Strassen multiplication over the integers

Peter Bruin on Sat, 25 Apr 2015 11:50:10 +0200

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Strassen multiplication over the integers

To: <pari-dev@pari.math.u-bordeaux.fr>
Subject: Strassen multiplication over the integers
From: Peter Bruin <P.J.Bruin@math.leidenuniv.nl>
Date: Sat, 25 Apr 2015 11:49:49 +0200
Delivery-date: Sat, 25 Apr 2015 11:50:10 +0200
User-agent: Gnus/5.13 (Gnus v5.13) Emacs/24.3 (gnu/linux)

Bonjour,

I have been working on a PARI implementation of Strassen's algorithm for
matrix multiplication (more precisely, Winograd's variant, which uses
fewer additions), in particular over the integers.  This has complexity
O(n^(log_2(7)) (instead of the classical O(n^3)) for n x n-matrices.

The code is in the attached ZM_mul_sw.patch; a program for tuning it is
in tune.c, and the output of running this tuning program on my laptop
(x86_64 Core i5-4210M with Gentoo GNU/Linux and PARI 2.8.0-development)
is in tune.txt.

Some remarks:

- The main function is ZM_mul_sw ("sw" stands for Strassen-Winograd).
  To add/subtract the various submatrices that occur in the algorithm,
  functions {add,subtract}_slices are used that implicitly pad with
  zeroes when one or more dimensions are odd.

- Tuning: for multiplications (m x n) * (n x k), a Strassen recursion
  step is done if min(m, n, k) >= b, where b is an adjustable parameter
  (called ZM_sw_bound in the code); otherwise classical multiplication
  is used.

- Optimal value of b: from the output in tune.txt, this seems to lie (on
  my laptop) around 28, and certainly 24 <= b <= 40.  I also did some
  tests with matrices containing only non-negative entries; in this case
  the optimal value of b increases to around 36.

- Finding the optimal b on a given system is not yet integrated into
  PARI's tuning framework, with which I am unfortunately not familiar.

- Speed increase: this appears to be roughly as follows (speedup factor
  relative to classical multiplication):
    size  speedup
      50   1.1
     100   1.5
     150   1.8
     200   2.8

- The results depend to some extent on the PARI stack size (I used a
  fixed stack of 16 MB).

- Garbage collection: there are currently a lot of gc_needed checks to
  avoid wasting memory.  Some of these could perhaps be removed.

- The user does not have to do anything special to use ZM_mul_sw; it is
  automatically called by ZM_mul for sufficiently large matrices.
  Furthermore, the new code is covered by the existing tests.

- Parameters: ZM_mul_sw takes the dimensions of the matrices as input,
  while ZM_mul_classical and ZM_mul_i expect these dimensions plus 1
  (due to lg = dim + 1).  I tried various possibilities and this seems
  to be a reasonable compromise between similarity to existing code and
  avoiding having to shift arguments by +1 or -1 all the time.

- Apart from matrices over the integers, matrices over non-prime finite
  fields of small characteristic (FlxqM) will also benefit from this
  functionality, thanks to Kronecker multiplication.

Comments are welcome!  Of course, I would be especially happy if this
code (with suitable changes if necessary) could be integrated into PARI.

Thanks,

Peter

diff --git a/src/basemath/ZV.c b/src/basemath/ZV.c
index c62f1c6..71e4eec 100644
--- a/src/basemath/ZV.c
+++ b/src/basemath/ZV.c
@@ -164,6 +164,179 @@ ZM_nm_mul(GEN x, GEN y)
   return z;
 }
 
+/* Strassen-Winograd algorithm */
+
+static inline GEN
+shallowmatslice(GEN A, long x1, long x2, long y1, long y2)
+{
+  return rowslice(vecslice(A, y1, y2), x1, x2);
+}
+
+/*
+  Return A[ma+1..ma+da, na+1..na+ea] - B[mb+1..mb+db, nb+1..nb+eb]
+  as an (m x n)-matrix, padding the input with zeroes as necessary.
+*/
+static GEN
+add_slices(long m, long n,
+	   GEN A, long ma, long da, long na, long ea,
+	   GEN B, long mb, long db, long nb, long eb)
+{
+  long min_d = minss(da, db), min_e = minss(ea, eb), i, j;
+  GEN M = cgetg(n + 1, t_MAT), C;
+
+  for (j = 1; j <= min_e; j++) {
+    gel(M, j) = C = cgetg(m + 1, t_COL);
+    for (i = 1; i <= min_d; i++)
+      gel(C, i) = addii(gcoeff(A, ma + i, na + j),
+			gcoeff(B, mb + i, nb + j));
+    for (; i <= da; i++)
+      gel(C, i) = gcoeff(A, ma + i, na + j);
+    for (; i <= db; i++)
+      gel(C, i) = gcoeff(B, mb + i, nb + j);
+    for (; i <= m; i++)
+      gel(C, i) = gen_0;
+  }
+  for (; j <= ea; j++) {
+    gel(M, j) = C = cgetg(m + 1, t_COL);
+    for (i = 1; i <= da; i++)
+      gel(C, i) = gcoeff(A, ma + i, na + j);
+    for (; i <= m; i++)
+      gel(C, i) = gen_0;
+  }
+  for (; j <= eb; j++) {
+    gel(M, j) = C = cgetg(m + 1, t_COL);
+    for (i = 1; i <= db; i++)
+      gel(C, i) = gcoeff(B, mb + i, nb + j);
+    for (; i <= m; i++)
+      gel(C, i) = gen_0;
+  }
+  for (; j <= n; j++)
+    gel(M, j) = zerocol(m);
+  return M;
+}
+
+/*
+  Return A[ma+1..ma+da, na+1..na+ea] - B[mb+1..mb+db, nb+1..nb+eb]
+  as an (m x n)-matrix, padding the input with zeroes as necessary.
+*/
+static GEN
+subtract_slices(long m, long n,
+		GEN A, long ma, long da, long na, long ea,
+		GEN B, long mb, long db, long nb, long eb)
+{
+  long min_d = minss(da, db), min_e = minss(ea, eb), i, j;
+  GEN M = cgetg(n + 1, t_MAT), C;
+
+  for (j = 1; j <= min_e; j++) {
+    gel(M, j) = C = cgetg(m + 1, t_COL);
+    for (i = 1; i <= min_d; i++)
+      gel(C, i) = subii(gcoeff(A, ma + i, na + j),
+			gcoeff(B, mb + i, nb + j));
+    for (; i <= da; i++)
+      gel(C, i) = gcoeff(A, ma + i, na + j);
+    for (; i <= db; i++)
+      gel(C, i) = negi(gcoeff(B, mb + i, nb + j));
+    for (; i <= m; i++)
+      gel(C, i) = gen_0;
+  }
+  for (; j <= ea; j++) {
+    gel(M, j) = C = cgetg(m + 1, t_COL);
+    for (i = 1; i <= da; i++)
+      gel(C, i) = gcoeff(A, ma + i, na + j);
+    for (; i <= m; i++)
+      gel(C, i) = gen_0;
+  }
+  for (; j <= eb; j++) {
+    gel(M, j) = C = cgetg(m + 1, t_COL);
+    for (i = 1; i <= db; i++)
+      gel(C, i) = negi(gcoeff(B, mb + i, nb + j));
+    for (; i <= m; i++)
+      gel(C, i) = gen_0;
+  }
+  for (; j <= n; j++)
+    gel(M, j) = zerocol(m);
+  return M;
+}
+
+static GEN ZM_mul_i(GEN x, GEN y, long l, long lx, long ly);
+
+/* Strassen-Winograd matrix product A (m x n) * B (n x p) */
+static GEN
+ZM_mul_sw(GEN A, GEN B, long m, long n, long p)
+{
+  pari_sp av = avma;
+  long m1 = (m + 1)/2, m2 = m/2,
+    n1 = (n + 1)/2, n2 = n/2,
+    p1 = (p + 1)/2, p2 = p/2;
+  GEN A11, A12, A22, B11, B21, B22,
+    S1, S2, S3, S4, T1, T2, T3, T4,
+    M1, M2, M3, M4, M5, M6, M7,
+    V1, V2, V3, C11, C12, C21, C22, C;
+
+  T2 = subtract_slices(n1, p2, B, 0, n1, p1, p2, B, n1, n2, p1, p2);
+  S1 = subtract_slices(m2, n1, A, m1, m2, 0, n1, A, 0, m2, 0, n1);
+  M2 = ZM_mul_i(S1, T2, m2 + 1, n1 + 1, p2 + 1);
+  if (gc_needed(av, 1))
+    gerepileall(av, 2, &T2, &M2);  /* destroy S1 */
+  T3 = subtract_slices(n1, p1, T2, 0, n1, 0, p2, B, 0, n1, 0, p1);
+  if (gc_needed(av, 1))
+    gerepileall(av, 2, &M2, &T3);  /* destroy T2 */
+  S2 = add_slices(m2, n1, A, m1, m2, 0, n1, A, m1, m2, n1, n2);
+  T1 = subtract_slices(n1, p1, B, 0, n1, p1, p2, B, 0, n1, 0, p2);
+  M3 = ZM_mul_i(S2, T1, m2 + 1, n1 + 1, p2 + 1);
+  if (gc_needed(av, 1))
+    gerepileall(av, 4, &M2, &T3, &S2, &M3);  /* destroy T1 */
+  S3 = subtract_slices(m1, n1, S2, 0, m2, 0, n1, A, 0, m1, 0, n1);
+  if (gc_needed(av, 1))
+    gerepileall(av, 4, &M2, &T3, &M3, &S3);  /* destroy S2 */
+  A11 = shallowmatslice(A, 1, m1, 1, n1);
+  B11 = shallowmatslice(B, 1, n1, 1, p1);
+  M1 = ZM_mul_i(A11, B11, m1 + 1, n1 + 1, p1 + 1);
+  if (gc_needed(av, 1))
+    gerepileall(av, 5, &M2, &T3, &M3, &S3, &M1);  /* destroy A11, B11 */
+  A12 = shallowmatslice(A, 1, m1, n1 + 1, n);
+  B21 = shallowmatslice(B, n1 + 1, n, 1, p1);
+  M4 = ZM_mul_i(A12, B21, m1 + 1, n2 + 1, p1 + 1);
+  if (gc_needed(av, 1))
+    gerepileall(av, 6, &M2, &T3, &M3, &S3, &M1, &M4);  /* destroy A12, B21 */
+  C11 = add_slices(m1, p1, M1, 0, m1, 0, p1, M4, 0, m1, 0, p1);
+  if (gc_needed(av, 1))
+    gerepileall(av, 6, &M2, &T3, &M3, &S3, &M1, &C11);  /* destroy M4 */
+  M5 = ZM_mul_i(S3, T3, m1 + 1, n1 + 1, p1 + 1);
+  S4 = subtract_slices(m1, n2, A, 0, m1, n1, n2, S3, 0, m1, 0, n2);
+  if (gc_needed(av, 1))
+    gerepileall(av, 7, &M2, &T3, &M3, &M1, &C11, &M5, &S4);  /* destroy S3 */
+  T4 = add_slices(n2, p1, B, n1, n2, 0, p1, T3, 0, n2, 0, p1);
+  if (gc_needed(av, 1))
+    gerepileall(av, 7, &M2, &M3, &M1, &C11, &M5, &S4, &T4);  /* destroy T3 */
+  V1 = subtract_slices(m1, p1, M1, 0, m1, 0, p1, M5, 0, m1, 0, p1);
+  if (gc_needed(av, 1))
+    gerepileall(av, 6, &M2, &M3, &S4, &T4, &C11, &V1);  /* destroy M1, M5 */
+  B22 = shallowmatslice(B, n1 + 1, n, p1 + 1, p);
+  M6 = ZM_mul_i(S4, B22, m1 + 1, n2 + 1, p2 + 1);
+  if (gc_needed(av, 1))
+    gerepileall(av, 6, &M2, &M3, &T4, &C11, &V1, &M6);  /* destroy S4, B22 */
+  A22 = shallowmatslice(A, m1 + 1, m, n1 + 1, n);
+  M7 = ZM_mul_i(A22, T4, m2 + 1, n2 + 1, p1 + 1);
+  if (gc_needed(av, 1))
+    gerepileall(av, 6, &M2, &M3, &C11, &V1, &M6, &M7);  /* destroy A22, T4 */
+  V3 = add_slices(m1, p2, V1, 0, m1, 0, p2, M3, 0, m2, 0, p2);
+  C12 = add_slices(m1, p2, V3, 0, m1, 0, p2, M6, 0, m1, 0, p2);
+  if (gc_needed(av, 1))
+    gerepileall(av, 6, &M2, &M3, &C11, &V1, &M7, &C12);  /* destroy V3, M6 */
+  V2 = add_slices(m2, p1, V1, 0, m2, 0, p1, M2, 0, m2, 0, p2);
+  if (gc_needed(av, 1))
+    gerepileall(av, 5, &M3, &C11, &M7, &C12, &V2);  /* destroy V1, M2 */
+  C21 = add_slices(m2, p1, V2, 0, m2, 0, p1, M7, 0, m2, 0, p1);
+  if (gc_needed(av, 1))
+    gerepileall(av, 5, &M3, &C11, &C12, &V2, &C21);  /* destroy M7 */
+  C22 = add_slices(m2, p2, V2, 0, m2, 0, p2, M3, 0, m2, 0, p2);
+  if (gc_needed(av, 1))
+    gerepileall(av, 4, &C11, &C12, &C21, &C22);  /* destroy V2, M3 */
+  C = mkmat2(mkcol2(C11, C21), mkcol2(C12, C22));
+  return gerepileupto(av, matconcat(C));
+}
+
 /* x[i,]*y. Assume lg(x) > 1 and 0 < i < lgcols(x) */
 static GEN
 ZMrow_ZC_mul_i(GEN x, GEN y, long i, long lx)
@@ -191,16 +364,35 @@ ZM_ZC_mul_i(GEN x, GEN y, long lx, long l)
   for (i=1; i<l; i++) gel(z,i) = ZMrow_ZC_mul_i(x,y,i,lx);
   return z;
 }
+
+static GEN
+ZM_mul_classical(GEN x, GEN y, long l, long lx, long ly)
+{
+  long j;
+  GEN z = cgetg(ly, t_MAT);
+  for (j = 1; j < ly; j++)
+    gel(z, j) = ZM_ZC_mul_i(x, gel(y, j), lx, l);
+  return z;
+}
+
+long ZM_sw_bound = 36;  /* Strassen-Winograd used for dim >= ZM_sw_bound */
+
+static GEN
+ZM_mul_i(GEN x, GEN y, long l, long lx, long ly)
+{
+  if (l <= ZM_sw_bound || lx <= ZM_sw_bound || ly <= ZM_sw_bound)
+    return ZM_mul_classical(x, y, l, lx, ly);
+  else
+    return ZM_mul_sw(x, y, l - 1, lx - 1, ly - 1);
+}
+
 GEN
 ZM_mul(GEN x, GEN y)
 {
-  long j, l, lx=lg(x), ly=lg(y);
-  GEN z;
+  long lx=lg(x), ly=lg(y);
   if (ly==1) return cgetg(1,t_MAT);
   if (lx==1) return zeromat(0, ly-1);
-  l = lgcols(x); z = cgetg(ly,t_MAT);
-  for (j=1; j<ly; j++) gel(z,j) = ZM_ZC_mul_i(x, gel(y,j), lx, l);
-  return z;
+  return ZM_mul_i(x, y, lgcols(x), lx, ly);
 }
 /* assume result is symmetric */
 GEN

#include <pari/pari.h>
#include <time.h>

extern long ZM_sw_bound;

static GEN
random_ZC(long m, GEN min, GEN max) {
  GEN C = cgetg(m + 1, t_COL);
  long i;
  for (i = 1; i <= m; i++)
    gel(C, i) = addii(randomi(subii(max, min)), min);
  return C;
}

static GEN
random_ZM(long m, long n, GEN min, GEN max) {
  GEN M = cgetg(n + 1, t_MAT);
  long i;
  for (i = 1; i <= n; i++)
    gel(M, i) = random_ZC(m, min, max);
  return M;
}

void test1(long m, long n, long k, GEN min, GEN max, long b,
	   time_t *t_old, time_t *t_new) {
  GEN A, B;
  time_t t0, t1, t2;
  pari_sp av = avma;

  A = random_ZM(m, n, min, max);
  B = random_ZM(n, k, min, max);
  ZM_sw_bound = b;
  t0 = clock();
  cgiv(ZM_mul(A, B));
  ZM_sw_bound = 10000;
  t1 = clock();
  cgiv(ZM_mul(A, B));
  t2 = clock();
  avma = av;
  *t_old = t2 - t1;
  *t_new = t1 - t0;
}

double test(long nmin, long nmax, long b) {
  long n;
  GEN max = stoi(1<<20), min = gneg(max);
  time_t t_old, t_new, T_old = 0, T_new = 0;
  double r;

  for (n = nmin; n <= nmax; n++) {
    test1(n, n, n, min, max, b, &t_old, &t_new);
    T_old += t_old;
    T_new += t_new;
    r = ((double) t_old) / t_new;
    printf("n = %li: %f\n", n, r);
  }
  return ((double) T_old) / T_new;
}

int main(int argc, char **argv) {
  long b, bmin = 16, bmax = 48, nmin = 16, nmax = 196;
  pari_init(1 << 24, 500000);
  for (b = bmin; b <= bmax; b++)
    printf("b = %li: %f\n", b, test(nmin, nmax, b));
  return 0;
}

n = 16: 0.750000
n = 17: 0.883041
n = 18: 1.036082
n = 19: 0.921739
n = 20: 1.034221
n = 21: 0.941176
n = 22: 0.904110
n = 23: 1.005013
n = 24: 1.038724
n = 25: 0.790244
n = 26: 0.987365
n = 27: 0.977671
n = 28: 1.010219
n = 29: 0.994764
n = 30: 1.028812
n = 31: 0.897585
n = 32: 0.923285
n = 33: 0.944490
n = 34: 0.939189
n = 35: 0.949045
n = 36: 0.973262
n = 37: 0.961141
n = 38: 0.971671
n = 39: 0.957194
n = 40: 0.999499
n = 41: 0.990817
n = 42: 1.003891
n = 43: 1.012540
n = 44: 1.030793
n = 45: 1.024217
n = 46: 1.039664
n = 47: 1.048842
n = 48: 1.070713
n = 49: 1.049286
n = 50: 1.065972
n = 51: 1.119535
n = 52: 1.087357
n = 53: 1.073857
n = 54: 1.096711
n = 55: 1.105393
n = 56: 1.131610
n = 57: 1.145795
n = 58: 1.191689
n = 59: 1.228615
n = 60: 1.259565
n = 61: 1.251330
n = 62: 1.228995
n = 63: 1.224371
n = 64: 1.219270
n = 65: 1.207827
n = 66: 1.217002
n = 67: 1.226224
n = 68: 1.262428
n = 69: 1.264114
n = 70: 1.274195
n = 71: 1.305866
n = 72: 1.316301
n = 73: 1.315014
n = 74: 1.304815
n = 75: 1.332829
n = 76: 1.323963
n = 77: 1.323994
n = 78: 1.337218
n = 79: 1.367465
n = 80: 1.382239
n = 81: 1.374139
n = 82: 1.366324
n = 83: 1.372225
n = 84: 1.412624
n = 85: 1.388417
n = 86: 1.418033
n = 87: 1.407960
n = 88: 1.433460
n = 89: 1.416809
n = 90: 1.428071
n = 91: 1.421015
n = 92: 1.453008
n = 93: 1.472794
n = 94: 1.459739
n = 95: 1.495596
n = 96: 1.482152
n = 97: 1.493739
n = 98: 1.470812
n = 99: 1.485682
n = 100: 1.486222
n = 101: 1.477575
n = 102: 1.524923
n = 103: 1.500186
n = 104: 1.541364
n = 105: 1.538881
n = 106: 1.514368
n = 107: 1.511930
n = 108: 1.569214
n = 109: 1.523140
n = 110: 1.534520
n = 111: 1.543261
n = 112: 1.564713
n = 113: 1.552097
n = 114: 1.567969
n = 115: 1.555144
n = 116: 1.565477
n = 117: 1.566211
n = 118: 1.584671
n = 119: 1.588149
n = 120: 1.599359
n = 121: 1.580301
n = 122: 1.603962
n = 123: 1.576970
n = 124: 1.563233
n = 125: 1.551753
n = 126: 1.537975
n = 127: 1.520579
n = 128: 1.503515
n = 129: 1.500562
n = 130: 1.491239
n = 131: 1.493385
n = 132: 1.503368
n = 133: 1.514181
n = 134: 1.517629
n = 135: 1.518274
n = 136: 1.528325
n = 137: 1.521870
n = 138: 1.537135
n = 139: 1.546079
n = 140: 1.565486
n = 141: 1.585261
n = 142: 1.596744
n = 143: 1.616293
n = 144: 1.629384
n = 145: 1.606136
n = 146: 1.623123
n = 147: 1.620257
n = 148: 1.671121
n = 149: 1.668866
n = 150: 1.679456
n = 151: 1.692421
n = 152: 1.756560
n = 153: 1.742970
n = 154: 1.747447
n = 155: 1.755114
n = 156: 1.776945
n = 157: 1.799361
n = 158: 1.796875
n = 159: 1.811059
n = 160: 1.857459
n = 161: 1.840381
n = 162: 1.918745
n = 163: 1.945092
n = 164: 1.980344
n = 165: 2.015516
n = 166: 1.982445
n = 167: 2.004558
n = 168: 2.062200
n = 169: 2.067725
n = 170: 2.077838
n = 171: 2.099074
n = 172: 2.130840
n = 173: 2.172667
n = 174: 2.198304
n = 175: 2.280999
n = 176: 2.288821
n = 177: 2.366419
n = 178: 2.411457
n = 179: 2.585644
n = 180: 2.429395
n = 181: 2.463217
n = 182: 2.507039
n = 183: 2.524642
n = 184: 2.585538
n = 185: 2.583893
n = 186: 2.630715
n = 187: 2.684189
n = 188: 2.708930
n = 189: 2.364858
n = 190: 2.403794
n = 191: 2.503915
n = 192: 2.456903
n = 193: 2.524675
n = 194: 2.251870
n = 195: 2.260716
n = 196: 2.287407
b = 16: 1.978040
n = 16: 0.992063
n = 17: 0.847458
n = 18: 0.908163
n = 19: 0.917031
n = 20: 0.953668
n = 21: 0.940594
n = 22: 0.959064
n = 23: 0.956633
n = 24: 0.995381
n = 25: 0.983838
n = 26: 1.001828
n = 27: 0.995138
n = 28: 1.005900
n = 29: 1.002642
n = 30: 1.023030
n = 31: 1.010881
n = 32: 1.035354
n = 33: 0.921376
n = 34: 0.957055
n = 35: 0.951807
n = 36: 0.971333
n = 37: 0.962264
n = 38: 0.978348
n = 39: 0.980403
n = 40: 1.003519
n = 41: 0.995845
n = 42: 1.006491
n = 43: 1.014593
n = 44: 1.034016
n = 45: 1.039615
n = 46: 1.041484
n = 47: 1.047242
n = 48: 1.077321
n = 49: 1.062694
n = 50: 1.064103
n = 51: 1.120091
n = 52: 1.088035
n = 53: 1.085266
n = 54: 1.095692
n = 55: 1.106746
n = 56: 1.151365
n = 57: 1.154459
n = 58: 1.194056
n = 59: 1.231094
n = 60: 1.264735
n = 61: 1.259862
n = 62: 1.269790
n = 63: 1.295059
n = 64: 1.339712
n = 65: 1.314417
n = 66: 1.298925
n = 67: 1.282106
n = 68: 1.260444
n = 69: 1.278564
n = 70: 1.271461
n = 71: 1.303478
n = 72: 1.315708
n = 73: 1.320981
n = 74: 1.310448
n = 75: 1.321123
n = 76: 1.325817
n = 77: 1.321492
n = 78: 1.337373
n = 79: 1.373677
n = 80: 1.379266
n = 81: 1.374633
n = 82: 1.371693
n = 83: 1.375311
n = 84: 1.415617
n = 85: 1.396468
n = 86: 1.421184
n = 87: 1.414626
n = 88: 1.442884
n = 89: 1.421836
n = 90: 1.429902
n = 91: 1.425648
n = 92: 1.453469
n = 93: 1.476538
n = 94: 1.458657
n = 95: 1.504910
n = 96: 1.483571
n = 97: 1.496876
n = 98: 1.474326
n = 99: 1.487015
n = 100: 1.489749
n = 101: 1.482381
n = 102: 1.522827
n = 103: 1.497350
n = 104: 1.547735
n = 105: 1.546296
n = 106: 1.516484
n = 107: 1.512143
n = 108: 1.564250
n = 109: 1.530633
n = 110: 1.543349
n = 111: 1.547255
n = 112: 1.572260
n = 113: 1.554941
n = 114: 1.578804
n = 115: 1.564479
n = 116: 1.567581
n = 117: 1.569721
n = 118: 1.583760
n = 119: 1.594501
n = 120: 1.604557
n = 121: 1.590809
n = 122: 1.616378
n = 123: 1.603021
n = 124: 1.609389
n = 125: 1.610465
n = 126: 1.618886
n = 127: 1.633009
n = 128: 1.638663
n = 129: 1.628342
n = 130: 1.610809
n = 131: 1.587743
n = 132: 1.598123
n = 133: 1.594863
n = 134: 1.563593
n = 135: 1.545852
n = 136: 1.532581
n = 137: 1.521360
n = 138: 1.528798
n = 139: 1.542534
n = 140: 1.562074
n = 141: 1.586382
n = 142: 1.602599
n = 143: 1.607338
n = 144: 1.629703
n = 145: 1.610431
n = 146: 1.627658
n = 147: 1.620884
n = 148: 1.668686
n = 149: 1.675234
n = 150: 1.682080
n = 151: 1.692685
n = 152: 1.756931
n = 153: 1.744741
n = 154: 1.757409
n = 155: 1.752630
n = 156: 1.785034
n = 157: 1.792223
n = 158: 1.796426
n = 159: 1.803518
n = 160: 1.865860
n = 161: 1.854728
n = 162: 1.912816
n = 163: 1.946260
n = 164: 1.989636
n = 165: 1.976285
n = 166: 1.987951
n = 167: 2.018808
n = 168: 2.062406
n = 169: 2.061882
n = 170: 2.084439
n = 171: 2.111998
n = 172: 2.141837
n = 173: 2.169392
n = 174: 2.192909
n = 175: 2.269146
n = 176: 2.278824
n = 177: 2.370802
n = 178: 2.397610
n = 179: 2.445993
n = 180: 2.427182
n = 181: 2.458137
n = 182: 2.499356
n = 183: 2.514071
n = 184: 2.574219
n = 185: 2.586495
n = 186: 2.628960
n = 187: 2.683935
n = 188: 2.704527
n = 189: 2.287590
n = 190: 2.316866
n = 191: 2.476606
n = 192: 2.464297
n = 193: 2.573640
n = 194: 2.227049
n = 195: 2.277503
n = 196: 2.304108
b = 17: 1.982747
n = 16: 1.000000
n = 17: 1.006667
n = 18: 0.886139
n = 19: 0.904762
n = 20: 0.942308
n = 21: 0.940789
n = 22: 0.970588
n = 23: 0.961637
n = 24: 0.983945
n = 25: 0.977778
n = 26: 1.003656
n = 27: 0.993517
n = 28: 1.010340
n = 29: 1.005298
n = 30: 1.025547
n = 31: 1.008705
n = 32: 1.034274
n = 33: 1.021858
n = 34: 1.055649
n = 35: 1.010518
n = 36: 0.977852
n = 37: 0.963415
n = 38: 0.998294
n = 39: 0.984093
n = 40: 1.006030
n = 41: 0.995849
n = 42: 1.004758
n = 43: 1.019113
n = 44: 1.032844
n = 45: 1.028224
n = 46: 1.043566
n = 47: 1.050492
n = 48: 1.073770
n = 49: 1.062252
n = 50: 1.064991
n = 51: 1.120071
n = 52: 1.087770
n = 53: 1.088469
n = 54: 1.104171
n = 55: 1.107569
n = 56: 1.134113
n = 57: 1.145984
n = 58: 1.199185
n = 59: 1.231913
n = 60: 1.264495
n = 61: 1.257099
n = 62: 1.273876
n = 63: 1.294902
n = 64: 1.335186
n = 65: 1.327485
n = 66: 1.322153
n = 67: 1.350183
n = 68: 1.377135
n = 69: 1.377017
n = 70: 1.356159
n = 71: 1.347638
n = 72: 1.328504
n = 73: 1.320373
n = 74: 1.314535
n = 75: 1.343069
n = 76: 1.327117
n = 77: 1.327083
n = 78: 1.335713
n = 79: 1.369740
n = 80: 1.378187
n = 81: 1.375881
n = 82: 1.366334
n = 83: 1.386522
n = 84: 1.405992
n = 85: 1.392247
n = 86: 1.414727
n = 87: 1.413821
n = 88: 1.446338
n = 89: 1.426263
n = 90: 1.447734
n = 91: 1.426970
n = 92: 1.453482
n = 93: 1.489836
n = 94: 1.458472
n = 95: 1.495119
n = 96: 1.494418
n = 97: 1.493384
n = 98: 1.475301
n = 99: 1.491769
n = 100: 1.486024
n = 101: 1.485577
n = 102: 1.520886
n = 103: 1.500406
n = 104: 1.542295
n = 105: 1.543064
n = 106: 1.514779
n = 107: 1.518110
n = 108: 1.558314
n = 109: 1.525219
n = 110: 1.536439
n = 111: 1.550303
n = 112: 1.567509
n = 113: 1.574447
n = 114: 1.580517
n = 115: 1.549263
n = 116: 1.567043
n = 117: 1.579706
n = 118: 1.574117
n = 119: 1.588567
n = 120: 1.603340
n = 121: 1.592479
n = 122: 1.610301
n = 123: 1.606175
n = 124: 1.610136
n = 125: 1.614672
n = 126: 1.606608
n = 127: 1.632392
n = 128: 1.637800
n = 129: 1.641910
n = 130: 1.627081
n = 131: 1.618035
n = 132: 1.632887
n = 133: 1.657351
n = 134: 1.660520
n = 135: 1.664890
n = 136: 1.676380
n = 137: 1.656493
n = 138: 1.652319
n = 139: 1.654636
n = 140: 1.651546
n = 141: 1.658264
n = 142: 1.648995
n = 143: 1.642285
n = 144: 1.623634
n = 145: 1.608369
n = 146: 1.625771
n = 147: 1.624084
n = 148: 1.672599
n = 149: 1.674085
n = 150: 1.673356
n = 151: 1.685899
n = 152: 1.761101
n = 153: 1.747898
n = 154: 1.758951
n = 155: 1.750030
n = 156: 1.777464
n = 157: 1.798724
n = 158: 1.785628
n = 159: 1.812364
n = 160: 1.851662
n = 161: 1.842790
n = 162: 1.913739
n = 163: 1.943131
n = 164: 1.985549
n = 165: 1.984541
n = 166: 1.987450
n = 167: 2.002666
n = 168: 2.064372
n = 169: 2.067729
n = 170: 2.074424
n = 171: 2.106171
n = 172: 2.131291
n = 173: 2.176969
n = 174: 2.200265
n = 175: 2.284233
n = 176: 2.282493
n = 177: 2.358527
n = 178: 2.396479
n = 179: 2.440407
n = 180: 2.421425
n = 181: 2.453536
n = 182: 2.504187
n = 183: 2.523263
n = 184: 2.586894
n = 185: 2.588950
n = 186: 2.626825
n = 187: 2.684810
n = 188: 2.705129
n = 189: 2.294140
n = 190: 2.334410
n = 191: 2.576744
n = 192: 2.462203
n = 193: 2.540339
n = 194: 2.256249
n = 195: 2.271264
n = 196: 2.298513
b = 18: 1.994695
n = 16: 0.992063
n = 17: 0.993377
n = 18: 1.000000
n = 19: 0.898305
n = 20: 0.945946
n = 21: 0.928105
n = 22: 0.976331
n = 23: 0.964010
n = 24: 0.986239
n = 25: 0.973896
n = 26: 0.998172
n = 27: 0.998377
n = 28: 1.016296
n = 29: 1.005298
n = 30: 1.025485
n = 31: 1.017505
n = 32: 1.034378
n = 33: 1.016334
n = 34: 1.060504
n = 35: 1.026902
n = 36: 1.048167
n = 37: 1.035054
n = 38: 0.964627
n = 39: 0.983078
n = 40: 1.005528
n = 41: 0.993551
n = 42: 1.006482
n = 43: 1.021087
n = 44: 1.032831
n = 45: 1.027887
n = 46: 1.039018
n = 47: 1.049762
n = 48: 1.075008
n = 49: 1.063896
n = 50: 1.068772
n = 51: 1.145063
n = 52: 1.086798
n = 53: 1.089152
n = 54: 1.087591
n = 55: 1.112276
n = 56: 1.135483
n = 57: 1.149378
n = 58: 1.203117
n = 59: 1.231757
n = 60: 1.263783
n = 61: 1.258793
n = 62: 1.263658
n = 63: 1.297616
n = 64: 1.336183
n = 65: 1.330341
n = 66: 1.341529
n = 67: 1.364044
n = 68: 1.379961
n = 69: 1.388353
n = 70: 1.385137
n = 71: 1.402605
n = 72: 1.416092
n = 73: 1.406150
n = 74: 1.379172
n = 75: 1.379175
n = 76: 1.324969
n = 77: 1.326436
n = 78: 1.343911
n = 79: 1.371786
n = 80: 1.383006
n = 81: 1.373053
n = 82: 1.367648
n = 83: 1.382183
n = 84: 1.407311
n = 85: 1.392768
n = 86: 1.414104
n = 87: 1.412043
n = 88: 1.443643
n = 89: 1.424021
n = 90: 1.455747
n = 91: 1.426160
n = 92: 1.452901
n = 93: 1.475805
n = 94: 1.458979
n = 95: 1.501987
n = 96: 1.481483
n = 97: 1.490669
n = 98: 1.472819
n = 99: 1.504753
n = 100: 1.488057
n = 101: 1.491570
n = 102: 1.522114
n = 103: 1.499543
n = 104: 1.536050
n = 105: 1.543087
n = 106: 1.524800
n = 107: 1.514270
n = 108: 1.565037
n = 109: 1.525486
n = 110: 1.537434
n = 111: 1.550751
n = 112: 1.573324
n = 113: 1.555422
n = 114: 1.578517
n = 115: 1.562831
n = 116: 1.571078
n = 117: 1.572104
n = 118: 1.582265
n = 119: 1.589446
n = 120: 1.607988
n = 121: 1.591233
n = 122: 1.617471
n = 123: 1.604206
n = 124: 1.604224
n = 125: 1.616713
n = 126: 1.610791
n = 127: 1.631818
n = 128: 1.639520
n = 129: 1.647926
n = 130: 1.625533
n = 131: 1.625011
n = 132: 1.632185
n = 133: 1.659539
n = 134: 1.662737
n = 135: 1.651755
n = 136: 1.674293
n = 137: 1.663864
n = 138: 1.665832
n = 139: 1.677514
n = 140: 1.694921
n = 141: 1.704906
n = 142: 1.713654
n = 143: 1.723881
n = 144: 1.735686
n = 145: 1.716422
n = 146: 1.727182
n = 147: 1.723253
n = 148: 1.749404
n = 149: 1.740315
n = 150: 1.722083
n = 151: 1.713006
n = 152: 1.751906
n = 153: 1.751364
n = 154: 1.753305
n = 155: 1.760402
n = 156: 1.778270
n = 157: 1.801949
n = 158: 1.801316
n = 159: 1.806905
n = 160: 1.873036
n = 161: 1.844291
n = 162: 1.919221
n = 163: 1.944254
n = 164: 1.982605
n = 165: 1.983412
n = 166: 1.995485
n = 167: 2.006709
n = 168: 2.055422
n = 169: 2.069779
n = 170: 2.094798
n = 171: 2.102081
n = 172: 2.117096
n = 173: 2.165272
n = 174: 2.196813
n = 175: 2.276745
n = 176: 2.282875
n = 177: 2.369460
n = 178: 2.405540
n = 179: 2.450684
n = 180: 2.428715
n = 181: 2.458723
n = 182: 2.504949
n = 183: 2.527977
n = 184: 2.581674
n = 185: 2.586177
n = 186: 2.623274
n = 187: 2.684341
n = 188: 2.705542
n = 189: 2.291416
n = 190: 2.290374
n = 191: 2.398950
n = 192: 2.460698
n = 193: 2.523776
n = 194: 2.250361
n = 195: 2.278330
n = 196: 2.267986
b = 19: 2.000259
n = 16: 0.992063
n = 17: 0.980263
n = 18: 0.994382
n = 19: 1.014354
n = 20: 0.921348
n = 21: 1.153605
n = 22: 0.964809
n = 23: 0.964286
n = 24: 0.979358
n = 25: 1.042424
n = 26: 0.994516
n = 27: 1.000000
n = 28: 1.014793
n = 29: 1.007916
n = 30: 1.020681
n = 31: 1.015317
n = 32: 1.036437
n = 33: 1.019126
n = 34: 1.059222
n = 35: 1.029208
n = 36: 1.039286
n = 37: 1.038108
n = 38: 1.050796
n = 39: 1.026578
n = 40: 1.003017
n = 41: 0.990323
n = 42: 1.005188
n = 43: 1.016240
n = 44: 1.038372
n = 45: 1.025375
n = 46: 1.043478
n = 47: 1.052448
n = 48: 1.074097
n = 49: 1.061634
n = 50: 1.067094
n = 51: 1.133789
n = 52: 1.088300
n = 53: 1.080645
n = 54: 1.098939
n = 55: 1.108258
n = 56: 1.131699
n = 57: 1.151301
n = 58: 1.195083
n = 59: 1.229666
n = 60: 1.272164
n = 61: 1.264363
n = 62: 1.261685
n = 63: 1.296026
n = 64: 1.337403
n = 65: 1.336243
n = 66: 1.346462
n = 67: 1.360156
n = 68: 1.383615
n = 69: 1.383424
n = 70: 1.382762
n = 71: 1.405727
n = 72: 1.411125
n = 73: 1.411194
n = 74: 1.424522
n = 75: 1.425539
n = 76: 1.425505
n = 77: 1.406095
n = 78: 1.399970
n = 79: 1.404103
n = 80: 1.381832
n = 81: 1.378117
n = 82: 1.369321
n = 83: 1.378137
n = 84: 1.411397
n = 85: 1.394086
n = 86: 1.419476
n = 87: 1.411410
n = 88: 1.436187
n = 89: 1.422022
n = 90: 1.432751
n = 91: 1.422952
n = 92: 1.464182
n = 93: 1.475308
n = 94: 1.460576
n = 95: 1.504783
n = 96: 1.495226
n = 97: 1.491733
n = 98: 1.465622
n = 99: 1.508353
n = 100: 1.491432
n = 101: 1.487479
n = 102: 1.521456
n = 103: 1.501860
n = 104: 1.548040
n = 105: 1.540343
n = 106: 1.516376
n = 107: 1.514528
n = 108: 1.565742
n = 109: 1.524531
n = 110: 1.542438
n = 111: 1.545935
n = 112: 1.571676
n = 113: 1.556028
n = 114: 1.579258
n = 115: 1.570415
n = 116: 1.568385
n = 117: 1.569504
n = 118: 1.582004
n = 119: 1.588345
n = 120: 1.602651
n = 121: 1.592364
n = 122: 1.618326
n = 123: 1.602699
n = 124: 1.608636
n = 125: 1.613940
n = 126: 1.620151
n = 127: 1.631494
n = 128: 1.640951
n = 129: 1.635649
n = 130: 1.634617
n = 131: 1.630367
n = 132: 1.639695
n = 133: 1.657255
n = 134: 1.657732
n = 135: 1.661245
n = 136: 1.679311
n = 137: 1.659142
n = 138: 1.665415
n = 139: 1.674313
n = 140: 1.688436
n = 141: 1.706059
n = 142: 1.718617
n = 143: 1.728571
n = 144: 1.738757
n = 145: 1.707983
n = 146: 1.740977
n = 147: 1.743892
n = 148: 1.786284
n = 149: 1.794115
n = 150: 1.803583
n = 151: 1.823660
n = 152: 1.874199
n = 153: 1.864575
n = 154: 1.858399
n = 155: 1.850476
n = 156: 1.857067
n = 157: 1.860786
n = 158: 1.847421
n = 159: 1.829953
n = 160: 1.867190
n = 161: 1.847126
n = 162: 1.916808
n = 163: 1.951253
n = 164: 1.978492
n = 165: 1.973641
n = 166: 1.992157
n = 167: 2.002257
n = 168: 2.057852
n = 169: 2.066551
n = 170: 2.089297
n = 171: 2.106922
n = 172: 2.127379
n = 173: 2.162979
n = 174: 2.197675
n = 175: 2.280617
n = 176: 2.313584
n = 177: 2.370025
n = 178: 2.410828
n = 179: 2.455363
n = 180: 2.433059
n = 181: 2.463436
n = 182: 2.507496
n = 183: 2.526051
n = 184: 2.584151
n = 185: 2.579725
n = 186: 2.632809
n = 187: 2.687868
n = 188: 2.708538
n = 189: 2.299182
n = 190: 2.286784
n = 191: 2.429703
n = 192: 2.474580
n = 193: 2.555368
n = 194: 2.246646
n = 195: 2.245494
n = 196: 2.299732
b = 20: 2.013637
n = 16: 1.007937
n = 17: 0.993333
n = 18: 1.005618
n = 19: 1.009569
n = 20: 1.004082
n = 21: 0.919614
n = 22: 0.976471
n = 23: 0.959184
n = 24: 0.986207
n = 25: 0.971944
n = 26: 0.998168
n = 27: 0.991909
n = 28: 1.017857
n = 29: 1.055556
n = 30: 1.026731
n = 31: 1.016411
n = 32: 1.035354
n = 33: 1.018149
n = 34: 1.057530
n = 35: 1.029186
n = 36: 1.044381
n = 37: 1.037426
n = 38: 1.050214
n = 39: 1.044532
n = 40: 1.056992
n = 41: 1.029693
n = 42: 0.965474
n = 43: 1.027519
n = 44: 1.031648
n = 45: 0.993430
n = 46: 1.067340
n = 47: 1.048193
n = 48: 1.076433
n = 49: 1.063012
n = 50: 1.069021
n = 51: 1.120503
n = 52: 1.080039
n = 53: 1.081517
n = 54: 1.100520
n = 55: 1.108691
n = 56: 1.135167
n = 57: 1.154618
n = 58: 1.197520
n = 59: 1.230106
n = 60: 1.265439
n = 61: 1.255001
n = 62: 1.271578
n = 63: 1.298470
n = 64: 1.341973
n = 65: 1.330725
n = 66: 1.340742
n = 67: 1.351412
n = 68: 1.387594
n = 69: 1.385391
n = 70: 1.381076
n = 71: 1.418719
n = 72: 1.411639
n = 73: 1.407999
n = 74: 1.403631
n = 75: 1.459247
n = 76: 1.428845
n = 77: 1.409743
n = 78: 1.433392
n = 79: 1.445889
n = 80: 1.454363
n = 81: 1.441470
n = 82: 1.418900
n = 83: 1.412177
n = 84: 1.407040
n = 85: 1.392235
n = 86: 1.421846
n = 87: 1.409854
n = 88: 1.445523
n = 89: 1.423826
n = 90: 1.448412
n = 91: 1.426348
n = 92: 1.451974
n = 93: 1.471932
n = 94: 1.456593
n = 95: 1.504363
n = 96: 1.479695
n = 97: 1.496075
n = 98: 1.470785
n = 99: 1.489227
n = 100: 1.483676
n = 101: 1.477759
n = 102: 1.522260
n = 103: 1.505640
n = 104: 1.541901
n = 105: 1.542250
n = 106: 1.517174
n = 107: 1.516146
n = 108: 1.563025
n = 109: 1.528337
n = 110: 1.535620
n = 111: 1.550216
n = 112: 1.574231
n = 113: 1.572899
n = 114: 1.601683
n = 115: 1.553832
n = 116: 1.563450
n = 117: 1.575491
n = 118: 1.577896
n = 119: 1.587376
n = 120: 1.608258
n = 121: 1.584732
n = 122: 1.611775
n = 123: 1.601207
n = 124: 1.608540
n = 125: 1.620150
n = 126: 1.608369
n = 127: 1.625546
n = 128: 1.637491
n = 129: 1.637569
n = 130: 1.634585
n = 131: 1.633007
n = 132: 1.644864
n = 133: 1.662906
n = 134: 1.659577
n = 135: 1.650906
n = 136: 1.685926
n = 137: 1.653067
n = 138: 1.659041
n = 139: 1.675182
n = 140: 1.690751
n = 141: 1.704856
n = 142: 1.709908
n = 143: 1.725170
n = 144: 1.742148
n = 145: 1.716018
n = 146: 1.738037
n = 147: 1.737855
n = 148: 1.786729
n = 149: 1.791763
n = 150: 1.801671
n = 151: 1.822929
n = 152: 1.882804
n = 153: 1.868654
n = 154: 1.869631
n = 155: 1.862723
n = 156: 1.884617
n = 157: 1.895529
n = 158: 1.907246
n = 159: 1.901906
n = 160: 1.963694
n = 161: 1.938269
n = 162: 1.999586
n = 163: 2.033372
n = 164: 2.052861
n = 165: 2.027217
n = 166: 2.031930
n = 167: 2.034364
n = 168: 2.063257
n = 169: 2.053967
n = 170: 2.089561
n = 171: 2.116748
n = 172: 2.133428
n = 173: 2.170707
n = 174: 2.187041
n = 175: 2.279514
n = 176: 2.285935
n = 177: 2.370218
n = 178: 2.409328
n = 179: 2.447777
n = 180: 2.429511
n = 181: 2.458491
n = 182: 2.502167
n = 183: 2.520189
n = 184: 2.582641
n = 185: 2.579314
n = 186: 2.627406
n = 187: 2.685562
n = 188: 2.705075
n = 189: 2.273654
n = 190: 2.302605
n = 191: 2.422098
n = 192: 2.448515
n = 193: 2.579127
n = 194: 2.237367
n = 195: 2.256911
n = 196: 2.295555
b = 21: 2.021763
n = 16: 0.984252
n = 17: 0.986842
n = 18: 1.000000
n = 19: 1.009479
n = 20: 0.995935
n = 21: 1.007042
n = 22: 0.945087
n = 23: 0.949495
n = 24: 0.986207
n = 25: 0.975855
n = 26: 0.996364
n = 27: 0.998374
n = 28: 1.014815
n = 29: 1.000000
n = 30: 1.023114
n = 31: 1.016340
n = 32: 1.034413
n = 33: 1.019091
n = 34: 1.057481
n = 35: 1.033051
n = 36: 1.044317
n = 37: 1.040053
n = 38: 1.050796
n = 39: 1.042159
n = 40: 1.053158
n = 41: 1.048152
n = 42: 1.060731
n = 43: 1.047320
n = 44: 1.037510
n = 45: 1.026805
n = 46: 1.041765
n = 47: 1.042453
n = 48: 1.072512
n = 49: 1.064990
n = 50: 1.067842
n = 51: 1.122315
n = 52: 1.089338
n = 53: 1.083466
n = 54: 1.092048
n = 55: 1.109218
n = 56: 1.134243
n = 57: 1.149777
n = 58: 1.197396
n = 59: 1.236864
n = 60: 1.264572
n = 61: 1.261397
n = 62: 1.273141
n = 63: 1.300084
n = 64: 1.346326
n = 65: 1.335163
n = 66: 1.345690
n = 67: 1.365332
n = 68: 1.387056
n = 69: 1.383499
n = 70: 1.383489
n = 71: 1.387420
n = 72: 1.413827
n = 73: 1.427094
n = 74: 1.404216
n = 75: 1.463210
n = 76: 1.432017
n = 77: 1.414162
n = 78: 1.429315
n = 79: 1.442641
n = 80: 1.455819
n = 81: 1.445252
n = 82: 1.443899
n = 83: 1.460051
n = 84: 1.481740
n = 85: 1.454210
n = 86: 1.453072
n = 87: 1.439406
n = 88: 1.442562
n = 89: 1.426771
n = 90: 1.451260
n = 91: 1.426590
n = 92: 1.453467
n = 93: 1.474736
n = 94: 1.453837
n = 95: 1.502858
n = 96: 1.482553
n = 97: 1.494922
n = 98: 1.474320
n = 99: 1.486174
n = 100: 1.491465
n = 101: 1.481312
n = 102: 1.519071
n = 103: 1.506491
n = 104: 1.543553
n = 105: 1.545580
n = 106: 1.513486
n = 107: 1.513863
n = 108: 1.566249
n = 109: 1.530615
n = 110: 1.539654
n = 111: 1.548909
n = 112: 1.568181
n = 113: 1.551785
n = 114: 1.578286
n = 115: 1.559625
n = 116: 1.567490
n = 117: 1.569108
n = 118: 1.585461
n = 119: 1.590784
n = 120: 1.607655
n = 121: 1.592849
n = 122: 1.617397
n = 123: 1.609726
n = 124: 1.610534
n = 125: 1.616779
n = 126: 1.605255
n = 127: 1.631358
n = 128: 1.639586
n = 129: 1.636800
n = 130: 1.648573
n = 131: 1.630971
n = 132: 1.635770
n = 133: 1.662607
n = 134: 1.663989
n = 135: 1.663159
n = 136: 1.679331
n = 137: 1.658359
n = 138: 1.666865
n = 139: 1.677007
n = 140: 1.684537
n = 141: 1.706402
n = 142: 1.712013
n = 143: 1.725485
n = 144: 1.742056
n = 145: 1.712356
n = 146: 1.737241
n = 147: 1.734520
n = 148: 1.785829
n = 149: 1.792015
n = 150: 1.801995
n = 151: 1.813246
n = 152: 1.884993
n = 153: 1.865313
n = 154: 1.869763
n = 155: 1.863940
n = 156: 1.882656
n = 157: 1.894032
n = 158: 1.908470
n = 159: 1.899519
n = 160: 1.961128
n = 161: 1.945279
n = 162: 2.009128
n = 163: 2.055661
n = 164: 2.086156
n = 165: 2.078282
n = 166: 2.100309
n = 167: 2.128024
n = 168: 2.175954
n = 169: 2.164439
n = 170: 2.184089
n = 171: 2.196148
n = 172: 2.202313
n = 173: 2.222729
n = 174: 2.231646
n = 175: 2.300185
n = 176: 2.280944
n = 177: 2.373498
n = 178: 2.398919
n = 179: 2.452831
n = 180: 2.446194
n = 181: 2.462432
n = 182: 2.507369
n = 183: 2.525889
n = 184: 2.585029
n = 185: 2.578245
n = 186: 2.629494
n = 187: 2.685530
n = 188: 2.704685
n = 189: 2.277833
n = 190: 2.282299
n = 191: 2.395570
n = 192: 2.450048
n = 193: 2.562534
n = 194: 2.253015
n = 195: 2.248896
n = 196: 2.302642
b = 22: 2.032756
n = 16: 0.992063
n = 17: 1.000000
n = 18: 0.988827
n = 19: 1.000000
n = 20: 0.995935
n = 21: 0.996479
n = 22: 1.000000
n = 23: 0.935323
n = 24: 0.988506
n = 25: 0.981891
n = 26: 0.998172
n = 27: 0.993517
n = 28: 1.014793
n = 29: 1.002646
n = 30: 1.026764
n = 31: 1.015267
n = 32: 1.038540
n = 33: 1.021838
n = 34: 1.055602
n = 35: 1.034695
n = 36: 1.042203
n = 37: 1.041393
n = 38: 1.050920
n = 39: 1.041011
n = 40: 1.054469
n = 41: 1.048058
n = 42: 1.063274
n = 43: 1.058400
n = 44: 1.069628
n = 45: 1.052381
n = 46: 1.043552
n = 47: 1.049825
n = 48: 1.087485
n = 49: 1.063366
n = 50: 1.070472
n = 51: 1.123860
n = 52: 1.093233
n = 53: 1.083276
n = 54: 1.101277
n = 55: 1.107847
n = 56: 1.136094
n = 57: 1.144046
n = 58: 1.206695
n = 59: 1.227334
n = 60: 1.265864
n = 61: 1.265397
n = 62: 1.273181
n = 63: 1.299705
n = 64: 1.348806
n = 65: 1.334145
n = 66: 1.342393
n = 67: 1.343629
n = 68: 1.387377
n = 69: 1.385425
n = 70: 1.385528
n = 71: 1.402343
n = 72: 1.413438
n = 73: 1.411118
n = 74: 1.412885
n = 75: 1.434838
n = 76: 1.428191
n = 77: 1.413911
n = 78: 1.414549
n = 79: 1.449402
n = 80: 1.453442
n = 81: 1.443577
n = 82: 1.446907
n = 83: 1.461144
n = 84: 1.482245
n = 85: 1.460702
n = 86: 1.476731
n = 87: 1.464535
n = 88: 1.496644
n = 89: 1.474616
n = 90: 1.485553
n = 91: 1.450048
n = 92: 1.457961
n = 93: 1.472693
n = 94: 1.463310
n = 95: 1.502624
n = 96: 1.485447
n = 97: 1.492474
n = 98: 1.473652
n = 99: 1.489278
n = 100: 1.486016
n = 101: 1.490766
n = 102: 1.516010
n = 103: 1.506194
n = 104: 1.529439
n = 105: 1.540369
n = 106: 1.514209
n = 107: 1.514944
n = 108: 1.565881
n = 109: 1.534108
n = 110: 1.538849
n = 111: 1.544260
n = 112: 1.564395
n = 113: 1.552451
n = 114: 1.579422
n = 115: 1.553714
n = 116: 1.564457
n = 117: 1.568819
n = 118: 1.578864
n = 119: 1.595109
n = 120: 1.605972
n = 121: 1.592683
n = 122: 1.617976
n = 123: 1.604317
n = 124: 1.610662
n = 125: 1.612130
n = 126: 1.617799
n = 127: 1.633566
n = 128: 1.641535
n = 129: 1.635462
n = 130: 1.637194
n = 131: 1.631820
n = 132: 1.643789
n = 133: 1.661790
n = 134: 1.657968
n = 135: 1.659354
n = 136: 1.683523
n = 137: 1.647074
n = 138: 1.656537
n = 139: 1.675065
n = 140: 1.687005
n = 141: 1.704779
n = 142: 1.719741
n = 143: 1.728667
n = 144: 1.744557
n = 145: 1.717143
n = 146: 1.734080
n = 147: 1.733266
n = 148: 1.786408
n = 149: 1.798275
n = 150: 1.802925
n = 151: 1.821323
n = 152: 1.883008
n = 153: 1.871861
n = 154: 1.866295
n = 155: 1.856917
n = 156: 1.889145
n = 157: 1.884088
n = 158: 1.891095
n = 159: 1.898591
n = 160: 1.961434
n = 161: 1.938298
n = 162: 2.010817
n = 163: 2.051986
n = 164: 2.082489
n = 165: 2.077453
n = 166: 2.100956
n = 167: 2.124360
n = 168: 2.175664
n = 169: 2.170846
n = 170: 2.189611
n = 171: 2.200540
n = 172: 2.222427
n = 173: 2.255163
n = 174: 2.281158
n = 175: 2.363929
n = 176: 2.364927
n = 177: 2.453585
n = 178: 2.485289
n = 179: 2.523580
n = 180: 2.493824
n = 181: 2.513511
n = 182: 2.547296
n = 183: 2.544045
n = 184: 2.583104
n = 185: 2.582380
n = 186: 2.622846
n = 187: 2.682221
n = 188: 2.708992
n = 189: 2.285877
n = 190: 2.330068
n = 191: 2.436135
n = 192: 2.434150
n = 193: 2.531168
n = 194: 2.241448
n = 195: 2.266526
n = 196: 2.271530
b = 23: 2.041462
n = 16: 0.992126
n = 17: 1.006623
n = 18: 1.000000
n = 19: 1.000000
n = 20: 1.000000
n = 21: 0.993031
n = 22: 1.006079
n = 23: 1.002660
n = 24: 0.979499
n = 25: 0.973843
n = 26: 1.005515
n = 27: 1.000000
n = 28: 1.014837
n = 29: 1.001319
n = 30: 1.019370
n = 31: 0.925447
n = 32: 1.035389
n = 33: 1.019091
n = 34: 1.056636
n = 35: 1.030769
n = 36: 1.042888
n = 37: 1.032005
n = 38: 1.055147
n = 39: 1.041550
n = 40: 1.053326
n = 41: 1.029637
n = 42: 1.064989
n = 43: 1.058749
n = 44: 1.069832
n = 45: 1.065975
n = 46: 1.081062
n = 47: 1.073400
n = 48: 1.071320
n = 49: 1.064498
n = 50: 1.067860
n = 51: 1.124082
n = 52: 1.088829
n = 53: 1.084280
n = 54: 1.095784
n = 55: 1.117937
n = 56: 1.132370
n = 57: 1.147234
n = 58: 1.204566
n = 59: 1.234976
n = 60: 1.268968
n = 61: 1.262439
n = 62: 1.274156
n = 63: 1.294109
n = 64: 1.344136
n = 65: 1.327389
n = 66: 1.341788
n = 67: 1.352795
n = 68: 1.388107
n = 69: 1.382433
n = 70: 1.388576
n = 71: 1.401981
n = 72: 1.414667
n = 73: 1.411895
n = 74: 1.408953
n = 75: 1.445972
n = 76: 1.429130
n = 77: 1.410740
n = 78: 1.417725
n = 79: 1.450277
n = 80: 1.453136
n = 81: 1.447569
n = 82: 1.448953
n = 83: 1.448591
n = 84: 1.492454
n = 85: 1.456949
n = 86: 1.473496
n = 87: 1.470040
n = 88: 1.498310
n = 89: 1.481412
n = 90: 1.503695
n = 91: 1.485314
n = 92: 1.512287
n = 93: 1.523772
n = 94: 1.492345
n = 95: 1.524674
n = 96: 1.481434
n = 97: 1.498110
n = 98: 1.478116
n = 99: 1.491281
n = 100: 1.485365
n = 101: 1.480419
n = 102: 1.520558
n = 103: 1.500372
n = 104: 1.540675
n = 105: 1.537546
n = 106: 1.524369
n = 107: 1.513951
n = 108: 1.562190
n = 109: 1.530753
n = 110: 1.543819
n = 111: 1.548680
n = 112: 1.566806
n = 113: 1.558146
n = 114: 1.580082
n = 115: 1.565188
n = 116: 1.566313
n = 117: 1.578926
n = 118: 1.579488
n = 119: 1.587328
n = 120: 1.610415
n = 121: 1.581710
n = 122: 1.618524
n = 123: 1.605572
n = 124: 1.609637
n = 125: 1.617745
n = 126: 1.617953
n = 127: 1.631509
n = 128: 1.635724
n = 129: 1.636234
n = 130: 1.633253
n = 131: 1.636744
n = 132: 1.636702
n = 133: 1.662489
n = 134: 1.667305
n = 135: 1.662029
n = 136: 1.679513
n = 137: 1.661829
n = 138: 1.665364
n = 139: 1.674781
n = 140: 1.683642
n = 141: 1.703360
n = 142: 1.735200
n = 143: 1.717805
n = 144: 1.738972
n = 145: 1.715235
n = 146: 1.736845
n = 147: 1.746086
n = 148: 1.787548
n = 149: 1.799902
n = 150: 1.788882
n = 151: 1.829245
n = 152: 1.883705
n = 153: 1.869773
n = 154: 1.867532
n = 155: 1.868459
n = 156: 1.886888
n = 157: 1.901180
n = 158: 1.900648
n = 159: 1.902469
n = 160: 1.963105
n = 161: 1.938340
n = 162: 2.018709
n = 163: 2.045837
n = 164: 2.086490
n = 165: 2.086918
n = 166: 2.101461
n = 167: 2.122837
n = 168: 2.173202
n = 169: 2.171412
n = 170: 2.198930
n = 171: 2.205755
n = 172: 2.222474
n = 173: 2.267601
n = 174: 2.288509
n = 175: 2.369857
n = 176: 2.372577
n = 177: 2.455825
n = 178: 2.494687
n = 179: 2.544723
n = 180: 2.527514
n = 181: 2.556847
n = 182: 2.607897
n = 183: 2.632448
n = 184: 2.793915
n = 185: 2.686032
n = 186: 2.715688
n = 187: 2.754375
n = 188: 2.771697
n = 189: 2.356955
n = 190: 2.422579
n = 191: 2.535951
n = 192: 2.441711
n = 193: 2.535207
n = 194: 2.255237
n = 195: 2.271403
n = 196: 2.273639
b = 24: 2.059571
n = 16: 0.992063
n = 17: 0.993377
n = 18: 1.000000
n = 19: 0.995261
n = 20: 1.004065
n = 21: 1.000000
n = 22: 0.996960
n = 23: 1.005305
n = 24: 1.006993
n = 25: 0.968000
n = 26: 1.001835
n = 27: 1.003257
n = 28: 1.014793
n = 29: 1.007947
n = 30: 1.029233
n = 31: 1.019672
n = 32: 1.035354
n = 33: 1.020985
n = 34: 1.057578
n = 35: 1.033846
n = 36: 1.043011
n = 37: 1.034595
n = 38: 1.054534
n = 39: 1.044432
n = 40: 1.054968
n = 41: 1.048567
n = 42: 1.066880
n = 43: 1.058326
n = 44: 1.069062
n = 45: 1.066370
n = 46: 1.083801
n = 47: 1.049794
n = 48: 1.113488
n = 49: 1.077275
n = 50: 1.064318
n = 51: 1.122723
n = 52: 1.085422
n = 53: 1.084811
n = 54: 1.098183
n = 55: 1.108236
n = 56: 1.127978
n = 57: 1.149545
n = 58: 1.209146
n = 59: 1.228514
n = 60: 1.266037
n = 61: 1.261083
n = 62: 1.270576
n = 63: 1.301852
n = 64: 1.347307
n = 65: 1.334446
n = 66: 1.342070
n = 67: 1.351281
n = 68: 1.385196
n = 69: 1.384957
n = 70: 1.387517
n = 71: 1.403006
n = 72: 1.414028
n = 73: 1.407233
n = 74: 1.407572
n = 75: 1.462190
n = 76: 1.434074
n = 77: 1.407675
n = 78: 1.424469
n = 79: 1.444831
n = 80: 1.454133
n = 81: 1.443525
n = 82: 1.441891
n = 83: 1.459506
n = 84: 1.484875
n = 85: 1.458535
n = 86: 1.473390
n = 87: 1.469795
n = 88: 1.497243
n = 89: 1.480401
n = 90: 1.496832
n = 91: 1.482943
n = 92: 1.513748
n = 93: 1.525460
n = 94: 1.502147
n = 95: 1.536845
n = 96: 1.508611
n = 97: 1.522092
n = 98: 1.502003
n = 99: 1.505962
n = 100: 1.483689
n = 101: 1.478923
n = 102: 1.518234
n = 103: 1.500017
n = 104: 1.542258
n = 105: 1.547578
n = 106: 1.517215
n = 107: 1.516209
n = 108: 1.567713
n = 109: 1.527334
n = 110: 1.537571
n = 111: 1.549666
n = 112: 1.569597
n = 113: 1.571317
n = 114: 1.593200
n = 115: 1.547896
n = 116: 1.566595
n = 117: 1.574042
n = 118: 1.580606
n = 119: 1.592536
n = 120: 1.608042
n = 121: 1.591649
n = 122: 1.618496
n = 123: 1.603079
n = 124: 1.608709
n = 125: 1.616600
n = 126: 1.614364
n = 127: 1.627318
n = 128: 1.648411
n = 129: 1.647033
n = 130: 1.623699
n = 131: 1.634083
n = 132: 1.641918
n = 133: 1.662525
n = 134: 1.666002
n = 135: 1.661213
n = 136: 1.677568
n = 137: 1.666555
n = 138: 1.663120
n = 139: 1.670827
n = 140: 1.692320
n = 141: 1.706120
n = 142: 1.717296
n = 143: 1.726251
n = 144: 1.736544
n = 145: 1.715811
n = 146: 1.738218
n = 147: 1.743170
n = 148: 1.785997
n = 149: 1.798726
n = 150: 1.802157
n = 151: 1.815029
n = 152: 1.880205
n = 153: 1.867302
n = 154: 1.863127
n = 155: 1.870174
n = 156: 1.886012
n = 157: 1.901242
n = 158: 1.883196
n = 159: 1.903569
n = 160: 1.956699
n = 161: 1.936563
n = 162: 2.019602
n = 163: 2.048587
n = 164: 2.082691
n = 165: 2.090507
n = 166: 2.095722
n = 167: 2.118566
n = 168: 2.178963
n = 169: 2.171126
n = 170: 2.183127
n = 171: 2.199282
n = 172: 2.232788
n = 173: 2.267589
n = 174: 2.284042
n = 175: 2.366423
n = 176: 2.364583
n = 177: 2.447587
n = 178: 2.483756
n = 179: 2.535439
n = 180: 2.517017
n = 181: 2.550595
n = 182: 2.597155
n = 183: 2.630048
n = 184: 2.691783
n = 185: 2.688874
n = 186: 2.720614
n = 187: 2.771137
n = 188: 2.786794
n = 189: 2.425373
n = 190: 2.409999
n = 191: 2.529421
n = 192: 2.542498
n = 193: 2.584707
n = 194: 2.308050
n = 195: 2.318064
n = 196: 2.334227
b = 25: 2.063227
n = 16: 1.000000
n = 17: 1.000000
n = 18: 1.005618
n = 19: 0.995261
n = 20: 1.000000
n = 21: 0.996491
n = 22: 1.006135
n = 23: 1.002653
n = 24: 1.004695
n = 25: 1.002066
n = 26: 0.987410
n = 27: 0.993528
n = 28: 1.011817
n = 29: 0.998684
n = 30: 1.031824
n = 31: 1.013100
n = 32: 1.027218
n = 33: 1.023723
n = 34: 1.051390
n = 35: 1.030746
n = 36: 1.046662
n = 37: 1.041366
n = 38: 1.055249
n = 39: 1.043968
n = 40: 1.053826
n = 41: 1.046625
n = 42: 1.064132
n = 43: 1.060670
n = 44: 1.068581
n = 45: 1.063657
n = 46: 1.081990
n = 47: 1.100914
n = 48: 1.095105
n = 49: 1.085235
n = 50: 1.099340
n = 51: 1.140220
n = 52: 1.090843
n = 53: 1.083333
n = 54: 1.095867
n = 55: 1.108308
n = 56: 1.135140
n = 57: 1.165460
n = 58: 1.213501
n = 59: 1.224089
n = 60: 1.265854
n = 61: 1.262366
n = 62: 1.271060
n = 63: 1.301431
n = 64: 1.344374
n = 65: 1.323661
n = 66: 1.342942
n = 67: 1.339829
n = 68: 1.369319
n = 69: 1.381159
n = 70: 1.378536
n = 71: 1.398659
n = 72: 1.411187
n = 73: 1.413353
n = 74: 1.404984
n = 75: 1.432916
n = 76: 1.425753
n = 77: 1.412971
n = 78: 1.419115
n = 79: 1.448744
n = 80: 1.463411
n = 81: 1.444711
n = 82: 1.444791
n = 83: 1.451667
n = 84: 1.489030
n = 85: 1.457831
n = 86: 1.477995
n = 87: 1.467085
n = 88: 1.485939
n = 89: 1.474127
n = 90: 1.482978
n = 91: 1.478173
n = 92: 1.515435
n = 93: 1.522962
n = 94: 1.505322
n = 95: 1.538758
n = 96: 1.507314
n = 97: 1.528899
n = 98: 1.511506
n = 99: 1.525540
n = 100: 1.529959
n = 101: 1.508225
n = 102: 1.540408
n = 103: 1.512798
n = 104: 1.544958
n = 105: 1.535532
n = 106: 1.522501
n = 107: 1.505307
n = 108: 1.566245
n = 109: 1.529574
n = 110: 1.540927
n = 111: 1.545829
n = 112: 1.571147
n = 113: 1.554897
n = 114: 1.578186
n = 115: 1.559792
n = 116: 1.566352
n = 117: 1.575549
n = 118: 1.581239
n = 119: 1.589582
n = 120: 1.609214
n = 121: 1.593604
n = 122: 1.618557
n = 123: 1.602662
n = 124: 1.609302
n = 125: 1.615011
n = 126: 1.616529
n = 127: 1.629369
n = 128: 1.643080
n = 129: 1.634120
n = 130: 1.634455
n = 131: 1.631738
n = 132: 1.647401
n = 133: 1.662536
n = 134: 1.661549
n = 135: 1.665866
n = 136: 1.675437
n = 137: 1.661148
n = 138: 1.657726
n = 139: 1.664977
n = 140: 1.688447
n = 141: 1.700942
n = 142: 1.715196
n = 143: 1.732293
n = 144: 1.736236
n = 145: 1.717100
n = 146: 1.737633
n = 147: 1.739010
n = 148: 1.772886
n = 149: 1.789400
n = 150: 1.807559
n = 151: 1.820535
n = 152: 1.906115
n = 153: 1.866130
n = 154: 1.869598
n = 155: 1.865752
n = 156: 1.883699
n = 157: 1.895973
n = 158: 1.884419
n = 159: 1.907333
n = 160: 1.950407
n = 161: 1.946626
n = 162: 2.013082
n = 163: 2.046547
n = 164: 2.093275
n = 165: 2.086320
n = 166: 2.094098
n = 167: 2.129052
n = 168: 2.183762
n = 169: 2.163847
n = 170: 2.180972
n = 171: 2.204439
n = 172: 2.231898
n = 173: 2.270110
n = 174: 2.276096
n = 175: 2.356317
n = 176: 2.358910
n = 177: 2.445898
n = 178: 2.489229
n = 179: 2.545431
n = 180: 2.530915
n = 181: 2.550246
n = 182: 2.597801
n = 183: 2.622038
n = 184: 2.690707
n = 185: 2.687022
n = 186: 2.726981
n = 187: 2.772425
n = 188: 2.783549
n = 189: 2.323110
n = 190: 2.366304
n = 191: 2.492825
n = 192: 2.541257
n = 193: 2.661718
n = 194: 2.279913
n = 195: 2.328014
n = 196: 2.573806
b = 26: 2.066079
n = 16: 0.992063
n = 17: 1.000000
n = 18: 1.011173
n = 19: 0.995261
n = 20: 1.012195
n = 21: 0.996491
n = 22: 0.996951
n = 23: 1.005319
n = 24: 1.000000
n = 25: 1.004141
n = 26: 1.001835
n = 27: 0.980800
n = 28: 1.014859
n = 29: 1.006640
n = 30: 1.024272
n = 31: 1.016393
n = 32: 1.035354
n = 33: 1.025547
n = 34: 1.057432
n = 35: 1.031611
n = 36: 1.040000
n = 37: 1.037353
n = 38: 1.052147
n = 39: 1.029461
n = 40: 1.053741
n = 41: 1.046625
n = 42: 1.064929
n = 43: 1.061681
n = 44: 1.081437
n = 45: 1.061391
n = 46: 1.085203
n = 47: 1.085211
n = 48: 1.095253
n = 49: 1.087107
n = 50: 1.096951
n = 51: 1.141425
n = 52: 1.101328
n = 53: 1.096878
n = 54: 1.098963
n = 55: 1.107714
n = 56: 1.131896
n = 57: 1.152499
n = 58: 1.210377
n = 59: 1.231977
n = 60: 1.266819
n = 61: 1.258346
n = 62: 1.273969
n = 63: 1.301416
n = 64: 1.345614
n = 65: 1.343594
n = 66: 1.342794
n = 67: 1.361782
n = 68: 1.385151
n = 69: 1.383776
n = 70: 1.390643
n = 71: 1.399560
n = 72: 1.413800
n = 73: 1.417875
n = 74: 1.404923
n = 75: 1.437976
n = 76: 1.427133
n = 77: 1.410676
n = 78: 1.421303
n = 79: 1.448281
n = 80: 1.454956
n = 81: 1.448295
n = 82: 1.444459
n = 83: 1.454679
n = 84: 1.489225
n = 85: 1.459885
n = 86: 1.480991
n = 87: 1.467114
n = 88: 1.489990
n = 89: 1.480178
n = 90: 1.501895
n = 91: 1.480467
n = 92: 1.503605
n = 93: 1.524807
n = 94: 1.492575
n = 95: 1.539488
n = 96: 1.509919
n = 97: 1.527863
n = 98: 1.510555
n = 99: 1.526885
n = 100: 1.525188
n = 101: 1.512510
n = 102: 1.535246
n = 103: 1.516057
n = 104: 1.557792
n = 105: 1.556763
n = 106: 1.521908
n = 107: 1.521194
n = 108: 1.561460
n = 109: 1.528470
n = 110: 1.539899
n = 111: 1.553085
n = 112: 1.574454
n = 113: 1.575282
n = 114: 1.593239
n = 115: 1.556730
n = 116: 1.565823
n = 117: 1.569051
n = 118: 1.582387
n = 119: 1.576945
n = 120: 1.609297
n = 121: 1.582745
n = 122: 1.614872
n = 123: 1.597186
n = 124: 1.611741
n = 125: 1.614957
n = 126: 1.608724
n = 127: 1.628847
n = 128: 1.645965
n = 129: 1.640656
n = 130: 1.635257
n = 131: 1.631290
n = 132: 1.646964
n = 133: 1.658296
n = 134: 1.663718
n = 135: 1.663741
n = 136: 1.673877
n = 137: 1.661045
n = 138: 1.665792
n = 139: 1.660244
n = 140: 1.685360
n = 141: 1.706852
n = 142: 1.716875
n = 143: 1.725913
n = 144: 1.733964
n = 145: 1.717441
n = 146: 1.729115
n = 147: 1.724454
n = 148: 1.791007
n = 149: 1.798503
n = 150: 1.808727
n = 151: 1.817918
n = 152: 1.888593
n = 153: 1.864555
n = 154: 1.874701
n = 155: 1.864952
n = 156: 1.889811
n = 157: 1.894958
n = 158: 1.902658
n = 159: 1.899514
n = 160: 1.950672
n = 161: 1.944229
n = 162: 2.008428
n = 163: 2.049818
n = 164: 2.088156
n = 165: 2.081150
n = 166: 2.082050
n = 167: 2.127805
n = 168: 2.177017
n = 169: 2.165241
n = 170: 2.185724
n = 171: 2.206577
n = 172: 2.229351
n = 173: 2.261401
n = 174: 2.274423
n = 175: 2.351444
n = 176: 2.364255
n = 177: 2.454597
n = 178: 2.488835
n = 179: 2.599162
n = 180: 3.441460
n = 181: 2.548167
n = 182: 2.601235
n = 183: 2.624658
n = 184: 2.689905
n = 185: 2.684139
n = 186: 2.724745
n = 187: 2.772729
n = 188: 2.784488
n = 189: 2.308983
n = 190: 2.417736
n = 191: 2.530756
n = 192: 2.536209
n = 193: 2.589242
n = 194: 2.279987
n = 195: 2.330649
n = 196: 2.355769
b = 27: 2.076677
n = 16: 0.984252
n = 17: 1.006711
n = 18: 0.994413
n = 19: 1.000000
n = 20: 1.000000
n = 21: 0.992982
n = 22: 1.000000
n = 23: 1.007958
n = 24: 1.000000
n = 25: 0.997934
n = 26: 1.001835
n = 27: 0.998366
n = 28: 1.004392
n = 29: 1.000000
n = 30: 1.026764
n = 31: 1.013072
n = 32: 1.028169
n = 33: 1.021898
n = 34: 1.053209
n = 35: 1.000745
n = 36: 1.044413
n = 37: 1.038058
n = 38: 1.048900
n = 39: 1.037704
n = 40: 1.073996
n = 41: 1.048058
n = 42: 1.063216
n = 43: 1.063136
n = 44: 1.069145
n = 45: 1.062245
n = 46: 1.082807
n = 47: 1.081999
n = 48: 1.097523
n = 49: 1.083430
n = 50: 1.095540
n = 51: 1.139039
n = 52: 1.101132
n = 53: 1.099538
n = 54: 1.114261
n = 55: 1.124897
n = 56: 1.133347
n = 57: 1.149118
n = 58: 1.211178
n = 59: 1.236735
n = 60: 1.269764
n = 61: 1.262318
n = 62: 1.273448
n = 63: 1.295629
n = 64: 1.340561
n = 65: 1.343261
n = 66: 1.340551
n = 67: 1.353441
n = 68: 1.386805
n = 69: 1.385866
n = 70: 1.382292
n = 71: 1.403660
n = 72: 1.417112
n = 73: 1.412172
n = 74: 1.409649
n = 75: 1.434872
n = 76: 1.436631
n = 77: 1.413243
n = 78: 1.419436
n = 79: 1.450532
n = 80: 1.456219
n = 81: 1.460878
n = 82: 1.449195
n = 83: 1.460445
n = 84: 1.488187
n = 85: 1.457832
n = 86: 1.480155
n = 87: 1.466361
n = 88: 1.485491
n = 89: 1.477291
n = 90: 1.482095
n = 91: 1.481338
n = 92: 1.512354
n = 93: 1.526057
n = 94: 1.497108
n = 95: 1.541710
n = 96: 1.515869
n = 97: 1.524629
n = 98: 1.515006
n = 99: 1.530206
n = 100: 1.529659
n = 101: 1.512566
n = 102: 1.535479
n = 103: 1.514638
n = 104: 1.561686
n = 105: 1.560420
n = 106: 1.545179
n = 107: 1.528554
n = 108: 1.594255
n = 109: 1.546173
n = 110: 1.551971
n = 111: 1.548775
n = 112: 1.572229
n = 113: 1.554897
n = 114: 1.578204
n = 115: 1.562714
n = 116: 1.567707
n = 117: 1.572901
n = 118: 1.586651
n = 119: 1.590490
n = 120: 1.608557
n = 121: 1.588825
n = 122: 1.620087
n = 123: 1.604993
n = 124: 1.610770
n = 125: 1.614804
n = 126: 1.619922
n = 127: 1.627556
n = 128: 1.642764
n = 129: 1.646025
n = 130: 1.629143
n = 131: 1.620095
n = 132: 1.637317
n = 133: 1.659622
n = 134: 1.660687
n = 135: 1.664671
n = 136: 1.671406
n = 137: 1.663843
n = 138: 1.665016
n = 139: 1.671319
n = 140: 1.689794
n = 141: 1.691629
n = 142: 1.715126
n = 143: 1.718480
n = 144: 1.726536
n = 145: 1.718153
n = 146: 1.740877
n = 147: 1.738376
n = 148: 1.791122
n = 149: 1.786398
n = 150: 1.807732
n = 151: 1.820189
n = 152: 1.889808
n = 153: 1.867999
n = 154: 1.871325
n = 155: 1.860922
n = 156: 1.884046
n = 157: 1.897310
n = 158: 1.900440
n = 159: 1.902365
n = 160: 1.936659
n = 161: 1.944198
n = 162: 2.007780
n = 163: 2.036935
n = 164: 2.091886
n = 165: 2.076645
n = 166: 2.099445
n = 167: 2.127399
n = 168: 2.176825
n = 169: 2.147221
n = 170: 2.182411
n = 171: 2.203689
n = 172: 2.234134
n = 173: 2.261538
n = 174: 2.268079
n = 175: 2.349766
n = 176: 2.362761
n = 177: 2.453315
n = 178: 2.486327
n = 179: 2.544305
n = 180: 2.525549
n = 181: 2.552354
n = 182: 2.604413
n = 183: 2.625692
n = 184: 2.689741
n = 185: 2.675614
n = 186: 2.723230
n = 187: 2.771354
n = 188: 2.785103
n = 189: 2.320661
n = 190: 2.395183
n = 191: 2.484654
n = 192: 2.507201
n = 193: 2.595113
n = 194: 2.301046
n = 195: 2.297693
n = 196: 2.357445
b = 28: 2.059831
n = 16: 0.992063
n = 17: 1.006667
n = 18: 0.988889
n = 19: 0.995261
n = 20: 0.995918
n = 21: 0.992982
n = 22: 1.000000
n = 23: 0.992063
n = 24: 1.004662
n = 25: 1.004149
n = 26: 1.001842
n = 27: 0.996737
n = 28: 1.001464
n = 29: 0.993455
n = 30: 1.025485
n = 31: 1.020788
n = 32: 1.032258
n = 33: 1.021858
n = 34: 1.054806
n = 35: 1.030722
n = 36: 1.042264
n = 37: 1.041257
n = 38: 1.052083
n = 39: 1.042649
n = 40: 1.055526
n = 41: 1.046117
n = 42: 1.063586
n = 43: 1.060914
n = 44: 1.069888
n = 45: 1.063310
n = 46: 1.084532
n = 47: 1.079153
n = 48: 1.096344
n = 49: 1.096476
n = 50: 1.096455
n = 51: 1.142527
n = 52: 1.102046
n = 53: 1.102286
n = 54: 1.117660
n = 55: 1.115702
n = 56: 1.133452
n = 57: 1.151763
n = 58: 1.207080
n = 59: 1.240324
n = 60: 1.271898
n = 61: 1.260190
n = 62: 1.272300
n = 63: 1.303835
n = 64: 1.341559
n = 65: 1.333034
n = 66: 1.343346
n = 67: 1.354053
n = 68: 1.388247
n = 69: 1.386107
n = 70: 1.391789
n = 71: 1.401399
n = 72: 1.411582
n = 73: 1.427660
n = 74: 1.409491
n = 75: 1.431499
n = 76: 1.428738
n = 77: 1.413342
n = 78: 1.416221
n = 79: 1.446988
n = 80: 1.453043
n = 81: 1.440992
n = 82: 1.444982
n = 83: 1.452443
n = 84: 1.486221
n = 85: 1.457734
n = 86: 1.481848
n = 87: 1.470891
n = 88: 1.484201
n = 89: 1.472851
n = 90: 1.484761
n = 91: 1.478867
n = 92: 1.512882
n = 93: 1.525477
n = 94: 1.499374
n = 95: 1.530138
n = 96: 1.522140
n = 97: 1.515975
n = 98: 1.501146
n = 99: 1.551804
n = 100: 1.524918
n = 101: 1.506579
n = 102: 1.545566
n = 103: 1.518373
n = 104: 1.560182
n = 105: 1.558657
n = 106: 1.535778
n = 107: 1.540230
n = 108: 1.585803
n = 109: 1.544764
n = 110: 1.545767
n = 111: 1.549086
n = 112: 1.567166
n = 113: 1.551406
n = 114: 1.580222
n = 115: 1.564547
n = 116: 1.561006
n = 117: 1.569440
n = 118: 1.582620
n = 119: 1.594593
n = 120: 1.602836
n = 121: 1.591962
n = 122: 1.616596
n = 123: 1.602425
n = 124: 1.600205
n = 125: 1.613882
n = 126: 1.618063
n = 127: 1.632601
n = 128: 1.644278
n = 129: 1.635269
n = 130: 1.630189
n = 131: 1.628274
n = 132: 1.643210
n = 133: 1.662076
n = 134: 1.659636
n = 135: 1.661451
n = 136: 1.677742
n = 137: 1.654508
n = 138: 1.665434
n = 139: 1.670811
n = 140: 1.686445
n = 141: 1.703029
n = 142: 1.720086
n = 143: 1.718493
n = 144: 1.729304
n = 145: 1.709676
n = 146: 1.726430
n = 147: 1.734813
n = 148: 1.789178
n = 149: 1.800432
n = 150: 1.804500
n = 151: 1.829494
n = 152: 1.874852
n = 153: 1.873583
n = 154: 1.863598
n = 155: 1.872344
n = 156: 1.884188
n = 157: 1.892948
n = 158: 1.895146
n = 159: 1.896014
n = 160: 1.959773
n = 161: 1.940567
n = 162: 2.018792
n = 163: 2.058052
n = 164: 2.081846
n = 165: 2.087892
n = 166: 2.104757
n = 167: 2.123438
n = 168: 2.175477
n = 169: 2.172777
n = 170: 2.186423
n = 171: 2.201360
n = 172: 2.215780
n = 173: 2.268691
n = 174: 2.279064
n = 175: 2.370241
n = 176: 2.371195
n = 177: 2.455790
n = 178: 2.494487
n = 179: 2.546160
n = 180: 2.535270
n = 181: 2.549537
n = 182: 2.623101
n = 183: 2.630912
n = 184: 2.693237
n = 185: 2.686886
n = 186: 2.723463
n = 187: 2.768393
n = 188: 2.788794
n = 189: 2.371259
n = 190: 2.447769
n = 191: 2.501723
n = 192: 2.492683
n = 193: 2.587741
n = 194: 2.302630
n = 195: 2.329662
n = 196: 2.340254
b = 29: 2.063705
n = 16: 1.000000
n = 17: 1.013333
n = 18: 1.005618
n = 19: 0.995283
n = 20: 0.980000
n = 21: 1.000000
n = 22: 0.996960
n = 23: 1.098143
n = 24: 0.995360
n = 25: 1.002066
n = 26: 0.996337
n = 27: 0.998366
n = 28: 1.000000
n = 29: 0.997368
n = 30: 1.016867
n = 31: 1.014192
n = 32: 1.031313
n = 33: 1.020036
n = 34: 1.057384
n = 35: 1.032283
n = 36: 1.057266
n = 37: 1.038033
n = 38: 1.047794
n = 39: 0.993583
n = 40: 1.053298
n = 41: 1.025190
n = 42: 1.067673
n = 43: 1.025410
n = 44: 1.078611
n = 45: 1.063404
n = 46: 1.083509
n = 47: 1.077876
n = 48: 1.088526
n = 49: 1.083742
n = 50: 1.098460
n = 51: 1.134513
n = 52: 1.099042
n = 53: 1.099193
n = 54: 1.115967
n = 55: 1.112670
n = 56: 1.131740
n = 57: 1.151661
n = 58: 1.207721
n = 59: 1.231701
n = 60: 1.275879
n = 61: 1.261236
n = 62: 1.272300
n = 63: 1.302609
n = 64: 1.339254
n = 65: 1.331155
n = 66: 1.342769
n = 67: 1.352830
n = 68: 1.381034
n = 69: 1.385900
n = 70: 1.380616
n = 71: 1.410770
n = 72: 1.412439
n = 73: 1.414296
n = 74: 1.406832
n = 75: 1.463804
n = 76: 1.434837
n = 77: 1.412208
n = 78: 1.414907
n = 79: 1.447265
n = 80: 1.456375
n = 81: 1.450165
n = 82: 1.445467
n = 83: 1.455694
n = 84: 1.486819
n = 85: 1.459996
n = 86: 1.482545
n = 87: 1.464521
n = 88: 1.483153
n = 89: 1.471866
n = 90: 1.489134
n = 91: 1.474769
n = 92: 1.512130
n = 93: 1.522726
n = 94: 1.502280
n = 95: 1.540817
n = 96: 1.511818
n = 97: 1.527977
n = 98: 1.509984
n = 99: 1.531154
n = 100: 1.525754
n = 101: 1.510875
n = 102: 1.541313
n = 103: 1.518698
n = 104: 1.556393
n = 105: 1.560405
n = 106: 1.528407
n = 107: 1.535366
n = 108: 1.587813
n = 109: 1.541977
n = 110: 1.549716
n = 111: 1.551490
n = 112: 1.567064
n = 113: 1.558204
n = 114: 1.581405
n = 115: 1.564017
n = 116: 1.569930
n = 117: 1.565362
n = 118: 1.577548
n = 119: 1.587753
n = 120: 1.602139
n = 121: 1.582359
n = 122: 1.616509
n = 123: 1.601817
n = 124: 1.609473
n = 125: 1.607892
n = 126: 1.616958
n = 127: 1.627816
n = 128: 1.651935
n = 129: 1.636675
n = 130: 1.635016
n = 131: 1.632625
n = 132: 1.640965
n = 133: 1.660807
n = 134: 1.659117
n = 135: 1.650489
n = 136: 1.676996
n = 137: 1.660108
n = 138: 1.664298
n = 139: 1.661238
n = 140: 1.692919
n = 141: 1.703832
n = 142: 1.715860
n = 143: 1.723228
n = 144: 1.737289
n = 145: 1.720823
n = 146: 1.741746
n = 147: 1.745241
n = 148: 1.789446
n = 149: 1.780176
n = 150: 1.798758
n = 151: 1.824251
n = 152: 1.871606
n = 153: 1.866966
n = 154: 1.864017
n = 155: 1.862566
n = 156: 1.884118
n = 157: 1.900027
n = 158: 1.897829
n = 159: 1.911562
n = 160: 1.944396
n = 161: 1.938020
n = 162: 2.015759
n = 163: 2.048850
n = 164: 2.084002
n = 165: 2.077337
n = 166: 2.086027
n = 167: 2.116228
n = 168: 2.181762
n = 169: 2.169350
n = 170: 2.183035
n = 171: 2.206309
n = 172: 2.228041
n = 173: 2.270014
n = 174: 2.283288
n = 175: 2.367812
n = 176: 2.361188
n = 177: 2.450797
n = 178: 2.477908
n = 179: 2.536521
n = 180: 2.526521
n = 181: 2.545225
n = 182: 2.599892
n = 183: 2.629552
n = 184: 2.693043
n = 185: 2.685079
n = 186: 2.725577
n = 187: 2.772576
n = 188: 2.780883
n = 189: 2.370182
n = 190: 2.461606
n = 191: 2.574264
n = 192: 2.630430
n = 193: 2.588475
n = 194: 2.300952
n = 195: 2.407580
n = 196: 2.357104
b = 30: 2.067955
n = 16: 0.992063
n = 17: 1.006667
n = 18: 0.994382
n = 19: 0.995261
n = 20: 0.995951
n = 21: 0.996491
n = 22: 0.984940
n = 23: 1.005362
n = 24: 1.000000
n = 25: 1.000000
n = 26: 1.000000
n = 27: 0.998366
n = 28: 0.998542
n = 29: 1.001325
n = 30: 1.003563
n = 31: 1.007592
n = 32: 1.027190
n = 33: 1.021878
n = 34: 1.054054
n = 35: 1.031514
n = 36: 1.042918
n = 37: 1.042735
n = 38: 1.053276
n = 39: 1.041034
n = 40: 1.053411
n = 41: 1.043668
n = 42: 1.061644
n = 43: 1.058824
n = 44: 1.069805
n = 45: 1.065234
n = 46: 1.085754
n = 47: 1.074468
n = 48: 1.092959
n = 49: 1.085475
n = 50: 1.094937
n = 51: 1.140468
n = 52: 1.102141
n = 53: 1.099033
n = 54: 1.116755
n = 55: 1.113496
n = 56: 1.133939
n = 57: 1.153389
n = 58: 1.207898
n = 59: 1.241576
n = 60: 1.245710
n = 61: 1.245283
n = 62: 1.269503
n = 63: 1.301489
n = 64: 1.339574
n = 65: 1.321460
n = 66: 1.337715
n = 67: 1.350467
n = 68: 1.383894
n = 69: 1.386978
n = 70: 1.382457
n = 71: 1.399380
n = 72: 1.415404
n = 73: 1.414481
n = 74: 1.405679
n = 75: 1.438962
n = 76: 1.432504
n = 77: 1.416343
n = 78: 1.420735
n = 79: 1.445314
n = 80: 1.461572
n = 81: 1.444269
n = 82: 1.446986
n = 83: 1.453888
n = 84: 1.489750
n = 85: 1.456751
n = 86: 1.477908
n = 87: 1.464352
n = 88: 1.480812
n = 89: 1.474119
n = 90: 1.483413
n = 91: 1.478996
n = 92: 1.499577
n = 93: 1.524079
n = 94: 1.502700
n = 95: 1.540627
n = 96: 1.504198
n = 97: 1.530847
n = 98: 1.511826
n = 99: 1.525928
n = 100: 1.529688
n = 101: 1.509046
n = 102: 1.541478
n = 103: 1.525179
n = 104: 1.556632
n = 105: 1.557414
n = 106: 1.532295
n = 107: 1.532975
n = 108: 1.587061
n = 109: 1.545365
n = 110: 1.550007
n = 111: 1.548774
n = 112: 1.569236
n = 113: 1.550876
n = 114: 1.579460
n = 115: 1.564684
n = 116: 1.568026
n = 117: 1.566017
n = 118: 1.570029
n = 119: 1.577798
n = 120: 1.587040
n = 121: 1.580713
n = 122: 1.607301
n = 123: 1.596544
n = 124: 1.609371
n = 125: 1.614050
n = 126: 1.616043
n = 127: 1.630634
n = 128: 1.648595
n = 129: 1.642775
n = 130: 1.626761
n = 131: 1.616397
n = 132: 1.640657
n = 133: 1.660142
n = 134: 1.664018
n = 135: 1.654972
n = 136: 1.679113
n = 137: 1.647424
n = 138: 1.661631
n = 139: 1.659867
n = 140: 1.689704
n = 141: 1.700964
n = 142: 1.714920
n = 143: 1.731101
n = 144: 1.737286
n = 145: 1.722227
n = 146: 1.722176
n = 147: 1.725855
n = 148: 1.788659
n = 149: 1.781533
n = 150: 1.805007
n = 151: 1.821144
n = 152: 1.886703
n = 153: 1.867100
n = 154: 1.866811
n = 155: 1.860843
n = 156: 1.879919
n = 157: 1.894617
n = 158: 1.895463
n = 159: 1.907628
n = 160: 1.953103
n = 161: 1.948024
n = 162: 2.008280
n = 163: 2.031467
n = 164: 2.087453
n = 165: 2.065877
n = 166: 2.093596
n = 167: 2.127535
n = 168: 2.184649
n = 169: 2.167052
n = 170: 2.176276
n = 171: 2.205810
n = 172: 2.229478
n = 173: 2.266525
n = 174: 2.274137
n = 175: 2.355087
n = 176: 2.358372
n = 177: 2.445348
n = 178: 2.483012
n = 179: 2.540296
n = 180: 2.532874
n = 181: 2.546228
n = 182: 2.594481
n = 183: 2.620318
n = 184: 2.694022
n = 185: 2.687043
n = 186: 2.728546
n = 187: 2.770704
n = 188: 2.786557
n = 189: 2.341833
n = 190: 2.362651
n = 191: 2.464634
n = 192: 2.543905
n = 193: 2.697746
n = 194: 2.279784
n = 195: 2.328215
n = 196: 2.350705
b = 31: 2.060844
n = 16: 1.000000
n = 17: 0.986842
n = 18: 0.994444
n = 19: 1.004785
n = 20: 1.004098
n = 21: 1.003521
n = 22: 1.003049
n = 23: 0.994695
n = 24: 0.912580
n = 25: 0.991786
n = 26: 0.996344
n = 27: 1.000000
n = 28: 1.000000
n = 29: 0.998682
n = 30: 1.001185
n = 31: 0.997849
n = 32: 1.024024
n = 33: 1.017241
n = 34: 1.059614
n = 35: 1.033001
n = 36: 1.045226
n = 37: 1.039948
n = 38: 1.048990
n = 39: 1.043356
n = 40: 1.054881
n = 41: 1.049196
n = 42: 1.062700
n = 43: 1.065199
n = 44: 1.072000
n = 45: 1.065113
n = 46: 1.084912
n = 47: 1.071798
n = 48: 1.093750
n = 49: 1.084848
n = 50: 1.096978
n = 51: 1.150783
n = 52: 1.103982
n = 53: 1.105798
n = 54: 1.114330
n = 55: 1.118486
n = 56: 1.134452
n = 57: 1.158922
n = 58: 1.206310
n = 59: 1.221999
n = 60: 1.256229
n = 61: 1.243862
n = 62: 1.255433
n = 63: 1.288772
n = 64: 1.342109
n = 65: 1.331794
n = 66: 1.348174
n = 67: 1.358406
n = 68: 1.398011
n = 69: 1.382289
n = 70: 1.388941
n = 71: 1.406688
n = 72: 1.415380
n = 73: 1.411184
n = 74: 1.408488
n = 75: 1.441580
n = 76: 1.426240
n = 77: 1.414307
n = 78: 1.423056
n = 79: 1.444559
n = 80: 1.455199
n = 81: 1.451469
n = 82: 1.442211
n = 83: 1.450368
n = 84: 1.493252
n = 85: 1.459584
n = 86: 1.483092
n = 87: 1.467043
n = 88: 1.482021
n = 89: 1.470116
n = 90: 1.479361
n = 91: 1.477740
n = 92: 1.513344
n = 93: 1.521919
n = 94: 1.501385
n = 95: 1.531024
n = 96: 1.513281
n = 97: 1.529031
n = 98: 1.510818
n = 99: 1.530907
n = 100: 1.525372
n = 101: 1.508829
n = 102: 1.546394
n = 103: 1.518812
n = 104: 1.554391
n = 105: 1.561157
n = 106: 1.535975
n = 107: 1.538256
n = 108: 1.588980
n = 109: 1.541213
n = 110: 1.549371
n = 111: 1.547325
n = 112: 1.568928
n = 113: 1.555326
n = 114: 1.579525
n = 115: 1.565998
n = 116: 1.571102
n = 117: 1.565639
n = 118: 1.574224
n = 119: 1.574250
n = 120: 1.581748
n = 121: 1.567529
n = 122: 1.601336
n = 123: 1.583462
n = 124: 1.595199
n = 125: 1.603860
n = 126: 1.609839
n = 127: 1.616712
n = 128: 1.646061
n = 129: 1.648350
n = 130: 1.629189
n = 131: 1.632722
n = 132: 1.645327
n = 133: 1.664228
n = 134: 1.656317
n = 135: 1.654351
n = 136: 1.682522
n = 137: 1.645689
n = 138: 1.657701
n = 139: 1.659395
n = 140: 1.687018
n = 141: 1.690810
n = 142: 1.713977
n = 143: 1.719038
n = 144: 1.742170
n = 145: 1.716016
n = 146: 1.742985
n = 147: 1.740207
n = 148: 1.787459
n = 149: 1.789921
n = 150: 1.802642
n = 151: 1.820682
n = 152: 1.883262
n = 153: 1.868700
n = 154: 1.864766
n = 155: 1.859274
n = 156: 1.891693
n = 157: 1.892538
n = 158: 1.900554
n = 159: 1.902704
n = 160: 1.958888
n = 161: 1.941806
n = 162: 2.012375
n = 163: 2.052937
n = 164: 2.081073
n = 165: 2.079922
n = 166: 2.103816
n = 167: 2.132718
n = 168: 2.179362
n = 169: 2.159072
n = 170: 2.182807
n = 171: 2.210382
n = 172: 2.227368
n = 173: 2.270896
n = 174: 2.272773
n = 175: 2.359103
n = 176: 2.371689
n = 177: 2.460617
n = 178: 2.476754
n = 179: 2.542575
n = 180: 2.533148
n = 181: 2.548003
n = 182: 2.613718
n = 183: 2.633199
n = 184: 2.692388
n = 185: 2.677945
n = 186: 2.721306
n = 187: 2.772302
n = 188: 2.790642
n = 189: 2.397279
n = 190: 2.369097
n = 191: 2.452489
n = 192: 2.514684
n = 193: 2.619147
n = 194: 2.305123
n = 195: 2.315402
n = 196: 2.328126
b = 32: 2.060658
n = 16: 1.054264
n = 17: 0.986755
n = 18: 0.988889
n = 19: 1.000000
n = 20: 1.004082
n = 21: 1.000000
n = 22: 0.993939
n = 23: 1.000000
n = 24: 1.004662
n = 25: 1.000000
n = 26: 1.000000
n = 27: 0.998366
n = 28: 0.998542
n = 29: 1.003968
n = 30: 1.000000
n = 31: 0.997843
n = 32: 0.999022
n = 33: 1.012658
n = 34: 1.052101
n = 35: 1.033898
n = 36: 1.045780
n = 37: 1.039344
n = 38: 1.026347
n = 39: 1.041573
n = 40: 1.052188
n = 41: 1.049172
n = 42: 1.062186
n = 43: 1.057082
n = 44: 1.066986
n = 45: 1.061738
n = 46: 1.080589
n = 47: 1.081566
n = 48: 1.095356
n = 49: 1.088150
n = 50: 1.097554
n = 51: 1.142269
n = 52: 1.100911
n = 53: 1.101061
n = 54: 1.128798
n = 55: 1.117915
n = 56: 1.131844
n = 57: 1.155646
n = 58: 1.201168
n = 59: 1.224753
n = 60: 1.249114
n = 61: 1.242691
n = 62: 1.261610
n = 63: 1.276766
n = 64: 1.302279
n = 65: 1.310462
n = 66: 1.340185
n = 67: 1.350378
n = 68: 1.377618
n = 69: 1.387846
n = 70: 1.379942
n = 71: 1.401400
n = 72: 1.419073
n = 73: 1.408915
n = 74: 1.417942
n = 75: 1.460965
n = 76: 1.428216
n = 77: 1.413793
n = 78: 1.430813
n = 79: 1.444248
n = 80: 1.455780
n = 81: 1.445596
n = 82: 1.447292
n = 83: 1.457576
n = 84: 1.487794
n = 85: 1.459026
n = 86: 1.476628
n = 87: 1.470344
n = 88: 1.487687
n = 89: 1.482474
n = 90: 1.504274
n = 91: 1.482882
n = 92: 1.508772
n = 93: 1.527040
n = 94: 1.499129
n = 95: 1.544384
n = 96: 1.503461
n = 97: 1.531203
n = 98: 1.504925
n = 99: 1.548506
n = 100: 1.527763
n = 101: 1.514209
n = 102: 1.544144
n = 103: 1.518171
n = 104: 1.558819
n = 105: 1.559612
n = 106: 1.533088
n = 107: 1.535723
n = 108: 1.584377
n = 109: 1.543883
n = 110: 1.551694
n = 111: 1.549504
n = 112: 1.569127
n = 113: 1.554110
n = 114: 1.580947
n = 115: 1.567074
n = 116: 1.568592
n = 117: 1.563503
n = 118: 1.574295
n = 119: 1.577961
n = 120: 1.577468
n = 121: 1.575974
n = 122: 1.604247
n = 123: 1.593408
n = 124: 1.601357
n = 125: 1.593754
n = 126: 1.597700
n = 127: 1.607128
n = 128: 1.615892
n = 129: 1.608600
n = 130: 1.611864
n = 131: 1.618599
n = 132: 1.642150
n = 133: 1.662711
n = 134: 1.664245
n = 135: 1.661805
n = 136: 1.679071
n = 137: 1.648210
n = 138: 1.663661
n = 139: 1.673332
n = 140: 1.682773
n = 141: 1.704927
n = 142: 1.720406
n = 143: 1.734453
n = 144: 1.740805
n = 145: 1.713091
n = 146: 1.737078
n = 147: 1.741986
n = 148: 1.784956
n = 149: 1.786734
n = 150: 1.802918
n = 151: 1.832484
n = 152: 1.882380
n = 153: 1.868837
n = 154: 1.863014
n = 155: 1.868588
n = 156: 1.878262
n = 157: 1.896056
n = 158: 1.897122
n = 159: 1.902808
n = 160: 1.962885
n = 161: 1.939325
n = 162: 2.015940
n = 163: 2.052255
n = 164: 2.083032
n = 165: 2.083125
n = 166: 2.094887
n = 167: 2.122228
n = 168: 2.170664
n = 169: 2.167552
n = 170: 2.190460
n = 171: 2.206830
n = 172: 2.217271
n = 173: 2.265165
n = 174: 2.282019
n = 175: 2.369295
n = 176: 2.370571
n = 177: 2.449058
n = 178: 2.489876
n = 179: 2.543943
n = 180: 2.534573
n = 181: 2.550452
n = 182: 2.611480
n = 183: 2.630603
n = 184: 2.697209
n = 185: 2.690302
n = 186: 2.743188
n = 187: 2.762139
n = 188: 2.782651
n = 189: 2.385467
n = 190: 2.485119
n = 191: 2.496342
n = 192: 2.497194
n = 193: 2.598725
n = 194: 2.301860
n = 195: 2.320698
n = 196: 2.337715
b = 33: 2.062811
n = 16: 0.781250
n = 17: 1.000000
n = 18: 0.994382
n = 19: 1.000000
n = 20: 1.000000
n = 21: 0.996491
n = 22: 1.012195
n = 23: 1.000000
n = 24: 1.000000
n = 25: 0.997934
n = 26: 1.000000
n = 27: 1.001631
n = 28: 0.998536
n = 29: 0.997365
n = 30: 1.002387
n = 31: 1.000000
n = 32: 0.998035
n = 33: 1.000000
n = 34: 1.057239
n = 35: 1.028396
n = 36: 1.046695
n = 37: 1.012141
n = 38: 1.053922
n = 39: 1.043944
n = 40: 1.055937
n = 41: 1.034102
n = 42: 1.067828
n = 43: 1.061812
n = 44: 1.071228
n = 45: 1.063240
n = 46: 1.081346
n = 47: 1.081566
n = 48: 1.095179
n = 49: 1.089647
n = 50: 1.092405
n = 51: 1.139589
n = 52: 1.075594
n = 53: 1.097904
n = 54: 1.121834
n = 55: 1.114345
n = 56: 1.126950
n = 57: 1.158364
n = 58: 1.205319
n = 59: 1.222631
n = 60: 1.246470
n = 61: 1.239061
n = 62: 1.253699
n = 63: 1.273003
n = 64: 1.300199
n = 65: 1.303450
n = 66: 1.317120
n = 67: 1.333721
n = 68: 1.376356
n = 69: 1.389334
n = 70: 1.383342
n = 71: 1.405446
n = 72: 1.412568
n = 73: 1.410145
n = 74: 1.410995
n = 75: 1.434705
n = 76: 1.429152
n = 77: 1.411830
n = 78: 1.435890
n = 79: 1.446970
n = 80: 1.451006
n = 81: 1.444795
n = 82: 1.445437
n = 83: 1.457039
n = 84: 1.489116
n = 85: 1.458669
n = 86: 1.476772
n = 87: 1.466987
n = 88: 1.496318
n = 89: 1.478050
n = 90: 1.506212
n = 91: 1.478397
n = 92: 1.510593
n = 93: 1.527423
n = 94: 1.498548
n = 95: 1.539330
n = 96: 1.510787
n = 97: 1.524757
n = 98: 1.506792
n = 99: 1.558316
n = 100: 1.524142
n = 101: 1.509393
n = 102: 1.541750
n = 103: 1.517948
n = 104: 1.557266
n = 105: 1.561203
n = 106: 1.526964
n = 107: 1.533979
n = 108: 1.587107
n = 109: 1.540639
n = 110: 1.549507
n = 111: 1.552203
n = 112: 1.567783
n = 113: 1.554418
n = 114: 1.581184
n = 115: 1.563348
n = 116: 1.572981
n = 117: 1.562368
n = 118: 1.573525
n = 119: 1.579207
n = 120: 1.581373
n = 121: 1.571812
n = 122: 1.601315
n = 123: 1.592704
n = 124: 1.601856
n = 125: 1.591747
n = 126: 1.594854
n = 127: 1.600190
n = 128: 1.620602
n = 129: 1.606336
n = 130: 1.608009
n = 131: 1.604253
n = 132: 1.618826
n = 133: 1.632411
n = 134: 1.638133
n = 135: 1.639758
n = 136: 1.676526
n = 137: 1.657956
n = 138: 1.663451
n = 139: 1.661872
n = 140: 1.687242
n = 141: 1.701074
n = 142: 1.716574
n = 143: 1.724455
n = 144: 1.730306
n = 145: 1.719981
n = 146: 1.728472
n = 147: 1.741521
n = 148: 1.788083
n = 149: 1.793362
n = 150: 1.801104
n = 151: 1.827855
n = 152: 1.877340
n = 153: 1.868075
n = 154: 1.861750
n = 155: 1.858339
n = 156: 1.883452
n = 157: 1.896241
n = 158: 1.898831
n = 159: 1.909796
n = 160: 1.954700
n = 161: 1.928221
n = 162: 2.018091
n = 163: 2.045903
n = 164: 2.084958
n = 165: 2.089003
n = 166: 2.087221
n = 167: 2.121175
n = 168: 2.181380
n = 169: 2.166762
n = 170: 2.180916
n = 171: 2.202653
n = 172: 2.229384
n = 173: 2.272258
n = 174: 2.280016
n = 175: 2.366726
n = 176: 2.362462
n = 177: 2.447569
n = 178: 2.476694
n = 179: 2.534892
n = 180: 2.530092
n = 181: 2.547722
n = 182: 2.602153
n = 183: 2.627444
n = 184: 2.694078
n = 185: 2.687460
n = 186: 2.728653
n = 187: 2.772655
n = 188: 2.774314
n = 189: 2.345764
n = 190: 2.446126
n = 191: 2.523846
n = 192: 2.587578
n = 193: 2.592862
n = 194: 2.311407
n = 195: 2.323677
n = 196: 2.345810
b = 34: 2.061185
n = 16: 0.992000
n = 17: 1.006667
n = 18: 1.005587
n = 19: 1.000000
n = 20: 1.000000
n = 21: 0.996491
n = 22: 1.000000
n = 23: 1.000000
n = 24: 1.000000
n = 25: 1.000000
n = 26: 1.001835
n = 27: 0.998363
n = 28: 0.995620
n = 29: 0.994737
n = 30: 0.998814
n = 31: 1.002160
n = 32: 0.998039
n = 33: 1.000894
n = 34: 0.998401
n = 35: 1.053476
n = 36: 1.041547
n = 37: 1.043307
n = 38: 1.052728
n = 39: 1.043234
n = 40: 1.052743
n = 41: 1.046557
n = 42: 1.063586
n = 43: 1.061389
n = 44: 1.071571
n = 45: 1.064815
n = 46: 1.083187
n = 47: 1.080834
n = 48: 1.097244
n = 49: 1.084996
n = 50: 1.095029
n = 51: 1.143371
n = 52: 1.108733
n = 53: 1.112111
n = 54: 1.116626
n = 55: 1.114144
n = 56: 1.131569
n = 57: 1.165490
n = 58: 1.203086
n = 59: 1.222297
n = 60: 1.248916
n = 61: 1.245678
n = 62: 1.238190
n = 63: 1.273116
n = 64: 1.283024
n = 65: 1.301430
n = 66: 1.309487
n = 67: 1.321786
n = 68: 1.327775
n = 69: 1.355943
n = 70: 1.382298
n = 71: 1.405852
n = 72: 1.406280
n = 73: 1.407076
n = 74: 1.406534
n = 75: 1.434481
n = 76: 1.426526
n = 77: 1.415596
n = 78: 1.420847
n = 79: 1.440637
n = 80: 1.455331
n = 81: 1.452662
n = 82: 1.441383
n = 83: 1.452250
n = 84: 1.493208
n = 85: 1.458930
n = 86: 1.478950
n = 87: 1.466265
n = 88: 1.483718
n = 89: 1.475105
n = 90: 1.484051
n = 91: 1.483988
n = 92: 1.514297
n = 93: 1.516759
n = 94: 1.499843
n = 95: 1.535370
n = 96: 1.514622
n = 97: 1.524707
n = 98: 1.510707
n = 99: 1.529815
n = 100: 1.523799
n = 101: 1.505587
n = 102: 1.541548
n = 103: 1.516490
n = 104: 1.554048
n = 105: 1.562520
n = 106: 1.533989
n = 107: 1.542416
n = 108: 1.585735
n = 109: 1.542262
n = 110: 1.546594
n = 111: 1.550047
n = 112: 1.570169
n = 113: 1.628276
n = 114: 1.580224
n = 115: 1.564661
n = 116: 1.572656
n = 117: 1.571912
n = 118: 1.573869
n = 119: 1.576873
n = 120: 1.581964
n = 121: 1.570131
n = 122: 1.602981
n = 123: 1.593035
n = 124: 1.600819
n = 125: 1.597964
n = 126: 1.596401
n = 127: 1.605433
n = 128: 1.616036
n = 129: 1.609935
n = 130: 1.598499
n = 131: 1.595332
n = 132: 1.619968
n = 133: 1.628803
n = 134: 1.622245
n = 135: 1.618124
n = 136: 1.625995
n = 137: 1.601891
n = 138: 1.635177
n = 139: 1.653540
n = 140: 1.685926
n = 141: 1.704050
n = 142: 1.714922
n = 143: 1.730435
n = 144: 1.737131
n = 145: 1.715576
n = 146: 1.736108
n = 147: 1.738884
n = 148: 1.791485
n = 149: 1.792184
n = 150: 1.807359
n = 151: 1.826224
n = 152: 1.884836
n = 153: 1.868302
n = 154: 1.867044
n = 155: 1.864474
n = 156: 1.889538
n = 157: 1.895546
n = 158: 1.893674
n = 159: 1.909552
n = 160: 1.941319
n = 161: 1.933713
n = 162: 2.010415
n = 163: 2.042250
n = 164: 2.086244
n = 165: 2.080296
n = 166: 2.098800
n = 167: 2.125621
n = 168: 2.183322
n = 169: 2.166126
n = 170: 2.177467
n = 171: 2.209576
n = 172: 2.230787
n = 173: 2.268108
n = 174: 2.272380
n = 175: 2.355560
n = 176: 2.361680
n = 177: 2.457658
n = 178: 2.484243
n = 179: 2.538352
n = 180: 2.532391
n = 181: 2.543594
n = 182: 2.611304
n = 183: 2.623247
n = 184: 2.681733
n = 185: 2.684481
n = 186: 2.725587
n = 187: 2.772504
n = 188: 2.787659
n = 189: 2.382664
n = 190: 2.409980
n = 191: 2.456560
n = 192: 2.526343
n = 193: 2.729098
n = 194: 2.277813
n = 195: 2.321315
n = 196: 2.353995
b = 35: 2.059508
n = 16: 1.008000
n = 17: 0.980263
n = 18: 0.994413
n = 19: 1.009479
n = 20: 1.000000
n = 21: 1.003509
n = 22: 0.996960
n = 23: 0.997340
n = 24: 0.997664
n = 25: 0.995885
n = 26: 1.000000
n = 27: 0.996748
n = 28: 1.060029
n = 29: 1.000000
n = 30: 0.998812
n = 31: 1.000000
n = 32: 1.000000
n = 33: 0.996429
n = 34: 1.000000
n = 35: 1.000749
n = 36: 1.033381
n = 37: 1.037884
n = 38: 1.053374
n = 39: 1.040472
n = 40: 1.055996
n = 41: 1.047133
n = 42: 1.061644
n = 43: 1.059720
n = 44: 1.071828
n = 45: 1.063657
n = 46: 1.082019
n = 47: 1.084097
n = 48: 1.093556
n = 49: 1.081385
n = 50: 1.093399
n = 51: 1.143188
n = 52: 1.096215
n = 53: 1.102948
n = 54: 1.116678
n = 55: 1.115894
n = 56: 1.130872
n = 57: 1.150604
n = 58: 1.205815
n = 59: 1.224438
n = 60: 1.249478
n = 61: 1.239717
n = 62: 1.260711
n = 63: 1.276552
n = 64: 1.302529
n = 65: 1.305055
n = 66: 1.316177
n = 67: 1.312815
n = 68: 1.311738
n = 69: 1.347345
n = 70: 1.346454
n = 71: 1.376049
n = 72: 1.412691
n = 73: 1.411167
n = 74: 1.410122
n = 75: 1.437869
n = 76: 1.424283
n = 77: 1.407970
n = 78: 1.421964
n = 79: 1.443010
n = 80: 1.452964
n = 81: 1.449610
n = 82: 1.445115
n = 83: 1.450826
n = 84: 1.500250
n = 85: 1.449617
n = 86: 1.481407
n = 87: 1.467424
n = 88: 1.492886
n = 89: 1.477235
n = 90: 1.502708
n = 91: 1.479787
n = 92: 1.513664
n = 93: 1.522993
n = 94: 1.505925
n = 95: 1.537410
n = 96: 1.515869
n = 97: 1.527625
n = 98: 1.507292
n = 99: 1.552286
n = 100: 1.527347
n = 101: 1.510257
n = 102: 1.544745
n = 103: 1.519235
n = 104: 1.554472
n = 105: 1.559776
n = 106: 1.533604
n = 107: 1.539273
n = 108: 1.591117
n = 109: 1.541744
n = 110: 1.543140
n = 111: 1.552073
n = 112: 1.566948
n = 113: 1.553183
n = 114: 1.576620
n = 115: 1.565067
n = 116: 1.570180
n = 117: 1.555597
n = 118: 1.578552
n = 119: 1.576497
n = 120: 1.581315
n = 121: 1.576816
n = 122: 1.604880
n = 123: 1.593720
n = 124: 1.601010
n = 125: 1.596219
n = 126: 1.600220
n = 127: 1.599625
n = 128: 1.615494
n = 129: 1.607550
n = 130: 1.605684
n = 131: 1.606074
n = 132: 1.623605
n = 133: 1.633016
n = 134: 1.622279
n = 135: 1.618852
n = 136: 1.627632
n = 137: 1.605528
n = 138: 1.623378
n = 139: 1.629305
n = 140: 1.652885
n = 141: 1.655802
n = 142: 1.684142
n = 143: 1.696947
n = 144: 1.728189
n = 145: 1.710181
n = 146: 1.731078
n = 147: 1.738076
n = 148: 1.794390
n = 149: 1.792556
n = 150: 1.799727
n = 151: 1.817059
n = 152: 1.882938
n = 153: 1.863227
n = 154: 1.874273
n = 155: 1.861437
n = 156: 1.892309
n = 157: 1.896549
n = 158: 1.902722
n = 159: 1.902415
n = 160: 1.957541
n = 161: 1.945818
n = 162: 2.013058
n = 163: 2.044017
n = 164: 2.087827
n = 165: 2.077893
n = 166: 2.104306
n = 167: 2.125695
n = 168: 2.165085
n = 169: 2.160609
n = 170: 2.184933
n = 171: 2.209171
n = 172: 2.234988
n = 173: 2.261162
n = 174: 2.272344
n = 175: 2.359290
n = 176: 2.368812
n = 177: 2.460535
n = 178: 2.489893
n = 179: 2.547935
n = 180: 2.528126
n = 181: 2.548481
n = 182: 2.642601
n = 183: 2.569242
n = 184: 2.700915
n = 185: 2.681769
n = 186: 2.720682
n = 187: 2.766666
n = 188: 2.781804
n = 189: 2.375654
n = 190: 2.400443
n = 191: 2.360717
n = 192: 2.570635
n = 193: 2.730535
n = 194: 2.280619
n = 195: 2.314418
n = 196: 2.354028
b = 36: 2.057417
n = 16: 1.000000
n = 17: 0.986842
n = 18: 0.994444
n = 19: 1.000000
n = 20: 0.991870
n = 21: 1.000000
n = 22: 0.993921
n = 23: 0.997347
n = 24: 0.988453
n = 25: 0.995902
n = 26: 0.996337
n = 27: 1.063725
n = 28: 1.000000
n = 29: 1.000000
n = 30: 1.001186
n = 31: 1.003236
n = 32: 1.001959
n = 33: 1.000000
n = 34: 0.999205
n = 35: 1.000746
n = 36: 0.998627
n = 37: 1.033943
n = 38: 1.052083
n = 39: 1.042159
n = 40: 1.056584
n = 41: 1.047665
n = 42: 1.063985
n = 43: 1.062685
n = 44: 1.071115
n = 45: 1.061715
n = 46: 1.081138
n = 47: 1.080745
n = 48: 1.094398
n = 49: 1.086919
n = 50: 1.101453
n = 51: 1.141288
n = 52: 1.101356
n = 53: 1.105494
n = 54: 1.119426
n = 55: 1.122208
n = 56: 1.131215
n = 57: 1.154203
n = 58: 1.211798
n = 59: 1.227364
n = 60: 1.253415
n = 61: 1.245713
n = 62: 1.266676
n = 63: 1.279785
n = 64: 1.300702
n = 65: 1.309027
n = 66: 1.324049
n = 67: 1.327358
n = 68: 1.347706
n = 69: 1.343119
n = 70: 1.347967
n = 71: 1.357959
n = 72: 1.360273
n = 73: 1.372907
n = 74: 1.411293
n = 75: 1.436646
n = 76: 1.431376
n = 77: 1.410945
n = 78: 1.434410
n = 79: 1.445741
n = 80: 1.454369
n = 81: 1.451085
n = 82: 1.440503
n = 83: 1.455911
n = 84: 1.484654
n = 85: 1.454033
n = 86: 1.478030
n = 87: 1.466100
n = 88: 1.496640
n = 89: 1.476568
n = 90: 1.504229
n = 91: 1.478261
n = 92: 1.513599
n = 93: 1.523941
n = 94: 1.497614
n = 95: 1.535184
n = 96: 1.512609
n = 97: 1.525527
n = 98: 1.508108
n = 99: 1.528254
n = 100: 1.524255
n = 101: 1.510648
n = 102: 1.549458
n = 103: 1.518192
n = 104: 1.552588
n = 105: 1.562812
n = 106: 1.535304
n = 107: 1.535964
n = 108: 1.585468
n = 109: 1.535637
n = 110: 1.549662
n = 111: 1.548355
n = 112: 1.569983
n = 113: 1.554653
n = 114: 1.578084
n = 115: 1.551912
n = 116: 1.569674
n = 117: 1.574190
n = 118: 1.567075
n = 119: 1.574386
n = 120: 1.587491
n = 121: 1.576533
n = 122: 1.602423
n = 123: 1.593077
n = 124: 1.601552
n = 125: 1.595550
n = 126: 1.599506
n = 127: 1.598783
n = 128: 1.619643
n = 129: 1.608580
n = 130: 1.603133
n = 131: 1.595838
n = 132: 1.614781
n = 133: 1.634242
n = 134: 1.621502
n = 135: 1.636836
n = 136: 1.624279
n = 137: 1.599258
n = 138: 1.615504
n = 139: 1.616854
n = 140: 1.650373
n = 141: 1.669212
n = 142: 1.668475
n = 143: 1.674632
n = 144: 1.678168
n = 145: 1.666288
n = 146: 1.704515
n = 147: 1.711116
n = 148: 1.793719
n = 149: 1.782675
n = 150: 1.788840
n = 151: 1.822176
n = 152: 1.884598
n = 153: 1.862897
n = 154: 1.864772
n = 155: 1.862813
n = 156: 1.897089
n = 157: 1.893073
n = 158: 2.036552
n = 159: 1.903843
n = 160: 1.952006
n = 161: 1.949011
n = 162: 2.008796
n = 163: 2.052638
n = 164: 2.090954
n = 165: 2.080560
n = 166: 2.104162
n = 167: 2.118727
n = 168: 2.175620
n = 169: 2.159656
n = 170: 2.192086
n = 171: 2.210315
n = 172: 2.232991
n = 173: 2.261605
n = 174: 2.275081
n = 175: 2.356251
n = 176: 2.367935
n = 177: 2.459864
n = 178: 2.486018
n = 179: 2.541862
n = 180: 2.539601
n = 181: 2.548931
n = 182: 2.615312
n = 183: 2.633267
n = 184: 2.690344
n = 185: 2.680922
n = 186: 2.725024
n = 187: 2.767990
n = 188: 2.783450
n = 189: 2.335859
n = 190: 2.379385
n = 191: 2.422300
n = 192: 2.508211
n = 193: 2.641303
n = 194: 2.300290
n = 195: 2.300750
n = 196: 2.346006
b = 37: 2.053280
n = 16: 1.000000
n = 17: 0.993377
n = 18: 0.994444
n = 19: 0.995283
n = 20: 1.012245
n = 21: 0.996503
n = 22: 0.993939
n = 23: 1.002660
n = 24: 1.000000
n = 25: 1.002066
n = 26: 1.001835
n = 27: 0.995098
n = 28: 1.000000
n = 29: 1.000000
n = 30: 1.000000
n = 31: 0.998921
n = 32: 0.999022
n = 33: 0.999108
n = 34: 0.999207
n = 35: 1.002237
n = 36: 1.001376
n = 37: 0.999368
n = 38: 1.045067
n = 39: 1.046840
n = 40: 1.057113
n = 41: 1.047596
n = 42: 1.061700
n = 43: 1.060888
n = 44: 1.073288
n = 45: 1.067112
n = 46: 1.083889
n = 47: 1.079987
n = 48: 1.093837
n = 49: 1.087258
n = 50: 1.084216
n = 51: 1.136948
n = 52: 1.098647
n = 53: 1.103734
n = 54: 1.115241
n = 55: 1.118097
n = 56: 1.131387
n = 57: 1.156389
n = 58: 1.210470
n = 59: 1.235966
n = 60: 1.247712
n = 61: 1.246925
n = 62: 1.262460
n = 63: 1.274869
n = 64: 1.301604
n = 65: 1.306079
n = 66: 1.313381
n = 67: 1.317769
n = 68: 1.334032
n = 69: 1.343789
n = 70: 1.353854
n = 71: 1.354832
n = 72: 1.358842
n = 73: 1.360625
n = 74: 1.361898
n = 75: 1.395657
n = 76: 1.430685
n = 77: 1.414862
n = 78: 1.415420
n = 79: 1.445700
n = 80: 1.452472
n = 81: 1.445434
n = 82: 1.447597
n = 83: 1.454289
n = 84: 1.489546
n = 85: 1.459592
n = 86: 1.480377
n = 87: 1.471394
n = 88: 1.485133
n = 89: 1.471791
n = 90: 1.487438
n = 91: 1.476808
n = 92: 1.518616
n = 93: 1.523242
n = 94: 1.501027
n = 95: 1.536766
n = 96: 1.502537
n = 97: 1.525739
n = 98: 1.509791
n = 99: 1.527895
n = 100: 1.524514
n = 101: 1.508762
n = 102: 1.544172
n = 103: 1.524262
n = 104: 1.549252
n = 105: 1.558012
n = 106: 1.535684
n = 107: 1.537879
n = 108: 1.588066
n = 109: 1.541457
n = 110: 1.547285
n = 111: 1.546506
n = 112: 1.566644
n = 113: 1.556299
n = 114: 1.580325
n = 115: 1.569221
n = 116: 1.571036
n = 117: 1.562018
n = 118: 1.570720
n = 119: 1.579149
n = 120: 1.583381
n = 121: 1.574986
n = 122: 1.605470
n = 123: 1.595413
n = 124: 1.599700
n = 125: 1.599110
n = 126: 1.588471
n = 127: 1.606187
n = 128: 1.622049
n = 129: 1.604425
n = 130: 1.604561
n = 131: 1.601289
n = 132: 1.624477
n = 133: 1.629657
n = 134: 1.618812
n = 135: 1.613933
n = 136: 1.621648
n = 137: 1.596891
n = 138: 1.613114
n = 139: 1.637638
n = 140: 1.647860
n = 141: 1.660535
n = 142: 1.668581
n = 143: 1.667912
n = 144: 1.681833
n = 145: 1.660149
n = 146: 1.682683
n = 147: 1.687284
n = 148: 1.733756
n = 149: 1.738794
n = 150: 1.763433
n = 151: 1.801897
n = 152: 1.874320
n = 153: 1.862185
n = 154: 1.860094
n = 155: 1.853968
n = 156: 1.884386
n = 157: 1.892227
n = 158: 1.899533
n = 159: 1.904793
n = 160: 1.957925
n = 161: 1.938837
n = 162: 2.007752
n = 163: 2.053074
n = 164: 2.078497
n = 165: 2.079897
n = 166: 2.094192
n = 167: 2.124747
n = 168: 2.178631
n = 169: 2.167528
n = 170: 2.192154
n = 171: 2.210623
n = 172: 2.220457
n = 173: 2.264790
n = 174: 2.273784
n = 175: 2.372423
n = 176: 2.370849
n = 177: 2.459742
n = 178: 2.496095
n = 179: 2.543472
n = 180: 2.535887
n = 181: 2.542780
n = 182: 2.618425
n = 183: 2.631386
n = 184: 2.694752
n = 185: 2.690646
n = 186: 2.718507
n = 187: 2.769702
n = 188: 2.789132
n = 189: 2.375249
n = 190: 2.430234
n = 191: 2.444117
n = 192: 2.496116
n = 193: 2.602380
n = 194: 2.308438
n = 195: 2.324092
n = 196: 2.333901
b = 38: 2.050683
n = 16: 1.000000
n = 17: 0.993421
n = 18: 1.005587
n = 19: 1.004785
n = 20: 1.000000
n = 21: 1.000000
n = 22: 1.000000
n = 23: 1.000000
n = 24: 1.004684
n = 25: 1.002075
n = 26: 1.000000
n = 27: 1.003263
n = 28: 0.995620
n = 29: 1.000000
n = 30: 0.998814
n = 31: 0.998922
n = 32: 1.002941
n = 33: 1.000000
n = 34: 0.996803
n = 35: 1.000749
n = 36: 0.962460
n = 37: 1.000000
n = 38: 1.023406
n = 39: 1.035196
n = 40: 1.099631
n = 41: 1.045609
n = 42: 1.072113
n = 43: 1.058302
n = 44: 1.104906
n = 45: 1.062477
n = 46: 1.097826
n = 47: 1.077449
n = 48: 1.095415
n = 49: 1.084223
n = 50: 1.095721
n = 51: 1.141720
n = 52: 1.105665
n = 53: 1.095260
n = 54: 1.115064
n = 55: 1.113293
n = 56: 1.130255
n = 57: 1.153004
n = 58: 1.199189
n = 59: 1.224551
n = 60: 1.246951
n = 61: 1.245220
n = 62: 1.257712
n = 63: 1.275017
n = 64: 1.307112
n = 65: 1.301043
n = 66: 1.320819
n = 67: 1.317460
n = 68: 1.331013
n = 69: 1.348472
n = 70: 1.346638
n = 71: 1.355014
n = 72: 1.361093
n = 73: 1.363101
n = 74: 1.358236
n = 75: 1.369596
n = 76: 1.375866
n = 77: 1.376289
n = 78: 1.418587
n = 79: 1.446480
n = 80: 1.454068
n = 81: 1.444460
n = 82: 1.441514
n = 83: 1.454278
n = 84: 1.487463
n = 85: 1.461451
n = 86: 1.475207
n = 87: 1.463567
n = 88: 1.492137
n = 89: 1.484956
n = 90: 1.502551
n = 91: 1.480228
n = 92: 1.510327
n = 93: 1.522909
n = 94: 1.496966
n = 95: 1.540642
n = 96: 1.511731
n = 97: 1.530285
n = 98: 1.516084
n = 99: 1.526629
n = 100: 1.529421
n = 101: 1.509172
n = 102: 1.540231
n = 103: 1.520203
n = 104: 1.553230
n = 105: 1.559572
n = 106: 1.533147
n = 107: 1.537196
n = 108: 1.588769
n = 109: 1.544966
n = 110: 1.548681
n = 111: 1.544775
n = 112: 1.562635
n = 113: 1.553174
n = 114: 1.577649
n = 115: 1.559074
n = 116: 1.567241
n = 117: 1.562243
n = 118: 1.570717
n = 119: 1.578339
n = 120: 1.585358
n = 121: 1.569744
n = 122: 1.605742
n = 123: 1.594489
n = 124: 1.607180
n = 125: 1.597696
n = 126: 1.596462
n = 127: 1.600861
n = 128: 1.614942
n = 129: 1.606942
n = 130: 1.600892
n = 131: 1.599037
n = 132: 1.624088
n = 133: 1.628190
n = 134: 1.625101
n = 135: 1.612207
n = 136: 1.620935
n = 137: 1.611343
n = 138: 1.623157
n = 139: 1.634877
n = 140: 1.651267
n = 141: 1.660336
n = 142: 1.672650
n = 143: 1.664569
n = 144: 1.678681
n = 145: 1.656825
n = 146: 1.684752
n = 147: 1.687402
n = 148: 1.735615
n = 149: 1.740453
n = 150: 1.737905
n = 151: 1.764120
n = 152: 1.805901
n = 153: 1.808785
n = 154: 1.815927
n = 155: 1.841393
n = 156: 1.883475
n = 157: 1.899995
n = 158: 1.894839
n = 159: 1.897930
n = 160: 1.952218
n = 161: 1.938912
n = 162: 2.017686
n = 163: 2.046732
n = 164: 2.078389
n = 165: 2.089718
n = 166: 2.110485
n = 167: 2.120905
n = 168: 2.173713
n = 169: 2.167067
n = 170: 2.188478
n = 171: 2.207500
n = 172: 2.221459
n = 173: 2.269930
n = 174: 2.283515
n = 175: 2.371119
n = 176: 2.375920
n = 177: 2.471505
n = 178: 2.497907
n = 179: 2.549392
n = 180: 2.536643
n = 181: 2.550844
n = 182: 2.619306
n = 183: 2.637884
n = 184: 2.694000
n = 185: 2.690014
n = 186: 2.731253
n = 187: 2.764803
n = 188: 2.784506
n = 189: 2.386655
n = 190: 2.463344
n = 191: 2.485816
n = 192: 2.502639
n = 193: 2.608298
n = 194: 2.306137
n = 195: 2.341687
n = 196: 2.349473
b = 39: 2.051153
n = 16: 1.000000
n = 17: 0.993377
n = 18: 0.994413
n = 19: 1.004762
n = 20: 0.995951
n = 21: 1.000000
n = 22: 1.003040
n = 23: 1.005333
n = 24: 1.002342
n = 25: 1.002075
n = 26: 1.005505
n = 27: 1.000000
n = 28: 0.998538
n = 29: 0.998682
n = 30: 0.998812
n = 31: 1.000000
n = 32: 1.002950
n = 33: 0.998216
n = 34: 1.000000
n = 35: 0.999253
n = 36: 1.000000
n = 37: 1.000000
n = 38: 1.000000
n = 39: 0.998920
n = 40: 1.050919
n = 41: 1.047087
n = 42: 1.064959
n = 43: 1.063243
n = 44: 1.066667
n = 45: 1.063240
n = 46: 1.083187
n = 47: 1.073534
n = 48: 1.094456
n = 49: 1.085186
n = 50: 1.105682
n = 51: 1.167266
n = 52: 1.101428
n = 53: 1.103806
n = 54: 1.115342
n = 55: 1.114185
n = 56: 1.132951
n = 57: 1.150621
n = 58: 1.206854
n = 59: 1.224312
n = 60: 1.243450
n = 61: 1.245332
n = 62: 1.255164
n = 63: 1.274167
n = 64: 1.300979
n = 65: 1.302086
n = 66: 1.312011
n = 67: 1.318129
n = 68: 1.332341
n = 69: 1.343128
n = 70: 1.345818
n = 71: 1.353203
n = 72: 1.357136
n = 73: 1.362768
n = 74: 1.362830
n = 75: 1.399524
n = 76: 1.367290
n = 77: 1.360648
n = 78: 1.365921
n = 79: 1.399256
n = 80: 1.453774
n = 81: 1.442512
n = 82: 1.443818
n = 83: 1.457117
n = 84: 1.483700
n = 85: 1.460143
n = 86: 1.477501
n = 87: 1.468446
n = 88: 1.496264
n = 89: 1.472069
n = 90: 1.510665
n = 91: 1.481209
n = 92: 1.515863
n = 93: 1.524024
n = 94: 1.525256
n = 95: 1.533039
n = 96: 1.524608
n = 97: 1.519397
n = 98: 1.502373
n = 99: 1.545862
n = 100: 1.528213
n = 101: 1.508364
n = 102: 1.546164
n = 103: 1.519054
n = 104: 1.556249
n = 105: 1.559129
n = 106: 1.527972
n = 107: 1.535119
n = 108: 1.590347
n = 109: 1.541594
n = 110: 1.548737
n = 111: 1.549161
n = 112: 1.564899
n = 113: 1.554164
n = 114: 1.579238
n = 115: 1.563602
n = 116: 1.573170
n = 117: 1.562042
n = 118: 1.571248
n = 119: 1.577370
n = 120: 1.581060
n = 121: 1.571496
n = 122: 1.606419
n = 123: 1.592846
n = 124: 1.602867
n = 125: 1.594924
n = 126: 1.595648
n = 127: 1.601834
n = 128: 1.627221
n = 129: 1.605585
n = 130: 1.604214
n = 131: 1.599953
n = 132: 1.614699
n = 133: 1.626314
n = 134: 1.619365
n = 135: 1.612342
n = 136: 1.620192
n = 137: 1.614463
n = 138: 1.621451
n = 139: 1.634469
n = 140: 1.657377
n = 141: 1.660426
n = 142: 1.667354
n = 143: 1.673567
n = 144: 1.677647
n = 145: 1.657310
n = 146: 1.676612
n = 147: 1.692577
n = 148: 1.734418
n = 149: 1.741875
n = 150: 1.739981
n = 151: 1.766534
n = 152: 1.808828
n = 153: 1.802399
n = 154: 1.798414
n = 155: 1.807976
n = 156: 1.822988
n = 157: 1.831766
n = 158: 1.845300
n = 159: 1.865178
n = 160: 1.959641
n = 161: 1.937640
n = 162: 2.020220
n = 163: 2.046047
n = 164: 2.081914
n = 165: 2.087862
n = 166: 2.105868
n = 167: 2.119773
n = 168: 2.183544
n = 169: 2.166322
n = 170: 2.181871
n = 171: 2.203261
n = 172: 2.224033
n = 173: 2.269168
n = 174: 2.284179
n = 175: 2.367193
n = 176: 2.373801
n = 177: 2.463160
n = 178: 2.501144
n = 179: 2.546925
n = 180: 2.532637
n = 181: 2.551788
n = 182: 2.620554
n = 183: 2.635701
n = 184: 2.692740
n = 185: 2.690663
n = 186: 2.727908
n = 187: 2.760477
n = 188: 2.788445
n = 189: 2.457809
n = 190: 2.460319
n = 191: 2.616999
n = 192: 2.528527
n = 193: 2.585469
n = 194: 2.308618
n = 195: 2.332726
n = 196: 2.348079
b = 40: 2.051168
n = 16: 1.000000
n = 17: 0.993377
n = 18: 1.005587
n = 19: 1.000000
n = 20: 1.004082
n = 21: 1.003509
n = 22: 1.000000
n = 23: 1.002660
n = 24: 1.000000
n = 25: 0.993814
n = 26: 1.001842
n = 27: 1.008183
n = 28: 0.997067
n = 29: 1.002642
n = 30: 1.000000
n = 31: 1.000000
n = 32: 1.000000
n = 33: 1.000000
n = 34: 1.001605
n = 35: 1.000747
n = 36: 1.002066
n = 37: 0.998736
n = 38: 0.998246
n = 39: 1.001082
n = 40: 0.999498
n = 41: 1.040658
n = 42: 1.063557
n = 43: 1.055790
n = 44: 1.069888
n = 45: 1.062940
n = 46: 1.080826
n = 47: 1.095440
n = 48: 1.083282
n = 49: 1.080761
n = 50: 1.098874
n = 51: 1.165595
n = 52: 1.100809
n = 53: 1.105215
n = 54: 1.119745
n = 55: 1.114409
n = 56: 1.131636
n = 57: 1.153332
n = 58: 1.211327
n = 59: 1.223658
n = 60: 1.246107
n = 61: 1.241887
n = 62: 1.260851
n = 63: 1.276247
n = 64: 1.304584
n = 65: 1.302116
n = 66: 1.316832
n = 67: 1.323614
n = 68: 1.331715
n = 69: 1.347982
n = 70: 1.341621
n = 71: 1.358215
n = 72: 1.359277
n = 73: 1.364124
n = 74: 1.360065
n = 75: 1.373330
n = 76: 1.364265
n = 77: 1.362516
n = 78: 1.370917
n = 79: 1.374903
n = 80: 1.380754
n = 81: 1.393568
n = 82: 1.442216
n = 83: 1.461573
n = 84: 1.484080
n = 85: 1.458082
n = 86: 1.473050
n = 87: 1.464835
n = 88: 1.488505
n = 89: 1.478390
n = 90: 1.508051
n = 91: 1.480276
n = 92: 1.511304
n = 93: 1.525006
n = 94: 1.520396
n = 95: 1.532351
n = 96: 1.523366
n = 97: 1.523398
n = 98: 1.503859
n = 99: 1.541340
n = 100: 1.531530
n = 101: 1.512380
n = 102: 1.543154
n = 103: 1.519118
n = 104: 1.553209
n = 105: 1.556795
n = 106: 1.527699
n = 107: 1.536778
n = 108: 1.587827
n = 109: 1.545650
n = 110: 1.550184
n = 111: 1.552270
n = 112: 1.565870
n = 113: 1.555675
n = 114: 1.596375
n = 115: 1.551059
n = 116: 1.572012
n = 117: 1.567092
n = 118: 1.566091
n = 119: 1.578039
n = 120: 1.586672
n = 121: 1.573722
n = 122: 1.607232
n = 123: 1.594167
n = 124: 1.599067
n = 125: 1.593285
n = 126: 1.593885
n = 127: 1.601214
n = 128: 1.625749
n = 129: 1.607330
n = 130: 1.606661
n = 131: 1.610731
n = 132: 1.624985
n = 133: 1.630398
n = 134: 1.624871
n = 135: 1.614636
n = 136: 1.622562
n = 137: 1.615893
n = 138: 1.624637
n = 139: 1.632750
n = 140: 1.649813
n = 141: 1.660669
n = 142: 1.669553
n = 143: 1.671320
n = 144: 1.677841
n = 145: 1.666059
n = 146: 1.682571
n = 147: 1.690619
n = 148: 1.734933
n = 149: 1.730530
n = 150: 1.739120
n = 151: 1.762773
n = 152: 1.807536
n = 153: 1.793407
n = 154: 1.799817
n = 155: 1.820896
n = 156: 1.822367
n = 157: 1.827902
n = 158: 1.817088
n = 159: 1.810545
n = 160: 1.862500
n = 161: 1.859609
n = 162: 1.954453
n = 163: 2.005398
n = 164: 2.077659
n = 165: 2.087373
n = 166: 2.105174
n = 167: 2.122438
n = 168: 2.174387
n = 169: 2.168431
n = 170: 2.193397
n = 171: 2.205252
n = 172: 2.219576
n = 173: 2.268028
n = 174: 2.282818
n = 175: 2.370922
n = 176: 2.382420
n = 177: 2.462969
n = 178: 2.503013
n = 179: 2.546729
n = 180: 2.536566
n = 181: 2.559057
n = 182: 2.620786
n = 183: 2.636823
n = 184: 2.695269
n = 185: 2.691660
n = 186: 2.728563
n = 187: 2.757916
n = 188: 2.782503
n = 189: 2.387920
n = 190: 2.484353
n = 191: 2.598857
n = 192: 2.510186
n = 193: 2.597685
n = 194: 2.308154
n = 195: 2.334296
n = 196: 2.329772
b = 41: 2.045460
n = 16: 1.000000
n = 17: 1.000000
n = 18: 0.994413
n = 19: 1.009524
n = 20: 0.995935
n = 21: 1.000000
n = 22: 0.993902
n = 23: 0.994695
n = 24: 0.997669
n = 25: 0.993840
n = 26: 0.992674
n = 27: 0.998369
n = 28: 1.001466
n = 29: 1.000000
n = 30: 1.000000
n = 31: 1.001076
n = 32: 1.000980
n = 33: 0.997321
n = 34: 1.000000
n = 35: 0.998509
n = 36: 0.997942
n = 37: 0.996841
n = 38: 0.999416
n = 39: 0.997838
n = 40: 1.000000
n = 41: 1.000932
n = 42: 1.075523
n = 43: 1.055720
n = 44: 1.067012
n = 45: 1.065258
n = 46: 1.082720
n = 47: 1.080078
n = 48: 1.096374
n = 49: 1.088150
n = 50: 1.066702
n = 51: 1.141170
n = 52: 1.102041
n = 53: 1.104801
n = 54: 1.118100
n = 55: 1.114598
n = 56: 1.125539
n = 57: 1.165335
n = 58: 1.206273
n = 59: 1.221664
n = 60: 1.249879
n = 61: 1.244991
n = 62: 1.259642
n = 63: 1.284080
n = 64: 1.305721
n = 65: 1.302600
n = 66: 1.315643
n = 67: 1.317862
n = 68: 1.333775
n = 69: 1.345165
n = 70: 1.348325
n = 71: 1.357392
n = 72: 1.358266
n = 73: 1.360075
n = 74: 1.359457
n = 75: 1.374949
n = 76: 1.371758
n = 77: 1.362980
n = 78: 1.365336
n = 79: 1.383015
n = 80: 1.374762
n = 81: 1.375881
n = 82: 1.373648
n = 83: 1.402512
n = 84: 1.489252
n = 85: 1.459044
n = 86: 1.479228
n = 87: 1.468299
n = 88: 1.491253
n = 89: 1.482093
n = 90: 1.498970
n = 91: 1.481930
n = 92: 1.511794
n = 93: 1.527848
n = 94: 1.498414
n = 95: 1.542514
n = 96: 1.512417
n = 97: 1.524013
n = 98: 1.510969
n = 99: 1.522215
n = 100: 1.524194
n = 101: 1.513522
n = 102: 1.545643
n = 103: 1.516728
n = 104: 1.554799
n = 105: 1.563705
n = 106: 1.532408
n = 107: 1.535157
n = 108: 1.583978
n = 109: 1.542774
n = 110: 1.551199
n = 111: 1.550151
n = 112: 1.566479
n = 113: 1.557629
n = 114: 1.580619
n = 115: 1.565731
n = 116: 1.569145
n = 117: 1.573907
n = 118: 1.571761
n = 119: 1.579345
n = 120: 1.582889
n = 121: 1.562282
n = 122: 1.604983
n = 123: 1.596088
n = 124: 1.607637
n = 125: 1.594793
n = 126: 1.595499
n = 127: 1.603273
n = 128: 1.622855
n = 129: 1.609546
n = 130: 1.605811
n = 131: 1.611362
n = 132: 1.624312
n = 133: 1.632167
n = 134: 1.627703
n = 135: 1.615798
n = 136: 1.621385
n = 137: 1.615075
n = 138: 1.621787
n = 139: 1.636033
n = 140: 1.656102
n = 141: 1.661474
n = 142: 1.663376
n = 143: 1.662908
n = 144: 1.671792
n = 145: 1.657253
n = 146: 1.683167
n = 147: 1.693643
n = 148: 1.735808
n = 149: 1.742654
n = 150: 1.740133
n = 151: 1.757520
n = 152: 1.805780
n = 153: 1.806621
n = 154: 1.797976
n = 155: 1.806285
n = 156: 1.822084
n = 157: 1.814880
n = 158: 1.818996
n = 159: 1.819524
n = 160: 1.871438
n = 161: 1.855999
n = 162: 1.929411
n = 163: 1.949625
n = 164: 1.991274
n = 165: 2.001607
n = 166: 2.040316
n = 167: 2.077045
n = 168: 2.178118
n = 169: 2.172230
n = 170: 2.194363
n = 171: 2.207531
n = 172: 2.219314
n = 173: 2.268288
n = 174: 2.288506
n = 175: 2.376058
n = 176: 2.377615
n = 177: 2.471326
n = 178: 2.505356
n = 179: 2.552060
n = 180: 2.533397
n = 181: 2.548183
n = 182: 2.619023
n = 183: 2.641116
n = 184: 2.698725
n = 185: 2.695349
n = 186: 2.730624
n = 187: 2.772042
n = 188: 2.789754
n = 189: 2.400669
n = 190: 2.507194
n = 191: 2.439893
n = 192: 2.498302
n = 193: 2.597614
n = 194: 2.313359
n = 195: 2.333354
n = 196: 2.334381
b = 42: 2.039156
n = 16: 1.032000
n = 17: 0.986667
n = 18: 1.000000
n = 19: 0.990610
n = 20: 1.000000
n = 21: 1.000000
n = 22: 1.000000
n = 23: 1.000000
n = 24: 0.997680
n = 25: 0.995876
n = 26: 0.994516
n = 27: 1.000000
n = 28: 1.001464
n = 29: 0.997372
n = 30: 0.998814
n = 31: 1.001076
n = 32: 0.959586
n = 33: 0.998216
n = 34: 0.998401
n = 35: 0.999254
n = 36: 0.997941
n = 37: 1.000631
n = 38: 0.998830
n = 39: 1.000540
n = 40: 0.997997
n = 41: 0.999069
n = 42: 0.998704
n = 43: 1.053849
n = 44: 1.071058
n = 45: 1.062454
n = 46: 1.083450
n = 47: 1.081593
n = 48: 1.064681
n = 49: 1.084104
n = 50: 1.095985
n = 51: 1.139338
n = 52: 1.111604
n = 53: 1.101131
n = 54: 1.117246
n = 55: 1.114717
n = 56: 1.130203
n = 57: 1.156401
n = 58: 1.206487
n = 59: 1.222502
n = 60: 1.246349
n = 61: 1.237426
n = 62: 1.259793
n = 63: 1.275995
n = 64: 1.303595
n = 65: 1.303248
n = 66: 1.314627
n = 67: 1.313187
n = 68: 1.333260
n = 69: 1.345184
n = 70: 1.345286
n = 71: 1.359244
n = 72: 1.358478
n = 73: 1.381999
n = 74: 1.357696
n = 75: 1.397789
n = 76: 1.365259
n = 77: 1.353403
n = 78: 1.378957
n = 79: 1.375977
n = 80: 1.377546
n = 81: 1.373785
n = 82: 1.373503
n = 83: 1.381969
n = 84: 1.401235
n = 85: 1.404822
n = 86: 1.475880
n = 87: 1.468678
n = 88: 1.495061
n = 89: 1.478200
n = 90: 1.502704
n = 91: 1.478148
n = 92: 1.510457
n = 93: 1.521955
n = 94: 1.499978
n = 95: 1.541786
n = 96: 1.513263
n = 97: 1.520873
n = 98: 1.505398
n = 99: 1.532146
n = 100: 1.525277
n = 101: 1.510358
n = 102: 1.544841
n = 103: 1.517764
n = 104: 1.542338
n = 105: 1.556910
n = 106: 1.545260
n = 107: 1.533219
n = 108: 1.586383
n = 109: 1.539701
n = 110: 1.542253
n = 111: 1.549561
n = 112: 1.568395
n = 113: 1.558019
n = 114: 1.581594
n = 115: 1.563530
n = 116: 1.573730
n = 117: 1.563948
n = 118: 1.571970
n = 119: 1.576927
n = 120: 1.584637
n = 121: 1.577154
n = 122: 1.605236
n = 123: 1.594558
n = 124: 1.605464
n = 125: 1.594360
n = 126: 1.594754
n = 127: 1.603271
n = 128: 1.622628
n = 129: 1.607708
n = 130: 1.606484
n = 131: 1.609797
n = 132: 1.622653
n = 133: 1.626643
n = 134: 1.626736
n = 135: 1.614199
n = 136: 1.620012
n = 137: 1.604959
n = 138: 1.622367
n = 139: 1.621487
n = 140: 1.656679
n = 141: 1.661290
n = 142: 1.674101
n = 143: 1.665255
n = 144: 1.673259
n = 145: 1.662569
n = 146: 1.671565
n = 147: 1.693302
n = 148: 1.734530
n = 149: 1.740840
n = 150: 1.741711
n = 151: 1.764419
n = 152: 1.804756
n = 153: 1.801172
n = 154: 1.800459
n = 155: 1.806948
n = 156: 1.820645
n = 157: 1.829903
n = 158: 1.818453
n = 159: 1.814010
n = 160: 1.869719
n = 161: 1.853628
n = 162: 1.921554
n = 163: 1.965012
n = 164: 1.990037
n = 165: 1.991613
n = 166: 2.009120
n = 167: 2.017071
n = 168: 2.055621
n = 169: 2.074470
n = 170: 2.120905
n = 171: 2.164914
n = 172: 2.223902
n = 173: 2.255180
n = 174: 2.285149
n = 175: 2.374096
n = 176: 2.374544
n = 177: 2.466448
n = 178: 2.503999
n = 179: 2.551115
n = 180: 2.532117
n = 181: 2.549514
n = 182: 2.619137
n = 183: 2.634388
n = 184: 2.695957
n = 185: 2.693880
n = 186: 2.725948
n = 187: 2.766078
n = 188: 2.785843
n = 189: 2.422146
n = 190: 2.429070
n = 191: 2.461155
n = 192: 2.500984
n = 193: 2.600206
n = 194: 2.304206
n = 195: 2.327039
n = 196: 2.318815
b = 43: 2.031354
n = 16: 1.000000
n = 17: 1.000000
n = 18: 1.005587
n = 19: 0.995261
n = 20: 1.004049
n = 21: 1.000000
n = 22: 1.000000
n = 23: 1.002660
n = 24: 1.000000
n = 25: 1.002075
n = 26: 1.000000
n = 27: 1.003284
n = 28: 0.994169
n = 29: 1.002642
n = 30: 0.998812
n = 31: 0.998922
n = 32: 0.999019
n = 33: 1.001787
n = 34: 0.999197
n = 35: 1.002992
n = 36: 0.999313
n = 37: 1.012642
n = 38: 0.998251
n = 39: 0.999458
n = 40: 0.996988
n = 41: 0.998140
n = 42: 0.999570
n = 43: 0.995598
n = 44: 1.091483
n = 45: 1.051667
n = 46: 1.080854
n = 47: 1.098270
n = 48: 1.090432
n = 49: 1.083285
n = 50: 1.092877
n = 51: 1.140950
n = 52: 1.101991
n = 53: 1.099355
n = 54: 1.120625
n = 55: 1.115972
n = 56: 1.128372
n = 57: 1.158462
n = 58: 1.214817
n = 59: 1.221664
n = 60: 1.250442
n = 61: 1.226704
n = 62: 1.247138
n = 63: 1.278977
n = 64: 1.308932
n = 65: 1.300188
n = 66: 1.311723
n = 67: 1.318600
n = 68: 1.328737
n = 69: 1.346032
n = 70: 1.340555
n = 71: 1.354149
n = 72: 1.359959
n = 73: 1.363003
n = 74: 1.351964
n = 75: 1.371593
n = 76: 1.370889
n = 77: 1.359884
n = 78: 1.379417
n = 79: 1.377781
n = 80: 1.379141
n = 81: 1.372516
n = 82: 1.371828
n = 83: 1.374373
n = 84: 1.403408
n = 85: 1.387274
n = 86: 1.402503
n = 87: 1.411470
n = 88: 1.489386
n = 89: 1.485176
n = 90: 1.498841
n = 91: 1.480920
n = 92: 1.507097
n = 93: 1.524743
n = 94: 1.498394
n = 95: 1.542803
n = 96: 1.513968
n = 97: 1.526930
n = 98: 1.513554
n = 99: 1.549837
n = 100: 1.527758
n = 101: 1.510022
n = 102: 1.543915
n = 103: 1.520412
n = 104: 1.555973
n = 105: 1.561077
n = 106: 1.532664
n = 107: 1.537530
n = 108: 1.591887
n = 109: 1.548026
n = 110: 1.549764
n = 111: 1.542527
n = 112: 1.566014
n = 113: 1.553882
n = 114: 1.580818
n = 115: 1.563568
n = 116: 1.566872
n = 117: 1.562014
n = 118: 1.574767
n = 119: 1.578976
n = 120: 1.589939
n = 121: 1.581389
n = 122: 1.604781
n = 123: 1.594427
n = 124: 1.608344
n = 125: 1.596855
n = 126: 1.596461
n = 127: 1.602782
n = 128: 1.615460
n = 129: 1.607803
n = 130: 1.608339
n = 131: 1.610166
n = 132: 1.625390
n = 133: 1.632213
n = 134: 1.627454
n = 135: 1.616675
n = 136: 1.620879
n = 137: 1.614314
n = 138: 1.622702
n = 139: 1.635794
n = 140: 1.649685
n = 141: 1.661719
n = 142: 1.671894
n = 143: 1.666024
n = 144: 1.670523
n = 145: 1.653785
n = 146: 1.682098
n = 147: 1.696565
n = 148: 1.737470
n = 149: 1.738123
n = 150: 1.728926
n = 151: 1.766029
n = 152: 1.806707
n = 153: 1.799959
n = 154: 1.797574
n = 155: 1.805200
n = 156: 1.822707
n = 157: 1.819267
n = 158: 1.820394
n = 159: 1.814174
n = 160: 1.866759
n = 161: 1.853143
n = 162: 1.918155
n = 163: 1.961329
n = 164: 1.992551
n = 165: 1.986013
n = 166: 2.010547
n = 167: 2.022182
n = 168: 2.066439
n = 169: 2.061509
n = 170: 2.088656
n = 171: 2.112349
n = 172: 2.130331
n = 173: 2.158234
n = 174: 2.189939
n = 175: 2.313228
n = 176: 2.373246
n = 177: 2.467443
n = 178: 2.503404
n = 179: 2.547183
n = 180: 2.527807
n = 181: 2.553125
n = 182: 2.622315
n = 183: 2.635169
n = 184: 2.694432
n = 185: 2.687241
n = 186: 2.721251
n = 187: 2.771372
n = 188: 2.786979
n = 189: 2.369708
n = 190: 2.379570
n = 191: 2.449432
n = 192: 2.531045
n = 193: 2.588748
n = 194: 2.306476
n = 195: 2.325916
n = 196: 2.326111
b = 44: 2.023895
n = 16: 0.968750
n = 17: 1.000000
n = 18: 1.000000
n = 19: 1.000000
n = 20: 0.995951
n = 21: 0.996503
n = 22: 1.003040
n = 23: 1.002674
n = 24: 0.997680
n = 25: 0.995868
n = 26: 0.990876
n = 27: 1.000000
n = 28: 1.002941
n = 29: 0.998686
n = 30: 0.998812
n = 31: 0.997847
n = 32: 0.997062
n = 33: 0.998216
n = 34: 0.997600
n = 35: 1.021626
n = 36: 1.060917
n = 37: 1.000633
n = 38: 0.999417
n = 39: 0.998378
n = 40: 0.998498
n = 41: 1.000931
n = 42: 0.999568
n = 43: 0.997200
n = 44: 0.998132
n = 45: 1.059019
n = 46: 1.084151
n = 47: 1.080287
n = 48: 1.095975
n = 49: 1.082516
n = 50: 1.094557
n = 51: 1.137365
n = 52: 1.102753
n = 53: 1.110650
n = 54: 1.120819
n = 55: 1.116188
n = 56: 1.127882
n = 57: 1.157445
n = 58: 1.205846
n = 59: 1.220922
n = 60: 1.246507
n = 61: 1.243736
n = 62: 1.252285
n = 63: 1.276584
n = 64: 1.308373
n = 65: 1.305076
n = 66: 1.313527
n = 67: 1.317748
n = 68: 1.329361
n = 69: 1.343354
n = 70: 1.349010
n = 71: 1.351140
n = 72: 1.352579
n = 73: 1.366690
n = 74: 1.357830
n = 75: 1.408659
n = 76: 1.363463
n = 77: 1.357355
n = 78: 1.374742
n = 79: 1.372823
n = 80: 1.376807
n = 81: 1.371002
n = 82: 1.372739
n = 83: 1.380525
n = 84: 1.404682
n = 85: 1.382128
n = 86: 1.401393
n = 87: 1.383572
n = 88: 1.408098
n = 89: 1.408016
n = 90: 1.538310
n = 91: 1.461022
n = 92: 1.511192
n = 93: 1.520478
n = 94: 1.501721
n = 95: 1.542774
n = 96: 1.514723
n = 97: 1.528368
n = 98: 1.503421
n = 99: 1.549101
n = 100: 1.528118
n = 101: 1.504309
n = 102: 1.548669
n = 103: 1.513522
n = 104: 1.548567
n = 105: 1.555128
n = 106: 1.543765
n = 107: 1.534071
n = 108: 1.588405
n = 109: 1.541571
n = 110: 1.553599
n = 111: 1.551419
n = 112: 1.569340
n = 113: 1.557768
n = 114: 1.569983
n = 115: 1.558059
n = 116: 1.569092
n = 117: 1.571351
n = 118: 1.570808
n = 119: 1.570827
n = 120: 1.586465
n = 121: 1.568749
n = 122: 1.606119
n = 123: 1.597196
n = 124: 1.596028
n = 125: 1.599969
n = 126: 1.597513
n = 127: 1.599466
n = 128: 1.612383
n = 129: 1.608651
n = 130: 1.608178
n = 131: 1.604801
n = 132: 1.620874
n = 133: 1.633781
n = 134: 1.626338
n = 135: 1.617830
n = 136: 1.623377
n = 137: 1.607990
n = 138: 1.619182
n = 139: 1.636445
n = 140: 1.648465
n = 141: 1.662056
n = 142: 1.675579
n = 143: 1.667296
n = 144: 1.681146
n = 145: 1.660061
n = 146: 1.685464
n = 147: 1.691680
n = 148: 1.734325
n = 149: 1.740524
n = 150: 1.744342
n = 151: 1.767387
n = 152: 1.806044
n = 153: 1.800215
n = 154: 1.800333
n = 155: 1.801354
n = 156: 1.820703
n = 157: 1.818187
n = 158: 1.822712
n = 159: 1.821628
n = 160: 1.868323
n = 161: 1.854209
n = 162: 1.922656
n = 163: 1.956937
n = 164: 1.992954
n = 165: 1.985608
n = 166: 2.009682
n = 167: 2.038402
n = 168: 2.065207
n = 169: 2.053001
n = 170: 2.078886
n = 171: 2.109605
n = 172: 2.131369
n = 173: 2.152006
n = 174: 2.153199
n = 175: 2.244638
n = 176: 2.242611
n = 177: 2.344909
n = 178: 2.412412
n = 179: 2.495039
n = 180: 2.531168
n = 181: 2.550047
n = 182: 2.622233
n = 183: 2.636475
n = 184: 2.694473
n = 185: 2.681866
n = 186: 2.731080
n = 187: 2.773415
n = 188: 2.790858
n = 189: 2.341066
n = 190: 2.406457
n = 191: 2.364557
n = 192: 2.573155
n = 193: 2.629643
n = 194: 2.312658
n = 195: 2.301843
n = 196: 2.345761
b = 45: 2.017313
n = 16: 1.000000
n = 17: 0.993333
n = 18: 1.000000
n = 19: 0.995238
n = 20: 1.000000
n = 21: 0.996479
n = 22: 1.003058
n = 23: 1.002653
n = 24: 0.997664
n = 25: 1.000000
n = 26: 1.001825
n = 27: 1.000000
n = 28: 0.998538
n = 29: 0.998684
n = 30: 0.998814
n = 31: 1.001078
n = 32: 0.999017
n = 33: 1.000894
n = 34: 1.000803
n = 35: 0.999254
n = 36: 0.997937
n = 37: 0.998098
n = 38: 0.998245
n = 39: 1.019438
n = 40: 0.998496
n = 41: 1.000000
n = 42: 0.998274
n = 43: 0.998800
n = 44: 0.998877
n = 45: 0.998953
n = 46: 1.077863
n = 47: 1.077098
n = 48: 1.094988
n = 49: 1.085541
n = 50: 1.098762
n = 51: 1.139523
n = 52: 1.098208
n = 53: 1.100507
n = 54: 1.126374
n = 55: 1.112188
n = 56: 1.130178
n = 57: 1.161290
n = 58: 1.208193
n = 59: 1.219194
n = 60: 1.248877
n = 61: 1.245369
n = 62: 1.264530
n = 63: 1.279355
n = 64: 1.308231
n = 65: 1.307160
n = 66: 1.317132
n = 67: 1.315215
n = 68: 1.323330
n = 69: 1.346743
n = 70: 1.345807
n = 71: 1.357399
n = 72: 1.364088
n = 73: 1.376950
n = 74: 1.358655
n = 75: 1.399426
n = 76: 1.362396
n = 77: 1.353617
n = 78: 1.376446
n = 79: 1.378555
n = 80: 1.378377
n = 81: 1.371587
n = 82: 1.369658
n = 83: 1.380643
n = 84: 1.406160
n = 85: 1.383161
n = 86: 1.402657
n = 87: 1.374079
n = 88: 1.404861
n = 89: 1.388957
n = 90: 1.415757
n = 91: 1.449243
n = 92: 1.547758
n = 93: 1.576759
n = 94: 1.504293
n = 95: 1.535518
n = 96: 1.509666
n = 97: 1.525406
n = 98: 1.512594
n = 99: 1.529428
n = 100: 1.522499
n = 101: 1.512678
n = 102: 1.546413
n = 103: 1.523277
n = 104: 1.552858
n = 105: 1.561476
n = 106: 1.531632
n = 107: 1.534221
n = 108: 1.584683
n = 109: 1.543164
n = 110: 1.546906
n = 111: 1.553755
n = 112: 1.567399
n = 113: 1.555654
n = 114: 1.580907
n = 115: 1.563356
n = 116: 1.570876
n = 117: 1.563887
n = 118: 1.570811
n = 119: 1.573361
n = 120: 1.590324
n = 121: 1.578862
n = 122: 1.607796
n = 123: 1.598829
n = 124: 1.600865
n = 125: 1.597462
n = 126: 1.599156
n = 127: 1.609752
n = 128: 1.616420
n = 129: 1.608396
n = 130: 1.609972
n = 131: 1.607239
n = 132: 1.622807
n = 133: 1.632341
n = 134: 1.618706
n = 135: 1.615142
n = 136: 1.628485
n = 137: 1.610979
n = 138: 1.622944
n = 139: 1.641084
n = 140: 1.653255
n = 141: 1.665542
n = 142: 1.667942
n = 143: 1.674197
n = 144: 1.686462
n = 145: 1.662996
n = 146: 1.683877
n = 147: 1.686047
n = 148: 1.739037
n = 149: 1.719036
n = 150: 1.742241
n = 151: 1.756148
n = 152: 1.807790
n = 153: 1.796151
n = 154: 1.796525
n = 155: 1.794531
n = 156: 1.828208
n = 157: 1.821948
n = 158: 1.822484
n = 159: 1.817534
n = 160: 1.860260
n = 161: 1.859514
n = 162: 1.926832
n = 163: 1.963603
n = 164: 1.984052
n = 165: 1.977417
n = 166: 2.008636
n = 167: 2.020436
n = 168: 2.054714
n = 169: 2.057339
n = 170: 2.086681
n = 171: 2.111227
n = 172: 2.134047
n = 173: 2.157556
n = 174: 2.155120
n = 175: 2.228577
n = 176: 2.238203
n = 177: 2.334037
n = 178: 2.381485
n = 179: 2.418062
n = 180: 2.407505
n = 181: 2.420490
n = 182: 2.508560
n = 183: 2.559381
n = 184: 2.687338
n = 185: 2.690304
n = 186: 2.727506
n = 187: 2.773436
n = 188: 2.783995
n = 189: 2.339305
n = 190: 2.385799
n = 191: 2.451525
n = 192: 2.557475
n = 193: 2.727898
n = 194: 2.280556
n = 195: 2.321069
n = 196: 2.342760
b = 46: 2.011690
n = 16: 0.992063
n = 17: 0.993377
n = 18: 1.005587
n = 19: 1.000000
n = 20: 1.004065
n = 21: 1.000000
n = 22: 0.996960
n = 23: 1.002667
n = 24: 1.009346
n = 25: 1.002066
n = 26: 1.003676
n = 27: 1.001639
n = 28: 0.998540
n = 29: 1.001323
n = 30: 0.997628
n = 31: 1.001076
n = 32: 1.000000
n = 33: 0.999106
n = 34: 0.998404
n = 35: 1.000000
n = 36: 1.000000
n = 37: 0.998737
n = 38: 0.997664
n = 39: 1.000539
n = 40: 1.000000
n = 41: 0.998606
n = 42: 0.999569
n = 43: 1.000801
n = 44: 0.998876
n = 45: 0.998258
n = 46: 0.997407
n = 47: 1.078425
n = 48: 1.095135
n = 49: 1.081962
n = 50: 1.108946
n = 51: 1.136748
n = 52: 1.096956
n = 53: 1.101269
n = 54: 1.113311
n = 55: 1.111799
n = 56: 1.129706
n = 57: 1.157895
n = 58: 1.204610
n = 59: 1.219655
n = 60: 1.241693
n = 61: 1.248330
n = 62: 1.259281
n = 63: 1.276499
n = 64: 1.309341
n = 65: 1.305272
n = 66: 1.325151
n = 67: 1.330266
n = 68: 1.330212
n = 69: 1.344475
n = 70: 1.347738
n = 71: 1.353849
n = 72: 1.358147
n = 73: 1.360682
n = 74: 1.360028
n = 75: 1.374457
n = 76: 1.366978
n = 77: 1.356730
n = 78: 1.364486
n = 79: 1.378070
n = 80: 1.377755
n = 81: 1.374203
n = 82: 1.374503
n = 83: 1.379214
n = 84: 1.395847
n = 85: 1.387625
n = 86: 1.398136
n = 87: 1.383548
n = 88: 1.404490
n = 89: 1.392310
n = 90: 1.418074
n = 91: 1.375969
n = 92: 1.437869
n = 93: 1.453021
n = 94: 1.543006
n = 95: 1.530048
n = 96: 1.523586
n = 97: 1.521178
n = 98: 1.504151
n = 99: 1.549312
n = 100: 1.532790
n = 101: 1.511398
n = 102: 1.541484
n = 103: 1.518716
n = 104: 1.556729
n = 105: 1.556665
n = 106: 1.532897
n = 107: 1.537388
n = 108: 1.595509
n = 109: 1.542243
n = 110: 1.547666
n = 111: 1.546475
n = 112: 1.566414
n = 113: 1.556542
n = 114: 1.580920
n = 115: 1.555616
n = 116: 1.568895
n = 117: 1.562739
n = 118: 1.573552
n = 119: 1.575559
n = 120: 1.587587
n = 121: 1.578409
n = 122: 1.612921
n = 123: 1.592821
n = 124: 1.602241
n = 125: 1.598681
n = 126: 1.589901
n = 127: 1.600412
n = 128: 1.618226
n = 129: 1.608904
n = 130: 1.604749
n = 131: 1.605578
n = 132: 1.614975
n = 133: 1.627090
n = 134: 1.619859
n = 135: 1.602180
n = 136: 1.619346
n = 137: 1.613342
n = 138: 1.622247
n = 139: 1.631925
n = 140: 1.652880
n = 141: 1.668232
n = 142: 1.667723
n = 143: 1.675862
n = 144: 1.673221
n = 145: 1.661349
n = 146: 1.687559
n = 147: 1.689962
n = 148: 1.741854
n = 149: 1.734844
n = 150: 1.749345
n = 151: 1.765443
n = 152: 1.810653
n = 153: 1.796938
n = 154: 1.805836
n = 155: 1.797382
n = 156: 1.826957
n = 157: 1.822104
n = 158: 1.812850
n = 159: 1.830482
n = 160: 1.861593
n = 161: 1.861510
n = 162: 1.925073
n = 163: 1.951431
n = 164: 1.995671
n = 165: 1.992127
n = 166: 1.994476
n = 167: 2.020321
n = 168: 2.074490
n = 169: 2.053866
n = 170: 2.078544
n = 171: 2.109143
n = 172: 2.157081
n = 173: 2.166024
n = 174: 2.166426
n = 175: 2.238867
n = 176: 2.240896
n = 177: 2.324741
n = 178: 2.374155
n = 179: 2.415874
n = 180: 2.400627
n = 181: 2.406671
n = 182: 2.578378
n = 183: 2.414904
n = 184: 2.534222
n = 185: 2.550252
n = 186: 2.621950
n = 187: 2.690810
n = 188: 2.788060
n = 189: 2.363328
n = 190: 2.409260
n = 191: 2.577408
n = 192: 2.524811
n = 193: 2.606808
n = 194: 2.310347
n = 195: 2.326990
n = 196: 2.352073
b = 47: 2.005786
n = 16: 0.984252
n = 17: 1.000000
n = 18: 0.988827
n = 19: 0.995261
n = 20: 0.995935
n = 21: 0.989547
n = 22: 0.996951
n = 23: 1.000000
n = 24: 0.997674
n = 25: 1.000000
n = 26: 0.996344
n = 27: 1.001637
n = 28: 1.001464
n = 29: 1.000000
n = 30: 0.998814
n = 31: 0.997845
n = 32: 1.000000
n = 33: 0.955409
n = 34: 1.001605
n = 35: 1.000000
n = 36: 0.969940
n = 37: 1.000000
n = 38: 1.052478
n = 39: 0.998379
n = 40: 1.010542
n = 41: 0.998605
n = 42: 0.998705
n = 43: 1.007197
n = 44: 0.999249
n = 45: 0.998255
n = 46: 0.999351
n = 47: 0.996073
n = 48: 1.076876
n = 49: 1.087471
n = 50: 1.093853
n = 51: 1.140144
n = 52: 1.100737
n = 53: 1.096707
n = 54: 1.093575
n = 55: 1.110996
n = 56: 1.126749
n = 57: 1.160067
n = 58: 1.208053
n = 59: 1.213371
n = 60: 1.248434
n = 61: 1.242595
n = 62: 1.257600
n = 63: 1.280028
n = 64: 1.307631
n = 65: 1.308196
n = 66: 1.315961
n = 67: 1.315166
n = 68: 1.335465
n = 69: 1.336927
n = 70: 1.343161
n = 71: 1.356022
n = 72: 1.357938
n = 73: 1.377016
n = 74: 1.354742
n = 75: 1.395248
n = 76: 1.366223
n = 77: 1.358447
n = 78: 1.383438
n = 79: 1.374068
n = 80: 1.381072
n = 81: 1.369385
n = 82: 1.372840
n = 83: 1.383098
n = 84: 1.401697
n = 85: 1.381831
n = 86: 1.403570
n = 87: 1.383788
n = 88: 1.400572
n = 89: 1.392922
n = 90: 1.418936
n = 91: 1.376248
n = 92: 1.403212
n = 93: 1.424952
n = 94: 1.428434
n = 95: 1.455981
n = 96: 1.525193
n = 97: 1.522466
n = 98: 1.501761
n = 99: 1.527670
n = 100: 1.526654
n = 101: 1.509865
n = 102: 1.540626
n = 103: 1.517712
n = 104: 1.558034
n = 105: 1.568200
n = 106: 1.529711
n = 107: 1.535565
n = 108: 1.587127
n = 109: 1.545130
n = 110: 1.549031
n = 111: 1.553950
n = 112: 1.565371
n = 113: 1.552286
n = 114: 1.581197
n = 115: 1.562722
n = 116: 1.571918
n = 117: 1.562485
n = 118: 1.572971
n = 119: 1.577317
n = 120: 1.585225
n = 121: 1.573864
n = 122: 1.606303
n = 123: 1.592804
n = 124: 1.606016
n = 125: 1.593198
n = 126: 1.595674
n = 127: 1.603135
n = 128: 1.619215
n = 129: 1.605661
n = 130: 1.609470
n = 131: 1.610065
n = 132: 1.622647
n = 133: 1.627684
n = 134: 1.619597
n = 135: 1.611185
n = 136: 1.622325
n = 137: 1.615493
n = 138: 1.622848
n = 139: 1.635967
n = 140: 1.659105
n = 141: 1.663193
n = 142: 1.664904
n = 143: 1.670899
n = 144: 1.678722
n = 145: 1.659713
n = 146: 1.682398
n = 147: 1.695945
n = 148: 1.738320
n = 149: 1.740993
n = 150: 1.741146
n = 151: 1.769169
n = 152: 1.805228
n = 153: 1.800243
n = 154: 1.798921
n = 155: 1.807430
n = 156: 1.819431
n = 157: 1.829063
n = 158: 1.818077
n = 159: 1.820196
n = 160: 1.871020
n = 161: 1.852522
n = 162: 1.929608
n = 163: 1.955307
n = 164: 1.985203
n = 165: 1.995037
n = 166: 2.010783
n = 167: 2.021500
n = 168: 2.066210
n = 169: 2.060216
n = 170: 2.087646
n = 171: 2.107776
n = 172: 2.127172
n = 173: 2.153526
n = 174: 2.164916
n = 175: 2.242795
n = 176: 2.247367
n = 177: 2.329753
n = 178: 2.384818
n = 179: 2.423444
n = 180: 2.408677
n = 181: 2.415472
n = 182: 2.470854
n = 183: 2.483664
n = 184: 2.535642
n = 185: 2.524304
n = 186: 2.577273
n = 187: 2.620823
n = 188: 2.636160
n = 189: 2.229418
n = 190: 2.301050
n = 191: 2.349704
n = 192: 2.519941
n = 193: 2.621947
n = 194: 2.295878
n = 195: 2.298101
n = 196: 2.348769
b = 48: 1.992683

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- Re: Strassen multiplication over the integers
  - From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>

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