Encoding of the first 500 critical Riemann zeta zeros

The data given below gives, for each of the zeros on the critical line, the y coordinate, the sign of the real part of the first derivative of zeta(s), the sign of the imaginary part of the fist derivative at the zero of zeta(s), the sign of the real part of the second derivative, the sign of the imaginary part of the second derivative, a checksum for these signs, the value of the anisotropy measure tan theta, and the encoding symbol A->H.

  1. 14.134725142, 1, 1, -1, -1, 0, 3.484902909627753, A
  2. 21.022039639, 1, -1, -1, 1, 0, -4.962678927864244, D
  3. 25.01085758, 1, 1, -1, -1, 0, 2.677290996452059, A
  4. 30.424876126, 1, -1, -1, 1, 0, -1.5586047896837238, D
  5. 32.935061588, 1, 1, -1, -1, 0, 1.3878187717570625, A
  6. 37.586178159, 1, -1, -1, 1, 0, -3.7388140692854344, D
  7. 40.918719012, 1, -1, -1, 1, 0, -4.362337701747673, D
  8. 43.327073281, 1, 1, -1, -1, 0, 1.2947596403616026, A
  9. 48.005150881, 1, -1, -1, 1, 0, -0.7388954088248779, D
  10. 49.773832478, 1, 1, -1, -1, 0, 1.6062108243319457, A
  11. 52.970321478, 1, 1, -1, -1, 0, 4.37244697635889, A
  12. 56.446247697, 1, -1, -1, 1, 0, -3.1843594284452905, D
  13. 59.347044003, 1, -1, -1, 1, 0, -1.6359984021384497, D
  14. 60.831778525, 1, 1, -1, -1, 0, 0.4057131131457224, A
  15. 65.112544048, 1, -1, -1, 1, 0, -1.048142518372168, D
  16. 67.079810529, 1, 1, -1, -1, 0, 8.669274345190077, A
  17. 69.546401711, 1, 1, -1, -1, 0, 4.640638431914339, A
  18. 72.067157674, 1, 1, -1, -1, 0, 2.9827866316974307, A
  19. 75.704690699, 1, -1, -1, 1, 0, -0.5030960583142499, D
  20. 77.144840069, 1, 1, -1, -1, 0, 2.2331457188675325, A
  21. 79.33737502, 1, 1, -1, -1, 0, 1.2226686537947058, A
  22. 82.910380854, 1, -1, -1, 1, 0, -1.2265720637351016, D
  23. 84.735492981, 1, 1, -1, -1, 0, 6.550129395646189, A
  24. 87.425274613, 1, -1, -1, 1, 0, -2.2538089850951817, D
  25. 88.809111208, 1, 1, -1, -1, 0, 0.47476635814924717, A
  26. 92.491899271, 1, -1, -1, 1, 0, -1.180042121648354, D
  27. 94.651344041, 1, -1, -1, 1, 0, -1.413051275352431, D
  28. 95.870634228, 1, 1, -1, -1, 0, 0.5299066307627971, A
  29. 98.831194218, 1, 1, -1, -1, 0, 197.55145808047246, A
  30. 101.317851006, 1, -1, -1, 1, 0, -4.941702213320838, D
  31. 103.72553804, 1, -1, -1, 1, 0, -2.0172079699943826, D
  32. 105.446623052, 1, 1, -1, -1, 0, 5.495591098939232, A
  33. 107.168611184, 1, 1, -1, -1, 0, 0.7119744019389307, A
  34. 111.029535543, 1, -1, 1, 1, 2, 0.43832498907590006, C
  35. 111.874659177, 1, 1, -1, -1, 0, 0.990554489724806, A
  36. 114.320220915, 1, 1, -1, -1, 0, 25.17066070520795, A
  37. 116.226680321, 1, 1, -1, -1, 0, 2.2298162970935613, A
  38. 118.790782866, 1, -1, -1, 1, 0, -10.579171149851302, D
  39. 121.370125002, 1, -1, -1, 1, 0, -1.001701769480149, D
  40. 122.946829294, 1, 1, -1, 1, 2, -14.695708701933773, B
  41. 124.256818554, 1, 1, 1, -1, 2, 0.20345594714660795, A
  42. 127.51668388, 1, -1, -1, 1, 0, -1.8825236401292929, D
  43. 129.5787042, 1, -1, -1, 1, 0, -1.917405405776955, D
  44. 131.087688531, 1, 1, -1, -1, 0, 2.606329398052542, A
  45. 133.497737203, 1, -1, -1, 1, 0, -2.919934827752366, D
  46. 134.756509753, 1, 1, -1, -1, 0, 0.4966002928838719, A
  47. 138.116042055, 1, -1, -1, 1, 0, -0.6097619294495522, D
  48. 139.736208952, 1, -1, -1, 1, 0, -2.830659043744565, D
  49. 141.123707404, 1, 1, -1, -1, 0, 1.48483759249775, A
  50. 143.111845808, 1, 1, -1, -1, 0, 1.5654694449863193, A
  51. 146.000982487, 1, -1, -1, 1, 0, -1.1081989754890156, D
  52. 147.422765343, 1, 1, -1, -1, 0, 3.71336980822533, A
  53. 150.053520421, 1, -1, -1, 1, 0, -0.5551422583719939, D
  54. 150.925257612, 1, 1, -1, -1, 0, 0.5429236509037039, A
  55. 153.024693811, 1, 1, -1, -1, 0, 1.4188766617870103, A
  56. 156.112909294, 1, -1, -1, 1, 0, -0.42590282049946887, D
  57. 157.597591818, 1, -1, -1, 1, 0, -2.9805859439293934, D
  58. 158.849988171, 1, 1, -1, -1, 0, 0.966646823007255, A
  59. 161.188964138, 1, 1, -1, -1, 0, 23.444460020355894, A
  60. 163.030709687, 1, 1, -1, -1, 0, 3.8422662044524354, A
  61. 165.537069188, 1, -1, -1, 1, 0, -1.4358600890298023, D
  62. 167.184439978, 1, -1, -1, 1, 0, -6.5451112526862065, D
  63. 169.094515416, 1, -1, -1, 1, 0, -1.7848985320612178, D
  64. 169.911976479, 1, 1, 1, -1, 2, -0.7787655268972481, B
  65. 173.41153652, 1, -1, -1, 1, 0, -0.44482121569072613, D
  66. 174.754191523, 1, -1, -1, 1, 0, -21.487054910013853, D
  67. 176.441434298, 1, 1, -1, -1, 0, 6.178451172260006, A
  68. 178.377407776, 1, 1, -1, -1, 0, -78.84180232021482, B
  69. 179.91648402, 1, 1, -1, -1, 0, 1.5396128321361244, A
  70. 182.207078484, 1, -1, -1, 1, 0, -30.34051813661849, D
  71. 184.874467848, 1, -1, 1, 1, 2, 0.4571731426503426, C
  72. 185.598783678, 1, 1, -1, -1, 0, 1.1156951704398024, A
  73. 187.228922584, 1, 1, -1, -1, 0, 0.9630682050317411, A
  74. 189.416158656, 1, 1, -1, -1, 0, 4.363461270046356, A
  75. 192.026656361, 1, -1, -1, 1, 0, -0.4641234269104473, D
  76. 193.079726604, 1, 1, -1, -1, 0, 2.048142850904004, A
  77. 195.26539668, 1, -1, -1, 1, 0, -3.307976358330546, D
  78. 196.876481841, 1, 1, -1, 1, 2, -13.233772416702994, B
  79. 198.015309676, 1, 1, 1, -1, 2, 0.11198218153602402, A
  80. 201.264751944, 1, -1, 1, 1, 2, -0.18831716736034287, D
  81. 202.493594514, 1, -1, -1, 1, 0, -16.613525699823168, D
  82. 204.189671803, 1, -1, -1, 1, 0, -8.556934997709408, D
  83. 205.394697202, 1, 1, -1, -1, 0, 0.5481734523268326, A
  84. 207.906258888, 1, -1, -1, 1, 0, -4.132090151479295, D
  85. 209.576509717, 1, -1, -1, -1, -2, 21.615863127275773, C
  86. 211.690862595, 1, -1, -1, 1, 0, -1.84286670219742, D
  87. 213.34791936, 1, -1, -1, 1, 0, -2.503772031372916, D
  88. 214.547044783, 1, 1, -1, -1, 0, 1.3921574321905446, A
  89. 216.169538508, 1, 1, -1, -1, 0, 0.7962149223185826, A
  90. 219.067596349, 1, -1, -1, 1, 0, -0.5801401465441607, D
  91. 220.714918839, 1, -1, -1, 1, 0, -0.6063532993677098, D
  92. 221.430705555, 1, 1, 1, -1, 2, 0.2586875962244637, A
  93. 224.007000255, 1, -1, -1, 1, 0, -1.535606125836665, D
  94. 224.98332467, 1, 1, -1, -1, 0, 0.5489829677061904, A
  95. 227.42144428, 1, -1, -1, 1, 0, -4.624917473864004, D
  96. 229.337413306, 1, -1, -1, 1, 0, -2.1676285154111388, D
  97. 231.2501887, 1, -1, -1, 1, 0, -0.5446913389340572, D
  98. 231.987235253, 1, 1, -1, -1, 0, 0.452730439079276, A
  99. 233.693404179, 1, 1, -1, -1, 0, 0.6797559384864499, A
  100. 236.524229666, 1, -1, -1, 1, 0, -0.6464611457497277, D
  101. 237.769820481, 1, -1, -1, 1, 0, 23.87119440437521, C
  102. 239.555477573, 1, -1, -1, 1, 0, -5.548594966179789, D
  103. 241.049157796, 1, 1, -1, -1, 0, 5.12233151584578, A
  104. 242.823271934, 1, 1, -1, -1, 0, -66.93346238312306, B
  105. 244.070898497, 1, 1, -1, -1, 0, 0.6250244080923771, A
  106. 247.136990075, 1, -1, 1, 1, 2, 0.42166934441616655, C
  107. 248.10199006, 1, -1, -1, -1, -2, 13.939613446895715, C
  108. 249.573689645, 1, 1, -1, -1, 0, 4.086603512161796, A
  109. 251.014947795, 1, 1, -1, -1, 0, 1.1412703976642968, A
  110. 253.069986748, 1, 1, -1, -1, 0, 9.150384139925926, A
  111. 255.306256455, 1, -1, -1, 1, 0, -0.8316695925105206, D
  112. 256.380713694, 1, 1, -1, -1, 0, 2.245899592856198, A
  113. 258.610439492, 1, -1, -1, 1, 0, -1.17808125464556, D
  114. 259.87440699, 1, 1, -1, 1, 2, -13.45463817467527, B
  115. 260.805084505, 1, 1, 1, -1, 2, -0.449753088965912, B
  116. 263.573893905, 1, -1, -1, 1, 0, -2.171059439883382, D
  117. 265.557851839, 1, -1, -1, 1, 0, -0.4153461535448356, D
  118. 266.614973782, 1, 1, -1, -1, 0, 7.041322628219283, A
  119. 267.921915083, 1, 1, -1, -1, 0, 1.1255396300204488, A
  120. 269.970449024, 1, 1, -1, 1, 2, -31.62533734531728, B
  121. 271.494055642, 1, 1, -1, -1, 0, 3.334780105969889, A
  122. 273.459609188, 1, -1, -1, 1, 0, -6.509081835003371, D
  123. 275.587492649, 1, -1, 1, 1, 2, -0.29290024141805526, D
  124. 276.452049503, 1, 1, -1, -1, 0, 1.684140525251563, A
  125. 278.25074353, 1, 1, -1, 1, 2, -10.136326190953145, B
  126. 279.229250928, 1, 1, 1, -1, 2, -0.2156417316571493, B
  127. 282.465114765, -1, -1, 1, 1, 0, 0.8312628905353894, G
  128. 283.211185733, 1, 1, -1, -1, 0, 2.260181765072384, A
  129. 284.835963981, 1, 1, -1, -1, 0, 5.611746130150903, A
  130. 286.667445363, 1, -1, -1, 1, 0, -4.059235495631246, D
  131. 287.911920501, 1, 1, -1, -1, 0, 1.7502074457055052, A
  132. 289.579854929, 1, 1, -1, -1, 0, 2.0361235552072685, A
  133. 291.846291329, 1, -1, -1, 1, 0, -1.6062211821596672, D
  134. 293.558434139, 1, -1, -1, 1, 0, -1.09214756207737, D
  135. 294.965369619, 1, -1, -1, 1, 0, -1.2425732213374914, D
  136. 295.573254879, -1, 1, 1, -1, 0, -0.9921225167469451, F
  137. 297.979277062, 1, 1, -1, -1, 0, 32.07640340081057, A
  138. 299.840326054, 1, -1, -1, 1, 0, -3.6256626052802297, D
  139. 301.649325462, 1, -1, -1, 1, 0, -1.172775820777226, D
  140. 302.69674959, 1, 1, -1, -1, 0, 1.8883349061175796, A
  141. 304.864371341, 1, -1, -1, 1, 0, -0.9757809378856183, D
  142. 305.728912602, 1, 1, -1, -1, 0, 0.9029657071780467, A
  143. 307.219496128, 1, 1, -1, -1, 0, 0.5965904660787817, A
  144. 310.109463147, 1, -1, 1, 1, 2, 0.238201554776322, C
  145. 311.16514153, 1, -1, -1, 1, 0, -5.123345996789718, D
  146. 312.427801181, 1, 1, -1, -1, 0, 3.107806471554846, A
  147. 313.985285731, 1, 1, -1, -1, 0, 3.2932530198110985, A
  148. 315.475616089, 1, 1, -1, -1, 0, 1.6078523190648344, A
  149. 317.734805942, 1, -1, -1, 1, 0, -1.3107820983261573, D
  150. 318.853104256, 1, 1, -1, -1, 0, 2.4184724644635387, A
  151. 321.160134309, 1, -1, -1, 1, 0, -0.38238922260627445, D
  152. 322.144558672, 1, 1, -1, -1, 0, 5.48602603489858, A
  153. 323.466969558, 1, 1, -1, -1, 0, 1.7093158028447735, A
  154. 324.862866052, 1, 1, -1, -1, 0, 0.6138714016046081, A
  155. 327.443901262, 1, -1, -1, 1, 0, -0.8915063307045042, D
  156. 329.03307168, 1, -1, -1, 1, 0, -0.7122715593127551, D
  157. 329.953239728, 1, 1, -1, -1, 0, 1.8662744676969303, A
  158. 331.474467583, 1, 1, -1, -1, 0, 2.009182026876637, A
  159. 333.645378525, 1, -1, -1, 1, 0, -0.6806249198677912, D
  160. 334.211354833, 1, 1, 1, -1, 2, -0.36494875465584403, B
  161. 336.841850428, 1, -1, -1, 1, 0, -1.3785476818579994, D
  162. 338.339992851, 1, -1, -1, 1, 0, -2.2844273419389167, D
  163. 339.858216725, 1, -1, -1, 1, 0, -2.2598620939401384, D
  164. 341.042261111, 1, 1, -1, -1, 0, 5.292449604350153, A
  165. 342.05487751, 1, 1, 1, -1, 2, -0.27831455398096083, B
  166. 344.66170294, 1, -1, -1, 1, 0, -1.6907691979420458, D
  167. 346.347870566, 1, -1, -1, 1, 0, -0.8357670964382145, D
  168. 347.272677584, 1, 1, -1, -1, 0, 1.5996055988017452, A
  169. 349.316260871, 1, -1, -1, 1, 0, -1.6135088958388972, D
  170. 350.408419349, 1, 1, -1, -1, 0, 2.43416073283005, A
  171. 351.878649025, 1, 1, -1, -1, 0, 1.9082187973968798, A
  172. 353.488900489, 1, 1, -1, -1, 0, 2.1233955452437097, A
  173. 356.017574977, 1, -1, 1, 1, 2, 0.24194540062111677, C
  174. 357.151302252, 1, -1, -1, 1, 0, -1.4151360694564885, D
  175. 357.952685102, 1, 1, -1, -1, 0, 0.5620086287357865, A
  176. 359.743754953, 1, 1, -1, -1, 0, 3.306562812483113, A
  177. 361.289361696, 1, 1, -1, -1, 0, 2.564905194176811, A
  178. 363.331330579, 1, -1, -1, 1, 0, -1.9132763124183052, D
  179. 364.736024114, 1, -1, -1, 1, 0, -6.218107439973309, D
  180. 366.212710288, 1, -1, -1, 1, 0, -26.941586372522806, D
  181. 367.993575482, 1, -1, -1, 1, 0, -1.2893978870573224, D
  182. 368.968438096, 1, 1, -1, -1, 0, 2.0139931901522687, A
  183. 370.050919212, 1, 1, 1, -1, 2, -0.35150301825782876, B
  184. 373.061928372, 1, -1, 1, 1, 2, 0.4677924388652097, C
  185. 373.864873911, 1, -1, -1, -1, -2, 3.4817400015178275, C
  186. 375.825912767, 1, -1, -1, 1, 0, -0.3612641970830922, D
  187. 376.324092231, 1, 1, 1, -1, 2, -0.17048221983081227, B
  188. 378.43668025, 1, 1, -1, -1, 0, -36.45428081941965, B
  189. 379.872975347, 1, 1, -1, -1, 0, 4.677066648153905, A
  190. 381.484468617, 1, 1, -1, -1, 0, 8.572536084456155, A
  191. 383.44352945, 1, -1, -1, 1, 0, -1.253281983854172, D
  192. 384.956116815, 1, -1, -1, 1, 0, -1.0150048996937209, D
  193. 385.861300846, 1, 1, -1, -1, 0, 1.6473360196481421, A
  194. 387.222890222, 1, 1, -1, -1, 0, 1.054285525184773, A
  195. 388.846128354, 1, 1, -1, -1, 0, 1.5874072858657244, A
  196. 391.456083564, -1, -1, 1, 1, 0, 0.7321285559509908, G
  197. 392.24508334, 1, -1, -1, -1, -2, 7.23038219030411, C
  198. 393.427743844, 1, 1, -1, -1, 0, 1.356609972817338, A
  199. 395.582870011, 1, -1, -1, 1, 0, -0.8939363864137041, D
  200. 396.381854223, 1, 1, -1, -1, 0, 0.8863263925397692, A
  201. 397.91873621, 1, 1, -1, -1, 0, 1.3300832745878506, A
  202. 399.985119876, 1, -1, -1, 1, 0, -3.1673923073697745, D
  203. 401.839228601, 1, -1, -1, 1, 0, -0.41492827627598916, D
  204. 402.861917764, 1, -1, -1, 1, 0, 61.489058238721476, C
  205. 404.2364418, 1, 1, -1, -1, 0, -52.0384915144852, B
  206. 405.13438746, 1, 1, 1, -1, 2, -0.2852493386840178, B
  207. 407.581460387, 1, -1, -1, 1, 0, -1.9359115268505167, D
  208. 408.947245502, 1, -1, -1, 1, 0, -8.527807102033593, D
  209. 410.513869193, 1, -1, -1, 1, 0, -3.812180536727697, D
  210. 411.972267804, 1, -1, -1, 1, 0, -4.662031733919943, D
  211. 413.26273607, 1, 1, -1, -1, 0, 5.5398716746895955, A
  212. 415.018809755, 1, -1, -1, 1, 0, -0.8444069751027914, D
  213. 415.455214996, -1, 1, 1, -1, 0, -7.509434881537031, F
  214. 418.38770579, 1, -1, -1, 1, 0, -0.46428027790237053, D
  215. 419.861364818, 1, -1, -1, 1, 0, -0.3829427042994517, D
  216. 420.643827625, 1, 1, -1, -1, 0, 1.629493950085014, A
  217. 422.076710059, 1, 1, -1, -1, 0, 2.0881912241649463, A
  218. 423.716579627, 1, 1, -1, -1, 0, 9.087002593746822, A
  219. 425.069882494, 1, 1, -1, -1, 0, 2.004973540678279, A
  220. 427.208825084, 1, -1, -1, 1, 0, -0.8163573896463242, D
  221. 428.127914077, 1, 1, -1, -1, 0, 1.8818186574070213, A
  222. 430.328745431, 1, -1, 1, 1, 2, -0.2859581646318212, D
  223. 431.301306931, 1, -1, -1, 1, 0, -7.5796315220936235, D
  224. 432.138641735, 1, 1, 1, -1, 2, -0.001955043900485127, B
  225. 433.889218481, 1, 1, -1, -1, 0, 1.4118360748548078, A
  226. 436.161006433, 1, -1, -1, 1, 0, -0.8637827603677071, D
  227. 437.581698168, 1, -1, -1, 1, 0, -1.1000903989084438, D
  228. 438.621738656, 1, 1, -1, -1, 0, 5.258201508085779, A
  229. 439.918442214, 1, 1, -1, -1, 0, 1.99050454180767, A
  230. 441.683199201, 1, -1, -1, 1, 0, -5.868824925396746, D
  231. 442.904546303, 1, 1, -1, -1, 0, 2.5922971558535064, A
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  460. 758.900238225, 1, 1, 1, -1, 2, 0.2979407783348307, A
  461. 760.282366984, 1, 1, -1, -1, 0, 0.7279170927289159, A
  462. 762.70003325, -1, -1, 1, 1, 0, 0.7972769571695038, G
  463. 763.593066173, 1, -1, -1, 1, 0, -1.518317490355908, D
  464. 764.307522724, 1, 1, -1, -1, 0, 0.7562427227139333, A
  465. 766.0875401, 1, -1, -1, 1, 0, -2.6847436785045633, D
  466. 767.218472156, 1, 1, -1, -1, 0, 92.58512577941852, A
  467. 768.281461807, 1, 1, -1, -1, 0, 1.5728597461081304, A
  468. 769.693407253, 1, 1, -1, -1, 0, 3.42322933500312, A
  469. 771.070839314, 1, 1, -1, -1, 0, 4.368665095775691, A
  470. 772.961617566, 1, -1, -1, 1, 0, -0.4005173862548548, D
  471. 774.117744628, 1, -1, -1, 1, 0, -1.110139462799011, D
  472. 775.047847097, 1, 1, -1, -1, 0, 12.874803184619282, A
  473. 775.999711963, 1, 1, -1, -1, 0, 0.8075027617664366, A
  474. 777.29974853, 1, 1, -1, -1, 0, 0.8768011783234304, A
  475. 779.157076949, 1, -1, -1, 1, 0, -2.6271251668623368, D
  476. 780.348925004, 1, -1, -1, 1, 0, -293.05450347576004, D
  477. 782.137664391, 1, -1, 1, 1, 2, 0.17170959533884386, C
  478. 782.597943946, 1, 1, -1, -1, 0, 0.539159446249617, A
  479. 784.288822612, 1, -1, -1, 1, 0, -6.02198649010478, D
  480. 785.739089701, 1, -1, -1, 1, 0, -1.22109063951801, D
  481. 786.461147451, 1, 1, -1, -1, 0, 0.9469973362366305, A
  482. 787.468463816, 1, 1, 1, -1, 2, -0.45496938869391634, B
  483. 790.059092364, 1, -1, 1, 1, 2, 0.5635134782473852, C
  484. 790.831620468, 1, -1, -1, 1, 0, 66.51067451285687, C
  485. 792.427707609, 1, -1, 1, 1, 2, -0.2507563303634125, D
  486. 792.888652563, 1, 1, 1, -1, 2, 0.22558910790710027, A
  487. 794.48379187, 1, 1, -1, -1, 0, 7.322992713056741, A
  488. 795.606596156, 1, 1, -1, -1, 0, 1.3722980607969582, A
  489. 797.263470038, 1, -1, -1, 1, 0, -7.253512526171401, D
  490. 798.707570166, 1, -1, -1, 1, 0, -1.954984980165169, D
  491. 799.654336211, 1, 1, -1, -1, 0, 2.1854769363691195, A
  492. 801.604246463, 1, -1, 1, 1, 2, -0.18312030550762967, D
  493. 802.541984878, 1, -1, -1, 1, 0, -2.301571881123993, D
  494. 803.243096204, 1, 1, -1, -1, 0, 0.37649758665319116, A
  495. 804.762239113, 1, 1, -1, -1, 0, 3.1584689496314624, A
  496. 805.861635667, 1, 1, -1, -1, 0, 0.6840771641836958, A
  497. 808.151814936, 1, -1, 1, 1, 2, 0.11058139771202492, C
  498. 809.197783363, 1, -1, -1, 1, 0, -1.1549561222357092, D
  499. 810.081804886, 1, 1, -1, -1, 0, 4.135623415945222, A
  500. 811.184358847, 1, 1, -1, -1, 0, 1.5049441682805962, A

    Last updated 7th April, 2002.