Properties

Label 177.10.a.d.1.12
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.23437 q^{2} +81.0000 q^{3} -510.476 q^{4} -1722.16 q^{5} +99.9839 q^{6} +4577.43 q^{7} -1262.11 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+1.23437 q^{2} +81.0000 q^{3} -510.476 q^{4} -1722.16 q^{5} +99.9839 q^{6} +4577.43 q^{7} -1262.11 q^{8} +6561.00 q^{9} -2125.78 q^{10} -75628.8 q^{11} -41348.6 q^{12} -128893. q^{13} +5650.24 q^{14} -139495. q^{15} +259806. q^{16} -7944.95 q^{17} +8098.70 q^{18} -291562. q^{19} +879120. q^{20} +370772. q^{21} -93353.9 q^{22} -586180. q^{23} -102231. q^{24} +1.01270e6 q^{25} -159102. q^{26} +531441. q^{27} -2.33667e6 q^{28} -4.07295e6 q^{29} -172188. q^{30} -2.85910e6 q^{31} +966899. q^{32} -6.12593e6 q^{33} -9807.01 q^{34} -7.88305e6 q^{35} -3.34924e6 q^{36} -1.13923e7 q^{37} -359895. q^{38} -1.04403e7 q^{39} +2.17356e6 q^{40} +2.10328e7 q^{41} +457669. q^{42} -1.69667e7 q^{43} +3.86067e7 q^{44} -1.12991e7 q^{45} -723563. q^{46} +2.55397e7 q^{47} +2.10443e7 q^{48} -1.94007e7 q^{49} +1.25004e6 q^{50} -643541. q^{51} +6.57969e7 q^{52} +4.62154e7 q^{53} +655995. q^{54} +1.30245e8 q^{55} -5.77724e6 q^{56} -2.36165e7 q^{57} -5.02752e6 q^{58} -1.21174e7 q^{59} +7.12087e7 q^{60} +577170. q^{61} -3.52918e6 q^{62} +3.00325e7 q^{63} -1.31827e8 q^{64} +2.21974e8 q^{65} -7.56167e6 q^{66} -1.20480e8 q^{67} +4.05571e6 q^{68} -4.74806e7 q^{69} -9.73060e6 q^{70} +2.52522e8 q^{71} -8.28073e6 q^{72} +1.25719e8 q^{73} -1.40623e7 q^{74} +8.20284e7 q^{75} +1.48835e8 q^{76} -3.46186e8 q^{77} -1.28872e7 q^{78} +1.68453e8 q^{79} -4.47426e8 q^{80} +4.30467e7 q^{81} +2.59622e7 q^{82} +2.60377e8 q^{83} -1.89270e8 q^{84} +1.36824e7 q^{85} -2.09432e7 q^{86} -3.29909e8 q^{87} +9.54522e7 q^{88} +6.26006e8 q^{89} -1.39472e7 q^{90} -5.89999e8 q^{91} +2.99231e8 q^{92} -2.31587e8 q^{93} +3.15254e7 q^{94} +5.02115e8 q^{95} +7.83188e7 q^{96} -3.81243e8 q^{97} -2.39477e7 q^{98} -4.96201e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.23437 0.0545519 0.0272760 0.999628i \(-0.491317\pi\)
0.0272760 + 0.999628i \(0.491317\pi\)
\(3\) 81.0000 0.577350
\(4\) −510.476 −0.997024
\(5\) −1722.16 −1.23227 −0.616137 0.787639i \(-0.711303\pi\)
−0.616137 + 0.787639i \(0.711303\pi\)
\(6\) 99.9839 0.0314956
\(7\) 4577.43 0.720577 0.360289 0.932841i \(-0.382678\pi\)
0.360289 + 0.932841i \(0.382678\pi\)
\(8\) −1262.11 −0.108942
\(9\) 6561.00 0.333333
\(10\) −2125.78 −0.0672230
\(11\) −75628.8 −1.55747 −0.778736 0.627352i \(-0.784139\pi\)
−0.778736 + 0.627352i \(0.784139\pi\)
\(12\) −41348.6 −0.575632
\(13\) −128893. −1.25165 −0.625827 0.779962i \(-0.715239\pi\)
−0.625827 + 0.779962i \(0.715239\pi\)
\(14\) 5650.24 0.0393089
\(15\) −139495. −0.711454
\(16\) 259806. 0.991081
\(17\) −7944.95 −0.0230713 −0.0115356 0.999933i \(-0.503672\pi\)
−0.0115356 + 0.999933i \(0.503672\pi\)
\(18\) 8098.70 0.0181840
\(19\) −291562. −0.513263 −0.256631 0.966509i \(-0.582613\pi\)
−0.256631 + 0.966509i \(0.582613\pi\)
\(20\) 879120. 1.22861
\(21\) 370772. 0.416025
\(22\) −93353.9 −0.0849631
\(23\) −586180. −0.436773 −0.218386 0.975862i \(-0.570079\pi\)
−0.218386 + 0.975862i \(0.570079\pi\)
\(24\) −102231. −0.0628974
\(25\) 1.01270e6 0.518501
\(26\) −159102. −0.0682802
\(27\) 531441. 0.192450
\(28\) −2.33667e6 −0.718433
\(29\) −4.07295e6 −1.06935 −0.534673 0.845059i \(-0.679565\pi\)
−0.534673 + 0.845059i \(0.679565\pi\)
\(30\) −172188. −0.0388112
\(31\) −2.85910e6 −0.556034 −0.278017 0.960576i \(-0.589677\pi\)
−0.278017 + 0.960576i \(0.589677\pi\)
\(32\) 966899. 0.163007
\(33\) −6.12593e6 −0.899207
\(34\) −9807.01 −0.00125858
\(35\) −7.88305e6 −0.887949
\(36\) −3.34924e6 −0.332341
\(37\) −1.13923e7 −0.999318 −0.499659 0.866222i \(-0.666541\pi\)
−0.499659 + 0.866222i \(0.666541\pi\)
\(38\) −359895. −0.0279995
\(39\) −1.04403e7 −0.722643
\(40\) 2.17356e6 0.134246
\(41\) 2.10328e7 1.16244 0.581218 0.813748i \(-0.302576\pi\)
0.581218 + 0.813748i \(0.302576\pi\)
\(42\) 457669. 0.0226950
\(43\) −1.69667e7 −0.756814 −0.378407 0.925639i \(-0.623528\pi\)
−0.378407 + 0.925639i \(0.623528\pi\)
\(44\) 3.86067e7 1.55284
\(45\) −1.12991e7 −0.410758
\(46\) −723563. −0.0238268
\(47\) 2.55397e7 0.763441 0.381721 0.924278i \(-0.375332\pi\)
0.381721 + 0.924278i \(0.375332\pi\)
\(48\) 2.10443e7 0.572201
\(49\) −1.94007e7 −0.480769
\(50\) 1.25004e6 0.0282852
\(51\) −643541. −0.0133202
\(52\) 6.57969e7 1.24793
\(53\) 4.62154e7 0.804536 0.402268 0.915522i \(-0.368222\pi\)
0.402268 + 0.915522i \(0.368222\pi\)
\(54\) 655995. 0.0104985
\(55\) 1.30245e8 1.91923
\(56\) −5.77724e6 −0.0785008
\(57\) −2.36165e7 −0.296332
\(58\) −5.02752e6 −0.0583349
\(59\) −1.21174e7 −0.130189
\(60\) 7.12087e7 0.709337
\(61\) 577170. 0.00533727 0.00266864 0.999996i \(-0.499151\pi\)
0.00266864 + 0.999996i \(0.499151\pi\)
\(62\) −3.52918e6 −0.0303327
\(63\) 3.00325e7 0.240192
\(64\) −1.31827e8 −0.982189
\(65\) 2.21974e8 1.54238
\(66\) −7.56167e6 −0.0490535
\(67\) −1.20480e8 −0.730427 −0.365213 0.930924i \(-0.619004\pi\)
−0.365213 + 0.930924i \(0.619004\pi\)
\(68\) 4.05571e6 0.0230026
\(69\) −4.74806e7 −0.252171
\(70\) −9.73060e6 −0.0484393
\(71\) 2.52522e8 1.17933 0.589667 0.807646i \(-0.299259\pi\)
0.589667 + 0.807646i \(0.299259\pi\)
\(72\) −8.28073e6 −0.0363138
\(73\) 1.25719e8 0.518140 0.259070 0.965859i \(-0.416584\pi\)
0.259070 + 0.965859i \(0.416584\pi\)
\(74\) −1.40623e7 −0.0545147
\(75\) 8.20284e7 0.299357
\(76\) 1.48835e8 0.511735
\(77\) −3.46186e8 −1.12228
\(78\) −1.28872e7 −0.0394216
\(79\) 1.68453e8 0.486584 0.243292 0.969953i \(-0.421773\pi\)
0.243292 + 0.969953i \(0.421773\pi\)
\(80\) −4.47426e8 −1.22128
\(81\) 4.30467e7 0.111111
\(82\) 2.59622e7 0.0634131
\(83\) 2.60377e8 0.602214 0.301107 0.953590i \(-0.402644\pi\)
0.301107 + 0.953590i \(0.402644\pi\)
\(84\) −1.89270e8 −0.414787
\(85\) 1.36824e7 0.0284301
\(86\) −2.09432e7 −0.0412857
\(87\) −3.29909e8 −0.617387
\(88\) 9.54522e7 0.169673
\(89\) 6.26006e8 1.05760 0.528802 0.848745i \(-0.322641\pi\)
0.528802 + 0.848745i \(0.322641\pi\)
\(90\) −1.39472e7 −0.0224077
\(91\) −5.89999e8 −0.901914
\(92\) 2.99231e8 0.435473
\(93\) −2.31587e8 −0.321026
\(94\) 3.15254e7 0.0416472
\(95\) 5.02115e8 0.632480
\(96\) 7.83188e7 0.0941121
\(97\) −3.81243e8 −0.437249 −0.218624 0.975809i \(-0.570157\pi\)
−0.218624 + 0.975809i \(0.570157\pi\)
\(98\) −2.39477e7 −0.0262269
\(99\) −4.96201e8 −0.519157
\(100\) −5.16958e8 −0.516958
\(101\) −1.79665e9 −1.71797 −0.858986 0.511999i \(-0.828905\pi\)
−0.858986 + 0.511999i \(0.828905\pi\)
\(102\) −794368. −0.000726643 0
\(103\) 1.89121e9 1.65567 0.827834 0.560973i \(-0.189573\pi\)
0.827834 + 0.560973i \(0.189573\pi\)
\(104\) 1.62678e8 0.136357
\(105\) −6.38527e8 −0.512658
\(106\) 5.70469e7 0.0438890
\(107\) 3.37128e8 0.248638 0.124319 0.992242i \(-0.460325\pi\)
0.124319 + 0.992242i \(0.460325\pi\)
\(108\) −2.71288e8 −0.191877
\(109\) 1.73641e9 1.17823 0.589117 0.808047i \(-0.299476\pi\)
0.589117 + 0.808047i \(0.299476\pi\)
\(110\) 1.60770e8 0.104698
\(111\) −9.22776e8 −0.576956
\(112\) 1.18924e9 0.714150
\(113\) 1.15382e9 0.665708 0.332854 0.942978i \(-0.391988\pi\)
0.332854 + 0.942978i \(0.391988\pi\)
\(114\) −2.91515e7 −0.0161655
\(115\) 1.00949e9 0.538224
\(116\) 2.07914e9 1.06616
\(117\) −8.45668e8 −0.417218
\(118\) −1.49573e7 −0.00710206
\(119\) −3.63675e7 −0.0166246
\(120\) 1.76058e8 0.0775069
\(121\) 3.36177e9 1.42572
\(122\) 712441. 0.000291159 0
\(123\) 1.70365e9 0.671133
\(124\) 1.45950e9 0.554379
\(125\) 1.61956e9 0.593339
\(126\) 3.70712e7 0.0131030
\(127\) 2.16551e9 0.738660 0.369330 0.929298i \(-0.379587\pi\)
0.369330 + 0.929298i \(0.379587\pi\)
\(128\) −6.57776e8 −0.216587
\(129\) −1.37430e9 −0.436947
\(130\) 2.73998e8 0.0841400
\(131\) −5.32788e8 −0.158064 −0.0790321 0.996872i \(-0.525183\pi\)
−0.0790321 + 0.996872i \(0.525183\pi\)
\(132\) 3.12714e9 0.896531
\(133\) −1.33460e9 −0.369845
\(134\) −1.48716e8 −0.0398462
\(135\) −9.15224e8 −0.237151
\(136\) 1.00274e7 0.00251342
\(137\) 5.97504e8 0.144910 0.0724550 0.997372i \(-0.476917\pi\)
0.0724550 + 0.997372i \(0.476917\pi\)
\(138\) −5.86086e7 −0.0137564
\(139\) −3.68105e9 −0.836383 −0.418192 0.908359i \(-0.637336\pi\)
−0.418192 + 0.908359i \(0.637336\pi\)
\(140\) 4.02411e9 0.885306
\(141\) 2.06872e9 0.440773
\(142\) 3.11706e8 0.0643350
\(143\) 9.74803e9 1.94942
\(144\) 1.70459e9 0.330360
\(145\) 7.01425e9 1.31773
\(146\) 1.55183e8 0.0282656
\(147\) −1.57146e9 −0.277572
\(148\) 5.81550e9 0.996344
\(149\) −8.72669e9 −1.45048 −0.725239 0.688497i \(-0.758271\pi\)
−0.725239 + 0.688497i \(0.758271\pi\)
\(150\) 1.01253e8 0.0163305
\(151\) 3.64829e9 0.571074 0.285537 0.958368i \(-0.407828\pi\)
0.285537 + 0.958368i \(0.407828\pi\)
\(152\) 3.67984e8 0.0559156
\(153\) −5.21268e7 −0.00769042
\(154\) −4.27321e8 −0.0612225
\(155\) 4.92381e9 0.685186
\(156\) 5.32955e9 0.720493
\(157\) −1.23067e10 −1.61657 −0.808283 0.588794i \(-0.799603\pi\)
−0.808283 + 0.588794i \(0.799603\pi\)
\(158\) 2.07934e8 0.0265441
\(159\) 3.74345e9 0.464499
\(160\) −1.66515e9 −0.200869
\(161\) −2.68320e9 −0.314729
\(162\) 5.31356e7 0.00606133
\(163\) −4.00912e8 −0.0444842 −0.0222421 0.999753i \(-0.507080\pi\)
−0.0222421 + 0.999753i \(0.507080\pi\)
\(164\) −1.07367e10 −1.15898
\(165\) 1.05498e10 1.10807
\(166\) 3.21401e8 0.0328520
\(167\) −5.01358e9 −0.498797 −0.249398 0.968401i \(-0.580233\pi\)
−0.249398 + 0.968401i \(0.580233\pi\)
\(168\) −4.67956e8 −0.0453225
\(169\) 6.00894e9 0.566640
\(170\) 1.68892e7 0.00155092
\(171\) −1.91294e9 −0.171088
\(172\) 8.66109e9 0.754562
\(173\) −1.13828e9 −0.0966145 −0.0483072 0.998833i \(-0.515383\pi\)
−0.0483072 + 0.998833i \(0.515383\pi\)
\(174\) −4.07229e8 −0.0336797
\(175\) 4.63555e9 0.373620
\(176\) −1.96488e10 −1.54358
\(177\) −9.81506e8 −0.0751646
\(178\) 7.72723e8 0.0576944
\(179\) 1.74893e10 1.27331 0.636655 0.771149i \(-0.280318\pi\)
0.636655 + 0.771149i \(0.280318\pi\)
\(180\) 5.76791e9 0.409536
\(181\) 8.61457e9 0.596596 0.298298 0.954473i \(-0.403581\pi\)
0.298298 + 0.954473i \(0.403581\pi\)
\(182\) −7.28277e8 −0.0492012
\(183\) 4.67508e7 0.00308148
\(184\) 7.39826e8 0.0475827
\(185\) 1.96193e10 1.23143
\(186\) −2.85864e8 −0.0175126
\(187\) 6.00867e8 0.0359328
\(188\) −1.30374e10 −0.761169
\(189\) 2.43263e9 0.138675
\(190\) 6.19796e8 0.0345030
\(191\) 1.63079e10 0.886643 0.443321 0.896363i \(-0.353800\pi\)
0.443321 + 0.896363i \(0.353800\pi\)
\(192\) −1.06780e10 −0.567067
\(193\) 4.83203e9 0.250681 0.125340 0.992114i \(-0.459998\pi\)
0.125340 + 0.992114i \(0.459998\pi\)
\(194\) −4.70594e8 −0.0238528
\(195\) 1.79799e10 0.890495
\(196\) 9.90362e9 0.479338
\(197\) 7.60149e9 0.359585 0.179792 0.983705i \(-0.442457\pi\)
0.179792 + 0.983705i \(0.442457\pi\)
\(198\) −6.12495e8 −0.0283210
\(199\) −2.00563e10 −0.906593 −0.453296 0.891360i \(-0.649752\pi\)
−0.453296 + 0.891360i \(0.649752\pi\)
\(200\) −1.27814e9 −0.0564863
\(201\) −9.75884e9 −0.421712
\(202\) −2.21772e9 −0.0937187
\(203\) −1.86436e10 −0.770546
\(204\) 3.28513e8 0.0132806
\(205\) −3.62217e10 −1.43244
\(206\) 2.33446e9 0.0903199
\(207\) −3.84593e9 −0.145591
\(208\) −3.34872e10 −1.24049
\(209\) 2.20505e10 0.799392
\(210\) −7.88178e8 −0.0279665
\(211\) −3.43734e10 −1.19386 −0.596928 0.802295i \(-0.703612\pi\)
−0.596928 + 0.802295i \(0.703612\pi\)
\(212\) −2.35919e10 −0.802141
\(213\) 2.04543e10 0.680889
\(214\) 4.16141e8 0.0135637
\(215\) 2.92193e10 0.932603
\(216\) −6.70739e8 −0.0209658
\(217\) −1.30873e10 −0.400665
\(218\) 2.14337e9 0.0642750
\(219\) 1.01832e10 0.299148
\(220\) −6.64868e10 −1.91352
\(221\) 1.02405e9 0.0288772
\(222\) −1.13905e9 −0.0314741
\(223\) 1.85618e10 0.502631 0.251315 0.967905i \(-0.419137\pi\)
0.251315 + 0.967905i \(0.419137\pi\)
\(224\) 4.42591e9 0.117459
\(225\) 6.64430e9 0.172834
\(226\) 1.42424e9 0.0363157
\(227\) 2.95817e10 0.739447 0.369724 0.929142i \(-0.379452\pi\)
0.369724 + 0.929142i \(0.379452\pi\)
\(228\) 1.20557e10 0.295450
\(229\) −7.00551e9 −0.168337 −0.0841686 0.996452i \(-0.526823\pi\)
−0.0841686 + 0.996452i \(0.526823\pi\)
\(230\) 1.24609e9 0.0293612
\(231\) −2.80410e10 −0.647948
\(232\) 5.14052e9 0.116496
\(233\) 7.20100e10 1.60063 0.800315 0.599580i \(-0.204666\pi\)
0.800315 + 0.599580i \(0.204666\pi\)
\(234\) −1.04387e9 −0.0227601
\(235\) −4.39834e10 −0.940769
\(236\) 6.18563e9 0.129801
\(237\) 1.36447e10 0.280929
\(238\) −4.48909e7 −0.000906905 0
\(239\) −4.52370e10 −0.896816 −0.448408 0.893829i \(-0.648009\pi\)
−0.448408 + 0.893829i \(0.648009\pi\)
\(240\) −3.62415e10 −0.705109
\(241\) −4.81152e10 −0.918767 −0.459384 0.888238i \(-0.651930\pi\)
−0.459384 + 0.888238i \(0.651930\pi\)
\(242\) 4.14967e9 0.0777758
\(243\) 3.48678e9 0.0641500
\(244\) −2.94632e8 −0.00532139
\(245\) 3.34111e10 0.592439
\(246\) 2.10294e9 0.0366116
\(247\) 3.75803e10 0.642428
\(248\) 3.60851e9 0.0605752
\(249\) 2.10905e10 0.347689
\(250\) 1.99914e9 0.0323678
\(251\) −3.37349e10 −0.536472 −0.268236 0.963353i \(-0.586441\pi\)
−0.268236 + 0.963353i \(0.586441\pi\)
\(252\) −1.53309e10 −0.239478
\(253\) 4.43321e10 0.680262
\(254\) 2.67305e9 0.0402953
\(255\) 1.10828e9 0.0164141
\(256\) 6.66836e10 0.970374
\(257\) 4.88383e10 0.698331 0.349165 0.937061i \(-0.386465\pi\)
0.349165 + 0.937061i \(0.386465\pi\)
\(258\) −1.69640e9 −0.0238363
\(259\) −5.21475e10 −0.720086
\(260\) −1.13313e11 −1.53779
\(261\) −2.67226e10 −0.356448
\(262\) −6.57657e8 −0.00862271
\(263\) −5.73393e10 −0.739012 −0.369506 0.929228i \(-0.620473\pi\)
−0.369506 + 0.929228i \(0.620473\pi\)
\(264\) 7.73163e9 0.0979610
\(265\) −7.95901e10 −0.991409
\(266\) −1.64739e9 −0.0201758
\(267\) 5.07065e10 0.610609
\(268\) 6.15020e10 0.728253
\(269\) 5.33586e10 0.621326 0.310663 0.950520i \(-0.399449\pi\)
0.310663 + 0.950520i \(0.399449\pi\)
\(270\) −1.12973e9 −0.0129371
\(271\) −4.34358e10 −0.489199 −0.244600 0.969624i \(-0.578656\pi\)
−0.244600 + 0.969624i \(0.578656\pi\)
\(272\) −2.06415e9 −0.0228655
\(273\) −4.77899e10 −0.520720
\(274\) 7.37541e8 0.00790512
\(275\) −7.65891e10 −0.807550
\(276\) 2.42377e10 0.251420
\(277\) 4.32531e10 0.441427 0.220713 0.975339i \(-0.429161\pi\)
0.220713 + 0.975339i \(0.429161\pi\)
\(278\) −4.54378e9 −0.0456263
\(279\) −1.87585e10 −0.185345
\(280\) 9.94930e9 0.0967345
\(281\) −7.68788e10 −0.735577 −0.367789 0.929909i \(-0.619885\pi\)
−0.367789 + 0.929909i \(0.619885\pi\)
\(282\) 2.55356e9 0.0240450
\(283\) 6.08362e10 0.563797 0.281899 0.959444i \(-0.409036\pi\)
0.281899 + 0.959444i \(0.409036\pi\)
\(284\) −1.28907e11 −1.17582
\(285\) 4.06713e10 0.365163
\(286\) 1.20327e10 0.106345
\(287\) 9.62760e10 0.837625
\(288\) 6.34382e9 0.0543357
\(289\) −1.18525e11 −0.999468
\(290\) 8.65818e9 0.0718846
\(291\) −3.08806e10 −0.252446
\(292\) −6.41765e10 −0.516598
\(293\) −1.08229e11 −0.857905 −0.428952 0.903327i \(-0.641117\pi\)
−0.428952 + 0.903327i \(0.641117\pi\)
\(294\) −1.93976e9 −0.0151421
\(295\) 2.08680e10 0.160428
\(296\) 1.43784e10 0.108867
\(297\) −4.01923e10 −0.299736
\(298\) −1.07720e10 −0.0791264
\(299\) 7.55546e10 0.546689
\(300\) −4.18736e10 −0.298466
\(301\) −7.76638e10 −0.545343
\(302\) 4.50333e9 0.0311532
\(303\) −1.45528e11 −0.991872
\(304\) −7.57495e10 −0.508685
\(305\) −9.93977e8 −0.00657699
\(306\) −6.43438e7 −0.000419527 0
\(307\) −1.72665e11 −1.10938 −0.554691 0.832056i \(-0.687164\pi\)
−0.554691 + 0.832056i \(0.687164\pi\)
\(308\) 1.76720e11 1.11894
\(309\) 1.53188e11 0.955900
\(310\) 6.07780e9 0.0373783
\(311\) −1.81316e10 −0.109904 −0.0549520 0.998489i \(-0.517501\pi\)
−0.0549520 + 0.998489i \(0.517501\pi\)
\(312\) 1.31769e10 0.0787259
\(313\) −3.00247e11 −1.76819 −0.884095 0.467308i \(-0.845224\pi\)
−0.884095 + 0.467308i \(0.845224\pi\)
\(314\) −1.51910e10 −0.0881868
\(315\) −5.17207e10 −0.295983
\(316\) −8.59914e10 −0.485136
\(317\) −3.28029e11 −1.82451 −0.912254 0.409625i \(-0.865660\pi\)
−0.912254 + 0.409625i \(0.865660\pi\)
\(318\) 4.62080e9 0.0253393
\(319\) 3.08032e11 1.66548
\(320\) 2.27027e11 1.21033
\(321\) 2.73074e10 0.143551
\(322\) −3.31206e9 −0.0171691
\(323\) 2.31645e9 0.0118416
\(324\) −2.19743e10 −0.110780
\(325\) −1.30530e11 −0.648984
\(326\) −4.94874e8 −0.00242670
\(327\) 1.40649e11 0.680254
\(328\) −2.65457e10 −0.126638
\(329\) 1.16906e11 0.550118
\(330\) 1.30224e10 0.0604474
\(331\) −4.20956e11 −1.92757 −0.963787 0.266672i \(-0.914076\pi\)
−0.963787 + 0.266672i \(0.914076\pi\)
\(332\) −1.32916e11 −0.600422
\(333\) −7.47449e10 −0.333106
\(334\) −6.18860e9 −0.0272103
\(335\) 2.07485e11 0.900087
\(336\) 9.63287e10 0.412315
\(337\) 1.86450e11 0.787458 0.393729 0.919226i \(-0.371185\pi\)
0.393729 + 0.919226i \(0.371185\pi\)
\(338\) 7.41725e9 0.0309113
\(339\) 9.34592e10 0.384347
\(340\) −6.98457e9 −0.0283455
\(341\) 2.16230e11 0.866007
\(342\) −2.36127e9 −0.00933316
\(343\) −2.73521e11 −1.06701
\(344\) 2.14139e10 0.0824485
\(345\) 8.17690e10 0.310744
\(346\) −1.40506e9 −0.00527051
\(347\) −3.20207e11 −1.18563 −0.592814 0.805339i \(-0.701983\pi\)
−0.592814 + 0.805339i \(0.701983\pi\)
\(348\) 1.68411e11 0.615550
\(349\) 4.15903e11 1.50065 0.750323 0.661072i \(-0.229898\pi\)
0.750323 + 0.661072i \(0.229898\pi\)
\(350\) 5.72198e9 0.0203817
\(351\) −6.84991e10 −0.240881
\(352\) −7.31254e10 −0.253879
\(353\) 2.67923e10 0.0918382 0.0459191 0.998945i \(-0.485378\pi\)
0.0459191 + 0.998945i \(0.485378\pi\)
\(354\) −1.21154e9 −0.00410038
\(355\) −4.34883e11 −1.45326
\(356\) −3.19561e11 −1.05446
\(357\) −2.94576e9 −0.00959823
\(358\) 2.15883e10 0.0694615
\(359\) 1.06956e11 0.339845 0.169922 0.985457i \(-0.445648\pi\)
0.169922 + 0.985457i \(0.445648\pi\)
\(360\) 1.42607e10 0.0447486
\(361\) −2.37679e11 −0.736562
\(362\) 1.06336e10 0.0325455
\(363\) 2.72303e11 0.823139
\(364\) 3.01181e11 0.899230
\(365\) −2.16507e11 −0.638491
\(366\) 5.77077e7 0.000168101 0
\(367\) −1.72987e11 −0.497755 −0.248877 0.968535i \(-0.580062\pi\)
−0.248877 + 0.968535i \(0.580062\pi\)
\(368\) −1.52293e11 −0.432877
\(369\) 1.37996e11 0.387479
\(370\) 2.42175e10 0.0671771
\(371\) 2.11548e11 0.579730
\(372\) 1.18220e11 0.320071
\(373\) 5.37786e11 1.43853 0.719267 0.694734i \(-0.244478\pi\)
0.719267 + 0.694734i \(0.244478\pi\)
\(374\) 7.41693e8 0.00196021
\(375\) 1.31185e11 0.342565
\(376\) −3.22340e10 −0.0831705
\(377\) 5.24975e11 1.33845
\(378\) 3.00277e9 0.00756500
\(379\) −3.86868e11 −0.963134 −0.481567 0.876409i \(-0.659932\pi\)
−0.481567 + 0.876409i \(0.659932\pi\)
\(380\) −2.56318e11 −0.630598
\(381\) 1.75407e11 0.426465
\(382\) 2.01300e10 0.0483681
\(383\) −5.21091e11 −1.23742 −0.618712 0.785618i \(-0.712345\pi\)
−0.618712 + 0.785618i \(0.712345\pi\)
\(384\) −5.32798e10 −0.125047
\(385\) 5.96186e11 1.38296
\(386\) 5.96451e9 0.0136751
\(387\) −1.11318e11 −0.252271
\(388\) 1.94615e11 0.435947
\(389\) 8.11858e11 1.79766 0.898829 0.438300i \(-0.144419\pi\)
0.898829 + 0.438300i \(0.144419\pi\)
\(390\) 2.21938e10 0.0485782
\(391\) 4.65717e9 0.0100769
\(392\) 2.44859e10 0.0523757
\(393\) −4.31558e10 −0.0912584
\(394\) 9.38305e9 0.0196160
\(395\) −2.90103e11 −0.599605
\(396\) 2.53299e11 0.517612
\(397\) 2.98669e11 0.603438 0.301719 0.953397i \(-0.402440\pi\)
0.301719 + 0.953397i \(0.402440\pi\)
\(398\) −2.47569e10 −0.0494564
\(399\) −1.08103e11 −0.213530
\(400\) 2.63105e11 0.513876
\(401\) 7.14419e11 1.37976 0.689879 0.723924i \(-0.257664\pi\)
0.689879 + 0.723924i \(0.257664\pi\)
\(402\) −1.20460e10 −0.0230052
\(403\) 3.68518e11 0.695963
\(404\) 9.17145e11 1.71286
\(405\) −7.41332e10 −0.136919
\(406\) −2.30131e10 −0.0420348
\(407\) 8.61586e11 1.55641
\(408\) 8.12222e8 0.00145112
\(409\) 7.98601e10 0.141116 0.0705578 0.997508i \(-0.477522\pi\)
0.0705578 + 0.997508i \(0.477522\pi\)
\(410\) −4.47110e10 −0.0781424
\(411\) 4.83978e10 0.0836638
\(412\) −9.65420e11 −1.65074
\(413\) −5.54664e10 −0.0938112
\(414\) −4.74729e9 −0.00794227
\(415\) −4.48410e11 −0.742094
\(416\) −1.24627e11 −0.204028
\(417\) −2.98165e11 −0.482886
\(418\) 2.72184e10 0.0436084
\(419\) 3.18506e11 0.504841 0.252420 0.967618i \(-0.418773\pi\)
0.252420 + 0.967618i \(0.418773\pi\)
\(420\) 3.25953e11 0.511132
\(421\) 9.50164e11 1.47411 0.737054 0.675834i \(-0.236216\pi\)
0.737054 + 0.675834i \(0.236216\pi\)
\(422\) −4.24295e10 −0.0651271
\(423\) 1.67566e11 0.254480
\(424\) −5.83291e10 −0.0876473
\(425\) −8.04583e9 −0.0119625
\(426\) 2.52482e10 0.0371438
\(427\) 2.64196e9 0.00384592
\(428\) −1.72096e11 −0.247898
\(429\) 7.89591e11 1.12550
\(430\) 3.60674e10 0.0508753
\(431\) 1.08204e11 0.151041 0.0755203 0.997144i \(-0.475938\pi\)
0.0755203 + 0.997144i \(0.475938\pi\)
\(432\) 1.38072e11 0.190734
\(433\) −8.27119e11 −1.13076 −0.565382 0.824829i \(-0.691271\pi\)
−0.565382 + 0.824829i \(0.691271\pi\)
\(434\) −1.61546e10 −0.0218571
\(435\) 5.68155e11 0.760790
\(436\) −8.86394e11 −1.17473
\(437\) 1.70908e11 0.224179
\(438\) 1.25699e10 0.0163191
\(439\) 1.41581e11 0.181935 0.0909674 0.995854i \(-0.471004\pi\)
0.0909674 + 0.995854i \(0.471004\pi\)
\(440\) −1.64384e11 −0.209084
\(441\) −1.27288e11 −0.160256
\(442\) 1.26406e9 0.00157531
\(443\) 1.32265e12 1.63165 0.815826 0.578297i \(-0.196283\pi\)
0.815826 + 0.578297i \(0.196283\pi\)
\(444\) 4.71055e11 0.575239
\(445\) −1.07808e12 −1.30326
\(446\) 2.29122e10 0.0274195
\(447\) −7.06862e11 −0.837434
\(448\) −6.03429e11 −0.707743
\(449\) 5.50408e11 0.639110 0.319555 0.947568i \(-0.396467\pi\)
0.319555 + 0.947568i \(0.396467\pi\)
\(450\) 8.20153e9 0.00942841
\(451\) −1.59068e12 −1.81046
\(452\) −5.88996e11 −0.663727
\(453\) 2.95511e11 0.329710
\(454\) 3.65148e10 0.0403383
\(455\) 1.01607e12 1.11141
\(456\) 2.98067e10 0.0322829
\(457\) 8.90772e11 0.955309 0.477654 0.878548i \(-0.341487\pi\)
0.477654 + 0.878548i \(0.341487\pi\)
\(458\) −8.64739e9 −0.00918312
\(459\) −4.22227e9 −0.00444006
\(460\) −5.15322e11 −0.536622
\(461\) 5.40229e11 0.557088 0.278544 0.960423i \(-0.410148\pi\)
0.278544 + 0.960423i \(0.410148\pi\)
\(462\) −3.46130e10 −0.0353468
\(463\) −1.15861e12 −1.17172 −0.585859 0.810413i \(-0.699243\pi\)
−0.585859 + 0.810413i \(0.699243\pi\)
\(464\) −1.05818e12 −1.05981
\(465\) 3.98829e11 0.395593
\(466\) 8.88869e10 0.0873175
\(467\) 3.39246e11 0.330057 0.165029 0.986289i \(-0.447228\pi\)
0.165029 + 0.986289i \(0.447228\pi\)
\(468\) 4.31693e11 0.415977
\(469\) −5.51487e11 −0.526329
\(470\) −5.42917e10 −0.0513208
\(471\) −9.96843e11 −0.933325
\(472\) 1.52935e10 0.0141830
\(473\) 1.28317e12 1.17872
\(474\) 1.68426e10 0.0153252
\(475\) −2.95264e11 −0.266127
\(476\) 1.85647e10 0.0165751
\(477\) 3.03219e11 0.268179
\(478\) −5.58392e10 −0.0489231
\(479\) −7.35605e10 −0.0638461 −0.0319231 0.999490i \(-0.510163\pi\)
−0.0319231 + 0.999490i \(0.510163\pi\)
\(480\) −1.34877e11 −0.115972
\(481\) 1.46839e12 1.25080
\(482\) −5.93919e10 −0.0501206
\(483\) −2.17339e11 −0.181709
\(484\) −1.71610e12 −1.42148
\(485\) 6.56559e11 0.538810
\(486\) 4.30398e9 0.00349951
\(487\) −1.42738e12 −1.14990 −0.574948 0.818190i \(-0.694978\pi\)
−0.574948 + 0.818190i \(0.694978\pi\)
\(488\) −7.28454e8 −0.000581451 0
\(489\) −3.24739e10 −0.0256829
\(490\) 4.12417e10 0.0323187
\(491\) 1.94184e12 1.50781 0.753906 0.656982i \(-0.228167\pi\)
0.753906 + 0.656982i \(0.228167\pi\)
\(492\) −8.69675e11 −0.669135
\(493\) 3.23594e10 0.0246711
\(494\) 4.63880e10 0.0350457
\(495\) 8.54535e11 0.639744
\(496\) −7.42810e11 −0.551075
\(497\) 1.15590e12 0.849802
\(498\) 2.60335e10 0.0189671
\(499\) −2.56548e12 −1.85232 −0.926159 0.377134i \(-0.876910\pi\)
−0.926159 + 0.377134i \(0.876910\pi\)
\(500\) −8.26749e11 −0.591574
\(501\) −4.06100e11 −0.287980
\(502\) −4.16413e10 −0.0292656
\(503\) 5.93035e11 0.413071 0.206535 0.978439i \(-0.433781\pi\)
0.206535 + 0.978439i \(0.433781\pi\)
\(504\) −3.79044e10 −0.0261669
\(505\) 3.09410e12 2.11701
\(506\) 5.47222e10 0.0371096
\(507\) 4.86724e11 0.327150
\(508\) −1.10544e12 −0.736462
\(509\) 1.72608e12 1.13981 0.569904 0.821711i \(-0.306980\pi\)
0.569904 + 0.821711i \(0.306980\pi\)
\(510\) 1.36803e9 0.000895423 0
\(511\) 5.75469e11 0.373360
\(512\) 4.19093e11 0.269523
\(513\) −1.54948e11 −0.0987774
\(514\) 6.02845e10 0.0380953
\(515\) −3.25697e12 −2.04024
\(516\) 7.01549e11 0.435646
\(517\) −1.93154e12 −1.18904
\(518\) −6.43692e10 −0.0392821
\(519\) −9.22008e10 −0.0557804
\(520\) −2.80157e11 −0.168030
\(521\) −5.35237e10 −0.0318256 −0.0159128 0.999873i \(-0.505065\pi\)
−0.0159128 + 0.999873i \(0.505065\pi\)
\(522\) −3.29856e10 −0.0194450
\(523\) 8.66933e11 0.506673 0.253337 0.967378i \(-0.418472\pi\)
0.253337 + 0.967378i \(0.418472\pi\)
\(524\) 2.71976e11 0.157594
\(525\) 3.75479e11 0.215710
\(526\) −7.07779e10 −0.0403145
\(527\) 2.27154e10 0.0128284
\(528\) −1.59155e12 −0.891187
\(529\) −1.45755e12 −0.809229
\(530\) −9.82436e10 −0.0540833
\(531\) −7.95020e10 −0.0433963
\(532\) 6.81284e11 0.368745
\(533\) −2.71098e12 −1.45497
\(534\) 6.25905e10 0.0333099
\(535\) −5.80587e11 −0.306391
\(536\) 1.52059e11 0.0795738
\(537\) 1.41663e12 0.735146
\(538\) 6.58643e10 0.0338945
\(539\) 1.46726e12 0.748784
\(540\) 4.67200e11 0.236446
\(541\) 3.04212e12 1.52682 0.763411 0.645913i \(-0.223523\pi\)
0.763411 + 0.645913i \(0.223523\pi\)
\(542\) −5.36158e10 −0.0266868
\(543\) 6.97781e11 0.344445
\(544\) −7.68197e9 −0.00376077
\(545\) −2.99036e12 −1.45191
\(546\) −5.89904e10 −0.0284063
\(547\) 3.02958e12 1.44691 0.723453 0.690374i \(-0.242554\pi\)
0.723453 + 0.690374i \(0.242554\pi\)
\(548\) −3.05012e11 −0.144479
\(549\) 3.78681e9 0.00177909
\(550\) −9.45392e10 −0.0440534
\(551\) 1.18752e12 0.548855
\(552\) 5.99259e10 0.0274719
\(553\) 7.71083e11 0.350621
\(554\) 5.33903e10 0.0240807
\(555\) 1.58916e12 0.710969
\(556\) 1.87909e12 0.833894
\(557\) −2.52749e12 −1.11261 −0.556303 0.830979i \(-0.687781\pi\)
−0.556303 + 0.830979i \(0.687781\pi\)
\(558\) −2.31550e10 −0.0101109
\(559\) 2.18689e12 0.947270
\(560\) −2.04806e12 −0.880029
\(561\) 4.86703e10 0.0207458
\(562\) −9.48969e10 −0.0401272
\(563\) 1.94482e12 0.815816 0.407908 0.913023i \(-0.366258\pi\)
0.407908 + 0.913023i \(0.366258\pi\)
\(564\) −1.05603e12 −0.439461
\(565\) −1.98705e12 −0.820335
\(566\) 7.50943e10 0.0307562
\(567\) 1.97043e11 0.0800641
\(568\) −3.18712e11 −0.128479
\(569\) 1.76979e12 0.707808 0.353904 0.935282i \(-0.384854\pi\)
0.353904 + 0.935282i \(0.384854\pi\)
\(570\) 5.02034e10 0.0199203
\(571\) −2.23937e12 −0.881584 −0.440792 0.897609i \(-0.645302\pi\)
−0.440792 + 0.897609i \(0.645302\pi\)
\(572\) −4.97614e12 −1.94362
\(573\) 1.32094e12 0.511903
\(574\) 1.18840e11 0.0456941
\(575\) −5.93623e11 −0.226467
\(576\) −8.64918e11 −0.327396
\(577\) 3.11152e12 1.16864 0.584322 0.811522i \(-0.301361\pi\)
0.584322 + 0.811522i \(0.301361\pi\)
\(578\) −1.46303e11 −0.0545229
\(579\) 3.91394e11 0.144731
\(580\) −3.58061e12 −1.31381
\(581\) 1.19186e12 0.433942
\(582\) −3.81181e10 −0.0137714
\(583\) −3.49522e12 −1.25304
\(584\) −1.58671e11 −0.0564470
\(585\) 1.45637e12 0.514128
\(586\) −1.33595e11 −0.0468004
\(587\) −3.40126e12 −1.18241 −0.591206 0.806521i \(-0.701348\pi\)
−0.591206 + 0.806521i \(0.701348\pi\)
\(588\) 8.02193e11 0.276746
\(589\) 8.33604e11 0.285391
\(590\) 2.57588e10 0.00875169
\(591\) 6.15721e11 0.207606
\(592\) −2.95979e12 −0.990405
\(593\) −1.25239e12 −0.415904 −0.207952 0.978139i \(-0.566680\pi\)
−0.207952 + 0.978139i \(0.566680\pi\)
\(594\) −4.96121e10 −0.0163512
\(595\) 6.26305e10 0.0204861
\(596\) 4.45477e12 1.44616
\(597\) −1.62456e12 −0.523422
\(598\) 9.32622e10 0.0298229
\(599\) −2.25023e12 −0.714178 −0.357089 0.934070i \(-0.616231\pi\)
−0.357089 + 0.934070i \(0.616231\pi\)
\(600\) −1.03529e11 −0.0326124
\(601\) 4.24405e12 1.32692 0.663462 0.748210i \(-0.269087\pi\)
0.663462 + 0.748210i \(0.269087\pi\)
\(602\) −9.58659e10 −0.0297495
\(603\) −7.90466e11 −0.243476
\(604\) −1.86236e12 −0.569375
\(605\) −5.78949e12 −1.75688
\(606\) −1.79636e11 −0.0541085
\(607\) −3.86858e12 −1.15665 −0.578326 0.815806i \(-0.696294\pi\)
−0.578326 + 0.815806i \(0.696294\pi\)
\(608\) −2.81911e11 −0.0836654
\(609\) −1.51013e12 −0.444875
\(610\) −1.22693e9 −0.000358787 0
\(611\) −3.29189e12 −0.955565
\(612\) 2.66095e10 0.00766753
\(613\) −1.24759e12 −0.356862 −0.178431 0.983952i \(-0.557102\pi\)
−0.178431 + 0.983952i \(0.557102\pi\)
\(614\) −2.13132e11 −0.0605190
\(615\) −2.93396e12 −0.827020
\(616\) 4.36926e11 0.122263
\(617\) −6.58800e12 −1.83008 −0.915040 0.403363i \(-0.867841\pi\)
−0.915040 + 0.403363i \(0.867841\pi\)
\(618\) 1.89091e11 0.0521462
\(619\) −6.62001e12 −1.81238 −0.906192 0.422866i \(-0.861024\pi\)
−0.906192 + 0.422866i \(0.861024\pi\)
\(620\) −2.51349e12 −0.683147
\(621\) −3.11520e11 −0.0840570
\(622\) −2.23810e10 −0.00599547
\(623\) 2.86550e12 0.762086
\(624\) −2.71246e12 −0.716198
\(625\) −4.76707e12 −1.24966
\(626\) −3.70615e11 −0.0964582
\(627\) 1.78609e12 0.461529
\(628\) 6.28228e12 1.61176
\(629\) 9.05113e10 0.0230555
\(630\) −6.38424e10 −0.0161464
\(631\) 7.31068e12 1.83580 0.917900 0.396811i \(-0.129883\pi\)
0.917900 + 0.396811i \(0.129883\pi\)
\(632\) −2.12607e11 −0.0530092
\(633\) −2.78425e12 −0.689273
\(634\) −4.04909e11 −0.0995305
\(635\) −3.72935e12 −0.910232
\(636\) −1.91094e12 −0.463116
\(637\) 2.50062e12 0.601756
\(638\) 3.80226e11 0.0908549
\(639\) 1.65680e12 0.393112
\(640\) 1.13279e12 0.266895
\(641\) −1.91229e12 −0.447397 −0.223698 0.974658i \(-0.571813\pi\)
−0.223698 + 0.974658i \(0.571813\pi\)
\(642\) 3.37074e10 0.00783101
\(643\) −2.85686e12 −0.659082 −0.329541 0.944141i \(-0.606894\pi\)
−0.329541 + 0.944141i \(0.606894\pi\)
\(644\) 1.36971e12 0.313792
\(645\) 2.36676e12 0.538438
\(646\) 2.85935e9 0.000645983 0
\(647\) 6.56091e12 1.47196 0.735978 0.677005i \(-0.236723\pi\)
0.735978 + 0.677005i \(0.236723\pi\)
\(648\) −5.43299e10 −0.0121046
\(649\) 9.16422e11 0.202766
\(650\) −1.61122e11 −0.0354033
\(651\) −1.06007e12 −0.231324
\(652\) 2.04656e11 0.0443518
\(653\) 7.12775e12 1.53406 0.767031 0.641610i \(-0.221733\pi\)
0.767031 + 0.641610i \(0.221733\pi\)
\(654\) 1.73613e11 0.0371092
\(655\) 9.17544e11 0.194779
\(656\) 5.46444e12 1.15207
\(657\) 8.24841e11 0.172713
\(658\) 1.44305e11 0.0300100
\(659\) 4.89769e12 1.01160 0.505798 0.862652i \(-0.331198\pi\)
0.505798 + 0.862652i \(0.331198\pi\)
\(660\) −5.38543e12 −1.10477
\(661\) 5.75298e12 1.17216 0.586080 0.810253i \(-0.300671\pi\)
0.586080 + 0.810253i \(0.300671\pi\)
\(662\) −5.19616e11 −0.105153
\(663\) 8.29480e10 0.0166723
\(664\) −3.28625e11 −0.0656062
\(665\) 2.29840e12 0.455751
\(666\) −9.22628e10 −0.0181716
\(667\) 2.38748e12 0.467061
\(668\) 2.55931e12 0.497312
\(669\) 1.50351e12 0.290194
\(670\) 2.56113e11 0.0491015
\(671\) −4.36507e10 −0.00831266
\(672\) 3.58499e11 0.0678150
\(673\) 4.61673e12 0.867494 0.433747 0.901035i \(-0.357191\pi\)
0.433747 + 0.901035i \(0.357191\pi\)
\(674\) 2.30148e11 0.0429574
\(675\) 5.38189e11 0.0997855
\(676\) −3.06742e12 −0.564954
\(677\) −8.67156e12 −1.58653 −0.793265 0.608877i \(-0.791620\pi\)
−0.793265 + 0.608877i \(0.791620\pi\)
\(678\) 1.15363e11 0.0209669
\(679\) −1.74511e12 −0.315071
\(680\) −1.72688e10 −0.00309722
\(681\) 2.39612e12 0.426920
\(682\) 2.66908e11 0.0472424
\(683\) 7.15878e12 1.25877 0.629385 0.777094i \(-0.283307\pi\)
0.629385 + 0.777094i \(0.283307\pi\)
\(684\) 9.76509e11 0.170578
\(685\) −1.02900e12 −0.178569
\(686\) −3.37626e11 −0.0582074
\(687\) −5.67446e11 −0.0971895
\(688\) −4.40805e12 −0.750064
\(689\) −5.95685e12 −1.00700
\(690\) 1.00933e11 0.0169517
\(691\) 9.45943e12 1.57839 0.789194 0.614144i \(-0.210499\pi\)
0.789194 + 0.614144i \(0.210499\pi\)
\(692\) 5.81066e11 0.0963270
\(693\) −2.27132e12 −0.374093
\(694\) −3.95254e11 −0.0646783
\(695\) 6.33935e12 1.03065
\(696\) 4.16382e11 0.0672591
\(697\) −1.67104e11 −0.0268189
\(698\) 5.13378e11 0.0818631
\(699\) 5.83281e12 0.924124
\(700\) −2.36634e12 −0.372508
\(701\) −2.18884e12 −0.342360 −0.171180 0.985240i \(-0.554758\pi\)
−0.171180 + 0.985240i \(0.554758\pi\)
\(702\) −8.45532e10 −0.0131405
\(703\) 3.32156e12 0.512912
\(704\) 9.96993e12 1.52973
\(705\) −3.56265e12 −0.543153
\(706\) 3.30716e10 0.00500995
\(707\) −8.22402e12 −1.23793
\(708\) 5.01036e11 0.0749409
\(709\) −6.30577e12 −0.937195 −0.468597 0.883412i \(-0.655241\pi\)
−0.468597 + 0.883412i \(0.655241\pi\)
\(710\) −5.36806e11 −0.0792784
\(711\) 1.10522e12 0.162195
\(712\) −7.90091e11 −0.115217
\(713\) 1.67595e12 0.242861
\(714\) −3.63616e9 −0.000523602 0
\(715\) −1.67876e13 −2.40222
\(716\) −8.92788e12 −1.26952
\(717\) −3.66420e12 −0.517777
\(718\) 1.32023e11 0.0185392
\(719\) 1.65166e12 0.230483 0.115242 0.993337i \(-0.463236\pi\)
0.115242 + 0.993337i \(0.463236\pi\)
\(720\) −2.93556e12 −0.407095
\(721\) 8.65690e12 1.19304
\(722\) −2.93384e11 −0.0401809
\(723\) −3.89733e12 −0.530451
\(724\) −4.39754e12 −0.594820
\(725\) −4.12466e12 −0.554456
\(726\) 3.36123e11 0.0449039
\(727\) 1.12273e13 1.49064 0.745319 0.666708i \(-0.232297\pi\)
0.745319 + 0.666708i \(0.232297\pi\)
\(728\) 7.44646e11 0.0982559
\(729\) 2.82430e11 0.0370370
\(730\) −2.67250e11 −0.0348309
\(731\) 1.34800e11 0.0174606
\(732\) −2.38652e10 −0.00307231
\(733\) 5.92897e12 0.758598 0.379299 0.925274i \(-0.376165\pi\)
0.379299 + 0.925274i \(0.376165\pi\)
\(734\) −2.13529e11 −0.0271535
\(735\) 2.70630e12 0.342045
\(736\) −5.66777e11 −0.0711970
\(737\) 9.11173e12 1.13762
\(738\) 1.70338e11 0.0211377
\(739\) −6.19162e11 −0.0763667 −0.0381834 0.999271i \(-0.512157\pi\)
−0.0381834 + 0.999271i \(0.512157\pi\)
\(740\) −1.00152e13 −1.22777
\(741\) 3.04401e12 0.370906
\(742\) 2.61128e11 0.0316254
\(743\) 6.89752e12 0.830316 0.415158 0.909749i \(-0.363726\pi\)
0.415158 + 0.909749i \(0.363726\pi\)
\(744\) 2.92289e11 0.0349731
\(745\) 1.50287e13 1.78739
\(746\) 6.63827e11 0.0784748
\(747\) 1.70833e12 0.200738
\(748\) −3.06729e11 −0.0358259
\(749\) 1.54318e12 0.179163
\(750\) 1.61930e11 0.0186876
\(751\) 1.12380e13 1.28916 0.644581 0.764536i \(-0.277032\pi\)
0.644581 + 0.764536i \(0.277032\pi\)
\(752\) 6.63537e12 0.756632
\(753\) −2.73252e12 −0.309732
\(754\) 6.48013e11 0.0730151
\(755\) −6.28292e12 −0.703720
\(756\) −1.24180e12 −0.138262
\(757\) −7.11433e11 −0.0787413 −0.0393707 0.999225i \(-0.512535\pi\)
−0.0393707 + 0.999225i \(0.512535\pi\)
\(758\) −4.77539e11 −0.0525408
\(759\) 3.59090e12 0.392749
\(760\) −6.33726e11 −0.0689034
\(761\) 7.84301e12 0.847719 0.423859 0.905728i \(-0.360675\pi\)
0.423859 + 0.905728i \(0.360675\pi\)
\(762\) 2.16517e11 0.0232645
\(763\) 7.94827e12 0.849009
\(764\) −8.32481e12 −0.884004
\(765\) 8.97706e10 0.00947671
\(766\) −6.43218e11 −0.0675039
\(767\) 1.56184e12 0.162952
\(768\) 5.40137e12 0.560245
\(769\) −1.61297e13 −1.66325 −0.831627 0.555335i \(-0.812590\pi\)
−0.831627 + 0.555335i \(0.812590\pi\)
\(770\) 7.35913e11 0.0754429
\(771\) 3.95590e12 0.403181
\(772\) −2.46663e12 −0.249935
\(773\) 2.75113e12 0.277142 0.138571 0.990352i \(-0.455749\pi\)
0.138571 + 0.990352i \(0.455749\pi\)
\(774\) −1.37408e11 −0.0137619
\(775\) −2.89540e12 −0.288304
\(776\) 4.81171e11 0.0476346
\(777\) −4.22394e12 −0.415742
\(778\) 1.00213e12 0.0980657
\(779\) −6.13235e12 −0.596635
\(780\) −9.17831e12 −0.887845
\(781\) −1.90980e13 −1.83678
\(782\) 5.74867e9 0.000549714 0
\(783\) −2.16453e12 −0.205796
\(784\) −5.04043e12 −0.476481
\(785\) 2.11941e13 1.99205
\(786\) −5.32703e10 −0.00497833
\(787\) 6.57985e12 0.611406 0.305703 0.952127i \(-0.401108\pi\)
0.305703 + 0.952127i \(0.401108\pi\)
\(788\) −3.88038e12 −0.358514
\(789\) −4.64448e12 −0.426669
\(790\) −3.58094e11 −0.0327096
\(791\) 5.28152e12 0.479694
\(792\) 6.26262e11 0.0565578
\(793\) −7.43932e10 −0.00668043
\(794\) 3.68668e11 0.0329187
\(795\) −6.44680e12 −0.572390
\(796\) 1.02383e13 0.903895
\(797\) −1.64506e13 −1.44418 −0.722088 0.691801i \(-0.756817\pi\)
−0.722088 + 0.691801i \(0.756817\pi\)
\(798\) −1.33439e11 −0.0116485
\(799\) −2.02912e11 −0.0176135
\(800\) 9.79175e11 0.0845192
\(801\) 4.10723e12 0.352535
\(802\) 8.81857e11 0.0752685
\(803\) −9.50796e12 −0.806989
\(804\) 4.98166e12 0.420457
\(805\) 4.62088e12 0.387832
\(806\) 4.54887e11 0.0379661
\(807\) 4.32205e12 0.358723
\(808\) 2.26757e12 0.187159
\(809\) 1.93194e13 1.58572 0.792859 0.609405i \(-0.208592\pi\)
0.792859 + 0.609405i \(0.208592\pi\)
\(810\) −9.15077e10 −0.00746922
\(811\) 2.50823e12 0.203598 0.101799 0.994805i \(-0.467540\pi\)
0.101799 + 0.994805i \(0.467540\pi\)
\(812\) 9.51714e12 0.768253
\(813\) −3.51830e12 −0.282439
\(814\) 1.06352e12 0.0849052
\(815\) 6.90434e11 0.0548167
\(816\) −1.67196e11 −0.0132014
\(817\) 4.94684e12 0.388444
\(818\) 9.85768e10 0.00769813
\(819\) −3.87098e12 −0.300638
\(820\) 1.84903e13 1.42818
\(821\) 2.08249e13 1.59970 0.799850 0.600200i \(-0.204912\pi\)
0.799850 + 0.600200i \(0.204912\pi\)
\(822\) 5.97408e10 0.00456402
\(823\) −1.22807e13 −0.933091 −0.466545 0.884497i \(-0.654502\pi\)
−0.466545 + 0.884497i \(0.654502\pi\)
\(824\) −2.38693e12 −0.180371
\(825\) −6.20371e12 −0.466239
\(826\) −6.84660e10 −0.00511758
\(827\) −2.51636e11 −0.0187068 −0.00935338 0.999956i \(-0.502977\pi\)
−0.00935338 + 0.999956i \(0.502977\pi\)
\(828\) 1.96325e12 0.145158
\(829\) −1.55316e12 −0.114214 −0.0571072 0.998368i \(-0.518188\pi\)
−0.0571072 + 0.998368i \(0.518188\pi\)
\(830\) −5.53503e11 −0.0404826
\(831\) 3.50350e12 0.254858
\(832\) 1.69916e13 1.22936
\(833\) 1.54138e11 0.0110919
\(834\) −3.68046e11 −0.0263424
\(835\) 8.63416e12 0.614654
\(836\) −1.12562e13 −0.797013
\(837\) −1.51944e12 −0.107009
\(838\) 3.93154e11 0.0275400
\(839\) −1.81673e12 −0.126579 −0.0632895 0.997995i \(-0.520159\pi\)
−0.0632895 + 0.997995i \(0.520159\pi\)
\(840\) 8.05894e11 0.0558497
\(841\) 2.08177e12 0.143499
\(842\) 1.17285e12 0.0804154
\(843\) −6.22719e12 −0.424686
\(844\) 1.75468e13 1.19030
\(845\) −1.03483e13 −0.698256
\(846\) 2.06838e11 0.0138824
\(847\) 1.53883e13 1.02734
\(848\) 1.20070e13 0.797360
\(849\) 4.92773e12 0.325509
\(850\) −9.93153e9 −0.000652576 0
\(851\) 6.67794e12 0.436475
\(852\) −1.04414e13 −0.678863
\(853\) 2.04844e13 1.32481 0.662403 0.749148i \(-0.269537\pi\)
0.662403 + 0.749148i \(0.269537\pi\)
\(854\) 3.26115e9 0.000209802 0
\(855\) 3.29438e12 0.210827
\(856\) −4.25494e11 −0.0270870
\(857\) −1.32055e13 −0.836263 −0.418131 0.908387i \(-0.637315\pi\)
−0.418131 + 0.908387i \(0.637315\pi\)
\(858\) 9.74647e11 0.0613980
\(859\) 1.73514e13 1.08734 0.543670 0.839299i \(-0.317034\pi\)
0.543670 + 0.839299i \(0.317034\pi\)
\(860\) −1.49158e13 −0.929827
\(861\) 7.79836e12 0.483603
\(862\) 1.33563e11 0.00823956
\(863\) −1.87435e13 −1.15028 −0.575138 0.818056i \(-0.695052\pi\)
−0.575138 + 0.818056i \(0.695052\pi\)
\(864\) 5.13850e11 0.0313707
\(865\) 1.96030e12 0.119056
\(866\) −1.02097e12 −0.0616854
\(867\) −9.60051e12 −0.577043
\(868\) 6.68076e12 0.399473
\(869\) −1.27399e13 −0.757841
\(870\) 7.01313e11 0.0415026
\(871\) 1.55290e13 0.914242
\(872\) −2.19154e12 −0.128359
\(873\) −2.50133e12 −0.145750
\(874\) 2.10963e11 0.0122294
\(875\) 7.41344e12 0.427547
\(876\) −5.19829e12 −0.298258
\(877\) 4.56616e12 0.260647 0.130323 0.991472i \(-0.458398\pi\)
0.130323 + 0.991472i \(0.458398\pi\)
\(878\) 1.74764e11 0.00992490
\(879\) −8.76654e12 −0.495312
\(880\) 3.38383e13 1.90212
\(881\) −4.31027e12 −0.241053 −0.120527 0.992710i \(-0.538458\pi\)
−0.120527 + 0.992710i \(0.538458\pi\)
\(882\) −1.57121e11 −0.00874229
\(883\) −1.02590e13 −0.567914 −0.283957 0.958837i \(-0.591647\pi\)
−0.283957 + 0.958837i \(0.591647\pi\)
\(884\) −5.22753e11 −0.0287913
\(885\) 1.69031e12 0.0926234
\(886\) 1.63264e12 0.0890098
\(887\) −1.22517e13 −0.664569 −0.332285 0.943179i \(-0.607819\pi\)
−0.332285 + 0.943179i \(0.607819\pi\)
\(888\) 1.16465e12 0.0628545
\(889\) 9.91249e12 0.532261
\(890\) −1.33075e12 −0.0710954
\(891\) −3.25557e12 −0.173052
\(892\) −9.47538e12 −0.501135
\(893\) −7.44641e12 −0.391846
\(894\) −8.72529e11 −0.0456837
\(895\) −3.01193e13 −1.56907
\(896\) −3.01092e12 −0.156068
\(897\) 6.11992e12 0.315631
\(898\) 6.79406e11 0.0348647
\(899\) 1.16450e13 0.594592
\(900\) −3.39176e12 −0.172319
\(901\) −3.67179e11 −0.0185616
\(902\) −1.96349e12 −0.0987642
\(903\) −6.29077e12 −0.314854
\(904\) −1.45625e12 −0.0725233
\(905\) −1.48356e13 −0.735170
\(906\) 3.64770e11 0.0179863
\(907\) 4.04322e12 0.198378 0.0991892 0.995069i \(-0.468375\pi\)
0.0991892 + 0.995069i \(0.468375\pi\)
\(908\) −1.51008e13 −0.737247
\(909\) −1.17878e13 −0.572657
\(910\) 1.25421e12 0.0606293
\(911\) 6.23447e12 0.299893 0.149947 0.988694i \(-0.452090\pi\)
0.149947 + 0.988694i \(0.452090\pi\)
\(912\) −6.13571e12 −0.293689
\(913\) −1.96920e13 −0.937932
\(914\) 1.09954e12 0.0521139
\(915\) −8.05121e10 −0.00379723
\(916\) 3.57615e12 0.167836
\(917\) −2.43880e12 −0.113897
\(918\) −5.21185e9 −0.000242214 0
\(919\) 1.21666e13 0.562663 0.281332 0.959611i \(-0.409224\pi\)
0.281332 + 0.959611i \(0.409224\pi\)
\(920\) −1.27410e12 −0.0586350
\(921\) −1.39859e13 −0.640502
\(922\) 6.66842e11 0.0303902
\(923\) −3.25484e13 −1.47612
\(924\) 1.43143e13 0.646020
\(925\) −1.15369e13 −0.518147
\(926\) −1.43015e12 −0.0639195
\(927\) 1.24083e13 0.551889
\(928\) −3.93813e12 −0.174311
\(929\) 1.94095e13 0.854955 0.427477 0.904026i \(-0.359402\pi\)
0.427477 + 0.904026i \(0.359402\pi\)
\(930\) 4.92302e11 0.0215803
\(931\) 5.65652e12 0.246760
\(932\) −3.67594e13 −1.59587
\(933\) −1.46866e12 −0.0634531
\(934\) 4.18756e11 0.0180053
\(935\) −1.03479e12 −0.0442791
\(936\) 1.06733e12 0.0454524
\(937\) 3.80869e13 1.61416 0.807082 0.590439i \(-0.201046\pi\)
0.807082 + 0.590439i \(0.201046\pi\)
\(938\) −6.80738e11 −0.0287123
\(939\) −2.43200e13 −1.02086
\(940\) 2.24525e13 0.937970
\(941\) −3.84217e13 −1.59743 −0.798717 0.601707i \(-0.794488\pi\)
−0.798717 + 0.601707i \(0.794488\pi\)
\(942\) −1.23047e12 −0.0509147
\(943\) −1.23290e13 −0.507720
\(944\) −3.14816e12 −0.129028
\(945\) −4.18938e12 −0.170886
\(946\) 1.58391e12 0.0643013
\(947\) −2.26959e13 −0.917008 −0.458504 0.888692i \(-0.651615\pi\)
−0.458504 + 0.888692i \(0.651615\pi\)
\(948\) −6.96531e12 −0.280093
\(949\) −1.62043e13 −0.648533
\(950\) −3.64465e11 −0.0145177
\(951\) −2.65704e13 −1.05338
\(952\) 4.58999e10 0.00181111
\(953\) −2.81368e13 −1.10498 −0.552492 0.833518i \(-0.686323\pi\)
−0.552492 + 0.833518i \(0.686323\pi\)
\(954\) 3.74285e11 0.0146297
\(955\) −2.80848e13 −1.09259
\(956\) 2.30924e13 0.894147
\(957\) 2.49506e13 0.961563
\(958\) −9.08008e10 −0.00348293
\(959\) 2.73503e12 0.104419
\(960\) 1.83892e13 0.698782
\(961\) −1.82652e13 −0.690826
\(962\) 1.81253e12 0.0682336
\(963\) 2.21190e12 0.0828794
\(964\) 2.45617e13 0.916033
\(965\) −8.32150e12 −0.308908
\(966\) −2.68277e11 −0.00991256
\(967\) −3.29680e13 −1.21248 −0.606238 0.795283i \(-0.707322\pi\)
−0.606238 + 0.795283i \(0.707322\pi\)
\(968\) −4.24294e12 −0.155320
\(969\) 1.87632e11 0.00683676
\(970\) 8.10437e11 0.0293932
\(971\) −3.55036e12 −0.128170 −0.0640849 0.997944i \(-0.520413\pi\)
−0.0640849 + 0.997944i \(0.520413\pi\)
\(972\) −1.77992e12 −0.0639591
\(973\) −1.68498e13 −0.602679
\(974\) −1.76191e12 −0.0627291
\(975\) −1.05729e13 −0.374691
\(976\) 1.49952e11 0.00528967
\(977\) −2.31998e13 −0.814625 −0.407313 0.913289i \(-0.633534\pi\)
−0.407313 + 0.913289i \(0.633534\pi\)
\(978\) −4.00848e10 −0.00140105
\(979\) −4.73441e13 −1.64719
\(980\) −1.70556e13 −0.590676
\(981\) 1.13926e13 0.392745
\(982\) 2.39695e12 0.0822541
\(983\) 5.95029e12 0.203258 0.101629 0.994822i \(-0.467595\pi\)
0.101629 + 0.994822i \(0.467595\pi\)
\(984\) −2.15021e12 −0.0731142
\(985\) −1.30910e13 −0.443107
\(986\) 3.99434e10 0.00134586
\(987\) 9.46940e12 0.317611
\(988\) −1.91839e13 −0.640516
\(989\) 9.94553e12 0.330556
\(990\) 1.05481e12 0.0348993
\(991\) 3.98196e13 1.31149 0.655745 0.754982i \(-0.272355\pi\)
0.655745 + 0.754982i \(0.272355\pi\)
\(992\) −2.76446e12 −0.0906374
\(993\) −3.40975e13 −1.11289
\(994\) 1.42681e12 0.0463583
\(995\) 3.45401e13 1.11717
\(996\) −1.07662e13 −0.346654
\(997\) 1.10377e13 0.353793 0.176897 0.984229i \(-0.443394\pi\)
0.176897 + 0.984229i \(0.443394\pi\)
\(998\) −3.16674e12 −0.101048
\(999\) −6.05434e12 −0.192319
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.10.a.d.1.12 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.12 22 1.1 even 1 trivial