Properties

Label 177.14.a.c.1.10
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $0$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(0\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-60.0941 q^{2} +729.000 q^{3} -4580.70 q^{4} -50851.6 q^{5} -43808.6 q^{6} -259334. q^{7} +767564. q^{8} +531441. q^{9} +O(q^{10})\) \(q-60.0941 q^{2} +729.000 q^{3} -4580.70 q^{4} -50851.6 q^{5} -43808.6 q^{6} -259334. q^{7} +767564. q^{8} +531441. q^{9} +3.05588e6 q^{10} -1.61611e6 q^{11} -3.33933e6 q^{12} +3.32755e6 q^{13} +1.55844e7 q^{14} -3.70708e7 q^{15} -8.60088e6 q^{16} -9.95689e7 q^{17} -3.19364e7 q^{18} +9.24640e7 q^{19} +2.32936e8 q^{20} -1.89055e8 q^{21} +9.71188e7 q^{22} -5.67360e8 q^{23} +5.59554e8 q^{24} +1.36518e9 q^{25} -1.99966e8 q^{26} +3.87420e8 q^{27} +1.18793e9 q^{28} +3.47908e9 q^{29} +2.22773e9 q^{30} -8.56644e9 q^{31} -5.77102e9 q^{32} -1.17815e9 q^{33} +5.98350e9 q^{34} +1.31876e10 q^{35} -2.43437e9 q^{36} -1.81122e10 q^{37} -5.55654e9 q^{38} +2.42579e9 q^{39} -3.90318e10 q^{40} -1.66711e8 q^{41} +1.13611e10 q^{42} -5.81369e10 q^{43} +7.40294e9 q^{44} -2.70246e10 q^{45} +3.40949e10 q^{46} -8.85067e10 q^{47} -6.27004e9 q^{48} -2.96348e10 q^{49} -8.20392e10 q^{50} -7.25857e10 q^{51} -1.52425e10 q^{52} -1.79141e11 q^{53} -2.32817e10 q^{54} +8.21819e10 q^{55} -1.99056e11 q^{56} +6.74063e10 q^{57} -2.09072e11 q^{58} -4.21805e10 q^{59} +1.69810e11 q^{60} -3.70046e11 q^{61} +5.14792e11 q^{62} -1.37821e11 q^{63} +4.17262e11 q^{64} -1.69211e11 q^{65} +7.07996e10 q^{66} -3.15486e11 q^{67} +4.56096e11 q^{68} -4.13605e11 q^{69} -7.92494e11 q^{70} -1.56042e12 q^{71} +4.07915e11 q^{72} +1.08742e12 q^{73} +1.08843e12 q^{74} +9.95216e11 q^{75} -4.23550e11 q^{76} +4.19114e11 q^{77} -1.45775e11 q^{78} +1.56095e12 q^{79} +4.37368e11 q^{80} +2.82430e11 q^{81} +1.00183e10 q^{82} +2.63040e12 q^{83} +8.66004e11 q^{84} +5.06324e12 q^{85} +3.49368e12 q^{86} +2.53625e12 q^{87} -1.24047e12 q^{88} -6.98019e12 q^{89} +1.62402e12 q^{90} -8.62948e11 q^{91} +2.59891e12 q^{92} -6.24493e12 q^{93} +5.31873e12 q^{94} -4.70194e12 q^{95} -4.20707e12 q^{96} -1.52218e13 q^{97} +1.78087e12 q^{98} -8.58869e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −60.0941 −0.663952 −0.331976 0.943288i \(-0.607715\pi\)
−0.331976 + 0.943288i \(0.607715\pi\)
\(3\) 729.000 0.577350
\(4\) −4580.70 −0.559168
\(5\) −50851.6 −1.45546 −0.727729 0.685865i \(-0.759424\pi\)
−0.727729 + 0.685865i \(0.759424\pi\)
\(6\) −43808.6 −0.383333
\(7\) −259334. −0.833149 −0.416574 0.909102i \(-0.636769\pi\)
−0.416574 + 0.909102i \(0.636769\pi\)
\(8\) 767564. 1.03521
\(9\) 531441. 0.333333
\(10\) 3.05588e6 0.966353
\(11\) −1.61611e6 −0.275055 −0.137527 0.990498i \(-0.543916\pi\)
−0.137527 + 0.990498i \(0.543916\pi\)
\(12\) −3.33933e6 −0.322836
\(13\) 3.32755e6 0.191202 0.0956012 0.995420i \(-0.469523\pi\)
0.0956012 + 0.995420i \(0.469523\pi\)
\(14\) 1.55844e7 0.553171
\(15\) −3.70708e7 −0.840309
\(16\) −8.60088e6 −0.128163
\(17\) −9.95689e7 −1.00047 −0.500237 0.865889i \(-0.666754\pi\)
−0.500237 + 0.865889i \(0.666754\pi\)
\(18\) −3.19364e7 −0.221317
\(19\) 9.24640e7 0.450894 0.225447 0.974255i \(-0.427616\pi\)
0.225447 + 0.974255i \(0.427616\pi\)
\(20\) 2.32936e8 0.813845
\(21\) −1.89055e8 −0.481019
\(22\) 9.71188e7 0.182623
\(23\) −5.67360e8 −0.799149 −0.399574 0.916701i \(-0.630842\pi\)
−0.399574 + 0.916701i \(0.630842\pi\)
\(24\) 5.59554e8 0.597680
\(25\) 1.36518e9 1.11836
\(26\) −1.99966e8 −0.126949
\(27\) 3.87420e8 0.192450
\(28\) 1.18793e9 0.465870
\(29\) 3.47908e9 1.08612 0.543060 0.839694i \(-0.317266\pi\)
0.543060 + 0.839694i \(0.317266\pi\)
\(30\) 2.22773e9 0.557924
\(31\) −8.56644e9 −1.73360 −0.866801 0.498655i \(-0.833827\pi\)
−0.866801 + 0.498655i \(0.833827\pi\)
\(32\) −5.77102e9 −0.950118
\(33\) −1.17815e9 −0.158803
\(34\) 5.98350e9 0.664266
\(35\) 1.31876e10 1.21261
\(36\) −2.43437e9 −0.186389
\(37\) −1.81122e10 −1.16054 −0.580269 0.814425i \(-0.697053\pi\)
−0.580269 + 0.814425i \(0.697053\pi\)
\(38\) −5.55654e9 −0.299372
\(39\) 2.42579e9 0.110391
\(40\) −3.90318e10 −1.50671
\(41\) −1.66711e8 −0.00548112 −0.00274056 0.999996i \(-0.500872\pi\)
−0.00274056 + 0.999996i \(0.500872\pi\)
\(42\) 1.13611e10 0.319373
\(43\) −5.81369e10 −1.40251 −0.701256 0.712909i \(-0.747377\pi\)
−0.701256 + 0.712909i \(0.747377\pi\)
\(44\) 7.40294e9 0.153802
\(45\) −2.70246e10 −0.485152
\(46\) 3.40949e10 0.530596
\(47\) −8.85067e10 −1.19768 −0.598839 0.800869i \(-0.704371\pi\)
−0.598839 + 0.800869i \(0.704371\pi\)
\(48\) −6.27004e9 −0.0739950
\(49\) −2.96348e10 −0.305863
\(50\) −8.20392e10 −0.742534
\(51\) −7.25857e10 −0.577624
\(52\) −1.52425e10 −0.106914
\(53\) −1.79141e11 −1.11020 −0.555100 0.831783i \(-0.687320\pi\)
−0.555100 + 0.831783i \(0.687320\pi\)
\(54\) −2.32817e10 −0.127778
\(55\) 8.21819e10 0.400331
\(56\) −1.99056e11 −0.862486
\(57\) 6.74063e10 0.260324
\(58\) −2.09072e11 −0.721131
\(59\) −4.21805e10 −0.130189
\(60\) 1.69810e11 0.469874
\(61\) −3.70046e11 −0.919626 −0.459813 0.888016i \(-0.652084\pi\)
−0.459813 + 0.888016i \(0.652084\pi\)
\(62\) 5.14792e11 1.15103
\(63\) −1.37821e11 −0.277716
\(64\) 4.17262e11 0.758996
\(65\) −1.69211e11 −0.278287
\(66\) 7.07996e10 0.105438
\(67\) −3.15486e11 −0.426083 −0.213042 0.977043i \(-0.568337\pi\)
−0.213042 + 0.977043i \(0.568337\pi\)
\(68\) 4.56096e11 0.559433
\(69\) −4.13605e11 −0.461389
\(70\) −7.92494e11 −0.805116
\(71\) −1.56042e12 −1.44565 −0.722825 0.691032i \(-0.757157\pi\)
−0.722825 + 0.691032i \(0.757157\pi\)
\(72\) 4.07915e11 0.345071
\(73\) 1.08742e12 0.841006 0.420503 0.907291i \(-0.361854\pi\)
0.420503 + 0.907291i \(0.361854\pi\)
\(74\) 1.08843e12 0.770542
\(75\) 9.95216e11 0.645683
\(76\) −4.23550e11 −0.252125
\(77\) 4.19114e11 0.229162
\(78\) −1.45775e11 −0.0732941
\(79\) 1.56095e12 0.722457 0.361229 0.932477i \(-0.382357\pi\)
0.361229 + 0.932477i \(0.382357\pi\)
\(80\) 4.37368e11 0.186536
\(81\) 2.82430e11 0.111111
\(82\) 1.00183e10 0.00363920
\(83\) 2.63040e12 0.883108 0.441554 0.897235i \(-0.354427\pi\)
0.441554 + 0.897235i \(0.354427\pi\)
\(84\) 8.66004e11 0.268970
\(85\) 5.06324e12 1.45615
\(86\) 3.49368e12 0.931201
\(87\) 2.53625e12 0.627072
\(88\) −1.24047e12 −0.284740
\(89\) −6.98019e12 −1.48879 −0.744393 0.667741i \(-0.767261\pi\)
−0.744393 + 0.667741i \(0.767261\pi\)
\(90\) 1.62402e12 0.322118
\(91\) −8.62948e11 −0.159300
\(92\) 2.59891e12 0.446858
\(93\) −6.24493e12 −1.00090
\(94\) 5.31873e12 0.795201
\(95\) −4.70194e12 −0.656257
\(96\) −4.20707e12 −0.548551
\(97\) −1.52218e13 −1.85546 −0.927728 0.373257i \(-0.878241\pi\)
−0.927728 + 0.373257i \(0.878241\pi\)
\(98\) 1.78087e12 0.203078
\(99\) −8.58869e11 −0.0916850
\(100\) −6.25348e12 −0.625348
\(101\) 4.49762e12 0.421594 0.210797 0.977530i \(-0.432394\pi\)
0.210797 + 0.977530i \(0.432394\pi\)
\(102\) 4.36197e12 0.383514
\(103\) 1.22877e12 0.101398 0.0506991 0.998714i \(-0.483855\pi\)
0.0506991 + 0.998714i \(0.483855\pi\)
\(104\) 2.55411e12 0.197935
\(105\) 9.61373e12 0.700102
\(106\) 1.07653e13 0.737120
\(107\) −1.24501e13 −0.802008 −0.401004 0.916076i \(-0.631339\pi\)
−0.401004 + 0.916076i \(0.631339\pi\)
\(108\) −1.77466e12 −0.107612
\(109\) 2.75070e13 1.57098 0.785490 0.618875i \(-0.212411\pi\)
0.785490 + 0.618875i \(0.212411\pi\)
\(110\) −4.93864e12 −0.265800
\(111\) −1.32038e13 −0.670037
\(112\) 2.23050e12 0.106779
\(113\) −1.25235e13 −0.565870 −0.282935 0.959139i \(-0.591308\pi\)
−0.282935 + 0.959139i \(0.591308\pi\)
\(114\) −4.05072e12 −0.172842
\(115\) 2.88511e13 1.16313
\(116\) −1.59367e13 −0.607324
\(117\) 1.76840e12 0.0637341
\(118\) 2.53480e12 0.0864392
\(119\) 2.58216e13 0.833544
\(120\) −2.84542e13 −0.869898
\(121\) −3.19109e13 −0.924345
\(122\) 2.22375e13 0.610588
\(123\) −1.21532e11 −0.00316453
\(124\) 3.92403e13 0.969374
\(125\) −7.34686e12 −0.172261
\(126\) 8.28221e12 0.184390
\(127\) −4.01254e13 −0.848584 −0.424292 0.905525i \(-0.639477\pi\)
−0.424292 + 0.905525i \(0.639477\pi\)
\(128\) 2.22012e13 0.446182
\(129\) −4.23818e13 −0.809741
\(130\) 1.01686e13 0.184769
\(131\) −5.35754e13 −0.926193 −0.463097 0.886308i \(-0.653262\pi\)
−0.463097 + 0.886308i \(0.653262\pi\)
\(132\) 5.39674e12 0.0887976
\(133\) −2.39791e13 −0.375662
\(134\) 1.89589e13 0.282899
\(135\) −1.97009e13 −0.280103
\(136\) −7.64255e13 −1.03570
\(137\) 2.14872e13 0.277648 0.138824 0.990317i \(-0.455668\pi\)
0.138824 + 0.990317i \(0.455668\pi\)
\(138\) 2.48552e13 0.306340
\(139\) −1.11909e13 −0.131604 −0.0658018 0.997833i \(-0.520961\pi\)
−0.0658018 + 0.997833i \(0.520961\pi\)
\(140\) −6.04083e13 −0.678054
\(141\) −6.45214e13 −0.691480
\(142\) 9.37721e13 0.959841
\(143\) −5.37770e12 −0.0525911
\(144\) −4.57086e12 −0.0427210
\(145\) −1.76917e14 −1.58080
\(146\) −6.53475e13 −0.558387
\(147\) −2.16037e13 −0.176590
\(148\) 8.29665e13 0.648936
\(149\) −1.68046e14 −1.25810 −0.629052 0.777364i \(-0.716557\pi\)
−0.629052 + 0.777364i \(0.716557\pi\)
\(150\) −5.98066e13 −0.428702
\(151\) −1.63072e14 −1.11951 −0.559757 0.828657i \(-0.689106\pi\)
−0.559757 + 0.828657i \(0.689106\pi\)
\(152\) 7.09720e13 0.466771
\(153\) −5.29150e13 −0.333491
\(154\) −2.51862e13 −0.152152
\(155\) 4.35617e14 2.52318
\(156\) −1.11118e13 −0.0617270
\(157\) 8.10870e13 0.432119 0.216060 0.976380i \(-0.430679\pi\)
0.216060 + 0.976380i \(0.430679\pi\)
\(158\) −9.38036e13 −0.479677
\(159\) −1.30594e14 −0.640975
\(160\) 2.93465e14 1.38286
\(161\) 1.47136e14 0.665810
\(162\) −1.69723e13 −0.0737724
\(163\) 1.62941e14 0.680472 0.340236 0.940340i \(-0.389493\pi\)
0.340236 + 0.940340i \(0.389493\pi\)
\(164\) 7.63654e11 0.00306487
\(165\) 5.99106e13 0.231131
\(166\) −1.58071e14 −0.586341
\(167\) −2.13090e13 −0.0760161 −0.0380081 0.999277i \(-0.512101\pi\)
−0.0380081 + 0.999277i \(0.512101\pi\)
\(168\) −1.45111e14 −0.497957
\(169\) −2.91802e14 −0.963442
\(170\) −3.04270e14 −0.966811
\(171\) 4.91392e13 0.150298
\(172\) 2.66308e14 0.784240
\(173\) 1.17673e14 0.333715 0.166857 0.985981i \(-0.446638\pi\)
0.166857 + 0.985981i \(0.446638\pi\)
\(174\) −1.52414e14 −0.416345
\(175\) −3.54038e14 −0.931756
\(176\) 1.39000e13 0.0352519
\(177\) −3.07496e13 −0.0751646
\(178\) 4.19468e14 0.988483
\(179\) 4.83367e14 1.09833 0.549164 0.835714i \(-0.314946\pi\)
0.549164 + 0.835714i \(0.314946\pi\)
\(180\) 1.23792e14 0.271282
\(181\) −8.13641e14 −1.71998 −0.859988 0.510315i \(-0.829529\pi\)
−0.859988 + 0.510315i \(0.829529\pi\)
\(182\) 5.18581e13 0.105768
\(183\) −2.69763e14 −0.530947
\(184\) −4.35485e14 −0.827289
\(185\) 9.21033e14 1.68911
\(186\) 3.75283e14 0.664546
\(187\) 1.60915e14 0.275185
\(188\) 4.05423e14 0.669703
\(189\) −1.00471e14 −0.160340
\(190\) 2.82559e14 0.435723
\(191\) 5.56459e14 0.829309 0.414654 0.909979i \(-0.363902\pi\)
0.414654 + 0.909979i \(0.363902\pi\)
\(192\) 3.04184e14 0.438206
\(193\) 1.36392e14 0.189962 0.0949812 0.995479i \(-0.469721\pi\)
0.0949812 + 0.995479i \(0.469721\pi\)
\(194\) 9.14742e14 1.23193
\(195\) −1.23355e14 −0.160669
\(196\) 1.35748e14 0.171029
\(197\) 1.02604e15 1.25064 0.625320 0.780368i \(-0.284968\pi\)
0.625320 + 0.780368i \(0.284968\pi\)
\(198\) 5.16129e13 0.0608744
\(199\) 2.51769e14 0.287381 0.143690 0.989623i \(-0.454103\pi\)
0.143690 + 0.989623i \(0.454103\pi\)
\(200\) 1.04786e15 1.15774
\(201\) −2.29990e14 −0.245999
\(202\) −2.70281e14 −0.279918
\(203\) −9.02246e14 −0.904900
\(204\) 3.32494e14 0.322989
\(205\) 8.47752e12 0.00797753
\(206\) −7.38420e13 −0.0673235
\(207\) −3.01518e14 −0.266383
\(208\) −2.86199e13 −0.0245051
\(209\) −1.49432e14 −0.124021
\(210\) −5.77728e14 −0.464834
\(211\) −1.32712e15 −1.03532 −0.517659 0.855587i \(-0.673196\pi\)
−0.517659 + 0.855587i \(0.673196\pi\)
\(212\) 8.20591e14 0.620789
\(213\) −1.13755e15 −0.834646
\(214\) 7.48178e14 0.532495
\(215\) 2.95635e15 2.04130
\(216\) 2.97370e14 0.199227
\(217\) 2.22157e15 1.44435
\(218\) −1.65301e15 −1.04305
\(219\) 7.92730e14 0.485555
\(220\) −3.76451e14 −0.223852
\(221\) −3.31321e14 −0.191293
\(222\) 7.93469e14 0.444872
\(223\) 2.42173e15 1.31870 0.659348 0.751838i \(-0.270832\pi\)
0.659348 + 0.751838i \(0.270832\pi\)
\(224\) 1.49662e15 0.791590
\(225\) 7.25512e14 0.372785
\(226\) 7.52589e14 0.375710
\(227\) −3.17178e14 −0.153863 −0.0769316 0.997036i \(-0.524512\pi\)
−0.0769316 + 0.997036i \(0.524512\pi\)
\(228\) −3.08768e14 −0.145565
\(229\) 4.14941e15 1.90132 0.950660 0.310234i \(-0.100407\pi\)
0.950660 + 0.310234i \(0.100407\pi\)
\(230\) −1.73378e15 −0.772260
\(231\) 3.05534e14 0.132307
\(232\) 2.67042e15 1.12437
\(233\) −1.02774e15 −0.420793 −0.210397 0.977616i \(-0.567476\pi\)
−0.210397 + 0.977616i \(0.567476\pi\)
\(234\) −1.06270e14 −0.0423164
\(235\) 4.50071e15 1.74317
\(236\) 1.93217e14 0.0727975
\(237\) 1.13793e15 0.417111
\(238\) −1.55173e15 −0.553433
\(239\) −3.04875e15 −1.05812 −0.529060 0.848584i \(-0.677455\pi\)
−0.529060 + 0.848584i \(0.677455\pi\)
\(240\) 3.18842e14 0.107697
\(241\) −4.17433e15 −1.37239 −0.686193 0.727419i \(-0.740720\pi\)
−0.686193 + 0.727419i \(0.740720\pi\)
\(242\) 1.91765e15 0.613720
\(243\) 2.05891e14 0.0641500
\(244\) 1.69507e15 0.514226
\(245\) 1.50697e15 0.445170
\(246\) 7.30337e12 0.00210109
\(247\) 3.07679e14 0.0862120
\(248\) −6.57528e15 −1.79465
\(249\) 1.91756e15 0.509862
\(250\) 4.41503e14 0.114373
\(251\) −3.46969e15 −0.875812 −0.437906 0.899021i \(-0.644280\pi\)
−0.437906 + 0.899021i \(0.644280\pi\)
\(252\) 6.31317e14 0.155290
\(253\) 9.16918e14 0.219810
\(254\) 2.41130e15 0.563419
\(255\) 3.69110e15 0.840707
\(256\) −4.75237e15 −1.05524
\(257\) −5.20108e15 −1.12597 −0.562986 0.826466i \(-0.690348\pi\)
−0.562986 + 0.826466i \(0.690348\pi\)
\(258\) 2.54689e15 0.537629
\(259\) 4.69711e15 0.966901
\(260\) 7.75107e14 0.155609
\(261\) 1.84893e15 0.362040
\(262\) 3.21956e15 0.614948
\(263\) 7.74985e15 1.44405 0.722023 0.691869i \(-0.243213\pi\)
0.722023 + 0.691869i \(0.243213\pi\)
\(264\) −9.04303e14 −0.164395
\(265\) 9.10959e15 1.61585
\(266\) 1.44100e15 0.249421
\(267\) −5.08856e15 −0.859551
\(268\) 1.44515e15 0.238252
\(269\) 6.57041e15 1.05731 0.528655 0.848837i \(-0.322696\pi\)
0.528655 + 0.848837i \(0.322696\pi\)
\(270\) 1.18391e15 0.185975
\(271\) 2.74962e15 0.421670 0.210835 0.977522i \(-0.432382\pi\)
0.210835 + 0.977522i \(0.432382\pi\)
\(272\) 8.56381e14 0.128224
\(273\) −6.29089e14 −0.0919719
\(274\) −1.29125e15 −0.184345
\(275\) −2.20629e15 −0.307609
\(276\) 1.89460e15 0.257994
\(277\) 8.55484e15 1.13787 0.568936 0.822382i \(-0.307355\pi\)
0.568936 + 0.822382i \(0.307355\pi\)
\(278\) 6.72505e14 0.0873785
\(279\) −4.55256e15 −0.577867
\(280\) 1.01223e16 1.25531
\(281\) 1.74791e15 0.211801 0.105901 0.994377i \(-0.466227\pi\)
0.105901 + 0.994377i \(0.466227\pi\)
\(282\) 3.87735e15 0.459109
\(283\) −8.40698e15 −0.972811 −0.486405 0.873733i \(-0.661692\pi\)
−0.486405 + 0.873733i \(0.661692\pi\)
\(284\) 7.14783e15 0.808361
\(285\) −3.42772e15 −0.378890
\(286\) 3.23168e14 0.0349180
\(287\) 4.32339e13 0.00456659
\(288\) −3.06696e15 −0.316706
\(289\) 9.39118e12 0.000948165 0
\(290\) 1.06317e16 1.04958
\(291\) −1.10967e16 −1.07125
\(292\) −4.98115e15 −0.470263
\(293\) 4.85086e15 0.447898 0.223949 0.974601i \(-0.428105\pi\)
0.223949 + 0.974601i \(0.428105\pi\)
\(294\) 1.29826e15 0.117247
\(295\) 2.14495e15 0.189484
\(296\) −1.39023e16 −1.20140
\(297\) −6.26115e14 −0.0529343
\(298\) 1.00985e16 0.835320
\(299\) −1.88792e15 −0.152799
\(300\) −4.55879e15 −0.361045
\(301\) 1.50769e16 1.16850
\(302\) 9.79967e15 0.743304
\(303\) 3.27877e15 0.243407
\(304\) −7.95272e14 −0.0577880
\(305\) 1.88174e16 1.33848
\(306\) 3.17988e15 0.221422
\(307\) −1.21767e16 −0.830098 −0.415049 0.909799i \(-0.636236\pi\)
−0.415049 + 0.909799i \(0.636236\pi\)
\(308\) −1.91984e15 −0.128140
\(309\) 8.95777e14 0.0585423
\(310\) −2.61780e16 −1.67527
\(311\) 2.99183e15 0.187497 0.0937485 0.995596i \(-0.470115\pi\)
0.0937485 + 0.995596i \(0.470115\pi\)
\(312\) 1.86195e15 0.114278
\(313\) −7.73766e15 −0.465127 −0.232563 0.972581i \(-0.574711\pi\)
−0.232563 + 0.972581i \(0.574711\pi\)
\(314\) −4.87285e15 −0.286906
\(315\) 7.00841e15 0.404204
\(316\) −7.15024e15 −0.403975
\(317\) −1.97145e16 −1.09119 −0.545596 0.838048i \(-0.683697\pi\)
−0.545596 + 0.838048i \(0.683697\pi\)
\(318\) 7.84790e15 0.425576
\(319\) −5.62259e15 −0.298743
\(320\) −2.12185e16 −1.10469
\(321\) −9.07614e15 −0.463040
\(322\) −8.84199e15 −0.442066
\(323\) −9.20654e15 −0.451108
\(324\) −1.29373e15 −0.0621298
\(325\) 4.54271e15 0.213832
\(326\) −9.79177e15 −0.451800
\(327\) 2.00526e16 0.907005
\(328\) −1.27961e14 −0.00567412
\(329\) 2.29528e16 0.997845
\(330\) −3.60027e15 −0.153460
\(331\) −9.82251e15 −0.410526 −0.205263 0.978707i \(-0.565805\pi\)
−0.205263 + 0.978707i \(0.565805\pi\)
\(332\) −1.20491e16 −0.493805
\(333\) −9.62556e15 −0.386846
\(334\) 1.28054e15 0.0504711
\(335\) 1.60430e16 0.620146
\(336\) 1.62604e15 0.0616489
\(337\) −4.07241e16 −1.51446 −0.757230 0.653149i \(-0.773448\pi\)
−0.757230 + 0.653149i \(0.773448\pi\)
\(338\) 1.75356e16 0.639679
\(339\) −9.12965e15 −0.326705
\(340\) −2.31932e16 −0.814231
\(341\) 1.38443e16 0.476835
\(342\) −2.95297e15 −0.0997906
\(343\) 3.28119e16 1.08798
\(344\) −4.46238e16 −1.45190
\(345\) 2.10325e16 0.671531
\(346\) −7.07142e15 −0.221571
\(347\) 4.15074e16 1.27639 0.638196 0.769874i \(-0.279681\pi\)
0.638196 + 0.769874i \(0.279681\pi\)
\(348\) −1.16178e16 −0.350638
\(349\) −5.66660e16 −1.67864 −0.839320 0.543638i \(-0.817046\pi\)
−0.839320 + 0.543638i \(0.817046\pi\)
\(350\) 2.12756e16 0.618641
\(351\) 1.28916e15 0.0367969
\(352\) 9.32662e15 0.261335
\(353\) 5.77632e16 1.58897 0.794485 0.607284i \(-0.207741\pi\)
0.794485 + 0.607284i \(0.207741\pi\)
\(354\) 1.84787e15 0.0499057
\(355\) 7.93499e16 2.10408
\(356\) 3.19742e16 0.832482
\(357\) 1.88240e16 0.481247
\(358\) −2.90475e16 −0.729237
\(359\) 4.44467e16 1.09579 0.547893 0.836548i \(-0.315430\pi\)
0.547893 + 0.836548i \(0.315430\pi\)
\(360\) −2.07431e16 −0.502236
\(361\) −3.35034e16 −0.796695
\(362\) 4.88950e16 1.14198
\(363\) −2.32630e16 −0.533671
\(364\) 3.95291e15 0.0890755
\(365\) −5.52970e16 −1.22405
\(366\) 1.62112e16 0.352523
\(367\) 5.59013e16 1.19424 0.597121 0.802151i \(-0.296311\pi\)
0.597121 + 0.802151i \(0.296311\pi\)
\(368\) 4.87979e15 0.102421
\(369\) −8.85971e13 −0.00182704
\(370\) −5.53486e16 −1.12149
\(371\) 4.64573e16 0.924962
\(372\) 2.86062e16 0.559669
\(373\) −3.17044e16 −0.609554 −0.304777 0.952424i \(-0.598582\pi\)
−0.304777 + 0.952424i \(0.598582\pi\)
\(374\) −9.67002e15 −0.182710
\(375\) −5.35586e15 −0.0994549
\(376\) −6.79346e16 −1.23985
\(377\) 1.15768e16 0.207669
\(378\) 6.03773e15 0.106458
\(379\) 4.78027e16 0.828509 0.414254 0.910161i \(-0.364042\pi\)
0.414254 + 0.910161i \(0.364042\pi\)
\(380\) 2.15382e16 0.366958
\(381\) −2.92514e16 −0.489930
\(382\) −3.34399e16 −0.550621
\(383\) 9.39040e16 1.52017 0.760085 0.649824i \(-0.225157\pi\)
0.760085 + 0.649824i \(0.225157\pi\)
\(384\) 1.61847e16 0.257603
\(385\) −2.13126e16 −0.333535
\(386\) −8.19638e15 −0.126126
\(387\) −3.08963e16 −0.467504
\(388\) 6.97267e16 1.03751
\(389\) 5.23650e16 0.766248 0.383124 0.923697i \(-0.374848\pi\)
0.383124 + 0.923697i \(0.374848\pi\)
\(390\) 7.41290e15 0.106676
\(391\) 5.64914e16 0.799527
\(392\) −2.27466e16 −0.316633
\(393\) −3.90564e16 −0.534738
\(394\) −6.16587e16 −0.830365
\(395\) −7.93766e16 −1.05151
\(396\) 3.93422e15 0.0512673
\(397\) 7.39522e16 0.948010 0.474005 0.880522i \(-0.342808\pi\)
0.474005 + 0.880522i \(0.342808\pi\)
\(398\) −1.51298e16 −0.190807
\(399\) −1.74808e16 −0.216888
\(400\) −1.17418e16 −0.143332
\(401\) 4.83656e16 0.580896 0.290448 0.956891i \(-0.406196\pi\)
0.290448 + 0.956891i \(0.406196\pi\)
\(402\) 1.38210e16 0.163332
\(403\) −2.85053e16 −0.331469
\(404\) −2.06023e16 −0.235742
\(405\) −1.43620e16 −0.161717
\(406\) 5.42196e16 0.600810
\(407\) 2.92713e16 0.319212
\(408\) −5.57142e16 −0.597963
\(409\) −1.51915e17 −1.60472 −0.802360 0.596840i \(-0.796423\pi\)
−0.802360 + 0.596840i \(0.796423\pi\)
\(410\) −5.09449e14 −0.00529670
\(411\) 1.56641e16 0.160300
\(412\) −5.62865e15 −0.0566986
\(413\) 1.09389e16 0.108467
\(414\) 1.81195e16 0.176865
\(415\) −1.33760e17 −1.28533
\(416\) −1.92034e16 −0.181665
\(417\) −8.15815e15 −0.0759814
\(418\) 8.98000e15 0.0823437
\(419\) 1.61912e17 1.46180 0.730901 0.682483i \(-0.239100\pi\)
0.730901 + 0.682483i \(0.239100\pi\)
\(420\) −4.40376e16 −0.391475
\(421\) −1.21796e16 −0.106610 −0.0533052 0.998578i \(-0.516976\pi\)
−0.0533052 + 0.998578i \(0.516976\pi\)
\(422\) 7.97520e16 0.687402
\(423\) −4.70361e16 −0.399226
\(424\) −1.37502e17 −1.14929
\(425\) −1.35929e17 −1.11889
\(426\) 6.83599e16 0.554165
\(427\) 9.59655e16 0.766186
\(428\) 5.70303e16 0.448457
\(429\) −3.92035e15 −0.0303635
\(430\) −1.77659e17 −1.35532
\(431\) −1.65911e17 −1.24673 −0.623365 0.781931i \(-0.714235\pi\)
−0.623365 + 0.781931i \(0.714235\pi\)
\(432\) −3.33216e15 −0.0246650
\(433\) −2.02278e17 −1.47495 −0.737476 0.675374i \(-0.763982\pi\)
−0.737476 + 0.675374i \(0.763982\pi\)
\(434\) −1.33503e17 −0.958977
\(435\) −1.28972e17 −0.912676
\(436\) −1.26001e17 −0.878441
\(437\) −5.24604e16 −0.360331
\(438\) −4.76383e16 −0.322385
\(439\) 1.02811e17 0.685519 0.342759 0.939423i \(-0.388638\pi\)
0.342759 + 0.939423i \(0.388638\pi\)
\(440\) 6.30799e16 0.414427
\(441\) −1.57491e16 −0.101954
\(442\) 1.99104e16 0.127009
\(443\) 2.13575e17 1.34254 0.671268 0.741215i \(-0.265750\pi\)
0.671268 + 0.741215i \(0.265750\pi\)
\(444\) 6.04826e16 0.374663
\(445\) 3.54954e17 2.16686
\(446\) −1.45532e17 −0.875550
\(447\) −1.22505e17 −0.726366
\(448\) −1.08210e17 −0.632357
\(449\) −2.67823e17 −1.54258 −0.771289 0.636485i \(-0.780388\pi\)
−0.771289 + 0.636485i \(0.780388\pi\)
\(450\) −4.35990e16 −0.247511
\(451\) 2.69424e14 0.00150761
\(452\) 5.73665e16 0.316416
\(453\) −1.18880e17 −0.646352
\(454\) 1.90605e16 0.102158
\(455\) 4.38823e16 0.231854
\(456\) 5.17386e16 0.269490
\(457\) −3.14940e16 −0.161723 −0.0808617 0.996725i \(-0.525767\pi\)
−0.0808617 + 0.996725i \(0.525767\pi\)
\(458\) −2.49355e17 −1.26239
\(459\) −3.85750e16 −0.192541
\(460\) −1.32159e17 −0.650383
\(461\) −5.04154e14 −0.00244629 −0.00122314 0.999999i \(-0.500389\pi\)
−0.00122314 + 0.999999i \(0.500389\pi\)
\(462\) −1.83608e16 −0.0878452
\(463\) 1.00687e17 0.475002 0.237501 0.971387i \(-0.423672\pi\)
0.237501 + 0.971387i \(0.423672\pi\)
\(464\) −2.99232e16 −0.139201
\(465\) 3.17565e17 1.45676
\(466\) 6.17610e16 0.279387
\(467\) −6.15520e16 −0.274589 −0.137294 0.990530i \(-0.543841\pi\)
−0.137294 + 0.990530i \(0.543841\pi\)
\(468\) −8.10051e15 −0.0356381
\(469\) 8.18164e16 0.354991
\(470\) −2.70466e17 −1.15738
\(471\) 5.91124e16 0.249484
\(472\) −3.23762e16 −0.134773
\(473\) 9.39558e16 0.385768
\(474\) −6.83829e16 −0.276941
\(475\) 1.26230e17 0.504260
\(476\) −1.18281e17 −0.466091
\(477\) −9.52028e16 −0.370067
\(478\) 1.83212e17 0.702541
\(479\) 9.25663e16 0.350165 0.175082 0.984554i \(-0.443981\pi\)
0.175082 + 0.984554i \(0.443981\pi\)
\(480\) 2.13936e17 0.798392
\(481\) −6.02692e16 −0.221898
\(482\) 2.50853e17 0.911198
\(483\) 1.07262e17 0.384405
\(484\) 1.46174e17 0.516864
\(485\) 7.74054e17 2.70054
\(486\) −1.23728e16 −0.0425925
\(487\) −5.04053e17 −1.71214 −0.856068 0.516864i \(-0.827099\pi\)
−0.856068 + 0.516864i \(0.827099\pi\)
\(488\) −2.84034e17 −0.952009
\(489\) 1.18784e17 0.392871
\(490\) −9.05602e16 −0.295572
\(491\) −2.25723e17 −0.727019 −0.363510 0.931590i \(-0.618422\pi\)
−0.363510 + 0.931590i \(0.618422\pi\)
\(492\) 5.56704e14 0.00176950
\(493\) −3.46409e17 −1.08663
\(494\) −1.84897e16 −0.0572406
\(495\) 4.36748e16 0.133444
\(496\) 7.36789e16 0.222184
\(497\) 4.04671e17 1.20444
\(498\) −1.15234e17 −0.338524
\(499\) −5.02541e17 −1.45720 −0.728598 0.684942i \(-0.759828\pi\)
−0.728598 + 0.684942i \(0.759828\pi\)
\(500\) 3.36538e16 0.0963228
\(501\) −1.55343e16 −0.0438879
\(502\) 2.08508e17 0.581497
\(503\) −5.56546e17 −1.53218 −0.766089 0.642735i \(-0.777800\pi\)
−0.766089 + 0.642735i \(0.777800\pi\)
\(504\) −1.05786e17 −0.287495
\(505\) −2.28711e17 −0.613612
\(506\) −5.51013e16 −0.145943
\(507\) −2.12724e17 −0.556243
\(508\) 1.83803e17 0.474501
\(509\) −9.61699e15 −0.0245117 −0.0122558 0.999925i \(-0.503901\pi\)
−0.0122558 + 0.999925i \(0.503901\pi\)
\(510\) −2.21813e17 −0.558189
\(511\) −2.82005e17 −0.700683
\(512\) 1.03717e17 0.254446
\(513\) 3.58225e16 0.0867746
\(514\) 3.12554e17 0.747592
\(515\) −6.24851e16 −0.147581
\(516\) 1.94138e17 0.452781
\(517\) 1.43037e17 0.329427
\(518\) −2.82268e17 −0.641976
\(519\) 8.57833e16 0.192670
\(520\) −1.29880e17 −0.288086
\(521\) 2.18076e17 0.477708 0.238854 0.971055i \(-0.423228\pi\)
0.238854 + 0.971055i \(0.423228\pi\)
\(522\) −1.11110e17 −0.240377
\(523\) −3.66482e17 −0.783054 −0.391527 0.920167i \(-0.628053\pi\)
−0.391527 + 0.920167i \(0.628053\pi\)
\(524\) 2.45413e17 0.517898
\(525\) −2.58094e17 −0.537950
\(526\) −4.65720e17 −0.958777
\(527\) 8.52951e17 1.73442
\(528\) 1.01331e16 0.0203527
\(529\) −1.82139e17 −0.361362
\(530\) −5.47432e17 −1.07285
\(531\) −2.24165e16 −0.0433963
\(532\) 1.09841e17 0.210058
\(533\) −5.54740e14 −0.00104800
\(534\) 3.05792e17 0.570701
\(535\) 6.33108e17 1.16729
\(536\) −2.42156e17 −0.441086
\(537\) 3.52374e17 0.634120
\(538\) −3.94843e17 −0.702003
\(539\) 4.78931e16 0.0841291
\(540\) 9.02442e16 0.156625
\(541\) 2.04481e17 0.350648 0.175324 0.984511i \(-0.443903\pi\)
0.175324 + 0.984511i \(0.443903\pi\)
\(542\) −1.65236e17 −0.279968
\(543\) −5.93145e17 −0.993028
\(544\) 5.74614e17 0.950569
\(545\) −1.39877e18 −2.28649
\(546\) 3.78045e16 0.0610649
\(547\) 2.66578e17 0.425507 0.212753 0.977106i \(-0.431757\pi\)
0.212753 + 0.977106i \(0.431757\pi\)
\(548\) −9.84263e16 −0.155252
\(549\) −1.96657e17 −0.306542
\(550\) 1.32585e17 0.204238
\(551\) 3.21690e17 0.489725
\(552\) −3.17468e17 −0.477635
\(553\) −4.04807e17 −0.601914
\(554\) −5.14095e17 −0.755492
\(555\) 6.71433e17 0.975210
\(556\) 5.12621e16 0.0735885
\(557\) 1.21966e18 1.73054 0.865268 0.501309i \(-0.167148\pi\)
0.865268 + 0.501309i \(0.167148\pi\)
\(558\) 2.73582e17 0.383676
\(559\) −1.93454e17 −0.268164
\(560\) −1.13425e17 −0.155412
\(561\) 1.17307e17 0.158878
\(562\) −1.05039e17 −0.140626
\(563\) 3.55279e17 0.470181 0.235090 0.971974i \(-0.424461\pi\)
0.235090 + 0.971974i \(0.424461\pi\)
\(564\) 2.95554e17 0.386653
\(565\) 6.36841e17 0.823599
\(566\) 5.05210e17 0.645899
\(567\) −7.32437e16 −0.0925721
\(568\) −1.19772e18 −1.49655
\(569\) −9.08963e17 −1.12284 −0.561418 0.827532i \(-0.689744\pi\)
−0.561418 + 0.827532i \(0.689744\pi\)
\(570\) 2.05985e17 0.251565
\(571\) −5.88871e16 −0.0711026 −0.0355513 0.999368i \(-0.511319\pi\)
−0.0355513 + 0.999368i \(0.511319\pi\)
\(572\) 2.46337e16 0.0294073
\(573\) 4.05659e17 0.478802
\(574\) −2.59810e15 −0.00303200
\(575\) −7.74548e17 −0.893732
\(576\) 2.21750e17 0.252999
\(577\) −4.27206e16 −0.0481941 −0.0240971 0.999710i \(-0.507671\pi\)
−0.0240971 + 0.999710i \(0.507671\pi\)
\(578\) −5.64354e14 −0.000629536 0
\(579\) 9.94301e16 0.109675
\(580\) 8.10404e17 0.883933
\(581\) −6.82152e17 −0.735760
\(582\) 6.66847e17 0.711257
\(583\) 2.89512e17 0.305366
\(584\) 8.34664e17 0.870619
\(585\) −8.99258e16 −0.0927623
\(586\) −2.91508e17 −0.297383
\(587\) 1.77715e17 0.179298 0.0896492 0.995973i \(-0.471425\pi\)
0.0896492 + 0.995973i \(0.471425\pi\)
\(588\) 9.89603e16 0.0987435
\(589\) −7.92087e17 −0.781670
\(590\) −1.28899e17 −0.125808
\(591\) 7.47981e17 0.722058
\(592\) 1.55781e17 0.148738
\(593\) −1.45819e18 −1.37708 −0.688541 0.725197i \(-0.741749\pi\)
−0.688541 + 0.725197i \(0.741749\pi\)
\(594\) 3.76258e16 0.0351459
\(595\) −1.31307e18 −1.21319
\(596\) 7.69767e17 0.703491
\(597\) 1.83540e17 0.165919
\(598\) 1.13453e17 0.101451
\(599\) 6.23019e16 0.0551096 0.0275548 0.999620i \(-0.491228\pi\)
0.0275548 + 0.999620i \(0.491228\pi\)
\(600\) 7.63892e17 0.668419
\(601\) −7.12658e17 −0.616875 −0.308437 0.951245i \(-0.599806\pi\)
−0.308437 + 0.951245i \(0.599806\pi\)
\(602\) −9.06031e17 −0.775829
\(603\) −1.67662e17 −0.142028
\(604\) 7.46985e17 0.625997
\(605\) 1.62272e18 1.34534
\(606\) −1.97034e17 −0.161611
\(607\) −1.59346e18 −1.29305 −0.646525 0.762893i \(-0.723778\pi\)
−0.646525 + 0.762893i \(0.723778\pi\)
\(608\) −5.33612e17 −0.428403
\(609\) −6.57737e17 −0.522444
\(610\) −1.13081e18 −0.888684
\(611\) −2.94511e17 −0.228999
\(612\) 2.42388e17 0.186478
\(613\) 1.53584e18 1.16910 0.584552 0.811356i \(-0.301270\pi\)
0.584552 + 0.811356i \(0.301270\pi\)
\(614\) 7.31746e17 0.551145
\(615\) 6.18011e15 0.00460583
\(616\) 3.21696e17 0.237231
\(617\) 1.69013e18 1.23329 0.616647 0.787240i \(-0.288491\pi\)
0.616647 + 0.787240i \(0.288491\pi\)
\(618\) −5.38308e16 −0.0388692
\(619\) −1.01975e18 −0.728628 −0.364314 0.931276i \(-0.618696\pi\)
−0.364314 + 0.931276i \(0.618696\pi\)
\(620\) −1.99543e18 −1.41088
\(621\) −2.19807e17 −0.153796
\(622\) −1.79791e17 −0.124489
\(623\) 1.81020e18 1.24038
\(624\) −2.08639e16 −0.0141480
\(625\) −1.29288e18 −0.867637
\(626\) 4.64987e17 0.308822
\(627\) −1.08936e17 −0.0716033
\(628\) −3.71436e17 −0.241627
\(629\) 1.80341e18 1.16109
\(630\) −4.21164e17 −0.268372
\(631\) 1.17079e18 0.738392 0.369196 0.929352i \(-0.379633\pi\)
0.369196 + 0.929352i \(0.379633\pi\)
\(632\) 1.19813e18 0.747897
\(633\) −9.67470e17 −0.597741
\(634\) 1.18473e18 0.724499
\(635\) 2.04044e18 1.23508
\(636\) 5.98211e17 0.358412
\(637\) −9.86112e16 −0.0584817
\(638\) 3.37884e17 0.198351
\(639\) −8.29272e17 −0.481883
\(640\) −1.12897e18 −0.649398
\(641\) 1.48643e17 0.0846381 0.0423191 0.999104i \(-0.486525\pi\)
0.0423191 + 0.999104i \(0.486525\pi\)
\(642\) 5.45422e17 0.307436
\(643\) 5.73901e17 0.320233 0.160116 0.987098i \(-0.448813\pi\)
0.160116 + 0.987098i \(0.448813\pi\)
\(644\) −6.73986e17 −0.372300
\(645\) 2.15518e18 1.17854
\(646\) 5.53259e17 0.299514
\(647\) −3.48724e18 −1.86898 −0.934489 0.355992i \(-0.884143\pi\)
−0.934489 + 0.355992i \(0.884143\pi\)
\(648\) 2.16783e17 0.115024
\(649\) 6.81685e16 0.0358091
\(650\) −2.72990e17 −0.141974
\(651\) 1.61952e18 0.833895
\(652\) −7.46383e17 −0.380498
\(653\) 1.51158e18 0.762950 0.381475 0.924379i \(-0.375416\pi\)
0.381475 + 0.924379i \(0.375416\pi\)
\(654\) −1.20504e18 −0.602208
\(655\) 2.72439e18 1.34803
\(656\) 1.43386e15 0.000702478 0
\(657\) 5.77900e17 0.280335
\(658\) −1.37933e18 −0.662521
\(659\) 8.36218e17 0.397708 0.198854 0.980029i \(-0.436278\pi\)
0.198854 + 0.980029i \(0.436278\pi\)
\(660\) −2.74433e17 −0.129241
\(661\) −6.16807e16 −0.0287634 −0.0143817 0.999897i \(-0.504578\pi\)
−0.0143817 + 0.999897i \(0.504578\pi\)
\(662\) 5.90274e17 0.272569
\(663\) −2.41533e17 −0.110443
\(664\) 2.01900e18 0.914204
\(665\) 1.21937e18 0.546760
\(666\) 5.78439e17 0.256847
\(667\) −1.97389e18 −0.867971
\(668\) 9.76102e16 0.0425058
\(669\) 1.76544e18 0.761349
\(670\) −9.64087e17 −0.411747
\(671\) 5.98036e17 0.252948
\(672\) 1.09104e18 0.457025
\(673\) −2.26568e17 −0.0939940 −0.0469970 0.998895i \(-0.514965\pi\)
−0.0469970 + 0.998895i \(0.514965\pi\)
\(674\) 2.44728e18 1.00553
\(675\) 5.28899e17 0.215228
\(676\) 1.33666e18 0.538726
\(677\) 3.02856e18 1.20895 0.604476 0.796623i \(-0.293382\pi\)
0.604476 + 0.796623i \(0.293382\pi\)
\(678\) 5.48638e17 0.216916
\(679\) 3.94754e18 1.54587
\(680\) 3.88636e18 1.50742
\(681\) −2.31223e17 −0.0888330
\(682\) −8.31962e17 −0.316596
\(683\) 4.54159e18 1.71188 0.855941 0.517074i \(-0.172979\pi\)
0.855941 + 0.517074i \(0.172979\pi\)
\(684\) −2.25092e17 −0.0840418
\(685\) −1.09266e18 −0.404105
\(686\) −1.97180e18 −0.722365
\(687\) 3.02492e18 1.09773
\(688\) 5.00028e17 0.179750
\(689\) −5.96101e17 −0.212273
\(690\) −1.26393e18 −0.445864
\(691\) −1.64481e18 −0.574788 −0.287394 0.957812i \(-0.592789\pi\)
−0.287394 + 0.957812i \(0.592789\pi\)
\(692\) −5.39023e17 −0.186603
\(693\) 2.22734e17 0.0763872
\(694\) −2.49435e18 −0.847462
\(695\) 5.69074e17 0.191543
\(696\) 1.94673e18 0.649152
\(697\) 1.65992e16 0.00548372
\(698\) 3.40529e18 1.11454
\(699\) −7.49221e17 −0.242945
\(700\) 1.62174e18 0.521008
\(701\) 3.67549e17 0.116990 0.0584949 0.998288i \(-0.481370\pi\)
0.0584949 + 0.998288i \(0.481370\pi\)
\(702\) −7.74710e16 −0.0244314
\(703\) −1.67473e18 −0.523280
\(704\) −6.74343e17 −0.208766
\(705\) 3.28102e18 1.00642
\(706\) −3.47123e18 −1.05500
\(707\) −1.16639e18 −0.351250
\(708\) 1.40855e17 0.0420296
\(709\) −4.11055e15 −0.00121534 −0.000607672 1.00000i \(-0.500193\pi\)
−0.000607672 1.00000i \(0.500193\pi\)
\(710\) −4.76846e18 −1.39701
\(711\) 8.29551e17 0.240819
\(712\) −5.35774e18 −1.54121
\(713\) 4.86025e18 1.38540
\(714\) −1.13121e18 −0.319525
\(715\) 2.73465e17 0.0765441
\(716\) −2.21416e18 −0.614150
\(717\) −2.22254e18 −0.610906
\(718\) −2.67099e18 −0.727550
\(719\) −2.98850e18 −0.806707 −0.403354 0.915044i \(-0.632156\pi\)
−0.403354 + 0.915044i \(0.632156\pi\)
\(720\) 2.32436e17 0.0621787
\(721\) −3.18663e17 −0.0844798
\(722\) 2.01335e18 0.528967
\(723\) −3.04309e18 −0.792348
\(724\) 3.72705e18 0.961755
\(725\) 4.74957e18 1.21467
\(726\) 1.39797e18 0.354332
\(727\) 4.78687e18 1.20248 0.601241 0.799068i \(-0.294673\pi\)
0.601241 + 0.799068i \(0.294673\pi\)
\(728\) −6.62368e17 −0.164909
\(729\) 1.50095e17 0.0370370
\(730\) 3.32302e18 0.812709
\(731\) 5.78863e18 1.40318
\(732\) 1.23571e18 0.296888
\(733\) 1.57343e18 0.374689 0.187344 0.982294i \(-0.440012\pi\)
0.187344 + 0.982294i \(0.440012\pi\)
\(734\) −3.35934e18 −0.792919
\(735\) 1.09858e18 0.257019
\(736\) 3.27424e18 0.759286
\(737\) 5.09862e17 0.117196
\(738\) 5.32416e15 0.00121307
\(739\) −3.70489e18 −0.836731 −0.418366 0.908279i \(-0.637397\pi\)
−0.418366 + 0.908279i \(0.637397\pi\)
\(740\) −4.21898e18 −0.944498
\(741\) 2.24298e17 0.0497745
\(742\) −2.79181e18 −0.614130
\(743\) −3.08237e18 −0.672136 −0.336068 0.941838i \(-0.609097\pi\)
−0.336068 + 0.941838i \(0.609097\pi\)
\(744\) −4.79338e18 −1.03614
\(745\) 8.54538e18 1.83112
\(746\) 1.90525e18 0.404715
\(747\) 1.39790e18 0.294369
\(748\) −7.37103e17 −0.153875
\(749\) 3.22874e18 0.668192
\(750\) 3.21855e17 0.0660332
\(751\) −4.35431e18 −0.885646 −0.442823 0.896609i \(-0.646023\pi\)
−0.442823 + 0.896609i \(0.646023\pi\)
\(752\) 7.61236e17 0.153498
\(753\) −2.52940e18 −0.505650
\(754\) −6.95699e17 −0.137882
\(755\) 8.29248e18 1.62941
\(756\) 4.60230e17 0.0896568
\(757\) 2.06249e18 0.398353 0.199177 0.979964i \(-0.436173\pi\)
0.199177 + 0.979964i \(0.436173\pi\)
\(758\) −2.87266e18 −0.550090
\(759\) 6.68433e17 0.126907
\(760\) −3.60904e18 −0.679365
\(761\) −9.83309e17 −0.183523 −0.0917613 0.995781i \(-0.529250\pi\)
−0.0917613 + 0.995781i \(0.529250\pi\)
\(762\) 1.75784e18 0.325290
\(763\) −7.13350e18 −1.30886
\(764\) −2.54897e18 −0.463723
\(765\) 2.69081e18 0.485382
\(766\) −5.64307e18 −1.00932
\(767\) −1.40358e17 −0.0248924
\(768\) −3.46448e18 −0.609242
\(769\) 1.44487e18 0.251946 0.125973 0.992034i \(-0.459795\pi\)
0.125973 + 0.992034i \(0.459795\pi\)
\(770\) 1.28076e18 0.221451
\(771\) −3.79158e18 −0.650081
\(772\) −6.24773e17 −0.106221
\(773\) −1.13834e19 −1.91914 −0.959568 0.281476i \(-0.909176\pi\)
−0.959568 + 0.281476i \(0.909176\pi\)
\(774\) 1.85669e18 0.310400
\(775\) −1.16947e19 −1.93878
\(776\) −1.16837e19 −1.92079
\(777\) 3.42419e18 0.558241
\(778\) −3.14683e18 −0.508751
\(779\) −1.54148e16 −0.00247140
\(780\) 5.65053e17 0.0898409
\(781\) 2.52182e18 0.397633
\(782\) −3.39480e18 −0.530848
\(783\) 1.34787e18 0.209024
\(784\) 2.54885e17 0.0392003
\(785\) −4.12340e18 −0.628931
\(786\) 2.34706e18 0.355040
\(787\) −6.01503e18 −0.902406 −0.451203 0.892421i \(-0.649005\pi\)
−0.451203 + 0.892421i \(0.649005\pi\)
\(788\) −4.69997e18 −0.699318
\(789\) 5.64964e18 0.833720
\(790\) 4.77006e18 0.698149
\(791\) 3.24778e18 0.471454
\(792\) −6.59237e17 −0.0949134
\(793\) −1.23135e18 −0.175835
\(794\) −4.44409e18 −0.629433
\(795\) 6.64089e18 0.932911
\(796\) −1.15328e18 −0.160694
\(797\) 1.50872e18 0.208511 0.104256 0.994551i \(-0.466754\pi\)
0.104256 + 0.994551i \(0.466754\pi\)
\(798\) 1.05049e18 0.144003
\(799\) 8.81252e18 1.19825
\(800\) −7.87848e18 −1.06257
\(801\) −3.70956e18 −0.496262
\(802\) −2.90648e18 −0.385687
\(803\) −1.75739e18 −0.231323
\(804\) 1.05351e18 0.137555
\(805\) −7.48209e18 −0.969057
\(806\) 1.71300e18 0.220079
\(807\) 4.78983e18 0.610439
\(808\) 3.45221e18 0.436439
\(809\) −5.57340e17 −0.0698964 −0.0349482 0.999389i \(-0.511127\pi\)
−0.0349482 + 0.999389i \(0.511127\pi\)
\(810\) 8.63070e17 0.107373
\(811\) 7.21194e18 0.890054 0.445027 0.895517i \(-0.353194\pi\)
0.445027 + 0.895517i \(0.353194\pi\)
\(812\) 4.13292e18 0.505991
\(813\) 2.00447e18 0.243451
\(814\) −1.75903e18 −0.211941
\(815\) −8.28579e18 −0.990397
\(816\) 6.24301e17 0.0740301
\(817\) −5.37557e18 −0.632384
\(818\) 9.12919e18 1.06546
\(819\) −4.58606e17 −0.0531000
\(820\) −3.88330e16 −0.00446078
\(821\) −1.02826e18 −0.117185 −0.0585925 0.998282i \(-0.518661\pi\)
−0.0585925 + 0.998282i \(0.518661\pi\)
\(822\) −9.41321e17 −0.106432
\(823\) −5.25999e18 −0.590046 −0.295023 0.955490i \(-0.595327\pi\)
−0.295023 + 0.955490i \(0.595327\pi\)
\(824\) 9.43163e17 0.104969
\(825\) −1.60838e18 −0.177598
\(826\) −6.57360e17 −0.0720167
\(827\) −4.84358e18 −0.526479 −0.263239 0.964731i \(-0.584791\pi\)
−0.263239 + 0.964731i \(0.584791\pi\)
\(828\) 1.38117e18 0.148953
\(829\) −5.32238e18 −0.569510 −0.284755 0.958600i \(-0.591912\pi\)
−0.284755 + 0.958600i \(0.591912\pi\)
\(830\) 8.03817e18 0.853394
\(831\) 6.23648e18 0.656951
\(832\) 1.38846e18 0.145122
\(833\) 2.95070e18 0.306008
\(834\) 4.90256e17 0.0504480
\(835\) 1.08360e18 0.110638
\(836\) 6.84506e17 0.0693484
\(837\) −3.31881e18 −0.333632
\(838\) −9.72997e18 −0.970566
\(839\) −1.15945e19 −1.14763 −0.573813 0.818986i \(-0.694536\pi\)
−0.573813 + 0.818986i \(0.694536\pi\)
\(840\) 7.37915e18 0.724754
\(841\) 1.84339e18 0.179657
\(842\) 7.31922e17 0.0707842
\(843\) 1.27423e18 0.122284
\(844\) 6.07914e18 0.578917
\(845\) 1.48386e19 1.40225
\(846\) 2.82659e18 0.265067
\(847\) 8.27559e18 0.770117
\(848\) 1.54077e18 0.142287
\(849\) −6.12869e18 −0.561652
\(850\) 8.16855e18 0.742886
\(851\) 1.02761e19 0.927443
\(852\) 5.21077e18 0.466707
\(853\) −1.81956e19 −1.61732 −0.808661 0.588275i \(-0.799807\pi\)
−0.808661 + 0.588275i \(0.799807\pi\)
\(854\) −5.76696e18 −0.508710
\(855\) −2.49880e18 −0.218752
\(856\) −9.55626e18 −0.830249
\(857\) −1.55587e17 −0.0134153 −0.00670763 0.999978i \(-0.502135\pi\)
−0.00670763 + 0.999978i \(0.502135\pi\)
\(858\) 2.35589e17 0.0201599
\(859\) −2.21845e19 −1.88406 −0.942030 0.335529i \(-0.891085\pi\)
−0.942030 + 0.335529i \(0.891085\pi\)
\(860\) −1.35422e19 −1.14143
\(861\) 3.15175e16 0.00263652
\(862\) 9.97025e18 0.827769
\(863\) −1.43516e19 −1.18258 −0.591289 0.806460i \(-0.701381\pi\)
−0.591289 + 0.806460i \(0.701381\pi\)
\(864\) −2.23581e18 −0.182850
\(865\) −5.98384e18 −0.485708
\(866\) 1.21557e19 0.979297
\(867\) 6.84617e15 0.000547423 0
\(868\) −1.01764e19 −0.807633
\(869\) −2.52267e18 −0.198715
\(870\) 7.75047e18 0.605973
\(871\) −1.04980e18 −0.0814681
\(872\) 2.11133e19 1.62630
\(873\) −8.08950e18 −0.618485
\(874\) 3.15256e18 0.239243
\(875\) 1.90529e18 0.143519
\(876\) −3.63126e18 −0.271507
\(877\) 2.37126e18 0.175988 0.0879939 0.996121i \(-0.471954\pi\)
0.0879939 + 0.996121i \(0.471954\pi\)
\(878\) −6.17832e18 −0.455151
\(879\) 3.53628e18 0.258594
\(880\) −7.06837e17 −0.0513076
\(881\) −1.27667e19 −0.919888 −0.459944 0.887948i \(-0.652130\pi\)
−0.459944 + 0.887948i \(0.652130\pi\)
\(882\) 9.46429e17 0.0676927
\(883\) 2.78599e18 0.197804 0.0989018 0.995097i \(-0.468467\pi\)
0.0989018 + 0.995097i \(0.468467\pi\)
\(884\) 1.51768e18 0.106965
\(885\) 1.56367e18 0.109399
\(886\) −1.28346e19 −0.891379
\(887\) −5.15165e18 −0.355175 −0.177588 0.984105i \(-0.556829\pi\)
−0.177588 + 0.984105i \(0.556829\pi\)
\(888\) −1.01347e19 −0.693631
\(889\) 1.04059e19 0.706997
\(890\) −2.13306e19 −1.43869
\(891\) −4.56438e17 −0.0305617
\(892\) −1.10932e19 −0.737373
\(893\) −8.18369e18 −0.540026
\(894\) 7.36184e18 0.482272
\(895\) −2.45800e19 −1.59857
\(896\) −5.75753e18 −0.371736
\(897\) −1.37629e18 −0.0882186
\(898\) 1.60946e19 1.02420
\(899\) −2.98033e19 −1.88290
\(900\) −3.32336e18 −0.208449
\(901\) 1.78369e19 1.11073
\(902\) −1.61908e16 −0.00100098
\(903\) 1.09910e19 0.674635
\(904\) −9.61260e18 −0.585796
\(905\) 4.13749e19 2.50335
\(906\) 7.14396e18 0.429147
\(907\) −1.31359e19 −0.783452 −0.391726 0.920082i \(-0.628122\pi\)
−0.391726 + 0.920082i \(0.628122\pi\)
\(908\) 1.45290e18 0.0860354
\(909\) 2.39022e18 0.140531
\(910\) −2.63706e18 −0.153940
\(911\) −1.27123e19 −0.736810 −0.368405 0.929665i \(-0.620096\pi\)
−0.368405 + 0.929665i \(0.620096\pi\)
\(912\) −5.79754e17 −0.0333639
\(913\) −4.25102e18 −0.242903
\(914\) 1.89260e18 0.107377
\(915\) 1.37179e19 0.772770
\(916\) −1.90072e19 −1.06316
\(917\) 1.38939e19 0.771657
\(918\) 2.31813e18 0.127838
\(919\) −2.80232e19 −1.53450 −0.767251 0.641347i \(-0.778376\pi\)
−0.767251 + 0.641347i \(0.778376\pi\)
\(920\) 2.21451e19 1.20408
\(921\) −8.87680e18 −0.479258
\(922\) 3.02967e16 0.00162422
\(923\) −5.19239e18 −0.276411
\(924\) −1.39956e18 −0.0739816
\(925\) −2.47264e19 −1.29789
\(926\) −6.05067e18 −0.315379
\(927\) 6.53021e17 0.0337994
\(928\) −2.00779e19 −1.03194
\(929\) 3.48107e19 1.77669 0.888343 0.459180i \(-0.151857\pi\)
0.888343 + 0.459180i \(0.151857\pi\)
\(930\) −1.90837e19 −0.967218
\(931\) −2.74015e18 −0.137912
\(932\) 4.70776e18 0.235294
\(933\) 2.18104e18 0.108251
\(934\) 3.69891e18 0.182314
\(935\) −8.18276e18 −0.400520
\(936\) 1.35736e18 0.0659783
\(937\) −1.42948e19 −0.690033 −0.345016 0.938597i \(-0.612127\pi\)
−0.345016 + 0.938597i \(0.612127\pi\)
\(938\) −4.91668e18 −0.235697
\(939\) −5.64075e18 −0.268541
\(940\) −2.06164e19 −0.974725
\(941\) 2.64152e19 1.24028 0.620141 0.784490i \(-0.287075\pi\)
0.620141 + 0.784490i \(0.287075\pi\)
\(942\) −3.55231e18 −0.165645
\(943\) 9.45851e16 0.00438023
\(944\) 3.62790e17 0.0166854
\(945\) 5.10913e18 0.233367
\(946\) −5.64618e18 −0.256131
\(947\) 3.19369e18 0.143886 0.0719429 0.997409i \(-0.477080\pi\)
0.0719429 + 0.997409i \(0.477080\pi\)
\(948\) −5.21252e18 −0.233235
\(949\) 3.61845e18 0.160802
\(950\) −7.58567e18 −0.334804
\(951\) −1.43719e19 −0.630000
\(952\) 1.98197e19 0.862895
\(953\) 1.15302e19 0.498576 0.249288 0.968429i \(-0.419803\pi\)
0.249288 + 0.968429i \(0.419803\pi\)
\(954\) 5.72112e18 0.245707
\(955\) −2.82968e19 −1.20702
\(956\) 1.39654e19 0.591667
\(957\) −4.09887e18 −0.172479
\(958\) −5.56269e18 −0.232492
\(959\) −5.57235e18 −0.231322
\(960\) −1.54683e19 −0.637791
\(961\) 4.89663e19 2.00537
\(962\) 3.62182e18 0.147329
\(963\) −6.61650e18 −0.267336
\(964\) 1.91214e19 0.767395
\(965\) −6.93577e18 −0.276482
\(966\) −6.44581e18 −0.255227
\(967\) 4.94665e17 0.0194554 0.00972768 0.999953i \(-0.496904\pi\)
0.00972768 + 0.999953i \(0.496904\pi\)
\(968\) −2.44936e19 −0.956893
\(969\) −6.71157e18 −0.260447
\(970\) −4.65160e19 −1.79303
\(971\) −1.35153e19 −0.517490 −0.258745 0.965946i \(-0.583309\pi\)
−0.258745 + 0.965946i \(0.583309\pi\)
\(972\) −9.43126e17 −0.0358706
\(973\) 2.90218e18 0.109645
\(974\) 3.02906e19 1.13678
\(975\) 3.31163e18 0.123456
\(976\) 3.18272e18 0.117862
\(977\) 2.64407e19 0.972655 0.486328 0.873777i \(-0.338336\pi\)
0.486328 + 0.873777i \(0.338336\pi\)
\(978\) −7.13820e18 −0.260847
\(979\) 1.12808e19 0.409498
\(980\) −6.90300e18 −0.248925
\(981\) 1.46183e19 0.523660
\(982\) 1.35646e19 0.482706
\(983\) 1.35645e19 0.479519 0.239759 0.970832i \(-0.422931\pi\)
0.239759 + 0.970832i \(0.422931\pi\)
\(984\) −9.32838e16 −0.00327596
\(985\) −5.21756e19 −1.82025
\(986\) 2.08171e19 0.721473
\(987\) 1.67326e19 0.576106
\(988\) −1.40939e18 −0.0482070
\(989\) 3.29845e19 1.12082
\(990\) −2.62460e18 −0.0886001
\(991\) 1.07510e19 0.360552 0.180276 0.983616i \(-0.442301\pi\)
0.180276 + 0.983616i \(0.442301\pi\)
\(992\) 4.94371e19 1.64713
\(993\) −7.16061e18 −0.237017
\(994\) −2.43183e19 −0.799691
\(995\) −1.28029e19 −0.418271
\(996\) −8.78377e18 −0.285099
\(997\) 4.04824e19 1.30541 0.652706 0.757612i \(-0.273634\pi\)
0.652706 + 0.757612i \(0.273634\pi\)
\(998\) 3.01997e19 0.967508
\(999\) −7.01703e18 −0.223346
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 177.14.a.c.1.10 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.10 31 1.1 even 1 trivial