Properties

Label 177.14.a.c.1.6
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 1.6
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-118.157 q^{2} +729.000 q^{3} +5769.07 q^{4} +218.169 q^{5} -86136.4 q^{6} +217680. q^{7} +286287. q^{8} +531441. q^{9} +O(q^{10})\) \(q-118.157 q^{2} +729.000 q^{3} +5769.07 q^{4} +218.169 q^{5} -86136.4 q^{6} +217680. q^{7} +286287. q^{8} +531441. q^{9} -25778.2 q^{10} +1.28409e6 q^{11} +4.20565e6 q^{12} -2.15032e7 q^{13} -2.57205e7 q^{14} +159045. q^{15} -8.10869e7 q^{16} -7.11178e7 q^{17} -6.27934e7 q^{18} +2.24678e8 q^{19} +1.25863e6 q^{20} +1.58689e8 q^{21} -1.51724e8 q^{22} -4.97569e8 q^{23} +2.08703e8 q^{24} -1.22066e9 q^{25} +2.54076e9 q^{26} +3.87420e8 q^{27} +1.25581e9 q^{28} -9.40726e8 q^{29} -1.87923e7 q^{30} +1.59649e9 q^{31} +7.23572e9 q^{32} +9.36098e8 q^{33} +8.40306e9 q^{34} +4.74912e7 q^{35} +3.06592e9 q^{36} +2.40599e10 q^{37} -2.65473e10 q^{38} -1.56759e10 q^{39} +6.24589e7 q^{40} +7.98989e9 q^{41} -1.87502e10 q^{42} -5.33738e10 q^{43} +7.40797e9 q^{44} +1.15944e8 q^{45} +5.87912e10 q^{46} -2.52267e10 q^{47} -5.91124e10 q^{48} -4.95042e10 q^{49} +1.44229e11 q^{50} -5.18449e10 q^{51} -1.24054e11 q^{52} +1.07921e11 q^{53} -4.57764e10 q^{54} +2.80148e8 q^{55} +6.23190e10 q^{56} +1.63790e11 q^{57} +1.11153e11 q^{58} -4.21805e10 q^{59} +9.17543e8 q^{60} +4.38247e11 q^{61} -1.88637e11 q^{62} +1.15684e11 q^{63} -1.90687e11 q^{64} -4.69134e9 q^{65} -1.10607e11 q^{66} +1.41653e12 q^{67} -4.10283e11 q^{68} -3.62728e11 q^{69} -5.61141e9 q^{70} +1.03171e12 q^{71} +1.52144e11 q^{72} -1.02339e12 q^{73} -2.84285e12 q^{74} -8.89858e11 q^{75} +1.29618e12 q^{76} +2.79520e11 q^{77} +1.85221e12 q^{78} +2.77802e12 q^{79} -1.76907e10 q^{80} +2.82430e11 q^{81} -9.44061e11 q^{82} +3.08697e12 q^{83} +9.15488e11 q^{84} -1.55157e10 q^{85} +6.30649e12 q^{86} -6.85790e11 q^{87} +3.67616e11 q^{88} -3.67055e12 q^{89} -1.36996e10 q^{90} -4.68083e12 q^{91} -2.87051e12 q^{92} +1.16384e12 q^{93} +2.98071e12 q^{94} +4.90178e10 q^{95} +5.27484e12 q^{96} -1.37717e13 q^{97} +5.84927e12 q^{98} +6.82416e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −118.157 −1.30546 −0.652731 0.757590i \(-0.726377\pi\)
−0.652731 + 0.757590i \(0.726377\pi\)
\(3\) 729.000 0.577350
\(4\) 5769.07 0.704232
\(5\) 218.169 0.00624437 0.00312218 0.999995i \(-0.499006\pi\)
0.00312218 + 0.999995i \(0.499006\pi\)
\(6\) −86136.4 −0.753709
\(7\) 217680. 0.699330 0.349665 0.936875i \(-0.386295\pi\)
0.349665 + 0.936875i \(0.386295\pi\)
\(8\) 286287. 0.386114
\(9\) 531441. 0.333333
\(10\) −25778.2 −0.00815178
\(11\) 1.28409e6 0.218545 0.109273 0.994012i \(-0.465148\pi\)
0.109273 + 0.994012i \(0.465148\pi\)
\(12\) 4.20565e6 0.406588
\(13\) −2.15032e7 −1.23558 −0.617791 0.786342i \(-0.711972\pi\)
−0.617791 + 0.786342i \(0.711972\pi\)
\(14\) −2.57205e7 −0.912949
\(15\) 159045. 0.00360519
\(16\) −8.10869e7 −1.20829
\(17\) −7.11178e7 −0.714596 −0.357298 0.933991i \(-0.616302\pi\)
−0.357298 + 0.933991i \(0.616302\pi\)
\(18\) −6.27934e7 −0.435154
\(19\) 2.24678e8 1.09562 0.547812 0.836601i \(-0.315461\pi\)
0.547812 + 0.836601i \(0.315461\pi\)
\(20\) 1.25863e6 0.00439748
\(21\) 1.58689e8 0.403758
\(22\) −1.51724e8 −0.285303
\(23\) −4.97569e8 −0.700846 −0.350423 0.936592i \(-0.613962\pi\)
−0.350423 + 0.936592i \(0.613962\pi\)
\(24\) 2.08703e8 0.222923
\(25\) −1.22066e9 −0.999961
\(26\) 2.54076e9 1.61301
\(27\) 3.87420e8 0.192450
\(28\) 1.25581e9 0.492490
\(29\) −9.40726e8 −0.293681 −0.146841 0.989160i \(-0.546910\pi\)
−0.146841 + 0.989160i \(0.546910\pi\)
\(30\) −1.87923e7 −0.00470643
\(31\) 1.59649e9 0.323084 0.161542 0.986866i \(-0.448353\pi\)
0.161542 + 0.986866i \(0.448353\pi\)
\(32\) 7.23572e9 1.19126
\(33\) 9.36098e8 0.126177
\(34\) 8.40306e9 0.932878
\(35\) 4.74912e7 0.00436687
\(36\) 3.06592e9 0.234744
\(37\) 2.40599e10 1.54164 0.770821 0.637052i \(-0.219846\pi\)
0.770821 + 0.637052i \(0.219846\pi\)
\(38\) −2.65473e10 −1.43030
\(39\) −1.56759e10 −0.713364
\(40\) 6.24589e7 0.00241104
\(41\) 7.98989e9 0.262691 0.131346 0.991337i \(-0.458070\pi\)
0.131346 + 0.991337i \(0.458070\pi\)
\(42\) −1.87502e10 −0.527091
\(43\) −5.33738e10 −1.28761 −0.643803 0.765191i \(-0.722645\pi\)
−0.643803 + 0.765191i \(0.722645\pi\)
\(44\) 7.40797e9 0.153906
\(45\) 1.15944e8 0.00208146
\(46\) 5.87912e10 0.914927
\(47\) −2.52267e10 −0.341369 −0.170685 0.985326i \(-0.554598\pi\)
−0.170685 + 0.985326i \(0.554598\pi\)
\(48\) −5.91124e10 −0.697606
\(49\) −4.95042e10 −0.510937
\(50\) 1.44229e11 1.30541
\(51\) −5.18449e10 −0.412572
\(52\) −1.24054e11 −0.870137
\(53\) 1.07921e11 0.668825 0.334413 0.942427i \(-0.391462\pi\)
0.334413 + 0.942427i \(0.391462\pi\)
\(54\) −4.57764e10 −0.251236
\(55\) 2.80148e8 0.00136468
\(56\) 6.23190e10 0.270021
\(57\) 1.63790e11 0.632559
\(58\) 1.11153e11 0.383390
\(59\) −4.21805e10 −0.130189
\(60\) 9.17543e8 0.00253889
\(61\) 4.38247e11 1.08912 0.544560 0.838722i \(-0.316697\pi\)
0.544560 + 0.838722i \(0.316697\pi\)
\(62\) −1.88637e11 −0.421774
\(63\) 1.15684e11 0.233110
\(64\) −1.90687e11 −0.346858
\(65\) −4.69134e9 −0.00771543
\(66\) −1.10607e11 −0.164720
\(67\) 1.41653e12 1.91311 0.956554 0.291556i \(-0.0941731\pi\)
0.956554 + 0.291556i \(0.0941731\pi\)
\(68\) −4.10283e11 −0.503241
\(69\) −3.62728e11 −0.404633
\(70\) −5.61141e9 −0.00570079
\(71\) 1.03171e12 0.955824 0.477912 0.878408i \(-0.341394\pi\)
0.477912 + 0.878408i \(0.341394\pi\)
\(72\) 1.52144e11 0.128705
\(73\) −1.02339e12 −0.791482 −0.395741 0.918362i \(-0.629512\pi\)
−0.395741 + 0.918362i \(0.629512\pi\)
\(74\) −2.84285e12 −2.01255
\(75\) −8.89858e11 −0.577328
\(76\) 1.29618e12 0.771574
\(77\) 2.79520e11 0.152835
\(78\) 1.85221e12 0.931270
\(79\) 2.77802e12 1.28576 0.642880 0.765967i \(-0.277739\pi\)
0.642880 + 0.765967i \(0.277739\pi\)
\(80\) −1.76907e10 −0.00754500
\(81\) 2.82430e11 0.111111
\(82\) −9.44061e11 −0.342934
\(83\) 3.08697e12 1.03639 0.518196 0.855262i \(-0.326604\pi\)
0.518196 + 0.855262i \(0.326604\pi\)
\(84\) 9.15488e11 0.284339
\(85\) −1.55157e10 −0.00446220
\(86\) 6.30649e12 1.68092
\(87\) −6.85790e11 −0.169557
\(88\) 3.67616e11 0.0843835
\(89\) −3.67055e12 −0.782881 −0.391441 0.920203i \(-0.628023\pi\)
−0.391441 + 0.920203i \(0.628023\pi\)
\(90\) −1.36996e10 −0.00271726
\(91\) −4.68083e12 −0.864080
\(92\) −2.87051e12 −0.493558
\(93\) 1.16384e12 0.186533
\(94\) 2.98071e12 0.445644
\(95\) 4.90178e10 0.00684148
\(96\) 5.27484e12 0.687775
\(97\) −1.37717e13 −1.67869 −0.839344 0.543600i \(-0.817061\pi\)
−0.839344 + 0.543600i \(0.817061\pi\)
\(98\) 5.84927e12 0.667009
\(99\) 6.82416e11 0.0728484
\(100\) −7.04204e12 −0.704204
\(101\) −1.38391e13 −1.29724 −0.648618 0.761115i \(-0.724653\pi\)
−0.648618 + 0.761115i \(0.724653\pi\)
\(102\) 6.12583e12 0.538597
\(103\) −2.38900e12 −0.197140 −0.0985699 0.995130i \(-0.531427\pi\)
−0.0985699 + 0.995130i \(0.531427\pi\)
\(104\) −6.15609e12 −0.477076
\(105\) 3.46211e10 0.00252122
\(106\) −1.27516e13 −0.873126
\(107\) 1.77681e12 0.114458 0.0572289 0.998361i \(-0.481774\pi\)
0.0572289 + 0.998361i \(0.481774\pi\)
\(108\) 2.23505e12 0.135529
\(109\) −6.89102e12 −0.393560 −0.196780 0.980448i \(-0.563049\pi\)
−0.196780 + 0.980448i \(0.563049\pi\)
\(110\) −3.31014e10 −0.00178153
\(111\) 1.75397e13 0.890067
\(112\) −1.76510e13 −0.844993
\(113\) 1.27590e13 0.576511 0.288255 0.957554i \(-0.406925\pi\)
0.288255 + 0.957554i \(0.406925\pi\)
\(114\) −1.93529e13 −0.825782
\(115\) −1.08554e11 −0.00437634
\(116\) −5.42711e12 −0.206820
\(117\) −1.14277e13 −0.411861
\(118\) 4.98392e12 0.169957
\(119\) −1.54810e13 −0.499738
\(120\) 4.55325e10 0.00139201
\(121\) −3.28738e13 −0.952238
\(122\) −5.17820e13 −1.42180
\(123\) 5.82463e12 0.151665
\(124\) 9.21027e12 0.227526
\(125\) −5.32629e11 −0.0124885
\(126\) −1.36689e13 −0.304316
\(127\) −9.02971e13 −1.90963 −0.954816 0.297198i \(-0.903948\pi\)
−0.954816 + 0.297198i \(0.903948\pi\)
\(128\) −3.67441e13 −0.738452
\(129\) −3.89095e13 −0.743400
\(130\) 5.54315e11 0.0100722
\(131\) 5.37302e13 0.928870 0.464435 0.885607i \(-0.346257\pi\)
0.464435 + 0.885607i \(0.346257\pi\)
\(132\) 5.40041e12 0.0888580
\(133\) 4.89080e13 0.766203
\(134\) −1.67373e14 −2.49749
\(135\) 8.45232e10 0.00120173
\(136\) −2.03601e13 −0.275916
\(137\) 1.09881e14 1.41984 0.709920 0.704283i \(-0.248731\pi\)
0.709920 + 0.704283i \(0.248731\pi\)
\(138\) 4.28588e13 0.528234
\(139\) 4.52947e13 0.532661 0.266331 0.963882i \(-0.414189\pi\)
0.266331 + 0.963882i \(0.414189\pi\)
\(140\) 2.73980e11 0.00307529
\(141\) −1.83903e13 −0.197090
\(142\) −1.21904e14 −1.24779
\(143\) −2.76120e13 −0.270031
\(144\) −4.30929e13 −0.402763
\(145\) −2.05237e11 −0.00183385
\(146\) 1.20920e14 1.03325
\(147\) −3.60886e13 −0.294990
\(148\) 1.38803e14 1.08567
\(149\) 1.54519e14 1.15683 0.578416 0.815742i \(-0.303671\pi\)
0.578416 + 0.815742i \(0.303671\pi\)
\(150\) 1.05143e14 0.753680
\(151\) −1.70906e14 −1.17329 −0.586646 0.809843i \(-0.699552\pi\)
−0.586646 + 0.809843i \(0.699552\pi\)
\(152\) 6.43223e13 0.423037
\(153\) −3.77949e13 −0.238199
\(154\) −3.30273e13 −0.199521
\(155\) 3.48305e11 0.00201746
\(156\) −9.04350e13 −0.502374
\(157\) 2.23059e14 1.18870 0.594350 0.804207i \(-0.297410\pi\)
0.594350 + 0.804207i \(0.297410\pi\)
\(158\) −3.28243e14 −1.67851
\(159\) 7.86744e13 0.386146
\(160\) 1.57861e12 0.00743867
\(161\) −1.08311e14 −0.490122
\(162\) −3.33710e13 −0.145051
\(163\) −5.23388e13 −0.218577 −0.109289 0.994010i \(-0.534857\pi\)
−0.109289 + 0.994010i \(0.534857\pi\)
\(164\) 4.60942e13 0.184995
\(165\) 2.04228e11 0.000787896 0
\(166\) −3.64747e14 −1.35297
\(167\) −7.33978e13 −0.261834 −0.130917 0.991393i \(-0.541792\pi\)
−0.130917 + 0.991393i \(0.541792\pi\)
\(168\) 4.54306e13 0.155897
\(169\) 1.59514e14 0.526665
\(170\) 1.83329e12 0.00582523
\(171\) 1.19403e14 0.365208
\(172\) −3.07917e14 −0.906773
\(173\) 6.36431e14 1.80490 0.902448 0.430800i \(-0.141768\pi\)
0.902448 + 0.430800i \(0.141768\pi\)
\(174\) 8.10308e13 0.221350
\(175\) −2.65713e14 −0.699303
\(176\) −1.04123e14 −0.264066
\(177\) −3.07496e13 −0.0751646
\(178\) 4.33701e14 1.02202
\(179\) −5.87474e14 −1.33488 −0.667442 0.744662i \(-0.732611\pi\)
−0.667442 + 0.744662i \(0.732611\pi\)
\(180\) 6.68889e11 0.00146583
\(181\) −5.87159e14 −1.24121 −0.620605 0.784123i \(-0.713113\pi\)
−0.620605 + 0.784123i \(0.713113\pi\)
\(182\) 5.53073e14 1.12802
\(183\) 3.19482e14 0.628803
\(184\) −1.42447e14 −0.270607
\(185\) 5.24914e12 0.00962657
\(186\) −1.37516e14 −0.243512
\(187\) −9.13213e13 −0.156171
\(188\) −1.45534e14 −0.240403
\(189\) 8.43339e13 0.134586
\(190\) −5.79179e12 −0.00893130
\(191\) 8.43064e14 1.25645 0.628223 0.778034i \(-0.283783\pi\)
0.628223 + 0.778034i \(0.283783\pi\)
\(192\) −1.39011e14 −0.200258
\(193\) 1.20396e15 1.67683 0.838415 0.545033i \(-0.183483\pi\)
0.838415 + 0.545033i \(0.183483\pi\)
\(194\) 1.62722e15 2.19146
\(195\) −3.41999e12 −0.00445451
\(196\) −2.85593e14 −0.359818
\(197\) −1.10425e15 −1.34598 −0.672990 0.739652i \(-0.734990\pi\)
−0.672990 + 0.739652i \(0.734990\pi\)
\(198\) −8.06321e13 −0.0951009
\(199\) −6.27234e14 −0.715953 −0.357976 0.933731i \(-0.616533\pi\)
−0.357976 + 0.933731i \(0.616533\pi\)
\(200\) −3.49457e14 −0.386099
\(201\) 1.03265e15 1.10453
\(202\) 1.63518e15 1.69349
\(203\) −2.04778e14 −0.205380
\(204\) −2.99096e14 −0.290546
\(205\) 1.74315e12 0.00164034
\(206\) 2.82277e14 0.257358
\(207\) −2.64429e14 −0.233615
\(208\) 1.74363e15 1.49294
\(209\) 2.88506e14 0.239444
\(210\) −4.09072e12 −0.00329135
\(211\) 1.51733e15 1.18371 0.591853 0.806046i \(-0.298397\pi\)
0.591853 + 0.806046i \(0.298397\pi\)
\(212\) 6.22603e14 0.471008
\(213\) 7.52116e14 0.551845
\(214\) −2.09942e14 −0.149420
\(215\) −1.16445e13 −0.00804029
\(216\) 1.10913e14 0.0743078
\(217\) 3.47525e14 0.225943
\(218\) 8.14222e14 0.513778
\(219\) −7.46048e14 −0.456962
\(220\) 1.61619e12 0.000961048 0
\(221\) 1.52926e15 0.882942
\(222\) −2.07244e15 −1.16195
\(223\) 6.83896e14 0.372399 0.186199 0.982512i \(-0.440383\pi\)
0.186199 + 0.982512i \(0.440383\pi\)
\(224\) 1.57508e15 0.833085
\(225\) −6.48706e14 −0.333320
\(226\) −1.50757e15 −0.752613
\(227\) 2.00349e15 0.971893 0.485947 0.873988i \(-0.338475\pi\)
0.485947 + 0.873988i \(0.338475\pi\)
\(228\) 9.44916e14 0.445468
\(229\) −5.07557e14 −0.232570 −0.116285 0.993216i \(-0.537099\pi\)
−0.116285 + 0.993216i \(0.537099\pi\)
\(230\) 1.28264e13 0.00571314
\(231\) 2.03770e14 0.0882395
\(232\) −2.69317e14 −0.113395
\(233\) 3.99269e15 1.63475 0.817376 0.576105i \(-0.195428\pi\)
0.817376 + 0.576105i \(0.195428\pi\)
\(234\) 1.35026e15 0.537669
\(235\) −5.50369e12 −0.00213163
\(236\) −2.43342e14 −0.0916831
\(237\) 2.02518e15 0.742334
\(238\) 1.82918e15 0.652389
\(239\) 4.90602e14 0.170272 0.0851359 0.996369i \(-0.472868\pi\)
0.0851359 + 0.996369i \(0.472868\pi\)
\(240\) −1.28965e13 −0.00435611
\(241\) 3.13435e15 1.03047 0.515236 0.857048i \(-0.327704\pi\)
0.515236 + 0.857048i \(0.327704\pi\)
\(242\) 3.88427e15 1.24311
\(243\) 2.05891e14 0.0641500
\(244\) 2.52828e15 0.766992
\(245\) −1.08003e13 −0.00319048
\(246\) −6.88220e14 −0.197993
\(247\) −4.83130e15 −1.35374
\(248\) 4.57054e14 0.124748
\(249\) 2.25040e15 0.598362
\(250\) 6.29338e13 0.0163032
\(251\) 4.36614e15 1.10209 0.551047 0.834474i \(-0.314229\pi\)
0.551047 + 0.834474i \(0.314229\pi\)
\(252\) 6.67390e14 0.164163
\(253\) −6.38921e14 −0.153167
\(254\) 1.06692e16 2.49295
\(255\) −1.13110e13 −0.00257625
\(256\) 5.90367e15 1.31088
\(257\) 2.74218e15 0.593650 0.296825 0.954932i \(-0.404072\pi\)
0.296825 + 0.954932i \(0.404072\pi\)
\(258\) 4.59743e15 0.970481
\(259\) 5.23738e15 1.07812
\(260\) −2.70647e13 −0.00543345
\(261\) −4.99941e14 −0.0978938
\(262\) −6.34860e15 −1.21261
\(263\) −6.48120e15 −1.20766 −0.603828 0.797115i \(-0.706359\pi\)
−0.603828 + 0.797115i \(0.706359\pi\)
\(264\) 2.67992e14 0.0487188
\(265\) 2.35450e13 0.00417639
\(266\) −5.77882e15 −1.00025
\(267\) −2.67583e15 −0.451997
\(268\) 8.17205e15 1.34727
\(269\) −7.20753e15 −1.15984 −0.579918 0.814675i \(-0.696915\pi\)
−0.579918 + 0.814675i \(0.696915\pi\)
\(270\) −9.98700e12 −0.00156881
\(271\) 1.69831e15 0.260445 0.130223 0.991485i \(-0.458431\pi\)
0.130223 + 0.991485i \(0.458431\pi\)
\(272\) 5.76672e15 0.863438
\(273\) −3.41233e15 −0.498877
\(274\) −1.29832e16 −1.85355
\(275\) −1.56743e15 −0.218537
\(276\) −2.09260e15 −0.284956
\(277\) 1.07690e16 1.43238 0.716191 0.697905i \(-0.245884\pi\)
0.716191 + 0.697905i \(0.245884\pi\)
\(278\) −5.35188e15 −0.695369
\(279\) 8.48441e14 0.107695
\(280\) 1.35961e13 0.00168611
\(281\) −3.43346e15 −0.416045 −0.208023 0.978124i \(-0.566703\pi\)
−0.208023 + 0.978124i \(0.566703\pi\)
\(282\) 2.17294e15 0.257293
\(283\) 3.84777e15 0.445244 0.222622 0.974905i \(-0.428538\pi\)
0.222622 + 0.974905i \(0.428538\pi\)
\(284\) 5.95200e15 0.673121
\(285\) 3.57340e13 0.00394993
\(286\) 3.26255e15 0.352515
\(287\) 1.73924e15 0.183708
\(288\) 3.84536e15 0.397087
\(289\) −4.84684e15 −0.489353
\(290\) 2.42502e13 0.00239403
\(291\) −1.00395e16 −0.969191
\(292\) −5.90398e15 −0.557386
\(293\) 1.96127e16 1.81092 0.905458 0.424436i \(-0.139528\pi\)
0.905458 + 0.424436i \(0.139528\pi\)
\(294\) 4.26412e15 0.385098
\(295\) −9.20249e12 −0.000812947 0
\(296\) 6.88804e15 0.595250
\(297\) 4.97481e14 0.0420591
\(298\) −1.82575e16 −1.51020
\(299\) 1.06993e16 0.865953
\(300\) −5.13365e15 −0.406572
\(301\) −1.16184e16 −0.900462
\(302\) 2.01937e16 1.53169
\(303\) −1.00887e16 −0.748959
\(304\) −1.82184e16 −1.32383
\(305\) 9.56120e13 0.00680086
\(306\) 4.46573e15 0.310959
\(307\) 2.18174e16 1.48731 0.743657 0.668561i \(-0.233089\pi\)
0.743657 + 0.668561i \(0.233089\pi\)
\(308\) 1.61257e15 0.107631
\(309\) −1.74158e15 −0.113819
\(310\) −4.11547e13 −0.00263371
\(311\) 1.35314e16 0.848007 0.424003 0.905661i \(-0.360624\pi\)
0.424003 + 0.905661i \(0.360624\pi\)
\(312\) −4.48779e15 −0.275440
\(313\) −1.11477e16 −0.670111 −0.335055 0.942198i \(-0.608755\pi\)
−0.335055 + 0.942198i \(0.608755\pi\)
\(314\) −2.63560e16 −1.55180
\(315\) 2.52388e13 0.00145562
\(316\) 1.60266e16 0.905472
\(317\) 1.09554e16 0.606376 0.303188 0.952931i \(-0.401949\pi\)
0.303188 + 0.952931i \(0.401949\pi\)
\(318\) −9.29592e15 −0.504099
\(319\) −1.20797e15 −0.0641827
\(320\) −4.16020e13 −0.00216591
\(321\) 1.29529e15 0.0660822
\(322\) 1.27977e16 0.639836
\(323\) −1.59786e16 −0.782929
\(324\) 1.62935e15 0.0782480
\(325\) 2.62480e16 1.23553
\(326\) 6.18420e15 0.285344
\(327\) −5.02355e15 −0.227222
\(328\) 2.28740e15 0.101429
\(329\) −5.49136e15 −0.238730
\(330\) −2.41309e13 −0.00102857
\(331\) −1.39087e16 −0.581306 −0.290653 0.956828i \(-0.593873\pi\)
−0.290653 + 0.956828i \(0.593873\pi\)
\(332\) 1.78089e16 0.729861
\(333\) 1.27864e16 0.513881
\(334\) 8.67246e15 0.341814
\(335\) 3.09043e14 0.0119461
\(336\) −1.28676e16 −0.487857
\(337\) 1.61764e16 0.601570 0.300785 0.953692i \(-0.402751\pi\)
0.300785 + 0.953692i \(0.402751\pi\)
\(338\) −1.88477e16 −0.687541
\(339\) 9.30133e15 0.332849
\(340\) −8.95111e13 −0.00314242
\(341\) 2.05003e15 0.0706085
\(342\) −1.41083e16 −0.476766
\(343\) −3.18669e16 −1.05664
\(344\) −1.52802e16 −0.497164
\(345\) −7.91360e13 −0.00252668
\(346\) −7.51988e16 −2.35622
\(347\) −3.83778e16 −1.18015 −0.590077 0.807347i \(-0.700902\pi\)
−0.590077 + 0.807347i \(0.700902\pi\)
\(348\) −3.95636e15 −0.119407
\(349\) −4.03032e16 −1.19392 −0.596959 0.802272i \(-0.703625\pi\)
−0.596959 + 0.802272i \(0.703625\pi\)
\(350\) 3.13958e16 0.912913
\(351\) −8.33079e15 −0.237788
\(352\) 9.29129e15 0.260345
\(353\) 3.80218e16 1.04592 0.522958 0.852359i \(-0.324829\pi\)
0.522958 + 0.852359i \(0.324829\pi\)
\(354\) 3.63328e15 0.0981245
\(355\) 2.25087e14 0.00596851
\(356\) −2.11756e16 −0.551330
\(357\) −1.12856e16 −0.288524
\(358\) 6.94141e16 1.74264
\(359\) −3.01081e16 −0.742282 −0.371141 0.928576i \(-0.621033\pi\)
−0.371141 + 0.928576i \(0.621033\pi\)
\(360\) 3.31932e13 0.000803680 0
\(361\) 8.42716e15 0.200394
\(362\) 6.93770e16 1.62035
\(363\) −2.39650e16 −0.549775
\(364\) −2.70040e16 −0.608513
\(365\) −2.23271e14 −0.00494230
\(366\) −3.77491e16 −0.820879
\(367\) −3.20870e16 −0.685487 −0.342744 0.939429i \(-0.611356\pi\)
−0.342744 + 0.939429i \(0.611356\pi\)
\(368\) 4.03463e16 0.846824
\(369\) 4.24615e15 0.0875638
\(370\) −6.20222e14 −0.0125671
\(371\) 2.34923e16 0.467729
\(372\) 6.71429e15 0.131362
\(373\) 4.35441e16 0.837186 0.418593 0.908174i \(-0.362523\pi\)
0.418593 + 0.908174i \(0.362523\pi\)
\(374\) 1.07902e16 0.203876
\(375\) −3.88287e14 −0.00721023
\(376\) −7.22206e15 −0.131808
\(377\) 2.02287e16 0.362868
\(378\) −9.96463e15 −0.175697
\(379\) −1.07507e16 −0.186330 −0.0931648 0.995651i \(-0.529698\pi\)
−0.0931648 + 0.995651i \(0.529698\pi\)
\(380\) 2.82787e14 0.00481799
\(381\) −6.58266e16 −1.10253
\(382\) −9.96138e16 −1.64024
\(383\) 5.47465e16 0.886266 0.443133 0.896456i \(-0.353867\pi\)
0.443133 + 0.896456i \(0.353867\pi\)
\(384\) −2.67864e16 −0.426346
\(385\) 6.09827e13 0.000954359 0
\(386\) −1.42256e17 −2.18904
\(387\) −2.83650e16 −0.429202
\(388\) −7.94496e16 −1.18219
\(389\) 1.32070e17 1.93255 0.966277 0.257505i \(-0.0829005\pi\)
0.966277 + 0.257505i \(0.0829005\pi\)
\(390\) 4.04095e14 0.00581519
\(391\) 3.53860e16 0.500821
\(392\) −1.41724e16 −0.197280
\(393\) 3.91693e16 0.536284
\(394\) 1.30475e17 1.75713
\(395\) 6.06079e14 0.00802875
\(396\) 3.93690e15 0.0513022
\(397\) 5.26848e16 0.675378 0.337689 0.941258i \(-0.390355\pi\)
0.337689 + 0.941258i \(0.390355\pi\)
\(398\) 7.41120e16 0.934650
\(399\) 3.56539e16 0.442368
\(400\) 9.89792e16 1.20824
\(401\) 1.39510e17 1.67559 0.837796 0.545984i \(-0.183844\pi\)
0.837796 + 0.545984i \(0.183844\pi\)
\(402\) −1.22015e17 −1.44193
\(403\) −3.43297e16 −0.399197
\(404\) −7.98386e16 −0.913554
\(405\) 6.16174e13 0.000693818 0
\(406\) 2.41959e16 0.268116
\(407\) 3.08950e16 0.336919
\(408\) −1.48425e16 −0.159300
\(409\) −1.00105e17 −1.05743 −0.528717 0.848798i \(-0.677327\pi\)
−0.528717 + 0.848798i \(0.677327\pi\)
\(410\) −2.05965e14 −0.00214140
\(411\) 8.01033e16 0.819744
\(412\) −1.37823e16 −0.138832
\(413\) −9.18188e15 −0.0910450
\(414\) 3.12441e16 0.304976
\(415\) 6.73481e14 0.00647162
\(416\) −1.55591e17 −1.47190
\(417\) 3.30198e16 0.307532
\(418\) −3.40889e16 −0.312585
\(419\) 2.00711e17 1.81209 0.906044 0.423184i \(-0.139088\pi\)
0.906044 + 0.423184i \(0.139088\pi\)
\(420\) 1.99731e14 0.00177552
\(421\) 3.40145e15 0.0297735 0.0148867 0.999889i \(-0.495261\pi\)
0.0148867 + 0.999889i \(0.495261\pi\)
\(422\) −1.79283e17 −1.54528
\(423\) −1.34065e16 −0.113790
\(424\) 3.08963e16 0.258243
\(425\) 8.68103e16 0.714568
\(426\) −8.88677e16 −0.720413
\(427\) 9.53979e16 0.761654
\(428\) 1.02505e16 0.0806048
\(429\) −2.01291e16 −0.155902
\(430\) 1.37588e15 0.0104963
\(431\) 7.01521e16 0.527155 0.263577 0.964638i \(-0.415098\pi\)
0.263577 + 0.964638i \(0.415098\pi\)
\(432\) −3.14147e16 −0.232535
\(433\) −1.17197e16 −0.0854565 −0.0427282 0.999087i \(-0.513605\pi\)
−0.0427282 + 0.999087i \(0.513605\pi\)
\(434\) −4.10625e16 −0.294959
\(435\) −1.49618e14 −0.00105878
\(436\) −3.97547e16 −0.277158
\(437\) −1.11793e17 −0.767864
\(438\) 8.81508e16 0.596547
\(439\) 2.16132e15 0.0144112 0.00720558 0.999974i \(-0.497706\pi\)
0.00720558 + 0.999974i \(0.497706\pi\)
\(440\) 8.02026e13 0.000526921 0
\(441\) −2.63086e16 −0.170312
\(442\) −1.80693e17 −1.15265
\(443\) 2.84823e17 1.79040 0.895201 0.445664i \(-0.147032\pi\)
0.895201 + 0.445664i \(0.147032\pi\)
\(444\) 1.01188e17 0.626813
\(445\) −8.00800e14 −0.00488860
\(446\) −8.08071e16 −0.486153
\(447\) 1.12644e17 0.667897
\(448\) −4.15089e16 −0.242568
\(449\) 1.16611e17 0.671641 0.335820 0.941926i \(-0.390986\pi\)
0.335820 + 0.941926i \(0.390986\pi\)
\(450\) 7.66492e16 0.435137
\(451\) 1.02597e16 0.0574099
\(452\) 7.36076e16 0.405997
\(453\) −1.24590e17 −0.677400
\(454\) −2.36726e17 −1.26877
\(455\) −1.02121e15 −0.00539563
\(456\) 4.68909e16 0.244240
\(457\) −5.01048e16 −0.257291 −0.128645 0.991691i \(-0.541063\pi\)
−0.128645 + 0.991691i \(0.541063\pi\)
\(458\) 5.99714e16 0.303612
\(459\) −2.75525e16 −0.137524
\(460\) −6.26256e14 −0.00308195
\(461\) −1.03469e17 −0.502058 −0.251029 0.967980i \(-0.580769\pi\)
−0.251029 + 0.967980i \(0.580769\pi\)
\(462\) −2.40769e16 −0.115193
\(463\) −3.19974e17 −1.50952 −0.754759 0.656002i \(-0.772246\pi\)
−0.754759 + 0.656002i \(0.772246\pi\)
\(464\) 7.62806e16 0.354852
\(465\) 2.53915e14 0.00116478
\(466\) −4.71764e17 −2.13411
\(467\) 2.29998e17 1.02604 0.513020 0.858377i \(-0.328527\pi\)
0.513020 + 0.858377i \(0.328527\pi\)
\(468\) −6.59271e16 −0.290046
\(469\) 3.08351e17 1.33789
\(470\) 6.50299e14 0.00278277
\(471\) 1.62610e17 0.686296
\(472\) −1.20757e16 −0.0502678
\(473\) −6.85365e16 −0.281400
\(474\) −2.39289e17 −0.969088
\(475\) −2.74254e17 −1.09558
\(476\) −8.93107e16 −0.351931
\(477\) 5.73536e16 0.222942
\(478\) −5.79680e16 −0.222283
\(479\) 4.04507e15 0.0153019 0.00765095 0.999971i \(-0.497565\pi\)
0.00765095 + 0.999971i \(0.497565\pi\)
\(480\) 1.15081e15 0.00429472
\(481\) −5.17367e17 −1.90483
\(482\) −3.70345e17 −1.34524
\(483\) −7.89588e16 −0.282972
\(484\) −1.89651e17 −0.670596
\(485\) −3.00455e15 −0.0104823
\(486\) −2.43275e16 −0.0837454
\(487\) −3.43808e17 −1.16782 −0.583912 0.811817i \(-0.698479\pi\)
−0.583912 + 0.811817i \(0.698479\pi\)
\(488\) 1.25464e17 0.420525
\(489\) −3.81550e16 −0.126196
\(490\) 1.27613e15 0.00416505
\(491\) 5.40973e17 1.74239 0.871196 0.490935i \(-0.163345\pi\)
0.871196 + 0.490935i \(0.163345\pi\)
\(492\) 3.36027e16 0.106807
\(493\) 6.69024e16 0.209863
\(494\) 5.70852e17 1.76725
\(495\) 1.48882e14 0.000454892 0
\(496\) −1.29455e17 −0.390379
\(497\) 2.24583e17 0.668436
\(498\) −2.65900e17 −0.781139
\(499\) 2.04271e17 0.592316 0.296158 0.955139i \(-0.404295\pi\)
0.296158 + 0.955139i \(0.404295\pi\)
\(500\) −3.07277e15 −0.00879479
\(501\) −5.35070e16 −0.151170
\(502\) −5.15890e17 −1.43874
\(503\) −2.22410e17 −0.612298 −0.306149 0.951984i \(-0.599041\pi\)
−0.306149 + 0.951984i \(0.599041\pi\)
\(504\) 3.31189e16 0.0900072
\(505\) −3.01926e15 −0.00810041
\(506\) 7.54930e16 0.199953
\(507\) 1.16286e17 0.304070
\(508\) −5.20930e17 −1.34482
\(509\) −3.82791e17 −0.975655 −0.487827 0.872940i \(-0.662210\pi\)
−0.487827 + 0.872940i \(0.662210\pi\)
\(510\) 1.33647e15 0.00336320
\(511\) −2.22771e17 −0.553507
\(512\) −3.96553e17 −0.972851
\(513\) 8.70448e16 0.210853
\(514\) −3.24008e17 −0.774988
\(515\) −5.21206e14 −0.00123101
\(516\) −2.24471e17 −0.523526
\(517\) −3.23932e16 −0.0746046
\(518\) −6.18833e17 −1.40744
\(519\) 4.63959e17 1.04206
\(520\) −1.34307e15 −0.00297904
\(521\) 2.64905e17 0.580290 0.290145 0.956983i \(-0.406296\pi\)
0.290145 + 0.956983i \(0.406296\pi\)
\(522\) 5.90715e16 0.127797
\(523\) −3.20781e17 −0.685406 −0.342703 0.939444i \(-0.611342\pi\)
−0.342703 + 0.939444i \(0.611342\pi\)
\(524\) 3.09973e17 0.654140
\(525\) −1.93705e17 −0.403743
\(526\) 7.65799e17 1.57655
\(527\) −1.13539e17 −0.230875
\(528\) −7.59053e16 −0.152459
\(529\) −2.56461e17 −0.508815
\(530\) −2.78201e15 −0.00545212
\(531\) −2.24165e16 −0.0433963
\(532\) 2.82153e17 0.539585
\(533\) −1.71808e17 −0.324577
\(534\) 3.16168e17 0.590065
\(535\) 3.87644e14 0.000714716 0
\(536\) 4.05533e17 0.738678
\(537\) −4.28268e17 −0.770696
\(538\) 8.51620e17 1.51412
\(539\) −6.35676e16 −0.111663
\(540\) 4.87620e14 0.000846295 0
\(541\) 9.89247e17 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(542\) −2.00667e17 −0.340001
\(543\) −4.28039e17 −0.716613
\(544\) −5.14589e17 −0.851270
\(545\) −1.50341e15 −0.00245753
\(546\) 4.03190e17 0.651265
\(547\) −8.63153e17 −1.37775 −0.688874 0.724881i \(-0.741895\pi\)
−0.688874 + 0.724881i \(0.741895\pi\)
\(548\) 6.33911e17 0.999895
\(549\) 2.32903e17 0.363040
\(550\) 1.85202e17 0.285291
\(551\) −2.11360e17 −0.321765
\(552\) −1.03844e17 −0.156235
\(553\) 6.04721e17 0.899170
\(554\) −1.27244e18 −1.86992
\(555\) 3.82662e15 0.00555790
\(556\) 2.61308e17 0.375117
\(557\) 2.76225e17 0.391927 0.195963 0.980611i \(-0.437217\pi\)
0.195963 + 0.980611i \(0.437217\pi\)
\(558\) −1.00249e17 −0.140591
\(559\) 1.14771e18 1.59094
\(560\) −3.85091e15 −0.00527645
\(561\) −6.65732e16 −0.0901657
\(562\) 4.05687e17 0.543132
\(563\) −6.74594e17 −0.892766 −0.446383 0.894842i \(-0.647288\pi\)
−0.446383 + 0.894842i \(0.647288\pi\)
\(564\) −1.06095e17 −0.138797
\(565\) 2.78363e15 0.00359995
\(566\) −4.54641e17 −0.581249
\(567\) 6.14794e16 0.0777033
\(568\) 2.95364e17 0.369057
\(569\) 1.41670e17 0.175004 0.0875022 0.996164i \(-0.472112\pi\)
0.0875022 + 0.996164i \(0.472112\pi\)
\(570\) −4.22222e15 −0.00515649
\(571\) −8.70534e17 −1.05112 −0.525559 0.850757i \(-0.676144\pi\)
−0.525559 + 0.850757i \(0.676144\pi\)
\(572\) −1.59295e17 −0.190164
\(573\) 6.14593e17 0.725409
\(574\) −2.05504e17 −0.239824
\(575\) 6.07360e17 0.700818
\(576\) −1.01339e17 −0.115619
\(577\) −6.55997e17 −0.740047 −0.370023 0.929022i \(-0.620650\pi\)
−0.370023 + 0.929022i \(0.620650\pi\)
\(578\) 5.72687e17 0.638832
\(579\) 8.77685e17 0.968118
\(580\) −1.18403e15 −0.00129146
\(581\) 6.71973e17 0.724781
\(582\) 1.18624e18 1.26524
\(583\) 1.38580e17 0.146169
\(584\) −2.92982e17 −0.305603
\(585\) −2.49317e15 −0.00257181
\(586\) −2.31738e18 −2.36408
\(587\) 2.13669e17 0.215573 0.107786 0.994174i \(-0.465624\pi\)
0.107786 + 0.994174i \(0.465624\pi\)
\(588\) −2.08197e17 −0.207741
\(589\) 3.58696e17 0.353979
\(590\) 1.08734e15 0.00106127
\(591\) −8.05001e17 −0.777102
\(592\) −1.95095e18 −1.86275
\(593\) −7.84408e17 −0.740775 −0.370387 0.928877i \(-0.620775\pi\)
−0.370387 + 0.928877i \(0.620775\pi\)
\(594\) −5.87808e16 −0.0549065
\(595\) −3.37747e15 −0.00312055
\(596\) 8.91428e17 0.814677
\(597\) −4.57253e17 −0.413356
\(598\) −1.26420e18 −1.13047
\(599\) −3.59041e17 −0.317592 −0.158796 0.987311i \(-0.550761\pi\)
−0.158796 + 0.987311i \(0.550761\pi\)
\(600\) −2.54754e17 −0.222915
\(601\) 1.41352e18 1.22354 0.611768 0.791037i \(-0.290459\pi\)
0.611768 + 0.791037i \(0.290459\pi\)
\(602\) 1.37280e18 1.17552
\(603\) 7.52802e17 0.637702
\(604\) −9.85966e17 −0.826269
\(605\) −7.17206e15 −0.00594612
\(606\) 1.19205e18 0.977738
\(607\) 2.27581e17 0.184676 0.0923379 0.995728i \(-0.470566\pi\)
0.0923379 + 0.995728i \(0.470566\pi\)
\(608\) 1.62571e18 1.30518
\(609\) −1.49283e17 −0.118576
\(610\) −1.12972e16 −0.00887826
\(611\) 5.42455e17 0.421790
\(612\) −2.18041e17 −0.167747
\(613\) 1.52616e18 1.16174 0.580869 0.813997i \(-0.302713\pi\)
0.580869 + 0.813997i \(0.302713\pi\)
\(614\) −2.57787e18 −1.94163
\(615\) 1.27075e15 0.000947051 0
\(616\) 8.00229e16 0.0590119
\(617\) −1.51369e18 −1.10455 −0.552274 0.833663i \(-0.686240\pi\)
−0.552274 + 0.833663i \(0.686240\pi\)
\(618\) 2.05780e17 0.148586
\(619\) 2.31320e18 1.65281 0.826406 0.563075i \(-0.190382\pi\)
0.826406 + 0.563075i \(0.190382\pi\)
\(620\) 2.00940e15 0.00142076
\(621\) −1.92768e17 −0.134878
\(622\) −1.59883e18 −1.10704
\(623\) −7.99007e17 −0.547492
\(624\) 1.27111e18 0.861950
\(625\) 1.48994e18 0.999883
\(626\) 1.31718e18 0.874804
\(627\) 2.10321e17 0.138243
\(628\) 1.28684e18 0.837119
\(629\) −1.71109e18 −1.10165
\(630\) −2.98213e15 −0.00190026
\(631\) −2.25313e18 −1.42100 −0.710501 0.703696i \(-0.751532\pi\)
−0.710501 + 0.703696i \(0.751532\pi\)
\(632\) 7.95311e17 0.496450
\(633\) 1.10613e18 0.683413
\(634\) −1.29445e18 −0.791602
\(635\) −1.97000e16 −0.0119244
\(636\) 4.53877e17 0.271936
\(637\) 1.06450e18 0.631305
\(638\) 1.42730e17 0.0837880
\(639\) 5.48292e17 0.318608
\(640\) −8.01642e15 −0.00461116
\(641\) 4.56005e17 0.259652 0.129826 0.991537i \(-0.458558\pi\)
0.129826 + 0.991537i \(0.458558\pi\)
\(642\) −1.53048e17 −0.0862679
\(643\) 1.38951e17 0.0775337 0.0387669 0.999248i \(-0.487657\pi\)
0.0387669 + 0.999248i \(0.487657\pi\)
\(644\) −6.24854e17 −0.345160
\(645\) −8.48885e15 −0.00464206
\(646\) 1.88798e18 1.02208
\(647\) 1.65177e18 0.885264 0.442632 0.896703i \(-0.354045\pi\)
0.442632 + 0.896703i \(0.354045\pi\)
\(648\) 8.08558e16 0.0429016
\(649\) −5.41634e16 −0.0284522
\(650\) −3.10139e18 −1.61294
\(651\) 2.53346e17 0.130448
\(652\) −3.01946e17 −0.153929
\(653\) 7.70105e17 0.388700 0.194350 0.980932i \(-0.437740\pi\)
0.194350 + 0.980932i \(0.437740\pi\)
\(654\) 5.93568e17 0.296630
\(655\) 1.17223e16 0.00580021
\(656\) −6.47876e17 −0.317407
\(657\) −5.43869e17 −0.263827
\(658\) 6.48842e17 0.311653
\(659\) 1.29640e18 0.616574 0.308287 0.951293i \(-0.400244\pi\)
0.308287 + 0.951293i \(0.400244\pi\)
\(660\) 1.17820e15 0.000554861 0
\(661\) 1.59296e18 0.742840 0.371420 0.928465i \(-0.378871\pi\)
0.371420 + 0.928465i \(0.378871\pi\)
\(662\) 1.64341e18 0.758874
\(663\) 1.11483e18 0.509767
\(664\) 8.83757e17 0.400166
\(665\) 1.06702e16 0.00478445
\(666\) −1.51081e18 −0.670852
\(667\) 4.68076e17 0.205825
\(668\) −4.23437e17 −0.184392
\(669\) 4.98560e17 0.215005
\(670\) −3.65156e16 −0.0155952
\(671\) 5.62747e17 0.238022
\(672\) 1.14823e18 0.480982
\(673\) 7.64288e17 0.317073 0.158537 0.987353i \(-0.449322\pi\)
0.158537 + 0.987353i \(0.449322\pi\)
\(674\) −1.91135e18 −0.785327
\(675\) −4.72907e17 −0.192443
\(676\) 9.20245e17 0.370894
\(677\) 1.17853e18 0.470452 0.235226 0.971941i \(-0.424417\pi\)
0.235226 + 0.971941i \(0.424417\pi\)
\(678\) −1.09902e18 −0.434522
\(679\) −2.99782e18 −1.17396
\(680\) −4.44194e15 −0.00172292
\(681\) 1.46054e18 0.561123
\(682\) −2.42226e17 −0.0921768
\(683\) −2.54053e18 −0.957613 −0.478807 0.877920i \(-0.658931\pi\)
−0.478807 + 0.877920i \(0.658931\pi\)
\(684\) 6.88844e17 0.257191
\(685\) 2.39727e16 0.00886599
\(686\) 3.76530e18 1.37941
\(687\) −3.70009e17 −0.134275
\(688\) 4.32792e18 1.55580
\(689\) −2.32065e18 −0.826389
\(690\) 9.35047e15 0.00329848
\(691\) 1.34331e18 0.469429 0.234715 0.972064i \(-0.424584\pi\)
0.234715 + 0.972064i \(0.424584\pi\)
\(692\) 3.67161e18 1.27106
\(693\) 1.48549e17 0.0509451
\(694\) 4.53460e18 1.54065
\(695\) 9.88190e15 0.00332613
\(696\) −1.96332e17 −0.0654684
\(697\) −5.68223e17 −0.187718
\(698\) 4.76211e18 1.55862
\(699\) 2.91067e18 0.943825
\(700\) −1.53291e18 −0.492471
\(701\) 4.56459e18 1.45290 0.726448 0.687221i \(-0.241170\pi\)
0.726448 + 0.687221i \(0.241170\pi\)
\(702\) 9.84341e17 0.310423
\(703\) 5.40574e18 1.68906
\(704\) −2.44858e17 −0.0758041
\(705\) −4.01219e15 −0.00123070
\(706\) −4.49254e18 −1.36540
\(707\) −3.01250e18 −0.907196
\(708\) −1.77396e17 −0.0529333
\(709\) 6.17963e18 1.82710 0.913549 0.406729i \(-0.133331\pi\)
0.913549 + 0.406729i \(0.133331\pi\)
\(710\) −2.65956e16 −0.00779167
\(711\) 1.47636e18 0.428586
\(712\) −1.05083e18 −0.302282
\(713\) −7.94365e17 −0.226432
\(714\) 1.33347e18 0.376657
\(715\) −6.02408e15 −0.00168617
\(716\) −3.38917e18 −0.940068
\(717\) 3.57649e17 0.0983064
\(718\) 3.55748e18 0.969022
\(719\) 4.19765e18 1.13310 0.566550 0.824028i \(-0.308278\pi\)
0.566550 + 0.824028i \(0.308278\pi\)
\(720\) −9.40155e15 −0.00251500
\(721\) −5.20039e17 −0.137866
\(722\) −9.95727e17 −0.261606
\(723\) 2.28494e18 0.594943
\(724\) −3.38736e18 −0.874099
\(725\) 1.14830e18 0.293670
\(726\) 2.83163e18 0.717710
\(727\) −6.06778e18 −1.52425 −0.762124 0.647431i \(-0.775844\pi\)
−0.762124 + 0.647431i \(0.775844\pi\)
\(728\) −1.34006e18 −0.333634
\(729\) 1.50095e17 0.0370370
\(730\) 2.63810e16 0.00645199
\(731\) 3.79583e18 0.920118
\(732\) 1.84311e18 0.442823
\(733\) −3.74219e18 −0.891147 −0.445574 0.895245i \(-0.647000\pi\)
−0.445574 + 0.895245i \(0.647000\pi\)
\(734\) 3.79130e18 0.894878
\(735\) −7.87341e15 −0.00184202
\(736\) −3.60027e18 −0.834891
\(737\) 1.81894e18 0.418101
\(738\) −5.01713e17 −0.114311
\(739\) −7.18460e18 −1.62261 −0.811304 0.584624i \(-0.801242\pi\)
−0.811304 + 0.584624i \(0.801242\pi\)
\(740\) 3.02826e16 0.00677934
\(741\) −3.52202e18 −0.781579
\(742\) −2.77578e18 −0.610603
\(743\) −7.38192e18 −1.60969 −0.804844 0.593486i \(-0.797751\pi\)
−0.804844 + 0.593486i \(0.797751\pi\)
\(744\) 3.33193e17 0.0720230
\(745\) 3.37112e16 0.00722368
\(746\) −5.14504e18 −1.09291
\(747\) 1.64054e18 0.345464
\(748\) −5.26839e17 −0.109981
\(749\) 3.86776e17 0.0800438
\(750\) 4.58788e16 0.00941268
\(751\) 4.82403e18 0.981185 0.490592 0.871389i \(-0.336780\pi\)
0.490592 + 0.871389i \(0.336780\pi\)
\(752\) 2.04556e18 0.412473
\(753\) 3.18292e18 0.636294
\(754\) −2.39016e18 −0.473710
\(755\) −3.72863e16 −0.00732646
\(756\) 4.86528e17 0.0947798
\(757\) 2.59728e18 0.501644 0.250822 0.968033i \(-0.419299\pi\)
0.250822 + 0.968033i \(0.419299\pi\)
\(758\) 1.27027e18 0.243246
\(759\) −4.65773e17 −0.0884307
\(760\) 1.40331e16 0.00264160
\(761\) −8.02151e18 −1.49712 −0.748559 0.663068i \(-0.769254\pi\)
−0.748559 + 0.663068i \(0.769254\pi\)
\(762\) 7.77787e18 1.43931
\(763\) −1.50004e18 −0.275229
\(764\) 4.86369e18 0.884828
\(765\) −8.24568e15 −0.00148740
\(766\) −6.46867e18 −1.15699
\(767\) 9.07018e17 0.160859
\(768\) 4.30378e18 0.756836
\(769\) 6.41075e18 1.11786 0.558931 0.829214i \(-0.311212\pi\)
0.558931 + 0.829214i \(0.311212\pi\)
\(770\) −7.20553e15 −0.00124588
\(771\) 1.99905e18 0.342744
\(772\) 6.94571e18 1.18088
\(773\) 1.06884e19 1.80196 0.900980 0.433861i \(-0.142849\pi\)
0.900980 + 0.433861i \(0.142849\pi\)
\(774\) 3.35153e18 0.560307
\(775\) −1.94877e18 −0.323072
\(776\) −3.94264e18 −0.648166
\(777\) 3.81805e18 0.622451
\(778\) −1.56050e19 −2.52288
\(779\) 1.79515e18 0.287811
\(780\) −1.97301e16 −0.00313700
\(781\) 1.32480e18 0.208891
\(782\) −4.18110e18 −0.653803
\(783\) −3.64457e17 −0.0565190
\(784\) 4.01414e18 0.617360
\(785\) 4.86646e16 0.00742267
\(786\) −4.62813e18 −0.700098
\(787\) −1.40570e17 −0.0210891 −0.0105445 0.999944i \(-0.503356\pi\)
−0.0105445 + 0.999944i \(0.503356\pi\)
\(788\) −6.37051e18 −0.947881
\(789\) −4.72480e18 −0.697241
\(790\) −7.16124e16 −0.0104812
\(791\) 2.77739e18 0.403172
\(792\) 1.95366e17 0.0281278
\(793\) −9.42373e18 −1.34570
\(794\) −6.22507e18 −0.881680
\(795\) 1.71643e16 0.00241124
\(796\) −3.61855e18 −0.504197
\(797\) −9.38764e17 −0.129741 −0.0648705 0.997894i \(-0.520663\pi\)
−0.0648705 + 0.997894i \(0.520663\pi\)
\(798\) −4.21276e18 −0.577494
\(799\) 1.79407e18 0.243941
\(800\) −8.83233e18 −1.19122
\(801\) −1.95068e18 −0.260960
\(802\) −1.64841e19 −2.18742
\(803\) −1.31411e18 −0.172975
\(804\) 5.95742e18 0.777847
\(805\) −2.36301e16 −0.00306050
\(806\) 4.05630e18 0.521137
\(807\) −5.25429e18 −0.669632
\(808\) −3.96195e18 −0.500881
\(809\) −5.09036e18 −0.638386 −0.319193 0.947690i \(-0.603412\pi\)
−0.319193 + 0.947690i \(0.603412\pi\)
\(810\) −7.28053e15 −0.000905754 0
\(811\) −1.71416e18 −0.211552 −0.105776 0.994390i \(-0.533733\pi\)
−0.105776 + 0.994390i \(0.533733\pi\)
\(812\) −1.18138e18 −0.144635
\(813\) 1.23807e18 0.150368
\(814\) −3.65046e18 −0.439834
\(815\) −1.14187e16 −0.00136488
\(816\) 4.20394e18 0.498506
\(817\) −1.19919e19 −1.41073
\(818\) 1.18281e19 1.38044
\(819\) −2.48759e18 −0.288027
\(820\) 1.00563e16 0.00115518
\(821\) −7.13051e18 −0.812625 −0.406313 0.913734i \(-0.633186\pi\)
−0.406313 + 0.913734i \(0.633186\pi\)
\(822\) −9.46476e18 −1.07015
\(823\) −2.67308e18 −0.299856 −0.149928 0.988697i \(-0.547904\pi\)
−0.149928 + 0.988697i \(0.547904\pi\)
\(824\) −6.83939e17 −0.0761185
\(825\) −1.14265e18 −0.126172
\(826\) 1.08490e18 0.118856
\(827\) 8.64840e18 0.940048 0.470024 0.882654i \(-0.344245\pi\)
0.470024 + 0.882654i \(0.344245\pi\)
\(828\) −1.52551e18 −0.164519
\(829\) −7.23666e18 −0.774343 −0.387172 0.922008i \(-0.626548\pi\)
−0.387172 + 0.922008i \(0.626548\pi\)
\(830\) −7.95765e16 −0.00844845
\(831\) 7.85063e18 0.826986
\(832\) 4.10039e18 0.428571
\(833\) 3.52063e18 0.365114
\(834\) −3.90152e18 −0.401472
\(835\) −1.60131e16 −0.00163499
\(836\) 1.66441e18 0.168624
\(837\) 6.18514e17 0.0621776
\(838\) −2.37154e19 −2.36561
\(839\) −2.13793e18 −0.211612 −0.105806 0.994387i \(-0.533742\pi\)
−0.105806 + 0.994387i \(0.533742\pi\)
\(840\) 9.91155e15 0.000973478 0
\(841\) −9.37566e18 −0.913751
\(842\) −4.01904e17 −0.0388682
\(843\) −2.50299e18 −0.240204
\(844\) 8.75357e18 0.833603
\(845\) 3.48010e16 0.00328869
\(846\) 1.58407e18 0.148548
\(847\) −7.15599e18 −0.665929
\(848\) −8.75098e18 −0.808134
\(849\) 2.80503e18 0.257062
\(850\) −1.02572e19 −0.932841
\(851\) −1.19715e19 −1.08045
\(852\) 4.33900e18 0.388627
\(853\) 9.16116e18 0.814295 0.407147 0.913362i \(-0.366524\pi\)
0.407147 + 0.913362i \(0.366524\pi\)
\(854\) −1.12719e19 −0.994310
\(855\) 2.60501e16 0.00228049
\(856\) 5.08676e17 0.0441938
\(857\) 1.52454e19 1.31451 0.657254 0.753669i \(-0.271718\pi\)
0.657254 + 0.753669i \(0.271718\pi\)
\(858\) 2.37840e18 0.203525
\(859\) 2.09334e19 1.77781 0.888904 0.458094i \(-0.151468\pi\)
0.888904 + 0.458094i \(0.151468\pi\)
\(860\) −6.71780e16 −0.00566222
\(861\) 1.26791e18 0.106064
\(862\) −8.28895e18 −0.688181
\(863\) −1.62203e19 −1.33656 −0.668279 0.743911i \(-0.732969\pi\)
−0.668279 + 0.743911i \(0.732969\pi\)
\(864\) 2.80327e18 0.229258
\(865\) 1.38850e17 0.0112704
\(866\) 1.38476e18 0.111560
\(867\) −3.53334e18 −0.282528
\(868\) 2.00490e18 0.159116
\(869\) 3.56722e18 0.280997
\(870\) 1.76784e16 0.00138219
\(871\) −3.04600e19 −2.36380
\(872\) −1.97281e18 −0.151959
\(873\) −7.31883e18 −0.559563
\(874\) 1.32091e19 1.00242
\(875\) −1.15943e17 −0.00873357
\(876\) −4.30400e18 −0.321807
\(877\) 1.29181e19 0.958739 0.479369 0.877613i \(-0.340865\pi\)
0.479369 + 0.877613i \(0.340865\pi\)
\(878\) −2.55374e17 −0.0188132
\(879\) 1.42977e19 1.04553
\(880\) −2.27163e16 −0.00164892
\(881\) 8.42062e18 0.606737 0.303369 0.952873i \(-0.401889\pi\)
0.303369 + 0.952873i \(0.401889\pi\)
\(882\) 3.10854e18 0.222336
\(883\) 6.23507e17 0.0442687 0.0221343 0.999755i \(-0.492954\pi\)
0.0221343 + 0.999755i \(0.492954\pi\)
\(884\) 8.82241e18 0.621796
\(885\) −6.70862e15 −0.000469355 0
\(886\) −3.36538e19 −2.33730
\(887\) −1.24814e19 −0.860518 −0.430259 0.902705i \(-0.641578\pi\)
−0.430259 + 0.902705i \(0.641578\pi\)
\(888\) 5.02138e18 0.343668
\(889\) −1.96559e19 −1.33546
\(890\) 9.46201e16 0.00638188
\(891\) 3.62664e17 0.0242828
\(892\) 3.94544e18 0.262255
\(893\) −5.66788e18 −0.374012
\(894\) −1.33097e19 −0.871914
\(895\) −1.28169e17 −0.00833551
\(896\) −7.99846e18 −0.516422
\(897\) 7.79982e18 0.499958
\(898\) −1.37784e19 −0.876802
\(899\) −1.50186e18 −0.0948838
\(900\) −3.74243e18 −0.234735
\(901\) −7.67510e18 −0.477939
\(902\) −1.21225e18 −0.0749465
\(903\) −8.46984e18 −0.519882
\(904\) 3.65274e18 0.222599
\(905\) −1.28100e17 −0.00775057
\(906\) 1.47212e19 0.884321
\(907\) −3.91182e18 −0.233309 −0.116654 0.993173i \(-0.537217\pi\)
−0.116654 + 0.993173i \(0.537217\pi\)
\(908\) 1.15583e19 0.684438
\(909\) −7.35466e18 −0.432412
\(910\) 1.20663e17 0.00704380
\(911\) −7.75067e18 −0.449231 −0.224615 0.974447i \(-0.572113\pi\)
−0.224615 + 0.974447i \(0.572113\pi\)
\(912\) −1.32812e19 −0.764315
\(913\) 3.96393e18 0.226499
\(914\) 5.92023e18 0.335883
\(915\) 6.97012e16 0.00392648
\(916\) −2.92813e18 −0.163783
\(917\) 1.16960e19 0.649587
\(918\) 3.25552e18 0.179532
\(919\) 1.47948e19 0.810137 0.405068 0.914286i \(-0.367248\pi\)
0.405068 + 0.914286i \(0.367248\pi\)
\(920\) −3.10776e16 −0.00168977
\(921\) 1.59049e19 0.858702
\(922\) 1.22256e19 0.655417
\(923\) −2.21851e19 −1.18100
\(924\) 1.17556e18 0.0621410
\(925\) −2.93689e19 −1.54158
\(926\) 3.78072e19 1.97062
\(927\) −1.26961e18 −0.0657132
\(928\) −6.80684e18 −0.349851
\(929\) 1.88038e19 0.959720 0.479860 0.877345i \(-0.340688\pi\)
0.479860 + 0.877345i \(0.340688\pi\)
\(930\) −3.00018e16 −0.00152057
\(931\) −1.11225e19 −0.559796
\(932\) 2.30341e19 1.15124
\(933\) 9.86437e18 0.489597
\(934\) −2.71758e19 −1.33946
\(935\) −1.99235e16 −0.000975192 0
\(936\) −3.27160e18 −0.159025
\(937\) 1.56979e19 0.757766 0.378883 0.925445i \(-0.376308\pi\)
0.378883 + 0.925445i \(0.376308\pi\)
\(938\) −3.64338e19 −1.74657
\(939\) −8.12666e18 −0.386889
\(940\) −3.17511e16 −0.00150116
\(941\) 1.50749e19 0.707820 0.353910 0.935279i \(-0.384852\pi\)
0.353910 + 0.935279i \(0.384852\pi\)
\(942\) −1.92135e19 −0.895933
\(943\) −3.97552e18 −0.184106
\(944\) 3.42029e18 0.157306
\(945\) 1.83990e16 0.000840405 0
\(946\) 8.09807e18 0.367358
\(947\) 4.53176e18 0.204170 0.102085 0.994776i \(-0.467449\pi\)
0.102085 + 0.994776i \(0.467449\pi\)
\(948\) 1.16834e19 0.522775
\(949\) 2.20061e19 0.977941
\(950\) 3.24050e19 1.43024
\(951\) 7.98647e18 0.350092
\(952\) −4.43199e18 −0.192956
\(953\) −3.51372e19 −1.51937 −0.759685 0.650292i \(-0.774647\pi\)
−0.759685 + 0.650292i \(0.774647\pi\)
\(954\) −6.77673e18 −0.291042
\(955\) 1.83930e17 0.00784570
\(956\) 2.83031e18 0.119911
\(957\) −8.80612e17 −0.0370559
\(958\) −4.77953e17 −0.0199760
\(959\) 2.39190e19 0.992936
\(960\) −3.03279e16 −0.00125049
\(961\) −2.18688e19 −0.895617
\(962\) 6.11305e19 2.48668
\(963\) 9.44267e17 0.0381526
\(964\) 1.80823e19 0.725691
\(965\) 2.62666e17 0.0104707
\(966\) 9.32953e18 0.369410
\(967\) 3.06736e19 1.20641 0.603203 0.797588i \(-0.293891\pi\)
0.603203 + 0.797588i \(0.293891\pi\)
\(968\) −9.41134e18 −0.367673
\(969\) −1.16484e19 −0.452024
\(970\) 3.55009e17 0.0136843
\(971\) 4.82739e19 1.84836 0.924182 0.381953i \(-0.124748\pi\)
0.924182 + 0.381953i \(0.124748\pi\)
\(972\) 1.18780e18 0.0451765
\(973\) 9.85977e18 0.372506
\(974\) 4.06233e19 1.52455
\(975\) 1.91348e19 0.713336
\(976\) −3.55361e19 −1.31597
\(977\) 4.71263e19 1.73360 0.866799 0.498658i \(-0.166174\pi\)
0.866799 + 0.498658i \(0.166174\pi\)
\(978\) 4.50828e18 0.164744
\(979\) −4.71330e18 −0.171095
\(980\) −6.23076e16 −0.00224684
\(981\) −3.66217e18 −0.131187
\(982\) −6.39197e19 −2.27463
\(983\) 5.36003e19 1.89483 0.947414 0.320011i \(-0.103687\pi\)
0.947414 + 0.320011i \(0.103687\pi\)
\(984\) 1.66751e18 0.0585600
\(985\) −2.40914e17 −0.00840479
\(986\) −7.90498e18 −0.273969
\(987\) −4.00320e18 −0.137831
\(988\) −2.78721e19 −0.953343
\(989\) 2.65572e19 0.902414
\(990\) −1.75914e16 −0.000593845 0
\(991\) 7.95774e18 0.266877 0.133438 0.991057i \(-0.457398\pi\)
0.133438 + 0.991057i \(0.457398\pi\)
\(992\) 1.15518e19 0.384878
\(993\) −1.01395e19 −0.335617
\(994\) −2.65360e19 −0.872619
\(995\) −1.36843e17 −0.00447067
\(996\) 1.29827e19 0.421385
\(997\) 4.41803e19 1.42466 0.712328 0.701847i \(-0.247641\pi\)
0.712328 + 0.701847i \(0.247641\pi\)
\(998\) −2.41361e19 −0.773246
\(999\) 9.32132e18 0.296689
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.1.6 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.6 31 1.1 even 1 trivial