Properties

Label 177.14.a.c.1.8
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 1.8
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-102.312 q^{2} +729.000 q^{3} +2275.81 q^{4} -9860.18 q^{5} -74585.7 q^{6} +439885. q^{7} +605299. q^{8} +531441. q^{9} +O(q^{10})\) \(q-102.312 q^{2} +729.000 q^{3} +2275.81 q^{4} -9860.18 q^{5} -74585.7 q^{6} +439885. q^{7} +605299. q^{8} +531441. q^{9} +1.00882e6 q^{10} -959631. q^{11} +1.65907e6 q^{12} +5.60936e6 q^{13} -4.50057e7 q^{14} -7.18807e6 q^{15} -8.05730e7 q^{16} -1.88295e8 q^{17} -5.43730e7 q^{18} -3.80650e6 q^{19} -2.24399e7 q^{20} +3.20677e8 q^{21} +9.81821e7 q^{22} +1.27095e9 q^{23} +4.41263e8 q^{24} -1.12348e9 q^{25} -5.73907e8 q^{26} +3.87420e8 q^{27} +1.00110e9 q^{28} +4.95175e9 q^{29} +7.35428e8 q^{30} +8.24954e9 q^{31} +3.28500e9 q^{32} -6.99571e8 q^{33} +1.92649e10 q^{34} -4.33735e9 q^{35} +1.20946e9 q^{36} -2.50637e10 q^{37} +3.89452e8 q^{38} +4.08922e9 q^{39} -5.96836e9 q^{40} -3.30388e10 q^{41} -3.28092e10 q^{42} +4.90496e10 q^{43} -2.18394e9 q^{44} -5.24010e9 q^{45} -1.30034e11 q^{46} +8.62871e10 q^{47} -5.87377e10 q^{48} +9.66102e10 q^{49} +1.14946e11 q^{50} -1.37267e11 q^{51} +1.27658e10 q^{52} +2.96825e11 q^{53} -3.96379e10 q^{54} +9.46214e9 q^{55} +2.66262e11 q^{56} -2.77494e9 q^{57} -5.06626e11 q^{58} -4.21805e10 q^{59} -1.63587e10 q^{60} -6.27896e11 q^{61} -8.44029e11 q^{62} +2.33773e11 q^{63} +3.23958e11 q^{64} -5.53093e10 q^{65} +7.15748e10 q^{66} -6.94025e11 q^{67} -4.28524e11 q^{68} +9.26520e11 q^{69} +4.43764e11 q^{70} +1.94174e11 q^{71} +3.21681e11 q^{72} +3.28001e11 q^{73} +2.56433e12 q^{74} -8.19017e11 q^{75} -8.66289e9 q^{76} -4.22128e11 q^{77} -4.18378e11 q^{78} +3.01833e10 q^{79} +7.94464e11 q^{80} +2.82430e11 q^{81} +3.38028e12 q^{82} +5.53645e11 q^{83} +7.29799e11 q^{84} +1.85662e12 q^{85} -5.01838e12 q^{86} +3.60983e12 q^{87} -5.80864e11 q^{88} -2.05690e12 q^{89} +5.36127e11 q^{90} +2.46748e12 q^{91} +2.89244e12 q^{92} +6.01391e12 q^{93} -8.82824e12 q^{94} +3.75328e10 q^{95} +2.39477e12 q^{96} +5.32259e12 q^{97} -9.88442e12 q^{98} -5.09988e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −102.312 −1.13040 −0.565201 0.824953i \(-0.691201\pi\)
−0.565201 + 0.824953i \(0.691201\pi\)
\(3\) 729.000 0.577350
\(4\) 2275.81 0.277809
\(5\) −9860.18 −0.282215 −0.141107 0.989994i \(-0.545066\pi\)
−0.141107 + 0.989994i \(0.545066\pi\)
\(6\) −74585.7 −0.652638
\(7\) 439885. 1.41320 0.706598 0.707615i \(-0.250229\pi\)
0.706598 + 0.707615i \(0.250229\pi\)
\(8\) 605299. 0.816366
\(9\) 531441. 0.333333
\(10\) 1.00882e6 0.319016
\(11\) −959631. −0.163325 −0.0816624 0.996660i \(-0.526023\pi\)
−0.0816624 + 0.996660i \(0.526023\pi\)
\(12\) 1.65907e6 0.160393
\(13\) 5.60936e6 0.322316 0.161158 0.986929i \(-0.448477\pi\)
0.161158 + 0.986929i \(0.448477\pi\)
\(14\) −4.50057e7 −1.59748
\(15\) −7.18807e6 −0.162937
\(16\) −8.05730e7 −1.20063
\(17\) −1.88295e8 −1.89200 −0.945999 0.324169i \(-0.894915\pi\)
−0.945999 + 0.324169i \(0.894915\pi\)
\(18\) −5.43730e7 −0.376801
\(19\) −3.80650e6 −0.0185621 −0.00928107 0.999957i \(-0.502954\pi\)
−0.00928107 + 0.999957i \(0.502954\pi\)
\(20\) −2.24399e7 −0.0784018
\(21\) 3.20677e8 0.815909
\(22\) 9.81821e7 0.184623
\(23\) 1.27095e9 1.79018 0.895089 0.445887i \(-0.147112\pi\)
0.895089 + 0.445887i \(0.147112\pi\)
\(24\) 4.41263e8 0.471329
\(25\) −1.12348e9 −0.920355
\(26\) −5.73907e8 −0.364346
\(27\) 3.87420e8 0.192450
\(28\) 1.00110e9 0.392599
\(29\) 4.95175e9 1.54587 0.772934 0.634487i \(-0.218789\pi\)
0.772934 + 0.634487i \(0.218789\pi\)
\(30\) 7.35428e8 0.184184
\(31\) 8.24954e9 1.66947 0.834735 0.550652i \(-0.185621\pi\)
0.834735 + 0.550652i \(0.185621\pi\)
\(32\) 3.28500e9 0.540830
\(33\) −6.99571e8 −0.0942956
\(34\) 1.92649e10 2.13872
\(35\) −4.33735e9 −0.398825
\(36\) 1.20946e9 0.0926030
\(37\) −2.50637e10 −1.60596 −0.802979 0.596008i \(-0.796753\pi\)
−0.802979 + 0.596008i \(0.796753\pi\)
\(38\) 3.89452e8 0.0209827
\(39\) 4.08922e9 0.186089
\(40\) −5.96836e9 −0.230391
\(41\) −3.30388e10 −1.08625 −0.543124 0.839652i \(-0.682759\pi\)
−0.543124 + 0.839652i \(0.682759\pi\)
\(42\) −3.28092e10 −0.922305
\(43\) 4.90496e10 1.18329 0.591644 0.806199i \(-0.298479\pi\)
0.591644 + 0.806199i \(0.298479\pi\)
\(44\) −2.18394e9 −0.0453731
\(45\) −5.24010e9 −0.0940716
\(46\) −1.30034e11 −2.02362
\(47\) 8.62871e10 1.16764 0.583821 0.811882i \(-0.301557\pi\)
0.583821 + 0.811882i \(0.301557\pi\)
\(48\) −5.87377e10 −0.693185
\(49\) 9.66102e10 0.997122
\(50\) 1.14946e11 1.04037
\(51\) −1.37267e11 −1.09235
\(52\) 1.27658e10 0.0895422
\(53\) 2.96825e11 1.83953 0.919767 0.392464i \(-0.128377\pi\)
0.919767 + 0.392464i \(0.128377\pi\)
\(54\) −3.96379e10 −0.217546
\(55\) 9.46214e9 0.0460927
\(56\) 2.66262e11 1.15369
\(57\) −2.77494e9 −0.0107169
\(58\) −5.06626e11 −1.74745
\(59\) −4.21805e10 −0.130189
\(60\) −1.63587e10 −0.0452653
\(61\) −6.27896e11 −1.56043 −0.780214 0.625513i \(-0.784890\pi\)
−0.780214 + 0.625513i \(0.784890\pi\)
\(62\) −8.44029e11 −1.88717
\(63\) 2.33773e11 0.471065
\(64\) 3.23958e11 0.589276
\(65\) −5.53093e10 −0.0909622
\(66\) 7.15748e10 0.106592
\(67\) −6.94025e11 −0.937323 −0.468661 0.883378i \(-0.655264\pi\)
−0.468661 + 0.883378i \(0.655264\pi\)
\(68\) −4.28524e11 −0.525614
\(69\) 9.26520e11 1.03356
\(70\) 4.43764e11 0.450832
\(71\) 1.94174e11 0.179892 0.0899460 0.995947i \(-0.471331\pi\)
0.0899460 + 0.995947i \(0.471331\pi\)
\(72\) 3.21681e11 0.272122
\(73\) 3.28001e11 0.253674 0.126837 0.991924i \(-0.459517\pi\)
0.126837 + 0.991924i \(0.459517\pi\)
\(74\) 2.56433e12 1.81538
\(75\) −8.19017e11 −0.531367
\(76\) −8.66289e9 −0.00515673
\(77\) −4.22128e11 −0.230810
\(78\) −4.18378e11 −0.210355
\(79\) 3.01833e10 0.0139698 0.00698491 0.999976i \(-0.497777\pi\)
0.00698491 + 0.999976i \(0.497777\pi\)
\(80\) 7.94464e11 0.338836
\(81\) 2.82430e11 0.111111
\(82\) 3.38028e12 1.22790
\(83\) 5.53645e11 0.185876 0.0929382 0.995672i \(-0.470374\pi\)
0.0929382 + 0.995672i \(0.470374\pi\)
\(84\) 7.29799e11 0.226667
\(85\) 1.85662e12 0.533950
\(86\) −5.01838e12 −1.33759
\(87\) 3.60983e12 0.892507
\(88\) −5.80864e11 −0.133333
\(89\) −2.05690e12 −0.438711 −0.219355 0.975645i \(-0.570395\pi\)
−0.219355 + 0.975645i \(0.570395\pi\)
\(90\) 5.36127e11 0.106339
\(91\) 2.46748e12 0.455495
\(92\) 2.89244e12 0.497328
\(93\) 6.01391e12 0.963869
\(94\) −8.82824e12 −1.31991
\(95\) 3.75328e10 0.00523851
\(96\) 2.39477e12 0.312248
\(97\) 5.32259e12 0.648794 0.324397 0.945921i \(-0.394839\pi\)
0.324397 + 0.945921i \(0.394839\pi\)
\(98\) −9.88442e12 −1.12715
\(99\) −5.09988e11 −0.0544416
\(100\) −2.55683e12 −0.255683
\(101\) 4.79471e12 0.449442 0.224721 0.974423i \(-0.427853\pi\)
0.224721 + 0.974423i \(0.427853\pi\)
\(102\) 1.40441e13 1.23479
\(103\) −1.39519e13 −1.15131 −0.575655 0.817693i \(-0.695253\pi\)
−0.575655 + 0.817693i \(0.695253\pi\)
\(104\) 3.39534e12 0.263128
\(105\) −3.16193e12 −0.230262
\(106\) −3.03689e13 −2.07941
\(107\) 8.69685e12 0.560232 0.280116 0.959966i \(-0.409627\pi\)
0.280116 + 0.959966i \(0.409627\pi\)
\(108\) 8.81696e11 0.0534644
\(109\) 2.50601e13 1.43123 0.715616 0.698494i \(-0.246146\pi\)
0.715616 + 0.698494i \(0.246146\pi\)
\(110\) −9.68093e11 −0.0521032
\(111\) −1.82714e13 −0.927200
\(112\) −3.54429e13 −1.69673
\(113\) −2.11671e13 −0.956424 −0.478212 0.878244i \(-0.658715\pi\)
−0.478212 + 0.878244i \(0.658715\pi\)
\(114\) 2.83911e11 0.0121144
\(115\) −1.25318e13 −0.505215
\(116\) 1.12693e13 0.429456
\(117\) 2.98104e12 0.107439
\(118\) 4.31559e12 0.147166
\(119\) −8.28282e13 −2.67376
\(120\) −4.35093e12 −0.133016
\(121\) −3.36018e13 −0.973325
\(122\) 6.42415e13 1.76391
\(123\) −2.40853e13 −0.627146
\(124\) 1.87744e13 0.463794
\(125\) 2.31141e13 0.541952
\(126\) −2.39179e13 −0.532493
\(127\) −1.50766e13 −0.318846 −0.159423 0.987210i \(-0.550963\pi\)
−0.159423 + 0.987210i \(0.550963\pi\)
\(128\) −6.00556e13 −1.20695
\(129\) 3.57572e13 0.683172
\(130\) 5.65882e12 0.102824
\(131\) −6.12475e13 −1.05883 −0.529413 0.848364i \(-0.677588\pi\)
−0.529413 + 0.848364i \(0.677588\pi\)
\(132\) −1.59209e12 −0.0261962
\(133\) −1.67443e12 −0.0262319
\(134\) 7.10073e13 1.05955
\(135\) −3.82003e12 −0.0543123
\(136\) −1.13975e14 −1.54456
\(137\) 6.52569e13 0.843224 0.421612 0.906776i \(-0.361464\pi\)
0.421612 + 0.906776i \(0.361464\pi\)
\(138\) −9.47944e13 −1.16834
\(139\) 7.06004e13 0.830254 0.415127 0.909763i \(-0.363737\pi\)
0.415127 + 0.909763i \(0.363737\pi\)
\(140\) −9.87099e12 −0.110797
\(141\) 6.29033e13 0.674139
\(142\) −1.98664e13 −0.203350
\(143\) −5.38292e12 −0.0526421
\(144\) −4.28198e13 −0.400210
\(145\) −4.88252e13 −0.436267
\(146\) −3.35585e13 −0.286754
\(147\) 7.04288e13 0.575689
\(148\) −5.70403e13 −0.446150
\(149\) −5.00979e13 −0.375067 −0.187533 0.982258i \(-0.560049\pi\)
−0.187533 + 0.982258i \(0.560049\pi\)
\(150\) 8.37955e13 0.600659
\(151\) −1.38699e14 −0.952191 −0.476096 0.879394i \(-0.657948\pi\)
−0.476096 + 0.879394i \(0.657948\pi\)
\(152\) −2.30407e12 −0.0151535
\(153\) −1.00068e14 −0.630666
\(154\) 4.31889e13 0.260908
\(155\) −8.13419e13 −0.471149
\(156\) 9.30630e12 0.0516972
\(157\) 3.48457e13 0.185696 0.0928479 0.995680i \(-0.470403\pi\)
0.0928479 + 0.995680i \(0.470403\pi\)
\(158\) −3.08813e12 −0.0157915
\(159\) 2.16386e14 1.06206
\(160\) −3.23907e13 −0.152630
\(161\) 5.59071e14 2.52987
\(162\) −2.88960e13 −0.125600
\(163\) 3.37036e12 0.0140753 0.00703763 0.999975i \(-0.497760\pi\)
0.00703763 + 0.999975i \(0.497760\pi\)
\(164\) −7.51901e13 −0.301770
\(165\) 6.89790e12 0.0266116
\(166\) −5.66447e13 −0.210115
\(167\) 9.27764e13 0.330964 0.165482 0.986213i \(-0.447082\pi\)
0.165482 + 0.986213i \(0.447082\pi\)
\(168\) 1.94105e14 0.666081
\(169\) −2.71410e14 −0.896113
\(170\) −1.89955e14 −0.603578
\(171\) −2.02293e12 −0.00618738
\(172\) 1.11628e14 0.328728
\(173\) −2.55428e14 −0.724383 −0.362192 0.932104i \(-0.617971\pi\)
−0.362192 + 0.932104i \(0.617971\pi\)
\(174\) −3.69330e14 −1.00889
\(175\) −4.94203e14 −1.30064
\(176\) 7.73204e13 0.196093
\(177\) −3.07496e13 −0.0751646
\(178\) 2.10446e14 0.495920
\(179\) 5.21459e14 1.18488 0.592441 0.805613i \(-0.298164\pi\)
0.592441 + 0.805613i \(0.298164\pi\)
\(180\) −1.19255e13 −0.0261339
\(181\) 1.91276e14 0.404343 0.202171 0.979350i \(-0.435200\pi\)
0.202171 + 0.979350i \(0.435200\pi\)
\(182\) −2.52453e14 −0.514893
\(183\) −4.57736e14 −0.900913
\(184\) 7.69303e14 1.46144
\(185\) 2.47133e14 0.453225
\(186\) −6.15297e14 −1.08956
\(187\) 1.80694e14 0.309010
\(188\) 1.96373e14 0.324382
\(189\) 1.70421e14 0.271970
\(190\) −3.84007e12 −0.00592162
\(191\) −3.71672e14 −0.553914 −0.276957 0.960882i \(-0.589326\pi\)
−0.276957 + 0.960882i \(0.589326\pi\)
\(192\) 2.36165e14 0.340219
\(193\) 3.74464e14 0.521540 0.260770 0.965401i \(-0.416024\pi\)
0.260770 + 0.965401i \(0.416024\pi\)
\(194\) −5.44567e14 −0.733398
\(195\) −4.03205e13 −0.0525171
\(196\) 2.19867e14 0.277010
\(197\) 1.03975e15 1.26735 0.633677 0.773598i \(-0.281545\pi\)
0.633677 + 0.773598i \(0.281545\pi\)
\(198\) 5.21780e13 0.0615409
\(199\) 1.58199e15 1.80575 0.902875 0.429903i \(-0.141452\pi\)
0.902875 + 0.429903i \(0.141452\pi\)
\(200\) −6.80041e14 −0.751347
\(201\) −5.05944e14 −0.541163
\(202\) −4.90558e14 −0.508050
\(203\) 2.17821e15 2.18461
\(204\) −3.12394e14 −0.303464
\(205\) 3.25768e14 0.306555
\(206\) 1.42745e15 1.30144
\(207\) 6.75433e14 0.596726
\(208\) −4.51963e14 −0.386982
\(209\) 3.65284e12 0.00303166
\(210\) 3.23504e14 0.260288
\(211\) −1.04660e15 −0.816481 −0.408241 0.912874i \(-0.633858\pi\)
−0.408241 + 0.912874i \(0.633858\pi\)
\(212\) 6.75519e14 0.511039
\(213\) 1.41553e14 0.103861
\(214\) −8.89795e14 −0.633287
\(215\) −4.83638e14 −0.333941
\(216\) 2.34505e14 0.157110
\(217\) 3.62885e15 2.35929
\(218\) −2.56395e15 −1.61787
\(219\) 2.39113e14 0.146459
\(220\) 2.15340e13 0.0128050
\(221\) −1.05621e15 −0.609821
\(222\) 1.86939e15 1.04811
\(223\) −7.62200e14 −0.415037 −0.207519 0.978231i \(-0.566539\pi\)
−0.207519 + 0.978231i \(0.566539\pi\)
\(224\) 1.44502e15 0.764299
\(225\) −5.97063e14 −0.306785
\(226\) 2.16565e15 1.08114
\(227\) 2.97374e15 1.44256 0.721282 0.692642i \(-0.243553\pi\)
0.721282 + 0.692642i \(0.243553\pi\)
\(228\) −6.31525e12 −0.00297724
\(229\) 3.26361e14 0.149544 0.0747719 0.997201i \(-0.476177\pi\)
0.0747719 + 0.997201i \(0.476177\pi\)
\(230\) 1.28215e15 0.571096
\(231\) −3.07731e14 −0.133258
\(232\) 2.99729e15 1.26199
\(233\) 2.53194e15 1.03667 0.518335 0.855178i \(-0.326552\pi\)
0.518335 + 0.855178i \(0.326552\pi\)
\(234\) −3.04997e14 −0.121449
\(235\) −8.50807e14 −0.329526
\(236\) −9.59950e13 −0.0361677
\(237\) 2.20036e13 0.00806548
\(238\) 8.47435e15 3.02243
\(239\) 1.47267e15 0.511117 0.255558 0.966794i \(-0.417741\pi\)
0.255558 + 0.966794i \(0.417741\pi\)
\(240\) 5.79164e14 0.195627
\(241\) 3.16431e15 1.04032 0.520161 0.854068i \(-0.325872\pi\)
0.520161 + 0.854068i \(0.325872\pi\)
\(242\) 3.43788e15 1.10025
\(243\) 2.05891e14 0.0641500
\(244\) −1.42897e15 −0.433501
\(245\) −9.52594e14 −0.281403
\(246\) 2.46422e15 0.708927
\(247\) −2.13521e13 −0.00598287
\(248\) 4.99343e15 1.36290
\(249\) 4.03607e14 0.107316
\(250\) −2.36485e15 −0.612624
\(251\) −4.90008e15 −1.23687 −0.618435 0.785836i \(-0.712233\pi\)
−0.618435 + 0.785836i \(0.712233\pi\)
\(252\) 5.32024e14 0.130866
\(253\) −1.21964e15 −0.292381
\(254\) 1.54253e15 0.360424
\(255\) 1.35348e15 0.308276
\(256\) 3.49057e15 0.775062
\(257\) 2.79467e15 0.605014 0.302507 0.953147i \(-0.402176\pi\)
0.302507 + 0.953147i \(0.402176\pi\)
\(258\) −3.65840e15 −0.772259
\(259\) −1.10252e16 −2.26953
\(260\) −1.25874e14 −0.0252701
\(261\) 2.63157e15 0.515289
\(262\) 6.26637e15 1.19690
\(263\) 6.06854e15 1.13076 0.565382 0.824829i \(-0.308729\pi\)
0.565382 + 0.824829i \(0.308729\pi\)
\(264\) −4.23450e14 −0.0769797
\(265\) −2.92675e15 −0.519144
\(266\) 1.71314e14 0.0296526
\(267\) −1.49948e15 −0.253290
\(268\) −1.57947e15 −0.260397
\(269\) −1.58413e15 −0.254919 −0.127459 0.991844i \(-0.540682\pi\)
−0.127459 + 0.991844i \(0.540682\pi\)
\(270\) 3.90837e14 0.0613947
\(271\) −6.06086e15 −0.929467 −0.464733 0.885451i \(-0.653850\pi\)
−0.464733 + 0.885451i \(0.653850\pi\)
\(272\) 1.51715e16 2.27159
\(273\) 1.79879e15 0.262980
\(274\) −6.67659e15 −0.953182
\(275\) 1.07813e15 0.150317
\(276\) 2.10859e15 0.287132
\(277\) −1.10110e16 −1.46456 −0.732279 0.681005i \(-0.761543\pi\)
−0.732279 + 0.681005i \(0.761543\pi\)
\(278\) −7.22329e15 −0.938521
\(279\) 4.38414e15 0.556490
\(280\) −2.62539e15 −0.325587
\(281\) 8.50276e15 1.03031 0.515156 0.857097i \(-0.327734\pi\)
0.515156 + 0.857097i \(0.327734\pi\)
\(282\) −6.43579e15 −0.762048
\(283\) 1.83458e15 0.212287 0.106144 0.994351i \(-0.466150\pi\)
0.106144 + 0.994351i \(0.466150\pi\)
\(284\) 4.41904e14 0.0499757
\(285\) 2.73614e13 0.00302445
\(286\) 5.50739e14 0.0595068
\(287\) −1.45333e16 −1.53508
\(288\) 1.74578e15 0.180277
\(289\) 2.55504e16 2.57966
\(290\) 4.99542e15 0.493157
\(291\) 3.88017e15 0.374581
\(292\) 7.46468e14 0.0704730
\(293\) −7.11647e15 −0.657090 −0.328545 0.944488i \(-0.606558\pi\)
−0.328545 + 0.944488i \(0.606558\pi\)
\(294\) −7.20574e15 −0.650760
\(295\) 4.15908e14 0.0367412
\(296\) −1.51710e16 −1.31105
\(297\) −3.71781e14 −0.0314319
\(298\) 5.12563e15 0.423976
\(299\) 7.12920e15 0.577003
\(300\) −1.86393e15 −0.147619
\(301\) 2.15762e16 1.67222
\(302\) 1.41906e16 1.07636
\(303\) 3.49534e15 0.259485
\(304\) 3.06702e14 0.0222863
\(305\) 6.19116e15 0.440376
\(306\) 1.02382e16 0.712906
\(307\) 3.06811e15 0.209157 0.104578 0.994517i \(-0.466651\pi\)
0.104578 + 0.994517i \(0.466651\pi\)
\(308\) −9.60684e14 −0.0641211
\(309\) −1.01709e16 −0.664709
\(310\) 8.32228e15 0.532588
\(311\) 2.41527e16 1.51364 0.756821 0.653623i \(-0.226752\pi\)
0.756821 + 0.653623i \(0.226752\pi\)
\(312\) 2.47520e15 0.151917
\(313\) −1.62698e16 −0.978010 −0.489005 0.872281i \(-0.662640\pi\)
−0.489005 + 0.872281i \(0.662640\pi\)
\(314\) −3.56515e15 −0.209911
\(315\) −2.30504e15 −0.132942
\(316\) 6.86916e13 0.00388094
\(317\) −1.23819e16 −0.685333 −0.342666 0.939457i \(-0.611330\pi\)
−0.342666 + 0.939457i \(0.611330\pi\)
\(318\) −2.21389e16 −1.20055
\(319\) −4.75186e15 −0.252478
\(320\) −3.19428e15 −0.166302
\(321\) 6.34001e15 0.323450
\(322\) −5.71999e16 −2.85977
\(323\) 7.16746e14 0.0351195
\(324\) 6.42757e14 0.0308677
\(325\) −6.30200e15 −0.296645
\(326\) −3.44829e14 −0.0159107
\(327\) 1.82688e16 0.826322
\(328\) −1.99984e16 −0.886777
\(329\) 3.79565e16 1.65011
\(330\) −7.05740e14 −0.0300818
\(331\) 2.36825e16 0.989797 0.494898 0.868951i \(-0.335205\pi\)
0.494898 + 0.868951i \(0.335205\pi\)
\(332\) 1.25999e15 0.0516381
\(333\) −1.33199e16 −0.535319
\(334\) −9.49217e15 −0.374122
\(335\) 6.84321e15 0.264526
\(336\) −2.58379e16 −0.979606
\(337\) −2.61147e16 −0.971161 −0.485580 0.874192i \(-0.661392\pi\)
−0.485580 + 0.874192i \(0.661392\pi\)
\(338\) 2.77686e16 1.01297
\(339\) −1.54308e16 −0.552192
\(340\) 4.22532e15 0.148336
\(341\) −7.91651e15 −0.272666
\(342\) 2.06971e14 0.00699423
\(343\) −1.22640e14 −0.00406651
\(344\) 2.96897e16 0.965996
\(345\) −9.13565e15 −0.291686
\(346\) 2.61334e16 0.818844
\(347\) 1.23055e16 0.378405 0.189202 0.981938i \(-0.439410\pi\)
0.189202 + 0.981938i \(0.439410\pi\)
\(348\) 8.21529e15 0.247947
\(349\) 1.37929e16 0.408591 0.204296 0.978909i \(-0.434510\pi\)
0.204296 + 0.978909i \(0.434510\pi\)
\(350\) 5.05630e16 1.47025
\(351\) 2.17318e15 0.0620297
\(352\) −3.15239e15 −0.0883309
\(353\) −4.63927e16 −1.27619 −0.638093 0.769960i \(-0.720276\pi\)
−0.638093 + 0.769960i \(0.720276\pi\)
\(354\) 3.14606e15 0.0849662
\(355\) −1.91459e15 −0.0507682
\(356\) −4.68112e15 −0.121878
\(357\) −6.03818e16 −1.54370
\(358\) −5.33517e16 −1.33939
\(359\) −1.44346e16 −0.355870 −0.177935 0.984042i \(-0.556942\pi\)
−0.177935 + 0.984042i \(0.556942\pi\)
\(360\) −3.17183e15 −0.0767969
\(361\) −4.20385e16 −0.999655
\(362\) −1.95699e16 −0.457070
\(363\) −2.44957e16 −0.561949
\(364\) 5.61551e15 0.126541
\(365\) −3.23415e15 −0.0715906
\(366\) 4.68320e16 1.01839
\(367\) 4.45889e16 0.952571 0.476286 0.879291i \(-0.341983\pi\)
0.476286 + 0.879291i \(0.341983\pi\)
\(368\) −1.02404e17 −2.14934
\(369\) −1.75582e16 −0.362083
\(370\) −2.52847e16 −0.512326
\(371\) 1.30569e17 2.59962
\(372\) 1.36865e16 0.267771
\(373\) 7.97536e16 1.53336 0.766678 0.642032i \(-0.221908\pi\)
0.766678 + 0.642032i \(0.221908\pi\)
\(374\) −1.84872e16 −0.349306
\(375\) 1.68502e16 0.312896
\(376\) 5.22295e16 0.953224
\(377\) 2.77762e16 0.498257
\(378\) −1.74361e16 −0.307435
\(379\) 5.34113e16 0.925717 0.462859 0.886432i \(-0.346824\pi\)
0.462859 + 0.886432i \(0.346824\pi\)
\(380\) 8.54176e13 0.00145531
\(381\) −1.09909e16 −0.184086
\(382\) 3.80266e16 0.626146
\(383\) 2.41068e16 0.390254 0.195127 0.980778i \(-0.437488\pi\)
0.195127 + 0.980778i \(0.437488\pi\)
\(384\) −4.37805e16 −0.696832
\(385\) 4.16226e15 0.0651380
\(386\) −3.83123e16 −0.589550
\(387\) 2.60670e16 0.394429
\(388\) 1.21132e16 0.180241
\(389\) 6.28632e16 0.919865 0.459933 0.887954i \(-0.347874\pi\)
0.459933 + 0.887954i \(0.347874\pi\)
\(390\) 4.12528e15 0.0593654
\(391\) −2.39313e17 −3.38702
\(392\) 5.84781e16 0.814017
\(393\) −4.46494e16 −0.611314
\(394\) −1.06379e17 −1.43262
\(395\) −2.97613e14 −0.00394249
\(396\) −1.16064e15 −0.0151244
\(397\) 4.95048e16 0.634613 0.317306 0.948323i \(-0.397222\pi\)
0.317306 + 0.948323i \(0.397222\pi\)
\(398\) −1.61857e17 −2.04122
\(399\) −1.22066e15 −0.0151450
\(400\) 9.05222e16 1.10501
\(401\) 7.60000e16 0.912799 0.456399 0.889775i \(-0.349139\pi\)
0.456399 + 0.889775i \(0.349139\pi\)
\(402\) 5.17644e16 0.611732
\(403\) 4.62746e16 0.538096
\(404\) 1.09119e16 0.124859
\(405\) −2.78481e15 −0.0313572
\(406\) −2.22857e17 −2.46949
\(407\) 2.40519e16 0.262293
\(408\) −8.30876e16 −0.891754
\(409\) 7.38271e16 0.779855 0.389928 0.920845i \(-0.372500\pi\)
0.389928 + 0.920845i \(0.372500\pi\)
\(410\) −3.33301e16 −0.346531
\(411\) 4.75723e16 0.486836
\(412\) −3.17520e16 −0.319844
\(413\) −1.85546e16 −0.183982
\(414\) −6.91051e16 −0.674541
\(415\) −5.45904e15 −0.0524570
\(416\) 1.84268e16 0.174318
\(417\) 5.14677e16 0.479347
\(418\) −3.73731e14 −0.00342699
\(419\) 5.18667e16 0.468271 0.234136 0.972204i \(-0.424774\pi\)
0.234136 + 0.972204i \(0.424774\pi\)
\(420\) −7.19595e15 −0.0639688
\(421\) 2.46988e16 0.216193 0.108096 0.994140i \(-0.465524\pi\)
0.108096 + 0.994140i \(0.465524\pi\)
\(422\) 1.07080e17 0.922952
\(423\) 4.58565e16 0.389214
\(424\) 1.79668e17 1.50173
\(425\) 2.11546e17 1.74131
\(426\) −1.44826e16 −0.117404
\(427\) −2.76202e17 −2.20519
\(428\) 1.97924e16 0.155637
\(429\) −3.92415e15 −0.0303929
\(430\) 4.94821e16 0.377488
\(431\) 2.15093e17 1.61630 0.808152 0.588974i \(-0.200468\pi\)
0.808152 + 0.588974i \(0.200468\pi\)
\(432\) −3.12156e16 −0.231062
\(433\) 2.35585e17 1.71782 0.858909 0.512128i \(-0.171143\pi\)
0.858909 + 0.512128i \(0.171143\pi\)
\(434\) −3.71276e17 −2.66694
\(435\) −3.55936e16 −0.251879
\(436\) 5.70320e16 0.397609
\(437\) −4.83787e15 −0.0332295
\(438\) −2.44642e16 −0.165557
\(439\) −1.21164e17 −0.807893 −0.403947 0.914783i \(-0.632362\pi\)
−0.403947 + 0.914783i \(0.632362\pi\)
\(440\) 5.72742e15 0.0376285
\(441\) 5.13426e16 0.332374
\(442\) 1.08064e17 0.689343
\(443\) −4.75701e16 −0.299026 −0.149513 0.988760i \(-0.547771\pi\)
−0.149513 + 0.988760i \(0.547771\pi\)
\(444\) −4.15824e16 −0.257585
\(445\) 2.02814e16 0.123811
\(446\) 7.79824e16 0.469159
\(447\) −3.65214e16 −0.216545
\(448\) 1.42504e17 0.832762
\(449\) 1.21062e17 0.697279 0.348640 0.937257i \(-0.386644\pi\)
0.348640 + 0.937257i \(0.386644\pi\)
\(450\) 6.10869e16 0.346790
\(451\) 3.17051e16 0.177411
\(452\) −4.81722e16 −0.265703
\(453\) −1.01112e17 −0.549748
\(454\) −3.04250e17 −1.63068
\(455\) −2.43297e16 −0.128547
\(456\) −1.67967e15 −0.00874888
\(457\) −2.45726e17 −1.26182 −0.630909 0.775857i \(-0.717318\pi\)
−0.630909 + 0.775857i \(0.717318\pi\)
\(458\) −3.33908e16 −0.169045
\(459\) −7.29493e16 −0.364115
\(460\) −2.85199e16 −0.140353
\(461\) 3.78798e17 1.83803 0.919013 0.394227i \(-0.128988\pi\)
0.919013 + 0.394227i \(0.128988\pi\)
\(462\) 3.14847e16 0.150635
\(463\) −2.59238e17 −1.22299 −0.611495 0.791248i \(-0.709432\pi\)
−0.611495 + 0.791248i \(0.709432\pi\)
\(464\) −3.98978e17 −1.85602
\(465\) −5.92982e16 −0.272018
\(466\) −2.59049e17 −1.17185
\(467\) 6.08852e16 0.271614 0.135807 0.990735i \(-0.456637\pi\)
0.135807 + 0.990735i \(0.456637\pi\)
\(468\) 6.78429e15 0.0298474
\(469\) −3.05292e17 −1.32462
\(470\) 8.70480e16 0.372497
\(471\) 2.54025e16 0.107211
\(472\) −2.55318e16 −0.106282
\(473\) −4.70695e16 −0.193260
\(474\) −2.25124e15 −0.00911724
\(475\) 4.27653e15 0.0170838
\(476\) −1.88501e17 −0.742796
\(477\) 1.57745e17 0.613178
\(478\) −1.50673e17 −0.577767
\(479\) 3.07859e17 1.16459 0.582293 0.812979i \(-0.302156\pi\)
0.582293 + 0.812979i \(0.302156\pi\)
\(480\) −2.36128e16 −0.0881211
\(481\) −1.40591e17 −0.517625
\(482\) −3.23748e17 −1.17598
\(483\) 4.07563e17 1.46062
\(484\) −7.64714e16 −0.270399
\(485\) −5.24817e16 −0.183099
\(486\) −2.10652e16 −0.0725153
\(487\) −1.84377e17 −0.626279 −0.313139 0.949707i \(-0.601381\pi\)
−0.313139 + 0.949707i \(0.601381\pi\)
\(488\) −3.80065e17 −1.27388
\(489\) 2.45699e15 0.00812636
\(490\) 9.74621e16 0.318098
\(491\) 2.52379e17 0.812873 0.406437 0.913679i \(-0.366771\pi\)
0.406437 + 0.913679i \(0.366771\pi\)
\(492\) −5.48136e16 −0.174227
\(493\) −9.32391e17 −2.92478
\(494\) 2.18458e15 0.00676305
\(495\) 5.02857e15 0.0153642
\(496\) −6.64690e17 −2.00442
\(497\) 8.54144e16 0.254223
\(498\) −4.12940e16 −0.121310
\(499\) −2.98918e17 −0.866760 −0.433380 0.901211i \(-0.642679\pi\)
−0.433380 + 0.901211i \(0.642679\pi\)
\(500\) 5.26033e16 0.150559
\(501\) 6.76340e16 0.191082
\(502\) 5.01338e17 1.39816
\(503\) 4.01278e17 1.10472 0.552362 0.833605i \(-0.313727\pi\)
0.552362 + 0.833605i \(0.313727\pi\)
\(504\) 1.41503e17 0.384562
\(505\) −4.72767e16 −0.126839
\(506\) 1.24784e17 0.330508
\(507\) −1.97858e17 −0.517371
\(508\) −3.43116e16 −0.0885782
\(509\) 6.16098e17 1.57030 0.785152 0.619303i \(-0.212585\pi\)
0.785152 + 0.619303i \(0.212585\pi\)
\(510\) −1.38477e17 −0.348476
\(511\) 1.44283e17 0.358491
\(512\) 1.34848e17 0.330817
\(513\) −1.47472e15 −0.00357229
\(514\) −2.85929e17 −0.683909
\(515\) 1.37568e17 0.324916
\(516\) 8.13766e16 0.189791
\(517\) −8.28039e16 −0.190705
\(518\) 1.12801e18 2.56548
\(519\) −1.86207e17 −0.418223
\(520\) −3.34786e16 −0.0742585
\(521\) −4.14914e17 −0.908892 −0.454446 0.890774i \(-0.650163\pi\)
−0.454446 + 0.890774i \(0.650163\pi\)
\(522\) −2.69242e17 −0.582484
\(523\) 3.78452e17 0.808630 0.404315 0.914620i \(-0.367510\pi\)
0.404315 + 0.914620i \(0.367510\pi\)
\(524\) −1.39388e17 −0.294152
\(525\) −3.60274e17 −0.750926
\(526\) −6.20886e17 −1.27822
\(527\) −1.55335e18 −3.15863
\(528\) 5.63666e16 0.113214
\(529\) 1.11127e18 2.20474
\(530\) 2.99443e17 0.586841
\(531\) −2.24165e16 −0.0433963
\(532\) −3.81068e15 −0.00728747
\(533\) −1.85327e17 −0.350115
\(534\) 1.53415e17 0.286319
\(535\) −8.57525e16 −0.158106
\(536\) −4.20093e17 −0.765198
\(537\) 3.80144e17 0.684092
\(538\) 1.62076e17 0.288161
\(539\) −9.27102e16 −0.162855
\(540\) −8.69368e15 −0.0150884
\(541\) 1.85708e17 0.318456 0.159228 0.987242i \(-0.449100\pi\)
0.159228 + 0.987242i \(0.449100\pi\)
\(542\) 6.20101e17 1.05067
\(543\) 1.39440e17 0.233447
\(544\) −6.18549e17 −1.02325
\(545\) −2.47097e17 −0.403915
\(546\) −1.84038e17 −0.297273
\(547\) −4.62369e17 −0.738026 −0.369013 0.929424i \(-0.620304\pi\)
−0.369013 + 0.929424i \(0.620304\pi\)
\(548\) 1.48513e17 0.234255
\(549\) −3.33690e17 −0.520142
\(550\) −1.10306e17 −0.169918
\(551\) −1.88489e16 −0.0286946
\(552\) 5.60822e17 0.843764
\(553\) 1.32772e16 0.0197421
\(554\) 1.12656e18 1.65554
\(555\) 1.80160e17 0.261670
\(556\) 1.60673e17 0.230652
\(557\) −1.03129e18 −1.46327 −0.731633 0.681699i \(-0.761242\pi\)
−0.731633 + 0.681699i \(0.761242\pi\)
\(558\) −4.48552e17 −0.629057
\(559\) 2.75137e17 0.381392
\(560\) 3.49473e17 0.478841
\(561\) 1.31726e17 0.178407
\(562\) −8.69937e17 −1.16467
\(563\) 8.59022e17 1.13684 0.568420 0.822738i \(-0.307555\pi\)
0.568420 + 0.822738i \(0.307555\pi\)
\(564\) 1.43156e17 0.187282
\(565\) 2.08711e17 0.269917
\(566\) −1.87700e17 −0.239970
\(567\) 1.24237e17 0.157022
\(568\) 1.17533e17 0.146858
\(569\) 5.29538e17 0.654135 0.327068 0.945001i \(-0.393939\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(570\) −2.79941e15 −0.00341885
\(571\) 1.43746e17 0.173565 0.0867825 0.996227i \(-0.472341\pi\)
0.0867825 + 0.996227i \(0.472341\pi\)
\(572\) −1.22505e16 −0.0146245
\(573\) −2.70949e17 −0.319803
\(574\) 1.48693e18 1.73526
\(575\) −1.42788e18 −1.64760
\(576\) 1.72164e17 0.196425
\(577\) 1.10842e18 1.25044 0.625219 0.780450i \(-0.285010\pi\)
0.625219 + 0.780450i \(0.285010\pi\)
\(578\) −2.61412e18 −2.91605
\(579\) 2.72984e17 0.301111
\(580\) −1.11117e17 −0.121199
\(581\) 2.43541e17 0.262680
\(582\) −3.96989e17 −0.423428
\(583\) −2.84843e17 −0.300442
\(584\) 1.98538e17 0.207091
\(585\) −2.93936e16 −0.0303207
\(586\) 7.28103e17 0.742776
\(587\) −1.21677e18 −1.22761 −0.613804 0.789458i \(-0.710362\pi\)
−0.613804 + 0.789458i \(0.710362\pi\)
\(588\) 1.60283e17 0.159932
\(589\) −3.14019e16 −0.0309889
\(590\) −4.25525e16 −0.0415324
\(591\) 7.57977e17 0.731707
\(592\) 2.01946e18 1.92816
\(593\) 1.51158e18 1.42750 0.713750 0.700401i \(-0.246995\pi\)
0.713750 + 0.700401i \(0.246995\pi\)
\(594\) 3.80378e16 0.0355306
\(595\) 8.16701e17 0.754576
\(596\) −1.14013e17 −0.104197
\(597\) 1.15327e18 1.04255
\(598\) −7.29405e17 −0.652245
\(599\) −1.83163e18 −1.62018 −0.810089 0.586307i \(-0.800581\pi\)
−0.810089 + 0.586307i \(0.800581\pi\)
\(600\) −4.95750e17 −0.433790
\(601\) −1.65935e17 −0.143633 −0.0718164 0.997418i \(-0.522880\pi\)
−0.0718164 + 0.997418i \(0.522880\pi\)
\(602\) −2.20751e18 −1.89028
\(603\) −3.68833e17 −0.312441
\(604\) −3.15654e17 −0.264527
\(605\) 3.31320e17 0.274687
\(606\) −3.57617e17 −0.293323
\(607\) −6.74725e17 −0.547520 −0.273760 0.961798i \(-0.588267\pi\)
−0.273760 + 0.961798i \(0.588267\pi\)
\(608\) −1.25044e16 −0.0100390
\(609\) 1.58791e18 1.26129
\(610\) −6.33432e17 −0.497802
\(611\) 4.84015e17 0.376350
\(612\) −2.27735e17 −0.175205
\(613\) −9.98298e17 −0.759919 −0.379960 0.925003i \(-0.624062\pi\)
−0.379960 + 0.925003i \(0.624062\pi\)
\(614\) −3.13906e17 −0.236431
\(615\) 2.37485e17 0.176990
\(616\) −2.55514e17 −0.188425
\(617\) −8.96065e17 −0.653862 −0.326931 0.945048i \(-0.606014\pi\)
−0.326931 + 0.945048i \(0.606014\pi\)
\(618\) 1.04061e18 0.751388
\(619\) −1.05232e18 −0.751897 −0.375948 0.926641i \(-0.622683\pi\)
−0.375948 + 0.926641i \(0.622683\pi\)
\(620\) −1.85119e17 −0.130889
\(621\) 4.92391e17 0.344520
\(622\) −2.47112e18 −1.71102
\(623\) −9.04801e17 −0.619984
\(624\) −3.29481e17 −0.223424
\(625\) 1.14353e18 0.767408
\(626\) 1.66460e18 1.10554
\(627\) 2.66292e15 0.00175033
\(628\) 7.93023e16 0.0515880
\(629\) 4.71937e18 3.03847
\(630\) 2.35835e17 0.150277
\(631\) 2.40986e16 0.0151985 0.00759927 0.999971i \(-0.497581\pi\)
0.00759927 + 0.999971i \(0.497581\pi\)
\(632\) 1.82699e16 0.0114045
\(633\) −7.62974e17 −0.471396
\(634\) 1.26682e18 0.774701
\(635\) 1.48658e17 0.0899830
\(636\) 4.92453e17 0.295049
\(637\) 5.41921e17 0.321388
\(638\) 4.86174e17 0.285402
\(639\) 1.03192e17 0.0599640
\(640\) 5.92159e17 0.340619
\(641\) 2.96151e17 0.168630 0.0843151 0.996439i \(-0.473130\pi\)
0.0843151 + 0.996439i \(0.473130\pi\)
\(642\) −6.48661e17 −0.365628
\(643\) −1.31913e18 −0.736065 −0.368032 0.929813i \(-0.619968\pi\)
−0.368032 + 0.929813i \(0.619968\pi\)
\(644\) 1.27234e18 0.702822
\(645\) −3.52572e17 −0.192801
\(646\) −7.33319e16 −0.0396992
\(647\) −1.31456e18 −0.704533 −0.352266 0.935900i \(-0.614589\pi\)
−0.352266 + 0.935900i \(0.614589\pi\)
\(648\) 1.70954e17 0.0907074
\(649\) 4.04778e16 0.0212631
\(650\) 6.44773e17 0.335328
\(651\) 2.64543e18 1.36214
\(652\) 7.67030e15 0.00391024
\(653\) 2.65086e18 1.33798 0.668992 0.743269i \(-0.266726\pi\)
0.668992 + 0.743269i \(0.266726\pi\)
\(654\) −1.86912e18 −0.934077
\(655\) 6.03911e17 0.298817
\(656\) 2.66204e18 1.30418
\(657\) 1.74313e17 0.0845580
\(658\) −3.88341e18 −1.86529
\(659\) 2.83726e18 1.34941 0.674706 0.738086i \(-0.264270\pi\)
0.674706 + 0.738086i \(0.264270\pi\)
\(660\) 1.56983e16 0.00739295
\(661\) −3.49795e18 −1.63119 −0.815594 0.578625i \(-0.803589\pi\)
−0.815594 + 0.578625i \(0.803589\pi\)
\(662\) −2.42301e18 −1.11887
\(663\) −7.69980e17 −0.352080
\(664\) 3.35121e17 0.151743
\(665\) 1.65101e16 0.00740304
\(666\) 1.36279e18 0.605126
\(667\) 6.29342e18 2.76738
\(668\) 2.11142e17 0.0919448
\(669\) −5.55644e17 −0.239622
\(670\) −7.00145e17 −0.299021
\(671\) 6.02548e17 0.254856
\(672\) 1.05342e18 0.441268
\(673\) 2.56691e18 1.06491 0.532455 0.846458i \(-0.321270\pi\)
0.532455 + 0.846458i \(0.321270\pi\)
\(674\) 2.67186e18 1.09780
\(675\) −4.35259e17 −0.177122
\(676\) −6.17679e17 −0.248948
\(677\) 2.29224e18 0.915028 0.457514 0.889202i \(-0.348740\pi\)
0.457514 + 0.889202i \(0.348740\pi\)
\(678\) 1.57876e18 0.624199
\(679\) 2.34133e18 0.916873
\(680\) 1.12381e18 0.435899
\(681\) 2.16786e18 0.832865
\(682\) 8.09957e17 0.308222
\(683\) −4.35324e18 −1.64088 −0.820442 0.571730i \(-0.806273\pi\)
−0.820442 + 0.571730i \(0.806273\pi\)
\(684\) −4.60382e15 −0.00171891
\(685\) −6.43445e17 −0.237970
\(686\) 1.25476e16 0.00459679
\(687\) 2.37918e17 0.0863391
\(688\) −3.95207e18 −1.42069
\(689\) 1.66500e18 0.592911
\(690\) 9.34690e17 0.329722
\(691\) 2.24198e18 0.783475 0.391737 0.920077i \(-0.371874\pi\)
0.391737 + 0.920077i \(0.371874\pi\)
\(692\) −5.81305e17 −0.201240
\(693\) −2.24336e17 −0.0769366
\(694\) −1.25900e18 −0.427750
\(695\) −6.96133e17 −0.234310
\(696\) 2.18503e18 0.728612
\(697\) 6.22104e18 2.05518
\(698\) −1.41118e18 −0.461873
\(699\) 1.84579e18 0.598521
\(700\) −1.12471e18 −0.361330
\(701\) 7.33703e17 0.233536 0.116768 0.993159i \(-0.462747\pi\)
0.116768 + 0.993159i \(0.462747\pi\)
\(702\) −2.22343e17 −0.0701185
\(703\) 9.54051e16 0.0298100
\(704\) −3.10880e17 −0.0962433
\(705\) −6.20238e17 −0.190252
\(706\) 4.74654e18 1.44260
\(707\) 2.10912e18 0.635149
\(708\) −6.99803e16 −0.0208814
\(709\) −1.88660e18 −0.557802 −0.278901 0.960320i \(-0.589970\pi\)
−0.278901 + 0.960320i \(0.589970\pi\)
\(710\) 1.95886e17 0.0573885
\(711\) 1.60407e16 0.00465661
\(712\) −1.24504e18 −0.358149
\(713\) 1.04847e19 2.98865
\(714\) 6.17780e18 1.74500
\(715\) 5.30765e16 0.0148564
\(716\) 1.18674e18 0.329171
\(717\) 1.07358e18 0.295093
\(718\) 1.47684e18 0.402277
\(719\) −4.39256e18 −1.18571 −0.592857 0.805308i \(-0.702000\pi\)
−0.592857 + 0.805308i \(0.702000\pi\)
\(720\) 4.22211e17 0.112945
\(721\) −6.13725e18 −1.62703
\(722\) 4.30106e18 1.13001
\(723\) 2.30678e18 0.600630
\(724\) 4.35308e17 0.112330
\(725\) −5.56320e18 −1.42275
\(726\) 2.50621e18 0.635229
\(727\) −4.05770e18 −1.01931 −0.509655 0.860379i \(-0.670227\pi\)
−0.509655 + 0.860379i \(0.670227\pi\)
\(728\) 1.49356e18 0.371851
\(729\) 1.50095e17 0.0370370
\(730\) 3.30893e17 0.0809261
\(731\) −9.23579e18 −2.23878
\(732\) −1.04172e18 −0.250282
\(733\) −6.78795e17 −0.161645 −0.0808226 0.996729i \(-0.525755\pi\)
−0.0808226 + 0.996729i \(0.525755\pi\)
\(734\) −4.56200e18 −1.07679
\(735\) −6.94441e17 −0.162468
\(736\) 4.17506e18 0.968182
\(737\) 6.66009e17 0.153088
\(738\) 1.79642e18 0.409299
\(739\) 3.45469e18 0.780225 0.390113 0.920767i \(-0.372436\pi\)
0.390113 + 0.920767i \(0.372436\pi\)
\(740\) 5.62427e17 0.125910
\(741\) −1.55656e16 −0.00345421
\(742\) −1.33588e19 −2.93862
\(743\) −5.30362e18 −1.15650 −0.578249 0.815860i \(-0.696264\pi\)
−0.578249 + 0.815860i \(0.696264\pi\)
\(744\) 3.64021e18 0.786870
\(745\) 4.93974e17 0.105849
\(746\) −8.15978e18 −1.73331
\(747\) 2.94230e17 0.0619588
\(748\) 4.11225e17 0.0858458
\(749\) 3.82562e18 0.791717
\(750\) −1.72398e18 −0.353699
\(751\) 6.33957e17 0.128944 0.0644719 0.997920i \(-0.479464\pi\)
0.0644719 + 0.997920i \(0.479464\pi\)
\(752\) −6.95241e18 −1.40191
\(753\) −3.57216e18 −0.714107
\(754\) −2.84184e18 −0.563231
\(755\) 1.36760e18 0.268722
\(756\) 3.87845e17 0.0755556
\(757\) −3.67271e18 −0.709355 −0.354677 0.934989i \(-0.615409\pi\)
−0.354677 + 0.934989i \(0.615409\pi\)
\(758\) −5.46463e18 −1.04643
\(759\) −8.89118e17 −0.168806
\(760\) 2.27186e16 0.00427654
\(761\) 1.00521e19 1.87611 0.938056 0.346485i \(-0.112625\pi\)
0.938056 + 0.346485i \(0.112625\pi\)
\(762\) 1.12450e18 0.208091
\(763\) 1.10236e19 2.02261
\(764\) −8.45855e17 −0.153882
\(765\) 9.86685e17 0.177983
\(766\) −2.46642e18 −0.441144
\(767\) −2.36606e17 −0.0419619
\(768\) 2.54462e18 0.447482
\(769\) 4.26376e18 0.743485 0.371742 0.928336i \(-0.378760\pi\)
0.371742 + 0.928336i \(0.378760\pi\)
\(770\) −4.25850e17 −0.0736321
\(771\) 2.03732e18 0.349305
\(772\) 8.52209e17 0.144888
\(773\) 6.88616e18 1.16094 0.580471 0.814281i \(-0.302869\pi\)
0.580471 + 0.814281i \(0.302869\pi\)
\(774\) −2.66697e18 −0.445864
\(775\) −9.26819e18 −1.53650
\(776\) 3.22176e18 0.529654
\(777\) −8.03734e18 −1.31032
\(778\) −6.43168e18 −1.03982
\(779\) 1.25762e17 0.0201631
\(780\) −9.17618e16 −0.0145897
\(781\) −1.86336e17 −0.0293808
\(782\) 2.44847e19 3.82869
\(783\) 1.91841e18 0.297502
\(784\) −7.78417e18 −1.19718
\(785\) −3.43585e17 −0.0524061
\(786\) 4.56819e18 0.691031
\(787\) 5.53498e18 0.830386 0.415193 0.909733i \(-0.363714\pi\)
0.415193 + 0.909733i \(0.363714\pi\)
\(788\) 2.36627e18 0.352083
\(789\) 4.42397e18 0.652847
\(790\) 3.04495e16 0.00445660
\(791\) −9.31108e18 −1.35161
\(792\) −3.08695e17 −0.0444443
\(793\) −3.52209e18 −0.502950
\(794\) −5.06495e18 −0.717368
\(795\) −2.13360e18 −0.299728
\(796\) 3.60030e18 0.501654
\(797\) −4.66478e18 −0.644691 −0.322346 0.946622i \(-0.604471\pi\)
−0.322346 + 0.946622i \(0.604471\pi\)
\(798\) 1.24888e17 0.0171200
\(799\) −1.62474e19 −2.20918
\(800\) −3.69063e18 −0.497755
\(801\) −1.09312e18 −0.146237
\(802\) −7.77574e18 −1.03183
\(803\) −3.14760e17 −0.0414313
\(804\) −1.15143e18 −0.150340
\(805\) −5.51254e18 −0.713968
\(806\) −4.73446e18 −0.608265
\(807\) −1.15483e18 −0.147177
\(808\) 2.90223e18 0.366909
\(809\) 1.15917e19 1.45373 0.726865 0.686781i \(-0.240977\pi\)
0.726865 + 0.686781i \(0.240977\pi\)
\(810\) 2.84920e17 0.0354462
\(811\) −1.26453e19 −1.56061 −0.780303 0.625401i \(-0.784935\pi\)
−0.780303 + 0.625401i \(0.784935\pi\)
\(812\) 4.95719e18 0.606905
\(813\) −4.41837e18 −0.536628
\(814\) −2.46081e18 −0.296496
\(815\) −3.32323e16 −0.00397225
\(816\) 1.10600e19 1.31150
\(817\) −1.86708e17 −0.0219644
\(818\) −7.55342e18 −0.881550
\(819\) 1.31132e18 0.151832
\(820\) 7.41388e17 0.0851639
\(821\) 5.27633e18 0.601314 0.300657 0.953732i \(-0.402794\pi\)
0.300657 + 0.953732i \(0.402794\pi\)
\(822\) −4.86723e18 −0.550320
\(823\) 1.62086e19 1.81822 0.909109 0.416558i \(-0.136764\pi\)
0.909109 + 0.416558i \(0.136764\pi\)
\(824\) −8.44508e18 −0.939890
\(825\) 7.85954e17 0.0867854
\(826\) 1.89836e18 0.207974
\(827\) 2.39103e18 0.259895 0.129948 0.991521i \(-0.458519\pi\)
0.129948 + 0.991521i \(0.458519\pi\)
\(828\) 1.53716e18 0.165776
\(829\) −5.11216e18 −0.547016 −0.273508 0.961870i \(-0.588184\pi\)
−0.273508 + 0.961870i \(0.588184\pi\)
\(830\) 5.58527e17 0.0592976
\(831\) −8.02699e18 −0.845563
\(832\) 1.81720e18 0.189933
\(833\) −1.81912e19 −1.88655
\(834\) −5.26578e18 −0.541855
\(835\) −9.14792e17 −0.0934029
\(836\) 8.31318e15 0.000842222 0
\(837\) 3.19604e18 0.321290
\(838\) −5.30661e18 −0.529335
\(839\) 1.31828e19 1.30484 0.652418 0.757859i \(-0.273755\pi\)
0.652418 + 0.757859i \(0.273755\pi\)
\(840\) −1.91391e18 −0.187978
\(841\) 1.42592e19 1.38971
\(842\) −2.52699e18 −0.244385
\(843\) 6.19851e18 0.594851
\(844\) −2.38187e18 −0.226826
\(845\) 2.67615e18 0.252896
\(846\) −4.69169e18 −0.439969
\(847\) −1.47810e19 −1.37550
\(848\) −2.39161e19 −2.20860
\(849\) 1.33741e18 0.122564
\(850\) −2.16437e19 −1.96838
\(851\) −3.18546e19 −2.87495
\(852\) 3.22148e17 0.0288535
\(853\) −6.75596e18 −0.600507 −0.300253 0.953859i \(-0.597071\pi\)
−0.300253 + 0.953859i \(0.597071\pi\)
\(854\) 2.82589e19 2.49275
\(855\) 1.99465e16 0.00174617
\(856\) 5.26420e18 0.457354
\(857\) −1.81595e19 −1.56577 −0.782885 0.622167i \(-0.786253\pi\)
−0.782885 + 0.622167i \(0.786253\pi\)
\(858\) 4.01489e17 0.0343563
\(859\) 8.37991e18 0.711678 0.355839 0.934547i \(-0.384195\pi\)
0.355839 + 0.934547i \(0.384195\pi\)
\(860\) −1.10067e18 −0.0927719
\(861\) −1.05948e19 −0.886280
\(862\) −2.20066e19 −1.82707
\(863\) 3.86530e18 0.318503 0.159251 0.987238i \(-0.449092\pi\)
0.159251 + 0.987238i \(0.449092\pi\)
\(864\) 1.27268e18 0.104083
\(865\) 2.51856e18 0.204432
\(866\) −2.41033e19 −1.94183
\(867\) 1.86263e19 1.48937
\(868\) 8.25858e18 0.655431
\(869\) −2.89649e16 −0.00228162
\(870\) 3.64166e18 0.284724
\(871\) −3.89304e18 −0.302114
\(872\) 1.51688e19 1.16841
\(873\) 2.82864e18 0.216265
\(874\) 4.94973e17 0.0375628
\(875\) 1.01675e19 0.765885
\(876\) 5.44175e17 0.0406876
\(877\) 6.56613e18 0.487317 0.243659 0.969861i \(-0.421652\pi\)
0.243659 + 0.969861i \(0.421652\pi\)
\(878\) 1.23966e19 0.913244
\(879\) −5.18791e18 −0.379371
\(880\) −7.62393e17 −0.0553403
\(881\) −2.31895e19 −1.67089 −0.835446 0.549572i \(-0.814791\pi\)
−0.835446 + 0.549572i \(0.814791\pi\)
\(882\) −5.25298e18 −0.375716
\(883\) −9.76153e18 −0.693064 −0.346532 0.938038i \(-0.612641\pi\)
−0.346532 + 0.938038i \(0.612641\pi\)
\(884\) −2.40374e18 −0.169414
\(885\) 3.03197e17 0.0212126
\(886\) 4.86700e18 0.338020
\(887\) 9.48722e18 0.654087 0.327044 0.945009i \(-0.393948\pi\)
0.327044 + 0.945009i \(0.393948\pi\)
\(888\) −1.10597e19 −0.756935
\(889\) −6.63200e18 −0.450591
\(890\) −2.07504e18 −0.139956
\(891\) −2.71028e17 −0.0181472
\(892\) −1.73462e18 −0.115301
\(893\) −3.28452e17 −0.0216739
\(894\) 3.73659e18 0.244783
\(895\) −5.14168e18 −0.334391
\(896\) −2.64176e19 −1.70565
\(897\) 5.19718e18 0.333133
\(898\) −1.23861e19 −0.788206
\(899\) 4.08497e19 2.58078
\(900\) −1.35880e18 −0.0852277
\(901\) −5.58907e19 −3.48040
\(902\) −3.24382e18 −0.200546
\(903\) 1.57291e19 0.965455
\(904\) −1.28124e19 −0.780792
\(905\) −1.88602e18 −0.114111
\(906\) 1.03450e19 0.621436
\(907\) 2.20544e19 1.31537 0.657686 0.753293i \(-0.271536\pi\)
0.657686 + 0.753293i \(0.271536\pi\)
\(908\) 6.76768e18 0.400757
\(909\) 2.54810e18 0.149814
\(910\) 2.48923e18 0.145310
\(911\) −9.61120e18 −0.557068 −0.278534 0.960426i \(-0.589848\pi\)
−0.278534 + 0.960426i \(0.589848\pi\)
\(912\) 2.23585e17 0.0128670
\(913\) −5.31296e17 −0.0303582
\(914\) 2.51408e19 1.42636
\(915\) 4.51336e18 0.254251
\(916\) 7.42737e17 0.0415446
\(917\) −2.69419e19 −1.49633
\(918\) 7.46362e18 0.411597
\(919\) −4.68978e18 −0.256804 −0.128402 0.991722i \(-0.540985\pi\)
−0.128402 + 0.991722i \(0.540985\pi\)
\(920\) −7.58546e18 −0.412440
\(921\) 2.23665e18 0.120757
\(922\) −3.87557e19 −2.07771
\(923\) 1.08919e18 0.0579820
\(924\) −7.00339e17 −0.0370203
\(925\) 2.81586e19 1.47805
\(926\) 2.65233e19 1.38247
\(927\) −7.41462e18 −0.383770
\(928\) 1.62665e19 0.836051
\(929\) −1.15841e19 −0.591236 −0.295618 0.955306i \(-0.595526\pi\)
−0.295618 + 0.955306i \(0.595526\pi\)
\(930\) 6.06694e18 0.307490
\(931\) −3.67747e17 −0.0185087
\(932\) 5.76222e18 0.287996
\(933\) 1.76073e19 0.873901
\(934\) −6.22931e18 −0.307033
\(935\) −1.78167e18 −0.0872072
\(936\) 1.80442e18 0.0877092
\(937\) 9.56007e18 0.461481 0.230741 0.973015i \(-0.425885\pi\)
0.230741 + 0.973015i \(0.425885\pi\)
\(938\) 3.12351e19 1.49735
\(939\) −1.18607e19 −0.564654
\(940\) −1.93628e18 −0.0915453
\(941\) 9.33756e18 0.438431 0.219215 0.975676i \(-0.429650\pi\)
0.219215 + 0.975676i \(0.429650\pi\)
\(942\) −2.59899e18 −0.121192
\(943\) −4.19906e19 −1.94458
\(944\) 3.39861e18 0.156309
\(945\) −1.68038e18 −0.0767539
\(946\) 4.81579e18 0.218462
\(947\) 2.92837e19 1.31932 0.659661 0.751563i \(-0.270700\pi\)
0.659661 + 0.751563i \(0.270700\pi\)
\(948\) 5.00761e16 0.00224066
\(949\) 1.83987e18 0.0817631
\(950\) −4.37542e17 −0.0193115
\(951\) −9.02639e18 −0.395677
\(952\) −5.01358e19 −2.18277
\(953\) −2.00892e19 −0.868679 −0.434340 0.900749i \(-0.643018\pi\)
−0.434340 + 0.900749i \(0.643018\pi\)
\(954\) −1.61393e19 −0.693138
\(955\) 3.66475e18 0.156323
\(956\) 3.35153e18 0.141993
\(957\) −3.46411e18 −0.145768
\(958\) −3.14978e19 −1.31645
\(959\) 2.87056e19 1.19164
\(960\) −2.32863e18 −0.0960147
\(961\) 4.36373e19 1.78713
\(962\) 1.43842e19 0.585125
\(963\) 4.62186e18 0.186744
\(964\) 7.20137e18 0.289011
\(965\) −3.69228e18 −0.147186
\(966\) −4.16987e19 −1.65109
\(967\) −7.24814e18 −0.285072 −0.142536 0.989790i \(-0.545526\pi\)
−0.142536 + 0.989790i \(0.545526\pi\)
\(968\) −2.03391e19 −0.794590
\(969\) 5.22508e17 0.0202763
\(970\) 5.36952e18 0.206976
\(971\) 3.66311e19 1.40257 0.701285 0.712881i \(-0.252610\pi\)
0.701285 + 0.712881i \(0.252610\pi\)
\(972\) 4.68570e17 0.0178215
\(973\) 3.10561e19 1.17331
\(974\) 1.88640e19 0.707947
\(975\) −4.59416e18 −0.171268
\(976\) 5.05914e19 1.87350
\(977\) 3.40906e19 1.25407 0.627033 0.778993i \(-0.284269\pi\)
0.627033 + 0.778993i \(0.284269\pi\)
\(978\) −2.51380e17 −0.00918605
\(979\) 1.97387e18 0.0716523
\(980\) −2.16792e18 −0.0781762
\(981\) 1.33180e19 0.477077
\(982\) −2.58214e19 −0.918873
\(983\) 1.21319e19 0.428874 0.214437 0.976738i \(-0.431208\pi\)
0.214437 + 0.976738i \(0.431208\pi\)
\(984\) −1.45788e19 −0.511981
\(985\) −1.02521e19 −0.357666
\(986\) 9.53950e19 3.30618
\(987\) 2.76703e19 0.952690
\(988\) −4.85933e16 −0.00166210
\(989\) 6.23394e19 2.11830
\(990\) −5.14484e17 −0.0173677
\(991\) 5.37442e19 1.80241 0.901204 0.433395i \(-0.142685\pi\)
0.901204 + 0.433395i \(0.142685\pi\)
\(992\) 2.70997e19 0.902899
\(993\) 1.72646e19 0.571460
\(994\) −8.73894e18 −0.287374
\(995\) −1.55987e19 −0.509609
\(996\) 9.18535e17 0.0298133
\(997\) −3.97542e19 −1.28193 −0.640964 0.767571i \(-0.721465\pi\)
−0.640964 + 0.767571i \(0.721465\pi\)
\(998\) 3.05830e19 0.979788
\(999\) −9.71019e18 −0.309067
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.1.8 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.8 31 1.1 even 1 trivial