Properties

Label 177.14.a.c.1.15
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $0$
Dimension $31$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.15
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.12446 q^{2} +729.000 q^{3} -8190.74 q^{4} -53521.6 q^{5} -819.732 q^{6} +445275. q^{7} +18421.7 q^{8} +531441. q^{9} +O(q^{10})\) \(q-1.12446 q^{2} +729.000 q^{3} -8190.74 q^{4} -53521.6 q^{5} -819.732 q^{6} +445275. q^{7} +18421.7 q^{8} +531441. q^{9} +60183.0 q^{10} +4.07152e6 q^{11} -5.97105e6 q^{12} +2.06685e7 q^{13} -500694. q^{14} -3.90173e7 q^{15} +6.70778e7 q^{16} +1.55027e7 q^{17} -597585. q^{18} -3.30972e8 q^{19} +4.38382e8 q^{20} +3.24605e8 q^{21} -4.57826e6 q^{22} -3.80918e8 q^{23} +1.34294e7 q^{24} +1.64386e9 q^{25} -2.32409e7 q^{26} +3.87420e8 q^{27} -3.64713e9 q^{28} +3.38409e9 q^{29} +4.38734e7 q^{30} +6.98563e9 q^{31} -2.26337e8 q^{32} +2.96814e9 q^{33} -1.74321e7 q^{34} -2.38318e10 q^{35} -4.35289e9 q^{36} +8.29474e9 q^{37} +3.72165e8 q^{38} +1.50673e10 q^{39} -9.85962e8 q^{40} +4.02532e10 q^{41} -3.65006e8 q^{42} -5.64046e10 q^{43} -3.33487e10 q^{44} -2.84436e10 q^{45} +4.28327e8 q^{46} -1.39143e11 q^{47} +4.88997e10 q^{48} +1.01381e11 q^{49} -1.84846e9 q^{50} +1.13014e10 q^{51} -1.69290e11 q^{52} +3.09377e10 q^{53} -4.35639e8 q^{54} -2.17914e11 q^{55} +8.20274e9 q^{56} -2.41279e11 q^{57} -3.80528e9 q^{58} -4.21805e10 q^{59} +3.19580e11 q^{60} -6.44956e11 q^{61} -7.85507e9 q^{62} +2.36637e11 q^{63} -5.49247e11 q^{64} -1.10621e12 q^{65} -3.33755e9 q^{66} -1.03241e12 q^{67} -1.26978e11 q^{68} -2.77689e11 q^{69} +2.67980e10 q^{70} +1.62556e12 q^{71} +9.79007e9 q^{72} -8.01233e11 q^{73} -9.32711e9 q^{74} +1.19838e12 q^{75} +2.71091e12 q^{76} +1.81295e12 q^{77} -1.69426e10 q^{78} -1.43639e12 q^{79} -3.59011e12 q^{80} +2.82430e11 q^{81} -4.52632e10 q^{82} +1.93924e12 q^{83} -2.65876e12 q^{84} -8.29728e11 q^{85} +6.34247e10 q^{86} +2.46700e12 q^{87} +7.50045e10 q^{88} +1.58905e12 q^{89} +3.19837e10 q^{90} +9.20317e12 q^{91} +3.12000e12 q^{92} +5.09252e12 q^{93} +1.56461e11 q^{94} +1.77142e13 q^{95} -1.65000e11 q^{96} +9.46461e12 q^{97} -1.13999e11 q^{98} +2.16377e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.12446 −0.0124237 −0.00621183 0.999981i \(-0.501977\pi\)
−0.00621183 + 0.999981i \(0.501977\pi\)
\(3\) 729.000 0.577350
\(4\) −8190.74 −0.999846
\(5\) −53521.6 −1.53188 −0.765939 0.642913i \(-0.777726\pi\)
−0.765939 + 0.642913i \(0.777726\pi\)
\(6\) −819.732 −0.00717280
\(7\) 445275. 1.43051 0.715255 0.698863i \(-0.246310\pi\)
0.715255 + 0.698863i \(0.246310\pi\)
\(8\) 18421.7 0.0248454
\(9\) 531441. 0.333333
\(10\) 60183.0 0.0190315
\(11\) 4.07152e6 0.692954 0.346477 0.938059i \(-0.387378\pi\)
0.346477 + 0.938059i \(0.387378\pi\)
\(12\) −5.97105e6 −0.577261
\(13\) 2.06685e7 1.18762 0.593810 0.804605i \(-0.297623\pi\)
0.593810 + 0.804605i \(0.297623\pi\)
\(14\) −500694. −0.0177722
\(15\) −3.90173e7 −0.884431
\(16\) 6.70778e7 0.999537
\(17\) 1.55027e7 0.155772 0.0778858 0.996962i \(-0.475183\pi\)
0.0778858 + 0.996962i \(0.475183\pi\)
\(18\) −597585. −0.00414122
\(19\) −3.30972e8 −1.61396 −0.806981 0.590578i \(-0.798900\pi\)
−0.806981 + 0.590578i \(0.798900\pi\)
\(20\) 4.38382e8 1.53164
\(21\) 3.24605e8 0.825906
\(22\) −4.57826e6 −0.00860901
\(23\) −3.80918e8 −0.536538 −0.268269 0.963344i \(-0.586452\pi\)
−0.268269 + 0.963344i \(0.586452\pi\)
\(24\) 1.34294e7 0.0143445
\(25\) 1.64386e9 1.34665
\(26\) −2.32409e7 −0.0147546
\(27\) 3.87420e8 0.192450
\(28\) −3.64713e9 −1.43029
\(29\) 3.38409e9 1.05646 0.528232 0.849100i \(-0.322855\pi\)
0.528232 + 0.849100i \(0.322855\pi\)
\(30\) 4.38734e7 0.0109879
\(31\) 6.98563e9 1.41369 0.706846 0.707368i \(-0.250118\pi\)
0.706846 + 0.707368i \(0.250118\pi\)
\(32\) −2.26337e8 −0.0372633
\(33\) 2.96814e9 0.400077
\(34\) −1.74321e7 −0.00193525
\(35\) −2.38318e10 −2.19137
\(36\) −4.35289e9 −0.333282
\(37\) 8.29474e9 0.531486 0.265743 0.964044i \(-0.414383\pi\)
0.265743 + 0.964044i \(0.414383\pi\)
\(38\) 3.72165e8 0.0200513
\(39\) 1.50673e10 0.685673
\(40\) −9.85962e8 −0.0380601
\(41\) 4.02532e10 1.32344 0.661722 0.749749i \(-0.269826\pi\)
0.661722 + 0.749749i \(0.269826\pi\)
\(42\) −3.65006e8 −0.0102608
\(43\) −5.64046e10 −1.36072 −0.680361 0.732877i \(-0.738177\pi\)
−0.680361 + 0.732877i \(0.738177\pi\)
\(44\) −3.33487e10 −0.692847
\(45\) −2.84436e10 −0.510626
\(46\) 4.28327e8 0.00666576
\(47\) −1.39143e11 −1.88290 −0.941448 0.337158i \(-0.890534\pi\)
−0.941448 + 0.337158i \(0.890534\pi\)
\(48\) 4.88997e10 0.577083
\(49\) 1.01381e11 1.04636
\(50\) −1.84846e9 −0.0167303
\(51\) 1.13014e10 0.0899347
\(52\) −1.69290e11 −1.18744
\(53\) 3.09377e10 0.191732 0.0958662 0.995394i \(-0.469438\pi\)
0.0958662 + 0.995394i \(0.469438\pi\)
\(54\) −4.35639e8 −0.00239093
\(55\) −2.17914e11 −1.06152
\(56\) 8.20274e9 0.0355416
\(57\) −2.41279e11 −0.931821
\(58\) −3.80528e9 −0.0131251
\(59\) −4.21805e10 −0.130189
\(60\) 3.19580e11 0.884294
\(61\) −6.44956e11 −1.60283 −0.801413 0.598111i \(-0.795918\pi\)
−0.801413 + 0.598111i \(0.795918\pi\)
\(62\) −7.85507e9 −0.0175632
\(63\) 2.36637e11 0.476837
\(64\) −5.49247e11 −0.999074
\(65\) −1.10621e12 −1.81929
\(66\) −3.33755e9 −0.00497042
\(67\) −1.03241e12 −1.39434 −0.697168 0.716908i \(-0.745557\pi\)
−0.697168 + 0.716908i \(0.745557\pi\)
\(68\) −1.26978e11 −0.155748
\(69\) −2.77689e11 −0.309771
\(70\) 2.67980e10 0.0272248
\(71\) 1.62556e12 1.50599 0.752997 0.658024i \(-0.228608\pi\)
0.752997 + 0.658024i \(0.228608\pi\)
\(72\) 9.79007e9 0.00828180
\(73\) −8.01233e11 −0.619669 −0.309835 0.950790i \(-0.600274\pi\)
−0.309835 + 0.950790i \(0.600274\pi\)
\(74\) −9.32711e9 −0.00660299
\(75\) 1.19838e12 0.777490
\(76\) 2.71091e12 1.61371
\(77\) 1.81295e12 0.991277
\(78\) −1.69426e10 −0.00851856
\(79\) −1.43639e12 −0.664809 −0.332405 0.943137i \(-0.607860\pi\)
−0.332405 + 0.943137i \(0.607860\pi\)
\(80\) −3.59011e12 −1.53117
\(81\) 2.82430e11 0.111111
\(82\) −4.52632e10 −0.0164420
\(83\) 1.93924e12 0.651065 0.325532 0.945531i \(-0.394457\pi\)
0.325532 + 0.945531i \(0.394457\pi\)
\(84\) −2.65876e12 −0.825778
\(85\) −8.29728e11 −0.238623
\(86\) 6.34247e10 0.0169051
\(87\) 2.46700e12 0.609950
\(88\) 7.50045e10 0.0172167
\(89\) 1.58905e12 0.338924 0.169462 0.985537i \(-0.445797\pi\)
0.169462 + 0.985537i \(0.445797\pi\)
\(90\) 3.19837e10 0.00634384
\(91\) 9.20317e12 1.69890
\(92\) 3.12000e12 0.536455
\(93\) 5.09252e12 0.816195
\(94\) 1.56461e11 0.0233924
\(95\) 1.77142e13 2.47239
\(96\) −1.65000e11 −0.0215140
\(97\) 9.46461e12 1.15368 0.576841 0.816856i \(-0.304285\pi\)
0.576841 + 0.816856i \(0.304285\pi\)
\(98\) −1.13999e11 −0.0129996
\(99\) 2.16377e12 0.230985
\(100\) −1.34644e13 −1.34644
\(101\) −4.54631e12 −0.426158 −0.213079 0.977035i \(-0.568349\pi\)
−0.213079 + 0.977035i \(0.568349\pi\)
\(102\) −1.27080e10 −0.00111732
\(103\) 1.34900e13 1.11319 0.556595 0.830784i \(-0.312108\pi\)
0.556595 + 0.830784i \(0.312108\pi\)
\(104\) 3.80750e11 0.0295069
\(105\) −1.73734e13 −1.26519
\(106\) −3.47883e10 −0.00238202
\(107\) 2.11168e13 1.36029 0.680147 0.733075i \(-0.261916\pi\)
0.680147 + 0.733075i \(0.261916\pi\)
\(108\) −3.17326e12 −0.192420
\(109\) −1.62894e13 −0.930324 −0.465162 0.885226i \(-0.654004\pi\)
−0.465162 + 0.885226i \(0.654004\pi\)
\(110\) 2.45036e11 0.0131880
\(111\) 6.04686e12 0.306853
\(112\) 2.98681e13 1.42985
\(113\) 2.30674e12 0.104229 0.0521144 0.998641i \(-0.483404\pi\)
0.0521144 + 0.998641i \(0.483404\pi\)
\(114\) 2.71308e11 0.0115766
\(115\) 2.03874e13 0.821912
\(116\) −2.77182e13 −1.05630
\(117\) 1.09841e13 0.395873
\(118\) 4.74304e10 0.00161742
\(119\) 6.90294e12 0.222833
\(120\) −7.18766e11 −0.0219740
\(121\) −1.79454e13 −0.519815
\(122\) 7.25228e11 0.0199130
\(123\) 2.93446e13 0.764091
\(124\) −5.72174e13 −1.41347
\(125\) −2.26482e13 −0.531029
\(126\) −2.66089e11 −0.00592405
\(127\) −4.24645e13 −0.898053 −0.449026 0.893519i \(-0.648229\pi\)
−0.449026 + 0.893519i \(0.648229\pi\)
\(128\) 2.47176e12 0.0496754
\(129\) −4.11189e13 −0.785613
\(130\) 1.24389e12 0.0226022
\(131\) 5.15262e13 0.890768 0.445384 0.895340i \(-0.353067\pi\)
0.445384 + 0.895340i \(0.353067\pi\)
\(132\) −2.43112e13 −0.400015
\(133\) −1.47374e14 −2.30879
\(134\) 1.16091e12 0.0173227
\(135\) −2.07354e13 −0.294810
\(136\) 2.85586e11 0.00387020
\(137\) 1.11549e14 1.44139 0.720695 0.693253i \(-0.243823\pi\)
0.720695 + 0.693253i \(0.243823\pi\)
\(138\) 3.12251e11 0.00384848
\(139\) −7.68261e13 −0.903467 −0.451734 0.892153i \(-0.649194\pi\)
−0.451734 + 0.892153i \(0.649194\pi\)
\(140\) 1.95200e14 2.19103
\(141\) −1.01435e14 −1.08709
\(142\) −1.82788e12 −0.0187099
\(143\) 8.41523e13 0.822965
\(144\) 3.56479e13 0.333179
\(145\) −1.81122e14 −1.61838
\(146\) 9.00955e11 0.00769856
\(147\) 7.39066e13 0.604116
\(148\) −6.79400e13 −0.531404
\(149\) 2.24493e14 1.68071 0.840354 0.542038i \(-0.182347\pi\)
0.840354 + 0.542038i \(0.182347\pi\)
\(150\) −1.34753e12 −0.00965927
\(151\) 4.25744e13 0.292279 0.146140 0.989264i \(-0.453315\pi\)
0.146140 + 0.989264i \(0.453315\pi\)
\(152\) −6.09709e12 −0.0400995
\(153\) 8.23875e12 0.0519238
\(154\) −2.03859e12 −0.0123153
\(155\) −3.73882e14 −2.16560
\(156\) −1.23413e14 −0.685567
\(157\) 1.87965e14 1.00168 0.500840 0.865540i \(-0.333024\pi\)
0.500840 + 0.865540i \(0.333024\pi\)
\(158\) 1.61517e12 0.00825936
\(159\) 2.25536e13 0.110697
\(160\) 1.21139e13 0.0570828
\(161\) −1.69613e14 −0.767524
\(162\) −3.17581e11 −0.00138041
\(163\) 4.26662e14 1.78182 0.890911 0.454178i \(-0.150067\pi\)
0.890911 + 0.454178i \(0.150067\pi\)
\(164\) −3.29703e14 −1.32324
\(165\) −1.58860e14 −0.612869
\(166\) −2.18060e12 −0.00808860
\(167\) −1.93549e14 −0.690452 −0.345226 0.938520i \(-0.612198\pi\)
−0.345226 + 0.938520i \(0.612198\pi\)
\(168\) 5.97980e12 0.0205199
\(169\) 1.24312e14 0.410441
\(170\) 9.32996e11 0.00296457
\(171\) −1.75892e14 −0.537987
\(172\) 4.61995e14 1.36051
\(173\) 3.70120e14 1.04965 0.524823 0.851212i \(-0.324132\pi\)
0.524823 + 0.851212i \(0.324132\pi\)
\(174\) −2.77405e12 −0.00757781
\(175\) 7.31971e14 1.92640
\(176\) 2.73109e14 0.692633
\(177\) −3.07496e13 −0.0751646
\(178\) −1.78682e12 −0.00421068
\(179\) 1.44118e14 0.327471 0.163735 0.986504i \(-0.447646\pi\)
0.163735 + 0.986504i \(0.447646\pi\)
\(180\) 2.32974e14 0.510547
\(181\) 4.26043e14 0.900623 0.450311 0.892872i \(-0.351313\pi\)
0.450311 + 0.892872i \(0.351313\pi\)
\(182\) −1.03486e13 −0.0211066
\(183\) −4.70173e14 −0.925392
\(184\) −7.01718e12 −0.0133305
\(185\) −4.43948e14 −0.814171
\(186\) −5.72634e12 −0.0101401
\(187\) 6.31194e13 0.107942
\(188\) 1.13969e15 1.88261
\(189\) 1.72509e14 0.275302
\(190\) −1.99189e13 −0.0307162
\(191\) 5.86860e14 0.874617 0.437308 0.899312i \(-0.355932\pi\)
0.437308 + 0.899312i \(0.355932\pi\)
\(192\) −4.00401e14 −0.576816
\(193\) 3.83722e14 0.534435 0.267217 0.963636i \(-0.413896\pi\)
0.267217 + 0.963636i \(0.413896\pi\)
\(194\) −1.06426e13 −0.0143329
\(195\) −8.06429e14 −1.05037
\(196\) −8.30383e14 −1.04620
\(197\) −1.46844e15 −1.78989 −0.894943 0.446181i \(-0.852784\pi\)
−0.894943 + 0.446181i \(0.852784\pi\)
\(198\) −2.43308e12 −0.00286967
\(199\) 1.36051e14 0.155295 0.0776475 0.996981i \(-0.475259\pi\)
0.0776475 + 0.996981i \(0.475259\pi\)
\(200\) 3.02828e13 0.0334581
\(201\) −7.52629e14 −0.805020
\(202\) 5.11215e12 0.00529444
\(203\) 1.50685e15 1.51128
\(204\) −9.25671e13 −0.0899209
\(205\) −2.15442e15 −2.02736
\(206\) −1.51690e13 −0.0138299
\(207\) −2.02436e14 −0.178846
\(208\) 1.38640e15 1.18707
\(209\) −1.34756e15 −1.11840
\(210\) 1.95357e13 0.0157182
\(211\) 1.48597e15 1.15925 0.579623 0.814885i \(-0.303200\pi\)
0.579623 + 0.814885i \(0.303200\pi\)
\(212\) −2.53403e14 −0.191703
\(213\) 1.18503e15 0.869486
\(214\) −2.37450e13 −0.0168998
\(215\) 3.01887e15 2.08446
\(216\) 7.13696e12 0.00478150
\(217\) 3.11053e15 2.02230
\(218\) 1.83168e13 0.0115580
\(219\) −5.84099e14 −0.357766
\(220\) 1.78488e15 1.06136
\(221\) 3.20417e14 0.184997
\(222\) −6.79946e12 −0.00381224
\(223\) 2.09683e15 1.14178 0.570888 0.821028i \(-0.306599\pi\)
0.570888 + 0.821028i \(0.306599\pi\)
\(224\) −1.00782e14 −0.0533055
\(225\) 8.73616e14 0.448884
\(226\) −2.59383e12 −0.00129490
\(227\) 1.30180e15 0.631505 0.315752 0.948842i \(-0.397743\pi\)
0.315752 + 0.948842i \(0.397743\pi\)
\(228\) 1.97625e15 0.931677
\(229\) −3.18073e15 −1.45746 −0.728729 0.684802i \(-0.759889\pi\)
−0.728729 + 0.684802i \(0.759889\pi\)
\(230\) −2.29248e13 −0.0102111
\(231\) 1.32164e15 0.572314
\(232\) 6.23408e13 0.0262483
\(233\) 6.38047e14 0.261240 0.130620 0.991433i \(-0.458303\pi\)
0.130620 + 0.991433i \(0.458303\pi\)
\(234\) −1.23512e13 −0.00491819
\(235\) 7.44718e15 2.88437
\(236\) 3.45490e14 0.130169
\(237\) −1.04713e15 −0.383828
\(238\) −7.76209e12 −0.00276840
\(239\) 6.97606e14 0.242116 0.121058 0.992645i \(-0.461371\pi\)
0.121058 + 0.992645i \(0.461371\pi\)
\(240\) −2.61719e15 −0.884021
\(241\) 2.84997e14 0.0936979 0.0468489 0.998902i \(-0.485082\pi\)
0.0468489 + 0.998902i \(0.485082\pi\)
\(242\) 2.01789e13 0.00645801
\(243\) 2.05891e14 0.0641500
\(244\) 5.28267e15 1.60258
\(245\) −5.42607e15 −1.60290
\(246\) −3.29968e13 −0.00949280
\(247\) −6.84070e15 −1.91677
\(248\) 1.28687e14 0.0351237
\(249\) 1.41371e15 0.375892
\(250\) 2.54670e13 0.00659732
\(251\) 3.10520e14 0.0783809 0.0391905 0.999232i \(-0.487522\pi\)
0.0391905 + 0.999232i \(0.487522\pi\)
\(252\) −1.93823e15 −0.476763
\(253\) −1.55092e15 −0.371796
\(254\) 4.77497e13 0.0111571
\(255\) −6.04871e14 −0.137769
\(256\) 4.49665e15 0.998457
\(257\) −3.87421e15 −0.838721 −0.419361 0.907820i \(-0.637746\pi\)
−0.419361 + 0.907820i \(0.637746\pi\)
\(258\) 4.62366e13 0.00976019
\(259\) 3.69344e15 0.760296
\(260\) 9.06070e15 1.81901
\(261\) 1.79844e15 0.352155
\(262\) −5.79392e13 −0.0110666
\(263\) −7.16286e15 −1.33467 −0.667335 0.744758i \(-0.732565\pi\)
−0.667335 + 0.744758i \(0.732565\pi\)
\(264\) 5.46783e13 0.00994007
\(265\) −1.65584e15 −0.293711
\(266\) 1.65716e14 0.0286836
\(267\) 1.15842e15 0.195678
\(268\) 8.45622e15 1.39412
\(269\) 8.10069e15 1.30356 0.651782 0.758407i \(-0.274022\pi\)
0.651782 + 0.758407i \(0.274022\pi\)
\(270\) 2.33161e13 0.00366262
\(271\) −1.42961e15 −0.219239 −0.109620 0.993974i \(-0.534963\pi\)
−0.109620 + 0.993974i \(0.534963\pi\)
\(272\) 1.03988e15 0.155699
\(273\) 6.70911e15 0.980862
\(274\) −1.25432e14 −0.0179073
\(275\) 6.69302e15 0.933168
\(276\) 2.27448e15 0.309723
\(277\) 3.07872e15 0.409499 0.204749 0.978814i \(-0.434362\pi\)
0.204749 + 0.978814i \(0.434362\pi\)
\(278\) 8.63879e13 0.0112244
\(279\) 3.71245e15 0.471230
\(280\) −4.39024e14 −0.0544454
\(281\) −1.00829e16 −1.22178 −0.610891 0.791714i \(-0.709189\pi\)
−0.610891 + 0.791714i \(0.709189\pi\)
\(282\) 1.14060e14 0.0135056
\(283\) −1.32688e16 −1.53539 −0.767696 0.640814i \(-0.778597\pi\)
−0.767696 + 0.640814i \(0.778597\pi\)
\(284\) −1.33145e16 −1.50576
\(285\) 1.29136e16 1.42744
\(286\) −9.46259e13 −0.0102242
\(287\) 1.79238e16 1.89320
\(288\) −1.20285e14 −0.0124211
\(289\) −9.66425e15 −0.975735
\(290\) 2.03665e14 0.0201061
\(291\) 6.89970e15 0.666079
\(292\) 6.56268e15 0.619574
\(293\) −2.25725e15 −0.208421 −0.104210 0.994555i \(-0.533231\pi\)
−0.104210 + 0.994555i \(0.533231\pi\)
\(294\) −8.31051e13 −0.00750533
\(295\) 2.25757e15 0.199434
\(296\) 1.52804e14 0.0132050
\(297\) 1.57739e15 0.133359
\(298\) −2.52434e14 −0.0208805
\(299\) −7.87301e15 −0.637203
\(300\) −9.81558e15 −0.777370
\(301\) −2.51156e16 −1.94653
\(302\) −4.78732e13 −0.00363118
\(303\) −3.31426e15 −0.246042
\(304\) −2.22009e16 −1.61321
\(305\) 3.45191e16 2.45534
\(306\) −9.26415e12 −0.000645084 0
\(307\) −1.24992e15 −0.0852085 −0.0426043 0.999092i \(-0.513565\pi\)
−0.0426043 + 0.999092i \(0.513565\pi\)
\(308\) −1.48494e16 −0.991124
\(309\) 9.83420e15 0.642701
\(310\) 4.20416e14 0.0269047
\(311\) 8.96059e15 0.561557 0.280779 0.959773i \(-0.409407\pi\)
0.280779 + 0.959773i \(0.409407\pi\)
\(312\) 2.77567e14 0.0170358
\(313\) 3.29749e16 1.98219 0.991094 0.133165i \(-0.0425140\pi\)
0.991094 + 0.133165i \(0.0425140\pi\)
\(314\) −2.11359e14 −0.0124445
\(315\) −1.26652e16 −0.730456
\(316\) 1.17651e16 0.664707
\(317\) −3.26982e16 −1.80983 −0.904916 0.425590i \(-0.860067\pi\)
−0.904916 + 0.425590i \(0.860067\pi\)
\(318\) −2.53606e13 −0.00137526
\(319\) 1.37784e16 0.732081
\(320\) 2.93966e16 1.53046
\(321\) 1.53941e16 0.785366
\(322\) 1.90723e14 0.00953545
\(323\) −5.13095e15 −0.251409
\(324\) −2.31331e15 −0.111094
\(325\) 3.39762e16 1.59931
\(326\) −4.79764e14 −0.0221367
\(327\) −1.18750e16 −0.537123
\(328\) 7.41534e14 0.0328815
\(329\) −6.19570e16 −2.69350
\(330\) 1.78631e14 0.00761408
\(331\) 7.92757e15 0.331328 0.165664 0.986182i \(-0.447023\pi\)
0.165664 + 0.986182i \(0.447023\pi\)
\(332\) −1.58838e16 −0.650964
\(333\) 4.40816e15 0.177162
\(334\) 2.17638e14 0.00857793
\(335\) 5.52564e16 2.13595
\(336\) 2.17738e16 0.825523
\(337\) −9.13829e15 −0.339837 −0.169918 0.985458i \(-0.554350\pi\)
−0.169918 + 0.985458i \(0.554350\pi\)
\(338\) −1.39784e14 −0.00509917
\(339\) 1.68161e15 0.0601766
\(340\) 6.79608e15 0.238586
\(341\) 2.84421e16 0.979622
\(342\) 1.97784e14 0.00668377
\(343\) 2.00008e15 0.0663186
\(344\) −1.03907e15 −0.0338077
\(345\) 1.48624e16 0.474531
\(346\) −4.16185e14 −0.0130404
\(347\) 5.15300e16 1.58460 0.792299 0.610133i \(-0.208884\pi\)
0.792299 + 0.610133i \(0.208884\pi\)
\(348\) −2.02066e16 −0.609856
\(349\) −2.85815e15 −0.0846680 −0.0423340 0.999104i \(-0.513479\pi\)
−0.0423340 + 0.999104i \(0.513479\pi\)
\(350\) −8.23072e14 −0.0239329
\(351\) 8.00741e15 0.228558
\(352\) −9.21537e14 −0.0258217
\(353\) 2.47280e16 0.680227 0.340114 0.940384i \(-0.389534\pi\)
0.340114 + 0.940384i \(0.389534\pi\)
\(354\) 3.45767e13 0.000933819 0
\(355\) −8.70025e16 −2.30700
\(356\) −1.30155e16 −0.338872
\(357\) 5.03225e15 0.128653
\(358\) −1.62055e14 −0.00406838
\(359\) 3.14105e16 0.774392 0.387196 0.921997i \(-0.373444\pi\)
0.387196 + 0.921997i \(0.373444\pi\)
\(360\) −5.23981e14 −0.0126867
\(361\) 6.74897e16 1.60487
\(362\) −4.79069e14 −0.0111890
\(363\) −1.30822e16 −0.300116
\(364\) −7.53807e16 −1.69864
\(365\) 4.28833e16 0.949258
\(366\) 5.28691e14 0.0114967
\(367\) 2.15939e16 0.461320 0.230660 0.973034i \(-0.425911\pi\)
0.230660 + 0.973034i \(0.425911\pi\)
\(368\) −2.55511e16 −0.536290
\(369\) 2.13922e16 0.441148
\(370\) 4.99202e14 0.0101150
\(371\) 1.37758e16 0.274275
\(372\) −4.17115e16 −0.816069
\(373\) 6.94694e16 1.33563 0.667815 0.744328i \(-0.267230\pi\)
0.667815 + 0.744328i \(0.267230\pi\)
\(374\) −7.09753e13 −0.00134104
\(375\) −1.65105e16 −0.306590
\(376\) −2.56326e15 −0.0467813
\(377\) 6.99441e16 1.25468
\(378\) −1.93979e14 −0.00342025
\(379\) −3.13899e16 −0.544045 −0.272022 0.962291i \(-0.587692\pi\)
−0.272022 + 0.962291i \(0.587692\pi\)
\(380\) −1.45092e17 −2.47201
\(381\) −3.09566e16 −0.518491
\(382\) −6.59901e14 −0.0108659
\(383\) 4.88712e16 0.791154 0.395577 0.918433i \(-0.370545\pi\)
0.395577 + 0.918433i \(0.370545\pi\)
\(384\) 1.80191e15 0.0286801
\(385\) −9.70318e16 −1.51852
\(386\) −4.31481e14 −0.00663963
\(387\) −2.99757e16 −0.453574
\(388\) −7.75221e16 −1.15350
\(389\) −1.97403e16 −0.288856 −0.144428 0.989515i \(-0.546134\pi\)
−0.144428 + 0.989515i \(0.546134\pi\)
\(390\) 9.06798e14 0.0130494
\(391\) −5.90524e15 −0.0835774
\(392\) 1.86761e15 0.0259972
\(393\) 3.75626e16 0.514285
\(394\) 1.65120e15 0.0222369
\(395\) 7.68781e16 1.01841
\(396\) −1.77229e16 −0.230949
\(397\) −9.34519e16 −1.19798 −0.598990 0.800756i \(-0.704431\pi\)
−0.598990 + 0.800756i \(0.704431\pi\)
\(398\) −1.52984e14 −0.00192933
\(399\) −1.07435e17 −1.33298
\(400\) 1.10267e17 1.34603
\(401\) 9.36404e16 1.12467 0.562335 0.826910i \(-0.309903\pi\)
0.562335 + 0.826910i \(0.309903\pi\)
\(402\) 8.46302e14 0.0100013
\(403\) 1.44383e17 1.67893
\(404\) 3.72377e16 0.426092
\(405\) −1.51161e16 −0.170209
\(406\) −1.69439e15 −0.0187757
\(407\) 3.37722e16 0.368295
\(408\) 2.08192e14 0.00223446
\(409\) 2.67006e16 0.282045 0.141023 0.990006i \(-0.454961\pi\)
0.141023 + 0.990006i \(0.454961\pi\)
\(410\) 2.42256e15 0.0251872
\(411\) 8.13191e16 0.832186
\(412\) −1.10493e17 −1.11302
\(413\) −1.87819e16 −0.186237
\(414\) 2.27631e14 0.00222192
\(415\) −1.03791e17 −0.997352
\(416\) −4.67805e15 −0.0442546
\(417\) −5.60062e16 −0.521617
\(418\) 1.51528e15 0.0138946
\(419\) −1.60374e17 −1.44792 −0.723959 0.689843i \(-0.757680\pi\)
−0.723959 + 0.689843i \(0.757680\pi\)
\(420\) 1.42301e17 1.26499
\(421\) 8.30141e15 0.0726638 0.0363319 0.999340i \(-0.488433\pi\)
0.0363319 + 0.999340i \(0.488433\pi\)
\(422\) −1.67092e15 −0.0144021
\(423\) −7.39465e16 −0.627632
\(424\) 5.69927e14 0.00476366
\(425\) 2.54842e16 0.209770
\(426\) −1.33252e15 −0.0108022
\(427\) −2.87183e17 −2.29286
\(428\) −1.72962e17 −1.36008
\(429\) 6.13470e16 0.475139
\(430\) −3.39460e15 −0.0258966
\(431\) 1.19959e17 0.901428 0.450714 0.892668i \(-0.351169\pi\)
0.450714 + 0.892668i \(0.351169\pi\)
\(432\) 2.59873e16 0.192361
\(433\) 2.48061e16 0.180879 0.0904393 0.995902i \(-0.471173\pi\)
0.0904393 + 0.995902i \(0.471173\pi\)
\(434\) −3.49766e15 −0.0251244
\(435\) −1.32038e17 −0.934369
\(436\) 1.33423e17 0.930180
\(437\) 1.26073e17 0.865952
\(438\) 6.56796e14 0.00444476
\(439\) −1.05987e17 −0.706696 −0.353348 0.935492i \(-0.614957\pi\)
−0.353348 + 0.935492i \(0.614957\pi\)
\(440\) −4.01436e15 −0.0263739
\(441\) 5.38779e16 0.348787
\(442\) −3.60296e14 −0.00229834
\(443\) −9.53388e16 −0.599301 −0.299651 0.954049i \(-0.596870\pi\)
−0.299651 + 0.954049i \(0.596870\pi\)
\(444\) −4.95283e16 −0.306806
\(445\) −8.50486e16 −0.519191
\(446\) −2.35780e15 −0.0141850
\(447\) 1.63655e17 0.970357
\(448\) −2.44566e17 −1.42919
\(449\) −9.16969e16 −0.528146 −0.264073 0.964503i \(-0.585066\pi\)
−0.264073 + 0.964503i \(0.585066\pi\)
\(450\) −9.82347e14 −0.00557678
\(451\) 1.63892e17 0.917085
\(452\) −1.88939e16 −0.104213
\(453\) 3.10367e16 0.168748
\(454\) −1.46382e15 −0.00784559
\(455\) −4.92569e17 −2.60251
\(456\) −4.44478e15 −0.0231515
\(457\) 2.27967e17 1.17062 0.585312 0.810808i \(-0.300972\pi\)
0.585312 + 0.810808i \(0.300972\pi\)
\(458\) 3.57660e15 0.0181070
\(459\) 6.00605e15 0.0299782
\(460\) −1.66987e17 −0.821785
\(461\) −3.71823e17 −1.80418 −0.902091 0.431546i \(-0.857968\pi\)
−0.902091 + 0.431546i \(0.857968\pi\)
\(462\) −1.48613e15 −0.00711023
\(463\) −1.92774e17 −0.909437 −0.454719 0.890635i \(-0.650260\pi\)
−0.454719 + 0.890635i \(0.650260\pi\)
\(464\) 2.26997e17 1.05598
\(465\) −2.72560e17 −1.25031
\(466\) −7.17458e14 −0.00324555
\(467\) −3.41906e17 −1.52527 −0.762635 0.646829i \(-0.776095\pi\)
−0.762635 + 0.646829i \(0.776095\pi\)
\(468\) −8.99678e16 −0.395812
\(469\) −4.59708e17 −1.99461
\(470\) −8.37406e15 −0.0358344
\(471\) 1.37027e17 0.578321
\(472\) −7.77039e14 −0.00323459
\(473\) −2.29652e17 −0.942917
\(474\) 1.17746e15 0.00476854
\(475\) −5.44073e17 −2.17345
\(476\) −5.65402e16 −0.222798
\(477\) 1.64416e16 0.0639108
\(478\) −7.84431e14 −0.00300797
\(479\) 3.99856e17 1.51259 0.756297 0.654228i \(-0.227006\pi\)
0.756297 + 0.654228i \(0.227006\pi\)
\(480\) 8.83106e15 0.0329568
\(481\) 1.71440e17 0.631203
\(482\) −3.20468e14 −0.00116407
\(483\) −1.23648e17 −0.443130
\(484\) 1.46986e17 0.519735
\(485\) −5.06561e17 −1.76730
\(486\) −2.31516e14 −0.000796978 0
\(487\) 3.49349e17 1.18665 0.593324 0.804964i \(-0.297815\pi\)
0.593324 + 0.804964i \(0.297815\pi\)
\(488\) −1.18812e16 −0.0398228
\(489\) 3.11036e17 1.02874
\(490\) 6.10140e15 0.0199138
\(491\) 1.16774e17 0.376112 0.188056 0.982158i \(-0.439781\pi\)
0.188056 + 0.982158i \(0.439781\pi\)
\(492\) −2.40354e17 −0.763973
\(493\) 5.24624e16 0.164567
\(494\) 7.69210e15 0.0238133
\(495\) −1.15809e17 −0.353840
\(496\) 4.68581e17 1.41304
\(497\) 7.23820e17 2.15434
\(498\) −1.58966e15 −0.00466996
\(499\) 3.16782e17 0.918558 0.459279 0.888292i \(-0.348108\pi\)
0.459279 + 0.888292i \(0.348108\pi\)
\(500\) 1.85505e17 0.530947
\(501\) −1.41097e17 −0.398632
\(502\) −3.49168e14 −0.000973778 0
\(503\) 6.06056e16 0.166848 0.0834239 0.996514i \(-0.473414\pi\)
0.0834239 + 0.996514i \(0.473414\pi\)
\(504\) 4.35927e15 0.0118472
\(505\) 2.43326e17 0.652822
\(506\) 1.74394e15 0.00461907
\(507\) 9.06237e16 0.236968
\(508\) 3.47815e17 0.897914
\(509\) 3.53468e16 0.0900917 0.0450458 0.998985i \(-0.485657\pi\)
0.0450458 + 0.998985i \(0.485657\pi\)
\(510\) 6.80154e14 0.00171160
\(511\) −3.56769e17 −0.886443
\(512\) −2.53050e16 −0.0620799
\(513\) −1.28225e17 −0.310607
\(514\) 4.35639e15 0.0104200
\(515\) −7.22006e17 −1.70527
\(516\) 3.36794e17 0.785492
\(517\) −5.66525e17 −1.30476
\(518\) −4.15313e15 −0.00944565
\(519\) 2.69817e17 0.606013
\(520\) −2.03784e16 −0.0452010
\(521\) 6.04157e17 1.32344 0.661720 0.749751i \(-0.269827\pi\)
0.661720 + 0.749751i \(0.269827\pi\)
\(522\) −2.02228e15 −0.00437505
\(523\) 3.36130e17 0.718202 0.359101 0.933299i \(-0.383083\pi\)
0.359101 + 0.933299i \(0.383083\pi\)
\(524\) −4.22038e17 −0.890631
\(525\) 5.33607e17 1.11221
\(526\) 8.05435e15 0.0165815
\(527\) 1.08296e17 0.220213
\(528\) 1.99096e17 0.399892
\(529\) −3.58938e17 −0.712127
\(530\) 1.86192e15 0.00364896
\(531\) −2.24165e16 −0.0433963
\(532\) 1.20710e18 2.30843
\(533\) 8.31974e17 1.57175
\(534\) −1.30259e15 −0.00243103
\(535\) −1.13020e18 −2.08381
\(536\) −1.90189e16 −0.0346428
\(537\) 1.05062e17 0.189065
\(538\) −9.10891e15 −0.0161950
\(539\) 4.12774e17 0.725079
\(540\) 1.69838e17 0.294765
\(541\) −6.98559e17 −1.19790 −0.598950 0.800786i \(-0.704415\pi\)
−0.598950 + 0.800786i \(0.704415\pi\)
\(542\) 1.60754e15 0.00272375
\(543\) 3.10586e17 0.519975
\(544\) −3.50883e15 −0.00580456
\(545\) 8.71838e17 1.42514
\(546\) −7.54413e15 −0.0121859
\(547\) −3.12942e17 −0.499512 −0.249756 0.968309i \(-0.580350\pi\)
−0.249756 + 0.968309i \(0.580350\pi\)
\(548\) −9.13667e17 −1.44117
\(549\) −3.42756e17 −0.534275
\(550\) −7.52604e15 −0.0115933
\(551\) −1.12004e18 −1.70509
\(552\) −5.11552e15 −0.00769637
\(553\) −6.39590e17 −0.951017
\(554\) −3.46190e15 −0.00508747
\(555\) −3.23638e17 −0.470062
\(556\) 6.29262e17 0.903328
\(557\) 1.01552e18 1.44089 0.720443 0.693514i \(-0.243938\pi\)
0.720443 + 0.693514i \(0.243938\pi\)
\(558\) −4.17450e15 −0.00585440
\(559\) −1.16580e18 −1.61602
\(560\) −1.59859e18 −2.19035
\(561\) 4.60140e16 0.0623206
\(562\) 1.13378e16 0.0151790
\(563\) 4.95596e17 0.655878 0.327939 0.944699i \(-0.393646\pi\)
0.327939 + 0.944699i \(0.393646\pi\)
\(564\) 8.30831e17 1.08692
\(565\) −1.23460e17 −0.159666
\(566\) 1.49202e16 0.0190752
\(567\) 1.25759e17 0.158946
\(568\) 2.99456e16 0.0374170
\(569\) −9.92143e17 −1.22559 −0.612794 0.790243i \(-0.709955\pi\)
−0.612794 + 0.790243i \(0.709955\pi\)
\(570\) −1.45209e16 −0.0177340
\(571\) 3.28537e17 0.396689 0.198345 0.980132i \(-0.436444\pi\)
0.198345 + 0.980132i \(0.436444\pi\)
\(572\) −6.89269e17 −0.822838
\(573\) 4.27821e17 0.504960
\(574\) −2.01546e16 −0.0235205
\(575\) −6.26177e17 −0.722530
\(576\) −2.91892e17 −0.333025
\(577\) 1.36727e18 1.54245 0.771223 0.636565i \(-0.219645\pi\)
0.771223 + 0.636565i \(0.219645\pi\)
\(578\) 1.08671e16 0.0121222
\(579\) 2.79734e17 0.308556
\(580\) 1.48352e18 1.61813
\(581\) 8.63495e17 0.931355
\(582\) −7.75844e15 −0.00827513
\(583\) 1.25964e17 0.132862
\(584\) −1.47601e16 −0.0153959
\(585\) −5.87887e17 −0.606430
\(586\) 2.53819e15 0.00258934
\(587\) −6.01986e16 −0.0607349 −0.0303675 0.999539i \(-0.509668\pi\)
−0.0303675 + 0.999539i \(0.509668\pi\)
\(588\) −6.05349e17 −0.604023
\(589\) −2.31205e18 −2.28164
\(590\) −2.53855e15 −0.00247769
\(591\) −1.07049e18 −1.03339
\(592\) 5.56393e17 0.531239
\(593\) 4.65893e17 0.439977 0.219989 0.975502i \(-0.429398\pi\)
0.219989 + 0.975502i \(0.429398\pi\)
\(594\) −1.77371e15 −0.00165681
\(595\) −3.69457e17 −0.341353
\(596\) −1.83876e18 −1.68045
\(597\) 9.91813e16 0.0896596
\(598\) 8.85289e15 0.00791639
\(599\) 1.36134e18 1.20419 0.602093 0.798426i \(-0.294333\pi\)
0.602093 + 0.798426i \(0.294333\pi\)
\(600\) 2.20762e16 0.0193170
\(601\) 2.18572e18 1.89195 0.945976 0.324238i \(-0.105108\pi\)
0.945976 + 0.324238i \(0.105108\pi\)
\(602\) 2.82415e16 0.0241830
\(603\) −5.48667e17 −0.464779
\(604\) −3.48716e17 −0.292234
\(605\) 9.60469e17 0.796294
\(606\) 3.72676e15 0.00305675
\(607\) 2.26851e18 1.84084 0.920418 0.390936i \(-0.127849\pi\)
0.920418 + 0.390936i \(0.127849\pi\)
\(608\) 7.49114e16 0.0601415
\(609\) 1.09849e18 0.872540
\(610\) −3.88154e16 −0.0305042
\(611\) −2.87589e18 −2.23616
\(612\) −6.74814e16 −0.0519158
\(613\) −7.43957e17 −0.566311 −0.283155 0.959074i \(-0.591381\pi\)
−0.283155 + 0.959074i \(0.591381\pi\)
\(614\) 1.40549e15 0.00105860
\(615\) −1.57057e18 −1.17049
\(616\) 3.33976e16 0.0246287
\(617\) −1.56850e16 −0.0114454 −0.00572271 0.999984i \(-0.501822\pi\)
−0.00572271 + 0.999984i \(0.501822\pi\)
\(618\) −1.10582e16 −0.00798469
\(619\) −1.65308e18 −1.18115 −0.590576 0.806982i \(-0.701099\pi\)
−0.590576 + 0.806982i \(0.701099\pi\)
\(620\) 3.06237e18 2.16527
\(621\) −1.47575e17 −0.103257
\(622\) −1.00758e16 −0.00697659
\(623\) 7.07564e17 0.484834
\(624\) 1.01068e18 0.685355
\(625\) −7.94500e17 −0.533180
\(626\) −3.70789e16 −0.0246260
\(627\) −9.82371e17 −0.645709
\(628\) −1.53957e18 −1.00153
\(629\) 1.28590e17 0.0827903
\(630\) 1.42415e16 0.00907493
\(631\) −2.83524e18 −1.78813 −0.894066 0.447936i \(-0.852159\pi\)
−0.894066 + 0.447936i \(0.852159\pi\)
\(632\) −2.64609e16 −0.0165174
\(633\) 1.08328e18 0.669290
\(634\) 3.67678e16 0.0224847
\(635\) 2.27277e18 1.37571
\(636\) −1.84731e17 −0.110680
\(637\) 2.09539e18 1.24268
\(638\) −1.54933e16 −0.00909512
\(639\) 8.63888e17 0.501998
\(640\) −1.32293e17 −0.0760967
\(641\) 3.20277e18 1.82368 0.911841 0.410543i \(-0.134661\pi\)
0.911841 + 0.410543i \(0.134661\pi\)
\(642\) −1.73101e16 −0.00975712
\(643\) 3.43410e18 1.91620 0.958102 0.286428i \(-0.0924679\pi\)
0.958102 + 0.286428i \(0.0924679\pi\)
\(644\) 1.38926e18 0.767405
\(645\) 2.20075e18 1.20346
\(646\) 5.76955e15 0.00312342
\(647\) −5.45681e17 −0.292456 −0.146228 0.989251i \(-0.546713\pi\)
−0.146228 + 0.989251i \(0.546713\pi\)
\(648\) 5.20284e15 0.00276060
\(649\) −1.71739e17 −0.0902149
\(650\) −3.82049e16 −0.0198693
\(651\) 2.26757e18 1.16758
\(652\) −3.49467e18 −1.78155
\(653\) −1.11656e17 −0.0563570 −0.0281785 0.999603i \(-0.508971\pi\)
−0.0281785 + 0.999603i \(0.508971\pi\)
\(654\) 1.33530e16 0.00667303
\(655\) −2.75777e18 −1.36455
\(656\) 2.70010e18 1.32283
\(657\) −4.25808e17 −0.206556
\(658\) 6.96683e16 0.0334631
\(659\) 3.58335e18 1.70425 0.852127 0.523336i \(-0.175313\pi\)
0.852127 + 0.523336i \(0.175313\pi\)
\(660\) 1.30118e18 0.612775
\(661\) −3.38067e18 −1.57650 −0.788248 0.615358i \(-0.789011\pi\)
−0.788248 + 0.615358i \(0.789011\pi\)
\(662\) −8.91424e15 −0.00411630
\(663\) 2.33584e17 0.106808
\(664\) 3.57242e16 0.0161760
\(665\) 7.88768e18 3.53678
\(666\) −4.95681e15 −0.00220100
\(667\) −1.28906e18 −0.566833
\(668\) 1.58531e18 0.690345
\(669\) 1.52859e18 0.659205
\(670\) −6.21337e16 −0.0265363
\(671\) −2.62595e18 −1.11068
\(672\) −7.34703e16 −0.0307760
\(673\) 1.07005e18 0.443920 0.221960 0.975056i \(-0.428755\pi\)
0.221960 + 0.975056i \(0.428755\pi\)
\(674\) 1.02756e16 0.00422202
\(675\) 6.36866e17 0.259163
\(676\) −1.01821e18 −0.410377
\(677\) 3.14098e18 1.25383 0.626915 0.779088i \(-0.284318\pi\)
0.626915 + 0.779088i \(0.284318\pi\)
\(678\) −1.89091e15 −0.000747613 0
\(679\) 4.21435e18 1.65035
\(680\) −1.52850e16 −0.00592868
\(681\) 9.49013e17 0.364599
\(682\) −3.19821e16 −0.0121705
\(683\) 3.36551e18 1.26858 0.634288 0.773097i \(-0.281293\pi\)
0.634288 + 0.773097i \(0.281293\pi\)
\(684\) 1.44069e18 0.537904
\(685\) −5.97028e18 −2.20803
\(686\) −2.24901e15 −0.000823919 0
\(687\) −2.31875e18 −0.841464
\(688\) −3.78350e18 −1.36009
\(689\) 6.39437e17 0.227705
\(690\) −1.67122e16 −0.00589541
\(691\) 3.37273e18 1.17862 0.589311 0.807907i \(-0.299399\pi\)
0.589311 + 0.807907i \(0.299399\pi\)
\(692\) −3.03155e18 −1.04948
\(693\) 9.63474e17 0.330426
\(694\) −5.79435e16 −0.0196865
\(695\) 4.11186e18 1.38400
\(696\) 4.54465e16 0.0151544
\(697\) 6.24032e17 0.206155
\(698\) 3.21387e15 0.00105189
\(699\) 4.65136e17 0.150827
\(700\) −5.99538e18 −1.92610
\(701\) 1.98301e18 0.631187 0.315594 0.948894i \(-0.397796\pi\)
0.315594 + 0.948894i \(0.397796\pi\)
\(702\) −9.00401e15 −0.00283952
\(703\) −2.74533e18 −0.857797
\(704\) −2.23627e18 −0.692312
\(705\) 5.42899e18 1.66529
\(706\) −2.78057e16 −0.00845091
\(707\) −2.02436e18 −0.609623
\(708\) 2.51862e17 0.0751530
\(709\) 2.34828e18 0.694303 0.347151 0.937809i \(-0.387149\pi\)
0.347151 + 0.937809i \(0.387149\pi\)
\(710\) 9.78309e16 0.0286614
\(711\) −7.63358e17 −0.221603
\(712\) 2.92731e16 0.00842070
\(713\) −2.66095e18 −0.758499
\(714\) −5.65856e15 −0.00159834
\(715\) −4.50397e18 −1.26068
\(716\) −1.18043e18 −0.327420
\(717\) 5.08555e17 0.139786
\(718\) −3.53199e16 −0.00962077
\(719\) −3.00538e18 −0.811264 −0.405632 0.914036i \(-0.632949\pi\)
−0.405632 + 0.914036i \(0.632949\pi\)
\(720\) −1.90793e18 −0.510390
\(721\) 6.00675e18 1.59243
\(722\) −7.58895e16 −0.0199384
\(723\) 2.07763e17 0.0540965
\(724\) −3.48961e18 −0.900484
\(725\) 5.56298e18 1.42269
\(726\) 1.47104e16 0.00372853
\(727\) 2.58278e18 0.648805 0.324403 0.945919i \(-0.394837\pi\)
0.324403 + 0.945919i \(0.394837\pi\)
\(728\) 1.69538e17 0.0422099
\(729\) 1.50095e17 0.0370370
\(730\) −4.82206e16 −0.0117933
\(731\) −8.74421e17 −0.211962
\(732\) 3.85106e18 0.925249
\(733\) −1.76946e18 −0.421371 −0.210686 0.977554i \(-0.567570\pi\)
−0.210686 + 0.977554i \(0.567570\pi\)
\(734\) −2.42815e16 −0.00573128
\(735\) −3.95560e18 −0.925433
\(736\) 8.62160e16 0.0199932
\(737\) −4.20349e18 −0.966210
\(738\) −2.40547e16 −0.00548067
\(739\) 5.41661e18 1.22332 0.611658 0.791122i \(-0.290503\pi\)
0.611658 + 0.791122i \(0.290503\pi\)
\(740\) 3.63626e18 0.814046
\(741\) −4.98687e18 −1.10665
\(742\) −1.54903e16 −0.00340750
\(743\) 6.37375e18 1.38985 0.694924 0.719083i \(-0.255438\pi\)
0.694924 + 0.719083i \(0.255438\pi\)
\(744\) 9.38132e16 0.0202787
\(745\) −1.20152e19 −2.57464
\(746\) −7.81156e16 −0.0165934
\(747\) 1.03059e18 0.217022
\(748\) −5.16994e17 −0.107926
\(749\) 9.40277e18 1.94592
\(750\) 1.85654e16 0.00380897
\(751\) −1.12823e18 −0.229476 −0.114738 0.993396i \(-0.536603\pi\)
−0.114738 + 0.993396i \(0.536603\pi\)
\(752\) −9.33343e18 −1.88202
\(753\) 2.26369e17 0.0452533
\(754\) −7.86494e16 −0.0155877
\(755\) −2.27865e18 −0.447737
\(756\) −1.41297e18 −0.275259
\(757\) −4.88523e18 −0.943544 −0.471772 0.881721i \(-0.656385\pi\)
−0.471772 + 0.881721i \(0.656385\pi\)
\(758\) 3.52967e16 0.00675902
\(759\) −1.13062e18 −0.214657
\(760\) 3.26326e17 0.0614276
\(761\) −3.48808e18 −0.651008 −0.325504 0.945541i \(-0.605534\pi\)
−0.325504 + 0.945541i \(0.605534\pi\)
\(762\) 3.48095e16 0.00644155
\(763\) −7.25328e18 −1.33084
\(764\) −4.80682e18 −0.874482
\(765\) −4.40951e17 −0.0795410
\(766\) −5.49537e16 −0.00982902
\(767\) −8.71809e17 −0.154615
\(768\) 3.27806e18 0.576459
\(769\) −6.70756e18 −1.16962 −0.584808 0.811172i \(-0.698830\pi\)
−0.584808 + 0.811172i \(0.698830\pi\)
\(770\) 1.09108e17 0.0188655
\(771\) −2.82430e18 −0.484236
\(772\) −3.14297e18 −0.534352
\(773\) 4.75122e18 0.801011 0.400505 0.916294i \(-0.368835\pi\)
0.400505 + 0.916294i \(0.368835\pi\)
\(774\) 3.37065e16 0.00563505
\(775\) 1.14834e19 1.90375
\(776\) 1.74355e17 0.0286637
\(777\) 2.69252e18 0.438957
\(778\) 2.21972e16 0.00358865
\(779\) −1.33227e19 −2.13599
\(780\) 6.60525e18 1.05021
\(781\) 6.61849e18 1.04358
\(782\) 6.64021e15 0.00103834
\(783\) 1.31107e18 0.203317
\(784\) 6.80040e18 1.04588
\(785\) −1.00602e19 −1.53445
\(786\) −4.22377e16 −0.00638930
\(787\) −1.78667e18 −0.268046 −0.134023 0.990978i \(-0.542790\pi\)
−0.134023 + 0.990978i \(0.542790\pi\)
\(788\) 1.20276e19 1.78961
\(789\) −5.22172e18 −0.770572
\(790\) −8.64464e16 −0.0126523
\(791\) 1.02713e18 0.149101
\(792\) 3.98605e16 0.00573890
\(793\) −1.33303e19 −1.90355
\(794\) 1.05083e17 0.0148833
\(795\) −1.20711e18 −0.169574
\(796\) −1.11436e18 −0.155271
\(797\) 6.89988e18 0.953591 0.476796 0.879014i \(-0.341798\pi\)
0.476796 + 0.879014i \(0.341798\pi\)
\(798\) 1.20807e17 0.0165605
\(799\) −2.15709e18 −0.293302
\(800\) −3.72067e17 −0.0501807
\(801\) 8.44486e17 0.112975
\(802\) −1.05295e17 −0.0139725
\(803\) −3.26223e18 −0.429402
\(804\) 6.16459e18 0.804896
\(805\) 9.07798e18 1.17575
\(806\) −1.62353e17 −0.0208584
\(807\) 5.90540e18 0.752613
\(808\) −8.37510e16 −0.0105881
\(809\) 8.48455e18 1.06405 0.532026 0.846728i \(-0.321431\pi\)
0.532026 + 0.846728i \(0.321431\pi\)
\(810\) 1.69975e16 0.00211461
\(811\) −2.81505e18 −0.347416 −0.173708 0.984797i \(-0.555575\pi\)
−0.173708 + 0.984797i \(0.555575\pi\)
\(812\) −1.23422e19 −1.51105
\(813\) −1.04219e18 −0.126578
\(814\) −3.79755e16 −0.00457557
\(815\) −2.28356e19 −2.72954
\(816\) 7.58075e17 0.0898931
\(817\) 1.86684e19 2.19615
\(818\) −3.00237e16 −0.00350404
\(819\) 4.89094e18 0.566301
\(820\) 1.76463e19 2.02704
\(821\) 6.28035e18 0.715737 0.357869 0.933772i \(-0.383504\pi\)
0.357869 + 0.933772i \(0.383504\pi\)
\(822\) −9.14401e16 −0.0103388
\(823\) 3.52404e18 0.395314 0.197657 0.980271i \(-0.436667\pi\)
0.197657 + 0.980271i \(0.436667\pi\)
\(824\) 2.48509e17 0.0276576
\(825\) 4.87921e18 0.538765
\(826\) 2.11195e16 0.00231374
\(827\) −6.15138e17 −0.0668631 −0.0334315 0.999441i \(-0.510644\pi\)
−0.0334315 + 0.999441i \(0.510644\pi\)
\(828\) 1.65810e18 0.178818
\(829\) 1.60126e19 1.71339 0.856695 0.515823i \(-0.172514\pi\)
0.856695 + 0.515823i \(0.172514\pi\)
\(830\) 1.16709e17 0.0123908
\(831\) 2.24439e18 0.236424
\(832\) −1.13521e19 −1.18652
\(833\) 1.57167e18 0.162993
\(834\) 6.29768e16 0.00648039
\(835\) 1.03590e19 1.05769
\(836\) 1.10375e19 1.11823
\(837\) 2.70638e18 0.272065
\(838\) 1.80335e17 0.0179884
\(839\) 7.18767e18 0.711435 0.355717 0.934594i \(-0.384237\pi\)
0.355717 + 0.934594i \(0.384237\pi\)
\(840\) −3.20049e17 −0.0314341
\(841\) 1.19143e18 0.116117
\(842\) −9.33460e15 −0.000902750 0
\(843\) −7.35043e18 −0.705397
\(844\) −1.21712e19 −1.15907
\(845\) −6.65340e18 −0.628746
\(846\) 8.31499e16 0.00779748
\(847\) −7.99065e18 −0.743601
\(848\) 2.07523e18 0.191644
\(849\) −9.67294e18 −0.886459
\(850\) −2.86560e16 −0.00260611
\(851\) −3.15962e18 −0.285162
\(852\) −9.70628e18 −0.869351
\(853\) 8.10442e18 0.720366 0.360183 0.932882i \(-0.382714\pi\)
0.360183 + 0.932882i \(0.382714\pi\)
\(854\) 3.22926e17 0.0284857
\(855\) 9.41404e18 0.824131
\(856\) 3.89008e17 0.0337970
\(857\) −9.13174e18 −0.787369 −0.393684 0.919246i \(-0.628800\pi\)
−0.393684 + 0.919246i \(0.628800\pi\)
\(858\) −6.89823e16 −0.00590297
\(859\) −3.12025e18 −0.264993 −0.132496 0.991184i \(-0.542299\pi\)
−0.132496 + 0.991184i \(0.542299\pi\)
\(860\) −2.47267e19 −2.08414
\(861\) 1.30664e19 1.09304
\(862\) −1.34889e17 −0.0111990
\(863\) −1.32191e19 −1.08926 −0.544629 0.838677i \(-0.683330\pi\)
−0.544629 + 0.838677i \(0.683330\pi\)
\(864\) −8.76877e16 −0.00717132
\(865\) −1.98094e19 −1.60793
\(866\) −2.78935e16 −0.00224717
\(867\) −7.04524e18 −0.563341
\(868\) −2.54775e19 −2.02199
\(869\) −5.84830e18 −0.460682
\(870\) 1.48471e17 0.0116083
\(871\) −2.13384e19 −1.65594
\(872\) −3.00080e17 −0.0231143
\(873\) 5.02988e18 0.384561
\(874\) −1.41765e17 −0.0107583
\(875\) −1.00847e19 −0.759643
\(876\) 4.78420e18 0.357711
\(877\) −7.08727e18 −0.525995 −0.262998 0.964796i \(-0.584711\pi\)
−0.262998 + 0.964796i \(0.584711\pi\)
\(878\) 1.19178e17 0.00877975
\(879\) −1.64554e18 −0.120332
\(880\) −1.46172e19 −1.06103
\(881\) 3.85374e18 0.277676 0.138838 0.990315i \(-0.455663\pi\)
0.138838 + 0.990315i \(0.455663\pi\)
\(882\) −6.05836e16 −0.00433320
\(883\) 1.09510e18 0.0777519 0.0388760 0.999244i \(-0.487622\pi\)
0.0388760 + 0.999244i \(0.487622\pi\)
\(884\) −2.62445e18 −0.184969
\(885\) 1.64577e18 0.115143
\(886\) 1.07205e17 0.00744551
\(887\) −9.84951e18 −0.679065 −0.339532 0.940594i \(-0.610269\pi\)
−0.339532 + 0.940594i \(0.610269\pi\)
\(888\) 1.11394e17 0.00762389
\(889\) −1.89084e19 −1.28467
\(890\) 9.56338e16 0.00645024
\(891\) 1.14992e18 0.0769948
\(892\) −1.71746e19 −1.14160
\(893\) 4.60526e19 3.03892
\(894\) −1.84024e17 −0.0120554
\(895\) −7.71341e18 −0.501645
\(896\) 1.10061e18 0.0710612
\(897\) −5.73942e18 −0.367890
\(898\) 1.03110e17 0.00656150
\(899\) 2.36400e19 1.49351
\(900\) −7.15556e18 −0.448815
\(901\) 4.79617e17 0.0298664
\(902\) −1.84290e17 −0.0113935
\(903\) −1.83092e19 −1.12383
\(904\) 4.24941e16 0.00258961
\(905\) −2.28025e19 −1.37964
\(906\) −3.48996e16 −0.00209646
\(907\) −1.44051e19 −0.859149 −0.429575 0.903031i \(-0.641336\pi\)
−0.429575 + 0.903031i \(0.641336\pi\)
\(908\) −1.06627e19 −0.631407
\(909\) −2.41610e18 −0.142053
\(910\) 5.53874e17 0.0323327
\(911\) 5.81274e18 0.336908 0.168454 0.985710i \(-0.446123\pi\)
0.168454 + 0.985710i \(0.446123\pi\)
\(912\) −1.61844e19 −0.931390
\(913\) 7.89566e18 0.451158
\(914\) −2.56340e17 −0.0145434
\(915\) 2.51644e19 1.41759
\(916\) 2.60525e19 1.45723
\(917\) 2.29433e19 1.27425
\(918\) −6.75356e15 −0.000372439 0
\(919\) 4.63641e18 0.253881 0.126941 0.991910i \(-0.459484\pi\)
0.126941 + 0.991910i \(0.459484\pi\)
\(920\) 3.75571e17 0.0204207
\(921\) −9.11192e17 −0.0491952
\(922\) 4.18101e17 0.0224145
\(923\) 3.35978e19 1.78855
\(924\) −1.08252e19 −0.572226
\(925\) 1.36354e19 0.715726
\(926\) 2.16767e17 0.0112985
\(927\) 7.16913e18 0.371063
\(928\) −7.65945e17 −0.0393673
\(929\) 4.69170e18 0.239457 0.119729 0.992807i \(-0.461798\pi\)
0.119729 + 0.992807i \(0.461798\pi\)
\(930\) 3.06483e17 0.0155334
\(931\) −3.35542e19 −1.68878
\(932\) −5.22607e18 −0.261199
\(933\) 6.53227e18 0.324215
\(934\) 3.84459e17 0.0189494
\(935\) −3.37825e18 −0.165355
\(936\) 2.02346e17 0.00983562
\(937\) −6.16165e18 −0.297433 −0.148717 0.988880i \(-0.547514\pi\)
−0.148717 + 0.988880i \(0.547514\pi\)
\(938\) 5.16923e17 0.0247804
\(939\) 2.40387e19 1.14442
\(940\) −6.09979e19 −2.88392
\(941\) −1.52437e19 −0.715742 −0.357871 0.933771i \(-0.616497\pi\)
−0.357871 + 0.933771i \(0.616497\pi\)
\(942\) −1.54081e17 −0.00718485
\(943\) −1.53332e19 −0.710078
\(944\) −2.82938e18 −0.130129
\(945\) −9.23295e18 −0.421729
\(946\) 2.58235e17 0.0117145
\(947\) −4.08281e19 −1.83943 −0.919717 0.392583i \(-0.871582\pi\)
−0.919717 + 0.392583i \(0.871582\pi\)
\(948\) 8.57677e18 0.383769
\(949\) −1.65603e19 −0.735932
\(950\) 6.11789e17 0.0270021
\(951\) −2.38370e19 −1.04491
\(952\) 1.27164e17 0.00553637
\(953\) 1.20791e18 0.0522312 0.0261156 0.999659i \(-0.491686\pi\)
0.0261156 + 0.999659i \(0.491686\pi\)
\(954\) −1.84879e16 −0.000794005 0
\(955\) −3.14097e19 −1.33981
\(956\) −5.71391e18 −0.242079
\(957\) 1.00444e19 0.422667
\(958\) −4.49622e17 −0.0187920
\(959\) 4.96699e19 2.06192
\(960\) 2.14301e19 0.883612
\(961\) 2.43815e19 0.998522
\(962\) −1.92777e17 −0.00784184
\(963\) 1.12223e19 0.453432
\(964\) −2.33434e18 −0.0936834
\(965\) −2.05374e19 −0.818689
\(966\) 1.39037e17 0.00550529
\(967\) 6.72408e18 0.264460 0.132230 0.991219i \(-0.457786\pi\)
0.132230 + 0.991219i \(0.457786\pi\)
\(968\) −3.30586e17 −0.0129150
\(969\) −3.74046e18 −0.145151
\(970\) 5.69608e17 0.0219563
\(971\) 2.78301e19 1.06559 0.532795 0.846244i \(-0.321141\pi\)
0.532795 + 0.846244i \(0.321141\pi\)
\(972\) −1.68640e18 −0.0641401
\(973\) −3.42087e19 −1.29242
\(974\) −3.92829e17 −0.0147425
\(975\) 2.47686e19 0.923363
\(976\) −4.32622e19 −1.60208
\(977\) −1.34400e19 −0.494408 −0.247204 0.968963i \(-0.579512\pi\)
−0.247204 + 0.968963i \(0.579512\pi\)
\(978\) −3.49748e17 −0.0127807
\(979\) 6.46985e18 0.234859
\(980\) 4.44435e19 1.60265
\(981\) −8.65688e18 −0.310108
\(982\) −1.31308e17 −0.00467268
\(983\) −3.07556e18 −0.108724 −0.0543620 0.998521i \(-0.517313\pi\)
−0.0543620 + 0.998521i \(0.517313\pi\)
\(984\) 5.40579e17 0.0189841
\(985\) 7.85932e19 2.74189
\(986\) −5.89919e16 −0.00204452
\(987\) −4.51667e19 −1.55509
\(988\) 5.60304e19 1.91648
\(989\) 2.14855e19 0.730080
\(990\) 1.30222e17 0.00439599
\(991\) 4.46469e18 0.149731 0.0748657 0.997194i \(-0.476147\pi\)
0.0748657 + 0.997194i \(0.476147\pi\)
\(992\) −1.58111e18 −0.0526788
\(993\) 5.77920e18 0.191292
\(994\) −8.13907e17 −0.0267648
\(995\) −7.28168e18 −0.237893
\(996\) −1.15793e19 −0.375834
\(997\) −4.98823e19 −1.60853 −0.804263 0.594274i \(-0.797439\pi\)
−0.804263 + 0.594274i \(0.797439\pi\)
\(998\) −3.56209e17 −0.0114119
\(999\) 3.21355e18 0.102284
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.1.15 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.15 31 1.1 even 1 trivial