Properties

Label 177.14.a.c.1.20
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 1.20
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+68.2207 q^{2} +729.000 q^{3} -3537.94 q^{4} -14307.6 q^{5} +49732.9 q^{6} -16077.5 q^{7} -800224. q^{8} +531441. q^{9} +O(q^{10})\) \(q+68.2207 q^{2} +729.000 q^{3} -3537.94 q^{4} -14307.6 q^{5} +49732.9 q^{6} -16077.5 q^{7} -800224. q^{8} +531441. q^{9} -976072. q^{10} -5.62969e6 q^{11} -2.57916e6 q^{12} -1.90389e7 q^{13} -1.09681e6 q^{14} -1.04302e7 q^{15} -2.56090e7 q^{16} +1.17014e8 q^{17} +3.62553e7 q^{18} +6.78180e7 q^{19} +5.06193e7 q^{20} -1.17205e7 q^{21} -3.84061e8 q^{22} -1.30559e9 q^{23} -5.83364e8 q^{24} -1.01600e9 q^{25} -1.29885e9 q^{26} +3.87420e8 q^{27} +5.68811e7 q^{28} +1.88273e8 q^{29} -7.11557e8 q^{30} -4.39205e9 q^{31} +4.80837e9 q^{32} -4.10404e9 q^{33} +7.98274e9 q^{34} +2.30029e8 q^{35} -1.88021e9 q^{36} +2.15668e10 q^{37} +4.62659e9 q^{38} -1.38794e10 q^{39} +1.14493e10 q^{40} +7.66988e9 q^{41} -7.99578e8 q^{42} +4.14186e10 q^{43} +1.99175e10 q^{44} -7.60363e9 q^{45} -8.90679e10 q^{46} -1.24725e11 q^{47} -1.86690e10 q^{48} -9.66305e10 q^{49} -6.93120e10 q^{50} +8.53029e10 q^{51} +6.73585e10 q^{52} +1.16632e11 q^{53} +2.64301e10 q^{54} +8.05471e10 q^{55} +1.28656e10 q^{56} +4.94393e10 q^{57} +1.28441e10 q^{58} -4.21805e10 q^{59} +3.69015e10 q^{60} +9.07189e10 q^{61} -2.99628e11 q^{62} -8.54422e9 q^{63} +5.37820e11 q^{64} +2.72400e11 q^{65} -2.79980e11 q^{66} +2.79779e11 q^{67} -4.13987e11 q^{68} -9.51772e11 q^{69} +1.56928e10 q^{70} +8.96606e11 q^{71} -4.25272e11 q^{72} +2.19719e9 q^{73} +1.47130e12 q^{74} -7.40661e11 q^{75} -2.39936e11 q^{76} +9.05110e10 q^{77} -9.46859e11 q^{78} -2.36194e12 q^{79} +3.66403e11 q^{80} +2.82430e11 q^{81} +5.23244e11 q^{82} +3.89435e12 q^{83} +4.14663e10 q^{84} -1.67418e12 q^{85} +2.82560e12 q^{86} +1.37251e11 q^{87} +4.50501e12 q^{88} +3.38545e12 q^{89} -5.18725e11 q^{90} +3.06097e11 q^{91} +4.61908e12 q^{92} -3.20180e12 q^{93} -8.50881e12 q^{94} -9.70311e11 q^{95} +3.50530e12 q^{96} -2.54230e12 q^{97} -6.59220e12 q^{98} -2.99185e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 68.2207 0.753739 0.376869 0.926266i \(-0.377001\pi\)
0.376869 + 0.926266i \(0.377001\pi\)
\(3\) 729.000 0.577350
\(4\) −3537.94 −0.431878
\(5\) −14307.6 −0.409507 −0.204753 0.978814i \(-0.565639\pi\)
−0.204753 + 0.978814i \(0.565639\pi\)
\(6\) 49732.9 0.435171
\(7\) −16077.5 −0.0516512 −0.0258256 0.999666i \(-0.508221\pi\)
−0.0258256 + 0.999666i \(0.508221\pi\)
\(8\) −800224. −1.07926
\(9\) 531441. 0.333333
\(10\) −976072. −0.308661
\(11\) −5.62969e6 −0.958146 −0.479073 0.877775i \(-0.659027\pi\)
−0.479073 + 0.877775i \(0.659027\pi\)
\(12\) −2.57916e6 −0.249345
\(13\) −1.90389e7 −1.09398 −0.546991 0.837139i \(-0.684227\pi\)
−0.546991 + 0.837139i \(0.684227\pi\)
\(14\) −1.09681e6 −0.0389315
\(15\) −1.04302e7 −0.236429
\(16\) −2.56090e7 −0.381604
\(17\) 1.17014e8 1.17576 0.587879 0.808949i \(-0.299963\pi\)
0.587879 + 0.808949i \(0.299963\pi\)
\(18\) 3.62553e7 0.251246
\(19\) 6.78180e7 0.330709 0.165355 0.986234i \(-0.447123\pi\)
0.165355 + 0.986234i \(0.447123\pi\)
\(20\) 5.06193e7 0.176857
\(21\) −1.17205e7 −0.0298208
\(22\) −3.84061e8 −0.722192
\(23\) −1.30559e9 −1.83897 −0.919485 0.393126i \(-0.871394\pi\)
−0.919485 + 0.393126i \(0.871394\pi\)
\(24\) −5.83364e8 −0.623112
\(25\) −1.01600e9 −0.832304
\(26\) −1.29885e9 −0.824577
\(27\) 3.87420e8 0.192450
\(28\) 5.68811e7 0.0223070
\(29\) 1.88273e8 0.0587761 0.0293881 0.999568i \(-0.490644\pi\)
0.0293881 + 0.999568i \(0.490644\pi\)
\(30\) −7.11557e8 −0.178206
\(31\) −4.39205e9 −0.888824 −0.444412 0.895822i \(-0.646587\pi\)
−0.444412 + 0.895822i \(0.646587\pi\)
\(32\) 4.80837e9 0.791632
\(33\) −4.10404e9 −0.553186
\(34\) 7.98274e9 0.886215
\(35\) 2.30029e8 0.0211515
\(36\) −1.88021e9 −0.143959
\(37\) 2.15668e10 1.38189 0.690945 0.722907i \(-0.257194\pi\)
0.690945 + 0.722907i \(0.257194\pi\)
\(38\) 4.62659e9 0.249269
\(39\) −1.38794e10 −0.631611
\(40\) 1.14493e10 0.441965
\(41\) 7.66988e9 0.252170 0.126085 0.992019i \(-0.459759\pi\)
0.126085 + 0.992019i \(0.459759\pi\)
\(42\) −7.99578e8 −0.0224771
\(43\) 4.14186e10 0.999195 0.499598 0.866258i \(-0.333481\pi\)
0.499598 + 0.866258i \(0.333481\pi\)
\(44\) 1.99175e10 0.413802
\(45\) −7.60363e9 −0.136502
\(46\) −8.90679e10 −1.38610
\(47\) −1.24725e11 −1.68778 −0.843892 0.536513i \(-0.819741\pi\)
−0.843892 + 0.536513i \(0.819741\pi\)
\(48\) −1.86690e10 −0.220319
\(49\) −9.66305e10 −0.997332
\(50\) −6.93120e10 −0.627340
\(51\) 8.53029e10 0.678825
\(52\) 6.73585e10 0.472466
\(53\) 1.16632e11 0.722812 0.361406 0.932409i \(-0.382297\pi\)
0.361406 + 0.932409i \(0.382297\pi\)
\(54\) 2.64301e10 0.145057
\(55\) 8.05471e10 0.392367
\(56\) 1.28656e10 0.0557451
\(57\) 4.94393e10 0.190935
\(58\) 1.28441e10 0.0443018
\(59\) −4.21805e10 −0.130189
\(60\) 3.69015e10 0.102108
\(61\) 9.07189e10 0.225452 0.112726 0.993626i \(-0.464042\pi\)
0.112726 + 0.993626i \(0.464042\pi\)
\(62\) −2.99628e11 −0.669941
\(63\) −8.54422e9 −0.0172171
\(64\) 5.37820e11 0.978288
\(65\) 2.72400e11 0.447993
\(66\) −2.79980e11 −0.416958
\(67\) 2.79779e11 0.377858 0.188929 0.981991i \(-0.439498\pi\)
0.188929 + 0.981991i \(0.439498\pi\)
\(68\) −4.13987e11 −0.507784
\(69\) −9.51772e11 −1.06173
\(70\) 1.56928e10 0.0159427
\(71\) 8.96606e11 0.830658 0.415329 0.909671i \(-0.363666\pi\)
0.415329 + 0.909671i \(0.363666\pi\)
\(72\) −4.25272e11 −0.359754
\(73\) 2.19719e9 0.00169930 0.000849649 1.00000i \(-0.499730\pi\)
0.000849649 1.00000i \(0.499730\pi\)
\(74\) 1.47130e12 1.04158
\(75\) −7.40661e11 −0.480531
\(76\) −2.39936e11 −0.142826
\(77\) 9.05110e10 0.0494893
\(78\) −9.46859e11 −0.476070
\(79\) −2.36194e12 −1.09318 −0.546591 0.837400i \(-0.684075\pi\)
−0.546591 + 0.837400i \(0.684075\pi\)
\(80\) 3.66403e11 0.156269
\(81\) 2.82430e11 0.111111
\(82\) 5.23244e11 0.190070
\(83\) 3.89435e12 1.30746 0.653729 0.756729i \(-0.273204\pi\)
0.653729 + 0.756729i \(0.273204\pi\)
\(84\) 4.14663e10 0.0128789
\(85\) −1.67418e12 −0.481481
\(86\) 2.82560e12 0.753132
\(87\) 1.37251e11 0.0339344
\(88\) 4.50501e12 1.03409
\(89\) 3.38545e12 0.722073 0.361036 0.932552i \(-0.382423\pi\)
0.361036 + 0.932552i \(0.382423\pi\)
\(90\) −5.18725e11 −0.102887
\(91\) 3.06097e11 0.0565054
\(92\) 4.61908e12 0.794209
\(93\) −3.20180e12 −0.513163
\(94\) −8.50881e12 −1.27215
\(95\) −9.70311e11 −0.135428
\(96\) 3.50530e12 0.457049
\(97\) −2.54230e12 −0.309893 −0.154946 0.987923i \(-0.549520\pi\)
−0.154946 + 0.987923i \(0.549520\pi\)
\(98\) −6.59220e12 −0.751728
\(99\) −2.99185e12 −0.319382
\(100\) 3.59454e12 0.359454
\(101\) 5.35425e12 0.501891 0.250946 0.968001i \(-0.419258\pi\)
0.250946 + 0.968001i \(0.419258\pi\)
\(102\) 5.81942e12 0.511657
\(103\) 1.13168e13 0.933863 0.466932 0.884293i \(-0.345359\pi\)
0.466932 + 0.884293i \(0.345359\pi\)
\(104\) 1.52354e13 1.18069
\(105\) 1.67691e11 0.0122118
\(106\) 7.95673e12 0.544812
\(107\) 1.59125e13 1.02505 0.512525 0.858673i \(-0.328710\pi\)
0.512525 + 0.858673i \(0.328710\pi\)
\(108\) −1.37067e12 −0.0831149
\(109\) 1.47025e13 0.839688 0.419844 0.907596i \(-0.362085\pi\)
0.419844 + 0.907596i \(0.362085\pi\)
\(110\) 5.49498e12 0.295742
\(111\) 1.57222e13 0.797835
\(112\) 4.11728e11 0.0197103
\(113\) −1.71973e13 −0.777053 −0.388526 0.921438i \(-0.627016\pi\)
−0.388526 + 0.921438i \(0.627016\pi\)
\(114\) 3.37278e12 0.143915
\(115\) 1.86798e13 0.753070
\(116\) −6.66098e11 −0.0253841
\(117\) −1.01181e13 −0.364661
\(118\) −2.87758e12 −0.0981285
\(119\) −1.88128e12 −0.0607293
\(120\) 8.34652e12 0.255169
\(121\) −2.82935e12 −0.0819562
\(122\) 6.18891e12 0.169932
\(123\) 5.59134e12 0.145590
\(124\) 1.55388e13 0.383863
\(125\) 3.20017e13 0.750341
\(126\) −5.82892e11 −0.0129772
\(127\) −9.22435e12 −0.195079 −0.0975397 0.995232i \(-0.531097\pi\)
−0.0975397 + 0.995232i \(0.531097\pi\)
\(128\) −2.69978e12 −0.0542580
\(129\) 3.01942e13 0.576886
\(130\) 1.85833e13 0.337670
\(131\) −3.50945e12 −0.0606702 −0.0303351 0.999540i \(-0.509657\pi\)
−0.0303351 + 0.999540i \(0.509657\pi\)
\(132\) 1.45199e13 0.238909
\(133\) −1.09034e12 −0.0170815
\(134\) 1.90867e13 0.284806
\(135\) −5.54305e12 −0.0788096
\(136\) −9.36371e13 −1.26895
\(137\) −6.75736e12 −0.0873159 −0.0436579 0.999047i \(-0.513901\pi\)
−0.0436579 + 0.999047i \(0.513901\pi\)
\(138\) −6.49305e13 −0.800267
\(139\) 5.30396e13 0.623740 0.311870 0.950125i \(-0.399045\pi\)
0.311870 + 0.950125i \(0.399045\pi\)
\(140\) −8.13830e11 −0.00913485
\(141\) −9.09244e13 −0.974443
\(142\) 6.11671e13 0.626100
\(143\) 1.07183e14 1.04819
\(144\) −1.36097e13 −0.127201
\(145\) −2.69373e12 −0.0240692
\(146\) 1.49894e11 0.00128083
\(147\) −7.04437e13 −0.575810
\(148\) −7.63019e13 −0.596808
\(149\) −9.35310e13 −0.700236 −0.350118 0.936706i \(-0.613859\pi\)
−0.350118 + 0.936706i \(0.613859\pi\)
\(150\) −5.05284e13 −0.362195
\(151\) 1.21235e14 0.832296 0.416148 0.909297i \(-0.363380\pi\)
0.416148 + 0.909297i \(0.363380\pi\)
\(152\) −5.42696e13 −0.356922
\(153\) 6.21858e13 0.391920
\(154\) 6.17472e12 0.0373021
\(155\) 6.28395e13 0.363979
\(156\) 4.91043e13 0.272778
\(157\) 1.43660e14 0.765574 0.382787 0.923837i \(-0.374964\pi\)
0.382787 + 0.923837i \(0.374964\pi\)
\(158\) −1.61133e14 −0.823974
\(159\) 8.50249e13 0.417316
\(160\) −6.87961e13 −0.324178
\(161\) 2.09905e13 0.0949849
\(162\) 1.92675e13 0.0837488
\(163\) −6.72578e13 −0.280881 −0.140441 0.990089i \(-0.544852\pi\)
−0.140441 + 0.990089i \(0.544852\pi\)
\(164\) −2.71356e13 −0.108907
\(165\) 5.87189e13 0.226533
\(166\) 2.65675e14 0.985482
\(167\) −3.82364e13 −0.136402 −0.0682009 0.997672i \(-0.521726\pi\)
−0.0682009 + 0.997672i \(0.521726\pi\)
\(168\) 9.37900e12 0.0321845
\(169\) 5.96046e13 0.196796
\(170\) −1.14214e14 −0.362911
\(171\) 3.60413e13 0.110236
\(172\) −1.46537e14 −0.431530
\(173\) 4.20171e14 1.19159 0.595794 0.803137i \(-0.296838\pi\)
0.595794 + 0.803137i \(0.296838\pi\)
\(174\) 9.36335e12 0.0255777
\(175\) 1.63346e13 0.0429895
\(176\) 1.44171e14 0.365633
\(177\) −3.07496e13 −0.0751646
\(178\) 2.30957e14 0.544254
\(179\) 5.91337e14 1.34366 0.671832 0.740704i \(-0.265508\pi\)
0.671832 + 0.740704i \(0.265508\pi\)
\(180\) 2.69012e13 0.0589522
\(181\) 2.38624e14 0.504433 0.252217 0.967671i \(-0.418840\pi\)
0.252217 + 0.967671i \(0.418840\pi\)
\(182\) 2.08821e13 0.0425903
\(183\) 6.61341e13 0.130165
\(184\) 1.04476e15 1.98473
\(185\) −3.08568e14 −0.565893
\(186\) −2.18429e14 −0.386791
\(187\) −6.58750e14 −1.12655
\(188\) 4.41269e14 0.728916
\(189\) −6.22874e12 −0.00994027
\(190\) −6.61952e13 −0.102077
\(191\) −4.91288e14 −0.732183 −0.366091 0.930579i \(-0.619304\pi\)
−0.366091 + 0.930579i \(0.619304\pi\)
\(192\) 3.92070e14 0.564815
\(193\) −1.19878e15 −1.66961 −0.834806 0.550544i \(-0.814420\pi\)
−0.834806 + 0.550544i \(0.814420\pi\)
\(194\) −1.73438e14 −0.233578
\(195\) 1.98580e14 0.258649
\(196\) 3.41873e14 0.430725
\(197\) −5.83934e14 −0.711760 −0.355880 0.934532i \(-0.615819\pi\)
−0.355880 + 0.934532i \(0.615819\pi\)
\(198\) −2.04106e14 −0.240731
\(199\) 1.08547e15 1.23900 0.619500 0.784997i \(-0.287335\pi\)
0.619500 + 0.784997i \(0.287335\pi\)
\(200\) 8.13025e14 0.898274
\(201\) 2.03959e14 0.218156
\(202\) 3.65271e14 0.378295
\(203\) −3.02695e12 −0.00303585
\(204\) −3.01797e14 −0.293169
\(205\) −1.09737e14 −0.103265
\(206\) 7.72042e14 0.703889
\(207\) −6.93842e14 −0.612990
\(208\) 4.87568e14 0.417468
\(209\) −3.81794e14 −0.316868
\(210\) 1.14400e13 0.00920452
\(211\) −6.59647e14 −0.514607 −0.257303 0.966331i \(-0.582834\pi\)
−0.257303 + 0.966331i \(0.582834\pi\)
\(212\) −4.12638e14 −0.312166
\(213\) 6.53626e14 0.479581
\(214\) 1.08556e15 0.772620
\(215\) −5.92599e14 −0.409177
\(216\) −3.10023e14 −0.207704
\(217\) 7.06129e13 0.0459088
\(218\) 1.00301e15 0.632906
\(219\) 1.60175e12 0.000981090 0
\(220\) −2.84971e14 −0.169455
\(221\) −2.22781e15 −1.28626
\(222\) 1.07258e15 0.601359
\(223\) 3.56431e14 0.194086 0.0970429 0.995280i \(-0.469062\pi\)
0.0970429 + 0.995280i \(0.469062\pi\)
\(224\) −7.73064e13 −0.0408887
\(225\) −5.39942e14 −0.277435
\(226\) −1.17321e15 −0.585695
\(227\) 1.97090e15 0.956085 0.478043 0.878337i \(-0.341346\pi\)
0.478043 + 0.878337i \(0.341346\pi\)
\(228\) −1.74913e14 −0.0824606
\(229\) 3.65385e15 1.67425 0.837124 0.547014i \(-0.184236\pi\)
0.837124 + 0.547014i \(0.184236\pi\)
\(230\) 1.27435e15 0.567618
\(231\) 6.59825e13 0.0285727
\(232\) −1.50661e14 −0.0634348
\(233\) −1.47105e14 −0.0602300 −0.0301150 0.999546i \(-0.509587\pi\)
−0.0301150 + 0.999546i \(0.509587\pi\)
\(234\) −6.90260e14 −0.274859
\(235\) 1.78451e15 0.691159
\(236\) 1.49232e14 0.0562257
\(237\) −1.72185e15 −0.631149
\(238\) −1.28342e14 −0.0457740
\(239\) 2.23241e15 0.774798 0.387399 0.921912i \(-0.373374\pi\)
0.387399 + 0.921912i \(0.373374\pi\)
\(240\) 2.67108e14 0.0902222
\(241\) −9.69707e13 −0.0318808 −0.0159404 0.999873i \(-0.505074\pi\)
−0.0159404 + 0.999873i \(0.505074\pi\)
\(242\) −1.93020e14 −0.0617736
\(243\) 2.05891e14 0.0641500
\(244\) −3.20958e14 −0.0973676
\(245\) 1.38255e15 0.408414
\(246\) 3.81445e14 0.109737
\(247\) −1.29118e15 −0.361790
\(248\) 3.51462e15 0.959274
\(249\) 2.83898e15 0.754861
\(250\) 2.18318e15 0.565561
\(251\) −4.62528e15 −1.16751 −0.583753 0.811931i \(-0.698416\pi\)
−0.583753 + 0.811931i \(0.698416\pi\)
\(252\) 3.02289e13 0.00743566
\(253\) 7.35004e15 1.76200
\(254\) −6.29291e14 −0.147039
\(255\) −1.22048e15 −0.277983
\(256\) −4.59000e15 −1.01918
\(257\) −1.85280e15 −0.401110 −0.200555 0.979682i \(-0.564275\pi\)
−0.200555 + 0.979682i \(0.564275\pi\)
\(258\) 2.05987e15 0.434821
\(259\) −3.46739e14 −0.0713763
\(260\) −9.63737e14 −0.193478
\(261\) 1.00056e14 0.0195920
\(262\) −2.39417e14 −0.0457295
\(263\) 8.13314e15 1.51546 0.757732 0.652566i \(-0.226307\pi\)
0.757732 + 0.652566i \(0.226307\pi\)
\(264\) 3.28415e15 0.597032
\(265\) −1.66872e15 −0.295996
\(266\) −7.43838e13 −0.0128750
\(267\) 2.46799e15 0.416889
\(268\) −9.89840e14 −0.163188
\(269\) −2.57796e15 −0.414845 −0.207423 0.978251i \(-0.566507\pi\)
−0.207423 + 0.978251i \(0.566507\pi\)
\(270\) −3.78150e14 −0.0594019
\(271\) 9.60115e15 1.47239 0.736195 0.676769i \(-0.236620\pi\)
0.736195 + 0.676769i \(0.236620\pi\)
\(272\) −2.99660e15 −0.448675
\(273\) 2.23145e14 0.0326234
\(274\) −4.60991e14 −0.0658134
\(275\) 5.71974e15 0.797469
\(276\) 3.36731e15 0.458537
\(277\) 2.44482e15 0.325183 0.162592 0.986693i \(-0.448015\pi\)
0.162592 + 0.986693i \(0.448015\pi\)
\(278\) 3.61839e15 0.470137
\(279\) −2.33411e15 −0.296275
\(280\) −1.84075e14 −0.0228280
\(281\) −5.47611e15 −0.663561 −0.331780 0.943357i \(-0.607649\pi\)
−0.331780 + 0.943357i \(0.607649\pi\)
\(282\) −6.20292e15 −0.734476
\(283\) −1.13967e15 −0.131877 −0.0659383 0.997824i \(-0.521004\pi\)
−0.0659383 + 0.997824i \(0.521004\pi\)
\(284\) −3.17214e15 −0.358743
\(285\) −7.07357e14 −0.0781892
\(286\) 7.31210e15 0.790065
\(287\) −1.23312e14 −0.0130249
\(288\) 2.55537e15 0.263877
\(289\) 3.78759e15 0.382408
\(290\) −1.83768e14 −0.0181419
\(291\) −1.85334e15 −0.178917
\(292\) −7.77353e12 −0.000733888 0
\(293\) −1.25752e16 −1.16111 −0.580556 0.814221i \(-0.697165\pi\)
−0.580556 + 0.814221i \(0.697165\pi\)
\(294\) −4.80571e15 −0.434010
\(295\) 6.03501e14 0.0533132
\(296\) −1.72582e16 −1.49142
\(297\) −2.18106e15 −0.184395
\(298\) −6.38075e15 −0.527796
\(299\) 2.48569e16 2.01180
\(300\) 2.62042e15 0.207531
\(301\) −6.65906e14 −0.0516096
\(302\) 8.27073e15 0.627334
\(303\) 3.90325e15 0.289767
\(304\) −1.73675e15 −0.126200
\(305\) −1.29797e15 −0.0923241
\(306\) 4.24236e15 0.295405
\(307\) −3.17745e15 −0.216610 −0.108305 0.994118i \(-0.534542\pi\)
−0.108305 + 0.994118i \(0.534542\pi\)
\(308\) −3.20223e14 −0.0213733
\(309\) 8.24998e15 0.539166
\(310\) 4.28695e15 0.274345
\(311\) −7.53782e15 −0.472392 −0.236196 0.971705i \(-0.575901\pi\)
−0.236196 + 0.971705i \(0.575901\pi\)
\(312\) 1.11066e16 0.681673
\(313\) 1.29776e16 0.780113 0.390056 0.920791i \(-0.372456\pi\)
0.390056 + 0.920791i \(0.372456\pi\)
\(314\) 9.80056e15 0.577043
\(315\) 1.22247e14 0.00705050
\(316\) 8.35640e15 0.472121
\(317\) 3.20214e16 1.77237 0.886186 0.463330i \(-0.153346\pi\)
0.886186 + 0.463330i \(0.153346\pi\)
\(318\) 5.80045e15 0.314547
\(319\) −1.05992e15 −0.0563161
\(320\) −7.69489e15 −0.400615
\(321\) 1.16002e16 0.591812
\(322\) 1.43199e15 0.0715938
\(323\) 7.93562e15 0.388834
\(324\) −9.99219e14 −0.0479864
\(325\) 1.93435e16 0.910526
\(326\) −4.58837e15 −0.211711
\(327\) 1.07181e16 0.484794
\(328\) −6.13762e15 −0.272158
\(329\) 2.00526e15 0.0871760
\(330\) 4.00584e15 0.170747
\(331\) 2.60836e16 1.09015 0.545073 0.838388i \(-0.316502\pi\)
0.545073 + 0.838388i \(0.316502\pi\)
\(332\) −1.37780e16 −0.564661
\(333\) 1.14615e16 0.460630
\(334\) −2.60851e15 −0.102811
\(335\) −4.00295e15 −0.154735
\(336\) 3.00150e14 0.0113797
\(337\) −1.94511e16 −0.723352 −0.361676 0.932304i \(-0.617795\pi\)
−0.361676 + 0.932304i \(0.617795\pi\)
\(338\) 4.06627e15 0.148333
\(339\) −1.25368e16 −0.448632
\(340\) 5.92315e15 0.207941
\(341\) 2.47258e16 0.851623
\(342\) 2.45876e15 0.0830895
\(343\) 3.11130e15 0.103165
\(344\) −3.31442e16 −1.07839
\(345\) 1.36175e16 0.434785
\(346\) 2.86643e16 0.898146
\(347\) 3.17367e16 0.975933 0.487966 0.872862i \(-0.337739\pi\)
0.487966 + 0.872862i \(0.337739\pi\)
\(348\) −4.85586e14 −0.0146555
\(349\) 1.90370e16 0.563939 0.281970 0.959423i \(-0.409012\pi\)
0.281970 + 0.959423i \(0.409012\pi\)
\(350\) 1.11436e15 0.0324028
\(351\) −7.37606e15 −0.210537
\(352\) −2.70696e16 −0.758499
\(353\) −5.22879e16 −1.43835 −0.719177 0.694827i \(-0.755481\pi\)
−0.719177 + 0.694827i \(0.755481\pi\)
\(354\) −2.09776e15 −0.0566545
\(355\) −1.28283e16 −0.340160
\(356\) −1.19775e16 −0.311847
\(357\) −1.37145e15 −0.0350621
\(358\) 4.03414e16 1.01277
\(359\) −1.28083e16 −0.315774 −0.157887 0.987457i \(-0.550468\pi\)
−0.157887 + 0.987457i \(0.550468\pi\)
\(360\) 6.08461e15 0.147322
\(361\) −3.74537e16 −0.890631
\(362\) 1.62791e16 0.380211
\(363\) −2.06260e15 −0.0473175
\(364\) −1.08295e15 −0.0244034
\(365\) −3.14365e13 −0.000695873 0
\(366\) 4.51171e15 0.0981102
\(367\) −2.23147e15 −0.0476718 −0.0238359 0.999716i \(-0.507588\pi\)
−0.0238359 + 0.999716i \(0.507588\pi\)
\(368\) 3.34348e16 0.701758
\(369\) 4.07609e15 0.0840567
\(370\) −2.10507e16 −0.426536
\(371\) −1.87515e15 −0.0373341
\(372\) 1.13278e16 0.221623
\(373\) 3.49809e16 0.672548 0.336274 0.941764i \(-0.390833\pi\)
0.336274 + 0.941764i \(0.390833\pi\)
\(374\) −4.49403e16 −0.849123
\(375\) 2.33293e16 0.433209
\(376\) 9.98079e16 1.82156
\(377\) −3.58451e15 −0.0643000
\(378\) −4.24928e14 −0.00749237
\(379\) 4.02456e16 0.697530 0.348765 0.937210i \(-0.386601\pi\)
0.348765 + 0.937210i \(0.386601\pi\)
\(380\) 3.43290e15 0.0584882
\(381\) −6.72455e15 −0.112629
\(382\) −3.35160e16 −0.551875
\(383\) −7.55162e16 −1.22250 −0.611249 0.791438i \(-0.709333\pi\)
−0.611249 + 0.791438i \(0.709333\pi\)
\(384\) −1.96814e15 −0.0313259
\(385\) −1.29499e15 −0.0202662
\(386\) −8.17813e16 −1.25845
\(387\) 2.20115e16 0.333065
\(388\) 8.99452e15 0.133836
\(389\) 1.02590e17 1.50117 0.750586 0.660772i \(-0.229771\pi\)
0.750586 + 0.660772i \(0.229771\pi\)
\(390\) 1.35473e16 0.194954
\(391\) −1.52771e17 −2.16218
\(392\) 7.73261e16 1.07638
\(393\) −2.55839e15 −0.0350280
\(394\) −3.98364e16 −0.536481
\(395\) 3.37936e16 0.447665
\(396\) 1.05850e16 0.137934
\(397\) −7.63990e16 −0.979376 −0.489688 0.871898i \(-0.662889\pi\)
−0.489688 + 0.871898i \(0.662889\pi\)
\(398\) 7.40512e16 0.933882
\(399\) −7.94858e14 −0.00986202
\(400\) 2.60187e16 0.317611
\(401\) −3.11585e16 −0.374229 −0.187115 0.982338i \(-0.559914\pi\)
−0.187115 + 0.982338i \(0.559914\pi\)
\(402\) 1.39142e16 0.164433
\(403\) 8.36197e16 0.972357
\(404\) −1.89430e16 −0.216756
\(405\) −4.04088e15 −0.0455007
\(406\) −2.06500e14 −0.00228824
\(407\) −1.21414e17 −1.32405
\(408\) −6.82614e16 −0.732630
\(409\) 2.97554e16 0.314314 0.157157 0.987574i \(-0.449767\pi\)
0.157157 + 0.987574i \(0.449767\pi\)
\(410\) −7.48636e15 −0.0778351
\(411\) −4.92611e15 −0.0504118
\(412\) −4.00383e16 −0.403315
\(413\) 6.78156e14 0.00672441
\(414\) −4.73343e16 −0.462034
\(415\) −5.57187e16 −0.535412
\(416\) −9.15461e16 −0.866031
\(417\) 3.86658e16 0.360117
\(418\) −2.60462e16 −0.238836
\(419\) 4.42811e16 0.399786 0.199893 0.979818i \(-0.435941\pi\)
0.199893 + 0.979818i \(0.435941\pi\)
\(420\) −5.93282e14 −0.00527401
\(421\) −1.57089e16 −0.137503 −0.0687516 0.997634i \(-0.521902\pi\)
−0.0687516 + 0.997634i \(0.521902\pi\)
\(422\) −4.50015e16 −0.387879
\(423\) −6.62839e16 −0.562595
\(424\) −9.33319e16 −0.780104
\(425\) −1.18885e17 −0.978589
\(426\) 4.45908e16 0.361479
\(427\) −1.45853e15 −0.0116449
\(428\) −5.62976e16 −0.442696
\(429\) 7.81364e16 0.605175
\(430\) −4.04275e16 −0.308413
\(431\) −4.64195e16 −0.348818 −0.174409 0.984673i \(-0.555801\pi\)
−0.174409 + 0.984673i \(0.555801\pi\)
\(432\) −9.92146e15 −0.0734398
\(433\) −1.74150e17 −1.26985 −0.634923 0.772575i \(-0.718968\pi\)
−0.634923 + 0.772575i \(0.718968\pi\)
\(434\) 4.81726e15 0.0346032
\(435\) −1.96373e15 −0.0138964
\(436\) −5.20165e16 −0.362643
\(437\) −8.85422e16 −0.608164
\(438\) 1.09273e14 0.000739486 0
\(439\) 9.81827e16 0.654660 0.327330 0.944910i \(-0.393851\pi\)
0.327330 + 0.944910i \(0.393851\pi\)
\(440\) −6.44558e16 −0.423467
\(441\) −5.13534e16 −0.332444
\(442\) −1.51983e17 −0.969503
\(443\) −6.64375e16 −0.417628 −0.208814 0.977955i \(-0.566960\pi\)
−0.208814 + 0.977955i \(0.566960\pi\)
\(444\) −5.56241e16 −0.344567
\(445\) −4.84375e16 −0.295694
\(446\) 2.43160e16 0.146290
\(447\) −6.81841e16 −0.404282
\(448\) −8.64677e15 −0.0505297
\(449\) −2.30121e17 −1.32542 −0.662712 0.748874i \(-0.730595\pi\)
−0.662712 + 0.748874i \(0.730595\pi\)
\(450\) −3.68352e16 −0.209113
\(451\) −4.31790e16 −0.241616
\(452\) 6.08430e16 0.335592
\(453\) 8.83803e16 0.480526
\(454\) 1.34456e17 0.720639
\(455\) −4.37951e15 −0.0231393
\(456\) −3.95625e16 −0.206069
\(457\) −3.07539e17 −1.57923 −0.789613 0.613605i \(-0.789719\pi\)
−0.789613 + 0.613605i \(0.789719\pi\)
\(458\) 2.49268e17 1.26195
\(459\) 4.53334e16 0.226275
\(460\) −6.60879e16 −0.325234
\(461\) −1.50288e17 −0.729235 −0.364617 0.931157i \(-0.618800\pi\)
−0.364617 + 0.931157i \(0.618800\pi\)
\(462\) 4.50137e15 0.0215363
\(463\) −1.70959e17 −0.806522 −0.403261 0.915085i \(-0.632123\pi\)
−0.403261 + 0.915085i \(0.632123\pi\)
\(464\) −4.82149e15 −0.0224292
\(465\) 4.58100e16 0.210144
\(466\) −1.00356e16 −0.0453977
\(467\) −2.26436e17 −1.01015 −0.505074 0.863076i \(-0.668535\pi\)
−0.505074 + 0.863076i \(0.668535\pi\)
\(468\) 3.57971e16 0.157489
\(469\) −4.49813e15 −0.0195168
\(470\) 1.21740e17 0.520953
\(471\) 1.04728e17 0.442004
\(472\) 3.37539e16 0.140508
\(473\) −2.33174e17 −0.957375
\(474\) −1.17466e17 −0.475722
\(475\) −6.89028e16 −0.275251
\(476\) 6.65586e15 0.0262276
\(477\) 6.19831e16 0.240937
\(478\) 1.52297e17 0.583995
\(479\) 1.64646e17 0.622831 0.311415 0.950274i \(-0.399197\pi\)
0.311415 + 0.950274i \(0.399197\pi\)
\(480\) −5.01524e16 −0.187165
\(481\) −4.10607e17 −1.51176
\(482\) −6.61540e15 −0.0240298
\(483\) 1.53021e16 0.0548395
\(484\) 1.00101e16 0.0353951
\(485\) 3.63742e16 0.126903
\(486\) 1.40460e16 0.0483524
\(487\) 8.54260e16 0.290170 0.145085 0.989419i \(-0.453654\pi\)
0.145085 + 0.989419i \(0.453654\pi\)
\(488\) −7.25955e16 −0.243322
\(489\) −4.90309e16 −0.162167
\(490\) 9.43184e16 0.307838
\(491\) −3.83545e17 −1.23534 −0.617670 0.786437i \(-0.711923\pi\)
−0.617670 + 0.786437i \(0.711923\pi\)
\(492\) −1.97818e16 −0.0628772
\(493\) 2.20305e16 0.0691065
\(494\) −8.80852e16 −0.272695
\(495\) 4.28060e16 0.130789
\(496\) 1.12476e17 0.339179
\(497\) −1.44151e16 −0.0429045
\(498\) 1.93677e17 0.568968
\(499\) 4.84648e17 1.40531 0.702656 0.711530i \(-0.251997\pi\)
0.702656 + 0.711530i \(0.251997\pi\)
\(500\) −1.13220e17 −0.324055
\(501\) −2.78743e16 −0.0787516
\(502\) −3.15540e17 −0.879995
\(503\) 2.36855e17 0.652063 0.326032 0.945359i \(-0.394288\pi\)
0.326032 + 0.945359i \(0.394288\pi\)
\(504\) 6.83729e15 0.0185817
\(505\) −7.66063e16 −0.205528
\(506\) 5.01424e17 1.32809
\(507\) 4.34518e16 0.113620
\(508\) 3.26352e16 0.0842504
\(509\) −2.52726e17 −0.644147 −0.322073 0.946715i \(-0.604380\pi\)
−0.322073 + 0.946715i \(0.604380\pi\)
\(510\) −8.32618e16 −0.209527
\(511\) −3.53252e13 −8.77707e−5 0
\(512\) −2.91016e17 −0.713941
\(513\) 2.62741e16 0.0636450
\(514\) −1.26399e17 −0.302332
\(515\) −1.61917e17 −0.382423
\(516\) −1.06825e17 −0.249144
\(517\) 7.02162e17 1.61714
\(518\) −2.36547e16 −0.0537991
\(519\) 3.06304e17 0.687964
\(520\) −2.17981e17 −0.483501
\(521\) −6.03304e17 −1.32157 −0.660786 0.750574i \(-0.729777\pi\)
−0.660786 + 0.750574i \(0.729777\pi\)
\(522\) 6.82588e15 0.0147673
\(523\) −1.80923e17 −0.386574 −0.193287 0.981142i \(-0.561915\pi\)
−0.193287 + 0.981142i \(0.561915\pi\)
\(524\) 1.24162e16 0.0262021
\(525\) 1.19080e16 0.0248200
\(526\) 5.54848e17 1.14226
\(527\) −5.13929e17 −1.04504
\(528\) 1.05101e17 0.211098
\(529\) 1.20052e18 2.38181
\(530\) −1.13841e17 −0.223104
\(531\) −2.24165e16 −0.0433963
\(532\) 3.85756e15 0.00737713
\(533\) −1.46026e17 −0.275869
\(534\) 1.68368e17 0.314225
\(535\) −2.27670e17 −0.419764
\(536\) −2.23886e17 −0.407808
\(537\) 4.31085e17 0.775764
\(538\) −1.75870e17 −0.312685
\(539\) 5.43999e17 0.955590
\(540\) 1.96110e16 0.0340361
\(541\) 4.78906e17 0.821236 0.410618 0.911807i \(-0.365313\pi\)
0.410618 + 0.911807i \(0.365313\pi\)
\(542\) 6.54997e17 1.10980
\(543\) 1.73957e17 0.291235
\(544\) 5.62645e17 0.930768
\(545\) −2.10357e17 −0.343858
\(546\) 1.52231e16 0.0245895
\(547\) −3.24068e17 −0.517272 −0.258636 0.965975i \(-0.583273\pi\)
−0.258636 + 0.965975i \(0.583273\pi\)
\(548\) 2.39071e16 0.0377098
\(549\) 4.82118e16 0.0751507
\(550\) 3.90205e17 0.601084
\(551\) 1.27683e16 0.0194378
\(552\) 7.61631e17 1.14588
\(553\) 3.79740e16 0.0564641
\(554\) 1.66787e17 0.245103
\(555\) −2.24946e17 −0.326719
\(556\) −1.87651e17 −0.269379
\(557\) −4.01406e16 −0.0569541 −0.0284771 0.999594i \(-0.509066\pi\)
−0.0284771 + 0.999594i \(0.509066\pi\)
\(558\) −1.59235e17 −0.223314
\(559\) −7.88564e17 −1.09310
\(560\) −5.89083e15 −0.00807150
\(561\) −4.80228e17 −0.650413
\(562\) −3.73584e17 −0.500152
\(563\) 1.07562e18 1.42349 0.711746 0.702437i \(-0.247905\pi\)
0.711746 + 0.702437i \(0.247905\pi\)
\(564\) 3.21685e17 0.420840
\(565\) 2.46052e17 0.318208
\(566\) −7.77492e16 −0.0994006
\(567\) −4.54075e15 −0.00573902
\(568\) −7.17486e17 −0.896498
\(569\) −8.84728e17 −1.09290 −0.546449 0.837492i \(-0.684021\pi\)
−0.546449 + 0.837492i \(0.684021\pi\)
\(570\) −4.82563e16 −0.0589342
\(571\) −4.11167e17 −0.496460 −0.248230 0.968701i \(-0.579849\pi\)
−0.248230 + 0.968701i \(0.579849\pi\)
\(572\) −3.79207e17 −0.452692
\(573\) −3.58149e17 −0.422726
\(574\) −8.41244e15 −0.00981736
\(575\) 1.32647e18 1.53058
\(576\) 2.85819e17 0.326096
\(577\) −8.47435e17 −0.956012 −0.478006 0.878357i \(-0.658640\pi\)
−0.478006 + 0.878357i \(0.658640\pi\)
\(578\) 2.58392e17 0.288236
\(579\) −8.73908e17 −0.963951
\(580\) 9.53025e15 0.0103949
\(581\) −6.26113e16 −0.0675317
\(582\) −1.26436e17 −0.134856
\(583\) −6.56603e17 −0.692559
\(584\) −1.75825e15 −0.00183399
\(585\) 1.44765e17 0.149331
\(586\) −8.57885e17 −0.875175
\(587\) 1.57040e18 1.58440 0.792198 0.610264i \(-0.208937\pi\)
0.792198 + 0.610264i \(0.208937\pi\)
\(588\) 2.49225e17 0.248679
\(589\) −2.97860e17 −0.293942
\(590\) 4.11712e16 0.0401842
\(591\) −4.25688e17 −0.410935
\(592\) −5.52304e17 −0.527335
\(593\) 7.08580e17 0.669165 0.334582 0.942366i \(-0.391405\pi\)
0.334582 + 0.942366i \(0.391405\pi\)
\(594\) −1.48793e17 −0.138986
\(595\) 2.69165e16 0.0248690
\(596\) 3.30907e17 0.302416
\(597\) 7.91305e17 0.715337
\(598\) 1.69576e18 1.51637
\(599\) 1.29626e18 1.14662 0.573308 0.819340i \(-0.305660\pi\)
0.573308 + 0.819340i \(0.305660\pi\)
\(600\) 5.92695e17 0.518619
\(601\) −1.79436e18 −1.55319 −0.776597 0.629998i \(-0.783056\pi\)
−0.776597 + 0.629998i \(0.783056\pi\)
\(602\) −4.54285e16 −0.0389002
\(603\) 1.48686e17 0.125953
\(604\) −4.28922e17 −0.359450
\(605\) 4.04811e16 0.0335616
\(606\) 2.66282e17 0.218409
\(607\) −1.09671e18 −0.889948 −0.444974 0.895543i \(-0.646787\pi\)
−0.444974 + 0.895543i \(0.646787\pi\)
\(608\) 3.26094e17 0.261800
\(609\) −2.20665e15 −0.00175275
\(610\) −8.85482e16 −0.0695882
\(611\) 2.37462e18 1.84641
\(612\) −2.20010e17 −0.169261
\(613\) 1.12867e17 0.0859163 0.0429582 0.999077i \(-0.486322\pi\)
0.0429582 + 0.999077i \(0.486322\pi\)
\(614\) −2.16768e17 −0.163268
\(615\) −7.99985e16 −0.0596202
\(616\) −7.24291e16 −0.0534120
\(617\) 1.11045e18 0.810299 0.405149 0.914250i \(-0.367219\pi\)
0.405149 + 0.914250i \(0.367219\pi\)
\(618\) 5.62819e17 0.406391
\(619\) −2.37317e18 −1.69567 −0.847833 0.530263i \(-0.822093\pi\)
−0.847833 + 0.530263i \(0.822093\pi\)
\(620\) −2.22322e17 −0.157194
\(621\) −5.05811e17 −0.353910
\(622\) −5.14235e17 −0.356061
\(623\) −5.44294e16 −0.0372959
\(624\) 3.55437e17 0.241025
\(625\) 7.82363e17 0.525035
\(626\) 8.85343e17 0.588001
\(627\) −2.78328e17 −0.182944
\(628\) −5.08259e17 −0.330634
\(629\) 2.52360e18 1.62477
\(630\) 8.33977e15 0.00531423
\(631\) −1.04868e18 −0.661379 −0.330690 0.943740i \(-0.607281\pi\)
−0.330690 + 0.943740i \(0.607281\pi\)
\(632\) 1.89008e18 1.17983
\(633\) −4.80882e17 −0.297108
\(634\) 2.18452e18 1.33591
\(635\) 1.31978e17 0.0798863
\(636\) −3.00813e17 −0.180229
\(637\) 1.83974e18 1.09106
\(638\) −7.23083e16 −0.0424476
\(639\) 4.76493e17 0.276886
\(640\) 3.86273e16 0.0222190
\(641\) 3.54450e16 0.0201826 0.0100913 0.999949i \(-0.496788\pi\)
0.0100913 + 0.999949i \(0.496788\pi\)
\(642\) 7.91376e17 0.446072
\(643\) −1.18886e18 −0.663376 −0.331688 0.943389i \(-0.607618\pi\)
−0.331688 + 0.943389i \(0.607618\pi\)
\(644\) −7.42631e16 −0.0410218
\(645\) −4.32005e17 −0.236238
\(646\) 5.41374e17 0.293080
\(647\) 1.24743e18 0.668559 0.334279 0.942474i \(-0.391507\pi\)
0.334279 + 0.942474i \(0.391507\pi\)
\(648\) −2.26007e17 −0.119918
\(649\) 2.37463e17 0.124740
\(650\) 1.31962e18 0.686299
\(651\) 5.14768e16 0.0265055
\(652\) 2.37954e17 0.121306
\(653\) −2.11743e18 −1.06875 −0.534373 0.845249i \(-0.679452\pi\)
−0.534373 + 0.845249i \(0.679452\pi\)
\(654\) 7.31196e17 0.365408
\(655\) 5.02117e16 0.0248449
\(656\) −1.96418e17 −0.0962292
\(657\) 1.16768e15 0.000566432 0
\(658\) 1.36800e17 0.0657080
\(659\) 4.39330e17 0.208947 0.104473 0.994528i \(-0.466684\pi\)
0.104473 + 0.994528i \(0.466684\pi\)
\(660\) −2.07744e17 −0.0978346
\(661\) −3.23741e17 −0.150969 −0.0754845 0.997147i \(-0.524050\pi\)
−0.0754845 + 0.997147i \(0.524050\pi\)
\(662\) 1.77944e18 0.821686
\(663\) −1.62407e18 −0.742622
\(664\) −3.11635e18 −1.41109
\(665\) 1.56001e16 0.00699500
\(666\) 7.81908e17 0.347195
\(667\) −2.45806e17 −0.108087
\(668\) 1.35278e17 0.0589088
\(669\) 2.59838e17 0.112055
\(670\) −2.73084e17 −0.116630
\(671\) −5.10719e17 −0.216016
\(672\) −5.63564e16 −0.0236071
\(673\) 2.95687e18 1.22669 0.613345 0.789815i \(-0.289824\pi\)
0.613345 + 0.789815i \(0.289824\pi\)
\(674\) −1.32697e18 −0.545218
\(675\) −3.93618e17 −0.160177
\(676\) −2.10878e17 −0.0849918
\(677\) −4.20450e18 −1.67837 −0.839185 0.543846i \(-0.816968\pi\)
−0.839185 + 0.543846i \(0.816968\pi\)
\(678\) −8.55271e17 −0.338151
\(679\) 4.08738e16 0.0160063
\(680\) 1.33972e18 0.519644
\(681\) 1.43679e18 0.551996
\(682\) 1.68681e18 0.641902
\(683\) 3.06840e18 1.15658 0.578292 0.815830i \(-0.303720\pi\)
0.578292 + 0.815830i \(0.303720\pi\)
\(684\) −1.27512e17 −0.0476086
\(685\) 9.66814e16 0.0357564
\(686\) 2.12255e17 0.0777591
\(687\) 2.66365e18 0.966627
\(688\) −1.06069e18 −0.381297
\(689\) −2.22055e18 −0.790743
\(690\) 9.28998e17 0.327715
\(691\) −5.62560e18 −1.96590 −0.982949 0.183876i \(-0.941136\pi\)
−0.982949 + 0.183876i \(0.941136\pi\)
\(692\) −1.48654e18 −0.514620
\(693\) 4.81013e16 0.0164964
\(694\) 2.16510e18 0.735598
\(695\) −7.58867e17 −0.255426
\(696\) −1.09832e17 −0.0366241
\(697\) 8.97480e17 0.296491
\(698\) 1.29871e18 0.425063
\(699\) −1.07239e17 −0.0347738
\(700\) −5.77910e16 −0.0185662
\(701\) 4.11353e18 1.30933 0.654663 0.755921i \(-0.272810\pi\)
0.654663 + 0.755921i \(0.272810\pi\)
\(702\) −5.03200e17 −0.158690
\(703\) 1.46261e18 0.457004
\(704\) −3.02776e18 −0.937343
\(705\) 1.30091e18 0.399041
\(706\) −3.56712e18 −1.08414
\(707\) −8.60827e16 −0.0259233
\(708\) 1.08790e17 0.0324619
\(709\) −1.08476e18 −0.320727 −0.160363 0.987058i \(-0.551267\pi\)
−0.160363 + 0.987058i \(0.551267\pi\)
\(710\) −8.75152e17 −0.256392
\(711\) −1.25523e18 −0.364394
\(712\) −2.70912e18 −0.779306
\(713\) 5.73419e18 1.63452
\(714\) −9.35615e16 −0.0264277
\(715\) −1.53353e18 −0.429242
\(716\) −2.09212e18 −0.580298
\(717\) 1.62743e18 0.447330
\(718\) −8.73789e17 −0.238011
\(719\) 5.12406e16 0.0138317 0.00691586 0.999976i \(-0.497799\pi\)
0.00691586 + 0.999976i \(0.497799\pi\)
\(720\) 1.94722e17 0.0520898
\(721\) −1.81946e17 −0.0482351
\(722\) −2.55512e18 −0.671304
\(723\) −7.06916e16 −0.0184064
\(724\) −8.44238e17 −0.217853
\(725\) −1.91285e17 −0.0489196
\(726\) −1.40712e17 −0.0356650
\(727\) −5.49897e18 −1.38136 −0.690682 0.723159i \(-0.742689\pi\)
−0.690682 + 0.723159i \(0.742689\pi\)
\(728\) −2.44946e17 −0.0609841
\(729\) 1.50095e17 0.0370370
\(730\) −2.14462e15 −0.000524507 0
\(731\) 4.84654e18 1.17481
\(732\) −2.33979e17 −0.0562152
\(733\) 7.36959e17 0.175496 0.0877480 0.996143i \(-0.472033\pi\)
0.0877480 + 0.996143i \(0.472033\pi\)
\(734\) −1.52232e17 −0.0359321
\(735\) 1.00788e18 0.235798
\(736\) −6.27774e18 −1.45579
\(737\) −1.57507e18 −0.362043
\(738\) 2.78073e17 0.0633568
\(739\) −9.89430e17 −0.223458 −0.111729 0.993739i \(-0.535639\pi\)
−0.111729 + 0.993739i \(0.535639\pi\)
\(740\) 1.09170e18 0.244397
\(741\) −9.41270e17 −0.208880
\(742\) −1.27924e17 −0.0281401
\(743\) 7.55374e18 1.64716 0.823578 0.567203i \(-0.191975\pi\)
0.823578 + 0.567203i \(0.191975\pi\)
\(744\) 2.56216e18 0.553837
\(745\) 1.33820e18 0.286751
\(746\) 2.38642e18 0.506926
\(747\) 2.06962e18 0.435819
\(748\) 2.33062e18 0.486531
\(749\) −2.55833e17 −0.0529450
\(750\) 1.59154e18 0.326527
\(751\) 2.68314e17 0.0545737 0.0272869 0.999628i \(-0.491313\pi\)
0.0272869 + 0.999628i \(0.491313\pi\)
\(752\) 3.19408e18 0.644066
\(753\) −3.37183e18 −0.674060
\(754\) −2.44538e17 −0.0484654
\(755\) −1.73458e18 −0.340831
\(756\) 2.20369e16 0.00429298
\(757\) 6.12937e18 1.18384 0.591919 0.805997i \(-0.298371\pi\)
0.591919 + 0.805997i \(0.298371\pi\)
\(758\) 2.74558e18 0.525756
\(759\) 5.35818e18 1.01729
\(760\) 7.76466e17 0.146162
\(761\) 8.37915e18 1.56387 0.781933 0.623362i \(-0.214234\pi\)
0.781933 + 0.623362i \(0.214234\pi\)
\(762\) −4.58753e17 −0.0848930
\(763\) −2.36378e17 −0.0433709
\(764\) 1.73815e18 0.316213
\(765\) −8.89728e17 −0.160494
\(766\) −5.15177e18 −0.921445
\(767\) 8.03071e17 0.142424
\(768\) −3.34611e18 −0.588426
\(769\) −6.77570e18 −1.18150 −0.590749 0.806856i \(-0.701167\pi\)
−0.590749 + 0.806856i \(0.701167\pi\)
\(770\) −8.83453e16 −0.0152754
\(771\) −1.35069e18 −0.231581
\(772\) 4.24120e18 0.721068
\(773\) 5.04035e18 0.849755 0.424877 0.905251i \(-0.360317\pi\)
0.424877 + 0.905251i \(0.360317\pi\)
\(774\) 1.50164e18 0.251044
\(775\) 4.46230e18 0.739772
\(776\) 2.03441e18 0.334455
\(777\) −2.52772e17 −0.0412091
\(778\) 6.99873e18 1.13149
\(779\) 5.20156e17 0.0833950
\(780\) −7.02564e17 −0.111705
\(781\) −5.04761e18 −0.795892
\(782\) −1.04222e19 −1.62972
\(783\) 7.29408e16 0.0113115
\(784\) 2.47461e18 0.380586
\(785\) −2.05542e18 −0.313508
\(786\) −1.74535e17 −0.0264019
\(787\) −5.19452e18 −0.779308 −0.389654 0.920961i \(-0.627405\pi\)
−0.389654 + 0.920961i \(0.627405\pi\)
\(788\) 2.06593e18 0.307393
\(789\) 5.92906e18 0.874954
\(790\) 2.30542e18 0.337423
\(791\) 2.76489e17 0.0401357
\(792\) 2.39415e18 0.344697
\(793\) −1.72719e18 −0.246640
\(794\) −5.21199e18 −0.738194
\(795\) −1.21650e18 −0.170894
\(796\) −3.84031e18 −0.535096
\(797\) 4.77261e18 0.659595 0.329797 0.944052i \(-0.393020\pi\)
0.329797 + 0.944052i \(0.393020\pi\)
\(798\) −5.42258e16 −0.00743339
\(799\) −1.45945e19 −1.98443
\(800\) −4.88529e18 −0.658879
\(801\) 1.79917e18 0.240691
\(802\) −2.12565e18 −0.282071
\(803\) −1.23695e16 −0.00162817
\(804\) −7.21594e17 −0.0942168
\(805\) −3.00323e17 −0.0388969
\(806\) 5.70459e18 0.732904
\(807\) −1.87933e18 −0.239511
\(808\) −4.28460e18 −0.541672
\(809\) −8.09008e18 −1.01458 −0.507291 0.861775i \(-0.669353\pi\)
−0.507291 + 0.861775i \(0.669353\pi\)
\(810\) −2.75672e17 −0.0342957
\(811\) −1.96586e18 −0.242615 −0.121307 0.992615i \(-0.538709\pi\)
−0.121307 + 0.992615i \(0.538709\pi\)
\(812\) 1.07092e16 0.00131112
\(813\) 6.99924e18 0.850085
\(814\) −8.28295e18 −0.997990
\(815\) 9.62295e17 0.115023
\(816\) −2.18452e18 −0.259042
\(817\) 2.80893e18 0.330443
\(818\) 2.02993e18 0.236911
\(819\) 1.62673e17 0.0188351
\(820\) 3.88244e17 0.0445980
\(821\) 1.11006e19 1.26507 0.632535 0.774531i \(-0.282014\pi\)
0.632535 + 0.774531i \(0.282014\pi\)
\(822\) −3.36063e17 −0.0379974
\(823\) −2.15363e18 −0.241587 −0.120793 0.992678i \(-0.538544\pi\)
−0.120793 + 0.992678i \(0.538544\pi\)
\(824\) −9.05601e18 −1.00788
\(825\) 4.16969e18 0.460419
\(826\) 4.62642e16 0.00506845
\(827\) 8.03212e18 0.873060 0.436530 0.899690i \(-0.356207\pi\)
0.436530 + 0.899690i \(0.356207\pi\)
\(828\) 2.45477e18 0.264736
\(829\) 9.02831e18 0.966055 0.483028 0.875605i \(-0.339537\pi\)
0.483028 + 0.875605i \(0.339537\pi\)
\(830\) −3.80117e18 −0.403561
\(831\) 1.78227e18 0.187745
\(832\) −1.02395e19 −1.07023
\(833\) −1.13071e19 −1.17262
\(834\) 2.63781e18 0.271434
\(835\) 5.47070e17 0.0558574
\(836\) 1.35076e18 0.136848
\(837\) −1.70157e18 −0.171054
\(838\) 3.02089e18 0.301334
\(839\) 1.37081e19 1.35683 0.678414 0.734680i \(-0.262668\pi\)
0.678414 + 0.734680i \(0.262668\pi\)
\(840\) −1.34191e17 −0.0131797
\(841\) −1.02252e19 −0.996545
\(842\) −1.07167e18 −0.103642
\(843\) −3.99208e18 −0.383107
\(844\) 2.33379e18 0.222247
\(845\) −8.52797e17 −0.0805893
\(846\) −4.52193e18 −0.424050
\(847\) 4.54888e16 0.00423313
\(848\) −2.98684e18 −0.275828
\(849\) −8.30821e17 −0.0761390
\(850\) −8.11044e18 −0.737601
\(851\) −2.81573e19 −2.54125
\(852\) −2.31249e18 −0.207120
\(853\) 9.37089e18 0.832937 0.416469 0.909150i \(-0.363268\pi\)
0.416469 + 0.909150i \(0.363268\pi\)
\(854\) −9.95019e16 −0.00877718
\(855\) −5.15663e17 −0.0451426
\(856\) −1.27336e19 −1.10630
\(857\) 5.26665e18 0.454108 0.227054 0.973882i \(-0.427091\pi\)
0.227054 + 0.973882i \(0.427091\pi\)
\(858\) 5.33052e18 0.456144
\(859\) 8.04270e18 0.683040 0.341520 0.939874i \(-0.389058\pi\)
0.341520 + 0.939874i \(0.389058\pi\)
\(860\) 2.09658e18 0.176714
\(861\) −8.98946e16 −0.00751991
\(862\) −3.16677e18 −0.262917
\(863\) 1.47717e19 1.21720 0.608598 0.793479i \(-0.291732\pi\)
0.608598 + 0.793479i \(0.291732\pi\)
\(864\) 1.86286e18 0.152350
\(865\) −6.01162e18 −0.487963
\(866\) −1.18806e19 −0.957133
\(867\) 2.76116e18 0.220784
\(868\) −2.49824e17 −0.0198270
\(869\) 1.32970e19 1.04743
\(870\) −1.33967e17 −0.0104742
\(871\) −5.32668e18 −0.413369
\(872\) −1.17653e19 −0.906244
\(873\) −1.35108e18 −0.103298
\(874\) −6.04041e18 −0.458397
\(875\) −5.14507e17 −0.0387560
\(876\) −5.66691e15 −0.000423711 0
\(877\) 2.26858e19 1.68367 0.841836 0.539734i \(-0.181475\pi\)
0.841836 + 0.539734i \(0.181475\pi\)
\(878\) 6.69809e18 0.493443
\(879\) −9.16729e18 −0.670368
\(880\) −2.06273e18 −0.149729
\(881\) 2.47327e19 1.78209 0.891044 0.453918i \(-0.149974\pi\)
0.891044 + 0.453918i \(0.149974\pi\)
\(882\) −3.50336e18 −0.250576
\(883\) −1.62910e19 −1.15665 −0.578327 0.815805i \(-0.696294\pi\)
−0.578327 + 0.815805i \(0.696294\pi\)
\(884\) 7.88186e18 0.555506
\(885\) 4.39952e17 0.0307804
\(886\) −4.53241e18 −0.314782
\(887\) −7.01228e18 −0.483454 −0.241727 0.970344i \(-0.577714\pi\)
−0.241727 + 0.970344i \(0.577714\pi\)
\(888\) −1.25813e19 −0.861073
\(889\) 1.48304e17 0.0100761
\(890\) −3.30444e18 −0.222876
\(891\) −1.58999e18 −0.106461
\(892\) −1.26103e18 −0.0838213
\(893\) −8.45859e18 −0.558166
\(894\) −4.65156e18 −0.304723
\(895\) −8.46060e18 −0.550239
\(896\) 4.34056e16 0.00280249
\(897\) 1.81207e19 1.16151
\(898\) −1.56990e19 −0.999024
\(899\) −8.26903e17 −0.0522416
\(900\) 1.91028e18 0.119818
\(901\) 1.36476e19 0.849853
\(902\) −2.94570e18 −0.182115
\(903\) −4.85445e17 −0.0297968
\(904\) 1.37617e19 0.838643
\(905\) −3.41413e18 −0.206569
\(906\) 6.02936e18 0.362191
\(907\) 2.17609e19 1.29786 0.648931 0.760847i \(-0.275216\pi\)
0.648931 + 0.760847i \(0.275216\pi\)
\(908\) −6.97293e18 −0.412912
\(909\) 2.84547e18 0.167297
\(910\) −2.98773e17 −0.0174410
\(911\) 5.88291e18 0.340975 0.170487 0.985360i \(-0.445466\pi\)
0.170487 + 0.985360i \(0.445466\pi\)
\(912\) −1.26609e18 −0.0728617
\(913\) −2.19240e19 −1.25274
\(914\) −2.09805e19 −1.19032
\(915\) −9.46218e17 −0.0533033
\(916\) −1.29271e19 −0.723070
\(917\) 5.64230e16 0.00313369
\(918\) 3.09268e18 0.170552
\(919\) −2.07394e18 −0.113565 −0.0567827 0.998387i \(-0.518084\pi\)
−0.0567827 + 0.998387i \(0.518084\pi\)
\(920\) −1.49480e19 −0.812760
\(921\) −2.31636e18 −0.125060
\(922\) −1.02527e19 −0.549652
\(923\) −1.70704e19 −0.908725
\(924\) −2.33442e17 −0.0123399
\(925\) −2.19118e19 −1.15015
\(926\) −1.16630e19 −0.607907
\(927\) 6.01423e18 0.311288
\(928\) 9.05286e17 0.0465290
\(929\) −2.07666e19 −1.05989 −0.529947 0.848031i \(-0.677788\pi\)
−0.529947 + 0.848031i \(0.677788\pi\)
\(930\) 3.12519e18 0.158393
\(931\) −6.55329e18 −0.329827
\(932\) 5.20448e17 0.0260120
\(933\) −5.49507e18 −0.272736
\(934\) −1.54476e19 −0.761388
\(935\) 9.42511e18 0.461329
\(936\) 8.09671e18 0.393564
\(937\) −1.34263e19 −0.648108 −0.324054 0.946039i \(-0.605046\pi\)
−0.324054 + 0.946039i \(0.605046\pi\)
\(938\) −3.06865e17 −0.0147106
\(939\) 9.46070e18 0.450398
\(940\) −6.31349e18 −0.298496
\(941\) 1.06489e19 0.500004 0.250002 0.968245i \(-0.419569\pi\)
0.250002 + 0.968245i \(0.419569\pi\)
\(942\) 7.14461e18 0.333156
\(943\) −1.00137e19 −0.463733
\(944\) 1.08020e18 0.0496806
\(945\) 8.91181e16 0.00407061
\(946\) −1.59073e19 −0.721611
\(947\) −3.41478e19 −1.53846 −0.769232 0.638969i \(-0.779361\pi\)
−0.769232 + 0.638969i \(0.779361\pi\)
\(948\) 6.09181e18 0.272579
\(949\) −4.18321e16 −0.00185900
\(950\) −4.70060e18 −0.207467
\(951\) 2.33436e19 1.02328
\(952\) 1.50545e18 0.0655428
\(953\) 1.27884e19 0.552985 0.276493 0.961016i \(-0.410828\pi\)
0.276493 + 0.961016i \(0.410828\pi\)
\(954\) 4.22853e18 0.181604
\(955\) 7.02914e18 0.299834
\(956\) −7.89815e18 −0.334618
\(957\) −7.72680e17 −0.0325141
\(958\) 1.12322e19 0.469452
\(959\) 1.08641e17 0.00450997
\(960\) −5.60958e18 −0.231295
\(961\) −5.12748e18 −0.209992
\(962\) −2.80119e19 −1.13947
\(963\) 8.45657e18 0.341683
\(964\) 3.43077e17 0.0137686
\(965\) 1.71516e19 0.683717
\(966\) 1.04392e18 0.0413347
\(967\) 3.66407e19 1.44109 0.720545 0.693408i \(-0.243892\pi\)
0.720545 + 0.693408i \(0.243892\pi\)
\(968\) 2.26412e18 0.0884522
\(969\) 5.78507e18 0.224494
\(970\) 2.48147e18 0.0956518
\(971\) 2.18984e19 0.838468 0.419234 0.907878i \(-0.362299\pi\)
0.419234 + 0.907878i \(0.362299\pi\)
\(972\) −7.28431e17 −0.0277050
\(973\) −8.52741e17 −0.0322169
\(974\) 5.82782e18 0.218712
\(975\) 1.41014e19 0.525692
\(976\) −2.32322e18 −0.0860334
\(977\) 3.15469e19 1.16049 0.580246 0.814441i \(-0.302956\pi\)
0.580246 + 0.814441i \(0.302956\pi\)
\(978\) −3.34492e18 −0.122232
\(979\) −1.90590e19 −0.691851
\(980\) −4.89137e18 −0.176385
\(981\) 7.81350e18 0.279896
\(982\) −2.61657e19 −0.931124
\(983\) −1.64360e19 −0.581029 −0.290514 0.956871i \(-0.593826\pi\)
−0.290514 + 0.956871i \(0.593826\pi\)
\(984\) −4.47433e18 −0.157130
\(985\) 8.35468e18 0.291470
\(986\) 1.50293e18 0.0520883
\(987\) 1.46183e18 0.0503311
\(988\) 4.56812e18 0.156249
\(989\) −5.40755e19 −1.83749
\(990\) 2.92026e18 0.0985808
\(991\) 2.50355e19 0.839610 0.419805 0.907614i \(-0.362098\pi\)
0.419805 + 0.907614i \(0.362098\pi\)
\(992\) −2.11186e19 −0.703621
\(993\) 1.90149e19 0.629396
\(994\) −9.83411e17 −0.0323388
\(995\) −1.55304e19 −0.507378
\(996\) −1.00442e19 −0.326007
\(997\) −4.00653e19 −1.29196 −0.645981 0.763354i \(-0.723551\pi\)
−0.645981 + 0.763354i \(0.723551\pi\)
\(998\) 3.30630e19 1.05924
\(999\) 8.35540e18 0.265945
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.1.20 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.20 31 1.1 even 1 trivial