Properties

Label 177.14.a.c.1.9
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 1.9
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-83.5640 q^{2} +729.000 q^{3} -1209.07 q^{4} +55860.4 q^{5} -60918.1 q^{6} -515369. q^{7} +785590. q^{8} +531441. q^{9} +O(q^{10})\) \(q-83.5640 q^{2} +729.000 q^{3} -1209.07 q^{4} +55860.4 q^{5} -60918.1 q^{6} -515369. q^{7} +785590. q^{8} +531441. q^{9} -4.66791e6 q^{10} +3.72299e6 q^{11} -881409. q^{12} -9.32855e6 q^{13} +4.30663e7 q^{14} +4.07222e7 q^{15} -5.57424e7 q^{16} -7.95874e6 q^{17} -4.44093e7 q^{18} -6.13400e7 q^{19} -6.75389e7 q^{20} -3.75704e8 q^{21} -3.11108e8 q^{22} +5.74053e8 q^{23} +5.72695e8 q^{24} +1.89968e9 q^{25} +7.79530e8 q^{26} +3.87420e8 q^{27} +6.23115e8 q^{28} -1.68012e9 q^{29} -3.40291e9 q^{30} -7.08624e9 q^{31} -1.77750e9 q^{32} +2.71406e9 q^{33} +6.65064e8 q^{34} -2.87887e10 q^{35} -6.42547e8 q^{36} -2.19046e9 q^{37} +5.12581e9 q^{38} -6.80051e9 q^{39} +4.38834e10 q^{40} +7.06872e9 q^{41} +3.13953e10 q^{42} +4.21711e10 q^{43} -4.50134e9 q^{44} +2.96865e10 q^{45} -4.79702e10 q^{46} +3.35142e10 q^{47} -4.06362e10 q^{48} +1.68716e11 q^{49} -1.58745e11 q^{50} -5.80192e9 q^{51} +1.12788e10 q^{52} +1.04251e11 q^{53} -3.23744e10 q^{54} +2.07967e11 q^{55} -4.04869e11 q^{56} -4.47168e10 q^{57} +1.40398e11 q^{58} -4.21805e10 q^{59} -4.92358e10 q^{60} +1.12562e11 q^{61} +5.92155e11 q^{62} -2.73888e11 q^{63} +6.05177e11 q^{64} -5.21096e11 q^{65} -2.26797e11 q^{66} +5.18952e11 q^{67} +9.62264e9 q^{68} +4.18485e11 q^{69} +2.40570e12 q^{70} -7.67141e11 q^{71} +4.17495e11 q^{72} -6.21825e11 q^{73} +1.83043e11 q^{74} +1.38486e12 q^{75} +7.41641e10 q^{76} -1.91871e12 q^{77} +5.68278e11 q^{78} +2.09547e12 q^{79} -3.11379e12 q^{80} +2.82430e11 q^{81} -5.90690e11 q^{82} +8.75347e11 q^{83} +4.54251e11 q^{84} -4.44578e11 q^{85} -3.52398e12 q^{86} -1.22481e12 q^{87} +2.92474e12 q^{88} +4.59522e12 q^{89} -2.48072e12 q^{90} +4.80765e12 q^{91} -6.94068e11 q^{92} -5.16587e12 q^{93} -2.80058e12 q^{94} -3.42647e12 q^{95} -1.29580e12 q^{96} -4.07043e12 q^{97} -1.40986e13 q^{98} +1.97855e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −83.5640 −0.923260 −0.461630 0.887073i \(-0.652735\pi\)
−0.461630 + 0.887073i \(0.652735\pi\)
\(3\) 729.000 0.577350
\(4\) −1209.07 −0.147591
\(5\) 55860.4 1.59882 0.799409 0.600788i \(-0.205146\pi\)
0.799409 + 0.600788i \(0.205146\pi\)
\(6\) −60918.1 −0.533044
\(7\) −515369. −1.65570 −0.827849 0.560951i \(-0.810436\pi\)
−0.827849 + 0.560951i \(0.810436\pi\)
\(8\) 785590. 1.05952
\(9\) 531441. 0.333333
\(10\) −4.66791e6 −1.47612
\(11\) 3.72299e6 0.633635 0.316817 0.948487i \(-0.397386\pi\)
0.316817 + 0.948487i \(0.397386\pi\)
\(12\) −881409. −0.0852117
\(13\) −9.32855e6 −0.536022 −0.268011 0.963416i \(-0.586366\pi\)
−0.268011 + 0.963416i \(0.586366\pi\)
\(14\) 4.30663e7 1.52864
\(15\) 4.07222e7 0.923077
\(16\) −5.57424e7 −0.830626
\(17\) −7.95874e6 −0.0799699 −0.0399849 0.999200i \(-0.512731\pi\)
−0.0399849 + 0.999200i \(0.512731\pi\)
\(18\) −4.44093e7 −0.307753
\(19\) −6.13400e7 −0.299120 −0.149560 0.988753i \(-0.547786\pi\)
−0.149560 + 0.988753i \(0.547786\pi\)
\(20\) −6.75389e7 −0.235971
\(21\) −3.75704e8 −0.955918
\(22\) −3.11108e8 −0.585010
\(23\) 5.74053e8 0.808577 0.404288 0.914632i \(-0.367519\pi\)
0.404288 + 0.914632i \(0.367519\pi\)
\(24\) 5.72695e8 0.611717
\(25\) 1.89968e9 1.55622
\(26\) 7.79530e8 0.494887
\(27\) 3.87420e8 0.192450
\(28\) 6.23115e8 0.244366
\(29\) −1.68012e9 −0.524511 −0.262255 0.964998i \(-0.584466\pi\)
−0.262255 + 0.964998i \(0.584466\pi\)
\(30\) −3.40291e9 −0.852240
\(31\) −7.08624e9 −1.43405 −0.717026 0.697046i \(-0.754497\pi\)
−0.717026 + 0.697046i \(0.754497\pi\)
\(32\) −1.77750e9 −0.292641
\(33\) 2.71406e9 0.365829
\(34\) 6.65064e8 0.0738330
\(35\) −2.87887e10 −2.64716
\(36\) −6.42547e8 −0.0491970
\(37\) −2.19046e9 −0.140354 −0.0701768 0.997535i \(-0.522356\pi\)
−0.0701768 + 0.997535i \(0.522356\pi\)
\(38\) 5.12581e9 0.276165
\(39\) −6.80051e9 −0.309472
\(40\) 4.38834e10 1.69399
\(41\) 7.06872e9 0.232405 0.116203 0.993226i \(-0.462928\pi\)
0.116203 + 0.993226i \(0.462928\pi\)
\(42\) 3.13953e10 0.882561
\(43\) 4.21711e10 1.01735 0.508674 0.860959i \(-0.330136\pi\)
0.508674 + 0.860959i \(0.330136\pi\)
\(44\) −4.50134e9 −0.0935188
\(45\) 2.96865e10 0.532939
\(46\) −4.79702e10 −0.746527
\(47\) 3.35142e10 0.453517 0.226758 0.973951i \(-0.427187\pi\)
0.226758 + 0.973951i \(0.427187\pi\)
\(48\) −4.06362e10 −0.479562
\(49\) 1.68716e11 1.74134
\(50\) −1.58745e11 −1.43679
\(51\) −5.80192e9 −0.0461706
\(52\) 1.12788e10 0.0791120
\(53\) 1.04251e11 0.646084 0.323042 0.946385i \(-0.395295\pi\)
0.323042 + 0.946385i \(0.395295\pi\)
\(54\) −3.23744e10 −0.177681
\(55\) 2.07967e11 1.01307
\(56\) −4.04869e11 −1.75425
\(57\) −4.47168e10 −0.172697
\(58\) 1.40398e11 0.484260
\(59\) −4.21805e10 −0.130189
\(60\) −4.92358e10 −0.136238
\(61\) 1.12562e11 0.279736 0.139868 0.990170i \(-0.455332\pi\)
0.139868 + 0.990170i \(0.455332\pi\)
\(62\) 5.92155e11 1.32400
\(63\) −2.73888e11 −0.551899
\(64\) 6.05177e11 1.10081
\(65\) −5.21096e11 −0.857000
\(66\) −2.26797e11 −0.337756
\(67\) 5.18952e11 0.700876 0.350438 0.936586i \(-0.386033\pi\)
0.350438 + 0.936586i \(0.386033\pi\)
\(68\) 9.62264e9 0.0118028
\(69\) 4.18485e11 0.466832
\(70\) 2.40570e12 2.44402
\(71\) −7.67141e11 −0.710715 −0.355358 0.934730i \(-0.615641\pi\)
−0.355358 + 0.934730i \(0.615641\pi\)
\(72\) 4.17495e11 0.353175
\(73\) −6.21825e11 −0.480916 −0.240458 0.970660i \(-0.577298\pi\)
−0.240458 + 0.970660i \(0.577298\pi\)
\(74\) 1.83043e11 0.129583
\(75\) 1.38486e12 0.898482
\(76\) 7.41641e10 0.0441474
\(77\) −1.91871e12 −1.04911
\(78\) 5.68278e11 0.285723
\(79\) 2.09547e12 0.969854 0.484927 0.874555i \(-0.338846\pi\)
0.484927 + 0.874555i \(0.338846\pi\)
\(80\) −3.11379e12 −1.32802
\(81\) 2.82430e11 0.111111
\(82\) −5.90690e11 −0.214570
\(83\) 8.75347e11 0.293882 0.146941 0.989145i \(-0.453057\pi\)
0.146941 + 0.989145i \(0.453057\pi\)
\(84\) 4.54251e11 0.141085
\(85\) −4.44578e11 −0.127857
\(86\) −3.52398e12 −0.939277
\(87\) −1.22481e12 −0.302826
\(88\) 2.92474e12 0.671352
\(89\) 4.59522e12 0.980102 0.490051 0.871694i \(-0.336978\pi\)
0.490051 + 0.871694i \(0.336978\pi\)
\(90\) −2.48072e12 −0.492041
\(91\) 4.80765e12 0.887490
\(92\) −6.94068e11 −0.119339
\(93\) −5.16587e12 −0.827951
\(94\) −2.80058e12 −0.418714
\(95\) −3.42647e12 −0.478238
\(96\) −1.29580e12 −0.168957
\(97\) −4.07043e12 −0.496162 −0.248081 0.968739i \(-0.579800\pi\)
−0.248081 + 0.968739i \(0.579800\pi\)
\(98\) −1.40986e13 −1.60771
\(99\) 1.97855e12 0.211212
\(100\) −2.29683e12 −0.229683
\(101\) −1.75220e13 −1.64246 −0.821230 0.570597i \(-0.806712\pi\)
−0.821230 + 0.570597i \(0.806712\pi\)
\(102\) 4.84832e11 0.0426275
\(103\) −5.35352e12 −0.441771 −0.220886 0.975300i \(-0.570895\pi\)
−0.220886 + 0.975300i \(0.570895\pi\)
\(104\) −7.32842e12 −0.567928
\(105\) −2.09870e13 −1.52834
\(106\) −8.71166e12 −0.596503
\(107\) 9.14307e12 0.588976 0.294488 0.955655i \(-0.404851\pi\)
0.294488 + 0.955655i \(0.404851\pi\)
\(108\) −4.68417e11 −0.0284039
\(109\) 2.30859e13 1.31848 0.659242 0.751931i \(-0.270877\pi\)
0.659242 + 0.751931i \(0.270877\pi\)
\(110\) −1.73786e13 −0.935324
\(111\) −1.59684e12 −0.0810332
\(112\) 2.87279e13 1.37527
\(113\) −1.78769e13 −0.807759 −0.403880 0.914812i \(-0.632339\pi\)
−0.403880 + 0.914812i \(0.632339\pi\)
\(114\) 3.73672e12 0.159444
\(115\) 3.20668e13 1.29277
\(116\) 2.03138e12 0.0774131
\(117\) −4.95757e12 −0.178674
\(118\) 3.52477e12 0.120198
\(119\) 4.10169e12 0.132406
\(120\) 3.19910e13 0.978023
\(121\) −2.06621e13 −0.598507
\(122\) −9.40614e12 −0.258269
\(123\) 5.15309e12 0.134179
\(124\) 8.56773e12 0.211653
\(125\) 3.79278e13 0.889287
\(126\) 2.28872e13 0.509547
\(127\) −6.19688e13 −1.31053 −0.655267 0.755397i \(-0.727444\pi\)
−0.655267 + 0.755397i \(0.727444\pi\)
\(128\) −3.60096e13 −0.723692
\(129\) 3.07427e13 0.587366
\(130\) 4.35449e13 0.791234
\(131\) 3.70185e13 0.639963 0.319982 0.947424i \(-0.396323\pi\)
0.319982 + 0.947424i \(0.396323\pi\)
\(132\) −3.28147e12 −0.0539931
\(133\) 3.16127e13 0.495252
\(134\) −4.33657e13 −0.647090
\(135\) 2.16415e13 0.307692
\(136\) −6.25231e12 −0.0847301
\(137\) −1.30239e14 −1.68290 −0.841451 0.540334i \(-0.818298\pi\)
−0.841451 + 0.540334i \(0.818298\pi\)
\(138\) −3.49702e13 −0.431007
\(139\) 1.01862e14 1.19789 0.598946 0.800790i \(-0.295587\pi\)
0.598946 + 0.800790i \(0.295587\pi\)
\(140\) 3.48074e13 0.390697
\(141\) 2.44319e13 0.261838
\(142\) 6.41053e13 0.656175
\(143\) −3.47301e13 −0.339642
\(144\) −2.96238e13 −0.276875
\(145\) −9.38524e13 −0.838597
\(146\) 5.19621e13 0.444011
\(147\) 1.22994e14 1.00536
\(148\) 2.64841e12 0.0207149
\(149\) 5.81338e13 0.435229 0.217614 0.976035i \(-0.430172\pi\)
0.217614 + 0.976035i \(0.430172\pi\)
\(150\) −1.15725e14 −0.829532
\(151\) 9.07930e12 0.0623307 0.0311654 0.999514i \(-0.490078\pi\)
0.0311654 + 0.999514i \(0.490078\pi\)
\(152\) −4.81881e13 −0.316925
\(153\) −4.22960e12 −0.0266566
\(154\) 1.60335e14 0.968600
\(155\) −3.95840e14 −2.29279
\(156\) 8.22227e12 0.0456753
\(157\) −9.06368e13 −0.483011 −0.241505 0.970400i \(-0.577641\pi\)
−0.241505 + 0.970400i \(0.577641\pi\)
\(158\) −1.75106e14 −0.895427
\(159\) 7.59993e13 0.373017
\(160\) −9.92920e13 −0.467880
\(161\) −2.95849e14 −1.33876
\(162\) −2.36009e13 −0.102584
\(163\) −4.00116e13 −0.167096 −0.0835481 0.996504i \(-0.526625\pi\)
−0.0835481 + 0.996504i \(0.526625\pi\)
\(164\) −8.54654e12 −0.0343009
\(165\) 1.51608e14 0.584894
\(166\) −7.31474e13 −0.271329
\(167\) 1.02841e14 0.366867 0.183433 0.983032i \(-0.441279\pi\)
0.183433 + 0.983032i \(0.441279\pi\)
\(168\) −2.95149e14 −1.01282
\(169\) −2.15853e14 −0.712681
\(170\) 3.71507e13 0.118045
\(171\) −3.25986e13 −0.0997066
\(172\) −5.09876e13 −0.150152
\(173\) 1.62858e14 0.461859 0.230929 0.972971i \(-0.425823\pi\)
0.230929 + 0.972971i \(0.425823\pi\)
\(174\) 1.02350e14 0.279588
\(175\) −9.79035e14 −2.57662
\(176\) −2.07528e14 −0.526314
\(177\) −3.07496e13 −0.0751646
\(178\) −3.83995e14 −0.904889
\(179\) −2.78658e14 −0.633180 −0.316590 0.948563i \(-0.602538\pi\)
−0.316590 + 0.948563i \(0.602538\pi\)
\(180\) −3.58929e13 −0.0786570
\(181\) 3.64782e14 0.771121 0.385561 0.922682i \(-0.374008\pi\)
0.385561 + 0.922682i \(0.374008\pi\)
\(182\) −4.01746e14 −0.819384
\(183\) 8.20579e13 0.161506
\(184\) 4.50971e14 0.856707
\(185\) −1.22360e14 −0.224400
\(186\) 4.31681e14 0.764414
\(187\) −2.96303e13 −0.0506717
\(188\) −4.05209e13 −0.0669350
\(189\) −1.99665e14 −0.318639
\(190\) 2.86330e14 0.441538
\(191\) 1.32894e15 1.98056 0.990282 0.139076i \(-0.0444133\pi\)
0.990282 + 0.139076i \(0.0444133\pi\)
\(192\) 4.41174e14 0.635553
\(193\) 7.90275e14 1.10067 0.550333 0.834945i \(-0.314501\pi\)
0.550333 + 0.834945i \(0.314501\pi\)
\(194\) 3.40141e14 0.458086
\(195\) −3.79879e14 −0.494789
\(196\) −2.03989e14 −0.257006
\(197\) 1.54814e15 1.88703 0.943517 0.331324i \(-0.107495\pi\)
0.943517 + 0.331324i \(0.107495\pi\)
\(198\) −1.65335e14 −0.195003
\(199\) 6.10207e14 0.696518 0.348259 0.937398i \(-0.386773\pi\)
0.348259 + 0.937398i \(0.386773\pi\)
\(200\) 1.49237e15 1.64885
\(201\) 3.78316e14 0.404651
\(202\) 1.46421e15 1.51642
\(203\) 8.65884e14 0.868432
\(204\) 7.01491e12 0.00681437
\(205\) 3.94861e14 0.371573
\(206\) 4.47361e14 0.407870
\(207\) 3.05075e14 0.269526
\(208\) 5.19995e14 0.445233
\(209\) −2.28368e14 −0.189533
\(210\) 1.75375e15 1.41105
\(211\) 8.00376e14 0.624393 0.312197 0.950018i \(-0.398935\pi\)
0.312197 + 0.950018i \(0.398935\pi\)
\(212\) −1.26047e14 −0.0953562
\(213\) −5.59246e14 −0.410332
\(214\) −7.64031e14 −0.543778
\(215\) 2.35569e15 1.62655
\(216\) 3.04354e14 0.203906
\(217\) 3.65203e15 2.37436
\(218\) −1.92915e15 −1.21730
\(219\) −4.53310e14 −0.277657
\(220\) −2.51446e14 −0.149519
\(221\) 7.42435e13 0.0428656
\(222\) 1.33439e14 0.0748147
\(223\) −1.00189e15 −0.545553 −0.272777 0.962077i \(-0.587942\pi\)
−0.272777 + 0.962077i \(0.587942\pi\)
\(224\) 9.16070e14 0.484526
\(225\) 1.00957e15 0.518739
\(226\) 1.49386e15 0.745772
\(227\) −3.52434e15 −1.70966 −0.854829 0.518909i \(-0.826338\pi\)
−0.854829 + 0.518909i \(0.826338\pi\)
\(228\) 5.40656e13 0.0254885
\(229\) 6.59620e14 0.302248 0.151124 0.988515i \(-0.451711\pi\)
0.151124 + 0.988515i \(0.451711\pi\)
\(230\) −2.67963e15 −1.19356
\(231\) −1.39874e15 −0.605703
\(232\) −1.31989e15 −0.555732
\(233\) 4.30079e15 1.76090 0.880450 0.474140i \(-0.157241\pi\)
0.880450 + 0.474140i \(0.157241\pi\)
\(234\) 4.14274e14 0.164962
\(235\) 1.87212e15 0.725090
\(236\) 5.09990e13 0.0192147
\(237\) 1.52760e15 0.559945
\(238\) −3.42754e14 −0.122245
\(239\) 1.93932e15 0.673075 0.336537 0.941670i \(-0.390744\pi\)
0.336537 + 0.941670i \(0.390744\pi\)
\(240\) −2.26995e15 −0.766732
\(241\) 1.38139e15 0.454157 0.227079 0.973876i \(-0.427083\pi\)
0.227079 + 0.973876i \(0.427083\pi\)
\(242\) 1.72660e15 0.552577
\(243\) 2.05891e14 0.0641500
\(244\) −1.36095e14 −0.0412866
\(245\) 9.42456e15 2.78408
\(246\) −4.30613e14 −0.123882
\(247\) 5.72213e14 0.160335
\(248\) −5.56688e15 −1.51941
\(249\) 6.38128e14 0.169673
\(250\) −3.16939e15 −0.821043
\(251\) 1.56790e15 0.395767 0.197883 0.980226i \(-0.436593\pi\)
0.197883 + 0.980226i \(0.436593\pi\)
\(252\) 3.31149e14 0.0814554
\(253\) 2.13719e15 0.512342
\(254\) 5.17835e15 1.20996
\(255\) −3.24098e14 −0.0738184
\(256\) −1.94850e15 −0.432654
\(257\) −1.82226e15 −0.394498 −0.197249 0.980353i \(-0.563201\pi\)
−0.197249 + 0.980353i \(0.563201\pi\)
\(258\) −2.56898e15 −0.542292
\(259\) 1.12889e15 0.232383
\(260\) 6.30039e14 0.126486
\(261\) −8.92887e14 −0.174837
\(262\) −3.09341e15 −0.590852
\(263\) 9.80099e15 1.82624 0.913119 0.407693i \(-0.133667\pi\)
0.913119 + 0.407693i \(0.133667\pi\)
\(264\) 2.13214e15 0.387605
\(265\) 5.82352e15 1.03297
\(266\) −2.64168e15 −0.457246
\(267\) 3.34992e15 0.565862
\(268\) −6.27447e14 −0.103443
\(269\) 1.08167e16 1.74062 0.870311 0.492502i \(-0.163918\pi\)
0.870311 + 0.492502i \(0.163918\pi\)
\(270\) −1.80845e15 −0.284080
\(271\) −6.40238e14 −0.0981841 −0.0490921 0.998794i \(-0.515633\pi\)
−0.0490921 + 0.998794i \(0.515633\pi\)
\(272\) 4.43639e14 0.0664251
\(273\) 3.50477e15 0.512393
\(274\) 1.08833e16 1.55376
\(275\) 7.07248e15 0.986073
\(276\) −5.05976e14 −0.0689002
\(277\) 4.12047e15 0.548060 0.274030 0.961721i \(-0.411643\pi\)
0.274030 + 0.961721i \(0.411643\pi\)
\(278\) −8.51202e15 −1.10596
\(279\) −3.76592e15 −0.478017
\(280\) −2.26161e16 −2.80473
\(281\) 7.69016e15 0.931846 0.465923 0.884825i \(-0.345722\pi\)
0.465923 + 0.884825i \(0.345722\pi\)
\(282\) −2.04162e15 −0.241744
\(283\) 1.20369e16 1.39285 0.696423 0.717632i \(-0.254774\pi\)
0.696423 + 0.717632i \(0.254774\pi\)
\(284\) 9.27524e14 0.104895
\(285\) −2.49790e15 −0.276111
\(286\) 2.90218e15 0.313578
\(287\) −3.64300e15 −0.384793
\(288\) −9.44638e14 −0.0975471
\(289\) −9.84124e15 −0.993605
\(290\) 7.84268e15 0.774243
\(291\) −2.96734e15 −0.286459
\(292\) 7.51827e14 0.0709789
\(293\) −1.22346e16 −1.12967 −0.564835 0.825204i \(-0.691060\pi\)
−0.564835 + 0.825204i \(0.691060\pi\)
\(294\) −1.02779e16 −0.928210
\(295\) −2.35622e15 −0.208148
\(296\) −1.72080e15 −0.148708
\(297\) 1.44236e15 0.121943
\(298\) −4.85789e15 −0.401829
\(299\) −5.35508e15 −0.433415
\(300\) −1.67439e15 −0.132608
\(301\) −2.17337e16 −1.68442
\(302\) −7.58702e14 −0.0575474
\(303\) −1.27735e16 −0.948275
\(304\) 3.41923e15 0.248457
\(305\) 6.28777e15 0.447247
\(306\) 3.53442e14 0.0246110
\(307\) 1.71522e16 1.16928 0.584642 0.811291i \(-0.301235\pi\)
0.584642 + 0.811291i \(0.301235\pi\)
\(308\) 2.31985e15 0.154839
\(309\) −3.90272e15 −0.255057
\(310\) 3.30780e16 2.11684
\(311\) 3.52488e15 0.220903 0.110451 0.993882i \(-0.464770\pi\)
0.110451 + 0.993882i \(0.464770\pi\)
\(312\) −5.34242e15 −0.327893
\(313\) −3.32294e15 −0.199749 −0.0998744 0.995000i \(-0.531844\pi\)
−0.0998744 + 0.995000i \(0.531844\pi\)
\(314\) 7.57397e15 0.445944
\(315\) −1.52995e16 −0.882386
\(316\) −2.53357e15 −0.143142
\(317\) 1.65296e16 0.914905 0.457453 0.889234i \(-0.348762\pi\)
0.457453 + 0.889234i \(0.348762\pi\)
\(318\) −6.35080e15 −0.344391
\(319\) −6.25508e15 −0.332348
\(320\) 3.38054e16 1.75999
\(321\) 6.66530e15 0.340045
\(322\) 2.47223e16 1.23602
\(323\) 4.88189e14 0.0239206
\(324\) −3.41476e14 −0.0163990
\(325\) −1.77212e16 −0.834165
\(326\) 3.34353e15 0.154273
\(327\) 1.68296e16 0.761227
\(328\) 5.55311e15 0.246239
\(329\) −1.72722e16 −0.750886
\(330\) −1.26690e16 −0.540009
\(331\) −1.38641e16 −0.579441 −0.289721 0.957111i \(-0.593562\pi\)
−0.289721 + 0.957111i \(0.593562\pi\)
\(332\) −1.05835e15 −0.0433743
\(333\) −1.16410e15 −0.0467846
\(334\) −8.59378e15 −0.338713
\(335\) 2.89888e16 1.12057
\(336\) 2.09426e16 0.794010
\(337\) 5.52508e15 0.205468 0.102734 0.994709i \(-0.467241\pi\)
0.102734 + 0.994709i \(0.467241\pi\)
\(338\) 1.80376e16 0.657990
\(339\) −1.30323e16 −0.466360
\(340\) 5.37524e14 0.0188706
\(341\) −2.63820e16 −0.908666
\(342\) 2.72407e15 0.0920551
\(343\) −3.70176e16 −1.22743
\(344\) 3.31292e16 1.07791
\(345\) 2.33767e16 0.746379
\(346\) −1.36090e16 −0.426416
\(347\) 4.31784e15 0.132778 0.0663889 0.997794i \(-0.478852\pi\)
0.0663889 + 0.997794i \(0.478852\pi\)
\(348\) 1.48088e15 0.0446945
\(349\) 3.12984e16 0.927165 0.463583 0.886054i \(-0.346564\pi\)
0.463583 + 0.886054i \(0.346564\pi\)
\(350\) 8.18121e16 2.37889
\(351\) −3.61407e15 −0.103157
\(352\) −6.61762e15 −0.185428
\(353\) −4.26852e16 −1.17420 −0.587100 0.809514i \(-0.699730\pi\)
−0.587100 + 0.809514i \(0.699730\pi\)
\(354\) 2.56956e15 0.0693965
\(355\) −4.28528e16 −1.13630
\(356\) −5.55593e15 −0.144654
\(357\) 2.99013e15 0.0764446
\(358\) 2.32858e16 0.584589
\(359\) 2.40663e16 0.593328 0.296664 0.954982i \(-0.404126\pi\)
0.296664 + 0.954982i \(0.404126\pi\)
\(360\) 2.33214e16 0.564662
\(361\) −3.82904e16 −0.910527
\(362\) −3.04826e16 −0.711946
\(363\) −1.50627e16 −0.345548
\(364\) −5.81276e15 −0.130986
\(365\) −3.47354e16 −0.768897
\(366\) −6.85708e15 −0.149112
\(367\) −2.70999e16 −0.578945 −0.289473 0.957186i \(-0.593480\pi\)
−0.289473 + 0.957186i \(0.593480\pi\)
\(368\) −3.19991e16 −0.671625
\(369\) 3.75661e15 0.0774683
\(370\) 1.02249e16 0.207179
\(371\) −5.37280e16 −1.06972
\(372\) 6.24588e15 0.122198
\(373\) 8.49106e16 1.63251 0.816253 0.577695i \(-0.196048\pi\)
0.816253 + 0.577695i \(0.196048\pi\)
\(374\) 2.47603e15 0.0467832
\(375\) 2.76493e16 0.513430
\(376\) 2.63284e16 0.480512
\(377\) 1.56731e16 0.281149
\(378\) 1.66848e16 0.294187
\(379\) 8.76162e16 1.51855 0.759276 0.650769i \(-0.225553\pi\)
0.759276 + 0.650769i \(0.225553\pi\)
\(380\) 4.14283e15 0.0705836
\(381\) −4.51752e16 −0.756638
\(382\) −1.11052e17 −1.82857
\(383\) −3.34691e16 −0.541817 −0.270908 0.962605i \(-0.587324\pi\)
−0.270908 + 0.962605i \(0.587324\pi\)
\(384\) −2.62510e16 −0.417824
\(385\) −1.07180e17 −1.67733
\(386\) −6.60385e16 −1.01620
\(387\) 2.24114e16 0.339116
\(388\) 4.92141e15 0.0732291
\(389\) −2.30023e16 −0.336588 −0.168294 0.985737i \(-0.553826\pi\)
−0.168294 + 0.985737i \(0.553826\pi\)
\(390\) 3.17442e16 0.456819
\(391\) −4.56874e15 −0.0646618
\(392\) 1.32542e17 1.84499
\(393\) 2.69865e16 0.369483
\(394\) −1.29369e17 −1.74222
\(395\) 1.17054e17 1.55062
\(396\) −2.39219e15 −0.0311729
\(397\) −5.74109e16 −0.735963 −0.367982 0.929833i \(-0.619951\pi\)
−0.367982 + 0.929833i \(0.619951\pi\)
\(398\) −5.09913e16 −0.643067
\(399\) 2.30457e16 0.285934
\(400\) −1.05893e17 −1.29263
\(401\) 1.62668e17 1.95372 0.976860 0.213878i \(-0.0686096\pi\)
0.976860 + 0.213878i \(0.0686096\pi\)
\(402\) −3.16136e16 −0.373598
\(403\) 6.61044e16 0.768683
\(404\) 2.11853e16 0.242412
\(405\) 1.57766e16 0.177646
\(406\) −7.23567e16 −0.801788
\(407\) −8.15505e15 −0.0889330
\(408\) −4.55793e15 −0.0489189
\(409\) 5.15674e16 0.544720 0.272360 0.962195i \(-0.412196\pi\)
0.272360 + 0.962195i \(0.412196\pi\)
\(410\) −3.29962e16 −0.343059
\(411\) −9.49445e16 −0.971624
\(412\) 6.47276e15 0.0652015
\(413\) 2.17385e16 0.215554
\(414\) −2.54933e16 −0.248842
\(415\) 4.88972e16 0.469863
\(416\) 1.65815e16 0.156862
\(417\) 7.42576e16 0.691603
\(418\) 1.90833e16 0.174988
\(419\) −1.02469e17 −0.925130 −0.462565 0.886585i \(-0.653071\pi\)
−0.462565 + 0.886585i \(0.653071\pi\)
\(420\) 2.53746e16 0.225569
\(421\) −1.46859e17 −1.28549 −0.642744 0.766081i \(-0.722204\pi\)
−0.642744 + 0.766081i \(0.722204\pi\)
\(422\) −6.68826e16 −0.576477
\(423\) 1.78108e16 0.151172
\(424\) 8.18989e16 0.684542
\(425\) −1.51190e16 −0.124450
\(426\) 4.67328e16 0.378843
\(427\) −5.80111e16 −0.463159
\(428\) −1.10546e16 −0.0869275
\(429\) −2.53182e16 −0.196092
\(430\) −1.96851e17 −1.50173
\(431\) −1.02127e17 −0.767430 −0.383715 0.923452i \(-0.625355\pi\)
−0.383715 + 0.923452i \(0.625355\pi\)
\(432\) −2.15957e16 −0.159854
\(433\) 5.61120e16 0.409152 0.204576 0.978851i \(-0.434418\pi\)
0.204576 + 0.978851i \(0.434418\pi\)
\(434\) −3.05178e17 −2.19215
\(435\) −6.84184e16 −0.484164
\(436\) −2.79124e16 −0.194596
\(437\) −3.52124e16 −0.241861
\(438\) 3.78804e16 0.256350
\(439\) 1.76400e17 1.17620 0.588098 0.808790i \(-0.299877\pi\)
0.588098 + 0.808790i \(0.299877\pi\)
\(440\) 1.63377e17 1.07337
\(441\) 8.96628e16 0.580445
\(442\) −6.20408e15 −0.0395761
\(443\) −6.99154e15 −0.0439489 −0.0219745 0.999759i \(-0.506995\pi\)
−0.0219745 + 0.999759i \(0.506995\pi\)
\(444\) 1.93069e15 0.0119598
\(445\) 2.56691e17 1.56700
\(446\) 8.37217e16 0.503688
\(447\) 4.23795e16 0.251279
\(448\) −3.11889e17 −1.82261
\(449\) −2.01295e16 −0.115939 −0.0579697 0.998318i \(-0.518463\pi\)
−0.0579697 + 0.998318i \(0.518463\pi\)
\(450\) −8.43634e16 −0.478931
\(451\) 2.63167e16 0.147260
\(452\) 2.16143e16 0.119218
\(453\) 6.61881e15 0.0359867
\(454\) 2.94508e17 1.57846
\(455\) 2.68557e17 1.41893
\(456\) −3.51291e16 −0.182977
\(457\) 1.52901e17 0.785156 0.392578 0.919719i \(-0.371583\pi\)
0.392578 + 0.919719i \(0.371583\pi\)
\(458\) −5.51205e16 −0.279053
\(459\) −3.08338e15 −0.0153902
\(460\) −3.87709e16 −0.190801
\(461\) 9.80386e16 0.475709 0.237854 0.971301i \(-0.423556\pi\)
0.237854 + 0.971301i \(0.423556\pi\)
\(462\) 1.16884e17 0.559221
\(463\) 3.94572e17 1.86144 0.930722 0.365726i \(-0.119179\pi\)
0.930722 + 0.365726i \(0.119179\pi\)
\(464\) 9.36541e16 0.435672
\(465\) −2.88567e17 −1.32374
\(466\) −3.59391e17 −1.62577
\(467\) −1.44630e17 −0.645205 −0.322602 0.946535i \(-0.604558\pi\)
−0.322602 + 0.946535i \(0.604558\pi\)
\(468\) 5.99403e15 0.0263707
\(469\) −2.67452e17 −1.16044
\(470\) −1.56441e17 −0.669446
\(471\) −6.60742e16 −0.278866
\(472\) −3.31366e16 −0.137938
\(473\) 1.57002e17 0.644628
\(474\) −1.27652e17 −0.516975
\(475\) −1.16526e17 −0.465495
\(476\) −4.95921e15 −0.0195419
\(477\) 5.54035e16 0.215361
\(478\) −1.62057e17 −0.621423
\(479\) 5.08752e17 1.92453 0.962267 0.272108i \(-0.0877208\pi\)
0.962267 + 0.272108i \(0.0877208\pi\)
\(480\) −7.23839e16 −0.270131
\(481\) 2.04338e16 0.0752326
\(482\) −1.15435e17 −0.419305
\(483\) −2.15674e17 −0.772933
\(484\) 2.49818e16 0.0883342
\(485\) −2.27375e17 −0.793272
\(486\) −1.72051e16 −0.0592272
\(487\) 4.72252e17 1.60412 0.802058 0.597246i \(-0.203739\pi\)
0.802058 + 0.597246i \(0.203739\pi\)
\(488\) 8.84278e16 0.296387
\(489\) −2.91685e16 −0.0964730
\(490\) −7.87553e17 −2.57043
\(491\) 5.42778e16 0.174821 0.0874103 0.996172i \(-0.472141\pi\)
0.0874103 + 0.996172i \(0.472141\pi\)
\(492\) −6.23043e15 −0.0198036
\(493\) 1.33717e16 0.0419451
\(494\) −4.78164e16 −0.148031
\(495\) 1.10522e17 0.337689
\(496\) 3.95004e17 1.19116
\(497\) 3.95361e17 1.17673
\(498\) −5.33245e16 −0.156652
\(499\) 6.89495e16 0.199930 0.0999649 0.994991i \(-0.468127\pi\)
0.0999649 + 0.994991i \(0.468127\pi\)
\(500\) −4.58572e16 −0.131251
\(501\) 7.49709e16 0.211811
\(502\) −1.31020e17 −0.365396
\(503\) −2.89523e17 −0.797059 −0.398530 0.917155i \(-0.630479\pi\)
−0.398530 + 0.917155i \(0.630479\pi\)
\(504\) −2.15164e17 −0.584751
\(505\) −9.78785e17 −2.62599
\(506\) −1.78592e17 −0.473025
\(507\) −1.57357e17 −0.411466
\(508\) 7.49243e16 0.193423
\(509\) −2.58627e17 −0.659188 −0.329594 0.944123i \(-0.606912\pi\)
−0.329594 + 0.944123i \(0.606912\pi\)
\(510\) 2.70829e16 0.0681536
\(511\) 3.20469e17 0.796252
\(512\) 4.57815e17 1.12314
\(513\) −2.37644e16 −0.0575656
\(514\) 1.52275e17 0.364224
\(515\) −2.99050e17 −0.706311
\(516\) −3.71700e16 −0.0866900
\(517\) 1.24773e17 0.287364
\(518\) −9.43349e16 −0.214550
\(519\) 1.18723e17 0.266654
\(520\) −4.09368e17 −0.908013
\(521\) −6.53363e17 −1.43123 −0.715615 0.698495i \(-0.753854\pi\)
−0.715615 + 0.698495i \(0.753854\pi\)
\(522\) 7.46132e16 0.161420
\(523\) 7.08667e17 1.51419 0.757097 0.653303i \(-0.226617\pi\)
0.757097 + 0.653303i \(0.226617\pi\)
\(524\) −4.47578e16 −0.0944528
\(525\) −7.13717e17 −1.48761
\(526\) −8.19009e17 −1.68609
\(527\) 5.63976e16 0.114681
\(528\) −1.51288e17 −0.303867
\(529\) −1.74499e17 −0.346204
\(530\) −4.86637e17 −0.953700
\(531\) −2.24165e16 −0.0433963
\(532\) −3.82219e16 −0.0730948
\(533\) −6.59409e16 −0.124574
\(534\) −2.79932e17 −0.522438
\(535\) 5.10735e17 0.941664
\(536\) 4.07684e17 0.742595
\(537\) −2.03142e17 −0.365566
\(538\) −9.03885e17 −1.60705
\(539\) 6.28129e17 1.10337
\(540\) −2.61659e16 −0.0454126
\(541\) −8.19026e17 −1.40448 −0.702240 0.711940i \(-0.747817\pi\)
−0.702240 + 0.711940i \(0.747817\pi\)
\(542\) 5.35008e16 0.0906495
\(543\) 2.65926e17 0.445207
\(544\) 1.41467e16 0.0234025
\(545\) 1.28959e18 2.10802
\(546\) −2.92873e17 −0.473072
\(547\) −2.29479e17 −0.366290 −0.183145 0.983086i \(-0.558628\pi\)
−0.183145 + 0.983086i \(0.558628\pi\)
\(548\) 1.57468e17 0.248381
\(549\) 5.98202e16 0.0932454
\(550\) −5.91004e17 −0.910401
\(551\) 1.03059e17 0.156892
\(552\) 3.28758e17 0.494620
\(553\) −1.07994e18 −1.60578
\(554\) −3.44322e17 −0.506001
\(555\) −8.92003e16 −0.129557
\(556\) −1.23158e17 −0.176798
\(557\) 4.44343e17 0.630463 0.315231 0.949015i \(-0.397918\pi\)
0.315231 + 0.949015i \(0.397918\pi\)
\(558\) 3.14695e17 0.441334
\(559\) −3.93395e17 −0.545321
\(560\) 1.60475e18 2.19880
\(561\) −2.16005e16 −0.0292553
\(562\) −6.42620e17 −0.860336
\(563\) 5.88678e17 0.779064 0.389532 0.921013i \(-0.372637\pi\)
0.389532 + 0.921013i \(0.372637\pi\)
\(564\) −2.95397e16 −0.0386449
\(565\) −9.98610e17 −1.29146
\(566\) −1.00585e18 −1.28596
\(567\) −1.45555e17 −0.183966
\(568\) −6.02658e17 −0.753021
\(569\) −3.38634e17 −0.418312 −0.209156 0.977882i \(-0.567072\pi\)
−0.209156 + 0.977882i \(0.567072\pi\)
\(570\) 2.08734e17 0.254922
\(571\) −1.82851e16 −0.0220781 −0.0110391 0.999939i \(-0.503514\pi\)
−0.0110391 + 0.999939i \(0.503514\pi\)
\(572\) 4.19909e16 0.0501281
\(573\) 9.68798e17 1.14348
\(574\) 3.04423e17 0.355264
\(575\) 1.09052e18 1.25832
\(576\) 3.21616e17 0.366937
\(577\) −3.76678e17 −0.424940 −0.212470 0.977168i \(-0.568151\pi\)
−0.212470 + 0.977168i \(0.568151\pi\)
\(578\) 8.22373e17 0.917356
\(579\) 5.76111e17 0.635470
\(580\) 1.13474e17 0.123769
\(581\) −4.51127e17 −0.486579
\(582\) 2.47963e17 0.264476
\(583\) 3.88127e17 0.409381
\(584\) −4.88499e17 −0.509543
\(585\) −2.76932e17 −0.285667
\(586\) 1.02237e18 1.04298
\(587\) 7.60927e17 0.767707 0.383853 0.923394i \(-0.374597\pi\)
0.383853 + 0.923394i \(0.374597\pi\)
\(588\) −1.48708e17 −0.148382
\(589\) 4.34670e17 0.428954
\(590\) 1.96895e17 0.192175
\(591\) 1.12859e18 1.08948
\(592\) 1.22101e17 0.116581
\(593\) 3.34908e17 0.316279 0.158139 0.987417i \(-0.449451\pi\)
0.158139 + 0.987417i \(0.449451\pi\)
\(594\) −1.20529e17 −0.112585
\(595\) 2.29122e17 0.211693
\(596\) −7.02875e16 −0.0642359
\(597\) 4.44841e17 0.402135
\(598\) 4.47492e17 0.400154
\(599\) −3.26843e17 −0.289111 −0.144555 0.989497i \(-0.546175\pi\)
−0.144555 + 0.989497i \(0.546175\pi\)
\(600\) 1.08794e18 0.951964
\(601\) 1.60372e17 0.138818 0.0694089 0.997588i \(-0.477889\pi\)
0.0694089 + 0.997588i \(0.477889\pi\)
\(602\) 1.81615e18 1.55516
\(603\) 2.75792e17 0.233625
\(604\) −1.09775e16 −0.00919945
\(605\) −1.15419e18 −0.956903
\(606\) 1.06741e18 0.875504
\(607\) 1.52099e18 1.23424 0.617120 0.786869i \(-0.288299\pi\)
0.617120 + 0.786869i \(0.288299\pi\)
\(608\) 1.09032e17 0.0875348
\(609\) 6.31230e17 0.501389
\(610\) −5.25431e17 −0.412925
\(611\) −3.12639e17 −0.243095
\(612\) 5.11387e15 0.00393428
\(613\) 1.84862e18 1.40720 0.703598 0.710598i \(-0.251576\pi\)
0.703598 + 0.710598i \(0.251576\pi\)
\(614\) −1.43331e18 −1.07955
\(615\) 2.87854e17 0.214528
\(616\) −1.50732e18 −1.11156
\(617\) 7.09719e17 0.517885 0.258942 0.965893i \(-0.416626\pi\)
0.258942 + 0.965893i \(0.416626\pi\)
\(618\) 3.26126e17 0.235484
\(619\) 1.82133e18 1.30137 0.650683 0.759350i \(-0.274483\pi\)
0.650683 + 0.759350i \(0.274483\pi\)
\(620\) 4.78597e17 0.338395
\(621\) 2.22400e17 0.155611
\(622\) −2.94553e17 −0.203951
\(623\) −2.36824e18 −1.62275
\(624\) 3.79077e17 0.257056
\(625\) −2.00284e17 −0.134408
\(626\) 2.77678e17 0.184420
\(627\) −1.66480e17 −0.109427
\(628\) 1.09586e17 0.0712880
\(629\) 1.74333e16 0.0112241
\(630\) 1.27849e18 0.814672
\(631\) 1.05239e18 0.663718 0.331859 0.943329i \(-0.392324\pi\)
0.331859 + 0.943329i \(0.392324\pi\)
\(632\) 1.64618e18 1.02758
\(633\) 5.83474e17 0.360493
\(634\) −1.38128e18 −0.844695
\(635\) −3.46160e18 −2.09531
\(636\) −9.18881e16 −0.0550539
\(637\) −1.57388e18 −0.933394
\(638\) 5.22699e17 0.306844
\(639\) −4.07690e17 −0.236905
\(640\) −2.01151e18 −1.15705
\(641\) −3.43637e18 −1.95669 −0.978346 0.206977i \(-0.933637\pi\)
−0.978346 + 0.206977i \(0.933637\pi\)
\(642\) −5.56979e17 −0.313950
\(643\) 8.38738e17 0.468010 0.234005 0.972235i \(-0.424817\pi\)
0.234005 + 0.972235i \(0.424817\pi\)
\(644\) 3.57701e17 0.197589
\(645\) 1.71730e18 0.939092
\(646\) −4.07950e16 −0.0220849
\(647\) −1.25796e18 −0.674202 −0.337101 0.941469i \(-0.609446\pi\)
−0.337101 + 0.941469i \(0.609446\pi\)
\(648\) 2.21874e17 0.117725
\(649\) −1.57038e17 −0.0824922
\(650\) 1.48086e18 0.770151
\(651\) 2.66233e18 1.37084
\(652\) 4.83767e16 0.0246619
\(653\) −2.84285e18 −1.43489 −0.717444 0.696616i \(-0.754688\pi\)
−0.717444 + 0.696616i \(0.754688\pi\)
\(654\) −1.40635e18 −0.702811
\(655\) 2.06787e18 1.02318
\(656\) −3.94027e17 −0.193042
\(657\) −3.30463e17 −0.160305
\(658\) 1.44333e18 0.693263
\(659\) −3.56178e18 −1.69399 −0.846997 0.531598i \(-0.821592\pi\)
−0.846997 + 0.531598i \(0.821592\pi\)
\(660\) −1.83304e17 −0.0863251
\(661\) 2.84891e18 1.32852 0.664262 0.747500i \(-0.268746\pi\)
0.664262 + 0.747500i \(0.268746\pi\)
\(662\) 1.15854e18 0.534975
\(663\) 5.41235e16 0.0247485
\(664\) 6.87664e17 0.311375
\(665\) 1.76590e18 0.791818
\(666\) 9.72768e16 0.0431943
\(667\) −9.64481e17 −0.424107
\(668\) −1.24341e17 −0.0541462
\(669\) −7.30376e17 −0.314975
\(670\) −2.42242e18 −1.03458
\(671\) 4.19068e17 0.177251
\(672\) 6.67815e17 0.279741
\(673\) 2.02250e18 0.839056 0.419528 0.907742i \(-0.362196\pi\)
0.419528 + 0.907742i \(0.362196\pi\)
\(674\) −4.61698e17 −0.189700
\(675\) 7.35974e17 0.299494
\(676\) 2.60981e17 0.105185
\(677\) −3.87383e18 −1.54637 −0.773185 0.634180i \(-0.781338\pi\)
−0.773185 + 0.634180i \(0.781338\pi\)
\(678\) 1.08903e18 0.430572
\(679\) 2.09777e18 0.821494
\(680\) −3.49256e17 −0.135468
\(681\) −2.56924e18 −0.987072
\(682\) 2.20458e18 0.838935
\(683\) −1.03330e18 −0.389485 −0.194742 0.980854i \(-0.562387\pi\)
−0.194742 + 0.980854i \(0.562387\pi\)
\(684\) 3.94138e16 0.0147158
\(685\) −7.27522e18 −2.69065
\(686\) 3.09334e18 1.13324
\(687\) 4.80863e17 0.174503
\(688\) −2.35072e18 −0.845036
\(689\) −9.72515e17 −0.346315
\(690\) −1.95345e18 −0.689102
\(691\) 3.95212e18 1.38109 0.690546 0.723288i \(-0.257370\pi\)
0.690546 + 0.723288i \(0.257370\pi\)
\(692\) −1.96906e17 −0.0681662
\(693\) −1.01968e18 −0.349703
\(694\) −3.60816e17 −0.122588
\(695\) 5.69007e18 1.91521
\(696\) −9.62199e17 −0.320852
\(697\) −5.62581e16 −0.0185854
\(698\) −2.61542e18 −0.856014
\(699\) 3.13527e18 1.01666
\(700\) 1.18372e18 0.380287
\(701\) 5.62189e18 1.78943 0.894716 0.446635i \(-0.147378\pi\)
0.894716 + 0.446635i \(0.147378\pi\)
\(702\) 3.02006e17 0.0952411
\(703\) 1.34363e17 0.0419826
\(704\) 2.25306e18 0.697512
\(705\) 1.36477e18 0.418631
\(706\) 3.56695e18 1.08409
\(707\) 9.03030e18 2.71942
\(708\) 3.71783e16 0.0110936
\(709\) −1.41248e18 −0.417619 −0.208810 0.977956i \(-0.566959\pi\)
−0.208810 + 0.977956i \(0.566959\pi\)
\(710\) 3.58095e18 1.04910
\(711\) 1.11362e18 0.323285
\(712\) 3.60996e18 1.03844
\(713\) −4.06788e18 −1.15954
\(714\) −2.49867e17 −0.0705783
\(715\) −1.94003e18 −0.543025
\(716\) 3.36916e17 0.0934516
\(717\) 1.41377e18 0.388600
\(718\) −2.01107e18 −0.547796
\(719\) 2.38512e16 0.00643833 0.00321917 0.999995i \(-0.498975\pi\)
0.00321917 + 0.999995i \(0.498975\pi\)
\(720\) −1.65479e18 −0.442673
\(721\) 2.75904e18 0.731440
\(722\) 3.19970e18 0.840653
\(723\) 1.00703e18 0.262208
\(724\) −4.41046e17 −0.113811
\(725\) −3.19169e18 −0.816252
\(726\) 1.25869e18 0.319031
\(727\) 7.36669e18 1.85054 0.925271 0.379307i \(-0.123838\pi\)
0.925271 + 0.379307i \(0.123838\pi\)
\(728\) 3.77684e18 0.940318
\(729\) 1.50095e17 0.0370370
\(730\) 2.90262e18 0.709892
\(731\) −3.35629e17 −0.0813573
\(732\) −9.92133e16 −0.0238368
\(733\) 4.19615e18 0.999252 0.499626 0.866241i \(-0.333471\pi\)
0.499626 + 0.866241i \(0.333471\pi\)
\(734\) 2.26457e18 0.534517
\(735\) 6.87050e18 1.60739
\(736\) −1.02038e18 −0.236623
\(737\) 1.93205e18 0.444099
\(738\) −3.13917e17 −0.0715234
\(739\) 2.45421e17 0.0554271 0.0277135 0.999616i \(-0.491177\pi\)
0.0277135 + 0.999616i \(0.491177\pi\)
\(740\) 1.47941e17 0.0331194
\(741\) 4.17143e17 0.0925693
\(742\) 4.48972e18 0.987630
\(743\) 2.08967e18 0.455671 0.227835 0.973700i \(-0.426835\pi\)
0.227835 + 0.973700i \(0.426835\pi\)
\(744\) −4.05826e18 −0.877234
\(745\) 3.24737e18 0.695851
\(746\) −7.09547e18 −1.50723
\(747\) 4.65195e17 0.0979606
\(748\) 3.58250e16 0.00747869
\(749\) −4.71206e18 −0.975166
\(750\) −2.31049e18 −0.474030
\(751\) 8.21538e17 0.167097 0.0835484 0.996504i \(-0.473375\pi\)
0.0835484 + 0.996504i \(0.473375\pi\)
\(752\) −1.86816e18 −0.376703
\(753\) 1.14300e18 0.228496
\(754\) −1.30971e18 −0.259574
\(755\) 5.07173e17 0.0996554
\(756\) 2.41408e17 0.0470283
\(757\) −4.94446e18 −0.954983 −0.477492 0.878636i \(-0.658454\pi\)
−0.477492 + 0.878636i \(0.658454\pi\)
\(758\) −7.32156e18 −1.40202
\(759\) 1.55801e18 0.295801
\(760\) −2.69180e18 −0.506705
\(761\) 9.65676e18 1.80232 0.901158 0.433490i \(-0.142718\pi\)
0.901158 + 0.433490i \(0.142718\pi\)
\(762\) 3.77502e18 0.698573
\(763\) −1.18978e19 −2.18301
\(764\) −1.60678e18 −0.292313
\(765\) −2.36267e17 −0.0426191
\(766\) 2.79681e18 0.500238
\(767\) 3.93483e17 0.0697841
\(768\) −1.42046e18 −0.249793
\(769\) −1.12349e19 −1.95907 −0.979535 0.201275i \(-0.935492\pi\)
−0.979535 + 0.201275i \(0.935492\pi\)
\(770\) 8.95639e18 1.54861
\(771\) −1.32843e18 −0.227764
\(772\) −9.55495e17 −0.162449
\(773\) 5.07788e18 0.856083 0.428041 0.903759i \(-0.359204\pi\)
0.428041 + 0.903759i \(0.359204\pi\)
\(774\) −1.87279e18 −0.313092
\(775\) −1.34616e19 −2.23170
\(776\) −3.19769e18 −0.525696
\(777\) 8.22964e17 0.134167
\(778\) 1.92216e18 0.310758
\(779\) −4.33595e17 −0.0695170
\(780\) 4.59299e17 0.0730265
\(781\) −2.85606e18 −0.450334
\(782\) 3.81782e17 0.0596996
\(783\) −6.50915e17 −0.100942
\(784\) −9.40465e18 −1.44640
\(785\) −5.06300e18 −0.772245
\(786\) −2.25510e18 −0.341129
\(787\) −3.40847e17 −0.0511356 −0.0255678 0.999673i \(-0.508139\pi\)
−0.0255678 + 0.999673i \(0.508139\pi\)
\(788\) −1.87180e18 −0.278509
\(789\) 7.14492e18 1.05438
\(790\) −9.78149e18 −1.43162
\(791\) 9.21320e18 1.33741
\(792\) 1.55433e18 0.223784
\(793\) −1.05004e18 −0.149945
\(794\) 4.79748e18 0.679486
\(795\) 4.24535e18 0.596385
\(796\) −7.37780e17 −0.102800
\(797\) 1.25420e18 0.173336 0.0866678 0.996237i \(-0.472378\pi\)
0.0866678 + 0.996237i \(0.472378\pi\)
\(798\) −1.92579e18 −0.263991
\(799\) −2.66731e17 −0.0362677
\(800\) −3.37668e18 −0.455413
\(801\) 2.44209e18 0.326701
\(802\) −1.35931e19 −1.80379
\(803\) −2.31505e18 −0.304725
\(804\) −4.57409e17 −0.0597228
\(805\) −1.65263e19 −2.14043
\(806\) −5.52394e18 −0.709694
\(807\) 7.88537e18 1.00495
\(808\) −1.37651e19 −1.74023
\(809\) −8.23011e18 −1.03214 −0.516072 0.856545i \(-0.672606\pi\)
−0.516072 + 0.856545i \(0.672606\pi\)
\(810\) −1.31836e18 −0.164014
\(811\) −1.24128e19 −1.53191 −0.765957 0.642892i \(-0.777734\pi\)
−0.765957 + 0.642892i \(0.777734\pi\)
\(812\) −1.04691e18 −0.128173
\(813\) −4.66734e17 −0.0566866
\(814\) 6.81468e17 0.0821083
\(815\) −2.23506e18 −0.267156
\(816\) 3.23413e17 0.0383505
\(817\) −2.58677e18 −0.304309
\(818\) −4.30917e18 −0.502918
\(819\) 2.55498e18 0.295830
\(820\) −4.77413e17 −0.0548409
\(821\) 8.33949e18 0.950406 0.475203 0.879876i \(-0.342375\pi\)
0.475203 + 0.879876i \(0.342375\pi\)
\(822\) 7.93394e18 0.897061
\(823\) −4.95643e18 −0.555994 −0.277997 0.960582i \(-0.589671\pi\)
−0.277997 + 0.960582i \(0.589671\pi\)
\(824\) −4.20567e18 −0.468068
\(825\) 5.15583e18 0.569309
\(826\) −1.81656e18 −0.199012
\(827\) −5.45088e18 −0.592489 −0.296245 0.955112i \(-0.595734\pi\)
−0.296245 + 0.955112i \(0.595734\pi\)
\(828\) −3.68856e17 −0.0397796
\(829\) 9.31288e18 0.996506 0.498253 0.867032i \(-0.333975\pi\)
0.498253 + 0.867032i \(0.333975\pi\)
\(830\) −4.08604e18 −0.433806
\(831\) 3.00382e18 0.316422
\(832\) −5.64542e18 −0.590058
\(833\) −1.34277e18 −0.139254
\(834\) −6.20526e18 −0.638529
\(835\) 5.74472e18 0.586553
\(836\) 2.76112e17 0.0279733
\(837\) −2.74536e18 −0.275984
\(838\) 8.56274e18 0.854136
\(839\) 1.64140e19 1.62466 0.812331 0.583197i \(-0.198198\pi\)
0.812331 + 0.583197i \(0.198198\pi\)
\(840\) −1.64872e19 −1.61931
\(841\) −7.43781e18 −0.724888
\(842\) 1.22722e19 1.18684
\(843\) 5.60613e18 0.538002
\(844\) −9.67707e17 −0.0921548
\(845\) −1.20576e19 −1.13945
\(846\) −1.48834e18 −0.139571
\(847\) 1.06486e19 0.990947
\(848\) −5.81122e18 −0.536654
\(849\) 8.77490e18 0.804160
\(850\) 1.26341e18 0.114900
\(851\) −1.25744e18 −0.113487
\(852\) 6.76165e17 0.0605613
\(853\) −1.68479e19 −1.49753 −0.748767 0.662833i \(-0.769354\pi\)
−0.748767 + 0.662833i \(0.769354\pi\)
\(854\) 4.84764e18 0.427616
\(855\) −1.82097e18 −0.159413
\(856\) 7.18270e18 0.624034
\(857\) −1.30913e19 −1.12877 −0.564385 0.825511i \(-0.690887\pi\)
−0.564385 + 0.825511i \(0.690887\pi\)
\(858\) 2.11569e18 0.181044
\(859\) −1.79226e19 −1.52211 −0.761053 0.648689i \(-0.775317\pi\)
−0.761053 + 0.648689i \(0.775317\pi\)
\(860\) −2.84819e18 −0.240065
\(861\) −2.65575e18 −0.222160
\(862\) 8.53414e18 0.708537
\(863\) 7.68168e18 0.632974 0.316487 0.948597i \(-0.397497\pi\)
0.316487 + 0.948597i \(0.397497\pi\)
\(864\) −6.88641e17 −0.0563188
\(865\) 9.09730e18 0.738427
\(866\) −4.68894e18 −0.377754
\(867\) −7.17426e18 −0.573658
\(868\) −4.41555e18 −0.350434
\(869\) 7.80142e18 0.614533
\(870\) 5.71731e18 0.447009
\(871\) −4.84107e18 −0.375684
\(872\) 1.81361e19 1.39697
\(873\) −2.16319e18 −0.165387
\(874\) 2.94249e18 0.223301
\(875\) −1.95468e19 −1.47239
\(876\) 5.48082e17 0.0409797
\(877\) 1.62154e19 1.20346 0.601730 0.798700i \(-0.294478\pi\)
0.601730 + 0.798700i \(0.294478\pi\)
\(878\) −1.47407e19 −1.08593
\(879\) −8.91905e18 −0.652215
\(880\) −1.15926e19 −0.841479
\(881\) 5.88155e18 0.423788 0.211894 0.977293i \(-0.432037\pi\)
0.211894 + 0.977293i \(0.432037\pi\)
\(882\) −7.49258e18 −0.535902
\(883\) −2.33752e19 −1.65963 −0.829815 0.558038i \(-0.811554\pi\)
−0.829815 + 0.558038i \(0.811554\pi\)
\(884\) −8.97653e16 −0.00632658
\(885\) −1.71768e18 −0.120174
\(886\) 5.84240e17 0.0405763
\(887\) 1.34784e19 0.929255 0.464628 0.885506i \(-0.346188\pi\)
0.464628 + 0.885506i \(0.346188\pi\)
\(888\) −1.25447e18 −0.0858567
\(889\) 3.19368e19 2.16985
\(890\) −2.14501e19 −1.44675
\(891\) 1.05148e18 0.0704039
\(892\) 1.21135e18 0.0805188
\(893\) −2.05576e18 −0.135656
\(894\) −3.54140e18 −0.231996
\(895\) −1.55659e19 −1.01234
\(896\) 1.85583e19 1.19822
\(897\) −3.90386e18 −0.250232
\(898\) 1.68210e18 0.107042
\(899\) 1.19058e19 0.752176
\(900\) −1.22063e18 −0.0765612
\(901\) −8.29710e17 −0.0516673
\(902\) −2.19913e18 −0.135959
\(903\) −1.58438e19 −0.972502
\(904\) −1.40439e19 −0.855841
\(905\) 2.03769e19 1.23288
\(906\) −5.53094e17 −0.0332250
\(907\) −1.01366e19 −0.604569 −0.302285 0.953218i \(-0.597749\pi\)
−0.302285 + 0.953218i \(0.597749\pi\)
\(908\) 4.26116e18 0.252330
\(909\) −9.31191e18 −0.547487
\(910\) −2.24417e19 −1.31004
\(911\) 1.21184e19 0.702385 0.351193 0.936303i \(-0.385776\pi\)
0.351193 + 0.936303i \(0.385776\pi\)
\(912\) 2.49262e18 0.143447
\(913\) 3.25890e18 0.186214
\(914\) −1.27770e19 −0.724903
\(915\) 4.58378e18 0.258218
\(916\) −7.97524e17 −0.0446091
\(917\) −1.90782e19 −1.05959
\(918\) 2.57659e17 0.0142092
\(919\) −3.21337e19 −1.75958 −0.879792 0.475360i \(-0.842318\pi\)
−0.879792 + 0.475360i \(0.842318\pi\)
\(920\) 2.51914e19 1.36972
\(921\) 1.25039e19 0.675087
\(922\) −8.19249e18 −0.439203
\(923\) 7.15631e18 0.380959
\(924\) 1.69117e18 0.0893963
\(925\) −4.16116e18 −0.218421
\(926\) −3.29720e19 −1.71860
\(927\) −2.84508e18 −0.147257
\(928\) 2.98643e18 0.153494
\(929\) −2.06077e19 −1.05179 −0.525894 0.850550i \(-0.676269\pi\)
−0.525894 + 0.850550i \(0.676269\pi\)
\(930\) 2.41138e19 1.22216
\(931\) −1.03491e19 −0.520868
\(932\) −5.19993e18 −0.259893
\(933\) 2.56963e18 0.127538
\(934\) 1.20858e19 0.595692
\(935\) −1.65516e18 −0.0810148
\(936\) −3.89462e18 −0.189309
\(937\) −4.34044e18 −0.209521 −0.104760 0.994498i \(-0.533408\pi\)
−0.104760 + 0.994498i \(0.533408\pi\)
\(938\) 2.23493e19 1.07139
\(939\) −2.42242e18 −0.115325
\(940\) −2.26351e18 −0.107017
\(941\) 1.54600e19 0.725902 0.362951 0.931808i \(-0.381769\pi\)
0.362951 + 0.931808i \(0.381769\pi\)
\(942\) 5.52142e18 0.257466
\(943\) 4.05782e18 0.187917
\(944\) 2.35124e18 0.108138
\(945\) −1.11533e19 −0.509446
\(946\) −1.31197e19 −0.595159
\(947\) 1.58525e19 0.714204 0.357102 0.934065i \(-0.383765\pi\)
0.357102 + 0.934065i \(0.383765\pi\)
\(948\) −1.84697e18 −0.0826429
\(949\) 5.80072e18 0.257781
\(950\) 9.73739e18 0.429773
\(951\) 1.20500e19 0.528221
\(952\) 3.22225e18 0.140287
\(953\) −3.84094e19 −1.66086 −0.830431 0.557122i \(-0.811906\pi\)
−0.830431 + 0.557122i \(0.811906\pi\)
\(954\) −4.62973e18 −0.198834
\(955\) 7.42351e19 3.16656
\(956\) −2.34477e18 −0.0993398
\(957\) −4.55996e18 −0.191881
\(958\) −4.25133e19 −1.77684
\(959\) 6.71214e19 2.78638
\(960\) 2.46441e19 1.01613
\(961\) 2.57973e19 1.05651
\(962\) −1.70753e18 −0.0694592
\(963\) 4.85900e18 0.196325
\(964\) −1.67019e18 −0.0670295
\(965\) 4.41451e19 1.75976
\(966\) 1.80226e19 0.713618
\(967\) 3.32794e19 1.30889 0.654446 0.756109i \(-0.272902\pi\)
0.654446 + 0.756109i \(0.272902\pi\)
\(968\) −1.62319e19 −0.634133
\(969\) 3.55890e17 0.0138106
\(970\) 1.90004e19 0.732396
\(971\) 2.86499e19 1.09698 0.548490 0.836157i \(-0.315203\pi\)
0.548490 + 0.836157i \(0.315203\pi\)
\(972\) −2.48936e17 −0.00946797
\(973\) −5.24967e19 −1.98335
\(974\) −3.94633e19 −1.48102
\(975\) −1.29188e19 −0.481606
\(976\) −6.27448e18 −0.232356
\(977\) 7.48660e18 0.275404 0.137702 0.990474i \(-0.456028\pi\)
0.137702 + 0.990474i \(0.456028\pi\)
\(978\) 2.43743e18 0.0890697
\(979\) 1.71080e19 0.621027
\(980\) −1.13949e19 −0.410905
\(981\) 1.22688e19 0.439495
\(982\) −4.53567e18 −0.161405
\(983\) −2.71555e19 −0.959975 −0.479987 0.877275i \(-0.659359\pi\)
−0.479987 + 0.877275i \(0.659359\pi\)
\(984\) 4.04822e18 0.142166
\(985\) 8.64797e19 3.01702
\(986\) −1.11739e18 −0.0387262
\(987\) −1.25914e19 −0.433524
\(988\) −6.91843e17 −0.0236640
\(989\) 2.42084e19 0.822604
\(990\) −9.23569e18 −0.311775
\(991\) −4.34033e19 −1.45561 −0.727803 0.685786i \(-0.759459\pi\)
−0.727803 + 0.685786i \(0.759459\pi\)
\(992\) 1.25958e19 0.419663
\(993\) −1.01069e19 −0.334540
\(994\) −3.30379e19 −1.08643
\(995\) 3.40864e19 1.11360
\(996\) −7.71538e17 −0.0250422
\(997\) −5.70975e19 −1.84119 −0.920595 0.390519i \(-0.872296\pi\)
−0.920595 + 0.390519i \(0.872296\pi\)
\(998\) −5.76170e18 −0.184587
\(999\) −8.48628e17 −0.0270111
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.1.9 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.9 31 1.1 even 1 trivial