Properties

Label 177.14.a.c.1.12
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 1.12
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-55.7627 q^{2} +729.000 q^{3} -5082.53 q^{4} +35389.9 q^{5} -40651.0 q^{6} +112882. q^{7} +740223. q^{8} +531441. q^{9} +O(q^{10})\) \(q-55.7627 q^{2} +729.000 q^{3} -5082.53 q^{4} +35389.9 q^{5} -40651.0 q^{6} +112882. q^{7} +740223. q^{8} +531441. q^{9} -1.97344e6 q^{10} -7.74091e6 q^{11} -3.70516e6 q^{12} -2.59034e7 q^{13} -6.29460e6 q^{14} +2.57993e7 q^{15} +359253. q^{16} -1.29900e8 q^{17} -2.96346e7 q^{18} -3.90885e8 q^{19} -1.79870e8 q^{20} +8.22910e7 q^{21} +4.31654e8 q^{22} -7.02596e8 q^{23} +5.39622e8 q^{24} +3.17454e7 q^{25} +1.44444e9 q^{26} +3.87420e8 q^{27} -5.73726e8 q^{28} +4.55351e9 q^{29} -1.43864e9 q^{30} -7.21548e8 q^{31} -6.08394e9 q^{32} -5.64312e9 q^{33} +7.24356e9 q^{34} +3.99489e9 q^{35} -2.70106e9 q^{36} +1.70177e10 q^{37} +2.17968e10 q^{38} -1.88836e10 q^{39} +2.61964e10 q^{40} +1.42424e10 q^{41} -4.58877e9 q^{42} +8.71016e9 q^{43} +3.93434e10 q^{44} +1.88077e10 q^{45} +3.91786e10 q^{46} +6.41381e10 q^{47} +2.61896e8 q^{48} -8.41466e10 q^{49} -1.77021e9 q^{50} -9.46969e10 q^{51} +1.31655e11 q^{52} -2.07313e11 q^{53} -2.16036e10 q^{54} -2.73950e11 q^{55} +8.35579e10 q^{56} -2.84955e11 q^{57} -2.53916e11 q^{58} -4.21805e10 q^{59} -1.31125e11 q^{60} +7.37636e11 q^{61} +4.02354e10 q^{62} +5.99902e10 q^{63} +3.36314e11 q^{64} -9.16720e11 q^{65} +3.14675e11 q^{66} -9.39581e11 q^{67} +6.60219e11 q^{68} -5.12192e11 q^{69} -2.22766e11 q^{70} +7.47914e11 q^{71} +3.93385e11 q^{72} +2.15376e12 q^{73} -9.48952e11 q^{74} +2.31424e10 q^{75} +1.98669e12 q^{76} -8.73810e11 q^{77} +1.05300e12 q^{78} +2.70570e12 q^{79} +1.27140e10 q^{80} +2.82430e11 q^{81} -7.94195e11 q^{82} +7.98844e11 q^{83} -4.18246e11 q^{84} -4.59715e12 q^{85} -4.85701e11 q^{86} +3.31951e12 q^{87} -5.73000e12 q^{88} +1.42309e12 q^{89} -1.04877e12 q^{90} -2.92403e12 q^{91} +3.57096e12 q^{92} -5.26008e11 q^{93} -3.57651e12 q^{94} -1.38334e13 q^{95} -4.43519e12 q^{96} +5.33688e12 q^{97} +4.69224e12 q^{98} -4.11384e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −55.7627 −0.616096 −0.308048 0.951371i \(-0.599676\pi\)
−0.308048 + 0.951371i \(0.599676\pi\)
\(3\) 729.000 0.577350
\(4\) −5082.53 −0.620425
\(5\) 35389.9 1.01292 0.506460 0.862264i \(-0.330954\pi\)
0.506460 + 0.862264i \(0.330954\pi\)
\(6\) −40651.0 −0.355703
\(7\) 112882. 0.362650 0.181325 0.983423i \(-0.441961\pi\)
0.181325 + 0.983423i \(0.441961\pi\)
\(8\) 740223. 0.998338
\(9\) 531441. 0.333333
\(10\) −1.97344e6 −0.624056
\(11\) −7.74091e6 −1.31747 −0.658733 0.752377i \(-0.728907\pi\)
−0.658733 + 0.752377i \(0.728907\pi\)
\(12\) −3.70516e6 −0.358203
\(13\) −2.59034e7 −1.48842 −0.744209 0.667947i \(-0.767173\pi\)
−0.744209 + 0.667947i \(0.767173\pi\)
\(14\) −6.29460e6 −0.223427
\(15\) 2.57993e7 0.584809
\(16\) 359253. 0.00535329
\(17\) −1.29900e8 −1.30524 −0.652620 0.757685i \(-0.726330\pi\)
−0.652620 + 0.757685i \(0.726330\pi\)
\(18\) −2.96346e7 −0.205365
\(19\) −3.90885e8 −1.90612 −0.953062 0.302776i \(-0.902087\pi\)
−0.953062 + 0.302776i \(0.902087\pi\)
\(20\) −1.79870e8 −0.628441
\(21\) 8.22910e7 0.209376
\(22\) 4.31654e8 0.811686
\(23\) −7.02596e8 −0.989634 −0.494817 0.868997i \(-0.664765\pi\)
−0.494817 + 0.868997i \(0.664765\pi\)
\(24\) 5.39622e8 0.576391
\(25\) 3.17454e7 0.0260058
\(26\) 1.44444e9 0.917009
\(27\) 3.87420e8 0.192450
\(28\) −5.73726e8 −0.224997
\(29\) 4.55351e9 1.42154 0.710770 0.703425i \(-0.248347\pi\)
0.710770 + 0.703425i \(0.248347\pi\)
\(30\) −1.43864e9 −0.360299
\(31\) −7.21548e8 −0.146021 −0.0730103 0.997331i \(-0.523261\pi\)
−0.0730103 + 0.997331i \(0.523261\pi\)
\(32\) −6.08394e9 −1.00164
\(33\) −5.64312e9 −0.760639
\(34\) 7.24356e9 0.804153
\(35\) 3.99489e9 0.367335
\(36\) −2.70106e9 −0.206808
\(37\) 1.70177e10 1.09041 0.545204 0.838303i \(-0.316452\pi\)
0.545204 + 0.838303i \(0.316452\pi\)
\(38\) 2.17968e10 1.17436
\(39\) −1.88836e10 −0.859339
\(40\) 2.61964e10 1.01124
\(41\) 1.42424e10 0.468262 0.234131 0.972205i \(-0.424776\pi\)
0.234131 + 0.972205i \(0.424776\pi\)
\(42\) −4.58877e9 −0.128996
\(43\) 8.71016e9 0.210127 0.105063 0.994466i \(-0.466495\pi\)
0.105063 + 0.994466i \(0.466495\pi\)
\(44\) 3.93434e10 0.817390
\(45\) 1.88077e10 0.337640
\(46\) 3.91786e10 0.609710
\(47\) 6.41381e10 0.867921 0.433960 0.900932i \(-0.357116\pi\)
0.433960 + 0.900932i \(0.357116\pi\)
\(48\) 2.61896e8 0.00309072
\(49\) −8.41466e10 −0.868485
\(50\) −1.77021e9 −0.0160221
\(51\) −9.46969e10 −0.753581
\(52\) 1.31655e11 0.923453
\(53\) −2.07313e11 −1.28479 −0.642396 0.766373i \(-0.722059\pi\)
−0.642396 + 0.766373i \(0.722059\pi\)
\(54\) −2.16036e10 −0.118568
\(55\) −2.73950e11 −1.33449
\(56\) 8.35579e10 0.362047
\(57\) −2.84955e11 −1.10050
\(58\) −2.53916e11 −0.875805
\(59\) −4.21805e10 −0.130189
\(60\) −1.31125e11 −0.362831
\(61\) 7.37636e11 1.83315 0.916575 0.399863i \(-0.130942\pi\)
0.916575 + 0.399863i \(0.130942\pi\)
\(62\) 4.02354e10 0.0899628
\(63\) 5.99902e10 0.120883
\(64\) 3.36314e11 0.611751
\(65\) −9.16720e11 −1.50765
\(66\) 3.14675e11 0.468627
\(67\) −9.39581e11 −1.26896 −0.634480 0.772939i \(-0.718786\pi\)
−0.634480 + 0.772939i \(0.718786\pi\)
\(68\) 6.60219e11 0.809804
\(69\) −5.12192e11 −0.571365
\(70\) −2.22766e11 −0.226314
\(71\) 7.47914e11 0.692903 0.346452 0.938068i \(-0.387386\pi\)
0.346452 + 0.938068i \(0.387386\pi\)
\(72\) 3.93385e11 0.332779
\(73\) 2.15376e12 1.66571 0.832853 0.553495i \(-0.186706\pi\)
0.832853 + 0.553495i \(0.186706\pi\)
\(74\) −9.48952e11 −0.671797
\(75\) 2.31424e10 0.0150145
\(76\) 1.98669e12 1.18261
\(77\) −8.73810e11 −0.477779
\(78\) 1.05300e12 0.529435
\(79\) 2.70570e12 1.25229 0.626144 0.779707i \(-0.284632\pi\)
0.626144 + 0.779707i \(0.284632\pi\)
\(80\) 1.27140e10 0.00542245
\(81\) 2.82430e11 0.111111
\(82\) −7.94195e11 −0.288494
\(83\) 7.98844e11 0.268197 0.134099 0.990968i \(-0.457186\pi\)
0.134099 + 0.990968i \(0.457186\pi\)
\(84\) −4.18246e11 −0.129902
\(85\) −4.59715e12 −1.32210
\(86\) −4.85701e11 −0.129458
\(87\) 3.31951e12 0.820726
\(88\) −5.73000e12 −1.31528
\(89\) 1.42309e12 0.303528 0.151764 0.988417i \(-0.451505\pi\)
0.151764 + 0.988417i \(0.451505\pi\)
\(90\) −1.04877e12 −0.208019
\(91\) −2.92403e12 −0.539775
\(92\) 3.57096e12 0.613994
\(93\) −5.26008e11 −0.0843050
\(94\) −3.57651e12 −0.534723
\(95\) −1.38334e13 −1.93075
\(96\) −4.43519e12 −0.578295
\(97\) 5.33688e12 0.650536 0.325268 0.945622i \(-0.394545\pi\)
0.325268 + 0.945622i \(0.394545\pi\)
\(98\) 4.69224e12 0.535070
\(99\) −4.11384e12 −0.439155
\(100\) −1.61347e11 −0.0161347
\(101\) 1.92748e12 0.180676 0.0903379 0.995911i \(-0.471205\pi\)
0.0903379 + 0.995911i \(0.471205\pi\)
\(102\) 5.28055e12 0.464278
\(103\) 2.16694e13 1.78816 0.894078 0.447910i \(-0.147832\pi\)
0.894078 + 0.447910i \(0.147832\pi\)
\(104\) −1.91743e13 −1.48594
\(105\) 2.91228e12 0.212081
\(106\) 1.15603e13 0.791555
\(107\) 8.12374e12 0.523313 0.261656 0.965161i \(-0.415731\pi\)
0.261656 + 0.965161i \(0.415731\pi\)
\(108\) −1.96907e12 −0.119401
\(109\) −2.43955e13 −1.39328 −0.696638 0.717423i \(-0.745321\pi\)
−0.696638 + 0.717423i \(0.745321\pi\)
\(110\) 1.52762e13 0.822172
\(111\) 1.24059e13 0.629548
\(112\) 4.05533e10 0.00194137
\(113\) −1.50096e13 −0.678201 −0.339100 0.940750i \(-0.610123\pi\)
−0.339100 + 0.940750i \(0.610123\pi\)
\(114\) 1.58899e13 0.678014
\(115\) −2.48648e13 −1.00242
\(116\) −2.31433e13 −0.881959
\(117\) −1.37661e13 −0.496139
\(118\) 2.35210e12 0.0802089
\(119\) −1.46634e13 −0.473345
\(120\) 1.90972e13 0.583837
\(121\) 2.53989e13 0.735717
\(122\) −4.11325e13 −1.12940
\(123\) 1.03827e13 0.270351
\(124\) 3.66729e12 0.0905949
\(125\) −4.20772e13 −0.986578
\(126\) −3.34521e12 −0.0744758
\(127\) 8.13608e13 1.72064 0.860322 0.509751i \(-0.170262\pi\)
0.860322 + 0.509751i \(0.170262\pi\)
\(128\) 3.10859e13 0.624739
\(129\) 6.34970e12 0.121317
\(130\) 5.11188e13 0.928856
\(131\) −3.74993e13 −0.648276 −0.324138 0.946010i \(-0.605074\pi\)
−0.324138 + 0.946010i \(0.605074\pi\)
\(132\) 2.86813e13 0.471920
\(133\) −4.41240e13 −0.691256
\(134\) 5.23935e13 0.781802
\(135\) 1.37108e13 0.194936
\(136\) −9.61548e13 −1.30307
\(137\) −8.77589e12 −0.113399 −0.0566993 0.998391i \(-0.518058\pi\)
−0.0566993 + 0.998391i \(0.518058\pi\)
\(138\) 2.85612e13 0.352016
\(139\) −6.68002e13 −0.785564 −0.392782 0.919632i \(-0.628487\pi\)
−0.392782 + 0.919632i \(0.628487\pi\)
\(140\) −2.03041e13 −0.227904
\(141\) 4.67567e13 0.501094
\(142\) −4.17057e13 −0.426895
\(143\) 2.00516e14 1.96094
\(144\) 1.90922e11 0.00178443
\(145\) 1.61148e14 1.43991
\(146\) −1.20099e14 −1.02623
\(147\) −6.13429e13 −0.501420
\(148\) −8.64928e13 −0.676518
\(149\) 1.38447e14 1.03651 0.518254 0.855227i \(-0.326582\pi\)
0.518254 + 0.855227i \(0.326582\pi\)
\(150\) −1.29048e12 −0.00925036
\(151\) 1.57694e14 1.08259 0.541295 0.840833i \(-0.317934\pi\)
0.541295 + 0.840833i \(0.317934\pi\)
\(152\) −2.89342e14 −1.90296
\(153\) −6.90341e13 −0.435080
\(154\) 4.87260e13 0.294358
\(155\) −2.55355e13 −0.147907
\(156\) 9.59763e13 0.533156
\(157\) −2.83769e14 −1.51223 −0.756113 0.654441i \(-0.772904\pi\)
−0.756113 + 0.654441i \(0.772904\pi\)
\(158\) −1.50877e14 −0.771530
\(159\) −1.51131e14 −0.741775
\(160\) −2.15310e14 −1.01458
\(161\) −7.93105e13 −0.358891
\(162\) −1.57490e13 −0.0684551
\(163\) 4.30080e14 1.79610 0.898049 0.439896i \(-0.144985\pi\)
0.898049 + 0.439896i \(0.144985\pi\)
\(164\) −7.23875e13 −0.290522
\(165\) −1.99710e14 −0.770466
\(166\) −4.45456e13 −0.165235
\(167\) −2.72981e14 −0.973812 −0.486906 0.873454i \(-0.661875\pi\)
−0.486906 + 0.873454i \(0.661875\pi\)
\(168\) 6.09137e13 0.209028
\(169\) 3.68111e14 1.21539
\(170\) 2.56349e14 0.814543
\(171\) −2.07733e14 −0.635375
\(172\) −4.42696e13 −0.130368
\(173\) −6.11310e14 −1.73365 −0.866825 0.498612i \(-0.833843\pi\)
−0.866825 + 0.498612i \(0.833843\pi\)
\(174\) −1.85104e14 −0.505646
\(175\) 3.58349e12 0.00943101
\(176\) −2.78095e12 −0.00705278
\(177\) −3.07496e13 −0.0751646
\(178\) −7.93555e13 −0.187002
\(179\) 1.01687e14 0.231058 0.115529 0.993304i \(-0.463144\pi\)
0.115529 + 0.993304i \(0.463144\pi\)
\(180\) −9.55905e13 −0.209480
\(181\) −3.26880e14 −0.691000 −0.345500 0.938419i \(-0.612291\pi\)
−0.345500 + 0.938419i \(0.612291\pi\)
\(182\) 1.63052e14 0.332553
\(183\) 5.37736e14 1.05837
\(184\) −5.20077e14 −0.987989
\(185\) 6.02255e14 1.10450
\(186\) 2.93316e13 0.0519400
\(187\) 1.00554e15 1.71961
\(188\) −3.25984e14 −0.538480
\(189\) 4.37328e13 0.0697920
\(190\) 7.71388e14 1.18953
\(191\) −1.58373e14 −0.236028 −0.118014 0.993012i \(-0.537653\pi\)
−0.118014 + 0.993012i \(0.537653\pi\)
\(192\) 2.45173e14 0.353195
\(193\) −4.12134e14 −0.574006 −0.287003 0.957930i \(-0.592659\pi\)
−0.287003 + 0.957930i \(0.592659\pi\)
\(194\) −2.97599e14 −0.400793
\(195\) −6.68289e14 −0.870441
\(196\) 4.27677e14 0.538830
\(197\) 1.49525e15 1.82257 0.911285 0.411775i \(-0.135091\pi\)
0.911285 + 0.411775i \(0.135091\pi\)
\(198\) 2.29398e14 0.270562
\(199\) 1.60159e15 1.82813 0.914063 0.405572i \(-0.132928\pi\)
0.914063 + 0.405572i \(0.132928\pi\)
\(200\) 2.34987e13 0.0259626
\(201\) −6.84955e14 −0.732635
\(202\) −1.07481e14 −0.111314
\(203\) 5.14009e14 0.515521
\(204\) 4.81300e14 0.467541
\(205\) 5.04038e14 0.474311
\(206\) −1.20835e15 −1.10168
\(207\) −3.73388e14 −0.329878
\(208\) −9.30588e12 −0.00796794
\(209\) 3.02581e15 2.51125
\(210\) −1.62396e14 −0.130662
\(211\) −4.16709e14 −0.325085 −0.162543 0.986702i \(-0.551970\pi\)
−0.162543 + 0.986702i \(0.551970\pi\)
\(212\) 1.05367e15 0.797117
\(213\) 5.45230e14 0.400048
\(214\) −4.53001e14 −0.322411
\(215\) 3.08252e14 0.212841
\(216\) 2.86778e14 0.192130
\(217\) −8.14498e13 −0.0529544
\(218\) 1.36036e15 0.858391
\(219\) 1.57009e15 0.961695
\(220\) 1.39236e15 0.827950
\(221\) 3.36485e15 1.94274
\(222\) −6.91786e14 −0.387862
\(223\) 1.26649e15 0.689639 0.344819 0.938669i \(-0.387940\pi\)
0.344819 + 0.938669i \(0.387940\pi\)
\(224\) −6.86768e14 −0.363243
\(225\) 1.68708e13 0.00866861
\(226\) 8.36973e14 0.417837
\(227\) −1.16866e15 −0.566919 −0.283459 0.958984i \(-0.591482\pi\)
−0.283459 + 0.958984i \(0.591482\pi\)
\(228\) 1.44829e15 0.682779
\(229\) −1.37038e15 −0.627930 −0.313965 0.949435i \(-0.601657\pi\)
−0.313965 + 0.949435i \(0.601657\pi\)
\(230\) 1.38653e15 0.617587
\(231\) −6.37007e14 −0.275846
\(232\) 3.37061e15 1.41918
\(233\) −7.05044e14 −0.288671 −0.144335 0.989529i \(-0.546104\pi\)
−0.144335 + 0.989529i \(0.546104\pi\)
\(234\) 7.67636e14 0.305670
\(235\) 2.26984e15 0.879134
\(236\) 2.14384e14 0.0807725
\(237\) 1.97246e15 0.723009
\(238\) 8.17668e14 0.291626
\(239\) −4.82720e15 −1.67536 −0.837682 0.546158i \(-0.816090\pi\)
−0.837682 + 0.546158i \(0.816090\pi\)
\(240\) 9.26847e12 0.00313065
\(241\) 4.23734e15 1.39310 0.696550 0.717508i \(-0.254718\pi\)
0.696550 + 0.717508i \(0.254718\pi\)
\(242\) −1.41631e15 −0.453272
\(243\) 2.05891e14 0.0641500
\(244\) −3.74905e15 −1.13733
\(245\) −2.97795e15 −0.879705
\(246\) −5.78968e14 −0.166562
\(247\) 1.01253e16 2.83711
\(248\) −5.34106e14 −0.145778
\(249\) 5.82357e14 0.154844
\(250\) 2.34633e15 0.607827
\(251\) 3.47724e15 0.877718 0.438859 0.898556i \(-0.355383\pi\)
0.438859 + 0.898556i \(0.355383\pi\)
\(252\) −3.04902e14 −0.0749991
\(253\) 5.43873e15 1.30381
\(254\) −4.53690e15 −1.06008
\(255\) −3.35132e15 −0.763316
\(256\) −4.48851e15 −0.996650
\(257\) 6.61181e15 1.43138 0.715690 0.698418i \(-0.246112\pi\)
0.715690 + 0.698418i \(0.246112\pi\)
\(258\) −3.54076e14 −0.0747427
\(259\) 1.92099e15 0.395437
\(260\) 4.65925e15 0.935383
\(261\) 2.41992e15 0.473847
\(262\) 2.09106e15 0.399400
\(263\) 6.55505e15 1.22142 0.610708 0.791856i \(-0.290885\pi\)
0.610708 + 0.791856i \(0.290885\pi\)
\(264\) −4.17717e15 −0.759375
\(265\) −7.33678e15 −1.30139
\(266\) 2.46047e15 0.425880
\(267\) 1.03744e15 0.175242
\(268\) 4.77545e15 0.787295
\(269\) 1.58276e15 0.254699 0.127349 0.991858i \(-0.459353\pi\)
0.127349 + 0.991858i \(0.459353\pi\)
\(270\) −7.64550e14 −0.120100
\(271\) −1.19736e16 −1.83622 −0.918108 0.396331i \(-0.870283\pi\)
−0.918108 + 0.396331i \(0.870283\pi\)
\(272\) −4.66669e13 −0.00698733
\(273\) −2.13162e15 −0.311639
\(274\) 4.89367e14 0.0698644
\(275\) −2.45738e14 −0.0342618
\(276\) 2.60323e15 0.354490
\(277\) −1.16282e16 −1.54666 −0.773329 0.634005i \(-0.781410\pi\)
−0.773329 + 0.634005i \(0.781410\pi\)
\(278\) 3.72496e15 0.483983
\(279\) −3.83460e14 −0.0486735
\(280\) 2.95711e15 0.366725
\(281\) −3.27561e15 −0.396918 −0.198459 0.980109i \(-0.563594\pi\)
−0.198459 + 0.980109i \(0.563594\pi\)
\(282\) −2.60728e15 −0.308722
\(283\) 3.41648e13 0.00395336 0.00197668 0.999998i \(-0.499371\pi\)
0.00197668 + 0.999998i \(0.499371\pi\)
\(284\) −3.80129e15 −0.429895
\(285\) −1.00846e16 −1.11472
\(286\) −1.11813e16 −1.20813
\(287\) 1.60771e15 0.169815
\(288\) −3.23325e15 −0.333879
\(289\) 6.96937e15 0.703651
\(290\) −8.98606e15 −0.887120
\(291\) 3.89059e15 0.375587
\(292\) −1.09465e16 −1.03345
\(293\) 1.29046e16 1.19153 0.595767 0.803158i \(-0.296848\pi\)
0.595767 + 0.803158i \(0.296848\pi\)
\(294\) 3.42064e15 0.308923
\(295\) −1.49277e15 −0.131871
\(296\) 1.25969e16 1.08860
\(297\) −2.99899e15 −0.253546
\(298\) −7.72017e15 −0.638589
\(299\) 1.81996e16 1.47299
\(300\) −1.17622e14 −0.00931536
\(301\) 9.83220e14 0.0762024
\(302\) −8.79342e15 −0.666980
\(303\) 1.40513e15 0.104313
\(304\) −1.40427e14 −0.0102040
\(305\) 2.61049e16 1.85683
\(306\) 3.84952e15 0.268051
\(307\) −8.62429e15 −0.587928 −0.293964 0.955817i \(-0.594975\pi\)
−0.293964 + 0.955817i \(0.594975\pi\)
\(308\) 4.44116e15 0.296426
\(309\) 1.57970e16 1.03239
\(310\) 1.42393e15 0.0911250
\(311\) 6.60329e15 0.413826 0.206913 0.978359i \(-0.433658\pi\)
0.206913 + 0.978359i \(0.433658\pi\)
\(312\) −1.39781e16 −0.857910
\(313\) 2.88885e16 1.73655 0.868273 0.496086i \(-0.165230\pi\)
0.868273 + 0.496086i \(0.165230\pi\)
\(314\) 1.58237e16 0.931677
\(315\) 2.12305e15 0.122445
\(316\) −1.37518e16 −0.776951
\(317\) 1.22993e16 0.680764 0.340382 0.940287i \(-0.389444\pi\)
0.340382 + 0.940287i \(0.389444\pi\)
\(318\) 8.42746e15 0.457004
\(319\) −3.52483e16 −1.87283
\(320\) 1.19021e16 0.619654
\(321\) 5.92220e15 0.302135
\(322\) 4.42256e15 0.221111
\(323\) 5.07759e16 2.48795
\(324\) −1.43546e15 −0.0689362
\(325\) −8.22314e14 −0.0387075
\(326\) −2.39824e16 −1.10657
\(327\) −1.77843e16 −0.804408
\(328\) 1.05426e16 0.467483
\(329\) 7.24004e15 0.314752
\(330\) 1.11363e16 0.474681
\(331\) −2.55496e16 −1.06783 −0.533914 0.845539i \(-0.679279\pi\)
−0.533914 + 0.845539i \(0.679279\pi\)
\(332\) −4.06014e15 −0.166396
\(333\) 9.04390e15 0.363470
\(334\) 1.52221e16 0.599962
\(335\) −3.32517e16 −1.28535
\(336\) 2.95633e13 0.00112085
\(337\) −6.15670e15 −0.228957 −0.114478 0.993426i \(-0.536520\pi\)
−0.114478 + 0.993426i \(0.536520\pi\)
\(338\) −2.05269e16 −0.748797
\(339\) −1.09420e16 −0.391559
\(340\) 2.33651e16 0.820266
\(341\) 5.58544e15 0.192377
\(342\) 1.15837e16 0.391452
\(343\) −2.04357e16 −0.677606
\(344\) 6.44746e15 0.209777
\(345\) −1.81265e16 −0.578747
\(346\) 3.40883e16 1.06810
\(347\) 1.84981e16 0.568835 0.284418 0.958700i \(-0.408200\pi\)
0.284418 + 0.958700i \(0.408200\pi\)
\(348\) −1.68715e16 −0.509200
\(349\) −3.31225e16 −0.981201 −0.490600 0.871385i \(-0.663223\pi\)
−0.490600 + 0.871385i \(0.663223\pi\)
\(350\) −1.99825e14 −0.00581041
\(351\) −1.00355e16 −0.286446
\(352\) 4.70952e16 1.31962
\(353\) −5.18852e16 −1.42728 −0.713638 0.700515i \(-0.752954\pi\)
−0.713638 + 0.700515i \(0.752954\pi\)
\(354\) 1.71468e15 0.0463086
\(355\) 2.64686e16 0.701855
\(356\) −7.23291e15 −0.188316
\(357\) −1.06896e16 −0.273286
\(358\) −5.67034e15 −0.142354
\(359\) −9.40818e15 −0.231949 −0.115974 0.993252i \(-0.536999\pi\)
−0.115974 + 0.993252i \(0.536999\pi\)
\(360\) 1.39219e16 0.337079
\(361\) 1.10738e17 2.63331
\(362\) 1.82277e16 0.425722
\(363\) 1.85158e16 0.424766
\(364\) 1.48615e16 0.334890
\(365\) 7.62213e16 1.68723
\(366\) −2.99856e16 −0.652058
\(367\) −4.62025e16 −0.987043 −0.493522 0.869734i \(-0.664291\pi\)
−0.493522 + 0.869734i \(0.664291\pi\)
\(368\) −2.52410e14 −0.00529780
\(369\) 7.56901e15 0.156087
\(370\) −3.35834e16 −0.680476
\(371\) −2.34019e16 −0.465930
\(372\) 2.67345e15 0.0523050
\(373\) −5.25352e16 −1.01005 −0.505025 0.863105i \(-0.668517\pi\)
−0.505025 + 0.863105i \(0.668517\pi\)
\(374\) −5.60717e16 −1.05944
\(375\) −3.06742e16 −0.569601
\(376\) 4.74765e16 0.866478
\(377\) −1.17951e17 −2.11585
\(378\) −2.43866e15 −0.0429986
\(379\) −7.83601e16 −1.35813 −0.679063 0.734080i \(-0.737614\pi\)
−0.679063 + 0.734080i \(0.737614\pi\)
\(380\) 7.03087e16 1.19789
\(381\) 5.93120e16 0.993414
\(382\) 8.83127e15 0.145416
\(383\) 7.07693e16 1.14565 0.572826 0.819677i \(-0.305847\pi\)
0.572826 + 0.819677i \(0.305847\pi\)
\(384\) 2.26616e16 0.360693
\(385\) −3.09241e16 −0.483952
\(386\) 2.29817e16 0.353643
\(387\) 4.62893e15 0.0700422
\(388\) −2.71248e16 −0.403609
\(389\) −4.03950e16 −0.591092 −0.295546 0.955329i \(-0.595502\pi\)
−0.295546 + 0.955329i \(0.595502\pi\)
\(390\) 3.72656e16 0.536275
\(391\) 9.12670e16 1.29171
\(392\) −6.22873e16 −0.867041
\(393\) −2.73370e16 −0.374282
\(394\) −8.33793e16 −1.12288
\(395\) 9.57547e16 1.26847
\(396\) 2.09087e16 0.272463
\(397\) −1.70754e16 −0.218893 −0.109446 0.993993i \(-0.534908\pi\)
−0.109446 + 0.993993i \(0.534908\pi\)
\(398\) −8.93089e16 −1.12630
\(399\) −3.21664e16 −0.399097
\(400\) 1.14046e13 0.000139217 0
\(401\) −5.15982e16 −0.619721 −0.309860 0.950782i \(-0.600282\pi\)
−0.309860 + 0.950782i \(0.600282\pi\)
\(402\) 3.81949e16 0.451373
\(403\) 1.86905e16 0.217340
\(404\) −9.79644e15 −0.112096
\(405\) 9.99517e15 0.112547
\(406\) −2.86625e16 −0.317611
\(407\) −1.31732e17 −1.43658
\(408\) −7.00968e16 −0.752328
\(409\) 3.80753e16 0.402200 0.201100 0.979571i \(-0.435548\pi\)
0.201100 + 0.979571i \(0.435548\pi\)
\(410\) −2.81065e16 −0.292221
\(411\) −6.39762e15 −0.0654707
\(412\) −1.10135e17 −1.10942
\(413\) −4.76143e15 −0.0472130
\(414\) 2.08211e16 0.203237
\(415\) 2.82710e16 0.271662
\(416\) 1.57595e17 1.49085
\(417\) −4.86973e16 −0.453546
\(418\) −1.68727e17 −1.54717
\(419\) 4.30196e16 0.388396 0.194198 0.980962i \(-0.437790\pi\)
0.194198 + 0.980962i \(0.437790\pi\)
\(420\) −1.48017e16 −0.131581
\(421\) −2.04885e16 −0.179340 −0.0896698 0.995972i \(-0.528581\pi\)
−0.0896698 + 0.995972i \(0.528581\pi\)
\(422\) 2.32368e16 0.200284
\(423\) 3.40856e16 0.289307
\(424\) −1.53458e17 −1.28266
\(425\) −4.12372e15 −0.0339438
\(426\) −3.04034e16 −0.246468
\(427\) 8.32659e16 0.664792
\(428\) −4.12891e16 −0.324677
\(429\) 1.46176e17 1.13215
\(430\) −1.71889e16 −0.131131
\(431\) 5.41548e16 0.406944 0.203472 0.979081i \(-0.434777\pi\)
0.203472 + 0.979081i \(0.434777\pi\)
\(432\) 1.39182e14 0.00103024
\(433\) −2.45592e17 −1.79078 −0.895390 0.445283i \(-0.853103\pi\)
−0.895390 + 0.445283i \(0.853103\pi\)
\(434\) 4.54186e15 0.0326250
\(435\) 1.17477e17 0.831330
\(436\) 1.23991e17 0.864423
\(437\) 2.74634e17 1.88636
\(438\) −8.75523e16 −0.592497
\(439\) 1.12802e17 0.752135 0.376068 0.926592i \(-0.377276\pi\)
0.376068 + 0.926592i \(0.377276\pi\)
\(440\) −2.02784e17 −1.33227
\(441\) −4.47190e16 −0.289495
\(442\) −1.87633e17 −1.19692
\(443\) 7.60744e16 0.478205 0.239103 0.970994i \(-0.423147\pi\)
0.239103 + 0.970994i \(0.423147\pi\)
\(444\) −6.30533e16 −0.390588
\(445\) 5.03632e16 0.307449
\(446\) −7.06231e16 −0.424884
\(447\) 1.00928e17 0.598428
\(448\) 3.79638e16 0.221851
\(449\) 3.03944e14 0.00175062 0.000875310 1.00000i \(-0.499721\pi\)
0.000875310 1.00000i \(0.499721\pi\)
\(450\) −9.40761e14 −0.00534070
\(451\) −1.10249e17 −0.616919
\(452\) 7.62865e16 0.420773
\(453\) 1.14959e17 0.625034
\(454\) 6.51677e16 0.349276
\(455\) −1.03481e17 −0.546749
\(456\) −2.10931e17 −1.09867
\(457\) −6.41357e16 −0.329340 −0.164670 0.986349i \(-0.552656\pi\)
−0.164670 + 0.986349i \(0.552656\pi\)
\(458\) 7.64162e16 0.386865
\(459\) −5.03258e16 −0.251194
\(460\) 1.26376e17 0.621927
\(461\) −2.60089e17 −1.26202 −0.631011 0.775774i \(-0.717360\pi\)
−0.631011 + 0.775774i \(0.717360\pi\)
\(462\) 3.55212e16 0.169948
\(463\) 1.55350e17 0.732884 0.366442 0.930441i \(-0.380576\pi\)
0.366442 + 0.930441i \(0.380576\pi\)
\(464\) 1.63586e15 0.00760992
\(465\) −1.86154e16 −0.0853942
\(466\) 3.93151e16 0.177849
\(467\) 3.24764e17 1.44880 0.724401 0.689379i \(-0.242117\pi\)
0.724401 + 0.689379i \(0.242117\pi\)
\(468\) 6.99667e16 0.307818
\(469\) −1.06062e17 −0.460189
\(470\) −1.26573e17 −0.541631
\(471\) −2.06867e17 −0.873084
\(472\) −3.12230e16 −0.129973
\(473\) −6.74245e16 −0.276835
\(474\) −1.09990e17 −0.445443
\(475\) −1.24088e16 −0.0495703
\(476\) 7.45269e16 0.293676
\(477\) −1.10174e17 −0.428264
\(478\) 2.69178e17 1.03219
\(479\) 1.41061e17 0.533611 0.266806 0.963750i \(-0.414032\pi\)
0.266806 + 0.963750i \(0.414032\pi\)
\(480\) −1.56961e17 −0.585766
\(481\) −4.40816e17 −1.62298
\(482\) −2.36285e17 −0.858283
\(483\) −5.78173e16 −0.207206
\(484\) −1.29091e17 −0.456457
\(485\) 1.88872e17 0.658941
\(486\) −1.14810e16 −0.0395226
\(487\) 2.40411e17 0.816612 0.408306 0.912845i \(-0.366120\pi\)
0.408306 + 0.912845i \(0.366120\pi\)
\(488\) 5.46015e17 1.83010
\(489\) 3.13528e17 1.03698
\(490\) 1.66058e17 0.541983
\(491\) −1.88402e17 −0.606815 −0.303407 0.952861i \(-0.598124\pi\)
−0.303407 + 0.952861i \(0.598124\pi\)
\(492\) −5.27705e16 −0.167733
\(493\) −5.91499e17 −1.85545
\(494\) −5.64612e17 −1.74793
\(495\) −1.45588e17 −0.444829
\(496\) −2.59218e14 −0.000781691 0
\(497\) 8.44261e16 0.251281
\(498\) −3.24738e16 −0.0953986
\(499\) 3.96915e17 1.15092 0.575458 0.817831i \(-0.304824\pi\)
0.575458 + 0.817831i \(0.304824\pi\)
\(500\) 2.13858e17 0.612098
\(501\) −1.99003e17 −0.562230
\(502\) −1.93900e17 −0.540759
\(503\) 1.41417e17 0.389322 0.194661 0.980871i \(-0.437639\pi\)
0.194661 + 0.980871i \(0.437639\pi\)
\(504\) 4.44061e16 0.120682
\(505\) 6.82133e16 0.183010
\(506\) −3.03278e17 −0.803272
\(507\) 2.68353e17 0.701705
\(508\) −4.13518e17 −1.06753
\(509\) −4.87285e17 −1.24199 −0.620994 0.783815i \(-0.713271\pi\)
−0.620994 + 0.783815i \(0.713271\pi\)
\(510\) 1.86878e17 0.470276
\(511\) 2.43121e17 0.604068
\(512\) −4.36415e15 −0.0107064
\(513\) −1.51437e17 −0.366834
\(514\) −3.68692e17 −0.881867
\(515\) 7.66880e17 1.81126
\(516\) −3.22725e16 −0.0752679
\(517\) −4.96487e17 −1.14346
\(518\) −1.07120e17 −0.243627
\(519\) −4.45645e17 −1.00092
\(520\) −6.78577e17 −1.50514
\(521\) 8.76008e16 0.191895 0.0959473 0.995386i \(-0.469412\pi\)
0.0959473 + 0.995386i \(0.469412\pi\)
\(522\) −1.34941e17 −0.291935
\(523\) −6.91313e17 −1.47711 −0.738557 0.674191i \(-0.764492\pi\)
−0.738557 + 0.674191i \(0.764492\pi\)
\(524\) 1.90591e17 0.402207
\(525\) 2.61236e15 0.00544500
\(526\) −3.65527e17 −0.752510
\(527\) 9.37289e16 0.190592
\(528\) −2.02731e15 −0.00407192
\(529\) −1.03957e16 −0.0206249
\(530\) 4.09119e17 0.801781
\(531\) −2.24165e16 −0.0433963
\(532\) 2.24261e17 0.428873
\(533\) −3.68927e17 −0.696969
\(534\) −5.78501e16 −0.107966
\(535\) 2.87499e17 0.530074
\(536\) −6.95500e17 −1.26685
\(537\) 7.41298e16 0.133401
\(538\) −8.82592e16 −0.156919
\(539\) 6.51371e17 1.14420
\(540\) −6.96854e16 −0.120944
\(541\) 4.44253e17 0.761813 0.380906 0.924614i \(-0.375612\pi\)
0.380906 + 0.924614i \(0.375612\pi\)
\(542\) 6.67679e17 1.13129
\(543\) −2.38296e17 −0.398949
\(544\) 7.90302e17 1.30738
\(545\) −8.63354e17 −1.41128
\(546\) 1.18865e17 0.192000
\(547\) −5.72288e17 −0.913476 −0.456738 0.889601i \(-0.650982\pi\)
−0.456738 + 0.889601i \(0.650982\pi\)
\(548\) 4.46037e16 0.0703553
\(549\) 3.92010e17 0.611050
\(550\) 1.37030e16 0.0211086
\(551\) −1.77990e18 −2.70963
\(552\) −3.79136e17 −0.570416
\(553\) 3.05426e17 0.454142
\(554\) 6.48420e17 0.952890
\(555\) 4.39044e17 0.637681
\(556\) 3.39514e17 0.487384
\(557\) 1.09323e18 1.55115 0.775575 0.631255i \(-0.217460\pi\)
0.775575 + 0.631255i \(0.217460\pi\)
\(558\) 2.13828e16 0.0299876
\(559\) −2.25623e17 −0.312756
\(560\) 1.43518e15 0.00196645
\(561\) 7.33040e17 0.992817
\(562\) 1.82656e17 0.244540
\(563\) −3.86699e17 −0.511763 −0.255882 0.966708i \(-0.582366\pi\)
−0.255882 + 0.966708i \(0.582366\pi\)
\(564\) −2.37642e17 −0.310892
\(565\) −5.31188e17 −0.686963
\(566\) −1.90512e15 −0.00243565
\(567\) 3.18812e16 0.0402944
\(568\) 5.53623e17 0.691752
\(569\) 1.07796e18 1.33160 0.665799 0.746131i \(-0.268091\pi\)
0.665799 + 0.746131i \(0.268091\pi\)
\(570\) 5.62342e17 0.686774
\(571\) −3.64277e17 −0.439843 −0.219921 0.975518i \(-0.570580\pi\)
−0.219921 + 0.975518i \(0.570580\pi\)
\(572\) −1.01913e18 −1.21662
\(573\) −1.15454e17 −0.136271
\(574\) −8.96504e16 −0.104622
\(575\) −2.23042e16 −0.0257362
\(576\) 1.78731e17 0.203917
\(577\) 8.86790e16 0.100041 0.0500205 0.998748i \(-0.484071\pi\)
0.0500205 + 0.998748i \(0.484071\pi\)
\(578\) −3.88631e17 −0.433517
\(579\) −3.00446e17 −0.331402
\(580\) −8.19041e17 −0.893354
\(581\) 9.01751e16 0.0972617
\(582\) −2.16950e17 −0.231398
\(583\) 1.60479e18 1.69267
\(584\) 1.59426e18 1.66294
\(585\) −4.87183e17 −0.502549
\(586\) −7.19597e17 −0.734099
\(587\) 1.16655e18 1.17694 0.588471 0.808519i \(-0.299730\pi\)
0.588471 + 0.808519i \(0.299730\pi\)
\(588\) 3.11777e17 0.311094
\(589\) 2.82043e17 0.278333
\(590\) 8.32407e16 0.0812451
\(591\) 1.09004e18 1.05226
\(592\) 6.11366e15 0.00583728
\(593\) −1.23991e18 −1.17094 −0.585470 0.810694i \(-0.699090\pi\)
−0.585470 + 0.810694i \(0.699090\pi\)
\(594\) 1.67231e17 0.156209
\(595\) −5.18935e17 −0.479461
\(596\) −7.03660e17 −0.643076
\(597\) 1.16756e18 1.05547
\(598\) −1.01486e18 −0.907503
\(599\) 2.98890e17 0.264385 0.132193 0.991224i \(-0.457798\pi\)
0.132193 + 0.991224i \(0.457798\pi\)
\(600\) 1.71305e16 0.0149895
\(601\) 1.47417e18 1.27604 0.638020 0.770020i \(-0.279754\pi\)
0.638020 + 0.770020i \(0.279754\pi\)
\(602\) −5.48270e16 −0.0469480
\(603\) −4.99332e17 −0.422987
\(604\) −8.01482e17 −0.671667
\(605\) 8.98867e17 0.745222
\(606\) −7.83538e16 −0.0642670
\(607\) 2.55738e17 0.207524 0.103762 0.994602i \(-0.466912\pi\)
0.103762 + 0.994602i \(0.466912\pi\)
\(608\) 2.37812e18 1.90924
\(609\) 3.74713e17 0.297636
\(610\) −1.45568e18 −1.14399
\(611\) −1.66140e18 −1.29183
\(612\) 3.50867e17 0.269935
\(613\) −1.27632e18 −0.971556 −0.485778 0.874082i \(-0.661464\pi\)
−0.485778 + 0.874082i \(0.661464\pi\)
\(614\) 4.80913e17 0.362220
\(615\) 3.67444e17 0.273844
\(616\) −6.46814e17 −0.476985
\(617\) −1.98750e18 −1.45029 −0.725143 0.688599i \(-0.758226\pi\)
−0.725143 + 0.688599i \(0.758226\pi\)
\(618\) −8.80884e17 −0.636053
\(619\) 1.46096e18 1.04388 0.521939 0.852983i \(-0.325209\pi\)
0.521939 + 0.852983i \(0.325209\pi\)
\(620\) 1.29785e17 0.0917654
\(621\) −2.72200e17 −0.190455
\(622\) −3.68217e17 −0.254956
\(623\) 1.60642e17 0.110074
\(624\) −6.78399e15 −0.00460029
\(625\) −1.52786e18 −1.02533
\(626\) −1.61090e18 −1.06988
\(627\) 2.20581e18 1.44987
\(628\) 1.44226e18 0.938224
\(629\) −2.21059e18 −1.42325
\(630\) −1.18387e17 −0.0754380
\(631\) −5.87590e17 −0.370582 −0.185291 0.982684i \(-0.559323\pi\)
−0.185291 + 0.982684i \(0.559323\pi\)
\(632\) 2.00282e18 1.25021
\(633\) −3.03781e17 −0.187688
\(634\) −6.85844e17 −0.419416
\(635\) 2.87935e18 1.74287
\(636\) 7.68127e17 0.460216
\(637\) 2.17968e18 1.29267
\(638\) 1.96554e18 1.15384
\(639\) 3.97472e17 0.230968
\(640\) 1.10013e18 0.632810
\(641\) 2.74499e18 1.56301 0.781507 0.623897i \(-0.214451\pi\)
0.781507 + 0.623897i \(0.214451\pi\)
\(642\) −3.30238e17 −0.186144
\(643\) 3.08333e18 1.72048 0.860238 0.509892i \(-0.170315\pi\)
0.860238 + 0.509892i \(0.170315\pi\)
\(644\) 4.03097e17 0.222665
\(645\) 2.24716e17 0.122884
\(646\) −2.83140e18 −1.53282
\(647\) −3.89479e17 −0.208740 −0.104370 0.994539i \(-0.533283\pi\)
−0.104370 + 0.994539i \(0.533283\pi\)
\(648\) 2.09061e17 0.110926
\(649\) 3.26516e17 0.171519
\(650\) 4.58544e16 0.0238476
\(651\) −5.93769e16 −0.0305732
\(652\) −2.18589e18 −1.11434
\(653\) −3.66726e18 −1.85100 −0.925500 0.378749i \(-0.876354\pi\)
−0.925500 + 0.378749i \(0.876354\pi\)
\(654\) 9.91700e17 0.495593
\(655\) −1.32710e18 −0.656651
\(656\) 5.11664e15 0.00250674
\(657\) 1.14459e18 0.555235
\(658\) −4.03724e17 −0.193917
\(659\) 1.66169e18 0.790303 0.395152 0.918616i \(-0.370692\pi\)
0.395152 + 0.918616i \(0.370692\pi\)
\(660\) 1.01503e18 0.478017
\(661\) 3.38080e18 1.57656 0.788279 0.615318i \(-0.210972\pi\)
0.788279 + 0.615318i \(0.210972\pi\)
\(662\) 1.42471e18 0.657885
\(663\) 2.45297e18 1.12164
\(664\) 5.91322e17 0.267751
\(665\) −1.56154e18 −0.700187
\(666\) −5.04312e17 −0.223932
\(667\) −3.19927e18 −1.40680
\(668\) 1.38743e18 0.604178
\(669\) 9.23275e17 0.398163
\(670\) 1.85421e18 0.791902
\(671\) −5.70997e18 −2.41511
\(672\) −5.00654e17 −0.209719
\(673\) 1.31123e18 0.543979 0.271990 0.962300i \(-0.412318\pi\)
0.271990 + 0.962300i \(0.412318\pi\)
\(674\) 3.43314e17 0.141059
\(675\) 1.22988e16 0.00500482
\(676\) −1.87093e18 −0.754058
\(677\) 4.09276e18 1.63377 0.816883 0.576804i \(-0.195700\pi\)
0.816883 + 0.576804i \(0.195700\pi\)
\(678\) 6.10154e17 0.241238
\(679\) 6.02438e17 0.235917
\(680\) −3.40291e18 −1.31991
\(681\) −8.51954e17 −0.327311
\(682\) −3.11459e17 −0.118523
\(683\) −1.85693e18 −0.699939 −0.349970 0.936761i \(-0.613808\pi\)
−0.349970 + 0.936761i \(0.613808\pi\)
\(684\) 1.05581e18 0.394203
\(685\) −3.10578e17 −0.114864
\(686\) 1.13955e18 0.417471
\(687\) −9.99009e17 −0.362535
\(688\) 3.12915e15 0.00112487
\(689\) 5.37010e18 1.91231
\(690\) 1.01078e18 0.356564
\(691\) 2.65304e18 0.927120 0.463560 0.886066i \(-0.346572\pi\)
0.463560 + 0.886066i \(0.346572\pi\)
\(692\) 3.10700e18 1.07560
\(693\) −4.64378e17 −0.159260
\(694\) −1.03151e18 −0.350457
\(695\) −2.36406e18 −0.795713
\(696\) 2.45717e18 0.819362
\(697\) −1.85009e18 −0.611194
\(698\) 1.84700e18 0.604514
\(699\) −5.13977e17 −0.166664
\(700\) −1.82132e16 −0.00585124
\(701\) 2.05507e18 0.654123 0.327062 0.945003i \(-0.393942\pi\)
0.327062 + 0.945003i \(0.393942\pi\)
\(702\) 5.59607e17 0.176478
\(703\) −6.65197e18 −2.07845
\(704\) −2.60337e18 −0.805961
\(705\) 1.65472e18 0.507568
\(706\) 2.89326e18 0.879339
\(707\) 2.17577e17 0.0655221
\(708\) 1.56286e17 0.0466340
\(709\) 5.06643e18 1.49796 0.748982 0.662591i \(-0.230543\pi\)
0.748982 + 0.662591i \(0.230543\pi\)
\(710\) −1.47596e18 −0.432410
\(711\) 1.43792e18 0.417429
\(712\) 1.05341e18 0.303023
\(713\) 5.06956e17 0.144507
\(714\) 5.96080e17 0.168370
\(715\) 7.09625e18 1.98627
\(716\) −5.16827e17 −0.143354
\(717\) −3.51903e18 −0.967272
\(718\) 5.24625e17 0.142903
\(719\) −2.40099e18 −0.648116 −0.324058 0.946037i \(-0.605047\pi\)
−0.324058 + 0.946037i \(0.605047\pi\)
\(720\) 6.75672e15 0.00180748
\(721\) 2.44609e18 0.648475
\(722\) −6.17507e18 −1.62237
\(723\) 3.08902e18 0.804306
\(724\) 1.66138e18 0.428714
\(725\) 1.44553e17 0.0369683
\(726\) −1.03249e18 −0.261697
\(727\) −3.72909e18 −0.936762 −0.468381 0.883526i \(-0.655163\pi\)
−0.468381 + 0.883526i \(0.655163\pi\)
\(728\) −2.16443e18 −0.538878
\(729\) 1.50095e17 0.0370370
\(730\) −4.25031e18 −1.03949
\(731\) −1.13145e18 −0.274266
\(732\) −2.73306e18 −0.656640
\(733\) −5.51789e18 −1.31401 −0.657003 0.753888i \(-0.728176\pi\)
−0.657003 + 0.753888i \(0.728176\pi\)
\(734\) 2.57638e18 0.608114
\(735\) −2.17092e18 −0.507898
\(736\) 4.27455e18 0.991253
\(737\) 7.27321e18 1.67181
\(738\) −4.22068e17 −0.0961648
\(739\) −2.12651e18 −0.480262 −0.240131 0.970741i \(-0.577190\pi\)
−0.240131 + 0.970741i \(0.577190\pi\)
\(740\) −3.06098e18 −0.685258
\(741\) 7.38132e18 1.63801
\(742\) 1.30495e18 0.287057
\(743\) 7.02153e18 1.53110 0.765551 0.643375i \(-0.222466\pi\)
0.765551 + 0.643375i \(0.222466\pi\)
\(744\) −3.89364e17 −0.0841649
\(745\) 4.89963e18 1.04990
\(746\) 2.92950e18 0.622288
\(747\) 4.24538e17 0.0893990
\(748\) −5.11069e18 −1.06689
\(749\) 9.17024e17 0.189779
\(750\) 1.71048e18 0.350929
\(751\) −4.88108e18 −0.992788 −0.496394 0.868097i \(-0.665343\pi\)
−0.496394 + 0.868097i \(0.665343\pi\)
\(752\) 2.30418e16 0.00464623
\(753\) 2.53491e18 0.506751
\(754\) 6.57728e18 1.30356
\(755\) 5.58077e18 1.09658
\(756\) −2.22273e17 −0.0433008
\(757\) −3.89271e18 −0.751845 −0.375923 0.926651i \(-0.622674\pi\)
−0.375923 + 0.926651i \(0.622674\pi\)
\(758\) 4.36957e18 0.836737
\(759\) 3.96483e18 0.752754
\(760\) −1.02398e19 −1.92754
\(761\) 7.13340e18 1.33136 0.665681 0.746237i \(-0.268141\pi\)
0.665681 + 0.746237i \(0.268141\pi\)
\(762\) −3.30740e18 −0.612039
\(763\) −2.75381e18 −0.505271
\(764\) 8.04932e17 0.146438
\(765\) −2.44311e18 −0.440701
\(766\) −3.94628e18 −0.705832
\(767\) 1.09262e18 0.193776
\(768\) −3.27213e18 −0.575416
\(769\) −1.33412e18 −0.232635 −0.116317 0.993212i \(-0.537109\pi\)
−0.116317 + 0.993212i \(0.537109\pi\)
\(770\) 1.72441e18 0.298161
\(771\) 4.82001e18 0.826407
\(772\) 2.09468e18 0.356128
\(773\) 2.34497e18 0.395339 0.197670 0.980269i \(-0.436663\pi\)
0.197670 + 0.980269i \(0.436663\pi\)
\(774\) −2.58122e17 −0.0431527
\(775\) −2.29058e16 −0.00379739
\(776\) 3.95048e18 0.649455
\(777\) 1.40040e18 0.228306
\(778\) 2.25253e18 0.364169
\(779\) −5.56715e18 −0.892565
\(780\) 3.39660e18 0.540044
\(781\) −5.78954e18 −0.912876
\(782\) −5.08929e18 −0.795817
\(783\) 1.76412e18 0.273575
\(784\) −3.02300e16 −0.00464925
\(785\) −1.00426e19 −1.53176
\(786\) 1.52438e18 0.230594
\(787\) −1.04240e18 −0.156387 −0.0781935 0.996938i \(-0.524915\pi\)
−0.0781935 + 0.996938i \(0.524915\pi\)
\(788\) −7.59967e18 −1.13077
\(789\) 4.77863e18 0.705185
\(790\) −5.33954e18 −0.781498
\(791\) −1.69431e18 −0.245950
\(792\) −3.04516e18 −0.438425
\(793\) −1.91073e19 −2.72849
\(794\) 9.52168e17 0.134859
\(795\) −5.34851e18 −0.751358
\(796\) −8.14012e18 −1.13422
\(797\) −8.26338e18 −1.14203 −0.571017 0.820938i \(-0.693451\pi\)
−0.571017 + 0.820938i \(0.693451\pi\)
\(798\) 1.79368e18 0.245882
\(799\) −8.33153e18 −1.13284
\(800\) −1.93137e17 −0.0260484
\(801\) 7.56290e17 0.101176
\(802\) 2.87725e18 0.381808
\(803\) −1.66720e19 −2.19451
\(804\) 3.48130e18 0.454545
\(805\) −2.80679e18 −0.363527
\(806\) −1.04223e18 −0.133902
\(807\) 1.15384e18 0.147050
\(808\) 1.42676e18 0.180375
\(809\) 9.98180e18 1.25182 0.625912 0.779894i \(-0.284727\pi\)
0.625912 + 0.779894i \(0.284727\pi\)
\(810\) −5.57357e17 −0.0693395
\(811\) 6.13636e18 0.757312 0.378656 0.925537i \(-0.376386\pi\)
0.378656 + 0.925537i \(0.376386\pi\)
\(812\) −2.61247e18 −0.319843
\(813\) −8.72874e18 −1.06014
\(814\) 7.34575e18 0.885069
\(815\) 1.52205e19 1.81930
\(816\) −3.40202e16 −0.00403414
\(817\) −3.40467e18 −0.400527
\(818\) −2.12318e18 −0.247794
\(819\) −1.55395e18 −0.179925
\(820\) −2.56179e18 −0.294275
\(821\) 9.34465e18 1.06496 0.532479 0.846443i \(-0.321261\pi\)
0.532479 + 0.846443i \(0.321261\pi\)
\(822\) 3.56748e17 0.0403362
\(823\) 2.28720e18 0.256570 0.128285 0.991737i \(-0.459053\pi\)
0.128285 + 0.991737i \(0.459053\pi\)
\(824\) 1.60402e19 1.78518
\(825\) −1.79143e17 −0.0197811
\(826\) 2.65510e17 0.0290878
\(827\) 7.13544e18 0.775595 0.387798 0.921745i \(-0.373236\pi\)
0.387798 + 0.921745i \(0.373236\pi\)
\(828\) 1.89775e18 0.204665
\(829\) −6.78150e18 −0.725640 −0.362820 0.931859i \(-0.618186\pi\)
−0.362820 + 0.931859i \(0.618186\pi\)
\(830\) −1.57647e18 −0.167370
\(831\) −8.47696e18 −0.892964
\(832\) −8.71167e18 −0.910541
\(833\) 1.09306e19 1.13358
\(834\) 2.71549e18 0.279428
\(835\) −9.66078e18 −0.986393
\(836\) −1.53787e19 −1.55805
\(837\) −2.79542e17 −0.0281017
\(838\) −2.39889e18 −0.239289
\(839\) −1.39131e18 −0.137711 −0.0688557 0.997627i \(-0.521935\pi\)
−0.0688557 + 0.997627i \(0.521935\pi\)
\(840\) 2.15573e18 0.211729
\(841\) 1.04738e19 1.02077
\(842\) 1.14249e18 0.110490
\(843\) −2.38792e18 −0.229161
\(844\) 2.11794e18 0.201691
\(845\) 1.30274e19 1.23109
\(846\) −1.90071e18 −0.178241
\(847\) 2.86708e18 0.266808
\(848\) −7.44777e16 −0.00687786
\(849\) 2.49061e16 0.00228248
\(850\) 2.29950e17 0.0209127
\(851\) −1.19566e19 −1.07911
\(852\) −2.77114e18 −0.248200
\(853\) −1.30566e19 −1.16055 −0.580273 0.814422i \(-0.697054\pi\)
−0.580273 + 0.814422i \(0.697054\pi\)
\(854\) −4.64313e18 −0.409576
\(855\) −7.35164e18 −0.643583
\(856\) 6.01338e18 0.522443
\(857\) −8.27918e18 −0.713859 −0.356929 0.934131i \(-0.616176\pi\)
−0.356929 + 0.934131i \(0.616176\pi\)
\(858\) −8.15117e18 −0.697513
\(859\) 7.43253e18 0.631220 0.315610 0.948889i \(-0.397791\pi\)
0.315610 + 0.948889i \(0.397791\pi\)
\(860\) −1.56670e18 −0.132052
\(861\) 1.17202e18 0.0980428
\(862\) −3.01982e18 −0.250717
\(863\) 1.64542e19 1.35583 0.677917 0.735138i \(-0.262883\pi\)
0.677917 + 0.735138i \(0.262883\pi\)
\(864\) −2.35704e18 −0.192765
\(865\) −2.16342e19 −1.75605
\(866\) 1.36948e19 1.10329
\(867\) 5.08067e18 0.406253
\(868\) 4.13971e17 0.0328543
\(869\) −2.09446e19 −1.64985
\(870\) −6.55084e18 −0.512179
\(871\) 2.43383e19 1.88874
\(872\) −1.80581e19 −1.39096
\(873\) 2.83624e18 0.216845
\(874\) −1.53143e19 −1.16218
\(875\) −4.74976e18 −0.357782
\(876\) −7.98002e18 −0.596660
\(877\) −6.72310e18 −0.498968 −0.249484 0.968379i \(-0.580261\pi\)
−0.249484 + 0.968379i \(0.580261\pi\)
\(878\) −6.29012e18 −0.463388
\(879\) 9.40748e18 0.687932
\(880\) −9.84176e16 −0.00714390
\(881\) −1.22874e19 −0.885355 −0.442677 0.896681i \(-0.645971\pi\)
−0.442677 + 0.896681i \(0.645971\pi\)
\(882\) 2.49365e18 0.178357
\(883\) −1.76396e19 −1.25241 −0.626203 0.779660i \(-0.715392\pi\)
−0.626203 + 0.779660i \(0.715392\pi\)
\(884\) −1.71019e19 −1.20533
\(885\) −1.08823e18 −0.0761357
\(886\) −4.24211e18 −0.294621
\(887\) 2.09206e19 1.44235 0.721174 0.692754i \(-0.243603\pi\)
0.721174 + 0.692754i \(0.243603\pi\)
\(888\) 9.18313e18 0.628502
\(889\) 9.18418e18 0.623992
\(890\) −2.80839e18 −0.189418
\(891\) −2.18626e18 −0.146385
\(892\) −6.43699e18 −0.427870
\(893\) −2.50707e19 −1.65436
\(894\) −5.62800e18 −0.368689
\(895\) 3.59870e18 0.234043
\(896\) 3.50904e18 0.226562
\(897\) 1.32675e19 0.850431
\(898\) −1.69487e16 −0.00107855
\(899\) −3.28557e18 −0.207574
\(900\) −8.57463e16 −0.00537823
\(901\) 2.69299e19 1.67696
\(902\) 6.14779e18 0.380081
\(903\) 7.16768e17 0.0439955
\(904\) −1.11104e19 −0.677074
\(905\) −1.15683e19 −0.699927
\(906\) −6.41040e18 −0.385081
\(907\) 4.88579e17 0.0291399 0.0145699 0.999894i \(-0.495362\pi\)
0.0145699 + 0.999894i \(0.495362\pi\)
\(908\) 5.93975e18 0.351731
\(909\) 1.02434e18 0.0602253
\(910\) 5.77039e18 0.336850
\(911\) 2.29445e18 0.132987 0.0664934 0.997787i \(-0.478819\pi\)
0.0664934 + 0.997787i \(0.478819\pi\)
\(912\) −1.02371e17 −0.00589130
\(913\) −6.18377e18 −0.353341
\(914\) 3.57638e18 0.202905
\(915\) 1.90305e19 1.07204
\(916\) 6.96500e18 0.389584
\(917\) −4.23300e18 −0.235097
\(918\) 2.80630e18 0.154759
\(919\) −1.90274e19 −1.04191 −0.520954 0.853585i \(-0.674424\pi\)
−0.520954 + 0.853585i \(0.674424\pi\)
\(920\) −1.84055e19 −1.00075
\(921\) −6.28711e18 −0.339440
\(922\) 1.45033e19 0.777527
\(923\) −1.93735e19 −1.03133
\(924\) 3.23761e18 0.171142
\(925\) 5.40233e17 0.0283570
\(926\) −8.66274e18 −0.451527
\(927\) 1.15160e19 0.596052
\(928\) −2.77033e19 −1.42387
\(929\) −2.53179e18 −0.129219 −0.0646094 0.997911i \(-0.520580\pi\)
−0.0646094 + 0.997911i \(0.520580\pi\)
\(930\) 1.03804e18 0.0526111
\(931\) 3.28917e19 1.65544
\(932\) 3.58341e18 0.179099
\(933\) 4.81380e18 0.238922
\(934\) −1.81097e19 −0.892601
\(935\) 3.55861e19 1.74183
\(936\) −1.01900e19 −0.495315
\(937\) 1.08706e19 0.524744 0.262372 0.964967i \(-0.415495\pi\)
0.262372 + 0.964967i \(0.415495\pi\)
\(938\) 5.91429e18 0.283520
\(939\) 2.10597e19 1.00260
\(940\) −1.15365e19 −0.545437
\(941\) −3.07512e19 −1.44388 −0.721938 0.691958i \(-0.756748\pi\)
−0.721938 + 0.691958i \(0.756748\pi\)
\(942\) 1.15355e19 0.537904
\(943\) −1.00067e19 −0.463408
\(944\) −1.51535e16 −0.000696939 0
\(945\) 1.54770e18 0.0706937
\(946\) 3.75977e18 0.170557
\(947\) 2.33777e19 1.05324 0.526620 0.850101i \(-0.323459\pi\)
0.526620 + 0.850101i \(0.323459\pi\)
\(948\) −1.00251e19 −0.448573
\(949\) −5.57896e19 −2.47927
\(950\) 6.91948e17 0.0305401
\(951\) 8.96622e18 0.393039
\(952\) −1.08542e19 −0.472559
\(953\) 3.92221e19 1.69600 0.848002 0.529992i \(-0.177805\pi\)
0.848002 + 0.529992i \(0.177805\pi\)
\(954\) 6.14362e18 0.263852
\(955\) −5.60480e18 −0.239077
\(956\) 2.45344e19 1.03944
\(957\) −2.56960e19 −1.08128
\(958\) −7.86591e18 −0.328756
\(959\) −9.90640e17 −0.0411240
\(960\) 8.67665e18 0.357758
\(961\) −2.38969e19 −0.978678
\(962\) 2.45811e19 0.999915
\(963\) 4.31729e18 0.174438
\(964\) −2.15364e19 −0.864315
\(965\) −1.45854e19 −0.581422
\(966\) 3.22405e18 0.127659
\(967\) −5.29017e18 −0.208064 −0.104032 0.994574i \(-0.533174\pi\)
−0.104032 + 0.994574i \(0.533174\pi\)
\(968\) 1.88009e19 0.734494
\(969\) 3.70156e19 1.43642
\(970\) −1.05320e19 −0.405971
\(971\) 4.26955e18 0.163477 0.0817387 0.996654i \(-0.473953\pi\)
0.0817387 + 0.996654i \(0.473953\pi\)
\(972\) −1.04645e18 −0.0398003
\(973\) −7.54055e18 −0.284885
\(974\) −1.34059e19 −0.503111
\(975\) −5.99467e17 −0.0223478
\(976\) 2.64998e17 0.00981339
\(977\) 4.80164e19 1.76634 0.883172 0.469049i \(-0.155403\pi\)
0.883172 + 0.469049i \(0.155403\pi\)
\(978\) −1.74832e19 −0.638878
\(979\) −1.10160e19 −0.399887
\(980\) 1.51355e19 0.545792
\(981\) −1.29648e19 −0.464425
\(982\) 1.05058e19 0.373856
\(983\) 1.28512e19 0.454302 0.227151 0.973859i \(-0.427059\pi\)
0.227151 + 0.973859i \(0.427059\pi\)
\(984\) 7.68553e18 0.269902
\(985\) 5.29170e19 1.84612
\(986\) 3.29836e19 1.14314
\(987\) 5.27799e18 0.181722
\(988\) −5.14619e19 −1.76022
\(989\) −6.11972e18 −0.207948
\(990\) 8.11840e18 0.274057
\(991\) 3.43466e19 1.15187 0.575937 0.817494i \(-0.304637\pi\)
0.575937 + 0.817494i \(0.304637\pi\)
\(992\) 4.38985e18 0.146260
\(993\) −1.86256e19 −0.616511
\(994\) −4.70782e18 −0.154813
\(995\) 5.66802e19 1.85174
\(996\) −2.95984e18 −0.0960690
\(997\) 2.00453e19 0.646389 0.323195 0.946333i \(-0.395243\pi\)
0.323195 + 0.946333i \(0.395243\pi\)
\(998\) −2.21330e19 −0.709075
\(999\) 6.59300e18 0.209849
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.1.12 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.12 31 1.1 even 1 trivial