Properties

Label 177.14.a.c.1.18
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 1.18
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+28.6646 q^{2} +729.000 q^{3} -7370.34 q^{4} -9309.96 q^{5} +20896.5 q^{6} +216532. q^{7} -446089. q^{8} +531441. q^{9} +O(q^{10})\) \(q+28.6646 q^{2} +729.000 q^{3} -7370.34 q^{4} -9309.96 q^{5} +20896.5 q^{6} +216532. q^{7} -446089. q^{8} +531441. q^{9} -266867. q^{10} +5.39906e6 q^{11} -5.37298e6 q^{12} +2.36936e7 q^{13} +6.20682e6 q^{14} -6.78696e6 q^{15} +4.75908e7 q^{16} +9.98122e7 q^{17} +1.52336e7 q^{18} +2.92098e8 q^{19} +6.86175e7 q^{20} +1.57852e8 q^{21} +1.54762e8 q^{22} -6.28110e8 q^{23} -3.25199e8 q^{24} -1.13403e9 q^{25} +6.79169e8 q^{26} +3.87420e8 q^{27} -1.59592e9 q^{28} -1.36461e9 q^{29} -1.94546e8 q^{30} +3.47253e8 q^{31} +5.01853e9 q^{32} +3.93592e9 q^{33} +2.86108e9 q^{34} -2.01591e9 q^{35} -3.91690e9 q^{36} -2.74111e9 q^{37} +8.37289e9 q^{38} +1.72726e10 q^{39} +4.15307e9 q^{40} -3.57931e10 q^{41} +4.52477e9 q^{42} -4.48542e10 q^{43} -3.97929e10 q^{44} -4.94769e9 q^{45} -1.80045e10 q^{46} +1.39902e11 q^{47} +3.46937e10 q^{48} -5.00028e10 q^{49} -3.25065e10 q^{50} +7.27631e10 q^{51} -1.74630e11 q^{52} -5.29436e9 q^{53} +1.11053e10 q^{54} -5.02650e10 q^{55} -9.65926e10 q^{56} +2.12940e11 q^{57} -3.91161e10 q^{58} -4.21805e10 q^{59} +5.00222e10 q^{60} +3.45027e11 q^{61} +9.95389e9 q^{62} +1.15074e11 q^{63} -2.46010e11 q^{64} -2.20587e11 q^{65} +1.12822e11 q^{66} -5.99003e11 q^{67} -7.35649e11 q^{68} -4.57892e11 q^{69} -5.77852e10 q^{70} -6.16912e11 q^{71} -2.37070e11 q^{72} +1.52900e12 q^{73} -7.85728e10 q^{74} -8.26706e11 q^{75} -2.15286e12 q^{76} +1.16907e12 q^{77} +4.95114e11 q^{78} +2.64250e12 q^{79} -4.43069e11 q^{80} +2.82430e11 q^{81} -1.02600e12 q^{82} +3.15524e12 q^{83} -1.16342e12 q^{84} -9.29247e11 q^{85} -1.28573e12 q^{86} -9.94803e11 q^{87} -2.40846e12 q^{88} +5.43970e12 q^{89} -1.41824e11 q^{90} +5.13043e12 q^{91} +4.62938e12 q^{92} +2.53147e11 q^{93} +4.01023e12 q^{94} -2.71942e12 q^{95} +3.65851e12 q^{96} -2.80648e12 q^{97} -1.43331e12 q^{98} +2.86928e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 28.6646 0.316703 0.158351 0.987383i \(-0.449382\pi\)
0.158351 + 0.987383i \(0.449382\pi\)
\(3\) 729.000 0.577350
\(4\) −7370.34 −0.899700
\(5\) −9309.96 −0.266467 −0.133233 0.991085i \(-0.542536\pi\)
−0.133233 + 0.991085i \(0.542536\pi\)
\(6\) 20896.5 0.182848
\(7\) 216532. 0.695641 0.347821 0.937561i \(-0.386922\pi\)
0.347821 + 0.937561i \(0.386922\pi\)
\(8\) −446089. −0.601640
\(9\) 531441. 0.333333
\(10\) −266867. −0.0843906
\(11\) 5.39906e6 0.918895 0.459448 0.888205i \(-0.348047\pi\)
0.459448 + 0.888205i \(0.348047\pi\)
\(12\) −5.37298e6 −0.519442
\(13\) 2.36936e7 1.36144 0.680722 0.732542i \(-0.261666\pi\)
0.680722 + 0.732542i \(0.261666\pi\)
\(14\) 6.20682e6 0.220311
\(15\) −6.78696e6 −0.153845
\(16\) 4.75908e7 0.709159
\(17\) 9.98122e7 1.00292 0.501459 0.865181i \(-0.332797\pi\)
0.501459 + 0.865181i \(0.332797\pi\)
\(18\) 1.52336e7 0.105568
\(19\) 2.92098e8 1.42440 0.712198 0.701979i \(-0.247700\pi\)
0.712198 + 0.701979i \(0.247700\pi\)
\(20\) 6.86175e7 0.239740
\(21\) 1.57852e8 0.401629
\(22\) 1.54762e8 0.291016
\(23\) −6.28110e8 −0.884717 −0.442359 0.896838i \(-0.645858\pi\)
−0.442359 + 0.896838i \(0.645858\pi\)
\(24\) −3.25199e8 −0.347357
\(25\) −1.13403e9 −0.928996
\(26\) 6.79169e8 0.431173
\(27\) 3.87420e8 0.192450
\(28\) −1.59592e9 −0.625868
\(29\) −1.36461e9 −0.426013 −0.213006 0.977051i \(-0.568325\pi\)
−0.213006 + 0.977051i \(0.568325\pi\)
\(30\) −1.94546e8 −0.0487229
\(31\) 3.47253e8 0.0702741 0.0351370 0.999383i \(-0.488813\pi\)
0.0351370 + 0.999383i \(0.488813\pi\)
\(32\) 5.01853e9 0.826232
\(33\) 3.93592e9 0.530524
\(34\) 2.86108e9 0.317627
\(35\) −2.01591e9 −0.185365
\(36\) −3.91690e9 −0.299900
\(37\) −2.74111e9 −0.175636 −0.0878182 0.996137i \(-0.527989\pi\)
−0.0878182 + 0.996137i \(0.527989\pi\)
\(38\) 8.37289e9 0.451110
\(39\) 1.72726e10 0.786030
\(40\) 4.15307e9 0.160317
\(41\) −3.57931e10 −1.17680 −0.588402 0.808568i \(-0.700243\pi\)
−0.588402 + 0.808568i \(0.700243\pi\)
\(42\) 4.52477e9 0.127197
\(43\) −4.48542e10 −1.08208 −0.541038 0.840998i \(-0.681968\pi\)
−0.541038 + 0.840998i \(0.681968\pi\)
\(44\) −3.97929e10 −0.826730
\(45\) −4.94769e9 −0.0888222
\(46\) −1.80045e10 −0.280192
\(47\) 1.39902e11 1.89316 0.946578 0.322474i \(-0.104514\pi\)
0.946578 + 0.322474i \(0.104514\pi\)
\(48\) 3.46937e10 0.409433
\(49\) −5.00028e10 −0.516084
\(50\) −3.25065e10 −0.294215
\(51\) 7.27631e10 0.579035
\(52\) −1.74630e11 −1.22489
\(53\) −5.29436e9 −0.0328111 −0.0164055 0.999865i \(-0.505222\pi\)
−0.0164055 + 0.999865i \(0.505222\pi\)
\(54\) 1.11053e10 0.0609494
\(55\) −5.02650e10 −0.244855
\(56\) −9.65926e10 −0.418525
\(57\) 2.12940e11 0.822375
\(58\) −3.91161e10 −0.134919
\(59\) −4.21805e10 −0.130189
\(60\) 5.00222e10 0.138414
\(61\) 3.45027e11 0.857452 0.428726 0.903435i \(-0.358963\pi\)
0.428726 + 0.903435i \(0.358963\pi\)
\(62\) 9.95389e9 0.0222560
\(63\) 1.15074e11 0.231880
\(64\) −2.46010e11 −0.447489
\(65\) −2.20587e11 −0.362779
\(66\) 1.12822e11 0.168018
\(67\) −5.99003e11 −0.808989 −0.404495 0.914540i \(-0.632553\pi\)
−0.404495 + 0.914540i \(0.632553\pi\)
\(68\) −7.35649e11 −0.902325
\(69\) −4.57892e11 −0.510792
\(70\) −5.77852e10 −0.0587056
\(71\) −6.16912e11 −0.571536 −0.285768 0.958299i \(-0.592249\pi\)
−0.285768 + 0.958299i \(0.592249\pi\)
\(72\) −2.37070e11 −0.200547
\(73\) 1.52900e12 1.18252 0.591259 0.806482i \(-0.298631\pi\)
0.591259 + 0.806482i \(0.298631\pi\)
\(74\) −7.85728e10 −0.0556245
\(75\) −8.26706e11 −0.536356
\(76\) −2.15286e12 −1.28153
\(77\) 1.16907e12 0.639221
\(78\) 4.95114e11 0.248938
\(79\) 2.64250e12 1.22304 0.611518 0.791230i \(-0.290559\pi\)
0.611518 + 0.791230i \(0.290559\pi\)
\(80\) −4.43069e11 −0.188967
\(81\) 2.82430e11 0.111111
\(82\) −1.02600e12 −0.372697
\(83\) 3.15524e12 1.05932 0.529658 0.848211i \(-0.322320\pi\)
0.529658 + 0.848211i \(0.322320\pi\)
\(84\) −1.16342e12 −0.361345
\(85\) −9.29247e11 −0.267244
\(86\) −1.28573e12 −0.342696
\(87\) −9.94803e11 −0.245959
\(88\) −2.40846e12 −0.552844
\(89\) 5.43970e12 1.16022 0.580109 0.814539i \(-0.303010\pi\)
0.580109 + 0.814539i \(0.303010\pi\)
\(90\) −1.41824e11 −0.0281302
\(91\) 5.13043e12 0.947076
\(92\) 4.62938e12 0.795980
\(93\) 2.53147e11 0.0405728
\(94\) 4.01023e12 0.599568
\(95\) −2.71942e12 −0.379554
\(96\) 3.65851e12 0.477025
\(97\) −2.80648e12 −0.342094 −0.171047 0.985263i \(-0.554715\pi\)
−0.171047 + 0.985263i \(0.554715\pi\)
\(98\) −1.43331e12 −0.163445
\(99\) 2.86928e12 0.306298
\(100\) 8.35817e12 0.835817
\(101\) 1.79795e13 1.68534 0.842671 0.538429i \(-0.180982\pi\)
0.842671 + 0.538429i \(0.180982\pi\)
\(102\) 2.08573e12 0.183382
\(103\) −1.22631e13 −1.01195 −0.505973 0.862549i \(-0.668867\pi\)
−0.505973 + 0.862549i \(0.668867\pi\)
\(104\) −1.05695e13 −0.819098
\(105\) −1.46959e12 −0.107021
\(106\) −1.51761e11 −0.0103913
\(107\) 2.81693e12 0.181460 0.0907301 0.995876i \(-0.471080\pi\)
0.0907301 + 0.995876i \(0.471080\pi\)
\(108\) −2.85542e12 −0.173147
\(109\) 1.61963e13 0.925006 0.462503 0.886618i \(-0.346951\pi\)
0.462503 + 0.886618i \(0.346951\pi\)
\(110\) −1.44083e12 −0.0775461
\(111\) −1.99827e12 −0.101404
\(112\) 1.03049e13 0.493320
\(113\) 2.60181e13 1.17562 0.587808 0.809001i \(-0.299991\pi\)
0.587808 + 0.809001i \(0.299991\pi\)
\(114\) 6.10384e12 0.260448
\(115\) 5.84767e12 0.235748
\(116\) 1.00577e13 0.383283
\(117\) 1.25918e13 0.453814
\(118\) −1.20909e12 −0.0412312
\(119\) 2.16125e13 0.697671
\(120\) 3.02759e12 0.0925590
\(121\) −5.37283e12 −0.155632
\(122\) 9.89009e12 0.271557
\(123\) −2.60932e13 −0.679429
\(124\) −2.55937e12 −0.0632255
\(125\) 2.19224e13 0.514013
\(126\) 3.29856e12 0.0734371
\(127\) −2.54106e13 −0.537391 −0.268695 0.963225i \(-0.586592\pi\)
−0.268695 + 0.963225i \(0.586592\pi\)
\(128\) −4.81636e13 −0.967953
\(129\) −3.26987e13 −0.624737
\(130\) −6.32303e12 −0.114893
\(131\) 2.68732e13 0.464575 0.232287 0.972647i \(-0.425379\pi\)
0.232287 + 0.972647i \(0.425379\pi\)
\(132\) −2.90090e13 −0.477312
\(133\) 6.32487e13 0.990868
\(134\) −1.71702e13 −0.256209
\(135\) −3.60687e12 −0.0512815
\(136\) −4.45251e13 −0.603395
\(137\) −8.59536e13 −1.11066 −0.555329 0.831631i \(-0.687408\pi\)
−0.555329 + 0.831631i \(0.687408\pi\)
\(138\) −1.31253e13 −0.161769
\(139\) 4.62143e13 0.543476 0.271738 0.962371i \(-0.412402\pi\)
0.271738 + 0.962371i \(0.412402\pi\)
\(140\) 1.48579e13 0.166773
\(141\) 1.01988e14 1.09301
\(142\) −1.76835e13 −0.181007
\(143\) 1.27923e14 1.25102
\(144\) 2.52917e13 0.236386
\(145\) 1.27045e13 0.113518
\(146\) 4.38281e13 0.374506
\(147\) −3.64521e13 −0.297961
\(148\) 2.02029e13 0.158020
\(149\) −1.36864e13 −0.102466 −0.0512328 0.998687i \(-0.516315\pi\)
−0.0512328 + 0.998687i \(0.516315\pi\)
\(150\) −2.36972e13 −0.169865
\(151\) −1.86371e14 −1.27946 −0.639732 0.768598i \(-0.720955\pi\)
−0.639732 + 0.768598i \(0.720955\pi\)
\(152\) −1.30302e14 −0.856973
\(153\) 5.30443e13 0.334306
\(154\) 3.35110e13 0.202443
\(155\) −3.23291e12 −0.0187257
\(156\) −1.27305e14 −0.707191
\(157\) −3.36680e14 −1.79420 −0.897098 0.441832i \(-0.854329\pi\)
−0.897098 + 0.441832i \(0.854329\pi\)
\(158\) 7.57464e13 0.387339
\(159\) −3.85959e12 −0.0189435
\(160\) −4.67223e13 −0.220163
\(161\) −1.36006e14 −0.615446
\(162\) 8.09574e12 0.0351892
\(163\) 4.64591e14 1.94022 0.970110 0.242665i \(-0.0780215\pi\)
0.970110 + 0.242665i \(0.0780215\pi\)
\(164\) 2.63807e14 1.05877
\(165\) −3.66432e13 −0.141367
\(166\) 9.04440e13 0.335488
\(167\) 1.82192e14 0.649937 0.324968 0.945725i \(-0.394646\pi\)
0.324968 + 0.945725i \(0.394646\pi\)
\(168\) −7.04160e13 −0.241636
\(169\) 2.58512e14 0.853528
\(170\) −2.66365e13 −0.0846369
\(171\) 1.55233e14 0.474799
\(172\) 3.30590e14 0.973543
\(173\) −4.23492e14 −1.20101 −0.600504 0.799622i \(-0.705033\pi\)
−0.600504 + 0.799622i \(0.705033\pi\)
\(174\) −2.85157e13 −0.0778957
\(175\) −2.45554e14 −0.646247
\(176\) 2.56946e14 0.651642
\(177\) −3.07496e13 −0.0751646
\(178\) 1.55927e14 0.367444
\(179\) −3.39561e14 −0.771567 −0.385783 0.922589i \(-0.626069\pi\)
−0.385783 + 0.922589i \(0.626069\pi\)
\(180\) 3.64662e13 0.0799133
\(181\) 2.38283e14 0.503711 0.251856 0.967765i \(-0.418959\pi\)
0.251856 + 0.967765i \(0.418959\pi\)
\(182\) 1.47062e14 0.299941
\(183\) 2.51525e14 0.495050
\(184\) 2.80193e14 0.532281
\(185\) 2.55196e13 0.0468012
\(186\) 7.25638e12 0.0128495
\(187\) 5.38892e14 0.921577
\(188\) −1.03112e15 −1.70327
\(189\) 8.38890e13 0.133876
\(190\) −7.79513e13 −0.120206
\(191\) −9.38453e14 −1.39861 −0.699303 0.714825i \(-0.746506\pi\)
−0.699303 + 0.714825i \(0.746506\pi\)
\(192\) −1.79341e14 −0.258358
\(193\) 4.43345e13 0.0617474 0.0308737 0.999523i \(-0.490171\pi\)
0.0308737 + 0.999523i \(0.490171\pi\)
\(194\) −8.04468e13 −0.108342
\(195\) −1.60808e14 −0.209451
\(196\) 3.68538e14 0.464320
\(197\) 3.95536e14 0.482121 0.241060 0.970510i \(-0.422505\pi\)
0.241060 + 0.970510i \(0.422505\pi\)
\(198\) 8.22470e13 0.0970055
\(199\) 9.44102e14 1.07764 0.538821 0.842421i \(-0.318870\pi\)
0.538821 + 0.842421i \(0.318870\pi\)
\(200\) 5.05877e14 0.558921
\(201\) −4.36673e14 −0.467070
\(202\) 5.15375e14 0.533752
\(203\) −2.95483e14 −0.296352
\(204\) −5.36288e14 −0.520958
\(205\) 3.33232e14 0.313579
\(206\) −3.51517e14 −0.320486
\(207\) −3.33803e14 −0.294906
\(208\) 1.12760e15 0.965479
\(209\) 1.57706e15 1.30887
\(210\) −4.21254e13 −0.0338937
\(211\) 1.72253e14 0.134379 0.0671893 0.997740i \(-0.478597\pi\)
0.0671893 + 0.997740i \(0.478597\pi\)
\(212\) 3.90212e13 0.0295201
\(213\) −4.49729e14 −0.329977
\(214\) 8.07463e13 0.0574689
\(215\) 4.17590e14 0.288337
\(216\) −1.72824e14 −0.115786
\(217\) 7.51915e13 0.0488855
\(218\) 4.64262e14 0.292952
\(219\) 1.11464e15 0.682727
\(220\) 3.70470e14 0.220296
\(221\) 2.36491e15 1.36542
\(222\) −5.72796e13 −0.0321148
\(223\) 2.68101e15 1.45988 0.729938 0.683513i \(-0.239549\pi\)
0.729938 + 0.683513i \(0.239549\pi\)
\(224\) 1.08667e15 0.574761
\(225\) −6.02669e14 −0.309665
\(226\) 7.45799e14 0.372320
\(227\) −2.87857e15 −1.39640 −0.698199 0.715903i \(-0.746015\pi\)
−0.698199 + 0.715903i \(0.746015\pi\)
\(228\) −1.56944e15 −0.739891
\(229\) 8.60452e14 0.394272 0.197136 0.980376i \(-0.436836\pi\)
0.197136 + 0.980376i \(0.436836\pi\)
\(230\) 1.67621e14 0.0746618
\(231\) 8.52253e14 0.369055
\(232\) 6.08739e14 0.256306
\(233\) 4.56845e15 1.87049 0.935246 0.353999i \(-0.115178\pi\)
0.935246 + 0.353999i \(0.115178\pi\)
\(234\) 3.60938e14 0.143724
\(235\) −1.30248e15 −0.504463
\(236\) 3.10885e14 0.117131
\(237\) 1.92639e15 0.706121
\(238\) 6.19516e14 0.220954
\(239\) 1.00186e15 0.347712 0.173856 0.984771i \(-0.444377\pi\)
0.173856 + 0.984771i \(0.444377\pi\)
\(240\) −3.22997e14 −0.109100
\(241\) −2.70267e15 −0.888551 −0.444276 0.895890i \(-0.646539\pi\)
−0.444276 + 0.895890i \(0.646539\pi\)
\(242\) −1.54010e14 −0.0492890
\(243\) 2.05891e14 0.0641500
\(244\) −2.54297e15 −0.771449
\(245\) 4.65524e14 0.137519
\(246\) −7.47952e14 −0.215177
\(247\) 6.92087e15 1.93923
\(248\) −1.54906e14 −0.0422797
\(249\) 2.30017e15 0.611596
\(250\) 6.28399e14 0.162789
\(251\) 4.19231e15 1.05822 0.529108 0.848554i \(-0.322527\pi\)
0.529108 + 0.848554i \(0.322527\pi\)
\(252\) −8.48135e14 −0.208623
\(253\) −3.39120e15 −0.812962
\(254\) −7.28385e14 −0.170193
\(255\) −6.77421e14 −0.154293
\(256\) 6.34718e14 0.140936
\(257\) −4.55534e15 −0.986179 −0.493089 0.869979i \(-0.664132\pi\)
−0.493089 + 0.869979i \(0.664132\pi\)
\(258\) −9.37296e14 −0.197856
\(259\) −5.93538e14 −0.122180
\(260\) 1.62580e15 0.326392
\(261\) −7.25211e14 −0.142004
\(262\) 7.70310e14 0.147132
\(263\) 6.22519e15 1.15995 0.579976 0.814634i \(-0.303062\pi\)
0.579976 + 0.814634i \(0.303062\pi\)
\(264\) −1.75577e15 −0.319184
\(265\) 4.92903e13 0.00874305
\(266\) 1.81300e15 0.313810
\(267\) 3.96554e15 0.669853
\(268\) 4.41485e15 0.727847
\(269\) −1.00784e16 −1.62181 −0.810906 0.585176i \(-0.801025\pi\)
−0.810906 + 0.585176i \(0.801025\pi\)
\(270\) −1.03390e14 −0.0162410
\(271\) −7.10285e15 −1.08926 −0.544631 0.838676i \(-0.683330\pi\)
−0.544631 + 0.838676i \(0.683330\pi\)
\(272\) 4.75014e15 0.711228
\(273\) 3.74008e15 0.546795
\(274\) −2.46383e15 −0.351748
\(275\) −6.12269e15 −0.853650
\(276\) 3.37482e15 0.459559
\(277\) −1.31312e15 −0.174657 −0.0873285 0.996180i \(-0.527833\pi\)
−0.0873285 + 0.996180i \(0.527833\pi\)
\(278\) 1.32472e15 0.172120
\(279\) 1.84545e14 0.0234247
\(280\) 8.99273e14 0.111523
\(281\) 7.47650e15 0.905957 0.452978 0.891522i \(-0.350362\pi\)
0.452978 + 0.891522i \(0.350362\pi\)
\(282\) 2.92346e15 0.346160
\(283\) 8.94157e15 1.03467 0.517335 0.855783i \(-0.326924\pi\)
0.517335 + 0.855783i \(0.326924\pi\)
\(284\) 4.54685e15 0.514211
\(285\) −1.98246e15 −0.219135
\(286\) 3.66688e15 0.396202
\(287\) −7.75036e15 −0.818634
\(288\) 2.66705e15 0.275411
\(289\) 5.78903e13 0.00584480
\(290\) 3.64170e14 0.0359515
\(291\) −2.04593e15 −0.197508
\(292\) −1.12692e16 −1.06391
\(293\) 8.88122e15 0.820036 0.410018 0.912077i \(-0.365522\pi\)
0.410018 + 0.912077i \(0.365522\pi\)
\(294\) −1.04489e15 −0.0943650
\(295\) 3.92699e14 0.0346910
\(296\) 1.22278e15 0.105670
\(297\) 2.09171e15 0.176841
\(298\) −3.92316e14 −0.0324511
\(299\) −1.48822e16 −1.20449
\(300\) 6.09311e15 0.482559
\(301\) −9.71237e15 −0.752736
\(302\) −5.34226e15 −0.405210
\(303\) 1.31070e16 0.973033
\(304\) 1.39012e16 1.01012
\(305\) −3.21219e15 −0.228482
\(306\) 1.52050e15 0.105876
\(307\) 2.88891e16 1.96940 0.984700 0.174257i \(-0.0557524\pi\)
0.984700 + 0.174257i \(0.0557524\pi\)
\(308\) −8.61645e15 −0.575107
\(309\) −8.93979e15 −0.584248
\(310\) −9.26702e13 −0.00593047
\(311\) 1.20012e16 0.752111 0.376055 0.926597i \(-0.377280\pi\)
0.376055 + 0.926597i \(0.377280\pi\)
\(312\) −7.70514e15 −0.472907
\(313\) 1.97347e16 1.18630 0.593148 0.805093i \(-0.297885\pi\)
0.593148 + 0.805093i \(0.297885\pi\)
\(314\) −9.65082e15 −0.568226
\(315\) −1.07133e15 −0.0617883
\(316\) −1.94761e16 −1.10037
\(317\) −8.35961e15 −0.462701 −0.231351 0.972870i \(-0.574314\pi\)
−0.231351 + 0.972870i \(0.574314\pi\)
\(318\) −1.10634e14 −0.00599945
\(319\) −7.36763e15 −0.391461
\(320\) 2.29034e15 0.119241
\(321\) 2.05354e15 0.104766
\(322\) −3.89856e15 −0.194913
\(323\) 2.91550e16 1.42855
\(324\) −2.08160e15 −0.0999666
\(325\) −2.68692e16 −1.26477
\(326\) 1.33173e16 0.614473
\(327\) 1.18071e16 0.534053
\(328\) 1.59669e16 0.708013
\(329\) 3.02932e16 1.31696
\(330\) −1.05036e15 −0.0447713
\(331\) 2.10739e16 0.880771 0.440385 0.897809i \(-0.354842\pi\)
0.440385 + 0.897809i \(0.354842\pi\)
\(332\) −2.32552e16 −0.953066
\(333\) −1.45674e15 −0.0585455
\(334\) 5.22245e15 0.205837
\(335\) 5.57669e15 0.215569
\(336\) 7.51231e15 0.284818
\(337\) 3.71003e16 1.37969 0.689847 0.723955i \(-0.257678\pi\)
0.689847 + 0.723955i \(0.257678\pi\)
\(338\) 7.41017e15 0.270315
\(339\) 1.89672e16 0.678742
\(340\) 6.84886e15 0.240439
\(341\) 1.87484e15 0.0645745
\(342\) 4.44970e15 0.150370
\(343\) −3.18068e16 −1.05465
\(344\) 2.00089e16 0.651020
\(345\) 4.26295e15 0.136109
\(346\) −1.21393e16 −0.380362
\(347\) 3.09426e16 0.951514 0.475757 0.879577i \(-0.342174\pi\)
0.475757 + 0.879577i \(0.342174\pi\)
\(348\) 7.33203e15 0.221289
\(349\) 5.69288e16 1.68642 0.843212 0.537581i \(-0.180662\pi\)
0.843212 + 0.537581i \(0.180662\pi\)
\(350\) −7.03870e15 −0.204668
\(351\) 9.17939e15 0.262010
\(352\) 2.70954e16 0.759221
\(353\) 8.38615e14 0.0230689 0.0115344 0.999933i \(-0.496328\pi\)
0.0115344 + 0.999933i \(0.496328\pi\)
\(354\) −8.81427e14 −0.0238048
\(355\) 5.74342e15 0.152295
\(356\) −4.00924e16 −1.04385
\(357\) 1.57555e16 0.402801
\(358\) −9.73340e15 −0.244357
\(359\) 3.37122e16 0.831138 0.415569 0.909562i \(-0.363582\pi\)
0.415569 + 0.909562i \(0.363582\pi\)
\(360\) 2.20711e15 0.0534389
\(361\) 4.32685e16 1.02890
\(362\) 6.83029e15 0.159527
\(363\) −3.91679e15 −0.0898540
\(364\) −3.78130e16 −0.852084
\(365\) −1.42349e16 −0.315101
\(366\) 7.20987e15 0.156784
\(367\) −6.86074e16 −1.46569 −0.732844 0.680397i \(-0.761808\pi\)
−0.732844 + 0.680397i \(0.761808\pi\)
\(368\) −2.98923e16 −0.627405
\(369\) −1.90219e16 −0.392268
\(370\) 7.31510e14 0.0148221
\(371\) −1.14640e15 −0.0228247
\(372\) −1.86578e15 −0.0365033
\(373\) −7.44207e16 −1.43083 −0.715413 0.698702i \(-0.753761\pi\)
−0.715413 + 0.698702i \(0.753761\pi\)
\(374\) 1.54472e16 0.291866
\(375\) 1.59815e16 0.296765
\(376\) −6.24085e16 −1.13900
\(377\) −3.23326e16 −0.579992
\(378\) 2.40465e15 0.0423989
\(379\) 1.37559e16 0.238416 0.119208 0.992869i \(-0.461965\pi\)
0.119208 + 0.992869i \(0.461965\pi\)
\(380\) 2.00431e16 0.341484
\(381\) −1.85243e16 −0.310263
\(382\) −2.69004e16 −0.442942
\(383\) −2.47689e16 −0.400973 −0.200487 0.979696i \(-0.564252\pi\)
−0.200487 + 0.979696i \(0.564252\pi\)
\(384\) −3.51113e16 −0.558848
\(385\) −1.08840e16 −0.170331
\(386\) 1.27083e15 0.0195556
\(387\) −2.38373e16 −0.360692
\(388\) 2.06847e16 0.307782
\(389\) 6.14774e16 0.899587 0.449793 0.893133i \(-0.351498\pi\)
0.449793 + 0.893133i \(0.351498\pi\)
\(390\) −4.60949e15 −0.0663335
\(391\) −6.26930e16 −0.887299
\(392\) 2.23057e16 0.310496
\(393\) 1.95906e16 0.268222
\(394\) 1.13379e16 0.152689
\(395\) −2.46016e16 −0.325898
\(396\) −2.11476e16 −0.275577
\(397\) 2.26904e16 0.290873 0.145437 0.989368i \(-0.453541\pi\)
0.145437 + 0.989368i \(0.453541\pi\)
\(398\) 2.70624e16 0.341292
\(399\) 4.61083e16 0.572078
\(400\) −5.39693e16 −0.658805
\(401\) 6.61849e16 0.794915 0.397458 0.917621i \(-0.369893\pi\)
0.397458 + 0.917621i \(0.369893\pi\)
\(402\) −1.25171e16 −0.147922
\(403\) 8.22768e15 0.0956742
\(404\) −1.32515e17 −1.51630
\(405\) −2.62941e15 −0.0296074
\(406\) −8.46990e15 −0.0938554
\(407\) −1.47994e16 −0.161392
\(408\) −3.24588e16 −0.348370
\(409\) −1.11947e17 −1.18253 −0.591265 0.806477i \(-0.701371\pi\)
−0.591265 + 0.806477i \(0.701371\pi\)
\(410\) 9.55199e15 0.0993113
\(411\) −6.26602e16 −0.641239
\(412\) 9.03831e16 0.910448
\(413\) −9.13344e15 −0.0905648
\(414\) −9.56835e15 −0.0933974
\(415\) −2.93752e16 −0.282272
\(416\) 1.18907e17 1.12487
\(417\) 3.36902e16 0.313776
\(418\) 4.52058e16 0.414523
\(419\) −1.11992e17 −1.01110 −0.505551 0.862797i \(-0.668711\pi\)
−0.505551 + 0.862797i \(0.668711\pi\)
\(420\) 1.08314e16 0.0962863
\(421\) 4.59146e16 0.401899 0.200950 0.979602i \(-0.435597\pi\)
0.200950 + 0.979602i \(0.435597\pi\)
\(422\) 4.93756e15 0.0425581
\(423\) 7.43494e16 0.631052
\(424\) 2.36176e15 0.0197404
\(425\) −1.13190e17 −0.931707
\(426\) −1.28913e16 −0.104504
\(427\) 7.47096e16 0.596479
\(428\) −2.07617e16 −0.163260
\(429\) 9.32561e16 0.722279
\(430\) 1.19701e16 0.0913170
\(431\) −4.95234e16 −0.372141 −0.186071 0.982536i \(-0.559575\pi\)
−0.186071 + 0.982536i \(0.559575\pi\)
\(432\) 1.84377e16 0.136478
\(433\) 5.90197e16 0.430354 0.215177 0.976575i \(-0.430967\pi\)
0.215177 + 0.976575i \(0.430967\pi\)
\(434\) 2.15534e15 0.0154822
\(435\) 9.26157e15 0.0655397
\(436\) −1.19373e17 −0.832228
\(437\) −1.83470e17 −1.26019
\(438\) 3.19507e16 0.216221
\(439\) −1.95409e17 −1.30294 −0.651470 0.758675i \(-0.725847\pi\)
−0.651470 + 0.758675i \(0.725847\pi\)
\(440\) 2.24227e16 0.147314
\(441\) −2.65735e16 −0.172028
\(442\) 6.77893e16 0.432431
\(443\) −2.63628e17 −1.65717 −0.828584 0.559864i \(-0.810853\pi\)
−0.828584 + 0.559864i \(0.810853\pi\)
\(444\) 1.47279e16 0.0912329
\(445\) −5.06434e16 −0.309159
\(446\) 7.68501e16 0.462347
\(447\) −9.97738e15 −0.0591586
\(448\) −5.32690e16 −0.311292
\(449\) −1.37870e17 −0.794090 −0.397045 0.917799i \(-0.629964\pi\)
−0.397045 + 0.917799i \(0.629964\pi\)
\(450\) −1.72753e16 −0.0980718
\(451\) −1.93249e17 −1.08136
\(452\) −1.91762e17 −1.05770
\(453\) −1.35864e17 −0.738699
\(454\) −8.25133e16 −0.442243
\(455\) −4.77641e16 −0.252364
\(456\) −9.49900e16 −0.494774
\(457\) 1.14822e17 0.589617 0.294808 0.955556i \(-0.404744\pi\)
0.294808 + 0.955556i \(0.404744\pi\)
\(458\) 2.46645e16 0.124867
\(459\) 3.86693e16 0.193012
\(460\) −4.30993e16 −0.212102
\(461\) −6.94164e16 −0.336826 −0.168413 0.985717i \(-0.553864\pi\)
−0.168413 + 0.985717i \(0.553864\pi\)
\(462\) 2.44295e16 0.116881
\(463\) −4.95155e16 −0.233596 −0.116798 0.993156i \(-0.537263\pi\)
−0.116798 + 0.993156i \(0.537263\pi\)
\(464\) −6.49431e16 −0.302111
\(465\) −2.35679e15 −0.0108113
\(466\) 1.30953e17 0.592389
\(467\) 2.23463e17 0.996886 0.498443 0.866923i \(-0.333905\pi\)
0.498443 + 0.866923i \(0.333905\pi\)
\(468\) −9.28055e16 −0.408297
\(469\) −1.29703e17 −0.562766
\(470\) −3.73351e16 −0.159765
\(471\) −2.45440e17 −1.03588
\(472\) 1.88163e16 0.0783268
\(473\) −2.42170e17 −0.994314
\(474\) 5.52191e16 0.223630
\(475\) −3.31248e17 −1.32326
\(476\) −1.59292e17 −0.627694
\(477\) −2.81364e15 −0.0109370
\(478\) 2.87179e16 0.110121
\(479\) 3.02476e17 1.14422 0.572111 0.820176i \(-0.306125\pi\)
0.572111 + 0.820176i \(0.306125\pi\)
\(480\) −3.40606e16 −0.127111
\(481\) −6.49467e16 −0.239119
\(482\) −7.74711e16 −0.281406
\(483\) −9.91483e16 −0.355328
\(484\) 3.95996e16 0.140022
\(485\) 2.61282e16 0.0911567
\(486\) 5.90180e15 0.0203165
\(487\) −3.10898e15 −0.0105604 −0.00528018 0.999986i \(-0.501681\pi\)
−0.00528018 + 0.999986i \(0.501681\pi\)
\(488\) −1.53913e17 −0.515877
\(489\) 3.38687e17 1.12019
\(490\) 1.33441e16 0.0435526
\(491\) 4.82801e17 1.55503 0.777515 0.628865i \(-0.216480\pi\)
0.777515 + 0.628865i \(0.216480\pi\)
\(492\) 1.92316e17 0.611282
\(493\) −1.36205e17 −0.427256
\(494\) 1.98384e17 0.614160
\(495\) −2.67129e16 −0.0816183
\(496\) 1.65261e16 0.0498355
\(497\) −1.33581e17 −0.397584
\(498\) 6.59336e16 0.193694
\(499\) −3.83978e17 −1.11341 −0.556703 0.830712i \(-0.687934\pi\)
−0.556703 + 0.830712i \(0.687934\pi\)
\(500\) −1.61576e17 −0.462457
\(501\) 1.32818e17 0.375241
\(502\) 1.20171e17 0.335140
\(503\) −4.43802e17 −1.22179 −0.610896 0.791711i \(-0.709191\pi\)
−0.610896 + 0.791711i \(0.709191\pi\)
\(504\) −5.13333e16 −0.139508
\(505\) −1.67388e17 −0.449087
\(506\) −9.72076e16 −0.257467
\(507\) 1.88456e17 0.492785
\(508\) 1.87284e17 0.483490
\(509\) 9.92092e16 0.252864 0.126432 0.991975i \(-0.459647\pi\)
0.126432 + 0.991975i \(0.459647\pi\)
\(510\) −1.94180e16 −0.0488651
\(511\) 3.31077e17 0.822608
\(512\) 4.12750e17 1.01259
\(513\) 1.13165e17 0.274125
\(514\) −1.30577e17 −0.312325
\(515\) 1.14169e17 0.269650
\(516\) 2.41000e17 0.562075
\(517\) 7.55338e17 1.73961
\(518\) −1.70135e16 −0.0386947
\(519\) −3.08726e17 −0.693402
\(520\) 9.84012e16 0.218262
\(521\) 5.01190e17 1.09789 0.548943 0.835860i \(-0.315030\pi\)
0.548943 + 0.835860i \(0.315030\pi\)
\(522\) −2.07879e16 −0.0449731
\(523\) 2.59670e17 0.554831 0.277415 0.960750i \(-0.410522\pi\)
0.277415 + 0.960750i \(0.410522\pi\)
\(524\) −1.98064e17 −0.417978
\(525\) −1.79009e17 −0.373111
\(526\) 1.78443e17 0.367360
\(527\) 3.46601e16 0.0704791
\(528\) 1.87314e17 0.376226
\(529\) −1.09515e17 −0.217275
\(530\) 1.41289e15 0.00276895
\(531\) −2.24165e16 −0.0433963
\(532\) −4.66164e17 −0.891484
\(533\) −8.48068e17 −1.60215
\(534\) 1.13671e17 0.212144
\(535\) −2.62255e16 −0.0483531
\(536\) 2.67209e17 0.486720
\(537\) −2.47540e17 −0.445464
\(538\) −2.88893e17 −0.513632
\(539\) −2.69968e17 −0.474227
\(540\) 2.65838e16 0.0461379
\(541\) 8.63101e17 1.48006 0.740030 0.672574i \(-0.234811\pi\)
0.740030 + 0.672574i \(0.234811\pi\)
\(542\) −2.03601e17 −0.344972
\(543\) 1.73708e17 0.290818
\(544\) 5.00911e17 0.828643
\(545\) −1.50787e17 −0.246483
\(546\) 1.07208e17 0.173171
\(547\) −9.16310e17 −1.46260 −0.731299 0.682057i \(-0.761085\pi\)
−0.731299 + 0.682057i \(0.761085\pi\)
\(548\) 6.33507e17 0.999259
\(549\) 1.83362e17 0.285817
\(550\) −1.75505e17 −0.270353
\(551\) −3.98601e17 −0.606811
\(552\) 2.04260e17 0.307313
\(553\) 5.72187e17 0.850795
\(554\) −3.76401e16 −0.0553143
\(555\) 1.86038e16 0.0270207
\(556\) −3.40615e17 −0.488965
\(557\) 4.86125e17 0.689746 0.344873 0.938649i \(-0.387922\pi\)
0.344873 + 0.938649i \(0.387922\pi\)
\(558\) 5.28990e15 0.00741866
\(559\) −1.06276e18 −1.47318
\(560\) −9.59386e16 −0.131453
\(561\) 3.92852e17 0.532073
\(562\) 2.14311e17 0.286919
\(563\) 2.64634e17 0.350220 0.175110 0.984549i \(-0.443972\pi\)
0.175110 + 0.984549i \(0.443972\pi\)
\(564\) −7.51688e17 −0.983385
\(565\) −2.42227e17 −0.313262
\(566\) 2.56307e17 0.327683
\(567\) 6.11551e16 0.0772935
\(568\) 2.75197e17 0.343859
\(569\) 6.30017e17 0.778256 0.389128 0.921184i \(-0.372776\pi\)
0.389128 + 0.921184i \(0.372776\pi\)
\(570\) −5.68265e16 −0.0694008
\(571\) −1.02890e18 −1.24234 −0.621168 0.783677i \(-0.713342\pi\)
−0.621168 + 0.783677i \(0.713342\pi\)
\(572\) −9.42838e17 −1.12555
\(573\) −6.84132e17 −0.807486
\(574\) −2.22161e17 −0.259263
\(575\) 7.12294e17 0.821898
\(576\) −1.30740e17 −0.149163
\(577\) −5.82838e17 −0.657514 −0.328757 0.944415i \(-0.606630\pi\)
−0.328757 + 0.944415i \(0.606630\pi\)
\(578\) 1.65941e15 0.00185106
\(579\) 3.23198e16 0.0356499
\(580\) −9.36364e16 −0.102132
\(581\) 6.83212e17 0.736904
\(582\) −5.86457e16 −0.0625514
\(583\) −2.85846e16 −0.0301499
\(584\) −6.82068e17 −0.711450
\(585\) −1.17229e17 −0.120926
\(586\) 2.54577e17 0.259708
\(587\) 1.71056e17 0.172581 0.0862903 0.996270i \(-0.472499\pi\)
0.0862903 + 0.996270i \(0.472499\pi\)
\(588\) 2.68664e17 0.268075
\(589\) 1.01432e17 0.100098
\(590\) 1.12566e16 0.0109867
\(591\) 2.88346e17 0.278352
\(592\) −1.30452e17 −0.124554
\(593\) −5.23667e17 −0.494538 −0.247269 0.968947i \(-0.579533\pi\)
−0.247269 + 0.968947i \(0.579533\pi\)
\(594\) 5.99581e16 0.0560061
\(595\) −2.01212e17 −0.185906
\(596\) 1.00873e17 0.0921883
\(597\) 6.88251e17 0.622176
\(598\) −4.26593e17 −0.381466
\(599\) −4.23616e17 −0.374712 −0.187356 0.982292i \(-0.559992\pi\)
−0.187356 + 0.982292i \(0.559992\pi\)
\(600\) 3.68784e17 0.322693
\(601\) −6.43390e17 −0.556917 −0.278458 0.960448i \(-0.589823\pi\)
−0.278458 + 0.960448i \(0.589823\pi\)
\(602\) −2.78402e17 −0.238394
\(603\) −3.18335e17 −0.269663
\(604\) 1.37362e18 1.15113
\(605\) 5.00208e16 0.0414706
\(606\) 3.75708e17 0.308162
\(607\) 6.08498e17 0.493779 0.246890 0.969044i \(-0.420591\pi\)
0.246890 + 0.969044i \(0.420591\pi\)
\(608\) 1.46591e18 1.17688
\(609\) −2.15407e17 −0.171099
\(610\) −9.20763e16 −0.0723609
\(611\) 3.31477e18 2.57743
\(612\) −3.90954e17 −0.300775
\(613\) 1.06005e18 0.806923 0.403462 0.914997i \(-0.367807\pi\)
0.403462 + 0.914997i \(0.367807\pi\)
\(614\) 8.28095e17 0.623714
\(615\) 2.42926e17 0.181045
\(616\) −5.21510e17 −0.384581
\(617\) 9.42378e17 0.687656 0.343828 0.939033i \(-0.388276\pi\)
0.343828 + 0.939033i \(0.388276\pi\)
\(618\) −2.56256e17 −0.185033
\(619\) −2.65447e18 −1.89666 −0.948329 0.317290i \(-0.897227\pi\)
−0.948329 + 0.317290i \(0.897227\pi\)
\(620\) 2.38276e16 0.0168475
\(621\) −2.43343e17 −0.170264
\(622\) 3.44010e17 0.238195
\(623\) 1.17787e18 0.807096
\(624\) 8.22020e17 0.557420
\(625\) 1.18021e18 0.792028
\(626\) 5.65689e17 0.375703
\(627\) 1.14967e18 0.755677
\(628\) 2.48145e18 1.61424
\(629\) −2.73596e17 −0.176149
\(630\) −3.07094e16 −0.0195685
\(631\) 4.03638e17 0.254566 0.127283 0.991866i \(-0.459374\pi\)
0.127283 + 0.991866i \(0.459374\pi\)
\(632\) −1.17879e18 −0.735827
\(633\) 1.25572e17 0.0775836
\(634\) −2.39625e17 −0.146539
\(635\) 2.36571e17 0.143197
\(636\) 2.84465e16 0.0170434
\(637\) −1.18475e18 −0.702618
\(638\) −2.11191e17 −0.123977
\(639\) −3.27852e17 −0.190512
\(640\) 4.48401e17 0.257927
\(641\) −5.77734e17 −0.328966 −0.164483 0.986380i \(-0.552596\pi\)
−0.164483 + 0.986380i \(0.552596\pi\)
\(642\) 5.88640e16 0.0331797
\(643\) −1.99793e18 −1.11483 −0.557415 0.830234i \(-0.688207\pi\)
−0.557415 + 0.830234i \(0.688207\pi\)
\(644\) 1.00241e18 0.553716
\(645\) 3.04423e17 0.166471
\(646\) 8.35717e17 0.452426
\(647\) −7.05000e17 −0.377843 −0.188922 0.981992i \(-0.560499\pi\)
−0.188922 + 0.981992i \(0.560499\pi\)
\(648\) −1.25989e17 −0.0668489
\(649\) −2.27735e17 −0.119630
\(650\) −7.70197e17 −0.400557
\(651\) 5.48146e16 0.0282241
\(652\) −3.42419e18 −1.74562
\(653\) 2.73122e18 1.37854 0.689272 0.724503i \(-0.257931\pi\)
0.689272 + 0.724503i \(0.257931\pi\)
\(654\) 3.38447e17 0.169136
\(655\) −2.50188e17 −0.123794
\(656\) −1.70342e18 −0.834541
\(657\) 8.12571e17 0.394173
\(658\) 8.68344e17 0.417084
\(659\) −9.55271e17 −0.454330 −0.227165 0.973856i \(-0.572946\pi\)
−0.227165 + 0.973856i \(0.572946\pi\)
\(660\) 2.70073e17 0.127188
\(661\) 4.95508e17 0.231069 0.115534 0.993303i \(-0.463142\pi\)
0.115534 + 0.993303i \(0.463142\pi\)
\(662\) 6.04076e17 0.278942
\(663\) 1.72402e18 0.788323
\(664\) −1.40752e18 −0.637326
\(665\) −5.88843e17 −0.264033
\(666\) −4.17568e16 −0.0185415
\(667\) 8.57127e17 0.376901
\(668\) −1.34281e18 −0.584748
\(669\) 1.95445e18 0.842860
\(670\) 1.59854e17 0.0682711
\(671\) 1.86283e18 0.787908
\(672\) 7.92185e17 0.331838
\(673\) −1.15745e18 −0.480180 −0.240090 0.970751i \(-0.577177\pi\)
−0.240090 + 0.970751i \(0.577177\pi\)
\(674\) 1.06347e18 0.436953
\(675\) −4.39346e17 −0.178785
\(676\) −1.90532e18 −0.767919
\(677\) 4.40348e18 1.75780 0.878899 0.477007i \(-0.158278\pi\)
0.878899 + 0.477007i \(0.158278\pi\)
\(678\) 5.43687e17 0.214959
\(679\) −6.07694e17 −0.237975
\(680\) 4.14527e17 0.160785
\(681\) −2.09848e18 −0.806211
\(682\) 5.37417e16 0.0204509
\(683\) 3.59605e18 1.35547 0.677737 0.735304i \(-0.262961\pi\)
0.677737 + 0.735304i \(0.262961\pi\)
\(684\) −1.14412e18 −0.427176
\(685\) 8.00224e17 0.295953
\(686\) −9.11731e17 −0.334010
\(687\) 6.27269e17 0.227633
\(688\) −2.13465e18 −0.767363
\(689\) −1.25443e17 −0.0446704
\(690\) 1.22196e17 0.0431060
\(691\) −2.36146e18 −0.825226 −0.412613 0.910906i \(-0.635384\pi\)
−0.412613 + 0.910906i \(0.635384\pi\)
\(692\) 3.12128e18 1.08055
\(693\) 6.21292e17 0.213074
\(694\) 8.86959e17 0.301347
\(695\) −4.30253e17 −0.144818
\(696\) 4.43770e17 0.147978
\(697\) −3.57259e18 −1.18024
\(698\) 1.63184e18 0.534095
\(699\) 3.33040e18 1.07993
\(700\) 1.80981e18 0.581429
\(701\) 4.90181e18 1.56023 0.780116 0.625635i \(-0.215160\pi\)
0.780116 + 0.625635i \(0.215160\pi\)
\(702\) 2.63124e17 0.0829792
\(703\) −8.00673e17 −0.250176
\(704\) −1.32822e18 −0.411195
\(705\) −9.49506e17 −0.291252
\(706\) 2.40386e16 0.00730598
\(707\) 3.89313e18 1.17239
\(708\) 2.26635e17 0.0676256
\(709\) −5.28943e17 −0.156390 −0.0781949 0.996938i \(-0.524916\pi\)
−0.0781949 + 0.996938i \(0.524916\pi\)
\(710\) 1.64633e17 0.0482323
\(711\) 1.40433e18 0.407679
\(712\) −2.42659e18 −0.698034
\(713\) −2.18113e17 −0.0621727
\(714\) 4.51627e17 0.127568
\(715\) −1.19096e18 −0.333356
\(716\) 2.50268e18 0.694178
\(717\) 7.30355e17 0.200752
\(718\) 9.66348e17 0.263224
\(719\) −3.32936e17 −0.0898718 −0.0449359 0.998990i \(-0.514308\pi\)
−0.0449359 + 0.998990i \(0.514308\pi\)
\(720\) −2.35465e17 −0.0629890
\(721\) −2.65535e18 −0.703952
\(722\) 1.24028e18 0.325856
\(723\) −1.97025e18 −0.513005
\(724\) −1.75622e18 −0.453189
\(725\) 1.54751e18 0.395764
\(726\) −1.12273e17 −0.0284570
\(727\) −4.92404e18 −1.23694 −0.618469 0.785810i \(-0.712247\pi\)
−0.618469 + 0.785810i \(0.712247\pi\)
\(728\) −2.28863e18 −0.569798
\(729\) 1.50095e17 0.0370370
\(730\) −4.08038e17 −0.0997934
\(731\) −4.47699e18 −1.08523
\(732\) −1.85382e18 −0.445396
\(733\) −3.40343e18 −0.810478 −0.405239 0.914211i \(-0.632812\pi\)
−0.405239 + 0.914211i \(0.632812\pi\)
\(734\) −1.96661e18 −0.464187
\(735\) 3.39367e17 0.0793966
\(736\) −3.15219e18 −0.730982
\(737\) −3.23406e18 −0.743376
\(738\) −5.45257e17 −0.124232
\(739\) 4.10703e18 0.927553 0.463777 0.885952i \(-0.346494\pi\)
0.463777 + 0.885952i \(0.346494\pi\)
\(740\) −1.88088e17 −0.0421071
\(741\) 5.04531e18 1.11962
\(742\) −3.28611e16 −0.00722865
\(743\) 2.15656e18 0.470256 0.235128 0.971964i \(-0.424449\pi\)
0.235128 + 0.971964i \(0.424449\pi\)
\(744\) −1.12926e17 −0.0244102
\(745\) 1.27420e17 0.0273037
\(746\) −2.13324e18 −0.453146
\(747\) 1.67683e18 0.353105
\(748\) −3.97182e18 −0.829142
\(749\) 6.09956e17 0.126231
\(750\) 4.58103e17 0.0939863
\(751\) −5.70403e18 −1.16017 −0.580086 0.814555i \(-0.696981\pi\)
−0.580086 + 0.814555i \(0.696981\pi\)
\(752\) 6.65803e18 1.34255
\(753\) 3.05619e18 0.610961
\(754\) −9.26803e17 −0.183685
\(755\) 1.73511e18 0.340934
\(756\) −6.18290e17 −0.120448
\(757\) 6.80967e18 1.31523 0.657617 0.753353i \(-0.271565\pi\)
0.657617 + 0.753353i \(0.271565\pi\)
\(758\) 3.94308e17 0.0755068
\(759\) −2.47219e18 −0.469364
\(760\) 1.21310e18 0.228355
\(761\) −7.27192e18 −1.35722 −0.678608 0.734501i \(-0.737417\pi\)
−0.678608 + 0.734501i \(0.737417\pi\)
\(762\) −5.30993e17 −0.0982610
\(763\) 3.50703e18 0.643472
\(764\) 6.91671e18 1.25833
\(765\) −4.93840e17 −0.0890814
\(766\) −7.09993e17 −0.126989
\(767\) −9.99409e17 −0.177245
\(768\) 4.62710e17 0.0813693
\(769\) −5.26207e18 −0.917562 −0.458781 0.888549i \(-0.651714\pi\)
−0.458781 + 0.888549i \(0.651714\pi\)
\(770\) −3.11986e17 −0.0539443
\(771\) −3.32084e18 −0.569371
\(772\) −3.26760e17 −0.0555541
\(773\) 5.20743e18 0.877924 0.438962 0.898506i \(-0.355346\pi\)
0.438962 + 0.898506i \(0.355346\pi\)
\(774\) −6.83289e17 −0.114232
\(775\) −3.93795e17 −0.0652843
\(776\) 1.25194e18 0.205818
\(777\) −4.32689e17 −0.0705406
\(778\) 1.76223e18 0.284901
\(779\) −1.04551e19 −1.67624
\(780\) 1.18521e18 0.188443
\(781\) −3.33074e18 −0.525182
\(782\) −1.79707e18 −0.281010
\(783\) −5.28679e17 −0.0819862
\(784\) −2.37968e18 −0.365985
\(785\) 3.13448e18 0.478093
\(786\) 5.61556e17 0.0849467
\(787\) 1.23580e19 1.85401 0.927006 0.375047i \(-0.122373\pi\)
0.927006 + 0.375047i \(0.122373\pi\)
\(788\) −2.91523e18 −0.433764
\(789\) 4.53816e18 0.669699
\(790\) −7.05196e17 −0.103213
\(791\) 5.63375e18 0.817806
\(792\) −1.27996e18 −0.184281
\(793\) 8.17495e18 1.16737
\(794\) 6.50412e17 0.0921202
\(795\) 3.59326e16 0.00504780
\(796\) −6.95835e18 −0.969553
\(797\) −4.92356e18 −0.680456 −0.340228 0.940343i \(-0.610504\pi\)
−0.340228 + 0.940343i \(0.610504\pi\)
\(798\) 1.32168e18 0.181179
\(799\) 1.39639e19 1.89868
\(800\) −5.69116e18 −0.767566
\(801\) 2.89088e18 0.386740
\(802\) 1.89717e18 0.251752
\(803\) 8.25514e18 1.08661
\(804\) 3.21843e18 0.420223
\(805\) 1.26621e18 0.163996
\(806\) 2.35844e17 0.0303003
\(807\) −7.34714e18 −0.936354
\(808\) −8.02044e18 −1.01397
\(809\) −7.88987e18 −0.989474 −0.494737 0.869043i \(-0.664736\pi\)
−0.494737 + 0.869043i \(0.664736\pi\)
\(810\) −7.53710e16 −0.00937674
\(811\) 1.10628e19 1.36531 0.682653 0.730743i \(-0.260826\pi\)
0.682653 + 0.730743i \(0.260826\pi\)
\(812\) 2.17781e18 0.266628
\(813\) −5.17798e18 −0.628885
\(814\) −4.24220e17 −0.0511131
\(815\) −4.32532e18 −0.517004
\(816\) 3.46286e18 0.410628
\(817\) −1.31018e19 −1.54130
\(818\) −3.20893e18 −0.374510
\(819\) 2.72652e18 0.315692
\(820\) −2.45604e18 −0.282127
\(821\) 4.81763e17 0.0549039 0.0274520 0.999623i \(-0.491261\pi\)
0.0274520 + 0.999623i \(0.491261\pi\)
\(822\) −1.79613e18 −0.203082
\(823\) 1.32130e19 1.48218 0.741092 0.671404i \(-0.234308\pi\)
0.741092 + 0.671404i \(0.234308\pi\)
\(824\) 5.47042e18 0.608827
\(825\) −4.46344e18 −0.492855
\(826\) −2.61807e17 −0.0286821
\(827\) 1.31017e18 0.142411 0.0712055 0.997462i \(-0.477315\pi\)
0.0712055 + 0.997462i \(0.477315\pi\)
\(828\) 2.46024e18 0.265327
\(829\) 3.40684e18 0.364542 0.182271 0.983248i \(-0.441655\pi\)
0.182271 + 0.983248i \(0.441655\pi\)
\(830\) −8.42029e17 −0.0893963
\(831\) −9.57264e17 −0.100838
\(832\) −5.82886e18 −0.609231
\(833\) −4.99089e18 −0.517590
\(834\) 9.65718e17 0.0993736
\(835\) −1.69620e18 −0.173186
\(836\) −1.16234e19 −1.17759
\(837\) 1.34533e17 0.0135243
\(838\) −3.21020e18 −0.320219
\(839\) −2.82067e18 −0.279190 −0.139595 0.990209i \(-0.544580\pi\)
−0.139595 + 0.990209i \(0.544580\pi\)
\(840\) 6.55570e17 0.0643878
\(841\) −8.39846e18 −0.818513
\(842\) 1.31613e18 0.127283
\(843\) 5.45037e18 0.523054
\(844\) −1.26956e18 −0.120900
\(845\) −2.40674e18 −0.227437
\(846\) 2.13120e18 0.199856
\(847\) −1.16339e18 −0.108264
\(848\) −2.51963e17 −0.0232683
\(849\) 6.51840e18 0.597367
\(850\) −3.24454e18 −0.295074
\(851\) 1.72172e18 0.155389
\(852\) 3.31465e18 0.296880
\(853\) −3.84425e17 −0.0341698 −0.0170849 0.999854i \(-0.505439\pi\)
−0.0170849 + 0.999854i \(0.505439\pi\)
\(854\) 2.14152e18 0.188906
\(855\) −1.44521e18 −0.126518
\(856\) −1.25660e18 −0.109174
\(857\) 3.39679e18 0.292882 0.146441 0.989219i \(-0.453218\pi\)
0.146441 + 0.989219i \(0.453218\pi\)
\(858\) 2.67315e18 0.228748
\(859\) −2.05123e19 −1.74204 −0.871022 0.491245i \(-0.836542\pi\)
−0.871022 + 0.491245i \(0.836542\pi\)
\(860\) −3.07778e18 −0.259417
\(861\) −5.65001e18 −0.472638
\(862\) −1.41957e18 −0.117858
\(863\) −4.66645e18 −0.384518 −0.192259 0.981344i \(-0.561581\pi\)
−0.192259 + 0.981344i \(0.561581\pi\)
\(864\) 1.94428e18 0.159008
\(865\) 3.94270e18 0.320028
\(866\) 1.69178e18 0.136294
\(867\) 4.22020e16 0.00337450
\(868\) −5.54187e17 −0.0439823
\(869\) 1.42670e19 1.12384
\(870\) 2.65480e17 0.0207566
\(871\) −1.41925e19 −1.10139
\(872\) −7.22501e18 −0.556520
\(873\) −1.49148e18 −0.114031
\(874\) −5.25910e18 −0.399105
\(875\) 4.74691e18 0.357568
\(876\) −8.21526e18 −0.614249
\(877\) −1.53247e19 −1.13735 −0.568676 0.822562i \(-0.692544\pi\)
−0.568676 + 0.822562i \(0.692544\pi\)
\(878\) −5.60132e18 −0.412644
\(879\) 6.47441e18 0.473448
\(880\) −2.39216e18 −0.173641
\(881\) 7.53364e18 0.542827 0.271414 0.962463i \(-0.412509\pi\)
0.271414 + 0.962463i \(0.412509\pi\)
\(882\) −7.61721e17 −0.0544817
\(883\) −1.72537e19 −1.22500 −0.612502 0.790469i \(-0.709837\pi\)
−0.612502 + 0.790469i \(0.709837\pi\)
\(884\) −1.74302e19 −1.22846
\(885\) 2.86278e17 0.0200288
\(886\) −7.55679e18 −0.524830
\(887\) −2.58215e17 −0.0178024 −0.00890120 0.999960i \(-0.502833\pi\)
−0.00890120 + 0.999960i \(0.502833\pi\)
\(888\) 8.91405e17 0.0610085
\(889\) −5.50221e18 −0.373831
\(890\) −1.45167e18 −0.0979116
\(891\) 1.52485e18 0.102099
\(892\) −1.97599e19 −1.31345
\(893\) 4.08650e19 2.69660
\(894\) −2.85998e17 −0.0187357
\(895\) 3.16130e18 0.205597
\(896\) −1.04290e19 −0.673348
\(897\) −1.08491e19 −0.695414
\(898\) −3.95201e18 −0.251490
\(899\) −4.73866e17 −0.0299376
\(900\) 4.44187e18 0.278606
\(901\) −5.28442e17 −0.0329068
\(902\) −5.53942e18 −0.342470
\(903\) −7.08032e18 −0.434593
\(904\) −1.16064e19 −0.707297
\(905\) −2.21840e18 −0.134222
\(906\) −3.89451e18 −0.233948
\(907\) −2.92969e19 −1.74733 −0.873664 0.486530i \(-0.838262\pi\)
−0.873664 + 0.486530i \(0.838262\pi\)
\(908\) 2.12161e19 1.25634
\(909\) 9.55503e18 0.561781
\(910\) −1.36914e18 −0.0799243
\(911\) 2.84837e19 1.65092 0.825462 0.564458i \(-0.190915\pi\)
0.825462 + 0.564458i \(0.190915\pi\)
\(912\) 1.01340e19 0.583195
\(913\) 1.70354e19 0.973400
\(914\) 3.29133e18 0.186733
\(915\) −2.34169e18 −0.131914
\(916\) −6.34182e18 −0.354726
\(917\) 5.81891e18 0.323177
\(918\) 1.10844e18 0.0611273
\(919\) −1.04671e19 −0.573161 −0.286580 0.958056i \(-0.592519\pi\)
−0.286580 + 0.958056i \(0.592519\pi\)
\(920\) −2.60858e18 −0.141835
\(921\) 2.10601e19 1.13703
\(922\) −1.98980e18 −0.106674
\(923\) −1.46169e19 −0.778114
\(924\) −6.28139e18 −0.332038
\(925\) 3.10849e18 0.163166
\(926\) −1.41934e18 −0.0739804
\(927\) −6.51710e18 −0.337316
\(928\) −6.84836e18 −0.351985
\(929\) 1.24768e19 0.636799 0.318399 0.947957i \(-0.396855\pi\)
0.318399 + 0.947957i \(0.396855\pi\)
\(930\) −6.75566e16 −0.00342396
\(931\) −1.46057e19 −0.735107
\(932\) −3.36711e19 −1.68288
\(933\) 8.74887e18 0.434231
\(934\) 6.40548e18 0.315716
\(935\) −5.01706e18 −0.245569
\(936\) −5.61704e18 −0.273033
\(937\) 2.05527e19 0.992112 0.496056 0.868291i \(-0.334781\pi\)
0.496056 + 0.868291i \(0.334781\pi\)
\(938\) −3.71790e18 −0.178229
\(939\) 1.43866e19 0.684908
\(940\) 9.59970e18 0.453865
\(941\) −3.02681e19 −1.42119 −0.710595 0.703601i \(-0.751574\pi\)
−0.710595 + 0.703601i \(0.751574\pi\)
\(942\) −7.03545e18 −0.328066
\(943\) 2.24820e19 1.04114
\(944\) −2.00741e18 −0.0923246
\(945\) −7.81003e17 −0.0356735
\(946\) −6.94173e18 −0.314902
\(947\) −3.41885e19 −1.54030 −0.770150 0.637862i \(-0.779819\pi\)
−0.770150 + 0.637862i \(0.779819\pi\)
\(948\) −1.41981e19 −0.635296
\(949\) 3.62274e19 1.60993
\(950\) −9.49510e18 −0.419079
\(951\) −6.09415e18 −0.267141
\(952\) −9.64112e18 −0.419747
\(953\) 1.70835e19 0.738710 0.369355 0.929288i \(-0.379579\pi\)
0.369355 + 0.929288i \(0.379579\pi\)
\(954\) −8.06520e16 −0.00346378
\(955\) 8.73695e18 0.372682
\(956\) −7.38404e18 −0.312837
\(957\) −5.37100e18 −0.226010
\(958\) 8.67036e18 0.362378
\(959\) −1.86117e19 −0.772620
\(960\) 1.66966e18 0.0688437
\(961\) −2.42970e19 −0.995062
\(962\) −1.86167e18 −0.0757296
\(963\) 1.49703e18 0.0604867
\(964\) 1.99196e19 0.799429
\(965\) −4.12752e17 −0.0164536
\(966\) −2.84205e18 −0.112533
\(967\) −4.48509e19 −1.76400 −0.882002 0.471246i \(-0.843804\pi\)
−0.882002 + 0.471246i \(0.843804\pi\)
\(968\) 2.39676e18 0.0936342
\(969\) 2.12540e19 0.824775
\(970\) 7.48956e17 0.0288696
\(971\) 3.21613e19 1.23143 0.615713 0.787971i \(-0.288868\pi\)
0.615713 + 0.787971i \(0.288868\pi\)
\(972\) −1.51749e18 −0.0577157
\(973\) 1.00069e19 0.378064
\(974\) −8.91177e16 −0.00334450
\(975\) −1.95877e19 −0.730218
\(976\) 1.64201e19 0.608069
\(977\) −1.01925e19 −0.374942 −0.187471 0.982270i \(-0.560029\pi\)
−0.187471 + 0.982270i \(0.560029\pi\)
\(978\) 9.70833e18 0.354766
\(979\) 2.93693e19 1.06612
\(980\) −3.43107e18 −0.123726
\(981\) 8.60740e18 0.308335
\(982\) 1.38393e19 0.492482
\(983\) 6.79418e18 0.240181 0.120091 0.992763i \(-0.461681\pi\)
0.120091 + 0.992763i \(0.461681\pi\)
\(984\) 1.16399e19 0.408771
\(985\) −3.68242e18 −0.128469
\(986\) −3.90427e18 −0.135313
\(987\) 2.20837e19 0.760346
\(988\) −5.10091e19 −1.74473
\(989\) 2.81733e19 0.957331
\(990\) −7.65716e17 −0.0258487
\(991\) −2.27185e19 −0.761905 −0.380952 0.924595i \(-0.624404\pi\)
−0.380952 + 0.924595i \(0.624404\pi\)
\(992\) 1.74270e18 0.0580627
\(993\) 1.53629e19 0.508513
\(994\) −3.82906e18 −0.125916
\(995\) −8.78955e18 −0.287155
\(996\) −1.69531e19 −0.550253
\(997\) −3.14471e19 −1.01406 −0.507028 0.861929i \(-0.669256\pi\)
−0.507028 + 0.861929i \(0.669256\pi\)
\(998\) −1.10066e19 −0.352618
\(999\) −1.06196e18 −0.0338013
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.1.18 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.18 31 1.1 even 1 trivial