Properties

Label 177.14.a.c.1.29
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 1.29
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+162.847 q^{2} +729.000 q^{3} +18327.1 q^{4} +27762.2 q^{5} +118715. q^{6} -59572.2 q^{7} +1.65046e6 q^{8} +531441. q^{9} +O(q^{10})\) \(q+162.847 q^{2} +729.000 q^{3} +18327.1 q^{4} +27762.2 q^{5} +118715. q^{6} -59572.2 q^{7} +1.65046e6 q^{8} +531441. q^{9} +4.52099e6 q^{10} -2.68286e6 q^{11} +1.33604e7 q^{12} -3.02892e6 q^{13} -9.70114e6 q^{14} +2.02387e7 q^{15} +1.18637e8 q^{16} +1.27291e8 q^{17} +8.65434e7 q^{18} +3.71145e8 q^{19} +5.08800e8 q^{20} -4.34281e7 q^{21} -4.36896e8 q^{22} -8.99791e8 q^{23} +1.20319e9 q^{24} -4.49962e8 q^{25} -4.93250e8 q^{26} +3.87420e8 q^{27} -1.09178e9 q^{28} +3.38875e9 q^{29} +3.29580e9 q^{30} +4.54415e9 q^{31} +5.79906e9 q^{32} -1.95581e9 q^{33} +2.07290e10 q^{34} -1.65386e9 q^{35} +9.73975e9 q^{36} -1.05156e10 q^{37} +6.04398e10 q^{38} -2.20808e9 q^{39} +4.58205e10 q^{40} -1.90780e10 q^{41} -7.07213e9 q^{42} +6.35415e10 q^{43} -4.91690e10 q^{44} +1.47540e10 q^{45} -1.46528e11 q^{46} +9.70295e10 q^{47} +8.64864e10 q^{48} -9.33402e10 q^{49} -7.32748e10 q^{50} +9.27953e10 q^{51} -5.55112e10 q^{52} +2.65128e11 q^{53} +6.30902e10 q^{54} -7.44823e10 q^{55} -9.83216e10 q^{56} +2.70565e11 q^{57} +5.51846e11 q^{58} -4.21805e10 q^{59} +3.70915e11 q^{60} +1.69822e11 q^{61} +7.40000e11 q^{62} -3.16591e10 q^{63} -2.75154e10 q^{64} -8.40896e10 q^{65} -3.18497e11 q^{66} +4.94258e11 q^{67} +2.33287e12 q^{68} -6.55947e11 q^{69} -2.69325e11 q^{70} +2.21765e10 q^{71} +8.77123e11 q^{72} +4.50606e11 q^{73} -1.71243e12 q^{74} -3.28022e11 q^{75} +6.80200e12 q^{76} +1.59824e11 q^{77} -3.59579e11 q^{78} -1.95067e12 q^{79} +3.29363e12 q^{80} +2.82430e11 q^{81} -3.10679e12 q^{82} -3.51604e12 q^{83} -7.95910e11 q^{84} +3.53389e12 q^{85} +1.03475e13 q^{86} +2.47040e12 q^{87} -4.42796e12 q^{88} +1.52322e12 q^{89} +2.40264e12 q^{90} +1.80440e11 q^{91} -1.64905e13 q^{92} +3.31269e12 q^{93} +1.58009e13 q^{94} +1.03038e13 q^{95} +4.22752e12 q^{96} +6.38953e12 q^{97} -1.52001e13 q^{98} -1.42578e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 162.847 1.79922 0.899610 0.436695i \(-0.143851\pi\)
0.899610 + 0.436695i \(0.143851\pi\)
\(3\) 729.000 0.577350
\(4\) 18327.1 2.23719
\(5\) 27762.2 0.794601 0.397301 0.917688i \(-0.369947\pi\)
0.397301 + 0.917688i \(0.369947\pi\)
\(6\) 118715. 1.03878
\(7\) −59572.2 −0.191384 −0.0956922 0.995411i \(-0.530506\pi\)
−0.0956922 + 0.995411i \(0.530506\pi\)
\(8\) 1.65046e6 2.22598
\(9\) 531441. 0.333333
\(10\) 4.52099e6 1.42966
\(11\) −2.68286e6 −0.456611 −0.228305 0.973590i \(-0.573318\pi\)
−0.228305 + 0.973590i \(0.573318\pi\)
\(12\) 1.33604e7 1.29164
\(13\) −3.02892e6 −0.174043 −0.0870214 0.996206i \(-0.527735\pi\)
−0.0870214 + 0.996206i \(0.527735\pi\)
\(14\) −9.70114e6 −0.344342
\(15\) 2.02387e7 0.458763
\(16\) 1.18637e8 1.76783
\(17\) 1.27291e8 1.27903 0.639514 0.768779i \(-0.279135\pi\)
0.639514 + 0.768779i \(0.279135\pi\)
\(18\) 8.65434e7 0.599740
\(19\) 3.71145e8 1.80986 0.904931 0.425559i \(-0.139923\pi\)
0.904931 + 0.425559i \(0.139923\pi\)
\(20\) 5.08800e8 1.77767
\(21\) −4.34281e7 −0.110496
\(22\) −4.36896e8 −0.821543
\(23\) −8.99791e8 −1.26739 −0.633695 0.773583i \(-0.718463\pi\)
−0.633695 + 0.773583i \(0.718463\pi\)
\(24\) 1.20319e9 1.28517
\(25\) −4.49962e8 −0.368609
\(26\) −4.93250e8 −0.313141
\(27\) 3.87420e8 0.192450
\(28\) −1.09178e9 −0.428163
\(29\) 3.38875e9 1.05792 0.528959 0.848647i \(-0.322582\pi\)
0.528959 + 0.848647i \(0.322582\pi\)
\(30\) 3.29580e9 0.825416
\(31\) 4.54415e9 0.919606 0.459803 0.888021i \(-0.347920\pi\)
0.459803 + 0.888021i \(0.347920\pi\)
\(32\) 5.79906e9 0.954735
\(33\) −1.95581e9 −0.263624
\(34\) 2.07290e10 2.30125
\(35\) −1.65386e9 −0.152074
\(36\) 9.73975e9 0.745730
\(37\) −1.05156e10 −0.673786 −0.336893 0.941543i \(-0.609376\pi\)
−0.336893 + 0.941543i \(0.609376\pi\)
\(38\) 6.04398e10 3.25634
\(39\) −2.20808e9 −0.100484
\(40\) 4.58205e10 1.76876
\(41\) −1.90780e10 −0.627246 −0.313623 0.949548i \(-0.601543\pi\)
−0.313623 + 0.949548i \(0.601543\pi\)
\(42\) −7.07213e9 −0.198806
\(43\) 6.35415e10 1.53290 0.766448 0.642306i \(-0.222022\pi\)
0.766448 + 0.642306i \(0.222022\pi\)
\(44\) −4.91690e10 −1.02153
\(45\) 1.47540e10 0.264867
\(46\) −1.46528e11 −2.28031
\(47\) 9.70295e10 1.31301 0.656504 0.754322i \(-0.272034\pi\)
0.656504 + 0.754322i \(0.272034\pi\)
\(48\) 8.64864e10 1.02066
\(49\) −9.33402e10 −0.963372
\(50\) −7.32748e10 −0.663208
\(51\) 9.27953e10 0.738448
\(52\) −5.55112e10 −0.389367
\(53\) 2.65128e11 1.64310 0.821548 0.570139i \(-0.193111\pi\)
0.821548 + 0.570139i \(0.193111\pi\)
\(54\) 6.30902e10 0.346260
\(55\) −7.44823e10 −0.362824
\(56\) −9.83216e10 −0.426017
\(57\) 2.70565e11 1.04492
\(58\) 5.51846e11 1.90343
\(59\) −4.21805e10 −0.130189
\(60\) 3.70915e11 1.02634
\(61\) 1.69822e11 0.422037 0.211019 0.977482i \(-0.432322\pi\)
0.211019 + 0.977482i \(0.432322\pi\)
\(62\) 7.40000e11 1.65457
\(63\) −3.16591e10 −0.0637948
\(64\) −2.75154e10 −0.0500502
\(65\) −8.40896e10 −0.138295
\(66\) −3.18497e11 −0.474318
\(67\) 4.94258e11 0.667525 0.333763 0.942657i \(-0.391682\pi\)
0.333763 + 0.942657i \(0.391682\pi\)
\(68\) 2.33287e12 2.86143
\(69\) −6.55947e11 −0.731728
\(70\) −2.69325e11 −0.273615
\(71\) 2.21765e10 0.0205453 0.0102727 0.999947i \(-0.496730\pi\)
0.0102727 + 0.999947i \(0.496730\pi\)
\(72\) 8.77123e11 0.741992
\(73\) 4.50606e11 0.348496 0.174248 0.984702i \(-0.444251\pi\)
0.174248 + 0.984702i \(0.444251\pi\)
\(74\) −1.71243e12 −1.21229
\(75\) −3.28022e11 −0.212816
\(76\) 6.80200e12 4.04900
\(77\) 1.59824e11 0.0873882
\(78\) −3.59579e11 −0.180792
\(79\) −1.95067e12 −0.902833 −0.451416 0.892313i \(-0.649081\pi\)
−0.451416 + 0.892313i \(0.649081\pi\)
\(80\) 3.29363e12 1.40472
\(81\) 2.82430e11 0.111111
\(82\) −3.10679e12 −1.12855
\(83\) −3.51604e12 −1.18045 −0.590224 0.807240i \(-0.700960\pi\)
−0.590224 + 0.807240i \(0.700960\pi\)
\(84\) −7.95910e11 −0.247200
\(85\) 3.53389e12 1.01632
\(86\) 1.03475e13 2.75802
\(87\) 2.47040e12 0.610790
\(88\) −4.42796e12 −1.01640
\(89\) 1.52322e12 0.324884 0.162442 0.986718i \(-0.448063\pi\)
0.162442 + 0.986718i \(0.448063\pi\)
\(90\) 2.40264e12 0.476554
\(91\) 1.80440e11 0.0333091
\(92\) −1.64905e13 −2.83539
\(93\) 3.31269e12 0.530935
\(94\) 1.58009e13 2.36239
\(95\) 1.03038e13 1.43812
\(96\) 4.22752e12 0.551217
\(97\) 6.38953e12 0.778848 0.389424 0.921059i \(-0.372674\pi\)
0.389424 + 0.921059i \(0.372674\pi\)
\(98\) −1.52001e13 −1.73332
\(99\) −1.42578e12 −0.152204
\(100\) −8.24647e12 −0.824647
\(101\) −5.94996e12 −0.557731 −0.278865 0.960330i \(-0.589958\pi\)
−0.278865 + 0.960330i \(0.589958\pi\)
\(102\) 1.51114e13 1.32863
\(103\) −2.14626e13 −1.77109 −0.885545 0.464554i \(-0.846215\pi\)
−0.885545 + 0.464554i \(0.846215\pi\)
\(104\) −4.99912e12 −0.387415
\(105\) −1.20566e12 −0.0878001
\(106\) 4.31753e13 2.95629
\(107\) −2.61584e13 −1.68506 −0.842531 0.538647i \(-0.818936\pi\)
−0.842531 + 0.538647i \(0.818936\pi\)
\(108\) 7.10028e12 0.430547
\(109\) −1.15642e13 −0.660454 −0.330227 0.943901i \(-0.607125\pi\)
−0.330227 + 0.943901i \(0.607125\pi\)
\(110\) −1.21292e13 −0.652799
\(111\) −7.66585e12 −0.389010
\(112\) −7.06747e12 −0.338335
\(113\) 3.23623e12 0.146228 0.0731139 0.997324i \(-0.476706\pi\)
0.0731139 + 0.997324i \(0.476706\pi\)
\(114\) 4.40606e13 1.88005
\(115\) −2.49802e13 −1.00707
\(116\) 6.21058e13 2.36676
\(117\) −1.60969e12 −0.0580143
\(118\) −6.86896e12 −0.234238
\(119\) −7.58302e12 −0.244786
\(120\) 3.34031e13 1.02120
\(121\) −2.73250e13 −0.791507
\(122\) 2.76550e13 0.759338
\(123\) −1.39079e13 −0.362141
\(124\) 8.32809e13 2.05733
\(125\) −4.63814e13 −1.08750
\(126\) −5.15558e12 −0.114781
\(127\) 5.78100e13 1.22258 0.611292 0.791405i \(-0.290650\pi\)
0.611292 + 0.791405i \(0.290650\pi\)
\(128\) −5.19867e13 −1.04479
\(129\) 4.63218e13 0.885018
\(130\) −1.36937e13 −0.248823
\(131\) −1.39914e13 −0.241878 −0.120939 0.992660i \(-0.538591\pi\)
−0.120939 + 0.992660i \(0.538591\pi\)
\(132\) −3.58442e13 −0.589778
\(133\) −2.21099e13 −0.346379
\(134\) 8.04883e13 1.20102
\(135\) 1.07557e13 0.152921
\(136\) 2.10089e14 2.84709
\(137\) 3.86259e13 0.499108 0.249554 0.968361i \(-0.419716\pi\)
0.249554 + 0.968361i \(0.419716\pi\)
\(138\) −1.06819e14 −1.31654
\(139\) 7.34165e13 0.863371 0.431686 0.902024i \(-0.357919\pi\)
0.431686 + 0.902024i \(0.357919\pi\)
\(140\) −3.03103e13 −0.340219
\(141\) 7.07345e13 0.758066
\(142\) 3.61136e12 0.0369655
\(143\) 8.12619e12 0.0794699
\(144\) 6.30486e13 0.589276
\(145\) 9.40792e13 0.840624
\(146\) 7.33797e13 0.627021
\(147\) −6.80450e13 −0.556203
\(148\) −1.92720e14 −1.50739
\(149\) 2.48102e14 1.85746 0.928732 0.370752i \(-0.120900\pi\)
0.928732 + 0.370752i \(0.120900\pi\)
\(150\) −5.34173e13 −0.382903
\(151\) 5.27940e11 0.00362439 0.00181219 0.999998i \(-0.499423\pi\)
0.00181219 + 0.999998i \(0.499423\pi\)
\(152\) 6.12561e14 4.02871
\(153\) 6.76478e13 0.426343
\(154\) 2.60268e13 0.157230
\(155\) 1.26156e14 0.730720
\(156\) −4.04677e13 −0.224801
\(157\) −2.22031e14 −1.18322 −0.591610 0.806224i \(-0.701507\pi\)
−0.591610 + 0.806224i \(0.701507\pi\)
\(158\) −3.17660e14 −1.62439
\(159\) 1.93279e14 0.948642
\(160\) 1.60995e14 0.758634
\(161\) 5.36025e13 0.242559
\(162\) 4.59927e13 0.199913
\(163\) 8.22901e13 0.343659 0.171830 0.985127i \(-0.445032\pi\)
0.171830 + 0.985127i \(0.445032\pi\)
\(164\) −3.49644e14 −1.40327
\(165\) −5.42976e13 −0.209476
\(166\) −5.72576e14 −2.12388
\(167\) −2.02218e14 −0.721379 −0.360690 0.932686i \(-0.617459\pi\)
−0.360690 + 0.932686i \(0.617459\pi\)
\(168\) −7.16765e13 −0.245961
\(169\) −2.93701e14 −0.969709
\(170\) 5.75482e14 1.82858
\(171\) 1.97242e14 0.603287
\(172\) 1.16453e15 3.42938
\(173\) −1.69653e14 −0.481129 −0.240564 0.970633i \(-0.577333\pi\)
−0.240564 + 0.970633i \(0.577333\pi\)
\(174\) 4.02296e14 1.09894
\(175\) 2.68052e13 0.0705459
\(176\) −3.18287e14 −0.807210
\(177\) −3.07496e13 −0.0751646
\(178\) 2.48052e14 0.584537
\(179\) 4.91796e14 1.11748 0.558740 0.829343i \(-0.311285\pi\)
0.558740 + 0.829343i \(0.311285\pi\)
\(180\) 2.70397e14 0.592558
\(181\) −7.85002e14 −1.65943 −0.829717 0.558185i \(-0.811498\pi\)
−0.829717 + 0.558185i \(0.811498\pi\)
\(182\) 2.93840e13 0.0599303
\(183\) 1.23800e14 0.243663
\(184\) −1.48507e15 −2.82118
\(185\) −2.91936e14 −0.535391
\(186\) 5.39460e14 0.955268
\(187\) −3.41505e14 −0.584018
\(188\) 1.77827e15 2.93745
\(189\) −2.30795e13 −0.0368319
\(190\) 1.67794e15 2.58749
\(191\) 1.10039e15 1.63995 0.819976 0.572398i \(-0.193987\pi\)
0.819976 + 0.572398i \(0.193987\pi\)
\(192\) −2.00587e13 −0.0288965
\(193\) 9.47937e14 1.32025 0.660126 0.751155i \(-0.270503\pi\)
0.660126 + 0.751155i \(0.270503\pi\)
\(194\) 1.04051e15 1.40132
\(195\) −6.13013e13 −0.0798445
\(196\) −1.71065e15 −2.15525
\(197\) 6.76201e14 0.824224 0.412112 0.911133i \(-0.364791\pi\)
0.412112 + 0.911133i \(0.364791\pi\)
\(198\) −2.32184e14 −0.273848
\(199\) −1.26155e15 −1.43999 −0.719997 0.693977i \(-0.755857\pi\)
−0.719997 + 0.693977i \(0.755857\pi\)
\(200\) −7.42644e14 −0.820514
\(201\) 3.60314e14 0.385396
\(202\) −9.68931e14 −1.00348
\(203\) −2.01875e14 −0.202469
\(204\) 1.70066e15 1.65205
\(205\) −5.29648e14 −0.498411
\(206\) −3.49512e15 −3.18658
\(207\) −4.78186e14 −0.422464
\(208\) −3.59342e14 −0.307678
\(209\) −9.95732e14 −0.826402
\(210\) −1.96338e14 −0.157972
\(211\) −1.40142e15 −1.09328 −0.546641 0.837367i \(-0.684094\pi\)
−0.546641 + 0.837367i \(0.684094\pi\)
\(212\) 4.85902e15 3.67592
\(213\) 1.61666e13 0.0118618
\(214\) −4.25980e15 −3.03180
\(215\) 1.76405e15 1.21804
\(216\) 6.39423e14 0.428389
\(217\) −2.70705e14 −0.175998
\(218\) −1.88319e15 −1.18830
\(219\) 3.28492e14 0.201204
\(220\) −1.36504e15 −0.811705
\(221\) −3.85555e14 −0.222606
\(222\) −1.24836e15 −0.699915
\(223\) −1.68731e15 −0.918784 −0.459392 0.888234i \(-0.651933\pi\)
−0.459392 + 0.888234i \(0.651933\pi\)
\(224\) −3.45463e14 −0.182721
\(225\) −2.39128e14 −0.122870
\(226\) 5.27010e14 0.263096
\(227\) −7.69795e14 −0.373428 −0.186714 0.982414i \(-0.559784\pi\)
−0.186714 + 0.982414i \(0.559784\pi\)
\(228\) 4.95866e15 2.33769
\(229\) 2.22614e15 1.02005 0.510024 0.860160i \(-0.329636\pi\)
0.510024 + 0.860160i \(0.329636\pi\)
\(230\) −4.06794e15 −1.81194
\(231\) 1.16512e14 0.0504536
\(232\) 5.59300e15 2.35490
\(233\) −1.40356e15 −0.574667 −0.287333 0.957831i \(-0.592769\pi\)
−0.287333 + 0.957831i \(0.592769\pi\)
\(234\) −2.62133e14 −0.104380
\(235\) 2.69376e15 1.04332
\(236\) −7.73045e14 −0.291257
\(237\) −1.42204e15 −0.521251
\(238\) −1.23487e15 −0.440424
\(239\) −4.41543e15 −1.53245 −0.766226 0.642571i \(-0.777868\pi\)
−0.766226 + 0.642571i \(0.777868\pi\)
\(240\) 2.40105e15 0.811015
\(241\) 4.28400e15 1.40844 0.704220 0.709982i \(-0.251297\pi\)
0.704220 + 0.709982i \(0.251297\pi\)
\(242\) −4.44978e15 −1.42409
\(243\) 2.05891e14 0.0641500
\(244\) 3.11234e15 0.944177
\(245\) −2.59133e15 −0.765497
\(246\) −2.26485e15 −0.651571
\(247\) −1.12417e15 −0.314993
\(248\) 7.49995e15 2.04702
\(249\) −2.56320e15 −0.681532
\(250\) −7.55306e15 −1.95665
\(251\) −3.63024e15 −0.916340 −0.458170 0.888865i \(-0.651495\pi\)
−0.458170 + 0.888865i \(0.651495\pi\)
\(252\) −5.80218e14 −0.142721
\(253\) 2.41402e15 0.578704
\(254\) 9.41416e15 2.19970
\(255\) 2.57620e15 0.586772
\(256\) −8.24046e15 −1.82975
\(257\) −9.10415e15 −1.97094 −0.985472 0.169838i \(-0.945676\pi\)
−0.985472 + 0.169838i \(0.945676\pi\)
\(258\) 7.54335e15 1.59234
\(259\) 6.26436e14 0.128952
\(260\) −1.54112e15 −0.309392
\(261\) 1.80092e15 0.352639
\(262\) −2.27845e15 −0.435192
\(263\) −7.03400e15 −1.31066 −0.655330 0.755343i \(-0.727470\pi\)
−0.655330 + 0.755343i \(0.727470\pi\)
\(264\) −3.22799e15 −0.586822
\(265\) 7.36056e15 1.30561
\(266\) −3.60053e15 −0.623212
\(267\) 1.11043e15 0.187572
\(268\) 9.05830e15 1.49338
\(269\) 1.22637e16 1.97347 0.986734 0.162347i \(-0.0519064\pi\)
0.986734 + 0.162347i \(0.0519064\pi\)
\(270\) 1.75152e15 0.275139
\(271\) −1.63408e15 −0.250595 −0.125297 0.992119i \(-0.539988\pi\)
−0.125297 + 0.992119i \(0.539988\pi\)
\(272\) 1.51014e16 2.26110
\(273\) 1.31540e14 0.0192310
\(274\) 6.29010e15 0.898005
\(275\) 1.20719e15 0.168311
\(276\) −1.20216e16 −1.63702
\(277\) 1.01889e16 1.35521 0.677605 0.735426i \(-0.263018\pi\)
0.677605 + 0.735426i \(0.263018\pi\)
\(278\) 1.19556e16 1.55339
\(279\) 2.41495e15 0.306535
\(280\) −2.72963e15 −0.338514
\(281\) −6.54038e14 −0.0792522 −0.0396261 0.999215i \(-0.512617\pi\)
−0.0396261 + 0.999215i \(0.512617\pi\)
\(282\) 1.15189e16 1.36393
\(283\) 3.12177e15 0.361234 0.180617 0.983554i \(-0.442191\pi\)
0.180617 + 0.983554i \(0.442191\pi\)
\(284\) 4.06429e14 0.0459638
\(285\) 7.51148e15 0.830298
\(286\) 1.32332e15 0.142984
\(287\) 1.13652e15 0.120045
\(288\) 3.08186e15 0.318245
\(289\) 6.29847e15 0.635915
\(290\) 1.53205e16 1.51247
\(291\) 4.65797e15 0.449668
\(292\) 8.25828e15 0.779652
\(293\) −1.25140e16 −1.15546 −0.577730 0.816228i \(-0.696061\pi\)
−0.577730 + 0.816228i \(0.696061\pi\)
\(294\) −1.10809e16 −1.00073
\(295\) −1.17103e15 −0.103448
\(296\) −1.73556e16 −1.49983
\(297\) −1.03940e15 −0.0878748
\(298\) 4.04027e16 3.34198
\(299\) 2.72540e15 0.220580
\(300\) −6.01168e15 −0.476110
\(301\) −3.78531e15 −0.293372
\(302\) 8.59733e13 0.00652107
\(303\) −4.33752e15 −0.322006
\(304\) 4.40315e16 3.19952
\(305\) 4.71465e15 0.335351
\(306\) 1.10162e16 0.767084
\(307\) 7.11289e15 0.484894 0.242447 0.970165i \(-0.422050\pi\)
0.242447 + 0.970165i \(0.422050\pi\)
\(308\) 2.92911e15 0.195504
\(309\) −1.56462e16 −1.02254
\(310\) 2.05441e16 1.31473
\(311\) 2.05093e16 1.28531 0.642654 0.766156i \(-0.277833\pi\)
0.642654 + 0.766156i \(0.277833\pi\)
\(312\) −3.64436e15 −0.223674
\(313\) −2.67164e16 −1.60598 −0.802989 0.595993i \(-0.796759\pi\)
−0.802989 + 0.595993i \(0.796759\pi\)
\(314\) −3.61570e16 −2.12887
\(315\) −8.78928e14 −0.0506914
\(316\) −3.57500e16 −2.01981
\(317\) 5.02011e15 0.277861 0.138931 0.990302i \(-0.455634\pi\)
0.138931 + 0.990302i \(0.455634\pi\)
\(318\) 3.14748e16 1.70682
\(319\) −9.09155e15 −0.483057
\(320\) −7.63888e14 −0.0397699
\(321\) −1.90694e16 −0.972871
\(322\) 8.72899e15 0.436416
\(323\) 4.72435e16 2.31486
\(324\) 5.17610e15 0.248577
\(325\) 1.36290e15 0.0641537
\(326\) 1.34007e16 0.618319
\(327\) −8.43029e15 −0.381314
\(328\) −3.14875e16 −1.39623
\(329\) −5.78026e15 −0.251289
\(330\) −8.84219e15 −0.376894
\(331\) 5.97840e14 0.0249864 0.0124932 0.999922i \(-0.496023\pi\)
0.0124932 + 0.999922i \(0.496023\pi\)
\(332\) −6.44387e16 −2.64088
\(333\) −5.58841e15 −0.224595
\(334\) −3.29306e16 −1.29792
\(335\) 1.37217e16 0.530417
\(336\) −5.15218e15 −0.195338
\(337\) 2.00409e16 0.745286 0.372643 0.927975i \(-0.378452\pi\)
0.372643 + 0.927975i \(0.378452\pi\)
\(338\) −4.78282e16 −1.74472
\(339\) 2.35921e15 0.0844247
\(340\) 6.47658e16 2.27370
\(341\) −1.21913e16 −0.419902
\(342\) 3.21202e16 1.08545
\(343\) 1.13324e16 0.375759
\(344\) 1.04873e17 3.41219
\(345\) −1.82106e16 −0.581432
\(346\) −2.76274e16 −0.865656
\(347\) −2.73765e16 −0.841854 −0.420927 0.907094i \(-0.638295\pi\)
−0.420927 + 0.907094i \(0.638295\pi\)
\(348\) 4.52751e16 1.36645
\(349\) 7.40036e15 0.219224 0.109612 0.993974i \(-0.465039\pi\)
0.109612 + 0.993974i \(0.465039\pi\)
\(350\) 4.36514e15 0.126928
\(351\) −1.17347e15 −0.0334946
\(352\) −1.55581e16 −0.435943
\(353\) −3.38573e16 −0.931358 −0.465679 0.884954i \(-0.654190\pi\)
−0.465679 + 0.884954i \(0.654190\pi\)
\(354\) −5.00747e15 −0.135238
\(355\) 6.15668e14 0.0163253
\(356\) 2.79162e16 0.726827
\(357\) −5.52802e15 −0.141327
\(358\) 8.00873e16 2.01059
\(359\) −2.55251e16 −0.629295 −0.314648 0.949209i \(-0.601886\pi\)
−0.314648 + 0.949209i \(0.601886\pi\)
\(360\) 2.43509e16 0.589588
\(361\) 9.56957e16 2.27560
\(362\) −1.27835e17 −2.98568
\(363\) −1.99199e16 −0.456977
\(364\) 3.30693e15 0.0745187
\(365\) 1.25098e16 0.276916
\(366\) 2.01605e16 0.438404
\(367\) 3.10453e16 0.663233 0.331616 0.943414i \(-0.392406\pi\)
0.331616 + 0.943414i \(0.392406\pi\)
\(368\) −1.06748e17 −2.24053
\(369\) −1.01388e16 −0.209082
\(370\) −4.75408e16 −0.963286
\(371\) −1.57943e16 −0.314463
\(372\) 6.07118e16 1.18780
\(373\) 6.86540e15 0.131995 0.0659976 0.997820i \(-0.478977\pi\)
0.0659976 + 0.997820i \(0.478977\pi\)
\(374\) −5.56130e16 −1.05078
\(375\) −3.38120e16 −0.627867
\(376\) 1.60143e17 2.92273
\(377\) −1.02642e16 −0.184123
\(378\) −3.75842e15 −0.0662687
\(379\) 3.37368e16 0.584722 0.292361 0.956308i \(-0.405559\pi\)
0.292361 + 0.956308i \(0.405559\pi\)
\(380\) 1.88839e17 3.21734
\(381\) 4.21435e16 0.705859
\(382\) 1.79196e17 2.95063
\(383\) −2.73031e16 −0.441998 −0.220999 0.975274i \(-0.570932\pi\)
−0.220999 + 0.975274i \(0.570932\pi\)
\(384\) −3.78983e16 −0.603208
\(385\) 4.43707e15 0.0694388
\(386\) 1.54368e17 2.37542
\(387\) 3.37686e16 0.510965
\(388\) 1.17101e17 1.74243
\(389\) −9.09678e16 −1.33111 −0.665557 0.746347i \(-0.731806\pi\)
−0.665557 + 0.746347i \(0.731806\pi\)
\(390\) −9.98272e15 −0.143658
\(391\) −1.14535e17 −1.62103
\(392\) −1.54054e17 −2.14444
\(393\) −1.01997e16 −0.139648
\(394\) 1.10117e17 1.48296
\(395\) −5.41549e16 −0.717392
\(396\) −2.61304e16 −0.340508
\(397\) 4.40801e16 0.565072 0.282536 0.959257i \(-0.408824\pi\)
0.282536 + 0.959257i \(0.408824\pi\)
\(398\) −2.05440e17 −2.59086
\(399\) −1.61181e16 −0.199982
\(400\) −5.33821e16 −0.651637
\(401\) −5.48202e16 −0.658419 −0.329209 0.944257i \(-0.606782\pi\)
−0.329209 + 0.944257i \(0.606782\pi\)
\(402\) 5.86760e16 0.693412
\(403\) −1.37639e16 −0.160051
\(404\) −1.09045e17 −1.24775
\(405\) 7.84087e15 0.0882891
\(406\) −3.28747e16 −0.364286
\(407\) 2.82119e16 0.307658
\(408\) 1.53155e17 1.64377
\(409\) −8.77365e16 −0.926785 −0.463392 0.886153i \(-0.653368\pi\)
−0.463392 + 0.886153i \(0.653368\pi\)
\(410\) −8.62515e16 −0.896750
\(411\) 2.81583e16 0.288160
\(412\) −3.93347e17 −3.96226
\(413\) 2.51279e15 0.0249161
\(414\) −7.78710e16 −0.760105
\(415\) −9.76132e16 −0.937985
\(416\) −1.75649e16 −0.166165
\(417\) 5.35206e16 0.498467
\(418\) −1.62152e17 −1.48688
\(419\) 7.73801e16 0.698616 0.349308 0.937008i \(-0.386417\pi\)
0.349308 + 0.937008i \(0.386417\pi\)
\(420\) −2.20962e16 −0.196426
\(421\) −1.39873e16 −0.122433 −0.0612166 0.998125i \(-0.519498\pi\)
−0.0612166 + 0.998125i \(0.519498\pi\)
\(422\) −2.28216e17 −1.96705
\(423\) 5.15655e16 0.437670
\(424\) 4.37584e17 3.65749
\(425\) −5.72761e16 −0.471461
\(426\) 2.63268e15 0.0213421
\(427\) −1.01167e16 −0.0807713
\(428\) −4.79406e17 −3.76981
\(429\) 5.92399e15 0.0458819
\(430\) 2.87271e17 2.19152
\(431\) −1.04418e16 −0.0784645 −0.0392322 0.999230i \(-0.512491\pi\)
−0.0392322 + 0.999230i \(0.512491\pi\)
\(432\) 4.59624e16 0.340219
\(433\) −1.00051e17 −0.729542 −0.364771 0.931097i \(-0.618853\pi\)
−0.364771 + 0.931097i \(0.618853\pi\)
\(434\) −4.40834e16 −0.316659
\(435\) 6.85837e16 0.485334
\(436\) −2.11938e17 −1.47756
\(437\) −3.33953e17 −2.29380
\(438\) 5.34938e16 0.362011
\(439\) −6.00729e16 −0.400552 −0.200276 0.979740i \(-0.564184\pi\)
−0.200276 + 0.979740i \(0.564184\pi\)
\(440\) −1.22930e17 −0.807637
\(441\) −4.96048e16 −0.321124
\(442\) −6.27864e16 −0.400517
\(443\) −1.05249e17 −0.661599 −0.330799 0.943701i \(-0.607318\pi\)
−0.330799 + 0.943701i \(0.607318\pi\)
\(444\) −1.40493e17 −0.870290
\(445\) 4.22880e16 0.258153
\(446\) −2.74773e17 −1.65309
\(447\) 1.80867e17 1.07241
\(448\) 1.63915e15 0.00957882
\(449\) −2.13071e17 −1.22722 −0.613610 0.789609i \(-0.710283\pi\)
−0.613610 + 0.789609i \(0.710283\pi\)
\(450\) −3.89412e16 −0.221069
\(451\) 5.11837e16 0.286407
\(452\) 5.93106e16 0.327139
\(453\) 3.84868e14 0.00209254
\(454\) −1.25359e17 −0.671879
\(455\) 5.00940e15 0.0264674
\(456\) 4.46557e17 2.32598
\(457\) −1.45809e17 −0.748737 −0.374369 0.927280i \(-0.622141\pi\)
−0.374369 + 0.927280i \(0.622141\pi\)
\(458\) 3.62519e17 1.83529
\(459\) 4.93152e16 0.246149
\(460\) −4.57814e17 −2.25301
\(461\) −3.26903e17 −1.58622 −0.793110 0.609078i \(-0.791539\pi\)
−0.793110 + 0.609078i \(0.791539\pi\)
\(462\) 1.89736e16 0.0907771
\(463\) −2.69753e16 −0.127259 −0.0636297 0.997974i \(-0.520268\pi\)
−0.0636297 + 0.997974i \(0.520268\pi\)
\(464\) 4.02031e17 1.87022
\(465\) 9.19676e16 0.421881
\(466\) −2.28564e17 −1.03395
\(467\) 3.22028e17 1.43660 0.718298 0.695736i \(-0.244922\pi\)
0.718298 + 0.695736i \(0.244922\pi\)
\(468\) −2.95009e16 −0.129789
\(469\) −2.94441e16 −0.127754
\(470\) 4.38669e17 1.87716
\(471\) −1.61860e17 −0.683132
\(472\) −6.96173e16 −0.289797
\(473\) −1.70473e17 −0.699937
\(474\) −2.31574e17 −0.937844
\(475\) −1.67001e17 −0.667130
\(476\) −1.38974e17 −0.547633
\(477\) 1.40900e17 0.547699
\(478\) −7.19039e17 −2.75722
\(479\) 9.04410e16 0.342125 0.171062 0.985260i \(-0.445280\pi\)
0.171062 + 0.985260i \(0.445280\pi\)
\(480\) 1.17365e17 0.437998
\(481\) 3.18509e16 0.117268
\(482\) 6.97635e17 2.53409
\(483\) 3.90762e16 0.140041
\(484\) −5.00786e17 −1.77075
\(485\) 1.77388e17 0.618874
\(486\) 3.35287e16 0.115420
\(487\) −4.00170e17 −1.35927 −0.679635 0.733550i \(-0.737862\pi\)
−0.679635 + 0.733550i \(0.737862\pi\)
\(488\) 2.80285e17 0.939445
\(489\) 5.99895e16 0.198412
\(490\) −4.21990e17 −1.37730
\(491\) 6.56325e16 0.211392 0.105696 0.994398i \(-0.466293\pi\)
0.105696 + 0.994398i \(0.466293\pi\)
\(492\) −2.54890e17 −0.810178
\(493\) 4.31358e17 1.35311
\(494\) −1.83067e17 −0.566742
\(495\) −3.95829e16 −0.120941
\(496\) 5.39104e17 1.62571
\(497\) −1.32110e15 −0.00393205
\(498\) −4.17408e17 −1.22622
\(499\) 2.45836e17 0.712839 0.356419 0.934326i \(-0.383997\pi\)
0.356419 + 0.934326i \(0.383997\pi\)
\(500\) −8.50034e17 −2.43294
\(501\) −1.47417e17 −0.416489
\(502\) −5.91174e17 −1.64870
\(503\) 7.17852e16 0.197626 0.0988128 0.995106i \(-0.468496\pi\)
0.0988128 + 0.995106i \(0.468496\pi\)
\(504\) −5.22521e16 −0.142006
\(505\) −1.65184e17 −0.443174
\(506\) 3.93115e17 1.04122
\(507\) −2.14108e17 −0.559862
\(508\) 1.05949e18 2.73515
\(509\) −5.87961e17 −1.49859 −0.749295 0.662237i \(-0.769607\pi\)
−0.749295 + 0.662237i \(0.769607\pi\)
\(510\) 4.19526e17 1.05573
\(511\) −2.68436e16 −0.0666967
\(512\) −9.16057e17 −2.24734
\(513\) 1.43789e17 0.348308
\(514\) −1.48258e18 −3.54616
\(515\) −5.95850e17 −1.40731
\(516\) 8.48942e17 1.97995
\(517\) −2.60317e17 −0.599534
\(518\) 1.02013e17 0.232013
\(519\) −1.23677e17 −0.277780
\(520\) −1.38787e17 −0.307841
\(521\) 2.11256e17 0.462769 0.231385 0.972862i \(-0.425674\pi\)
0.231385 + 0.972862i \(0.425674\pi\)
\(522\) 2.93274e17 0.634476
\(523\) −1.25075e16 −0.0267246 −0.0133623 0.999911i \(-0.504253\pi\)
−0.0133623 + 0.999911i \(0.504253\pi\)
\(524\) −2.56421e17 −0.541127
\(525\) 1.95410e16 0.0407297
\(526\) −1.14546e18 −2.35816
\(527\) 5.78430e17 1.17620
\(528\) −2.32031e17 −0.466043
\(529\) 3.05587e17 0.606279
\(530\) 1.19864e18 2.34907
\(531\) −2.24165e16 −0.0433963
\(532\) −4.05210e17 −0.774916
\(533\) 5.77858e16 0.109168
\(534\) 1.80830e17 0.337483
\(535\) −7.26215e17 −1.33895
\(536\) 8.15754e17 1.48590
\(537\) 3.58519e17 0.645178
\(538\) 1.99710e18 3.55070
\(539\) 2.50419e17 0.439886
\(540\) 1.97120e17 0.342114
\(541\) −3.49458e17 −0.599256 −0.299628 0.954056i \(-0.596863\pi\)
−0.299628 + 0.954056i \(0.596863\pi\)
\(542\) −2.66104e17 −0.450875
\(543\) −5.72266e17 −0.958074
\(544\) 7.38170e17 1.22113
\(545\) −3.21048e17 −0.524798
\(546\) 2.14209e16 0.0346008
\(547\) 6.74542e17 1.07669 0.538346 0.842724i \(-0.319049\pi\)
0.538346 + 0.842724i \(0.319049\pi\)
\(548\) 7.07899e17 1.11660
\(549\) 9.02505e16 0.140679
\(550\) 1.96586e17 0.302828
\(551\) 1.25772e18 1.91469
\(552\) −1.08262e18 −1.62881
\(553\) 1.16206e17 0.172788
\(554\) 1.65922e18 2.43832
\(555\) −2.12821e17 −0.309108
\(556\) 1.34551e18 1.93152
\(557\) 3.51419e17 0.498616 0.249308 0.968424i \(-0.419797\pi\)
0.249308 + 0.968424i \(0.419797\pi\)
\(558\) 3.93266e17 0.551524
\(559\) −1.92462e17 −0.266790
\(560\) −1.96209e17 −0.268841
\(561\) −2.48957e17 −0.337183
\(562\) −1.06508e17 −0.142592
\(563\) −6.96299e17 −0.921491 −0.460745 0.887532i \(-0.652418\pi\)
−0.460745 + 0.887532i \(0.652418\pi\)
\(564\) 1.29636e18 1.69594
\(565\) 8.98451e16 0.116193
\(566\) 5.08369e17 0.649939
\(567\) −1.68250e16 −0.0212649
\(568\) 3.66014e16 0.0457334
\(569\) 3.66255e17 0.452433 0.226216 0.974077i \(-0.427364\pi\)
0.226216 + 0.974077i \(0.427364\pi\)
\(570\) 1.22322e18 1.49389
\(571\) −3.71004e15 −0.00447965 −0.00223982 0.999997i \(-0.500713\pi\)
−0.00223982 + 0.999997i \(0.500713\pi\)
\(572\) 1.48929e17 0.177789
\(573\) 8.02187e17 0.946827
\(574\) 1.85078e17 0.215987
\(575\) 4.04871e17 0.467171
\(576\) −1.46228e16 −0.0166834
\(577\) 1.15792e18 1.30628 0.653141 0.757236i \(-0.273451\pi\)
0.653141 + 0.757236i \(0.273451\pi\)
\(578\) 1.02569e18 1.14415
\(579\) 6.91046e17 0.762248
\(580\) 1.72419e18 1.88063
\(581\) 2.09458e17 0.225919
\(582\) 7.58535e17 0.809052
\(583\) −7.11303e17 −0.750256
\(584\) 7.43707e17 0.775744
\(585\) −4.46887e16 −0.0460982
\(586\) −2.03786e18 −2.07893
\(587\) −1.85019e18 −1.86667 −0.933337 0.359000i \(-0.883118\pi\)
−0.933337 + 0.359000i \(0.883118\pi\)
\(588\) −1.24706e18 −1.24433
\(589\) 1.68654e18 1.66436
\(590\) −1.90698e17 −0.186126
\(591\) 4.92950e17 0.475866
\(592\) −1.24754e18 −1.19114
\(593\) −1.80740e18 −1.70686 −0.853431 0.521206i \(-0.825482\pi\)
−0.853431 + 0.521206i \(0.825482\pi\)
\(594\) −1.69262e17 −0.158106
\(595\) −2.10521e17 −0.194507
\(596\) 4.54699e18 4.15550
\(597\) −9.19672e17 −0.831381
\(598\) 4.43822e17 0.396872
\(599\) 9.10508e17 0.805396 0.402698 0.915333i \(-0.368072\pi\)
0.402698 + 0.915333i \(0.368072\pi\)
\(600\) −5.41388e17 −0.473724
\(601\) −1.40863e18 −1.21931 −0.609654 0.792668i \(-0.708692\pi\)
−0.609654 + 0.792668i \(0.708692\pi\)
\(602\) −6.16425e17 −0.527841
\(603\) 2.62669e17 0.222508
\(604\) 9.67559e15 0.00810844
\(605\) −7.58602e17 −0.628932
\(606\) −7.06351e17 −0.579360
\(607\) 9.92919e17 0.805726 0.402863 0.915260i \(-0.368015\pi\)
0.402863 + 0.915260i \(0.368015\pi\)
\(608\) 2.15229e18 1.72794
\(609\) −1.47167e17 −0.116896
\(610\) 7.67765e17 0.603371
\(611\) −2.93895e17 −0.228520
\(612\) 1.23978e18 0.953810
\(613\) 2.91842e17 0.222155 0.111077 0.993812i \(-0.464570\pi\)
0.111077 + 0.993812i \(0.464570\pi\)
\(614\) 1.15831e18 0.872431
\(615\) −3.86114e17 −0.287758
\(616\) 2.63784e17 0.194524
\(617\) −1.79700e18 −1.31128 −0.655638 0.755075i \(-0.727600\pi\)
−0.655638 + 0.755075i \(0.727600\pi\)
\(618\) −2.54794e18 −1.83977
\(619\) 5.45005e17 0.389413 0.194707 0.980862i \(-0.437624\pi\)
0.194707 + 0.980862i \(0.437624\pi\)
\(620\) 2.31206e18 1.63476
\(621\) −3.48597e17 −0.243909
\(622\) 3.33987e18 2.31255
\(623\) −9.07417e16 −0.0621777
\(624\) −2.61960e17 −0.177638
\(625\) −7.38381e17 −0.495519
\(626\) −4.35068e18 −2.88951
\(627\) −7.25888e17 −0.477124
\(628\) −4.06917e18 −2.64709
\(629\) −1.33854e18 −0.861791
\(630\) −1.43131e17 −0.0912050
\(631\) −2.83897e18 −1.79048 −0.895242 0.445581i \(-0.852997\pi\)
−0.895242 + 0.445581i \(0.852997\pi\)
\(632\) −3.21950e18 −2.00968
\(633\) −1.02163e18 −0.631206
\(634\) 8.17508e17 0.499933
\(635\) 1.60493e18 0.971467
\(636\) 3.54223e18 2.12229
\(637\) 2.82720e17 0.167668
\(638\) −1.48053e18 −0.869126
\(639\) 1.17855e16 0.00684844
\(640\) −1.44327e18 −0.830189
\(641\) −1.15734e18 −0.659000 −0.329500 0.944156i \(-0.606880\pi\)
−0.329500 + 0.944156i \(0.606880\pi\)
\(642\) −3.10540e18 −1.75041
\(643\) −1.72656e18 −0.963410 −0.481705 0.876333i \(-0.659982\pi\)
−0.481705 + 0.876333i \(0.659982\pi\)
\(644\) 9.82376e17 0.542650
\(645\) 1.28600e18 0.703237
\(646\) 7.69345e18 4.16495
\(647\) 2.77189e18 1.48559 0.742793 0.669521i \(-0.233501\pi\)
0.742793 + 0.669521i \(0.233501\pi\)
\(648\) 4.66139e17 0.247331
\(649\) 1.13165e17 0.0594457
\(650\) 2.21944e17 0.115427
\(651\) −1.97344e17 −0.101613
\(652\) 1.50814e18 0.768831
\(653\) −1.65704e18 −0.836370 −0.418185 0.908362i \(-0.637334\pi\)
−0.418185 + 0.908362i \(0.637334\pi\)
\(654\) −1.37285e18 −0.686067
\(655\) −3.88432e17 −0.192197
\(656\) −2.26336e18 −1.10886
\(657\) 2.39470e17 0.116165
\(658\) −9.41297e17 −0.452125
\(659\) −4.56344e17 −0.217038 −0.108519 0.994094i \(-0.534611\pi\)
−0.108519 + 0.994094i \(0.534611\pi\)
\(660\) −9.95115e17 −0.468638
\(661\) −2.24313e18 −1.04603 −0.523017 0.852323i \(-0.675193\pi\)
−0.523017 + 0.852323i \(0.675193\pi\)
\(662\) 9.73563e16 0.0449559
\(663\) −2.81070e17 −0.128522
\(664\) −5.80309e18 −2.62765
\(665\) −6.13821e17 −0.275233
\(666\) −9.10054e17 −0.404096
\(667\) −3.04916e18 −1.34080
\(668\) −3.70607e18 −1.61386
\(669\) −1.23005e18 −0.530460
\(670\) 2.23454e18 0.954336
\(671\) −4.55610e17 −0.192707
\(672\) −2.51843e17 −0.105494
\(673\) −1.26622e18 −0.525304 −0.262652 0.964891i \(-0.584597\pi\)
−0.262652 + 0.964891i \(0.584597\pi\)
\(674\) 3.26359e18 1.34093
\(675\) −1.74324e17 −0.0709387
\(676\) −5.38267e18 −2.16942
\(677\) 3.19946e18 1.27717 0.638587 0.769550i \(-0.279519\pi\)
0.638587 + 0.769550i \(0.279519\pi\)
\(678\) 3.84190e17 0.151898
\(679\) −3.80638e17 −0.149059
\(680\) 5.83254e18 2.26230
\(681\) −5.61181e17 −0.215599
\(682\) −1.98532e18 −0.755496
\(683\) −2.21315e18 −0.834212 −0.417106 0.908858i \(-0.636956\pi\)
−0.417106 + 0.908858i \(0.636956\pi\)
\(684\) 3.61486e18 1.34967
\(685\) 1.07234e18 0.396592
\(686\) 1.84544e18 0.676072
\(687\) 1.62285e18 0.588925
\(688\) 7.53838e18 2.70990
\(689\) −8.03053e17 −0.285969
\(690\) −2.96553e18 −1.04612
\(691\) 3.58037e18 1.25118 0.625591 0.780151i \(-0.284858\pi\)
0.625591 + 0.780151i \(0.284858\pi\)
\(692\) −3.10924e18 −1.07638
\(693\) 8.49371e16 0.0291294
\(694\) −4.45818e18 −1.51468
\(695\) 2.03821e18 0.686036
\(696\) 4.07729e18 1.35960
\(697\) −2.42846e18 −0.802266
\(698\) 1.20512e18 0.394431
\(699\) −1.02319e18 −0.331784
\(700\) 4.91261e17 0.157825
\(701\) −8.45015e17 −0.268966 −0.134483 0.990916i \(-0.542937\pi\)
−0.134483 + 0.990916i \(0.542937\pi\)
\(702\) −1.91095e17 −0.0602641
\(703\) −3.90280e18 −1.21946
\(704\) 7.38200e16 0.0228535
\(705\) 1.96375e18 0.602360
\(706\) −5.51355e18 −1.67572
\(707\) 3.54452e17 0.106741
\(708\) −5.63550e17 −0.168157
\(709\) 1.87350e18 0.553928 0.276964 0.960880i \(-0.410672\pi\)
0.276964 + 0.960880i \(0.410672\pi\)
\(710\) 1.00260e17 0.0293729
\(711\) −1.03667e18 −0.300944
\(712\) 2.51402e18 0.723183
\(713\) −4.08878e18 −1.16550
\(714\) −9.00220e17 −0.254279
\(715\) 2.25601e17 0.0631469
\(716\) 9.01317e18 2.50002
\(717\) −3.21885e18 −0.884762
\(718\) −4.15669e18 −1.13224
\(719\) −2.95003e17 −0.0796322 −0.0398161 0.999207i \(-0.512677\pi\)
−0.0398161 + 0.999207i \(0.512677\pi\)
\(720\) 1.75037e18 0.468240
\(721\) 1.27858e18 0.338959
\(722\) 1.55837e19 4.09430
\(723\) 3.12303e18 0.813163
\(724\) −1.43868e19 −3.71247
\(725\) −1.52481e18 −0.389958
\(726\) −3.24389e18 −0.822201
\(727\) 1.45871e18 0.366435 0.183217 0.983072i \(-0.441349\pi\)
0.183217 + 0.983072i \(0.441349\pi\)
\(728\) 2.97808e17 0.0741452
\(729\) 1.50095e17 0.0370370
\(730\) 2.03718e18 0.498232
\(731\) 8.08828e18 1.96062
\(732\) 2.26890e18 0.545121
\(733\) 1.93655e17 0.0461161 0.0230581 0.999734i \(-0.492660\pi\)
0.0230581 + 0.999734i \(0.492660\pi\)
\(734\) 5.05562e18 1.19330
\(735\) −1.88908e18 −0.441960
\(736\) −5.21794e18 −1.21002
\(737\) −1.32603e18 −0.304799
\(738\) −1.65108e18 −0.376184
\(739\) 4.83038e18 1.09092 0.545459 0.838138i \(-0.316355\pi\)
0.545459 + 0.838138i \(0.316355\pi\)
\(740\) −5.35033e18 −1.19777
\(741\) −8.19519e17 −0.181862
\(742\) −2.57205e18 −0.565788
\(743\) 1.58218e18 0.345009 0.172504 0.985009i \(-0.444814\pi\)
0.172504 + 0.985009i \(0.444814\pi\)
\(744\) 5.46746e18 1.18185
\(745\) 6.88788e18 1.47594
\(746\) 1.11801e18 0.237488
\(747\) −1.86857e18 −0.393482
\(748\) −6.25878e18 −1.30656
\(749\) 1.55831e18 0.322495
\(750\) −5.50618e18 −1.12967
\(751\) 4.08665e17 0.0831205 0.0415602 0.999136i \(-0.486767\pi\)
0.0415602 + 0.999136i \(0.486767\pi\)
\(752\) 1.15113e19 2.32117
\(753\) −2.64645e18 −0.529049
\(754\) −1.67150e18 −0.331278
\(755\) 1.46568e16 0.00287994
\(756\) −4.22979e17 −0.0824000
\(757\) 8.55834e18 1.65298 0.826488 0.562955i \(-0.190335\pi\)
0.826488 + 0.562955i \(0.190335\pi\)
\(758\) 5.49393e18 1.05204
\(759\) 1.75982e18 0.334115
\(760\) 1.70060e19 3.20122
\(761\) 7.22831e18 1.34908 0.674538 0.738240i \(-0.264343\pi\)
0.674538 + 0.738240i \(0.264343\pi\)
\(762\) 6.86293e18 1.26999
\(763\) 6.88904e17 0.126401
\(764\) 2.01670e19 3.66888
\(765\) 1.87805e18 0.338773
\(766\) −4.44623e18 −0.795252
\(767\) 1.27762e17 0.0226585
\(768\) −6.00730e18 −1.05641
\(769\) −1.04746e19 −1.82648 −0.913242 0.407417i \(-0.866430\pi\)
−0.913242 + 0.407417i \(0.866430\pi\)
\(770\) 7.22563e17 0.124936
\(771\) −6.63693e18 −1.13793
\(772\) 1.73729e19 2.95365
\(773\) 7.19454e18 1.21293 0.606466 0.795110i \(-0.292587\pi\)
0.606466 + 0.795110i \(0.292587\pi\)
\(774\) 5.49910e18 0.919339
\(775\) −2.04469e18 −0.338975
\(776\) 1.05457e19 1.73370
\(777\) 4.56672e17 0.0744505
\(778\) −1.48138e19 −2.39497
\(779\) −7.08071e18 −1.13523
\(780\) −1.12347e18 −0.178627
\(781\) −5.94964e16 −0.00938122
\(782\) −1.86517e19 −2.91659
\(783\) 1.31287e18 0.203597
\(784\) −1.10736e19 −1.70308
\(785\) −6.16407e18 −0.940188
\(786\) −1.66099e18 −0.251258
\(787\) −9.23676e17 −0.138575 −0.0692873 0.997597i \(-0.522073\pi\)
−0.0692873 + 0.997597i \(0.522073\pi\)
\(788\) 1.23928e19 1.84395
\(789\) −5.12779e18 −0.756710
\(790\) −8.81895e18 −1.29075
\(791\) −1.92790e17 −0.0279857
\(792\) −2.35320e18 −0.338802
\(793\) −5.14378e17 −0.0734526
\(794\) 7.17829e18 1.01669
\(795\) 5.36585e18 0.753792
\(796\) −2.31206e19 −3.22154
\(797\) 1.02280e19 1.41355 0.706777 0.707436i \(-0.250148\pi\)
0.706777 + 0.707436i \(0.250148\pi\)
\(798\) −2.62479e18 −0.359812
\(799\) 1.23510e19 1.67938
\(800\) −2.60936e18 −0.351924
\(801\) 8.09502e17 0.108295
\(802\) −8.92729e18 −1.18464
\(803\) −1.20891e18 −0.159127
\(804\) 6.60350e18 0.862204
\(805\) 1.48813e18 0.192738
\(806\) −2.24140e18 −0.287967
\(807\) 8.94020e18 1.13938
\(808\) −9.82017e18 −1.24150
\(809\) −2.79977e18 −0.351121 −0.175560 0.984469i \(-0.556174\pi\)
−0.175560 + 0.984469i \(0.556174\pi\)
\(810\) 1.27686e18 0.158851
\(811\) 4.99698e18 0.616697 0.308348 0.951273i \(-0.400224\pi\)
0.308348 + 0.951273i \(0.400224\pi\)
\(812\) −3.69978e18 −0.452962
\(813\) −1.19124e18 −0.144681
\(814\) 4.59421e18 0.553544
\(815\) 2.28456e18 0.273072
\(816\) 1.10090e19 1.30545
\(817\) 2.35831e19 2.77433
\(818\) −1.42876e19 −1.66749
\(819\) 9.58930e16 0.0111030
\(820\) −9.70689e18 −1.11504
\(821\) 8.44738e18 0.962701 0.481350 0.876528i \(-0.340146\pi\)
0.481350 + 0.876528i \(0.340146\pi\)
\(822\) 4.58548e18 0.518463
\(823\) −1.22309e19 −1.37201 −0.686007 0.727594i \(-0.740638\pi\)
−0.686007 + 0.727594i \(0.740638\pi\)
\(824\) −3.54232e19 −3.94240
\(825\) 8.80038e17 0.0971742
\(826\) 4.09199e17 0.0448296
\(827\) 5.16881e18 0.561830 0.280915 0.959733i \(-0.409362\pi\)
0.280915 + 0.959733i \(0.409362\pi\)
\(828\) −8.76374e18 −0.945131
\(829\) 6.02973e18 0.645199 0.322600 0.946536i \(-0.395443\pi\)
0.322600 + 0.946536i \(0.395443\pi\)
\(830\) −1.58960e19 −1.68764
\(831\) 7.42768e18 0.782431
\(832\) 8.33419e16 0.00871088
\(833\) −1.18814e19 −1.23218
\(834\) 8.71566e18 0.896852
\(835\) −5.61404e18 −0.573209
\(836\) −1.82488e19 −1.84882
\(837\) 1.76050e18 0.176978
\(838\) 1.26011e19 1.25696
\(839\) 2.15630e18 0.213430 0.106715 0.994290i \(-0.465967\pi\)
0.106715 + 0.994290i \(0.465967\pi\)
\(840\) −1.98990e18 −0.195441
\(841\) 1.22298e18 0.119191
\(842\) −2.27778e18 −0.220284
\(843\) −4.76793e17 −0.0457563
\(844\) −2.56839e19 −2.44588
\(845\) −8.15379e18 −0.770532
\(846\) 8.39727e18 0.787464
\(847\) 1.62781e18 0.151482
\(848\) 3.14540e19 2.90471
\(849\) 2.27577e18 0.208558
\(850\) −9.32723e18 −0.848262
\(851\) 9.46182e18 0.853950
\(852\) 2.96287e17 0.0265372
\(853\) −1.52135e19 −1.35226 −0.676132 0.736780i \(-0.736345\pi\)
−0.676132 + 0.736780i \(0.736345\pi\)
\(854\) −1.64747e18 −0.145325
\(855\) 5.47587e18 0.479373
\(856\) −4.31734e19 −3.75091
\(857\) 5.10916e18 0.440529 0.220264 0.975440i \(-0.429308\pi\)
0.220264 + 0.975440i \(0.429308\pi\)
\(858\) 9.64702e17 0.0825517
\(859\) 1.71058e19 1.45274 0.726372 0.687302i \(-0.241205\pi\)
0.726372 + 0.687302i \(0.241205\pi\)
\(860\) 3.23299e19 2.72499
\(861\) 8.28523e17 0.0693081
\(862\) −1.70041e18 −0.141175
\(863\) −8.30852e18 −0.684626 −0.342313 0.939586i \(-0.611210\pi\)
−0.342313 + 0.939586i \(0.611210\pi\)
\(864\) 2.24668e18 0.183739
\(865\) −4.70994e18 −0.382306
\(866\) −1.62930e19 −1.31261
\(867\) 4.59158e18 0.367146
\(868\) −4.96123e18 −0.393741
\(869\) 5.23338e18 0.412243
\(870\) 1.11686e19 0.873223
\(871\) −1.49707e18 −0.116178
\(872\) −1.90862e19 −1.47016
\(873\) 3.39566e18 0.259616
\(874\) −5.43831e19 −4.12705
\(875\) 2.76304e18 0.208130
\(876\) 6.02028e18 0.450132
\(877\) 8.52752e18 0.632886 0.316443 0.948612i \(-0.397511\pi\)
0.316443 + 0.948612i \(0.397511\pi\)
\(878\) −9.78267e18 −0.720681
\(879\) −9.12267e18 −0.667105
\(880\) −8.83635e18 −0.641410
\(881\) 2.06956e18 0.149120 0.0745598 0.997217i \(-0.476245\pi\)
0.0745598 + 0.997217i \(0.476245\pi\)
\(882\) −8.07798e18 −0.577772
\(883\) 3.49059e18 0.247830 0.123915 0.992293i \(-0.460455\pi\)
0.123915 + 0.992293i \(0.460455\pi\)
\(884\) −7.06609e18 −0.498012
\(885\) −8.53678e17 −0.0597259
\(886\) −1.71395e19 −1.19036
\(887\) 6.91170e18 0.476520 0.238260 0.971201i \(-0.423423\pi\)
0.238260 + 0.971201i \(0.423423\pi\)
\(888\) −1.26522e19 −0.865928
\(889\) −3.44387e18 −0.233983
\(890\) 6.88647e18 0.464474
\(891\) −7.57720e17 −0.0507345
\(892\) −3.09234e19 −2.05549
\(893\) 3.60120e19 2.37636
\(894\) 2.94535e19 1.92950
\(895\) 1.36534e19 0.887952
\(896\) 3.09696e18 0.199956
\(897\) 1.98681e18 0.127352
\(898\) −3.46979e19 −2.20804
\(899\) 1.53990e19 0.972868
\(900\) −4.38251e18 −0.274882
\(901\) 3.37485e19 2.10157
\(902\) 8.33510e18 0.515310
\(903\) −2.75949e18 −0.169379
\(904\) 5.34128e18 0.325500
\(905\) −2.17934e19 −1.31859
\(906\) 6.26746e16 0.00376494
\(907\) −1.77163e18 −0.105663 −0.0528317 0.998603i \(-0.516825\pi\)
−0.0528317 + 0.998603i \(0.516825\pi\)
\(908\) −1.41081e19 −0.835430
\(909\) −3.16205e18 −0.185910
\(910\) 8.15765e17 0.0476207
\(911\) 2.60354e19 1.50902 0.754509 0.656289i \(-0.227875\pi\)
0.754509 + 0.656289i \(0.227875\pi\)
\(912\) 3.20990e19 1.84725
\(913\) 9.43307e18 0.539005
\(914\) −2.37445e19 −1.34714
\(915\) 3.43698e18 0.193615
\(916\) 4.07985e19 2.28204
\(917\) 8.33496e17 0.0462917
\(918\) 8.03082e18 0.442876
\(919\) −1.43989e19 −0.788457 −0.394228 0.919012i \(-0.628988\pi\)
−0.394228 + 0.919012i \(0.628988\pi\)
\(920\) −4.12288e19 −2.24171
\(921\) 5.18530e18 0.279954
\(922\) −5.32352e19 −2.85396
\(923\) −6.71708e16 −0.00357577
\(924\) 2.13532e18 0.112874
\(925\) 4.73160e18 0.248363
\(926\) −4.39284e18 −0.228967
\(927\) −1.14061e19 −0.590363
\(928\) 1.96516e19 1.01003
\(929\) 1.78752e19 0.912323 0.456162 0.889897i \(-0.349224\pi\)
0.456162 + 0.889897i \(0.349224\pi\)
\(930\) 1.49766e19 0.759057
\(931\) −3.46427e19 −1.74357
\(932\) −2.57230e19 −1.28564
\(933\) 1.49513e19 0.742073
\(934\) 5.24413e19 2.58475
\(935\) −9.48094e18 −0.464062
\(936\) −2.65674e18 −0.129138
\(937\) −2.91622e19 −1.40771 −0.703855 0.710343i \(-0.748540\pi\)
−0.703855 + 0.710343i \(0.748540\pi\)
\(938\) −4.79487e18 −0.229857
\(939\) −1.94763e19 −0.927212
\(940\) 4.93686e19 2.33410
\(941\) 6.10375e18 0.286592 0.143296 0.989680i \(-0.454230\pi\)
0.143296 + 0.989680i \(0.454230\pi\)
\(942\) −2.63584e19 −1.22910
\(943\) 1.71662e19 0.794966
\(944\) −5.00417e18 −0.230152
\(945\) −6.40738e17 −0.0292667
\(946\) −2.77610e19 −1.25934
\(947\) 3.52519e19 1.58821 0.794104 0.607782i \(-0.207940\pi\)
0.794104 + 0.607782i \(0.207940\pi\)
\(948\) −2.60618e19 −1.16614
\(949\) −1.36485e18 −0.0606533
\(950\) −2.71956e19 −1.20031
\(951\) 3.65966e18 0.160423
\(952\) −1.25155e19 −0.544888
\(953\) 6.76761e18 0.292638 0.146319 0.989237i \(-0.453257\pi\)
0.146319 + 0.989237i \(0.453257\pi\)
\(954\) 2.29451e19 0.985430
\(955\) 3.05494e19 1.30311
\(956\) −8.09219e19 −3.42839
\(957\) −6.62774e18 −0.278893
\(958\) 1.47280e19 0.615557
\(959\) −2.30103e18 −0.0955215
\(960\) −5.56875e17 −0.0229612
\(961\) −3.76824e18 −0.154325
\(962\) 5.18681e18 0.210990
\(963\) −1.39016e19 −0.561688
\(964\) 7.85131e19 3.15095
\(965\) 2.63168e19 1.04907
\(966\) 6.36344e18 0.251965
\(967\) 4.30947e19 1.69493 0.847464 0.530853i \(-0.178128\pi\)
0.847464 + 0.530853i \(0.178128\pi\)
\(968\) −4.50988e19 −1.76187
\(969\) 3.44405e19 1.33649
\(970\) 2.88870e19 1.11349
\(971\) 1.27778e18 0.0489248 0.0244624 0.999701i \(-0.492213\pi\)
0.0244624 + 0.999701i \(0.492213\pi\)
\(972\) 3.77338e18 0.143516
\(973\) −4.37358e18 −0.165236
\(974\) −6.51663e19 −2.44563
\(975\) 9.93553e17 0.0370391
\(976\) 2.01472e19 0.746090
\(977\) −2.44489e19 −0.899385 −0.449692 0.893184i \(-0.648466\pi\)
−0.449692 + 0.893184i \(0.648466\pi\)
\(978\) 9.76909e18 0.356986
\(979\) −4.08660e18 −0.148345
\(980\) −4.74915e19 −1.71256
\(981\) −6.14568e18 −0.220151
\(982\) 1.06880e19 0.380341
\(983\) 2.72043e19 0.961699 0.480849 0.876803i \(-0.340328\pi\)
0.480849 + 0.876803i \(0.340328\pi\)
\(984\) −2.29544e19 −0.806117
\(985\) 1.87728e19 0.654929
\(986\) 7.02452e19 2.43454
\(987\) −4.21381e18 −0.145082
\(988\) −2.06027e19 −0.704700
\(989\) −5.71741e19 −1.94278
\(990\) −6.44595e18 −0.217600
\(991\) 2.65383e19 0.890008 0.445004 0.895529i \(-0.353202\pi\)
0.445004 + 0.895529i \(0.353202\pi\)
\(992\) 2.63518e19 0.877980
\(993\) 4.35825e17 0.0144259
\(994\) −2.15137e17 −0.00707463
\(995\) −3.50235e19 −1.14422
\(996\) −4.69758e19 −1.52472
\(997\) 5.24836e19 1.69241 0.846205 0.532858i \(-0.178882\pi\)
0.846205 + 0.532858i \(0.178882\pi\)
\(998\) 4.00335e19 1.28255
\(999\) −4.07395e18 −0.129670
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.1.29 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.29 31 1.1 even 1 trivial