Properties

Label 177.14.a.c.1.17
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 1.17
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+28.6118 q^{2} +729.000 q^{3} -7373.36 q^{4} +60045.3 q^{5} +20858.0 q^{6} +428045. q^{7} -445354. q^{8} +531441. q^{9} +O(q^{10})\) \(q+28.6118 q^{2} +729.000 q^{3} -7373.36 q^{4} +60045.3 q^{5} +20858.0 q^{6} +428045. q^{7} -445354. q^{8} +531441. q^{9} +1.71801e6 q^{10} -5.05028e6 q^{11} -5.37518e6 q^{12} +8.30885e6 q^{13} +1.22472e7 q^{14} +4.37730e7 q^{15} +4.76602e7 q^{16} -3.21092e7 q^{17} +1.52055e7 q^{18} +9.20230e7 q^{19} -4.42736e8 q^{20} +3.12045e8 q^{21} -1.44498e8 q^{22} +2.82456e8 q^{23} -3.24663e8 q^{24} +2.38473e9 q^{25} +2.37732e8 q^{26} +3.87420e8 q^{27} -3.15613e9 q^{28} -1.86463e9 q^{29} +1.25243e9 q^{30} -1.29741e9 q^{31} +5.01198e9 q^{32} -3.68166e9 q^{33} -9.18703e8 q^{34} +2.57021e10 q^{35} -3.91851e9 q^{36} -5.91028e9 q^{37} +2.63295e9 q^{38} +6.05716e9 q^{39} -2.67414e10 q^{40} +4.67448e10 q^{41} +8.92817e9 q^{42} +5.00850e10 q^{43} +3.72376e10 q^{44} +3.19105e10 q^{45} +8.08158e9 q^{46} +5.50206e10 q^{47} +3.47443e10 q^{48} +8.63335e10 q^{49} +6.82315e10 q^{50} -2.34076e10 q^{51} -6.12642e10 q^{52} -5.12531e10 q^{53} +1.10848e10 q^{54} -3.03246e11 q^{55} -1.90631e11 q^{56} +6.70848e10 q^{57} -5.33504e10 q^{58} -4.21805e10 q^{59} -3.22754e11 q^{60} +4.21271e11 q^{61} -3.71212e10 q^{62} +2.27481e11 q^{63} -2.47031e11 q^{64} +4.98907e11 q^{65} -1.05339e11 q^{66} -6.77755e9 q^{67} +2.36753e11 q^{68} +2.05910e11 q^{69} +7.35384e11 q^{70} +6.84243e11 q^{71} -2.36679e11 q^{72} -1.74954e12 q^{73} -1.69104e11 q^{74} +1.73847e12 q^{75} -6.78519e11 q^{76} -2.16175e12 q^{77} +1.73306e11 q^{78} -4.15612e12 q^{79} +2.86177e12 q^{80} +2.82430e11 q^{81} +1.33745e12 q^{82} +1.01331e12 q^{83} -2.30082e12 q^{84} -1.92801e12 q^{85} +1.43302e12 q^{86} -1.35931e12 q^{87} +2.24916e12 q^{88} -4.21516e12 q^{89} +9.13018e11 q^{90} +3.55656e12 q^{91} -2.08265e12 q^{92} -9.45810e11 q^{93} +1.57424e12 q^{94} +5.52555e12 q^{95} +3.65373e12 q^{96} -3.08119e12 q^{97} +2.47016e12 q^{98} -2.68393e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 28.6118 0.316119 0.158060 0.987430i \(-0.449476\pi\)
0.158060 + 0.987430i \(0.449476\pi\)
\(3\) 729.000 0.577350
\(4\) −7373.36 −0.900069
\(5\) 60045.3 1.71860 0.859298 0.511475i \(-0.170901\pi\)
0.859298 + 0.511475i \(0.170901\pi\)
\(6\) 20858.0 0.182511
\(7\) 428045. 1.37516 0.687578 0.726110i \(-0.258674\pi\)
0.687578 + 0.726110i \(0.258674\pi\)
\(8\) −445354. −0.600648
\(9\) 531441. 0.333333
\(10\) 1.71801e6 0.543281
\(11\) −5.05028e6 −0.859535 −0.429767 0.902940i \(-0.641404\pi\)
−0.429767 + 0.902940i \(0.641404\pi\)
\(12\) −5.37518e6 −0.519655
\(13\) 8.30885e6 0.477430 0.238715 0.971090i \(-0.423274\pi\)
0.238715 + 0.971090i \(0.423274\pi\)
\(14\) 1.22472e7 0.434713
\(15\) 4.37730e7 0.992232
\(16\) 4.76602e7 0.710193
\(17\) −3.21092e7 −0.322635 −0.161318 0.986903i \(-0.551574\pi\)
−0.161318 + 0.986903i \(0.551574\pi\)
\(18\) 1.52055e7 0.105373
\(19\) 9.20230e7 0.448744 0.224372 0.974504i \(-0.427967\pi\)
0.224372 + 0.974504i \(0.427967\pi\)
\(20\) −4.42736e8 −1.54685
\(21\) 3.12045e8 0.793947
\(22\) −1.44498e8 −0.271715
\(23\) 2.82456e8 0.397851 0.198925 0.980015i \(-0.436255\pi\)
0.198925 + 0.980015i \(0.436255\pi\)
\(24\) −3.24663e8 −0.346784
\(25\) 2.38473e9 1.95357
\(26\) 2.37732e8 0.150925
\(27\) 3.87420e8 0.192450
\(28\) −3.15613e9 −1.23774
\(29\) −1.86463e9 −0.582110 −0.291055 0.956706i \(-0.594006\pi\)
−0.291055 + 0.956706i \(0.594006\pi\)
\(30\) 1.25243e9 0.313663
\(31\) −1.29741e9 −0.262558 −0.131279 0.991345i \(-0.541908\pi\)
−0.131279 + 0.991345i \(0.541908\pi\)
\(32\) 5.01198e9 0.825153
\(33\) −3.68166e9 −0.496253
\(34\) −9.18703e8 −0.101991
\(35\) 2.57021e10 2.36334
\(36\) −3.91851e9 −0.300023
\(37\) −5.91028e9 −0.378701 −0.189351 0.981910i \(-0.560638\pi\)
−0.189351 + 0.981910i \(0.560638\pi\)
\(38\) 2.63295e9 0.141856
\(39\) 6.05716e9 0.275644
\(40\) −2.67414e10 −1.03227
\(41\) 4.67448e10 1.53687 0.768437 0.639926i \(-0.221035\pi\)
0.768437 + 0.639926i \(0.221035\pi\)
\(42\) 8.92817e9 0.250982
\(43\) 5.00850e10 1.20827 0.604134 0.796883i \(-0.293519\pi\)
0.604134 + 0.796883i \(0.293519\pi\)
\(44\) 3.72376e10 0.773640
\(45\) 3.19105e10 0.572865
\(46\) 8.08158e9 0.125768
\(47\) 5.50206e10 0.744542 0.372271 0.928124i \(-0.378579\pi\)
0.372271 + 0.928124i \(0.378579\pi\)
\(48\) 3.47443e10 0.410030
\(49\) 8.63335e10 0.891056
\(50\) 6.82315e10 0.617561
\(51\) −2.34076e10 −0.186273
\(52\) −6.12642e10 −0.429720
\(53\) −5.12531e10 −0.317634 −0.158817 0.987308i \(-0.550768\pi\)
−0.158817 + 0.987308i \(0.550768\pi\)
\(54\) 1.10848e10 0.0608371
\(55\) −3.03246e11 −1.47719
\(56\) −1.90631e11 −0.825985
\(57\) 6.70848e10 0.259082
\(58\) −5.33504e10 −0.184016
\(59\) −4.21805e10 −0.130189
\(60\) −3.22754e11 −0.893077
\(61\) 4.21271e11 1.04693 0.523465 0.852047i \(-0.324639\pi\)
0.523465 + 0.852047i \(0.324639\pi\)
\(62\) −3.71212e10 −0.0829996
\(63\) 2.27481e11 0.458386
\(64\) −2.47031e11 −0.449346
\(65\) 4.98907e11 0.820509
\(66\) −1.05339e11 −0.156875
\(67\) −6.77755e9 −0.00915348 −0.00457674 0.999990i \(-0.501457\pi\)
−0.00457674 + 0.999990i \(0.501457\pi\)
\(68\) 2.36753e11 0.290394
\(69\) 2.05910e11 0.229699
\(70\) 7.35384e11 0.747096
\(71\) 6.84243e11 0.633915 0.316958 0.948440i \(-0.397339\pi\)
0.316958 + 0.948440i \(0.397339\pi\)
\(72\) −2.36679e11 −0.200216
\(73\) −1.74954e12 −1.35308 −0.676542 0.736404i \(-0.736522\pi\)
−0.676542 + 0.736404i \(0.736522\pi\)
\(74\) −1.69104e11 −0.119715
\(75\) 1.73847e12 1.12790
\(76\) −6.78519e11 −0.403900
\(77\) −2.16175e12 −1.18199
\(78\) 1.73306e11 0.0871364
\(79\) −4.15612e12 −1.92359 −0.961794 0.273773i \(-0.911728\pi\)
−0.961794 + 0.273773i \(0.911728\pi\)
\(80\) 2.86177e12 1.22053
\(81\) 2.82430e11 0.111111
\(82\) 1.33745e12 0.485835
\(83\) 1.01331e12 0.340201 0.170101 0.985427i \(-0.445591\pi\)
0.170101 + 0.985427i \(0.445591\pi\)
\(84\) −2.30082e12 −0.714607
\(85\) −1.92801e12 −0.554479
\(86\) 1.43302e12 0.381956
\(87\) −1.35931e12 −0.336081
\(88\) 2.24916e12 0.516278
\(89\) −4.21516e12 −0.899039 −0.449520 0.893270i \(-0.648405\pi\)
−0.449520 + 0.893270i \(0.648405\pi\)
\(90\) 9.13018e11 0.181094
\(91\) 3.55656e12 0.656541
\(92\) −2.08265e12 −0.358093
\(93\) −9.45810e11 −0.151588
\(94\) 1.57424e12 0.235364
\(95\) 5.52555e12 0.771209
\(96\) 3.65373e12 0.476402
\(97\) −3.08119e12 −0.375580 −0.187790 0.982209i \(-0.560132\pi\)
−0.187790 + 0.982209i \(0.560132\pi\)
\(98\) 2.47016e12 0.281680
\(99\) −2.68393e12 −0.286512
\(100\) −1.75835e13 −1.75835
\(101\) 3.98600e12 0.373635 0.186818 0.982395i \(-0.440183\pi\)
0.186818 + 0.982395i \(0.440183\pi\)
\(102\) −6.69734e11 −0.0588846
\(103\) −6.75982e12 −0.557818 −0.278909 0.960317i \(-0.589973\pi\)
−0.278909 + 0.960317i \(0.589973\pi\)
\(104\) −3.70038e12 −0.286767
\(105\) 1.87368e13 1.36447
\(106\) −1.46644e12 −0.100410
\(107\) 1.94180e13 1.25086 0.625432 0.780279i \(-0.284923\pi\)
0.625432 + 0.780279i \(0.284923\pi\)
\(108\) −2.85659e12 −0.173218
\(109\) 3.32706e13 1.90015 0.950076 0.312018i \(-0.101005\pi\)
0.950076 + 0.312018i \(0.101005\pi\)
\(110\) −8.67642e12 −0.466969
\(111\) −4.30859e12 −0.218643
\(112\) 2.04007e13 0.976626
\(113\) 2.33760e13 1.05623 0.528116 0.849172i \(-0.322899\pi\)
0.528116 + 0.849172i \(0.322899\pi\)
\(114\) 1.91942e12 0.0819008
\(115\) 1.69602e13 0.683744
\(116\) 1.37486e13 0.523939
\(117\) 4.41567e12 0.159143
\(118\) −1.20686e12 −0.0411552
\(119\) −1.37442e13 −0.443674
\(120\) −1.94945e13 −0.595982
\(121\) −9.01734e12 −0.261200
\(122\) 1.20533e13 0.330955
\(123\) 3.40769e13 0.887314
\(124\) 9.56625e12 0.236320
\(125\) 6.98944e13 1.63881
\(126\) 6.50864e12 0.144904
\(127\) −2.01180e13 −0.425461 −0.212730 0.977111i \(-0.568236\pi\)
−0.212730 + 0.977111i \(0.568236\pi\)
\(128\) −4.81261e13 −0.967200
\(129\) 3.65120e13 0.697593
\(130\) 1.42747e13 0.259378
\(131\) −1.03263e14 −1.78517 −0.892587 0.450876i \(-0.851112\pi\)
−0.892587 + 0.450876i \(0.851112\pi\)
\(132\) 2.71462e13 0.446661
\(133\) 3.93900e13 0.617093
\(134\) −1.93918e11 −0.00289359
\(135\) 2.32628e13 0.330744
\(136\) 1.42999e13 0.193790
\(137\) −3.98625e13 −0.515088 −0.257544 0.966267i \(-0.582913\pi\)
−0.257544 + 0.966267i \(0.582913\pi\)
\(138\) 5.89148e12 0.0726123
\(139\) 8.28297e13 0.974069 0.487035 0.873383i \(-0.338079\pi\)
0.487035 + 0.873383i \(0.338079\pi\)
\(140\) −1.89511e14 −2.12717
\(141\) 4.01100e13 0.429862
\(142\) 1.95774e13 0.200393
\(143\) −4.19621e13 −0.410367
\(144\) 2.53286e13 0.236731
\(145\) −1.11962e14 −1.00041
\(146\) −5.00575e13 −0.427735
\(147\) 6.29371e13 0.514451
\(148\) 4.35786e13 0.340857
\(149\) 1.89703e14 1.42024 0.710122 0.704079i \(-0.248640\pi\)
0.710122 + 0.704079i \(0.248640\pi\)
\(150\) 4.97408e13 0.356549
\(151\) 4.48388e12 0.0307825 0.0153913 0.999882i \(-0.495101\pi\)
0.0153913 + 0.999882i \(0.495101\pi\)
\(152\) −4.09828e13 −0.269537
\(153\) −1.70641e13 −0.107545
\(154\) −6.18516e13 −0.373651
\(155\) −7.79032e13 −0.451231
\(156\) −4.46616e13 −0.248099
\(157\) 1.71354e14 0.913159 0.456579 0.889683i \(-0.349074\pi\)
0.456579 + 0.889683i \(0.349074\pi\)
\(158\) −1.18914e14 −0.608083
\(159\) −3.73635e13 −0.183386
\(160\) 3.00946e14 1.41811
\(161\) 1.20904e14 0.547107
\(162\) 8.08083e12 0.0351243
\(163\) 3.63350e14 1.51742 0.758709 0.651429i \(-0.225830\pi\)
0.758709 + 0.651429i \(0.225830\pi\)
\(164\) −3.44666e14 −1.38329
\(165\) −2.21066e14 −0.852858
\(166\) 2.89927e13 0.107544
\(167\) −2.08346e14 −0.743240 −0.371620 0.928385i \(-0.621197\pi\)
−0.371620 + 0.928385i \(0.621197\pi\)
\(168\) −1.38970e14 −0.476883
\(169\) −2.33838e14 −0.772061
\(170\) −5.51638e13 −0.175281
\(171\) 4.89048e13 0.149581
\(172\) −3.69295e14 −1.08752
\(173\) 1.06883e14 0.303115 0.151558 0.988448i \(-0.451571\pi\)
0.151558 + 0.988448i \(0.451571\pi\)
\(174\) −3.88924e13 −0.106242
\(175\) 1.02077e15 2.68647
\(176\) −2.40698e14 −0.610435
\(177\) −3.07496e13 −0.0751646
\(178\) −1.20603e14 −0.284203
\(179\) 7.38037e13 0.167700 0.0838501 0.996478i \(-0.473278\pi\)
0.0838501 + 0.996478i \(0.473278\pi\)
\(180\) −2.35288e14 −0.515618
\(181\) 4.34002e13 0.0917446 0.0458723 0.998947i \(-0.485393\pi\)
0.0458723 + 0.998947i \(0.485393\pi\)
\(182\) 1.01760e14 0.207545
\(183\) 3.07107e14 0.604445
\(184\) −1.25793e14 −0.238968
\(185\) −3.54884e14 −0.650834
\(186\) −2.70613e13 −0.0479198
\(187\) 1.62161e14 0.277316
\(188\) −4.05687e14 −0.670139
\(189\) 1.65833e14 0.264649
\(190\) 1.58096e14 0.243794
\(191\) 6.53880e14 0.974498 0.487249 0.873263i \(-0.338000\pi\)
0.487249 + 0.873263i \(0.338000\pi\)
\(192\) −1.80085e14 −0.259430
\(193\) 2.02162e14 0.281564 0.140782 0.990041i \(-0.455038\pi\)
0.140782 + 0.990041i \(0.455038\pi\)
\(194\) −8.81585e13 −0.118728
\(195\) 3.63704e14 0.473721
\(196\) −6.36568e14 −0.802012
\(197\) −5.32924e14 −0.649583 −0.324791 0.945786i \(-0.605294\pi\)
−0.324791 + 0.945786i \(0.605294\pi\)
\(198\) −7.67921e13 −0.0905718
\(199\) −5.68355e14 −0.648746 −0.324373 0.945929i \(-0.605153\pi\)
−0.324373 + 0.945929i \(0.605153\pi\)
\(200\) −1.06205e15 −1.17341
\(201\) −4.94083e12 −0.00528477
\(202\) 1.14047e14 0.118113
\(203\) −7.98144e14 −0.800492
\(204\) 1.72593e14 0.167659
\(205\) 2.80680e15 2.64126
\(206\) −1.93411e14 −0.176337
\(207\) 1.50109e14 0.132617
\(208\) 3.96002e14 0.339067
\(209\) −4.64743e14 −0.385711
\(210\) 5.36095e14 0.431336
\(211\) 1.67860e15 1.30952 0.654758 0.755839i \(-0.272771\pi\)
0.654758 + 0.755839i \(0.272771\pi\)
\(212\) 3.77908e14 0.285892
\(213\) 4.98813e14 0.365991
\(214\) 5.55584e14 0.395422
\(215\) 3.00737e15 2.07652
\(216\) −1.72539e14 −0.115595
\(217\) −5.55349e14 −0.361058
\(218\) 9.51933e14 0.600674
\(219\) −1.27541e15 −0.781203
\(220\) 2.23594e15 1.32958
\(221\) −2.66791e14 −0.154036
\(222\) −1.23277e14 −0.0691173
\(223\) 3.31081e15 1.80282 0.901410 0.432966i \(-0.142533\pi\)
0.901410 + 0.432966i \(0.142533\pi\)
\(224\) 2.14535e15 1.13472
\(225\) 1.26734e15 0.651191
\(226\) 6.68829e14 0.333895
\(227\) 1.02924e15 0.499287 0.249643 0.968338i \(-0.419687\pi\)
0.249643 + 0.968338i \(0.419687\pi\)
\(228\) −4.94641e14 −0.233192
\(229\) 9.90704e14 0.453955 0.226978 0.973900i \(-0.427116\pi\)
0.226978 + 0.973900i \(0.427116\pi\)
\(230\) 4.85261e14 0.216145
\(231\) −1.57592e15 −0.682425
\(232\) 8.30418e14 0.349643
\(233\) 1.52144e15 0.622931 0.311466 0.950257i \(-0.399180\pi\)
0.311466 + 0.950257i \(0.399180\pi\)
\(234\) 1.26340e14 0.0503082
\(235\) 3.30373e15 1.27957
\(236\) 3.11012e14 0.117179
\(237\) −3.02981e15 −1.11058
\(238\) −3.93246e14 −0.140254
\(239\) −1.07681e15 −0.373726 −0.186863 0.982386i \(-0.559832\pi\)
−0.186863 + 0.982386i \(0.559832\pi\)
\(240\) 2.08623e15 0.704676
\(241\) 2.34050e15 0.769481 0.384741 0.923025i \(-0.374291\pi\)
0.384741 + 0.923025i \(0.374291\pi\)
\(242\) −2.58002e14 −0.0825703
\(243\) 2.05891e14 0.0641500
\(244\) −3.10618e15 −0.942309
\(245\) 5.18392e15 1.53137
\(246\) 9.75004e14 0.280497
\(247\) 7.64606e14 0.214243
\(248\) 5.77805e14 0.157705
\(249\) 7.38705e14 0.196415
\(250\) 1.99981e15 0.518058
\(251\) 3.17723e15 0.801992 0.400996 0.916080i \(-0.368664\pi\)
0.400996 + 0.916080i \(0.368664\pi\)
\(252\) −1.67730e15 −0.412579
\(253\) −1.42648e15 −0.341966
\(254\) −5.75611e14 −0.134496
\(255\) −1.40552e15 −0.320129
\(256\) 6.46697e14 0.143596
\(257\) 2.52119e15 0.545809 0.272905 0.962041i \(-0.412016\pi\)
0.272905 + 0.962041i \(0.412016\pi\)
\(258\) 1.04467e15 0.220523
\(259\) −2.52986e15 −0.520773
\(260\) −3.67863e15 −0.738514
\(261\) −9.90939e14 −0.194037
\(262\) −2.95454e15 −0.564327
\(263\) −9.14713e14 −0.170440 −0.0852202 0.996362i \(-0.527159\pi\)
−0.0852202 + 0.996362i \(0.527159\pi\)
\(264\) 1.63964e15 0.298073
\(265\) −3.07750e15 −0.545884
\(266\) 1.12702e15 0.195075
\(267\) −3.07285e15 −0.519061
\(268\) 4.99733e13 0.00823876
\(269\) 9.66114e15 1.55467 0.777336 0.629086i \(-0.216571\pi\)
0.777336 + 0.629086i \(0.216571\pi\)
\(270\) 6.65590e14 0.104554
\(271\) −1.13859e16 −1.74610 −0.873048 0.487635i \(-0.837860\pi\)
−0.873048 + 0.487635i \(0.837860\pi\)
\(272\) −1.53033e15 −0.229133
\(273\) 2.59274e15 0.379054
\(274\) −1.14054e15 −0.162829
\(275\) −1.20436e16 −1.67916
\(276\) −1.51825e15 −0.206745
\(277\) −1.05903e16 −1.40861 −0.704304 0.709899i \(-0.748741\pi\)
−0.704304 + 0.709899i \(0.748741\pi\)
\(278\) 2.36991e15 0.307922
\(279\) −6.89495e14 −0.0875193
\(280\) −1.14465e16 −1.41953
\(281\) −9.53225e15 −1.15506 −0.577529 0.816370i \(-0.695983\pi\)
−0.577529 + 0.816370i \(0.695983\pi\)
\(282\) 1.14762e15 0.135887
\(283\) −4.46032e15 −0.516124 −0.258062 0.966128i \(-0.583084\pi\)
−0.258062 + 0.966128i \(0.583084\pi\)
\(284\) −5.04517e15 −0.570567
\(285\) 4.02813e15 0.445258
\(286\) −1.20061e15 −0.129725
\(287\) 2.00089e16 2.11344
\(288\) 2.66357e15 0.275051
\(289\) −8.87358e15 −0.895907
\(290\) −3.20344e15 −0.316249
\(291\) −2.24619e15 −0.216841
\(292\) 1.29000e16 1.21787
\(293\) 1.77460e16 1.63855 0.819277 0.573398i \(-0.194375\pi\)
0.819277 + 0.573398i \(0.194375\pi\)
\(294\) 1.80075e15 0.162628
\(295\) −2.53274e15 −0.223742
\(296\) 2.63216e15 0.227466
\(297\) −1.95658e15 −0.165418
\(298\) 5.42774e15 0.448966
\(299\) 2.34689e15 0.189946
\(300\) −1.28184e16 −1.01518
\(301\) 2.14386e16 1.66156
\(302\) 1.28292e14 0.00973094
\(303\) 2.90579e15 0.215718
\(304\) 4.38584e15 0.318694
\(305\) 2.52953e16 1.79925
\(306\) −4.88236e14 −0.0339970
\(307\) 1.42327e16 0.970259 0.485129 0.874442i \(-0.338772\pi\)
0.485129 + 0.874442i \(0.338772\pi\)
\(308\) 1.59394e16 1.06388
\(309\) −4.92791e15 −0.322057
\(310\) −2.22895e15 −0.142643
\(311\) 6.96725e15 0.436636 0.218318 0.975878i \(-0.429943\pi\)
0.218318 + 0.975878i \(0.429943\pi\)
\(312\) −2.69758e15 −0.165565
\(313\) −1.86288e16 −1.11981 −0.559907 0.828556i \(-0.689163\pi\)
−0.559907 + 0.828556i \(0.689163\pi\)
\(314\) 4.90275e15 0.288667
\(315\) 1.36591e16 0.787780
\(316\) 3.06446e16 1.73136
\(317\) 2.34802e15 0.129962 0.0649810 0.997887i \(-0.479301\pi\)
0.0649810 + 0.997887i \(0.479301\pi\)
\(318\) −1.06904e15 −0.0579718
\(319\) 9.41690e15 0.500344
\(320\) −1.48330e16 −0.772244
\(321\) 1.41557e16 0.722186
\(322\) 3.45928e15 0.172951
\(323\) −2.95479e15 −0.144780
\(324\) −2.08246e15 −0.100008
\(325\) 1.98144e16 0.932693
\(326\) 1.03961e16 0.479685
\(327\) 2.42543e16 1.09705
\(328\) −2.08180e16 −0.923120
\(329\) 2.35513e16 1.02386
\(330\) −6.32511e15 −0.269605
\(331\) −2.75150e16 −1.14997 −0.574986 0.818163i \(-0.694992\pi\)
−0.574986 + 0.818163i \(0.694992\pi\)
\(332\) −7.47152e15 −0.306204
\(333\) −3.14096e15 −0.126234
\(334\) −5.96117e15 −0.234952
\(335\) −4.06960e14 −0.0157311
\(336\) 1.48721e16 0.563855
\(337\) 3.01597e16 1.12159 0.560794 0.827956i \(-0.310496\pi\)
0.560794 + 0.827956i \(0.310496\pi\)
\(338\) −6.69053e15 −0.244063
\(339\) 1.70411e16 0.609816
\(340\) 1.42159e16 0.499069
\(341\) 6.55227e15 0.225678
\(342\) 1.39926e15 0.0472855
\(343\) −4.51822e15 −0.149815
\(344\) −2.23055e16 −0.725743
\(345\) 1.23640e16 0.394760
\(346\) 3.05811e15 0.0958205
\(347\) 2.92206e16 0.898562 0.449281 0.893391i \(-0.351680\pi\)
0.449281 + 0.893391i \(0.351680\pi\)
\(348\) 1.00227e16 0.302496
\(349\) 2.57396e16 0.762494 0.381247 0.924473i \(-0.375495\pi\)
0.381247 + 0.924473i \(0.375495\pi\)
\(350\) 2.92062e16 0.849244
\(351\) 3.21902e15 0.0918814
\(352\) −2.53119e16 −0.709248
\(353\) 1.98344e16 0.545610 0.272805 0.962069i \(-0.412049\pi\)
0.272805 + 0.962069i \(0.412049\pi\)
\(354\) −8.79803e14 −0.0237610
\(355\) 4.10856e16 1.08944
\(356\) 3.10799e16 0.809197
\(357\) −1.00195e16 −0.256155
\(358\) 2.11166e15 0.0530132
\(359\) −6.75022e16 −1.66419 −0.832097 0.554630i \(-0.812860\pi\)
−0.832097 + 0.554630i \(0.812860\pi\)
\(360\) −1.42115e16 −0.344090
\(361\) −3.35847e16 −0.798629
\(362\) 1.24176e15 0.0290022
\(363\) −6.57364e15 −0.150804
\(364\) −2.62238e16 −0.590932
\(365\) −1.05051e17 −2.32540
\(366\) 8.78688e15 0.191077
\(367\) 6.55766e16 1.40094 0.700470 0.713682i \(-0.252974\pi\)
0.700470 + 0.713682i \(0.252974\pi\)
\(368\) 1.34619e16 0.282550
\(369\) 2.48421e16 0.512291
\(370\) −1.01539e16 −0.205741
\(371\) −2.19386e16 −0.436796
\(372\) 6.97380e15 0.136440
\(373\) 3.93729e16 0.756989 0.378495 0.925603i \(-0.376442\pi\)
0.378495 + 0.925603i \(0.376442\pi\)
\(374\) 4.63971e15 0.0876649
\(375\) 5.09530e16 0.946165
\(376\) −2.45036e16 −0.447208
\(377\) −1.54929e16 −0.277917
\(378\) 4.74480e15 0.0836606
\(379\) −2.09052e16 −0.362326 −0.181163 0.983453i \(-0.557986\pi\)
−0.181163 + 0.983453i \(0.557986\pi\)
\(380\) −4.07419e16 −0.694141
\(381\) −1.46660e16 −0.245640
\(382\) 1.87087e16 0.308057
\(383\) −4.89324e16 −0.792145 −0.396073 0.918219i \(-0.629627\pi\)
−0.396073 + 0.918219i \(0.629627\pi\)
\(384\) −3.50840e16 −0.558413
\(385\) −1.29803e17 −2.03137
\(386\) 5.78423e15 0.0890078
\(387\) 2.66172e16 0.402756
\(388\) 2.27187e16 0.338048
\(389\) 6.05798e15 0.0886452 0.0443226 0.999017i \(-0.485887\pi\)
0.0443226 + 0.999017i \(0.485887\pi\)
\(390\) 1.04062e16 0.149752
\(391\) −9.06944e15 −0.128361
\(392\) −3.84489e16 −0.535211
\(393\) −7.52786e16 −1.03067
\(394\) −1.52479e16 −0.205346
\(395\) −2.49556e17 −3.30587
\(396\) 1.97896e16 0.257880
\(397\) −1.10851e16 −0.142103 −0.0710513 0.997473i \(-0.522635\pi\)
−0.0710513 + 0.997473i \(0.522635\pi\)
\(398\) −1.62617e16 −0.205081
\(399\) 2.87153e16 0.356279
\(400\) 1.13657e17 1.38741
\(401\) −1.48299e17 −1.78115 −0.890574 0.454838i \(-0.849697\pi\)
−0.890574 + 0.454838i \(0.849697\pi\)
\(402\) −1.41366e14 −0.00167062
\(403\) −1.07800e16 −0.125353
\(404\) −2.93902e16 −0.336298
\(405\) 1.69586e16 0.190955
\(406\) −2.28364e16 −0.253051
\(407\) 2.98486e16 0.325507
\(408\) 1.04247e16 0.111885
\(409\) −6.53952e16 −0.690787 −0.345393 0.938458i \(-0.612255\pi\)
−0.345393 + 0.938458i \(0.612255\pi\)
\(410\) 8.03078e16 0.834954
\(411\) −2.90598e16 −0.297386
\(412\) 4.98426e16 0.502075
\(413\) −1.80552e16 −0.179030
\(414\) 4.29489e15 0.0419227
\(415\) 6.08446e16 0.584668
\(416\) 4.16438e16 0.393953
\(417\) 6.03828e16 0.562379
\(418\) −1.32971e16 −0.121930
\(419\) −2.96994e16 −0.268137 −0.134069 0.990972i \(-0.542804\pi\)
−0.134069 + 0.990972i \(0.542804\pi\)
\(420\) −1.38153e17 −1.22812
\(421\) −3.74709e16 −0.327990 −0.163995 0.986461i \(-0.552438\pi\)
−0.163995 + 0.986461i \(0.552438\pi\)
\(422\) 4.80277e16 0.413963
\(423\) 2.92402e16 0.248181
\(424\) 2.28257e16 0.190786
\(425\) −7.65718e16 −0.630291
\(426\) 1.42720e16 0.115697
\(427\) 1.80323e17 1.43969
\(428\) −1.43176e17 −1.12586
\(429\) −3.05904e16 −0.236926
\(430\) 8.60463e16 0.656428
\(431\) 2.25892e17 1.69745 0.848727 0.528831i \(-0.177369\pi\)
0.848727 + 0.528831i \(0.177369\pi\)
\(432\) 1.84645e16 0.136677
\(433\) −3.17126e16 −0.231238 −0.115619 0.993294i \(-0.536885\pi\)
−0.115619 + 0.993294i \(0.536885\pi\)
\(434\) −1.58895e16 −0.114137
\(435\) −8.16203e16 −0.577588
\(436\) −2.45316e17 −1.71027
\(437\) 2.59925e16 0.178533
\(438\) −3.64919e16 −0.246953
\(439\) −5.45505e16 −0.363730 −0.181865 0.983324i \(-0.558213\pi\)
−0.181865 + 0.983324i \(0.558213\pi\)
\(440\) 1.35052e17 0.887273
\(441\) 4.58812e16 0.297019
\(442\) −7.63337e15 −0.0486936
\(443\) 5.75290e16 0.361628 0.180814 0.983517i \(-0.442127\pi\)
0.180814 + 0.983517i \(0.442127\pi\)
\(444\) 3.17688e16 0.196794
\(445\) −2.53100e17 −1.54509
\(446\) 9.47283e16 0.569906
\(447\) 1.38293e17 0.819978
\(448\) −1.05740e17 −0.617921
\(449\) −2.78144e17 −1.60202 −0.801011 0.598649i \(-0.795704\pi\)
−0.801011 + 0.598649i \(0.795704\pi\)
\(450\) 3.62610e16 0.205854
\(451\) −2.36074e17 −1.32100
\(452\) −1.72359e17 −0.950682
\(453\) 3.26875e15 0.0177723
\(454\) 2.94485e16 0.157834
\(455\) 2.13555e17 1.12833
\(456\) −2.98764e16 −0.155617
\(457\) −3.44104e17 −1.76699 −0.883496 0.468438i \(-0.844817\pi\)
−0.883496 + 0.468438i \(0.844817\pi\)
\(458\) 2.83459e16 0.143504
\(459\) −1.24398e16 −0.0620911
\(460\) −1.25053e17 −0.615417
\(461\) 2.94568e17 1.42932 0.714660 0.699472i \(-0.246582\pi\)
0.714660 + 0.699472i \(0.246582\pi\)
\(462\) −4.50898e16 −0.215728
\(463\) 2.54307e16 0.119972 0.0599862 0.998199i \(-0.480894\pi\)
0.0599862 + 0.998199i \(0.480894\pi\)
\(464\) −8.88685e16 −0.413410
\(465\) −5.67914e16 −0.260518
\(466\) 4.35311e16 0.196920
\(467\) −8.60939e16 −0.384072 −0.192036 0.981388i \(-0.561509\pi\)
−0.192036 + 0.981388i \(0.561509\pi\)
\(468\) −3.25583e16 −0.143240
\(469\) −2.90110e15 −0.0125875
\(470\) 9.45257e16 0.404496
\(471\) 1.24917e17 0.527212
\(472\) 1.87852e16 0.0781977
\(473\) −2.52944e17 −1.03855
\(474\) −8.66885e16 −0.351077
\(475\) 2.19450e17 0.876653
\(476\) 1.01341e17 0.399337
\(477\) −2.72380e16 −0.105878
\(478\) −3.08096e16 −0.118142
\(479\) −1.88707e17 −0.713852 −0.356926 0.934133i \(-0.616175\pi\)
−0.356926 + 0.934133i \(0.616175\pi\)
\(480\) 2.19390e17 0.818743
\(481\) −4.91076e16 −0.180803
\(482\) 6.69660e16 0.243248
\(483\) 8.81390e16 0.315872
\(484\) 6.64881e16 0.235098
\(485\) −1.85011e17 −0.645470
\(486\) 5.89092e15 0.0202790
\(487\) −4.58622e17 −1.55782 −0.778908 0.627138i \(-0.784226\pi\)
−0.778908 + 0.627138i \(0.784226\pi\)
\(488\) −1.87615e17 −0.628836
\(489\) 2.64882e17 0.876082
\(490\) 1.48321e17 0.484094
\(491\) −4.21466e17 −1.35748 −0.678739 0.734380i \(-0.737473\pi\)
−0.678739 + 0.734380i \(0.737473\pi\)
\(492\) −2.51262e17 −0.798644
\(493\) 5.98717e16 0.187809
\(494\) 2.18768e16 0.0677264
\(495\) −1.61157e17 −0.492398
\(496\) −6.18347e16 −0.186467
\(497\) 2.92887e17 0.871733
\(498\) 2.11357e16 0.0620906
\(499\) 4.93358e17 1.43057 0.715285 0.698833i \(-0.246297\pi\)
0.715285 + 0.698833i \(0.246297\pi\)
\(500\) −5.15357e17 −1.47504
\(501\) −1.51884e17 −0.429110
\(502\) 9.09065e16 0.253525
\(503\) −3.34056e17 −0.919661 −0.459831 0.888007i \(-0.652090\pi\)
−0.459831 + 0.888007i \(0.652090\pi\)
\(504\) −1.01309e17 −0.275328
\(505\) 2.39340e17 0.642128
\(506\) −4.08143e16 −0.108102
\(507\) −1.70468e17 −0.445750
\(508\) 1.48337e17 0.382944
\(509\) 6.63987e17 1.69236 0.846182 0.532894i \(-0.178896\pi\)
0.846182 + 0.532894i \(0.178896\pi\)
\(510\) −4.02144e16 −0.101199
\(511\) −7.48881e17 −1.86070
\(512\) 4.12753e17 1.01259
\(513\) 3.56516e16 0.0863607
\(514\) 7.21360e16 0.172541
\(515\) −4.05895e17 −0.958665
\(516\) −2.69216e17 −0.627882
\(517\) −2.77870e17 −0.639960
\(518\) −7.23840e16 −0.164626
\(519\) 7.79175e16 0.175004
\(520\) −2.22190e17 −0.492837
\(521\) −2.59732e17 −0.568958 −0.284479 0.958682i \(-0.591821\pi\)
−0.284479 + 0.958682i \(0.591821\pi\)
\(522\) −2.83526e16 −0.0613387
\(523\) −2.00639e17 −0.428701 −0.214350 0.976757i \(-0.568763\pi\)
−0.214350 + 0.976757i \(0.568763\pi\)
\(524\) 7.61394e17 1.60678
\(525\) 7.44143e17 1.55103
\(526\) −2.61716e16 −0.0538795
\(527\) 4.16587e16 0.0847104
\(528\) −1.75469e17 −0.352435
\(529\) −4.24255e17 −0.841715
\(530\) −8.80530e16 −0.172564
\(531\) −2.24165e16 −0.0433963
\(532\) −2.90437e17 −0.555426
\(533\) 3.88396e17 0.733749
\(534\) −8.79198e16 −0.164085
\(535\) 1.16596e18 2.14973
\(536\) 3.01840e15 0.00549802
\(537\) 5.38029e16 0.0968217
\(538\) 2.76423e17 0.491461
\(539\) −4.36009e17 −0.765894
\(540\) −1.71525e17 −0.297692
\(541\) −2.36614e17 −0.405750 −0.202875 0.979205i \(-0.565028\pi\)
−0.202875 + 0.979205i \(0.565028\pi\)
\(542\) −3.25772e17 −0.551974
\(543\) 3.16387e16 0.0529688
\(544\) −1.60931e17 −0.266223
\(545\) 1.99774e18 3.26559
\(546\) 7.41829e16 0.119826
\(547\) 2.15614e17 0.344159 0.172079 0.985083i \(-0.444951\pi\)
0.172079 + 0.985083i \(0.444951\pi\)
\(548\) 2.93921e17 0.463614
\(549\) 2.23881e17 0.348977
\(550\) −3.44589e17 −0.530815
\(551\) −1.71589e17 −0.261218
\(552\) −9.17030e16 −0.137968
\(553\) −1.77901e18 −2.64524
\(554\) −3.03008e17 −0.445288
\(555\) −2.58711e17 −0.375759
\(556\) −6.10733e17 −0.876729
\(557\) −8.75029e17 −1.24155 −0.620774 0.783990i \(-0.713182\pi\)
−0.620774 + 0.783990i \(0.713182\pi\)
\(558\) −1.97277e16 −0.0276665
\(559\) 4.16149e17 0.576863
\(560\) 1.22497e18 1.67843
\(561\) 1.18215e17 0.160108
\(562\) −2.72735e17 −0.365136
\(563\) 9.12606e17 1.20775 0.603877 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(564\) −2.95746e17 −0.386905
\(565\) 1.40362e18 1.81524
\(566\) −1.27618e17 −0.163157
\(567\) 1.20893e17 0.152795
\(568\) −3.04730e17 −0.380760
\(569\) −4.32429e17 −0.534177 −0.267089 0.963672i \(-0.586062\pi\)
−0.267089 + 0.963672i \(0.586062\pi\)
\(570\) 1.15252e17 0.140754
\(571\) −3.05605e17 −0.368999 −0.184500 0.982833i \(-0.559066\pi\)
−0.184500 + 0.982833i \(0.559066\pi\)
\(572\) 3.09402e17 0.369359
\(573\) 4.76678e17 0.562627
\(574\) 5.72490e17 0.668099
\(575\) 6.73582e17 0.777230
\(576\) −1.31282e17 −0.149782
\(577\) 2.04890e17 0.231141 0.115571 0.993299i \(-0.463130\pi\)
0.115571 + 0.993299i \(0.463130\pi\)
\(578\) −2.53889e17 −0.283213
\(579\) 1.47376e17 0.162561
\(580\) 8.25537e17 0.900440
\(581\) 4.33743e17 0.467830
\(582\) −6.42676e16 −0.0685476
\(583\) 2.58843e17 0.273017
\(584\) 7.79162e17 0.812727
\(585\) 2.65140e17 0.273503
\(586\) 5.07745e17 0.517978
\(587\) −8.18615e17 −0.825909 −0.412954 0.910752i \(-0.635503\pi\)
−0.412954 + 0.910752i \(0.635503\pi\)
\(588\) −4.64058e17 −0.463042
\(589\) −1.19391e17 −0.117821
\(590\) −7.24664e16 −0.0707292
\(591\) −3.88501e17 −0.375037
\(592\) −2.81685e17 −0.268951
\(593\) −2.63935e17 −0.249254 −0.124627 0.992204i \(-0.539773\pi\)
−0.124627 + 0.992204i \(0.539773\pi\)
\(594\) −5.59814e16 −0.0522916
\(595\) −8.25273e17 −0.762496
\(596\) −1.39875e18 −1.27832
\(597\) −4.14331e17 −0.374554
\(598\) 6.71487e16 0.0600454
\(599\) 6.06960e17 0.536890 0.268445 0.963295i \(-0.413490\pi\)
0.268445 + 0.963295i \(0.413490\pi\)
\(600\) −7.74234e17 −0.677468
\(601\) −9.28222e17 −0.803467 −0.401733 0.915757i \(-0.631592\pi\)
−0.401733 + 0.915757i \(0.631592\pi\)
\(602\) 6.13399e17 0.525250
\(603\) −3.60187e15 −0.00305116
\(604\) −3.30613e16 −0.0277064
\(605\) −5.41448e17 −0.448897
\(606\) 8.31400e16 0.0681927
\(607\) −1.02008e18 −0.827766 −0.413883 0.910330i \(-0.635828\pi\)
−0.413883 + 0.910330i \(0.635828\pi\)
\(608\) 4.61218e17 0.370282
\(609\) −5.81847e17 −0.462165
\(610\) 7.23746e17 0.568777
\(611\) 4.57158e17 0.355466
\(612\) 1.25820e17 0.0967979
\(613\) 1.38898e18 1.05731 0.528655 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(614\) 4.07223e17 0.306717
\(615\) 2.04616e18 1.52493
\(616\) 9.62743e17 0.709963
\(617\) 1.27962e18 0.933740 0.466870 0.884326i \(-0.345382\pi\)
0.466870 + 0.884326i \(0.345382\pi\)
\(618\) −1.40996e17 −0.101808
\(619\) 7.14427e17 0.510468 0.255234 0.966879i \(-0.417847\pi\)
0.255234 + 0.966879i \(0.417847\pi\)
\(620\) 5.74408e17 0.406139
\(621\) 1.09429e17 0.0765664
\(622\) 1.99346e17 0.138029
\(623\) −1.80428e18 −1.23632
\(624\) 2.88685e17 0.195760
\(625\) 1.28578e18 0.862873
\(626\) −5.33003e17 −0.353994
\(627\) −3.38797e17 −0.222690
\(628\) −1.26345e18 −0.821906
\(629\) 1.89774e17 0.122182
\(630\) 3.90813e17 0.249032
\(631\) 1.73070e18 1.09152 0.545758 0.837943i \(-0.316242\pi\)
0.545758 + 0.837943i \(0.316242\pi\)
\(632\) 1.85094e18 1.15540
\(633\) 1.22370e18 0.756049
\(634\) 6.71811e16 0.0410835
\(635\) −1.20799e18 −0.731195
\(636\) 2.75495e17 0.165060
\(637\) 7.17333e17 0.425417
\(638\) 2.69435e17 0.158168
\(639\) 3.63635e17 0.211305
\(640\) −2.88975e18 −1.66223
\(641\) 1.48780e18 0.847163 0.423581 0.905858i \(-0.360773\pi\)
0.423581 + 0.905858i \(0.360773\pi\)
\(642\) 4.05021e17 0.228297
\(643\) 1.41403e18 0.789016 0.394508 0.918892i \(-0.370915\pi\)
0.394508 + 0.918892i \(0.370915\pi\)
\(644\) −8.91468e17 −0.492434
\(645\) 2.19237e18 1.19888
\(646\) −8.45418e16 −0.0457678
\(647\) 2.03762e18 1.09206 0.546029 0.837766i \(-0.316139\pi\)
0.546029 + 0.837766i \(0.316139\pi\)
\(648\) −1.25781e17 −0.0667387
\(649\) 2.13024e17 0.111902
\(650\) 5.66926e17 0.294842
\(651\) −4.04849e17 −0.208457
\(652\) −2.67911e18 −1.36578
\(653\) −9.92522e17 −0.500962 −0.250481 0.968122i \(-0.580589\pi\)
−0.250481 + 0.968122i \(0.580589\pi\)
\(654\) 6.93959e17 0.346800
\(655\) −6.20044e18 −3.06799
\(656\) 2.22787e18 1.09148
\(657\) −9.29776e17 −0.451028
\(658\) 6.73846e17 0.323662
\(659\) 1.22480e17 0.0582520 0.0291260 0.999576i \(-0.490728\pi\)
0.0291260 + 0.999576i \(0.490728\pi\)
\(660\) 1.63000e18 0.767631
\(661\) 3.12167e17 0.145572 0.0727860 0.997348i \(-0.476811\pi\)
0.0727860 + 0.997348i \(0.476811\pi\)
\(662\) −7.87254e17 −0.363528
\(663\) −1.94490e17 −0.0889325
\(664\) −4.51282e17 −0.204341
\(665\) 2.36518e18 1.06053
\(666\) −8.98687e16 −0.0399049
\(667\) −5.26675e17 −0.231593
\(668\) 1.53621e18 0.668967
\(669\) 2.41358e18 1.04086
\(670\) −1.16439e16 −0.00497291
\(671\) −2.12754e18 −0.899873
\(672\) 1.56396e18 0.655128
\(673\) −2.67413e18 −1.10939 −0.554696 0.832053i \(-0.687166\pi\)
−0.554696 + 0.832053i \(0.687166\pi\)
\(674\) 8.62925e17 0.354555
\(675\) 9.23894e17 0.375965
\(676\) 1.72417e18 0.694908
\(677\) −4.28300e18 −1.70971 −0.854854 0.518868i \(-0.826354\pi\)
−0.854854 + 0.518868i \(0.826354\pi\)
\(678\) 4.87576e17 0.192774
\(679\) −1.31889e18 −0.516481
\(680\) 8.58644e17 0.333047
\(681\) 7.50319e17 0.288263
\(682\) 1.87473e17 0.0713410
\(683\) −7.31913e17 −0.275883 −0.137941 0.990440i \(-0.544049\pi\)
−0.137941 + 0.990440i \(0.544049\pi\)
\(684\) −3.60593e17 −0.134633
\(685\) −2.39356e18 −0.885228
\(686\) −1.29275e17 −0.0473594
\(687\) 7.22223e17 0.262091
\(688\) 2.38706e18 0.858102
\(689\) −4.25854e17 −0.151648
\(690\) 3.53755e17 0.124791
\(691\) 7.91680e17 0.276657 0.138329 0.990386i \(-0.455827\pi\)
0.138329 + 0.990386i \(0.455827\pi\)
\(692\) −7.88085e17 −0.272825
\(693\) −1.14884e18 −0.393998
\(694\) 8.36055e17 0.284052
\(695\) 4.97353e18 1.67403
\(696\) 6.05375e17 0.201867
\(697\) −1.50094e18 −0.495849
\(698\) 7.36457e17 0.241039
\(699\) 1.10913e18 0.359650
\(700\) −7.52653e18 −2.41801
\(701\) 1.65035e18 0.525302 0.262651 0.964891i \(-0.415403\pi\)
0.262651 + 0.964891i \(0.415403\pi\)
\(702\) 9.21021e16 0.0290455
\(703\) −5.43882e17 −0.169940
\(704\) 1.24757e18 0.386228
\(705\) 2.40842e18 0.738758
\(706\) 5.67497e17 0.172478
\(707\) 1.70619e18 0.513807
\(708\) 2.26728e17 0.0676533
\(709\) −6.24771e18 −1.84723 −0.923614 0.383324i \(-0.874779\pi\)
−0.923614 + 0.383324i \(0.874779\pi\)
\(710\) 1.17553e18 0.344394
\(711\) −2.20873e18 −0.641196
\(712\) 1.87723e18 0.540006
\(713\) −3.66460e17 −0.104459
\(714\) −2.86676e17 −0.0809755
\(715\) −2.51962e18 −0.705256
\(716\) −5.44182e17 −0.150942
\(717\) −7.84996e17 −0.215771
\(718\) −1.93136e18 −0.526083
\(719\) 5.85211e18 1.57970 0.789850 0.613300i \(-0.210158\pi\)
0.789850 + 0.613300i \(0.210158\pi\)
\(720\) 1.52086e18 0.406845
\(721\) −2.89351e18 −0.767088
\(722\) −9.60921e17 −0.252462
\(723\) 1.70623e18 0.444260
\(724\) −3.20005e17 −0.0825765
\(725\) −4.44664e18 −1.13719
\(726\) −1.88084e17 −0.0476720
\(727\) 1.76655e17 0.0443765 0.0221882 0.999754i \(-0.492937\pi\)
0.0221882 + 0.999754i \(0.492937\pi\)
\(728\) −1.58393e18 −0.394350
\(729\) 1.50095e17 0.0370370
\(730\) −3.00571e18 −0.735104
\(731\) −1.60819e18 −0.389829
\(732\) −2.26441e18 −0.544042
\(733\) 3.03756e18 0.723350 0.361675 0.932304i \(-0.382205\pi\)
0.361675 + 0.932304i \(0.382205\pi\)
\(734\) 1.87627e18 0.442864
\(735\) 3.77908e18 0.884134
\(736\) 1.41566e18 0.328288
\(737\) 3.42285e16 0.00786774
\(738\) 7.10778e17 0.161945
\(739\) −4.10920e18 −0.928044 −0.464022 0.885824i \(-0.653594\pi\)
−0.464022 + 0.885824i \(0.653594\pi\)
\(740\) 2.61669e18 0.585795
\(741\) 5.57398e17 0.123694
\(742\) −6.27704e17 −0.138080
\(743\) −7.88870e18 −1.72020 −0.860098 0.510128i \(-0.829598\pi\)
−0.860098 + 0.510128i \(0.829598\pi\)
\(744\) 4.21220e17 0.0910510
\(745\) 1.13908e19 2.44083
\(746\) 1.12653e18 0.239299
\(747\) 5.38516e17 0.113400
\(748\) −1.19567e18 −0.249603
\(749\) 8.31178e18 1.72013
\(750\) 1.45786e18 0.299101
\(751\) −2.55663e18 −0.520006 −0.260003 0.965608i \(-0.583724\pi\)
−0.260003 + 0.965608i \(0.583724\pi\)
\(752\) 2.62229e18 0.528768
\(753\) 2.31620e18 0.463030
\(754\) −4.43281e17 −0.0878547
\(755\) 2.69236e17 0.0529027
\(756\) −1.22275e18 −0.238202
\(757\) 5.09571e18 0.984195 0.492098 0.870540i \(-0.336230\pi\)
0.492098 + 0.870540i \(0.336230\pi\)
\(758\) −5.98136e17 −0.114538
\(759\) −1.03991e18 −0.197434
\(760\) −2.46082e18 −0.463225
\(761\) −3.34517e18 −0.624336 −0.312168 0.950027i \(-0.601055\pi\)
−0.312168 + 0.950027i \(0.601055\pi\)
\(762\) −4.19621e17 −0.0776515
\(763\) 1.42413e19 2.61301
\(764\) −4.82129e18 −0.877115
\(765\) −1.02462e18 −0.184826
\(766\) −1.40005e18 −0.250412
\(767\) −3.50472e17 −0.0621560
\(768\) 4.71442e17 0.0829049
\(769\) 3.54959e18 0.618952 0.309476 0.950907i \(-0.399846\pi\)
0.309476 + 0.950907i \(0.399846\pi\)
\(770\) −3.71390e18 −0.642155
\(771\) 1.83795e18 0.315123
\(772\) −1.49062e18 −0.253427
\(773\) −2.46328e18 −0.415285 −0.207643 0.978205i \(-0.566579\pi\)
−0.207643 + 0.978205i \(0.566579\pi\)
\(774\) 7.61568e17 0.127319
\(775\) −3.09397e18 −0.512926
\(776\) 1.37222e18 0.225591
\(777\) −1.84427e18 −0.300669
\(778\) 1.73330e17 0.0280224
\(779\) 4.30160e18 0.689662
\(780\) −2.68172e18 −0.426381
\(781\) −3.45562e18 −0.544872
\(782\) −2.59493e17 −0.0405772
\(783\) −7.22395e17 −0.112027
\(784\) 4.11467e18 0.632821
\(785\) 1.02890e19 1.56935
\(786\) −2.15386e18 −0.325815
\(787\) −5.08722e18 −0.763211 −0.381605 0.924325i \(-0.624629\pi\)
−0.381605 + 0.924325i \(0.624629\pi\)
\(788\) 3.92944e18 0.584669
\(789\) −6.66826e17 −0.0984038
\(790\) −7.14024e18 −1.04505
\(791\) 1.00060e19 1.45248
\(792\) 1.19530e18 0.172093
\(793\) 3.50028e18 0.499835
\(794\) −3.17166e17 −0.0449214
\(795\) −2.24350e18 −0.315166
\(796\) 4.19069e18 0.583916
\(797\) −9.51239e18 −1.31465 −0.657325 0.753607i \(-0.728312\pi\)
−0.657325 + 0.753607i \(0.728312\pi\)
\(798\) 8.21598e17 0.112626
\(799\) −1.76667e18 −0.240215
\(800\) 1.19522e19 1.61200
\(801\) −2.24011e18 −0.299680
\(802\) −4.24311e18 −0.563055
\(803\) 8.83566e18 1.16302
\(804\) 3.64306e16 0.00475665
\(805\) 7.25971e18 0.940256
\(806\) −3.08435e17 −0.0396265
\(807\) 7.04297e18 0.897590
\(808\) −1.77518e18 −0.224423
\(809\) 4.48219e18 0.562114 0.281057 0.959691i \(-0.409315\pi\)
0.281057 + 0.959691i \(0.409315\pi\)
\(810\) 4.85215e17 0.0603645
\(811\) −1.01306e19 −1.25025 −0.625127 0.780523i \(-0.714953\pi\)
−0.625127 + 0.780523i \(0.714953\pi\)
\(812\) 5.88501e18 0.720498
\(813\) −8.30034e18 −1.00811
\(814\) 8.54022e17 0.102899
\(815\) 2.18174e19 2.60783
\(816\) −1.11561e18 −0.132290
\(817\) 4.60898e18 0.542202
\(818\) −1.87108e18 −0.218371
\(819\) 1.89010e18 0.218847
\(820\) −2.06956e19 −2.37732
\(821\) −1.44455e19 −1.64627 −0.823136 0.567845i \(-0.807777\pi\)
−0.823136 + 0.567845i \(0.807777\pi\)
\(822\) −8.31454e17 −0.0940094
\(823\) −1.87229e18 −0.210026 −0.105013 0.994471i \(-0.533488\pi\)
−0.105013 + 0.994471i \(0.533488\pi\)
\(824\) 3.01051e18 0.335053
\(825\) −8.77977e18 −0.969465
\(826\) −5.16591e17 −0.0565948
\(827\) −8.21859e18 −0.893329 −0.446665 0.894701i \(-0.647388\pi\)
−0.446665 + 0.894701i \(0.647388\pi\)
\(828\) −1.10681e18 −0.119364
\(829\) −6.85548e18 −0.733557 −0.366778 0.930308i \(-0.619539\pi\)
−0.366778 + 0.930308i \(0.619539\pi\)
\(830\) 1.74088e18 0.184825
\(831\) −7.72033e18 −0.813260
\(832\) −2.05254e18 −0.214531
\(833\) −2.77210e18 −0.287486
\(834\) 1.72766e18 0.177779
\(835\) −1.25102e19 −1.27733
\(836\) 3.42672e18 0.347166
\(837\) −5.02642e17 −0.0505293
\(838\) −8.49755e17 −0.0847633
\(839\) −1.29934e19 −1.28608 −0.643041 0.765832i \(-0.722327\pi\)
−0.643041 + 0.765832i \(0.722327\pi\)
\(840\) −8.34451e18 −0.819569
\(841\) −6.78379e18 −0.661148
\(842\) −1.07211e18 −0.103684
\(843\) −6.94901e18 −0.666874
\(844\) −1.23769e19 −1.17865
\(845\) −1.40409e19 −1.32686
\(846\) 8.36616e17 0.0784546
\(847\) −3.85983e18 −0.359191
\(848\) −2.44273e18 −0.225581
\(849\) −3.25157e18 −0.297984
\(850\) −2.19086e18 −0.199247
\(851\) −1.66939e18 −0.150666
\(852\) −3.67793e18 −0.329417
\(853\) −6.44498e18 −0.572866 −0.286433 0.958100i \(-0.592470\pi\)
−0.286433 + 0.958100i \(0.592470\pi\)
\(854\) 5.15937e18 0.455114
\(855\) 2.93650e18 0.257070
\(856\) −8.64787e18 −0.751329
\(857\) −1.91734e19 −1.65319 −0.826596 0.562795i \(-0.809726\pi\)
−0.826596 + 0.562795i \(0.809726\pi\)
\(858\) −8.75246e17 −0.0748967
\(859\) 1.33684e19 1.13533 0.567667 0.823259i \(-0.307846\pi\)
0.567667 + 0.823259i \(0.307846\pi\)
\(860\) −2.21744e19 −1.86901
\(861\) 1.45865e19 1.22020
\(862\) 6.46318e18 0.536598
\(863\) 1.08501e19 0.894056 0.447028 0.894520i \(-0.352482\pi\)
0.447028 + 0.894520i \(0.352482\pi\)
\(864\) 1.94174e18 0.158801
\(865\) 6.41780e18 0.520933
\(866\) −9.07354e17 −0.0730989
\(867\) −6.46884e18 −0.517252
\(868\) 4.09479e18 0.324977
\(869\) 2.09896e19 1.65339
\(870\) −2.33531e18 −0.182587
\(871\) −5.63137e16 −0.00437014
\(872\) −1.48172e19 −1.14132
\(873\) −1.63747e18 −0.125193
\(874\) 7.43692e17 0.0564376
\(875\) 2.99180e19 2.25361
\(876\) 9.40408e18 0.703136
\(877\) −7.91821e18 −0.587665 −0.293832 0.955857i \(-0.594931\pi\)
−0.293832 + 0.955857i \(0.594931\pi\)
\(878\) −1.56079e18 −0.114982
\(879\) 1.29368e19 0.946020
\(880\) −1.44528e19 −1.04909
\(881\) 2.63411e18 0.189797 0.0948987 0.995487i \(-0.469747\pi\)
0.0948987 + 0.995487i \(0.469747\pi\)
\(882\) 1.31274e18 0.0938933
\(883\) 2.30340e19 1.63540 0.817702 0.575641i \(-0.195248\pi\)
0.817702 + 0.575641i \(0.195248\pi\)
\(884\) 1.96714e18 0.138643
\(885\) −1.84637e18 −0.129178
\(886\) 1.64601e18 0.114318
\(887\) 4.21937e18 0.290901 0.145450 0.989366i \(-0.453537\pi\)
0.145450 + 0.989366i \(0.453537\pi\)
\(888\) 1.91885e18 0.131328
\(889\) −8.61139e18 −0.585075
\(890\) −7.24166e18 −0.488431
\(891\) −1.42635e18 −0.0955039
\(892\) −2.44118e19 −1.62266
\(893\) 5.06316e18 0.334108
\(894\) 3.95683e18 0.259211
\(895\) 4.43156e18 0.288209
\(896\) −2.06002e19 −1.33005
\(897\) 1.71088e18 0.109665
\(898\) −7.95821e18 −0.506430
\(899\) 2.41918e18 0.152838
\(900\) −9.34459e18 −0.586116
\(901\) 1.64570e18 0.102480
\(902\) −6.75452e18 −0.417592
\(903\) 1.56288e19 0.959300
\(904\) −1.04106e19 −0.634424
\(905\) 2.60598e18 0.157672
\(906\) 9.35249e16 0.00561816
\(907\) −2.00406e18 −0.119526 −0.0597631 0.998213i \(-0.519035\pi\)
−0.0597631 + 0.998213i \(0.519035\pi\)
\(908\) −7.58899e18 −0.449392
\(909\) 2.11832e18 0.124545
\(910\) 6.11020e18 0.356686
\(911\) 1.33766e19 0.775311 0.387656 0.921804i \(-0.373285\pi\)
0.387656 + 0.921804i \(0.373285\pi\)
\(912\) 3.19728e18 0.183998
\(913\) −5.11752e18 −0.292415
\(914\) −9.84545e18 −0.558580
\(915\) 1.84403e19 1.03880
\(916\) −7.30482e18 −0.408591
\(917\) −4.42011e19 −2.45489
\(918\) −3.55924e17 −0.0196282
\(919\) −5.46503e18 −0.299255 −0.149628 0.988742i \(-0.547808\pi\)
−0.149628 + 0.988742i \(0.547808\pi\)
\(920\) −7.55326e18 −0.410690
\(921\) 1.03756e19 0.560179
\(922\) 8.42812e18 0.451835
\(923\) 5.68528e18 0.302650
\(924\) 1.16198e19 0.614229
\(925\) −1.40944e19 −0.739820
\(926\) 7.27618e17 0.0379256
\(927\) −3.59244e18 −0.185939
\(928\) −9.34548e18 −0.480330
\(929\) 2.03703e19 1.03967 0.519834 0.854267i \(-0.325994\pi\)
0.519834 + 0.854267i \(0.325994\pi\)
\(930\) −1.62491e18 −0.0823548
\(931\) 7.94467e18 0.399856
\(932\) −1.12181e19 −0.560681
\(933\) 5.07913e18 0.252092
\(934\) −2.46331e18 −0.121413
\(935\) 9.73698e18 0.476594
\(936\) −1.96653e18 −0.0955890
\(937\) −2.26477e19 −1.09324 −0.546621 0.837380i \(-0.684086\pi\)
−0.546621 + 0.837380i \(0.684086\pi\)
\(938\) −8.30057e16 −0.00397914
\(939\) −1.35804e19 −0.646525
\(940\) −2.43596e19 −1.15170
\(941\) −4.52873e17 −0.0212639 −0.0106320 0.999943i \(-0.503384\pi\)
−0.0106320 + 0.999943i \(0.503384\pi\)
\(942\) 3.57410e18 0.166662
\(943\) 1.32033e19 0.611446
\(944\) −2.01033e18 −0.0924592
\(945\) 9.95751e18 0.454825
\(946\) −7.23718e18 −0.328305
\(947\) 2.29988e19 1.03617 0.518083 0.855330i \(-0.326646\pi\)
0.518083 + 0.855330i \(0.326646\pi\)
\(948\) 2.23399e19 0.999602
\(949\) −1.45366e19 −0.646002
\(950\) 6.27887e18 0.277127
\(951\) 1.71171e18 0.0750336
\(952\) 6.12102e18 0.266492
\(953\) 3.27952e19 1.41810 0.709050 0.705158i \(-0.249124\pi\)
0.709050 + 0.705158i \(0.249124\pi\)
\(954\) −7.79329e17 −0.0334700
\(955\) 3.92624e19 1.67477
\(956\) 7.93973e18 0.336379
\(957\) 6.86492e18 0.288874
\(958\) −5.39927e18 −0.225662
\(959\) −1.70630e19 −0.708326
\(960\) −1.08133e19 −0.445855
\(961\) −2.27343e19 −0.931063
\(962\) −1.40506e18 −0.0571553
\(963\) 1.03195e19 0.416954
\(964\) −1.72574e19 −0.692586
\(965\) 1.21389e19 0.483895
\(966\) 2.52182e18 0.0998532
\(967\) 2.96901e19 1.16772 0.583861 0.811853i \(-0.301541\pi\)
0.583861 + 0.811853i \(0.301541\pi\)
\(968\) 4.01590e18 0.156889
\(969\) −2.15404e18 −0.0835890
\(970\) −5.29350e18 −0.204045
\(971\) −1.17847e19 −0.451225 −0.225613 0.974217i \(-0.572438\pi\)
−0.225613 + 0.974217i \(0.572438\pi\)
\(972\) −1.51811e18 −0.0577394
\(973\) 3.54548e19 1.33950
\(974\) −1.31220e19 −0.492455
\(975\) 1.44447e19 0.538491
\(976\) 2.00779e19 0.743522
\(977\) −4.47194e19 −1.64506 −0.822529 0.568723i \(-0.807438\pi\)
−0.822529 + 0.568723i \(0.807438\pi\)
\(978\) 7.57876e18 0.276946
\(979\) 2.12877e19 0.772755
\(980\) −3.82229e19 −1.37833
\(981\) 1.76814e19 0.633384
\(982\) −1.20589e19 −0.429125
\(983\) −1.95000e19 −0.689345 −0.344673 0.938723i \(-0.612010\pi\)
−0.344673 + 0.938723i \(0.612010\pi\)
\(984\) −1.51763e19 −0.532963
\(985\) −3.19996e19 −1.11637
\(986\) 1.71304e18 0.0593700
\(987\) 1.71689e19 0.591127
\(988\) −5.63772e18 −0.192834
\(989\) 1.41468e19 0.480710
\(990\) −4.61100e18 −0.155656
\(991\) 3.83680e18 0.128674 0.0643369 0.997928i \(-0.479507\pi\)
0.0643369 + 0.997928i \(0.479507\pi\)
\(992\) −6.50258e18 −0.216651
\(993\) −2.00584e19 −0.663936
\(994\) 8.38003e18 0.275571
\(995\) −3.41270e19 −1.11493
\(996\) −5.44674e18 −0.176787
\(997\) −9.82416e18 −0.316794 −0.158397 0.987376i \(-0.550633\pi\)
−0.158397 + 0.987376i \(0.550633\pi\)
\(998\) 1.41159e19 0.452230
\(999\) −2.28976e18 −0.0728811
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.1.17 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.17 31 1.1 even 1 trivial