Properties

Label 177.12.a.d.1.26
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.26
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+79.9794 q^{2} +243.000 q^{3} +4348.71 q^{4} +3572.54 q^{5} +19435.0 q^{6} +34298.8 q^{7} +184010. q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+79.9794 q^{2} +243.000 q^{3} +4348.71 q^{4} +3572.54 q^{5} +19435.0 q^{6} +34298.8 q^{7} +184010. q^{8} +59049.0 q^{9} +285730. q^{10} +561469. q^{11} +1.05674e6 q^{12} -841746. q^{13} +2.74320e6 q^{14} +868128. q^{15} +5.81083e6 q^{16} -1.34277e6 q^{17} +4.72271e6 q^{18} -1.30792e6 q^{19} +1.55360e7 q^{20} +8.33461e6 q^{21} +4.49060e7 q^{22} +5.35592e7 q^{23} +4.47143e7 q^{24} -3.60651e7 q^{25} -6.73224e7 q^{26} +1.43489e7 q^{27} +1.49156e8 q^{28} +7.22123e7 q^{29} +6.94324e7 q^{30} +1.64321e8 q^{31} +8.78949e7 q^{32} +1.36437e8 q^{33} -1.07394e8 q^{34} +1.22534e8 q^{35} +2.56787e8 q^{36} -2.58614e8 q^{37} -1.04607e8 q^{38} -2.04544e8 q^{39} +6.57382e8 q^{40} -5.88764e8 q^{41} +6.66597e8 q^{42} +6.19956e8 q^{43} +2.44167e9 q^{44} +2.10955e8 q^{45} +4.28363e9 q^{46} -1.16783e9 q^{47} +1.41203e9 q^{48} -8.00919e8 q^{49} -2.88446e9 q^{50} -3.26294e8 q^{51} -3.66051e9 q^{52} -1.57562e9 q^{53} +1.14762e9 q^{54} +2.00587e9 q^{55} +6.31131e9 q^{56} -3.17825e8 q^{57} +5.77550e9 q^{58} +7.14924e8 q^{59} +3.77524e9 q^{60} +7.71700e9 q^{61} +1.31423e10 q^{62} +2.02531e9 q^{63} -4.87079e9 q^{64} -3.00717e9 q^{65} +1.09122e10 q^{66} -3.30544e9 q^{67} -5.83933e9 q^{68} +1.30149e10 q^{69} +9.80020e9 q^{70} -1.03471e10 q^{71} +1.08656e10 q^{72} +2.59913e10 q^{73} -2.06838e10 q^{74} -8.76381e9 q^{75} -5.68777e9 q^{76} +1.92577e10 q^{77} -1.63593e10 q^{78} +4.26792e9 q^{79} +2.07594e10 q^{80} +3.48678e9 q^{81} -4.70890e10 q^{82} -3.07597e10 q^{83} +3.62448e10 q^{84} -4.79711e9 q^{85} +4.95837e10 q^{86} +1.75476e10 q^{87} +1.03316e11 q^{88} -8.23783e10 q^{89} +1.68721e10 q^{90} -2.88709e10 q^{91} +2.32913e11 q^{92} +3.99301e10 q^{93} -9.34021e10 q^{94} -4.67260e9 q^{95} +2.13585e10 q^{96} +1.52034e10 q^{97} -6.40571e10 q^{98} +3.31542e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + O(q^{10}) \) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + 616281q^{10} + 1082362q^{11} + 7099002q^{12} + 503712q^{13} + 1321669q^{14} + 6454566q^{15} + 34870338q^{16} + 13513579q^{17} + 5668704q^{18} + 35971687q^{19} + 96105997q^{20} + 34586919q^{21} - 47598882q^{22} + 61380539q^{23} + 80756433q^{24} + 294744746q^{25} + 62820734q^{26} + 401769396q^{27} + 148068294q^{28} + 322339307q^{29} + 149756283q^{30} + 151247077q^{31} + 466383494q^{32} + 263013966q^{33} + 684479860q^{34} + 960297361q^{35} + 1725057486q^{36} + 863508437q^{37} + 992640509q^{38} + 122402016q^{39} + 3067680252q^{40} + 3081170377q^{41} + 321165567q^{42} + 2554238300q^{43} + 4350123570q^{44} + 1568459538q^{45} - 1987059155q^{46} + 6203398333q^{47} + 8473492134q^{48} + 10327857997q^{49} + 17577682253q^{50} + 3283799697q^{51} + 32137181618q^{52} + 14571770754q^{53} + 1377495072q^{54} + 18251419334q^{55} + 33498842836q^{56} + 8741119941q^{57} + 11860778276q^{58} + 20017880372q^{59} + 23353757271q^{60} + 2761613771q^{61} + 13785829526q^{62} + 8404621317q^{63} + 86547545293q^{64} + 32034985256q^{65} - 11566528326q^{66} + 39381333296q^{67} + 38995496621q^{68} + 14915470977q^{69} + 8551800364q^{70} + 26130020296q^{71} + 19623813219q^{72} + 41382402799q^{73} + 23815315058q^{74} + 71622973278q^{75} + 10611720128q^{76} - 8426124313q^{77} + 15265438362q^{78} + 59825111206q^{79} + 4009687655q^{80} + 97629963228q^{81} - 39592715115q^{82} + 35433122727q^{83} + 35980595442q^{84} - 8950496085q^{85} - 182032360688q^{86} + 78328451601q^{87} - 220003602335q^{88} + 102303043039q^{89} + 36390776769q^{90} - 111146323655q^{91} - 163000203526q^{92} + 36753039711q^{93} - 81314346008q^{94} + 208102168887q^{95} + 113331189042q^{96} - 171891031490q^{97} + 72304707792q^{98} + 63912393738q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 79.9794 1.76731 0.883656 0.468136i \(-0.155074\pi\)
0.883656 + 0.468136i \(0.155074\pi\)
\(3\) 243.000 0.577350
\(4\) 4348.71 2.12339
\(5\) 3572.54 0.511261 0.255630 0.966775i \(-0.417717\pi\)
0.255630 + 0.966775i \(0.417717\pi\)
\(6\) 19435.0 1.02036
\(7\) 34298.8 0.771329 0.385665 0.922639i \(-0.373972\pi\)
0.385665 + 0.922639i \(0.373972\pi\)
\(8\) 184010. 1.98539
\(9\) 59049.0 0.333333
\(10\) 285730. 0.903558
\(11\) 561469. 1.05115 0.525577 0.850746i \(-0.323850\pi\)
0.525577 + 0.850746i \(0.323850\pi\)
\(12\) 1.05674e6 1.22594
\(13\) −841746. −0.628771 −0.314386 0.949295i \(-0.601798\pi\)
−0.314386 + 0.949295i \(0.601798\pi\)
\(14\) 2.74320e6 1.36318
\(15\) 868128. 0.295177
\(16\) 5.81083e6 1.38541
\(17\) −1.34277e6 −0.229368 −0.114684 0.993402i \(-0.536586\pi\)
−0.114684 + 0.993402i \(0.536586\pi\)
\(18\) 4.72271e6 0.589104
\(19\) −1.30792e6 −0.121182 −0.0605908 0.998163i \(-0.519298\pi\)
−0.0605908 + 0.998163i \(0.519298\pi\)
\(20\) 1.55360e7 1.08561
\(21\) 8.33461e6 0.445327
\(22\) 4.49060e7 1.85772
\(23\) 5.35592e7 1.73512 0.867562 0.497328i \(-0.165686\pi\)
0.867562 + 0.497328i \(0.165686\pi\)
\(24\) 4.47143e7 1.14626
\(25\) −3.60651e7 −0.738612
\(26\) −6.73224e7 −1.11123
\(27\) 1.43489e7 0.192450
\(28\) 1.49156e8 1.63784
\(29\) 7.22123e7 0.653766 0.326883 0.945065i \(-0.394002\pi\)
0.326883 + 0.945065i \(0.394002\pi\)
\(30\) 6.94324e7 0.521669
\(31\) 1.64321e8 1.03087 0.515436 0.856928i \(-0.327630\pi\)
0.515436 + 0.856928i \(0.327630\pi\)
\(32\) 8.78949e7 0.463062
\(33\) 1.36437e8 0.606884
\(34\) −1.07394e8 −0.405365
\(35\) 1.22534e8 0.394350
\(36\) 2.56787e8 0.707798
\(37\) −2.58614e8 −0.613115 −0.306558 0.951852i \(-0.599177\pi\)
−0.306558 + 0.951852i \(0.599177\pi\)
\(38\) −1.04607e8 −0.214166
\(39\) −2.04544e8 −0.363021
\(40\) 6.57382e8 1.01505
\(41\) −5.88764e8 −0.793651 −0.396826 0.917894i \(-0.629888\pi\)
−0.396826 + 0.917894i \(0.629888\pi\)
\(42\) 6.66597e8 0.787032
\(43\) 6.19956e8 0.643109 0.321554 0.946891i \(-0.395795\pi\)
0.321554 + 0.946891i \(0.395795\pi\)
\(44\) 2.44167e9 2.23201
\(45\) 2.10955e8 0.170420
\(46\) 4.28363e9 3.06651
\(47\) −1.16783e9 −0.742745 −0.371373 0.928484i \(-0.621113\pi\)
−0.371373 + 0.928484i \(0.621113\pi\)
\(48\) 1.41203e9 0.799866
\(49\) −8.00919e8 −0.405051
\(50\) −2.88446e9 −1.30536
\(51\) −3.26294e8 −0.132426
\(52\) −3.66051e9 −1.33513
\(53\) −1.57562e9 −0.517528 −0.258764 0.965941i \(-0.583315\pi\)
−0.258764 + 0.965941i \(0.583315\pi\)
\(54\) 1.14762e9 0.340119
\(55\) 2.00587e9 0.537413
\(56\) 6.31131e9 1.53139
\(57\) −3.17825e8 −0.0699642
\(58\) 5.77550e9 1.15541
\(59\) 7.14924e8 0.130189
\(60\) 3.77524e9 0.626776
\(61\) 7.71700e9 1.16986 0.584930 0.811083i \(-0.301122\pi\)
0.584930 + 0.811083i \(0.301122\pi\)
\(62\) 1.31423e10 1.82187
\(63\) 2.02531e9 0.257110
\(64\) −4.87079e9 −0.567034
\(65\) −3.00717e9 −0.321466
\(66\) 1.09122e10 1.07255
\(67\) −3.30544e9 −0.299101 −0.149550 0.988754i \(-0.547783\pi\)
−0.149550 + 0.988754i \(0.547783\pi\)
\(68\) −5.83933e9 −0.487039
\(69\) 1.30149e10 1.00177
\(70\) 9.80020e9 0.696940
\(71\) −1.03471e10 −0.680609 −0.340304 0.940315i \(-0.610530\pi\)
−0.340304 + 0.940315i \(0.610530\pi\)
\(72\) 1.08656e10 0.661796
\(73\) 2.59913e10 1.46741 0.733705 0.679468i \(-0.237789\pi\)
0.733705 + 0.679468i \(0.237789\pi\)
\(74\) −2.06838e10 −1.08357
\(75\) −8.76381e9 −0.426438
\(76\) −5.68777e9 −0.257316
\(77\) 1.92577e10 0.810785
\(78\) −1.63593e10 −0.641572
\(79\) 4.26792e9 0.156051 0.0780257 0.996951i \(-0.475138\pi\)
0.0780257 + 0.996951i \(0.475138\pi\)
\(80\) 2.07594e10 0.708305
\(81\) 3.48678e9 0.111111
\(82\) −4.70890e10 −1.40263
\(83\) −3.07597e10 −0.857141 −0.428571 0.903508i \(-0.640983\pi\)
−0.428571 + 0.903508i \(0.640983\pi\)
\(84\) 3.62448e10 0.945605
\(85\) −4.79711e9 −0.117267
\(86\) 4.95837e10 1.13657
\(87\) 1.75476e10 0.377452
\(88\) 1.03316e11 2.08695
\(89\) −8.23783e10 −1.56375 −0.781876 0.623434i \(-0.785737\pi\)
−0.781876 + 0.623434i \(0.785737\pi\)
\(90\) 1.68721e10 0.301186
\(91\) −2.88709e10 −0.484989
\(92\) 2.32913e11 3.68435
\(93\) 3.99301e10 0.595175
\(94\) −9.34021e10 −1.31266
\(95\) −4.67260e9 −0.0619554
\(96\) 2.13585e10 0.267349
\(97\) 1.52034e10 0.179761 0.0898806 0.995953i \(-0.471351\pi\)
0.0898806 + 0.995953i \(0.471351\pi\)
\(98\) −6.40571e10 −0.715853
\(99\) 3.31542e10 0.350384
\(100\) −1.56837e11 −1.56837
\(101\) 8.95263e10 0.847585 0.423793 0.905759i \(-0.360699\pi\)
0.423793 + 0.905759i \(0.360699\pi\)
\(102\) −2.60968e10 −0.234038
\(103\) 5.26327e9 0.0447354 0.0223677 0.999750i \(-0.492880\pi\)
0.0223677 + 0.999750i \(0.492880\pi\)
\(104\) −1.54889e11 −1.24835
\(105\) 2.97758e10 0.227678
\(106\) −1.26017e11 −0.914634
\(107\) −7.94295e10 −0.547483 −0.273742 0.961803i \(-0.588261\pi\)
−0.273742 + 0.961803i \(0.588261\pi\)
\(108\) 6.23993e10 0.408647
\(109\) 8.71745e10 0.542680 0.271340 0.962484i \(-0.412533\pi\)
0.271340 + 0.962484i \(0.412533\pi\)
\(110\) 1.60429e11 0.949778
\(111\) −6.28432e10 −0.353982
\(112\) 1.99304e11 1.06861
\(113\) 3.06361e11 1.56423 0.782117 0.623131i \(-0.214140\pi\)
0.782117 + 0.623131i \(0.214140\pi\)
\(114\) −2.54194e10 −0.123649
\(115\) 1.91342e11 0.887101
\(116\) 3.14031e11 1.38820
\(117\) −4.97042e10 −0.209590
\(118\) 5.71792e10 0.230085
\(119\) −4.60555e10 −0.176918
\(120\) 1.59744e11 0.586040
\(121\) 2.99358e10 0.104923
\(122\) 6.17201e11 2.06751
\(123\) −1.43070e11 −0.458215
\(124\) 7.14587e11 2.18895
\(125\) −3.03285e11 −0.888884
\(126\) 1.61983e11 0.454393
\(127\) 4.86702e10 0.130720 0.0653601 0.997862i \(-0.479180\pi\)
0.0653601 + 0.997862i \(0.479180\pi\)
\(128\) −5.69571e11 −1.46519
\(129\) 1.50649e11 0.371299
\(130\) −2.40512e11 −0.568131
\(131\) 5.88093e11 1.33184 0.665922 0.746021i \(-0.268038\pi\)
0.665922 + 0.746021i \(0.268038\pi\)
\(132\) 5.93325e11 1.28865
\(133\) −4.48601e10 −0.0934709
\(134\) −2.64367e11 −0.528605
\(135\) 5.12621e10 0.0983922
\(136\) −2.47083e11 −0.455385
\(137\) 8.79493e10 0.155693 0.0778466 0.996965i \(-0.475196\pi\)
0.0778466 + 0.996965i \(0.475196\pi\)
\(138\) 1.04092e12 1.77045
\(139\) −1.38697e10 −0.0226719 −0.0113359 0.999936i \(-0.503608\pi\)
−0.0113359 + 0.999936i \(0.503608\pi\)
\(140\) 5.32865e11 0.837361
\(141\) −2.83782e11 −0.428824
\(142\) −8.27555e11 −1.20285
\(143\) −4.72614e11 −0.660935
\(144\) 3.43123e11 0.461803
\(145\) 2.57982e11 0.334245
\(146\) 2.07877e12 2.59337
\(147\) −1.94623e11 −0.233857
\(148\) −1.12464e12 −1.30189
\(149\) 9.30625e10 0.103813 0.0519063 0.998652i \(-0.483470\pi\)
0.0519063 + 0.998652i \(0.483470\pi\)
\(150\) −7.00925e11 −0.753649
\(151\) −8.33215e11 −0.863742 −0.431871 0.901935i \(-0.642146\pi\)
−0.431871 + 0.901935i \(0.642146\pi\)
\(152\) −2.40670e11 −0.240592
\(153\) −7.92894e10 −0.0764561
\(154\) 1.54022e12 1.43291
\(155\) 5.87046e11 0.527045
\(156\) −8.89504e11 −0.770837
\(157\) 1.06013e11 0.0886978 0.0443489 0.999016i \(-0.485879\pi\)
0.0443489 + 0.999016i \(0.485879\pi\)
\(158\) 3.41346e11 0.275791
\(159\) −3.82875e11 −0.298795
\(160\) 3.14008e11 0.236745
\(161\) 1.83702e12 1.33835
\(162\) 2.78871e11 0.196368
\(163\) −2.01619e12 −1.37246 −0.686230 0.727385i \(-0.740735\pi\)
−0.686230 + 0.727385i \(0.740735\pi\)
\(164\) −2.56036e12 −1.68523
\(165\) 4.87427e11 0.310276
\(166\) −2.46014e12 −1.51484
\(167\) −2.42962e12 −1.44743 −0.723715 0.690099i \(-0.757567\pi\)
−0.723715 + 0.690099i \(0.757567\pi\)
\(168\) 1.53365e12 0.884147
\(169\) −1.08362e12 −0.604647
\(170\) −3.83670e11 −0.207247
\(171\) −7.72314e10 −0.0403938
\(172\) 2.69601e12 1.36557
\(173\) 2.10687e12 1.03367 0.516837 0.856084i \(-0.327109\pi\)
0.516837 + 0.856084i \(0.327109\pi\)
\(174\) 1.40345e12 0.667076
\(175\) −1.23699e12 −0.569713
\(176\) 3.26260e12 1.45628
\(177\) 1.73727e11 0.0751646
\(178\) −6.58857e12 −2.76364
\(179\) 2.02471e12 0.823514 0.411757 0.911294i \(-0.364915\pi\)
0.411757 + 0.911294i \(0.364915\pi\)
\(180\) 9.17383e11 0.361869
\(181\) −1.86962e12 −0.715352 −0.357676 0.933846i \(-0.616431\pi\)
−0.357676 + 0.933846i \(0.616431\pi\)
\(182\) −2.30908e12 −0.857128
\(183\) 1.87523e12 0.675419
\(184\) 9.85540e12 3.44490
\(185\) −9.23909e11 −0.313462
\(186\) 3.19359e12 1.05186
\(187\) −7.53925e11 −0.241101
\(188\) −5.07854e12 −1.57714
\(189\) 4.92150e11 0.148442
\(190\) −3.73712e11 −0.109495
\(191\) −5.41601e12 −1.54168 −0.770842 0.637026i \(-0.780164\pi\)
−0.770842 + 0.637026i \(0.780164\pi\)
\(192\) −1.18360e12 −0.327377
\(193\) 6.88015e11 0.184941 0.0924705 0.995715i \(-0.470524\pi\)
0.0924705 + 0.995715i \(0.470524\pi\)
\(194\) 1.21596e12 0.317694
\(195\) −7.30743e11 −0.185598
\(196\) −3.48297e12 −0.860084
\(197\) −3.58885e12 −0.861770 −0.430885 0.902407i \(-0.641799\pi\)
−0.430885 + 0.902407i \(0.641799\pi\)
\(198\) 2.65165e12 0.619239
\(199\) −2.32985e12 −0.529219 −0.264609 0.964356i \(-0.585243\pi\)
−0.264609 + 0.964356i \(0.585243\pi\)
\(200\) −6.63632e12 −1.46643
\(201\) −8.03222e11 −0.172686
\(202\) 7.16027e12 1.49795
\(203\) 2.47680e12 0.504269
\(204\) −1.41896e12 −0.281192
\(205\) −2.10338e12 −0.405763
\(206\) 4.20954e11 0.0790614
\(207\) 3.16262e12 0.578375
\(208\) −4.89124e12 −0.871105
\(209\) −7.34357e11 −0.127380
\(210\) 2.38145e12 0.402379
\(211\) 2.97692e12 0.490021 0.245010 0.969520i \(-0.421209\pi\)
0.245010 + 0.969520i \(0.421209\pi\)
\(212\) −6.85191e12 −1.09892
\(213\) −2.51434e12 −0.392950
\(214\) −6.35272e12 −0.967574
\(215\) 2.21482e12 0.328796
\(216\) 2.64034e12 0.382088
\(217\) 5.63603e12 0.795142
\(218\) 6.97217e12 0.959085
\(219\) 6.31587e12 0.847210
\(220\) 8.72296e12 1.14114
\(221\) 1.13027e12 0.144220
\(222\) −5.02616e12 −0.625597
\(223\) 3.54917e12 0.430972 0.215486 0.976507i \(-0.430866\pi\)
0.215486 + 0.976507i \(0.430866\pi\)
\(224\) 3.01469e12 0.357173
\(225\) −2.12961e12 −0.246204
\(226\) 2.45026e13 2.76449
\(227\) −7.30662e12 −0.804589 −0.402295 0.915510i \(-0.631787\pi\)
−0.402295 + 0.915510i \(0.631787\pi\)
\(228\) −1.38213e12 −0.148562
\(229\) 1.39308e13 1.46177 0.730886 0.682499i \(-0.239107\pi\)
0.730886 + 0.682499i \(0.239107\pi\)
\(230\) 1.53035e13 1.56779
\(231\) 4.67962e12 0.468107
\(232\) 1.32878e13 1.29798
\(233\) −1.29379e13 −1.23426 −0.617129 0.786862i \(-0.711704\pi\)
−0.617129 + 0.786862i \(0.711704\pi\)
\(234\) −3.97532e12 −0.370412
\(235\) −4.17211e12 −0.379737
\(236\) 3.10900e12 0.276442
\(237\) 1.03710e12 0.0900963
\(238\) −3.68349e12 −0.312670
\(239\) −1.86912e13 −1.55042 −0.775209 0.631705i \(-0.782356\pi\)
−0.775209 + 0.631705i \(0.782356\pi\)
\(240\) 5.04454e12 0.408940
\(241\) 2.45800e13 1.94755 0.973773 0.227521i \(-0.0730621\pi\)
0.973773 + 0.227521i \(0.0730621\pi\)
\(242\) 2.39424e12 0.185432
\(243\) 8.47289e11 0.0641500
\(244\) 3.35590e13 2.48408
\(245\) −2.86132e12 −0.207087
\(246\) −1.14426e13 −0.809809
\(247\) 1.10094e12 0.0761954
\(248\) 3.02367e13 2.04668
\(249\) −7.47460e12 −0.494871
\(250\) −2.42565e13 −1.57094
\(251\) 1.55098e13 0.982657 0.491329 0.870974i \(-0.336511\pi\)
0.491329 + 0.870974i \(0.336511\pi\)
\(252\) 8.80749e12 0.545945
\(253\) 3.00718e13 1.82388
\(254\) 3.89262e12 0.231024
\(255\) −1.16570e12 −0.0677041
\(256\) −3.55786e13 −2.02241
\(257\) 1.52741e13 0.849815 0.424907 0.905237i \(-0.360307\pi\)
0.424907 + 0.905237i \(0.360307\pi\)
\(258\) 1.20488e13 0.656201
\(259\) −8.87014e12 −0.472914
\(260\) −1.30773e13 −0.682599
\(261\) 4.26406e12 0.217922
\(262\) 4.70353e13 2.35379
\(263\) 1.10164e13 0.539863 0.269931 0.962880i \(-0.412999\pi\)
0.269931 + 0.962880i \(0.412999\pi\)
\(264\) 2.51057e13 1.20490
\(265\) −5.62897e12 −0.264592
\(266\) −3.58789e12 −0.165192
\(267\) −2.00179e13 −0.902833
\(268\) −1.43744e13 −0.635109
\(269\) 5.21846e12 0.225894 0.112947 0.993601i \(-0.463971\pi\)
0.112947 + 0.993601i \(0.463971\pi\)
\(270\) 4.09991e12 0.173890
\(271\) −4.48531e12 −0.186406 −0.0932032 0.995647i \(-0.529711\pi\)
−0.0932032 + 0.995647i \(0.529711\pi\)
\(272\) −7.80261e12 −0.317769
\(273\) −7.01562e12 −0.280009
\(274\) 7.03414e12 0.275158
\(275\) −2.02494e13 −0.776395
\(276\) 5.65979e13 2.12716
\(277\) −1.35475e13 −0.499137 −0.249568 0.968357i \(-0.580289\pi\)
−0.249568 + 0.968357i \(0.580289\pi\)
\(278\) −1.10929e12 −0.0400683
\(279\) 9.70302e12 0.343624
\(280\) 2.25474e13 0.782939
\(281\) −3.84766e13 −1.31012 −0.655062 0.755575i \(-0.727358\pi\)
−0.655062 + 0.755575i \(0.727358\pi\)
\(282\) −2.26967e13 −0.757866
\(283\) 1.31918e12 0.0431997 0.0215998 0.999767i \(-0.493124\pi\)
0.0215998 + 0.999767i \(0.493124\pi\)
\(284\) −4.49965e13 −1.44520
\(285\) −1.13544e12 −0.0357700
\(286\) −3.77994e13 −1.16808
\(287\) −2.01939e13 −0.612166
\(288\) 5.19011e12 0.154354
\(289\) −3.24689e13 −0.947390
\(290\) 2.06332e13 0.590715
\(291\) 3.69443e12 0.103785
\(292\) 1.13028e14 3.11589
\(293\) −2.28631e13 −0.618532 −0.309266 0.950976i \(-0.600083\pi\)
−0.309266 + 0.950976i \(0.600083\pi\)
\(294\) −1.55659e13 −0.413298
\(295\) 2.55410e12 0.0665605
\(296\) −4.75874e13 −1.21727
\(297\) 8.05647e12 0.202295
\(298\) 7.44309e12 0.183469
\(299\) −4.50832e13 −1.09100
\(300\) −3.81113e13 −0.905496
\(301\) 2.12637e13 0.496048
\(302\) −6.66401e13 −1.52650
\(303\) 2.17549e13 0.489353
\(304\) −7.60010e12 −0.167886
\(305\) 2.75693e13 0.598104
\(306\) −6.34152e12 −0.135122
\(307\) −1.45153e13 −0.303783 −0.151892 0.988397i \(-0.548536\pi\)
−0.151892 + 0.988397i \(0.548536\pi\)
\(308\) 8.37462e13 1.72162
\(309\) 1.27898e12 0.0258280
\(310\) 4.69516e13 0.931453
\(311\) −5.42173e13 −1.05671 −0.528355 0.849023i \(-0.677191\pi\)
−0.528355 + 0.849023i \(0.677191\pi\)
\(312\) −3.76381e13 −0.720738
\(313\) 5.61660e13 1.05677 0.528384 0.849005i \(-0.322798\pi\)
0.528384 + 0.849005i \(0.322798\pi\)
\(314\) 8.47890e12 0.156757
\(315\) 7.23551e12 0.131450
\(316\) 1.85600e13 0.331358
\(317\) −5.86840e13 −1.02966 −0.514830 0.857292i \(-0.672145\pi\)
−0.514830 + 0.857292i \(0.672145\pi\)
\(318\) −3.06222e13 −0.528064
\(319\) 4.05450e13 0.687208
\(320\) −1.74011e13 −0.289902
\(321\) −1.93014e13 −0.316090
\(322\) 1.46923e14 2.36529
\(323\) 1.75624e12 0.0277952
\(324\) 1.51630e13 0.235933
\(325\) 3.03576e13 0.464418
\(326\) −1.61254e14 −2.42556
\(327\) 2.11834e13 0.313316
\(328\) −1.08338e14 −1.57571
\(329\) −4.00550e13 −0.572901
\(330\) 3.89841e13 0.548354
\(331\) 2.77443e13 0.383813 0.191906 0.981413i \(-0.438533\pi\)
0.191906 + 0.981413i \(0.438533\pi\)
\(332\) −1.33765e14 −1.82005
\(333\) −1.52709e13 −0.204372
\(334\) −1.94319e14 −2.55806
\(335\) −1.18088e13 −0.152919
\(336\) 4.84310e13 0.616960
\(337\) 8.92104e12 0.111802 0.0559012 0.998436i \(-0.482197\pi\)
0.0559012 + 0.998436i \(0.482197\pi\)
\(338\) −8.66677e13 −1.06860
\(339\) 7.44457e13 0.903111
\(340\) −2.08613e13 −0.249004
\(341\) 9.22614e13 1.08360
\(342\) −6.17692e12 −0.0713886
\(343\) −9.52905e13 −1.08376
\(344\) 1.14078e14 1.27682
\(345\) 4.64962e13 0.512168
\(346\) 1.68506e14 1.82683
\(347\) −1.23395e13 −0.131670 −0.0658350 0.997831i \(-0.520971\pi\)
−0.0658350 + 0.997831i \(0.520971\pi\)
\(348\) 7.63094e13 0.801479
\(349\) 2.06884e13 0.213888 0.106944 0.994265i \(-0.465893\pi\)
0.106944 + 0.994265i \(0.465893\pi\)
\(350\) −9.89336e13 −1.00686
\(351\) −1.20781e13 −0.121007
\(352\) 4.93503e13 0.486749
\(353\) 7.96972e13 0.773895 0.386947 0.922102i \(-0.373529\pi\)
0.386947 + 0.922102i \(0.373529\pi\)
\(354\) 1.38946e13 0.132839
\(355\) −3.69654e13 −0.347969
\(356\) −3.58240e14 −3.32046
\(357\) −1.11915e13 −0.102144
\(358\) 1.61935e14 1.45541
\(359\) −1.58028e14 −1.39867 −0.699335 0.714794i \(-0.746520\pi\)
−0.699335 + 0.714794i \(0.746520\pi\)
\(360\) 3.88178e13 0.338350
\(361\) −1.14780e14 −0.985315
\(362\) −1.49531e14 −1.26425
\(363\) 7.27439e12 0.0605773
\(364\) −1.25551e14 −1.02982
\(365\) 9.28549e13 0.750229
\(366\) 1.49980e14 1.19368
\(367\) −2.16424e14 −1.69685 −0.848423 0.529319i \(-0.822448\pi\)
−0.848423 + 0.529319i \(0.822448\pi\)
\(368\) 3.11223e14 2.40386
\(369\) −3.47659e13 −0.264550
\(370\) −7.38937e13 −0.553985
\(371\) −5.40418e13 −0.399184
\(372\) 1.73645e14 1.26379
\(373\) −2.24017e14 −1.60651 −0.803254 0.595637i \(-0.796900\pi\)
−0.803254 + 0.595637i \(0.796900\pi\)
\(374\) −6.02985e13 −0.426101
\(375\) −7.36982e13 −0.513198
\(376\) −2.14891e14 −1.47464
\(377\) −6.07844e13 −0.411069
\(378\) 3.93619e13 0.262344
\(379\) −1.47661e14 −0.969949 −0.484974 0.874528i \(-0.661171\pi\)
−0.484974 + 0.874528i \(0.661171\pi\)
\(380\) −2.03198e13 −0.131556
\(381\) 1.18269e13 0.0754714
\(382\) −4.33169e14 −2.72464
\(383\) 1.58886e14 0.985125 0.492562 0.870277i \(-0.336060\pi\)
0.492562 + 0.870277i \(0.336060\pi\)
\(384\) −1.38406e14 −0.845927
\(385\) 6.87990e13 0.414523
\(386\) 5.50271e13 0.326848
\(387\) 3.66078e13 0.214370
\(388\) 6.61152e13 0.381704
\(389\) −1.38859e14 −0.790405 −0.395203 0.918594i \(-0.629326\pi\)
−0.395203 + 0.918594i \(0.629326\pi\)
\(390\) −5.84444e13 −0.328011
\(391\) −7.19178e13 −0.397983
\(392\) −1.47377e14 −0.804185
\(393\) 1.42906e14 0.768941
\(394\) −2.87034e14 −1.52302
\(395\) 1.52473e13 0.0797829
\(396\) 1.44178e14 0.744004
\(397\) −1.52121e14 −0.774179 −0.387090 0.922042i \(-0.626520\pi\)
−0.387090 + 0.922042i \(0.626520\pi\)
\(398\) −1.86340e14 −0.935295
\(399\) −1.09010e13 −0.0539654
\(400\) −2.09568e14 −1.02328
\(401\) 4.48848e13 0.216175 0.108087 0.994141i \(-0.465527\pi\)
0.108087 + 0.994141i \(0.465527\pi\)
\(402\) −6.42412e13 −0.305190
\(403\) −1.38317e14 −0.648183
\(404\) 3.89324e14 1.79976
\(405\) 1.24567e13 0.0568068
\(406\) 1.98093e14 0.891200
\(407\) −1.45204e14 −0.644478
\(408\) −6.00412e13 −0.262917
\(409\) −1.18153e14 −0.510468 −0.255234 0.966879i \(-0.582152\pi\)
−0.255234 + 0.966879i \(0.582152\pi\)
\(410\) −1.68227e14 −0.717110
\(411\) 2.13717e13 0.0898895
\(412\) 2.28885e13 0.0949909
\(413\) 2.45210e13 0.100418
\(414\) 2.52944e14 1.02217
\(415\) −1.09890e14 −0.438223
\(416\) −7.39852e13 −0.291160
\(417\) −3.37035e12 −0.0130896
\(418\) −5.87334e13 −0.225121
\(419\) −1.87467e14 −0.709165 −0.354582 0.935025i \(-0.615377\pi\)
−0.354582 + 0.935025i \(0.615377\pi\)
\(420\) 1.29486e14 0.483451
\(421\) −2.67548e14 −0.985938 −0.492969 0.870047i \(-0.664088\pi\)
−0.492969 + 0.870047i \(0.664088\pi\)
\(422\) 2.38093e14 0.866020
\(423\) −6.89590e13 −0.247582
\(424\) −2.89929e14 −1.02749
\(425\) 4.84272e13 0.169414
\(426\) −2.01096e14 −0.694465
\(427\) 2.64684e14 0.902348
\(428\) −3.45416e14 −1.16252
\(429\) −1.14845e14 −0.381591
\(430\) 1.77140e14 0.581086
\(431\) 3.55171e14 1.15030 0.575152 0.818046i \(-0.304943\pi\)
0.575152 + 0.818046i \(0.304943\pi\)
\(432\) 8.33790e13 0.266622
\(433\) −1.83266e14 −0.578628 −0.289314 0.957234i \(-0.593427\pi\)
−0.289314 + 0.957234i \(0.593427\pi\)
\(434\) 4.50766e14 1.40526
\(435\) 6.26895e13 0.192976
\(436\) 3.79097e14 1.15232
\(437\) −7.00511e13 −0.210265
\(438\) 5.05140e14 1.49728
\(439\) 1.75742e14 0.514424 0.257212 0.966355i \(-0.417196\pi\)
0.257212 + 0.966355i \(0.417196\pi\)
\(440\) 3.69100e14 1.06697
\(441\) −4.72935e13 −0.135017
\(442\) 9.03986e13 0.254882
\(443\) 2.35033e14 0.654499 0.327249 0.944938i \(-0.393878\pi\)
0.327249 + 0.944938i \(0.393878\pi\)
\(444\) −2.73287e14 −0.751644
\(445\) −2.94300e14 −0.799485
\(446\) 2.83860e14 0.761663
\(447\) 2.26142e13 0.0599363
\(448\) −1.67062e14 −0.437370
\(449\) −4.79472e13 −0.123996 −0.0619981 0.998076i \(-0.519747\pi\)
−0.0619981 + 0.998076i \(0.519747\pi\)
\(450\) −1.70325e14 −0.435120
\(451\) −3.30572e14 −0.834249
\(452\) 1.33227e15 3.32149
\(453\) −2.02471e14 −0.498681
\(454\) −5.84379e14 −1.42196
\(455\) −1.03142e14 −0.247956
\(456\) −5.84828e13 −0.138906
\(457\) 2.63461e14 0.618269 0.309134 0.951018i \(-0.399961\pi\)
0.309134 + 0.951018i \(0.399961\pi\)
\(458\) 1.11417e15 2.58341
\(459\) −1.92673e13 −0.0441419
\(460\) 8.32093e14 1.88367
\(461\) 7.90062e12 0.0176728 0.00883641 0.999961i \(-0.497187\pi\)
0.00883641 + 0.999961i \(0.497187\pi\)
\(462\) 3.74274e14 0.827291
\(463\) 2.36642e13 0.0516887 0.0258444 0.999666i \(-0.491773\pi\)
0.0258444 + 0.999666i \(0.491773\pi\)
\(464\) 4.19613e14 0.905733
\(465\) 1.42652e14 0.304289
\(466\) −1.03477e15 −2.18132
\(467\) −5.01380e14 −1.04454 −0.522269 0.852781i \(-0.674914\pi\)
−0.522269 + 0.852781i \(0.674914\pi\)
\(468\) −2.16149e14 −0.445043
\(469\) −1.13373e14 −0.230705
\(470\) −3.33683e14 −0.671113
\(471\) 2.57613e13 0.0512097
\(472\) 1.31553e14 0.258476
\(473\) 3.48086e14 0.676006
\(474\) 8.29471e13 0.159228
\(475\) 4.71702e13 0.0895062
\(476\) −2.00282e14 −0.375668
\(477\) −9.30387e13 −0.172509
\(478\) −1.49491e15 −2.74007
\(479\) 3.41620e14 0.619010 0.309505 0.950898i \(-0.399837\pi\)
0.309505 + 0.950898i \(0.399837\pi\)
\(480\) 7.63040e13 0.136685
\(481\) 2.17687e14 0.385509
\(482\) 1.96589e15 3.44192
\(483\) 4.46395e14 0.772698
\(484\) 1.30182e14 0.222793
\(485\) 5.43148e13 0.0919049
\(486\) 6.77657e13 0.113373
\(487\) 4.67082e14 0.772652 0.386326 0.922362i \(-0.373744\pi\)
0.386326 + 0.922362i \(0.373744\pi\)
\(488\) 1.42000e15 2.32263
\(489\) −4.89934e14 −0.792390
\(490\) −2.28847e14 −0.365987
\(491\) 6.11829e14 0.967569 0.483784 0.875187i \(-0.339262\pi\)
0.483784 + 0.875187i \(0.339262\pi\)
\(492\) −6.22168e14 −0.972970
\(493\) −9.69647e13 −0.149953
\(494\) 8.80523e13 0.134661
\(495\) 1.18445e14 0.179138
\(496\) 9.54843e14 1.42818
\(497\) −3.54893e14 −0.524973
\(498\) −5.97815e14 −0.874591
\(499\) 1.18221e15 1.71057 0.855283 0.518160i \(-0.173383\pi\)
0.855283 + 0.518160i \(0.173383\pi\)
\(500\) −1.31890e15 −1.88745
\(501\) −5.90397e14 −0.835674
\(502\) 1.24047e15 1.73666
\(503\) −9.30484e14 −1.28850 −0.644251 0.764814i \(-0.722831\pi\)
−0.644251 + 0.764814i \(0.722831\pi\)
\(504\) 3.72676e14 0.510463
\(505\) 3.19837e14 0.433337
\(506\) 2.40513e15 3.22337
\(507\) −2.63321e14 −0.349093
\(508\) 2.11653e14 0.277571
\(509\) 1.32830e15 1.72325 0.861627 0.507542i \(-0.169446\pi\)
0.861627 + 0.507542i \(0.169446\pi\)
\(510\) −9.32319e13 −0.119654
\(511\) 8.91469e14 1.13186
\(512\) −1.67908e15 −2.10905
\(513\) −1.87672e13 −0.0233214
\(514\) 1.22162e15 1.50189
\(515\) 1.88033e13 0.0228715
\(516\) 6.55130e14 0.788414
\(517\) −6.55698e14 −0.780739
\(518\) −7.09429e14 −0.835786
\(519\) 5.11969e14 0.596792
\(520\) −5.53349e14 −0.638235
\(521\) −5.69906e14 −0.650422 −0.325211 0.945641i \(-0.605435\pi\)
−0.325211 + 0.945641i \(0.605435\pi\)
\(522\) 3.41038e14 0.385136
\(523\) 5.33919e14 0.596645 0.298323 0.954465i \(-0.403573\pi\)
0.298323 + 0.954465i \(0.403573\pi\)
\(524\) 2.55744e15 2.82803
\(525\) −3.00588e14 −0.328924
\(526\) 8.81086e14 0.954106
\(527\) −2.20646e14 −0.236449
\(528\) 7.92811e14 0.840782
\(529\) 1.91577e15 2.01066
\(530\) −4.50202e14 −0.467616
\(531\) 4.22156e13 0.0433963
\(532\) −1.95084e14 −0.198475
\(533\) 4.95589e14 0.499025
\(534\) −1.60102e15 −1.59559
\(535\) −2.83765e14 −0.279907
\(536\) −6.08233e14 −0.593832
\(537\) 4.92004e14 0.475456
\(538\) 4.17370e14 0.399226
\(539\) −4.49691e14 −0.425771
\(540\) 2.22924e14 0.208925
\(541\) −1.12465e15 −1.04336 −0.521679 0.853142i \(-0.674694\pi\)
−0.521679 + 0.853142i \(0.674694\pi\)
\(542\) −3.58732e14 −0.329439
\(543\) −4.54316e14 −0.413009
\(544\) −1.18023e14 −0.106212
\(545\) 3.11435e14 0.277451
\(546\) −5.61106e14 −0.494863
\(547\) −4.20520e14 −0.367161 −0.183580 0.983005i \(-0.558769\pi\)
−0.183580 + 0.983005i \(0.558769\pi\)
\(548\) 3.82466e14 0.330598
\(549\) 4.55681e14 0.389954
\(550\) −1.61954e15 −1.37213
\(551\) −9.44480e13 −0.0792244
\(552\) 2.39486e15 1.98891
\(553\) 1.46385e14 0.120367
\(554\) −1.08352e15 −0.882131
\(555\) −2.24510e14 −0.180977
\(556\) −6.03155e13 −0.0481413
\(557\) −1.70913e15 −1.35074 −0.675369 0.737480i \(-0.736016\pi\)
−0.675369 + 0.737480i \(0.736016\pi\)
\(558\) 7.76042e14 0.607291
\(559\) −5.21845e14 −0.404368
\(560\) 7.12023e14 0.546336
\(561\) −1.83204e14 −0.139200
\(562\) −3.07734e15 −2.31540
\(563\) −7.02850e14 −0.523680 −0.261840 0.965111i \(-0.584329\pi\)
−0.261840 + 0.965111i \(0.584329\pi\)
\(564\) −1.23408e15 −0.910563
\(565\) 1.09449e15 0.799732
\(566\) 1.05508e14 0.0763473
\(567\) 1.19593e14 0.0857032
\(568\) −1.90396e15 −1.35127
\(569\) −7.52563e14 −0.528963 −0.264481 0.964391i \(-0.585201\pi\)
−0.264481 + 0.964391i \(0.585201\pi\)
\(570\) −9.08120e13 −0.0632167
\(571\) −7.63440e14 −0.526352 −0.263176 0.964748i \(-0.584770\pi\)
−0.263176 + 0.964748i \(0.584770\pi\)
\(572\) −2.05526e15 −1.40342
\(573\) −1.31609e15 −0.890092
\(574\) −1.61510e15 −1.08189
\(575\) −1.93161e15 −1.28158
\(576\) −2.87615e14 −0.189011
\(577\) 4.05246e14 0.263786 0.131893 0.991264i \(-0.457894\pi\)
0.131893 + 0.991264i \(0.457894\pi\)
\(578\) −2.59684e15 −1.67433
\(579\) 1.67188e14 0.106776
\(580\) 1.12189e15 0.709734
\(581\) −1.05502e15 −0.661138
\(582\) 2.95478e14 0.183421
\(583\) −8.84661e14 −0.544001
\(584\) 4.78264e15 2.91338
\(585\) −1.77571e14 −0.107155
\(586\) −1.82857e15 −1.09314
\(587\) 2.81960e15 1.66985 0.834926 0.550363i \(-0.185511\pi\)
0.834926 + 0.550363i \(0.185511\pi\)
\(588\) −8.46361e14 −0.496570
\(589\) −2.14919e14 −0.124923
\(590\) 2.04275e14 0.117633
\(591\) −8.72091e14 −0.497543
\(592\) −1.50276e15 −0.849415
\(593\) 1.71000e14 0.0957622 0.0478811 0.998853i \(-0.484753\pi\)
0.0478811 + 0.998853i \(0.484753\pi\)
\(594\) 6.44352e14 0.357518
\(595\) −1.64535e14 −0.0904514
\(596\) 4.04702e14 0.220435
\(597\) −5.66152e14 −0.305545
\(598\) −3.60573e15 −1.92813
\(599\) 1.28350e15 0.680062 0.340031 0.940414i \(-0.389562\pi\)
0.340031 + 0.940414i \(0.389562\pi\)
\(600\) −1.61263e15 −0.846645
\(601\) −7.80949e14 −0.406268 −0.203134 0.979151i \(-0.565113\pi\)
−0.203134 + 0.979151i \(0.565113\pi\)
\(602\) 1.70066e15 0.876672
\(603\) −1.95183e14 −0.0997003
\(604\) −3.62341e15 −1.83406
\(605\) 1.06947e14 0.0536430
\(606\) 1.73994e15 0.864841
\(607\) −1.58644e15 −0.781423 −0.390712 0.920513i \(-0.627771\pi\)
−0.390712 + 0.920513i \(0.627771\pi\)
\(608\) −1.14960e14 −0.0561145
\(609\) 6.01861e14 0.291140
\(610\) 2.20498e15 1.05704
\(611\) 9.83013e14 0.467017
\(612\) −3.44807e14 −0.162346
\(613\) −7.34991e14 −0.342965 −0.171482 0.985187i \(-0.554856\pi\)
−0.171482 + 0.985187i \(0.554856\pi\)
\(614\) −1.16092e15 −0.536880
\(615\) −5.11122e14 −0.234267
\(616\) 3.54360e15 1.60972
\(617\) 3.87074e15 1.74271 0.871356 0.490652i \(-0.163241\pi\)
0.871356 + 0.490652i \(0.163241\pi\)
\(618\) 1.02292e14 0.0456461
\(619\) −1.48567e15 −0.657089 −0.328545 0.944488i \(-0.606558\pi\)
−0.328545 + 0.944488i \(0.606558\pi\)
\(620\) 2.55289e15 1.11912
\(621\) 7.68515e14 0.333925
\(622\) −4.33627e15 −1.86754
\(623\) −2.82548e15 −1.20617
\(624\) −1.18857e15 −0.502933
\(625\) 6.77492e14 0.284161
\(626\) 4.49213e15 1.86764
\(627\) −1.78449e14 −0.0735431
\(628\) 4.61022e14 0.188340
\(629\) 3.47259e14 0.140629
\(630\) 5.78692e14 0.232313
\(631\) 3.20662e15 1.27611 0.638053 0.769993i \(-0.279740\pi\)
0.638053 + 0.769993i \(0.279740\pi\)
\(632\) 7.85339e14 0.309823
\(633\) 7.23393e14 0.282914
\(634\) −4.69351e15 −1.81973
\(635\) 1.73876e14 0.0668321
\(636\) −1.66501e15 −0.634459
\(637\) 6.74170e14 0.254685
\(638\) 3.24276e15 1.21451
\(639\) −6.10986e14 −0.226870
\(640\) −2.03482e15 −0.749093
\(641\) 1.69427e15 0.618393 0.309196 0.950998i \(-0.399940\pi\)
0.309196 + 0.950998i \(0.399940\pi\)
\(642\) −1.54371e15 −0.558629
\(643\) −1.21733e15 −0.436765 −0.218382 0.975863i \(-0.570078\pi\)
−0.218382 + 0.975863i \(0.570078\pi\)
\(644\) 7.98865e15 2.84185
\(645\) 5.38201e14 0.189831
\(646\) 1.40463e14 0.0491228
\(647\) −3.53897e15 −1.22717 −0.613584 0.789630i \(-0.710273\pi\)
−0.613584 + 0.789630i \(0.710273\pi\)
\(648\) 6.41602e14 0.220599
\(649\) 4.01408e14 0.136848
\(650\) 2.42798e15 0.820772
\(651\) 1.36956e15 0.459075
\(652\) −8.76782e15 −2.91427
\(653\) 2.33782e15 0.770530 0.385265 0.922806i \(-0.374110\pi\)
0.385265 + 0.922806i \(0.374110\pi\)
\(654\) 1.69424e15 0.553728
\(655\) 2.10099e15 0.680920
\(656\) −3.42120e15 −1.09953
\(657\) 1.53476e15 0.489137
\(658\) −3.20358e15 −1.01250
\(659\) 1.65395e15 0.518385 0.259192 0.965826i \(-0.416544\pi\)
0.259192 + 0.965826i \(0.416544\pi\)
\(660\) 2.11968e15 0.658838
\(661\) 2.69598e15 0.831015 0.415508 0.909590i \(-0.363604\pi\)
0.415508 + 0.909590i \(0.363604\pi\)
\(662\) 2.21897e15 0.678317
\(663\) 2.74656e14 0.0832655
\(664\) −5.66008e15 −1.70176
\(665\) −1.60265e14 −0.0477880
\(666\) −1.22136e15 −0.361189
\(667\) 3.86763e15 1.13437
\(668\) −1.05657e16 −3.07346
\(669\) 8.62447e14 0.248822
\(670\) −9.44463e14 −0.270255
\(671\) 4.33285e15 1.22970
\(672\) 7.32570e14 0.206214
\(673\) 2.56365e15 0.715775 0.357888 0.933765i \(-0.383497\pi\)
0.357888 + 0.933765i \(0.383497\pi\)
\(674\) 7.13500e14 0.197590
\(675\) −5.17494e14 −0.142146
\(676\) −4.71237e15 −1.28390
\(677\) 1.34304e15 0.362953 0.181476 0.983395i \(-0.441912\pi\)
0.181476 + 0.983395i \(0.441912\pi\)
\(678\) 5.95412e15 1.59608
\(679\) 5.21458e14 0.138655
\(680\) −8.82715e14 −0.232821
\(681\) −1.77551e15 −0.464530
\(682\) 7.37902e15 1.91507
\(683\) 2.87848e15 0.741053 0.370527 0.928822i \(-0.379177\pi\)
0.370527 + 0.928822i \(0.379177\pi\)
\(684\) −3.35857e14 −0.0857721
\(685\) 3.14203e14 0.0795998
\(686\) −7.62128e15 −1.91534
\(687\) 3.38517e15 0.843955
\(688\) 3.60246e15 0.890968
\(689\) 1.32627e15 0.325407
\(690\) 3.71874e15 0.905161
\(691\) 5.82940e15 1.40765 0.703824 0.710374i \(-0.251474\pi\)
0.703824 + 0.710374i \(0.251474\pi\)
\(692\) 9.16216e15 2.19490
\(693\) 1.13715e15 0.270262
\(694\) −9.86910e14 −0.232702
\(695\) −4.95503e13 −0.0115912
\(696\) 3.22893e15 0.749389
\(697\) 7.90575e14 0.182038
\(698\) 1.65465e15 0.378007
\(699\) −3.14391e15 −0.712599
\(700\) −5.37930e15 −1.20973
\(701\) 3.84624e15 0.858197 0.429098 0.903258i \(-0.358831\pi\)
0.429098 + 0.903258i \(0.358831\pi\)
\(702\) −9.66002e14 −0.213857
\(703\) 3.38246e14 0.0742983
\(704\) −2.73480e15 −0.596040
\(705\) −1.01382e15 −0.219241
\(706\) 6.37413e15 1.36771
\(707\) 3.07065e15 0.653767
\(708\) 7.55487e14 0.159604
\(709\) 3.06847e15 0.643231 0.321616 0.946870i \(-0.395774\pi\)
0.321616 + 0.946870i \(0.395774\pi\)
\(710\) −2.95648e15 −0.614969
\(711\) 2.52016e14 0.0520171
\(712\) −1.51584e16 −3.10466
\(713\) 8.80092e15 1.78869
\(714\) −8.95088e14 −0.180520
\(715\) −1.68843e15 −0.337910
\(716\) 8.80488e15 1.74865
\(717\) −4.54196e15 −0.895134
\(718\) −1.26390e16 −2.47189
\(719\) 6.87669e15 1.33466 0.667330 0.744762i \(-0.267437\pi\)
0.667330 + 0.744762i \(0.267437\pi\)
\(720\) 1.22582e15 0.236102
\(721\) 1.80524e14 0.0345057
\(722\) −9.18001e15 −1.74136
\(723\) 5.97293e15 1.12442
\(724\) −8.13042e15 −1.51898
\(725\) −2.60434e15 −0.482880
\(726\) 5.81802e14 0.107059
\(727\) 6.86387e15 1.25351 0.626757 0.779214i \(-0.284382\pi\)
0.626757 + 0.779214i \(0.284382\pi\)
\(728\) −5.31252e15 −0.962892
\(729\) 2.05891e14 0.0370370
\(730\) 7.42648e15 1.32589
\(731\) −8.32460e14 −0.147509
\(732\) 8.15483e15 1.43418
\(733\) −4.45996e15 −0.778501 −0.389251 0.921132i \(-0.627266\pi\)
−0.389251 + 0.921132i \(0.627266\pi\)
\(734\) −1.73095e16 −2.99886
\(735\) −6.95300e14 −0.119562
\(736\) 4.70758e15 0.803470
\(737\) −1.85590e15 −0.314401
\(738\) −2.78056e15 −0.467543
\(739\) −2.66547e15 −0.444866 −0.222433 0.974948i \(-0.571400\pi\)
−0.222433 + 0.974948i \(0.571400\pi\)
\(740\) −4.01781e15 −0.665603
\(741\) 2.67528e14 0.0439915
\(742\) −4.32223e15 −0.705484
\(743\) −5.44547e15 −0.882261 −0.441131 0.897443i \(-0.645422\pi\)
−0.441131 + 0.897443i \(0.645422\pi\)
\(744\) 7.34752e15 1.18165
\(745\) 3.32470e14 0.0530754
\(746\) −1.79168e16 −2.83920
\(747\) −1.81633e15 −0.285714
\(748\) −3.27860e15 −0.511953
\(749\) −2.72433e15 −0.422290
\(750\) −5.89434e15 −0.906981
\(751\) 1.41234e15 0.215735 0.107868 0.994165i \(-0.465598\pi\)
0.107868 + 0.994165i \(0.465598\pi\)
\(752\) −6.78603e15 −1.02901
\(753\) 3.76889e15 0.567337
\(754\) −4.86150e15 −0.726488
\(755\) −2.97670e15 −0.441597
\(756\) 2.14022e15 0.315202
\(757\) 1.28316e16 1.87609 0.938045 0.346514i \(-0.112635\pi\)
0.938045 + 0.346514i \(0.112635\pi\)
\(758\) −1.18098e16 −1.71420
\(759\) 7.30745e15 1.05302
\(760\) −8.59804e14 −0.123006
\(761\) −1.15160e15 −0.163563 −0.0817813 0.996650i \(-0.526061\pi\)
−0.0817813 + 0.996650i \(0.526061\pi\)
\(762\) 9.45906e14 0.133382
\(763\) 2.98998e15 0.418585
\(764\) −2.35526e16 −3.27360
\(765\) −2.83265e14 −0.0390890
\(766\) 1.27076e16 1.74102
\(767\) −6.01785e14 −0.0818590
\(768\) −8.64561e15 −1.16764
\(769\) −1.81080e14 −0.0242815 −0.0121407 0.999926i \(-0.503865\pi\)
−0.0121407 + 0.999926i \(0.503865\pi\)
\(770\) 5.50251e15 0.732591
\(771\) 3.71161e15 0.490641
\(772\) 2.99198e15 0.392702
\(773\) 1.46772e16 1.91274 0.956368 0.292165i \(-0.0943756\pi\)
0.956368 + 0.292165i \(0.0943756\pi\)
\(774\) 2.92787e15 0.378858
\(775\) −5.92626e15 −0.761415
\(776\) 2.79757e15 0.356896
\(777\) −2.15544e15 −0.273037
\(778\) −1.11058e16 −1.39689
\(779\) 7.70056e14 0.0961759
\(780\) −3.17779e15 −0.394099
\(781\) −5.80957e15 −0.715424
\(782\) −5.75194e15 −0.703360
\(783\) 1.03617e15 0.125817
\(784\) −4.65400e15 −0.561162
\(785\) 3.78738e14 0.0453477
\(786\) 1.14296e16 1.35896
\(787\) 3.83560e15 0.452869 0.226435 0.974026i \(-0.427293\pi\)
0.226435 + 0.974026i \(0.427293\pi\)
\(788\) −1.56069e16 −1.82988
\(789\) 2.67699e15 0.311690
\(790\) 1.21947e15 0.141001
\(791\) 1.05078e16 1.20654
\(792\) 6.10069e15 0.695649
\(793\) −6.49575e15 −0.735575
\(794\) −1.21666e16 −1.36822
\(795\) −1.36784e15 −0.152762
\(796\) −1.01318e16 −1.12374
\(797\) 1.05481e16 1.16186 0.580929 0.813954i \(-0.302690\pi\)
0.580929 + 0.813954i \(0.302690\pi\)
\(798\) −8.71856e14 −0.0953738
\(799\) 1.56812e15 0.170362
\(800\) −3.16993e15 −0.342023
\(801\) −4.86436e15 −0.521251
\(802\) 3.58986e15 0.382049
\(803\) 1.45933e16 1.54247
\(804\) −3.49298e15 −0.366681
\(805\) 6.56282e15 0.684247
\(806\) −1.10625e16 −1.14554
\(807\) 1.26809e15 0.130420
\(808\) 1.64737e16 1.68279
\(809\) 5.79101e15 0.587540 0.293770 0.955876i \(-0.405090\pi\)
0.293770 + 0.955876i \(0.405090\pi\)
\(810\) 9.96279e14 0.100395
\(811\) −1.64492e16 −1.64638 −0.823190 0.567767i \(-0.807808\pi\)
−0.823190 + 0.567767i \(0.807808\pi\)
\(812\) 1.07709e16 1.07076
\(813\) −1.08993e15 −0.107622
\(814\) −1.16133e16 −1.13899
\(815\) −7.20292e15 −0.701685
\(816\) −1.89604e15 −0.183464
\(817\) −8.10853e14 −0.0779329
\(818\) −9.44985e15 −0.902156
\(819\) −1.70480e15 −0.161663
\(820\) −9.14701e15 −0.861594
\(821\) −1.68942e16 −1.58070 −0.790350 0.612655i \(-0.790101\pi\)
−0.790350 + 0.612655i \(0.790101\pi\)
\(822\) 1.70930e15 0.158863
\(823\) 7.50053e15 0.692457 0.346228 0.938150i \(-0.387462\pi\)
0.346228 + 0.938150i \(0.387462\pi\)
\(824\) 9.68493e14 0.0888171
\(825\) −4.92061e15 −0.448252
\(826\) 1.96118e15 0.177471
\(827\) 1.69067e16 1.51977 0.759887 0.650055i \(-0.225254\pi\)
0.759887 + 0.650055i \(0.225254\pi\)
\(828\) 1.37533e16 1.22812
\(829\) −3.61894e15 −0.321020 −0.160510 0.987034i \(-0.551314\pi\)
−0.160510 + 0.987034i \(0.551314\pi\)
\(830\) −8.78897e15 −0.774476
\(831\) −3.29204e15 −0.288177
\(832\) 4.09996e15 0.356535
\(833\) 1.07545e15 0.0929059
\(834\) −2.69559e14 −0.0231334
\(835\) −8.67992e15 −0.740014
\(836\) −3.19351e15 −0.270479
\(837\) 2.35783e15 0.198392
\(838\) −1.49935e16 −1.25332
\(839\) 1.98137e16 1.64541 0.822707 0.568466i \(-0.192463\pi\)
0.822707 + 0.568466i \(0.192463\pi\)
\(840\) 5.47902e15 0.452030
\(841\) −6.98589e15 −0.572590
\(842\) −2.13983e16 −1.74246
\(843\) −9.34982e15 −0.756401
\(844\) 1.29458e16 1.04051
\(845\) −3.87130e15 −0.309132
\(846\) −5.51530e15 −0.437554
\(847\) 1.02676e15 0.0809302
\(848\) −9.15564e15 −0.716988
\(849\) 3.20562e14 0.0249413
\(850\) 3.87318e15 0.299408
\(851\) −1.38511e16 −1.06383
\(852\) −1.09342e16 −0.834387
\(853\) 2.28015e16 1.72879 0.864397 0.502809i \(-0.167700\pi\)
0.864397 + 0.502809i \(0.167700\pi\)
\(854\) 2.11693e16 1.59473
\(855\) −2.75912e14 −0.0206518
\(856\) −1.46158e16 −1.08697
\(857\) −1.99033e15 −0.147072 −0.0735359 0.997293i \(-0.523428\pi\)
−0.0735359 + 0.997293i \(0.523428\pi\)
\(858\) −9.18526e15 −0.674390
\(859\) −4.83946e15 −0.353049 −0.176524 0.984296i \(-0.556485\pi\)
−0.176524 + 0.984296i \(0.556485\pi\)
\(860\) 9.63161e15 0.698164
\(861\) −4.90711e15 −0.353434
\(862\) 2.84064e16 2.03295
\(863\) 1.58331e16 1.12592 0.562960 0.826484i \(-0.309663\pi\)
0.562960 + 0.826484i \(0.309663\pi\)
\(864\) 1.26120e15 0.0891162
\(865\) 7.52688e15 0.528477
\(866\) −1.46575e16 −1.02262
\(867\) −7.88993e15 −0.546976
\(868\) 2.45095e16 1.68840
\(869\) 2.39631e15 0.164034
\(870\) 5.01387e15 0.341050
\(871\) 2.78234e15 0.188066
\(872\) 1.60409e16 1.07743
\(873\) 8.97746e14 0.0599204
\(874\) −5.60265e15 −0.371604
\(875\) −1.04023e16 −0.685622
\(876\) 2.74659e16 1.79896
\(877\) 2.47298e16 1.60962 0.804808 0.593536i \(-0.202268\pi\)
0.804808 + 0.593536i \(0.202268\pi\)
\(878\) 1.40558e16 0.909148
\(879\) −5.55572e15 −0.357110
\(880\) 1.16558e16 0.744537
\(881\) 1.84220e15 0.116942 0.0584710 0.998289i \(-0.481377\pi\)
0.0584710 + 0.998289i \(0.481377\pi\)
\(882\) −3.78251e15 −0.238618
\(883\) 1.86832e16 1.17130 0.585648 0.810565i \(-0.300840\pi\)
0.585648 + 0.810565i \(0.300840\pi\)
\(884\) 4.91523e15 0.306236
\(885\) 6.20646e14 0.0384287
\(886\) 1.87978e16 1.15670
\(887\) 2.73600e16 1.67316 0.836578 0.547848i \(-0.184553\pi\)
0.836578 + 0.547848i \(0.184553\pi\)
\(888\) −1.15637e16 −0.702793
\(889\) 1.66933e15 0.100828
\(890\) −2.35380e16 −1.41294
\(891\) 1.95772e15 0.116795
\(892\) 1.54343e16 0.915124
\(893\) 1.52742e15 0.0900070
\(894\) 1.80867e15 0.105926
\(895\) 7.23336e15 0.421031
\(896\) −1.95356e16 −1.13014
\(897\) −1.09552e16 −0.629887
\(898\) −3.83479e15 −0.219140
\(899\) 1.18660e16 0.673949
\(900\) −9.26104e15 −0.522788
\(901\) 2.11570e15 0.118704
\(902\) −2.64390e16 −1.47438
\(903\) 5.16709e15 0.286394
\(904\) 5.63733e16 3.10561
\(905\) −6.67928e15 −0.365732
\(906\) −1.61935e16 −0.881326
\(907\) −6.43997e14 −0.0348372 −0.0174186 0.999848i \(-0.505545\pi\)
−0.0174186 + 0.999848i \(0.505545\pi\)
\(908\) −3.17744e16 −1.70846
\(909\) 5.28644e15 0.282528
\(910\) −8.24927e15 −0.438216
\(911\) −1.57513e16 −0.831696 −0.415848 0.909434i \(-0.636515\pi\)
−0.415848 + 0.909434i \(0.636515\pi\)
\(912\) −1.84682e15 −0.0969290
\(913\) −1.72706e16 −0.900987
\(914\) 2.10715e16 1.09267
\(915\) 6.69934e15 0.345316
\(916\) 6.05809e16 3.10392
\(917\) 2.01709e16 1.02729
\(918\) −1.54099e15 −0.0780126
\(919\) −2.79204e16 −1.40503 −0.702516 0.711668i \(-0.747940\pi\)
−0.702516 + 0.711668i \(0.747940\pi\)
\(920\) 3.52088e16 1.76124
\(921\) −3.52721e15 −0.175389
\(922\) 6.31887e14 0.0312334
\(923\) 8.70962e15 0.427947
\(924\) 2.03503e16 0.993976
\(925\) 9.32692e15 0.452855
\(926\) 1.89265e15 0.0913501
\(927\) 3.10791e14 0.0149118
\(928\) 6.34709e15 0.302734
\(929\) −7.89495e15 −0.374337 −0.187169 0.982328i \(-0.559931\pi\)
−0.187169 + 0.982328i \(0.559931\pi\)
\(930\) 1.14092e16 0.537775
\(931\) 1.04754e15 0.0490848
\(932\) −5.62632e16 −2.62082
\(933\) −1.31748e16 −0.610092
\(934\) −4.01001e16 −1.84602
\(935\) −2.69343e15 −0.123266
\(936\) −9.14606e15 −0.416118
\(937\) −1.31134e16 −0.593126 −0.296563 0.955013i \(-0.595840\pi\)
−0.296563 + 0.955013i \(0.595840\pi\)
\(938\) −9.06748e15 −0.407728
\(939\) 1.36483e16 0.610126
\(940\) −1.81433e16 −0.806330
\(941\) −2.58260e16 −1.14107 −0.570537 0.821272i \(-0.693265\pi\)
−0.570537 + 0.821272i \(0.693265\pi\)
\(942\) 2.06037e15 0.0905036
\(943\) −3.15337e16 −1.37708
\(944\) 4.15430e15 0.180365
\(945\) 1.75823e15 0.0758928
\(946\) 2.78397e16 1.19471
\(947\) 1.15258e15 0.0491751 0.0245875 0.999698i \(-0.492173\pi\)
0.0245875 + 0.999698i \(0.492173\pi\)
\(948\) 4.51007e15 0.191310
\(949\) −2.18780e16 −0.922665
\(950\) 3.77265e15 0.158185
\(951\) −1.42602e16 −0.594474
\(952\) −8.47465e15 −0.351252
\(953\) −2.71230e16 −1.11770 −0.558852 0.829267i \(-0.688758\pi\)
−0.558852 + 0.829267i \(0.688758\pi\)
\(954\) −7.44118e15 −0.304878
\(955\) −1.93489e16 −0.788203
\(956\) −8.12827e16 −3.29215
\(957\) 9.85243e15 0.396760
\(958\) 2.73226e16 1.09399
\(959\) 3.01656e15 0.120091
\(960\) −4.22847e15 −0.167375
\(961\) 1.59307e15 0.0626982
\(962\) 1.74105e16 0.681315
\(963\) −4.69023e15 −0.182494
\(964\) 1.06891e17 4.13541
\(965\) 2.45797e15 0.0945530
\(966\) 3.57024e16 1.36560
\(967\) −6.11822e15 −0.232691 −0.116346 0.993209i \(-0.537118\pi\)
−0.116346 + 0.993209i \(0.537118\pi\)
\(968\) 5.50847e15 0.208313
\(969\) 4.26766e14 0.0160476
\(970\) 4.34407e15 0.162425
\(971\) −1.74742e16 −0.649668 −0.324834 0.945771i \(-0.605308\pi\)
−0.324834 + 0.945771i \(0.605308\pi\)
\(972\) 3.68461e15 0.136216
\(973\) −4.75716e14 −0.0174875
\(974\) 3.73570e16 1.36552
\(975\) 7.37690e15 0.268132
\(976\) 4.48421e16 1.62074
\(977\) 4.04578e16 1.45406 0.727030 0.686606i \(-0.240900\pi\)
0.727030 + 0.686606i \(0.240900\pi\)
\(978\) −3.91846e16 −1.40040
\(979\) −4.62529e16 −1.64374
\(980\) −1.24430e16 −0.439727
\(981\) 5.14757e15 0.180893
\(982\) 4.89337e16 1.71000
\(983\) −8.70149e15 −0.302377 −0.151189 0.988505i \(-0.548310\pi\)
−0.151189 + 0.988505i \(0.548310\pi\)
\(984\) −2.63262e16 −0.909734
\(985\) −1.28213e16 −0.440589
\(986\) −7.75518e15 −0.265014
\(987\) −9.73337e15 −0.330765
\(988\) 4.78765e15 0.161793
\(989\) 3.32043e16 1.11587
\(990\) 9.47315e15 0.316593
\(991\) −2.22000e16 −0.737817 −0.368909 0.929466i \(-0.620268\pi\)
−0.368909 + 0.929466i \(0.620268\pi\)
\(992\) 1.44430e16 0.477357
\(993\) 6.74186e15 0.221594
\(994\) −2.83841e16 −0.927792
\(995\) −8.32347e15 −0.270569
\(996\) −3.25049e16 −1.05081
\(997\) −2.56007e16 −0.823055 −0.411528 0.911397i \(-0.635005\pi\)
−0.411528 + 0.911397i \(0.635005\pi\)
\(998\) 9.45522e16 3.02311
\(999\) −3.71083e15 −0.117994
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 177.12.a.d.1.26 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.d.1.26 28 1.1 even 1 trivial