Properties

Label 177.12.a.a.1.14
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $26$
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: \(1\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+9.61747 q^{2} -243.000 q^{3} -1955.50 q^{4} -8978.47 q^{5} -2337.04 q^{6} +1935.43 q^{7} -38503.6 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+9.61747 q^{2} -243.000 q^{3} -1955.50 q^{4} -8978.47 q^{5} -2337.04 q^{6} +1935.43 q^{7} -38503.6 q^{8} +59049.0 q^{9} -86350.1 q^{10} -908857. q^{11} +475188. q^{12} -1.01344e6 q^{13} +18614.0 q^{14} +2.18177e6 q^{15} +3.63457e6 q^{16} +1.33915e6 q^{17} +567902. q^{18} +1.42736e7 q^{19} +1.75574e7 q^{20} -470311. q^{21} -8.74091e6 q^{22} +7.93240e6 q^{23} +9.35637e6 q^{24} +3.17848e7 q^{25} -9.74668e6 q^{26} -1.43489e7 q^{27} -3.78475e6 q^{28} +6.25466e6 q^{29} +2.09831e7 q^{30} -1.62098e8 q^{31} +1.13811e8 q^{32} +2.20852e8 q^{33} +1.28792e7 q^{34} -1.73772e7 q^{35} -1.15471e8 q^{36} +1.71173e8 q^{37} +1.37276e8 q^{38} +2.46265e8 q^{39} +3.45703e8 q^{40} +5.36286e8 q^{41} -4.52320e6 q^{42} +1.25115e9 q^{43} +1.77727e9 q^{44} -5.30170e8 q^{45} +7.62896e7 q^{46} +1.92164e9 q^{47} -8.83200e8 q^{48} -1.97358e9 q^{49} +3.05689e8 q^{50} -3.25413e8 q^{51} +1.98178e9 q^{52} +3.11202e9 q^{53} -1.38000e8 q^{54} +8.16015e9 q^{55} -7.45211e7 q^{56} -3.46849e9 q^{57} +6.01540e7 q^{58} +7.14924e8 q^{59} -4.26646e9 q^{60} -8.48149e9 q^{61} -1.55897e9 q^{62} +1.14285e8 q^{63} -6.34902e9 q^{64} +9.09910e9 q^{65} +2.12404e9 q^{66} +4.77009e9 q^{67} -2.61871e9 q^{68} -1.92757e9 q^{69} -1.67125e8 q^{70} +5.10131e8 q^{71} -2.27360e9 q^{72} +1.18698e10 q^{73} +1.64625e9 q^{74} -7.72370e9 q^{75} -2.79122e10 q^{76} -1.75903e9 q^{77} +2.36844e9 q^{78} -2.99691e10 q^{79} -3.26328e10 q^{80} +3.48678e9 q^{81} +5.15771e9 q^{82} +5.44332e10 q^{83} +9.19694e8 q^{84} -1.20235e10 q^{85} +1.20329e10 q^{86} -1.51988e9 q^{87} +3.49943e10 q^{88} -2.89450e10 q^{89} -5.09889e9 q^{90} -1.96144e9 q^{91} -1.55118e10 q^{92} +3.93898e10 q^{93} +1.84814e10 q^{94} -1.28155e11 q^{95} -2.76560e10 q^{96} +1.91150e10 q^{97} -1.89808e10 q^{98} -5.36671e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.61747 0.212518 0.106259 0.994338i \(-0.466113\pi\)
0.106259 + 0.994338i \(0.466113\pi\)
\(3\) −243.000 −0.577350
\(4\) −1955.50 −0.954836
\(5\) −8978.47 −1.28489 −0.642447 0.766330i \(-0.722081\pi\)
−0.642447 + 0.766330i \(0.722081\pi\)
\(6\) −2337.04 −0.122697
\(7\) 1935.43 0.0435250 0.0217625 0.999763i \(-0.493072\pi\)
0.0217625 + 0.999763i \(0.493072\pi\)
\(8\) −38503.6 −0.415438
\(9\) 59049.0 0.333333
\(10\) −86350.1 −0.273063
\(11\) −908857. −1.70152 −0.850758 0.525558i \(-0.823857\pi\)
−0.850758 + 0.525558i \(0.823857\pi\)
\(12\) 475188. 0.551275
\(13\) −1.01344e6 −0.757020 −0.378510 0.925597i \(-0.623564\pi\)
−0.378510 + 0.925597i \(0.623564\pi\)
\(14\) 18614.0 0.00924986
\(15\) 2.18177e6 0.741834
\(16\) 3.63457e6 0.866548
\(17\) 1.33915e6 0.228750 0.114375 0.993438i \(-0.463514\pi\)
0.114375 + 0.993438i \(0.463514\pi\)
\(18\) 567902. 0.0708393
\(19\) 1.42736e7 1.32248 0.661241 0.750174i \(-0.270030\pi\)
0.661241 + 0.750174i \(0.270030\pi\)
\(20\) 1.75574e7 1.22686
\(21\) −470311. −0.0251292
\(22\) −8.74091e6 −0.361603
\(23\) 7.93240e6 0.256981 0.128491 0.991711i \(-0.458987\pi\)
0.128491 + 0.991711i \(0.458987\pi\)
\(24\) 9.35637e6 0.239853
\(25\) 3.17848e7 0.650952
\(26\) −9.74668e6 −0.160880
\(27\) −1.43489e7 −0.192450
\(28\) −3.78475e6 −0.0415593
\(29\) 6.25466e6 0.0566258 0.0283129 0.999599i \(-0.490987\pi\)
0.0283129 + 0.999599i \(0.490987\pi\)
\(30\) 2.09831e7 0.157653
\(31\) −1.62098e8 −1.01692 −0.508462 0.861084i \(-0.669786\pi\)
−0.508462 + 0.861084i \(0.669786\pi\)
\(32\) 1.13811e8 0.599595
\(33\) 2.20852e8 0.982371
\(34\) 1.28792e7 0.0486134
\(35\) −1.73772e7 −0.0559251
\(36\) −1.15471e8 −0.318279
\(37\) 1.71173e8 0.405813 0.202907 0.979198i \(-0.434961\pi\)
0.202907 + 0.979198i \(0.434961\pi\)
\(38\) 1.37276e8 0.281051
\(39\) 2.46265e8 0.437066
\(40\) 3.45703e8 0.533794
\(41\) 5.36286e8 0.722912 0.361456 0.932389i \(-0.382280\pi\)
0.361456 + 0.932389i \(0.382280\pi\)
\(42\) −4.52320e6 −0.00534041
\(43\) 1.25115e9 1.29788 0.648938 0.760841i \(-0.275213\pi\)
0.648938 + 0.760841i \(0.275213\pi\)
\(44\) 1.77727e9 1.62467
\(45\) −5.30170e8 −0.428298
\(46\) 7.62896e7 0.0546132
\(47\) 1.92164e9 1.22218 0.611090 0.791562i \(-0.290732\pi\)
0.611090 + 0.791562i \(0.290732\pi\)
\(48\) −8.83200e8 −0.500302
\(49\) −1.97358e9 −0.998106
\(50\) 3.05689e8 0.138339
\(51\) −3.25413e8 −0.132069
\(52\) 1.98178e9 0.722830
\(53\) 3.11202e9 1.02217 0.511087 0.859529i \(-0.329243\pi\)
0.511087 + 0.859529i \(0.329243\pi\)
\(54\) −1.38000e8 −0.0408991
\(55\) 8.16015e9 2.18627
\(56\) −7.45211e7 −0.0180820
\(57\) −3.46849e9 −0.763535
\(58\) 6.01540e7 0.0120340
\(59\) 7.14924e8 0.130189
\(60\) −4.26646e9 −0.708330
\(61\) −8.48149e9 −1.28575 −0.642877 0.765969i \(-0.722259\pi\)
−0.642877 + 0.765969i \(0.722259\pi\)
\(62\) −1.55897e9 −0.216115
\(63\) 1.14285e8 0.0145083
\(64\) −6.34902e9 −0.739123
\(65\) 9.09910e9 0.972691
\(66\) 2.12404e9 0.208771
\(67\) 4.77009e9 0.431634 0.215817 0.976434i \(-0.430759\pi\)
0.215817 + 0.976434i \(0.430759\pi\)
\(68\) −2.61871e9 −0.218418
\(69\) −1.92757e9 −0.148368
\(70\) −1.67125e8 −0.0118851
\(71\) 5.10131e8 0.0335553 0.0167776 0.999859i \(-0.494659\pi\)
0.0167776 + 0.999859i \(0.494659\pi\)
\(72\) −2.27360e9 −0.138479
\(73\) 1.18698e10 0.670144 0.335072 0.942192i \(-0.391239\pi\)
0.335072 + 0.942192i \(0.391239\pi\)
\(74\) 1.64625e9 0.0862426
\(75\) −7.72370e9 −0.375827
\(76\) −2.79122e10 −1.26275
\(77\) −1.75903e9 −0.0740585
\(78\) 2.36844e9 0.0928844
\(79\) −2.99691e10 −1.09578 −0.547891 0.836550i \(-0.684569\pi\)
−0.547891 + 0.836550i \(0.684569\pi\)
\(80\) −3.26328e10 −1.11342
\(81\) 3.48678e9 0.111111
\(82\) 5.15771e9 0.153632
\(83\) 5.44332e10 1.51682 0.758411 0.651777i \(-0.225976\pi\)
0.758411 + 0.651777i \(0.225976\pi\)
\(84\) 9.19694e8 0.0239943
\(85\) −1.20235e10 −0.293919
\(86\) 1.20329e10 0.275822
\(87\) −1.51988e9 −0.0326929
\(88\) 3.49943e10 0.706874
\(89\) −2.89450e10 −0.549451 −0.274725 0.961523i \(-0.588587\pi\)
−0.274725 + 0.961523i \(0.588587\pi\)
\(90\) −5.09889e9 −0.0910210
\(91\) −1.96144e9 −0.0329493
\(92\) −1.55118e10 −0.245375
\(93\) 3.93898e10 0.587121
\(94\) 1.84814e10 0.259735
\(95\) −1.28155e11 −1.69925
\(96\) −2.76560e10 −0.346176
\(97\) 1.91150e10 0.226011 0.113005 0.993594i \(-0.463952\pi\)
0.113005 + 0.993594i \(0.463952\pi\)
\(98\) −1.89808e10 −0.212115
\(99\) −5.36671e10 −0.567172
\(100\) −6.21553e10 −0.621553
\(101\) 6.28414e10 0.594947 0.297474 0.954730i \(-0.403856\pi\)
0.297474 + 0.954730i \(0.403856\pi\)
\(102\) −3.12965e9 −0.0280670
\(103\) −1.47830e11 −1.25649 −0.628243 0.778017i \(-0.716226\pi\)
−0.628243 + 0.778017i \(0.716226\pi\)
\(104\) 3.90209e10 0.314495
\(105\) 4.22267e9 0.0322884
\(106\) 2.99297e10 0.217230
\(107\) 8.34678e10 0.575319 0.287659 0.957733i \(-0.407123\pi\)
0.287659 + 0.957733i \(0.407123\pi\)
\(108\) 2.80593e10 0.183758
\(109\) −1.65315e11 −1.02912 −0.514559 0.857455i \(-0.672044\pi\)
−0.514559 + 0.857455i \(0.672044\pi\)
\(110\) 7.84800e10 0.464621
\(111\) −4.15951e10 −0.234296
\(112\) 7.03446e9 0.0377165
\(113\) 2.12923e10 0.108716 0.0543578 0.998522i \(-0.482689\pi\)
0.0543578 + 0.998522i \(0.482689\pi\)
\(114\) −3.33581e10 −0.162265
\(115\) −7.12208e10 −0.330194
\(116\) −1.22310e10 −0.0540684
\(117\) −5.98423e10 −0.252340
\(118\) 6.87576e9 0.0276675
\(119\) 2.59184e9 0.00995633
\(120\) −8.40059e10 −0.308186
\(121\) 5.40710e11 1.89516
\(122\) −8.15704e10 −0.273246
\(123\) −1.30318e11 −0.417373
\(124\) 3.16983e11 0.970996
\(125\) 1.53023e11 0.448489
\(126\) 1.09914e9 0.00308329
\(127\) −5.38389e10 −0.144602 −0.0723012 0.997383i \(-0.523034\pi\)
−0.0723012 + 0.997383i \(0.523034\pi\)
\(128\) −2.94146e11 −0.756672
\(129\) −3.04030e11 −0.749329
\(130\) 8.75103e10 0.206714
\(131\) −5.33391e11 −1.20796 −0.603981 0.796999i \(-0.706420\pi\)
−0.603981 + 0.796999i \(0.706420\pi\)
\(132\) −4.31878e11 −0.938003
\(133\) 2.76257e10 0.0575611
\(134\) 4.58762e10 0.0917299
\(135\) 1.28831e11 0.247278
\(136\) −5.15621e10 −0.0950312
\(137\) −1.81390e11 −0.321107 −0.160554 0.987027i \(-0.551328\pi\)
−0.160554 + 0.987027i \(0.551328\pi\)
\(138\) −1.85384e10 −0.0315309
\(139\) −6.69082e11 −1.09370 −0.546850 0.837231i \(-0.684173\pi\)
−0.546850 + 0.837231i \(0.684173\pi\)
\(140\) 3.39813e10 0.0533993
\(141\) −4.66960e11 −0.705625
\(142\) 4.90617e9 0.00713110
\(143\) 9.21068e11 1.28808
\(144\) 2.14617e11 0.288849
\(145\) −5.61573e10 −0.0727582
\(146\) 1.14158e11 0.142418
\(147\) 4.79580e11 0.576257
\(148\) −3.34730e11 −0.387485
\(149\) −1.17113e12 −1.30641 −0.653205 0.757181i \(-0.726576\pi\)
−0.653205 + 0.757181i \(0.726576\pi\)
\(150\) −7.42824e10 −0.0798701
\(151\) −6.40012e11 −0.663460 −0.331730 0.943374i \(-0.607632\pi\)
−0.331730 + 0.943374i \(0.607632\pi\)
\(152\) −5.49586e11 −0.549409
\(153\) 7.90755e10 0.0762498
\(154\) −1.69174e10 −0.0157388
\(155\) 1.45539e12 1.30664
\(156\) −4.81572e11 −0.417326
\(157\) −4.28861e11 −0.358813 −0.179407 0.983775i \(-0.557418\pi\)
−0.179407 + 0.983775i \(0.557418\pi\)
\(158\) −2.88227e11 −0.232874
\(159\) −7.56220e11 −0.590152
\(160\) −1.02185e12 −0.770416
\(161\) 1.53526e10 0.0111851
\(162\) 3.35340e10 0.0236131
\(163\) 1.51544e12 1.03159 0.515793 0.856713i \(-0.327497\pi\)
0.515793 + 0.856713i \(0.327497\pi\)
\(164\) −1.04871e12 −0.690262
\(165\) −1.98292e12 −1.26224
\(166\) 5.23510e11 0.322352
\(167\) 2.00802e11 0.119626 0.0598132 0.998210i \(-0.480949\pi\)
0.0598132 + 0.998210i \(0.480949\pi\)
\(168\) 1.81086e10 0.0104396
\(169\) −7.65109e11 −0.426920
\(170\) −1.15636e11 −0.0624631
\(171\) 8.42844e11 0.440827
\(172\) −2.44663e12 −1.23926
\(173\) −9.66265e9 −0.00474070 −0.00237035 0.999997i \(-0.500755\pi\)
−0.00237035 + 0.999997i \(0.500755\pi\)
\(174\) −1.46174e10 −0.00694784
\(175\) 6.15174e10 0.0283327
\(176\) −3.30330e12 −1.47445
\(177\) −1.73727e11 −0.0751646
\(178\) −2.78378e11 −0.116768
\(179\) 1.75496e12 0.713797 0.356899 0.934143i \(-0.383834\pi\)
0.356899 + 0.934143i \(0.383834\pi\)
\(180\) 1.03675e12 0.408954
\(181\) 3.25190e12 1.24424 0.622121 0.782921i \(-0.286271\pi\)
0.622121 + 0.782921i \(0.286271\pi\)
\(182\) −1.88641e10 −0.00700233
\(183\) 2.06100e12 0.742331
\(184\) −3.05426e11 −0.106760
\(185\) −1.53687e12 −0.521427
\(186\) 3.78830e11 0.124774
\(187\) −1.21710e12 −0.389221
\(188\) −3.75778e12 −1.16698
\(189\) −2.77714e10 −0.00837640
\(190\) −1.23253e12 −0.361121
\(191\) 2.17402e12 0.618843 0.309421 0.950925i \(-0.399865\pi\)
0.309421 + 0.950925i \(0.399865\pi\)
\(192\) 1.54281e12 0.426733
\(193\) 4.37751e12 1.17669 0.588345 0.808610i \(-0.299780\pi\)
0.588345 + 0.808610i \(0.299780\pi\)
\(194\) 1.83838e11 0.0480314
\(195\) −2.21108e12 −0.561583
\(196\) 3.85935e12 0.953027
\(197\) −1.77709e12 −0.426721 −0.213361 0.976974i \(-0.568441\pi\)
−0.213361 + 0.976974i \(0.568441\pi\)
\(198\) −5.16142e11 −0.120534
\(199\) 6.76559e12 1.53679 0.768393 0.639978i \(-0.221057\pi\)
0.768393 + 0.639978i \(0.221057\pi\)
\(200\) −1.22383e12 −0.270430
\(201\) −1.15913e12 −0.249204
\(202\) 6.04375e11 0.126437
\(203\) 1.21055e10 0.00246464
\(204\) 6.36347e11 0.126104
\(205\) −4.81503e12 −0.928865
\(206\) −1.42175e12 −0.267026
\(207\) 4.68400e11 0.0856604
\(208\) −3.68340e12 −0.655995
\(209\) −1.29727e13 −2.25022
\(210\) 4.06114e10 0.00686186
\(211\) 2.79045e12 0.459326 0.229663 0.973270i \(-0.426238\pi\)
0.229663 + 0.973270i \(0.426238\pi\)
\(212\) −6.08556e12 −0.976008
\(213\) −1.23962e11 −0.0193732
\(214\) 8.02749e11 0.122266
\(215\) −1.12334e13 −1.66763
\(216\) 5.52484e11 0.0799511
\(217\) −3.13730e11 −0.0442617
\(218\) −1.58991e12 −0.218706
\(219\) −2.88437e12 −0.386908
\(220\) −1.59572e13 −2.08753
\(221\) −1.35714e12 −0.173168
\(222\) −4.00039e11 −0.0497922
\(223\) −1.46989e13 −1.78488 −0.892438 0.451171i \(-0.851006\pi\)
−0.892438 + 0.451171i \(0.851006\pi\)
\(224\) 2.20273e11 0.0260974
\(225\) 1.87686e12 0.216984
\(226\) 2.04778e11 0.0231040
\(227\) 7.12599e12 0.784698 0.392349 0.919816i \(-0.371662\pi\)
0.392349 + 0.919816i \(0.371662\pi\)
\(228\) 6.78265e12 0.729051
\(229\) 4.09823e12 0.430033 0.215016 0.976610i \(-0.431019\pi\)
0.215016 + 0.976610i \(0.431019\pi\)
\(230\) −6.84964e11 −0.0701721
\(231\) 4.27445e11 0.0427577
\(232\) −2.40827e11 −0.0235245
\(233\) −4.91911e11 −0.0469276 −0.0234638 0.999725i \(-0.507469\pi\)
−0.0234638 + 0.999725i \(0.507469\pi\)
\(234\) −5.75532e11 −0.0536268
\(235\) −1.72534e13 −1.57037
\(236\) −1.39804e12 −0.124309
\(237\) 7.28249e12 0.632650
\(238\) 2.49269e10 0.00211590
\(239\) −6.14857e12 −0.510018 −0.255009 0.966939i \(-0.582078\pi\)
−0.255009 + 0.966939i \(0.582078\pi\)
\(240\) 7.92978e12 0.642835
\(241\) 4.98321e12 0.394835 0.197417 0.980320i \(-0.436745\pi\)
0.197417 + 0.980320i \(0.436745\pi\)
\(242\) 5.20026e12 0.402755
\(243\) −8.47289e11 −0.0641500
\(244\) 1.65856e13 1.22768
\(245\) 1.77197e13 1.28246
\(246\) −1.25332e12 −0.0886994
\(247\) −1.44654e13 −1.00115
\(248\) 6.24135e12 0.422469
\(249\) −1.32273e13 −0.875737
\(250\) 1.47170e12 0.0953120
\(251\) −3.17460e12 −0.201133 −0.100567 0.994930i \(-0.532066\pi\)
−0.100567 + 0.994930i \(0.532066\pi\)
\(252\) −2.23486e11 −0.0138531
\(253\) −7.20942e12 −0.437258
\(254\) −5.17793e11 −0.0307306
\(255\) 2.92171e12 0.169694
\(256\) 1.01739e13 0.578317
\(257\) −2.00280e13 −1.11431 −0.557153 0.830410i \(-0.688106\pi\)
−0.557153 + 0.830410i \(0.688106\pi\)
\(258\) −2.92400e12 −0.159246
\(259\) 3.31294e11 0.0176630
\(260\) −1.77933e13 −0.928760
\(261\) 3.69331e11 0.0188753
\(262\) −5.12987e12 −0.256714
\(263\) 1.25346e13 0.614260 0.307130 0.951668i \(-0.400631\pi\)
0.307130 + 0.951668i \(0.400631\pi\)
\(264\) −8.50360e12 −0.408114
\(265\) −2.79411e13 −1.31338
\(266\) 2.65689e11 0.0122328
\(267\) 7.03364e12 0.317226
\(268\) −9.32794e12 −0.412140
\(269\) 2.94360e13 1.27421 0.637105 0.770777i \(-0.280132\pi\)
0.637105 + 0.770777i \(0.280132\pi\)
\(270\) 1.23903e12 0.0525510
\(271\) 5.64401e11 0.0234562 0.0117281 0.999931i \(-0.496267\pi\)
0.0117281 + 0.999931i \(0.496267\pi\)
\(272\) 4.86723e12 0.198222
\(273\) 4.76629e11 0.0190233
\(274\) −1.74451e12 −0.0682411
\(275\) −2.88878e13 −1.10761
\(276\) 3.76938e12 0.141667
\(277\) −5.72696e12 −0.211002 −0.105501 0.994419i \(-0.533645\pi\)
−0.105501 + 0.994419i \(0.533645\pi\)
\(278\) −6.43487e12 −0.232431
\(279\) −9.57173e12 −0.338975
\(280\) 6.69086e11 0.0232334
\(281\) 3.08258e13 1.04961 0.524806 0.851222i \(-0.324138\pi\)
0.524806 + 0.851222i \(0.324138\pi\)
\(282\) −4.49097e12 −0.149958
\(283\) −4.57961e12 −0.149969 −0.0749847 0.997185i \(-0.523891\pi\)
−0.0749847 + 0.997185i \(0.523891\pi\)
\(284\) −9.97564e11 −0.0320398
\(285\) 3.11418e13 0.981062
\(286\) 8.85834e12 0.273741
\(287\) 1.03795e12 0.0314648
\(288\) 6.72040e12 0.199865
\(289\) −3.24786e13 −0.947674
\(290\) −5.40091e11 −0.0154624
\(291\) −4.64494e12 −0.130487
\(292\) −2.32115e13 −0.639878
\(293\) −2.28588e13 −0.618417 −0.309209 0.950994i \(-0.600064\pi\)
−0.309209 + 0.950994i \(0.600064\pi\)
\(294\) 4.61235e12 0.122465
\(295\) −6.41893e12 −0.167279
\(296\) −6.59078e12 −0.168590
\(297\) 1.30411e13 0.327457
\(298\) −1.12633e13 −0.277635
\(299\) −8.03898e12 −0.194540
\(300\) 1.51037e13 0.358854
\(301\) 2.42152e12 0.0564901
\(302\) −6.15529e12 −0.140997
\(303\) −1.52705e13 −0.343493
\(304\) 5.18785e13 1.14599
\(305\) 7.61508e13 1.65206
\(306\) 7.60506e11 0.0162045
\(307\) 1.67173e13 0.349870 0.174935 0.984580i \(-0.444029\pi\)
0.174935 + 0.984580i \(0.444029\pi\)
\(308\) 3.43980e12 0.0707138
\(309\) 3.59227e13 0.725433
\(310\) 1.39972e13 0.277684
\(311\) −1.89410e13 −0.369166 −0.184583 0.982817i \(-0.559093\pi\)
−0.184583 + 0.982817i \(0.559093\pi\)
\(312\) −9.48207e12 −0.181574
\(313\) −1.17436e13 −0.220956 −0.110478 0.993879i \(-0.535238\pi\)
−0.110478 + 0.993879i \(0.535238\pi\)
\(314\) −4.12456e12 −0.0762543
\(315\) −1.02611e12 −0.0186417
\(316\) 5.86047e13 1.04629
\(317\) 8.62862e13 1.51396 0.756982 0.653436i \(-0.226673\pi\)
0.756982 + 0.653436i \(0.226673\pi\)
\(318\) −7.27292e12 −0.125418
\(319\) −5.68459e12 −0.0963497
\(320\) 5.70045e13 0.949695
\(321\) −2.02827e13 −0.332160
\(322\) 1.47654e11 0.00237704
\(323\) 1.91145e13 0.302517
\(324\) −6.81842e12 −0.106093
\(325\) −3.22118e13 −0.492784
\(326\) 1.45747e13 0.219231
\(327\) 4.01714e13 0.594162
\(328\) −2.06489e13 −0.300325
\(329\) 3.71922e12 0.0531954
\(330\) −1.90706e13 −0.268249
\(331\) 2.92656e13 0.404859 0.202430 0.979297i \(-0.435116\pi\)
0.202430 + 0.979297i \(0.435116\pi\)
\(332\) −1.06444e14 −1.44832
\(333\) 1.01076e13 0.135271
\(334\) 1.93120e12 0.0254228
\(335\) −4.28281e13 −0.554604
\(336\) −1.70937e12 −0.0217757
\(337\) 1.32340e14 1.65855 0.829274 0.558842i \(-0.188754\pi\)
0.829274 + 0.558842i \(0.188754\pi\)
\(338\) −7.35841e12 −0.0907282
\(339\) −5.17404e12 −0.0627670
\(340\) 2.35120e13 0.280644
\(341\) 1.47324e14 1.73031
\(342\) 8.10602e12 0.0936837
\(343\) −7.64672e12 −0.0869676
\(344\) −4.81738e13 −0.539187
\(345\) 1.73067e13 0.190637
\(346\) −9.29302e10 −0.00100748
\(347\) 3.67543e13 0.392190 0.196095 0.980585i \(-0.437174\pi\)
0.196095 + 0.980585i \(0.437174\pi\)
\(348\) 2.97214e12 0.0312164
\(349\) −1.29785e14 −1.34180 −0.670898 0.741550i \(-0.734091\pi\)
−0.670898 + 0.741550i \(0.734091\pi\)
\(350\) 5.91641e11 0.00602121
\(351\) 1.45417e13 0.145689
\(352\) −1.03438e14 −1.02022
\(353\) 1.04977e14 1.01937 0.509687 0.860360i \(-0.329761\pi\)
0.509687 + 0.860360i \(0.329761\pi\)
\(354\) −1.67081e12 −0.0159738
\(355\) −4.58020e12 −0.0431150
\(356\) 5.66021e13 0.524636
\(357\) −6.29816e11 −0.00574829
\(358\) 1.68782e13 0.151695
\(359\) 9.26261e13 0.819811 0.409906 0.912128i \(-0.365562\pi\)
0.409906 + 0.912128i \(0.365562\pi\)
\(360\) 2.04134e13 0.177931
\(361\) 8.72464e13 0.748958
\(362\) 3.12750e13 0.264424
\(363\) −1.31393e14 −1.09417
\(364\) 3.83560e12 0.0314612
\(365\) −1.06573e14 −0.861064
\(366\) 1.98216e13 0.157759
\(367\) 2.10505e14 1.65044 0.825219 0.564813i \(-0.191052\pi\)
0.825219 + 0.564813i \(0.191052\pi\)
\(368\) 2.88308e13 0.222687
\(369\) 3.16672e13 0.240971
\(370\) −1.47808e13 −0.110813
\(371\) 6.02310e12 0.0444902
\(372\) −7.70270e13 −0.560605
\(373\) −3.70839e13 −0.265942 −0.132971 0.991120i \(-0.542452\pi\)
−0.132971 + 0.991120i \(0.542452\pi\)
\(374\) −1.17054e13 −0.0827165
\(375\) −3.71846e13 −0.258935
\(376\) −7.39902e13 −0.507739
\(377\) −6.33869e12 −0.0428669
\(378\) −2.67090e11 −0.00178014
\(379\) 4.29231e13 0.281952 0.140976 0.990013i \(-0.454976\pi\)
0.140976 + 0.990013i \(0.454976\pi\)
\(380\) 2.50608e14 1.62250
\(381\) 1.30828e13 0.0834862
\(382\) 2.09086e13 0.131515
\(383\) 1.09831e14 0.680975 0.340488 0.940249i \(-0.389408\pi\)
0.340488 + 0.940249i \(0.389408\pi\)
\(384\) 7.14774e13 0.436865
\(385\) 1.57934e13 0.0951574
\(386\) 4.21006e13 0.250068
\(387\) 7.38792e13 0.432625
\(388\) −3.73794e13 −0.215803
\(389\) −2.86161e14 −1.62887 −0.814436 0.580253i \(-0.802954\pi\)
−0.814436 + 0.580253i \(0.802954\pi\)
\(390\) −2.12650e13 −0.119347
\(391\) 1.06227e13 0.0587844
\(392\) 7.59899e13 0.414651
\(393\) 1.29614e14 0.697417
\(394\) −1.70911e13 −0.0906860
\(395\) 2.69076e14 1.40796
\(396\) 1.04946e14 0.541556
\(397\) −1.19227e14 −0.606775 −0.303387 0.952867i \(-0.598118\pi\)
−0.303387 + 0.952867i \(0.598118\pi\)
\(398\) 6.50678e13 0.326595
\(399\) −6.71304e12 −0.0332329
\(400\) 1.15524e14 0.564081
\(401\) 7.47737e13 0.360126 0.180063 0.983655i \(-0.442370\pi\)
0.180063 + 0.983655i \(0.442370\pi\)
\(402\) −1.11479e13 −0.0529603
\(403\) 1.64276e14 0.769832
\(404\) −1.22887e14 −0.568077
\(405\) −3.13060e13 −0.142766
\(406\) 1.16424e11 0.000523781 0
\(407\) −1.55572e14 −0.690497
\(408\) 1.25296e13 0.0548663
\(409\) 2.85390e14 1.23299 0.616495 0.787358i \(-0.288552\pi\)
0.616495 + 0.787358i \(0.288552\pi\)
\(410\) −4.63084e13 −0.197401
\(411\) 4.40778e13 0.185391
\(412\) 2.89082e14 1.19974
\(413\) 1.38369e12 0.00566648
\(414\) 4.50483e12 0.0182044
\(415\) −4.88727e14 −1.94895
\(416\) −1.15340e14 −0.453906
\(417\) 1.62587e14 0.631448
\(418\) −1.24764e14 −0.478213
\(419\) −1.04792e13 −0.0396416 −0.0198208 0.999804i \(-0.506310\pi\)
−0.0198208 + 0.999804i \(0.506310\pi\)
\(420\) −8.25745e12 −0.0308301
\(421\) −1.74954e14 −0.644721 −0.322361 0.946617i \(-0.604476\pi\)
−0.322361 + 0.946617i \(0.604476\pi\)
\(422\) 2.68371e13 0.0976151
\(423\) 1.13471e14 0.407393
\(424\) −1.19824e14 −0.424650
\(425\) 4.25646e13 0.148905
\(426\) −1.19220e12 −0.00411714
\(427\) −1.64154e13 −0.0559625
\(428\) −1.63222e14 −0.549335
\(429\) −2.23820e14 −0.743675
\(430\) −1.08037e14 −0.354402
\(431\) −3.00307e14 −0.972613 −0.486306 0.873788i \(-0.661656\pi\)
−0.486306 + 0.873788i \(0.661656\pi\)
\(432\) −5.21521e13 −0.166767
\(433\) 2.80926e14 0.886968 0.443484 0.896282i \(-0.353742\pi\)
0.443484 + 0.896282i \(0.353742\pi\)
\(434\) −3.01729e12 −0.00940640
\(435\) 1.36462e13 0.0420070
\(436\) 3.23273e14 0.982639
\(437\) 1.13224e14 0.339853
\(438\) −2.77403e13 −0.0822249
\(439\) −5.81821e14 −1.70308 −0.851540 0.524290i \(-0.824331\pi\)
−0.851540 + 0.524290i \(0.824331\pi\)
\(440\) −3.14195e14 −0.908258
\(441\) −1.16538e14 −0.332702
\(442\) −1.30523e13 −0.0368013
\(443\) −5.40109e13 −0.150404 −0.0752022 0.997168i \(-0.523960\pi\)
−0.0752022 + 0.997168i \(0.523960\pi\)
\(444\) 8.13393e13 0.223715
\(445\) 2.59882e14 0.705986
\(446\) −1.41366e14 −0.379318
\(447\) 2.84584e14 0.754256
\(448\) −1.22881e13 −0.0321704
\(449\) −6.26344e14 −1.61979 −0.809894 0.586576i \(-0.800476\pi\)
−0.809894 + 0.586576i \(0.800476\pi\)
\(450\) 1.80506e13 0.0461130
\(451\) −4.87408e14 −1.23005
\(452\) −4.16372e13 −0.103806
\(453\) 1.55523e14 0.383049
\(454\) 6.85339e13 0.166763
\(455\) 1.76107e13 0.0423364
\(456\) 1.33549e14 0.317201
\(457\) 1.70392e14 0.399861 0.199931 0.979810i \(-0.435928\pi\)
0.199931 + 0.979810i \(0.435928\pi\)
\(458\) 3.94146e13 0.0913897
\(459\) −1.92153e13 −0.0440229
\(460\) 1.39273e14 0.315281
\(461\) 3.38574e14 0.757354 0.378677 0.925529i \(-0.376379\pi\)
0.378677 + 0.925529i \(0.376379\pi\)
\(462\) 4.11094e12 0.00908679
\(463\) 2.87373e14 0.627697 0.313849 0.949473i \(-0.398382\pi\)
0.313849 + 0.949473i \(0.398382\pi\)
\(464\) 2.27330e13 0.0490690
\(465\) −3.53660e14 −0.754389
\(466\) −4.73093e12 −0.00997296
\(467\) 7.74798e14 1.61416 0.807078 0.590444i \(-0.201048\pi\)
0.807078 + 0.590444i \(0.201048\pi\)
\(468\) 1.17022e14 0.240943
\(469\) 9.23220e12 0.0187869
\(470\) −1.65934e14 −0.333732
\(471\) 1.04213e14 0.207161
\(472\) −2.75271e13 −0.0540854
\(473\) −1.13712e15 −2.20836
\(474\) 7.00391e13 0.134450
\(475\) 4.53684e14 0.860873
\(476\) −5.06835e12 −0.00950667
\(477\) 1.83761e14 0.340725
\(478\) −5.91336e13 −0.108388
\(479\) −7.02364e13 −0.127267 −0.0636337 0.997973i \(-0.520269\pi\)
−0.0636337 + 0.997973i \(0.520269\pi\)
\(480\) 2.48308e14 0.444800
\(481\) −1.73473e14 −0.307209
\(482\) 4.79258e13 0.0839094
\(483\) −3.73069e12 −0.00645773
\(484\) −1.05736e15 −1.80956
\(485\) −1.71623e14 −0.290400
\(486\) −8.14877e12 −0.0136330
\(487\) −5.05024e14 −0.835416 −0.417708 0.908581i \(-0.637166\pi\)
−0.417708 + 0.908581i \(0.637166\pi\)
\(488\) 3.26568e14 0.534151
\(489\) −3.68251e14 −0.595587
\(490\) 1.70419e14 0.272546
\(491\) 6.74170e14 1.06616 0.533079 0.846066i \(-0.321035\pi\)
0.533079 + 0.846066i \(0.321035\pi\)
\(492\) 2.54836e14 0.398523
\(493\) 8.37593e12 0.0129531
\(494\) −1.39121e14 −0.212761
\(495\) 4.81849e14 0.728756
\(496\) −5.89156e14 −0.881213
\(497\) 9.87325e11 0.00146050
\(498\) −1.27213e14 −0.186110
\(499\) −2.91391e13 −0.0421622 −0.0210811 0.999778i \(-0.506711\pi\)
−0.0210811 + 0.999778i \(0.506711\pi\)
\(500\) −2.99237e14 −0.428234
\(501\) −4.87948e13 −0.0690663
\(502\) −3.05316e13 −0.0427444
\(503\) 1.55483e14 0.215307 0.107654 0.994188i \(-0.465666\pi\)
0.107654 + 0.994188i \(0.465666\pi\)
\(504\) −4.40040e12 −0.00602732
\(505\) −5.64220e14 −0.764444
\(506\) −6.93364e13 −0.0929252
\(507\) 1.85922e14 0.246482
\(508\) 1.05282e14 0.138072
\(509\) −7.58496e14 −0.984024 −0.492012 0.870588i \(-0.663738\pi\)
−0.492012 + 0.870588i \(0.663738\pi\)
\(510\) 2.80995e13 0.0360631
\(511\) 2.29733e13 0.0291681
\(512\) 7.00257e14 0.879575
\(513\) −2.04811e14 −0.254512
\(514\) −1.92618e14 −0.236810
\(515\) 1.32729e15 1.61445
\(516\) 5.94531e14 0.715487
\(517\) −1.74650e15 −2.07956
\(518\) 3.18621e12 0.00375371
\(519\) 2.34802e12 0.00273705
\(520\) −3.50348e14 −0.404093
\(521\) 1.45929e15 1.66546 0.832728 0.553682i \(-0.186778\pi\)
0.832728 + 0.553682i \(0.186778\pi\)
\(522\) 3.55203e12 0.00401134
\(523\) −1.72020e15 −1.92229 −0.961146 0.276039i \(-0.910978\pi\)
−0.961146 + 0.276039i \(0.910978\pi\)
\(524\) 1.04305e15 1.15341
\(525\) −1.49487e13 −0.0163579
\(526\) 1.20551e14 0.130541
\(527\) −2.17074e14 −0.232621
\(528\) 8.02702e14 0.851271
\(529\) −8.89887e14 −0.933961
\(530\) −2.68723e14 −0.279118
\(531\) 4.22156e13 0.0433963
\(532\) −5.40221e13 −0.0549614
\(533\) −5.43491e14 −0.547259
\(534\) 6.76458e13 0.0674162
\(535\) −7.49413e14 −0.739223
\(536\) −1.83666e14 −0.179317
\(537\) −4.26455e14 −0.412111
\(538\) 2.83099e14 0.270792
\(539\) 1.79370e15 1.69829
\(540\) −2.51930e14 −0.236110
\(541\) −2.14899e15 −1.99365 −0.996826 0.0796149i \(-0.974631\pi\)
−0.996826 + 0.0796149i \(0.974631\pi\)
\(542\) 5.42811e12 0.00498485
\(543\) −7.90212e14 −0.718364
\(544\) 1.52410e14 0.137157
\(545\) 1.48427e15 1.32231
\(546\) 4.58397e12 0.00404280
\(547\) −1.09027e15 −0.951930 −0.475965 0.879464i \(-0.657901\pi\)
−0.475965 + 0.879464i \(0.657901\pi\)
\(548\) 3.54709e14 0.306605
\(549\) −5.00823e14 −0.428585
\(550\) −2.77828e14 −0.235386
\(551\) 8.92767e13 0.0748866
\(552\) 7.42185e13 0.0616378
\(553\) −5.80032e13 −0.0476940
\(554\) −5.50789e13 −0.0448416
\(555\) 3.73460e14 0.301046
\(556\) 1.30839e15 1.04430
\(557\) 1.71044e15 1.35177 0.675887 0.737006i \(-0.263761\pi\)
0.675887 + 0.737006i \(0.263761\pi\)
\(558\) −9.20558e13 −0.0720382
\(559\) −1.26796e15 −0.982519
\(560\) −6.31587e13 −0.0484618
\(561\) 2.95754e14 0.224717
\(562\) 2.96466e14 0.223062
\(563\) 2.29132e15 1.70722 0.853610 0.520912i \(-0.174408\pi\)
0.853610 + 0.520912i \(0.174408\pi\)
\(564\) 9.13142e14 0.673757
\(565\) −1.91172e14 −0.139688
\(566\) −4.40442e13 −0.0318712
\(567\) 6.74844e12 0.00483612
\(568\) −1.96419e13 −0.0139401
\(569\) −2.79540e15 −1.96484 −0.982418 0.186693i \(-0.940223\pi\)
−0.982418 + 0.186693i \(0.940223\pi\)
\(570\) 2.99505e14 0.208493
\(571\) −8.74818e14 −0.603142 −0.301571 0.953444i \(-0.597511\pi\)
−0.301571 + 0.953444i \(0.597511\pi\)
\(572\) −1.80115e15 −1.22991
\(573\) −5.28287e14 −0.357289
\(574\) 9.98242e12 0.00668683
\(575\) 2.52130e14 0.167283
\(576\) −3.74903e14 −0.246374
\(577\) −1.83319e15 −1.19328 −0.596638 0.802510i \(-0.703497\pi\)
−0.596638 + 0.802510i \(0.703497\pi\)
\(578\) −3.12362e14 −0.201398
\(579\) −1.06374e15 −0.679363
\(580\) 1.09816e14 0.0694721
\(581\) 1.05352e14 0.0660197
\(582\) −4.46726e13 −0.0277309
\(583\) −2.82838e15 −1.73924
\(584\) −4.57030e14 −0.278403
\(585\) 5.37293e14 0.324230
\(586\) −2.19844e14 −0.131425
\(587\) −2.67588e15 −1.58473 −0.792367 0.610044i \(-0.791152\pi\)
−0.792367 + 0.610044i \(0.791152\pi\)
\(588\) −9.37821e14 −0.550231
\(589\) −2.31373e15 −1.34486
\(590\) −6.17338e13 −0.0355498
\(591\) 4.31832e14 0.246368
\(592\) 6.22140e14 0.351657
\(593\) 5.40731e14 0.302817 0.151409 0.988471i \(-0.451619\pi\)
0.151409 + 0.988471i \(0.451619\pi\)
\(594\) 1.25422e14 0.0695905
\(595\) −2.32707e13 −0.0127928
\(596\) 2.29014e15 1.24741
\(597\) −1.64404e15 −0.887264
\(598\) −7.73146e13 −0.0413433
\(599\) 3.38091e15 1.79138 0.895688 0.444683i \(-0.146684\pi\)
0.895688 + 0.444683i \(0.146684\pi\)
\(600\) 2.97390e14 0.156133
\(601\) −2.57256e15 −1.33831 −0.669153 0.743125i \(-0.733343\pi\)
−0.669153 + 0.743125i \(0.733343\pi\)
\(602\) 2.32889e13 0.0120052
\(603\) 2.81669e14 0.143878
\(604\) 1.25155e15 0.633496
\(605\) −4.85475e15 −2.43507
\(606\) −1.46863e14 −0.0729985
\(607\) −3.05746e14 −0.150599 −0.0752997 0.997161i \(-0.523991\pi\)
−0.0752997 + 0.997161i \(0.523991\pi\)
\(608\) 1.62449e15 0.792953
\(609\) −2.94163e12 −0.00142296
\(610\) 7.32378e14 0.351092
\(611\) −1.94746e15 −0.925214
\(612\) −1.54632e14 −0.0728061
\(613\) 3.74944e15 1.74958 0.874789 0.484504i \(-0.161000\pi\)
0.874789 + 0.484504i \(0.161000\pi\)
\(614\) 1.60778e14 0.0743536
\(615\) 1.17005e15 0.536280
\(616\) 6.77291e13 0.0307667
\(617\) −1.74630e15 −0.786232 −0.393116 0.919489i \(-0.628603\pi\)
−0.393116 + 0.919489i \(0.628603\pi\)
\(618\) 3.45485e14 0.154167
\(619\) −2.66563e15 −1.17896 −0.589482 0.807781i \(-0.700668\pi\)
−0.589482 + 0.807781i \(0.700668\pi\)
\(620\) −2.84603e15 −1.24763
\(621\) −1.13821e14 −0.0494561
\(622\) −1.82165e14 −0.0784544
\(623\) −5.60212e13 −0.0239149
\(624\) 8.95066e14 0.378739
\(625\) −2.92590e15 −1.22721
\(626\) −1.12943e14 −0.0469571
\(627\) 3.15237e15 1.29917
\(628\) 8.38639e14 0.342608
\(629\) 2.29227e14 0.0928296
\(630\) −9.86856e12 −0.00396169
\(631\) −3.39794e15 −1.35224 −0.676121 0.736791i \(-0.736340\pi\)
−0.676121 + 0.736791i \(0.736340\pi\)
\(632\) 1.15392e15 0.455230
\(633\) −6.78080e14 −0.265192
\(634\) 8.29855e14 0.321745
\(635\) 4.83390e14 0.185799
\(636\) 1.47879e15 0.563499
\(637\) 2.00010e15 0.755586
\(638\) −5.46714e13 −0.0204761
\(639\) 3.01227e13 0.0111851
\(640\) 2.64098e15 0.972243
\(641\) 2.60956e15 0.952464 0.476232 0.879320i \(-0.342002\pi\)
0.476232 + 0.879320i \(0.342002\pi\)
\(642\) −1.95068e14 −0.0705900
\(643\) 4.18378e15 1.50109 0.750547 0.660817i \(-0.229790\pi\)
0.750547 + 0.660817i \(0.229790\pi\)
\(644\) −3.00222e13 −0.0106800
\(645\) 2.72972e15 0.962809
\(646\) 1.83833e14 0.0642903
\(647\) 1.52285e15 0.528059 0.264030 0.964515i \(-0.414948\pi\)
0.264030 + 0.964515i \(0.414948\pi\)
\(648\) −1.34254e14 −0.0461598
\(649\) −6.49764e14 −0.221518
\(650\) −3.09796e14 −0.104725
\(651\) 7.62364e13 0.0255545
\(652\) −2.96344e15 −0.984996
\(653\) 2.27823e14 0.0750888 0.0375444 0.999295i \(-0.488046\pi\)
0.0375444 + 0.999295i \(0.488046\pi\)
\(654\) 3.86347e14 0.126270
\(655\) 4.78903e15 1.55210
\(656\) 1.94917e15 0.626438
\(657\) 7.00901e14 0.223381
\(658\) 3.57694e13 0.0113050
\(659\) 2.20006e15 0.689549 0.344774 0.938686i \(-0.387955\pi\)
0.344774 + 0.938686i \(0.387955\pi\)
\(660\) 3.87760e15 1.20523
\(661\) 4.21838e15 1.30028 0.650141 0.759814i \(-0.274710\pi\)
0.650141 + 0.759814i \(0.274710\pi\)
\(662\) 2.81461e14 0.0860398
\(663\) 3.29785e14 0.0999786
\(664\) −2.09587e15 −0.630145
\(665\) −2.48036e14 −0.0739599
\(666\) 9.72095e13 0.0287475
\(667\) 4.96145e13 0.0145518
\(668\) −3.92669e14 −0.114224
\(669\) 3.57183e15 1.03050
\(670\) −4.11898e14 −0.117863
\(671\) 7.70846e15 2.18773
\(672\) −5.35263e13 −0.0150673
\(673\) −2.92053e15 −0.815414 −0.407707 0.913113i \(-0.633672\pi\)
−0.407707 + 0.913113i \(0.633672\pi\)
\(674\) 1.27278e15 0.352471
\(675\) −4.56077e14 −0.125276
\(676\) 1.49617e15 0.407639
\(677\) 2.76749e15 0.747910 0.373955 0.927447i \(-0.378002\pi\)
0.373955 + 0.927447i \(0.378002\pi\)
\(678\) −4.97611e13 −0.0133391
\(679\) 3.69958e13 0.00983713
\(680\) 4.62948e14 0.122105
\(681\) −1.73161e15 −0.453046
\(682\) 1.41688e15 0.367722
\(683\) −5.44228e15 −1.40109 −0.700547 0.713606i \(-0.747061\pi\)
−0.700547 + 0.713606i \(0.747061\pi\)
\(684\) −1.64818e15 −0.420918
\(685\) 1.62860e15 0.412589
\(686\) −7.35421e13 −0.0184822
\(687\) −9.95871e14 −0.248280
\(688\) 4.54739e15 1.12467
\(689\) −3.15383e15 −0.773806
\(690\) 1.66446e14 0.0405139
\(691\) −2.91161e15 −0.703079 −0.351540 0.936173i \(-0.614342\pi\)
−0.351540 + 0.936173i \(0.614342\pi\)
\(692\) 1.88954e13 0.00452659
\(693\) −1.03869e14 −0.0246862
\(694\) 3.53484e14 0.0833474
\(695\) 6.00733e15 1.40529
\(696\) 5.85209e13 0.0135819
\(697\) 7.18168e14 0.165366
\(698\) −1.24821e15 −0.285156
\(699\) 1.19534e14 0.0270937
\(700\) −1.20297e14 −0.0270531
\(701\) −5.11697e15 −1.14173 −0.570865 0.821044i \(-0.693392\pi\)
−0.570865 + 0.821044i \(0.693392\pi\)
\(702\) 1.39854e14 0.0309615
\(703\) 2.44326e15 0.536681
\(704\) 5.77035e15 1.25763
\(705\) 4.19258e15 0.906654
\(706\) 1.00961e15 0.216635
\(707\) 1.21625e14 0.0258951
\(708\) 3.39723e14 0.0717699
\(709\) 4.25185e14 0.0891300 0.0445650 0.999006i \(-0.485810\pi\)
0.0445650 + 0.999006i \(0.485810\pi\)
\(710\) −4.40499e13 −0.00916271
\(711\) −1.76964e15 −0.365261
\(712\) 1.11449e15 0.228263
\(713\) −1.28583e15 −0.261330
\(714\) −6.05724e12 −0.00122162
\(715\) −8.26978e15 −1.65505
\(716\) −3.43183e15 −0.681559
\(717\) 1.49410e15 0.294459
\(718\) 8.90828e14 0.174225
\(719\) 1.41112e15 0.273877 0.136938 0.990580i \(-0.456274\pi\)
0.136938 + 0.990580i \(0.456274\pi\)
\(720\) −1.92694e15 −0.371141
\(721\) −2.86115e14 −0.0546886
\(722\) 8.39089e14 0.159167
\(723\) −1.21092e15 −0.227958
\(724\) −6.35911e15 −1.18805
\(725\) 1.98803e14 0.0368607
\(726\) −1.26366e15 −0.232531
\(727\) −6.89870e14 −0.125988 −0.0629938 0.998014i \(-0.520065\pi\)
−0.0629938 + 0.998014i \(0.520065\pi\)
\(728\) 7.55223e13 0.0136884
\(729\) 2.05891e14 0.0370370
\(730\) −1.02496e15 −0.182992
\(731\) 1.67548e15 0.296889
\(732\) −4.03030e15 −0.708804
\(733\) −4.64231e15 −0.810330 −0.405165 0.914244i \(-0.632786\pi\)
−0.405165 + 0.914244i \(0.632786\pi\)
\(734\) 2.02453e15 0.350748
\(735\) −4.30590e15 −0.740428
\(736\) 9.02792e14 0.154085
\(737\) −4.33533e15 −0.734432
\(738\) 3.04558e14 0.0512106
\(739\) 5.83938e15 0.974592 0.487296 0.873237i \(-0.337983\pi\)
0.487296 + 0.873237i \(0.337983\pi\)
\(740\) 3.00536e15 0.497877
\(741\) 3.51509e15 0.578012
\(742\) 5.79270e13 0.00945496
\(743\) −1.97794e15 −0.320460 −0.160230 0.987080i \(-0.551224\pi\)
−0.160230 + 0.987080i \(0.551224\pi\)
\(744\) −1.51665e15 −0.243912
\(745\) 1.05149e16 1.67860
\(746\) −3.56653e14 −0.0565175
\(747\) 3.21423e15 0.505607
\(748\) 2.38004e15 0.371642
\(749\) 1.61547e14 0.0250408
\(750\) −3.57622e14 −0.0550284
\(751\) −5.77666e15 −0.882384 −0.441192 0.897413i \(-0.645444\pi\)
−0.441192 + 0.897413i \(0.645444\pi\)
\(752\) 6.98434e15 1.05908
\(753\) 7.71428e14 0.116124
\(754\) −6.09621e13 −0.00910999
\(755\) 5.74633e15 0.852476
\(756\) 5.43070e13 0.00799809
\(757\) 6.34073e15 0.927069 0.463535 0.886079i \(-0.346581\pi\)
0.463535 + 0.886079i \(0.346581\pi\)
\(758\) 4.12812e14 0.0599200
\(759\) 1.75189e15 0.252451
\(760\) 4.93444e15 0.705932
\(761\) −1.27884e16 −1.81635 −0.908176 0.418589i \(-0.862525\pi\)
−0.908176 + 0.418589i \(0.862525\pi\)
\(762\) 1.25824e14 0.0177423
\(763\) −3.19955e14 −0.0447924
\(764\) −4.25131e15 −0.590893
\(765\) −7.09977e14 −0.0979730
\(766\) 1.05629e15 0.144719
\(767\) −7.24529e14 −0.0985557
\(768\) −2.47225e15 −0.333891
\(769\) −7.46048e15 −1.00040 −0.500198 0.865911i \(-0.666739\pi\)
−0.500198 + 0.865911i \(0.666739\pi\)
\(770\) 1.51893e14 0.0202227
\(771\) 4.86679e15 0.643345
\(772\) −8.56025e15 −1.12355
\(773\) −6.32191e15 −0.823874 −0.411937 0.911212i \(-0.635148\pi\)
−0.411937 + 0.911212i \(0.635148\pi\)
\(774\) 7.10531e14 0.0919407
\(775\) −5.15225e15 −0.661969
\(776\) −7.35995e14 −0.0938935
\(777\) −8.05045e13 −0.0101978
\(778\) −2.75214e15 −0.346165
\(779\) 7.65475e15 0.956038
\(780\) 4.32378e15 0.536220
\(781\) −4.63636e14 −0.0570948
\(782\) 1.02163e14 0.0124927
\(783\) −8.97475e13 −0.0108976
\(784\) −7.17311e15 −0.864906
\(785\) 3.85051e15 0.461037
\(786\) 1.24656e15 0.148214
\(787\) 3.28483e15 0.387839 0.193920 0.981017i \(-0.437880\pi\)
0.193920 + 0.981017i \(0.437880\pi\)
\(788\) 3.47510e15 0.407449
\(789\) −3.04590e15 −0.354643
\(790\) 2.58783e15 0.299218
\(791\) 4.12099e13 0.00473185
\(792\) 2.06638e15 0.235625
\(793\) 8.59544e15 0.973342
\(794\) −1.14666e15 −0.128951
\(795\) 6.78970e15 0.758283
\(796\) −1.32301e16 −1.46738
\(797\) −1.22059e16 −1.34446 −0.672232 0.740341i \(-0.734664\pi\)
−0.672232 + 0.740341i \(0.734664\pi\)
\(798\) −6.45624e13 −0.00706259
\(799\) 2.57337e15 0.279573
\(800\) 3.61745e15 0.390308
\(801\) −1.70917e15 −0.183150
\(802\) 7.19134e14 0.0765333
\(803\) −1.07880e16 −1.14026
\(804\) 2.26669e15 0.237949
\(805\) −1.37843e14 −0.0143717
\(806\) 1.57992e15 0.163603
\(807\) −7.15294e15 −0.735665
\(808\) −2.41962e15 −0.247164
\(809\) 1.51655e16 1.53865 0.769324 0.638859i \(-0.220593\pi\)
0.769324 + 0.638859i \(0.220593\pi\)
\(810\) −3.01084e14 −0.0303403
\(811\) 1.41376e15 0.141502 0.0707509 0.997494i \(-0.477460\pi\)
0.0707509 + 0.997494i \(0.477460\pi\)
\(812\) −2.36723e13 −0.00235333
\(813\) −1.37149e14 −0.0135424
\(814\) −1.49621e15 −0.146743
\(815\) −1.36063e16 −1.32548
\(816\) −1.18274e15 −0.114444
\(817\) 1.78585e16 1.71642
\(818\) 2.74472e15 0.262033
\(819\) −1.15821e14 −0.0109831
\(820\) 9.41581e15 0.886914
\(821\) 2.57332e15 0.240772 0.120386 0.992727i \(-0.461587\pi\)
0.120386 + 0.992727i \(0.461587\pi\)
\(822\) 4.23917e14 0.0393990
\(823\) −1.91485e16 −1.76781 −0.883906 0.467665i \(-0.845095\pi\)
−0.883906 + 0.467665i \(0.845095\pi\)
\(824\) 5.69198e15 0.521992
\(825\) 7.01974e15 0.639476
\(826\) 1.33076e13 0.00120423
\(827\) −1.88291e16 −1.69258 −0.846289 0.532724i \(-0.821168\pi\)
−0.846289 + 0.532724i \(0.821168\pi\)
\(828\) −9.15959e14 −0.0817917
\(829\) 6.78530e15 0.601892 0.300946 0.953641i \(-0.402698\pi\)
0.300946 + 0.953641i \(0.402698\pi\)
\(830\) −4.70031e15 −0.414188
\(831\) 1.39165e15 0.121822
\(832\) 6.43432e15 0.559531
\(833\) −2.64292e15 −0.228316
\(834\) 1.56367e15 0.134194
\(835\) −1.80289e15 −0.153707
\(836\) 2.53682e16 2.14859
\(837\) 2.32593e15 0.195707
\(838\) −1.00783e14 −0.00842456
\(839\) 4.04318e15 0.335762 0.167881 0.985807i \(-0.446308\pi\)
0.167881 + 0.985807i \(0.446308\pi\)
\(840\) −1.62588e14 −0.0134138
\(841\) −1.21614e16 −0.996794
\(842\) −1.68261e15 −0.137015
\(843\) −7.49066e15 −0.605994
\(844\) −5.45675e15 −0.438581
\(845\) 6.86951e15 0.548547
\(846\) 1.09131e15 0.0865783
\(847\) 1.04651e15 0.0824867
\(848\) 1.13108e16 0.885763
\(849\) 1.11284e15 0.0865849
\(850\) 4.09364e14 0.0316450
\(851\) 1.35781e15 0.104286
\(852\) 2.42408e14 0.0184982
\(853\) −1.59369e16 −1.20833 −0.604164 0.796860i \(-0.706493\pi\)
−0.604164 + 0.796860i \(0.706493\pi\)
\(854\) −1.57874e14 −0.0118930
\(855\) −7.56745e15 −0.566416
\(856\) −3.21381e15 −0.239009
\(857\) −2.96888e15 −0.219381 −0.109690 0.993966i \(-0.534986\pi\)
−0.109690 + 0.993966i \(0.534986\pi\)
\(858\) −2.15258e15 −0.158044
\(859\) 1.55831e16 1.13682 0.568411 0.822745i \(-0.307558\pi\)
0.568411 + 0.822745i \(0.307558\pi\)
\(860\) 2.19670e16 1.59232
\(861\) −2.52221e14 −0.0181662
\(862\) −2.88819e15 −0.206698
\(863\) 4.27803e15 0.304218 0.152109 0.988364i \(-0.451394\pi\)
0.152109 + 0.988364i \(0.451394\pi\)
\(864\) −1.63306e15 −0.115392
\(865\) 8.67558e13 0.00609130
\(866\) 2.70179e15 0.188497
\(867\) 7.89229e15 0.547140
\(868\) 6.13501e14 0.0422626
\(869\) 2.72376e16 1.86449
\(870\) 1.31242e14 0.00892723
\(871\) −4.83418e15 −0.326756
\(872\) 6.36520e15 0.427535
\(873\) 1.12872e15 0.0753369
\(874\) 1.08893e15 0.0722249
\(875\) 2.96166e14 0.0195205
\(876\) 5.64039e15 0.369434
\(877\) −1.12838e16 −0.734441 −0.367221 0.930134i \(-0.619691\pi\)
−0.367221 + 0.930134i \(0.619691\pi\)
\(878\) −5.59565e15 −0.361935
\(879\) 5.55469e15 0.357043
\(880\) 2.96586e16 1.89451
\(881\) −5.86659e15 −0.372407 −0.186204 0.982511i \(-0.559618\pi\)
−0.186204 + 0.982511i \(0.559618\pi\)
\(882\) −1.12080e15 −0.0707051
\(883\) 1.09029e16 0.683530 0.341765 0.939785i \(-0.388975\pi\)
0.341765 + 0.939785i \(0.388975\pi\)
\(884\) 2.65390e15 0.165347
\(885\) 1.55980e15 0.0965785
\(886\) −5.19448e14 −0.0319636
\(887\) −2.39091e16 −1.46212 −0.731062 0.682311i \(-0.760975\pi\)
−0.731062 + 0.682311i \(0.760975\pi\)
\(888\) 1.60156e15 0.0973356
\(889\) −1.04202e14 −0.00629382
\(890\) 2.49941e15 0.150035
\(891\) −3.16899e15 −0.189057
\(892\) 2.87437e16 1.70426
\(893\) 2.74288e16 1.61631
\(894\) 2.73697e15 0.160293
\(895\) −1.57568e16 −0.917154
\(896\) −5.69300e14 −0.0329342
\(897\) 1.95347e15 0.112318
\(898\) −6.02385e15 −0.344234
\(899\) −1.01387e15 −0.0575842
\(900\) −3.67021e15 −0.207184
\(901\) 4.16746e15 0.233822
\(902\) −4.68763e15 −0.261407
\(903\) −5.88430e14 −0.0326146
\(904\) −8.19831e14 −0.0451646
\(905\) −2.91971e16 −1.59872
\(906\) 1.49574e15 0.0814048
\(907\) −5.18038e15 −0.280234 −0.140117 0.990135i \(-0.544748\pi\)
−0.140117 + 0.990135i \(0.544748\pi\)
\(908\) −1.39349e16 −0.749258
\(909\) 3.71072e15 0.198316
\(910\) 1.69370e14 0.00899725
\(911\) −3.53724e16 −1.86773 −0.933863 0.357631i \(-0.883584\pi\)
−0.933863 + 0.357631i \(0.883584\pi\)
\(912\) −1.26065e16 −0.661640
\(913\) −4.94720e16 −2.58090
\(914\) 1.63874e15 0.0849777
\(915\) −1.85046e16 −0.953816
\(916\) −8.01412e15 −0.410611
\(917\) −1.03234e15 −0.0525766
\(918\) −1.84803e14 −0.00935565
\(919\) −2.34017e16 −1.17764 −0.588820 0.808264i \(-0.700407\pi\)
−0.588820 + 0.808264i \(0.700407\pi\)
\(920\) 2.74226e15 0.137175
\(921\) −4.06231e15 −0.201997
\(922\) 3.25623e15 0.160951
\(923\) −5.16985e14 −0.0254020
\(924\) −8.35871e14 −0.0408266
\(925\) 5.44070e15 0.264165
\(926\) 2.76380e15 0.133397
\(927\) −8.72921e15 −0.418829
\(928\) 7.11847e14 0.0339526
\(929\) −9.47653e15 −0.449328 −0.224664 0.974436i \(-0.572128\pi\)
−0.224664 + 0.974436i \(0.572128\pi\)
\(930\) −3.40132e15 −0.160321
\(931\) −2.81702e16 −1.31998
\(932\) 9.61933e14 0.0448082
\(933\) 4.60267e15 0.213138
\(934\) 7.45159e15 0.343037
\(935\) 1.09277e16 0.500108
\(936\) 2.30414e15 0.104832
\(937\) −1.38527e16 −0.626566 −0.313283 0.949660i \(-0.601429\pi\)
−0.313283 + 0.949660i \(0.601429\pi\)
\(938\) 8.87904e13 0.00399255
\(939\) 2.85368e15 0.127569
\(940\) 3.37391e16 1.49945
\(941\) −4.29714e16 −1.89862 −0.949308 0.314348i \(-0.898214\pi\)
−0.949308 + 0.314348i \(0.898214\pi\)
\(942\) 1.00227e15 0.0440254
\(943\) 4.25404e15 0.185775
\(944\) 2.59844e15 0.112815
\(945\) 2.49344e14 0.0107628
\(946\) −1.09362e16 −0.469316
\(947\) 4.38038e15 0.186890 0.0934452 0.995624i \(-0.470212\pi\)
0.0934452 + 0.995624i \(0.470212\pi\)
\(948\) −1.42409e16 −0.604077
\(949\) −1.20293e16 −0.507313
\(950\) 4.36329e15 0.182951
\(951\) −2.09676e16 −0.874088
\(952\) −9.97950e13 −0.00413624
\(953\) −3.70592e16 −1.52716 −0.763580 0.645713i \(-0.776560\pi\)
−0.763580 + 0.645713i \(0.776560\pi\)
\(954\) 1.76732e15 0.0724101
\(955\) −1.95194e16 −0.795147
\(956\) 1.20236e16 0.486984
\(957\) 1.38136e15 0.0556275
\(958\) −6.75496e14 −0.0270466
\(959\) −3.51068e14 −0.0139762
\(960\) −1.38521e16 −0.548307
\(961\) 8.67298e14 0.0341342
\(962\) −1.66837e15 −0.0652874
\(963\) 4.92869e15 0.191773
\(964\) −9.74468e15 −0.377002
\(965\) −3.93034e16 −1.51192
\(966\) −3.58798e13 −0.00137238
\(967\) −3.18540e15 −0.121148 −0.0605742 0.998164i \(-0.519293\pi\)
−0.0605742 + 0.998164i \(0.519293\pi\)
\(968\) −2.08193e16 −0.787319
\(969\) −4.64483e15 −0.174658
\(970\) −1.65058e15 −0.0617152
\(971\) −1.07743e16 −0.400575 −0.200287 0.979737i \(-0.564188\pi\)
−0.200287 + 0.979737i \(0.564188\pi\)
\(972\) 1.65688e15 0.0612528
\(973\) −1.29496e15 −0.0476033
\(974\) −4.85705e15 −0.177541
\(975\) 7.82747e15 0.284509
\(976\) −3.08265e16 −1.11417
\(977\) 5.03107e16 1.80817 0.904087 0.427348i \(-0.140552\pi\)
0.904087 + 0.427348i \(0.140552\pi\)
\(978\) −3.54164e15 −0.126573
\(979\) 2.63069e16 0.934899
\(980\) −3.46510e16 −1.22454
\(981\) −9.76166e15 −0.343039
\(982\) 6.48381e15 0.226578
\(983\) 1.83781e16 0.638639 0.319319 0.947647i \(-0.396546\pi\)
0.319319 + 0.947647i \(0.396546\pi\)
\(984\) 5.01769e15 0.173393
\(985\) 1.59555e16 0.548292
\(986\) 8.05552e13 0.00275277
\(987\) −9.03770e14 −0.0307124
\(988\) 2.82872e16 0.955930
\(989\) 9.92463e15 0.333530
\(990\) 4.63416e15 0.154874
\(991\) −2.39571e16 −0.796214 −0.398107 0.917339i \(-0.630333\pi\)
−0.398107 + 0.917339i \(0.630333\pi\)
\(992\) −1.84485e16 −0.609742
\(993\) −7.11155e15 −0.233745
\(994\) 9.49557e12 0.000310382 0
\(995\) −6.07446e16 −1.97461
\(996\) 2.58660e16 0.836186
\(997\) 5.69539e16 1.83105 0.915526 0.402260i \(-0.131775\pi\)
0.915526 + 0.402260i \(0.131775\pi\)
\(998\) −2.80244e14 −0.00896023
\(999\) −2.45615e15 −0.0780988
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.a.1.14 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.14 26 1.1 even 1 trivial