Properties

Label 177.12.a.c.1.8
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $27$
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: \(27\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-41.9561 q^{2} -243.000 q^{3} -287.686 q^{4} -4799.69 q^{5} +10195.3 q^{6} -40967.8 q^{7} +97996.3 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-41.9561 q^{2} -243.000 q^{3} -287.686 q^{4} -4799.69 q^{5} +10195.3 q^{6} -40967.8 q^{7} +97996.3 q^{8} +59049.0 q^{9} +201376. q^{10} +261833. q^{11} +69907.8 q^{12} -320404. q^{13} +1.71885e6 q^{14} +1.16632e6 q^{15} -3.52236e6 q^{16} +8.00961e6 q^{17} -2.47747e6 q^{18} +4.69006e6 q^{19} +1.38080e6 q^{20} +9.95518e6 q^{21} -1.09855e7 q^{22} +2.01048e7 q^{23} -2.38131e7 q^{24} -2.57911e7 q^{25} +1.34429e7 q^{26} -1.43489e7 q^{27} +1.17859e7 q^{28} +9.30191e7 q^{29} -4.89344e7 q^{30} +4.66282e7 q^{31} -5.29119e7 q^{32} -6.36253e7 q^{33} -3.36052e8 q^{34} +1.96633e8 q^{35} -1.69876e7 q^{36} -4.29096e8 q^{37} -1.96776e8 q^{38} +7.78581e7 q^{39} -4.70352e8 q^{40} +1.99434e7 q^{41} -4.17680e8 q^{42} +1.68610e8 q^{43} -7.53256e7 q^{44} -2.83417e8 q^{45} -8.43519e8 q^{46} -5.76398e8 q^{47} +8.55933e8 q^{48} -2.98964e8 q^{49} +1.08209e9 q^{50} -1.94633e9 q^{51} +9.21758e7 q^{52} +4.39963e9 q^{53} +6.02024e8 q^{54} -1.25672e9 q^{55} -4.01469e9 q^{56} -1.13968e9 q^{57} -3.90272e9 q^{58} -7.14924e8 q^{59} -3.35536e8 q^{60} -2.27729e9 q^{61} -1.95634e9 q^{62} -2.41911e9 q^{63} +9.43377e9 q^{64} +1.53784e9 q^{65} +2.66947e9 q^{66} +1.03436e10 q^{67} -2.30425e9 q^{68} -4.88547e9 q^{69} -8.24995e9 q^{70} -2.02693e10 q^{71} +5.78658e9 q^{72} -3.07148e10 q^{73} +1.80032e10 q^{74} +6.26724e9 q^{75} -1.34926e9 q^{76} -1.07267e10 q^{77} -3.26662e9 q^{78} -2.51513e10 q^{79} +1.69062e10 q^{80} +3.48678e9 q^{81} -8.36747e8 q^{82} -1.75237e10 q^{83} -2.86397e9 q^{84} -3.84436e10 q^{85} -7.07423e9 q^{86} -2.26036e10 q^{87} +2.56586e10 q^{88} -1.52045e10 q^{89} +1.18911e10 q^{90} +1.31262e10 q^{91} -5.78388e9 q^{92} -1.13307e10 q^{93} +2.41834e10 q^{94} -2.25108e10 q^{95} +1.28576e10 q^{96} +1.56615e10 q^{97} +1.25434e10 q^{98} +1.54610e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −41.9561 −0.927107 −0.463554 0.886069i \(-0.653426\pi\)
−0.463554 + 0.886069i \(0.653426\pi\)
\(3\) −243.000 −0.577350
\(4\) −287.686 −0.140472
\(5\) −4799.69 −0.686876 −0.343438 0.939175i \(-0.611591\pi\)
−0.343438 + 0.939175i \(0.611591\pi\)
\(6\) 10195.3 0.535266
\(7\) −40967.8 −0.921305 −0.460653 0.887580i \(-0.652385\pi\)
−0.460653 + 0.887580i \(0.652385\pi\)
\(8\) 97996.3 1.05734
\(9\) 59049.0 0.333333
\(10\) 201376. 0.636808
\(11\) 261833. 0.490189 0.245095 0.969499i \(-0.421181\pi\)
0.245095 + 0.969499i \(0.421181\pi\)
\(12\) 69907.8 0.0811014
\(13\) −320404. −0.239337 −0.119668 0.992814i \(-0.538183\pi\)
−0.119668 + 0.992814i \(0.538183\pi\)
\(14\) 1.71885e6 0.854149
\(15\) 1.16632e6 0.396568
\(16\) −3.52236e6 −0.839796
\(17\) 8.00961e6 1.36818 0.684088 0.729399i \(-0.260200\pi\)
0.684088 + 0.729399i \(0.260200\pi\)
\(18\) −2.47747e6 −0.309036
\(19\) 4.69006e6 0.434543 0.217272 0.976111i \(-0.430284\pi\)
0.217272 + 0.976111i \(0.430284\pi\)
\(20\) 1.38080e6 0.0964867
\(21\) 9.95518e6 0.531916
\(22\) −1.09855e7 −0.454458
\(23\) 2.01048e7 0.651324 0.325662 0.945486i \(-0.394413\pi\)
0.325662 + 0.945486i \(0.394413\pi\)
\(24\) −2.38131e7 −0.610455
\(25\) −2.57911e7 −0.528202
\(26\) 1.34429e7 0.221891
\(27\) −1.43489e7 −0.192450
\(28\) 1.17859e7 0.129417
\(29\) 9.30191e7 0.842138 0.421069 0.907029i \(-0.361655\pi\)
0.421069 + 0.907029i \(0.361655\pi\)
\(30\) −4.89344e7 −0.367661
\(31\) 4.66282e7 0.292523 0.146261 0.989246i \(-0.453276\pi\)
0.146261 + 0.989246i \(0.453276\pi\)
\(32\) −5.29119e7 −0.278759
\(33\) −6.36253e7 −0.283011
\(34\) −3.36052e8 −1.26845
\(35\) 1.96633e8 0.632822
\(36\) −1.69876e7 −0.0468239
\(37\) −4.29096e8 −1.01729 −0.508645 0.860976i \(-0.669854\pi\)
−0.508645 + 0.860976i \(0.669854\pi\)
\(38\) −1.96776e8 −0.402868
\(39\) 7.78581e7 0.138181
\(40\) −4.70352e8 −0.726261
\(41\) 1.99434e7 0.0268836 0.0134418 0.999910i \(-0.495721\pi\)
0.0134418 + 0.999910i \(0.495721\pi\)
\(42\) −4.17680e8 −0.493143
\(43\) 1.68610e8 0.174907 0.0874536 0.996169i \(-0.472127\pi\)
0.0874536 + 0.996169i \(0.472127\pi\)
\(44\) −7.53256e7 −0.0688578
\(45\) −2.83417e8 −0.228959
\(46\) −8.43519e8 −0.603847
\(47\) −5.76398e8 −0.366593 −0.183296 0.983058i \(-0.558677\pi\)
−0.183296 + 0.983058i \(0.558677\pi\)
\(48\) 8.55933e8 0.484856
\(49\) −2.98964e8 −0.151196
\(50\) 1.08209e9 0.489700
\(51\) −1.94633e9 −0.789917
\(52\) 9.21758e7 0.0336201
\(53\) 4.39963e9 1.44510 0.722551 0.691317i \(-0.242969\pi\)
0.722551 + 0.691317i \(0.242969\pi\)
\(54\) 6.02024e8 0.178422
\(55\) −1.25672e9 −0.336699
\(56\) −4.01469e9 −0.974133
\(57\) −1.13968e9 −0.250884
\(58\) −3.90272e9 −0.780752
\(59\) −7.14924e8 −0.130189
\(60\) −3.35536e8 −0.0557066
\(61\) −2.27729e9 −0.345227 −0.172613 0.984990i \(-0.555221\pi\)
−0.172613 + 0.984990i \(0.555221\pi\)
\(62\) −1.95634e9 −0.271200
\(63\) −2.41911e9 −0.307102
\(64\) 9.43377e9 1.09824
\(65\) 1.53784e9 0.164395
\(66\) 2.66947e9 0.262382
\(67\) 1.03436e10 0.935970 0.467985 0.883736i \(-0.344980\pi\)
0.467985 + 0.883736i \(0.344980\pi\)
\(68\) −2.30425e9 −0.192190
\(69\) −4.88547e9 −0.376042
\(70\) −8.24995e9 −0.586694
\(71\) −2.02693e10 −1.33327 −0.666635 0.745384i \(-0.732266\pi\)
−0.666635 + 0.745384i \(0.732266\pi\)
\(72\) 5.78658e9 0.352447
\(73\) −3.07148e10 −1.73409 −0.867046 0.498227i \(-0.833985\pi\)
−0.867046 + 0.498227i \(0.833985\pi\)
\(74\) 1.80032e10 0.943138
\(75\) 6.26724e9 0.304957
\(76\) −1.34926e9 −0.0610411
\(77\) −1.07267e10 −0.451614
\(78\) −3.26662e9 −0.128109
\(79\) −2.51513e10 −0.919626 −0.459813 0.888016i \(-0.652083\pi\)
−0.459813 + 0.888016i \(0.652083\pi\)
\(80\) 1.69062e10 0.576835
\(81\) 3.48678e9 0.111111
\(82\) −8.36747e8 −0.0249240
\(83\) −1.75237e10 −0.488312 −0.244156 0.969736i \(-0.578511\pi\)
−0.244156 + 0.969736i \(0.578511\pi\)
\(84\) −2.86397e9 −0.0747192
\(85\) −3.84436e10 −0.939767
\(86\) −7.07423e9 −0.162158
\(87\) −2.26036e10 −0.486208
\(88\) 2.56586e10 0.518297
\(89\) −1.52045e10 −0.288621 −0.144310 0.989532i \(-0.546096\pi\)
−0.144310 + 0.989532i \(0.546096\pi\)
\(90\) 1.18911e10 0.212269
\(91\) 1.31262e10 0.220502
\(92\) −5.78388e9 −0.0914926
\(93\) −1.13307e10 −0.168888
\(94\) 2.41834e10 0.339871
\(95\) −2.25108e10 −0.298477
\(96\) 1.28576e10 0.160942
\(97\) 1.56615e10 0.185178 0.0925889 0.995704i \(-0.470486\pi\)
0.0925889 + 0.995704i \(0.470486\pi\)
\(98\) 1.25434e10 0.140175
\(99\) 1.54610e10 0.163396
\(100\) 7.41975e9 0.0741975
\(101\) 1.14234e11 1.08151 0.540753 0.841182i \(-0.318139\pi\)
0.540753 + 0.841182i \(0.318139\pi\)
\(102\) 8.16606e10 0.732338
\(103\) −2.14743e11 −1.82522 −0.912610 0.408831i \(-0.865937\pi\)
−0.912610 + 0.408831i \(0.865937\pi\)
\(104\) −3.13984e10 −0.253060
\(105\) −4.77818e10 −0.365360
\(106\) −1.84591e11 −1.33977
\(107\) −7.73008e10 −0.532811 −0.266406 0.963861i \(-0.585836\pi\)
−0.266406 + 0.963861i \(0.585836\pi\)
\(108\) 4.12798e9 0.0270338
\(109\) 1.16831e11 0.727300 0.363650 0.931536i \(-0.381530\pi\)
0.363650 + 0.931536i \(0.381530\pi\)
\(110\) 5.27269e10 0.312156
\(111\) 1.04270e11 0.587333
\(112\) 1.44303e11 0.773709
\(113\) 3.30169e10 0.168580 0.0842899 0.996441i \(-0.473138\pi\)
0.0842899 + 0.996441i \(0.473138\pi\)
\(114\) 4.78167e10 0.232596
\(115\) −9.64968e10 −0.447378
\(116\) −2.67603e10 −0.118297
\(117\) −1.89195e10 −0.0797789
\(118\) 2.99954e10 0.120699
\(119\) −3.28136e11 −1.26051
\(120\) 1.14295e11 0.419307
\(121\) −2.16755e11 −0.759714
\(122\) 9.55462e10 0.320062
\(123\) −4.84624e9 −0.0155213
\(124\) −1.34143e10 −0.0410912
\(125\) 3.58149e11 1.04968
\(126\) 1.01496e11 0.284716
\(127\) 3.12876e11 0.840333 0.420166 0.907447i \(-0.361972\pi\)
0.420166 + 0.907447i \(0.361972\pi\)
\(128\) −2.87440e11 −0.739423
\(129\) −4.09723e10 −0.100983
\(130\) −6.45217e10 −0.152411
\(131\) −2.09307e11 −0.474014 −0.237007 0.971508i \(-0.576166\pi\)
−0.237007 + 0.971508i \(0.576166\pi\)
\(132\) 1.83041e10 0.0397551
\(133\) −1.92141e11 −0.400347
\(134\) −4.33979e11 −0.867745
\(135\) 6.88703e10 0.132189
\(136\) 7.84912e11 1.44663
\(137\) −6.26380e11 −1.10886 −0.554428 0.832232i \(-0.687063\pi\)
−0.554428 + 0.832232i \(0.687063\pi\)
\(138\) 2.04975e11 0.348631
\(139\) 8.36338e11 1.36710 0.683550 0.729903i \(-0.260435\pi\)
0.683550 + 0.729903i \(0.260435\pi\)
\(140\) −5.65686e10 −0.0888937
\(141\) 1.40065e11 0.211653
\(142\) 8.50422e11 1.23609
\(143\) −8.38922e10 −0.117320
\(144\) −2.07992e11 −0.279932
\(145\) −4.46463e11 −0.578444
\(146\) 1.28867e12 1.60769
\(147\) 7.26483e10 0.0872932
\(148\) 1.23445e11 0.142901
\(149\) −7.28067e11 −0.812170 −0.406085 0.913835i \(-0.633106\pi\)
−0.406085 + 0.913835i \(0.633106\pi\)
\(150\) −2.62949e11 −0.282728
\(151\) 1.11462e12 1.15546 0.577730 0.816228i \(-0.303939\pi\)
0.577730 + 0.816228i \(0.303939\pi\)
\(152\) 4.59608e11 0.459460
\(153\) 4.72959e11 0.456059
\(154\) 4.50051e11 0.418695
\(155\) −2.23801e11 −0.200927
\(156\) −2.23987e10 −0.0194106
\(157\) 1.18440e12 0.990944 0.495472 0.868624i \(-0.334995\pi\)
0.495472 + 0.868624i \(0.334995\pi\)
\(158\) 1.05525e12 0.852592
\(159\) −1.06911e12 −0.834330
\(160\) 2.53961e11 0.191473
\(161\) −8.23650e11 −0.600068
\(162\) −1.46292e11 −0.103012
\(163\) 1.05240e12 0.716387 0.358194 0.933647i \(-0.383393\pi\)
0.358194 + 0.933647i \(0.383393\pi\)
\(164\) −5.73744e9 −0.00377639
\(165\) 3.05382e11 0.194393
\(166\) 7.35228e11 0.452717
\(167\) 4.67477e11 0.278496 0.139248 0.990258i \(-0.455531\pi\)
0.139248 + 0.990258i \(0.455531\pi\)
\(168\) 9.75571e11 0.562416
\(169\) −1.68950e12 −0.942718
\(170\) 1.61294e12 0.871265
\(171\) 2.76943e11 0.144848
\(172\) −4.85069e10 −0.0245695
\(173\) 2.74846e12 1.34845 0.674227 0.738524i \(-0.264477\pi\)
0.674227 + 0.738524i \(0.264477\pi\)
\(174\) 9.48360e11 0.450767
\(175\) 1.05661e12 0.486635
\(176\) −9.22268e11 −0.411659
\(177\) 1.73727e11 0.0751646
\(178\) 6.37922e11 0.267583
\(179\) 1.23655e12 0.502946 0.251473 0.967864i \(-0.419085\pi\)
0.251473 + 0.967864i \(0.419085\pi\)
\(180\) 8.15351e10 0.0321622
\(181\) −2.36395e12 −0.904497 −0.452248 0.891892i \(-0.649378\pi\)
−0.452248 + 0.891892i \(0.649378\pi\)
\(182\) −5.50726e11 −0.204429
\(183\) 5.53381e11 0.199317
\(184\) 1.97020e12 0.688671
\(185\) 2.05953e12 0.698752
\(186\) 4.75390e11 0.156577
\(187\) 2.09718e12 0.670666
\(188\) 1.65822e11 0.0514960
\(189\) 5.87843e11 0.177305
\(190\) 9.44466e11 0.276721
\(191\) 1.66476e12 0.473879 0.236939 0.971524i \(-0.423856\pi\)
0.236939 + 0.971524i \(0.423856\pi\)
\(192\) −2.29241e12 −0.634066
\(193\) 2.43187e12 0.653696 0.326848 0.945077i \(-0.394014\pi\)
0.326848 + 0.945077i \(0.394014\pi\)
\(194\) −6.57096e11 −0.171680
\(195\) −3.73695e11 −0.0949132
\(196\) 8.60079e10 0.0212388
\(197\) 4.03087e12 0.967910 0.483955 0.875093i \(-0.339200\pi\)
0.483955 + 0.875093i \(0.339200\pi\)
\(198\) −6.48681e11 −0.151486
\(199\) 2.52695e12 0.573991 0.286996 0.957932i \(-0.407343\pi\)
0.286996 + 0.957932i \(0.407343\pi\)
\(200\) −2.52743e12 −0.558489
\(201\) −2.51350e12 −0.540382
\(202\) −4.79282e12 −1.00267
\(203\) −3.81079e12 −0.775866
\(204\) 5.59934e11 0.110961
\(205\) −9.57221e10 −0.0184657
\(206\) 9.00980e12 1.69218
\(207\) 1.18717e12 0.217108
\(208\) 1.12858e12 0.200994
\(209\) 1.22801e12 0.213009
\(210\) 2.00474e12 0.338728
\(211\) −3.90004e12 −0.641971 −0.320985 0.947084i \(-0.604014\pi\)
−0.320985 + 0.947084i \(0.604014\pi\)
\(212\) −1.26571e12 −0.202996
\(213\) 4.92545e12 0.769764
\(214\) 3.24324e12 0.493973
\(215\) −8.09277e11 −0.120139
\(216\) −1.40614e12 −0.203485
\(217\) −1.91026e12 −0.269503
\(218\) −4.90179e12 −0.674285
\(219\) 7.46370e12 1.00118
\(220\) 3.61540e11 0.0472967
\(221\) −2.56631e12 −0.327455
\(222\) −4.37478e12 −0.544521
\(223\) −4.30330e12 −0.522546 −0.261273 0.965265i \(-0.584142\pi\)
−0.261273 + 0.965265i \(0.584142\pi\)
\(224\) 2.16769e12 0.256822
\(225\) −1.52294e12 −0.176067
\(226\) −1.38526e12 −0.156291
\(227\) 6.55576e12 0.721907 0.360953 0.932584i \(-0.382451\pi\)
0.360953 + 0.932584i \(0.382451\pi\)
\(228\) 3.27871e11 0.0352421
\(229\) 1.14174e13 1.19805 0.599023 0.800731i \(-0.295556\pi\)
0.599023 + 0.800731i \(0.295556\pi\)
\(230\) 4.04863e12 0.414768
\(231\) 2.60659e12 0.260740
\(232\) 9.11552e12 0.890426
\(233\) 1.28113e13 1.22218 0.611090 0.791561i \(-0.290731\pi\)
0.611090 + 0.791561i \(0.290731\pi\)
\(234\) 7.93790e11 0.0739636
\(235\) 2.76653e12 0.251804
\(236\) 2.05674e11 0.0182879
\(237\) 6.11176e12 0.530946
\(238\) 1.37673e13 1.16863
\(239\) −2.88344e12 −0.239179 −0.119589 0.992823i \(-0.538158\pi\)
−0.119589 + 0.992823i \(0.538158\pi\)
\(240\) −4.10821e12 −0.333036
\(241\) 9.71704e12 0.769911 0.384955 0.922935i \(-0.374217\pi\)
0.384955 + 0.922935i \(0.374217\pi\)
\(242\) 9.09421e12 0.704337
\(243\) −8.47289e11 −0.0641500
\(244\) 6.55145e11 0.0484946
\(245\) 1.43494e12 0.103853
\(246\) 2.03329e11 0.0143899
\(247\) −1.50271e12 −0.104002
\(248\) 4.56939e12 0.309296
\(249\) 4.25827e12 0.281927
\(250\) −1.50265e13 −0.973170
\(251\) 6.06579e12 0.384310 0.192155 0.981365i \(-0.438452\pi\)
0.192155 + 0.981365i \(0.438452\pi\)
\(252\) 6.95944e11 0.0431392
\(253\) 5.26409e12 0.319272
\(254\) −1.31270e13 −0.779079
\(255\) 9.34180e12 0.542575
\(256\) −7.26048e12 −0.412711
\(257\) 6.71155e12 0.373414 0.186707 0.982416i \(-0.440219\pi\)
0.186707 + 0.982416i \(0.440219\pi\)
\(258\) 1.71904e12 0.0936218
\(259\) 1.75791e13 0.937235
\(260\) −4.42415e11 −0.0230928
\(261\) 5.49268e12 0.280713
\(262\) 8.78169e12 0.439462
\(263\) −3.03108e13 −1.48539 −0.742696 0.669629i \(-0.766453\pi\)
−0.742696 + 0.669629i \(0.766453\pi\)
\(264\) −6.23504e12 −0.299239
\(265\) −2.11168e13 −0.992606
\(266\) 8.06150e12 0.371165
\(267\) 3.69470e12 0.166635
\(268\) −2.97572e12 −0.131477
\(269\) −3.36364e13 −1.45604 −0.728018 0.685558i \(-0.759558\pi\)
−0.728018 + 0.685558i \(0.759558\pi\)
\(270\) −2.88953e12 −0.122554
\(271\) 8.58630e12 0.356841 0.178420 0.983954i \(-0.442901\pi\)
0.178420 + 0.983954i \(0.442901\pi\)
\(272\) −2.82127e13 −1.14899
\(273\) −3.18968e12 −0.127307
\(274\) 2.62805e13 1.02803
\(275\) −6.75295e12 −0.258919
\(276\) 1.40548e12 0.0528233
\(277\) −4.36554e13 −1.60842 −0.804210 0.594345i \(-0.797411\pi\)
−0.804210 + 0.594345i \(0.797411\pi\)
\(278\) −3.50895e13 −1.26745
\(279\) 2.75335e12 0.0975075
\(280\) 1.92693e13 0.669108
\(281\) −4.91273e13 −1.67278 −0.836390 0.548136i \(-0.815338\pi\)
−0.836390 + 0.548136i \(0.815338\pi\)
\(282\) −5.87657e12 −0.196225
\(283\) −5.03326e13 −1.64825 −0.824127 0.566405i \(-0.808334\pi\)
−0.824127 + 0.566405i \(0.808334\pi\)
\(284\) 5.83121e12 0.187287
\(285\) 5.47013e12 0.172326
\(286\) 3.51979e12 0.108769
\(287\) −8.17037e11 −0.0247680
\(288\) −3.12440e12 −0.0929196
\(289\) 2.98819e13 0.871907
\(290\) 1.87318e13 0.536280
\(291\) −3.80575e12 −0.106912
\(292\) 8.83624e12 0.243591
\(293\) −3.72144e13 −1.00679 −0.503396 0.864056i \(-0.667916\pi\)
−0.503396 + 0.864056i \(0.667916\pi\)
\(294\) −3.04804e12 −0.0809302
\(295\) 3.43141e12 0.0894236
\(296\) −4.20498e13 −1.07562
\(297\) −3.75701e12 −0.0943370
\(298\) 3.05469e13 0.752969
\(299\) −6.44166e12 −0.155886
\(300\) −1.80300e12 −0.0428379
\(301\) −6.90760e12 −0.161143
\(302\) −4.67653e13 −1.07124
\(303\) −2.77589e13 −0.624407
\(304\) −1.65201e13 −0.364928
\(305\) 1.09303e13 0.237128
\(306\) −1.98435e13 −0.422816
\(307\) 4.67400e13 0.978199 0.489100 0.872228i \(-0.337325\pi\)
0.489100 + 0.872228i \(0.337325\pi\)
\(308\) 3.08593e12 0.0634391
\(309\) 5.21827e13 1.05379
\(310\) 9.38981e12 0.186281
\(311\) −1.49199e13 −0.290792 −0.145396 0.989374i \(-0.546446\pi\)
−0.145396 + 0.989374i \(0.546446\pi\)
\(312\) 7.62981e12 0.146104
\(313\) 2.38159e13 0.448097 0.224049 0.974578i \(-0.428073\pi\)
0.224049 + 0.974578i \(0.428073\pi\)
\(314\) −4.96927e13 −0.918712
\(315\) 1.16110e13 0.210941
\(316\) 7.23568e12 0.129181
\(317\) −5.45968e13 −0.957947 −0.478973 0.877829i \(-0.658991\pi\)
−0.478973 + 0.877829i \(0.658991\pi\)
\(318\) 4.48557e13 0.773514
\(319\) 2.43554e13 0.412807
\(320\) −4.52792e13 −0.754351
\(321\) 1.87841e13 0.307619
\(322\) 3.45571e13 0.556328
\(323\) 3.75655e13 0.594532
\(324\) −1.00310e12 −0.0156080
\(325\) 8.26357e12 0.126418
\(326\) −4.41545e13 −0.664168
\(327\) −2.83900e13 −0.419907
\(328\) 1.95438e12 0.0284251
\(329\) 2.36138e13 0.337744
\(330\) −1.28126e13 −0.180224
\(331\) 4.03726e13 0.558512 0.279256 0.960217i \(-0.409912\pi\)
0.279256 + 0.960217i \(0.409912\pi\)
\(332\) 5.04134e12 0.0685940
\(333\) −2.53377e13 −0.339097
\(334\) −1.96135e13 −0.258196
\(335\) −4.96463e13 −0.642895
\(336\) −3.50657e13 −0.446701
\(337\) −2.58730e12 −0.0324251 −0.0162126 0.999869i \(-0.505161\pi\)
−0.0162126 + 0.999869i \(0.505161\pi\)
\(338\) 7.08849e13 0.874001
\(339\) −8.02311e12 −0.0973295
\(340\) 1.10597e13 0.132011
\(341\) 1.22088e13 0.143391
\(342\) −1.16195e13 −0.134289
\(343\) 9.32547e13 1.06060
\(344\) 1.65232e13 0.184936
\(345\) 2.34487e13 0.258294
\(346\) −1.15315e14 −1.25016
\(347\) −1.16111e14 −1.23897 −0.619486 0.785008i \(-0.712659\pi\)
−0.619486 + 0.785008i \(0.712659\pi\)
\(348\) 6.50276e12 0.0682986
\(349\) −8.24104e12 −0.0852005 −0.0426002 0.999092i \(-0.513564\pi\)
−0.0426002 + 0.999092i \(0.513564\pi\)
\(350\) −4.43310e13 −0.451163
\(351\) 4.59745e12 0.0460604
\(352\) −1.38541e13 −0.136645
\(353\) 1.18877e14 1.15435 0.577174 0.816621i \(-0.304156\pi\)
0.577174 + 0.816621i \(0.304156\pi\)
\(354\) −7.28889e12 −0.0696857
\(355\) 9.72865e13 0.915791
\(356\) 4.37413e12 0.0405431
\(357\) 7.97371e13 0.727755
\(358\) −5.18810e13 −0.466285
\(359\) 1.53675e14 1.36014 0.680070 0.733147i \(-0.261949\pi\)
0.680070 + 0.733147i \(0.261949\pi\)
\(360\) −2.77738e13 −0.242087
\(361\) −9.44936e13 −0.811172
\(362\) 9.91823e13 0.838565
\(363\) 5.26716e13 0.438621
\(364\) −3.77624e12 −0.0309743
\(365\) 1.47422e14 1.19111
\(366\) −2.32177e13 −0.184788
\(367\) 2.07126e13 0.162394 0.0811972 0.996698i \(-0.474126\pi\)
0.0811972 + 0.996698i \(0.474126\pi\)
\(368\) −7.08164e13 −0.546979
\(369\) 1.17764e12 0.00896121
\(370\) −8.64097e13 −0.647818
\(371\) −1.80243e14 −1.33138
\(372\) 3.25967e12 0.0237240
\(373\) 7.14846e13 0.512642 0.256321 0.966592i \(-0.417490\pi\)
0.256321 + 0.966592i \(0.417490\pi\)
\(374\) −8.79893e13 −0.621779
\(375\) −8.70302e13 −0.606036
\(376\) −5.64848e13 −0.387613
\(377\) −2.98037e13 −0.201554
\(378\) −2.46636e13 −0.164381
\(379\) −1.47308e14 −0.967633 −0.483816 0.875170i \(-0.660750\pi\)
−0.483816 + 0.875170i \(0.660750\pi\)
\(380\) 6.47605e12 0.0419277
\(381\) −7.60288e13 −0.485166
\(382\) −6.98467e13 −0.439336
\(383\) −2.62373e14 −1.62677 −0.813386 0.581725i \(-0.802378\pi\)
−0.813386 + 0.581725i \(0.802378\pi\)
\(384\) 6.98480e13 0.426906
\(385\) 5.14849e13 0.310203
\(386\) −1.02032e14 −0.606046
\(387\) 9.95627e12 0.0583024
\(388\) −4.50560e12 −0.0260123
\(389\) −8.11217e13 −0.461758 −0.230879 0.972982i \(-0.574160\pi\)
−0.230879 + 0.972982i \(0.574160\pi\)
\(390\) 1.56788e13 0.0879948
\(391\) 1.61032e14 0.891126
\(392\) −2.92974e13 −0.159866
\(393\) 5.08615e13 0.273672
\(394\) −1.69120e14 −0.897357
\(395\) 1.20718e14 0.631668
\(396\) −4.44790e12 −0.0229526
\(397\) −1.00735e14 −0.512663 −0.256331 0.966589i \(-0.582514\pi\)
−0.256331 + 0.966589i \(0.582514\pi\)
\(398\) −1.06021e14 −0.532152
\(399\) 4.66904e13 0.231141
\(400\) 9.08455e13 0.443582
\(401\) −1.25734e14 −0.605564 −0.302782 0.953060i \(-0.597915\pi\)
−0.302782 + 0.953060i \(0.597915\pi\)
\(402\) 1.05457e14 0.500993
\(403\) −1.49399e13 −0.0700114
\(404\) −3.28636e13 −0.151921
\(405\) −1.67355e13 −0.0763195
\(406\) 1.59886e14 0.719311
\(407\) −1.12351e14 −0.498665
\(408\) −1.90734e14 −0.835211
\(409\) −1.64182e14 −0.709329 −0.354664 0.934994i \(-0.615405\pi\)
−0.354664 + 0.934994i \(0.615405\pi\)
\(410\) 4.01612e12 0.0171197
\(411\) 1.52210e14 0.640198
\(412\) 6.17788e13 0.256392
\(413\) 2.92889e13 0.119944
\(414\) −4.98090e13 −0.201282
\(415\) 8.41085e13 0.335409
\(416\) 1.69532e13 0.0667172
\(417\) −2.03230e14 −0.789296
\(418\) −5.15225e13 −0.197482
\(419\) 4.55120e13 0.172167 0.0860834 0.996288i \(-0.472565\pi\)
0.0860834 + 0.996288i \(0.472565\pi\)
\(420\) 1.37462e13 0.0513228
\(421\) 1.11206e14 0.409804 0.204902 0.978782i \(-0.434312\pi\)
0.204902 + 0.978782i \(0.434312\pi\)
\(422\) 1.63630e14 0.595176
\(423\) −3.40357e13 −0.122198
\(424\) 4.31147e14 1.52796
\(425\) −2.06577e14 −0.722673
\(426\) −2.06652e14 −0.713654
\(427\) 9.32956e13 0.318059
\(428\) 2.22384e13 0.0748450
\(429\) 2.03858e13 0.0677349
\(430\) 3.39541e13 0.111382
\(431\) 5.12340e14 1.65933 0.829667 0.558259i \(-0.188531\pi\)
0.829667 + 0.558259i \(0.188531\pi\)
\(432\) 5.05420e13 0.161619
\(433\) 5.37809e14 1.69803 0.849014 0.528370i \(-0.177197\pi\)
0.849014 + 0.528370i \(0.177197\pi\)
\(434\) 8.01469e13 0.249858
\(435\) 1.08490e14 0.333965
\(436\) −3.36108e13 −0.102165
\(437\) 9.42927e13 0.283028
\(438\) −3.13148e14 −0.928201
\(439\) −5.56321e13 −0.162844 −0.0814219 0.996680i \(-0.525946\pi\)
−0.0814219 + 0.996680i \(0.525946\pi\)
\(440\) −1.23153e14 −0.356005
\(441\) −1.76535e13 −0.0503987
\(442\) 1.07672e14 0.303586
\(443\) −9.33511e13 −0.259955 −0.129978 0.991517i \(-0.541491\pi\)
−0.129978 + 0.991517i \(0.541491\pi\)
\(444\) −2.99971e13 −0.0825037
\(445\) 7.29770e13 0.198247
\(446\) 1.80550e14 0.484456
\(447\) 1.76920e14 0.468907
\(448\) −3.86481e14 −1.01181
\(449\) 1.14106e14 0.295089 0.147544 0.989055i \(-0.452863\pi\)
0.147544 + 0.989055i \(0.452863\pi\)
\(450\) 6.38966e13 0.163233
\(451\) 5.22183e12 0.0131781
\(452\) −9.49852e12 −0.0236807
\(453\) −2.70854e14 −0.667106
\(454\) −2.75054e14 −0.669285
\(455\) −6.30019e13 −0.151458
\(456\) −1.11685e14 −0.265269
\(457\) −4.34785e13 −0.102032 −0.0510159 0.998698i \(-0.516246\pi\)
−0.0510159 + 0.998698i \(0.516246\pi\)
\(458\) −4.79031e14 −1.11072
\(459\) −1.14929e14 −0.263306
\(460\) 2.77608e13 0.0628441
\(461\) −3.79992e14 −0.850000 −0.425000 0.905193i \(-0.639726\pi\)
−0.425000 + 0.905193i \(0.639726\pi\)
\(462\) −1.09362e14 −0.241734
\(463\) 4.53675e14 0.990945 0.495472 0.868624i \(-0.334995\pi\)
0.495472 + 0.868624i \(0.334995\pi\)
\(464\) −3.27647e14 −0.707224
\(465\) 5.43836e13 0.116005
\(466\) −5.37512e14 −1.13309
\(467\) 2.87881e14 0.599750 0.299875 0.953978i \(-0.403055\pi\)
0.299875 + 0.953978i \(0.403055\pi\)
\(468\) 5.44289e12 0.0112067
\(469\) −4.23756e14 −0.862314
\(470\) −1.16073e14 −0.233449
\(471\) −2.87808e14 −0.572122
\(472\) −7.00599e13 −0.137654
\(473\) 4.41477e13 0.0857377
\(474\) −2.56426e14 −0.492244
\(475\) −1.20962e14 −0.229527
\(476\) 9.44003e13 0.177066
\(477\) 2.59794e14 0.481701
\(478\) 1.20978e14 0.221744
\(479\) 1.77660e14 0.321917 0.160959 0.986961i \(-0.448541\pi\)
0.160959 + 0.986961i \(0.448541\pi\)
\(480\) −6.17125e13 −0.110547
\(481\) 1.37484e14 0.243475
\(482\) −4.07689e14 −0.713790
\(483\) 2.00147e14 0.346449
\(484\) 6.23575e13 0.106718
\(485\) −7.51704e13 −0.127194
\(486\) 3.55489e13 0.0594740
\(487\) 2.41589e14 0.399639 0.199820 0.979833i \(-0.435964\pi\)
0.199820 + 0.979833i \(0.435964\pi\)
\(488\) −2.23166e14 −0.365022
\(489\) −2.55732e14 −0.413606
\(490\) −6.02043e13 −0.0962829
\(491\) −1.18877e14 −0.187997 −0.0939986 0.995572i \(-0.529965\pi\)
−0.0939986 + 0.995572i \(0.529965\pi\)
\(492\) 1.39420e12 0.00218030
\(493\) 7.45046e14 1.15219
\(494\) 6.30479e13 0.0964212
\(495\) −7.42078e13 −0.112233
\(496\) −1.64241e14 −0.245659
\(497\) 8.30390e14 1.22835
\(498\) −1.78660e14 −0.261377
\(499\) 1.20282e15 1.74040 0.870200 0.492698i \(-0.163989\pi\)
0.870200 + 0.492698i \(0.163989\pi\)
\(500\) −1.03035e14 −0.147451
\(501\) −1.13597e14 −0.160790
\(502\) −2.54497e14 −0.356297
\(503\) −7.53438e14 −1.04333 −0.521667 0.853149i \(-0.674690\pi\)
−0.521667 + 0.853149i \(0.674690\pi\)
\(504\) −2.37064e14 −0.324711
\(505\) −5.48289e14 −0.742860
\(506\) −2.20861e14 −0.295999
\(507\) 4.10549e14 0.544278
\(508\) −9.00100e13 −0.118043
\(509\) −1.40721e14 −0.182562 −0.0912811 0.995825i \(-0.529096\pi\)
−0.0912811 + 0.995825i \(0.529096\pi\)
\(510\) −3.91945e14 −0.503025
\(511\) 1.25832e15 1.59763
\(512\) 8.93299e14 1.12205
\(513\) −6.72972e13 −0.0836279
\(514\) −2.81590e14 −0.346195
\(515\) 1.03070e15 1.25370
\(516\) 1.17872e13 0.0141852
\(517\) −1.50920e14 −0.179700
\(518\) −7.37552e14 −0.868918
\(519\) −6.67877e14 −0.778531
\(520\) 1.50703e14 0.173821
\(521\) −2.48690e14 −0.283825 −0.141913 0.989879i \(-0.545325\pi\)
−0.141913 + 0.989879i \(0.545325\pi\)
\(522\) −2.30452e14 −0.260251
\(523\) −2.98483e14 −0.333550 −0.166775 0.985995i \(-0.553335\pi\)
−0.166775 + 0.985995i \(0.553335\pi\)
\(524\) 6.02147e13 0.0665856
\(525\) −2.56755e14 −0.280959
\(526\) 1.27172e15 1.37712
\(527\) 3.73474e14 0.400223
\(528\) 2.24111e14 0.237671
\(529\) −5.48606e14 −0.575777
\(530\) 8.85980e14 0.920252
\(531\) −4.22156e13 −0.0433963
\(532\) 5.52764e13 0.0562375
\(533\) −6.38994e12 −0.00643424
\(534\) −1.55015e14 −0.154489
\(535\) 3.71020e14 0.365975
\(536\) 1.01364e15 0.989638
\(537\) −3.00483e14 −0.290376
\(538\) 1.41125e15 1.34990
\(539\) −7.82786e13 −0.0741148
\(540\) −1.98130e13 −0.0185689
\(541\) 1.12984e15 1.04817 0.524085 0.851666i \(-0.324407\pi\)
0.524085 + 0.851666i \(0.324407\pi\)
\(542\) −3.60247e14 −0.330830
\(543\) 5.74441e14 0.522211
\(544\) −4.23804e14 −0.381391
\(545\) −5.60754e14 −0.499565
\(546\) 1.33826e14 0.118027
\(547\) 1.49689e15 1.30695 0.653475 0.756948i \(-0.273311\pi\)
0.653475 + 0.756948i \(0.273311\pi\)
\(548\) 1.80201e14 0.155763
\(549\) −1.34472e14 −0.115076
\(550\) 2.83327e14 0.240046
\(551\) 4.36265e14 0.365945
\(552\) −4.78758e14 −0.397604
\(553\) 1.03039e15 0.847256
\(554\) 1.83161e15 1.49118
\(555\) −5.00465e14 −0.403425
\(556\) −2.40603e14 −0.192039
\(557\) 2.00238e15 1.58250 0.791250 0.611493i \(-0.209431\pi\)
0.791250 + 0.611493i \(0.209431\pi\)
\(558\) −1.15520e14 −0.0904000
\(559\) −5.40234e13 −0.0418617
\(560\) −6.92611e14 −0.531442
\(561\) −5.09614e14 −0.387209
\(562\) 2.06119e15 1.55085
\(563\) 9.06475e14 0.675398 0.337699 0.941254i \(-0.390351\pi\)
0.337699 + 0.941254i \(0.390351\pi\)
\(564\) −4.02947e13 −0.0297312
\(565\) −1.58471e14 −0.115793
\(566\) 2.11176e15 1.52811
\(567\) −1.42846e14 −0.102367
\(568\) −1.98632e15 −1.40972
\(569\) 1.54826e14 0.108824 0.0544122 0.998519i \(-0.482672\pi\)
0.0544122 + 0.998519i \(0.482672\pi\)
\(570\) −2.29505e14 −0.159765
\(571\) −5.86212e13 −0.0404163 −0.0202081 0.999796i \(-0.506433\pi\)
−0.0202081 + 0.999796i \(0.506433\pi\)
\(572\) 2.41346e13 0.0164802
\(573\) −4.04536e14 −0.273594
\(574\) 3.42797e13 0.0229626
\(575\) −5.18525e14 −0.344030
\(576\) 5.57055e14 0.366078
\(577\) 1.96260e15 1.27751 0.638754 0.769411i \(-0.279450\pi\)
0.638754 + 0.769411i \(0.279450\pi\)
\(578\) −1.25373e15 −0.808351
\(579\) −5.90945e14 −0.377411
\(580\) 1.28441e14 0.0812551
\(581\) 7.17909e14 0.449884
\(582\) 1.59674e14 0.0991194
\(583\) 1.15197e15 0.708374
\(584\) −3.00994e15 −1.83353
\(585\) 9.08079e13 0.0547982
\(586\) 1.56137e15 0.933404
\(587\) 1.27919e15 0.757575 0.378787 0.925484i \(-0.376341\pi\)
0.378787 + 0.925484i \(0.376341\pi\)
\(588\) −2.08999e13 −0.0122622
\(589\) 2.18689e14 0.127114
\(590\) −1.43969e14 −0.0829053
\(591\) −9.79502e14 −0.558823
\(592\) 1.51143e15 0.854316
\(593\) 1.19686e15 0.670259 0.335130 0.942172i \(-0.391220\pi\)
0.335130 + 0.942172i \(0.391220\pi\)
\(594\) 1.57630e14 0.0874605
\(595\) 1.57495e15 0.865813
\(596\) 2.09455e14 0.114087
\(597\) −6.14050e14 −0.331394
\(598\) 2.70267e14 0.144523
\(599\) −1.51517e15 −0.802812 −0.401406 0.915900i \(-0.631478\pi\)
−0.401406 + 0.915900i \(0.631478\pi\)
\(600\) 6.14166e14 0.322444
\(601\) 1.56048e15 0.811797 0.405899 0.913918i \(-0.366959\pi\)
0.405899 + 0.913918i \(0.366959\pi\)
\(602\) 2.89816e14 0.149397
\(603\) 6.10781e14 0.311990
\(604\) −3.20662e14 −0.162310
\(605\) 1.04036e15 0.521829
\(606\) 1.16466e15 0.578893
\(607\) −1.37734e15 −0.678426 −0.339213 0.940710i \(-0.610161\pi\)
−0.339213 + 0.940710i \(0.610161\pi\)
\(608\) −2.48160e14 −0.121133
\(609\) 9.26022e14 0.447947
\(610\) −4.58592e14 −0.219843
\(611\) 1.84680e14 0.0877392
\(612\) −1.36064e14 −0.0640634
\(613\) −9.68578e14 −0.451962 −0.225981 0.974132i \(-0.572559\pi\)
−0.225981 + 0.974132i \(0.572559\pi\)
\(614\) −1.96103e15 −0.906896
\(615\) 2.32605e13 0.0106612
\(616\) −1.05118e15 −0.477510
\(617\) 3.92444e15 1.76689 0.883445 0.468534i \(-0.155218\pi\)
0.883445 + 0.468534i \(0.155218\pi\)
\(618\) −2.18938e15 −0.976978
\(619\) −1.85431e15 −0.820132 −0.410066 0.912056i \(-0.634494\pi\)
−0.410066 + 0.912056i \(0.634494\pi\)
\(620\) 6.43845e13 0.0282245
\(621\) −2.88482e14 −0.125347
\(622\) 6.25979e14 0.269596
\(623\) 6.22896e14 0.265908
\(624\) −2.74244e14 −0.116044
\(625\) −4.59673e14 −0.192801
\(626\) −9.99221e14 −0.415435
\(627\) −2.98406e14 −0.122981
\(628\) −3.40735e14 −0.139200
\(629\) −3.43689e15 −1.39183
\(630\) −4.87151e14 −0.195565
\(631\) −1.90250e14 −0.0757119 −0.0378560 0.999283i \(-0.512053\pi\)
−0.0378560 + 0.999283i \(0.512053\pi\)
\(632\) −2.46473e15 −0.972357
\(633\) 9.47709e14 0.370642
\(634\) 2.29067e15 0.888120
\(635\) −1.50171e15 −0.577204
\(636\) 3.07568e14 0.117200
\(637\) 9.57893e13 0.0361868
\(638\) −1.02186e15 −0.382716
\(639\) −1.19688e15 −0.444424
\(640\) 1.37963e15 0.507892
\(641\) 7.34660e14 0.268144 0.134072 0.990972i \(-0.457195\pi\)
0.134072 + 0.990972i \(0.457195\pi\)
\(642\) −7.88107e14 −0.285196
\(643\) −1.60145e15 −0.574584 −0.287292 0.957843i \(-0.592755\pi\)
−0.287292 + 0.957843i \(0.592755\pi\)
\(644\) 2.36953e14 0.0842927
\(645\) 1.96654e14 0.0693626
\(646\) −1.57610e15 −0.551195
\(647\) 3.09071e15 1.07173 0.535865 0.844304i \(-0.319986\pi\)
0.535865 + 0.844304i \(0.319986\pi\)
\(648\) 3.41692e14 0.117482
\(649\) −1.87190e14 −0.0638172
\(650\) −3.46707e14 −0.117203
\(651\) 4.64192e14 0.155597
\(652\) −3.02760e14 −0.100632
\(653\) 3.29713e14 0.108671 0.0543356 0.998523i \(-0.482696\pi\)
0.0543356 + 0.998523i \(0.482696\pi\)
\(654\) 1.19113e15 0.389299
\(655\) 1.00461e15 0.325589
\(656\) −7.02478e13 −0.0225768
\(657\) −1.81368e15 −0.578031
\(658\) −9.90741e14 −0.313125
\(659\) −4.91143e15 −1.53935 −0.769676 0.638435i \(-0.779582\pi\)
−0.769676 + 0.638435i \(0.779582\pi\)
\(660\) −8.78542e13 −0.0273068
\(661\) 5.93341e15 1.82893 0.914464 0.404668i \(-0.132613\pi\)
0.914464 + 0.404668i \(0.132613\pi\)
\(662\) −1.69387e15 −0.517800
\(663\) 6.23613e14 0.189056
\(664\) −1.71726e15 −0.516312
\(665\) 9.22219e14 0.274989
\(666\) 1.06307e15 0.314379
\(667\) 1.87013e15 0.548504
\(668\) −1.34487e14 −0.0391209
\(669\) 1.04570e15 0.301692
\(670\) 2.08296e15 0.596033
\(671\) −5.96269e14 −0.169226
\(672\) −5.26748e14 −0.148276
\(673\) −3.55768e15 −0.993307 −0.496653 0.867949i \(-0.665438\pi\)
−0.496653 + 0.867949i \(0.665438\pi\)
\(674\) 1.08553e14 0.0300616
\(675\) 3.70074e14 0.101652
\(676\) 4.86046e14 0.132425
\(677\) −5.94589e15 −1.60686 −0.803432 0.595397i \(-0.796995\pi\)
−0.803432 + 0.595397i \(0.796995\pi\)
\(678\) 3.36619e14 0.0902349
\(679\) −6.41618e14 −0.170605
\(680\) −3.76733e15 −0.993653
\(681\) −1.59305e15 −0.416793
\(682\) −5.12233e14 −0.132939
\(683\) −2.82331e15 −0.726849 −0.363424 0.931624i \(-0.618392\pi\)
−0.363424 + 0.931624i \(0.618392\pi\)
\(684\) −7.96727e13 −0.0203470
\(685\) 3.00643e15 0.761646
\(686\) −3.91260e15 −0.983293
\(687\) −2.77444e15 −0.691693
\(688\) −5.93906e14 −0.146886
\(689\) −1.40966e15 −0.345866
\(690\) −9.83817e14 −0.239466
\(691\) −3.19635e15 −0.771835 −0.385918 0.922533i \(-0.626115\pi\)
−0.385918 + 0.922533i \(0.626115\pi\)
\(692\) −7.90695e14 −0.189420
\(693\) −6.33402e14 −0.150538
\(694\) 4.87156e15 1.14866
\(695\) −4.01416e15 −0.939028
\(696\) −2.21507e15 −0.514088
\(697\) 1.59739e14 0.0367815
\(698\) 3.45762e14 0.0789900
\(699\) −3.11314e15 −0.705626
\(700\) −3.03971e14 −0.0683585
\(701\) 3.84612e15 0.858172 0.429086 0.903264i \(-0.358836\pi\)
0.429086 + 0.903264i \(0.358836\pi\)
\(702\) −1.92891e14 −0.0427029
\(703\) −2.01248e15 −0.442057
\(704\) 2.47007e15 0.538343
\(705\) −6.72267e14 −0.145379
\(706\) −4.98761e15 −1.07020
\(707\) −4.67993e15 −0.996397
\(708\) −4.99788e13 −0.0105585
\(709\) −4.86982e15 −1.02084 −0.510421 0.859924i \(-0.670511\pi\)
−0.510421 + 0.859924i \(0.670511\pi\)
\(710\) −4.08176e15 −0.849037
\(711\) −1.48516e15 −0.306542
\(712\) −1.48999e15 −0.305170
\(713\) 9.37451e14 0.190527
\(714\) −3.34546e15 −0.674707
\(715\) 4.02656e14 0.0805845
\(716\) −3.55740e14 −0.0706497
\(717\) 7.00676e14 0.138090
\(718\) −6.44760e15 −1.26100
\(719\) 3.04461e15 0.590913 0.295456 0.955356i \(-0.404528\pi\)
0.295456 + 0.955356i \(0.404528\pi\)
\(720\) 9.98296e14 0.192278
\(721\) 8.79757e15 1.68159
\(722\) 3.96458e15 0.752044
\(723\) −2.36124e15 −0.444508
\(724\) 6.80077e14 0.127056
\(725\) −2.39907e15 −0.444819
\(726\) −2.20989e15 −0.406649
\(727\) −2.20618e15 −0.402903 −0.201452 0.979498i \(-0.564566\pi\)
−0.201452 + 0.979498i \(0.564566\pi\)
\(728\) 1.28632e15 0.233146
\(729\) 2.05891e14 0.0370370
\(730\) −6.18524e15 −1.10428
\(731\) 1.35050e15 0.239304
\(732\) −1.59200e14 −0.0279984
\(733\) −5.07430e15 −0.885737 −0.442868 0.896587i \(-0.646039\pi\)
−0.442868 + 0.896587i \(0.646039\pi\)
\(734\) −8.69020e14 −0.150557
\(735\) −3.48689e14 −0.0599596
\(736\) −1.06378e15 −0.181562
\(737\) 2.70830e15 0.458803
\(738\) −4.94091e13 −0.00830800
\(739\) −5.59265e14 −0.0933411 −0.0466706 0.998910i \(-0.514861\pi\)
−0.0466706 + 0.998910i \(0.514861\pi\)
\(740\) −5.92498e14 −0.0981550
\(741\) 3.65159e14 0.0600457
\(742\) 7.56230e15 1.23433
\(743\) 9.49565e14 0.153846 0.0769230 0.997037i \(-0.475490\pi\)
0.0769230 + 0.997037i \(0.475490\pi\)
\(744\) −1.11036e15 −0.178572
\(745\) 3.49450e15 0.557860
\(746\) −2.99921e15 −0.475274
\(747\) −1.03476e15 −0.162771
\(748\) −6.03329e14 −0.0942096
\(749\) 3.16685e15 0.490882
\(750\) 3.65145e15 0.561860
\(751\) 8.88342e15 1.35694 0.678470 0.734628i \(-0.262643\pi\)
0.678470 + 0.734628i \(0.262643\pi\)
\(752\) 2.03028e15 0.307863
\(753\) −1.47399e15 −0.221882
\(754\) 1.25045e15 0.186863
\(755\) −5.34985e15 −0.793658
\(756\) −1.69115e14 −0.0249064
\(757\) −1.55458e15 −0.227292 −0.113646 0.993521i \(-0.536253\pi\)
−0.113646 + 0.993521i \(0.536253\pi\)
\(758\) 6.18047e15 0.897099
\(759\) −1.27918e15 −0.184332
\(760\) −2.20598e15 −0.315592
\(761\) −1.08463e16 −1.54052 −0.770261 0.637729i \(-0.779874\pi\)
−0.770261 + 0.637729i \(0.779874\pi\)
\(762\) 3.18987e15 0.449801
\(763\) −4.78633e15 −0.670066
\(764\) −4.78927e14 −0.0665666
\(765\) −2.27006e15 −0.313256
\(766\) 1.10082e16 1.50819
\(767\) 2.29065e14 0.0311590
\(768\) 1.76430e15 0.238279
\(769\) −1.24330e15 −0.166718 −0.0833590 0.996520i \(-0.526565\pi\)
−0.0833590 + 0.996520i \(0.526565\pi\)
\(770\) −2.16010e15 −0.287591
\(771\) −1.63091e15 −0.215591
\(772\) −6.99616e14 −0.0918258
\(773\) 5.01623e15 0.653718 0.326859 0.945073i \(-0.394010\pi\)
0.326859 + 0.945073i \(0.394010\pi\)
\(774\) −4.17726e14 −0.0540526
\(775\) −1.20259e15 −0.154511
\(776\) 1.53477e15 0.195796
\(777\) −4.27173e15 −0.541113
\(778\) 3.40355e15 0.428099
\(779\) 9.35356e13 0.0116821
\(780\) 1.07507e14 0.0133326
\(781\) −5.30717e15 −0.653555
\(782\) −6.75626e15 −0.826169
\(783\) −1.33472e15 −0.162069
\(784\) 1.05306e15 0.126974
\(785\) −5.68474e15 −0.680655
\(786\) −2.13395e15 −0.253723
\(787\) 1.08821e16 1.28485 0.642423 0.766350i \(-0.277929\pi\)
0.642423 + 0.766350i \(0.277929\pi\)
\(788\) −1.15963e15 −0.135964
\(789\) 7.36553e15 0.857591
\(790\) −5.06487e15 −0.585625
\(791\) −1.35263e15 −0.155313
\(792\) 1.51512e15 0.172766
\(793\) 7.29652e14 0.0826254
\(794\) 4.22644e15 0.475293
\(795\) 5.13139e15 0.573081
\(796\) −7.26970e14 −0.0806296
\(797\) −5.27896e15 −0.581470 −0.290735 0.956804i \(-0.593900\pi\)
−0.290735 + 0.956804i \(0.593900\pi\)
\(798\) −1.95894e15 −0.214292
\(799\) −4.61672e15 −0.501564
\(800\) 1.36466e15 0.147241
\(801\) −8.97812e14 −0.0962069
\(802\) 5.27532e15 0.561422
\(803\) −8.04214e15 −0.850034
\(804\) 7.23101e14 0.0759085
\(805\) 3.95327e15 0.412172
\(806\) 6.26818e14 0.0649081
\(807\) 8.17364e15 0.840642
\(808\) 1.11945e16 1.14352
\(809\) −8.64287e14 −0.0876882 −0.0438441 0.999038i \(-0.513960\pi\)
−0.0438441 + 0.999038i \(0.513960\pi\)
\(810\) 7.02155e14 0.0707564
\(811\) −2.23191e15 −0.223389 −0.111694 0.993743i \(-0.535628\pi\)
−0.111694 + 0.993743i \(0.535628\pi\)
\(812\) 1.09631e15 0.108987
\(813\) −2.08647e15 −0.206022
\(814\) 4.71382e15 0.462316
\(815\) −5.05118e15 −0.492069
\(816\) 6.85569e15 0.663369
\(817\) 7.90792e14 0.0760048
\(818\) 6.88844e15 0.657624
\(819\) 7.75092e14 0.0735007
\(820\) 2.75379e13 0.00259391
\(821\) −9.98068e15 −0.933841 −0.466920 0.884299i \(-0.654637\pi\)
−0.466920 + 0.884299i \(0.654637\pi\)
\(822\) −6.38615e15 −0.593532
\(823\) 1.41483e16 1.30619 0.653095 0.757276i \(-0.273470\pi\)
0.653095 + 0.757276i \(0.273470\pi\)
\(824\) −2.10441e16 −1.92988
\(825\) 1.64097e15 0.149487
\(826\) −1.22885e15 −0.111201
\(827\) 1.34308e16 1.20732 0.603660 0.797242i \(-0.293708\pi\)
0.603660 + 0.797242i \(0.293708\pi\)
\(828\) −3.41532e14 −0.0304975
\(829\) 1.75970e16 1.56095 0.780475 0.625187i \(-0.214977\pi\)
0.780475 + 0.625187i \(0.214977\pi\)
\(830\) −3.52886e15 −0.310961
\(831\) 1.06083e16 0.928622
\(832\) −3.02262e15 −0.262848
\(833\) −2.39459e15 −0.206863
\(834\) 8.52674e15 0.731762
\(835\) −2.24374e15 −0.191292
\(836\) −3.53282e14 −0.0299217
\(837\) −6.69064e14 −0.0562960
\(838\) −1.90951e15 −0.159617
\(839\) 1.83671e16 1.52528 0.762640 0.646823i \(-0.223903\pi\)
0.762640 + 0.646823i \(0.223903\pi\)
\(840\) −4.68244e15 −0.386310
\(841\) −3.54796e15 −0.290804
\(842\) −4.66576e15 −0.379932
\(843\) 1.19379e16 0.965779
\(844\) 1.12199e15 0.0901788
\(845\) 8.10908e15 0.647530
\(846\) 1.42801e15 0.113290
\(847\) 8.87999e15 0.699929
\(848\) −1.54971e16 −1.21359
\(849\) 1.22308e16 0.951620
\(850\) 8.66715e15 0.669996
\(851\) −8.62690e15 −0.662586
\(852\) −1.41698e15 −0.108130
\(853\) 1.35599e16 1.02810 0.514052 0.857759i \(-0.328144\pi\)
0.514052 + 0.857759i \(0.328144\pi\)
\(854\) −3.91432e15 −0.294875
\(855\) −1.32924e15 −0.0994924
\(856\) −7.57519e15 −0.563363
\(857\) −1.56281e15 −0.115481 −0.0577406 0.998332i \(-0.518390\pi\)
−0.0577406 + 0.998332i \(0.518390\pi\)
\(858\) −8.55309e14 −0.0627976
\(859\) −1.35473e16 −0.988301 −0.494150 0.869376i \(-0.664521\pi\)
−0.494150 + 0.869376i \(0.664521\pi\)
\(860\) 2.32818e14 0.0168762
\(861\) 1.98540e14 0.0142998
\(862\) −2.14958e16 −1.53838
\(863\) 7.25297e15 0.515771 0.257885 0.966176i \(-0.416974\pi\)
0.257885 + 0.966176i \(0.416974\pi\)
\(864\) 7.59228e14 0.0536472
\(865\) −1.31918e16 −0.926221
\(866\) −2.25644e16 −1.57425
\(867\) −7.26130e15 −0.503396
\(868\) 5.49555e14 0.0378575
\(869\) −6.58542e15 −0.450791
\(870\) −4.55184e15 −0.309621
\(871\) −3.31414e15 −0.224012
\(872\) 1.14490e16 0.769003
\(873\) 9.24796e14 0.0617260
\(874\) −3.95615e15 −0.262398
\(875\) −1.46726e16 −0.967080
\(876\) −2.14721e15 −0.140637
\(877\) 1.26953e16 0.826312 0.413156 0.910660i \(-0.364426\pi\)
0.413156 + 0.910660i \(0.364426\pi\)
\(878\) 2.33411e15 0.150974
\(879\) 9.04311e15 0.581271
\(880\) 4.42660e15 0.282759
\(881\) 7.00994e15 0.444987 0.222493 0.974934i \(-0.428580\pi\)
0.222493 + 0.974934i \(0.428580\pi\)
\(882\) 7.40674e14 0.0467251
\(883\) −8.35461e15 −0.523772 −0.261886 0.965099i \(-0.584344\pi\)
−0.261886 + 0.965099i \(0.584344\pi\)
\(884\) 7.38292e14 0.0459982
\(885\) −8.33834e14 −0.0516287
\(886\) 3.91665e15 0.241007
\(887\) 2.16567e16 1.32438 0.662191 0.749335i \(-0.269627\pi\)
0.662191 + 0.749335i \(0.269627\pi\)
\(888\) 1.02181e16 0.621011
\(889\) −1.28178e16 −0.774203
\(890\) −3.06183e15 −0.183796
\(891\) 9.12954e14 0.0544655
\(892\) 1.23800e15 0.0734030
\(893\) −2.70334e15 −0.159301
\(894\) −7.42288e15 −0.434727
\(895\) −5.93507e15 −0.345461
\(896\) 1.17758e16 0.681235
\(897\) 1.56532e15 0.0900006
\(898\) −4.78743e15 −0.273579
\(899\) 4.33731e15 0.246344
\(900\) 4.38129e14 0.0247325
\(901\) 3.52393e16 1.97716
\(902\) −2.19088e14 −0.0122175
\(903\) 1.67855e15 0.0930359
\(904\) 3.23554e15 0.178246
\(905\) 1.13462e16 0.621277
\(906\) 1.13640e16 0.618478
\(907\) 3.43091e15 0.185596 0.0927981 0.995685i \(-0.470419\pi\)
0.0927981 + 0.995685i \(0.470419\pi\)
\(908\) −1.88600e15 −0.101408
\(909\) 6.74542e15 0.360502
\(910\) 2.64331e15 0.140417
\(911\) 2.56366e16 1.35366 0.676830 0.736139i \(-0.263353\pi\)
0.676830 + 0.736139i \(0.263353\pi\)
\(912\) 4.01437e15 0.210691
\(913\) −4.58829e15 −0.239365
\(914\) 1.82419e15 0.0945944
\(915\) −2.65606e15 −0.136906
\(916\) −3.28464e15 −0.168292
\(917\) 8.57484e15 0.436712
\(918\) 4.82198e15 0.244113
\(919\) 8.39129e15 0.422273 0.211137 0.977457i \(-0.432284\pi\)
0.211137 + 0.977457i \(0.432284\pi\)
\(920\) −9.45633e15 −0.473031
\(921\) −1.13578e16 −0.564764
\(922\) 1.59430e16 0.788041
\(923\) 6.49437e15 0.319101
\(924\) −7.49880e14 −0.0366266
\(925\) 1.10669e16 0.537335
\(926\) −1.90344e16 −0.918712
\(927\) −1.26804e16 −0.608407
\(928\) −4.92182e15 −0.234753
\(929\) 3.81194e16 1.80742 0.903712 0.428141i \(-0.140831\pi\)
0.903712 + 0.428141i \(0.140831\pi\)
\(930\) −2.28172e15 −0.107549
\(931\) −1.40216e15 −0.0657013
\(932\) −3.68563e15 −0.171682
\(933\) 3.62553e15 0.167889
\(934\) −1.20784e16 −0.556033
\(935\) −1.00658e16 −0.460664
\(936\) −1.85404e15 −0.0843534
\(937\) 1.21249e16 0.548416 0.274208 0.961670i \(-0.411584\pi\)
0.274208 + 0.961670i \(0.411584\pi\)
\(938\) 1.77792e16 0.799458
\(939\) −5.78726e15 −0.258709
\(940\) −7.95893e14 −0.0353713
\(941\) 1.82977e16 0.808449 0.404224 0.914660i \(-0.367541\pi\)
0.404224 + 0.914660i \(0.367541\pi\)
\(942\) 1.20753e16 0.530418
\(943\) 4.00958e14 0.0175099
\(944\) 2.51822e15 0.109332
\(945\) −2.82147e15 −0.121787
\(946\) −1.85226e15 −0.0794880
\(947\) 2.31106e16 0.986022 0.493011 0.870023i \(-0.335896\pi\)
0.493011 + 0.870023i \(0.335896\pi\)
\(948\) −1.75827e15 −0.0745830
\(949\) 9.84115e15 0.415032
\(950\) 5.07508e15 0.212796
\(951\) 1.32670e16 0.553071
\(952\) −3.21561e16 −1.33279
\(953\) 1.47887e16 0.609424 0.304712 0.952445i \(-0.401440\pi\)
0.304712 + 0.952445i \(0.401440\pi\)
\(954\) −1.08999e16 −0.446588
\(955\) −7.99031e15 −0.325496
\(956\) 8.29526e14 0.0335978
\(957\) −5.91837e15 −0.238334
\(958\) −7.45392e15 −0.298452
\(959\) 2.56614e16 1.02159
\(960\) 1.10028e16 0.435525
\(961\) −2.32343e16 −0.914431
\(962\) −5.76829e15 −0.225727
\(963\) −4.56454e15 −0.177604
\(964\) −2.79546e15 −0.108151
\(965\) −1.16722e16 −0.449008
\(966\) −8.39739e15 −0.321196
\(967\) 1.32924e16 0.505542 0.252771 0.967526i \(-0.418658\pi\)
0.252771 + 0.967526i \(0.418658\pi\)
\(968\) −2.12412e16 −0.803276
\(969\) −9.12842e15 −0.343253
\(970\) 3.15386e15 0.117923
\(971\) 1.37842e16 0.512479 0.256239 0.966613i \(-0.417516\pi\)
0.256239 + 0.966613i \(0.417516\pi\)
\(972\) 2.43753e14 0.00901127
\(973\) −3.42630e16 −1.25952
\(974\) −1.01361e16 −0.370508
\(975\) −2.00805e15 −0.0729875
\(976\) 8.02143e15 0.289920
\(977\) 4.44842e15 0.159877 0.0799384 0.996800i \(-0.474528\pi\)
0.0799384 + 0.996800i \(0.474528\pi\)
\(978\) 1.07295e16 0.383457
\(979\) −3.98104e15 −0.141479
\(980\) −4.12811e14 −0.0145884
\(981\) 6.89877e15 0.242433
\(982\) 4.98763e15 0.174294
\(983\) 4.39070e16 1.52577 0.762885 0.646534i \(-0.223782\pi\)
0.762885 + 0.646534i \(0.223782\pi\)
\(984\) −4.74914e14 −0.0164113
\(985\) −1.93469e16 −0.664834
\(986\) −3.12592e16 −1.06821
\(987\) −5.73815e15 −0.194997
\(988\) 4.32310e14 0.0146094
\(989\) 3.38988e15 0.113921
\(990\) 3.11347e15 0.104052
\(991\) −5.42054e15 −0.180151 −0.0900756 0.995935i \(-0.528711\pi\)
−0.0900756 + 0.995935i \(0.528711\pi\)
\(992\) −2.46719e15 −0.0815433
\(993\) −9.81053e15 −0.322457
\(994\) −3.48399e16 −1.13881
\(995\) −1.21286e16 −0.394261
\(996\) −1.22505e15 −0.0396028
\(997\) −2.96023e15 −0.0951705 −0.0475852 0.998867i \(-0.515153\pi\)
−0.0475852 + 0.998867i \(0.515153\pi\)
\(998\) −5.04658e16 −1.61354
\(999\) 6.15706e15 0.195778
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.c.1.8 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.8 27 1.1 even 1 trivial