Properties

Label 177.12.a.c.1.18
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 1.18
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+24.9877 q^{2} -243.000 q^{3} -1423.61 q^{4} +11346.7 q^{5} -6072.02 q^{6} -46106.7 q^{7} -86747.8 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+24.9877 q^{2} -243.000 q^{3} -1423.61 q^{4} +11346.7 q^{5} -6072.02 q^{6} -46106.7 q^{7} -86747.8 q^{8} +59049.0 q^{9} +283528. q^{10} -158942. q^{11} +345938. q^{12} -2.30733e6 q^{13} -1.15210e6 q^{14} -2.75724e6 q^{15} +747929. q^{16} -3.64274e6 q^{17} +1.47550e6 q^{18} +8.79583e6 q^{19} -1.61533e7 q^{20} +1.12039e7 q^{21} -3.97161e6 q^{22} -4.28026e6 q^{23} +2.10797e7 q^{24} +7.99192e7 q^{25} -5.76548e7 q^{26} -1.43489e7 q^{27} +6.56381e7 q^{28} -9.38699e7 q^{29} -6.88973e7 q^{30} -1.47835e8 q^{31} +1.96348e8 q^{32} +3.86230e7 q^{33} -9.10238e7 q^{34} -5.23159e8 q^{35} -8.40629e7 q^{36} +3.64192e8 q^{37} +2.19788e8 q^{38} +5.60680e8 q^{39} -9.84300e8 q^{40} -1.41920e8 q^{41} +2.79961e8 q^{42} +2.12648e7 q^{43} +2.26272e8 q^{44} +6.70011e8 q^{45} -1.06954e8 q^{46} -9.13862e7 q^{47} -1.81747e8 q^{48} +1.48504e8 q^{49} +1.99700e9 q^{50} +8.85186e8 q^{51} +3.28474e9 q^{52} +2.00062e9 q^{53} -3.58547e8 q^{54} -1.80347e9 q^{55} +3.99966e9 q^{56} -2.13739e9 q^{57} -2.34560e9 q^{58} -7.14924e8 q^{59} +3.92525e9 q^{60} -3.63962e9 q^{61} -3.69407e9 q^{62} -2.72256e9 q^{63} +3.37455e9 q^{64} -2.61805e10 q^{65} +9.65101e8 q^{66} +7.77012e8 q^{67} +5.18585e9 q^{68} +1.04010e9 q^{69} -1.30725e10 q^{70} -2.23660e10 q^{71} -5.12237e9 q^{72} -2.80490e10 q^{73} +9.10033e9 q^{74} -1.94204e10 q^{75} -1.25219e10 q^{76} +7.32831e9 q^{77} +1.40101e10 q^{78} +4.41096e10 q^{79} +8.48652e9 q^{80} +3.48678e9 q^{81} -3.54626e9 q^{82} +2.91614e10 q^{83} -1.59501e10 q^{84} -4.13330e10 q^{85} +5.31358e8 q^{86} +2.28104e10 q^{87} +1.37879e10 q^{88} +2.60526e10 q^{89} +1.67420e10 q^{90} +1.06383e11 q^{91} +6.09343e9 q^{92} +3.59240e10 q^{93} -2.28354e9 q^{94} +9.98035e10 q^{95} -4.77127e10 q^{96} +4.00595e9 q^{97} +3.71077e9 q^{98} -9.38539e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 24.9877 0.552156 0.276078 0.961135i \(-0.410965\pi\)
0.276078 + 0.961135i \(0.410965\pi\)
\(3\) −243.000 −0.577350
\(4\) −1423.61 −0.695124
\(5\) 11346.7 1.62381 0.811903 0.583793i \(-0.198432\pi\)
0.811903 + 0.583793i \(0.198432\pi\)
\(6\) −6072.02 −0.318788
\(7\) −46106.7 −1.03687 −0.518436 0.855116i \(-0.673486\pi\)
−0.518436 + 0.855116i \(0.673486\pi\)
\(8\) −86747.8 −0.935973
\(9\) 59049.0 0.333333
\(10\) 283528. 0.896594
\(11\) −158942. −0.297564 −0.148782 0.988870i \(-0.547535\pi\)
−0.148782 + 0.988870i \(0.547535\pi\)
\(12\) 345938. 0.401330
\(13\) −2.30733e6 −1.72354 −0.861768 0.507302i \(-0.830643\pi\)
−0.861768 + 0.507302i \(0.830643\pi\)
\(14\) −1.15210e6 −0.572515
\(15\) −2.75724e6 −0.937505
\(16\) 747929. 0.178320
\(17\) −3.64274e6 −0.622242 −0.311121 0.950370i \(-0.600704\pi\)
−0.311121 + 0.950370i \(0.600704\pi\)
\(18\) 1.47550e6 0.184052
\(19\) 8.79583e6 0.814952 0.407476 0.913216i \(-0.366409\pi\)
0.407476 + 0.913216i \(0.366409\pi\)
\(20\) −1.61533e7 −1.12875
\(21\) 1.12039e7 0.598638
\(22\) −3.97161e6 −0.164302
\(23\) −4.28026e6 −0.138665 −0.0693325 0.997594i \(-0.522087\pi\)
−0.0693325 + 0.997594i \(0.522087\pi\)
\(24\) 2.10797e7 0.540384
\(25\) 7.99192e7 1.63674
\(26\) −5.76548e7 −0.951661
\(27\) −1.43489e7 −0.192450
\(28\) 6.56381e7 0.720754
\(29\) −9.38699e7 −0.849840 −0.424920 0.905231i \(-0.639698\pi\)
−0.424920 + 0.905231i \(0.639698\pi\)
\(30\) −6.88973e7 −0.517649
\(31\) −1.47835e8 −0.927447 −0.463723 0.885980i \(-0.653487\pi\)
−0.463723 + 0.885980i \(0.653487\pi\)
\(32\) 1.96348e8 1.03443
\(33\) 3.86230e7 0.171798
\(34\) −9.10238e7 −0.343575
\(35\) −5.23159e8 −1.68368
\(36\) −8.40629e7 −0.231708
\(37\) 3.64192e8 0.863417 0.431709 0.902013i \(-0.357911\pi\)
0.431709 + 0.902013i \(0.357911\pi\)
\(38\) 2.19788e8 0.449981
\(39\) 5.60680e8 0.995084
\(40\) −9.84300e8 −1.51984
\(41\) −1.41920e8 −0.191308 −0.0956538 0.995415i \(-0.530494\pi\)
−0.0956538 + 0.995415i \(0.530494\pi\)
\(42\) 2.79961e8 0.330542
\(43\) 2.12648e7 0.0220589 0.0110295 0.999939i \(-0.496489\pi\)
0.0110295 + 0.999939i \(0.496489\pi\)
\(44\) 2.26272e8 0.206843
\(45\) 6.70011e8 0.541269
\(46\) −1.06954e8 −0.0765647
\(47\) −9.13862e7 −0.0581223 −0.0290611 0.999578i \(-0.509252\pi\)
−0.0290611 + 0.999578i \(0.509252\pi\)
\(48\) −1.81747e8 −0.102953
\(49\) 1.48504e8 0.0751032
\(50\) 1.99700e9 0.903739
\(51\) 8.85186e8 0.359251
\(52\) 3.28474e9 1.19807
\(53\) 2.00062e9 0.657124 0.328562 0.944482i \(-0.393436\pi\)
0.328562 + 0.944482i \(0.393436\pi\)
\(54\) −3.58547e8 −0.106263
\(55\) −1.80347e9 −0.483186
\(56\) 3.99966e9 0.970484
\(57\) −2.13739e9 −0.470513
\(58\) −2.34560e9 −0.469245
\(59\) −7.14924e8 −0.130189
\(60\) 3.92525e9 0.651681
\(61\) −3.63962e9 −0.551750 −0.275875 0.961194i \(-0.588968\pi\)
−0.275875 + 0.961194i \(0.588968\pi\)
\(62\) −3.69407e9 −0.512095
\(63\) −2.72256e9 −0.345624
\(64\) 3.37455e9 0.392849
\(65\) −2.61805e10 −2.79869
\(66\) 9.65101e8 0.0948596
\(67\) 7.77012e8 0.0703099 0.0351549 0.999382i \(-0.488808\pi\)
0.0351549 + 0.999382i \(0.488808\pi\)
\(68\) 5.18585e9 0.432535
\(69\) 1.04010e9 0.0800583
\(70\) −1.30725e10 −0.929653
\(71\) −2.23660e10 −1.47119 −0.735594 0.677422i \(-0.763097\pi\)
−0.735594 + 0.677422i \(0.763097\pi\)
\(72\) −5.12237e9 −0.311991
\(73\) −2.80490e10 −1.58359 −0.791794 0.610788i \(-0.790853\pi\)
−0.791794 + 0.610788i \(0.790853\pi\)
\(74\) 9.10033e9 0.476741
\(75\) −1.94204e10 −0.944975
\(76\) −1.25219e10 −0.566492
\(77\) 7.32831e9 0.308535
\(78\) 1.40101e10 0.549442
\(79\) 4.41096e10 1.61281 0.806406 0.591362i \(-0.201410\pi\)
0.806406 + 0.591362i \(0.201410\pi\)
\(80\) 8.48652e9 0.289557
\(81\) 3.48678e9 0.111111
\(82\) −3.54626e9 −0.105632
\(83\) 2.91614e10 0.812602 0.406301 0.913739i \(-0.366818\pi\)
0.406301 + 0.913739i \(0.366818\pi\)
\(84\) −1.59501e10 −0.416127
\(85\) −4.13330e10 −1.01040
\(86\) 5.31358e8 0.0121800
\(87\) 2.28104e10 0.490656
\(88\) 1.37879e10 0.278512
\(89\) 2.60526e10 0.494545 0.247272 0.968946i \(-0.420466\pi\)
0.247272 + 0.968946i \(0.420466\pi\)
\(90\) 1.67420e10 0.298865
\(91\) 1.06383e11 1.78709
\(92\) 6.09343e9 0.0963893
\(93\) 3.59240e10 0.535462
\(94\) −2.28354e9 −0.0320926
\(95\) 9.98035e10 1.32332
\(96\) −4.77127e10 −0.597231
\(97\) 4.00595e9 0.0473653 0.0236827 0.999720i \(-0.492461\pi\)
0.0236827 + 0.999720i \(0.492461\pi\)
\(98\) 3.71077e9 0.0414687
\(99\) −9.38539e9 −0.0991879
\(100\) −1.13774e11 −1.13774
\(101\) 1.36683e11 1.29404 0.647020 0.762473i \(-0.276015\pi\)
0.647020 + 0.762473i \(0.276015\pi\)
\(102\) 2.21188e10 0.198363
\(103\) 3.32592e10 0.282688 0.141344 0.989961i \(-0.454858\pi\)
0.141344 + 0.989961i \(0.454858\pi\)
\(104\) 2.00155e11 1.61318
\(105\) 1.27128e11 0.972072
\(106\) 4.99910e10 0.362835
\(107\) 2.20332e11 1.51868 0.759340 0.650694i \(-0.225522\pi\)
0.759340 + 0.650694i \(0.225522\pi\)
\(108\) 2.04273e10 0.133777
\(109\) 3.41039e10 0.212304 0.106152 0.994350i \(-0.466147\pi\)
0.106152 + 0.994350i \(0.466147\pi\)
\(110\) −4.50646e10 −0.266794
\(111\) −8.84986e10 −0.498494
\(112\) −3.44846e10 −0.184895
\(113\) 1.78537e11 0.911582 0.455791 0.890087i \(-0.349356\pi\)
0.455791 + 0.890087i \(0.349356\pi\)
\(114\) −5.34084e10 −0.259796
\(115\) −4.85667e10 −0.225165
\(116\) 1.33634e11 0.590744
\(117\) −1.36245e11 −0.574512
\(118\) −1.78643e10 −0.0718846
\(119\) 1.67955e11 0.645185
\(120\) 2.39185e11 0.877479
\(121\) −2.60049e11 −0.911456
\(122\) −9.09460e10 −0.304652
\(123\) 3.44865e10 0.110451
\(124\) 2.10460e11 0.644690
\(125\) 3.52780e11 1.03395
\(126\) −6.80305e10 −0.190838
\(127\) −3.67519e11 −0.987095 −0.493547 0.869719i \(-0.664300\pi\)
−0.493547 + 0.869719i \(0.664300\pi\)
\(128\) −3.17799e11 −0.817520
\(129\) −5.16734e9 −0.0127357
\(130\) −6.54191e11 −1.54531
\(131\) 8.20347e11 1.85783 0.928914 0.370296i \(-0.120744\pi\)
0.928914 + 0.370296i \(0.120744\pi\)
\(132\) −5.49842e10 −0.119421
\(133\) −4.05547e11 −0.845001
\(134\) 1.94158e10 0.0388220
\(135\) −1.62813e11 −0.312502
\(136\) 3.16000e11 0.582402
\(137\) 4.76223e11 0.843038 0.421519 0.906820i \(-0.361497\pi\)
0.421519 + 0.906820i \(0.361497\pi\)
\(138\) 2.59898e10 0.0442047
\(139\) 5.05261e11 0.825913 0.412957 0.910751i \(-0.364496\pi\)
0.412957 + 0.910751i \(0.364496\pi\)
\(140\) 7.44775e11 1.17036
\(141\) 2.22069e10 0.0335569
\(142\) −5.58877e11 −0.812326
\(143\) 3.66732e11 0.512862
\(144\) 4.41645e10 0.0594401
\(145\) −1.06511e12 −1.37998
\(146\) −7.00882e11 −0.874388
\(147\) −3.60864e10 −0.0433608
\(148\) −5.18468e11 −0.600181
\(149\) 4.01963e11 0.448396 0.224198 0.974544i \(-0.428024\pi\)
0.224198 + 0.974544i \(0.428024\pi\)
\(150\) −4.85271e11 −0.521774
\(151\) 7.98467e11 0.827720 0.413860 0.910340i \(-0.364180\pi\)
0.413860 + 0.910340i \(0.364180\pi\)
\(152\) −7.63018e11 −0.762773
\(153\) −2.15100e11 −0.207414
\(154\) 1.83118e11 0.170360
\(155\) −1.67744e12 −1.50599
\(156\) −7.98191e11 −0.691706
\(157\) 1.89568e12 1.58605 0.793023 0.609191i \(-0.208506\pi\)
0.793023 + 0.609191i \(0.208506\pi\)
\(158\) 1.10220e12 0.890524
\(159\) −4.86151e11 −0.379391
\(160\) 2.22790e12 1.67972
\(161\) 1.97349e11 0.143778
\(162\) 8.71269e10 0.0613507
\(163\) 5.31502e11 0.361804 0.180902 0.983501i \(-0.442098\pi\)
0.180902 + 0.983501i \(0.442098\pi\)
\(164\) 2.02039e11 0.132982
\(165\) 4.38243e11 0.278967
\(166\) 7.28676e11 0.448684
\(167\) 7.57455e10 0.0451249 0.0225625 0.999745i \(-0.492818\pi\)
0.0225625 + 0.999745i \(0.492818\pi\)
\(168\) −9.71916e11 −0.560309
\(169\) 3.53159e12 1.97058
\(170\) −1.03282e12 −0.557899
\(171\) 5.19385e11 0.271651
\(172\) −3.02728e10 −0.0153337
\(173\) −1.34894e12 −0.661821 −0.330911 0.943662i \(-0.607356\pi\)
−0.330911 + 0.943662i \(0.607356\pi\)
\(174\) 5.69980e11 0.270919
\(175\) −3.68481e12 −1.69709
\(176\) −1.18878e11 −0.0530616
\(177\) 1.73727e11 0.0751646
\(178\) 6.50995e11 0.273066
\(179\) 2.42722e12 0.987229 0.493614 0.869681i \(-0.335675\pi\)
0.493614 + 0.869681i \(0.335675\pi\)
\(180\) −9.53836e11 −0.376248
\(181\) −4.50546e11 −0.172388 −0.0861940 0.996278i \(-0.527470\pi\)
−0.0861940 + 0.996278i \(0.527470\pi\)
\(182\) 2.65828e12 0.986751
\(183\) 8.84428e11 0.318553
\(184\) 3.71303e11 0.129787
\(185\) 4.13237e12 1.40202
\(186\) 8.97659e11 0.295658
\(187\) 5.78986e11 0.185157
\(188\) 1.30099e11 0.0404022
\(189\) 6.61581e11 0.199546
\(190\) 2.49386e12 0.730681
\(191\) −7.48171e11 −0.212970 −0.106485 0.994314i \(-0.533960\pi\)
−0.106485 + 0.994314i \(0.533960\pi\)
\(192\) −8.20014e11 −0.226811
\(193\) −1.99875e12 −0.537272 −0.268636 0.963242i \(-0.586573\pi\)
−0.268636 + 0.963242i \(0.586573\pi\)
\(194\) 1.00100e11 0.0261531
\(195\) 6.36186e12 1.61582
\(196\) −2.11412e11 −0.0522060
\(197\) 2.36660e12 0.568279 0.284139 0.958783i \(-0.408292\pi\)
0.284139 + 0.958783i \(0.408292\pi\)
\(198\) −2.34520e11 −0.0547672
\(199\) −8.64639e11 −0.196401 −0.0982004 0.995167i \(-0.531309\pi\)
−0.0982004 + 0.995167i \(0.531309\pi\)
\(200\) −6.93281e12 −1.53195
\(201\) −1.88814e11 −0.0405934
\(202\) 3.41541e12 0.714513
\(203\) 4.32803e12 0.881176
\(204\) −1.26016e12 −0.249724
\(205\) −1.61032e12 −0.310646
\(206\) 8.31072e11 0.156088
\(207\) −2.52745e11 −0.0462217
\(208\) −1.72572e12 −0.307341
\(209\) −1.39803e12 −0.242500
\(210\) 3.17663e12 0.536736
\(211\) −9.33836e12 −1.53715 −0.768577 0.639758i \(-0.779035\pi\)
−0.768577 + 0.639758i \(0.779035\pi\)
\(212\) −2.84811e12 −0.456782
\(213\) 5.43495e12 0.849391
\(214\) 5.50559e12 0.838549
\(215\) 2.41285e11 0.0358194
\(216\) 1.24474e12 0.180128
\(217\) 6.81620e12 0.961643
\(218\) 8.52178e11 0.117225
\(219\) 6.81592e12 0.914285
\(220\) 2.56744e12 0.335874
\(221\) 8.40499e12 1.07246
\(222\) −2.21138e12 −0.275247
\(223\) −2.98323e12 −0.362251 −0.181125 0.983460i \(-0.557974\pi\)
−0.181125 + 0.983460i \(0.557974\pi\)
\(224\) −9.05298e12 −1.07258
\(225\) 4.71915e12 0.545582
\(226\) 4.46122e12 0.503336
\(227\) 5.65977e12 0.623241 0.311621 0.950207i \(-0.399128\pi\)
0.311621 + 0.950207i \(0.399128\pi\)
\(228\) 3.04281e12 0.327064
\(229\) 5.53904e11 0.0581218 0.0290609 0.999578i \(-0.490748\pi\)
0.0290609 + 0.999578i \(0.490748\pi\)
\(230\) −1.21357e12 −0.124326
\(231\) −1.78078e12 −0.178133
\(232\) 8.14300e12 0.795428
\(233\) −6.26960e12 −0.598111 −0.299056 0.954236i \(-0.596672\pi\)
−0.299056 + 0.954236i \(0.596672\pi\)
\(234\) −3.40446e12 −0.317220
\(235\) −1.03693e12 −0.0943793
\(236\) 1.01778e12 0.0904974
\(237\) −1.07186e13 −0.931158
\(238\) 4.19681e12 0.356243
\(239\) −1.63168e13 −1.35347 −0.676733 0.736228i \(-0.736605\pi\)
−0.676733 + 0.736228i \(0.736605\pi\)
\(240\) −2.06222e12 −0.167176
\(241\) 6.93338e10 0.00549353 0.00274676 0.999996i \(-0.499126\pi\)
0.00274676 + 0.999996i \(0.499126\pi\)
\(242\) −6.49804e12 −0.503266
\(243\) −8.47289e11 −0.0641500
\(244\) 5.18141e12 0.383534
\(245\) 1.68502e12 0.121953
\(246\) 8.61741e11 0.0609865
\(247\) −2.02948e13 −1.40460
\(248\) 1.28244e13 0.868065
\(249\) −7.08621e12 −0.469156
\(250\) 8.81519e12 0.570902
\(251\) 1.77996e13 1.12773 0.563866 0.825866i \(-0.309314\pi\)
0.563866 + 0.825866i \(0.309314\pi\)
\(252\) 3.87587e12 0.240251
\(253\) 6.80314e11 0.0412617
\(254\) −9.18346e12 −0.545030
\(255\) 1.00439e13 0.583355
\(256\) −1.48522e13 −0.844247
\(257\) 2.62327e13 1.45952 0.729762 0.683701i \(-0.239631\pi\)
0.729762 + 0.683701i \(0.239631\pi\)
\(258\) −1.29120e11 −0.00703211
\(259\) −1.67917e13 −0.895253
\(260\) 3.72709e13 1.94543
\(261\) −5.54292e12 −0.283280
\(262\) 2.04986e13 1.02581
\(263\) 3.26150e13 1.59831 0.799154 0.601127i \(-0.205281\pi\)
0.799154 + 0.601127i \(0.205281\pi\)
\(264\) −3.35046e12 −0.160799
\(265\) 2.27004e13 1.06704
\(266\) −1.01337e13 −0.466572
\(267\) −6.33078e12 −0.285526
\(268\) −1.10616e12 −0.0488740
\(269\) −2.34861e13 −1.01665 −0.508327 0.861164i \(-0.669736\pi\)
−0.508327 + 0.861164i \(0.669736\pi\)
\(270\) −4.06832e12 −0.172550
\(271\) 5.02136e12 0.208685 0.104342 0.994541i \(-0.466726\pi\)
0.104342 + 0.994541i \(0.466726\pi\)
\(272\) −2.72451e12 −0.110958
\(273\) −2.58511e13 −1.03177
\(274\) 1.18997e13 0.465489
\(275\) −1.27025e13 −0.487036
\(276\) −1.48070e12 −0.0556504
\(277\) 1.70115e13 0.626764 0.313382 0.949627i \(-0.398538\pi\)
0.313382 + 0.949627i \(0.398538\pi\)
\(278\) 1.26253e13 0.456033
\(279\) −8.72953e12 −0.309149
\(280\) 4.53828e13 1.57588
\(281\) −1.28857e13 −0.438756 −0.219378 0.975640i \(-0.570403\pi\)
−0.219378 + 0.975640i \(0.570403\pi\)
\(282\) 5.54899e11 0.0185287
\(283\) 4.68660e13 1.53473 0.767366 0.641210i \(-0.221567\pi\)
0.767366 + 0.641210i \(0.221567\pi\)
\(284\) 3.18406e13 1.02266
\(285\) −2.42523e13 −0.764021
\(286\) 9.16380e12 0.283180
\(287\) 6.54346e12 0.198361
\(288\) 1.15942e13 0.344811
\(289\) −2.10023e13 −0.612815
\(290\) −2.66147e13 −0.761962
\(291\) −9.73445e11 −0.0273464
\(292\) 3.99310e13 1.10079
\(293\) 7.34035e13 1.98584 0.992922 0.118769i \(-0.0378947\pi\)
0.992922 + 0.118769i \(0.0378947\pi\)
\(294\) −9.01716e11 −0.0239420
\(295\) −8.11202e12 −0.211401
\(296\) −3.15928e13 −0.808135
\(297\) 2.28065e12 0.0572662
\(298\) 1.00441e13 0.247585
\(299\) 9.87595e12 0.238994
\(300\) 2.76471e13 0.656874
\(301\) −9.80449e11 −0.0228723
\(302\) 1.99519e13 0.457031
\(303\) −3.32140e13 −0.747115
\(304\) 6.57866e12 0.145322
\(305\) −4.12977e13 −0.895935
\(306\) −5.37487e12 −0.114525
\(307\) 3.58069e13 0.749386 0.374693 0.927149i \(-0.377748\pi\)
0.374693 + 0.927149i \(0.377748\pi\)
\(308\) −1.04327e13 −0.214470
\(309\) −8.08198e12 −0.163210
\(310\) −4.19155e13 −0.831544
\(311\) −1.02620e13 −0.200009 −0.100004 0.994987i \(-0.531886\pi\)
−0.100004 + 0.994987i \(0.531886\pi\)
\(312\) −4.86377e13 −0.931372
\(313\) −9.38393e13 −1.76559 −0.882797 0.469754i \(-0.844343\pi\)
−0.882797 + 0.469754i \(0.844343\pi\)
\(314\) 4.73686e13 0.875745
\(315\) −3.08920e13 −0.561226
\(316\) −6.27950e13 −1.12110
\(317\) −7.53558e13 −1.32218 −0.661090 0.750306i \(-0.729906\pi\)
−0.661090 + 0.750306i \(0.729906\pi\)
\(318\) −1.21478e13 −0.209483
\(319\) 1.49199e13 0.252882
\(320\) 3.82899e13 0.637910
\(321\) −5.35406e13 −0.876810
\(322\) 4.93130e12 0.0793878
\(323\) −3.20409e13 −0.507097
\(324\) −4.96383e12 −0.0772359
\(325\) −1.84400e14 −2.82099
\(326\) 1.32810e13 0.199772
\(327\) −8.28724e12 −0.122574
\(328\) 1.23112e13 0.179059
\(329\) 4.21352e12 0.0602653
\(330\) 1.09507e13 0.154034
\(331\) −1.30987e14 −1.81207 −0.906035 0.423202i \(-0.860906\pi\)
−0.906035 + 0.423202i \(0.860906\pi\)
\(332\) −4.15145e13 −0.564859
\(333\) 2.15052e13 0.287806
\(334\) 1.89271e12 0.0249160
\(335\) 8.81651e12 0.114170
\(336\) 8.37975e12 0.106749
\(337\) 3.42343e13 0.429039 0.214520 0.976720i \(-0.431181\pi\)
0.214520 + 0.976720i \(0.431181\pi\)
\(338\) 8.82465e13 1.08807
\(339\) −4.33844e13 −0.526302
\(340\) 5.88422e13 0.702353
\(341\) 2.34973e13 0.275974
\(342\) 1.29783e13 0.149994
\(343\) 8.43211e13 0.958999
\(344\) −1.84467e12 −0.0206466
\(345\) 1.18017e13 0.129999
\(346\) −3.37071e13 −0.365429
\(347\) −7.09428e13 −0.757001 −0.378500 0.925601i \(-0.623560\pi\)
−0.378500 + 0.925601i \(0.623560\pi\)
\(348\) −3.24732e13 −0.341066
\(349\) −7.61162e13 −0.786932 −0.393466 0.919339i \(-0.628724\pi\)
−0.393466 + 0.919339i \(0.628724\pi\)
\(350\) −9.20751e13 −0.937061
\(351\) 3.31076e13 0.331695
\(352\) −3.12081e13 −0.307810
\(353\) −3.44627e13 −0.334648 −0.167324 0.985902i \(-0.553513\pi\)
−0.167324 + 0.985902i \(0.553513\pi\)
\(354\) 4.34103e12 0.0415026
\(355\) −2.53781e14 −2.38892
\(356\) −3.70888e13 −0.343770
\(357\) −4.08130e13 −0.372498
\(358\) 6.06508e13 0.545105
\(359\) 1.32771e14 1.17512 0.587561 0.809180i \(-0.300088\pi\)
0.587561 + 0.809180i \(0.300088\pi\)
\(360\) −5.81219e13 −0.506613
\(361\) −3.91237e13 −0.335853
\(362\) −1.12581e13 −0.0951851
\(363\) 6.31919e13 0.526229
\(364\) −1.51449e14 −1.24225
\(365\) −3.18264e14 −2.57144
\(366\) 2.20999e13 0.175891
\(367\) −4.06463e13 −0.318682 −0.159341 0.987224i \(-0.550937\pi\)
−0.159341 + 0.987224i \(0.550937\pi\)
\(368\) −3.20133e12 −0.0247268
\(369\) −8.38023e12 −0.0637692
\(370\) 1.03259e14 0.774135
\(371\) −9.22421e13 −0.681353
\(372\) −5.11419e13 −0.372212
\(373\) 1.60092e14 1.14808 0.574038 0.818828i \(-0.305376\pi\)
0.574038 + 0.818828i \(0.305376\pi\)
\(374\) 1.44675e13 0.102235
\(375\) −8.57256e13 −0.596951
\(376\) 7.92755e12 0.0544009
\(377\) 2.16588e14 1.46473
\(378\) 1.65314e13 0.110181
\(379\) −6.88174e13 −0.452046 −0.226023 0.974122i \(-0.572572\pi\)
−0.226023 + 0.974122i \(0.572572\pi\)
\(380\) −1.42082e14 −0.919873
\(381\) 8.93070e13 0.569899
\(382\) −1.86951e13 −0.117592
\(383\) 1.17164e14 0.726444 0.363222 0.931703i \(-0.381677\pi\)
0.363222 + 0.931703i \(0.381677\pi\)
\(384\) 7.72253e13 0.471995
\(385\) 8.31521e13 0.501001
\(386\) −4.99443e13 −0.296658
\(387\) 1.25566e12 0.00735297
\(388\) −5.70292e12 −0.0329248
\(389\) −2.48888e14 −1.41671 −0.708355 0.705856i \(-0.750562\pi\)
−0.708355 + 0.705856i \(0.750562\pi\)
\(390\) 1.58969e14 0.892187
\(391\) 1.55919e13 0.0862831
\(392\) −1.28823e13 −0.0702945
\(393\) −1.99344e14 −1.07262
\(394\) 5.91361e13 0.313779
\(395\) 5.00498e14 2.61889
\(396\) 1.33612e13 0.0689478
\(397\) −3.77720e14 −1.92230 −0.961151 0.276023i \(-0.910983\pi\)
−0.961151 + 0.276023i \(0.910983\pi\)
\(398\) −2.16054e13 −0.108444
\(399\) 9.85479e13 0.487861
\(400\) 5.97739e13 0.291865
\(401\) 1.13652e14 0.547371 0.273686 0.961819i \(-0.411757\pi\)
0.273686 + 0.961819i \(0.411757\pi\)
\(402\) −4.71803e12 −0.0224139
\(403\) 3.41104e14 1.59849
\(404\) −1.94584e14 −0.899518
\(405\) 3.95635e13 0.180423
\(406\) 1.08148e14 0.486547
\(407\) −5.78855e13 −0.256922
\(408\) −7.67879e13 −0.336250
\(409\) 1.19370e14 0.515724 0.257862 0.966182i \(-0.416982\pi\)
0.257862 + 0.966182i \(0.416982\pi\)
\(410\) −4.02383e13 −0.171525
\(411\) −1.15722e14 −0.486728
\(412\) −4.73482e13 −0.196503
\(413\) 3.29628e13 0.134989
\(414\) −6.31552e12 −0.0255216
\(415\) 3.30885e14 1.31951
\(416\) −4.53040e14 −1.78288
\(417\) −1.22778e14 −0.476841
\(418\) −3.49336e13 −0.133898
\(419\) 2.87309e14 1.08686 0.543428 0.839456i \(-0.317126\pi\)
0.543428 + 0.839456i \(0.317126\pi\)
\(420\) −1.80980e14 −0.675710
\(421\) 3.25120e14 1.19810 0.599049 0.800712i \(-0.295545\pi\)
0.599049 + 0.800712i \(0.295545\pi\)
\(422\) −2.33344e14 −0.848749
\(423\) −5.39627e12 −0.0193741
\(424\) −1.73549e14 −0.615050
\(425\) −2.91125e14 −1.01845
\(426\) 1.35807e14 0.468997
\(427\) 1.67811e14 0.572094
\(428\) −3.13667e14 −1.05567
\(429\) −8.91158e13 −0.296101
\(430\) 6.02916e12 0.0197779
\(431\) 4.11329e14 1.33219 0.666093 0.745869i \(-0.267966\pi\)
0.666093 + 0.745869i \(0.267966\pi\)
\(432\) −1.07320e13 −0.0343177
\(433\) 2.50637e13 0.0791337 0.0395669 0.999217i \(-0.487402\pi\)
0.0395669 + 0.999217i \(0.487402\pi\)
\(434\) 1.70322e14 0.530977
\(435\) 2.58822e14 0.796729
\(436\) −4.85507e13 −0.147577
\(437\) −3.76484e13 −0.113005
\(438\) 1.70314e14 0.504828
\(439\) 9.80836e13 0.287106 0.143553 0.989643i \(-0.454147\pi\)
0.143553 + 0.989643i \(0.454147\pi\)
\(440\) 1.56447e14 0.452249
\(441\) 8.76898e12 0.0250344
\(442\) 2.10022e14 0.592163
\(443\) −2.21763e14 −0.617546 −0.308773 0.951136i \(-0.599918\pi\)
−0.308773 + 0.951136i \(0.599918\pi\)
\(444\) 1.25988e14 0.346515
\(445\) 2.95610e14 0.803045
\(446\) −7.45441e13 −0.200019
\(447\) −9.76770e13 −0.258881
\(448\) −1.55589e14 −0.407334
\(449\) −1.67607e14 −0.433448 −0.216724 0.976233i \(-0.569537\pi\)
−0.216724 + 0.976233i \(0.569537\pi\)
\(450\) 1.17921e14 0.301246
\(451\) 2.25571e13 0.0569262
\(452\) −2.54167e14 −0.633662
\(453\) −1.94027e14 −0.477885
\(454\) 1.41425e14 0.344127
\(455\) 1.20710e15 2.90188
\(456\) 1.85413e14 0.440387
\(457\) −6.66669e14 −1.56448 −0.782242 0.622974i \(-0.785924\pi\)
−0.782242 + 0.622974i \(0.785924\pi\)
\(458\) 1.38408e13 0.0320923
\(459\) 5.22693e13 0.119750
\(460\) 6.91402e13 0.156517
\(461\) −5.09805e14 −1.14038 −0.570189 0.821513i \(-0.693130\pi\)
−0.570189 + 0.821513i \(0.693130\pi\)
\(462\) −4.44977e13 −0.0983572
\(463\) 1.18421e13 0.0258662 0.0129331 0.999916i \(-0.495883\pi\)
0.0129331 + 0.999916i \(0.495883\pi\)
\(464\) −7.02080e13 −0.151544
\(465\) 4.07618e14 0.869486
\(466\) −1.56663e14 −0.330251
\(467\) −7.86087e14 −1.63767 −0.818837 0.574026i \(-0.805381\pi\)
−0.818837 + 0.574026i \(0.805381\pi\)
\(468\) 1.93961e14 0.399357
\(469\) −3.58255e13 −0.0729023
\(470\) −2.59106e13 −0.0521121
\(471\) −4.60649e14 −0.915704
\(472\) 6.20181e13 0.121853
\(473\) −3.37987e12 −0.00656393
\(474\) −2.67834e14 −0.514144
\(475\) 7.02955e14 1.33387
\(476\) −2.39103e14 −0.448483
\(477\) 1.18135e14 0.219041
\(478\) −4.07721e14 −0.747325
\(479\) −3.44582e14 −0.624377 −0.312188 0.950020i \(-0.601062\pi\)
−0.312188 + 0.950020i \(0.601062\pi\)
\(480\) −5.41381e14 −0.969786
\(481\) −8.40309e14 −1.48813
\(482\) 1.73250e12 0.00303329
\(483\) −4.79557e13 −0.0830102
\(484\) 3.70209e14 0.633574
\(485\) 4.54542e13 0.0769121
\(486\) −2.11718e13 −0.0354208
\(487\) −6.12126e14 −1.01259 −0.506293 0.862362i \(-0.668984\pi\)
−0.506293 + 0.862362i \(0.668984\pi\)
\(488\) 3.15729e14 0.516423
\(489\) −1.29155e14 −0.208887
\(490\) 4.21049e13 0.0673371
\(491\) −8.24882e14 −1.30450 −0.652249 0.758005i \(-0.726174\pi\)
−0.652249 + 0.758005i \(0.726174\pi\)
\(492\) −4.90955e13 −0.0767774
\(493\) 3.41944e14 0.528806
\(494\) −5.07122e14 −0.775558
\(495\) −1.06493e14 −0.161062
\(496\) −1.10570e14 −0.165382
\(497\) 1.03123e15 1.52543
\(498\) −1.77068e14 −0.259048
\(499\) 1.05005e15 1.51934 0.759670 0.650308i \(-0.225360\pi\)
0.759670 + 0.650308i \(0.225360\pi\)
\(500\) −5.02223e14 −0.718723
\(501\) −1.84062e13 −0.0260529
\(502\) 4.44773e14 0.622684
\(503\) 7.43308e14 1.02931 0.514653 0.857398i \(-0.327921\pi\)
0.514653 + 0.857398i \(0.327921\pi\)
\(504\) 2.36176e14 0.323495
\(505\) 1.55090e15 2.10127
\(506\) 1.69995e13 0.0227829
\(507\) −8.58177e14 −1.13771
\(508\) 5.23204e14 0.686153
\(509\) 4.36328e14 0.566063 0.283032 0.959111i \(-0.408660\pi\)
0.283032 + 0.959111i \(0.408660\pi\)
\(510\) 2.50975e14 0.322103
\(511\) 1.29325e15 1.64198
\(512\) 2.79731e14 0.351363
\(513\) −1.26211e14 −0.156838
\(514\) 6.55496e14 0.805885
\(515\) 3.77382e14 0.459030
\(516\) 7.35629e12 0.00885290
\(517\) 1.45251e13 0.0172951
\(518\) −4.19586e14 −0.494319
\(519\) 3.27794e14 0.382103
\(520\) 2.27110e15 2.61950
\(521\) −1.34886e15 −1.53942 −0.769712 0.638392i \(-0.779600\pi\)
−0.769712 + 0.638392i \(0.779600\pi\)
\(522\) −1.38505e14 −0.156415
\(523\) 2.29606e14 0.256580 0.128290 0.991737i \(-0.459051\pi\)
0.128290 + 0.991737i \(0.459051\pi\)
\(524\) −1.16786e15 −1.29142
\(525\) 8.95409e14 0.979818
\(526\) 8.14974e14 0.882516
\(527\) 5.38526e14 0.577096
\(528\) 2.88873e13 0.0306351
\(529\) −9.34489e14 −0.980772
\(530\) 5.67232e14 0.589174
\(531\) −4.22156e13 −0.0433963
\(532\) 5.77342e14 0.587380
\(533\) 3.27456e14 0.329726
\(534\) −1.58192e14 −0.157655
\(535\) 2.50004e15 2.46604
\(536\) −6.74040e13 −0.0658081
\(537\) −5.89815e14 −0.569977
\(538\) −5.86864e14 −0.561352
\(539\) −2.36035e13 −0.0223480
\(540\) 2.31782e14 0.217227
\(541\) 1.15412e15 1.07069 0.535347 0.844632i \(-0.320181\pi\)
0.535347 + 0.844632i \(0.320181\pi\)
\(542\) 1.25472e14 0.115226
\(543\) 1.09483e14 0.0995282
\(544\) −7.15247e14 −0.643668
\(545\) 3.86966e14 0.344740
\(546\) −6.45961e14 −0.569701
\(547\) 2.08672e15 1.82194 0.910970 0.412472i \(-0.135335\pi\)
0.910970 + 0.412472i \(0.135335\pi\)
\(548\) −6.77957e14 −0.586016
\(549\) −2.14916e14 −0.183917
\(550\) −3.17408e14 −0.268920
\(551\) −8.25664e14 −0.692579
\(552\) −9.02266e13 −0.0749324
\(553\) −2.03375e15 −1.67228
\(554\) 4.25079e14 0.346071
\(555\) −1.00417e15 −0.809457
\(556\) −7.19296e14 −0.574112
\(557\) 5.49786e14 0.434500 0.217250 0.976116i \(-0.430291\pi\)
0.217250 + 0.976116i \(0.430291\pi\)
\(558\) −2.18131e14 −0.170698
\(559\) −4.90647e13 −0.0380193
\(560\) −3.91286e14 −0.300234
\(561\) −1.40694e14 −0.106900
\(562\) −3.21985e14 −0.242262
\(563\) 1.07926e15 0.804134 0.402067 0.915610i \(-0.368292\pi\)
0.402067 + 0.915610i \(0.368292\pi\)
\(564\) −3.16140e13 −0.0233262
\(565\) 2.02580e15 1.48023
\(566\) 1.17107e15 0.847411
\(567\) −1.60764e14 −0.115208
\(568\) 1.94020e15 1.37699
\(569\) 1.60362e14 0.112716 0.0563578 0.998411i \(-0.482051\pi\)
0.0563578 + 0.998411i \(0.482051\pi\)
\(570\) −6.06009e14 −0.421859
\(571\) −2.36698e15 −1.63191 −0.815956 0.578115i \(-0.803789\pi\)
−0.815956 + 0.578115i \(0.803789\pi\)
\(572\) −5.22084e14 −0.356502
\(573\) 1.81806e14 0.122958
\(574\) 1.63506e14 0.109527
\(575\) −3.42075e14 −0.226959
\(576\) 1.99264e14 0.130950
\(577\) −1.07977e15 −0.702854 −0.351427 0.936215i \(-0.614304\pi\)
−0.351427 + 0.936215i \(0.614304\pi\)
\(578\) −5.24801e14 −0.338370
\(579\) 4.85697e14 0.310194
\(580\) 1.51631e15 0.959253
\(581\) −1.34453e15 −0.842565
\(582\) −2.43242e13 −0.0150995
\(583\) −3.17983e14 −0.195536
\(584\) 2.43319e15 1.48220
\(585\) −1.54593e15 −0.932896
\(586\) 1.83419e15 1.09650
\(587\) 2.34278e15 1.38746 0.693732 0.720233i \(-0.255965\pi\)
0.693732 + 0.720233i \(0.255965\pi\)
\(588\) 5.13730e13 0.0301411
\(589\) −1.30033e15 −0.755824
\(590\) −2.02701e14 −0.116727
\(591\) −5.75085e14 −0.328096
\(592\) 2.72390e14 0.153965
\(593\) −1.16395e14 −0.0651829 −0.0325915 0.999469i \(-0.510376\pi\)
−0.0325915 + 0.999469i \(0.510376\pi\)
\(594\) 5.69883e13 0.0316199
\(595\) 1.90573e15 1.04766
\(596\) −5.72240e14 −0.311690
\(597\) 2.10107e14 0.113392
\(598\) 2.46778e14 0.131962
\(599\) −2.24089e15 −1.18734 −0.593668 0.804710i \(-0.702321\pi\)
−0.593668 + 0.804710i \(0.702321\pi\)
\(600\) 1.68467e15 0.884471
\(601\) −1.18510e15 −0.616520 −0.308260 0.951302i \(-0.599747\pi\)
−0.308260 + 0.951302i \(0.599747\pi\)
\(602\) −2.44992e13 −0.0126291
\(603\) 4.58818e13 0.0234366
\(604\) −1.13671e15 −0.575368
\(605\) −2.95069e15 −1.48003
\(606\) −8.29944e14 −0.412524
\(607\) 3.64904e15 1.79738 0.898692 0.438581i \(-0.144519\pi\)
0.898692 + 0.438581i \(0.144519\pi\)
\(608\) 1.72705e15 0.843014
\(609\) −1.05171e15 −0.508747
\(610\) −1.03194e15 −0.494696
\(611\) 2.10858e14 0.100176
\(612\) 3.06219e14 0.144178
\(613\) −2.47416e15 −1.15450 −0.577251 0.816566i \(-0.695875\pi\)
−0.577251 + 0.816566i \(0.695875\pi\)
\(614\) 8.94734e14 0.413778
\(615\) 3.91308e14 0.179352
\(616\) −6.35715e14 −0.288781
\(617\) 2.04469e15 0.920577 0.460288 0.887769i \(-0.347746\pi\)
0.460288 + 0.887769i \(0.347746\pi\)
\(618\) −2.01950e14 −0.0901173
\(619\) 1.43884e15 0.636374 0.318187 0.948028i \(-0.396926\pi\)
0.318187 + 0.948028i \(0.396926\pi\)
\(620\) 2.38803e15 1.04685
\(621\) 6.14170e13 0.0266861
\(622\) −2.56424e14 −0.110436
\(623\) −1.20120e15 −0.512780
\(624\) 4.19349e14 0.177444
\(625\) 1.00586e14 0.0421887
\(626\) −2.34483e15 −0.974884
\(627\) 3.39721e14 0.140007
\(628\) −2.69871e15 −1.10250
\(629\) −1.32666e15 −0.537254
\(630\) −7.71921e14 −0.309884
\(631\) 1.86730e15 0.743108 0.371554 0.928411i \(-0.378825\pi\)
0.371554 + 0.928411i \(0.378825\pi\)
\(632\) −3.82641e15 −1.50955
\(633\) 2.26922e15 0.887476
\(634\) −1.88297e15 −0.730050
\(635\) −4.17012e15 −1.60285
\(636\) 6.92090e14 0.263723
\(637\) −3.42646e14 −0.129443
\(638\) 3.72815e14 0.139630
\(639\) −1.32069e15 −0.490396
\(640\) −3.60597e15 −1.32749
\(641\) −2.42900e15 −0.886561 −0.443281 0.896383i \(-0.646185\pi\)
−0.443281 + 0.896383i \(0.646185\pi\)
\(642\) −1.33786e15 −0.484136
\(643\) 1.94259e15 0.696980 0.348490 0.937313i \(-0.386695\pi\)
0.348490 + 0.937313i \(0.386695\pi\)
\(644\) −2.80948e14 −0.0999433
\(645\) −5.86322e13 −0.0206803
\(646\) −8.00630e14 −0.279997
\(647\) 2.89049e15 1.00230 0.501150 0.865360i \(-0.332910\pi\)
0.501150 + 0.865360i \(0.332910\pi\)
\(648\) −3.02471e14 −0.103997
\(649\) 1.13632e14 0.0387395
\(650\) −4.60773e15 −1.55763
\(651\) −1.65634e15 −0.555205
\(652\) −7.56653e14 −0.251498
\(653\) 4.48440e15 1.47803 0.739013 0.673691i \(-0.235292\pi\)
0.739013 + 0.673691i \(0.235292\pi\)
\(654\) −2.07079e14 −0.0676798
\(655\) 9.30822e15 3.01675
\(656\) −1.06146e14 −0.0341140
\(657\) −1.65627e15 −0.527863
\(658\) 1.05286e14 0.0332759
\(659\) 6.73335e14 0.211038 0.105519 0.994417i \(-0.466350\pi\)
0.105519 + 0.994417i \(0.466350\pi\)
\(660\) −6.23888e14 −0.193917
\(661\) −2.74625e14 −0.0846508 −0.0423254 0.999104i \(-0.513477\pi\)
−0.0423254 + 0.999104i \(0.513477\pi\)
\(662\) −3.27308e15 −1.00055
\(663\) −2.04241e15 −0.619183
\(664\) −2.52968e15 −0.760574
\(665\) −4.60161e15 −1.37212
\(666\) 5.37365e14 0.158914
\(667\) 4.01787e14 0.117843
\(668\) −1.07832e14 −0.0313674
\(669\) 7.24924e14 0.209146
\(670\) 2.20305e14 0.0630394
\(671\) 5.78490e14 0.164181
\(672\) 2.19988e15 0.619251
\(673\) −8.34894e14 −0.233103 −0.116552 0.993185i \(-0.537184\pi\)
−0.116552 + 0.993185i \(0.537184\pi\)
\(674\) 8.55438e14 0.236897
\(675\) −1.14675e15 −0.314992
\(676\) −5.02762e15 −1.36979
\(677\) 3.97083e15 1.07311 0.536554 0.843866i \(-0.319726\pi\)
0.536554 + 0.843866i \(0.319726\pi\)
\(678\) −1.08408e15 −0.290601
\(679\) −1.84701e14 −0.0491118
\(680\) 3.58555e15 0.945707
\(681\) −1.37532e15 −0.359829
\(682\) 5.87144e14 0.152381
\(683\) −1.11756e15 −0.287711 −0.143856 0.989599i \(-0.545950\pi\)
−0.143856 + 0.989599i \(0.545950\pi\)
\(684\) −7.39403e14 −0.188831
\(685\) 5.40355e15 1.36893
\(686\) 2.10699e15 0.529518
\(687\) −1.34599e14 −0.0335566
\(688\) 1.59045e13 0.00393355
\(689\) −4.61608e15 −1.13258
\(690\) 2.94898e14 0.0717798
\(691\) 1.51192e15 0.365089 0.182545 0.983198i \(-0.441567\pi\)
0.182545 + 0.983198i \(0.441567\pi\)
\(692\) 1.92038e15 0.460047
\(693\) 4.32730e14 0.102845
\(694\) −1.77270e15 −0.417983
\(695\) 5.73304e15 1.34112
\(696\) −1.97875e15 −0.459240
\(697\) 5.16978e14 0.119040
\(698\) −1.90197e15 −0.434509
\(699\) 1.52351e15 0.345320
\(700\) 5.24575e15 1.17969
\(701\) 7.06634e15 1.57669 0.788343 0.615236i \(-0.210939\pi\)
0.788343 + 0.615236i \(0.210939\pi\)
\(702\) 8.27284e14 0.183147
\(703\) 3.20337e15 0.703643
\(704\) −5.36358e14 −0.116898
\(705\) 2.51974e14 0.0544899
\(706\) −8.61144e14 −0.184778
\(707\) −6.30202e15 −1.34175
\(708\) −2.47319e14 −0.0522487
\(709\) 8.67632e15 1.81878 0.909392 0.415939i \(-0.136547\pi\)
0.909392 + 0.415939i \(0.136547\pi\)
\(710\) −6.34140e15 −1.31906
\(711\) 2.60463e15 0.537604
\(712\) −2.26000e15 −0.462881
\(713\) 6.32773e14 0.128604
\(714\) −1.01983e15 −0.205677
\(715\) 4.16119e15 0.832788
\(716\) −3.45543e15 −0.686246
\(717\) 3.96499e15 0.781424
\(718\) 3.31764e15 0.648851
\(719\) −2.70240e15 −0.524495 −0.262247 0.965001i \(-0.584464\pi\)
−0.262247 + 0.965001i \(0.584464\pi\)
\(720\) 5.01120e14 0.0965191
\(721\) −1.53347e15 −0.293111
\(722\) −9.77612e14 −0.185444
\(723\) −1.68481e13 −0.00317169
\(724\) 6.41403e14 0.119831
\(725\) −7.50201e15 −1.39097
\(726\) 1.57902e15 0.290561
\(727\) 3.41265e15 0.623236 0.311618 0.950207i \(-0.399129\pi\)
0.311618 + 0.950207i \(0.399129\pi\)
\(728\) −9.22851e15 −1.67266
\(729\) 2.05891e14 0.0370370
\(730\) −7.95269e15 −1.41984
\(731\) −7.74620e13 −0.0137260
\(732\) −1.25908e15 −0.221434
\(733\) −9.45746e15 −1.65083 −0.825416 0.564525i \(-0.809059\pi\)
−0.825416 + 0.564525i \(0.809059\pi\)
\(734\) −1.01566e15 −0.175962
\(735\) −4.09461e14 −0.0704096
\(736\) −8.40422e14 −0.143440
\(737\) −1.23500e14 −0.0209217
\(738\) −2.09403e14 −0.0352106
\(739\) 2.54064e14 0.0424033 0.0212016 0.999775i \(-0.493251\pi\)
0.0212016 + 0.999775i \(0.493251\pi\)
\(740\) −5.88289e15 −0.974578
\(741\) 4.93165e15 0.810946
\(742\) −2.30492e15 −0.376214
\(743\) −8.07197e15 −1.30780 −0.653900 0.756581i \(-0.726868\pi\)
−0.653900 + 0.756581i \(0.726868\pi\)
\(744\) −3.11633e15 −0.501178
\(745\) 4.56095e15 0.728108
\(746\) 4.00034e15 0.633918
\(747\) 1.72195e15 0.270867
\(748\) −8.24252e14 −0.128707
\(749\) −1.01588e16 −1.57468
\(750\) −2.14209e15 −0.329610
\(751\) 4.23375e15 0.646705 0.323352 0.946279i \(-0.395190\pi\)
0.323352 + 0.946279i \(0.395190\pi\)
\(752\) −6.83504e13 −0.0103644
\(753\) −4.32531e15 −0.651096
\(754\) 5.41205e15 0.808760
\(755\) 9.05995e15 1.34406
\(756\) −9.41835e14 −0.138709
\(757\) 8.54159e15 1.24885 0.624427 0.781083i \(-0.285333\pi\)
0.624427 + 0.781083i \(0.285333\pi\)
\(758\) −1.71959e15 −0.249600
\(759\) −1.65316e14 −0.0238224
\(760\) −8.65773e15 −1.23859
\(761\) −7.25893e15 −1.03100 −0.515498 0.856891i \(-0.672393\pi\)
−0.515498 + 0.856891i \(0.672393\pi\)
\(762\) 2.23158e15 0.314673
\(763\) −1.57242e15 −0.220132
\(764\) 1.06511e15 0.148040
\(765\) −2.44067e15 −0.336800
\(766\) 2.92767e15 0.401110
\(767\) 1.64956e15 0.224385
\(768\) 3.60907e15 0.487426
\(769\) −9.20046e15 −1.23371 −0.616857 0.787075i \(-0.711595\pi\)
−0.616857 + 0.787075i \(0.711595\pi\)
\(770\) 2.07778e15 0.276631
\(771\) −6.37455e15 −0.842656
\(772\) 2.84545e15 0.373470
\(773\) 1.01836e16 1.32713 0.663565 0.748118i \(-0.269043\pi\)
0.663565 + 0.748118i \(0.269043\pi\)
\(774\) 3.13762e13 0.00405999
\(775\) −1.18149e16 −1.51799
\(776\) −3.47507e14 −0.0443327
\(777\) 4.08038e15 0.516874
\(778\) −6.21915e15 −0.782245
\(779\) −1.24830e15 −0.155906
\(780\) −9.05683e15 −1.12320
\(781\) 3.55491e15 0.437772
\(782\) 3.89606e14 0.0476418
\(783\) 1.34693e15 0.163552
\(784\) 1.11070e14 0.0133924
\(785\) 2.15096e16 2.57543
\(786\) −4.98116e15 −0.592252
\(787\) −1.49460e16 −1.76467 −0.882336 0.470620i \(-0.844030\pi\)
−0.882336 + 0.470620i \(0.844030\pi\)
\(788\) −3.36913e15 −0.395024
\(789\) −7.92544e15 −0.922783
\(790\) 1.25063e16 1.44604
\(791\) −8.23174e15 −0.945194
\(792\) 8.14161e14 0.0928372
\(793\) 8.39780e15 0.950961
\(794\) −9.43836e15 −1.06141
\(795\) −5.51620e15 −0.616057
\(796\) 1.23091e15 0.136523
\(797\) −1.60985e16 −1.77323 −0.886613 0.462512i \(-0.846948\pi\)
−0.886613 + 0.462512i \(0.846948\pi\)
\(798\) 2.46249e15 0.269376
\(799\) 3.32896e14 0.0361661
\(800\) 1.56920e16 1.69310
\(801\) 1.53838e15 0.164848
\(802\) 2.83990e15 0.302234
\(803\) 4.45818e15 0.471218
\(804\) 2.68798e14 0.0282174
\(805\) 2.23925e15 0.233467
\(806\) 8.52342e15 0.882615
\(807\) 5.70712e15 0.586965
\(808\) −1.18570e16 −1.21119
\(809\) 1.31507e16 1.33424 0.667119 0.744951i \(-0.267527\pi\)
0.667119 + 0.744951i \(0.267527\pi\)
\(810\) 9.88601e14 0.0996216
\(811\) 1.83930e16 1.84093 0.920466 0.390823i \(-0.127809\pi\)
0.920466 + 0.390823i \(0.127809\pi\)
\(812\) −6.16144e15 −0.612526
\(813\) −1.22019e15 −0.120484
\(814\) −1.44643e15 −0.141861
\(815\) 6.03078e15 0.587499
\(816\) 6.62056e14 0.0640618
\(817\) 1.87041e14 0.0179770
\(818\) 2.98279e15 0.284760
\(819\) 6.28182e15 0.595695
\(820\) 2.29247e15 0.215938
\(821\) 2.16713e15 0.202768 0.101384 0.994847i \(-0.467673\pi\)
0.101384 + 0.994847i \(0.467673\pi\)
\(822\) −2.89164e15 −0.268750
\(823\) −1.42522e16 −1.31578 −0.657891 0.753113i \(-0.728551\pi\)
−0.657891 + 0.753113i \(0.728551\pi\)
\(824\) −2.88516e15 −0.264588
\(825\) 3.08672e15 0.281190
\(826\) 8.23666e14 0.0745351
\(827\) 1.02767e16 0.923789 0.461894 0.886935i \(-0.347170\pi\)
0.461894 + 0.886935i \(0.347170\pi\)
\(828\) 3.59811e14 0.0321298
\(829\) −1.09609e16 −0.972290 −0.486145 0.873878i \(-0.661597\pi\)
−0.486145 + 0.873878i \(0.661597\pi\)
\(830\) 8.26806e15 0.728575
\(831\) −4.13379e15 −0.361862
\(832\) −7.78617e15 −0.677089
\(833\) −5.40960e14 −0.0467323
\(834\) −3.06796e15 −0.263291
\(835\) 8.59461e14 0.0732741
\(836\) 1.99025e15 0.168567
\(837\) 2.12128e15 0.178487
\(838\) 7.17920e15 0.600115
\(839\) −3.71803e15 −0.308761 −0.154380 0.988011i \(-0.549338\pi\)
−0.154380 + 0.988011i \(0.549338\pi\)
\(840\) −1.10280e16 −0.909833
\(841\) −3.38895e15 −0.277771
\(842\) 8.12402e15 0.661537
\(843\) 3.13123e15 0.253316
\(844\) 1.32942e16 1.06851
\(845\) 4.00719e16 3.19983
\(846\) −1.34840e14 −0.0106975
\(847\) 1.19900e16 0.945063
\(848\) 1.49632e15 0.117178
\(849\) −1.13884e16 −0.886077
\(850\) −7.27455e15 −0.562344
\(851\) −1.55883e15 −0.119726
\(852\) −7.73726e15 −0.590432
\(853\) −1.95258e16 −1.48043 −0.740216 0.672370i \(-0.765277\pi\)
−0.740216 + 0.672370i \(0.765277\pi\)
\(854\) 4.19322e15 0.315885
\(855\) 5.89330e15 0.441108
\(856\) −1.91133e16 −1.42144
\(857\) 2.10648e16 1.55655 0.778275 0.627924i \(-0.216095\pi\)
0.778275 + 0.627924i \(0.216095\pi\)
\(858\) −2.22680e15 −0.163494
\(859\) 4.27980e15 0.312220 0.156110 0.987740i \(-0.450105\pi\)
0.156110 + 0.987740i \(0.450105\pi\)
\(860\) −3.43496e14 −0.0248989
\(861\) −1.59006e15 −0.114524
\(862\) 1.02782e16 0.735574
\(863\) −1.94699e16 −1.38454 −0.692270 0.721639i \(-0.743389\pi\)
−0.692270 + 0.721639i \(0.743389\pi\)
\(864\) −2.81739e15 −0.199077
\(865\) −1.53061e16 −1.07467
\(866\) 6.26285e14 0.0436942
\(867\) 5.10357e15 0.353809
\(868\) −9.70364e15 −0.668461
\(869\) −7.01088e15 −0.479914
\(870\) 6.46738e15 0.439919
\(871\) −1.79282e15 −0.121182
\(872\) −2.95843e15 −0.198711
\(873\) 2.36547e14 0.0157884
\(874\) −9.40749e14 −0.0623966
\(875\) −1.62656e16 −1.07207
\(876\) −9.70323e15 −0.635541
\(877\) −1.03948e16 −0.676580 −0.338290 0.941042i \(-0.609849\pi\)
−0.338290 + 0.941042i \(0.609849\pi\)
\(878\) 2.45089e15 0.158527
\(879\) −1.78371e16 −1.14653
\(880\) −1.34887e15 −0.0861617
\(881\) −1.97751e16 −1.25531 −0.627654 0.778492i \(-0.715985\pi\)
−0.627654 + 0.778492i \(0.715985\pi\)
\(882\) 2.19117e14 0.0138229
\(883\) 9.09389e15 0.570120 0.285060 0.958510i \(-0.407987\pi\)
0.285060 + 0.958510i \(0.407987\pi\)
\(884\) −1.19654e16 −0.745490
\(885\) 1.97122e15 0.122053
\(886\) −5.54136e15 −0.340982
\(887\) −2.81999e15 −0.172452 −0.0862259 0.996276i \(-0.527481\pi\)
−0.0862259 + 0.996276i \(0.527481\pi\)
\(888\) 7.67705e15 0.466577
\(889\) 1.69451e16 1.02349
\(890\) 7.38664e15 0.443406
\(891\) −5.54198e14 −0.0330626
\(892\) 4.24696e15 0.251809
\(893\) −8.03818e14 −0.0473669
\(894\) −2.44073e15 −0.142943
\(895\) 2.75409e16 1.60307
\(896\) 1.46527e16 0.847663
\(897\) −2.39986e15 −0.137983
\(898\) −4.18812e15 −0.239331
\(899\) 1.38773e16 0.788182
\(900\) −6.71824e15 −0.379247
\(901\) −7.28774e15 −0.408890
\(902\) 5.63651e14 0.0314321
\(903\) 2.38249e14 0.0132053
\(904\) −1.54876e16 −0.853216
\(905\) −5.11220e15 −0.279924
\(906\) −4.84831e15 −0.263867
\(907\) 4.87855e15 0.263907 0.131953 0.991256i \(-0.457875\pi\)
0.131953 + 0.991256i \(0.457875\pi\)
\(908\) −8.05732e15 −0.433230
\(909\) 8.07101e15 0.431347
\(910\) 3.01626e16 1.60229
\(911\) 2.85112e16 1.50545 0.752723 0.658337i \(-0.228740\pi\)
0.752723 + 0.658337i \(0.228740\pi\)
\(912\) −1.59861e15 −0.0839019
\(913\) −4.63497e15 −0.241801
\(914\) −1.66586e16 −0.863840
\(915\) 1.00353e16 0.517268
\(916\) −7.88545e14 −0.0404018
\(917\) −3.78235e16 −1.92633
\(918\) 1.30609e15 0.0661210
\(919\) −1.16794e16 −0.587741 −0.293870 0.955845i \(-0.594943\pi\)
−0.293870 + 0.955845i \(0.594943\pi\)
\(920\) 4.21306e15 0.210748
\(921\) −8.70108e15 −0.432658
\(922\) −1.27389e16 −0.629667
\(923\) 5.16058e16 2.53565
\(924\) 2.53514e15 0.123824
\(925\) 2.91059e16 1.41319
\(926\) 2.95907e14 0.0142822
\(927\) 1.96392e15 0.0942292
\(928\) −1.84312e16 −0.879103
\(929\) −9.14172e14 −0.0433453 −0.0216726 0.999765i \(-0.506899\pi\)
−0.0216726 + 0.999765i \(0.506899\pi\)
\(930\) 1.01855e16 0.480092
\(931\) 1.30621e15 0.0612055
\(932\) 8.92548e15 0.415761
\(933\) 2.49366e15 0.115475
\(934\) −1.96425e16 −0.904252
\(935\) 6.56957e15 0.300658
\(936\) 1.18190e16 0.537728
\(937\) −3.46960e16 −1.56932 −0.784661 0.619925i \(-0.787163\pi\)
−0.784661 + 0.619925i \(0.787163\pi\)
\(938\) −8.95198e14 −0.0402535
\(939\) 2.28030e16 1.01937
\(940\) 1.47619e15 0.0656053
\(941\) 1.95869e16 0.865413 0.432707 0.901535i \(-0.357559\pi\)
0.432707 + 0.901535i \(0.357559\pi\)
\(942\) −1.15106e16 −0.505612
\(943\) 6.07454e14 0.0265277
\(944\) −5.34713e14 −0.0232153
\(945\) 7.50675e15 0.324024
\(946\) −8.44554e13 −0.00362432
\(947\) 1.54606e16 0.659631 0.329816 0.944045i \(-0.393013\pi\)
0.329816 + 0.944045i \(0.393013\pi\)
\(948\) 1.52592e16 0.647270
\(949\) 6.47183e16 2.72937
\(950\) 1.75653e16 0.736504
\(951\) 1.83115e16 0.763361
\(952\) −1.45697e16 −0.603876
\(953\) −2.84619e16 −1.17288 −0.586439 0.809994i \(-0.699470\pi\)
−0.586439 + 0.809994i \(0.699470\pi\)
\(954\) 2.95192e15 0.120945
\(955\) −8.48927e15 −0.345821
\(956\) 2.32289e16 0.940826
\(957\) −3.62554e15 −0.146001
\(958\) −8.61031e15 −0.344754
\(959\) −2.19571e16 −0.874123
\(960\) −9.30445e15 −0.368298
\(961\) −3.55319e15 −0.139843
\(962\) −2.09974e16 −0.821681
\(963\) 1.30104e16 0.506227
\(964\) −9.87045e13 −0.00381868
\(965\) −2.26792e16 −0.872425
\(966\) −1.19831e15 −0.0458346
\(967\) 3.63956e16 1.38421 0.692106 0.721796i \(-0.256683\pi\)
0.692106 + 0.721796i \(0.256683\pi\)
\(968\) 2.25587e16 0.853098
\(969\) 7.78594e15 0.292773
\(970\) 1.13580e15 0.0424675
\(971\) −4.89750e15 −0.182083 −0.0910414 0.995847i \(-0.529020\pi\)
−0.0910414 + 0.995847i \(0.529020\pi\)
\(972\) 1.20621e15 0.0445922
\(973\) −2.32959e16 −0.856366
\(974\) −1.52956e16 −0.559105
\(975\) 4.48091e16 1.62870
\(976\) −2.72218e15 −0.0983882
\(977\) −7.30223e15 −0.262443 −0.131222 0.991353i \(-0.541890\pi\)
−0.131222 + 0.991353i \(0.541890\pi\)
\(978\) −3.22729e15 −0.115338
\(979\) −4.14086e15 −0.147159
\(980\) −2.39882e15 −0.0847724
\(981\) 2.01380e15 0.0707679
\(982\) −2.06119e16 −0.720287
\(983\) 2.87349e16 0.998541 0.499271 0.866446i \(-0.333601\pi\)
0.499271 + 0.866446i \(0.333601\pi\)
\(984\) −2.99163e15 −0.103380
\(985\) 2.68531e16 0.922774
\(986\) 8.54440e15 0.291984
\(987\) −1.02389e15 −0.0347942
\(988\) 2.88920e16 0.976370
\(989\) −9.10187e13 −0.00305880
\(990\) −2.66102e15 −0.0889313
\(991\) 4.57403e16 1.52018 0.760089 0.649820i \(-0.225156\pi\)
0.760089 + 0.649820i \(0.225156\pi\)
\(992\) −2.90272e16 −0.959382
\(993\) 3.18299e16 1.04620
\(994\) 2.57680e16 0.842278
\(995\) −9.81079e15 −0.318917
\(996\) 1.00880e16 0.326122
\(997\) 5.16771e16 1.66140 0.830701 0.556719i \(-0.187940\pi\)
0.830701 + 0.556719i \(0.187940\pi\)
\(998\) 2.62383e16 0.838914
\(999\) −5.22575e15 −0.166165
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.1.18 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.18 27 1.1 even 1 trivial