Properties

Label 177.12.a.a.1.12
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $26$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(1\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-16.5456 q^{2} -243.000 q^{3} -1774.24 q^{4} +2844.36 q^{5} +4020.58 q^{6} +41460.7 q^{7} +63241.3 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-16.5456 q^{2} -243.000 q^{3} -1774.24 q^{4} +2844.36 q^{5} +4020.58 q^{6} +41460.7 q^{7} +63241.3 q^{8} +59049.0 q^{9} -47061.6 q^{10} +49404.8 q^{11} +431141. q^{12} -2.15805e6 q^{13} -685992. q^{14} -691179. q^{15} +2.58728e6 q^{16} +2.16906e6 q^{17} -977001. q^{18} +7.65694e6 q^{19} -5.04658e6 q^{20} -1.00749e7 q^{21} -817432. q^{22} -2.58011e7 q^{23} -1.53676e7 q^{24} -4.07377e7 q^{25} +3.57062e7 q^{26} -1.43489e7 q^{27} -7.35613e7 q^{28} -5.29779e7 q^{29} +1.14360e7 q^{30} -7.09513e6 q^{31} -1.72326e8 q^{32} -1.20054e7 q^{33} -3.58884e7 q^{34} +1.17929e8 q^{35} -1.04767e8 q^{36} +1.02432e7 q^{37} -1.26689e8 q^{38} +5.24405e8 q^{39} +1.79881e8 q^{40} +1.31085e9 q^{41} +1.66696e8 q^{42} +1.41318e9 q^{43} -8.76561e7 q^{44} +1.67957e8 q^{45} +4.26895e8 q^{46} -9.75486e8 q^{47} -6.28710e8 q^{48} -2.58341e8 q^{49} +6.74031e8 q^{50} -5.27081e8 q^{51} +3.82890e9 q^{52} -9.42664e8 q^{53} +2.37411e8 q^{54} +1.40525e8 q^{55} +2.62203e9 q^{56} -1.86064e9 q^{57} +8.76551e8 q^{58} +7.14924e8 q^{59} +1.22632e9 q^{60} +7.22349e9 q^{61} +1.17393e8 q^{62} +2.44821e9 q^{63} -2.44751e9 q^{64} -6.13826e9 q^{65} +1.98636e8 q^{66} +1.55270e10 q^{67} -3.84844e9 q^{68} +6.26966e9 q^{69} -1.95121e9 q^{70} +1.91439e10 q^{71} +3.73434e9 q^{72} -1.37117e10 q^{73} -1.69481e8 q^{74} +9.89927e9 q^{75} -1.35853e10 q^{76} +2.04835e9 q^{77} -8.67660e9 q^{78} -3.29619e9 q^{79} +7.35916e9 q^{80} +3.48678e9 q^{81} -2.16889e10 q^{82} -6.18447e10 q^{83} +1.78754e10 q^{84} +6.16958e9 q^{85} -2.33819e10 q^{86} +1.28736e10 q^{87} +3.12442e9 q^{88} +7.94446e10 q^{89} -2.77894e9 q^{90} -8.94740e10 q^{91} +4.57774e10 q^{92} +1.72412e9 q^{93} +1.61400e10 q^{94} +2.17791e10 q^{95} +4.18753e10 q^{96} -1.08245e11 q^{97} +4.27441e9 q^{98} +2.91730e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.5456 −0.365610 −0.182805 0.983149i \(-0.558518\pi\)
−0.182805 + 0.983149i \(0.558518\pi\)
\(3\) −243.000 −0.577350
\(4\) −1774.24 −0.866330
\(5\) 2844.36 0.407051 0.203526 0.979070i \(-0.434760\pi\)
0.203526 + 0.979070i \(0.434760\pi\)
\(6\) 4020.58 0.211085
\(7\) 41460.7 0.932388 0.466194 0.884682i \(-0.345625\pi\)
0.466194 + 0.884682i \(0.345625\pi\)
\(8\) 63241.3 0.682348
\(9\) 59049.0 0.333333
\(10\) −47061.6 −0.148822
\(11\) 49404.8 0.0924931 0.0462465 0.998930i \(-0.485274\pi\)
0.0462465 + 0.998930i \(0.485274\pi\)
\(12\) 431141. 0.500176
\(13\) −2.15805e6 −1.61203 −0.806013 0.591898i \(-0.798379\pi\)
−0.806013 + 0.591898i \(0.798379\pi\)
\(14\) −685992. −0.340890
\(15\) −691179. −0.235011
\(16\) 2.58728e6 0.616856
\(17\) 2.16906e6 0.370512 0.185256 0.982690i \(-0.440689\pi\)
0.185256 + 0.982690i \(0.440689\pi\)
\(18\) −977001. −0.121870
\(19\) 7.65694e6 0.709431 0.354716 0.934974i \(-0.384578\pi\)
0.354716 + 0.934974i \(0.384578\pi\)
\(20\) −5.04658e6 −0.352641
\(21\) −1.00749e7 −0.538315
\(22\) −817432. −0.0338164
\(23\) −2.58011e7 −0.835863 −0.417931 0.908479i \(-0.637245\pi\)
−0.417931 + 0.908479i \(0.637245\pi\)
\(24\) −1.53676e7 −0.393954
\(25\) −4.07377e7 −0.834309
\(26\) 3.57062e7 0.589372
\(27\) −1.43489e7 −0.192450
\(28\) −7.35613e7 −0.807756
\(29\) −5.29779e7 −0.479629 −0.239814 0.970819i \(-0.577087\pi\)
−0.239814 + 0.970819i \(0.577087\pi\)
\(30\) 1.14360e7 0.0859224
\(31\) −7.09513e6 −0.0445114 −0.0222557 0.999752i \(-0.507085\pi\)
−0.0222557 + 0.999752i \(0.507085\pi\)
\(32\) −1.72326e8 −0.907877
\(33\) −1.20054e7 −0.0534009
\(34\) −3.58884e7 −0.135463
\(35\) 1.17929e8 0.379530
\(36\) −1.04767e8 −0.288777
\(37\) 1.02432e7 0.0242844 0.0121422 0.999926i \(-0.496135\pi\)
0.0121422 + 0.999926i \(0.496135\pi\)
\(38\) −1.26689e8 −0.259375
\(39\) 5.24405e8 0.930704
\(40\) 1.79881e8 0.277751
\(41\) 1.31085e9 1.76703 0.883514 0.468405i \(-0.155171\pi\)
0.883514 + 0.468405i \(0.155171\pi\)
\(42\) 1.66696e8 0.196813
\(43\) 1.41318e9 1.46595 0.732977 0.680253i \(-0.238130\pi\)
0.732977 + 0.680253i \(0.238130\pi\)
\(44\) −8.76561e7 −0.0801295
\(45\) 1.67957e8 0.135684
\(46\) 4.26895e8 0.305599
\(47\) −9.75486e8 −0.620416 −0.310208 0.950669i \(-0.600399\pi\)
−0.310208 + 0.950669i \(0.600399\pi\)
\(48\) −6.28710e8 −0.356142
\(49\) −2.58341e8 −0.130652
\(50\) 6.74031e8 0.305031
\(51\) −5.27081e8 −0.213915
\(52\) 3.82890e9 1.39655
\(53\) −9.42664e8 −0.309628 −0.154814 0.987944i \(-0.549478\pi\)
−0.154814 + 0.987944i \(0.549478\pi\)
\(54\) 2.37411e8 0.0703616
\(55\) 1.40525e8 0.0376494
\(56\) 2.62203e9 0.636214
\(57\) −1.86064e9 −0.409590
\(58\) 8.76551e8 0.175357
\(59\) 7.14924e8 0.130189
\(60\) 1.22632e9 0.203597
\(61\) 7.22349e9 1.09505 0.547524 0.836790i \(-0.315571\pi\)
0.547524 + 0.836790i \(0.315571\pi\)
\(62\) 1.17393e8 0.0162738
\(63\) 2.44821e9 0.310796
\(64\) −2.44751e9 −0.284928
\(65\) −6.13826e9 −0.656178
\(66\) 1.98636e8 0.0195239
\(67\) 1.55270e10 1.40500 0.702500 0.711684i \(-0.252067\pi\)
0.702500 + 0.711684i \(0.252067\pi\)
\(68\) −3.84844e9 −0.320985
\(69\) 6.26966e9 0.482585
\(70\) −1.95121e9 −0.138760
\(71\) 1.91439e10 1.25924 0.629621 0.776902i \(-0.283210\pi\)
0.629621 + 0.776902i \(0.283210\pi\)
\(72\) 3.73434e9 0.227449
\(73\) −1.37117e10 −0.774134 −0.387067 0.922052i \(-0.626512\pi\)
−0.387067 + 0.922052i \(0.626512\pi\)
\(74\) −1.69481e8 −0.00887863
\(75\) 9.89927e9 0.481689
\(76\) −1.35853e10 −0.614601
\(77\) 2.04835e9 0.0862395
\(78\) −8.67660e9 −0.340274
\(79\) −3.29619e9 −0.120521 −0.0602605 0.998183i \(-0.519193\pi\)
−0.0602605 + 0.998183i \(0.519193\pi\)
\(80\) 7.35916e9 0.251092
\(81\) 3.48678e9 0.111111
\(82\) −2.16889e10 −0.646043
\(83\) −6.18447e10 −1.72335 −0.861674 0.507462i \(-0.830584\pi\)
−0.861674 + 0.507462i \(0.830584\pi\)
\(84\) 1.78754e10 0.466358
\(85\) 6.16958e9 0.150817
\(86\) −2.33819e10 −0.535967
\(87\) 1.28736e10 0.276914
\(88\) 3.12442e9 0.0631125
\(89\) 7.94446e10 1.50806 0.754032 0.656838i \(-0.228107\pi\)
0.754032 + 0.656838i \(0.228107\pi\)
\(90\) −2.77894e9 −0.0496073
\(91\) −8.94740e10 −1.50303
\(92\) 4.57774e10 0.724132
\(93\) 1.72412e9 0.0256987
\(94\) 1.61400e10 0.226830
\(95\) 2.17791e10 0.288775
\(96\) 4.18753e10 0.524163
\(97\) −1.08245e11 −1.27987 −0.639933 0.768431i \(-0.721038\pi\)
−0.639933 + 0.768431i \(0.721038\pi\)
\(98\) 4.27441e9 0.0477675
\(99\) 2.91730e9 0.0308310
\(100\) 7.22787e10 0.722787
\(101\) −1.15397e11 −1.09252 −0.546259 0.837616i \(-0.683949\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(102\) 8.72088e9 0.0782094
\(103\) 8.55381e10 0.727034 0.363517 0.931588i \(-0.381576\pi\)
0.363517 + 0.931588i \(0.381576\pi\)
\(104\) −1.36478e11 −1.09996
\(105\) −2.86567e10 −0.219122
\(106\) 1.55970e10 0.113203
\(107\) −1.05757e10 −0.0728949 −0.0364475 0.999336i \(-0.511604\pi\)
−0.0364475 + 0.999336i \(0.511604\pi\)
\(108\) 2.54584e10 0.166725
\(109\) 2.13576e11 1.32956 0.664779 0.747040i \(-0.268526\pi\)
0.664779 + 0.747040i \(0.268526\pi\)
\(110\) −2.32507e9 −0.0137650
\(111\) −2.48911e9 −0.0140206
\(112\) 1.07270e11 0.575150
\(113\) −2.24026e11 −1.14385 −0.571923 0.820307i \(-0.693803\pi\)
−0.571923 + 0.820307i \(0.693803\pi\)
\(114\) 3.07854e10 0.149750
\(115\) −7.33875e10 −0.340239
\(116\) 9.39956e10 0.415517
\(117\) −1.27430e11 −0.537342
\(118\) −1.18289e10 −0.0475983
\(119\) 8.99306e10 0.345461
\(120\) −4.37111e10 −0.160360
\(121\) −2.82871e11 −0.991445
\(122\) −1.19517e11 −0.400360
\(123\) −3.18538e11 −1.02019
\(124\) 1.25885e10 0.0385615
\(125\) −2.54757e11 −0.746658
\(126\) −4.05071e10 −0.113630
\(127\) −8.92835e10 −0.239801 −0.119900 0.992786i \(-0.538258\pi\)
−0.119900 + 0.992786i \(0.538258\pi\)
\(128\) 3.93420e11 1.01205
\(129\) −3.43402e11 −0.846369
\(130\) 1.01561e11 0.239905
\(131\) 1.39957e11 0.316958 0.158479 0.987362i \(-0.449341\pi\)
0.158479 + 0.987362i \(0.449341\pi\)
\(132\) 2.13004e10 0.0462628
\(133\) 3.17462e11 0.661466
\(134\) −2.56904e11 −0.513682
\(135\) −4.08134e10 −0.0783371
\(136\) 1.37174e11 0.252818
\(137\) −5.16655e11 −0.914613 −0.457306 0.889309i \(-0.651186\pi\)
−0.457306 + 0.889309i \(0.651186\pi\)
\(138\) −1.03735e11 −0.176438
\(139\) 6.30410e11 1.03049 0.515243 0.857044i \(-0.327702\pi\)
0.515243 + 0.857044i \(0.327702\pi\)
\(140\) −2.09235e11 −0.328798
\(141\) 2.37043e11 0.358197
\(142\) −3.16747e11 −0.460391
\(143\) −1.06618e11 −0.149101
\(144\) 1.52777e11 0.205619
\(145\) −1.50688e11 −0.195234
\(146\) 2.26869e11 0.283031
\(147\) 6.27769e10 0.0754318
\(148\) −1.81740e10 −0.0210383
\(149\) −9.13502e10 −0.101903 −0.0509513 0.998701i \(-0.516225\pi\)
−0.0509513 + 0.998701i \(0.516225\pi\)
\(150\) −1.63789e11 −0.176110
\(151\) 9.49321e11 0.984102 0.492051 0.870566i \(-0.336247\pi\)
0.492051 + 0.870566i \(0.336247\pi\)
\(152\) 4.84235e11 0.484079
\(153\) 1.28081e11 0.123504
\(154\) −3.38913e10 −0.0315300
\(155\) −2.01811e10 −0.0181184
\(156\) −9.30422e11 −0.806296
\(157\) 1.26333e11 0.105698 0.0528491 0.998603i \(-0.483170\pi\)
0.0528491 + 0.998603i \(0.483170\pi\)
\(158\) 5.45374e10 0.0440636
\(159\) 2.29067e11 0.178764
\(160\) −4.90158e11 −0.369553
\(161\) −1.06973e12 −0.779349
\(162\) −5.76910e10 −0.0406233
\(163\) −1.75646e12 −1.19566 −0.597828 0.801625i \(-0.703969\pi\)
−0.597828 + 0.801625i \(0.703969\pi\)
\(164\) −2.32577e12 −1.53083
\(165\) −3.41475e10 −0.0217369
\(166\) 1.02326e12 0.630073
\(167\) −8.26293e11 −0.492259 −0.246129 0.969237i \(-0.579159\pi\)
−0.246129 + 0.969237i \(0.579159\pi\)
\(168\) −6.37152e11 −0.367318
\(169\) 2.86500e12 1.59863
\(170\) −1.02079e11 −0.0551403
\(171\) 4.52135e11 0.236477
\(172\) −2.50732e12 −1.27000
\(173\) −1.77758e12 −0.872118 −0.436059 0.899918i \(-0.643626\pi\)
−0.436059 + 0.899918i \(0.643626\pi\)
\(174\) −2.13002e11 −0.101242
\(175\) −1.68901e12 −0.777900
\(176\) 1.27824e11 0.0570549
\(177\) −1.73727e11 −0.0751646
\(178\) −1.31446e12 −0.551363
\(179\) −3.18380e12 −1.29495 −0.647477 0.762085i \(-0.724176\pi\)
−0.647477 + 0.762085i \(0.724176\pi\)
\(180\) −2.97996e11 −0.117547
\(181\) −6.48052e11 −0.247958 −0.123979 0.992285i \(-0.539565\pi\)
−0.123979 + 0.992285i \(0.539565\pi\)
\(182\) 1.48040e12 0.549524
\(183\) −1.75531e12 −0.632226
\(184\) −1.63169e12 −0.570349
\(185\) 2.91355e10 0.00988502
\(186\) −2.85266e10 −0.00939568
\(187\) 1.07162e11 0.0342698
\(188\) 1.73075e12 0.537484
\(189\) −5.94915e11 −0.179438
\(190\) −3.60348e11 −0.105579
\(191\) 6.04436e11 0.172055 0.0860274 0.996293i \(-0.472583\pi\)
0.0860274 + 0.996293i \(0.472583\pi\)
\(192\) 5.94745e11 0.164503
\(193\) −6.09808e12 −1.63919 −0.819593 0.572947i \(-0.805800\pi\)
−0.819593 + 0.572947i \(0.805800\pi\)
\(194\) 1.79098e12 0.467931
\(195\) 1.49160e12 0.378844
\(196\) 4.58360e11 0.113187
\(197\) −3.12704e12 −0.750878 −0.375439 0.926847i \(-0.622508\pi\)
−0.375439 + 0.926847i \(0.622508\pi\)
\(198\) −4.82685e10 −0.0112721
\(199\) 7.35466e11 0.167059 0.0835297 0.996505i \(-0.473381\pi\)
0.0835297 + 0.996505i \(0.473381\pi\)
\(200\) −2.57631e12 −0.569289
\(201\) −3.77306e12 −0.811177
\(202\) 1.90932e12 0.399435
\(203\) −2.19650e12 −0.447201
\(204\) 9.35170e11 0.185321
\(205\) 3.72854e12 0.719271
\(206\) −1.41528e12 −0.265811
\(207\) −1.52353e12 −0.278621
\(208\) −5.58348e12 −0.994389
\(209\) 3.78289e11 0.0656175
\(210\) 4.74143e11 0.0801131
\(211\) −3.01668e12 −0.496564 −0.248282 0.968688i \(-0.579866\pi\)
−0.248282 + 0.968688i \(0.579866\pi\)
\(212\) 1.67252e12 0.268240
\(213\) −4.65196e12 −0.727024
\(214\) 1.74981e11 0.0266511
\(215\) 4.01959e12 0.596719
\(216\) −9.07444e11 −0.131318
\(217\) −2.94169e11 −0.0415019
\(218\) −3.53375e12 −0.486099
\(219\) 3.33195e12 0.446947
\(220\) −2.49325e11 −0.0326168
\(221\) −4.68093e12 −0.597275
\(222\) 4.11838e10 0.00512608
\(223\) 2.13109e12 0.258776 0.129388 0.991594i \(-0.458699\pi\)
0.129388 + 0.991594i \(0.458699\pi\)
\(224\) −7.14477e12 −0.846494
\(225\) −2.40552e12 −0.278103
\(226\) 3.70665e12 0.418201
\(227\) 1.14890e13 1.26515 0.632573 0.774501i \(-0.281999\pi\)
0.632573 + 0.774501i \(0.281999\pi\)
\(228\) 3.30122e12 0.354840
\(229\) −1.83816e13 −1.92881 −0.964404 0.264432i \(-0.914816\pi\)
−0.964404 + 0.264432i \(0.914816\pi\)
\(230\) 1.21424e12 0.124395
\(231\) −4.97750e11 −0.0497904
\(232\) −3.35039e12 −0.327274
\(233\) −7.86981e12 −0.750769 −0.375385 0.926869i \(-0.622489\pi\)
−0.375385 + 0.926869i \(0.622489\pi\)
\(234\) 2.10841e12 0.196457
\(235\) −2.77463e12 −0.252541
\(236\) −1.26845e12 −0.112787
\(237\) 8.00973e11 0.0695828
\(238\) −1.48796e12 −0.126304
\(239\) 1.67805e12 0.139193 0.0695964 0.997575i \(-0.477829\pi\)
0.0695964 + 0.997575i \(0.477829\pi\)
\(240\) −1.78828e12 −0.144968
\(241\) 9.79471e12 0.776064 0.388032 0.921646i \(-0.373155\pi\)
0.388032 + 0.921646i \(0.373155\pi\)
\(242\) 4.68027e12 0.362482
\(243\) −8.47289e11 −0.0641500
\(244\) −1.28162e13 −0.948672
\(245\) −7.34815e11 −0.0531820
\(246\) 5.27040e12 0.372993
\(247\) −1.65240e13 −1.14362
\(248\) −4.48705e11 −0.0303723
\(249\) 1.50283e13 0.994975
\(250\) 4.21512e12 0.272985
\(251\) 7.32224e12 0.463915 0.231957 0.972726i \(-0.425487\pi\)
0.231957 + 0.972726i \(0.425487\pi\)
\(252\) −4.34372e12 −0.269252
\(253\) −1.27470e12 −0.0773115
\(254\) 1.47725e12 0.0876735
\(255\) −1.49921e12 −0.0870745
\(256\) −1.49687e12 −0.0850872
\(257\) 2.22220e13 1.23637 0.618187 0.786031i \(-0.287867\pi\)
0.618187 + 0.786031i \(0.287867\pi\)
\(258\) 5.68180e12 0.309441
\(259\) 4.24692e11 0.0226425
\(260\) 1.08908e13 0.568466
\(261\) −3.12829e12 −0.159876
\(262\) −2.31567e12 −0.115883
\(263\) 1.95089e13 0.956039 0.478020 0.878349i \(-0.341355\pi\)
0.478020 + 0.878349i \(0.341355\pi\)
\(264\) −7.59235e11 −0.0364380
\(265\) −2.68128e12 −0.126034
\(266\) −5.25260e12 −0.241838
\(267\) −1.93050e13 −0.870681
\(268\) −2.75487e13 −1.21719
\(269\) −9.39033e12 −0.406484 −0.203242 0.979129i \(-0.565148\pi\)
−0.203242 + 0.979129i \(0.565148\pi\)
\(270\) 6.75283e11 0.0286408
\(271\) −9.28184e12 −0.385747 −0.192874 0.981224i \(-0.561781\pi\)
−0.192874 + 0.981224i \(0.561781\pi\)
\(272\) 5.61197e12 0.228553
\(273\) 2.17422e13 0.867778
\(274\) 8.54836e12 0.334391
\(275\) −2.01264e12 −0.0771678
\(276\) −1.11239e13 −0.418078
\(277\) −2.18617e13 −0.805463 −0.402731 0.915318i \(-0.631939\pi\)
−0.402731 + 0.915318i \(0.631939\pi\)
\(278\) −1.04305e13 −0.376755
\(279\) −4.18960e11 −0.0148371
\(280\) 7.45798e12 0.258972
\(281\) 1.68565e13 0.573962 0.286981 0.957936i \(-0.407348\pi\)
0.286981 + 0.957936i \(0.407348\pi\)
\(282\) −3.92202e12 −0.130960
\(283\) −5.37145e13 −1.75900 −0.879500 0.475899i \(-0.842123\pi\)
−0.879500 + 0.475899i \(0.842123\pi\)
\(284\) −3.39659e13 −1.09092
\(285\) −5.29232e12 −0.166724
\(286\) 1.76406e12 0.0545129
\(287\) 5.43489e13 1.64756
\(288\) −1.01757e13 −0.302626
\(289\) −2.95671e13 −0.862721
\(290\) 2.49322e12 0.0713793
\(291\) 2.63036e13 0.738931
\(292\) 2.43279e13 0.670655
\(293\) −4.19452e13 −1.13478 −0.567388 0.823451i \(-0.692046\pi\)
−0.567388 + 0.823451i \(0.692046\pi\)
\(294\) −1.03868e12 −0.0275786
\(295\) 2.03350e12 0.0529936
\(296\) 6.47797e11 0.0165704
\(297\) −7.08905e11 −0.0178003
\(298\) 1.51144e12 0.0372565
\(299\) 5.56799e13 1.34743
\(300\) −1.75637e13 −0.417301
\(301\) 5.85913e13 1.36684
\(302\) −1.57071e13 −0.359797
\(303\) 2.80416e13 0.630766
\(304\) 1.98107e13 0.437617
\(305\) 2.05462e13 0.445741
\(306\) −2.11917e12 −0.0451542
\(307\) 1.16139e13 0.243063 0.121531 0.992588i \(-0.461220\pi\)
0.121531 + 0.992588i \(0.461220\pi\)
\(308\) −3.63428e12 −0.0747118
\(309\) −2.07858e13 −0.419753
\(310\) 3.33908e11 0.00662427
\(311\) −2.32744e13 −0.453624 −0.226812 0.973939i \(-0.572830\pi\)
−0.226812 + 0.973939i \(0.572830\pi\)
\(312\) 3.31641e13 0.635064
\(313\) −3.25730e13 −0.612863 −0.306432 0.951893i \(-0.599135\pi\)
−0.306432 + 0.951893i \(0.599135\pi\)
\(314\) −2.09025e12 −0.0386443
\(315\) 6.96359e12 0.126510
\(316\) 5.84823e12 0.104411
\(317\) −1.66067e13 −0.291378 −0.145689 0.989330i \(-0.546540\pi\)
−0.145689 + 0.989330i \(0.546540\pi\)
\(318\) −3.79006e12 −0.0653577
\(319\) −2.61736e12 −0.0443624
\(320\) −6.96160e12 −0.115980
\(321\) 2.56989e12 0.0420859
\(322\) 1.76993e13 0.284937
\(323\) 1.66083e13 0.262853
\(324\) −6.18640e12 −0.0962588
\(325\) 8.79139e13 1.34493
\(326\) 2.90617e13 0.437143
\(327\) −5.18990e13 −0.767621
\(328\) 8.29002e13 1.20573
\(329\) −4.04443e13 −0.578468
\(330\) 5.64992e11 0.00794723
\(331\) 8.26670e13 1.14361 0.571805 0.820389i \(-0.306243\pi\)
0.571805 + 0.820389i \(0.306243\pi\)
\(332\) 1.09728e14 1.49299
\(333\) 6.04854e11 0.00809482
\(334\) 1.36715e13 0.179975
\(335\) 4.41644e13 0.571907
\(336\) −2.60667e13 −0.332063
\(337\) −4.67427e13 −0.585800 −0.292900 0.956143i \(-0.594620\pi\)
−0.292900 + 0.956143i \(0.594620\pi\)
\(338\) −4.74032e13 −0.584474
\(339\) 5.44384e13 0.660400
\(340\) −1.09463e13 −0.130658
\(341\) −3.50533e11 −0.00411699
\(342\) −7.48084e12 −0.0864583
\(343\) −9.26922e13 −1.05421
\(344\) 8.93713e13 1.00029
\(345\) 1.78332e13 0.196437
\(346\) 2.94111e13 0.318855
\(347\) 1.56968e14 1.67494 0.837469 0.546485i \(-0.184034\pi\)
0.837469 + 0.546485i \(0.184034\pi\)
\(348\) −2.28409e13 −0.239899
\(349\) 7.50899e13 0.776322 0.388161 0.921592i \(-0.373110\pi\)
0.388161 + 0.921592i \(0.373110\pi\)
\(350\) 2.79458e13 0.284408
\(351\) 3.09656e13 0.310235
\(352\) −8.51375e12 −0.0839723
\(353\) 1.15618e14 1.12270 0.561350 0.827579i \(-0.310282\pi\)
0.561350 + 0.827579i \(0.310282\pi\)
\(354\) 2.87441e12 0.0274809
\(355\) 5.44521e13 0.512576
\(356\) −1.40954e14 −1.30648
\(357\) −2.18531e13 −0.199452
\(358\) 5.26779e13 0.473448
\(359\) −1.55424e14 −1.37562 −0.687811 0.725890i \(-0.741428\pi\)
−0.687811 + 0.725890i \(0.741428\pi\)
\(360\) 1.06218e13 0.0925836
\(361\) −5.78615e13 −0.496707
\(362\) 1.07224e13 0.0906557
\(363\) 6.87376e13 0.572411
\(364\) 1.58749e14 1.30212
\(365\) −3.90011e13 −0.315112
\(366\) 2.90426e13 0.231148
\(367\) −1.54518e14 −1.21148 −0.605739 0.795663i \(-0.707123\pi\)
−0.605739 + 0.795663i \(0.707123\pi\)
\(368\) −6.67547e13 −0.515607
\(369\) 7.74047e13 0.589009
\(370\) −4.82064e11 −0.00361406
\(371\) −3.90835e13 −0.288693
\(372\) −3.05900e12 −0.0222635
\(373\) −1.43977e14 −1.03251 −0.516256 0.856434i \(-0.672675\pi\)
−0.516256 + 0.856434i \(0.672675\pi\)
\(374\) −1.77306e12 −0.0125294
\(375\) 6.19061e13 0.431083
\(376\) −6.16910e13 −0.423340
\(377\) 1.14329e14 0.773175
\(378\) 9.84323e12 0.0656044
\(379\) −1.71279e14 −1.12509 −0.562547 0.826765i \(-0.690179\pi\)
−0.562547 + 0.826765i \(0.690179\pi\)
\(380\) −3.86414e13 −0.250174
\(381\) 2.16959e13 0.138449
\(382\) −1.00008e13 −0.0629049
\(383\) −5.17030e13 −0.320570 −0.160285 0.987071i \(-0.551241\pi\)
−0.160285 + 0.987071i \(0.551241\pi\)
\(384\) −9.56011e13 −0.584307
\(385\) 5.82625e12 0.0351039
\(386\) 1.00896e14 0.599302
\(387\) 8.34468e13 0.488651
\(388\) 1.92053e14 1.10879
\(389\) 1.07061e14 0.609407 0.304704 0.952447i \(-0.401443\pi\)
0.304704 + 0.952447i \(0.401443\pi\)
\(390\) −2.46794e13 −0.138509
\(391\) −5.59640e13 −0.309697
\(392\) −1.63378e13 −0.0891499
\(393\) −3.40095e13 −0.182996
\(394\) 5.17388e13 0.274528
\(395\) −9.37553e12 −0.0490582
\(396\) −5.17600e12 −0.0267098
\(397\) 1.22203e14 0.621919 0.310959 0.950423i \(-0.399350\pi\)
0.310959 + 0.950423i \(0.399350\pi\)
\(398\) −1.21687e13 −0.0610785
\(399\) −7.71432e13 −0.381897
\(400\) −1.05400e14 −0.514649
\(401\) 2.29196e14 1.10386 0.551928 0.833892i \(-0.313892\pi\)
0.551928 + 0.833892i \(0.313892\pi\)
\(402\) 6.24276e13 0.296574
\(403\) 1.53116e13 0.0717535
\(404\) 2.04743e14 0.946481
\(405\) 9.91766e12 0.0452279
\(406\) 3.63424e13 0.163501
\(407\) 5.06065e11 0.00224614
\(408\) −3.33333e13 −0.145965
\(409\) −2.66904e14 −1.15313 −0.576563 0.817053i \(-0.695606\pi\)
−0.576563 + 0.817053i \(0.695606\pi\)
\(410\) −6.16910e13 −0.262973
\(411\) 1.25547e14 0.528052
\(412\) −1.51765e14 −0.629851
\(413\) 2.96412e13 0.121387
\(414\) 2.52077e13 0.101866
\(415\) −1.75908e14 −0.701491
\(416\) 3.71888e14 1.46352
\(417\) −1.53190e14 −0.594951
\(418\) −6.25903e12 −0.0239904
\(419\) −2.26201e14 −0.855693 −0.427846 0.903852i \(-0.640728\pi\)
−0.427846 + 0.903852i \(0.640728\pi\)
\(420\) 5.08440e13 0.189832
\(421\) −2.91017e14 −1.07243 −0.536213 0.844083i \(-0.680146\pi\)
−0.536213 + 0.844083i \(0.680146\pi\)
\(422\) 4.99128e13 0.181549
\(423\) −5.76015e13 −0.206805
\(424\) −5.96154e13 −0.211274
\(425\) −8.83625e13 −0.309121
\(426\) 7.69696e13 0.265807
\(427\) 2.99491e14 1.02101
\(428\) 1.87638e13 0.0631510
\(429\) 2.59081e13 0.0860837
\(430\) −6.65065e13 −0.218166
\(431\) 5.44197e14 1.76251 0.881254 0.472644i \(-0.156700\pi\)
0.881254 + 0.472644i \(0.156700\pi\)
\(432\) −3.71247e13 −0.118714
\(433\) −2.85221e14 −0.900531 −0.450265 0.892895i \(-0.648671\pi\)
−0.450265 + 0.892895i \(0.648671\pi\)
\(434\) 4.86720e12 0.0151735
\(435\) 3.66172e13 0.112718
\(436\) −3.78936e14 −1.15184
\(437\) −1.97557e14 −0.592987
\(438\) −5.51291e13 −0.163408
\(439\) 3.89958e14 1.14147 0.570733 0.821135i \(-0.306659\pi\)
0.570733 + 0.821135i \(0.306659\pi\)
\(440\) 8.88698e12 0.0256900
\(441\) −1.52548e13 −0.0435506
\(442\) 7.74488e13 0.218369
\(443\) −4.51653e14 −1.25772 −0.628861 0.777518i \(-0.716479\pi\)
−0.628861 + 0.777518i \(0.716479\pi\)
\(444\) 4.41628e12 0.0121465
\(445\) 2.25969e14 0.613859
\(446\) −3.52601e13 −0.0946110
\(447\) 2.21981e13 0.0588334
\(448\) −1.01475e14 −0.265663
\(449\) −1.64956e14 −0.426592 −0.213296 0.976988i \(-0.568420\pi\)
−0.213296 + 0.976988i \(0.568420\pi\)
\(450\) 3.98008e13 0.101677
\(451\) 6.47625e13 0.163438
\(452\) 3.97477e14 0.990948
\(453\) −2.30685e14 −0.568172
\(454\) −1.90093e14 −0.462549
\(455\) −2.54496e14 −0.611813
\(456\) −1.17669e14 −0.279483
\(457\) 6.44813e14 1.51319 0.756597 0.653882i \(-0.226861\pi\)
0.756597 + 0.653882i \(0.226861\pi\)
\(458\) 3.04135e14 0.705191
\(459\) −3.11236e13 −0.0713050
\(460\) 1.30207e14 0.294759
\(461\) −2.06718e14 −0.462405 −0.231202 0.972906i \(-0.574266\pi\)
−0.231202 + 0.972906i \(0.574266\pi\)
\(462\) 8.23558e12 0.0182038
\(463\) −3.31636e14 −0.724380 −0.362190 0.932104i \(-0.617971\pi\)
−0.362190 + 0.932104i \(0.617971\pi\)
\(464\) −1.37069e14 −0.295862
\(465\) 4.90401e12 0.0104607
\(466\) 1.30211e14 0.274489
\(467\) 6.31321e14 1.31525 0.657623 0.753347i \(-0.271562\pi\)
0.657623 + 0.753347i \(0.271562\pi\)
\(468\) 2.26093e14 0.465515
\(469\) 6.43760e14 1.31001
\(470\) 4.59080e13 0.0923315
\(471\) −3.06988e13 −0.0610249
\(472\) 4.52128e13 0.0888342
\(473\) 6.98177e13 0.135591
\(474\) −1.32526e13 −0.0254402
\(475\) −3.11926e14 −0.591885
\(476\) −1.59559e14 −0.299283
\(477\) −5.56634e13 −0.103209
\(478\) −2.77644e13 −0.0508902
\(479\) 2.58208e14 0.467869 0.233935 0.972252i \(-0.424840\pi\)
0.233935 + 0.972252i \(0.424840\pi\)
\(480\) 1.19108e14 0.213361
\(481\) −2.21054e13 −0.0391472
\(482\) −1.62059e14 −0.283737
\(483\) 2.59944e14 0.449957
\(484\) 5.01882e14 0.858918
\(485\) −3.07888e14 −0.520971
\(486\) 1.40189e13 0.0234539
\(487\) −7.53305e14 −1.24613 −0.623063 0.782172i \(-0.714112\pi\)
−0.623063 + 0.782172i \(0.714112\pi\)
\(488\) 4.56823e14 0.747204
\(489\) 4.26819e14 0.690312
\(490\) 1.21580e13 0.0194438
\(491\) −8.96454e14 −1.41769 −0.708843 0.705367i \(-0.750782\pi\)
−0.708843 + 0.705367i \(0.750782\pi\)
\(492\) 5.65163e14 0.883824
\(493\) −1.14912e14 −0.177708
\(494\) 2.73400e14 0.418119
\(495\) 8.29785e12 0.0125498
\(496\) −1.83571e13 −0.0274571
\(497\) 7.93718e14 1.17410
\(498\) −2.48652e14 −0.363773
\(499\) −1.31048e15 −1.89617 −0.948086 0.318014i \(-0.896984\pi\)
−0.948086 + 0.318014i \(0.896984\pi\)
\(500\) 4.52002e14 0.646852
\(501\) 2.00789e14 0.284206
\(502\) −1.21151e14 −0.169612
\(503\) 5.74181e14 0.795106 0.397553 0.917579i \(-0.369859\pi\)
0.397553 + 0.917579i \(0.369859\pi\)
\(504\) 1.54828e14 0.212071
\(505\) −3.28232e14 −0.444711
\(506\) 2.10906e13 0.0282658
\(507\) −6.96195e14 −0.922969
\(508\) 1.58411e14 0.207746
\(509\) −9.19197e14 −1.19251 −0.596254 0.802796i \(-0.703345\pi\)
−0.596254 + 0.802796i \(0.703345\pi\)
\(510\) 2.48053e13 0.0318353
\(511\) −5.68497e14 −0.721794
\(512\) −7.80958e14 −0.980941
\(513\) −1.09869e14 −0.136530
\(514\) −3.67676e14 −0.452031
\(515\) 2.43301e14 0.295940
\(516\) 6.09279e14 0.733234
\(517\) −4.81937e13 −0.0573841
\(518\) −7.02678e12 −0.00827833
\(519\) 4.31952e14 0.503518
\(520\) −3.88191e14 −0.447742
\(521\) −1.39135e15 −1.58792 −0.793958 0.607973i \(-0.791983\pi\)
−0.793958 + 0.607973i \(0.791983\pi\)
\(522\) 5.17594e13 0.0584523
\(523\) −3.26568e14 −0.364933 −0.182467 0.983212i \(-0.558408\pi\)
−0.182467 + 0.983212i \(0.558408\pi\)
\(524\) −2.48317e14 −0.274590
\(525\) 4.10430e14 0.449121
\(526\) −3.22786e14 −0.349537
\(527\) −1.53897e13 −0.0164920
\(528\) −3.10613e13 −0.0329407
\(529\) −2.87114e14 −0.301334
\(530\) 4.43633e13 0.0460794
\(531\) 4.22156e13 0.0433963
\(532\) −5.63254e14 −0.573047
\(533\) −2.82888e15 −2.84850
\(534\) 3.19414e14 0.318329
\(535\) −3.00810e13 −0.0296720
\(536\) 9.81949e14 0.958700
\(537\) 7.73664e14 0.747642
\(538\) 1.55369e14 0.148614
\(539\) −1.27633e13 −0.0120844
\(540\) 7.24129e13 0.0678657
\(541\) −5.99446e14 −0.556115 −0.278058 0.960564i \(-0.589691\pi\)
−0.278058 + 0.960564i \(0.589691\pi\)
\(542\) 1.53574e14 0.141033
\(543\) 1.57477e14 0.143158
\(544\) −3.73786e14 −0.336379
\(545\) 6.07488e14 0.541199
\(546\) −3.59737e14 −0.317268
\(547\) −7.46132e14 −0.651456 −0.325728 0.945463i \(-0.605609\pi\)
−0.325728 + 0.945463i \(0.605609\pi\)
\(548\) 9.16671e14 0.792356
\(549\) 4.26540e14 0.365016
\(550\) 3.33003e13 0.0282133
\(551\) −4.05648e14 −0.340264
\(552\) 3.96502e14 0.329291
\(553\) −1.36662e14 −0.112372
\(554\) 3.61715e14 0.294485
\(555\) −7.07992e12 −0.00570712
\(556\) −1.11850e15 −0.892740
\(557\) 1.38536e15 1.09486 0.547432 0.836850i \(-0.315605\pi\)
0.547432 + 0.836850i \(0.315605\pi\)
\(558\) 6.93195e12 0.00542460
\(559\) −3.04970e15 −2.36316
\(560\) 3.05116e14 0.234116
\(561\) −2.60403e13 −0.0197857
\(562\) −2.78901e14 −0.209846
\(563\) −7.17447e14 −0.534557 −0.267278 0.963619i \(-0.586124\pi\)
−0.267278 + 0.963619i \(0.586124\pi\)
\(564\) −4.20572e14 −0.310317
\(565\) −6.37211e14 −0.465604
\(566\) 8.88738e14 0.643107
\(567\) 1.44564e14 0.103599
\(568\) 1.21068e15 0.859241
\(569\) −3.65447e14 −0.256866 −0.128433 0.991718i \(-0.540995\pi\)
−0.128433 + 0.991718i \(0.540995\pi\)
\(570\) 8.75646e13 0.0609560
\(571\) −8.60431e14 −0.593222 −0.296611 0.954998i \(-0.595857\pi\)
−0.296611 + 0.954998i \(0.595857\pi\)
\(572\) 1.89166e14 0.129171
\(573\) −1.46878e14 −0.0993359
\(574\) −8.99235e14 −0.602363
\(575\) 1.05108e15 0.697368
\(576\) −1.44523e14 −0.0949760
\(577\) −2.43951e15 −1.58795 −0.793974 0.607952i \(-0.791991\pi\)
−0.793974 + 0.607952i \(0.791991\pi\)
\(578\) 4.89205e14 0.315419
\(579\) 1.48183e15 0.946384
\(580\) 2.67357e14 0.169137
\(581\) −2.56412e15 −1.60683
\(582\) −4.35209e14 −0.270160
\(583\) −4.65721e13 −0.0286384
\(584\) −8.67148e14 −0.528229
\(585\) −3.62458e14 −0.218726
\(586\) 6.94008e14 0.414885
\(587\) −2.16572e15 −1.28261 −0.641303 0.767288i \(-0.721606\pi\)
−0.641303 + 0.767288i \(0.721606\pi\)
\(588\) −1.11381e14 −0.0653488
\(589\) −5.43270e13 −0.0315778
\(590\) −3.36455e13 −0.0193750
\(591\) 7.59871e14 0.433520
\(592\) 2.65022e13 0.0149800
\(593\) −2.96460e15 −1.66022 −0.830110 0.557599i \(-0.811723\pi\)
−0.830110 + 0.557599i \(0.811723\pi\)
\(594\) 1.17293e13 0.00650796
\(595\) 2.55795e14 0.140620
\(596\) 1.62077e14 0.0882812
\(597\) −1.78718e14 −0.0964518
\(598\) −9.21258e14 −0.492634
\(599\) −1.93205e14 −0.102369 −0.0511847 0.998689i \(-0.516300\pi\)
−0.0511847 + 0.998689i \(0.516300\pi\)
\(600\) 6.26043e14 0.328679
\(601\) 1.00117e15 0.520835 0.260418 0.965496i \(-0.416140\pi\)
0.260418 + 0.965496i \(0.416140\pi\)
\(602\) −9.69428e14 −0.499729
\(603\) 9.16855e14 0.468333
\(604\) −1.68433e15 −0.852557
\(605\) −8.04586e14 −0.403569
\(606\) −4.63965e14 −0.230614
\(607\) −1.85054e15 −0.911509 −0.455754 0.890106i \(-0.650630\pi\)
−0.455754 + 0.890106i \(0.650630\pi\)
\(608\) −1.31949e15 −0.644076
\(609\) 5.33749e14 0.258191
\(610\) −3.39949e14 −0.162967
\(611\) 2.10514e15 1.00013
\(612\) −2.27246e14 −0.106995
\(613\) 1.13216e15 0.528292 0.264146 0.964483i \(-0.414910\pi\)
0.264146 + 0.964483i \(0.414910\pi\)
\(614\) −1.92159e14 −0.0888660
\(615\) −9.06036e14 −0.415271
\(616\) 1.29541e14 0.0588453
\(617\) 2.96469e15 1.33478 0.667392 0.744707i \(-0.267411\pi\)
0.667392 + 0.744707i \(0.267411\pi\)
\(618\) 3.43913e14 0.153466
\(619\) −1.13102e15 −0.500234 −0.250117 0.968216i \(-0.580469\pi\)
−0.250117 + 0.968216i \(0.580469\pi\)
\(620\) 3.58062e13 0.0156965
\(621\) 3.70217e14 0.160862
\(622\) 3.85089e14 0.165849
\(623\) 3.29383e15 1.40610
\(624\) 1.35678e15 0.574111
\(625\) 1.26453e15 0.530381
\(626\) 5.38940e14 0.224069
\(627\) −9.19243e13 −0.0378843
\(628\) −2.24145e14 −0.0915695
\(629\) 2.22182e13 0.00899767
\(630\) −1.15217e14 −0.0462533
\(631\) −2.46195e15 −0.979755 −0.489878 0.871791i \(-0.662959\pi\)
−0.489878 + 0.871791i \(0.662959\pi\)
\(632\) −2.08455e14 −0.0822373
\(633\) 7.33053e14 0.286691
\(634\) 2.74768e14 0.106531
\(635\) −2.53954e14 −0.0976112
\(636\) −4.06421e14 −0.154868
\(637\) 5.57512e14 0.210614
\(638\) 4.33058e13 0.0162193
\(639\) 1.13043e15 0.419747
\(640\) 1.11903e15 0.411956
\(641\) 1.10162e15 0.402082 0.201041 0.979583i \(-0.435568\pi\)
0.201041 + 0.979583i \(0.435568\pi\)
\(642\) −4.25204e13 −0.0153870
\(643\) −5.45536e14 −0.195733 −0.0978664 0.995200i \(-0.531202\pi\)
−0.0978664 + 0.995200i \(0.531202\pi\)
\(644\) 1.89796e15 0.675173
\(645\) −9.76759e14 −0.344516
\(646\) −2.74795e14 −0.0961015
\(647\) 6.85317e14 0.237639 0.118820 0.992916i \(-0.462089\pi\)
0.118820 + 0.992916i \(0.462089\pi\)
\(648\) 2.20509e14 0.0758165
\(649\) 3.53207e13 0.0120416
\(650\) −1.45459e15 −0.491719
\(651\) 7.14830e13 0.0239611
\(652\) 3.11638e15 1.03583
\(653\) 4.88769e15 1.61095 0.805473 0.592633i \(-0.201912\pi\)
0.805473 + 0.592633i \(0.201912\pi\)
\(654\) 8.58701e14 0.280650
\(655\) 3.98087e14 0.129018
\(656\) 3.39155e15 1.09000
\(657\) −8.09664e14 −0.258045
\(658\) 6.69175e14 0.211494
\(659\) 2.33955e15 0.733268 0.366634 0.930365i \(-0.380510\pi\)
0.366634 + 0.930365i \(0.380510\pi\)
\(660\) 6.05860e13 0.0188313
\(661\) 9.05484e14 0.279108 0.139554 0.990214i \(-0.455433\pi\)
0.139554 + 0.990214i \(0.455433\pi\)
\(662\) −1.36778e15 −0.418115
\(663\) 1.13746e15 0.344837
\(664\) −3.91114e15 −1.17592
\(665\) 9.02975e14 0.269251
\(666\) −1.00077e13 −0.00295954
\(667\) 1.36689e15 0.400904
\(668\) 1.46604e15 0.426458
\(669\) −5.17854e14 −0.149404
\(670\) −7.30727e14 −0.209095
\(671\) 3.56875e14 0.101284
\(672\) 1.73618e15 0.488724
\(673\) 4.27924e15 1.19477 0.597384 0.801956i \(-0.296207\pi\)
0.597384 + 0.801956i \(0.296207\pi\)
\(674\) 7.73387e14 0.214174
\(675\) 5.84542e14 0.160563
\(676\) −5.08321e15 −1.38494
\(677\) 1.05288e14 0.0284537 0.0142269 0.999899i \(-0.495471\pi\)
0.0142269 + 0.999899i \(0.495471\pi\)
\(678\) −9.00717e14 −0.241449
\(679\) −4.48792e15 −1.19333
\(680\) 3.90172e14 0.102910
\(681\) −2.79183e15 −0.730432
\(682\) 5.79979e12 0.00150521
\(683\) 7.50102e15 1.93111 0.965554 0.260202i \(-0.0837891\pi\)
0.965554 + 0.260202i \(0.0837891\pi\)
\(684\) −8.02197e14 −0.204867
\(685\) −1.46955e15 −0.372294
\(686\) 1.53365e15 0.385428
\(687\) 4.46674e15 1.11360
\(688\) 3.65629e15 0.904283
\(689\) 2.03431e15 0.499128
\(690\) −2.95061e14 −0.0718193
\(691\) 3.16800e15 0.764990 0.382495 0.923957i \(-0.375065\pi\)
0.382495 + 0.923957i \(0.375065\pi\)
\(692\) 3.15386e15 0.755542
\(693\) 1.20953e14 0.0287465
\(694\) −2.59713e15 −0.612374
\(695\) 1.79311e15 0.419461
\(696\) 8.14145e14 0.188952
\(697\) 2.84332e15 0.654705
\(698\) −1.24241e15 −0.283831
\(699\) 1.91236e15 0.433457
\(700\) 2.99672e15 0.673918
\(701\) −3.78543e15 −0.844628 −0.422314 0.906449i \(-0.638782\pi\)
−0.422314 + 0.906449i \(0.638782\pi\)
\(702\) −5.12345e14 −0.113425
\(703\) 7.84319e13 0.0172281
\(704\) −1.20919e14 −0.0263539
\(705\) 6.74235e14 0.145805
\(706\) −1.91296e15 −0.410470
\(707\) −4.78445e15 −1.01865
\(708\) 3.08233e14 0.0651173
\(709\) −8.63490e15 −1.81010 −0.905051 0.425303i \(-0.860167\pi\)
−0.905051 + 0.425303i \(0.860167\pi\)
\(710\) −9.00943e14 −0.187403
\(711\) −1.94636e14 −0.0401737
\(712\) 5.02418e15 1.02902
\(713\) 1.83062e14 0.0372054
\(714\) 3.61573e14 0.0729216
\(715\) −3.03259e14 −0.0606919
\(716\) 5.64884e15 1.12186
\(717\) −4.07767e14 −0.0803630
\(718\) 2.57159e15 0.502941
\(719\) −7.12634e15 −1.38311 −0.691557 0.722322i \(-0.743075\pi\)
−0.691557 + 0.722322i \(0.743075\pi\)
\(720\) 4.34551e14 0.0836974
\(721\) 3.54646e15 0.677878
\(722\) 9.57354e14 0.181601
\(723\) −2.38011e15 −0.448061
\(724\) 1.14980e15 0.214813
\(725\) 2.15820e15 0.400159
\(726\) −1.13731e15 −0.209279
\(727\) −4.80671e15 −0.877826 −0.438913 0.898529i \(-0.644636\pi\)
−0.438913 + 0.898529i \(0.644636\pi\)
\(728\) −5.65845e15 −1.02559
\(729\) 2.05891e14 0.0370370
\(730\) 6.45296e14 0.115208
\(731\) 3.06526e15 0.543153
\(732\) 3.11434e15 0.547716
\(733\) 4.93840e15 0.862015 0.431007 0.902348i \(-0.358158\pi\)
0.431007 + 0.902348i \(0.358158\pi\)
\(734\) 2.55659e15 0.442928
\(735\) 1.78560e14 0.0307046
\(736\) 4.44621e15 0.758860
\(737\) 7.67109e14 0.129953
\(738\) −1.28071e15 −0.215348
\(739\) 1.12139e16 1.87160 0.935798 0.352536i \(-0.114680\pi\)
0.935798 + 0.352536i \(0.114680\pi\)
\(740\) −5.16934e13 −0.00856368
\(741\) 4.01534e15 0.660271
\(742\) 6.46660e14 0.105549
\(743\) −9.98430e15 −1.61763 −0.808815 0.588064i \(-0.799890\pi\)
−0.808815 + 0.588064i \(0.799890\pi\)
\(744\) 1.09035e14 0.0175354
\(745\) −2.59833e14 −0.0414796
\(746\) 2.38219e15 0.377497
\(747\) −3.65187e15 −0.574449
\(748\) −1.90131e14 −0.0296889
\(749\) −4.38474e14 −0.0679664
\(750\) −1.02427e15 −0.157608
\(751\) −9.54628e15 −1.45819 −0.729096 0.684412i \(-0.760059\pi\)
−0.729096 + 0.684412i \(0.760059\pi\)
\(752\) −2.52386e15 −0.382707
\(753\) −1.77930e15 −0.267841
\(754\) −1.89164e15 −0.282680
\(755\) 2.70021e15 0.400580
\(756\) 1.05552e15 0.155453
\(757\) −5.84451e15 −0.854517 −0.427258 0.904130i \(-0.640520\pi\)
−0.427258 + 0.904130i \(0.640520\pi\)
\(758\) 2.83392e15 0.411345
\(759\) 3.09751e14 0.0446358
\(760\) 1.37734e15 0.197045
\(761\) −3.51497e14 −0.0499236 −0.0249618 0.999688i \(-0.507946\pi\)
−0.0249618 + 0.999688i \(0.507946\pi\)
\(762\) −3.58971e14 −0.0506183
\(763\) 8.85501e15 1.23966
\(764\) −1.07242e15 −0.149056
\(765\) 3.64307e14 0.0502725
\(766\) 8.55458e14 0.117203
\(767\) −1.54284e15 −0.209868
\(768\) 3.63739e14 0.0491251
\(769\) −2.12882e15 −0.285459 −0.142730 0.989762i \(-0.545588\pi\)
−0.142730 + 0.989762i \(0.545588\pi\)
\(770\) −9.63989e13 −0.0128343
\(771\) −5.39994e15 −0.713821
\(772\) 1.08195e16 1.42007
\(773\) 1.51816e16 1.97848 0.989240 0.146303i \(-0.0467374\pi\)
0.989240 + 0.146303i \(0.0467374\pi\)
\(774\) −1.38068e15 −0.178656
\(775\) 2.89040e14 0.0371362
\(776\) −6.84557e15 −0.873314
\(777\) −1.03200e14 −0.0130727
\(778\) −1.77139e15 −0.222805
\(779\) 1.00371e16 1.25359
\(780\) −2.64645e15 −0.328204
\(781\) 9.45799e14 0.116471
\(782\) 9.25959e14 0.113228
\(783\) 7.60174e14 0.0923046
\(784\) −6.68402e14 −0.0805933
\(785\) 3.59335e14 0.0430246
\(786\) 5.62708e14 0.0669051
\(787\) −2.45701e15 −0.290099 −0.145050 0.989424i \(-0.546334\pi\)
−0.145050 + 0.989424i \(0.546334\pi\)
\(788\) 5.54813e15 0.650508
\(789\) −4.74066e15 −0.551969
\(790\) 1.55124e14 0.0179362
\(791\) −9.28828e15 −1.06651
\(792\) 1.84494e14 0.0210375
\(793\) −1.55886e16 −1.76525
\(794\) −2.02192e15 −0.227380
\(795\) 6.51550e14 0.0727660
\(796\) −1.30490e15 −0.144728
\(797\) −8.50843e15 −0.937192 −0.468596 0.883413i \(-0.655240\pi\)
−0.468596 + 0.883413i \(0.655240\pi\)
\(798\) 1.27638e15 0.139625
\(799\) −2.11589e15 −0.229871
\(800\) 7.02019e15 0.757450
\(801\) 4.69113e15 0.502688
\(802\) −3.79218e15 −0.403580
\(803\) −6.77425e14 −0.0716021
\(804\) 6.69433e15 0.702747
\(805\) −3.04270e15 −0.317235
\(806\) −2.53340e14 −0.0262338
\(807\) 2.28185e15 0.234684
\(808\) −7.29789e15 −0.745478
\(809\) 7.02046e15 0.712276 0.356138 0.934433i \(-0.384093\pi\)
0.356138 + 0.934433i \(0.384093\pi\)
\(810\) −1.64094e14 −0.0165358
\(811\) −1.72598e16 −1.72752 −0.863758 0.503907i \(-0.831895\pi\)
−0.863758 + 0.503907i \(0.831895\pi\)
\(812\) 3.89712e15 0.387423
\(813\) 2.25549e15 0.222711
\(814\) −8.37316e12 −0.000821212 0
\(815\) −4.99600e15 −0.486693
\(816\) −1.36371e15 −0.131955
\(817\) 1.08206e16 1.03999
\(818\) 4.41609e15 0.421594
\(819\) −5.28335e15 −0.501012
\(820\) −6.61534e15 −0.623126
\(821\) −1.53967e16 −1.44059 −0.720295 0.693668i \(-0.755993\pi\)
−0.720295 + 0.693668i \(0.755993\pi\)
\(822\) −2.07725e15 −0.193061
\(823\) 8.63994e15 0.797649 0.398824 0.917027i \(-0.369418\pi\)
0.398824 + 0.917027i \(0.369418\pi\)
\(824\) 5.40954e15 0.496090
\(825\) 4.89071e14 0.0445529
\(826\) −4.90432e14 −0.0443801
\(827\) 2.35190e15 0.211416 0.105708 0.994397i \(-0.466289\pi\)
0.105708 + 0.994397i \(0.466289\pi\)
\(828\) 2.70311e15 0.241377
\(829\) 1.30697e16 1.15935 0.579677 0.814847i \(-0.303179\pi\)
0.579677 + 0.814847i \(0.303179\pi\)
\(830\) 2.91051e15 0.256472
\(831\) 5.31240e15 0.465034
\(832\) 5.28184e15 0.459311
\(833\) −5.60357e14 −0.0484080
\(834\) 2.53462e15 0.217520
\(835\) −2.35027e15 −0.200375
\(836\) −6.71177e14 −0.0568464
\(837\) 1.01807e14 0.00856622
\(838\) 3.74264e15 0.312850
\(839\) −2.20551e15 −0.183155 −0.0915776 0.995798i \(-0.529191\pi\)
−0.0915776 + 0.995798i \(0.529191\pi\)
\(840\) −1.81229e15 −0.149517
\(841\) −9.39386e15 −0.769956
\(842\) 4.81506e15 0.392089
\(843\) −4.09613e15 −0.331377
\(844\) 5.35232e15 0.430188
\(845\) 8.14909e15 0.650724
\(846\) 9.53051e14 0.0756100
\(847\) −1.17280e16 −0.924412
\(848\) −2.43894e15 −0.190996
\(849\) 1.30526e16 1.01556
\(850\) 1.46201e15 0.113018
\(851\) −2.64287e14 −0.0202985
\(852\) 8.25371e15 0.629842
\(853\) −4.82327e15 −0.365697 −0.182849 0.983141i \(-0.558532\pi\)
−0.182849 + 0.983141i \(0.558532\pi\)
\(854\) −4.95525e15 −0.373291
\(855\) 1.28603e15 0.0962584
\(856\) −6.68820e14 −0.0497397
\(857\) 1.82356e16 1.34749 0.673743 0.738965i \(-0.264685\pi\)
0.673743 + 0.738965i \(0.264685\pi\)
\(858\) −4.28665e14 −0.0314730
\(859\) 1.35505e16 0.988538 0.494269 0.869309i \(-0.335436\pi\)
0.494269 + 0.869309i \(0.335436\pi\)
\(860\) −7.13172e15 −0.516955
\(861\) −1.32068e16 −0.951217
\(862\) −9.00406e15 −0.644390
\(863\) 3.58064e15 0.254625 0.127313 0.991863i \(-0.459365\pi\)
0.127313 + 0.991863i \(0.459365\pi\)
\(864\) 2.47270e15 0.174721
\(865\) −5.05607e15 −0.354997
\(866\) 4.71916e15 0.329243
\(867\) 7.18480e15 0.498092
\(868\) 5.21927e14 0.0359543
\(869\) −1.62847e14 −0.0111474
\(870\) −6.05854e14 −0.0412109
\(871\) −3.35080e16 −2.26490
\(872\) 1.35068e16 0.907222
\(873\) −6.39177e15 −0.426622
\(874\) 3.26871e15 0.216802
\(875\) −1.05624e16 −0.696176
\(876\) −5.91169e15 −0.387203
\(877\) 1.08631e16 0.707060 0.353530 0.935423i \(-0.384981\pi\)
0.353530 + 0.935423i \(0.384981\pi\)
\(878\) −6.45210e15 −0.417331
\(879\) 1.01927e16 0.655163
\(880\) 3.63578e14 0.0232243
\(881\) 1.47375e16 0.935524 0.467762 0.883854i \(-0.345060\pi\)
0.467762 + 0.883854i \(0.345060\pi\)
\(882\) 2.52400e14 0.0159225
\(883\) −1.93222e16 −1.21136 −0.605680 0.795709i \(-0.707099\pi\)
−0.605680 + 0.795709i \(0.707099\pi\)
\(884\) 8.30510e15 0.517437
\(885\) −4.94141e14 −0.0305959
\(886\) 7.47288e15 0.459836
\(887\) −2.98238e16 −1.82383 −0.911913 0.410384i \(-0.865395\pi\)
−0.911913 + 0.410384i \(0.865395\pi\)
\(888\) −1.57415e14 −0.00956695
\(889\) −3.70175e15 −0.223587
\(890\) −3.73879e15 −0.224433
\(891\) 1.72264e14 0.0102770
\(892\) −3.78106e15 −0.224185
\(893\) −7.46924e15 −0.440142
\(894\) −3.67281e14 −0.0215101
\(895\) −9.05588e15 −0.527113
\(896\) 1.63115e16 0.943623
\(897\) −1.35302e16 −0.777941
\(898\) 2.72929e15 0.155966
\(899\) 3.75885e14 0.0213489
\(900\) 4.26798e15 0.240929
\(901\) −2.04469e15 −0.114721
\(902\) −1.07153e15 −0.0597545
\(903\) −1.42377e16 −0.789145
\(904\) −1.41677e16 −0.780502
\(905\) −1.84329e15 −0.100931
\(906\) 3.81683e15 0.207729
\(907\) −2.12927e16 −1.15183 −0.575917 0.817508i \(-0.695355\pi\)
−0.575917 + 0.817508i \(0.695355\pi\)
\(908\) −2.03843e16 −1.09603
\(909\) −6.81411e15 −0.364173
\(910\) 4.21079e15 0.223685
\(911\) 3.26708e14 0.0172508 0.00862540 0.999963i \(-0.497254\pi\)
0.00862540 + 0.999963i \(0.497254\pi\)
\(912\) −4.81399e15 −0.252658
\(913\) −3.05542e15 −0.159398
\(914\) −1.06688e16 −0.553238
\(915\) −4.99272e15 −0.257348
\(916\) 3.26135e16 1.67098
\(917\) 5.80270e15 0.295528
\(918\) 5.14959e14 0.0260698
\(919\) −1.89702e16 −0.954633 −0.477316 0.878732i \(-0.658390\pi\)
−0.477316 + 0.878732i \(0.658390\pi\)
\(920\) −4.64113e15 −0.232162
\(921\) −2.82218e15 −0.140332
\(922\) 3.42027e15 0.169060
\(923\) −4.13134e16 −2.02993
\(924\) 8.83130e14 0.0431349
\(925\) −4.17287e14 −0.0202607
\(926\) 5.48712e15 0.264840
\(927\) 5.05094e15 0.242345
\(928\) 9.12948e15 0.435444
\(929\) 4.78262e15 0.226767 0.113383 0.993551i \(-0.463831\pi\)
0.113383 + 0.993551i \(0.463831\pi\)
\(930\) −8.11397e13 −0.00382452
\(931\) −1.97810e15 −0.0926884
\(932\) 1.39629e16 0.650414
\(933\) 5.65568e15 0.261900
\(934\) −1.04456e16 −0.480867
\(935\) 3.04807e14 0.0139496
\(936\) −8.05887e15 −0.366654
\(937\) 3.44010e16 1.55598 0.777989 0.628277i \(-0.216240\pi\)
0.777989 + 0.628277i \(0.216240\pi\)
\(938\) −1.06514e16 −0.478951
\(939\) 7.91523e15 0.353837
\(940\) 4.92287e15 0.218784
\(941\) −2.78341e16 −1.22980 −0.614901 0.788605i \(-0.710804\pi\)
−0.614901 + 0.788605i \(0.710804\pi\)
\(942\) 5.07931e14 0.0223113
\(943\) −3.38215e16 −1.47699
\(944\) 1.84971e15 0.0803079
\(945\) −1.69215e15 −0.0730406
\(946\) −1.15518e15 −0.0495732
\(947\) 2.68749e16 1.14663 0.573314 0.819336i \(-0.305657\pi\)
0.573314 + 0.819336i \(0.305657\pi\)
\(948\) −1.42112e15 −0.0602817
\(949\) 2.95905e16 1.24792
\(950\) 5.16101e15 0.216399
\(951\) 4.03542e15 0.168227
\(952\) 5.68733e15 0.235725
\(953\) 1.03588e16 0.426873 0.213437 0.976957i \(-0.431534\pi\)
0.213437 + 0.976957i \(0.431534\pi\)
\(954\) 9.20985e14 0.0377343
\(955\) 1.71923e15 0.0700352
\(956\) −2.97727e15 −0.120587
\(957\) 6.36018e14 0.0256126
\(958\) −4.27221e15 −0.171058
\(959\) −2.14208e16 −0.852774
\(960\) 1.69167e15 0.0669613
\(961\) −2.53581e16 −0.998019
\(962\) 3.65747e14 0.0143126
\(963\) −6.24483e14 −0.0242983
\(964\) −1.73782e16 −0.672327
\(965\) −1.73451e16 −0.667233
\(966\) −4.30094e15 −0.164509
\(967\) 1.97119e16 0.749692 0.374846 0.927087i \(-0.377696\pi\)
0.374846 + 0.927087i \(0.377696\pi\)
\(968\) −1.78891e16 −0.676511
\(969\) −4.03583e15 −0.151758
\(970\) 5.09420e15 0.190472
\(971\) 1.13357e16 0.421445 0.210722 0.977546i \(-0.432418\pi\)
0.210722 + 0.977546i \(0.432418\pi\)
\(972\) 1.50330e15 0.0555751
\(973\) 2.61372e16 0.960813
\(974\) 1.24639e16 0.455596
\(975\) −2.13631e16 −0.776495
\(976\) 1.86892e16 0.675487
\(977\) 1.73424e16 0.623288 0.311644 0.950199i \(-0.399120\pi\)
0.311644 + 0.950199i \(0.399120\pi\)
\(978\) −7.06198e15 −0.252385
\(979\) 3.92494e15 0.139485
\(980\) 1.30374e15 0.0460731
\(981\) 1.26115e16 0.443186
\(982\) 1.48324e16 0.518320
\(983\) −5.57930e16 −1.93881 −0.969406 0.245464i \(-0.921060\pi\)
−0.969406 + 0.245464i \(0.921060\pi\)
\(984\) −2.01447e16 −0.696128
\(985\) −8.89443e15 −0.305646
\(986\) 1.90129e15 0.0649718
\(987\) 9.82796e15 0.333979
\(988\) 2.93176e16 0.990754
\(989\) −3.64615e16 −1.22534
\(990\) −1.37293e14 −0.00458833
\(991\) 4.68425e16 1.55681 0.778404 0.627764i \(-0.216030\pi\)
0.778404 + 0.627764i \(0.216030\pi\)
\(992\) 1.22268e15 0.0404108
\(993\) −2.00881e16 −0.660264
\(994\) −1.31325e16 −0.429263
\(995\) 2.09193e15 0.0680018
\(996\) −2.66638e16 −0.861976
\(997\) 4.70992e16 1.51422 0.757112 0.653285i \(-0.226610\pi\)
0.757112 + 0.653285i \(0.226610\pi\)
\(998\) 2.16827e16 0.693259
\(999\) −1.46979e14 −0.00467354
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.12.a.a.1.12 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.12 26 1.1 even 1 trivial