Properties

Label 43.10.a.a.1.13
Level 43
Weight 10
Character 43.1
Self dual yes
Analytic conductor 22.147
Analytic rank 1
Dimension 15
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.1465409550\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: multiple of \( 2^{10}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(-28.3075\) of \(x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} - 11474166224 x^{9} + 47465836576 x^{8} + 5986976782464 x^{7} - 32493903147264 x^{6} - 1516975415483904 x^{5} + 10892588268404224 x^{4} + 139803541742443008 x^{3} - 1349125586394823680 x^{2} + 2103623681144094720 x + 529838441422848000\)
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q+26.3075 q^{2} -164.924 q^{3} +180.084 q^{4} +879.044 q^{5} -4338.73 q^{6} +8431.97 q^{7} -8731.88 q^{8} +7516.88 q^{9} +O(q^{10})\) \(q+26.3075 q^{2} -164.924 q^{3} +180.084 q^{4} +879.044 q^{5} -4338.73 q^{6} +8431.97 q^{7} -8731.88 q^{8} +7516.88 q^{9} +23125.4 q^{10} -44408.6 q^{11} -29700.2 q^{12} -47197.0 q^{13} +221824. q^{14} -144975. q^{15} -321917. q^{16} +106312. q^{17} +197750. q^{18} -840557. q^{19} +158302. q^{20} -1.39063e6 q^{21} -1.16828e6 q^{22} -2.20694e6 q^{23} +1.44009e6 q^{24} -1.18041e6 q^{25} -1.24163e6 q^{26} +2.00648e6 q^{27} +1.51846e6 q^{28} -5.29576e6 q^{29} -3.81394e6 q^{30} +8.55848e6 q^{31} -3.99810e6 q^{32} +7.32404e6 q^{33} +2.79681e6 q^{34} +7.41208e6 q^{35} +1.35367e6 q^{36} +1.40897e7 q^{37} -2.21129e7 q^{38} +7.78391e6 q^{39} -7.67571e6 q^{40} -3.26833e7 q^{41} -3.65841e7 q^{42} -3.41880e6 q^{43} -7.99729e6 q^{44} +6.60767e6 q^{45} -5.80590e7 q^{46} +1.82676e7 q^{47} +5.30918e7 q^{48} +3.07445e7 q^{49} -3.10535e7 q^{50} -1.75334e7 q^{51} -8.49942e6 q^{52} -1.58212e7 q^{53} +5.27855e7 q^{54} -3.90372e7 q^{55} -7.36269e7 q^{56} +1.38628e8 q^{57} -1.39318e8 q^{58} +5.21983e7 q^{59} -2.61078e7 q^{60} -5.19929e7 q^{61} +2.25152e8 q^{62} +6.33821e7 q^{63} +5.96414e7 q^{64} -4.14882e7 q^{65} +1.92677e8 q^{66} -5.12923e7 q^{67} +1.91451e7 q^{68} +3.63977e8 q^{69} +1.94993e8 q^{70} +1.33738e8 q^{71} -6.56365e7 q^{72} +2.51019e8 q^{73} +3.70665e8 q^{74} +1.94677e8 q^{75} -1.51371e8 q^{76} -3.74452e8 q^{77} +2.04775e8 q^{78} -5.19381e8 q^{79} -2.82979e8 q^{80} -4.78872e8 q^{81} -8.59815e8 q^{82} -9.09782e6 q^{83} -2.50431e8 q^{84} +9.34532e7 q^{85} -8.99401e7 q^{86} +8.73397e8 q^{87} +3.87771e8 q^{88} +2.78479e8 q^{89} +1.73831e8 q^{90} -3.97963e8 q^{91} -3.97434e8 q^{92} -1.41150e9 q^{93} +4.80576e8 q^{94} -7.38887e8 q^{95} +6.59382e8 q^{96} +1.06067e9 q^{97} +8.08811e8 q^{98} -3.33815e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} + O(q^{10}) \) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} - 36237q^{10} - 104484q^{11} - 266395q^{12} - 116174q^{13} + 416064q^{14} + 415388q^{15} + 996762q^{16} - 884265q^{17} - 588735q^{18} - 689535q^{19} - 3077879q^{20} - 2070198q^{21} - 7276218q^{22} - 2504077q^{23} - 11534895q^{24} + 1315350q^{25} - 13343414q^{26} - 12546986q^{27} - 28059568q^{28} - 18406221q^{29} - 39503820q^{30} - 12033699q^{31} - 18952630q^{32} - 14197716q^{33} - 30383125q^{34} - 27855546q^{35} - 18372959q^{36} - 8722847q^{37} - 63941843q^{38} - 30955510q^{39} - 39665611q^{40} - 18689389q^{41} - 73185310q^{42} - 51282015q^{43} - 68723220q^{44} - 216992888q^{45} - 2067521q^{46} - 104960741q^{47} - 145362479q^{48} + 92663095q^{49} - 42446347q^{50} + 37433407q^{51} + 149226080q^{52} - 215907800q^{53} + 419158122q^{54} + 384379852q^{55} + 430441344q^{56} + 258744488q^{57} + 295963139q^{58} + 185924544q^{59} + 973236172q^{60} + 247538102q^{61} + 139798853q^{62} + 405429926q^{63} + 848556290q^{64} + 94294394q^{65} + 667230492q^{66} + 467904656q^{67} - 88234341q^{68} + 163914994q^{69} + 647526126q^{70} - 8252944q^{71} + 889796745q^{72} - 715627902q^{73} + 725122989q^{74} - 18301762q^{75} + 346300359q^{76} - 1236779964q^{77} + 2058642146q^{78} + 560681783q^{79} - 1157214179q^{80} - 752010645q^{81} + 941346367q^{82} - 1442854698q^{83} + 1895248718q^{84} + 699302088q^{85} + 109401632q^{86} - 2094576907q^{87} - 1464507256q^{88} - 396710008q^{89} + 1411356270q^{90} - 3278076852q^{91} + 155864647q^{92} - 1424759183q^{93} + 4666638949q^{94} - 3854114395q^{95} - 952489551q^{96} - 3063837815q^{97} - 6161086984q^{98} - 6576160348q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 26.3075 1.16264 0.581319 0.813676i \(-0.302537\pi\)
0.581319 + 0.813676i \(0.302537\pi\)
\(3\) −164.924 −1.17554 −0.587771 0.809028i \(-0.699994\pi\)
−0.587771 + 0.809028i \(0.699994\pi\)
\(4\) 180.084 0.351727
\(5\) 879.044 0.628993 0.314496 0.949259i \(-0.398164\pi\)
0.314496 + 0.949259i \(0.398164\pi\)
\(6\) −4338.73 −1.36673
\(7\) 8431.97 1.32736 0.663679 0.748018i \(-0.268994\pi\)
0.663679 + 0.748018i \(0.268994\pi\)
\(8\) −8731.88 −0.753707
\(9\) 7516.88 0.381897
\(10\) 23125.4 0.731291
\(11\) −44408.6 −0.914535 −0.457268 0.889329i \(-0.651172\pi\)
−0.457268 + 0.889329i \(0.651172\pi\)
\(12\) −29700.2 −0.413469
\(13\) −47197.0 −0.458320 −0.229160 0.973389i \(-0.573598\pi\)
−0.229160 + 0.973389i \(0.573598\pi\)
\(14\) 221824. 1.54324
\(15\) −144975. −0.739407
\(16\) −321917. −1.22801
\(17\) 106312. 0.308719 0.154359 0.988015i \(-0.450669\pi\)
0.154359 + 0.988015i \(0.450669\pi\)
\(18\) 197750. 0.444008
\(19\) −840557. −1.47971 −0.739854 0.672768i \(-0.765105\pi\)
−0.739854 + 0.672768i \(0.765105\pi\)
\(20\) 158302. 0.221234
\(21\) −1.39063e6 −1.56036
\(22\) −1.16828e6 −1.06327
\(23\) −2.20694e6 −1.64443 −0.822214 0.569178i \(-0.807262\pi\)
−0.822214 + 0.569178i \(0.807262\pi\)
\(24\) 1.44009e6 0.886014
\(25\) −1.18041e6 −0.604368
\(26\) −1.24163e6 −0.532860
\(27\) 2.00648e6 0.726605
\(28\) 1.51846e6 0.466867
\(29\) −5.29576e6 −1.39039 −0.695196 0.718820i \(-0.744683\pi\)
−0.695196 + 0.718820i \(0.744683\pi\)
\(30\) −3.81394e6 −0.859663
\(31\) 8.55848e6 1.66444 0.832222 0.554443i \(-0.187068\pi\)
0.832222 + 0.554443i \(0.187068\pi\)
\(32\) −3.99810e6 −0.674029
\(33\) 7.32404e6 1.07507
\(34\) 2.79681e6 0.358928
\(35\) 7.41208e6 0.834898
\(36\) 1.35367e6 0.134323
\(37\) 1.40897e7 1.23593 0.617965 0.786205i \(-0.287957\pi\)
0.617965 + 0.786205i \(0.287957\pi\)
\(38\) −2.21129e7 −1.72036
\(39\) 7.78391e6 0.538774
\(40\) −7.67571e6 −0.474076
\(41\) −3.26833e7 −1.80633 −0.903167 0.429288i \(-0.858764\pi\)
−0.903167 + 0.429288i \(0.858764\pi\)
\(42\) −3.65841e7 −1.81414
\(43\) −3.41880e6 −0.152499
\(44\) −7.99729e6 −0.321666
\(45\) 6.60767e6 0.240211
\(46\) −5.80590e7 −1.91187
\(47\) 1.82676e7 0.546062 0.273031 0.962005i \(-0.411974\pi\)
0.273031 + 0.962005i \(0.411974\pi\)
\(48\) 5.30918e7 1.44358
\(49\) 3.07445e7 0.761878
\(50\) −3.10535e7 −0.702661
\(51\) −1.75334e7 −0.362912
\(52\) −8.49942e6 −0.161203
\(53\) −1.58212e7 −0.275422 −0.137711 0.990472i \(-0.543974\pi\)
−0.137711 + 0.990472i \(0.543974\pi\)
\(54\) 5.27855e7 0.844779
\(55\) −3.90372e7 −0.575236
\(56\) −7.36269e7 −1.00044
\(57\) 1.38628e8 1.73946
\(58\) −1.39318e8 −1.61652
\(59\) 5.21983e7 0.560819 0.280409 0.959881i \(-0.409530\pi\)
0.280409 + 0.959881i \(0.409530\pi\)
\(60\) −2.61078e7 −0.260069
\(61\) −5.19929e7 −0.480794 −0.240397 0.970675i \(-0.577278\pi\)
−0.240397 + 0.970675i \(0.577278\pi\)
\(62\) 2.25152e8 1.93515
\(63\) 6.33821e7 0.506914
\(64\) 5.96414e7 0.444363
\(65\) −4.14882e7 −0.288280
\(66\) 1.92677e8 1.24992
\(67\) −5.12923e7 −0.310968 −0.155484 0.987838i \(-0.549694\pi\)
−0.155484 + 0.987838i \(0.549694\pi\)
\(68\) 1.91451e7 0.108585
\(69\) 3.63977e8 1.93309
\(70\) 1.94993e8 0.970685
\(71\) 1.33738e8 0.624588 0.312294 0.949986i \(-0.398903\pi\)
0.312294 + 0.949986i \(0.398903\pi\)
\(72\) −6.56365e7 −0.287839
\(73\) 2.51019e8 1.03455 0.517277 0.855818i \(-0.326946\pi\)
0.517277 + 0.855818i \(0.326946\pi\)
\(74\) 3.70665e8 1.43694
\(75\) 1.94677e8 0.710459
\(76\) −1.51371e8 −0.520453
\(77\) −3.74452e8 −1.21391
\(78\) 2.04775e8 0.626399
\(79\) −5.19381e8 −1.50025 −0.750126 0.661295i \(-0.770007\pi\)
−0.750126 + 0.661295i \(0.770007\pi\)
\(80\) −2.82979e8 −0.772413
\(81\) −4.78872e8 −1.23605
\(82\) −8.59815e8 −2.10011
\(83\) −9.09782e6 −0.0210419 −0.0105210 0.999945i \(-0.503349\pi\)
−0.0105210 + 0.999945i \(0.503349\pi\)
\(84\) −2.50431e8 −0.548821
\(85\) 9.34532e7 0.194182
\(86\) −8.99401e7 −0.177301
\(87\) 8.73397e8 1.63446
\(88\) 3.87771e8 0.689292
\(89\) 2.78479e8 0.470476 0.235238 0.971938i \(-0.424413\pi\)
0.235238 + 0.971938i \(0.424413\pi\)
\(90\) 1.73831e8 0.279278
\(91\) −3.97963e8 −0.608355
\(92\) −3.97434e8 −0.578389
\(93\) −1.41150e9 −1.95662
\(94\) 4.80576e8 0.634873
\(95\) −7.38887e8 −0.930726
\(96\) 6.59382e8 0.792349
\(97\) 1.06067e9 1.21649 0.608244 0.793750i \(-0.291874\pi\)
0.608244 + 0.793750i \(0.291874\pi\)
\(98\) 8.08811e8 0.885788
\(99\) −3.33815e8 −0.349258
\(100\) −2.12572e8 −0.212572
\(101\) −9.68968e8 −0.926538 −0.463269 0.886218i \(-0.653324\pi\)
−0.463269 + 0.886218i \(0.653324\pi\)
\(102\) −4.61261e8 −0.421935
\(103\) −9.31835e8 −0.815777 −0.407888 0.913032i \(-0.633735\pi\)
−0.407888 + 0.913032i \(0.633735\pi\)
\(104\) 4.12118e8 0.345439
\(105\) −1.22243e9 −0.981458
\(106\) −4.16216e8 −0.320216
\(107\) 4.53416e8 0.334403 0.167202 0.985923i \(-0.446527\pi\)
0.167202 + 0.985923i \(0.446527\pi\)
\(108\) 3.61336e8 0.255566
\(109\) −2.45730e8 −0.166740 −0.0833698 0.996519i \(-0.526568\pi\)
−0.0833698 + 0.996519i \(0.526568\pi\)
\(110\) −1.02697e9 −0.668791
\(111\) −2.32373e9 −1.45289
\(112\) −2.71439e9 −1.63001
\(113\) 1.88661e9 1.08850 0.544251 0.838922i \(-0.316814\pi\)
0.544251 + 0.838922i \(0.316814\pi\)
\(114\) 3.64695e9 2.02236
\(115\) −1.94000e9 −1.03433
\(116\) −9.53682e8 −0.489038
\(117\) −3.54774e8 −0.175031
\(118\) 1.37321e9 0.652029
\(119\) 8.96422e8 0.409780
\(120\) 1.26591e9 0.557296
\(121\) −3.85821e8 −0.163626
\(122\) −1.36780e9 −0.558990
\(123\) 5.39025e9 2.12342
\(124\) 1.54125e9 0.585429
\(125\) −2.75451e9 −1.00914
\(126\) 1.66743e9 0.589358
\(127\) 4.85598e9 1.65638 0.828190 0.560447i \(-0.189371\pi\)
0.828190 + 0.560447i \(0.189371\pi\)
\(128\) 3.61604e9 1.19066
\(129\) 5.63842e8 0.179268
\(130\) −1.09145e9 −0.335165
\(131\) −2.84855e9 −0.845089 −0.422545 0.906342i \(-0.638863\pi\)
−0.422545 + 0.906342i \(0.638863\pi\)
\(132\) 1.31894e9 0.378132
\(133\) −7.08755e9 −1.96410
\(134\) −1.34937e9 −0.361543
\(135\) 1.76379e9 0.457030
\(136\) −9.28305e8 −0.232684
\(137\) −2.63584e9 −0.639258 −0.319629 0.947543i \(-0.603558\pi\)
−0.319629 + 0.947543i \(0.603558\pi\)
\(138\) 9.57532e9 2.24749
\(139\) −1.99731e9 −0.453814 −0.226907 0.973916i \(-0.572861\pi\)
−0.226907 + 0.973916i \(0.572861\pi\)
\(140\) 1.33480e9 0.293656
\(141\) −3.01277e9 −0.641919
\(142\) 3.51832e9 0.726169
\(143\) 2.09595e9 0.419150
\(144\) −2.41981e9 −0.468976
\(145\) −4.65521e9 −0.874547
\(146\) 6.60368e9 1.20281
\(147\) −5.07051e9 −0.895619
\(148\) 2.53733e9 0.434710
\(149\) 1.72984e9 0.287520 0.143760 0.989613i \(-0.454081\pi\)
0.143760 + 0.989613i \(0.454081\pi\)
\(150\) 5.12147e9 0.826007
\(151\) 9.37624e8 0.146768 0.0733841 0.997304i \(-0.476620\pi\)
0.0733841 + 0.997304i \(0.476620\pi\)
\(152\) 7.33964e9 1.11527
\(153\) 7.99137e8 0.117899
\(154\) −9.85090e9 −1.41134
\(155\) 7.52329e9 1.04692
\(156\) 1.40176e9 0.189501
\(157\) 7.92803e9 1.04140 0.520699 0.853740i \(-0.325671\pi\)
0.520699 + 0.853740i \(0.325671\pi\)
\(158\) −1.36636e10 −1.74425
\(159\) 2.60929e9 0.323770
\(160\) −3.51451e9 −0.423960
\(161\) −1.86088e10 −2.18274
\(162\) −1.25979e10 −1.43708
\(163\) 2.00486e9 0.222454 0.111227 0.993795i \(-0.464522\pi\)
0.111227 + 0.993795i \(0.464522\pi\)
\(164\) −5.88574e9 −0.635336
\(165\) 6.43816e9 0.676214
\(166\) −2.39341e8 −0.0244642
\(167\) 1.17331e10 1.16731 0.583656 0.812001i \(-0.301622\pi\)
0.583656 + 0.812001i \(0.301622\pi\)
\(168\) 1.21428e10 1.17606
\(169\) −8.37695e9 −0.789943
\(170\) 2.45852e9 0.225763
\(171\) −6.31837e9 −0.565096
\(172\) −6.15671e8 −0.0536378
\(173\) −4.43977e9 −0.376837 −0.188418 0.982089i \(-0.560336\pi\)
−0.188418 + 0.982089i \(0.560336\pi\)
\(174\) 2.29769e10 1.90029
\(175\) −9.95315e9 −0.802212
\(176\) 1.42959e10 1.12306
\(177\) −8.60875e9 −0.659265
\(178\) 7.32608e9 0.546993
\(179\) 8.09413e8 0.0589294 0.0294647 0.999566i \(-0.490620\pi\)
0.0294647 + 0.999566i \(0.490620\pi\)
\(180\) 1.18994e9 0.0844885
\(181\) −2.74859e10 −1.90352 −0.951758 0.306850i \(-0.900725\pi\)
−0.951758 + 0.306850i \(0.900725\pi\)
\(182\) −1.04694e10 −0.707296
\(183\) 8.57486e9 0.565194
\(184\) 1.92707e10 1.23942
\(185\) 1.23855e10 0.777391
\(186\) −3.71330e10 −2.27484
\(187\) −4.72118e9 −0.282334
\(188\) 3.28971e9 0.192065
\(189\) 1.69186e10 0.964465
\(190\) −1.94383e10 −1.08210
\(191\) 2.57143e10 1.39805 0.699027 0.715095i \(-0.253617\pi\)
0.699027 + 0.715095i \(0.253617\pi\)
\(192\) −9.83629e9 −0.522367
\(193\) −3.15862e10 −1.63866 −0.819330 0.573322i \(-0.805654\pi\)
−0.819330 + 0.573322i \(0.805654\pi\)
\(194\) 2.79036e10 1.41433
\(195\) 6.84240e9 0.338885
\(196\) 5.53660e9 0.267973
\(197\) −8.04167e9 −0.380407 −0.190203 0.981745i \(-0.560915\pi\)
−0.190203 + 0.981745i \(0.560915\pi\)
\(198\) −8.78182e9 −0.406061
\(199\) 2.69320e10 1.21739 0.608695 0.793404i \(-0.291693\pi\)
0.608695 + 0.793404i \(0.291693\pi\)
\(200\) 1.03072e10 0.455516
\(201\) 8.45933e9 0.365556
\(202\) −2.54911e10 −1.07723
\(203\) −4.46537e10 −1.84555
\(204\) −3.15749e9 −0.127646
\(205\) −2.87301e10 −1.13617
\(206\) −2.45142e10 −0.948453
\(207\) −1.65893e10 −0.628003
\(208\) 1.51935e10 0.562824
\(209\) 3.73280e10 1.35324
\(210\) −3.21590e10 −1.14108
\(211\) 3.31590e10 1.15168 0.575838 0.817564i \(-0.304676\pi\)
0.575838 + 0.817564i \(0.304676\pi\)
\(212\) −2.84915e9 −0.0968731
\(213\) −2.20566e10 −0.734228
\(214\) 1.19282e10 0.388790
\(215\) −3.00528e9 −0.0959205
\(216\) −1.75204e10 −0.547648
\(217\) 7.21649e10 2.20931
\(218\) −6.46454e9 −0.193858
\(219\) −4.13990e10 −1.21616
\(220\) −7.02997e9 −0.202326
\(221\) −5.01762e9 −0.141492
\(222\) −6.11314e10 −1.68918
\(223\) −9.20954e8 −0.0249383 −0.0124691 0.999922i \(-0.503969\pi\)
−0.0124691 + 0.999922i \(0.503969\pi\)
\(224\) −3.37119e10 −0.894678
\(225\) −8.87298e9 −0.230806
\(226\) 4.96320e10 1.26553
\(227\) −1.44593e10 −0.361436 −0.180718 0.983535i \(-0.557842\pi\)
−0.180718 + 0.983535i \(0.557842\pi\)
\(228\) 2.49647e10 0.611814
\(229\) 1.65510e10 0.397709 0.198855 0.980029i \(-0.436278\pi\)
0.198855 + 0.980029i \(0.436278\pi\)
\(230\) −5.10365e10 −1.20256
\(231\) 6.17561e10 1.42701
\(232\) 4.62419e10 1.04795
\(233\) 3.78508e10 0.841344 0.420672 0.907213i \(-0.361794\pi\)
0.420672 + 0.907213i \(0.361794\pi\)
\(234\) −9.33322e9 −0.203498
\(235\) 1.60581e10 0.343469
\(236\) 9.40008e9 0.197255
\(237\) 8.56583e10 1.76361
\(238\) 2.35826e10 0.476426
\(239\) −8.76102e10 −1.73686 −0.868429 0.495814i \(-0.834870\pi\)
−0.868429 + 0.495814i \(0.834870\pi\)
\(240\) 4.66700e10 0.908003
\(241\) 1.20041e10 0.229221 0.114610 0.993411i \(-0.463438\pi\)
0.114610 + 0.993411i \(0.463438\pi\)
\(242\) −1.01500e10 −0.190237
\(243\) 3.94838e10 0.726425
\(244\) −9.36308e9 −0.169108
\(245\) 2.70258e10 0.479216
\(246\) 1.41804e11 2.46877
\(247\) 3.96717e10 0.678180
\(248\) −7.47316e10 −1.25450
\(249\) 1.50045e9 0.0247357
\(250\) −7.24643e10 −1.17326
\(251\) −3.64728e10 −0.580013 −0.290006 0.957025i \(-0.593657\pi\)
−0.290006 + 0.957025i \(0.593657\pi\)
\(252\) 1.14141e10 0.178295
\(253\) 9.80071e10 1.50389
\(254\) 1.27749e11 1.92577
\(255\) −1.54127e10 −0.228269
\(256\) 6.45926e10 0.939946
\(257\) −5.66916e10 −0.810624 −0.405312 0.914178i \(-0.632837\pi\)
−0.405312 + 0.914178i \(0.632837\pi\)
\(258\) 1.48333e10 0.208424
\(259\) 1.18804e11 1.64052
\(260\) −7.47137e9 −0.101396
\(261\) −3.98076e10 −0.530987
\(262\) −7.49381e10 −0.982533
\(263\) 1.18478e11 1.52700 0.763498 0.645811i \(-0.223480\pi\)
0.763498 + 0.645811i \(0.223480\pi\)
\(264\) −6.39526e10 −0.810291
\(265\) −1.39075e10 −0.173238
\(266\) −1.86456e11 −2.28354
\(267\) −4.59278e10 −0.553064
\(268\) −9.23693e9 −0.109376
\(269\) −1.35889e11 −1.58234 −0.791168 0.611598i \(-0.790527\pi\)
−0.791168 + 0.611598i \(0.790527\pi\)
\(270\) 4.64008e10 0.531360
\(271\) 1.48062e11 1.66756 0.833782 0.552094i \(-0.186171\pi\)
0.833782 + 0.552094i \(0.186171\pi\)
\(272\) −3.42237e10 −0.379111
\(273\) 6.56337e10 0.715146
\(274\) −6.93422e10 −0.743225
\(275\) 5.24202e10 0.552716
\(276\) 6.55464e10 0.679921
\(277\) −1.40075e11 −1.42955 −0.714777 0.699353i \(-0.753472\pi\)
−0.714777 + 0.699353i \(0.753472\pi\)
\(278\) −5.25441e10 −0.527621
\(279\) 6.43331e10 0.635647
\(280\) −6.47213e10 −0.629269
\(281\) −1.76496e11 −1.68872 −0.844358 0.535780i \(-0.820018\pi\)
−0.844358 + 0.535780i \(0.820018\pi\)
\(282\) −7.92584e10 −0.746319
\(283\) −1.68090e11 −1.55776 −0.778882 0.627170i \(-0.784213\pi\)
−0.778882 + 0.627170i \(0.784213\pi\)
\(284\) 2.40841e10 0.219684
\(285\) 1.21860e11 1.09411
\(286\) 5.51393e10 0.487319
\(287\) −2.75584e11 −2.39765
\(288\) −3.00533e10 −0.257410
\(289\) −1.07286e11 −0.904693
\(290\) −1.22467e11 −1.01678
\(291\) −1.74930e11 −1.43003
\(292\) 4.52045e10 0.363880
\(293\) 1.44737e11 1.14729 0.573646 0.819103i \(-0.305529\pi\)
0.573646 + 0.819103i \(0.305529\pi\)
\(294\) −1.33392e11 −1.04128
\(295\) 4.58846e10 0.352751
\(296\) −1.23030e11 −0.931530
\(297\) −8.91052e10 −0.664506
\(298\) 4.55079e10 0.334282
\(299\) 1.04161e11 0.753675
\(300\) 3.50582e10 0.249887
\(301\) −2.88272e10 −0.202420
\(302\) 2.46665e10 0.170638
\(303\) 1.59806e11 1.08918
\(304\) 2.70589e11 1.81710
\(305\) −4.57040e10 −0.302416
\(306\) 2.10233e10 0.137074
\(307\) −5.43835e10 −0.349418 −0.174709 0.984620i \(-0.555898\pi\)
−0.174709 + 0.984620i \(0.555898\pi\)
\(308\) −6.74329e10 −0.426966
\(309\) 1.53682e11 0.958979
\(310\) 1.97919e11 1.21719
\(311\) 2.25354e10 0.136598 0.0682990 0.997665i \(-0.478243\pi\)
0.0682990 + 0.997665i \(0.478243\pi\)
\(312\) −6.79681e10 −0.406078
\(313\) −1.33449e11 −0.785896 −0.392948 0.919561i \(-0.628545\pi\)
−0.392948 + 0.919561i \(0.628545\pi\)
\(314\) 2.08567e11 1.21077
\(315\) 5.57157e10 0.318845
\(316\) −9.35322e10 −0.527678
\(317\) −1.53990e11 −0.856495 −0.428247 0.903662i \(-0.640869\pi\)
−0.428247 + 0.903662i \(0.640869\pi\)
\(318\) 6.86440e10 0.376427
\(319\) 2.35178e11 1.27156
\(320\) 5.24274e10 0.279501
\(321\) −7.47792e10 −0.393105
\(322\) −4.89552e11 −2.53774
\(323\) −8.93615e10 −0.456814
\(324\) −8.62372e10 −0.434752
\(325\) 5.57116e10 0.276994
\(326\) 5.27429e10 0.258633
\(327\) 4.05267e10 0.196009
\(328\) 2.85386e11 1.36145
\(329\) 1.54032e11 0.724820
\(330\) 1.69372e11 0.786192
\(331\) 2.39934e11 1.09867 0.549333 0.835603i \(-0.314882\pi\)
0.549333 + 0.835603i \(0.314882\pi\)
\(332\) −1.63837e9 −0.00740101
\(333\) 1.05911e11 0.471998
\(334\) 3.08667e11 1.35716
\(335\) −4.50882e10 −0.195597
\(336\) 4.47668e11 1.91615
\(337\) 3.87512e10 0.163663 0.0818315 0.996646i \(-0.473923\pi\)
0.0818315 + 0.996646i \(0.473923\pi\)
\(338\) −2.20376e11 −0.918417
\(339\) −3.11147e11 −1.27958
\(340\) 1.68294e10 0.0682990
\(341\) −3.80071e11 −1.52219
\(342\) −1.66220e11 −0.657002
\(343\) −8.10235e10 −0.316073
\(344\) 2.98525e10 0.114939
\(345\) 3.19952e11 1.21590
\(346\) −1.16799e11 −0.438124
\(347\) −5.45577e10 −0.202010 −0.101005 0.994886i \(-0.532206\pi\)
−0.101005 + 0.994886i \(0.532206\pi\)
\(348\) 1.57285e11 0.574884
\(349\) −6.33934e10 −0.228733 −0.114367 0.993439i \(-0.536484\pi\)
−0.114367 + 0.993439i \(0.536484\pi\)
\(350\) −2.61842e11 −0.932682
\(351\) −9.46999e10 −0.333018
\(352\) 1.77550e11 0.616424
\(353\) −1.99546e11 −0.684002 −0.342001 0.939700i \(-0.611105\pi\)
−0.342001 + 0.939700i \(0.611105\pi\)
\(354\) −2.26475e11 −0.766487
\(355\) 1.17562e11 0.392861
\(356\) 5.01496e10 0.165479
\(357\) −1.47841e11 −0.481714
\(358\) 2.12936e10 0.0685135
\(359\) 4.39428e11 1.39625 0.698125 0.715976i \(-0.254018\pi\)
0.698125 + 0.715976i \(0.254018\pi\)
\(360\) −5.76974e10 −0.181048
\(361\) 3.83848e11 1.18954
\(362\) −7.23085e11 −2.21310
\(363\) 6.36310e10 0.192349
\(364\) −7.16669e10 −0.213975
\(365\) 2.20657e11 0.650728
\(366\) 2.25583e11 0.657116
\(367\) −2.34148e11 −0.673742 −0.336871 0.941551i \(-0.609369\pi\)
−0.336871 + 0.941551i \(0.609369\pi\)
\(368\) 7.10451e11 2.01938
\(369\) −2.45676e11 −0.689834
\(370\) 3.25831e11 0.903825
\(371\) −1.33404e11 −0.365583
\(372\) −2.54188e11 −0.688196
\(373\) 5.75087e11 1.53831 0.769155 0.639063i \(-0.220678\pi\)
0.769155 + 0.639063i \(0.220678\pi\)
\(374\) −1.24202e11 −0.328252
\(375\) 4.54285e11 1.18628
\(376\) −1.59511e11 −0.411571
\(377\) 2.49944e11 0.637245
\(378\) 4.45086e11 1.12132
\(379\) −3.66818e11 −0.913218 −0.456609 0.889667i \(-0.650936\pi\)
−0.456609 + 0.889667i \(0.650936\pi\)
\(380\) −1.33062e11 −0.327361
\(381\) −8.00867e11 −1.94714
\(382\) 6.76478e11 1.62543
\(383\) 5.74114e11 1.36334 0.681669 0.731660i \(-0.261254\pi\)
0.681669 + 0.731660i \(0.261254\pi\)
\(384\) −5.96372e11 −1.39967
\(385\) −3.29160e11 −0.763544
\(386\) −8.30953e11 −1.90517
\(387\) −2.56987e10 −0.0582388
\(388\) 1.91010e11 0.427871
\(389\) −2.56613e11 −0.568205 −0.284102 0.958794i \(-0.591696\pi\)
−0.284102 + 0.958794i \(0.591696\pi\)
\(390\) 1.80006e11 0.394001
\(391\) −2.34625e11 −0.507666
\(392\) −2.68457e11 −0.574233
\(393\) 4.69794e11 0.993437
\(394\) −2.11556e11 −0.442275
\(395\) −4.56559e11 −0.943647
\(396\) −6.01147e10 −0.122843
\(397\) 4.87408e11 0.984771 0.492385 0.870377i \(-0.336125\pi\)
0.492385 + 0.870377i \(0.336125\pi\)
\(398\) 7.08513e11 1.41538
\(399\) 1.16891e12 2.30888
\(400\) 3.79993e11 0.742173
\(401\) −2.25451e10 −0.0435414 −0.0217707 0.999763i \(-0.506930\pi\)
−0.0217707 + 0.999763i \(0.506930\pi\)
\(402\) 2.22544e11 0.425009
\(403\) −4.03934e11 −0.762848
\(404\) −1.74496e11 −0.325888
\(405\) −4.20949e11 −0.777468
\(406\) −1.17473e12 −2.14570
\(407\) −6.25704e11 −1.13030
\(408\) 1.53100e11 0.273529
\(409\) −5.20640e11 −0.919988 −0.459994 0.887922i \(-0.652149\pi\)
−0.459994 + 0.887922i \(0.652149\pi\)
\(410\) −7.55816e11 −1.32096
\(411\) 4.34712e11 0.751474
\(412\) −1.67809e11 −0.286930
\(413\) 4.40135e11 0.744407
\(414\) −4.36423e11 −0.730140
\(415\) −7.99738e9 −0.0132352
\(416\) 1.88698e11 0.308921
\(417\) 3.29403e11 0.533477
\(418\) 9.82006e11 1.57333
\(419\) −8.78483e11 −1.39242 −0.696210 0.717838i \(-0.745132\pi\)
−0.696210 + 0.717838i \(0.745132\pi\)
\(420\) −2.20140e11 −0.345205
\(421\) 7.17609e10 0.111332 0.0556658 0.998449i \(-0.482272\pi\)
0.0556658 + 0.998449i \(0.482272\pi\)
\(422\) 8.72329e11 1.33898
\(423\) 1.37316e11 0.208540
\(424\) 1.38149e11 0.207587
\(425\) −1.25492e11 −0.186580
\(426\) −5.80255e11 −0.853642
\(427\) −4.38402e11 −0.638186
\(428\) 8.16531e10 0.117618
\(429\) −3.45673e11 −0.492728
\(430\) −7.90613e10 −0.111521
\(431\) −1.77962e11 −0.248416 −0.124208 0.992256i \(-0.539639\pi\)
−0.124208 + 0.992256i \(0.539639\pi\)
\(432\) −6.45921e11 −0.892282
\(433\) −1.21148e12 −1.65622 −0.828112 0.560563i \(-0.810585\pi\)
−0.828112 + 0.560563i \(0.810585\pi\)
\(434\) 1.89848e12 2.56863
\(435\) 7.67755e11 1.02807
\(436\) −4.42520e10 −0.0586468
\(437\) 1.85506e12 2.43327
\(438\) −1.08910e12 −1.41396
\(439\) −5.87231e11 −0.754603 −0.377302 0.926090i \(-0.623148\pi\)
−0.377302 + 0.926090i \(0.623148\pi\)
\(440\) 3.40868e11 0.433560
\(441\) 2.31103e11 0.290959
\(442\) −1.32001e11 −0.164504
\(443\) −1.21527e12 −1.49919 −0.749593 0.661899i \(-0.769751\pi\)
−0.749593 + 0.661899i \(0.769751\pi\)
\(444\) −4.18466e11 −0.511019
\(445\) 2.44795e11 0.295926
\(446\) −2.42280e10 −0.0289942
\(447\) −2.85293e11 −0.337992
\(448\) 5.02894e11 0.589828
\(449\) −1.69159e12 −1.96421 −0.982103 0.188342i \(-0.939689\pi\)
−0.982103 + 0.188342i \(0.939689\pi\)
\(450\) −2.33426e11 −0.268344
\(451\) 1.45142e12 1.65196
\(452\) 3.39749e11 0.382855
\(453\) −1.54637e11 −0.172532
\(454\) −3.80388e11 −0.420219
\(455\) −3.49827e11 −0.382651
\(456\) −1.21048e12 −1.31104
\(457\) −3.52686e11 −0.378239 −0.189119 0.981954i \(-0.560563\pi\)
−0.189119 + 0.981954i \(0.560563\pi\)
\(458\) 4.35416e11 0.462392
\(459\) 2.13314e11 0.224317
\(460\) −3.49362e11 −0.363803
\(461\) −7.83575e11 −0.808028 −0.404014 0.914753i \(-0.632385\pi\)
−0.404014 + 0.914753i \(0.632385\pi\)
\(462\) 1.62465e12 1.65909
\(463\) 8.28011e11 0.837378 0.418689 0.908130i \(-0.362490\pi\)
0.418689 + 0.908130i \(0.362490\pi\)
\(464\) 1.70479e12 1.70742
\(465\) −1.24077e12 −1.23070
\(466\) 9.95760e11 0.978179
\(467\) −9.44763e11 −0.919172 −0.459586 0.888133i \(-0.652002\pi\)
−0.459586 + 0.888133i \(0.652002\pi\)
\(468\) −6.38891e10 −0.0615631
\(469\) −4.32495e11 −0.412766
\(470\) 4.22447e11 0.399330
\(471\) −1.30752e12 −1.22421
\(472\) −4.55789e11 −0.422693
\(473\) 1.51824e11 0.139465
\(474\) 2.25345e12 2.05044
\(475\) 9.92199e11 0.894288
\(476\) 1.61431e11 0.144131
\(477\) −1.18926e11 −0.105183
\(478\) −2.30480e12 −2.01934
\(479\) −1.31925e12 −1.14503 −0.572514 0.819895i \(-0.694032\pi\)
−0.572514 + 0.819895i \(0.694032\pi\)
\(480\) 5.79626e11 0.498382
\(481\) −6.64991e11 −0.566452
\(482\) 3.15798e11 0.266500
\(483\) 3.06904e12 2.56591
\(484\) −6.94801e10 −0.0575515
\(485\) 9.32376e11 0.765162
\(486\) 1.03872e12 0.844569
\(487\) −7.98399e11 −0.643190 −0.321595 0.946877i \(-0.604219\pi\)
−0.321595 + 0.946877i \(0.604219\pi\)
\(488\) 4.53995e11 0.362378
\(489\) −3.30649e11 −0.261504
\(490\) 7.10981e11 0.557154
\(491\) 9.36951e11 0.727529 0.363765 0.931491i \(-0.381491\pi\)
0.363765 + 0.931491i \(0.381491\pi\)
\(492\) 9.70698e11 0.746864
\(493\) −5.63004e11 −0.429240
\(494\) 1.04366e12 0.788478
\(495\) −2.93438e11 −0.219681
\(496\) −2.75512e12 −2.04396
\(497\) 1.12768e12 0.829051
\(498\) 3.94730e10 0.0287586
\(499\) 6.92404e11 0.499928 0.249964 0.968255i \(-0.419581\pi\)
0.249964 + 0.968255i \(0.419581\pi\)
\(500\) −4.96044e11 −0.354940
\(501\) −1.93506e12 −1.37222
\(502\) −9.59508e11 −0.674345
\(503\) 4.51453e11 0.314454 0.157227 0.987563i \(-0.449745\pi\)
0.157227 + 0.987563i \(0.449745\pi\)
\(504\) −5.53445e11 −0.382065
\(505\) −8.51766e11 −0.582786
\(506\) 2.57832e12 1.74848
\(507\) 1.38156e12 0.928610
\(508\) 8.74484e11 0.582593
\(509\) −1.19633e12 −0.789987 −0.394993 0.918684i \(-0.629253\pi\)
−0.394993 + 0.918684i \(0.629253\pi\)
\(510\) −4.05468e11 −0.265394
\(511\) 2.11658e12 1.37322
\(512\) −1.52144e11 −0.0978454
\(513\) −1.68656e12 −1.07516
\(514\) −1.49141e12 −0.942462
\(515\) −8.19124e11 −0.513118
\(516\) 1.01539e11 0.0630535
\(517\) −8.11241e11 −0.499393
\(518\) 3.12543e12 1.90733
\(519\) 7.32224e11 0.442987
\(520\) 3.62270e11 0.217279
\(521\) −2.45881e12 −1.46203 −0.731013 0.682364i \(-0.760952\pi\)
−0.731013 + 0.682364i \(0.760952\pi\)
\(522\) −1.04724e12 −0.617346
\(523\) 7.38007e11 0.431323 0.215662 0.976468i \(-0.430809\pi\)
0.215662 + 0.976468i \(0.430809\pi\)
\(524\) −5.12978e11 −0.297240
\(525\) 1.64151e12 0.943034
\(526\) 3.11686e12 1.77534
\(527\) 9.09872e11 0.513845
\(528\) −2.35773e12 −1.32021
\(529\) 3.06943e12 1.70415
\(530\) −3.65872e11 −0.201413
\(531\) 3.92369e11 0.214175
\(532\) −1.27635e12 −0.690827
\(533\) 1.54255e12 0.827880
\(534\) −1.20825e12 −0.643013
\(535\) 3.98573e11 0.210337
\(536\) 4.47878e11 0.234379
\(537\) −1.33492e11 −0.0692739
\(538\) −3.57490e12 −1.83968
\(539\) −1.36532e12 −0.696764
\(540\) 3.17630e11 0.160749
\(541\) −5.43907e11 −0.272984 −0.136492 0.990641i \(-0.543583\pi\)
−0.136492 + 0.990641i \(0.543583\pi\)
\(542\) 3.89514e12 1.93877
\(543\) 4.53308e12 2.23766
\(544\) −4.25047e11 −0.208086
\(545\) −2.16008e11 −0.104878
\(546\) 1.72666e12 0.831456
\(547\) 3.81622e12 1.82260 0.911298 0.411747i \(-0.135081\pi\)
0.911298 + 0.411747i \(0.135081\pi\)
\(548\) −4.74672e11 −0.224844
\(549\) −3.90824e11 −0.183614
\(550\) 1.37904e12 0.642608
\(551\) 4.45139e12 2.05737
\(552\) −3.17820e12 −1.45699
\(553\) −4.37940e12 −1.99137
\(554\) −3.68501e12 −1.66205
\(555\) −2.04266e12 −0.913856
\(556\) −3.59683e11 −0.159618
\(557\) 3.04799e12 1.34173 0.670865 0.741580i \(-0.265923\pi\)
0.670865 + 0.741580i \(0.265923\pi\)
\(558\) 1.69244e12 0.739027
\(559\) 1.61357e11 0.0698932
\(560\) −2.38607e12 −1.02527
\(561\) 7.78636e11 0.331896
\(562\) −4.64317e12 −1.96336
\(563\) −3.04470e12 −1.27719 −0.638597 0.769542i \(-0.720485\pi\)
−0.638597 + 0.769542i \(0.720485\pi\)
\(564\) −5.42552e11 −0.225780
\(565\) 1.65842e12 0.684661
\(566\) −4.42201e12 −1.81112
\(567\) −4.03783e12 −1.64068
\(568\) −1.16779e12 −0.470756
\(569\) 1.54929e12 0.619624 0.309812 0.950798i \(-0.399734\pi\)
0.309812 + 0.950798i \(0.399734\pi\)
\(570\) 3.20583e12 1.27205
\(571\) 3.65555e11 0.143910 0.0719549 0.997408i \(-0.477076\pi\)
0.0719549 + 0.997408i \(0.477076\pi\)
\(572\) 3.77448e11 0.147426
\(573\) −4.24090e12 −1.64347
\(574\) −7.24994e12 −2.78760
\(575\) 2.60508e12 0.993840
\(576\) 4.48317e11 0.169701
\(577\) −7.02681e11 −0.263917 −0.131958 0.991255i \(-0.542127\pi\)
−0.131958 + 0.991255i \(0.542127\pi\)
\(578\) −2.82241e12 −1.05183
\(579\) 5.20931e12 1.92631
\(580\) −8.38329e11 −0.307601
\(581\) −7.67125e10 −0.0279302
\(582\) −4.60197e12 −1.66261
\(583\) 7.02598e11 0.251883
\(584\) −2.19187e12 −0.779751
\(585\) −3.11862e11 −0.110093
\(586\) 3.80765e12 1.33388
\(587\) −1.17216e12 −0.407488 −0.203744 0.979024i \(-0.565311\pi\)
−0.203744 + 0.979024i \(0.565311\pi\)
\(588\) −9.13117e11 −0.315013
\(589\) −7.19389e12 −2.46289
\(590\) 1.20711e12 0.410122
\(591\) 1.32626e12 0.447184
\(592\) −4.53571e12 −1.51774
\(593\) −2.02177e12 −0.671406 −0.335703 0.941968i \(-0.608974\pi\)
−0.335703 + 0.941968i \(0.608974\pi\)
\(594\) −2.34413e12 −0.772580
\(595\) 7.87995e11 0.257749
\(596\) 3.11517e11 0.101129
\(597\) −4.44173e12 −1.43109
\(598\) 2.74021e12 0.876251
\(599\) 3.38829e12 1.07538 0.537688 0.843144i \(-0.319298\pi\)
0.537688 + 0.843144i \(0.319298\pi\)
\(600\) −1.69990e12 −0.535478
\(601\) 3.27712e12 1.02461 0.512303 0.858805i \(-0.328792\pi\)
0.512303 + 0.858805i \(0.328792\pi\)
\(602\) −7.58372e11 −0.235341
\(603\) −3.85558e11 −0.118758
\(604\) 1.68851e11 0.0516223
\(605\) −3.39153e11 −0.102919
\(606\) 4.20409e12 1.26633
\(607\) 2.63454e12 0.787692 0.393846 0.919177i \(-0.371144\pi\)
0.393846 + 0.919177i \(0.371144\pi\)
\(608\) 3.36063e12 0.997367
\(609\) 7.36446e12 2.16952
\(610\) −1.20236e12 −0.351601
\(611\) −8.62177e11 −0.250271
\(612\) 1.43912e11 0.0414682
\(613\) 1.97763e12 0.565682 0.282841 0.959167i \(-0.408723\pi\)
0.282841 + 0.959167i \(0.408723\pi\)
\(614\) −1.43069e12 −0.406246
\(615\) 4.73827e12 1.33562
\(616\) 3.26967e12 0.914936
\(617\) −1.80428e12 −0.501211 −0.250605 0.968089i \(-0.580630\pi\)
−0.250605 + 0.968089i \(0.580630\pi\)
\(618\) 4.04298e12 1.11495
\(619\) 4.19267e12 1.14784 0.573922 0.818910i \(-0.305421\pi\)
0.573922 + 0.818910i \(0.305421\pi\)
\(620\) 1.35482e12 0.368231
\(621\) −4.42819e12 −1.19485
\(622\) 5.92851e11 0.158814
\(623\) 2.34813e12 0.624489
\(624\) −2.50577e12 −0.661623
\(625\) −1.15858e11 −0.0303715
\(626\) −3.51070e12 −0.913712
\(627\) −6.15628e12 −1.59079
\(628\) 1.42771e12 0.366288
\(629\) 1.49791e12 0.381555
\(630\) 1.46574e12 0.370702
\(631\) 7.60008e12 1.90847 0.954236 0.299054i \(-0.0966711\pi\)
0.954236 + 0.299054i \(0.0966711\pi\)
\(632\) 4.53517e12 1.13075
\(633\) −5.46871e12 −1.35384
\(634\) −4.05108e12 −0.995793
\(635\) 4.26862e12 1.04185
\(636\) 4.69892e11 0.113878
\(637\) −1.45105e12 −0.349184
\(638\) 6.18693e12 1.47837
\(639\) 1.00530e12 0.238528
\(640\) 3.17866e12 0.748918
\(641\) 2.51743e12 0.588974 0.294487 0.955655i \(-0.404851\pi\)
0.294487 + 0.955655i \(0.404851\pi\)
\(642\) −1.96725e12 −0.457038
\(643\) 1.22772e12 0.283238 0.141619 0.989921i \(-0.454769\pi\)
0.141619 + 0.989921i \(0.454769\pi\)
\(644\) −3.35116e12 −0.767729
\(645\) 4.95642e11 0.112759
\(646\) −2.35088e12 −0.531109
\(647\) −1.27600e12 −0.286274 −0.143137 0.989703i \(-0.545719\pi\)
−0.143137 + 0.989703i \(0.545719\pi\)
\(648\) 4.18145e12 0.931621
\(649\) −2.31806e12 −0.512888
\(650\) 1.46563e12 0.322044
\(651\) −1.19017e13 −2.59714
\(652\) 3.61043e11 0.0782430
\(653\) −5.09778e12 −1.09717 −0.548583 0.836096i \(-0.684832\pi\)
−0.548583 + 0.836096i \(0.684832\pi\)
\(654\) 1.06616e12 0.227888
\(655\) −2.50400e12 −0.531555
\(656\) 1.05213e13 2.21821
\(657\) 1.88688e12 0.395094
\(658\) 4.05220e12 0.842703
\(659\) −5.41368e12 −1.11817 −0.559085 0.829110i \(-0.688847\pi\)
−0.559085 + 0.829110i \(0.688847\pi\)
\(660\) 1.15941e12 0.237842
\(661\) −6.99933e11 −0.142610 −0.0713050 0.997455i \(-0.522716\pi\)
−0.0713050 + 0.997455i \(0.522716\pi\)
\(662\) 6.31206e12 1.27735
\(663\) 8.27525e11 0.166330
\(664\) 7.94410e10 0.0158595
\(665\) −6.23027e12 −1.23541
\(666\) 2.78624e12 0.548763
\(667\) 1.16874e13 2.28640
\(668\) 2.11294e12 0.410575
\(669\) 1.51887e11 0.0293159
\(670\) −1.18616e12 −0.227408
\(671\) 2.30893e12 0.439703
\(672\) 5.55989e12 1.05173
\(673\) 9.59739e12 1.80337 0.901686 0.432391i \(-0.142330\pi\)
0.901686 + 0.432391i \(0.142330\pi\)
\(674\) 1.01945e12 0.190281
\(675\) −2.36846e12 −0.439137
\(676\) −1.50855e12 −0.277844
\(677\) 6.93140e12 1.26815 0.634077 0.773270i \(-0.281380\pi\)
0.634077 + 0.773270i \(0.281380\pi\)
\(678\) −8.18550e12 −1.48769
\(679\) 8.94354e12 1.61471
\(680\) −8.16022e11 −0.146356
\(681\) 2.38469e12 0.424883
\(682\) −9.99870e12 −1.76976
\(683\) −1.01426e13 −1.78343 −0.891715 0.452597i \(-0.850497\pi\)
−0.891715 + 0.452597i \(0.850497\pi\)
\(684\) −1.13784e12 −0.198759
\(685\) −2.31702e12 −0.402089
\(686\) −2.13152e12 −0.367478
\(687\) −2.72966e12 −0.467523
\(688\) 1.10057e12 0.187271
\(689\) 7.46713e11 0.126231
\(690\) 8.41713e12 1.41365
\(691\) −1.50973e12 −0.251911 −0.125955 0.992036i \(-0.540200\pi\)
−0.125955 + 0.992036i \(0.540200\pi\)
\(692\) −7.99532e11 −0.132543
\(693\) −2.81471e12 −0.463591
\(694\) −1.43528e12 −0.234865
\(695\) −1.75572e12 −0.285446
\(696\) −7.62640e12 −1.23191
\(697\) −3.47463e12 −0.557650
\(698\) −1.66772e12 −0.265934
\(699\) −6.24251e12 −0.989035
\(700\) −1.79240e12 −0.282159
\(701\) 3.00850e12 0.470565 0.235282 0.971927i \(-0.424399\pi\)
0.235282 + 0.971927i \(0.424399\pi\)
\(702\) −2.49132e12 −0.387179
\(703\) −1.18432e13 −1.82882
\(704\) −2.64859e12 −0.406385
\(705\) −2.64836e12 −0.403762
\(706\) −5.24956e12 −0.795247
\(707\) −8.17031e12 −1.22985
\(708\) −1.55030e12 −0.231881
\(709\) 6.68286e12 0.993240 0.496620 0.867968i \(-0.334574\pi\)
0.496620 + 0.867968i \(0.334574\pi\)
\(710\) 3.09276e12 0.456755
\(711\) −3.90413e12 −0.572942
\(712\) −2.43164e12 −0.354601
\(713\) −1.88880e13 −2.73706
\(714\) −3.88934e12 −0.560059
\(715\) 1.84244e12 0.263642
\(716\) 1.45762e11 0.0207270
\(717\) 1.44490e13 2.04175
\(718\) 1.15603e13 1.62333
\(719\) −4.40326e12 −0.614461 −0.307230 0.951635i \(-0.599402\pi\)
−0.307230 + 0.951635i \(0.599402\pi\)
\(720\) −2.12712e12 −0.294982
\(721\) −7.85720e12 −1.08283
\(722\) 1.00981e13 1.38300
\(723\) −1.97977e12 −0.269458
\(724\) −4.94977e12 −0.669517
\(725\) 6.25115e12 0.840309
\(726\) 1.67397e12 0.223632
\(727\) 5.60251e11 0.0743837 0.0371919 0.999308i \(-0.488159\pi\)
0.0371919 + 0.999308i \(0.488159\pi\)
\(728\) 3.47497e12 0.458521
\(729\) 2.91382e12 0.382110
\(730\) 5.80492e12 0.756560
\(731\) −3.63460e11 −0.0470792
\(732\) 1.54420e12 0.198794
\(733\) 1.16288e13 1.48787 0.743937 0.668249i \(-0.232956\pi\)
0.743937 + 0.668249i \(0.232956\pi\)
\(734\) −6.15985e12 −0.783317
\(735\) −4.45720e12 −0.563338
\(736\) 8.82357e12 1.10839
\(737\) 2.27782e12 0.284391
\(738\) −6.46313e12 −0.802027
\(739\) −8.52376e12 −1.05131 −0.525656 0.850697i \(-0.676180\pi\)
−0.525656 + 0.850697i \(0.676180\pi\)
\(740\) 2.23043e12 0.273429
\(741\) −6.54282e12 −0.797229
\(742\) −3.50952e12 −0.425041
\(743\) 7.66343e12 0.922515 0.461258 0.887266i \(-0.347398\pi\)
0.461258 + 0.887266i \(0.347398\pi\)
\(744\) 1.23250e13 1.47472
\(745\) 1.52061e12 0.180848
\(746\) 1.51291e13 1.78850
\(747\) −6.83872e10 −0.00803586
\(748\) −8.50209e11 −0.0993045
\(749\) 3.82319e12 0.443872
\(750\) 1.19511e13 1.37922
\(751\) −3.80411e12 −0.436389 −0.218194 0.975905i \(-0.570017\pi\)
−0.218194 + 0.975905i \(0.570017\pi\)
\(752\) −5.88066e12 −0.670573
\(753\) 6.01524e12 0.681829
\(754\) 6.57540e12 0.740885
\(755\) 8.24213e11 0.0923162
\(756\) 3.04677e12 0.339228
\(757\) −1.39063e13 −1.53915 −0.769575 0.638556i \(-0.779532\pi\)
−0.769575 + 0.638556i \(0.779532\pi\)
\(758\) −9.65007e12 −1.06174
\(759\) −1.61637e13 −1.76788
\(760\) 6.45187e12 0.701495
\(761\) 1.60656e13 1.73646 0.868230 0.496162i \(-0.165258\pi\)
0.868230 + 0.496162i \(0.165258\pi\)
\(762\) −2.10688e13 −2.26382
\(763\) −2.07199e12 −0.221323
\(764\) 4.63073e12 0.491733
\(765\) 7.02477e11 0.0741576
\(766\) 1.51035e13 1.58507
\(767\) −2.46360e12 −0.257034
\(768\) −1.06529e13 −1.10495
\(769\) 9.39173e12 0.968449 0.484225 0.874944i \(-0.339102\pi\)
0.484225 + 0.874944i \(0.339102\pi\)
\(770\) −8.65938e12 −0.887725
\(771\) 9.34979e12 0.952922
\(772\) −5.68816e12 −0.576360
\(773\) 7.25850e11 0.0731205 0.0365602 0.999331i \(-0.488360\pi\)
0.0365602 + 0.999331i \(0.488360\pi\)
\(774\) −6.76069e11 −0.0677106
\(775\) −1.01025e13 −1.00594
\(776\) −9.26164e12 −0.916875
\(777\) −1.95936e13 −1.92850
\(778\) −6.75083e12 −0.660616
\(779\) 2.74722e13 2.67285
\(780\) 1.23221e12 0.119195
\(781\) −5.93914e12 −0.571207
\(782\) −6.17239e12 −0.590232
\(783\) −1.06259e13 −1.01027
\(784\) −9.89718e12 −0.935598
\(785\) 6.96909e12 0.655032
\(786\) 1.23591e13 1.15501
\(787\) 2.02032e12 0.187730 0.0938649 0.995585i \(-0.470078\pi\)
0.0938649 + 0.995585i \(0.470078\pi\)
\(788\) −1.44818e12 −0.133799
\(789\) −1.95399e13 −1.79505
\(790\) −1.20109e13 −1.09712
\(791\) 1.59079e13 1.44483
\(792\) 2.91483e12 0.263239
\(793\) 2.45391e12 0.220358
\(794\) 1.28225e13 1.14493
\(795\) 2.29369e12 0.203649
\(796\) 4.85002e12 0.428189
\(797\) −1.88088e13 −1.65119 −0.825597 0.564260i \(-0.809162\pi\)
−0.825597 + 0.564260i \(0.809162\pi\)
\(798\) 3.07510e13 2.68439
\(799\) 1.94207e12 0.168580
\(800\) 4.71938e12 0.407362
\(801\) 2.09329e12 0.179673
\(802\) −5.93104e11 −0.0506228
\(803\) −1.11474e13 −0.946136
\(804\) 1.52339e12 0.128576
\(805\) −1.63580e13 −1.37293
\(806\) −1.06265e13 −0.886916
\(807\) 2.24113e13 1.86010
\(808\) 8.46091e12 0.698338
\(809\) −7.98963e12 −0.655780 −0.327890 0.944716i \(-0.606338\pi\)
−0.327890 + 0.944716i \(0.606338\pi\)
\(810\) −1.10741e13 −0.903913
\(811\) 1.98323e13 1.60982 0.804912 0.593395i \(-0.202213\pi\)
0.804912 + 0.593395i \(0.202213\pi\)
\(812\) −8.04142e12 −0.649128
\(813\) −2.44190e13 −1.96029
\(814\) −1.64607e13 −1.31413
\(815\) 1.76236e12 0.139922
\(816\) 5.64430e12 0.445661
\(817\) 2.87370e12 0.225653
\(818\) −1.36967e13 −1.06961
\(819\) −2.99144e12 −0.232329
\(820\) −5.17382e12 −0.399622
\(821\) 1.32468e13 1.01757 0.508787 0.860892i \(-0.330094\pi\)
0.508787 + 0.860892i \(0.330094\pi\)
\(822\) 1.14362e13 0.873692
\(823\) −1.59550e13 −1.21227 −0.606133 0.795363i \(-0.707280\pi\)
−0.606133 + 0.795363i \(0.707280\pi\)
\(824\) 8.13667e12 0.614857
\(825\) −8.64535e12 −0.649740
\(826\) 1.15788e13 0.865475
\(827\) −1.55293e13 −1.15445 −0.577226 0.816584i \(-0.695865\pi\)
−0.577226 + 0.816584i \(0.695865\pi\)
\(828\) −2.98747e12 −0.220885
\(829\) 9.57611e12 0.704196 0.352098 0.935963i \(-0.385468\pi\)
0.352098 + 0.935963i \(0.385468\pi\)
\(830\) −2.10391e11 −0.0153878
\(831\) 2.31016e13 1.68050
\(832\) −2.81489e12 −0.203660
\(833\) 3.26852e12 0.235206
\(834\) 8.66578e12 0.620241
\(835\) 1.03139e13 0.734231
\(836\) 6.72217e12 0.475972
\(837\) 1.71725e13 1.20939
\(838\) −2.31107e13 −1.61888
\(839\) 7.28075e12 0.507279 0.253640 0.967299i \(-0.418372\pi\)
0.253640 + 0.967299i \(0.418372\pi\)
\(840\) 1.06741e13 0.739732
\(841\) 1.35379e13 0.933191
\(842\) 1.88785e12 0.129438
\(843\) 2.91084e13 1.98515
\(844\) 5.97140e12 0.405075
\(845\) −7.36371e12 −0.496868
\(846\) 3.61243e12 0.242456
\(847\) −3.25323e12 −0.217190
\(848\) 5.09311e12 0.338222
\(849\) 2.77220e13 1.83122
\(850\) −3.30137e12 −0.216925
\(851\) −3.10951e13 −2.03240
\(852\) −3.97205e12 −0.258248
\(853\) −1.46073e13 −0.944710 −0.472355 0.881408i \(-0.656596\pi\)
−0.472355 + 0.881408i \(0.656596\pi\)
\(854\) −1.15333e13 −0.741979
\(855\) −5.55413e12 −0.355442
\(856\) −3.95918e12 −0.252042
\(857\) −5.33231e12 −0.337677 −0.168839 0.985644i \(-0.554002\pi\)
−0.168839 + 0.985644i \(0.554002\pi\)
\(858\) −9.09378e12 −0.572864
\(859\) −2.80034e13 −1.75486 −0.877429 0.479707i \(-0.840743\pi\)
−0.877429 + 0.479707i \(0.840743\pi\)
\(860\) −5.41202e11 −0.0337378
\(861\) 4.54505e13 2.81854
\(862\) −4.68174e12 −0.288818
\(863\) 1.68340e13 1.03309 0.516545 0.856260i \(-0.327218\pi\)
0.516545 + 0.856260i \(0.327218\pi\)
\(864\) −8.02212e12 −0.489753
\(865\) −3.90275e12 −0.237027
\(866\) −3.18709e13 −1.92559
\(867\) 1.76940e13 1.06350
\(868\) 1.29957e13 0.777074
\(869\) 2.30650e13 1.37203
\(870\) 2.01977e13 1.19527
\(871\) 2.42084e12 0.142523
\(872\) 2.14568e12 0.125673
\(873\) 7.97294e12 0.464573
\(874\) 4.88019e13 2.82902
\(875\) −2.32260e13 −1.33948
\(876\) −7.45530e12 −0.427756
\(877\) 2.28783e13 1.30595 0.652973 0.757381i \(-0.273522\pi\)
0.652973 + 0.757381i \(0.273522\pi\)
\(878\) −1.54486e13 −0.877330
\(879\) −2.38705e13 −1.34869
\(880\) 1.25667e13 0.706398
\(881\) 2.40339e13 1.34410 0.672052 0.740504i \(-0.265413\pi\)
0.672052 + 0.740504i \(0.265413\pi\)
\(882\) 6.07974e12 0.338280
\(883\) −2.37323e13 −1.31376 −0.656882 0.753993i \(-0.728125\pi\)
−0.656882 + 0.753993i \(0.728125\pi\)
\(884\) −9.03592e11 −0.0497665
\(885\) −7.56747e12 −0.414673
\(886\) −3.19707e13 −1.74301
\(887\) 1.92837e12 0.104600 0.0523002 0.998631i \(-0.483345\pi\)
0.0523002 + 0.998631i \(0.483345\pi\)
\(888\) 2.02905e13 1.09505
\(889\) 4.09455e13 2.19861
\(890\) 6.43995e12 0.344055
\(891\) 2.12660e13 1.13041
\(892\) −1.65849e11 −0.00877145
\(893\) −1.53550e13 −0.808013
\(894\) −7.50533e12 −0.392962
\(895\) 7.11510e11 0.0370661
\(896\) 3.04904e13 1.58043
\(897\) −1.71786e13 −0.885976
\(898\) −4.45016e13 −2.28366
\(899\) −4.53237e13 −2.31423
\(900\) −1.59788e12 −0.0811808
\(901\) −1.68199e12 −0.0850279
\(902\) 3.81832e13 1.92063
\(903\) 4.75430e12 0.237953
\(904\) −1.64737e13 −0.820412
\(905\) −2.41613e13 −1.19730
\(906\) −4.06810e12 −0.200592
\(907\) −7.87264e12 −0.386267 −0.193134 0.981172i \(-0.561865\pi\)
−0.193134 + 0.981172i \(0.561865\pi\)
\(908\) −2.60389e12 −0.127127
\(909\) −7.28362e12 −0.353842
\(910\) −9.20308e12 −0.444884
\(911\) 5.84560e12 0.281188 0.140594 0.990067i \(-0.455099\pi\)
0.140594 + 0.990067i \(0.455099\pi\)
\(912\) −4.46267e13 −2.13608
\(913\) 4.04022e11 0.0192436
\(914\) −9.27830e12 −0.439755
\(915\) 7.53769e12 0.355503
\(916\) 2.98058e12 0.139885
\(917\) −2.40189e13 −1.12174
\(918\) 5.61175e12 0.260799
\(919\) 1.30582e13 0.603898 0.301949 0.953324i \(-0.402363\pi\)
0.301949 + 0.953324i \(0.402363\pi\)
\(920\) 1.69398e13 0.779585
\(921\) 8.96914e12 0.410755
\(922\) −2.06139e13 −0.939444
\(923\) −6.31204e12 −0.286261
\(924\) 1.11213e13 0.501916
\(925\) −1.66316e13 −0.746957
\(926\) 2.17829e13 0.973567
\(927\) −7.00449e12 −0.311543
\(928\) 2.11730e13 0.937165
\(929\) 3.22164e11 0.0141908 0.00709538 0.999975i \(-0.497741\pi\)
0.00709538 + 0.999975i \(0.497741\pi\)
\(930\) −3.26415e13 −1.43086
\(931\) −2.58425e13 −1.12736
\(932\) 6.81633e12 0.295923
\(933\) −3.71663e12 −0.160576
\(934\) −2.48543e13 −1.06866
\(935\) −4.15013e12 −0.177586
\(936\) 3.09784e12 0.131922
\(937\) −2.39611e13 −1.01550 −0.507748 0.861506i \(-0.669522\pi\)
−0.507748 + 0.861506i \(0.669522\pi\)
\(938\) −1.13779e13 −0.479897
\(939\) 2.20089e13 0.923853
\(940\) 2.89180e12 0.120807
\(941\) 1.17349e13 0.487895 0.243947 0.969788i \(-0.421558\pi\)
0.243947 + 0.969788i \(0.421558\pi\)
\(942\) −3.43976e13 −1.42331
\(943\) 7.21300e13 2.97039
\(944\) −1.68035e13 −0.688694
\(945\) 1.48722e13 0.606642
\(946\) 3.99412e12 0.162148
\(947\) −4.64389e13 −1.87632 −0.938160 0.346203i \(-0.887471\pi\)
−0.938160 + 0.346203i \(0.887471\pi\)
\(948\) 1.54257e13 0.620308
\(949\) −1.18473e13 −0.474157
\(950\) 2.61023e13 1.03973
\(951\) 2.53966e13 1.00685
\(952\) −7.82744e12 −0.308854
\(953\) −8.15486e12 −0.320257 −0.160128 0.987096i \(-0.551191\pi\)
−0.160128 + 0.987096i \(0.551191\pi\)
\(954\) −3.12865e12 −0.122289
\(955\) 2.26040e13 0.879366
\(956\) −1.57772e13 −0.610899
\(957\) −3.87864e13 −1.49477
\(958\) −3.47060e13 −1.33125
\(959\) −2.22253e13 −0.848523
\(960\) −8.64653e12 −0.328565
\(961\) 4.68080e13 1.77037
\(962\) −1.74942e13 −0.658578
\(963\) 3.40828e12 0.127708
\(964\) 2.16175e12 0.0806230
\(965\) −2.77656e13 −1.03071
\(966\) 8.07388e13 2.98322
\(967\) 2.76860e13 1.01822 0.509109 0.860702i \(-0.329975\pi\)
0.509109 + 0.860702i \(0.329975\pi\)
\(968\) 3.36894e12 0.123326
\(969\) 1.47378e13 0.537003
\(970\) 2.45285e13 0.889606
\(971\) −2.46465e13 −0.889750 −0.444875 0.895593i \(-0.646752\pi\)
−0.444875 + 0.895593i \(0.646752\pi\)
\(972\) 7.11040e12 0.255503
\(973\) −1.68412e13 −0.602373
\(974\) −2.10039e13 −0.747797
\(975\) −9.18817e12 −0.325618
\(976\) 1.67374e13 0.590423
\(977\) −4.94639e12 −0.173685 −0.0868427 0.996222i \(-0.527678\pi\)
−0.0868427 + 0.996222i \(0.527678\pi\)
\(978\) −8.69856e12 −0.304034
\(979\) −1.23669e13 −0.430267
\(980\) 4.86691e12 0.168553
\(981\) −1.84712e12 −0.0636774
\(982\) 2.46488e13 0.845853
\(983\) −3.98081e13 −1.35982 −0.679908 0.733297i \(-0.737980\pi\)
−0.679908 + 0.733297i \(0.737980\pi\)
\(984\) −4.70670e13 −1.60044
\(985\) −7.06899e12 −0.239273
\(986\) −1.48112e13 −0.499051
\(987\) −2.54036e13 −0.852056
\(988\) 7.14425e12 0.238534
\(989\) 7.54508e12 0.250773
\(990\) −7.71961e12 −0.255410
\(991\) 2.28757e13 0.753430 0.376715 0.926329i \(-0.377054\pi\)
0.376715 + 0.926329i \(0.377054\pi\)
\(992\) −3.42177e13 −1.12188
\(993\) −3.95709e13 −1.29153
\(994\) 2.96664e13 0.963886
\(995\) 2.36744e13 0.765730
\(996\) 2.70207e11 0.00870019
\(997\) 4.85768e13 1.55704 0.778521 0.627618i \(-0.215970\pi\)
0.778521 + 0.627618i \(0.215970\pi\)
\(998\) 1.82154e13 0.581235
\(999\) 2.82707e13 0.898034
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 43.10.a.a.1.13 15
3.2 odd 2 387.10.a.c.1.3 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.10.a.a.1.13 15 1.1 even 1 trivial
387.10.a.c.1.3 15 3.2 odd 2