Properties

Label 8003.2.a.c.1.15
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.40631 q^{2}\) \(+0.956408 q^{3}\) \(+3.79032 q^{4}\) \(+0.737910 q^{5}\) \(-2.30141 q^{6}\) \(-3.66716 q^{7}\) \(-4.30806 q^{8}\) \(-2.08528 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.40631 q^{2}\) \(+0.956408 q^{3}\) \(+3.79032 q^{4}\) \(+0.737910 q^{5}\) \(-2.30141 q^{6}\) \(-3.66716 q^{7}\) \(-4.30806 q^{8}\) \(-2.08528 q^{9}\) \(-1.77564 q^{10}\) \(+1.41720 q^{11}\) \(+3.62509 q^{12}\) \(+1.85413 q^{13}\) \(+8.82431 q^{14}\) \(+0.705743 q^{15}\) \(+2.78588 q^{16}\) \(+6.47350 q^{17}\) \(+5.01783 q^{18}\) \(+6.02287 q^{19}\) \(+2.79691 q^{20}\) \(-3.50730 q^{21}\) \(-3.41023 q^{22}\) \(-1.32910 q^{23}\) \(-4.12026 q^{24}\) \(-4.45549 q^{25}\) \(-4.46160 q^{26}\) \(-4.86361 q^{27}\) \(-13.8997 q^{28}\) \(+9.16119 q^{29}\) \(-1.69824 q^{30}\) \(-7.11229 q^{31}\) \(+1.91243 q^{32}\) \(+1.35543 q^{33}\) \(-15.5772 q^{34}\) \(-2.70603 q^{35}\) \(-7.90389 q^{36}\) \(-9.66734 q^{37}\) \(-14.4929 q^{38}\) \(+1.77330 q^{39}\) \(-3.17896 q^{40}\) \(+4.45502 q^{41}\) \(+8.43964 q^{42}\) \(+5.74808 q^{43}\) \(+5.37166 q^{44}\) \(-1.53875 q^{45}\) \(+3.19823 q^{46}\) \(+7.90190 q^{47}\) \(+2.66444 q^{48}\) \(+6.44804 q^{49}\) \(+10.7213 q^{50}\) \(+6.19131 q^{51}\) \(+7.02773 q^{52}\) \(-1.00000 q^{53}\) \(+11.7033 q^{54}\) \(+1.04577 q^{55}\) \(+15.7983 q^{56}\) \(+5.76033 q^{57}\) \(-22.0446 q^{58}\) \(+3.47977 q^{59}\) \(+2.67499 q^{60}\) \(+2.52155 q^{61}\) \(+17.1144 q^{62}\) \(+7.64706 q^{63}\) \(-10.1737 q^{64}\) \(+1.36818 q^{65}\) \(-3.26157 q^{66}\) \(+11.4639 q^{67}\) \(+24.5366 q^{68}\) \(-1.27116 q^{69}\) \(+6.51154 q^{70}\) \(-9.38012 q^{71}\) \(+8.98352 q^{72}\) \(-14.6044 q^{73}\) \(+23.2626 q^{74}\) \(-4.26127 q^{75}\) \(+22.8286 q^{76}\) \(-5.19711 q^{77}\) \(-4.26711 q^{78}\) \(-1.60709 q^{79}\) \(+2.05573 q^{80}\) \(+1.60425 q^{81}\) \(-10.7201 q^{82}\) \(+14.1268 q^{83}\) \(-13.2938 q^{84}\) \(+4.77686 q^{85}\) \(-13.8316 q^{86}\) \(+8.76184 q^{87}\) \(-6.10540 q^{88}\) \(-13.0935 q^{89}\) \(+3.70271 q^{90}\) \(-6.79937 q^{91}\) \(-5.03772 q^{92}\) \(-6.80226 q^{93}\) \(-19.0144 q^{94}\) \(+4.44434 q^{95}\) \(+1.82907 q^{96}\) \(+10.1986 q^{97}\) \(-15.5160 q^{98}\) \(-2.95527 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.40631 −1.70152 −0.850758 0.525557i \(-0.823857\pi\)
−0.850758 + 0.525557i \(0.823857\pi\)
\(3\) 0.956408 0.552183 0.276091 0.961131i \(-0.410961\pi\)
0.276091 + 0.961131i \(0.410961\pi\)
\(4\) 3.79032 1.89516
\(5\) 0.737910 0.330003 0.165002 0.986293i \(-0.447237\pi\)
0.165002 + 0.986293i \(0.447237\pi\)
\(6\) −2.30141 −0.939548
\(7\) −3.66716 −1.38605 −0.693027 0.720911i \(-0.743724\pi\)
−0.693027 + 0.720911i \(0.743724\pi\)
\(8\) −4.30806 −1.52313
\(9\) −2.08528 −0.695094
\(10\) −1.77564 −0.561506
\(11\) 1.41720 0.427303 0.213652 0.976910i \(-0.431464\pi\)
0.213652 + 0.976910i \(0.431464\pi\)
\(12\) 3.62509 1.04647
\(13\) 1.85413 0.514242 0.257121 0.966379i \(-0.417226\pi\)
0.257121 + 0.966379i \(0.417226\pi\)
\(14\) 8.82431 2.35840
\(15\) 0.705743 0.182222
\(16\) 2.78588 0.696470
\(17\) 6.47350 1.57005 0.785027 0.619462i \(-0.212649\pi\)
0.785027 + 0.619462i \(0.212649\pi\)
\(18\) 5.01783 1.18271
\(19\) 6.02287 1.38174 0.690871 0.722978i \(-0.257227\pi\)
0.690871 + 0.722978i \(0.257227\pi\)
\(20\) 2.79691 0.625409
\(21\) −3.50730 −0.765356
\(22\) −3.41023 −0.727064
\(23\) −1.32910 −0.277137 −0.138568 0.990353i \(-0.544250\pi\)
−0.138568 + 0.990353i \(0.544250\pi\)
\(24\) −4.12026 −0.841045
\(25\) −4.45549 −0.891098
\(26\) −4.46160 −0.874991
\(27\) −4.86361 −0.936002
\(28\) −13.8997 −2.62680
\(29\) 9.16119 1.70119 0.850595 0.525821i \(-0.176242\pi\)
0.850595 + 0.525821i \(0.176242\pi\)
\(30\) −1.69824 −0.310054
\(31\) −7.11229 −1.27741 −0.638703 0.769454i \(-0.720529\pi\)
−0.638703 + 0.769454i \(0.720529\pi\)
\(32\) 1.91243 0.338074
\(33\) 1.35543 0.235949
\(34\) −15.5772 −2.67147
\(35\) −2.70603 −0.457403
\(36\) −7.90389 −1.31731
\(37\) −9.66734 −1.58930 −0.794651 0.607067i \(-0.792346\pi\)
−0.794651 + 0.607067i \(0.792346\pi\)
\(38\) −14.4929 −2.35106
\(39\) 1.77330 0.283956
\(40\) −3.17896 −0.502638
\(41\) 4.45502 0.695757 0.347879 0.937540i \(-0.386902\pi\)
0.347879 + 0.937540i \(0.386902\pi\)
\(42\) 8.43964 1.30227
\(43\) 5.74808 0.876573 0.438287 0.898835i \(-0.355585\pi\)
0.438287 + 0.898835i \(0.355585\pi\)
\(44\) 5.37166 0.809808
\(45\) −1.53875 −0.229383
\(46\) 3.19823 0.471553
\(47\) 7.90190 1.15261 0.576305 0.817234i \(-0.304494\pi\)
0.576305 + 0.817234i \(0.304494\pi\)
\(48\) 2.66444 0.384579
\(49\) 6.44804 0.921148
\(50\) 10.7213 1.51622
\(51\) 6.19131 0.866957
\(52\) 7.02773 0.974571
\(53\) −1.00000 −0.137361
\(54\) 11.7033 1.59262
\(55\) 1.04577 0.141012
\(56\) 15.7983 2.11114
\(57\) 5.76033 0.762974
\(58\) −22.0446 −2.89460
\(59\) 3.47977 0.453027 0.226514 0.974008i \(-0.427267\pi\)
0.226514 + 0.974008i \(0.427267\pi\)
\(60\) 2.67499 0.345340
\(61\) 2.52155 0.322851 0.161426 0.986885i \(-0.448391\pi\)
0.161426 + 0.986885i \(0.448391\pi\)
\(62\) 17.1144 2.17353
\(63\) 7.64706 0.963439
\(64\) −10.1737 −1.27171
\(65\) 1.36818 0.169702
\(66\) −3.26157 −0.401472
\(67\) 11.4639 1.40054 0.700272 0.713876i \(-0.253062\pi\)
0.700272 + 0.713876i \(0.253062\pi\)
\(68\) 24.5366 2.97550
\(69\) −1.27116 −0.153030
\(70\) 6.51154 0.778278
\(71\) −9.38012 −1.11321 −0.556607 0.830776i \(-0.687897\pi\)
−0.556607 + 0.830776i \(0.687897\pi\)
\(72\) 8.98352 1.05872
\(73\) −14.6044 −1.70931 −0.854655 0.519196i \(-0.826232\pi\)
−0.854655 + 0.519196i \(0.826232\pi\)
\(74\) 23.2626 2.70422
\(75\) −4.26127 −0.492049
\(76\) 22.8286 2.61862
\(77\) −5.19711 −0.592266
\(78\) −4.26711 −0.483155
\(79\) −1.60709 −0.180812 −0.0904058 0.995905i \(-0.528816\pi\)
−0.0904058 + 0.995905i \(0.528816\pi\)
\(80\) 2.05573 0.229837
\(81\) 1.60425 0.178250
\(82\) −10.7201 −1.18384
\(83\) 14.1268 1.55061 0.775307 0.631585i \(-0.217595\pi\)
0.775307 + 0.631585i \(0.217595\pi\)
\(84\) −13.2938 −1.45047
\(85\) 4.77686 0.518123
\(86\) −13.8316 −1.49150
\(87\) 8.76184 0.939368
\(88\) −6.10540 −0.650838
\(89\) −13.0935 −1.38790 −0.693952 0.720022i \(-0.744132\pi\)
−0.693952 + 0.720022i \(0.744132\pi\)
\(90\) 3.70271 0.390300
\(91\) −6.79937 −0.712768
\(92\) −5.03772 −0.525219
\(93\) −6.80226 −0.705361
\(94\) −19.0144 −1.96119
\(95\) 4.44434 0.455979
\(96\) 1.82907 0.186678
\(97\) 10.1986 1.03551 0.517754 0.855529i \(-0.326768\pi\)
0.517754 + 0.855529i \(0.326768\pi\)
\(98\) −15.5160 −1.56735
\(99\) −2.95527 −0.297016
\(100\) −16.8877 −1.68877
\(101\) −3.08520 −0.306989 −0.153495 0.988149i \(-0.549053\pi\)
−0.153495 + 0.988149i \(0.549053\pi\)
\(102\) −14.8982 −1.47514
\(103\) 2.86454 0.282252 0.141126 0.989992i \(-0.454928\pi\)
0.141126 + 0.989992i \(0.454928\pi\)
\(104\) −7.98768 −0.783257
\(105\) −2.58807 −0.252570
\(106\) 2.40631 0.233721
\(107\) −5.75229 −0.556095 −0.278048 0.960567i \(-0.589687\pi\)
−0.278048 + 0.960567i \(0.589687\pi\)
\(108\) −18.4346 −1.77387
\(109\) 2.77310 0.265615 0.132808 0.991142i \(-0.457601\pi\)
0.132808 + 0.991142i \(0.457601\pi\)
\(110\) −2.51644 −0.239933
\(111\) −9.24593 −0.877585
\(112\) −10.2163 −0.965345
\(113\) −17.4290 −1.63959 −0.819793 0.572660i \(-0.805912\pi\)
−0.819793 + 0.572660i \(0.805912\pi\)
\(114\) −13.8611 −1.29821
\(115\) −0.980758 −0.0914561
\(116\) 34.7238 3.22403
\(117\) −3.86638 −0.357447
\(118\) −8.37339 −0.770833
\(119\) −23.7393 −2.17618
\(120\) −3.04038 −0.277548
\(121\) −8.99153 −0.817412
\(122\) −6.06763 −0.549337
\(123\) 4.26082 0.384185
\(124\) −26.9579 −2.42089
\(125\) −6.97730 −0.624069
\(126\) −18.4012 −1.63931
\(127\) 13.7500 1.22012 0.610060 0.792355i \(-0.291145\pi\)
0.610060 + 0.792355i \(0.291145\pi\)
\(128\) 20.6561 1.82576
\(129\) 5.49751 0.484029
\(130\) −3.29226 −0.288750
\(131\) −2.38933 −0.208756 −0.104378 0.994538i \(-0.533285\pi\)
−0.104378 + 0.994538i \(0.533285\pi\)
\(132\) 5.13750 0.447162
\(133\) −22.0868 −1.91517
\(134\) −27.5858 −2.38305
\(135\) −3.58890 −0.308884
\(136\) −27.8882 −2.39139
\(137\) −7.29527 −0.623277 −0.311638 0.950201i \(-0.600878\pi\)
−0.311638 + 0.950201i \(0.600878\pi\)
\(138\) 3.05881 0.260383
\(139\) −1.75507 −0.148863 −0.0744314 0.997226i \(-0.523714\pi\)
−0.0744314 + 0.997226i \(0.523714\pi\)
\(140\) −10.2567 −0.866851
\(141\) 7.55745 0.636452
\(142\) 22.5714 1.89415
\(143\) 2.62768 0.219737
\(144\) −5.80935 −0.484112
\(145\) 6.76013 0.561398
\(146\) 35.1426 2.90842
\(147\) 6.16696 0.508642
\(148\) −36.6423 −3.01198
\(149\) 8.67854 0.710974 0.355487 0.934681i \(-0.384315\pi\)
0.355487 + 0.934681i \(0.384315\pi\)
\(150\) 10.2539 0.837229
\(151\) 1.00000 0.0813788
\(152\) −25.9469 −2.10457
\(153\) −13.4991 −1.09134
\(154\) 12.5059 1.00775
\(155\) −5.24823 −0.421548
\(156\) 6.72138 0.538141
\(157\) 13.8022 1.10154 0.550768 0.834658i \(-0.314335\pi\)
0.550768 + 0.834658i \(0.314335\pi\)
\(158\) 3.86715 0.307654
\(159\) −0.956408 −0.0758481
\(160\) 1.41120 0.111565
\(161\) 4.87403 0.384127
\(162\) −3.86033 −0.303296
\(163\) 12.5161 0.980333 0.490166 0.871629i \(-0.336936\pi\)
0.490166 + 0.871629i \(0.336936\pi\)
\(164\) 16.8859 1.31857
\(165\) 1.00018 0.0778641
\(166\) −33.9933 −2.63840
\(167\) 5.87085 0.454300 0.227150 0.973860i \(-0.427059\pi\)
0.227150 + 0.973860i \(0.427059\pi\)
\(168\) 15.1097 1.16574
\(169\) −9.56222 −0.735555
\(170\) −11.4946 −0.881595
\(171\) −12.5594 −0.960441
\(172\) 21.7870 1.66125
\(173\) −7.73110 −0.587784 −0.293892 0.955839i \(-0.594951\pi\)
−0.293892 + 0.955839i \(0.594951\pi\)
\(174\) −21.0837 −1.59835
\(175\) 16.3390 1.23511
\(176\) 3.94816 0.297604
\(177\) 3.32808 0.250154
\(178\) 31.5069 2.36154
\(179\) −4.18187 −0.312568 −0.156284 0.987712i \(-0.549951\pi\)
−0.156284 + 0.987712i \(0.549951\pi\)
\(180\) −5.83236 −0.434718
\(181\) 23.1087 1.71766 0.858828 0.512263i \(-0.171193\pi\)
0.858828 + 0.512263i \(0.171193\pi\)
\(182\) 16.3614 1.21279
\(183\) 2.41163 0.178273
\(184\) 5.72585 0.422115
\(185\) −7.13363 −0.524475
\(186\) 16.3683 1.20018
\(187\) 9.17427 0.670889
\(188\) 29.9507 2.18438
\(189\) 17.8356 1.29735
\(190\) −10.6944 −0.775856
\(191\) −3.80968 −0.275658 −0.137829 0.990456i \(-0.544013\pi\)
−0.137829 + 0.990456i \(0.544013\pi\)
\(192\) −9.73018 −0.702215
\(193\) −7.60617 −0.547504 −0.273752 0.961800i \(-0.588265\pi\)
−0.273752 + 0.961800i \(0.588265\pi\)
\(194\) −24.5409 −1.76194
\(195\) 1.30854 0.0937063
\(196\) 24.4401 1.74572
\(197\) 17.6356 1.25648 0.628242 0.778018i \(-0.283775\pi\)
0.628242 + 0.778018i \(0.283775\pi\)
\(198\) 7.11130 0.505378
\(199\) 16.3861 1.16158 0.580791 0.814052i \(-0.302743\pi\)
0.580791 + 0.814052i \(0.302743\pi\)
\(200\) 19.1945 1.35726
\(201\) 10.9642 0.773356
\(202\) 7.42395 0.522347
\(203\) −33.5955 −2.35794
\(204\) 23.4670 1.64302
\(205\) 3.28740 0.229602
\(206\) −6.89297 −0.480256
\(207\) 2.77155 0.192636
\(208\) 5.16537 0.358154
\(209\) 8.53564 0.590423
\(210\) 6.22770 0.429752
\(211\) −18.7283 −1.28931 −0.644656 0.764473i \(-0.722999\pi\)
−0.644656 + 0.764473i \(0.722999\pi\)
\(212\) −3.79032 −0.260320
\(213\) −8.97122 −0.614698
\(214\) 13.8418 0.946205
\(215\) 4.24156 0.289272
\(216\) 20.9527 1.42565
\(217\) 26.0819 1.77055
\(218\) −6.67294 −0.451949
\(219\) −13.9677 −0.943852
\(220\) 3.96380 0.267239
\(221\) 12.0027 0.807388
\(222\) 22.2486 1.49323
\(223\) −4.57398 −0.306296 −0.153148 0.988203i \(-0.548941\pi\)
−0.153148 + 0.988203i \(0.548941\pi\)
\(224\) −7.01319 −0.468589
\(225\) 9.29096 0.619397
\(226\) 41.9396 2.78978
\(227\) −14.8256 −0.984012 −0.492006 0.870592i \(-0.663736\pi\)
−0.492006 + 0.870592i \(0.663736\pi\)
\(228\) 21.8335 1.44596
\(229\) −6.13894 −0.405672 −0.202836 0.979213i \(-0.565016\pi\)
−0.202836 + 0.979213i \(0.565016\pi\)
\(230\) 2.36000 0.155614
\(231\) −4.97056 −0.327039
\(232\) −39.4669 −2.59113
\(233\) 21.9606 1.43869 0.719345 0.694653i \(-0.244442\pi\)
0.719345 + 0.694653i \(0.244442\pi\)
\(234\) 9.30369 0.608202
\(235\) 5.83089 0.380365
\(236\) 13.1894 0.858559
\(237\) −1.53703 −0.0998410
\(238\) 57.1241 3.70281
\(239\) −17.6247 −1.14004 −0.570022 0.821629i \(-0.693065\pi\)
−0.570022 + 0.821629i \(0.693065\pi\)
\(240\) 1.96612 0.126912
\(241\) 5.27943 0.340078 0.170039 0.985437i \(-0.445611\pi\)
0.170039 + 0.985437i \(0.445611\pi\)
\(242\) 21.6364 1.39084
\(243\) 16.1251 1.03443
\(244\) 9.55748 0.611855
\(245\) 4.75807 0.303982
\(246\) −10.2528 −0.653697
\(247\) 11.1672 0.710550
\(248\) 30.6402 1.94565
\(249\) 13.5110 0.856222
\(250\) 16.7895 1.06186
\(251\) −29.7638 −1.87867 −0.939336 0.342998i \(-0.888558\pi\)
−0.939336 + 0.342998i \(0.888558\pi\)
\(252\) 28.9848 1.82587
\(253\) −1.88361 −0.118422
\(254\) −33.0869 −2.07605
\(255\) 4.56863 0.286099
\(256\) −29.3576 −1.83485
\(257\) 14.5436 0.907203 0.453601 0.891205i \(-0.350139\pi\)
0.453601 + 0.891205i \(0.350139\pi\)
\(258\) −13.2287 −0.823583
\(259\) 35.4517 2.20286
\(260\) 5.18583 0.321612
\(261\) −19.1037 −1.18249
\(262\) 5.74946 0.355203
\(263\) 6.25554 0.385733 0.192867 0.981225i \(-0.438222\pi\)
0.192867 + 0.981225i \(0.438222\pi\)
\(264\) −5.83926 −0.359381
\(265\) −0.737910 −0.0453294
\(266\) 53.1477 3.25869
\(267\) −12.5227 −0.766376
\(268\) 43.4520 2.65425
\(269\) 1.82671 0.111377 0.0556883 0.998448i \(-0.482265\pi\)
0.0556883 + 0.998448i \(0.482265\pi\)
\(270\) 8.63601 0.525571
\(271\) 14.9325 0.907085 0.453543 0.891235i \(-0.350160\pi\)
0.453543 + 0.891235i \(0.350160\pi\)
\(272\) 18.0344 1.09350
\(273\) −6.50297 −0.393578
\(274\) 17.5547 1.06052
\(275\) −6.31434 −0.380769
\(276\) −4.81812 −0.290017
\(277\) −4.23907 −0.254701 −0.127350 0.991858i \(-0.540647\pi\)
−0.127350 + 0.991858i \(0.540647\pi\)
\(278\) 4.22323 0.253292
\(279\) 14.8311 0.887917
\(280\) 11.6577 0.696683
\(281\) 4.87738 0.290960 0.145480 0.989361i \(-0.453527\pi\)
0.145480 + 0.989361i \(0.453527\pi\)
\(282\) −18.1855 −1.08293
\(283\) −14.3524 −0.853162 −0.426581 0.904449i \(-0.640282\pi\)
−0.426581 + 0.904449i \(0.640282\pi\)
\(284\) −35.5536 −2.10972
\(285\) 4.25060 0.251784
\(286\) −6.32300 −0.373887
\(287\) −16.3373 −0.964358
\(288\) −3.98797 −0.234993
\(289\) 24.9062 1.46507
\(290\) −16.2670 −0.955229
\(291\) 9.75401 0.571790
\(292\) −55.3552 −3.23942
\(293\) 33.2411 1.94196 0.970982 0.239151i \(-0.0768693\pi\)
0.970982 + 0.239151i \(0.0768693\pi\)
\(294\) −14.8396 −0.865463
\(295\) 2.56775 0.149500
\(296\) 41.6475 2.42071
\(297\) −6.89273 −0.399957
\(298\) −20.8832 −1.20973
\(299\) −2.46432 −0.142515
\(300\) −16.1516 −0.932511
\(301\) −21.0791 −1.21498
\(302\) −2.40631 −0.138467
\(303\) −2.95072 −0.169514
\(304\) 16.7790 0.962341
\(305\) 1.86068 0.106542
\(306\) 32.4829 1.85693
\(307\) 33.0910 1.88860 0.944301 0.329083i \(-0.106740\pi\)
0.944301 + 0.329083i \(0.106740\pi\)
\(308\) −19.6987 −1.12244
\(309\) 2.73967 0.155855
\(310\) 12.6289 0.717271
\(311\) 12.4401 0.705414 0.352707 0.935734i \(-0.385261\pi\)
0.352707 + 0.935734i \(0.385261\pi\)
\(312\) −7.63949 −0.432501
\(313\) −12.4430 −0.703319 −0.351660 0.936128i \(-0.614383\pi\)
−0.351660 + 0.936128i \(0.614383\pi\)
\(314\) −33.2124 −1.87428
\(315\) 5.64284 0.317938
\(316\) −6.09138 −0.342667
\(317\) 26.7941 1.50491 0.752453 0.658646i \(-0.228871\pi\)
0.752453 + 0.658646i \(0.228871\pi\)
\(318\) 2.30141 0.129057
\(319\) 12.9833 0.726924
\(320\) −7.50725 −0.419668
\(321\) −5.50154 −0.307066
\(322\) −11.7284 −0.653599
\(323\) 38.9891 2.16941
\(324\) 6.08063 0.337813
\(325\) −8.26104 −0.458240
\(326\) −30.1175 −1.66805
\(327\) 2.65222 0.146668
\(328\) −19.1925 −1.05973
\(329\) −28.9775 −1.59758
\(330\) −2.40675 −0.132487
\(331\) −15.0578 −0.827653 −0.413826 0.910356i \(-0.635808\pi\)
−0.413826 + 0.910356i \(0.635808\pi\)
\(332\) 53.5449 2.93866
\(333\) 20.1591 1.10471
\(334\) −14.1271 −0.773000
\(335\) 8.45936 0.462184
\(336\) −9.77091 −0.533047
\(337\) 7.30515 0.397937 0.198968 0.980006i \(-0.436241\pi\)
0.198968 + 0.980006i \(0.436241\pi\)
\(338\) 23.0096 1.25156
\(339\) −16.6693 −0.905351
\(340\) 18.1058 0.981926
\(341\) −10.0796 −0.545840
\(342\) 30.2218 1.63421
\(343\) 2.02413 0.109293
\(344\) −24.7631 −1.33513
\(345\) −0.938005 −0.0505005
\(346\) 18.6034 1.00013
\(347\) −19.2437 −1.03306 −0.516528 0.856271i \(-0.672776\pi\)
−0.516528 + 0.856271i \(0.672776\pi\)
\(348\) 33.2102 1.78025
\(349\) 31.7682 1.70051 0.850256 0.526370i \(-0.176447\pi\)
0.850256 + 0.526370i \(0.176447\pi\)
\(350\) −39.3166 −2.10156
\(351\) −9.01774 −0.481331
\(352\) 2.71031 0.144460
\(353\) 26.5258 1.41182 0.705912 0.708300i \(-0.250538\pi\)
0.705912 + 0.708300i \(0.250538\pi\)
\(354\) −8.00838 −0.425641
\(355\) −6.92168 −0.367365
\(356\) −49.6284 −2.63030
\(357\) −22.7045 −1.20165
\(358\) 10.0629 0.531839
\(359\) −15.9940 −0.844132 −0.422066 0.906565i \(-0.638695\pi\)
−0.422066 + 0.906565i \(0.638695\pi\)
\(360\) 6.62903 0.349380
\(361\) 17.2750 0.909210
\(362\) −55.6067 −2.92262
\(363\) −8.59958 −0.451361
\(364\) −25.7718 −1.35081
\(365\) −10.7767 −0.564078
\(366\) −5.80313 −0.303334
\(367\) −36.2800 −1.89380 −0.946899 0.321530i \(-0.895803\pi\)
−0.946899 + 0.321530i \(0.895803\pi\)
\(368\) −3.70272 −0.193018
\(369\) −9.28997 −0.483617
\(370\) 17.1657 0.892403
\(371\) 3.66716 0.190389
\(372\) −25.7827 −1.33677
\(373\) 7.69968 0.398674 0.199337 0.979931i \(-0.436121\pi\)
0.199337 + 0.979931i \(0.436121\pi\)
\(374\) −22.0761 −1.14153
\(375\) −6.67315 −0.344600
\(376\) −34.0419 −1.75557
\(377\) 16.9860 0.874823
\(378\) −42.9180 −2.20746
\(379\) −14.7255 −0.756397 −0.378199 0.925724i \(-0.623456\pi\)
−0.378199 + 0.925724i \(0.623456\pi\)
\(380\) 16.8455 0.864154
\(381\) 13.1507 0.673729
\(382\) 9.16725 0.469038
\(383\) −19.4174 −0.992184 −0.496092 0.868270i \(-0.665232\pi\)
−0.496092 + 0.868270i \(0.665232\pi\)
\(384\) 19.7557 1.00815
\(385\) −3.83500 −0.195450
\(386\) 18.3028 0.931587
\(387\) −11.9864 −0.609301
\(388\) 38.6559 1.96245
\(389\) −2.60892 −0.132278 −0.0661388 0.997810i \(-0.521068\pi\)
−0.0661388 + 0.997810i \(0.521068\pi\)
\(390\) −3.14874 −0.159443
\(391\) −8.60394 −0.435120
\(392\) −27.7785 −1.40303
\(393\) −2.28517 −0.115272
\(394\) −42.4366 −2.13793
\(395\) −1.18589 −0.0596684
\(396\) −11.2014 −0.562893
\(397\) −7.64012 −0.383447 −0.191723 0.981449i \(-0.561408\pi\)
−0.191723 + 0.981449i \(0.561408\pi\)
\(398\) −39.4301 −1.97645
\(399\) −21.1240 −1.05752
\(400\) −12.4125 −0.620623
\(401\) 30.8910 1.54262 0.771311 0.636459i \(-0.219601\pi\)
0.771311 + 0.636459i \(0.219601\pi\)
\(402\) −26.3833 −1.31588
\(403\) −13.1871 −0.656896
\(404\) −11.6939 −0.581794
\(405\) 1.18379 0.0588232
\(406\) 80.8412 4.01208
\(407\) −13.7006 −0.679114
\(408\) −26.6725 −1.32049
\(409\) −25.5752 −1.26461 −0.632306 0.774719i \(-0.717891\pi\)
−0.632306 + 0.774719i \(0.717891\pi\)
\(410\) −7.91050 −0.390672
\(411\) −6.97726 −0.344163
\(412\) 10.8575 0.534912
\(413\) −12.7609 −0.627920
\(414\) −6.66921 −0.327774
\(415\) 10.4243 0.511708
\(416\) 3.54589 0.173852
\(417\) −1.67856 −0.0821994
\(418\) −20.5394 −1.00461
\(419\) 14.5256 0.709623 0.354811 0.934938i \(-0.384545\pi\)
0.354811 + 0.934938i \(0.384545\pi\)
\(420\) −9.80961 −0.478660
\(421\) 2.58121 0.125800 0.0629002 0.998020i \(-0.479965\pi\)
0.0629002 + 0.998020i \(0.479965\pi\)
\(422\) 45.0661 2.19379
\(423\) −16.4777 −0.801173
\(424\) 4.30806 0.209218
\(425\) −28.8426 −1.39907
\(426\) 21.5875 1.04592
\(427\) −9.24692 −0.447490
\(428\) −21.8030 −1.05389
\(429\) 2.51313 0.121335
\(430\) −10.2065 −0.492201
\(431\) 22.0958 1.06432 0.532158 0.846645i \(-0.321381\pi\)
0.532158 + 0.846645i \(0.321381\pi\)
\(432\) −13.5494 −0.651897
\(433\) 16.0791 0.772712 0.386356 0.922350i \(-0.373734\pi\)
0.386356 + 0.922350i \(0.373734\pi\)
\(434\) −62.7611 −3.01263
\(435\) 6.46545 0.309994
\(436\) 10.5109 0.503383
\(437\) −8.00501 −0.382932
\(438\) 33.6107 1.60598
\(439\) 36.3475 1.73477 0.867387 0.497634i \(-0.165798\pi\)
0.867387 + 0.497634i \(0.165798\pi\)
\(440\) −4.50524 −0.214779
\(441\) −13.4460 −0.640285
\(442\) −28.8821 −1.37378
\(443\) 24.8116 1.17883 0.589417 0.807829i \(-0.299357\pi\)
0.589417 + 0.807829i \(0.299357\pi\)
\(444\) −35.0450 −1.66316
\(445\) −9.66179 −0.458013
\(446\) 11.0064 0.521168
\(447\) 8.30023 0.392587
\(448\) 37.3084 1.76266
\(449\) 31.0553 1.46559 0.732795 0.680450i \(-0.238216\pi\)
0.732795 + 0.680450i \(0.238216\pi\)
\(450\) −22.3569 −1.05391
\(451\) 6.31367 0.297299
\(452\) −66.0616 −3.10728
\(453\) 0.956408 0.0449360
\(454\) 35.6751 1.67431
\(455\) −5.01732 −0.235216
\(456\) −24.8158 −1.16211
\(457\) 2.54467 0.119035 0.0595174 0.998227i \(-0.481044\pi\)
0.0595174 + 0.998227i \(0.481044\pi\)
\(458\) 14.7722 0.690258
\(459\) −31.4846 −1.46957
\(460\) −3.71738 −0.173324
\(461\) 30.7029 1.42998 0.714988 0.699136i \(-0.246432\pi\)
0.714988 + 0.699136i \(0.246432\pi\)
\(462\) 11.9607 0.556462
\(463\) 11.2728 0.523892 0.261946 0.965083i \(-0.415636\pi\)
0.261946 + 0.965083i \(0.415636\pi\)
\(464\) 25.5220 1.18483
\(465\) −5.01945 −0.232772
\(466\) −52.8441 −2.44795
\(467\) −32.4537 −1.50178 −0.750889 0.660429i \(-0.770375\pi\)
−0.750889 + 0.660429i \(0.770375\pi\)
\(468\) −14.6548 −0.677418
\(469\) −42.0401 −1.94123
\(470\) −14.0309 −0.647198
\(471\) 13.2006 0.608250
\(472\) −14.9910 −0.690019
\(473\) 8.14620 0.374563
\(474\) 3.69857 0.169881
\(475\) −26.8348 −1.23127
\(476\) −89.9796 −4.12421
\(477\) 2.08528 0.0954785
\(478\) 42.4104 1.93981
\(479\) −13.3883 −0.611727 −0.305864 0.952075i \(-0.598945\pi\)
−0.305864 + 0.952075i \(0.598945\pi\)
\(480\) 1.34969 0.0616045
\(481\) −17.9245 −0.817285
\(482\) −12.7039 −0.578649
\(483\) 4.66156 0.212108
\(484\) −34.0808 −1.54913
\(485\) 7.52563 0.341721
\(486\) −38.8021 −1.76010
\(487\) 6.73003 0.304967 0.152483 0.988306i \(-0.451273\pi\)
0.152483 + 0.988306i \(0.451273\pi\)
\(488\) −10.8630 −0.491744
\(489\) 11.9705 0.541323
\(490\) −11.4494 −0.517230
\(491\) −5.36715 −0.242216 −0.121108 0.992639i \(-0.538645\pi\)
−0.121108 + 0.992639i \(0.538645\pi\)
\(492\) 16.1499 0.728092
\(493\) 59.3049 2.67096
\(494\) −26.8716 −1.20901
\(495\) −2.18072 −0.0980163
\(496\) −19.8140 −0.889674
\(497\) 34.3984 1.54298
\(498\) −32.5115 −1.45688
\(499\) 31.9919 1.43216 0.716078 0.698021i \(-0.245936\pi\)
0.716078 + 0.698021i \(0.245936\pi\)
\(500\) −26.4462 −1.18271
\(501\) 5.61493 0.250857
\(502\) 71.6208 3.19659
\(503\) 25.2322 1.12505 0.562523 0.826781i \(-0.309831\pi\)
0.562523 + 0.826781i \(0.309831\pi\)
\(504\) −32.9440 −1.46744
\(505\) −2.27660 −0.101307
\(506\) 4.53255 0.201496
\(507\) −9.14539 −0.406161
\(508\) 52.1171 2.31232
\(509\) 35.9506 1.59348 0.796741 0.604321i \(-0.206555\pi\)
0.796741 + 0.604321i \(0.206555\pi\)
\(510\) −10.9935 −0.486801
\(511\) 53.5565 2.36920
\(512\) 29.3313 1.29627
\(513\) −29.2929 −1.29331
\(514\) −34.9963 −1.54362
\(515\) 2.11377 0.0931441
\(516\) 20.8373 0.917312
\(517\) 11.1986 0.492514
\(518\) −85.3076 −3.74820
\(519\) −7.39409 −0.324564
\(520\) −5.89419 −0.258477
\(521\) 7.11980 0.311924 0.155962 0.987763i \(-0.450152\pi\)
0.155962 + 0.987763i \(0.450152\pi\)
\(522\) 45.9693 2.01202
\(523\) 27.6699 1.20992 0.604959 0.796256i \(-0.293189\pi\)
0.604959 + 0.796256i \(0.293189\pi\)
\(524\) −9.05631 −0.395627
\(525\) 15.6267 0.682007
\(526\) −15.0528 −0.656332
\(527\) −46.0414 −2.00560
\(528\) 3.77605 0.164332
\(529\) −21.2335 −0.923195
\(530\) 1.77564 0.0771288
\(531\) −7.25630 −0.314897
\(532\) −83.7161 −3.62955
\(533\) 8.26017 0.357788
\(534\) 30.1334 1.30400
\(535\) −4.24467 −0.183513
\(536\) −49.3874 −2.13321
\(537\) −3.99958 −0.172594
\(538\) −4.39563 −0.189509
\(539\) 9.13819 0.393610
\(540\) −13.6031 −0.585384
\(541\) 27.8997 1.19950 0.599750 0.800187i \(-0.295267\pi\)
0.599750 + 0.800187i \(0.295267\pi\)
\(542\) −35.9322 −1.54342
\(543\) 22.1014 0.948460
\(544\) 12.3801 0.530794
\(545\) 2.04630 0.0876539
\(546\) 15.6482 0.669679
\(547\) 4.81047 0.205681 0.102840 0.994698i \(-0.467207\pi\)
0.102840 + 0.994698i \(0.467207\pi\)
\(548\) −27.6514 −1.18121
\(549\) −5.25814 −0.224412
\(550\) 15.1942 0.647885
\(551\) 55.1767 2.35061
\(552\) 5.47625 0.233085
\(553\) 5.89344 0.250615
\(554\) 10.2005 0.433378
\(555\) −6.82266 −0.289606
\(556\) −6.65226 −0.282119
\(557\) 21.4791 0.910097 0.455049 0.890467i \(-0.349622\pi\)
0.455049 + 0.890467i \(0.349622\pi\)
\(558\) −35.6883 −1.51081
\(559\) 10.6577 0.450771
\(560\) −7.53868 −0.318567
\(561\) 8.77435 0.370453
\(562\) −11.7365 −0.495074
\(563\) −38.4088 −1.61874 −0.809369 0.587300i \(-0.800191\pi\)
−0.809369 + 0.587300i \(0.800191\pi\)
\(564\) 28.6451 1.20618
\(565\) −12.8611 −0.541069
\(566\) 34.5363 1.45167
\(567\) −5.88305 −0.247065
\(568\) 40.4101 1.69557
\(569\) −21.3407 −0.894649 −0.447325 0.894372i \(-0.647623\pi\)
−0.447325 + 0.894372i \(0.647623\pi\)
\(570\) −10.2283 −0.428415
\(571\) 27.8834 1.16688 0.583442 0.812155i \(-0.301705\pi\)
0.583442 + 0.812155i \(0.301705\pi\)
\(572\) 9.95973 0.416437
\(573\) −3.64361 −0.152214
\(574\) 39.3125 1.64087
\(575\) 5.92180 0.246956
\(576\) 21.2150 0.883957
\(577\) 25.1872 1.04856 0.524279 0.851547i \(-0.324335\pi\)
0.524279 + 0.851547i \(0.324335\pi\)
\(578\) −59.9319 −2.49284
\(579\) −7.27461 −0.302322
\(580\) 25.6231 1.06394
\(581\) −51.8051 −2.14924
\(582\) −23.4711 −0.972910
\(583\) −1.41720 −0.0586946
\(584\) 62.9164 2.60350
\(585\) −2.85304 −0.117959
\(586\) −79.9883 −3.30429
\(587\) −25.2037 −1.04027 −0.520135 0.854084i \(-0.674118\pi\)
−0.520135 + 0.854084i \(0.674118\pi\)
\(588\) 23.3747 0.963958
\(589\) −42.8364 −1.76504
\(590\) −6.17881 −0.254378
\(591\) 16.8668 0.693808
\(592\) −26.9320 −1.10690
\(593\) −8.04071 −0.330193 −0.165096 0.986277i \(-0.552793\pi\)
−0.165096 + 0.986277i \(0.552793\pi\)
\(594\) 16.5860 0.680533
\(595\) −17.5175 −0.718147
\(596\) 32.8944 1.34741
\(597\) 15.6718 0.641406
\(598\) 5.92992 0.242492
\(599\) −19.9914 −0.816824 −0.408412 0.912798i \(-0.633917\pi\)
−0.408412 + 0.912798i \(0.633917\pi\)
\(600\) 18.3578 0.749454
\(601\) −7.64055 −0.311664 −0.155832 0.987784i \(-0.549806\pi\)
−0.155832 + 0.987784i \(0.549806\pi\)
\(602\) 50.7228 2.06731
\(603\) −23.9056 −0.973510
\(604\) 3.79032 0.154226
\(605\) −6.63494 −0.269749
\(606\) 7.10033 0.288431
\(607\) −2.29298 −0.0930694 −0.0465347 0.998917i \(-0.514818\pi\)
−0.0465347 + 0.998917i \(0.514818\pi\)
\(608\) 11.5183 0.467131
\(609\) −32.1310 −1.30202
\(610\) −4.47736 −0.181283
\(611\) 14.6511 0.592721
\(612\) −51.1658 −2.06825
\(613\) 4.20940 0.170016 0.0850080 0.996380i \(-0.472908\pi\)
0.0850080 + 0.996380i \(0.472908\pi\)
\(614\) −79.6271 −3.21349
\(615\) 3.14410 0.126782
\(616\) 22.3895 0.902097
\(617\) −24.8660 −1.00107 −0.500533 0.865718i \(-0.666863\pi\)
−0.500533 + 0.865718i \(0.666863\pi\)
\(618\) −6.59250 −0.265189
\(619\) −20.4245 −0.820930 −0.410465 0.911876i \(-0.634634\pi\)
−0.410465 + 0.911876i \(0.634634\pi\)
\(620\) −19.8925 −0.798901
\(621\) 6.46423 0.259401
\(622\) −29.9347 −1.20027
\(623\) 48.0157 1.92371
\(624\) 4.94020 0.197766
\(625\) 17.1288 0.685153
\(626\) 29.9417 1.19671
\(627\) 8.16356 0.326021
\(628\) 52.3148 2.08759
\(629\) −62.5815 −2.49529
\(630\) −13.5784 −0.540977
\(631\) 42.3764 1.68698 0.843488 0.537147i \(-0.180498\pi\)
0.843488 + 0.537147i \(0.180498\pi\)
\(632\) 6.92343 0.275399
\(633\) −17.9119 −0.711935
\(634\) −64.4748 −2.56062
\(635\) 10.1463 0.402643
\(636\) −3.62509 −0.143744
\(637\) 11.9555 0.473693
\(638\) −31.2418 −1.23687
\(639\) 19.5602 0.773789
\(640\) 15.2423 0.602506
\(641\) −28.7801 −1.13675 −0.568373 0.822771i \(-0.692427\pi\)
−0.568373 + 0.822771i \(0.692427\pi\)
\(642\) 13.2384 0.522478
\(643\) −10.7371 −0.423430 −0.211715 0.977331i \(-0.567905\pi\)
−0.211715 + 0.977331i \(0.567905\pi\)
\(644\) 18.4741 0.727982
\(645\) 4.05667 0.159731
\(646\) −93.8197 −3.69129
\(647\) 26.8116 1.05407 0.527037 0.849842i \(-0.323303\pi\)
0.527037 + 0.849842i \(0.323303\pi\)
\(648\) −6.91122 −0.271498
\(649\) 4.93154 0.193580
\(650\) 19.8786 0.779703
\(651\) 24.9449 0.977669
\(652\) 47.4398 1.85789
\(653\) −4.59137 −0.179674 −0.0898371 0.995956i \(-0.528635\pi\)
−0.0898371 + 0.995956i \(0.528635\pi\)
\(654\) −6.38206 −0.249558
\(655\) −1.76311 −0.0688903
\(656\) 12.4111 0.484574
\(657\) 30.4542 1.18813
\(658\) 69.7288 2.71831
\(659\) 9.49241 0.369772 0.184886 0.982760i \(-0.440808\pi\)
0.184886 + 0.982760i \(0.440808\pi\)
\(660\) 3.79101 0.147565
\(661\) 9.75368 0.379374 0.189687 0.981845i \(-0.439253\pi\)
0.189687 + 0.981845i \(0.439253\pi\)
\(662\) 36.2338 1.40827
\(663\) 11.4795 0.445825
\(664\) −60.8589 −2.36178
\(665\) −16.2981 −0.632012
\(666\) −48.5091 −1.87969
\(667\) −12.1762 −0.471463
\(668\) 22.2524 0.860971
\(669\) −4.37459 −0.169131
\(670\) −20.3558 −0.786414
\(671\) 3.57355 0.137955
\(672\) −6.70748 −0.258747
\(673\) −2.38737 −0.0920265 −0.0460132 0.998941i \(-0.514652\pi\)
−0.0460132 + 0.998941i \(0.514652\pi\)
\(674\) −17.5784 −0.677096
\(675\) 21.6698 0.834069
\(676\) −36.2439 −1.39399
\(677\) −26.6691 −1.02498 −0.512489 0.858694i \(-0.671276\pi\)
−0.512489 + 0.858694i \(0.671276\pi\)
\(678\) 40.1114 1.54047
\(679\) −37.3998 −1.43527
\(680\) −20.5790 −0.789168
\(681\) −14.1794 −0.543355
\(682\) 24.2546 0.928755
\(683\) 2.95639 0.113123 0.0565616 0.998399i \(-0.481986\pi\)
0.0565616 + 0.998399i \(0.481986\pi\)
\(684\) −47.6041 −1.82019
\(685\) −5.38325 −0.205683
\(686\) −4.87068 −0.185964
\(687\) −5.87133 −0.224005
\(688\) 16.0134 0.610507
\(689\) −1.85413 −0.0706366
\(690\) 2.25713 0.0859274
\(691\) −35.7988 −1.36185 −0.680925 0.732353i \(-0.738422\pi\)
−0.680925 + 0.732353i \(0.738422\pi\)
\(692\) −29.3033 −1.11395
\(693\) 10.8374 0.411681
\(694\) 46.3062 1.75776
\(695\) −1.29508 −0.0491252
\(696\) −37.7465 −1.43078
\(697\) 28.8396 1.09238
\(698\) −76.4440 −2.89345
\(699\) 21.0033 0.794419
\(700\) 61.9299 2.34073
\(701\) 48.3418 1.82584 0.912922 0.408134i \(-0.133820\pi\)
0.912922 + 0.408134i \(0.133820\pi\)
\(702\) 21.6995 0.818993
\(703\) −58.2252 −2.19600
\(704\) −14.4182 −0.543405
\(705\) 5.57671 0.210031
\(706\) −63.8291 −2.40224
\(707\) 11.3139 0.425504
\(708\) 12.6145 0.474081
\(709\) 24.6762 0.926736 0.463368 0.886166i \(-0.346641\pi\)
0.463368 + 0.886166i \(0.346641\pi\)
\(710\) 16.6557 0.625077
\(711\) 3.35123 0.125681
\(712\) 56.4074 2.11396
\(713\) 9.45296 0.354016
\(714\) 54.6340 2.04463
\(715\) 1.93899 0.0725140
\(716\) −15.8506 −0.592366
\(717\) −16.8564 −0.629513
\(718\) 38.4865 1.43630
\(719\) 19.0169 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(720\) −4.28677 −0.159759
\(721\) −10.5047 −0.391217
\(722\) −41.5689 −1.54704
\(723\) 5.04929 0.187785
\(724\) 87.5894 3.25523
\(725\) −40.8176 −1.51593
\(726\) 20.6932 0.767998
\(727\) −14.9259 −0.553572 −0.276786 0.960932i \(-0.589269\pi\)
−0.276786 + 0.960932i \(0.589269\pi\)
\(728\) 29.2921 1.08564
\(729\) 10.6095 0.392943
\(730\) 25.9321 0.959788
\(731\) 37.2102 1.37627
\(732\) 9.14085 0.337856
\(733\) 43.7513 1.61599 0.807995 0.589189i \(-0.200553\pi\)
0.807995 + 0.589189i \(0.200553\pi\)
\(734\) 87.3008 3.22233
\(735\) 4.55066 0.167854
\(736\) −2.54182 −0.0936927
\(737\) 16.2468 0.598457
\(738\) 22.3545 0.822882
\(739\) −17.9533 −0.660423 −0.330212 0.943907i \(-0.607120\pi\)
−0.330212 + 0.943907i \(0.607120\pi\)
\(740\) −27.0387 −0.993963
\(741\) 10.6804 0.392353
\(742\) −8.82431 −0.323951
\(743\) 14.4400 0.529753 0.264877 0.964282i \(-0.414669\pi\)
0.264877 + 0.964282i \(0.414669\pi\)
\(744\) 29.3045 1.07436
\(745\) 6.40398 0.234624
\(746\) −18.5278 −0.678351
\(747\) −29.4583 −1.07782
\(748\) 34.7734 1.27144
\(749\) 21.0946 0.770778
\(750\) 16.0576 0.586342
\(751\) −48.7782 −1.77994 −0.889972 0.456016i \(-0.849276\pi\)
−0.889972 + 0.456016i \(0.849276\pi\)
\(752\) 22.0137 0.802759
\(753\) −28.4663 −1.03737
\(754\) −40.8735 −1.48853
\(755\) 0.737910 0.0268553
\(756\) 67.6027 2.45868
\(757\) 50.6616 1.84133 0.920663 0.390357i \(-0.127649\pi\)
0.920663 + 0.390357i \(0.127649\pi\)
\(758\) 35.4340 1.28702
\(759\) −1.80150 −0.0653903
\(760\) −19.1465 −0.694515
\(761\) −25.4705 −0.923306 −0.461653 0.887061i \(-0.652743\pi\)
−0.461653 + 0.887061i \(0.652743\pi\)
\(762\) −31.6445 −1.14636
\(763\) −10.1694 −0.368157
\(764\) −14.4399 −0.522417
\(765\) −9.96110 −0.360144
\(766\) 46.7243 1.68822
\(767\) 6.45193 0.232966
\(768\) −28.0779 −1.01317
\(769\) −39.0215 −1.40715 −0.703576 0.710621i \(-0.748414\pi\)
−0.703576 + 0.710621i \(0.748414\pi\)
\(770\) 9.22819 0.332561
\(771\) 13.9096 0.500942
\(772\) −28.8298 −1.03761
\(773\) −13.4734 −0.484606 −0.242303 0.970201i \(-0.577903\pi\)
−0.242303 + 0.970201i \(0.577903\pi\)
\(774\) 28.8429 1.03674
\(775\) 31.6887 1.13829
\(776\) −43.9361 −1.57721
\(777\) 33.9063 1.21638
\(778\) 6.27787 0.225073
\(779\) 26.8320 0.961357
\(780\) 4.95977 0.177588
\(781\) −13.2935 −0.475680
\(782\) 20.7037 0.740364
\(783\) −44.5564 −1.59232
\(784\) 17.9635 0.641552
\(785\) 10.1848 0.363511
\(786\) 5.49883 0.196137
\(787\) 12.6509 0.450954 0.225477 0.974248i \(-0.427606\pi\)
0.225477 + 0.974248i \(0.427606\pi\)
\(788\) 66.8445 2.38124
\(789\) 5.98286 0.212995
\(790\) 2.85361 0.101527
\(791\) 63.9150 2.27256
\(792\) 12.7315 0.452394
\(793\) 4.67527 0.166024
\(794\) 18.3845 0.652441
\(795\) −0.705743 −0.0250301
\(796\) 62.1087 2.20138
\(797\) 30.8417 1.09247 0.546234 0.837632i \(-0.316061\pi\)
0.546234 + 0.837632i \(0.316061\pi\)
\(798\) 50.8309 1.79939
\(799\) 51.1529 1.80966
\(800\) −8.52083 −0.301257
\(801\) 27.3036 0.964724
\(802\) −74.3332 −2.62480
\(803\) −20.6974 −0.730394
\(804\) 41.5579 1.46563
\(805\) 3.59659 0.126763
\(806\) 31.7322 1.11772
\(807\) 1.74708 0.0615002
\(808\) 13.2912 0.467584
\(809\) 6.78850 0.238671 0.119335 0.992854i \(-0.461924\pi\)
0.119335 + 0.992854i \(0.461924\pi\)
\(810\) −2.84857 −0.100089
\(811\) −14.5189 −0.509829 −0.254915 0.966964i \(-0.582047\pi\)
−0.254915 + 0.966964i \(0.582047\pi\)
\(812\) −127.338 −4.46868
\(813\) 14.2816 0.500877
\(814\) 32.9679 1.15552
\(815\) 9.23572 0.323513
\(816\) 17.2482 0.603809
\(817\) 34.6199 1.21120
\(818\) 61.5418 2.15176
\(819\) 14.1786 0.495441
\(820\) 12.4603 0.435133
\(821\) −19.8277 −0.691992 −0.345996 0.938236i \(-0.612459\pi\)
−0.345996 + 0.938236i \(0.612459\pi\)
\(822\) 16.7894 0.585599
\(823\) 4.15675 0.144895 0.0724477 0.997372i \(-0.476919\pi\)
0.0724477 + 0.997372i \(0.476919\pi\)
\(824\) −12.3406 −0.429906
\(825\) −6.03909 −0.210254
\(826\) 30.7065 1.06842
\(827\) −5.79734 −0.201593 −0.100797 0.994907i \(-0.532139\pi\)
−0.100797 + 0.994907i \(0.532139\pi\)
\(828\) 10.5051 0.365077
\(829\) −7.89597 −0.274238 −0.137119 0.990555i \(-0.543784\pi\)
−0.137119 + 0.990555i \(0.543784\pi\)
\(830\) −25.0840 −0.870679
\(831\) −4.05428 −0.140641
\(832\) −18.8633 −0.653966
\(833\) 41.7414 1.44625
\(834\) 4.03913 0.139864
\(835\) 4.33216 0.149921
\(836\) 32.3528 1.11895
\(837\) 34.5914 1.19565
\(838\) −34.9531 −1.20744
\(839\) 30.5294 1.05399 0.526996 0.849868i \(-0.323318\pi\)
0.526996 + 0.849868i \(0.323318\pi\)
\(840\) 11.1496 0.384696
\(841\) 54.9274 1.89405
\(842\) −6.21118 −0.214052
\(843\) 4.66477 0.160663
\(844\) −70.9863 −2.44345
\(845\) −7.05605 −0.242736
\(846\) 39.6504 1.36321
\(847\) 32.9734 1.13298
\(848\) −2.78588 −0.0956675
\(849\) −13.7268 −0.471101
\(850\) 69.4042 2.38054
\(851\) 12.8489 0.440454
\(852\) −34.0038 −1.16495
\(853\) 37.5914 1.28710 0.643552 0.765402i \(-0.277460\pi\)
0.643552 + 0.765402i \(0.277460\pi\)
\(854\) 22.2509 0.761411
\(855\) −9.26770 −0.316949
\(856\) 24.7812 0.847005
\(857\) 35.0317 1.19666 0.598331 0.801249i \(-0.295831\pi\)
0.598331 + 0.801249i \(0.295831\pi\)
\(858\) −6.04737 −0.206454
\(859\) −11.7167 −0.399769 −0.199885 0.979819i \(-0.564057\pi\)
−0.199885 + 0.979819i \(0.564057\pi\)
\(860\) 16.0769 0.548217
\(861\) −15.6251 −0.532502
\(862\) −53.1692 −1.81095
\(863\) −26.1446 −0.889973 −0.444987 0.895537i \(-0.646792\pi\)
−0.444987 + 0.895537i \(0.646792\pi\)
\(864\) −9.30133 −0.316438
\(865\) −5.70485 −0.193971
\(866\) −38.6913 −1.31478
\(867\) 23.8205 0.808986
\(868\) 98.8587 3.35548
\(869\) −2.27757 −0.0772614
\(870\) −15.5579 −0.527461
\(871\) 21.2556 0.720219
\(872\) −11.9467 −0.404566
\(873\) −21.2669 −0.719776
\(874\) 19.2625 0.651565
\(875\) 25.5868 0.864993
\(876\) −52.9421 −1.78875
\(877\) 20.4646 0.691041 0.345520 0.938411i \(-0.387702\pi\)
0.345520 + 0.938411i \(0.387702\pi\)
\(878\) −87.4634 −2.95175
\(879\) 31.7920 1.07232
\(880\) 2.91339 0.0982103
\(881\) 15.3637 0.517615 0.258808 0.965929i \(-0.416670\pi\)
0.258808 + 0.965929i \(0.416670\pi\)
\(882\) 32.3552 1.08946
\(883\) −21.7801 −0.732958 −0.366479 0.930426i \(-0.619437\pi\)
−0.366479 + 0.930426i \(0.619437\pi\)
\(884\) 45.4940 1.53013
\(885\) 2.45582 0.0825516
\(886\) −59.7043 −2.00581
\(887\) 41.0417 1.37805 0.689023 0.724740i \(-0.258040\pi\)
0.689023 + 0.724740i \(0.258040\pi\)
\(888\) 39.8320 1.33667
\(889\) −50.4236 −1.69115
\(890\) 23.2492 0.779316
\(891\) 2.27356 0.0761670
\(892\) −17.3368 −0.580480
\(893\) 47.5921 1.59261
\(894\) −19.9729 −0.667994
\(895\) −3.08584 −0.103148
\(896\) −75.7492 −2.53060
\(897\) −2.35690 −0.0786946
\(898\) −74.7286 −2.49372
\(899\) −65.1571 −2.17311
\(900\) 35.2157 1.17386
\(901\) −6.47350 −0.215663
\(902\) −15.1926 −0.505860
\(903\) −20.1602 −0.670890
\(904\) 75.0853 2.49730
\(905\) 17.0521 0.566832
\(906\) −2.30141 −0.0764593
\(907\) 15.8391 0.525927 0.262964 0.964806i \(-0.415300\pi\)
0.262964 + 0.964806i \(0.415300\pi\)
\(908\) −56.1939 −1.86486
\(909\) 6.43352 0.213387
\(910\) 12.0732 0.400223
\(911\) −3.41029 −0.112988 −0.0564940 0.998403i \(-0.517992\pi\)
−0.0564940 + 0.998403i \(0.517992\pi\)
\(912\) 16.0476 0.531388
\(913\) 20.0205 0.662582
\(914\) −6.12327 −0.202540
\(915\) 1.77957 0.0588307
\(916\) −23.2685 −0.768814
\(917\) 8.76204 0.289348
\(918\) 75.7615 2.50050
\(919\) 26.6931 0.880525 0.440262 0.897869i \(-0.354885\pi\)
0.440262 + 0.897869i \(0.354885\pi\)
\(920\) 4.22516 0.139299
\(921\) 31.6485 1.04285
\(922\) −73.8806 −2.43313
\(923\) −17.3919 −0.572462
\(924\) −18.8400 −0.619791
\(925\) 43.0727 1.41622
\(926\) −27.1258 −0.891410
\(927\) −5.97338 −0.196192
\(928\) 17.5202 0.575128
\(929\) −31.6053 −1.03693 −0.518467 0.855097i \(-0.673497\pi\)
−0.518467 + 0.855097i \(0.673497\pi\)
\(930\) 12.0784 0.396065
\(931\) 38.8357 1.27279
\(932\) 83.2378 2.72655
\(933\) 11.8978 0.389517
\(934\) 78.0936 2.55530
\(935\) 6.76979 0.221396
\(936\) 16.6566 0.544437
\(937\) −11.8568 −0.387344 −0.193672 0.981066i \(-0.562040\pi\)
−0.193672 + 0.981066i \(0.562040\pi\)
\(938\) 101.161 3.30304
\(939\) −11.9006 −0.388361
\(940\) 22.1009 0.720853
\(941\) −8.81925 −0.287499 −0.143750 0.989614i \(-0.545916\pi\)
−0.143750 + 0.989614i \(0.545916\pi\)
\(942\) −31.7646 −1.03495
\(943\) −5.92118 −0.192820
\(944\) 9.69421 0.315520
\(945\) 13.1611 0.428130
\(946\) −19.6023 −0.637325
\(947\) −42.6784 −1.38686 −0.693431 0.720523i \(-0.743902\pi\)
−0.693431 + 0.720523i \(0.743902\pi\)
\(948\) −5.82584 −0.189215
\(949\) −27.0783 −0.878999
\(950\) 64.5729 2.09502
\(951\) 25.6261 0.830983
\(952\) 102.270 3.31460
\(953\) −38.3936 −1.24369 −0.621845 0.783140i \(-0.713617\pi\)
−0.621845 + 0.783140i \(0.713617\pi\)
\(954\) −5.01783 −0.162458
\(955\) −2.81120 −0.0909682
\(956\) −66.8031 −2.16057
\(957\) 12.4173 0.401395
\(958\) 32.2164 1.04086
\(959\) 26.7529 0.863896
\(960\) −7.17999 −0.231733
\(961\) 19.5847 0.631765
\(962\) 43.1318 1.39063
\(963\) 11.9952 0.386539
\(964\) 20.0107 0.644502
\(965\) −5.61267 −0.180678
\(966\) −11.2171 −0.360906
\(967\) 24.3034 0.781545 0.390773 0.920487i \(-0.372208\pi\)
0.390773 + 0.920487i \(0.372208\pi\)
\(968\) 38.7360 1.24502
\(969\) 37.2895 1.19791
\(970\) −18.1090 −0.581445
\(971\) −29.6550 −0.951673 −0.475836 0.879534i \(-0.657855\pi\)
−0.475836 + 0.879534i \(0.657855\pi\)
\(972\) 61.1194 1.96041
\(973\) 6.43610 0.206332
\(974\) −16.1945 −0.518906
\(975\) −7.90093 −0.253032
\(976\) 7.02473 0.224856
\(977\) 3.33044 0.106550 0.0532751 0.998580i \(-0.483034\pi\)
0.0532751 + 0.998580i \(0.483034\pi\)
\(978\) −28.8046 −0.921070
\(979\) −18.5561 −0.593056
\(980\) 18.0346 0.576094
\(981\) −5.78270 −0.184628
\(982\) 12.9150 0.412135
\(983\) −41.1771 −1.31335 −0.656673 0.754176i \(-0.728037\pi\)
−0.656673 + 0.754176i \(0.728037\pi\)
\(984\) −18.3559 −0.585163
\(985\) 13.0135 0.414644
\(986\) −142.706 −4.54468
\(987\) −27.7143 −0.882157
\(988\) 42.3271 1.34660
\(989\) −7.63978 −0.242931
\(990\) 5.24750 0.166776
\(991\) −12.0106 −0.381529 −0.190765 0.981636i \(-0.561097\pi\)
−0.190765 + 0.981636i \(0.561097\pi\)
\(992\) −13.6018 −0.431857
\(993\) −14.4014 −0.457016
\(994\) −82.7730 −2.62540
\(995\) 12.0915 0.383326
\(996\) 51.2108 1.62268
\(997\) 30.9197 0.979235 0.489618 0.871937i \(-0.337136\pi\)
0.489618 + 0.871937i \(0.337136\pi\)
\(998\) −76.9824 −2.43684
\(999\) 47.0182 1.48759
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 \(a_p\))