Properties

Label 8018.2.a.f.1.5
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.56521 q^{3}\) \(+1.00000 q^{4}\) \(+3.62382 q^{5}\) \(+2.56521 q^{6}\) \(+4.81473 q^{7}\) \(-1.00000 q^{8}\) \(+3.58031 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.56521 q^{3}\) \(+1.00000 q^{4}\) \(+3.62382 q^{5}\) \(+2.56521 q^{6}\) \(+4.81473 q^{7}\) \(-1.00000 q^{8}\) \(+3.58031 q^{9}\) \(-3.62382 q^{10}\) \(+0.483333 q^{11}\) \(-2.56521 q^{12}\) \(-5.40690 q^{13}\) \(-4.81473 q^{14}\) \(-9.29586 q^{15}\) \(+1.00000 q^{16}\) \(-5.64515 q^{17}\) \(-3.58031 q^{18}\) \(-1.00000 q^{19}\) \(+3.62382 q^{20}\) \(-12.3508 q^{21}\) \(-0.483333 q^{22}\) \(-3.29287 q^{23}\) \(+2.56521 q^{24}\) \(+8.13206 q^{25}\) \(+5.40690 q^{26}\) \(-1.48862 q^{27}\) \(+4.81473 q^{28}\) \(+7.39723 q^{29}\) \(+9.29586 q^{30}\) \(-3.65660 q^{31}\) \(-1.00000 q^{32}\) \(-1.23985 q^{33}\) \(+5.64515 q^{34}\) \(+17.4477 q^{35}\) \(+3.58031 q^{36}\) \(-4.09678 q^{37}\) \(+1.00000 q^{38}\) \(+13.8698 q^{39}\) \(-3.62382 q^{40}\) \(+3.25360 q^{41}\) \(+12.3508 q^{42}\) \(-9.51322 q^{43}\) \(+0.483333 q^{44}\) \(+12.9744 q^{45}\) \(+3.29287 q^{46}\) \(-1.74149 q^{47}\) \(-2.56521 q^{48}\) \(+16.1816 q^{49}\) \(-8.13206 q^{50}\) \(+14.4810 q^{51}\) \(-5.40690 q^{52}\) \(-10.5836 q^{53}\) \(+1.48862 q^{54}\) \(+1.75151 q^{55}\) \(-4.81473 q^{56}\) \(+2.56521 q^{57}\) \(-7.39723 q^{58}\) \(+3.36884 q^{59}\) \(-9.29586 q^{60}\) \(+0.239416 q^{61}\) \(+3.65660 q^{62}\) \(+17.2382 q^{63}\) \(+1.00000 q^{64}\) \(-19.5936 q^{65}\) \(+1.23985 q^{66}\) \(-2.95102 q^{67}\) \(-5.64515 q^{68}\) \(+8.44691 q^{69}\) \(-17.4477 q^{70}\) \(+0.0139607 q^{71}\) \(-3.58031 q^{72}\) \(+8.52837 q^{73}\) \(+4.09678 q^{74}\) \(-20.8605 q^{75}\) \(-1.00000 q^{76}\) \(+2.32711 q^{77}\) \(-13.8698 q^{78}\) \(+4.43438 q^{79}\) \(+3.62382 q^{80}\) \(-6.92230 q^{81}\) \(-3.25360 q^{82}\) \(-3.63352 q^{83}\) \(-12.3508 q^{84}\) \(-20.4570 q^{85}\) \(+9.51322 q^{86}\) \(-18.9755 q^{87}\) \(-0.483333 q^{88}\) \(-13.1060 q^{89}\) \(-12.9744 q^{90}\) \(-26.0327 q^{91}\) \(-3.29287 q^{92}\) \(+9.37996 q^{93}\) \(+1.74149 q^{94}\) \(-3.62382 q^{95}\) \(+2.56521 q^{96}\) \(-7.06235 q^{97}\) \(-16.1816 q^{98}\) \(+1.73048 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.56521 −1.48103 −0.740513 0.672042i \(-0.765417\pi\)
−0.740513 + 0.672042i \(0.765417\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.62382 1.62062 0.810311 0.586001i \(-0.199298\pi\)
0.810311 + 0.586001i \(0.199298\pi\)
\(6\) 2.56521 1.04724
\(7\) 4.81473 1.81980 0.909898 0.414833i \(-0.136160\pi\)
0.909898 + 0.414833i \(0.136160\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.58031 1.19344
\(10\) −3.62382 −1.14595
\(11\) 0.483333 0.145730 0.0728651 0.997342i \(-0.476786\pi\)
0.0728651 + 0.997342i \(0.476786\pi\)
\(12\) −2.56521 −0.740513
\(13\) −5.40690 −1.49960 −0.749802 0.661662i \(-0.769851\pi\)
−0.749802 + 0.661662i \(0.769851\pi\)
\(14\) −4.81473 −1.28679
\(15\) −9.29586 −2.40018
\(16\) 1.00000 0.250000
\(17\) −5.64515 −1.36915 −0.684575 0.728943i \(-0.740012\pi\)
−0.684575 + 0.728943i \(0.740012\pi\)
\(18\) −3.58031 −0.843888
\(19\) −1.00000 −0.229416
\(20\) 3.62382 0.810311
\(21\) −12.3508 −2.69516
\(22\) −0.483333 −0.103047
\(23\) −3.29287 −0.686611 −0.343306 0.939224i \(-0.611547\pi\)
−0.343306 + 0.939224i \(0.611547\pi\)
\(24\) 2.56521 0.523622
\(25\) 8.13206 1.62641
\(26\) 5.40690 1.06038
\(27\) −1.48862 −0.286486
\(28\) 4.81473 0.909898
\(29\) 7.39723 1.37363 0.686816 0.726832i \(-0.259008\pi\)
0.686816 + 0.726832i \(0.259008\pi\)
\(30\) 9.29586 1.69718
\(31\) −3.65660 −0.656745 −0.328373 0.944548i \(-0.606500\pi\)
−0.328373 + 0.944548i \(0.606500\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.23985 −0.215830
\(34\) 5.64515 0.968135
\(35\) 17.4477 2.94920
\(36\) 3.58031 0.596719
\(37\) −4.09678 −0.673507 −0.336754 0.941593i \(-0.609329\pi\)
−0.336754 + 0.941593i \(0.609329\pi\)
\(38\) 1.00000 0.162221
\(39\) 13.8698 2.22095
\(40\) −3.62382 −0.572976
\(41\) 3.25360 0.508126 0.254063 0.967188i \(-0.418233\pi\)
0.254063 + 0.967188i \(0.418233\pi\)
\(42\) 12.3508 1.90577
\(43\) −9.51322 −1.45075 −0.725376 0.688353i \(-0.758334\pi\)
−0.725376 + 0.688353i \(0.758334\pi\)
\(44\) 0.483333 0.0728651
\(45\) 12.9744 1.93411
\(46\) 3.29287 0.485508
\(47\) −1.74149 −0.254023 −0.127012 0.991901i \(-0.540539\pi\)
−0.127012 + 0.991901i \(0.540539\pi\)
\(48\) −2.56521 −0.370256
\(49\) 16.1816 2.31165
\(50\) −8.13206 −1.15005
\(51\) 14.4810 2.02775
\(52\) −5.40690 −0.749802
\(53\) −10.5836 −1.45377 −0.726887 0.686757i \(-0.759034\pi\)
−0.726887 + 0.686757i \(0.759034\pi\)
\(54\) 1.48862 0.202576
\(55\) 1.75151 0.236174
\(56\) −4.81473 −0.643395
\(57\) 2.56521 0.339771
\(58\) −7.39723 −0.971304
\(59\) 3.36884 0.438586 0.219293 0.975659i \(-0.429625\pi\)
0.219293 + 0.975659i \(0.429625\pi\)
\(60\) −9.29586 −1.20009
\(61\) 0.239416 0.0306541 0.0153271 0.999883i \(-0.495121\pi\)
0.0153271 + 0.999883i \(0.495121\pi\)
\(62\) 3.65660 0.464389
\(63\) 17.2382 2.17181
\(64\) 1.00000 0.125000
\(65\) −19.5936 −2.43029
\(66\) 1.23985 0.152615
\(67\) −2.95102 −0.360525 −0.180262 0.983619i \(-0.557695\pi\)
−0.180262 + 0.983619i \(0.557695\pi\)
\(68\) −5.64515 −0.684575
\(69\) 8.44691 1.01689
\(70\) −17.4477 −2.08540
\(71\) 0.0139607 0.00165683 0.000828416 1.00000i \(-0.499736\pi\)
0.000828416 1.00000i \(0.499736\pi\)
\(72\) −3.58031 −0.421944
\(73\) 8.52837 0.998170 0.499085 0.866553i \(-0.333669\pi\)
0.499085 + 0.866553i \(0.333669\pi\)
\(74\) 4.09678 0.476241
\(75\) −20.8605 −2.40876
\(76\) −1.00000 −0.114708
\(77\) 2.32711 0.265199
\(78\) −13.8698 −1.57045
\(79\) 4.43438 0.498907 0.249454 0.968387i \(-0.419749\pi\)
0.249454 + 0.968387i \(0.419749\pi\)
\(80\) 3.62382 0.405155
\(81\) −6.92230 −0.769145
\(82\) −3.25360 −0.359299
\(83\) −3.63352 −0.398831 −0.199415 0.979915i \(-0.563904\pi\)
−0.199415 + 0.979915i \(0.563904\pi\)
\(84\) −12.3508 −1.34758
\(85\) −20.4570 −2.21887
\(86\) 9.51322 1.02584
\(87\) −18.9755 −2.03438
\(88\) −0.483333 −0.0515234
\(89\) −13.1060 −1.38924 −0.694618 0.719378i \(-0.744427\pi\)
−0.694618 + 0.719378i \(0.744427\pi\)
\(90\) −12.9744 −1.36762
\(91\) −26.0327 −2.72897
\(92\) −3.29287 −0.343306
\(93\) 9.37996 0.972657
\(94\) 1.74149 0.179621
\(95\) −3.62382 −0.371796
\(96\) 2.56521 0.261811
\(97\) −7.06235 −0.717073 −0.358536 0.933516i \(-0.616724\pi\)
−0.358536 + 0.933516i \(0.616724\pi\)
\(98\) −16.1816 −1.63459
\(99\) 1.73048 0.173920
\(100\) 8.13206 0.813206
\(101\) 17.3847 1.72984 0.864921 0.501907i \(-0.167368\pi\)
0.864921 + 0.501907i \(0.167368\pi\)
\(102\) −14.4810 −1.43383
\(103\) 1.16071 0.114368 0.0571839 0.998364i \(-0.481788\pi\)
0.0571839 + 0.998364i \(0.481788\pi\)
\(104\) 5.40690 0.530190
\(105\) −44.7570 −4.36784
\(106\) 10.5836 1.02797
\(107\) −1.98841 −0.192227 −0.0961135 0.995370i \(-0.530641\pi\)
−0.0961135 + 0.995370i \(0.530641\pi\)
\(108\) −1.48862 −0.143243
\(109\) 6.13451 0.587580 0.293790 0.955870i \(-0.405083\pi\)
0.293790 + 0.955870i \(0.405083\pi\)
\(110\) −1.75151 −0.167000
\(111\) 10.5091 0.997481
\(112\) 4.81473 0.454949
\(113\) −14.2125 −1.33700 −0.668500 0.743712i \(-0.733063\pi\)
−0.668500 + 0.743712i \(0.733063\pi\)
\(114\) −2.56521 −0.240254
\(115\) −11.9328 −1.11274
\(116\) 7.39723 0.686816
\(117\) −19.3584 −1.78968
\(118\) −3.36884 −0.310127
\(119\) −27.1798 −2.49157
\(120\) 9.29586 0.848592
\(121\) −10.7664 −0.978763
\(122\) −0.239416 −0.0216757
\(123\) −8.34616 −0.752548
\(124\) −3.65660 −0.328373
\(125\) 11.3500 1.01518
\(126\) −17.2382 −1.53570
\(127\) −0.471433 −0.0418329 −0.0209165 0.999781i \(-0.506658\pi\)
−0.0209165 + 0.999781i \(0.506658\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 24.4034 2.14860
\(130\) 19.5936 1.71847
\(131\) −19.0185 −1.66165 −0.830825 0.556533i \(-0.812131\pi\)
−0.830825 + 0.556533i \(0.812131\pi\)
\(132\) −1.23985 −0.107915
\(133\) −4.81473 −0.417490
\(134\) 2.95102 0.254929
\(135\) −5.39450 −0.464285
\(136\) 5.64515 0.484067
\(137\) −3.39468 −0.290027 −0.145013 0.989430i \(-0.546323\pi\)
−0.145013 + 0.989430i \(0.546323\pi\)
\(138\) −8.44691 −0.719049
\(139\) 4.92798 0.417986 0.208993 0.977917i \(-0.432981\pi\)
0.208993 + 0.977917i \(0.432981\pi\)
\(140\) 17.4477 1.47460
\(141\) 4.46730 0.376215
\(142\) −0.0139607 −0.00117156
\(143\) −2.61333 −0.218538
\(144\) 3.58031 0.298359
\(145\) 26.8062 2.22614
\(146\) −8.52837 −0.705813
\(147\) −41.5092 −3.42362
\(148\) −4.09678 −0.336754
\(149\) −12.9917 −1.06432 −0.532160 0.846644i \(-0.678620\pi\)
−0.532160 + 0.846644i \(0.678620\pi\)
\(150\) 20.8605 1.70325
\(151\) −18.6205 −1.51532 −0.757659 0.652651i \(-0.773657\pi\)
−0.757659 + 0.652651i \(0.773657\pi\)
\(152\) 1.00000 0.0811107
\(153\) −20.2114 −1.63399
\(154\) −2.32711 −0.187524
\(155\) −13.2509 −1.06434
\(156\) 13.8698 1.11048
\(157\) 4.81982 0.384664 0.192332 0.981330i \(-0.438395\pi\)
0.192332 + 0.981330i \(0.438395\pi\)
\(158\) −4.43438 −0.352781
\(159\) 27.1493 2.15308
\(160\) −3.62382 −0.286488
\(161\) −15.8543 −1.24949
\(162\) 6.92230 0.543867
\(163\) 10.5352 0.825179 0.412590 0.910917i \(-0.364624\pi\)
0.412590 + 0.910917i \(0.364624\pi\)
\(164\) 3.25360 0.254063
\(165\) −4.49299 −0.349779
\(166\) 3.63352 0.282016
\(167\) −9.47281 −0.733028 −0.366514 0.930413i \(-0.619449\pi\)
−0.366514 + 0.930413i \(0.619449\pi\)
\(168\) 12.3508 0.952884
\(169\) 16.2346 1.24881
\(170\) 20.4570 1.56898
\(171\) −3.58031 −0.273793
\(172\) −9.51322 −0.725376
\(173\) −17.6072 −1.33865 −0.669326 0.742969i \(-0.733417\pi\)
−0.669326 + 0.742969i \(0.733417\pi\)
\(174\) 18.9755 1.43853
\(175\) 39.1536 2.95974
\(176\) 0.483333 0.0364326
\(177\) −8.64179 −0.649557
\(178\) 13.1060 0.982339
\(179\) 16.1982 1.21071 0.605355 0.795956i \(-0.293031\pi\)
0.605355 + 0.795956i \(0.293031\pi\)
\(180\) 12.9744 0.967055
\(181\) −14.9491 −1.11116 −0.555578 0.831464i \(-0.687503\pi\)
−0.555578 + 0.831464i \(0.687503\pi\)
\(182\) 26.0327 1.92967
\(183\) −0.614154 −0.0453996
\(184\) 3.29287 0.242754
\(185\) −14.8460 −1.09150
\(186\) −9.37996 −0.687772
\(187\) −2.72848 −0.199526
\(188\) −1.74149 −0.127012
\(189\) −7.16731 −0.521345
\(190\) 3.62382 0.262899
\(191\) 16.5906 1.20045 0.600226 0.799831i \(-0.295077\pi\)
0.600226 + 0.799831i \(0.295077\pi\)
\(192\) −2.56521 −0.185128
\(193\) −19.7455 −1.42131 −0.710656 0.703540i \(-0.751602\pi\)
−0.710656 + 0.703540i \(0.751602\pi\)
\(194\) 7.06235 0.507047
\(195\) 50.2618 3.59932
\(196\) 16.1816 1.15583
\(197\) 18.8208 1.34093 0.670465 0.741941i \(-0.266095\pi\)
0.670465 + 0.741941i \(0.266095\pi\)
\(198\) −1.73048 −0.122980
\(199\) −11.5459 −0.818464 −0.409232 0.912430i \(-0.634203\pi\)
−0.409232 + 0.912430i \(0.634203\pi\)
\(200\) −8.13206 −0.575024
\(201\) 7.57000 0.533946
\(202\) −17.3847 −1.22318
\(203\) 35.6156 2.49973
\(204\) 14.4810 1.01387
\(205\) 11.7904 0.823480
\(206\) −1.16071 −0.0808702
\(207\) −11.7895 −0.819428
\(208\) −5.40690 −0.374901
\(209\) −0.483333 −0.0334328
\(210\) 44.7570 3.08853
\(211\) −1.00000 −0.0688428
\(212\) −10.5836 −0.726887
\(213\) −0.0358122 −0.00245381
\(214\) 1.98841 0.135925
\(215\) −34.4742 −2.35112
\(216\) 1.48862 0.101288
\(217\) −17.6055 −1.19514
\(218\) −6.13451 −0.415482
\(219\) −21.8771 −1.47832
\(220\) 1.75151 0.118087
\(221\) 30.5227 2.05318
\(222\) −10.5091 −0.705326
\(223\) −23.0712 −1.54496 −0.772479 0.635040i \(-0.780984\pi\)
−0.772479 + 0.635040i \(0.780984\pi\)
\(224\) −4.81473 −0.321697
\(225\) 29.1153 1.94102
\(226\) 14.2125 0.945402
\(227\) 16.5721 1.09993 0.549963 0.835189i \(-0.314642\pi\)
0.549963 + 0.835189i \(0.314642\pi\)
\(228\) 2.56521 0.169885
\(229\) 3.42397 0.226263 0.113131 0.993580i \(-0.463912\pi\)
0.113131 + 0.993580i \(0.463912\pi\)
\(230\) 11.9328 0.786824
\(231\) −5.96954 −0.392767
\(232\) −7.39723 −0.485652
\(233\) 5.79695 0.379770 0.189885 0.981806i \(-0.439188\pi\)
0.189885 + 0.981806i \(0.439188\pi\)
\(234\) 19.3584 1.26550
\(235\) −6.31086 −0.411675
\(236\) 3.36884 0.219293
\(237\) −11.3751 −0.738894
\(238\) 27.1798 1.76181
\(239\) −0.233983 −0.0151351 −0.00756755 0.999971i \(-0.502409\pi\)
−0.00756755 + 0.999971i \(0.502409\pi\)
\(240\) −9.29586 −0.600045
\(241\) 9.45390 0.608980 0.304490 0.952516i \(-0.401514\pi\)
0.304490 + 0.952516i \(0.401514\pi\)
\(242\) 10.7664 0.692090
\(243\) 22.2230 1.42561
\(244\) 0.239416 0.0153271
\(245\) 58.6391 3.74631
\(246\) 8.34616 0.532132
\(247\) 5.40690 0.344033
\(248\) 3.65660 0.232195
\(249\) 9.32075 0.590679
\(250\) −11.3500 −0.717839
\(251\) −14.1920 −0.895788 −0.447894 0.894087i \(-0.647826\pi\)
−0.447894 + 0.894087i \(0.647826\pi\)
\(252\) 17.2382 1.08591
\(253\) −1.59155 −0.100060
\(254\) 0.471433 0.0295803
\(255\) 52.4765 3.28621
\(256\) 1.00000 0.0625000
\(257\) 25.7696 1.60746 0.803731 0.594992i \(-0.202845\pi\)
0.803731 + 0.594992i \(0.202845\pi\)
\(258\) −24.4034 −1.51929
\(259\) −19.7249 −1.22564
\(260\) −19.5936 −1.21515
\(261\) 26.4844 1.63934
\(262\) 19.0185 1.17496
\(263\) −26.3234 −1.62317 −0.811586 0.584233i \(-0.801395\pi\)
−0.811586 + 0.584233i \(0.801395\pi\)
\(264\) 1.23985 0.0763075
\(265\) −38.3532 −2.35602
\(266\) 4.81473 0.295210
\(267\) 33.6197 2.05750
\(268\) −2.95102 −0.180262
\(269\) 24.6133 1.50070 0.750349 0.661042i \(-0.229886\pi\)
0.750349 + 0.661042i \(0.229886\pi\)
\(270\) 5.39450 0.328299
\(271\) −14.8630 −0.902862 −0.451431 0.892306i \(-0.649086\pi\)
−0.451431 + 0.892306i \(0.649086\pi\)
\(272\) −5.64515 −0.342287
\(273\) 66.7795 4.04168
\(274\) 3.39468 0.205080
\(275\) 3.93049 0.237018
\(276\) 8.44691 0.508445
\(277\) 3.58959 0.215678 0.107839 0.994168i \(-0.465607\pi\)
0.107839 + 0.994168i \(0.465607\pi\)
\(278\) −4.92798 −0.295560
\(279\) −13.0918 −0.783785
\(280\) −17.4477 −1.04270
\(281\) 26.4608 1.57852 0.789261 0.614059i \(-0.210464\pi\)
0.789261 + 0.614059i \(0.210464\pi\)
\(282\) −4.46730 −0.266024
\(283\) 14.6346 0.869937 0.434969 0.900446i \(-0.356759\pi\)
0.434969 + 0.900446i \(0.356759\pi\)
\(284\) 0.0139607 0.000828416 0
\(285\) 9.29586 0.550639
\(286\) 2.61333 0.154530
\(287\) 15.6652 0.924686
\(288\) −3.58031 −0.210972
\(289\) 14.8677 0.874570
\(290\) −26.8062 −1.57412
\(291\) 18.1164 1.06200
\(292\) 8.52837 0.499085
\(293\) 19.7157 1.15180 0.575901 0.817520i \(-0.304652\pi\)
0.575901 + 0.817520i \(0.304652\pi\)
\(294\) 41.5092 2.42086
\(295\) 12.2081 0.710782
\(296\) 4.09678 0.238121
\(297\) −0.719500 −0.0417496
\(298\) 12.9917 0.752588
\(299\) 17.8042 1.02965
\(300\) −20.8605 −1.20438
\(301\) −45.8035 −2.64007
\(302\) 18.6205 1.07149
\(303\) −44.5955 −2.56194
\(304\) −1.00000 −0.0573539
\(305\) 0.867602 0.0496787
\(306\) 20.2114 1.15541
\(307\) −30.0320 −1.71402 −0.857008 0.515303i \(-0.827679\pi\)
−0.857008 + 0.515303i \(0.827679\pi\)
\(308\) 2.32711 0.132600
\(309\) −2.97746 −0.169382
\(310\) 13.2509 0.752599
\(311\) −33.1178 −1.87794 −0.938968 0.344003i \(-0.888217\pi\)
−0.938968 + 0.344003i \(0.888217\pi\)
\(312\) −13.8698 −0.785225
\(313\) 0.709517 0.0401043 0.0200521 0.999799i \(-0.493617\pi\)
0.0200521 + 0.999799i \(0.493617\pi\)
\(314\) −4.81982 −0.271998
\(315\) 62.4682 3.51968
\(316\) 4.43438 0.249454
\(317\) 2.38483 0.133946 0.0669728 0.997755i \(-0.478666\pi\)
0.0669728 + 0.997755i \(0.478666\pi\)
\(318\) −27.1493 −1.52246
\(319\) 3.57532 0.200180
\(320\) 3.62382 0.202578
\(321\) 5.10070 0.284693
\(322\) 15.8543 0.883524
\(323\) 5.64515 0.314104
\(324\) −6.92230 −0.384572
\(325\) −43.9692 −2.43897
\(326\) −10.5352 −0.583490
\(327\) −15.7363 −0.870221
\(328\) −3.25360 −0.179650
\(329\) −8.38482 −0.462270
\(330\) 4.49299 0.247331
\(331\) −29.5601 −1.62477 −0.812386 0.583120i \(-0.801832\pi\)
−0.812386 + 0.583120i \(0.801832\pi\)
\(332\) −3.63352 −0.199415
\(333\) −14.6678 −0.803789
\(334\) 9.47281 0.518329
\(335\) −10.6940 −0.584274
\(336\) −12.3508 −0.673791
\(337\) −11.6149 −0.632705 −0.316352 0.948642i \(-0.602458\pi\)
−0.316352 + 0.948642i \(0.602458\pi\)
\(338\) −16.2346 −0.883044
\(339\) 36.4581 1.98013
\(340\) −20.4570 −1.10944
\(341\) −1.76736 −0.0957077
\(342\) 3.58031 0.193601
\(343\) 44.2068 2.38694
\(344\) 9.51322 0.512918
\(345\) 30.6101 1.64799
\(346\) 17.6072 0.946570
\(347\) 1.42388 0.0764377 0.0382189 0.999269i \(-0.487832\pi\)
0.0382189 + 0.999269i \(0.487832\pi\)
\(348\) −18.9755 −1.01719
\(349\) −6.02755 −0.322647 −0.161324 0.986902i \(-0.551576\pi\)
−0.161324 + 0.986902i \(0.551576\pi\)
\(350\) −39.1536 −2.09285
\(351\) 8.04883 0.429615
\(352\) −0.483333 −0.0257617
\(353\) −1.61861 −0.0861499 −0.0430750 0.999072i \(-0.513715\pi\)
−0.0430750 + 0.999072i \(0.513715\pi\)
\(354\) 8.64179 0.459306
\(355\) 0.0505911 0.00268510
\(356\) −13.1060 −0.694618
\(357\) 69.7220 3.69008
\(358\) −16.1982 −0.856101
\(359\) −20.7395 −1.09459 −0.547294 0.836940i \(-0.684342\pi\)
−0.547294 + 0.836940i \(0.684342\pi\)
\(360\) −12.9744 −0.683811
\(361\) 1.00000 0.0526316
\(362\) 14.9491 0.785706
\(363\) 27.6181 1.44957
\(364\) −26.0327 −1.36449
\(365\) 30.9053 1.61766
\(366\) 0.614154 0.0321023
\(367\) −7.59985 −0.396709 −0.198355 0.980130i \(-0.563560\pi\)
−0.198355 + 0.980130i \(0.563560\pi\)
\(368\) −3.29287 −0.171653
\(369\) 11.6489 0.606417
\(370\) 14.8460 0.771807
\(371\) −50.9573 −2.64557
\(372\) 9.37996 0.486328
\(373\) 24.5031 1.26872 0.634362 0.773036i \(-0.281263\pi\)
0.634362 + 0.773036i \(0.281263\pi\)
\(374\) 2.72848 0.141087
\(375\) −29.1152 −1.50350
\(376\) 1.74149 0.0898107
\(377\) −39.9961 −2.05990
\(378\) 7.16731 0.368647
\(379\) −8.53571 −0.438450 −0.219225 0.975674i \(-0.570353\pi\)
−0.219225 + 0.975674i \(0.570353\pi\)
\(380\) −3.62382 −0.185898
\(381\) 1.20933 0.0619556
\(382\) −16.5906 −0.848848
\(383\) −11.7009 −0.597889 −0.298945 0.954270i \(-0.596635\pi\)
−0.298945 + 0.954270i \(0.596635\pi\)
\(384\) 2.56521 0.130905
\(385\) 8.43304 0.429787
\(386\) 19.7455 1.00502
\(387\) −34.0603 −1.73138
\(388\) −7.06235 −0.358536
\(389\) 24.3028 1.23220 0.616100 0.787668i \(-0.288712\pi\)
0.616100 + 0.787668i \(0.288712\pi\)
\(390\) −50.2618 −2.54511
\(391\) 18.5887 0.940073
\(392\) −16.1816 −0.817293
\(393\) 48.7864 2.46095
\(394\) −18.8208 −0.948180
\(395\) 16.0694 0.808540
\(396\) 1.73048 0.0869600
\(397\) −27.2367 −1.36697 −0.683486 0.729964i \(-0.739537\pi\)
−0.683486 + 0.729964i \(0.739537\pi\)
\(398\) 11.5459 0.578741
\(399\) 12.3508 0.618313
\(400\) 8.13206 0.406603
\(401\) −18.5289 −0.925287 −0.462643 0.886544i \(-0.653099\pi\)
−0.462643 + 0.886544i \(0.653099\pi\)
\(402\) −7.57000 −0.377557
\(403\) 19.7709 0.984858
\(404\) 17.3847 0.864921
\(405\) −25.0852 −1.24649
\(406\) −35.6156 −1.76757
\(407\) −1.98011 −0.0981504
\(408\) −14.4810 −0.716916
\(409\) −14.8965 −0.736584 −0.368292 0.929710i \(-0.620057\pi\)
−0.368292 + 0.929710i \(0.620057\pi\)
\(410\) −11.7904 −0.582288
\(411\) 8.70806 0.429537
\(412\) 1.16071 0.0571839
\(413\) 16.2201 0.798137
\(414\) 11.7895 0.579423
\(415\) −13.1672 −0.646354
\(416\) 5.40690 0.265095
\(417\) −12.6413 −0.619047
\(418\) 0.483333 0.0236406
\(419\) 0.854101 0.0417256 0.0208628 0.999782i \(-0.493359\pi\)
0.0208628 + 0.999782i \(0.493359\pi\)
\(420\) −44.7570 −2.18392
\(421\) −17.8339 −0.869171 −0.434585 0.900631i \(-0.643105\pi\)
−0.434585 + 0.900631i \(0.643105\pi\)
\(422\) 1.00000 0.0486792
\(423\) −6.23509 −0.303161
\(424\) 10.5836 0.513987
\(425\) −45.9067 −2.22680
\(426\) 0.0358122 0.00173511
\(427\) 1.15272 0.0557842
\(428\) −1.98841 −0.0961135
\(429\) 6.70375 0.323660
\(430\) 34.4742 1.66249
\(431\) −28.9693 −1.39540 −0.697701 0.716389i \(-0.745794\pi\)
−0.697701 + 0.716389i \(0.745794\pi\)
\(432\) −1.48862 −0.0716214
\(433\) 24.0138 1.15403 0.577015 0.816734i \(-0.304217\pi\)
0.577015 + 0.816734i \(0.304217\pi\)
\(434\) 17.6055 0.845093
\(435\) −68.7636 −3.29696
\(436\) 6.13451 0.293790
\(437\) 3.29287 0.157519
\(438\) 21.8771 1.04533
\(439\) 13.1530 0.627758 0.313879 0.949463i \(-0.398371\pi\)
0.313879 + 0.949463i \(0.398371\pi\)
\(440\) −1.75151 −0.0835000
\(441\) 57.9351 2.75881
\(442\) −30.5227 −1.45182
\(443\) −8.78113 −0.417204 −0.208602 0.978001i \(-0.566891\pi\)
−0.208602 + 0.978001i \(0.566891\pi\)
\(444\) 10.5091 0.498741
\(445\) −47.4939 −2.25143
\(446\) 23.0712 1.09245
\(447\) 33.3264 1.57629
\(448\) 4.81473 0.227474
\(449\) 17.6450 0.832719 0.416359 0.909200i \(-0.363306\pi\)
0.416359 + 0.909200i \(0.363306\pi\)
\(450\) −29.1153 −1.37251
\(451\) 1.57257 0.0740494
\(452\) −14.2125 −0.668500
\(453\) 47.7656 2.24422
\(454\) −16.5721 −0.777765
\(455\) −94.3379 −4.42263
\(456\) −2.56521 −0.120127
\(457\) −21.8845 −1.02371 −0.511856 0.859071i \(-0.671042\pi\)
−0.511856 + 0.859071i \(0.671042\pi\)
\(458\) −3.42397 −0.159992
\(459\) 8.40350 0.392242
\(460\) −11.9328 −0.556368
\(461\) −4.83115 −0.225009 −0.112505 0.993651i \(-0.535887\pi\)
−0.112505 + 0.993651i \(0.535887\pi\)
\(462\) 5.96954 0.277728
\(463\) 5.95116 0.276574 0.138287 0.990392i \(-0.455840\pi\)
0.138287 + 0.990392i \(0.455840\pi\)
\(464\) 7.39723 0.343408
\(465\) 33.9913 1.57631
\(466\) −5.79695 −0.268538
\(467\) −0.943463 −0.0436583 −0.0218291 0.999762i \(-0.506949\pi\)
−0.0218291 + 0.999762i \(0.506949\pi\)
\(468\) −19.3584 −0.894842
\(469\) −14.2084 −0.656081
\(470\) 6.31086 0.291098
\(471\) −12.3639 −0.569697
\(472\) −3.36884 −0.155064
\(473\) −4.59805 −0.211418
\(474\) 11.3751 0.522477
\(475\) −8.13206 −0.373125
\(476\) −27.1798 −1.24579
\(477\) −37.8927 −1.73499
\(478\) 0.233983 0.0107021
\(479\) −28.7216 −1.31232 −0.656162 0.754620i \(-0.727821\pi\)
−0.656162 + 0.754620i \(0.727821\pi\)
\(480\) 9.29586 0.424296
\(481\) 22.1509 1.00999
\(482\) −9.45390 −0.430614
\(483\) 40.6696 1.85053
\(484\) −10.7664 −0.489381
\(485\) −25.5927 −1.16210
\(486\) −22.2230 −1.00806
\(487\) 21.1829 0.959890 0.479945 0.877299i \(-0.340657\pi\)
0.479945 + 0.877299i \(0.340657\pi\)
\(488\) −0.239416 −0.0108379
\(489\) −27.0250 −1.22211
\(490\) −58.6391 −2.64904
\(491\) −8.36445 −0.377482 −0.188741 0.982027i \(-0.560441\pi\)
−0.188741 + 0.982027i \(0.560441\pi\)
\(492\) −8.34616 −0.376274
\(493\) −41.7585 −1.88071
\(494\) −5.40690 −0.243268
\(495\) 6.27095 0.281858
\(496\) −3.65660 −0.164186
\(497\) 0.0672170 0.00301510
\(498\) −9.32075 −0.417673
\(499\) 23.5808 1.05562 0.527810 0.849362i \(-0.323013\pi\)
0.527810 + 0.849362i \(0.323013\pi\)
\(500\) 11.3500 0.507589
\(501\) 24.2998 1.08563
\(502\) 14.1920 0.633418
\(503\) −21.0962 −0.940635 −0.470318 0.882497i \(-0.655861\pi\)
−0.470318 + 0.882497i \(0.655861\pi\)
\(504\) −17.2382 −0.767851
\(505\) 62.9990 2.80342
\(506\) 1.59155 0.0707531
\(507\) −41.6451 −1.84952
\(508\) −0.471433 −0.0209165
\(509\) 7.33577 0.325152 0.162576 0.986696i \(-0.448020\pi\)
0.162576 + 0.986696i \(0.448020\pi\)
\(510\) −52.4765 −2.32370
\(511\) 41.0618 1.81647
\(512\) −1.00000 −0.0441942
\(513\) 1.48862 0.0657243
\(514\) −25.7696 −1.13665
\(515\) 4.20619 0.185347
\(516\) 24.4034 1.07430
\(517\) −0.841721 −0.0370189
\(518\) 19.7249 0.866662
\(519\) 45.1662 1.98258
\(520\) 19.5936 0.859237
\(521\) 12.7746 0.559665 0.279833 0.960049i \(-0.409721\pi\)
0.279833 + 0.960049i \(0.409721\pi\)
\(522\) −26.4844 −1.15919
\(523\) −26.6711 −1.16624 −0.583122 0.812384i \(-0.698169\pi\)
−0.583122 + 0.812384i \(0.698169\pi\)
\(524\) −19.0185 −0.830825
\(525\) −100.437 −4.38345
\(526\) 26.3234 1.14776
\(527\) 20.6421 0.899183
\(528\) −1.23985 −0.0539576
\(529\) −12.1570 −0.528565
\(530\) 38.3532 1.66596
\(531\) 12.0615 0.523425
\(532\) −4.81473 −0.208745
\(533\) −17.5919 −0.761988
\(534\) −33.6197 −1.45487
\(535\) −7.20565 −0.311527
\(536\) 2.95102 0.127465
\(537\) −41.5518 −1.79309
\(538\) −24.6133 −1.06115
\(539\) 7.82108 0.336878
\(540\) −5.39450 −0.232142
\(541\) −7.48518 −0.321813 −0.160907 0.986970i \(-0.551442\pi\)
−0.160907 + 0.986970i \(0.551442\pi\)
\(542\) 14.8630 0.638420
\(543\) 38.3475 1.64565
\(544\) 5.64515 0.242034
\(545\) 22.2304 0.952244
\(546\) −66.7795 −2.85790
\(547\) −25.8450 −1.10505 −0.552526 0.833496i \(-0.686336\pi\)
−0.552526 + 0.833496i \(0.686336\pi\)
\(548\) −3.39468 −0.145013
\(549\) 0.857185 0.0365838
\(550\) −3.93049 −0.167597
\(551\) −7.39723 −0.315133
\(552\) −8.44691 −0.359525
\(553\) 21.3503 0.907909
\(554\) −3.58959 −0.152507
\(555\) 38.0831 1.61654
\(556\) 4.92798 0.208993
\(557\) −29.4861 −1.24937 −0.624684 0.780878i \(-0.714772\pi\)
−0.624684 + 0.780878i \(0.714772\pi\)
\(558\) 13.0918 0.554219
\(559\) 51.4370 2.17555
\(560\) 17.4477 0.737300
\(561\) 6.99914 0.295504
\(562\) −26.4608 −1.11618
\(563\) 1.73847 0.0732676 0.0366338 0.999329i \(-0.488336\pi\)
0.0366338 + 0.999329i \(0.488336\pi\)
\(564\) 4.46730 0.188107
\(565\) −51.5036 −2.16677
\(566\) −14.6346 −0.615138
\(567\) −33.3290 −1.39969
\(568\) −0.0139607 −0.000585779 0
\(569\) 36.4497 1.52805 0.764025 0.645186i \(-0.223220\pi\)
0.764025 + 0.645186i \(0.223220\pi\)
\(570\) −9.29586 −0.389361
\(571\) 2.10049 0.0879028 0.0439514 0.999034i \(-0.486005\pi\)
0.0439514 + 0.999034i \(0.486005\pi\)
\(572\) −2.61333 −0.109269
\(573\) −42.5583 −1.77790
\(574\) −15.6652 −0.653851
\(575\) −26.7778 −1.11671
\(576\) 3.58031 0.149180
\(577\) 35.9192 1.49534 0.747668 0.664073i \(-0.231174\pi\)
0.747668 + 0.664073i \(0.231174\pi\)
\(578\) −14.8677 −0.618414
\(579\) 50.6514 2.10500
\(580\) 26.8062 1.11307
\(581\) −17.4944 −0.725790
\(582\) −18.1164 −0.750949
\(583\) −5.11542 −0.211859
\(584\) −8.52837 −0.352907
\(585\) −70.1513 −2.90040
\(586\) −19.7157 −0.814446
\(587\) 42.6923 1.76210 0.881049 0.473025i \(-0.156838\pi\)
0.881049 + 0.473025i \(0.156838\pi\)
\(588\) −41.5092 −1.71181
\(589\) 3.65660 0.150668
\(590\) −12.2081 −0.502598
\(591\) −48.2794 −1.98595
\(592\) −4.09678 −0.168377
\(593\) 16.6590 0.684105 0.342052 0.939681i \(-0.388878\pi\)
0.342052 + 0.939681i \(0.388878\pi\)
\(594\) 0.719500 0.0295214
\(595\) −98.4948 −4.03789
\(596\) −12.9917 −0.532160
\(597\) 29.6176 1.21217
\(598\) −17.8042 −0.728069
\(599\) −19.6946 −0.804702 −0.402351 0.915486i \(-0.631807\pi\)
−0.402351 + 0.915486i \(0.631807\pi\)
\(600\) 20.8605 0.851625
\(601\) 21.3739 0.871859 0.435930 0.899981i \(-0.356420\pi\)
0.435930 + 0.899981i \(0.356420\pi\)
\(602\) 45.8035 1.86681
\(603\) −10.5656 −0.430264
\(604\) −18.6205 −0.757659
\(605\) −39.0154 −1.58620
\(606\) 44.5955 1.81157
\(607\) 16.5595 0.672131 0.336066 0.941839i \(-0.390904\pi\)
0.336066 + 0.941839i \(0.390904\pi\)
\(608\) 1.00000 0.0405554
\(609\) −91.3616 −3.70216
\(610\) −0.867602 −0.0351282
\(611\) 9.41609 0.380934
\(612\) −20.2114 −0.816997
\(613\) −20.0082 −0.808125 −0.404062 0.914731i \(-0.632402\pi\)
−0.404062 + 0.914731i \(0.632402\pi\)
\(614\) 30.0320 1.21199
\(615\) −30.2450 −1.21960
\(616\) −2.32711 −0.0937621
\(617\) −1.54570 −0.0622274 −0.0311137 0.999516i \(-0.509905\pi\)
−0.0311137 + 0.999516i \(0.509905\pi\)
\(618\) 2.97746 0.119771
\(619\) −28.7093 −1.15392 −0.576962 0.816771i \(-0.695762\pi\)
−0.576962 + 0.816771i \(0.695762\pi\)
\(620\) −13.2509 −0.532168
\(621\) 4.90184 0.196704
\(622\) 33.1178 1.32790
\(623\) −63.1019 −2.52813
\(624\) 13.8698 0.555238
\(625\) 0.470126 0.0188050
\(626\) −0.709517 −0.0283580
\(627\) 1.23985 0.0495149
\(628\) 4.81982 0.192332
\(629\) 23.1269 0.922132
\(630\) −62.4682 −2.48879
\(631\) −32.6313 −1.29903 −0.649516 0.760348i \(-0.725028\pi\)
−0.649516 + 0.760348i \(0.725028\pi\)
\(632\) −4.43438 −0.176390
\(633\) 2.56521 0.101958
\(634\) −2.38483 −0.0947139
\(635\) −1.70839 −0.0677953
\(636\) 27.1493 1.07654
\(637\) −87.4922 −3.46657
\(638\) −3.57532 −0.141548
\(639\) 0.0499837 0.00197733
\(640\) −3.62382 −0.143244
\(641\) 29.4825 1.16449 0.582245 0.813014i \(-0.302175\pi\)
0.582245 + 0.813014i \(0.302175\pi\)
\(642\) −5.10070 −0.201309
\(643\) 26.1111 1.02972 0.514861 0.857274i \(-0.327844\pi\)
0.514861 + 0.857274i \(0.327844\pi\)
\(644\) −15.8543 −0.624746
\(645\) 88.4335 3.48207
\(646\) −5.64515 −0.222105
\(647\) 34.3605 1.35085 0.675425 0.737428i \(-0.263960\pi\)
0.675425 + 0.737428i \(0.263960\pi\)
\(648\) 6.92230 0.271934
\(649\) 1.62827 0.0639152
\(650\) 43.9692 1.72462
\(651\) 45.1619 1.77004
\(652\) 10.5352 0.412590
\(653\) −40.3342 −1.57840 −0.789200 0.614137i \(-0.789504\pi\)
−0.789200 + 0.614137i \(0.789504\pi\)
\(654\) 15.7363 0.615339
\(655\) −68.9195 −2.69291
\(656\) 3.25360 0.127032
\(657\) 30.5342 1.19125
\(658\) 8.38482 0.326874
\(659\) 17.7621 0.691915 0.345957 0.938250i \(-0.387554\pi\)
0.345957 + 0.938250i \(0.387554\pi\)
\(660\) −4.49299 −0.174890
\(661\) 37.7222 1.46722 0.733612 0.679568i \(-0.237833\pi\)
0.733612 + 0.679568i \(0.237833\pi\)
\(662\) 29.5601 1.14889
\(663\) −78.2973 −3.04082
\(664\) 3.63352 0.141008
\(665\) −17.4477 −0.676592
\(666\) 14.6678 0.568364
\(667\) −24.3581 −0.943151
\(668\) −9.47281 −0.366514
\(669\) 59.1824 2.28812
\(670\) 10.6940 0.413144
\(671\) 0.115718 0.00446723
\(672\) 12.3508 0.476442
\(673\) 34.8916 1.34497 0.672486 0.740109i \(-0.265226\pi\)
0.672486 + 0.740109i \(0.265226\pi\)
\(674\) 11.6149 0.447390
\(675\) −12.1056 −0.465944
\(676\) 16.2346 0.624406
\(677\) −30.7839 −1.18312 −0.591560 0.806261i \(-0.701488\pi\)
−0.591560 + 0.806261i \(0.701488\pi\)
\(678\) −36.4581 −1.40016
\(679\) −34.0033 −1.30493
\(680\) 20.4570 0.784490
\(681\) −42.5108 −1.62902
\(682\) 1.76736 0.0676756
\(683\) 29.6790 1.13564 0.567819 0.823154i \(-0.307788\pi\)
0.567819 + 0.823154i \(0.307788\pi\)
\(684\) −3.58031 −0.136897
\(685\) −12.3017 −0.470023
\(686\) −44.2068 −1.68782
\(687\) −8.78322 −0.335101
\(688\) −9.51322 −0.362688
\(689\) 57.2247 2.18009
\(690\) −30.6101 −1.16531
\(691\) 5.38223 0.204750 0.102375 0.994746i \(-0.467356\pi\)
0.102375 + 0.994746i \(0.467356\pi\)
\(692\) −17.6072 −0.669326
\(693\) 8.33179 0.316499
\(694\) −1.42388 −0.0540496
\(695\) 17.8581 0.677396
\(696\) 18.9755 0.719263
\(697\) −18.3670 −0.695701
\(698\) 6.02755 0.228146
\(699\) −14.8704 −0.562450
\(700\) 39.1536 1.47987
\(701\) −0.881147 −0.0332805 −0.0166402 0.999862i \(-0.505297\pi\)
−0.0166402 + 0.999862i \(0.505297\pi\)
\(702\) −8.04883 −0.303784
\(703\) 4.09678 0.154513
\(704\) 0.483333 0.0182163
\(705\) 16.1887 0.609702
\(706\) 1.61861 0.0609172
\(707\) 83.7026 3.14796
\(708\) −8.64179 −0.324779
\(709\) 35.1686 1.32078 0.660391 0.750922i \(-0.270390\pi\)
0.660391 + 0.750922i \(0.270390\pi\)
\(710\) −0.0505911 −0.00189865
\(711\) 15.8765 0.595415
\(712\) 13.1060 0.491169
\(713\) 12.0407 0.450929
\(714\) −69.7220 −2.60928
\(715\) −9.47024 −0.354167
\(716\) 16.1982 0.605355
\(717\) 0.600216 0.0224155
\(718\) 20.7395 0.773991
\(719\) −23.4978 −0.876320 −0.438160 0.898897i \(-0.644370\pi\)
−0.438160 + 0.898897i \(0.644370\pi\)
\(720\) 12.9744 0.483527
\(721\) 5.58848 0.208126
\(722\) −1.00000 −0.0372161
\(723\) −24.2513 −0.901914
\(724\) −14.9491 −0.555578
\(725\) 60.1547 2.23409
\(726\) −27.6181 −1.02500
\(727\) 31.7852 1.17885 0.589423 0.807824i \(-0.299355\pi\)
0.589423 + 0.807824i \(0.299355\pi\)
\(728\) 26.0327 0.964837
\(729\) −36.2399 −1.34222
\(730\) −30.9053 −1.14386
\(731\) 53.7035 1.98630
\(732\) −0.614154 −0.0226998
\(733\) 47.8357 1.76685 0.883425 0.468572i \(-0.155231\pi\)
0.883425 + 0.468572i \(0.155231\pi\)
\(734\) 7.59985 0.280516
\(735\) −150.422 −5.54839
\(736\) 3.29287 0.121377
\(737\) −1.42633 −0.0525394
\(738\) −11.6489 −0.428801
\(739\) −51.1768 −1.88257 −0.941284 0.337615i \(-0.890380\pi\)
−0.941284 + 0.337615i \(0.890380\pi\)
\(740\) −14.8460 −0.545750
\(741\) −13.8698 −0.509521
\(742\) 50.9573 1.87070
\(743\) −16.8041 −0.616484 −0.308242 0.951308i \(-0.599741\pi\)
−0.308242 + 0.951308i \(0.599741\pi\)
\(744\) −9.37996 −0.343886
\(745\) −47.0795 −1.72486
\(746\) −24.5031 −0.897123
\(747\) −13.0091 −0.475980
\(748\) −2.72848 −0.0997632
\(749\) −9.57366 −0.349814
\(750\) 29.1152 1.06314
\(751\) −23.7296 −0.865905 −0.432953 0.901417i \(-0.642528\pi\)
−0.432953 + 0.901417i \(0.642528\pi\)
\(752\) −1.74149 −0.0635058
\(753\) 36.4054 1.32669
\(754\) 39.9961 1.45657
\(755\) −67.4775 −2.45576
\(756\) −7.16731 −0.260673
\(757\) −5.90532 −0.214632 −0.107316 0.994225i \(-0.534226\pi\)
−0.107316 + 0.994225i \(0.534226\pi\)
\(758\) 8.53571 0.310031
\(759\) 4.08267 0.148192
\(760\) 3.62382 0.131450
\(761\) 47.0067 1.70399 0.851997 0.523547i \(-0.175392\pi\)
0.851997 + 0.523547i \(0.175392\pi\)
\(762\) −1.20933 −0.0438093
\(763\) 29.5360 1.06927
\(764\) 16.5906 0.600226
\(765\) −73.2424 −2.64808
\(766\) 11.7009 0.422771
\(767\) −18.2150 −0.657705
\(768\) −2.56521 −0.0925641
\(769\) −23.1141 −0.833517 −0.416758 0.909017i \(-0.636834\pi\)
−0.416758 + 0.909017i \(0.636834\pi\)
\(770\) −8.43304 −0.303906
\(771\) −66.1044 −2.38069
\(772\) −19.7455 −0.710656
\(773\) 24.5982 0.884734 0.442367 0.896834i \(-0.354139\pi\)
0.442367 + 0.896834i \(0.354139\pi\)
\(774\) 34.0603 1.22427
\(775\) −29.7357 −1.06814
\(776\) 7.06235 0.253523
\(777\) 50.5985 1.81521
\(778\) −24.3028 −0.871298
\(779\) −3.25360 −0.116572
\(780\) 50.2618 1.79966
\(781\) 0.00674767 0.000241451 0
\(782\) −18.5887 −0.664732
\(783\) −11.0117 −0.393526
\(784\) 16.1816 0.577913
\(785\) 17.4662 0.623394
\(786\) −48.7864 −1.74015
\(787\) −13.4320 −0.478799 −0.239400 0.970921i \(-0.576951\pi\)
−0.239400 + 0.970921i \(0.576951\pi\)
\(788\) 18.8208 0.670465
\(789\) 67.5252 2.40396
\(790\) −16.0694 −0.571724
\(791\) −68.4293 −2.43307
\(792\) −1.73048 −0.0614900
\(793\) −1.29450 −0.0459691
\(794\) 27.2367 0.966595
\(795\) 98.3841 3.48932
\(796\) −11.5459 −0.409232
\(797\) 22.9776 0.813908 0.406954 0.913449i \(-0.366591\pi\)
0.406954 + 0.913449i \(0.366591\pi\)
\(798\) −12.3508 −0.437213
\(799\) 9.83099 0.347796
\(800\) −8.13206 −0.287512
\(801\) −46.9237 −1.65797
\(802\) 18.5289 0.654277
\(803\) 4.12204 0.145464
\(804\) 7.57000 0.266973
\(805\) −57.4530 −2.02495
\(806\) −19.7709 −0.696400
\(807\) −63.1382 −2.22257
\(808\) −17.3847 −0.611592
\(809\) −39.7478 −1.39746 −0.698729 0.715386i \(-0.746251\pi\)
−0.698729 + 0.715386i \(0.746251\pi\)
\(810\) 25.0852 0.881403
\(811\) 21.6945 0.761797 0.380898 0.924617i \(-0.375615\pi\)
0.380898 + 0.924617i \(0.375615\pi\)
\(812\) 35.6156 1.24986
\(813\) 38.1267 1.33716
\(814\) 1.98011 0.0694028
\(815\) 38.1776 1.33730
\(816\) 14.4810 0.506936
\(817\) 9.51322 0.332825
\(818\) 14.8965 0.520844
\(819\) −93.2053 −3.25686
\(820\) 11.7904 0.411740
\(821\) 0.906308 0.0316304 0.0158152 0.999875i \(-0.494966\pi\)
0.0158152 + 0.999875i \(0.494966\pi\)
\(822\) −8.70806 −0.303729
\(823\) −33.4016 −1.16431 −0.582154 0.813079i \(-0.697790\pi\)
−0.582154 + 0.813079i \(0.697790\pi\)
\(824\) −1.16071 −0.0404351
\(825\) −10.0825 −0.351029
\(826\) −16.2201 −0.564368
\(827\) −48.4821 −1.68589 −0.842944 0.538002i \(-0.819179\pi\)
−0.842944 + 0.538002i \(0.819179\pi\)
\(828\) −11.7895 −0.409714
\(829\) 21.1802 0.735619 0.367810 0.929901i \(-0.380108\pi\)
0.367810 + 0.929901i \(0.380108\pi\)
\(830\) 13.1672 0.457041
\(831\) −9.20806 −0.319424
\(832\) −5.40690 −0.187451
\(833\) −91.3474 −3.16500
\(834\) 12.6413 0.437733
\(835\) −34.3277 −1.18796
\(836\) −0.483333 −0.0167164
\(837\) 5.44330 0.188148
\(838\) −0.854101 −0.0295044
\(839\) 55.3200 1.90986 0.954930 0.296831i \(-0.0959299\pi\)
0.954930 + 0.296831i \(0.0959299\pi\)
\(840\) 44.7570 1.54426
\(841\) 25.7190 0.886863
\(842\) 17.8339 0.614597
\(843\) −67.8776 −2.33783
\(844\) −1.00000 −0.0344214
\(845\) 58.8311 2.02385
\(846\) 6.23509 0.214367
\(847\) −51.8372 −1.78115
\(848\) −10.5836 −0.363444
\(849\) −37.5409 −1.28840
\(850\) 45.9067 1.57459
\(851\) 13.4902 0.462438
\(852\) −0.0358122 −0.00122691
\(853\) 46.8225 1.60317 0.801585 0.597880i \(-0.203990\pi\)
0.801585 + 0.597880i \(0.203990\pi\)
\(854\) −1.15272 −0.0394454
\(855\) −12.9744 −0.443715
\(856\) 1.98841 0.0679625
\(857\) −3.25186 −0.111082 −0.0555408 0.998456i \(-0.517688\pi\)
−0.0555408 + 0.998456i \(0.517688\pi\)
\(858\) −6.70375 −0.228862
\(859\) −14.1103 −0.481438 −0.240719 0.970595i \(-0.577383\pi\)
−0.240719 + 0.970595i \(0.577383\pi\)
\(860\) −34.4742 −1.17556
\(861\) −40.1845 −1.36948
\(862\) 28.9693 0.986698
\(863\) 2.88423 0.0981804 0.0490902 0.998794i \(-0.484368\pi\)
0.0490902 + 0.998794i \(0.484368\pi\)
\(864\) 1.48862 0.0506440
\(865\) −63.8054 −2.16945
\(866\) −24.0138 −0.816022
\(867\) −38.1388 −1.29526
\(868\) −17.6055 −0.597571
\(869\) 2.14328 0.0727059
\(870\) 68.7636 2.33131
\(871\) 15.9559 0.540644
\(872\) −6.13451 −0.207741
\(873\) −25.2854 −0.855781
\(874\) −3.29287 −0.111383
\(875\) 54.6473 1.84741
\(876\) −21.8771 −0.739158
\(877\) 52.5613 1.77487 0.887435 0.460933i \(-0.152485\pi\)
0.887435 + 0.460933i \(0.152485\pi\)
\(878\) −13.1530 −0.443892
\(879\) −50.5748 −1.70585
\(880\) 1.75151 0.0590434
\(881\) −2.76352 −0.0931054 −0.0465527 0.998916i \(-0.514824\pi\)
−0.0465527 + 0.998916i \(0.514824\pi\)
\(882\) −57.9351 −1.95078
\(883\) −18.1987 −0.612434 −0.306217 0.951962i \(-0.599063\pi\)
−0.306217 + 0.951962i \(0.599063\pi\)
\(884\) 30.5227 1.02659
\(885\) −31.3163 −1.05269
\(886\) 8.78113 0.295008
\(887\) −31.3928 −1.05407 −0.527034 0.849844i \(-0.676696\pi\)
−0.527034 + 0.849844i \(0.676696\pi\)
\(888\) −10.5091 −0.352663
\(889\) −2.26982 −0.0761273
\(890\) 47.4939 1.59200
\(891\) −3.34577 −0.112088
\(892\) −23.0712 −0.772479
\(893\) 1.74149 0.0582769
\(894\) −33.3264 −1.11460
\(895\) 58.6993 1.96210
\(896\) −4.81473 −0.160849
\(897\) −45.6716 −1.52493
\(898\) −17.6450 −0.588821
\(899\) −27.0487 −0.902126
\(900\) 29.1153 0.970511
\(901\) 59.7462 1.99043
\(902\) −1.57257 −0.0523608
\(903\) 117.496 3.91001
\(904\) 14.2125 0.472701
\(905\) −54.1727 −1.80076
\(906\) −47.7656 −1.58691
\(907\) −0.694013 −0.0230443 −0.0115222 0.999934i \(-0.503668\pi\)
−0.0115222 + 0.999934i \(0.503668\pi\)
\(908\) 16.5721 0.549963
\(909\) 62.2427 2.06446
\(910\) 94.3379 3.12727
\(911\) 49.4228 1.63745 0.818726 0.574185i \(-0.194681\pi\)
0.818726 + 0.574185i \(0.194681\pi\)
\(912\) 2.56521 0.0849427
\(913\) −1.75620 −0.0581217
\(914\) 21.8845 0.723874
\(915\) −2.22558 −0.0735755
\(916\) 3.42397 0.113131
\(917\) −91.5687 −3.02386
\(918\) −8.40350 −0.277357
\(919\) −35.4504 −1.16940 −0.584700 0.811249i \(-0.698788\pi\)
−0.584700 + 0.811249i \(0.698788\pi\)
\(920\) 11.9328 0.393412
\(921\) 77.0384 2.53850
\(922\) 4.83115 0.159105
\(923\) −0.0754842 −0.00248459
\(924\) −5.96954 −0.196383
\(925\) −33.3153 −1.09540
\(926\) −5.95116 −0.195567
\(927\) 4.15569 0.136491
\(928\) −7.39723 −0.242826
\(929\) −42.7113 −1.40131 −0.700657 0.713498i \(-0.747110\pi\)
−0.700657 + 0.713498i \(0.747110\pi\)
\(930\) −33.9913 −1.11462
\(931\) −16.1816 −0.530330
\(932\) 5.79695 0.189885
\(933\) 84.9541 2.78127
\(934\) 0.943463 0.0308710
\(935\) −9.88753 −0.323357
\(936\) 19.3584 0.632749
\(937\) −37.5728 −1.22745 −0.613725 0.789520i \(-0.710330\pi\)
−0.613725 + 0.789520i \(0.710330\pi\)
\(938\) 14.2084 0.463919
\(939\) −1.82006 −0.0593955
\(940\) −6.31086 −0.205838
\(941\) −49.3760 −1.60961 −0.804805 0.593539i \(-0.797730\pi\)
−0.804805 + 0.593539i \(0.797730\pi\)
\(942\) 12.3639 0.402836
\(943\) −10.7137 −0.348885
\(944\) 3.36884 0.109646
\(945\) −25.9730 −0.844903
\(946\) 4.59805 0.149495
\(947\) 20.2355 0.657566 0.328783 0.944405i \(-0.393361\pi\)
0.328783 + 0.944405i \(0.393361\pi\)
\(948\) −11.3751 −0.369447
\(949\) −46.1121 −1.49686
\(950\) 8.13206 0.263839
\(951\) −6.11760 −0.198377
\(952\) 27.1798 0.880903
\(953\) 37.6841 1.22071 0.610355 0.792128i \(-0.291027\pi\)
0.610355 + 0.792128i \(0.291027\pi\)
\(954\) 37.8927 1.22682
\(955\) 60.1212 1.94548
\(956\) −0.233983 −0.00756755
\(957\) −9.17146 −0.296471
\(958\) 28.7216 0.927953
\(959\) −16.3444 −0.527789
\(960\) −9.29586 −0.300023
\(961\) −17.6292 −0.568685
\(962\) −22.1509 −0.714174
\(963\) −7.11914 −0.229411
\(964\) 9.45390 0.304490
\(965\) −71.5541 −2.30341
\(966\) −40.6696 −1.30852
\(967\) 25.1088 0.807445 0.403722 0.914882i \(-0.367716\pi\)
0.403722 + 0.914882i \(0.367716\pi\)
\(968\) 10.7664 0.346045
\(969\) −14.4810 −0.465197
\(970\) 25.5927 0.821731
\(971\) 9.66498 0.310164 0.155082 0.987902i \(-0.450436\pi\)
0.155082 + 0.987902i \(0.450436\pi\)
\(972\) 22.2230 0.712804
\(973\) 23.7269 0.760648
\(974\) −21.1829 −0.678745
\(975\) 112.790 3.61218
\(976\) 0.239416 0.00766353
\(977\) 41.3547 1.32305 0.661527 0.749921i \(-0.269909\pi\)
0.661527 + 0.749921i \(0.269909\pi\)
\(978\) 27.0250 0.864164
\(979\) −6.33457 −0.202454
\(980\) 58.6391 1.87316
\(981\) 21.9635 0.701240
\(982\) 8.36445 0.266920
\(983\) 36.1878 1.15421 0.577105 0.816670i \(-0.304182\pi\)
0.577105 + 0.816670i \(0.304182\pi\)
\(984\) 8.34616 0.266066
\(985\) 68.2033 2.17314
\(986\) 41.7585 1.32986
\(987\) 21.5088 0.684634
\(988\) 5.40690 0.172016
\(989\) 31.3258 0.996103
\(990\) −6.27095 −0.199304
\(991\) −50.1090 −1.59176 −0.795882 0.605452i \(-0.792992\pi\)
−0.795882 + 0.605452i \(0.792992\pi\)
\(992\) 3.65660 0.116097
\(993\) 75.8280 2.40633
\(994\) −0.0672170 −0.00213199
\(995\) −41.8401 −1.32642
\(996\) 9.32075 0.295339
\(997\) −46.9996 −1.48849 −0.744247 0.667905i \(-0.767191\pi\)
−0.744247 + 0.667905i \(0.767191\pi\)
\(998\) −23.5808 −0.746436
\(999\) 6.09857 0.192950
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 \(a_p\))