Properties

Label 8018.2.a.f.1.11
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 1.11
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.91986 q^{3}\) \(+1.00000 q^{4}\) \(+0.472260 q^{5}\) \(+1.91986 q^{6}\) \(+4.62137 q^{7}\) \(-1.00000 q^{8}\) \(+0.685870 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.91986 q^{3}\) \(+1.00000 q^{4}\) \(+0.472260 q^{5}\) \(+1.91986 q^{6}\) \(+4.62137 q^{7}\) \(-1.00000 q^{8}\) \(+0.685870 q^{9}\) \(-0.472260 q^{10}\) \(-0.111615 q^{11}\) \(-1.91986 q^{12}\) \(+0.272381 q^{13}\) \(-4.62137 q^{14}\) \(-0.906673 q^{15}\) \(+1.00000 q^{16}\) \(+2.02660 q^{17}\) \(-0.685870 q^{18}\) \(-1.00000 q^{19}\) \(+0.472260 q^{20}\) \(-8.87239 q^{21}\) \(+0.111615 q^{22}\) \(+5.62701 q^{23}\) \(+1.91986 q^{24}\) \(-4.77697 q^{25}\) \(-0.272381 q^{26}\) \(+4.44281 q^{27}\) \(+4.62137 q^{28}\) \(-4.88771 q^{29}\) \(+0.906673 q^{30}\) \(-8.39165 q^{31}\) \(-1.00000 q^{32}\) \(+0.214285 q^{33}\) \(-2.02660 q^{34}\) \(+2.18249 q^{35}\) \(+0.685870 q^{36}\) \(+7.54400 q^{37}\) \(+1.00000 q^{38}\) \(-0.522934 q^{39}\) \(-0.472260 q^{40}\) \(-5.51603 q^{41}\) \(+8.87239 q^{42}\) \(+0.252608 q^{43}\) \(-0.111615 q^{44}\) \(+0.323909 q^{45}\) \(-5.62701 q^{46}\) \(+3.79423 q^{47}\) \(-1.91986 q^{48}\) \(+14.3571 q^{49}\) \(+4.77697 q^{50}\) \(-3.89079 q^{51}\) \(+0.272381 q^{52}\) \(-2.47409 q^{53}\) \(-4.44281 q^{54}\) \(-0.0527112 q^{55}\) \(-4.62137 q^{56}\) \(+1.91986 q^{57}\) \(+4.88771 q^{58}\) \(-10.5518 q^{59}\) \(-0.906673 q^{60}\) \(-7.76848 q^{61}\) \(+8.39165 q^{62}\) \(+3.16966 q^{63}\) \(+1.00000 q^{64}\) \(+0.128634 q^{65}\) \(-0.214285 q^{66}\) \(-13.7548 q^{67}\) \(+2.02660 q^{68}\) \(-10.8031 q^{69}\) \(-2.18249 q^{70}\) \(+7.29402 q^{71}\) \(-0.685870 q^{72}\) \(-9.98277 q^{73}\) \(-7.54400 q^{74}\) \(+9.17112 q^{75}\) \(-1.00000 q^{76}\) \(-0.515814 q^{77}\) \(+0.522934 q^{78}\) \(-8.19692 q^{79}\) \(+0.472260 q^{80}\) \(-10.5872 q^{81}\) \(+5.51603 q^{82}\) \(+4.34992 q^{83}\) \(-8.87239 q^{84}\) \(+0.957080 q^{85}\) \(-0.252608 q^{86}\) \(+9.38373 q^{87}\) \(+0.111615 q^{88}\) \(+1.85112 q^{89}\) \(-0.323909 q^{90}\) \(+1.25877 q^{91}\) \(+5.62701 q^{92}\) \(+16.1108 q^{93}\) \(-3.79423 q^{94}\) \(-0.472260 q^{95}\) \(+1.91986 q^{96}\) \(-4.37494 q^{97}\) \(-14.3571 q^{98}\) \(-0.0765533 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.91986 −1.10843 −0.554216 0.832373i \(-0.686982\pi\)
−0.554216 + 0.832373i \(0.686982\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.472260 0.211201 0.105600 0.994409i \(-0.466324\pi\)
0.105600 + 0.994409i \(0.466324\pi\)
\(6\) 1.91986 0.783780
\(7\) 4.62137 1.74671 0.873357 0.487081i \(-0.161938\pi\)
0.873357 + 0.487081i \(0.161938\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.685870 0.228623
\(10\) −0.472260 −0.149342
\(11\) −0.111615 −0.0336531 −0.0168266 0.999858i \(-0.505356\pi\)
−0.0168266 + 0.999858i \(0.505356\pi\)
\(12\) −1.91986 −0.554216
\(13\) 0.272381 0.0755449 0.0377724 0.999286i \(-0.487974\pi\)
0.0377724 + 0.999286i \(0.487974\pi\)
\(14\) −4.62137 −1.23511
\(15\) −0.906673 −0.234102
\(16\) 1.00000 0.250000
\(17\) 2.02660 0.491522 0.245761 0.969330i \(-0.420962\pi\)
0.245761 + 0.969330i \(0.420962\pi\)
\(18\) −0.685870 −0.161661
\(19\) −1.00000 −0.229416
\(20\) 0.472260 0.105600
\(21\) −8.87239 −1.93612
\(22\) 0.111615 0.0237964
\(23\) 5.62701 1.17331 0.586657 0.809836i \(-0.300444\pi\)
0.586657 + 0.809836i \(0.300444\pi\)
\(24\) 1.91986 0.391890
\(25\) −4.77697 −0.955394
\(26\) −0.272381 −0.0534183
\(27\) 4.44281 0.855019
\(28\) 4.62137 0.873357
\(29\) −4.88771 −0.907625 −0.453812 0.891097i \(-0.649936\pi\)
−0.453812 + 0.891097i \(0.649936\pi\)
\(30\) 0.906673 0.165535
\(31\) −8.39165 −1.50719 −0.753593 0.657342i \(-0.771681\pi\)
−0.753593 + 0.657342i \(0.771681\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.214285 0.0373022
\(34\) −2.02660 −0.347559
\(35\) 2.18249 0.368908
\(36\) 0.685870 0.114312
\(37\) 7.54400 1.24023 0.620113 0.784513i \(-0.287087\pi\)
0.620113 + 0.784513i \(0.287087\pi\)
\(38\) 1.00000 0.162221
\(39\) −0.522934 −0.0837364
\(40\) −0.472260 −0.0746708
\(41\) −5.51603 −0.861460 −0.430730 0.902481i \(-0.641744\pi\)
−0.430730 + 0.902481i \(0.641744\pi\)
\(42\) 8.87239 1.36904
\(43\) 0.252608 0.0385224 0.0192612 0.999814i \(-0.493869\pi\)
0.0192612 + 0.999814i \(0.493869\pi\)
\(44\) −0.111615 −0.0168266
\(45\) 0.323909 0.0482855
\(46\) −5.62701 −0.829658
\(47\) 3.79423 0.553445 0.276722 0.960950i \(-0.410752\pi\)
0.276722 + 0.960950i \(0.410752\pi\)
\(48\) −1.91986 −0.277108
\(49\) 14.3571 2.05101
\(50\) 4.77697 0.675566
\(51\) −3.89079 −0.544819
\(52\) 0.272381 0.0377724
\(53\) −2.47409 −0.339842 −0.169921 0.985458i \(-0.554351\pi\)
−0.169921 + 0.985458i \(0.554351\pi\)
\(54\) −4.44281 −0.604590
\(55\) −0.0527112 −0.00710757
\(56\) −4.62137 −0.617557
\(57\) 1.91986 0.254292
\(58\) 4.88771 0.641788
\(59\) −10.5518 −1.37373 −0.686865 0.726785i \(-0.741014\pi\)
−0.686865 + 0.726785i \(0.741014\pi\)
\(60\) −0.906673 −0.117051
\(61\) −7.76848 −0.994652 −0.497326 0.867564i \(-0.665685\pi\)
−0.497326 + 0.867564i \(0.665685\pi\)
\(62\) 8.39165 1.06574
\(63\) 3.16966 0.399340
\(64\) 1.00000 0.125000
\(65\) 0.128634 0.0159551
\(66\) −0.214285 −0.0263767
\(67\) −13.7548 −1.68042 −0.840209 0.542263i \(-0.817567\pi\)
−0.840209 + 0.542263i \(0.817567\pi\)
\(68\) 2.02660 0.245761
\(69\) −10.8031 −1.30054
\(70\) −2.18249 −0.260857
\(71\) 7.29402 0.865641 0.432820 0.901480i \(-0.357518\pi\)
0.432820 + 0.901480i \(0.357518\pi\)
\(72\) −0.685870 −0.0808306
\(73\) −9.98277 −1.16839 −0.584197 0.811612i \(-0.698591\pi\)
−0.584197 + 0.811612i \(0.698591\pi\)
\(74\) −7.54400 −0.876972
\(75\) 9.17112 1.05899
\(76\) −1.00000 −0.114708
\(77\) −0.515814 −0.0587824
\(78\) 0.522934 0.0592106
\(79\) −8.19692 −0.922225 −0.461113 0.887342i \(-0.652550\pi\)
−0.461113 + 0.887342i \(0.652550\pi\)
\(80\) 0.472260 0.0528002
\(81\) −10.5872 −1.17635
\(82\) 5.51603 0.609144
\(83\) 4.34992 0.477465 0.238733 0.971085i \(-0.423268\pi\)
0.238733 + 0.971085i \(0.423268\pi\)
\(84\) −8.87239 −0.968058
\(85\) 0.957080 0.103810
\(86\) −0.252608 −0.0272394
\(87\) 9.38373 1.00604
\(88\) 0.111615 0.0118982
\(89\) 1.85112 0.196219 0.0981093 0.995176i \(-0.468721\pi\)
0.0981093 + 0.995176i \(0.468721\pi\)
\(90\) −0.323909 −0.0341430
\(91\) 1.25877 0.131955
\(92\) 5.62701 0.586657
\(93\) 16.1108 1.67061
\(94\) −3.79423 −0.391345
\(95\) −0.472260 −0.0484528
\(96\) 1.91986 0.195945
\(97\) −4.37494 −0.444208 −0.222104 0.975023i \(-0.571292\pi\)
−0.222104 + 0.975023i \(0.571292\pi\)
\(98\) −14.3571 −1.45028
\(99\) −0.0765533 −0.00769389
\(100\) −4.77697 −0.477697
\(101\) −9.21439 −0.916866 −0.458433 0.888729i \(-0.651589\pi\)
−0.458433 + 0.888729i \(0.651589\pi\)
\(102\) 3.89079 0.385245
\(103\) −4.24953 −0.418719 −0.209360 0.977839i \(-0.567138\pi\)
−0.209360 + 0.977839i \(0.567138\pi\)
\(104\) −0.272381 −0.0267091
\(105\) −4.19007 −0.408909
\(106\) 2.47409 0.240305
\(107\) 4.84308 0.468198 0.234099 0.972213i \(-0.424786\pi\)
0.234099 + 0.972213i \(0.424786\pi\)
\(108\) 4.44281 0.427510
\(109\) −8.35783 −0.800535 −0.400268 0.916398i \(-0.631083\pi\)
−0.400268 + 0.916398i \(0.631083\pi\)
\(110\) 0.0527112 0.00502581
\(111\) −14.4834 −1.37471
\(112\) 4.62137 0.436678
\(113\) −1.90512 −0.179219 −0.0896095 0.995977i \(-0.528562\pi\)
−0.0896095 + 0.995977i \(0.528562\pi\)
\(114\) −1.91986 −0.179812
\(115\) 2.65741 0.247805
\(116\) −4.88771 −0.453812
\(117\) 0.186818 0.0172713
\(118\) 10.5518 0.971374
\(119\) 9.36566 0.858548
\(120\) 0.906673 0.0827676
\(121\) −10.9875 −0.998867
\(122\) 7.76848 0.703325
\(123\) 10.5900 0.954870
\(124\) −8.39165 −0.753593
\(125\) −4.61727 −0.412981
\(126\) −3.16966 −0.282376
\(127\) −13.6337 −1.20980 −0.604899 0.796302i \(-0.706787\pi\)
−0.604899 + 0.796302i \(0.706787\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.484973 −0.0426995
\(130\) −0.128634 −0.0112820
\(131\) −9.39429 −0.820783 −0.410391 0.911909i \(-0.634608\pi\)
−0.410391 + 0.911909i \(0.634608\pi\)
\(132\) 0.214285 0.0186511
\(133\) −4.62137 −0.400724
\(134\) 13.7548 1.18823
\(135\) 2.09816 0.180581
\(136\) −2.02660 −0.173779
\(137\) −16.8861 −1.44268 −0.721339 0.692582i \(-0.756473\pi\)
−0.721339 + 0.692582i \(0.756473\pi\)
\(138\) 10.8031 0.919620
\(139\) 16.6058 1.40849 0.704243 0.709959i \(-0.251286\pi\)
0.704243 + 0.709959i \(0.251286\pi\)
\(140\) 2.18249 0.184454
\(141\) −7.28439 −0.613456
\(142\) −7.29402 −0.612100
\(143\) −0.0304018 −0.00254232
\(144\) 0.685870 0.0571558
\(145\) −2.30827 −0.191691
\(146\) 9.98277 0.826180
\(147\) −27.5636 −2.27341
\(148\) 7.54400 0.620113
\(149\) 2.75899 0.226026 0.113013 0.993594i \(-0.463950\pi\)
0.113013 + 0.993594i \(0.463950\pi\)
\(150\) −9.17112 −0.748819
\(151\) −16.5692 −1.34838 −0.674192 0.738556i \(-0.735508\pi\)
−0.674192 + 0.738556i \(0.735508\pi\)
\(152\) 1.00000 0.0811107
\(153\) 1.38998 0.112373
\(154\) 0.515814 0.0415654
\(155\) −3.96304 −0.318319
\(156\) −0.522934 −0.0418682
\(157\) 22.1872 1.77073 0.885367 0.464893i \(-0.153907\pi\)
0.885367 + 0.464893i \(0.153907\pi\)
\(158\) 8.19692 0.652112
\(159\) 4.74991 0.376692
\(160\) −0.472260 −0.0373354
\(161\) 26.0045 2.04944
\(162\) 10.5872 0.831808
\(163\) 18.7445 1.46818 0.734090 0.679052i \(-0.237609\pi\)
0.734090 + 0.679052i \(0.237609\pi\)
\(164\) −5.51603 −0.430730
\(165\) 0.101198 0.00787827
\(166\) −4.34992 −0.337619
\(167\) 11.2702 0.872115 0.436057 0.899919i \(-0.356375\pi\)
0.436057 + 0.899919i \(0.356375\pi\)
\(168\) 8.87239 0.684520
\(169\) −12.9258 −0.994293
\(170\) −0.957080 −0.0734047
\(171\) −0.685870 −0.0524498
\(172\) 0.252608 0.0192612
\(173\) 16.3680 1.24444 0.622218 0.782844i \(-0.286232\pi\)
0.622218 + 0.782844i \(0.286232\pi\)
\(174\) −9.38373 −0.711378
\(175\) −22.0762 −1.66880
\(176\) −0.111615 −0.00841329
\(177\) 20.2580 1.52269
\(178\) −1.85112 −0.138747
\(179\) 6.99012 0.522466 0.261233 0.965276i \(-0.415871\pi\)
0.261233 + 0.965276i \(0.415871\pi\)
\(180\) 0.323909 0.0241427
\(181\) 10.2038 0.758439 0.379219 0.925307i \(-0.376193\pi\)
0.379219 + 0.925307i \(0.376193\pi\)
\(182\) −1.25877 −0.0933065
\(183\) 14.9144 1.10251
\(184\) −5.62701 −0.414829
\(185\) 3.56272 0.261937
\(186\) −16.1108 −1.18130
\(187\) −0.226198 −0.0165413
\(188\) 3.79423 0.276722
\(189\) 20.5319 1.49347
\(190\) 0.472260 0.0342613
\(191\) −11.5053 −0.832494 −0.416247 0.909252i \(-0.636655\pi\)
−0.416247 + 0.909252i \(0.636655\pi\)
\(192\) −1.91986 −0.138554
\(193\) 6.94976 0.500254 0.250127 0.968213i \(-0.419528\pi\)
0.250127 + 0.968213i \(0.419528\pi\)
\(194\) 4.37494 0.314102
\(195\) −0.246960 −0.0176852
\(196\) 14.3571 1.02550
\(197\) −0.472969 −0.0336977 −0.0168488 0.999858i \(-0.505363\pi\)
−0.0168488 + 0.999858i \(0.505363\pi\)
\(198\) 0.0765533 0.00544041
\(199\) −2.12016 −0.150294 −0.0751472 0.997172i \(-0.523943\pi\)
−0.0751472 + 0.997172i \(0.523943\pi\)
\(200\) 4.77697 0.337783
\(201\) 26.4073 1.86263
\(202\) 9.21439 0.648322
\(203\) −22.5879 −1.58536
\(204\) −3.89079 −0.272410
\(205\) −2.60500 −0.181941
\(206\) 4.24953 0.296079
\(207\) 3.85940 0.268247
\(208\) 0.272381 0.0188862
\(209\) 0.111615 0.00772056
\(210\) 4.19007 0.289142
\(211\) −1.00000 −0.0688428
\(212\) −2.47409 −0.169921
\(213\) −14.0035 −0.959505
\(214\) −4.84308 −0.331066
\(215\) 0.119297 0.00813596
\(216\) −4.44281 −0.302295
\(217\) −38.7809 −2.63262
\(218\) 8.35783 0.566064
\(219\) 19.1655 1.29509
\(220\) −0.0527112 −0.00355379
\(221\) 0.552006 0.0371320
\(222\) 14.4834 0.972064
\(223\) 23.2965 1.56005 0.780025 0.625748i \(-0.215206\pi\)
0.780025 + 0.625748i \(0.215206\pi\)
\(224\) −4.62137 −0.308778
\(225\) −3.27638 −0.218425
\(226\) 1.90512 0.126727
\(227\) −11.2543 −0.746972 −0.373486 0.927636i \(-0.621838\pi\)
−0.373486 + 0.927636i \(0.621838\pi\)
\(228\) 1.91986 0.127146
\(229\) −18.2204 −1.20404 −0.602018 0.798483i \(-0.705636\pi\)
−0.602018 + 0.798483i \(0.705636\pi\)
\(230\) −2.65741 −0.175224
\(231\) 0.990291 0.0651564
\(232\) 4.88771 0.320894
\(233\) 20.8797 1.36788 0.683938 0.729540i \(-0.260266\pi\)
0.683938 + 0.729540i \(0.260266\pi\)
\(234\) −0.186818 −0.0122127
\(235\) 1.79186 0.116888
\(236\) −10.5518 −0.686865
\(237\) 15.7370 1.02222
\(238\) −9.36566 −0.607085
\(239\) −6.35982 −0.411383 −0.205691 0.978617i \(-0.565944\pi\)
−0.205691 + 0.978617i \(0.565944\pi\)
\(240\) −0.906673 −0.0585255
\(241\) −27.5421 −1.77414 −0.887072 0.461631i \(-0.847265\pi\)
−0.887072 + 0.461631i \(0.847265\pi\)
\(242\) 10.9875 0.706306
\(243\) 6.99752 0.448891
\(244\) −7.76848 −0.497326
\(245\) 6.78026 0.433175
\(246\) −10.5900 −0.675195
\(247\) −0.272381 −0.0173312
\(248\) 8.39165 0.532870
\(249\) −8.35124 −0.529238
\(250\) 4.61727 0.292022
\(251\) 25.8059 1.62886 0.814428 0.580265i \(-0.197051\pi\)
0.814428 + 0.580265i \(0.197051\pi\)
\(252\) 3.16966 0.199670
\(253\) −0.628058 −0.0394857
\(254\) 13.6337 0.855457
\(255\) −1.83746 −0.115066
\(256\) 1.00000 0.0625000
\(257\) −27.3503 −1.70606 −0.853032 0.521859i \(-0.825239\pi\)
−0.853032 + 0.521859i \(0.825239\pi\)
\(258\) 0.484973 0.0301931
\(259\) 34.8636 2.16632
\(260\) 0.128634 0.00797757
\(261\) −3.35233 −0.207504
\(262\) 9.39429 0.580381
\(263\) −20.0329 −1.23528 −0.617642 0.786459i \(-0.711912\pi\)
−0.617642 + 0.786459i \(0.711912\pi\)
\(264\) −0.214285 −0.0131883
\(265\) −1.16841 −0.0717750
\(266\) 4.62137 0.283354
\(267\) −3.55390 −0.217495
\(268\) −13.7548 −0.840209
\(269\) −17.9291 −1.09316 −0.546579 0.837408i \(-0.684070\pi\)
−0.546579 + 0.837408i \(0.684070\pi\)
\(270\) −2.09816 −0.127690
\(271\) −29.8009 −1.81028 −0.905139 0.425116i \(-0.860233\pi\)
−0.905139 + 0.425116i \(0.860233\pi\)
\(272\) 2.02660 0.122880
\(273\) −2.41667 −0.146264
\(274\) 16.8861 1.02013
\(275\) 0.533181 0.0321520
\(276\) −10.8031 −0.650269
\(277\) 30.3358 1.82270 0.911351 0.411631i \(-0.135041\pi\)
0.911351 + 0.411631i \(0.135041\pi\)
\(278\) −16.6058 −0.995950
\(279\) −5.75558 −0.344578
\(280\) −2.18249 −0.130429
\(281\) 8.78673 0.524173 0.262086 0.965044i \(-0.415589\pi\)
0.262086 + 0.965044i \(0.415589\pi\)
\(282\) 7.28439 0.433779
\(283\) −1.62138 −0.0963808 −0.0481904 0.998838i \(-0.515345\pi\)
−0.0481904 + 0.998838i \(0.515345\pi\)
\(284\) 7.29402 0.432820
\(285\) 0.906673 0.0537067
\(286\) 0.0304018 0.00179769
\(287\) −25.4916 −1.50472
\(288\) −0.685870 −0.0404153
\(289\) −12.8929 −0.758406
\(290\) 2.30827 0.135546
\(291\) 8.39928 0.492375
\(292\) −9.98277 −0.584197
\(293\) 32.3187 1.88808 0.944041 0.329829i \(-0.106991\pi\)
0.944041 + 0.329829i \(0.106991\pi\)
\(294\) 27.5636 1.60754
\(295\) −4.98320 −0.290133
\(296\) −7.54400 −0.438486
\(297\) −0.495884 −0.0287741
\(298\) −2.75899 −0.159824
\(299\) 1.53269 0.0886378
\(300\) 9.17112 0.529495
\(301\) 1.16740 0.0672876
\(302\) 16.5692 0.953452
\(303\) 17.6904 1.01628
\(304\) −1.00000 −0.0573539
\(305\) −3.66874 −0.210071
\(306\) −1.38998 −0.0794600
\(307\) 26.3266 1.50254 0.751268 0.659997i \(-0.229443\pi\)
0.751268 + 0.659997i \(0.229443\pi\)
\(308\) −0.515814 −0.0293912
\(309\) 8.15852 0.464122
\(310\) 3.96304 0.225085
\(311\) 22.1733 1.25733 0.628666 0.777676i \(-0.283601\pi\)
0.628666 + 0.777676i \(0.283601\pi\)
\(312\) 0.522934 0.0296053
\(313\) −10.6795 −0.603640 −0.301820 0.953365i \(-0.597594\pi\)
−0.301820 + 0.953365i \(0.597594\pi\)
\(314\) −22.1872 −1.25210
\(315\) 1.49690 0.0843409
\(316\) −8.19692 −0.461113
\(317\) 9.60508 0.539475 0.269737 0.962934i \(-0.413063\pi\)
0.269737 + 0.962934i \(0.413063\pi\)
\(318\) −4.74991 −0.266362
\(319\) 0.545541 0.0305444
\(320\) 0.472260 0.0264001
\(321\) −9.29805 −0.518966
\(322\) −26.0045 −1.44917
\(323\) −2.02660 −0.112763
\(324\) −10.5872 −0.588177
\(325\) −1.30116 −0.0721751
\(326\) −18.7445 −1.03816
\(327\) 16.0459 0.887339
\(328\) 5.51603 0.304572
\(329\) 17.5345 0.966710
\(330\) −0.101198 −0.00557078
\(331\) −2.66520 −0.146492 −0.0732462 0.997314i \(-0.523336\pi\)
−0.0732462 + 0.997314i \(0.523336\pi\)
\(332\) 4.34992 0.238733
\(333\) 5.17420 0.283544
\(334\) −11.2702 −0.616678
\(335\) −6.49584 −0.354906
\(336\) −8.87239 −0.484029
\(337\) −0.227011 −0.0123661 −0.00618304 0.999981i \(-0.501968\pi\)
−0.00618304 + 0.999981i \(0.501968\pi\)
\(338\) 12.9258 0.703071
\(339\) 3.65757 0.198652
\(340\) 0.957080 0.0519049
\(341\) 0.936633 0.0507215
\(342\) 0.685870 0.0370876
\(343\) 33.9997 1.83581
\(344\) −0.252608 −0.0136197
\(345\) −5.10186 −0.274675
\(346\) −16.3680 −0.879949
\(347\) 13.8514 0.743584 0.371792 0.928316i \(-0.378743\pi\)
0.371792 + 0.928316i \(0.378743\pi\)
\(348\) 9.38373 0.503020
\(349\) −31.8668 −1.70579 −0.852896 0.522081i \(-0.825156\pi\)
−0.852896 + 0.522081i \(0.825156\pi\)
\(350\) 22.0762 1.18002
\(351\) 1.21014 0.0645923
\(352\) 0.111615 0.00594909
\(353\) 16.6465 0.886002 0.443001 0.896521i \(-0.353914\pi\)
0.443001 + 0.896521i \(0.353914\pi\)
\(354\) −20.2580 −1.07670
\(355\) 3.44467 0.182824
\(356\) 1.85112 0.0981093
\(357\) −17.9808 −0.951643
\(358\) −6.99012 −0.369439
\(359\) 26.3584 1.39114 0.695571 0.718457i \(-0.255152\pi\)
0.695571 + 0.718457i \(0.255152\pi\)
\(360\) −0.323909 −0.0170715
\(361\) 1.00000 0.0526316
\(362\) −10.2038 −0.536297
\(363\) 21.0946 1.10718
\(364\) 1.25877 0.0659776
\(365\) −4.71446 −0.246766
\(366\) −14.9144 −0.779589
\(367\) −25.7657 −1.34496 −0.672480 0.740116i \(-0.734771\pi\)
−0.672480 + 0.740116i \(0.734771\pi\)
\(368\) 5.62701 0.293328
\(369\) −3.78328 −0.196950
\(370\) −3.56272 −0.185217
\(371\) −11.4337 −0.593607
\(372\) 16.1108 0.835307
\(373\) 28.1372 1.45689 0.728444 0.685105i \(-0.240244\pi\)
0.728444 + 0.685105i \(0.240244\pi\)
\(374\) 0.226198 0.0116964
\(375\) 8.86452 0.457762
\(376\) −3.79423 −0.195672
\(377\) −1.33132 −0.0685664
\(378\) −20.5319 −1.05605
\(379\) −13.5334 −0.695163 −0.347581 0.937650i \(-0.612997\pi\)
−0.347581 + 0.937650i \(0.612997\pi\)
\(380\) −0.472260 −0.0242264
\(381\) 26.1749 1.34098
\(382\) 11.5053 0.588662
\(383\) −24.5134 −1.25257 −0.626287 0.779592i \(-0.715426\pi\)
−0.626287 + 0.779592i \(0.715426\pi\)
\(384\) 1.91986 0.0979725
\(385\) −0.243598 −0.0124149
\(386\) −6.94976 −0.353733
\(387\) 0.173256 0.00880712
\(388\) −4.37494 −0.222104
\(389\) 16.4578 0.834444 0.417222 0.908804i \(-0.363004\pi\)
0.417222 + 0.908804i \(0.363004\pi\)
\(390\) 0.246960 0.0125053
\(391\) 11.4037 0.576709
\(392\) −14.3571 −0.725141
\(393\) 18.0357 0.909783
\(394\) 0.472969 0.0238278
\(395\) −3.87107 −0.194775
\(396\) −0.0765533 −0.00384695
\(397\) 5.94014 0.298127 0.149063 0.988828i \(-0.452374\pi\)
0.149063 + 0.988828i \(0.452374\pi\)
\(398\) 2.12016 0.106274
\(399\) 8.87239 0.444175
\(400\) −4.77697 −0.238849
\(401\) 28.2705 1.41176 0.705880 0.708332i \(-0.250552\pi\)
0.705880 + 0.708332i \(0.250552\pi\)
\(402\) −26.4073 −1.31708
\(403\) −2.28573 −0.113860
\(404\) −9.21439 −0.458433
\(405\) −4.99990 −0.248447
\(406\) 22.5879 1.12102
\(407\) −0.842022 −0.0417375
\(408\) 3.89079 0.192623
\(409\) −8.18671 −0.404807 −0.202403 0.979302i \(-0.564875\pi\)
−0.202403 + 0.979302i \(0.564875\pi\)
\(410\) 2.60500 0.128652
\(411\) 32.4190 1.59911
\(412\) −4.24953 −0.209360
\(413\) −48.7639 −2.39951
\(414\) −3.85940 −0.189679
\(415\) 2.05429 0.100841
\(416\) −0.272381 −0.0133546
\(417\) −31.8809 −1.56121
\(418\) −0.111615 −0.00545926
\(419\) 21.3479 1.04291 0.521456 0.853278i \(-0.325389\pi\)
0.521456 + 0.853278i \(0.325389\pi\)
\(420\) −4.19007 −0.204455
\(421\) 12.7248 0.620167 0.310084 0.950709i \(-0.399643\pi\)
0.310084 + 0.950709i \(0.399643\pi\)
\(422\) 1.00000 0.0486792
\(423\) 2.60235 0.126530
\(424\) 2.47409 0.120152
\(425\) −9.68099 −0.469597
\(426\) 14.0035 0.678472
\(427\) −35.9010 −1.73737
\(428\) 4.84308 0.234099
\(429\) 0.0583672 0.00281799
\(430\) −0.119297 −0.00575300
\(431\) −29.0466 −1.39913 −0.699564 0.714570i \(-0.746622\pi\)
−0.699564 + 0.714570i \(0.746622\pi\)
\(432\) 4.44281 0.213755
\(433\) −26.0853 −1.25358 −0.626791 0.779188i \(-0.715632\pi\)
−0.626791 + 0.779188i \(0.715632\pi\)
\(434\) 38.7809 1.86154
\(435\) 4.43155 0.212477
\(436\) −8.35783 −0.400268
\(437\) −5.62701 −0.269177
\(438\) −19.1655 −0.915765
\(439\) 9.67726 0.461870 0.230935 0.972969i \(-0.425821\pi\)
0.230935 + 0.972969i \(0.425821\pi\)
\(440\) 0.0527112 0.00251291
\(441\) 9.84708 0.468909
\(442\) −0.552006 −0.0262563
\(443\) −36.4375 −1.73120 −0.865599 0.500738i \(-0.833062\pi\)
−0.865599 + 0.500738i \(0.833062\pi\)
\(444\) −14.4834 −0.687353
\(445\) 0.874210 0.0414415
\(446\) −23.2965 −1.10312
\(447\) −5.29689 −0.250534
\(448\) 4.62137 0.218339
\(449\) 41.2136 1.94499 0.972496 0.232920i \(-0.0748282\pi\)
0.972496 + 0.232920i \(0.0748282\pi\)
\(450\) 3.27638 0.154450
\(451\) 0.615671 0.0289908
\(452\) −1.90512 −0.0896095
\(453\) 31.8106 1.49459
\(454\) 11.2543 0.528189
\(455\) 0.594468 0.0278691
\(456\) −1.91986 −0.0899058
\(457\) −25.3327 −1.18501 −0.592507 0.805565i \(-0.701862\pi\)
−0.592507 + 0.805565i \(0.701862\pi\)
\(458\) 18.2204 0.851382
\(459\) 9.00379 0.420261
\(460\) 2.65741 0.123902
\(461\) −24.6118 −1.14629 −0.573143 0.819456i \(-0.694276\pi\)
−0.573143 + 0.819456i \(0.694276\pi\)
\(462\) −0.990291 −0.0460725
\(463\) 14.9610 0.695295 0.347648 0.937625i \(-0.386981\pi\)
0.347648 + 0.937625i \(0.386981\pi\)
\(464\) −4.88771 −0.226906
\(465\) 7.60849 0.352835
\(466\) −20.8797 −0.967235
\(467\) −12.6145 −0.583730 −0.291865 0.956460i \(-0.594276\pi\)
−0.291865 + 0.956460i \(0.594276\pi\)
\(468\) 0.186818 0.00863566
\(469\) −63.5661 −2.93521
\(470\) −1.79186 −0.0826523
\(471\) −42.5964 −1.96274
\(472\) 10.5518 0.485687
\(473\) −0.0281948 −0.00129640
\(474\) −15.7370 −0.722822
\(475\) 4.77697 0.219182
\(476\) 9.36566 0.429274
\(477\) −1.69690 −0.0776959
\(478\) 6.35982 0.290891
\(479\) −6.67518 −0.304997 −0.152498 0.988304i \(-0.548732\pi\)
−0.152498 + 0.988304i \(0.548732\pi\)
\(480\) 0.906673 0.0413838
\(481\) 2.05484 0.0936927
\(482\) 27.5421 1.25451
\(483\) −49.9251 −2.27167
\(484\) −10.9875 −0.499434
\(485\) −2.06611 −0.0938171
\(486\) −6.99752 −0.317414
\(487\) −26.2374 −1.18893 −0.594465 0.804121i \(-0.702636\pi\)
−0.594465 + 0.804121i \(0.702636\pi\)
\(488\) 7.76848 0.351663
\(489\) −35.9868 −1.62738
\(490\) −6.78026 −0.306301
\(491\) −22.9290 −1.03477 −0.517385 0.855753i \(-0.673095\pi\)
−0.517385 + 0.855753i \(0.673095\pi\)
\(492\) 10.5900 0.477435
\(493\) −9.90541 −0.446117
\(494\) 0.272381 0.0122550
\(495\) −0.0361530 −0.00162496
\(496\) −8.39165 −0.376796
\(497\) 33.7084 1.51203
\(498\) 8.35124 0.374228
\(499\) −16.2548 −0.727666 −0.363833 0.931464i \(-0.618532\pi\)
−0.363833 + 0.931464i \(0.618532\pi\)
\(500\) −4.61727 −0.206490
\(501\) −21.6372 −0.966680
\(502\) −25.8059 −1.15177
\(503\) 24.5006 1.09243 0.546214 0.837646i \(-0.316069\pi\)
0.546214 + 0.837646i \(0.316069\pi\)
\(504\) −3.16966 −0.141188
\(505\) −4.35158 −0.193643
\(506\) 0.628058 0.0279206
\(507\) 24.8158 1.10211
\(508\) −13.6337 −0.604899
\(509\) 19.8209 0.878546 0.439273 0.898354i \(-0.355236\pi\)
0.439273 + 0.898354i \(0.355236\pi\)
\(510\) 1.83746 0.0813641
\(511\) −46.1341 −2.04085
\(512\) −1.00000 −0.0441942
\(513\) −4.44281 −0.196155
\(514\) 27.3503 1.20637
\(515\) −2.00688 −0.0884338
\(516\) −0.484973 −0.0213497
\(517\) −0.423492 −0.0186252
\(518\) −34.8636 −1.53182
\(519\) −31.4243 −1.37937
\(520\) −0.128634 −0.00564100
\(521\) −2.52355 −0.110559 −0.0552794 0.998471i \(-0.517605\pi\)
−0.0552794 + 0.998471i \(0.517605\pi\)
\(522\) 3.35233 0.146728
\(523\) 17.4823 0.764449 0.382224 0.924070i \(-0.375158\pi\)
0.382224 + 0.924070i \(0.375158\pi\)
\(524\) −9.39429 −0.410391
\(525\) 42.3832 1.84975
\(526\) 20.0329 0.873478
\(527\) −17.0065 −0.740815
\(528\) 0.214285 0.00932556
\(529\) 8.66327 0.376664
\(530\) 1.16841 0.0507526
\(531\) −7.23718 −0.314067
\(532\) −4.62137 −0.200362
\(533\) −1.50246 −0.0650789
\(534\) 3.55390 0.153792
\(535\) 2.28719 0.0988839
\(536\) 13.7548 0.594117
\(537\) −13.4201 −0.579118
\(538\) 17.9291 0.772979
\(539\) −1.60246 −0.0690229
\(540\) 2.09816 0.0902904
\(541\) 8.02592 0.345061 0.172531 0.985004i \(-0.444806\pi\)
0.172531 + 0.985004i \(0.444806\pi\)
\(542\) 29.8009 1.28006
\(543\) −19.5898 −0.840679
\(544\) −2.02660 −0.0868896
\(545\) −3.94707 −0.169074
\(546\) 2.41667 0.103424
\(547\) −40.5232 −1.73265 −0.866324 0.499483i \(-0.833523\pi\)
−0.866324 + 0.499483i \(0.833523\pi\)
\(548\) −16.8861 −0.721339
\(549\) −5.32817 −0.227401
\(550\) −0.533181 −0.0227349
\(551\) 4.88771 0.208223
\(552\) 10.8031 0.459810
\(553\) −37.8810 −1.61086
\(554\) −30.3358 −1.28884
\(555\) −6.83994 −0.290339
\(556\) 16.6058 0.704243
\(557\) 30.5384 1.29395 0.646977 0.762510i \(-0.276033\pi\)
0.646977 + 0.762510i \(0.276033\pi\)
\(558\) 5.75558 0.243653
\(559\) 0.0688057 0.00291017
\(560\) 2.18249 0.0922269
\(561\) 0.434270 0.0183349
\(562\) −8.78673 −0.370646
\(563\) −31.7971 −1.34009 −0.670044 0.742321i \(-0.733725\pi\)
−0.670044 + 0.742321i \(0.733725\pi\)
\(564\) −7.28439 −0.306728
\(565\) −0.899713 −0.0378512
\(566\) 1.62138 0.0681515
\(567\) −48.9273 −2.05476
\(568\) −7.29402 −0.306050
\(569\) −8.51692 −0.357048 −0.178524 0.983936i \(-0.557132\pi\)
−0.178524 + 0.983936i \(0.557132\pi\)
\(570\) −0.906673 −0.0379764
\(571\) 24.6385 1.03109 0.515544 0.856863i \(-0.327590\pi\)
0.515544 + 0.856863i \(0.327590\pi\)
\(572\) −0.0304018 −0.00127116
\(573\) 22.0886 0.922764
\(574\) 25.4916 1.06400
\(575\) −26.8801 −1.12098
\(576\) 0.685870 0.0285779
\(577\) 13.6248 0.567208 0.283604 0.958942i \(-0.408470\pi\)
0.283604 + 0.958942i \(0.408470\pi\)
\(578\) 12.8929 0.536274
\(579\) −13.3426 −0.554498
\(580\) −2.30827 −0.0958456
\(581\) 20.1026 0.833995
\(582\) −8.39928 −0.348161
\(583\) 0.276145 0.0114368
\(584\) 9.98277 0.413090
\(585\) 0.0882266 0.00364772
\(586\) −32.3187 −1.33508
\(587\) −31.3795 −1.29517 −0.647586 0.761992i \(-0.724221\pi\)
−0.647586 + 0.761992i \(0.724221\pi\)
\(588\) −27.5636 −1.13670
\(589\) 8.39165 0.345772
\(590\) 4.98320 0.205155
\(591\) 0.908035 0.0373516
\(592\) 7.54400 0.310056
\(593\) 36.9806 1.51861 0.759305 0.650735i \(-0.225539\pi\)
0.759305 + 0.650735i \(0.225539\pi\)
\(594\) 0.495884 0.0203463
\(595\) 4.42302 0.181326
\(596\) 2.75899 0.113013
\(597\) 4.07042 0.166591
\(598\) −1.53269 −0.0626764
\(599\) −32.6016 −1.33207 −0.666034 0.745922i \(-0.732009\pi\)
−0.666034 + 0.745922i \(0.732009\pi\)
\(600\) −9.17112 −0.374410
\(601\) −22.7501 −0.927997 −0.463999 0.885836i \(-0.653586\pi\)
−0.463999 + 0.885836i \(0.653586\pi\)
\(602\) −1.16740 −0.0475795
\(603\) −9.43401 −0.384183
\(604\) −16.5692 −0.674192
\(605\) −5.18897 −0.210962
\(606\) −17.6904 −0.718622
\(607\) −25.7053 −1.04335 −0.521673 0.853145i \(-0.674692\pi\)
−0.521673 + 0.853145i \(0.674692\pi\)
\(608\) 1.00000 0.0405554
\(609\) 43.3657 1.75727
\(610\) 3.66874 0.148543
\(611\) 1.03348 0.0418099
\(612\) 1.38998 0.0561867
\(613\) −30.0177 −1.21240 −0.606202 0.795311i \(-0.707308\pi\)
−0.606202 + 0.795311i \(0.707308\pi\)
\(614\) −26.3266 −1.06245
\(615\) 5.00124 0.201669
\(616\) 0.515814 0.0207827
\(617\) −28.4706 −1.14618 −0.573092 0.819491i \(-0.694256\pi\)
−0.573092 + 0.819491i \(0.694256\pi\)
\(618\) −8.15852 −0.328184
\(619\) −9.44005 −0.379428 −0.189714 0.981839i \(-0.560756\pi\)
−0.189714 + 0.981839i \(0.560756\pi\)
\(620\) −3.96304 −0.159159
\(621\) 24.9997 1.00321
\(622\) −22.1733 −0.889068
\(623\) 8.55472 0.342738
\(624\) −0.522934 −0.0209341
\(625\) 21.7043 0.868172
\(626\) 10.6795 0.426838
\(627\) −0.214285 −0.00855772
\(628\) 22.1872 0.885367
\(629\) 15.2886 0.609598
\(630\) −1.49690 −0.0596380
\(631\) −19.1209 −0.761189 −0.380595 0.924742i \(-0.624281\pi\)
−0.380595 + 0.924742i \(0.624281\pi\)
\(632\) 8.19692 0.326056
\(633\) 1.91986 0.0763077
\(634\) −9.60508 −0.381466
\(635\) −6.43866 −0.255511
\(636\) 4.74991 0.188346
\(637\) 3.91059 0.154943
\(638\) −0.545541 −0.0215982
\(639\) 5.00275 0.197906
\(640\) −0.472260 −0.0186677
\(641\) −5.39138 −0.212947 −0.106473 0.994316i \(-0.533956\pi\)
−0.106473 + 0.994316i \(0.533956\pi\)
\(642\) 9.29805 0.366965
\(643\) −36.3332 −1.43284 −0.716421 0.697668i \(-0.754221\pi\)
−0.716421 + 0.697668i \(0.754221\pi\)
\(644\) 26.0045 1.02472
\(645\) −0.229033 −0.00901817
\(646\) 2.02660 0.0797354
\(647\) 0.622710 0.0244813 0.0122406 0.999925i \(-0.496104\pi\)
0.0122406 + 0.999925i \(0.496104\pi\)
\(648\) 10.5872 0.415904
\(649\) 1.17774 0.0462303
\(650\) 1.30116 0.0510355
\(651\) 74.4540 2.91808
\(652\) 18.7445 0.734090
\(653\) −37.2732 −1.45861 −0.729306 0.684188i \(-0.760157\pi\)
−0.729306 + 0.684188i \(0.760157\pi\)
\(654\) −16.0459 −0.627444
\(655\) −4.43654 −0.173350
\(656\) −5.51603 −0.215365
\(657\) −6.84688 −0.267122
\(658\) −17.5345 −0.683567
\(659\) −38.7745 −1.51044 −0.755221 0.655470i \(-0.772470\pi\)
−0.755221 + 0.655470i \(0.772470\pi\)
\(660\) 0.101198 0.00393913
\(661\) −12.6203 −0.490872 −0.245436 0.969413i \(-0.578931\pi\)
−0.245436 + 0.969413i \(0.578931\pi\)
\(662\) 2.66520 0.103586
\(663\) −1.05978 −0.0411583
\(664\) −4.34992 −0.168809
\(665\) −2.18249 −0.0846332
\(666\) −5.17420 −0.200496
\(667\) −27.5032 −1.06493
\(668\) 11.2702 0.436057
\(669\) −44.7261 −1.72921
\(670\) 6.49584 0.250956
\(671\) 0.867078 0.0334732
\(672\) 8.87239 0.342260
\(673\) 0.576782 0.0222333 0.0111166 0.999938i \(-0.496461\pi\)
0.0111166 + 0.999938i \(0.496461\pi\)
\(674\) 0.227011 0.00874414
\(675\) −21.2232 −0.816880
\(676\) −12.9258 −0.497146
\(677\) 1.72191 0.0661782 0.0330891 0.999452i \(-0.489465\pi\)
0.0330891 + 0.999452i \(0.489465\pi\)
\(678\) −3.65757 −0.140468
\(679\) −20.2182 −0.775904
\(680\) −0.957080 −0.0367023
\(681\) 21.6066 0.827968
\(682\) −0.936633 −0.0358655
\(683\) −25.2785 −0.967254 −0.483627 0.875274i \(-0.660681\pi\)
−0.483627 + 0.875274i \(0.660681\pi\)
\(684\) −0.685870 −0.0262249
\(685\) −7.97463 −0.304695
\(686\) −33.9997 −1.29812
\(687\) 34.9806 1.33459
\(688\) 0.252608 0.00963060
\(689\) −0.673895 −0.0256734
\(690\) 5.10186 0.194225
\(691\) −6.74199 −0.256477 −0.128239 0.991743i \(-0.540932\pi\)
−0.128239 + 0.991743i \(0.540932\pi\)
\(692\) 16.3680 0.622218
\(693\) −0.353781 −0.0134390
\(694\) −13.8514 −0.525794
\(695\) 7.84225 0.297474
\(696\) −9.38373 −0.355689
\(697\) −11.1788 −0.423426
\(698\) 31.8668 1.20618
\(699\) −40.0862 −1.51620
\(700\) −22.0762 −0.834400
\(701\) −1.00611 −0.0380003 −0.0190001 0.999819i \(-0.506048\pi\)
−0.0190001 + 0.999819i \(0.506048\pi\)
\(702\) −1.21014 −0.0456737
\(703\) −7.54400 −0.284527
\(704\) −0.111615 −0.00420664
\(705\) −3.44012 −0.129563
\(706\) −16.6465 −0.626498
\(707\) −42.5831 −1.60150
\(708\) 20.2580 0.761344
\(709\) 9.38550 0.352480 0.176240 0.984347i \(-0.443607\pi\)
0.176240 + 0.984347i \(0.443607\pi\)
\(710\) −3.44467 −0.129276
\(711\) −5.62202 −0.210842
\(712\) −1.85112 −0.0693737
\(713\) −47.2199 −1.76840
\(714\) 17.9808 0.672913
\(715\) −0.0143575 −0.000536941 0
\(716\) 6.99012 0.261233
\(717\) 12.2100 0.455990
\(718\) −26.3584 −0.983686
\(719\) 33.4334 1.24685 0.623427 0.781881i \(-0.285740\pi\)
0.623427 + 0.781881i \(0.285740\pi\)
\(720\) 0.323909 0.0120714
\(721\) −19.6387 −0.731382
\(722\) −1.00000 −0.0372161
\(723\) 52.8771 1.96652
\(724\) 10.2038 0.379219
\(725\) 23.3484 0.867139
\(726\) −21.0946 −0.782893
\(727\) −11.8978 −0.441264 −0.220632 0.975357i \(-0.570812\pi\)
−0.220632 + 0.975357i \(0.570812\pi\)
\(728\) −1.25877 −0.0466532
\(729\) 18.3273 0.678789
\(730\) 4.71446 0.174490
\(731\) 0.511935 0.0189346
\(732\) 14.9144 0.551253
\(733\) −17.3766 −0.641818 −0.320909 0.947110i \(-0.603988\pi\)
−0.320909 + 0.947110i \(0.603988\pi\)
\(734\) 25.7657 0.951030
\(735\) −13.0172 −0.480145
\(736\) −5.62701 −0.207414
\(737\) 1.53524 0.0565513
\(738\) 3.78328 0.139265
\(739\) −23.7805 −0.874780 −0.437390 0.899272i \(-0.644097\pi\)
−0.437390 + 0.899272i \(0.644097\pi\)
\(740\) 3.56272 0.130968
\(741\) 0.522934 0.0192105
\(742\) 11.4337 0.419744
\(743\) −21.9105 −0.803817 −0.401909 0.915680i \(-0.631653\pi\)
−0.401909 + 0.915680i \(0.631653\pi\)
\(744\) −16.1108 −0.590651
\(745\) 1.30296 0.0477368
\(746\) −28.1372 −1.03018
\(747\) 2.98348 0.109160
\(748\) −0.226198 −0.00827063
\(749\) 22.3817 0.817808
\(750\) −8.86452 −0.323686
\(751\) −21.3312 −0.778387 −0.389194 0.921156i \(-0.627246\pi\)
−0.389194 + 0.921156i \(0.627246\pi\)
\(752\) 3.79423 0.138361
\(753\) −49.5438 −1.80548
\(754\) 1.33132 0.0484838
\(755\) −7.82497 −0.284780
\(756\) 20.5319 0.746737
\(757\) −9.54262 −0.346832 −0.173416 0.984849i \(-0.555481\pi\)
−0.173416 + 0.984849i \(0.555481\pi\)
\(758\) 13.5334 0.491554
\(759\) 1.20578 0.0437672
\(760\) 0.472260 0.0171307
\(761\) 49.9803 1.81178 0.905892 0.423508i \(-0.139201\pi\)
0.905892 + 0.423508i \(0.139201\pi\)
\(762\) −26.1749 −0.948216
\(763\) −38.6246 −1.39831
\(764\) −11.5053 −0.416247
\(765\) 0.656432 0.0237334
\(766\) 24.5134 0.885704
\(767\) −2.87412 −0.103778
\(768\) −1.91986 −0.0692771
\(769\) 27.8025 1.00258 0.501291 0.865279i \(-0.332859\pi\)
0.501291 + 0.865279i \(0.332859\pi\)
\(770\) 0.243598 0.00877866
\(771\) 52.5088 1.89106
\(772\) 6.94976 0.250127
\(773\) −26.8412 −0.965409 −0.482705 0.875783i \(-0.660346\pi\)
−0.482705 + 0.875783i \(0.660346\pi\)
\(774\) −0.173256 −0.00622757
\(775\) 40.0867 1.43996
\(776\) 4.37494 0.157051
\(777\) −66.9333 −2.40122
\(778\) −16.4578 −0.590041
\(779\) 5.51603 0.197632
\(780\) −0.246960 −0.00884260
\(781\) −0.814121 −0.0291315
\(782\) −11.4037 −0.407795
\(783\) −21.7152 −0.776036
\(784\) 14.3571 0.512752
\(785\) 10.4781 0.373981
\(786\) −18.0357 −0.643313
\(787\) 50.9265 1.81533 0.907667 0.419692i \(-0.137862\pi\)
0.907667 + 0.419692i \(0.137862\pi\)
\(788\) −0.472969 −0.0168488
\(789\) 38.4605 1.36923
\(790\) 3.87107 0.137727
\(791\) −8.80428 −0.313044
\(792\) 0.0765533 0.00272020
\(793\) −2.11599 −0.0751409
\(794\) −5.94014 −0.210808
\(795\) 2.24319 0.0795578
\(796\) −2.12016 −0.0751472
\(797\) 39.2707 1.39104 0.695519 0.718507i \(-0.255174\pi\)
0.695519 + 0.718507i \(0.255174\pi\)
\(798\) −8.87239 −0.314079
\(799\) 7.68937 0.272030
\(800\) 4.77697 0.168891
\(801\) 1.26963 0.0448601
\(802\) −28.2705 −0.998265
\(803\) 1.11423 0.0393201
\(804\) 26.4073 0.931315
\(805\) 12.2809 0.432844
\(806\) 2.28573 0.0805113
\(807\) 34.4214 1.21169
\(808\) 9.21439 0.324161
\(809\) 23.1539 0.814049 0.407025 0.913417i \(-0.366566\pi\)
0.407025 + 0.913417i \(0.366566\pi\)
\(810\) 4.99990 0.175679
\(811\) 27.1373 0.952918 0.476459 0.879197i \(-0.341920\pi\)
0.476459 + 0.879197i \(0.341920\pi\)
\(812\) −22.5879 −0.792680
\(813\) 57.2137 2.00657
\(814\) 0.842022 0.0295129
\(815\) 8.85226 0.310081
\(816\) −3.89079 −0.136205
\(817\) −0.252608 −0.00883764
\(818\) 8.18671 0.286242
\(819\) 0.863355 0.0301681
\(820\) −2.60500 −0.0909705
\(821\) −17.1421 −0.598265 −0.299132 0.954212i \(-0.596697\pi\)
−0.299132 + 0.954212i \(0.596697\pi\)
\(822\) −32.4190 −1.13074
\(823\) −45.7326 −1.59414 −0.797069 0.603888i \(-0.793617\pi\)
−0.797069 + 0.603888i \(0.793617\pi\)
\(824\) 4.24953 0.148040
\(825\) −1.02363 −0.0356384
\(826\) 48.7639 1.69671
\(827\) 16.0868 0.559393 0.279697 0.960088i \(-0.409766\pi\)
0.279697 + 0.960088i \(0.409766\pi\)
\(828\) 3.85940 0.134123
\(829\) −31.4246 −1.09142 −0.545711 0.837973i \(-0.683740\pi\)
−0.545711 + 0.837973i \(0.683740\pi\)
\(830\) −2.05429 −0.0713054
\(831\) −58.2405 −2.02034
\(832\) 0.272381 0.00944311
\(833\) 29.0960 1.00812
\(834\) 31.8809 1.10394
\(835\) 5.32246 0.184191
\(836\) 0.111615 0.00386028
\(837\) −37.2825 −1.28867
\(838\) −21.3479 −0.737450
\(839\) −8.18920 −0.282722 −0.141361 0.989958i \(-0.545148\pi\)
−0.141361 + 0.989958i \(0.545148\pi\)
\(840\) 4.19007 0.144571
\(841\) −5.11031 −0.176218
\(842\) −12.7248 −0.438525
\(843\) −16.8693 −0.581010
\(844\) −1.00000 −0.0344214
\(845\) −6.10434 −0.209996
\(846\) −2.60235 −0.0894705
\(847\) −50.7775 −1.74474
\(848\) −2.47409 −0.0849606
\(849\) 3.11282 0.106832
\(850\) 9.68099 0.332055
\(851\) 42.4502 1.45517
\(852\) −14.0035 −0.479752
\(853\) 6.06450 0.207645 0.103822 0.994596i \(-0.466893\pi\)
0.103822 + 0.994596i \(0.466893\pi\)
\(854\) 35.9010 1.22851
\(855\) −0.323909 −0.0110774
\(856\) −4.84308 −0.165533
\(857\) 0.554792 0.0189513 0.00947567 0.999955i \(-0.496984\pi\)
0.00947567 + 0.999955i \(0.496984\pi\)
\(858\) −0.0583672 −0.00199262
\(859\) −51.2323 −1.74803 −0.874013 0.485903i \(-0.838491\pi\)
−0.874013 + 0.485903i \(0.838491\pi\)
\(860\) 0.119297 0.00406798
\(861\) 48.9404 1.66788
\(862\) 29.0466 0.989332
\(863\) −12.4317 −0.423179 −0.211590 0.977359i \(-0.567864\pi\)
−0.211590 + 0.977359i \(0.567864\pi\)
\(864\) −4.44281 −0.151147
\(865\) 7.72994 0.262826
\(866\) 26.0853 0.886416
\(867\) 24.7526 0.840642
\(868\) −38.7809 −1.31631
\(869\) 0.914898 0.0310358
\(870\) −4.43155 −0.150244
\(871\) −3.74655 −0.126947
\(872\) 8.35783 0.283032
\(873\) −3.00064 −0.101556
\(874\) 5.62701 0.190337
\(875\) −21.3381 −0.721360
\(876\) 19.1655 0.647543
\(877\) −45.6458 −1.54135 −0.770675 0.637229i \(-0.780081\pi\)
−0.770675 + 0.637229i \(0.780081\pi\)
\(878\) −9.67726 −0.326592
\(879\) −62.0475 −2.09281
\(880\) −0.0527112 −0.00177689
\(881\) −35.1750 −1.18507 −0.592537 0.805543i \(-0.701874\pi\)
−0.592537 + 0.805543i \(0.701874\pi\)
\(882\) −9.84708 −0.331569
\(883\) 24.5711 0.826884 0.413442 0.910530i \(-0.364326\pi\)
0.413442 + 0.910530i \(0.364326\pi\)
\(884\) 0.552006 0.0185660
\(885\) 9.56705 0.321593
\(886\) 36.4375 1.22414
\(887\) 21.0111 0.705485 0.352743 0.935720i \(-0.385249\pi\)
0.352743 + 0.935720i \(0.385249\pi\)
\(888\) 14.4834 0.486032
\(889\) −63.0066 −2.11317
\(890\) −0.874210 −0.0293036
\(891\) 1.18169 0.0395880
\(892\) 23.2965 0.780025
\(893\) −3.79423 −0.126969
\(894\) 5.29689 0.177154
\(895\) 3.30115 0.110345
\(896\) −4.62137 −0.154389
\(897\) −2.94256 −0.0982491
\(898\) −41.2136 −1.37532
\(899\) 41.0159 1.36796
\(900\) −3.27638 −0.109213
\(901\) −5.01398 −0.167040
\(902\) −0.615671 −0.0204996
\(903\) −2.24124 −0.0745838
\(904\) 1.90512 0.0633635
\(905\) 4.81882 0.160183
\(906\) −31.8106 −1.05684
\(907\) −29.0385 −0.964209 −0.482104 0.876114i \(-0.660127\pi\)
−0.482104 + 0.876114i \(0.660127\pi\)
\(908\) −11.2543 −0.373486
\(909\) −6.31988 −0.209617
\(910\) −0.594468 −0.0197064
\(911\) 49.5077 1.64026 0.820132 0.572175i \(-0.193900\pi\)
0.820132 + 0.572175i \(0.193900\pi\)
\(912\) 1.91986 0.0635730
\(913\) −0.485515 −0.0160682
\(914\) 25.3327 0.837932
\(915\) 7.04348 0.232850
\(916\) −18.2204 −0.602018
\(917\) −43.4145 −1.43367
\(918\) −9.00379 −0.297169
\(919\) −31.6305 −1.04339 −0.521697 0.853131i \(-0.674701\pi\)
−0.521697 + 0.853131i \(0.674701\pi\)
\(920\) −2.65741 −0.0876122
\(921\) −50.5434 −1.66546
\(922\) 24.6118 0.810546
\(923\) 1.98675 0.0653947
\(924\) 0.990291 0.0325782
\(925\) −36.0374 −1.18490
\(926\) −14.9610 −0.491648
\(927\) −2.91463 −0.0957290
\(928\) 4.88771 0.160447
\(929\) 22.1704 0.727386 0.363693 0.931519i \(-0.381516\pi\)
0.363693 + 0.931519i \(0.381516\pi\)
\(930\) −7.60849 −0.249492
\(931\) −14.3571 −0.470534
\(932\) 20.8797 0.683938
\(933\) −42.5696 −1.39367
\(934\) 12.6145 0.412759
\(935\) −0.106824 −0.00349353
\(936\) −0.186818 −0.00610634
\(937\) −41.9507 −1.37047 −0.685234 0.728323i \(-0.740300\pi\)
−0.685234 + 0.728323i \(0.740300\pi\)
\(938\) 63.5661 2.07551
\(939\) 20.5031 0.669094
\(940\) 1.79186 0.0584440
\(941\) 16.3507 0.533017 0.266509 0.963833i \(-0.414130\pi\)
0.266509 + 0.963833i \(0.414130\pi\)
\(942\) 42.5964 1.38787
\(943\) −31.0388 −1.01076
\(944\) −10.5518 −0.343433
\(945\) 9.69637 0.315423
\(946\) 0.0281948 0.000916693 0
\(947\) −8.77637 −0.285194 −0.142597 0.989781i \(-0.545545\pi\)
−0.142597 + 0.989781i \(0.545545\pi\)
\(948\) 15.7370 0.511112
\(949\) −2.71912 −0.0882662
\(950\) −4.77697 −0.154985
\(951\) −18.4404 −0.597972
\(952\) −9.36566 −0.303543
\(953\) 38.8286 1.25778 0.628890 0.777494i \(-0.283509\pi\)
0.628890 + 0.777494i \(0.283509\pi\)
\(954\) 1.69690 0.0549393
\(955\) −5.43349 −0.175824
\(956\) −6.35982 −0.205691
\(957\) −1.04736 −0.0338564
\(958\) 6.67518 0.215665
\(959\) −78.0370 −2.51995
\(960\) −0.906673 −0.0292628
\(961\) 39.4198 1.27161
\(962\) −2.05484 −0.0662507
\(963\) 3.32172 0.107041
\(964\) −27.5421 −0.887072
\(965\) 3.28209 0.105654
\(966\) 49.9251 1.60631
\(967\) 16.0077 0.514772 0.257386 0.966309i \(-0.417139\pi\)
0.257386 + 0.966309i \(0.417139\pi\)
\(968\) 10.9875 0.353153
\(969\) 3.89079 0.124990
\(970\) 2.06611 0.0663387
\(971\) −50.8387 −1.63149 −0.815745 0.578411i \(-0.803673\pi\)
−0.815745 + 0.578411i \(0.803673\pi\)
\(972\) 6.99752 0.224446
\(973\) 76.7416 2.46022
\(974\) 26.2374 0.840700
\(975\) 2.49804 0.0800013
\(976\) −7.76848 −0.248663
\(977\) −17.2482 −0.551818 −0.275909 0.961184i \(-0.588979\pi\)
−0.275909 + 0.961184i \(0.588979\pi\)
\(978\) 35.9868 1.15073
\(979\) −0.206613 −0.00660337
\(980\) 6.78026 0.216588
\(981\) −5.73239 −0.183021
\(982\) 22.9290 0.731693
\(983\) 42.2447 1.34740 0.673698 0.739007i \(-0.264705\pi\)
0.673698 + 0.739007i \(0.264705\pi\)
\(984\) −10.5900 −0.337598
\(985\) −0.223364 −0.00711697
\(986\) 9.90541 0.315453
\(987\) −33.6639 −1.07153
\(988\) −0.272381 −0.00866559
\(989\) 1.42143 0.0451988
\(990\) 0.0361530 0.00114902
\(991\) 48.6224 1.54454 0.772271 0.635293i \(-0.219121\pi\)
0.772271 + 0.635293i \(0.219121\pi\)
\(992\) 8.39165 0.266435
\(993\) 5.11681 0.162377
\(994\) −33.7084 −1.06916
\(995\) −1.00127 −0.0317423
\(996\) −8.35124 −0.264619
\(997\) 21.0111 0.665427 0.332713 0.943028i \(-0.392036\pi\)
0.332713 + 0.943028i \(0.392036\pi\)
\(998\) 16.2548 0.514538
\(999\) 33.5165 1.06042
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 \(a_p\))