Properties

Label 6018.2.a.p.1.5
Level 6018
Weight 2
Character 6018.1
Self dual Yes
Analytic conductor 48.054
Analytic rank 0
Dimension 5
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.1668357.1
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-1.53628\)
Character \(\chi\) = 6018.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.05778 q^{5} -1.00000 q^{6} +1.53628 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.05778 q^{5} -1.00000 q^{6} +1.53628 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.05778 q^{10} -3.38200 q^{11} +1.00000 q^{12} -1.02340 q^{13} -1.53628 q^{14} +3.05778 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.86050 q^{19} +3.05778 q^{20} +1.53628 q^{21} +3.38200 q^{22} +3.31561 q^{23} -1.00000 q^{24} +4.34999 q^{25} +1.02340 q^{26} +1.00000 q^{27} +1.53628 q^{28} +9.99843 q^{29} -3.05778 q^{30} -0.616436 q^{31} -1.00000 q^{32} -3.38200 q^{33} +1.00000 q^{34} +4.69761 q^{35} +1.00000 q^{36} +6.96745 q^{37} -3.86050 q^{38} -1.02340 q^{39} -3.05778 q^{40} +3.75695 q^{41} -1.53628 q^{42} -10.5037 q^{43} -3.38200 q^{44} +3.05778 q^{45} -3.31561 q^{46} +1.24801 q^{47} +1.00000 q^{48} -4.63983 q^{49} -4.34999 q^{50} -1.00000 q^{51} -1.02340 q^{52} -4.62844 q^{53} -1.00000 q^{54} -10.3414 q^{55} -1.53628 q^{56} +3.86050 q^{57} -9.99843 q^{58} -1.00000 q^{59} +3.05778 q^{60} -7.29167 q^{61} +0.616436 q^{62} +1.53628 q^{63} +1.00000 q^{64} -3.12932 q^{65} +3.38200 q^{66} +11.4731 q^{67} -1.00000 q^{68} +3.31561 q^{69} -4.69761 q^{70} +3.33520 q^{71} -1.00000 q^{72} -6.75436 q^{73} -6.96745 q^{74} +4.34999 q^{75} +3.86050 q^{76} -5.19570 q^{77} +1.02340 q^{78} +9.75174 q^{79} +3.05778 q^{80} +1.00000 q^{81} -3.75695 q^{82} +10.3190 q^{83} +1.53628 q^{84} -3.05778 q^{85} +10.5037 q^{86} +9.99843 q^{87} +3.38200 q^{88} +6.45613 q^{89} -3.05778 q^{90} -1.57223 q^{91} +3.31561 q^{92} -0.616436 q^{93} -1.24801 q^{94} +11.8046 q^{95} -1.00000 q^{96} +3.62504 q^{97} +4.63983 q^{98} -3.38200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - q^{7} - 5q^{8} + 5q^{9} + O(q^{10}) \) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - q^{7} - 5q^{8} + 5q^{9} + q^{10} + 6q^{11} + 5q^{12} - 2q^{13} + q^{14} - q^{15} + 5q^{16} - 5q^{17} - 5q^{18} + 4q^{19} - q^{20} - q^{21} - 6q^{22} + 12q^{23} - 5q^{24} + 4q^{25} + 2q^{26} + 5q^{27} - q^{28} + 19q^{29} + q^{30} + 5q^{31} - 5q^{32} + 6q^{33} + 5q^{34} - 4q^{35} + 5q^{36} - 11q^{37} - 4q^{38} - 2q^{39} + q^{40} + 6q^{41} + q^{42} + 2q^{43} + 6q^{44} - q^{45} - 12q^{46} + 22q^{47} + 5q^{48} - 12q^{49} - 4q^{50} - 5q^{51} - 2q^{52} + 15q^{53} - 5q^{54} - 36q^{55} + q^{56} + 4q^{57} - 19q^{58} - 5q^{59} - q^{60} + 16q^{61} - 5q^{62} - q^{63} + 5q^{64} - 2q^{65} - 6q^{66} + 25q^{67} - 5q^{68} + 12q^{69} + 4q^{70} - 5q^{72} - 10q^{73} + 11q^{74} + 4q^{75} + 4q^{76} + 6q^{77} + 2q^{78} + 10q^{79} - q^{80} + 5q^{81} - 6q^{82} + 19q^{83} - q^{84} + q^{85} - 2q^{86} + 19q^{87} - 6q^{88} + 23q^{89} + q^{90} - 17q^{91} + 12q^{92} + 5q^{93} - 22q^{94} + q^{95} - 5q^{96} + 8q^{97} + 12q^{98} + 6q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 3.05778 1.36748 0.683739 0.729726i \(-0.260353\pi\)
0.683739 + 0.729726i \(0.260353\pi\)
\(6\) −1.00000 −0.408248
\(7\) 1.53628 0.580660 0.290330 0.956927i \(-0.406235\pi\)
0.290330 + 0.956927i \(0.406235\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −3.05778 −0.966954
\(11\) −3.38200 −1.01971 −0.509855 0.860260i \(-0.670301\pi\)
−0.509855 + 0.860260i \(0.670301\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.02340 −0.283840 −0.141920 0.989878i \(-0.545327\pi\)
−0.141920 + 0.989878i \(0.545327\pi\)
\(14\) −1.53628 −0.410589
\(15\) 3.05778 0.789514
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) 3.86050 0.885660 0.442830 0.896606i \(-0.353974\pi\)
0.442830 + 0.896606i \(0.353974\pi\)
\(20\) 3.05778 0.683739
\(21\) 1.53628 0.335244
\(22\) 3.38200 0.721044
\(23\) 3.31561 0.691353 0.345677 0.938354i \(-0.387649\pi\)
0.345677 + 0.938354i \(0.387649\pi\)
\(24\) −1.00000 −0.204124
\(25\) 4.34999 0.869998
\(26\) 1.02340 0.200705
\(27\) 1.00000 0.192450
\(28\) 1.53628 0.290330
\(29\) 9.99843 1.85666 0.928331 0.371755i \(-0.121244\pi\)
0.928331 + 0.371755i \(0.121244\pi\)
\(30\) −3.05778 −0.558271
\(31\) −0.616436 −0.110715 −0.0553576 0.998467i \(-0.517630\pi\)
−0.0553576 + 0.998467i \(0.517630\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.38200 −0.588730
\(34\) 1.00000 0.171499
\(35\) 4.69761 0.794041
\(36\) 1.00000 0.166667
\(37\) 6.96745 1.14544 0.572721 0.819751i \(-0.305888\pi\)
0.572721 + 0.819751i \(0.305888\pi\)
\(38\) −3.86050 −0.626256
\(39\) −1.02340 −0.163875
\(40\) −3.05778 −0.483477
\(41\) 3.75695 0.586737 0.293369 0.955999i \(-0.405224\pi\)
0.293369 + 0.955999i \(0.405224\pi\)
\(42\) −1.53628 −0.237054
\(43\) −10.5037 −1.60180 −0.800902 0.598795i \(-0.795646\pi\)
−0.800902 + 0.598795i \(0.795646\pi\)
\(44\) −3.38200 −0.509855
\(45\) 3.05778 0.455826
\(46\) −3.31561 −0.488861
\(47\) 1.24801 0.182041 0.0910204 0.995849i \(-0.470987\pi\)
0.0910204 + 0.995849i \(0.470987\pi\)
\(48\) 1.00000 0.144338
\(49\) −4.63983 −0.662833
\(50\) −4.34999 −0.615182
\(51\) −1.00000 −0.140028
\(52\) −1.02340 −0.141920
\(53\) −4.62844 −0.635765 −0.317882 0.948130i \(-0.602972\pi\)
−0.317882 + 0.948130i \(0.602972\pi\)
\(54\) −1.00000 −0.136083
\(55\) −10.3414 −1.39443
\(56\) −1.53628 −0.205294
\(57\) 3.86050 0.511336
\(58\) −9.99843 −1.31286
\(59\) −1.00000 −0.130189
\(60\) 3.05778 0.394757
\(61\) −7.29167 −0.933602 −0.466801 0.884362i \(-0.654594\pi\)
−0.466801 + 0.884362i \(0.654594\pi\)
\(62\) 0.616436 0.0782874
\(63\) 1.53628 0.193553
\(64\) 1.00000 0.125000
\(65\) −3.12932 −0.388145
\(66\) 3.38200 0.416295
\(67\) 11.4731 1.40167 0.700833 0.713326i \(-0.252812\pi\)
0.700833 + 0.713326i \(0.252812\pi\)
\(68\) −1.00000 −0.121268
\(69\) 3.31561 0.399153
\(70\) −4.69761 −0.561472
\(71\) 3.33520 0.395815 0.197908 0.980221i \(-0.436585\pi\)
0.197908 + 0.980221i \(0.436585\pi\)
\(72\) −1.00000 −0.117851
\(73\) −6.75436 −0.790539 −0.395269 0.918565i \(-0.629349\pi\)
−0.395269 + 0.918565i \(0.629349\pi\)
\(74\) −6.96745 −0.809949
\(75\) 4.34999 0.502294
\(76\) 3.86050 0.442830
\(77\) −5.19570 −0.592105
\(78\) 1.02340 0.115877
\(79\) 9.75174 1.09716 0.548578 0.836099i \(-0.315169\pi\)
0.548578 + 0.836099i \(0.315169\pi\)
\(80\) 3.05778 0.341870
\(81\) 1.00000 0.111111
\(82\) −3.75695 −0.414886
\(83\) 10.3190 1.13266 0.566329 0.824179i \(-0.308363\pi\)
0.566329 + 0.824179i \(0.308363\pi\)
\(84\) 1.53628 0.167622
\(85\) −3.05778 −0.331662
\(86\) 10.5037 1.13265
\(87\) 9.99843 1.07194
\(88\) 3.38200 0.360522
\(89\) 6.45613 0.684348 0.342174 0.939637i \(-0.388837\pi\)
0.342174 + 0.939637i \(0.388837\pi\)
\(90\) −3.05778 −0.322318
\(91\) −1.57223 −0.164814
\(92\) 3.31561 0.345677
\(93\) −0.616436 −0.0639214
\(94\) −1.24801 −0.128722
\(95\) 11.8046 1.21112
\(96\) −1.00000 −0.102062
\(97\) 3.62504 0.368067 0.184034 0.982920i \(-0.441084\pi\)
0.184034 + 0.982920i \(0.441084\pi\)
\(98\) 4.63983 0.468694
\(99\) −3.38200 −0.339903
\(100\) 4.34999 0.434999
\(101\) 2.67082 0.265756 0.132878 0.991132i \(-0.457578\pi\)
0.132878 + 0.991132i \(0.457578\pi\)
\(102\) 1.00000 0.0990148
\(103\) 1.34525 0.132551 0.0662755 0.997801i \(-0.478888\pi\)
0.0662755 + 0.997801i \(0.478888\pi\)
\(104\) 1.02340 0.100352
\(105\) 4.69761 0.458440
\(106\) 4.62844 0.449553
\(107\) 11.1785 1.08067 0.540335 0.841450i \(-0.318297\pi\)
0.540335 + 0.841450i \(0.318297\pi\)
\(108\) 1.00000 0.0962250
\(109\) −7.90967 −0.757609 −0.378805 0.925477i \(-0.623665\pi\)
−0.378805 + 0.925477i \(0.623665\pi\)
\(110\) 10.3414 0.986012
\(111\) 6.96745 0.661321
\(112\) 1.53628 0.145165
\(113\) −5.61589 −0.528298 −0.264149 0.964482i \(-0.585091\pi\)
−0.264149 + 0.964482i \(0.585091\pi\)
\(114\) −3.86050 −0.361569
\(115\) 10.1384 0.945411
\(116\) 9.99843 0.928331
\(117\) −1.02340 −0.0946132
\(118\) 1.00000 0.0920575
\(119\) −1.53628 −0.140831
\(120\) −3.05778 −0.279135
\(121\) 0.437896 0.0398087
\(122\) 7.29167 0.660157
\(123\) 3.75695 0.338753
\(124\) −0.616436 −0.0553576
\(125\) −1.98758 −0.177775
\(126\) −1.53628 −0.136863
\(127\) 22.2111 1.97092 0.985458 0.169919i \(-0.0543505\pi\)
0.985458 + 0.169919i \(0.0543505\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −10.5037 −0.924802
\(130\) 3.12932 0.274460
\(131\) 4.20710 0.367576 0.183788 0.982966i \(-0.441164\pi\)
0.183788 + 0.982966i \(0.441164\pi\)
\(132\) −3.38200 −0.294365
\(133\) 5.93083 0.514268
\(134\) −11.4731 −0.991127
\(135\) 3.05778 0.263171
\(136\) 1.00000 0.0857493
\(137\) 6.31269 0.539330 0.269665 0.962954i \(-0.413087\pi\)
0.269665 + 0.962954i \(0.413087\pi\)
\(138\) −3.31561 −0.282244
\(139\) 10.5233 0.892576 0.446288 0.894889i \(-0.352746\pi\)
0.446288 + 0.894889i \(0.352746\pi\)
\(140\) 4.69761 0.397020
\(141\) 1.24801 0.105101
\(142\) −3.33520 −0.279884
\(143\) 3.46113 0.289434
\(144\) 1.00000 0.0833333
\(145\) 30.5730 2.53895
\(146\) 6.75436 0.558995
\(147\) −4.63983 −0.382687
\(148\) 6.96745 0.572721
\(149\) −11.0906 −0.908576 −0.454288 0.890855i \(-0.650106\pi\)
−0.454288 + 0.890855i \(0.650106\pi\)
\(150\) −4.34999 −0.355175
\(151\) −3.05298 −0.248448 −0.124224 0.992254i \(-0.539644\pi\)
−0.124224 + 0.992254i \(0.539644\pi\)
\(152\) −3.86050 −0.313128
\(153\) −1.00000 −0.0808452
\(154\) 5.19570 0.418682
\(155\) −1.88492 −0.151401
\(156\) −1.02340 −0.0819374
\(157\) 1.96927 0.157165 0.0785823 0.996908i \(-0.474961\pi\)
0.0785823 + 0.996908i \(0.474961\pi\)
\(158\) −9.75174 −0.775807
\(159\) −4.62844 −0.367059
\(160\) −3.05778 −0.241738
\(161\) 5.09372 0.401441
\(162\) −1.00000 −0.0785674
\(163\) −7.74059 −0.606290 −0.303145 0.952944i \(-0.598037\pi\)
−0.303145 + 0.952944i \(0.598037\pi\)
\(164\) 3.75695 0.293369
\(165\) −10.3414 −0.805076
\(166\) −10.3190 −0.800910
\(167\) −11.9612 −0.925586 −0.462793 0.886466i \(-0.653153\pi\)
−0.462793 + 0.886466i \(0.653153\pi\)
\(168\) −1.53628 −0.118527
\(169\) −11.9527 −0.919435
\(170\) 3.05778 0.234521
\(171\) 3.86050 0.295220
\(172\) −10.5037 −0.800902
\(173\) 9.90009 0.752690 0.376345 0.926480i \(-0.377181\pi\)
0.376345 + 0.926480i \(0.377181\pi\)
\(174\) −9.99843 −0.757979
\(175\) 6.68282 0.505174
\(176\) −3.38200 −0.254928
\(177\) −1.00000 −0.0751646
\(178\) −6.45613 −0.483907
\(179\) 11.8577 0.886287 0.443144 0.896451i \(-0.353863\pi\)
0.443144 + 0.896451i \(0.353863\pi\)
\(180\) 3.05778 0.227913
\(181\) −8.80388 −0.654387 −0.327194 0.944957i \(-0.606103\pi\)
−0.327194 + 0.944957i \(0.606103\pi\)
\(182\) 1.57223 0.116541
\(183\) −7.29167 −0.539016
\(184\) −3.31561 −0.244430
\(185\) 21.3049 1.56637
\(186\) 0.616436 0.0451993
\(187\) 3.38200 0.247316
\(188\) 1.24801 0.0910204
\(189\) 1.53628 0.111748
\(190\) −11.8046 −0.856392
\(191\) 3.26517 0.236260 0.118130 0.992998i \(-0.462310\pi\)
0.118130 + 0.992998i \(0.462310\pi\)
\(192\) 1.00000 0.0721688
\(193\) −0.975034 −0.0701845 −0.0350922 0.999384i \(-0.511172\pi\)
−0.0350922 + 0.999384i \(0.511172\pi\)
\(194\) −3.62504 −0.260263
\(195\) −3.12932 −0.224095
\(196\) −4.63983 −0.331417
\(197\) 6.24305 0.444799 0.222399 0.974956i \(-0.428611\pi\)
0.222399 + 0.974956i \(0.428611\pi\)
\(198\) 3.38200 0.240348
\(199\) −14.1931 −1.00612 −0.503060 0.864251i \(-0.667793\pi\)
−0.503060 + 0.864251i \(0.667793\pi\)
\(200\) −4.34999 −0.307591
\(201\) 11.4731 0.809252
\(202\) −2.67082 −0.187918
\(203\) 15.3604 1.07809
\(204\) −1.00000 −0.0700140
\(205\) 11.4879 0.802351
\(206\) −1.34525 −0.0937277
\(207\) 3.31561 0.230451
\(208\) −1.02340 −0.0709599
\(209\) −13.0562 −0.903117
\(210\) −4.69761 −0.324166
\(211\) 1.85088 0.127420 0.0637098 0.997968i \(-0.479707\pi\)
0.0637098 + 0.997968i \(0.479707\pi\)
\(212\) −4.62844 −0.317882
\(213\) 3.33520 0.228524
\(214\) −11.1785 −0.764149
\(215\) −32.1181 −2.19043
\(216\) −1.00000 −0.0680414
\(217\) −0.947020 −0.0642879
\(218\) 7.90967 0.535711
\(219\) −6.75436 −0.456418
\(220\) −10.3414 −0.697216
\(221\) 1.02340 0.0688412
\(222\) −6.96745 −0.467624
\(223\) −10.7496 −0.719848 −0.359924 0.932982i \(-0.617197\pi\)
−0.359924 + 0.932982i \(0.617197\pi\)
\(224\) −1.53628 −0.102647
\(225\) 4.34999 0.289999
\(226\) 5.61589 0.373563
\(227\) 10.3425 0.686458 0.343229 0.939252i \(-0.388479\pi\)
0.343229 + 0.939252i \(0.388479\pi\)
\(228\) 3.86050 0.255668
\(229\) 6.28585 0.415381 0.207690 0.978195i \(-0.433405\pi\)
0.207690 + 0.978195i \(0.433405\pi\)
\(230\) −10.1384 −0.668506
\(231\) −5.19570 −0.341852
\(232\) −9.99843 −0.656429
\(233\) 18.9550 1.24179 0.620893 0.783896i \(-0.286770\pi\)
0.620893 + 0.783896i \(0.286770\pi\)
\(234\) 1.02340 0.0669016
\(235\) 3.81613 0.248937
\(236\) −1.00000 −0.0650945
\(237\) 9.75174 0.633444
\(238\) 1.53628 0.0995825
\(239\) 12.1587 0.786481 0.393241 0.919436i \(-0.371354\pi\)
0.393241 + 0.919436i \(0.371354\pi\)
\(240\) 3.05778 0.197379
\(241\) 12.7987 0.824434 0.412217 0.911086i \(-0.364754\pi\)
0.412217 + 0.911086i \(0.364754\pi\)
\(242\) −0.437896 −0.0281490
\(243\) 1.00000 0.0641500
\(244\) −7.29167 −0.466801
\(245\) −14.1876 −0.906411
\(246\) −3.75695 −0.239535
\(247\) −3.95083 −0.251385
\(248\) 0.616436 0.0391437
\(249\) 10.3190 0.653940
\(250\) 1.98758 0.125706
\(251\) −21.4380 −1.35315 −0.676576 0.736373i \(-0.736537\pi\)
−0.676576 + 0.736373i \(0.736537\pi\)
\(252\) 1.53628 0.0967767
\(253\) −11.2134 −0.704980
\(254\) −22.2111 −1.39365
\(255\) −3.05778 −0.191485
\(256\) 1.00000 0.0625000
\(257\) −1.26962 −0.0791968 −0.0395984 0.999216i \(-0.512608\pi\)
−0.0395984 + 0.999216i \(0.512608\pi\)
\(258\) 10.5037 0.653934
\(259\) 10.7040 0.665113
\(260\) −3.12932 −0.194072
\(261\) 9.99843 0.618887
\(262\) −4.20710 −0.259916
\(263\) −19.9569 −1.23059 −0.615296 0.788296i \(-0.710964\pi\)
−0.615296 + 0.788296i \(0.710964\pi\)
\(264\) 3.38200 0.208147
\(265\) −14.1527 −0.869395
\(266\) −5.93083 −0.363642
\(267\) 6.45613 0.395109
\(268\) 11.4731 0.700833
\(269\) −13.9073 −0.847943 −0.423972 0.905676i \(-0.639364\pi\)
−0.423972 + 0.905676i \(0.639364\pi\)
\(270\) −3.05778 −0.186090
\(271\) 13.8785 0.843060 0.421530 0.906814i \(-0.361493\pi\)
0.421530 + 0.906814i \(0.361493\pi\)
\(272\) −1.00000 −0.0606339
\(273\) −1.57223 −0.0951556
\(274\) −6.31269 −0.381364
\(275\) −14.7117 −0.887146
\(276\) 3.31561 0.199576
\(277\) 15.5930 0.936895 0.468447 0.883491i \(-0.344814\pi\)
0.468447 + 0.883491i \(0.344814\pi\)
\(278\) −10.5233 −0.631147
\(279\) −0.616436 −0.0369050
\(280\) −4.69761 −0.280736
\(281\) 2.76080 0.164695 0.0823477 0.996604i \(-0.473758\pi\)
0.0823477 + 0.996604i \(0.473758\pi\)
\(282\) −1.24801 −0.0743178
\(283\) −30.9950 −1.84246 −0.921232 0.389014i \(-0.872816\pi\)
−0.921232 + 0.389014i \(0.872816\pi\)
\(284\) 3.33520 0.197908
\(285\) 11.8046 0.699241
\(286\) −3.46113 −0.204661
\(287\) 5.77174 0.340695
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) −30.5730 −1.79531
\(291\) 3.62504 0.212504
\(292\) −6.75436 −0.395269
\(293\) 16.4014 0.958180 0.479090 0.877766i \(-0.340967\pi\)
0.479090 + 0.877766i \(0.340967\pi\)
\(294\) 4.63983 0.270601
\(295\) −3.05778 −0.178031
\(296\) −6.96745 −0.404975
\(297\) −3.38200 −0.196243
\(298\) 11.0906 0.642460
\(299\) −3.39319 −0.196233
\(300\) 4.34999 0.251147
\(301\) −16.1367 −0.930104
\(302\) 3.05298 0.175679
\(303\) 2.67082 0.153434
\(304\) 3.86050 0.221415
\(305\) −22.2963 −1.27668
\(306\) 1.00000 0.0571662
\(307\) 34.1464 1.94884 0.974419 0.224738i \(-0.0721525\pi\)
0.974419 + 0.224738i \(0.0721525\pi\)
\(308\) −5.19570 −0.296053
\(309\) 1.34525 0.0765283
\(310\) 1.88492 0.107056
\(311\) 3.87360 0.219652 0.109826 0.993951i \(-0.464971\pi\)
0.109826 + 0.993951i \(0.464971\pi\)
\(312\) 1.02340 0.0579385
\(313\) −17.8845 −1.01089 −0.505446 0.862858i \(-0.668672\pi\)
−0.505446 + 0.862858i \(0.668672\pi\)
\(314\) −1.96927 −0.111132
\(315\) 4.69761 0.264680
\(316\) 9.75174 0.548578
\(317\) −1.56824 −0.0880810 −0.0440405 0.999030i \(-0.514023\pi\)
−0.0440405 + 0.999030i \(0.514023\pi\)
\(318\) 4.62844 0.259550
\(319\) −33.8147 −1.89326
\(320\) 3.05778 0.170935
\(321\) 11.1785 0.623925
\(322\) −5.09372 −0.283862
\(323\) −3.86050 −0.214804
\(324\) 1.00000 0.0555556
\(325\) −4.45177 −0.246940
\(326\) 7.74059 0.428712
\(327\) −7.90967 −0.437406
\(328\) −3.75695 −0.207443
\(329\) 1.91729 0.105704
\(330\) 10.3414 0.569274
\(331\) 8.06808 0.443462 0.221731 0.975108i \(-0.428829\pi\)
0.221731 + 0.975108i \(0.428829\pi\)
\(332\) 10.3190 0.566329
\(333\) 6.96745 0.381814
\(334\) 11.9612 0.654488
\(335\) 35.0822 1.91675
\(336\) 1.53628 0.0838111
\(337\) −15.9269 −0.867593 −0.433796 0.901011i \(-0.642826\pi\)
−0.433796 + 0.901011i \(0.642826\pi\)
\(338\) 11.9527 0.650139
\(339\) −5.61589 −0.305013
\(340\) −3.05778 −0.165831
\(341\) 2.08478 0.112897
\(342\) −3.86050 −0.208752
\(343\) −17.8821 −0.965542
\(344\) 10.5037 0.566323
\(345\) 10.1384 0.545833
\(346\) −9.90009 −0.532232
\(347\) 1.86486 0.100111 0.0500555 0.998746i \(-0.484060\pi\)
0.0500555 + 0.998746i \(0.484060\pi\)
\(348\) 9.99843 0.535972
\(349\) −26.4402 −1.41531 −0.707655 0.706559i \(-0.750247\pi\)
−0.707655 + 0.706559i \(0.750247\pi\)
\(350\) −6.68282 −0.357212
\(351\) −1.02340 −0.0546249
\(352\) 3.38200 0.180261
\(353\) 20.1982 1.07504 0.537522 0.843250i \(-0.319361\pi\)
0.537522 + 0.843250i \(0.319361\pi\)
\(354\) 1.00000 0.0531494
\(355\) 10.1983 0.541269
\(356\) 6.45613 0.342174
\(357\) −1.53628 −0.0813087
\(358\) −11.8577 −0.626700
\(359\) −16.8608 −0.889877 −0.444938 0.895561i \(-0.646774\pi\)
−0.444938 + 0.895561i \(0.646774\pi\)
\(360\) −3.05778 −0.161159
\(361\) −4.09651 −0.215606
\(362\) 8.80388 0.462722
\(363\) 0.437896 0.0229836
\(364\) −1.57223 −0.0824072
\(365\) −20.6533 −1.08104
\(366\) 7.29167 0.381142
\(367\) −31.4836 −1.64343 −0.821714 0.569900i \(-0.806982\pi\)
−0.821714 + 0.569900i \(0.806982\pi\)
\(368\) 3.31561 0.172838
\(369\) 3.75695 0.195579
\(370\) −21.3049 −1.10759
\(371\) −7.11059 −0.369163
\(372\) −0.616436 −0.0319607
\(373\) −1.57431 −0.0815145 −0.0407572 0.999169i \(-0.512977\pi\)
−0.0407572 + 0.999169i \(0.512977\pi\)
\(374\) −3.38200 −0.174879
\(375\) −1.98758 −0.102638
\(376\) −1.24801 −0.0643611
\(377\) −10.2324 −0.526994
\(378\) −1.53628 −0.0790179
\(379\) 23.0239 1.18266 0.591328 0.806431i \(-0.298604\pi\)
0.591328 + 0.806431i \(0.298604\pi\)
\(380\) 11.8046 0.605561
\(381\) 22.2111 1.13791
\(382\) −3.26517 −0.167061
\(383\) 9.17617 0.468880 0.234440 0.972131i \(-0.424674\pi\)
0.234440 + 0.972131i \(0.424674\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −15.8873 −0.809692
\(386\) 0.975034 0.0496279
\(387\) −10.5037 −0.533935
\(388\) 3.62504 0.184034
\(389\) 8.17625 0.414552 0.207276 0.978282i \(-0.433540\pi\)
0.207276 + 0.978282i \(0.433540\pi\)
\(390\) 3.12932 0.158459
\(391\) −3.31561 −0.167678
\(392\) 4.63983 0.234347
\(393\) 4.20710 0.212220
\(394\) −6.24305 −0.314520
\(395\) 29.8186 1.50034
\(396\) −3.38200 −0.169952
\(397\) −25.7166 −1.29068 −0.645341 0.763895i \(-0.723285\pi\)
−0.645341 + 0.763895i \(0.723285\pi\)
\(398\) 14.1931 0.711435
\(399\) 5.93083 0.296913
\(400\) 4.34999 0.217500
\(401\) 6.66798 0.332983 0.166491 0.986043i \(-0.446756\pi\)
0.166491 + 0.986043i \(0.446756\pi\)
\(402\) −11.4731 −0.572228
\(403\) 0.630859 0.0314253
\(404\) 2.67082 0.132878
\(405\) 3.05778 0.151942
\(406\) −15.3604 −0.762325
\(407\) −23.5639 −1.16802
\(408\) 1.00000 0.0495074
\(409\) −1.00352 −0.0496206 −0.0248103 0.999692i \(-0.507898\pi\)
−0.0248103 + 0.999692i \(0.507898\pi\)
\(410\) −11.4879 −0.567348
\(411\) 6.31269 0.311382
\(412\) 1.34525 0.0662755
\(413\) −1.53628 −0.0755956
\(414\) −3.31561 −0.162954
\(415\) 31.5532 1.54889
\(416\) 1.02340 0.0501762
\(417\) 10.5233 0.515329
\(418\) 13.0562 0.638600
\(419\) −21.4897 −1.04984 −0.524919 0.851152i \(-0.675905\pi\)
−0.524919 + 0.851152i \(0.675905\pi\)
\(420\) 4.69761 0.229220
\(421\) 2.94777 0.143666 0.0718329 0.997417i \(-0.477115\pi\)
0.0718329 + 0.997417i \(0.477115\pi\)
\(422\) −1.85088 −0.0900992
\(423\) 1.24801 0.0606803
\(424\) 4.62844 0.224777
\(425\) −4.34999 −0.211006
\(426\) −3.33520 −0.161591
\(427\) −11.2021 −0.542106
\(428\) 11.1785 0.540335
\(429\) 3.46113 0.167105
\(430\) 32.1181 1.54887
\(431\) 34.9160 1.68185 0.840923 0.541155i \(-0.182013\pi\)
0.840923 + 0.541155i \(0.182013\pi\)
\(432\) 1.00000 0.0481125
\(433\) −30.4654 −1.46407 −0.732037 0.681265i \(-0.761430\pi\)
−0.732037 + 0.681265i \(0.761430\pi\)
\(434\) 0.947020 0.0454584
\(435\) 30.5730 1.46586
\(436\) −7.90967 −0.378805
\(437\) 12.7999 0.612304
\(438\) 6.75436 0.322736
\(439\) 25.7830 1.23055 0.615277 0.788311i \(-0.289044\pi\)
0.615277 + 0.788311i \(0.289044\pi\)
\(440\) 10.3414 0.493006
\(441\) −4.63983 −0.220944
\(442\) −1.02340 −0.0486781
\(443\) 22.9987 1.09270 0.546350 0.837557i \(-0.316017\pi\)
0.546350 + 0.837557i \(0.316017\pi\)
\(444\) 6.96745 0.330660
\(445\) 19.7414 0.935832
\(446\) 10.7496 0.509009
\(447\) −11.0906 −0.524567
\(448\) 1.53628 0.0725826
\(449\) 16.8056 0.793104 0.396552 0.918012i \(-0.370207\pi\)
0.396552 + 0.918012i \(0.370207\pi\)
\(450\) −4.34999 −0.205061
\(451\) −12.7060 −0.598302
\(452\) −5.61589 −0.264149
\(453\) −3.05298 −0.143442
\(454\) −10.3425 −0.485399
\(455\) −4.80752 −0.225380
\(456\) −3.86050 −0.180785
\(457\) −6.66524 −0.311787 −0.155893 0.987774i \(-0.549826\pi\)
−0.155893 + 0.987774i \(0.549826\pi\)
\(458\) −6.28585 −0.293719
\(459\) −1.00000 −0.0466760
\(460\) 10.1384 0.472705
\(461\) −8.84232 −0.411828 −0.205914 0.978570i \(-0.566017\pi\)
−0.205914 + 0.978570i \(0.566017\pi\)
\(462\) 5.19570 0.241726
\(463\) −12.9431 −0.601516 −0.300758 0.953701i \(-0.597240\pi\)
−0.300758 + 0.953701i \(0.597240\pi\)
\(464\) 9.99843 0.464166
\(465\) −1.88492 −0.0874112
\(466\) −18.9550 −0.878075
\(467\) 34.7988 1.61030 0.805149 0.593072i \(-0.202085\pi\)
0.805149 + 0.593072i \(0.202085\pi\)
\(468\) −1.02340 −0.0473066
\(469\) 17.6260 0.813892
\(470\) −3.81613 −0.176025
\(471\) 1.96927 0.0907391
\(472\) 1.00000 0.0460287
\(473\) 35.5236 1.63338
\(474\) −9.75174 −0.447912
\(475\) 16.7932 0.770523
\(476\) −1.53628 −0.0704154
\(477\) −4.62844 −0.211922
\(478\) −12.1587 −0.556126
\(479\) 1.23920 0.0566205 0.0283103 0.999599i \(-0.490987\pi\)
0.0283103 + 0.999599i \(0.490987\pi\)
\(480\) −3.05778 −0.139568
\(481\) −7.13047 −0.325122
\(482\) −12.7987 −0.582963
\(483\) 5.09372 0.231772
\(484\) 0.437896 0.0199044
\(485\) 11.0846 0.503324
\(486\) −1.00000 −0.0453609
\(487\) 23.1162 1.04750 0.523748 0.851873i \(-0.324533\pi\)
0.523748 + 0.851873i \(0.324533\pi\)
\(488\) 7.29167 0.330078
\(489\) −7.74059 −0.350042
\(490\) 14.1876 0.640929
\(491\) 7.59394 0.342710 0.171355 0.985209i \(-0.445186\pi\)
0.171355 + 0.985209i \(0.445186\pi\)
\(492\) 3.75695 0.169377
\(493\) −9.99843 −0.450307
\(494\) 3.95083 0.177756
\(495\) −10.3414 −0.464811
\(496\) −0.616436 −0.0276788
\(497\) 5.12381 0.229834
\(498\) −10.3190 −0.462406
\(499\) −5.98394 −0.267878 −0.133939 0.990990i \(-0.542763\pi\)
−0.133939 + 0.990990i \(0.542763\pi\)
\(500\) −1.98758 −0.0888874
\(501\) −11.9612 −0.534388
\(502\) 21.4380 0.956823
\(503\) −17.8750 −0.797005 −0.398503 0.917167i \(-0.630470\pi\)
−0.398503 + 0.917167i \(0.630470\pi\)
\(504\) −1.53628 −0.0684315
\(505\) 8.16676 0.363416
\(506\) 11.2134 0.498496
\(507\) −11.9527 −0.530836
\(508\) 22.2111 0.985458
\(509\) −18.2491 −0.808876 −0.404438 0.914566i \(-0.632533\pi\)
−0.404438 + 0.914566i \(0.632533\pi\)
\(510\) 3.05778 0.135401
\(511\) −10.3766 −0.459034
\(512\) −1.00000 −0.0441942
\(513\) 3.86050 0.170445
\(514\) 1.26962 0.0560006
\(515\) 4.11346 0.181261
\(516\) −10.5037 −0.462401
\(517\) −4.22076 −0.185629
\(518\) −10.7040 −0.470306
\(519\) 9.90009 0.434566
\(520\) 3.12932 0.137230
\(521\) −29.4612 −1.29072 −0.645359 0.763880i \(-0.723292\pi\)
−0.645359 + 0.763880i \(0.723292\pi\)
\(522\) −9.99843 −0.437619
\(523\) −1.39480 −0.0609901 −0.0304951 0.999535i \(-0.509708\pi\)
−0.0304951 + 0.999535i \(0.509708\pi\)
\(524\) 4.20710 0.183788
\(525\) 6.68282 0.291662
\(526\) 19.9569 0.870160
\(527\) 0.616436 0.0268524
\(528\) −3.38200 −0.147182
\(529\) −12.0067 −0.522031
\(530\) 14.1527 0.614755
\(531\) −1.00000 −0.0433963
\(532\) 5.93083 0.257134
\(533\) −3.84486 −0.166539
\(534\) −6.45613 −0.279384
\(535\) 34.1815 1.47779
\(536\) −11.4731 −0.495564
\(537\) 11.8577 0.511698
\(538\) 13.9073 0.599586
\(539\) 15.6919 0.675898
\(540\) 3.05778 0.131586
\(541\) −16.4269 −0.706249 −0.353124 0.935576i \(-0.614881\pi\)
−0.353124 + 0.935576i \(0.614881\pi\)
\(542\) −13.8785 −0.596134
\(543\) −8.80388 −0.377811
\(544\) 1.00000 0.0428746
\(545\) −24.1860 −1.03601
\(546\) 1.57223 0.0672852
\(547\) −14.7145 −0.629146 −0.314573 0.949233i \(-0.601861\pi\)
−0.314573 + 0.949233i \(0.601861\pi\)
\(548\) 6.31269 0.269665
\(549\) −7.29167 −0.311201
\(550\) 14.7117 0.627307
\(551\) 38.5990 1.64437
\(552\) −3.31561 −0.141122
\(553\) 14.9814 0.637075
\(554\) −15.5930 −0.662485
\(555\) 21.3049 0.904342
\(556\) 10.5233 0.446288
\(557\) −3.30447 −0.140015 −0.0700074 0.997546i \(-0.522302\pi\)
−0.0700074 + 0.997546i \(0.522302\pi\)
\(558\) 0.616436 0.0260958
\(559\) 10.7495 0.454655
\(560\) 4.69761 0.198510
\(561\) 3.38200 0.142788
\(562\) −2.76080 −0.116457
\(563\) −0.999402 −0.0421198 −0.0210599 0.999778i \(-0.506704\pi\)
−0.0210599 + 0.999778i \(0.506704\pi\)
\(564\) 1.24801 0.0525506
\(565\) −17.1721 −0.722437
\(566\) 30.9950 1.30282
\(567\) 1.53628 0.0645178
\(568\) −3.33520 −0.139942
\(569\) 40.3931 1.69337 0.846684 0.532097i \(-0.178596\pi\)
0.846684 + 0.532097i \(0.178596\pi\)
\(570\) −11.8046 −0.494438
\(571\) 11.4501 0.479171 0.239585 0.970875i \(-0.422989\pi\)
0.239585 + 0.970875i \(0.422989\pi\)
\(572\) 3.46113 0.144717
\(573\) 3.26517 0.136405
\(574\) −5.77174 −0.240908
\(575\) 14.4229 0.601476
\(576\) 1.00000 0.0416667
\(577\) −21.1757 −0.881556 −0.440778 0.897616i \(-0.645297\pi\)
−0.440778 + 0.897616i \(0.645297\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −0.975034 −0.0405210
\(580\) 30.5730 1.26947
\(581\) 15.8529 0.657690
\(582\) −3.62504 −0.150263
\(583\) 15.6534 0.648296
\(584\) 6.75436 0.279498
\(585\) −3.12932 −0.129382
\(586\) −16.4014 −0.677536
\(587\) −12.9790 −0.535701 −0.267851 0.963460i \(-0.586313\pi\)
−0.267851 + 0.963460i \(0.586313\pi\)
\(588\) −4.63983 −0.191344
\(589\) −2.37975 −0.0980560
\(590\) 3.05778 0.125887
\(591\) 6.24305 0.256805
\(592\) 6.96745 0.286360
\(593\) 30.2200 1.24098 0.620492 0.784212i \(-0.286933\pi\)
0.620492 + 0.784212i \(0.286933\pi\)
\(594\) 3.38200 0.138765
\(595\) −4.69761 −0.192583
\(596\) −11.0906 −0.454288
\(597\) −14.1931 −0.580884
\(598\) 3.39319 0.138758
\(599\) 1.20562 0.0492604 0.0246302 0.999697i \(-0.492159\pi\)
0.0246302 + 0.999697i \(0.492159\pi\)
\(600\) −4.34999 −0.177588
\(601\) −35.4744 −1.44703 −0.723516 0.690307i \(-0.757475\pi\)
−0.723516 + 0.690307i \(0.757475\pi\)
\(602\) 16.1367 0.657683
\(603\) 11.4731 0.467222
\(604\) −3.05298 −0.124224
\(605\) 1.33899 0.0544376
\(606\) −2.67082 −0.108495
\(607\) −14.3527 −0.582557 −0.291278 0.956638i \(-0.594081\pi\)
−0.291278 + 0.956638i \(0.594081\pi\)
\(608\) −3.86050 −0.156564
\(609\) 15.3604 0.622436
\(610\) 22.2963 0.902750
\(611\) −1.27721 −0.0516704
\(612\) −1.00000 −0.0404226
\(613\) −25.5760 −1.03301 −0.516503 0.856286i \(-0.672766\pi\)
−0.516503 + 0.856286i \(0.672766\pi\)
\(614\) −34.1464 −1.37804
\(615\) 11.4879 0.463238
\(616\) 5.19570 0.209341
\(617\) 0.275470 0.0110900 0.00554500 0.999985i \(-0.498235\pi\)
0.00554500 + 0.999985i \(0.498235\pi\)
\(618\) −1.34525 −0.0541137
\(619\) −7.83256 −0.314817 −0.157409 0.987534i \(-0.550314\pi\)
−0.157409 + 0.987534i \(0.550314\pi\)
\(620\) −1.88492 −0.0757003
\(621\) 3.31561 0.133051
\(622\) −3.87360 −0.155317
\(623\) 9.91845 0.397374
\(624\) −1.02340 −0.0409687
\(625\) −27.8275 −1.11310
\(626\) 17.8845 0.714809
\(627\) −13.0562 −0.521415
\(628\) 1.96927 0.0785823
\(629\) −6.96745 −0.277810
\(630\) −4.69761 −0.187157
\(631\) 3.49029 0.138946 0.0694731 0.997584i \(-0.477868\pi\)
0.0694731 + 0.997584i \(0.477868\pi\)
\(632\) −9.75174 −0.387903
\(633\) 1.85088 0.0735657
\(634\) 1.56824 0.0622827
\(635\) 67.9165 2.69519
\(636\) −4.62844 −0.183529
\(637\) 4.74840 0.188138
\(638\) 33.8147 1.33873
\(639\) 3.33520 0.131938
\(640\) −3.05778 −0.120869
\(641\) 4.58902 0.181255 0.0906276 0.995885i \(-0.471113\pi\)
0.0906276 + 0.995885i \(0.471113\pi\)
\(642\) −11.1785 −0.441182
\(643\) −29.3717 −1.15831 −0.579153 0.815219i \(-0.696617\pi\)
−0.579153 + 0.815219i \(0.696617\pi\)
\(644\) 5.09372 0.200721
\(645\) −32.1181 −1.26465
\(646\) 3.86050 0.151889
\(647\) −25.2818 −0.993929 −0.496964 0.867771i \(-0.665552\pi\)
−0.496964 + 0.867771i \(0.665552\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 3.38200 0.132755
\(650\) 4.45177 0.174613
\(651\) −0.947020 −0.0371166
\(652\) −7.74059 −0.303145
\(653\) 20.7127 0.810552 0.405276 0.914194i \(-0.367175\pi\)
0.405276 + 0.914194i \(0.367175\pi\)
\(654\) 7.90967 0.309293
\(655\) 12.8644 0.502653
\(656\) 3.75695 0.146684
\(657\) −6.75436 −0.263513
\(658\) −1.91729 −0.0747439
\(659\) −38.2348 −1.48941 −0.744707 0.667391i \(-0.767411\pi\)
−0.744707 + 0.667391i \(0.767411\pi\)
\(660\) −10.3414 −0.402538
\(661\) −32.9603 −1.28201 −0.641004 0.767538i \(-0.721482\pi\)
−0.641004 + 0.767538i \(0.721482\pi\)
\(662\) −8.06808 −0.313575
\(663\) 1.02340 0.0397455
\(664\) −10.3190 −0.400455
\(665\) 18.1351 0.703250
\(666\) −6.96745 −0.269983
\(667\) 33.1509 1.28361
\(668\) −11.9612 −0.462793
\(669\) −10.7496 −0.415604
\(670\) −35.0822 −1.35535
\(671\) 24.6604 0.952004
\(672\) −1.53628 −0.0592634
\(673\) 6.85541 0.264257 0.132128 0.991233i \(-0.457819\pi\)
0.132128 + 0.991233i \(0.457819\pi\)
\(674\) 15.9269 0.613481
\(675\) 4.34999 0.167431
\(676\) −11.9527 −0.459718
\(677\) 42.2197 1.62263 0.811317 0.584607i \(-0.198751\pi\)
0.811317 + 0.584607i \(0.198751\pi\)
\(678\) 5.61589 0.215677
\(679\) 5.56909 0.213722
\(680\) 3.05778 0.117260
\(681\) 10.3425 0.396327
\(682\) −2.08478 −0.0798305
\(683\) −43.9874 −1.68313 −0.841565 0.540156i \(-0.818365\pi\)
−0.841565 + 0.540156i \(0.818365\pi\)
\(684\) 3.86050 0.147610
\(685\) 19.3028 0.737522
\(686\) 17.8821 0.682741
\(687\) 6.28585 0.239820
\(688\) −10.5037 −0.400451
\(689\) 4.73673 0.180455
\(690\) −10.1384 −0.385962
\(691\) 18.2747 0.695203 0.347601 0.937642i \(-0.386996\pi\)
0.347601 + 0.937642i \(0.386996\pi\)
\(692\) 9.90009 0.376345
\(693\) −5.19570 −0.197368
\(694\) −1.86486 −0.0707892
\(695\) 32.1779 1.22058
\(696\) −9.99843 −0.378990
\(697\) −3.75695 −0.142305
\(698\) 26.4402 1.00077
\(699\) 18.9550 0.716945
\(700\) 6.68282 0.252587
\(701\) −37.1275 −1.40229 −0.701143 0.713020i \(-0.747327\pi\)
−0.701143 + 0.713020i \(0.747327\pi\)
\(702\) 1.02340 0.0386257
\(703\) 26.8979 1.01447
\(704\) −3.38200 −0.127464
\(705\) 3.81613 0.143724
\(706\) −20.1982 −0.760171
\(707\) 4.10313 0.154314
\(708\) −1.00000 −0.0375823
\(709\) 4.42022 0.166005 0.0830025 0.996549i \(-0.473549\pi\)
0.0830025 + 0.996549i \(0.473549\pi\)
\(710\) −10.1983 −0.382735
\(711\) 9.75174 0.365719
\(712\) −6.45613 −0.241954
\(713\) −2.04386 −0.0765433
\(714\) 1.53628 0.0574940
\(715\) 10.5834 0.395795
\(716\) 11.8577 0.443144
\(717\) 12.1587 0.454075
\(718\) 16.8608 0.629238
\(719\) 18.2091 0.679085 0.339543 0.940591i \(-0.389728\pi\)
0.339543 + 0.940591i \(0.389728\pi\)
\(720\) 3.05778 0.113957
\(721\) 2.06668 0.0769671
\(722\) 4.09651 0.152456
\(723\) 12.7987 0.475987
\(724\) −8.80388 −0.327194
\(725\) 43.4931 1.61529
\(726\) −0.437896 −0.0162518
\(727\) 22.8229 0.846453 0.423227 0.906024i \(-0.360897\pi\)
0.423227 + 0.906024i \(0.360897\pi\)
\(728\) 1.57223 0.0582707
\(729\) 1.00000 0.0370370
\(730\) 20.6533 0.764414
\(731\) 10.5037 0.388495
\(732\) −7.29167 −0.269508
\(733\) −14.8713 −0.549285 −0.274642 0.961546i \(-0.588559\pi\)
−0.274642 + 0.961546i \(0.588559\pi\)
\(734\) 31.4836 1.16208
\(735\) −14.1876 −0.523316
\(736\) −3.31561 −0.122215
\(737\) −38.8021 −1.42929
\(738\) −3.75695 −0.138295
\(739\) 29.3269 1.07881 0.539404 0.842047i \(-0.318649\pi\)
0.539404 + 0.842047i \(0.318649\pi\)
\(740\) 21.3049 0.783183
\(741\) −3.95083 −0.145137
\(742\) 7.11059 0.261038
\(743\) −52.6541 −1.93169 −0.965846 0.259115i \(-0.916569\pi\)
−0.965846 + 0.259115i \(0.916569\pi\)
\(744\) 0.616436 0.0225996
\(745\) −33.9125 −1.24246
\(746\) 1.57431 0.0576394
\(747\) 10.3190 0.377553
\(748\) 3.38200 0.123658
\(749\) 17.1734 0.627503
\(750\) 1.98758 0.0725762
\(751\) −38.6248 −1.40944 −0.704719 0.709486i \(-0.748927\pi\)
−0.704719 + 0.709486i \(0.748927\pi\)
\(752\) 1.24801 0.0455102
\(753\) −21.4380 −0.781242
\(754\) 10.2324 0.372641
\(755\) −9.33533 −0.339747
\(756\) 1.53628 0.0558741
\(757\) 41.6929 1.51536 0.757678 0.652629i \(-0.226334\pi\)
0.757678 + 0.652629i \(0.226334\pi\)
\(758\) −23.0239 −0.836265
\(759\) −11.2134 −0.407020
\(760\) −11.8046 −0.428196
\(761\) −9.92565 −0.359804 −0.179902 0.983684i \(-0.557578\pi\)
−0.179902 + 0.983684i \(0.557578\pi\)
\(762\) −22.2111 −0.804623
\(763\) −12.1515 −0.439914
\(764\) 3.26517 0.118130
\(765\) −3.05778 −0.110554
\(766\) −9.17617 −0.331548
\(767\) 1.02340 0.0369528
\(768\) 1.00000 0.0360844
\(769\) 10.0493 0.362387 0.181193 0.983447i \(-0.442004\pi\)
0.181193 + 0.983447i \(0.442004\pi\)
\(770\) 15.8873 0.572538
\(771\) −1.26962 −0.0457243
\(772\) −0.975034 −0.0350922
\(773\) −17.5416 −0.630929 −0.315464 0.948937i \(-0.602160\pi\)
−0.315464 + 0.948937i \(0.602160\pi\)
\(774\) 10.5037 0.377549
\(775\) −2.68149 −0.0963220
\(776\) −3.62504 −0.130131
\(777\) 10.7040 0.384003
\(778\) −8.17625 −0.293133
\(779\) 14.5037 0.519650
\(780\) −3.12932 −0.112048
\(781\) −11.2796 −0.403617
\(782\) 3.31561 0.118566
\(783\) 9.99843 0.357315
\(784\) −4.63983 −0.165708
\(785\) 6.02158 0.214919
\(786\) −4.20710 −0.150062
\(787\) −18.3262 −0.653260 −0.326630 0.945152i \(-0.605913\pi\)
−0.326630 + 0.945152i \(0.605913\pi\)
\(788\) 6.24305 0.222399
\(789\) −19.9569 −0.710483
\(790\) −29.8186 −1.06090
\(791\) −8.62760 −0.306762
\(792\) 3.38200 0.120174
\(793\) 7.46228 0.264993
\(794\) 25.7166 0.912650
\(795\) −14.1527 −0.501945
\(796\) −14.1931 −0.503060
\(797\) 7.85337 0.278181 0.139090 0.990280i \(-0.455582\pi\)
0.139090 + 0.990280i \(0.455582\pi\)
\(798\) −5.93083 −0.209949
\(799\) −1.24801 −0.0441514
\(800\) −4.34999 −0.153795
\(801\) 6.45613 0.228116
\(802\) −6.66798 −0.235454
\(803\) 22.8432 0.806120
\(804\) 11.4731 0.404626
\(805\) 15.5755 0.548963
\(806\) −0.630859 −0.0222211
\(807\) −13.9073 −0.489560
\(808\) −2.67082 −0.0939590
\(809\) 2.33219 0.0819956 0.0409978 0.999159i \(-0.486946\pi\)
0.0409978 + 0.999159i \(0.486946\pi\)
\(810\) −3.05778 −0.107439
\(811\) 7.21354 0.253302 0.126651 0.991947i \(-0.459577\pi\)
0.126651 + 0.991947i \(0.459577\pi\)
\(812\) 15.3604 0.539045
\(813\) 13.8785 0.486741
\(814\) 23.5639 0.825914
\(815\) −23.6690 −0.829089
\(816\) −1.00000 −0.0350070
\(817\) −40.5497 −1.41865
\(818\) 1.00352 0.0350871
\(819\) −1.57223 −0.0549381
\(820\) 11.4879 0.401176
\(821\) 11.1461 0.389001 0.194500 0.980902i \(-0.437691\pi\)
0.194500 + 0.980902i \(0.437691\pi\)
\(822\) −6.31269 −0.220180
\(823\) 34.9332 1.21769 0.608847 0.793288i \(-0.291632\pi\)
0.608847 + 0.793288i \(0.291632\pi\)
\(824\) −1.34525 −0.0468639
\(825\) −14.7117 −0.512194
\(826\) 1.53628 0.0534541
\(827\) 34.2325 1.19038 0.595189 0.803585i \(-0.297077\pi\)
0.595189 + 0.803585i \(0.297077\pi\)
\(828\) 3.31561 0.115226
\(829\) −55.3841 −1.92357 −0.961784 0.273808i \(-0.911717\pi\)
−0.961784 + 0.273808i \(0.911717\pi\)
\(830\) −31.5532 −1.09523
\(831\) 15.5930 0.540916
\(832\) −1.02340 −0.0354799
\(833\) 4.63983 0.160761
\(834\) −10.5233 −0.364393
\(835\) −36.5747 −1.26572
\(836\) −13.0562 −0.451558
\(837\) −0.616436 −0.0213071
\(838\) 21.4897 0.742348
\(839\) −13.6335 −0.470680 −0.235340 0.971913i \(-0.575620\pi\)
−0.235340 + 0.971913i \(0.575620\pi\)
\(840\) −4.69761 −0.162083
\(841\) 70.9686 2.44719
\(842\) −2.94777 −0.101587
\(843\) 2.76080 0.0950870
\(844\) 1.85088 0.0637098
\(845\) −36.5485 −1.25731
\(846\) −1.24801 −0.0429074
\(847\) 0.672732 0.0231154
\(848\) −4.62844 −0.158941
\(849\) −30.9950 −1.06375
\(850\) 4.34999 0.149203
\(851\) 23.1014 0.791905
\(852\) 3.33520 0.114262
\(853\) −6.56804 −0.224885 −0.112443 0.993658i \(-0.535867\pi\)
−0.112443 + 0.993658i \(0.535867\pi\)
\(854\) 11.2021 0.383327
\(855\) 11.8046 0.403707
\(856\) −11.1785 −0.382075
\(857\) 40.5970 1.38677 0.693384 0.720568i \(-0.256119\pi\)
0.693384 + 0.720568i \(0.256119\pi\)
\(858\) −3.46113 −0.118161
\(859\) −26.7597 −0.913028 −0.456514 0.889716i \(-0.650902\pi\)
−0.456514 + 0.889716i \(0.650902\pi\)
\(860\) −32.1181 −1.09522
\(861\) 5.77174 0.196701
\(862\) −34.9160 −1.18924
\(863\) −25.3027 −0.861315 −0.430658 0.902515i \(-0.641718\pi\)
−0.430658 + 0.902515i \(0.641718\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 30.2723 1.02929
\(866\) 30.4654 1.03526
\(867\) 1.00000 0.0339618
\(868\) −0.947020 −0.0321440
\(869\) −32.9803 −1.11878
\(870\) −30.5730 −1.03652
\(871\) −11.7416 −0.397848
\(872\) 7.90967 0.267855
\(873\) 3.62504 0.122689
\(874\) −12.7999 −0.432964
\(875\) −3.05349 −0.103227
\(876\) −6.75436 −0.228209
\(877\) −24.1892 −0.816810 −0.408405 0.912801i \(-0.633915\pi\)
−0.408405 + 0.912801i \(0.633915\pi\)
\(878\) −25.7830 −0.870133
\(879\) 16.4014 0.553206
\(880\) −10.3414 −0.348608
\(881\) 17.6275 0.593884 0.296942 0.954895i \(-0.404033\pi\)
0.296942 + 0.954895i \(0.404033\pi\)
\(882\) 4.63983 0.156231
\(883\) 44.8845 1.51048 0.755242 0.655446i \(-0.227519\pi\)
0.755242 + 0.655446i \(0.227519\pi\)
\(884\) 1.02340 0.0344206
\(885\) −3.05778 −0.102786
\(886\) −22.9987 −0.772656
\(887\) −16.9012 −0.567486 −0.283743 0.958900i \(-0.591576\pi\)
−0.283743 + 0.958900i \(0.591576\pi\)
\(888\) −6.96745 −0.233812
\(889\) 34.1225 1.14443
\(890\) −19.7414 −0.661733
\(891\) −3.38200 −0.113301
\(892\) −10.7496 −0.359924
\(893\) 4.81794 0.161226
\(894\) 11.0906 0.370925
\(895\) 36.2582 1.21198
\(896\) −1.53628 −0.0513236
\(897\) −3.39319 −0.113295
\(898\) −16.8056 −0.560809
\(899\) −6.16339 −0.205561
\(900\) 4.34999 0.145000
\(901\) 4.62844 0.154196
\(902\) 12.7060 0.423064
\(903\) −16.1367 −0.536996
\(904\) 5.61589 0.186782
\(905\) −26.9203 −0.894861
\(906\) 3.05298 0.101428
\(907\) −42.9219 −1.42520 −0.712598 0.701572i \(-0.752482\pi\)
−0.712598 + 0.701572i \(0.752482\pi\)
\(908\) 10.3425 0.343229
\(909\) 2.67082 0.0885854
\(910\) 4.80752 0.159368
\(911\) 6.63455 0.219812 0.109906 0.993942i \(-0.464945\pi\)
0.109906 + 0.993942i \(0.464945\pi\)
\(912\) 3.86050 0.127834
\(913\) −34.8988 −1.15498
\(914\) 6.66524 0.220466
\(915\) −22.2963 −0.737092
\(916\) 6.28585 0.207690
\(917\) 6.46330 0.213437
\(918\) 1.00000 0.0330049
\(919\) 40.4623 1.33473 0.667364 0.744732i \(-0.267423\pi\)
0.667364 + 0.744732i \(0.267423\pi\)
\(920\) −10.1384 −0.334253
\(921\) 34.1464 1.12516
\(922\) 8.84232 0.291206
\(923\) −3.41324 −0.112348
\(924\) −5.19570 −0.170926
\(925\) 30.3083 0.996532
\(926\) 12.9431 0.425336
\(927\) 1.34525 0.0441837
\(928\) −9.99843 −0.328215
\(929\) 55.6656 1.82633 0.913165 0.407590i \(-0.133631\pi\)
0.913165 + 0.407590i \(0.133631\pi\)
\(930\) 1.88492 0.0618090
\(931\) −17.9121 −0.587045
\(932\) 18.9550 0.620893
\(933\) 3.87360 0.126816
\(934\) −34.7988 −1.13865
\(935\) 10.3414 0.338199
\(936\) 1.02340 0.0334508
\(937\) 5.06188 0.165364 0.0826821 0.996576i \(-0.473651\pi\)
0.0826821 + 0.996576i \(0.473651\pi\)
\(938\) −17.6260 −0.575508
\(939\) −17.8845 −0.583639
\(940\) 3.81613 0.124468
\(941\) −10.2625 −0.334548 −0.167274 0.985910i \(-0.553496\pi\)
−0.167274 + 0.985910i \(0.553496\pi\)
\(942\) −1.96927 −0.0641622
\(943\) 12.4566 0.405643
\(944\) −1.00000 −0.0325472
\(945\) 4.69761 0.152813
\(946\) −35.5236 −1.15497
\(947\) 2.01141 0.0653619 0.0326809 0.999466i \(-0.489595\pi\)
0.0326809 + 0.999466i \(0.489595\pi\)
\(948\) 9.75174 0.316722
\(949\) 6.91240 0.224386
\(950\) −16.7932 −0.544842
\(951\) −1.56824 −0.0508536
\(952\) 1.53628 0.0497912
\(953\) 37.6195 1.21862 0.609308 0.792934i \(-0.291447\pi\)
0.609308 + 0.792934i \(0.291447\pi\)
\(954\) 4.62844 0.149851
\(955\) 9.98416 0.323080
\(956\) 12.1587 0.393241
\(957\) −33.8147 −1.09307
\(958\) −1.23920 −0.0400367
\(959\) 9.69808 0.313167
\(960\) 3.05778 0.0986893
\(961\) −30.6200 −0.987742
\(962\) 7.13047 0.229896
\(963\) 11.1785 0.360223
\(964\) 12.7987 0.412217
\(965\) −2.98143 −0.0959758
\(966\) −5.09372 −0.163888
\(967\) 9.67552 0.311144 0.155572 0.987825i \(-0.450278\pi\)
0.155572 + 0.987825i \(0.450278\pi\)
\(968\) −0.437896 −0.0140745
\(969\) −3.86050 −0.124017
\(970\) −11.0846 −0.355904
\(971\) 61.1703 1.96305 0.981524 0.191340i \(-0.0612832\pi\)
0.981524 + 0.191340i \(0.0612832\pi\)
\(972\) 1.00000 0.0320750
\(973\) 16.1668 0.518284
\(974\) −23.1162 −0.740692
\(975\) −4.45177 −0.142571
\(976\) −7.29167 −0.233401
\(977\) −11.6550 −0.372877 −0.186439 0.982467i \(-0.559695\pi\)
−0.186439 + 0.982467i \(0.559695\pi\)
\(978\) 7.74059 0.247517
\(979\) −21.8346 −0.697837
\(980\) −14.1876 −0.453205
\(981\) −7.90967 −0.252536
\(982\) −7.59394 −0.242332
\(983\) −10.2688 −0.327525 −0.163762 0.986500i \(-0.552363\pi\)
−0.163762 + 0.986500i \(0.552363\pi\)
\(984\) −3.75695 −0.119767
\(985\) 19.0898 0.608253
\(986\) 9.99843 0.318415
\(987\) 1.91729 0.0610282
\(988\) −3.95083 −0.125693
\(989\) −34.8263 −1.10741
\(990\) 10.3414 0.328671
\(991\) 7.99009 0.253814 0.126907 0.991915i \(-0.459495\pi\)
0.126907 + 0.991915i \(0.459495\pi\)
\(992\) 0.616436 0.0195719
\(993\) 8.06808 0.256033
\(994\) −5.12381 −0.162517
\(995\) −43.3993 −1.37585
\(996\) 10.3190 0.326970
\(997\) −27.3092 −0.864892 −0.432446 0.901660i \(-0.642349\pi\)
−0.432446 + 0.901660i \(0.642349\pi\)
\(998\) 5.98394 0.189418
\(999\) 6.96745 0.220440
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 \(a_p\))