Properties

Label 8015.2.a.l.1.40
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.40
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.970097 q^{2} -0.396968 q^{3} -1.05891 q^{4} -1.00000 q^{5} -0.385098 q^{6} -1.00000 q^{7} -2.96744 q^{8} -2.84242 q^{9} +O(q^{10})\) \(q+0.970097 q^{2} -0.396968 q^{3} -1.05891 q^{4} -1.00000 q^{5} -0.385098 q^{6} -1.00000 q^{7} -2.96744 q^{8} -2.84242 q^{9} -0.970097 q^{10} -2.20338 q^{11} +0.420355 q^{12} +4.66808 q^{13} -0.970097 q^{14} +0.396968 q^{15} -0.760881 q^{16} -3.82317 q^{17} -2.75742 q^{18} -5.08764 q^{19} +1.05891 q^{20} +0.396968 q^{21} -2.13749 q^{22} -8.61116 q^{23} +1.17798 q^{24} +1.00000 q^{25} +4.52849 q^{26} +2.31925 q^{27} +1.05891 q^{28} -6.53813 q^{29} +0.385098 q^{30} -3.90594 q^{31} +5.19675 q^{32} +0.874671 q^{33} -3.70885 q^{34} +1.00000 q^{35} +3.00987 q^{36} +1.56682 q^{37} -4.93550 q^{38} -1.85308 q^{39} +2.96744 q^{40} -10.3901 q^{41} +0.385098 q^{42} -5.42344 q^{43} +2.33318 q^{44} +2.84242 q^{45} -8.35365 q^{46} +4.14775 q^{47} +0.302046 q^{48} +1.00000 q^{49} +0.970097 q^{50} +1.51768 q^{51} -4.94309 q^{52} -1.57645 q^{53} +2.24990 q^{54} +2.20338 q^{55} +2.96744 q^{56} +2.01963 q^{57} -6.34262 q^{58} +8.65116 q^{59} -0.420355 q^{60} +1.84183 q^{61} -3.78914 q^{62} +2.84242 q^{63} +6.56312 q^{64} -4.66808 q^{65} +0.848516 q^{66} +10.0744 q^{67} +4.04840 q^{68} +3.41836 q^{69} +0.970097 q^{70} +2.25770 q^{71} +8.43470 q^{72} -10.5309 q^{73} +1.51997 q^{74} -0.396968 q^{75} +5.38736 q^{76} +2.20338 q^{77} -1.79767 q^{78} +8.74949 q^{79} +0.760881 q^{80} +7.60658 q^{81} -10.0794 q^{82} -13.9029 q^{83} -0.420355 q^{84} +3.82317 q^{85} -5.26126 q^{86} +2.59543 q^{87} +6.53839 q^{88} -8.53761 q^{89} +2.75742 q^{90} -4.66808 q^{91} +9.11846 q^{92} +1.55053 q^{93} +4.02372 q^{94} +5.08764 q^{95} -2.06295 q^{96} -14.8303 q^{97} +0.970097 q^{98} +6.26291 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.970097 0.685962 0.342981 0.939342i \(-0.388563\pi\)
0.342981 + 0.939342i \(0.388563\pi\)
\(3\) −0.396968 −0.229190 −0.114595 0.993412i \(-0.536557\pi\)
−0.114595 + 0.993412i \(0.536557\pi\)
\(4\) −1.05891 −0.529456
\(5\) −1.00000 −0.447214
\(6\) −0.385098 −0.157216
\(7\) −1.00000 −0.377964
\(8\) −2.96744 −1.04915
\(9\) −2.84242 −0.947472
\(10\) −0.970097 −0.306772
\(11\) −2.20338 −0.664343 −0.332172 0.943219i \(-0.607781\pi\)
−0.332172 + 0.943219i \(0.607781\pi\)
\(12\) 0.420355 0.121346
\(13\) 4.66808 1.29469 0.647347 0.762196i \(-0.275879\pi\)
0.647347 + 0.762196i \(0.275879\pi\)
\(14\) −0.970097 −0.259269
\(15\) 0.396968 0.102497
\(16\) −0.760881 −0.190220
\(17\) −3.82317 −0.927255 −0.463628 0.886030i \(-0.653452\pi\)
−0.463628 + 0.886030i \(0.653452\pi\)
\(18\) −2.75742 −0.649930
\(19\) −5.08764 −1.16718 −0.583592 0.812047i \(-0.698353\pi\)
−0.583592 + 0.812047i \(0.698353\pi\)
\(20\) 1.05891 0.236780
\(21\) 0.396968 0.0866256
\(22\) −2.13749 −0.455714
\(23\) −8.61116 −1.79555 −0.897775 0.440454i \(-0.854817\pi\)
−0.897775 + 0.440454i \(0.854817\pi\)
\(24\) 1.17798 0.240454
\(25\) 1.00000 0.200000
\(26\) 4.52849 0.888110
\(27\) 2.31925 0.446341
\(28\) 1.05891 0.200116
\(29\) −6.53813 −1.21410 −0.607050 0.794664i \(-0.707647\pi\)
−0.607050 + 0.794664i \(0.707647\pi\)
\(30\) 0.385098 0.0703089
\(31\) −3.90594 −0.701527 −0.350764 0.936464i \(-0.614078\pi\)
−0.350764 + 0.936464i \(0.614078\pi\)
\(32\) 5.19675 0.918665
\(33\) 0.874671 0.152261
\(34\) −3.70885 −0.636062
\(35\) 1.00000 0.169031
\(36\) 3.00987 0.501645
\(37\) 1.56682 0.257584 0.128792 0.991672i \(-0.458890\pi\)
0.128792 + 0.991672i \(0.458890\pi\)
\(38\) −4.93550 −0.800644
\(39\) −1.85308 −0.296731
\(40\) 2.96744 0.469194
\(41\) −10.3901 −1.62265 −0.811327 0.584592i \(-0.801254\pi\)
−0.811327 + 0.584592i \(0.801254\pi\)
\(42\) 0.385098 0.0594219
\(43\) −5.42344 −0.827067 −0.413533 0.910489i \(-0.635705\pi\)
−0.413533 + 0.910489i \(0.635705\pi\)
\(44\) 2.33318 0.351740
\(45\) 2.84242 0.423722
\(46\) −8.35365 −1.23168
\(47\) 4.14775 0.605011 0.302505 0.953148i \(-0.402177\pi\)
0.302505 + 0.953148i \(0.402177\pi\)
\(48\) 0.302046 0.0435966
\(49\) 1.00000 0.142857
\(50\) 0.970097 0.137192
\(51\) 1.51768 0.212517
\(52\) −4.94309 −0.685483
\(53\) −1.57645 −0.216541 −0.108271 0.994121i \(-0.534531\pi\)
−0.108271 + 0.994121i \(0.534531\pi\)
\(54\) 2.24990 0.306173
\(55\) 2.20338 0.297103
\(56\) 2.96744 0.396541
\(57\) 2.01963 0.267507
\(58\) −6.34262 −0.832827
\(59\) 8.65116 1.12628 0.563142 0.826360i \(-0.309592\pi\)
0.563142 + 0.826360i \(0.309592\pi\)
\(60\) −0.420355 −0.0542675
\(61\) 1.84183 0.235822 0.117911 0.993024i \(-0.462380\pi\)
0.117911 + 0.993024i \(0.462380\pi\)
\(62\) −3.78914 −0.481221
\(63\) 2.84242 0.358111
\(64\) 6.56312 0.820390
\(65\) −4.66808 −0.579004
\(66\) 0.848516 0.104445
\(67\) 10.0744 1.23078 0.615392 0.788222i \(-0.288998\pi\)
0.615392 + 0.788222i \(0.288998\pi\)
\(68\) 4.04840 0.490941
\(69\) 3.41836 0.411522
\(70\) 0.970097 0.115949
\(71\) 2.25770 0.267939 0.133970 0.990985i \(-0.457228\pi\)
0.133970 + 0.990985i \(0.457228\pi\)
\(72\) 8.43470 0.994039
\(73\) −10.5309 −1.23255 −0.616275 0.787531i \(-0.711359\pi\)
−0.616275 + 0.787531i \(0.711359\pi\)
\(74\) 1.51997 0.176693
\(75\) −0.396968 −0.0458380
\(76\) 5.38736 0.617973
\(77\) 2.20338 0.251098
\(78\) −1.79767 −0.203546
\(79\) 8.74949 0.984394 0.492197 0.870484i \(-0.336194\pi\)
0.492197 + 0.870484i \(0.336194\pi\)
\(80\) 0.760881 0.0850691
\(81\) 7.60658 0.845175
\(82\) −10.0794 −1.11308
\(83\) −13.9029 −1.52604 −0.763022 0.646373i \(-0.776285\pi\)
−0.763022 + 0.646373i \(0.776285\pi\)
\(84\) −0.420355 −0.0458645
\(85\) 3.82317 0.414681
\(86\) −5.26126 −0.567336
\(87\) 2.59543 0.278259
\(88\) 6.53839 0.696995
\(89\) −8.53761 −0.904985 −0.452492 0.891768i \(-0.649465\pi\)
−0.452492 + 0.891768i \(0.649465\pi\)
\(90\) 2.75742 0.290657
\(91\) −4.66808 −0.489348
\(92\) 9.11846 0.950665
\(93\) 1.55053 0.160783
\(94\) 4.02372 0.415015
\(95\) 5.08764 0.521981
\(96\) −2.06295 −0.210549
\(97\) −14.8303 −1.50578 −0.752892 0.658144i \(-0.771342\pi\)
−0.752892 + 0.658144i \(0.771342\pi\)
\(98\) 0.970097 0.0979946
\(99\) 6.26291 0.629446
\(100\) −1.05891 −0.105891
\(101\) 3.96350 0.394383 0.197191 0.980365i \(-0.436818\pi\)
0.197191 + 0.980365i \(0.436818\pi\)
\(102\) 1.47229 0.145779
\(103\) −8.14891 −0.802936 −0.401468 0.915873i \(-0.631500\pi\)
−0.401468 + 0.915873i \(0.631500\pi\)
\(104\) −13.8523 −1.35833
\(105\) −0.396968 −0.0387402
\(106\) −1.52931 −0.148539
\(107\) −9.09956 −0.879688 −0.439844 0.898074i \(-0.644966\pi\)
−0.439844 + 0.898074i \(0.644966\pi\)
\(108\) −2.45589 −0.236318
\(109\) 11.2079 1.07352 0.536760 0.843735i \(-0.319648\pi\)
0.536760 + 0.843735i \(0.319648\pi\)
\(110\) 2.13749 0.203802
\(111\) −0.621979 −0.0590356
\(112\) 0.760881 0.0718965
\(113\) 0.420027 0.0395129 0.0197564 0.999805i \(-0.493711\pi\)
0.0197564 + 0.999805i \(0.493711\pi\)
\(114\) 1.95924 0.183499
\(115\) 8.61116 0.802994
\(116\) 6.92330 0.642813
\(117\) −13.2686 −1.22669
\(118\) 8.39246 0.772589
\(119\) 3.82317 0.350470
\(120\) −1.17798 −0.107534
\(121\) −6.14513 −0.558648
\(122\) 1.78675 0.161765
\(123\) 4.12452 0.371896
\(124\) 4.13605 0.371428
\(125\) −1.00000 −0.0894427
\(126\) 2.75742 0.245650
\(127\) 4.25797 0.377834 0.188917 0.981993i \(-0.439502\pi\)
0.188917 + 0.981993i \(0.439502\pi\)
\(128\) −4.02665 −0.355909
\(129\) 2.15293 0.189555
\(130\) −4.52849 −0.397175
\(131\) −8.77509 −0.766683 −0.383342 0.923607i \(-0.625227\pi\)
−0.383342 + 0.923607i \(0.625227\pi\)
\(132\) −0.926200 −0.0806153
\(133\) 5.08764 0.441154
\(134\) 9.77314 0.844271
\(135\) −2.31925 −0.199610
\(136\) 11.3450 0.972829
\(137\) −0.00613626 −0.000524256 0 −0.000262128 1.00000i \(-0.500083\pi\)
−0.000262128 1.00000i \(0.500083\pi\)
\(138\) 3.31614 0.282288
\(139\) −9.63822 −0.817503 −0.408752 0.912646i \(-0.634036\pi\)
−0.408752 + 0.912646i \(0.634036\pi\)
\(140\) −1.05891 −0.0894944
\(141\) −1.64652 −0.138662
\(142\) 2.19018 0.183796
\(143\) −10.2855 −0.860120
\(144\) 2.16274 0.180228
\(145\) 6.53813 0.542962
\(146\) −10.2160 −0.845483
\(147\) −0.396968 −0.0327414
\(148\) −1.65913 −0.136379
\(149\) 13.3212 1.09131 0.545657 0.838009i \(-0.316280\pi\)
0.545657 + 0.838009i \(0.316280\pi\)
\(150\) −0.385098 −0.0314431
\(151\) −5.14788 −0.418929 −0.209464 0.977816i \(-0.567172\pi\)
−0.209464 + 0.977816i \(0.567172\pi\)
\(152\) 15.0973 1.22455
\(153\) 10.8670 0.878548
\(154\) 2.13749 0.172244
\(155\) 3.90594 0.313733
\(156\) 1.96225 0.157106
\(157\) 9.06063 0.723117 0.361558 0.932349i \(-0.382245\pi\)
0.361558 + 0.932349i \(0.382245\pi\)
\(158\) 8.48785 0.675257
\(159\) 0.625799 0.0496291
\(160\) −5.19675 −0.410839
\(161\) 8.61116 0.678654
\(162\) 7.37912 0.579758
\(163\) −0.996155 −0.0780249 −0.0390124 0.999239i \(-0.512421\pi\)
−0.0390124 + 0.999239i \(0.512421\pi\)
\(164\) 11.0022 0.859124
\(165\) −0.874671 −0.0680930
\(166\) −13.4872 −1.04681
\(167\) −12.3079 −0.952412 −0.476206 0.879334i \(-0.657988\pi\)
−0.476206 + 0.879334i \(0.657988\pi\)
\(168\) −1.17798 −0.0908832
\(169\) 8.79100 0.676231
\(170\) 3.70885 0.284456
\(171\) 14.4612 1.10587
\(172\) 5.74294 0.437895
\(173\) 16.4452 1.25031 0.625154 0.780501i \(-0.285036\pi\)
0.625154 + 0.780501i \(0.285036\pi\)
\(174\) 2.51782 0.190875
\(175\) −1.00000 −0.0755929
\(176\) 1.67651 0.126372
\(177\) −3.43424 −0.258133
\(178\) −8.28231 −0.620785
\(179\) 5.29031 0.395416 0.197708 0.980261i \(-0.436650\pi\)
0.197708 + 0.980261i \(0.436650\pi\)
\(180\) −3.00987 −0.224342
\(181\) 11.0371 0.820378 0.410189 0.912001i \(-0.365463\pi\)
0.410189 + 0.912001i \(0.365463\pi\)
\(182\) −4.52849 −0.335674
\(183\) −0.731149 −0.0540481
\(184\) 25.5531 1.88380
\(185\) −1.56682 −0.115195
\(186\) 1.50417 0.110291
\(187\) 8.42389 0.616016
\(188\) −4.39210 −0.320327
\(189\) −2.31925 −0.168701
\(190\) 4.93550 0.358059
\(191\) −11.7995 −0.853782 −0.426891 0.904303i \(-0.640391\pi\)
−0.426891 + 0.904303i \(0.640391\pi\)
\(192\) −2.60535 −0.188025
\(193\) 6.22737 0.448256 0.224128 0.974560i \(-0.428047\pi\)
0.224128 + 0.974560i \(0.428047\pi\)
\(194\) −14.3868 −1.03291
\(195\) 1.85308 0.132702
\(196\) −1.05891 −0.0756366
\(197\) −6.52208 −0.464679 −0.232339 0.972635i \(-0.574638\pi\)
−0.232339 + 0.972635i \(0.574638\pi\)
\(198\) 6.07563 0.431776
\(199\) −0.945655 −0.0670357 −0.0335179 0.999438i \(-0.510671\pi\)
−0.0335179 + 0.999438i \(0.510671\pi\)
\(200\) −2.96744 −0.209830
\(201\) −3.99922 −0.282083
\(202\) 3.84497 0.270531
\(203\) 6.53813 0.458887
\(204\) −1.60709 −0.112519
\(205\) 10.3901 0.725673
\(206\) −7.90524 −0.550784
\(207\) 24.4765 1.70123
\(208\) −3.55186 −0.246277
\(209\) 11.2100 0.775410
\(210\) −0.385098 −0.0265743
\(211\) −2.49474 −0.171745 −0.0858725 0.996306i \(-0.527368\pi\)
−0.0858725 + 0.996306i \(0.527368\pi\)
\(212\) 1.66932 0.114649
\(213\) −0.896234 −0.0614089
\(214\) −8.82746 −0.603433
\(215\) 5.42344 0.369875
\(216\) −6.88225 −0.468278
\(217\) 3.90594 0.265152
\(218\) 10.8727 0.736394
\(219\) 4.18044 0.282488
\(220\) −2.33318 −0.157303
\(221\) −17.8469 −1.20051
\(222\) −0.603380 −0.0404962
\(223\) 23.9274 1.60230 0.801149 0.598465i \(-0.204222\pi\)
0.801149 + 0.598465i \(0.204222\pi\)
\(224\) −5.19675 −0.347223
\(225\) −2.84242 −0.189494
\(226\) 0.407467 0.0271043
\(227\) 12.3622 0.820510 0.410255 0.911971i \(-0.365440\pi\)
0.410255 + 0.911971i \(0.365440\pi\)
\(228\) −2.13861 −0.141633
\(229\) 1.00000 0.0660819
\(230\) 8.35365 0.550824
\(231\) −0.874671 −0.0575491
\(232\) 19.4015 1.27377
\(233\) −21.9933 −1.44083 −0.720414 0.693544i \(-0.756048\pi\)
−0.720414 + 0.693544i \(0.756048\pi\)
\(234\) −12.8719 −0.841460
\(235\) −4.14775 −0.270569
\(236\) −9.16081 −0.596318
\(237\) −3.47327 −0.225613
\(238\) 3.70885 0.240409
\(239\) 16.6728 1.07847 0.539236 0.842155i \(-0.318713\pi\)
0.539236 + 0.842155i \(0.318713\pi\)
\(240\) −0.302046 −0.0194970
\(241\) 5.79359 0.373198 0.186599 0.982436i \(-0.440254\pi\)
0.186599 + 0.982436i \(0.440254\pi\)
\(242\) −5.96137 −0.383212
\(243\) −9.97733 −0.640046
\(244\) −1.95034 −0.124858
\(245\) −1.00000 −0.0638877
\(246\) 4.00119 0.255106
\(247\) −23.7495 −1.51115
\(248\) 11.5906 0.736007
\(249\) 5.51902 0.349754
\(250\) −0.970097 −0.0613543
\(251\) 22.9827 1.45066 0.725328 0.688404i \(-0.241688\pi\)
0.725328 + 0.688404i \(0.241688\pi\)
\(252\) −3.00987 −0.189604
\(253\) 18.9736 1.19286
\(254\) 4.13065 0.259180
\(255\) −1.51768 −0.0950407
\(256\) −17.0325 −1.06453
\(257\) 9.03120 0.563351 0.281675 0.959510i \(-0.409110\pi\)
0.281675 + 0.959510i \(0.409110\pi\)
\(258\) 2.08855 0.130028
\(259\) −1.56682 −0.0973576
\(260\) 4.94309 0.306557
\(261\) 18.5841 1.15033
\(262\) −8.51269 −0.525915
\(263\) −7.40733 −0.456755 −0.228378 0.973573i \(-0.573342\pi\)
−0.228378 + 0.973573i \(0.573342\pi\)
\(264\) −2.59553 −0.159744
\(265\) 1.57645 0.0968403
\(266\) 4.93550 0.302615
\(267\) 3.38916 0.207413
\(268\) −10.6679 −0.651646
\(269\) 16.2546 0.991063 0.495531 0.868590i \(-0.334973\pi\)
0.495531 + 0.868590i \(0.334973\pi\)
\(270\) −2.24990 −0.136925
\(271\) 25.9362 1.57551 0.787757 0.615986i \(-0.211242\pi\)
0.787757 + 0.615986i \(0.211242\pi\)
\(272\) 2.90898 0.176383
\(273\) 1.85308 0.112154
\(274\) −0.00595277 −0.000359620 0
\(275\) −2.20338 −0.132869
\(276\) −3.61974 −0.217883
\(277\) −7.44191 −0.447141 −0.223570 0.974688i \(-0.571771\pi\)
−0.223570 + 0.974688i \(0.571771\pi\)
\(278\) −9.35001 −0.560776
\(279\) 11.1023 0.664678
\(280\) −2.96744 −0.177339
\(281\) −17.8273 −1.06349 −0.531743 0.846906i \(-0.678463\pi\)
−0.531743 + 0.846906i \(0.678463\pi\)
\(282\) −1.59729 −0.0951171
\(283\) 11.3850 0.676768 0.338384 0.941008i \(-0.390120\pi\)
0.338384 + 0.941008i \(0.390120\pi\)
\(284\) −2.39070 −0.141862
\(285\) −2.01963 −0.119633
\(286\) −9.97797 −0.590010
\(287\) 10.3901 0.613306
\(288\) −14.7713 −0.870409
\(289\) −2.38336 −0.140198
\(290\) 6.34262 0.372451
\(291\) 5.88715 0.345111
\(292\) 11.1513 0.652581
\(293\) −14.6010 −0.852997 −0.426498 0.904488i \(-0.640253\pi\)
−0.426498 + 0.904488i \(0.640253\pi\)
\(294\) −0.385098 −0.0224594
\(295\) −8.65116 −0.503690
\(296\) −4.64945 −0.270244
\(297\) −5.11019 −0.296523
\(298\) 12.9228 0.748600
\(299\) −40.1976 −2.32469
\(300\) 0.420355 0.0242692
\(301\) 5.42344 0.312602
\(302\) −4.99394 −0.287369
\(303\) −1.57338 −0.0903885
\(304\) 3.87109 0.222022
\(305\) −1.84183 −0.105463
\(306\) 10.5421 0.602651
\(307\) 4.07326 0.232473 0.116237 0.993222i \(-0.462917\pi\)
0.116237 + 0.993222i \(0.462917\pi\)
\(308\) −2.33318 −0.132945
\(309\) 3.23486 0.184025
\(310\) 3.78914 0.215209
\(311\) 6.74219 0.382314 0.191157 0.981559i \(-0.438776\pi\)
0.191157 + 0.981559i \(0.438776\pi\)
\(312\) 5.49891 0.311314
\(313\) 4.88163 0.275926 0.137963 0.990437i \(-0.455944\pi\)
0.137963 + 0.990437i \(0.455944\pi\)
\(314\) 8.78969 0.496031
\(315\) −2.84242 −0.160152
\(316\) −9.26494 −0.521193
\(317\) 26.1274 1.46746 0.733729 0.679442i \(-0.237778\pi\)
0.733729 + 0.679442i \(0.237778\pi\)
\(318\) 0.607086 0.0340437
\(319\) 14.4060 0.806579
\(320\) −6.56312 −0.366889
\(321\) 3.61224 0.201616
\(322\) 8.35365 0.465531
\(323\) 19.4509 1.08228
\(324\) −8.05470 −0.447483
\(325\) 4.66808 0.258939
\(326\) −0.966367 −0.0535221
\(327\) −4.44917 −0.246040
\(328\) 30.8319 1.70241
\(329\) −4.14775 −0.228673
\(330\) −0.848516 −0.0467092
\(331\) 24.1488 1.32734 0.663669 0.748026i \(-0.268998\pi\)
0.663669 + 0.748026i \(0.268998\pi\)
\(332\) 14.7220 0.807973
\(333\) −4.45356 −0.244054
\(334\) −11.9398 −0.653318
\(335\) −10.0744 −0.550423
\(336\) −0.302046 −0.0164779
\(337\) 31.0135 1.68941 0.844707 0.535230i \(-0.179775\pi\)
0.844707 + 0.535230i \(0.179775\pi\)
\(338\) 8.52812 0.463869
\(339\) −0.166738 −0.00905594
\(340\) −4.04840 −0.219555
\(341\) 8.60626 0.466055
\(342\) 14.0287 0.758588
\(343\) −1.00000 −0.0539949
\(344\) 16.0937 0.867716
\(345\) −3.41836 −0.184038
\(346\) 15.9535 0.857664
\(347\) 0.0306680 0.00164634 0.000823172 1.00000i \(-0.499738\pi\)
0.000823172 1.00000i \(0.499738\pi\)
\(348\) −2.74833 −0.147326
\(349\) 21.6364 1.15817 0.579085 0.815267i \(-0.303410\pi\)
0.579085 + 0.815267i \(0.303410\pi\)
\(350\) −0.970097 −0.0518539
\(351\) 10.8265 0.577874
\(352\) −11.4504 −0.610309
\(353\) 2.83747 0.151023 0.0755117 0.997145i \(-0.475941\pi\)
0.0755117 + 0.997145i \(0.475941\pi\)
\(354\) −3.33154 −0.177069
\(355\) −2.25770 −0.119826
\(356\) 9.04058 0.479150
\(357\) −1.51768 −0.0803241
\(358\) 5.13211 0.271241
\(359\) −33.7911 −1.78342 −0.891712 0.452603i \(-0.850495\pi\)
−0.891712 + 0.452603i \(0.850495\pi\)
\(360\) −8.43470 −0.444548
\(361\) 6.88405 0.362318
\(362\) 10.7070 0.562748
\(363\) 2.43942 0.128037
\(364\) 4.94309 0.259088
\(365\) 10.5309 0.551213
\(366\) −0.709285 −0.0370749
\(367\) 6.12803 0.319881 0.159940 0.987127i \(-0.448870\pi\)
0.159940 + 0.987127i \(0.448870\pi\)
\(368\) 6.55207 0.341550
\(369\) 29.5329 1.53742
\(370\) −1.51997 −0.0790194
\(371\) 1.57645 0.0818450
\(372\) −1.64188 −0.0851275
\(373\) 11.3406 0.587195 0.293597 0.955929i \(-0.405148\pi\)
0.293597 + 0.955929i \(0.405148\pi\)
\(374\) 8.17199 0.422563
\(375\) 0.396968 0.0204994
\(376\) −12.3082 −0.634746
\(377\) −30.5205 −1.57189
\(378\) −2.24990 −0.115722
\(379\) −34.4420 −1.76917 −0.884583 0.466383i \(-0.845557\pi\)
−0.884583 + 0.466383i \(0.845557\pi\)
\(380\) −5.38736 −0.276366
\(381\) −1.69028 −0.0865957
\(382\) −11.4467 −0.585662
\(383\) −36.0412 −1.84162 −0.920810 0.390010i \(-0.872471\pi\)
−0.920810 + 0.390010i \(0.872471\pi\)
\(384\) 1.59845 0.0815707
\(385\) −2.20338 −0.112294
\(386\) 6.04115 0.307487
\(387\) 15.4157 0.783623
\(388\) 15.7039 0.797247
\(389\) 30.7369 1.55842 0.779211 0.626762i \(-0.215620\pi\)
0.779211 + 0.626762i \(0.215620\pi\)
\(390\) 1.79767 0.0910285
\(391\) 32.9219 1.66493
\(392\) −2.96744 −0.149878
\(393\) 3.48343 0.175716
\(394\) −6.32705 −0.318752
\(395\) −8.74949 −0.440234
\(396\) −6.63187 −0.333264
\(397\) 25.6295 1.28631 0.643153 0.765737i \(-0.277626\pi\)
0.643153 + 0.765737i \(0.277626\pi\)
\(398\) −0.917377 −0.0459839
\(399\) −2.01963 −0.101108
\(400\) −0.760881 −0.0380441
\(401\) 1.76129 0.0879547 0.0439773 0.999033i \(-0.485997\pi\)
0.0439773 + 0.999033i \(0.485997\pi\)
\(402\) −3.87963 −0.193498
\(403\) −18.2333 −0.908263
\(404\) −4.19699 −0.208808
\(405\) −7.60658 −0.377974
\(406\) 6.34262 0.314779
\(407\) −3.45230 −0.171124
\(408\) −4.50362 −0.222962
\(409\) 22.9828 1.13643 0.568214 0.822881i \(-0.307635\pi\)
0.568214 + 0.822881i \(0.307635\pi\)
\(410\) 10.0794 0.497784
\(411\) 0.00243590 0.000120154 0
\(412\) 8.62898 0.425119
\(413\) −8.65116 −0.425696
\(414\) 23.7446 1.16698
\(415\) 13.9029 0.682467
\(416\) 24.2589 1.18939
\(417\) 3.82607 0.187363
\(418\) 10.8748 0.531902
\(419\) −12.9493 −0.632614 −0.316307 0.948657i \(-0.602443\pi\)
−0.316307 + 0.948657i \(0.602443\pi\)
\(420\) 0.420355 0.0205112
\(421\) −29.2841 −1.42722 −0.713610 0.700543i \(-0.752941\pi\)
−0.713610 + 0.700543i \(0.752941\pi\)
\(422\) −2.42014 −0.117811
\(423\) −11.7896 −0.573231
\(424\) 4.67801 0.227184
\(425\) −3.82317 −0.185451
\(426\) −0.869434 −0.0421242
\(427\) −1.84183 −0.0891324
\(428\) 9.63564 0.465756
\(429\) 4.08304 0.197131
\(430\) 5.26126 0.253721
\(431\) 14.3388 0.690675 0.345337 0.938479i \(-0.387765\pi\)
0.345337 + 0.938479i \(0.387765\pi\)
\(432\) −1.76468 −0.0849031
\(433\) 5.82467 0.279916 0.139958 0.990157i \(-0.455303\pi\)
0.139958 + 0.990157i \(0.455303\pi\)
\(434\) 3.78914 0.181885
\(435\) −2.59543 −0.124441
\(436\) −11.8682 −0.568382
\(437\) 43.8104 2.09574
\(438\) 4.05543 0.193776
\(439\) −33.2124 −1.58514 −0.792570 0.609780i \(-0.791258\pi\)
−0.792570 + 0.609780i \(0.791258\pi\)
\(440\) −6.53839 −0.311706
\(441\) −2.84242 −0.135353
\(442\) −17.3132 −0.823505
\(443\) −16.1169 −0.765738 −0.382869 0.923803i \(-0.625064\pi\)
−0.382869 + 0.923803i \(0.625064\pi\)
\(444\) 0.658621 0.0312568
\(445\) 8.53761 0.404721
\(446\) 23.2119 1.09912
\(447\) −5.28809 −0.250118
\(448\) −6.56312 −0.310078
\(449\) 0.840226 0.0396527 0.0198264 0.999803i \(-0.493689\pi\)
0.0198264 + 0.999803i \(0.493689\pi\)
\(450\) −2.75742 −0.129986
\(451\) 22.8932 1.07800
\(452\) −0.444772 −0.0209203
\(453\) 2.04355 0.0960142
\(454\) 11.9926 0.562839
\(455\) 4.66808 0.218843
\(456\) −5.99314 −0.280654
\(457\) −9.74058 −0.455645 −0.227823 0.973703i \(-0.573161\pi\)
−0.227823 + 0.973703i \(0.573161\pi\)
\(458\) 0.970097 0.0453297
\(459\) −8.86691 −0.413872
\(460\) −9.11846 −0.425150
\(461\) −14.7555 −0.687231 −0.343615 0.939110i \(-0.611652\pi\)
−0.343615 + 0.939110i \(0.611652\pi\)
\(462\) −0.848516 −0.0394765
\(463\) −17.7643 −0.825577 −0.412788 0.910827i \(-0.635445\pi\)
−0.412788 + 0.910827i \(0.635445\pi\)
\(464\) 4.97474 0.230946
\(465\) −1.55053 −0.0719043
\(466\) −21.3356 −0.988353
\(467\) 11.1165 0.514410 0.257205 0.966357i \(-0.417198\pi\)
0.257205 + 0.966357i \(0.417198\pi\)
\(468\) 14.0503 0.649476
\(469\) −10.0744 −0.465192
\(470\) −4.02372 −0.185600
\(471\) −3.59678 −0.165731
\(472\) −25.6718 −1.18164
\(473\) 11.9499 0.549456
\(474\) −3.36941 −0.154762
\(475\) −5.08764 −0.233437
\(476\) −4.04840 −0.185558
\(477\) 4.48092 0.205167
\(478\) 16.1742 0.739790
\(479\) −40.0322 −1.82912 −0.914559 0.404452i \(-0.867462\pi\)
−0.914559 + 0.404452i \(0.867462\pi\)
\(480\) 2.06295 0.0941602
\(481\) 7.31406 0.333492
\(482\) 5.62034 0.255999
\(483\) −3.41836 −0.155541
\(484\) 6.50715 0.295780
\(485\) 14.8303 0.673408
\(486\) −9.67898 −0.439048
\(487\) −16.2358 −0.735716 −0.367858 0.929882i \(-0.619909\pi\)
−0.367858 + 0.929882i \(0.619909\pi\)
\(488\) −5.46552 −0.247413
\(489\) 0.395442 0.0178825
\(490\) −0.970097 −0.0438245
\(491\) −22.9333 −1.03497 −0.517483 0.855694i \(-0.673131\pi\)
−0.517483 + 0.855694i \(0.673131\pi\)
\(492\) −4.36751 −0.196903
\(493\) 24.9964 1.12578
\(494\) −23.0393 −1.03659
\(495\) −6.26291 −0.281497
\(496\) 2.97196 0.133445
\(497\) −2.25770 −0.101271
\(498\) 5.35398 0.239918
\(499\) 17.0699 0.764154 0.382077 0.924131i \(-0.375209\pi\)
0.382077 + 0.924131i \(0.375209\pi\)
\(500\) 1.05891 0.0473560
\(501\) 4.88584 0.218283
\(502\) 22.2954 0.995094
\(503\) −15.3081 −0.682554 −0.341277 0.939963i \(-0.610859\pi\)
−0.341277 + 0.939963i \(0.610859\pi\)
\(504\) −8.43470 −0.375711
\(505\) −3.96350 −0.176373
\(506\) 18.4062 0.818257
\(507\) −3.48975 −0.154985
\(508\) −4.50882 −0.200046
\(509\) −9.62930 −0.426811 −0.213406 0.976964i \(-0.568456\pi\)
−0.213406 + 0.976964i \(0.568456\pi\)
\(510\) −1.47229 −0.0651943
\(511\) 10.5309 0.465860
\(512\) −8.46985 −0.374318
\(513\) −11.7995 −0.520962
\(514\) 8.76114 0.386437
\(515\) 8.14891 0.359084
\(516\) −2.27977 −0.100361
\(517\) −9.13905 −0.401935
\(518\) −1.51997 −0.0667836
\(519\) −6.52824 −0.286558
\(520\) 13.8523 0.607462
\(521\) 3.33359 0.146047 0.0730237 0.997330i \(-0.476735\pi\)
0.0730237 + 0.997330i \(0.476735\pi\)
\(522\) 18.0284 0.789080
\(523\) −10.8231 −0.473262 −0.236631 0.971600i \(-0.576043\pi\)
−0.236631 + 0.971600i \(0.576043\pi\)
\(524\) 9.29205 0.405925
\(525\) 0.396968 0.0173251
\(526\) −7.18583 −0.313317
\(527\) 14.9331 0.650495
\(528\) −0.665521 −0.0289631
\(529\) 51.1520 2.22400
\(530\) 1.52931 0.0664288
\(531\) −24.5902 −1.06712
\(532\) −5.38736 −0.233572
\(533\) −48.5017 −2.10084
\(534\) 3.28781 0.142278
\(535\) 9.09956 0.393408
\(536\) −29.8952 −1.29127
\(537\) −2.10009 −0.0906254
\(538\) 15.7686 0.679832
\(539\) −2.20338 −0.0949061
\(540\) 2.45589 0.105685
\(541\) 30.1401 1.29582 0.647911 0.761716i \(-0.275643\pi\)
0.647911 + 0.761716i \(0.275643\pi\)
\(542\) 25.1607 1.08074
\(543\) −4.38136 −0.188022
\(544\) −19.8681 −0.851837
\(545\) −11.2079 −0.480093
\(546\) 1.79767 0.0769331
\(547\) −22.9241 −0.980166 −0.490083 0.871676i \(-0.663033\pi\)
−0.490083 + 0.871676i \(0.663033\pi\)
\(548\) 0.00649776 0.000277571 0
\(549\) −5.23525 −0.223435
\(550\) −2.13749 −0.0911428
\(551\) 33.2636 1.41708
\(552\) −10.1438 −0.431748
\(553\) −8.74949 −0.372066
\(554\) −7.21937 −0.306722
\(555\) 0.621979 0.0264015
\(556\) 10.2060 0.432832
\(557\) 9.20116 0.389866 0.194933 0.980817i \(-0.437551\pi\)
0.194933 + 0.980817i \(0.437551\pi\)
\(558\) 10.7703 0.455944
\(559\) −25.3171 −1.07080
\(560\) −0.760881 −0.0321531
\(561\) −3.34402 −0.141184
\(562\) −17.2942 −0.729511
\(563\) −21.4310 −0.903207 −0.451604 0.892219i \(-0.649148\pi\)
−0.451604 + 0.892219i \(0.649148\pi\)
\(564\) 1.74352 0.0734156
\(565\) −0.420027 −0.0176707
\(566\) 11.0446 0.464237
\(567\) −7.60658 −0.319446
\(568\) −6.69958 −0.281108
\(569\) 4.44920 0.186520 0.0932600 0.995642i \(-0.470271\pi\)
0.0932600 + 0.995642i \(0.470271\pi\)
\(570\) −1.95924 −0.0820634
\(571\) −42.8836 −1.79462 −0.897312 0.441397i \(-0.854483\pi\)
−0.897312 + 0.441397i \(0.854483\pi\)
\(572\) 10.8915 0.455396
\(573\) 4.68403 0.195678
\(574\) 10.0794 0.420704
\(575\) −8.61116 −0.359110
\(576\) −18.6551 −0.777296
\(577\) −35.9822 −1.49796 −0.748979 0.662594i \(-0.769455\pi\)
−0.748979 + 0.662594i \(0.769455\pi\)
\(578\) −2.31209 −0.0961703
\(579\) −2.47207 −0.102736
\(580\) −6.92330 −0.287474
\(581\) 13.9029 0.576790
\(582\) 5.71110 0.236733
\(583\) 3.47350 0.143858
\(584\) 31.2499 1.29313
\(585\) 13.2686 0.548590
\(586\) −14.1643 −0.585124
\(587\) −3.77637 −0.155867 −0.0779337 0.996959i \(-0.524832\pi\)
−0.0779337 + 0.996959i \(0.524832\pi\)
\(588\) 0.420355 0.0173351
\(589\) 19.8720 0.818812
\(590\) −8.39246 −0.345512
\(591\) 2.58906 0.106500
\(592\) −1.19217 −0.0489977
\(593\) −47.9537 −1.96922 −0.984612 0.174755i \(-0.944087\pi\)
−0.984612 + 0.174755i \(0.944087\pi\)
\(594\) −4.95738 −0.203404
\(595\) −3.82317 −0.156735
\(596\) −14.1060 −0.577803
\(597\) 0.375395 0.0153639
\(598\) −38.9956 −1.59465
\(599\) 8.62497 0.352407 0.176203 0.984354i \(-0.443618\pi\)
0.176203 + 0.984354i \(0.443618\pi\)
\(600\) 1.17798 0.0480908
\(601\) −25.0778 −1.02294 −0.511471 0.859300i \(-0.670899\pi\)
−0.511471 + 0.859300i \(0.670899\pi\)
\(602\) 5.26126 0.214433
\(603\) −28.6356 −1.16613
\(604\) 5.45115 0.221804
\(605\) 6.14513 0.249835
\(606\) −1.52633 −0.0620031
\(607\) 22.0772 0.896088 0.448044 0.894012i \(-0.352121\pi\)
0.448044 + 0.894012i \(0.352121\pi\)
\(608\) −26.4392 −1.07225
\(609\) −2.59543 −0.105172
\(610\) −1.78675 −0.0723436
\(611\) 19.3620 0.783304
\(612\) −11.5072 −0.465153
\(613\) 22.9679 0.927664 0.463832 0.885923i \(-0.346474\pi\)
0.463832 + 0.885923i \(0.346474\pi\)
\(614\) 3.95146 0.159468
\(615\) −4.12452 −0.166317
\(616\) −6.53839 −0.263439
\(617\) −42.8701 −1.72589 −0.862943 0.505301i \(-0.831381\pi\)
−0.862943 + 0.505301i \(0.831381\pi\)
\(618\) 3.13813 0.126234
\(619\) −8.22940 −0.330767 −0.165384 0.986229i \(-0.552886\pi\)
−0.165384 + 0.986229i \(0.552886\pi\)
\(620\) −4.13605 −0.166108
\(621\) −19.9715 −0.801427
\(622\) 6.54058 0.262253
\(623\) 8.53761 0.342052
\(624\) 1.40997 0.0564442
\(625\) 1.00000 0.0400000
\(626\) 4.73566 0.189275
\(627\) −4.45001 −0.177716
\(628\) −9.59441 −0.382859
\(629\) −5.99023 −0.238846
\(630\) −2.75742 −0.109858
\(631\) 6.97229 0.277562 0.138781 0.990323i \(-0.455682\pi\)
0.138781 + 0.990323i \(0.455682\pi\)
\(632\) −25.9636 −1.03278
\(633\) 0.990333 0.0393622
\(634\) 25.3461 1.00662
\(635\) −4.25797 −0.168972
\(636\) −0.662666 −0.0262764
\(637\) 4.66808 0.184956
\(638\) 13.9752 0.553282
\(639\) −6.41731 −0.253865
\(640\) 4.02665 0.159167
\(641\) 20.5071 0.809980 0.404990 0.914321i \(-0.367275\pi\)
0.404990 + 0.914321i \(0.367275\pi\)
\(642\) 3.50422 0.138301
\(643\) 8.28256 0.326632 0.163316 0.986574i \(-0.447781\pi\)
0.163316 + 0.986574i \(0.447781\pi\)
\(644\) −9.11846 −0.359317
\(645\) −2.15293 −0.0847717
\(646\) 18.8693 0.742401
\(647\) 13.7628 0.541073 0.270536 0.962710i \(-0.412799\pi\)
0.270536 + 0.962710i \(0.412799\pi\)
\(648\) −22.5721 −0.886715
\(649\) −19.0618 −0.748239
\(650\) 4.52849 0.177622
\(651\) −1.55053 −0.0607702
\(652\) 1.05484 0.0413107
\(653\) −15.1249 −0.591882 −0.295941 0.955206i \(-0.595633\pi\)
−0.295941 + 0.955206i \(0.595633\pi\)
\(654\) −4.31613 −0.168774
\(655\) 8.77509 0.342871
\(656\) 7.90560 0.308662
\(657\) 29.9333 1.16781
\(658\) −4.02372 −0.156861
\(659\) −13.4571 −0.524216 −0.262108 0.965039i \(-0.584418\pi\)
−0.262108 + 0.965039i \(0.584418\pi\)
\(660\) 0.926200 0.0360523
\(661\) −36.1753 −1.40706 −0.703528 0.710667i \(-0.748393\pi\)
−0.703528 + 0.710667i \(0.748393\pi\)
\(662\) 23.4267 0.910504
\(663\) 7.08465 0.275145
\(664\) 41.2561 1.60105
\(665\) −5.08764 −0.197290
\(666\) −4.32039 −0.167412
\(667\) 56.3008 2.17998
\(668\) 13.0330 0.504260
\(669\) −9.49843 −0.367230
\(670\) −9.77314 −0.377569
\(671\) −4.05825 −0.156667
\(672\) 2.06295 0.0795799
\(673\) −33.6626 −1.29760 −0.648799 0.760959i \(-0.724729\pi\)
−0.648799 + 0.760959i \(0.724729\pi\)
\(674\) 30.0861 1.15887
\(675\) 2.31925 0.0892682
\(676\) −9.30889 −0.358034
\(677\) −11.3713 −0.437033 −0.218517 0.975833i \(-0.570122\pi\)
−0.218517 + 0.975833i \(0.570122\pi\)
\(678\) −0.161752 −0.00621203
\(679\) 14.8303 0.569133
\(680\) −11.3450 −0.435062
\(681\) −4.90741 −0.188052
\(682\) 8.34890 0.319696
\(683\) −11.6951 −0.447502 −0.223751 0.974646i \(-0.571830\pi\)
−0.223751 + 0.974646i \(0.571830\pi\)
\(684\) −15.3131 −0.585512
\(685\) 0.00613626 0.000234455 0
\(686\) −0.970097 −0.0370385
\(687\) −0.396968 −0.0151453
\(688\) 4.12659 0.157325
\(689\) −7.35898 −0.280355
\(690\) −3.31614 −0.126243
\(691\) −27.1242 −1.03185 −0.515927 0.856632i \(-0.672552\pi\)
−0.515927 + 0.856632i \(0.672552\pi\)
\(692\) −17.4141 −0.661983
\(693\) −6.26291 −0.237908
\(694\) 0.0297509 0.00112933
\(695\) 9.63822 0.365599
\(696\) −7.70179 −0.291935
\(697\) 39.7230 1.50461
\(698\) 20.9894 0.794461
\(699\) 8.73064 0.330223
\(700\) 1.05891 0.0400231
\(701\) 28.6667 1.08272 0.541362 0.840789i \(-0.317909\pi\)
0.541362 + 0.840789i \(0.317909\pi\)
\(702\) 10.5027 0.396400
\(703\) −7.97142 −0.300648
\(704\) −14.4610 −0.545020
\(705\) 1.64652 0.0620117
\(706\) 2.75262 0.103596
\(707\) −3.96350 −0.149063
\(708\) 3.63655 0.136670
\(709\) −28.2128 −1.05955 −0.529776 0.848137i \(-0.677724\pi\)
−0.529776 + 0.848137i \(0.677724\pi\)
\(710\) −2.19018 −0.0821961
\(711\) −24.8697 −0.932686
\(712\) 25.3349 0.949464
\(713\) 33.6347 1.25963
\(714\) −1.47229 −0.0550993
\(715\) 10.2855 0.384658
\(716\) −5.60197 −0.209356
\(717\) −6.61856 −0.247175
\(718\) −32.7806 −1.22336
\(719\) −9.99293 −0.372674 −0.186337 0.982486i \(-0.559662\pi\)
−0.186337 + 0.982486i \(0.559662\pi\)
\(720\) −2.16274 −0.0806006
\(721\) 8.14891 0.303481
\(722\) 6.67819 0.248537
\(723\) −2.29987 −0.0855331
\(724\) −11.6873 −0.434354
\(725\) −6.53813 −0.242820
\(726\) 2.36648 0.0878282
\(727\) 20.9421 0.776699 0.388350 0.921512i \(-0.373045\pi\)
0.388350 + 0.921512i \(0.373045\pi\)
\(728\) 13.8523 0.513399
\(729\) −18.8590 −0.698483
\(730\) 10.2160 0.378112
\(731\) 20.7347 0.766902
\(732\) 0.774222 0.0286161
\(733\) 21.0024 0.775740 0.387870 0.921714i \(-0.373211\pi\)
0.387870 + 0.921714i \(0.373211\pi\)
\(734\) 5.94478 0.219426
\(735\) 0.396968 0.0146424
\(736\) −44.7501 −1.64951
\(737\) −22.1977 −0.817662
\(738\) 28.6497 1.05461
\(739\) 14.8485 0.546210 0.273105 0.961984i \(-0.411949\pi\)
0.273105 + 0.961984i \(0.411949\pi\)
\(740\) 1.65913 0.0609907
\(741\) 9.42781 0.346339
\(742\) 1.52931 0.0561426
\(743\) −33.9274 −1.24468 −0.622338 0.782749i \(-0.713817\pi\)
−0.622338 + 0.782749i \(0.713817\pi\)
\(744\) −4.60112 −0.168685
\(745\) −13.3212 −0.488050
\(746\) 11.0015 0.402793
\(747\) 39.5179 1.44588
\(748\) −8.92015 −0.326153
\(749\) 9.09956 0.332491
\(750\) 0.385098 0.0140618
\(751\) −43.6902 −1.59428 −0.797139 0.603795i \(-0.793654\pi\)
−0.797139 + 0.603795i \(0.793654\pi\)
\(752\) −3.15594 −0.115085
\(753\) −9.12341 −0.332475
\(754\) −29.6079 −1.07825
\(755\) 5.14788 0.187351
\(756\) 2.45589 0.0893197
\(757\) 15.9082 0.578194 0.289097 0.957300i \(-0.406645\pi\)
0.289097 + 0.957300i \(0.406645\pi\)
\(758\) −33.4121 −1.21358
\(759\) −7.53193 −0.273392
\(760\) −15.0973 −0.547635
\(761\) −16.0488 −0.581768 −0.290884 0.956758i \(-0.593949\pi\)
−0.290884 + 0.956758i \(0.593949\pi\)
\(762\) −1.63974 −0.0594014
\(763\) −11.2079 −0.405752
\(764\) 12.4946 0.452040
\(765\) −10.8670 −0.392899
\(766\) −34.9635 −1.26328
\(767\) 40.3843 1.45819
\(768\) 6.76135 0.243979
\(769\) −43.2353 −1.55911 −0.779553 0.626337i \(-0.784554\pi\)
−0.779553 + 0.626337i \(0.784554\pi\)
\(770\) −2.13749 −0.0770297
\(771\) −3.58510 −0.129114
\(772\) −6.59424 −0.237332
\(773\) −4.00538 −0.144064 −0.0720318 0.997402i \(-0.522948\pi\)
−0.0720318 + 0.997402i \(0.522948\pi\)
\(774\) 14.9547 0.537535
\(775\) −3.90594 −0.140305
\(776\) 44.0079 1.57979
\(777\) 0.621979 0.0223134
\(778\) 29.8177 1.06902
\(779\) 52.8608 1.89394
\(780\) −1.96225 −0.0702598
\(781\) −4.97455 −0.178004
\(782\) 31.9375 1.14208
\(783\) −15.1636 −0.541902
\(784\) −0.760881 −0.0271743
\(785\) −9.06063 −0.323388
\(786\) 3.37927 0.120534
\(787\) 38.6808 1.37882 0.689411 0.724370i \(-0.257869\pi\)
0.689411 + 0.724370i \(0.257869\pi\)
\(788\) 6.90631 0.246027
\(789\) 2.94048 0.104684
\(790\) −8.48785 −0.301984
\(791\) −0.420027 −0.0149345
\(792\) −18.5848 −0.660383
\(793\) 8.59782 0.305318
\(794\) 24.8631 0.882358
\(795\) −0.625799 −0.0221948
\(796\) 1.00137 0.0354925
\(797\) 0.586778 0.0207847 0.0103924 0.999946i \(-0.496692\pi\)
0.0103924 + 0.999946i \(0.496692\pi\)
\(798\) −1.95924 −0.0693563
\(799\) −15.8575 −0.561000
\(800\) 5.19675 0.183733
\(801\) 24.2674 0.857448
\(802\) 1.70862 0.0603336
\(803\) 23.2036 0.818837
\(804\) 4.23482 0.149351
\(805\) −8.61116 −0.303503
\(806\) −17.6880 −0.623034
\(807\) −6.45258 −0.227142
\(808\) −11.7614 −0.413766
\(809\) −43.0287 −1.51281 −0.756404 0.654104i \(-0.773046\pi\)
−0.756404 + 0.654104i \(0.773046\pi\)
\(810\) −7.37912 −0.259276
\(811\) −42.8131 −1.50337 −0.751686 0.659521i \(-0.770759\pi\)
−0.751686 + 0.659521i \(0.770759\pi\)
\(812\) −6.92330 −0.242960
\(813\) −10.2959 −0.361092
\(814\) −3.34906 −0.117385
\(815\) 0.996155 0.0348938
\(816\) −1.15477 −0.0404251
\(817\) 27.5925 0.965339
\(818\) 22.2956 0.779546
\(819\) 13.2686 0.463644
\(820\) −11.0022 −0.384212
\(821\) 35.5694 1.24138 0.620690 0.784056i \(-0.286852\pi\)
0.620690 + 0.784056i \(0.286852\pi\)
\(822\) 0.00236306 8.24213e−5 0
\(823\) −9.24595 −0.322293 −0.161147 0.986930i \(-0.551519\pi\)
−0.161147 + 0.986930i \(0.551519\pi\)
\(824\) 24.1814 0.842400
\(825\) 0.874671 0.0304521
\(826\) −8.39246 −0.292011
\(827\) 21.7702 0.757025 0.378513 0.925596i \(-0.376436\pi\)
0.378513 + 0.925596i \(0.376436\pi\)
\(828\) −25.9184 −0.900728
\(829\) 32.8043 1.13934 0.569671 0.821873i \(-0.307071\pi\)
0.569671 + 0.821873i \(0.307071\pi\)
\(830\) 13.4872 0.468147
\(831\) 2.95420 0.102480
\(832\) 30.6372 1.06215
\(833\) −3.82317 −0.132465
\(834\) 3.71166 0.128524
\(835\) 12.3079 0.425932
\(836\) −11.8704 −0.410546
\(837\) −9.05887 −0.313120
\(838\) −12.5621 −0.433949
\(839\) 21.9111 0.756456 0.378228 0.925712i \(-0.376534\pi\)
0.378228 + 0.925712i \(0.376534\pi\)
\(840\) 1.17798 0.0406442
\(841\) 13.7471 0.474039
\(842\) −28.4084 −0.979019
\(843\) 7.07687 0.243740
\(844\) 2.64171 0.0909314
\(845\) −8.79100 −0.302420
\(846\) −11.4371 −0.393215
\(847\) 6.14513 0.211149
\(848\) 1.19949 0.0411906
\(849\) −4.51949 −0.155108
\(850\) −3.70885 −0.127212
\(851\) −13.4921 −0.462505
\(852\) 0.949033 0.0325133
\(853\) 27.1671 0.930183 0.465091 0.885263i \(-0.346021\pi\)
0.465091 + 0.885263i \(0.346021\pi\)
\(854\) −1.78675 −0.0611415
\(855\) −14.4612 −0.494562
\(856\) 27.0024 0.922924
\(857\) 46.1986 1.57812 0.789058 0.614319i \(-0.210569\pi\)
0.789058 + 0.614319i \(0.210569\pi\)
\(858\) 3.96094 0.135224
\(859\) −11.6704 −0.398190 −0.199095 0.979980i \(-0.563800\pi\)
−0.199095 + 0.979980i \(0.563800\pi\)
\(860\) −5.74294 −0.195833
\(861\) −4.12452 −0.140563
\(862\) 13.9100 0.473777
\(863\) 15.2359 0.518635 0.259317 0.965792i \(-0.416502\pi\)
0.259317 + 0.965792i \(0.416502\pi\)
\(864\) 12.0526 0.410038
\(865\) −16.4452 −0.559155
\(866\) 5.65050 0.192012
\(867\) 0.946119 0.0321319
\(868\) −4.13605 −0.140387
\(869\) −19.2784 −0.653975
\(870\) −2.51782 −0.0853621
\(871\) 47.0281 1.59349
\(872\) −33.2587 −1.12628
\(873\) 42.1538 1.42669
\(874\) 42.5004 1.43760
\(875\) 1.00000 0.0338062
\(876\) −4.42672 −0.149565
\(877\) −7.57101 −0.255655 −0.127827 0.991796i \(-0.540800\pi\)
−0.127827 + 0.991796i \(0.540800\pi\)
\(878\) −32.2192 −1.08735
\(879\) 5.79612 0.195498
\(880\) −1.67651 −0.0565151
\(881\) −2.47954 −0.0835379 −0.0417689 0.999127i \(-0.513299\pi\)
−0.0417689 + 0.999127i \(0.513299\pi\)
\(882\) −2.75742 −0.0928471
\(883\) −31.3125 −1.05375 −0.526874 0.849943i \(-0.676636\pi\)
−0.526874 + 0.849943i \(0.676636\pi\)
\(884\) 18.8983 0.635618
\(885\) 3.43424 0.115441
\(886\) −15.6350 −0.525267
\(887\) 2.61870 0.0879272 0.0439636 0.999033i \(-0.486001\pi\)
0.0439636 + 0.999033i \(0.486001\pi\)
\(888\) 1.84569 0.0619372
\(889\) −4.25797 −0.142808
\(890\) 8.28231 0.277624
\(891\) −16.7602 −0.561486
\(892\) −25.3370 −0.848346
\(893\) −21.1022 −0.706159
\(894\) −5.12996 −0.171571
\(895\) −5.29031 −0.176836
\(896\) 4.02665 0.134521
\(897\) 15.9572 0.532794
\(898\) 0.815101 0.0272003
\(899\) 25.5375 0.851724
\(900\) 3.00987 0.100329
\(901\) 6.02702 0.200789
\(902\) 22.2086 0.739467
\(903\) −2.15293 −0.0716452
\(904\) −1.24641 −0.0414549
\(905\) −11.0371 −0.366884
\(906\) 1.98244 0.0658621
\(907\) −2.40941 −0.0800032 −0.0400016 0.999200i \(-0.512736\pi\)
−0.0400016 + 0.999200i \(0.512736\pi\)
\(908\) −13.0905 −0.434424
\(909\) −11.2659 −0.373666
\(910\) 4.52849 0.150118
\(911\) 12.5161 0.414676 0.207338 0.978269i \(-0.433520\pi\)
0.207338 + 0.978269i \(0.433520\pi\)
\(912\) −1.53670 −0.0508852
\(913\) 30.6334 1.01382
\(914\) −9.44931 −0.312555
\(915\) 0.731149 0.0241710
\(916\) −1.05891 −0.0349874
\(917\) 8.77509 0.289779
\(918\) −8.60176 −0.283900
\(919\) −5.20958 −0.171848 −0.0859242 0.996302i \(-0.527384\pi\)
−0.0859242 + 0.996302i \(0.527384\pi\)
\(920\) −25.5531 −0.842461
\(921\) −1.61696 −0.0532805
\(922\) −14.3142 −0.471414
\(923\) 10.5391 0.346899
\(924\) 0.926200 0.0304697
\(925\) 1.56682 0.0515168
\(926\) −17.2331 −0.566314
\(927\) 23.1626 0.760760
\(928\) −33.9770 −1.11535
\(929\) 41.4038 1.35841 0.679207 0.733947i \(-0.262324\pi\)
0.679207 + 0.733947i \(0.262324\pi\)
\(930\) −1.50417 −0.0493236
\(931\) −5.08764 −0.166741
\(932\) 23.2890 0.762855
\(933\) −2.67644 −0.0876226
\(934\) 10.7841 0.352866
\(935\) −8.42389 −0.275491
\(936\) 39.3739 1.28698
\(937\) 13.0517 0.426379 0.213190 0.977011i \(-0.431615\pi\)
0.213190 + 0.977011i \(0.431615\pi\)
\(938\) −9.77314 −0.319104
\(939\) −1.93785 −0.0632395
\(940\) 4.39210 0.143254
\(941\) −43.4066 −1.41501 −0.707507 0.706706i \(-0.750180\pi\)
−0.707507 + 0.706706i \(0.750180\pi\)
\(942\) −3.48923 −0.113685
\(943\) 89.4704 2.91356
\(944\) −6.58250 −0.214242
\(945\) 2.31925 0.0754454
\(946\) 11.5925 0.376906
\(947\) 45.7348 1.48618 0.743091 0.669191i \(-0.233359\pi\)
0.743091 + 0.669191i \(0.233359\pi\)
\(948\) 3.67789 0.119452
\(949\) −49.1592 −1.59578
\(950\) −4.93550 −0.160129
\(951\) −10.3717 −0.336326
\(952\) −11.3450 −0.367695
\(953\) −36.0278 −1.16706 −0.583528 0.812093i \(-0.698328\pi\)
−0.583528 + 0.812093i \(0.698328\pi\)
\(954\) 4.34692 0.140737
\(955\) 11.7995 0.381823
\(956\) −17.6550 −0.571003
\(957\) −5.71871 −0.184860
\(958\) −38.8351 −1.25471
\(959\) 0.00613626 0.000198150 0
\(960\) 2.60535 0.0840873
\(961\) −15.7436 −0.507859
\(962\) 7.09534 0.228763
\(963\) 25.8647 0.833480
\(964\) −6.13490 −0.197592
\(965\) −6.22737 −0.200466
\(966\) −3.31614 −0.106695
\(967\) −31.8922 −1.02558 −0.512792 0.858513i \(-0.671389\pi\)
−0.512792 + 0.858513i \(0.671389\pi\)
\(968\) 18.2353 0.586105
\(969\) −7.72140 −0.248047
\(970\) 14.3868 0.461932
\(971\) 39.9911 1.28338 0.641688 0.766966i \(-0.278234\pi\)
0.641688 + 0.766966i \(0.278234\pi\)
\(972\) 10.5651 0.338876
\(973\) 9.63822 0.308987
\(974\) −15.7503 −0.504674
\(975\) −1.85308 −0.0593461
\(976\) −1.40141 −0.0448582
\(977\) 26.3668 0.843549 0.421774 0.906701i \(-0.361407\pi\)
0.421774 + 0.906701i \(0.361407\pi\)
\(978\) 0.383617 0.0122667
\(979\) 18.8116 0.601220
\(980\) 1.05891 0.0338257
\(981\) −31.8574 −1.01713
\(982\) −22.2475 −0.709947
\(983\) 6.84062 0.218182 0.109091 0.994032i \(-0.465206\pi\)
0.109091 + 0.994032i \(0.465206\pi\)
\(984\) −12.2393 −0.390174
\(985\) 6.52208 0.207811
\(986\) 24.2489 0.772243
\(987\) 1.64652 0.0524094
\(988\) 25.1486 0.800085
\(989\) 46.7021 1.48504
\(990\) −6.07563 −0.193096
\(991\) −10.4466 −0.331847 −0.165924 0.986139i \(-0.553061\pi\)
−0.165924 + 0.986139i \(0.553061\pi\)
\(992\) −20.2982 −0.644469
\(993\) −9.58632 −0.304213
\(994\) −2.19018 −0.0694684
\(995\) 0.945655 0.0299793
\(996\) −5.84415 −0.185179
\(997\) −33.4358 −1.05892 −0.529461 0.848334i \(-0.677606\pi\)
−0.529461 + 0.848334i \(0.677606\pi\)
\(998\) 16.5595 0.524180
\(999\) 3.63386 0.114970
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 \(a_p\))