Properties

Label 4017.2.a.j.1.17
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.39323 q^{2} -1.00000 q^{3} -0.0589163 q^{4} +0.623512 q^{5} -1.39323 q^{6} -3.51013 q^{7} -2.86854 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.39323 q^{2} -1.00000 q^{3} -0.0589163 q^{4} +0.623512 q^{5} -1.39323 q^{6} -3.51013 q^{7} -2.86854 q^{8} +1.00000 q^{9} +0.868695 q^{10} -5.58599 q^{11} +0.0589163 q^{12} +1.00000 q^{13} -4.89041 q^{14} -0.623512 q^{15} -3.87870 q^{16} -2.32558 q^{17} +1.39323 q^{18} +1.21481 q^{19} -0.0367350 q^{20} +3.51013 q^{21} -7.78256 q^{22} +3.37640 q^{23} +2.86854 q^{24} -4.61123 q^{25} +1.39323 q^{26} -1.00000 q^{27} +0.206804 q^{28} +0.198494 q^{29} -0.868695 q^{30} +7.68697 q^{31} +0.333171 q^{32} +5.58599 q^{33} -3.24006 q^{34} -2.18861 q^{35} -0.0589163 q^{36} -6.15059 q^{37} +1.69250 q^{38} -1.00000 q^{39} -1.78857 q^{40} -0.138445 q^{41} +4.89041 q^{42} +2.99205 q^{43} +0.329106 q^{44} +0.623512 q^{45} +4.70410 q^{46} +10.0482 q^{47} +3.87870 q^{48} +5.32103 q^{49} -6.42450 q^{50} +2.32558 q^{51} -0.0589163 q^{52} -4.89477 q^{53} -1.39323 q^{54} -3.48293 q^{55} +10.0690 q^{56} -1.21481 q^{57} +0.276548 q^{58} -2.53206 q^{59} +0.0367350 q^{60} -10.9607 q^{61} +10.7097 q^{62} -3.51013 q^{63} +8.22158 q^{64} +0.623512 q^{65} +7.78256 q^{66} +11.8383 q^{67} +0.137014 q^{68} -3.37640 q^{69} -3.04923 q^{70} +12.6126 q^{71} -2.86854 q^{72} +13.3432 q^{73} -8.56917 q^{74} +4.61123 q^{75} -0.0715718 q^{76} +19.6076 q^{77} -1.39323 q^{78} -1.41353 q^{79} -2.41841 q^{80} +1.00000 q^{81} -0.192886 q^{82} -7.93349 q^{83} -0.206804 q^{84} -1.45003 q^{85} +4.16861 q^{86} -0.198494 q^{87} +16.0236 q^{88} +5.72890 q^{89} +0.868695 q^{90} -3.51013 q^{91} -0.198925 q^{92} -7.68697 q^{93} +13.9995 q^{94} +0.757446 q^{95} -0.333171 q^{96} -6.43788 q^{97} +7.41341 q^{98} -5.58599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39323 0.985161 0.492580 0.870267i \(-0.336054\pi\)
0.492580 + 0.870267i \(0.336054\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.0589163 −0.0294581
\(5\) 0.623512 0.278843 0.139422 0.990233i \(-0.455476\pi\)
0.139422 + 0.990233i \(0.455476\pi\)
\(6\) −1.39323 −0.568783
\(7\) −3.51013 −1.32671 −0.663353 0.748307i \(-0.730867\pi\)
−0.663353 + 0.748307i \(0.730867\pi\)
\(8\) −2.86854 −1.01418
\(9\) 1.00000 0.333333
\(10\) 0.868695 0.274705
\(11\) −5.58599 −1.68424 −0.842120 0.539291i \(-0.818692\pi\)
−0.842120 + 0.539291i \(0.818692\pi\)
\(12\) 0.0589163 0.0170077
\(13\) 1.00000 0.277350
\(14\) −4.89041 −1.30702
\(15\) −0.623512 −0.160990
\(16\) −3.87870 −0.969674
\(17\) −2.32558 −0.564036 −0.282018 0.959409i \(-0.591004\pi\)
−0.282018 + 0.959409i \(0.591004\pi\)
\(18\) 1.39323 0.328387
\(19\) 1.21481 0.278695 0.139348 0.990244i \(-0.455499\pi\)
0.139348 + 0.990244i \(0.455499\pi\)
\(20\) −0.0367350 −0.00821420
\(21\) 3.51013 0.765974
\(22\) −7.78256 −1.65925
\(23\) 3.37640 0.704029 0.352014 0.935995i \(-0.385497\pi\)
0.352014 + 0.935995i \(0.385497\pi\)
\(24\) 2.86854 0.585538
\(25\) −4.61123 −0.922246
\(26\) 1.39323 0.273234
\(27\) −1.00000 −0.192450
\(28\) 0.206804 0.0390823
\(29\) 0.198494 0.0368595 0.0184297 0.999830i \(-0.494133\pi\)
0.0184297 + 0.999830i \(0.494133\pi\)
\(30\) −0.868695 −0.158601
\(31\) 7.68697 1.38062 0.690311 0.723513i \(-0.257474\pi\)
0.690311 + 0.723513i \(0.257474\pi\)
\(32\) 0.333171 0.0588969
\(33\) 5.58599 0.972396
\(34\) −3.24006 −0.555666
\(35\) −2.18861 −0.369943
\(36\) −0.0589163 −0.00981938
\(37\) −6.15059 −1.01115 −0.505575 0.862782i \(-0.668720\pi\)
−0.505575 + 0.862782i \(0.668720\pi\)
\(38\) 1.69250 0.274560
\(39\) −1.00000 −0.160128
\(40\) −1.78857 −0.282798
\(41\) −0.138445 −0.0216215 −0.0108108 0.999942i \(-0.503441\pi\)
−0.0108108 + 0.999942i \(0.503441\pi\)
\(42\) 4.89041 0.754607
\(43\) 2.99205 0.456284 0.228142 0.973628i \(-0.426735\pi\)
0.228142 + 0.973628i \(0.426735\pi\)
\(44\) 0.329106 0.0496145
\(45\) 0.623512 0.0929477
\(46\) 4.70410 0.693582
\(47\) 10.0482 1.46569 0.732843 0.680397i \(-0.238193\pi\)
0.732843 + 0.680397i \(0.238193\pi\)
\(48\) 3.87870 0.559842
\(49\) 5.32103 0.760148
\(50\) −6.42450 −0.908561
\(51\) 2.32558 0.325646
\(52\) −0.0589163 −0.00817021
\(53\) −4.89477 −0.672348 −0.336174 0.941800i \(-0.609133\pi\)
−0.336174 + 0.941800i \(0.609133\pi\)
\(54\) −1.39323 −0.189594
\(55\) −3.48293 −0.469639
\(56\) 10.0690 1.34552
\(57\) −1.21481 −0.160905
\(58\) 0.276548 0.0363125
\(59\) −2.53206 −0.329646 −0.164823 0.986323i \(-0.552705\pi\)
−0.164823 + 0.986323i \(0.552705\pi\)
\(60\) 0.0367350 0.00474247
\(61\) −10.9607 −1.40337 −0.701685 0.712487i \(-0.747569\pi\)
−0.701685 + 0.712487i \(0.747569\pi\)
\(62\) 10.7097 1.36013
\(63\) −3.51013 −0.442235
\(64\) 8.22158 1.02770
\(65\) 0.623512 0.0773372
\(66\) 7.78256 0.957967
\(67\) 11.8383 1.44628 0.723138 0.690704i \(-0.242699\pi\)
0.723138 + 0.690704i \(0.242699\pi\)
\(68\) 0.137014 0.0166154
\(69\) −3.37640 −0.406471
\(70\) −3.04923 −0.364453
\(71\) 12.6126 1.49683 0.748417 0.663228i \(-0.230814\pi\)
0.748417 + 0.663228i \(0.230814\pi\)
\(72\) −2.86854 −0.338061
\(73\) 13.3432 1.56170 0.780850 0.624718i \(-0.214786\pi\)
0.780850 + 0.624718i \(0.214786\pi\)
\(74\) −8.56917 −0.996146
\(75\) 4.61123 0.532459
\(76\) −0.0715718 −0.00820985
\(77\) 19.6076 2.23449
\(78\) −1.39323 −0.157752
\(79\) −1.41353 −0.159034 −0.0795172 0.996833i \(-0.525338\pi\)
−0.0795172 + 0.996833i \(0.525338\pi\)
\(80\) −2.41841 −0.270387
\(81\) 1.00000 0.111111
\(82\) −0.192886 −0.0213007
\(83\) −7.93349 −0.870814 −0.435407 0.900234i \(-0.643396\pi\)
−0.435407 + 0.900234i \(0.643396\pi\)
\(84\) −0.206804 −0.0225642
\(85\) −1.45003 −0.157278
\(86\) 4.16861 0.449513
\(87\) −0.198494 −0.0212808
\(88\) 16.0236 1.70813
\(89\) 5.72890 0.607262 0.303631 0.952790i \(-0.401801\pi\)
0.303631 + 0.952790i \(0.401801\pi\)
\(90\) 0.868695 0.0915685
\(91\) −3.51013 −0.367962
\(92\) −0.198925 −0.0207394
\(93\) −7.68697 −0.797102
\(94\) 13.9995 1.44394
\(95\) 0.757446 0.0777123
\(96\) −0.333171 −0.0340041
\(97\) −6.43788 −0.653667 −0.326834 0.945082i \(-0.605982\pi\)
−0.326834 + 0.945082i \(0.605982\pi\)
\(98\) 7.41341 0.748868
\(99\) −5.58599 −0.561413
\(100\) 0.271677 0.0271677
\(101\) 14.9176 1.48436 0.742178 0.670203i \(-0.233793\pi\)
0.742178 + 0.670203i \(0.233793\pi\)
\(102\) 3.24006 0.320814
\(103\) −1.00000 −0.0985329
\(104\) −2.86854 −0.281283
\(105\) 2.18861 0.213587
\(106\) −6.81952 −0.662371
\(107\) 5.92763 0.573046 0.286523 0.958073i \(-0.407501\pi\)
0.286523 + 0.958073i \(0.407501\pi\)
\(108\) 0.0589163 0.00566922
\(109\) −11.2495 −1.07751 −0.538755 0.842462i \(-0.681105\pi\)
−0.538755 + 0.842462i \(0.681105\pi\)
\(110\) −4.85252 −0.462670
\(111\) 6.15059 0.583788
\(112\) 13.6147 1.28647
\(113\) 8.05742 0.757978 0.378989 0.925401i \(-0.376272\pi\)
0.378989 + 0.925401i \(0.376272\pi\)
\(114\) −1.69250 −0.158517
\(115\) 2.10523 0.196314
\(116\) −0.0116945 −0.00108581
\(117\) 1.00000 0.0924500
\(118\) −3.52773 −0.324754
\(119\) 8.16309 0.748309
\(120\) 1.78857 0.163273
\(121\) 20.2033 1.83666
\(122\) −15.2707 −1.38254
\(123\) 0.138445 0.0124832
\(124\) −0.452888 −0.0406705
\(125\) −5.99272 −0.536005
\(126\) −4.89041 −0.435673
\(127\) −9.49994 −0.842984 −0.421492 0.906832i \(-0.638493\pi\)
−0.421492 + 0.906832i \(0.638493\pi\)
\(128\) 10.7882 0.953550
\(129\) −2.99205 −0.263435
\(130\) 0.868695 0.0761896
\(131\) 7.24489 0.632989 0.316495 0.948594i \(-0.397494\pi\)
0.316495 + 0.948594i \(0.397494\pi\)
\(132\) −0.329106 −0.0286450
\(133\) −4.26413 −0.369747
\(134\) 16.4934 1.42481
\(135\) −0.623512 −0.0536634
\(136\) 6.67102 0.572035
\(137\) −14.1521 −1.20910 −0.604549 0.796568i \(-0.706647\pi\)
−0.604549 + 0.796568i \(0.706647\pi\)
\(138\) −4.70410 −0.400440
\(139\) 6.78145 0.575195 0.287597 0.957751i \(-0.407143\pi\)
0.287597 + 0.957751i \(0.407143\pi\)
\(140\) 0.128945 0.0108978
\(141\) −10.0482 −0.846215
\(142\) 17.5722 1.47462
\(143\) −5.58599 −0.467124
\(144\) −3.87870 −0.323225
\(145\) 0.123764 0.0102780
\(146\) 18.5901 1.53853
\(147\) −5.32103 −0.438871
\(148\) 0.362370 0.0297866
\(149\) −10.6460 −0.872153 −0.436076 0.899910i \(-0.643632\pi\)
−0.436076 + 0.899910i \(0.643632\pi\)
\(150\) 6.42450 0.524558
\(151\) −10.0387 −0.816935 −0.408468 0.912773i \(-0.633937\pi\)
−0.408468 + 0.912773i \(0.633937\pi\)
\(152\) −3.48472 −0.282648
\(153\) −2.32558 −0.188012
\(154\) 27.3178 2.20133
\(155\) 4.79292 0.384977
\(156\) 0.0589163 0.00471708
\(157\) 15.6058 1.24548 0.622738 0.782430i \(-0.286020\pi\)
0.622738 + 0.782430i \(0.286020\pi\)
\(158\) −1.96937 −0.156674
\(159\) 4.89477 0.388180
\(160\) 0.207736 0.0164230
\(161\) −11.8516 −0.934039
\(162\) 1.39323 0.109462
\(163\) −18.7849 −1.47135 −0.735674 0.677336i \(-0.763134\pi\)
−0.735674 + 0.677336i \(0.763134\pi\)
\(164\) 0.00815668 0.000636930 0
\(165\) 3.48293 0.271146
\(166\) −11.0532 −0.857892
\(167\) 17.1601 1.32789 0.663946 0.747780i \(-0.268880\pi\)
0.663946 + 0.747780i \(0.268880\pi\)
\(168\) −10.0690 −0.776837
\(169\) 1.00000 0.0769231
\(170\) −2.02022 −0.154944
\(171\) 1.21481 0.0928985
\(172\) −0.176280 −0.0134413
\(173\) −14.5383 −1.10532 −0.552662 0.833406i \(-0.686388\pi\)
−0.552662 + 0.833406i \(0.686388\pi\)
\(174\) −0.276548 −0.0209650
\(175\) 16.1860 1.22355
\(176\) 21.6664 1.63316
\(177\) 2.53206 0.190321
\(178\) 7.98166 0.598251
\(179\) −9.18888 −0.686809 −0.343405 0.939188i \(-0.611580\pi\)
−0.343405 + 0.939188i \(0.611580\pi\)
\(180\) −0.0367350 −0.00273807
\(181\) 2.04116 0.151718 0.0758590 0.997119i \(-0.475830\pi\)
0.0758590 + 0.997119i \(0.475830\pi\)
\(182\) −4.89041 −0.362502
\(183\) 10.9607 0.810236
\(184\) −9.68535 −0.714013
\(185\) −3.83497 −0.281953
\(186\) −10.7097 −0.785274
\(187\) 12.9907 0.949971
\(188\) −0.592005 −0.0431764
\(189\) 3.51013 0.255325
\(190\) 1.05529 0.0765591
\(191\) 14.3314 1.03698 0.518490 0.855084i \(-0.326494\pi\)
0.518490 + 0.855084i \(0.326494\pi\)
\(192\) −8.22158 −0.593341
\(193\) 9.12754 0.657014 0.328507 0.944501i \(-0.393454\pi\)
0.328507 + 0.944501i \(0.393454\pi\)
\(194\) −8.96943 −0.643967
\(195\) −0.623512 −0.0446506
\(196\) −0.313495 −0.0223925
\(197\) −15.9455 −1.13607 −0.568034 0.823005i \(-0.692296\pi\)
−0.568034 + 0.823005i \(0.692296\pi\)
\(198\) −7.78256 −0.553082
\(199\) 9.81013 0.695422 0.347711 0.937602i \(-0.386959\pi\)
0.347711 + 0.937602i \(0.386959\pi\)
\(200\) 13.2275 0.935326
\(201\) −11.8383 −0.835007
\(202\) 20.7836 1.46233
\(203\) −0.696741 −0.0489016
\(204\) −0.137014 −0.00959293
\(205\) −0.0863224 −0.00602902
\(206\) −1.39323 −0.0970708
\(207\) 3.37640 0.234676
\(208\) −3.87870 −0.268939
\(209\) −6.78589 −0.469390
\(210\) 3.04923 0.210417
\(211\) −19.3221 −1.33019 −0.665095 0.746758i \(-0.731609\pi\)
−0.665095 + 0.746758i \(0.731609\pi\)
\(212\) 0.288381 0.0198061
\(213\) −12.6126 −0.864198
\(214\) 8.25854 0.564542
\(215\) 1.86558 0.127232
\(216\) 2.86854 0.195179
\(217\) −26.9823 −1.83168
\(218\) −15.6732 −1.06152
\(219\) −13.3432 −0.901648
\(220\) 0.205201 0.0138347
\(221\) −2.32558 −0.156435
\(222\) 8.56917 0.575125
\(223\) 8.65778 0.579768 0.289884 0.957062i \(-0.406383\pi\)
0.289884 + 0.957062i \(0.406383\pi\)
\(224\) −1.16947 −0.0781388
\(225\) −4.61123 −0.307415
\(226\) 11.2258 0.746730
\(227\) 13.9306 0.924604 0.462302 0.886722i \(-0.347024\pi\)
0.462302 + 0.886722i \(0.347024\pi\)
\(228\) 0.0715718 0.00473996
\(229\) 26.1342 1.72700 0.863500 0.504350i \(-0.168268\pi\)
0.863500 + 0.504350i \(0.168268\pi\)
\(230\) 2.93306 0.193401
\(231\) −19.6076 −1.29008
\(232\) −0.569389 −0.0373822
\(233\) 23.5545 1.54311 0.771553 0.636165i \(-0.219480\pi\)
0.771553 + 0.636165i \(0.219480\pi\)
\(234\) 1.39323 0.0910782
\(235\) 6.26520 0.408697
\(236\) 0.149179 0.00971075
\(237\) 1.41353 0.0918185
\(238\) 11.3730 0.737205
\(239\) −8.80497 −0.569546 −0.284773 0.958595i \(-0.591918\pi\)
−0.284773 + 0.958595i \(0.591918\pi\)
\(240\) 2.41841 0.156108
\(241\) 14.9700 0.964303 0.482152 0.876088i \(-0.339855\pi\)
0.482152 + 0.876088i \(0.339855\pi\)
\(242\) 28.1478 1.80941
\(243\) −1.00000 −0.0641500
\(244\) 0.645762 0.0413406
\(245\) 3.31773 0.211962
\(246\) 0.192886 0.0122980
\(247\) 1.21481 0.0772962
\(248\) −22.0504 −1.40020
\(249\) 7.93349 0.502765
\(250\) −8.34923 −0.528051
\(251\) −1.59917 −0.100938 −0.0504692 0.998726i \(-0.516072\pi\)
−0.0504692 + 0.998726i \(0.516072\pi\)
\(252\) 0.206804 0.0130274
\(253\) −18.8606 −1.18575
\(254\) −13.2356 −0.830475
\(255\) 1.45003 0.0908042
\(256\) −1.41275 −0.0882969
\(257\) −13.0861 −0.816290 −0.408145 0.912917i \(-0.633824\pi\)
−0.408145 + 0.912917i \(0.633824\pi\)
\(258\) −4.16861 −0.259526
\(259\) 21.5894 1.34150
\(260\) −0.0367350 −0.00227821
\(261\) 0.198494 0.0122865
\(262\) 10.0938 0.623596
\(263\) −4.71375 −0.290662 −0.145331 0.989383i \(-0.546425\pi\)
−0.145331 + 0.989383i \(0.546425\pi\)
\(264\) −16.0236 −0.986187
\(265\) −3.05195 −0.187480
\(266\) −5.94090 −0.364260
\(267\) −5.72890 −0.350603
\(268\) −0.697467 −0.0426046
\(269\) −0.151544 −0.00923980 −0.00461990 0.999989i \(-0.501471\pi\)
−0.00461990 + 0.999989i \(0.501471\pi\)
\(270\) −0.868695 −0.0528671
\(271\) 9.25680 0.562310 0.281155 0.959662i \(-0.409282\pi\)
0.281155 + 0.959662i \(0.409282\pi\)
\(272\) 9.02022 0.546931
\(273\) 3.51013 0.212443
\(274\) −19.7171 −1.19116
\(275\) 25.7583 1.55328
\(276\) 0.198925 0.0119739
\(277\) 24.5898 1.47746 0.738728 0.674004i \(-0.235427\pi\)
0.738728 + 0.674004i \(0.235427\pi\)
\(278\) 9.44810 0.566660
\(279\) 7.68697 0.460207
\(280\) 6.27812 0.375189
\(281\) −7.66509 −0.457261 −0.228630 0.973513i \(-0.573425\pi\)
−0.228630 + 0.973513i \(0.573425\pi\)
\(282\) −13.9995 −0.833658
\(283\) 30.8950 1.83652 0.918260 0.395978i \(-0.129595\pi\)
0.918260 + 0.395978i \(0.129595\pi\)
\(284\) −0.743084 −0.0440939
\(285\) −0.757446 −0.0448672
\(286\) −7.78256 −0.460192
\(287\) 0.485962 0.0286854
\(288\) 0.333171 0.0196323
\(289\) −11.5917 −0.681864
\(290\) 0.172431 0.0101255
\(291\) 6.43788 0.377395
\(292\) −0.786130 −0.0460048
\(293\) −8.39607 −0.490504 −0.245252 0.969459i \(-0.578871\pi\)
−0.245252 + 0.969459i \(0.578871\pi\)
\(294\) −7.41341 −0.432359
\(295\) −1.57877 −0.0919195
\(296\) 17.6432 1.02549
\(297\) 5.58599 0.324132
\(298\) −14.8323 −0.859211
\(299\) 3.37640 0.195262
\(300\) −0.271677 −0.0156853
\(301\) −10.5025 −0.605354
\(302\) −13.9861 −0.804812
\(303\) −14.9176 −0.856994
\(304\) −4.71186 −0.270244
\(305\) −6.83411 −0.391320
\(306\) −3.24006 −0.185222
\(307\) 16.9044 0.964787 0.482393 0.875955i \(-0.339768\pi\)
0.482393 + 0.875955i \(0.339768\pi\)
\(308\) −1.15520 −0.0658239
\(309\) 1.00000 0.0568880
\(310\) 6.67763 0.379264
\(311\) 14.1865 0.804441 0.402221 0.915543i \(-0.368238\pi\)
0.402221 + 0.915543i \(0.368238\pi\)
\(312\) 2.86854 0.162399
\(313\) 20.0222 1.13172 0.565861 0.824501i \(-0.308544\pi\)
0.565861 + 0.824501i \(0.308544\pi\)
\(314\) 21.7424 1.22699
\(315\) −2.18861 −0.123314
\(316\) 0.0832798 0.00468485
\(317\) −21.0736 −1.18361 −0.591807 0.806080i \(-0.701585\pi\)
−0.591807 + 0.806080i \(0.701585\pi\)
\(318\) 6.81952 0.382420
\(319\) −1.10879 −0.0620802
\(320\) 5.12625 0.286566
\(321\) −5.92763 −0.330848
\(322\) −16.5120 −0.920179
\(323\) −2.82513 −0.157194
\(324\) −0.0589163 −0.00327313
\(325\) −4.61123 −0.255785
\(326\) −26.1716 −1.44951
\(327\) 11.2495 0.622101
\(328\) 0.397136 0.0219282
\(329\) −35.2707 −1.94453
\(330\) 4.85252 0.267122
\(331\) −21.6470 −1.18982 −0.594912 0.803791i \(-0.702813\pi\)
−0.594912 + 0.803791i \(0.702813\pi\)
\(332\) 0.467412 0.0256525
\(333\) −6.15059 −0.337050
\(334\) 23.9080 1.30819
\(335\) 7.38131 0.403284
\(336\) −13.6147 −0.742745
\(337\) 7.03473 0.383206 0.191603 0.981473i \(-0.438631\pi\)
0.191603 + 0.981473i \(0.438631\pi\)
\(338\) 1.39323 0.0757816
\(339\) −8.05742 −0.437619
\(340\) 0.0854302 0.00463310
\(341\) −42.9394 −2.32530
\(342\) 1.69250 0.0915200
\(343\) 5.89340 0.318214
\(344\) −8.58282 −0.462755
\(345\) −2.10523 −0.113342
\(346\) −20.2551 −1.08892
\(347\) −3.75732 −0.201704 −0.100852 0.994901i \(-0.532157\pi\)
−0.100852 + 0.994901i \(0.532157\pi\)
\(348\) 0.0116945 0.000626893 0
\(349\) −17.4340 −0.933220 −0.466610 0.884463i \(-0.654525\pi\)
−0.466610 + 0.884463i \(0.654525\pi\)
\(350\) 22.5508 1.20539
\(351\) −1.00000 −0.0533761
\(352\) −1.86109 −0.0991965
\(353\) 1.22134 0.0650054 0.0325027 0.999472i \(-0.489652\pi\)
0.0325027 + 0.999472i \(0.489652\pi\)
\(354\) 3.52773 0.187497
\(355\) 7.86408 0.417382
\(356\) −0.337525 −0.0178888
\(357\) −8.16309 −0.432037
\(358\) −12.8022 −0.676618
\(359\) 6.72978 0.355184 0.177592 0.984104i \(-0.443169\pi\)
0.177592 + 0.984104i \(0.443169\pi\)
\(360\) −1.78857 −0.0942659
\(361\) −17.5242 −0.922329
\(362\) 2.84380 0.149467
\(363\) −20.2033 −1.06040
\(364\) 0.206804 0.0108395
\(365\) 8.31963 0.435469
\(366\) 15.2707 0.798213
\(367\) 26.8652 1.40235 0.701177 0.712987i \(-0.252658\pi\)
0.701177 + 0.712987i \(0.252658\pi\)
\(368\) −13.0960 −0.682679
\(369\) −0.138445 −0.00720718
\(370\) −5.34299 −0.277769
\(371\) 17.1813 0.892007
\(372\) 0.452888 0.0234811
\(373\) −32.8670 −1.70179 −0.850895 0.525335i \(-0.823940\pi\)
−0.850895 + 0.525335i \(0.823940\pi\)
\(374\) 18.0990 0.935875
\(375\) 5.99272 0.309463
\(376\) −28.8238 −1.48647
\(377\) 0.198494 0.0102230
\(378\) 4.89041 0.251536
\(379\) 4.08694 0.209932 0.104966 0.994476i \(-0.466527\pi\)
0.104966 + 0.994476i \(0.466527\pi\)
\(380\) −0.0446259 −0.00228926
\(381\) 9.49994 0.486697
\(382\) 19.9668 1.02159
\(383\) 15.9831 0.816699 0.408349 0.912826i \(-0.366104\pi\)
0.408349 + 0.912826i \(0.366104\pi\)
\(384\) −10.7882 −0.550532
\(385\) 12.2256 0.623072
\(386\) 12.7167 0.647265
\(387\) 2.99205 0.152095
\(388\) 0.379296 0.0192558
\(389\) 16.2958 0.826232 0.413116 0.910678i \(-0.364440\pi\)
0.413116 + 0.910678i \(0.364440\pi\)
\(390\) −0.868695 −0.0439881
\(391\) −7.85209 −0.397098
\(392\) −15.2636 −0.770928
\(393\) −7.24489 −0.365456
\(394\) −22.2157 −1.11921
\(395\) −0.881352 −0.0443456
\(396\) 0.329106 0.0165382
\(397\) −2.71844 −0.136434 −0.0682172 0.997670i \(-0.521731\pi\)
−0.0682172 + 0.997670i \(0.521731\pi\)
\(398\) 13.6677 0.685102
\(399\) 4.26413 0.213473
\(400\) 17.8856 0.894279
\(401\) −12.3564 −0.617049 −0.308524 0.951216i \(-0.599835\pi\)
−0.308524 + 0.951216i \(0.599835\pi\)
\(402\) −16.4934 −0.822617
\(403\) 7.68697 0.382915
\(404\) −0.878889 −0.0437264
\(405\) 0.623512 0.0309826
\(406\) −0.970719 −0.0481760
\(407\) 34.3571 1.70302
\(408\) −6.67102 −0.330264
\(409\) −19.4791 −0.963181 −0.481591 0.876396i \(-0.659941\pi\)
−0.481591 + 0.876396i \(0.659941\pi\)
\(410\) −0.120267 −0.00593955
\(411\) 14.1521 0.698073
\(412\) 0.0589163 0.00290260
\(413\) 8.88786 0.437343
\(414\) 4.70410 0.231194
\(415\) −4.94663 −0.242821
\(416\) 0.333171 0.0163351
\(417\) −6.78145 −0.332089
\(418\) −9.45429 −0.462425
\(419\) 6.50214 0.317650 0.158825 0.987307i \(-0.449229\pi\)
0.158825 + 0.987307i \(0.449229\pi\)
\(420\) −0.128945 −0.00629186
\(421\) −30.5827 −1.49051 −0.745255 0.666780i \(-0.767672\pi\)
−0.745255 + 0.666780i \(0.767672\pi\)
\(422\) −26.9201 −1.31045
\(423\) 10.0482 0.488562
\(424\) 14.0408 0.681883
\(425\) 10.7238 0.520180
\(426\) −17.5722 −0.851374
\(427\) 38.4734 1.86186
\(428\) −0.349234 −0.0168809
\(429\) 5.58599 0.269694
\(430\) 2.59918 0.125344
\(431\) 32.7855 1.57922 0.789611 0.613607i \(-0.210282\pi\)
0.789611 + 0.613607i \(0.210282\pi\)
\(432\) 3.87870 0.186614
\(433\) −19.3376 −0.929305 −0.464653 0.885493i \(-0.653821\pi\)
−0.464653 + 0.885493i \(0.653821\pi\)
\(434\) −37.5925 −1.80450
\(435\) −0.123764 −0.00593401
\(436\) 0.662780 0.0317414
\(437\) 4.10167 0.196210
\(438\) −18.5901 −0.888268
\(439\) −30.5692 −1.45899 −0.729493 0.683988i \(-0.760244\pi\)
−0.729493 + 0.683988i \(0.760244\pi\)
\(440\) 9.99093 0.476299
\(441\) 5.32103 0.253383
\(442\) −3.24006 −0.154114
\(443\) −27.4515 −1.30426 −0.652130 0.758107i \(-0.726124\pi\)
−0.652130 + 0.758107i \(0.726124\pi\)
\(444\) −0.362370 −0.0171973
\(445\) 3.57204 0.169331
\(446\) 12.0623 0.571164
\(447\) 10.6460 0.503538
\(448\) −28.8588 −1.36345
\(449\) 34.0830 1.60847 0.804237 0.594308i \(-0.202574\pi\)
0.804237 + 0.594308i \(0.202574\pi\)
\(450\) −6.42450 −0.302854
\(451\) 0.773355 0.0364158
\(452\) −0.474713 −0.0223286
\(453\) 10.0387 0.471658
\(454\) 19.4085 0.910884
\(455\) −2.18861 −0.102604
\(456\) 3.48472 0.163187
\(457\) −1.83623 −0.0858953 −0.0429476 0.999077i \(-0.513675\pi\)
−0.0429476 + 0.999077i \(0.513675\pi\)
\(458\) 36.4109 1.70137
\(459\) 2.32558 0.108549
\(460\) −0.124032 −0.00578303
\(461\) 32.5255 1.51486 0.757432 0.652914i \(-0.226454\pi\)
0.757432 + 0.652914i \(0.226454\pi\)
\(462\) −27.3178 −1.27094
\(463\) 4.40056 0.204511 0.102256 0.994758i \(-0.467394\pi\)
0.102256 + 0.994758i \(0.467394\pi\)
\(464\) −0.769899 −0.0357417
\(465\) −4.79292 −0.222266
\(466\) 32.8168 1.52021
\(467\) 22.8375 1.05679 0.528396 0.848998i \(-0.322794\pi\)
0.528396 + 0.848998i \(0.322794\pi\)
\(468\) −0.0589163 −0.00272340
\(469\) −41.5539 −1.91878
\(470\) 8.72885 0.402632
\(471\) −15.6058 −0.719076
\(472\) 7.26331 0.334321
\(473\) −16.7136 −0.768491
\(474\) 1.96937 0.0904560
\(475\) −5.60175 −0.257026
\(476\) −0.480939 −0.0220438
\(477\) −4.89477 −0.224116
\(478\) −12.2673 −0.561095
\(479\) −12.1490 −0.555101 −0.277551 0.960711i \(-0.589523\pi\)
−0.277551 + 0.960711i \(0.589523\pi\)
\(480\) −0.207736 −0.00948182
\(481\) −6.15059 −0.280443
\(482\) 20.8566 0.949994
\(483\) 11.8516 0.539268
\(484\) −1.19030 −0.0541046
\(485\) −4.01409 −0.182271
\(486\) −1.39323 −0.0631981
\(487\) −28.5484 −1.29365 −0.646826 0.762638i \(-0.723904\pi\)
−0.646826 + 0.762638i \(0.723904\pi\)
\(488\) 31.4411 1.42327
\(489\) 18.7849 0.849483
\(490\) 4.62235 0.208817
\(491\) 7.58496 0.342304 0.171152 0.985245i \(-0.445251\pi\)
0.171152 + 0.985245i \(0.445251\pi\)
\(492\) −0.00815668 −0.000367732 0
\(493\) −0.461614 −0.0207901
\(494\) 1.69250 0.0761492
\(495\) −3.48293 −0.156546
\(496\) −29.8154 −1.33875
\(497\) −44.2717 −1.98586
\(498\) 11.0532 0.495304
\(499\) 21.0538 0.942499 0.471250 0.882000i \(-0.343803\pi\)
0.471250 + 0.882000i \(0.343803\pi\)
\(500\) 0.353069 0.0157897
\(501\) −17.1601 −0.766659
\(502\) −2.22800 −0.0994406
\(503\) −11.6612 −0.519946 −0.259973 0.965616i \(-0.583714\pi\)
−0.259973 + 0.965616i \(0.583714\pi\)
\(504\) 10.0690 0.448507
\(505\) 9.30131 0.413903
\(506\) −26.2771 −1.16816
\(507\) −1.00000 −0.0444116
\(508\) 0.559701 0.0248327
\(509\) 34.5093 1.52960 0.764798 0.644270i \(-0.222839\pi\)
0.764798 + 0.644270i \(0.222839\pi\)
\(510\) 2.02022 0.0894568
\(511\) −46.8363 −2.07192
\(512\) −23.5447 −1.04054
\(513\) −1.21481 −0.0536350
\(514\) −18.2319 −0.804177
\(515\) −0.623512 −0.0274752
\(516\) 0.176280 0.00776032
\(517\) −56.1294 −2.46857
\(518\) 30.0789 1.32159
\(519\) 14.5383 0.638159
\(520\) −1.78857 −0.0784340
\(521\) 24.2192 1.06106 0.530531 0.847665i \(-0.321992\pi\)
0.530531 + 0.847665i \(0.321992\pi\)
\(522\) 0.276548 0.0121042
\(523\) −37.5545 −1.64214 −0.821071 0.570826i \(-0.806623\pi\)
−0.821071 + 0.570826i \(0.806623\pi\)
\(524\) −0.426842 −0.0186467
\(525\) −16.1860 −0.706417
\(526\) −6.56733 −0.286349
\(527\) −17.8767 −0.778720
\(528\) −21.6664 −0.942907
\(529\) −11.5999 −0.504343
\(530\) −4.25206 −0.184698
\(531\) −2.53206 −0.109882
\(532\) 0.251226 0.0108920
\(533\) −0.138445 −0.00599673
\(534\) −7.98166 −0.345400
\(535\) 3.69595 0.159790
\(536\) −33.9586 −1.46679
\(537\) 9.18888 0.396529
\(538\) −0.211135 −0.00910269
\(539\) −29.7232 −1.28027
\(540\) 0.0367350 0.00158082
\(541\) 7.66595 0.329585 0.164792 0.986328i \(-0.447305\pi\)
0.164792 + 0.986328i \(0.447305\pi\)
\(542\) 12.8968 0.553966
\(543\) −2.04116 −0.0875944
\(544\) −0.774816 −0.0332200
\(545\) −7.01422 −0.300456
\(546\) 4.89041 0.209290
\(547\) 30.3058 1.29578 0.647892 0.761732i \(-0.275651\pi\)
0.647892 + 0.761732i \(0.275651\pi\)
\(548\) 0.833791 0.0356178
\(549\) −10.9607 −0.467790
\(550\) 35.8872 1.53023
\(551\) 0.241132 0.0102726
\(552\) 9.68535 0.412236
\(553\) 4.96167 0.210992
\(554\) 34.2592 1.45553
\(555\) 3.83497 0.162785
\(556\) −0.399538 −0.0169442
\(557\) −21.0984 −0.893969 −0.446985 0.894542i \(-0.647502\pi\)
−0.446985 + 0.894542i \(0.647502\pi\)
\(558\) 10.7097 0.453378
\(559\) 2.99205 0.126550
\(560\) 8.48896 0.358724
\(561\) −12.9907 −0.548466
\(562\) −10.6792 −0.450476
\(563\) −1.49987 −0.0632119 −0.0316060 0.999500i \(-0.510062\pi\)
−0.0316060 + 0.999500i \(0.510062\pi\)
\(564\) 0.592005 0.0249279
\(565\) 5.02390 0.211357
\(566\) 43.0438 1.80927
\(567\) −3.51013 −0.147412
\(568\) −36.1796 −1.51806
\(569\) 1.58922 0.0666238 0.0333119 0.999445i \(-0.489395\pi\)
0.0333119 + 0.999445i \(0.489395\pi\)
\(570\) −1.05529 −0.0442014
\(571\) 19.7581 0.826851 0.413426 0.910538i \(-0.364332\pi\)
0.413426 + 0.910538i \(0.364332\pi\)
\(572\) 0.329106 0.0137606
\(573\) −14.3314 −0.598701
\(574\) 0.677055 0.0282597
\(575\) −15.5694 −0.649288
\(576\) 8.22158 0.342566
\(577\) 27.2376 1.13391 0.566957 0.823747i \(-0.308120\pi\)
0.566957 + 0.823747i \(0.308120\pi\)
\(578\) −16.1499 −0.671745
\(579\) −9.12754 −0.379327
\(580\) −0.00729169 −0.000302771 0
\(581\) 27.8476 1.15531
\(582\) 8.96943 0.371795
\(583\) 27.3421 1.13239
\(584\) −38.2754 −1.58385
\(585\) 0.623512 0.0257791
\(586\) −11.6976 −0.483225
\(587\) 21.6708 0.894448 0.447224 0.894422i \(-0.352413\pi\)
0.447224 + 0.894422i \(0.352413\pi\)
\(588\) 0.313495 0.0129283
\(589\) 9.33818 0.384773
\(590\) −2.19959 −0.0905555
\(591\) 15.9455 0.655909
\(592\) 23.8563 0.980487
\(593\) 1.93250 0.0793584 0.0396792 0.999212i \(-0.487366\pi\)
0.0396792 + 0.999212i \(0.487366\pi\)
\(594\) 7.78256 0.319322
\(595\) 5.08979 0.208661
\(596\) 0.627221 0.0256920
\(597\) −9.81013 −0.401502
\(598\) 4.70410 0.192365
\(599\) 27.8408 1.13754 0.568771 0.822496i \(-0.307419\pi\)
0.568771 + 0.822496i \(0.307419\pi\)
\(600\) −13.2275 −0.540011
\(601\) −31.1724 −1.27155 −0.635774 0.771875i \(-0.719319\pi\)
−0.635774 + 0.771875i \(0.719319\pi\)
\(602\) −14.6324 −0.596371
\(603\) 11.8383 0.482092
\(604\) 0.591441 0.0240654
\(605\) 12.5970 0.512141
\(606\) −20.7836 −0.844277
\(607\) −40.6348 −1.64932 −0.824659 0.565631i \(-0.808633\pi\)
−0.824659 + 0.565631i \(0.808633\pi\)
\(608\) 0.404738 0.0164143
\(609\) 0.696741 0.0282334
\(610\) −9.52147 −0.385513
\(611\) 10.0482 0.406508
\(612\) 0.137014 0.00553848
\(613\) 20.6548 0.834241 0.417120 0.908851i \(-0.363039\pi\)
0.417120 + 0.908851i \(0.363039\pi\)
\(614\) 23.5517 0.950470
\(615\) 0.0863224 0.00348085
\(616\) −56.2451 −2.26618
\(617\) 35.6280 1.43433 0.717164 0.696905i \(-0.245440\pi\)
0.717164 + 0.696905i \(0.245440\pi\)
\(618\) 1.39323 0.0560438
\(619\) −14.6429 −0.588547 −0.294274 0.955721i \(-0.595078\pi\)
−0.294274 + 0.955721i \(0.595078\pi\)
\(620\) −0.282381 −0.0113407
\(621\) −3.37640 −0.135490
\(622\) 19.7650 0.792504
\(623\) −20.1092 −0.805658
\(624\) 3.87870 0.155272
\(625\) 19.3196 0.772785
\(626\) 27.8955 1.11493
\(627\) 6.78589 0.271002
\(628\) −0.919434 −0.0366894
\(629\) 14.3037 0.570325
\(630\) −3.04923 −0.121484
\(631\) −7.38635 −0.294046 −0.147023 0.989133i \(-0.546969\pi\)
−0.147023 + 0.989133i \(0.546969\pi\)
\(632\) 4.05476 0.161290
\(633\) 19.3221 0.767986
\(634\) −29.3604 −1.16605
\(635\) −5.92333 −0.235060
\(636\) −0.288381 −0.0114351
\(637\) 5.32103 0.210827
\(638\) −1.54479 −0.0611589
\(639\) 12.6126 0.498945
\(640\) 6.72657 0.265891
\(641\) −11.1588 −0.440746 −0.220373 0.975416i \(-0.570728\pi\)
−0.220373 + 0.975416i \(0.570728\pi\)
\(642\) −8.25854 −0.325939
\(643\) 34.2972 1.35255 0.676275 0.736650i \(-0.263593\pi\)
0.676275 + 0.736650i \(0.263593\pi\)
\(644\) 0.698253 0.0275150
\(645\) −1.86558 −0.0734572
\(646\) −3.93604 −0.154862
\(647\) −12.3868 −0.486976 −0.243488 0.969904i \(-0.578292\pi\)
−0.243488 + 0.969904i \(0.578292\pi\)
\(648\) −2.86854 −0.112687
\(649\) 14.1441 0.555203
\(650\) −6.42450 −0.251990
\(651\) 26.9823 1.05752
\(652\) 1.10674 0.0433431
\(653\) 15.8968 0.622088 0.311044 0.950396i \(-0.399321\pi\)
0.311044 + 0.950396i \(0.399321\pi\)
\(654\) 15.6732 0.612869
\(655\) 4.51728 0.176505
\(656\) 0.536988 0.0209658
\(657\) 13.3432 0.520567
\(658\) −49.1401 −1.91568
\(659\) 0.893369 0.0348007 0.0174003 0.999849i \(-0.494461\pi\)
0.0174003 + 0.999849i \(0.494461\pi\)
\(660\) −0.205201 −0.00798745
\(661\) −2.77680 −0.108005 −0.0540025 0.998541i \(-0.517198\pi\)
−0.0540025 + 0.998541i \(0.517198\pi\)
\(662\) −30.1591 −1.17217
\(663\) 2.32558 0.0903180
\(664\) 22.7575 0.883164
\(665\) −2.65874 −0.103101
\(666\) −8.56917 −0.332049
\(667\) 0.670197 0.0259501
\(668\) −1.01101 −0.0391172
\(669\) −8.65778 −0.334729
\(670\) 10.2838 0.397300
\(671\) 61.2262 2.36361
\(672\) 1.16947 0.0451135
\(673\) 23.6763 0.912653 0.456326 0.889812i \(-0.349165\pi\)
0.456326 + 0.889812i \(0.349165\pi\)
\(674\) 9.80098 0.377520
\(675\) 4.61123 0.177486
\(676\) −0.0589163 −0.00226601
\(677\) 8.05264 0.309488 0.154744 0.987955i \(-0.450545\pi\)
0.154744 + 0.987955i \(0.450545\pi\)
\(678\) −11.2258 −0.431125
\(679\) 22.5978 0.867224
\(680\) 4.15946 0.159508
\(681\) −13.9306 −0.533821
\(682\) −59.8243 −2.29079
\(683\) 22.0387 0.843287 0.421643 0.906762i \(-0.361453\pi\)
0.421643 + 0.906762i \(0.361453\pi\)
\(684\) −0.0715718 −0.00273662
\(685\) −8.82403 −0.337149
\(686\) 8.21084 0.313491
\(687\) −26.1342 −0.997083
\(688\) −11.6053 −0.442446
\(689\) −4.89477 −0.186476
\(690\) −2.93306 −0.111660
\(691\) 0.281085 0.0106930 0.00534649 0.999986i \(-0.498298\pi\)
0.00534649 + 0.999986i \(0.498298\pi\)
\(692\) 0.856540 0.0325608
\(693\) 19.6076 0.744830
\(694\) −5.23481 −0.198711
\(695\) 4.22832 0.160389
\(696\) 0.569389 0.0215826
\(697\) 0.321966 0.0121953
\(698\) −24.2895 −0.919372
\(699\) −23.5545 −0.890913
\(700\) −0.953621 −0.0360435
\(701\) −12.7370 −0.481069 −0.240534 0.970641i \(-0.577323\pi\)
−0.240534 + 0.970641i \(0.577323\pi\)
\(702\) −1.39323 −0.0525840
\(703\) −7.47177 −0.281803
\(704\) −45.9256 −1.73089
\(705\) −6.26520 −0.235961
\(706\) 1.70161 0.0640408
\(707\) −52.3628 −1.96930
\(708\) −0.149179 −0.00560650
\(709\) −46.4397 −1.74408 −0.872039 0.489436i \(-0.837203\pi\)
−0.872039 + 0.489436i \(0.837203\pi\)
\(710\) 10.9565 0.411188
\(711\) −1.41353 −0.0530115
\(712\) −16.4336 −0.615874
\(713\) 25.9543 0.971997
\(714\) −11.3730 −0.425626
\(715\) −3.48293 −0.130254
\(716\) 0.541374 0.0202321
\(717\) 8.80497 0.328828
\(718\) 9.37612 0.349914
\(719\) −0.212425 −0.00792212 −0.00396106 0.999992i \(-0.501261\pi\)
−0.00396106 + 0.999992i \(0.501261\pi\)
\(720\) −2.41841 −0.0901290
\(721\) 3.51013 0.130724
\(722\) −24.4153 −0.908642
\(723\) −14.9700 −0.556741
\(724\) −0.120257 −0.00446933
\(725\) −0.915303 −0.0339935
\(726\) −28.1478 −1.04466
\(727\) −47.5945 −1.76518 −0.882591 0.470142i \(-0.844203\pi\)
−0.882591 + 0.470142i \(0.844203\pi\)
\(728\) 10.0690 0.373180
\(729\) 1.00000 0.0370370
\(730\) 11.5911 0.429007
\(731\) −6.95825 −0.257360
\(732\) −0.645762 −0.0238680
\(733\) −15.5758 −0.575306 −0.287653 0.957735i \(-0.592875\pi\)
−0.287653 + 0.957735i \(0.592875\pi\)
\(734\) 37.4294 1.38154
\(735\) −3.31773 −0.122376
\(736\) 1.12492 0.0414651
\(737\) −66.1285 −2.43587
\(738\) −0.192886 −0.00710023
\(739\) 26.3314 0.968616 0.484308 0.874897i \(-0.339071\pi\)
0.484308 + 0.874897i \(0.339071\pi\)
\(740\) 0.225942 0.00830579
\(741\) −1.21481 −0.0446270
\(742\) 23.9374 0.878771
\(743\) 39.0347 1.43205 0.716023 0.698077i \(-0.245961\pi\)
0.716023 + 0.698077i \(0.245961\pi\)
\(744\) 22.0504 0.808406
\(745\) −6.63790 −0.243194
\(746\) −45.7913 −1.67654
\(747\) −7.93349 −0.290271
\(748\) −0.765361 −0.0279844
\(749\) −20.8068 −0.760263
\(750\) 8.34923 0.304871
\(751\) 8.77940 0.320365 0.160182 0.987087i \(-0.448792\pi\)
0.160182 + 0.987087i \(0.448792\pi\)
\(752\) −38.9741 −1.42124
\(753\) 1.59917 0.0582768
\(754\) 0.276548 0.0100713
\(755\) −6.25923 −0.227797
\(756\) −0.206804 −0.00752138
\(757\) −0.806275 −0.0293046 −0.0146523 0.999893i \(-0.504664\pi\)
−0.0146523 + 0.999893i \(0.504664\pi\)
\(758\) 5.69404 0.206817
\(759\) 18.8606 0.684595
\(760\) −2.17276 −0.0788144
\(761\) −33.1652 −1.20224 −0.601119 0.799160i \(-0.705278\pi\)
−0.601119 + 0.799160i \(0.705278\pi\)
\(762\) 13.2356 0.479475
\(763\) 39.4874 1.42954
\(764\) −0.844350 −0.0305475
\(765\) −1.45003 −0.0524258
\(766\) 22.2681 0.804580
\(767\) −2.53206 −0.0914273
\(768\) 1.41275 0.0509783
\(769\) −8.04302 −0.290039 −0.145019 0.989429i \(-0.546324\pi\)
−0.145019 + 0.989429i \(0.546324\pi\)
\(770\) 17.0330 0.613826
\(771\) 13.0861 0.471285
\(772\) −0.537760 −0.0193544
\(773\) 6.13164 0.220540 0.110270 0.993902i \(-0.464828\pi\)
0.110270 + 0.993902i \(0.464828\pi\)
\(774\) 4.16861 0.149838
\(775\) −35.4464 −1.27327
\(776\) 18.4673 0.662937
\(777\) −21.5894 −0.774515
\(778\) 22.7038 0.813971
\(779\) −0.168184 −0.00602582
\(780\) 0.0367350 0.00131532
\(781\) −70.4536 −2.52103
\(782\) −10.9398 −0.391205
\(783\) −0.198494 −0.00709361
\(784\) −20.6387 −0.737095
\(785\) 9.73039 0.347293
\(786\) −10.0938 −0.360033
\(787\) −1.36104 −0.0485160 −0.0242580 0.999706i \(-0.507722\pi\)
−0.0242580 + 0.999706i \(0.507722\pi\)
\(788\) 0.939447 0.0334664
\(789\) 4.71375 0.167814
\(790\) −1.22792 −0.0436876
\(791\) −28.2826 −1.00561
\(792\) 16.0236 0.569375
\(793\) −10.9607 −0.389225
\(794\) −3.78740 −0.134410
\(795\) 3.05195 0.108241
\(796\) −0.577976 −0.0204858
\(797\) −33.5832 −1.18958 −0.594788 0.803882i \(-0.702764\pi\)
−0.594788 + 0.803882i \(0.702764\pi\)
\(798\) 5.94090 0.210306
\(799\) −23.3680 −0.826700
\(800\) −1.53633 −0.0543175
\(801\) 5.72890 0.202421
\(802\) −17.2153 −0.607892
\(803\) −74.5348 −2.63028
\(804\) 0.697467 0.0245978
\(805\) −7.38964 −0.260450
\(806\) 10.7097 0.377233
\(807\) 0.151544 0.00533460
\(808\) −42.7917 −1.50541
\(809\) 51.2511 1.80189 0.900947 0.433929i \(-0.142873\pi\)
0.900947 + 0.433929i \(0.142873\pi\)
\(810\) 0.868695 0.0305228
\(811\) −30.0690 −1.05587 −0.527933 0.849286i \(-0.677033\pi\)
−0.527933 + 0.849286i \(0.677033\pi\)
\(812\) 0.0410494 0.00144055
\(813\) −9.25680 −0.324650
\(814\) 47.8673 1.67775
\(815\) −11.7126 −0.410275
\(816\) −9.02022 −0.315771
\(817\) 3.63476 0.127164
\(818\) −27.1389 −0.948888
\(819\) −3.51013 −0.122654
\(820\) 0.00508579 0.000177604 0
\(821\) 33.5984 1.17259 0.586296 0.810097i \(-0.300586\pi\)
0.586296 + 0.810097i \(0.300586\pi\)
\(822\) 19.7171 0.687714
\(823\) 4.22395 0.147238 0.0736189 0.997286i \(-0.476545\pi\)
0.0736189 + 0.997286i \(0.476545\pi\)
\(824\) 2.86854 0.0999303
\(825\) −25.7583 −0.896789
\(826\) 12.3828 0.430853
\(827\) 8.27238 0.287659 0.143829 0.989603i \(-0.454058\pi\)
0.143829 + 0.989603i \(0.454058\pi\)
\(828\) −0.198925 −0.00691312
\(829\) −29.0396 −1.00859 −0.504294 0.863532i \(-0.668247\pi\)
−0.504294 + 0.863532i \(0.668247\pi\)
\(830\) −6.89178 −0.239217
\(831\) −24.5898 −0.853010
\(832\) 8.22158 0.285032
\(833\) −12.3745 −0.428750
\(834\) −9.44810 −0.327161
\(835\) 10.6996 0.370274
\(836\) 0.399799 0.0138273
\(837\) −7.68697 −0.265701
\(838\) 9.05896 0.312937
\(839\) −31.5299 −1.08853 −0.544267 0.838912i \(-0.683192\pi\)
−0.544267 + 0.838912i \(0.683192\pi\)
\(840\) −6.27812 −0.216616
\(841\) −28.9606 −0.998641
\(842\) −42.6087 −1.46839
\(843\) 7.66509 0.264000
\(844\) 1.13839 0.0391849
\(845\) 0.623512 0.0214495
\(846\) 13.9995 0.481312
\(847\) −70.9162 −2.43671
\(848\) 18.9853 0.651958
\(849\) −30.8950 −1.06032
\(850\) 14.9407 0.512461
\(851\) −20.7669 −0.711879
\(852\) 0.743084 0.0254576
\(853\) 16.2194 0.555342 0.277671 0.960676i \(-0.410438\pi\)
0.277671 + 0.960676i \(0.410438\pi\)
\(854\) 53.6022 1.83423
\(855\) 0.757446 0.0259041
\(856\) −17.0036 −0.581173
\(857\) −6.11563 −0.208906 −0.104453 0.994530i \(-0.533309\pi\)
−0.104453 + 0.994530i \(0.533309\pi\)
\(858\) 7.78256 0.265692
\(859\) 49.2920 1.68182 0.840911 0.541173i \(-0.182020\pi\)
0.840911 + 0.541173i \(0.182020\pi\)
\(860\) −0.109913 −0.00374800
\(861\) −0.485962 −0.0165615
\(862\) 45.6777 1.55579
\(863\) 30.1735 1.02712 0.513558 0.858055i \(-0.328327\pi\)
0.513558 + 0.858055i \(0.328327\pi\)
\(864\) −0.333171 −0.0113347
\(865\) −9.06479 −0.308212
\(866\) −26.9417 −0.915515
\(867\) 11.5917 0.393674
\(868\) 1.58970 0.0539578
\(869\) 7.89596 0.267852
\(870\) −0.172431 −0.00584595
\(871\) 11.8383 0.401125
\(872\) 32.2697 1.09279
\(873\) −6.43788 −0.217889
\(874\) 5.71457 0.193298
\(875\) 21.0352 0.711121
\(876\) 0.786130 0.0265609
\(877\) −40.3418 −1.36225 −0.681124 0.732168i \(-0.738508\pi\)
−0.681124 + 0.732168i \(0.738508\pi\)
\(878\) −42.5898 −1.43734
\(879\) 8.39607 0.283192
\(880\) 13.5092 0.455396
\(881\) −23.7382 −0.799760 −0.399880 0.916568i \(-0.630948\pi\)
−0.399880 + 0.916568i \(0.630948\pi\)
\(882\) 7.41341 0.249623
\(883\) 47.4707 1.59752 0.798758 0.601652i \(-0.205491\pi\)
0.798758 + 0.601652i \(0.205491\pi\)
\(884\) 0.137014 0.00460829
\(885\) 1.57877 0.0530697
\(886\) −38.2462 −1.28491
\(887\) −42.1842 −1.41641 −0.708203 0.706009i \(-0.750494\pi\)
−0.708203 + 0.706009i \(0.750494\pi\)
\(888\) −17.6432 −0.592067
\(889\) 33.3461 1.11839
\(890\) 4.97666 0.166818
\(891\) −5.58599 −0.187138
\(892\) −0.510084 −0.0170789
\(893\) 12.2067 0.408480
\(894\) 14.8323 0.496066
\(895\) −5.72938 −0.191512
\(896\) −37.8680 −1.26508
\(897\) −3.37640 −0.112735
\(898\) 47.4853 1.58461
\(899\) 1.52582 0.0508889
\(900\) 0.271677 0.00905588
\(901\) 11.3832 0.379228
\(902\) 1.07746 0.0358755
\(903\) 10.5025 0.349501
\(904\) −23.1130 −0.768728
\(905\) 1.27269 0.0423055
\(906\) 13.9861 0.464659
\(907\) −9.59254 −0.318515 −0.159258 0.987237i \(-0.550910\pi\)
−0.159258 + 0.987237i \(0.550910\pi\)
\(908\) −0.820737 −0.0272371
\(909\) 14.9176 0.494785
\(910\) −3.04923 −0.101081
\(911\) −22.1358 −0.733390 −0.366695 0.930341i \(-0.619511\pi\)
−0.366695 + 0.930341i \(0.619511\pi\)
\(912\) 4.71186 0.156025
\(913\) 44.3164 1.46666
\(914\) −2.55829 −0.0846207
\(915\) 6.83411 0.225929
\(916\) −1.53973 −0.0508742
\(917\) −25.4305 −0.839790
\(918\) 3.24006 0.106938
\(919\) −22.2798 −0.734942 −0.367471 0.930035i \(-0.619776\pi\)
−0.367471 + 0.930035i \(0.619776\pi\)
\(920\) −6.03893 −0.199098
\(921\) −16.9044 −0.557020
\(922\) 45.3154 1.49238
\(923\) 12.6126 0.415147
\(924\) 1.15520 0.0380034
\(925\) 28.3618 0.932530
\(926\) 6.13098 0.201477
\(927\) −1.00000 −0.0328443
\(928\) 0.0661326 0.00217091
\(929\) 44.2081 1.45042 0.725211 0.688527i \(-0.241742\pi\)
0.725211 + 0.688527i \(0.241742\pi\)
\(930\) −6.67763 −0.218968
\(931\) 6.46402 0.211850
\(932\) −1.38774 −0.0454570
\(933\) −14.1865 −0.464444
\(934\) 31.8178 1.04111
\(935\) 8.09984 0.264893
\(936\) −2.86854 −0.0937611
\(937\) −35.1138 −1.14712 −0.573558 0.819165i \(-0.694437\pi\)
−0.573558 + 0.819165i \(0.694437\pi\)
\(938\) −57.8941 −1.89031
\(939\) −20.0222 −0.653400
\(940\) −0.369122 −0.0120394
\(941\) 8.68663 0.283176 0.141588 0.989926i \(-0.454779\pi\)
0.141588 + 0.989926i \(0.454779\pi\)
\(942\) −21.7424 −0.708406
\(943\) −0.467448 −0.0152222
\(944\) 9.82108 0.319649
\(945\) 2.18861 0.0711955
\(946\) −23.2858 −0.757087
\(947\) −33.2171 −1.07941 −0.539705 0.841854i \(-0.681464\pi\)
−0.539705 + 0.841854i \(0.681464\pi\)
\(948\) −0.0832798 −0.00270480
\(949\) 13.3432 0.433138
\(950\) −7.80451 −0.253212
\(951\) 21.0736 0.683360
\(952\) −23.4161 −0.758922
\(953\) 26.7923 0.867889 0.433944 0.900940i \(-0.357121\pi\)
0.433944 + 0.900940i \(0.357121\pi\)
\(954\) −6.81952 −0.220790
\(955\) 8.93578 0.289155
\(956\) 0.518756 0.0167778
\(957\) 1.10879 0.0358420
\(958\) −16.9263 −0.546864
\(959\) 49.6759 1.60412
\(960\) −5.12625 −0.165449
\(961\) 28.0896 0.906115
\(962\) −8.56917 −0.276281
\(963\) 5.92763 0.191015
\(964\) −0.881977 −0.0284066
\(965\) 5.69113 0.183204
\(966\) 16.5120 0.531265
\(967\) 29.5840 0.951358 0.475679 0.879619i \(-0.342202\pi\)
0.475679 + 0.879619i \(0.342202\pi\)
\(968\) −57.9539 −1.86271
\(969\) 2.82513 0.0907561
\(970\) −5.59255 −0.179566
\(971\) −6.03890 −0.193798 −0.0968988 0.995294i \(-0.530892\pi\)
−0.0968988 + 0.995294i \(0.530892\pi\)
\(972\) 0.0589163 0.00188974
\(973\) −23.8038 −0.763114
\(974\) −39.7744 −1.27446
\(975\) 4.61123 0.147678
\(976\) 42.5131 1.36081
\(977\) 31.6161 1.01149 0.505744 0.862684i \(-0.331218\pi\)
0.505744 + 0.862684i \(0.331218\pi\)
\(978\) 26.1716 0.836877
\(979\) −32.0016 −1.02277
\(980\) −0.195468 −0.00624400
\(981\) −11.2495 −0.359170
\(982\) 10.5676 0.337225
\(983\) 58.8338 1.87651 0.938254 0.345948i \(-0.112443\pi\)
0.938254 + 0.345948i \(0.112443\pi\)
\(984\) −0.397136 −0.0126602
\(985\) −9.94219 −0.316785
\(986\) −0.643134 −0.0204815
\(987\) 35.2707 1.12268
\(988\) −0.0715718 −0.00227700
\(989\) 10.1024 0.321237
\(990\) −4.85252 −0.154223
\(991\) 6.31025 0.200452 0.100226 0.994965i \(-0.468043\pi\)
0.100226 + 0.994965i \(0.468043\pi\)
\(992\) 2.56108 0.0813143
\(993\) 21.6470 0.686945
\(994\) −61.6806 −1.95639
\(995\) 6.11674 0.193914
\(996\) −0.467412 −0.0148105
\(997\) −8.71738 −0.276082 −0.138041 0.990426i \(-0.544081\pi\)
−0.138041 + 0.990426i \(0.544081\pi\)
\(998\) 29.3328 0.928514
\(999\) 6.15059 0.194596
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 \(a_p\))