Properties

Label 8002.2.a.e.1.1
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.18344 q^{3} +1.00000 q^{4} -0.604370 q^{5} +3.18344 q^{6} +1.50072 q^{7} -1.00000 q^{8} +7.13428 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.18344 q^{3} +1.00000 q^{4} -0.604370 q^{5} +3.18344 q^{6} +1.50072 q^{7} -1.00000 q^{8} +7.13428 q^{9} +0.604370 q^{10} +0.0174264 q^{11} -3.18344 q^{12} -0.0590342 q^{13} -1.50072 q^{14} +1.92398 q^{15} +1.00000 q^{16} -2.14364 q^{17} -7.13428 q^{18} -0.224806 q^{19} -0.604370 q^{20} -4.77744 q^{21} -0.0174264 q^{22} +7.15199 q^{23} +3.18344 q^{24} -4.63474 q^{25} +0.0590342 q^{26} -13.1612 q^{27} +1.50072 q^{28} -0.660126 q^{29} -1.92398 q^{30} +3.62722 q^{31} -1.00000 q^{32} -0.0554757 q^{33} +2.14364 q^{34} -0.906989 q^{35} +7.13428 q^{36} +4.14091 q^{37} +0.224806 q^{38} +0.187932 q^{39} +0.604370 q^{40} +8.68900 q^{41} +4.77744 q^{42} -3.52694 q^{43} +0.0174264 q^{44} -4.31175 q^{45} -7.15199 q^{46} -0.591863 q^{47} -3.18344 q^{48} -4.74785 q^{49} +4.63474 q^{50} +6.82414 q^{51} -0.0590342 q^{52} +1.46621 q^{53} +13.1612 q^{54} -0.0105320 q^{55} -1.50072 q^{56} +0.715655 q^{57} +0.660126 q^{58} -7.29811 q^{59} +1.92398 q^{60} +2.27389 q^{61} -3.62722 q^{62} +10.7065 q^{63} +1.00000 q^{64} +0.0356785 q^{65} +0.0554757 q^{66} +7.74449 q^{67} -2.14364 q^{68} -22.7679 q^{69} +0.906989 q^{70} +4.41174 q^{71} -7.13428 q^{72} +14.7536 q^{73} -4.14091 q^{74} +14.7544 q^{75} -0.224806 q^{76} +0.0261520 q^{77} -0.187932 q^{78} -9.38290 q^{79} -0.604370 q^{80} +20.4951 q^{81} -8.68900 q^{82} +14.3568 q^{83} -4.77744 q^{84} +1.29555 q^{85} +3.52694 q^{86} +2.10147 q^{87} -0.0174264 q^{88} -1.18035 q^{89} +4.31175 q^{90} -0.0885937 q^{91} +7.15199 q^{92} -11.5470 q^{93} +0.591863 q^{94} +0.135866 q^{95} +3.18344 q^{96} +2.46087 q^{97} +4.74785 q^{98} +0.124324 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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
\(3\) −3.18344 −1.83796 −0.918980 0.394305i \(-0.870985\pi\)
−0.918980 + 0.394305i \(0.870985\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.604370 −0.270283 −0.135141 0.990826i \(-0.543149\pi\)
−0.135141 + 0.990826i \(0.543149\pi\)
\(6\) 3.18344 1.29963
\(7\) 1.50072 0.567218 0.283609 0.958940i \(-0.408468\pi\)
0.283609 + 0.958940i \(0.408468\pi\)
\(8\) −1.00000 −0.353553
\(9\) 7.13428 2.37809
\(10\) 0.604370 0.191119
\(11\) 0.0174264 0.00525424 0.00262712 0.999997i \(-0.499164\pi\)
0.00262712 + 0.999997i \(0.499164\pi\)
\(12\) −3.18344 −0.918980
\(13\) −0.0590342 −0.0163731 −0.00818657 0.999966i \(-0.502606\pi\)
−0.00818657 + 0.999966i \(0.502606\pi\)
\(14\) −1.50072 −0.401084
\(15\) 1.92398 0.496768
\(16\) 1.00000 0.250000
\(17\) −2.14364 −0.519909 −0.259954 0.965621i \(-0.583708\pi\)
−0.259954 + 0.965621i \(0.583708\pi\)
\(18\) −7.13428 −1.68157
\(19\) −0.224806 −0.0515739 −0.0257870 0.999667i \(-0.508209\pi\)
−0.0257870 + 0.999667i \(0.508209\pi\)
\(20\) −0.604370 −0.135141
\(21\) −4.77744 −1.04252
\(22\) −0.0174264 −0.00371531
\(23\) 7.15199 1.49129 0.745647 0.666342i \(-0.232141\pi\)
0.745647 + 0.666342i \(0.232141\pi\)
\(24\) 3.18344 0.649817
\(25\) −4.63474 −0.926947
\(26\) 0.0590342 0.0115776
\(27\) −13.1612 −2.53288
\(28\) 1.50072 0.283609
\(29\) −0.660126 −0.122582 −0.0612912 0.998120i \(-0.519522\pi\)
−0.0612912 + 0.998120i \(0.519522\pi\)
\(30\) −1.92398 −0.351268
\(31\) 3.62722 0.651467 0.325734 0.945462i \(-0.394389\pi\)
0.325734 + 0.945462i \(0.394389\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.0554757 −0.00965708
\(34\) 2.14364 0.367631
\(35\) −0.906989 −0.153309
\(36\) 7.13428 1.18905
\(37\) 4.14091 0.680761 0.340381 0.940288i \(-0.389444\pi\)
0.340381 + 0.940288i \(0.389444\pi\)
\(38\) 0.224806 0.0364683
\(39\) 0.187932 0.0300932
\(40\) 0.604370 0.0955593
\(41\) 8.68900 1.35699 0.678497 0.734603i \(-0.262632\pi\)
0.678497 + 0.734603i \(0.262632\pi\)
\(42\) 4.77744 0.737175
\(43\) −3.52694 −0.537853 −0.268927 0.963161i \(-0.586669\pi\)
−0.268927 + 0.963161i \(0.586669\pi\)
\(44\) 0.0174264 0.00262712
\(45\) −4.31175 −0.642757
\(46\) −7.15199 −1.05450
\(47\) −0.591863 −0.0863320 −0.0431660 0.999068i \(-0.513744\pi\)
−0.0431660 + 0.999068i \(0.513744\pi\)
\(48\) −3.18344 −0.459490
\(49\) −4.74785 −0.678264
\(50\) 4.63474 0.655451
\(51\) 6.82414 0.955571
\(52\) −0.0590342 −0.00818657
\(53\) 1.46621 0.201400 0.100700 0.994917i \(-0.467892\pi\)
0.100700 + 0.994917i \(0.467892\pi\)
\(54\) 13.1612 1.79102
\(55\) −0.0105320 −0.00142013
\(56\) −1.50072 −0.200542
\(57\) 0.715655 0.0947908
\(58\) 0.660126 0.0866788
\(59\) −7.29811 −0.950133 −0.475066 0.879950i \(-0.657576\pi\)
−0.475066 + 0.879950i \(0.657576\pi\)
\(60\) 1.92398 0.248384
\(61\) 2.27389 0.291141 0.145571 0.989348i \(-0.453498\pi\)
0.145571 + 0.989348i \(0.453498\pi\)
\(62\) −3.62722 −0.460657
\(63\) 10.7065 1.34890
\(64\) 1.00000 0.125000
\(65\) 0.0356785 0.00442538
\(66\) 0.0554757 0.00682859
\(67\) 7.74449 0.946140 0.473070 0.881025i \(-0.343146\pi\)
0.473070 + 0.881025i \(0.343146\pi\)
\(68\) −2.14364 −0.259954
\(69\) −22.7679 −2.74094
\(70\) 0.906989 0.108406
\(71\) 4.41174 0.523578 0.261789 0.965125i \(-0.415688\pi\)
0.261789 + 0.965125i \(0.415688\pi\)
\(72\) −7.13428 −0.840783
\(73\) 14.7536 1.72678 0.863391 0.504535i \(-0.168336\pi\)
0.863391 + 0.504535i \(0.168336\pi\)
\(74\) −4.14091 −0.481371
\(75\) 14.7544 1.70369
\(76\) −0.224806 −0.0257870
\(77\) 0.0261520 0.00298030
\(78\) −0.187932 −0.0212791
\(79\) −9.38290 −1.05566 −0.527829 0.849351i \(-0.676994\pi\)
−0.527829 + 0.849351i \(0.676994\pi\)
\(80\) −0.604370 −0.0675707
\(81\) 20.4951 2.27723
\(82\) −8.68900 −0.959540
\(83\) 14.3568 1.57587 0.787933 0.615761i \(-0.211151\pi\)
0.787933 + 0.615761i \(0.211151\pi\)
\(84\) −4.77744 −0.521262
\(85\) 1.29555 0.140522
\(86\) 3.52694 0.380320
\(87\) 2.10147 0.225301
\(88\) −0.0174264 −0.00185766
\(89\) −1.18035 −0.125117 −0.0625586 0.998041i \(-0.519926\pi\)
−0.0625586 + 0.998041i \(0.519926\pi\)
\(90\) 4.31175 0.454498
\(91\) −0.0885937 −0.00928714
\(92\) 7.15199 0.745647
\(93\) −11.5470 −1.19737
\(94\) 0.591863 0.0610460
\(95\) 0.135866 0.0139395
\(96\) 3.18344 0.324908
\(97\) 2.46087 0.249863 0.124932 0.992165i \(-0.460129\pi\)
0.124932 + 0.992165i \(0.460129\pi\)
\(98\) 4.74785 0.479605
\(99\) 0.124324 0.0124951
\(100\) −4.63474 −0.463474
\(101\) 4.48024 0.445800 0.222900 0.974841i \(-0.428448\pi\)
0.222900 + 0.974841i \(0.428448\pi\)
\(102\) −6.82414 −0.675691
\(103\) −0.889295 −0.0876248 −0.0438124 0.999040i \(-0.513950\pi\)
−0.0438124 + 0.999040i \(0.513950\pi\)
\(104\) 0.0590342 0.00578878
\(105\) 2.88734 0.281776
\(106\) −1.46621 −0.142411
\(107\) 0.501109 0.0484440 0.0242220 0.999707i \(-0.492289\pi\)
0.0242220 + 0.999707i \(0.492289\pi\)
\(108\) −13.1612 −1.26644
\(109\) −5.17723 −0.495888 −0.247944 0.968774i \(-0.579755\pi\)
−0.247944 + 0.968774i \(0.579755\pi\)
\(110\) 0.0105320 0.00100418
\(111\) −13.1823 −1.25121
\(112\) 1.50072 0.141804
\(113\) 15.3138 1.44060 0.720300 0.693663i \(-0.244004\pi\)
0.720300 + 0.693663i \(0.244004\pi\)
\(114\) −0.715655 −0.0670272
\(115\) −4.32245 −0.403071
\(116\) −0.660126 −0.0612912
\(117\) −0.421167 −0.0389369
\(118\) 7.29811 0.671845
\(119\) −3.21700 −0.294902
\(120\) −1.92398 −0.175634
\(121\) −10.9997 −0.999972
\(122\) −2.27389 −0.205868
\(123\) −27.6609 −2.49410
\(124\) 3.62722 0.325734
\(125\) 5.82295 0.520820
\(126\) −10.7065 −0.953814
\(127\) 12.9413 1.14835 0.574176 0.818732i \(-0.305322\pi\)
0.574176 + 0.818732i \(0.305322\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 11.2278 0.988553
\(130\) −0.0356785 −0.00312921
\(131\) −10.1579 −0.887498 −0.443749 0.896151i \(-0.646352\pi\)
−0.443749 + 0.896151i \(0.646352\pi\)
\(132\) −0.0554757 −0.00482854
\(133\) −0.337370 −0.0292537
\(134\) −7.74449 −0.669022
\(135\) 7.95425 0.684593
\(136\) 2.14364 0.183815
\(137\) −11.6130 −0.992162 −0.496081 0.868276i \(-0.665228\pi\)
−0.496081 + 0.868276i \(0.665228\pi\)
\(138\) 22.7679 1.93813
\(139\) 1.53504 0.130200 0.0651002 0.997879i \(-0.479263\pi\)
0.0651002 + 0.997879i \(0.479263\pi\)
\(140\) −0.906989 −0.0766546
\(141\) 1.88416 0.158675
\(142\) −4.41174 −0.370225
\(143\) −0.00102875 −8.60285e−5 0
\(144\) 7.13428 0.594523
\(145\) 0.398961 0.0331319
\(146\) −14.7536 −1.22102
\(147\) 15.1145 1.24662
\(148\) 4.14091 0.340381
\(149\) 2.82586 0.231503 0.115752 0.993278i \(-0.463072\pi\)
0.115752 + 0.993278i \(0.463072\pi\)
\(150\) −14.7544 −1.20469
\(151\) 6.24550 0.508252 0.254126 0.967171i \(-0.418212\pi\)
0.254126 + 0.967171i \(0.418212\pi\)
\(152\) 0.224806 0.0182341
\(153\) −15.2933 −1.23639
\(154\) −0.0261520 −0.00210739
\(155\) −2.19218 −0.176080
\(156\) 0.187932 0.0150466
\(157\) 16.0038 1.27724 0.638622 0.769520i \(-0.279505\pi\)
0.638622 + 0.769520i \(0.279505\pi\)
\(158\) 9.38290 0.746463
\(159\) −4.66759 −0.370164
\(160\) 0.604370 0.0477797
\(161\) 10.7331 0.845888
\(162\) −20.4951 −1.61025
\(163\) −15.8760 −1.24350 −0.621751 0.783215i \(-0.713578\pi\)
−0.621751 + 0.783215i \(0.713578\pi\)
\(164\) 8.68900 0.678497
\(165\) 0.0335279 0.00261014
\(166\) −14.3568 −1.11431
\(167\) −2.14245 −0.165787 −0.0828937 0.996558i \(-0.526416\pi\)
−0.0828937 + 0.996558i \(0.526416\pi\)
\(168\) 4.77744 0.368588
\(169\) −12.9965 −0.999732
\(170\) −1.29555 −0.0993643
\(171\) −1.60383 −0.122648
\(172\) −3.52694 −0.268927
\(173\) −2.68055 −0.203798 −0.101899 0.994795i \(-0.532492\pi\)
−0.101899 + 0.994795i \(0.532492\pi\)
\(174\) −2.10147 −0.159312
\(175\) −6.95543 −0.525781
\(176\) 0.0174264 0.00131356
\(177\) 23.2331 1.74631
\(178\) 1.18035 0.0884713
\(179\) −11.4744 −0.857639 −0.428819 0.903390i \(-0.641070\pi\)
−0.428819 + 0.903390i \(0.641070\pi\)
\(180\) −4.31175 −0.321379
\(181\) −19.5969 −1.45663 −0.728314 0.685244i \(-0.759696\pi\)
−0.728314 + 0.685244i \(0.759696\pi\)
\(182\) 0.0885937 0.00656700
\(183\) −7.23878 −0.535106
\(184\) −7.15199 −0.527252
\(185\) −2.50264 −0.183998
\(186\) 11.5470 0.846669
\(187\) −0.0373558 −0.00273173
\(188\) −0.591863 −0.0431660
\(189\) −19.7513 −1.43669
\(190\) −0.135866 −0.00985674
\(191\) 4.41240 0.319270 0.159635 0.987176i \(-0.448968\pi\)
0.159635 + 0.987176i \(0.448968\pi\)
\(192\) −3.18344 −0.229745
\(193\) −12.3834 −0.891376 −0.445688 0.895188i \(-0.647041\pi\)
−0.445688 + 0.895188i \(0.647041\pi\)
\(194\) −2.46087 −0.176680
\(195\) −0.113580 −0.00813366
\(196\) −4.74785 −0.339132
\(197\) −18.5648 −1.32268 −0.661342 0.750085i \(-0.730013\pi\)
−0.661342 + 0.750085i \(0.730013\pi\)
\(198\) −0.124324 −0.00883536
\(199\) −15.5232 −1.10041 −0.550205 0.835030i \(-0.685450\pi\)
−0.550205 + 0.835030i \(0.685450\pi\)
\(200\) 4.63474 0.327725
\(201\) −24.6541 −1.73897
\(202\) −4.48024 −0.315228
\(203\) −0.990663 −0.0695309
\(204\) 6.82414 0.477785
\(205\) −5.25137 −0.366772
\(206\) 0.889295 0.0619601
\(207\) 51.0243 3.54643
\(208\) −0.0590342 −0.00409329
\(209\) −0.00391754 −0.000270982 0
\(210\) −2.88734 −0.199246
\(211\) −15.2842 −1.05220 −0.526102 0.850421i \(-0.676347\pi\)
−0.526102 + 0.850421i \(0.676347\pi\)
\(212\) 1.46621 0.100700
\(213\) −14.0445 −0.962315
\(214\) −0.501109 −0.0342551
\(215\) 2.13158 0.145372
\(216\) 13.1612 0.895508
\(217\) 5.44343 0.369524
\(218\) 5.17723 0.350646
\(219\) −46.9673 −3.17376
\(220\) −0.0105320 −0.000710065 0
\(221\) 0.126548 0.00851254
\(222\) 13.1823 0.884740
\(223\) 19.8535 1.32949 0.664746 0.747069i \(-0.268540\pi\)
0.664746 + 0.747069i \(0.268540\pi\)
\(224\) −1.50072 −0.100271
\(225\) −33.0655 −2.20437
\(226\) −15.3138 −1.01866
\(227\) −6.60886 −0.438646 −0.219323 0.975652i \(-0.570385\pi\)
−0.219323 + 0.975652i \(0.570385\pi\)
\(228\) 0.715655 0.0473954
\(229\) −19.5632 −1.29277 −0.646387 0.763010i \(-0.723721\pi\)
−0.646387 + 0.763010i \(0.723721\pi\)
\(230\) 4.32245 0.285014
\(231\) −0.0832534 −0.00547767
\(232\) 0.660126 0.0433394
\(233\) −29.1896 −1.91228 −0.956139 0.292915i \(-0.905375\pi\)
−0.956139 + 0.292915i \(0.905375\pi\)
\(234\) 0.421167 0.0275325
\(235\) 0.357704 0.0233341
\(236\) −7.29811 −0.475066
\(237\) 29.8699 1.94026
\(238\) 3.21700 0.208527
\(239\) 12.4416 0.804779 0.402390 0.915468i \(-0.368180\pi\)
0.402390 + 0.915468i \(0.368180\pi\)
\(240\) 1.92398 0.124192
\(241\) −11.4327 −0.736447 −0.368224 0.929737i \(-0.620034\pi\)
−0.368224 + 0.929737i \(0.620034\pi\)
\(242\) 10.9997 0.707087
\(243\) −25.7612 −1.65258
\(244\) 2.27389 0.145571
\(245\) 2.86946 0.183323
\(246\) 27.6609 1.76359
\(247\) 0.0132712 0.000844427 0
\(248\) −3.62722 −0.230328
\(249\) −45.7041 −2.89638
\(250\) −5.82295 −0.368276
\(251\) 19.9787 1.26104 0.630521 0.776172i \(-0.282841\pi\)
0.630521 + 0.776172i \(0.282841\pi\)
\(252\) 10.7065 0.674449
\(253\) 0.124633 0.00783562
\(254\) −12.9413 −0.812008
\(255\) −4.12431 −0.258274
\(256\) 1.00000 0.0625000
\(257\) 20.3257 1.26788 0.633942 0.773381i \(-0.281436\pi\)
0.633942 + 0.773381i \(0.281436\pi\)
\(258\) −11.2278 −0.699012
\(259\) 6.21434 0.386140
\(260\) 0.0356785 0.00221269
\(261\) −4.70953 −0.291512
\(262\) 10.1579 0.627556
\(263\) 24.8060 1.52960 0.764801 0.644267i \(-0.222837\pi\)
0.764801 + 0.644267i \(0.222837\pi\)
\(264\) 0.0554757 0.00341429
\(265\) −0.886135 −0.0544348
\(266\) 0.337370 0.0206855
\(267\) 3.75758 0.229960
\(268\) 7.74449 0.473070
\(269\) −14.7917 −0.901865 −0.450932 0.892558i \(-0.648908\pi\)
−0.450932 + 0.892558i \(0.648908\pi\)
\(270\) −7.95425 −0.484081
\(271\) −8.85440 −0.537866 −0.268933 0.963159i \(-0.586671\pi\)
−0.268933 + 0.963159i \(0.586671\pi\)
\(272\) −2.14364 −0.129977
\(273\) 0.282032 0.0170694
\(274\) 11.6130 0.701564
\(275\) −0.0807665 −0.00487041
\(276\) −22.7679 −1.37047
\(277\) 11.1070 0.667356 0.333678 0.942687i \(-0.391710\pi\)
0.333678 + 0.942687i \(0.391710\pi\)
\(278\) −1.53504 −0.0920655
\(279\) 25.8776 1.54925
\(280\) 0.906989 0.0542030
\(281\) 22.8345 1.36219 0.681095 0.732195i \(-0.261504\pi\)
0.681095 + 0.732195i \(0.261504\pi\)
\(282\) −1.88416 −0.112200
\(283\) 28.3530 1.68541 0.842705 0.538376i \(-0.180962\pi\)
0.842705 + 0.538376i \(0.180962\pi\)
\(284\) 4.41174 0.261789
\(285\) −0.432520 −0.0256203
\(286\) 0.00102875 6.08313e−5 0
\(287\) 13.0397 0.769711
\(288\) −7.13428 −0.420391
\(289\) −12.4048 −0.729695
\(290\) −0.398961 −0.0234278
\(291\) −7.83402 −0.459238
\(292\) 14.7536 0.863391
\(293\) −8.21460 −0.479902 −0.239951 0.970785i \(-0.577131\pi\)
−0.239951 + 0.970785i \(0.577131\pi\)
\(294\) −15.1145 −0.881494
\(295\) 4.41076 0.256804
\(296\) −4.14091 −0.240686
\(297\) −0.229352 −0.0133084
\(298\) −2.82586 −0.163697
\(299\) −0.422212 −0.0244172
\(300\) 14.7544 0.851846
\(301\) −5.29294 −0.305080
\(302\) −6.24550 −0.359388
\(303\) −14.2626 −0.819362
\(304\) −0.224806 −0.0128935
\(305\) −1.37427 −0.0786905
\(306\) 15.2933 0.874261
\(307\) 28.1230 1.60506 0.802532 0.596609i \(-0.203486\pi\)
0.802532 + 0.596609i \(0.203486\pi\)
\(308\) 0.0261520 0.00149015
\(309\) 2.83102 0.161051
\(310\) 2.19218 0.124508
\(311\) 25.4678 1.44415 0.722073 0.691817i \(-0.243190\pi\)
0.722073 + 0.691817i \(0.243190\pi\)
\(312\) −0.187932 −0.0106395
\(313\) 24.8869 1.40669 0.703345 0.710848i \(-0.251689\pi\)
0.703345 + 0.710848i \(0.251689\pi\)
\(314\) −16.0038 −0.903148
\(315\) −6.47071 −0.364583
\(316\) −9.38290 −0.527829
\(317\) −30.7031 −1.72446 −0.862229 0.506519i \(-0.830932\pi\)
−0.862229 + 0.506519i \(0.830932\pi\)
\(318\) 4.66759 0.261746
\(319\) −0.0115036 −0.000644078 0
\(320\) −0.604370 −0.0337853
\(321\) −1.59525 −0.0890382
\(322\) −10.7331 −0.598133
\(323\) 0.481902 0.0268137
\(324\) 20.4951 1.13862
\(325\) 0.273608 0.0151770
\(326\) 15.8760 0.879289
\(327\) 16.4814 0.911423
\(328\) −8.68900 −0.479770
\(329\) −0.888219 −0.0489691
\(330\) −0.0335279 −0.00184565
\(331\) −23.6049 −1.29744 −0.648721 0.761026i \(-0.724696\pi\)
−0.648721 + 0.761026i \(0.724696\pi\)
\(332\) 14.3568 0.787933
\(333\) 29.5424 1.61891
\(334\) 2.14245 0.117229
\(335\) −4.68054 −0.255725
\(336\) −4.77744 −0.260631
\(337\) −32.2397 −1.75621 −0.878103 0.478471i \(-0.841191\pi\)
−0.878103 + 0.478471i \(0.841191\pi\)
\(338\) 12.9965 0.706917
\(339\) −48.7505 −2.64776
\(340\) 1.29555 0.0702611
\(341\) 0.0632092 0.00342297
\(342\) 1.60383 0.0867250
\(343\) −17.6302 −0.951941
\(344\) 3.52694 0.190160
\(345\) 13.7603 0.740827
\(346\) 2.68055 0.144107
\(347\) −7.31946 −0.392929 −0.196465 0.980511i \(-0.562946\pi\)
−0.196465 + 0.980511i \(0.562946\pi\)
\(348\) 2.10147 0.112651
\(349\) −8.44644 −0.452127 −0.226064 0.974113i \(-0.572586\pi\)
−0.226064 + 0.974113i \(0.572586\pi\)
\(350\) 6.95543 0.371783
\(351\) 0.776962 0.0414712
\(352\) −0.0174264 −0.000928828 0
\(353\) 9.05255 0.481819 0.240909 0.970548i \(-0.422554\pi\)
0.240909 + 0.970548i \(0.422554\pi\)
\(354\) −23.2331 −1.23482
\(355\) −2.66633 −0.141514
\(356\) −1.18035 −0.0625586
\(357\) 10.2411 0.542017
\(358\) 11.4744 0.606442
\(359\) 20.3524 1.07416 0.537080 0.843531i \(-0.319527\pi\)
0.537080 + 0.843531i \(0.319527\pi\)
\(360\) 4.31175 0.227249
\(361\) −18.9495 −0.997340
\(362\) 19.5969 1.02999
\(363\) 35.0169 1.83791
\(364\) −0.0885937 −0.00464357
\(365\) −8.91666 −0.466719
\(366\) 7.23878 0.378377
\(367\) −30.9737 −1.61681 −0.808406 0.588625i \(-0.799669\pi\)
−0.808406 + 0.588625i \(0.799669\pi\)
\(368\) 7.15199 0.372823
\(369\) 61.9898 3.22706
\(370\) 2.50264 0.130106
\(371\) 2.20037 0.114237
\(372\) −11.5470 −0.598685
\(373\) −10.8622 −0.562422 −0.281211 0.959646i \(-0.590736\pi\)
−0.281211 + 0.959646i \(0.590736\pi\)
\(374\) 0.0373558 0.00193162
\(375\) −18.5370 −0.957247
\(376\) 0.591863 0.0305230
\(377\) 0.0389700 0.00200706
\(378\) 19.7513 1.01590
\(379\) 24.5552 1.26132 0.630659 0.776060i \(-0.282785\pi\)
0.630659 + 0.776060i \(0.282785\pi\)
\(380\) 0.135866 0.00696977
\(381\) −41.1977 −2.11062
\(382\) −4.41240 −0.225758
\(383\) 15.5837 0.796291 0.398146 0.917322i \(-0.369654\pi\)
0.398146 + 0.917322i \(0.369654\pi\)
\(384\) 3.18344 0.162454
\(385\) −0.0158055 −0.000805523 0
\(386\) 12.3834 0.630298
\(387\) −25.1622 −1.27907
\(388\) 2.46087 0.124932
\(389\) −2.47204 −0.125338 −0.0626688 0.998034i \(-0.519961\pi\)
−0.0626688 + 0.998034i \(0.519961\pi\)
\(390\) 0.113580 0.00575137
\(391\) −15.3313 −0.775336
\(392\) 4.74785 0.239802
\(393\) 32.3370 1.63118
\(394\) 18.5648 0.935279
\(395\) 5.67074 0.285326
\(396\) 0.124324 0.00624754
\(397\) 14.5896 0.732231 0.366116 0.930569i \(-0.380687\pi\)
0.366116 + 0.930569i \(0.380687\pi\)
\(398\) 15.5232 0.778107
\(399\) 1.07400 0.0537670
\(400\) −4.63474 −0.231737
\(401\) 6.94449 0.346792 0.173396 0.984852i \(-0.444526\pi\)
0.173396 + 0.984852i \(0.444526\pi\)
\(402\) 24.6541 1.22964
\(403\) −0.214130 −0.0106666
\(404\) 4.48024 0.222900
\(405\) −12.3866 −0.615497
\(406\) 0.990663 0.0491658
\(407\) 0.0721610 0.00357689
\(408\) −6.82414 −0.337845
\(409\) 29.0157 1.43473 0.717367 0.696696i \(-0.245347\pi\)
0.717367 + 0.696696i \(0.245347\pi\)
\(410\) 5.25137 0.259347
\(411\) 36.9691 1.82355
\(412\) −0.889295 −0.0438124
\(413\) −10.9524 −0.538932
\(414\) −51.0243 −2.50771
\(415\) −8.67684 −0.425929
\(416\) 0.0590342 0.00289439
\(417\) −4.88670 −0.239303
\(418\) 0.00391754 0.000191613 0
\(419\) 31.2135 1.52488 0.762441 0.647058i \(-0.224001\pi\)
0.762441 + 0.647058i \(0.224001\pi\)
\(420\) 2.88734 0.140888
\(421\) −2.86136 −0.139454 −0.0697272 0.997566i \(-0.522213\pi\)
−0.0697272 + 0.997566i \(0.522213\pi\)
\(422\) 15.2842 0.744021
\(423\) −4.22251 −0.205306
\(424\) −1.46621 −0.0712055
\(425\) 9.93520 0.481928
\(426\) 14.0445 0.680459
\(427\) 3.41246 0.165141
\(428\) 0.501109 0.0242220
\(429\) 0.00327496 0.000158117 0
\(430\) −2.13158 −0.102794
\(431\) 28.0698 1.35207 0.676037 0.736868i \(-0.263696\pi\)
0.676037 + 0.736868i \(0.263696\pi\)
\(432\) −13.1612 −0.633220
\(433\) 13.5090 0.649199 0.324600 0.945851i \(-0.394770\pi\)
0.324600 + 0.945851i \(0.394770\pi\)
\(434\) −5.44343 −0.261293
\(435\) −1.27007 −0.0608950
\(436\) −5.17723 −0.247944
\(437\) −1.60781 −0.0769119
\(438\) 46.9673 2.24418
\(439\) 10.3121 0.492170 0.246085 0.969248i \(-0.420856\pi\)
0.246085 + 0.969248i \(0.420856\pi\)
\(440\) 0.0105320 0.000502092 0
\(441\) −33.8725 −1.61297
\(442\) −0.126548 −0.00601927
\(443\) 1.79175 0.0851288 0.0425644 0.999094i \(-0.486447\pi\)
0.0425644 + 0.999094i \(0.486447\pi\)
\(444\) −13.1823 −0.625606
\(445\) 0.713371 0.0338170
\(446\) −19.8535 −0.940093
\(447\) −8.99594 −0.425493
\(448\) 1.50072 0.0709022
\(449\) 27.1173 1.27974 0.639872 0.768481i \(-0.278987\pi\)
0.639872 + 0.768481i \(0.278987\pi\)
\(450\) 33.0655 1.55872
\(451\) 0.151418 0.00712998
\(452\) 15.3138 0.720300
\(453\) −19.8822 −0.934146
\(454\) 6.60886 0.310169
\(455\) 0.0535434 0.00251015
\(456\) −0.715655 −0.0335136
\(457\) −13.2661 −0.620561 −0.310281 0.950645i \(-0.600423\pi\)
−0.310281 + 0.950645i \(0.600423\pi\)
\(458\) 19.5632 0.914129
\(459\) 28.2129 1.31687
\(460\) −4.32245 −0.201535
\(461\) −5.09856 −0.237464 −0.118732 0.992926i \(-0.537883\pi\)
−0.118732 + 0.992926i \(0.537883\pi\)
\(462\) 0.0832534 0.00387330
\(463\) 31.6491 1.47086 0.735430 0.677601i \(-0.236980\pi\)
0.735430 + 0.677601i \(0.236980\pi\)
\(464\) −0.660126 −0.0306456
\(465\) 6.97868 0.323628
\(466\) 29.1896 1.35218
\(467\) −13.9190 −0.644094 −0.322047 0.946724i \(-0.604371\pi\)
−0.322047 + 0.946724i \(0.604371\pi\)
\(468\) −0.421167 −0.0194684
\(469\) 11.6223 0.536668
\(470\) −0.357704 −0.0164997
\(471\) −50.9472 −2.34752
\(472\) 7.29811 0.335923
\(473\) −0.0614617 −0.00282601
\(474\) −29.8699 −1.37197
\(475\) 1.04191 0.0478063
\(476\) −3.21700 −0.147451
\(477\) 10.4604 0.478947
\(478\) −12.4416 −0.569065
\(479\) 34.6909 1.58507 0.792533 0.609829i \(-0.208762\pi\)
0.792533 + 0.609829i \(0.208762\pi\)
\(480\) −1.92398 −0.0878171
\(481\) −0.244455 −0.0111462
\(482\) 11.4327 0.520747
\(483\) −34.1682 −1.55471
\(484\) −10.9997 −0.499986
\(485\) −1.48727 −0.0675337
\(486\) 25.7612 1.16855
\(487\) −21.3944 −0.969473 −0.484736 0.874660i \(-0.661084\pi\)
−0.484736 + 0.874660i \(0.661084\pi\)
\(488\) −2.27389 −0.102934
\(489\) 50.5402 2.28551
\(490\) −2.86946 −0.129629
\(491\) 5.14953 0.232395 0.116198 0.993226i \(-0.462929\pi\)
0.116198 + 0.993226i \(0.462929\pi\)
\(492\) −27.6609 −1.24705
\(493\) 1.41507 0.0637316
\(494\) −0.0132712 −0.000597100 0
\(495\) −0.0751380 −0.00337720
\(496\) 3.62722 0.162867
\(497\) 6.62078 0.296983
\(498\) 45.7041 2.04805
\(499\) −6.44849 −0.288674 −0.144337 0.989529i \(-0.546105\pi\)
−0.144337 + 0.989529i \(0.546105\pi\)
\(500\) 5.82295 0.260410
\(501\) 6.82034 0.304710
\(502\) −19.9787 −0.891691
\(503\) −15.0149 −0.669482 −0.334741 0.942310i \(-0.608649\pi\)
−0.334741 + 0.942310i \(0.608649\pi\)
\(504\) −10.7065 −0.476907
\(505\) −2.70772 −0.120492
\(506\) −0.124633 −0.00554062
\(507\) 41.3736 1.83747
\(508\) 12.9413 0.574176
\(509\) −8.90039 −0.394503 −0.197251 0.980353i \(-0.563202\pi\)
−0.197251 + 0.980353i \(0.563202\pi\)
\(510\) 4.12431 0.182627
\(511\) 22.1410 0.979462
\(512\) −1.00000 −0.0441942
\(513\) 2.95872 0.130631
\(514\) −20.3257 −0.896529
\(515\) 0.537464 0.0236835
\(516\) 11.2278 0.494276
\(517\) −0.0103140 −0.000453609 0
\(518\) −6.21434 −0.273042
\(519\) 8.53336 0.374573
\(520\) −0.0356785 −0.00156461
\(521\) 1.25845 0.0551339 0.0275669 0.999620i \(-0.491224\pi\)
0.0275669 + 0.999620i \(0.491224\pi\)
\(522\) 4.70953 0.206130
\(523\) 20.5407 0.898181 0.449090 0.893486i \(-0.351748\pi\)
0.449090 + 0.893486i \(0.351748\pi\)
\(524\) −10.1579 −0.443749
\(525\) 22.1422 0.966364
\(526\) −24.8060 −1.08159
\(527\) −7.77544 −0.338704
\(528\) −0.0554757 −0.00241427
\(529\) 28.1510 1.22396
\(530\) 0.886135 0.0384912
\(531\) −52.0667 −2.25950
\(532\) −0.337370 −0.0146268
\(533\) −0.512948 −0.0222183
\(534\) −3.75758 −0.162607
\(535\) −0.302855 −0.0130936
\(536\) −7.74449 −0.334511
\(537\) 36.5281 1.57631
\(538\) 14.7917 0.637715
\(539\) −0.0827376 −0.00356376
\(540\) 7.95425 0.342297
\(541\) −12.6751 −0.544947 −0.272473 0.962163i \(-0.587842\pi\)
−0.272473 + 0.962163i \(0.587842\pi\)
\(542\) 8.85440 0.380329
\(543\) 62.3856 2.67722
\(544\) 2.14364 0.0919077
\(545\) 3.12896 0.134030
\(546\) −0.282032 −0.0120699
\(547\) 44.6231 1.90795 0.953973 0.299892i \(-0.0969508\pi\)
0.953973 + 0.299892i \(0.0969508\pi\)
\(548\) −11.6130 −0.496081
\(549\) 16.2225 0.692361
\(550\) 0.0807665 0.00344390
\(551\) 0.148400 0.00632206
\(552\) 22.7679 0.969067
\(553\) −14.0811 −0.598788
\(554\) −11.1070 −0.471892
\(555\) 7.96701 0.338181
\(556\) 1.53504 0.0651002
\(557\) −33.5356 −1.42095 −0.710475 0.703722i \(-0.751520\pi\)
−0.710475 + 0.703722i \(0.751520\pi\)
\(558\) −25.8776 −1.09549
\(559\) 0.208210 0.00880635
\(560\) −0.906989 −0.0383273
\(561\) 0.118920 0.00502080
\(562\) −22.8345 −0.963214
\(563\) 24.7387 1.04261 0.521307 0.853369i \(-0.325445\pi\)
0.521307 + 0.853369i \(0.325445\pi\)
\(564\) 1.88416 0.0793374
\(565\) −9.25520 −0.389369
\(566\) −28.3530 −1.19176
\(567\) 30.7574 1.29169
\(568\) −4.41174 −0.185113
\(569\) −12.0702 −0.506011 −0.253005 0.967465i \(-0.581419\pi\)
−0.253005 + 0.967465i \(0.581419\pi\)
\(570\) 0.432520 0.0181163
\(571\) 14.6425 0.612768 0.306384 0.951908i \(-0.400881\pi\)
0.306384 + 0.951908i \(0.400881\pi\)
\(572\) −0.00102875 −4.30142e−5 0
\(573\) −14.0466 −0.586805
\(574\) −13.0397 −0.544268
\(575\) −33.1476 −1.38235
\(576\) 7.13428 0.297262
\(577\) −12.7708 −0.531654 −0.265827 0.964021i \(-0.585645\pi\)
−0.265827 + 0.964021i \(0.585645\pi\)
\(578\) 12.4048 0.515972
\(579\) 39.4218 1.63831
\(580\) 0.398961 0.0165659
\(581\) 21.5455 0.893860
\(582\) 7.83402 0.324730
\(583\) 0.0255507 0.00105820
\(584\) −14.7536 −0.610510
\(585\) 0.254541 0.0105240
\(586\) 8.21460 0.339342
\(587\) 14.4010 0.594391 0.297196 0.954817i \(-0.403949\pi\)
0.297196 + 0.954817i \(0.403949\pi\)
\(588\) 15.1145 0.623311
\(589\) −0.815419 −0.0335987
\(590\) −4.41076 −0.181588
\(591\) 59.0997 2.43104
\(592\) 4.14091 0.170190
\(593\) 15.3305 0.629550 0.314775 0.949166i \(-0.398071\pi\)
0.314775 + 0.949166i \(0.398071\pi\)
\(594\) 0.229352 0.00941043
\(595\) 1.94426 0.0797068
\(596\) 2.82586 0.115752
\(597\) 49.4171 2.02251
\(598\) 0.422212 0.0172655
\(599\) 45.2886 1.85044 0.925221 0.379430i \(-0.123880\pi\)
0.925221 + 0.379430i \(0.123880\pi\)
\(600\) −14.7544 −0.602346
\(601\) −13.0778 −0.533453 −0.266726 0.963772i \(-0.585942\pi\)
−0.266726 + 0.963772i \(0.585942\pi\)
\(602\) 5.29294 0.215724
\(603\) 55.2514 2.25001
\(604\) 6.24550 0.254126
\(605\) 6.64789 0.270275
\(606\) 14.2626 0.579377
\(607\) −30.0392 −1.21925 −0.609626 0.792689i \(-0.708680\pi\)
−0.609626 + 0.792689i \(0.708680\pi\)
\(608\) 0.224806 0.00911707
\(609\) 3.15371 0.127795
\(610\) 1.37427 0.0556426
\(611\) 0.0349401 0.00141353
\(612\) −15.2933 −0.618196
\(613\) −32.9717 −1.33172 −0.665858 0.746078i \(-0.731934\pi\)
−0.665858 + 0.746078i \(0.731934\pi\)
\(614\) −28.1230 −1.13495
\(615\) 16.7174 0.674112
\(616\) −0.0261520 −0.00105370
\(617\) 46.3278 1.86509 0.932544 0.361057i \(-0.117584\pi\)
0.932544 + 0.361057i \(0.117584\pi\)
\(618\) −2.83102 −0.113880
\(619\) −8.14525 −0.327385 −0.163693 0.986511i \(-0.552341\pi\)
−0.163693 + 0.986511i \(0.552341\pi\)
\(620\) −2.19218 −0.0880402
\(621\) −94.1290 −3.77727
\(622\) −25.4678 −1.02117
\(623\) −1.77138 −0.0709687
\(624\) 0.187932 0.00752329
\(625\) 19.6545 0.786179
\(626\) −24.8869 −0.994680
\(627\) 0.0124713 0.000498054 0
\(628\) 16.0038 0.638622
\(629\) −8.87661 −0.353934
\(630\) 6.47071 0.257799
\(631\) −13.6883 −0.544923 −0.272462 0.962167i \(-0.587838\pi\)
−0.272462 + 0.962167i \(0.587838\pi\)
\(632\) 9.38290 0.373232
\(633\) 48.6562 1.93391
\(634\) 30.7031 1.21938
\(635\) −7.82132 −0.310380
\(636\) −4.66759 −0.185082
\(637\) 0.280285 0.0111053
\(638\) 0.0115036 0.000455432 0
\(639\) 31.4746 1.24512
\(640\) 0.604370 0.0238898
\(641\) 34.7150 1.37116 0.685581 0.727997i \(-0.259548\pi\)
0.685581 + 0.727997i \(0.259548\pi\)
\(642\) 1.59525 0.0629595
\(643\) 30.6143 1.20731 0.603655 0.797246i \(-0.293710\pi\)
0.603655 + 0.797246i \(0.293710\pi\)
\(644\) 10.7331 0.422944
\(645\) −6.78575 −0.267189
\(646\) −0.481902 −0.0189602
\(647\) 14.5762 0.573051 0.286526 0.958073i \(-0.407500\pi\)
0.286526 + 0.958073i \(0.407500\pi\)
\(648\) −20.4951 −0.805124
\(649\) −0.127179 −0.00499223
\(650\) −0.273608 −0.0107318
\(651\) −17.3288 −0.679170
\(652\) −15.8760 −0.621751
\(653\) −1.10036 −0.0430603 −0.0215301 0.999768i \(-0.506854\pi\)
−0.0215301 + 0.999768i \(0.506854\pi\)
\(654\) −16.4814 −0.644473
\(655\) 6.13912 0.239875
\(656\) 8.68900 0.339248
\(657\) 105.257 4.10645
\(658\) 0.888219 0.0346264
\(659\) −17.2652 −0.672555 −0.336278 0.941763i \(-0.609168\pi\)
−0.336278 + 0.941763i \(0.609168\pi\)
\(660\) 0.0335279 0.00130507
\(661\) −33.9762 −1.32152 −0.660761 0.750596i \(-0.729766\pi\)
−0.660761 + 0.750596i \(0.729766\pi\)
\(662\) 23.6049 0.917430
\(663\) −0.402858 −0.0156457
\(664\) −14.3568 −0.557153
\(665\) 0.203896 0.00790676
\(666\) −29.5424 −1.14475
\(667\) −4.72122 −0.182806
\(668\) −2.14245 −0.0828937
\(669\) −63.2025 −2.44355
\(670\) 4.68054 0.180825
\(671\) 0.0396256 0.00152973
\(672\) 4.77744 0.184294
\(673\) −6.42557 −0.247687 −0.123844 0.992302i \(-0.539522\pi\)
−0.123844 + 0.992302i \(0.539522\pi\)
\(674\) 32.2397 1.24183
\(675\) 60.9988 2.34785
\(676\) −12.9965 −0.499866
\(677\) −18.3007 −0.703354 −0.351677 0.936121i \(-0.614389\pi\)
−0.351677 + 0.936121i \(0.614389\pi\)
\(678\) 48.7505 1.87225
\(679\) 3.69307 0.141727
\(680\) −1.29555 −0.0496821
\(681\) 21.0389 0.806213
\(682\) −0.0632092 −0.00242040
\(683\) −7.28953 −0.278926 −0.139463 0.990227i \(-0.544538\pi\)
−0.139463 + 0.990227i \(0.544538\pi\)
\(684\) −1.60383 −0.0613238
\(685\) 7.01853 0.268164
\(686\) 17.6302 0.673124
\(687\) 62.2783 2.37607
\(688\) −3.52694 −0.134463
\(689\) −0.0865566 −0.00329754
\(690\) −13.7603 −0.523844
\(691\) −17.5780 −0.668697 −0.334349 0.942449i \(-0.608516\pi\)
−0.334349 + 0.942449i \(0.608516\pi\)
\(692\) −2.68055 −0.101899
\(693\) 0.186576 0.00708743
\(694\) 7.31946 0.277843
\(695\) −0.927732 −0.0351909
\(696\) −2.10147 −0.0796561
\(697\) −18.6261 −0.705513
\(698\) 8.44644 0.319702
\(699\) 92.9234 3.51469
\(700\) −6.95543 −0.262891
\(701\) 27.7384 1.04766 0.523832 0.851822i \(-0.324502\pi\)
0.523832 + 0.851822i \(0.324502\pi\)
\(702\) −0.776962 −0.0293246
\(703\) −0.930900 −0.0351095
\(704\) 0.0174264 0.000656780 0
\(705\) −1.13873 −0.0428870
\(706\) −9.05255 −0.340697
\(707\) 6.72357 0.252866
\(708\) 23.2331 0.873153
\(709\) −14.5059 −0.544780 −0.272390 0.962187i \(-0.587814\pi\)
−0.272390 + 0.962187i \(0.587814\pi\)
\(710\) 2.66633 0.100065
\(711\) −66.9402 −2.51045
\(712\) 1.18035 0.0442356
\(713\) 25.9418 0.971529
\(714\) −10.2411 −0.383264
\(715\) 0.000621746 0 2.32520e−5 0
\(716\) −11.4744 −0.428819
\(717\) −39.6070 −1.47915
\(718\) −20.3524 −0.759546
\(719\) 37.7221 1.40680 0.703399 0.710795i \(-0.251665\pi\)
0.703399 + 0.710795i \(0.251665\pi\)
\(720\) −4.31175 −0.160689
\(721\) −1.33458 −0.0497024
\(722\) 18.9495 0.705226
\(723\) 36.3954 1.35356
\(724\) −19.5969 −0.728314
\(725\) 3.05951 0.113627
\(726\) −35.0169 −1.29960
\(727\) 15.6300 0.579685 0.289843 0.957074i \(-0.406397\pi\)
0.289843 + 0.957074i \(0.406397\pi\)
\(728\) 0.0885937 0.00328350
\(729\) 20.5240 0.760148
\(730\) 8.91666 0.330020
\(731\) 7.56049 0.279635
\(732\) −7.23878 −0.267553
\(733\) 12.0991 0.446889 0.223445 0.974717i \(-0.428270\pi\)
0.223445 + 0.974717i \(0.428270\pi\)
\(734\) 30.9737 1.14326
\(735\) −9.13474 −0.336940
\(736\) −7.15199 −0.263626
\(737\) 0.134958 0.00497125
\(738\) −61.9898 −2.28187
\(739\) −22.3901 −0.823634 −0.411817 0.911267i \(-0.635106\pi\)
−0.411817 + 0.911267i \(0.635106\pi\)
\(740\) −2.50264 −0.0919990
\(741\) −0.0422481 −0.00155202
\(742\) −2.20037 −0.0807781
\(743\) −50.5510 −1.85454 −0.927269 0.374396i \(-0.877850\pi\)
−0.927269 + 0.374396i \(0.877850\pi\)
\(744\) 11.5470 0.423334
\(745\) −1.70786 −0.0625713
\(746\) 10.8622 0.397693
\(747\) 102.426 3.74756
\(748\) −0.0373558 −0.00136586
\(749\) 0.752023 0.0274783
\(750\) 18.5370 0.676876
\(751\) 13.7291 0.500982 0.250491 0.968119i \(-0.419408\pi\)
0.250491 + 0.968119i \(0.419408\pi\)
\(752\) −0.591863 −0.0215830
\(753\) −63.6008 −2.31774
\(754\) −0.0389700 −0.00141920
\(755\) −3.77460 −0.137372
\(756\) −19.7513 −0.718347
\(757\) 23.0398 0.837396 0.418698 0.908125i \(-0.362487\pi\)
0.418698 + 0.908125i \(0.362487\pi\)
\(758\) −24.5552 −0.891886
\(759\) −0.396762 −0.0144015
\(760\) −0.135866 −0.00492837
\(761\) 2.86627 0.103902 0.0519512 0.998650i \(-0.483456\pi\)
0.0519512 + 0.998650i \(0.483456\pi\)
\(762\) 41.1977 1.49244
\(763\) −7.76956 −0.281277
\(764\) 4.41240 0.159635
\(765\) 9.24283 0.334175
\(766\) −15.5837 −0.563063
\(767\) 0.430838 0.0155567
\(768\) −3.18344 −0.114872
\(769\) 22.2005 0.800571 0.400285 0.916391i \(-0.368911\pi\)
0.400285 + 0.916391i \(0.368911\pi\)
\(770\) 0.0158055 0.000569591 0
\(771\) −64.7057 −2.33032
\(772\) −12.3834 −0.445688
\(773\) 10.5737 0.380311 0.190156 0.981754i \(-0.439101\pi\)
0.190156 + 0.981754i \(0.439101\pi\)
\(774\) 25.1622 0.904436
\(775\) −16.8112 −0.603876
\(776\) −2.46087 −0.0883400
\(777\) −19.7830 −0.709710
\(778\) 2.47204 0.0886270
\(779\) −1.95334 −0.0699855
\(780\) −0.113580 −0.00406683
\(781\) 0.0768806 0.00275100
\(782\) 15.3313 0.548246
\(783\) 8.68807 0.310486
\(784\) −4.74785 −0.169566
\(785\) −9.67224 −0.345217
\(786\) −32.3370 −1.15342
\(787\) −12.7549 −0.454663 −0.227331 0.973817i \(-0.573000\pi\)
−0.227331 + 0.973817i \(0.573000\pi\)
\(788\) −18.5648 −0.661342
\(789\) −78.9683 −2.81135
\(790\) −5.67074 −0.201756
\(791\) 22.9817 0.817134
\(792\) −0.124324 −0.00441768
\(793\) −0.134237 −0.00476690
\(794\) −14.5896 −0.517766
\(795\) 2.82096 0.100049
\(796\) −15.5232 −0.550205
\(797\) 40.9497 1.45051 0.725257 0.688478i \(-0.241721\pi\)
0.725257 + 0.688478i \(0.241721\pi\)
\(798\) −1.07400 −0.0380190
\(799\) 1.26874 0.0448848
\(800\) 4.63474 0.163863
\(801\) −8.42097 −0.297541
\(802\) −6.94449 −0.245219
\(803\) 0.257102 0.00907293
\(804\) −24.6541 −0.869483
\(805\) −6.48678 −0.228629
\(806\) 0.214130 0.00754240
\(807\) 47.0884 1.65759
\(808\) −4.48024 −0.157614
\(809\) 25.6502 0.901812 0.450906 0.892572i \(-0.351101\pi\)
0.450906 + 0.892572i \(0.351101\pi\)
\(810\) 12.3866 0.435222
\(811\) −7.90218 −0.277483 −0.138742 0.990329i \(-0.544306\pi\)
−0.138742 + 0.990329i \(0.544306\pi\)
\(812\) −0.990663 −0.0347655
\(813\) 28.1874 0.988576
\(814\) −0.0721610 −0.00252924
\(815\) 9.59497 0.336097
\(816\) 6.82414 0.238893
\(817\) 0.792876 0.0277392
\(818\) −29.0157 −1.01451
\(819\) −0.632052 −0.0220857
\(820\) −5.25137 −0.183386
\(821\) 17.2097 0.600622 0.300311 0.953841i \(-0.402910\pi\)
0.300311 + 0.953841i \(0.402910\pi\)
\(822\) −36.9691 −1.28945
\(823\) 51.7322 1.80327 0.901635 0.432498i \(-0.142368\pi\)
0.901635 + 0.432498i \(0.142368\pi\)
\(824\) 0.889295 0.0309801
\(825\) 0.257115 0.00895161
\(826\) 10.9524 0.381083
\(827\) 51.1713 1.77940 0.889699 0.456547i \(-0.150914\pi\)
0.889699 + 0.456547i \(0.150914\pi\)
\(828\) 51.0243 1.77322
\(829\) −12.8622 −0.446723 −0.223362 0.974736i \(-0.571703\pi\)
−0.223362 + 0.974736i \(0.571703\pi\)
\(830\) 8.67684 0.301177
\(831\) −35.3585 −1.22657
\(832\) −0.0590342 −0.00204664
\(833\) 10.1777 0.352635
\(834\) 4.88670 0.169213
\(835\) 1.29483 0.0448095
\(836\) −0.00391754 −0.000135491 0
\(837\) −47.7386 −1.65009
\(838\) −31.2135 −1.07825
\(839\) −4.64426 −0.160338 −0.0801688 0.996781i \(-0.525546\pi\)
−0.0801688 + 0.996781i \(0.525546\pi\)
\(840\) −2.88734 −0.0996228
\(841\) −28.5642 −0.984974
\(842\) 2.86136 0.0986091
\(843\) −72.6921 −2.50365
\(844\) −15.2842 −0.526102
\(845\) 7.85471 0.270210
\(846\) 4.22251 0.145173
\(847\) −16.5074 −0.567202
\(848\) 1.46621 0.0503499
\(849\) −90.2599 −3.09771
\(850\) −9.93520 −0.340775
\(851\) 29.6158 1.01521
\(852\) −14.0445 −0.481157
\(853\) 54.3453 1.86075 0.930374 0.366612i \(-0.119482\pi\)
0.930374 + 0.366612i \(0.119482\pi\)
\(854\) −3.41246 −0.116772
\(855\) 0.969305 0.0331495
\(856\) −0.501109 −0.0171276
\(857\) −5.22896 −0.178618 −0.0893090 0.996004i \(-0.528466\pi\)
−0.0893090 + 0.996004i \(0.528466\pi\)
\(858\) −0.00327496 −0.000111805 0
\(859\) 14.5173 0.495324 0.247662 0.968847i \(-0.420338\pi\)
0.247662 + 0.968847i \(0.420338\pi\)
\(860\) 2.13158 0.0726862
\(861\) −41.5112 −1.41470
\(862\) −28.0698 −0.956061
\(863\) −32.4738 −1.10542 −0.552710 0.833374i \(-0.686406\pi\)
−0.552710 + 0.833374i \(0.686406\pi\)
\(864\) 13.1612 0.447754
\(865\) 1.62004 0.0550832
\(866\) −13.5090 −0.459053
\(867\) 39.4900 1.34115
\(868\) 5.44343 0.184762
\(869\) −0.163510 −0.00554668
\(870\) 1.27007 0.0430593
\(871\) −0.457190 −0.0154913
\(872\) 5.17723 0.175323
\(873\) 17.5565 0.594198
\(874\) 1.60781 0.0543849
\(875\) 8.73860 0.295419
\(876\) −46.9673 −1.58688
\(877\) −47.9595 −1.61948 −0.809739 0.586790i \(-0.800391\pi\)
−0.809739 + 0.586790i \(0.800391\pi\)
\(878\) −10.3121 −0.348017
\(879\) 26.1507 0.882040
\(880\) −0.0105320 −0.000355033 0
\(881\) −18.5582 −0.625241 −0.312620 0.949878i \(-0.601207\pi\)
−0.312620 + 0.949878i \(0.601207\pi\)
\(882\) 33.8725 1.14055
\(883\) 7.75882 0.261105 0.130553 0.991441i \(-0.458325\pi\)
0.130553 + 0.991441i \(0.458325\pi\)
\(884\) 0.126548 0.00425627
\(885\) −14.0414 −0.471996
\(886\) −1.79175 −0.0601952
\(887\) −38.4240 −1.29015 −0.645076 0.764118i \(-0.723174\pi\)
−0.645076 + 0.764118i \(0.723174\pi\)
\(888\) 13.1823 0.442370
\(889\) 19.4212 0.651366
\(890\) −0.713371 −0.0239122
\(891\) 0.357155 0.0119651
\(892\) 19.8535 0.664746
\(893\) 0.133054 0.00445248
\(894\) 8.99594 0.300869
\(895\) 6.93480 0.231805
\(896\) −1.50072 −0.0501355
\(897\) 1.34409 0.0448777
\(898\) −27.1173 −0.904916
\(899\) −2.39442 −0.0798584
\(900\) −33.0655 −1.10218
\(901\) −3.14303 −0.104709
\(902\) −0.151418 −0.00504165
\(903\) 16.8498 0.560725
\(904\) −15.3138 −0.509329
\(905\) 11.8438 0.393701
\(906\) 19.8822 0.660541
\(907\) −19.7292 −0.655096 −0.327548 0.944834i \(-0.606222\pi\)
−0.327548 + 0.944834i \(0.606222\pi\)
\(908\) −6.60886 −0.219323
\(909\) 31.9633 1.06015
\(910\) −0.0535434 −0.00177495
\(911\) 28.7443 0.952341 0.476171 0.879353i \(-0.342024\pi\)
0.476171 + 0.879353i \(0.342024\pi\)
\(912\) 0.715655 0.0236977
\(913\) 0.250187 0.00827998
\(914\) 13.2661 0.438803
\(915\) 4.37490 0.144630
\(916\) −19.5632 −0.646387
\(917\) −15.2441 −0.503405
\(918\) −28.2129 −0.931165
\(919\) 51.7779 1.70799 0.853997 0.520277i \(-0.174171\pi\)
0.853997 + 0.520277i \(0.174171\pi\)
\(920\) 4.32245 0.142507
\(921\) −89.5278 −2.95004
\(922\) 5.09856 0.167912
\(923\) −0.260444 −0.00857261
\(924\) −0.0832534 −0.00273884
\(925\) −19.1920 −0.631030
\(926\) −31.6491 −1.04005
\(927\) −6.34448 −0.208380
\(928\) 0.660126 0.0216697
\(929\) −20.7475 −0.680703 −0.340352 0.940298i \(-0.610546\pi\)
−0.340352 + 0.940298i \(0.610546\pi\)
\(930\) −6.97868 −0.228840
\(931\) 1.06734 0.0349807
\(932\) −29.1896 −0.956139
\(933\) −81.0751 −2.65428
\(934\) 13.9190 0.455443
\(935\) 0.0225767 0.000738338 0
\(936\) 0.421167 0.0137663
\(937\) 45.4265 1.48402 0.742010 0.670389i \(-0.233873\pi\)
0.742010 + 0.670389i \(0.233873\pi\)
\(938\) −11.6223 −0.379481
\(939\) −79.2259 −2.58544
\(940\) 0.357704 0.0116670
\(941\) −28.2055 −0.919473 −0.459736 0.888055i \(-0.652056\pi\)
−0.459736 + 0.888055i \(0.652056\pi\)
\(942\) 50.9472 1.65995
\(943\) 62.1437 2.02368
\(944\) −7.29811 −0.237533
\(945\) 11.9371 0.388314
\(946\) 0.0614617 0.00199829
\(947\) 21.0618 0.684416 0.342208 0.939624i \(-0.388825\pi\)
0.342208 + 0.939624i \(0.388825\pi\)
\(948\) 29.8699 0.970128
\(949\) −0.870969 −0.0282729
\(950\) −1.04191 −0.0338042
\(951\) 97.7414 3.16948
\(952\) 3.21700 0.104263
\(953\) −6.63702 −0.214994 −0.107497 0.994205i \(-0.534284\pi\)
−0.107497 + 0.994205i \(0.534284\pi\)
\(954\) −10.4604 −0.338667
\(955\) −2.66672 −0.0862932
\(956\) 12.4416 0.402390
\(957\) 0.0366210 0.00118379
\(958\) −34.6909 −1.12081
\(959\) −17.4278 −0.562772
\(960\) 1.92398 0.0620960
\(961\) −17.8433 −0.575590
\(962\) 0.244455 0.00788156
\(963\) 3.57505 0.115204
\(964\) −11.4327 −0.368224
\(965\) 7.48415 0.240923
\(966\) 34.1682 1.09934
\(967\) −22.4294 −0.721282 −0.360641 0.932705i \(-0.617442\pi\)
−0.360641 + 0.932705i \(0.617442\pi\)
\(968\) 10.9997 0.353544
\(969\) −1.53411 −0.0492826
\(970\) 1.48727 0.0477535
\(971\) −0.810915 −0.0260235 −0.0130118 0.999915i \(-0.504142\pi\)
−0.0130118 + 0.999915i \(0.504142\pi\)
\(972\) −25.7612 −0.826292
\(973\) 2.30366 0.0738519
\(974\) 21.3944 0.685521
\(975\) −0.871014 −0.0278948
\(976\) 2.27389 0.0727854
\(977\) −12.2192 −0.390925 −0.195463 0.980711i \(-0.562621\pi\)
−0.195463 + 0.980711i \(0.562621\pi\)
\(978\) −50.5402 −1.61610
\(979\) −0.0205693 −0.000657396 0
\(980\) 2.86946 0.0916615
\(981\) −36.9358 −1.17927
\(982\) −5.14953 −0.164328
\(983\) −7.37146 −0.235113 −0.117556 0.993066i \(-0.537506\pi\)
−0.117556 + 0.993066i \(0.537506\pi\)
\(984\) 27.6609 0.881797
\(985\) 11.2200 0.357498
\(986\) −1.41507 −0.0450651
\(987\) 2.82759 0.0900032
\(988\) 0.0132712 0.000422214 0
\(989\) −25.2246 −0.802097
\(990\) 0.0751380 0.00238804
\(991\) 28.7194 0.912303 0.456152 0.889902i \(-0.349227\pi\)
0.456152 + 0.889902i \(0.349227\pi\)
\(992\) −3.62722 −0.115164
\(993\) 75.1447 2.38465
\(994\) −6.62078 −0.209998
\(995\) 9.38175 0.297422
\(996\) −45.7041 −1.44819
\(997\) 1.38001 0.0437055 0.0218527 0.999761i \(-0.493044\pi\)
0.0218527 + 0.999761i \(0.493044\pi\)
\(998\) 6.44849 0.204123
\(999\) −54.4995 −1.72429
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 \(a_p\))