Properties

Label 8007.2.a.j.1.3
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.69904 q^{2}\) \(-1.00000 q^{3}\) \(+5.28480 q^{4}\) \(-1.39519 q^{5}\) \(+2.69904 q^{6}\) \(-4.02432 q^{7}\) \(-8.86580 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.69904 q^{2}\) \(-1.00000 q^{3}\) \(+5.28480 q^{4}\) \(-1.39519 q^{5}\) \(+2.69904 q^{6}\) \(-4.02432 q^{7}\) \(-8.86580 q^{8}\) \(+1.00000 q^{9}\) \(+3.76567 q^{10}\) \(-4.50878 q^{11}\) \(-5.28480 q^{12}\) \(+6.27088 q^{13}\) \(+10.8618 q^{14}\) \(+1.39519 q^{15}\) \(+13.3595 q^{16}\) \(+1.00000 q^{17}\) \(-2.69904 q^{18}\) \(-0.936912 q^{19}\) \(-7.37329 q^{20}\) \(+4.02432 q^{21}\) \(+12.1694 q^{22}\) \(-3.43565 q^{23}\) \(+8.86580 q^{24}\) \(-3.05345 q^{25}\) \(-16.9253 q^{26}\) \(-1.00000 q^{27}\) \(-21.2677 q^{28}\) \(-0.713369 q^{29}\) \(-3.76567 q^{30}\) \(-4.52582 q^{31}\) \(-18.3262 q^{32}\) \(+4.50878 q^{33}\) \(-2.69904 q^{34}\) \(+5.61469 q^{35}\) \(+5.28480 q^{36}\) \(-4.09969 q^{37}\) \(+2.52876 q^{38}\) \(-6.27088 q^{39}\) \(+12.3695 q^{40}\) \(-3.33697 q^{41}\) \(-10.8618 q^{42}\) \(+0.999978 q^{43}\) \(-23.8280 q^{44}\) \(-1.39519 q^{45}\) \(+9.27296 q^{46}\) \(+6.04485 q^{47}\) \(-13.3595 q^{48}\) \(+9.19517 q^{49}\) \(+8.24137 q^{50}\) \(-1.00000 q^{51}\) \(+33.1404 q^{52}\) \(+3.14493 q^{53}\) \(+2.69904 q^{54}\) \(+6.29059 q^{55}\) \(+35.6788 q^{56}\) \(+0.936912 q^{57}\) \(+1.92541 q^{58}\) \(-13.9294 q^{59}\) \(+7.37329 q^{60}\) \(+14.5661 q^{61}\) \(+12.2154 q^{62}\) \(-4.02432 q^{63}\) \(+22.7442 q^{64}\) \(-8.74906 q^{65}\) \(-12.1694 q^{66}\) \(+7.10967 q^{67}\) \(+5.28480 q^{68}\) \(+3.43565 q^{69}\) \(-15.1543 q^{70}\) \(-8.69442 q^{71}\) \(-8.86580 q^{72}\) \(+3.71040 q^{73}\) \(+11.0652 q^{74}\) \(+3.05345 q^{75}\) \(-4.95139 q^{76}\) \(+18.1448 q^{77}\) \(+16.9253 q^{78}\) \(-11.0868 q^{79}\) \(-18.6390 q^{80}\) \(+1.00000 q^{81}\) \(+9.00660 q^{82}\) \(-14.9149 q^{83}\) \(+21.2677 q^{84}\) \(-1.39519 q^{85}\) \(-2.69898 q^{86}\) \(+0.713369 q^{87}\) \(+39.9739 q^{88}\) \(-10.9723 q^{89}\) \(+3.76567 q^{90}\) \(-25.2360 q^{91}\) \(-18.1567 q^{92}\) \(+4.52582 q^{93}\) \(-16.3153 q^{94}\) \(+1.30717 q^{95}\) \(+18.3262 q^{96}\) \(-15.2770 q^{97}\) \(-24.8181 q^{98}\) \(-4.50878 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69904 −1.90851 −0.954254 0.298998i \(-0.903348\pi\)
−0.954254 + 0.298998i \(0.903348\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.28480 2.64240
\(5\) −1.39519 −0.623947 −0.311974 0.950091i \(-0.600990\pi\)
−0.311974 + 0.950091i \(0.600990\pi\)
\(6\) 2.69904 1.10188
\(7\) −4.02432 −1.52105 −0.760525 0.649308i \(-0.775059\pi\)
−0.760525 + 0.649308i \(0.775059\pi\)
\(8\) −8.86580 −3.13453
\(9\) 1.00000 0.333333
\(10\) 3.76567 1.19081
\(11\) −4.50878 −1.35945 −0.679723 0.733468i \(-0.737900\pi\)
−0.679723 + 0.733468i \(0.737900\pi\)
\(12\) −5.28480 −1.52559
\(13\) 6.27088 1.73923 0.869615 0.493731i \(-0.164367\pi\)
0.869615 + 0.493731i \(0.164367\pi\)
\(14\) 10.8618 2.90294
\(15\) 1.39519 0.360236
\(16\) 13.3595 3.33988
\(17\) 1.00000 0.242536
\(18\) −2.69904 −0.636169
\(19\) −0.936912 −0.214942 −0.107471 0.994208i \(-0.534275\pi\)
−0.107471 + 0.994208i \(0.534275\pi\)
\(20\) −7.37329 −1.64872
\(21\) 4.02432 0.878179
\(22\) 12.1694 2.59451
\(23\) −3.43565 −0.716383 −0.358192 0.933648i \(-0.616607\pi\)
−0.358192 + 0.933648i \(0.616607\pi\)
\(24\) 8.86580 1.80972
\(25\) −3.05345 −0.610690
\(26\) −16.9253 −3.31933
\(27\) −1.00000 −0.192450
\(28\) −21.2677 −4.01923
\(29\) −0.713369 −0.132469 −0.0662346 0.997804i \(-0.521099\pi\)
−0.0662346 + 0.997804i \(0.521099\pi\)
\(30\) −3.76567 −0.687513
\(31\) −4.52582 −0.812862 −0.406431 0.913682i \(-0.633227\pi\)
−0.406431 + 0.913682i \(0.633227\pi\)
\(32\) −18.3262 −3.23965
\(33\) 4.50878 0.784877
\(34\) −2.69904 −0.462881
\(35\) 5.61469 0.949055
\(36\) 5.28480 0.880800
\(37\) −4.09969 −0.673984 −0.336992 0.941507i \(-0.609410\pi\)
−0.336992 + 0.941507i \(0.609410\pi\)
\(38\) 2.52876 0.410219
\(39\) −6.27088 −1.00414
\(40\) 12.3695 1.95578
\(41\) −3.33697 −0.521147 −0.260573 0.965454i \(-0.583912\pi\)
−0.260573 + 0.965454i \(0.583912\pi\)
\(42\) −10.8618 −1.67601
\(43\) 0.999978 0.152495 0.0762476 0.997089i \(-0.475706\pi\)
0.0762476 + 0.997089i \(0.475706\pi\)
\(44\) −23.8280 −3.59220
\(45\) −1.39519 −0.207982
\(46\) 9.27296 1.36722
\(47\) 6.04485 0.881732 0.440866 0.897573i \(-0.354671\pi\)
0.440866 + 0.897573i \(0.354671\pi\)
\(48\) −13.3595 −1.92828
\(49\) 9.19517 1.31360
\(50\) 8.24137 1.16551
\(51\) −1.00000 −0.140028
\(52\) 33.1404 4.59574
\(53\) 3.14493 0.431990 0.215995 0.976394i \(-0.430701\pi\)
0.215995 + 0.976394i \(0.430701\pi\)
\(54\) 2.69904 0.367292
\(55\) 6.29059 0.848223
\(56\) 35.6788 4.76779
\(57\) 0.936912 0.124097
\(58\) 1.92541 0.252819
\(59\) −13.9294 −1.81346 −0.906730 0.421713i \(-0.861429\pi\)
−0.906730 + 0.421713i \(0.861429\pi\)
\(60\) 7.37329 0.951888
\(61\) 14.5661 1.86500 0.932499 0.361172i \(-0.117623\pi\)
0.932499 + 0.361172i \(0.117623\pi\)
\(62\) 12.2154 1.55135
\(63\) −4.02432 −0.507017
\(64\) 22.7442 2.84302
\(65\) −8.74906 −1.08519
\(66\) −12.1694 −1.49794
\(67\) 7.10967 0.868584 0.434292 0.900772i \(-0.356999\pi\)
0.434292 + 0.900772i \(0.356999\pi\)
\(68\) 5.28480 0.640876
\(69\) 3.43565 0.413604
\(70\) −15.1543 −1.81128
\(71\) −8.69442 −1.03184 −0.515919 0.856637i \(-0.672549\pi\)
−0.515919 + 0.856637i \(0.672549\pi\)
\(72\) −8.86580 −1.04484
\(73\) 3.71040 0.434270 0.217135 0.976142i \(-0.430329\pi\)
0.217135 + 0.976142i \(0.430329\pi\)
\(74\) 11.0652 1.28630
\(75\) 3.05345 0.352582
\(76\) −4.95139 −0.567964
\(77\) 18.1448 2.06779
\(78\) 16.9253 1.91642
\(79\) −11.0868 −1.24736 −0.623681 0.781679i \(-0.714364\pi\)
−0.623681 + 0.781679i \(0.714364\pi\)
\(80\) −18.6390 −2.08391
\(81\) 1.00000 0.111111
\(82\) 9.00660 0.994613
\(83\) −14.9149 −1.63713 −0.818564 0.574415i \(-0.805229\pi\)
−0.818564 + 0.574415i \(0.805229\pi\)
\(84\) 21.2677 2.32050
\(85\) −1.39519 −0.151329
\(86\) −2.69898 −0.291038
\(87\) 0.713369 0.0764812
\(88\) 39.9739 4.26123
\(89\) −10.9723 −1.16306 −0.581530 0.813525i \(-0.697546\pi\)
−0.581530 + 0.813525i \(0.697546\pi\)
\(90\) 3.76567 0.396936
\(91\) −25.2360 −2.64546
\(92\) −18.1567 −1.89297
\(93\) 4.52582 0.469306
\(94\) −16.3153 −1.68279
\(95\) 1.30717 0.134113
\(96\) 18.3262 1.87041
\(97\) −15.2770 −1.55114 −0.775570 0.631261i \(-0.782538\pi\)
−0.775570 + 0.631261i \(0.782538\pi\)
\(98\) −24.8181 −2.50701
\(99\) −4.50878 −0.453149
\(100\) −16.1369 −1.61369
\(101\) 14.2076 1.41371 0.706855 0.707358i \(-0.250113\pi\)
0.706855 + 0.707358i \(0.250113\pi\)
\(102\) 2.69904 0.267244
\(103\) 11.4058 1.12385 0.561926 0.827188i \(-0.310061\pi\)
0.561926 + 0.827188i \(0.310061\pi\)
\(104\) −55.5964 −5.45167
\(105\) −5.61469 −0.547937
\(106\) −8.48830 −0.824456
\(107\) 1.93080 0.186657 0.0933286 0.995635i \(-0.470249\pi\)
0.0933286 + 0.995635i \(0.470249\pi\)
\(108\) −5.28480 −0.508530
\(109\) −16.3094 −1.56216 −0.781081 0.624430i \(-0.785331\pi\)
−0.781081 + 0.624430i \(0.785331\pi\)
\(110\) −16.9785 −1.61884
\(111\) 4.09969 0.389125
\(112\) −53.7630 −5.08013
\(113\) −4.04417 −0.380443 −0.190222 0.981741i \(-0.560921\pi\)
−0.190222 + 0.981741i \(0.560921\pi\)
\(114\) −2.52876 −0.236840
\(115\) 4.79338 0.446985
\(116\) −3.77001 −0.350037
\(117\) 6.27088 0.579743
\(118\) 37.5961 3.46100
\(119\) −4.02432 −0.368909
\(120\) −12.3695 −1.12917
\(121\) 9.32905 0.848096
\(122\) −39.3144 −3.55936
\(123\) 3.33697 0.300884
\(124\) −23.9181 −2.14791
\(125\) 11.2361 1.00499
\(126\) 10.8618 0.967646
\(127\) −20.7353 −1.83996 −0.919982 0.391960i \(-0.871797\pi\)
−0.919982 + 0.391960i \(0.871797\pi\)
\(128\) −24.7349 −2.18627
\(129\) −0.999978 −0.0880431
\(130\) 23.6140 2.07109
\(131\) −3.58003 −0.312789 −0.156395 0.987695i \(-0.549987\pi\)
−0.156395 + 0.987695i \(0.549987\pi\)
\(132\) 23.8280 2.07396
\(133\) 3.77043 0.326938
\(134\) −19.1893 −1.65770
\(135\) 1.39519 0.120079
\(136\) −8.86580 −0.760236
\(137\) −5.26133 −0.449506 −0.224753 0.974416i \(-0.572158\pi\)
−0.224753 + 0.974416i \(0.572158\pi\)
\(138\) −9.27296 −0.789366
\(139\) −1.88082 −0.159529 −0.0797646 0.996814i \(-0.525417\pi\)
−0.0797646 + 0.996814i \(0.525417\pi\)
\(140\) 29.6725 2.50778
\(141\) −6.04485 −0.509068
\(142\) 23.4666 1.96927
\(143\) −28.2740 −2.36439
\(144\) 13.3595 1.11329
\(145\) 0.995284 0.0826538
\(146\) −10.0145 −0.828807
\(147\) −9.19517 −0.758405
\(148\) −21.6660 −1.78094
\(149\) −16.2738 −1.33320 −0.666601 0.745414i \(-0.732252\pi\)
−0.666601 + 0.745414i \(0.732252\pi\)
\(150\) −8.24137 −0.672905
\(151\) 4.31638 0.351262 0.175631 0.984456i \(-0.443803\pi\)
0.175631 + 0.984456i \(0.443803\pi\)
\(152\) 8.30647 0.673744
\(153\) 1.00000 0.0808452
\(154\) −48.9734 −3.94639
\(155\) 6.31437 0.507183
\(156\) −33.1404 −2.65335
\(157\) −1.00000 −0.0798087
\(158\) 29.9237 2.38060
\(159\) −3.14493 −0.249410
\(160\) 25.5686 2.02137
\(161\) 13.8262 1.08966
\(162\) −2.69904 −0.212056
\(163\) 20.7002 1.62136 0.810682 0.585487i \(-0.199097\pi\)
0.810682 + 0.585487i \(0.199097\pi\)
\(164\) −17.6352 −1.37708
\(165\) −6.29059 −0.489722
\(166\) 40.2560 3.12447
\(167\) 19.6736 1.52239 0.761193 0.648526i \(-0.224614\pi\)
0.761193 + 0.648526i \(0.224614\pi\)
\(168\) −35.6788 −2.75268
\(169\) 26.3239 2.02492
\(170\) 3.76567 0.288813
\(171\) −0.936912 −0.0716474
\(172\) 5.28468 0.402953
\(173\) −5.04254 −0.383377 −0.191689 0.981456i \(-0.561396\pi\)
−0.191689 + 0.981456i \(0.561396\pi\)
\(174\) −1.92541 −0.145965
\(175\) 12.2881 0.928890
\(176\) −60.2351 −4.54039
\(177\) 13.9294 1.04700
\(178\) 29.6146 2.21971
\(179\) 5.27729 0.394443 0.197221 0.980359i \(-0.436808\pi\)
0.197221 + 0.980359i \(0.436808\pi\)
\(180\) −7.37329 −0.549573
\(181\) −21.2415 −1.57887 −0.789435 0.613834i \(-0.789626\pi\)
−0.789435 + 0.613834i \(0.789626\pi\)
\(182\) 68.1130 5.04887
\(183\) −14.5661 −1.07676
\(184\) 30.4598 2.24553
\(185\) 5.71984 0.420531
\(186\) −12.2154 −0.895674
\(187\) −4.50878 −0.329714
\(188\) 31.9458 2.32989
\(189\) 4.02432 0.292726
\(190\) −3.52810 −0.255955
\(191\) −24.1190 −1.74519 −0.872597 0.488442i \(-0.837566\pi\)
−0.872597 + 0.488442i \(0.837566\pi\)
\(192\) −22.7442 −1.64142
\(193\) −12.5692 −0.904754 −0.452377 0.891827i \(-0.649424\pi\)
−0.452377 + 0.891827i \(0.649424\pi\)
\(194\) 41.2331 2.96036
\(195\) 8.74906 0.626533
\(196\) 48.5946 3.47105
\(197\) −11.5162 −0.820494 −0.410247 0.911975i \(-0.634557\pi\)
−0.410247 + 0.911975i \(0.634557\pi\)
\(198\) 12.1694 0.864838
\(199\) −17.6821 −1.25345 −0.626724 0.779241i \(-0.715605\pi\)
−0.626724 + 0.779241i \(0.715605\pi\)
\(200\) 27.0713 1.91423
\(201\) −7.10967 −0.501477
\(202\) −38.3469 −2.69808
\(203\) 2.87083 0.201492
\(204\) −5.28480 −0.370010
\(205\) 4.65570 0.325168
\(206\) −30.7848 −2.14488
\(207\) −3.43565 −0.238794
\(208\) 83.7760 5.80882
\(209\) 4.22432 0.292203
\(210\) 15.1543 1.04574
\(211\) 12.2510 0.843391 0.421695 0.906738i \(-0.361435\pi\)
0.421695 + 0.906738i \(0.361435\pi\)
\(212\) 16.6204 1.14149
\(213\) 8.69442 0.595732
\(214\) −5.21129 −0.356237
\(215\) −1.39516 −0.0951489
\(216\) 8.86580 0.603241
\(217\) 18.2134 1.23640
\(218\) 44.0198 2.98140
\(219\) −3.71040 −0.250726
\(220\) 33.2445 2.24135
\(221\) 6.27088 0.421825
\(222\) −11.0652 −0.742648
\(223\) −25.4810 −1.70633 −0.853167 0.521638i \(-0.825321\pi\)
−0.853167 + 0.521638i \(0.825321\pi\)
\(224\) 73.7507 4.92768
\(225\) −3.05345 −0.203563
\(226\) 10.9154 0.726079
\(227\) −5.35227 −0.355243 −0.177621 0.984099i \(-0.556840\pi\)
−0.177621 + 0.984099i \(0.556840\pi\)
\(228\) 4.95139 0.327914
\(229\) 8.83483 0.583822 0.291911 0.956445i \(-0.405709\pi\)
0.291911 + 0.956445i \(0.405709\pi\)
\(230\) −12.9375 −0.853075
\(231\) −18.1448 −1.19384
\(232\) 6.32459 0.415229
\(233\) −16.2168 −1.06240 −0.531200 0.847247i \(-0.678259\pi\)
−0.531200 + 0.847247i \(0.678259\pi\)
\(234\) −16.9253 −1.10644
\(235\) −8.43370 −0.550154
\(236\) −73.6143 −4.79189
\(237\) 11.0868 0.720165
\(238\) 10.8618 0.704066
\(239\) −20.5714 −1.33065 −0.665327 0.746552i \(-0.731708\pi\)
−0.665327 + 0.746552i \(0.731708\pi\)
\(240\) 18.6390 1.20315
\(241\) 0.336297 0.0216628 0.0108314 0.999941i \(-0.496552\pi\)
0.0108314 + 0.999941i \(0.496552\pi\)
\(242\) −25.1795 −1.61860
\(243\) −1.00000 −0.0641500
\(244\) 76.9790 4.92807
\(245\) −12.8290 −0.819614
\(246\) −9.00660 −0.574240
\(247\) −5.87526 −0.373834
\(248\) 40.1250 2.54794
\(249\) 14.9149 0.945196
\(250\) −30.3266 −1.91802
\(251\) −8.39917 −0.530151 −0.265075 0.964228i \(-0.585397\pi\)
−0.265075 + 0.964228i \(0.585397\pi\)
\(252\) −21.2677 −1.33974
\(253\) 15.4906 0.973885
\(254\) 55.9655 3.51159
\(255\) 1.39519 0.0873701
\(256\) 21.2720 1.32950
\(257\) 21.0428 1.31261 0.656307 0.754494i \(-0.272117\pi\)
0.656307 + 0.754494i \(0.272117\pi\)
\(258\) 2.69898 0.168031
\(259\) 16.4985 1.02516
\(260\) −46.2370 −2.86750
\(261\) −0.713369 −0.0441564
\(262\) 9.66265 0.596960
\(263\) 30.9109 1.90605 0.953024 0.302894i \(-0.0979529\pi\)
0.953024 + 0.302894i \(0.0979529\pi\)
\(264\) −39.9739 −2.46022
\(265\) −4.38778 −0.269539
\(266\) −10.1765 −0.623964
\(267\) 10.9723 0.671493
\(268\) 37.5732 2.29515
\(269\) −2.47144 −0.150686 −0.0753432 0.997158i \(-0.524005\pi\)
−0.0753432 + 0.997158i \(0.524005\pi\)
\(270\) −3.76567 −0.229171
\(271\) −27.2477 −1.65518 −0.827589 0.561334i \(-0.810288\pi\)
−0.827589 + 0.561334i \(0.810288\pi\)
\(272\) 13.3595 0.810040
\(273\) 25.2360 1.52735
\(274\) 14.2005 0.857886
\(275\) 13.7673 0.830200
\(276\) 18.1567 1.09291
\(277\) −24.4154 −1.46698 −0.733490 0.679700i \(-0.762110\pi\)
−0.733490 + 0.679700i \(0.762110\pi\)
\(278\) 5.07640 0.304463
\(279\) −4.52582 −0.270954
\(280\) −49.7787 −2.97485
\(281\) −6.77651 −0.404252 −0.202126 0.979359i \(-0.564785\pi\)
−0.202126 + 0.979359i \(0.564785\pi\)
\(282\) 16.3153 0.971560
\(283\) 6.54969 0.389338 0.194669 0.980869i \(-0.437637\pi\)
0.194669 + 0.980869i \(0.437637\pi\)
\(284\) −45.9483 −2.72653
\(285\) −1.30717 −0.0774300
\(286\) 76.3125 4.51246
\(287\) 13.4290 0.792691
\(288\) −18.3262 −1.07988
\(289\) 1.00000 0.0588235
\(290\) −2.68631 −0.157745
\(291\) 15.2770 0.895551
\(292\) 19.6087 1.14751
\(293\) −10.4943 −0.613081 −0.306541 0.951858i \(-0.599172\pi\)
−0.306541 + 0.951858i \(0.599172\pi\)
\(294\) 24.8181 1.44742
\(295\) 19.4342 1.13150
\(296\) 36.3470 2.11263
\(297\) 4.50878 0.261626
\(298\) 43.9236 2.54443
\(299\) −21.5446 −1.24595
\(300\) 16.1369 0.931663
\(301\) −4.02423 −0.231953
\(302\) −11.6501 −0.670386
\(303\) −14.2076 −0.816206
\(304\) −12.5167 −0.717882
\(305\) −20.3225 −1.16366
\(306\) −2.69904 −0.154294
\(307\) −22.9157 −1.30787 −0.653935 0.756550i \(-0.726883\pi\)
−0.653935 + 0.756550i \(0.726883\pi\)
\(308\) 95.8915 5.46392
\(309\) −11.4058 −0.648856
\(310\) −17.0427 −0.967962
\(311\) −1.52904 −0.0867040 −0.0433520 0.999060i \(-0.513804\pi\)
−0.0433520 + 0.999060i \(0.513804\pi\)
\(312\) 55.5964 3.14752
\(313\) −10.0254 −0.566668 −0.283334 0.959021i \(-0.591440\pi\)
−0.283334 + 0.959021i \(0.591440\pi\)
\(314\) 2.69904 0.152315
\(315\) 5.61469 0.316352
\(316\) −58.5915 −3.29603
\(317\) 18.6589 1.04799 0.523993 0.851723i \(-0.324442\pi\)
0.523993 + 0.851723i \(0.324442\pi\)
\(318\) 8.48830 0.476000
\(319\) 3.21642 0.180085
\(320\) −31.7324 −1.77390
\(321\) −1.93080 −0.107767
\(322\) −37.3174 −2.07962
\(323\) −0.936912 −0.0521312
\(324\) 5.28480 0.293600
\(325\) −19.1478 −1.06213
\(326\) −55.8706 −3.09438
\(327\) 16.3094 0.901914
\(328\) 29.5849 1.63355
\(329\) −24.3264 −1.34116
\(330\) 16.9785 0.934638
\(331\) −2.56682 −0.141085 −0.0705425 0.997509i \(-0.522473\pi\)
−0.0705425 + 0.997509i \(0.522473\pi\)
\(332\) −78.8225 −4.32595
\(333\) −4.09969 −0.224661
\(334\) −53.0997 −2.90548
\(335\) −9.91932 −0.541951
\(336\) 53.7630 2.93301
\(337\) −18.7750 −1.02274 −0.511370 0.859361i \(-0.670862\pi\)
−0.511370 + 0.859361i \(0.670862\pi\)
\(338\) −71.0493 −3.86457
\(339\) 4.04417 0.219649
\(340\) −7.37329 −0.399873
\(341\) 20.4059 1.10504
\(342\) 2.52876 0.136740
\(343\) −8.83407 −0.476995
\(344\) −8.86560 −0.478001
\(345\) −4.79338 −0.258067
\(346\) 13.6100 0.731678
\(347\) −16.4101 −0.880940 −0.440470 0.897767i \(-0.645188\pi\)
−0.440470 + 0.897767i \(0.645188\pi\)
\(348\) 3.77001 0.202094
\(349\) 32.2739 1.72758 0.863792 0.503848i \(-0.168083\pi\)
0.863792 + 0.503848i \(0.168083\pi\)
\(350\) −33.1659 −1.77279
\(351\) −6.27088 −0.334715
\(352\) 82.6289 4.40414
\(353\) 27.0957 1.44216 0.721079 0.692853i \(-0.243647\pi\)
0.721079 + 0.692853i \(0.243647\pi\)
\(354\) −37.5961 −1.99821
\(355\) 12.1304 0.643812
\(356\) −57.9864 −3.07327
\(357\) 4.02432 0.212990
\(358\) −14.2436 −0.752797
\(359\) 4.74384 0.250370 0.125185 0.992133i \(-0.460048\pi\)
0.125185 + 0.992133i \(0.460048\pi\)
\(360\) 12.3695 0.651928
\(361\) −18.1222 −0.953800
\(362\) 57.3317 3.01329
\(363\) −9.32905 −0.489648
\(364\) −133.367 −6.99035
\(365\) −5.17671 −0.270961
\(366\) 39.3144 2.05500
\(367\) 22.2165 1.15969 0.579845 0.814727i \(-0.303113\pi\)
0.579845 + 0.814727i \(0.303113\pi\)
\(368\) −45.8987 −2.39263
\(369\) −3.33697 −0.173716
\(370\) −15.4381 −0.802586
\(371\) −12.6562 −0.657079
\(372\) 23.9181 1.24009
\(373\) 28.6253 1.48216 0.741081 0.671416i \(-0.234313\pi\)
0.741081 + 0.671416i \(0.234313\pi\)
\(374\) 12.1694 0.629262
\(375\) −11.2361 −0.580229
\(376\) −53.5924 −2.76382
\(377\) −4.47345 −0.230394
\(378\) −10.8618 −0.558670
\(379\) −15.4649 −0.794379 −0.397190 0.917737i \(-0.630014\pi\)
−0.397190 + 0.917737i \(0.630014\pi\)
\(380\) 6.90813 0.354379
\(381\) 20.7353 1.06230
\(382\) 65.0982 3.33071
\(383\) −13.8251 −0.706430 −0.353215 0.935542i \(-0.614912\pi\)
−0.353215 + 0.935542i \(0.614912\pi\)
\(384\) 24.7349 1.26225
\(385\) −25.3154 −1.29019
\(386\) 33.9248 1.72673
\(387\) 0.999978 0.0508317
\(388\) −80.7357 −4.09873
\(389\) 1.74249 0.0883477 0.0441739 0.999024i \(-0.485934\pi\)
0.0441739 + 0.999024i \(0.485934\pi\)
\(390\) −23.6140 −1.19574
\(391\) −3.43565 −0.173748
\(392\) −81.5225 −4.11751
\(393\) 3.58003 0.180589
\(394\) 31.0826 1.56592
\(395\) 15.4682 0.778289
\(396\) −23.8280 −1.19740
\(397\) 32.0326 1.60767 0.803836 0.594851i \(-0.202789\pi\)
0.803836 + 0.594851i \(0.202789\pi\)
\(398\) 47.7245 2.39221
\(399\) −3.77043 −0.188758
\(400\) −40.7926 −2.03963
\(401\) −34.0906 −1.70240 −0.851202 0.524837i \(-0.824126\pi\)
−0.851202 + 0.524837i \(0.824126\pi\)
\(402\) 19.1893 0.957073
\(403\) −28.3809 −1.41375
\(404\) 75.0844 3.73559
\(405\) −1.39519 −0.0693275
\(406\) −7.74847 −0.384550
\(407\) 18.4846 0.916246
\(408\) 8.86580 0.438923
\(409\) 23.6999 1.17188 0.585941 0.810354i \(-0.300725\pi\)
0.585941 + 0.810354i \(0.300725\pi\)
\(410\) −12.5659 −0.620586
\(411\) 5.26133 0.259522
\(412\) 60.2776 2.96967
\(413\) 56.0566 2.75836
\(414\) 9.27296 0.455741
\(415\) 20.8092 1.02148
\(416\) −114.922 −5.63450
\(417\) 1.88082 0.0921042
\(418\) −11.4016 −0.557671
\(419\) −16.0805 −0.785586 −0.392793 0.919627i \(-0.628491\pi\)
−0.392793 + 0.919627i \(0.628491\pi\)
\(420\) −29.6725 −1.44787
\(421\) −8.34538 −0.406729 −0.203365 0.979103i \(-0.565188\pi\)
−0.203365 + 0.979103i \(0.565188\pi\)
\(422\) −33.0658 −1.60962
\(423\) 6.04485 0.293911
\(424\) −27.8824 −1.35409
\(425\) −3.05345 −0.148114
\(426\) −23.4666 −1.13696
\(427\) −58.6187 −2.83676
\(428\) 10.2039 0.493223
\(429\) 28.2740 1.36508
\(430\) 3.76558 0.181592
\(431\) 13.6817 0.659025 0.329513 0.944151i \(-0.393116\pi\)
0.329513 + 0.944151i \(0.393116\pi\)
\(432\) −13.3595 −0.642760
\(433\) −20.4247 −0.981549 −0.490774 0.871287i \(-0.663286\pi\)
−0.490774 + 0.871287i \(0.663286\pi\)
\(434\) −49.1585 −2.35969
\(435\) −0.995284 −0.0477202
\(436\) −86.1922 −4.12786
\(437\) 3.21890 0.153981
\(438\) 10.0145 0.478512
\(439\) −6.07071 −0.289739 −0.144870 0.989451i \(-0.546276\pi\)
−0.144870 + 0.989451i \(0.546276\pi\)
\(440\) −55.7711 −2.65878
\(441\) 9.19517 0.437865
\(442\) −16.9253 −0.805056
\(443\) 11.9603 0.568250 0.284125 0.958787i \(-0.408297\pi\)
0.284125 + 0.958787i \(0.408297\pi\)
\(444\) 21.6660 1.02822
\(445\) 15.3084 0.725688
\(446\) 68.7742 3.25655
\(447\) 16.2738 0.769725
\(448\) −91.5299 −4.32438
\(449\) 16.5254 0.779884 0.389942 0.920839i \(-0.372495\pi\)
0.389942 + 0.920839i \(0.372495\pi\)
\(450\) 8.24137 0.388502
\(451\) 15.0456 0.708471
\(452\) −21.3726 −1.00528
\(453\) −4.31638 −0.202801
\(454\) 14.4460 0.677983
\(455\) 35.2090 1.65063
\(456\) −8.30647 −0.388986
\(457\) 26.2389 1.22741 0.613703 0.789537i \(-0.289679\pi\)
0.613703 + 0.789537i \(0.289679\pi\)
\(458\) −23.8455 −1.11423
\(459\) −1.00000 −0.0466760
\(460\) 25.3321 1.18111
\(461\) 8.72840 0.406522 0.203261 0.979125i \(-0.434846\pi\)
0.203261 + 0.979125i \(0.434846\pi\)
\(462\) 48.9734 2.27845
\(463\) −21.2582 −0.987951 −0.493975 0.869476i \(-0.664457\pi\)
−0.493975 + 0.869476i \(0.664457\pi\)
\(464\) −9.53027 −0.442431
\(465\) −6.31437 −0.292822
\(466\) 43.7698 2.02760
\(467\) −10.2415 −0.473922 −0.236961 0.971519i \(-0.576151\pi\)
−0.236961 + 0.971519i \(0.576151\pi\)
\(468\) 33.1404 1.53191
\(469\) −28.6116 −1.32116
\(470\) 22.7629 1.04997
\(471\) 1.00000 0.0460776
\(472\) 123.496 5.68435
\(473\) −4.50867 −0.207309
\(474\) −29.9237 −1.37444
\(475\) 2.86081 0.131263
\(476\) −21.2677 −0.974805
\(477\) 3.14493 0.143997
\(478\) 55.5230 2.53956
\(479\) 39.8665 1.82155 0.910774 0.412905i \(-0.135486\pi\)
0.910774 + 0.412905i \(0.135486\pi\)
\(480\) −25.5686 −1.16704
\(481\) −25.7086 −1.17221
\(482\) −0.907678 −0.0413436
\(483\) −13.8262 −0.629113
\(484\) 49.3022 2.24101
\(485\) 21.3142 0.967830
\(486\) 2.69904 0.122431
\(487\) 10.4861 0.475171 0.237585 0.971367i \(-0.423644\pi\)
0.237585 + 0.971367i \(0.423644\pi\)
\(488\) −129.140 −5.84590
\(489\) −20.7002 −0.936095
\(490\) 34.6259 1.56424
\(491\) −43.2487 −1.95179 −0.975893 0.218250i \(-0.929965\pi\)
−0.975893 + 0.218250i \(0.929965\pi\)
\(492\) 17.6352 0.795057
\(493\) −0.713369 −0.0321285
\(494\) 15.8575 0.713465
\(495\) 6.29059 0.282741
\(496\) −60.4628 −2.71486
\(497\) 34.9892 1.56948
\(498\) −40.2560 −1.80391
\(499\) 21.6555 0.969435 0.484718 0.874671i \(-0.338922\pi\)
0.484718 + 0.874671i \(0.338922\pi\)
\(500\) 59.3804 2.65557
\(501\) −19.6736 −0.878950
\(502\) 22.6697 1.01180
\(503\) −2.17687 −0.0970617 −0.0485308 0.998822i \(-0.515454\pi\)
−0.0485308 + 0.998822i \(0.515454\pi\)
\(504\) 35.6788 1.58926
\(505\) −19.8223 −0.882081
\(506\) −41.8097 −1.85867
\(507\) −26.3239 −1.16909
\(508\) −109.582 −4.86192
\(509\) −12.8570 −0.569876 −0.284938 0.958546i \(-0.591973\pi\)
−0.284938 + 0.958546i \(0.591973\pi\)
\(510\) −3.76567 −0.166746
\(511\) −14.9319 −0.660546
\(512\) −7.94414 −0.351085
\(513\) 0.936912 0.0413657
\(514\) −56.7953 −2.50514
\(515\) −15.9133 −0.701224
\(516\) −5.28468 −0.232645
\(517\) −27.2549 −1.19867
\(518\) −44.5300 −1.95653
\(519\) 5.04254 0.221343
\(520\) 77.5674 3.40156
\(521\) −3.90165 −0.170934 −0.0854671 0.996341i \(-0.527238\pi\)
−0.0854671 + 0.996341i \(0.527238\pi\)
\(522\) 1.92541 0.0842729
\(523\) 29.9664 1.31034 0.655169 0.755483i \(-0.272598\pi\)
0.655169 + 0.755483i \(0.272598\pi\)
\(524\) −18.9198 −0.826514
\(525\) −12.2881 −0.536295
\(526\) −83.4297 −3.63771
\(527\) −4.52582 −0.197148
\(528\) 60.2351 2.62140
\(529\) −11.1963 −0.486795
\(530\) 11.8428 0.514417
\(531\) −13.9294 −0.604486
\(532\) 19.9260 0.863902
\(533\) −20.9257 −0.906394
\(534\) −29.6146 −1.28155
\(535\) −2.69383 −0.116464
\(536\) −63.0329 −2.72261
\(537\) −5.27729 −0.227732
\(538\) 6.67051 0.287586
\(539\) −41.4590 −1.78576
\(540\) 7.37329 0.317296
\(541\) −10.7641 −0.462784 −0.231392 0.972861i \(-0.574328\pi\)
−0.231392 + 0.972861i \(0.574328\pi\)
\(542\) 73.5425 3.15892
\(543\) 21.2415 0.911561
\(544\) −18.3262 −0.785731
\(545\) 22.7547 0.974706
\(546\) −68.1130 −2.91497
\(547\) 22.8408 0.976602 0.488301 0.872675i \(-0.337617\pi\)
0.488301 + 0.872675i \(0.337617\pi\)
\(548\) −27.8051 −1.18777
\(549\) 14.5661 0.621666
\(550\) −37.1585 −1.58444
\(551\) 0.668364 0.0284732
\(552\) −30.4598 −1.29646
\(553\) 44.6169 1.89730
\(554\) 65.8981 2.79974
\(555\) −5.71984 −0.242794
\(556\) −9.93976 −0.421540
\(557\) 31.2493 1.32408 0.662038 0.749470i \(-0.269692\pi\)
0.662038 + 0.749470i \(0.269692\pi\)
\(558\) 12.2154 0.517117
\(559\) 6.27074 0.265224
\(560\) 75.0095 3.16973
\(561\) 4.50878 0.190361
\(562\) 18.2900 0.771519
\(563\) −5.75846 −0.242690 −0.121345 0.992610i \(-0.538721\pi\)
−0.121345 + 0.992610i \(0.538721\pi\)
\(564\) −31.9458 −1.34516
\(565\) 5.64238 0.237377
\(566\) −17.6778 −0.743055
\(567\) −4.02432 −0.169006
\(568\) 77.0830 3.23433
\(569\) −25.4846 −1.06837 −0.534184 0.845368i \(-0.679381\pi\)
−0.534184 + 0.845368i \(0.679381\pi\)
\(570\) 3.52810 0.147776
\(571\) −43.3410 −1.81377 −0.906883 0.421383i \(-0.861545\pi\)
−0.906883 + 0.421383i \(0.861545\pi\)
\(572\) −149.422 −6.24766
\(573\) 24.1190 1.00759
\(574\) −36.2455 −1.51286
\(575\) 10.4906 0.437488
\(576\) 22.7442 0.947674
\(577\) −25.7345 −1.07134 −0.535671 0.844427i \(-0.679941\pi\)
−0.535671 + 0.844427i \(0.679941\pi\)
\(578\) −2.69904 −0.112265
\(579\) 12.5692 0.522360
\(580\) 5.25988 0.218405
\(581\) 60.0226 2.49016
\(582\) −41.2331 −1.70917
\(583\) −14.1798 −0.587267
\(584\) −32.8957 −1.36123
\(585\) −8.74906 −0.361729
\(586\) 28.3244 1.17007
\(587\) −12.1617 −0.501967 −0.250984 0.967991i \(-0.580754\pi\)
−0.250984 + 0.967991i \(0.580754\pi\)
\(588\) −48.5946 −2.00401
\(589\) 4.24030 0.174718
\(590\) −52.4536 −2.15948
\(591\) 11.5162 0.473712
\(592\) −54.7699 −2.25103
\(593\) 2.22220 0.0912547 0.0456274 0.998959i \(-0.485471\pi\)
0.0456274 + 0.998959i \(0.485471\pi\)
\(594\) −12.1694 −0.499315
\(595\) 5.61469 0.230180
\(596\) −86.0039 −3.52286
\(597\) 17.6821 0.723679
\(598\) 58.1496 2.37791
\(599\) −16.4260 −0.671150 −0.335575 0.942013i \(-0.608931\pi\)
−0.335575 + 0.942013i \(0.608931\pi\)
\(600\) −27.0713 −1.10518
\(601\) −15.5393 −0.633863 −0.316932 0.948448i \(-0.602653\pi\)
−0.316932 + 0.948448i \(0.602653\pi\)
\(602\) 10.8616 0.442684
\(603\) 7.10967 0.289528
\(604\) 22.8112 0.928174
\(605\) −13.0158 −0.529167
\(606\) 38.3469 1.55774
\(607\) −1.32603 −0.0538217 −0.0269109 0.999638i \(-0.508567\pi\)
−0.0269109 + 0.999638i \(0.508567\pi\)
\(608\) 17.1701 0.696338
\(609\) −2.87083 −0.116332
\(610\) 54.8511 2.22085
\(611\) 37.9065 1.53353
\(612\) 5.28480 0.213625
\(613\) −11.4453 −0.462273 −0.231137 0.972921i \(-0.574244\pi\)
−0.231137 + 0.972921i \(0.574244\pi\)
\(614\) 61.8504 2.49608
\(615\) −4.65570 −0.187736
\(616\) −160.868 −6.48155
\(617\) −6.20638 −0.249859 −0.124930 0.992166i \(-0.539871\pi\)
−0.124930 + 0.992166i \(0.539871\pi\)
\(618\) 30.7848 1.23835
\(619\) 37.3524 1.50132 0.750660 0.660689i \(-0.229736\pi\)
0.750660 + 0.660689i \(0.229736\pi\)
\(620\) 33.3702 1.34018
\(621\) 3.43565 0.137868
\(622\) 4.12694 0.165475
\(623\) 44.1560 1.76907
\(624\) −83.7760 −3.35372
\(625\) −0.409202 −0.0163681
\(626\) 27.0589 1.08149
\(627\) −4.22432 −0.168703
\(628\) −5.28480 −0.210887
\(629\) −4.09969 −0.163465
\(630\) −15.1543 −0.603760
\(631\) 29.3635 1.16894 0.584471 0.811415i \(-0.301302\pi\)
0.584471 + 0.811415i \(0.301302\pi\)
\(632\) 98.2934 3.90990
\(633\) −12.2510 −0.486932
\(634\) −50.3610 −2.00009
\(635\) 28.9297 1.14804
\(636\) −16.6204 −0.659040
\(637\) 57.6618 2.28464
\(638\) −8.68124 −0.343693
\(639\) −8.69442 −0.343946
\(640\) 34.5098 1.36412
\(641\) 42.4131 1.67522 0.837608 0.546271i \(-0.183953\pi\)
0.837608 + 0.546271i \(0.183953\pi\)
\(642\) 5.21129 0.205673
\(643\) 7.99193 0.315171 0.157585 0.987505i \(-0.449629\pi\)
0.157585 + 0.987505i \(0.449629\pi\)
\(644\) 73.0686 2.87931
\(645\) 1.39516 0.0549343
\(646\) 2.52876 0.0994927
\(647\) −30.2235 −1.18821 −0.594105 0.804387i \(-0.702494\pi\)
−0.594105 + 0.804387i \(0.702494\pi\)
\(648\) −8.86580 −0.348282
\(649\) 62.8047 2.46530
\(650\) 51.6807 2.02708
\(651\) −18.2134 −0.713838
\(652\) 109.396 4.28429
\(653\) −19.6509 −0.768997 −0.384499 0.923126i \(-0.625626\pi\)
−0.384499 + 0.923126i \(0.625626\pi\)
\(654\) −44.0198 −1.72131
\(655\) 4.99482 0.195164
\(656\) −44.5803 −1.74057
\(657\) 3.71040 0.144757
\(658\) 65.6579 2.55961
\(659\) 23.6072 0.919606 0.459803 0.888021i \(-0.347920\pi\)
0.459803 + 0.888021i \(0.347920\pi\)
\(660\) −33.2445 −1.29404
\(661\) 1.05620 0.0410815 0.0205408 0.999789i \(-0.493461\pi\)
0.0205408 + 0.999789i \(0.493461\pi\)
\(662\) 6.92794 0.269262
\(663\) −6.27088 −0.243541
\(664\) 132.233 5.13163
\(665\) −5.26047 −0.203992
\(666\) 11.0652 0.428768
\(667\) 2.45089 0.0948988
\(668\) 103.971 4.02275
\(669\) 25.4810 0.985153
\(670\) 26.7726 1.03432
\(671\) −65.6753 −2.53537
\(672\) −73.7507 −2.84500
\(673\) −11.7935 −0.454606 −0.227303 0.973824i \(-0.572991\pi\)
−0.227303 + 0.973824i \(0.572991\pi\)
\(674\) 50.6744 1.95191
\(675\) 3.05345 0.117527
\(676\) 139.117 5.35065
\(677\) 31.9014 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(678\) −10.9154 −0.419202
\(679\) 61.4794 2.35936
\(680\) 12.3695 0.474347
\(681\) 5.35227 0.205099
\(682\) −55.0763 −2.10898
\(683\) −21.0274 −0.804591 −0.402296 0.915510i \(-0.631788\pi\)
−0.402296 + 0.915510i \(0.631788\pi\)
\(684\) −4.95139 −0.189321
\(685\) 7.34055 0.280468
\(686\) 23.8435 0.910349
\(687\) −8.83483 −0.337070
\(688\) 13.3592 0.509316
\(689\) 19.7215 0.751330
\(690\) 12.9375 0.492523
\(691\) −17.4800 −0.664970 −0.332485 0.943109i \(-0.607887\pi\)
−0.332485 + 0.943109i \(0.607887\pi\)
\(692\) −26.6488 −1.01304
\(693\) 18.1448 0.689263
\(694\) 44.2914 1.68128
\(695\) 2.62410 0.0995378
\(696\) −6.32459 −0.239733
\(697\) −3.33697 −0.126397
\(698\) −87.1086 −3.29711
\(699\) 16.2168 0.613376
\(700\) 64.9400 2.45450
\(701\) −1.16361 −0.0439488 −0.0219744 0.999759i \(-0.506995\pi\)
−0.0219744 + 0.999759i \(0.506995\pi\)
\(702\) 16.9253 0.638806
\(703\) 3.84105 0.144868
\(704\) −102.548 −3.86494
\(705\) 8.43370 0.317632
\(706\) −73.1322 −2.75237
\(707\) −57.1760 −2.15033
\(708\) 73.6143 2.76660
\(709\) 40.1600 1.50824 0.754120 0.656737i \(-0.228064\pi\)
0.754120 + 0.656737i \(0.228064\pi\)
\(710\) −32.7403 −1.22872
\(711\) −11.0868 −0.415788
\(712\) 97.2781 3.64565
\(713\) 15.5492 0.582320
\(714\) −10.8618 −0.406492
\(715\) 39.4475 1.47525
\(716\) 27.8894 1.04228
\(717\) 20.5714 0.768254
\(718\) −12.8038 −0.477833
\(719\) 32.9365 1.22833 0.614163 0.789179i \(-0.289494\pi\)
0.614163 + 0.789179i \(0.289494\pi\)
\(720\) −18.6390 −0.694636
\(721\) −45.9008 −1.70944
\(722\) 48.9125 1.82033
\(723\) −0.336297 −0.0125070
\(724\) −112.257 −4.17201
\(725\) 2.17824 0.0808976
\(726\) 25.1795 0.934498
\(727\) 47.0662 1.74559 0.872795 0.488087i \(-0.162305\pi\)
0.872795 + 0.488087i \(0.162305\pi\)
\(728\) 223.738 8.29227
\(729\) 1.00000 0.0370370
\(730\) 13.9721 0.517132
\(731\) 0.999978 0.0369855
\(732\) −76.9790 −2.84522
\(733\) 12.1862 0.450108 0.225054 0.974346i \(-0.427744\pi\)
0.225054 + 0.974346i \(0.427744\pi\)
\(734\) −59.9631 −2.21328
\(735\) 12.8290 0.473205
\(736\) 62.9626 2.32083
\(737\) −32.0559 −1.18079
\(738\) 9.00660 0.331538
\(739\) −28.3800 −1.04397 −0.521987 0.852953i \(-0.674809\pi\)
−0.521987 + 0.852953i \(0.674809\pi\)
\(740\) 30.2282 1.11121
\(741\) 5.87526 0.215833
\(742\) 34.1596 1.25404
\(743\) 30.1024 1.10435 0.552174 0.833729i \(-0.313798\pi\)
0.552174 + 0.833729i \(0.313798\pi\)
\(744\) −40.1250 −1.47106
\(745\) 22.7050 0.831848
\(746\) −77.2608 −2.82872
\(747\) −14.9149 −0.545709
\(748\) −23.8280 −0.871237
\(749\) −7.77015 −0.283915
\(750\) 30.3266 1.10737
\(751\) −45.4570 −1.65875 −0.829375 0.558693i \(-0.811303\pi\)
−0.829375 + 0.558693i \(0.811303\pi\)
\(752\) 80.7563 2.94488
\(753\) 8.39917 0.306083
\(754\) 12.0740 0.439709
\(755\) −6.02216 −0.219169
\(756\) 21.2677 0.773500
\(757\) 23.0324 0.837126 0.418563 0.908188i \(-0.362534\pi\)
0.418563 + 0.908188i \(0.362534\pi\)
\(758\) 41.7404 1.51608
\(759\) −15.4906 −0.562273
\(760\) −11.5891 −0.420381
\(761\) −8.12503 −0.294532 −0.147266 0.989097i \(-0.547047\pi\)
−0.147266 + 0.989097i \(0.547047\pi\)
\(762\) −55.9655 −2.02742
\(763\) 65.6344 2.37613
\(764\) −127.464 −4.61150
\(765\) −1.39519 −0.0504431
\(766\) 37.3145 1.34823
\(767\) −87.3499 −3.15402
\(768\) −21.2720 −0.767586
\(769\) 6.57902 0.237246 0.118623 0.992939i \(-0.462152\pi\)
0.118623 + 0.992939i \(0.462152\pi\)
\(770\) 68.3271 2.46234
\(771\) −21.0428 −0.757839
\(772\) −66.4259 −2.39072
\(773\) 18.3616 0.660420 0.330210 0.943907i \(-0.392880\pi\)
0.330210 + 0.943907i \(0.392880\pi\)
\(774\) −2.69898 −0.0970127
\(775\) 13.8194 0.496406
\(776\) 135.443 4.86210
\(777\) −16.4985 −0.591879
\(778\) −4.70304 −0.168612
\(779\) 3.12644 0.112017
\(780\) 46.2370 1.65555
\(781\) 39.2012 1.40273
\(782\) 9.27296 0.331600
\(783\) 0.713369 0.0254937
\(784\) 122.843 4.38725
\(785\) 1.39519 0.0497964
\(786\) −9.66265 −0.344655
\(787\) 37.3127 1.33005 0.665027 0.746819i \(-0.268420\pi\)
0.665027 + 0.746819i \(0.268420\pi\)
\(788\) −60.8607 −2.16807
\(789\) −30.9109 −1.10046
\(790\) −41.7492 −1.48537
\(791\) 16.2750 0.578674
\(792\) 39.9739 1.42041
\(793\) 91.3423 3.24366
\(794\) −86.4573 −3.06825
\(795\) 4.38778 0.155618
\(796\) −93.4462 −3.31211
\(797\) 24.9166 0.882591 0.441296 0.897362i \(-0.354519\pi\)
0.441296 + 0.897362i \(0.354519\pi\)
\(798\) 10.1765 0.360246
\(799\) 6.04485 0.213851
\(800\) 55.9583 1.97842
\(801\) −10.9723 −0.387687
\(802\) 92.0119 3.24905
\(803\) −16.7294 −0.590367
\(804\) −37.5732 −1.32510
\(805\) −19.2901 −0.679887
\(806\) 76.6011 2.69816
\(807\) 2.47144 0.0869988
\(808\) −125.962 −4.43132
\(809\) −48.7765 −1.71489 −0.857444 0.514577i \(-0.827949\pi\)
−0.857444 + 0.514577i \(0.827949\pi\)
\(810\) 3.76567 0.132312
\(811\) 22.7258 0.798012 0.399006 0.916948i \(-0.369355\pi\)
0.399006 + 0.916948i \(0.369355\pi\)
\(812\) 15.1717 0.532424
\(813\) 27.2477 0.955618
\(814\) −49.8905 −1.74866
\(815\) −28.8807 −1.01165
\(816\) −13.3595 −0.467677
\(817\) −0.936891 −0.0327777
\(818\) −63.9668 −2.23655
\(819\) −25.2360 −0.881819
\(820\) 24.6044 0.859225
\(821\) −1.65874 −0.0578905 −0.0289452 0.999581i \(-0.509215\pi\)
−0.0289452 + 0.999581i \(0.509215\pi\)
\(822\) −14.2005 −0.495300
\(823\) 3.01399 0.105061 0.0525305 0.998619i \(-0.483271\pi\)
0.0525305 + 0.998619i \(0.483271\pi\)
\(824\) −101.122 −3.52275
\(825\) −13.7673 −0.479316
\(826\) −151.299 −5.26436
\(827\) 3.89927 0.135591 0.0677954 0.997699i \(-0.478403\pi\)
0.0677954 + 0.997699i \(0.478403\pi\)
\(828\) −18.1567 −0.630990
\(829\) −10.4469 −0.362837 −0.181419 0.983406i \(-0.558069\pi\)
−0.181419 + 0.983406i \(0.558069\pi\)
\(830\) −56.1647 −1.94951
\(831\) 24.4154 0.846962
\(832\) 142.626 4.94466
\(833\) 9.19517 0.318594
\(834\) −5.07640 −0.175782
\(835\) −27.4483 −0.949888
\(836\) 22.3247 0.772116
\(837\) 4.52582 0.156435
\(838\) 43.4020 1.49930
\(839\) 3.61150 0.124683 0.0623413 0.998055i \(-0.480143\pi\)
0.0623413 + 0.998055i \(0.480143\pi\)
\(840\) 49.7787 1.71753
\(841\) −28.4911 −0.982452
\(842\) 22.5245 0.776245
\(843\) 6.77651 0.233395
\(844\) 64.7439 2.22858
\(845\) −36.7269 −1.26344
\(846\) −16.3153 −0.560931
\(847\) −37.5431 −1.29000
\(848\) 42.0148 1.44279
\(849\) −6.54969 −0.224785
\(850\) 8.24137 0.282677
\(851\) 14.0851 0.482831
\(852\) 45.9483 1.57416
\(853\) −13.4090 −0.459114 −0.229557 0.973295i \(-0.573728\pi\)
−0.229557 + 0.973295i \(0.573728\pi\)
\(854\) 158.214 5.41397
\(855\) 1.30717 0.0447042
\(856\) −17.1181 −0.585083
\(857\) −1.71381 −0.0585426 −0.0292713 0.999572i \(-0.509319\pi\)
−0.0292713 + 0.999572i \(0.509319\pi\)
\(858\) −76.3125 −2.60527
\(859\) 34.3192 1.17096 0.585478 0.810688i \(-0.300907\pi\)
0.585478 + 0.810688i \(0.300907\pi\)
\(860\) −7.37313 −0.251422
\(861\) −13.4290 −0.457660
\(862\) −36.9275 −1.25775
\(863\) −40.5851 −1.38153 −0.690767 0.723077i \(-0.742727\pi\)
−0.690767 + 0.723077i \(0.742727\pi\)
\(864\) 18.3262 0.623471
\(865\) 7.03530 0.239207
\(866\) 55.1270 1.87329
\(867\) −1.00000 −0.0339618
\(868\) 96.2540 3.26707
\(869\) 49.9879 1.69572
\(870\) 2.68631 0.0910744
\(871\) 44.5839 1.51067
\(872\) 144.596 4.89665
\(873\) −15.2770 −0.517047
\(874\) −8.68794 −0.293874
\(875\) −45.2176 −1.52863
\(876\) −19.6087 −0.662518
\(877\) −27.3672 −0.924125 −0.462063 0.886847i \(-0.652890\pi\)
−0.462063 + 0.886847i \(0.652890\pi\)
\(878\) 16.3851 0.552970
\(879\) 10.4943 0.353963
\(880\) 84.0393 2.83296
\(881\) 53.9615 1.81801 0.909005 0.416786i \(-0.136844\pi\)
0.909005 + 0.416786i \(0.136844\pi\)
\(882\) −24.8181 −0.835669
\(883\) −41.4535 −1.39502 −0.697510 0.716575i \(-0.745709\pi\)
−0.697510 + 0.716575i \(0.745709\pi\)
\(884\) 33.1404 1.11463
\(885\) −19.4342 −0.653273
\(886\) −32.2813 −1.08451
\(887\) 2.87080 0.0963922 0.0481961 0.998838i \(-0.484653\pi\)
0.0481961 + 0.998838i \(0.484653\pi\)
\(888\) −36.3470 −1.21973
\(889\) 83.4457 2.79868
\(890\) −41.3180 −1.38498
\(891\) −4.50878 −0.151050
\(892\) −134.662 −4.50882
\(893\) −5.66349 −0.189521
\(894\) −43.9236 −1.46903
\(895\) −7.36281 −0.246112
\(896\) 99.5411 3.32543
\(897\) 21.5446 0.719352
\(898\) −44.6028 −1.48841
\(899\) 3.22858 0.107679
\(900\) −16.1369 −0.537896
\(901\) 3.14493 0.104773
\(902\) −40.6087 −1.35212
\(903\) 4.02423 0.133918
\(904\) 35.8548 1.19251
\(905\) 29.6359 0.985132
\(906\) 11.6501 0.387047
\(907\) −10.6288 −0.352924 −0.176462 0.984307i \(-0.556465\pi\)
−0.176462 + 0.984307i \(0.556465\pi\)
\(908\) −28.2857 −0.938693
\(909\) 14.2076 0.471237
\(910\) −95.0305 −3.15023
\(911\) 32.7399 1.08472 0.542361 0.840146i \(-0.317531\pi\)
0.542361 + 0.840146i \(0.317531\pi\)
\(912\) 12.5167 0.414469
\(913\) 67.2481 2.22559
\(914\) −70.8198 −2.34251
\(915\) 20.3225 0.671840
\(916\) 46.6903 1.54269
\(917\) 14.4072 0.475768
\(918\) 2.69904 0.0890815
\(919\) −31.1715 −1.02825 −0.514127 0.857714i \(-0.671884\pi\)
−0.514127 + 0.857714i \(0.671884\pi\)
\(920\) −42.4972 −1.40109
\(921\) 22.9157 0.755099
\(922\) −23.5583 −0.775850
\(923\) −54.5217 −1.79460
\(924\) −95.8915 −3.15460
\(925\) 12.5182 0.411595
\(926\) 57.3766 1.88551
\(927\) 11.4058 0.374617
\(928\) 13.0734 0.429154
\(929\) 12.1769 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(930\) 17.0427 0.558853
\(931\) −8.61506 −0.282347
\(932\) −85.7027 −2.80728
\(933\) 1.52904 0.0500586
\(934\) 27.6423 0.904483
\(935\) 6.29059 0.205724
\(936\) −55.5964 −1.81722
\(937\) 41.0500 1.34105 0.670523 0.741889i \(-0.266070\pi\)
0.670523 + 0.741889i \(0.266070\pi\)
\(938\) 77.2237 2.52144
\(939\) 10.0254 0.327166
\(940\) −44.5704 −1.45373
\(941\) 11.6761 0.380629 0.190314 0.981723i \(-0.439049\pi\)
0.190314 + 0.981723i \(0.439049\pi\)
\(942\) −2.69904 −0.0879394
\(943\) 11.4647 0.373341
\(944\) −186.091 −6.05674
\(945\) −5.61469 −0.182646
\(946\) 12.1691 0.395651
\(947\) −27.7067 −0.900348 −0.450174 0.892941i \(-0.648638\pi\)
−0.450174 + 0.892941i \(0.648638\pi\)
\(948\) 58.5915 1.90296
\(949\) 23.2675 0.755294
\(950\) −7.72144 −0.250517
\(951\) −18.6589 −0.605055
\(952\) 35.6788 1.15636
\(953\) 17.8327 0.577657 0.288829 0.957381i \(-0.406734\pi\)
0.288829 + 0.957381i \(0.406734\pi\)
\(954\) −8.48830 −0.274819
\(955\) 33.6506 1.08891
\(956\) −108.716 −3.51612
\(957\) −3.21642 −0.103972
\(958\) −107.601 −3.47644
\(959\) 21.1733 0.683721
\(960\) 31.7324 1.02416
\(961\) −10.5169 −0.339256
\(962\) 69.3886 2.23718
\(963\) 1.93080 0.0622191
\(964\) 1.77726 0.0572418
\(965\) 17.5365 0.564519
\(966\) 37.3174 1.20067
\(967\) −26.1834 −0.842000 −0.421000 0.907061i \(-0.638321\pi\)
−0.421000 + 0.907061i \(0.638321\pi\)
\(968\) −82.7095 −2.65839
\(969\) 0.936912 0.0300979
\(970\) −57.5279 −1.84711
\(971\) −24.6119 −0.789833 −0.394916 0.918717i \(-0.629226\pi\)
−0.394916 + 0.918717i \(0.629226\pi\)
\(972\) −5.28480 −0.169510
\(973\) 7.56903 0.242652
\(974\) −28.3024 −0.906867
\(975\) 19.1478 0.613221
\(976\) 194.596 6.22887
\(977\) 58.8177 1.88174 0.940872 0.338763i \(-0.110008\pi\)
0.940872 + 0.338763i \(0.110008\pi\)
\(978\) 55.8706 1.78654
\(979\) 49.4716 1.58112
\(980\) −67.7987 −2.16575
\(981\) −16.3094 −0.520720
\(982\) 116.730 3.72500
\(983\) 13.7855 0.439689 0.219844 0.975535i \(-0.429445\pi\)
0.219844 + 0.975535i \(0.429445\pi\)
\(984\) −29.5849 −0.943132
\(985\) 16.0672 0.511945
\(986\) 1.92541 0.0613175
\(987\) 24.3264 0.774318
\(988\) −31.0496 −0.987819
\(989\) −3.43558 −0.109245
\(990\) −16.9785 −0.539613
\(991\) −2.98210 −0.0947297 −0.0473648 0.998878i \(-0.515082\pi\)
−0.0473648 + 0.998878i \(0.515082\pi\)
\(992\) 82.9413 2.63339
\(993\) 2.56682 0.0814555
\(994\) −94.4370 −2.99536
\(995\) 24.6698 0.782085
\(996\) 78.8225 2.49759
\(997\) 34.3559 1.08806 0.544030 0.839065i \(-0.316898\pi\)
0.544030 + 0.839065i \(0.316898\pi\)
\(998\) −58.4491 −1.85017
\(999\) 4.09969 0.129708
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 \(a_p\))