Properties

Label 6008.2.a.e.1.48
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.48
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.08580 q^{3} -3.00553 q^{5} +4.90892 q^{7} +6.52215 q^{9} +O(q^{10})\) \(q+3.08580 q^{3} -3.00553 q^{5} +4.90892 q^{7} +6.52215 q^{9} -0.849994 q^{11} +3.14160 q^{13} -9.27445 q^{15} +0.172702 q^{17} -5.46033 q^{19} +15.1479 q^{21} -1.77175 q^{23} +4.03319 q^{25} +10.8686 q^{27} +4.39026 q^{29} -1.76048 q^{31} -2.62291 q^{33} -14.7539 q^{35} +7.37710 q^{37} +9.69434 q^{39} +7.48177 q^{41} +10.5633 q^{43} -19.6025 q^{45} -12.9228 q^{47} +17.0975 q^{49} +0.532925 q^{51} +4.69453 q^{53} +2.55468 q^{55} -16.8495 q^{57} +6.35178 q^{59} +7.33912 q^{61} +32.0167 q^{63} -9.44216 q^{65} -12.2594 q^{67} -5.46726 q^{69} -4.18800 q^{71} +3.73696 q^{73} +12.4456 q^{75} -4.17256 q^{77} -13.9088 q^{79} +13.9719 q^{81} +0.877723 q^{83} -0.519062 q^{85} +13.5475 q^{87} -7.18554 q^{89} +15.4219 q^{91} -5.43250 q^{93} +16.4112 q^{95} +14.1722 q^{97} -5.54378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.08580 1.78159 0.890793 0.454409i \(-0.150150\pi\)
0.890793 + 0.454409i \(0.150150\pi\)
\(4\) 0 0
\(5\) −3.00553 −1.34411 −0.672056 0.740500i \(-0.734589\pi\)
−0.672056 + 0.740500i \(0.734589\pi\)
\(6\) 0 0
\(7\) 4.90892 1.85540 0.927699 0.373328i \(-0.121783\pi\)
0.927699 + 0.373328i \(0.121783\pi\)
\(8\) 0 0
\(9\) 6.52215 2.17405
\(10\) 0 0
\(11\) −0.849994 −0.256283 −0.128141 0.991756i \(-0.540901\pi\)
−0.128141 + 0.991756i \(0.540901\pi\)
\(12\) 0 0
\(13\) 3.14160 0.871323 0.435661 0.900111i \(-0.356515\pi\)
0.435661 + 0.900111i \(0.356515\pi\)
\(14\) 0 0
\(15\) −9.27445 −2.39465
\(16\) 0 0
\(17\) 0.172702 0.0418865 0.0209433 0.999781i \(-0.493333\pi\)
0.0209433 + 0.999781i \(0.493333\pi\)
\(18\) 0 0
\(19\) −5.46033 −1.25269 −0.626343 0.779548i \(-0.715449\pi\)
−0.626343 + 0.779548i \(0.715449\pi\)
\(20\) 0 0
\(21\) 15.1479 3.30555
\(22\) 0 0
\(23\) −1.77175 −0.369436 −0.184718 0.982792i \(-0.559137\pi\)
−0.184718 + 0.982792i \(0.559137\pi\)
\(24\) 0 0
\(25\) 4.03319 0.806638
\(26\) 0 0
\(27\) 10.8686 2.09167
\(28\) 0 0
\(29\) 4.39026 0.815251 0.407626 0.913149i \(-0.366357\pi\)
0.407626 + 0.913149i \(0.366357\pi\)
\(30\) 0 0
\(31\) −1.76048 −0.316192 −0.158096 0.987424i \(-0.550536\pi\)
−0.158096 + 0.987424i \(0.550536\pi\)
\(32\) 0 0
\(33\) −2.62291 −0.456590
\(34\) 0 0
\(35\) −14.7539 −2.49386
\(36\) 0 0
\(37\) 7.37710 1.21279 0.606394 0.795164i \(-0.292615\pi\)
0.606394 + 0.795164i \(0.292615\pi\)
\(38\) 0 0
\(39\) 9.69434 1.55234
\(40\) 0 0
\(41\) 7.48177 1.16846 0.584228 0.811589i \(-0.301397\pi\)
0.584228 + 0.811589i \(0.301397\pi\)
\(42\) 0 0
\(43\) 10.5633 1.61089 0.805444 0.592671i \(-0.201927\pi\)
0.805444 + 0.592671i \(0.201927\pi\)
\(44\) 0 0
\(45\) −19.6025 −2.92217
\(46\) 0 0
\(47\) −12.9228 −1.88498 −0.942491 0.334233i \(-0.891523\pi\)
−0.942491 + 0.334233i \(0.891523\pi\)
\(48\) 0 0
\(49\) 17.0975 2.44250
\(50\) 0 0
\(51\) 0.532925 0.0746244
\(52\) 0 0
\(53\) 4.69453 0.644843 0.322421 0.946596i \(-0.395503\pi\)
0.322421 + 0.946596i \(0.395503\pi\)
\(54\) 0 0
\(55\) 2.55468 0.344473
\(56\) 0 0
\(57\) −16.8495 −2.23177
\(58\) 0 0
\(59\) 6.35178 0.826932 0.413466 0.910520i \(-0.364318\pi\)
0.413466 + 0.910520i \(0.364318\pi\)
\(60\) 0 0
\(61\) 7.33912 0.939678 0.469839 0.882752i \(-0.344312\pi\)
0.469839 + 0.882752i \(0.344312\pi\)
\(62\) 0 0
\(63\) 32.0167 4.03373
\(64\) 0 0
\(65\) −9.44216 −1.17116
\(66\) 0 0
\(67\) −12.2594 −1.49772 −0.748862 0.662726i \(-0.769399\pi\)
−0.748862 + 0.662726i \(0.769399\pi\)
\(68\) 0 0
\(69\) −5.46726 −0.658181
\(70\) 0 0
\(71\) −4.18800 −0.497024 −0.248512 0.968629i \(-0.579942\pi\)
−0.248512 + 0.968629i \(0.579942\pi\)
\(72\) 0 0
\(73\) 3.73696 0.437378 0.218689 0.975795i \(-0.429822\pi\)
0.218689 + 0.975795i \(0.429822\pi\)
\(74\) 0 0
\(75\) 12.4456 1.43709
\(76\) 0 0
\(77\) −4.17256 −0.475507
\(78\) 0 0
\(79\) −13.9088 −1.56487 −0.782433 0.622735i \(-0.786021\pi\)
−0.782433 + 0.622735i \(0.786021\pi\)
\(80\) 0 0
\(81\) 13.9719 1.55244
\(82\) 0 0
\(83\) 0.877723 0.0963426 0.0481713 0.998839i \(-0.484661\pi\)
0.0481713 + 0.998839i \(0.484661\pi\)
\(84\) 0 0
\(85\) −0.519062 −0.0563002
\(86\) 0 0
\(87\) 13.5475 1.45244
\(88\) 0 0
\(89\) −7.18554 −0.761665 −0.380833 0.924644i \(-0.624363\pi\)
−0.380833 + 0.924644i \(0.624363\pi\)
\(90\) 0 0
\(91\) 15.4219 1.61665
\(92\) 0 0
\(93\) −5.43250 −0.563324
\(94\) 0 0
\(95\) 16.4112 1.68375
\(96\) 0 0
\(97\) 14.1722 1.43897 0.719484 0.694509i \(-0.244379\pi\)
0.719484 + 0.694509i \(0.244379\pi\)
\(98\) 0 0
\(99\) −5.54378 −0.557171
\(100\) 0 0
\(101\) 8.17030 0.812975 0.406488 0.913656i \(-0.366753\pi\)
0.406488 + 0.913656i \(0.366753\pi\)
\(102\) 0 0
\(103\) 17.0847 1.68341 0.841705 0.539938i \(-0.181552\pi\)
0.841705 + 0.539938i \(0.181552\pi\)
\(104\) 0 0
\(105\) −45.5275 −4.44303
\(106\) 0 0
\(107\) −4.22945 −0.408877 −0.204438 0.978879i \(-0.565537\pi\)
−0.204438 + 0.978879i \(0.565537\pi\)
\(108\) 0 0
\(109\) 9.38410 0.898834 0.449417 0.893322i \(-0.351632\pi\)
0.449417 + 0.893322i \(0.351632\pi\)
\(110\) 0 0
\(111\) 22.7643 2.16069
\(112\) 0 0
\(113\) −14.0346 −1.32026 −0.660131 0.751151i \(-0.729499\pi\)
−0.660131 + 0.751151i \(0.729499\pi\)
\(114\) 0 0
\(115\) 5.32504 0.496563
\(116\) 0 0
\(117\) 20.4900 1.89430
\(118\) 0 0
\(119\) 0.847783 0.0777162
\(120\) 0 0
\(121\) −10.2775 −0.934319
\(122\) 0 0
\(123\) 23.0872 2.08171
\(124\) 0 0
\(125\) 2.90578 0.259901
\(126\) 0 0
\(127\) 12.8238 1.13793 0.568966 0.822361i \(-0.307343\pi\)
0.568966 + 0.822361i \(0.307343\pi\)
\(128\) 0 0
\(129\) 32.5962 2.86994
\(130\) 0 0
\(131\) −17.4621 −1.52567 −0.762837 0.646591i \(-0.776194\pi\)
−0.762837 + 0.646591i \(0.776194\pi\)
\(132\) 0 0
\(133\) −26.8043 −2.32423
\(134\) 0 0
\(135\) −32.6659 −2.81144
\(136\) 0 0
\(137\) −8.05531 −0.688211 −0.344106 0.938931i \(-0.611818\pi\)
−0.344106 + 0.938931i \(0.611818\pi\)
\(138\) 0 0
\(139\) −12.3211 −1.04506 −0.522532 0.852620i \(-0.675013\pi\)
−0.522532 + 0.852620i \(0.675013\pi\)
\(140\) 0 0
\(141\) −39.8771 −3.35826
\(142\) 0 0
\(143\) −2.67034 −0.223305
\(144\) 0 0
\(145\) −13.1950 −1.09579
\(146\) 0 0
\(147\) 52.7595 4.35153
\(148\) 0 0
\(149\) 9.77241 0.800587 0.400293 0.916387i \(-0.368908\pi\)
0.400293 + 0.916387i \(0.368908\pi\)
\(150\) 0 0
\(151\) 22.8681 1.86098 0.930489 0.366320i \(-0.119382\pi\)
0.930489 + 0.366320i \(0.119382\pi\)
\(152\) 0 0
\(153\) 1.12639 0.0910633
\(154\) 0 0
\(155\) 5.29118 0.424998
\(156\) 0 0
\(157\) −5.34574 −0.426637 −0.213318 0.976983i \(-0.568427\pi\)
−0.213318 + 0.976983i \(0.568427\pi\)
\(158\) 0 0
\(159\) 14.4864 1.14884
\(160\) 0 0
\(161\) −8.69739 −0.685450
\(162\) 0 0
\(163\) 1.53197 0.119993 0.0599967 0.998199i \(-0.480891\pi\)
0.0599967 + 0.998199i \(0.480891\pi\)
\(164\) 0 0
\(165\) 7.88322 0.613708
\(166\) 0 0
\(167\) 7.09636 0.549133 0.274566 0.961568i \(-0.411466\pi\)
0.274566 + 0.961568i \(0.411466\pi\)
\(168\) 0 0
\(169\) −3.13035 −0.240796
\(170\) 0 0
\(171\) −35.6131 −2.72340
\(172\) 0 0
\(173\) −3.31550 −0.252073 −0.126036 0.992026i \(-0.540226\pi\)
−0.126036 + 0.992026i \(0.540226\pi\)
\(174\) 0 0
\(175\) 19.7986 1.49663
\(176\) 0 0
\(177\) 19.6003 1.47325
\(178\) 0 0
\(179\) −0.496922 −0.0371417 −0.0185708 0.999828i \(-0.505912\pi\)
−0.0185708 + 0.999828i \(0.505912\pi\)
\(180\) 0 0
\(181\) −25.1294 −1.86785 −0.933926 0.357465i \(-0.883641\pi\)
−0.933926 + 0.357465i \(0.883641\pi\)
\(182\) 0 0
\(183\) 22.6470 1.67412
\(184\) 0 0
\(185\) −22.1721 −1.63012
\(186\) 0 0
\(187\) −0.146796 −0.0107348
\(188\) 0 0
\(189\) 53.3533 3.88088
\(190\) 0 0
\(191\) −13.6779 −0.989698 −0.494849 0.868979i \(-0.664777\pi\)
−0.494849 + 0.868979i \(0.664777\pi\)
\(192\) 0 0
\(193\) −0.968154 −0.0696892 −0.0348446 0.999393i \(-0.511094\pi\)
−0.0348446 + 0.999393i \(0.511094\pi\)
\(194\) 0 0
\(195\) −29.1366 −2.08651
\(196\) 0 0
\(197\) 24.9818 1.77988 0.889941 0.456076i \(-0.150745\pi\)
0.889941 + 0.456076i \(0.150745\pi\)
\(198\) 0 0
\(199\) −14.8012 −1.04923 −0.524616 0.851339i \(-0.675791\pi\)
−0.524616 + 0.851339i \(0.675791\pi\)
\(200\) 0 0
\(201\) −37.8300 −2.66832
\(202\) 0 0
\(203\) 21.5515 1.51262
\(204\) 0 0
\(205\) −22.4867 −1.57054
\(206\) 0 0
\(207\) −11.5556 −0.803171
\(208\) 0 0
\(209\) 4.64125 0.321042
\(210\) 0 0
\(211\) −19.4904 −1.34177 −0.670886 0.741560i \(-0.734086\pi\)
−0.670886 + 0.741560i \(0.734086\pi\)
\(212\) 0 0
\(213\) −12.9233 −0.885491
\(214\) 0 0
\(215\) −31.7483 −2.16522
\(216\) 0 0
\(217\) −8.64208 −0.586663
\(218\) 0 0
\(219\) 11.5315 0.779227
\(220\) 0 0
\(221\) 0.542562 0.0364967
\(222\) 0 0
\(223\) 9.80484 0.656580 0.328290 0.944577i \(-0.393528\pi\)
0.328290 + 0.944577i \(0.393528\pi\)
\(224\) 0 0
\(225\) 26.3050 1.75367
\(226\) 0 0
\(227\) 1.76043 0.116844 0.0584218 0.998292i \(-0.481393\pi\)
0.0584218 + 0.998292i \(0.481393\pi\)
\(228\) 0 0
\(229\) 3.16511 0.209156 0.104578 0.994517i \(-0.466651\pi\)
0.104578 + 0.994517i \(0.466651\pi\)
\(230\) 0 0
\(231\) −12.8757 −0.847156
\(232\) 0 0
\(233\) −0.980144 −0.0642114 −0.0321057 0.999484i \(-0.510221\pi\)
−0.0321057 + 0.999484i \(0.510221\pi\)
\(234\) 0 0
\(235\) 38.8398 2.53363
\(236\) 0 0
\(237\) −42.9198 −2.78794
\(238\) 0 0
\(239\) 14.1600 0.915935 0.457967 0.888969i \(-0.348578\pi\)
0.457967 + 0.888969i \(0.348578\pi\)
\(240\) 0 0
\(241\) 22.7300 1.46417 0.732085 0.681213i \(-0.238547\pi\)
0.732085 + 0.681213i \(0.238547\pi\)
\(242\) 0 0
\(243\) 10.5087 0.674134
\(244\) 0 0
\(245\) −51.3871 −3.28300
\(246\) 0 0
\(247\) −17.1542 −1.09149
\(248\) 0 0
\(249\) 2.70847 0.171643
\(250\) 0 0
\(251\) −2.76643 −0.174616 −0.0873079 0.996181i \(-0.527826\pi\)
−0.0873079 + 0.996181i \(0.527826\pi\)
\(252\) 0 0
\(253\) 1.50598 0.0946800
\(254\) 0 0
\(255\) −1.60172 −0.100304
\(256\) 0 0
\(257\) −10.7251 −0.669014 −0.334507 0.942393i \(-0.608570\pi\)
−0.334507 + 0.942393i \(0.608570\pi\)
\(258\) 0 0
\(259\) 36.2136 2.25021
\(260\) 0 0
\(261\) 28.6339 1.77240
\(262\) 0 0
\(263\) −7.01264 −0.432418 −0.216209 0.976347i \(-0.569369\pi\)
−0.216209 + 0.976347i \(0.569369\pi\)
\(264\) 0 0
\(265\) −14.1095 −0.866741
\(266\) 0 0
\(267\) −22.1731 −1.35697
\(268\) 0 0
\(269\) −6.84967 −0.417632 −0.208816 0.977955i \(-0.566961\pi\)
−0.208816 + 0.977955i \(0.566961\pi\)
\(270\) 0 0
\(271\) −11.9347 −0.724979 −0.362490 0.931988i \(-0.618073\pi\)
−0.362490 + 0.931988i \(0.618073\pi\)
\(272\) 0 0
\(273\) 47.5888 2.88020
\(274\) 0 0
\(275\) −3.42819 −0.206727
\(276\) 0 0
\(277\) 17.3557 1.04280 0.521401 0.853312i \(-0.325410\pi\)
0.521401 + 0.853312i \(0.325410\pi\)
\(278\) 0 0
\(279\) −11.4821 −0.687417
\(280\) 0 0
\(281\) 7.73252 0.461283 0.230642 0.973039i \(-0.425918\pi\)
0.230642 + 0.973039i \(0.425918\pi\)
\(282\) 0 0
\(283\) −25.4626 −1.51360 −0.756798 0.653649i \(-0.773237\pi\)
−0.756798 + 0.653649i \(0.773237\pi\)
\(284\) 0 0
\(285\) 50.6415 2.99975
\(286\) 0 0
\(287\) 36.7274 2.16795
\(288\) 0 0
\(289\) −16.9702 −0.998246
\(290\) 0 0
\(291\) 43.7325 2.56364
\(292\) 0 0
\(293\) 1.81414 0.105983 0.0529915 0.998595i \(-0.483124\pi\)
0.0529915 + 0.998595i \(0.483124\pi\)
\(294\) 0 0
\(295\) −19.0904 −1.11149
\(296\) 0 0
\(297\) −9.23827 −0.536059
\(298\) 0 0
\(299\) −5.56613 −0.321898
\(300\) 0 0
\(301\) 51.8545 2.98884
\(302\) 0 0
\(303\) 25.2119 1.44839
\(304\) 0 0
\(305\) −22.0579 −1.26303
\(306\) 0 0
\(307\) −6.62368 −0.378034 −0.189017 0.981974i \(-0.560530\pi\)
−0.189017 + 0.981974i \(0.560530\pi\)
\(308\) 0 0
\(309\) 52.7200 2.99914
\(310\) 0 0
\(311\) −5.20576 −0.295192 −0.147596 0.989048i \(-0.547153\pi\)
−0.147596 + 0.989048i \(0.547153\pi\)
\(312\) 0 0
\(313\) 19.9901 1.12991 0.564953 0.825123i \(-0.308894\pi\)
0.564953 + 0.825123i \(0.308894\pi\)
\(314\) 0 0
\(315\) −96.2271 −5.42178
\(316\) 0 0
\(317\) −11.4146 −0.641111 −0.320555 0.947230i \(-0.603869\pi\)
−0.320555 + 0.947230i \(0.603869\pi\)
\(318\) 0 0
\(319\) −3.73170 −0.208935
\(320\) 0 0
\(321\) −13.0512 −0.728449
\(322\) 0 0
\(323\) −0.943013 −0.0524706
\(324\) 0 0
\(325\) 12.6707 0.702842
\(326\) 0 0
\(327\) 28.9574 1.60135
\(328\) 0 0
\(329\) −63.4369 −3.49739
\(330\) 0 0
\(331\) 14.4352 0.793433 0.396716 0.917941i \(-0.370150\pi\)
0.396716 + 0.917941i \(0.370150\pi\)
\(332\) 0 0
\(333\) 48.1146 2.63666
\(334\) 0 0
\(335\) 36.8459 2.01311
\(336\) 0 0
\(337\) −10.7553 −0.585880 −0.292940 0.956131i \(-0.594634\pi\)
−0.292940 + 0.956131i \(0.594634\pi\)
\(338\) 0 0
\(339\) −43.3078 −2.35216
\(340\) 0 0
\(341\) 1.49640 0.0810347
\(342\) 0 0
\(343\) 49.5680 2.67642
\(344\) 0 0
\(345\) 16.4320 0.884670
\(346\) 0 0
\(347\) 29.7298 1.59598 0.797990 0.602671i \(-0.205897\pi\)
0.797990 + 0.602671i \(0.205897\pi\)
\(348\) 0 0
\(349\) 18.4030 0.985090 0.492545 0.870287i \(-0.336067\pi\)
0.492545 + 0.870287i \(0.336067\pi\)
\(350\) 0 0
\(351\) 34.1449 1.82252
\(352\) 0 0
\(353\) 16.5287 0.879731 0.439866 0.898064i \(-0.355026\pi\)
0.439866 + 0.898064i \(0.355026\pi\)
\(354\) 0 0
\(355\) 12.5871 0.668056
\(356\) 0 0
\(357\) 2.61609 0.138458
\(358\) 0 0
\(359\) −21.3513 −1.12688 −0.563438 0.826158i \(-0.690522\pi\)
−0.563438 + 0.826158i \(0.690522\pi\)
\(360\) 0 0
\(361\) 10.8152 0.569222
\(362\) 0 0
\(363\) −31.7143 −1.66457
\(364\) 0 0
\(365\) −11.2315 −0.587885
\(366\) 0 0
\(367\) −30.2930 −1.58128 −0.790642 0.612279i \(-0.790253\pi\)
−0.790642 + 0.612279i \(0.790253\pi\)
\(368\) 0 0
\(369\) 48.7972 2.54028
\(370\) 0 0
\(371\) 23.0451 1.19644
\(372\) 0 0
\(373\) −6.31523 −0.326990 −0.163495 0.986544i \(-0.552277\pi\)
−0.163495 + 0.986544i \(0.552277\pi\)
\(374\) 0 0
\(375\) 8.96664 0.463035
\(376\) 0 0
\(377\) 13.7924 0.710347
\(378\) 0 0
\(379\) 5.57418 0.286327 0.143163 0.989699i \(-0.454273\pi\)
0.143163 + 0.989699i \(0.454273\pi\)
\(380\) 0 0
\(381\) 39.5718 2.02732
\(382\) 0 0
\(383\) 3.24541 0.165833 0.0829164 0.996557i \(-0.473577\pi\)
0.0829164 + 0.996557i \(0.473577\pi\)
\(384\) 0 0
\(385\) 12.5407 0.639135
\(386\) 0 0
\(387\) 68.8954 3.50215
\(388\) 0 0
\(389\) 33.3075 1.68876 0.844378 0.535748i \(-0.179970\pi\)
0.844378 + 0.535748i \(0.179970\pi\)
\(390\) 0 0
\(391\) −0.305986 −0.0154744
\(392\) 0 0
\(393\) −53.8846 −2.71812
\(394\) 0 0
\(395\) 41.8033 2.10335
\(396\) 0 0
\(397\) 32.3583 1.62401 0.812007 0.583647i \(-0.198375\pi\)
0.812007 + 0.583647i \(0.198375\pi\)
\(398\) 0 0
\(399\) −82.7128 −4.14082
\(400\) 0 0
\(401\) 27.0097 1.34880 0.674401 0.738366i \(-0.264402\pi\)
0.674401 + 0.738366i \(0.264402\pi\)
\(402\) 0 0
\(403\) −5.53074 −0.275506
\(404\) 0 0
\(405\) −41.9930 −2.08665
\(406\) 0 0
\(407\) −6.27050 −0.310817
\(408\) 0 0
\(409\) −19.0459 −0.941761 −0.470881 0.882197i \(-0.656064\pi\)
−0.470881 + 0.882197i \(0.656064\pi\)
\(410\) 0 0
\(411\) −24.8570 −1.22611
\(412\) 0 0
\(413\) 31.1804 1.53429
\(414\) 0 0
\(415\) −2.63802 −0.129495
\(416\) 0 0
\(417\) −38.0205 −1.86187
\(418\) 0 0
\(419\) 21.0836 1.03000 0.515000 0.857190i \(-0.327792\pi\)
0.515000 + 0.857190i \(0.327792\pi\)
\(420\) 0 0
\(421\) 12.5467 0.611491 0.305745 0.952113i \(-0.401094\pi\)
0.305745 + 0.952113i \(0.401094\pi\)
\(422\) 0 0
\(423\) −84.2842 −4.09804
\(424\) 0 0
\(425\) 0.696542 0.0337872
\(426\) 0 0
\(427\) 36.0272 1.74348
\(428\) 0 0
\(429\) −8.24013 −0.397837
\(430\) 0 0
\(431\) −37.1322 −1.78860 −0.894298 0.447471i \(-0.852325\pi\)
−0.894298 + 0.447471i \(0.852325\pi\)
\(432\) 0 0
\(433\) 13.7904 0.662723 0.331361 0.943504i \(-0.392492\pi\)
0.331361 + 0.943504i \(0.392492\pi\)
\(434\) 0 0
\(435\) −40.7172 −1.95224
\(436\) 0 0
\(437\) 9.67435 0.462787
\(438\) 0 0
\(439\) 7.02188 0.335136 0.167568 0.985861i \(-0.446409\pi\)
0.167568 + 0.985861i \(0.446409\pi\)
\(440\) 0 0
\(441\) 111.513 5.31012
\(442\) 0 0
\(443\) −34.9978 −1.66280 −0.831398 0.555677i \(-0.812459\pi\)
−0.831398 + 0.555677i \(0.812459\pi\)
\(444\) 0 0
\(445\) 21.5963 1.02376
\(446\) 0 0
\(447\) 30.1557 1.42631
\(448\) 0 0
\(449\) −28.6892 −1.35393 −0.676963 0.736017i \(-0.736704\pi\)
−0.676963 + 0.736017i \(0.736704\pi\)
\(450\) 0 0
\(451\) −6.35946 −0.299455
\(452\) 0 0
\(453\) 70.5663 3.31549
\(454\) 0 0
\(455\) −46.3508 −2.17296
\(456\) 0 0
\(457\) −6.33327 −0.296258 −0.148129 0.988968i \(-0.547325\pi\)
−0.148129 + 0.988968i \(0.547325\pi\)
\(458\) 0 0
\(459\) 1.87704 0.0876127
\(460\) 0 0
\(461\) 33.7309 1.57101 0.785503 0.618858i \(-0.212404\pi\)
0.785503 + 0.618858i \(0.212404\pi\)
\(462\) 0 0
\(463\) −1.33042 −0.0618296 −0.0309148 0.999522i \(-0.509842\pi\)
−0.0309148 + 0.999522i \(0.509842\pi\)
\(464\) 0 0
\(465\) 16.3275 0.757170
\(466\) 0 0
\(467\) −38.7824 −1.79463 −0.897317 0.441386i \(-0.854487\pi\)
−0.897317 + 0.441386i \(0.854487\pi\)
\(468\) 0 0
\(469\) −60.1805 −2.77888
\(470\) 0 0
\(471\) −16.4959 −0.760090
\(472\) 0 0
\(473\) −8.97875 −0.412843
\(474\) 0 0
\(475\) −22.0225 −1.01046
\(476\) 0 0
\(477\) 30.6184 1.40192
\(478\) 0 0
\(479\) 6.05881 0.276834 0.138417 0.990374i \(-0.455799\pi\)
0.138417 + 0.990374i \(0.455799\pi\)
\(480\) 0 0
\(481\) 23.1759 1.05673
\(482\) 0 0
\(483\) −26.8384 −1.22119
\(484\) 0 0
\(485\) −42.5949 −1.93413
\(486\) 0 0
\(487\) −11.8084 −0.535092 −0.267546 0.963545i \(-0.586213\pi\)
−0.267546 + 0.963545i \(0.586213\pi\)
\(488\) 0 0
\(489\) 4.72736 0.213779
\(490\) 0 0
\(491\) 20.9540 0.945639 0.472819 0.881159i \(-0.343236\pi\)
0.472819 + 0.881159i \(0.343236\pi\)
\(492\) 0 0
\(493\) 0.758209 0.0341480
\(494\) 0 0
\(495\) 16.6620 0.748901
\(496\) 0 0
\(497\) −20.5586 −0.922178
\(498\) 0 0
\(499\) −9.79481 −0.438476 −0.219238 0.975671i \(-0.570357\pi\)
−0.219238 + 0.975671i \(0.570357\pi\)
\(500\) 0 0
\(501\) 21.8979 0.978328
\(502\) 0 0
\(503\) 6.08455 0.271297 0.135648 0.990757i \(-0.456688\pi\)
0.135648 + 0.990757i \(0.456688\pi\)
\(504\) 0 0
\(505\) −24.5561 −1.09273
\(506\) 0 0
\(507\) −9.65964 −0.429000
\(508\) 0 0
\(509\) 10.5870 0.469260 0.234630 0.972085i \(-0.424612\pi\)
0.234630 + 0.972085i \(0.424612\pi\)
\(510\) 0 0
\(511\) 18.3444 0.811511
\(512\) 0 0
\(513\) −59.3463 −2.62020
\(514\) 0 0
\(515\) −51.3486 −2.26269
\(516\) 0 0
\(517\) 10.9843 0.483088
\(518\) 0 0
\(519\) −10.2310 −0.449089
\(520\) 0 0
\(521\) −18.7980 −0.823554 −0.411777 0.911285i \(-0.635092\pi\)
−0.411777 + 0.911285i \(0.635092\pi\)
\(522\) 0 0
\(523\) 36.4479 1.59376 0.796878 0.604140i \(-0.206483\pi\)
0.796878 + 0.604140i \(0.206483\pi\)
\(524\) 0 0
\(525\) 61.0945 2.66638
\(526\) 0 0
\(527\) −0.304040 −0.0132442
\(528\) 0 0
\(529\) −19.8609 −0.863517
\(530\) 0 0
\(531\) 41.4272 1.79779
\(532\) 0 0
\(533\) 23.5047 1.01810
\(534\) 0 0
\(535\) 12.7117 0.549576
\(536\) 0 0
\(537\) −1.53340 −0.0661711
\(538\) 0 0
\(539\) −14.5328 −0.625972
\(540\) 0 0
\(541\) −24.2001 −1.04045 −0.520223 0.854031i \(-0.674151\pi\)
−0.520223 + 0.854031i \(0.674151\pi\)
\(542\) 0 0
\(543\) −77.5442 −3.32774
\(544\) 0 0
\(545\) −28.2042 −1.20813
\(546\) 0 0
\(547\) 4.68909 0.200491 0.100245 0.994963i \(-0.468037\pi\)
0.100245 + 0.994963i \(0.468037\pi\)
\(548\) 0 0
\(549\) 47.8668 2.04291
\(550\) 0 0
\(551\) −23.9723 −1.02125
\(552\) 0 0
\(553\) −68.2774 −2.90345
\(554\) 0 0
\(555\) −68.4186 −2.90421
\(556\) 0 0
\(557\) −40.6042 −1.72045 −0.860227 0.509911i \(-0.829678\pi\)
−0.860227 + 0.509911i \(0.829678\pi\)
\(558\) 0 0
\(559\) 33.1857 1.40360
\(560\) 0 0
\(561\) −0.452983 −0.0191250
\(562\) 0 0
\(563\) −30.7338 −1.29527 −0.647637 0.761949i \(-0.724243\pi\)
−0.647637 + 0.761949i \(0.724243\pi\)
\(564\) 0 0
\(565\) 42.1813 1.77458
\(566\) 0 0
\(567\) 68.5872 2.88039
\(568\) 0 0
\(569\) −38.7893 −1.62613 −0.813065 0.582173i \(-0.802203\pi\)
−0.813065 + 0.582173i \(0.802203\pi\)
\(570\) 0 0
\(571\) −3.20361 −0.134067 −0.0670335 0.997751i \(-0.521353\pi\)
−0.0670335 + 0.997751i \(0.521353\pi\)
\(572\) 0 0
\(573\) −42.2072 −1.76323
\(574\) 0 0
\(575\) −7.14581 −0.298001
\(576\) 0 0
\(577\) −45.4151 −1.89066 −0.945328 0.326123i \(-0.894258\pi\)
−0.945328 + 0.326123i \(0.894258\pi\)
\(578\) 0 0
\(579\) −2.98753 −0.124157
\(580\) 0 0
\(581\) 4.30867 0.178754
\(582\) 0 0
\(583\) −3.99032 −0.165262
\(584\) 0 0
\(585\) −61.5831 −2.54615
\(586\) 0 0
\(587\) −22.2499 −0.918354 −0.459177 0.888345i \(-0.651856\pi\)
−0.459177 + 0.888345i \(0.651856\pi\)
\(588\) 0 0
\(589\) 9.61283 0.396090
\(590\) 0 0
\(591\) 77.0889 3.17101
\(592\) 0 0
\(593\) −13.1505 −0.540027 −0.270013 0.962857i \(-0.587028\pi\)
−0.270013 + 0.962857i \(0.587028\pi\)
\(594\) 0 0
\(595\) −2.54803 −0.104459
\(596\) 0 0
\(597\) −45.6736 −1.86930
\(598\) 0 0
\(599\) −34.8226 −1.42281 −0.711406 0.702781i \(-0.751941\pi\)
−0.711406 + 0.702781i \(0.751941\pi\)
\(600\) 0 0
\(601\) −1.65276 −0.0674176 −0.0337088 0.999432i \(-0.510732\pi\)
−0.0337088 + 0.999432i \(0.510732\pi\)
\(602\) 0 0
\(603\) −79.9576 −3.25612
\(604\) 0 0
\(605\) 30.8893 1.25583
\(606\) 0 0
\(607\) 12.7664 0.518173 0.259087 0.965854i \(-0.416578\pi\)
0.259087 + 0.965854i \(0.416578\pi\)
\(608\) 0 0
\(609\) 66.5034 2.69486
\(610\) 0 0
\(611\) −40.5982 −1.64243
\(612\) 0 0
\(613\) −3.26224 −0.131761 −0.0658804 0.997828i \(-0.520986\pi\)
−0.0658804 + 0.997828i \(0.520986\pi\)
\(614\) 0 0
\(615\) −69.3893 −2.79805
\(616\) 0 0
\(617\) −2.35479 −0.0948002 −0.0474001 0.998876i \(-0.515094\pi\)
−0.0474001 + 0.998876i \(0.515094\pi\)
\(618\) 0 0
\(619\) −24.9975 −1.00474 −0.502368 0.864654i \(-0.667538\pi\)
−0.502368 + 0.864654i \(0.667538\pi\)
\(620\) 0 0
\(621\) −19.2565 −0.772737
\(622\) 0 0
\(623\) −35.2733 −1.41319
\(624\) 0 0
\(625\) −28.8993 −1.15597
\(626\) 0 0
\(627\) 14.3220 0.571964
\(628\) 0 0
\(629\) 1.27404 0.0507995
\(630\) 0 0
\(631\) −4.92512 −0.196066 −0.0980330 0.995183i \(-0.531255\pi\)
−0.0980330 + 0.995183i \(0.531255\pi\)
\(632\) 0 0
\(633\) −60.1433 −2.39048
\(634\) 0 0
\(635\) −38.5424 −1.52951
\(636\) 0 0
\(637\) 53.7136 2.12821
\(638\) 0 0
\(639\) −27.3147 −1.08055
\(640\) 0 0
\(641\) −41.6086 −1.64344 −0.821720 0.569891i \(-0.806985\pi\)
−0.821720 + 0.569891i \(0.806985\pi\)
\(642\) 0 0
\(643\) −12.0815 −0.476449 −0.238225 0.971210i \(-0.576565\pi\)
−0.238225 + 0.971210i \(0.576565\pi\)
\(644\) 0 0
\(645\) −97.9688 −3.85752
\(646\) 0 0
\(647\) 2.43603 0.0957701 0.0478851 0.998853i \(-0.484752\pi\)
0.0478851 + 0.998853i \(0.484752\pi\)
\(648\) 0 0
\(649\) −5.39898 −0.211928
\(650\) 0 0
\(651\) −26.6677 −1.04519
\(652\) 0 0
\(653\) −24.2825 −0.950249 −0.475125 0.879918i \(-0.657597\pi\)
−0.475125 + 0.879918i \(0.657597\pi\)
\(654\) 0 0
\(655\) 52.4829 2.05068
\(656\) 0 0
\(657\) 24.3730 0.950881
\(658\) 0 0
\(659\) 3.97727 0.154933 0.0774663 0.996995i \(-0.475317\pi\)
0.0774663 + 0.996995i \(0.475317\pi\)
\(660\) 0 0
\(661\) 5.92623 0.230504 0.115252 0.993336i \(-0.463232\pi\)
0.115252 + 0.993336i \(0.463232\pi\)
\(662\) 0 0
\(663\) 1.67424 0.0650220
\(664\) 0 0
\(665\) 80.5612 3.12403
\(666\) 0 0
\(667\) −7.77845 −0.301183
\(668\) 0 0
\(669\) 30.2557 1.16975
\(670\) 0 0
\(671\) −6.23821 −0.240823
\(672\) 0 0
\(673\) −4.42299 −0.170494 −0.0852469 0.996360i \(-0.527168\pi\)
−0.0852469 + 0.996360i \(0.527168\pi\)
\(674\) 0 0
\(675\) 43.8352 1.68722
\(676\) 0 0
\(677\) −10.1540 −0.390251 −0.195126 0.980778i \(-0.562511\pi\)
−0.195126 + 0.980778i \(0.562511\pi\)
\(678\) 0 0
\(679\) 69.5702 2.66986
\(680\) 0 0
\(681\) 5.43232 0.208167
\(682\) 0 0
\(683\) −4.26271 −0.163108 −0.0815540 0.996669i \(-0.525988\pi\)
−0.0815540 + 0.996669i \(0.525988\pi\)
\(684\) 0 0
\(685\) 24.2104 0.925033
\(686\) 0 0
\(687\) 9.76689 0.372630
\(688\) 0 0
\(689\) 14.7483 0.561866
\(690\) 0 0
\(691\) 41.5796 1.58176 0.790882 0.611969i \(-0.209622\pi\)
0.790882 + 0.611969i \(0.209622\pi\)
\(692\) 0 0
\(693\) −27.2140 −1.03377
\(694\) 0 0
\(695\) 37.0315 1.40468
\(696\) 0 0
\(697\) 1.29212 0.0489426
\(698\) 0 0
\(699\) −3.02453 −0.114398
\(700\) 0 0
\(701\) 33.8219 1.27744 0.638718 0.769441i \(-0.279465\pi\)
0.638718 + 0.769441i \(0.279465\pi\)
\(702\) 0 0
\(703\) −40.2814 −1.51924
\(704\) 0 0
\(705\) 119.852 4.51387
\(706\) 0 0
\(707\) 40.1074 1.50839
\(708\) 0 0
\(709\) 36.3368 1.36466 0.682328 0.731046i \(-0.260968\pi\)
0.682328 + 0.731046i \(0.260968\pi\)
\(710\) 0 0
\(711\) −90.7154 −3.40209
\(712\) 0 0
\(713\) 3.11914 0.116813
\(714\) 0 0
\(715\) 8.02578 0.300147
\(716\) 0 0
\(717\) 43.6949 1.63182
\(718\) 0 0
\(719\) 3.25595 0.121426 0.0607132 0.998155i \(-0.480662\pi\)
0.0607132 + 0.998155i \(0.480662\pi\)
\(720\) 0 0
\(721\) 83.8677 3.12340
\(722\) 0 0
\(723\) 70.1403 2.60855
\(724\) 0 0
\(725\) 17.7068 0.657612
\(726\) 0 0
\(727\) −33.5554 −1.24450 −0.622251 0.782818i \(-0.713782\pi\)
−0.622251 + 0.782818i \(0.713782\pi\)
\(728\) 0 0
\(729\) −9.48809 −0.351411
\(730\) 0 0
\(731\) 1.82431 0.0674745
\(732\) 0 0
\(733\) 39.9157 1.47432 0.737160 0.675718i \(-0.236166\pi\)
0.737160 + 0.675718i \(0.236166\pi\)
\(734\) 0 0
\(735\) −158.570 −5.84895
\(736\) 0 0
\(737\) 10.4204 0.383841
\(738\) 0 0
\(739\) 22.7446 0.836674 0.418337 0.908292i \(-0.362613\pi\)
0.418337 + 0.908292i \(0.362613\pi\)
\(740\) 0 0
\(741\) −52.9343 −1.94459
\(742\) 0 0
\(743\) 3.59269 0.131803 0.0659015 0.997826i \(-0.479008\pi\)
0.0659015 + 0.997826i \(0.479008\pi\)
\(744\) 0 0
\(745\) −29.3712 −1.07608
\(746\) 0 0
\(747\) 5.72464 0.209453
\(748\) 0 0
\(749\) −20.7621 −0.758629
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −8.53665 −0.311093
\(754\) 0 0
\(755\) −68.7306 −2.50136
\(756\) 0 0
\(757\) −25.7694 −0.936603 −0.468302 0.883569i \(-0.655134\pi\)
−0.468302 + 0.883569i \(0.655134\pi\)
\(758\) 0 0
\(759\) 4.64714 0.168681
\(760\) 0 0
\(761\) −13.0413 −0.472747 −0.236373 0.971662i \(-0.575959\pi\)
−0.236373 + 0.971662i \(0.575959\pi\)
\(762\) 0 0
\(763\) 46.0658 1.66770
\(764\) 0 0
\(765\) −3.38540 −0.122399
\(766\) 0 0
\(767\) 19.9548 0.720524
\(768\) 0 0
\(769\) −40.7333 −1.46888 −0.734439 0.678674i \(-0.762555\pi\)
−0.734439 + 0.678674i \(0.762555\pi\)
\(770\) 0 0
\(771\) −33.0955 −1.19191
\(772\) 0 0
\(773\) −15.1877 −0.546265 −0.273133 0.961976i \(-0.588060\pi\)
−0.273133 + 0.961976i \(0.588060\pi\)
\(774\) 0 0
\(775\) −7.10036 −0.255053
\(776\) 0 0
\(777\) 111.748 4.00894
\(778\) 0 0
\(779\) −40.8530 −1.46371
\(780\) 0 0
\(781\) 3.55977 0.127379
\(782\) 0 0
\(783\) 47.7161 1.70523
\(784\) 0 0
\(785\) 16.0668 0.573448
\(786\) 0 0
\(787\) 31.5078 1.12313 0.561567 0.827432i \(-0.310199\pi\)
0.561567 + 0.827432i \(0.310199\pi\)
\(788\) 0 0
\(789\) −21.6396 −0.770389
\(790\) 0 0
\(791\) −68.8946 −2.44961
\(792\) 0 0
\(793\) 23.0566 0.818763
\(794\) 0 0
\(795\) −43.5391 −1.54417
\(796\) 0 0
\(797\) −38.8212 −1.37512 −0.687559 0.726129i \(-0.741318\pi\)
−0.687559 + 0.726129i \(0.741318\pi\)
\(798\) 0 0
\(799\) −2.23180 −0.0789553
\(800\) 0 0
\(801\) −46.8651 −1.65590
\(802\) 0 0
\(803\) −3.17639 −0.112092
\(804\) 0 0
\(805\) 26.1402 0.921322
\(806\) 0 0
\(807\) −21.1367 −0.744047
\(808\) 0 0
\(809\) 44.3592 1.55959 0.779794 0.626036i \(-0.215324\pi\)
0.779794 + 0.626036i \(0.215324\pi\)
\(810\) 0 0
\(811\) −9.17475 −0.322169 −0.161085 0.986941i \(-0.551499\pi\)
−0.161085 + 0.986941i \(0.551499\pi\)
\(812\) 0 0
\(813\) −36.8280 −1.29161
\(814\) 0 0
\(815\) −4.60439 −0.161285
\(816\) 0 0
\(817\) −57.6791 −2.01794
\(818\) 0 0
\(819\) 100.584 3.51468
\(820\) 0 0
\(821\) −35.7167 −1.24652 −0.623260 0.782014i \(-0.714192\pi\)
−0.623260 + 0.782014i \(0.714192\pi\)
\(822\) 0 0
\(823\) 33.3257 1.16166 0.580831 0.814024i \(-0.302728\pi\)
0.580831 + 0.814024i \(0.302728\pi\)
\(824\) 0 0
\(825\) −10.5787 −0.368303
\(826\) 0 0
\(827\) 30.1967 1.05004 0.525021 0.851089i \(-0.324058\pi\)
0.525021 + 0.851089i \(0.324058\pi\)
\(828\) 0 0
\(829\) 29.1745 1.01327 0.506637 0.862160i \(-0.330889\pi\)
0.506637 + 0.862160i \(0.330889\pi\)
\(830\) 0 0
\(831\) 53.5561 1.85784
\(832\) 0 0
\(833\) 2.95279 0.102308
\(834\) 0 0
\(835\) −21.3283 −0.738096
\(836\) 0 0
\(837\) −19.1340 −0.661369
\(838\) 0 0
\(839\) −1.04312 −0.0360125 −0.0180063 0.999838i \(-0.505732\pi\)
−0.0180063 + 0.999838i \(0.505732\pi\)
\(840\) 0 0
\(841\) −9.72560 −0.335366
\(842\) 0 0
\(843\) 23.8610 0.821816
\(844\) 0 0
\(845\) 9.40836 0.323657
\(846\) 0 0
\(847\) −50.4515 −1.73353
\(848\) 0 0
\(849\) −78.5725 −2.69660
\(850\) 0 0
\(851\) −13.0704 −0.448047
\(852\) 0 0
\(853\) −22.6944 −0.777043 −0.388521 0.921440i \(-0.627014\pi\)
−0.388521 + 0.921440i \(0.627014\pi\)
\(854\) 0 0
\(855\) 107.036 3.66056
\(856\) 0 0
\(857\) 32.8976 1.12376 0.561880 0.827219i \(-0.310078\pi\)
0.561880 + 0.827219i \(0.310078\pi\)
\(858\) 0 0
\(859\) −6.18870 −0.211156 −0.105578 0.994411i \(-0.533669\pi\)
−0.105578 + 0.994411i \(0.533669\pi\)
\(860\) 0 0
\(861\) 113.333 3.86239
\(862\) 0 0
\(863\) −42.7305 −1.45456 −0.727281 0.686339i \(-0.759216\pi\)
−0.727281 + 0.686339i \(0.759216\pi\)
\(864\) 0 0
\(865\) 9.96482 0.338814
\(866\) 0 0
\(867\) −52.3665 −1.77846
\(868\) 0 0
\(869\) 11.8224 0.401048
\(870\) 0 0
\(871\) −38.5141 −1.30500
\(872\) 0 0
\(873\) 92.4330 3.12838
\(874\) 0 0
\(875\) 14.2642 0.482219
\(876\) 0 0
\(877\) −22.3009 −0.753048 −0.376524 0.926407i \(-0.622881\pi\)
−0.376524 + 0.926407i \(0.622881\pi\)
\(878\) 0 0
\(879\) 5.59806 0.188818
\(880\) 0 0
\(881\) −49.7586 −1.67641 −0.838204 0.545356i \(-0.816394\pi\)
−0.838204 + 0.545356i \(0.816394\pi\)
\(882\) 0 0
\(883\) −28.4745 −0.958243 −0.479122 0.877748i \(-0.659045\pi\)
−0.479122 + 0.877748i \(0.659045\pi\)
\(884\) 0 0
\(885\) −58.9093 −1.98021
\(886\) 0 0
\(887\) 39.9822 1.34247 0.671236 0.741244i \(-0.265764\pi\)
0.671236 + 0.741244i \(0.265764\pi\)
\(888\) 0 0
\(889\) 62.9513 2.11132
\(890\) 0 0
\(891\) −11.8761 −0.397863
\(892\) 0 0
\(893\) 70.5627 2.36129
\(894\) 0 0
\(895\) 1.49351 0.0499226
\(896\) 0 0
\(897\) −17.1760 −0.573488
\(898\) 0 0
\(899\) −7.72899 −0.257776
\(900\) 0 0
\(901\) 0.810756 0.0270102
\(902\) 0 0
\(903\) 160.012 5.32488
\(904\) 0 0
\(905\) 75.5270 2.51060
\(906\) 0 0
\(907\) −14.0133 −0.465304 −0.232652 0.972560i \(-0.574740\pi\)
−0.232652 + 0.972560i \(0.574740\pi\)
\(908\) 0 0
\(909\) 53.2879 1.76745
\(910\) 0 0
\(911\) −38.8620 −1.28756 −0.643778 0.765213i \(-0.722634\pi\)
−0.643778 + 0.765213i \(0.722634\pi\)
\(912\) 0 0
\(913\) −0.746059 −0.0246910
\(914\) 0 0
\(915\) −68.0663 −2.25020
\(916\) 0 0
\(917\) −85.7202 −2.83073
\(918\) 0 0
\(919\) 56.1238 1.85135 0.925676 0.378318i \(-0.123497\pi\)
0.925676 + 0.378318i \(0.123497\pi\)
\(920\) 0 0
\(921\) −20.4393 −0.673499
\(922\) 0 0
\(923\) −13.1570 −0.433068
\(924\) 0 0
\(925\) 29.7533 0.978281
\(926\) 0 0
\(927\) 111.429 3.65981
\(928\) 0 0
\(929\) 7.53682 0.247275 0.123637 0.992327i \(-0.460544\pi\)
0.123637 + 0.992327i \(0.460544\pi\)
\(930\) 0 0
\(931\) −93.3582 −3.05969
\(932\) 0 0
\(933\) −16.0639 −0.525909
\(934\) 0 0
\(935\) 0.441199 0.0144288
\(936\) 0 0
\(937\) 19.6885 0.643196 0.321598 0.946876i \(-0.395780\pi\)
0.321598 + 0.946876i \(0.395780\pi\)
\(938\) 0 0
\(939\) 61.6853 2.01302
\(940\) 0 0
\(941\) 20.1273 0.656130 0.328065 0.944655i \(-0.393603\pi\)
0.328065 + 0.944655i \(0.393603\pi\)
\(942\) 0 0
\(943\) −13.2558 −0.431669
\(944\) 0 0
\(945\) −160.355 −5.21634
\(946\) 0 0
\(947\) 0.220832 0.00717609 0.00358805 0.999994i \(-0.498858\pi\)
0.00358805 + 0.999994i \(0.498858\pi\)
\(948\) 0 0
\(949\) 11.7400 0.381097
\(950\) 0 0
\(951\) −35.2233 −1.14219
\(952\) 0 0
\(953\) −56.4140 −1.82743 −0.913715 0.406356i \(-0.866799\pi\)
−0.913715 + 0.406356i \(0.866799\pi\)
\(954\) 0 0
\(955\) 41.1093 1.33027
\(956\) 0 0
\(957\) −11.5153 −0.372235
\(958\) 0 0
\(959\) −39.5429 −1.27691
\(960\) 0 0
\(961\) −27.9007 −0.900022
\(962\) 0 0
\(963\) −27.5851 −0.888918
\(964\) 0 0
\(965\) 2.90981 0.0936702
\(966\) 0 0
\(967\) −14.1085 −0.453697 −0.226849 0.973930i \(-0.572842\pi\)
−0.226849 + 0.973930i \(0.572842\pi\)
\(968\) 0 0
\(969\) −2.90995 −0.0934809
\(970\) 0 0
\(971\) −14.1387 −0.453734 −0.226867 0.973926i \(-0.572848\pi\)
−0.226867 + 0.973926i \(0.572848\pi\)
\(972\) 0 0
\(973\) −60.4835 −1.93901
\(974\) 0 0
\(975\) 39.0991 1.25217
\(976\) 0 0
\(977\) 29.8439 0.954792 0.477396 0.878688i \(-0.341581\pi\)
0.477396 + 0.878688i \(0.341581\pi\)
\(978\) 0 0
\(979\) 6.10766 0.195202
\(980\) 0 0
\(981\) 61.2045 1.95411
\(982\) 0 0
\(983\) −49.6855 −1.58472 −0.792361 0.610053i \(-0.791148\pi\)
−0.792361 + 0.610053i \(0.791148\pi\)
\(984\) 0 0
\(985\) −75.0836 −2.39236
\(986\) 0 0
\(987\) −195.754 −6.23090
\(988\) 0 0
\(989\) −18.7155 −0.595120
\(990\) 0 0
\(991\) 21.7426 0.690677 0.345338 0.938478i \(-0.387764\pi\)
0.345338 + 0.938478i \(0.387764\pi\)
\(992\) 0 0
\(993\) 44.5442 1.41357
\(994\) 0 0
\(995\) 44.4855 1.41029
\(996\) 0 0
\(997\) 8.62639 0.273200 0.136600 0.990626i \(-0.456382\pi\)
0.136600 + 0.990626i \(0.456382\pi\)
\(998\) 0 0
\(999\) 80.1790 2.53675
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 \(a_p\))