Properties

Label 6008.2.a.e.1.15
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 1.15
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.34723 q^{3} +0.0749039 q^{5} -4.25247 q^{7} -1.18497 q^{9} +O(q^{10})\) \(q-1.34723 q^{3} +0.0749039 q^{5} -4.25247 q^{7} -1.18497 q^{9} +1.12257 q^{11} -0.485811 q^{13} -0.100913 q^{15} +6.54264 q^{17} -3.86478 q^{19} +5.72905 q^{21} -8.49829 q^{23} -4.99439 q^{25} +5.63812 q^{27} -1.99956 q^{29} -6.58629 q^{31} -1.51236 q^{33} -0.318526 q^{35} +5.71347 q^{37} +0.654499 q^{39} +4.59627 q^{41} -6.88895 q^{43} -0.0887591 q^{45} +2.43998 q^{47} +11.0835 q^{49} -8.81444 q^{51} -10.3855 q^{53} +0.0840846 q^{55} +5.20675 q^{57} -5.14682 q^{59} -5.48484 q^{61} +5.03906 q^{63} -0.0363891 q^{65} -8.24807 q^{67} +11.4492 q^{69} +14.5585 q^{71} -14.0072 q^{73} +6.72859 q^{75} -4.77368 q^{77} -1.73234 q^{79} -4.04092 q^{81} -11.8143 q^{83} +0.490069 q^{85} +2.69386 q^{87} -6.39261 q^{89} +2.06590 q^{91} +8.87324 q^{93} -0.289487 q^{95} -12.5205 q^{97} -1.33021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −1.34723 −0.777823 −0.388912 0.921275i \(-0.627149\pi\)
−0.388912 + 0.921275i \(0.627149\pi\)
\(4\) 0 0
\(5\) 0.0749039 0.0334980 0.0167490 0.999860i \(-0.494668\pi\)
0.0167490 + 0.999860i \(0.494668\pi\)
\(6\) 0 0
\(7\) −4.25247 −1.60728 −0.803641 0.595114i \(-0.797107\pi\)
−0.803641 + 0.595114i \(0.797107\pi\)
\(8\) 0 0
\(9\) −1.18497 −0.394991
\(10\) 0 0
\(11\) 1.12257 0.338467 0.169233 0.985576i \(-0.445871\pi\)
0.169233 + 0.985576i \(0.445871\pi\)
\(12\) 0 0
\(13\) −0.485811 −0.134740 −0.0673698 0.997728i \(-0.521461\pi\)
−0.0673698 + 0.997728i \(0.521461\pi\)
\(14\) 0 0
\(15\) −0.100913 −0.0260555
\(16\) 0 0
\(17\) 6.54264 1.58682 0.793412 0.608685i \(-0.208303\pi\)
0.793412 + 0.608685i \(0.208303\pi\)
\(18\) 0 0
\(19\) −3.86478 −0.886641 −0.443321 0.896363i \(-0.646200\pi\)
−0.443321 + 0.896363i \(0.646200\pi\)
\(20\) 0 0
\(21\) 5.72905 1.25018
\(22\) 0 0
\(23\) −8.49829 −1.77202 −0.886008 0.463669i \(-0.846533\pi\)
−0.886008 + 0.463669i \(0.846533\pi\)
\(24\) 0 0
\(25\) −4.99439 −0.998878
\(26\) 0 0
\(27\) 5.63812 1.08506
\(28\) 0 0
\(29\) −1.99956 −0.371309 −0.185654 0.982615i \(-0.559440\pi\)
−0.185654 + 0.982615i \(0.559440\pi\)
\(30\) 0 0
\(31\) −6.58629 −1.18293 −0.591466 0.806330i \(-0.701451\pi\)
−0.591466 + 0.806330i \(0.701451\pi\)
\(32\) 0 0
\(33\) −1.51236 −0.263267
\(34\) 0 0
\(35\) −0.318526 −0.0538408
\(36\) 0 0
\(37\) 5.71347 0.939289 0.469645 0.882856i \(-0.344382\pi\)
0.469645 + 0.882856i \(0.344382\pi\)
\(38\) 0 0
\(39\) 0.654499 0.104804
\(40\) 0 0
\(41\) 4.59627 0.717816 0.358908 0.933373i \(-0.383149\pi\)
0.358908 + 0.933373i \(0.383149\pi\)
\(42\) 0 0
\(43\) −6.88895 −1.05055 −0.525277 0.850931i \(-0.676038\pi\)
−0.525277 + 0.850931i \(0.676038\pi\)
\(44\) 0 0
\(45\) −0.0887591 −0.0132314
\(46\) 0 0
\(47\) 2.43998 0.355908 0.177954 0.984039i \(-0.443052\pi\)
0.177954 + 0.984039i \(0.443052\pi\)
\(48\) 0 0
\(49\) 11.0835 1.58336
\(50\) 0 0
\(51\) −8.81444 −1.23427
\(52\) 0 0
\(53\) −10.3855 −1.42656 −0.713280 0.700879i \(-0.752791\pi\)
−0.713280 + 0.700879i \(0.752791\pi\)
\(54\) 0 0
\(55\) 0.0840846 0.0113380
\(56\) 0 0
\(57\) 5.20675 0.689650
\(58\) 0 0
\(59\) −5.14682 −0.670059 −0.335029 0.942208i \(-0.608746\pi\)
−0.335029 + 0.942208i \(0.608746\pi\)
\(60\) 0 0
\(61\) −5.48484 −0.702262 −0.351131 0.936326i \(-0.614203\pi\)
−0.351131 + 0.936326i \(0.614203\pi\)
\(62\) 0 0
\(63\) 5.03906 0.634862
\(64\) 0 0
\(65\) −0.0363891 −0.00451351
\(66\) 0 0
\(67\) −8.24807 −1.00766 −0.503831 0.863802i \(-0.668077\pi\)
−0.503831 + 0.863802i \(0.668077\pi\)
\(68\) 0 0
\(69\) 11.4492 1.37832
\(70\) 0 0
\(71\) 14.5585 1.72777 0.863886 0.503688i \(-0.168024\pi\)
0.863886 + 0.503688i \(0.168024\pi\)
\(72\) 0 0
\(73\) −14.0072 −1.63942 −0.819710 0.572779i \(-0.805865\pi\)
−0.819710 + 0.572779i \(0.805865\pi\)
\(74\) 0 0
\(75\) 6.72859 0.776950
\(76\) 0 0
\(77\) −4.77368 −0.544012
\(78\) 0 0
\(79\) −1.73234 −0.194903 −0.0974517 0.995240i \(-0.531069\pi\)
−0.0974517 + 0.995240i \(0.531069\pi\)
\(80\) 0 0
\(81\) −4.04092 −0.448991
\(82\) 0 0
\(83\) −11.8143 −1.29679 −0.648394 0.761305i \(-0.724559\pi\)
−0.648394 + 0.761305i \(0.724559\pi\)
\(84\) 0 0
\(85\) 0.490069 0.0531555
\(86\) 0 0
\(87\) 2.69386 0.288813
\(88\) 0 0
\(89\) −6.39261 −0.677615 −0.338808 0.940856i \(-0.610024\pi\)
−0.338808 + 0.940856i \(0.610024\pi\)
\(90\) 0 0
\(91\) 2.06590 0.216565
\(92\) 0 0
\(93\) 8.87324 0.920112
\(94\) 0 0
\(95\) −0.289487 −0.0297007
\(96\) 0 0
\(97\) −12.5205 −1.27126 −0.635630 0.771994i \(-0.719260\pi\)
−0.635630 + 0.771994i \(0.719260\pi\)
\(98\) 0 0
\(99\) −1.33021 −0.133691
\(100\) 0 0
\(101\) 14.1855 1.41151 0.705755 0.708456i \(-0.250608\pi\)
0.705755 + 0.708456i \(0.250608\pi\)
\(102\) 0 0
\(103\) 18.3729 1.81034 0.905169 0.425051i \(-0.139744\pi\)
0.905169 + 0.425051i \(0.139744\pi\)
\(104\) 0 0
\(105\) 0.429128 0.0418786
\(106\) 0 0
\(107\) 20.4669 1.97861 0.989304 0.145866i \(-0.0465968\pi\)
0.989304 + 0.145866i \(0.0465968\pi\)
\(108\) 0 0
\(109\) −0.248709 −0.0238220 −0.0119110 0.999929i \(-0.503791\pi\)
−0.0119110 + 0.999929i \(0.503791\pi\)
\(110\) 0 0
\(111\) −7.69736 −0.730601
\(112\) 0 0
\(113\) 8.74307 0.822479 0.411240 0.911527i \(-0.365096\pi\)
0.411240 + 0.911527i \(0.365096\pi\)
\(114\) 0 0
\(115\) −0.636555 −0.0593591
\(116\) 0 0
\(117\) 0.575673 0.0532210
\(118\) 0 0
\(119\) −27.8224 −2.55047
\(120\) 0 0
\(121\) −9.73984 −0.885440
\(122\) 0 0
\(123\) −6.19223 −0.558334
\(124\) 0 0
\(125\) −0.748618 −0.0669585
\(126\) 0 0
\(127\) 3.99042 0.354092 0.177046 0.984203i \(-0.443346\pi\)
0.177046 + 0.984203i \(0.443346\pi\)
\(128\) 0 0
\(129\) 9.28100 0.817146
\(130\) 0 0
\(131\) −17.2850 −1.51020 −0.755101 0.655609i \(-0.772412\pi\)
−0.755101 + 0.655609i \(0.772412\pi\)
\(132\) 0 0
\(133\) 16.4349 1.42508
\(134\) 0 0
\(135\) 0.422317 0.0363473
\(136\) 0 0
\(137\) 18.7194 1.59930 0.799652 0.600464i \(-0.205017\pi\)
0.799652 + 0.600464i \(0.205017\pi\)
\(138\) 0 0
\(139\) −15.8730 −1.34633 −0.673166 0.739491i \(-0.735066\pi\)
−0.673166 + 0.739491i \(0.735066\pi\)
\(140\) 0 0
\(141\) −3.28721 −0.276833
\(142\) 0 0
\(143\) −0.545355 −0.0456049
\(144\) 0 0
\(145\) −0.149775 −0.0124381
\(146\) 0 0
\(147\) −14.9320 −1.23157
\(148\) 0 0
\(149\) 9.08337 0.744138 0.372069 0.928205i \(-0.378648\pi\)
0.372069 + 0.928205i \(0.378648\pi\)
\(150\) 0 0
\(151\) −0.180064 −0.0146534 −0.00732669 0.999973i \(-0.502332\pi\)
−0.00732669 + 0.999973i \(0.502332\pi\)
\(152\) 0 0
\(153\) −7.75285 −0.626781
\(154\) 0 0
\(155\) −0.493338 −0.0396259
\(156\) 0 0
\(157\) 10.7585 0.858622 0.429311 0.903157i \(-0.358756\pi\)
0.429311 + 0.903157i \(0.358756\pi\)
\(158\) 0 0
\(159\) 13.9917 1.10961
\(160\) 0 0
\(161\) 36.1387 2.84813
\(162\) 0 0
\(163\) −0.259605 −0.0203338 −0.0101669 0.999948i \(-0.503236\pi\)
−0.0101669 + 0.999948i \(0.503236\pi\)
\(164\) 0 0
\(165\) −0.113281 −0.00881894
\(166\) 0 0
\(167\) 19.8973 1.53970 0.769851 0.638224i \(-0.220331\pi\)
0.769851 + 0.638224i \(0.220331\pi\)
\(168\) 0 0
\(169\) −12.7640 −0.981845
\(170\) 0 0
\(171\) 4.57966 0.350215
\(172\) 0 0
\(173\) 5.36173 0.407645 0.203822 0.979008i \(-0.434663\pi\)
0.203822 + 0.979008i \(0.434663\pi\)
\(174\) 0 0
\(175\) 21.2385 1.60548
\(176\) 0 0
\(177\) 6.93395 0.521187
\(178\) 0 0
\(179\) 9.66315 0.722258 0.361129 0.932516i \(-0.382391\pi\)
0.361129 + 0.932516i \(0.382391\pi\)
\(180\) 0 0
\(181\) 3.25833 0.242190 0.121095 0.992641i \(-0.461359\pi\)
0.121095 + 0.992641i \(0.461359\pi\)
\(182\) 0 0
\(183\) 7.38934 0.546236
\(184\) 0 0
\(185\) 0.427961 0.0314643
\(186\) 0 0
\(187\) 7.34456 0.537087
\(188\) 0 0
\(189\) −23.9759 −1.74399
\(190\) 0 0
\(191\) 8.85083 0.640423 0.320212 0.947346i \(-0.396246\pi\)
0.320212 + 0.947346i \(0.396246\pi\)
\(192\) 0 0
\(193\) −11.4779 −0.826195 −0.413098 0.910687i \(-0.635553\pi\)
−0.413098 + 0.910687i \(0.635553\pi\)
\(194\) 0 0
\(195\) 0.0490245 0.00351072
\(196\) 0 0
\(197\) 11.6058 0.826882 0.413441 0.910531i \(-0.364327\pi\)
0.413441 + 0.910531i \(0.364327\pi\)
\(198\) 0 0
\(199\) 5.37936 0.381333 0.190666 0.981655i \(-0.438935\pi\)
0.190666 + 0.981655i \(0.438935\pi\)
\(200\) 0 0
\(201\) 11.1120 0.783783
\(202\) 0 0
\(203\) 8.50306 0.596798
\(204\) 0 0
\(205\) 0.344278 0.0240454
\(206\) 0 0
\(207\) 10.0702 0.699931
\(208\) 0 0
\(209\) −4.33848 −0.300099
\(210\) 0 0
\(211\) −12.2353 −0.842310 −0.421155 0.906989i \(-0.638375\pi\)
−0.421155 + 0.906989i \(0.638375\pi\)
\(212\) 0 0
\(213\) −19.6136 −1.34390
\(214\) 0 0
\(215\) −0.516009 −0.0351915
\(216\) 0 0
\(217\) 28.0080 1.90131
\(218\) 0 0
\(219\) 18.8709 1.27518
\(220\) 0 0
\(221\) −3.17849 −0.213808
\(222\) 0 0
\(223\) −16.5361 −1.10734 −0.553670 0.832736i \(-0.686773\pi\)
−0.553670 + 0.832736i \(0.686773\pi\)
\(224\) 0 0
\(225\) 5.91822 0.394548
\(226\) 0 0
\(227\) 10.6412 0.706281 0.353141 0.935570i \(-0.385114\pi\)
0.353141 + 0.935570i \(0.385114\pi\)
\(228\) 0 0
\(229\) 17.7209 1.17103 0.585514 0.810662i \(-0.300893\pi\)
0.585514 + 0.810662i \(0.300893\pi\)
\(230\) 0 0
\(231\) 6.43124 0.423145
\(232\) 0 0
\(233\) 26.8468 1.75879 0.879397 0.476089i \(-0.157946\pi\)
0.879397 + 0.476089i \(0.157946\pi\)
\(234\) 0 0
\(235\) 0.182764 0.0119222
\(236\) 0 0
\(237\) 2.33386 0.151600
\(238\) 0 0
\(239\) −15.0812 −0.975522 −0.487761 0.872977i \(-0.662186\pi\)
−0.487761 + 0.872977i \(0.662186\pi\)
\(240\) 0 0
\(241\) −5.68364 −0.366116 −0.183058 0.983102i \(-0.558600\pi\)
−0.183058 + 0.983102i \(0.558600\pi\)
\(242\) 0 0
\(243\) −11.4703 −0.735821
\(244\) 0 0
\(245\) 0.830196 0.0530393
\(246\) 0 0
\(247\) 1.87755 0.119466
\(248\) 0 0
\(249\) 15.9166 1.00867
\(250\) 0 0
\(251\) −17.6892 −1.11653 −0.558266 0.829662i \(-0.688533\pi\)
−0.558266 + 0.829662i \(0.688533\pi\)
\(252\) 0 0
\(253\) −9.53991 −0.599769
\(254\) 0 0
\(255\) −0.660236 −0.0413456
\(256\) 0 0
\(257\) 2.60681 0.162608 0.0813041 0.996689i \(-0.474092\pi\)
0.0813041 + 0.996689i \(0.474092\pi\)
\(258\) 0 0
\(259\) −24.2964 −1.50970
\(260\) 0 0
\(261\) 2.36942 0.146664
\(262\) 0 0
\(263\) 20.3704 1.25609 0.628045 0.778177i \(-0.283855\pi\)
0.628045 + 0.778177i \(0.283855\pi\)
\(264\) 0 0
\(265\) −0.777915 −0.0477869
\(266\) 0 0
\(267\) 8.61231 0.527065
\(268\) 0 0
\(269\) 27.5197 1.67791 0.838954 0.544203i \(-0.183168\pi\)
0.838954 + 0.544203i \(0.183168\pi\)
\(270\) 0 0
\(271\) 15.9867 0.971124 0.485562 0.874202i \(-0.338615\pi\)
0.485562 + 0.874202i \(0.338615\pi\)
\(272\) 0 0
\(273\) −2.78323 −0.168449
\(274\) 0 0
\(275\) −5.60654 −0.338087
\(276\) 0 0
\(277\) 13.9604 0.838799 0.419399 0.907802i \(-0.362241\pi\)
0.419399 + 0.907802i \(0.362241\pi\)
\(278\) 0 0
\(279\) 7.80457 0.467247
\(280\) 0 0
\(281\) 5.69579 0.339782 0.169891 0.985463i \(-0.445658\pi\)
0.169891 + 0.985463i \(0.445658\pi\)
\(282\) 0 0
\(283\) 11.4291 0.679389 0.339695 0.940536i \(-0.389676\pi\)
0.339695 + 0.940536i \(0.389676\pi\)
\(284\) 0 0
\(285\) 0.390005 0.0231019
\(286\) 0 0
\(287\) −19.5455 −1.15373
\(288\) 0 0
\(289\) 25.8062 1.51801
\(290\) 0 0
\(291\) 16.8679 0.988816
\(292\) 0 0
\(293\) 7.91999 0.462691 0.231345 0.972872i \(-0.425687\pi\)
0.231345 + 0.972872i \(0.425687\pi\)
\(294\) 0 0
\(295\) −0.385517 −0.0224456
\(296\) 0 0
\(297\) 6.32917 0.367256
\(298\) 0 0
\(299\) 4.12856 0.238761
\(300\) 0 0
\(301\) 29.2950 1.68854
\(302\) 0 0
\(303\) −19.1111 −1.09790
\(304\) 0 0
\(305\) −0.410836 −0.0235244
\(306\) 0 0
\(307\) 14.1653 0.808454 0.404227 0.914659i \(-0.367541\pi\)
0.404227 + 0.914659i \(0.367541\pi\)
\(308\) 0 0
\(309\) −24.7525 −1.40812
\(310\) 0 0
\(311\) −16.0761 −0.911593 −0.455797 0.890084i \(-0.650646\pi\)
−0.455797 + 0.890084i \(0.650646\pi\)
\(312\) 0 0
\(313\) −15.0069 −0.848242 −0.424121 0.905606i \(-0.639417\pi\)
−0.424121 + 0.905606i \(0.639417\pi\)
\(314\) 0 0
\(315\) 0.377445 0.0212666
\(316\) 0 0
\(317\) −18.0571 −1.01419 −0.507094 0.861891i \(-0.669280\pi\)
−0.507094 + 0.861891i \(0.669280\pi\)
\(318\) 0 0
\(319\) −2.24464 −0.125676
\(320\) 0 0
\(321\) −27.5736 −1.53901
\(322\) 0 0
\(323\) −25.2859 −1.40694
\(324\) 0 0
\(325\) 2.42633 0.134588
\(326\) 0 0
\(327\) 0.335068 0.0185293
\(328\) 0 0
\(329\) −10.3759 −0.572044
\(330\) 0 0
\(331\) −10.1118 −0.555793 −0.277896 0.960611i \(-0.589637\pi\)
−0.277896 + 0.960611i \(0.589637\pi\)
\(332\) 0 0
\(333\) −6.77031 −0.371011
\(334\) 0 0
\(335\) −0.617812 −0.0337547
\(336\) 0 0
\(337\) −11.4575 −0.624131 −0.312066 0.950061i \(-0.601021\pi\)
−0.312066 + 0.950061i \(0.601021\pi\)
\(338\) 0 0
\(339\) −11.7789 −0.639743
\(340\) 0 0
\(341\) −7.39355 −0.400383
\(342\) 0 0
\(343\) −17.3649 −0.937616
\(344\) 0 0
\(345\) 0.857586 0.0461709
\(346\) 0 0
\(347\) −18.9404 −1.01677 −0.508386 0.861129i \(-0.669758\pi\)
−0.508386 + 0.861129i \(0.669758\pi\)
\(348\) 0 0
\(349\) −12.8108 −0.685745 −0.342873 0.939382i \(-0.611400\pi\)
−0.342873 + 0.939382i \(0.611400\pi\)
\(350\) 0 0
\(351\) −2.73906 −0.146200
\(352\) 0 0
\(353\) 22.8842 1.21800 0.609002 0.793169i \(-0.291570\pi\)
0.609002 + 0.793169i \(0.291570\pi\)
\(354\) 0 0
\(355\) 1.09049 0.0578769
\(356\) 0 0
\(357\) 37.4831 1.98382
\(358\) 0 0
\(359\) −0.0696918 −0.00367819 −0.00183910 0.999998i \(-0.500585\pi\)
−0.00183910 + 0.999998i \(0.500585\pi\)
\(360\) 0 0
\(361\) −4.06347 −0.213867
\(362\) 0 0
\(363\) 13.1218 0.688716
\(364\) 0 0
\(365\) −1.04919 −0.0549173
\(366\) 0 0
\(367\) −17.6779 −0.922778 −0.461389 0.887198i \(-0.652649\pi\)
−0.461389 + 0.887198i \(0.652649\pi\)
\(368\) 0 0
\(369\) −5.44645 −0.283531
\(370\) 0 0
\(371\) 44.1641 2.29288
\(372\) 0 0
\(373\) 8.47111 0.438617 0.219309 0.975656i \(-0.429620\pi\)
0.219309 + 0.975656i \(0.429620\pi\)
\(374\) 0 0
\(375\) 1.00856 0.0520819
\(376\) 0 0
\(377\) 0.971407 0.0500300
\(378\) 0 0
\(379\) −13.7732 −0.707482 −0.353741 0.935343i \(-0.615091\pi\)
−0.353741 + 0.935343i \(0.615091\pi\)
\(380\) 0 0
\(381\) −5.37601 −0.275421
\(382\) 0 0
\(383\) 8.75113 0.447162 0.223581 0.974685i \(-0.428225\pi\)
0.223581 + 0.974685i \(0.428225\pi\)
\(384\) 0 0
\(385\) −0.357567 −0.0182233
\(386\) 0 0
\(387\) 8.16322 0.414960
\(388\) 0 0
\(389\) 2.08771 0.105851 0.0529255 0.998598i \(-0.483145\pi\)
0.0529255 + 0.998598i \(0.483145\pi\)
\(390\) 0 0
\(391\) −55.6013 −2.81188
\(392\) 0 0
\(393\) 23.2869 1.17467
\(394\) 0 0
\(395\) −0.129759 −0.00652888
\(396\) 0 0
\(397\) 27.3393 1.37212 0.686059 0.727546i \(-0.259339\pi\)
0.686059 + 0.727546i \(0.259339\pi\)
\(398\) 0 0
\(399\) −22.1415 −1.10846
\(400\) 0 0
\(401\) 9.56123 0.477465 0.238732 0.971085i \(-0.423268\pi\)
0.238732 + 0.971085i \(0.423268\pi\)
\(402\) 0 0
\(403\) 3.19969 0.159388
\(404\) 0 0
\(405\) −0.302681 −0.0150403
\(406\) 0 0
\(407\) 6.41376 0.317918
\(408\) 0 0
\(409\) −15.1693 −0.750074 −0.375037 0.927010i \(-0.622370\pi\)
−0.375037 + 0.927010i \(0.622370\pi\)
\(410\) 0 0
\(411\) −25.2193 −1.24398
\(412\) 0 0
\(413\) 21.8867 1.07697
\(414\) 0 0
\(415\) −0.884937 −0.0434398
\(416\) 0 0
\(417\) 21.3846 1.04721
\(418\) 0 0
\(419\) 11.6001 0.566703 0.283352 0.959016i \(-0.408554\pi\)
0.283352 + 0.959016i \(0.408554\pi\)
\(420\) 0 0
\(421\) 17.5008 0.852936 0.426468 0.904503i \(-0.359758\pi\)
0.426468 + 0.904503i \(0.359758\pi\)
\(422\) 0 0
\(423\) −2.89131 −0.140580
\(424\) 0 0
\(425\) −32.6765 −1.58504
\(426\) 0 0
\(427\) 23.3241 1.12873
\(428\) 0 0
\(429\) 0.734719 0.0354726
\(430\) 0 0
\(431\) 11.1444 0.536808 0.268404 0.963306i \(-0.413504\pi\)
0.268404 + 0.963306i \(0.413504\pi\)
\(432\) 0 0
\(433\) −37.4822 −1.80128 −0.900639 0.434568i \(-0.856901\pi\)
−0.900639 + 0.434568i \(0.856901\pi\)
\(434\) 0 0
\(435\) 0.201781 0.00967465
\(436\) 0 0
\(437\) 32.8440 1.57114
\(438\) 0 0
\(439\) −5.57251 −0.265961 −0.132981 0.991119i \(-0.542455\pi\)
−0.132981 + 0.991119i \(0.542455\pi\)
\(440\) 0 0
\(441\) −13.1336 −0.625411
\(442\) 0 0
\(443\) 16.3877 0.778603 0.389301 0.921110i \(-0.372716\pi\)
0.389301 + 0.921110i \(0.372716\pi\)
\(444\) 0 0
\(445\) −0.478831 −0.0226988
\(446\) 0 0
\(447\) −12.2374 −0.578808
\(448\) 0 0
\(449\) 1.50787 0.0711609 0.0355805 0.999367i \(-0.488672\pi\)
0.0355805 + 0.999367i \(0.488672\pi\)
\(450\) 0 0
\(451\) 5.15962 0.242957
\(452\) 0 0
\(453\) 0.242587 0.0113977
\(454\) 0 0
\(455\) 0.154744 0.00725449
\(456\) 0 0
\(457\) 39.8861 1.86579 0.932896 0.360147i \(-0.117273\pi\)
0.932896 + 0.360147i \(0.117273\pi\)
\(458\) 0 0
\(459\) 36.8882 1.72179
\(460\) 0 0
\(461\) 21.8959 1.01980 0.509898 0.860235i \(-0.329683\pi\)
0.509898 + 0.860235i \(0.329683\pi\)
\(462\) 0 0
\(463\) −19.7923 −0.919827 −0.459913 0.887964i \(-0.652120\pi\)
−0.459913 + 0.887964i \(0.652120\pi\)
\(464\) 0 0
\(465\) 0.664640 0.0308219
\(466\) 0 0
\(467\) 38.4128 1.77753 0.888767 0.458359i \(-0.151563\pi\)
0.888767 + 0.458359i \(0.151563\pi\)
\(468\) 0 0
\(469\) 35.0747 1.61960
\(470\) 0 0
\(471\) −14.4942 −0.667856
\(472\) 0 0
\(473\) −7.73331 −0.355578
\(474\) 0 0
\(475\) 19.3022 0.885647
\(476\) 0 0
\(477\) 12.3065 0.563478
\(478\) 0 0
\(479\) −1.06727 −0.0487646 −0.0243823 0.999703i \(-0.507762\pi\)
−0.0243823 + 0.999703i \(0.507762\pi\)
\(480\) 0 0
\(481\) −2.77567 −0.126560
\(482\) 0 0
\(483\) −48.6872 −2.21534
\(484\) 0 0
\(485\) −0.937831 −0.0425847
\(486\) 0 0
\(487\) 12.8081 0.580393 0.290196 0.956967i \(-0.406279\pi\)
0.290196 + 0.956967i \(0.406279\pi\)
\(488\) 0 0
\(489\) 0.349747 0.0158161
\(490\) 0 0
\(491\) 5.67129 0.255942 0.127971 0.991778i \(-0.459154\pi\)
0.127971 + 0.991778i \(0.459154\pi\)
\(492\) 0 0
\(493\) −13.0824 −0.589201
\(494\) 0 0
\(495\) −0.0996380 −0.00447840
\(496\) 0 0
\(497\) −61.9094 −2.77702
\(498\) 0 0
\(499\) 16.9907 0.760609 0.380304 0.924861i \(-0.375819\pi\)
0.380304 + 0.924861i \(0.375819\pi\)
\(500\) 0 0
\(501\) −26.8063 −1.19762
\(502\) 0 0
\(503\) −6.19038 −0.276015 −0.138008 0.990431i \(-0.544070\pi\)
−0.138008 + 0.990431i \(0.544070\pi\)
\(504\) 0 0
\(505\) 1.06255 0.0472828
\(506\) 0 0
\(507\) 17.1960 0.763702
\(508\) 0 0
\(509\) −0.283868 −0.0125822 −0.00629111 0.999980i \(-0.502003\pi\)
−0.00629111 + 0.999980i \(0.502003\pi\)
\(510\) 0 0
\(511\) 59.5652 2.63501
\(512\) 0 0
\(513\) −21.7901 −0.962056
\(514\) 0 0
\(515\) 1.37620 0.0606428
\(516\) 0 0
\(517\) 2.73904 0.120463
\(518\) 0 0
\(519\) −7.22348 −0.317076
\(520\) 0 0
\(521\) −36.1674 −1.58452 −0.792261 0.610183i \(-0.791096\pi\)
−0.792261 + 0.610183i \(0.791096\pi\)
\(522\) 0 0
\(523\) 5.62713 0.246057 0.123029 0.992403i \(-0.460739\pi\)
0.123029 + 0.992403i \(0.460739\pi\)
\(524\) 0 0
\(525\) −28.6131 −1.24878
\(526\) 0 0
\(527\) −43.0917 −1.87710
\(528\) 0 0
\(529\) 49.2210 2.14004
\(530\) 0 0
\(531\) 6.09884 0.264667
\(532\) 0 0
\(533\) −2.23292 −0.0967183
\(534\) 0 0
\(535\) 1.53305 0.0662795
\(536\) 0 0
\(537\) −13.0185 −0.561789
\(538\) 0 0
\(539\) 12.4420 0.535913
\(540\) 0 0
\(541\) −20.2787 −0.871850 −0.435925 0.899983i \(-0.643579\pi\)
−0.435925 + 0.899983i \(0.643579\pi\)
\(542\) 0 0
\(543\) −4.38972 −0.188381
\(544\) 0 0
\(545\) −0.0186293 −0.000797991 0
\(546\) 0 0
\(547\) −33.7625 −1.44358 −0.721791 0.692111i \(-0.756681\pi\)
−0.721791 + 0.692111i \(0.756681\pi\)
\(548\) 0 0
\(549\) 6.49939 0.277387
\(550\) 0 0
\(551\) 7.72785 0.329218
\(552\) 0 0
\(553\) 7.36672 0.313265
\(554\) 0 0
\(555\) −0.576562 −0.0244737
\(556\) 0 0
\(557\) −33.0877 −1.40197 −0.700985 0.713176i \(-0.747256\pi\)
−0.700985 + 0.713176i \(0.747256\pi\)
\(558\) 0 0
\(559\) 3.34673 0.141551
\(560\) 0 0
\(561\) −9.89480 −0.417759
\(562\) 0 0
\(563\) −37.2463 −1.56974 −0.784872 0.619658i \(-0.787271\pi\)
−0.784872 + 0.619658i \(0.787271\pi\)
\(564\) 0 0
\(565\) 0.654890 0.0275514
\(566\) 0 0
\(567\) 17.1839 0.721655
\(568\) 0 0
\(569\) 32.9211 1.38012 0.690062 0.723750i \(-0.257583\pi\)
0.690062 + 0.723750i \(0.257583\pi\)
\(570\) 0 0
\(571\) 35.9815 1.50578 0.752890 0.658147i \(-0.228659\pi\)
0.752890 + 0.658147i \(0.228659\pi\)
\(572\) 0 0
\(573\) −11.9241 −0.498136
\(574\) 0 0
\(575\) 42.4438 1.77003
\(576\) 0 0
\(577\) −20.8605 −0.868433 −0.434217 0.900808i \(-0.642975\pi\)
−0.434217 + 0.900808i \(0.642975\pi\)
\(578\) 0 0
\(579\) 15.4633 0.642634
\(580\) 0 0
\(581\) 50.2399 2.08430
\(582\) 0 0
\(583\) −11.6584 −0.482843
\(584\) 0 0
\(585\) 0.0431201 0.00178280
\(586\) 0 0
\(587\) −16.3158 −0.673426 −0.336713 0.941607i \(-0.609315\pi\)
−0.336713 + 0.941607i \(0.609315\pi\)
\(588\) 0 0
\(589\) 25.4546 1.04884
\(590\) 0 0
\(591\) −15.6357 −0.643168
\(592\) 0 0
\(593\) −9.87672 −0.405588 −0.202794 0.979221i \(-0.565002\pi\)
−0.202794 + 0.979221i \(0.565002\pi\)
\(594\) 0 0
\(595\) −2.08400 −0.0854358
\(596\) 0 0
\(597\) −7.24723 −0.296610
\(598\) 0 0
\(599\) 35.7750 1.46173 0.730863 0.682524i \(-0.239118\pi\)
0.730863 + 0.682524i \(0.239118\pi\)
\(600\) 0 0
\(601\) −15.7084 −0.640761 −0.320380 0.947289i \(-0.603811\pi\)
−0.320380 + 0.947289i \(0.603811\pi\)
\(602\) 0 0
\(603\) 9.77374 0.398017
\(604\) 0 0
\(605\) −0.729552 −0.0296605
\(606\) 0 0
\(607\) 9.93044 0.403064 0.201532 0.979482i \(-0.435408\pi\)
0.201532 + 0.979482i \(0.435408\pi\)
\(608\) 0 0
\(609\) −11.4556 −0.464203
\(610\) 0 0
\(611\) −1.18537 −0.0479549
\(612\) 0 0
\(613\) 45.4527 1.83582 0.917908 0.396793i \(-0.129877\pi\)
0.917908 + 0.396793i \(0.129877\pi\)
\(614\) 0 0
\(615\) −0.463822 −0.0187031
\(616\) 0 0
\(617\) −27.1035 −1.09115 −0.545574 0.838063i \(-0.683688\pi\)
−0.545574 + 0.838063i \(0.683688\pi\)
\(618\) 0 0
\(619\) 28.9676 1.16431 0.582153 0.813079i \(-0.302211\pi\)
0.582153 + 0.813079i \(0.302211\pi\)
\(620\) 0 0
\(621\) −47.9144 −1.92274
\(622\) 0 0
\(623\) 27.1844 1.08912
\(624\) 0 0
\(625\) 24.9159 0.996635
\(626\) 0 0
\(627\) 5.84492 0.233424
\(628\) 0 0
\(629\) 37.3812 1.49049
\(630\) 0 0
\(631\) 20.8230 0.828950 0.414475 0.910061i \(-0.363965\pi\)
0.414475 + 0.910061i \(0.363965\pi\)
\(632\) 0 0
\(633\) 16.4837 0.655168
\(634\) 0 0
\(635\) 0.298898 0.0118614
\(636\) 0 0
\(637\) −5.38448 −0.213341
\(638\) 0 0
\(639\) −17.2514 −0.682454
\(640\) 0 0
\(641\) −33.1908 −1.31096 −0.655480 0.755213i \(-0.727533\pi\)
−0.655480 + 0.755213i \(0.727533\pi\)
\(642\) 0 0
\(643\) −2.76533 −0.109054 −0.0545270 0.998512i \(-0.517365\pi\)
−0.0545270 + 0.998512i \(0.517365\pi\)
\(644\) 0 0
\(645\) 0.695183 0.0273728
\(646\) 0 0
\(647\) 5.18596 0.203881 0.101941 0.994790i \(-0.467495\pi\)
0.101941 + 0.994790i \(0.467495\pi\)
\(648\) 0 0
\(649\) −5.77765 −0.226793
\(650\) 0 0
\(651\) −37.7332 −1.47888
\(652\) 0 0
\(653\) 12.7366 0.498423 0.249212 0.968449i \(-0.419829\pi\)
0.249212 + 0.968449i \(0.419829\pi\)
\(654\) 0 0
\(655\) −1.29472 −0.0505888
\(656\) 0 0
\(657\) 16.5982 0.647556
\(658\) 0 0
\(659\) 13.9110 0.541895 0.270947 0.962594i \(-0.412663\pi\)
0.270947 + 0.962594i \(0.412663\pi\)
\(660\) 0 0
\(661\) 14.1006 0.548452 0.274226 0.961665i \(-0.411578\pi\)
0.274226 + 0.961665i \(0.411578\pi\)
\(662\) 0 0
\(663\) 4.28215 0.166305
\(664\) 0 0
\(665\) 1.23103 0.0477375
\(666\) 0 0
\(667\) 16.9928 0.657965
\(668\) 0 0
\(669\) 22.2779 0.861314
\(670\) 0 0
\(671\) −6.15710 −0.237692
\(672\) 0 0
\(673\) −34.9497 −1.34721 −0.673607 0.739090i \(-0.735256\pi\)
−0.673607 + 0.739090i \(0.735256\pi\)
\(674\) 0 0
\(675\) −28.1590 −1.08384
\(676\) 0 0
\(677\) −20.0280 −0.769738 −0.384869 0.922971i \(-0.625753\pi\)
−0.384869 + 0.922971i \(0.625753\pi\)
\(678\) 0 0
\(679\) 53.2429 2.04327
\(680\) 0 0
\(681\) −14.3361 −0.549362
\(682\) 0 0
\(683\) 20.5757 0.787308 0.393654 0.919259i \(-0.371211\pi\)
0.393654 + 0.919259i \(0.371211\pi\)
\(684\) 0 0
\(685\) 1.40215 0.0535735
\(686\) 0 0
\(687\) −23.8741 −0.910853
\(688\) 0 0
\(689\) 5.04539 0.192214
\(690\) 0 0
\(691\) −3.16945 −0.120571 −0.0602857 0.998181i \(-0.519201\pi\)
−0.0602857 + 0.998181i \(0.519201\pi\)
\(692\) 0 0
\(693\) 5.65668 0.214880
\(694\) 0 0
\(695\) −1.18895 −0.0450995
\(696\) 0 0
\(697\) 30.0717 1.13905
\(698\) 0 0
\(699\) −36.1688 −1.36803
\(700\) 0 0
\(701\) −21.7344 −0.820897 −0.410448 0.911884i \(-0.634628\pi\)
−0.410448 + 0.911884i \(0.634628\pi\)
\(702\) 0 0
\(703\) −22.0813 −0.832813
\(704\) 0 0
\(705\) −0.246225 −0.00927337
\(706\) 0 0
\(707\) −60.3234 −2.26869
\(708\) 0 0
\(709\) −11.1719 −0.419569 −0.209784 0.977748i \(-0.567276\pi\)
−0.209784 + 0.977748i \(0.567276\pi\)
\(710\) 0 0
\(711\) 2.05278 0.0769851
\(712\) 0 0
\(713\) 55.9722 2.09618
\(714\) 0 0
\(715\) −0.0408492 −0.00152767
\(716\) 0 0
\(717\) 20.3178 0.758783
\(718\) 0 0
\(719\) −21.5011 −0.801855 −0.400927 0.916110i \(-0.631312\pi\)
−0.400927 + 0.916110i \(0.631312\pi\)
\(720\) 0 0
\(721\) −78.1303 −2.90972
\(722\) 0 0
\(723\) 7.65717 0.284773
\(724\) 0 0
\(725\) 9.98657 0.370892
\(726\) 0 0
\(727\) 8.71945 0.323386 0.161693 0.986841i \(-0.448304\pi\)
0.161693 + 0.986841i \(0.448304\pi\)
\(728\) 0 0
\(729\) 27.5759 1.02133
\(730\) 0 0
\(731\) −45.0719 −1.66705
\(732\) 0 0
\(733\) 4.45443 0.164528 0.0822640 0.996611i \(-0.473785\pi\)
0.0822640 + 0.996611i \(0.473785\pi\)
\(734\) 0 0
\(735\) −1.11846 −0.0412552
\(736\) 0 0
\(737\) −9.25901 −0.341060
\(738\) 0 0
\(739\) −9.99944 −0.367835 −0.183918 0.982942i \(-0.558878\pi\)
−0.183918 + 0.982942i \(0.558878\pi\)
\(740\) 0 0
\(741\) −2.52949 −0.0929233
\(742\) 0 0
\(743\) 30.6417 1.12414 0.562068 0.827091i \(-0.310006\pi\)
0.562068 + 0.827091i \(0.310006\pi\)
\(744\) 0 0
\(745\) 0.680379 0.0249272
\(746\) 0 0
\(747\) 13.9996 0.512219
\(748\) 0 0
\(749\) −87.0348 −3.18018
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 23.8314 0.868465
\(754\) 0 0
\(755\) −0.0134875 −0.000490859 0
\(756\) 0 0
\(757\) −46.2342 −1.68041 −0.840206 0.542268i \(-0.817566\pi\)
−0.840206 + 0.542268i \(0.817566\pi\)
\(758\) 0 0
\(759\) 12.8524 0.466514
\(760\) 0 0
\(761\) 31.2829 1.13401 0.567003 0.823716i \(-0.308103\pi\)
0.567003 + 0.823716i \(0.308103\pi\)
\(762\) 0 0
\(763\) 1.05763 0.0382887
\(764\) 0 0
\(765\) −0.580719 −0.0209959
\(766\) 0 0
\(767\) 2.50038 0.0902835
\(768\) 0 0
\(769\) 20.8600 0.752229 0.376115 0.926573i \(-0.377260\pi\)
0.376115 + 0.926573i \(0.377260\pi\)
\(770\) 0 0
\(771\) −3.51197 −0.126480
\(772\) 0 0
\(773\) 45.6621 1.64235 0.821176 0.570676i \(-0.193319\pi\)
0.821176 + 0.570676i \(0.193319\pi\)
\(774\) 0 0
\(775\) 32.8945 1.18160
\(776\) 0 0
\(777\) 32.7328 1.17428
\(778\) 0 0
\(779\) −17.7636 −0.636446
\(780\) 0 0
\(781\) 16.3429 0.584793
\(782\) 0 0
\(783\) −11.2737 −0.402891
\(784\) 0 0
\(785\) 0.805854 0.0287621
\(786\) 0 0
\(787\) 6.91001 0.246315 0.123158 0.992387i \(-0.460698\pi\)
0.123158 + 0.992387i \(0.460698\pi\)
\(788\) 0 0
\(789\) −27.4435 −0.977016
\(790\) 0 0
\(791\) −37.1796 −1.32196
\(792\) 0 0
\(793\) 2.66459 0.0946225
\(794\) 0 0
\(795\) 1.04803 0.0371698
\(796\) 0 0
\(797\) −31.7434 −1.12441 −0.562205 0.826998i \(-0.690047\pi\)
−0.562205 + 0.826998i \(0.690047\pi\)
\(798\) 0 0
\(799\) 15.9639 0.564763
\(800\) 0 0
\(801\) 7.57507 0.267652
\(802\) 0 0
\(803\) −15.7240 −0.554889
\(804\) 0 0
\(805\) 2.70693 0.0954068
\(806\) 0 0
\(807\) −37.0754 −1.30512
\(808\) 0 0
\(809\) 3.73470 0.131305 0.0656526 0.997843i \(-0.479087\pi\)
0.0656526 + 0.997843i \(0.479087\pi\)
\(810\) 0 0
\(811\) 53.5714 1.88114 0.940572 0.339593i \(-0.110289\pi\)
0.940572 + 0.339593i \(0.110289\pi\)
\(812\) 0 0
\(813\) −21.5378 −0.755363
\(814\) 0 0
\(815\) −0.0194454 −0.000681142 0
\(816\) 0 0
\(817\) 26.6243 0.931466
\(818\) 0 0
\(819\) −2.44803 −0.0855411
\(820\) 0 0
\(821\) −4.05328 −0.141461 −0.0707303 0.997495i \(-0.522533\pi\)
−0.0707303 + 0.997495i \(0.522533\pi\)
\(822\) 0 0
\(823\) 16.0611 0.559856 0.279928 0.960021i \(-0.409689\pi\)
0.279928 + 0.960021i \(0.409689\pi\)
\(824\) 0 0
\(825\) 7.55329 0.262972
\(826\) 0 0
\(827\) −4.25680 −0.148024 −0.0740118 0.997257i \(-0.523580\pi\)
−0.0740118 + 0.997257i \(0.523580\pi\)
\(828\) 0 0
\(829\) 22.5583 0.783482 0.391741 0.920076i \(-0.371873\pi\)
0.391741 + 0.920076i \(0.371873\pi\)
\(830\) 0 0
\(831\) −18.8079 −0.652437
\(832\) 0 0
\(833\) 72.5153 2.51251
\(834\) 0 0
\(835\) 1.49039 0.0515770
\(836\) 0 0
\(837\) −37.1343 −1.28355
\(838\) 0 0
\(839\) −30.5380 −1.05429 −0.527145 0.849776i \(-0.676737\pi\)
−0.527145 + 0.849776i \(0.676737\pi\)
\(840\) 0 0
\(841\) −25.0018 −0.862130
\(842\) 0 0
\(843\) −7.67353 −0.264291
\(844\) 0 0
\(845\) −0.956072 −0.0328899
\(846\) 0 0
\(847\) 41.4184 1.42315
\(848\) 0 0
\(849\) −15.3976 −0.528445
\(850\) 0 0
\(851\) −48.5548 −1.66444
\(852\) 0 0
\(853\) 3.74804 0.128330 0.0641652 0.997939i \(-0.479562\pi\)
0.0641652 + 0.997939i \(0.479562\pi\)
\(854\) 0 0
\(855\) 0.343034 0.0117315
\(856\) 0 0
\(857\) 1.28672 0.0439535 0.0219767 0.999758i \(-0.493004\pi\)
0.0219767 + 0.999758i \(0.493004\pi\)
\(858\) 0 0
\(859\) −8.31880 −0.283834 −0.141917 0.989879i \(-0.545327\pi\)
−0.141917 + 0.989879i \(0.545327\pi\)
\(860\) 0 0
\(861\) 26.3322 0.897401
\(862\) 0 0
\(863\) 5.84487 0.198962 0.0994808 0.995039i \(-0.468282\pi\)
0.0994808 + 0.995039i \(0.468282\pi\)
\(864\) 0 0
\(865\) 0.401614 0.0136553
\(866\) 0 0
\(867\) −34.7668 −1.18074
\(868\) 0 0
\(869\) −1.94467 −0.0659683
\(870\) 0 0
\(871\) 4.00700 0.135772
\(872\) 0 0
\(873\) 14.8364 0.502136
\(874\) 0 0
\(875\) 3.18348 0.107621
\(876\) 0 0
\(877\) 49.1131 1.65843 0.829217 0.558927i \(-0.188787\pi\)
0.829217 + 0.558927i \(0.188787\pi\)
\(878\) 0 0
\(879\) −10.6700 −0.359892
\(880\) 0 0
\(881\) 18.4500 0.621597 0.310799 0.950476i \(-0.399404\pi\)
0.310799 + 0.950476i \(0.399404\pi\)
\(882\) 0 0
\(883\) 39.0972 1.31573 0.657864 0.753137i \(-0.271460\pi\)
0.657864 + 0.753137i \(0.271460\pi\)
\(884\) 0 0
\(885\) 0.519379 0.0174587
\(886\) 0 0
\(887\) −48.2198 −1.61906 −0.809532 0.587076i \(-0.800279\pi\)
−0.809532 + 0.587076i \(0.800279\pi\)
\(888\) 0 0
\(889\) −16.9691 −0.569126
\(890\) 0 0
\(891\) −4.53621 −0.151969
\(892\) 0 0
\(893\) −9.42999 −0.315563
\(894\) 0 0
\(895\) 0.723808 0.0241942
\(896\) 0 0
\(897\) −5.56212 −0.185714
\(898\) 0 0
\(899\) 13.1697 0.439233
\(900\) 0 0
\(901\) −67.9487 −2.26370
\(902\) 0 0
\(903\) −39.4671 −1.31338
\(904\) 0 0
\(905\) 0.244062 0.00811288
\(906\) 0 0
\(907\) 30.4977 1.01266 0.506329 0.862340i \(-0.331002\pi\)
0.506329 + 0.862340i \(0.331002\pi\)
\(908\) 0 0
\(909\) −16.8094 −0.557533
\(910\) 0 0
\(911\) −15.5291 −0.514502 −0.257251 0.966345i \(-0.582817\pi\)
−0.257251 + 0.966345i \(0.582817\pi\)
\(912\) 0 0
\(913\) −13.2623 −0.438920
\(914\) 0 0
\(915\) 0.553490 0.0182978
\(916\) 0 0
\(917\) 73.5041 2.42732
\(918\) 0 0
\(919\) −54.7722 −1.80677 −0.903384 0.428832i \(-0.858925\pi\)
−0.903384 + 0.428832i \(0.858925\pi\)
\(920\) 0 0
\(921\) −19.0838 −0.628834
\(922\) 0 0
\(923\) −7.07266 −0.232799
\(924\) 0 0
\(925\) −28.5353 −0.938235
\(926\) 0 0
\(927\) −21.7714 −0.715067
\(928\) 0 0
\(929\) 13.9121 0.456440 0.228220 0.973610i \(-0.426709\pi\)
0.228220 + 0.973610i \(0.426709\pi\)
\(930\) 0 0
\(931\) −42.8352 −1.40387
\(932\) 0 0
\(933\) 21.6582 0.709058
\(934\) 0 0
\(935\) 0.550136 0.0179914
\(936\) 0 0
\(937\) −11.9858 −0.391559 −0.195779 0.980648i \(-0.562724\pi\)
−0.195779 + 0.980648i \(0.562724\pi\)
\(938\) 0 0
\(939\) 20.2178 0.659782
\(940\) 0 0
\(941\) −58.8007 −1.91685 −0.958424 0.285349i \(-0.907891\pi\)
−0.958424 + 0.285349i \(0.907891\pi\)
\(942\) 0 0
\(943\) −39.0604 −1.27198
\(944\) 0 0
\(945\) −1.79589 −0.0584203
\(946\) 0 0
\(947\) 3.68932 0.119887 0.0599435 0.998202i \(-0.480908\pi\)
0.0599435 + 0.998202i \(0.480908\pi\)
\(948\) 0 0
\(949\) 6.80485 0.220895
\(950\) 0 0
\(951\) 24.3271 0.788859
\(952\) 0 0
\(953\) 25.3743 0.821954 0.410977 0.911646i \(-0.365188\pi\)
0.410977 + 0.911646i \(0.365188\pi\)
\(954\) 0 0
\(955\) 0.662961 0.0214529
\(956\) 0 0
\(957\) 3.02404 0.0977534
\(958\) 0 0
\(959\) −79.6035 −2.57053
\(960\) 0 0
\(961\) 12.3792 0.399328
\(962\) 0 0
\(963\) −24.2527 −0.781533
\(964\) 0 0
\(965\) −0.859737 −0.0276759
\(966\) 0 0
\(967\) 30.0166 0.965270 0.482635 0.875822i \(-0.339680\pi\)
0.482635 + 0.875822i \(0.339680\pi\)
\(968\) 0 0
\(969\) 34.0659 1.09435
\(970\) 0 0
\(971\) 2.26870 0.0728061 0.0364030 0.999337i \(-0.488410\pi\)
0.0364030 + 0.999337i \(0.488410\pi\)
\(972\) 0 0
\(973\) 67.4995 2.16393
\(974\) 0 0
\(975\) −3.26882 −0.104686
\(976\) 0 0
\(977\) −0.536664 −0.0171694 −0.00858470 0.999963i \(-0.502733\pi\)
−0.00858470 + 0.999963i \(0.502733\pi\)
\(978\) 0 0
\(979\) −7.17613 −0.229350
\(980\) 0 0
\(981\) 0.294714 0.00940948
\(982\) 0 0
\(983\) 10.8763 0.346899 0.173450 0.984843i \(-0.444509\pi\)
0.173450 + 0.984843i \(0.444509\pi\)
\(984\) 0 0
\(985\) 0.869322 0.0276989
\(986\) 0 0
\(987\) 13.9788 0.444949
\(988\) 0 0
\(989\) 58.5443 1.86160
\(990\) 0 0
\(991\) −52.5065 −1.66792 −0.833961 0.551823i \(-0.813933\pi\)
−0.833961 + 0.551823i \(0.813933\pi\)
\(992\) 0 0
\(993\) 13.6229 0.432308
\(994\) 0 0
\(995\) 0.402935 0.0127739
\(996\) 0 0
\(997\) 12.8794 0.407895 0.203947 0.978982i \(-0.434623\pi\)
0.203947 + 0.978982i \(0.434623\pi\)
\(998\) 0 0
\(999\) 32.2132 1.01918
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 \(a_p\))