Properties

Label 6008.2.a.e.1.26
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

Related objects

Downloads

Learn more about

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 1.26
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.325374 q^{3} -3.38648 q^{5} +0.980947 q^{7} -2.89413 q^{9} +O(q^{10})\) \(q+0.325374 q^{3} -3.38648 q^{5} +0.980947 q^{7} -2.89413 q^{9} -2.93018 q^{11} +4.83935 q^{13} -1.10187 q^{15} +7.26129 q^{17} -3.24836 q^{19} +0.319174 q^{21} -4.67797 q^{23} +6.46823 q^{25} -1.91780 q^{27} +0.705257 q^{29} -2.40928 q^{31} -0.953404 q^{33} -3.32196 q^{35} +3.15042 q^{37} +1.57460 q^{39} -7.63708 q^{41} +0.860565 q^{43} +9.80091 q^{45} -7.21523 q^{47} -6.03774 q^{49} +2.36263 q^{51} -4.24924 q^{53} +9.92299 q^{55} -1.05693 q^{57} -8.60491 q^{59} +3.47883 q^{61} -2.83899 q^{63} -16.3883 q^{65} +12.7506 q^{67} -1.52209 q^{69} -0.381676 q^{71} +1.63372 q^{73} +2.10459 q^{75} -2.87435 q^{77} -3.41258 q^{79} +8.05840 q^{81} +6.72394 q^{83} -24.5902 q^{85} +0.229472 q^{87} +2.86150 q^{89} +4.74714 q^{91} -0.783917 q^{93} +11.0005 q^{95} +14.6477 q^{97} +8.48033 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 0.325374 0.187855 0.0939273 0.995579i \(-0.470058\pi\)
0.0939273 + 0.995579i \(0.470058\pi\)
\(4\) 0 0
\(5\) −3.38648 −1.51448 −0.757239 0.653138i \(-0.773452\pi\)
−0.757239 + 0.653138i \(0.773452\pi\)
\(6\) 0 0
\(7\) 0.980947 0.370763 0.185382 0.982667i \(-0.440648\pi\)
0.185382 + 0.982667i \(0.440648\pi\)
\(8\) 0 0
\(9\) −2.89413 −0.964711
\(10\) 0 0
\(11\) −2.93018 −0.883482 −0.441741 0.897143i \(-0.645639\pi\)
−0.441741 + 0.897143i \(0.645639\pi\)
\(12\) 0 0
\(13\) 4.83935 1.34219 0.671097 0.741370i \(-0.265824\pi\)
0.671097 + 0.741370i \(0.265824\pi\)
\(14\) 0 0
\(15\) −1.10187 −0.284502
\(16\) 0 0
\(17\) 7.26129 1.76112 0.880561 0.473933i \(-0.157166\pi\)
0.880561 + 0.473933i \(0.157166\pi\)
\(18\) 0 0
\(19\) −3.24836 −0.745225 −0.372613 0.927987i \(-0.621538\pi\)
−0.372613 + 0.927987i \(0.621538\pi\)
\(20\) 0 0
\(21\) 0.319174 0.0696496
\(22\) 0 0
\(23\) −4.67797 −0.975424 −0.487712 0.873004i \(-0.662168\pi\)
−0.487712 + 0.873004i \(0.662168\pi\)
\(24\) 0 0
\(25\) 6.46823 1.29365
\(26\) 0 0
\(27\) −1.91780 −0.369080
\(28\) 0 0
\(29\) 0.705257 0.130963 0.0654814 0.997854i \(-0.479142\pi\)
0.0654814 + 0.997854i \(0.479142\pi\)
\(30\) 0 0
\(31\) −2.40928 −0.432720 −0.216360 0.976314i \(-0.569418\pi\)
−0.216360 + 0.976314i \(0.569418\pi\)
\(32\) 0 0
\(33\) −0.953404 −0.165966
\(34\) 0 0
\(35\) −3.32196 −0.561513
\(36\) 0 0
\(37\) 3.15042 0.517926 0.258963 0.965887i \(-0.416619\pi\)
0.258963 + 0.965887i \(0.416619\pi\)
\(38\) 0 0
\(39\) 1.57460 0.252137
\(40\) 0 0
\(41\) −7.63708 −1.19271 −0.596356 0.802720i \(-0.703385\pi\)
−0.596356 + 0.802720i \(0.703385\pi\)
\(42\) 0 0
\(43\) 0.860565 0.131235 0.0656175 0.997845i \(-0.479098\pi\)
0.0656175 + 0.997845i \(0.479098\pi\)
\(44\) 0 0
\(45\) 9.80091 1.46103
\(46\) 0 0
\(47\) −7.21523 −1.05245 −0.526225 0.850346i \(-0.676393\pi\)
−0.526225 + 0.850346i \(0.676393\pi\)
\(48\) 0 0
\(49\) −6.03774 −0.862535
\(50\) 0 0
\(51\) 2.36263 0.330835
\(52\) 0 0
\(53\) −4.24924 −0.583678 −0.291839 0.956468i \(-0.594267\pi\)
−0.291839 + 0.956468i \(0.594267\pi\)
\(54\) 0 0
\(55\) 9.92299 1.33802
\(56\) 0 0
\(57\) −1.05693 −0.139994
\(58\) 0 0
\(59\) −8.60491 −1.12026 −0.560132 0.828403i \(-0.689250\pi\)
−0.560132 + 0.828403i \(0.689250\pi\)
\(60\) 0 0
\(61\) 3.47883 0.445418 0.222709 0.974885i \(-0.428510\pi\)
0.222709 + 0.974885i \(0.428510\pi\)
\(62\) 0 0
\(63\) −2.83899 −0.357679
\(64\) 0 0
\(65\) −16.3883 −2.03272
\(66\) 0 0
\(67\) 12.7506 1.55773 0.778866 0.627190i \(-0.215795\pi\)
0.778866 + 0.627190i \(0.215795\pi\)
\(68\) 0 0
\(69\) −1.52209 −0.183238
\(70\) 0 0
\(71\) −0.381676 −0.0452966 −0.0226483 0.999743i \(-0.507210\pi\)
−0.0226483 + 0.999743i \(0.507210\pi\)
\(72\) 0 0
\(73\) 1.63372 0.191213 0.0956065 0.995419i \(-0.469521\pi\)
0.0956065 + 0.995419i \(0.469521\pi\)
\(74\) 0 0
\(75\) 2.10459 0.243017
\(76\) 0 0
\(77\) −2.87435 −0.327563
\(78\) 0 0
\(79\) −3.41258 −0.383945 −0.191973 0.981400i \(-0.561489\pi\)
−0.191973 + 0.981400i \(0.561489\pi\)
\(80\) 0 0
\(81\) 8.05840 0.895377
\(82\) 0 0
\(83\) 6.72394 0.738049 0.369024 0.929420i \(-0.379692\pi\)
0.369024 + 0.929420i \(0.379692\pi\)
\(84\) 0 0
\(85\) −24.5902 −2.66718
\(86\) 0 0
\(87\) 0.229472 0.0246020
\(88\) 0 0
\(89\) 2.86150 0.303318 0.151659 0.988433i \(-0.451538\pi\)
0.151659 + 0.988433i \(0.451538\pi\)
\(90\) 0 0
\(91\) 4.74714 0.497636
\(92\) 0 0
\(93\) −0.783917 −0.0812884
\(94\) 0 0
\(95\) 11.0005 1.12863
\(96\) 0 0
\(97\) 14.6477 1.48725 0.743626 0.668596i \(-0.233105\pi\)
0.743626 + 0.668596i \(0.233105\pi\)
\(98\) 0 0
\(99\) 8.48033 0.852305
\(100\) 0 0
\(101\) −12.7322 −1.26691 −0.633453 0.773781i \(-0.718363\pi\)
−0.633453 + 0.773781i \(0.718363\pi\)
\(102\) 0 0
\(103\) 8.94224 0.881105 0.440552 0.897727i \(-0.354783\pi\)
0.440552 + 0.897727i \(0.354783\pi\)
\(104\) 0 0
\(105\) −1.08088 −0.105483
\(106\) 0 0
\(107\) −9.67961 −0.935764 −0.467882 0.883791i \(-0.654983\pi\)
−0.467882 + 0.883791i \(0.654983\pi\)
\(108\) 0 0
\(109\) 7.27681 0.696992 0.348496 0.937310i \(-0.386693\pi\)
0.348496 + 0.937310i \(0.386693\pi\)
\(110\) 0 0
\(111\) 1.02506 0.0972948
\(112\) 0 0
\(113\) 0.975504 0.0917677 0.0458838 0.998947i \(-0.485390\pi\)
0.0458838 + 0.998947i \(0.485390\pi\)
\(114\) 0 0
\(115\) 15.8418 1.47726
\(116\) 0 0
\(117\) −14.0057 −1.29483
\(118\) 0 0
\(119\) 7.12295 0.652959
\(120\) 0 0
\(121\) −2.41405 −0.219459
\(122\) 0 0
\(123\) −2.48490 −0.224056
\(124\) 0 0
\(125\) −4.97212 −0.444720
\(126\) 0 0
\(127\) −18.6668 −1.65641 −0.828205 0.560426i \(-0.810637\pi\)
−0.828205 + 0.560426i \(0.810637\pi\)
\(128\) 0 0
\(129\) 0.280005 0.0246531
\(130\) 0 0
\(131\) 18.6390 1.62850 0.814249 0.580516i \(-0.197149\pi\)
0.814249 + 0.580516i \(0.197149\pi\)
\(132\) 0 0
\(133\) −3.18647 −0.276302
\(134\) 0 0
\(135\) 6.49457 0.558964
\(136\) 0 0
\(137\) 11.8063 1.00868 0.504342 0.863504i \(-0.331735\pi\)
0.504342 + 0.863504i \(0.331735\pi\)
\(138\) 0 0
\(139\) 17.6784 1.49946 0.749729 0.661745i \(-0.230184\pi\)
0.749729 + 0.661745i \(0.230184\pi\)
\(140\) 0 0
\(141\) −2.34765 −0.197707
\(142\) 0 0
\(143\) −14.1802 −1.18580
\(144\) 0 0
\(145\) −2.38834 −0.198341
\(146\) 0 0
\(147\) −1.96452 −0.162031
\(148\) 0 0
\(149\) 21.8028 1.78615 0.893076 0.449906i \(-0.148543\pi\)
0.893076 + 0.449906i \(0.148543\pi\)
\(150\) 0 0
\(151\) 17.2206 1.40139 0.700696 0.713460i \(-0.252873\pi\)
0.700696 + 0.713460i \(0.252873\pi\)
\(152\) 0 0
\(153\) −21.0151 −1.69897
\(154\) 0 0
\(155\) 8.15897 0.655345
\(156\) 0 0
\(157\) 14.2403 1.13650 0.568250 0.822856i \(-0.307621\pi\)
0.568250 + 0.822856i \(0.307621\pi\)
\(158\) 0 0
\(159\) −1.38259 −0.109647
\(160\) 0 0
\(161\) −4.58884 −0.361651
\(162\) 0 0
\(163\) −12.7027 −0.994949 −0.497474 0.867479i \(-0.665739\pi\)
−0.497474 + 0.867479i \(0.665739\pi\)
\(164\) 0 0
\(165\) 3.22868 0.251352
\(166\) 0 0
\(167\) 13.9001 1.07562 0.537812 0.843065i \(-0.319251\pi\)
0.537812 + 0.843065i \(0.319251\pi\)
\(168\) 0 0
\(169\) 10.4193 0.801482
\(170\) 0 0
\(171\) 9.40119 0.718927
\(172\) 0 0
\(173\) 2.63995 0.200711 0.100356 0.994952i \(-0.468002\pi\)
0.100356 + 0.994952i \(0.468002\pi\)
\(174\) 0 0
\(175\) 6.34499 0.479636
\(176\) 0 0
\(177\) −2.79981 −0.210447
\(178\) 0 0
\(179\) 19.5349 1.46011 0.730054 0.683389i \(-0.239495\pi\)
0.730054 + 0.683389i \(0.239495\pi\)
\(180\) 0 0
\(181\) 17.2303 1.28072 0.640358 0.768077i \(-0.278786\pi\)
0.640358 + 0.768077i \(0.278786\pi\)
\(182\) 0 0
\(183\) 1.13192 0.0836739
\(184\) 0 0
\(185\) −10.6688 −0.784388
\(186\) 0 0
\(187\) −21.2769 −1.55592
\(188\) 0 0
\(189\) −1.88126 −0.136841
\(190\) 0 0
\(191\) 11.5169 0.833337 0.416669 0.909058i \(-0.363198\pi\)
0.416669 + 0.909058i \(0.363198\pi\)
\(192\) 0 0
\(193\) −5.32103 −0.383016 −0.191508 0.981491i \(-0.561338\pi\)
−0.191508 + 0.981491i \(0.561338\pi\)
\(194\) 0 0
\(195\) −5.33233 −0.381856
\(196\) 0 0
\(197\) 10.9254 0.778406 0.389203 0.921152i \(-0.372750\pi\)
0.389203 + 0.921152i \(0.372750\pi\)
\(198\) 0 0
\(199\) 12.6818 0.898991 0.449496 0.893283i \(-0.351604\pi\)
0.449496 + 0.893283i \(0.351604\pi\)
\(200\) 0 0
\(201\) 4.14871 0.292627
\(202\) 0 0
\(203\) 0.691820 0.0485562
\(204\) 0 0
\(205\) 25.8628 1.80634
\(206\) 0 0
\(207\) 13.5387 0.941002
\(208\) 0 0
\(209\) 9.51828 0.658393
\(210\) 0 0
\(211\) 6.47480 0.445744 0.222872 0.974848i \(-0.428457\pi\)
0.222872 + 0.974848i \(0.428457\pi\)
\(212\) 0 0
\(213\) −0.124187 −0.00850918
\(214\) 0 0
\(215\) −2.91429 −0.198753
\(216\) 0 0
\(217\) −2.36338 −0.160436
\(218\) 0 0
\(219\) 0.531571 0.0359202
\(220\) 0 0
\(221\) 35.1399 2.36377
\(222\) 0 0
\(223\) −17.4768 −1.17033 −0.585166 0.810913i \(-0.698971\pi\)
−0.585166 + 0.810913i \(0.698971\pi\)
\(224\) 0 0
\(225\) −18.7199 −1.24799
\(226\) 0 0
\(227\) −7.45740 −0.494965 −0.247483 0.968892i \(-0.579603\pi\)
−0.247483 + 0.968892i \(0.579603\pi\)
\(228\) 0 0
\(229\) 5.28630 0.349329 0.174664 0.984628i \(-0.444116\pi\)
0.174664 + 0.984628i \(0.444116\pi\)
\(230\) 0 0
\(231\) −0.935238 −0.0615342
\(232\) 0 0
\(233\) −2.11458 −0.138531 −0.0692655 0.997598i \(-0.522066\pi\)
−0.0692655 + 0.997598i \(0.522066\pi\)
\(234\) 0 0
\(235\) 24.4342 1.59391
\(236\) 0 0
\(237\) −1.11036 −0.0721259
\(238\) 0 0
\(239\) 4.46049 0.288525 0.144262 0.989539i \(-0.453919\pi\)
0.144262 + 0.989539i \(0.453919\pi\)
\(240\) 0 0
\(241\) −16.2174 −1.04465 −0.522327 0.852745i \(-0.674936\pi\)
−0.522327 + 0.852745i \(0.674936\pi\)
\(242\) 0 0
\(243\) 8.37538 0.537281
\(244\) 0 0
\(245\) 20.4467 1.30629
\(246\) 0 0
\(247\) −15.7199 −1.00024
\(248\) 0 0
\(249\) 2.18780 0.138646
\(250\) 0 0
\(251\) −11.3620 −0.717161 −0.358581 0.933499i \(-0.616739\pi\)
−0.358581 + 0.933499i \(0.616739\pi\)
\(252\) 0 0
\(253\) 13.7073 0.861770
\(254\) 0 0
\(255\) −8.00101 −0.501042
\(256\) 0 0
\(257\) −22.1107 −1.37923 −0.689614 0.724177i \(-0.742220\pi\)
−0.689614 + 0.724177i \(0.742220\pi\)
\(258\) 0 0
\(259\) 3.09040 0.192028
\(260\) 0 0
\(261\) −2.04111 −0.126341
\(262\) 0 0
\(263\) −13.3247 −0.821637 −0.410819 0.911717i \(-0.634757\pi\)
−0.410819 + 0.911717i \(0.634757\pi\)
\(264\) 0 0
\(265\) 14.3899 0.883967
\(266\) 0 0
\(267\) 0.931056 0.0569797
\(268\) 0 0
\(269\) 2.35083 0.143333 0.0716663 0.997429i \(-0.477168\pi\)
0.0716663 + 0.997429i \(0.477168\pi\)
\(270\) 0 0
\(271\) 0.879378 0.0534184 0.0267092 0.999643i \(-0.491497\pi\)
0.0267092 + 0.999643i \(0.491497\pi\)
\(272\) 0 0
\(273\) 1.54460 0.0934832
\(274\) 0 0
\(275\) −18.9531 −1.14291
\(276\) 0 0
\(277\) −2.43286 −0.146176 −0.0730882 0.997325i \(-0.523285\pi\)
−0.0730882 + 0.997325i \(0.523285\pi\)
\(278\) 0 0
\(279\) 6.97278 0.417449
\(280\) 0 0
\(281\) 16.7384 0.998532 0.499266 0.866449i \(-0.333603\pi\)
0.499266 + 0.866449i \(0.333603\pi\)
\(282\) 0 0
\(283\) 5.69773 0.338695 0.169347 0.985556i \(-0.445834\pi\)
0.169347 + 0.985556i \(0.445834\pi\)
\(284\) 0 0
\(285\) 3.57928 0.212018
\(286\) 0 0
\(287\) −7.49157 −0.442213
\(288\) 0 0
\(289\) 35.7264 2.10155
\(290\) 0 0
\(291\) 4.76599 0.279387
\(292\) 0 0
\(293\) 32.2603 1.88467 0.942333 0.334677i \(-0.108627\pi\)
0.942333 + 0.334677i \(0.108627\pi\)
\(294\) 0 0
\(295\) 29.1403 1.69662
\(296\) 0 0
\(297\) 5.61949 0.326076
\(298\) 0 0
\(299\) −22.6383 −1.30921
\(300\) 0 0
\(301\) 0.844169 0.0486571
\(302\) 0 0
\(303\) −4.14274 −0.237994
\(304\) 0 0
\(305\) −11.7810 −0.674576
\(306\) 0 0
\(307\) −0.928452 −0.0529895 −0.0264948 0.999649i \(-0.508435\pi\)
−0.0264948 + 0.999649i \(0.508435\pi\)
\(308\) 0 0
\(309\) 2.90957 0.165520
\(310\) 0 0
\(311\) 6.09507 0.345619 0.172810 0.984955i \(-0.444715\pi\)
0.172810 + 0.984955i \(0.444715\pi\)
\(312\) 0 0
\(313\) −28.4959 −1.61068 −0.805341 0.592812i \(-0.798018\pi\)
−0.805341 + 0.592812i \(0.798018\pi\)
\(314\) 0 0
\(315\) 9.61418 0.541697
\(316\) 0 0
\(317\) 2.47666 0.139103 0.0695516 0.997578i \(-0.477843\pi\)
0.0695516 + 0.997578i \(0.477843\pi\)
\(318\) 0 0
\(319\) −2.06653 −0.115703
\(320\) 0 0
\(321\) −3.14949 −0.175788
\(322\) 0 0
\(323\) −23.5873 −1.31243
\(324\) 0 0
\(325\) 31.3020 1.73632
\(326\) 0 0
\(327\) 2.36768 0.130933
\(328\) 0 0
\(329\) −7.07776 −0.390209
\(330\) 0 0
\(331\) −10.3182 −0.567141 −0.283571 0.958951i \(-0.591519\pi\)
−0.283571 + 0.958951i \(0.591519\pi\)
\(332\) 0 0
\(333\) −9.11773 −0.499649
\(334\) 0 0
\(335\) −43.1796 −2.35915
\(336\) 0 0
\(337\) 12.5304 0.682572 0.341286 0.939960i \(-0.389138\pi\)
0.341286 + 0.939960i \(0.389138\pi\)
\(338\) 0 0
\(339\) 0.317403 0.0172390
\(340\) 0 0
\(341\) 7.05963 0.382300
\(342\) 0 0
\(343\) −12.7893 −0.690559
\(344\) 0 0
\(345\) 5.15452 0.277510
\(346\) 0 0
\(347\) 10.2613 0.550857 0.275429 0.961322i \(-0.411180\pi\)
0.275429 + 0.961322i \(0.411180\pi\)
\(348\) 0 0
\(349\) −13.5683 −0.726296 −0.363148 0.931731i \(-0.618298\pi\)
−0.363148 + 0.931731i \(0.618298\pi\)
\(350\) 0 0
\(351\) −9.28088 −0.495377
\(352\) 0 0
\(353\) 17.9948 0.957766 0.478883 0.877879i \(-0.341042\pi\)
0.478883 + 0.877879i \(0.341042\pi\)
\(354\) 0 0
\(355\) 1.29254 0.0686008
\(356\) 0 0
\(357\) 2.31762 0.122661
\(358\) 0 0
\(359\) −10.9258 −0.576643 −0.288322 0.957534i \(-0.593097\pi\)
−0.288322 + 0.957534i \(0.593097\pi\)
\(360\) 0 0
\(361\) −8.44814 −0.444639
\(362\) 0 0
\(363\) −0.785468 −0.0412264
\(364\) 0 0
\(365\) −5.53257 −0.289588
\(366\) 0 0
\(367\) 24.7073 1.28971 0.644855 0.764305i \(-0.276918\pi\)
0.644855 + 0.764305i \(0.276918\pi\)
\(368\) 0 0
\(369\) 22.1027 1.15062
\(370\) 0 0
\(371\) −4.16828 −0.216406
\(372\) 0 0
\(373\) 24.8403 1.28618 0.643092 0.765789i \(-0.277651\pi\)
0.643092 + 0.765789i \(0.277651\pi\)
\(374\) 0 0
\(375\) −1.61780 −0.0835427
\(376\) 0 0
\(377\) 3.41298 0.175778
\(378\) 0 0
\(379\) −2.66407 −0.136844 −0.0684222 0.997656i \(-0.521796\pi\)
−0.0684222 + 0.997656i \(0.521796\pi\)
\(380\) 0 0
\(381\) −6.07368 −0.311164
\(382\) 0 0
\(383\) −6.22225 −0.317942 −0.158971 0.987283i \(-0.550818\pi\)
−0.158971 + 0.987283i \(0.550818\pi\)
\(384\) 0 0
\(385\) 9.73392 0.496087
\(386\) 0 0
\(387\) −2.49059 −0.126604
\(388\) 0 0
\(389\) −8.40510 −0.426155 −0.213078 0.977035i \(-0.568349\pi\)
−0.213078 + 0.977035i \(0.568349\pi\)
\(390\) 0 0
\(391\) −33.9681 −1.71784
\(392\) 0 0
\(393\) 6.06464 0.305921
\(394\) 0 0
\(395\) 11.5566 0.581477
\(396\) 0 0
\(397\) 0.187258 0.00939823 0.00469912 0.999989i \(-0.498504\pi\)
0.00469912 + 0.999989i \(0.498504\pi\)
\(398\) 0 0
\(399\) −1.03679 −0.0519046
\(400\) 0 0
\(401\) 10.3224 0.515475 0.257738 0.966215i \(-0.417023\pi\)
0.257738 + 0.966215i \(0.417023\pi\)
\(402\) 0 0
\(403\) −11.6593 −0.580793
\(404\) 0 0
\(405\) −27.2896 −1.35603
\(406\) 0 0
\(407\) −9.23129 −0.457578
\(408\) 0 0
\(409\) −4.98644 −0.246564 −0.123282 0.992372i \(-0.539342\pi\)
−0.123282 + 0.992372i \(0.539342\pi\)
\(410\) 0 0
\(411\) 3.84147 0.189486
\(412\) 0 0
\(413\) −8.44096 −0.415353
\(414\) 0 0
\(415\) −22.7705 −1.11776
\(416\) 0 0
\(417\) 5.75207 0.281680
\(418\) 0 0
\(419\) −32.1370 −1.56999 −0.784997 0.619500i \(-0.787335\pi\)
−0.784997 + 0.619500i \(0.787335\pi\)
\(420\) 0 0
\(421\) 17.8353 0.869241 0.434620 0.900614i \(-0.356883\pi\)
0.434620 + 0.900614i \(0.356883\pi\)
\(422\) 0 0
\(423\) 20.8818 1.01531
\(424\) 0 0
\(425\) 46.9677 2.27827
\(426\) 0 0
\(427\) 3.41255 0.165145
\(428\) 0 0
\(429\) −4.61385 −0.222759
\(430\) 0 0
\(431\) −8.24739 −0.397263 −0.198631 0.980074i \(-0.563650\pi\)
−0.198631 + 0.980074i \(0.563650\pi\)
\(432\) 0 0
\(433\) 5.05087 0.242729 0.121365 0.992608i \(-0.461273\pi\)
0.121365 + 0.992608i \(0.461273\pi\)
\(434\) 0 0
\(435\) −0.777102 −0.0372592
\(436\) 0 0
\(437\) 15.1957 0.726911
\(438\) 0 0
\(439\) −23.4052 −1.11707 −0.558535 0.829481i \(-0.688636\pi\)
−0.558535 + 0.829481i \(0.688636\pi\)
\(440\) 0 0
\(441\) 17.4740 0.832096
\(442\) 0 0
\(443\) 5.09062 0.241863 0.120931 0.992661i \(-0.461412\pi\)
0.120931 + 0.992661i \(0.461412\pi\)
\(444\) 0 0
\(445\) −9.69039 −0.459369
\(446\) 0 0
\(447\) 7.09405 0.335537
\(448\) 0 0
\(449\) 25.6395 1.21000 0.605001 0.796225i \(-0.293173\pi\)
0.605001 + 0.796225i \(0.293173\pi\)
\(450\) 0 0
\(451\) 22.3780 1.05374
\(452\) 0 0
\(453\) 5.60313 0.263258
\(454\) 0 0
\(455\) −16.0761 −0.753659
\(456\) 0 0
\(457\) −25.9163 −1.21231 −0.606156 0.795345i \(-0.707289\pi\)
−0.606156 + 0.795345i \(0.707289\pi\)
\(458\) 0 0
\(459\) −13.9257 −0.649995
\(460\) 0 0
\(461\) −4.85042 −0.225906 −0.112953 0.993600i \(-0.536031\pi\)
−0.112953 + 0.993600i \(0.536031\pi\)
\(462\) 0 0
\(463\) 25.8229 1.20009 0.600046 0.799965i \(-0.295149\pi\)
0.600046 + 0.799965i \(0.295149\pi\)
\(464\) 0 0
\(465\) 2.65472 0.123110
\(466\) 0 0
\(467\) −0.530213 −0.0245353 −0.0122677 0.999925i \(-0.503905\pi\)
−0.0122677 + 0.999925i \(0.503905\pi\)
\(468\) 0 0
\(469\) 12.5077 0.577550
\(470\) 0 0
\(471\) 4.63342 0.213497
\(472\) 0 0
\(473\) −2.52161 −0.115944
\(474\) 0 0
\(475\) −21.0111 −0.964057
\(476\) 0 0
\(477\) 12.2979 0.563080
\(478\) 0 0
\(479\) 3.50480 0.160138 0.0800691 0.996789i \(-0.474486\pi\)
0.0800691 + 0.996789i \(0.474486\pi\)
\(480\) 0 0
\(481\) 15.2460 0.695156
\(482\) 0 0
\(483\) −1.49309 −0.0679379
\(484\) 0 0
\(485\) −49.6042 −2.25241
\(486\) 0 0
\(487\) 26.8777 1.21795 0.608973 0.793191i \(-0.291582\pi\)
0.608973 + 0.793191i \(0.291582\pi\)
\(488\) 0 0
\(489\) −4.13311 −0.186906
\(490\) 0 0
\(491\) −22.8720 −1.03220 −0.516099 0.856529i \(-0.672616\pi\)
−0.516099 + 0.856529i \(0.672616\pi\)
\(492\) 0 0
\(493\) 5.12108 0.230642
\(494\) 0 0
\(495\) −28.7184 −1.29080
\(496\) 0 0
\(497\) −0.374404 −0.0167943
\(498\) 0 0
\(499\) 33.0977 1.48166 0.740829 0.671693i \(-0.234433\pi\)
0.740829 + 0.671693i \(0.234433\pi\)
\(500\) 0 0
\(501\) 4.52273 0.202061
\(502\) 0 0
\(503\) −31.8957 −1.42216 −0.711080 0.703111i \(-0.751794\pi\)
−0.711080 + 0.703111i \(0.751794\pi\)
\(504\) 0 0
\(505\) 43.1174 1.91870
\(506\) 0 0
\(507\) 3.39016 0.150562
\(508\) 0 0
\(509\) −17.7795 −0.788064 −0.394032 0.919097i \(-0.628920\pi\)
−0.394032 + 0.919097i \(0.628920\pi\)
\(510\) 0 0
\(511\) 1.60260 0.0708947
\(512\) 0 0
\(513\) 6.22970 0.275048
\(514\) 0 0
\(515\) −30.2827 −1.33441
\(516\) 0 0
\(517\) 21.1419 0.929820
\(518\) 0 0
\(519\) 0.858969 0.0377046
\(520\) 0 0
\(521\) −16.4500 −0.720688 −0.360344 0.932820i \(-0.617341\pi\)
−0.360344 + 0.932820i \(0.617341\pi\)
\(522\) 0 0
\(523\) −41.5433 −1.81656 −0.908282 0.418359i \(-0.862605\pi\)
−0.908282 + 0.418359i \(0.862605\pi\)
\(524\) 0 0
\(525\) 2.06449 0.0901019
\(526\) 0 0
\(527\) −17.4945 −0.762072
\(528\) 0 0
\(529\) −1.11659 −0.0485473
\(530\) 0 0
\(531\) 24.9037 1.08073
\(532\) 0 0
\(533\) −36.9585 −1.60085
\(534\) 0 0
\(535\) 32.7798 1.41719
\(536\) 0 0
\(537\) 6.35615 0.274288
\(538\) 0 0
\(539\) 17.6917 0.762034
\(540\) 0 0
\(541\) 40.2181 1.72911 0.864556 0.502537i \(-0.167600\pi\)
0.864556 + 0.502537i \(0.167600\pi\)
\(542\) 0 0
\(543\) 5.60627 0.240588
\(544\) 0 0
\(545\) −24.6427 −1.05558
\(546\) 0 0
\(547\) 1.75359 0.0749780 0.0374890 0.999297i \(-0.488064\pi\)
0.0374890 + 0.999297i \(0.488064\pi\)
\(548\) 0 0
\(549\) −10.0682 −0.429700
\(550\) 0 0
\(551\) −2.29093 −0.0975969
\(552\) 0 0
\(553\) −3.34756 −0.142353
\(554\) 0 0
\(555\) −3.47136 −0.147351
\(556\) 0 0
\(557\) 20.5762 0.871842 0.435921 0.899985i \(-0.356423\pi\)
0.435921 + 0.899985i \(0.356423\pi\)
\(558\) 0 0
\(559\) 4.16457 0.176143
\(560\) 0 0
\(561\) −6.92294 −0.292287
\(562\) 0 0
\(563\) 4.34244 0.183012 0.0915060 0.995805i \(-0.470832\pi\)
0.0915060 + 0.995805i \(0.470832\pi\)
\(564\) 0 0
\(565\) −3.30352 −0.138980
\(566\) 0 0
\(567\) 7.90486 0.331973
\(568\) 0 0
\(569\) −5.32669 −0.223306 −0.111653 0.993747i \(-0.535615\pi\)
−0.111653 + 0.993747i \(0.535615\pi\)
\(570\) 0 0
\(571\) 9.48575 0.396966 0.198483 0.980104i \(-0.436398\pi\)
0.198483 + 0.980104i \(0.436398\pi\)
\(572\) 0 0
\(573\) 3.74731 0.156546
\(574\) 0 0
\(575\) −30.2582 −1.26185
\(576\) 0 0
\(577\) −8.16813 −0.340044 −0.170022 0.985440i \(-0.554384\pi\)
−0.170022 + 0.985440i \(0.554384\pi\)
\(578\) 0 0
\(579\) −1.73132 −0.0719513
\(580\) 0 0
\(581\) 6.59583 0.273641
\(582\) 0 0
\(583\) 12.4510 0.515669
\(584\) 0 0
\(585\) 47.4300 1.96099
\(586\) 0 0
\(587\) −18.9722 −0.783068 −0.391534 0.920164i \(-0.628055\pi\)
−0.391534 + 0.920164i \(0.628055\pi\)
\(588\) 0 0
\(589\) 7.82622 0.322474
\(590\) 0 0
\(591\) 3.55485 0.146227
\(592\) 0 0
\(593\) 4.94720 0.203157 0.101579 0.994828i \(-0.467611\pi\)
0.101579 + 0.994828i \(0.467611\pi\)
\(594\) 0 0
\(595\) −24.1217 −0.988893
\(596\) 0 0
\(597\) 4.12634 0.168880
\(598\) 0 0
\(599\) 33.0329 1.34969 0.674843 0.737961i \(-0.264211\pi\)
0.674843 + 0.737961i \(0.264211\pi\)
\(600\) 0 0
\(601\) −20.3306 −0.829303 −0.414652 0.909980i \(-0.636097\pi\)
−0.414652 + 0.909980i \(0.636097\pi\)
\(602\) 0 0
\(603\) −36.9019 −1.50276
\(604\) 0 0
\(605\) 8.17512 0.332366
\(606\) 0 0
\(607\) −1.35601 −0.0550386 −0.0275193 0.999621i \(-0.508761\pi\)
−0.0275193 + 0.999621i \(0.508761\pi\)
\(608\) 0 0
\(609\) 0.225100 0.00912151
\(610\) 0 0
\(611\) −34.9170 −1.41259
\(612\) 0 0
\(613\) 37.7337 1.52405 0.762025 0.647548i \(-0.224205\pi\)
0.762025 + 0.647548i \(0.224205\pi\)
\(614\) 0 0
\(615\) 8.41507 0.339329
\(616\) 0 0
\(617\) −12.5979 −0.507174 −0.253587 0.967313i \(-0.581610\pi\)
−0.253587 + 0.967313i \(0.581610\pi\)
\(618\) 0 0
\(619\) 4.48413 0.180232 0.0901161 0.995931i \(-0.471276\pi\)
0.0901161 + 0.995931i \(0.471276\pi\)
\(620\) 0 0
\(621\) 8.97139 0.360010
\(622\) 0 0
\(623\) 2.80698 0.112459
\(624\) 0 0
\(625\) −15.5032 −0.620127
\(626\) 0 0
\(627\) 3.09700 0.123682
\(628\) 0 0
\(629\) 22.8761 0.912131
\(630\) 0 0
\(631\) 29.3761 1.16945 0.584723 0.811233i \(-0.301203\pi\)
0.584723 + 0.811233i \(0.301203\pi\)
\(632\) 0 0
\(633\) 2.10673 0.0837350
\(634\) 0 0
\(635\) 63.2146 2.50860
\(636\) 0 0
\(637\) −29.2187 −1.15769
\(638\) 0 0
\(639\) 1.10462 0.0436982
\(640\) 0 0
\(641\) 9.57893 0.378345 0.189172 0.981944i \(-0.439419\pi\)
0.189172 + 0.981944i \(0.439419\pi\)
\(642\) 0 0
\(643\) −11.1231 −0.438653 −0.219327 0.975651i \(-0.570386\pi\)
−0.219327 + 0.975651i \(0.570386\pi\)
\(644\) 0 0
\(645\) −0.948232 −0.0373366
\(646\) 0 0
\(647\) 20.6967 0.813673 0.406837 0.913501i \(-0.366632\pi\)
0.406837 + 0.913501i \(0.366632\pi\)
\(648\) 0 0
\(649\) 25.2139 0.989733
\(650\) 0 0
\(651\) −0.768981 −0.0301387
\(652\) 0 0
\(653\) 2.78120 0.108837 0.0544183 0.998518i \(-0.482670\pi\)
0.0544183 + 0.998518i \(0.482670\pi\)
\(654\) 0 0
\(655\) −63.1206 −2.46632
\(656\) 0 0
\(657\) −4.72821 −0.184465
\(658\) 0 0
\(659\) −4.82839 −0.188087 −0.0940436 0.995568i \(-0.529979\pi\)
−0.0940436 + 0.995568i \(0.529979\pi\)
\(660\) 0 0
\(661\) 22.7121 0.883399 0.441699 0.897163i \(-0.354376\pi\)
0.441699 + 0.897163i \(0.354376\pi\)
\(662\) 0 0
\(663\) 11.4336 0.444044
\(664\) 0 0
\(665\) 10.7909 0.418454
\(666\) 0 0
\(667\) −3.29917 −0.127744
\(668\) 0 0
\(669\) −5.68649 −0.219852
\(670\) 0 0
\(671\) −10.1936 −0.393519
\(672\) 0 0
\(673\) 12.4100 0.478370 0.239185 0.970974i \(-0.423120\pi\)
0.239185 + 0.970974i \(0.423120\pi\)
\(674\) 0 0
\(675\) −12.4047 −0.477459
\(676\) 0 0
\(677\) −12.5670 −0.482990 −0.241495 0.970402i \(-0.577638\pi\)
−0.241495 + 0.970402i \(0.577638\pi\)
\(678\) 0 0
\(679\) 14.3686 0.551418
\(680\) 0 0
\(681\) −2.42644 −0.0929815
\(682\) 0 0
\(683\) 2.76729 0.105888 0.0529438 0.998597i \(-0.483140\pi\)
0.0529438 + 0.998597i \(0.483140\pi\)
\(684\) 0 0
\(685\) −39.9819 −1.52763
\(686\) 0 0
\(687\) 1.72002 0.0656230
\(688\) 0 0
\(689\) −20.5635 −0.783408
\(690\) 0 0
\(691\) 28.2383 1.07424 0.537118 0.843507i \(-0.319513\pi\)
0.537118 + 0.843507i \(0.319513\pi\)
\(692\) 0 0
\(693\) 8.31875 0.316003
\(694\) 0 0
\(695\) −59.8673 −2.27090
\(696\) 0 0
\(697\) −55.4551 −2.10051
\(698\) 0 0
\(699\) −0.688030 −0.0260237
\(700\) 0 0
\(701\) −13.0454 −0.492716 −0.246358 0.969179i \(-0.579234\pi\)
−0.246358 + 0.969179i \(0.579234\pi\)
\(702\) 0 0
\(703\) −10.2337 −0.385971
\(704\) 0 0
\(705\) 7.95025 0.299424
\(706\) 0 0
\(707\) −12.4897 −0.469722
\(708\) 0 0
\(709\) −12.3975 −0.465597 −0.232799 0.972525i \(-0.574788\pi\)
−0.232799 + 0.972525i \(0.574788\pi\)
\(710\) 0 0
\(711\) 9.87646 0.370396
\(712\) 0 0
\(713\) 11.2705 0.422085
\(714\) 0 0
\(715\) 48.0208 1.79587
\(716\) 0 0
\(717\) 1.45133 0.0542007
\(718\) 0 0
\(719\) 19.0452 0.710266 0.355133 0.934816i \(-0.384436\pi\)
0.355133 + 0.934816i \(0.384436\pi\)
\(720\) 0 0
\(721\) 8.77186 0.326681
\(722\) 0 0
\(723\) −5.27672 −0.196243
\(724\) 0 0
\(725\) 4.56176 0.169420
\(726\) 0 0
\(727\) 8.34849 0.309628 0.154814 0.987944i \(-0.450522\pi\)
0.154814 + 0.987944i \(0.450522\pi\)
\(728\) 0 0
\(729\) −21.4501 −0.794447
\(730\) 0 0
\(731\) 6.24882 0.231121
\(732\) 0 0
\(733\) 41.2981 1.52538 0.762691 0.646763i \(-0.223878\pi\)
0.762691 + 0.646763i \(0.223878\pi\)
\(734\) 0 0
\(735\) 6.65281 0.245393
\(736\) 0 0
\(737\) −37.3615 −1.37623
\(738\) 0 0
\(739\) −24.6059 −0.905144 −0.452572 0.891728i \(-0.649494\pi\)
−0.452572 + 0.891728i \(0.649494\pi\)
\(740\) 0 0
\(741\) −5.11486 −0.187899
\(742\) 0 0
\(743\) −26.6199 −0.976591 −0.488295 0.872678i \(-0.662381\pi\)
−0.488295 + 0.872678i \(0.662381\pi\)
\(744\) 0 0
\(745\) −73.8345 −2.70509
\(746\) 0 0
\(747\) −19.4600 −0.712004
\(748\) 0 0
\(749\) −9.49519 −0.346947
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −3.69689 −0.134722
\(754\) 0 0
\(755\) −58.3172 −2.12238
\(756\) 0 0
\(757\) 27.3819 0.995212 0.497606 0.867403i \(-0.334213\pi\)
0.497606 + 0.867403i \(0.334213\pi\)
\(758\) 0 0
\(759\) 4.45999 0.161888
\(760\) 0 0
\(761\) −40.8639 −1.48132 −0.740658 0.671882i \(-0.765486\pi\)
−0.740658 + 0.671882i \(0.765486\pi\)
\(762\) 0 0
\(763\) 7.13817 0.258419
\(764\) 0 0
\(765\) 71.1673 2.57306
\(766\) 0 0
\(767\) −41.6421 −1.50361
\(768\) 0 0
\(769\) 21.6250 0.779817 0.389908 0.920854i \(-0.372507\pi\)
0.389908 + 0.920854i \(0.372507\pi\)
\(770\) 0 0
\(771\) −7.19424 −0.259094
\(772\) 0 0
\(773\) 40.3624 1.45174 0.725868 0.687834i \(-0.241438\pi\)
0.725868 + 0.687834i \(0.241438\pi\)
\(774\) 0 0
\(775\) −15.5838 −0.559786
\(776\) 0 0
\(777\) 1.00553 0.0360733
\(778\) 0 0
\(779\) 24.8080 0.888839
\(780\) 0 0
\(781\) 1.11838 0.0400188
\(782\) 0 0
\(783\) −1.35254 −0.0483358
\(784\) 0 0
\(785\) −48.2245 −1.72121
\(786\) 0 0
\(787\) 33.4325 1.19174 0.595870 0.803081i \(-0.296808\pi\)
0.595870 + 0.803081i \(0.296808\pi\)
\(788\) 0 0
\(789\) −4.33551 −0.154348
\(790\) 0 0
\(791\) 0.956918 0.0340241
\(792\) 0 0
\(793\) 16.8353 0.597837
\(794\) 0 0
\(795\) 4.68211 0.166057
\(796\) 0 0
\(797\) 25.6478 0.908492 0.454246 0.890876i \(-0.349909\pi\)
0.454246 + 0.890876i \(0.349909\pi\)
\(798\) 0 0
\(799\) −52.3919 −1.85349
\(800\) 0 0
\(801\) −8.28155 −0.292614
\(802\) 0 0
\(803\) −4.78710 −0.168933
\(804\) 0 0
\(805\) 15.5400 0.547713
\(806\) 0 0
\(807\) 0.764898 0.0269257
\(808\) 0 0
\(809\) 32.0703 1.12753 0.563766 0.825935i \(-0.309352\pi\)
0.563766 + 0.825935i \(0.309352\pi\)
\(810\) 0 0
\(811\) 25.7578 0.904479 0.452240 0.891896i \(-0.350625\pi\)
0.452240 + 0.891896i \(0.350625\pi\)
\(812\) 0 0
\(813\) 0.286126 0.0100349
\(814\) 0 0
\(815\) 43.0172 1.50683
\(816\) 0 0
\(817\) −2.79543 −0.0977997
\(818\) 0 0
\(819\) −13.7389 −0.480075
\(820\) 0 0
\(821\) 1.80881 0.0631281 0.0315640 0.999502i \(-0.489951\pi\)
0.0315640 + 0.999502i \(0.489951\pi\)
\(822\) 0 0
\(823\) −5.42577 −0.189130 −0.0945652 0.995519i \(-0.530146\pi\)
−0.0945652 + 0.995519i \(0.530146\pi\)
\(824\) 0 0
\(825\) −6.16683 −0.214701
\(826\) 0 0
\(827\) 0.890182 0.0309547 0.0154773 0.999880i \(-0.495073\pi\)
0.0154773 + 0.999880i \(0.495073\pi\)
\(828\) 0 0
\(829\) −7.56934 −0.262894 −0.131447 0.991323i \(-0.541962\pi\)
−0.131447 + 0.991323i \(0.541962\pi\)
\(830\) 0 0
\(831\) −0.791589 −0.0274599
\(832\) 0 0
\(833\) −43.8418 −1.51903
\(834\) 0 0
\(835\) −47.0724 −1.62901
\(836\) 0 0
\(837\) 4.62051 0.159708
\(838\) 0 0
\(839\) 2.64242 0.0912266 0.0456133 0.998959i \(-0.485476\pi\)
0.0456133 + 0.998959i \(0.485476\pi\)
\(840\) 0 0
\(841\) −28.5026 −0.982849
\(842\) 0 0
\(843\) 5.44625 0.187579
\(844\) 0 0
\(845\) −35.2846 −1.21383
\(846\) 0 0
\(847\) −2.36805 −0.0813673
\(848\) 0 0
\(849\) 1.85389 0.0636254
\(850\) 0 0
\(851\) −14.7376 −0.505197
\(852\) 0 0
\(853\) −38.9393 −1.33326 −0.666629 0.745390i \(-0.732263\pi\)
−0.666629 + 0.745390i \(0.732263\pi\)
\(854\) 0 0
\(855\) −31.8369 −1.08880
\(856\) 0 0
\(857\) 28.6786 0.979644 0.489822 0.871823i \(-0.337062\pi\)
0.489822 + 0.871823i \(0.337062\pi\)
\(858\) 0 0
\(859\) 54.5112 1.85990 0.929948 0.367690i \(-0.119851\pi\)
0.929948 + 0.367690i \(0.119851\pi\)
\(860\) 0 0
\(861\) −2.43756 −0.0830718
\(862\) 0 0
\(863\) −37.5516 −1.27827 −0.639136 0.769094i \(-0.720708\pi\)
−0.639136 + 0.769094i \(0.720708\pi\)
\(864\) 0 0
\(865\) −8.94012 −0.303973
\(866\) 0 0
\(867\) 11.6244 0.394786
\(868\) 0 0
\(869\) 9.99948 0.339209
\(870\) 0 0
\(871\) 61.7045 2.09078
\(872\) 0 0
\(873\) −42.3924 −1.43477
\(874\) 0 0
\(875\) −4.87739 −0.164886
\(876\) 0 0
\(877\) −30.0598 −1.01505 −0.507523 0.861638i \(-0.669439\pi\)
−0.507523 + 0.861638i \(0.669439\pi\)
\(878\) 0 0
\(879\) 10.4966 0.354043
\(880\) 0 0
\(881\) −11.3371 −0.381958 −0.190979 0.981594i \(-0.561166\pi\)
−0.190979 + 0.981594i \(0.561166\pi\)
\(882\) 0 0
\(883\) 5.23356 0.176123 0.0880617 0.996115i \(-0.471933\pi\)
0.0880617 + 0.996115i \(0.471933\pi\)
\(884\) 0 0
\(885\) 9.48150 0.318717
\(886\) 0 0
\(887\) 18.1560 0.609618 0.304809 0.952413i \(-0.401407\pi\)
0.304809 + 0.952413i \(0.401407\pi\)
\(888\) 0 0
\(889\) −18.3111 −0.614136
\(890\) 0 0
\(891\) −23.6125 −0.791050
\(892\) 0 0
\(893\) 23.4377 0.784312
\(894\) 0 0
\(895\) −66.1546 −2.21130
\(896\) 0 0
\(897\) −7.36592 −0.245941
\(898\) 0 0
\(899\) −1.69916 −0.0566702
\(900\) 0 0
\(901\) −30.8550 −1.02793
\(902\) 0 0
\(903\) 0.274671 0.00914046
\(904\) 0 0
\(905\) −58.3499 −1.93962
\(906\) 0 0
\(907\) −58.5778 −1.94504 −0.972522 0.232812i \(-0.925207\pi\)
−0.972522 + 0.232812i \(0.925207\pi\)
\(908\) 0 0
\(909\) 36.8488 1.22220
\(910\) 0 0
\(911\) −27.5561 −0.912975 −0.456488 0.889730i \(-0.650893\pi\)
−0.456488 + 0.889730i \(0.650893\pi\)
\(912\) 0 0
\(913\) −19.7024 −0.652053
\(914\) 0 0
\(915\) −3.83322 −0.126722
\(916\) 0 0
\(917\) 18.2839 0.603787
\(918\) 0 0
\(919\) 38.1780 1.25938 0.629688 0.776848i \(-0.283183\pi\)
0.629688 + 0.776848i \(0.283183\pi\)
\(920\) 0 0
\(921\) −0.302094 −0.00995433
\(922\) 0 0
\(923\) −1.84706 −0.0607968
\(924\) 0 0
\(925\) 20.3776 0.670012
\(926\) 0 0
\(927\) −25.8800 −0.850011
\(928\) 0 0
\(929\) 19.4504 0.638148 0.319074 0.947730i \(-0.396628\pi\)
0.319074 + 0.947730i \(0.396628\pi\)
\(930\) 0 0
\(931\) 19.6128 0.642783
\(932\) 0 0
\(933\) 1.98317 0.0649262
\(934\) 0 0
\(935\) 72.0537 2.35641
\(936\) 0 0
\(937\) −46.0860 −1.50556 −0.752782 0.658270i \(-0.771288\pi\)
−0.752782 + 0.658270i \(0.771288\pi\)
\(938\) 0 0
\(939\) −9.27181 −0.302574
\(940\) 0 0
\(941\) 32.3167 1.05349 0.526747 0.850022i \(-0.323411\pi\)
0.526747 + 0.850022i \(0.323411\pi\)
\(942\) 0 0
\(943\) 35.7260 1.16340
\(944\) 0 0
\(945\) 6.37083 0.207243
\(946\) 0 0
\(947\) −24.9224 −0.809870 −0.404935 0.914345i \(-0.632706\pi\)
−0.404935 + 0.914345i \(0.632706\pi\)
\(948\) 0 0
\(949\) 7.90616 0.256645
\(950\) 0 0
\(951\) 0.805841 0.0261312
\(952\) 0 0
\(953\) 54.6130 1.76909 0.884544 0.466456i \(-0.154469\pi\)
0.884544 + 0.466456i \(0.154469\pi\)
\(954\) 0 0
\(955\) −39.0019 −1.26207
\(956\) 0 0
\(957\) −0.672394 −0.0217354
\(958\) 0 0
\(959\) 11.5814 0.373983
\(960\) 0 0
\(961\) −25.1954 −0.812754
\(962\) 0 0
\(963\) 28.0141 0.902741
\(964\) 0 0
\(965\) 18.0195 0.580069
\(966\) 0 0
\(967\) 37.0859 1.19260 0.596301 0.802761i \(-0.296637\pi\)
0.596301 + 0.802761i \(0.296637\pi\)
\(968\) 0 0
\(969\) −7.67469 −0.246547
\(970\) 0 0
\(971\) −47.6621 −1.52955 −0.764776 0.644297i \(-0.777150\pi\)
−0.764776 + 0.644297i \(0.777150\pi\)
\(972\) 0 0
\(973\) 17.3415 0.555944
\(974\) 0 0
\(975\) 10.1848 0.326176
\(976\) 0 0
\(977\) −40.9441 −1.30992 −0.654960 0.755664i \(-0.727314\pi\)
−0.654960 + 0.755664i \(0.727314\pi\)
\(978\) 0 0
\(979\) −8.38470 −0.267976
\(980\) 0 0
\(981\) −21.0600 −0.672396
\(982\) 0 0
\(983\) 16.1264 0.514352 0.257176 0.966365i \(-0.417208\pi\)
0.257176 + 0.966365i \(0.417208\pi\)
\(984\) 0 0
\(985\) −36.9988 −1.17888
\(986\) 0 0
\(987\) −2.30292 −0.0733026
\(988\) 0 0
\(989\) −4.02570 −0.128010
\(990\) 0 0
\(991\) 48.7527 1.54868 0.774340 0.632770i \(-0.218082\pi\)
0.774340 + 0.632770i \(0.218082\pi\)
\(992\) 0 0
\(993\) −3.35728 −0.106540
\(994\) 0 0
\(995\) −42.9467 −1.36150
\(996\) 0 0
\(997\) 17.8374 0.564917 0.282459 0.959279i \(-0.408850\pi\)
0.282459 + 0.959279i \(0.408850\pi\)
\(998\) 0 0
\(999\) −6.04186 −0.191156
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 \(a_p\))