Properties

Label 8008.2.a.p.1.8
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(2.24883\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.24883 q^{3} -0.903831 q^{5} -1.00000 q^{7} +2.05724 q^{9} +O(q^{10})\) \(q+2.24883 q^{3} -0.903831 q^{5} -1.00000 q^{7} +2.05724 q^{9} +1.00000 q^{11} +1.00000 q^{13} -2.03256 q^{15} +6.24184 q^{17} -3.18001 q^{19} -2.24883 q^{21} -3.89934 q^{23} -4.18309 q^{25} -2.12010 q^{27} -7.45322 q^{29} -5.90291 q^{31} +2.24883 q^{33} +0.903831 q^{35} -5.53086 q^{37} +2.24883 q^{39} +1.74830 q^{41} +1.93088 q^{43} -1.85940 q^{45} +6.48238 q^{47} +1.00000 q^{49} +14.0368 q^{51} -5.50070 q^{53} -0.903831 q^{55} -7.15130 q^{57} +4.02967 q^{59} -9.49947 q^{61} -2.05724 q^{63} -0.903831 q^{65} +3.09877 q^{67} -8.76896 q^{69} +7.68736 q^{71} -7.41380 q^{73} -9.40707 q^{75} -1.00000 q^{77} -11.6456 q^{79} -10.9395 q^{81} -5.15710 q^{83} -5.64157 q^{85} -16.7610 q^{87} -6.64006 q^{89} -1.00000 q^{91} -13.2747 q^{93} +2.87419 q^{95} -7.18680 q^{97} +2.05724 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + O(q^{10}) \) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + 9q^{11} + 9q^{13} - 9q^{15} - 11q^{17} + 10q^{19} - q^{21} - 14q^{23} - q^{25} - 5q^{27} - 10q^{29} + 5q^{31} + q^{33} + 4q^{35} - 16q^{37} + q^{39} + 2q^{41} + 4q^{43} - 30q^{45} + 9q^{49} + 3q^{51} - 23q^{53} - 4q^{55} + 14q^{57} + 9q^{59} - 14q^{61} - 4q^{63} - 4q^{65} + 8q^{67} - 26q^{69} - 20q^{71} - 23q^{73} + 32q^{75} - 9q^{77} + 2q^{79} - 11q^{81} - 9q^{83} - 3q^{85} - 7q^{87} - 6q^{89} - 9q^{91} - 19q^{93} - 4q^{95} - 3q^{97} + 4q^{99} + O(q^{100}) \)

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
\(3\) 2.24883 1.29836 0.649182 0.760633i \(-0.275111\pi\)
0.649182 + 0.760633i \(0.275111\pi\)
\(4\) 0 0
\(5\) −0.903831 −0.404205 −0.202103 0.979364i \(-0.564777\pi\)
−0.202103 + 0.979364i \(0.564777\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 2.05724 0.685748
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −2.03256 −0.524806
\(16\) 0 0
\(17\) 6.24184 1.51387 0.756934 0.653491i \(-0.226696\pi\)
0.756934 + 0.653491i \(0.226696\pi\)
\(18\) 0 0
\(19\) −3.18001 −0.729544 −0.364772 0.931097i \(-0.618853\pi\)
−0.364772 + 0.931097i \(0.618853\pi\)
\(20\) 0 0
\(21\) −2.24883 −0.490735
\(22\) 0 0
\(23\) −3.89934 −0.813068 −0.406534 0.913636i \(-0.633263\pi\)
−0.406534 + 0.913636i \(0.633263\pi\)
\(24\) 0 0
\(25\) −4.18309 −0.836618
\(26\) 0 0
\(27\) −2.12010 −0.408013
\(28\) 0 0
\(29\) −7.45322 −1.38403 −0.692015 0.721884i \(-0.743277\pi\)
−0.692015 + 0.721884i \(0.743277\pi\)
\(30\) 0 0
\(31\) −5.90291 −1.06019 −0.530097 0.847937i \(-0.677845\pi\)
−0.530097 + 0.847937i \(0.677845\pi\)
\(32\) 0 0
\(33\) 2.24883 0.391471
\(34\) 0 0
\(35\) 0.903831 0.152775
\(36\) 0 0
\(37\) −5.53086 −0.909269 −0.454634 0.890678i \(-0.650230\pi\)
−0.454634 + 0.890678i \(0.650230\pi\)
\(38\) 0 0
\(39\) 2.24883 0.360101
\(40\) 0 0
\(41\) 1.74830 0.273038 0.136519 0.990637i \(-0.456408\pi\)
0.136519 + 0.990637i \(0.456408\pi\)
\(42\) 0 0
\(43\) 1.93088 0.294456 0.147228 0.989103i \(-0.452965\pi\)
0.147228 + 0.989103i \(0.452965\pi\)
\(44\) 0 0
\(45\) −1.85940 −0.277183
\(46\) 0 0
\(47\) 6.48238 0.945552 0.472776 0.881183i \(-0.343252\pi\)
0.472776 + 0.881183i \(0.343252\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 14.0368 1.96555
\(52\) 0 0
\(53\) −5.50070 −0.755579 −0.377789 0.925892i \(-0.623316\pi\)
−0.377789 + 0.925892i \(0.623316\pi\)
\(54\) 0 0
\(55\) −0.903831 −0.121873
\(56\) 0 0
\(57\) −7.15130 −0.947213
\(58\) 0 0
\(59\) 4.02967 0.524618 0.262309 0.964984i \(-0.415516\pi\)
0.262309 + 0.964984i \(0.415516\pi\)
\(60\) 0 0
\(61\) −9.49947 −1.21628 −0.608141 0.793829i \(-0.708084\pi\)
−0.608141 + 0.793829i \(0.708084\pi\)
\(62\) 0 0
\(63\) −2.05724 −0.259188
\(64\) 0 0
\(65\) −0.903831 −0.112106
\(66\) 0 0
\(67\) 3.09877 0.378575 0.189288 0.981922i \(-0.439382\pi\)
0.189288 + 0.981922i \(0.439382\pi\)
\(68\) 0 0
\(69\) −8.76896 −1.05566
\(70\) 0 0
\(71\) 7.68736 0.912322 0.456161 0.889897i \(-0.349224\pi\)
0.456161 + 0.889897i \(0.349224\pi\)
\(72\) 0 0
\(73\) −7.41380 −0.867720 −0.433860 0.900980i \(-0.642849\pi\)
−0.433860 + 0.900980i \(0.642849\pi\)
\(74\) 0 0
\(75\) −9.40707 −1.08623
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −11.6456 −1.31023 −0.655116 0.755528i \(-0.727380\pi\)
−0.655116 + 0.755528i \(0.727380\pi\)
\(80\) 0 0
\(81\) −10.9395 −1.21550
\(82\) 0 0
\(83\) −5.15710 −0.566065 −0.283033 0.959110i \(-0.591340\pi\)
−0.283033 + 0.959110i \(0.591340\pi\)
\(84\) 0 0
\(85\) −5.64157 −0.611914
\(86\) 0 0
\(87\) −16.7610 −1.79697
\(88\) 0 0
\(89\) −6.64006 −0.703845 −0.351923 0.936029i \(-0.614472\pi\)
−0.351923 + 0.936029i \(0.614472\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −13.2747 −1.37652
\(94\) 0 0
\(95\) 2.87419 0.294886
\(96\) 0 0
\(97\) −7.18680 −0.729709 −0.364855 0.931064i \(-0.618881\pi\)
−0.364855 + 0.931064i \(0.618881\pi\)
\(98\) 0 0
\(99\) 2.05724 0.206761
\(100\) 0 0
\(101\) 10.2582 1.02073 0.510366 0.859957i \(-0.329510\pi\)
0.510366 + 0.859957i \(0.329510\pi\)
\(102\) 0 0
\(103\) −15.7974 −1.55657 −0.778284 0.627913i \(-0.783910\pi\)
−0.778284 + 0.627913i \(0.783910\pi\)
\(104\) 0 0
\(105\) 2.03256 0.198358
\(106\) 0 0
\(107\) 9.13768 0.883372 0.441686 0.897170i \(-0.354380\pi\)
0.441686 + 0.897170i \(0.354380\pi\)
\(108\) 0 0
\(109\) 10.8358 1.03788 0.518939 0.854811i \(-0.326327\pi\)
0.518939 + 0.854811i \(0.326327\pi\)
\(110\) 0 0
\(111\) −12.4380 −1.18056
\(112\) 0 0
\(113\) 15.4913 1.45730 0.728648 0.684889i \(-0.240149\pi\)
0.728648 + 0.684889i \(0.240149\pi\)
\(114\) 0 0
\(115\) 3.52434 0.328647
\(116\) 0 0
\(117\) 2.05724 0.190192
\(118\) 0 0
\(119\) −6.24184 −0.572188
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 3.93163 0.354503
\(124\) 0 0
\(125\) 8.29996 0.742371
\(126\) 0 0
\(127\) −4.77207 −0.423452 −0.211726 0.977329i \(-0.567909\pi\)
−0.211726 + 0.977329i \(0.567909\pi\)
\(128\) 0 0
\(129\) 4.34222 0.382312
\(130\) 0 0
\(131\) −12.3855 −1.08212 −0.541062 0.840982i \(-0.681978\pi\)
−0.541062 + 0.840982i \(0.681978\pi\)
\(132\) 0 0
\(133\) 3.18001 0.275742
\(134\) 0 0
\(135\) 1.91621 0.164921
\(136\) 0 0
\(137\) −5.16125 −0.440955 −0.220478 0.975392i \(-0.570762\pi\)
−0.220478 + 0.975392i \(0.570762\pi\)
\(138\) 0 0
\(139\) 8.79830 0.746262 0.373131 0.927779i \(-0.378284\pi\)
0.373131 + 0.927779i \(0.378284\pi\)
\(140\) 0 0
\(141\) 14.5778 1.22767
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 6.73645 0.559432
\(146\) 0 0
\(147\) 2.24883 0.185481
\(148\) 0 0
\(149\) 12.2202 1.00112 0.500558 0.865703i \(-0.333128\pi\)
0.500558 + 0.865703i \(0.333128\pi\)
\(150\) 0 0
\(151\) 17.5452 1.42781 0.713903 0.700245i \(-0.246926\pi\)
0.713903 + 0.700245i \(0.246926\pi\)
\(152\) 0 0
\(153\) 12.8410 1.03813
\(154\) 0 0
\(155\) 5.33524 0.428536
\(156\) 0 0
\(157\) 7.40036 0.590613 0.295307 0.955403i \(-0.404578\pi\)
0.295307 + 0.955403i \(0.404578\pi\)
\(158\) 0 0
\(159\) −12.3701 −0.981016
\(160\) 0 0
\(161\) 3.89934 0.307311
\(162\) 0 0
\(163\) 14.8288 1.16148 0.580741 0.814088i \(-0.302763\pi\)
0.580741 + 0.814088i \(0.302763\pi\)
\(164\) 0 0
\(165\) −2.03256 −0.158235
\(166\) 0 0
\(167\) −20.5373 −1.58923 −0.794613 0.607117i \(-0.792326\pi\)
−0.794613 + 0.607117i \(0.792326\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −6.54205 −0.500283
\(172\) 0 0
\(173\) −11.5283 −0.876480 −0.438240 0.898858i \(-0.644398\pi\)
−0.438240 + 0.898858i \(0.644398\pi\)
\(174\) 0 0
\(175\) 4.18309 0.316212
\(176\) 0 0
\(177\) 9.06204 0.681145
\(178\) 0 0
\(179\) −16.0348 −1.19850 −0.599250 0.800562i \(-0.704534\pi\)
−0.599250 + 0.800562i \(0.704534\pi\)
\(180\) 0 0
\(181\) −23.3798 −1.73781 −0.868903 0.494982i \(-0.835175\pi\)
−0.868903 + 0.494982i \(0.835175\pi\)
\(182\) 0 0
\(183\) −21.3627 −1.57918
\(184\) 0 0
\(185\) 4.99897 0.367531
\(186\) 0 0
\(187\) 6.24184 0.456448
\(188\) 0 0
\(189\) 2.12010 0.154215
\(190\) 0 0
\(191\) −9.17954 −0.664208 −0.332104 0.943243i \(-0.607758\pi\)
−0.332104 + 0.943243i \(0.607758\pi\)
\(192\) 0 0
\(193\) 6.87634 0.494970 0.247485 0.968892i \(-0.420396\pi\)
0.247485 + 0.968892i \(0.420396\pi\)
\(194\) 0 0
\(195\) −2.03256 −0.145555
\(196\) 0 0
\(197\) −20.9814 −1.49486 −0.747431 0.664339i \(-0.768713\pi\)
−0.747431 + 0.664339i \(0.768713\pi\)
\(198\) 0 0
\(199\) 4.74468 0.336341 0.168171 0.985758i \(-0.446214\pi\)
0.168171 + 0.985758i \(0.446214\pi\)
\(200\) 0 0
\(201\) 6.96862 0.491528
\(202\) 0 0
\(203\) 7.45322 0.523114
\(204\) 0 0
\(205\) −1.58017 −0.110364
\(206\) 0 0
\(207\) −8.02189 −0.557560
\(208\) 0 0
\(209\) −3.18001 −0.219966
\(210\) 0 0
\(211\) −18.1416 −1.24892 −0.624459 0.781058i \(-0.714680\pi\)
−0.624459 + 0.781058i \(0.714680\pi\)
\(212\) 0 0
\(213\) 17.2876 1.18453
\(214\) 0 0
\(215\) −1.74519 −0.119021
\(216\) 0 0
\(217\) 5.90291 0.400716
\(218\) 0 0
\(219\) −16.6724 −1.12662
\(220\) 0 0
\(221\) 6.24184 0.419871
\(222\) 0 0
\(223\) 13.4791 0.902625 0.451313 0.892366i \(-0.350956\pi\)
0.451313 + 0.892366i \(0.350956\pi\)
\(224\) 0 0
\(225\) −8.60564 −0.573709
\(226\) 0 0
\(227\) 8.81639 0.585164 0.292582 0.956240i \(-0.405485\pi\)
0.292582 + 0.956240i \(0.405485\pi\)
\(228\) 0 0
\(229\) −7.45110 −0.492383 −0.246191 0.969221i \(-0.579179\pi\)
−0.246191 + 0.969221i \(0.579179\pi\)
\(230\) 0 0
\(231\) −2.24883 −0.147962
\(232\) 0 0
\(233\) −3.47202 −0.227460 −0.113730 0.993512i \(-0.536280\pi\)
−0.113730 + 0.993512i \(0.536280\pi\)
\(234\) 0 0
\(235\) −5.85897 −0.382197
\(236\) 0 0
\(237\) −26.1890 −1.70116
\(238\) 0 0
\(239\) −17.2438 −1.11541 −0.557704 0.830040i \(-0.688318\pi\)
−0.557704 + 0.830040i \(0.688318\pi\)
\(240\) 0 0
\(241\) −18.1758 −1.17080 −0.585402 0.810743i \(-0.699063\pi\)
−0.585402 + 0.810743i \(0.699063\pi\)
\(242\) 0 0
\(243\) −18.2407 −1.17014
\(244\) 0 0
\(245\) −0.903831 −0.0577436
\(246\) 0 0
\(247\) −3.18001 −0.202339
\(248\) 0 0
\(249\) −11.5975 −0.734959
\(250\) 0 0
\(251\) 25.5228 1.61099 0.805493 0.592605i \(-0.201900\pi\)
0.805493 + 0.592605i \(0.201900\pi\)
\(252\) 0 0
\(253\) −3.89934 −0.245149
\(254\) 0 0
\(255\) −12.6869 −0.794486
\(256\) 0 0
\(257\) −28.7020 −1.79038 −0.895190 0.445685i \(-0.852960\pi\)
−0.895190 + 0.445685i \(0.852960\pi\)
\(258\) 0 0
\(259\) 5.53086 0.343671
\(260\) 0 0
\(261\) −15.3331 −0.949095
\(262\) 0 0
\(263\) −4.38449 −0.270359 −0.135180 0.990821i \(-0.543161\pi\)
−0.135180 + 0.990821i \(0.543161\pi\)
\(264\) 0 0
\(265\) 4.97170 0.305409
\(266\) 0 0
\(267\) −14.9324 −0.913847
\(268\) 0 0
\(269\) 7.19130 0.438461 0.219231 0.975673i \(-0.429645\pi\)
0.219231 + 0.975673i \(0.429645\pi\)
\(270\) 0 0
\(271\) 17.1267 1.04037 0.520187 0.854053i \(-0.325862\pi\)
0.520187 + 0.854053i \(0.325862\pi\)
\(272\) 0 0
\(273\) −2.24883 −0.136105
\(274\) 0 0
\(275\) −4.18309 −0.252250
\(276\) 0 0
\(277\) −2.61283 −0.156990 −0.0784950 0.996915i \(-0.525011\pi\)
−0.0784950 + 0.996915i \(0.525011\pi\)
\(278\) 0 0
\(279\) −12.1437 −0.727027
\(280\) 0 0
\(281\) −2.10599 −0.125633 −0.0628165 0.998025i \(-0.520008\pi\)
−0.0628165 + 0.998025i \(0.520008\pi\)
\(282\) 0 0
\(283\) 4.85673 0.288703 0.144351 0.989526i \(-0.453890\pi\)
0.144351 + 0.989526i \(0.453890\pi\)
\(284\) 0 0
\(285\) 6.46357 0.382869
\(286\) 0 0
\(287\) −1.74830 −0.103199
\(288\) 0 0
\(289\) 21.9605 1.29180
\(290\) 0 0
\(291\) −16.1619 −0.947428
\(292\) 0 0
\(293\) −9.09597 −0.531392 −0.265696 0.964057i \(-0.585602\pi\)
−0.265696 + 0.964057i \(0.585602\pi\)
\(294\) 0 0
\(295\) −3.64214 −0.212053
\(296\) 0 0
\(297\) −2.12010 −0.123021
\(298\) 0 0
\(299\) −3.89934 −0.225505
\(300\) 0 0
\(301\) −1.93088 −0.111294
\(302\) 0 0
\(303\) 23.0690 1.32528
\(304\) 0 0
\(305\) 8.58591 0.491628
\(306\) 0 0
\(307\) −31.2366 −1.78277 −0.891383 0.453251i \(-0.850264\pi\)
−0.891383 + 0.453251i \(0.850264\pi\)
\(308\) 0 0
\(309\) −35.5258 −2.02099
\(310\) 0 0
\(311\) −27.8100 −1.57696 −0.788481 0.615059i \(-0.789132\pi\)
−0.788481 + 0.615059i \(0.789132\pi\)
\(312\) 0 0
\(313\) −7.79549 −0.440627 −0.220314 0.975429i \(-0.570708\pi\)
−0.220314 + 0.975429i \(0.570708\pi\)
\(314\) 0 0
\(315\) 1.85940 0.104765
\(316\) 0 0
\(317\) 24.4193 1.37152 0.685762 0.727826i \(-0.259469\pi\)
0.685762 + 0.727826i \(0.259469\pi\)
\(318\) 0 0
\(319\) −7.45322 −0.417300
\(320\) 0 0
\(321\) 20.5491 1.14694
\(322\) 0 0
\(323\) −19.8491 −1.10443
\(324\) 0 0
\(325\) −4.18309 −0.232036
\(326\) 0 0
\(327\) 24.3678 1.34754
\(328\) 0 0
\(329\) −6.48238 −0.357385
\(330\) 0 0
\(331\) −7.27763 −0.400014 −0.200007 0.979794i \(-0.564097\pi\)
−0.200007 + 0.979794i \(0.564097\pi\)
\(332\) 0 0
\(333\) −11.3783 −0.623529
\(334\) 0 0
\(335\) −2.80077 −0.153022
\(336\) 0 0
\(337\) 14.6862 0.800007 0.400004 0.916514i \(-0.369009\pi\)
0.400004 + 0.916514i \(0.369009\pi\)
\(338\) 0 0
\(339\) 34.8372 1.89210
\(340\) 0 0
\(341\) −5.90291 −0.319661
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 7.92565 0.426703
\(346\) 0 0
\(347\) 16.5963 0.890939 0.445469 0.895297i \(-0.353037\pi\)
0.445469 + 0.895297i \(0.353037\pi\)
\(348\) 0 0
\(349\) −0.874980 −0.0468366 −0.0234183 0.999726i \(-0.507455\pi\)
−0.0234183 + 0.999726i \(0.507455\pi\)
\(350\) 0 0
\(351\) −2.12010 −0.113163
\(352\) 0 0
\(353\) 26.2033 1.39466 0.697331 0.716750i \(-0.254371\pi\)
0.697331 + 0.716750i \(0.254371\pi\)
\(354\) 0 0
\(355\) −6.94807 −0.368765
\(356\) 0 0
\(357\) −14.0368 −0.742909
\(358\) 0 0
\(359\) −8.60660 −0.454239 −0.227120 0.973867i \(-0.572931\pi\)
−0.227120 + 0.973867i \(0.572931\pi\)
\(360\) 0 0
\(361\) −8.88755 −0.467766
\(362\) 0 0
\(363\) 2.24883 0.118033
\(364\) 0 0
\(365\) 6.70082 0.350737
\(366\) 0 0
\(367\) −3.27914 −0.171170 −0.0855848 0.996331i \(-0.527276\pi\)
−0.0855848 + 0.996331i \(0.527276\pi\)
\(368\) 0 0
\(369\) 3.59668 0.187235
\(370\) 0 0
\(371\) 5.50070 0.285582
\(372\) 0 0
\(373\) −26.3670 −1.36523 −0.682615 0.730778i \(-0.739157\pi\)
−0.682615 + 0.730778i \(0.739157\pi\)
\(374\) 0 0
\(375\) 18.6652 0.963867
\(376\) 0 0
\(377\) −7.45322 −0.383861
\(378\) 0 0
\(379\) −20.3220 −1.04387 −0.521935 0.852985i \(-0.674790\pi\)
−0.521935 + 0.852985i \(0.674790\pi\)
\(380\) 0 0
\(381\) −10.7316 −0.549795
\(382\) 0 0
\(383\) 3.69412 0.188761 0.0943804 0.995536i \(-0.469913\pi\)
0.0943804 + 0.995536i \(0.469913\pi\)
\(384\) 0 0
\(385\) 0.903831 0.0460635
\(386\) 0 0
\(387\) 3.97229 0.201923
\(388\) 0 0
\(389\) −12.3981 −0.628608 −0.314304 0.949322i \(-0.601771\pi\)
−0.314304 + 0.949322i \(0.601771\pi\)
\(390\) 0 0
\(391\) −24.3390 −1.23088
\(392\) 0 0
\(393\) −27.8529 −1.40499
\(394\) 0 0
\(395\) 10.5257 0.529603
\(396\) 0 0
\(397\) −13.5349 −0.679296 −0.339648 0.940553i \(-0.610308\pi\)
−0.339648 + 0.940553i \(0.610308\pi\)
\(398\) 0 0
\(399\) 7.15130 0.358013
\(400\) 0 0
\(401\) −20.3061 −1.01404 −0.507020 0.861934i \(-0.669253\pi\)
−0.507020 + 0.861934i \(0.669253\pi\)
\(402\) 0 0
\(403\) −5.90291 −0.294045
\(404\) 0 0
\(405\) 9.88744 0.491311
\(406\) 0 0
\(407\) −5.53086 −0.274155
\(408\) 0 0
\(409\) −15.9099 −0.786692 −0.393346 0.919391i \(-0.628682\pi\)
−0.393346 + 0.919391i \(0.628682\pi\)
\(410\) 0 0
\(411\) −11.6068 −0.572520
\(412\) 0 0
\(413\) −4.02967 −0.198287
\(414\) 0 0
\(415\) 4.66115 0.228807
\(416\) 0 0
\(417\) 19.7859 0.968920
\(418\) 0 0
\(419\) −3.60713 −0.176220 −0.0881100 0.996111i \(-0.528083\pi\)
−0.0881100 + 0.996111i \(0.528083\pi\)
\(420\) 0 0
\(421\) 37.9364 1.84891 0.924455 0.381292i \(-0.124521\pi\)
0.924455 + 0.381292i \(0.124521\pi\)
\(422\) 0 0
\(423\) 13.3358 0.648411
\(424\) 0 0
\(425\) −26.1102 −1.26653
\(426\) 0 0
\(427\) 9.49947 0.459711
\(428\) 0 0
\(429\) 2.24883 0.108575
\(430\) 0 0
\(431\) 13.6439 0.657205 0.328602 0.944468i \(-0.393422\pi\)
0.328602 + 0.944468i \(0.393422\pi\)
\(432\) 0 0
\(433\) 3.93517 0.189112 0.0945560 0.995520i \(-0.469857\pi\)
0.0945560 + 0.995520i \(0.469857\pi\)
\(434\) 0 0
\(435\) 15.1491 0.726346
\(436\) 0 0
\(437\) 12.3999 0.593169
\(438\) 0 0
\(439\) −8.99749 −0.429427 −0.214713 0.976677i \(-0.568882\pi\)
−0.214713 + 0.976677i \(0.568882\pi\)
\(440\) 0 0
\(441\) 2.05724 0.0979640
\(442\) 0 0
\(443\) 11.7651 0.558979 0.279490 0.960149i \(-0.409835\pi\)
0.279490 + 0.960149i \(0.409835\pi\)
\(444\) 0 0
\(445\) 6.00149 0.284498
\(446\) 0 0
\(447\) 27.4811 1.29981
\(448\) 0 0
\(449\) −7.69749 −0.363267 −0.181634 0.983366i \(-0.558138\pi\)
−0.181634 + 0.983366i \(0.558138\pi\)
\(450\) 0 0
\(451\) 1.74830 0.0823241
\(452\) 0 0
\(453\) 39.4561 1.85381
\(454\) 0 0
\(455\) 0.903831 0.0423722
\(456\) 0 0
\(457\) 34.1264 1.59636 0.798182 0.602417i \(-0.205795\pi\)
0.798182 + 0.602417i \(0.205795\pi\)
\(458\) 0 0
\(459\) −13.2333 −0.617678
\(460\) 0 0
\(461\) 30.9635 1.44211 0.721057 0.692875i \(-0.243656\pi\)
0.721057 + 0.692875i \(0.243656\pi\)
\(462\) 0 0
\(463\) −1.61862 −0.0752238 −0.0376119 0.999292i \(-0.511975\pi\)
−0.0376119 + 0.999292i \(0.511975\pi\)
\(464\) 0 0
\(465\) 11.9980 0.556396
\(466\) 0 0
\(467\) 2.82037 0.130511 0.0652557 0.997869i \(-0.479214\pi\)
0.0652557 + 0.997869i \(0.479214\pi\)
\(468\) 0 0
\(469\) −3.09877 −0.143088
\(470\) 0 0
\(471\) 16.6422 0.766831
\(472\) 0 0
\(473\) 1.93088 0.0887820
\(474\) 0 0
\(475\) 13.3023 0.610350
\(476\) 0 0
\(477\) −11.3163 −0.518137
\(478\) 0 0
\(479\) 12.8970 0.589279 0.294639 0.955609i \(-0.404800\pi\)
0.294639 + 0.955609i \(0.404800\pi\)
\(480\) 0 0
\(481\) −5.53086 −0.252186
\(482\) 0 0
\(483\) 8.76896 0.399001
\(484\) 0 0
\(485\) 6.49565 0.294952
\(486\) 0 0
\(487\) 23.1931 1.05098 0.525490 0.850800i \(-0.323882\pi\)
0.525490 + 0.850800i \(0.323882\pi\)
\(488\) 0 0
\(489\) 33.3475 1.50803
\(490\) 0 0
\(491\) −22.4553 −1.01339 −0.506696 0.862125i \(-0.669133\pi\)
−0.506696 + 0.862125i \(0.669133\pi\)
\(492\) 0 0
\(493\) −46.5218 −2.09524
\(494\) 0 0
\(495\) −1.85940 −0.0835738
\(496\) 0 0
\(497\) −7.68736 −0.344825
\(498\) 0 0
\(499\) 6.82022 0.305315 0.152657 0.988279i \(-0.451217\pi\)
0.152657 + 0.988279i \(0.451217\pi\)
\(500\) 0 0
\(501\) −46.1850 −2.06339
\(502\) 0 0
\(503\) −10.2676 −0.457808 −0.228904 0.973449i \(-0.573514\pi\)
−0.228904 + 0.973449i \(0.573514\pi\)
\(504\) 0 0
\(505\) −9.27171 −0.412586
\(506\) 0 0
\(507\) 2.24883 0.0998741
\(508\) 0 0
\(509\) −24.1361 −1.06982 −0.534908 0.844911i \(-0.679654\pi\)
−0.534908 + 0.844911i \(0.679654\pi\)
\(510\) 0 0
\(511\) 7.41380 0.327967
\(512\) 0 0
\(513\) 6.74193 0.297664
\(514\) 0 0
\(515\) 14.2782 0.629173
\(516\) 0 0
\(517\) 6.48238 0.285095
\(518\) 0 0
\(519\) −25.9252 −1.13799
\(520\) 0 0
\(521\) 28.7456 1.25937 0.629684 0.776851i \(-0.283184\pi\)
0.629684 + 0.776851i \(0.283184\pi\)
\(522\) 0 0
\(523\) −1.90369 −0.0832427 −0.0416213 0.999133i \(-0.513252\pi\)
−0.0416213 + 0.999133i \(0.513252\pi\)
\(524\) 0 0
\(525\) 9.40707 0.410558
\(526\) 0 0
\(527\) −36.8450 −1.60500
\(528\) 0 0
\(529\) −7.79515 −0.338920
\(530\) 0 0
\(531\) 8.29001 0.359756
\(532\) 0 0
\(533\) 1.74830 0.0757272
\(534\) 0 0
\(535\) −8.25891 −0.357064
\(536\) 0 0
\(537\) −36.0596 −1.55609
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −22.4335 −0.964491 −0.482245 0.876036i \(-0.660179\pi\)
−0.482245 + 0.876036i \(0.660179\pi\)
\(542\) 0 0
\(543\) −52.5772 −2.25630
\(544\) 0 0
\(545\) −9.79370 −0.419516
\(546\) 0 0
\(547\) 20.1066 0.859695 0.429847 0.902902i \(-0.358567\pi\)
0.429847 + 0.902902i \(0.358567\pi\)
\(548\) 0 0
\(549\) −19.5427 −0.834063
\(550\) 0 0
\(551\) 23.7013 1.00971
\(552\) 0 0
\(553\) 11.6456 0.495221
\(554\) 0 0
\(555\) 11.2418 0.477189
\(556\) 0 0
\(557\) −13.9569 −0.591371 −0.295686 0.955285i \(-0.595548\pi\)
−0.295686 + 0.955285i \(0.595548\pi\)
\(558\) 0 0
\(559\) 1.93088 0.0816675
\(560\) 0 0
\(561\) 14.0368 0.592636
\(562\) 0 0
\(563\) 38.2900 1.61373 0.806867 0.590734i \(-0.201162\pi\)
0.806867 + 0.590734i \(0.201162\pi\)
\(564\) 0 0
\(565\) −14.0015 −0.589047
\(566\) 0 0
\(567\) 10.9395 0.459415
\(568\) 0 0
\(569\) −38.8497 −1.62866 −0.814331 0.580400i \(-0.802896\pi\)
−0.814331 + 0.580400i \(0.802896\pi\)
\(570\) 0 0
\(571\) −15.1303 −0.633185 −0.316592 0.948562i \(-0.602539\pi\)
−0.316592 + 0.948562i \(0.602539\pi\)
\(572\) 0 0
\(573\) −20.6432 −0.862383
\(574\) 0 0
\(575\) 16.3113 0.680228
\(576\) 0 0
\(577\) 19.1643 0.797818 0.398909 0.916990i \(-0.369389\pi\)
0.398909 + 0.916990i \(0.369389\pi\)
\(578\) 0 0
\(579\) 15.4637 0.642651
\(580\) 0 0
\(581\) 5.15710 0.213953
\(582\) 0 0
\(583\) −5.50070 −0.227816
\(584\) 0 0
\(585\) −1.85940 −0.0768767
\(586\) 0 0
\(587\) 28.6383 1.18203 0.591014 0.806661i \(-0.298728\pi\)
0.591014 + 0.806661i \(0.298728\pi\)
\(588\) 0 0
\(589\) 18.7713 0.773459
\(590\) 0 0
\(591\) −47.1836 −1.94087
\(592\) 0 0
\(593\) −5.02360 −0.206295 −0.103147 0.994666i \(-0.532891\pi\)
−0.103147 + 0.994666i \(0.532891\pi\)
\(594\) 0 0
\(595\) 5.64157 0.231282
\(596\) 0 0
\(597\) 10.6700 0.436693
\(598\) 0 0
\(599\) 3.48066 0.142216 0.0711080 0.997469i \(-0.477347\pi\)
0.0711080 + 0.997469i \(0.477347\pi\)
\(600\) 0 0
\(601\) 19.5135 0.795974 0.397987 0.917391i \(-0.369709\pi\)
0.397987 + 0.917391i \(0.369709\pi\)
\(602\) 0 0
\(603\) 6.37493 0.259607
\(604\) 0 0
\(605\) −0.903831 −0.0367459
\(606\) 0 0
\(607\) −0.256535 −0.0104124 −0.00520622 0.999986i \(-0.501657\pi\)
−0.00520622 + 0.999986i \(0.501657\pi\)
\(608\) 0 0
\(609\) 16.7610 0.679192
\(610\) 0 0
\(611\) 6.48238 0.262249
\(612\) 0 0
\(613\) −6.79629 −0.274500 −0.137250 0.990536i \(-0.543826\pi\)
−0.137250 + 0.990536i \(0.543826\pi\)
\(614\) 0 0
\(615\) −3.55353 −0.143292
\(616\) 0 0
\(617\) 2.84201 0.114415 0.0572075 0.998362i \(-0.481780\pi\)
0.0572075 + 0.998362i \(0.481780\pi\)
\(618\) 0 0
\(619\) 27.4698 1.10410 0.552052 0.833809i \(-0.313845\pi\)
0.552052 + 0.833809i \(0.313845\pi\)
\(620\) 0 0
\(621\) 8.26699 0.331743
\(622\) 0 0
\(623\) 6.64006 0.266029
\(624\) 0 0
\(625\) 13.4137 0.536548
\(626\) 0 0
\(627\) −7.15130 −0.285596
\(628\) 0 0
\(629\) −34.5228 −1.37651
\(630\) 0 0
\(631\) 28.1742 1.12160 0.560799 0.827952i \(-0.310494\pi\)
0.560799 + 0.827952i \(0.310494\pi\)
\(632\) 0 0
\(633\) −40.7974 −1.62155
\(634\) 0 0
\(635\) 4.31314 0.171162
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) 15.8148 0.625623
\(640\) 0 0
\(641\) −49.2209 −1.94411 −0.972054 0.234758i \(-0.924570\pi\)
−0.972054 + 0.234758i \(0.924570\pi\)
\(642\) 0 0
\(643\) 30.3937 1.19861 0.599305 0.800521i \(-0.295444\pi\)
0.599305 + 0.800521i \(0.295444\pi\)
\(644\) 0 0
\(645\) −3.92464 −0.154532
\(646\) 0 0
\(647\) 6.68020 0.262626 0.131313 0.991341i \(-0.458081\pi\)
0.131313 + 0.991341i \(0.458081\pi\)
\(648\) 0 0
\(649\) 4.02967 0.158178
\(650\) 0 0
\(651\) 13.2747 0.520275
\(652\) 0 0
\(653\) 41.4104 1.62052 0.810258 0.586073i \(-0.199327\pi\)
0.810258 + 0.586073i \(0.199327\pi\)
\(654\) 0 0
\(655\) 11.1944 0.437401
\(656\) 0 0
\(657\) −15.2520 −0.595037
\(658\) 0 0
\(659\) −50.9177 −1.98347 −0.991736 0.128292i \(-0.959051\pi\)
−0.991736 + 0.128292i \(0.959051\pi\)
\(660\) 0 0
\(661\) 11.9014 0.462912 0.231456 0.972845i \(-0.425651\pi\)
0.231456 + 0.972845i \(0.425651\pi\)
\(662\) 0 0
\(663\) 14.0368 0.545146
\(664\) 0 0
\(665\) −2.87419 −0.111456
\(666\) 0 0
\(667\) 29.0627 1.12531
\(668\) 0 0
\(669\) 30.3122 1.17194
\(670\) 0 0
\(671\) −9.49947 −0.366723
\(672\) 0 0
\(673\) −2.53354 −0.0976609 −0.0488304 0.998807i \(-0.515549\pi\)
−0.0488304 + 0.998807i \(0.515549\pi\)
\(674\) 0 0
\(675\) 8.86857 0.341351
\(676\) 0 0
\(677\) 33.1578 1.27436 0.637178 0.770716i \(-0.280101\pi\)
0.637178 + 0.770716i \(0.280101\pi\)
\(678\) 0 0
\(679\) 7.18680 0.275804
\(680\) 0 0
\(681\) 19.8266 0.759756
\(682\) 0 0
\(683\) 25.0003 0.956610 0.478305 0.878194i \(-0.341251\pi\)
0.478305 + 0.878194i \(0.341251\pi\)
\(684\) 0 0
\(685\) 4.66489 0.178236
\(686\) 0 0
\(687\) −16.7563 −0.639292
\(688\) 0 0
\(689\) −5.50070 −0.209560
\(690\) 0 0
\(691\) 24.4918 0.931712 0.465856 0.884861i \(-0.345747\pi\)
0.465856 + 0.884861i \(0.345747\pi\)
\(692\) 0 0
\(693\) −2.05724 −0.0781482
\(694\) 0 0
\(695\) −7.95218 −0.301643
\(696\) 0 0
\(697\) 10.9126 0.413344
\(698\) 0 0
\(699\) −7.80799 −0.295325
\(700\) 0 0
\(701\) −48.0349 −1.81425 −0.907127 0.420857i \(-0.861729\pi\)
−0.907127 + 0.420857i \(0.861729\pi\)
\(702\) 0 0
\(703\) 17.5882 0.663351
\(704\) 0 0
\(705\) −13.1758 −0.496231
\(706\) 0 0
\(707\) −10.2582 −0.385801
\(708\) 0 0
\(709\) −17.2347 −0.647261 −0.323631 0.946184i \(-0.604904\pi\)
−0.323631 + 0.946184i \(0.604904\pi\)
\(710\) 0 0
\(711\) −23.9578 −0.898489
\(712\) 0 0
\(713\) 23.0175 0.862011
\(714\) 0 0
\(715\) −0.903831 −0.0338014
\(716\) 0 0
\(717\) −38.7784 −1.44821
\(718\) 0 0
\(719\) 42.7531 1.59442 0.797212 0.603700i \(-0.206307\pi\)
0.797212 + 0.603700i \(0.206307\pi\)
\(720\) 0 0
\(721\) 15.7974 0.588327
\(722\) 0 0
\(723\) −40.8743 −1.52013
\(724\) 0 0
\(725\) 31.1775 1.15790
\(726\) 0 0
\(727\) 42.0677 1.56021 0.780103 0.625652i \(-0.215167\pi\)
0.780103 + 0.625652i \(0.215167\pi\)
\(728\) 0 0
\(729\) −8.20194 −0.303776
\(730\) 0 0
\(731\) 12.0522 0.445768
\(732\) 0 0
\(733\) −36.9129 −1.36341 −0.681705 0.731627i \(-0.738761\pi\)
−0.681705 + 0.731627i \(0.738761\pi\)
\(734\) 0 0
\(735\) −2.03256 −0.0749722
\(736\) 0 0
\(737\) 3.09877 0.114145
\(738\) 0 0
\(739\) 9.60434 0.353302 0.176651 0.984274i \(-0.443474\pi\)
0.176651 + 0.984274i \(0.443474\pi\)
\(740\) 0 0
\(741\) −7.15130 −0.262710
\(742\) 0 0
\(743\) 11.8614 0.435153 0.217577 0.976043i \(-0.430185\pi\)
0.217577 + 0.976043i \(0.430185\pi\)
\(744\) 0 0
\(745\) −11.0450 −0.404657
\(746\) 0 0
\(747\) −10.6094 −0.388178
\(748\) 0 0
\(749\) −9.13768 −0.333883
\(750\) 0 0
\(751\) 34.2351 1.24925 0.624627 0.780923i \(-0.285251\pi\)
0.624627 + 0.780923i \(0.285251\pi\)
\(752\) 0 0
\(753\) 57.3965 2.09165
\(754\) 0 0
\(755\) −15.8579 −0.577127
\(756\) 0 0
\(757\) 1.55940 0.0566774 0.0283387 0.999598i \(-0.490978\pi\)
0.0283387 + 0.999598i \(0.490978\pi\)
\(758\) 0 0
\(759\) −8.76896 −0.318293
\(760\) 0 0
\(761\) −2.70245 −0.0979636 −0.0489818 0.998800i \(-0.515598\pi\)
−0.0489818 + 0.998800i \(0.515598\pi\)
\(762\) 0 0
\(763\) −10.8358 −0.392281
\(764\) 0 0
\(765\) −11.6061 −0.419619
\(766\) 0 0
\(767\) 4.02967 0.145503
\(768\) 0 0
\(769\) −25.1828 −0.908116 −0.454058 0.890972i \(-0.650024\pi\)
−0.454058 + 0.890972i \(0.650024\pi\)
\(770\) 0 0
\(771\) −64.5459 −2.32456
\(772\) 0 0
\(773\) −29.9513 −1.07727 −0.538637 0.842538i \(-0.681061\pi\)
−0.538637 + 0.842538i \(0.681061\pi\)
\(774\) 0 0
\(775\) 24.6924 0.886978
\(776\) 0 0
\(777\) 12.4380 0.446210
\(778\) 0 0
\(779\) −5.55960 −0.199193
\(780\) 0 0
\(781\) 7.68736 0.275075
\(782\) 0 0
\(783\) 15.8016 0.564702
\(784\) 0 0
\(785\) −6.68867 −0.238729
\(786\) 0 0
\(787\) 16.2431 0.579002 0.289501 0.957178i \(-0.406511\pi\)
0.289501 + 0.957178i \(0.406511\pi\)
\(788\) 0 0
\(789\) −9.85997 −0.351024
\(790\) 0 0
\(791\) −15.4913 −0.550806
\(792\) 0 0
\(793\) −9.49947 −0.337336
\(794\) 0 0
\(795\) 11.1805 0.396532
\(796\) 0 0
\(797\) −42.5277 −1.50641 −0.753204 0.657787i \(-0.771493\pi\)
−0.753204 + 0.657787i \(0.771493\pi\)
\(798\) 0 0
\(799\) 40.4620 1.43144
\(800\) 0 0
\(801\) −13.6602 −0.482661
\(802\) 0 0
\(803\) −7.41380 −0.261627
\(804\) 0 0
\(805\) −3.52434 −0.124217
\(806\) 0 0
\(807\) 16.1720 0.569282
\(808\) 0 0
\(809\) 51.1758 1.79925 0.899623 0.436666i \(-0.143841\pi\)
0.899623 + 0.436666i \(0.143841\pi\)
\(810\) 0 0
\(811\) −26.9466 −0.946222 −0.473111 0.881003i \(-0.656869\pi\)
−0.473111 + 0.881003i \(0.656869\pi\)
\(812\) 0 0
\(813\) 38.5151 1.35078
\(814\) 0 0
\(815\) −13.4027 −0.469478
\(816\) 0 0
\(817\) −6.14021 −0.214819
\(818\) 0 0
\(819\) −2.05724 −0.0718859
\(820\) 0 0
\(821\) −20.0890 −0.701110 −0.350555 0.936542i \(-0.614007\pi\)
−0.350555 + 0.936542i \(0.614007\pi\)
\(822\) 0 0
\(823\) −11.6383 −0.405686 −0.202843 0.979211i \(-0.565018\pi\)
−0.202843 + 0.979211i \(0.565018\pi\)
\(824\) 0 0
\(825\) −9.40707 −0.327512
\(826\) 0 0
\(827\) 13.2406 0.460422 0.230211 0.973141i \(-0.426058\pi\)
0.230211 + 0.973141i \(0.426058\pi\)
\(828\) 0 0
\(829\) 10.4082 0.361493 0.180746 0.983530i \(-0.442149\pi\)
0.180746 + 0.983530i \(0.442149\pi\)
\(830\) 0 0
\(831\) −5.87583 −0.203830
\(832\) 0 0
\(833\) 6.24184 0.216267
\(834\) 0 0
\(835\) 18.5623 0.642374
\(836\) 0 0
\(837\) 12.5148 0.432574
\(838\) 0 0
\(839\) −36.0596 −1.24492 −0.622458 0.782653i \(-0.713866\pi\)
−0.622458 + 0.782653i \(0.713866\pi\)
\(840\) 0 0
\(841\) 26.5506 0.915536
\(842\) 0 0
\(843\) −4.73602 −0.163117
\(844\) 0 0
\(845\) −0.903831 −0.0310927
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 10.9220 0.374841
\(850\) 0 0
\(851\) 21.5667 0.739298
\(852\) 0 0
\(853\) 28.0126 0.959133 0.479567 0.877506i \(-0.340794\pi\)
0.479567 + 0.877506i \(0.340794\pi\)
\(854\) 0 0
\(855\) 5.91291 0.202217
\(856\) 0 0
\(857\) −15.5237 −0.530280 −0.265140 0.964210i \(-0.585418\pi\)
−0.265140 + 0.964210i \(0.585418\pi\)
\(858\) 0 0
\(859\) 7.70075 0.262746 0.131373 0.991333i \(-0.458061\pi\)
0.131373 + 0.991333i \(0.458061\pi\)
\(860\) 0 0
\(861\) −3.93163 −0.133990
\(862\) 0 0
\(863\) −32.7843 −1.11599 −0.557995 0.829844i \(-0.688429\pi\)
−0.557995 + 0.829844i \(0.688429\pi\)
\(864\) 0 0
\(865\) 10.4196 0.354278
\(866\) 0 0
\(867\) 49.3856 1.67722
\(868\) 0 0
\(869\) −11.6456 −0.395050
\(870\) 0 0
\(871\) 3.09877 0.104998
\(872\) 0 0
\(873\) −14.7850 −0.500397
\(874\) 0 0
\(875\) −8.29996 −0.280590
\(876\) 0 0
\(877\) 38.1649 1.28874 0.644369 0.764715i \(-0.277120\pi\)
0.644369 + 0.764715i \(0.277120\pi\)
\(878\) 0 0
\(879\) −20.4553 −0.689940
\(880\) 0 0
\(881\) 38.2191 1.28763 0.643817 0.765179i \(-0.277350\pi\)
0.643817 + 0.765179i \(0.277350\pi\)
\(882\) 0 0
\(883\) 5.52445 0.185912 0.0929562 0.995670i \(-0.470368\pi\)
0.0929562 + 0.995670i \(0.470368\pi\)
\(884\) 0 0
\(885\) −8.19055 −0.275322
\(886\) 0 0
\(887\) −21.7944 −0.731785 −0.365892 0.930657i \(-0.619236\pi\)
−0.365892 + 0.930657i \(0.619236\pi\)
\(888\) 0 0
\(889\) 4.77207 0.160050
\(890\) 0 0
\(891\) −10.9395 −0.366486
\(892\) 0 0
\(893\) −20.6140 −0.689822
\(894\) 0 0
\(895\) 14.4928 0.484440
\(896\) 0 0
\(897\) −8.76896 −0.292787
\(898\) 0 0
\(899\) 43.9957 1.46734
\(900\) 0 0
\(901\) −34.3345 −1.14385
\(902\) 0 0
\(903\) −4.34222 −0.144500
\(904\) 0 0
\(905\) 21.1314 0.702431
\(906\) 0 0
\(907\) 19.7630 0.656218 0.328109 0.944640i \(-0.393589\pi\)
0.328109 + 0.944640i \(0.393589\pi\)
\(908\) 0 0
\(909\) 21.1037 0.699965
\(910\) 0 0
\(911\) −38.6305 −1.27988 −0.639942 0.768423i \(-0.721042\pi\)
−0.639942 + 0.768423i \(0.721042\pi\)
\(912\) 0 0
\(913\) −5.15710 −0.170675
\(914\) 0 0
\(915\) 19.3083 0.638312
\(916\) 0 0
\(917\) 12.3855 0.409005
\(918\) 0 0
\(919\) −22.5736 −0.744635 −0.372318 0.928105i \(-0.621437\pi\)
−0.372318 + 0.928105i \(0.621437\pi\)
\(920\) 0 0
\(921\) −70.2458 −2.31468
\(922\) 0 0
\(923\) 7.68736 0.253033
\(924\) 0 0
\(925\) 23.1361 0.760710
\(926\) 0 0
\(927\) −32.4992 −1.06741
\(928\) 0 0
\(929\) 46.7458 1.53368 0.766840 0.641839i \(-0.221828\pi\)
0.766840 + 0.641839i \(0.221828\pi\)
\(930\) 0 0
\(931\) −3.18001 −0.104221
\(932\) 0 0
\(933\) −62.5401 −2.04747
\(934\) 0 0
\(935\) −5.64157 −0.184499
\(936\) 0 0
\(937\) 24.3401 0.795157 0.397578 0.917568i \(-0.369851\pi\)
0.397578 + 0.917568i \(0.369851\pi\)
\(938\) 0 0
\(939\) −17.5307 −0.572094
\(940\) 0 0
\(941\) 17.9933 0.586566 0.293283 0.956026i \(-0.405252\pi\)
0.293283 + 0.956026i \(0.405252\pi\)
\(942\) 0 0
\(943\) −6.81721 −0.221999
\(944\) 0 0
\(945\) −1.91621 −0.0623343
\(946\) 0 0
\(947\) 19.3456 0.628649 0.314324 0.949316i \(-0.398222\pi\)
0.314324 + 0.949316i \(0.398222\pi\)
\(948\) 0 0
\(949\) −7.41380 −0.240662
\(950\) 0 0
\(951\) 54.9149 1.78074
\(952\) 0 0
\(953\) 27.3362 0.885505 0.442753 0.896644i \(-0.354002\pi\)
0.442753 + 0.896644i \(0.354002\pi\)
\(954\) 0 0
\(955\) 8.29675 0.268476
\(956\) 0 0
\(957\) −16.7610 −0.541808
\(958\) 0 0
\(959\) 5.16125 0.166665
\(960\) 0 0
\(961\) 3.84440 0.124013
\(962\) 0 0
\(963\) 18.7984 0.605771
\(964\) 0 0
\(965\) −6.21505 −0.200069
\(966\) 0 0
\(967\) −45.4186 −1.46056 −0.730282 0.683145i \(-0.760612\pi\)
−0.730282 + 0.683145i \(0.760612\pi\)
\(968\) 0 0
\(969\) −44.6373 −1.43396
\(970\) 0 0
\(971\) 60.0810 1.92809 0.964045 0.265739i \(-0.0856160\pi\)
0.964045 + 0.265739i \(0.0856160\pi\)
\(972\) 0 0
\(973\) −8.79830 −0.282061
\(974\) 0 0
\(975\) −9.40707 −0.301267
\(976\) 0 0
\(977\) 42.5380 1.36091 0.680456 0.732789i \(-0.261782\pi\)
0.680456 + 0.732789i \(0.261782\pi\)
\(978\) 0 0
\(979\) −6.64006 −0.212217
\(980\) 0 0
\(981\) 22.2918 0.711723
\(982\) 0 0
\(983\) 18.0985 0.577254 0.288627 0.957442i \(-0.406801\pi\)
0.288627 + 0.957442i \(0.406801\pi\)
\(984\) 0 0
\(985\) 18.9636 0.604231
\(986\) 0 0
\(987\) −14.5778 −0.464016
\(988\) 0 0
\(989\) −7.52916 −0.239413
\(990\) 0 0
\(991\) 39.7987 1.26425 0.632123 0.774868i \(-0.282184\pi\)
0.632123 + 0.774868i \(0.282184\pi\)
\(992\) 0 0
\(993\) −16.3662 −0.519364
\(994\) 0 0
\(995\) −4.28838 −0.135951
\(996\) 0 0
\(997\) −62.5265 −1.98023 −0.990116 0.140248i \(-0.955210\pi\)
−0.990116 + 0.140248i \(0.955210\pi\)
\(998\) 0 0
\(999\) 11.7260 0.370994
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 \(a_p\))