Properties

Label 8036.2.a.p.1.7
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(1.20067\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.20067 q^{3} -0.960855 q^{5} -1.55839 q^{9} +O(q^{10})\) \(q+1.20067 q^{3} -0.960855 q^{5} -1.55839 q^{9} -4.42245 q^{11} +0.696329 q^{13} -1.15367 q^{15} +1.02043 q^{17} -7.03402 q^{19} -4.50530 q^{23} -4.07676 q^{25} -5.47312 q^{27} +8.50757 q^{29} +2.30265 q^{31} -5.30991 q^{33} +6.54332 q^{37} +0.836062 q^{39} +1.00000 q^{41} +6.37372 q^{43} +1.49739 q^{45} +0.286914 q^{47} +1.22520 q^{51} +6.03283 q^{53} +4.24934 q^{55} -8.44553 q^{57} -14.2347 q^{59} +5.32167 q^{61} -0.669072 q^{65} +0.778309 q^{67} -5.40938 q^{69} -0.249785 q^{71} +6.06573 q^{73} -4.89484 q^{75} +1.79493 q^{79} -1.89624 q^{81} +0.273880 q^{83} -0.980482 q^{85} +10.2148 q^{87} +10.8123 q^{89} +2.76472 q^{93} +6.75867 q^{95} +18.9582 q^{97} +6.89192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + O(q^{10}) \) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + 6q^{13} - 4q^{15} + 12q^{17} + 8q^{19} + 4q^{23} + 16q^{25} + 8q^{27} + 2q^{29} + 8q^{31} - 6q^{33} - 2q^{37} - 2q^{39} + 10q^{41} - 2q^{43} + 44q^{45} - 14q^{47} + 14q^{51} + 8q^{53} + 8q^{55} - 10q^{57} + 24q^{59} + 14q^{61} + 2q^{65} - 8q^{67} + 16q^{69} + 10q^{71} + 44q^{73} - 50q^{75} + 10q^{79} - 14q^{81} + 20q^{83} + 8q^{85} + 20q^{87} + 6q^{89} + 8q^{93} + 4q^{95} + 46q^{97} + 2q^{99} + O(q^{100}) \)

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
\(3\) 1.20067 0.693207 0.346604 0.938012i \(-0.387335\pi\)
0.346604 + 0.938012i \(0.387335\pi\)
\(4\) 0 0
\(5\) −0.960855 −0.429708 −0.214854 0.976646i \(-0.568927\pi\)
−0.214854 + 0.976646i \(0.568927\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −1.55839 −0.519464
\(10\) 0 0
\(11\) −4.42245 −1.33342 −0.666710 0.745317i \(-0.732298\pi\)
−0.666710 + 0.745317i \(0.732298\pi\)
\(12\) 0 0
\(13\) 0.696329 0.193127 0.0965635 0.995327i \(-0.469215\pi\)
0.0965635 + 0.995327i \(0.469215\pi\)
\(14\) 0 0
\(15\) −1.15367 −0.297876
\(16\) 0 0
\(17\) 1.02043 0.247490 0.123745 0.992314i \(-0.460510\pi\)
0.123745 + 0.992314i \(0.460510\pi\)
\(18\) 0 0
\(19\) −7.03402 −1.61371 −0.806857 0.590747i \(-0.798833\pi\)
−0.806857 + 0.590747i \(0.798833\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.50530 −0.939420 −0.469710 0.882821i \(-0.655641\pi\)
−0.469710 + 0.882821i \(0.655641\pi\)
\(24\) 0 0
\(25\) −4.07676 −0.815351
\(26\) 0 0
\(27\) −5.47312 −1.05330
\(28\) 0 0
\(29\) 8.50757 1.57982 0.789909 0.613225i \(-0.210128\pi\)
0.789909 + 0.613225i \(0.210128\pi\)
\(30\) 0 0
\(31\) 2.30265 0.413568 0.206784 0.978387i \(-0.433700\pi\)
0.206784 + 0.978387i \(0.433700\pi\)
\(32\) 0 0
\(33\) −5.30991 −0.924336
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.54332 1.07572 0.537858 0.843036i \(-0.319234\pi\)
0.537858 + 0.843036i \(0.319234\pi\)
\(38\) 0 0
\(39\) 0.836062 0.133877
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 6.37372 0.971983 0.485992 0.873964i \(-0.338459\pi\)
0.485992 + 0.873964i \(0.338459\pi\)
\(44\) 0 0
\(45\) 1.49739 0.223218
\(46\) 0 0
\(47\) 0.286914 0.0418507 0.0209253 0.999781i \(-0.493339\pi\)
0.0209253 + 0.999781i \(0.493339\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 1.22520 0.171562
\(52\) 0 0
\(53\) 6.03283 0.828673 0.414337 0.910124i \(-0.364014\pi\)
0.414337 + 0.910124i \(0.364014\pi\)
\(54\) 0 0
\(55\) 4.24934 0.572981
\(56\) 0 0
\(57\) −8.44553 −1.11864
\(58\) 0 0
\(59\) −14.2347 −1.85319 −0.926597 0.376055i \(-0.877280\pi\)
−0.926597 + 0.376055i \(0.877280\pi\)
\(60\) 0 0
\(61\) 5.32167 0.681370 0.340685 0.940177i \(-0.389341\pi\)
0.340685 + 0.940177i \(0.389341\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.669072 −0.0829881
\(66\) 0 0
\(67\) 0.778309 0.0950856 0.0475428 0.998869i \(-0.484861\pi\)
0.0475428 + 0.998869i \(0.484861\pi\)
\(68\) 0 0
\(69\) −5.40938 −0.651212
\(70\) 0 0
\(71\) −0.249785 −0.0296441 −0.0148220 0.999890i \(-0.504718\pi\)
−0.0148220 + 0.999890i \(0.504718\pi\)
\(72\) 0 0
\(73\) 6.06573 0.709939 0.354970 0.934878i \(-0.384491\pi\)
0.354970 + 0.934878i \(0.384491\pi\)
\(74\) 0 0
\(75\) −4.89484 −0.565207
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.79493 0.201945 0.100973 0.994889i \(-0.467805\pi\)
0.100973 + 0.994889i \(0.467805\pi\)
\(80\) 0 0
\(81\) −1.89624 −0.210693
\(82\) 0 0
\(83\) 0.273880 0.0300622 0.0150311 0.999887i \(-0.495215\pi\)
0.0150311 + 0.999887i \(0.495215\pi\)
\(84\) 0 0
\(85\) −0.980482 −0.106348
\(86\) 0 0
\(87\) 10.2148 1.09514
\(88\) 0 0
\(89\) 10.8123 1.14610 0.573052 0.819519i \(-0.305759\pi\)
0.573052 + 0.819519i \(0.305759\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 2.76472 0.286689
\(94\) 0 0
\(95\) 6.75867 0.693425
\(96\) 0 0
\(97\) 18.9582 1.92492 0.962458 0.271431i \(-0.0874969\pi\)
0.962458 + 0.271431i \(0.0874969\pi\)
\(98\) 0 0
\(99\) 6.89192 0.692664
\(100\) 0 0
\(101\) 18.2970 1.82062 0.910309 0.413929i \(-0.135844\pi\)
0.910309 + 0.413929i \(0.135844\pi\)
\(102\) 0 0
\(103\) 0.562381 0.0554130 0.0277065 0.999616i \(-0.491180\pi\)
0.0277065 + 0.999616i \(0.491180\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.07805 −0.104219 −0.0521094 0.998641i \(-0.516594\pi\)
−0.0521094 + 0.998641i \(0.516594\pi\)
\(108\) 0 0
\(109\) −2.25003 −0.215514 −0.107757 0.994177i \(-0.534367\pi\)
−0.107757 + 0.994177i \(0.534367\pi\)
\(110\) 0 0
\(111\) 7.85637 0.745693
\(112\) 0 0
\(113\) 8.09996 0.761980 0.380990 0.924579i \(-0.375583\pi\)
0.380990 + 0.924579i \(0.375583\pi\)
\(114\) 0 0
\(115\) 4.32894 0.403676
\(116\) 0 0
\(117\) −1.08515 −0.100323
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 8.55811 0.778010
\(122\) 0 0
\(123\) 1.20067 0.108261
\(124\) 0 0
\(125\) 8.72145 0.780070
\(126\) 0 0
\(127\) 9.24445 0.820313 0.410156 0.912015i \(-0.365474\pi\)
0.410156 + 0.912015i \(0.365474\pi\)
\(128\) 0 0
\(129\) 7.65273 0.673785
\(130\) 0 0
\(131\) −5.82273 −0.508734 −0.254367 0.967108i \(-0.581867\pi\)
−0.254367 + 0.967108i \(0.581867\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 5.25888 0.452612
\(136\) 0 0
\(137\) −22.0115 −1.88057 −0.940285 0.340388i \(-0.889442\pi\)
−0.940285 + 0.340388i \(0.889442\pi\)
\(138\) 0 0
\(139\) 12.8321 1.08841 0.544204 0.838953i \(-0.316832\pi\)
0.544204 + 0.838953i \(0.316832\pi\)
\(140\) 0 0
\(141\) 0.344489 0.0290112
\(142\) 0 0
\(143\) −3.07948 −0.257519
\(144\) 0 0
\(145\) −8.17455 −0.678859
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 14.9482 1.22460 0.612301 0.790625i \(-0.290244\pi\)
0.612301 + 0.790625i \(0.290244\pi\)
\(150\) 0 0
\(151\) −15.6267 −1.27169 −0.635843 0.771818i \(-0.719347\pi\)
−0.635843 + 0.771818i \(0.719347\pi\)
\(152\) 0 0
\(153\) −1.59022 −0.128562
\(154\) 0 0
\(155\) −2.21251 −0.177713
\(156\) 0 0
\(157\) 14.8900 1.18835 0.594175 0.804336i \(-0.297479\pi\)
0.594175 + 0.804336i \(0.297479\pi\)
\(158\) 0 0
\(159\) 7.24344 0.574442
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −3.18475 −0.249449 −0.124724 0.992191i \(-0.539805\pi\)
−0.124724 + 0.992191i \(0.539805\pi\)
\(164\) 0 0
\(165\) 5.10205 0.397194
\(166\) 0 0
\(167\) 14.1043 1.09142 0.545712 0.837973i \(-0.316259\pi\)
0.545712 + 0.837973i \(0.316259\pi\)
\(168\) 0 0
\(169\) −12.5151 −0.962702
\(170\) 0 0
\(171\) 10.9618 0.838266
\(172\) 0 0
\(173\) −7.31878 −0.556436 −0.278218 0.960518i \(-0.589744\pi\)
−0.278218 + 0.960518i \(0.589744\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −17.0911 −1.28465
\(178\) 0 0
\(179\) −5.41426 −0.404681 −0.202340 0.979315i \(-0.564855\pi\)
−0.202340 + 0.979315i \(0.564855\pi\)
\(180\) 0 0
\(181\) −19.4477 −1.44554 −0.722768 0.691090i \(-0.757131\pi\)
−0.722768 + 0.691090i \(0.757131\pi\)
\(182\) 0 0
\(183\) 6.38957 0.472331
\(184\) 0 0
\(185\) −6.28718 −0.462243
\(186\) 0 0
\(187\) −4.51279 −0.330008
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −13.1177 −0.949165 −0.474583 0.880211i \(-0.657401\pi\)
−0.474583 + 0.880211i \(0.657401\pi\)
\(192\) 0 0
\(193\) 1.64643 0.118512 0.0592561 0.998243i \(-0.481127\pi\)
0.0592561 + 0.998243i \(0.481127\pi\)
\(194\) 0 0
\(195\) −0.803334 −0.0575279
\(196\) 0 0
\(197\) 7.34791 0.523517 0.261758 0.965133i \(-0.415698\pi\)
0.261758 + 0.965133i \(0.415698\pi\)
\(198\) 0 0
\(199\) −5.91693 −0.419440 −0.209720 0.977761i \(-0.567255\pi\)
−0.209720 + 0.977761i \(0.567255\pi\)
\(200\) 0 0
\(201\) 0.934492 0.0659140
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −0.960855 −0.0671090
\(206\) 0 0
\(207\) 7.02102 0.487995
\(208\) 0 0
\(209\) 31.1076 2.15176
\(210\) 0 0
\(211\) −23.2386 −1.59981 −0.799906 0.600125i \(-0.795117\pi\)
−0.799906 + 0.600125i \(0.795117\pi\)
\(212\) 0 0
\(213\) −0.299910 −0.0205495
\(214\) 0 0
\(215\) −6.12422 −0.417668
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 7.28293 0.492135
\(220\) 0 0
\(221\) 0.710553 0.0477970
\(222\) 0 0
\(223\) 22.8794 1.53212 0.766059 0.642771i \(-0.222215\pi\)
0.766059 + 0.642771i \(0.222215\pi\)
\(224\) 0 0
\(225\) 6.35319 0.423546
\(226\) 0 0
\(227\) −16.7210 −1.10981 −0.554905 0.831914i \(-0.687245\pi\)
−0.554905 + 0.831914i \(0.687245\pi\)
\(228\) 0 0
\(229\) 5.07185 0.335157 0.167579 0.985859i \(-0.446405\pi\)
0.167579 + 0.985859i \(0.446405\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.6473 0.959577 0.479789 0.877384i \(-0.340713\pi\)
0.479789 + 0.877384i \(0.340713\pi\)
\(234\) 0 0
\(235\) −0.275683 −0.0179835
\(236\) 0 0
\(237\) 2.15512 0.139990
\(238\) 0 0
\(239\) 12.1788 0.787779 0.393890 0.919158i \(-0.371129\pi\)
0.393890 + 0.919158i \(0.371129\pi\)
\(240\) 0 0
\(241\) 24.2926 1.56482 0.782411 0.622763i \(-0.213990\pi\)
0.782411 + 0.622763i \(0.213990\pi\)
\(242\) 0 0
\(243\) 14.1426 0.907249
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.89799 −0.311652
\(248\) 0 0
\(249\) 0.328839 0.0208393
\(250\) 0 0
\(251\) −21.7394 −1.37218 −0.686089 0.727518i \(-0.740674\pi\)
−0.686089 + 0.727518i \(0.740674\pi\)
\(252\) 0 0
\(253\) 19.9245 1.25264
\(254\) 0 0
\(255\) −1.17724 −0.0737213
\(256\) 0 0
\(257\) −25.2802 −1.57693 −0.788466 0.615078i \(-0.789125\pi\)
−0.788466 + 0.615078i \(0.789125\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −13.2581 −0.820658
\(262\) 0 0
\(263\) 27.7075 1.70852 0.854260 0.519846i \(-0.174011\pi\)
0.854260 + 0.519846i \(0.174011\pi\)
\(264\) 0 0
\(265\) −5.79668 −0.356087
\(266\) 0 0
\(267\) 12.9820 0.794487
\(268\) 0 0
\(269\) 12.1912 0.743311 0.371655 0.928371i \(-0.378790\pi\)
0.371655 + 0.928371i \(0.378790\pi\)
\(270\) 0 0
\(271\) 23.2192 1.41046 0.705232 0.708977i \(-0.250843\pi\)
0.705232 + 0.708977i \(0.250843\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 18.0293 1.08721
\(276\) 0 0
\(277\) −9.58468 −0.575888 −0.287944 0.957647i \(-0.592972\pi\)
−0.287944 + 0.957647i \(0.592972\pi\)
\(278\) 0 0
\(279\) −3.58843 −0.214834
\(280\) 0 0
\(281\) −16.2612 −0.970062 −0.485031 0.874497i \(-0.661192\pi\)
−0.485031 + 0.874497i \(0.661192\pi\)
\(282\) 0 0
\(283\) 6.92241 0.411495 0.205747 0.978605i \(-0.434038\pi\)
0.205747 + 0.978605i \(0.434038\pi\)
\(284\) 0 0
\(285\) 8.11493 0.480687
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −15.9587 −0.938749
\(290\) 0 0
\(291\) 22.7626 1.33437
\(292\) 0 0
\(293\) 8.64464 0.505025 0.252513 0.967594i \(-0.418743\pi\)
0.252513 + 0.967594i \(0.418743\pi\)
\(294\) 0 0
\(295\) 13.6774 0.796332
\(296\) 0 0
\(297\) 24.2046 1.40450
\(298\) 0 0
\(299\) −3.13717 −0.181427
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 21.9686 1.26207
\(304\) 0 0
\(305\) −5.11336 −0.292790
\(306\) 0 0
\(307\) 14.4004 0.821875 0.410937 0.911664i \(-0.365201\pi\)
0.410937 + 0.911664i \(0.365201\pi\)
\(308\) 0 0
\(309\) 0.675233 0.0384127
\(310\) 0 0
\(311\) 22.3514 1.26743 0.633716 0.773566i \(-0.281529\pi\)
0.633716 + 0.773566i \(0.281529\pi\)
\(312\) 0 0
\(313\) −22.8805 −1.29328 −0.646641 0.762795i \(-0.723827\pi\)
−0.646641 + 0.762795i \(0.723827\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −23.1999 −1.30303 −0.651517 0.758634i \(-0.725867\pi\)
−0.651517 + 0.758634i \(0.725867\pi\)
\(318\) 0 0
\(319\) −37.6244 −2.10656
\(320\) 0 0
\(321\) −1.29438 −0.0722452
\(322\) 0 0
\(323\) −7.17770 −0.399378
\(324\) 0 0
\(325\) −2.83877 −0.157466
\(326\) 0 0
\(327\) −2.70154 −0.149396
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 13.1383 0.722147 0.361073 0.932537i \(-0.382410\pi\)
0.361073 + 0.932537i \(0.382410\pi\)
\(332\) 0 0
\(333\) −10.1971 −0.558795
\(334\) 0 0
\(335\) −0.747842 −0.0408590
\(336\) 0 0
\(337\) −28.4357 −1.54899 −0.774495 0.632580i \(-0.781996\pi\)
−0.774495 + 0.632580i \(0.781996\pi\)
\(338\) 0 0
\(339\) 9.72538 0.528210
\(340\) 0 0
\(341\) −10.1834 −0.551460
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 5.19763 0.279831
\(346\) 0 0
\(347\) 4.99947 0.268386 0.134193 0.990955i \(-0.457156\pi\)
0.134193 + 0.990955i \(0.457156\pi\)
\(348\) 0 0
\(349\) −7.09183 −0.379617 −0.189809 0.981821i \(-0.560787\pi\)
−0.189809 + 0.981821i \(0.560787\pi\)
\(350\) 0 0
\(351\) −3.81110 −0.203421
\(352\) 0 0
\(353\) 3.71132 0.197533 0.0987667 0.995111i \(-0.468510\pi\)
0.0987667 + 0.995111i \(0.468510\pi\)
\(354\) 0 0
\(355\) 0.240007 0.0127383
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.5218 0.555320 0.277660 0.960679i \(-0.410441\pi\)
0.277660 + 0.960679i \(0.410441\pi\)
\(360\) 0 0
\(361\) 30.4774 1.60407
\(362\) 0 0
\(363\) 10.2755 0.539322
\(364\) 0 0
\(365\) −5.82828 −0.305066
\(366\) 0 0
\(367\) 25.2458 1.31782 0.658910 0.752222i \(-0.271018\pi\)
0.658910 + 0.752222i \(0.271018\pi\)
\(368\) 0 0
\(369\) −1.55839 −0.0811266
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −2.71198 −0.140421 −0.0702106 0.997532i \(-0.522367\pi\)
−0.0702106 + 0.997532i \(0.522367\pi\)
\(374\) 0 0
\(375\) 10.4716 0.540750
\(376\) 0 0
\(377\) 5.92407 0.305105
\(378\) 0 0
\(379\) 28.8541 1.48214 0.741069 0.671429i \(-0.234319\pi\)
0.741069 + 0.671429i \(0.234319\pi\)
\(380\) 0 0
\(381\) 11.0995 0.568647
\(382\) 0 0
\(383\) −28.3527 −1.44876 −0.724379 0.689402i \(-0.757873\pi\)
−0.724379 + 0.689402i \(0.757873\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −9.93275 −0.504910
\(388\) 0 0
\(389\) 19.2733 0.977195 0.488598 0.872509i \(-0.337509\pi\)
0.488598 + 0.872509i \(0.337509\pi\)
\(390\) 0 0
\(391\) −4.59733 −0.232497
\(392\) 0 0
\(393\) −6.99118 −0.352658
\(394\) 0 0
\(395\) −1.72467 −0.0867774
\(396\) 0 0
\(397\) 32.8499 1.64869 0.824346 0.566087i \(-0.191543\pi\)
0.824346 + 0.566087i \(0.191543\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.8111 0.689695 0.344847 0.938659i \(-0.387931\pi\)
0.344847 + 0.938659i \(0.387931\pi\)
\(402\) 0 0
\(403\) 1.60340 0.0798712
\(404\) 0 0
\(405\) 1.82201 0.0905364
\(406\) 0 0
\(407\) −28.9375 −1.43438
\(408\) 0 0
\(409\) −11.9398 −0.590385 −0.295193 0.955438i \(-0.595384\pi\)
−0.295193 + 0.955438i \(0.595384\pi\)
\(410\) 0 0
\(411\) −26.4286 −1.30362
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −0.263159 −0.0129180
\(416\) 0 0
\(417\) 15.4072 0.754492
\(418\) 0 0
\(419\) −7.86680 −0.384318 −0.192159 0.981364i \(-0.561549\pi\)
−0.192159 + 0.981364i \(0.561549\pi\)
\(420\) 0 0
\(421\) −25.6643 −1.25080 −0.625400 0.780304i \(-0.715064\pi\)
−0.625400 + 0.780304i \(0.715064\pi\)
\(422\) 0 0
\(423\) −0.447124 −0.0217399
\(424\) 0 0
\(425\) −4.16003 −0.201791
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −3.69744 −0.178514
\(430\) 0 0
\(431\) 12.4449 0.599449 0.299725 0.954026i \(-0.403105\pi\)
0.299725 + 0.954026i \(0.403105\pi\)
\(432\) 0 0
\(433\) 1.50279 0.0722196 0.0361098 0.999348i \(-0.488503\pi\)
0.0361098 + 0.999348i \(0.488503\pi\)
\(434\) 0 0
\(435\) −9.81493 −0.470590
\(436\) 0 0
\(437\) 31.6903 1.51595
\(438\) 0 0
\(439\) −30.8960 −1.47459 −0.737293 0.675573i \(-0.763896\pi\)
−0.737293 + 0.675573i \(0.763896\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −14.8122 −0.703749 −0.351874 0.936047i \(-0.614456\pi\)
−0.351874 + 0.936047i \(0.614456\pi\)
\(444\) 0 0
\(445\) −10.3891 −0.492489
\(446\) 0 0
\(447\) 17.9478 0.848902
\(448\) 0 0
\(449\) −38.4709 −1.81555 −0.907776 0.419455i \(-0.862221\pi\)
−0.907776 + 0.419455i \(0.862221\pi\)
\(450\) 0 0
\(451\) −4.42245 −0.208245
\(452\) 0 0
\(453\) −18.7626 −0.881542
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 25.5711 1.19616 0.598082 0.801435i \(-0.295930\pi\)
0.598082 + 0.801435i \(0.295930\pi\)
\(458\) 0 0
\(459\) −5.58492 −0.260682
\(460\) 0 0
\(461\) 7.94612 0.370088 0.185044 0.982730i \(-0.440757\pi\)
0.185044 + 0.982730i \(0.440757\pi\)
\(462\) 0 0
\(463\) 33.6444 1.56359 0.781795 0.623536i \(-0.214305\pi\)
0.781795 + 0.623536i \(0.214305\pi\)
\(464\) 0 0
\(465\) −2.65650 −0.123192
\(466\) 0 0
\(467\) −36.6702 −1.69690 −0.848448 0.529279i \(-0.822463\pi\)
−0.848448 + 0.529279i \(0.822463\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 17.8780 0.823773
\(472\) 0 0
\(473\) −28.1875 −1.29606
\(474\) 0 0
\(475\) 28.6760 1.31574
\(476\) 0 0
\(477\) −9.40152 −0.430466
\(478\) 0 0
\(479\) 19.4725 0.889722 0.444861 0.895600i \(-0.353253\pi\)
0.444861 + 0.895600i \(0.353253\pi\)
\(480\) 0 0
\(481\) 4.55631 0.207750
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −18.2161 −0.827151
\(486\) 0 0
\(487\) 22.6738 1.02745 0.513723 0.857956i \(-0.328266\pi\)
0.513723 + 0.857956i \(0.328266\pi\)
\(488\) 0 0
\(489\) −3.82383 −0.172920
\(490\) 0 0
\(491\) 16.6279 0.750408 0.375204 0.926942i \(-0.377573\pi\)
0.375204 + 0.926942i \(0.377573\pi\)
\(492\) 0 0
\(493\) 8.68136 0.390989
\(494\) 0 0
\(495\) −6.62214 −0.297643
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −30.6666 −1.37282 −0.686412 0.727213i \(-0.740815\pi\)
−0.686412 + 0.727213i \(0.740815\pi\)
\(500\) 0 0
\(501\) 16.9346 0.756583
\(502\) 0 0
\(503\) −5.49221 −0.244885 −0.122443 0.992476i \(-0.539073\pi\)
−0.122443 + 0.992476i \(0.539073\pi\)
\(504\) 0 0
\(505\) −17.5808 −0.782333
\(506\) 0 0
\(507\) −15.0265 −0.667352
\(508\) 0 0
\(509\) 20.8187 0.922774 0.461387 0.887199i \(-0.347352\pi\)
0.461387 + 0.887199i \(0.347352\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 38.4980 1.69973
\(514\) 0 0
\(515\) −0.540366 −0.0238114
\(516\) 0 0
\(517\) −1.26886 −0.0558045
\(518\) 0 0
\(519\) −8.78743 −0.385725
\(520\) 0 0
\(521\) −15.7425 −0.689692 −0.344846 0.938659i \(-0.612069\pi\)
−0.344846 + 0.938659i \(0.612069\pi\)
\(522\) 0 0
\(523\) 19.2884 0.843425 0.421713 0.906730i \(-0.361429\pi\)
0.421713 + 0.906730i \(0.361429\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.34969 0.102354
\(528\) 0 0
\(529\) −2.70228 −0.117490
\(530\) 0 0
\(531\) 22.1832 0.962668
\(532\) 0 0
\(533\) 0.696329 0.0301614
\(534\) 0 0
\(535\) 1.03585 0.0447836
\(536\) 0 0
\(537\) −6.50074 −0.280527
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −16.2247 −0.697555 −0.348777 0.937206i \(-0.613403\pi\)
−0.348777 + 0.937206i \(0.613403\pi\)
\(542\) 0 0
\(543\) −23.3503 −1.00206
\(544\) 0 0
\(545\) 2.16195 0.0926079
\(546\) 0 0
\(547\) 5.86146 0.250618 0.125309 0.992118i \(-0.460008\pi\)
0.125309 + 0.992118i \(0.460008\pi\)
\(548\) 0 0
\(549\) −8.29325 −0.353947
\(550\) 0 0
\(551\) −59.8424 −2.54937
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −7.54883 −0.320430
\(556\) 0 0
\(557\) −41.9290 −1.77659 −0.888295 0.459273i \(-0.848110\pi\)
−0.888295 + 0.459273i \(0.848110\pi\)
\(558\) 0 0
\(559\) 4.43821 0.187716
\(560\) 0 0
\(561\) −5.41837 −0.228764
\(562\) 0 0
\(563\) 25.1667 1.06065 0.530325 0.847795i \(-0.322070\pi\)
0.530325 + 0.847795i \(0.322070\pi\)
\(564\) 0 0
\(565\) −7.78289 −0.327429
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −20.0437 −0.840276 −0.420138 0.907460i \(-0.638018\pi\)
−0.420138 + 0.907460i \(0.638018\pi\)
\(570\) 0 0
\(571\) 30.0571 1.25785 0.628925 0.777466i \(-0.283495\pi\)
0.628925 + 0.777466i \(0.283495\pi\)
\(572\) 0 0
\(573\) −15.7501 −0.657968
\(574\) 0 0
\(575\) 18.3670 0.765957
\(576\) 0 0
\(577\) 34.7832 1.44805 0.724023 0.689776i \(-0.242291\pi\)
0.724023 + 0.689776i \(0.242291\pi\)
\(578\) 0 0
\(579\) 1.97681 0.0821535
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −26.6799 −1.10497
\(584\) 0 0
\(585\) 1.04268 0.0431093
\(586\) 0 0
\(587\) 38.7289 1.59851 0.799256 0.600991i \(-0.205227\pi\)
0.799256 + 0.600991i \(0.205227\pi\)
\(588\) 0 0
\(589\) −16.1969 −0.667381
\(590\) 0 0
\(591\) 8.82241 0.362905
\(592\) 0 0
\(593\) 31.3187 1.28611 0.643053 0.765821i \(-0.277667\pi\)
0.643053 + 0.765821i \(0.277667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −7.10428 −0.290759
\(598\) 0 0
\(599\) −31.7113 −1.29569 −0.647845 0.761772i \(-0.724329\pi\)
−0.647845 + 0.761772i \(0.724329\pi\)
\(600\) 0 0
\(601\) 7.97320 0.325234 0.162617 0.986689i \(-0.448007\pi\)
0.162617 + 0.986689i \(0.448007\pi\)
\(602\) 0 0
\(603\) −1.21291 −0.0493935
\(604\) 0 0
\(605\) −8.22310 −0.334317
\(606\) 0 0
\(607\) −10.7159 −0.434944 −0.217472 0.976067i \(-0.569781\pi\)
−0.217472 + 0.976067i \(0.569781\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.199786 0.00808249
\(612\) 0 0
\(613\) 6.31151 0.254919 0.127460 0.991844i \(-0.459318\pi\)
0.127460 + 0.991844i \(0.459318\pi\)
\(614\) 0 0
\(615\) −1.15367 −0.0465205
\(616\) 0 0
\(617\) 19.7164 0.793752 0.396876 0.917872i \(-0.370094\pi\)
0.396876 + 0.917872i \(0.370094\pi\)
\(618\) 0 0
\(619\) −23.0555 −0.926678 −0.463339 0.886181i \(-0.653349\pi\)
−0.463339 + 0.886181i \(0.653349\pi\)
\(620\) 0 0
\(621\) 24.6581 0.989494
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 12.0037 0.480149
\(626\) 0 0
\(627\) 37.3500 1.49161
\(628\) 0 0
\(629\) 6.67698 0.266229
\(630\) 0 0
\(631\) −17.4544 −0.694847 −0.347424 0.937708i \(-0.612943\pi\)
−0.347424 + 0.937708i \(0.612943\pi\)
\(632\) 0 0
\(633\) −27.9019 −1.10900
\(634\) 0 0
\(635\) −8.88258 −0.352495
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0.389263 0.0153990
\(640\) 0 0
\(641\) 2.45391 0.0969235 0.0484618 0.998825i \(-0.484568\pi\)
0.0484618 + 0.998825i \(0.484568\pi\)
\(642\) 0 0
\(643\) 2.18234 0.0860631 0.0430315 0.999074i \(-0.486298\pi\)
0.0430315 + 0.999074i \(0.486298\pi\)
\(644\) 0 0
\(645\) −7.35317 −0.289531
\(646\) 0 0
\(647\) −8.23779 −0.323861 −0.161930 0.986802i \(-0.551772\pi\)
−0.161930 + 0.986802i \(0.551772\pi\)
\(648\) 0 0
\(649\) 62.9521 2.47109
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −39.5156 −1.54636 −0.773182 0.634184i \(-0.781336\pi\)
−0.773182 + 0.634184i \(0.781336\pi\)
\(654\) 0 0
\(655\) 5.59480 0.218607
\(656\) 0 0
\(657\) −9.45278 −0.368788
\(658\) 0 0
\(659\) −0.710018 −0.0276584 −0.0138292 0.999904i \(-0.504402\pi\)
−0.0138292 + 0.999904i \(0.504402\pi\)
\(660\) 0 0
\(661\) −3.85365 −0.149889 −0.0749447 0.997188i \(-0.523878\pi\)
−0.0749447 + 0.997188i \(0.523878\pi\)
\(662\) 0 0
\(663\) 0.853139 0.0331332
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −38.3292 −1.48411
\(668\) 0 0
\(669\) 27.4706 1.06207
\(670\) 0 0
\(671\) −23.5349 −0.908553
\(672\) 0 0
\(673\) 6.80389 0.262271 0.131135 0.991364i \(-0.458138\pi\)
0.131135 + 0.991364i \(0.458138\pi\)
\(674\) 0 0
\(675\) 22.3126 0.858812
\(676\) 0 0
\(677\) 26.1026 1.00320 0.501602 0.865098i \(-0.332744\pi\)
0.501602 + 0.865098i \(0.332744\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −20.0764 −0.769328
\(682\) 0 0
\(683\) −11.7058 −0.447910 −0.223955 0.974600i \(-0.571897\pi\)
−0.223955 + 0.974600i \(0.571897\pi\)
\(684\) 0 0
\(685\) 21.1499 0.808095
\(686\) 0 0
\(687\) 6.08962 0.232333
\(688\) 0 0
\(689\) 4.20084 0.160039
\(690\) 0 0
\(691\) 27.9879 1.06471 0.532355 0.846521i \(-0.321307\pi\)
0.532355 + 0.846521i \(0.321307\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −12.3298 −0.467697
\(696\) 0 0
\(697\) 1.02043 0.0386514
\(698\) 0 0
\(699\) 17.5866 0.665186
\(700\) 0 0
\(701\) −0.331564 −0.0125230 −0.00626149 0.999980i \(-0.501993\pi\)
−0.00626149 + 0.999980i \(0.501993\pi\)
\(702\) 0 0
\(703\) −46.0258 −1.73590
\(704\) 0 0
\(705\) −0.331004 −0.0124663
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 19.2339 0.722345 0.361172 0.932499i \(-0.382377\pi\)
0.361172 + 0.932499i \(0.382377\pi\)
\(710\) 0 0
\(711\) −2.79720 −0.104903
\(712\) 0 0
\(713\) −10.3741 −0.388514
\(714\) 0 0
\(715\) 2.95894 0.110658
\(716\) 0 0
\(717\) 14.6227 0.546094
\(718\) 0 0
\(719\) −14.2799 −0.532550 −0.266275 0.963897i \(-0.585793\pi\)
−0.266275 + 0.963897i \(0.585793\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 29.1673 1.08475
\(724\) 0 0
\(725\) −34.6833 −1.28811
\(726\) 0 0
\(727\) 43.4351 1.61092 0.805460 0.592650i \(-0.201918\pi\)
0.805460 + 0.592650i \(0.201918\pi\)
\(728\) 0 0
\(729\) 22.6693 0.839605
\(730\) 0 0
\(731\) 6.50391 0.240556
\(732\) 0 0
\(733\) 51.2125 1.89158 0.945789 0.324782i \(-0.105291\pi\)
0.945789 + 0.324782i \(0.105291\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.44204 −0.126789
\(738\) 0 0
\(739\) 7.81873 0.287617 0.143808 0.989606i \(-0.454065\pi\)
0.143808 + 0.989606i \(0.454065\pi\)
\(740\) 0 0
\(741\) −5.88087 −0.216039
\(742\) 0 0
\(743\) −46.1171 −1.69187 −0.845935 0.533285i \(-0.820957\pi\)
−0.845935 + 0.533285i \(0.820957\pi\)
\(744\) 0 0
\(745\) −14.3630 −0.526220
\(746\) 0 0
\(747\) −0.426812 −0.0156162
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −44.2495 −1.61469 −0.807343 0.590083i \(-0.799095\pi\)
−0.807343 + 0.590083i \(0.799095\pi\)
\(752\) 0 0
\(753\) −26.1018 −0.951203
\(754\) 0 0
\(755\) 15.0150 0.546453
\(756\) 0 0
\(757\) 33.9225 1.23293 0.616466 0.787381i \(-0.288564\pi\)
0.616466 + 0.787381i \(0.288564\pi\)
\(758\) 0 0
\(759\) 23.9227 0.868340
\(760\) 0 0
\(761\) −3.04413 −0.110350 −0.0551748 0.998477i \(-0.517572\pi\)
−0.0551748 + 0.998477i \(0.517572\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 1.52798 0.0552441
\(766\) 0 0
\(767\) −9.91201 −0.357902
\(768\) 0 0
\(769\) −10.2605 −0.370003 −0.185002 0.982738i \(-0.559229\pi\)
−0.185002 + 0.982738i \(0.559229\pi\)
\(770\) 0 0
\(771\) −30.3531 −1.09314
\(772\) 0 0
\(773\) 42.1375 1.51558 0.757791 0.652497i \(-0.226279\pi\)
0.757791 + 0.652497i \(0.226279\pi\)
\(774\) 0 0
\(775\) −9.38735 −0.337204
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.03402 −0.252020
\(780\) 0 0
\(781\) 1.10466 0.0395280
\(782\) 0 0
\(783\) −46.5630 −1.66403
\(784\) 0 0
\(785\) −14.3071 −0.510643
\(786\) 0 0
\(787\) 6.73060 0.239920 0.119960 0.992779i \(-0.461723\pi\)
0.119960 + 0.992779i \(0.461723\pi\)
\(788\) 0 0
\(789\) 33.2676 1.18436
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 3.70564 0.131591
\(794\) 0 0
\(795\) −6.95990 −0.246842
\(796\) 0 0
\(797\) −38.8945 −1.37771 −0.688857 0.724897i \(-0.741887\pi\)
−0.688857 + 0.724897i \(0.741887\pi\)
\(798\) 0 0
\(799\) 0.292774 0.0103576
\(800\) 0 0
\(801\) −16.8498 −0.595359
\(802\) 0 0
\(803\) −26.8254 −0.946648
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 14.6376 0.515268
\(808\) 0 0
\(809\) 5.28280 0.185733 0.0928667 0.995679i \(-0.470397\pi\)
0.0928667 + 0.995679i \(0.470397\pi\)
\(810\) 0 0
\(811\) 55.9839 1.96586 0.982929 0.183983i \(-0.0588990\pi\)
0.982929 + 0.183983i \(0.0588990\pi\)
\(812\) 0 0
\(813\) 27.8786 0.977744
\(814\) 0 0
\(815\) 3.06008 0.107190
\(816\) 0 0
\(817\) −44.8328 −1.56850
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 8.60213 0.300217 0.150108 0.988670i \(-0.452038\pi\)
0.150108 + 0.988670i \(0.452038\pi\)
\(822\) 0 0
\(823\) 4.71187 0.164246 0.0821228 0.996622i \(-0.473830\pi\)
0.0821228 + 0.996622i \(0.473830\pi\)
\(824\) 0 0
\(825\) 21.6472 0.753659
\(826\) 0 0
\(827\) 27.2953 0.949152 0.474576 0.880215i \(-0.342601\pi\)
0.474576 + 0.880215i \(0.342601\pi\)
\(828\) 0 0
\(829\) 3.32378 0.115440 0.0577199 0.998333i \(-0.481617\pi\)
0.0577199 + 0.998333i \(0.481617\pi\)
\(830\) 0 0
\(831\) −11.5080 −0.399209
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −13.5522 −0.468993
\(836\) 0 0
\(837\) −12.6027 −0.435613
\(838\) 0 0
\(839\) 1.30879 0.0451844 0.0225922 0.999745i \(-0.492808\pi\)
0.0225922 + 0.999745i \(0.492808\pi\)
\(840\) 0 0
\(841\) 43.3788 1.49582
\(842\) 0 0
\(843\) −19.5243 −0.672454
\(844\) 0 0
\(845\) 12.0252 0.413680
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 8.31153 0.285251
\(850\) 0 0
\(851\) −29.4796 −1.01055
\(852\) 0 0
\(853\) 32.9494 1.12817 0.564084 0.825718i \(-0.309230\pi\)
0.564084 + 0.825718i \(0.309230\pi\)
\(854\) 0 0
\(855\) −10.5327 −0.360209
\(856\) 0 0
\(857\) 12.5820 0.429792 0.214896 0.976637i \(-0.431059\pi\)
0.214896 + 0.976637i \(0.431059\pi\)
\(858\) 0 0
\(859\) 44.1748 1.50723 0.753613 0.657319i \(-0.228309\pi\)
0.753613 + 0.657319i \(0.228309\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 7.62354 0.259508 0.129754 0.991546i \(-0.458581\pi\)
0.129754 + 0.991546i \(0.458581\pi\)
\(864\) 0 0
\(865\) 7.03228 0.239105
\(866\) 0 0
\(867\) −19.1612 −0.650747
\(868\) 0 0
\(869\) −7.93799 −0.269278
\(870\) 0 0
\(871\) 0.541959 0.0183636
\(872\) 0 0
\(873\) −29.5443 −0.999924
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 40.5396 1.36892 0.684462 0.729049i \(-0.260037\pi\)
0.684462 + 0.729049i \(0.260037\pi\)
\(878\) 0 0
\(879\) 10.3794 0.350087
\(880\) 0 0
\(881\) 15.9206 0.536379 0.268189 0.963366i \(-0.413575\pi\)
0.268189 + 0.963366i \(0.413575\pi\)
\(882\) 0 0
\(883\) 17.8403 0.600374 0.300187 0.953880i \(-0.402951\pi\)
0.300187 + 0.953880i \(0.402951\pi\)
\(884\) 0 0
\(885\) 16.4221 0.552023
\(886\) 0 0
\(887\) −17.0709 −0.573185 −0.286592 0.958053i \(-0.592523\pi\)
−0.286592 + 0.958053i \(0.592523\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 8.38603 0.280943
\(892\) 0 0
\(893\) −2.01816 −0.0675350
\(894\) 0 0
\(895\) 5.20232 0.173894
\(896\) 0 0
\(897\) −3.76671 −0.125767
\(898\) 0 0
\(899\) 19.5900 0.653362
\(900\) 0 0
\(901\) 6.15606 0.205088
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 18.6864 0.621158
\(906\) 0 0
\(907\) 43.5612 1.44643 0.723213 0.690625i \(-0.242664\pi\)
0.723213 + 0.690625i \(0.242664\pi\)
\(908\) 0 0
\(909\) −28.5139 −0.945746
\(910\) 0 0
\(911\) −42.9086 −1.42162 −0.710812 0.703382i \(-0.751673\pi\)
−0.710812 + 0.703382i \(0.751673\pi\)
\(912\) 0 0
\(913\) −1.21122 −0.0400856
\(914\) 0 0
\(915\) −6.13945 −0.202964
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 31.5185 1.03970 0.519849 0.854258i \(-0.325988\pi\)
0.519849 + 0.854258i \(0.325988\pi\)
\(920\) 0 0
\(921\) 17.2901 0.569729
\(922\) 0 0
\(923\) −0.173933 −0.00572507
\(924\) 0 0
\(925\) −26.6755 −0.877086
\(926\) 0 0
\(927\) −0.876409 −0.0287851
\(928\) 0 0
\(929\) 13.8605 0.454747 0.227374 0.973808i \(-0.426986\pi\)
0.227374 + 0.973808i \(0.426986\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 26.8367 0.878593
\(934\) 0 0
\(935\) 4.33614 0.141807
\(936\) 0 0
\(937\) −19.8346 −0.647967 −0.323983 0.946063i \(-0.605022\pi\)
−0.323983 + 0.946063i \(0.605022\pi\)
\(938\) 0 0
\(939\) −27.4719 −0.896512
\(940\) 0 0
\(941\) 3.35579 0.109396 0.0546978 0.998503i \(-0.482580\pi\)
0.0546978 + 0.998503i \(0.482580\pi\)
\(942\) 0 0
\(943\) −4.50530 −0.146713
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 28.4951 0.925965 0.462983 0.886367i \(-0.346779\pi\)
0.462983 + 0.886367i \(0.346779\pi\)
\(948\) 0 0
\(949\) 4.22374 0.137108
\(950\) 0 0
\(951\) −27.8554 −0.903273
\(952\) 0 0
\(953\) −22.8478 −0.740114 −0.370057 0.929009i \(-0.620662\pi\)
−0.370057 + 0.929009i \(0.620662\pi\)
\(954\) 0 0
\(955\) 12.6042 0.407863
\(956\) 0 0
\(957\) −45.1744 −1.46028
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −25.6978 −0.828961
\(962\) 0 0
\(963\) 1.68002 0.0541379
\(964\) 0 0
\(965\) −1.58198 −0.0509256
\(966\) 0 0
\(967\) −43.2554 −1.39100 −0.695500 0.718526i \(-0.744817\pi\)
−0.695500 + 0.718526i \(0.744817\pi\)
\(968\) 0 0
\(969\) −8.61804 −0.276851
\(970\) 0 0
\(971\) 7.07103 0.226920 0.113460 0.993543i \(-0.463807\pi\)
0.113460 + 0.993543i \(0.463807\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −3.40842 −0.109157
\(976\) 0 0
\(977\) 2.10191 0.0672461 0.0336230 0.999435i \(-0.489295\pi\)
0.0336230 + 0.999435i \(0.489295\pi\)
\(978\) 0 0
\(979\) −47.8170 −1.52824
\(980\) 0 0
\(981\) 3.50643 0.111952
\(982\) 0 0
\(983\) −9.55506 −0.304759 −0.152379 0.988322i \(-0.548694\pi\)
−0.152379 + 0.988322i \(0.548694\pi\)
\(984\) 0 0
\(985\) −7.06027 −0.224959
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −28.7155 −0.913100
\(990\) 0 0
\(991\) −22.5928 −0.717685 −0.358843 0.933398i \(-0.616829\pi\)
−0.358843 + 0.933398i \(0.616829\pi\)
\(992\) 0 0
\(993\) 15.7748 0.500597
\(994\) 0 0
\(995\) 5.68531 0.180237
\(996\) 0 0
\(997\) −0.674933 −0.0213754 −0.0106877 0.999943i \(-0.503402\pi\)
−0.0106877 + 0.999943i \(0.503402\pi\)
\(998\) 0 0
\(999\) −35.8124 −1.13305
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 \(a_p\))