Properties

Label 4032.2.j.e.2591.4
Level 4032
Weight 2
Character 4032.2591
Analytic conductor 32.196
Analytic rank 0
Dimension 16
CM No
Inner twists 8

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Newspace parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.j (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.195682095\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: 16.0.162447943996702457856.1
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{18} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2591.4
Root \(-1.40721 + 0.140577i\)
Character \(\chi\) = 4032.2591
Dual form 4032.2.j.e.2591.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.09557 q^{5} +1.00000i q^{7} +O(q^{10})\) \(q-3.09557 q^{5} +1.00000i q^{7} +0.646084i q^{11} +4.37780i q^{13} -0.295164i q^{17} -5.29150 q^{19} +3.94748 q^{23} +4.58258 q^{25} +5.03383 q^{29} +9.16515i q^{31} -3.09557i q^{35} +2.55040i q^{37} -10.4282i q^{41} -1.63670 q^{43} +5.65685 q^{47} -1.00000 q^{49} -8.64064 q^{53} -2.00000i q^{55} +6.92820i q^{61} -13.5518i q^{65} -2.55040 q^{67} -1.11905 q^{71} -9.58258 q^{73} -0.646084 q^{77} -16.7477i q^{79} -8.50579i q^{83} +0.913701i q^{85} +10.4282i q^{89} -4.37780 q^{91} +16.3802 q^{95} -2.41742 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 16q^{49} - 80q^{73} - 112q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1793\) \(3781\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(-1\)

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 0
\(4\) 0 0
\(5\) −3.09557 −1.38438 −0.692191 0.721714i \(-0.743355\pi\)
−0.692191 + 0.721714i \(0.743355\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.646084i 0.194802i 0.995245 + 0.0974008i \(0.0310529\pi\)
−0.995245 + 0.0974008i \(0.968947\pi\)
\(12\) 0 0
\(13\) 4.37780i 1.21418i 0.794632 + 0.607092i \(0.207664\pi\)
−0.794632 + 0.607092i \(0.792336\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 0.295164i − 0.0715877i −0.999359 0.0357938i \(-0.988604\pi\)
0.999359 0.0357938i \(-0.0113960\pi\)
\(18\) 0 0
\(19\) −5.29150 −1.21395 −0.606977 0.794719i \(-0.707618\pi\)
−0.606977 + 0.794719i \(0.707618\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.94748 0.823106 0.411553 0.911386i \(-0.364987\pi\)
0.411553 + 0.911386i \(0.364987\pi\)
\(24\) 0 0
\(25\) 4.58258 0.916515
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.03383 0.934758 0.467379 0.884057i \(-0.345198\pi\)
0.467379 + 0.884057i \(0.345198\pi\)
\(30\) 0 0
\(31\) 9.16515i 1.64611i 0.567962 + 0.823055i \(0.307732\pi\)
−0.567962 + 0.823055i \(0.692268\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 3.09557i − 0.523247i
\(36\) 0 0
\(37\) 2.55040i 0.419283i 0.977778 + 0.209642i \(0.0672297\pi\)
−0.977778 + 0.209642i \(0.932770\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 10.4282i − 1.62861i −0.580434 0.814307i \(-0.697117\pi\)
0.580434 0.814307i \(-0.302883\pi\)
\(42\) 0 0
\(43\) −1.63670 −0.249595 −0.124797 0.992182i \(-0.539828\pi\)
−0.124797 + 0.992182i \(0.539828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.65685 0.825137 0.412568 0.910927i \(-0.364632\pi\)
0.412568 + 0.910927i \(0.364632\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −8.64064 −1.18688 −0.593441 0.804877i \(-0.702231\pi\)
−0.593441 + 0.804877i \(0.702231\pi\)
\(54\) 0 0
\(55\) − 2.00000i − 0.269680i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 6.92820i 0.887066i 0.896258 + 0.443533i \(0.146275\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) − 13.5518i − 1.68089i
\(66\) 0 0
\(67\) −2.55040 −0.311581 −0.155791 0.987790i \(-0.549792\pi\)
−0.155791 + 0.987790i \(0.549792\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.11905 −0.132807 −0.0664034 0.997793i \(-0.521152\pi\)
−0.0664034 + 0.997793i \(0.521152\pi\)
\(72\) 0 0
\(73\) −9.58258 −1.12156 −0.560778 0.827966i \(-0.689498\pi\)
−0.560778 + 0.827966i \(0.689498\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.646084 −0.0736281
\(78\) 0 0
\(79\) − 16.7477i − 1.88427i −0.335239 0.942133i \(-0.608817\pi\)
0.335239 0.942133i \(-0.391183\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 8.50579i − 0.933632i −0.884354 0.466816i \(-0.845401\pi\)
0.884354 0.466816i \(-0.154599\pi\)
\(84\) 0 0
\(85\) 0.913701i 0.0991047i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 10.4282i 1.10539i 0.833384 + 0.552694i \(0.186400\pi\)
−0.833384 + 0.552694i \(0.813600\pi\)
\(90\) 0 0
\(91\) −4.37780 −0.458918
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 16.3802 1.68058
\(96\) 0 0
\(97\) −2.41742 −0.245452 −0.122726 0.992441i \(-0.539164\pi\)
−0.122726 + 0.992441i \(0.539164\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −17.7925 −1.77042 −0.885211 0.465191i \(-0.845986\pi\)
−0.885211 + 0.465191i \(0.845986\pi\)
\(102\) 0 0
\(103\) 2.00000i 0.197066i 0.995134 + 0.0985329i \(0.0314150\pi\)
−0.995134 + 0.0985329i \(0.968585\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 10.4440i − 1.00966i −0.863218 0.504832i \(-0.831554\pi\)
0.863218 0.504832i \(-0.168446\pi\)
\(108\) 0 0
\(109\) 5.29150i 0.506834i 0.967357 + 0.253417i \(0.0815545\pi\)
−0.967357 + 0.253417i \(0.918446\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 9.89949i − 0.931266i −0.884978 0.465633i \(-0.845827\pi\)
0.884978 0.465633i \(-0.154173\pi\)
\(114\) 0 0
\(115\) −12.2197 −1.13949
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.295164 0.0270576
\(120\) 0 0
\(121\) 10.5826 0.962052
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.29217 0.115575
\(126\) 0 0
\(127\) − 13.5826i − 1.20526i −0.798021 0.602629i \(-0.794120\pi\)
0.798021 0.602629i \(-0.205880\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 3.60681i − 0.315129i −0.987509 0.157564i \(-0.949636\pi\)
0.987509 0.157564i \(-0.0503642\pi\)
\(132\) 0 0
\(133\) − 5.29150i − 0.458831i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 20.0325i 1.71150i 0.517393 + 0.855748i \(0.326903\pi\)
−0.517393 + 0.855748i \(0.673097\pi\)
\(138\) 0 0
\(139\) −8.75560 −0.742641 −0.371320 0.928505i \(-0.621095\pi\)
−0.371320 + 0.928505i \(0.621095\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.82843 −0.236525
\(144\) 0 0
\(145\) −15.5826 −1.29406
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.76413 −0.390293 −0.195147 0.980774i \(-0.562518\pi\)
−0.195147 + 0.980774i \(0.562518\pi\)
\(150\) 0 0
\(151\) − 4.83485i − 0.393454i −0.980458 0.196727i \(-0.936969\pi\)
0.980458 0.196727i \(-0.0630313\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 28.3714i − 2.27885i
\(156\) 0 0
\(157\) 5.10080i 0.407088i 0.979066 + 0.203544i \(0.0652461\pi\)
−0.979066 + 0.203544i \(0.934754\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.94748i 0.311105i
\(162\) 0 0
\(163\) 23.7164 1.85761 0.928806 0.370565i \(-0.120836\pi\)
0.928806 + 0.370565i \(0.120836\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.06653 −0.392060 −0.196030 0.980598i \(-0.562805\pi\)
−0.196030 + 0.980598i \(0.562805\pi\)
\(168\) 0 0
\(169\) −6.16515 −0.474242
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −19.0847 −1.45098 −0.725491 0.688232i \(-0.758387\pi\)
−0.725491 + 0.688232i \(0.758387\pi\)
\(174\) 0 0
\(175\) 4.58258i 0.346410i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 15.3430i − 1.14679i −0.819279 0.573396i \(-0.805626\pi\)
0.819279 0.573396i \(-0.194374\pi\)
\(180\) 0 0
\(181\) − 6.20520i − 0.461229i −0.973045 0.230615i \(-0.925926\pi\)
0.973045 0.230615i \(-0.0740736\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 7.89495i − 0.580449i
\(186\) 0 0
\(187\) 0.190700 0.0139454
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −24.8039 −1.79475 −0.897374 0.441271i \(-0.854528\pi\)
−0.897374 + 0.441271i \(0.854528\pi\)
\(192\) 0 0
\(193\) −20.7477 −1.49345 −0.746727 0.665131i \(-0.768376\pi\)
−0.746727 + 0.665131i \(0.768376\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −20.0005 −1.42497 −0.712487 0.701686i \(-0.752431\pi\)
−0.712487 + 0.701686i \(0.752431\pi\)
\(198\) 0 0
\(199\) 0.834849i 0.0591808i 0.999562 + 0.0295904i \(0.00942030\pi\)
−0.999562 + 0.0295904i \(0.990580\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.03383i 0.353305i
\(204\) 0 0
\(205\) 32.2813i 2.25462i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 3.41875i − 0.236480i
\(210\) 0 0
\(211\) −20.9753 −1.44400 −0.722000 0.691893i \(-0.756777\pi\)
−0.722000 + 0.691893i \(0.756777\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5.06653 0.345534
\(216\) 0 0
\(217\) −9.16515 −0.622171
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.29217 0.0869206
\(222\) 0 0
\(223\) − 20.0000i − 1.33930i −0.742677 0.669650i \(-0.766444\pi\)
0.742677 0.669650i \(-0.233556\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.60681i 0.239393i 0.992811 + 0.119696i \(0.0381921\pi\)
−0.992811 + 0.119696i \(0.961808\pi\)
\(228\) 0 0
\(229\) − 14.9608i − 0.988638i −0.869281 0.494319i \(-0.835417\pi\)
0.869281 0.494319i \(-0.164583\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 7.07107i − 0.463241i −0.972806 0.231621i \(-0.925597\pi\)
0.972806 0.231621i \(-0.0744028\pi\)
\(234\) 0 0
\(235\) −17.5112 −1.14231
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 12.4328 0.804208 0.402104 0.915594i \(-0.368279\pi\)
0.402104 + 0.915594i \(0.368279\pi\)
\(240\) 0 0
\(241\) −29.5826 −1.90558 −0.952791 0.303628i \(-0.901802\pi\)
−0.952791 + 0.303628i \(0.901802\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.09557 0.197769
\(246\) 0 0
\(247\) − 23.1652i − 1.47396i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 23.4724i − 1.48157i −0.671744 0.740783i \(-0.734455\pi\)
0.671744 0.740783i \(-0.265545\pi\)
\(252\) 0 0
\(253\) 2.55040i 0.160342i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 16.6754i − 1.04018i −0.854111 0.520091i \(-0.825898\pi\)
0.854111 0.520091i \(-0.174102\pi\)
\(258\) 0 0
\(259\) −2.55040 −0.158474
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 17.4993 1.07905 0.539526 0.841969i \(-0.318603\pi\)
0.539526 + 0.841969i \(0.318603\pi\)
\(264\) 0 0
\(265\) 26.7477 1.64310
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −21.3993 −1.30474 −0.652370 0.757901i \(-0.726225\pi\)
−0.652370 + 0.757901i \(0.726225\pi\)
\(270\) 0 0
\(271\) 13.1652i 0.799726i 0.916575 + 0.399863i \(0.130942\pi\)
−0.916575 + 0.399863i \(0.869058\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.96073i 0.178539i
\(276\) 0 0
\(277\) − 11.4967i − 0.690770i −0.938461 0.345385i \(-0.887748\pi\)
0.938461 0.345385i \(-0.112252\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7.66139i 0.457041i 0.973539 + 0.228520i \(0.0733887\pi\)
−0.973539 + 0.228520i \(0.926611\pi\)
\(282\) 0 0
\(283\) 17.3205 1.02960 0.514799 0.857311i \(-0.327867\pi\)
0.514799 + 0.857311i \(0.327867\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.4282 0.615558
\(288\) 0 0
\(289\) 16.9129 0.994875
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 11.8711 0.693514 0.346757 0.937955i \(-0.387283\pi\)
0.346757 + 0.937955i \(0.387283\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 17.2813i 0.999402i
\(300\) 0 0
\(301\) − 1.63670i − 0.0943379i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 21.4468i − 1.22804i
\(306\) 0 0
\(307\) 8.94630 0.510593 0.255296 0.966863i \(-0.417827\pi\)
0.255296 + 0.966863i \(0.417827\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 21.4468 1.21613 0.608067 0.793886i \(-0.291945\pi\)
0.608067 + 0.793886i \(0.291945\pi\)
\(312\) 0 0
\(313\) −9.16515 −0.518045 −0.259022 0.965871i \(-0.583400\pi\)
−0.259022 + 0.965871i \(0.583400\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.8318 −0.833036 −0.416518 0.909127i \(-0.636750\pi\)
−0.416518 + 0.909127i \(0.636750\pi\)
\(318\) 0 0
\(319\) 3.25227i 0.182092i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.56186i 0.0869041i
\(324\) 0 0
\(325\) 20.0616i 1.11282i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5.65685i 0.311872i
\(330\) 0 0
\(331\) −22.8027 −1.25335 −0.626675 0.779281i \(-0.715585\pi\)
−0.626675 + 0.779281i \(0.715585\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7.89495 0.431347
\(336\) 0 0
\(337\) 14.3303 0.780621 0.390311 0.920683i \(-0.372368\pi\)
0.390311 + 0.920683i \(0.372368\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5.92146 −0.320665
\(342\) 0 0
\(343\) − 1.00000i − 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 5.27537i − 0.283197i −0.989924 0.141598i \(-0.954776\pi\)
0.989924 0.141598i \(-0.0452242\pi\)
\(348\) 0 0
\(349\) 21.1660i 1.13299i 0.824065 + 0.566495i \(0.191701\pi\)
−0.824065 + 0.566495i \(0.808299\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 15.0276i − 0.799840i −0.916550 0.399920i \(-0.869038\pi\)
0.916550 0.399920i \(-0.130962\pi\)
\(354\) 0 0
\(355\) 3.46410 0.183855
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −28.2227 −1.48954 −0.744768 0.667324i \(-0.767440\pi\)
−0.744768 + 0.667324i \(0.767440\pi\)
\(360\) 0 0
\(361\) 9.00000 0.473684
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 29.6636 1.55266
\(366\) 0 0
\(367\) 19.1652i 1.00041i 0.865906 + 0.500206i \(0.166743\pi\)
−0.865906 + 0.500206i \(0.833257\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 8.64064i − 0.448600i
\(372\) 0 0
\(373\) 21.1660i 1.09593i 0.836500 + 0.547967i \(0.184598\pi\)
−0.836500 + 0.547967i \(0.815402\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 22.0371i 1.13497i
\(378\) 0 0
\(379\) 29.7309 1.52717 0.763587 0.645705i \(-0.223436\pi\)
0.763587 + 0.645705i \(0.223436\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 22.0371 1.12604 0.563021 0.826442i \(-0.309639\pi\)
0.563021 + 0.826442i \(0.309639\pi\)
\(384\) 0 0
\(385\) 2.00000 0.101929
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 15.8543 0.803843 0.401921 0.915674i \(-0.368342\pi\)
0.401921 + 0.915674i \(0.368342\pi\)
\(390\) 0 0
\(391\) − 1.16515i − 0.0589242i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 51.8438i 2.60855i
\(396\) 0 0
\(397\) 1.82740i 0.0917146i 0.998948 + 0.0458573i \(0.0146020\pi\)
−0.998948 + 0.0458573i \(0.985398\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 32.5269i − 1.62432i −0.583437 0.812158i \(-0.698293\pi\)
0.583437 0.812158i \(-0.301707\pi\)
\(402\) 0 0
\(403\) −40.1232 −1.99868
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.64777 −0.0816771
\(408\) 0 0
\(409\) −1.58258 −0.0782533 −0.0391267 0.999234i \(-0.512458\pi\)
−0.0391267 + 0.999234i \(0.512458\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 26.3303i 1.29250i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 10.0677i − 0.491837i −0.969291 0.245918i \(-0.920910\pi\)
0.969291 0.245918i \(-0.0790895\pi\)
\(420\) 0 0
\(421\) 6.01450i 0.293129i 0.989201 + 0.146564i \(0.0468216\pi\)
−0.989201 + 0.146564i \(0.953178\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 1.35261i − 0.0656112i
\(426\) 0 0
\(427\) −6.92820 −0.335279
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −27.6323 −1.33100 −0.665501 0.746397i \(-0.731782\pi\)
−0.665501 + 0.746397i \(0.731782\pi\)
\(432\) 0 0
\(433\) 2.83485 0.136234 0.0681171 0.997677i \(-0.478301\pi\)
0.0681171 + 0.997677i \(0.478301\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −20.8881 −0.999213
\(438\) 0 0
\(439\) 18.3303i 0.874858i 0.899253 + 0.437429i \(0.144111\pi\)
−0.899253 + 0.437429i \(0.855889\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 10.7137i − 0.509025i −0.967070 0.254512i \(-0.918085\pi\)
0.967070 0.254512i \(-0.0819150\pi\)
\(444\) 0 0
\(445\) − 32.2813i − 1.53028i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9.89949i 0.467186i 0.972334 + 0.233593i \(0.0750483\pi\)
−0.972334 + 0.233593i \(0.924952\pi\)
\(450\) 0 0
\(451\) 6.73750 0.317257
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 13.5518 0.635319
\(456\) 0 0
\(457\) 15.1652 0.709396 0.354698 0.934981i \(-0.384584\pi\)
0.354698 + 0.934981i \(0.384584\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −9.55641 −0.445086 −0.222543 0.974923i \(-0.571436\pi\)
−0.222543 + 0.974923i \(0.571436\pi\)
\(462\) 0 0
\(463\) − 2.41742i − 0.112347i −0.998421 0.0561736i \(-0.982110\pi\)
0.998421 0.0561736i \(-0.0178900\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 18.8431i − 0.871956i −0.899957 0.435978i \(-0.856403\pi\)
0.899957 0.435978i \(-0.143597\pi\)
\(468\) 0 0
\(469\) − 2.55040i − 0.117767i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 1.05745i − 0.0486214i
\(474\) 0 0
\(475\) −24.2487 −1.11261
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9.66594 −0.441648 −0.220824 0.975314i \(-0.570875\pi\)
−0.220824 + 0.975314i \(0.570875\pi\)
\(480\) 0 0
\(481\) −11.1652 −0.509087
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.48331 0.339800
\(486\) 0 0
\(487\) 14.3303i 0.649368i 0.945823 + 0.324684i \(0.105258\pi\)
−0.945823 + 0.324684i \(0.894742\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 20.2420i − 0.913509i −0.889593 0.456754i \(-0.849012\pi\)
0.889593 0.456754i \(-0.150988\pi\)
\(492\) 0 0
\(493\) − 1.48580i − 0.0669171i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 1.11905i − 0.0501963i
\(498\) 0 0
\(499\) 33.0043 1.47748 0.738738 0.673993i \(-0.235422\pi\)
0.738738 + 0.673993i \(0.235422\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 14.7325 0.656888 0.328444 0.944523i \(-0.393476\pi\)
0.328444 + 0.944523i \(0.393476\pi\)
\(504\) 0 0
\(505\) 55.0780 2.45094
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2.07310 −0.0918884 −0.0459442 0.998944i \(-0.514630\pi\)
−0.0459442 + 0.998944i \(0.514630\pi\)
\(510\) 0 0
\(511\) − 9.58258i − 0.423908i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 6.19115i − 0.272815i
\(516\) 0 0
\(517\) 3.65480i 0.160738i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 31.8750i 1.39647i 0.715869 + 0.698234i \(0.246031\pi\)
−0.715869 + 0.698234i \(0.753969\pi\)
\(522\) 0 0
\(523\) −33.5764 −1.46819 −0.734097 0.679045i \(-0.762394\pi\)
−0.734097 + 0.679045i \(0.762394\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.70522 0.117841
\(528\) 0 0
\(529\) −7.41742 −0.322497
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 45.6527 1.97744
\(534\) 0 0
\(535\) 32.3303i 1.39776i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 0.646084i − 0.0278288i
\(540\) 0 0
\(541\) − 20.2523i − 0.870715i −0.900258 0.435357i \(-0.856622\pi\)
0.900258 0.435357i \(-0.143378\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) − 16.3802i − 0.701652i
\(546\) 0 0
\(547\) −44.5010 −1.90273 −0.951363 0.308072i \(-0.900316\pi\)
−0.951363 + 0.308072i \(0.900316\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −26.6365 −1.13475
\(552\) 0 0
\(553\) 16.7477 0.712186
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 41.9110 1.77583 0.887913 0.460011i \(-0.152154\pi\)
0.887913 + 0.460011i \(0.152154\pi\)
\(558\) 0 0
\(559\) − 7.16515i − 0.303054i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 44.3605i 1.86957i 0.355211 + 0.934786i \(0.384409\pi\)
−0.355211 + 0.934786i \(0.615591\pi\)
\(564\) 0 0
\(565\) 30.6446i 1.28923i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.25172i 0.345930i 0.984928 + 0.172965i \(0.0553348\pi\)
−0.984928 + 0.172965i \(0.944665\pi\)
\(570\) 0 0
\(571\) 44.8824 1.87827 0.939135 0.343547i \(-0.111628\pi\)
0.939135 + 0.343547i \(0.111628\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 18.0896 0.754389
\(576\) 0 0
\(577\) −13.1652 −0.548072 −0.274036 0.961719i \(-0.588359\pi\)
−0.274036 + 0.961719i \(0.588359\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8.50579 0.352880
\(582\) 0 0
\(583\) − 5.58258i − 0.231207i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 23.7421i 0.979942i 0.871739 + 0.489971i \(0.162993\pi\)
−0.871739 + 0.489971i \(0.837007\pi\)
\(588\) 0 0
\(589\) − 48.4974i − 1.99830i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 12.1992i − 0.500961i −0.968122 0.250481i \(-0.919411\pi\)
0.968122 0.250481i \(-0.0805886\pi\)
\(594\) 0 0
\(595\) −0.913701 −0.0374581
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7.95656 0.325096 0.162548 0.986701i \(-0.448029\pi\)
0.162548 + 0.986701i \(0.448029\pi\)
\(600\) 0 0
\(601\) 6.83485 0.278799 0.139400 0.990236i \(-0.455483\pi\)
0.139400 + 0.990236i \(0.455483\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −32.7591 −1.33185
\(606\) 0 0
\(607\) − 22.3303i − 0.906359i −0.891419 0.453180i \(-0.850290\pi\)
0.891419 0.453180i \(-0.149710\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 24.7646i 1.00187i
\(612\) 0 0
\(613\) 0.381401i 0.0154046i 0.999970 + 0.00770232i \(0.00245175\pi\)
−0.999970 + 0.00770232i \(0.997548\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 37.0031i 1.48969i 0.667238 + 0.744845i \(0.267476\pi\)
−0.667238 + 0.744845i \(0.732524\pi\)
\(618\) 0 0
\(619\) 41.9506 1.68614 0.843069 0.537806i \(-0.180747\pi\)
0.843069 + 0.537806i \(0.180747\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −10.4282 −0.417798
\(624\) 0 0
\(625\) −26.9129 −1.07652
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.752785 0.0300155
\(630\) 0 0
\(631\) − 31.9129i − 1.27043i −0.772335 0.635216i \(-0.780911\pi\)
0.772335 0.635216i \(-0.219089\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 42.0459i 1.66854i
\(636\) 0 0
\(637\) − 4.37780i − 0.173455i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 26.7468i 1.05644i 0.849108 + 0.528219i \(0.177140\pi\)
−0.849108 + 0.528219i \(0.822860\pi\)
\(642\) 0 0
\(643\) 41.7599 1.64685 0.823425 0.567425i \(-0.192060\pi\)
0.823425 + 0.567425i \(0.192060\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −33.3508 −1.31116 −0.655578 0.755128i \(-0.727575\pi\)
−0.655578 + 0.755128i \(0.727575\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.07878 −0.277014 −0.138507 0.990361i \(-0.544230\pi\)
−0.138507 + 0.990361i \(0.544230\pi\)
\(654\) 0 0
\(655\) 11.1652i 0.436259i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 24.1185i 0.939524i 0.882793 + 0.469762i \(0.155660\pi\)
−0.882793 + 0.469762i \(0.844340\pi\)
\(660\) 0 0
\(661\) 19.3386i 0.752185i 0.926582 + 0.376092i \(0.122732\pi\)
−0.926582 + 0.376092i \(0.877268\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 16.3802i 0.635198i
\(666\) 0 0
\(667\) 19.8709 0.769405
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.47620 −0.172802
\(672\) 0 0
\(673\) −39.9129 −1.53853 −0.769264 0.638931i \(-0.779377\pi\)
−0.769264 + 0.638931i \(0.779377\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 24.2534 0.932132 0.466066 0.884750i \(-0.345671\pi\)
0.466066 + 0.884750i \(0.345671\pi\)
\(678\) 0 0
\(679\) − 2.41742i − 0.0927722i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 49.1528i − 1.88078i −0.340099 0.940390i \(-0.610461\pi\)
0.340099 0.940390i \(-0.389539\pi\)
\(684\) 0 0
\(685\) − 62.0122i − 2.36937i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 37.8270i − 1.44109i
\(690\) 0 0
\(691\) 36.8498 1.40183 0.700917 0.713243i \(-0.252775\pi\)
0.700917 + 0.713243i \(0.252775\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 27.1036 1.02810
\(696\) 0 0
\(697\) −3.07803 −0.116589
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 8.37095 0.316166 0.158083 0.987426i \(-0.449469\pi\)
0.158083 + 0.987426i \(0.449469\pi\)
\(702\) 0 0
\(703\) − 13.4955i − 0.508991i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 17.7925i − 0.669156i
\(708\) 0 0
\(709\) − 2.01810i − 0.0757914i −0.999282 0.0378957i \(-0.987935\pi\)
0.999282 0.0378957i \(-0.0120655\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 36.1792i 1.35492i
\(714\) 0 0
\(715\) 8.75560 0.327441
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −42.3032 −1.57764 −0.788822 0.614622i \(-0.789308\pi\)
−0.788822 + 0.614622i \(0.789308\pi\)
\(720\) 0 0
\(721\) −2.00000 −0.0744839
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 23.0679 0.856720
\(726\) 0 0
\(727\) − 35.4955i − 1.31645i −0.752820 0.658227i \(-0.771307\pi\)
0.752820 0.658227i \(-0.228693\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.483094i 0.0178679i
\(732\) 0 0
\(733\) − 28.8172i − 1.06439i −0.846622 0.532194i \(-0.821368\pi\)
0.846622 0.532194i \(-0.178632\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 1.64777i − 0.0606965i
\(738\) 0 0
\(739\) 2.55040 0.0938180 0.0469090 0.998899i \(-0.485063\pi\)
0.0469090 + 0.998899i \(0.485063\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.17650 0.0798479 0.0399239 0.999203i \(-0.487288\pi\)
0.0399239 + 0.999203i \(0.487288\pi\)
\(744\) 0 0
\(745\) 14.7477 0.540315
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 10.4440 0.381617
\(750\) 0 0
\(751\) 16.8348i 0.614312i 0.951659 + 0.307156i \(0.0993774\pi\)
−0.951659 + 0.307156i \(0.900623\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 14.9666i 0.544691i
\(756\) 0 0
\(757\) − 20.5939i − 0.748498i −0.927328 0.374249i \(-0.877900\pi\)
0.927328 0.374249i \(-0.122100\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 40.3603i 1.46306i 0.681810 + 0.731529i \(0.261193\pi\)
−0.681810 + 0.731529i \(0.738807\pi\)
\(762\) 0 0
\(763\) −5.29150 −0.191565
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −28.6129 −1.02914 −0.514568 0.857450i \(-0.672048\pi\)
−0.514568 + 0.857450i \(0.672048\pi\)
\(774\) 0 0
\(775\) 42.0000i 1.50868i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 55.1809i 1.97706i
\(780\) 0 0
\(781\) − 0.723000i − 0.0258710i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 15.7899i − 0.563566i
\(786\) 0 0
\(787\) 22.2306 0.792436 0.396218 0.918157i \(-0.370323\pi\)
0.396218 + 0.918157i \(0.370323\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 9.89949 0.351986
\(792\) 0 0
\(793\) −30.3303 −1.07706
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 50.0404 1.77252 0.886261 0.463186i \(-0.153294\pi\)
0.886261 + 0.463186i \(0.153294\pi\)
\(798\) 0 0
\(799\) − 1.66970i − 0.0590696i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 6.19115i − 0.218481i
\(804\) 0 0
\(805\) − 12.2197i − 0.430688i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 8.84205i 0.310870i 0.987846 + 0.155435i \(0.0496779\pi\)
−0.987846 + 0.155435i \(0.950322\pi\)
\(810\) 0 0
\(811\) −26.2668 −0.922353 −0.461176 0.887309i \(-0.652572\pi\)
−0.461176 + 0.887309i \(0.652572\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −73.4159 −2.57165
\(816\) 0 0
\(817\) 8.66061 0.302996
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.74166 −0.130585 −0.0652924 0.997866i \(-0.520798\pi\)
−0.0652924 + 0.997866i \(0.520798\pi\)
\(822\) 0 0
\(823\) − 43.9129i − 1.53071i −0.643610 0.765353i \(-0.722564\pi\)
0.643610 0.765353i \(-0.277436\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 47.8606i − 1.66428i −0.554568 0.832138i \(-0.687117\pi\)
0.554568 0.832138i \(-0.312883\pi\)
\(828\) 0 0
\(829\) 27.3712i 0.950642i 0.879813 + 0.475321i \(0.157668\pi\)
−0.879813 + 0.475321i \(0.842332\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0.295164i 0.0102268i
\(834\) 0 0
\(835\) 15.6838 0.542761
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −26.0462 −0.899214 −0.449607 0.893227i \(-0.648436\pi\)
−0.449607 + 0.893227i \(0.648436\pi\)
\(840\) 0 0
\(841\) −3.66061 −0.126228
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 19.0847 0.656533
\(846\) 0 0
\(847\) 10.5826i 0.363622i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 10.0677i 0.345115i
\(852\) 0 0
\(853\) − 7.30960i − 0.250276i −0.992139 0.125138i \(-0.960063\pi\)
0.992139 0.125138i \(-0.0399374\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 19.5038i − 0.666238i −0.942885 0.333119i \(-0.891899\pi\)
0.942885 0.333119i \(-0.108101\pi\)
\(858\) 0 0
\(859\) 27.5221 0.939042 0.469521 0.882921i \(-0.344427\pi\)
0.469521 + 0.882921i \(0.344427\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −10.1947 −0.347030 −0.173515 0.984831i \(-0.555513\pi\)
−0.173515 + 0.984831i \(0.555513\pi\)
\(864\) 0 0
\(865\) 59.0780 2.00871
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 10.8204 0.367058
\(870\) 0 0
\(871\) − 11.1652i − 0.378317i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.29217i 0.0436832i
\(876\) 0 0
\(877\) − 35.0224i − 1.18262i −0.806443 0.591311i \(-0.798610\pi\)
0.806443 0.591311i \(-0.201390\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 11.6089i 0.391113i 0.980692 + 0.195556i \(0.0626513\pi\)
−0.980692 + 0.195556i \(0.937349\pi\)
\(882\) 0 0
\(883\) −24.2487 −0.816034 −0.408017 0.912974i \(-0.633780\pi\)
−0.408017 + 0.912974i \(0.633780\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −42.3032 −1.42040 −0.710201 0.703999i \(-0.751396\pi\)
−0.710201 + 0.703999i \(0.751396\pi\)
\(888\) 0 0
\(889\) 13.5826 0.455545
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −29.9333 −1.00168
\(894\) 0 0
\(895\) 47.4955i 1.58760i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 46.1358i 1.53871i
\(900\) 0 0
\(901\) 2.55040i 0.0849662i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 19.2087i 0.638518i
\(906\) 0 0
\(907\) −34.8317 −1.15657 −0.578284 0.815835i \(-0.696277\pi\)
−0.578284 + 0.815835i \(0.696277\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 6.18558 0.204937 0.102469 0.994736i \(-0.467326\pi\)
0.102469 + 0.994736i \(0.467326\pi\)
\(912\) 0 0
\(913\) 5.49545 0.181873
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.60681 0.119107
\(918\) 0 0
\(919\) 31.1652i 1.02804i 0.857777 + 0.514022i \(0.171845\pi\)
−0.857777 + 0.514022i \(0.828155\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 4.89898i − 0.161252i
\(924\) 0 0
\(925\) 11.6874i 0.384280i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 5.36169i 0.175911i 0.996124 + 0.0879557i \(0.0280334\pi\)
−0.996124 + 0.0879557i \(0.971967\pi\)
\(930\) 0 0
\(931\) 5.29150 0.173422
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −0.590327 −0.0193058
\(936\) 0 0
\(937\) −15.4955 −0.506214 −0.253107 0.967438i \(-0.581453\pi\)
−0.253107 + 0.967438i \(0.581453\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −23.9837 −0.781845 −0.390922 0.920424i \(-0.627844\pi\)
−0.390922 + 0.920424i \(0.627844\pi\)
\(942\) 0 0
\(943\) − 41.1652i − 1.34052i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 53.7821i 1.74768i 0.486211 + 0.873841i \(0.338379\pi\)
−0.486211 + 0.873841i \(0.661621\pi\)
\(948\) 0 0
\(949\) − 41.9506i − 1.36177i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 40.4219i 1.30939i 0.755892 + 0.654696i \(0.227203\pi\)
−0.755892 + 0.654696i \(0.772797\pi\)
\(954\) 0 0
\(955\) 76.7823 2.48462
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −20.0325 −0.646885
\(960\) 0 0
\(961\) −53.0000 −1.70968
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 64.2261 2.06751
\(966\) 0 0
\(967\) 51.0780i 1.64256i 0.570526 + 0.821279i \(0.306739\pi\)
−0.570526 + 0.821279i \(0.693261\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 39.4615i 1.26638i 0.773996 + 0.633190i \(0.218255\pi\)
−0.773996 + 0.633190i \(0.781745\pi\)
\(972\) 0 0
\(973\) − 8.75560i − 0.280692i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 44.8981i 1.43642i 0.695828 + 0.718208i \(0.255037\pi\)
−0.695828 + 0.718208i \(0.744963\pi\)
\(978\) 0 0
\(979\) −6.73750 −0.215332
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −50.1982 −1.60107 −0.800536 0.599284i \(-0.795452\pi\)
−0.800536 + 0.599284i \(0.795452\pi\)
\(984\) 0 0
\(985\) 61.9129 1.97271
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −6.46084 −0.205443
\(990\) 0 0
\(991\) − 20.0000i − 0.635321i −0.948205 0.317660i \(-0.897103\pi\)
0.948205 0.317660i \(-0.102897\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 2.58434i − 0.0819289i
\(996\) 0 0
\(997\) 48.8788i 1.54801i 0.633181 + 0.774004i \(0.281749\pi\)
−0.633181 + 0.774004i \(0.718251\pi\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))