Properties

Label 6048.2.a.be.1.2
Level 6048
Weight 2
Character 6048.1
Self dual Yes
Analytic conductor 48.294
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.56155\)
Character \(\chi\) = 6048.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.56155 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+2.56155 q^{5} -1.00000 q^{7} +5.12311 q^{11} -2.43845 q^{13} +4.12311 q^{17} +3.12311 q^{19} +8.68466 q^{23} +1.56155 q^{25} +9.56155 q^{29} +1.56155 q^{31} -2.56155 q^{35} -0.561553 q^{37} -7.43845 q^{41} -7.24621 q^{43} +0.561553 q^{47} +1.00000 q^{49} -6.68466 q^{53} +13.1231 q^{55} -8.12311 q^{59} -8.24621 q^{61} -6.24621 q^{65} +3.31534 q^{67} +1.56155 q^{71} -7.12311 q^{73} -5.12311 q^{77} +8.56155 q^{79} +2.56155 q^{83} +10.5616 q^{85} -1.31534 q^{89} +2.43845 q^{91} +8.00000 q^{95} -1.75379 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{5} - 2q^{7} + O(q^{10}) \) \( 2q + q^{5} - 2q^{7} + 2q^{11} - 9q^{13} - 2q^{19} + 5q^{23} - q^{25} + 15q^{29} - q^{31} - q^{35} + 3q^{37} - 19q^{41} + 2q^{43} - 3q^{47} + 2q^{49} - q^{53} + 18q^{55} - 8q^{59} + 4q^{65} + 19q^{67} - q^{71} - 6q^{73} - 2q^{77} + 13q^{79} + q^{83} + 17q^{85} - 15q^{89} + 9q^{91} + 16q^{95} - 20q^{97} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 2.56155 1.14556 0.572781 0.819709i \(-0.305865\pi\)
0.572781 + 0.819709i \(0.305865\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.12311 1.54467 0.772337 0.635213i \(-0.219088\pi\)
0.772337 + 0.635213i \(0.219088\pi\)
\(12\) 0 0
\(13\) −2.43845 −0.676304 −0.338152 0.941092i \(-0.609802\pi\)
−0.338152 + 0.941092i \(0.609802\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.12311 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 0 0
\(19\) 3.12311 0.716490 0.358245 0.933628i \(-0.383375\pi\)
0.358245 + 0.933628i \(0.383375\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 8.68466 1.81088 0.905438 0.424478i \(-0.139542\pi\)
0.905438 + 0.424478i \(0.139542\pi\)
\(24\) 0 0
\(25\) 1.56155 0.312311
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 9.56155 1.77554 0.887768 0.460291i \(-0.152255\pi\)
0.887768 + 0.460291i \(0.152255\pi\)
\(30\) 0 0
\(31\) 1.56155 0.280463 0.140232 0.990119i \(-0.455215\pi\)
0.140232 + 0.990119i \(0.455215\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.56155 −0.432981
\(36\) 0 0
\(37\) −0.561553 −0.0923187 −0.0461594 0.998934i \(-0.514698\pi\)
−0.0461594 + 0.998934i \(0.514698\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.43845 −1.16169 −0.580845 0.814014i \(-0.697278\pi\)
−0.580845 + 0.814014i \(0.697278\pi\)
\(42\) 0 0
\(43\) −7.24621 −1.10504 −0.552518 0.833501i \(-0.686333\pi\)
−0.552518 + 0.833501i \(0.686333\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.561553 0.0819109 0.0409554 0.999161i \(-0.486960\pi\)
0.0409554 + 0.999161i \(0.486960\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6.68466 −0.918208 −0.459104 0.888382i \(-0.651830\pi\)
−0.459104 + 0.888382i \(0.651830\pi\)
\(54\) 0 0
\(55\) 13.1231 1.76952
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.12311 −1.05754 −0.528769 0.848766i \(-0.677346\pi\)
−0.528769 + 0.848766i \(0.677346\pi\)
\(60\) 0 0
\(61\) −8.24621 −1.05582 −0.527910 0.849301i \(-0.677024\pi\)
−0.527910 + 0.849301i \(0.677024\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.24621 −0.774747
\(66\) 0 0
\(67\) 3.31534 0.405033 0.202517 0.979279i \(-0.435088\pi\)
0.202517 + 0.979279i \(0.435088\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.56155 0.185322 0.0926611 0.995698i \(-0.470463\pi\)
0.0926611 + 0.995698i \(0.470463\pi\)
\(72\) 0 0
\(73\) −7.12311 −0.833696 −0.416848 0.908976i \(-0.636865\pi\)
−0.416848 + 0.908976i \(0.636865\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −5.12311 −0.583832
\(78\) 0 0
\(79\) 8.56155 0.963250 0.481625 0.876377i \(-0.340047\pi\)
0.481625 + 0.876377i \(0.340047\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.56155 0.281167 0.140583 0.990069i \(-0.455102\pi\)
0.140583 + 0.990069i \(0.455102\pi\)
\(84\) 0 0
\(85\) 10.5616 1.14556
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.31534 −0.139426 −0.0697130 0.997567i \(-0.522208\pi\)
−0.0697130 + 0.997567i \(0.522208\pi\)
\(90\) 0 0
\(91\) 2.43845 0.255619
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 8.00000 0.820783
\(96\) 0 0
\(97\) −1.75379 −0.178070 −0.0890351 0.996028i \(-0.528378\pi\)
−0.0890351 + 0.996028i \(0.528378\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 0 0
\(103\) 6.43845 0.634399 0.317200 0.948359i \(-0.397258\pi\)
0.317200 + 0.948359i \(0.397258\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.4924 1.59438 0.797191 0.603727i \(-0.206318\pi\)
0.797191 + 0.603727i \(0.206318\pi\)
\(108\) 0 0
\(109\) −16.8078 −1.60989 −0.804946 0.593348i \(-0.797806\pi\)
−0.804946 + 0.593348i \(0.797806\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −5.12311 −0.481941 −0.240971 0.970532i \(-0.577466\pi\)
−0.240971 + 0.970532i \(0.577466\pi\)
\(114\) 0 0
\(115\) 22.2462 2.07447
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −4.12311 −0.377964
\(120\) 0 0
\(121\) 15.2462 1.38602
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −8.80776 −0.787790
\(126\) 0 0
\(127\) 18.5616 1.64707 0.823536 0.567264i \(-0.191998\pi\)
0.823536 + 0.567264i \(0.191998\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.31534 0.289663 0.144831 0.989456i \(-0.453736\pi\)
0.144831 + 0.989456i \(0.453736\pi\)
\(132\) 0 0
\(133\) −3.12311 −0.270808
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.12311 −0.608568 −0.304284 0.952581i \(-0.598417\pi\)
−0.304284 + 0.952581i \(0.598417\pi\)
\(138\) 0 0
\(139\) −18.4924 −1.56851 −0.784253 0.620441i \(-0.786954\pi\)
−0.784253 + 0.620441i \(0.786954\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −12.4924 −1.04467
\(144\) 0 0
\(145\) 24.4924 2.03398
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 12.9309 1.05934 0.529669 0.848204i \(-0.322316\pi\)
0.529669 + 0.848204i \(0.322316\pi\)
\(150\) 0 0
\(151\) −0.561553 −0.0456985 −0.0228493 0.999739i \(-0.507274\pi\)
−0.0228493 + 0.999739i \(0.507274\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) 18.9309 1.51085 0.755424 0.655236i \(-0.227431\pi\)
0.755424 + 0.655236i \(0.227431\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −8.68466 −0.684447
\(162\) 0 0
\(163\) 14.3693 1.12549 0.562746 0.826630i \(-0.309745\pi\)
0.562746 + 0.826630i \(0.309745\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.315342 −0.0244019 −0.0122009 0.999926i \(-0.503884\pi\)
−0.0122009 + 0.999926i \(0.503884\pi\)
\(168\) 0 0
\(169\) −7.05398 −0.542613
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 19.3693 1.47262 0.736311 0.676643i \(-0.236566\pi\)
0.736311 + 0.676643i \(0.236566\pi\)
\(174\) 0 0
\(175\) −1.56155 −0.118042
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −14.8769 −1.11195 −0.555976 0.831199i \(-0.687655\pi\)
−0.555976 + 0.831199i \(0.687655\pi\)
\(180\) 0 0
\(181\) −19.5616 −1.45400 −0.726999 0.686638i \(-0.759086\pi\)
−0.726999 + 0.686638i \(0.759086\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.43845 −0.105757
\(186\) 0 0
\(187\) 21.1231 1.54467
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 9.12311 0.660125 0.330062 0.943959i \(-0.392930\pi\)
0.330062 + 0.943959i \(0.392930\pi\)
\(192\) 0 0
\(193\) 22.6155 1.62790 0.813951 0.580934i \(-0.197313\pi\)
0.813951 + 0.580934i \(0.197313\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −15.1231 −1.07748 −0.538738 0.842473i \(-0.681099\pi\)
−0.538738 + 0.842473i \(0.681099\pi\)
\(198\) 0 0
\(199\) −6.68466 −0.473863 −0.236931 0.971526i \(-0.576142\pi\)
−0.236931 + 0.971526i \(0.576142\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −9.56155 −0.671089
\(204\) 0 0
\(205\) −19.0540 −1.33079
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) 26.0540 1.79363 0.896815 0.442406i \(-0.145875\pi\)
0.896815 + 0.442406i \(0.145875\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −18.5616 −1.26589
\(216\) 0 0
\(217\) −1.56155 −0.106005
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −10.0540 −0.676304
\(222\) 0 0
\(223\) 10.2462 0.686137 0.343069 0.939310i \(-0.388534\pi\)
0.343069 + 0.939310i \(0.388534\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −23.8078 −1.58018 −0.790088 0.612993i \(-0.789965\pi\)
−0.790088 + 0.612993i \(0.789965\pi\)
\(228\) 0 0
\(229\) −26.4924 −1.75067 −0.875334 0.483518i \(-0.839359\pi\)
−0.875334 + 0.483518i \(0.839359\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.75379 −0.376943 −0.188472 0.982079i \(-0.560353\pi\)
−0.188472 + 0.982079i \(0.560353\pi\)
\(234\) 0 0
\(235\) 1.43845 0.0938339
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.87689 −0.444829 −0.222415 0.974952i \(-0.571394\pi\)
−0.222415 + 0.974952i \(0.571394\pi\)
\(240\) 0 0
\(241\) 0.876894 0.0564857 0.0282429 0.999601i \(-0.491009\pi\)
0.0282429 + 0.999601i \(0.491009\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.56155 0.163652
\(246\) 0 0
\(247\) −7.61553 −0.484564
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.3153 0.777337 0.388669 0.921378i \(-0.372935\pi\)
0.388669 + 0.921378i \(0.372935\pi\)
\(252\) 0 0
\(253\) 44.4924 2.79721
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.00000 0.124757 0.0623783 0.998053i \(-0.480131\pi\)
0.0623783 + 0.998053i \(0.480131\pi\)
\(258\) 0 0
\(259\) 0.561553 0.0348932
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −13.1771 −0.812534 −0.406267 0.913754i \(-0.633170\pi\)
−0.406267 + 0.913754i \(0.633170\pi\)
\(264\) 0 0
\(265\) −17.1231 −1.05186
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 21.3002 1.29870 0.649348 0.760492i \(-0.275042\pi\)
0.649348 + 0.760492i \(0.275042\pi\)
\(270\) 0 0
\(271\) −20.0540 −1.21819 −0.609096 0.793096i \(-0.708468\pi\)
−0.609096 + 0.793096i \(0.708468\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 8.00000 0.482418
\(276\) 0 0
\(277\) 2.56155 0.153909 0.0769544 0.997035i \(-0.475480\pi\)
0.0769544 + 0.997035i \(0.475480\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −29.3693 −1.75203 −0.876013 0.482287i \(-0.839806\pi\)
−0.876013 + 0.482287i \(0.839806\pi\)
\(282\) 0 0
\(283\) 21.6155 1.28491 0.642455 0.766324i \(-0.277916\pi\)
0.642455 + 0.766324i \(0.277916\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 7.43845 0.439078
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 24.5616 1.43490 0.717451 0.696609i \(-0.245309\pi\)
0.717451 + 0.696609i \(0.245309\pi\)
\(294\) 0 0
\(295\) −20.8078 −1.21147
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −21.1771 −1.22470
\(300\) 0 0
\(301\) 7.24621 0.417665
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −21.1231 −1.20951
\(306\) 0 0
\(307\) 12.8769 0.734923 0.367462 0.930039i \(-0.380227\pi\)
0.367462 + 0.930039i \(0.380227\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 15.6847 0.889395 0.444698 0.895681i \(-0.353311\pi\)
0.444698 + 0.895681i \(0.353311\pi\)
\(312\) 0 0
\(313\) −24.2462 −1.37048 −0.685238 0.728319i \(-0.740302\pi\)
−0.685238 + 0.728319i \(0.740302\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 31.1231 1.74805 0.874024 0.485883i \(-0.161502\pi\)
0.874024 + 0.485883i \(0.161502\pi\)
\(318\) 0 0
\(319\) 48.9848 2.74262
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 12.8769 0.716490
\(324\) 0 0
\(325\) −3.80776 −0.211217
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −0.561553 −0.0309594
\(330\) 0 0
\(331\) 22.1231 1.21600 0.607998 0.793939i \(-0.291973\pi\)
0.607998 + 0.793939i \(0.291973\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 8.49242 0.463991
\(336\) 0 0
\(337\) 0.753789 0.0410615 0.0205307 0.999789i \(-0.493464\pi\)
0.0205307 + 0.999789i \(0.493464\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 8.00000 0.433224
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −29.8617 −1.60306 −0.801531 0.597953i \(-0.795981\pi\)
−0.801531 + 0.597953i \(0.795981\pi\)
\(348\) 0 0
\(349\) 29.1771 1.56181 0.780907 0.624648i \(-0.214757\pi\)
0.780907 + 0.624648i \(0.214757\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 33.9848 1.80883 0.904415 0.426653i \(-0.140307\pi\)
0.904415 + 0.426653i \(0.140307\pi\)
\(354\) 0 0
\(355\) 4.00000 0.212298
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −25.8078 −1.36208 −0.681041 0.732245i \(-0.738472\pi\)
−0.681041 + 0.732245i \(0.738472\pi\)
\(360\) 0 0
\(361\) −9.24621 −0.486643
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −18.2462 −0.955050
\(366\) 0 0
\(367\) −0.0539753 −0.00281749 −0.00140874 0.999999i \(-0.500448\pi\)
−0.00140874 + 0.999999i \(0.500448\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6.68466 0.347050
\(372\) 0 0
\(373\) 2.80776 0.145381 0.0726903 0.997355i \(-0.476842\pi\)
0.0726903 + 0.997355i \(0.476842\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −23.3153 −1.20080
\(378\) 0 0
\(379\) 4.31534 0.221664 0.110832 0.993839i \(-0.464648\pi\)
0.110832 + 0.993839i \(0.464648\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −19.0540 −0.973613 −0.486806 0.873510i \(-0.661838\pi\)
−0.486806 + 0.873510i \(0.661838\pi\)
\(384\) 0 0
\(385\) −13.1231 −0.668815
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 32.2462 1.63495 0.817474 0.575966i \(-0.195374\pi\)
0.817474 + 0.575966i \(0.195374\pi\)
\(390\) 0 0
\(391\) 35.8078 1.81088
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 21.9309 1.10346
\(396\) 0 0
\(397\) 7.61553 0.382212 0.191106 0.981569i \(-0.438793\pi\)
0.191106 + 0.981569i \(0.438793\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 14.4924 0.723717 0.361859 0.932233i \(-0.382142\pi\)
0.361859 + 0.932233i \(0.382142\pi\)
\(402\) 0 0
\(403\) −3.80776 −0.189678
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.87689 −0.142602
\(408\) 0 0
\(409\) −5.36932 −0.265496 −0.132748 0.991150i \(-0.542380\pi\)
−0.132748 + 0.991150i \(0.542380\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.12311 0.399712
\(414\) 0 0
\(415\) 6.56155 0.322094
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4.75379 −0.232238 −0.116119 0.993235i \(-0.537045\pi\)
−0.116119 + 0.993235i \(0.537045\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 6.43845 0.312311
\(426\) 0 0
\(427\) 8.24621 0.399062
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 0 0
\(433\) −38.1080 −1.83135 −0.915676 0.401918i \(-0.868344\pi\)
−0.915676 + 0.401918i \(0.868344\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 27.1231 1.29747
\(438\) 0 0
\(439\) 16.0540 0.766214 0.383107 0.923704i \(-0.374854\pi\)
0.383107 + 0.923704i \(0.374854\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −0.876894 −0.0416625 −0.0208313 0.999783i \(-0.506631\pi\)
−0.0208313 + 0.999783i \(0.506631\pi\)
\(444\) 0 0
\(445\) −3.36932 −0.159721
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −32.4924 −1.53341 −0.766706 0.641998i \(-0.778106\pi\)
−0.766706 + 0.641998i \(0.778106\pi\)
\(450\) 0 0
\(451\) −38.1080 −1.79443
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6.24621 0.292827
\(456\) 0 0
\(457\) −29.8078 −1.39435 −0.697174 0.716902i \(-0.745560\pi\)
−0.697174 + 0.716902i \(0.745560\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −32.4233 −1.51010 −0.755052 0.655665i \(-0.772388\pi\)
−0.755052 + 0.655665i \(0.772388\pi\)
\(462\) 0 0
\(463\) 11.4384 0.531590 0.265795 0.964030i \(-0.414366\pi\)
0.265795 + 0.964030i \(0.414366\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.24621 0.103942 0.0519711 0.998649i \(-0.483450\pi\)
0.0519711 + 0.998649i \(0.483450\pi\)
\(468\) 0 0
\(469\) −3.31534 −0.153088
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −37.1231 −1.70692
\(474\) 0 0
\(475\) 4.87689 0.223767
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 19.0540 0.870598 0.435299 0.900286i \(-0.356643\pi\)
0.435299 + 0.900286i \(0.356643\pi\)
\(480\) 0 0
\(481\) 1.36932 0.0624355
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.49242 −0.203990
\(486\) 0 0
\(487\) 6.63068 0.300465 0.150232 0.988651i \(-0.451998\pi\)
0.150232 + 0.988651i \(0.451998\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.75379 −0.0791474 −0.0395737 0.999217i \(-0.512600\pi\)
−0.0395737 + 0.999217i \(0.512600\pi\)
\(492\) 0 0
\(493\) 39.4233 1.77554
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.56155 −0.0700452
\(498\) 0 0
\(499\) −25.9309 −1.16083 −0.580413 0.814323i \(-0.697109\pi\)
−0.580413 + 0.814323i \(0.697109\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.19224 0.320686 0.160343 0.987061i \(-0.448740\pi\)
0.160343 + 0.987061i \(0.448740\pi\)
\(504\) 0 0
\(505\) 25.6155 1.13988
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −17.0540 −0.755904 −0.377952 0.925825i \(-0.623372\pi\)
−0.377952 + 0.925825i \(0.623372\pi\)
\(510\) 0 0
\(511\) 7.12311 0.315108
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 16.4924 0.726743
\(516\) 0 0
\(517\) 2.87689 0.126526
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −40.3693 −1.76861 −0.884306 0.466908i \(-0.845368\pi\)
−0.884306 + 0.466908i \(0.845368\pi\)
\(522\) 0 0
\(523\) 4.63068 0.202486 0.101243 0.994862i \(-0.467718\pi\)
0.101243 + 0.994862i \(0.467718\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.43845 0.280463
\(528\) 0 0
\(529\) 52.4233 2.27927
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 18.1383 0.785655
\(534\) 0 0
\(535\) 42.2462 1.82646
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5.12311 0.220668
\(540\) 0 0
\(541\) −11.1922 −0.481192 −0.240596 0.970625i \(-0.577343\pi\)
−0.240596 + 0.970625i \(0.577343\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −43.0540 −1.84423
\(546\) 0 0
\(547\) 31.6847 1.35474 0.677369 0.735643i \(-0.263120\pi\)
0.677369 + 0.735643i \(0.263120\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 29.8617 1.27215
\(552\) 0 0
\(553\) −8.56155 −0.364074
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12.1922 −0.516602 −0.258301 0.966065i \(-0.583163\pi\)
−0.258301 + 0.966065i \(0.583163\pi\)
\(558\) 0 0
\(559\) 17.6695 0.747340
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10.9309 0.460681 0.230341 0.973110i \(-0.426016\pi\)
0.230341 + 0.973110i \(0.426016\pi\)
\(564\) 0 0
\(565\) −13.1231 −0.552093
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10.2462 0.429544 0.214772 0.976664i \(-0.431099\pi\)
0.214772 + 0.976664i \(0.431099\pi\)
\(570\) 0 0
\(571\) −36.1231 −1.51170 −0.755852 0.654742i \(-0.772777\pi\)
−0.755852 + 0.654742i \(0.772777\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 13.5616 0.565556
\(576\) 0 0
\(577\) 6.00000 0.249783 0.124892 0.992170i \(-0.460142\pi\)
0.124892 + 0.992170i \(0.460142\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.56155 −0.106271
\(582\) 0 0
\(583\) −34.2462 −1.41833
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 28.6847 1.18394 0.591971 0.805959i \(-0.298350\pi\)
0.591971 + 0.805959i \(0.298350\pi\)
\(588\) 0 0
\(589\) 4.87689 0.200949
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −41.0540 −1.68588 −0.842942 0.538004i \(-0.819179\pi\)
−0.842942 + 0.538004i \(0.819179\pi\)
\(594\) 0 0
\(595\) −10.5616 −0.432981
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 36.9309 1.50895 0.754477 0.656326i \(-0.227890\pi\)
0.754477 + 0.656326i \(0.227890\pi\)
\(600\) 0 0
\(601\) 16.4924 0.672740 0.336370 0.941730i \(-0.390801\pi\)
0.336370 + 0.941730i \(0.390801\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 39.0540 1.58777
\(606\) 0 0
\(607\) 4.43845 0.180151 0.0900755 0.995935i \(-0.471289\pi\)
0.0900755 + 0.995935i \(0.471289\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.36932 −0.0553966
\(612\) 0 0
\(613\) −8.73863 −0.352950 −0.176475 0.984305i \(-0.556469\pi\)
−0.176475 + 0.984305i \(0.556469\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.12311 −0.286765 −0.143383 0.989667i \(-0.545798\pi\)
−0.143383 + 0.989667i \(0.545798\pi\)
\(618\) 0 0
\(619\) −31.6155 −1.27074 −0.635368 0.772210i \(-0.719151\pi\)
−0.635368 + 0.772210i \(0.719151\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.31534 0.0526980
\(624\) 0 0
\(625\) −30.3693 −1.21477
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.31534 −0.0923187
\(630\) 0 0
\(631\) −27.1922 −1.08251 −0.541253 0.840860i \(-0.682050\pi\)
−0.541253 + 0.840860i \(0.682050\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 47.5464 1.88682
\(636\) 0 0
\(637\) −2.43845 −0.0966148
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 16.6307 0.656872 0.328436 0.944526i \(-0.393478\pi\)
0.328436 + 0.944526i \(0.393478\pi\)
\(642\) 0 0
\(643\) −35.3693 −1.39483 −0.697415 0.716668i \(-0.745666\pi\)
−0.697415 + 0.716668i \(0.745666\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.8769 0.506243 0.253121 0.967435i \(-0.418543\pi\)
0.253121 + 0.967435i \(0.418543\pi\)
\(648\) 0 0
\(649\) −41.6155 −1.63355
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.05398 0.158644 0.0793222 0.996849i \(-0.474724\pi\)
0.0793222 + 0.996849i \(0.474724\pi\)
\(654\) 0 0
\(655\) 8.49242 0.331826
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 22.8769 0.891157 0.445579 0.895243i \(-0.352998\pi\)
0.445579 + 0.895243i \(0.352998\pi\)
\(660\) 0 0
\(661\) −2.49242 −0.0969440 −0.0484720 0.998825i \(-0.515435\pi\)
−0.0484720 + 0.998825i \(0.515435\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −8.00000 −0.310227
\(666\) 0 0
\(667\) 83.0388 3.21528
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −42.2462 −1.63090
\(672\) 0 0
\(673\) 30.1922 1.16383 0.581913 0.813251i \(-0.302305\pi\)
0.581913 + 0.813251i \(0.302305\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 30.8769 1.18670 0.593348 0.804946i \(-0.297806\pi\)
0.593348 + 0.804946i \(0.297806\pi\)
\(678\) 0 0
\(679\) 1.75379 0.0673042
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.49242 0.171898 0.0859489 0.996300i \(-0.472608\pi\)
0.0859489 + 0.996300i \(0.472608\pi\)
\(684\) 0 0
\(685\) −18.2462 −0.697152
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 16.3002 0.620988
\(690\) 0 0
\(691\) 5.61553 0.213625 0.106812 0.994279i \(-0.465936\pi\)
0.106812 + 0.994279i \(0.465936\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −47.3693 −1.79682
\(696\) 0 0
\(697\) −30.6695 −1.16169
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 10.0000 0.377695 0.188847 0.982006i \(-0.439525\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 0 0
\(703\) −1.75379 −0.0661454
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10.0000 −0.376089
\(708\) 0 0
\(709\) 9.93087 0.372962 0.186481 0.982459i \(-0.440292\pi\)
0.186481 + 0.982459i \(0.440292\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 13.5616 0.507884
\(714\) 0 0
\(715\) −32.0000 −1.19673
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 44.1771 1.64753 0.823764 0.566934i \(-0.191870\pi\)
0.823764 + 0.566934i \(0.191870\pi\)
\(720\) 0 0
\(721\) −6.43845 −0.239780
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 14.9309 0.554519
\(726\) 0 0
\(727\) −10.4384 −0.387141 −0.193570 0.981086i \(-0.562007\pi\)
−0.193570 + 0.981086i \(0.562007\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −29.8769 −1.10504
\(732\) 0 0
\(733\) −10.1922 −0.376459 −0.188229 0.982125i \(-0.560275\pi\)
−0.188229 + 0.982125i \(0.560275\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 16.9848 0.625645
\(738\) 0 0
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −29.5616 −1.08451 −0.542254 0.840215i \(-0.682429\pi\)
−0.542254 + 0.840215i \(0.682429\pi\)
\(744\) 0 0
\(745\) 33.1231 1.21354
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −16.4924 −0.602620
\(750\) 0 0
\(751\) −52.1080 −1.90145 −0.950723 0.310041i \(-0.899657\pi\)
−0.950723 + 0.310041i \(0.899657\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.43845 −0.0523505
\(756\) 0 0
\(757\) 23.1922 0.842936 0.421468 0.906843i \(-0.361515\pi\)
0.421468 + 0.906843i \(0.361515\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −29.8769 −1.08304 −0.541518 0.840689i \(-0.682150\pi\)
−0.541518 + 0.840689i \(0.682150\pi\)
\(762\) 0 0
\(763\) 16.8078 0.608482
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 19.8078 0.715217
\(768\) 0 0
\(769\) −39.8617 −1.43745 −0.718726 0.695294i \(-0.755274\pi\)
−0.718726 + 0.695294i \(0.755274\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9.43845 0.339477 0.169739 0.985489i \(-0.445708\pi\)
0.169739 + 0.985489i \(0.445708\pi\)
\(774\) 0 0
\(775\) 2.43845 0.0875916
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −23.2311 −0.832339
\(780\) 0 0
\(781\) 8.00000 0.286263
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 48.4924 1.73077
\(786\) 0 0
\(787\) −29.3693 −1.04690 −0.523452 0.852055i \(-0.675356\pi\)
−0.523452 + 0.852055i \(0.675356\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 5.12311 0.182157
\(792\) 0 0
\(793\) 20.1080 0.714054
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 22.9848 0.814165 0.407082 0.913391i \(-0.366546\pi\)
0.407082 + 0.913391i \(0.366546\pi\)
\(798\) 0 0
\(799\) 2.31534 0.0819109
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −36.4924 −1.28779
\(804\) 0 0
\(805\) −22.2462 −0.784076
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 19.3693 0.680989 0.340494 0.940247i \(-0.389406\pi\)
0.340494 + 0.940247i \(0.389406\pi\)
\(810\) 0 0
\(811\) −34.4924 −1.21119 −0.605596 0.795772i \(-0.707065\pi\)
−0.605596 + 0.795772i \(0.707065\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 36.8078 1.28932
\(816\) 0 0
\(817\) −22.6307 −0.791747
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 38.9309 1.35870 0.679348 0.733816i \(-0.262263\pi\)
0.679348 + 0.733816i \(0.262263\pi\)
\(822\) 0 0
\(823\) −4.56155 −0.159006 −0.0795029 0.996835i \(-0.525333\pi\)
−0.0795029 + 0.996835i \(0.525333\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −34.4924 −1.19942 −0.599710 0.800218i \(-0.704717\pi\)
−0.599710 + 0.800218i \(0.704717\pi\)
\(828\) 0 0
\(829\) 43.1231 1.49773 0.748864 0.662724i \(-0.230600\pi\)
0.748864 + 0.662724i \(0.230600\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 4.12311 0.142857
\(834\) 0 0
\(835\) −0.807764 −0.0279538
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −44.9157 −1.55066 −0.775331 0.631555i \(-0.782417\pi\)
−0.775331 + 0.631555i \(0.782417\pi\)
\(840\) 0 0
\(841\) 62.4233 2.15253
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −18.0691 −0.621597
\(846\) 0 0
\(847\) −15.2462 −0.523866
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −4.87689 −0.167178
\(852\) 0 0
\(853\) 36.0540 1.23446 0.617232 0.786781i \(-0.288254\pi\)
0.617232 + 0.786781i \(0.288254\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 42.1231 1.43890 0.719449 0.694545i \(-0.244394\pi\)
0.719449 + 0.694545i \(0.244394\pi\)
\(858\) 0 0
\(859\) −13.5076 −0.460873 −0.230436 0.973087i \(-0.574015\pi\)
−0.230436 + 0.973087i \(0.574015\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −29.8078 −1.01467 −0.507334 0.861749i \(-0.669369\pi\)
−0.507334 + 0.861749i \(0.669369\pi\)
\(864\) 0 0
\(865\) 49.6155 1.68698
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 43.8617 1.48791
\(870\) 0 0
\(871\) −8.08429 −0.273926
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 8.80776 0.297757
\(876\) 0 0
\(877\) −31.6847 −1.06991 −0.534957 0.844879i \(-0.679672\pi\)
−0.534957 + 0.844879i \(0.679672\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −33.4233 −1.12606 −0.563030 0.826437i \(-0.690364\pi\)
−0.563030 + 0.826437i \(0.690364\pi\)
\(882\) 0 0
\(883\) 48.2311 1.62310 0.811552 0.584280i \(-0.198623\pi\)
0.811552 + 0.584280i \(0.198623\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 21.4384 0.719833 0.359916 0.932985i \(-0.382805\pi\)
0.359916 + 0.932985i \(0.382805\pi\)
\(888\) 0 0
\(889\) −18.5616 −0.622535
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.75379 0.0586883
\(894\) 0 0
\(895\) −38.1080 −1.27381
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 14.9309 0.497972
\(900\) 0 0
\(901\) −27.5616 −0.918208
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −50.1080 −1.66564
\(906\) 0 0
\(907\) 26.5616 0.881962 0.440981 0.897516i \(-0.354631\pi\)
0.440981 + 0.897516i \(0.354631\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0.630683 0.0208955 0.0104477 0.999945i \(-0.496674\pi\)
0.0104477 + 0.999945i \(0.496674\pi\)
\(912\) 0 0
\(913\) 13.1231 0.434311
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3.31534 −0.109482
\(918\) 0 0
\(919\) 30.1771 0.995450 0.497725 0.867335i \(-0.334169\pi\)
0.497725 + 0.867335i \(0.334169\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −3.80776 −0.125334
\(924\) 0 0
\(925\) −0.876894 −0.0288321
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.56155 0.149660 0.0748298 0.997196i \(-0.476159\pi\)
0.0748298 + 0.997196i \(0.476159\pi\)
\(930\) 0 0
\(931\) 3.12311 0.102356
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 54.1080 1.76952
\(936\) 0 0
\(937\) 9.75379 0.318642 0.159321 0.987227i \(-0.449069\pi\)
0.159321 + 0.987227i \(0.449069\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −30.8078 −1.00430 −0.502152 0.864779i \(-0.667458\pi\)
−0.502152 + 0.864779i \(0.667458\pi\)
\(942\) 0 0
\(943\) −64.6004 −2.10368
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 14.6307 0.475433 0.237717 0.971335i \(-0.423601\pi\)
0.237717 + 0.971335i \(0.423601\pi\)
\(948\) 0 0
\(949\) 17.3693 0.563832
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −23.5076 −0.761485 −0.380743 0.924681i \(-0.624332\pi\)
−0.380743 + 0.924681i \(0.624332\pi\)
\(954\) 0 0
\(955\) 23.3693 0.756213
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 7.12311 0.230017
\(960\) 0 0
\(961\) −28.5616 −0.921340
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 57.9309 1.86486
\(966\) 0 0
\(967\) −8.98485 −0.288933 −0.144467 0.989510i \(-0.546147\pi\)
−0.144467 + 0.989510i \(0.546147\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −30.1231 −0.966696 −0.483348 0.875428i \(-0.660579\pi\)
−0.483348 + 0.875428i \(0.660579\pi\)
\(972\) 0 0
\(973\) 18.4924 0.592840
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 22.0000 0.703842 0.351921 0.936030i \(-0.385529\pi\)
0.351921 + 0.936030i \(0.385529\pi\)
\(978\) 0 0
\(979\) −6.73863 −0.215368
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −12.8078 −0.408504 −0.204252 0.978918i \(-0.565476\pi\)
−0.204252 + 0.978918i \(0.565476\pi\)
\(984\) 0 0
\(985\) −38.7386 −1.23432
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −62.9309 −2.00109
\(990\) 0 0
\(991\) −56.4233 −1.79234 −0.896172 0.443706i \(-0.853663\pi\)
−0.896172 + 0.443706i \(0.853663\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −17.1231 −0.542839
\(996\) 0 0
\(997\) −45.6695 −1.44637 −0.723184 0.690656i \(-0.757322\pi\)
−0.723184 + 0.690656i \(0.757322\pi\)
\(998\) 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 \(a_p\))