Properties

Label 8008.2.a.v.1.1
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 11
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.33407\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.33407 q^{3} -0.131360 q^{5} -1.00000 q^{7} +8.11603 q^{9} +O(q^{10})\) \(q-3.33407 q^{3} -0.131360 q^{5} -1.00000 q^{7} +8.11603 q^{9} +1.00000 q^{11} -1.00000 q^{13} +0.437964 q^{15} +4.35509 q^{17} +0.765047 q^{19} +3.33407 q^{21} -2.35398 q^{23} -4.98274 q^{25} -17.0572 q^{27} +1.55007 q^{29} +3.44072 q^{31} -3.33407 q^{33} +0.131360 q^{35} -6.91967 q^{37} +3.33407 q^{39} +7.35180 q^{41} -9.25933 q^{43} -1.06612 q^{45} -2.35398 q^{47} +1.00000 q^{49} -14.5202 q^{51} +6.98712 q^{53} -0.131360 q^{55} -2.55072 q^{57} -0.151719 q^{59} -7.77746 q^{61} -8.11603 q^{63} +0.131360 q^{65} -7.77938 q^{67} +7.84834 q^{69} -0.493113 q^{71} -3.05167 q^{73} +16.6128 q^{75} -1.00000 q^{77} +1.38849 q^{79} +32.5219 q^{81} +4.49597 q^{83} -0.572085 q^{85} -5.16804 q^{87} +6.66657 q^{89} +1.00000 q^{91} -11.4716 q^{93} -0.100497 q^{95} +18.6373 q^{97} +8.11603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + O(q^{10}) \) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + 11q^{11} - 11q^{13} - 7q^{15} - 4q^{17} - 16q^{19} + 2q^{21} - 3q^{23} + 11q^{25} - 11q^{27} + q^{29} + 14q^{31} - 2q^{33} - 2q^{35} - 8q^{37} + 2q^{39} + 4q^{41} - 30q^{43} + 13q^{45} - 3q^{47} + 11q^{49} - 14q^{51} - 5q^{53} + 2q^{55} - 22q^{57} + 11q^{59} + 15q^{61} - 9q^{63} - 2q^{65} - 41q^{67} + 12q^{69} + q^{71} - 8q^{73} - 24q^{75} - 11q^{77} - 26q^{79} + 19q^{81} - 31q^{83} - 27q^{85} - 25q^{87} + 2q^{89} + 11q^{91} - 37q^{93} - 6q^{97} + 9q^{99} + O(q^{100}) \)

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
\(3\) −3.33407 −1.92493 −0.962463 0.271411i \(-0.912510\pi\)
−0.962463 + 0.271411i \(0.912510\pi\)
\(4\) 0 0
\(5\) −0.131360 −0.0587461 −0.0293730 0.999569i \(-0.509351\pi\)
−0.0293730 + 0.999569i \(0.509351\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 8.11603 2.70534
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0.437964 0.113082
\(16\) 0 0
\(17\) 4.35509 1.05626 0.528132 0.849162i \(-0.322893\pi\)
0.528132 + 0.849162i \(0.322893\pi\)
\(18\) 0 0
\(19\) 0.765047 0.175514 0.0877569 0.996142i \(-0.472030\pi\)
0.0877569 + 0.996142i \(0.472030\pi\)
\(20\) 0 0
\(21\) 3.33407 0.727554
\(22\) 0 0
\(23\) −2.35398 −0.490839 −0.245419 0.969417i \(-0.578926\pi\)
−0.245419 + 0.969417i \(0.578926\pi\)
\(24\) 0 0
\(25\) −4.98274 −0.996549
\(26\) 0 0
\(27\) −17.0572 −3.28266
\(28\) 0 0
\(29\) 1.55007 0.287840 0.143920 0.989589i \(-0.454029\pi\)
0.143920 + 0.989589i \(0.454029\pi\)
\(30\) 0 0
\(31\) 3.44072 0.617971 0.308985 0.951067i \(-0.400011\pi\)
0.308985 + 0.951067i \(0.400011\pi\)
\(32\) 0 0
\(33\) −3.33407 −0.580387
\(34\) 0 0
\(35\) 0.131360 0.0222039
\(36\) 0 0
\(37\) −6.91967 −1.13759 −0.568793 0.822481i \(-0.692589\pi\)
−0.568793 + 0.822481i \(0.692589\pi\)
\(38\) 0 0
\(39\) 3.33407 0.533879
\(40\) 0 0
\(41\) 7.35180 1.14816 0.574079 0.818800i \(-0.305360\pi\)
0.574079 + 0.818800i \(0.305360\pi\)
\(42\) 0 0
\(43\) −9.25933 −1.41203 −0.706017 0.708195i \(-0.749510\pi\)
−0.706017 + 0.708195i \(0.749510\pi\)
\(44\) 0 0
\(45\) −1.06612 −0.158928
\(46\) 0 0
\(47\) −2.35398 −0.343363 −0.171682 0.985152i \(-0.554920\pi\)
−0.171682 + 0.985152i \(0.554920\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −14.5202 −2.03323
\(52\) 0 0
\(53\) 6.98712 0.959754 0.479877 0.877336i \(-0.340681\pi\)
0.479877 + 0.877336i \(0.340681\pi\)
\(54\) 0 0
\(55\) −0.131360 −0.0177126
\(56\) 0 0
\(57\) −2.55072 −0.337851
\(58\) 0 0
\(59\) −0.151719 −0.0197521 −0.00987604 0.999951i \(-0.503144\pi\)
−0.00987604 + 0.999951i \(0.503144\pi\)
\(60\) 0 0
\(61\) −7.77746 −0.995802 −0.497901 0.867234i \(-0.665896\pi\)
−0.497901 + 0.867234i \(0.665896\pi\)
\(62\) 0 0
\(63\) −8.11603 −1.02252
\(64\) 0 0
\(65\) 0.131360 0.0162932
\(66\) 0 0
\(67\) −7.77938 −0.950402 −0.475201 0.879877i \(-0.657625\pi\)
−0.475201 + 0.879877i \(0.657625\pi\)
\(68\) 0 0
\(69\) 7.84834 0.944829
\(70\) 0 0
\(71\) −0.493113 −0.0585217 −0.0292609 0.999572i \(-0.509315\pi\)
−0.0292609 + 0.999572i \(0.509315\pi\)
\(72\) 0 0
\(73\) −3.05167 −0.357170 −0.178585 0.983924i \(-0.557152\pi\)
−0.178585 + 0.983924i \(0.557152\pi\)
\(74\) 0 0
\(75\) 16.6128 1.91828
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 1.38849 0.156217 0.0781087 0.996945i \(-0.475112\pi\)
0.0781087 + 0.996945i \(0.475112\pi\)
\(80\) 0 0
\(81\) 32.5219 3.61354
\(82\) 0 0
\(83\) 4.49597 0.493497 0.246748 0.969080i \(-0.420638\pi\)
0.246748 + 0.969080i \(0.420638\pi\)
\(84\) 0 0
\(85\) −0.572085 −0.0620513
\(86\) 0 0
\(87\) −5.16804 −0.554072
\(88\) 0 0
\(89\) 6.66657 0.706655 0.353327 0.935500i \(-0.385050\pi\)
0.353327 + 0.935500i \(0.385050\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −11.4716 −1.18955
\(94\) 0 0
\(95\) −0.100497 −0.0103107
\(96\) 0 0
\(97\) 18.6373 1.89233 0.946166 0.323681i \(-0.104921\pi\)
0.946166 + 0.323681i \(0.104921\pi\)
\(98\) 0 0
\(99\) 8.11603 0.815692
\(100\) 0 0
\(101\) 15.4024 1.53259 0.766297 0.642486i \(-0.222097\pi\)
0.766297 + 0.642486i \(0.222097\pi\)
\(102\) 0 0
\(103\) −3.82506 −0.376895 −0.188447 0.982083i \(-0.560345\pi\)
−0.188447 + 0.982083i \(0.560345\pi\)
\(104\) 0 0
\(105\) −0.437964 −0.0427409
\(106\) 0 0
\(107\) 5.58414 0.539839 0.269920 0.962883i \(-0.413003\pi\)
0.269920 + 0.962883i \(0.413003\pi\)
\(108\) 0 0
\(109\) −2.66796 −0.255544 −0.127772 0.991804i \(-0.540783\pi\)
−0.127772 + 0.991804i \(0.540783\pi\)
\(110\) 0 0
\(111\) 23.0707 2.18977
\(112\) 0 0
\(113\) −14.9938 −1.41050 −0.705251 0.708958i \(-0.749166\pi\)
−0.705251 + 0.708958i \(0.749166\pi\)
\(114\) 0 0
\(115\) 0.309219 0.0288348
\(116\) 0 0
\(117\) −8.11603 −0.750327
\(118\) 0 0
\(119\) −4.35509 −0.399230
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −24.5114 −2.21012
\(124\) 0 0
\(125\) 1.31134 0.117289
\(126\) 0 0
\(127\) 2.20075 0.195285 0.0976424 0.995222i \(-0.468870\pi\)
0.0976424 + 0.995222i \(0.468870\pi\)
\(128\) 0 0
\(129\) 30.8713 2.71806
\(130\) 0 0
\(131\) −1.36405 −0.119178 −0.0595888 0.998223i \(-0.518979\pi\)
−0.0595888 + 0.998223i \(0.518979\pi\)
\(132\) 0 0
\(133\) −0.765047 −0.0663380
\(134\) 0 0
\(135\) 2.24064 0.192843
\(136\) 0 0
\(137\) −6.02782 −0.514991 −0.257496 0.966279i \(-0.582897\pi\)
−0.257496 + 0.966279i \(0.582897\pi\)
\(138\) 0 0
\(139\) −10.0216 −0.850019 −0.425009 0.905189i \(-0.639729\pi\)
−0.425009 + 0.905189i \(0.639729\pi\)
\(140\) 0 0
\(141\) 7.84834 0.660949
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) −0.203617 −0.0169095
\(146\) 0 0
\(147\) −3.33407 −0.274990
\(148\) 0 0
\(149\) 19.0745 1.56264 0.781322 0.624128i \(-0.214546\pi\)
0.781322 + 0.624128i \(0.214546\pi\)
\(150\) 0 0
\(151\) −11.7413 −0.955498 −0.477749 0.878497i \(-0.658547\pi\)
−0.477749 + 0.878497i \(0.658547\pi\)
\(152\) 0 0
\(153\) 35.3460 2.85756
\(154\) 0 0
\(155\) −0.451973 −0.0363034
\(156\) 0 0
\(157\) −13.6860 −1.09226 −0.546129 0.837701i \(-0.683899\pi\)
−0.546129 + 0.837701i \(0.683899\pi\)
\(158\) 0 0
\(159\) −23.2955 −1.84746
\(160\) 0 0
\(161\) 2.35398 0.185520
\(162\) 0 0
\(163\) 7.12800 0.558308 0.279154 0.960246i \(-0.409946\pi\)
0.279154 + 0.960246i \(0.409946\pi\)
\(164\) 0 0
\(165\) 0.437964 0.0340955
\(166\) 0 0
\(167\) 19.7445 1.52787 0.763937 0.645291i \(-0.223264\pi\)
0.763937 + 0.645291i \(0.223264\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 6.20915 0.474825
\(172\) 0 0
\(173\) 6.64607 0.505291 0.252646 0.967559i \(-0.418699\pi\)
0.252646 + 0.967559i \(0.418699\pi\)
\(174\) 0 0
\(175\) 4.98274 0.376660
\(176\) 0 0
\(177\) 0.505841 0.0380213
\(178\) 0 0
\(179\) −14.7828 −1.10492 −0.552460 0.833539i \(-0.686311\pi\)
−0.552460 + 0.833539i \(0.686311\pi\)
\(180\) 0 0
\(181\) 9.96875 0.740972 0.370486 0.928838i \(-0.379191\pi\)
0.370486 + 0.928838i \(0.379191\pi\)
\(182\) 0 0
\(183\) 25.9306 1.91685
\(184\) 0 0
\(185\) 0.908968 0.0668287
\(186\) 0 0
\(187\) 4.35509 0.318476
\(188\) 0 0
\(189\) 17.0572 1.24073
\(190\) 0 0
\(191\) −21.6792 −1.56865 −0.784324 0.620351i \(-0.786990\pi\)
−0.784324 + 0.620351i \(0.786990\pi\)
\(192\) 0 0
\(193\) 7.76049 0.558612 0.279306 0.960202i \(-0.409896\pi\)
0.279306 + 0.960202i \(0.409896\pi\)
\(194\) 0 0
\(195\) −0.437964 −0.0313633
\(196\) 0 0
\(197\) −10.4152 −0.742052 −0.371026 0.928622i \(-0.620994\pi\)
−0.371026 + 0.928622i \(0.620994\pi\)
\(198\) 0 0
\(199\) 10.6780 0.756940 0.378470 0.925614i \(-0.376450\pi\)
0.378470 + 0.925614i \(0.376450\pi\)
\(200\) 0 0
\(201\) 25.9370 1.82946
\(202\) 0 0
\(203\) −1.55007 −0.108793
\(204\) 0 0
\(205\) −0.965734 −0.0674498
\(206\) 0 0
\(207\) −19.1050 −1.32789
\(208\) 0 0
\(209\) 0.765047 0.0529194
\(210\) 0 0
\(211\) 16.6665 1.14737 0.573683 0.819077i \(-0.305514\pi\)
0.573683 + 0.819077i \(0.305514\pi\)
\(212\) 0 0
\(213\) 1.64407 0.112650
\(214\) 0 0
\(215\) 1.21631 0.0829514
\(216\) 0 0
\(217\) −3.44072 −0.233571
\(218\) 0 0
\(219\) 10.1745 0.687527
\(220\) 0 0
\(221\) −4.35509 −0.292955
\(222\) 0 0
\(223\) 17.4843 1.17084 0.585418 0.810732i \(-0.300930\pi\)
0.585418 + 0.810732i \(0.300930\pi\)
\(224\) 0 0
\(225\) −40.4401 −2.69601
\(226\) 0 0
\(227\) 9.07798 0.602527 0.301263 0.953541i \(-0.402592\pi\)
0.301263 + 0.953541i \(0.402592\pi\)
\(228\) 0 0
\(229\) −5.14364 −0.339901 −0.169951 0.985453i \(-0.554361\pi\)
−0.169951 + 0.985453i \(0.554361\pi\)
\(230\) 0 0
\(231\) 3.33407 0.219366
\(232\) 0 0
\(233\) 8.89654 0.582832 0.291416 0.956596i \(-0.405874\pi\)
0.291416 + 0.956596i \(0.405874\pi\)
\(234\) 0 0
\(235\) 0.309219 0.0201712
\(236\) 0 0
\(237\) −4.62933 −0.300707
\(238\) 0 0
\(239\) 5.98466 0.387116 0.193558 0.981089i \(-0.437997\pi\)
0.193558 + 0.981089i \(0.437997\pi\)
\(240\) 0 0
\(241\) −20.7900 −1.33920 −0.669600 0.742722i \(-0.733534\pi\)
−0.669600 + 0.742722i \(0.733534\pi\)
\(242\) 0 0
\(243\) −57.2586 −3.67314
\(244\) 0 0
\(245\) −0.131360 −0.00839229
\(246\) 0 0
\(247\) −0.765047 −0.0486788
\(248\) 0 0
\(249\) −14.9899 −0.949945
\(250\) 0 0
\(251\) −7.73079 −0.487963 −0.243982 0.969780i \(-0.578454\pi\)
−0.243982 + 0.969780i \(0.578454\pi\)
\(252\) 0 0
\(253\) −2.35398 −0.147993
\(254\) 0 0
\(255\) 1.90737 0.119444
\(256\) 0 0
\(257\) 8.98032 0.560177 0.280089 0.959974i \(-0.409636\pi\)
0.280089 + 0.959974i \(0.409636\pi\)
\(258\) 0 0
\(259\) 6.91967 0.429967
\(260\) 0 0
\(261\) 12.5804 0.778707
\(262\) 0 0
\(263\) −8.88531 −0.547892 −0.273946 0.961745i \(-0.588329\pi\)
−0.273946 + 0.961745i \(0.588329\pi\)
\(264\) 0 0
\(265\) −0.917829 −0.0563818
\(266\) 0 0
\(267\) −22.2268 −1.36026
\(268\) 0 0
\(269\) −1.70873 −0.104183 −0.0520915 0.998642i \(-0.516589\pi\)
−0.0520915 + 0.998642i \(0.516589\pi\)
\(270\) 0 0
\(271\) 14.3865 0.873920 0.436960 0.899481i \(-0.356055\pi\)
0.436960 + 0.899481i \(0.356055\pi\)
\(272\) 0 0
\(273\) −3.33407 −0.201787
\(274\) 0 0
\(275\) −4.98274 −0.300471
\(276\) 0 0
\(277\) −7.21972 −0.433791 −0.216895 0.976195i \(-0.569593\pi\)
−0.216895 + 0.976195i \(0.569593\pi\)
\(278\) 0 0
\(279\) 27.9250 1.67182
\(280\) 0 0
\(281\) 23.1518 1.38112 0.690560 0.723275i \(-0.257364\pi\)
0.690560 + 0.723275i \(0.257364\pi\)
\(282\) 0 0
\(283\) −27.4350 −1.63084 −0.815421 0.578868i \(-0.803494\pi\)
−0.815421 + 0.578868i \(0.803494\pi\)
\(284\) 0 0
\(285\) 0.335063 0.0198474
\(286\) 0 0
\(287\) −7.35180 −0.433963
\(288\) 0 0
\(289\) 1.96678 0.115693
\(290\) 0 0
\(291\) −62.1381 −3.64260
\(292\) 0 0
\(293\) −15.5213 −0.906765 −0.453382 0.891316i \(-0.649783\pi\)
−0.453382 + 0.891316i \(0.649783\pi\)
\(294\) 0 0
\(295\) 0.0199298 0.00116036
\(296\) 0 0
\(297\) −17.0572 −0.989760
\(298\) 0 0
\(299\) 2.35398 0.136134
\(300\) 0 0
\(301\) 9.25933 0.533699
\(302\) 0 0
\(303\) −51.3527 −2.95013
\(304\) 0 0
\(305\) 1.02165 0.0584995
\(306\) 0 0
\(307\) −19.8814 −1.13469 −0.567346 0.823480i \(-0.692030\pi\)
−0.567346 + 0.823480i \(0.692030\pi\)
\(308\) 0 0
\(309\) 12.7530 0.725495
\(310\) 0 0
\(311\) −16.2048 −0.918890 −0.459445 0.888206i \(-0.651952\pi\)
−0.459445 + 0.888206i \(0.651952\pi\)
\(312\) 0 0
\(313\) −14.0158 −0.792220 −0.396110 0.918203i \(-0.629640\pi\)
−0.396110 + 0.918203i \(0.629640\pi\)
\(314\) 0 0
\(315\) 1.06612 0.0600692
\(316\) 0 0
\(317\) −12.2844 −0.689959 −0.344979 0.938610i \(-0.612114\pi\)
−0.344979 + 0.938610i \(0.612114\pi\)
\(318\) 0 0
\(319\) 1.55007 0.0867871
\(320\) 0 0
\(321\) −18.6179 −1.03915
\(322\) 0 0
\(323\) 3.33185 0.185389
\(324\) 0 0
\(325\) 4.98274 0.276393
\(326\) 0 0
\(327\) 8.89516 0.491904
\(328\) 0 0
\(329\) 2.35398 0.129779
\(330\) 0 0
\(331\) −3.87931 −0.213226 −0.106613 0.994301i \(-0.534001\pi\)
−0.106613 + 0.994301i \(0.534001\pi\)
\(332\) 0 0
\(333\) −56.1602 −3.07756
\(334\) 0 0
\(335\) 1.02190 0.0558324
\(336\) 0 0
\(337\) 15.0265 0.818544 0.409272 0.912412i \(-0.365783\pi\)
0.409272 + 0.912412i \(0.365783\pi\)
\(338\) 0 0
\(339\) 49.9905 2.71511
\(340\) 0 0
\(341\) 3.44072 0.186325
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −1.03096 −0.0555050
\(346\) 0 0
\(347\) −34.2138 −1.83669 −0.918347 0.395777i \(-0.870475\pi\)
−0.918347 + 0.395777i \(0.870475\pi\)
\(348\) 0 0
\(349\) 34.3616 1.83933 0.919667 0.392700i \(-0.128459\pi\)
0.919667 + 0.392700i \(0.128459\pi\)
\(350\) 0 0
\(351\) 17.0572 0.910447
\(352\) 0 0
\(353\) −34.8717 −1.85604 −0.928018 0.372536i \(-0.878488\pi\)
−0.928018 + 0.372536i \(0.878488\pi\)
\(354\) 0 0
\(355\) 0.0647754 0.00343792
\(356\) 0 0
\(357\) 14.5202 0.768489
\(358\) 0 0
\(359\) −10.4610 −0.552108 −0.276054 0.961142i \(-0.589027\pi\)
−0.276054 + 0.961142i \(0.589027\pi\)
\(360\) 0 0
\(361\) −18.4147 −0.969195
\(362\) 0 0
\(363\) −3.33407 −0.174993
\(364\) 0 0
\(365\) 0.400867 0.0209824
\(366\) 0 0
\(367\) 30.9235 1.61419 0.807096 0.590420i \(-0.201038\pi\)
0.807096 + 0.590420i \(0.201038\pi\)
\(368\) 0 0
\(369\) 59.6674 3.10616
\(370\) 0 0
\(371\) −6.98712 −0.362753
\(372\) 0 0
\(373\) −19.5450 −1.01200 −0.506001 0.862533i \(-0.668877\pi\)
−0.506001 + 0.862533i \(0.668877\pi\)
\(374\) 0 0
\(375\) −4.37208 −0.225773
\(376\) 0 0
\(377\) −1.55007 −0.0798325
\(378\) 0 0
\(379\) −11.8988 −0.611200 −0.305600 0.952160i \(-0.598857\pi\)
−0.305600 + 0.952160i \(0.598857\pi\)
\(380\) 0 0
\(381\) −7.33745 −0.375909
\(382\) 0 0
\(383\) 8.14824 0.416356 0.208178 0.978091i \(-0.433247\pi\)
0.208178 + 0.978091i \(0.433247\pi\)
\(384\) 0 0
\(385\) 0.131360 0.00669473
\(386\) 0 0
\(387\) −75.1490 −3.82004
\(388\) 0 0
\(389\) 39.0264 1.97872 0.989359 0.145493i \(-0.0464770\pi\)
0.989359 + 0.145493i \(0.0464770\pi\)
\(390\) 0 0
\(391\) −10.2518 −0.518455
\(392\) 0 0
\(393\) 4.54784 0.229408
\(394\) 0 0
\(395\) −0.182392 −0.00917716
\(396\) 0 0
\(397\) −6.18126 −0.310228 −0.155114 0.987897i \(-0.549575\pi\)
−0.155114 + 0.987897i \(0.549575\pi\)
\(398\) 0 0
\(399\) 2.55072 0.127696
\(400\) 0 0
\(401\) −33.0280 −1.64934 −0.824669 0.565616i \(-0.808638\pi\)
−0.824669 + 0.565616i \(0.808638\pi\)
\(402\) 0 0
\(403\) −3.44072 −0.171394
\(404\) 0 0
\(405\) −4.27208 −0.212281
\(406\) 0 0
\(407\) −6.91967 −0.342995
\(408\) 0 0
\(409\) −35.1053 −1.73585 −0.867923 0.496698i \(-0.834545\pi\)
−0.867923 + 0.496698i \(0.834545\pi\)
\(410\) 0 0
\(411\) 20.0972 0.991321
\(412\) 0 0
\(413\) 0.151719 0.00746558
\(414\) 0 0
\(415\) −0.590591 −0.0289910
\(416\) 0 0
\(417\) 33.4126 1.63622
\(418\) 0 0
\(419\) −3.69266 −0.180398 −0.0901991 0.995924i \(-0.528750\pi\)
−0.0901991 + 0.995924i \(0.528750\pi\)
\(420\) 0 0
\(421\) −21.5864 −1.05206 −0.526029 0.850467i \(-0.676320\pi\)
−0.526029 + 0.850467i \(0.676320\pi\)
\(422\) 0 0
\(423\) −19.1050 −0.928916
\(424\) 0 0
\(425\) −21.7003 −1.05262
\(426\) 0 0
\(427\) 7.77746 0.376378
\(428\) 0 0
\(429\) 3.33407 0.160970
\(430\) 0 0
\(431\) 25.0783 1.20798 0.603990 0.796992i \(-0.293577\pi\)
0.603990 + 0.796992i \(0.293577\pi\)
\(432\) 0 0
\(433\) 4.64244 0.223102 0.111551 0.993759i \(-0.464418\pi\)
0.111551 + 0.993759i \(0.464418\pi\)
\(434\) 0 0
\(435\) 0.678874 0.0325495
\(436\) 0 0
\(437\) −1.80091 −0.0861490
\(438\) 0 0
\(439\) 20.1516 0.961785 0.480893 0.876780i \(-0.340313\pi\)
0.480893 + 0.876780i \(0.340313\pi\)
\(440\) 0 0
\(441\) 8.11603 0.386478
\(442\) 0 0
\(443\) 16.0015 0.760256 0.380128 0.924934i \(-0.375880\pi\)
0.380128 + 0.924934i \(0.375880\pi\)
\(444\) 0 0
\(445\) −0.875721 −0.0415132
\(446\) 0 0
\(447\) −63.5958 −3.00798
\(448\) 0 0
\(449\) −19.5565 −0.922929 −0.461465 0.887159i \(-0.652676\pi\)
−0.461465 + 0.887159i \(0.652676\pi\)
\(450\) 0 0
\(451\) 7.35180 0.346183
\(452\) 0 0
\(453\) 39.1465 1.83926
\(454\) 0 0
\(455\) −0.131360 −0.00615826
\(456\) 0 0
\(457\) −25.5393 −1.19468 −0.597338 0.801989i \(-0.703775\pi\)
−0.597338 + 0.801989i \(0.703775\pi\)
\(458\) 0 0
\(459\) −74.2857 −3.46736
\(460\) 0 0
\(461\) 1.76652 0.0822750 0.0411375 0.999153i \(-0.486902\pi\)
0.0411375 + 0.999153i \(0.486902\pi\)
\(462\) 0 0
\(463\) 26.4558 1.22951 0.614753 0.788720i \(-0.289256\pi\)
0.614753 + 0.788720i \(0.289256\pi\)
\(464\) 0 0
\(465\) 1.50691 0.0698813
\(466\) 0 0
\(467\) 7.49460 0.346809 0.173404 0.984851i \(-0.444523\pi\)
0.173404 + 0.984851i \(0.444523\pi\)
\(468\) 0 0
\(469\) 7.77938 0.359218
\(470\) 0 0
\(471\) 45.6299 2.10252
\(472\) 0 0
\(473\) −9.25933 −0.425744
\(474\) 0 0
\(475\) −3.81203 −0.174908
\(476\) 0 0
\(477\) 56.7076 2.59646
\(478\) 0 0
\(479\) −38.1474 −1.74300 −0.871500 0.490395i \(-0.836852\pi\)
−0.871500 + 0.490395i \(0.836852\pi\)
\(480\) 0 0
\(481\) 6.91967 0.315510
\(482\) 0 0
\(483\) −7.84834 −0.357112
\(484\) 0 0
\(485\) −2.44820 −0.111167
\(486\) 0 0
\(487\) −4.23729 −0.192010 −0.0960050 0.995381i \(-0.530606\pi\)
−0.0960050 + 0.995381i \(0.530606\pi\)
\(488\) 0 0
\(489\) −23.7653 −1.07470
\(490\) 0 0
\(491\) 4.21926 0.190413 0.0952063 0.995458i \(-0.469649\pi\)
0.0952063 + 0.995458i \(0.469649\pi\)
\(492\) 0 0
\(493\) 6.75068 0.304035
\(494\) 0 0
\(495\) −1.06612 −0.0479187
\(496\) 0 0
\(497\) 0.493113 0.0221191
\(498\) 0 0
\(499\) −12.5672 −0.562584 −0.281292 0.959622i \(-0.590763\pi\)
−0.281292 + 0.959622i \(0.590763\pi\)
\(500\) 0 0
\(501\) −65.8295 −2.94105
\(502\) 0 0
\(503\) 0.278377 0.0124122 0.00620610 0.999981i \(-0.498025\pi\)
0.00620610 + 0.999981i \(0.498025\pi\)
\(504\) 0 0
\(505\) −2.02326 −0.0900339
\(506\) 0 0
\(507\) −3.33407 −0.148071
\(508\) 0 0
\(509\) 5.55657 0.246291 0.123145 0.992389i \(-0.460702\pi\)
0.123145 + 0.992389i \(0.460702\pi\)
\(510\) 0 0
\(511\) 3.05167 0.134998
\(512\) 0 0
\(513\) −13.0496 −0.576153
\(514\) 0 0
\(515\) 0.502461 0.0221411
\(516\) 0 0
\(517\) −2.35398 −0.103528
\(518\) 0 0
\(519\) −22.1585 −0.972649
\(520\) 0 0
\(521\) −39.3183 −1.72257 −0.861284 0.508124i \(-0.830339\pi\)
−0.861284 + 0.508124i \(0.830339\pi\)
\(522\) 0 0
\(523\) −15.7210 −0.687433 −0.343717 0.939073i \(-0.611686\pi\)
−0.343717 + 0.939073i \(0.611686\pi\)
\(524\) 0 0
\(525\) −16.6128 −0.725043
\(526\) 0 0
\(527\) 14.9846 0.652740
\(528\) 0 0
\(529\) −17.4588 −0.759077
\(530\) 0 0
\(531\) −1.23135 −0.0534362
\(532\) 0 0
\(533\) −7.35180 −0.318442
\(534\) 0 0
\(535\) −0.733534 −0.0317134
\(536\) 0 0
\(537\) 49.2870 2.12689
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −2.41251 −0.103722 −0.0518610 0.998654i \(-0.516515\pi\)
−0.0518610 + 0.998654i \(0.516515\pi\)
\(542\) 0 0
\(543\) −33.2365 −1.42632
\(544\) 0 0
\(545\) 0.350463 0.0150122
\(546\) 0 0
\(547\) −6.56886 −0.280864 −0.140432 0.990090i \(-0.544849\pi\)
−0.140432 + 0.990090i \(0.544849\pi\)
\(548\) 0 0
\(549\) −63.1221 −2.69399
\(550\) 0 0
\(551\) 1.18587 0.0505200
\(552\) 0 0
\(553\) −1.38849 −0.0590447
\(554\) 0 0
\(555\) −3.03057 −0.128640
\(556\) 0 0
\(557\) −4.40486 −0.186640 −0.0933200 0.995636i \(-0.529748\pi\)
−0.0933200 + 0.995636i \(0.529748\pi\)
\(558\) 0 0
\(559\) 9.25933 0.391628
\(560\) 0 0
\(561\) −14.5202 −0.613042
\(562\) 0 0
\(563\) −22.7506 −0.958825 −0.479412 0.877590i \(-0.659150\pi\)
−0.479412 + 0.877590i \(0.659150\pi\)
\(564\) 0 0
\(565\) 1.96959 0.0828614
\(566\) 0 0
\(567\) −32.5219 −1.36579
\(568\) 0 0
\(569\) −1.11234 −0.0466319 −0.0233159 0.999728i \(-0.507422\pi\)
−0.0233159 + 0.999728i \(0.507422\pi\)
\(570\) 0 0
\(571\) −24.2442 −1.01459 −0.507294 0.861773i \(-0.669354\pi\)
−0.507294 + 0.861773i \(0.669354\pi\)
\(572\) 0 0
\(573\) 72.2799 3.01953
\(574\) 0 0
\(575\) 11.7293 0.489145
\(576\) 0 0
\(577\) 39.2412 1.63363 0.816815 0.576899i \(-0.195737\pi\)
0.816815 + 0.576899i \(0.195737\pi\)
\(578\) 0 0
\(579\) −25.8740 −1.07529
\(580\) 0 0
\(581\) −4.49597 −0.186524
\(582\) 0 0
\(583\) 6.98712 0.289377
\(584\) 0 0
\(585\) 1.06612 0.0440788
\(586\) 0 0
\(587\) −23.3803 −0.965007 −0.482504 0.875894i \(-0.660273\pi\)
−0.482504 + 0.875894i \(0.660273\pi\)
\(588\) 0 0
\(589\) 2.63231 0.108462
\(590\) 0 0
\(591\) 34.7250 1.42840
\(592\) 0 0
\(593\) 7.97296 0.327410 0.163705 0.986509i \(-0.447655\pi\)
0.163705 + 0.986509i \(0.447655\pi\)
\(594\) 0 0
\(595\) 0.572085 0.0234532
\(596\) 0 0
\(597\) −35.6011 −1.45705
\(598\) 0 0
\(599\) −19.8961 −0.812932 −0.406466 0.913666i \(-0.633239\pi\)
−0.406466 + 0.913666i \(0.633239\pi\)
\(600\) 0 0
\(601\) 18.5273 0.755743 0.377871 0.925858i \(-0.376656\pi\)
0.377871 + 0.925858i \(0.376656\pi\)
\(602\) 0 0
\(603\) −63.1377 −2.57117
\(604\) 0 0
\(605\) −0.131360 −0.00534055
\(606\) 0 0
\(607\) −1.20417 −0.0488756 −0.0244378 0.999701i \(-0.507780\pi\)
−0.0244378 + 0.999701i \(0.507780\pi\)
\(608\) 0 0
\(609\) 5.16804 0.209419
\(610\) 0 0
\(611\) 2.35398 0.0952318
\(612\) 0 0
\(613\) −37.4757 −1.51363 −0.756814 0.653630i \(-0.773245\pi\)
−0.756814 + 0.653630i \(0.773245\pi\)
\(614\) 0 0
\(615\) 3.21983 0.129836
\(616\) 0 0
\(617\) −7.47398 −0.300891 −0.150446 0.988618i \(-0.548071\pi\)
−0.150446 + 0.988618i \(0.548071\pi\)
\(618\) 0 0
\(619\) 21.3392 0.857696 0.428848 0.903377i \(-0.358920\pi\)
0.428848 + 0.903377i \(0.358920\pi\)
\(620\) 0 0
\(621\) 40.1523 1.61126
\(622\) 0 0
\(623\) −6.66657 −0.267090
\(624\) 0 0
\(625\) 24.7415 0.989659
\(626\) 0 0
\(627\) −2.55072 −0.101866
\(628\) 0 0
\(629\) −30.1357 −1.20159
\(630\) 0 0
\(631\) −26.5065 −1.05521 −0.527604 0.849490i \(-0.676910\pi\)
−0.527604 + 0.849490i \(0.676910\pi\)
\(632\) 0 0
\(633\) −55.5671 −2.20860
\(634\) 0 0
\(635\) −0.289090 −0.0114722
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −4.00212 −0.158321
\(640\) 0 0
\(641\) −22.0146 −0.869526 −0.434763 0.900545i \(-0.643168\pi\)
−0.434763 + 0.900545i \(0.643168\pi\)
\(642\) 0 0
\(643\) −40.6392 −1.60266 −0.801328 0.598226i \(-0.795873\pi\)
−0.801328 + 0.598226i \(0.795873\pi\)
\(644\) 0 0
\(645\) −4.05525 −0.159675
\(646\) 0 0
\(647\) 46.9827 1.84708 0.923540 0.383503i \(-0.125282\pi\)
0.923540 + 0.383503i \(0.125282\pi\)
\(648\) 0 0
\(649\) −0.151719 −0.00595548
\(650\) 0 0
\(651\) 11.4716 0.449607
\(652\) 0 0
\(653\) −9.69116 −0.379245 −0.189622 0.981857i \(-0.560726\pi\)
−0.189622 + 0.981857i \(0.560726\pi\)
\(654\) 0 0
\(655\) 0.179182 0.00700121
\(656\) 0 0
\(657\) −24.7674 −0.966269
\(658\) 0 0
\(659\) 27.5066 1.07151 0.535753 0.844375i \(-0.320028\pi\)
0.535753 + 0.844375i \(0.320028\pi\)
\(660\) 0 0
\(661\) −21.0568 −0.819016 −0.409508 0.912307i \(-0.634300\pi\)
−0.409508 + 0.912307i \(0.634300\pi\)
\(662\) 0 0
\(663\) 14.5202 0.563917
\(664\) 0 0
\(665\) 0.100497 0.00389710
\(666\) 0 0
\(667\) −3.64883 −0.141283
\(668\) 0 0
\(669\) −58.2939 −2.25377
\(670\) 0 0
\(671\) −7.77746 −0.300246
\(672\) 0 0
\(673\) 23.8236 0.918334 0.459167 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(674\) 0 0
\(675\) 84.9917 3.27133
\(676\) 0 0
\(677\) −38.2567 −1.47033 −0.735163 0.677891i \(-0.762894\pi\)
−0.735163 + 0.677891i \(0.762894\pi\)
\(678\) 0 0
\(679\) −18.6373 −0.715234
\(680\) 0 0
\(681\) −30.2666 −1.15982
\(682\) 0 0
\(683\) 48.5941 1.85940 0.929701 0.368315i \(-0.120065\pi\)
0.929701 + 0.368315i \(0.120065\pi\)
\(684\) 0 0
\(685\) 0.791815 0.0302537
\(686\) 0 0
\(687\) 17.1493 0.654285
\(688\) 0 0
\(689\) −6.98712 −0.266188
\(690\) 0 0
\(691\) −4.14380 −0.157638 −0.0788188 0.996889i \(-0.525115\pi\)
−0.0788188 + 0.996889i \(0.525115\pi\)
\(692\) 0 0
\(693\) −8.11603 −0.308303
\(694\) 0 0
\(695\) 1.31644 0.0499352
\(696\) 0 0
\(697\) 32.0177 1.21276
\(698\) 0 0
\(699\) −29.6617 −1.12191
\(700\) 0 0
\(701\) 8.94798 0.337961 0.168980 0.985619i \(-0.445953\pi\)
0.168980 + 0.985619i \(0.445953\pi\)
\(702\) 0 0
\(703\) −5.29387 −0.199662
\(704\) 0 0
\(705\) −1.03096 −0.0388282
\(706\) 0 0
\(707\) −15.4024 −0.579266
\(708\) 0 0
\(709\) −35.0954 −1.31803 −0.659017 0.752128i \(-0.729028\pi\)
−0.659017 + 0.752128i \(0.729028\pi\)
\(710\) 0 0
\(711\) 11.2690 0.422622
\(712\) 0 0
\(713\) −8.09938 −0.303324
\(714\) 0 0
\(715\) 0.131360 0.00491259
\(716\) 0 0
\(717\) −19.9533 −0.745169
\(718\) 0 0
\(719\) 18.8101 0.701500 0.350750 0.936469i \(-0.385927\pi\)
0.350750 + 0.936469i \(0.385927\pi\)
\(720\) 0 0
\(721\) 3.82506 0.142453
\(722\) 0 0
\(723\) 69.3152 2.57786
\(724\) 0 0
\(725\) −7.72359 −0.286847
\(726\) 0 0
\(727\) −30.4039 −1.12762 −0.563809 0.825905i \(-0.690664\pi\)
−0.563809 + 0.825905i \(0.690664\pi\)
\(728\) 0 0
\(729\) 93.3387 3.45699
\(730\) 0 0
\(731\) −40.3252 −1.49148
\(732\) 0 0
\(733\) −22.8265 −0.843114 −0.421557 0.906802i \(-0.638516\pi\)
−0.421557 + 0.906802i \(0.638516\pi\)
\(734\) 0 0
\(735\) 0.437964 0.0161546
\(736\) 0 0
\(737\) −7.77938 −0.286557
\(738\) 0 0
\(739\) 10.4878 0.385798 0.192899 0.981219i \(-0.438211\pi\)
0.192899 + 0.981219i \(0.438211\pi\)
\(740\) 0 0
\(741\) 2.55072 0.0937031
\(742\) 0 0
\(743\) −21.8544 −0.801759 −0.400880 0.916131i \(-0.631295\pi\)
−0.400880 + 0.916131i \(0.631295\pi\)
\(744\) 0 0
\(745\) −2.50563 −0.0917992
\(746\) 0 0
\(747\) 36.4894 1.33508
\(748\) 0 0
\(749\) −5.58414 −0.204040
\(750\) 0 0
\(751\) −10.0271 −0.365895 −0.182947 0.983123i \(-0.558564\pi\)
−0.182947 + 0.983123i \(0.558564\pi\)
\(752\) 0 0
\(753\) 25.7750 0.939293
\(754\) 0 0
\(755\) 1.54235 0.0561317
\(756\) 0 0
\(757\) −36.8082 −1.33781 −0.668907 0.743346i \(-0.733238\pi\)
−0.668907 + 0.743346i \(0.733238\pi\)
\(758\) 0 0
\(759\) 7.84834 0.284877
\(760\) 0 0
\(761\) 12.3389 0.447286 0.223643 0.974671i \(-0.428205\pi\)
0.223643 + 0.974671i \(0.428205\pi\)
\(762\) 0 0
\(763\) 2.66796 0.0965865
\(764\) 0 0
\(765\) −4.64306 −0.167870
\(766\) 0 0
\(767\) 0.151719 0.00547824
\(768\) 0 0
\(769\) 27.4637 0.990365 0.495182 0.868789i \(-0.335101\pi\)
0.495182 + 0.868789i \(0.335101\pi\)
\(770\) 0 0
\(771\) −29.9410 −1.07830
\(772\) 0 0
\(773\) −21.2895 −0.765731 −0.382865 0.923804i \(-0.625063\pi\)
−0.382865 + 0.923804i \(0.625063\pi\)
\(774\) 0 0
\(775\) −17.1442 −0.615838
\(776\) 0 0
\(777\) −23.0707 −0.827655
\(778\) 0 0
\(779\) 5.62447 0.201518
\(780\) 0 0
\(781\) −0.493113 −0.0176450
\(782\) 0 0
\(783\) −26.4398 −0.944883
\(784\) 0 0
\(785\) 1.79779 0.0641658
\(786\) 0 0
\(787\) −50.9382 −1.81575 −0.907875 0.419240i \(-0.862297\pi\)
−0.907875 + 0.419240i \(0.862297\pi\)
\(788\) 0 0
\(789\) 29.6242 1.05465
\(790\) 0 0
\(791\) 14.9938 0.533120
\(792\) 0 0
\(793\) 7.77746 0.276186
\(794\) 0 0
\(795\) 3.06011 0.108531
\(796\) 0 0
\(797\) 12.5689 0.445214 0.222607 0.974908i \(-0.428543\pi\)
0.222607 + 0.974908i \(0.428543\pi\)
\(798\) 0 0
\(799\) −10.2518 −0.362682
\(800\) 0 0
\(801\) 54.1061 1.91174
\(802\) 0 0
\(803\) −3.05167 −0.107691
\(804\) 0 0
\(805\) −0.309219 −0.0108985
\(806\) 0 0
\(807\) 5.69702 0.200545
\(808\) 0 0
\(809\) 24.0565 0.845783 0.422891 0.906180i \(-0.361015\pi\)
0.422891 + 0.906180i \(0.361015\pi\)
\(810\) 0 0
\(811\) −10.4503 −0.366961 −0.183480 0.983023i \(-0.558736\pi\)
−0.183480 + 0.983023i \(0.558736\pi\)
\(812\) 0 0
\(813\) −47.9658 −1.68223
\(814\) 0 0
\(815\) −0.936335 −0.0327984
\(816\) 0 0
\(817\) −7.08382 −0.247832
\(818\) 0 0
\(819\) 8.11603 0.283597
\(820\) 0 0
\(821\) 14.4334 0.503729 0.251864 0.967763i \(-0.418956\pi\)
0.251864 + 0.967763i \(0.418956\pi\)
\(822\) 0 0
\(823\) 15.1010 0.526388 0.263194 0.964743i \(-0.415224\pi\)
0.263194 + 0.964743i \(0.415224\pi\)
\(824\) 0 0
\(825\) 16.6128 0.578384
\(826\) 0 0
\(827\) −4.92095 −0.171118 −0.0855592 0.996333i \(-0.527268\pi\)
−0.0855592 + 0.996333i \(0.527268\pi\)
\(828\) 0 0
\(829\) −2.48798 −0.0864111 −0.0432055 0.999066i \(-0.513757\pi\)
−0.0432055 + 0.999066i \(0.513757\pi\)
\(830\) 0 0
\(831\) 24.0711 0.835016
\(832\) 0 0
\(833\) 4.35509 0.150895
\(834\) 0 0
\(835\) −2.59364 −0.0897566
\(836\) 0 0
\(837\) −58.6890 −2.02859
\(838\) 0 0
\(839\) 44.1545 1.52438 0.762192 0.647351i \(-0.224123\pi\)
0.762192 + 0.647351i \(0.224123\pi\)
\(840\) 0 0
\(841\) −26.5973 −0.917148
\(842\) 0 0
\(843\) −77.1897 −2.65855
\(844\) 0 0
\(845\) −0.131360 −0.00451893
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 91.4703 3.13925
\(850\) 0 0
\(851\) 16.2888 0.558371
\(852\) 0 0
\(853\) 25.7989 0.883336 0.441668 0.897179i \(-0.354387\pi\)
0.441668 + 0.897179i \(0.354387\pi\)
\(854\) 0 0
\(855\) −0.815635 −0.0278941
\(856\) 0 0
\(857\) −8.87595 −0.303197 −0.151598 0.988442i \(-0.548442\pi\)
−0.151598 + 0.988442i \(0.548442\pi\)
\(858\) 0 0
\(859\) 25.8810 0.883049 0.441524 0.897249i \(-0.354438\pi\)
0.441524 + 0.897249i \(0.354438\pi\)
\(860\) 0 0
\(861\) 24.5114 0.835347
\(862\) 0 0
\(863\) −21.7619 −0.740785 −0.370393 0.928875i \(-0.620777\pi\)
−0.370393 + 0.928875i \(0.620777\pi\)
\(864\) 0 0
\(865\) −0.873029 −0.0296839
\(866\) 0 0
\(867\) −6.55740 −0.222701
\(868\) 0 0
\(869\) 1.38849 0.0471013
\(870\) 0 0
\(871\) 7.77938 0.263594
\(872\) 0 0
\(873\) 151.261 5.11941
\(874\) 0 0
\(875\) −1.31134 −0.0443312
\(876\) 0 0
\(877\) −2.16341 −0.0730530 −0.0365265 0.999333i \(-0.511629\pi\)
−0.0365265 + 0.999333i \(0.511629\pi\)
\(878\) 0 0
\(879\) 51.7492 1.74546
\(880\) 0 0
\(881\) −1.39781 −0.0470935 −0.0235468 0.999723i \(-0.507496\pi\)
−0.0235468 + 0.999723i \(0.507496\pi\)
\(882\) 0 0
\(883\) 19.5992 0.659565 0.329783 0.944057i \(-0.393025\pi\)
0.329783 + 0.944057i \(0.393025\pi\)
\(884\) 0 0
\(885\) −0.0664473 −0.00223360
\(886\) 0 0
\(887\) 0.151305 0.00508033 0.00254016 0.999997i \(-0.499191\pi\)
0.00254016 + 0.999997i \(0.499191\pi\)
\(888\) 0 0
\(889\) −2.20075 −0.0738107
\(890\) 0 0
\(891\) 32.5219 1.08952
\(892\) 0 0
\(893\) −1.80091 −0.0602650
\(894\) 0 0
\(895\) 1.94187 0.0649097
\(896\) 0 0
\(897\) −7.84834 −0.262048
\(898\) 0 0
\(899\) 5.33334 0.177877
\(900\) 0 0
\(901\) 30.4295 1.01375
\(902\) 0 0
\(903\) −30.8713 −1.02733
\(904\) 0 0
\(905\) −1.30950 −0.0435292
\(906\) 0 0
\(907\) 51.7316 1.71772 0.858859 0.512211i \(-0.171174\pi\)
0.858859 + 0.512211i \(0.171174\pi\)
\(908\) 0 0
\(909\) 125.006 4.14620
\(910\) 0 0
\(911\) 7.05918 0.233881 0.116941 0.993139i \(-0.462691\pi\)
0.116941 + 0.993139i \(0.462691\pi\)
\(912\) 0 0
\(913\) 4.49597 0.148795
\(914\) 0 0
\(915\) −3.40625 −0.112607
\(916\) 0 0
\(917\) 1.36405 0.0450449
\(918\) 0 0
\(919\) −57.2866 −1.88971 −0.944855 0.327488i \(-0.893798\pi\)
−0.944855 + 0.327488i \(0.893798\pi\)
\(920\) 0 0
\(921\) 66.2860 2.18420
\(922\) 0 0
\(923\) 0.493113 0.0162310
\(924\) 0 0
\(925\) 34.4789 1.13366
\(926\) 0 0
\(927\) −31.0443 −1.01963
\(928\) 0 0
\(929\) 35.9526 1.17957 0.589784 0.807561i \(-0.299213\pi\)
0.589784 + 0.807561i \(0.299213\pi\)
\(930\) 0 0
\(931\) 0.765047 0.0250734
\(932\) 0 0
\(933\) 54.0280 1.76880
\(934\) 0 0
\(935\) −0.572085 −0.0187092
\(936\) 0 0
\(937\) 23.4837 0.767180 0.383590 0.923504i \(-0.374688\pi\)
0.383590 + 0.923504i \(0.374688\pi\)
\(938\) 0 0
\(939\) 46.7297 1.52497
\(940\) 0 0
\(941\) −27.1625 −0.885471 −0.442736 0.896652i \(-0.645992\pi\)
−0.442736 + 0.896652i \(0.645992\pi\)
\(942\) 0 0
\(943\) −17.3060 −0.563561
\(944\) 0 0
\(945\) −2.24064 −0.0728880
\(946\) 0 0
\(947\) −57.1940 −1.85855 −0.929277 0.369383i \(-0.879569\pi\)
−0.929277 + 0.369383i \(0.879569\pi\)
\(948\) 0 0
\(949\) 3.05167 0.0990612
\(950\) 0 0
\(951\) 40.9569 1.32812
\(952\) 0 0
\(953\) −16.5759 −0.536947 −0.268474 0.963287i \(-0.586519\pi\)
−0.268474 + 0.963287i \(0.586519\pi\)
\(954\) 0 0
\(955\) 2.84778 0.0921519
\(956\) 0 0
\(957\) −5.16804 −0.167059
\(958\) 0 0
\(959\) 6.02782 0.194648
\(960\) 0 0
\(961\) −19.1615 −0.618112
\(962\) 0 0
\(963\) 45.3211 1.46045
\(964\) 0 0
\(965\) −1.01942 −0.0328162
\(966\) 0 0
\(967\) 10.2590 0.329908 0.164954 0.986301i \(-0.447252\pi\)
0.164954 + 0.986301i \(0.447252\pi\)
\(968\) 0 0
\(969\) −11.1086 −0.356860
\(970\) 0 0
\(971\) −40.7338 −1.30721 −0.653605 0.756836i \(-0.726744\pi\)
−0.653605 + 0.756836i \(0.726744\pi\)
\(972\) 0 0
\(973\) 10.0216 0.321277
\(974\) 0 0
\(975\) −16.6128 −0.532036
\(976\) 0 0
\(977\) −2.37413 −0.0759552 −0.0379776 0.999279i \(-0.512092\pi\)
−0.0379776 + 0.999279i \(0.512092\pi\)
\(978\) 0 0
\(979\) 6.66657 0.213064
\(980\) 0 0
\(981\) −21.6532 −0.691334
\(982\) 0 0
\(983\) 36.8610 1.17568 0.587842 0.808976i \(-0.299978\pi\)
0.587842 + 0.808976i \(0.299978\pi\)
\(984\) 0 0
\(985\) 1.36814 0.0435926
\(986\) 0 0
\(987\) −7.84834 −0.249815
\(988\) 0 0
\(989\) 21.7963 0.693081
\(990\) 0 0
\(991\) −22.0726 −0.701159 −0.350580 0.936533i \(-0.614015\pi\)
−0.350580 + 0.936533i \(0.614015\pi\)
\(992\) 0 0
\(993\) 12.9339 0.410444
\(994\) 0 0
\(995\) −1.40266 −0.0444672
\(996\) 0 0
\(997\) 48.3632 1.53168 0.765839 0.643032i \(-0.222324\pi\)
0.765839 + 0.643032i \(0.222324\pi\)
\(998\) 0 0
\(999\) 118.030 3.73431
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 \(a_p\))