Properties

Label 8036.2.a.q.1.8
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(0.515082\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.515082 q^{3} +2.19964 q^{5} -2.73469 q^{9} +O(q^{10})\) \(q-0.515082 q^{3} +2.19964 q^{5} -2.73469 q^{9} +4.22160 q^{11} +3.63941 q^{13} -1.13299 q^{15} -7.98698 q^{17} +1.14014 q^{19} -7.43446 q^{23} -0.161604 q^{25} +2.95383 q^{27} +6.08068 q^{29} -1.33243 q^{31} -2.17447 q^{33} -2.87776 q^{37} -1.87460 q^{39} -1.00000 q^{41} +5.14701 q^{43} -6.01532 q^{45} +8.12473 q^{47} +4.11395 q^{51} -1.63075 q^{53} +9.28598 q^{55} -0.587265 q^{57} -2.97978 q^{59} +10.2708 q^{61} +8.00538 q^{65} +2.46808 q^{67} +3.82935 q^{69} +13.0326 q^{71} +11.5199 q^{73} +0.0832393 q^{75} +9.06941 q^{79} +6.68261 q^{81} +7.51957 q^{83} -17.5684 q^{85} -3.13205 q^{87} -17.9819 q^{89} +0.686309 q^{93} +2.50789 q^{95} +13.2426 q^{97} -11.5448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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
\(3\) −0.515082 −0.297383 −0.148691 0.988884i \(-0.547506\pi\)
−0.148691 + 0.988884i \(0.547506\pi\)
\(4\) 0 0
\(5\) 2.19964 0.983707 0.491853 0.870678i \(-0.336320\pi\)
0.491853 + 0.870678i \(0.336320\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.73469 −0.911564
\(10\) 0 0
\(11\) 4.22160 1.27286 0.636430 0.771335i \(-0.280410\pi\)
0.636430 + 0.771335i \(0.280410\pi\)
\(12\) 0 0
\(13\) 3.63941 1.00939 0.504696 0.863297i \(-0.331605\pi\)
0.504696 + 0.863297i \(0.331605\pi\)
\(14\) 0 0
\(15\) −1.13299 −0.292537
\(16\) 0 0
\(17\) −7.98698 −1.93713 −0.968563 0.248768i \(-0.919974\pi\)
−0.968563 + 0.248768i \(0.919974\pi\)
\(18\) 0 0
\(19\) 1.14014 0.261566 0.130783 0.991411i \(-0.458251\pi\)
0.130783 + 0.991411i \(0.458251\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.43446 −1.55019 −0.775096 0.631844i \(-0.782298\pi\)
−0.775096 + 0.631844i \(0.782298\pi\)
\(24\) 0 0
\(25\) −0.161604 −0.0323208
\(26\) 0 0
\(27\) 2.95383 0.568466
\(28\) 0 0
\(29\) 6.08068 1.12915 0.564577 0.825380i \(-0.309039\pi\)
0.564577 + 0.825380i \(0.309039\pi\)
\(30\) 0 0
\(31\) −1.33243 −0.239311 −0.119655 0.992815i \(-0.538179\pi\)
−0.119655 + 0.992815i \(0.538179\pi\)
\(32\) 0 0
\(33\) −2.17447 −0.378526
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.87776 −0.473101 −0.236551 0.971619i \(-0.576017\pi\)
−0.236551 + 0.971619i \(0.576017\pi\)
\(38\) 0 0
\(39\) −1.87460 −0.300176
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 5.14701 0.784912 0.392456 0.919771i \(-0.371626\pi\)
0.392456 + 0.919771i \(0.371626\pi\)
\(44\) 0 0
\(45\) −6.01532 −0.896711
\(46\) 0 0
\(47\) 8.12473 1.18511 0.592557 0.805529i \(-0.298119\pi\)
0.592557 + 0.805529i \(0.298119\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 4.11395 0.576068
\(52\) 0 0
\(53\) −1.63075 −0.224001 −0.112001 0.993708i \(-0.535726\pi\)
−0.112001 + 0.993708i \(0.535726\pi\)
\(54\) 0 0
\(55\) 9.28598 1.25212
\(56\) 0 0
\(57\) −0.587265 −0.0777852
\(58\) 0 0
\(59\) −2.97978 −0.387935 −0.193967 0.981008i \(-0.562136\pi\)
−0.193967 + 0.981008i \(0.562136\pi\)
\(60\) 0 0
\(61\) 10.2708 1.31505 0.657524 0.753434i \(-0.271604\pi\)
0.657524 + 0.753434i \(0.271604\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 8.00538 0.992946
\(66\) 0 0
\(67\) 2.46808 0.301525 0.150762 0.988570i \(-0.451827\pi\)
0.150762 + 0.988570i \(0.451827\pi\)
\(68\) 0 0
\(69\) 3.82935 0.461000
\(70\) 0 0
\(71\) 13.0326 1.54668 0.773342 0.633989i \(-0.218584\pi\)
0.773342 + 0.633989i \(0.218584\pi\)
\(72\) 0 0
\(73\) 11.5199 1.34831 0.674154 0.738591i \(-0.264509\pi\)
0.674154 + 0.738591i \(0.264509\pi\)
\(74\) 0 0
\(75\) 0.0832393 0.00961165
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 9.06941 1.02039 0.510194 0.860059i \(-0.329573\pi\)
0.510194 + 0.860059i \(0.329573\pi\)
\(80\) 0 0
\(81\) 6.68261 0.742512
\(82\) 0 0
\(83\) 7.51957 0.825380 0.412690 0.910872i \(-0.364589\pi\)
0.412690 + 0.910872i \(0.364589\pi\)
\(84\) 0 0
\(85\) −17.5684 −1.90556
\(86\) 0 0
\(87\) −3.13205 −0.335791
\(88\) 0 0
\(89\) −17.9819 −1.90608 −0.953041 0.302840i \(-0.902065\pi\)
−0.953041 + 0.302840i \(0.902065\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0.686309 0.0711669
\(94\) 0 0
\(95\) 2.50789 0.257304
\(96\) 0 0
\(97\) 13.2426 1.34459 0.672293 0.740285i \(-0.265309\pi\)
0.672293 + 0.740285i \(0.265309\pi\)
\(98\) 0 0
\(99\) −11.5448 −1.16029
\(100\) 0 0
\(101\) 5.90610 0.587678 0.293839 0.955855i \(-0.405067\pi\)
0.293839 + 0.955855i \(0.405067\pi\)
\(102\) 0 0
\(103\) −4.32873 −0.426522 −0.213261 0.976995i \(-0.568409\pi\)
−0.213261 + 0.976995i \(0.568409\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.6786 −1.12901 −0.564504 0.825430i \(-0.690933\pi\)
−0.564504 + 0.825430i \(0.690933\pi\)
\(108\) 0 0
\(109\) 15.2466 1.46036 0.730178 0.683257i \(-0.239437\pi\)
0.730178 + 0.683257i \(0.239437\pi\)
\(110\) 0 0
\(111\) 1.48228 0.140692
\(112\) 0 0
\(113\) 17.2122 1.61919 0.809594 0.586990i \(-0.199687\pi\)
0.809594 + 0.586990i \(0.199687\pi\)
\(114\) 0 0
\(115\) −16.3531 −1.52493
\(116\) 0 0
\(117\) −9.95267 −0.920125
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 6.82189 0.620172
\(122\) 0 0
\(123\) 0.515082 0.0464434
\(124\) 0 0
\(125\) −11.3536 −1.01550
\(126\) 0 0
\(127\) −8.42630 −0.747713 −0.373857 0.927487i \(-0.621965\pi\)
−0.373857 + 0.927487i \(0.621965\pi\)
\(128\) 0 0
\(129\) −2.65113 −0.233419
\(130\) 0 0
\(131\) −11.8466 −1.03504 −0.517522 0.855670i \(-0.673145\pi\)
−0.517522 + 0.855670i \(0.673145\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 6.49736 0.559204
\(136\) 0 0
\(137\) −17.6176 −1.50518 −0.752589 0.658491i \(-0.771195\pi\)
−0.752589 + 0.658491i \(0.771195\pi\)
\(138\) 0 0
\(139\) −3.43664 −0.291492 −0.145746 0.989322i \(-0.546558\pi\)
−0.145746 + 0.989322i \(0.546558\pi\)
\(140\) 0 0
\(141\) −4.18490 −0.352432
\(142\) 0 0
\(143\) 15.3641 1.28481
\(144\) 0 0
\(145\) 13.3753 1.11076
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 20.2855 1.66185 0.830926 0.556383i \(-0.187811\pi\)
0.830926 + 0.556383i \(0.187811\pi\)
\(150\) 0 0
\(151\) 0.792622 0.0645027 0.0322513 0.999480i \(-0.489732\pi\)
0.0322513 + 0.999480i \(0.489732\pi\)
\(152\) 0 0
\(153\) 21.8419 1.76581
\(154\) 0 0
\(155\) −2.93085 −0.235412
\(156\) 0 0
\(157\) 5.29832 0.422852 0.211426 0.977394i \(-0.432189\pi\)
0.211426 + 0.977394i \(0.432189\pi\)
\(158\) 0 0
\(159\) 0.839972 0.0666141
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 9.33217 0.730952 0.365476 0.930821i \(-0.380906\pi\)
0.365476 + 0.930821i \(0.380906\pi\)
\(164\) 0 0
\(165\) −4.78304 −0.372359
\(166\) 0 0
\(167\) 5.22005 0.403939 0.201970 0.979392i \(-0.435266\pi\)
0.201970 + 0.979392i \(0.435266\pi\)
\(168\) 0 0
\(169\) 0.245336 0.0188720
\(170\) 0 0
\(171\) −3.11793 −0.238434
\(172\) 0 0
\(173\) −0.187866 −0.0142832 −0.00714158 0.999974i \(-0.502273\pi\)
−0.00714158 + 0.999974i \(0.502273\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1.53483 0.115365
\(178\) 0 0
\(179\) 13.3865 1.00055 0.500277 0.865865i \(-0.333231\pi\)
0.500277 + 0.865865i \(0.333231\pi\)
\(180\) 0 0
\(181\) −0.303123 −0.0225309 −0.0112655 0.999937i \(-0.503586\pi\)
−0.0112655 + 0.999937i \(0.503586\pi\)
\(182\) 0 0
\(183\) −5.29033 −0.391072
\(184\) 0 0
\(185\) −6.33003 −0.465393
\(186\) 0 0
\(187\) −33.7178 −2.46569
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.01783 −0.0736479 −0.0368239 0.999322i \(-0.511724\pi\)
−0.0368239 + 0.999322i \(0.511724\pi\)
\(192\) 0 0
\(193\) 17.1199 1.23231 0.616157 0.787623i \(-0.288689\pi\)
0.616157 + 0.787623i \(0.288689\pi\)
\(194\) 0 0
\(195\) −4.12343 −0.295285
\(196\) 0 0
\(197\) −4.81082 −0.342757 −0.171379 0.985205i \(-0.554822\pi\)
−0.171379 + 0.985205i \(0.554822\pi\)
\(198\) 0 0
\(199\) −12.5535 −0.889892 −0.444946 0.895557i \(-0.646777\pi\)
−0.444946 + 0.895557i \(0.646777\pi\)
\(200\) 0 0
\(201\) −1.27127 −0.0896681
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2.19964 −0.153629
\(206\) 0 0
\(207\) 20.3309 1.41310
\(208\) 0 0
\(209\) 4.81321 0.332937
\(210\) 0 0
\(211\) 20.7515 1.42859 0.714297 0.699843i \(-0.246747\pi\)
0.714297 + 0.699843i \(0.246747\pi\)
\(212\) 0 0
\(213\) −6.71285 −0.459957
\(214\) 0 0
\(215\) 11.3215 0.772123
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −5.93371 −0.400963
\(220\) 0 0
\(221\) −29.0679 −1.95532
\(222\) 0 0
\(223\) −11.6034 −0.777022 −0.388511 0.921444i \(-0.627010\pi\)
−0.388511 + 0.921444i \(0.627010\pi\)
\(224\) 0 0
\(225\) 0.441937 0.0294625
\(226\) 0 0
\(227\) −0.694596 −0.0461020 −0.0230510 0.999734i \(-0.507338\pi\)
−0.0230510 + 0.999734i \(0.507338\pi\)
\(228\) 0 0
\(229\) 25.1712 1.66336 0.831681 0.555254i \(-0.187379\pi\)
0.831681 + 0.555254i \(0.187379\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.94397 0.192866 0.0964330 0.995339i \(-0.469257\pi\)
0.0964330 + 0.995339i \(0.469257\pi\)
\(234\) 0 0
\(235\) 17.8714 1.16580
\(236\) 0 0
\(237\) −4.67149 −0.303446
\(238\) 0 0
\(239\) 7.56259 0.489183 0.244592 0.969626i \(-0.421346\pi\)
0.244592 + 0.969626i \(0.421346\pi\)
\(240\) 0 0
\(241\) −7.59060 −0.488953 −0.244477 0.969655i \(-0.578616\pi\)
−0.244477 + 0.969655i \(0.578616\pi\)
\(242\) 0 0
\(243\) −12.3036 −0.789276
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4.14944 0.264023
\(248\) 0 0
\(249\) −3.87319 −0.245454
\(250\) 0 0
\(251\) −23.7549 −1.49940 −0.749698 0.661780i \(-0.769801\pi\)
−0.749698 + 0.661780i \(0.769801\pi\)
\(252\) 0 0
\(253\) −31.3853 −1.97318
\(254\) 0 0
\(255\) 9.04918 0.566682
\(256\) 0 0
\(257\) −1.53771 −0.0959198 −0.0479599 0.998849i \(-0.515272\pi\)
−0.0479599 + 0.998849i \(0.515272\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −16.6288 −1.02930
\(262\) 0 0
\(263\) 16.3727 1.00958 0.504791 0.863242i \(-0.331570\pi\)
0.504791 + 0.863242i \(0.331570\pi\)
\(264\) 0 0
\(265\) −3.58707 −0.220352
\(266\) 0 0
\(267\) 9.26217 0.566836
\(268\) 0 0
\(269\) 18.6581 1.13760 0.568801 0.822475i \(-0.307407\pi\)
0.568801 + 0.822475i \(0.307407\pi\)
\(270\) 0 0
\(271\) 16.3271 0.991800 0.495900 0.868380i \(-0.334838\pi\)
0.495900 + 0.868380i \(0.334838\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.682228 −0.0411399
\(276\) 0 0
\(277\) −19.2494 −1.15659 −0.578293 0.815829i \(-0.696281\pi\)
−0.578293 + 0.815829i \(0.696281\pi\)
\(278\) 0 0
\(279\) 3.64378 0.218147
\(280\) 0 0
\(281\) 25.4587 1.51874 0.759369 0.650660i \(-0.225508\pi\)
0.759369 + 0.650660i \(0.225508\pi\)
\(282\) 0 0
\(283\) −6.72536 −0.399781 −0.199891 0.979818i \(-0.564059\pi\)
−0.199891 + 0.979818i \(0.564059\pi\)
\(284\) 0 0
\(285\) −1.29177 −0.0765178
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 46.7918 2.75246
\(290\) 0 0
\(291\) −6.82104 −0.399857
\(292\) 0 0
\(293\) −14.0817 −0.822660 −0.411330 0.911487i \(-0.634936\pi\)
−0.411330 + 0.911487i \(0.634936\pi\)
\(294\) 0 0
\(295\) −6.55444 −0.381614
\(296\) 0 0
\(297\) 12.4699 0.723577
\(298\) 0 0
\(299\) −27.0571 −1.56475
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −3.04212 −0.174765
\(304\) 0 0
\(305\) 22.5921 1.29362
\(306\) 0 0
\(307\) −22.4646 −1.28212 −0.641062 0.767489i \(-0.721506\pi\)
−0.641062 + 0.767489i \(0.721506\pi\)
\(308\) 0 0
\(309\) 2.22965 0.126840
\(310\) 0 0
\(311\) −15.1252 −0.857671 −0.428835 0.903383i \(-0.641076\pi\)
−0.428835 + 0.903383i \(0.641076\pi\)
\(312\) 0 0
\(313\) −19.4123 −1.09725 −0.548625 0.836068i \(-0.684849\pi\)
−0.548625 + 0.836068i \(0.684849\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.76362 0.0990546 0.0495273 0.998773i \(-0.484229\pi\)
0.0495273 + 0.998773i \(0.484229\pi\)
\(318\) 0 0
\(319\) 25.6702 1.43725
\(320\) 0 0
\(321\) 6.01541 0.335747
\(322\) 0 0
\(323\) −9.10627 −0.506686
\(324\) 0 0
\(325\) −0.588144 −0.0326244
\(326\) 0 0
\(327\) −7.85322 −0.434284
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 12.1176 0.666045 0.333023 0.942919i \(-0.391931\pi\)
0.333023 + 0.942919i \(0.391931\pi\)
\(332\) 0 0
\(333\) 7.86979 0.431262
\(334\) 0 0
\(335\) 5.42889 0.296612
\(336\) 0 0
\(337\) 5.78905 0.315349 0.157675 0.987491i \(-0.449600\pi\)
0.157675 + 0.987491i \(0.449600\pi\)
\(338\) 0 0
\(339\) −8.86569 −0.481518
\(340\) 0 0
\(341\) −5.62497 −0.304609
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 8.42318 0.453489
\(346\) 0 0
\(347\) 11.9344 0.640672 0.320336 0.947304i \(-0.396204\pi\)
0.320336 + 0.947304i \(0.396204\pi\)
\(348\) 0 0
\(349\) −3.41253 −0.182669 −0.0913344 0.995820i \(-0.529113\pi\)
−0.0913344 + 0.995820i \(0.529113\pi\)
\(350\) 0 0
\(351\) 10.7502 0.573805
\(352\) 0 0
\(353\) −3.72027 −0.198010 −0.0990049 0.995087i \(-0.531566\pi\)
−0.0990049 + 0.995087i \(0.531566\pi\)
\(354\) 0 0
\(355\) 28.6669 1.52148
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 25.3819 1.33961 0.669803 0.742539i \(-0.266379\pi\)
0.669803 + 0.742539i \(0.266379\pi\)
\(360\) 0 0
\(361\) −17.7001 −0.931583
\(362\) 0 0
\(363\) −3.51383 −0.184428
\(364\) 0 0
\(365\) 25.3397 1.32634
\(366\) 0 0
\(367\) −7.66006 −0.399852 −0.199926 0.979811i \(-0.564070\pi\)
−0.199926 + 0.979811i \(0.564070\pi\)
\(368\) 0 0
\(369\) 2.73469 0.142362
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 32.1886 1.66666 0.833331 0.552774i \(-0.186431\pi\)
0.833331 + 0.552774i \(0.186431\pi\)
\(374\) 0 0
\(375\) 5.84806 0.301992
\(376\) 0 0
\(377\) 22.1301 1.13976
\(378\) 0 0
\(379\) −4.38797 −0.225395 −0.112697 0.993629i \(-0.535949\pi\)
−0.112697 + 0.993629i \(0.535949\pi\)
\(380\) 0 0
\(381\) 4.34023 0.222357
\(382\) 0 0
\(383\) 5.35384 0.273568 0.136784 0.990601i \(-0.456323\pi\)
0.136784 + 0.990601i \(0.456323\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −14.0755 −0.715497
\(388\) 0 0
\(389\) 1.67620 0.0849866 0.0424933 0.999097i \(-0.486470\pi\)
0.0424933 + 0.999097i \(0.486470\pi\)
\(390\) 0 0
\(391\) 59.3788 3.00292
\(392\) 0 0
\(393\) 6.10198 0.307804
\(394\) 0 0
\(395\) 19.9494 1.00376
\(396\) 0 0
\(397\) 7.85249 0.394105 0.197053 0.980393i \(-0.436863\pi\)
0.197053 + 0.980393i \(0.436863\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.10274 0.254819 0.127409 0.991850i \(-0.459334\pi\)
0.127409 + 0.991850i \(0.459334\pi\)
\(402\) 0 0
\(403\) −4.84925 −0.241559
\(404\) 0 0
\(405\) 14.6993 0.730414
\(406\) 0 0
\(407\) −12.1488 −0.602192
\(408\) 0 0
\(409\) 21.6135 1.06872 0.534360 0.845257i \(-0.320553\pi\)
0.534360 + 0.845257i \(0.320553\pi\)
\(410\) 0 0
\(411\) 9.07453 0.447614
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 16.5403 0.811932
\(416\) 0 0
\(417\) 1.77015 0.0866848
\(418\) 0 0
\(419\) −29.2736 −1.43011 −0.715054 0.699069i \(-0.753598\pi\)
−0.715054 + 0.699069i \(0.753598\pi\)
\(420\) 0 0
\(421\) −1.32720 −0.0646837 −0.0323419 0.999477i \(-0.510297\pi\)
−0.0323419 + 0.999477i \(0.510297\pi\)
\(422\) 0 0
\(423\) −22.2186 −1.08031
\(424\) 0 0
\(425\) 1.29073 0.0626095
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −7.91379 −0.382081
\(430\) 0 0
\(431\) −13.2691 −0.639151 −0.319575 0.947561i \(-0.603540\pi\)
−0.319575 + 0.947561i \(0.603540\pi\)
\(432\) 0 0
\(433\) −20.4388 −0.982225 −0.491113 0.871096i \(-0.663410\pi\)
−0.491113 + 0.871096i \(0.663410\pi\)
\(434\) 0 0
\(435\) −6.88936 −0.330320
\(436\) 0 0
\(437\) −8.47632 −0.405477
\(438\) 0 0
\(439\) 1.64250 0.0783922 0.0391961 0.999232i \(-0.487520\pi\)
0.0391961 + 0.999232i \(0.487520\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −16.3859 −0.778518 −0.389259 0.921128i \(-0.627269\pi\)
−0.389259 + 0.921128i \(0.627269\pi\)
\(444\) 0 0
\(445\) −39.5537 −1.87503
\(446\) 0 0
\(447\) −10.4487 −0.494206
\(448\) 0 0
\(449\) 39.6265 1.87009 0.935045 0.354528i \(-0.115358\pi\)
0.935045 + 0.354528i \(0.115358\pi\)
\(450\) 0 0
\(451\) −4.22160 −0.198787
\(452\) 0 0
\(453\) −0.408265 −0.0191820
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 7.21966 0.337721 0.168861 0.985640i \(-0.445991\pi\)
0.168861 + 0.985640i \(0.445991\pi\)
\(458\) 0 0
\(459\) −23.5922 −1.10119
\(460\) 0 0
\(461\) 19.4564 0.906176 0.453088 0.891466i \(-0.350322\pi\)
0.453088 + 0.891466i \(0.350322\pi\)
\(462\) 0 0
\(463\) −17.9014 −0.831950 −0.415975 0.909376i \(-0.636560\pi\)
−0.415975 + 0.909376i \(0.636560\pi\)
\(464\) 0 0
\(465\) 1.50963 0.0700074
\(466\) 0 0
\(467\) −1.60602 −0.0743176 −0.0371588 0.999309i \(-0.511831\pi\)
−0.0371588 + 0.999309i \(0.511831\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −2.72907 −0.125749
\(472\) 0 0
\(473\) 21.7286 0.999082
\(474\) 0 0
\(475\) −0.184251 −0.00845403
\(476\) 0 0
\(477\) 4.45961 0.204191
\(478\) 0 0
\(479\) 1.93345 0.0883415 0.0441708 0.999024i \(-0.485935\pi\)
0.0441708 + 0.999024i \(0.485935\pi\)
\(480\) 0 0
\(481\) −10.4734 −0.477545
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 29.1290 1.32268
\(486\) 0 0
\(487\) 31.5340 1.42894 0.714471 0.699665i \(-0.246667\pi\)
0.714471 + 0.699665i \(0.246667\pi\)
\(488\) 0 0
\(489\) −4.80683 −0.217372
\(490\) 0 0
\(491\) −41.6704 −1.88056 −0.940279 0.340404i \(-0.889436\pi\)
−0.940279 + 0.340404i \(0.889436\pi\)
\(492\) 0 0
\(493\) −48.5663 −2.18731
\(494\) 0 0
\(495\) −25.3943 −1.14139
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 5.75198 0.257494 0.128747 0.991677i \(-0.458904\pi\)
0.128747 + 0.991677i \(0.458904\pi\)
\(500\) 0 0
\(501\) −2.68875 −0.120125
\(502\) 0 0
\(503\) 40.6067 1.81057 0.905283 0.424810i \(-0.139659\pi\)
0.905283 + 0.424810i \(0.139659\pi\)
\(504\) 0 0
\(505\) 12.9913 0.578103
\(506\) 0 0
\(507\) −0.126368 −0.00561220
\(508\) 0 0
\(509\) −13.1720 −0.583837 −0.291919 0.956443i \(-0.594294\pi\)
−0.291919 + 0.956443i \(0.594294\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 3.36778 0.148691
\(514\) 0 0
\(515\) −9.52163 −0.419573
\(516\) 0 0
\(517\) 34.2993 1.50848
\(518\) 0 0
\(519\) 0.0967662 0.00424757
\(520\) 0 0
\(521\) 34.1957 1.49814 0.749070 0.662491i \(-0.230501\pi\)
0.749070 + 0.662491i \(0.230501\pi\)
\(522\) 0 0
\(523\) 35.1253 1.53592 0.767961 0.640497i \(-0.221271\pi\)
0.767961 + 0.640497i \(0.221271\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.6421 0.463576
\(528\) 0 0
\(529\) 32.2711 1.40309
\(530\) 0 0
\(531\) 8.14879 0.353627
\(532\) 0 0
\(533\) −3.63941 −0.157641
\(534\) 0 0
\(535\) −25.6886 −1.11061
\(536\) 0 0
\(537\) −6.89515 −0.297548
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 24.0445 1.03376 0.516878 0.856059i \(-0.327094\pi\)
0.516878 + 0.856059i \(0.327094\pi\)
\(542\) 0 0
\(543\) 0.156133 0.00670031
\(544\) 0 0
\(545\) 33.5369 1.43656
\(546\) 0 0
\(547\) −34.5404 −1.47684 −0.738421 0.674340i \(-0.764428\pi\)
−0.738421 + 0.674340i \(0.764428\pi\)
\(548\) 0 0
\(549\) −28.0876 −1.19875
\(550\) 0 0
\(551\) 6.93283 0.295348
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 3.26048 0.138400
\(556\) 0 0
\(557\) 26.6174 1.12782 0.563908 0.825837i \(-0.309297\pi\)
0.563908 + 0.825837i \(0.309297\pi\)
\(558\) 0 0
\(559\) 18.7321 0.792283
\(560\) 0 0
\(561\) 17.3674 0.733253
\(562\) 0 0
\(563\) −38.4714 −1.62137 −0.810687 0.585479i \(-0.800906\pi\)
−0.810687 + 0.585479i \(0.800906\pi\)
\(564\) 0 0
\(565\) 37.8606 1.59281
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22.1979 −0.930583 −0.465291 0.885158i \(-0.654050\pi\)
−0.465291 + 0.885158i \(0.654050\pi\)
\(570\) 0 0
\(571\) −32.3436 −1.35354 −0.676769 0.736196i \(-0.736620\pi\)
−0.676769 + 0.736196i \(0.736620\pi\)
\(572\) 0 0
\(573\) 0.524268 0.0219016
\(574\) 0 0
\(575\) 1.20144 0.0501035
\(576\) 0 0
\(577\) 23.4107 0.974599 0.487299 0.873235i \(-0.337982\pi\)
0.487299 + 0.873235i \(0.337982\pi\)
\(578\) 0 0
\(579\) −8.81813 −0.366469
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −6.88439 −0.285122
\(584\) 0 0
\(585\) −21.8923 −0.905133
\(586\) 0 0
\(587\) −6.45509 −0.266430 −0.133215 0.991087i \(-0.542530\pi\)
−0.133215 + 0.991087i \(0.542530\pi\)
\(588\) 0 0
\(589\) −1.51915 −0.0625956
\(590\) 0 0
\(591\) 2.47797 0.101930
\(592\) 0 0
\(593\) −38.1095 −1.56497 −0.782484 0.622671i \(-0.786048\pi\)
−0.782484 + 0.622671i \(0.786048\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 6.46606 0.264638
\(598\) 0 0
\(599\) −16.4950 −0.673967 −0.336983 0.941511i \(-0.609407\pi\)
−0.336983 + 0.941511i \(0.609407\pi\)
\(600\) 0 0
\(601\) 4.14054 0.168896 0.0844482 0.996428i \(-0.473087\pi\)
0.0844482 + 0.996428i \(0.473087\pi\)
\(602\) 0 0
\(603\) −6.74945 −0.274859
\(604\) 0 0
\(605\) 15.0057 0.610067
\(606\) 0 0
\(607\) −40.8860 −1.65951 −0.829756 0.558127i \(-0.811520\pi\)
−0.829756 + 0.558127i \(0.811520\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 29.5693 1.19624
\(612\) 0 0
\(613\) 38.5223 1.55590 0.777951 0.628325i \(-0.216259\pi\)
0.777951 + 0.628325i \(0.216259\pi\)
\(614\) 0 0
\(615\) 1.13299 0.0456867
\(616\) 0 0
\(617\) −26.2855 −1.05822 −0.529108 0.848555i \(-0.677473\pi\)
−0.529108 + 0.848555i \(0.677473\pi\)
\(618\) 0 0
\(619\) −47.3181 −1.90188 −0.950938 0.309383i \(-0.899878\pi\)
−0.950938 + 0.309383i \(0.899878\pi\)
\(620\) 0 0
\(621\) −21.9602 −0.881231
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −24.1659 −0.966635
\(626\) 0 0
\(627\) −2.47920 −0.0990096
\(628\) 0 0
\(629\) 22.9846 0.916457
\(630\) 0 0
\(631\) 4.48510 0.178549 0.0892746 0.996007i \(-0.471545\pi\)
0.0892746 + 0.996007i \(0.471545\pi\)
\(632\) 0 0
\(633\) −10.6887 −0.424839
\(634\) 0 0
\(635\) −18.5348 −0.735531
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −35.6401 −1.40990
\(640\) 0 0
\(641\) −35.7692 −1.41280 −0.706399 0.707814i \(-0.749682\pi\)
−0.706399 + 0.707814i \(0.749682\pi\)
\(642\) 0 0
\(643\) 30.7547 1.21285 0.606424 0.795142i \(-0.292603\pi\)
0.606424 + 0.795142i \(0.292603\pi\)
\(644\) 0 0
\(645\) −5.83152 −0.229616
\(646\) 0 0
\(647\) 44.6457 1.75520 0.877602 0.479391i \(-0.159142\pi\)
0.877602 + 0.479391i \(0.159142\pi\)
\(648\) 0 0
\(649\) −12.5795 −0.493787
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −29.4217 −1.15136 −0.575680 0.817675i \(-0.695263\pi\)
−0.575680 + 0.817675i \(0.695263\pi\)
\(654\) 0 0
\(655\) −26.0583 −1.01818
\(656\) 0 0
\(657\) −31.5035 −1.22907
\(658\) 0 0
\(659\) 39.7367 1.54792 0.773961 0.633234i \(-0.218273\pi\)
0.773961 + 0.633234i \(0.218273\pi\)
\(660\) 0 0
\(661\) −9.58987 −0.373003 −0.186501 0.982455i \(-0.559715\pi\)
−0.186501 + 0.982455i \(0.559715\pi\)
\(662\) 0 0
\(663\) 14.9724 0.581478
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −45.2066 −1.75040
\(668\) 0 0
\(669\) 5.97670 0.231073
\(670\) 0 0
\(671\) 43.3594 1.67387
\(672\) 0 0
\(673\) 28.1956 1.08686 0.543431 0.839454i \(-0.317125\pi\)
0.543431 + 0.839454i \(0.317125\pi\)
\(674\) 0 0
\(675\) −0.477352 −0.0183733
\(676\) 0 0
\(677\) −9.29576 −0.357265 −0.178633 0.983916i \(-0.557167\pi\)
−0.178633 + 0.983916i \(0.557167\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.357774 0.0137099
\(682\) 0 0
\(683\) 13.2127 0.505570 0.252785 0.967522i \(-0.418653\pi\)
0.252785 + 0.967522i \(0.418653\pi\)
\(684\) 0 0
\(685\) −38.7524 −1.48065
\(686\) 0 0
\(687\) −12.9652 −0.494655
\(688\) 0 0
\(689\) −5.93499 −0.226105
\(690\) 0 0
\(691\) −6.77498 −0.257732 −0.128866 0.991662i \(-0.541134\pi\)
−0.128866 + 0.991662i \(0.541134\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7.55937 −0.286743
\(696\) 0 0
\(697\) 7.98698 0.302528
\(698\) 0 0
\(699\) −1.51639 −0.0573550
\(700\) 0 0
\(701\) 29.8871 1.12882 0.564410 0.825494i \(-0.309104\pi\)
0.564410 + 0.825494i \(0.309104\pi\)
\(702\) 0 0
\(703\) −3.28105 −0.123747
\(704\) 0 0
\(705\) −9.20525 −0.346690
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 4.95367 0.186039 0.0930194 0.995664i \(-0.470348\pi\)
0.0930194 + 0.995664i \(0.470348\pi\)
\(710\) 0 0
\(711\) −24.8020 −0.930149
\(712\) 0 0
\(713\) 9.90587 0.370978
\(714\) 0 0
\(715\) 33.7955 1.26388
\(716\) 0 0
\(717\) −3.89535 −0.145475
\(718\) 0 0
\(719\) −18.8348 −0.702418 −0.351209 0.936297i \(-0.614229\pi\)
−0.351209 + 0.936297i \(0.614229\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 3.90978 0.145406
\(724\) 0 0
\(725\) −0.982663 −0.0364952
\(726\) 0 0
\(727\) −42.1079 −1.56169 −0.780847 0.624722i \(-0.785212\pi\)
−0.780847 + 0.624722i \(0.785212\pi\)
\(728\) 0 0
\(729\) −13.7105 −0.507795
\(730\) 0 0
\(731\) −41.1090 −1.52047
\(732\) 0 0
\(733\) 15.6455 0.577881 0.288940 0.957347i \(-0.406697\pi\)
0.288940 + 0.957347i \(0.406697\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.4193 0.383798
\(738\) 0 0
\(739\) 32.1517 1.18272 0.591360 0.806407i \(-0.298591\pi\)
0.591360 + 0.806407i \(0.298591\pi\)
\(740\) 0 0
\(741\) −2.13730 −0.0785157
\(742\) 0 0
\(743\) −3.81171 −0.139838 −0.0699190 0.997553i \(-0.522274\pi\)
−0.0699190 + 0.997553i \(0.522274\pi\)
\(744\) 0 0
\(745\) 44.6207 1.63478
\(746\) 0 0
\(747\) −20.5637 −0.752386
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −19.1017 −0.697030 −0.348515 0.937303i \(-0.613314\pi\)
−0.348515 + 0.937303i \(0.613314\pi\)
\(752\) 0 0
\(753\) 12.2357 0.445894
\(754\) 0 0
\(755\) 1.74348 0.0634517
\(756\) 0 0
\(757\) 30.1926 1.09737 0.548684 0.836030i \(-0.315129\pi\)
0.548684 + 0.836030i \(0.315129\pi\)
\(758\) 0 0
\(759\) 16.1660 0.586788
\(760\) 0 0
\(761\) 51.0772 1.85155 0.925774 0.378076i \(-0.123414\pi\)
0.925774 + 0.378076i \(0.123414\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 48.0442 1.73704
\(766\) 0 0
\(767\) −10.8447 −0.391578
\(768\) 0 0
\(769\) −30.8036 −1.11081 −0.555404 0.831581i \(-0.687436\pi\)
−0.555404 + 0.831581i \(0.687436\pi\)
\(770\) 0 0
\(771\) 0.792047 0.0285249
\(772\) 0 0
\(773\) 31.1901 1.12183 0.560916 0.827873i \(-0.310449\pi\)
0.560916 + 0.827873i \(0.310449\pi\)
\(774\) 0 0
\(775\) 0.215326 0.00773473
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.14014 −0.0408498
\(780\) 0 0
\(781\) 55.0184 1.96871
\(782\) 0 0
\(783\) 17.9613 0.641885
\(784\) 0 0
\(785\) 11.6544 0.415963
\(786\) 0 0
\(787\) 12.4267 0.442963 0.221481 0.975165i \(-0.428911\pi\)
0.221481 + 0.975165i \(0.428911\pi\)
\(788\) 0 0
\(789\) −8.43326 −0.300232
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 37.3799 1.32740
\(794\) 0 0
\(795\) 1.84763 0.0655287
\(796\) 0 0
\(797\) 17.3519 0.614636 0.307318 0.951607i \(-0.400568\pi\)
0.307318 + 0.951607i \(0.400568\pi\)
\(798\) 0 0
\(799\) −64.8920 −2.29571
\(800\) 0 0
\(801\) 49.1751 1.73752
\(802\) 0 0
\(803\) 48.6326 1.71621
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −9.61043 −0.338303
\(808\) 0 0
\(809\) 26.0371 0.915416 0.457708 0.889103i \(-0.348670\pi\)
0.457708 + 0.889103i \(0.348670\pi\)
\(810\) 0 0
\(811\) 16.2483 0.570557 0.285278 0.958445i \(-0.407914\pi\)
0.285278 + 0.958445i \(0.407914\pi\)
\(812\) 0 0
\(813\) −8.40978 −0.294944
\(814\) 0 0
\(815\) 20.5274 0.719042
\(816\) 0 0
\(817\) 5.86831 0.205306
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 30.5449 1.06603 0.533013 0.846107i \(-0.321060\pi\)
0.533013 + 0.846107i \(0.321060\pi\)
\(822\) 0 0
\(823\) −47.3618 −1.65093 −0.825464 0.564455i \(-0.809086\pi\)
−0.825464 + 0.564455i \(0.809086\pi\)
\(824\) 0 0
\(825\) 0.351403 0.0122343
\(826\) 0 0
\(827\) −49.3914 −1.71751 −0.858754 0.512388i \(-0.828761\pi\)
−0.858754 + 0.512388i \(0.828761\pi\)
\(828\) 0 0
\(829\) −1.74976 −0.0607717 −0.0303859 0.999538i \(-0.509674\pi\)
−0.0303859 + 0.999538i \(0.509674\pi\)
\(830\) 0 0
\(831\) 9.91502 0.343948
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 11.4822 0.397358
\(836\) 0 0
\(837\) −3.93577 −0.136040
\(838\) 0 0
\(839\) 48.9756 1.69083 0.845413 0.534113i \(-0.179354\pi\)
0.845413 + 0.534113i \(0.179354\pi\)
\(840\) 0 0
\(841\) 7.97468 0.274989
\(842\) 0 0
\(843\) −13.1133 −0.451646
\(844\) 0 0
\(845\) 0.539649 0.0185645
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 3.46411 0.118888
\(850\) 0 0
\(851\) 21.3946 0.733397
\(852\) 0 0
\(853\) −26.3270 −0.901420 −0.450710 0.892670i \(-0.648829\pi\)
−0.450710 + 0.892670i \(0.648829\pi\)
\(854\) 0 0
\(855\) −6.85831 −0.234549
\(856\) 0 0
\(857\) −41.2096 −1.40769 −0.703847 0.710352i \(-0.748536\pi\)
−0.703847 + 0.710352i \(0.748536\pi\)
\(858\) 0 0
\(859\) −13.1281 −0.447925 −0.223962 0.974598i \(-0.571899\pi\)
−0.223962 + 0.974598i \(0.571899\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −33.7054 −1.14735 −0.573673 0.819084i \(-0.694482\pi\)
−0.573673 + 0.819084i \(0.694482\pi\)
\(864\) 0 0
\(865\) −0.413236 −0.0140505
\(866\) 0 0
\(867\) −24.1016 −0.818533
\(868\) 0 0
\(869\) 38.2874 1.29881
\(870\) 0 0
\(871\) 8.98238 0.304356
\(872\) 0 0
\(873\) −36.2145 −1.22568
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 12.0469 0.406795 0.203398 0.979096i \(-0.434802\pi\)
0.203398 + 0.979096i \(0.434802\pi\)
\(878\) 0 0
\(879\) 7.25321 0.244645
\(880\) 0 0
\(881\) −25.8023 −0.869302 −0.434651 0.900599i \(-0.643128\pi\)
−0.434651 + 0.900599i \(0.643128\pi\)
\(882\) 0 0
\(883\) 55.2747 1.86014 0.930070 0.367381i \(-0.119746\pi\)
0.930070 + 0.367381i \(0.119746\pi\)
\(884\) 0 0
\(885\) 3.37607 0.113485
\(886\) 0 0
\(887\) 52.5771 1.76536 0.882682 0.469970i \(-0.155735\pi\)
0.882682 + 0.469970i \(0.155735\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 28.2113 0.945113
\(892\) 0 0
\(893\) 9.26333 0.309985
\(894\) 0 0
\(895\) 29.4454 0.984252
\(896\) 0 0
\(897\) 13.9366 0.465330
\(898\) 0 0
\(899\) −8.10206 −0.270219
\(900\) 0 0
\(901\) 13.0248 0.433919
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −0.666759 −0.0221638
\(906\) 0 0
\(907\) −35.7961 −1.18859 −0.594294 0.804248i \(-0.702569\pi\)
−0.594294 + 0.804248i \(0.702569\pi\)
\(908\) 0 0
\(909\) −16.1513 −0.535706
\(910\) 0 0
\(911\) 5.12715 0.169870 0.0849350 0.996386i \(-0.472932\pi\)
0.0849350 + 0.996386i \(0.472932\pi\)
\(912\) 0 0
\(913\) 31.7446 1.05059
\(914\) 0 0
\(915\) −11.6368 −0.384700
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 2.73713 0.0902897 0.0451449 0.998980i \(-0.485625\pi\)
0.0451449 + 0.998980i \(0.485625\pi\)
\(920\) 0 0
\(921\) 11.5711 0.381281
\(922\) 0 0
\(923\) 47.4310 1.56121
\(924\) 0 0
\(925\) 0.465058 0.0152910
\(926\) 0 0
\(927\) 11.8377 0.388802
\(928\) 0 0
\(929\) 13.6670 0.448399 0.224199 0.974543i \(-0.428023\pi\)
0.224199 + 0.974543i \(0.428023\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 7.79071 0.255056
\(934\) 0 0
\(935\) −74.1669 −2.42552
\(936\) 0 0
\(937\) 6.96389 0.227500 0.113750 0.993509i \(-0.463714\pi\)
0.113750 + 0.993509i \(0.463714\pi\)
\(938\) 0 0
\(939\) 9.99895 0.326303
\(940\) 0 0
\(941\) −22.5498 −0.735102 −0.367551 0.930003i \(-0.619804\pi\)
−0.367551 + 0.930003i \(0.619804\pi\)
\(942\) 0 0
\(943\) 7.43446 0.242099
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −43.9769 −1.42906 −0.714528 0.699607i \(-0.753358\pi\)
−0.714528 + 0.699607i \(0.753358\pi\)
\(948\) 0 0
\(949\) 41.9258 1.36097
\(950\) 0 0
\(951\) −0.908407 −0.0294571
\(952\) 0 0
\(953\) 6.89729 0.223425 0.111713 0.993741i \(-0.464366\pi\)
0.111713 + 0.993741i \(0.464366\pi\)
\(954\) 0 0
\(955\) −2.23886 −0.0724479
\(956\) 0 0
\(957\) −13.2222 −0.427415
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −29.2246 −0.942730
\(962\) 0 0
\(963\) 31.9372 1.02916
\(964\) 0 0
\(965\) 37.6574 1.21224
\(966\) 0 0
\(967\) 24.7226 0.795025 0.397512 0.917597i \(-0.369874\pi\)
0.397512 + 0.917597i \(0.369874\pi\)
\(968\) 0 0
\(969\) 4.69047 0.150680
\(970\) 0 0
\(971\) 51.8477 1.66387 0.831937 0.554871i \(-0.187232\pi\)
0.831937 + 0.554871i \(0.187232\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0.302942 0.00970192
\(976\) 0 0
\(977\) 9.99891 0.319893 0.159947 0.987126i \(-0.448868\pi\)
0.159947 + 0.987126i \(0.448868\pi\)
\(978\) 0 0
\(979\) −75.9126 −2.42618
\(980\) 0 0
\(981\) −41.6946 −1.33121
\(982\) 0 0
\(983\) 1.22767 0.0391566 0.0195783 0.999808i \(-0.493768\pi\)
0.0195783 + 0.999808i \(0.493768\pi\)
\(984\) 0 0
\(985\) −10.5821 −0.337172
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −38.2652 −1.21676
\(990\) 0 0
\(991\) 43.7198 1.38881 0.694403 0.719586i \(-0.255669\pi\)
0.694403 + 0.719586i \(0.255669\pi\)
\(992\) 0 0
\(993\) −6.24157 −0.198070
\(994\) 0 0
\(995\) −27.6131 −0.875393
\(996\) 0 0
\(997\) 5.79205 0.183436 0.0917180 0.995785i \(-0.470764\pi\)
0.0917180 + 0.995785i \(0.470764\pi\)
\(998\) 0 0
\(999\) −8.50044 −0.268942
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 \(a_p\))