Properties

Label 4004.2.a.j.1.4
Level 4004
Weight 2
Character 4004.1
Self dual Yes
Analytic conductor 31.972
Analytic rank 0
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9721009693\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
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 1.4
Root \(0.672934\)
Character \(\chi\) = 4004.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.672934 q^{3} +0.538228 q^{5} -1.00000 q^{7} -2.54716 q^{9} +O(q^{10})\) \(q-0.672934 q^{3} +0.538228 q^{5} -1.00000 q^{7} -2.54716 q^{9} -1.00000 q^{11} -1.00000 q^{13} -0.362192 q^{15} -1.70606 q^{17} +4.21645 q^{19} +0.672934 q^{21} +3.56036 q^{23} -4.71031 q^{25} +3.73287 q^{27} +9.32798 q^{29} -5.69704 q^{31} +0.672934 q^{33} -0.538228 q^{35} -8.10326 q^{37} +0.672934 q^{39} -6.73633 q^{41} -12.5566 q^{43} -1.37095 q^{45} +12.2622 q^{47} +1.00000 q^{49} +1.14806 q^{51} +7.52462 q^{53} -0.538228 q^{55} -2.83739 q^{57} +1.63094 q^{59} +8.27727 q^{61} +2.54716 q^{63} -0.538228 q^{65} -8.26536 q^{67} -2.39589 q^{69} +9.58999 q^{71} +7.50579 q^{73} +3.16973 q^{75} +1.00000 q^{77} +12.6682 q^{79} +5.12950 q^{81} -10.4121 q^{83} -0.918247 q^{85} -6.27712 q^{87} +0.0335338 q^{89} +1.00000 q^{91} +3.83373 q^{93} +2.26941 q^{95} +12.7427 q^{97} +2.54716 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} + O(q^{10}) \) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} - 10q^{11} - 10q^{13} - 4q^{15} + 9q^{17} + 3q^{19} + 2q^{21} - 4q^{23} + 22q^{25} - 8q^{27} + 13q^{29} - 17q^{31} + 2q^{33} + 2q^{35} + 11q^{37} + 2q^{39} + 8q^{41} + 21q^{43} - 15q^{45} + q^{47} + 10q^{49} + 19q^{51} + 22q^{53} + 2q^{55} + 8q^{57} - 24q^{59} + 16q^{61} - 10q^{63} + 2q^{65} + 19q^{67} + 51q^{69} - 25q^{71} + 22q^{73} + 28q^{75} + 10q^{77} + 41q^{79} + 54q^{81} + 8q^{83} + 9q^{85} - 5q^{87} + 36q^{89} + 10q^{91} + 12q^{93} + 13q^{95} - 5q^{97} - 10q^{99} + O(q^{100}) \)

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
\(3\) −0.672934 −0.388519 −0.194259 0.980950i \(-0.562230\pi\)
−0.194259 + 0.980950i \(0.562230\pi\)
\(4\) 0 0
\(5\) 0.538228 0.240703 0.120351 0.992731i \(-0.461598\pi\)
0.120351 + 0.992731i \(0.461598\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.54716 −0.849053
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −0.362192 −0.0935176
\(16\) 0 0
\(17\) −1.70606 −0.413779 −0.206890 0.978364i \(-0.566334\pi\)
−0.206890 + 0.978364i \(0.566334\pi\)
\(18\) 0 0
\(19\) 4.21645 0.967320 0.483660 0.875256i \(-0.339307\pi\)
0.483660 + 0.875256i \(0.339307\pi\)
\(20\) 0 0
\(21\) 0.672934 0.146846
\(22\) 0 0
\(23\) 3.56036 0.742387 0.371194 0.928555i \(-0.378949\pi\)
0.371194 + 0.928555i \(0.378949\pi\)
\(24\) 0 0
\(25\) −4.71031 −0.942062
\(26\) 0 0
\(27\) 3.73287 0.718392
\(28\) 0 0
\(29\) 9.32798 1.73216 0.866081 0.499903i \(-0.166631\pi\)
0.866081 + 0.499903i \(0.166631\pi\)
\(30\) 0 0
\(31\) −5.69704 −1.02322 −0.511609 0.859218i \(-0.670951\pi\)
−0.511609 + 0.859218i \(0.670951\pi\)
\(32\) 0 0
\(33\) 0.672934 0.117143
\(34\) 0 0
\(35\) −0.538228 −0.0909772
\(36\) 0 0
\(37\) −8.10326 −1.33217 −0.666084 0.745877i \(-0.732031\pi\)
−0.666084 + 0.745877i \(0.732031\pi\)
\(38\) 0 0
\(39\) 0.672934 0.107756
\(40\) 0 0
\(41\) −6.73633 −1.05204 −0.526019 0.850473i \(-0.676316\pi\)
−0.526019 + 0.850473i \(0.676316\pi\)
\(42\) 0 0
\(43\) −12.5566 −1.91486 −0.957432 0.288660i \(-0.906790\pi\)
−0.957432 + 0.288660i \(0.906790\pi\)
\(44\) 0 0
\(45\) −1.37095 −0.204370
\(46\) 0 0
\(47\) 12.2622 1.78863 0.894313 0.447441i \(-0.147665\pi\)
0.894313 + 0.447441i \(0.147665\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 1.14806 0.160761
\(52\) 0 0
\(53\) 7.52462 1.03359 0.516793 0.856110i \(-0.327126\pi\)
0.516793 + 0.856110i \(0.327126\pi\)
\(54\) 0 0
\(55\) −0.538228 −0.0725747
\(56\) 0 0
\(57\) −2.83739 −0.375822
\(58\) 0 0
\(59\) 1.63094 0.212330 0.106165 0.994349i \(-0.466143\pi\)
0.106165 + 0.994349i \(0.466143\pi\)
\(60\) 0 0
\(61\) 8.27727 1.05980 0.529898 0.848061i \(-0.322230\pi\)
0.529898 + 0.848061i \(0.322230\pi\)
\(62\) 0 0
\(63\) 2.54716 0.320912
\(64\) 0 0
\(65\) −0.538228 −0.0667590
\(66\) 0 0
\(67\) −8.26536 −1.00977 −0.504887 0.863185i \(-0.668466\pi\)
−0.504887 + 0.863185i \(0.668466\pi\)
\(68\) 0 0
\(69\) −2.39589 −0.288431
\(70\) 0 0
\(71\) 9.58999 1.13812 0.569061 0.822295i \(-0.307307\pi\)
0.569061 + 0.822295i \(0.307307\pi\)
\(72\) 0 0
\(73\) 7.50579 0.878486 0.439243 0.898368i \(-0.355247\pi\)
0.439243 + 0.898368i \(0.355247\pi\)
\(74\) 0 0
\(75\) 3.16973 0.366009
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 12.6682 1.42529 0.712644 0.701526i \(-0.247498\pi\)
0.712644 + 0.701526i \(0.247498\pi\)
\(80\) 0 0
\(81\) 5.12950 0.569945
\(82\) 0 0
\(83\) −10.4121 −1.14288 −0.571438 0.820645i \(-0.693614\pi\)
−0.571438 + 0.820645i \(0.693614\pi\)
\(84\) 0 0
\(85\) −0.918247 −0.0995979
\(86\) 0 0
\(87\) −6.27712 −0.672977
\(88\) 0 0
\(89\) 0.0335338 0.00355458 0.00177729 0.999998i \(-0.499434\pi\)
0.00177729 + 0.999998i \(0.499434\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 3.83373 0.397540
\(94\) 0 0
\(95\) 2.26941 0.232837
\(96\) 0 0
\(97\) 12.7427 1.29382 0.646910 0.762566i \(-0.276061\pi\)
0.646910 + 0.762566i \(0.276061\pi\)
\(98\) 0 0
\(99\) 2.54716 0.255999
\(100\) 0 0
\(101\) 11.1490 1.10936 0.554681 0.832063i \(-0.312840\pi\)
0.554681 + 0.832063i \(0.312840\pi\)
\(102\) 0 0
\(103\) 5.61935 0.553691 0.276846 0.960914i \(-0.410711\pi\)
0.276846 + 0.960914i \(0.410711\pi\)
\(104\) 0 0
\(105\) 0.362192 0.0353463
\(106\) 0 0
\(107\) 7.13010 0.689292 0.344646 0.938733i \(-0.387999\pi\)
0.344646 + 0.938733i \(0.387999\pi\)
\(108\) 0 0
\(109\) 15.3848 1.47360 0.736798 0.676112i \(-0.236337\pi\)
0.736798 + 0.676112i \(0.236337\pi\)
\(110\) 0 0
\(111\) 5.45296 0.517572
\(112\) 0 0
\(113\) 12.5604 1.18158 0.590789 0.806826i \(-0.298816\pi\)
0.590789 + 0.806826i \(0.298816\pi\)
\(114\) 0 0
\(115\) 1.91629 0.178695
\(116\) 0 0
\(117\) 2.54716 0.235485
\(118\) 0 0
\(119\) 1.70606 0.156394
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 4.53311 0.408736
\(124\) 0 0
\(125\) −5.22636 −0.467460
\(126\) 0 0
\(127\) −17.4061 −1.54455 −0.772273 0.635291i \(-0.780880\pi\)
−0.772273 + 0.635291i \(0.780880\pi\)
\(128\) 0 0
\(129\) 8.44976 0.743960
\(130\) 0 0
\(131\) −15.8268 −1.38280 −0.691398 0.722474i \(-0.743005\pi\)
−0.691398 + 0.722474i \(0.743005\pi\)
\(132\) 0 0
\(133\) −4.21645 −0.365612
\(134\) 0 0
\(135\) 2.00914 0.172919
\(136\) 0 0
\(137\) −5.89307 −0.503479 −0.251739 0.967795i \(-0.581003\pi\)
−0.251739 + 0.967795i \(0.581003\pi\)
\(138\) 0 0
\(139\) −11.8018 −1.00102 −0.500509 0.865731i \(-0.666854\pi\)
−0.500509 + 0.865731i \(0.666854\pi\)
\(140\) 0 0
\(141\) −8.25165 −0.694915
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 5.02058 0.416937
\(146\) 0 0
\(147\) −0.672934 −0.0555027
\(148\) 0 0
\(149\) −20.5371 −1.68246 −0.841231 0.540676i \(-0.818168\pi\)
−0.841231 + 0.540676i \(0.818168\pi\)
\(150\) 0 0
\(151\) 7.85237 0.639017 0.319508 0.947583i \(-0.396482\pi\)
0.319508 + 0.947583i \(0.396482\pi\)
\(152\) 0 0
\(153\) 4.34560 0.351321
\(154\) 0 0
\(155\) −3.06631 −0.246292
\(156\) 0 0
\(157\) −12.0690 −0.963215 −0.481607 0.876387i \(-0.659947\pi\)
−0.481607 + 0.876387i \(0.659947\pi\)
\(158\) 0 0
\(159\) −5.06357 −0.401567
\(160\) 0 0
\(161\) −3.56036 −0.280596
\(162\) 0 0
\(163\) 20.3458 1.59361 0.796804 0.604237i \(-0.206522\pi\)
0.796804 + 0.604237i \(0.206522\pi\)
\(164\) 0 0
\(165\) 0.362192 0.0281966
\(166\) 0 0
\(167\) −0.151712 −0.0117398 −0.00586990 0.999983i \(-0.501868\pi\)
−0.00586990 + 0.999983i \(0.501868\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −10.7400 −0.821306
\(172\) 0 0
\(173\) 9.52069 0.723845 0.361922 0.932208i \(-0.382121\pi\)
0.361922 + 0.932208i \(0.382121\pi\)
\(174\) 0 0
\(175\) 4.71031 0.356066
\(176\) 0 0
\(177\) −1.09751 −0.0824943
\(178\) 0 0
\(179\) 1.92886 0.144170 0.0720850 0.997398i \(-0.477035\pi\)
0.0720850 + 0.997398i \(0.477035\pi\)
\(180\) 0 0
\(181\) 21.7724 1.61833 0.809166 0.587580i \(-0.199919\pi\)
0.809166 + 0.587580i \(0.199919\pi\)
\(182\) 0 0
\(183\) −5.57005 −0.411750
\(184\) 0 0
\(185\) −4.36140 −0.320657
\(186\) 0 0
\(187\) 1.70606 0.124759
\(188\) 0 0
\(189\) −3.73287 −0.271526
\(190\) 0 0
\(191\) −2.82575 −0.204464 −0.102232 0.994761i \(-0.532598\pi\)
−0.102232 + 0.994761i \(0.532598\pi\)
\(192\) 0 0
\(193\) 19.2031 1.38227 0.691134 0.722727i \(-0.257111\pi\)
0.691134 + 0.722727i \(0.257111\pi\)
\(194\) 0 0
\(195\) 0.362192 0.0259371
\(196\) 0 0
\(197\) 15.8466 1.12903 0.564513 0.825424i \(-0.309064\pi\)
0.564513 + 0.825424i \(0.309064\pi\)
\(198\) 0 0
\(199\) 7.57704 0.537122 0.268561 0.963263i \(-0.413452\pi\)
0.268561 + 0.963263i \(0.413452\pi\)
\(200\) 0 0
\(201\) 5.56204 0.392316
\(202\) 0 0
\(203\) −9.32798 −0.654696
\(204\) 0 0
\(205\) −3.62568 −0.253229
\(206\) 0 0
\(207\) −9.06882 −0.630326
\(208\) 0 0
\(209\) −4.21645 −0.291658
\(210\) 0 0
\(211\) 6.62864 0.456334 0.228167 0.973622i \(-0.426727\pi\)
0.228167 + 0.973622i \(0.426727\pi\)
\(212\) 0 0
\(213\) −6.45343 −0.442182
\(214\) 0 0
\(215\) −6.75831 −0.460913
\(216\) 0 0
\(217\) 5.69704 0.386740
\(218\) 0 0
\(219\) −5.05090 −0.341308
\(220\) 0 0
\(221\) 1.70606 0.114762
\(222\) 0 0
\(223\) −11.9808 −0.802291 −0.401146 0.916014i \(-0.631388\pi\)
−0.401146 + 0.916014i \(0.631388\pi\)
\(224\) 0 0
\(225\) 11.9979 0.799861
\(226\) 0 0
\(227\) −16.1516 −1.07202 −0.536011 0.844211i \(-0.680069\pi\)
−0.536011 + 0.844211i \(0.680069\pi\)
\(228\) 0 0
\(229\) 25.4721 1.68324 0.841621 0.540068i \(-0.181602\pi\)
0.841621 + 0.540068i \(0.181602\pi\)
\(230\) 0 0
\(231\) −0.672934 −0.0442758
\(232\) 0 0
\(233\) 20.2582 1.32716 0.663579 0.748106i \(-0.269037\pi\)
0.663579 + 0.748106i \(0.269037\pi\)
\(234\) 0 0
\(235\) 6.59986 0.430528
\(236\) 0 0
\(237\) −8.52488 −0.553751
\(238\) 0 0
\(239\) 11.9477 0.772831 0.386415 0.922325i \(-0.373713\pi\)
0.386415 + 0.922325i \(0.373713\pi\)
\(240\) 0 0
\(241\) 26.9032 1.73299 0.866493 0.499189i \(-0.166369\pi\)
0.866493 + 0.499189i \(0.166369\pi\)
\(242\) 0 0
\(243\) −14.6504 −0.939826
\(244\) 0 0
\(245\) 0.538228 0.0343861
\(246\) 0 0
\(247\) −4.21645 −0.268286
\(248\) 0 0
\(249\) 7.00666 0.444029
\(250\) 0 0
\(251\) 1.52645 0.0963490 0.0481745 0.998839i \(-0.484660\pi\)
0.0481745 + 0.998839i \(0.484660\pi\)
\(252\) 0 0
\(253\) −3.56036 −0.223838
\(254\) 0 0
\(255\) 0.617919 0.0386956
\(256\) 0 0
\(257\) 9.33923 0.582565 0.291283 0.956637i \(-0.405918\pi\)
0.291283 + 0.956637i \(0.405918\pi\)
\(258\) 0 0
\(259\) 8.10326 0.503512
\(260\) 0 0
\(261\) −23.7599 −1.47070
\(262\) 0 0
\(263\) −10.5211 −0.648758 −0.324379 0.945927i \(-0.605155\pi\)
−0.324379 + 0.945927i \(0.605155\pi\)
\(264\) 0 0
\(265\) 4.04996 0.248787
\(266\) 0 0
\(267\) −0.0225661 −0.00138102
\(268\) 0 0
\(269\) 12.1026 0.737908 0.368954 0.929448i \(-0.379716\pi\)
0.368954 + 0.929448i \(0.379716\pi\)
\(270\) 0 0
\(271\) 11.7953 0.716515 0.358258 0.933623i \(-0.383371\pi\)
0.358258 + 0.933623i \(0.383371\pi\)
\(272\) 0 0
\(273\) −0.672934 −0.0407278
\(274\) 0 0
\(275\) 4.71031 0.284042
\(276\) 0 0
\(277\) −7.83652 −0.470851 −0.235425 0.971892i \(-0.575648\pi\)
−0.235425 + 0.971892i \(0.575648\pi\)
\(278\) 0 0
\(279\) 14.5113 0.868767
\(280\) 0 0
\(281\) −1.38147 −0.0824113 −0.0412057 0.999151i \(-0.513120\pi\)
−0.0412057 + 0.999151i \(0.513120\pi\)
\(282\) 0 0
\(283\) 21.4298 1.27387 0.636934 0.770918i \(-0.280202\pi\)
0.636934 + 0.770918i \(0.280202\pi\)
\(284\) 0 0
\(285\) −1.52716 −0.0904614
\(286\) 0 0
\(287\) 6.73633 0.397633
\(288\) 0 0
\(289\) −14.0894 −0.828787
\(290\) 0 0
\(291\) −8.57497 −0.502673
\(292\) 0 0
\(293\) −16.4337 −0.960066 −0.480033 0.877250i \(-0.659375\pi\)
−0.480033 + 0.877250i \(0.659375\pi\)
\(294\) 0 0
\(295\) 0.877818 0.0511085
\(296\) 0 0
\(297\) −3.73287 −0.216603
\(298\) 0 0
\(299\) −3.56036 −0.205901
\(300\) 0 0
\(301\) 12.5566 0.723750
\(302\) 0 0
\(303\) −7.50251 −0.431008
\(304\) 0 0
\(305\) 4.45506 0.255096
\(306\) 0 0
\(307\) 25.4134 1.45042 0.725209 0.688529i \(-0.241743\pi\)
0.725209 + 0.688529i \(0.241743\pi\)
\(308\) 0 0
\(309\) −3.78145 −0.215119
\(310\) 0 0
\(311\) −22.2211 −1.26004 −0.630021 0.776578i \(-0.716954\pi\)
−0.630021 + 0.776578i \(0.716954\pi\)
\(312\) 0 0
\(313\) −17.4758 −0.987793 −0.493896 0.869521i \(-0.664428\pi\)
−0.493896 + 0.869521i \(0.664428\pi\)
\(314\) 0 0
\(315\) 1.37095 0.0772445
\(316\) 0 0
\(317\) 5.35194 0.300595 0.150297 0.988641i \(-0.451977\pi\)
0.150297 + 0.988641i \(0.451977\pi\)
\(318\) 0 0
\(319\) −9.32798 −0.522267
\(320\) 0 0
\(321\) −4.79808 −0.267803
\(322\) 0 0
\(323\) −7.19349 −0.400257
\(324\) 0 0
\(325\) 4.71031 0.261281
\(326\) 0 0
\(327\) −10.3530 −0.572520
\(328\) 0 0
\(329\) −12.2622 −0.676037
\(330\) 0 0
\(331\) −33.5298 −1.84297 −0.921483 0.388419i \(-0.873021\pi\)
−0.921483 + 0.388419i \(0.873021\pi\)
\(332\) 0 0
\(333\) 20.6403 1.13108
\(334\) 0 0
\(335\) −4.44865 −0.243056
\(336\) 0 0
\(337\) 25.5363 1.39105 0.695527 0.718500i \(-0.255171\pi\)
0.695527 + 0.718500i \(0.255171\pi\)
\(338\) 0 0
\(339\) −8.45229 −0.459065
\(340\) 0 0
\(341\) 5.69704 0.308512
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −1.28954 −0.0694262
\(346\) 0 0
\(347\) 19.2720 1.03458 0.517288 0.855811i \(-0.326942\pi\)
0.517288 + 0.855811i \(0.326942\pi\)
\(348\) 0 0
\(349\) −13.0534 −0.698731 −0.349365 0.936987i \(-0.613603\pi\)
−0.349365 + 0.936987i \(0.613603\pi\)
\(350\) 0 0
\(351\) −3.73287 −0.199246
\(352\) 0 0
\(353\) 17.3319 0.922485 0.461243 0.887274i \(-0.347404\pi\)
0.461243 + 0.887274i \(0.347404\pi\)
\(354\) 0 0
\(355\) 5.16160 0.273949
\(356\) 0 0
\(357\) −1.14806 −0.0607619
\(358\) 0 0
\(359\) 0.598945 0.0316111 0.0158056 0.999875i \(-0.494969\pi\)
0.0158056 + 0.999875i \(0.494969\pi\)
\(360\) 0 0
\(361\) −1.22156 −0.0642927
\(362\) 0 0
\(363\) −0.672934 −0.0353199
\(364\) 0 0
\(365\) 4.03983 0.211454
\(366\) 0 0
\(367\) 6.57145 0.343027 0.171513 0.985182i \(-0.445134\pi\)
0.171513 + 0.985182i \(0.445134\pi\)
\(368\) 0 0
\(369\) 17.1585 0.893237
\(370\) 0 0
\(371\) −7.52462 −0.390659
\(372\) 0 0
\(373\) 15.7645 0.816253 0.408126 0.912925i \(-0.366182\pi\)
0.408126 + 0.912925i \(0.366182\pi\)
\(374\) 0 0
\(375\) 3.51700 0.181617
\(376\) 0 0
\(377\) −9.32798 −0.480416
\(378\) 0 0
\(379\) 11.9448 0.613565 0.306783 0.951780i \(-0.400747\pi\)
0.306783 + 0.951780i \(0.400747\pi\)
\(380\) 0 0
\(381\) 11.7132 0.600084
\(382\) 0 0
\(383\) 18.4537 0.942942 0.471471 0.881882i \(-0.343723\pi\)
0.471471 + 0.881882i \(0.343723\pi\)
\(384\) 0 0
\(385\) 0.538228 0.0274306
\(386\) 0 0
\(387\) 31.9837 1.62582
\(388\) 0 0
\(389\) 28.4060 1.44024 0.720122 0.693848i \(-0.244086\pi\)
0.720122 + 0.693848i \(0.244086\pi\)
\(390\) 0 0
\(391\) −6.07418 −0.307184
\(392\) 0 0
\(393\) 10.6504 0.537242
\(394\) 0 0
\(395\) 6.81840 0.343071
\(396\) 0 0
\(397\) −2.07267 −0.104024 −0.0520122 0.998646i \(-0.516563\pi\)
−0.0520122 + 0.998646i \(0.516563\pi\)
\(398\) 0 0
\(399\) 2.83739 0.142047
\(400\) 0 0
\(401\) 13.8582 0.692045 0.346022 0.938226i \(-0.387532\pi\)
0.346022 + 0.938226i \(0.387532\pi\)
\(402\) 0 0
\(403\) 5.69704 0.283790
\(404\) 0 0
\(405\) 2.76084 0.137187
\(406\) 0 0
\(407\) 8.10326 0.401664
\(408\) 0 0
\(409\) −18.5491 −0.917192 −0.458596 0.888645i \(-0.651647\pi\)
−0.458596 + 0.888645i \(0.651647\pi\)
\(410\) 0 0
\(411\) 3.96565 0.195611
\(412\) 0 0
\(413\) −1.63094 −0.0802533
\(414\) 0 0
\(415\) −5.60408 −0.275094
\(416\) 0 0
\(417\) 7.94185 0.388914
\(418\) 0 0
\(419\) −20.4582 −0.999450 −0.499725 0.866184i \(-0.666566\pi\)
−0.499725 + 0.866184i \(0.666566\pi\)
\(420\) 0 0
\(421\) −5.02752 −0.245026 −0.122513 0.992467i \(-0.539095\pi\)
−0.122513 + 0.992467i \(0.539095\pi\)
\(422\) 0 0
\(423\) −31.2338 −1.51864
\(424\) 0 0
\(425\) 8.03605 0.389806
\(426\) 0 0
\(427\) −8.27727 −0.400565
\(428\) 0 0
\(429\) −0.672934 −0.0324896
\(430\) 0 0
\(431\) 4.12654 0.198769 0.0993843 0.995049i \(-0.468313\pi\)
0.0993843 + 0.995049i \(0.468313\pi\)
\(432\) 0 0
\(433\) −34.7599 −1.67045 −0.835227 0.549905i \(-0.814664\pi\)
−0.835227 + 0.549905i \(0.814664\pi\)
\(434\) 0 0
\(435\) −3.37852 −0.161988
\(436\) 0 0
\(437\) 15.0121 0.718126
\(438\) 0 0
\(439\) −0.778157 −0.0371394 −0.0185697 0.999828i \(-0.505911\pi\)
−0.0185697 + 0.999828i \(0.505911\pi\)
\(440\) 0 0
\(441\) −2.54716 −0.121293
\(442\) 0 0
\(443\) 34.6935 1.64834 0.824169 0.566343i \(-0.191642\pi\)
0.824169 + 0.566343i \(0.191642\pi\)
\(444\) 0 0
\(445\) 0.0180489 0.000855598 0
\(446\) 0 0
\(447\) 13.8201 0.653668
\(448\) 0 0
\(449\) −19.4109 −0.916056 −0.458028 0.888938i \(-0.651444\pi\)
−0.458028 + 0.888938i \(0.651444\pi\)
\(450\) 0 0
\(451\) 6.73633 0.317201
\(452\) 0 0
\(453\) −5.28413 −0.248270
\(454\) 0 0
\(455\) 0.538228 0.0252325
\(456\) 0 0
\(457\) −11.2186 −0.524783 −0.262391 0.964962i \(-0.584511\pi\)
−0.262391 + 0.964962i \(0.584511\pi\)
\(458\) 0 0
\(459\) −6.36849 −0.297255
\(460\) 0 0
\(461\) −5.58868 −0.260291 −0.130145 0.991495i \(-0.541544\pi\)
−0.130145 + 0.991495i \(0.541544\pi\)
\(462\) 0 0
\(463\) −22.4767 −1.04458 −0.522290 0.852768i \(-0.674922\pi\)
−0.522290 + 0.852768i \(0.674922\pi\)
\(464\) 0 0
\(465\) 2.06342 0.0956889
\(466\) 0 0
\(467\) −13.2930 −0.615129 −0.307564 0.951527i \(-0.599514\pi\)
−0.307564 + 0.951527i \(0.599514\pi\)
\(468\) 0 0
\(469\) 8.26536 0.381659
\(470\) 0 0
\(471\) 8.12167 0.374227
\(472\) 0 0
\(473\) 12.5566 0.577353
\(474\) 0 0
\(475\) −19.8608 −0.911275
\(476\) 0 0
\(477\) −19.1664 −0.877569
\(478\) 0 0
\(479\) 11.4999 0.525445 0.262723 0.964871i \(-0.415380\pi\)
0.262723 + 0.964871i \(0.415380\pi\)
\(480\) 0 0
\(481\) 8.10326 0.369477
\(482\) 0 0
\(483\) 2.39589 0.109017
\(484\) 0 0
\(485\) 6.85846 0.311426
\(486\) 0 0
\(487\) −16.4335 −0.744671 −0.372335 0.928098i \(-0.621443\pi\)
−0.372335 + 0.928098i \(0.621443\pi\)
\(488\) 0 0
\(489\) −13.6914 −0.619147
\(490\) 0 0
\(491\) −25.4190 −1.14714 −0.573572 0.819155i \(-0.694443\pi\)
−0.573572 + 0.819155i \(0.694443\pi\)
\(492\) 0 0
\(493\) −15.9141 −0.716733
\(494\) 0 0
\(495\) 1.37095 0.0616198
\(496\) 0 0
\(497\) −9.58999 −0.430170
\(498\) 0 0
\(499\) 10.0845 0.451446 0.225723 0.974191i \(-0.427526\pi\)
0.225723 + 0.974191i \(0.427526\pi\)
\(500\) 0 0
\(501\) 0.102092 0.00456113
\(502\) 0 0
\(503\) −24.2866 −1.08289 −0.541443 0.840738i \(-0.682122\pi\)
−0.541443 + 0.840738i \(0.682122\pi\)
\(504\) 0 0
\(505\) 6.00068 0.267027
\(506\) 0 0
\(507\) −0.672934 −0.0298860
\(508\) 0 0
\(509\) 10.3881 0.460444 0.230222 0.973138i \(-0.426055\pi\)
0.230222 + 0.973138i \(0.426055\pi\)
\(510\) 0 0
\(511\) −7.50579 −0.332036
\(512\) 0 0
\(513\) 15.7395 0.694914
\(514\) 0 0
\(515\) 3.02449 0.133275
\(516\) 0 0
\(517\) −12.2622 −0.539291
\(518\) 0 0
\(519\) −6.40680 −0.281227
\(520\) 0 0
\(521\) −41.4927 −1.81783 −0.908915 0.416981i \(-0.863088\pi\)
−0.908915 + 0.416981i \(0.863088\pi\)
\(522\) 0 0
\(523\) 2.19012 0.0957674 0.0478837 0.998853i \(-0.484752\pi\)
0.0478837 + 0.998853i \(0.484752\pi\)
\(524\) 0 0
\(525\) −3.16973 −0.138338
\(526\) 0 0
\(527\) 9.71947 0.423387
\(528\) 0 0
\(529\) −10.3238 −0.448861
\(530\) 0 0
\(531\) −4.15427 −0.180280
\(532\) 0 0
\(533\) 6.73633 0.291783
\(534\) 0 0
\(535\) 3.83762 0.165915
\(536\) 0 0
\(537\) −1.29800 −0.0560127
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 40.0027 1.71985 0.859925 0.510420i \(-0.170510\pi\)
0.859925 + 0.510420i \(0.170510\pi\)
\(542\) 0 0
\(543\) −14.6514 −0.628752
\(544\) 0 0
\(545\) 8.28053 0.354699
\(546\) 0 0
\(547\) 7.70909 0.329617 0.164809 0.986326i \(-0.447299\pi\)
0.164809 + 0.986326i \(0.447299\pi\)
\(548\) 0 0
\(549\) −21.0835 −0.899823
\(550\) 0 0
\(551\) 39.3310 1.67556
\(552\) 0 0
\(553\) −12.6682 −0.538708
\(554\) 0 0
\(555\) 2.93493 0.124581
\(556\) 0 0
\(557\) 38.8851 1.64761 0.823807 0.566871i \(-0.191846\pi\)
0.823807 + 0.566871i \(0.191846\pi\)
\(558\) 0 0
\(559\) 12.5566 0.531087
\(560\) 0 0
\(561\) −1.14806 −0.0484712
\(562\) 0 0
\(563\) −40.3929 −1.70236 −0.851179 0.524875i \(-0.824112\pi\)
−0.851179 + 0.524875i \(0.824112\pi\)
\(564\) 0 0
\(565\) 6.76034 0.284409
\(566\) 0 0
\(567\) −5.12950 −0.215419
\(568\) 0 0
\(569\) 10.1163 0.424099 0.212049 0.977259i \(-0.431986\pi\)
0.212049 + 0.977259i \(0.431986\pi\)
\(570\) 0 0
\(571\) 42.2032 1.76615 0.883074 0.469234i \(-0.155470\pi\)
0.883074 + 0.469234i \(0.155470\pi\)
\(572\) 0 0
\(573\) 1.90154 0.0794382
\(574\) 0 0
\(575\) −16.7704 −0.699375
\(576\) 0 0
\(577\) −34.0021 −1.41553 −0.707764 0.706449i \(-0.750296\pi\)
−0.707764 + 0.706449i \(0.750296\pi\)
\(578\) 0 0
\(579\) −12.9224 −0.537037
\(580\) 0 0
\(581\) 10.4121 0.431967
\(582\) 0 0
\(583\) −7.52462 −0.311638
\(584\) 0 0
\(585\) 1.37095 0.0566819
\(586\) 0 0
\(587\) −11.7956 −0.486857 −0.243428 0.969919i \(-0.578272\pi\)
−0.243428 + 0.969919i \(0.578272\pi\)
\(588\) 0 0
\(589\) −24.0213 −0.989780
\(590\) 0 0
\(591\) −10.6637 −0.438647
\(592\) 0 0
\(593\) −45.8832 −1.88420 −0.942099 0.335334i \(-0.891151\pi\)
−0.942099 + 0.335334i \(0.891151\pi\)
\(594\) 0 0
\(595\) 0.918247 0.0376445
\(596\) 0 0
\(597\) −5.09885 −0.208682
\(598\) 0 0
\(599\) 34.7991 1.42185 0.710927 0.703266i \(-0.248276\pi\)
0.710927 + 0.703266i \(0.248276\pi\)
\(600\) 0 0
\(601\) 35.8665 1.46302 0.731512 0.681828i \(-0.238815\pi\)
0.731512 + 0.681828i \(0.238815\pi\)
\(602\) 0 0
\(603\) 21.0532 0.857352
\(604\) 0 0
\(605\) 0.538228 0.0218821
\(606\) 0 0
\(607\) 12.5866 0.510874 0.255437 0.966826i \(-0.417781\pi\)
0.255437 + 0.966826i \(0.417781\pi\)
\(608\) 0 0
\(609\) 6.27712 0.254362
\(610\) 0 0
\(611\) −12.2622 −0.496076
\(612\) 0 0
\(613\) −28.3997 −1.14705 −0.573527 0.819186i \(-0.694425\pi\)
−0.573527 + 0.819186i \(0.694425\pi\)
\(614\) 0 0
\(615\) 2.43985 0.0983841
\(616\) 0 0
\(617\) −26.3564 −1.06107 −0.530534 0.847663i \(-0.678009\pi\)
−0.530534 + 0.847663i \(0.678009\pi\)
\(618\) 0 0
\(619\) 11.1729 0.449076 0.224538 0.974465i \(-0.427913\pi\)
0.224538 + 0.974465i \(0.427913\pi\)
\(620\) 0 0
\(621\) 13.2904 0.533325
\(622\) 0 0
\(623\) −0.0335338 −0.00134351
\(624\) 0 0
\(625\) 20.7386 0.829543
\(626\) 0 0
\(627\) 2.83739 0.113314
\(628\) 0 0
\(629\) 13.8246 0.551223
\(630\) 0 0
\(631\) −34.1256 −1.35852 −0.679259 0.733898i \(-0.737699\pi\)
−0.679259 + 0.733898i \(0.737699\pi\)
\(632\) 0 0
\(633\) −4.46063 −0.177294
\(634\) 0 0
\(635\) −9.36847 −0.371776
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −24.4272 −0.966327
\(640\) 0 0
\(641\) 5.35218 0.211398 0.105699 0.994398i \(-0.466292\pi\)
0.105699 + 0.994398i \(0.466292\pi\)
\(642\) 0 0
\(643\) −49.1919 −1.93994 −0.969970 0.243226i \(-0.921794\pi\)
−0.969970 + 0.243226i \(0.921794\pi\)
\(644\) 0 0
\(645\) 4.54790 0.179073
\(646\) 0 0
\(647\) −10.2193 −0.401763 −0.200881 0.979616i \(-0.564381\pi\)
−0.200881 + 0.979616i \(0.564381\pi\)
\(648\) 0 0
\(649\) −1.63094 −0.0640200
\(650\) 0 0
\(651\) −3.83373 −0.150256
\(652\) 0 0
\(653\) −1.76322 −0.0690003 −0.0345001 0.999405i \(-0.510984\pi\)
−0.0345001 + 0.999405i \(0.510984\pi\)
\(654\) 0 0
\(655\) −8.51844 −0.332843
\(656\) 0 0
\(657\) −19.1184 −0.745881
\(658\) 0 0
\(659\) −3.27817 −0.127699 −0.0638496 0.997960i \(-0.520338\pi\)
−0.0638496 + 0.997960i \(0.520338\pi\)
\(660\) 0 0
\(661\) 17.2156 0.669608 0.334804 0.942288i \(-0.391330\pi\)
0.334804 + 0.942288i \(0.391330\pi\)
\(662\) 0 0
\(663\) −1.14806 −0.0445870
\(664\) 0 0
\(665\) −2.26941 −0.0880040
\(666\) 0 0
\(667\) 33.2110 1.28594
\(668\) 0 0
\(669\) 8.06226 0.311705
\(670\) 0 0
\(671\) −8.27727 −0.319540
\(672\) 0 0
\(673\) 11.5166 0.443931 0.221966 0.975054i \(-0.428753\pi\)
0.221966 + 0.975054i \(0.428753\pi\)
\(674\) 0 0
\(675\) −17.5830 −0.676769
\(676\) 0 0
\(677\) 7.99010 0.307084 0.153542 0.988142i \(-0.450932\pi\)
0.153542 + 0.988142i \(0.450932\pi\)
\(678\) 0 0
\(679\) −12.7427 −0.489018
\(680\) 0 0
\(681\) 10.8690 0.416500
\(682\) 0 0
\(683\) 2.67293 0.102277 0.0511384 0.998692i \(-0.483715\pi\)
0.0511384 + 0.998692i \(0.483715\pi\)
\(684\) 0 0
\(685\) −3.17182 −0.121189
\(686\) 0 0
\(687\) −17.1410 −0.653971
\(688\) 0 0
\(689\) −7.52462 −0.286665
\(690\) 0 0
\(691\) 22.7347 0.864867 0.432434 0.901666i \(-0.357655\pi\)
0.432434 + 0.901666i \(0.357655\pi\)
\(692\) 0 0
\(693\) −2.54716 −0.0967586
\(694\) 0 0
\(695\) −6.35208 −0.240948
\(696\) 0 0
\(697\) 11.4926 0.435312
\(698\) 0 0
\(699\) −13.6324 −0.515625
\(700\) 0 0
\(701\) 13.0708 0.493678 0.246839 0.969056i \(-0.420608\pi\)
0.246839 + 0.969056i \(0.420608\pi\)
\(702\) 0 0
\(703\) −34.1670 −1.28863
\(704\) 0 0
\(705\) −4.44127 −0.167268
\(706\) 0 0
\(707\) −11.1490 −0.419300
\(708\) 0 0
\(709\) 24.2329 0.910086 0.455043 0.890470i \(-0.349624\pi\)
0.455043 + 0.890470i \(0.349624\pi\)
\(710\) 0 0
\(711\) −32.2680 −1.21015
\(712\) 0 0
\(713\) −20.2835 −0.759625
\(714\) 0 0
\(715\) 0.538228 0.0201286
\(716\) 0 0
\(717\) −8.03999 −0.300259
\(718\) 0 0
\(719\) −40.5402 −1.51189 −0.755947 0.654632i \(-0.772823\pi\)
−0.755947 + 0.654632i \(0.772823\pi\)
\(720\) 0 0
\(721\) −5.61935 −0.209276
\(722\) 0 0
\(723\) −18.1041 −0.673297
\(724\) 0 0
\(725\) −43.9377 −1.63180
\(726\) 0 0
\(727\) 8.38603 0.311021 0.155510 0.987834i \(-0.450298\pi\)
0.155510 + 0.987834i \(0.450298\pi\)
\(728\) 0 0
\(729\) −5.52974 −0.204805
\(730\) 0 0
\(731\) 21.4222 0.792330
\(732\) 0 0
\(733\) −23.7946 −0.878873 −0.439437 0.898274i \(-0.644822\pi\)
−0.439437 + 0.898274i \(0.644822\pi\)
\(734\) 0 0
\(735\) −0.362192 −0.0133597
\(736\) 0 0
\(737\) 8.26536 0.304458
\(738\) 0 0
\(739\) 27.3233 1.00510 0.502552 0.864547i \(-0.332395\pi\)
0.502552 + 0.864547i \(0.332395\pi\)
\(740\) 0 0
\(741\) 2.83739 0.104234
\(742\) 0 0
\(743\) −32.2512 −1.18318 −0.591592 0.806238i \(-0.701500\pi\)
−0.591592 + 0.806238i \(0.701500\pi\)
\(744\) 0 0
\(745\) −11.0536 −0.404973
\(746\) 0 0
\(747\) 26.5213 0.970363
\(748\) 0 0
\(749\) −7.13010 −0.260528
\(750\) 0 0
\(751\) −3.78681 −0.138183 −0.0690913 0.997610i \(-0.522010\pi\)
−0.0690913 + 0.997610i \(0.522010\pi\)
\(752\) 0 0
\(753\) −1.02720 −0.0374334
\(754\) 0 0
\(755\) 4.22637 0.153813
\(756\) 0 0
\(757\) 20.6522 0.750619 0.375309 0.926900i \(-0.377536\pi\)
0.375309 + 0.926900i \(0.377536\pi\)
\(758\) 0 0
\(759\) 2.39589 0.0869653
\(760\) 0 0
\(761\) 21.1253 0.765790 0.382895 0.923792i \(-0.374927\pi\)
0.382895 + 0.923792i \(0.374927\pi\)
\(762\) 0 0
\(763\) −15.3848 −0.556967
\(764\) 0 0
\(765\) 2.33892 0.0845639
\(766\) 0 0
\(767\) −1.63094 −0.0588898
\(768\) 0 0
\(769\) −7.64664 −0.275745 −0.137872 0.990450i \(-0.544026\pi\)
−0.137872 + 0.990450i \(0.544026\pi\)
\(770\) 0 0
\(771\) −6.28468 −0.226337
\(772\) 0 0
\(773\) −17.0537 −0.613379 −0.306689 0.951810i \(-0.599221\pi\)
−0.306689 + 0.951810i \(0.599221\pi\)
\(774\) 0 0
\(775\) 26.8348 0.963936
\(776\) 0 0
\(777\) −5.45296 −0.195624
\(778\) 0 0
\(779\) −28.4034 −1.01766
\(780\) 0 0
\(781\) −9.58999 −0.343157
\(782\) 0 0
\(783\) 34.8202 1.24437
\(784\) 0 0
\(785\) −6.49590 −0.231849
\(786\) 0 0
\(787\) −16.1001 −0.573905 −0.286953 0.957945i \(-0.592642\pi\)
−0.286953 + 0.957945i \(0.592642\pi\)
\(788\) 0 0
\(789\) 7.08000 0.252055
\(790\) 0 0
\(791\) −12.5604 −0.446595
\(792\) 0 0
\(793\) −8.27727 −0.293934
\(794\) 0 0
\(795\) −2.72536 −0.0966584
\(796\) 0 0
\(797\) 40.1516 1.42224 0.711122 0.703069i \(-0.248187\pi\)
0.711122 + 0.703069i \(0.248187\pi\)
\(798\) 0 0
\(799\) −20.9200 −0.740096
\(800\) 0 0
\(801\) −0.0854161 −0.00301803
\(802\) 0 0
\(803\) −7.50579 −0.264873
\(804\) 0 0
\(805\) −1.91629 −0.0675403
\(806\) 0 0
\(807\) −8.14424 −0.286691
\(808\) 0 0
\(809\) −36.0345 −1.26690 −0.633452 0.773782i \(-0.718363\pi\)
−0.633452 + 0.773782i \(0.718363\pi\)
\(810\) 0 0
\(811\) −42.0083 −1.47511 −0.737555 0.675287i \(-0.764020\pi\)
−0.737555 + 0.675287i \(0.764020\pi\)
\(812\) 0 0
\(813\) −7.93748 −0.278380
\(814\) 0 0
\(815\) 10.9507 0.383586
\(816\) 0 0
\(817\) −52.9442 −1.85228
\(818\) 0 0
\(819\) −2.54716 −0.0890050
\(820\) 0 0
\(821\) −16.2213 −0.566126 −0.283063 0.959101i \(-0.591350\pi\)
−0.283063 + 0.959101i \(0.591350\pi\)
\(822\) 0 0
\(823\) −28.3340 −0.987661 −0.493830 0.869558i \(-0.664404\pi\)
−0.493830 + 0.869558i \(0.664404\pi\)
\(824\) 0 0
\(825\) −3.16973 −0.110356
\(826\) 0 0
\(827\) 31.0942 1.08125 0.540625 0.841264i \(-0.318188\pi\)
0.540625 + 0.841264i \(0.318188\pi\)
\(828\) 0 0
\(829\) 12.2909 0.426882 0.213441 0.976956i \(-0.431533\pi\)
0.213441 + 0.976956i \(0.431533\pi\)
\(830\) 0 0
\(831\) 5.27346 0.182934
\(832\) 0 0
\(833\) −1.70606 −0.0591113
\(834\) 0 0
\(835\) −0.0816555 −0.00282581
\(836\) 0 0
\(837\) −21.2663 −0.735072
\(838\) 0 0
\(839\) −49.0450 −1.69322 −0.846611 0.532213i \(-0.821361\pi\)
−0.846611 + 0.532213i \(0.821361\pi\)
\(840\) 0 0
\(841\) 58.0112 2.00039
\(842\) 0 0
\(843\) 0.929635 0.0320183
\(844\) 0 0
\(845\) 0.538228 0.0185156
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −14.4208 −0.494921
\(850\) 0 0
\(851\) −28.8506 −0.988984
\(852\) 0 0
\(853\) −16.8025 −0.575305 −0.287653 0.957735i \(-0.592875\pi\)
−0.287653 + 0.957735i \(0.592875\pi\)
\(854\) 0 0
\(855\) −5.78055 −0.197691
\(856\) 0 0
\(857\) 21.6045 0.737995 0.368998 0.929430i \(-0.379701\pi\)
0.368998 + 0.929430i \(0.379701\pi\)
\(858\) 0 0
\(859\) −7.06380 −0.241014 −0.120507 0.992712i \(-0.538452\pi\)
−0.120507 + 0.992712i \(0.538452\pi\)
\(860\) 0 0
\(861\) −4.53311 −0.154488
\(862\) 0 0
\(863\) −40.6779 −1.38469 −0.692345 0.721567i \(-0.743422\pi\)
−0.692345 + 0.721567i \(0.743422\pi\)
\(864\) 0 0
\(865\) 5.12430 0.174232
\(866\) 0 0
\(867\) 9.48122 0.321999
\(868\) 0 0
\(869\) −12.6682 −0.429740
\(870\) 0 0
\(871\) 8.26536 0.280061
\(872\) 0 0
\(873\) −32.4576 −1.09852
\(874\) 0 0
\(875\) 5.22636 0.176683
\(876\) 0 0
\(877\) 55.7205 1.88155 0.940775 0.339033i \(-0.110100\pi\)
0.940775 + 0.339033i \(0.110100\pi\)
\(878\) 0 0
\(879\) 11.0588 0.373004
\(880\) 0 0
\(881\) 17.3931 0.585989 0.292994 0.956114i \(-0.405348\pi\)
0.292994 + 0.956114i \(0.405348\pi\)
\(882\) 0 0
\(883\) 18.4938 0.622367 0.311183 0.950350i \(-0.399275\pi\)
0.311183 + 0.950350i \(0.399275\pi\)
\(884\) 0 0
\(885\) −0.590713 −0.0198566
\(886\) 0 0
\(887\) 5.90249 0.198186 0.0990931 0.995078i \(-0.468406\pi\)
0.0990931 + 0.995078i \(0.468406\pi\)
\(888\) 0 0
\(889\) 17.4061 0.583783
\(890\) 0 0
\(891\) −5.12950 −0.171845
\(892\) 0 0
\(893\) 51.7030 1.73017
\(894\) 0 0
\(895\) 1.03817 0.0347021
\(896\) 0 0
\(897\) 2.39589 0.0799964
\(898\) 0 0
\(899\) −53.1419 −1.77238
\(900\) 0 0
\(901\) −12.8374 −0.427676
\(902\) 0 0
\(903\) −8.44976 −0.281190
\(904\) 0 0
\(905\) 11.7185 0.389537
\(906\) 0 0
\(907\) 22.0760 0.733022 0.366511 0.930414i \(-0.380552\pi\)
0.366511 + 0.930414i \(0.380552\pi\)
\(908\) 0 0
\(909\) −28.3982 −0.941908
\(910\) 0 0
\(911\) 10.2537 0.339720 0.169860 0.985468i \(-0.445668\pi\)
0.169860 + 0.985468i \(0.445668\pi\)
\(912\) 0 0
\(913\) 10.4121 0.344590
\(914\) 0 0
\(915\) −2.99796 −0.0991095
\(916\) 0 0
\(917\) 15.8268 0.522648
\(918\) 0 0
\(919\) −6.10317 −0.201325 −0.100663 0.994921i \(-0.532096\pi\)
−0.100663 + 0.994921i \(0.532096\pi\)
\(920\) 0 0
\(921\) −17.1015 −0.563514
\(922\) 0 0
\(923\) −9.58999 −0.315658
\(924\) 0 0
\(925\) 38.1689 1.25498
\(926\) 0 0
\(927\) −14.3134 −0.470113
\(928\) 0 0
\(929\) 49.8438 1.63532 0.817660 0.575701i \(-0.195271\pi\)
0.817660 + 0.575701i \(0.195271\pi\)
\(930\) 0 0
\(931\) 4.21645 0.138189
\(932\) 0 0
\(933\) 14.9533 0.489550
\(934\) 0 0
\(935\) 0.918247 0.0300299
\(936\) 0 0
\(937\) 2.75458 0.0899881 0.0449941 0.998987i \(-0.485673\pi\)
0.0449941 + 0.998987i \(0.485673\pi\)
\(938\) 0 0
\(939\) 11.7601 0.383776
\(940\) 0 0
\(941\) −56.1728 −1.83118 −0.915591 0.402111i \(-0.868276\pi\)
−0.915591 + 0.402111i \(0.868276\pi\)
\(942\) 0 0
\(943\) −23.9838 −0.781020
\(944\) 0 0
\(945\) −2.00914 −0.0653572
\(946\) 0 0
\(947\) −7.86955 −0.255726 −0.127863 0.991792i \(-0.540812\pi\)
−0.127863 + 0.991792i \(0.540812\pi\)
\(948\) 0 0
\(949\) −7.50579 −0.243648
\(950\) 0 0
\(951\) −3.60150 −0.116787
\(952\) 0 0
\(953\) −5.62240 −0.182127 −0.0910637 0.995845i \(-0.529027\pi\)
−0.0910637 + 0.995845i \(0.529027\pi\)
\(954\) 0 0
\(955\) −1.52090 −0.0492152
\(956\) 0 0
\(957\) 6.27712 0.202910
\(958\) 0 0
\(959\) 5.89307 0.190297
\(960\) 0 0
\(961\) 1.45629 0.0469769
\(962\) 0 0
\(963\) −18.1615 −0.585246
\(964\) 0 0
\(965\) 10.3356 0.332716
\(966\) 0 0
\(967\) 50.0719 1.61020 0.805102 0.593137i \(-0.202111\pi\)
0.805102 + 0.593137i \(0.202111\pi\)
\(968\) 0 0
\(969\) 4.84075 0.155507
\(970\) 0 0
\(971\) 38.6410 1.24005 0.620024 0.784582i \(-0.287123\pi\)
0.620024 + 0.784582i \(0.287123\pi\)
\(972\) 0 0
\(973\) 11.8018 0.378349
\(974\) 0 0
\(975\) −3.16973 −0.101513
\(976\) 0 0
\(977\) −10.1764 −0.325573 −0.162786 0.986661i \(-0.552048\pi\)
−0.162786 + 0.986661i \(0.552048\pi\)
\(978\) 0 0
\(979\) −0.0335338 −0.00107175
\(980\) 0 0
\(981\) −39.1876 −1.25116
\(982\) 0 0
\(983\) 10.8713 0.346741 0.173371 0.984857i \(-0.444534\pi\)
0.173371 + 0.984857i \(0.444534\pi\)
\(984\) 0 0
\(985\) 8.52910 0.271760
\(986\) 0 0
\(987\) 8.25165 0.262653
\(988\) 0 0
\(989\) −44.7061 −1.42157
\(990\) 0 0
\(991\) 24.8489 0.789353 0.394676 0.918820i \(-0.370857\pi\)
0.394676 + 0.918820i \(0.370857\pi\)
\(992\) 0 0
\(993\) 22.5634 0.716026
\(994\) 0 0
\(995\) 4.07818 0.129287
\(996\) 0 0
\(997\) −19.4611 −0.616340 −0.308170 0.951331i \(-0.599717\pi\)
−0.308170 + 0.951331i \(0.599717\pi\)
\(998\) 0 0
\(999\) −30.2484 −0.957018
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 \(a_p\))