Properties

Label 8008.2.a.p.1.5
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 9
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: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.141545\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.141545 q^{3} +0.343768 q^{5} -1.00000 q^{7} -2.97996 q^{9} +O(q^{10})\) \(q+0.141545 q^{3} +0.343768 q^{5} -1.00000 q^{7} -2.97996 q^{9} +1.00000 q^{11} +1.00000 q^{13} +0.0486587 q^{15} -1.94296 q^{17} -0.383972 q^{19} -0.141545 q^{21} -1.66573 q^{23} -4.88182 q^{25} -0.846436 q^{27} +3.52781 q^{29} +8.92433 q^{31} +0.141545 q^{33} -0.343768 q^{35} +5.87381 q^{37} +0.141545 q^{39} +6.78021 q^{41} -1.87960 q^{43} -1.02442 q^{45} +2.51467 q^{47} +1.00000 q^{49} -0.275017 q^{51} +0.793466 q^{53} +0.343768 q^{55} -0.0543494 q^{57} -14.0287 q^{59} +6.36966 q^{61} +2.97996 q^{63} +0.343768 q^{65} -8.05936 q^{67} -0.235776 q^{69} +0.428251 q^{71} -12.1299 q^{73} -0.690999 q^{75} -1.00000 q^{77} +9.37219 q^{79} +8.82009 q^{81} -4.37797 q^{83} -0.667928 q^{85} +0.499346 q^{87} -4.95758 q^{89} -1.00000 q^{91} +1.26320 q^{93} -0.131997 q^{95} -13.5322 q^{97} -2.97996 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + O(q^{10}) \) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + 9q^{11} + 9q^{13} - 9q^{15} - 11q^{17} + 10q^{19} - q^{21} - 14q^{23} - q^{25} - 5q^{27} - 10q^{29} + 5q^{31} + q^{33} + 4q^{35} - 16q^{37} + q^{39} + 2q^{41} + 4q^{43} - 30q^{45} + 9q^{49} + 3q^{51} - 23q^{53} - 4q^{55} + 14q^{57} + 9q^{59} - 14q^{61} - 4q^{63} - 4q^{65} + 8q^{67} - 26q^{69} - 20q^{71} - 23q^{73} + 32q^{75} - 9q^{77} + 2q^{79} - 11q^{81} - 9q^{83} - 3q^{85} - 7q^{87} - 6q^{89} - 9q^{91} - 19q^{93} - 4q^{95} - 3q^{97} + 4q^{99} + O(q^{100}) \)

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
\(3\) 0.141545 0.0817212 0.0408606 0.999165i \(-0.486990\pi\)
0.0408606 + 0.999165i \(0.486990\pi\)
\(4\) 0 0
\(5\) 0.343768 0.153738 0.0768688 0.997041i \(-0.475508\pi\)
0.0768688 + 0.997041i \(0.475508\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.97996 −0.993322
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0.0486587 0.0125636
\(16\) 0 0
\(17\) −1.94296 −0.471238 −0.235619 0.971846i \(-0.575712\pi\)
−0.235619 + 0.971846i \(0.575712\pi\)
\(18\) 0 0
\(19\) −0.383972 −0.0880892 −0.0440446 0.999030i \(-0.514024\pi\)
−0.0440446 + 0.999030i \(0.514024\pi\)
\(20\) 0 0
\(21\) −0.141545 −0.0308877
\(22\) 0 0
\(23\) −1.66573 −0.347328 −0.173664 0.984805i \(-0.555561\pi\)
−0.173664 + 0.984805i \(0.555561\pi\)
\(24\) 0 0
\(25\) −4.88182 −0.976365
\(26\) 0 0
\(27\) −0.846436 −0.162897
\(28\) 0 0
\(29\) 3.52781 0.655098 0.327549 0.944834i \(-0.393777\pi\)
0.327549 + 0.944834i \(0.393777\pi\)
\(30\) 0 0
\(31\) 8.92433 1.60286 0.801429 0.598090i \(-0.204074\pi\)
0.801429 + 0.598090i \(0.204074\pi\)
\(32\) 0 0
\(33\) 0.141545 0.0246399
\(34\) 0 0
\(35\) −0.343768 −0.0581074
\(36\) 0 0
\(37\) 5.87381 0.965649 0.482825 0.875717i \(-0.339611\pi\)
0.482825 + 0.875717i \(0.339611\pi\)
\(38\) 0 0
\(39\) 0.141545 0.0226654
\(40\) 0 0
\(41\) 6.78021 1.05889 0.529446 0.848344i \(-0.322400\pi\)
0.529446 + 0.848344i \(0.322400\pi\)
\(42\) 0 0
\(43\) −1.87960 −0.286636 −0.143318 0.989677i \(-0.545777\pi\)
−0.143318 + 0.989677i \(0.545777\pi\)
\(44\) 0 0
\(45\) −1.02442 −0.152711
\(46\) 0 0
\(47\) 2.51467 0.366803 0.183401 0.983038i \(-0.441289\pi\)
0.183401 + 0.983038i \(0.441289\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −0.275017 −0.0385101
\(52\) 0 0
\(53\) 0.793466 0.108991 0.0544954 0.998514i \(-0.482645\pi\)
0.0544954 + 0.998514i \(0.482645\pi\)
\(54\) 0 0
\(55\) 0.343768 0.0463536
\(56\) 0 0
\(57\) −0.0543494 −0.00719876
\(58\) 0 0
\(59\) −14.0287 −1.82638 −0.913191 0.407531i \(-0.866390\pi\)
−0.913191 + 0.407531i \(0.866390\pi\)
\(60\) 0 0
\(61\) 6.36966 0.815551 0.407776 0.913082i \(-0.366305\pi\)
0.407776 + 0.913082i \(0.366305\pi\)
\(62\) 0 0
\(63\) 2.97996 0.375440
\(64\) 0 0
\(65\) 0.343768 0.0426392
\(66\) 0 0
\(67\) −8.05936 −0.984607 −0.492304 0.870423i \(-0.663845\pi\)
−0.492304 + 0.870423i \(0.663845\pi\)
\(68\) 0 0
\(69\) −0.235776 −0.0283841
\(70\) 0 0
\(71\) 0.428251 0.0508241 0.0254120 0.999677i \(-0.491910\pi\)
0.0254120 + 0.999677i \(0.491910\pi\)
\(72\) 0 0
\(73\) −12.1299 −1.41970 −0.709848 0.704354i \(-0.751237\pi\)
−0.709848 + 0.704354i \(0.751237\pi\)
\(74\) 0 0
\(75\) −0.690999 −0.0797897
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 9.37219 1.05445 0.527227 0.849725i \(-0.323232\pi\)
0.527227 + 0.849725i \(0.323232\pi\)
\(80\) 0 0
\(81\) 8.82009 0.980010
\(82\) 0 0
\(83\) −4.37797 −0.480544 −0.240272 0.970706i \(-0.577237\pi\)
−0.240272 + 0.970706i \(0.577237\pi\)
\(84\) 0 0
\(85\) −0.667928 −0.0724470
\(86\) 0 0
\(87\) 0.499346 0.0535355
\(88\) 0 0
\(89\) −4.95758 −0.525502 −0.262751 0.964864i \(-0.584630\pi\)
−0.262751 + 0.964864i \(0.584630\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 1.26320 0.130987
\(94\) 0 0
\(95\) −0.131997 −0.0135426
\(96\) 0 0
\(97\) −13.5322 −1.37399 −0.686994 0.726664i \(-0.741070\pi\)
−0.686994 + 0.726664i \(0.741070\pi\)
\(98\) 0 0
\(99\) −2.97996 −0.299498
\(100\) 0 0
\(101\) −5.38219 −0.535548 −0.267774 0.963482i \(-0.586288\pi\)
−0.267774 + 0.963482i \(0.586288\pi\)
\(102\) 0 0
\(103\) −12.3682 −1.21868 −0.609339 0.792910i \(-0.708565\pi\)
−0.609339 + 0.792910i \(0.708565\pi\)
\(104\) 0 0
\(105\) −0.0486587 −0.00474861
\(106\) 0 0
\(107\) −0.508008 −0.0491110 −0.0245555 0.999698i \(-0.507817\pi\)
−0.0245555 + 0.999698i \(0.507817\pi\)
\(108\) 0 0
\(109\) 1.42923 0.136896 0.0684478 0.997655i \(-0.478195\pi\)
0.0684478 + 0.997655i \(0.478195\pi\)
\(110\) 0 0
\(111\) 0.831411 0.0789141
\(112\) 0 0
\(113\) −9.14399 −0.860194 −0.430097 0.902783i \(-0.641521\pi\)
−0.430097 + 0.902783i \(0.641521\pi\)
\(114\) 0 0
\(115\) −0.572623 −0.0533974
\(116\) 0 0
\(117\) −2.97996 −0.275498
\(118\) 0 0
\(119\) 1.94296 0.178111
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0.959707 0.0865339
\(124\) 0 0
\(125\) −3.39705 −0.303842
\(126\) 0 0
\(127\) −13.2998 −1.18017 −0.590083 0.807343i \(-0.700905\pi\)
−0.590083 + 0.807343i \(0.700905\pi\)
\(128\) 0 0
\(129\) −0.266048 −0.0234242
\(130\) 0 0
\(131\) 17.2076 1.50344 0.751719 0.659483i \(-0.229225\pi\)
0.751719 + 0.659483i \(0.229225\pi\)
\(132\) 0 0
\(133\) 0.383972 0.0332946
\(134\) 0 0
\(135\) −0.290978 −0.0250434
\(136\) 0 0
\(137\) −16.9509 −1.44822 −0.724109 0.689686i \(-0.757749\pi\)
−0.724109 + 0.689686i \(0.757749\pi\)
\(138\) 0 0
\(139\) −11.0975 −0.941275 −0.470638 0.882327i \(-0.655976\pi\)
−0.470638 + 0.882327i \(0.655976\pi\)
\(140\) 0 0
\(141\) 0.355940 0.0299756
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 1.21275 0.100713
\(146\) 0 0
\(147\) 0.141545 0.0116745
\(148\) 0 0
\(149\) −10.3649 −0.849127 −0.424563 0.905398i \(-0.639572\pi\)
−0.424563 + 0.905398i \(0.639572\pi\)
\(150\) 0 0
\(151\) 6.99428 0.569187 0.284593 0.958648i \(-0.408141\pi\)
0.284593 + 0.958648i \(0.408141\pi\)
\(152\) 0 0
\(153\) 5.78996 0.468091
\(154\) 0 0
\(155\) 3.06790 0.246420
\(156\) 0 0
\(157\) −5.89153 −0.470195 −0.235098 0.971972i \(-0.575541\pi\)
−0.235098 + 0.971972i \(0.575541\pi\)
\(158\) 0 0
\(159\) 0.112311 0.00890687
\(160\) 0 0
\(161\) 1.66573 0.131278
\(162\) 0 0
\(163\) 1.13057 0.0885533 0.0442767 0.999019i \(-0.485902\pi\)
0.0442767 + 0.999019i \(0.485902\pi\)
\(164\) 0 0
\(165\) 0.0486587 0.00378808
\(166\) 0 0
\(167\) −15.9501 −1.23425 −0.617127 0.786864i \(-0.711703\pi\)
−0.617127 + 0.786864i \(0.711703\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 1.14422 0.0875009
\(172\) 0 0
\(173\) −22.4356 −1.70574 −0.852872 0.522120i \(-0.825141\pi\)
−0.852872 + 0.522120i \(0.825141\pi\)
\(174\) 0 0
\(175\) 4.88182 0.369031
\(176\) 0 0
\(177\) −1.98570 −0.149254
\(178\) 0 0
\(179\) 12.9674 0.969228 0.484614 0.874728i \(-0.338960\pi\)
0.484614 + 0.874728i \(0.338960\pi\)
\(180\) 0 0
\(181\) −0.833575 −0.0619591 −0.0309796 0.999520i \(-0.509863\pi\)
−0.0309796 + 0.999520i \(0.509863\pi\)
\(182\) 0 0
\(183\) 0.901595 0.0666478
\(184\) 0 0
\(185\) 2.01923 0.148457
\(186\) 0 0
\(187\) −1.94296 −0.142084
\(188\) 0 0
\(189\) 0.846436 0.0615692
\(190\) 0 0
\(191\) 16.3507 1.18309 0.591547 0.806271i \(-0.298517\pi\)
0.591547 + 0.806271i \(0.298517\pi\)
\(192\) 0 0
\(193\) 18.1486 1.30636 0.653182 0.757201i \(-0.273434\pi\)
0.653182 + 0.757201i \(0.273434\pi\)
\(194\) 0 0
\(195\) 0.0486587 0.00348452
\(196\) 0 0
\(197\) −22.4904 −1.60237 −0.801186 0.598416i \(-0.795797\pi\)
−0.801186 + 0.598416i \(0.795797\pi\)
\(198\) 0 0
\(199\) 13.1359 0.931182 0.465591 0.885000i \(-0.345842\pi\)
0.465591 + 0.885000i \(0.345842\pi\)
\(200\) 0 0
\(201\) −1.14076 −0.0804633
\(202\) 0 0
\(203\) −3.52781 −0.247604
\(204\) 0 0
\(205\) 2.33082 0.162791
\(206\) 0 0
\(207\) 4.96380 0.345008
\(208\) 0 0
\(209\) −0.383972 −0.0265599
\(210\) 0 0
\(211\) −18.0317 −1.24135 −0.620677 0.784066i \(-0.713142\pi\)
−0.620677 + 0.784066i \(0.713142\pi\)
\(212\) 0 0
\(213\) 0.0606170 0.00415341
\(214\) 0 0
\(215\) −0.646145 −0.0440667
\(216\) 0 0
\(217\) −8.92433 −0.605823
\(218\) 0 0
\(219\) −1.71693 −0.116019
\(220\) 0 0
\(221\) −1.94296 −0.130698
\(222\) 0 0
\(223\) 6.34803 0.425096 0.212548 0.977151i \(-0.431824\pi\)
0.212548 + 0.977151i \(0.431824\pi\)
\(224\) 0 0
\(225\) 14.5477 0.969844
\(226\) 0 0
\(227\) −3.57190 −0.237075 −0.118538 0.992950i \(-0.537821\pi\)
−0.118538 + 0.992950i \(0.537821\pi\)
\(228\) 0 0
\(229\) −6.43178 −0.425024 −0.212512 0.977158i \(-0.568164\pi\)
−0.212512 + 0.977158i \(0.568164\pi\)
\(230\) 0 0
\(231\) −0.141545 −0.00931300
\(232\) 0 0
\(233\) 11.7243 0.768085 0.384043 0.923315i \(-0.374532\pi\)
0.384043 + 0.923315i \(0.374532\pi\)
\(234\) 0 0
\(235\) 0.864463 0.0563914
\(236\) 0 0
\(237\) 1.32659 0.0861713
\(238\) 0 0
\(239\) −13.8255 −0.894299 −0.447150 0.894459i \(-0.647561\pi\)
−0.447150 + 0.894459i \(0.647561\pi\)
\(240\) 0 0
\(241\) −14.5623 −0.938040 −0.469020 0.883187i \(-0.655393\pi\)
−0.469020 + 0.883187i \(0.655393\pi\)
\(242\) 0 0
\(243\) 3.78775 0.242984
\(244\) 0 0
\(245\) 0.343768 0.0219625
\(246\) 0 0
\(247\) −0.383972 −0.0244315
\(248\) 0 0
\(249\) −0.619681 −0.0392707
\(250\) 0 0
\(251\) 9.48632 0.598771 0.299386 0.954132i \(-0.403218\pi\)
0.299386 + 0.954132i \(0.403218\pi\)
\(252\) 0 0
\(253\) −1.66573 −0.104723
\(254\) 0 0
\(255\) −0.0945421 −0.00592046
\(256\) 0 0
\(257\) 14.0937 0.879143 0.439572 0.898208i \(-0.355130\pi\)
0.439572 + 0.898208i \(0.355130\pi\)
\(258\) 0 0
\(259\) −5.87381 −0.364981
\(260\) 0 0
\(261\) −10.5128 −0.650723
\(262\) 0 0
\(263\) 15.5786 0.960615 0.480307 0.877100i \(-0.340525\pi\)
0.480307 + 0.877100i \(0.340525\pi\)
\(264\) 0 0
\(265\) 0.272768 0.0167560
\(266\) 0 0
\(267\) −0.701722 −0.0429447
\(268\) 0 0
\(269\) −16.3016 −0.993924 −0.496962 0.867772i \(-0.665551\pi\)
−0.496962 + 0.867772i \(0.665551\pi\)
\(270\) 0 0
\(271\) 3.78877 0.230151 0.115076 0.993357i \(-0.463289\pi\)
0.115076 + 0.993357i \(0.463289\pi\)
\(272\) 0 0
\(273\) −0.141545 −0.00856671
\(274\) 0 0
\(275\) −4.88182 −0.294385
\(276\) 0 0
\(277\) −19.7291 −1.18541 −0.592703 0.805421i \(-0.701939\pi\)
−0.592703 + 0.805421i \(0.701939\pi\)
\(278\) 0 0
\(279\) −26.5942 −1.59215
\(280\) 0 0
\(281\) −18.8178 −1.12257 −0.561286 0.827622i \(-0.689693\pi\)
−0.561286 + 0.827622i \(0.689693\pi\)
\(282\) 0 0
\(283\) −6.57588 −0.390895 −0.195448 0.980714i \(-0.562616\pi\)
−0.195448 + 0.980714i \(0.562616\pi\)
\(284\) 0 0
\(285\) −0.0186836 −0.00110672
\(286\) 0 0
\(287\) −6.78021 −0.400223
\(288\) 0 0
\(289\) −13.2249 −0.777935
\(290\) 0 0
\(291\) −1.91542 −0.112284
\(292\) 0 0
\(293\) 8.44965 0.493634 0.246817 0.969062i \(-0.420615\pi\)
0.246817 + 0.969062i \(0.420615\pi\)
\(294\) 0 0
\(295\) −4.82262 −0.280784
\(296\) 0 0
\(297\) −0.846436 −0.0491152
\(298\) 0 0
\(299\) −1.66573 −0.0963314
\(300\) 0 0
\(301\) 1.87960 0.108338
\(302\) 0 0
\(303\) −0.761824 −0.0437656
\(304\) 0 0
\(305\) 2.18968 0.125381
\(306\) 0 0
\(307\) −0.311354 −0.0177699 −0.00888496 0.999961i \(-0.502828\pi\)
−0.00888496 + 0.999961i \(0.502828\pi\)
\(308\) 0 0
\(309\) −1.75067 −0.0995919
\(310\) 0 0
\(311\) −16.0877 −0.912249 −0.456125 0.889916i \(-0.650763\pi\)
−0.456125 + 0.889916i \(0.650763\pi\)
\(312\) 0 0
\(313\) 17.5991 0.994758 0.497379 0.867533i \(-0.334296\pi\)
0.497379 + 0.867533i \(0.334296\pi\)
\(314\) 0 0
\(315\) 1.02442 0.0577193
\(316\) 0 0
\(317\) −19.0753 −1.07138 −0.535688 0.844416i \(-0.679948\pi\)
−0.535688 + 0.844416i \(0.679948\pi\)
\(318\) 0 0
\(319\) 3.52781 0.197520
\(320\) 0 0
\(321\) −0.0719061 −0.00401341
\(322\) 0 0
\(323\) 0.746043 0.0415109
\(324\) 0 0
\(325\) −4.88182 −0.270795
\(326\) 0 0
\(327\) 0.202301 0.0111873
\(328\) 0 0
\(329\) −2.51467 −0.138638
\(330\) 0 0
\(331\) −34.2735 −1.88384 −0.941922 0.335832i \(-0.890983\pi\)
−0.941922 + 0.335832i \(0.890983\pi\)
\(332\) 0 0
\(333\) −17.5038 −0.959200
\(334\) 0 0
\(335\) −2.77055 −0.151371
\(336\) 0 0
\(337\) 20.3206 1.10693 0.553466 0.832872i \(-0.313305\pi\)
0.553466 + 0.832872i \(0.313305\pi\)
\(338\) 0 0
\(339\) −1.29429 −0.0702961
\(340\) 0 0
\(341\) 8.92433 0.483280
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −0.0810521 −0.00436370
\(346\) 0 0
\(347\) −1.03772 −0.0557080 −0.0278540 0.999612i \(-0.508867\pi\)
−0.0278540 + 0.999612i \(0.508867\pi\)
\(348\) 0 0
\(349\) −13.8448 −0.741096 −0.370548 0.928813i \(-0.620830\pi\)
−0.370548 + 0.928813i \(0.620830\pi\)
\(350\) 0 0
\(351\) −0.846436 −0.0451794
\(352\) 0 0
\(353\) −16.0955 −0.856678 −0.428339 0.903618i \(-0.640901\pi\)
−0.428339 + 0.903618i \(0.640901\pi\)
\(354\) 0 0
\(355\) 0.147219 0.00781357
\(356\) 0 0
\(357\) 0.275017 0.0145555
\(358\) 0 0
\(359\) 3.89822 0.205740 0.102870 0.994695i \(-0.467197\pi\)
0.102870 + 0.994695i \(0.467197\pi\)
\(360\) 0 0
\(361\) −18.8526 −0.992240
\(362\) 0 0
\(363\) 0.141545 0.00742920
\(364\) 0 0
\(365\) −4.16987 −0.218261
\(366\) 0 0
\(367\) 35.9022 1.87408 0.937041 0.349220i \(-0.113553\pi\)
0.937041 + 0.349220i \(0.113553\pi\)
\(368\) 0 0
\(369\) −20.2048 −1.05182
\(370\) 0 0
\(371\) −0.793466 −0.0411947
\(372\) 0 0
\(373\) −17.8176 −0.922563 −0.461281 0.887254i \(-0.652610\pi\)
−0.461281 + 0.887254i \(0.652610\pi\)
\(374\) 0 0
\(375\) −0.480837 −0.0248303
\(376\) 0 0
\(377\) 3.52781 0.181692
\(378\) 0 0
\(379\) 0.508512 0.0261205 0.0130603 0.999915i \(-0.495843\pi\)
0.0130603 + 0.999915i \(0.495843\pi\)
\(380\) 0 0
\(381\) −1.88252 −0.0964446
\(382\) 0 0
\(383\) 31.2777 1.59822 0.799109 0.601187i \(-0.205305\pi\)
0.799109 + 0.601187i \(0.205305\pi\)
\(384\) 0 0
\(385\) −0.343768 −0.0175200
\(386\) 0 0
\(387\) 5.60114 0.284722
\(388\) 0 0
\(389\) −10.1369 −0.513963 −0.256981 0.966416i \(-0.582728\pi\)
−0.256981 + 0.966416i \(0.582728\pi\)
\(390\) 0 0
\(391\) 3.23644 0.163674
\(392\) 0 0
\(393\) 2.43566 0.122863
\(394\) 0 0
\(395\) 3.22186 0.162109
\(396\) 0 0
\(397\) −2.86914 −0.143998 −0.0719989 0.997405i \(-0.522938\pi\)
−0.0719989 + 0.997405i \(0.522938\pi\)
\(398\) 0 0
\(399\) 0.0543494 0.00272087
\(400\) 0 0
\(401\) 24.7925 1.23808 0.619040 0.785359i \(-0.287522\pi\)
0.619040 + 0.785359i \(0.287522\pi\)
\(402\) 0 0
\(403\) 8.92433 0.444553
\(404\) 0 0
\(405\) 3.03206 0.150664
\(406\) 0 0
\(407\) 5.87381 0.291154
\(408\) 0 0
\(409\) 18.9450 0.936769 0.468384 0.883525i \(-0.344836\pi\)
0.468384 + 0.883525i \(0.344836\pi\)
\(410\) 0 0
\(411\) −2.39933 −0.118350
\(412\) 0 0
\(413\) 14.0287 0.690308
\(414\) 0 0
\(415\) −1.50500 −0.0738778
\(416\) 0 0
\(417\) −1.57080 −0.0769222
\(418\) 0 0
\(419\) 1.32966 0.0649579 0.0324790 0.999472i \(-0.489660\pi\)
0.0324790 + 0.999472i \(0.489660\pi\)
\(420\) 0 0
\(421\) −8.02264 −0.390999 −0.195500 0.980704i \(-0.562633\pi\)
−0.195500 + 0.980704i \(0.562633\pi\)
\(422\) 0 0
\(423\) −7.49363 −0.364353
\(424\) 0 0
\(425\) 9.48520 0.460100
\(426\) 0 0
\(427\) −6.36966 −0.308249
\(428\) 0 0
\(429\) 0.141545 0.00683387
\(430\) 0 0
\(431\) −9.68512 −0.466516 −0.233258 0.972415i \(-0.574939\pi\)
−0.233258 + 0.972415i \(0.574939\pi\)
\(432\) 0 0
\(433\) −28.7157 −1.37999 −0.689994 0.723815i \(-0.742387\pi\)
−0.689994 + 0.723815i \(0.742387\pi\)
\(434\) 0 0
\(435\) 0.171659 0.00823042
\(436\) 0 0
\(437\) 0.639592 0.0305958
\(438\) 0 0
\(439\) −8.65803 −0.413225 −0.206613 0.978423i \(-0.566244\pi\)
−0.206613 + 0.978423i \(0.566244\pi\)
\(440\) 0 0
\(441\) −2.97996 −0.141903
\(442\) 0 0
\(443\) −20.9580 −0.995745 −0.497872 0.867250i \(-0.665885\pi\)
−0.497872 + 0.867250i \(0.665885\pi\)
\(444\) 0 0
\(445\) −1.70426 −0.0807895
\(446\) 0 0
\(447\) −1.46710 −0.0693917
\(448\) 0 0
\(449\) −33.5646 −1.58401 −0.792006 0.610513i \(-0.790963\pi\)
−0.792006 + 0.610513i \(0.790963\pi\)
\(450\) 0 0
\(451\) 6.78021 0.319268
\(452\) 0 0
\(453\) 0.990008 0.0465146
\(454\) 0 0
\(455\) −0.343768 −0.0161161
\(456\) 0 0
\(457\) −21.1902 −0.991235 −0.495617 0.868541i \(-0.665058\pi\)
−0.495617 + 0.868541i \(0.665058\pi\)
\(458\) 0 0
\(459\) 1.64459 0.0767631
\(460\) 0 0
\(461\) 36.6365 1.70633 0.853166 0.521640i \(-0.174680\pi\)
0.853166 + 0.521640i \(0.174680\pi\)
\(462\) 0 0
\(463\) −17.3814 −0.807782 −0.403891 0.914807i \(-0.632342\pi\)
−0.403891 + 0.914807i \(0.632342\pi\)
\(464\) 0 0
\(465\) 0.434247 0.0201377
\(466\) 0 0
\(467\) 25.9327 1.20002 0.600012 0.799991i \(-0.295163\pi\)
0.600012 + 0.799991i \(0.295163\pi\)
\(468\) 0 0
\(469\) 8.05936 0.372147
\(470\) 0 0
\(471\) −0.833919 −0.0384250
\(472\) 0 0
\(473\) −1.87960 −0.0864240
\(474\) 0 0
\(475\) 1.87448 0.0860072
\(476\) 0 0
\(477\) −2.36450 −0.108263
\(478\) 0 0
\(479\) −21.2850 −0.972537 −0.486268 0.873810i \(-0.661642\pi\)
−0.486268 + 0.873810i \(0.661642\pi\)
\(480\) 0 0
\(481\) 5.87381 0.267823
\(482\) 0 0
\(483\) 0.235776 0.0107282
\(484\) 0 0
\(485\) −4.65194 −0.211234
\(486\) 0 0
\(487\) 29.4443 1.33425 0.667123 0.744947i \(-0.267525\pi\)
0.667123 + 0.744947i \(0.267525\pi\)
\(488\) 0 0
\(489\) 0.160027 0.00723669
\(490\) 0 0
\(491\) 23.7655 1.07252 0.536261 0.844053i \(-0.319836\pi\)
0.536261 + 0.844053i \(0.319836\pi\)
\(492\) 0 0
\(493\) −6.85441 −0.308707
\(494\) 0 0
\(495\) −1.02442 −0.0460441
\(496\) 0 0
\(497\) −0.428251 −0.0192097
\(498\) 0 0
\(499\) 39.2462 1.75690 0.878451 0.477833i \(-0.158578\pi\)
0.878451 + 0.477833i \(0.158578\pi\)
\(500\) 0 0
\(501\) −2.25766 −0.100865
\(502\) 0 0
\(503\) −14.9003 −0.664370 −0.332185 0.943214i \(-0.607786\pi\)
−0.332185 + 0.943214i \(0.607786\pi\)
\(504\) 0 0
\(505\) −1.85022 −0.0823339
\(506\) 0 0
\(507\) 0.141545 0.00628625
\(508\) 0 0
\(509\) 15.3793 0.681677 0.340838 0.940122i \(-0.389289\pi\)
0.340838 + 0.940122i \(0.389289\pi\)
\(510\) 0 0
\(511\) 12.1299 0.536595
\(512\) 0 0
\(513\) 0.325008 0.0143494
\(514\) 0 0
\(515\) −4.25180 −0.187357
\(516\) 0 0
\(517\) 2.51467 0.110595
\(518\) 0 0
\(519\) −3.17565 −0.139396
\(520\) 0 0
\(521\) −44.8745 −1.96599 −0.982994 0.183636i \(-0.941213\pi\)
−0.982994 + 0.183636i \(0.941213\pi\)
\(522\) 0 0
\(523\) 35.0853 1.53417 0.767086 0.641544i \(-0.221706\pi\)
0.767086 + 0.641544i \(0.221706\pi\)
\(524\) 0 0
\(525\) 0.690999 0.0301577
\(526\) 0 0
\(527\) −17.3396 −0.755327
\(528\) 0 0
\(529\) −20.2254 −0.879363
\(530\) 0 0
\(531\) 41.8051 1.81419
\(532\) 0 0
\(533\) 6.78021 0.293684
\(534\) 0 0
\(535\) −0.174637 −0.00755021
\(536\) 0 0
\(537\) 1.83547 0.0792065
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 5.41564 0.232836 0.116418 0.993200i \(-0.462859\pi\)
0.116418 + 0.993200i \(0.462859\pi\)
\(542\) 0 0
\(543\) −0.117989 −0.00506338
\(544\) 0 0
\(545\) 0.491324 0.0210460
\(546\) 0 0
\(547\) 8.15207 0.348557 0.174279 0.984696i \(-0.444241\pi\)
0.174279 + 0.984696i \(0.444241\pi\)
\(548\) 0 0
\(549\) −18.9814 −0.810104
\(550\) 0 0
\(551\) −1.35458 −0.0577071
\(552\) 0 0
\(553\) −9.37219 −0.398546
\(554\) 0 0
\(555\) 0.285812 0.0121321
\(556\) 0 0
\(557\) 41.6501 1.76477 0.882385 0.470528i \(-0.155937\pi\)
0.882385 + 0.470528i \(0.155937\pi\)
\(558\) 0 0
\(559\) −1.87960 −0.0794985
\(560\) 0 0
\(561\) −0.275017 −0.0116112
\(562\) 0 0
\(563\) −24.1701 −1.01865 −0.509324 0.860575i \(-0.670105\pi\)
−0.509324 + 0.860575i \(0.670105\pi\)
\(564\) 0 0
\(565\) −3.14341 −0.132244
\(566\) 0 0
\(567\) −8.82009 −0.370409
\(568\) 0 0
\(569\) 11.0116 0.461631 0.230815 0.972998i \(-0.425861\pi\)
0.230815 + 0.972998i \(0.425861\pi\)
\(570\) 0 0
\(571\) −16.2224 −0.678885 −0.339443 0.940627i \(-0.610238\pi\)
−0.339443 + 0.940627i \(0.610238\pi\)
\(572\) 0 0
\(573\) 2.31436 0.0966839
\(574\) 0 0
\(575\) 8.13178 0.339119
\(576\) 0 0
\(577\) 9.16422 0.381512 0.190756 0.981638i \(-0.438906\pi\)
0.190756 + 0.981638i \(0.438906\pi\)
\(578\) 0 0
\(579\) 2.56885 0.106758
\(580\) 0 0
\(581\) 4.37797 0.181629
\(582\) 0 0
\(583\) 0.793466 0.0328620
\(584\) 0 0
\(585\) −1.02442 −0.0423544
\(586\) 0 0
\(587\) −28.4842 −1.17567 −0.587834 0.808982i \(-0.700019\pi\)
−0.587834 + 0.808982i \(0.700019\pi\)
\(588\) 0 0
\(589\) −3.42669 −0.141194
\(590\) 0 0
\(591\) −3.18341 −0.130948
\(592\) 0 0
\(593\) 11.2059 0.460172 0.230086 0.973170i \(-0.426099\pi\)
0.230086 + 0.973170i \(0.426099\pi\)
\(594\) 0 0
\(595\) 0.667928 0.0273824
\(596\) 0 0
\(597\) 1.85933 0.0760974
\(598\) 0 0
\(599\) 13.8800 0.567123 0.283561 0.958954i \(-0.408484\pi\)
0.283561 + 0.958954i \(0.408484\pi\)
\(600\) 0 0
\(601\) 11.7232 0.478200 0.239100 0.970995i \(-0.423148\pi\)
0.239100 + 0.970995i \(0.423148\pi\)
\(602\) 0 0
\(603\) 24.0166 0.978032
\(604\) 0 0
\(605\) 0.343768 0.0139762
\(606\) 0 0
\(607\) −18.3454 −0.744618 −0.372309 0.928109i \(-0.621434\pi\)
−0.372309 + 0.928109i \(0.621434\pi\)
\(608\) 0 0
\(609\) −0.499346 −0.0202345
\(610\) 0 0
\(611\) 2.51467 0.101733
\(612\) 0 0
\(613\) −10.2327 −0.413296 −0.206648 0.978415i \(-0.566255\pi\)
−0.206648 + 0.978415i \(0.566255\pi\)
\(614\) 0 0
\(615\) 0.329917 0.0133035
\(616\) 0 0
\(617\) 2.92459 0.117739 0.0588697 0.998266i \(-0.481250\pi\)
0.0588697 + 0.998266i \(0.481250\pi\)
\(618\) 0 0
\(619\) 38.5588 1.54981 0.774904 0.632079i \(-0.217798\pi\)
0.774904 + 0.632079i \(0.217798\pi\)
\(620\) 0 0
\(621\) 1.40993 0.0565786
\(622\) 0 0
\(623\) 4.95758 0.198621
\(624\) 0 0
\(625\) 23.2413 0.929653
\(626\) 0 0
\(627\) −0.0543494 −0.00217051
\(628\) 0 0
\(629\) −11.4126 −0.455050
\(630\) 0 0
\(631\) 31.8716 1.26879 0.634395 0.773009i \(-0.281249\pi\)
0.634395 + 0.773009i \(0.281249\pi\)
\(632\) 0 0
\(633\) −2.55230 −0.101445
\(634\) 0 0
\(635\) −4.57204 −0.181436
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) −1.27617 −0.0504846
\(640\) 0 0
\(641\) 40.7019 1.60763 0.803815 0.594879i \(-0.202800\pi\)
0.803815 + 0.594879i \(0.202800\pi\)
\(642\) 0 0
\(643\) −28.5035 −1.12407 −0.562033 0.827114i \(-0.689981\pi\)
−0.562033 + 0.827114i \(0.689981\pi\)
\(644\) 0 0
\(645\) −0.0914589 −0.00360119
\(646\) 0 0
\(647\) −38.3960 −1.50950 −0.754751 0.656012i \(-0.772242\pi\)
−0.754751 + 0.656012i \(0.772242\pi\)
\(648\) 0 0
\(649\) −14.0287 −0.550675
\(650\) 0 0
\(651\) −1.26320 −0.0495086
\(652\) 0 0
\(653\) −25.3523 −0.992111 −0.496055 0.868291i \(-0.665219\pi\)
−0.496055 + 0.868291i \(0.665219\pi\)
\(654\) 0 0
\(655\) 5.91543 0.231135
\(656\) 0 0
\(657\) 36.1467 1.41022
\(658\) 0 0
\(659\) −3.42625 −0.133468 −0.0667339 0.997771i \(-0.521258\pi\)
−0.0667339 + 0.997771i \(0.521258\pi\)
\(660\) 0 0
\(661\) −21.9669 −0.854413 −0.427207 0.904154i \(-0.640502\pi\)
−0.427207 + 0.904154i \(0.640502\pi\)
\(662\) 0 0
\(663\) −0.275017 −0.0106808
\(664\) 0 0
\(665\) 0.131997 0.00511863
\(666\) 0 0
\(667\) −5.87637 −0.227534
\(668\) 0 0
\(669\) 0.898534 0.0347393
\(670\) 0 0
\(671\) 6.36966 0.245898
\(672\) 0 0
\(673\) −23.5578 −0.908087 −0.454044 0.890979i \(-0.650019\pi\)
−0.454044 + 0.890979i \(0.650019\pi\)
\(674\) 0 0
\(675\) 4.13215 0.159047
\(676\) 0 0
\(677\) −45.9949 −1.76773 −0.883863 0.467745i \(-0.845066\pi\)
−0.883863 + 0.467745i \(0.845066\pi\)
\(678\) 0 0
\(679\) 13.5322 0.519318
\(680\) 0 0
\(681\) −0.505586 −0.0193741
\(682\) 0 0
\(683\) −5.43705 −0.208043 −0.104021 0.994575i \(-0.533171\pi\)
−0.104021 + 0.994575i \(0.533171\pi\)
\(684\) 0 0
\(685\) −5.82719 −0.222646
\(686\) 0 0
\(687\) −0.910388 −0.0347335
\(688\) 0 0
\(689\) 0.793466 0.0302286
\(690\) 0 0
\(691\) 26.9640 1.02576 0.512880 0.858460i \(-0.328579\pi\)
0.512880 + 0.858460i \(0.328579\pi\)
\(692\) 0 0
\(693\) 2.97996 0.113200
\(694\) 0 0
\(695\) −3.81495 −0.144709
\(696\) 0 0
\(697\) −13.1737 −0.498989
\(698\) 0 0
\(699\) 1.65952 0.0627689
\(700\) 0 0
\(701\) −43.3979 −1.63911 −0.819557 0.572997i \(-0.805781\pi\)
−0.819557 + 0.572997i \(0.805781\pi\)
\(702\) 0 0
\(703\) −2.25538 −0.0850632
\(704\) 0 0
\(705\) 0.122361 0.00460837
\(706\) 0 0
\(707\) 5.38219 0.202418
\(708\) 0 0
\(709\) 48.5676 1.82399 0.911997 0.410196i \(-0.134540\pi\)
0.911997 + 0.410196i \(0.134540\pi\)
\(710\) 0 0
\(711\) −27.9288 −1.04741
\(712\) 0 0
\(713\) −14.8655 −0.556717
\(714\) 0 0
\(715\) 0.343768 0.0128562
\(716\) 0 0
\(717\) −1.95694 −0.0730833
\(718\) 0 0
\(719\) −40.5701 −1.51301 −0.756504 0.653989i \(-0.773094\pi\)
−0.756504 + 0.653989i \(0.773094\pi\)
\(720\) 0 0
\(721\) 12.3682 0.460617
\(722\) 0 0
\(723\) −2.06123 −0.0766578
\(724\) 0 0
\(725\) −17.2222 −0.639615
\(726\) 0 0
\(727\) 15.9922 0.593117 0.296559 0.955015i \(-0.404161\pi\)
0.296559 + 0.955015i \(0.404161\pi\)
\(728\) 0 0
\(729\) −25.9241 −0.960153
\(730\) 0 0
\(731\) 3.65199 0.135074
\(732\) 0 0
\(733\) −17.4403 −0.644172 −0.322086 0.946710i \(-0.604384\pi\)
−0.322086 + 0.946710i \(0.604384\pi\)
\(734\) 0 0
\(735\) 0.0486587 0.00179480
\(736\) 0 0
\(737\) −8.05936 −0.296870
\(738\) 0 0
\(739\) −26.7320 −0.983352 −0.491676 0.870778i \(-0.663616\pi\)
−0.491676 + 0.870778i \(0.663616\pi\)
\(740\) 0 0
\(741\) −0.0543494 −0.00199658
\(742\) 0 0
\(743\) 8.12671 0.298140 0.149070 0.988827i \(-0.452372\pi\)
0.149070 + 0.988827i \(0.452372\pi\)
\(744\) 0 0
\(745\) −3.56312 −0.130543
\(746\) 0 0
\(747\) 13.0462 0.477335
\(748\) 0 0
\(749\) 0.508008 0.0185622
\(750\) 0 0
\(751\) 5.68036 0.207279 0.103640 0.994615i \(-0.466951\pi\)
0.103640 + 0.994615i \(0.466951\pi\)
\(752\) 0 0
\(753\) 1.34274 0.0489323
\(754\) 0 0
\(755\) 2.40441 0.0875054
\(756\) 0 0
\(757\) −30.9880 −1.12628 −0.563138 0.826363i \(-0.690406\pi\)
−0.563138 + 0.826363i \(0.690406\pi\)
\(758\) 0 0
\(759\) −0.235776 −0.00855812
\(760\) 0 0
\(761\) −10.4708 −0.379566 −0.189783 0.981826i \(-0.560778\pi\)
−0.189783 + 0.981826i \(0.560778\pi\)
\(762\) 0 0
\(763\) −1.42923 −0.0517417
\(764\) 0 0
\(765\) 1.99040 0.0719632
\(766\) 0 0
\(767\) −14.0287 −0.506547
\(768\) 0 0
\(769\) −42.0177 −1.51520 −0.757599 0.652720i \(-0.773628\pi\)
−0.757599 + 0.652720i \(0.773628\pi\)
\(770\) 0 0
\(771\) 1.99490 0.0718447
\(772\) 0 0
\(773\) 25.6652 0.923113 0.461557 0.887111i \(-0.347291\pi\)
0.461557 + 0.887111i \(0.347291\pi\)
\(774\) 0 0
\(775\) −43.5670 −1.56497
\(776\) 0 0
\(777\) −0.831411 −0.0298267
\(778\) 0 0
\(779\) −2.60341 −0.0932768
\(780\) 0 0
\(781\) 0.428251 0.0153240
\(782\) 0 0
\(783\) −2.98607 −0.106713
\(784\) 0 0
\(785\) −2.02532 −0.0722868
\(786\) 0 0
\(787\) 39.4566 1.40648 0.703238 0.710955i \(-0.251737\pi\)
0.703238 + 0.710955i \(0.251737\pi\)
\(788\) 0 0
\(789\) 2.20507 0.0785026
\(790\) 0 0
\(791\) 9.14399 0.325123
\(792\) 0 0
\(793\) 6.36966 0.226193
\(794\) 0 0
\(795\) 0.0386090 0.00136932
\(796\) 0 0
\(797\) 0.454799 0.0161098 0.00805490 0.999968i \(-0.497436\pi\)
0.00805490 + 0.999968i \(0.497436\pi\)
\(798\) 0 0
\(799\) −4.88591 −0.172851
\(800\) 0 0
\(801\) 14.7734 0.521993
\(802\) 0 0
\(803\) −12.1299 −0.428055
\(804\) 0 0
\(805\) 0.572623 0.0201823
\(806\) 0 0
\(807\) −2.30741 −0.0812247
\(808\) 0 0
\(809\) 28.6757 1.00818 0.504092 0.863650i \(-0.331827\pi\)
0.504092 + 0.863650i \(0.331827\pi\)
\(810\) 0 0
\(811\) 24.3682 0.855682 0.427841 0.903854i \(-0.359274\pi\)
0.427841 + 0.903854i \(0.359274\pi\)
\(812\) 0 0
\(813\) 0.536282 0.0188082
\(814\) 0 0
\(815\) 0.388655 0.0136140
\(816\) 0 0
\(817\) 0.721712 0.0252495
\(818\) 0 0
\(819\) 2.97996 0.104128
\(820\) 0 0
\(821\) 38.7715 1.35313 0.676567 0.736381i \(-0.263467\pi\)
0.676567 + 0.736381i \(0.263467\pi\)
\(822\) 0 0
\(823\) 7.94497 0.276944 0.138472 0.990366i \(-0.455781\pi\)
0.138472 + 0.990366i \(0.455781\pi\)
\(824\) 0 0
\(825\) −0.690999 −0.0240575
\(826\) 0 0
\(827\) 17.1512 0.596406 0.298203 0.954502i \(-0.403613\pi\)
0.298203 + 0.954502i \(0.403613\pi\)
\(828\) 0 0
\(829\) 14.6830 0.509961 0.254981 0.966946i \(-0.417931\pi\)
0.254981 + 0.966946i \(0.417931\pi\)
\(830\) 0 0
\(831\) −2.79256 −0.0968729
\(832\) 0 0
\(833\) −1.94296 −0.0673197
\(834\) 0 0
\(835\) −5.48312 −0.189751
\(836\) 0 0
\(837\) −7.55388 −0.261100
\(838\) 0 0
\(839\) 5.17883 0.178793 0.0893966 0.995996i \(-0.471506\pi\)
0.0893966 + 0.995996i \(0.471506\pi\)
\(840\) 0 0
\(841\) −16.5545 −0.570846
\(842\) 0 0
\(843\) −2.66357 −0.0917381
\(844\) 0 0
\(845\) 0.343768 0.0118260
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −0.930785 −0.0319444
\(850\) 0 0
\(851\) −9.78417 −0.335397
\(852\) 0 0
\(853\) 3.44234 0.117864 0.0589318 0.998262i \(-0.481231\pi\)
0.0589318 + 0.998262i \(0.481231\pi\)
\(854\) 0 0
\(855\) 0.393347 0.0134522
\(856\) 0 0
\(857\) −16.5475 −0.565252 −0.282626 0.959230i \(-0.591206\pi\)
−0.282626 + 0.959230i \(0.591206\pi\)
\(858\) 0 0
\(859\) −37.9475 −1.29475 −0.647376 0.762171i \(-0.724133\pi\)
−0.647376 + 0.762171i \(0.724133\pi\)
\(860\) 0 0
\(861\) −0.959707 −0.0327067
\(862\) 0 0
\(863\) 21.1359 0.719476 0.359738 0.933053i \(-0.382866\pi\)
0.359738 + 0.933053i \(0.382866\pi\)
\(864\) 0 0
\(865\) −7.71262 −0.262237
\(866\) 0 0
\(867\) −1.87192 −0.0635738
\(868\) 0 0
\(869\) 9.37219 0.317930
\(870\) 0 0
\(871\) −8.05936 −0.273081
\(872\) 0 0
\(873\) 40.3255 1.36481
\(874\) 0 0
\(875\) 3.39705 0.114841
\(876\) 0 0
\(877\) −31.7514 −1.07217 −0.536085 0.844164i \(-0.680097\pi\)
−0.536085 + 0.844164i \(0.680097\pi\)
\(878\) 0 0
\(879\) 1.19601 0.0403404
\(880\) 0 0
\(881\) −26.7648 −0.901729 −0.450864 0.892593i \(-0.648884\pi\)
−0.450864 + 0.892593i \(0.648884\pi\)
\(882\) 0 0
\(883\) −40.5131 −1.36338 −0.681688 0.731643i \(-0.738754\pi\)
−0.681688 + 0.731643i \(0.738754\pi\)
\(884\) 0 0
\(885\) −0.682619 −0.0229460
\(886\) 0 0
\(887\) 27.5458 0.924897 0.462448 0.886646i \(-0.346971\pi\)
0.462448 + 0.886646i \(0.346971\pi\)
\(888\) 0 0
\(889\) 13.2998 0.446061
\(890\) 0 0
\(891\) 8.82009 0.295484
\(892\) 0 0
\(893\) −0.965563 −0.0323113
\(894\) 0 0
\(895\) 4.45777 0.149007
\(896\) 0 0
\(897\) −0.235776 −0.00787232
\(898\) 0 0
\(899\) 31.4834 1.05003
\(900\) 0 0
\(901\) −1.54167 −0.0513606
\(902\) 0 0
\(903\) 0.266048 0.00885353
\(904\) 0 0
\(905\) −0.286556 −0.00952545
\(906\) 0 0
\(907\) 21.6514 0.718925 0.359462 0.933160i \(-0.382960\pi\)
0.359462 + 0.933160i \(0.382960\pi\)
\(908\) 0 0
\(909\) 16.0387 0.531971
\(910\) 0 0
\(911\) −37.6600 −1.24773 −0.623866 0.781532i \(-0.714439\pi\)
−0.623866 + 0.781532i \(0.714439\pi\)
\(912\) 0 0
\(913\) −4.37797 −0.144890
\(914\) 0 0
\(915\) 0.309940 0.0102463
\(916\) 0 0
\(917\) −17.2076 −0.568246
\(918\) 0 0
\(919\) −45.8544 −1.51260 −0.756298 0.654227i \(-0.772994\pi\)
−0.756298 + 0.654227i \(0.772994\pi\)
\(920\) 0 0
\(921\) −0.0440707 −0.00145218
\(922\) 0 0
\(923\) 0.428251 0.0140961
\(924\) 0 0
\(925\) −28.6749 −0.942826
\(926\) 0 0
\(927\) 36.8569 1.21054
\(928\) 0 0
\(929\) 3.81073 0.125026 0.0625130 0.998044i \(-0.480089\pi\)
0.0625130 + 0.998044i \(0.480089\pi\)
\(930\) 0 0
\(931\) −0.383972 −0.0125842
\(932\) 0 0
\(933\) −2.27714 −0.0745501
\(934\) 0 0
\(935\) −0.667928 −0.0218436
\(936\) 0 0
\(937\) 30.5064 0.996600 0.498300 0.867005i \(-0.333958\pi\)
0.498300 + 0.867005i \(0.333958\pi\)
\(938\) 0 0
\(939\) 2.49107 0.0812929
\(940\) 0 0
\(941\) 36.0054 1.17374 0.586871 0.809681i \(-0.300360\pi\)
0.586871 + 0.809681i \(0.300360\pi\)
\(942\) 0 0
\(943\) −11.2940 −0.367782
\(944\) 0 0
\(945\) 0.290978 0.00946550
\(946\) 0 0
\(947\) 2.75429 0.0895023 0.0447512 0.998998i \(-0.485751\pi\)
0.0447512 + 0.998998i \(0.485751\pi\)
\(948\) 0 0
\(949\) −12.1299 −0.393753
\(950\) 0 0
\(951\) −2.70002 −0.0875543
\(952\) 0 0
\(953\) −56.0079 −1.81427 −0.907137 0.420836i \(-0.861737\pi\)
−0.907137 + 0.420836i \(0.861737\pi\)
\(954\) 0 0
\(955\) 5.62084 0.181886
\(956\) 0 0
\(957\) 0.499346 0.0161415
\(958\) 0 0
\(959\) 16.9509 0.547375
\(960\) 0 0
\(961\) 48.6437 1.56915
\(962\) 0 0
\(963\) 1.51385 0.0487830
\(964\) 0 0
\(965\) 6.23890 0.200837
\(966\) 0 0
\(967\) −46.0658 −1.48138 −0.740688 0.671849i \(-0.765500\pi\)
−0.740688 + 0.671849i \(0.765500\pi\)
\(968\) 0 0
\(969\) 0.105599 0.00339233
\(970\) 0 0
\(971\) −20.6368 −0.662268 −0.331134 0.943584i \(-0.607431\pi\)
−0.331134 + 0.943584i \(0.607431\pi\)
\(972\) 0 0
\(973\) 11.0975 0.355769
\(974\) 0 0
\(975\) −0.690999 −0.0221297
\(976\) 0 0
\(977\) 6.08573 0.194700 0.0973498 0.995250i \(-0.468963\pi\)
0.0973498 + 0.995250i \(0.468963\pi\)
\(978\) 0 0
\(979\) −4.95758 −0.158445
\(980\) 0 0
\(981\) −4.25906 −0.135981
\(982\) 0 0
\(983\) 4.52353 0.144278 0.0721391 0.997395i \(-0.477017\pi\)
0.0721391 + 0.997395i \(0.477017\pi\)
\(984\) 0 0
\(985\) −7.73146 −0.246345
\(986\) 0 0
\(987\) −0.355940 −0.0113297
\(988\) 0 0
\(989\) 3.13089 0.0995567
\(990\) 0 0
\(991\) −12.0636 −0.383212 −0.191606 0.981472i \(-0.561370\pi\)
−0.191606 + 0.981472i \(0.561370\pi\)
\(992\) 0 0
\(993\) −4.85126 −0.153950
\(994\) 0 0
\(995\) 4.51572 0.143158
\(996\) 0 0
\(997\) 10.8318 0.343045 0.171523 0.985180i \(-0.445131\pi\)
0.171523 + 0.985180i \(0.445131\pi\)
\(998\) 0 0
\(999\) −4.97181 −0.157301
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 \(a_p\))