Properties

Label 4004.2.a.j.1.6
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 1.6
Root \(-0.0962745\)
Character \(\chi\) = 4004.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.0962745 q^{3} -1.48698 q^{5} -1.00000 q^{7} -2.99073 q^{9} +O(q^{10})\) \(q+0.0962745 q^{3} -1.48698 q^{5} -1.00000 q^{7} -2.99073 q^{9} -1.00000 q^{11} -1.00000 q^{13} -0.143158 q^{15} -7.53478 q^{17} +7.59969 q^{19} -0.0962745 q^{21} -3.71789 q^{23} -2.78889 q^{25} -0.576755 q^{27} -9.29580 q^{29} +6.27772 q^{31} -0.0962745 q^{33} +1.48698 q^{35} +0.976345 q^{37} -0.0962745 q^{39} +4.24087 q^{41} +11.8980 q^{43} +4.44716 q^{45} +12.9010 q^{47} +1.00000 q^{49} -0.725407 q^{51} -4.71919 q^{53} +1.48698 q^{55} +0.731656 q^{57} -5.01808 q^{59} -3.65793 q^{61} +2.99073 q^{63} +1.48698 q^{65} +5.47832 q^{67} -0.357938 q^{69} -9.99423 q^{71} +8.02335 q^{73} -0.268499 q^{75} +1.00000 q^{77} +2.16743 q^{79} +8.91667 q^{81} -12.0745 q^{83} +11.2041 q^{85} -0.894948 q^{87} +12.1364 q^{89} +1.00000 q^{91} +0.604385 q^{93} -11.3006 q^{95} -9.20899 q^{97} +2.99073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} + O(q^{10}) \) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} - 10q^{11} - 10q^{13} - 4q^{15} + 9q^{17} + 3q^{19} + 2q^{21} - 4q^{23} + 22q^{25} - 8q^{27} + 13q^{29} - 17q^{31} + 2q^{33} + 2q^{35} + 11q^{37} + 2q^{39} + 8q^{41} + 21q^{43} - 15q^{45} + q^{47} + 10q^{49} + 19q^{51} + 22q^{53} + 2q^{55} + 8q^{57} - 24q^{59} + 16q^{61} - 10q^{63} + 2q^{65} + 19q^{67} + 51q^{69} - 25q^{71} + 22q^{73} + 28q^{75} + 10q^{77} + 41q^{79} + 54q^{81} + 8q^{83} + 9q^{85} - 5q^{87} + 36q^{89} + 10q^{91} + 12q^{93} + 13q^{95} - 5q^{97} - 10q^{99} + O(q^{100}) \)

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
\(3\) 0.0962745 0.0555841 0.0277920 0.999614i \(-0.491152\pi\)
0.0277920 + 0.999614i \(0.491152\pi\)
\(4\) 0 0
\(5\) −1.48698 −0.664998 −0.332499 0.943104i \(-0.607892\pi\)
−0.332499 + 0.943104i \(0.607892\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.99073 −0.996910
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −0.143158 −0.0369633
\(16\) 0 0
\(17\) −7.53478 −1.82745 −0.913726 0.406331i \(-0.866808\pi\)
−0.913726 + 0.406331i \(0.866808\pi\)
\(18\) 0 0
\(19\) 7.59969 1.74349 0.871744 0.489961i \(-0.162989\pi\)
0.871744 + 0.489961i \(0.162989\pi\)
\(20\) 0 0
\(21\) −0.0962745 −0.0210088
\(22\) 0 0
\(23\) −3.71789 −0.775233 −0.387616 0.921821i \(-0.626701\pi\)
−0.387616 + 0.921821i \(0.626701\pi\)
\(24\) 0 0
\(25\) −2.78889 −0.557778
\(26\) 0 0
\(27\) −0.576755 −0.110996
\(28\) 0 0
\(29\) −9.29580 −1.72619 −0.863093 0.505044i \(-0.831476\pi\)
−0.863093 + 0.505044i \(0.831476\pi\)
\(30\) 0 0
\(31\) 6.27772 1.12751 0.563756 0.825941i \(-0.309356\pi\)
0.563756 + 0.825941i \(0.309356\pi\)
\(32\) 0 0
\(33\) −0.0962745 −0.0167592
\(34\) 0 0
\(35\) 1.48698 0.251345
\(36\) 0 0
\(37\) 0.976345 0.160510 0.0802551 0.996774i \(-0.474427\pi\)
0.0802551 + 0.996774i \(0.474427\pi\)
\(38\) 0 0
\(39\) −0.0962745 −0.0154163
\(40\) 0 0
\(41\) 4.24087 0.662312 0.331156 0.943576i \(-0.392561\pi\)
0.331156 + 0.943576i \(0.392561\pi\)
\(42\) 0 0
\(43\) 11.8980 1.81443 0.907217 0.420663i \(-0.138202\pi\)
0.907217 + 0.420663i \(0.138202\pi\)
\(44\) 0 0
\(45\) 4.44716 0.662943
\(46\) 0 0
\(47\) 12.9010 1.88180 0.940901 0.338681i \(-0.109981\pi\)
0.940901 + 0.338681i \(0.109981\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −0.725407 −0.101577
\(52\) 0 0
\(53\) −4.71919 −0.648231 −0.324116 0.946017i \(-0.605067\pi\)
−0.324116 + 0.946017i \(0.605067\pi\)
\(54\) 0 0
\(55\) 1.48698 0.200504
\(56\) 0 0
\(57\) 0.731656 0.0969102
\(58\) 0 0
\(59\) −5.01808 −0.653298 −0.326649 0.945146i \(-0.605919\pi\)
−0.326649 + 0.945146i \(0.605919\pi\)
\(60\) 0 0
\(61\) −3.65793 −0.468350 −0.234175 0.972194i \(-0.575239\pi\)
−0.234175 + 0.972194i \(0.575239\pi\)
\(62\) 0 0
\(63\) 2.99073 0.376797
\(64\) 0 0
\(65\) 1.48698 0.184437
\(66\) 0 0
\(67\) 5.47832 0.669283 0.334641 0.942346i \(-0.391385\pi\)
0.334641 + 0.942346i \(0.391385\pi\)
\(68\) 0 0
\(69\) −0.357938 −0.0430906
\(70\) 0 0
\(71\) −9.99423 −1.18610 −0.593049 0.805167i \(-0.702076\pi\)
−0.593049 + 0.805167i \(0.702076\pi\)
\(72\) 0 0
\(73\) 8.02335 0.939062 0.469531 0.882916i \(-0.344423\pi\)
0.469531 + 0.882916i \(0.344423\pi\)
\(74\) 0 0
\(75\) −0.268499 −0.0310036
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 2.16743 0.243855 0.121927 0.992539i \(-0.461093\pi\)
0.121927 + 0.992539i \(0.461093\pi\)
\(80\) 0 0
\(81\) 8.91667 0.990741
\(82\) 0 0
\(83\) −12.0745 −1.32535 −0.662673 0.748909i \(-0.730578\pi\)
−0.662673 + 0.748909i \(0.730578\pi\)
\(84\) 0 0
\(85\) 11.2041 1.21525
\(86\) 0 0
\(87\) −0.894948 −0.0959485
\(88\) 0 0
\(89\) 12.1364 1.28645 0.643226 0.765676i \(-0.277596\pi\)
0.643226 + 0.765676i \(0.277596\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 0.604385 0.0626718
\(94\) 0 0
\(95\) −11.3006 −1.15942
\(96\) 0 0
\(97\) −9.20899 −0.935031 −0.467515 0.883985i \(-0.654851\pi\)
−0.467515 + 0.883985i \(0.654851\pi\)
\(98\) 0 0
\(99\) 2.99073 0.300580
\(100\) 0 0
\(101\) 4.95809 0.493348 0.246674 0.969098i \(-0.420662\pi\)
0.246674 + 0.969098i \(0.420662\pi\)
\(102\) 0 0
\(103\) −0.232419 −0.0229009 −0.0114504 0.999934i \(-0.503645\pi\)
−0.0114504 + 0.999934i \(0.503645\pi\)
\(104\) 0 0
\(105\) 0.143158 0.0139708
\(106\) 0 0
\(107\) 2.52905 0.244492 0.122246 0.992500i \(-0.460990\pi\)
0.122246 + 0.992500i \(0.460990\pi\)
\(108\) 0 0
\(109\) 1.23676 0.118460 0.0592301 0.998244i \(-0.481135\pi\)
0.0592301 + 0.998244i \(0.481135\pi\)
\(110\) 0 0
\(111\) 0.0939972 0.00892181
\(112\) 0 0
\(113\) −4.71296 −0.443358 −0.221679 0.975120i \(-0.571154\pi\)
−0.221679 + 0.975120i \(0.571154\pi\)
\(114\) 0 0
\(115\) 5.52842 0.515528
\(116\) 0 0
\(117\) 2.99073 0.276493
\(118\) 0 0
\(119\) 7.53478 0.690712
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0.408287 0.0368140
\(124\) 0 0
\(125\) 11.5819 1.03592
\(126\) 0 0
\(127\) 20.6384 1.83137 0.915683 0.401902i \(-0.131651\pi\)
0.915683 + 0.401902i \(0.131651\pi\)
\(128\) 0 0
\(129\) 1.14548 0.100854
\(130\) 0 0
\(131\) −1.43721 −0.125570 −0.0627850 0.998027i \(-0.519998\pi\)
−0.0627850 + 0.998027i \(0.519998\pi\)
\(132\) 0 0
\(133\) −7.59969 −0.658977
\(134\) 0 0
\(135\) 0.857622 0.0738124
\(136\) 0 0
\(137\) 21.9061 1.87156 0.935782 0.352580i \(-0.114695\pi\)
0.935782 + 0.352580i \(0.114695\pi\)
\(138\) 0 0
\(139\) −4.33207 −0.367441 −0.183721 0.982978i \(-0.558814\pi\)
−0.183721 + 0.982978i \(0.558814\pi\)
\(140\) 0 0
\(141\) 1.24204 0.104598
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 13.8227 1.14791
\(146\) 0 0
\(147\) 0.0962745 0.00794059
\(148\) 0 0
\(149\) 12.4447 1.01951 0.509755 0.860320i \(-0.329736\pi\)
0.509755 + 0.860320i \(0.329736\pi\)
\(150\) 0 0
\(151\) 20.1067 1.63626 0.818132 0.575031i \(-0.195010\pi\)
0.818132 + 0.575031i \(0.195010\pi\)
\(152\) 0 0
\(153\) 22.5345 1.82181
\(154\) 0 0
\(155\) −9.33485 −0.749793
\(156\) 0 0
\(157\) 5.44888 0.434868 0.217434 0.976075i \(-0.430231\pi\)
0.217434 + 0.976075i \(0.430231\pi\)
\(158\) 0 0
\(159\) −0.454338 −0.0360313
\(160\) 0 0
\(161\) 3.71789 0.293011
\(162\) 0 0
\(163\) −3.33546 −0.261253 −0.130627 0.991432i \(-0.541699\pi\)
−0.130627 + 0.991432i \(0.541699\pi\)
\(164\) 0 0
\(165\) 0.143158 0.0111449
\(166\) 0 0
\(167\) −17.6360 −1.36471 −0.682356 0.731020i \(-0.739045\pi\)
−0.682356 + 0.731020i \(0.739045\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −22.7286 −1.73810
\(172\) 0 0
\(173\) −17.9723 −1.36641 −0.683204 0.730227i \(-0.739414\pi\)
−0.683204 + 0.730227i \(0.739414\pi\)
\(174\) 0 0
\(175\) 2.78889 0.210820
\(176\) 0 0
\(177\) −0.483113 −0.0363130
\(178\) 0 0
\(179\) 10.5233 0.786547 0.393273 0.919422i \(-0.371343\pi\)
0.393273 + 0.919422i \(0.371343\pi\)
\(180\) 0 0
\(181\) −5.25277 −0.390436 −0.195218 0.980760i \(-0.562541\pi\)
−0.195218 + 0.980760i \(0.562541\pi\)
\(182\) 0 0
\(183\) −0.352165 −0.0260328
\(184\) 0 0
\(185\) −1.45181 −0.106739
\(186\) 0 0
\(187\) 7.53478 0.550997
\(188\) 0 0
\(189\) 0.576755 0.0419527
\(190\) 0 0
\(191\) 11.5412 0.835091 0.417545 0.908656i \(-0.362890\pi\)
0.417545 + 0.908656i \(0.362890\pi\)
\(192\) 0 0
\(193\) 0.170184 0.0122501 0.00612505 0.999981i \(-0.498050\pi\)
0.00612505 + 0.999981i \(0.498050\pi\)
\(194\) 0 0
\(195\) 0.143158 0.0102518
\(196\) 0 0
\(197\) −27.4451 −1.95538 −0.977691 0.210047i \(-0.932638\pi\)
−0.977691 + 0.210047i \(0.932638\pi\)
\(198\) 0 0
\(199\) −13.2838 −0.941664 −0.470832 0.882223i \(-0.656046\pi\)
−0.470832 + 0.882223i \(0.656046\pi\)
\(200\) 0 0
\(201\) 0.527422 0.0372015
\(202\) 0 0
\(203\) 9.29580 0.652437
\(204\) 0 0
\(205\) −6.30609 −0.440436
\(206\) 0 0
\(207\) 11.1192 0.772838
\(208\) 0 0
\(209\) −7.59969 −0.525682
\(210\) 0 0
\(211\) 4.47275 0.307917 0.153958 0.988077i \(-0.450798\pi\)
0.153958 + 0.988077i \(0.450798\pi\)
\(212\) 0 0
\(213\) −0.962190 −0.0659281
\(214\) 0 0
\(215\) −17.6921 −1.20659
\(216\) 0 0
\(217\) −6.27772 −0.426160
\(218\) 0 0
\(219\) 0.772444 0.0521969
\(220\) 0 0
\(221\) 7.53478 0.506844
\(222\) 0 0
\(223\) −16.6613 −1.11573 −0.557863 0.829933i \(-0.688378\pi\)
−0.557863 + 0.829933i \(0.688378\pi\)
\(224\) 0 0
\(225\) 8.34082 0.556055
\(226\) 0 0
\(227\) 27.9568 1.85556 0.927779 0.373130i \(-0.121716\pi\)
0.927779 + 0.373130i \(0.121716\pi\)
\(228\) 0 0
\(229\) 9.91041 0.654898 0.327449 0.944869i \(-0.393811\pi\)
0.327449 + 0.944869i \(0.393811\pi\)
\(230\) 0 0
\(231\) 0.0962745 0.00633440
\(232\) 0 0
\(233\) −13.0561 −0.855334 −0.427667 0.903936i \(-0.640664\pi\)
−0.427667 + 0.903936i \(0.640664\pi\)
\(234\) 0 0
\(235\) −19.1835 −1.25139
\(236\) 0 0
\(237\) 0.208668 0.0135544
\(238\) 0 0
\(239\) 14.8509 0.960623 0.480311 0.877098i \(-0.340524\pi\)
0.480311 + 0.877098i \(0.340524\pi\)
\(240\) 0 0
\(241\) 5.60632 0.361135 0.180567 0.983563i \(-0.442207\pi\)
0.180567 + 0.983563i \(0.442207\pi\)
\(242\) 0 0
\(243\) 2.58871 0.166066
\(244\) 0 0
\(245\) −1.48698 −0.0949997
\(246\) 0 0
\(247\) −7.59969 −0.483557
\(248\) 0 0
\(249\) −1.16246 −0.0736682
\(250\) 0 0
\(251\) 6.74971 0.426038 0.213019 0.977048i \(-0.431670\pi\)
0.213019 + 0.977048i \(0.431670\pi\)
\(252\) 0 0
\(253\) 3.71789 0.233742
\(254\) 0 0
\(255\) 1.07867 0.0675486
\(256\) 0 0
\(257\) −15.1654 −0.945992 −0.472996 0.881065i \(-0.656828\pi\)
−0.472996 + 0.881065i \(0.656828\pi\)
\(258\) 0 0
\(259\) −0.976345 −0.0606672
\(260\) 0 0
\(261\) 27.8012 1.72085
\(262\) 0 0
\(263\) 18.9930 1.17116 0.585578 0.810616i \(-0.300867\pi\)
0.585578 + 0.810616i \(0.300867\pi\)
\(264\) 0 0
\(265\) 7.01735 0.431072
\(266\) 0 0
\(267\) 1.16842 0.0715063
\(268\) 0 0
\(269\) 26.4136 1.61046 0.805231 0.592961i \(-0.202041\pi\)
0.805231 + 0.592961i \(0.202041\pi\)
\(270\) 0 0
\(271\) −13.3654 −0.811888 −0.405944 0.913898i \(-0.633057\pi\)
−0.405944 + 0.913898i \(0.633057\pi\)
\(272\) 0 0
\(273\) 0.0962745 0.00582680
\(274\) 0 0
\(275\) 2.78889 0.168176
\(276\) 0 0
\(277\) 31.7062 1.90504 0.952521 0.304473i \(-0.0984802\pi\)
0.952521 + 0.304473i \(0.0984802\pi\)
\(278\) 0 0
\(279\) −18.7750 −1.12403
\(280\) 0 0
\(281\) −14.7863 −0.882074 −0.441037 0.897489i \(-0.645389\pi\)
−0.441037 + 0.897489i \(0.645389\pi\)
\(282\) 0 0
\(283\) −27.6881 −1.64589 −0.822943 0.568124i \(-0.807669\pi\)
−0.822943 + 0.568124i \(0.807669\pi\)
\(284\) 0 0
\(285\) −1.08796 −0.0644451
\(286\) 0 0
\(287\) −4.24087 −0.250331
\(288\) 0 0
\(289\) 39.7729 2.33958
\(290\) 0 0
\(291\) −0.886590 −0.0519728
\(292\) 0 0
\(293\) 2.36339 0.138071 0.0690355 0.997614i \(-0.478008\pi\)
0.0690355 + 0.997614i \(0.478008\pi\)
\(294\) 0 0
\(295\) 7.46178 0.434442
\(296\) 0 0
\(297\) 0.576755 0.0334667
\(298\) 0 0
\(299\) 3.71789 0.215011
\(300\) 0 0
\(301\) −11.8980 −0.685792
\(302\) 0 0
\(303\) 0.477337 0.0274223
\(304\) 0 0
\(305\) 5.43927 0.311452
\(306\) 0 0
\(307\) 11.1239 0.634875 0.317438 0.948279i \(-0.397178\pi\)
0.317438 + 0.948279i \(0.397178\pi\)
\(308\) 0 0
\(309\) −0.0223760 −0.00127293
\(310\) 0 0
\(311\) 7.39075 0.419091 0.209546 0.977799i \(-0.432802\pi\)
0.209546 + 0.977799i \(0.432802\pi\)
\(312\) 0 0
\(313\) 18.1279 1.02465 0.512325 0.858792i \(-0.328784\pi\)
0.512325 + 0.858792i \(0.328784\pi\)
\(314\) 0 0
\(315\) −4.44716 −0.250569
\(316\) 0 0
\(317\) 11.9342 0.670293 0.335147 0.942166i \(-0.391214\pi\)
0.335147 + 0.942166i \(0.391214\pi\)
\(318\) 0 0
\(319\) 9.29580 0.520465
\(320\) 0 0
\(321\) 0.243483 0.0135899
\(322\) 0 0
\(323\) −57.2620 −3.18614
\(324\) 0 0
\(325\) 2.78889 0.154700
\(326\) 0 0
\(327\) 0.119068 0.00658450
\(328\) 0 0
\(329\) −12.9010 −0.711254
\(330\) 0 0
\(331\) −27.7216 −1.52372 −0.761858 0.647744i \(-0.775713\pi\)
−0.761858 + 0.647744i \(0.775713\pi\)
\(332\) 0 0
\(333\) −2.91999 −0.160014
\(334\) 0 0
\(335\) −8.14614 −0.445071
\(336\) 0 0
\(337\) −14.3079 −0.779400 −0.389700 0.920942i \(-0.627421\pi\)
−0.389700 + 0.920942i \(0.627421\pi\)
\(338\) 0 0
\(339\) −0.453738 −0.0246437
\(340\) 0 0
\(341\) −6.27772 −0.339958
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0.532246 0.0286552
\(346\) 0 0
\(347\) 19.2795 1.03498 0.517489 0.855690i \(-0.326867\pi\)
0.517489 + 0.855690i \(0.326867\pi\)
\(348\) 0 0
\(349\) −9.55297 −0.511359 −0.255679 0.966762i \(-0.582299\pi\)
−0.255679 + 0.966762i \(0.582299\pi\)
\(350\) 0 0
\(351\) 0.576755 0.0307849
\(352\) 0 0
\(353\) 13.4085 0.713664 0.356832 0.934169i \(-0.383857\pi\)
0.356832 + 0.934169i \(0.383857\pi\)
\(354\) 0 0
\(355\) 14.8612 0.788752
\(356\) 0 0
\(357\) 0.725407 0.0383926
\(358\) 0 0
\(359\) 30.0564 1.58632 0.793159 0.609014i \(-0.208435\pi\)
0.793159 + 0.609014i \(0.208435\pi\)
\(360\) 0 0
\(361\) 38.7553 2.03975
\(362\) 0 0
\(363\) 0.0962745 0.00505310
\(364\) 0 0
\(365\) −11.9306 −0.624474
\(366\) 0 0
\(367\) −1.13021 −0.0589963 −0.0294982 0.999565i \(-0.509391\pi\)
−0.0294982 + 0.999565i \(0.509391\pi\)
\(368\) 0 0
\(369\) −12.6833 −0.660266
\(370\) 0 0
\(371\) 4.71919 0.245008
\(372\) 0 0
\(373\) −24.2307 −1.25462 −0.627309 0.778770i \(-0.715844\pi\)
−0.627309 + 0.778770i \(0.715844\pi\)
\(374\) 0 0
\(375\) 1.11504 0.0575806
\(376\) 0 0
\(377\) 9.29580 0.478758
\(378\) 0 0
\(379\) −14.5563 −0.747705 −0.373852 0.927488i \(-0.621963\pi\)
−0.373852 + 0.927488i \(0.621963\pi\)
\(380\) 0 0
\(381\) 1.98696 0.101795
\(382\) 0 0
\(383\) 10.1806 0.520202 0.260101 0.965581i \(-0.416244\pi\)
0.260101 + 0.965581i \(0.416244\pi\)
\(384\) 0 0
\(385\) −1.48698 −0.0757835
\(386\) 0 0
\(387\) −35.5838 −1.80883
\(388\) 0 0
\(389\) 0.101396 0.00514100 0.00257050 0.999997i \(-0.499182\pi\)
0.00257050 + 0.999997i \(0.499182\pi\)
\(390\) 0 0
\(391\) 28.0134 1.41670
\(392\) 0 0
\(393\) −0.138367 −0.00697970
\(394\) 0 0
\(395\) −3.22292 −0.162163
\(396\) 0 0
\(397\) −32.8536 −1.64888 −0.824438 0.565953i \(-0.808508\pi\)
−0.824438 + 0.565953i \(0.808508\pi\)
\(398\) 0 0
\(399\) −0.731656 −0.0366286
\(400\) 0 0
\(401\) −22.2263 −1.10993 −0.554964 0.831874i \(-0.687268\pi\)
−0.554964 + 0.831874i \(0.687268\pi\)
\(402\) 0 0
\(403\) −6.27772 −0.312716
\(404\) 0 0
\(405\) −13.2589 −0.658840
\(406\) 0 0
\(407\) −0.976345 −0.0483956
\(408\) 0 0
\(409\) 7.74445 0.382939 0.191469 0.981499i \(-0.438675\pi\)
0.191469 + 0.981499i \(0.438675\pi\)
\(410\) 0 0
\(411\) 2.10900 0.104029
\(412\) 0 0
\(413\) 5.01808 0.246923
\(414\) 0 0
\(415\) 17.9545 0.881352
\(416\) 0 0
\(417\) −0.417068 −0.0204239
\(418\) 0 0
\(419\) 32.4417 1.58488 0.792440 0.609950i \(-0.208811\pi\)
0.792440 + 0.609950i \(0.208811\pi\)
\(420\) 0 0
\(421\) −27.2537 −1.32827 −0.664133 0.747614i \(-0.731199\pi\)
−0.664133 + 0.747614i \(0.731199\pi\)
\(422\) 0 0
\(423\) −38.5834 −1.87599
\(424\) 0 0
\(425\) 21.0137 1.01931
\(426\) 0 0
\(427\) 3.65793 0.177020
\(428\) 0 0
\(429\) 0.0962745 0.00464818
\(430\) 0 0
\(431\) 21.3245 1.02716 0.513582 0.858040i \(-0.328318\pi\)
0.513582 + 0.858040i \(0.328318\pi\)
\(432\) 0 0
\(433\) −1.57252 −0.0755706 −0.0377853 0.999286i \(-0.512030\pi\)
−0.0377853 + 0.999286i \(0.512030\pi\)
\(434\) 0 0
\(435\) 1.33077 0.0638055
\(436\) 0 0
\(437\) −28.2548 −1.35161
\(438\) 0 0
\(439\) −25.4666 −1.21546 −0.607728 0.794145i \(-0.707919\pi\)
−0.607728 + 0.794145i \(0.707919\pi\)
\(440\) 0 0
\(441\) −2.99073 −0.142416
\(442\) 0 0
\(443\) 34.9443 1.66025 0.830126 0.557576i \(-0.188268\pi\)
0.830126 + 0.557576i \(0.188268\pi\)
\(444\) 0 0
\(445\) −18.0465 −0.855488
\(446\) 0 0
\(447\) 1.19811 0.0566685
\(448\) 0 0
\(449\) 21.6772 1.02301 0.511505 0.859281i \(-0.329088\pi\)
0.511505 + 0.859281i \(0.329088\pi\)
\(450\) 0 0
\(451\) −4.24087 −0.199695
\(452\) 0 0
\(453\) 1.93577 0.0909502
\(454\) 0 0
\(455\) −1.48698 −0.0697107
\(456\) 0 0
\(457\) −13.2417 −0.619418 −0.309709 0.950831i \(-0.600232\pi\)
−0.309709 + 0.950831i \(0.600232\pi\)
\(458\) 0 0
\(459\) 4.34572 0.202841
\(460\) 0 0
\(461\) 37.1588 1.73066 0.865328 0.501206i \(-0.167110\pi\)
0.865328 + 0.501206i \(0.167110\pi\)
\(462\) 0 0
\(463\) −0.624236 −0.0290107 −0.0145054 0.999895i \(-0.504617\pi\)
−0.0145054 + 0.999895i \(0.504617\pi\)
\(464\) 0 0
\(465\) −0.898708 −0.0416766
\(466\) 0 0
\(467\) −4.53216 −0.209723 −0.104862 0.994487i \(-0.533440\pi\)
−0.104862 + 0.994487i \(0.533440\pi\)
\(468\) 0 0
\(469\) −5.47832 −0.252965
\(470\) 0 0
\(471\) 0.524588 0.0241717
\(472\) 0 0
\(473\) −11.8980 −0.547072
\(474\) 0 0
\(475\) −21.1947 −0.972480
\(476\) 0 0
\(477\) 14.1138 0.646228
\(478\) 0 0
\(479\) −22.2480 −1.01654 −0.508269 0.861199i \(-0.669714\pi\)
−0.508269 + 0.861199i \(0.669714\pi\)
\(480\) 0 0
\(481\) −0.976345 −0.0445175
\(482\) 0 0
\(483\) 0.357938 0.0162867
\(484\) 0 0
\(485\) 13.6936 0.621793
\(486\) 0 0
\(487\) −9.46077 −0.428709 −0.214354 0.976756i \(-0.568765\pi\)
−0.214354 + 0.976756i \(0.568765\pi\)
\(488\) 0 0
\(489\) −0.321119 −0.0145215
\(490\) 0 0
\(491\) 24.2146 1.09279 0.546394 0.837528i \(-0.316000\pi\)
0.546394 + 0.837528i \(0.316000\pi\)
\(492\) 0 0
\(493\) 70.0418 3.15452
\(494\) 0 0
\(495\) −4.44716 −0.199885
\(496\) 0 0
\(497\) 9.99423 0.448303
\(498\) 0 0
\(499\) 31.3417 1.40305 0.701523 0.712646i \(-0.252504\pi\)
0.701523 + 0.712646i \(0.252504\pi\)
\(500\) 0 0
\(501\) −1.69789 −0.0758563
\(502\) 0 0
\(503\) −33.5662 −1.49664 −0.748322 0.663335i \(-0.769140\pi\)
−0.748322 + 0.663335i \(0.769140\pi\)
\(504\) 0 0
\(505\) −7.37258 −0.328075
\(506\) 0 0
\(507\) 0.0962745 0.00427570
\(508\) 0 0
\(509\) −15.5318 −0.688436 −0.344218 0.938890i \(-0.611856\pi\)
−0.344218 + 0.938890i \(0.611856\pi\)
\(510\) 0 0
\(511\) −8.02335 −0.354932
\(512\) 0 0
\(513\) −4.38316 −0.193521
\(514\) 0 0
\(515\) 0.345602 0.0152290
\(516\) 0 0
\(517\) −12.9010 −0.567385
\(518\) 0 0
\(519\) −1.73027 −0.0759506
\(520\) 0 0
\(521\) −27.3683 −1.19903 −0.599514 0.800364i \(-0.704640\pi\)
−0.599514 + 0.800364i \(0.704640\pi\)
\(522\) 0 0
\(523\) −7.82671 −0.342238 −0.171119 0.985250i \(-0.554738\pi\)
−0.171119 + 0.985250i \(0.554738\pi\)
\(524\) 0 0
\(525\) 0.268499 0.0117183
\(526\) 0 0
\(527\) −47.3013 −2.06047
\(528\) 0 0
\(529\) −9.17732 −0.399014
\(530\) 0 0
\(531\) 15.0077 0.651280
\(532\) 0 0
\(533\) −4.24087 −0.183692
\(534\) 0 0
\(535\) −3.76064 −0.162587
\(536\) 0 0
\(537\) 1.01312 0.0437195
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −6.75618 −0.290471 −0.145235 0.989397i \(-0.546394\pi\)
−0.145235 + 0.989397i \(0.546394\pi\)
\(542\) 0 0
\(543\) −0.505708 −0.0217020
\(544\) 0 0
\(545\) −1.83904 −0.0787757
\(546\) 0 0
\(547\) −24.9014 −1.06471 −0.532354 0.846522i \(-0.678692\pi\)
−0.532354 + 0.846522i \(0.678692\pi\)
\(548\) 0 0
\(549\) 10.9399 0.466903
\(550\) 0 0
\(551\) −70.6452 −3.00959
\(552\) 0 0
\(553\) −2.16743 −0.0921684
\(554\) 0 0
\(555\) −0.139772 −0.00593299
\(556\) 0 0
\(557\) 30.6165 1.29726 0.648632 0.761102i \(-0.275341\pi\)
0.648632 + 0.761102i \(0.275341\pi\)
\(558\) 0 0
\(559\) −11.8980 −0.503233
\(560\) 0 0
\(561\) 0.725407 0.0306267
\(562\) 0 0
\(563\) 3.43712 0.144857 0.0724286 0.997374i \(-0.476925\pi\)
0.0724286 + 0.997374i \(0.476925\pi\)
\(564\) 0 0
\(565\) 7.00808 0.294832
\(566\) 0 0
\(567\) −8.91667 −0.374465
\(568\) 0 0
\(569\) −7.77965 −0.326140 −0.163070 0.986615i \(-0.552140\pi\)
−0.163070 + 0.986615i \(0.552140\pi\)
\(570\) 0 0
\(571\) 44.9038 1.87916 0.939582 0.342324i \(-0.111214\pi\)
0.939582 + 0.342324i \(0.111214\pi\)
\(572\) 0 0
\(573\) 1.11112 0.0464178
\(574\) 0 0
\(575\) 10.3688 0.432408
\(576\) 0 0
\(577\) 4.01254 0.167044 0.0835221 0.996506i \(-0.473383\pi\)
0.0835221 + 0.996506i \(0.473383\pi\)
\(578\) 0 0
\(579\) 0.0163844 0.000680911 0
\(580\) 0 0
\(581\) 12.0745 0.500934
\(582\) 0 0
\(583\) 4.71919 0.195449
\(584\) 0 0
\(585\) −4.44716 −0.183867
\(586\) 0 0
\(587\) 37.6248 1.55294 0.776471 0.630152i \(-0.217008\pi\)
0.776471 + 0.630152i \(0.217008\pi\)
\(588\) 0 0
\(589\) 47.7088 1.96581
\(590\) 0 0
\(591\) −2.64226 −0.108688
\(592\) 0 0
\(593\) 35.3853 1.45310 0.726551 0.687113i \(-0.241122\pi\)
0.726551 + 0.687113i \(0.241122\pi\)
\(594\) 0 0
\(595\) −11.2041 −0.459322
\(596\) 0 0
\(597\) −1.27889 −0.0523415
\(598\) 0 0
\(599\) −19.7877 −0.808503 −0.404252 0.914648i \(-0.632468\pi\)
−0.404252 + 0.914648i \(0.632468\pi\)
\(600\) 0 0
\(601\) 3.93876 0.160666 0.0803328 0.996768i \(-0.474402\pi\)
0.0803328 + 0.996768i \(0.474402\pi\)
\(602\) 0 0
\(603\) −16.3842 −0.667215
\(604\) 0 0
\(605\) −1.48698 −0.0604543
\(606\) 0 0
\(607\) 46.0332 1.86843 0.934215 0.356711i \(-0.116102\pi\)
0.934215 + 0.356711i \(0.116102\pi\)
\(608\) 0 0
\(609\) 0.894948 0.0362651
\(610\) 0 0
\(611\) −12.9010 −0.521918
\(612\) 0 0
\(613\) −4.74471 −0.191637 −0.0958186 0.995399i \(-0.530547\pi\)
−0.0958186 + 0.995399i \(0.530547\pi\)
\(614\) 0 0
\(615\) −0.607115 −0.0244812
\(616\) 0 0
\(617\) −12.5014 −0.503289 −0.251645 0.967820i \(-0.580971\pi\)
−0.251645 + 0.967820i \(0.580971\pi\)
\(618\) 0 0
\(619\) 1.53170 0.0615644 0.0307822 0.999526i \(-0.490200\pi\)
0.0307822 + 0.999526i \(0.490200\pi\)
\(620\) 0 0
\(621\) 2.14431 0.0860481
\(622\) 0 0
\(623\) −12.1364 −0.486233
\(624\) 0 0
\(625\) −3.27763 −0.131105
\(626\) 0 0
\(627\) −0.731656 −0.0292195
\(628\) 0 0
\(629\) −7.35655 −0.293325
\(630\) 0 0
\(631\) −17.9627 −0.715083 −0.357542 0.933897i \(-0.616385\pi\)
−0.357542 + 0.933897i \(0.616385\pi\)
\(632\) 0 0
\(633\) 0.430612 0.0171153
\(634\) 0 0
\(635\) −30.6890 −1.21785
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 29.8901 1.18243
\(640\) 0 0
\(641\) −22.6689 −0.895367 −0.447683 0.894192i \(-0.647751\pi\)
−0.447683 + 0.894192i \(0.647751\pi\)
\(642\) 0 0
\(643\) −9.22386 −0.363753 −0.181877 0.983321i \(-0.558217\pi\)
−0.181877 + 0.983321i \(0.558217\pi\)
\(644\) 0 0
\(645\) −1.70330 −0.0670675
\(646\) 0 0
\(647\) −32.0275 −1.25913 −0.629566 0.776947i \(-0.716767\pi\)
−0.629566 + 0.776947i \(0.716767\pi\)
\(648\) 0 0
\(649\) 5.01808 0.196977
\(650\) 0 0
\(651\) −0.604385 −0.0236877
\(652\) 0 0
\(653\) −22.9334 −0.897452 −0.448726 0.893669i \(-0.648122\pi\)
−0.448726 + 0.893669i \(0.648122\pi\)
\(654\) 0 0
\(655\) 2.13711 0.0835037
\(656\) 0 0
\(657\) −23.9957 −0.936161
\(658\) 0 0
\(659\) 27.1761 1.05863 0.529316 0.848425i \(-0.322449\pi\)
0.529316 + 0.848425i \(0.322449\pi\)
\(660\) 0 0
\(661\) 30.0555 1.16902 0.584512 0.811385i \(-0.301286\pi\)
0.584512 + 0.811385i \(0.301286\pi\)
\(662\) 0 0
\(663\) 0.725407 0.0281725
\(664\) 0 0
\(665\) 11.3006 0.438218
\(666\) 0 0
\(667\) 34.5607 1.33820
\(668\) 0 0
\(669\) −1.60406 −0.0620166
\(670\) 0 0
\(671\) 3.65793 0.141213
\(672\) 0 0
\(673\) 12.1199 0.467186 0.233593 0.972334i \(-0.424952\pi\)
0.233593 + 0.972334i \(0.424952\pi\)
\(674\) 0 0
\(675\) 1.60851 0.0619114
\(676\) 0 0
\(677\) 2.61418 0.100471 0.0502356 0.998737i \(-0.484003\pi\)
0.0502356 + 0.998737i \(0.484003\pi\)
\(678\) 0 0
\(679\) 9.20899 0.353408
\(680\) 0 0
\(681\) 2.69153 0.103140
\(682\) 0 0
\(683\) −34.1398 −1.30632 −0.653161 0.757219i \(-0.726558\pi\)
−0.653161 + 0.757219i \(0.726558\pi\)
\(684\) 0 0
\(685\) −32.5739 −1.24459
\(686\) 0 0
\(687\) 0.954119 0.0364019
\(688\) 0 0
\(689\) 4.71919 0.179787
\(690\) 0 0
\(691\) 36.7273 1.39717 0.698586 0.715526i \(-0.253813\pi\)
0.698586 + 0.715526i \(0.253813\pi\)
\(692\) 0 0
\(693\) −2.99073 −0.113608
\(694\) 0 0
\(695\) 6.44170 0.244348
\(696\) 0 0
\(697\) −31.9540 −1.21034
\(698\) 0 0
\(699\) −1.25697 −0.0475429
\(700\) 0 0
\(701\) 30.5869 1.15525 0.577626 0.816301i \(-0.303979\pi\)
0.577626 + 0.816301i \(0.303979\pi\)
\(702\) 0 0
\(703\) 7.41992 0.279848
\(704\) 0 0
\(705\) −1.84688 −0.0695576
\(706\) 0 0
\(707\) −4.95809 −0.186468
\(708\) 0 0
\(709\) 22.2292 0.834836 0.417418 0.908715i \(-0.362935\pi\)
0.417418 + 0.908715i \(0.362935\pi\)
\(710\) 0 0
\(711\) −6.48219 −0.243101
\(712\) 0 0
\(713\) −23.3399 −0.874085
\(714\) 0 0
\(715\) −1.48698 −0.0556099
\(716\) 0 0
\(717\) 1.42976 0.0533953
\(718\) 0 0
\(719\) −23.0582 −0.859925 −0.429963 0.902847i \(-0.641473\pi\)
−0.429963 + 0.902847i \(0.641473\pi\)
\(720\) 0 0
\(721\) 0.232419 0.00865572
\(722\) 0 0
\(723\) 0.539745 0.0200733
\(724\) 0 0
\(725\) 25.9250 0.962829
\(726\) 0 0
\(727\) −37.1745 −1.37873 −0.689364 0.724415i \(-0.742110\pi\)
−0.689364 + 0.724415i \(0.742110\pi\)
\(728\) 0 0
\(729\) −26.5008 −0.981510
\(730\) 0 0
\(731\) −89.6491 −3.31579
\(732\) 0 0
\(733\) 22.7524 0.840380 0.420190 0.907436i \(-0.361963\pi\)
0.420190 + 0.907436i \(0.361963\pi\)
\(734\) 0 0
\(735\) −0.143158 −0.00528047
\(736\) 0 0
\(737\) −5.47832 −0.201796
\(738\) 0 0
\(739\) −21.0686 −0.775020 −0.387510 0.921866i \(-0.626665\pi\)
−0.387510 + 0.921866i \(0.626665\pi\)
\(740\) 0 0
\(741\) −0.731656 −0.0268781
\(742\) 0 0
\(743\) −41.6490 −1.52795 −0.763976 0.645244i \(-0.776756\pi\)
−0.763976 + 0.645244i \(0.776756\pi\)
\(744\) 0 0
\(745\) −18.5050 −0.677972
\(746\) 0 0
\(747\) 36.1115 1.32125
\(748\) 0 0
\(749\) −2.52905 −0.0924093
\(750\) 0 0
\(751\) −0.399650 −0.0145834 −0.00729171 0.999973i \(-0.502321\pi\)
−0.00729171 + 0.999973i \(0.502321\pi\)
\(752\) 0 0
\(753\) 0.649825 0.0236809
\(754\) 0 0
\(755\) −29.8983 −1.08811
\(756\) 0 0
\(757\) 32.1194 1.16740 0.583699 0.811970i \(-0.301605\pi\)
0.583699 + 0.811970i \(0.301605\pi\)
\(758\) 0 0
\(759\) 0.357938 0.0129923
\(760\) 0 0
\(761\) −28.5139 −1.03363 −0.516815 0.856097i \(-0.672882\pi\)
−0.516815 + 0.856097i \(0.672882\pi\)
\(762\) 0 0
\(763\) −1.23676 −0.0447737
\(764\) 0 0
\(765\) −33.5083 −1.21150
\(766\) 0 0
\(767\) 5.01808 0.181192
\(768\) 0 0
\(769\) 0.500827 0.0180603 0.00903014 0.999959i \(-0.497126\pi\)
0.00903014 + 0.999959i \(0.497126\pi\)
\(770\) 0 0
\(771\) −1.46004 −0.0525821
\(772\) 0 0
\(773\) −25.6976 −0.924277 −0.462138 0.886808i \(-0.652918\pi\)
−0.462138 + 0.886808i \(0.652918\pi\)
\(774\) 0 0
\(775\) −17.5079 −0.628902
\(776\) 0 0
\(777\) −0.0939972 −0.00337213
\(778\) 0 0
\(779\) 32.2293 1.15473
\(780\) 0 0
\(781\) 9.99423 0.357622
\(782\) 0 0
\(783\) 5.36140 0.191601
\(784\) 0 0
\(785\) −8.10237 −0.289186
\(786\) 0 0
\(787\) −26.7939 −0.955100 −0.477550 0.878605i \(-0.658475\pi\)
−0.477550 + 0.878605i \(0.658475\pi\)
\(788\) 0 0
\(789\) 1.82854 0.0650977
\(790\) 0 0
\(791\) 4.71296 0.167574
\(792\) 0 0
\(793\) 3.65793 0.129897
\(794\) 0 0
\(795\) 0.675591 0.0239608
\(796\) 0 0
\(797\) −24.6618 −0.873567 −0.436784 0.899567i \(-0.643882\pi\)
−0.436784 + 0.899567i \(0.643882\pi\)
\(798\) 0 0
\(799\) −97.2061 −3.43890
\(800\) 0 0
\(801\) −36.2966 −1.28248
\(802\) 0 0
\(803\) −8.02335 −0.283138
\(804\) 0 0
\(805\) −5.52842 −0.194851
\(806\) 0 0
\(807\) 2.54295 0.0895161
\(808\) 0 0
\(809\) 13.7534 0.483542 0.241771 0.970333i \(-0.422272\pi\)
0.241771 + 0.970333i \(0.422272\pi\)
\(810\) 0 0
\(811\) −7.54296 −0.264869 −0.132435 0.991192i \(-0.542279\pi\)
−0.132435 + 0.991192i \(0.542279\pi\)
\(812\) 0 0
\(813\) −1.28674 −0.0451280
\(814\) 0 0
\(815\) 4.95975 0.173733
\(816\) 0 0
\(817\) 90.4214 3.16345
\(818\) 0 0
\(819\) −2.99073 −0.104505
\(820\) 0 0
\(821\) −26.8612 −0.937461 −0.468730 0.883341i \(-0.655288\pi\)
−0.468730 + 0.883341i \(0.655288\pi\)
\(822\) 0 0
\(823\) −49.5461 −1.72707 −0.863534 0.504290i \(-0.831754\pi\)
−0.863534 + 0.504290i \(0.831754\pi\)
\(824\) 0 0
\(825\) 0.268499 0.00934794
\(826\) 0 0
\(827\) 17.0075 0.591407 0.295704 0.955280i \(-0.404446\pi\)
0.295704 + 0.955280i \(0.404446\pi\)
\(828\) 0 0
\(829\) −4.12070 −0.143118 −0.0715589 0.997436i \(-0.522797\pi\)
−0.0715589 + 0.997436i \(0.522797\pi\)
\(830\) 0 0
\(831\) 3.05250 0.105890
\(832\) 0 0
\(833\) −7.53478 −0.261065
\(834\) 0 0
\(835\) 26.2243 0.907530
\(836\) 0 0
\(837\) −3.62071 −0.125150
\(838\) 0 0
\(839\) −24.9638 −0.861846 −0.430923 0.902389i \(-0.641812\pi\)
−0.430923 + 0.902389i \(0.641812\pi\)
\(840\) 0 0
\(841\) 57.4119 1.97972
\(842\) 0 0
\(843\) −1.42354 −0.0490293
\(844\) 0 0
\(845\) −1.48698 −0.0511537
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −2.66566 −0.0914851
\(850\) 0 0
\(851\) −3.62994 −0.124433
\(852\) 0 0
\(853\) 8.42469 0.288456 0.144228 0.989544i \(-0.453930\pi\)
0.144228 + 0.989544i \(0.453930\pi\)
\(854\) 0 0
\(855\) 33.7970 1.15583
\(856\) 0 0
\(857\) −36.9461 −1.26205 −0.631027 0.775761i \(-0.717366\pi\)
−0.631027 + 0.775761i \(0.717366\pi\)
\(858\) 0 0
\(859\) 52.5551 1.79316 0.896579 0.442884i \(-0.146045\pi\)
0.896579 + 0.442884i \(0.146045\pi\)
\(860\) 0 0
\(861\) −0.408287 −0.0139144
\(862\) 0 0
\(863\) 53.4110 1.81813 0.909066 0.416653i \(-0.136797\pi\)
0.909066 + 0.416653i \(0.136797\pi\)
\(864\) 0 0
\(865\) 26.7244 0.908658
\(866\) 0 0
\(867\) 3.82911 0.130043
\(868\) 0 0
\(869\) −2.16743 −0.0735249
\(870\) 0 0
\(871\) −5.47832 −0.185626
\(872\) 0 0
\(873\) 27.5416 0.932142
\(874\) 0 0
\(875\) −11.5819 −0.391540
\(876\) 0 0
\(877\) −45.8164 −1.54711 −0.773556 0.633728i \(-0.781524\pi\)
−0.773556 + 0.633728i \(0.781524\pi\)
\(878\) 0 0
\(879\) 0.227535 0.00767455
\(880\) 0 0
\(881\) −45.1659 −1.52168 −0.760839 0.648941i \(-0.775212\pi\)
−0.760839 + 0.648941i \(0.775212\pi\)
\(882\) 0 0
\(883\) −4.93907 −0.166213 −0.0831064 0.996541i \(-0.526484\pi\)
−0.0831064 + 0.996541i \(0.526484\pi\)
\(884\) 0 0
\(885\) 0.718379 0.0241480
\(886\) 0 0
\(887\) 56.1806 1.88636 0.943179 0.332284i \(-0.107819\pi\)
0.943179 + 0.332284i \(0.107819\pi\)
\(888\) 0 0
\(889\) −20.6384 −0.692191
\(890\) 0 0
\(891\) −8.91667 −0.298720
\(892\) 0 0
\(893\) 98.0435 3.28090
\(894\) 0 0
\(895\) −15.6479 −0.523052
\(896\) 0 0
\(897\) 0.357938 0.0119512
\(898\) 0 0
\(899\) −58.3565 −1.94630
\(900\) 0 0
\(901\) 35.5581 1.18461
\(902\) 0 0
\(903\) −1.14548 −0.0381191
\(904\) 0 0
\(905\) 7.81077 0.259639
\(906\) 0 0
\(907\) −0.175012 −0.00581117 −0.00290559 0.999996i \(-0.500925\pi\)
−0.00290559 + 0.999996i \(0.500925\pi\)
\(908\) 0 0
\(909\) −14.8283 −0.491824
\(910\) 0 0
\(911\) −28.3521 −0.939348 −0.469674 0.882840i \(-0.655628\pi\)
−0.469674 + 0.882840i \(0.655628\pi\)
\(912\) 0 0
\(913\) 12.0745 0.399607
\(914\) 0 0
\(915\) 0.523663 0.0173118
\(916\) 0 0
\(917\) 1.43721 0.0474610
\(918\) 0 0
\(919\) −11.6918 −0.385676 −0.192838 0.981231i \(-0.561769\pi\)
−0.192838 + 0.981231i \(0.561769\pi\)
\(920\) 0 0
\(921\) 1.07095 0.0352890
\(922\) 0 0
\(923\) 9.99423 0.328964
\(924\) 0 0
\(925\) −2.72292 −0.0895291
\(926\) 0 0
\(927\) 0.695102 0.0228301
\(928\) 0 0
\(929\) 17.3318 0.568639 0.284320 0.958730i \(-0.408232\pi\)
0.284320 + 0.958730i \(0.408232\pi\)
\(930\) 0 0
\(931\) 7.59969 0.249070
\(932\) 0 0
\(933\) 0.711541 0.0232948
\(934\) 0 0
\(935\) −11.2041 −0.366412
\(936\) 0 0
\(937\) 31.4827 1.02849 0.514247 0.857642i \(-0.328072\pi\)
0.514247 + 0.857642i \(0.328072\pi\)
\(938\) 0 0
\(939\) 1.74526 0.0569543
\(940\) 0 0
\(941\) −33.6213 −1.09602 −0.548011 0.836471i \(-0.684615\pi\)
−0.548011 + 0.836471i \(0.684615\pi\)
\(942\) 0 0
\(943\) −15.7671 −0.513446
\(944\) 0 0
\(945\) −0.857622 −0.0278985
\(946\) 0 0
\(947\) 24.1792 0.785720 0.392860 0.919598i \(-0.371486\pi\)
0.392860 + 0.919598i \(0.371486\pi\)
\(948\) 0 0
\(949\) −8.02335 −0.260449
\(950\) 0 0
\(951\) 1.14896 0.0372576
\(952\) 0 0
\(953\) −18.3155 −0.593297 −0.296649 0.954987i \(-0.595869\pi\)
−0.296649 + 0.954987i \(0.595869\pi\)
\(954\) 0 0
\(955\) −17.1615 −0.555333
\(956\) 0 0
\(957\) 0.894948 0.0289296
\(958\) 0 0
\(959\) −21.9061 −0.707385
\(960\) 0 0
\(961\) 8.40982 0.271284
\(962\) 0 0
\(963\) −7.56370 −0.243737
\(964\) 0 0
\(965\) −0.253060 −0.00814629
\(966\) 0 0
\(967\) 25.0244 0.804731 0.402365 0.915479i \(-0.368188\pi\)
0.402365 + 0.915479i \(0.368188\pi\)
\(968\) 0 0
\(969\) −5.51287 −0.177099
\(970\) 0 0
\(971\) 8.74207 0.280547 0.140273 0.990113i \(-0.455202\pi\)
0.140273 + 0.990113i \(0.455202\pi\)
\(972\) 0 0
\(973\) 4.33207 0.138880
\(974\) 0 0
\(975\) 0.268499 0.00859885
\(976\) 0 0
\(977\) −4.82118 −0.154243 −0.0771216 0.997022i \(-0.524573\pi\)
−0.0771216 + 0.997022i \(0.524573\pi\)
\(978\) 0 0
\(979\) −12.1364 −0.387880
\(980\) 0 0
\(981\) −3.69882 −0.118094
\(982\) 0 0
\(983\) 1.55814 0.0496968 0.0248484 0.999691i \(-0.492090\pi\)
0.0248484 + 0.999691i \(0.492090\pi\)
\(984\) 0 0
\(985\) 40.8103 1.30032
\(986\) 0 0
\(987\) −1.24204 −0.0395344
\(988\) 0 0
\(989\) −44.2356 −1.40661
\(990\) 0 0
\(991\) 23.5716 0.748776 0.374388 0.927272i \(-0.377853\pi\)
0.374388 + 0.927272i \(0.377853\pi\)
\(992\) 0 0
\(993\) −2.66888 −0.0846944
\(994\) 0 0
\(995\) 19.7527 0.626204
\(996\) 0 0
\(997\) 38.9566 1.23377 0.616884 0.787054i \(-0.288395\pi\)
0.616884 + 0.787054i \(0.288395\pi\)
\(998\) 0 0
\(999\) −0.563112 −0.0178161
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 \(a_p\))