Properties

Label 8008.2.a.n.1.2
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
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: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.00639\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.00639 q^{3} +2.62191 q^{5} -1.00000 q^{7} +6.03838 q^{9} +O(q^{10})\) \(q-3.00639 q^{3} +2.62191 q^{5} -1.00000 q^{7} +6.03838 q^{9} +1.00000 q^{11} -1.00000 q^{13} -7.88249 q^{15} -0.640640 q^{17} -5.26451 q^{19} +3.00639 q^{21} +3.73795 q^{23} +1.87442 q^{25} -9.13457 q^{27} -2.10721 q^{29} -10.8285 q^{31} -3.00639 q^{33} -2.62191 q^{35} -5.89549 q^{37} +3.00639 q^{39} +10.7215 q^{41} +2.17775 q^{43} +15.8321 q^{45} +3.39933 q^{47} +1.00000 q^{49} +1.92601 q^{51} +3.38742 q^{53} +2.62191 q^{55} +15.8272 q^{57} -3.21236 q^{59} +14.8242 q^{61} -6.03838 q^{63} -2.62191 q^{65} +7.51329 q^{67} -11.2377 q^{69} -2.60540 q^{71} -0.811910 q^{73} -5.63524 q^{75} -1.00000 q^{77} +9.43761 q^{79} +9.34693 q^{81} -16.0593 q^{83} -1.67970 q^{85} +6.33511 q^{87} -8.41905 q^{89} +1.00000 q^{91} +32.5546 q^{93} -13.8031 q^{95} +8.56933 q^{97} +6.03838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + O(q^{10}) \) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + 9q^{11} - 9q^{13} + 11q^{15} + 7q^{17} - 17q^{19} + 3q^{21} + 11q^{23} + 18q^{25} - 9q^{27} + 9q^{29} - 8q^{31} - 3q^{33} - q^{35} + 2q^{37} + 3q^{39} + 18q^{41} + 7q^{43} + 5q^{45} + 15q^{47} + 9q^{49} - 7q^{51} - 4q^{53} + q^{55} + 22q^{57} - 23q^{59} + 12q^{61} - 12q^{63} - q^{65} - 16q^{67} - 32q^{69} - 6q^{71} + 4q^{73} - 14q^{75} - 9q^{77} + 21q^{79} + 5q^{81} - 16q^{83} + 53q^{85} + 41q^{87} + 5q^{89} + 9q^{91} + 29q^{93} + 19q^{95} + 18q^{97} + 12q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.00639 −1.73574 −0.867870 0.496791i \(-0.834512\pi\)
−0.867870 + 0.496791i \(0.834512\pi\)
\(4\) 0 0
\(5\) 2.62191 1.17255 0.586277 0.810110i \(-0.300593\pi\)
0.586277 + 0.810110i \(0.300593\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 6.03838 2.01279
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −7.88249 −2.03525
\(16\) 0 0
\(17\) −0.640640 −0.155378 −0.0776890 0.996978i \(-0.524754\pi\)
−0.0776890 + 0.996978i \(0.524754\pi\)
\(18\) 0 0
\(19\) −5.26451 −1.20776 −0.603881 0.797075i \(-0.706380\pi\)
−0.603881 + 0.797075i \(0.706380\pi\)
\(20\) 0 0
\(21\) 3.00639 0.656048
\(22\) 0 0
\(23\) 3.73795 0.779416 0.389708 0.920939i \(-0.372576\pi\)
0.389708 + 0.920939i \(0.372576\pi\)
\(24\) 0 0
\(25\) 1.87442 0.374884
\(26\) 0 0
\(27\) −9.13457 −1.75795
\(28\) 0 0
\(29\) −2.10721 −0.391300 −0.195650 0.980674i \(-0.562682\pi\)
−0.195650 + 0.980674i \(0.562682\pi\)
\(30\) 0 0
\(31\) −10.8285 −1.94485 −0.972427 0.233210i \(-0.925077\pi\)
−0.972427 + 0.233210i \(0.925077\pi\)
\(32\) 0 0
\(33\) −3.00639 −0.523345
\(34\) 0 0
\(35\) −2.62191 −0.443184
\(36\) 0 0
\(37\) −5.89549 −0.969213 −0.484607 0.874732i \(-0.661037\pi\)
−0.484607 + 0.874732i \(0.661037\pi\)
\(38\) 0 0
\(39\) 3.00639 0.481408
\(40\) 0 0
\(41\) 10.7215 1.67442 0.837212 0.546879i \(-0.184184\pi\)
0.837212 + 0.546879i \(0.184184\pi\)
\(42\) 0 0
\(43\) 2.17775 0.332104 0.166052 0.986117i \(-0.446898\pi\)
0.166052 + 0.986117i \(0.446898\pi\)
\(44\) 0 0
\(45\) 15.8321 2.36011
\(46\) 0 0
\(47\) 3.39933 0.495843 0.247921 0.968780i \(-0.420253\pi\)
0.247921 + 0.968780i \(0.420253\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 1.92601 0.269696
\(52\) 0 0
\(53\) 3.38742 0.465298 0.232649 0.972561i \(-0.425261\pi\)
0.232649 + 0.972561i \(0.425261\pi\)
\(54\) 0 0
\(55\) 2.62191 0.353539
\(56\) 0 0
\(57\) 15.8272 2.09636
\(58\) 0 0
\(59\) −3.21236 −0.418213 −0.209107 0.977893i \(-0.567056\pi\)
−0.209107 + 0.977893i \(0.567056\pi\)
\(60\) 0 0
\(61\) 14.8242 1.89805 0.949024 0.315203i \(-0.102073\pi\)
0.949024 + 0.315203i \(0.102073\pi\)
\(62\) 0 0
\(63\) −6.03838 −0.760765
\(64\) 0 0
\(65\) −2.62191 −0.325208
\(66\) 0 0
\(67\) 7.51329 0.917895 0.458947 0.888463i \(-0.348227\pi\)
0.458947 + 0.888463i \(0.348227\pi\)
\(68\) 0 0
\(69\) −11.2377 −1.35286
\(70\) 0 0
\(71\) −2.60540 −0.309205 −0.154602 0.987977i \(-0.549410\pi\)
−0.154602 + 0.987977i \(0.549410\pi\)
\(72\) 0 0
\(73\) −0.811910 −0.0950269 −0.0475135 0.998871i \(-0.515130\pi\)
−0.0475135 + 0.998871i \(0.515130\pi\)
\(74\) 0 0
\(75\) −5.63524 −0.650702
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 9.43761 1.06181 0.530907 0.847430i \(-0.321851\pi\)
0.530907 + 0.847430i \(0.321851\pi\)
\(80\) 0 0
\(81\) 9.34693 1.03855
\(82\) 0 0
\(83\) −16.0593 −1.76273 −0.881367 0.472432i \(-0.843376\pi\)
−0.881367 + 0.472432i \(0.843376\pi\)
\(84\) 0 0
\(85\) −1.67970 −0.182189
\(86\) 0 0
\(87\) 6.33511 0.679195
\(88\) 0 0
\(89\) −8.41905 −0.892417 −0.446209 0.894929i \(-0.647226\pi\)
−0.446209 + 0.894929i \(0.647226\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 32.5546 3.37576
\(94\) 0 0
\(95\) −13.8031 −1.41617
\(96\) 0 0
\(97\) 8.56933 0.870084 0.435042 0.900410i \(-0.356734\pi\)
0.435042 + 0.900410i \(0.356734\pi\)
\(98\) 0 0
\(99\) 6.03838 0.606880
\(100\) 0 0
\(101\) −16.7195 −1.66365 −0.831827 0.555034i \(-0.812705\pi\)
−0.831827 + 0.555034i \(0.812705\pi\)
\(102\) 0 0
\(103\) 4.15665 0.409567 0.204784 0.978807i \(-0.434351\pi\)
0.204784 + 0.978807i \(0.434351\pi\)
\(104\) 0 0
\(105\) 7.88249 0.769252
\(106\) 0 0
\(107\) 11.7552 1.13642 0.568209 0.822884i \(-0.307636\pi\)
0.568209 + 0.822884i \(0.307636\pi\)
\(108\) 0 0
\(109\) 18.0693 1.73073 0.865363 0.501145i \(-0.167088\pi\)
0.865363 + 0.501145i \(0.167088\pi\)
\(110\) 0 0
\(111\) 17.7242 1.68230
\(112\) 0 0
\(113\) 0.147481 0.0138739 0.00693694 0.999976i \(-0.497792\pi\)
0.00693694 + 0.999976i \(0.497792\pi\)
\(114\) 0 0
\(115\) 9.80057 0.913908
\(116\) 0 0
\(117\) −6.03838 −0.558249
\(118\) 0 0
\(119\) 0.640640 0.0587273
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −32.2331 −2.90636
\(124\) 0 0
\(125\) −8.19499 −0.732982
\(126\) 0 0
\(127\) −9.12294 −0.809530 −0.404765 0.914421i \(-0.632647\pi\)
−0.404765 + 0.914421i \(0.632647\pi\)
\(128\) 0 0
\(129\) −6.54718 −0.576447
\(130\) 0 0
\(131\) 0.635495 0.0555235 0.0277617 0.999615i \(-0.491162\pi\)
0.0277617 + 0.999615i \(0.491162\pi\)
\(132\) 0 0
\(133\) 5.26451 0.456491
\(134\) 0 0
\(135\) −23.9500 −2.06129
\(136\) 0 0
\(137\) 16.6993 1.42672 0.713358 0.700799i \(-0.247173\pi\)
0.713358 + 0.700799i \(0.247173\pi\)
\(138\) 0 0
\(139\) −2.98332 −0.253042 −0.126521 0.991964i \(-0.540381\pi\)
−0.126521 + 0.991964i \(0.540381\pi\)
\(140\) 0 0
\(141\) −10.2197 −0.860654
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) −5.52493 −0.458821
\(146\) 0 0
\(147\) −3.00639 −0.247963
\(148\) 0 0
\(149\) −10.1030 −0.827671 −0.413835 0.910352i \(-0.635811\pi\)
−0.413835 + 0.910352i \(0.635811\pi\)
\(150\) 0 0
\(151\) −9.67817 −0.787598 −0.393799 0.919196i \(-0.628839\pi\)
−0.393799 + 0.919196i \(0.628839\pi\)
\(152\) 0 0
\(153\) −3.86843 −0.312744
\(154\) 0 0
\(155\) −28.3913 −2.28045
\(156\) 0 0
\(157\) −8.82238 −0.704102 −0.352051 0.935981i \(-0.614516\pi\)
−0.352051 + 0.935981i \(0.614516\pi\)
\(158\) 0 0
\(159\) −10.1839 −0.807637
\(160\) 0 0
\(161\) −3.73795 −0.294591
\(162\) 0 0
\(163\) 3.41996 0.267872 0.133936 0.990990i \(-0.457238\pi\)
0.133936 + 0.990990i \(0.457238\pi\)
\(164\) 0 0
\(165\) −7.88249 −0.613651
\(166\) 0 0
\(167\) 1.94831 0.150764 0.0753822 0.997155i \(-0.475982\pi\)
0.0753822 + 0.997155i \(0.475982\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −31.7891 −2.43098
\(172\) 0 0
\(173\) 24.9934 1.90022 0.950108 0.311922i \(-0.100973\pi\)
0.950108 + 0.311922i \(0.100973\pi\)
\(174\) 0 0
\(175\) −1.87442 −0.141693
\(176\) 0 0
\(177\) 9.65760 0.725910
\(178\) 0 0
\(179\) 10.4326 0.779766 0.389883 0.920864i \(-0.372515\pi\)
0.389883 + 0.920864i \(0.372515\pi\)
\(180\) 0 0
\(181\) −3.34840 −0.248884 −0.124442 0.992227i \(-0.539714\pi\)
−0.124442 + 0.992227i \(0.539714\pi\)
\(182\) 0 0
\(183\) −44.5674 −3.29452
\(184\) 0 0
\(185\) −15.4575 −1.13646
\(186\) 0 0
\(187\) −0.640640 −0.0468482
\(188\) 0 0
\(189\) 9.13457 0.664442
\(190\) 0 0
\(191\) 0.0717404 0.00519096 0.00259548 0.999997i \(-0.499174\pi\)
0.00259548 + 0.999997i \(0.499174\pi\)
\(192\) 0 0
\(193\) 13.7086 0.986768 0.493384 0.869812i \(-0.335760\pi\)
0.493384 + 0.869812i \(0.335760\pi\)
\(194\) 0 0
\(195\) 7.88249 0.564477
\(196\) 0 0
\(197\) −10.9890 −0.782934 −0.391467 0.920192i \(-0.628032\pi\)
−0.391467 + 0.920192i \(0.628032\pi\)
\(198\) 0 0
\(199\) 26.7225 1.89431 0.947154 0.320779i \(-0.103945\pi\)
0.947154 + 0.320779i \(0.103945\pi\)
\(200\) 0 0
\(201\) −22.5879 −1.59323
\(202\) 0 0
\(203\) 2.10721 0.147897
\(204\) 0 0
\(205\) 28.1109 1.96335
\(206\) 0 0
\(207\) 22.5712 1.56880
\(208\) 0 0
\(209\) −5.26451 −0.364154
\(210\) 0 0
\(211\) −17.8725 −1.23040 −0.615198 0.788373i \(-0.710924\pi\)
−0.615198 + 0.788373i \(0.710924\pi\)
\(212\) 0 0
\(213\) 7.83286 0.536699
\(214\) 0 0
\(215\) 5.70988 0.389411
\(216\) 0 0
\(217\) 10.8285 0.735085
\(218\) 0 0
\(219\) 2.44092 0.164942
\(220\) 0 0
\(221\) 0.640640 0.0430941
\(222\) 0 0
\(223\) 28.5819 1.91399 0.956993 0.290110i \(-0.0936920\pi\)
0.956993 + 0.290110i \(0.0936920\pi\)
\(224\) 0 0
\(225\) 11.3185 0.754565
\(226\) 0 0
\(227\) 7.63926 0.507036 0.253518 0.967331i \(-0.418412\pi\)
0.253518 + 0.967331i \(0.418412\pi\)
\(228\) 0 0
\(229\) −7.03493 −0.464881 −0.232441 0.972611i \(-0.574671\pi\)
−0.232441 + 0.972611i \(0.574671\pi\)
\(230\) 0 0
\(231\) 3.00639 0.197806
\(232\) 0 0
\(233\) −11.8395 −0.775630 −0.387815 0.921737i \(-0.626770\pi\)
−0.387815 + 0.921737i \(0.626770\pi\)
\(234\) 0 0
\(235\) 8.91273 0.581402
\(236\) 0 0
\(237\) −28.3732 −1.84303
\(238\) 0 0
\(239\) 3.04360 0.196874 0.0984370 0.995143i \(-0.468616\pi\)
0.0984370 + 0.995143i \(0.468616\pi\)
\(240\) 0 0
\(241\) 15.3595 0.989394 0.494697 0.869066i \(-0.335279\pi\)
0.494697 + 0.869066i \(0.335279\pi\)
\(242\) 0 0
\(243\) −0.696807 −0.0447002
\(244\) 0 0
\(245\) 2.62191 0.167508
\(246\) 0 0
\(247\) 5.26451 0.334973
\(248\) 0 0
\(249\) 48.2804 3.05965
\(250\) 0 0
\(251\) −23.1777 −1.46297 −0.731483 0.681859i \(-0.761172\pi\)
−0.731483 + 0.681859i \(0.761172\pi\)
\(252\) 0 0
\(253\) 3.73795 0.235003
\(254\) 0 0
\(255\) 5.04984 0.316233
\(256\) 0 0
\(257\) −11.4778 −0.715964 −0.357982 0.933728i \(-0.616535\pi\)
−0.357982 + 0.933728i \(0.616535\pi\)
\(258\) 0 0
\(259\) 5.89549 0.366328
\(260\) 0 0
\(261\) −12.7242 −0.787606
\(262\) 0 0
\(263\) −18.2082 −1.12277 −0.561383 0.827556i \(-0.689730\pi\)
−0.561383 + 0.827556i \(0.689730\pi\)
\(264\) 0 0
\(265\) 8.88152 0.545587
\(266\) 0 0
\(267\) 25.3109 1.54900
\(268\) 0 0
\(269\) −8.10349 −0.494078 −0.247039 0.969005i \(-0.579458\pi\)
−0.247039 + 0.969005i \(0.579458\pi\)
\(270\) 0 0
\(271\) 16.4840 1.00133 0.500667 0.865640i \(-0.333088\pi\)
0.500667 + 0.865640i \(0.333088\pi\)
\(272\) 0 0
\(273\) −3.00639 −0.181955
\(274\) 0 0
\(275\) 1.87442 0.113032
\(276\) 0 0
\(277\) 29.0211 1.74371 0.871855 0.489764i \(-0.162917\pi\)
0.871855 + 0.489764i \(0.162917\pi\)
\(278\) 0 0
\(279\) −65.3865 −3.91459
\(280\) 0 0
\(281\) −12.4263 −0.741293 −0.370646 0.928774i \(-0.620864\pi\)
−0.370646 + 0.928774i \(0.620864\pi\)
\(282\) 0 0
\(283\) −15.1671 −0.901593 −0.450796 0.892627i \(-0.648860\pi\)
−0.450796 + 0.892627i \(0.648860\pi\)
\(284\) 0 0
\(285\) 41.4975 2.45810
\(286\) 0 0
\(287\) −10.7215 −0.632873
\(288\) 0 0
\(289\) −16.5896 −0.975858
\(290\) 0 0
\(291\) −25.7628 −1.51024
\(292\) 0 0
\(293\) 13.6503 0.797456 0.398728 0.917069i \(-0.369452\pi\)
0.398728 + 0.917069i \(0.369452\pi\)
\(294\) 0 0
\(295\) −8.42252 −0.490378
\(296\) 0 0
\(297\) −9.13457 −0.530041
\(298\) 0 0
\(299\) −3.73795 −0.216171
\(300\) 0 0
\(301\) −2.17775 −0.125524
\(302\) 0 0
\(303\) 50.2654 2.88767
\(304\) 0 0
\(305\) 38.8678 2.22557
\(306\) 0 0
\(307\) −8.36347 −0.477328 −0.238664 0.971102i \(-0.576710\pi\)
−0.238664 + 0.971102i \(0.576710\pi\)
\(308\) 0 0
\(309\) −12.4965 −0.710902
\(310\) 0 0
\(311\) 10.0374 0.569169 0.284585 0.958651i \(-0.408144\pi\)
0.284585 + 0.958651i \(0.408144\pi\)
\(312\) 0 0
\(313\) 10.2185 0.577583 0.288792 0.957392i \(-0.406747\pi\)
0.288792 + 0.957392i \(0.406747\pi\)
\(314\) 0 0
\(315\) −15.8321 −0.892038
\(316\) 0 0
\(317\) 20.0912 1.12844 0.564218 0.825626i \(-0.309178\pi\)
0.564218 + 0.825626i \(0.309178\pi\)
\(318\) 0 0
\(319\) −2.10721 −0.117981
\(320\) 0 0
\(321\) −35.3407 −1.97253
\(322\) 0 0
\(323\) 3.37265 0.187660
\(324\) 0 0
\(325\) −1.87442 −0.103974
\(326\) 0 0
\(327\) −54.3234 −3.00409
\(328\) 0 0
\(329\) −3.39933 −0.187411
\(330\) 0 0
\(331\) −0.159166 −0.00874854 −0.00437427 0.999990i \(-0.501392\pi\)
−0.00437427 + 0.999990i \(0.501392\pi\)
\(332\) 0 0
\(333\) −35.5993 −1.95083
\(334\) 0 0
\(335\) 19.6992 1.07628
\(336\) 0 0
\(337\) −17.1801 −0.935858 −0.467929 0.883766i \(-0.655000\pi\)
−0.467929 + 0.883766i \(0.655000\pi\)
\(338\) 0 0
\(339\) −0.443387 −0.0240815
\(340\) 0 0
\(341\) −10.8285 −0.586395
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −29.4643 −1.58631
\(346\) 0 0
\(347\) 22.3482 1.19971 0.599857 0.800107i \(-0.295224\pi\)
0.599857 + 0.800107i \(0.295224\pi\)
\(348\) 0 0
\(349\) −22.6192 −1.21078 −0.605389 0.795930i \(-0.706982\pi\)
−0.605389 + 0.795930i \(0.706982\pi\)
\(350\) 0 0
\(351\) 9.13457 0.487567
\(352\) 0 0
\(353\) −10.6490 −0.566788 −0.283394 0.959004i \(-0.591460\pi\)
−0.283394 + 0.959004i \(0.591460\pi\)
\(354\) 0 0
\(355\) −6.83114 −0.362559
\(356\) 0 0
\(357\) −1.92601 −0.101935
\(358\) 0 0
\(359\) 17.2862 0.912332 0.456166 0.889895i \(-0.349222\pi\)
0.456166 + 0.889895i \(0.349222\pi\)
\(360\) 0 0
\(361\) 8.71508 0.458688
\(362\) 0 0
\(363\) −3.00639 −0.157795
\(364\) 0 0
\(365\) −2.12876 −0.111424
\(366\) 0 0
\(367\) −15.6465 −0.816739 −0.408370 0.912817i \(-0.633903\pi\)
−0.408370 + 0.912817i \(0.633903\pi\)
\(368\) 0 0
\(369\) 64.7408 3.37027
\(370\) 0 0
\(371\) −3.38742 −0.175866
\(372\) 0 0
\(373\) 27.8567 1.44236 0.721182 0.692746i \(-0.243599\pi\)
0.721182 + 0.692746i \(0.243599\pi\)
\(374\) 0 0
\(375\) 24.6373 1.27227
\(376\) 0 0
\(377\) 2.10721 0.108527
\(378\) 0 0
\(379\) 28.8132 1.48004 0.740019 0.672586i \(-0.234817\pi\)
0.740019 + 0.672586i \(0.234817\pi\)
\(380\) 0 0
\(381\) 27.4271 1.40513
\(382\) 0 0
\(383\) 5.23069 0.267276 0.133638 0.991030i \(-0.457334\pi\)
0.133638 + 0.991030i \(0.457334\pi\)
\(384\) 0 0
\(385\) −2.62191 −0.133625
\(386\) 0 0
\(387\) 13.1501 0.668458
\(388\) 0 0
\(389\) −17.6693 −0.895868 −0.447934 0.894067i \(-0.647840\pi\)
−0.447934 + 0.894067i \(0.647840\pi\)
\(390\) 0 0
\(391\) −2.39468 −0.121104
\(392\) 0 0
\(393\) −1.91055 −0.0963743
\(394\) 0 0
\(395\) 24.7446 1.24504
\(396\) 0 0
\(397\) −2.47696 −0.124315 −0.0621575 0.998066i \(-0.519798\pi\)
−0.0621575 + 0.998066i \(0.519798\pi\)
\(398\) 0 0
\(399\) −15.8272 −0.792350
\(400\) 0 0
\(401\) 39.0987 1.95250 0.976248 0.216656i \(-0.0695151\pi\)
0.976248 + 0.216656i \(0.0695151\pi\)
\(402\) 0 0
\(403\) 10.8285 0.539405
\(404\) 0 0
\(405\) 24.5068 1.21775
\(406\) 0 0
\(407\) −5.89549 −0.292229
\(408\) 0 0
\(409\) −3.61951 −0.178973 −0.0894866 0.995988i \(-0.528523\pi\)
−0.0894866 + 0.995988i \(0.528523\pi\)
\(410\) 0 0
\(411\) −50.2046 −2.47641
\(412\) 0 0
\(413\) 3.21236 0.158070
\(414\) 0 0
\(415\) −42.1060 −2.06690
\(416\) 0 0
\(417\) 8.96903 0.439215
\(418\) 0 0
\(419\) −21.4317 −1.04701 −0.523503 0.852024i \(-0.675375\pi\)
−0.523503 + 0.852024i \(0.675375\pi\)
\(420\) 0 0
\(421\) 1.84175 0.0897614 0.0448807 0.998992i \(-0.485709\pi\)
0.0448807 + 0.998992i \(0.485709\pi\)
\(422\) 0 0
\(423\) 20.5264 0.998029
\(424\) 0 0
\(425\) −1.20083 −0.0582488
\(426\) 0 0
\(427\) −14.8242 −0.717395
\(428\) 0 0
\(429\) 3.00639 0.145150
\(430\) 0 0
\(431\) 35.4834 1.70918 0.854589 0.519306i \(-0.173809\pi\)
0.854589 + 0.519306i \(0.173809\pi\)
\(432\) 0 0
\(433\) −2.68908 −0.129229 −0.0646144 0.997910i \(-0.520582\pi\)
−0.0646144 + 0.997910i \(0.520582\pi\)
\(434\) 0 0
\(435\) 16.6101 0.796393
\(436\) 0 0
\(437\) −19.6785 −0.941349
\(438\) 0 0
\(439\) −25.3807 −1.21135 −0.605677 0.795710i \(-0.707098\pi\)
−0.605677 + 0.795710i \(0.707098\pi\)
\(440\) 0 0
\(441\) 6.03838 0.287542
\(442\) 0 0
\(443\) −3.24993 −0.154409 −0.0772044 0.997015i \(-0.524599\pi\)
−0.0772044 + 0.997015i \(0.524599\pi\)
\(444\) 0 0
\(445\) −22.0740 −1.04641
\(446\) 0 0
\(447\) 30.3736 1.43662
\(448\) 0 0
\(449\) 30.7838 1.45278 0.726390 0.687283i \(-0.241197\pi\)
0.726390 + 0.687283i \(0.241197\pi\)
\(450\) 0 0
\(451\) 10.7215 0.504858
\(452\) 0 0
\(453\) 29.0964 1.36707
\(454\) 0 0
\(455\) 2.62191 0.122917
\(456\) 0 0
\(457\) 5.91634 0.276755 0.138377 0.990380i \(-0.455811\pi\)
0.138377 + 0.990380i \(0.455811\pi\)
\(458\) 0 0
\(459\) 5.85197 0.273146
\(460\) 0 0
\(461\) −0.223628 −0.0104154 −0.00520771 0.999986i \(-0.501658\pi\)
−0.00520771 + 0.999986i \(0.501658\pi\)
\(462\) 0 0
\(463\) −2.64416 −0.122885 −0.0614423 0.998111i \(-0.519570\pi\)
−0.0614423 + 0.998111i \(0.519570\pi\)
\(464\) 0 0
\(465\) 85.3554 3.95826
\(466\) 0 0
\(467\) 18.9325 0.876093 0.438046 0.898952i \(-0.355671\pi\)
0.438046 + 0.898952i \(0.355671\pi\)
\(468\) 0 0
\(469\) −7.51329 −0.346932
\(470\) 0 0
\(471\) 26.5235 1.22214
\(472\) 0 0
\(473\) 2.17775 0.100133
\(474\) 0 0
\(475\) −9.86792 −0.452771
\(476\) 0 0
\(477\) 20.4546 0.936550
\(478\) 0 0
\(479\) 26.3722 1.20498 0.602488 0.798128i \(-0.294176\pi\)
0.602488 + 0.798128i \(0.294176\pi\)
\(480\) 0 0
\(481\) 5.89549 0.268811
\(482\) 0 0
\(483\) 11.2377 0.511334
\(484\) 0 0
\(485\) 22.4680 1.02022
\(486\) 0 0
\(487\) 19.2556 0.872553 0.436276 0.899813i \(-0.356297\pi\)
0.436276 + 0.899813i \(0.356297\pi\)
\(488\) 0 0
\(489\) −10.2817 −0.464956
\(490\) 0 0
\(491\) 23.3647 1.05443 0.527217 0.849731i \(-0.323236\pi\)
0.527217 + 0.849731i \(0.323236\pi\)
\(492\) 0 0
\(493\) 1.34997 0.0607994
\(494\) 0 0
\(495\) 15.8321 0.711600
\(496\) 0 0
\(497\) 2.60540 0.116868
\(498\) 0 0
\(499\) −25.8930 −1.15913 −0.579565 0.814926i \(-0.696777\pi\)
−0.579565 + 0.814926i \(0.696777\pi\)
\(500\) 0 0
\(501\) −5.85737 −0.261688
\(502\) 0 0
\(503\) 38.4397 1.71394 0.856972 0.515363i \(-0.172343\pi\)
0.856972 + 0.515363i \(0.172343\pi\)
\(504\) 0 0
\(505\) −43.8371 −1.95073
\(506\) 0 0
\(507\) −3.00639 −0.133518
\(508\) 0 0
\(509\) −0.0129086 −0.000572166 0 −0.000286083 1.00000i \(-0.500091\pi\)
−0.000286083 1.00000i \(0.500091\pi\)
\(510\) 0 0
\(511\) 0.811910 0.0359168
\(512\) 0 0
\(513\) 48.0890 2.12318
\(514\) 0 0
\(515\) 10.8984 0.480240
\(516\) 0 0
\(517\) 3.39933 0.149502
\(518\) 0 0
\(519\) −75.1400 −3.29828
\(520\) 0 0
\(521\) −12.5988 −0.551965 −0.275983 0.961163i \(-0.589003\pi\)
−0.275983 + 0.961163i \(0.589003\pi\)
\(522\) 0 0
\(523\) 31.5723 1.38056 0.690280 0.723542i \(-0.257487\pi\)
0.690280 + 0.723542i \(0.257487\pi\)
\(524\) 0 0
\(525\) 5.63524 0.245942
\(526\) 0 0
\(527\) 6.93715 0.302187
\(528\) 0 0
\(529\) −9.02775 −0.392511
\(530\) 0 0
\(531\) −19.3975 −0.841778
\(532\) 0 0
\(533\) −10.7215 −0.464402
\(534\) 0 0
\(535\) 30.8211 1.33251
\(536\) 0 0
\(537\) −31.3643 −1.35347
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 35.7034 1.53501 0.767504 0.641045i \(-0.221499\pi\)
0.767504 + 0.641045i \(0.221499\pi\)
\(542\) 0 0
\(543\) 10.0666 0.431998
\(544\) 0 0
\(545\) 47.3762 2.02937
\(546\) 0 0
\(547\) 28.6308 1.22416 0.612082 0.790794i \(-0.290332\pi\)
0.612082 + 0.790794i \(0.290332\pi\)
\(548\) 0 0
\(549\) 89.5144 3.82038
\(550\) 0 0
\(551\) 11.0935 0.472597
\(552\) 0 0
\(553\) −9.43761 −0.401328
\(554\) 0 0
\(555\) 46.4712 1.97259
\(556\) 0 0
\(557\) 23.4323 0.992860 0.496430 0.868077i \(-0.334644\pi\)
0.496430 + 0.868077i \(0.334644\pi\)
\(558\) 0 0
\(559\) −2.17775 −0.0921092
\(560\) 0 0
\(561\) 1.92601 0.0813163
\(562\) 0 0
\(563\) 27.8530 1.17386 0.586932 0.809636i \(-0.300336\pi\)
0.586932 + 0.809636i \(0.300336\pi\)
\(564\) 0 0
\(565\) 0.386683 0.0162679
\(566\) 0 0
\(567\) −9.34693 −0.392534
\(568\) 0 0
\(569\) 20.2369 0.848374 0.424187 0.905575i \(-0.360560\pi\)
0.424187 + 0.905575i \(0.360560\pi\)
\(570\) 0 0
\(571\) −10.7462 −0.449716 −0.224858 0.974392i \(-0.572192\pi\)
−0.224858 + 0.974392i \(0.572192\pi\)
\(572\) 0 0
\(573\) −0.215680 −0.00901015
\(574\) 0 0
\(575\) 7.00649 0.292191
\(576\) 0 0
\(577\) 40.2497 1.67561 0.837807 0.545966i \(-0.183837\pi\)
0.837807 + 0.545966i \(0.183837\pi\)
\(578\) 0 0
\(579\) −41.2135 −1.71277
\(580\) 0 0
\(581\) 16.0593 0.666251
\(582\) 0 0
\(583\) 3.38742 0.140293
\(584\) 0 0
\(585\) −15.8321 −0.654577
\(586\) 0 0
\(587\) 32.0025 1.32088 0.660442 0.750877i \(-0.270369\pi\)
0.660442 + 0.750877i \(0.270369\pi\)
\(588\) 0 0
\(589\) 57.0067 2.34892
\(590\) 0 0
\(591\) 33.0372 1.35897
\(592\) 0 0
\(593\) −20.1994 −0.829491 −0.414746 0.909937i \(-0.636129\pi\)
−0.414746 + 0.909937i \(0.636129\pi\)
\(594\) 0 0
\(595\) 1.67970 0.0688610
\(596\) 0 0
\(597\) −80.3383 −3.28803
\(598\) 0 0
\(599\) 2.86763 0.117168 0.0585840 0.998282i \(-0.481341\pi\)
0.0585840 + 0.998282i \(0.481341\pi\)
\(600\) 0 0
\(601\) 23.3415 0.952119 0.476059 0.879413i \(-0.342065\pi\)
0.476059 + 0.879413i \(0.342065\pi\)
\(602\) 0 0
\(603\) 45.3682 1.84753
\(604\) 0 0
\(605\) 2.62191 0.106596
\(606\) 0 0
\(607\) 2.78759 0.113145 0.0565724 0.998398i \(-0.481983\pi\)
0.0565724 + 0.998398i \(0.481983\pi\)
\(608\) 0 0
\(609\) −6.33511 −0.256712
\(610\) 0 0
\(611\) −3.39933 −0.137522
\(612\) 0 0
\(613\) −24.0657 −0.972004 −0.486002 0.873958i \(-0.661545\pi\)
−0.486002 + 0.873958i \(0.661545\pi\)
\(614\) 0 0
\(615\) −84.5125 −3.40787
\(616\) 0 0
\(617\) 11.5876 0.466501 0.233250 0.972417i \(-0.425064\pi\)
0.233250 + 0.972417i \(0.425064\pi\)
\(618\) 0 0
\(619\) 28.4011 1.14154 0.570768 0.821111i \(-0.306645\pi\)
0.570768 + 0.821111i \(0.306645\pi\)
\(620\) 0 0
\(621\) −34.1445 −1.37017
\(622\) 0 0
\(623\) 8.41905 0.337302
\(624\) 0 0
\(625\) −30.8587 −1.23435
\(626\) 0 0
\(627\) 15.8272 0.632077
\(628\) 0 0
\(629\) 3.77689 0.150594
\(630\) 0 0
\(631\) 39.5351 1.57387 0.786934 0.617037i \(-0.211667\pi\)
0.786934 + 0.617037i \(0.211667\pi\)
\(632\) 0 0
\(633\) 53.7318 2.13565
\(634\) 0 0
\(635\) −23.9195 −0.949218
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −15.7324 −0.622365
\(640\) 0 0
\(641\) −26.5690 −1.04941 −0.524706 0.851284i \(-0.675825\pi\)
−0.524706 + 0.851284i \(0.675825\pi\)
\(642\) 0 0
\(643\) −2.30572 −0.0909287 −0.0454644 0.998966i \(-0.514477\pi\)
−0.0454644 + 0.998966i \(0.514477\pi\)
\(644\) 0 0
\(645\) −17.1661 −0.675916
\(646\) 0 0
\(647\) −0.403023 −0.0158445 −0.00792223 0.999969i \(-0.502522\pi\)
−0.00792223 + 0.999969i \(0.502522\pi\)
\(648\) 0 0
\(649\) −3.21236 −0.126096
\(650\) 0 0
\(651\) −32.5546 −1.27592
\(652\) 0 0
\(653\) −25.2173 −0.986829 −0.493415 0.869794i \(-0.664251\pi\)
−0.493415 + 0.869794i \(0.664251\pi\)
\(654\) 0 0
\(655\) 1.66621 0.0651043
\(656\) 0 0
\(657\) −4.90263 −0.191270
\(658\) 0 0
\(659\) −8.45316 −0.329289 −0.164644 0.986353i \(-0.552648\pi\)
−0.164644 + 0.986353i \(0.552648\pi\)
\(660\) 0 0
\(661\) 37.9491 1.47605 0.738025 0.674773i \(-0.235758\pi\)
0.738025 + 0.674773i \(0.235758\pi\)
\(662\) 0 0
\(663\) −1.92601 −0.0748001
\(664\) 0 0
\(665\) 13.8031 0.535261
\(666\) 0 0
\(667\) −7.87666 −0.304985
\(668\) 0 0
\(669\) −85.9284 −3.32218
\(670\) 0 0
\(671\) 14.8242 0.572283
\(672\) 0 0
\(673\) 41.9745 1.61800 0.808998 0.587811i \(-0.200010\pi\)
0.808998 + 0.587811i \(0.200010\pi\)
\(674\) 0 0
\(675\) −17.1220 −0.659027
\(676\) 0 0
\(677\) 6.75283 0.259532 0.129766 0.991545i \(-0.458577\pi\)
0.129766 + 0.991545i \(0.458577\pi\)
\(678\) 0 0
\(679\) −8.56933 −0.328861
\(680\) 0 0
\(681\) −22.9666 −0.880082
\(682\) 0 0
\(683\) 3.11326 0.119126 0.0595628 0.998225i \(-0.481029\pi\)
0.0595628 + 0.998225i \(0.481029\pi\)
\(684\) 0 0
\(685\) 43.7841 1.67290
\(686\) 0 0
\(687\) 21.1498 0.806913
\(688\) 0 0
\(689\) −3.38742 −0.129050
\(690\) 0 0
\(691\) −2.14985 −0.0817842 −0.0408921 0.999164i \(-0.513020\pi\)
−0.0408921 + 0.999164i \(0.513020\pi\)
\(692\) 0 0
\(693\) −6.03838 −0.229379
\(694\) 0 0
\(695\) −7.82201 −0.296706
\(696\) 0 0
\(697\) −6.86864 −0.260168
\(698\) 0 0
\(699\) 35.5941 1.34629
\(700\) 0 0
\(701\) −34.5343 −1.30434 −0.652171 0.758072i \(-0.726142\pi\)
−0.652171 + 0.758072i \(0.726142\pi\)
\(702\) 0 0
\(703\) 31.0369 1.17058
\(704\) 0 0
\(705\) −26.7951 −1.00916
\(706\) 0 0
\(707\) 16.7195 0.628802
\(708\) 0 0
\(709\) 21.2520 0.798135 0.399068 0.916922i \(-0.369334\pi\)
0.399068 + 0.916922i \(0.369334\pi\)
\(710\) 0 0
\(711\) 56.9879 2.13721
\(712\) 0 0
\(713\) −40.4763 −1.51585
\(714\) 0 0
\(715\) −2.62191 −0.0980539
\(716\) 0 0
\(717\) −9.15024 −0.341722
\(718\) 0 0
\(719\) −42.0739 −1.56909 −0.784546 0.620070i \(-0.787104\pi\)
−0.784546 + 0.620070i \(0.787104\pi\)
\(720\) 0 0
\(721\) −4.15665 −0.154802
\(722\) 0 0
\(723\) −46.1767 −1.71733
\(724\) 0 0
\(725\) −3.94981 −0.146692
\(726\) 0 0
\(727\) 11.6948 0.433735 0.216868 0.976201i \(-0.430416\pi\)
0.216868 + 0.976201i \(0.430416\pi\)
\(728\) 0 0
\(729\) −25.9459 −0.960959
\(730\) 0 0
\(731\) −1.39516 −0.0516017
\(732\) 0 0
\(733\) −9.01427 −0.332950 −0.166475 0.986046i \(-0.553238\pi\)
−0.166475 + 0.986046i \(0.553238\pi\)
\(734\) 0 0
\(735\) −7.88249 −0.290750
\(736\) 0 0
\(737\) 7.51329 0.276756
\(738\) 0 0
\(739\) −12.8353 −0.472153 −0.236077 0.971734i \(-0.575862\pi\)
−0.236077 + 0.971734i \(0.575862\pi\)
\(740\) 0 0
\(741\) −15.8272 −0.581426
\(742\) 0 0
\(743\) 27.8116 1.02031 0.510154 0.860083i \(-0.329588\pi\)
0.510154 + 0.860083i \(0.329588\pi\)
\(744\) 0 0
\(745\) −26.4892 −0.970489
\(746\) 0 0
\(747\) −96.9721 −3.54802
\(748\) 0 0
\(749\) −11.7552 −0.429526
\(750\) 0 0
\(751\) 16.1453 0.589149 0.294574 0.955629i \(-0.404822\pi\)
0.294574 + 0.955629i \(0.404822\pi\)
\(752\) 0 0
\(753\) 69.6814 2.53933
\(754\) 0 0
\(755\) −25.3753 −0.923502
\(756\) 0 0
\(757\) 0.449041 0.0163207 0.00816033 0.999967i \(-0.497402\pi\)
0.00816033 + 0.999967i \(0.497402\pi\)
\(758\) 0 0
\(759\) −11.2377 −0.407904
\(760\) 0 0
\(761\) 38.6952 1.40270 0.701351 0.712816i \(-0.252581\pi\)
0.701351 + 0.712816i \(0.252581\pi\)
\(762\) 0 0
\(763\) −18.0693 −0.654153
\(764\) 0 0
\(765\) −10.1427 −0.366709
\(766\) 0 0
\(767\) 3.21236 0.115992
\(768\) 0 0
\(769\) −19.9355 −0.718891 −0.359446 0.933166i \(-0.617034\pi\)
−0.359446 + 0.933166i \(0.617034\pi\)
\(770\) 0 0
\(771\) 34.5067 1.24273
\(772\) 0 0
\(773\) −34.0010 −1.22293 −0.611466 0.791270i \(-0.709420\pi\)
−0.611466 + 0.791270i \(0.709420\pi\)
\(774\) 0 0
\(775\) −20.2971 −0.729095
\(776\) 0 0
\(777\) −17.7242 −0.635851
\(778\) 0 0
\(779\) −56.4437 −2.02230
\(780\) 0 0
\(781\) −2.60540 −0.0932287
\(782\) 0 0
\(783\) 19.2485 0.687885
\(784\) 0 0
\(785\) −23.1315 −0.825599
\(786\) 0 0
\(787\) 47.6131 1.69722 0.848612 0.529016i \(-0.177439\pi\)
0.848612 + 0.529016i \(0.177439\pi\)
\(788\) 0 0
\(789\) 54.7409 1.94883
\(790\) 0 0
\(791\) −0.147481 −0.00524384
\(792\) 0 0
\(793\) −14.8242 −0.526424
\(794\) 0 0
\(795\) −26.7013 −0.946998
\(796\) 0 0
\(797\) 20.4579 0.724657 0.362328 0.932050i \(-0.381982\pi\)
0.362328 + 0.932050i \(0.381982\pi\)
\(798\) 0 0
\(799\) −2.17774 −0.0770430
\(800\) 0 0
\(801\) −50.8374 −1.79625
\(802\) 0 0
\(803\) −0.811910 −0.0286517
\(804\) 0 0
\(805\) −9.80057 −0.345425
\(806\) 0 0
\(807\) 24.3622 0.857592
\(808\) 0 0
\(809\) 33.2328 1.16840 0.584201 0.811609i \(-0.301408\pi\)
0.584201 + 0.811609i \(0.301408\pi\)
\(810\) 0 0
\(811\) −11.2418 −0.394752 −0.197376 0.980328i \(-0.563242\pi\)
−0.197376 + 0.980328i \(0.563242\pi\)
\(812\) 0 0
\(813\) −49.5574 −1.73805
\(814\) 0 0
\(815\) 8.96683 0.314094
\(816\) 0 0
\(817\) −11.4648 −0.401103
\(818\) 0 0
\(819\) 6.03838 0.210998
\(820\) 0 0
\(821\) −29.9929 −1.04676 −0.523379 0.852100i \(-0.675329\pi\)
−0.523379 + 0.852100i \(0.675329\pi\)
\(822\) 0 0
\(823\) 18.9024 0.658897 0.329448 0.944174i \(-0.393137\pi\)
0.329448 + 0.944174i \(0.393137\pi\)
\(824\) 0 0
\(825\) −5.63524 −0.196194
\(826\) 0 0
\(827\) 3.44487 0.119790 0.0598949 0.998205i \(-0.480923\pi\)
0.0598949 + 0.998205i \(0.480923\pi\)
\(828\) 0 0
\(829\) −26.7370 −0.928616 −0.464308 0.885674i \(-0.653697\pi\)
−0.464308 + 0.885674i \(0.653697\pi\)
\(830\) 0 0
\(831\) −87.2488 −3.02663
\(832\) 0 0
\(833\) −0.640640 −0.0221968
\(834\) 0 0
\(835\) 5.10829 0.176780
\(836\) 0 0
\(837\) 98.9135 3.41895
\(838\) 0 0
\(839\) −12.3535 −0.426491 −0.213246 0.976999i \(-0.568403\pi\)
−0.213246 + 0.976999i \(0.568403\pi\)
\(840\) 0 0
\(841\) −24.5596 −0.846884
\(842\) 0 0
\(843\) 37.3584 1.28669
\(844\) 0 0
\(845\) 2.62191 0.0901965
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 45.5983 1.56493
\(850\) 0 0
\(851\) −22.0370 −0.755420
\(852\) 0 0
\(853\) −50.6873 −1.73550 −0.867750 0.497002i \(-0.834434\pi\)
−0.867750 + 0.497002i \(0.834434\pi\)
\(854\) 0 0
\(855\) −83.3483 −2.85045
\(856\) 0 0
\(857\) −13.4844 −0.460620 −0.230310 0.973117i \(-0.573974\pi\)
−0.230310 + 0.973117i \(0.573974\pi\)
\(858\) 0 0
\(859\) 4.09174 0.139608 0.0698041 0.997561i \(-0.477763\pi\)
0.0698041 + 0.997561i \(0.477763\pi\)
\(860\) 0 0
\(861\) 32.2331 1.09850
\(862\) 0 0
\(863\) 44.6753 1.52077 0.760383 0.649475i \(-0.225011\pi\)
0.760383 + 0.649475i \(0.225011\pi\)
\(864\) 0 0
\(865\) 65.5306 2.22811
\(866\) 0 0
\(867\) 49.8748 1.69384
\(868\) 0 0
\(869\) 9.43761 0.320149
\(870\) 0 0
\(871\) −7.51329 −0.254578
\(872\) 0 0
\(873\) 51.7449 1.75130
\(874\) 0 0
\(875\) 8.19499 0.277041
\(876\) 0 0
\(877\) −35.5232 −1.19953 −0.599767 0.800175i \(-0.704740\pi\)
−0.599767 + 0.800175i \(0.704740\pi\)
\(878\) 0 0
\(879\) −41.0380 −1.38418
\(880\) 0 0
\(881\) −15.1895 −0.511748 −0.255874 0.966710i \(-0.582363\pi\)
−0.255874 + 0.966710i \(0.582363\pi\)
\(882\) 0 0
\(883\) −3.51926 −0.118433 −0.0592163 0.998245i \(-0.518860\pi\)
−0.0592163 + 0.998245i \(0.518860\pi\)
\(884\) 0 0
\(885\) 25.3214 0.851169
\(886\) 0 0
\(887\) −18.4868 −0.620726 −0.310363 0.950618i \(-0.600451\pi\)
−0.310363 + 0.950618i \(0.600451\pi\)
\(888\) 0 0
\(889\) 9.12294 0.305974
\(890\) 0 0
\(891\) 9.34693 0.313134
\(892\) 0 0
\(893\) −17.8958 −0.598860
\(894\) 0 0
\(895\) 27.3533 0.914318
\(896\) 0 0
\(897\) 11.2377 0.375217
\(898\) 0 0
\(899\) 22.8179 0.761021
\(900\) 0 0
\(901\) −2.17012 −0.0722971
\(902\) 0 0
\(903\) 6.54718 0.217877
\(904\) 0 0
\(905\) −8.77920 −0.291830
\(906\) 0 0
\(907\) −41.1041 −1.36484 −0.682419 0.730961i \(-0.739072\pi\)
−0.682419 + 0.730961i \(0.739072\pi\)
\(908\) 0 0
\(909\) −100.959 −3.34860
\(910\) 0 0
\(911\) −23.6347 −0.783051 −0.391525 0.920167i \(-0.628053\pi\)
−0.391525 + 0.920167i \(0.628053\pi\)
\(912\) 0 0
\(913\) −16.0593 −0.531484
\(914\) 0 0
\(915\) −116.852 −3.86300
\(916\) 0 0
\(917\) −0.635495 −0.0209859
\(918\) 0 0
\(919\) −10.3341 −0.340890 −0.170445 0.985367i \(-0.554520\pi\)
−0.170445 + 0.985367i \(0.554520\pi\)
\(920\) 0 0
\(921\) 25.1439 0.828518
\(922\) 0 0
\(923\) 2.60540 0.0857579
\(924\) 0 0
\(925\) −11.0506 −0.363343
\(926\) 0 0
\(927\) 25.0995 0.824374
\(928\) 0 0
\(929\) 4.88488 0.160268 0.0801338 0.996784i \(-0.474465\pi\)
0.0801338 + 0.996784i \(0.474465\pi\)
\(930\) 0 0
\(931\) −5.26451 −0.172537
\(932\) 0 0
\(933\) −30.1764 −0.987930
\(934\) 0 0
\(935\) −1.67970 −0.0549321
\(936\) 0 0
\(937\) −10.6863 −0.349106 −0.174553 0.984648i \(-0.555848\pi\)
−0.174553 + 0.984648i \(0.555848\pi\)
\(938\) 0 0
\(939\) −30.7208 −1.00253
\(940\) 0 0
\(941\) −4.59053 −0.149647 −0.0748234 0.997197i \(-0.523839\pi\)
−0.0748234 + 0.997197i \(0.523839\pi\)
\(942\) 0 0
\(943\) 40.0766 1.30507
\(944\) 0 0
\(945\) 23.9500 0.779095
\(946\) 0 0
\(947\) 52.8670 1.71795 0.858973 0.512021i \(-0.171103\pi\)
0.858973 + 0.512021i \(0.171103\pi\)
\(948\) 0 0
\(949\) 0.811910 0.0263557
\(950\) 0 0
\(951\) −60.4021 −1.95867
\(952\) 0 0
\(953\) 53.8607 1.74472 0.872359 0.488865i \(-0.162589\pi\)
0.872359 + 0.488865i \(0.162589\pi\)
\(954\) 0 0
\(955\) 0.188097 0.00608668
\(956\) 0 0
\(957\) 6.33511 0.204785
\(958\) 0 0
\(959\) −16.6993 −0.539248
\(960\) 0 0
\(961\) 86.2560 2.78245
\(962\) 0 0
\(963\) 70.9824 2.28738
\(964\) 0 0
\(965\) 35.9428 1.15704
\(966\) 0 0
\(967\) −13.9767 −0.449462 −0.224731 0.974421i \(-0.572150\pi\)
−0.224731 + 0.974421i \(0.572150\pi\)
\(968\) 0 0
\(969\) −10.1395 −0.325728
\(970\) 0 0
\(971\) −28.1830 −0.904436 −0.452218 0.891908i \(-0.649367\pi\)
−0.452218 + 0.891908i \(0.649367\pi\)
\(972\) 0 0
\(973\) 2.98332 0.0956409
\(974\) 0 0
\(975\) 5.63524 0.180472
\(976\) 0 0
\(977\) 61.0613 1.95352 0.976762 0.214329i \(-0.0687564\pi\)
0.976762 + 0.214329i \(0.0687564\pi\)
\(978\) 0 0
\(979\) −8.41905 −0.269074
\(980\) 0 0
\(981\) 109.109 3.48360
\(982\) 0 0
\(983\) −47.2785 −1.50795 −0.753975 0.656904i \(-0.771866\pi\)
−0.753975 + 0.656904i \(0.771866\pi\)
\(984\) 0 0
\(985\) −28.8122 −0.918033
\(986\) 0 0
\(987\) 10.2197 0.325297
\(988\) 0 0
\(989\) 8.14033 0.258847
\(990\) 0 0
\(991\) −16.9842 −0.539522 −0.269761 0.962927i \(-0.586945\pi\)
−0.269761 + 0.962927i \(0.586945\pi\)
\(992\) 0 0
\(993\) 0.478515 0.0151852
\(994\) 0 0
\(995\) 70.0641 2.22118
\(996\) 0 0
\(997\) 21.1064 0.668447 0.334224 0.942494i \(-0.391526\pi\)
0.334224 + 0.942494i \(0.391526\pi\)
\(998\) 0 0
\(999\) 53.8528 1.70383
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 \(a_p\))