Properties

Label 8008.2.a.y.1.11
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 14
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: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-1.85932\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.85932 q^{3} +1.13919 q^{5} +1.00000 q^{7} +0.457073 q^{9} +O(q^{10})\) \(q+1.85932 q^{3} +1.13919 q^{5} +1.00000 q^{7} +0.457073 q^{9} -1.00000 q^{11} -1.00000 q^{13} +2.11812 q^{15} -2.43965 q^{17} -4.36447 q^{19} +1.85932 q^{21} +4.06162 q^{23} -3.70225 q^{25} -4.72812 q^{27} -0.412473 q^{29} -8.12679 q^{31} -1.85932 q^{33} +1.13919 q^{35} -7.51813 q^{37} -1.85932 q^{39} -0.210128 q^{41} +8.57641 q^{43} +0.520692 q^{45} -8.98496 q^{47} +1.00000 q^{49} -4.53608 q^{51} +8.77822 q^{53} -1.13919 q^{55} -8.11495 q^{57} -2.23049 q^{59} -6.23803 q^{61} +0.457073 q^{63} -1.13919 q^{65} +11.2185 q^{67} +7.55186 q^{69} -7.84719 q^{71} -15.8894 q^{73} -6.88367 q^{75} -1.00000 q^{77} -5.38936 q^{79} -10.1623 q^{81} -5.74479 q^{83} -2.77921 q^{85} -0.766920 q^{87} +0.577855 q^{89} -1.00000 q^{91} -15.1103 q^{93} -4.97195 q^{95} -2.41830 q^{97} -0.457073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

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
\(3\) 1.85932 1.07348 0.536740 0.843748i \(-0.319656\pi\)
0.536740 + 0.843748i \(0.319656\pi\)
\(4\) 0 0
\(5\) 1.13919 0.509460 0.254730 0.967012i \(-0.418013\pi\)
0.254730 + 0.967012i \(0.418013\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0.457073 0.152358
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 2.11812 0.546895
\(16\) 0 0
\(17\) −2.43965 −0.591701 −0.295850 0.955234i \(-0.595603\pi\)
−0.295850 + 0.955234i \(0.595603\pi\)
\(18\) 0 0
\(19\) −4.36447 −1.00128 −0.500639 0.865656i \(-0.666902\pi\)
−0.500639 + 0.865656i \(0.666902\pi\)
\(20\) 0 0
\(21\) 1.85932 0.405737
\(22\) 0 0
\(23\) 4.06162 0.846907 0.423454 0.905918i \(-0.360818\pi\)
0.423454 + 0.905918i \(0.360818\pi\)
\(24\) 0 0
\(25\) −3.70225 −0.740450
\(26\) 0 0
\(27\) −4.72812 −0.909927
\(28\) 0 0
\(29\) −0.412473 −0.0765943 −0.0382972 0.999266i \(-0.512193\pi\)
−0.0382972 + 0.999266i \(0.512193\pi\)
\(30\) 0 0
\(31\) −8.12679 −1.45961 −0.729807 0.683653i \(-0.760390\pi\)
−0.729807 + 0.683653i \(0.760390\pi\)
\(32\) 0 0
\(33\) −1.85932 −0.323666
\(34\) 0 0
\(35\) 1.13919 0.192558
\(36\) 0 0
\(37\) −7.51813 −1.23597 −0.617986 0.786189i \(-0.712051\pi\)
−0.617986 + 0.786189i \(0.712051\pi\)
\(38\) 0 0
\(39\) −1.85932 −0.297730
\(40\) 0 0
\(41\) −0.210128 −0.0328165 −0.0164083 0.999865i \(-0.505223\pi\)
−0.0164083 + 0.999865i \(0.505223\pi\)
\(42\) 0 0
\(43\) 8.57641 1.30789 0.653945 0.756542i \(-0.273113\pi\)
0.653945 + 0.756542i \(0.273113\pi\)
\(44\) 0 0
\(45\) 0.520692 0.0776201
\(46\) 0 0
\(47\) −8.98496 −1.31059 −0.655296 0.755372i \(-0.727456\pi\)
−0.655296 + 0.755372i \(0.727456\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −4.53608 −0.635179
\(52\) 0 0
\(53\) 8.77822 1.20578 0.602891 0.797824i \(-0.294016\pi\)
0.602891 + 0.797824i \(0.294016\pi\)
\(54\) 0 0
\(55\) −1.13919 −0.153608
\(56\) 0 0
\(57\) −8.11495 −1.07485
\(58\) 0 0
\(59\) −2.23049 −0.290385 −0.145192 0.989403i \(-0.546380\pi\)
−0.145192 + 0.989403i \(0.546380\pi\)
\(60\) 0 0
\(61\) −6.23803 −0.798698 −0.399349 0.916799i \(-0.630764\pi\)
−0.399349 + 0.916799i \(0.630764\pi\)
\(62\) 0 0
\(63\) 0.457073 0.0575857
\(64\) 0 0
\(65\) −1.13919 −0.141299
\(66\) 0 0
\(67\) 11.2185 1.37056 0.685281 0.728279i \(-0.259679\pi\)
0.685281 + 0.728279i \(0.259679\pi\)
\(68\) 0 0
\(69\) 7.55186 0.909137
\(70\) 0 0
\(71\) −7.84719 −0.931290 −0.465645 0.884972i \(-0.654178\pi\)
−0.465645 + 0.884972i \(0.654178\pi\)
\(72\) 0 0
\(73\) −15.8894 −1.85971 −0.929857 0.367921i \(-0.880070\pi\)
−0.929857 + 0.367921i \(0.880070\pi\)
\(74\) 0 0
\(75\) −6.88367 −0.794858
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −5.38936 −0.606351 −0.303175 0.952935i \(-0.598047\pi\)
−0.303175 + 0.952935i \(0.598047\pi\)
\(80\) 0 0
\(81\) −10.1623 −1.12914
\(82\) 0 0
\(83\) −5.74479 −0.630572 −0.315286 0.948997i \(-0.602100\pi\)
−0.315286 + 0.948997i \(0.602100\pi\)
\(84\) 0 0
\(85\) −2.77921 −0.301448
\(86\) 0 0
\(87\) −0.766920 −0.0822224
\(88\) 0 0
\(89\) 0.577855 0.0612525 0.0306262 0.999531i \(-0.490250\pi\)
0.0306262 + 0.999531i \(0.490250\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −15.1103 −1.56687
\(94\) 0 0
\(95\) −4.97195 −0.510111
\(96\) 0 0
\(97\) −2.41830 −0.245541 −0.122770 0.992435i \(-0.539178\pi\)
−0.122770 + 0.992435i \(0.539178\pi\)
\(98\) 0 0
\(99\) −0.457073 −0.0459375
\(100\) 0 0
\(101\) 3.57116 0.355344 0.177672 0.984090i \(-0.443143\pi\)
0.177672 + 0.984090i \(0.443143\pi\)
\(102\) 0 0
\(103\) −10.8044 −1.06459 −0.532295 0.846559i \(-0.678670\pi\)
−0.532295 + 0.846559i \(0.678670\pi\)
\(104\) 0 0
\(105\) 2.11812 0.206707
\(106\) 0 0
\(107\) 13.8099 1.33505 0.667526 0.744587i \(-0.267353\pi\)
0.667526 + 0.744587i \(0.267353\pi\)
\(108\) 0 0
\(109\) −5.49058 −0.525903 −0.262951 0.964809i \(-0.584696\pi\)
−0.262951 + 0.964809i \(0.584696\pi\)
\(110\) 0 0
\(111\) −13.9786 −1.32679
\(112\) 0 0
\(113\) 8.64277 0.813043 0.406522 0.913641i \(-0.366742\pi\)
0.406522 + 0.913641i \(0.366742\pi\)
\(114\) 0 0
\(115\) 4.62695 0.431466
\(116\) 0 0
\(117\) −0.457073 −0.0422564
\(118\) 0 0
\(119\) −2.43965 −0.223642
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −0.390696 −0.0352279
\(124\) 0 0
\(125\) −9.91350 −0.886690
\(126\) 0 0
\(127\) 18.6357 1.65365 0.826824 0.562460i \(-0.190145\pi\)
0.826824 + 0.562460i \(0.190145\pi\)
\(128\) 0 0
\(129\) 15.9463 1.40399
\(130\) 0 0
\(131\) −0.760163 −0.0664157 −0.0332079 0.999448i \(-0.510572\pi\)
−0.0332079 + 0.999448i \(0.510572\pi\)
\(132\) 0 0
\(133\) −4.36447 −0.378447
\(134\) 0 0
\(135\) −5.38621 −0.463572
\(136\) 0 0
\(137\) 15.1918 1.29792 0.648962 0.760821i \(-0.275203\pi\)
0.648962 + 0.760821i \(0.275203\pi\)
\(138\) 0 0
\(139\) −14.1907 −1.20364 −0.601820 0.798632i \(-0.705558\pi\)
−0.601820 + 0.798632i \(0.705558\pi\)
\(140\) 0 0
\(141\) −16.7059 −1.40689
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −0.469884 −0.0390218
\(146\) 0 0
\(147\) 1.85932 0.153354
\(148\) 0 0
\(149\) −6.84598 −0.560845 −0.280422 0.959877i \(-0.590475\pi\)
−0.280422 + 0.959877i \(0.590475\pi\)
\(150\) 0 0
\(151\) 0.713259 0.0580442 0.0290221 0.999579i \(-0.490761\pi\)
0.0290221 + 0.999579i \(0.490761\pi\)
\(152\) 0 0
\(153\) −1.11509 −0.0901501
\(154\) 0 0
\(155\) −9.25794 −0.743616
\(156\) 0 0
\(157\) 10.6338 0.848673 0.424337 0.905505i \(-0.360507\pi\)
0.424337 + 0.905505i \(0.360507\pi\)
\(158\) 0 0
\(159\) 16.3215 1.29438
\(160\) 0 0
\(161\) 4.06162 0.320101
\(162\) 0 0
\(163\) 11.2140 0.878350 0.439175 0.898401i \(-0.355271\pi\)
0.439175 + 0.898401i \(0.355271\pi\)
\(164\) 0 0
\(165\) −2.11812 −0.164895
\(166\) 0 0
\(167\) 3.40870 0.263773 0.131887 0.991265i \(-0.457896\pi\)
0.131887 + 0.991265i \(0.457896\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −1.99488 −0.152552
\(172\) 0 0
\(173\) −7.50127 −0.570311 −0.285155 0.958481i \(-0.592045\pi\)
−0.285155 + 0.958481i \(0.592045\pi\)
\(174\) 0 0
\(175\) −3.70225 −0.279864
\(176\) 0 0
\(177\) −4.14719 −0.311722
\(178\) 0 0
\(179\) −16.0679 −1.20097 −0.600485 0.799636i \(-0.705026\pi\)
−0.600485 + 0.799636i \(0.705026\pi\)
\(180\) 0 0
\(181\) −16.1109 −1.19751 −0.598756 0.800931i \(-0.704338\pi\)
−0.598756 + 0.800931i \(0.704338\pi\)
\(182\) 0 0
\(183\) −11.5985 −0.857386
\(184\) 0 0
\(185\) −8.56456 −0.629679
\(186\) 0 0
\(187\) 2.43965 0.178405
\(188\) 0 0
\(189\) −4.72812 −0.343920
\(190\) 0 0
\(191\) −3.59700 −0.260270 −0.130135 0.991496i \(-0.541541\pi\)
−0.130135 + 0.991496i \(0.541541\pi\)
\(192\) 0 0
\(193\) −4.52564 −0.325762 −0.162881 0.986646i \(-0.552079\pi\)
−0.162881 + 0.986646i \(0.552079\pi\)
\(194\) 0 0
\(195\) −2.11812 −0.151681
\(196\) 0 0
\(197\) 15.1491 1.07933 0.539666 0.841879i \(-0.318551\pi\)
0.539666 + 0.841879i \(0.318551\pi\)
\(198\) 0 0
\(199\) −4.59654 −0.325840 −0.162920 0.986639i \(-0.552091\pi\)
−0.162920 + 0.986639i \(0.552091\pi\)
\(200\) 0 0
\(201\) 20.8588 1.47127
\(202\) 0 0
\(203\) −0.412473 −0.0289499
\(204\) 0 0
\(205\) −0.239376 −0.0167187
\(206\) 0 0
\(207\) 1.85646 0.129033
\(208\) 0 0
\(209\) 4.36447 0.301897
\(210\) 0 0
\(211\) −7.54087 −0.519135 −0.259568 0.965725i \(-0.583580\pi\)
−0.259568 + 0.965725i \(0.583580\pi\)
\(212\) 0 0
\(213\) −14.5904 −0.999720
\(214\) 0 0
\(215\) 9.77014 0.666318
\(216\) 0 0
\(217\) −8.12679 −0.551682
\(218\) 0 0
\(219\) −29.5435 −1.99636
\(220\) 0 0
\(221\) 2.43965 0.164108
\(222\) 0 0
\(223\) −26.8067 −1.79511 −0.897555 0.440902i \(-0.854659\pi\)
−0.897555 + 0.440902i \(0.854659\pi\)
\(224\) 0 0
\(225\) −1.69220 −0.112813
\(226\) 0 0
\(227\) −1.96930 −0.130707 −0.0653535 0.997862i \(-0.520818\pi\)
−0.0653535 + 0.997862i \(0.520818\pi\)
\(228\) 0 0
\(229\) 20.9526 1.38459 0.692294 0.721616i \(-0.256600\pi\)
0.692294 + 0.721616i \(0.256600\pi\)
\(230\) 0 0
\(231\) −1.85932 −0.122334
\(232\) 0 0
\(233\) −15.7952 −1.03478 −0.517389 0.855750i \(-0.673096\pi\)
−0.517389 + 0.855750i \(0.673096\pi\)
\(234\) 0 0
\(235\) −10.2356 −0.667694
\(236\) 0 0
\(237\) −10.0206 −0.650905
\(238\) 0 0
\(239\) 24.4833 1.58369 0.791845 0.610722i \(-0.209121\pi\)
0.791845 + 0.610722i \(0.209121\pi\)
\(240\) 0 0
\(241\) 11.0133 0.709426 0.354713 0.934975i \(-0.384579\pi\)
0.354713 + 0.934975i \(0.384579\pi\)
\(242\) 0 0
\(243\) −4.71063 −0.302187
\(244\) 0 0
\(245\) 1.13919 0.0727801
\(246\) 0 0
\(247\) 4.36447 0.277704
\(248\) 0 0
\(249\) −10.6814 −0.676906
\(250\) 0 0
\(251\) 4.01223 0.253250 0.126625 0.991951i \(-0.459586\pi\)
0.126625 + 0.991951i \(0.459586\pi\)
\(252\) 0 0
\(253\) −4.06162 −0.255352
\(254\) 0 0
\(255\) −5.16745 −0.323598
\(256\) 0 0
\(257\) −3.02186 −0.188498 −0.0942492 0.995549i \(-0.530045\pi\)
−0.0942492 + 0.995549i \(0.530045\pi\)
\(258\) 0 0
\(259\) −7.51813 −0.467154
\(260\) 0 0
\(261\) −0.188530 −0.0116697
\(262\) 0 0
\(263\) −0.513650 −0.0316730 −0.0158365 0.999875i \(-0.505041\pi\)
−0.0158365 + 0.999875i \(0.505041\pi\)
\(264\) 0 0
\(265\) 10.0000 0.614298
\(266\) 0 0
\(267\) 1.07442 0.0657532
\(268\) 0 0
\(269\) −26.5185 −1.61686 −0.808429 0.588593i \(-0.799682\pi\)
−0.808429 + 0.588593i \(0.799682\pi\)
\(270\) 0 0
\(271\) 31.5252 1.91502 0.957509 0.288404i \(-0.0931247\pi\)
0.957509 + 0.288404i \(0.0931247\pi\)
\(272\) 0 0
\(273\) −1.85932 −0.112531
\(274\) 0 0
\(275\) 3.70225 0.223254
\(276\) 0 0
\(277\) 27.9907 1.68180 0.840899 0.541192i \(-0.182027\pi\)
0.840899 + 0.541192i \(0.182027\pi\)
\(278\) 0 0
\(279\) −3.71453 −0.222383
\(280\) 0 0
\(281\) 27.3440 1.63120 0.815602 0.578613i \(-0.196406\pi\)
0.815602 + 0.578613i \(0.196406\pi\)
\(282\) 0 0
\(283\) 5.18505 0.308219 0.154110 0.988054i \(-0.450749\pi\)
0.154110 + 0.988054i \(0.450749\pi\)
\(284\) 0 0
\(285\) −9.24445 −0.547594
\(286\) 0 0
\(287\) −0.210128 −0.0124035
\(288\) 0 0
\(289\) −11.0481 −0.649890
\(290\) 0 0
\(291\) −4.49639 −0.263583
\(292\) 0 0
\(293\) −28.6760 −1.67527 −0.837636 0.546229i \(-0.816063\pi\)
−0.837636 + 0.546229i \(0.816063\pi\)
\(294\) 0 0
\(295\) −2.54094 −0.147939
\(296\) 0 0
\(297\) 4.72812 0.274353
\(298\) 0 0
\(299\) −4.06162 −0.234890
\(300\) 0 0
\(301\) 8.57641 0.494336
\(302\) 0 0
\(303\) 6.63994 0.381454
\(304\) 0 0
\(305\) −7.10629 −0.406905
\(306\) 0 0
\(307\) −1.21096 −0.0691130 −0.0345565 0.999403i \(-0.511002\pi\)
−0.0345565 + 0.999403i \(0.511002\pi\)
\(308\) 0 0
\(309\) −20.0889 −1.14282
\(310\) 0 0
\(311\) −3.12676 −0.177302 −0.0886512 0.996063i \(-0.528256\pi\)
−0.0886512 + 0.996063i \(0.528256\pi\)
\(312\) 0 0
\(313\) −17.1075 −0.966972 −0.483486 0.875352i \(-0.660630\pi\)
−0.483486 + 0.875352i \(0.660630\pi\)
\(314\) 0 0
\(315\) 0.520692 0.0293377
\(316\) 0 0
\(317\) 28.7586 1.61524 0.807621 0.589702i \(-0.200755\pi\)
0.807621 + 0.589702i \(0.200755\pi\)
\(318\) 0 0
\(319\) 0.412473 0.0230941
\(320\) 0 0
\(321\) 25.6770 1.43315
\(322\) 0 0
\(323\) 10.6478 0.592457
\(324\) 0 0
\(325\) 3.70225 0.205364
\(326\) 0 0
\(327\) −10.2088 −0.564545
\(328\) 0 0
\(329\) −8.98496 −0.495357
\(330\) 0 0
\(331\) −31.1599 −1.71270 −0.856352 0.516392i \(-0.827275\pi\)
−0.856352 + 0.516392i \(0.827275\pi\)
\(332\) 0 0
\(333\) −3.43633 −0.188310
\(334\) 0 0
\(335\) 12.7800 0.698247
\(336\) 0 0
\(337\) −3.21637 −0.175207 −0.0876034 0.996155i \(-0.527921\pi\)
−0.0876034 + 0.996155i \(0.527921\pi\)
\(338\) 0 0
\(339\) 16.0697 0.872785
\(340\) 0 0
\(341\) 8.12679 0.440090
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 8.60299 0.463169
\(346\) 0 0
\(347\) 3.25621 0.174802 0.0874012 0.996173i \(-0.472144\pi\)
0.0874012 + 0.996173i \(0.472144\pi\)
\(348\) 0 0
\(349\) 4.70551 0.251880 0.125940 0.992038i \(-0.459805\pi\)
0.125940 + 0.992038i \(0.459805\pi\)
\(350\) 0 0
\(351\) 4.72812 0.252368
\(352\) 0 0
\(353\) −5.76977 −0.307094 −0.153547 0.988141i \(-0.549070\pi\)
−0.153547 + 0.988141i \(0.549070\pi\)
\(354\) 0 0
\(355\) −8.93942 −0.474455
\(356\) 0 0
\(357\) −4.53608 −0.240075
\(358\) 0 0
\(359\) −9.48183 −0.500432 −0.250216 0.968190i \(-0.580502\pi\)
−0.250216 + 0.968190i \(0.580502\pi\)
\(360\) 0 0
\(361\) 0.0485854 0.00255712
\(362\) 0 0
\(363\) 1.85932 0.0975890
\(364\) 0 0
\(365\) −18.1010 −0.947451
\(366\) 0 0
\(367\) 28.0919 1.46638 0.733192 0.680022i \(-0.238030\pi\)
0.733192 + 0.680022i \(0.238030\pi\)
\(368\) 0 0
\(369\) −0.0960439 −0.00499985
\(370\) 0 0
\(371\) 8.77822 0.455743
\(372\) 0 0
\(373\) 6.47251 0.335134 0.167567 0.985861i \(-0.446409\pi\)
0.167567 + 0.985861i \(0.446409\pi\)
\(374\) 0 0
\(375\) −18.4324 −0.951844
\(376\) 0 0
\(377\) 0.412473 0.0212434
\(378\) 0 0
\(379\) −22.6820 −1.16510 −0.582549 0.812796i \(-0.697945\pi\)
−0.582549 + 0.812796i \(0.697945\pi\)
\(380\) 0 0
\(381\) 34.6497 1.77516
\(382\) 0 0
\(383\) −24.3230 −1.24285 −0.621424 0.783475i \(-0.713446\pi\)
−0.621424 + 0.783475i \(0.713446\pi\)
\(384\) 0 0
\(385\) −1.13919 −0.0580584
\(386\) 0 0
\(387\) 3.92004 0.199267
\(388\) 0 0
\(389\) 9.23244 0.468103 0.234052 0.972224i \(-0.424802\pi\)
0.234052 + 0.972224i \(0.424802\pi\)
\(390\) 0 0
\(391\) −9.90892 −0.501116
\(392\) 0 0
\(393\) −1.41339 −0.0712959
\(394\) 0 0
\(395\) −6.13950 −0.308912
\(396\) 0 0
\(397\) 10.7358 0.538814 0.269407 0.963026i \(-0.413172\pi\)
0.269407 + 0.963026i \(0.413172\pi\)
\(398\) 0 0
\(399\) −8.11495 −0.406255
\(400\) 0 0
\(401\) −5.44508 −0.271914 −0.135957 0.990715i \(-0.543411\pi\)
−0.135957 + 0.990715i \(0.543411\pi\)
\(402\) 0 0
\(403\) 8.12679 0.404824
\(404\) 0 0
\(405\) −11.5768 −0.575255
\(406\) 0 0
\(407\) 7.51813 0.372660
\(408\) 0 0
\(409\) 24.7840 1.22549 0.612744 0.790281i \(-0.290066\pi\)
0.612744 + 0.790281i \(0.290066\pi\)
\(410\) 0 0
\(411\) 28.2465 1.39329
\(412\) 0 0
\(413\) −2.23049 −0.109755
\(414\) 0 0
\(415\) −6.54439 −0.321252
\(416\) 0 0
\(417\) −26.3851 −1.29208
\(418\) 0 0
\(419\) 8.58148 0.419233 0.209616 0.977784i \(-0.432778\pi\)
0.209616 + 0.977784i \(0.432778\pi\)
\(420\) 0 0
\(421\) 6.89799 0.336187 0.168094 0.985771i \(-0.446239\pi\)
0.168094 + 0.985771i \(0.446239\pi\)
\(422\) 0 0
\(423\) −4.10678 −0.199678
\(424\) 0 0
\(425\) 9.03218 0.438125
\(426\) 0 0
\(427\) −6.23803 −0.301880
\(428\) 0 0
\(429\) 1.85932 0.0897688
\(430\) 0 0
\(431\) −22.8518 −1.10073 −0.550367 0.834923i \(-0.685512\pi\)
−0.550367 + 0.834923i \(0.685512\pi\)
\(432\) 0 0
\(433\) 23.9326 1.15013 0.575063 0.818109i \(-0.304977\pi\)
0.575063 + 0.818109i \(0.304977\pi\)
\(434\) 0 0
\(435\) −0.873666 −0.0418891
\(436\) 0 0
\(437\) −17.7268 −0.847989
\(438\) 0 0
\(439\) −4.28669 −0.204593 −0.102296 0.994754i \(-0.532619\pi\)
−0.102296 + 0.994754i \(0.532619\pi\)
\(440\) 0 0
\(441\) 0.457073 0.0217654
\(442\) 0 0
\(443\) 15.9434 0.757494 0.378747 0.925500i \(-0.376355\pi\)
0.378747 + 0.925500i \(0.376355\pi\)
\(444\) 0 0
\(445\) 0.658285 0.0312057
\(446\) 0 0
\(447\) −12.7289 −0.602055
\(448\) 0 0
\(449\) −3.69766 −0.174504 −0.0872518 0.996186i \(-0.527808\pi\)
−0.0872518 + 0.996186i \(0.527808\pi\)
\(450\) 0 0
\(451\) 0.210128 0.00989456
\(452\) 0 0
\(453\) 1.32618 0.0623093
\(454\) 0 0
\(455\) −1.13919 −0.0534060
\(456\) 0 0
\(457\) −25.2958 −1.18329 −0.591644 0.806200i \(-0.701521\pi\)
−0.591644 + 0.806200i \(0.701521\pi\)
\(458\) 0 0
\(459\) 11.5349 0.538404
\(460\) 0 0
\(461\) 35.3046 1.64430 0.822149 0.569273i \(-0.192775\pi\)
0.822149 + 0.569273i \(0.192775\pi\)
\(462\) 0 0
\(463\) 19.9855 0.928806 0.464403 0.885624i \(-0.346269\pi\)
0.464403 + 0.885624i \(0.346269\pi\)
\(464\) 0 0
\(465\) −17.2135 −0.798256
\(466\) 0 0
\(467\) 31.8835 1.47539 0.737695 0.675134i \(-0.235914\pi\)
0.737695 + 0.675134i \(0.235914\pi\)
\(468\) 0 0
\(469\) 11.2185 0.518024
\(470\) 0 0
\(471\) 19.7717 0.911033
\(472\) 0 0
\(473\) −8.57641 −0.394344
\(474\) 0 0
\(475\) 16.1584 0.741396
\(476\) 0 0
\(477\) 4.01228 0.183710
\(478\) 0 0
\(479\) −35.9578 −1.64295 −0.821477 0.570241i \(-0.806850\pi\)
−0.821477 + 0.570241i \(0.806850\pi\)
\(480\) 0 0
\(481\) 7.51813 0.342797
\(482\) 0 0
\(483\) 7.55186 0.343622
\(484\) 0 0
\(485\) −2.75489 −0.125093
\(486\) 0 0
\(487\) −23.1605 −1.04950 −0.524752 0.851255i \(-0.675842\pi\)
−0.524752 + 0.851255i \(0.675842\pi\)
\(488\) 0 0
\(489\) 20.8505 0.942891
\(490\) 0 0
\(491\) −29.3914 −1.32642 −0.663208 0.748435i \(-0.730806\pi\)
−0.663208 + 0.748435i \(0.730806\pi\)
\(492\) 0 0
\(493\) 1.00629 0.0453209
\(494\) 0 0
\(495\) −0.520692 −0.0234034
\(496\) 0 0
\(497\) −7.84719 −0.351994
\(498\) 0 0
\(499\) −24.1855 −1.08269 −0.541346 0.840800i \(-0.682085\pi\)
−0.541346 + 0.840800i \(0.682085\pi\)
\(500\) 0 0
\(501\) 6.33787 0.283155
\(502\) 0 0
\(503\) 26.0053 1.15952 0.579760 0.814787i \(-0.303146\pi\)
0.579760 + 0.814787i \(0.303146\pi\)
\(504\) 0 0
\(505\) 4.06823 0.181034
\(506\) 0 0
\(507\) 1.85932 0.0825753
\(508\) 0 0
\(509\) −20.3224 −0.900773 −0.450387 0.892834i \(-0.648714\pi\)
−0.450387 + 0.892834i \(0.648714\pi\)
\(510\) 0 0
\(511\) −15.8894 −0.702906
\(512\) 0 0
\(513\) 20.6357 0.911089
\(514\) 0 0
\(515\) −12.3083 −0.542367
\(516\) 0 0
\(517\) 8.98496 0.395158
\(518\) 0 0
\(519\) −13.9473 −0.612217
\(520\) 0 0
\(521\) −33.3536 −1.46125 −0.730625 0.682779i \(-0.760771\pi\)
−0.730625 + 0.682779i \(0.760771\pi\)
\(522\) 0 0
\(523\) −18.3051 −0.800428 −0.400214 0.916422i \(-0.631064\pi\)
−0.400214 + 0.916422i \(0.631064\pi\)
\(524\) 0 0
\(525\) −6.88367 −0.300428
\(526\) 0 0
\(527\) 19.8265 0.863655
\(528\) 0 0
\(529\) −6.50320 −0.282748
\(530\) 0 0
\(531\) −1.01949 −0.0442423
\(532\) 0 0
\(533\) 0.210128 0.00910167
\(534\) 0 0
\(535\) 15.7321 0.680156
\(536\) 0 0
\(537\) −29.8753 −1.28922
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −7.53976 −0.324160 −0.162080 0.986778i \(-0.551820\pi\)
−0.162080 + 0.986778i \(0.551820\pi\)
\(542\) 0 0
\(543\) −29.9553 −1.28550
\(544\) 0 0
\(545\) −6.25481 −0.267927
\(546\) 0 0
\(547\) 7.12726 0.304740 0.152370 0.988324i \(-0.451310\pi\)
0.152370 + 0.988324i \(0.451310\pi\)
\(548\) 0 0
\(549\) −2.85123 −0.121688
\(550\) 0 0
\(551\) 1.80023 0.0766922
\(552\) 0 0
\(553\) −5.38936 −0.229179
\(554\) 0 0
\(555\) −15.9243 −0.675947
\(556\) 0 0
\(557\) 18.7729 0.795433 0.397717 0.917508i \(-0.369803\pi\)
0.397717 + 0.917508i \(0.369803\pi\)
\(558\) 0 0
\(559\) −8.57641 −0.362743
\(560\) 0 0
\(561\) 4.53608 0.191514
\(562\) 0 0
\(563\) −18.8497 −0.794420 −0.397210 0.917728i \(-0.630022\pi\)
−0.397210 + 0.917728i \(0.630022\pi\)
\(564\) 0 0
\(565\) 9.84574 0.414213
\(566\) 0 0
\(567\) −10.1623 −0.426777
\(568\) 0 0
\(569\) 12.8921 0.540463 0.270232 0.962795i \(-0.412900\pi\)
0.270232 + 0.962795i \(0.412900\pi\)
\(570\) 0 0
\(571\) 39.4783 1.65212 0.826058 0.563585i \(-0.190578\pi\)
0.826058 + 0.563585i \(0.190578\pi\)
\(572\) 0 0
\(573\) −6.68798 −0.279394
\(574\) 0 0
\(575\) −15.0372 −0.627093
\(576\) 0 0
\(577\) −11.9135 −0.495966 −0.247983 0.968764i \(-0.579768\pi\)
−0.247983 + 0.968764i \(0.579768\pi\)
\(578\) 0 0
\(579\) −8.41461 −0.349699
\(580\) 0 0
\(581\) −5.74479 −0.238334
\(582\) 0 0
\(583\) −8.77822 −0.363557
\(584\) 0 0
\(585\) −0.520692 −0.0215280
\(586\) 0 0
\(587\) −16.9659 −0.700259 −0.350130 0.936701i \(-0.613862\pi\)
−0.350130 + 0.936701i \(0.613862\pi\)
\(588\) 0 0
\(589\) 35.4691 1.46148
\(590\) 0 0
\(591\) 28.1671 1.15864
\(592\) 0 0
\(593\) 6.95059 0.285426 0.142713 0.989764i \(-0.454417\pi\)
0.142713 + 0.989764i \(0.454417\pi\)
\(594\) 0 0
\(595\) −2.77921 −0.113937
\(596\) 0 0
\(597\) −8.54645 −0.349783
\(598\) 0 0
\(599\) −42.4976 −1.73640 −0.868202 0.496210i \(-0.834724\pi\)
−0.868202 + 0.496210i \(0.834724\pi\)
\(600\) 0 0
\(601\) 6.23112 0.254173 0.127086 0.991892i \(-0.459437\pi\)
0.127086 + 0.991892i \(0.459437\pi\)
\(602\) 0 0
\(603\) 5.12768 0.208815
\(604\) 0 0
\(605\) 1.13919 0.0463146
\(606\) 0 0
\(607\) 24.6593 1.00089 0.500445 0.865768i \(-0.333170\pi\)
0.500445 + 0.865768i \(0.333170\pi\)
\(608\) 0 0
\(609\) −0.766920 −0.0310772
\(610\) 0 0
\(611\) 8.98496 0.363493
\(612\) 0 0
\(613\) 15.7158 0.634756 0.317378 0.948299i \(-0.397198\pi\)
0.317378 + 0.948299i \(0.397198\pi\)
\(614\) 0 0
\(615\) −0.445076 −0.0179472
\(616\) 0 0
\(617\) 11.5791 0.466158 0.233079 0.972458i \(-0.425120\pi\)
0.233079 + 0.972458i \(0.425120\pi\)
\(618\) 0 0
\(619\) 7.22023 0.290205 0.145103 0.989417i \(-0.453649\pi\)
0.145103 + 0.989417i \(0.453649\pi\)
\(620\) 0 0
\(621\) −19.2038 −0.770623
\(622\) 0 0
\(623\) 0.577855 0.0231513
\(624\) 0 0
\(625\) 7.21791 0.288716
\(626\) 0 0
\(627\) 8.11495 0.324080
\(628\) 0 0
\(629\) 18.3416 0.731326
\(630\) 0 0
\(631\) 22.2384 0.885298 0.442649 0.896695i \(-0.354039\pi\)
0.442649 + 0.896695i \(0.354039\pi\)
\(632\) 0 0
\(633\) −14.0209 −0.557281
\(634\) 0 0
\(635\) 21.2295 0.842468
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −3.58673 −0.141889
\(640\) 0 0
\(641\) −31.6804 −1.25130 −0.625651 0.780103i \(-0.715167\pi\)
−0.625651 + 0.780103i \(0.715167\pi\)
\(642\) 0 0
\(643\) −37.3281 −1.47208 −0.736038 0.676941i \(-0.763305\pi\)
−0.736038 + 0.676941i \(0.763305\pi\)
\(644\) 0 0
\(645\) 18.1658 0.715279
\(646\) 0 0
\(647\) 32.0364 1.25948 0.629739 0.776806i \(-0.283162\pi\)
0.629739 + 0.776806i \(0.283162\pi\)
\(648\) 0 0
\(649\) 2.23049 0.0875542
\(650\) 0 0
\(651\) −15.1103 −0.592220
\(652\) 0 0
\(653\) −40.4097 −1.58135 −0.790676 0.612235i \(-0.790271\pi\)
−0.790676 + 0.612235i \(0.790271\pi\)
\(654\) 0 0
\(655\) −0.865968 −0.0338362
\(656\) 0 0
\(657\) −7.26261 −0.283341
\(658\) 0 0
\(659\) −8.45813 −0.329482 −0.164741 0.986337i \(-0.552679\pi\)
−0.164741 + 0.986337i \(0.552679\pi\)
\(660\) 0 0
\(661\) −17.1707 −0.667862 −0.333931 0.942597i \(-0.608375\pi\)
−0.333931 + 0.942597i \(0.608375\pi\)
\(662\) 0 0
\(663\) 4.53608 0.176167
\(664\) 0 0
\(665\) −4.97195 −0.192804
\(666\) 0 0
\(667\) −1.67531 −0.0648683
\(668\) 0 0
\(669\) −49.8423 −1.92701
\(670\) 0 0
\(671\) 6.23803 0.240817
\(672\) 0 0
\(673\) 30.3578 1.17021 0.585104 0.810958i \(-0.301054\pi\)
0.585104 + 0.810958i \(0.301054\pi\)
\(674\) 0 0
\(675\) 17.5047 0.673755
\(676\) 0 0
\(677\) 13.6466 0.524482 0.262241 0.965002i \(-0.415539\pi\)
0.262241 + 0.965002i \(0.415539\pi\)
\(678\) 0 0
\(679\) −2.41830 −0.0928057
\(680\) 0 0
\(681\) −3.66156 −0.140311
\(682\) 0 0
\(683\) −43.0332 −1.64662 −0.823310 0.567592i \(-0.807875\pi\)
−0.823310 + 0.567592i \(0.807875\pi\)
\(684\) 0 0
\(685\) 17.3063 0.661241
\(686\) 0 0
\(687\) 38.9576 1.48633
\(688\) 0 0
\(689\) −8.77822 −0.334424
\(690\) 0 0
\(691\) −11.3082 −0.430183 −0.215092 0.976594i \(-0.569005\pi\)
−0.215092 + 0.976594i \(0.569005\pi\)
\(692\) 0 0
\(693\) −0.457073 −0.0173628
\(694\) 0 0
\(695\) −16.1659 −0.613207
\(696\) 0 0
\(697\) 0.512639 0.0194176
\(698\) 0 0
\(699\) −29.3684 −1.11081
\(700\) 0 0
\(701\) 27.0712 1.02246 0.511232 0.859442i \(-0.329189\pi\)
0.511232 + 0.859442i \(0.329189\pi\)
\(702\) 0 0
\(703\) 32.8126 1.23755
\(704\) 0 0
\(705\) −19.0312 −0.716756
\(706\) 0 0
\(707\) 3.57116 0.134307
\(708\) 0 0
\(709\) 28.6143 1.07463 0.537316 0.843381i \(-0.319438\pi\)
0.537316 + 0.843381i \(0.319438\pi\)
\(710\) 0 0
\(711\) −2.46333 −0.0923821
\(712\) 0 0
\(713\) −33.0080 −1.23616
\(714\) 0 0
\(715\) 1.13919 0.0426032
\(716\) 0 0
\(717\) 45.5222 1.70006
\(718\) 0 0
\(719\) 7.89921 0.294591 0.147295 0.989093i \(-0.452943\pi\)
0.147295 + 0.989093i \(0.452943\pi\)
\(720\) 0 0
\(721\) −10.8044 −0.402377
\(722\) 0 0
\(723\) 20.4772 0.761554
\(724\) 0 0
\(725\) 1.52708 0.0567143
\(726\) 0 0
\(727\) −1.67249 −0.0620292 −0.0310146 0.999519i \(-0.509874\pi\)
−0.0310146 + 0.999519i \(0.509874\pi\)
\(728\) 0 0
\(729\) 21.7283 0.804753
\(730\) 0 0
\(731\) −20.9234 −0.773880
\(732\) 0 0
\(733\) 35.7021 1.31869 0.659344 0.751841i \(-0.270834\pi\)
0.659344 + 0.751841i \(0.270834\pi\)
\(734\) 0 0
\(735\) 2.11812 0.0781279
\(736\) 0 0
\(737\) −11.2185 −0.413240
\(738\) 0 0
\(739\) −24.9259 −0.916915 −0.458457 0.888716i \(-0.651598\pi\)
−0.458457 + 0.888716i \(0.651598\pi\)
\(740\) 0 0
\(741\) 8.11495 0.298110
\(742\) 0 0
\(743\) 10.9776 0.402729 0.201365 0.979516i \(-0.435462\pi\)
0.201365 + 0.979516i \(0.435462\pi\)
\(744\) 0 0
\(745\) −7.79886 −0.285728
\(746\) 0 0
\(747\) −2.62578 −0.0960724
\(748\) 0 0
\(749\) 13.8099 0.504602
\(750\) 0 0
\(751\) 1.54131 0.0562431 0.0281215 0.999605i \(-0.491047\pi\)
0.0281215 + 0.999605i \(0.491047\pi\)
\(752\) 0 0
\(753\) 7.46002 0.271858
\(754\) 0 0
\(755\) 0.812537 0.0295712
\(756\) 0 0
\(757\) 20.8138 0.756490 0.378245 0.925705i \(-0.376528\pi\)
0.378245 + 0.925705i \(0.376528\pi\)
\(758\) 0 0
\(759\) −7.55186 −0.274115
\(760\) 0 0
\(761\) 6.52690 0.236600 0.118300 0.992978i \(-0.462256\pi\)
0.118300 + 0.992978i \(0.462256\pi\)
\(762\) 0 0
\(763\) −5.49058 −0.198772
\(764\) 0 0
\(765\) −1.27030 −0.0459279
\(766\) 0 0
\(767\) 2.23049 0.0805382
\(768\) 0 0
\(769\) 28.9745 1.04485 0.522424 0.852686i \(-0.325028\pi\)
0.522424 + 0.852686i \(0.325028\pi\)
\(770\) 0 0
\(771\) −5.61861 −0.202349
\(772\) 0 0
\(773\) −10.4044 −0.374220 −0.187110 0.982339i \(-0.559912\pi\)
−0.187110 + 0.982339i \(0.559912\pi\)
\(774\) 0 0
\(775\) 30.0874 1.08077
\(776\) 0 0
\(777\) −13.9786 −0.501480
\(778\) 0 0
\(779\) 0.917099 0.0328585
\(780\) 0 0
\(781\) 7.84719 0.280794
\(782\) 0 0
\(783\) 1.95022 0.0696952
\(784\) 0 0
\(785\) 12.1139 0.432365
\(786\) 0 0
\(787\) 11.2258 0.400155 0.200078 0.979780i \(-0.435881\pi\)
0.200078 + 0.979780i \(0.435881\pi\)
\(788\) 0 0
\(789\) −0.955040 −0.0340003
\(790\) 0 0
\(791\) 8.64277 0.307301
\(792\) 0 0
\(793\) 6.23803 0.221519
\(794\) 0 0
\(795\) 18.5933 0.659436
\(796\) 0 0
\(797\) 18.2894 0.647845 0.323922 0.946084i \(-0.394998\pi\)
0.323922 + 0.946084i \(0.394998\pi\)
\(798\) 0 0
\(799\) 21.9201 0.775478
\(800\) 0 0
\(801\) 0.264122 0.00933228
\(802\) 0 0
\(803\) 15.8894 0.560725
\(804\) 0 0
\(805\) 4.62695 0.163079
\(806\) 0 0
\(807\) −49.3063 −1.73566
\(808\) 0 0
\(809\) −4.09275 −0.143893 −0.0719467 0.997408i \(-0.522921\pi\)
−0.0719467 + 0.997408i \(0.522921\pi\)
\(810\) 0 0
\(811\) −53.3329 −1.87277 −0.936385 0.350973i \(-0.885851\pi\)
−0.936385 + 0.350973i \(0.885851\pi\)
\(812\) 0 0
\(813\) 58.6154 2.05573
\(814\) 0 0
\(815\) 12.7749 0.447485
\(816\) 0 0
\(817\) −37.4315 −1.30956
\(818\) 0 0
\(819\) −0.457073 −0.0159714
\(820\) 0 0
\(821\) −31.4574 −1.09787 −0.548935 0.835865i \(-0.684966\pi\)
−0.548935 + 0.835865i \(0.684966\pi\)
\(822\) 0 0
\(823\) 55.3033 1.92775 0.963876 0.266351i \(-0.0858179\pi\)
0.963876 + 0.266351i \(0.0858179\pi\)
\(824\) 0 0
\(825\) 6.88367 0.239659
\(826\) 0 0
\(827\) −52.1998 −1.81516 −0.907582 0.419875i \(-0.862074\pi\)
−0.907582 + 0.419875i \(0.862074\pi\)
\(828\) 0 0
\(829\) 19.2170 0.667435 0.333717 0.942673i \(-0.391697\pi\)
0.333717 + 0.942673i \(0.391697\pi\)
\(830\) 0 0
\(831\) 52.0437 1.80537
\(832\) 0 0
\(833\) −2.43965 −0.0845287
\(834\) 0 0
\(835\) 3.88316 0.134382
\(836\) 0 0
\(837\) 38.4244 1.32814
\(838\) 0 0
\(839\) −33.5682 −1.15890 −0.579451 0.815007i \(-0.696733\pi\)
−0.579451 + 0.815007i \(0.696733\pi\)
\(840\) 0 0
\(841\) −28.8299 −0.994133
\(842\) 0 0
\(843\) 50.8412 1.75106
\(844\) 0 0
\(845\) 1.13919 0.0391893
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 9.64067 0.330867
\(850\) 0 0
\(851\) −30.5358 −1.04675
\(852\) 0 0
\(853\) 28.2442 0.967064 0.483532 0.875327i \(-0.339354\pi\)
0.483532 + 0.875327i \(0.339354\pi\)
\(854\) 0 0
\(855\) −2.27254 −0.0777193
\(856\) 0 0
\(857\) 10.6777 0.364742 0.182371 0.983230i \(-0.441623\pi\)
0.182371 + 0.983230i \(0.441623\pi\)
\(858\) 0 0
\(859\) −30.0048 −1.02375 −0.511875 0.859060i \(-0.671049\pi\)
−0.511875 + 0.859060i \(0.671049\pi\)
\(860\) 0 0
\(861\) −0.390696 −0.0133149
\(862\) 0 0
\(863\) −58.1989 −1.98112 −0.990558 0.137097i \(-0.956223\pi\)
−0.990558 + 0.137097i \(0.956223\pi\)
\(864\) 0 0
\(865\) −8.54535 −0.290551
\(866\) 0 0
\(867\) −20.5420 −0.697643
\(868\) 0 0
\(869\) 5.38936 0.182822
\(870\) 0 0
\(871\) −11.2185 −0.380125
\(872\) 0 0
\(873\) −1.10534 −0.0374100
\(874\) 0 0
\(875\) −9.91350 −0.335137
\(876\) 0 0
\(877\) −39.8675 −1.34623 −0.673115 0.739538i \(-0.735044\pi\)
−0.673115 + 0.739538i \(0.735044\pi\)
\(878\) 0 0
\(879\) −53.3179 −1.79837
\(880\) 0 0
\(881\) −24.3519 −0.820437 −0.410218 0.911987i \(-0.634547\pi\)
−0.410218 + 0.911987i \(0.634547\pi\)
\(882\) 0 0
\(883\) −15.3434 −0.516345 −0.258173 0.966099i \(-0.583120\pi\)
−0.258173 + 0.966099i \(0.583120\pi\)
\(884\) 0 0
\(885\) −4.72443 −0.158810
\(886\) 0 0
\(887\) −12.7397 −0.427757 −0.213878 0.976860i \(-0.568610\pi\)
−0.213878 + 0.976860i \(0.568610\pi\)
\(888\) 0 0
\(889\) 18.6357 0.625020
\(890\) 0 0
\(891\) 10.1623 0.340450
\(892\) 0 0
\(893\) 39.2146 1.31227
\(894\) 0 0
\(895\) −18.3043 −0.611846
\(896\) 0 0
\(897\) −7.55186 −0.252149
\(898\) 0 0
\(899\) 3.35208 0.111798
\(900\) 0 0
\(901\) −21.4157 −0.713462
\(902\) 0 0
\(903\) 15.9463 0.530659
\(904\) 0 0
\(905\) −18.3533 −0.610085
\(906\) 0 0
\(907\) −29.2984 −0.972839 −0.486419 0.873725i \(-0.661697\pi\)
−0.486419 + 0.873725i \(0.661697\pi\)
\(908\) 0 0
\(909\) 1.63228 0.0541393
\(910\) 0 0
\(911\) −26.0771 −0.863973 −0.431987 0.901880i \(-0.642187\pi\)
−0.431987 + 0.901880i \(0.642187\pi\)
\(912\) 0 0
\(913\) 5.74479 0.190125
\(914\) 0 0
\(915\) −13.2129 −0.436804
\(916\) 0 0
\(917\) −0.760163 −0.0251028
\(918\) 0 0
\(919\) −7.38215 −0.243515 −0.121757 0.992560i \(-0.538853\pi\)
−0.121757 + 0.992560i \(0.538853\pi\)
\(920\) 0 0
\(921\) −2.25156 −0.0741913
\(922\) 0 0
\(923\) 7.84719 0.258293
\(924\) 0 0
\(925\) 27.8340 0.915176
\(926\) 0 0
\(927\) −4.93840 −0.162198
\(928\) 0 0
\(929\) −41.2805 −1.35437 −0.677185 0.735813i \(-0.736800\pi\)
−0.677185 + 0.735813i \(0.736800\pi\)
\(930\) 0 0
\(931\) −4.36447 −0.143040
\(932\) 0 0
\(933\) −5.81365 −0.190330
\(934\) 0 0
\(935\) 2.77921 0.0908900
\(936\) 0 0
\(937\) −27.6346 −0.902782 −0.451391 0.892326i \(-0.649072\pi\)
−0.451391 + 0.892326i \(0.649072\pi\)
\(938\) 0 0
\(939\) −31.8083 −1.03802
\(940\) 0 0
\(941\) 18.2613 0.595303 0.297651 0.954675i \(-0.403797\pi\)
0.297651 + 0.954675i \(0.403797\pi\)
\(942\) 0 0
\(943\) −0.853463 −0.0277926
\(944\) 0 0
\(945\) −5.38621 −0.175214
\(946\) 0 0
\(947\) −5.38628 −0.175031 −0.0875153 0.996163i \(-0.527893\pi\)
−0.0875153 + 0.996163i \(0.527893\pi\)
\(948\) 0 0
\(949\) 15.8894 0.515792
\(950\) 0 0
\(951\) 53.4714 1.73393
\(952\) 0 0
\(953\) 26.4840 0.857900 0.428950 0.903328i \(-0.358884\pi\)
0.428950 + 0.903328i \(0.358884\pi\)
\(954\) 0 0
\(955\) −4.09766 −0.132597
\(956\) 0 0
\(957\) 0.766920 0.0247910
\(958\) 0 0
\(959\) 15.1918 0.490569
\(960\) 0 0
\(961\) 35.0447 1.13047
\(962\) 0 0
\(963\) 6.31212 0.203405
\(964\) 0 0
\(965\) −5.15555 −0.165963
\(966\) 0 0
\(967\) −26.4189 −0.849574 −0.424787 0.905293i \(-0.639651\pi\)
−0.424787 + 0.905293i \(0.639651\pi\)
\(968\) 0 0
\(969\) 19.7976 0.635990
\(970\) 0 0
\(971\) 7.54863 0.242247 0.121123 0.992637i \(-0.461350\pi\)
0.121123 + 0.992637i \(0.461350\pi\)
\(972\) 0 0
\(973\) −14.1907 −0.454933
\(974\) 0 0
\(975\) 6.88367 0.220454
\(976\) 0 0
\(977\) 22.3574 0.715277 0.357639 0.933860i \(-0.383582\pi\)
0.357639 + 0.933860i \(0.383582\pi\)
\(978\) 0 0
\(979\) −0.577855 −0.0184683
\(980\) 0 0
\(981\) −2.50960 −0.0801252
\(982\) 0 0
\(983\) 29.6401 0.945373 0.472687 0.881231i \(-0.343284\pi\)
0.472687 + 0.881231i \(0.343284\pi\)
\(984\) 0 0
\(985\) 17.2577 0.549877
\(986\) 0 0
\(987\) −16.7059 −0.531755
\(988\) 0 0
\(989\) 34.8342 1.10766
\(990\) 0 0
\(991\) −40.4495 −1.28492 −0.642461 0.766318i \(-0.722087\pi\)
−0.642461 + 0.766318i \(0.722087\pi\)
\(992\) 0 0
\(993\) −57.9363 −1.83855
\(994\) 0 0
\(995\) −5.23633 −0.166003
\(996\) 0 0
\(997\) −22.0197 −0.697372 −0.348686 0.937240i \(-0.613372\pi\)
−0.348686 + 0.937240i \(0.613372\pi\)
\(998\) 0 0
\(999\) 35.5466 1.12464
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 \(a_p\))