Properties

Label 8008.2.a.n.1.1
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 1.1
Root \(3.07040\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.07040 q^{3} -3.53994 q^{5} -1.00000 q^{7} +6.42735 q^{9} +O(q^{10})\) \(q-3.07040 q^{3} -3.53994 q^{5} -1.00000 q^{7} +6.42735 q^{9} +1.00000 q^{11} -1.00000 q^{13} +10.8690 q^{15} +1.83553 q^{17} -0.318127 q^{19} +3.07040 q^{21} +1.10506 q^{23} +7.53117 q^{25} -10.5233 q^{27} -1.36170 q^{29} -1.34508 q^{31} -3.07040 q^{33} +3.53994 q^{35} +10.6497 q^{37} +3.07040 q^{39} +0.852734 q^{41} -2.13797 q^{43} -22.7524 q^{45} +10.5005 q^{47} +1.00000 q^{49} -5.63580 q^{51} -1.45473 q^{53} -3.53994 q^{55} +0.976776 q^{57} -5.50546 q^{59} -4.79694 q^{61} -6.42735 q^{63} +3.53994 q^{65} +1.55735 q^{67} -3.39297 q^{69} +0.673836 q^{71} +2.83968 q^{73} -23.1237 q^{75} -1.00000 q^{77} -6.33566 q^{79} +13.0288 q^{81} -4.51924 q^{83} -6.49766 q^{85} +4.18097 q^{87} -13.3709 q^{89} +1.00000 q^{91} +4.12992 q^{93} +1.12615 q^{95} -3.08525 q^{97} +6.42735 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + O(q^{10}) \) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + 9q^{11} - 9q^{13} + 11q^{15} + 7q^{17} - 17q^{19} + 3q^{21} + 11q^{23} + 18q^{25} - 9q^{27} + 9q^{29} - 8q^{31} - 3q^{33} - q^{35} + 2q^{37} + 3q^{39} + 18q^{41} + 7q^{43} + 5q^{45} + 15q^{47} + 9q^{49} - 7q^{51} - 4q^{53} + q^{55} + 22q^{57} - 23q^{59} + 12q^{61} - 12q^{63} - q^{65} - 16q^{67} - 32q^{69} - 6q^{71} + 4q^{73} - 14q^{75} - 9q^{77} + 21q^{79} + 5q^{81} - 16q^{83} + 53q^{85} + 41q^{87} + 5q^{89} + 9q^{91} + 29q^{93} + 19q^{95} + 18q^{97} + 12q^{99} + O(q^{100}) \)

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
\(3\) −3.07040 −1.77270 −0.886348 0.463020i \(-0.846766\pi\)
−0.886348 + 0.463020i \(0.846766\pi\)
\(4\) 0 0
\(5\) −3.53994 −1.58311 −0.791554 0.611099i \(-0.790728\pi\)
−0.791554 + 0.611099i \(0.790728\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 6.42735 2.14245
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 10.8690 2.80637
\(16\) 0 0
\(17\) 1.83553 0.445181 0.222590 0.974912i \(-0.428549\pi\)
0.222590 + 0.974912i \(0.428549\pi\)
\(18\) 0 0
\(19\) −0.318127 −0.0729833 −0.0364916 0.999334i \(-0.511618\pi\)
−0.0364916 + 0.999334i \(0.511618\pi\)
\(20\) 0 0
\(21\) 3.07040 0.670016
\(22\) 0 0
\(23\) 1.10506 0.230421 0.115210 0.993341i \(-0.463246\pi\)
0.115210 + 0.993341i \(0.463246\pi\)
\(24\) 0 0
\(25\) 7.53117 1.50623
\(26\) 0 0
\(27\) −10.5233 −2.02522
\(28\) 0 0
\(29\) −1.36170 −0.252862 −0.126431 0.991975i \(-0.540352\pi\)
−0.126431 + 0.991975i \(0.540352\pi\)
\(30\) 0 0
\(31\) −1.34508 −0.241583 −0.120791 0.992678i \(-0.538543\pi\)
−0.120791 + 0.992678i \(0.538543\pi\)
\(32\) 0 0
\(33\) −3.07040 −0.534488
\(34\) 0 0
\(35\) 3.53994 0.598359
\(36\) 0 0
\(37\) 10.6497 1.75080 0.875399 0.483400i \(-0.160598\pi\)
0.875399 + 0.483400i \(0.160598\pi\)
\(38\) 0 0
\(39\) 3.07040 0.491657
\(40\) 0 0
\(41\) 0.852734 0.133175 0.0665874 0.997781i \(-0.478789\pi\)
0.0665874 + 0.997781i \(0.478789\pi\)
\(42\) 0 0
\(43\) −2.13797 −0.326037 −0.163018 0.986623i \(-0.552123\pi\)
−0.163018 + 0.986623i \(0.552123\pi\)
\(44\) 0 0
\(45\) −22.7524 −3.39173
\(46\) 0 0
\(47\) 10.5005 1.53166 0.765831 0.643042i \(-0.222328\pi\)
0.765831 + 0.643042i \(0.222328\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −5.63580 −0.789170
\(52\) 0 0
\(53\) −1.45473 −0.199823 −0.0999115 0.994996i \(-0.531856\pi\)
−0.0999115 + 0.994996i \(0.531856\pi\)
\(54\) 0 0
\(55\) −3.53994 −0.477325
\(56\) 0 0
\(57\) 0.976776 0.129377
\(58\) 0 0
\(59\) −5.50546 −0.716750 −0.358375 0.933578i \(-0.616669\pi\)
−0.358375 + 0.933578i \(0.616669\pi\)
\(60\) 0 0
\(61\) −4.79694 −0.614185 −0.307093 0.951680i \(-0.599356\pi\)
−0.307093 + 0.951680i \(0.599356\pi\)
\(62\) 0 0
\(63\) −6.42735 −0.809770
\(64\) 0 0
\(65\) 3.53994 0.439075
\(66\) 0 0
\(67\) 1.55735 0.190260 0.0951302 0.995465i \(-0.469673\pi\)
0.0951302 + 0.995465i \(0.469673\pi\)
\(68\) 0 0
\(69\) −3.39297 −0.408466
\(70\) 0 0
\(71\) 0.673836 0.0799696 0.0399848 0.999200i \(-0.487269\pi\)
0.0399848 + 0.999200i \(0.487269\pi\)
\(72\) 0 0
\(73\) 2.83968 0.332359 0.166179 0.986096i \(-0.446857\pi\)
0.166179 + 0.986096i \(0.446857\pi\)
\(74\) 0 0
\(75\) −23.1237 −2.67009
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −6.33566 −0.712818 −0.356409 0.934330i \(-0.615999\pi\)
−0.356409 + 0.934330i \(0.615999\pi\)
\(80\) 0 0
\(81\) 13.0288 1.44764
\(82\) 0 0
\(83\) −4.51924 −0.496051 −0.248025 0.968754i \(-0.579782\pi\)
−0.248025 + 0.968754i \(0.579782\pi\)
\(84\) 0 0
\(85\) −6.49766 −0.704770
\(86\) 0 0
\(87\) 4.18097 0.448247
\(88\) 0 0
\(89\) −13.3709 −1.41731 −0.708654 0.705556i \(-0.750697\pi\)
−0.708654 + 0.705556i \(0.750697\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 4.12992 0.428253
\(94\) 0 0
\(95\) 1.12615 0.115540
\(96\) 0 0
\(97\) −3.08525 −0.313260 −0.156630 0.987657i \(-0.550063\pi\)
−0.156630 + 0.987657i \(0.550063\pi\)
\(98\) 0 0
\(99\) 6.42735 0.645973
\(100\) 0 0
\(101\) 14.2620 1.41912 0.709559 0.704646i \(-0.248894\pi\)
0.709559 + 0.704646i \(0.248894\pi\)
\(102\) 0 0
\(103\) −15.8325 −1.56002 −0.780010 0.625767i \(-0.784786\pi\)
−0.780010 + 0.625767i \(0.784786\pi\)
\(104\) 0 0
\(105\) −10.8690 −1.06071
\(106\) 0 0
\(107\) −14.7426 −1.42522 −0.712612 0.701558i \(-0.752488\pi\)
−0.712612 + 0.701558i \(0.752488\pi\)
\(108\) 0 0
\(109\) −10.4349 −0.999480 −0.499740 0.866176i \(-0.666571\pi\)
−0.499740 + 0.866176i \(0.666571\pi\)
\(110\) 0 0
\(111\) −32.6988 −3.10363
\(112\) 0 0
\(113\) 9.85354 0.926943 0.463472 0.886112i \(-0.346604\pi\)
0.463472 + 0.886112i \(0.346604\pi\)
\(114\) 0 0
\(115\) −3.91184 −0.364781
\(116\) 0 0
\(117\) −6.42735 −0.594209
\(118\) 0 0
\(119\) −1.83553 −0.168263
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −2.61824 −0.236078
\(124\) 0 0
\(125\) −8.96018 −0.801423
\(126\) 0 0
\(127\) 2.56257 0.227391 0.113696 0.993516i \(-0.463731\pi\)
0.113696 + 0.993516i \(0.463731\pi\)
\(128\) 0 0
\(129\) 6.56441 0.577964
\(130\) 0 0
\(131\) −6.39260 −0.558524 −0.279262 0.960215i \(-0.590090\pi\)
−0.279262 + 0.960215i \(0.590090\pi\)
\(132\) 0 0
\(133\) 0.318127 0.0275851
\(134\) 0 0
\(135\) 37.2520 3.20614
\(136\) 0 0
\(137\) 5.06708 0.432910 0.216455 0.976293i \(-0.430551\pi\)
0.216455 + 0.976293i \(0.430551\pi\)
\(138\) 0 0
\(139\) −12.7171 −1.07865 −0.539325 0.842098i \(-0.681321\pi\)
−0.539325 + 0.842098i \(0.681321\pi\)
\(140\) 0 0
\(141\) −32.2409 −2.71517
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 4.82034 0.400307
\(146\) 0 0
\(147\) −3.07040 −0.253242
\(148\) 0 0
\(149\) −13.4741 −1.10384 −0.551921 0.833896i \(-0.686105\pi\)
−0.551921 + 0.833896i \(0.686105\pi\)
\(150\) 0 0
\(151\) 23.3013 1.89623 0.948117 0.317922i \(-0.102985\pi\)
0.948117 + 0.317922i \(0.102985\pi\)
\(152\) 0 0
\(153\) 11.7976 0.953778
\(154\) 0 0
\(155\) 4.76148 0.382452
\(156\) 0 0
\(157\) −6.46455 −0.515927 −0.257964 0.966155i \(-0.583051\pi\)
−0.257964 + 0.966155i \(0.583051\pi\)
\(158\) 0 0
\(159\) 4.46661 0.354225
\(160\) 0 0
\(161\) −1.10506 −0.0870908
\(162\) 0 0
\(163\) −22.0285 −1.72540 −0.862702 0.505713i \(-0.831230\pi\)
−0.862702 + 0.505713i \(0.831230\pi\)
\(164\) 0 0
\(165\) 10.8690 0.846153
\(166\) 0 0
\(167\) −12.8268 −0.992566 −0.496283 0.868161i \(-0.665302\pi\)
−0.496283 + 0.868161i \(0.665302\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −2.04471 −0.156363
\(172\) 0 0
\(173\) 0.896457 0.0681564 0.0340782 0.999419i \(-0.489150\pi\)
0.0340782 + 0.999419i \(0.489150\pi\)
\(174\) 0 0
\(175\) −7.53117 −0.569303
\(176\) 0 0
\(177\) 16.9040 1.27058
\(178\) 0 0
\(179\) 14.6403 1.09427 0.547134 0.837045i \(-0.315719\pi\)
0.547134 + 0.837045i \(0.315719\pi\)
\(180\) 0 0
\(181\) 7.12159 0.529344 0.264672 0.964339i \(-0.414736\pi\)
0.264672 + 0.964339i \(0.414736\pi\)
\(182\) 0 0
\(183\) 14.7285 1.08876
\(184\) 0 0
\(185\) −37.6993 −2.77171
\(186\) 0 0
\(187\) 1.83553 0.134227
\(188\) 0 0
\(189\) 10.5233 0.765460
\(190\) 0 0
\(191\) 4.81282 0.348244 0.174122 0.984724i \(-0.444291\pi\)
0.174122 + 0.984724i \(0.444291\pi\)
\(192\) 0 0
\(193\) 1.49734 0.107781 0.0538903 0.998547i \(-0.482838\pi\)
0.0538903 + 0.998547i \(0.482838\pi\)
\(194\) 0 0
\(195\) −10.8690 −0.778347
\(196\) 0 0
\(197\) −11.5736 −0.824582 −0.412291 0.911052i \(-0.635271\pi\)
−0.412291 + 0.911052i \(0.635271\pi\)
\(198\) 0 0
\(199\) −15.1145 −1.07144 −0.535718 0.844397i \(-0.679959\pi\)
−0.535718 + 0.844397i \(0.679959\pi\)
\(200\) 0 0
\(201\) −4.78168 −0.337274
\(202\) 0 0
\(203\) 1.36170 0.0955727
\(204\) 0 0
\(205\) −3.01863 −0.210830
\(206\) 0 0
\(207\) 7.10260 0.493665
\(208\) 0 0
\(209\) −0.318127 −0.0220053
\(210\) 0 0
\(211\) −6.20348 −0.427065 −0.213532 0.976936i \(-0.568497\pi\)
−0.213532 + 0.976936i \(0.568497\pi\)
\(212\) 0 0
\(213\) −2.06895 −0.141762
\(214\) 0 0
\(215\) 7.56827 0.516151
\(216\) 0 0
\(217\) 1.34508 0.0913097
\(218\) 0 0
\(219\) −8.71894 −0.589171
\(220\) 0 0
\(221\) −1.83553 −0.123471
\(222\) 0 0
\(223\) −13.9688 −0.935421 −0.467711 0.883882i \(-0.654921\pi\)
−0.467711 + 0.883882i \(0.654921\pi\)
\(224\) 0 0
\(225\) 48.4055 3.22703
\(226\) 0 0
\(227\) −4.25786 −0.282604 −0.141302 0.989967i \(-0.545129\pi\)
−0.141302 + 0.989967i \(0.545129\pi\)
\(228\) 0 0
\(229\) 2.43864 0.161150 0.0805751 0.996749i \(-0.474324\pi\)
0.0805751 + 0.996749i \(0.474324\pi\)
\(230\) 0 0
\(231\) 3.07040 0.202017
\(232\) 0 0
\(233\) 24.0686 1.57678 0.788392 0.615173i \(-0.210914\pi\)
0.788392 + 0.615173i \(0.210914\pi\)
\(234\) 0 0
\(235\) −37.1713 −2.42479
\(236\) 0 0
\(237\) 19.4530 1.26361
\(238\) 0 0
\(239\) 12.0385 0.778703 0.389351 0.921089i \(-0.372699\pi\)
0.389351 + 0.921089i \(0.372699\pi\)
\(240\) 0 0
\(241\) 15.3026 0.985730 0.492865 0.870106i \(-0.335950\pi\)
0.492865 + 0.870106i \(0.335950\pi\)
\(242\) 0 0
\(243\) −8.43361 −0.541016
\(244\) 0 0
\(245\) −3.53994 −0.226158
\(246\) 0 0
\(247\) 0.318127 0.0202419
\(248\) 0 0
\(249\) 13.8759 0.879347
\(250\) 0 0
\(251\) −0.800260 −0.0505120 −0.0252560 0.999681i \(-0.508040\pi\)
−0.0252560 + 0.999681i \(0.508040\pi\)
\(252\) 0 0
\(253\) 1.10506 0.0694744
\(254\) 0 0
\(255\) 19.9504 1.24934
\(256\) 0 0
\(257\) 19.3486 1.20693 0.603467 0.797388i \(-0.293786\pi\)
0.603467 + 0.797388i \(0.293786\pi\)
\(258\) 0 0
\(259\) −10.6497 −0.661740
\(260\) 0 0
\(261\) −8.75213 −0.541743
\(262\) 0 0
\(263\) 19.4405 1.19876 0.599378 0.800466i \(-0.295415\pi\)
0.599378 + 0.800466i \(0.295415\pi\)
\(264\) 0 0
\(265\) 5.14967 0.316341
\(266\) 0 0
\(267\) 41.0539 2.51246
\(268\) 0 0
\(269\) 17.2124 1.04946 0.524731 0.851268i \(-0.324166\pi\)
0.524731 + 0.851268i \(0.324166\pi\)
\(270\) 0 0
\(271\) 10.5128 0.638609 0.319304 0.947652i \(-0.396551\pi\)
0.319304 + 0.947652i \(0.396551\pi\)
\(272\) 0 0
\(273\) −3.07040 −0.185829
\(274\) 0 0
\(275\) 7.53117 0.454146
\(276\) 0 0
\(277\) 25.6416 1.54065 0.770327 0.637649i \(-0.220093\pi\)
0.770327 + 0.637649i \(0.220093\pi\)
\(278\) 0 0
\(279\) −8.64527 −0.517579
\(280\) 0 0
\(281\) 15.0875 0.900045 0.450022 0.893017i \(-0.351416\pi\)
0.450022 + 0.893017i \(0.351416\pi\)
\(282\) 0 0
\(283\) −12.7746 −0.759373 −0.379686 0.925115i \(-0.623968\pi\)
−0.379686 + 0.925115i \(0.623968\pi\)
\(284\) 0 0
\(285\) −3.45773 −0.204818
\(286\) 0 0
\(287\) −0.852734 −0.0503353
\(288\) 0 0
\(289\) −13.6308 −0.801814
\(290\) 0 0
\(291\) 9.47296 0.555315
\(292\) 0 0
\(293\) 4.45302 0.260148 0.130074 0.991504i \(-0.458478\pi\)
0.130074 + 0.991504i \(0.458478\pi\)
\(294\) 0 0
\(295\) 19.4890 1.13469
\(296\) 0 0
\(297\) −10.5233 −0.610626
\(298\) 0 0
\(299\) −1.10506 −0.0639072
\(300\) 0 0
\(301\) 2.13797 0.123230
\(302\) 0 0
\(303\) −43.7899 −2.51567
\(304\) 0 0
\(305\) 16.9809 0.972322
\(306\) 0 0
\(307\) −2.92416 −0.166890 −0.0834452 0.996512i \(-0.526592\pi\)
−0.0834452 + 0.996512i \(0.526592\pi\)
\(308\) 0 0
\(309\) 48.6120 2.76544
\(310\) 0 0
\(311\) 4.81577 0.273077 0.136539 0.990635i \(-0.456402\pi\)
0.136539 + 0.990635i \(0.456402\pi\)
\(312\) 0 0
\(313\) −11.6350 −0.657652 −0.328826 0.944391i \(-0.606653\pi\)
−0.328826 + 0.944391i \(0.606653\pi\)
\(314\) 0 0
\(315\) 22.7524 1.28195
\(316\) 0 0
\(317\) −0.568439 −0.0319267 −0.0159634 0.999873i \(-0.505082\pi\)
−0.0159634 + 0.999873i \(0.505082\pi\)
\(318\) 0 0
\(319\) −1.36170 −0.0762406
\(320\) 0 0
\(321\) 45.2658 2.52649
\(322\) 0 0
\(323\) −0.583930 −0.0324908
\(324\) 0 0
\(325\) −7.53117 −0.417754
\(326\) 0 0
\(327\) 32.0392 1.77177
\(328\) 0 0
\(329\) −10.5005 −0.578914
\(330\) 0 0
\(331\) −3.42000 −0.187980 −0.0939901 0.995573i \(-0.529962\pi\)
−0.0939901 + 0.995573i \(0.529962\pi\)
\(332\) 0 0
\(333\) 68.4493 3.75100
\(334\) 0 0
\(335\) −5.51292 −0.301203
\(336\) 0 0
\(337\) 12.4942 0.680601 0.340300 0.940317i \(-0.389471\pi\)
0.340300 + 0.940317i \(0.389471\pi\)
\(338\) 0 0
\(339\) −30.2543 −1.64319
\(340\) 0 0
\(341\) −1.34508 −0.0728399
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 12.0109 0.646646
\(346\) 0 0
\(347\) 7.94152 0.426323 0.213161 0.977017i \(-0.431624\pi\)
0.213161 + 0.977017i \(0.431624\pi\)
\(348\) 0 0
\(349\) 34.6625 1.85544 0.927719 0.373278i \(-0.121766\pi\)
0.927719 + 0.373278i \(0.121766\pi\)
\(350\) 0 0
\(351\) 10.5233 0.561694
\(352\) 0 0
\(353\) 0.488574 0.0260041 0.0130021 0.999915i \(-0.495861\pi\)
0.0130021 + 0.999915i \(0.495861\pi\)
\(354\) 0 0
\(355\) −2.38534 −0.126601
\(356\) 0 0
\(357\) 5.63580 0.298278
\(358\) 0 0
\(359\) −28.8639 −1.52338 −0.761688 0.647944i \(-0.775629\pi\)
−0.761688 + 0.647944i \(0.775629\pi\)
\(360\) 0 0
\(361\) −18.8988 −0.994673
\(362\) 0 0
\(363\) −3.07040 −0.161154
\(364\) 0 0
\(365\) −10.0523 −0.526160
\(366\) 0 0
\(367\) −1.96410 −0.102525 −0.0512625 0.998685i \(-0.516325\pi\)
−0.0512625 + 0.998685i \(0.516325\pi\)
\(368\) 0 0
\(369\) 5.48083 0.285320
\(370\) 0 0
\(371\) 1.45473 0.0755260
\(372\) 0 0
\(373\) 16.7295 0.866219 0.433109 0.901341i \(-0.357416\pi\)
0.433109 + 0.901341i \(0.357416\pi\)
\(374\) 0 0
\(375\) 27.5113 1.42068
\(376\) 0 0
\(377\) 1.36170 0.0701312
\(378\) 0 0
\(379\) −17.4701 −0.897380 −0.448690 0.893687i \(-0.648109\pi\)
−0.448690 + 0.893687i \(0.648109\pi\)
\(380\) 0 0
\(381\) −7.86812 −0.403096
\(382\) 0 0
\(383\) −8.87459 −0.453471 −0.226735 0.973956i \(-0.572805\pi\)
−0.226735 + 0.973956i \(0.572805\pi\)
\(384\) 0 0
\(385\) 3.53994 0.180412
\(386\) 0 0
\(387\) −13.7415 −0.698517
\(388\) 0 0
\(389\) −14.8454 −0.752691 −0.376346 0.926479i \(-0.622820\pi\)
−0.376346 + 0.926479i \(0.622820\pi\)
\(390\) 0 0
\(391\) 2.02837 0.102579
\(392\) 0 0
\(393\) 19.6278 0.990093
\(394\) 0 0
\(395\) 22.4279 1.12847
\(396\) 0 0
\(397\) 20.4087 1.02428 0.512142 0.858901i \(-0.328852\pi\)
0.512142 + 0.858901i \(0.328852\pi\)
\(398\) 0 0
\(399\) −0.976776 −0.0489000
\(400\) 0 0
\(401\) −13.1461 −0.656485 −0.328242 0.944594i \(-0.606456\pi\)
−0.328242 + 0.944594i \(0.606456\pi\)
\(402\) 0 0
\(403\) 1.34508 0.0670030
\(404\) 0 0
\(405\) −46.1212 −2.29178
\(406\) 0 0
\(407\) 10.6497 0.527886
\(408\) 0 0
\(409\) −1.67209 −0.0826796 −0.0413398 0.999145i \(-0.513163\pi\)
−0.0413398 + 0.999145i \(0.513163\pi\)
\(410\) 0 0
\(411\) −15.5580 −0.767418
\(412\) 0 0
\(413\) 5.50546 0.270906
\(414\) 0 0
\(415\) 15.9978 0.785302
\(416\) 0 0
\(417\) 39.0466 1.91212
\(418\) 0 0
\(419\) −9.99163 −0.488123 −0.244061 0.969760i \(-0.578480\pi\)
−0.244061 + 0.969760i \(0.578480\pi\)
\(420\) 0 0
\(421\) 23.2254 1.13194 0.565969 0.824426i \(-0.308502\pi\)
0.565969 + 0.824426i \(0.308502\pi\)
\(422\) 0 0
\(423\) 67.4907 3.28151
\(424\) 0 0
\(425\) 13.8237 0.670546
\(426\) 0 0
\(427\) 4.79694 0.232140
\(428\) 0 0
\(429\) 3.07040 0.148240
\(430\) 0 0
\(431\) 23.7865 1.14576 0.572878 0.819640i \(-0.305827\pi\)
0.572878 + 0.819640i \(0.305827\pi\)
\(432\) 0 0
\(433\) 18.6525 0.896382 0.448191 0.893938i \(-0.352068\pi\)
0.448191 + 0.893938i \(0.352068\pi\)
\(434\) 0 0
\(435\) −14.8004 −0.709623
\(436\) 0 0
\(437\) −0.351549 −0.0168169
\(438\) 0 0
\(439\) −19.4711 −0.929306 −0.464653 0.885493i \(-0.653821\pi\)
−0.464653 + 0.885493i \(0.653821\pi\)
\(440\) 0 0
\(441\) 6.42735 0.306064
\(442\) 0 0
\(443\) 31.0959 1.47741 0.738706 0.674028i \(-0.235437\pi\)
0.738706 + 0.674028i \(0.235437\pi\)
\(444\) 0 0
\(445\) 47.3320 2.24375
\(446\) 0 0
\(447\) 41.3709 1.95678
\(448\) 0 0
\(449\) −15.6766 −0.739823 −0.369911 0.929067i \(-0.620612\pi\)
−0.369911 + 0.929067i \(0.620612\pi\)
\(450\) 0 0
\(451\) 0.852734 0.0401537
\(452\) 0 0
\(453\) −71.5443 −3.36145
\(454\) 0 0
\(455\) −3.53994 −0.165955
\(456\) 0 0
\(457\) 24.4595 1.14417 0.572084 0.820195i \(-0.306135\pi\)
0.572084 + 0.820195i \(0.306135\pi\)
\(458\) 0 0
\(459\) −19.3159 −0.901588
\(460\) 0 0
\(461\) −21.5634 −1.00431 −0.502154 0.864778i \(-0.667459\pi\)
−0.502154 + 0.864778i \(0.667459\pi\)
\(462\) 0 0
\(463\) −18.6525 −0.866856 −0.433428 0.901188i \(-0.642696\pi\)
−0.433428 + 0.901188i \(0.642696\pi\)
\(464\) 0 0
\(465\) −14.6197 −0.677970
\(466\) 0 0
\(467\) −19.7416 −0.913532 −0.456766 0.889587i \(-0.650992\pi\)
−0.456766 + 0.889587i \(0.650992\pi\)
\(468\) 0 0
\(469\) −1.55735 −0.0719117
\(470\) 0 0
\(471\) 19.8487 0.914582
\(472\) 0 0
\(473\) −2.13797 −0.0983037
\(474\) 0 0
\(475\) −2.39587 −0.109930
\(476\) 0 0
\(477\) −9.35008 −0.428111
\(478\) 0 0
\(479\) 22.5165 1.02880 0.514402 0.857549i \(-0.328014\pi\)
0.514402 + 0.857549i \(0.328014\pi\)
\(480\) 0 0
\(481\) −10.6497 −0.485584
\(482\) 0 0
\(483\) 3.39297 0.154386
\(484\) 0 0
\(485\) 10.9216 0.495925
\(486\) 0 0
\(487\) 1.47178 0.0666929 0.0333464 0.999444i \(-0.489384\pi\)
0.0333464 + 0.999444i \(0.489384\pi\)
\(488\) 0 0
\(489\) 67.6362 3.05862
\(490\) 0 0
\(491\) −27.8596 −1.25729 −0.628644 0.777693i \(-0.716390\pi\)
−0.628644 + 0.777693i \(0.716390\pi\)
\(492\) 0 0
\(493\) −2.49944 −0.112569
\(494\) 0 0
\(495\) −22.7524 −1.02265
\(496\) 0 0
\(497\) −0.673836 −0.0302257
\(498\) 0 0
\(499\) −23.6808 −1.06010 −0.530048 0.847967i \(-0.677826\pi\)
−0.530048 + 0.847967i \(0.677826\pi\)
\(500\) 0 0
\(501\) 39.3833 1.75952
\(502\) 0 0
\(503\) 23.7351 1.05829 0.529147 0.848530i \(-0.322512\pi\)
0.529147 + 0.848530i \(0.322512\pi\)
\(504\) 0 0
\(505\) −50.4865 −2.24662
\(506\) 0 0
\(507\) −3.07040 −0.136361
\(508\) 0 0
\(509\) −21.0502 −0.933032 −0.466516 0.884513i \(-0.654491\pi\)
−0.466516 + 0.884513i \(0.654491\pi\)
\(510\) 0 0
\(511\) −2.83968 −0.125620
\(512\) 0 0
\(513\) 3.34776 0.147807
\(514\) 0 0
\(515\) 56.0460 2.46968
\(516\) 0 0
\(517\) 10.5005 0.461813
\(518\) 0 0
\(519\) −2.75248 −0.120821
\(520\) 0 0
\(521\) −13.2797 −0.581795 −0.290897 0.956754i \(-0.593954\pi\)
−0.290897 + 0.956754i \(0.593954\pi\)
\(522\) 0 0
\(523\) 35.0330 1.53189 0.765944 0.642907i \(-0.222272\pi\)
0.765944 + 0.642907i \(0.222272\pi\)
\(524\) 0 0
\(525\) 23.1237 1.00920
\(526\) 0 0
\(527\) −2.46892 −0.107548
\(528\) 0 0
\(529\) −21.7788 −0.946906
\(530\) 0 0
\(531\) −35.3856 −1.53560
\(532\) 0 0
\(533\) −0.852734 −0.0369360
\(534\) 0 0
\(535\) 52.1880 2.25628
\(536\) 0 0
\(537\) −44.9516 −1.93980
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −11.0767 −0.476224 −0.238112 0.971238i \(-0.576529\pi\)
−0.238112 + 0.971238i \(0.576529\pi\)
\(542\) 0 0
\(543\) −21.8661 −0.938365
\(544\) 0 0
\(545\) 36.9388 1.58228
\(546\) 0 0
\(547\) −44.4467 −1.90040 −0.950202 0.311634i \(-0.899124\pi\)
−0.950202 + 0.311634i \(0.899124\pi\)
\(548\) 0 0
\(549\) −30.8316 −1.31586
\(550\) 0 0
\(551\) 0.433193 0.0184547
\(552\) 0 0
\(553\) 6.33566 0.269420
\(554\) 0 0
\(555\) 115.752 4.91339
\(556\) 0 0
\(557\) 2.34468 0.0993473 0.0496736 0.998766i \(-0.484182\pi\)
0.0496736 + 0.998766i \(0.484182\pi\)
\(558\) 0 0
\(559\) 2.13797 0.0904263
\(560\) 0 0
\(561\) −5.63580 −0.237944
\(562\) 0 0
\(563\) 25.2348 1.06352 0.531760 0.846895i \(-0.321531\pi\)
0.531760 + 0.846895i \(0.321531\pi\)
\(564\) 0 0
\(565\) −34.8809 −1.46745
\(566\) 0 0
\(567\) −13.0288 −0.547158
\(568\) 0 0
\(569\) −39.5541 −1.65819 −0.829097 0.559105i \(-0.811145\pi\)
−0.829097 + 0.559105i \(0.811145\pi\)
\(570\) 0 0
\(571\) 1.28447 0.0537532 0.0268766 0.999639i \(-0.491444\pi\)
0.0268766 + 0.999639i \(0.491444\pi\)
\(572\) 0 0
\(573\) −14.7773 −0.617330
\(574\) 0 0
\(575\) 8.32238 0.347067
\(576\) 0 0
\(577\) −14.5395 −0.605288 −0.302644 0.953104i \(-0.597869\pi\)
−0.302644 + 0.953104i \(0.597869\pi\)
\(578\) 0 0
\(579\) −4.59742 −0.191062
\(580\) 0 0
\(581\) 4.51924 0.187490
\(582\) 0 0
\(583\) −1.45473 −0.0602489
\(584\) 0 0
\(585\) 22.7524 0.940697
\(586\) 0 0
\(587\) −32.1511 −1.32702 −0.663510 0.748168i \(-0.730934\pi\)
−0.663510 + 0.748168i \(0.730934\pi\)
\(588\) 0 0
\(589\) 0.427904 0.0176315
\(590\) 0 0
\(591\) 35.5355 1.46173
\(592\) 0 0
\(593\) 31.1241 1.27811 0.639057 0.769159i \(-0.279325\pi\)
0.639057 + 0.769159i \(0.279325\pi\)
\(594\) 0 0
\(595\) 6.49766 0.266378
\(596\) 0 0
\(597\) 46.4074 1.89933
\(598\) 0 0
\(599\) 27.8698 1.13873 0.569364 0.822085i \(-0.307189\pi\)
0.569364 + 0.822085i \(0.307189\pi\)
\(600\) 0 0
\(601\) −24.7458 −1.00940 −0.504701 0.863294i \(-0.668397\pi\)
−0.504701 + 0.863294i \(0.668397\pi\)
\(602\) 0 0
\(603\) 10.0096 0.407624
\(604\) 0 0
\(605\) −3.53994 −0.143919
\(606\) 0 0
\(607\) 26.0137 1.05586 0.527931 0.849287i \(-0.322968\pi\)
0.527931 + 0.849287i \(0.322968\pi\)
\(608\) 0 0
\(609\) −4.18097 −0.169421
\(610\) 0 0
\(611\) −10.5005 −0.424806
\(612\) 0 0
\(613\) −4.72789 −0.190958 −0.0954788 0.995431i \(-0.530438\pi\)
−0.0954788 + 0.995431i \(0.530438\pi\)
\(614\) 0 0
\(615\) 9.26839 0.373738
\(616\) 0 0
\(617\) 34.5562 1.39118 0.695591 0.718438i \(-0.255143\pi\)
0.695591 + 0.718438i \(0.255143\pi\)
\(618\) 0 0
\(619\) 22.3735 0.899268 0.449634 0.893213i \(-0.351554\pi\)
0.449634 + 0.893213i \(0.351554\pi\)
\(620\) 0 0
\(621\) −11.6289 −0.466652
\(622\) 0 0
\(623\) 13.3709 0.535692
\(624\) 0 0
\(625\) −5.93735 −0.237494
\(626\) 0 0
\(627\) 0.976776 0.0390087
\(628\) 0 0
\(629\) 19.5478 0.779422
\(630\) 0 0
\(631\) 7.63999 0.304143 0.152072 0.988369i \(-0.451406\pi\)
0.152072 + 0.988369i \(0.451406\pi\)
\(632\) 0 0
\(633\) 19.0471 0.757056
\(634\) 0 0
\(635\) −9.07135 −0.359985
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 4.33098 0.171331
\(640\) 0 0
\(641\) 27.2348 1.07571 0.537855 0.843037i \(-0.319235\pi\)
0.537855 + 0.843037i \(0.319235\pi\)
\(642\) 0 0
\(643\) 37.4951 1.47866 0.739331 0.673342i \(-0.235142\pi\)
0.739331 + 0.673342i \(0.235142\pi\)
\(644\) 0 0
\(645\) −23.2376 −0.914980
\(646\) 0 0
\(647\) 29.2852 1.15132 0.575660 0.817689i \(-0.304745\pi\)
0.575660 + 0.817689i \(0.304745\pi\)
\(648\) 0 0
\(649\) −5.50546 −0.216108
\(650\) 0 0
\(651\) −4.12992 −0.161864
\(652\) 0 0
\(653\) 3.97367 0.155502 0.0777509 0.996973i \(-0.475226\pi\)
0.0777509 + 0.996973i \(0.475226\pi\)
\(654\) 0 0
\(655\) 22.6294 0.884204
\(656\) 0 0
\(657\) 18.2516 0.712063
\(658\) 0 0
\(659\) −32.6580 −1.27218 −0.636088 0.771617i \(-0.719448\pi\)
−0.636088 + 0.771617i \(0.719448\pi\)
\(660\) 0 0
\(661\) 38.9618 1.51544 0.757718 0.652582i \(-0.226314\pi\)
0.757718 + 0.652582i \(0.226314\pi\)
\(662\) 0 0
\(663\) 5.63580 0.218877
\(664\) 0 0
\(665\) −1.12615 −0.0436702
\(666\) 0 0
\(667\) −1.50476 −0.0582645
\(668\) 0 0
\(669\) 42.8899 1.65822
\(670\) 0 0
\(671\) −4.79694 −0.185184
\(672\) 0 0
\(673\) −8.12969 −0.313376 −0.156688 0.987648i \(-0.550082\pi\)
−0.156688 + 0.987648i \(0.550082\pi\)
\(674\) 0 0
\(675\) −79.2530 −3.05045
\(676\) 0 0
\(677\) 17.3465 0.666682 0.333341 0.942806i \(-0.391824\pi\)
0.333341 + 0.942806i \(0.391824\pi\)
\(678\) 0 0
\(679\) 3.08525 0.118401
\(680\) 0 0
\(681\) 13.0733 0.500971
\(682\) 0 0
\(683\) 26.1608 1.00101 0.500507 0.865733i \(-0.333147\pi\)
0.500507 + 0.865733i \(0.333147\pi\)
\(684\) 0 0
\(685\) −17.9372 −0.685344
\(686\) 0 0
\(687\) −7.48761 −0.285670
\(688\) 0 0
\(689\) 1.45473 0.0554209
\(690\) 0 0
\(691\) −36.7575 −1.39832 −0.699161 0.714964i \(-0.746443\pi\)
−0.699161 + 0.714964i \(0.746443\pi\)
\(692\) 0 0
\(693\) −6.42735 −0.244155
\(694\) 0 0
\(695\) 45.0178 1.70762
\(696\) 0 0
\(697\) 1.56522 0.0592869
\(698\) 0 0
\(699\) −73.9001 −2.79516
\(700\) 0 0
\(701\) 49.2156 1.85885 0.929424 0.369014i \(-0.120305\pi\)
0.929424 + 0.369014i \(0.120305\pi\)
\(702\) 0 0
\(703\) −3.38795 −0.127779
\(704\) 0 0
\(705\) 114.131 4.29841
\(706\) 0 0
\(707\) −14.2620 −0.536376
\(708\) 0 0
\(709\) −42.0710 −1.58001 −0.790004 0.613102i \(-0.789922\pi\)
−0.790004 + 0.613102i \(0.789922\pi\)
\(710\) 0 0
\(711\) −40.7215 −1.52718
\(712\) 0 0
\(713\) −1.48639 −0.0556656
\(714\) 0 0
\(715\) 3.53994 0.132386
\(716\) 0 0
\(717\) −36.9629 −1.38040
\(718\) 0 0
\(719\) −30.9972 −1.15600 −0.578001 0.816036i \(-0.696167\pi\)
−0.578001 + 0.816036i \(0.696167\pi\)
\(720\) 0 0
\(721\) 15.8325 0.589632
\(722\) 0 0
\(723\) −46.9852 −1.74740
\(724\) 0 0
\(725\) −10.2552 −0.380869
\(726\) 0 0
\(727\) −48.4255 −1.79600 −0.898002 0.439991i \(-0.854981\pi\)
−0.898002 + 0.439991i \(0.854981\pi\)
\(728\) 0 0
\(729\) −13.1919 −0.488588
\(730\) 0 0
\(731\) −3.92430 −0.145145
\(732\) 0 0
\(733\) 39.8393 1.47150 0.735748 0.677255i \(-0.236831\pi\)
0.735748 + 0.677255i \(0.236831\pi\)
\(734\) 0 0
\(735\) 10.8690 0.400910
\(736\) 0 0
\(737\) 1.55735 0.0573657
\(738\) 0 0
\(739\) −5.50888 −0.202647 −0.101324 0.994854i \(-0.532308\pi\)
−0.101324 + 0.994854i \(0.532308\pi\)
\(740\) 0 0
\(741\) −0.976776 −0.0358828
\(742\) 0 0
\(743\) 4.63743 0.170131 0.0850653 0.996375i \(-0.472890\pi\)
0.0850653 + 0.996375i \(0.472890\pi\)
\(744\) 0 0
\(745\) 47.6975 1.74750
\(746\) 0 0
\(747\) −29.0467 −1.06276
\(748\) 0 0
\(749\) 14.7426 0.538684
\(750\) 0 0
\(751\) 12.0160 0.438469 0.219235 0.975672i \(-0.429644\pi\)
0.219235 + 0.975672i \(0.429644\pi\)
\(752\) 0 0
\(753\) 2.45712 0.0895424
\(754\) 0 0
\(755\) −82.4852 −3.00194
\(756\) 0 0
\(757\) −45.2755 −1.64557 −0.822783 0.568355i \(-0.807580\pi\)
−0.822783 + 0.568355i \(0.807580\pi\)
\(758\) 0 0
\(759\) −3.39297 −0.123157
\(760\) 0 0
\(761\) −16.6581 −0.603854 −0.301927 0.953331i \(-0.597630\pi\)
−0.301927 + 0.953331i \(0.597630\pi\)
\(762\) 0 0
\(763\) 10.4349 0.377768
\(764\) 0 0
\(765\) −41.7627 −1.50993
\(766\) 0 0
\(767\) 5.50546 0.198791
\(768\) 0 0
\(769\) −34.4831 −1.24349 −0.621746 0.783219i \(-0.713576\pi\)
−0.621746 + 0.783219i \(0.713576\pi\)
\(770\) 0 0
\(771\) −59.4080 −2.13953
\(772\) 0 0
\(773\) 13.4753 0.484672 0.242336 0.970192i \(-0.422086\pi\)
0.242336 + 0.970192i \(0.422086\pi\)
\(774\) 0 0
\(775\) −10.1300 −0.363880
\(776\) 0 0
\(777\) 32.6988 1.17306
\(778\) 0 0
\(779\) −0.271278 −0.00971953
\(780\) 0 0
\(781\) 0.673836 0.0241117
\(782\) 0 0
\(783\) 14.3296 0.512100
\(784\) 0 0
\(785\) 22.8841 0.816769
\(786\) 0 0
\(787\) 39.7684 1.41759 0.708795 0.705414i \(-0.249239\pi\)
0.708795 + 0.705414i \(0.249239\pi\)
\(788\) 0 0
\(789\) −59.6902 −2.12503
\(790\) 0 0
\(791\) −9.85354 −0.350352
\(792\) 0 0
\(793\) 4.79694 0.170344
\(794\) 0 0
\(795\) −15.8115 −0.560777
\(796\) 0 0
\(797\) 42.5289 1.50645 0.753226 0.657762i \(-0.228497\pi\)
0.753226 + 0.657762i \(0.228497\pi\)
\(798\) 0 0
\(799\) 19.2740 0.681866
\(800\) 0 0
\(801\) −85.9393 −3.03651
\(802\) 0 0
\(803\) 2.83968 0.100210
\(804\) 0 0
\(805\) 3.91184 0.137874
\(806\) 0 0
\(807\) −52.8491 −1.86038
\(808\) 0 0
\(809\) 1.59554 0.0560963 0.0280481 0.999607i \(-0.491071\pi\)
0.0280481 + 0.999607i \(0.491071\pi\)
\(810\) 0 0
\(811\) 24.0024 0.842837 0.421418 0.906866i \(-0.361532\pi\)
0.421418 + 0.906866i \(0.361532\pi\)
\(812\) 0 0
\(813\) −32.2786 −1.13206
\(814\) 0 0
\(815\) 77.9795 2.73150
\(816\) 0 0
\(817\) 0.680144 0.0237952
\(818\) 0 0
\(819\) 6.42735 0.224590
\(820\) 0 0
\(821\) 33.6833 1.17556 0.587778 0.809022i \(-0.300003\pi\)
0.587778 + 0.809022i \(0.300003\pi\)
\(822\) 0 0
\(823\) 12.5993 0.439185 0.219592 0.975592i \(-0.429527\pi\)
0.219592 + 0.975592i \(0.429527\pi\)
\(824\) 0 0
\(825\) −23.1237 −0.805064
\(826\) 0 0
\(827\) −28.2424 −0.982084 −0.491042 0.871136i \(-0.663384\pi\)
−0.491042 + 0.871136i \(0.663384\pi\)
\(828\) 0 0
\(829\) 30.7396 1.06763 0.533816 0.845601i \(-0.320758\pi\)
0.533816 + 0.845601i \(0.320758\pi\)
\(830\) 0 0
\(831\) −78.7299 −2.73111
\(832\) 0 0
\(833\) 1.83553 0.0635973
\(834\) 0 0
\(835\) 45.4060 1.57134
\(836\) 0 0
\(837\) 14.1547 0.489258
\(838\) 0 0
\(839\) 29.8066 1.02904 0.514518 0.857479i \(-0.327971\pi\)
0.514518 + 0.857479i \(0.327971\pi\)
\(840\) 0 0
\(841\) −27.1458 −0.936061
\(842\) 0 0
\(843\) −46.3247 −1.59551
\(844\) 0 0
\(845\) −3.53994 −0.121778
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 39.2232 1.34614
\(850\) 0 0
\(851\) 11.7685 0.403420
\(852\) 0 0
\(853\) 4.99204 0.170924 0.0854620 0.996341i \(-0.472763\pi\)
0.0854620 + 0.996341i \(0.472763\pi\)
\(854\) 0 0
\(855\) 7.23816 0.247540
\(856\) 0 0
\(857\) −28.1557 −0.961779 −0.480889 0.876781i \(-0.659686\pi\)
−0.480889 + 0.876781i \(0.659686\pi\)
\(858\) 0 0
\(859\) −51.0735 −1.74260 −0.871302 0.490747i \(-0.836724\pi\)
−0.871302 + 0.490747i \(0.836724\pi\)
\(860\) 0 0
\(861\) 2.61824 0.0892292
\(862\) 0 0
\(863\) 28.1643 0.958723 0.479362 0.877617i \(-0.340868\pi\)
0.479362 + 0.877617i \(0.340868\pi\)
\(864\) 0 0
\(865\) −3.17340 −0.107899
\(866\) 0 0
\(867\) 41.8521 1.42137
\(868\) 0 0
\(869\) −6.33566 −0.214923
\(870\) 0 0
\(871\) −1.55735 −0.0527687
\(872\) 0 0
\(873\) −19.8300 −0.671144
\(874\) 0 0
\(875\) 8.96018 0.302909
\(876\) 0 0
\(877\) −34.4567 −1.16352 −0.581760 0.813361i \(-0.697636\pi\)
−0.581760 + 0.813361i \(0.697636\pi\)
\(878\) 0 0
\(879\) −13.6726 −0.461164
\(880\) 0 0
\(881\) −22.8794 −0.770828 −0.385414 0.922744i \(-0.625941\pi\)
−0.385414 + 0.922744i \(0.625941\pi\)
\(882\) 0 0
\(883\) −10.3514 −0.348353 −0.174176 0.984714i \(-0.555726\pi\)
−0.174176 + 0.984714i \(0.555726\pi\)
\(884\) 0 0
\(885\) −59.8390 −2.01147
\(886\) 0 0
\(887\) −57.3639 −1.92609 −0.963046 0.269337i \(-0.913195\pi\)
−0.963046 + 0.269337i \(0.913195\pi\)
\(888\) 0 0
\(889\) −2.56257 −0.0859459
\(890\) 0 0
\(891\) 13.0288 0.436481
\(892\) 0 0
\(893\) −3.34050 −0.111786
\(894\) 0 0
\(895\) −51.8258 −1.73234
\(896\) 0 0
\(897\) 3.39297 0.113288
\(898\) 0 0
\(899\) 1.83159 0.0610870
\(900\) 0 0
\(901\) −2.67020 −0.0889574
\(902\) 0 0
\(903\) −6.56441 −0.218450
\(904\) 0 0
\(905\) −25.2100 −0.838008
\(906\) 0 0
\(907\) 18.9637 0.629681 0.314840 0.949145i \(-0.398049\pi\)
0.314840 + 0.949145i \(0.398049\pi\)
\(908\) 0 0
\(909\) 91.6667 3.04039
\(910\) 0 0
\(911\) −4.91143 −0.162723 −0.0813615 0.996685i \(-0.525927\pi\)
−0.0813615 + 0.996685i \(0.525927\pi\)
\(912\) 0 0
\(913\) −4.51924 −0.149565
\(914\) 0 0
\(915\) −52.1381 −1.72363
\(916\) 0 0
\(917\) 6.39260 0.211102
\(918\) 0 0
\(919\) −17.8744 −0.589622 −0.294811 0.955556i \(-0.595257\pi\)
−0.294811 + 0.955556i \(0.595257\pi\)
\(920\) 0 0
\(921\) 8.97833 0.295846
\(922\) 0 0
\(923\) −0.673836 −0.0221796
\(924\) 0 0
\(925\) 80.2046 2.63711
\(926\) 0 0
\(927\) −101.761 −3.34227
\(928\) 0 0
\(929\) −6.43045 −0.210976 −0.105488 0.994421i \(-0.533640\pi\)
−0.105488 + 0.994421i \(0.533640\pi\)
\(930\) 0 0
\(931\) −0.318127 −0.0104262
\(932\) 0 0
\(933\) −14.7863 −0.484083
\(934\) 0 0
\(935\) −6.49766 −0.212496
\(936\) 0 0
\(937\) 17.8778 0.584041 0.292021 0.956412i \(-0.405672\pi\)
0.292021 + 0.956412i \(0.405672\pi\)
\(938\) 0 0
\(939\) 35.7242 1.16582
\(940\) 0 0
\(941\) 17.3162 0.564493 0.282246 0.959342i \(-0.408920\pi\)
0.282246 + 0.959342i \(0.408920\pi\)
\(942\) 0 0
\(943\) 0.942322 0.0306862
\(944\) 0 0
\(945\) −37.2520 −1.21181
\(946\) 0 0
\(947\) 43.4657 1.41245 0.706223 0.707990i \(-0.250398\pi\)
0.706223 + 0.707990i \(0.250398\pi\)
\(948\) 0 0
\(949\) −2.83968 −0.0921798
\(950\) 0 0
\(951\) 1.74533 0.0565964
\(952\) 0 0
\(953\) 3.13801 0.101650 0.0508251 0.998708i \(-0.483815\pi\)
0.0508251 + 0.998708i \(0.483815\pi\)
\(954\) 0 0
\(955\) −17.0371 −0.551308
\(956\) 0 0
\(957\) 4.18097 0.135151
\(958\) 0 0
\(959\) −5.06708 −0.163625
\(960\) 0 0
\(961\) −29.1908 −0.941638
\(962\) 0 0
\(963\) −94.7561 −3.05347
\(964\) 0 0
\(965\) −5.30048 −0.170628
\(966\) 0 0
\(967\) 54.4418 1.75073 0.875366 0.483462i \(-0.160621\pi\)
0.875366 + 0.483462i \(0.160621\pi\)
\(968\) 0 0
\(969\) 1.79290 0.0575962
\(970\) 0 0
\(971\) 51.2136 1.64352 0.821761 0.569832i \(-0.192992\pi\)
0.821761 + 0.569832i \(0.192992\pi\)
\(972\) 0 0
\(973\) 12.7171 0.407692
\(974\) 0 0
\(975\) 23.1237 0.740551
\(976\) 0 0
\(977\) 30.2400 0.967462 0.483731 0.875217i \(-0.339281\pi\)
0.483731 + 0.875217i \(0.339281\pi\)
\(978\) 0 0
\(979\) −13.3709 −0.427335
\(980\) 0 0
\(981\) −67.0686 −2.14134
\(982\) 0 0
\(983\) −6.54306 −0.208691 −0.104346 0.994541i \(-0.533275\pi\)
−0.104346 + 0.994541i \(0.533275\pi\)
\(984\) 0 0
\(985\) 40.9697 1.30540
\(986\) 0 0
\(987\) 32.2409 1.02624
\(988\) 0 0
\(989\) −2.36258 −0.0751256
\(990\) 0 0
\(991\) −52.3945 −1.66437 −0.832183 0.554501i \(-0.812909\pi\)
−0.832183 + 0.554501i \(0.812909\pi\)
\(992\) 0 0
\(993\) 10.5008 0.333232
\(994\) 0 0
\(995\) 53.5043 1.69620
\(996\) 0 0
\(997\) 43.6151 1.38130 0.690652 0.723188i \(-0.257324\pi\)
0.690652 + 0.723188i \(0.257324\pi\)
\(998\) 0 0
\(999\) −112.070 −3.54575
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 \(a_p\))