Properties

Label 8036.2.a.p.1.5
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 10
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-0.284914\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.284914 q^{3} +2.38934 q^{5} -2.91882 q^{9} +O(q^{10})\) \(q-0.284914 q^{3} +2.38934 q^{5} -2.91882 q^{9} +5.72114 q^{11} +5.63894 q^{13} -0.680755 q^{15} +0.225296 q^{17} -1.88313 q^{19} +1.32240 q^{23} +0.708922 q^{25} +1.68636 q^{27} +0.835045 q^{29} -4.68008 q^{31} -1.63003 q^{33} +5.80526 q^{37} -1.60661 q^{39} +1.00000 q^{41} -0.313719 q^{43} -6.97405 q^{45} -0.467063 q^{47} -0.0641900 q^{51} +11.1454 q^{53} +13.6697 q^{55} +0.536530 q^{57} +7.92358 q^{59} -4.62009 q^{61} +13.4733 q^{65} +0.187114 q^{67} -0.376771 q^{69} +2.39451 q^{71} +6.57946 q^{73} -0.201982 q^{75} -3.56412 q^{79} +8.27600 q^{81} +14.4593 q^{83} +0.538308 q^{85} -0.237916 q^{87} +8.14466 q^{89} +1.33342 q^{93} -4.49943 q^{95} -17.7258 q^{97} -16.6990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + O(q^{10}) \) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + 6q^{13} - 4q^{15} + 12q^{17} + 8q^{19} + 4q^{23} + 16q^{25} + 8q^{27} + 2q^{29} + 8q^{31} - 6q^{33} - 2q^{37} - 2q^{39} + 10q^{41} - 2q^{43} + 44q^{45} - 14q^{47} + 14q^{51} + 8q^{53} + 8q^{55} - 10q^{57} + 24q^{59} + 14q^{61} + 2q^{65} - 8q^{67} + 16q^{69} + 10q^{71} + 44q^{73} - 50q^{75} + 10q^{79} - 14q^{81} + 20q^{83} + 8q^{85} + 20q^{87} + 6q^{89} + 8q^{93} + 4q^{95} + 46q^{97} + 2q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.284914 −0.164495 −0.0822476 0.996612i \(-0.526210\pi\)
−0.0822476 + 0.996612i \(0.526210\pi\)
\(4\) 0 0
\(5\) 2.38934 1.06854 0.534272 0.845313i \(-0.320586\pi\)
0.534272 + 0.845313i \(0.320586\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.91882 −0.972941
\(10\) 0 0
\(11\) 5.72114 1.72499 0.862494 0.506068i \(-0.168901\pi\)
0.862494 + 0.506068i \(0.168901\pi\)
\(12\) 0 0
\(13\) 5.63894 1.56396 0.781980 0.623304i \(-0.214210\pi\)
0.781980 + 0.623304i \(0.214210\pi\)
\(14\) 0 0
\(15\) −0.680755 −0.175770
\(16\) 0 0
\(17\) 0.225296 0.0546423 0.0273212 0.999627i \(-0.491302\pi\)
0.0273212 + 0.999627i \(0.491302\pi\)
\(18\) 0 0
\(19\) −1.88313 −0.432019 −0.216010 0.976391i \(-0.569304\pi\)
−0.216010 + 0.976391i \(0.569304\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.32240 0.275740 0.137870 0.990450i \(-0.455974\pi\)
0.137870 + 0.990450i \(0.455974\pi\)
\(24\) 0 0
\(25\) 0.708922 0.141784
\(26\) 0 0
\(27\) 1.68636 0.324540
\(28\) 0 0
\(29\) 0.835045 0.155064 0.0775320 0.996990i \(-0.475296\pi\)
0.0775320 + 0.996990i \(0.475296\pi\)
\(30\) 0 0
\(31\) −4.68008 −0.840567 −0.420283 0.907393i \(-0.638069\pi\)
−0.420283 + 0.907393i \(0.638069\pi\)
\(32\) 0 0
\(33\) −1.63003 −0.283752
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.80526 0.954380 0.477190 0.878800i \(-0.341655\pi\)
0.477190 + 0.878800i \(0.341655\pi\)
\(38\) 0 0
\(39\) −1.60661 −0.257264
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −0.313719 −0.0478417 −0.0239209 0.999714i \(-0.507615\pi\)
−0.0239209 + 0.999714i \(0.507615\pi\)
\(44\) 0 0
\(45\) −6.97405 −1.03963
\(46\) 0 0
\(47\) −0.467063 −0.0681282 −0.0340641 0.999420i \(-0.510845\pi\)
−0.0340641 + 0.999420i \(0.510845\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −0.0641900 −0.00898840
\(52\) 0 0
\(53\) 11.1454 1.53094 0.765468 0.643474i \(-0.222508\pi\)
0.765468 + 0.643474i \(0.222508\pi\)
\(54\) 0 0
\(55\) 13.6697 1.84322
\(56\) 0 0
\(57\) 0.536530 0.0710652
\(58\) 0 0
\(59\) 7.92358 1.03156 0.515781 0.856720i \(-0.327502\pi\)
0.515781 + 0.856720i \(0.327502\pi\)
\(60\) 0 0
\(61\) −4.62009 −0.591542 −0.295771 0.955259i \(-0.595576\pi\)
−0.295771 + 0.955259i \(0.595576\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 13.4733 1.67116
\(66\) 0 0
\(67\) 0.187114 0.0228596 0.0114298 0.999935i \(-0.496362\pi\)
0.0114298 + 0.999935i \(0.496362\pi\)
\(68\) 0 0
\(69\) −0.376771 −0.0453579
\(70\) 0 0
\(71\) 2.39451 0.284176 0.142088 0.989854i \(-0.454618\pi\)
0.142088 + 0.989854i \(0.454618\pi\)
\(72\) 0 0
\(73\) 6.57946 0.770068 0.385034 0.922902i \(-0.374190\pi\)
0.385034 + 0.922902i \(0.374190\pi\)
\(74\) 0 0
\(75\) −0.201982 −0.0233229
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −3.56412 −0.400995 −0.200498 0.979694i \(-0.564256\pi\)
−0.200498 + 0.979694i \(0.564256\pi\)
\(80\) 0 0
\(81\) 8.27600 0.919556
\(82\) 0 0
\(83\) 14.4593 1.58712 0.793558 0.608495i \(-0.208226\pi\)
0.793558 + 0.608495i \(0.208226\pi\)
\(84\) 0 0
\(85\) 0.538308 0.0583877
\(86\) 0 0
\(87\) −0.237916 −0.0255073
\(88\) 0 0
\(89\) 8.14466 0.863332 0.431666 0.902033i \(-0.357926\pi\)
0.431666 + 0.902033i \(0.357926\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1.33342 0.138269
\(94\) 0 0
\(95\) −4.49943 −0.461631
\(96\) 0 0
\(97\) −17.7258 −1.79979 −0.899893 0.436112i \(-0.856355\pi\)
−0.899893 + 0.436112i \(0.856355\pi\)
\(98\) 0 0
\(99\) −16.6990 −1.67831
\(100\) 0 0
\(101\) 9.59821 0.955057 0.477529 0.878616i \(-0.341533\pi\)
0.477529 + 0.878616i \(0.341533\pi\)
\(102\) 0 0
\(103\) −6.43285 −0.633847 −0.316924 0.948451i \(-0.602650\pi\)
−0.316924 + 0.948451i \(0.602650\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −13.6742 −1.32194 −0.660969 0.750413i \(-0.729855\pi\)
−0.660969 + 0.750413i \(0.729855\pi\)
\(108\) 0 0
\(109\) −13.7242 −1.31454 −0.657270 0.753655i \(-0.728289\pi\)
−0.657270 + 0.753655i \(0.728289\pi\)
\(110\) 0 0
\(111\) −1.65400 −0.156991
\(112\) 0 0
\(113\) −18.4103 −1.73189 −0.865947 0.500137i \(-0.833283\pi\)
−0.865947 + 0.500137i \(0.833283\pi\)
\(114\) 0 0
\(115\) 3.15966 0.294640
\(116\) 0 0
\(117\) −16.4591 −1.52164
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 21.7314 1.97558
\(122\) 0 0
\(123\) −0.284914 −0.0256898
\(124\) 0 0
\(125\) −10.2528 −0.917040
\(126\) 0 0
\(127\) −3.04644 −0.270327 −0.135164 0.990823i \(-0.543156\pi\)
−0.135164 + 0.990823i \(0.543156\pi\)
\(128\) 0 0
\(129\) 0.0893831 0.00786974
\(130\) 0 0
\(131\) −9.24397 −0.807649 −0.403825 0.914836i \(-0.632319\pi\)
−0.403825 + 0.914836i \(0.632319\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 4.02927 0.346784
\(136\) 0 0
\(137\) 12.2287 1.04477 0.522386 0.852709i \(-0.325042\pi\)
0.522386 + 0.852709i \(0.325042\pi\)
\(138\) 0 0
\(139\) 7.60223 0.644813 0.322407 0.946601i \(-0.395508\pi\)
0.322407 + 0.946601i \(0.395508\pi\)
\(140\) 0 0
\(141\) 0.133073 0.0112068
\(142\) 0 0
\(143\) 32.2611 2.69781
\(144\) 0 0
\(145\) 1.99520 0.165693
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.38712 −0.523253 −0.261627 0.965169i \(-0.584259\pi\)
−0.261627 + 0.965169i \(0.584259\pi\)
\(150\) 0 0
\(151\) −5.05067 −0.411018 −0.205509 0.978655i \(-0.565885\pi\)
−0.205509 + 0.978655i \(0.565885\pi\)
\(152\) 0 0
\(153\) −0.657599 −0.0531638
\(154\) 0 0
\(155\) −11.1823 −0.898182
\(156\) 0 0
\(157\) 5.41932 0.432509 0.216255 0.976337i \(-0.430616\pi\)
0.216255 + 0.976337i \(0.430616\pi\)
\(158\) 0 0
\(159\) −3.17548 −0.251832
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 7.39830 0.579480 0.289740 0.957105i \(-0.406431\pi\)
0.289740 + 0.957105i \(0.406431\pi\)
\(164\) 0 0
\(165\) −3.89469 −0.303202
\(166\) 0 0
\(167\) 7.05784 0.546152 0.273076 0.961992i \(-0.411959\pi\)
0.273076 + 0.961992i \(0.411959\pi\)
\(168\) 0 0
\(169\) 18.7976 1.44597
\(170\) 0 0
\(171\) 5.49652 0.420330
\(172\) 0 0
\(173\) 8.90963 0.677387 0.338693 0.940897i \(-0.390015\pi\)
0.338693 + 0.940897i \(0.390015\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −2.25754 −0.169687
\(178\) 0 0
\(179\) −7.91862 −0.591865 −0.295933 0.955209i \(-0.595630\pi\)
−0.295933 + 0.955209i \(0.595630\pi\)
\(180\) 0 0
\(181\) 0.182128 0.0135375 0.00676874 0.999977i \(-0.497845\pi\)
0.00676874 + 0.999977i \(0.497845\pi\)
\(182\) 0 0
\(183\) 1.31633 0.0973058
\(184\) 0 0
\(185\) 13.8707 1.01980
\(186\) 0 0
\(187\) 1.28895 0.0942573
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −15.7058 −1.13643 −0.568215 0.822880i \(-0.692366\pi\)
−0.568215 + 0.822880i \(0.692366\pi\)
\(192\) 0 0
\(193\) −8.44563 −0.607930 −0.303965 0.952683i \(-0.598311\pi\)
−0.303965 + 0.952683i \(0.598311\pi\)
\(194\) 0 0
\(195\) −3.83874 −0.274898
\(196\) 0 0
\(197\) 16.6247 1.18446 0.592230 0.805769i \(-0.298248\pi\)
0.592230 + 0.805769i \(0.298248\pi\)
\(198\) 0 0
\(199\) 23.5536 1.66967 0.834835 0.550500i \(-0.185563\pi\)
0.834835 + 0.550500i \(0.185563\pi\)
\(200\) 0 0
\(201\) −0.0533113 −0.00376029
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2.38934 0.166878
\(206\) 0 0
\(207\) −3.85986 −0.268279
\(208\) 0 0
\(209\) −10.7736 −0.745228
\(210\) 0 0
\(211\) −8.47900 −0.583719 −0.291859 0.956461i \(-0.594274\pi\)
−0.291859 + 0.956461i \(0.594274\pi\)
\(212\) 0 0
\(213\) −0.682229 −0.0467456
\(214\) 0 0
\(215\) −0.749580 −0.0511210
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.87458 −0.126673
\(220\) 0 0
\(221\) 1.27043 0.0854584
\(222\) 0 0
\(223\) 19.0449 1.27534 0.637672 0.770308i \(-0.279898\pi\)
0.637672 + 0.770308i \(0.279898\pi\)
\(224\) 0 0
\(225\) −2.06922 −0.137948
\(226\) 0 0
\(227\) −22.4620 −1.49085 −0.745427 0.666588i \(-0.767754\pi\)
−0.745427 + 0.666588i \(0.767754\pi\)
\(228\) 0 0
\(229\) −13.4786 −0.890689 −0.445345 0.895359i \(-0.646919\pi\)
−0.445345 + 0.895359i \(0.646919\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.63269 −0.237986 −0.118993 0.992895i \(-0.537967\pi\)
−0.118993 + 0.992895i \(0.537967\pi\)
\(234\) 0 0
\(235\) −1.11597 −0.0727979
\(236\) 0 0
\(237\) 1.01547 0.0659618
\(238\) 0 0
\(239\) 11.8940 0.769358 0.384679 0.923050i \(-0.374312\pi\)
0.384679 + 0.923050i \(0.374312\pi\)
\(240\) 0 0
\(241\) 19.4290 1.25153 0.625766 0.780011i \(-0.284787\pi\)
0.625766 + 0.780011i \(0.284787\pi\)
\(242\) 0 0
\(243\) −7.41702 −0.475802
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −10.6188 −0.675661
\(248\) 0 0
\(249\) −4.11966 −0.261073
\(250\) 0 0
\(251\) −8.54770 −0.539526 −0.269763 0.962927i \(-0.586945\pi\)
−0.269763 + 0.962927i \(0.586945\pi\)
\(252\) 0 0
\(253\) 7.56564 0.475648
\(254\) 0 0
\(255\) −0.153372 −0.00960450
\(256\) 0 0
\(257\) 14.1942 0.885411 0.442706 0.896667i \(-0.354019\pi\)
0.442706 + 0.896667i \(0.354019\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −2.43735 −0.150868
\(262\) 0 0
\(263\) 23.1055 1.42475 0.712374 0.701800i \(-0.247620\pi\)
0.712374 + 0.701800i \(0.247620\pi\)
\(264\) 0 0
\(265\) 26.6300 1.63587
\(266\) 0 0
\(267\) −2.32053 −0.142014
\(268\) 0 0
\(269\) 8.03904 0.490149 0.245075 0.969504i \(-0.421188\pi\)
0.245075 + 0.969504i \(0.421188\pi\)
\(270\) 0 0
\(271\) −14.0642 −0.854339 −0.427169 0.904172i \(-0.640489\pi\)
−0.427169 + 0.904172i \(0.640489\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.05584 0.244576
\(276\) 0 0
\(277\) 2.91125 0.174920 0.0874601 0.996168i \(-0.472125\pi\)
0.0874601 + 0.996168i \(0.472125\pi\)
\(278\) 0 0
\(279\) 13.6603 0.817822
\(280\) 0 0
\(281\) −8.63718 −0.515251 −0.257625 0.966245i \(-0.582940\pi\)
−0.257625 + 0.966245i \(0.582940\pi\)
\(282\) 0 0
\(283\) −13.6433 −0.811010 −0.405505 0.914093i \(-0.632904\pi\)
−0.405505 + 0.914093i \(0.632904\pi\)
\(284\) 0 0
\(285\) 1.28195 0.0759362
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.9492 −0.997014
\(290\) 0 0
\(291\) 5.05034 0.296056
\(292\) 0 0
\(293\) 1.58934 0.0928503 0.0464252 0.998922i \(-0.485217\pi\)
0.0464252 + 0.998922i \(0.485217\pi\)
\(294\) 0 0
\(295\) 18.9321 1.10227
\(296\) 0 0
\(297\) 9.64788 0.559827
\(298\) 0 0
\(299\) 7.45694 0.431246
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −2.73467 −0.157102
\(304\) 0 0
\(305\) −11.0389 −0.632088
\(306\) 0 0
\(307\) 23.7023 1.35276 0.676382 0.736551i \(-0.263547\pi\)
0.676382 + 0.736551i \(0.263547\pi\)
\(308\) 0 0
\(309\) 1.83281 0.104265
\(310\) 0 0
\(311\) 28.2042 1.59931 0.799657 0.600457i \(-0.205015\pi\)
0.799657 + 0.600457i \(0.205015\pi\)
\(312\) 0 0
\(313\) 13.5469 0.765715 0.382858 0.923807i \(-0.374940\pi\)
0.382858 + 0.923807i \(0.374940\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.07490 0.228869 0.114435 0.993431i \(-0.463494\pi\)
0.114435 + 0.993431i \(0.463494\pi\)
\(318\) 0 0
\(319\) 4.77741 0.267484
\(320\) 0 0
\(321\) 3.89598 0.217453
\(322\) 0 0
\(323\) −0.424262 −0.0236065
\(324\) 0 0
\(325\) 3.99757 0.221745
\(326\) 0 0
\(327\) 3.91022 0.216236
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −29.8518 −1.64080 −0.820401 0.571788i \(-0.806250\pi\)
−0.820401 + 0.571788i \(0.806250\pi\)
\(332\) 0 0
\(333\) −16.9445 −0.928555
\(334\) 0 0
\(335\) 0.447077 0.0244264
\(336\) 0 0
\(337\) 1.23104 0.0670590 0.0335295 0.999438i \(-0.489325\pi\)
0.0335295 + 0.999438i \(0.489325\pi\)
\(338\) 0 0
\(339\) 5.24535 0.284888
\(340\) 0 0
\(341\) −26.7754 −1.44997
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −0.900232 −0.0484669
\(346\) 0 0
\(347\) 9.00756 0.483551 0.241775 0.970332i \(-0.422270\pi\)
0.241775 + 0.970332i \(0.422270\pi\)
\(348\) 0 0
\(349\) 11.0534 0.591676 0.295838 0.955238i \(-0.404401\pi\)
0.295838 + 0.955238i \(0.404401\pi\)
\(350\) 0 0
\(351\) 9.50926 0.507567
\(352\) 0 0
\(353\) 24.0375 1.27939 0.639695 0.768629i \(-0.279061\pi\)
0.639695 + 0.768629i \(0.279061\pi\)
\(354\) 0 0
\(355\) 5.72128 0.303654
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −15.3867 −0.812080 −0.406040 0.913855i \(-0.633091\pi\)
−0.406040 + 0.913855i \(0.633091\pi\)
\(360\) 0 0
\(361\) −15.4538 −0.813359
\(362\) 0 0
\(363\) −6.19158 −0.324974
\(364\) 0 0
\(365\) 15.7205 0.822851
\(366\) 0 0
\(367\) −19.0729 −0.995599 −0.497799 0.867292i \(-0.665858\pi\)
−0.497799 + 0.867292i \(0.665858\pi\)
\(368\) 0 0
\(369\) −2.91882 −0.151948
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 13.7210 0.710447 0.355223 0.934781i \(-0.384405\pi\)
0.355223 + 0.934781i \(0.384405\pi\)
\(374\) 0 0
\(375\) 2.92117 0.150849
\(376\) 0 0
\(377\) 4.70877 0.242514
\(378\) 0 0
\(379\) −19.5626 −1.00486 −0.502432 0.864617i \(-0.667561\pi\)
−0.502432 + 0.864617i \(0.667561\pi\)
\(380\) 0 0
\(381\) 0.867973 0.0444676
\(382\) 0 0
\(383\) −3.84968 −0.196709 −0.0983547 0.995151i \(-0.531358\pi\)
−0.0983547 + 0.995151i \(0.531358\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.915691 0.0465472
\(388\) 0 0
\(389\) 11.6658 0.591478 0.295739 0.955269i \(-0.404434\pi\)
0.295739 + 0.955269i \(0.404434\pi\)
\(390\) 0 0
\(391\) 0.297932 0.0150671
\(392\) 0 0
\(393\) 2.63374 0.132855
\(394\) 0 0
\(395\) −8.51588 −0.428480
\(396\) 0 0
\(397\) 15.5657 0.781218 0.390609 0.920557i \(-0.372264\pi\)
0.390609 + 0.920557i \(0.372264\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −29.0383 −1.45010 −0.725051 0.688696i \(-0.758184\pi\)
−0.725051 + 0.688696i \(0.758184\pi\)
\(402\) 0 0
\(403\) −26.3907 −1.31461
\(404\) 0 0
\(405\) 19.7741 0.982585
\(406\) 0 0
\(407\) 33.2127 1.64629
\(408\) 0 0
\(409\) −10.5338 −0.520863 −0.260432 0.965492i \(-0.583865\pi\)
−0.260432 + 0.965492i \(0.583865\pi\)
\(410\) 0 0
\(411\) −3.48414 −0.171860
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 34.5481 1.69590
\(416\) 0 0
\(417\) −2.16598 −0.106069
\(418\) 0 0
\(419\) 32.6004 1.59263 0.796316 0.604880i \(-0.206779\pi\)
0.796316 + 0.604880i \(0.206779\pi\)
\(420\) 0 0
\(421\) −0.624956 −0.0304585 −0.0152293 0.999884i \(-0.504848\pi\)
−0.0152293 + 0.999884i \(0.504848\pi\)
\(422\) 0 0
\(423\) 1.36328 0.0662847
\(424\) 0 0
\(425\) 0.159717 0.00774743
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −9.19165 −0.443777
\(430\) 0 0
\(431\) 7.11125 0.342537 0.171268 0.985224i \(-0.445213\pi\)
0.171268 + 0.985224i \(0.445213\pi\)
\(432\) 0 0
\(433\) 39.2606 1.88675 0.943373 0.331734i \(-0.107634\pi\)
0.943373 + 0.331734i \(0.107634\pi\)
\(434\) 0 0
\(435\) −0.568462 −0.0272557
\(436\) 0 0
\(437\) −2.49025 −0.119125
\(438\) 0 0
\(439\) −38.2853 −1.82726 −0.913630 0.406548i \(-0.866733\pi\)
−0.913630 + 0.406548i \(0.866733\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.5341 0.595515 0.297758 0.954642i \(-0.403761\pi\)
0.297758 + 0.954642i \(0.403761\pi\)
\(444\) 0 0
\(445\) 19.4603 0.922508
\(446\) 0 0
\(447\) 1.81978 0.0860727
\(448\) 0 0
\(449\) 35.8296 1.69090 0.845451 0.534053i \(-0.179332\pi\)
0.845451 + 0.534053i \(0.179332\pi\)
\(450\) 0 0
\(451\) 5.72114 0.269398
\(452\) 0 0
\(453\) 1.43901 0.0676105
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11.8056 0.552245 0.276122 0.961122i \(-0.410950\pi\)
0.276122 + 0.961122i \(0.410950\pi\)
\(458\) 0 0
\(459\) 0.379930 0.0177336
\(460\) 0 0
\(461\) 34.3509 1.59988 0.799941 0.600079i \(-0.204864\pi\)
0.799941 + 0.600079i \(0.204864\pi\)
\(462\) 0 0
\(463\) −29.1253 −1.35357 −0.676784 0.736181i \(-0.736627\pi\)
−0.676784 + 0.736181i \(0.736627\pi\)
\(464\) 0 0
\(465\) 3.18599 0.147747
\(466\) 0 0
\(467\) 10.6140 0.491159 0.245579 0.969376i \(-0.421022\pi\)
0.245579 + 0.969376i \(0.421022\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.54404 −0.0711457
\(472\) 0 0
\(473\) −1.79483 −0.0825264
\(474\) 0 0
\(475\) −1.33499 −0.0612536
\(476\) 0 0
\(477\) −32.5314 −1.48951
\(478\) 0 0
\(479\) 8.03739 0.367238 0.183619 0.982998i \(-0.441219\pi\)
0.183619 + 0.982998i \(0.441219\pi\)
\(480\) 0 0
\(481\) 32.7355 1.49261
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −42.3529 −1.92315
\(486\) 0 0
\(487\) 22.3245 1.01162 0.505811 0.862645i \(-0.331193\pi\)
0.505811 + 0.862645i \(0.331193\pi\)
\(488\) 0 0
\(489\) −2.10788 −0.0953217
\(490\) 0 0
\(491\) −16.5660 −0.747611 −0.373806 0.927507i \(-0.621947\pi\)
−0.373806 + 0.927507i \(0.621947\pi\)
\(492\) 0 0
\(493\) 0.188132 0.00847306
\(494\) 0 0
\(495\) −39.8995 −1.79335
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −10.8446 −0.485472 −0.242736 0.970092i \(-0.578045\pi\)
−0.242736 + 0.970092i \(0.578045\pi\)
\(500\) 0 0
\(501\) −2.01088 −0.0898394
\(502\) 0 0
\(503\) 34.6678 1.54576 0.772881 0.634552i \(-0.218815\pi\)
0.772881 + 0.634552i \(0.218815\pi\)
\(504\) 0 0
\(505\) 22.9333 1.02052
\(506\) 0 0
\(507\) −5.35571 −0.237855
\(508\) 0 0
\(509\) −10.1641 −0.450515 −0.225258 0.974299i \(-0.572322\pi\)
−0.225258 + 0.974299i \(0.572322\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −3.17563 −0.140207
\(514\) 0 0
\(515\) −15.3702 −0.677293
\(516\) 0 0
\(517\) −2.67213 −0.117520
\(518\) 0 0
\(519\) −2.53848 −0.111427
\(520\) 0 0
\(521\) 32.3278 1.41630 0.708152 0.706060i \(-0.249529\pi\)
0.708152 + 0.706060i \(0.249529\pi\)
\(522\) 0 0
\(523\) −13.4973 −0.590197 −0.295099 0.955467i \(-0.595353\pi\)
−0.295099 + 0.955467i \(0.595353\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.05440 −0.0459305
\(528\) 0 0
\(529\) −21.2513 −0.923968
\(530\) 0 0
\(531\) −23.1275 −1.00365
\(532\) 0 0
\(533\) 5.63894 0.244250
\(534\) 0 0
\(535\) −32.6723 −1.41255
\(536\) 0 0
\(537\) 2.25613 0.0973590
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 21.0207 0.903749 0.451874 0.892082i \(-0.350755\pi\)
0.451874 + 0.892082i \(0.350755\pi\)
\(542\) 0 0
\(543\) −0.0518909 −0.00222685
\(544\) 0 0
\(545\) −32.7917 −1.40464
\(546\) 0 0
\(547\) −37.0787 −1.58537 −0.792685 0.609631i \(-0.791318\pi\)
−0.792685 + 0.609631i \(0.791318\pi\)
\(548\) 0 0
\(549\) 13.4852 0.575535
\(550\) 0 0
\(551\) −1.57250 −0.0669907
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −3.95197 −0.167752
\(556\) 0 0
\(557\) −7.78331 −0.329789 −0.164895 0.986311i \(-0.552728\pi\)
−0.164895 + 0.986311i \(0.552728\pi\)
\(558\) 0 0
\(559\) −1.76904 −0.0748226
\(560\) 0 0
\(561\) −0.367240 −0.0155049
\(562\) 0 0
\(563\) −16.9855 −0.715854 −0.357927 0.933750i \(-0.616516\pi\)
−0.357927 + 0.933750i \(0.616516\pi\)
\(564\) 0 0
\(565\) −43.9883 −1.85060
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 46.1734 1.93569 0.967844 0.251551i \(-0.0809407\pi\)
0.967844 + 0.251551i \(0.0809407\pi\)
\(570\) 0 0
\(571\) −32.7866 −1.37208 −0.686038 0.727566i \(-0.740652\pi\)
−0.686038 + 0.727566i \(0.740652\pi\)
\(572\) 0 0
\(573\) 4.47480 0.186937
\(574\) 0 0
\(575\) 0.937479 0.0390956
\(576\) 0 0
\(577\) 15.9785 0.665192 0.332596 0.943069i \(-0.392075\pi\)
0.332596 + 0.943069i \(0.392075\pi\)
\(578\) 0 0
\(579\) 2.40628 0.100002
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 63.7642 2.64084
\(584\) 0 0
\(585\) −39.3262 −1.62594
\(586\) 0 0
\(587\) −12.4963 −0.515777 −0.257888 0.966175i \(-0.583027\pi\)
−0.257888 + 0.966175i \(0.583027\pi\)
\(588\) 0 0
\(589\) 8.81319 0.363141
\(590\) 0 0
\(591\) −4.73661 −0.194838
\(592\) 0 0
\(593\) −12.3518 −0.507229 −0.253614 0.967305i \(-0.581619\pi\)
−0.253614 + 0.967305i \(0.581619\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6.71076 −0.274653
\(598\) 0 0
\(599\) −31.1090 −1.27108 −0.635541 0.772068i \(-0.719223\pi\)
−0.635541 + 0.772068i \(0.719223\pi\)
\(600\) 0 0
\(601\) −18.9355 −0.772393 −0.386197 0.922416i \(-0.626211\pi\)
−0.386197 + 0.922416i \(0.626211\pi\)
\(602\) 0 0
\(603\) −0.546152 −0.0222410
\(604\) 0 0
\(605\) 51.9236 2.11099
\(606\) 0 0
\(607\) −10.0928 −0.409655 −0.204828 0.978798i \(-0.565663\pi\)
−0.204828 + 0.978798i \(0.565663\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.63374 −0.106550
\(612\) 0 0
\(613\) 14.2143 0.574111 0.287055 0.957914i \(-0.407324\pi\)
0.287055 + 0.957914i \(0.407324\pi\)
\(614\) 0 0
\(615\) −0.680755 −0.0274507
\(616\) 0 0
\(617\) 0.265395 0.0106844 0.00534220 0.999986i \(-0.498300\pi\)
0.00534220 + 0.999986i \(0.498300\pi\)
\(618\) 0 0
\(619\) 39.5133 1.58817 0.794086 0.607806i \(-0.207950\pi\)
0.794086 + 0.607806i \(0.207950\pi\)
\(620\) 0 0
\(621\) 2.23004 0.0894885
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −28.0420 −1.12168
\(626\) 0 0
\(627\) 3.06956 0.122587
\(628\) 0 0
\(629\) 1.30790 0.0521495
\(630\) 0 0
\(631\) −20.7060 −0.824293 −0.412146 0.911118i \(-0.635221\pi\)
−0.412146 + 0.911118i \(0.635221\pi\)
\(632\) 0 0
\(633\) 2.41579 0.0960190
\(634\) 0 0
\(635\) −7.27895 −0.288857
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −6.98915 −0.276486
\(640\) 0 0
\(641\) 25.7099 1.01548 0.507741 0.861510i \(-0.330481\pi\)
0.507741 + 0.861510i \(0.330481\pi\)
\(642\) 0 0
\(643\) −22.1357 −0.872947 −0.436474 0.899717i \(-0.643773\pi\)
−0.436474 + 0.899717i \(0.643773\pi\)
\(644\) 0 0
\(645\) 0.213566 0.00840916
\(646\) 0 0
\(647\) −2.96781 −0.116677 −0.0583384 0.998297i \(-0.518580\pi\)
−0.0583384 + 0.998297i \(0.518580\pi\)
\(648\) 0 0
\(649\) 45.3319 1.77943
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 17.5485 0.686725 0.343362 0.939203i \(-0.388434\pi\)
0.343362 + 0.939203i \(0.388434\pi\)
\(654\) 0 0
\(655\) −22.0869 −0.863008
\(656\) 0 0
\(657\) −19.2043 −0.749231
\(658\) 0 0
\(659\) −42.4886 −1.65512 −0.827560 0.561378i \(-0.810272\pi\)
−0.827560 + 0.561378i \(0.810272\pi\)
\(660\) 0 0
\(661\) −6.53462 −0.254167 −0.127084 0.991892i \(-0.540562\pi\)
−0.127084 + 0.991892i \(0.540562\pi\)
\(662\) 0 0
\(663\) −0.361964 −0.0140575
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1.10427 0.0427573
\(668\) 0 0
\(669\) −5.42617 −0.209788
\(670\) 0 0
\(671\) −26.4322 −1.02040
\(672\) 0 0
\(673\) 23.0722 0.889367 0.444684 0.895688i \(-0.353316\pi\)
0.444684 + 0.895688i \(0.353316\pi\)
\(674\) 0 0
\(675\) 1.19550 0.0460146
\(676\) 0 0
\(677\) 4.35184 0.167255 0.0836274 0.996497i \(-0.473349\pi\)
0.0836274 + 0.996497i \(0.473349\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 6.39973 0.245238
\(682\) 0 0
\(683\) 47.1520 1.80422 0.902110 0.431507i \(-0.142018\pi\)
0.902110 + 0.431507i \(0.142018\pi\)
\(684\) 0 0
\(685\) 29.2185 1.11638
\(686\) 0 0
\(687\) 3.84024 0.146514
\(688\) 0 0
\(689\) 62.8481 2.39432
\(690\) 0 0
\(691\) 15.4736 0.588642 0.294321 0.955707i \(-0.404907\pi\)
0.294321 + 0.955707i \(0.404907\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 18.1643 0.689011
\(696\) 0 0
\(697\) 0.225296 0.00853370
\(698\) 0 0
\(699\) 1.03501 0.0391475
\(700\) 0 0
\(701\) −20.7147 −0.782385 −0.391192 0.920309i \(-0.627937\pi\)
−0.391192 + 0.920309i \(0.627937\pi\)
\(702\) 0 0
\(703\) −10.9321 −0.412311
\(704\) 0 0
\(705\) 0.317956 0.0119749
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −18.0362 −0.677365 −0.338683 0.940901i \(-0.609981\pi\)
−0.338683 + 0.940901i \(0.609981\pi\)
\(710\) 0 0
\(711\) 10.4030 0.390145
\(712\) 0 0
\(713\) −6.18894 −0.231778
\(714\) 0 0
\(715\) 77.0827 2.88273
\(716\) 0 0
\(717\) −3.38877 −0.126556
\(718\) 0 0
\(719\) −22.5833 −0.842214 −0.421107 0.907011i \(-0.638358\pi\)
−0.421107 + 0.907011i \(0.638358\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −5.53560 −0.205871
\(724\) 0 0
\(725\) 0.591982 0.0219857
\(726\) 0 0
\(727\) −15.3118 −0.567882 −0.283941 0.958842i \(-0.591642\pi\)
−0.283941 + 0.958842i \(0.591642\pi\)
\(728\) 0 0
\(729\) −22.7148 −0.841289
\(730\) 0 0
\(731\) −0.0706797 −0.00261418
\(732\) 0 0
\(733\) 18.2825 0.675279 0.337639 0.941276i \(-0.390372\pi\)
0.337639 + 0.941276i \(0.390372\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.07050 0.0394325
\(738\) 0 0
\(739\) 8.46264 0.311303 0.155652 0.987812i \(-0.450252\pi\)
0.155652 + 0.987812i \(0.450252\pi\)
\(740\) 0 0
\(741\) 3.02546 0.111143
\(742\) 0 0
\(743\) 28.7597 1.05509 0.527545 0.849527i \(-0.323113\pi\)
0.527545 + 0.849527i \(0.323113\pi\)
\(744\) 0 0
\(745\) −15.2610 −0.559119
\(746\) 0 0
\(747\) −42.2042 −1.54417
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 33.0211 1.20496 0.602478 0.798135i \(-0.294180\pi\)
0.602478 + 0.798135i \(0.294180\pi\)
\(752\) 0 0
\(753\) 2.43536 0.0887495
\(754\) 0 0
\(755\) −12.0677 −0.439190
\(756\) 0 0
\(757\) −9.70050 −0.352571 −0.176285 0.984339i \(-0.556408\pi\)
−0.176285 + 0.984339i \(0.556408\pi\)
\(758\) 0 0
\(759\) −2.15556 −0.0782418
\(760\) 0 0
\(761\) −45.3326 −1.64331 −0.821653 0.569988i \(-0.806948\pi\)
−0.821653 + 0.569988i \(0.806948\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −1.57123 −0.0568078
\(766\) 0 0
\(767\) 44.6806 1.61332
\(768\) 0 0
\(769\) 54.9681 1.98220 0.991100 0.133121i \(-0.0425000\pi\)
0.991100 + 0.133121i \(0.0425000\pi\)
\(770\) 0 0
\(771\) −4.04413 −0.145646
\(772\) 0 0
\(773\) −33.7153 −1.21265 −0.606327 0.795215i \(-0.707358\pi\)
−0.606327 + 0.795215i \(0.707358\pi\)
\(774\) 0 0
\(775\) −3.31781 −0.119179
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.88313 −0.0674701
\(780\) 0 0
\(781\) 13.6993 0.490200
\(782\) 0 0
\(783\) 1.40818 0.0503244
\(784\) 0 0
\(785\) 12.9486 0.462155
\(786\) 0 0
\(787\) −30.6525 −1.09264 −0.546322 0.837575i \(-0.683973\pi\)
−0.546322 + 0.837575i \(0.683973\pi\)
\(788\) 0 0
\(789\) −6.58309 −0.234364
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −26.0524 −0.925148
\(794\) 0 0
\(795\) −7.58728 −0.269093
\(796\) 0 0
\(797\) −33.9994 −1.20432 −0.602160 0.798375i \(-0.705693\pi\)
−0.602160 + 0.798375i \(0.705693\pi\)
\(798\) 0 0
\(799\) −0.105227 −0.00372268
\(800\) 0 0
\(801\) −23.7728 −0.839971
\(802\) 0 0
\(803\) 37.6420 1.32836
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −2.29044 −0.0806272
\(808\) 0 0
\(809\) 20.7327 0.728924 0.364462 0.931218i \(-0.381253\pi\)
0.364462 + 0.931218i \(0.381253\pi\)
\(810\) 0 0
\(811\) 10.6026 0.372308 0.186154 0.982521i \(-0.440398\pi\)
0.186154 + 0.982521i \(0.440398\pi\)
\(812\) 0 0
\(813\) 4.00709 0.140535
\(814\) 0 0
\(815\) 17.6770 0.619199
\(816\) 0 0
\(817\) 0.590774 0.0206686
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 17.4066 0.607495 0.303748 0.952752i \(-0.401762\pi\)
0.303748 + 0.952752i \(0.401762\pi\)
\(822\) 0 0
\(823\) 15.4934 0.540068 0.270034 0.962851i \(-0.412965\pi\)
0.270034 + 0.962851i \(0.412965\pi\)
\(824\) 0 0
\(825\) −1.15557 −0.0402316
\(826\) 0 0
\(827\) −31.9844 −1.11221 −0.556103 0.831113i \(-0.687704\pi\)
−0.556103 + 0.831113i \(0.687704\pi\)
\(828\) 0 0
\(829\) 52.1808 1.81231 0.906157 0.422942i \(-0.139002\pi\)
0.906157 + 0.422942i \(0.139002\pi\)
\(830\) 0 0
\(831\) −0.829457 −0.0287735
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 16.8635 0.583587
\(836\) 0 0
\(837\) −7.89228 −0.272797
\(838\) 0 0
\(839\) −24.0140 −0.829054 −0.414527 0.910037i \(-0.636053\pi\)
−0.414527 + 0.910037i \(0.636053\pi\)
\(840\) 0 0
\(841\) −28.3027 −0.975955
\(842\) 0 0
\(843\) 2.46085 0.0847563
\(844\) 0 0
\(845\) 44.9138 1.54508
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 3.88717 0.133407
\(850\) 0 0
\(851\) 7.67689 0.263160
\(852\) 0 0
\(853\) 20.5132 0.702359 0.351179 0.936308i \(-0.385781\pi\)
0.351179 + 0.936308i \(0.385781\pi\)
\(854\) 0 0
\(855\) 13.1330 0.449140
\(856\) 0 0
\(857\) −4.73663 −0.161800 −0.0809001 0.996722i \(-0.525779\pi\)
−0.0809001 + 0.996722i \(0.525779\pi\)
\(858\) 0 0
\(859\) −28.8070 −0.982881 −0.491441 0.870911i \(-0.663530\pi\)
−0.491441 + 0.870911i \(0.663530\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −27.5865 −0.939056 −0.469528 0.882918i \(-0.655576\pi\)
−0.469528 + 0.882918i \(0.655576\pi\)
\(864\) 0 0
\(865\) 21.2881 0.723817
\(866\) 0 0
\(867\) 4.82908 0.164004
\(868\) 0 0
\(869\) −20.3908 −0.691711
\(870\) 0 0
\(871\) 1.05512 0.0357514
\(872\) 0 0
\(873\) 51.7386 1.75109
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 41.4167 1.39854 0.699271 0.714857i \(-0.253508\pi\)
0.699271 + 0.714857i \(0.253508\pi\)
\(878\) 0 0
\(879\) −0.452826 −0.0152734
\(880\) 0 0
\(881\) −16.5018 −0.555960 −0.277980 0.960587i \(-0.589665\pi\)
−0.277980 + 0.960587i \(0.589665\pi\)
\(882\) 0 0
\(883\) −54.4787 −1.83335 −0.916676 0.399630i \(-0.869138\pi\)
−0.916676 + 0.399630i \(0.869138\pi\)
\(884\) 0 0
\(885\) −5.39402 −0.181318
\(886\) 0 0
\(887\) −17.5866 −0.590499 −0.295250 0.955420i \(-0.595403\pi\)
−0.295250 + 0.955420i \(0.595403\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 47.3481 1.58622
\(892\) 0 0
\(893\) 0.879540 0.0294327
\(894\) 0 0
\(895\) −18.9202 −0.632434
\(896\) 0 0
\(897\) −2.12459 −0.0709379
\(898\) 0 0
\(899\) −3.90808 −0.130342
\(900\) 0 0
\(901\) 2.51101 0.0836539
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0.435165 0.0144654
\(906\) 0 0
\(907\) −27.1953 −0.903004 −0.451502 0.892270i \(-0.649112\pi\)
−0.451502 + 0.892270i \(0.649112\pi\)
\(908\) 0 0
\(909\) −28.0155 −0.929215
\(910\) 0 0
\(911\) 25.7790 0.854097 0.427048 0.904229i \(-0.359553\pi\)
0.427048 + 0.904229i \(0.359553\pi\)
\(912\) 0 0
\(913\) 82.7237 2.73775
\(914\) 0 0
\(915\) 3.14515 0.103975
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −19.6407 −0.647885 −0.323943 0.946077i \(-0.605009\pi\)
−0.323943 + 0.946077i \(0.605009\pi\)
\(920\) 0 0
\(921\) −6.75313 −0.222523
\(922\) 0 0
\(923\) 13.5025 0.444440
\(924\) 0 0
\(925\) 4.11548 0.135316
\(926\) 0 0
\(927\) 18.7764 0.616696
\(928\) 0 0
\(929\) 30.4274 0.998290 0.499145 0.866519i \(-0.333648\pi\)
0.499145 + 0.866519i \(0.333648\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −8.03578 −0.263080
\(934\) 0 0
\(935\) 3.07973 0.100718
\(936\) 0 0
\(937\) −29.4086 −0.960737 −0.480368 0.877067i \(-0.659497\pi\)
−0.480368 + 0.877067i \(0.659497\pi\)
\(938\) 0 0
\(939\) −3.85970 −0.125957
\(940\) 0 0
\(941\) −32.3930 −1.05598 −0.527991 0.849250i \(-0.677055\pi\)
−0.527991 + 0.849250i \(0.677055\pi\)
\(942\) 0 0
\(943\) 1.32240 0.0430633
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −32.3938 −1.05266 −0.526329 0.850281i \(-0.676432\pi\)
−0.526329 + 0.850281i \(0.676432\pi\)
\(948\) 0 0
\(949\) 37.1012 1.20436
\(950\) 0 0
\(951\) −1.16100 −0.0376479
\(952\) 0 0
\(953\) −19.3888 −0.628065 −0.314033 0.949412i \(-0.601680\pi\)
−0.314033 + 0.949412i \(0.601680\pi\)
\(954\) 0 0
\(955\) −37.5263 −1.21432
\(956\) 0 0
\(957\) −1.36115 −0.0439998
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −9.09688 −0.293448
\(962\) 0 0
\(963\) 39.9127 1.28617
\(964\) 0 0
\(965\) −20.1794 −0.649599
\(966\) 0 0
\(967\) 18.8317 0.605587 0.302794 0.953056i \(-0.402081\pi\)
0.302794 + 0.953056i \(0.402081\pi\)
\(968\) 0 0
\(969\) 0.120878 0.00388316
\(970\) 0 0
\(971\) 27.3721 0.878414 0.439207 0.898386i \(-0.355259\pi\)
0.439207 + 0.898386i \(0.355259\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −1.13896 −0.0364760
\(976\) 0 0
\(977\) 26.5113 0.848172 0.424086 0.905622i \(-0.360595\pi\)
0.424086 + 0.905622i \(0.360595\pi\)
\(978\) 0 0
\(979\) 46.5967 1.48924
\(980\) 0 0
\(981\) 40.0586 1.27897
\(982\) 0 0
\(983\) −37.4952 −1.19591 −0.597956 0.801529i \(-0.704020\pi\)
−0.597956 + 0.801529i \(0.704020\pi\)
\(984\) 0 0
\(985\) 39.7219 1.26565
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −0.414863 −0.0131919
\(990\) 0 0
\(991\) 28.4033 0.902262 0.451131 0.892458i \(-0.351021\pi\)
0.451131 + 0.892458i \(0.351021\pi\)
\(992\) 0 0
\(993\) 8.50520 0.269904
\(994\) 0 0
\(995\) 56.2775 1.78412
\(996\) 0 0
\(997\) −30.3006 −0.959629 −0.479815 0.877370i \(-0.659296\pi\)
−0.479815 + 0.877370i \(0.659296\pi\)
\(998\) 0 0
\(999\) 9.78975 0.309734
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 \(a_p\))