Properties

Label 8036.2.a.q.1.6
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
CM No
Inner twists 1

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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: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.40418\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.40418 q^{3} +3.61567 q^{5} -1.02828 q^{9} +O(q^{10})\) \(q-1.40418 q^{3} +3.61567 q^{5} -1.02828 q^{9} -5.64929 q^{11} +6.54345 q^{13} -5.07705 q^{15} +3.39066 q^{17} +5.19738 q^{19} -2.81011 q^{23} +8.07310 q^{25} +5.65643 q^{27} +2.17600 q^{29} +6.26055 q^{31} +7.93262 q^{33} +0.641460 q^{37} -9.18818 q^{39} -1.00000 q^{41} -4.44365 q^{43} -3.71793 q^{45} +6.69641 q^{47} -4.76109 q^{51} +4.95277 q^{53} -20.4260 q^{55} -7.29805 q^{57} -11.0289 q^{59} -12.0389 q^{61} +23.6590 q^{65} +10.5842 q^{67} +3.94589 q^{69} -8.70411 q^{71} +0.422919 q^{73} -11.3361 q^{75} -14.2265 q^{79} -4.85779 q^{81} +5.06521 q^{83} +12.2595 q^{85} -3.05549 q^{87} -1.56457 q^{89} -8.79093 q^{93} +18.7920 q^{95} +16.4451 q^{97} +5.80907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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
\(3\) −1.40418 −0.810703 −0.405351 0.914161i \(-0.632851\pi\)
−0.405351 + 0.914161i \(0.632851\pi\)
\(4\) 0 0
\(5\) 3.61567 1.61698 0.808489 0.588511i \(-0.200286\pi\)
0.808489 + 0.588511i \(0.200286\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −1.02828 −0.342761
\(10\) 0 0
\(11\) −5.64929 −1.70333 −0.851663 0.524090i \(-0.824406\pi\)
−0.851663 + 0.524090i \(0.824406\pi\)
\(12\) 0 0
\(13\) 6.54345 1.81483 0.907414 0.420238i \(-0.138053\pi\)
0.907414 + 0.420238i \(0.138053\pi\)
\(14\) 0 0
\(15\) −5.07705 −1.31089
\(16\) 0 0
\(17\) 3.39066 0.822356 0.411178 0.911555i \(-0.365118\pi\)
0.411178 + 0.911555i \(0.365118\pi\)
\(18\) 0 0
\(19\) 5.19738 1.19236 0.596181 0.802850i \(-0.296684\pi\)
0.596181 + 0.802850i \(0.296684\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.81011 −0.585948 −0.292974 0.956120i \(-0.594645\pi\)
−0.292974 + 0.956120i \(0.594645\pi\)
\(24\) 0 0
\(25\) 8.07310 1.61462
\(26\) 0 0
\(27\) 5.65643 1.08858
\(28\) 0 0
\(29\) 2.17600 0.404072 0.202036 0.979378i \(-0.435244\pi\)
0.202036 + 0.979378i \(0.435244\pi\)
\(30\) 0 0
\(31\) 6.26055 1.12443 0.562214 0.826992i \(-0.309950\pi\)
0.562214 + 0.826992i \(0.309950\pi\)
\(32\) 0 0
\(33\) 7.93262 1.38089
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.641460 0.105455 0.0527277 0.998609i \(-0.483208\pi\)
0.0527277 + 0.998609i \(0.483208\pi\)
\(38\) 0 0
\(39\) −9.18818 −1.47129
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −4.44365 −0.677650 −0.338825 0.940849i \(-0.610029\pi\)
−0.338825 + 0.940849i \(0.610029\pi\)
\(44\) 0 0
\(45\) −3.71793 −0.554237
\(46\) 0 0
\(47\) 6.69641 0.976772 0.488386 0.872628i \(-0.337586\pi\)
0.488386 + 0.872628i \(0.337586\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −4.76109 −0.666686
\(52\) 0 0
\(53\) 4.95277 0.680316 0.340158 0.940368i \(-0.389519\pi\)
0.340158 + 0.940368i \(0.389519\pi\)
\(54\) 0 0
\(55\) −20.4260 −2.75424
\(56\) 0 0
\(57\) −7.29805 −0.966651
\(58\) 0 0
\(59\) −11.0289 −1.43584 −0.717922 0.696124i \(-0.754906\pi\)
−0.717922 + 0.696124i \(0.754906\pi\)
\(60\) 0 0
\(61\) −12.0389 −1.54143 −0.770713 0.637182i \(-0.780100\pi\)
−0.770713 + 0.637182i \(0.780100\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 23.6590 2.93454
\(66\) 0 0
\(67\) 10.5842 1.29306 0.646531 0.762888i \(-0.276219\pi\)
0.646531 + 0.762888i \(0.276219\pi\)
\(68\) 0 0
\(69\) 3.94589 0.475030
\(70\) 0 0
\(71\) −8.70411 −1.03299 −0.516494 0.856291i \(-0.672763\pi\)
−0.516494 + 0.856291i \(0.672763\pi\)
\(72\) 0 0
\(73\) 0.422919 0.0494990 0.0247495 0.999694i \(-0.492121\pi\)
0.0247495 + 0.999694i \(0.492121\pi\)
\(74\) 0 0
\(75\) −11.3361 −1.30898
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −14.2265 −1.60061 −0.800305 0.599594i \(-0.795329\pi\)
−0.800305 + 0.599594i \(0.795329\pi\)
\(80\) 0 0
\(81\) −4.85779 −0.539754
\(82\) 0 0
\(83\) 5.06521 0.555979 0.277989 0.960584i \(-0.410332\pi\)
0.277989 + 0.960584i \(0.410332\pi\)
\(84\) 0 0
\(85\) 12.2595 1.32973
\(86\) 0 0
\(87\) −3.05549 −0.327583
\(88\) 0 0
\(89\) −1.56457 −0.165844 −0.0829218 0.996556i \(-0.526425\pi\)
−0.0829218 + 0.996556i \(0.526425\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −8.79093 −0.911577
\(94\) 0 0
\(95\) 18.7920 1.92802
\(96\) 0 0
\(97\) 16.4451 1.66975 0.834873 0.550442i \(-0.185541\pi\)
0.834873 + 0.550442i \(0.185541\pi\)
\(98\) 0 0
\(99\) 5.80907 0.583833
\(100\) 0 0
\(101\) −11.1405 −1.10852 −0.554260 0.832343i \(-0.686999\pi\)
−0.554260 + 0.832343i \(0.686999\pi\)
\(102\) 0 0
\(103\) −5.00165 −0.492827 −0.246414 0.969165i \(-0.579252\pi\)
−0.246414 + 0.969165i \(0.579252\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.29287 −0.801702 −0.400851 0.916143i \(-0.631285\pi\)
−0.400851 + 0.916143i \(0.631285\pi\)
\(108\) 0 0
\(109\) 11.0279 1.05629 0.528143 0.849156i \(-0.322889\pi\)
0.528143 + 0.849156i \(0.322889\pi\)
\(110\) 0 0
\(111\) −0.900725 −0.0854930
\(112\) 0 0
\(113\) −8.26658 −0.777654 −0.388827 0.921311i \(-0.627120\pi\)
−0.388827 + 0.921311i \(0.627120\pi\)
\(114\) 0 0
\(115\) −10.1604 −0.947465
\(116\) 0 0
\(117\) −6.72852 −0.622052
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 20.9145 1.90132
\(122\) 0 0
\(123\) 1.40418 0.126611
\(124\) 0 0
\(125\) 11.1113 0.993828
\(126\) 0 0
\(127\) 1.12925 0.100205 0.0501024 0.998744i \(-0.484045\pi\)
0.0501024 + 0.998744i \(0.484045\pi\)
\(128\) 0 0
\(129\) 6.23967 0.549373
\(130\) 0 0
\(131\) 18.9249 1.65348 0.826739 0.562586i \(-0.190194\pi\)
0.826739 + 0.562586i \(0.190194\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 20.4518 1.76021
\(136\) 0 0
\(137\) 8.36226 0.714436 0.357218 0.934021i \(-0.383725\pi\)
0.357218 + 0.934021i \(0.383725\pi\)
\(138\) 0 0
\(139\) 18.1952 1.54330 0.771648 0.636050i \(-0.219433\pi\)
0.771648 + 0.636050i \(0.219433\pi\)
\(140\) 0 0
\(141\) −9.40296 −0.791872
\(142\) 0 0
\(143\) −36.9659 −3.09124
\(144\) 0 0
\(145\) 7.86769 0.653376
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −12.0464 −0.986877 −0.493438 0.869781i \(-0.664260\pi\)
−0.493438 + 0.869781i \(0.664260\pi\)
\(150\) 0 0
\(151\) 5.44182 0.442849 0.221424 0.975178i \(-0.428929\pi\)
0.221424 + 0.975178i \(0.428929\pi\)
\(152\) 0 0
\(153\) −3.48656 −0.281871
\(154\) 0 0
\(155\) 22.6361 1.81818
\(156\) 0 0
\(157\) 20.9240 1.66992 0.834960 0.550311i \(-0.185491\pi\)
0.834960 + 0.550311i \(0.185491\pi\)
\(158\) 0 0
\(159\) −6.95458 −0.551534
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 17.0858 1.33826 0.669132 0.743144i \(-0.266666\pi\)
0.669132 + 0.743144i \(0.266666\pi\)
\(164\) 0 0
\(165\) 28.6818 2.23287
\(166\) 0 0
\(167\) 13.0854 1.01258 0.506289 0.862364i \(-0.331017\pi\)
0.506289 + 0.862364i \(0.331017\pi\)
\(168\) 0 0
\(169\) 29.8168 2.29360
\(170\) 0 0
\(171\) −5.34438 −0.408695
\(172\) 0 0
\(173\) 19.2270 1.46180 0.730902 0.682482i \(-0.239100\pi\)
0.730902 + 0.682482i \(0.239100\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 15.4866 1.16404
\(178\) 0 0
\(179\) −8.73014 −0.652521 −0.326261 0.945280i \(-0.605789\pi\)
−0.326261 + 0.945280i \(0.605789\pi\)
\(180\) 0 0
\(181\) −11.2949 −0.839544 −0.419772 0.907630i \(-0.637890\pi\)
−0.419772 + 0.907630i \(0.637890\pi\)
\(182\) 0 0
\(183\) 16.9048 1.24964
\(184\) 0 0
\(185\) 2.31931 0.170519
\(186\) 0 0
\(187\) −19.1548 −1.40074
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −16.9084 −1.22345 −0.611724 0.791071i \(-0.709524\pi\)
−0.611724 + 0.791071i \(0.709524\pi\)
\(192\) 0 0
\(193\) 3.98688 0.286982 0.143491 0.989652i \(-0.454167\pi\)
0.143491 + 0.989652i \(0.454167\pi\)
\(194\) 0 0
\(195\) −33.2215 −2.37904
\(196\) 0 0
\(197\) −12.0163 −0.856124 −0.428062 0.903749i \(-0.640803\pi\)
−0.428062 + 0.903749i \(0.640803\pi\)
\(198\) 0 0
\(199\) −10.9253 −0.774475 −0.387238 0.921980i \(-0.626571\pi\)
−0.387238 + 0.921980i \(0.626571\pi\)
\(200\) 0 0
\(201\) −14.8621 −1.04829
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3.61567 −0.252530
\(206\) 0 0
\(207\) 2.88958 0.200840
\(208\) 0 0
\(209\) −29.3615 −2.03098
\(210\) 0 0
\(211\) −7.98904 −0.549988 −0.274994 0.961446i \(-0.588676\pi\)
−0.274994 + 0.961446i \(0.588676\pi\)
\(212\) 0 0
\(213\) 12.2221 0.837446
\(214\) 0 0
\(215\) −16.0668 −1.09575
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −0.593854 −0.0401290
\(220\) 0 0
\(221\) 22.1866 1.49243
\(222\) 0 0
\(223\) 27.5999 1.84823 0.924115 0.382116i \(-0.124804\pi\)
0.924115 + 0.382116i \(0.124804\pi\)
\(224\) 0 0
\(225\) −8.30143 −0.553429
\(226\) 0 0
\(227\) −24.3315 −1.61494 −0.807468 0.589911i \(-0.799163\pi\)
−0.807468 + 0.589911i \(0.799163\pi\)
\(228\) 0 0
\(229\) 0.109735 0.00725149 0.00362574 0.999993i \(-0.498846\pi\)
0.00362574 + 0.999993i \(0.498846\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.22953 −0.539134 −0.269567 0.962982i \(-0.586881\pi\)
−0.269567 + 0.962982i \(0.586881\pi\)
\(234\) 0 0
\(235\) 24.2120 1.57942
\(236\) 0 0
\(237\) 19.9766 1.29762
\(238\) 0 0
\(239\) 7.13997 0.461846 0.230923 0.972972i \(-0.425825\pi\)
0.230923 + 0.972972i \(0.425825\pi\)
\(240\) 0 0
\(241\) 12.3191 0.793543 0.396771 0.917917i \(-0.370131\pi\)
0.396771 + 0.917917i \(0.370131\pi\)
\(242\) 0 0
\(243\) −10.1481 −0.651000
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 34.0088 2.16393
\(248\) 0 0
\(249\) −7.11245 −0.450734
\(250\) 0 0
\(251\) −6.03854 −0.381149 −0.190575 0.981673i \(-0.561035\pi\)
−0.190575 + 0.981673i \(0.561035\pi\)
\(252\) 0 0
\(253\) 15.8751 0.998060
\(254\) 0 0
\(255\) −17.2146 −1.07802
\(256\) 0 0
\(257\) 28.5716 1.78225 0.891123 0.453763i \(-0.149919\pi\)
0.891123 + 0.453763i \(0.149919\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −2.23754 −0.138500
\(262\) 0 0
\(263\) −30.7054 −1.89338 −0.946690 0.322147i \(-0.895595\pi\)
−0.946690 + 0.322147i \(0.895595\pi\)
\(264\) 0 0
\(265\) 17.9076 1.10006
\(266\) 0 0
\(267\) 2.19693 0.134450
\(268\) 0 0
\(269\) 12.1607 0.741451 0.370726 0.928742i \(-0.379109\pi\)
0.370726 + 0.928742i \(0.379109\pi\)
\(270\) 0 0
\(271\) 5.84160 0.354852 0.177426 0.984134i \(-0.443223\pi\)
0.177426 + 0.984134i \(0.443223\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −45.6073 −2.75022
\(276\) 0 0
\(277\) −22.7835 −1.36893 −0.684463 0.729047i \(-0.739963\pi\)
−0.684463 + 0.729047i \(0.739963\pi\)
\(278\) 0 0
\(279\) −6.43761 −0.385410
\(280\) 0 0
\(281\) −2.36022 −0.140799 −0.0703995 0.997519i \(-0.522427\pi\)
−0.0703995 + 0.997519i \(0.522427\pi\)
\(282\) 0 0
\(283\) 0.0967397 0.00575058 0.00287529 0.999996i \(-0.499085\pi\)
0.00287529 + 0.999996i \(0.499085\pi\)
\(284\) 0 0
\(285\) −26.3874 −1.56305
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −5.50343 −0.323731
\(290\) 0 0
\(291\) −23.0919 −1.35367
\(292\) 0 0
\(293\) 24.8023 1.44897 0.724484 0.689292i \(-0.242078\pi\)
0.724484 + 0.689292i \(0.242078\pi\)
\(294\) 0 0
\(295\) −39.8770 −2.32173
\(296\) 0 0
\(297\) −31.9548 −1.85421
\(298\) 0 0
\(299\) −18.3878 −1.06339
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 15.6432 0.898681
\(304\) 0 0
\(305\) −43.5288 −2.49245
\(306\) 0 0
\(307\) −3.46391 −0.197696 −0.0988480 0.995103i \(-0.531516\pi\)
−0.0988480 + 0.995103i \(0.531516\pi\)
\(308\) 0 0
\(309\) 7.02321 0.399537
\(310\) 0 0
\(311\) 26.0188 1.47539 0.737697 0.675132i \(-0.235913\pi\)
0.737697 + 0.675132i \(0.235913\pi\)
\(312\) 0 0
\(313\) 4.95821 0.280255 0.140127 0.990133i \(-0.455249\pi\)
0.140127 + 0.990133i \(0.455249\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 17.0035 0.955012 0.477506 0.878629i \(-0.341541\pi\)
0.477506 + 0.878629i \(0.341541\pi\)
\(318\) 0 0
\(319\) −12.2928 −0.688267
\(320\) 0 0
\(321\) 11.6447 0.649942
\(322\) 0 0
\(323\) 17.6226 0.980545
\(324\) 0 0
\(325\) 52.8260 2.93026
\(326\) 0 0
\(327\) −15.4852 −0.856334
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 11.2694 0.619424 0.309712 0.950830i \(-0.399767\pi\)
0.309712 + 0.950830i \(0.399767\pi\)
\(332\) 0 0
\(333\) −0.659602 −0.0361460
\(334\) 0 0
\(335\) 38.2689 2.09085
\(336\) 0 0
\(337\) 29.7342 1.61972 0.809862 0.586620i \(-0.199542\pi\)
0.809862 + 0.586620i \(0.199542\pi\)
\(338\) 0 0
\(339\) 11.6077 0.630446
\(340\) 0 0
\(341\) −35.3677 −1.91527
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 14.2671 0.768113
\(346\) 0 0
\(347\) 13.6670 0.733683 0.366841 0.930283i \(-0.380439\pi\)
0.366841 + 0.930283i \(0.380439\pi\)
\(348\) 0 0
\(349\) −21.4570 −1.14857 −0.574284 0.818656i \(-0.694720\pi\)
−0.574284 + 0.818656i \(0.694720\pi\)
\(350\) 0 0
\(351\) 37.0126 1.97559
\(352\) 0 0
\(353\) 20.1025 1.06995 0.534974 0.844868i \(-0.320321\pi\)
0.534974 + 0.844868i \(0.320321\pi\)
\(354\) 0 0
\(355\) −31.4712 −1.67032
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −13.7108 −0.723629 −0.361814 0.932250i \(-0.617843\pi\)
−0.361814 + 0.932250i \(0.617843\pi\)
\(360\) 0 0
\(361\) 8.01278 0.421725
\(362\) 0 0
\(363\) −29.3677 −1.54140
\(364\) 0 0
\(365\) 1.52914 0.0800388
\(366\) 0 0
\(367\) 27.1307 1.41621 0.708105 0.706107i \(-0.249550\pi\)
0.708105 + 0.706107i \(0.249550\pi\)
\(368\) 0 0
\(369\) 1.02828 0.0535302
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −10.5573 −0.546636 −0.273318 0.961924i \(-0.588121\pi\)
−0.273318 + 0.961924i \(0.588121\pi\)
\(374\) 0 0
\(375\) −15.6023 −0.805699
\(376\) 0 0
\(377\) 14.2385 0.733322
\(378\) 0 0
\(379\) 24.9019 1.27913 0.639563 0.768739i \(-0.279115\pi\)
0.639563 + 0.768739i \(0.279115\pi\)
\(380\) 0 0
\(381\) −1.58567 −0.0812364
\(382\) 0 0
\(383\) 8.74847 0.447026 0.223513 0.974701i \(-0.428248\pi\)
0.223513 + 0.974701i \(0.428248\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.56932 0.232272
\(388\) 0 0
\(389\) −5.28198 −0.267807 −0.133903 0.990994i \(-0.542751\pi\)
−0.133903 + 0.990994i \(0.542751\pi\)
\(390\) 0 0
\(391\) −9.52812 −0.481858
\(392\) 0 0
\(393\) −26.5740 −1.34048
\(394\) 0 0
\(395\) −51.4385 −2.58815
\(396\) 0 0
\(397\) −8.19379 −0.411235 −0.205617 0.978632i \(-0.565920\pi\)
−0.205617 + 0.978632i \(0.565920\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11.7598 0.587256 0.293628 0.955920i \(-0.405137\pi\)
0.293628 + 0.955920i \(0.405137\pi\)
\(402\) 0 0
\(403\) 40.9656 2.04064
\(404\) 0 0
\(405\) −17.5642 −0.872771
\(406\) 0 0
\(407\) −3.62380 −0.179625
\(408\) 0 0
\(409\) −14.1419 −0.699274 −0.349637 0.936885i \(-0.613695\pi\)
−0.349637 + 0.936885i \(0.613695\pi\)
\(410\) 0 0
\(411\) −11.7421 −0.579196
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 18.3141 0.899006
\(416\) 0 0
\(417\) −25.5493 −1.25115
\(418\) 0 0
\(419\) −3.94153 −0.192556 −0.0962781 0.995354i \(-0.530694\pi\)
−0.0962781 + 0.995354i \(0.530694\pi\)
\(420\) 0 0
\(421\) −28.9273 −1.40983 −0.704914 0.709292i \(-0.749015\pi\)
−0.704914 + 0.709292i \(0.749015\pi\)
\(422\) 0 0
\(423\) −6.88580 −0.334799
\(424\) 0 0
\(425\) 27.3731 1.32779
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 51.9067 2.50608
\(430\) 0 0
\(431\) 4.29158 0.206718 0.103359 0.994644i \(-0.467041\pi\)
0.103359 + 0.994644i \(0.467041\pi\)
\(432\) 0 0
\(433\) 1.69228 0.0813259 0.0406629 0.999173i \(-0.487053\pi\)
0.0406629 + 0.999173i \(0.487053\pi\)
\(434\) 0 0
\(435\) −11.0476 −0.529694
\(436\) 0 0
\(437\) −14.6052 −0.698661
\(438\) 0 0
\(439\) −4.55266 −0.217287 −0.108643 0.994081i \(-0.534651\pi\)
−0.108643 + 0.994081i \(0.534651\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.59951 0.218529 0.109265 0.994013i \(-0.465150\pi\)
0.109265 + 0.994013i \(0.465150\pi\)
\(444\) 0 0
\(445\) −5.65696 −0.268166
\(446\) 0 0
\(447\) 16.9153 0.800064
\(448\) 0 0
\(449\) 4.72931 0.223190 0.111595 0.993754i \(-0.464404\pi\)
0.111595 + 0.993754i \(0.464404\pi\)
\(450\) 0 0
\(451\) 5.64929 0.266015
\(452\) 0 0
\(453\) −7.64128 −0.359019
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 19.5087 0.912581 0.456290 0.889831i \(-0.349178\pi\)
0.456290 + 0.889831i \(0.349178\pi\)
\(458\) 0 0
\(459\) 19.1790 0.895200
\(460\) 0 0
\(461\) 1.57849 0.0735178 0.0367589 0.999324i \(-0.488297\pi\)
0.0367589 + 0.999324i \(0.488297\pi\)
\(462\) 0 0
\(463\) 4.94122 0.229638 0.114819 0.993386i \(-0.463371\pi\)
0.114819 + 0.993386i \(0.463371\pi\)
\(464\) 0 0
\(465\) −31.7851 −1.47400
\(466\) 0 0
\(467\) 23.2577 1.07624 0.538120 0.842868i \(-0.319135\pi\)
0.538120 + 0.842868i \(0.319135\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −29.3811 −1.35381
\(472\) 0 0
\(473\) 25.1035 1.15426
\(474\) 0 0
\(475\) 41.9590 1.92521
\(476\) 0 0
\(477\) −5.09285 −0.233186
\(478\) 0 0
\(479\) 15.5270 0.709449 0.354724 0.934971i \(-0.384575\pi\)
0.354724 + 0.934971i \(0.384575\pi\)
\(480\) 0 0
\(481\) 4.19737 0.191383
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 59.4601 2.69995
\(486\) 0 0
\(487\) 15.9614 0.723279 0.361640 0.932318i \(-0.382217\pi\)
0.361640 + 0.932318i \(0.382217\pi\)
\(488\) 0 0
\(489\) −23.9915 −1.08493
\(490\) 0 0
\(491\) −4.11148 −0.185548 −0.0927742 0.995687i \(-0.529573\pi\)
−0.0927742 + 0.995687i \(0.529573\pi\)
\(492\) 0 0
\(493\) 7.37806 0.332291
\(494\) 0 0
\(495\) 21.0037 0.944046
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −7.15438 −0.320274 −0.160137 0.987095i \(-0.551194\pi\)
−0.160137 + 0.987095i \(0.551194\pi\)
\(500\) 0 0
\(501\) −18.3742 −0.820901
\(502\) 0 0
\(503\) 4.71388 0.210182 0.105091 0.994463i \(-0.466487\pi\)
0.105091 + 0.994463i \(0.466487\pi\)
\(504\) 0 0
\(505\) −40.2804 −1.79245
\(506\) 0 0
\(507\) −41.8681 −1.85943
\(508\) 0 0
\(509\) −18.2184 −0.807516 −0.403758 0.914866i \(-0.632296\pi\)
−0.403758 + 0.914866i \(0.632296\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 29.3986 1.29798
\(514\) 0 0
\(515\) −18.0843 −0.796891
\(516\) 0 0
\(517\) −37.8300 −1.66376
\(518\) 0 0
\(519\) −26.9982 −1.18509
\(520\) 0 0
\(521\) 10.9519 0.479811 0.239905 0.970796i \(-0.422884\pi\)
0.239905 + 0.970796i \(0.422884\pi\)
\(522\) 0 0
\(523\) 19.6211 0.857972 0.428986 0.903311i \(-0.358871\pi\)
0.428986 + 0.903311i \(0.358871\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 21.2274 0.924679
\(528\) 0 0
\(529\) −15.1033 −0.656665
\(530\) 0 0
\(531\) 11.3408 0.492151
\(532\) 0 0
\(533\) −6.54345 −0.283428
\(534\) 0 0
\(535\) −29.9843 −1.29633
\(536\) 0 0
\(537\) 12.2587 0.529001
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 22.4723 0.966160 0.483080 0.875576i \(-0.339518\pi\)
0.483080 + 0.875576i \(0.339518\pi\)
\(542\) 0 0
\(543\) 15.8601 0.680621
\(544\) 0 0
\(545\) 39.8734 1.70799
\(546\) 0 0
\(547\) −5.78852 −0.247499 −0.123750 0.992313i \(-0.539492\pi\)
−0.123750 + 0.992313i \(0.539492\pi\)
\(548\) 0 0
\(549\) 12.3794 0.528340
\(550\) 0 0
\(551\) 11.3095 0.481800
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −3.25673 −0.138240
\(556\) 0 0
\(557\) 8.22507 0.348507 0.174254 0.984701i \(-0.444249\pi\)
0.174254 + 0.984701i \(0.444249\pi\)
\(558\) 0 0
\(559\) −29.0768 −1.22982
\(560\) 0 0
\(561\) 26.8968 1.13558
\(562\) 0 0
\(563\) −20.5297 −0.865223 −0.432611 0.901580i \(-0.642408\pi\)
−0.432611 + 0.901580i \(0.642408\pi\)
\(564\) 0 0
\(565\) −29.8892 −1.25745
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −23.9665 −1.00473 −0.502364 0.864656i \(-0.667536\pi\)
−0.502364 + 0.864656i \(0.667536\pi\)
\(570\) 0 0
\(571\) 34.4864 1.44321 0.721605 0.692306i \(-0.243405\pi\)
0.721605 + 0.692306i \(0.243405\pi\)
\(572\) 0 0
\(573\) 23.7424 0.991853
\(574\) 0 0
\(575\) −22.6863 −0.946083
\(576\) 0 0
\(577\) −41.0357 −1.70834 −0.854168 0.519996i \(-0.825933\pi\)
−0.854168 + 0.519996i \(0.825933\pi\)
\(578\) 0 0
\(579\) −5.59829 −0.232657
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −27.9797 −1.15880
\(584\) 0 0
\(585\) −24.3281 −1.00584
\(586\) 0 0
\(587\) 6.21910 0.256690 0.128345 0.991730i \(-0.459034\pi\)
0.128345 + 0.991730i \(0.459034\pi\)
\(588\) 0 0
\(589\) 32.5385 1.34072
\(590\) 0 0
\(591\) 16.8730 0.694062
\(592\) 0 0
\(593\) −2.92318 −0.120041 −0.0600204 0.998197i \(-0.519117\pi\)
−0.0600204 + 0.998197i \(0.519117\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 15.3411 0.627869
\(598\) 0 0
\(599\) −13.4830 −0.550901 −0.275450 0.961315i \(-0.588827\pi\)
−0.275450 + 0.961315i \(0.588827\pi\)
\(600\) 0 0
\(601\) −35.1493 −1.43377 −0.716886 0.697191i \(-0.754433\pi\)
−0.716886 + 0.697191i \(0.754433\pi\)
\(602\) 0 0
\(603\) −10.8835 −0.443211
\(604\) 0 0
\(605\) 75.6201 3.07439
\(606\) 0 0
\(607\) 31.7046 1.28685 0.643425 0.765509i \(-0.277513\pi\)
0.643425 + 0.765509i \(0.277513\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 43.8177 1.77267
\(612\) 0 0
\(613\) 0.747674 0.0301983 0.0150991 0.999886i \(-0.495194\pi\)
0.0150991 + 0.999886i \(0.495194\pi\)
\(614\) 0 0
\(615\) 5.07705 0.204727
\(616\) 0 0
\(617\) 16.6618 0.670780 0.335390 0.942079i \(-0.391132\pi\)
0.335390 + 0.942079i \(0.391132\pi\)
\(618\) 0 0
\(619\) −27.0691 −1.08800 −0.543999 0.839086i \(-0.683091\pi\)
−0.543999 + 0.839086i \(0.683091\pi\)
\(620\) 0 0
\(621\) −15.8952 −0.637851
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.190547 −0.00762189
\(626\) 0 0
\(627\) 41.2288 1.64652
\(628\) 0 0
\(629\) 2.17497 0.0867219
\(630\) 0 0
\(631\) −23.1258 −0.920625 −0.460312 0.887757i \(-0.652263\pi\)
−0.460312 + 0.887757i \(0.652263\pi\)
\(632\) 0 0
\(633\) 11.2180 0.445877
\(634\) 0 0
\(635\) 4.08301 0.162029
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 8.95028 0.354068
\(640\) 0 0
\(641\) 13.8551 0.547244 0.273622 0.961837i \(-0.411778\pi\)
0.273622 + 0.961837i \(0.411778\pi\)
\(642\) 0 0
\(643\) −6.61525 −0.260880 −0.130440 0.991456i \(-0.541639\pi\)
−0.130440 + 0.991456i \(0.541639\pi\)
\(644\) 0 0
\(645\) 22.5606 0.888324
\(646\) 0 0
\(647\) 5.04073 0.198172 0.0990858 0.995079i \(-0.468408\pi\)
0.0990858 + 0.995079i \(0.468408\pi\)
\(648\) 0 0
\(649\) 62.3056 2.44571
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 15.9694 0.624931 0.312465 0.949929i \(-0.398845\pi\)
0.312465 + 0.949929i \(0.398845\pi\)
\(654\) 0 0
\(655\) 68.4263 2.67364
\(656\) 0 0
\(657\) −0.434881 −0.0169663
\(658\) 0 0
\(659\) 4.81563 0.187590 0.0937952 0.995592i \(-0.470100\pi\)
0.0937952 + 0.995592i \(0.470100\pi\)
\(660\) 0 0
\(661\) −22.6400 −0.880593 −0.440296 0.897853i \(-0.645127\pi\)
−0.440296 + 0.897853i \(0.645127\pi\)
\(662\) 0 0
\(663\) −31.1540 −1.20992
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −6.11478 −0.236765
\(668\) 0 0
\(669\) −38.7553 −1.49836
\(670\) 0 0
\(671\) 68.0114 2.62555
\(672\) 0 0
\(673\) −15.0840 −0.581446 −0.290723 0.956807i \(-0.593896\pi\)
−0.290723 + 0.956807i \(0.593896\pi\)
\(674\) 0 0
\(675\) 45.6649 1.75764
\(676\) 0 0
\(677\) 29.4473 1.13175 0.565876 0.824490i \(-0.308538\pi\)
0.565876 + 0.824490i \(0.308538\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 34.1657 1.30923
\(682\) 0 0
\(683\) 0.575409 0.0220174 0.0110087 0.999939i \(-0.496496\pi\)
0.0110087 + 0.999939i \(0.496496\pi\)
\(684\) 0 0
\(685\) 30.2352 1.15523
\(686\) 0 0
\(687\) −0.154087 −0.00587880
\(688\) 0 0
\(689\) 32.4082 1.23466
\(690\) 0 0
\(691\) −37.5440 −1.42824 −0.714120 0.700023i \(-0.753173\pi\)
−0.714120 + 0.700023i \(0.753173\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 65.7879 2.49548
\(696\) 0 0
\(697\) −3.39066 −0.128430
\(698\) 0 0
\(699\) 11.5557 0.437078
\(700\) 0 0
\(701\) −31.1046 −1.17480 −0.587402 0.809295i \(-0.699849\pi\)
−0.587402 + 0.809295i \(0.699849\pi\)
\(702\) 0 0
\(703\) 3.33391 0.125741
\(704\) 0 0
\(705\) −33.9980 −1.28044
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −5.85434 −0.219864 −0.109932 0.993939i \(-0.535063\pi\)
−0.109932 + 0.993939i \(0.535063\pi\)
\(710\) 0 0
\(711\) 14.6289 0.548626
\(712\) 0 0
\(713\) −17.5928 −0.658856
\(714\) 0 0
\(715\) −133.657 −4.99847
\(716\) 0 0
\(717\) −10.0258 −0.374420
\(718\) 0 0
\(719\) 27.7937 1.03653 0.518264 0.855220i \(-0.326578\pi\)
0.518264 + 0.855220i \(0.326578\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −17.2982 −0.643328
\(724\) 0 0
\(725\) 17.5670 0.652423
\(726\) 0 0
\(727\) 15.5974 0.578474 0.289237 0.957257i \(-0.406598\pi\)
0.289237 + 0.957257i \(0.406598\pi\)
\(728\) 0 0
\(729\) 28.8231 1.06752
\(730\) 0 0
\(731\) −15.0669 −0.557269
\(732\) 0 0
\(733\) −39.6572 −1.46477 −0.732386 0.680889i \(-0.761594\pi\)
−0.732386 + 0.680889i \(0.761594\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −59.7930 −2.20250
\(738\) 0 0
\(739\) −12.9478 −0.476292 −0.238146 0.971229i \(-0.576540\pi\)
−0.238146 + 0.971229i \(0.576540\pi\)
\(740\) 0 0
\(741\) −47.7545 −1.75430
\(742\) 0 0
\(743\) −5.12957 −0.188186 −0.0940929 0.995563i \(-0.529995\pi\)
−0.0940929 + 0.995563i \(0.529995\pi\)
\(744\) 0 0
\(745\) −43.5557 −1.59576
\(746\) 0 0
\(747\) −5.20846 −0.190568
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 19.0378 0.694697 0.347349 0.937736i \(-0.387082\pi\)
0.347349 + 0.937736i \(0.387082\pi\)
\(752\) 0 0
\(753\) 8.47919 0.308999
\(754\) 0 0
\(755\) 19.6758 0.716077
\(756\) 0 0
\(757\) 32.8052 1.19233 0.596163 0.802864i \(-0.296691\pi\)
0.596163 + 0.802864i \(0.296691\pi\)
\(758\) 0 0
\(759\) −22.2915 −0.809130
\(760\) 0 0
\(761\) 41.2671 1.49593 0.747966 0.663737i \(-0.231031\pi\)
0.747966 + 0.663737i \(0.231031\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −12.6062 −0.455780
\(766\) 0 0
\(767\) −72.1672 −2.60581
\(768\) 0 0
\(769\) 36.2060 1.30562 0.652811 0.757520i \(-0.273589\pi\)
0.652811 + 0.757520i \(0.273589\pi\)
\(770\) 0 0
\(771\) −40.1196 −1.44487
\(772\) 0 0
\(773\) −23.6296 −0.849898 −0.424949 0.905217i \(-0.639708\pi\)
−0.424949 + 0.905217i \(0.639708\pi\)
\(774\) 0 0
\(775\) 50.5420 1.81552
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.19738 −0.186216
\(780\) 0 0
\(781\) 49.1721 1.75951
\(782\) 0 0
\(783\) 12.3084 0.439865
\(784\) 0 0
\(785\) 75.6545 2.70022
\(786\) 0 0
\(787\) 9.23570 0.329217 0.164609 0.986359i \(-0.447364\pi\)
0.164609 + 0.986359i \(0.447364\pi\)
\(788\) 0 0
\(789\) 43.1159 1.53497
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −78.7761 −2.79742
\(794\) 0 0
\(795\) −25.1455 −0.891819
\(796\) 0 0
\(797\) 41.1963 1.45925 0.729624 0.683848i \(-0.239695\pi\)
0.729624 + 0.683848i \(0.239695\pi\)
\(798\) 0 0
\(799\) 22.7052 0.803254
\(800\) 0 0
\(801\) 1.60881 0.0568447
\(802\) 0 0
\(803\) −2.38920 −0.0843129
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −17.0758 −0.601097
\(808\) 0 0
\(809\) 4.01458 0.141145 0.0705725 0.997507i \(-0.477517\pi\)
0.0705725 + 0.997507i \(0.477517\pi\)
\(810\) 0 0
\(811\) 26.1749 0.919124 0.459562 0.888146i \(-0.348006\pi\)
0.459562 + 0.888146i \(0.348006\pi\)
\(812\) 0 0
\(813\) −8.20264 −0.287679
\(814\) 0 0
\(815\) 61.7767 2.16394
\(816\) 0 0
\(817\) −23.0953 −0.808003
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −40.0484 −1.39770 −0.698849 0.715269i \(-0.746304\pi\)
−0.698849 + 0.715269i \(0.746304\pi\)
\(822\) 0 0
\(823\) 17.6884 0.616577 0.308289 0.951293i \(-0.400244\pi\)
0.308289 + 0.951293i \(0.400244\pi\)
\(824\) 0 0
\(825\) 64.0408 2.22961
\(826\) 0 0
\(827\) 27.9098 0.970520 0.485260 0.874370i \(-0.338725\pi\)
0.485260 + 0.874370i \(0.338725\pi\)
\(828\) 0 0
\(829\) 55.4075 1.92438 0.962191 0.272377i \(-0.0878098\pi\)
0.962191 + 0.272377i \(0.0878098\pi\)
\(830\) 0 0
\(831\) 31.9921 1.10979
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 47.3126 1.63732
\(836\) 0 0
\(837\) 35.4123 1.22403
\(838\) 0 0
\(839\) −46.1671 −1.59386 −0.796932 0.604069i \(-0.793545\pi\)
−0.796932 + 0.604069i \(0.793545\pi\)
\(840\) 0 0
\(841\) −24.2650 −0.836726
\(842\) 0 0
\(843\) 3.31417 0.114146
\(844\) 0 0
\(845\) 107.808 3.70870
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −0.135840 −0.00466201
\(850\) 0 0
\(851\) −1.80257 −0.0617914
\(852\) 0 0
\(853\) −46.7110 −1.59935 −0.799677 0.600430i \(-0.794996\pi\)
−0.799677 + 0.600430i \(0.794996\pi\)
\(854\) 0 0
\(855\) −19.3235 −0.660851
\(856\) 0 0
\(857\) 28.0091 0.956773 0.478387 0.878149i \(-0.341222\pi\)
0.478387 + 0.878149i \(0.341222\pi\)
\(858\) 0 0
\(859\) 9.73604 0.332189 0.166095 0.986110i \(-0.446884\pi\)
0.166095 + 0.986110i \(0.446884\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 10.8036 0.367759 0.183880 0.982949i \(-0.441134\pi\)
0.183880 + 0.982949i \(0.441134\pi\)
\(864\) 0 0
\(865\) 69.5187 2.36371
\(866\) 0 0
\(867\) 7.72780 0.262450
\(868\) 0 0
\(869\) 80.3698 2.72636
\(870\) 0 0
\(871\) 69.2570 2.34668
\(872\) 0 0
\(873\) −16.9102 −0.572324
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 14.1267 0.477026 0.238513 0.971139i \(-0.423340\pi\)
0.238513 + 0.971139i \(0.423340\pi\)
\(878\) 0 0
\(879\) −34.8269 −1.17468
\(880\) 0 0
\(881\) −37.6737 −1.26926 −0.634630 0.772816i \(-0.718847\pi\)
−0.634630 + 0.772816i \(0.718847\pi\)
\(882\) 0 0
\(883\) 20.1033 0.676531 0.338266 0.941051i \(-0.390160\pi\)
0.338266 + 0.941051i \(0.390160\pi\)
\(884\) 0 0
\(885\) 55.9944 1.88223
\(886\) 0 0
\(887\) −44.1332 −1.48185 −0.740924 0.671589i \(-0.765612\pi\)
−0.740924 + 0.671589i \(0.765612\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 27.4431 0.919377
\(892\) 0 0
\(893\) 34.8038 1.16466
\(894\) 0 0
\(895\) −31.5653 −1.05511
\(896\) 0 0
\(897\) 25.8198 0.862097
\(898\) 0 0
\(899\) 13.6229 0.454350
\(900\) 0 0
\(901\) 16.7932 0.559462
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −40.8387 −1.35753
\(906\) 0 0
\(907\) 1.85749 0.0616770 0.0308385 0.999524i \(-0.490182\pi\)
0.0308385 + 0.999524i \(0.490182\pi\)
\(908\) 0 0
\(909\) 11.4556 0.379957
\(910\) 0 0
\(911\) 14.5018 0.480466 0.240233 0.970715i \(-0.422776\pi\)
0.240233 + 0.970715i \(0.422776\pi\)
\(912\) 0 0
\(913\) −28.6148 −0.947013
\(914\) 0 0
\(915\) 61.1222 2.02064
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 21.1624 0.698082 0.349041 0.937107i \(-0.386507\pi\)
0.349041 + 0.937107i \(0.386507\pi\)
\(920\) 0 0
\(921\) 4.86395 0.160273
\(922\) 0 0
\(923\) −56.9549 −1.87469
\(924\) 0 0
\(925\) 5.17857 0.170270
\(926\) 0 0
\(927\) 5.14311 0.168922
\(928\) 0 0
\(929\) −59.7145 −1.95917 −0.979585 0.201029i \(-0.935571\pi\)
−0.979585 + 0.201029i \(0.935571\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −36.5351 −1.19611
\(934\) 0 0
\(935\) −69.2576 −2.26497
\(936\) 0 0
\(937\) −12.1335 −0.396384 −0.198192 0.980163i \(-0.563507\pi\)
−0.198192 + 0.980163i \(0.563507\pi\)
\(938\) 0 0
\(939\) −6.96221 −0.227203
\(940\) 0 0
\(941\) 12.8135 0.417710 0.208855 0.977947i \(-0.433026\pi\)
0.208855 + 0.977947i \(0.433026\pi\)
\(942\) 0 0
\(943\) 2.81011 0.0915097
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −17.2252 −0.559744 −0.279872 0.960037i \(-0.590292\pi\)
−0.279872 + 0.960037i \(0.590292\pi\)
\(948\) 0 0
\(949\) 2.76735 0.0898321
\(950\) 0 0
\(951\) −23.8760 −0.774231
\(952\) 0 0
\(953\) 15.2346 0.493496 0.246748 0.969080i \(-0.420638\pi\)
0.246748 + 0.969080i \(0.420638\pi\)
\(954\) 0 0
\(955\) −61.1352 −1.97829
\(956\) 0 0
\(957\) 17.2613 0.557980
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 8.19445 0.264337
\(962\) 0 0
\(963\) 8.52741 0.274792
\(964\) 0 0
\(965\) 14.4152 0.464043
\(966\) 0 0
\(967\) −27.5678 −0.886522 −0.443261 0.896393i \(-0.646179\pi\)
−0.443261 + 0.896393i \(0.646179\pi\)
\(968\) 0 0
\(969\) −24.7452 −0.794931
\(970\) 0 0
\(971\) −10.8096 −0.346896 −0.173448 0.984843i \(-0.555491\pi\)
−0.173448 + 0.984843i \(0.555491\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −74.1771 −2.37557
\(976\) 0 0
\(977\) −42.4703 −1.35875 −0.679373 0.733793i \(-0.737748\pi\)
−0.679373 + 0.733793i \(0.737748\pi\)
\(978\) 0 0
\(979\) 8.83869 0.282486
\(980\) 0 0
\(981\) −11.3398 −0.362053
\(982\) 0 0
\(983\) 61.6165 1.96526 0.982630 0.185576i \(-0.0594151\pi\)
0.982630 + 0.185576i \(0.0594151\pi\)
\(984\) 0 0
\(985\) −43.4469 −1.38433
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 12.4871 0.397067
\(990\) 0 0
\(991\) 42.2933 1.34349 0.671745 0.740782i \(-0.265545\pi\)
0.671745 + 0.740782i \(0.265545\pi\)
\(992\) 0 0
\(993\) −15.8243 −0.502169
\(994\) 0 0
\(995\) −39.5024 −1.25231
\(996\) 0 0
\(997\) 25.3094 0.801557 0.400778 0.916175i \(-0.368740\pi\)
0.400778 + 0.916175i \(0.368740\pi\)
\(998\) 0 0
\(999\) 3.62837 0.114797
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 \(a_p\))