Properties

Label 8036.2.a.p.1.3
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 10
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: \(10\)
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 1.3
Root \(-1.73395\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73395 q^{3} -3.41343 q^{5} +0.00658743 q^{9} +O(q^{10})\) \(q-1.73395 q^{3} -3.41343 q^{5} +0.00658743 q^{9} +1.67665 q^{11} +6.13889 q^{13} +5.91872 q^{15} +3.78979 q^{17} +3.86873 q^{19} -5.49935 q^{23} +6.65149 q^{25} +5.19043 q^{27} -0.172699 q^{29} +7.15470 q^{31} -2.90724 q^{33} -4.80199 q^{37} -10.6445 q^{39} +1.00000 q^{41} +0.845176 q^{43} -0.0224857 q^{45} +4.65792 q^{47} -6.57131 q^{51} +4.46567 q^{53} -5.72314 q^{55} -6.70819 q^{57} -3.38395 q^{59} +0.643064 q^{61} -20.9547 q^{65} -2.25183 q^{67} +9.53561 q^{69} -4.77826 q^{71} +9.42378 q^{73} -11.5334 q^{75} +3.64751 q^{79} -9.01972 q^{81} -12.7027 q^{83} -12.9362 q^{85} +0.299452 q^{87} +6.83667 q^{89} -12.4059 q^{93} -13.2056 q^{95} -0.615292 q^{97} +0.0110448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + O(q^{10}) \) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + 6q^{13} - 4q^{15} + 12q^{17} + 8q^{19} + 4q^{23} + 16q^{25} + 8q^{27} + 2q^{29} + 8q^{31} - 6q^{33} - 2q^{37} - 2q^{39} + 10q^{41} - 2q^{43} + 44q^{45} - 14q^{47} + 14q^{51} + 8q^{53} + 8q^{55} - 10q^{57} + 24q^{59} + 14q^{61} + 2q^{65} - 8q^{67} + 16q^{69} + 10q^{71} + 44q^{73} - 50q^{75} + 10q^{79} - 14q^{81} + 20q^{83} + 8q^{85} + 20q^{87} + 6q^{89} + 8q^{93} + 4q^{95} + 46q^{97} + 2q^{99} + O(q^{100}) \)

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
\(3\) −1.73395 −1.00110 −0.500549 0.865708i \(-0.666868\pi\)
−0.500549 + 0.865708i \(0.666868\pi\)
\(4\) 0 0
\(5\) −3.41343 −1.52653 −0.763266 0.646085i \(-0.776405\pi\)
−0.763266 + 0.646085i \(0.776405\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0.00658743 0.00219581
\(10\) 0 0
\(11\) 1.67665 0.505530 0.252765 0.967528i \(-0.418660\pi\)
0.252765 + 0.967528i \(0.418660\pi\)
\(12\) 0 0
\(13\) 6.13889 1.70262 0.851311 0.524661i \(-0.175808\pi\)
0.851311 + 0.524661i \(0.175808\pi\)
\(14\) 0 0
\(15\) 5.91872 1.52821
\(16\) 0 0
\(17\) 3.78979 0.919159 0.459580 0.888137i \(-0.348000\pi\)
0.459580 + 0.888137i \(0.348000\pi\)
\(18\) 0 0
\(19\) 3.86873 0.887547 0.443774 0.896139i \(-0.353639\pi\)
0.443774 + 0.896139i \(0.353639\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.49935 −1.14669 −0.573347 0.819312i \(-0.694355\pi\)
−0.573347 + 0.819312i \(0.694355\pi\)
\(24\) 0 0
\(25\) 6.65149 1.33030
\(26\) 0 0
\(27\) 5.19043 0.998899
\(28\) 0 0
\(29\) −0.172699 −0.0320695 −0.0160347 0.999871i \(-0.505104\pi\)
−0.0160347 + 0.999871i \(0.505104\pi\)
\(30\) 0 0
\(31\) 7.15470 1.28502 0.642511 0.766276i \(-0.277893\pi\)
0.642511 + 0.766276i \(0.277893\pi\)
\(32\) 0 0
\(33\) −2.90724 −0.506085
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.80199 −0.789443 −0.394721 0.918801i \(-0.629159\pi\)
−0.394721 + 0.918801i \(0.629159\pi\)
\(38\) 0 0
\(39\) −10.6445 −1.70449
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 0.845176 0.128888 0.0644441 0.997921i \(-0.479473\pi\)
0.0644441 + 0.997921i \(0.479473\pi\)
\(44\) 0 0
\(45\) −0.0224857 −0.00335197
\(46\) 0 0
\(47\) 4.65792 0.679428 0.339714 0.940529i \(-0.389670\pi\)
0.339714 + 0.940529i \(0.389670\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −6.57131 −0.920168
\(52\) 0 0
\(53\) 4.46567 0.613407 0.306703 0.951805i \(-0.400774\pi\)
0.306703 + 0.951805i \(0.400774\pi\)
\(54\) 0 0
\(55\) −5.72314 −0.771708
\(56\) 0 0
\(57\) −6.70819 −0.888521
\(58\) 0 0
\(59\) −3.38395 −0.440553 −0.220276 0.975437i \(-0.570696\pi\)
−0.220276 + 0.975437i \(0.570696\pi\)
\(60\) 0 0
\(61\) 0.643064 0.0823359 0.0411679 0.999152i \(-0.486892\pi\)
0.0411679 + 0.999152i \(0.486892\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −20.9547 −2.59911
\(66\) 0 0
\(67\) −2.25183 −0.275105 −0.137553 0.990494i \(-0.543924\pi\)
−0.137553 + 0.990494i \(0.543924\pi\)
\(68\) 0 0
\(69\) 9.53561 1.14795
\(70\) 0 0
\(71\) −4.77826 −0.567076 −0.283538 0.958961i \(-0.591508\pi\)
−0.283538 + 0.958961i \(0.591508\pi\)
\(72\) 0 0
\(73\) 9.42378 1.10297 0.551485 0.834185i \(-0.314061\pi\)
0.551485 + 0.834185i \(0.314061\pi\)
\(74\) 0 0
\(75\) −11.5334 −1.33176
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 3.64751 0.410377 0.205189 0.978722i \(-0.434219\pi\)
0.205189 + 0.978722i \(0.434219\pi\)
\(80\) 0 0
\(81\) −9.01972 −1.00219
\(82\) 0 0
\(83\) −12.7027 −1.39430 −0.697149 0.716926i \(-0.745548\pi\)
−0.697149 + 0.716926i \(0.745548\pi\)
\(84\) 0 0
\(85\) −12.9362 −1.40313
\(86\) 0 0
\(87\) 0.299452 0.0321046
\(88\) 0 0
\(89\) 6.83667 0.724685 0.362343 0.932045i \(-0.381977\pi\)
0.362343 + 0.932045i \(0.381977\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −12.4059 −1.28643
\(94\) 0 0
\(95\) −13.2056 −1.35487
\(96\) 0 0
\(97\) −0.615292 −0.0624734 −0.0312367 0.999512i \(-0.509945\pi\)
−0.0312367 + 0.999512i \(0.509945\pi\)
\(98\) 0 0
\(99\) 0.0110448 0.00111005
\(100\) 0 0
\(101\) −6.55350 −0.652098 −0.326049 0.945353i \(-0.605717\pi\)
−0.326049 + 0.945353i \(0.605717\pi\)
\(102\) 0 0
\(103\) −9.40980 −0.927175 −0.463588 0.886051i \(-0.653438\pi\)
−0.463588 + 0.886051i \(0.653438\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.66303 0.354119 0.177059 0.984200i \(-0.443342\pi\)
0.177059 + 0.984200i \(0.443342\pi\)
\(108\) 0 0
\(109\) 10.1194 0.969263 0.484632 0.874718i \(-0.338954\pi\)
0.484632 + 0.874718i \(0.338954\pi\)
\(110\) 0 0
\(111\) 8.32642 0.790309
\(112\) 0 0
\(113\) −11.0216 −1.03683 −0.518413 0.855131i \(-0.673477\pi\)
−0.518413 + 0.855131i \(0.673477\pi\)
\(114\) 0 0
\(115\) 18.7717 1.75047
\(116\) 0 0
\(117\) 0.0404395 0.00373863
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −8.18883 −0.744439
\(122\) 0 0
\(123\) −1.73395 −0.156345
\(124\) 0 0
\(125\) −5.63724 −0.504210
\(126\) 0 0
\(127\) 15.1077 1.34059 0.670296 0.742094i \(-0.266167\pi\)
0.670296 + 0.742094i \(0.266167\pi\)
\(128\) 0 0
\(129\) −1.46549 −0.129030
\(130\) 0 0
\(131\) 5.99133 0.523465 0.261732 0.965140i \(-0.415706\pi\)
0.261732 + 0.965140i \(0.415706\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −17.7172 −1.52485
\(136\) 0 0
\(137\) −12.1656 −1.03938 −0.519688 0.854356i \(-0.673952\pi\)
−0.519688 + 0.854356i \(0.673952\pi\)
\(138\) 0 0
\(139\) −5.02141 −0.425910 −0.212955 0.977062i \(-0.568309\pi\)
−0.212955 + 0.977062i \(0.568309\pi\)
\(140\) 0 0
\(141\) −8.07661 −0.680173
\(142\) 0 0
\(143\) 10.2928 0.860728
\(144\) 0 0
\(145\) 0.589497 0.0489550
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.7546 0.881055 0.440528 0.897739i \(-0.354791\pi\)
0.440528 + 0.897739i \(0.354791\pi\)
\(150\) 0 0
\(151\) −14.3236 −1.16564 −0.582818 0.812602i \(-0.698050\pi\)
−0.582818 + 0.812602i \(0.698050\pi\)
\(152\) 0 0
\(153\) 0.0249650 0.00201830
\(154\) 0 0
\(155\) −24.4221 −1.96163
\(156\) 0 0
\(157\) −16.9304 −1.35119 −0.675596 0.737272i \(-0.736114\pi\)
−0.675596 + 0.737272i \(0.736114\pi\)
\(158\) 0 0
\(159\) −7.74325 −0.614080
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −5.72220 −0.448197 −0.224099 0.974566i \(-0.571944\pi\)
−0.224099 + 0.974566i \(0.571944\pi\)
\(164\) 0 0
\(165\) 9.92365 0.772555
\(166\) 0 0
\(167\) 11.3051 0.874812 0.437406 0.899264i \(-0.355897\pi\)
0.437406 + 0.899264i \(0.355897\pi\)
\(168\) 0 0
\(169\) 24.6860 1.89892
\(170\) 0 0
\(171\) 0.0254850 0.00194888
\(172\) 0 0
\(173\) −19.4786 −1.48093 −0.740465 0.672095i \(-0.765395\pi\)
−0.740465 + 0.672095i \(0.765395\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.86761 0.441036
\(178\) 0 0
\(179\) 1.59474 0.119197 0.0595983 0.998222i \(-0.481018\pi\)
0.0595983 + 0.998222i \(0.481018\pi\)
\(180\) 0 0
\(181\) 7.25966 0.539607 0.269803 0.962915i \(-0.413041\pi\)
0.269803 + 0.962915i \(0.413041\pi\)
\(182\) 0 0
\(183\) −1.11504 −0.0824262
\(184\) 0 0
\(185\) 16.3913 1.20511
\(186\) 0 0
\(187\) 6.35417 0.464663
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 23.7348 1.71739 0.858694 0.512488i \(-0.171276\pi\)
0.858694 + 0.512488i \(0.171276\pi\)
\(192\) 0 0
\(193\) 20.2501 1.45763 0.728817 0.684709i \(-0.240071\pi\)
0.728817 + 0.684709i \(0.240071\pi\)
\(194\) 0 0
\(195\) 36.3344 2.60196
\(196\) 0 0
\(197\) −16.4401 −1.17131 −0.585654 0.810561i \(-0.699162\pi\)
−0.585654 + 0.810561i \(0.699162\pi\)
\(198\) 0 0
\(199\) −13.2785 −0.941291 −0.470646 0.882322i \(-0.655979\pi\)
−0.470646 + 0.882322i \(0.655979\pi\)
\(200\) 0 0
\(201\) 3.90457 0.275407
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3.41343 −0.238404
\(206\) 0 0
\(207\) −0.0362266 −0.00251792
\(208\) 0 0
\(209\) 6.48652 0.448682
\(210\) 0 0
\(211\) 1.73436 0.119398 0.0596991 0.998216i \(-0.480986\pi\)
0.0596991 + 0.998216i \(0.480986\pi\)
\(212\) 0 0
\(213\) 8.28528 0.567698
\(214\) 0 0
\(215\) −2.88495 −0.196752
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −16.3404 −1.10418
\(220\) 0 0
\(221\) 23.2651 1.56498
\(222\) 0 0
\(223\) 26.4764 1.77299 0.886496 0.462737i \(-0.153132\pi\)
0.886496 + 0.462737i \(0.153132\pi\)
\(224\) 0 0
\(225\) 0.0438162 0.00292108
\(226\) 0 0
\(227\) 16.7320 1.11054 0.555271 0.831669i \(-0.312614\pi\)
0.555271 + 0.831669i \(0.312614\pi\)
\(228\) 0 0
\(229\) 6.74483 0.445711 0.222855 0.974852i \(-0.428462\pi\)
0.222855 + 0.974852i \(0.428462\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.7713 0.967697 0.483849 0.875152i \(-0.339239\pi\)
0.483849 + 0.875152i \(0.339239\pi\)
\(234\) 0 0
\(235\) −15.8995 −1.03717
\(236\) 0 0
\(237\) −6.32461 −0.410828
\(238\) 0 0
\(239\) −16.2994 −1.05432 −0.527161 0.849766i \(-0.676743\pi\)
−0.527161 + 0.849766i \(0.676743\pi\)
\(240\) 0 0
\(241\) 8.34464 0.537526 0.268763 0.963206i \(-0.413385\pi\)
0.268763 + 0.963206i \(0.413385\pi\)
\(242\) 0 0
\(243\) 0.0684584 0.00439161
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 23.7497 1.51116
\(248\) 0 0
\(249\) 22.0258 1.39583
\(250\) 0 0
\(251\) −2.21866 −0.140041 −0.0700204 0.997546i \(-0.522306\pi\)
−0.0700204 + 0.997546i \(0.522306\pi\)
\(252\) 0 0
\(253\) −9.22052 −0.579689
\(254\) 0 0
\(255\) 22.4307 1.40467
\(256\) 0 0
\(257\) −24.4944 −1.52792 −0.763961 0.645263i \(-0.776748\pi\)
−0.763961 + 0.645263i \(0.776748\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.00113764 −7.04184e−5 0
\(262\) 0 0
\(263\) −7.53312 −0.464512 −0.232256 0.972655i \(-0.574611\pi\)
−0.232256 + 0.972655i \(0.574611\pi\)
\(264\) 0 0
\(265\) −15.2432 −0.936385
\(266\) 0 0
\(267\) −11.8544 −0.725480
\(268\) 0 0
\(269\) 22.0410 1.34386 0.671931 0.740614i \(-0.265465\pi\)
0.671931 + 0.740614i \(0.265465\pi\)
\(270\) 0 0
\(271\) −21.4621 −1.30373 −0.651864 0.758336i \(-0.726013\pi\)
−0.651864 + 0.758336i \(0.726013\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 11.1523 0.672506
\(276\) 0 0
\(277\) 31.7745 1.90915 0.954573 0.297977i \(-0.0963119\pi\)
0.954573 + 0.297977i \(0.0963119\pi\)
\(278\) 0 0
\(279\) 0.0471311 0.00282166
\(280\) 0 0
\(281\) −5.66405 −0.337889 −0.168944 0.985626i \(-0.554036\pi\)
−0.168944 + 0.985626i \(0.554036\pi\)
\(282\) 0 0
\(283\) 22.1824 1.31860 0.659302 0.751878i \(-0.270852\pi\)
0.659302 + 0.751878i \(0.270852\pi\)
\(284\) 0 0
\(285\) 22.8979 1.35636
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −2.63748 −0.155146
\(290\) 0 0
\(291\) 1.06689 0.0625419
\(292\) 0 0
\(293\) −0.662844 −0.0387238 −0.0193619 0.999813i \(-0.506163\pi\)
−0.0193619 + 0.999813i \(0.506163\pi\)
\(294\) 0 0
\(295\) 11.5509 0.672518
\(296\) 0 0
\(297\) 8.70256 0.504974
\(298\) 0 0
\(299\) −33.7599 −1.95239
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 11.3635 0.652813
\(304\) 0 0
\(305\) −2.19505 −0.125688
\(306\) 0 0
\(307\) 11.6945 0.667438 0.333719 0.942673i \(-0.391696\pi\)
0.333719 + 0.942673i \(0.391696\pi\)
\(308\) 0 0
\(309\) 16.3161 0.928193
\(310\) 0 0
\(311\) −10.1939 −0.578044 −0.289022 0.957322i \(-0.593330\pi\)
−0.289022 + 0.957322i \(0.593330\pi\)
\(312\) 0 0
\(313\) 3.90892 0.220945 0.110473 0.993879i \(-0.464764\pi\)
0.110473 + 0.993879i \(0.464764\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 19.2084 1.07885 0.539427 0.842033i \(-0.318641\pi\)
0.539427 + 0.842033i \(0.318641\pi\)
\(318\) 0 0
\(319\) −0.289557 −0.0162121
\(320\) 0 0
\(321\) −6.35152 −0.354507
\(322\) 0 0
\(323\) 14.6617 0.815798
\(324\) 0 0
\(325\) 40.8328 2.26500
\(326\) 0 0
\(327\) −17.5466 −0.970327
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 25.3104 1.39119 0.695594 0.718435i \(-0.255141\pi\)
0.695594 + 0.718435i \(0.255141\pi\)
\(332\) 0 0
\(333\) −0.0316328 −0.00173346
\(334\) 0 0
\(335\) 7.68647 0.419957
\(336\) 0 0
\(337\) 34.5103 1.87990 0.939948 0.341319i \(-0.110873\pi\)
0.939948 + 0.341319i \(0.110873\pi\)
\(338\) 0 0
\(339\) 19.1109 1.03796
\(340\) 0 0
\(341\) 11.9960 0.649618
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −32.5491 −1.75239
\(346\) 0 0
\(347\) 19.5932 1.05182 0.525910 0.850540i \(-0.323725\pi\)
0.525910 + 0.850540i \(0.323725\pi\)
\(348\) 0 0
\(349\) 27.0415 1.44750 0.723750 0.690063i \(-0.242417\pi\)
0.723750 + 0.690063i \(0.242417\pi\)
\(350\) 0 0
\(351\) 31.8635 1.70075
\(352\) 0 0
\(353\) 28.6917 1.52711 0.763553 0.645745i \(-0.223453\pi\)
0.763553 + 0.645745i \(0.223453\pi\)
\(354\) 0 0
\(355\) 16.3103 0.865659
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −28.4429 −1.50116 −0.750578 0.660782i \(-0.770225\pi\)
−0.750578 + 0.660782i \(0.770225\pi\)
\(360\) 0 0
\(361\) −4.03293 −0.212260
\(362\) 0 0
\(363\) 14.1990 0.745256
\(364\) 0 0
\(365\) −32.1674 −1.68372
\(366\) 0 0
\(367\) −27.2393 −1.42188 −0.710939 0.703254i \(-0.751730\pi\)
−0.710939 + 0.703254i \(0.751730\pi\)
\(368\) 0 0
\(369\) 0.00658743 0.000342928 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 12.0603 0.624461 0.312230 0.950006i \(-0.398924\pi\)
0.312230 + 0.950006i \(0.398924\pi\)
\(374\) 0 0
\(375\) 9.77471 0.504764
\(376\) 0 0
\(377\) −1.06018 −0.0546022
\(378\) 0 0
\(379\) 28.8577 1.48232 0.741160 0.671329i \(-0.234276\pi\)
0.741160 + 0.671329i \(0.234276\pi\)
\(380\) 0 0
\(381\) −26.1960 −1.34206
\(382\) 0 0
\(383\) −13.6206 −0.695982 −0.347991 0.937498i \(-0.613136\pi\)
−0.347991 + 0.937498i \(0.613136\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.00556753 0.000283014 0
\(388\) 0 0
\(389\) −12.1436 −0.615704 −0.307852 0.951434i \(-0.599610\pi\)
−0.307852 + 0.951434i \(0.599610\pi\)
\(390\) 0 0
\(391\) −20.8414 −1.05400
\(392\) 0 0
\(393\) −10.3887 −0.524039
\(394\) 0 0
\(395\) −12.4505 −0.626454
\(396\) 0 0
\(397\) −24.1841 −1.21376 −0.606882 0.794792i \(-0.707580\pi\)
−0.606882 + 0.794792i \(0.707580\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.87866 −0.343504 −0.171752 0.985140i \(-0.554943\pi\)
−0.171752 + 0.985140i \(0.554943\pi\)
\(402\) 0 0
\(403\) 43.9220 2.18791
\(404\) 0 0
\(405\) 30.7882 1.52988
\(406\) 0 0
\(407\) −8.05128 −0.399087
\(408\) 0 0
\(409\) 8.83930 0.437075 0.218538 0.975829i \(-0.429871\pi\)
0.218538 + 0.975829i \(0.429871\pi\)
\(410\) 0 0
\(411\) 21.0945 1.04052
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 43.3596 2.12844
\(416\) 0 0
\(417\) 8.70687 0.426377
\(418\) 0 0
\(419\) 18.1974 0.889000 0.444500 0.895779i \(-0.353381\pi\)
0.444500 + 0.895779i \(0.353381\pi\)
\(420\) 0 0
\(421\) −13.7003 −0.667711 −0.333856 0.942624i \(-0.608350\pi\)
−0.333856 + 0.942624i \(0.608350\pi\)
\(422\) 0 0
\(423\) 0.0306837 0.00149189
\(424\) 0 0
\(425\) 25.2078 1.22276
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −17.8472 −0.861672
\(430\) 0 0
\(431\) −29.1190 −1.40261 −0.701307 0.712859i \(-0.747400\pi\)
−0.701307 + 0.712859i \(0.747400\pi\)
\(432\) 0 0
\(433\) 5.49135 0.263897 0.131949 0.991257i \(-0.457877\pi\)
0.131949 + 0.991257i \(0.457877\pi\)
\(434\) 0 0
\(435\) −1.02216 −0.0490087
\(436\) 0 0
\(437\) −21.2755 −1.01775
\(438\) 0 0
\(439\) −8.58453 −0.409717 −0.204859 0.978792i \(-0.565673\pi\)
−0.204859 + 0.978792i \(0.565673\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 33.1993 1.57734 0.788672 0.614814i \(-0.210769\pi\)
0.788672 + 0.614814i \(0.210769\pi\)
\(444\) 0 0
\(445\) −23.3365 −1.10625
\(446\) 0 0
\(447\) −18.6480 −0.882022
\(448\) 0 0
\(449\) 17.3746 0.819960 0.409980 0.912094i \(-0.365536\pi\)
0.409980 + 0.912094i \(0.365536\pi\)
\(450\) 0 0
\(451\) 1.67665 0.0789506
\(452\) 0 0
\(453\) 24.8364 1.16692
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −7.33864 −0.343287 −0.171644 0.985159i \(-0.554908\pi\)
−0.171644 + 0.985159i \(0.554908\pi\)
\(458\) 0 0
\(459\) 19.6707 0.918148
\(460\) 0 0
\(461\) 2.46073 0.114608 0.0573038 0.998357i \(-0.481750\pi\)
0.0573038 + 0.998357i \(0.481750\pi\)
\(462\) 0 0
\(463\) −35.1206 −1.63219 −0.816097 0.577915i \(-0.803866\pi\)
−0.816097 + 0.577915i \(0.803866\pi\)
\(464\) 0 0
\(465\) 42.3467 1.96378
\(466\) 0 0
\(467\) 11.4411 0.529433 0.264716 0.964326i \(-0.414722\pi\)
0.264716 + 0.964326i \(0.414722\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 29.3565 1.35268
\(472\) 0 0
\(473\) 1.41707 0.0651569
\(474\) 0 0
\(475\) 25.7328 1.18070
\(476\) 0 0
\(477\) 0.0294173 0.00134692
\(478\) 0 0
\(479\) −12.8860 −0.588778 −0.294389 0.955686i \(-0.595116\pi\)
−0.294389 + 0.955686i \(0.595116\pi\)
\(480\) 0 0
\(481\) −29.4789 −1.34412
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.10025 0.0953676
\(486\) 0 0
\(487\) −29.5691 −1.33990 −0.669952 0.742405i \(-0.733685\pi\)
−0.669952 + 0.742405i \(0.733685\pi\)
\(488\) 0 0
\(489\) 9.92201 0.448689
\(490\) 0 0
\(491\) −28.3180 −1.27797 −0.638986 0.769218i \(-0.720646\pi\)
−0.638986 + 0.769218i \(0.720646\pi\)
\(492\) 0 0
\(493\) −0.654494 −0.0294769
\(494\) 0 0
\(495\) −0.0377008 −0.00169452
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −9.71814 −0.435044 −0.217522 0.976055i \(-0.569797\pi\)
−0.217522 + 0.976055i \(0.569797\pi\)
\(500\) 0 0
\(501\) −19.6024 −0.875772
\(502\) 0 0
\(503\) 27.2237 1.21385 0.606923 0.794760i \(-0.292403\pi\)
0.606923 + 0.794760i \(0.292403\pi\)
\(504\) 0 0
\(505\) 22.3699 0.995448
\(506\) 0 0
\(507\) −42.8043 −1.90101
\(508\) 0 0
\(509\) 34.2038 1.51606 0.758028 0.652222i \(-0.226163\pi\)
0.758028 + 0.652222i \(0.226163\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 20.0804 0.886570
\(514\) 0 0
\(515\) 32.1197 1.41536
\(516\) 0 0
\(517\) 7.80973 0.343471
\(518\) 0 0
\(519\) 33.7749 1.48255
\(520\) 0 0
\(521\) 37.2153 1.63043 0.815216 0.579157i \(-0.196618\pi\)
0.815216 + 0.579157i \(0.196618\pi\)
\(522\) 0 0
\(523\) −10.9891 −0.480519 −0.240259 0.970709i \(-0.577233\pi\)
−0.240259 + 0.970709i \(0.577233\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 27.1148 1.18114
\(528\) 0 0
\(529\) 7.24290 0.314909
\(530\) 0 0
\(531\) −0.0222915 −0.000967370 0
\(532\) 0 0
\(533\) 6.13889 0.265905
\(534\) 0 0
\(535\) −12.5035 −0.540573
\(536\) 0 0
\(537\) −2.76520 −0.119327
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −12.7378 −0.547643 −0.273821 0.961781i \(-0.588288\pi\)
−0.273821 + 0.961781i \(0.588288\pi\)
\(542\) 0 0
\(543\) −12.5879 −0.540199
\(544\) 0 0
\(545\) −34.5419 −1.47961
\(546\) 0 0
\(547\) 16.0176 0.684865 0.342432 0.939542i \(-0.388749\pi\)
0.342432 + 0.939542i \(0.388749\pi\)
\(548\) 0 0
\(549\) 0.00423614 0.000180794 0
\(550\) 0 0
\(551\) −0.668127 −0.0284632
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −28.4216 −1.20643
\(556\) 0 0
\(557\) −39.0799 −1.65587 −0.827935 0.560824i \(-0.810484\pi\)
−0.827935 + 0.560824i \(0.810484\pi\)
\(558\) 0 0
\(559\) 5.18845 0.219448
\(560\) 0 0
\(561\) −11.0178 −0.465173
\(562\) 0 0
\(563\) −29.1641 −1.22912 −0.614561 0.788869i \(-0.710667\pi\)
−0.614561 + 0.788869i \(0.710667\pi\)
\(564\) 0 0
\(565\) 37.6215 1.58275
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10.6973 −0.448453 −0.224226 0.974537i \(-0.571986\pi\)
−0.224226 + 0.974537i \(0.571986\pi\)
\(570\) 0 0
\(571\) −6.67889 −0.279503 −0.139751 0.990187i \(-0.544630\pi\)
−0.139751 + 0.990187i \(0.544630\pi\)
\(572\) 0 0
\(573\) −41.1550 −1.71927
\(574\) 0 0
\(575\) −36.5789 −1.52545
\(576\) 0 0
\(577\) 21.7440 0.905213 0.452607 0.891710i \(-0.350494\pi\)
0.452607 + 0.891710i \(0.350494\pi\)
\(578\) 0 0
\(579\) −35.1127 −1.45923
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 7.48739 0.310096
\(584\) 0 0
\(585\) −0.138037 −0.00570714
\(586\) 0 0
\(587\) −30.7691 −1.26998 −0.634988 0.772522i \(-0.718995\pi\)
−0.634988 + 0.772522i \(0.718995\pi\)
\(588\) 0 0
\(589\) 27.6796 1.14052
\(590\) 0 0
\(591\) 28.5063 1.17259
\(592\) 0 0
\(593\) −27.2968 −1.12095 −0.560473 0.828173i \(-0.689381\pi\)
−0.560473 + 0.828173i \(0.689381\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 23.0244 0.942324
\(598\) 0 0
\(599\) −3.15083 −0.128739 −0.0643697 0.997926i \(-0.520504\pi\)
−0.0643697 + 0.997926i \(0.520504\pi\)
\(600\) 0 0
\(601\) 42.4377 1.73107 0.865534 0.500850i \(-0.166979\pi\)
0.865534 + 0.500850i \(0.166979\pi\)
\(602\) 0 0
\(603\) −0.0148338 −0.000604079 0
\(604\) 0 0
\(605\) 27.9520 1.13641
\(606\) 0 0
\(607\) −31.1857 −1.26579 −0.632894 0.774239i \(-0.718133\pi\)
−0.632894 + 0.774239i \(0.718133\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 28.5945 1.15681
\(612\) 0 0
\(613\) 36.9343 1.49176 0.745880 0.666080i \(-0.232029\pi\)
0.745880 + 0.666080i \(0.232029\pi\)
\(614\) 0 0
\(615\) 5.91872 0.238666
\(616\) 0 0
\(617\) −15.8487 −0.638045 −0.319023 0.947747i \(-0.603355\pi\)
−0.319023 + 0.947747i \(0.603355\pi\)
\(618\) 0 0
\(619\) −23.2914 −0.936159 −0.468080 0.883686i \(-0.655054\pi\)
−0.468080 + 0.883686i \(0.655054\pi\)
\(620\) 0 0
\(621\) −28.5440 −1.14543
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −14.0151 −0.560605
\(626\) 0 0
\(627\) −11.2473 −0.449175
\(628\) 0 0
\(629\) −18.1985 −0.725624
\(630\) 0 0
\(631\) 17.4445 0.694453 0.347227 0.937781i \(-0.387123\pi\)
0.347227 + 0.937781i \(0.387123\pi\)
\(632\) 0 0
\(633\) −3.00730 −0.119529
\(634\) 0 0
\(635\) −51.5690 −2.04646
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −0.0314765 −0.00124519
\(640\) 0 0
\(641\) −28.8551 −1.13971 −0.569855 0.821746i \(-0.693000\pi\)
−0.569855 + 0.821746i \(0.693000\pi\)
\(642\) 0 0
\(643\) 17.4989 0.690090 0.345045 0.938586i \(-0.387864\pi\)
0.345045 + 0.938586i \(0.387864\pi\)
\(644\) 0 0
\(645\) 5.00236 0.196968
\(646\) 0 0
\(647\) 22.7880 0.895887 0.447944 0.894062i \(-0.352157\pi\)
0.447944 + 0.894062i \(0.352157\pi\)
\(648\) 0 0
\(649\) −5.67372 −0.222713
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 43.1360 1.68804 0.844021 0.536311i \(-0.180182\pi\)
0.844021 + 0.536311i \(0.180182\pi\)
\(654\) 0 0
\(655\) −20.4510 −0.799086
\(656\) 0 0
\(657\) 0.0620785 0.00242191
\(658\) 0 0
\(659\) 10.9211 0.425424 0.212712 0.977115i \(-0.431770\pi\)
0.212712 + 0.977115i \(0.431770\pi\)
\(660\) 0 0
\(661\) −28.4575 −1.10687 −0.553434 0.832893i \(-0.686683\pi\)
−0.553434 + 0.832893i \(0.686683\pi\)
\(662\) 0 0
\(663\) −40.3406 −1.56670
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.949735 0.0367739
\(668\) 0 0
\(669\) −45.9088 −1.77494
\(670\) 0 0
\(671\) 1.07820 0.0416233
\(672\) 0 0
\(673\) −37.3470 −1.43962 −0.719810 0.694171i \(-0.755771\pi\)
−0.719810 + 0.694171i \(0.755771\pi\)
\(674\) 0 0
\(675\) 34.5241 1.32883
\(676\) 0 0
\(677\) 19.5079 0.749748 0.374874 0.927076i \(-0.377686\pi\)
0.374874 + 0.927076i \(0.377686\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −29.0125 −1.11176
\(682\) 0 0
\(683\) −46.3804 −1.77469 −0.887347 0.461101i \(-0.847454\pi\)
−0.887347 + 0.461101i \(0.847454\pi\)
\(684\) 0 0
\(685\) 41.5264 1.58664
\(686\) 0 0
\(687\) −11.6952 −0.446200
\(688\) 0 0
\(689\) 27.4143 1.04440
\(690\) 0 0
\(691\) −4.07303 −0.154945 −0.0774726 0.996994i \(-0.524685\pi\)
−0.0774726 + 0.996994i \(0.524685\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 17.1402 0.650165
\(696\) 0 0
\(697\) 3.78979 0.143549
\(698\) 0 0
\(699\) −25.6126 −0.968759
\(700\) 0 0
\(701\) 47.2407 1.78426 0.892128 0.451783i \(-0.149212\pi\)
0.892128 + 0.451783i \(0.149212\pi\)
\(702\) 0 0
\(703\) −18.5776 −0.700668
\(704\) 0 0
\(705\) 27.5689 1.03831
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −15.8445 −0.595053 −0.297526 0.954714i \(-0.596162\pi\)
−0.297526 + 0.954714i \(0.596162\pi\)
\(710\) 0 0
\(711\) 0.0240277 0.000901110 0
\(712\) 0 0
\(713\) −39.3462 −1.47353
\(714\) 0 0
\(715\) −35.1337 −1.31393
\(716\) 0 0
\(717\) 28.2624 1.05548
\(718\) 0 0
\(719\) 46.2097 1.72333 0.861665 0.507478i \(-0.169422\pi\)
0.861665 + 0.507478i \(0.169422\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −14.4692 −0.538115
\(724\) 0 0
\(725\) −1.14871 −0.0426619
\(726\) 0 0
\(727\) −46.2962 −1.71703 −0.858515 0.512788i \(-0.828613\pi\)
−0.858515 + 0.512788i \(0.828613\pi\)
\(728\) 0 0
\(729\) 26.9405 0.997795
\(730\) 0 0
\(731\) 3.20304 0.118469
\(732\) 0 0
\(733\) 14.3823 0.531222 0.265611 0.964080i \(-0.414426\pi\)
0.265611 + 0.964080i \(0.414426\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.77555 −0.139074
\(738\) 0 0
\(739\) −23.1656 −0.852161 −0.426080 0.904685i \(-0.640106\pi\)
−0.426080 + 0.904685i \(0.640106\pi\)
\(740\) 0 0
\(741\) −41.1808 −1.51282
\(742\) 0 0
\(743\) 8.59555 0.315340 0.157670 0.987492i \(-0.449602\pi\)
0.157670 + 0.987492i \(0.449602\pi\)
\(744\) 0 0
\(745\) −36.7102 −1.34496
\(746\) 0 0
\(747\) −0.0836778 −0.00306161
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 34.6291 1.26363 0.631817 0.775118i \(-0.282310\pi\)
0.631817 + 0.775118i \(0.282310\pi\)
\(752\) 0 0
\(753\) 3.84706 0.140194
\(754\) 0 0
\(755\) 48.8925 1.77938
\(756\) 0 0
\(757\) 35.3458 1.28467 0.642333 0.766426i \(-0.277967\pi\)
0.642333 + 0.766426i \(0.277967\pi\)
\(758\) 0 0
\(759\) 15.9879 0.580325
\(760\) 0 0
\(761\) 22.9971 0.833645 0.416823 0.908988i \(-0.363144\pi\)
0.416823 + 0.908988i \(0.363144\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.0852161 −0.00308100
\(766\) 0 0
\(767\) −20.7737 −0.750095
\(768\) 0 0
\(769\) 15.5231 0.559776 0.279888 0.960033i \(-0.409703\pi\)
0.279888 + 0.960033i \(0.409703\pi\)
\(770\) 0 0
\(771\) 42.4722 1.52960
\(772\) 0 0
\(773\) 40.7953 1.46731 0.733653 0.679524i \(-0.237814\pi\)
0.733653 + 0.679524i \(0.237814\pi\)
\(774\) 0 0
\(775\) 47.5894 1.70946
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.86873 0.138612
\(780\) 0 0
\(781\) −8.01150 −0.286674
\(782\) 0 0
\(783\) −0.896384 −0.0320341
\(784\) 0 0
\(785\) 57.7907 2.06264
\(786\) 0 0
\(787\) 14.2880 0.509313 0.254656 0.967032i \(-0.418038\pi\)
0.254656 + 0.967032i \(0.418038\pi\)
\(788\) 0 0
\(789\) 13.0621 0.465022
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 3.94770 0.140187
\(794\) 0 0
\(795\) 26.4310 0.937412
\(796\) 0 0
\(797\) 44.9428 1.59196 0.795978 0.605326i \(-0.206957\pi\)
0.795978 + 0.605326i \(0.206957\pi\)
\(798\) 0 0
\(799\) 17.6526 0.624502
\(800\) 0 0
\(801\) 0.0450360 0.00159127
\(802\) 0 0
\(803\) 15.8004 0.557585
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −38.2180 −1.34534
\(808\) 0 0
\(809\) −50.8169 −1.78663 −0.893314 0.449432i \(-0.851626\pi\)
−0.893314 + 0.449432i \(0.851626\pi\)
\(810\) 0 0
\(811\) 23.6587 0.830769 0.415385 0.909646i \(-0.363647\pi\)
0.415385 + 0.909646i \(0.363647\pi\)
\(812\) 0 0
\(813\) 37.2142 1.30516
\(814\) 0 0
\(815\) 19.5323 0.684187
\(816\) 0 0
\(817\) 3.26976 0.114394
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −29.0297 −1.01314 −0.506572 0.862198i \(-0.669087\pi\)
−0.506572 + 0.862198i \(0.669087\pi\)
\(822\) 0 0
\(823\) −53.7149 −1.87238 −0.936192 0.351488i \(-0.885676\pi\)
−0.936192 + 0.351488i \(0.885676\pi\)
\(824\) 0 0
\(825\) −19.3375 −0.673244
\(826\) 0 0
\(827\) 6.55779 0.228037 0.114018 0.993479i \(-0.463628\pi\)
0.114018 + 0.993479i \(0.463628\pi\)
\(828\) 0 0
\(829\) 53.1994 1.84769 0.923847 0.382763i \(-0.125027\pi\)
0.923847 + 0.382763i \(0.125027\pi\)
\(830\) 0 0
\(831\) −55.0955 −1.91124
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −38.5890 −1.33543
\(836\) 0 0
\(837\) 37.1360 1.28361
\(838\) 0 0
\(839\) 22.3780 0.772574 0.386287 0.922379i \(-0.373758\pi\)
0.386287 + 0.922379i \(0.373758\pi\)
\(840\) 0 0
\(841\) −28.9702 −0.998972
\(842\) 0 0
\(843\) 9.82119 0.338260
\(844\) 0 0
\(845\) −84.2639 −2.89877
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −38.4631 −1.32005
\(850\) 0 0
\(851\) 26.4079 0.905250
\(852\) 0 0
\(853\) 30.5227 1.04508 0.522539 0.852615i \(-0.324985\pi\)
0.522539 + 0.852615i \(0.324985\pi\)
\(854\) 0 0
\(855\) −0.0869911 −0.00297503
\(856\) 0 0
\(857\) −41.8325 −1.42897 −0.714485 0.699651i \(-0.753339\pi\)
−0.714485 + 0.699651i \(0.753339\pi\)
\(858\) 0 0
\(859\) 19.8918 0.678699 0.339349 0.940660i \(-0.389793\pi\)
0.339349 + 0.940660i \(0.389793\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.48686 0.0506134 0.0253067 0.999680i \(-0.491944\pi\)
0.0253067 + 0.999680i \(0.491944\pi\)
\(864\) 0 0
\(865\) 66.4888 2.26069
\(866\) 0 0
\(867\) 4.57326 0.155316
\(868\) 0 0
\(869\) 6.11562 0.207458
\(870\) 0 0
\(871\) −13.8238 −0.468400
\(872\) 0 0
\(873\) −0.00405319 −0.000137180 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −44.8377 −1.51406 −0.757032 0.653378i \(-0.773351\pi\)
−0.757032 + 0.653378i \(0.773351\pi\)
\(878\) 0 0
\(879\) 1.14934 0.0387663
\(880\) 0 0
\(881\) 43.5372 1.46681 0.733404 0.679794i \(-0.237931\pi\)
0.733404 + 0.679794i \(0.237931\pi\)
\(882\) 0 0
\(883\) 0.769970 0.0259116 0.0129558 0.999916i \(-0.495876\pi\)
0.0129558 + 0.999916i \(0.495876\pi\)
\(884\) 0 0
\(885\) −20.0287 −0.673256
\(886\) 0 0
\(887\) −16.9096 −0.567770 −0.283885 0.958858i \(-0.591623\pi\)
−0.283885 + 0.958858i \(0.591623\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −15.1230 −0.506638
\(892\) 0 0
\(893\) 18.0202 0.603024
\(894\) 0 0
\(895\) −5.44354 −0.181957
\(896\) 0 0
\(897\) 58.5381 1.95453
\(898\) 0 0
\(899\) −1.23561 −0.0412100
\(900\) 0 0
\(901\) 16.9240 0.563819
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −24.7803 −0.823726
\(906\) 0 0
\(907\) 55.6035 1.84628 0.923142 0.384459i \(-0.125612\pi\)
0.923142 + 0.384459i \(0.125612\pi\)
\(908\) 0 0
\(909\) −0.0431707 −0.00143188
\(910\) 0 0
\(911\) 16.1374 0.534655 0.267327 0.963606i \(-0.413859\pi\)
0.267327 + 0.963606i \(0.413859\pi\)
\(912\) 0 0
\(913\) −21.2980 −0.704860
\(914\) 0 0
\(915\) 3.80611 0.125826
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 27.8317 0.918082 0.459041 0.888415i \(-0.348193\pi\)
0.459041 + 0.888415i \(0.348193\pi\)
\(920\) 0 0
\(921\) −20.2776 −0.668171
\(922\) 0 0
\(923\) −29.3333 −0.965516
\(924\) 0 0
\(925\) −31.9404 −1.05019
\(926\) 0 0
\(927\) −0.0619864 −0.00203590
\(928\) 0 0
\(929\) 28.1727 0.924315 0.462157 0.886798i \(-0.347075\pi\)
0.462157 + 0.886798i \(0.347075\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 17.6757 0.578678
\(934\) 0 0
\(935\) −21.6895 −0.709323
\(936\) 0 0
\(937\) 31.3030 1.02262 0.511312 0.859395i \(-0.329160\pi\)
0.511312 + 0.859395i \(0.329160\pi\)
\(938\) 0 0
\(939\) −6.77787 −0.221187
\(940\) 0 0
\(941\) 55.2328 1.80054 0.900270 0.435333i \(-0.143369\pi\)
0.900270 + 0.435333i \(0.143369\pi\)
\(942\) 0 0
\(943\) −5.49935 −0.179084
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −15.7591 −0.512101 −0.256050 0.966663i \(-0.582421\pi\)
−0.256050 + 0.966663i \(0.582421\pi\)
\(948\) 0 0
\(949\) 57.8516 1.87794
\(950\) 0 0
\(951\) −33.3065 −1.08004
\(952\) 0 0
\(953\) −49.2694 −1.59599 −0.797996 0.602662i \(-0.794107\pi\)
−0.797996 + 0.602662i \(0.794107\pi\)
\(954\) 0 0
\(955\) −81.0170 −2.62165
\(956\) 0 0
\(957\) 0.502078 0.0162299
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 20.1898 0.651283
\(962\) 0 0
\(963\) 0.0241299 0.000777576 0
\(964\) 0 0
\(965\) −69.1223 −2.22512
\(966\) 0 0
\(967\) −25.6867 −0.826030 −0.413015 0.910724i \(-0.635524\pi\)
−0.413015 + 0.910724i \(0.635524\pi\)
\(968\) 0 0
\(969\) −25.4226 −0.816693
\(970\) 0 0
\(971\) −29.0629 −0.932672 −0.466336 0.884608i \(-0.654426\pi\)
−0.466336 + 0.884608i \(0.654426\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −70.8021 −2.26748
\(976\) 0 0
\(977\) 13.0637 0.417946 0.208973 0.977921i \(-0.432988\pi\)
0.208973 + 0.977921i \(0.432988\pi\)
\(978\) 0 0
\(979\) 11.4627 0.366350
\(980\) 0 0
\(981\) 0.0666608 0.00212832
\(982\) 0 0
\(983\) −29.4830 −0.940361 −0.470180 0.882570i \(-0.655811\pi\)
−0.470180 + 0.882570i \(0.655811\pi\)
\(984\) 0 0
\(985\) 56.1171 1.78804
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4.64792 −0.147795
\(990\) 0 0
\(991\) −36.9953 −1.17520 −0.587598 0.809153i \(-0.699926\pi\)
−0.587598 + 0.809153i \(0.699926\pi\)
\(992\) 0 0
\(993\) −43.8871 −1.39271
\(994\) 0 0
\(995\) 45.3254 1.43691
\(996\) 0 0
\(997\) 21.6514 0.685707 0.342854 0.939389i \(-0.388606\pi\)
0.342854 + 0.939389i \(0.388606\pi\)
\(998\) 0 0
\(999\) −24.9244 −0.788573
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 \(a_p\))