Properties

Label 8036.2.a.p.1.10
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 1.10
Root \(2.71781\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.71781 q^{3} -0.521406 q^{5} +4.38650 q^{9} +O(q^{10})\) \(q+2.71781 q^{3} -0.521406 q^{5} +4.38650 q^{9} -0.0523876 q^{11} -5.95553 q^{13} -1.41708 q^{15} +8.06280 q^{17} +4.41423 q^{19} +5.28903 q^{23} -4.72814 q^{25} +3.76825 q^{27} +4.73584 q^{29} -8.03532 q^{31} -0.142380 q^{33} -5.28272 q^{37} -16.1860 q^{39} +1.00000 q^{41} +3.65780 q^{43} -2.28715 q^{45} +4.87355 q^{47} +21.9132 q^{51} -1.13119 q^{53} +0.0273152 q^{55} +11.9970 q^{57} +5.21861 q^{59} +10.2952 q^{61} +3.10525 q^{65} +9.37745 q^{67} +14.3746 q^{69} +9.25115 q^{71} +15.6348 q^{73} -12.8502 q^{75} -7.46946 q^{79} -2.91811 q^{81} +6.66344 q^{83} -4.20399 q^{85} +12.8711 q^{87} +15.1869 q^{89} -21.8385 q^{93} -2.30160 q^{95} -8.41390 q^{97} -0.229798 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + O(q^{10}) \) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + 6q^{13} - 4q^{15} + 12q^{17} + 8q^{19} + 4q^{23} + 16q^{25} + 8q^{27} + 2q^{29} + 8q^{31} - 6q^{33} - 2q^{37} - 2q^{39} + 10q^{41} - 2q^{43} + 44q^{45} - 14q^{47} + 14q^{51} + 8q^{53} + 8q^{55} - 10q^{57} + 24q^{59} + 14q^{61} + 2q^{65} - 8q^{67} + 16q^{69} + 10q^{71} + 44q^{73} - 50q^{75} + 10q^{79} - 14q^{81} + 20q^{83} + 8q^{85} + 20q^{87} + 6q^{89} + 8q^{93} + 4q^{95} + 46q^{97} + 2q^{99} + O(q^{100}) \)

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
\(3\) 2.71781 1.56913 0.784565 0.620047i \(-0.212886\pi\)
0.784565 + 0.620047i \(0.212886\pi\)
\(4\) 0 0
\(5\) −0.521406 −0.233180 −0.116590 0.993180i \(-0.537196\pi\)
−0.116590 + 0.993180i \(0.537196\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 4.38650 1.46217
\(10\) 0 0
\(11\) −0.0523876 −0.0157954 −0.00789772 0.999969i \(-0.502514\pi\)
−0.00789772 + 0.999969i \(0.502514\pi\)
\(12\) 0 0
\(13\) −5.95553 −1.65177 −0.825884 0.563840i \(-0.809323\pi\)
−0.825884 + 0.563840i \(0.809323\pi\)
\(14\) 0 0
\(15\) −1.41708 −0.365889
\(16\) 0 0
\(17\) 8.06280 1.95552 0.977758 0.209736i \(-0.0672603\pi\)
0.977758 + 0.209736i \(0.0672603\pi\)
\(18\) 0 0
\(19\) 4.41423 1.01269 0.506346 0.862330i \(-0.330996\pi\)
0.506346 + 0.862330i \(0.330996\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.28903 1.10284 0.551420 0.834228i \(-0.314086\pi\)
0.551420 + 0.834228i \(0.314086\pi\)
\(24\) 0 0
\(25\) −4.72814 −0.945627
\(26\) 0 0
\(27\) 3.76825 0.725200
\(28\) 0 0
\(29\) 4.73584 0.879424 0.439712 0.898139i \(-0.355081\pi\)
0.439712 + 0.898139i \(0.355081\pi\)
\(30\) 0 0
\(31\) −8.03532 −1.44319 −0.721593 0.692317i \(-0.756590\pi\)
−0.721593 + 0.692317i \(0.756590\pi\)
\(32\) 0 0
\(33\) −0.142380 −0.0247851
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.28272 −0.868474 −0.434237 0.900799i \(-0.642982\pi\)
−0.434237 + 0.900799i \(0.642982\pi\)
\(38\) 0 0
\(39\) −16.1860 −2.59184
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 3.65780 0.557809 0.278904 0.960319i \(-0.410029\pi\)
0.278904 + 0.960319i \(0.410029\pi\)
\(44\) 0 0
\(45\) −2.28715 −0.340948
\(46\) 0 0
\(47\) 4.87355 0.710880 0.355440 0.934699i \(-0.384331\pi\)
0.355440 + 0.934699i \(0.384331\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 21.9132 3.06846
\(52\) 0 0
\(53\) −1.13119 −0.155381 −0.0776907 0.996978i \(-0.524755\pi\)
−0.0776907 + 0.996978i \(0.524755\pi\)
\(54\) 0 0
\(55\) 0.0273152 0.00368318
\(56\) 0 0
\(57\) 11.9970 1.58905
\(58\) 0 0
\(59\) 5.21861 0.679406 0.339703 0.940533i \(-0.389674\pi\)
0.339703 + 0.940533i \(0.389674\pi\)
\(60\) 0 0
\(61\) 10.2952 1.31816 0.659080 0.752073i \(-0.270946\pi\)
0.659080 + 0.752073i \(0.270946\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.10525 0.385159
\(66\) 0 0
\(67\) 9.37745 1.14564 0.572819 0.819682i \(-0.305850\pi\)
0.572819 + 0.819682i \(0.305850\pi\)
\(68\) 0 0
\(69\) 14.3746 1.73050
\(70\) 0 0
\(71\) 9.25115 1.09791 0.548955 0.835852i \(-0.315026\pi\)
0.548955 + 0.835852i \(0.315026\pi\)
\(72\) 0 0
\(73\) 15.6348 1.82992 0.914959 0.403547i \(-0.132223\pi\)
0.914959 + 0.403547i \(0.132223\pi\)
\(74\) 0 0
\(75\) −12.8502 −1.48381
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −7.46946 −0.840380 −0.420190 0.907436i \(-0.638037\pi\)
−0.420190 + 0.907436i \(0.638037\pi\)
\(80\) 0 0
\(81\) −2.91811 −0.324234
\(82\) 0 0
\(83\) 6.66344 0.731407 0.365704 0.930731i \(-0.380828\pi\)
0.365704 + 0.930731i \(0.380828\pi\)
\(84\) 0 0
\(85\) −4.20399 −0.455987
\(86\) 0 0
\(87\) 12.8711 1.37993
\(88\) 0 0
\(89\) 15.1869 1.60980 0.804902 0.593408i \(-0.202218\pi\)
0.804902 + 0.593408i \(0.202218\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −21.8385 −2.26455
\(94\) 0 0
\(95\) −2.30160 −0.236139
\(96\) 0 0
\(97\) −8.41390 −0.854302 −0.427151 0.904180i \(-0.640483\pi\)
−0.427151 + 0.904180i \(0.640483\pi\)
\(98\) 0 0
\(99\) −0.229798 −0.0230956
\(100\) 0 0
\(101\) −7.66350 −0.762547 −0.381273 0.924462i \(-0.624514\pi\)
−0.381273 + 0.924462i \(0.624514\pi\)
\(102\) 0 0
\(103\) −12.7118 −1.25253 −0.626265 0.779610i \(-0.715417\pi\)
−0.626265 + 0.779610i \(0.715417\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.4948 1.30459 0.652297 0.757963i \(-0.273805\pi\)
0.652297 + 0.757963i \(0.273805\pi\)
\(108\) 0 0
\(109\) −7.25475 −0.694879 −0.347439 0.937702i \(-0.612949\pi\)
−0.347439 + 0.937702i \(0.612949\pi\)
\(110\) 0 0
\(111\) −14.3574 −1.36275
\(112\) 0 0
\(113\) −9.99151 −0.939923 −0.469961 0.882687i \(-0.655732\pi\)
−0.469961 + 0.882687i \(0.655732\pi\)
\(114\) 0 0
\(115\) −2.75773 −0.257160
\(116\) 0 0
\(117\) −26.1240 −2.41516
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.9973 −0.999751
\(122\) 0 0
\(123\) 2.71781 0.245057
\(124\) 0 0
\(125\) 5.07230 0.453681
\(126\) 0 0
\(127\) 13.2019 1.17147 0.585737 0.810501i \(-0.300805\pi\)
0.585737 + 0.810501i \(0.300805\pi\)
\(128\) 0 0
\(129\) 9.94120 0.875274
\(130\) 0 0
\(131\) −21.0053 −1.83524 −0.917619 0.397460i \(-0.869892\pi\)
−0.917619 + 0.397460i \(0.869892\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1.96479 −0.169102
\(136\) 0 0
\(137\) 16.7936 1.43478 0.717388 0.696674i \(-0.245338\pi\)
0.717388 + 0.696674i \(0.245338\pi\)
\(138\) 0 0
\(139\) 11.3023 0.958645 0.479323 0.877639i \(-0.340882\pi\)
0.479323 + 0.877639i \(0.340882\pi\)
\(140\) 0 0
\(141\) 13.2454 1.11546
\(142\) 0 0
\(143\) 0.311996 0.0260904
\(144\) 0 0
\(145\) −2.46929 −0.205064
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 16.3854 1.34234 0.671172 0.741302i \(-0.265791\pi\)
0.671172 + 0.741302i \(0.265791\pi\)
\(150\) 0 0
\(151\) 8.53086 0.694231 0.347116 0.937822i \(-0.387161\pi\)
0.347116 + 0.937822i \(0.387161\pi\)
\(152\) 0 0
\(153\) 35.3675 2.85929
\(154\) 0 0
\(155\) 4.18966 0.336522
\(156\) 0 0
\(157\) −18.4731 −1.47432 −0.737158 0.675721i \(-0.763833\pi\)
−0.737158 + 0.675721i \(0.763833\pi\)
\(158\) 0 0
\(159\) −3.07437 −0.243814
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −17.1837 −1.34593 −0.672965 0.739674i \(-0.734980\pi\)
−0.672965 + 0.739674i \(0.734980\pi\)
\(164\) 0 0
\(165\) 0.0742375 0.00577938
\(166\) 0 0
\(167\) −5.03913 −0.389939 −0.194970 0.980809i \(-0.562461\pi\)
−0.194970 + 0.980809i \(0.562461\pi\)
\(168\) 0 0
\(169\) 22.4684 1.72834
\(170\) 0 0
\(171\) 19.3630 1.48073
\(172\) 0 0
\(173\) 2.34776 0.178497 0.0892483 0.996009i \(-0.471554\pi\)
0.0892483 + 0.996009i \(0.471554\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 14.1832 1.06608
\(178\) 0 0
\(179\) 9.00985 0.673428 0.336714 0.941607i \(-0.390684\pi\)
0.336714 + 0.941607i \(0.390684\pi\)
\(180\) 0 0
\(181\) 7.24384 0.538430 0.269215 0.963080i \(-0.413236\pi\)
0.269215 + 0.963080i \(0.413236\pi\)
\(182\) 0 0
\(183\) 27.9803 2.06836
\(184\) 0 0
\(185\) 2.75444 0.202510
\(186\) 0 0
\(187\) −0.422390 −0.0308882
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 10.3381 0.748039 0.374020 0.927421i \(-0.377979\pi\)
0.374020 + 0.927421i \(0.377979\pi\)
\(192\) 0 0
\(193\) −23.6485 −1.70226 −0.851130 0.524955i \(-0.824082\pi\)
−0.851130 + 0.524955i \(0.824082\pi\)
\(194\) 0 0
\(195\) 8.43948 0.604364
\(196\) 0 0
\(197\) 8.34901 0.594842 0.297421 0.954746i \(-0.403873\pi\)
0.297421 + 0.954746i \(0.403873\pi\)
\(198\) 0 0
\(199\) 8.31844 0.589678 0.294839 0.955547i \(-0.404734\pi\)
0.294839 + 0.955547i \(0.404734\pi\)
\(200\) 0 0
\(201\) 25.4861 1.79765
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −0.521406 −0.0364165
\(206\) 0 0
\(207\) 23.2003 1.61254
\(208\) 0 0
\(209\) −0.231251 −0.0159959
\(210\) 0 0
\(211\) −5.92332 −0.407778 −0.203889 0.978994i \(-0.565358\pi\)
−0.203889 + 0.978994i \(0.565358\pi\)
\(212\) 0 0
\(213\) 25.1429 1.72276
\(214\) 0 0
\(215\) −1.90720 −0.130070
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 42.4925 2.87138
\(220\) 0 0
\(221\) −48.0183 −3.23006
\(222\) 0 0
\(223\) 22.0457 1.47629 0.738143 0.674644i \(-0.235703\pi\)
0.738143 + 0.674644i \(0.235703\pi\)
\(224\) 0 0
\(225\) −20.7400 −1.38267
\(226\) 0 0
\(227\) 22.8145 1.51425 0.757125 0.653270i \(-0.226603\pi\)
0.757125 + 0.653270i \(0.226603\pi\)
\(228\) 0 0
\(229\) −3.11879 −0.206095 −0.103048 0.994676i \(-0.532859\pi\)
−0.103048 + 0.994676i \(0.532859\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 26.5258 1.73777 0.868883 0.495018i \(-0.164838\pi\)
0.868883 + 0.495018i \(0.164838\pi\)
\(234\) 0 0
\(235\) −2.54110 −0.165763
\(236\) 0 0
\(237\) −20.3006 −1.31866
\(238\) 0 0
\(239\) −26.6422 −1.72334 −0.861669 0.507470i \(-0.830581\pi\)
−0.861669 + 0.507470i \(0.830581\pi\)
\(240\) 0 0
\(241\) −27.5162 −1.77248 −0.886238 0.463231i \(-0.846690\pi\)
−0.886238 + 0.463231i \(0.846690\pi\)
\(242\) 0 0
\(243\) −19.2356 −1.23397
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −26.2891 −1.67273
\(248\) 0 0
\(249\) 18.1100 1.14767
\(250\) 0 0
\(251\) 8.34125 0.526495 0.263248 0.964728i \(-0.415206\pi\)
0.263248 + 0.964728i \(0.415206\pi\)
\(252\) 0 0
\(253\) −0.277079 −0.0174198
\(254\) 0 0
\(255\) −11.4257 −0.715502
\(256\) 0 0
\(257\) 5.08474 0.317177 0.158589 0.987345i \(-0.449306\pi\)
0.158589 + 0.987345i \(0.449306\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 20.7738 1.28586
\(262\) 0 0
\(263\) 9.84288 0.606938 0.303469 0.952841i \(-0.401855\pi\)
0.303469 + 0.952841i \(0.401855\pi\)
\(264\) 0 0
\(265\) 0.589811 0.0362318
\(266\) 0 0
\(267\) 41.2750 2.52599
\(268\) 0 0
\(269\) 8.97791 0.547393 0.273696 0.961816i \(-0.411754\pi\)
0.273696 + 0.961816i \(0.411754\pi\)
\(270\) 0 0
\(271\) −1.29679 −0.0787741 −0.0393871 0.999224i \(-0.512541\pi\)
−0.0393871 + 0.999224i \(0.512541\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.247696 0.0149366
\(276\) 0 0
\(277\) −8.86652 −0.532738 −0.266369 0.963871i \(-0.585824\pi\)
−0.266369 + 0.963871i \(0.585824\pi\)
\(278\) 0 0
\(279\) −35.2470 −2.11018
\(280\) 0 0
\(281\) −1.25681 −0.0749752 −0.0374876 0.999297i \(-0.511935\pi\)
−0.0374876 + 0.999297i \(0.511935\pi\)
\(282\) 0 0
\(283\) 0.661785 0.0393390 0.0196695 0.999807i \(-0.493739\pi\)
0.0196695 + 0.999807i \(0.493739\pi\)
\(284\) 0 0
\(285\) −6.25532 −0.370533
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 48.0087 2.82404
\(290\) 0 0
\(291\) −22.8674 −1.34051
\(292\) 0 0
\(293\) 26.8784 1.57025 0.785126 0.619336i \(-0.212598\pi\)
0.785126 + 0.619336i \(0.212598\pi\)
\(294\) 0 0
\(295\) −2.72101 −0.158424
\(296\) 0 0
\(297\) −0.197409 −0.0114549
\(298\) 0 0
\(299\) −31.4990 −1.82163
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −20.8280 −1.19653
\(304\) 0 0
\(305\) −5.36796 −0.307368
\(306\) 0 0
\(307\) 16.4296 0.937689 0.468845 0.883281i \(-0.344670\pi\)
0.468845 + 0.883281i \(0.344670\pi\)
\(308\) 0 0
\(309\) −34.5483 −1.96538
\(310\) 0 0
\(311\) −5.95638 −0.337755 −0.168878 0.985637i \(-0.554014\pi\)
−0.168878 + 0.985637i \(0.554014\pi\)
\(312\) 0 0
\(313\) −13.6393 −0.770937 −0.385468 0.922721i \(-0.625960\pi\)
−0.385468 + 0.922721i \(0.625960\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.1941 −0.684891 −0.342446 0.939538i \(-0.611255\pi\)
−0.342446 + 0.939538i \(0.611255\pi\)
\(318\) 0 0
\(319\) −0.248099 −0.0138909
\(320\) 0 0
\(321\) 36.6764 2.04708
\(322\) 0 0
\(323\) 35.5910 1.98034
\(324\) 0 0
\(325\) 28.1586 1.56196
\(326\) 0 0
\(327\) −19.7170 −1.09035
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −33.4381 −1.83792 −0.918962 0.394345i \(-0.870971\pi\)
−0.918962 + 0.394345i \(0.870971\pi\)
\(332\) 0 0
\(333\) −23.1727 −1.26985
\(334\) 0 0
\(335\) −4.88945 −0.267139
\(336\) 0 0
\(337\) −20.6785 −1.12643 −0.563216 0.826310i \(-0.690436\pi\)
−0.563216 + 0.826310i \(0.690436\pi\)
\(338\) 0 0
\(339\) −27.1551 −1.47486
\(340\) 0 0
\(341\) 0.420951 0.0227958
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −7.49499 −0.403517
\(346\) 0 0
\(347\) −3.52816 −0.189401 −0.0947007 0.995506i \(-0.530189\pi\)
−0.0947007 + 0.995506i \(0.530189\pi\)
\(348\) 0 0
\(349\) 21.8147 1.16771 0.583857 0.811856i \(-0.301543\pi\)
0.583857 + 0.811856i \(0.301543\pi\)
\(350\) 0 0
\(351\) −22.4419 −1.19786
\(352\) 0 0
\(353\) 9.82379 0.522868 0.261434 0.965221i \(-0.415805\pi\)
0.261434 + 0.965221i \(0.415805\pi\)
\(354\) 0 0
\(355\) −4.82360 −0.256010
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −20.3688 −1.07503 −0.537513 0.843255i \(-0.680636\pi\)
−0.537513 + 0.843255i \(0.680636\pi\)
\(360\) 0 0
\(361\) 0.485391 0.0255469
\(362\) 0 0
\(363\) −29.8885 −1.56874
\(364\) 0 0
\(365\) −8.15208 −0.426700
\(366\) 0 0
\(367\) 1.77124 0.0924578 0.0462289 0.998931i \(-0.485280\pi\)
0.0462289 + 0.998931i \(0.485280\pi\)
\(368\) 0 0
\(369\) 4.38650 0.228352
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −26.1930 −1.35622 −0.678112 0.734959i \(-0.737201\pi\)
−0.678112 + 0.734959i \(0.737201\pi\)
\(374\) 0 0
\(375\) 13.7856 0.711884
\(376\) 0 0
\(377\) −28.2045 −1.45260
\(378\) 0 0
\(379\) −7.75824 −0.398514 −0.199257 0.979947i \(-0.563853\pi\)
−0.199257 + 0.979947i \(0.563853\pi\)
\(380\) 0 0
\(381\) 35.8802 1.83820
\(382\) 0 0
\(383\) 26.6322 1.36084 0.680421 0.732822i \(-0.261797\pi\)
0.680421 + 0.732822i \(0.261797\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 16.0449 0.815610
\(388\) 0 0
\(389\) −14.5184 −0.736110 −0.368055 0.929804i \(-0.619976\pi\)
−0.368055 + 0.929804i \(0.619976\pi\)
\(390\) 0 0
\(391\) 42.6444 2.15662
\(392\) 0 0
\(393\) −57.0884 −2.87973
\(394\) 0 0
\(395\) 3.89462 0.195959
\(396\) 0 0
\(397\) −2.84163 −0.142618 −0.0713088 0.997454i \(-0.522718\pi\)
−0.0713088 + 0.997454i \(0.522718\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −19.1476 −0.956186 −0.478093 0.878309i \(-0.658672\pi\)
−0.478093 + 0.878309i \(0.658672\pi\)
\(402\) 0 0
\(403\) 47.8546 2.38381
\(404\) 0 0
\(405\) 1.52152 0.0756048
\(406\) 0 0
\(407\) 0.276749 0.0137179
\(408\) 0 0
\(409\) 31.5456 1.55983 0.779915 0.625886i \(-0.215262\pi\)
0.779915 + 0.625886i \(0.215262\pi\)
\(410\) 0 0
\(411\) 45.6419 2.25135
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −3.47435 −0.170549
\(416\) 0 0
\(417\) 30.7174 1.50424
\(418\) 0 0
\(419\) 34.9308 1.70648 0.853240 0.521519i \(-0.174634\pi\)
0.853240 + 0.521519i \(0.174634\pi\)
\(420\) 0 0
\(421\) −40.2206 −1.96023 −0.980115 0.198429i \(-0.936416\pi\)
−0.980115 + 0.198429i \(0.936416\pi\)
\(422\) 0 0
\(423\) 21.3778 1.03943
\(424\) 0 0
\(425\) −38.1220 −1.84919
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0.847946 0.0409392
\(430\) 0 0
\(431\) −0.0998975 −0.00481190 −0.00240595 0.999997i \(-0.500766\pi\)
−0.00240595 + 0.999997i \(0.500766\pi\)
\(432\) 0 0
\(433\) −19.3357 −0.929216 −0.464608 0.885516i \(-0.653805\pi\)
−0.464608 + 0.885516i \(0.653805\pi\)
\(434\) 0 0
\(435\) −6.71108 −0.321772
\(436\) 0 0
\(437\) 23.3470 1.11684
\(438\) 0 0
\(439\) 8.70056 0.415255 0.207628 0.978208i \(-0.433426\pi\)
0.207628 + 0.978208i \(0.433426\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.62748 0.0773239 0.0386619 0.999252i \(-0.487690\pi\)
0.0386619 + 0.999252i \(0.487690\pi\)
\(444\) 0 0
\(445\) −7.91851 −0.375373
\(446\) 0 0
\(447\) 44.5324 2.10631
\(448\) 0 0
\(449\) 10.9660 0.517519 0.258759 0.965942i \(-0.416686\pi\)
0.258759 + 0.965942i \(0.416686\pi\)
\(450\) 0 0
\(451\) −0.0523876 −0.00246683
\(452\) 0 0
\(453\) 23.1853 1.08934
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −16.9173 −0.791358 −0.395679 0.918389i \(-0.629491\pi\)
−0.395679 + 0.918389i \(0.629491\pi\)
\(458\) 0 0
\(459\) 30.3827 1.41814
\(460\) 0 0
\(461\) 12.2523 0.570648 0.285324 0.958431i \(-0.407899\pi\)
0.285324 + 0.958431i \(0.407899\pi\)
\(462\) 0 0
\(463\) −15.4046 −0.715911 −0.357956 0.933739i \(-0.616526\pi\)
−0.357956 + 0.933739i \(0.616526\pi\)
\(464\) 0 0
\(465\) 11.3867 0.528046
\(466\) 0 0
\(467\) 1.55604 0.0720048 0.0360024 0.999352i \(-0.488538\pi\)
0.0360024 + 0.999352i \(0.488538\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −50.2065 −2.31339
\(472\) 0 0
\(473\) −0.191623 −0.00881084
\(474\) 0 0
\(475\) −20.8711 −0.957630
\(476\) 0 0
\(477\) −4.96199 −0.227194
\(478\) 0 0
\(479\) −7.48168 −0.341847 −0.170923 0.985284i \(-0.554675\pi\)
−0.170923 + 0.985284i \(0.554675\pi\)
\(480\) 0 0
\(481\) 31.4614 1.43452
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.38705 0.199206
\(486\) 0 0
\(487\) −4.12986 −0.187142 −0.0935709 0.995613i \(-0.529828\pi\)
−0.0935709 + 0.995613i \(0.529828\pi\)
\(488\) 0 0
\(489\) −46.7021 −2.11194
\(490\) 0 0
\(491\) 3.37953 0.152516 0.0762581 0.997088i \(-0.475703\pi\)
0.0762581 + 0.997088i \(0.475703\pi\)
\(492\) 0 0
\(493\) 38.1842 1.71973
\(494\) 0 0
\(495\) 0.119818 0.00538542
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0.714451 0.0319832 0.0159916 0.999872i \(-0.494909\pi\)
0.0159916 + 0.999872i \(0.494909\pi\)
\(500\) 0 0
\(501\) −13.6954 −0.611865
\(502\) 0 0
\(503\) −31.1268 −1.38788 −0.693938 0.720035i \(-0.744126\pi\)
−0.693938 + 0.720035i \(0.744126\pi\)
\(504\) 0 0
\(505\) 3.99579 0.177810
\(506\) 0 0
\(507\) 61.0648 2.71198
\(508\) 0 0
\(509\) −18.1459 −0.804302 −0.402151 0.915573i \(-0.631737\pi\)
−0.402151 + 0.915573i \(0.631737\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 16.6339 0.734405
\(514\) 0 0
\(515\) 6.62800 0.292065
\(516\) 0 0
\(517\) −0.255313 −0.0112287
\(518\) 0 0
\(519\) 6.38076 0.280084
\(520\) 0 0
\(521\) −20.2199 −0.885851 −0.442925 0.896558i \(-0.646059\pi\)
−0.442925 + 0.896558i \(0.646059\pi\)
\(522\) 0 0
\(523\) 10.7117 0.468391 0.234196 0.972189i \(-0.424754\pi\)
0.234196 + 0.972189i \(0.424754\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −64.7872 −2.82217
\(528\) 0 0
\(529\) 4.97386 0.216255
\(530\) 0 0
\(531\) 22.8915 0.993405
\(532\) 0 0
\(533\) −5.95553 −0.257963
\(534\) 0 0
\(535\) −7.03628 −0.304205
\(536\) 0 0
\(537\) 24.4871 1.05670
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −3.09928 −0.133248 −0.0666242 0.997778i \(-0.521223\pi\)
−0.0666242 + 0.997778i \(0.521223\pi\)
\(542\) 0 0
\(543\) 19.6874 0.844867
\(544\) 0 0
\(545\) 3.78267 0.162032
\(546\) 0 0
\(547\) 15.4370 0.660038 0.330019 0.943974i \(-0.392945\pi\)
0.330019 + 0.943974i \(0.392945\pi\)
\(548\) 0 0
\(549\) 45.1598 1.92737
\(550\) 0 0
\(551\) 20.9051 0.890586
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 7.48605 0.317765
\(556\) 0 0
\(557\) 29.1785 1.23633 0.618167 0.786047i \(-0.287876\pi\)
0.618167 + 0.786047i \(0.287876\pi\)
\(558\) 0 0
\(559\) −21.7841 −0.921370
\(560\) 0 0
\(561\) −1.14798 −0.0484677
\(562\) 0 0
\(563\) −33.1730 −1.39808 −0.699038 0.715084i \(-0.746388\pi\)
−0.699038 + 0.715084i \(0.746388\pi\)
\(564\) 0 0
\(565\) 5.20963 0.219171
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −32.0718 −1.34452 −0.672261 0.740315i \(-0.734677\pi\)
−0.672261 + 0.740315i \(0.734677\pi\)
\(570\) 0 0
\(571\) 36.3618 1.52169 0.760846 0.648932i \(-0.224784\pi\)
0.760846 + 0.648932i \(0.224784\pi\)
\(572\) 0 0
\(573\) 28.0970 1.17377
\(574\) 0 0
\(575\) −25.0073 −1.04287
\(576\) 0 0
\(577\) −29.2809 −1.21898 −0.609490 0.792794i \(-0.708626\pi\)
−0.609490 + 0.792794i \(0.708626\pi\)
\(578\) 0 0
\(579\) −64.2723 −2.67107
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.0592605 0.00245432
\(584\) 0 0
\(585\) 13.6212 0.563166
\(586\) 0 0
\(587\) 0.283450 0.0116992 0.00584962 0.999983i \(-0.498138\pi\)
0.00584962 + 0.999983i \(0.498138\pi\)
\(588\) 0 0
\(589\) −35.4697 −1.46150
\(590\) 0 0
\(591\) 22.6910 0.933385
\(592\) 0 0
\(593\) −19.9652 −0.819872 −0.409936 0.912114i \(-0.634449\pi\)
−0.409936 + 0.912114i \(0.634449\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 22.6079 0.925282
\(598\) 0 0
\(599\) −7.15375 −0.292294 −0.146147 0.989263i \(-0.546687\pi\)
−0.146147 + 0.989263i \(0.546687\pi\)
\(600\) 0 0
\(601\) 11.5662 0.471794 0.235897 0.971778i \(-0.424197\pi\)
0.235897 + 0.971778i \(0.424197\pi\)
\(602\) 0 0
\(603\) 41.1342 1.67511
\(604\) 0 0
\(605\) 5.73403 0.233121
\(606\) 0 0
\(607\) 5.37175 0.218033 0.109016 0.994040i \(-0.465230\pi\)
0.109016 + 0.994040i \(0.465230\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −29.0246 −1.17421
\(612\) 0 0
\(613\) −10.5142 −0.424667 −0.212333 0.977197i \(-0.568106\pi\)
−0.212333 + 0.977197i \(0.568106\pi\)
\(614\) 0 0
\(615\) −1.41708 −0.0571423
\(616\) 0 0
\(617\) 11.5370 0.464461 0.232231 0.972661i \(-0.425398\pi\)
0.232231 + 0.972661i \(0.425398\pi\)
\(618\) 0 0
\(619\) 19.8935 0.799586 0.399793 0.916606i \(-0.369082\pi\)
0.399793 + 0.916606i \(0.369082\pi\)
\(620\) 0 0
\(621\) 19.9304 0.799779
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 20.9960 0.839838
\(626\) 0 0
\(627\) −0.628495 −0.0250997
\(628\) 0 0
\(629\) −42.5935 −1.69831
\(630\) 0 0
\(631\) 8.58885 0.341917 0.170958 0.985278i \(-0.445314\pi\)
0.170958 + 0.985278i \(0.445314\pi\)
\(632\) 0 0
\(633\) −16.0985 −0.639857
\(634\) 0 0
\(635\) −6.88352 −0.273164
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 40.5802 1.60533
\(640\) 0 0
\(641\) −35.0485 −1.38433 −0.692166 0.721738i \(-0.743343\pi\)
−0.692166 + 0.721738i \(0.743343\pi\)
\(642\) 0 0
\(643\) 9.10398 0.359026 0.179513 0.983756i \(-0.442548\pi\)
0.179513 + 0.983756i \(0.442548\pi\)
\(644\) 0 0
\(645\) −5.18340 −0.204096
\(646\) 0 0
\(647\) −44.6739 −1.75631 −0.878156 0.478375i \(-0.841226\pi\)
−0.878156 + 0.478375i \(0.841226\pi\)
\(648\) 0 0
\(649\) −0.273390 −0.0107315
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.524446 0.0205232 0.0102616 0.999947i \(-0.496734\pi\)
0.0102616 + 0.999947i \(0.496734\pi\)
\(654\) 0 0
\(655\) 10.9523 0.427940
\(656\) 0 0
\(657\) 68.5822 2.67565
\(658\) 0 0
\(659\) −47.3824 −1.84576 −0.922878 0.385092i \(-0.874170\pi\)
−0.922878 + 0.385092i \(0.874170\pi\)
\(660\) 0 0
\(661\) 12.8569 0.500076 0.250038 0.968236i \(-0.419557\pi\)
0.250038 + 0.968236i \(0.419557\pi\)
\(662\) 0 0
\(663\) −130.505 −5.06838
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 25.0480 0.969863
\(668\) 0 0
\(669\) 59.9159 2.31648
\(670\) 0 0
\(671\) −0.539339 −0.0208209
\(672\) 0 0
\(673\) 27.1973 1.04838 0.524189 0.851602i \(-0.324369\pi\)
0.524189 + 0.851602i \(0.324369\pi\)
\(674\) 0 0
\(675\) −17.8168 −0.685769
\(676\) 0 0
\(677\) 18.4835 0.710379 0.355189 0.934794i \(-0.384416\pi\)
0.355189 + 0.934794i \(0.384416\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 62.0055 2.37606
\(682\) 0 0
\(683\) 9.16977 0.350872 0.175436 0.984491i \(-0.443867\pi\)
0.175436 + 0.984491i \(0.443867\pi\)
\(684\) 0 0
\(685\) −8.75628 −0.334560
\(686\) 0 0
\(687\) −8.47628 −0.323390
\(688\) 0 0
\(689\) 6.73686 0.256654
\(690\) 0 0
\(691\) −10.4993 −0.399414 −0.199707 0.979856i \(-0.563999\pi\)
−0.199707 + 0.979856i \(0.563999\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −5.89306 −0.223537
\(696\) 0 0
\(697\) 8.06280 0.305400
\(698\) 0 0
\(699\) 72.0923 2.72678
\(700\) 0 0
\(701\) 36.9734 1.39647 0.698233 0.715871i \(-0.253970\pi\)
0.698233 + 0.715871i \(0.253970\pi\)
\(702\) 0 0
\(703\) −23.3191 −0.879497
\(704\) 0 0
\(705\) −6.90622 −0.260103
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −41.6159 −1.56292 −0.781460 0.623956i \(-0.785525\pi\)
−0.781460 + 0.623956i \(0.785525\pi\)
\(710\) 0 0
\(711\) −32.7648 −1.22878
\(712\) 0 0
\(713\) −42.4991 −1.59160
\(714\) 0 0
\(715\) −0.162676 −0.00608375
\(716\) 0 0
\(717\) −72.4084 −2.70414
\(718\) 0 0
\(719\) 26.5108 0.988687 0.494343 0.869267i \(-0.335409\pi\)
0.494343 + 0.869267i \(0.335409\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −74.7839 −2.78124
\(724\) 0 0
\(725\) −22.3917 −0.831607
\(726\) 0 0
\(727\) 28.4464 1.05502 0.527510 0.849549i \(-0.323126\pi\)
0.527510 + 0.849549i \(0.323126\pi\)
\(728\) 0 0
\(729\) −43.5245 −1.61202
\(730\) 0 0
\(731\) 29.4921 1.09080
\(732\) 0 0
\(733\) 11.9478 0.441300 0.220650 0.975353i \(-0.429182\pi\)
0.220650 + 0.975353i \(0.429182\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.491262 −0.0180959
\(738\) 0 0
\(739\) −6.44140 −0.236951 −0.118475 0.992957i \(-0.537801\pi\)
−0.118475 + 0.992957i \(0.537801\pi\)
\(740\) 0 0
\(741\) −71.4487 −2.62473
\(742\) 0 0
\(743\) −39.7507 −1.45831 −0.729156 0.684348i \(-0.760087\pi\)
−0.729156 + 0.684348i \(0.760087\pi\)
\(744\) 0 0
\(745\) −8.54344 −0.313007
\(746\) 0 0
\(747\) 29.2292 1.06944
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 26.0681 0.951240 0.475620 0.879651i \(-0.342224\pi\)
0.475620 + 0.879651i \(0.342224\pi\)
\(752\) 0 0
\(753\) 22.6700 0.826139
\(754\) 0 0
\(755\) −4.44804 −0.161881
\(756\) 0 0
\(757\) −17.8431 −0.648517 −0.324259 0.945968i \(-0.605115\pi\)
−0.324259 + 0.945968i \(0.605115\pi\)
\(758\) 0 0
\(759\) −0.753050 −0.0273340
\(760\) 0 0
\(761\) −20.9632 −0.759916 −0.379958 0.925004i \(-0.624062\pi\)
−0.379958 + 0.925004i \(0.624062\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −18.4408 −0.666729
\(766\) 0 0
\(767\) −31.0796 −1.12222
\(768\) 0 0
\(769\) 7.95390 0.286825 0.143413 0.989663i \(-0.454192\pi\)
0.143413 + 0.989663i \(0.454192\pi\)
\(770\) 0 0
\(771\) 13.8194 0.497692
\(772\) 0 0
\(773\) 17.3869 0.625364 0.312682 0.949858i \(-0.398773\pi\)
0.312682 + 0.949858i \(0.398773\pi\)
\(774\) 0 0
\(775\) 37.9921 1.36472
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.41423 0.158156
\(780\) 0 0
\(781\) −0.484645 −0.0173420
\(782\) 0 0
\(783\) 17.8458 0.637758
\(784\) 0 0
\(785\) 9.63199 0.343780
\(786\) 0 0
\(787\) 15.1912 0.541508 0.270754 0.962649i \(-0.412727\pi\)
0.270754 + 0.962649i \(0.412727\pi\)
\(788\) 0 0
\(789\) 26.7511 0.952364
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −61.3132 −2.17729
\(794\) 0 0
\(795\) 1.60300 0.0568524
\(796\) 0 0
\(797\) −11.4142 −0.404311 −0.202156 0.979353i \(-0.564795\pi\)
−0.202156 + 0.979353i \(0.564795\pi\)
\(798\) 0 0
\(799\) 39.2945 1.39014
\(800\) 0 0
\(801\) 66.6172 2.35380
\(802\) 0 0
\(803\) −0.819070 −0.0289044
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 24.4003 0.858930
\(808\) 0 0
\(809\) −8.40298 −0.295433 −0.147716 0.989030i \(-0.547192\pi\)
−0.147716 + 0.989030i \(0.547192\pi\)
\(810\) 0 0
\(811\) 42.3090 1.48567 0.742835 0.669474i \(-0.233481\pi\)
0.742835 + 0.669474i \(0.233481\pi\)
\(812\) 0 0
\(813\) −3.52442 −0.123607
\(814\) 0 0
\(815\) 8.95967 0.313844
\(816\) 0 0
\(817\) 16.1463 0.564889
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −7.23403 −0.252470 −0.126235 0.992000i \(-0.540289\pi\)
−0.126235 + 0.992000i \(0.540289\pi\)
\(822\) 0 0
\(823\) −48.5809 −1.69342 −0.846712 0.532052i \(-0.821421\pi\)
−0.846712 + 0.532052i \(0.821421\pi\)
\(824\) 0 0
\(825\) 0.673190 0.0234375
\(826\) 0 0
\(827\) 6.30440 0.219225 0.109613 0.993974i \(-0.465039\pi\)
0.109613 + 0.993974i \(0.465039\pi\)
\(828\) 0 0
\(829\) −28.8484 −1.00194 −0.500972 0.865463i \(-0.667024\pi\)
−0.500972 + 0.865463i \(0.667024\pi\)
\(830\) 0 0
\(831\) −24.0975 −0.835934
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 2.62743 0.0909259
\(836\) 0 0
\(837\) −30.2791 −1.04660
\(838\) 0 0
\(839\) −0.912239 −0.0314940 −0.0157470 0.999876i \(-0.505013\pi\)
−0.0157470 + 0.999876i \(0.505013\pi\)
\(840\) 0 0
\(841\) −6.57179 −0.226613
\(842\) 0 0
\(843\) −3.41578 −0.117646
\(844\) 0 0
\(845\) −11.7151 −0.403013
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 1.79861 0.0617280
\(850\) 0 0
\(851\) −27.9405 −0.957787
\(852\) 0 0
\(853\) −5.28786 −0.181053 −0.0905264 0.995894i \(-0.528855\pi\)
−0.0905264 + 0.995894i \(0.528855\pi\)
\(854\) 0 0
\(855\) −10.0960 −0.345275
\(856\) 0 0
\(857\) −35.7176 −1.22009 −0.610046 0.792366i \(-0.708849\pi\)
−0.610046 + 0.792366i \(0.708849\pi\)
\(858\) 0 0
\(859\) 23.0888 0.787778 0.393889 0.919158i \(-0.371129\pi\)
0.393889 + 0.919158i \(0.371129\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −28.4626 −0.968879 −0.484439 0.874825i \(-0.660976\pi\)
−0.484439 + 0.874825i \(0.660976\pi\)
\(864\) 0 0
\(865\) −1.22413 −0.0416218
\(866\) 0 0
\(867\) 130.479 4.43129
\(868\) 0 0
\(869\) 0.391307 0.0132742
\(870\) 0 0
\(871\) −55.8477 −1.89233
\(872\) 0 0
\(873\) −36.9076 −1.24913
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 28.1917 0.951967 0.475983 0.879454i \(-0.342092\pi\)
0.475983 + 0.879454i \(0.342092\pi\)
\(878\) 0 0
\(879\) 73.0504 2.46393
\(880\) 0 0
\(881\) −5.41597 −0.182469 −0.0912343 0.995829i \(-0.529081\pi\)
−0.0912343 + 0.995829i \(0.529081\pi\)
\(882\) 0 0
\(883\) −0.811514 −0.0273096 −0.0136548 0.999907i \(-0.504347\pi\)
−0.0136548 + 0.999907i \(0.504347\pi\)
\(884\) 0 0
\(885\) −7.39520 −0.248587
\(886\) 0 0
\(887\) −42.7334 −1.43485 −0.717424 0.696636i \(-0.754679\pi\)
−0.717424 + 0.696636i \(0.754679\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.152873 0.00512142
\(892\) 0 0
\(893\) 21.5130 0.719904
\(894\) 0 0
\(895\) −4.69779 −0.157030
\(896\) 0 0
\(897\) −85.6084 −2.85838
\(898\) 0 0
\(899\) −38.0540 −1.26917
\(900\) 0 0
\(901\) −9.12059 −0.303851
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −3.77698 −0.125551
\(906\) 0 0
\(907\) −20.5541 −0.682487 −0.341244 0.939975i \(-0.610848\pi\)
−0.341244 + 0.939975i \(0.610848\pi\)
\(908\) 0 0
\(909\) −33.6160 −1.11497
\(910\) 0 0
\(911\) 25.8456 0.856302 0.428151 0.903707i \(-0.359165\pi\)
0.428151 + 0.903707i \(0.359165\pi\)
\(912\) 0 0
\(913\) −0.349081 −0.0115529
\(914\) 0 0
\(915\) −14.5891 −0.482301
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −24.5311 −0.809205 −0.404602 0.914493i \(-0.632590\pi\)
−0.404602 + 0.914493i \(0.632590\pi\)
\(920\) 0 0
\(921\) 44.6527 1.47136
\(922\) 0 0
\(923\) −55.0955 −1.81349
\(924\) 0 0
\(925\) 24.9774 0.821253
\(926\) 0 0
\(927\) −55.7603 −1.83141
\(928\) 0 0
\(929\) −15.2592 −0.500639 −0.250319 0.968163i \(-0.580536\pi\)
−0.250319 + 0.968163i \(0.580536\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −16.1883 −0.529982
\(934\) 0 0
\(935\) 0.220237 0.00720251
\(936\) 0 0
\(937\) −20.6093 −0.673276 −0.336638 0.941634i \(-0.609290\pi\)
−0.336638 + 0.941634i \(0.609290\pi\)
\(938\) 0 0
\(939\) −37.0689 −1.20970
\(940\) 0 0
\(941\) 5.76678 0.187992 0.0939958 0.995573i \(-0.470036\pi\)
0.0939958 + 0.995573i \(0.470036\pi\)
\(942\) 0 0
\(943\) 5.28903 0.172235
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −18.2002 −0.591427 −0.295713 0.955277i \(-0.595557\pi\)
−0.295713 + 0.955277i \(0.595557\pi\)
\(948\) 0 0
\(949\) −93.1137 −3.02260
\(950\) 0 0
\(951\) −33.1414 −1.07468
\(952\) 0 0
\(953\) −11.8833 −0.384938 −0.192469 0.981303i \(-0.561649\pi\)
−0.192469 + 0.981303i \(0.561649\pi\)
\(954\) 0 0
\(955\) −5.39035 −0.174428
\(956\) 0 0
\(957\) −0.674287 −0.0217966
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 33.5664 1.08279
\(962\) 0 0
\(963\) 59.1951 1.90754
\(964\) 0 0
\(965\) 12.3305 0.396932
\(966\) 0 0
\(967\) 60.5653 1.94765 0.973825 0.227299i \(-0.0729894\pi\)
0.973825 + 0.227299i \(0.0729894\pi\)
\(968\) 0 0
\(969\) 96.7297 3.10741
\(970\) 0 0
\(971\) −52.2238 −1.67594 −0.837970 0.545716i \(-0.816258\pi\)
−0.837970 + 0.545716i \(0.816258\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 76.5297 2.45091
\(976\) 0 0
\(977\) −3.44437 −0.110195 −0.0550976 0.998481i \(-0.517547\pi\)
−0.0550976 + 0.998481i \(0.517547\pi\)
\(978\) 0 0
\(979\) −0.795602 −0.0254276
\(980\) 0 0
\(981\) −31.8230 −1.01603
\(982\) 0 0
\(983\) 44.5887 1.42216 0.711079 0.703112i \(-0.248207\pi\)
0.711079 + 0.703112i \(0.248207\pi\)
\(984\) 0 0
\(985\) −4.35322 −0.138705
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 19.3462 0.615173
\(990\) 0 0
\(991\) −22.3007 −0.708406 −0.354203 0.935169i \(-0.615248\pi\)
−0.354203 + 0.935169i \(0.615248\pi\)
\(992\) 0 0
\(993\) −90.8785 −2.88394
\(994\) 0 0
\(995\) −4.33728 −0.137501
\(996\) 0 0
\(997\) −12.5700 −0.398097 −0.199048 0.979990i \(-0.563785\pi\)
−0.199048 + 0.979990i \(0.563785\pi\)
\(998\) 0 0
\(999\) −19.9066 −0.629817
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 \(a_p\))