Properties

Label 6008.2.a.e.1.17
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.03653 q^{3} +2.53205 q^{5} -0.333645 q^{7} -1.92561 q^{9} +O(q^{10})\) \(q-1.03653 q^{3} +2.53205 q^{5} -0.333645 q^{7} -1.92561 q^{9} -4.00849 q^{11} -1.11706 q^{13} -2.62454 q^{15} +7.29433 q^{17} -5.63287 q^{19} +0.345833 q^{21} -4.25451 q^{23} +1.41125 q^{25} +5.10553 q^{27} -1.89980 q^{29} +9.43795 q^{31} +4.15491 q^{33} -0.844805 q^{35} -0.479113 q^{37} +1.15787 q^{39} -2.92963 q^{41} -2.67273 q^{43} -4.87573 q^{45} -5.38038 q^{47} -6.88868 q^{49} -7.56078 q^{51} +11.0743 q^{53} -10.1497 q^{55} +5.83863 q^{57} +13.7733 q^{59} +9.57938 q^{61} +0.642470 q^{63} -2.82845 q^{65} -9.91497 q^{67} +4.40992 q^{69} -12.2338 q^{71} +11.3112 q^{73} -1.46280 q^{75} +1.33741 q^{77} +8.09784 q^{79} +0.484799 q^{81} +4.23590 q^{83} +18.4696 q^{85} +1.96919 q^{87} +0.712086 q^{89} +0.372702 q^{91} -9.78270 q^{93} -14.2627 q^{95} +5.75930 q^{97} +7.71878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −1.03653 −0.598440 −0.299220 0.954184i \(-0.596726\pi\)
−0.299220 + 0.954184i \(0.596726\pi\)
\(4\) 0 0
\(5\) 2.53205 1.13237 0.566183 0.824280i \(-0.308420\pi\)
0.566183 + 0.824280i \(0.308420\pi\)
\(6\) 0 0
\(7\) −0.333645 −0.126106 −0.0630530 0.998010i \(-0.520084\pi\)
−0.0630530 + 0.998010i \(0.520084\pi\)
\(8\) 0 0
\(9\) −1.92561 −0.641870
\(10\) 0 0
\(11\) −4.00849 −1.20860 −0.604302 0.796755i \(-0.706548\pi\)
−0.604302 + 0.796755i \(0.706548\pi\)
\(12\) 0 0
\(13\) −1.11706 −0.309817 −0.154909 0.987929i \(-0.549508\pi\)
−0.154909 + 0.987929i \(0.549508\pi\)
\(14\) 0 0
\(15\) −2.62454 −0.677652
\(16\) 0 0
\(17\) 7.29433 1.76914 0.884568 0.466412i \(-0.154453\pi\)
0.884568 + 0.466412i \(0.154453\pi\)
\(18\) 0 0
\(19\) −5.63287 −1.29227 −0.646134 0.763224i \(-0.723615\pi\)
−0.646134 + 0.763224i \(0.723615\pi\)
\(20\) 0 0
\(21\) 0.345833 0.0754669
\(22\) 0 0
\(23\) −4.25451 −0.887126 −0.443563 0.896243i \(-0.646286\pi\)
−0.443563 + 0.896243i \(0.646286\pi\)
\(24\) 0 0
\(25\) 1.41125 0.282251
\(26\) 0 0
\(27\) 5.10553 0.982560
\(28\) 0 0
\(29\) −1.89980 −0.352784 −0.176392 0.984320i \(-0.556443\pi\)
−0.176392 + 0.984320i \(0.556443\pi\)
\(30\) 0 0
\(31\) 9.43795 1.69511 0.847553 0.530711i \(-0.178075\pi\)
0.847553 + 0.530711i \(0.178075\pi\)
\(32\) 0 0
\(33\) 4.15491 0.723277
\(34\) 0 0
\(35\) −0.844805 −0.142798
\(36\) 0 0
\(37\) −0.479113 −0.0787657 −0.0393828 0.999224i \(-0.512539\pi\)
−0.0393828 + 0.999224i \(0.512539\pi\)
\(38\) 0 0
\(39\) 1.15787 0.185407
\(40\) 0 0
\(41\) −2.92963 −0.457532 −0.228766 0.973481i \(-0.573469\pi\)
−0.228766 + 0.973481i \(0.573469\pi\)
\(42\) 0 0
\(43\) −2.67273 −0.407588 −0.203794 0.979014i \(-0.565327\pi\)
−0.203794 + 0.979014i \(0.565327\pi\)
\(44\) 0 0
\(45\) −4.87573 −0.726831
\(46\) 0 0
\(47\) −5.38038 −0.784809 −0.392404 0.919793i \(-0.628357\pi\)
−0.392404 + 0.919793i \(0.628357\pi\)
\(48\) 0 0
\(49\) −6.88868 −0.984097
\(50\) 0 0
\(51\) −7.56078 −1.05872
\(52\) 0 0
\(53\) 11.0743 1.52117 0.760584 0.649239i \(-0.224913\pi\)
0.760584 + 0.649239i \(0.224913\pi\)
\(54\) 0 0
\(55\) −10.1497 −1.36858
\(56\) 0 0
\(57\) 5.83863 0.773345
\(58\) 0 0
\(59\) 13.7733 1.79313 0.896564 0.442914i \(-0.146055\pi\)
0.896564 + 0.442914i \(0.146055\pi\)
\(60\) 0 0
\(61\) 9.57938 1.22651 0.613257 0.789883i \(-0.289859\pi\)
0.613257 + 0.789883i \(0.289859\pi\)
\(62\) 0 0
\(63\) 0.642470 0.0809437
\(64\) 0 0
\(65\) −2.82845 −0.350826
\(66\) 0 0
\(67\) −9.91497 −1.21131 −0.605653 0.795729i \(-0.707088\pi\)
−0.605653 + 0.795729i \(0.707088\pi\)
\(68\) 0 0
\(69\) 4.40992 0.530892
\(70\) 0 0
\(71\) −12.2338 −1.45189 −0.725945 0.687753i \(-0.758597\pi\)
−0.725945 + 0.687753i \(0.758597\pi\)
\(72\) 0 0
\(73\) 11.3112 1.32387 0.661935 0.749561i \(-0.269735\pi\)
0.661935 + 0.749561i \(0.269735\pi\)
\(74\) 0 0
\(75\) −1.46280 −0.168910
\(76\) 0 0
\(77\) 1.33741 0.152412
\(78\) 0 0
\(79\) 8.09784 0.911079 0.455539 0.890216i \(-0.349446\pi\)
0.455539 + 0.890216i \(0.349446\pi\)
\(80\) 0 0
\(81\) 0.484799 0.0538665
\(82\) 0 0
\(83\) 4.23590 0.464951 0.232475 0.972602i \(-0.425318\pi\)
0.232475 + 0.972602i \(0.425318\pi\)
\(84\) 0 0
\(85\) 18.4696 2.00331
\(86\) 0 0
\(87\) 1.96919 0.211120
\(88\) 0 0
\(89\) 0.712086 0.0754809 0.0377405 0.999288i \(-0.487984\pi\)
0.0377405 + 0.999288i \(0.487984\pi\)
\(90\) 0 0
\(91\) 0.372702 0.0390698
\(92\) 0 0
\(93\) −9.78270 −1.01442
\(94\) 0 0
\(95\) −14.2627 −1.46332
\(96\) 0 0
\(97\) 5.75930 0.584769 0.292384 0.956301i \(-0.405551\pi\)
0.292384 + 0.956301i \(0.405551\pi\)
\(98\) 0 0
\(99\) 7.71878 0.775767
\(100\) 0 0
\(101\) 15.4644 1.53876 0.769381 0.638791i \(-0.220565\pi\)
0.769381 + 0.638791i \(0.220565\pi\)
\(102\) 0 0
\(103\) −8.14373 −0.802426 −0.401213 0.915985i \(-0.631411\pi\)
−0.401213 + 0.915985i \(0.631411\pi\)
\(104\) 0 0
\(105\) 0.875664 0.0854561
\(106\) 0 0
\(107\) 20.3670 1.96895 0.984475 0.175527i \(-0.0561631\pi\)
0.984475 + 0.175527i \(0.0561631\pi\)
\(108\) 0 0
\(109\) 8.19367 0.784811 0.392406 0.919792i \(-0.371643\pi\)
0.392406 + 0.919792i \(0.371643\pi\)
\(110\) 0 0
\(111\) 0.496614 0.0471365
\(112\) 0 0
\(113\) 2.82473 0.265728 0.132864 0.991134i \(-0.457583\pi\)
0.132864 + 0.991134i \(0.457583\pi\)
\(114\) 0 0
\(115\) −10.7726 −1.00455
\(116\) 0 0
\(117\) 2.15102 0.198862
\(118\) 0 0
\(119\) −2.43372 −0.223099
\(120\) 0 0
\(121\) 5.06798 0.460725
\(122\) 0 0
\(123\) 3.03665 0.273805
\(124\) 0 0
\(125\) −9.08687 −0.812754
\(126\) 0 0
\(127\) 16.6619 1.47851 0.739253 0.673428i \(-0.235179\pi\)
0.739253 + 0.673428i \(0.235179\pi\)
\(128\) 0 0
\(129\) 2.77036 0.243917
\(130\) 0 0
\(131\) 9.30397 0.812892 0.406446 0.913675i \(-0.366768\pi\)
0.406446 + 0.913675i \(0.366768\pi\)
\(132\) 0 0
\(133\) 1.87938 0.162963
\(134\) 0 0
\(135\) 12.9274 1.11262
\(136\) 0 0
\(137\) −1.24260 −0.106163 −0.0530814 0.998590i \(-0.516904\pi\)
−0.0530814 + 0.998590i \(0.516904\pi\)
\(138\) 0 0
\(139\) 2.75676 0.233826 0.116913 0.993142i \(-0.462700\pi\)
0.116913 + 0.993142i \(0.462700\pi\)
\(140\) 0 0
\(141\) 5.57691 0.469661
\(142\) 0 0
\(143\) 4.47773 0.374447
\(144\) 0 0
\(145\) −4.81037 −0.399480
\(146\) 0 0
\(147\) 7.14031 0.588923
\(148\) 0 0
\(149\) 16.3242 1.33733 0.668663 0.743565i \(-0.266867\pi\)
0.668663 + 0.743565i \(0.266867\pi\)
\(150\) 0 0
\(151\) 8.82551 0.718210 0.359105 0.933297i \(-0.383082\pi\)
0.359105 + 0.933297i \(0.383082\pi\)
\(152\) 0 0
\(153\) −14.0460 −1.13555
\(154\) 0 0
\(155\) 23.8973 1.91948
\(156\) 0 0
\(157\) −9.71273 −0.775160 −0.387580 0.921836i \(-0.626689\pi\)
−0.387580 + 0.921836i \(0.626689\pi\)
\(158\) 0 0
\(159\) −11.4788 −0.910328
\(160\) 0 0
\(161\) 1.41950 0.111872
\(162\) 0 0
\(163\) −18.7758 −1.47063 −0.735317 0.677723i \(-0.762967\pi\)
−0.735317 + 0.677723i \(0.762967\pi\)
\(164\) 0 0
\(165\) 10.5204 0.819014
\(166\) 0 0
\(167\) −24.4140 −1.88921 −0.944607 0.328202i \(-0.893557\pi\)
−0.944607 + 0.328202i \(0.893557\pi\)
\(168\) 0 0
\(169\) −11.7522 −0.904013
\(170\) 0 0
\(171\) 10.8467 0.829468
\(172\) 0 0
\(173\) −11.3839 −0.865505 −0.432753 0.901513i \(-0.642458\pi\)
−0.432753 + 0.901513i \(0.642458\pi\)
\(174\) 0 0
\(175\) −0.470858 −0.0355935
\(176\) 0 0
\(177\) −14.2764 −1.07308
\(178\) 0 0
\(179\) −3.39117 −0.253468 −0.126734 0.991937i \(-0.540449\pi\)
−0.126734 + 0.991937i \(0.540449\pi\)
\(180\) 0 0
\(181\) −16.5572 −1.23069 −0.615344 0.788259i \(-0.710983\pi\)
−0.615344 + 0.788259i \(0.710983\pi\)
\(182\) 0 0
\(183\) −9.92930 −0.733995
\(184\) 0 0
\(185\) −1.21314 −0.0891915
\(186\) 0 0
\(187\) −29.2392 −2.13819
\(188\) 0 0
\(189\) −1.70344 −0.123907
\(190\) 0 0
\(191\) 10.9196 0.790116 0.395058 0.918656i \(-0.370725\pi\)
0.395058 + 0.918656i \(0.370725\pi\)
\(192\) 0 0
\(193\) 14.3531 1.03316 0.516580 0.856239i \(-0.327205\pi\)
0.516580 + 0.856239i \(0.327205\pi\)
\(194\) 0 0
\(195\) 2.93177 0.209948
\(196\) 0 0
\(197\) 1.40276 0.0999423 0.0499712 0.998751i \(-0.484087\pi\)
0.0499712 + 0.998751i \(0.484087\pi\)
\(198\) 0 0
\(199\) 7.37657 0.522911 0.261455 0.965216i \(-0.415798\pi\)
0.261455 + 0.965216i \(0.415798\pi\)
\(200\) 0 0
\(201\) 10.2771 0.724894
\(202\) 0 0
\(203\) 0.633858 0.0444881
\(204\) 0 0
\(205\) −7.41796 −0.518093
\(206\) 0 0
\(207\) 8.19252 0.569420
\(208\) 0 0
\(209\) 22.5793 1.56184
\(210\) 0 0
\(211\) 13.8794 0.955499 0.477750 0.878496i \(-0.341453\pi\)
0.477750 + 0.878496i \(0.341453\pi\)
\(212\) 0 0
\(213\) 12.6807 0.868869
\(214\) 0 0
\(215\) −6.76748 −0.461538
\(216\) 0 0
\(217\) −3.14893 −0.213763
\(218\) 0 0
\(219\) −11.7243 −0.792257
\(220\) 0 0
\(221\) −8.14822 −0.548109
\(222\) 0 0
\(223\) −11.2011 −0.750082 −0.375041 0.927008i \(-0.622371\pi\)
−0.375041 + 0.927008i \(0.622371\pi\)
\(224\) 0 0
\(225\) −2.71752 −0.181168
\(226\) 0 0
\(227\) 26.6371 1.76797 0.883985 0.467516i \(-0.154851\pi\)
0.883985 + 0.467516i \(0.154851\pi\)
\(228\) 0 0
\(229\) 17.0506 1.12673 0.563367 0.826207i \(-0.309506\pi\)
0.563367 + 0.826207i \(0.309506\pi\)
\(230\) 0 0
\(231\) −1.38627 −0.0912096
\(232\) 0 0
\(233\) −16.6402 −1.09013 −0.545067 0.838393i \(-0.683496\pi\)
−0.545067 + 0.838393i \(0.683496\pi\)
\(234\) 0 0
\(235\) −13.6234 −0.888690
\(236\) 0 0
\(237\) −8.39364 −0.545226
\(238\) 0 0
\(239\) 4.49038 0.290459 0.145229 0.989398i \(-0.453608\pi\)
0.145229 + 0.989398i \(0.453608\pi\)
\(240\) 0 0
\(241\) −5.12770 −0.330304 −0.165152 0.986268i \(-0.552812\pi\)
−0.165152 + 0.986268i \(0.552812\pi\)
\(242\) 0 0
\(243\) −15.8191 −1.01480
\(244\) 0 0
\(245\) −17.4425 −1.11436
\(246\) 0 0
\(247\) 6.29226 0.400367
\(248\) 0 0
\(249\) −4.39063 −0.278245
\(250\) 0 0
\(251\) 21.6896 1.36903 0.684517 0.728997i \(-0.260013\pi\)
0.684517 + 0.728997i \(0.260013\pi\)
\(252\) 0 0
\(253\) 17.0541 1.07219
\(254\) 0 0
\(255\) −19.1442 −1.19886
\(256\) 0 0
\(257\) −12.7772 −0.797019 −0.398510 0.917164i \(-0.630472\pi\)
−0.398510 + 0.917164i \(0.630472\pi\)
\(258\) 0 0
\(259\) 0.159854 0.00993283
\(260\) 0 0
\(261\) 3.65827 0.226441
\(262\) 0 0
\(263\) −4.02954 −0.248472 −0.124236 0.992253i \(-0.539648\pi\)
−0.124236 + 0.992253i \(0.539648\pi\)
\(264\) 0 0
\(265\) 28.0406 1.72252
\(266\) 0 0
\(267\) −0.738097 −0.0451708
\(268\) 0 0
\(269\) −21.8554 −1.33254 −0.666272 0.745709i \(-0.732111\pi\)
−0.666272 + 0.745709i \(0.732111\pi\)
\(270\) 0 0
\(271\) −6.58932 −0.400273 −0.200136 0.979768i \(-0.564139\pi\)
−0.200136 + 0.979768i \(0.564139\pi\)
\(272\) 0 0
\(273\) −0.386317 −0.0233809
\(274\) 0 0
\(275\) −5.65699 −0.341129
\(276\) 0 0
\(277\) 18.7032 1.12377 0.561884 0.827216i \(-0.310077\pi\)
0.561884 + 0.827216i \(0.310077\pi\)
\(278\) 0 0
\(279\) −18.1738 −1.08804
\(280\) 0 0
\(281\) 22.1897 1.32373 0.661863 0.749625i \(-0.269766\pi\)
0.661863 + 0.749625i \(0.269766\pi\)
\(282\) 0 0
\(283\) −11.2094 −0.666328 −0.333164 0.942869i \(-0.608116\pi\)
−0.333164 + 0.942869i \(0.608116\pi\)
\(284\) 0 0
\(285\) 14.7837 0.875709
\(286\) 0 0
\(287\) 0.977458 0.0576975
\(288\) 0 0
\(289\) 36.2073 2.12984
\(290\) 0 0
\(291\) −5.96968 −0.349949
\(292\) 0 0
\(293\) 12.8818 0.752564 0.376282 0.926505i \(-0.377202\pi\)
0.376282 + 0.926505i \(0.377202\pi\)
\(294\) 0 0
\(295\) 34.8746 2.03048
\(296\) 0 0
\(297\) −20.4655 −1.18753
\(298\) 0 0
\(299\) 4.75255 0.274847
\(300\) 0 0
\(301\) 0.891745 0.0513993
\(302\) 0 0
\(303\) −16.0292 −0.920856
\(304\) 0 0
\(305\) 24.2554 1.38886
\(306\) 0 0
\(307\) 19.4035 1.10741 0.553707 0.832711i \(-0.313213\pi\)
0.553707 + 0.832711i \(0.313213\pi\)
\(308\) 0 0
\(309\) 8.44121 0.480204
\(310\) 0 0
\(311\) 20.6297 1.16980 0.584901 0.811104i \(-0.301133\pi\)
0.584901 + 0.811104i \(0.301133\pi\)
\(312\) 0 0
\(313\) 23.7872 1.34453 0.672266 0.740310i \(-0.265321\pi\)
0.672266 + 0.740310i \(0.265321\pi\)
\(314\) 0 0
\(315\) 1.62676 0.0916578
\(316\) 0 0
\(317\) 27.4129 1.53966 0.769831 0.638248i \(-0.220341\pi\)
0.769831 + 0.638248i \(0.220341\pi\)
\(318\) 0 0
\(319\) 7.61532 0.426376
\(320\) 0 0
\(321\) −21.1109 −1.17830
\(322\) 0 0
\(323\) −41.0880 −2.28620
\(324\) 0 0
\(325\) −1.57646 −0.0874461
\(326\) 0 0
\(327\) −8.49297 −0.469662
\(328\) 0 0
\(329\) 1.79514 0.0989691
\(330\) 0 0
\(331\) −21.3830 −1.17532 −0.587658 0.809110i \(-0.699950\pi\)
−0.587658 + 0.809110i \(0.699950\pi\)
\(332\) 0 0
\(333\) 0.922584 0.0505573
\(334\) 0 0
\(335\) −25.1052 −1.37164
\(336\) 0 0
\(337\) 8.03958 0.437944 0.218972 0.975731i \(-0.429730\pi\)
0.218972 + 0.975731i \(0.429730\pi\)
\(338\) 0 0
\(339\) −2.92791 −0.159022
\(340\) 0 0
\(341\) −37.8319 −2.04871
\(342\) 0 0
\(343\) 4.63389 0.250207
\(344\) 0 0
\(345\) 11.1661 0.601163
\(346\) 0 0
\(347\) −3.40048 −0.182547 −0.0912737 0.995826i \(-0.529094\pi\)
−0.0912737 + 0.995826i \(0.529094\pi\)
\(348\) 0 0
\(349\) 8.80924 0.471548 0.235774 0.971808i \(-0.424238\pi\)
0.235774 + 0.971808i \(0.424238\pi\)
\(350\) 0 0
\(351\) −5.70320 −0.304414
\(352\) 0 0
\(353\) 21.4924 1.14393 0.571963 0.820280i \(-0.306182\pi\)
0.571963 + 0.820280i \(0.306182\pi\)
\(354\) 0 0
\(355\) −30.9766 −1.64407
\(356\) 0 0
\(357\) 2.52262 0.133511
\(358\) 0 0
\(359\) 15.6038 0.823537 0.411769 0.911288i \(-0.364911\pi\)
0.411769 + 0.911288i \(0.364911\pi\)
\(360\) 0 0
\(361\) 12.7292 0.669958
\(362\) 0 0
\(363\) −5.25310 −0.275716
\(364\) 0 0
\(365\) 28.6403 1.49910
\(366\) 0 0
\(367\) −20.1545 −1.05206 −0.526028 0.850467i \(-0.676319\pi\)
−0.526028 + 0.850467i \(0.676319\pi\)
\(368\) 0 0
\(369\) 5.64133 0.293676
\(370\) 0 0
\(371\) −3.69488 −0.191829
\(372\) 0 0
\(373\) −35.8287 −1.85514 −0.927570 0.373649i \(-0.878107\pi\)
−0.927570 + 0.373649i \(0.878107\pi\)
\(374\) 0 0
\(375\) 9.41880 0.486385
\(376\) 0 0
\(377\) 2.12219 0.109298
\(378\) 0 0
\(379\) 4.98404 0.256013 0.128007 0.991773i \(-0.459142\pi\)
0.128007 + 0.991773i \(0.459142\pi\)
\(380\) 0 0
\(381\) −17.2705 −0.884797
\(382\) 0 0
\(383\) −10.5401 −0.538572 −0.269286 0.963060i \(-0.586788\pi\)
−0.269286 + 0.963060i \(0.586788\pi\)
\(384\) 0 0
\(385\) 3.38639 0.172586
\(386\) 0 0
\(387\) 5.14664 0.261618
\(388\) 0 0
\(389\) −13.0652 −0.662432 −0.331216 0.943555i \(-0.607459\pi\)
−0.331216 + 0.943555i \(0.607459\pi\)
\(390\) 0 0
\(391\) −31.0338 −1.56945
\(392\) 0 0
\(393\) −9.64383 −0.486467
\(394\) 0 0
\(395\) 20.5041 1.03167
\(396\) 0 0
\(397\) 31.1313 1.56244 0.781218 0.624259i \(-0.214599\pi\)
0.781218 + 0.624259i \(0.214599\pi\)
\(398\) 0 0
\(399\) −1.94803 −0.0975235
\(400\) 0 0
\(401\) −19.0218 −0.949904 −0.474952 0.880012i \(-0.657535\pi\)
−0.474952 + 0.880012i \(0.657535\pi\)
\(402\) 0 0
\(403\) −10.5428 −0.525173
\(404\) 0 0
\(405\) 1.22753 0.0609966
\(406\) 0 0
\(407\) 1.92052 0.0951965
\(408\) 0 0
\(409\) −14.4726 −0.715624 −0.357812 0.933794i \(-0.616477\pi\)
−0.357812 + 0.933794i \(0.616477\pi\)
\(410\) 0 0
\(411\) 1.28799 0.0635320
\(412\) 0 0
\(413\) −4.59539 −0.226124
\(414\) 0 0
\(415\) 10.7255 0.526494
\(416\) 0 0
\(417\) −2.85746 −0.139930
\(418\) 0 0
\(419\) 22.5646 1.10235 0.551177 0.834388i \(-0.314179\pi\)
0.551177 + 0.834388i \(0.314179\pi\)
\(420\) 0 0
\(421\) −23.5020 −1.14542 −0.572709 0.819759i \(-0.694108\pi\)
−0.572709 + 0.819759i \(0.694108\pi\)
\(422\) 0 0
\(423\) 10.3605 0.503745
\(424\) 0 0
\(425\) 10.2941 0.499340
\(426\) 0 0
\(427\) −3.19612 −0.154671
\(428\) 0 0
\(429\) −4.64129 −0.224084
\(430\) 0 0
\(431\) 11.6189 0.559664 0.279832 0.960049i \(-0.409721\pi\)
0.279832 + 0.960049i \(0.409721\pi\)
\(432\) 0 0
\(433\) 16.8523 0.809869 0.404934 0.914346i \(-0.367294\pi\)
0.404934 + 0.914346i \(0.367294\pi\)
\(434\) 0 0
\(435\) 4.98609 0.239065
\(436\) 0 0
\(437\) 23.9651 1.14641
\(438\) 0 0
\(439\) −32.6896 −1.56019 −0.780096 0.625660i \(-0.784830\pi\)
−0.780096 + 0.625660i \(0.784830\pi\)
\(440\) 0 0
\(441\) 13.2649 0.631662
\(442\) 0 0
\(443\) 14.7830 0.702360 0.351180 0.936308i \(-0.385781\pi\)
0.351180 + 0.936308i \(0.385781\pi\)
\(444\) 0 0
\(445\) 1.80303 0.0854720
\(446\) 0 0
\(447\) −16.9204 −0.800310
\(448\) 0 0
\(449\) 21.6703 1.02269 0.511343 0.859377i \(-0.329148\pi\)
0.511343 + 0.859377i \(0.329148\pi\)
\(450\) 0 0
\(451\) 11.7434 0.552975
\(452\) 0 0
\(453\) −9.14789 −0.429805
\(454\) 0 0
\(455\) 0.943700 0.0442413
\(456\) 0 0
\(457\) 28.1372 1.31620 0.658101 0.752929i \(-0.271360\pi\)
0.658101 + 0.752929i \(0.271360\pi\)
\(458\) 0 0
\(459\) 37.2415 1.73828
\(460\) 0 0
\(461\) −16.4770 −0.767409 −0.383705 0.923456i \(-0.625352\pi\)
−0.383705 + 0.923456i \(0.625352\pi\)
\(462\) 0 0
\(463\) −36.2859 −1.68635 −0.843174 0.537641i \(-0.819315\pi\)
−0.843174 + 0.537641i \(0.819315\pi\)
\(464\) 0 0
\(465\) −24.7702 −1.14869
\(466\) 0 0
\(467\) −9.94066 −0.459999 −0.229999 0.973191i \(-0.573872\pi\)
−0.229999 + 0.973191i \(0.573872\pi\)
\(468\) 0 0
\(469\) 3.30808 0.152753
\(470\) 0 0
\(471\) 10.0675 0.463887
\(472\) 0 0
\(473\) 10.7136 0.492613
\(474\) 0 0
\(475\) −7.94940 −0.364744
\(476\) 0 0
\(477\) −21.3247 −0.976392
\(478\) 0 0
\(479\) −12.1853 −0.556762 −0.278381 0.960471i \(-0.589798\pi\)
−0.278381 + 0.960471i \(0.589798\pi\)
\(480\) 0 0
\(481\) 0.535199 0.0244030
\(482\) 0 0
\(483\) −1.47135 −0.0669487
\(484\) 0 0
\(485\) 14.5828 0.662172
\(486\) 0 0
\(487\) 23.6953 1.07374 0.536869 0.843666i \(-0.319607\pi\)
0.536869 + 0.843666i \(0.319607\pi\)
\(488\) 0 0
\(489\) 19.4617 0.880087
\(490\) 0 0
\(491\) 27.3741 1.23537 0.617687 0.786424i \(-0.288070\pi\)
0.617687 + 0.786424i \(0.288070\pi\)
\(492\) 0 0
\(493\) −13.8578 −0.624122
\(494\) 0 0
\(495\) 19.5443 0.878451
\(496\) 0 0
\(497\) 4.08176 0.183092
\(498\) 0 0
\(499\) −6.41437 −0.287146 −0.143573 0.989640i \(-0.545859\pi\)
−0.143573 + 0.989640i \(0.545859\pi\)
\(500\) 0 0
\(501\) 25.3058 1.13058
\(502\) 0 0
\(503\) 5.49851 0.245167 0.122583 0.992458i \(-0.460882\pi\)
0.122583 + 0.992458i \(0.460882\pi\)
\(504\) 0 0
\(505\) 39.1565 1.74244
\(506\) 0 0
\(507\) 12.1815 0.540998
\(508\) 0 0
\(509\) −18.8142 −0.833924 −0.416962 0.908924i \(-0.636905\pi\)
−0.416962 + 0.908924i \(0.636905\pi\)
\(510\) 0 0
\(511\) −3.77391 −0.166948
\(512\) 0 0
\(513\) −28.7588 −1.26973
\(514\) 0 0
\(515\) −20.6203 −0.908639
\(516\) 0 0
\(517\) 21.5672 0.948523
\(518\) 0 0
\(519\) 11.7998 0.517953
\(520\) 0 0
\(521\) −8.75170 −0.383419 −0.191709 0.981452i \(-0.561403\pi\)
−0.191709 + 0.981452i \(0.561403\pi\)
\(522\) 0 0
\(523\) 22.4680 0.982458 0.491229 0.871030i \(-0.336548\pi\)
0.491229 + 0.871030i \(0.336548\pi\)
\(524\) 0 0
\(525\) 0.488057 0.0213006
\(526\) 0 0
\(527\) 68.8435 2.99887
\(528\) 0 0
\(529\) −4.89916 −0.213007
\(530\) 0 0
\(531\) −26.5220 −1.15095
\(532\) 0 0
\(533\) 3.27258 0.141751
\(534\) 0 0
\(535\) 51.5701 2.22957
\(536\) 0 0
\(537\) 3.51505 0.151685
\(538\) 0 0
\(539\) 27.6132 1.18938
\(540\) 0 0
\(541\) 29.1157 1.25178 0.625891 0.779910i \(-0.284735\pi\)
0.625891 + 0.779910i \(0.284735\pi\)
\(542\) 0 0
\(543\) 17.1620 0.736493
\(544\) 0 0
\(545\) 20.7467 0.888693
\(546\) 0 0
\(547\) 45.9869 1.96626 0.983128 0.182919i \(-0.0585547\pi\)
0.983128 + 0.182919i \(0.0585547\pi\)
\(548\) 0 0
\(549\) −18.4461 −0.787262
\(550\) 0 0
\(551\) 10.7013 0.455891
\(552\) 0 0
\(553\) −2.70181 −0.114893
\(554\) 0 0
\(555\) 1.25745 0.0533757
\(556\) 0 0
\(557\) 21.3860 0.906153 0.453076 0.891472i \(-0.350326\pi\)
0.453076 + 0.891472i \(0.350326\pi\)
\(558\) 0 0
\(559\) 2.98561 0.126278
\(560\) 0 0
\(561\) 30.3073 1.27958
\(562\) 0 0
\(563\) −36.3102 −1.53029 −0.765146 0.643856i \(-0.777333\pi\)
−0.765146 + 0.643856i \(0.777333\pi\)
\(564\) 0 0
\(565\) 7.15233 0.300901
\(566\) 0 0
\(567\) −0.161751 −0.00679289
\(568\) 0 0
\(569\) 32.9668 1.38204 0.691020 0.722836i \(-0.257162\pi\)
0.691020 + 0.722836i \(0.257162\pi\)
\(570\) 0 0
\(571\) 31.6514 1.32457 0.662284 0.749253i \(-0.269587\pi\)
0.662284 + 0.749253i \(0.269587\pi\)
\(572\) 0 0
\(573\) −11.3185 −0.472837
\(574\) 0 0
\(575\) −6.00419 −0.250392
\(576\) 0 0
\(577\) 41.4459 1.72542 0.862709 0.505701i \(-0.168766\pi\)
0.862709 + 0.505701i \(0.168766\pi\)
\(578\) 0 0
\(579\) −14.8774 −0.618284
\(580\) 0 0
\(581\) −1.41329 −0.0586331
\(582\) 0 0
\(583\) −44.3911 −1.83849
\(584\) 0 0
\(585\) 5.44649 0.225185
\(586\) 0 0
\(587\) −25.6584 −1.05903 −0.529517 0.848299i \(-0.677627\pi\)
−0.529517 + 0.848299i \(0.677627\pi\)
\(588\) 0 0
\(589\) −53.1627 −2.19053
\(590\) 0 0
\(591\) −1.45400 −0.0598095
\(592\) 0 0
\(593\) −18.7863 −0.771460 −0.385730 0.922612i \(-0.626050\pi\)
−0.385730 + 0.922612i \(0.626050\pi\)
\(594\) 0 0
\(595\) −6.16229 −0.252629
\(596\) 0 0
\(597\) −7.64602 −0.312931
\(598\) 0 0
\(599\) 27.4579 1.12190 0.560950 0.827850i \(-0.310436\pi\)
0.560950 + 0.827850i \(0.310436\pi\)
\(600\) 0 0
\(601\) 3.60426 0.147021 0.0735105 0.997294i \(-0.476580\pi\)
0.0735105 + 0.997294i \(0.476580\pi\)
\(602\) 0 0
\(603\) 19.0924 0.777501
\(604\) 0 0
\(605\) 12.8324 0.521709
\(606\) 0 0
\(607\) −23.2924 −0.945410 −0.472705 0.881221i \(-0.656722\pi\)
−0.472705 + 0.881221i \(0.656722\pi\)
\(608\) 0 0
\(609\) −0.657012 −0.0266235
\(610\) 0 0
\(611\) 6.01022 0.243147
\(612\) 0 0
\(613\) 11.5942 0.468284 0.234142 0.972202i \(-0.424772\pi\)
0.234142 + 0.972202i \(0.424772\pi\)
\(614\) 0 0
\(615\) 7.68893 0.310048
\(616\) 0 0
\(617\) −18.3176 −0.737438 −0.368719 0.929541i \(-0.620204\pi\)
−0.368719 + 0.929541i \(0.620204\pi\)
\(618\) 0 0
\(619\) 23.9145 0.961206 0.480603 0.876938i \(-0.340418\pi\)
0.480603 + 0.876938i \(0.340418\pi\)
\(620\) 0 0
\(621\) −21.7215 −0.871655
\(622\) 0 0
\(623\) −0.237584 −0.00951860
\(624\) 0 0
\(625\) −30.0646 −1.20259
\(626\) 0 0
\(627\) −23.4041 −0.934668
\(628\) 0 0
\(629\) −3.49481 −0.139347
\(630\) 0 0
\(631\) −5.59809 −0.222857 −0.111428 0.993772i \(-0.535543\pi\)
−0.111428 + 0.993772i \(0.535543\pi\)
\(632\) 0 0
\(633\) −14.3864 −0.571809
\(634\) 0 0
\(635\) 42.1887 1.67421
\(636\) 0 0
\(637\) 7.69508 0.304890
\(638\) 0 0
\(639\) 23.5576 0.931924
\(640\) 0 0
\(641\) 27.4040 1.08239 0.541197 0.840896i \(-0.317971\pi\)
0.541197 + 0.840896i \(0.317971\pi\)
\(642\) 0 0
\(643\) 13.7877 0.543735 0.271868 0.962335i \(-0.412359\pi\)
0.271868 + 0.962335i \(0.412359\pi\)
\(644\) 0 0
\(645\) 7.01468 0.276203
\(646\) 0 0
\(647\) −36.5366 −1.43640 −0.718200 0.695837i \(-0.755034\pi\)
−0.718200 + 0.695837i \(0.755034\pi\)
\(648\) 0 0
\(649\) −55.2100 −2.16718
\(650\) 0 0
\(651\) 3.26395 0.127924
\(652\) 0 0
\(653\) 43.3663 1.69706 0.848528 0.529151i \(-0.177489\pi\)
0.848528 + 0.529151i \(0.177489\pi\)
\(654\) 0 0
\(655\) 23.5581 0.920490
\(656\) 0 0
\(657\) −21.7809 −0.849752
\(658\) 0 0
\(659\) 2.56728 0.100007 0.0500035 0.998749i \(-0.484077\pi\)
0.0500035 + 0.998749i \(0.484077\pi\)
\(660\) 0 0
\(661\) 6.35014 0.246992 0.123496 0.992345i \(-0.460589\pi\)
0.123496 + 0.992345i \(0.460589\pi\)
\(662\) 0 0
\(663\) 8.44586 0.328010
\(664\) 0 0
\(665\) 4.75867 0.184533
\(666\) 0 0
\(667\) 8.08270 0.312964
\(668\) 0 0
\(669\) 11.6103 0.448879
\(670\) 0 0
\(671\) −38.3988 −1.48237
\(672\) 0 0
\(673\) −43.6943 −1.68429 −0.842147 0.539248i \(-0.818708\pi\)
−0.842147 + 0.539248i \(0.818708\pi\)
\(674\) 0 0
\(675\) 7.20520 0.277328
\(676\) 0 0
\(677\) −26.6785 −1.02534 −0.512669 0.858586i \(-0.671343\pi\)
−0.512669 + 0.858586i \(0.671343\pi\)
\(678\) 0 0
\(679\) −1.92156 −0.0737429
\(680\) 0 0
\(681\) −27.6102 −1.05802
\(682\) 0 0
\(683\) −36.1599 −1.38362 −0.691811 0.722079i \(-0.743187\pi\)
−0.691811 + 0.722079i \(0.743187\pi\)
\(684\) 0 0
\(685\) −3.14633 −0.120215
\(686\) 0 0
\(687\) −17.6734 −0.674282
\(688\) 0 0
\(689\) −12.3706 −0.471284
\(690\) 0 0
\(691\) 23.9787 0.912191 0.456095 0.889931i \(-0.349248\pi\)
0.456095 + 0.889931i \(0.349248\pi\)
\(692\) 0 0
\(693\) −2.57534 −0.0978289
\(694\) 0 0
\(695\) 6.98025 0.264776
\(696\) 0 0
\(697\) −21.3697 −0.809436
\(698\) 0 0
\(699\) 17.2480 0.652379
\(700\) 0 0
\(701\) 21.5218 0.812866 0.406433 0.913681i \(-0.366772\pi\)
0.406433 + 0.913681i \(0.366772\pi\)
\(702\) 0 0
\(703\) 2.69878 0.101786
\(704\) 0 0
\(705\) 14.1210 0.531827
\(706\) 0 0
\(707\) −5.15961 −0.194047
\(708\) 0 0
\(709\) −48.1227 −1.80729 −0.903643 0.428287i \(-0.859117\pi\)
−0.903643 + 0.428287i \(0.859117\pi\)
\(710\) 0 0
\(711\) −15.5933 −0.584794
\(712\) 0 0
\(713\) −40.1538 −1.50377
\(714\) 0 0
\(715\) 11.3378 0.424010
\(716\) 0 0
\(717\) −4.65441 −0.173822
\(718\) 0 0
\(719\) −26.6998 −0.995736 −0.497868 0.867253i \(-0.665884\pi\)
−0.497868 + 0.867253i \(0.665884\pi\)
\(720\) 0 0
\(721\) 2.71712 0.101191
\(722\) 0 0
\(723\) 5.31501 0.197667
\(724\) 0 0
\(725\) −2.68109 −0.0995733
\(726\) 0 0
\(727\) 45.3867 1.68330 0.841651 0.540023i \(-0.181584\pi\)
0.841651 + 0.540023i \(0.181584\pi\)
\(728\) 0 0
\(729\) 14.9426 0.553428
\(730\) 0 0
\(731\) −19.4958 −0.721078
\(732\) 0 0
\(733\) 27.2436 1.00627 0.503133 0.864209i \(-0.332180\pi\)
0.503133 + 0.864209i \(0.332180\pi\)
\(734\) 0 0
\(735\) 18.0796 0.666876
\(736\) 0 0
\(737\) 39.7441 1.46399
\(738\) 0 0
\(739\) −29.6122 −1.08930 −0.544651 0.838663i \(-0.683338\pi\)
−0.544651 + 0.838663i \(0.683338\pi\)
\(740\) 0 0
\(741\) −6.52211 −0.239596
\(742\) 0 0
\(743\) −5.94812 −0.218215 −0.109108 0.994030i \(-0.534799\pi\)
−0.109108 + 0.994030i \(0.534799\pi\)
\(744\) 0 0
\(745\) 41.3335 1.51434
\(746\) 0 0
\(747\) −8.15669 −0.298438
\(748\) 0 0
\(749\) −6.79534 −0.248296
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −22.4819 −0.819284
\(754\) 0 0
\(755\) 22.3466 0.813276
\(756\) 0 0
\(757\) 7.16070 0.260260 0.130130 0.991497i \(-0.458460\pi\)
0.130130 + 0.991497i \(0.458460\pi\)
\(758\) 0 0
\(759\) −17.6771 −0.641638
\(760\) 0 0
\(761\) 8.61876 0.312430 0.156215 0.987723i \(-0.450071\pi\)
0.156215 + 0.987723i \(0.450071\pi\)
\(762\) 0 0
\(763\) −2.73378 −0.0989695
\(764\) 0 0
\(765\) −35.5652 −1.28586
\(766\) 0 0
\(767\) −15.3856 −0.555542
\(768\) 0 0
\(769\) 22.7333 0.819785 0.409892 0.912134i \(-0.365566\pi\)
0.409892 + 0.912134i \(0.365566\pi\)
\(770\) 0 0
\(771\) 13.2439 0.476968
\(772\) 0 0
\(773\) 22.2371 0.799812 0.399906 0.916556i \(-0.369043\pi\)
0.399906 + 0.916556i \(0.369043\pi\)
\(774\) 0 0
\(775\) 13.3193 0.478445
\(776\) 0 0
\(777\) −0.165693 −0.00594420
\(778\) 0 0
\(779\) 16.5022 0.591254
\(780\) 0 0
\(781\) 49.0392 1.75476
\(782\) 0 0
\(783\) −9.69948 −0.346631
\(784\) 0 0
\(785\) −24.5931 −0.877764
\(786\) 0 0
\(787\) 30.5341 1.08842 0.544212 0.838948i \(-0.316829\pi\)
0.544212 + 0.838948i \(0.316829\pi\)
\(788\) 0 0
\(789\) 4.17673 0.148696
\(790\) 0 0
\(791\) −0.942457 −0.0335099
\(792\) 0 0
\(793\) −10.7008 −0.379995
\(794\) 0 0
\(795\) −29.0648 −1.03082
\(796\) 0 0
\(797\) 14.0680 0.498314 0.249157 0.968463i \(-0.419846\pi\)
0.249157 + 0.968463i \(0.419846\pi\)
\(798\) 0 0
\(799\) −39.2463 −1.38843
\(800\) 0 0
\(801\) −1.37120 −0.0484489
\(802\) 0 0
\(803\) −45.3406 −1.60004
\(804\) 0 0
\(805\) 3.59423 0.126680
\(806\) 0 0
\(807\) 22.6537 0.797448
\(808\) 0 0
\(809\) −6.60709 −0.232293 −0.116147 0.993232i \(-0.537054\pi\)
−0.116147 + 0.993232i \(0.537054\pi\)
\(810\) 0 0
\(811\) −8.83123 −0.310106 −0.155053 0.987906i \(-0.549555\pi\)
−0.155053 + 0.987906i \(0.549555\pi\)
\(812\) 0 0
\(813\) 6.83002 0.239539
\(814\) 0 0
\(815\) −47.5412 −1.66530
\(816\) 0 0
\(817\) 15.0551 0.526713
\(818\) 0 0
\(819\) −0.717679 −0.0250777
\(820\) 0 0
\(821\) −33.7581 −1.17816 −0.589082 0.808073i \(-0.700511\pi\)
−0.589082 + 0.808073i \(0.700511\pi\)
\(822\) 0 0
\(823\) 28.8890 1.00701 0.503504 0.863993i \(-0.332044\pi\)
0.503504 + 0.863993i \(0.332044\pi\)
\(824\) 0 0
\(825\) 5.86363 0.204145
\(826\) 0 0
\(827\) 29.2028 1.01548 0.507740 0.861511i \(-0.330481\pi\)
0.507740 + 0.861511i \(0.330481\pi\)
\(828\) 0 0
\(829\) 33.0765 1.14879 0.574396 0.818577i \(-0.305237\pi\)
0.574396 + 0.818577i \(0.305237\pi\)
\(830\) 0 0
\(831\) −19.3864 −0.672507
\(832\) 0 0
\(833\) −50.2483 −1.74100
\(834\) 0 0
\(835\) −61.8174 −2.13928
\(836\) 0 0
\(837\) 48.1858 1.66554
\(838\) 0 0
\(839\) 25.6450 0.885362 0.442681 0.896679i \(-0.354027\pi\)
0.442681 + 0.896679i \(0.354027\pi\)
\(840\) 0 0
\(841\) −25.3908 −0.875544
\(842\) 0 0
\(843\) −23.0002 −0.792170
\(844\) 0 0
\(845\) −29.7570 −1.02367
\(846\) 0 0
\(847\) −1.69091 −0.0581003
\(848\) 0 0
\(849\) 11.6188 0.398757
\(850\) 0 0
\(851\) 2.03839 0.0698751
\(852\) 0 0
\(853\) −14.8656 −0.508988 −0.254494 0.967074i \(-0.581909\pi\)
−0.254494 + 0.967074i \(0.581909\pi\)
\(854\) 0 0
\(855\) 27.4643 0.939261
\(856\) 0 0
\(857\) 3.29898 0.112691 0.0563455 0.998411i \(-0.482055\pi\)
0.0563455 + 0.998411i \(0.482055\pi\)
\(858\) 0 0
\(859\) −39.6126 −1.35157 −0.675783 0.737101i \(-0.736194\pi\)
−0.675783 + 0.737101i \(0.736194\pi\)
\(860\) 0 0
\(861\) −1.01316 −0.0345285
\(862\) 0 0
\(863\) −18.4041 −0.626481 −0.313241 0.949674i \(-0.601415\pi\)
−0.313241 + 0.949674i \(0.601415\pi\)
\(864\) 0 0
\(865\) −28.8247 −0.980068
\(866\) 0 0
\(867\) −37.5299 −1.27458
\(868\) 0 0
\(869\) −32.4601 −1.10113
\(870\) 0 0
\(871\) 11.0756 0.375284
\(872\) 0 0
\(873\) −11.0902 −0.375345
\(874\) 0 0
\(875\) 3.03179 0.102493
\(876\) 0 0
\(877\) −40.4029 −1.36431 −0.682154 0.731208i \(-0.738957\pi\)
−0.682154 + 0.731208i \(0.738957\pi\)
\(878\) 0 0
\(879\) −13.3524 −0.450365
\(880\) 0 0
\(881\) −31.4302 −1.05891 −0.529455 0.848338i \(-0.677603\pi\)
−0.529455 + 0.848338i \(0.677603\pi\)
\(882\) 0 0
\(883\) 11.3012 0.380316 0.190158 0.981753i \(-0.439100\pi\)
0.190158 + 0.981753i \(0.439100\pi\)
\(884\) 0 0
\(885\) −36.1485 −1.21512
\(886\) 0 0
\(887\) −25.1227 −0.843536 −0.421768 0.906704i \(-0.638590\pi\)
−0.421768 + 0.906704i \(0.638590\pi\)
\(888\) 0 0
\(889\) −5.55917 −0.186449
\(890\) 0 0
\(891\) −1.94331 −0.0651033
\(892\) 0 0
\(893\) 30.3070 1.01418
\(894\) 0 0
\(895\) −8.58661 −0.287019
\(896\) 0 0
\(897\) −4.92615 −0.164479
\(898\) 0 0
\(899\) −17.9302 −0.598005
\(900\) 0 0
\(901\) 80.7794 2.69115
\(902\) 0 0
\(903\) −0.924319 −0.0307594
\(904\) 0 0
\(905\) −41.9236 −1.39359
\(906\) 0 0
\(907\) −23.0128 −0.764127 −0.382063 0.924136i \(-0.624786\pi\)
−0.382063 + 0.924136i \(0.624786\pi\)
\(908\) 0 0
\(909\) −29.7783 −0.987684
\(910\) 0 0
\(911\) 9.07981 0.300828 0.150414 0.988623i \(-0.451939\pi\)
0.150414 + 0.988623i \(0.451939\pi\)
\(912\) 0 0
\(913\) −16.9796 −0.561942
\(914\) 0 0
\(915\) −25.1414 −0.831150
\(916\) 0 0
\(917\) −3.10423 −0.102511
\(918\) 0 0
\(919\) −27.4842 −0.906621 −0.453310 0.891353i \(-0.649757\pi\)
−0.453310 + 0.891353i \(0.649757\pi\)
\(920\) 0 0
\(921\) −20.1122 −0.662721
\(922\) 0 0
\(923\) 13.6660 0.449820
\(924\) 0 0
\(925\) −0.676149 −0.0222317
\(926\) 0 0
\(927\) 15.6816 0.515053
\(928\) 0 0
\(929\) 53.6788 1.76115 0.880573 0.473911i \(-0.157158\pi\)
0.880573 + 0.473911i \(0.157158\pi\)
\(930\) 0 0
\(931\) 38.8030 1.27172
\(932\) 0 0
\(933\) −21.3833 −0.700057
\(934\) 0 0
\(935\) −74.0351 −2.42121
\(936\) 0 0
\(937\) 4.32473 0.141283 0.0706414 0.997502i \(-0.477495\pi\)
0.0706414 + 0.997502i \(0.477495\pi\)
\(938\) 0 0
\(939\) −24.6561 −0.804621
\(940\) 0 0
\(941\) −21.3622 −0.696386 −0.348193 0.937423i \(-0.613205\pi\)
−0.348193 + 0.937423i \(0.613205\pi\)
\(942\) 0 0
\(943\) 12.4642 0.405889
\(944\) 0 0
\(945\) −4.31318 −0.140308
\(946\) 0 0
\(947\) −26.8998 −0.874126 −0.437063 0.899431i \(-0.643981\pi\)
−0.437063 + 0.899431i \(0.643981\pi\)
\(948\) 0 0
\(949\) −12.6353 −0.410158
\(950\) 0 0
\(951\) −28.4142 −0.921395
\(952\) 0 0
\(953\) −56.9505 −1.84481 −0.922404 0.386228i \(-0.873778\pi\)
−0.922404 + 0.386228i \(0.873778\pi\)
\(954\) 0 0
\(955\) 27.6490 0.894699
\(956\) 0 0
\(957\) −7.89349 −0.255160
\(958\) 0 0
\(959\) 0.414589 0.0133878
\(960\) 0 0
\(961\) 58.0749 1.87338
\(962\) 0 0
\(963\) −39.2188 −1.26381
\(964\) 0 0
\(965\) 36.3428 1.16991
\(966\) 0 0
\(967\) −20.2950 −0.652642 −0.326321 0.945259i \(-0.605809\pi\)
−0.326321 + 0.945259i \(0.605809\pi\)
\(968\) 0 0
\(969\) 42.5889 1.36815
\(970\) 0 0
\(971\) −28.2148 −0.905457 −0.452728 0.891649i \(-0.649549\pi\)
−0.452728 + 0.891649i \(0.649549\pi\)
\(972\) 0 0
\(973\) −0.919781 −0.0294868
\(974\) 0 0
\(975\) 1.63404 0.0523312
\(976\) 0 0
\(977\) 6.06986 0.194192 0.0970961 0.995275i \(-0.469045\pi\)
0.0970961 + 0.995275i \(0.469045\pi\)
\(978\) 0 0
\(979\) −2.85439 −0.0912266
\(980\) 0 0
\(981\) −15.7778 −0.503747
\(982\) 0 0
\(983\) 17.6903 0.564233 0.282116 0.959380i \(-0.408964\pi\)
0.282116 + 0.959380i \(0.408964\pi\)
\(984\) 0 0
\(985\) 3.55184 0.113171
\(986\) 0 0
\(987\) −1.86071 −0.0592271
\(988\) 0 0
\(989\) 11.3712 0.361582
\(990\) 0 0
\(991\) −0.428154 −0.0136008 −0.00680038 0.999977i \(-0.502165\pi\)
−0.00680038 + 0.999977i \(0.502165\pi\)
\(992\) 0 0
\(993\) 22.1641 0.703356
\(994\) 0 0
\(995\) 18.6778 0.592126
\(996\) 0 0
\(997\) 1.76540 0.0559109 0.0279554 0.999609i \(-0.491100\pi\)
0.0279554 + 0.999609i \(0.491100\pi\)
\(998\) 0 0
\(999\) −2.44613 −0.0773920
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 \(a_p\))