Properties

Label 6036.2.a.g.1.1
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.01525\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-4.01525 q^{5}\) \(-3.41124 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-4.01525 q^{5}\) \(-3.41124 q^{7}\) \(+1.00000 q^{9}\) \(-0.942703 q^{11}\) \(-0.0524594 q^{13}\) \(-4.01525 q^{15}\) \(+2.46892 q^{17}\) \(+6.45629 q^{19}\) \(-3.41124 q^{21}\) \(-1.91648 q^{23}\) \(+11.1223 q^{25}\) \(+1.00000 q^{27}\) \(-1.42443 q^{29}\) \(+3.96306 q^{31}\) \(-0.942703 q^{33}\) \(+13.6970 q^{35}\) \(+6.45415 q^{37}\) \(-0.0524594 q^{39}\) \(+4.79510 q^{41}\) \(+3.95926 q^{43}\) \(-4.01525 q^{45}\) \(-7.81224 q^{47}\) \(+4.63656 q^{49}\) \(+2.46892 q^{51}\) \(-5.37123 q^{53}\) \(+3.78519 q^{55}\) \(+6.45629 q^{57}\) \(+1.63643 q^{59}\) \(-3.15845 q^{61}\) \(-3.41124 q^{63}\) \(+0.210638 q^{65}\) \(-2.49181 q^{67}\) \(-1.91648 q^{69}\) \(+3.47255 q^{71}\) \(-11.3160 q^{73}\) \(+11.1223 q^{75}\) \(+3.21578 q^{77}\) \(-5.58817 q^{79}\) \(+1.00000 q^{81}\) \(-6.10715 q^{83}\) \(-9.91333 q^{85}\) \(-1.42443 q^{87}\) \(-11.5017 q^{89}\) \(+0.178952 q^{91}\) \(+3.96306 q^{93}\) \(-25.9236 q^{95}\) \(-4.98650 q^{97}\) \(-0.942703 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 11q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut -\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 13q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −4.01525 −1.79568 −0.897838 0.440326i \(-0.854863\pi\)
−0.897838 + 0.440326i \(0.854863\pi\)
\(6\) 0 0
\(7\) −3.41124 −1.28933 −0.644664 0.764466i \(-0.723003\pi\)
−0.644664 + 0.764466i \(0.723003\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.942703 −0.284236 −0.142118 0.989850i \(-0.545391\pi\)
−0.142118 + 0.989850i \(0.545391\pi\)
\(12\) 0 0
\(13\) −0.0524594 −0.0145496 −0.00727481 0.999974i \(-0.502316\pi\)
−0.00727481 + 0.999974i \(0.502316\pi\)
\(14\) 0 0
\(15\) −4.01525 −1.03673
\(16\) 0 0
\(17\) 2.46892 0.598800 0.299400 0.954128i \(-0.403213\pi\)
0.299400 + 0.954128i \(0.403213\pi\)
\(18\) 0 0
\(19\) 6.45629 1.48117 0.740587 0.671960i \(-0.234547\pi\)
0.740587 + 0.671960i \(0.234547\pi\)
\(20\) 0 0
\(21\) −3.41124 −0.744394
\(22\) 0 0
\(23\) −1.91648 −0.399613 −0.199807 0.979835i \(-0.564031\pi\)
−0.199807 + 0.979835i \(0.564031\pi\)
\(24\) 0 0
\(25\) 11.1223 2.22445
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.42443 −0.264510 −0.132255 0.991216i \(-0.542222\pi\)
−0.132255 + 0.991216i \(0.542222\pi\)
\(30\) 0 0
\(31\) 3.96306 0.711787 0.355894 0.934526i \(-0.384177\pi\)
0.355894 + 0.934526i \(0.384177\pi\)
\(32\) 0 0
\(33\) −0.942703 −0.164103
\(34\) 0 0
\(35\) 13.6970 2.31521
\(36\) 0 0
\(37\) 6.45415 1.06106 0.530528 0.847667i \(-0.321994\pi\)
0.530528 + 0.847667i \(0.321994\pi\)
\(38\) 0 0
\(39\) −0.0524594 −0.00840023
\(40\) 0 0
\(41\) 4.79510 0.748869 0.374434 0.927253i \(-0.377837\pi\)
0.374434 + 0.927253i \(0.377837\pi\)
\(42\) 0 0
\(43\) 3.95926 0.603782 0.301891 0.953342i \(-0.402382\pi\)
0.301891 + 0.953342i \(0.402382\pi\)
\(44\) 0 0
\(45\) −4.01525 −0.598559
\(46\) 0 0
\(47\) −7.81224 −1.13953 −0.569766 0.821807i \(-0.692966\pi\)
−0.569766 + 0.821807i \(0.692966\pi\)
\(48\) 0 0
\(49\) 4.63656 0.662365
\(50\) 0 0
\(51\) 2.46892 0.345717
\(52\) 0 0
\(53\) −5.37123 −0.737796 −0.368898 0.929470i \(-0.620265\pi\)
−0.368898 + 0.929470i \(0.620265\pi\)
\(54\) 0 0
\(55\) 3.78519 0.510395
\(56\) 0 0
\(57\) 6.45629 0.855156
\(58\) 0 0
\(59\) 1.63643 0.213046 0.106523 0.994310i \(-0.466028\pi\)
0.106523 + 0.994310i \(0.466028\pi\)
\(60\) 0 0
\(61\) −3.15845 −0.404398 −0.202199 0.979344i \(-0.564809\pi\)
−0.202199 + 0.979344i \(0.564809\pi\)
\(62\) 0 0
\(63\) −3.41124 −0.429776
\(64\) 0 0
\(65\) 0.210638 0.0261264
\(66\) 0 0
\(67\) −2.49181 −0.304423 −0.152211 0.988348i \(-0.548639\pi\)
−0.152211 + 0.988348i \(0.548639\pi\)
\(68\) 0 0
\(69\) −1.91648 −0.230717
\(70\) 0 0
\(71\) 3.47255 0.412116 0.206058 0.978540i \(-0.433936\pi\)
0.206058 + 0.978540i \(0.433936\pi\)
\(72\) 0 0
\(73\) −11.3160 −1.32443 −0.662217 0.749312i \(-0.730385\pi\)
−0.662217 + 0.749312i \(0.730385\pi\)
\(74\) 0 0
\(75\) 11.1223 1.28429
\(76\) 0 0
\(77\) 3.21578 0.366473
\(78\) 0 0
\(79\) −5.58817 −0.628718 −0.314359 0.949304i \(-0.601790\pi\)
−0.314359 + 0.949304i \(0.601790\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −6.10715 −0.670347 −0.335173 0.942157i \(-0.608795\pi\)
−0.335173 + 0.942157i \(0.608795\pi\)
\(84\) 0 0
\(85\) −9.91333 −1.07525
\(86\) 0 0
\(87\) −1.42443 −0.152715
\(88\) 0 0
\(89\) −11.5017 −1.21918 −0.609588 0.792719i \(-0.708665\pi\)
−0.609588 + 0.792719i \(0.708665\pi\)
\(90\) 0 0
\(91\) 0.178952 0.0187592
\(92\) 0 0
\(93\) 3.96306 0.410951
\(94\) 0 0
\(95\) −25.9236 −2.65971
\(96\) 0 0
\(97\) −4.98650 −0.506302 −0.253151 0.967427i \(-0.581467\pi\)
−0.253151 + 0.967427i \(0.581467\pi\)
\(98\) 0 0
\(99\) −0.942703 −0.0947452
\(100\) 0 0
\(101\) −4.36685 −0.434518 −0.217259 0.976114i \(-0.569712\pi\)
−0.217259 + 0.976114i \(0.569712\pi\)
\(102\) 0 0
\(103\) 15.8204 1.55883 0.779417 0.626506i \(-0.215516\pi\)
0.779417 + 0.626506i \(0.215516\pi\)
\(104\) 0 0
\(105\) 13.6970 1.33669
\(106\) 0 0
\(107\) −7.31076 −0.706758 −0.353379 0.935480i \(-0.614967\pi\)
−0.353379 + 0.935480i \(0.614967\pi\)
\(108\) 0 0
\(109\) −8.19561 −0.784997 −0.392498 0.919753i \(-0.628389\pi\)
−0.392498 + 0.919753i \(0.628389\pi\)
\(110\) 0 0
\(111\) 6.45415 0.612601
\(112\) 0 0
\(113\) 5.76691 0.542505 0.271253 0.962508i \(-0.412562\pi\)
0.271253 + 0.962508i \(0.412562\pi\)
\(114\) 0 0
\(115\) 7.69515 0.717576
\(116\) 0 0
\(117\) −0.0524594 −0.00484987
\(118\) 0 0
\(119\) −8.42207 −0.772050
\(120\) 0 0
\(121\) −10.1113 −0.919210
\(122\) 0 0
\(123\) 4.79510 0.432360
\(124\) 0 0
\(125\) −24.5824 −2.19872
\(126\) 0 0
\(127\) −11.5005 −1.02050 −0.510251 0.860026i \(-0.670447\pi\)
−0.510251 + 0.860026i \(0.670447\pi\)
\(128\) 0 0
\(129\) 3.95926 0.348594
\(130\) 0 0
\(131\) −6.13043 −0.535618 −0.267809 0.963472i \(-0.586300\pi\)
−0.267809 + 0.963472i \(0.586300\pi\)
\(132\) 0 0
\(133\) −22.0240 −1.90972
\(134\) 0 0
\(135\) −4.01525 −0.345578
\(136\) 0 0
\(137\) 16.6493 1.42244 0.711222 0.702968i \(-0.248142\pi\)
0.711222 + 0.702968i \(0.248142\pi\)
\(138\) 0 0
\(139\) −10.5493 −0.894778 −0.447389 0.894340i \(-0.647646\pi\)
−0.447389 + 0.894340i \(0.647646\pi\)
\(140\) 0 0
\(141\) −7.81224 −0.657910
\(142\) 0 0
\(143\) 0.0494536 0.00413552
\(144\) 0 0
\(145\) 5.71945 0.474974
\(146\) 0 0
\(147\) 4.63656 0.382417
\(148\) 0 0
\(149\) 12.3008 1.00772 0.503862 0.863784i \(-0.331912\pi\)
0.503862 + 0.863784i \(0.331912\pi\)
\(150\) 0 0
\(151\) −10.3433 −0.841723 −0.420862 0.907125i \(-0.638272\pi\)
−0.420862 + 0.907125i \(0.638272\pi\)
\(152\) 0 0
\(153\) 2.46892 0.199600
\(154\) 0 0
\(155\) −15.9127 −1.27814
\(156\) 0 0
\(157\) −8.50057 −0.678419 −0.339210 0.940711i \(-0.610160\pi\)
−0.339210 + 0.940711i \(0.610160\pi\)
\(158\) 0 0
\(159\) −5.37123 −0.425967
\(160\) 0 0
\(161\) 6.53757 0.515232
\(162\) 0 0
\(163\) 19.4328 1.52209 0.761045 0.648699i \(-0.224686\pi\)
0.761045 + 0.648699i \(0.224686\pi\)
\(164\) 0 0
\(165\) 3.78519 0.294677
\(166\) 0 0
\(167\) 17.0642 1.32047 0.660233 0.751061i \(-0.270458\pi\)
0.660233 + 0.751061i \(0.270458\pi\)
\(168\) 0 0
\(169\) −12.9972 −0.999788
\(170\) 0 0
\(171\) 6.45629 0.493725
\(172\) 0 0
\(173\) −2.00293 −0.152280 −0.0761399 0.997097i \(-0.524260\pi\)
−0.0761399 + 0.997097i \(0.524260\pi\)
\(174\) 0 0
\(175\) −37.9407 −2.86805
\(176\) 0 0
\(177\) 1.63643 0.123002
\(178\) 0 0
\(179\) −14.2827 −1.06754 −0.533769 0.845630i \(-0.679225\pi\)
−0.533769 + 0.845630i \(0.679225\pi\)
\(180\) 0 0
\(181\) −1.09829 −0.0816352 −0.0408176 0.999167i \(-0.512996\pi\)
−0.0408176 + 0.999167i \(0.512996\pi\)
\(182\) 0 0
\(183\) −3.15845 −0.233479
\(184\) 0 0
\(185\) −25.9151 −1.90531
\(186\) 0 0
\(187\) −2.32745 −0.170200
\(188\) 0 0
\(189\) −3.41124 −0.248131
\(190\) 0 0
\(191\) −6.22913 −0.450724 −0.225362 0.974275i \(-0.572356\pi\)
−0.225362 + 0.974275i \(0.572356\pi\)
\(192\) 0 0
\(193\) 25.3301 1.82330 0.911652 0.410963i \(-0.134807\pi\)
0.911652 + 0.410963i \(0.134807\pi\)
\(194\) 0 0
\(195\) 0.210638 0.0150841
\(196\) 0 0
\(197\) −4.06948 −0.289938 −0.144969 0.989436i \(-0.546308\pi\)
−0.144969 + 0.989436i \(0.546308\pi\)
\(198\) 0 0
\(199\) 12.3837 0.877856 0.438928 0.898522i \(-0.355358\pi\)
0.438928 + 0.898522i \(0.355358\pi\)
\(200\) 0 0
\(201\) −2.49181 −0.175759
\(202\) 0 0
\(203\) 4.85907 0.341040
\(204\) 0 0
\(205\) −19.2535 −1.34473
\(206\) 0 0
\(207\) −1.91648 −0.133204
\(208\) 0 0
\(209\) −6.08636 −0.421002
\(210\) 0 0
\(211\) 5.37012 0.369694 0.184847 0.982767i \(-0.440821\pi\)
0.184847 + 0.982767i \(0.440821\pi\)
\(212\) 0 0
\(213\) 3.47255 0.237935
\(214\) 0 0
\(215\) −15.8974 −1.08420
\(216\) 0 0
\(217\) −13.5190 −0.917727
\(218\) 0 0
\(219\) −11.3160 −0.764663
\(220\) 0 0
\(221\) −0.129518 −0.00871232
\(222\) 0 0
\(223\) −2.15780 −0.144497 −0.0722486 0.997387i \(-0.523018\pi\)
−0.0722486 + 0.997387i \(0.523018\pi\)
\(224\) 0 0
\(225\) 11.1223 0.741484
\(226\) 0 0
\(227\) 12.5187 0.830893 0.415446 0.909618i \(-0.363625\pi\)
0.415446 + 0.909618i \(0.363625\pi\)
\(228\) 0 0
\(229\) 0.848259 0.0560545 0.0280273 0.999607i \(-0.491077\pi\)
0.0280273 + 0.999607i \(0.491077\pi\)
\(230\) 0 0
\(231\) 3.21578 0.211583
\(232\) 0 0
\(233\) 14.9314 0.978190 0.489095 0.872230i \(-0.337327\pi\)
0.489095 + 0.872230i \(0.337327\pi\)
\(234\) 0 0
\(235\) 31.3681 2.04623
\(236\) 0 0
\(237\) −5.58817 −0.362990
\(238\) 0 0
\(239\) −14.7836 −0.956268 −0.478134 0.878287i \(-0.658687\pi\)
−0.478134 + 0.878287i \(0.658687\pi\)
\(240\) 0 0
\(241\) −5.09764 −0.328368 −0.164184 0.986430i \(-0.552499\pi\)
−0.164184 + 0.986430i \(0.552499\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −18.6170 −1.18939
\(246\) 0 0
\(247\) −0.338693 −0.0215505
\(248\) 0 0
\(249\) −6.10715 −0.387025
\(250\) 0 0
\(251\) −26.6622 −1.68290 −0.841452 0.540331i \(-0.818299\pi\)
−0.841452 + 0.540331i \(0.818299\pi\)
\(252\) 0 0
\(253\) 1.80667 0.113584
\(254\) 0 0
\(255\) −9.91333 −0.620797
\(256\) 0 0
\(257\) −13.5964 −0.848120 −0.424060 0.905634i \(-0.639395\pi\)
−0.424060 + 0.905634i \(0.639395\pi\)
\(258\) 0 0
\(259\) −22.0167 −1.36805
\(260\) 0 0
\(261\) −1.42443 −0.0881700
\(262\) 0 0
\(263\) −29.7649 −1.83539 −0.917693 0.397291i \(-0.869950\pi\)
−0.917693 + 0.397291i \(0.869950\pi\)
\(264\) 0 0
\(265\) 21.5669 1.32484
\(266\) 0 0
\(267\) −11.5017 −0.703891
\(268\) 0 0
\(269\) 14.1573 0.863183 0.431591 0.902069i \(-0.357952\pi\)
0.431591 + 0.902069i \(0.357952\pi\)
\(270\) 0 0
\(271\) −2.79431 −0.169742 −0.0848710 0.996392i \(-0.527048\pi\)
−0.0848710 + 0.996392i \(0.527048\pi\)
\(272\) 0 0
\(273\) 0.178952 0.0108306
\(274\) 0 0
\(275\) −10.4850 −0.632269
\(276\) 0 0
\(277\) −14.4653 −0.869134 −0.434567 0.900640i \(-0.643099\pi\)
−0.434567 + 0.900640i \(0.643099\pi\)
\(278\) 0 0
\(279\) 3.96306 0.237262
\(280\) 0 0
\(281\) −13.6796 −0.816056 −0.408028 0.912969i \(-0.633783\pi\)
−0.408028 + 0.912969i \(0.633783\pi\)
\(282\) 0 0
\(283\) 29.1116 1.73050 0.865252 0.501337i \(-0.167158\pi\)
0.865252 + 0.501337i \(0.167158\pi\)
\(284\) 0 0
\(285\) −25.9236 −1.53558
\(286\) 0 0
\(287\) −16.3572 −0.965537
\(288\) 0 0
\(289\) −10.9045 −0.641438
\(290\) 0 0
\(291\) −4.98650 −0.292314
\(292\) 0 0
\(293\) −13.3512 −0.779986 −0.389993 0.920818i \(-0.627523\pi\)
−0.389993 + 0.920818i \(0.627523\pi\)
\(294\) 0 0
\(295\) −6.57070 −0.382561
\(296\) 0 0
\(297\) −0.942703 −0.0547011
\(298\) 0 0
\(299\) 0.100537 0.00581422
\(300\) 0 0
\(301\) −13.5060 −0.778472
\(302\) 0 0
\(303\) −4.36685 −0.250869
\(304\) 0 0
\(305\) 12.6820 0.726168
\(306\) 0 0
\(307\) 20.6026 1.17585 0.587926 0.808914i \(-0.299944\pi\)
0.587926 + 0.808914i \(0.299944\pi\)
\(308\) 0 0
\(309\) 15.8204 0.899993
\(310\) 0 0
\(311\) −16.5899 −0.940727 −0.470363 0.882473i \(-0.655877\pi\)
−0.470363 + 0.882473i \(0.655877\pi\)
\(312\) 0 0
\(313\) 4.08435 0.230861 0.115431 0.993316i \(-0.463175\pi\)
0.115431 + 0.993316i \(0.463175\pi\)
\(314\) 0 0
\(315\) 13.6970 0.771738
\(316\) 0 0
\(317\) −11.3455 −0.637228 −0.318614 0.947885i \(-0.603217\pi\)
−0.318614 + 0.947885i \(0.603217\pi\)
\(318\) 0 0
\(319\) 1.34281 0.0751831
\(320\) 0 0
\(321\) −7.31076 −0.408047
\(322\) 0 0
\(323\) 15.9400 0.886928
\(324\) 0 0
\(325\) −0.583468 −0.0323650
\(326\) 0 0
\(327\) −8.19561 −0.453218
\(328\) 0 0
\(329\) 26.6494 1.46923
\(330\) 0 0
\(331\) −16.1841 −0.889558 −0.444779 0.895640i \(-0.646718\pi\)
−0.444779 + 0.895640i \(0.646718\pi\)
\(332\) 0 0
\(333\) 6.45415 0.353685
\(334\) 0 0
\(335\) 10.0052 0.546645
\(336\) 0 0
\(337\) 26.6985 1.45436 0.727181 0.686446i \(-0.240830\pi\)
0.727181 + 0.686446i \(0.240830\pi\)
\(338\) 0 0
\(339\) 5.76691 0.313216
\(340\) 0 0
\(341\) −3.73599 −0.202315
\(342\) 0 0
\(343\) 8.06227 0.435321
\(344\) 0 0
\(345\) 7.69515 0.414293
\(346\) 0 0
\(347\) −11.9383 −0.640879 −0.320440 0.947269i \(-0.603831\pi\)
−0.320440 + 0.947269i \(0.603831\pi\)
\(348\) 0 0
\(349\) 30.9836 1.65851 0.829256 0.558868i \(-0.188764\pi\)
0.829256 + 0.558868i \(0.188764\pi\)
\(350\) 0 0
\(351\) −0.0524594 −0.00280008
\(352\) 0 0
\(353\) −27.1829 −1.44680 −0.723399 0.690430i \(-0.757421\pi\)
−0.723399 + 0.690430i \(0.757421\pi\)
\(354\) 0 0
\(355\) −13.9432 −0.740027
\(356\) 0 0
\(357\) −8.42207 −0.445743
\(358\) 0 0
\(359\) 25.8032 1.36184 0.680920 0.732358i \(-0.261580\pi\)
0.680920 + 0.732358i \(0.261580\pi\)
\(360\) 0 0
\(361\) 22.6837 1.19388
\(362\) 0 0
\(363\) −10.1113 −0.530706
\(364\) 0 0
\(365\) 45.4365 2.37826
\(366\) 0 0
\(367\) −16.8585 −0.880005 −0.440002 0.897997i \(-0.645022\pi\)
−0.440002 + 0.897997i \(0.645022\pi\)
\(368\) 0 0
\(369\) 4.79510 0.249623
\(370\) 0 0
\(371\) 18.3226 0.951260
\(372\) 0 0
\(373\) −8.49097 −0.439646 −0.219823 0.975540i \(-0.570548\pi\)
−0.219823 + 0.975540i \(0.570548\pi\)
\(374\) 0 0
\(375\) −24.5824 −1.26943
\(376\) 0 0
\(377\) 0.0747248 0.00384852
\(378\) 0 0
\(379\) −9.73575 −0.500092 −0.250046 0.968234i \(-0.580446\pi\)
−0.250046 + 0.968234i \(0.580446\pi\)
\(380\) 0 0
\(381\) −11.5005 −0.589187
\(382\) 0 0
\(383\) −0.901542 −0.0460667 −0.0230333 0.999735i \(-0.507332\pi\)
−0.0230333 + 0.999735i \(0.507332\pi\)
\(384\) 0 0
\(385\) −12.9122 −0.658066
\(386\) 0 0
\(387\) 3.95926 0.201261
\(388\) 0 0
\(389\) −15.3424 −0.777891 −0.388945 0.921261i \(-0.627161\pi\)
−0.388945 + 0.921261i \(0.627161\pi\)
\(390\) 0 0
\(391\) −4.73162 −0.239289
\(392\) 0 0
\(393\) −6.13043 −0.309239
\(394\) 0 0
\(395\) 22.4379 1.12897
\(396\) 0 0
\(397\) 11.6130 0.582842 0.291421 0.956595i \(-0.405872\pi\)
0.291421 + 0.956595i \(0.405872\pi\)
\(398\) 0 0
\(399\) −22.0240 −1.10258
\(400\) 0 0
\(401\) −33.6967 −1.68273 −0.841365 0.540467i \(-0.818248\pi\)
−0.841365 + 0.540467i \(0.818248\pi\)
\(402\) 0 0
\(403\) −0.207900 −0.0103562
\(404\) 0 0
\(405\) −4.01525 −0.199520
\(406\) 0 0
\(407\) −6.08435 −0.301590
\(408\) 0 0
\(409\) 9.24538 0.457155 0.228577 0.973526i \(-0.426593\pi\)
0.228577 + 0.973526i \(0.426593\pi\)
\(410\) 0 0
\(411\) 16.6493 0.821248
\(412\) 0 0
\(413\) −5.58227 −0.274686
\(414\) 0 0
\(415\) 24.5217 1.20373
\(416\) 0 0
\(417\) −10.5493 −0.516600
\(418\) 0 0
\(419\) −32.0393 −1.56522 −0.782611 0.622510i \(-0.786113\pi\)
−0.782611 + 0.622510i \(0.786113\pi\)
\(420\) 0 0
\(421\) −2.80651 −0.136781 −0.0683905 0.997659i \(-0.521786\pi\)
−0.0683905 + 0.997659i \(0.521786\pi\)
\(422\) 0 0
\(423\) −7.81224 −0.379844
\(424\) 0 0
\(425\) 27.4599 1.33200
\(426\) 0 0
\(427\) 10.7742 0.521402
\(428\) 0 0
\(429\) 0.0494536 0.00238764
\(430\) 0 0
\(431\) −0.919689 −0.0442998 −0.0221499 0.999755i \(-0.507051\pi\)
−0.0221499 + 0.999755i \(0.507051\pi\)
\(432\) 0 0
\(433\) −18.2734 −0.878165 −0.439082 0.898447i \(-0.644696\pi\)
−0.439082 + 0.898447i \(0.644696\pi\)
\(434\) 0 0
\(435\) 5.71945 0.274227
\(436\) 0 0
\(437\) −12.3733 −0.591897
\(438\) 0 0
\(439\) −23.9702 −1.14403 −0.572017 0.820242i \(-0.693839\pi\)
−0.572017 + 0.820242i \(0.693839\pi\)
\(440\) 0 0
\(441\) 4.63656 0.220788
\(442\) 0 0
\(443\) 7.76147 0.368759 0.184379 0.982855i \(-0.440973\pi\)
0.184379 + 0.982855i \(0.440973\pi\)
\(444\) 0 0
\(445\) 46.1822 2.18924
\(446\) 0 0
\(447\) 12.3008 0.581810
\(448\) 0 0
\(449\) 5.53865 0.261385 0.130692 0.991423i \(-0.458280\pi\)
0.130692 + 0.991423i \(0.458280\pi\)
\(450\) 0 0
\(451\) −4.52035 −0.212855
\(452\) 0 0
\(453\) −10.3433 −0.485969
\(454\) 0 0
\(455\) −0.718536 −0.0336855
\(456\) 0 0
\(457\) 34.0935 1.59483 0.797413 0.603433i \(-0.206201\pi\)
0.797413 + 0.603433i \(0.206201\pi\)
\(458\) 0 0
\(459\) 2.46892 0.115239
\(460\) 0 0
\(461\) −30.5906 −1.42475 −0.712373 0.701801i \(-0.752380\pi\)
−0.712373 + 0.701801i \(0.752380\pi\)
\(462\) 0 0
\(463\) −22.4639 −1.04398 −0.521992 0.852950i \(-0.674811\pi\)
−0.521992 + 0.852950i \(0.674811\pi\)
\(464\) 0 0
\(465\) −15.9127 −0.737934
\(466\) 0 0
\(467\) −3.61860 −0.167449 −0.0837244 0.996489i \(-0.526682\pi\)
−0.0837244 + 0.996489i \(0.526682\pi\)
\(468\) 0 0
\(469\) 8.50016 0.392501
\(470\) 0 0
\(471\) −8.50057 −0.391686
\(472\) 0 0
\(473\) −3.73241 −0.171616
\(474\) 0 0
\(475\) 71.8086 3.29480
\(476\) 0 0
\(477\) −5.37123 −0.245932
\(478\) 0 0
\(479\) −24.3435 −1.11228 −0.556142 0.831088i \(-0.687719\pi\)
−0.556142 + 0.831088i \(0.687719\pi\)
\(480\) 0 0
\(481\) −0.338581 −0.0154380
\(482\) 0 0
\(483\) 6.53757 0.297470
\(484\) 0 0
\(485\) 20.0220 0.909154
\(486\) 0 0
\(487\) 3.68270 0.166879 0.0834395 0.996513i \(-0.473409\pi\)
0.0834395 + 0.996513i \(0.473409\pi\)
\(488\) 0 0
\(489\) 19.4328 0.878780
\(490\) 0 0
\(491\) 19.1346 0.863531 0.431765 0.901986i \(-0.357891\pi\)
0.431765 + 0.901986i \(0.357891\pi\)
\(492\) 0 0
\(493\) −3.51680 −0.158389
\(494\) 0 0
\(495\) 3.78519 0.170132
\(496\) 0 0
\(497\) −11.8457 −0.531352
\(498\) 0 0
\(499\) 17.3020 0.774543 0.387272 0.921966i \(-0.373418\pi\)
0.387272 + 0.921966i \(0.373418\pi\)
\(500\) 0 0
\(501\) 17.0642 0.762371
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 17.5340 0.780254
\(506\) 0 0
\(507\) −12.9972 −0.577228
\(508\) 0 0
\(509\) 22.8033 1.01074 0.505368 0.862904i \(-0.331357\pi\)
0.505368 + 0.862904i \(0.331357\pi\)
\(510\) 0 0
\(511\) 38.6015 1.70763
\(512\) 0 0
\(513\) 6.45629 0.285052
\(514\) 0 0
\(515\) −63.5230 −2.79916
\(516\) 0 0
\(517\) 7.36462 0.323896
\(518\) 0 0
\(519\) −2.00293 −0.0879188
\(520\) 0 0
\(521\) −15.7216 −0.688778 −0.344389 0.938827i \(-0.611914\pi\)
−0.344389 + 0.938827i \(0.611914\pi\)
\(522\) 0 0
\(523\) 32.3305 1.41372 0.706858 0.707356i \(-0.250112\pi\)
0.706858 + 0.707356i \(0.250112\pi\)
\(524\) 0 0
\(525\) −37.9407 −1.65587
\(526\) 0 0
\(527\) 9.78448 0.426218
\(528\) 0 0
\(529\) −19.3271 −0.840309
\(530\) 0 0
\(531\) 1.63643 0.0710152
\(532\) 0 0
\(533\) −0.251548 −0.0108958
\(534\) 0 0
\(535\) 29.3546 1.26911
\(536\) 0 0
\(537\) −14.2827 −0.616344
\(538\) 0 0
\(539\) −4.37090 −0.188268
\(540\) 0 0
\(541\) −2.43532 −0.104703 −0.0523513 0.998629i \(-0.516672\pi\)
−0.0523513 + 0.998629i \(0.516672\pi\)
\(542\) 0 0
\(543\) −1.09829 −0.0471321
\(544\) 0 0
\(545\) 32.9074 1.40960
\(546\) 0 0
\(547\) 5.13952 0.219750 0.109875 0.993945i \(-0.464955\pi\)
0.109875 + 0.993945i \(0.464955\pi\)
\(548\) 0 0
\(549\) −3.15845 −0.134799
\(550\) 0 0
\(551\) −9.19653 −0.391785
\(552\) 0 0
\(553\) 19.0626 0.810623
\(554\) 0 0
\(555\) −25.9151 −1.10003
\(556\) 0 0
\(557\) 1.82366 0.0772710 0.0386355 0.999253i \(-0.487699\pi\)
0.0386355 + 0.999253i \(0.487699\pi\)
\(558\) 0 0
\(559\) −0.207701 −0.00878480
\(560\) 0 0
\(561\) −2.32745 −0.0982652
\(562\) 0 0
\(563\) −14.0557 −0.592379 −0.296189 0.955129i \(-0.595716\pi\)
−0.296189 + 0.955129i \(0.595716\pi\)
\(564\) 0 0
\(565\) −23.1556 −0.974164
\(566\) 0 0
\(567\) −3.41124 −0.143259
\(568\) 0 0
\(569\) 19.8848 0.833616 0.416808 0.908994i \(-0.363149\pi\)
0.416808 + 0.908994i \(0.363149\pi\)
\(570\) 0 0
\(571\) −5.24281 −0.219405 −0.109702 0.993964i \(-0.534990\pi\)
−0.109702 + 0.993964i \(0.534990\pi\)
\(572\) 0 0
\(573\) −6.22913 −0.260226
\(574\) 0 0
\(575\) −21.3156 −0.888921
\(576\) 0 0
\(577\) −35.1315 −1.46254 −0.731272 0.682086i \(-0.761073\pi\)
−0.731272 + 0.682086i \(0.761073\pi\)
\(578\) 0 0
\(579\) 25.3301 1.05269
\(580\) 0 0
\(581\) 20.8329 0.864296
\(582\) 0 0
\(583\) 5.06348 0.209708
\(584\) 0 0
\(585\) 0.210638 0.00870880
\(586\) 0 0
\(587\) −28.1708 −1.16273 −0.581366 0.813642i \(-0.697482\pi\)
−0.581366 + 0.813642i \(0.697482\pi\)
\(588\) 0 0
\(589\) 25.5867 1.05428
\(590\) 0 0
\(591\) −4.06948 −0.167396
\(592\) 0 0
\(593\) 10.3812 0.426304 0.213152 0.977019i \(-0.431627\pi\)
0.213152 + 0.977019i \(0.431627\pi\)
\(594\) 0 0
\(595\) 33.8167 1.38635
\(596\) 0 0
\(597\) 12.3837 0.506830
\(598\) 0 0
\(599\) −13.0820 −0.534516 −0.267258 0.963625i \(-0.586118\pi\)
−0.267258 + 0.963625i \(0.586118\pi\)
\(600\) 0 0
\(601\) −3.47942 −0.141928 −0.0709642 0.997479i \(-0.522608\pi\)
−0.0709642 + 0.997479i \(0.522608\pi\)
\(602\) 0 0
\(603\) −2.49181 −0.101474
\(604\) 0 0
\(605\) 40.5995 1.65060
\(606\) 0 0
\(607\) −6.26320 −0.254216 −0.127108 0.991889i \(-0.540569\pi\)
−0.127108 + 0.991889i \(0.540569\pi\)
\(608\) 0 0
\(609\) 4.85907 0.196900
\(610\) 0 0
\(611\) 0.409826 0.0165798
\(612\) 0 0
\(613\) −20.4156 −0.824580 −0.412290 0.911053i \(-0.635271\pi\)
−0.412290 + 0.911053i \(0.635271\pi\)
\(614\) 0 0
\(615\) −19.2535 −0.776378
\(616\) 0 0
\(617\) 22.1908 0.893369 0.446684 0.894692i \(-0.352605\pi\)
0.446684 + 0.894692i \(0.352605\pi\)
\(618\) 0 0
\(619\) 1.70540 0.0685457 0.0342729 0.999413i \(-0.489088\pi\)
0.0342729 + 0.999413i \(0.489088\pi\)
\(620\) 0 0
\(621\) −1.91648 −0.0769056
\(622\) 0 0
\(623\) 39.2350 1.57192
\(624\) 0 0
\(625\) 43.0935 1.72374
\(626\) 0 0
\(627\) −6.08636 −0.243066
\(628\) 0 0
\(629\) 15.9348 0.635361
\(630\) 0 0
\(631\) 13.3902 0.533056 0.266528 0.963827i \(-0.414124\pi\)
0.266528 + 0.963827i \(0.414124\pi\)
\(632\) 0 0
\(633\) 5.37012 0.213443
\(634\) 0 0
\(635\) 46.1773 1.83249
\(636\) 0 0
\(637\) −0.243231 −0.00963717
\(638\) 0 0
\(639\) 3.47255 0.137372
\(640\) 0 0
\(641\) −35.7869 −1.41350 −0.706748 0.707465i \(-0.749839\pi\)
−0.706748 + 0.707465i \(0.749839\pi\)
\(642\) 0 0
\(643\) 18.2097 0.718120 0.359060 0.933315i \(-0.383097\pi\)
0.359060 + 0.933315i \(0.383097\pi\)
\(644\) 0 0
\(645\) −15.8974 −0.625961
\(646\) 0 0
\(647\) 31.5405 1.23998 0.619992 0.784608i \(-0.287136\pi\)
0.619992 + 0.784608i \(0.287136\pi\)
\(648\) 0 0
\(649\) −1.54267 −0.0605551
\(650\) 0 0
\(651\) −13.5190 −0.529850
\(652\) 0 0
\(653\) −4.10196 −0.160522 −0.0802611 0.996774i \(-0.525575\pi\)
−0.0802611 + 0.996774i \(0.525575\pi\)
\(654\) 0 0
\(655\) 24.6152 0.961796
\(656\) 0 0
\(657\) −11.3160 −0.441478
\(658\) 0 0
\(659\) −0.307285 −0.0119701 −0.00598505 0.999982i \(-0.501905\pi\)
−0.00598505 + 0.999982i \(0.501905\pi\)
\(660\) 0 0
\(661\) 37.7726 1.46918 0.734592 0.678509i \(-0.237374\pi\)
0.734592 + 0.678509i \(0.237374\pi\)
\(662\) 0 0
\(663\) −0.129518 −0.00503006
\(664\) 0 0
\(665\) 88.4318 3.42924
\(666\) 0 0
\(667\) 2.72989 0.105702
\(668\) 0 0
\(669\) −2.15780 −0.0834255
\(670\) 0 0
\(671\) 2.97748 0.114944
\(672\) 0 0
\(673\) −36.4713 −1.40586 −0.702932 0.711257i \(-0.748126\pi\)
−0.702932 + 0.711257i \(0.748126\pi\)
\(674\) 0 0
\(675\) 11.1223 0.428096
\(676\) 0 0
\(677\) −9.31919 −0.358165 −0.179083 0.983834i \(-0.557313\pi\)
−0.179083 + 0.983834i \(0.557313\pi\)
\(678\) 0 0
\(679\) 17.0101 0.652789
\(680\) 0 0
\(681\) 12.5187 0.479716
\(682\) 0 0
\(683\) 22.6181 0.865459 0.432730 0.901524i \(-0.357550\pi\)
0.432730 + 0.901524i \(0.357550\pi\)
\(684\) 0 0
\(685\) −66.8511 −2.55425
\(686\) 0 0
\(687\) 0.848259 0.0323631
\(688\) 0 0
\(689\) 0.281772 0.0107347
\(690\) 0 0
\(691\) −39.0277 −1.48468 −0.742341 0.670022i \(-0.766285\pi\)
−0.742341 + 0.670022i \(0.766285\pi\)
\(692\) 0 0
\(693\) 3.21578 0.122158
\(694\) 0 0
\(695\) 42.3580 1.60673
\(696\) 0 0
\(697\) 11.8387 0.448423
\(698\) 0 0
\(699\) 14.9314 0.564759
\(700\) 0 0
\(701\) −21.5411 −0.813598 −0.406799 0.913518i \(-0.633355\pi\)
−0.406799 + 0.913518i \(0.633355\pi\)
\(702\) 0 0
\(703\) 41.6699 1.57161
\(704\) 0 0
\(705\) 31.3681 1.18139
\(706\) 0 0
\(707\) 14.8964 0.560236
\(708\) 0 0
\(709\) 29.6541 1.11368 0.556841 0.830619i \(-0.312013\pi\)
0.556841 + 0.830619i \(0.312013\pi\)
\(710\) 0 0
\(711\) −5.58817 −0.209573
\(712\) 0 0
\(713\) −7.59512 −0.284440
\(714\) 0 0
\(715\) −0.198569 −0.00742605
\(716\) 0 0
\(717\) −14.7836 −0.552102
\(718\) 0 0
\(719\) −1.61658 −0.0602882 −0.0301441 0.999546i \(-0.509597\pi\)
−0.0301441 + 0.999546i \(0.509597\pi\)
\(720\) 0 0
\(721\) −53.9673 −2.00985
\(722\) 0 0
\(723\) −5.09764 −0.189583
\(724\) 0 0
\(725\) −15.8429 −0.588390
\(726\) 0 0
\(727\) 15.6379 0.579978 0.289989 0.957030i \(-0.406348\pi\)
0.289989 + 0.957030i \(0.406348\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 9.77509 0.361545
\(732\) 0 0
\(733\) −26.0045 −0.960499 −0.480249 0.877132i \(-0.659454\pi\)
−0.480249 + 0.877132i \(0.659454\pi\)
\(734\) 0 0
\(735\) −18.6170 −0.686697
\(736\) 0 0
\(737\) 2.34904 0.0865278
\(738\) 0 0
\(739\) −30.6613 −1.12790 −0.563948 0.825811i \(-0.690718\pi\)
−0.563948 + 0.825811i \(0.690718\pi\)
\(740\) 0 0
\(741\) −0.338693 −0.0124422
\(742\) 0 0
\(743\) −26.0081 −0.954145 −0.477072 0.878864i \(-0.658302\pi\)
−0.477072 + 0.878864i \(0.658302\pi\)
\(744\) 0 0
\(745\) −49.3910 −1.80955
\(746\) 0 0
\(747\) −6.10715 −0.223449
\(748\) 0 0
\(749\) 24.9388 0.911242
\(750\) 0 0
\(751\) 25.0453 0.913918 0.456959 0.889488i \(-0.348939\pi\)
0.456959 + 0.889488i \(0.348939\pi\)
\(752\) 0 0
\(753\) −26.6622 −0.971625
\(754\) 0 0
\(755\) 41.5309 1.51146
\(756\) 0 0
\(757\) 5.14742 0.187086 0.0935430 0.995615i \(-0.470181\pi\)
0.0935430 + 0.995615i \(0.470181\pi\)
\(758\) 0 0
\(759\) 1.80667 0.0655779
\(760\) 0 0
\(761\) −36.4361 −1.32081 −0.660404 0.750910i \(-0.729615\pi\)
−0.660404 + 0.750910i \(0.729615\pi\)
\(762\) 0 0
\(763\) 27.9572 1.01212
\(764\) 0 0
\(765\) −9.91333 −0.358417
\(766\) 0 0
\(767\) −0.0858464 −0.00309973
\(768\) 0 0
\(769\) −7.30809 −0.263537 −0.131768 0.991281i \(-0.542065\pi\)
−0.131768 + 0.991281i \(0.542065\pi\)
\(770\) 0 0
\(771\) −13.5964 −0.489663
\(772\) 0 0
\(773\) 24.0791 0.866067 0.433033 0.901378i \(-0.357443\pi\)
0.433033 + 0.901378i \(0.357443\pi\)
\(774\) 0 0
\(775\) 44.0782 1.58334
\(776\) 0 0
\(777\) −22.0167 −0.789844
\(778\) 0 0
\(779\) 30.9586 1.10921
\(780\) 0 0
\(781\) −3.27358 −0.117138
\(782\) 0 0
\(783\) −1.42443 −0.0509050
\(784\) 0 0
\(785\) 34.1319 1.21822
\(786\) 0 0
\(787\) −30.8437 −1.09946 −0.549729 0.835343i \(-0.685269\pi\)
−0.549729 + 0.835343i \(0.685269\pi\)
\(788\) 0 0
\(789\) −29.7649 −1.05966
\(790\) 0 0
\(791\) −19.6723 −0.699467
\(792\) 0 0
\(793\) 0.165690 0.00588384
\(794\) 0 0
\(795\) 21.5669 0.764898
\(796\) 0 0
\(797\) 21.1040 0.747541 0.373771 0.927521i \(-0.378065\pi\)
0.373771 + 0.927521i \(0.378065\pi\)
\(798\) 0 0
\(799\) −19.2878 −0.682353
\(800\) 0 0
\(801\) −11.5017 −0.406392
\(802\) 0 0
\(803\) 10.6676 0.376451
\(804\) 0 0
\(805\) −26.2500 −0.925190
\(806\) 0 0
\(807\) 14.1573 0.498359
\(808\) 0 0
\(809\) −42.6345 −1.49895 −0.749474 0.662034i \(-0.769694\pi\)
−0.749474 + 0.662034i \(0.769694\pi\)
\(810\) 0 0
\(811\) −30.1661 −1.05928 −0.529638 0.848224i \(-0.677672\pi\)
−0.529638 + 0.848224i \(0.677672\pi\)
\(812\) 0 0
\(813\) −2.79431 −0.0980006
\(814\) 0 0
\(815\) −78.0274 −2.73318
\(816\) 0 0
\(817\) 25.5621 0.894306
\(818\) 0 0
\(819\) 0.178952 0.00625308
\(820\) 0 0
\(821\) 9.00173 0.314163 0.157081 0.987586i \(-0.449792\pi\)
0.157081 + 0.987586i \(0.449792\pi\)
\(822\) 0 0
\(823\) 8.24095 0.287262 0.143631 0.989631i \(-0.454122\pi\)
0.143631 + 0.989631i \(0.454122\pi\)
\(824\) 0 0
\(825\) −10.4850 −0.365040
\(826\) 0 0
\(827\) −15.8965 −0.552775 −0.276387 0.961046i \(-0.589137\pi\)
−0.276387 + 0.961046i \(0.589137\pi\)
\(828\) 0 0
\(829\) −22.8729 −0.794410 −0.397205 0.917730i \(-0.630020\pi\)
−0.397205 + 0.917730i \(0.630020\pi\)
\(830\) 0 0
\(831\) −14.4653 −0.501795
\(832\) 0 0
\(833\) 11.4473 0.396625
\(834\) 0 0
\(835\) −68.5170 −2.37113
\(836\) 0 0
\(837\) 3.96306 0.136984
\(838\) 0 0
\(839\) −3.82681 −0.132116 −0.0660581 0.997816i \(-0.521042\pi\)
−0.0660581 + 0.997816i \(0.521042\pi\)
\(840\) 0 0
\(841\) −26.9710 −0.930034
\(842\) 0 0
\(843\) −13.6796 −0.471150
\(844\) 0 0
\(845\) 52.1873 1.79530
\(846\) 0 0
\(847\) 34.4921 1.18516
\(848\) 0 0
\(849\) 29.1116 0.999107
\(850\) 0 0
\(851\) −12.3692 −0.424012
\(852\) 0 0
\(853\) −36.3471 −1.24450 −0.622250 0.782819i \(-0.713781\pi\)
−0.622250 + 0.782819i \(0.713781\pi\)
\(854\) 0 0
\(855\) −25.9236 −0.886570
\(856\) 0 0
\(857\) −15.6160 −0.533432 −0.266716 0.963775i \(-0.585938\pi\)
−0.266716 + 0.963775i \(0.585938\pi\)
\(858\) 0 0
\(859\) 18.0884 0.617169 0.308585 0.951197i \(-0.400145\pi\)
0.308585 + 0.951197i \(0.400145\pi\)
\(860\) 0 0
\(861\) −16.3572 −0.557453
\(862\) 0 0
\(863\) 7.47419 0.254424 0.127212 0.991876i \(-0.459397\pi\)
0.127212 + 0.991876i \(0.459397\pi\)
\(864\) 0 0
\(865\) 8.04226 0.273445
\(866\) 0 0
\(867\) −10.9045 −0.370335
\(868\) 0 0
\(869\) 5.26798 0.178704
\(870\) 0 0
\(871\) 0.130719 0.00442924
\(872\) 0 0
\(873\) −4.98650 −0.168767
\(874\) 0 0
\(875\) 83.8566 2.83487
\(876\) 0 0
\(877\) −22.9554 −0.775150 −0.387575 0.921838i \(-0.626687\pi\)
−0.387575 + 0.921838i \(0.626687\pi\)
\(878\) 0 0
\(879\) −13.3512 −0.450325
\(880\) 0 0
\(881\) −3.84769 −0.129632 −0.0648160 0.997897i \(-0.520646\pi\)
−0.0648160 + 0.997897i \(0.520646\pi\)
\(882\) 0 0
\(883\) −21.1281 −0.711016 −0.355508 0.934673i \(-0.615692\pi\)
−0.355508 + 0.934673i \(0.615692\pi\)
\(884\) 0 0
\(885\) −6.57070 −0.220872
\(886\) 0 0
\(887\) −15.7929 −0.530275 −0.265137 0.964211i \(-0.585417\pi\)
−0.265137 + 0.964211i \(0.585417\pi\)
\(888\) 0 0
\(889\) 39.2308 1.31576
\(890\) 0 0
\(891\) −0.942703 −0.0315817
\(892\) 0 0
\(893\) −50.4381 −1.68785
\(894\) 0 0
\(895\) 57.3487 1.91695
\(896\) 0 0
\(897\) 0.100537 0.00335684
\(898\) 0 0
\(899\) −5.64511 −0.188275
\(900\) 0 0
\(901\) −13.2611 −0.441792
\(902\) 0 0
\(903\) −13.5060 −0.449451
\(904\) 0 0
\(905\) 4.40991 0.146590
\(906\) 0 0
\(907\) 33.3706 1.10805 0.554027 0.832499i \(-0.313091\pi\)
0.554027 + 0.832499i \(0.313091\pi\)
\(908\) 0 0
\(909\) −4.36685 −0.144839
\(910\) 0 0
\(911\) −14.0757 −0.466349 −0.233174 0.972435i \(-0.574911\pi\)
−0.233174 + 0.972435i \(0.574911\pi\)
\(912\) 0 0
\(913\) 5.75722 0.190536
\(914\) 0 0
\(915\) 12.6820 0.419253
\(916\) 0 0
\(917\) 20.9124 0.690587
\(918\) 0 0
\(919\) 14.5296 0.479288 0.239644 0.970861i \(-0.422969\pi\)
0.239644 + 0.970861i \(0.422969\pi\)
\(920\) 0 0
\(921\) 20.6026 0.678879
\(922\) 0 0
\(923\) −0.182168 −0.00599613
\(924\) 0 0
\(925\) 71.7848 2.36027
\(926\) 0 0
\(927\) 15.8204 0.519611
\(928\) 0 0
\(929\) 20.2952 0.665863 0.332932 0.942951i \(-0.391962\pi\)
0.332932 + 0.942951i \(0.391962\pi\)
\(930\) 0 0
\(931\) 29.9350 0.981079
\(932\) 0 0
\(933\) −16.5899 −0.543129
\(934\) 0 0
\(935\) 9.34532 0.305625
\(936\) 0 0
\(937\) −53.8327 −1.75864 −0.879319 0.476234i \(-0.842002\pi\)
−0.879319 + 0.476234i \(0.842002\pi\)
\(938\) 0 0
\(939\) 4.08435 0.133288
\(940\) 0 0
\(941\) 38.4127 1.25222 0.626109 0.779735i \(-0.284646\pi\)
0.626109 + 0.779735i \(0.284646\pi\)
\(942\) 0 0
\(943\) −9.18970 −0.299258
\(944\) 0 0
\(945\) 13.6970 0.445563
\(946\) 0 0
\(947\) 48.5325 1.57710 0.788548 0.614973i \(-0.210833\pi\)
0.788548 + 0.614973i \(0.210833\pi\)
\(948\) 0 0
\(949\) 0.593630 0.0192700
\(950\) 0 0
\(951\) −11.3455 −0.367904
\(952\) 0 0
\(953\) −42.4334 −1.37455 −0.687276 0.726396i \(-0.741194\pi\)
−0.687276 + 0.726396i \(0.741194\pi\)
\(954\) 0 0
\(955\) 25.0115 0.809354
\(956\) 0 0
\(957\) 1.34281 0.0434070
\(958\) 0 0
\(959\) −56.7947 −1.83400
\(960\) 0 0
\(961\) −15.2941 −0.493359
\(962\) 0 0
\(963\) −7.31076 −0.235586
\(964\) 0 0
\(965\) −101.707 −3.27406
\(966\) 0 0
\(967\) 20.7743 0.668057 0.334029 0.942563i \(-0.391592\pi\)
0.334029 + 0.942563i \(0.391592\pi\)
\(968\) 0 0
\(969\) 15.9400 0.512068
\(970\) 0 0
\(971\) −0.881250 −0.0282807 −0.0141403 0.999900i \(-0.504501\pi\)
−0.0141403 + 0.999900i \(0.504501\pi\)
\(972\) 0 0
\(973\) 35.9861 1.15366
\(974\) 0 0
\(975\) −0.583468 −0.0186859
\(976\) 0 0
\(977\) −32.8981 −1.05250 −0.526252 0.850328i \(-0.676403\pi\)
−0.526252 + 0.850328i \(0.676403\pi\)
\(978\) 0 0
\(979\) 10.8427 0.346533
\(980\) 0 0
\(981\) −8.19561 −0.261666
\(982\) 0 0
\(983\) −17.2826 −0.551230 −0.275615 0.961268i \(-0.588882\pi\)
−0.275615 + 0.961268i \(0.588882\pi\)
\(984\) 0 0
\(985\) 16.3400 0.520635
\(986\) 0 0
\(987\) 26.6494 0.848261
\(988\) 0 0
\(989\) −7.58784 −0.241279
\(990\) 0 0
\(991\) −18.2559 −0.579916 −0.289958 0.957039i \(-0.593641\pi\)
−0.289958 + 0.957039i \(0.593641\pi\)
\(992\) 0 0
\(993\) −16.1841 −0.513587
\(994\) 0 0
\(995\) −49.7236 −1.57634
\(996\) 0 0
\(997\) −17.2774 −0.547181 −0.273591 0.961846i \(-0.588211\pi\)
−0.273591 + 0.961846i \(0.588211\pi\)
\(998\) 0 0
\(999\) 6.45415 0.204200
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 \(a_p\))