Properties

Label 8004.2.a.d.1.8
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 1
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(1.87214\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+2.74094 q^{5}\) \(-3.17108 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+2.74094 q^{5}\) \(-3.17108 q^{7}\) \(+1.00000 q^{9}\) \(-0.319748 q^{11}\) \(-0.778524 q^{13}\) \(+2.74094 q^{15}\) \(-1.46825 q^{17}\) \(-0.913678 q^{19}\) \(-3.17108 q^{21}\) \(+1.00000 q^{23}\) \(+2.51273 q^{25}\) \(+1.00000 q^{27}\) \(+1.00000 q^{29}\) \(-0.759923 q^{31}\) \(-0.319748 q^{33}\) \(-8.69172 q^{35}\) \(-7.77804 q^{37}\) \(-0.778524 q^{39}\) \(-10.1559 q^{41}\) \(-4.11821 q^{43}\) \(+2.74094 q^{45}\) \(-0.0564046 q^{47}\) \(+3.05572 q^{49}\) \(-1.46825 q^{51}\) \(-11.1853 q^{53}\) \(-0.876409 q^{55}\) \(-0.913678 q^{57}\) \(+11.6998 q^{59}\) \(+10.6382 q^{61}\) \(-3.17108 q^{63}\) \(-2.13388 q^{65}\) \(+0.276436 q^{67}\) \(+1.00000 q^{69}\) \(-8.70814 q^{71}\) \(-11.0869 q^{73}\) \(+2.51273 q^{75}\) \(+1.01394 q^{77}\) \(-4.66744 q^{79}\) \(+1.00000 q^{81}\) \(+1.81955 q^{83}\) \(-4.02437 q^{85}\) \(+1.00000 q^{87}\) \(-15.6397 q^{89}\) \(+2.46876 q^{91}\) \(-0.759923 q^{93}\) \(-2.50433 q^{95}\) \(+9.80700 q^{97}\) \(-0.319748 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 11q^{41} \) \(\mathstrut -\mathstrut 7q^{43} \) \(\mathstrut -\mathstrut 5q^{45} \) \(\mathstrut -\mathstrut 14q^{47} \) \(\mathstrut -\mathstrut 18q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut -\mathstrut 15q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 5q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut -\mathstrut 21q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 8q^{81} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut +\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 2q^{93} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 7q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 2.74094 1.22578 0.612892 0.790167i \(-0.290006\pi\)
0.612892 + 0.790167i \(0.290006\pi\)
\(6\) 0 0
\(7\) −3.17108 −1.19855 −0.599277 0.800542i \(-0.704545\pi\)
−0.599277 + 0.800542i \(0.704545\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.319748 −0.0964076 −0.0482038 0.998838i \(-0.515350\pi\)
−0.0482038 + 0.998838i \(0.515350\pi\)
\(12\) 0 0
\(13\) −0.778524 −0.215924 −0.107962 0.994155i \(-0.534432\pi\)
−0.107962 + 0.994155i \(0.534432\pi\)
\(14\) 0 0
\(15\) 2.74094 0.707707
\(16\) 0 0
\(17\) −1.46825 −0.356102 −0.178051 0.984021i \(-0.556979\pi\)
−0.178051 + 0.984021i \(0.556979\pi\)
\(18\) 0 0
\(19\) −0.913678 −0.209612 −0.104806 0.994493i \(-0.533422\pi\)
−0.104806 + 0.994493i \(0.533422\pi\)
\(20\) 0 0
\(21\) −3.17108 −0.691985
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 2.51273 0.502546
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −0.759923 −0.136486 −0.0682431 0.997669i \(-0.521739\pi\)
−0.0682431 + 0.997669i \(0.521739\pi\)
\(32\) 0 0
\(33\) −0.319748 −0.0556610
\(34\) 0 0
\(35\) −8.69172 −1.46917
\(36\) 0 0
\(37\) −7.77804 −1.27870 −0.639351 0.768915i \(-0.720797\pi\)
−0.639351 + 0.768915i \(0.720797\pi\)
\(38\) 0 0
\(39\) −0.778524 −0.124664
\(40\) 0 0
\(41\) −10.1559 −1.58609 −0.793043 0.609165i \(-0.791505\pi\)
−0.793043 + 0.609165i \(0.791505\pi\)
\(42\) 0 0
\(43\) −4.11821 −0.628021 −0.314011 0.949419i \(-0.601673\pi\)
−0.314011 + 0.949419i \(0.601673\pi\)
\(44\) 0 0
\(45\) 2.74094 0.408595
\(46\) 0 0
\(47\) −0.0564046 −0.00822745 −0.00411373 0.999992i \(-0.501309\pi\)
−0.00411373 + 0.999992i \(0.501309\pi\)
\(48\) 0 0
\(49\) 3.05572 0.436532
\(50\) 0 0
\(51\) −1.46825 −0.205595
\(52\) 0 0
\(53\) −11.1853 −1.53641 −0.768207 0.640201i \(-0.778851\pi\)
−0.768207 + 0.640201i \(0.778851\pi\)
\(54\) 0 0
\(55\) −0.876409 −0.118175
\(56\) 0 0
\(57\) −0.913678 −0.121020
\(58\) 0 0
\(59\) 11.6998 1.52318 0.761589 0.648060i \(-0.224419\pi\)
0.761589 + 0.648060i \(0.224419\pi\)
\(60\) 0 0
\(61\) 10.6382 1.36208 0.681042 0.732244i \(-0.261527\pi\)
0.681042 + 0.732244i \(0.261527\pi\)
\(62\) 0 0
\(63\) −3.17108 −0.399518
\(64\) 0 0
\(65\) −2.13388 −0.264676
\(66\) 0 0
\(67\) 0.276436 0.0337720 0.0168860 0.999857i \(-0.494625\pi\)
0.0168860 + 0.999857i \(0.494625\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −8.70814 −1.03347 −0.516733 0.856147i \(-0.672852\pi\)
−0.516733 + 0.856147i \(0.672852\pi\)
\(72\) 0 0
\(73\) −11.0869 −1.29762 −0.648811 0.760950i \(-0.724733\pi\)
−0.648811 + 0.760950i \(0.724733\pi\)
\(74\) 0 0
\(75\) 2.51273 0.290145
\(76\) 0 0
\(77\) 1.01394 0.115550
\(78\) 0 0
\(79\) −4.66744 −0.525128 −0.262564 0.964915i \(-0.584568\pi\)
−0.262564 + 0.964915i \(0.584568\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 1.81955 0.199722 0.0998610 0.995001i \(-0.468160\pi\)
0.0998610 + 0.995001i \(0.468160\pi\)
\(84\) 0 0
\(85\) −4.02437 −0.436504
\(86\) 0 0
\(87\) 1.00000 0.107211
\(88\) 0 0
\(89\) −15.6397 −1.65780 −0.828900 0.559397i \(-0.811033\pi\)
−0.828900 + 0.559397i \(0.811033\pi\)
\(90\) 0 0
\(91\) 2.46876 0.258796
\(92\) 0 0
\(93\) −0.759923 −0.0788004
\(94\) 0 0
\(95\) −2.50433 −0.256939
\(96\) 0 0
\(97\) 9.80700 0.995750 0.497875 0.867249i \(-0.334114\pi\)
0.497875 + 0.867249i \(0.334114\pi\)
\(98\) 0 0
\(99\) −0.319748 −0.0321359
\(100\) 0 0
\(101\) −0.127442 −0.0126810 −0.00634048 0.999980i \(-0.502018\pi\)
−0.00634048 + 0.999980i \(0.502018\pi\)
\(102\) 0 0
\(103\) 2.60543 0.256721 0.128361 0.991728i \(-0.459029\pi\)
0.128361 + 0.991728i \(0.459029\pi\)
\(104\) 0 0
\(105\) −8.69172 −0.848225
\(106\) 0 0
\(107\) 7.32175 0.707821 0.353910 0.935279i \(-0.384852\pi\)
0.353910 + 0.935279i \(0.384852\pi\)
\(108\) 0 0
\(109\) 8.76847 0.839867 0.419934 0.907555i \(-0.362053\pi\)
0.419934 + 0.907555i \(0.362053\pi\)
\(110\) 0 0
\(111\) −7.77804 −0.738259
\(112\) 0 0
\(113\) −7.11868 −0.669669 −0.334835 0.942277i \(-0.608680\pi\)
−0.334835 + 0.942277i \(0.608680\pi\)
\(114\) 0 0
\(115\) 2.74094 0.255594
\(116\) 0 0
\(117\) −0.778524 −0.0719745
\(118\) 0 0
\(119\) 4.65592 0.426807
\(120\) 0 0
\(121\) −10.8978 −0.990706
\(122\) 0 0
\(123\) −10.1559 −0.915727
\(124\) 0 0
\(125\) −6.81744 −0.609771
\(126\) 0 0
\(127\) 13.5344 1.20099 0.600494 0.799629i \(-0.294971\pi\)
0.600494 + 0.799629i \(0.294971\pi\)
\(128\) 0 0
\(129\) −4.11821 −0.362588
\(130\) 0 0
\(131\) −2.98124 −0.260472 −0.130236 0.991483i \(-0.541574\pi\)
−0.130236 + 0.991483i \(0.541574\pi\)
\(132\) 0 0
\(133\) 2.89734 0.251232
\(134\) 0 0
\(135\) 2.74094 0.235902
\(136\) 0 0
\(137\) 15.4718 1.32185 0.660923 0.750453i \(-0.270165\pi\)
0.660923 + 0.750453i \(0.270165\pi\)
\(138\) 0 0
\(139\) 6.12909 0.519863 0.259931 0.965627i \(-0.416300\pi\)
0.259931 + 0.965627i \(0.416300\pi\)
\(140\) 0 0
\(141\) −0.0564046 −0.00475012
\(142\) 0 0
\(143\) 0.248931 0.0208167
\(144\) 0 0
\(145\) 2.74094 0.227622
\(146\) 0 0
\(147\) 3.05572 0.252032
\(148\) 0 0
\(149\) −10.8122 −0.885773 −0.442887 0.896578i \(-0.646046\pi\)
−0.442887 + 0.896578i \(0.646046\pi\)
\(150\) 0 0
\(151\) 0.0371443 0.00302276 0.00151138 0.999999i \(-0.499519\pi\)
0.00151138 + 0.999999i \(0.499519\pi\)
\(152\) 0 0
\(153\) −1.46825 −0.118701
\(154\) 0 0
\(155\) −2.08290 −0.167303
\(156\) 0 0
\(157\) −0.229620 −0.0183257 −0.00916283 0.999958i \(-0.502917\pi\)
−0.00916283 + 0.999958i \(0.502917\pi\)
\(158\) 0 0
\(159\) −11.1853 −0.887050
\(160\) 0 0
\(161\) −3.17108 −0.249916
\(162\) 0 0
\(163\) −13.6219 −1.06695 −0.533475 0.845816i \(-0.679114\pi\)
−0.533475 + 0.845816i \(0.679114\pi\)
\(164\) 0 0
\(165\) −0.876409 −0.0682283
\(166\) 0 0
\(167\) −11.0692 −0.856561 −0.428280 0.903646i \(-0.640880\pi\)
−0.428280 + 0.903646i \(0.640880\pi\)
\(168\) 0 0
\(169\) −12.3939 −0.953377
\(170\) 0 0
\(171\) −0.913678 −0.0698707
\(172\) 0 0
\(173\) −10.3603 −0.787676 −0.393838 0.919180i \(-0.628853\pi\)
−0.393838 + 0.919180i \(0.628853\pi\)
\(174\) 0 0
\(175\) −7.96806 −0.602329
\(176\) 0 0
\(177\) 11.6998 0.879408
\(178\) 0 0
\(179\) −11.9142 −0.890506 −0.445253 0.895405i \(-0.646886\pi\)
−0.445253 + 0.895405i \(0.646886\pi\)
\(180\) 0 0
\(181\) −10.8691 −0.807896 −0.403948 0.914782i \(-0.632362\pi\)
−0.403948 + 0.914782i \(0.632362\pi\)
\(182\) 0 0
\(183\) 10.6382 0.786400
\(184\) 0 0
\(185\) −21.3191 −1.56741
\(186\) 0 0
\(187\) 0.469468 0.0343309
\(188\) 0 0
\(189\) −3.17108 −0.230662
\(190\) 0 0
\(191\) 10.8586 0.785700 0.392850 0.919603i \(-0.371489\pi\)
0.392850 + 0.919603i \(0.371489\pi\)
\(192\) 0 0
\(193\) 6.28047 0.452078 0.226039 0.974118i \(-0.427422\pi\)
0.226039 + 0.974118i \(0.427422\pi\)
\(194\) 0 0
\(195\) −2.13388 −0.152811
\(196\) 0 0
\(197\) −22.1081 −1.57513 −0.787567 0.616228i \(-0.788660\pi\)
−0.787567 + 0.616228i \(0.788660\pi\)
\(198\) 0 0
\(199\) −9.76637 −0.692320 −0.346160 0.938176i \(-0.612515\pi\)
−0.346160 + 0.938176i \(0.612515\pi\)
\(200\) 0 0
\(201\) 0.276436 0.0194983
\(202\) 0 0
\(203\) −3.17108 −0.222566
\(204\) 0 0
\(205\) −27.8367 −1.94420
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 0.292147 0.0202082
\(210\) 0 0
\(211\) 13.2681 0.913415 0.456708 0.889617i \(-0.349029\pi\)
0.456708 + 0.889617i \(0.349029\pi\)
\(212\) 0 0
\(213\) −8.70814 −0.596672
\(214\) 0 0
\(215\) −11.2878 −0.769819
\(216\) 0 0
\(217\) 2.40977 0.163586
\(218\) 0 0
\(219\) −11.0869 −0.749182
\(220\) 0 0
\(221\) 1.14306 0.0768908
\(222\) 0 0
\(223\) 12.5412 0.839820 0.419910 0.907566i \(-0.362062\pi\)
0.419910 + 0.907566i \(0.362062\pi\)
\(224\) 0 0
\(225\) 2.51273 0.167515
\(226\) 0 0
\(227\) 11.4671 0.761097 0.380549 0.924761i \(-0.375735\pi\)
0.380549 + 0.924761i \(0.375735\pi\)
\(228\) 0 0
\(229\) 11.5362 0.762332 0.381166 0.924507i \(-0.375523\pi\)
0.381166 + 0.924507i \(0.375523\pi\)
\(230\) 0 0
\(231\) 1.01394 0.0667127
\(232\) 0 0
\(233\) 25.9119 1.69755 0.848773 0.528757i \(-0.177342\pi\)
0.848773 + 0.528757i \(0.177342\pi\)
\(234\) 0 0
\(235\) −0.154601 −0.0100851
\(236\) 0 0
\(237\) −4.66744 −0.303183
\(238\) 0 0
\(239\) −18.4313 −1.19222 −0.596111 0.802902i \(-0.703288\pi\)
−0.596111 + 0.802902i \(0.703288\pi\)
\(240\) 0 0
\(241\) −8.44255 −0.543832 −0.271916 0.962321i \(-0.587657\pi\)
−0.271916 + 0.962321i \(0.587657\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 8.37554 0.535094
\(246\) 0 0
\(247\) 0.711320 0.0452602
\(248\) 0 0
\(249\) 1.81955 0.115310
\(250\) 0 0
\(251\) −16.0222 −1.01131 −0.505657 0.862734i \(-0.668750\pi\)
−0.505657 + 0.862734i \(0.668750\pi\)
\(252\) 0 0
\(253\) −0.319748 −0.0201024
\(254\) 0 0
\(255\) −4.02437 −0.252016
\(256\) 0 0
\(257\) −12.0434 −0.751249 −0.375624 0.926772i \(-0.622572\pi\)
−0.375624 + 0.926772i \(0.622572\pi\)
\(258\) 0 0
\(259\) 24.6648 1.53259
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) 25.9976 1.60308 0.801540 0.597942i \(-0.204015\pi\)
0.801540 + 0.597942i \(0.204015\pi\)
\(264\) 0 0
\(265\) −30.6581 −1.88331
\(266\) 0 0
\(267\) −15.6397 −0.957131
\(268\) 0 0
\(269\) −18.1511 −1.10669 −0.553346 0.832952i \(-0.686649\pi\)
−0.553346 + 0.832952i \(0.686649\pi\)
\(270\) 0 0
\(271\) −13.2450 −0.804578 −0.402289 0.915513i \(-0.631785\pi\)
−0.402289 + 0.915513i \(0.631785\pi\)
\(272\) 0 0
\(273\) 2.46876 0.149416
\(274\) 0 0
\(275\) −0.803441 −0.0484493
\(276\) 0 0
\(277\) 4.86516 0.292319 0.146160 0.989261i \(-0.453309\pi\)
0.146160 + 0.989261i \(0.453309\pi\)
\(278\) 0 0
\(279\) −0.759923 −0.0454954
\(280\) 0 0
\(281\) −25.5871 −1.52640 −0.763198 0.646164i \(-0.776372\pi\)
−0.763198 + 0.646164i \(0.776372\pi\)
\(282\) 0 0
\(283\) −10.1261 −0.601936 −0.300968 0.953634i \(-0.597310\pi\)
−0.300968 + 0.953634i \(0.597310\pi\)
\(284\) 0 0
\(285\) −2.50433 −0.148344
\(286\) 0 0
\(287\) 32.2052 1.90101
\(288\) 0 0
\(289\) −14.8443 −0.873191
\(290\) 0 0
\(291\) 9.80700 0.574897
\(292\) 0 0
\(293\) 27.6514 1.61541 0.807705 0.589587i \(-0.200709\pi\)
0.807705 + 0.589587i \(0.200709\pi\)
\(294\) 0 0
\(295\) 32.0683 1.86709
\(296\) 0 0
\(297\) −0.319748 −0.0185537
\(298\) 0 0
\(299\) −0.778524 −0.0450232
\(300\) 0 0
\(301\) 13.0592 0.752718
\(302\) 0 0
\(303\) −0.127442 −0.00732135
\(304\) 0 0
\(305\) 29.1587 1.66962
\(306\) 0 0
\(307\) 28.8959 1.64918 0.824589 0.565732i \(-0.191406\pi\)
0.824589 + 0.565732i \(0.191406\pi\)
\(308\) 0 0
\(309\) 2.60543 0.148218
\(310\) 0 0
\(311\) −0.879658 −0.0498808 −0.0249404 0.999689i \(-0.507940\pi\)
−0.0249404 + 0.999689i \(0.507940\pi\)
\(312\) 0 0
\(313\) −23.7373 −1.34171 −0.670855 0.741589i \(-0.734073\pi\)
−0.670855 + 0.741589i \(0.734073\pi\)
\(314\) 0 0
\(315\) −8.69172 −0.489723
\(316\) 0 0
\(317\) −4.87172 −0.273623 −0.136811 0.990597i \(-0.543685\pi\)
−0.136811 + 0.990597i \(0.543685\pi\)
\(318\) 0 0
\(319\) −0.319748 −0.0179024
\(320\) 0 0
\(321\) 7.32175 0.408660
\(322\) 0 0
\(323\) 1.34150 0.0746433
\(324\) 0 0
\(325\) −1.95622 −0.108512
\(326\) 0 0
\(327\) 8.76847 0.484898
\(328\) 0 0
\(329\) 0.178863 0.00986104
\(330\) 0 0
\(331\) −2.02968 −0.111561 −0.0557807 0.998443i \(-0.517765\pi\)
−0.0557807 + 0.998443i \(0.517765\pi\)
\(332\) 0 0
\(333\) −7.77804 −0.426234
\(334\) 0 0
\(335\) 0.757692 0.0413971
\(336\) 0 0
\(337\) 22.2073 1.20971 0.604854 0.796336i \(-0.293231\pi\)
0.604854 + 0.796336i \(0.293231\pi\)
\(338\) 0 0
\(339\) −7.11868 −0.386634
\(340\) 0 0
\(341\) 0.242984 0.0131583
\(342\) 0 0
\(343\) 12.5076 0.675347
\(344\) 0 0
\(345\) 2.74094 0.147567
\(346\) 0 0
\(347\) −3.65654 −0.196293 −0.0981466 0.995172i \(-0.531291\pi\)
−0.0981466 + 0.995172i \(0.531291\pi\)
\(348\) 0 0
\(349\) −7.99437 −0.427929 −0.213964 0.976841i \(-0.568638\pi\)
−0.213964 + 0.976841i \(0.568638\pi\)
\(350\) 0 0
\(351\) −0.778524 −0.0415545
\(352\) 0 0
\(353\) 15.0602 0.801571 0.400786 0.916172i \(-0.368737\pi\)
0.400786 + 0.916172i \(0.368737\pi\)
\(354\) 0 0
\(355\) −23.8684 −1.26681
\(356\) 0 0
\(357\) 4.65592 0.246417
\(358\) 0 0
\(359\) 19.0451 1.00516 0.502581 0.864530i \(-0.332384\pi\)
0.502581 + 0.864530i \(0.332384\pi\)
\(360\) 0 0
\(361\) −18.1652 −0.956063
\(362\) 0 0
\(363\) −10.8978 −0.571984
\(364\) 0 0
\(365\) −30.3884 −1.59060
\(366\) 0 0
\(367\) −25.0628 −1.30827 −0.654135 0.756378i \(-0.726967\pi\)
−0.654135 + 0.756378i \(0.726967\pi\)
\(368\) 0 0
\(369\) −10.1559 −0.528695
\(370\) 0 0
\(371\) 35.4693 1.84148
\(372\) 0 0
\(373\) 13.6205 0.705241 0.352621 0.935766i \(-0.385291\pi\)
0.352621 + 0.935766i \(0.385291\pi\)
\(374\) 0 0
\(375\) −6.81744 −0.352051
\(376\) 0 0
\(377\) −0.778524 −0.0400960
\(378\) 0 0
\(379\) −3.03758 −0.156030 −0.0780149 0.996952i \(-0.524858\pi\)
−0.0780149 + 0.996952i \(0.524858\pi\)
\(380\) 0 0
\(381\) 13.5344 0.693390
\(382\) 0 0
\(383\) −3.08959 −0.157871 −0.0789353 0.996880i \(-0.525152\pi\)
−0.0789353 + 0.996880i \(0.525152\pi\)
\(384\) 0 0
\(385\) 2.77916 0.141639
\(386\) 0 0
\(387\) −4.11821 −0.209340
\(388\) 0 0
\(389\) −38.9192 −1.97328 −0.986640 0.162914i \(-0.947911\pi\)
−0.986640 + 0.162914i \(0.947911\pi\)
\(390\) 0 0
\(391\) −1.46825 −0.0742524
\(392\) 0 0
\(393\) −2.98124 −0.150384
\(394\) 0 0
\(395\) −12.7932 −0.643694
\(396\) 0 0
\(397\) −16.5420 −0.830222 −0.415111 0.909771i \(-0.636257\pi\)
−0.415111 + 0.909771i \(0.636257\pi\)
\(398\) 0 0
\(399\) 2.89734 0.145049
\(400\) 0 0
\(401\) 11.7079 0.584665 0.292333 0.956317i \(-0.405569\pi\)
0.292333 + 0.956317i \(0.405569\pi\)
\(402\) 0 0
\(403\) 0.591618 0.0294706
\(404\) 0 0
\(405\) 2.74094 0.136198
\(406\) 0 0
\(407\) 2.48701 0.123277
\(408\) 0 0
\(409\) −10.8671 −0.537343 −0.268671 0.963232i \(-0.586585\pi\)
−0.268671 + 0.963232i \(0.586585\pi\)
\(410\) 0 0
\(411\) 15.4718 0.763169
\(412\) 0 0
\(413\) −37.1008 −1.82561
\(414\) 0 0
\(415\) 4.98728 0.244816
\(416\) 0 0
\(417\) 6.12909 0.300143
\(418\) 0 0
\(419\) −4.60704 −0.225068 −0.112534 0.993648i \(-0.535897\pi\)
−0.112534 + 0.993648i \(0.535897\pi\)
\(420\) 0 0
\(421\) 21.1985 1.03315 0.516577 0.856241i \(-0.327206\pi\)
0.516577 + 0.856241i \(0.327206\pi\)
\(422\) 0 0
\(423\) −0.0564046 −0.00274248
\(424\) 0 0
\(425\) −3.68931 −0.178958
\(426\) 0 0
\(427\) −33.7346 −1.63253
\(428\) 0 0
\(429\) 0.248931 0.0120185
\(430\) 0 0
\(431\) 35.7258 1.72085 0.860425 0.509577i \(-0.170198\pi\)
0.860425 + 0.509577i \(0.170198\pi\)
\(432\) 0 0
\(433\) 3.59244 0.172642 0.0863209 0.996267i \(-0.472489\pi\)
0.0863209 + 0.996267i \(0.472489\pi\)
\(434\) 0 0
\(435\) 2.74094 0.131418
\(436\) 0 0
\(437\) −0.913678 −0.0437072
\(438\) 0 0
\(439\) 11.7197 0.559349 0.279674 0.960095i \(-0.409773\pi\)
0.279674 + 0.960095i \(0.409773\pi\)
\(440\) 0 0
\(441\) 3.05572 0.145511
\(442\) 0 0
\(443\) −23.0195 −1.09369 −0.546845 0.837234i \(-0.684171\pi\)
−0.546845 + 0.837234i \(0.684171\pi\)
\(444\) 0 0
\(445\) −42.8673 −2.03210
\(446\) 0 0
\(447\) −10.8122 −0.511401
\(448\) 0 0
\(449\) −23.3026 −1.09972 −0.549858 0.835258i \(-0.685318\pi\)
−0.549858 + 0.835258i \(0.685318\pi\)
\(450\) 0 0
\(451\) 3.24733 0.152911
\(452\) 0 0
\(453\) 0.0371443 0.00174519
\(454\) 0 0
\(455\) 6.76671 0.317228
\(456\) 0 0
\(457\) −10.1758 −0.476004 −0.238002 0.971265i \(-0.576493\pi\)
−0.238002 + 0.971265i \(0.576493\pi\)
\(458\) 0 0
\(459\) −1.46825 −0.0685318
\(460\) 0 0
\(461\) 28.6775 1.33565 0.667823 0.744320i \(-0.267226\pi\)
0.667823 + 0.744320i \(0.267226\pi\)
\(462\) 0 0
\(463\) −1.26235 −0.0586666 −0.0293333 0.999570i \(-0.509338\pi\)
−0.0293333 + 0.999570i \(0.509338\pi\)
\(464\) 0 0
\(465\) −2.08290 −0.0965922
\(466\) 0 0
\(467\) −15.4777 −0.716221 −0.358111 0.933679i \(-0.616579\pi\)
−0.358111 + 0.933679i \(0.616579\pi\)
\(468\) 0 0
\(469\) −0.876598 −0.0404775
\(470\) 0 0
\(471\) −0.229620 −0.0105803
\(472\) 0 0
\(473\) 1.31679 0.0605460
\(474\) 0 0
\(475\) −2.29583 −0.105340
\(476\) 0 0
\(477\) −11.1853 −0.512138
\(478\) 0 0
\(479\) −23.1503 −1.05776 −0.528882 0.848695i \(-0.677389\pi\)
−0.528882 + 0.848695i \(0.677389\pi\)
\(480\) 0 0
\(481\) 6.05539 0.276102
\(482\) 0 0
\(483\) −3.17108 −0.144289
\(484\) 0 0
\(485\) 26.8804 1.22057
\(486\) 0 0
\(487\) 15.5288 0.703677 0.351839 0.936061i \(-0.385557\pi\)
0.351839 + 0.936061i \(0.385557\pi\)
\(488\) 0 0
\(489\) −13.6219 −0.616004
\(490\) 0 0
\(491\) 31.1097 1.40396 0.701979 0.712197i \(-0.252300\pi\)
0.701979 + 0.712197i \(0.252300\pi\)
\(492\) 0 0
\(493\) −1.46825 −0.0661265
\(494\) 0 0
\(495\) −0.876409 −0.0393916
\(496\) 0 0
\(497\) 27.6142 1.23866
\(498\) 0 0
\(499\) 17.5446 0.785404 0.392702 0.919666i \(-0.371540\pi\)
0.392702 + 0.919666i \(0.371540\pi\)
\(500\) 0 0
\(501\) −11.0692 −0.494536
\(502\) 0 0
\(503\) −3.56113 −0.158783 −0.0793915 0.996844i \(-0.525298\pi\)
−0.0793915 + 0.996844i \(0.525298\pi\)
\(504\) 0 0
\(505\) −0.349311 −0.0155441
\(506\) 0 0
\(507\) −12.3939 −0.550432
\(508\) 0 0
\(509\) −4.37498 −0.193918 −0.0969588 0.995288i \(-0.530912\pi\)
−0.0969588 + 0.995288i \(0.530912\pi\)
\(510\) 0 0
\(511\) 35.1574 1.55527
\(512\) 0 0
\(513\) −0.913678 −0.0403399
\(514\) 0 0
\(515\) 7.14133 0.314685
\(516\) 0 0
\(517\) 0.0180352 0.000793189 0
\(518\) 0 0
\(519\) −10.3603 −0.454765
\(520\) 0 0
\(521\) 12.2906 0.538463 0.269231 0.963076i \(-0.413230\pi\)
0.269231 + 0.963076i \(0.413230\pi\)
\(522\) 0 0
\(523\) 10.9510 0.478852 0.239426 0.970915i \(-0.423041\pi\)
0.239426 + 0.970915i \(0.423041\pi\)
\(524\) 0 0
\(525\) −7.96806 −0.347755
\(526\) 0 0
\(527\) 1.11575 0.0486030
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 11.6998 0.507726
\(532\) 0 0
\(533\) 7.90662 0.342474
\(534\) 0 0
\(535\) 20.0685 0.867635
\(536\) 0 0
\(537\) −11.9142 −0.514134
\(538\) 0 0
\(539\) −0.977061 −0.0420850
\(540\) 0 0
\(541\) 20.8769 0.897570 0.448785 0.893640i \(-0.351857\pi\)
0.448785 + 0.893640i \(0.351857\pi\)
\(542\) 0 0
\(543\) −10.8691 −0.466439
\(544\) 0 0
\(545\) 24.0338 1.02950
\(546\) 0 0
\(547\) −6.70207 −0.286560 −0.143280 0.989682i \(-0.545765\pi\)
−0.143280 + 0.989682i \(0.545765\pi\)
\(548\) 0 0
\(549\) 10.6382 0.454028
\(550\) 0 0
\(551\) −0.913678 −0.0389240
\(552\) 0 0
\(553\) 14.8008 0.629394
\(554\) 0 0
\(555\) −21.3191 −0.904946
\(556\) 0 0
\(557\) 41.6614 1.76525 0.882625 0.470078i \(-0.155774\pi\)
0.882625 + 0.470078i \(0.155774\pi\)
\(558\) 0 0
\(559\) 3.20613 0.135605
\(560\) 0 0
\(561\) 0.469468 0.0198210
\(562\) 0 0
\(563\) 29.6449 1.24938 0.624691 0.780872i \(-0.285225\pi\)
0.624691 + 0.780872i \(0.285225\pi\)
\(564\) 0 0
\(565\) −19.5119 −0.820870
\(566\) 0 0
\(567\) −3.17108 −0.133173
\(568\) 0 0
\(569\) 2.80536 0.117607 0.0588034 0.998270i \(-0.481272\pi\)
0.0588034 + 0.998270i \(0.481272\pi\)
\(570\) 0 0
\(571\) −36.5749 −1.53061 −0.765306 0.643667i \(-0.777412\pi\)
−0.765306 + 0.643667i \(0.777412\pi\)
\(572\) 0 0
\(573\) 10.8586 0.453624
\(574\) 0 0
\(575\) 2.51273 0.104788
\(576\) 0 0
\(577\) −14.9213 −0.621180 −0.310590 0.950544i \(-0.600527\pi\)
−0.310590 + 0.950544i \(0.600527\pi\)
\(578\) 0 0
\(579\) 6.28047 0.261007
\(580\) 0 0
\(581\) −5.76995 −0.239378
\(582\) 0 0
\(583\) 3.57647 0.148122
\(584\) 0 0
\(585\) −2.13388 −0.0882252
\(586\) 0 0
\(587\) 29.4095 1.21386 0.606930 0.794755i \(-0.292401\pi\)
0.606930 + 0.794755i \(0.292401\pi\)
\(588\) 0 0
\(589\) 0.694325 0.0286092
\(590\) 0 0
\(591\) −22.1081 −0.909405
\(592\) 0 0
\(593\) −15.3090 −0.628664 −0.314332 0.949313i \(-0.601780\pi\)
−0.314332 + 0.949313i \(0.601780\pi\)
\(594\) 0 0
\(595\) 12.7616 0.523174
\(596\) 0 0
\(597\) −9.76637 −0.399711
\(598\) 0 0
\(599\) −21.3689 −0.873109 −0.436555 0.899678i \(-0.643801\pi\)
−0.436555 + 0.899678i \(0.643801\pi\)
\(600\) 0 0
\(601\) −37.6068 −1.53401 −0.767006 0.641640i \(-0.778254\pi\)
−0.767006 + 0.641640i \(0.778254\pi\)
\(602\) 0 0
\(603\) 0.276436 0.0112573
\(604\) 0 0
\(605\) −29.8701 −1.21439
\(606\) 0 0
\(607\) −8.27447 −0.335850 −0.167925 0.985800i \(-0.553707\pi\)
−0.167925 + 0.985800i \(0.553707\pi\)
\(608\) 0 0
\(609\) −3.17108 −0.128498
\(610\) 0 0
\(611\) 0.0439123 0.00177650
\(612\) 0 0
\(613\) 29.1148 1.17594 0.587969 0.808884i \(-0.299928\pi\)
0.587969 + 0.808884i \(0.299928\pi\)
\(614\) 0 0
\(615\) −27.8367 −1.12248
\(616\) 0 0
\(617\) −18.3528 −0.738856 −0.369428 0.929259i \(-0.620446\pi\)
−0.369428 + 0.929259i \(0.620446\pi\)
\(618\) 0 0
\(619\) 37.7224 1.51619 0.758096 0.652143i \(-0.226130\pi\)
0.758096 + 0.652143i \(0.226130\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 49.5945 1.98696
\(624\) 0 0
\(625\) −31.2498 −1.24999
\(626\) 0 0
\(627\) 0.292147 0.0116672
\(628\) 0 0
\(629\) 11.4201 0.455348
\(630\) 0 0
\(631\) −21.1508 −0.842002 −0.421001 0.907060i \(-0.638321\pi\)
−0.421001 + 0.907060i \(0.638321\pi\)
\(632\) 0 0
\(633\) 13.2681 0.527361
\(634\) 0 0
\(635\) 37.0970 1.47215
\(636\) 0 0
\(637\) −2.37895 −0.0942575
\(638\) 0 0
\(639\) −8.70814 −0.344489
\(640\) 0 0
\(641\) −3.50898 −0.138596 −0.0692982 0.997596i \(-0.522076\pi\)
−0.0692982 + 0.997596i \(0.522076\pi\)
\(642\) 0 0
\(643\) 6.23550 0.245904 0.122952 0.992413i \(-0.460764\pi\)
0.122952 + 0.992413i \(0.460764\pi\)
\(644\) 0 0
\(645\) −11.2878 −0.444455
\(646\) 0 0
\(647\) −8.42133 −0.331077 −0.165538 0.986203i \(-0.552936\pi\)
−0.165538 + 0.986203i \(0.552936\pi\)
\(648\) 0 0
\(649\) −3.74097 −0.146846
\(650\) 0 0
\(651\) 2.40977 0.0944465
\(652\) 0 0
\(653\) 38.9460 1.52408 0.762038 0.647532i \(-0.224199\pi\)
0.762038 + 0.647532i \(0.224199\pi\)
\(654\) 0 0
\(655\) −8.17139 −0.319283
\(656\) 0 0
\(657\) −11.0869 −0.432541
\(658\) 0 0
\(659\) 27.4963 1.07110 0.535552 0.844503i \(-0.320104\pi\)
0.535552 + 0.844503i \(0.320104\pi\)
\(660\) 0 0
\(661\) 2.68466 0.104421 0.0522106 0.998636i \(-0.483373\pi\)
0.0522106 + 0.998636i \(0.483373\pi\)
\(662\) 0 0
\(663\) 1.14306 0.0443929
\(664\) 0 0
\(665\) 7.94143 0.307956
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 0 0
\(669\) 12.5412 0.484870
\(670\) 0 0
\(671\) −3.40155 −0.131315
\(672\) 0 0
\(673\) −10.7614 −0.414820 −0.207410 0.978254i \(-0.566503\pi\)
−0.207410 + 0.978254i \(0.566503\pi\)
\(674\) 0 0
\(675\) 2.51273 0.0967151
\(676\) 0 0
\(677\) −3.71712 −0.142860 −0.0714302 0.997446i \(-0.522756\pi\)
−0.0714302 + 0.997446i \(0.522756\pi\)
\(678\) 0 0
\(679\) −31.0988 −1.19346
\(680\) 0 0
\(681\) 11.4671 0.439420
\(682\) 0 0
\(683\) 42.4607 1.62471 0.812357 0.583161i \(-0.198184\pi\)
0.812357 + 0.583161i \(0.198184\pi\)
\(684\) 0 0
\(685\) 42.4073 1.62030
\(686\) 0 0
\(687\) 11.5362 0.440132
\(688\) 0 0
\(689\) 8.70800 0.331748
\(690\) 0 0
\(691\) 6.56195 0.249628 0.124814 0.992180i \(-0.460167\pi\)
0.124814 + 0.992180i \(0.460167\pi\)
\(692\) 0 0
\(693\) 1.01394 0.0385166
\(694\) 0 0
\(695\) 16.7994 0.637239
\(696\) 0 0
\(697\) 14.9114 0.564808
\(698\) 0 0
\(699\) 25.9119 0.980079
\(700\) 0 0
\(701\) −3.96758 −0.149854 −0.0749268 0.997189i \(-0.523872\pi\)
−0.0749268 + 0.997189i \(0.523872\pi\)
\(702\) 0 0
\(703\) 7.10663 0.268031
\(704\) 0 0
\(705\) −0.154601 −0.00582262
\(706\) 0 0
\(707\) 0.404128 0.0151988
\(708\) 0 0
\(709\) −34.0976 −1.28056 −0.640282 0.768140i \(-0.721182\pi\)
−0.640282 + 0.768140i \(0.721182\pi\)
\(710\) 0 0
\(711\) −4.66744 −0.175043
\(712\) 0 0
\(713\) −0.759923 −0.0284593
\(714\) 0 0
\(715\) 0.682305 0.0255168
\(716\) 0 0
\(717\) −18.4313 −0.688330
\(718\) 0 0
\(719\) −6.94170 −0.258882 −0.129441 0.991587i \(-0.541318\pi\)
−0.129441 + 0.991587i \(0.541318\pi\)
\(720\) 0 0
\(721\) −8.26203 −0.307694
\(722\) 0 0
\(723\) −8.44255 −0.313982
\(724\) 0 0
\(725\) 2.51273 0.0933205
\(726\) 0 0
\(727\) −36.7564 −1.36322 −0.681611 0.731715i \(-0.738720\pi\)
−0.681611 + 0.731715i \(0.738720\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 6.04655 0.223640
\(732\) 0 0
\(733\) 50.2866 1.85738 0.928690 0.370857i \(-0.120936\pi\)
0.928690 + 0.370857i \(0.120936\pi\)
\(734\) 0 0
\(735\) 8.37554 0.308936
\(736\) 0 0
\(737\) −0.0883897 −0.00325588
\(738\) 0 0
\(739\) −6.94487 −0.255471 −0.127736 0.991808i \(-0.540771\pi\)
−0.127736 + 0.991808i \(0.540771\pi\)
\(740\) 0 0
\(741\) 0.711320 0.0261310
\(742\) 0 0
\(743\) 0.278485 0.0102166 0.00510831 0.999987i \(-0.498374\pi\)
0.00510831 + 0.999987i \(0.498374\pi\)
\(744\) 0 0
\(745\) −29.6357 −1.08577
\(746\) 0 0
\(747\) 1.81955 0.0665740
\(748\) 0 0
\(749\) −23.2178 −0.848361
\(750\) 0 0
\(751\) −40.6746 −1.48424 −0.742118 0.670269i \(-0.766179\pi\)
−0.742118 + 0.670269i \(0.766179\pi\)
\(752\) 0 0
\(753\) −16.0222 −0.583883
\(754\) 0 0
\(755\) 0.101810 0.00370525
\(756\) 0 0
\(757\) −29.3657 −1.06732 −0.533658 0.845700i \(-0.679183\pi\)
−0.533658 + 0.845700i \(0.679183\pi\)
\(758\) 0 0
\(759\) −0.319748 −0.0116061
\(760\) 0 0
\(761\) −12.1509 −0.440471 −0.220236 0.975447i \(-0.570683\pi\)
−0.220236 + 0.975447i \(0.570683\pi\)
\(762\) 0 0
\(763\) −27.8055 −1.00663
\(764\) 0 0
\(765\) −4.02437 −0.145501
\(766\) 0 0
\(767\) −9.10854 −0.328890
\(768\) 0 0
\(769\) −2.20534 −0.0795266 −0.0397633 0.999209i \(-0.512660\pi\)
−0.0397633 + 0.999209i \(0.512660\pi\)
\(770\) 0 0
\(771\) −12.0434 −0.433734
\(772\) 0 0
\(773\) −13.6949 −0.492570 −0.246285 0.969198i \(-0.579210\pi\)
−0.246285 + 0.969198i \(0.579210\pi\)
\(774\) 0 0
\(775\) −1.90948 −0.0685907
\(776\) 0 0
\(777\) 24.6648 0.884843
\(778\) 0 0
\(779\) 9.27923 0.332463
\(780\) 0 0
\(781\) 2.78441 0.0996340
\(782\) 0 0
\(783\) 1.00000 0.0357371
\(784\) 0 0
\(785\) −0.629374 −0.0224633
\(786\) 0 0
\(787\) −34.4934 −1.22956 −0.614779 0.788699i \(-0.710755\pi\)
−0.614779 + 0.788699i \(0.710755\pi\)
\(788\) 0 0
\(789\) 25.9976 0.925538
\(790\) 0 0
\(791\) 22.5739 0.802635
\(792\) 0 0
\(793\) −8.28211 −0.294106
\(794\) 0 0
\(795\) −30.6581 −1.08733
\(796\) 0 0
\(797\) 44.3779 1.57195 0.785973 0.618261i \(-0.212163\pi\)
0.785973 + 0.618261i \(0.212163\pi\)
\(798\) 0 0
\(799\) 0.0828157 0.00292981
\(800\) 0 0
\(801\) −15.6397 −0.552600
\(802\) 0 0
\(803\) 3.54501 0.125101
\(804\) 0 0
\(805\) −8.69172 −0.306343
\(806\) 0 0
\(807\) −18.1511 −0.638949
\(808\) 0 0
\(809\) 34.8304 1.22457 0.612286 0.790637i \(-0.290250\pi\)
0.612286 + 0.790637i \(0.290250\pi\)
\(810\) 0 0
\(811\) −26.8425 −0.942567 −0.471283 0.881982i \(-0.656209\pi\)
−0.471283 + 0.881982i \(0.656209\pi\)
\(812\) 0 0
\(813\) −13.2450 −0.464523
\(814\) 0 0
\(815\) −37.3368 −1.30785
\(816\) 0 0
\(817\) 3.76272 0.131641
\(818\) 0 0
\(819\) 2.46876 0.0862654
\(820\) 0 0
\(821\) 23.0110 0.803091 0.401545 0.915839i \(-0.368473\pi\)
0.401545 + 0.915839i \(0.368473\pi\)
\(822\) 0 0
\(823\) −26.5219 −0.924496 −0.462248 0.886751i \(-0.652957\pi\)
−0.462248 + 0.886751i \(0.652957\pi\)
\(824\) 0 0
\(825\) −0.803441 −0.0279722
\(826\) 0 0
\(827\) 54.9516 1.91086 0.955428 0.295224i \(-0.0953944\pi\)
0.955428 + 0.295224i \(0.0953944\pi\)
\(828\) 0 0
\(829\) 42.6804 1.48235 0.741176 0.671310i \(-0.234268\pi\)
0.741176 + 0.671310i \(0.234268\pi\)
\(830\) 0 0
\(831\) 4.86516 0.168771
\(832\) 0 0
\(833\) −4.48655 −0.155450
\(834\) 0 0
\(835\) −30.3400 −1.04996
\(836\) 0 0
\(837\) −0.759923 −0.0262668
\(838\) 0 0
\(839\) −20.0404 −0.691871 −0.345936 0.938258i \(-0.612438\pi\)
−0.345936 + 0.938258i \(0.612438\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −25.5871 −0.881266
\(844\) 0 0
\(845\) −33.9709 −1.16863
\(846\) 0 0
\(847\) 34.5576 1.18741
\(848\) 0 0
\(849\) −10.1261 −0.347528
\(850\) 0 0
\(851\) −7.77804 −0.266628
\(852\) 0 0
\(853\) −11.1868 −0.383028 −0.191514 0.981490i \(-0.561340\pi\)
−0.191514 + 0.981490i \(0.561340\pi\)
\(854\) 0 0
\(855\) −2.50433 −0.0856464
\(856\) 0 0
\(857\) −52.6242 −1.79761 −0.898805 0.438349i \(-0.855563\pi\)
−0.898805 + 0.438349i \(0.855563\pi\)
\(858\) 0 0
\(859\) −6.92802 −0.236381 −0.118191 0.992991i \(-0.537709\pi\)
−0.118191 + 0.992991i \(0.537709\pi\)
\(860\) 0 0
\(861\) 32.2052 1.09755
\(862\) 0 0
\(863\) −49.1189 −1.67203 −0.836013 0.548710i \(-0.815119\pi\)
−0.836013 + 0.548710i \(0.815119\pi\)
\(864\) 0 0
\(865\) −28.3968 −0.965520
\(866\) 0 0
\(867\) −14.8443 −0.504137
\(868\) 0 0
\(869\) 1.49240 0.0506264
\(870\) 0 0
\(871\) −0.215212 −0.00729217
\(872\) 0 0
\(873\) 9.80700 0.331917
\(874\) 0 0
\(875\) 21.6186 0.730843
\(876\) 0 0
\(877\) 15.9647 0.539090 0.269545 0.962988i \(-0.413127\pi\)
0.269545 + 0.962988i \(0.413127\pi\)
\(878\) 0 0
\(879\) 27.6514 0.932658
\(880\) 0 0
\(881\) 36.7371 1.23770 0.618852 0.785507i \(-0.287598\pi\)
0.618852 + 0.785507i \(0.287598\pi\)
\(882\) 0 0
\(883\) −39.0226 −1.31321 −0.656607 0.754233i \(-0.728009\pi\)
−0.656607 + 0.754233i \(0.728009\pi\)
\(884\) 0 0
\(885\) 32.0683 1.07796
\(886\) 0 0
\(887\) 14.0804 0.472772 0.236386 0.971659i \(-0.424037\pi\)
0.236386 + 0.971659i \(0.424037\pi\)
\(888\) 0 0
\(889\) −42.9187 −1.43945
\(890\) 0 0
\(891\) −0.319748 −0.0107120
\(892\) 0 0
\(893\) 0.0515356 0.00172457
\(894\) 0 0
\(895\) −32.6559 −1.09157
\(896\) 0 0
\(897\) −0.778524 −0.0259942
\(898\) 0 0
\(899\) −0.759923 −0.0253449
\(900\) 0 0
\(901\) 16.4227 0.547120
\(902\) 0 0
\(903\) 13.0592 0.434582
\(904\) 0 0
\(905\) −29.7916 −0.990307
\(906\) 0 0
\(907\) −48.8506 −1.62206 −0.811028 0.585007i \(-0.801092\pi\)
−0.811028 + 0.585007i \(0.801092\pi\)
\(908\) 0 0
\(909\) −0.127442 −0.00422699
\(910\) 0 0
\(911\) 2.02211 0.0669954 0.0334977 0.999439i \(-0.489335\pi\)
0.0334977 + 0.999439i \(0.489335\pi\)
\(912\) 0 0
\(913\) −0.581799 −0.0192547
\(914\) 0 0
\(915\) 29.1587 0.963956
\(916\) 0 0
\(917\) 9.45374 0.312190
\(918\) 0 0
\(919\) 39.3164 1.29693 0.648465 0.761245i \(-0.275411\pi\)
0.648465 + 0.761245i \(0.275411\pi\)
\(920\) 0 0
\(921\) 28.8959 0.952153
\(922\) 0 0
\(923\) 6.77949 0.223150
\(924\) 0 0
\(925\) −19.5441 −0.642607
\(926\) 0 0
\(927\) 2.60543 0.0855737
\(928\) 0 0
\(929\) −26.6454 −0.874206 −0.437103 0.899412i \(-0.643995\pi\)
−0.437103 + 0.899412i \(0.643995\pi\)
\(930\) 0 0
\(931\) −2.79195 −0.0915024
\(932\) 0 0
\(933\) −0.879658 −0.0287987
\(934\) 0 0
\(935\) 1.28678 0.0420823
\(936\) 0 0
\(937\) −0.670073 −0.0218903 −0.0109452 0.999940i \(-0.503484\pi\)
−0.0109452 + 0.999940i \(0.503484\pi\)
\(938\) 0 0
\(939\) −23.7373 −0.774636
\(940\) 0 0
\(941\) 11.8283 0.385593 0.192797 0.981239i \(-0.438244\pi\)
0.192797 + 0.981239i \(0.438244\pi\)
\(942\) 0 0
\(943\) −10.1559 −0.330722
\(944\) 0 0
\(945\) −8.69172 −0.282742
\(946\) 0 0
\(947\) −34.0658 −1.10699 −0.553494 0.832853i \(-0.686706\pi\)
−0.553494 + 0.832853i \(0.686706\pi\)
\(948\) 0 0
\(949\) 8.63140 0.280187
\(950\) 0 0
\(951\) −4.87172 −0.157976
\(952\) 0 0
\(953\) 24.8288 0.804285 0.402142 0.915577i \(-0.368266\pi\)
0.402142 + 0.915577i \(0.368266\pi\)
\(954\) 0 0
\(955\) 29.7627 0.963099
\(956\) 0 0
\(957\) −0.319748 −0.0103360
\(958\) 0 0
\(959\) −49.0623 −1.58430
\(960\) 0 0
\(961\) −30.4225 −0.981372
\(962\) 0 0
\(963\) 7.32175 0.235940
\(964\) 0 0
\(965\) 17.2144 0.554150
\(966\) 0 0
\(967\) 1.04696 0.0336681 0.0168340 0.999858i \(-0.494641\pi\)
0.0168340 + 0.999858i \(0.494641\pi\)
\(968\) 0 0
\(969\) 1.34150 0.0430953
\(970\) 0 0
\(971\) −27.3776 −0.878590 −0.439295 0.898343i \(-0.644772\pi\)
−0.439295 + 0.898343i \(0.644772\pi\)
\(972\) 0 0
\(973\) −19.4358 −0.623083
\(974\) 0 0
\(975\) −1.95622 −0.0626492
\(976\) 0 0
\(977\) −12.0324 −0.384949 −0.192475 0.981302i \(-0.561651\pi\)
−0.192475 + 0.981302i \(0.561651\pi\)
\(978\) 0 0
\(979\) 5.00075 0.159825
\(980\) 0 0
\(981\) 8.76847 0.279956
\(982\) 0 0
\(983\) 39.1661 1.24921 0.624603 0.780943i \(-0.285261\pi\)
0.624603 + 0.780943i \(0.285261\pi\)
\(984\) 0 0
\(985\) −60.5968 −1.93078
\(986\) 0 0
\(987\) 0.178863 0.00569328
\(988\) 0 0
\(989\) −4.11821 −0.130952
\(990\) 0 0
\(991\) 30.0370 0.954156 0.477078 0.878861i \(-0.341696\pi\)
0.477078 + 0.878861i \(0.341696\pi\)
\(992\) 0 0
\(993\) −2.02968 −0.0644100
\(994\) 0 0
\(995\) −26.7690 −0.848634
\(996\) 0 0
\(997\) 3.90829 0.123777 0.0618884 0.998083i \(-0.480288\pi\)
0.0618884 + 0.998083i \(0.480288\pi\)
\(998\) 0 0
\(999\) −7.77804 −0.246086
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 \(a_p\))