Properties

Label 8004.2.a.d.1.7
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 1.7
Root \(0.411238\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+1.71910 q^{5}\) \(+0.210007 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+1.71910 q^{5}\) \(+0.210007 q^{7}\) \(+1.00000 q^{9}\) \(-2.37289 q^{11}\) \(-3.22411 q^{13}\) \(+1.71910 q^{15}\) \(-1.22874 q^{17}\) \(-7.29204 q^{19}\) \(+0.210007 q^{21}\) \(+1.00000 q^{23}\) \(-2.04468 q^{25}\) \(+1.00000 q^{27}\) \(+1.00000 q^{29}\) \(+3.68744 q^{31}\) \(-2.37289 q^{33}\) \(+0.361024 q^{35}\) \(+7.65306 q^{37}\) \(-3.22411 q^{39}\) \(+2.82840 q^{41}\) \(+9.02791 q^{43}\) \(+1.71910 q^{45}\) \(-5.43500 q^{47}\) \(-6.95590 q^{49}\) \(-1.22874 q^{51}\) \(-2.49073 q^{53}\) \(-4.07924 q^{55}\) \(-7.29204 q^{57}\) \(-3.55638 q^{59}\) \(-7.27294 q^{61}\) \(+0.210007 q^{63}\) \(-5.54258 q^{65}\) \(+9.41000 q^{67}\) \(+1.00000 q^{69}\) \(-7.53494 q^{71}\) \(+3.75783 q^{73}\) \(-2.04468 q^{75}\) \(-0.498323 q^{77}\) \(+0.807221 q^{79}\) \(+1.00000 q^{81}\) \(+5.58455 q^{83}\) \(-2.11233 q^{85}\) \(+1.00000 q^{87}\) \(-11.2438 q^{89}\) \(-0.677086 q^{91}\) \(+3.68744 q^{93}\) \(-12.5358 q^{95}\) \(-11.5915 q^{97}\) \(-2.37289 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 11q^{41} \) \(\mathstrut -\mathstrut 7q^{43} \) \(\mathstrut -\mathstrut 5q^{45} \) \(\mathstrut -\mathstrut 14q^{47} \) \(\mathstrut -\mathstrut 18q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut -\mathstrut 15q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 5q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut -\mathstrut 21q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 8q^{81} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut +\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 2q^{93} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 7q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 1.71910 0.768807 0.384403 0.923165i \(-0.374407\pi\)
0.384403 + 0.923165i \(0.374407\pi\)
\(6\) 0 0
\(7\) 0.210007 0.0793752 0.0396876 0.999212i \(-0.487364\pi\)
0.0396876 + 0.999212i \(0.487364\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.37289 −0.715453 −0.357726 0.933826i \(-0.616448\pi\)
−0.357726 + 0.933826i \(0.616448\pi\)
\(12\) 0 0
\(13\) −3.22411 −0.894207 −0.447104 0.894482i \(-0.647545\pi\)
−0.447104 + 0.894482i \(0.647545\pi\)
\(14\) 0 0
\(15\) 1.71910 0.443871
\(16\) 0 0
\(17\) −1.22874 −0.298013 −0.149007 0.988836i \(-0.547608\pi\)
−0.149007 + 0.988836i \(0.547608\pi\)
\(18\) 0 0
\(19\) −7.29204 −1.67291 −0.836454 0.548037i \(-0.815375\pi\)
−0.836454 + 0.548037i \(0.815375\pi\)
\(20\) 0 0
\(21\) 0.210007 0.0458273
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −2.04468 −0.408937
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 3.68744 0.662283 0.331142 0.943581i \(-0.392566\pi\)
0.331142 + 0.943581i \(0.392566\pi\)
\(32\) 0 0
\(33\) −2.37289 −0.413067
\(34\) 0 0
\(35\) 0.361024 0.0610241
\(36\) 0 0
\(37\) 7.65306 1.25816 0.629078 0.777342i \(-0.283433\pi\)
0.629078 + 0.777342i \(0.283433\pi\)
\(38\) 0 0
\(39\) −3.22411 −0.516271
\(40\) 0 0
\(41\) 2.82840 0.441722 0.220861 0.975305i \(-0.429113\pi\)
0.220861 + 0.975305i \(0.429113\pi\)
\(42\) 0 0
\(43\) 9.02791 1.37674 0.688372 0.725358i \(-0.258326\pi\)
0.688372 + 0.725358i \(0.258326\pi\)
\(44\) 0 0
\(45\) 1.71910 0.256269
\(46\) 0 0
\(47\) −5.43500 −0.792776 −0.396388 0.918083i \(-0.629736\pi\)
−0.396388 + 0.918083i \(0.629736\pi\)
\(48\) 0 0
\(49\) −6.95590 −0.993700
\(50\) 0 0
\(51\) −1.22874 −0.172058
\(52\) 0 0
\(53\) −2.49073 −0.342128 −0.171064 0.985260i \(-0.554720\pi\)
−0.171064 + 0.985260i \(0.554720\pi\)
\(54\) 0 0
\(55\) −4.07924 −0.550045
\(56\) 0 0
\(57\) −7.29204 −0.965854
\(58\) 0 0
\(59\) −3.55638 −0.463002 −0.231501 0.972835i \(-0.574364\pi\)
−0.231501 + 0.972835i \(0.574364\pi\)
\(60\) 0 0
\(61\) −7.27294 −0.931205 −0.465602 0.884994i \(-0.654162\pi\)
−0.465602 + 0.884994i \(0.654162\pi\)
\(62\) 0 0
\(63\) 0.210007 0.0264584
\(64\) 0 0
\(65\) −5.54258 −0.687472
\(66\) 0 0
\(67\) 9.41000 1.14961 0.574807 0.818289i \(-0.305077\pi\)
0.574807 + 0.818289i \(0.305077\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −7.53494 −0.894233 −0.447117 0.894476i \(-0.647549\pi\)
−0.447117 + 0.894476i \(0.647549\pi\)
\(72\) 0 0
\(73\) 3.75783 0.439820 0.219910 0.975520i \(-0.429424\pi\)
0.219910 + 0.975520i \(0.429424\pi\)
\(74\) 0 0
\(75\) −2.04468 −0.236100
\(76\) 0 0
\(77\) −0.498323 −0.0567892
\(78\) 0 0
\(79\) 0.807221 0.0908194 0.0454097 0.998968i \(-0.485541\pi\)
0.0454097 + 0.998968i \(0.485541\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 5.58455 0.612984 0.306492 0.951873i \(-0.400845\pi\)
0.306492 + 0.951873i \(0.400845\pi\)
\(84\) 0 0
\(85\) −2.11233 −0.229114
\(86\) 0 0
\(87\) 1.00000 0.107211
\(88\) 0 0
\(89\) −11.2438 −1.19184 −0.595919 0.803044i \(-0.703212\pi\)
−0.595919 + 0.803044i \(0.703212\pi\)
\(90\) 0 0
\(91\) −0.677086 −0.0709779
\(92\) 0 0
\(93\) 3.68744 0.382370
\(94\) 0 0
\(95\) −12.5358 −1.28614
\(96\) 0 0
\(97\) −11.5915 −1.17694 −0.588471 0.808519i \(-0.700270\pi\)
−0.588471 + 0.808519i \(0.700270\pi\)
\(98\) 0 0
\(99\) −2.37289 −0.238484
\(100\) 0 0
\(101\) −1.54449 −0.153683 −0.0768413 0.997043i \(-0.524483\pi\)
−0.0768413 + 0.997043i \(0.524483\pi\)
\(102\) 0 0
\(103\) −14.7680 −1.45513 −0.727567 0.686037i \(-0.759349\pi\)
−0.727567 + 0.686037i \(0.759349\pi\)
\(104\) 0 0
\(105\) 0.361024 0.0352323
\(106\) 0 0
\(107\) −12.0255 −1.16255 −0.581273 0.813708i \(-0.697445\pi\)
−0.581273 + 0.813708i \(0.697445\pi\)
\(108\) 0 0
\(109\) −3.79224 −0.363230 −0.181615 0.983370i \(-0.558133\pi\)
−0.181615 + 0.983370i \(0.558133\pi\)
\(110\) 0 0
\(111\) 7.65306 0.726396
\(112\) 0 0
\(113\) −15.1915 −1.42909 −0.714546 0.699588i \(-0.753367\pi\)
−0.714546 + 0.699588i \(0.753367\pi\)
\(114\) 0 0
\(115\) 1.71910 0.160307
\(116\) 0 0
\(117\) −3.22411 −0.298069
\(118\) 0 0
\(119\) −0.258044 −0.0236548
\(120\) 0 0
\(121\) −5.36940 −0.488128
\(122\) 0 0
\(123\) 2.82840 0.255029
\(124\) 0 0
\(125\) −12.1105 −1.08320
\(126\) 0 0
\(127\) −13.6613 −1.21225 −0.606123 0.795371i \(-0.707276\pi\)
−0.606123 + 0.795371i \(0.707276\pi\)
\(128\) 0 0
\(129\) 9.02791 0.794863
\(130\) 0 0
\(131\) 0.920826 0.0804530 0.0402265 0.999191i \(-0.487192\pi\)
0.0402265 + 0.999191i \(0.487192\pi\)
\(132\) 0 0
\(133\) −1.53138 −0.132787
\(134\) 0 0
\(135\) 1.71910 0.147957
\(136\) 0 0
\(137\) −1.57814 −0.134830 −0.0674148 0.997725i \(-0.521475\pi\)
−0.0674148 + 0.997725i \(0.521475\pi\)
\(138\) 0 0
\(139\) 7.64986 0.648852 0.324426 0.945911i \(-0.394829\pi\)
0.324426 + 0.945911i \(0.394829\pi\)
\(140\) 0 0
\(141\) −5.43500 −0.457709
\(142\) 0 0
\(143\) 7.65045 0.639763
\(144\) 0 0
\(145\) 1.71910 0.142764
\(146\) 0 0
\(147\) −6.95590 −0.573713
\(148\) 0 0
\(149\) 0.562591 0.0460893 0.0230446 0.999734i \(-0.492664\pi\)
0.0230446 + 0.999734i \(0.492664\pi\)
\(150\) 0 0
\(151\) −4.59101 −0.373611 −0.186806 0.982397i \(-0.559813\pi\)
−0.186806 + 0.982397i \(0.559813\pi\)
\(152\) 0 0
\(153\) −1.22874 −0.0993377
\(154\) 0 0
\(155\) 6.33909 0.509168
\(156\) 0 0
\(157\) −17.6359 −1.40750 −0.703750 0.710448i \(-0.748492\pi\)
−0.703750 + 0.710448i \(0.748492\pi\)
\(158\) 0 0
\(159\) −2.49073 −0.197528
\(160\) 0 0
\(161\) 0.210007 0.0165509
\(162\) 0 0
\(163\) −9.54677 −0.747761 −0.373880 0.927477i \(-0.621973\pi\)
−0.373880 + 0.927477i \(0.621973\pi\)
\(164\) 0 0
\(165\) −4.07924 −0.317568
\(166\) 0 0
\(167\) −18.8167 −1.45608 −0.728042 0.685533i \(-0.759569\pi\)
−0.728042 + 0.685533i \(0.759569\pi\)
\(168\) 0 0
\(169\) −2.60511 −0.200393
\(170\) 0 0
\(171\) −7.29204 −0.557636
\(172\) 0 0
\(173\) 0.0827733 0.00629314 0.00314657 0.999995i \(-0.498998\pi\)
0.00314657 + 0.999995i \(0.498998\pi\)
\(174\) 0 0
\(175\) −0.429398 −0.0324594
\(176\) 0 0
\(177\) −3.55638 −0.267314
\(178\) 0 0
\(179\) 9.20992 0.688382 0.344191 0.938900i \(-0.388153\pi\)
0.344191 + 0.938900i \(0.388153\pi\)
\(180\) 0 0
\(181\) −9.17306 −0.681828 −0.340914 0.940094i \(-0.610736\pi\)
−0.340914 + 0.940094i \(0.610736\pi\)
\(182\) 0 0
\(183\) −7.27294 −0.537631
\(184\) 0 0
\(185\) 13.1564 0.967278
\(186\) 0 0
\(187\) 2.91566 0.213214
\(188\) 0 0
\(189\) 0.210007 0.0152758
\(190\) 0 0
\(191\) −1.71415 −0.124031 −0.0620156 0.998075i \(-0.519753\pi\)
−0.0620156 + 0.998075i \(0.519753\pi\)
\(192\) 0 0
\(193\) 3.98986 0.287196 0.143598 0.989636i \(-0.454133\pi\)
0.143598 + 0.989636i \(0.454133\pi\)
\(194\) 0 0
\(195\) −5.54258 −0.396912
\(196\) 0 0
\(197\) −3.34272 −0.238159 −0.119080 0.992885i \(-0.537994\pi\)
−0.119080 + 0.992885i \(0.537994\pi\)
\(198\) 0 0
\(199\) 18.4507 1.30793 0.653967 0.756523i \(-0.273104\pi\)
0.653967 + 0.756523i \(0.273104\pi\)
\(200\) 0 0
\(201\) 9.41000 0.663730
\(202\) 0 0
\(203\) 0.210007 0.0147396
\(204\) 0 0
\(205\) 4.86232 0.339599
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 17.3032 1.19689
\(210\) 0 0
\(211\) 20.7086 1.42564 0.712818 0.701349i \(-0.247418\pi\)
0.712818 + 0.701349i \(0.247418\pi\)
\(212\) 0 0
\(213\) −7.53494 −0.516286
\(214\) 0 0
\(215\) 15.5199 1.05845
\(216\) 0 0
\(217\) 0.774388 0.0525689
\(218\) 0 0
\(219\) 3.75783 0.253930
\(220\) 0 0
\(221\) 3.96159 0.266486
\(222\) 0 0
\(223\) −12.1547 −0.813936 −0.406968 0.913442i \(-0.633414\pi\)
−0.406968 + 0.913442i \(0.633414\pi\)
\(224\) 0 0
\(225\) −2.04468 −0.136312
\(226\) 0 0
\(227\) 12.9879 0.862035 0.431017 0.902344i \(-0.358155\pi\)
0.431017 + 0.902344i \(0.358155\pi\)
\(228\) 0 0
\(229\) 9.91961 0.655506 0.327753 0.944763i \(-0.393709\pi\)
0.327753 + 0.944763i \(0.393709\pi\)
\(230\) 0 0
\(231\) −0.498323 −0.0327872
\(232\) 0 0
\(233\) 13.0401 0.854285 0.427143 0.904184i \(-0.359520\pi\)
0.427143 + 0.904184i \(0.359520\pi\)
\(234\) 0 0
\(235\) −9.34332 −0.609491
\(236\) 0 0
\(237\) 0.807221 0.0524346
\(238\) 0 0
\(239\) −4.25253 −0.275073 −0.137537 0.990497i \(-0.543918\pi\)
−0.137537 + 0.990497i \(0.543918\pi\)
\(240\) 0 0
\(241\) −1.22996 −0.0792289 −0.0396144 0.999215i \(-0.512613\pi\)
−0.0396144 + 0.999215i \(0.512613\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −11.9579 −0.763963
\(246\) 0 0
\(247\) 23.5103 1.49593
\(248\) 0 0
\(249\) 5.58455 0.353907
\(250\) 0 0
\(251\) 12.4225 0.784100 0.392050 0.919944i \(-0.371766\pi\)
0.392050 + 0.919944i \(0.371766\pi\)
\(252\) 0 0
\(253\) −2.37289 −0.149182
\(254\) 0 0
\(255\) −2.11233 −0.132279
\(256\) 0 0
\(257\) 3.16912 0.197684 0.0988422 0.995103i \(-0.468486\pi\)
0.0988422 + 0.995103i \(0.468486\pi\)
\(258\) 0 0
\(259\) 1.60720 0.0998663
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) −11.4038 −0.703190 −0.351595 0.936152i \(-0.614361\pi\)
−0.351595 + 0.936152i \(0.614361\pi\)
\(264\) 0 0
\(265\) −4.28182 −0.263030
\(266\) 0 0
\(267\) −11.2438 −0.688108
\(268\) 0 0
\(269\) 3.50827 0.213903 0.106952 0.994264i \(-0.465891\pi\)
0.106952 + 0.994264i \(0.465891\pi\)
\(270\) 0 0
\(271\) 2.74651 0.166839 0.0834193 0.996515i \(-0.473416\pi\)
0.0834193 + 0.996515i \(0.473416\pi\)
\(272\) 0 0
\(273\) −0.677086 −0.0409791
\(274\) 0 0
\(275\) 4.85180 0.292575
\(276\) 0 0
\(277\) −26.2225 −1.57556 −0.787780 0.615957i \(-0.788769\pi\)
−0.787780 + 0.615957i \(0.788769\pi\)
\(278\) 0 0
\(279\) 3.68744 0.220761
\(280\) 0 0
\(281\) 13.9533 0.832382 0.416191 0.909277i \(-0.363365\pi\)
0.416191 + 0.909277i \(0.363365\pi\)
\(282\) 0 0
\(283\) 0.0948723 0.00563957 0.00281979 0.999996i \(-0.499102\pi\)
0.00281979 + 0.999996i \(0.499102\pi\)
\(284\) 0 0
\(285\) −12.5358 −0.742555
\(286\) 0 0
\(287\) 0.593984 0.0350618
\(288\) 0 0
\(289\) −15.4902 −0.911188
\(290\) 0 0
\(291\) −11.5915 −0.679507
\(292\) 0 0
\(293\) −19.3283 −1.12917 −0.564586 0.825374i \(-0.690964\pi\)
−0.564586 + 0.825374i \(0.690964\pi\)
\(294\) 0 0
\(295\) −6.11379 −0.355959
\(296\) 0 0
\(297\) −2.37289 −0.137689
\(298\) 0 0
\(299\) −3.22411 −0.186455
\(300\) 0 0
\(301\) 1.89592 0.109279
\(302\) 0 0
\(303\) −1.54449 −0.0887287
\(304\) 0 0
\(305\) −12.5029 −0.715916
\(306\) 0 0
\(307\) −27.8115 −1.58729 −0.793644 0.608382i \(-0.791819\pi\)
−0.793644 + 0.608382i \(0.791819\pi\)
\(308\) 0 0
\(309\) −14.7680 −0.840122
\(310\) 0 0
\(311\) 4.91082 0.278467 0.139234 0.990260i \(-0.455536\pi\)
0.139234 + 0.990260i \(0.455536\pi\)
\(312\) 0 0
\(313\) 3.32210 0.187776 0.0938881 0.995583i \(-0.470070\pi\)
0.0938881 + 0.995583i \(0.470070\pi\)
\(314\) 0 0
\(315\) 0.361024 0.0203414
\(316\) 0 0
\(317\) 11.0295 0.619477 0.309738 0.950822i \(-0.399759\pi\)
0.309738 + 0.950822i \(0.399759\pi\)
\(318\) 0 0
\(319\) −2.37289 −0.132856
\(320\) 0 0
\(321\) −12.0255 −0.671197
\(322\) 0 0
\(323\) 8.96002 0.498549
\(324\) 0 0
\(325\) 6.59228 0.365674
\(326\) 0 0
\(327\) −3.79224 −0.209711
\(328\) 0 0
\(329\) −1.14139 −0.0629267
\(330\) 0 0
\(331\) −14.1235 −0.776295 −0.388148 0.921597i \(-0.626885\pi\)
−0.388148 + 0.921597i \(0.626885\pi\)
\(332\) 0 0
\(333\) 7.65306 0.419385
\(334\) 0 0
\(335\) 16.1768 0.883831
\(336\) 0 0
\(337\) −27.3246 −1.48846 −0.744232 0.667921i \(-0.767184\pi\)
−0.744232 + 0.667921i \(0.767184\pi\)
\(338\) 0 0
\(339\) −15.1915 −0.825087
\(340\) 0 0
\(341\) −8.74988 −0.473832
\(342\) 0 0
\(343\) −2.93084 −0.158250
\(344\) 0 0
\(345\) 1.71910 0.0925534
\(346\) 0 0
\(347\) −11.1666 −0.599456 −0.299728 0.954025i \(-0.596896\pi\)
−0.299728 + 0.954025i \(0.596896\pi\)
\(348\) 0 0
\(349\) 16.7330 0.895697 0.447849 0.894109i \(-0.352190\pi\)
0.447849 + 0.894109i \(0.352190\pi\)
\(350\) 0 0
\(351\) −3.22411 −0.172090
\(352\) 0 0
\(353\) 28.3617 1.50954 0.754771 0.655988i \(-0.227748\pi\)
0.754771 + 0.655988i \(0.227748\pi\)
\(354\) 0 0
\(355\) −12.9533 −0.687492
\(356\) 0 0
\(357\) −0.258044 −0.0136571
\(358\) 0 0
\(359\) 26.6653 1.40734 0.703670 0.710527i \(-0.251543\pi\)
0.703670 + 0.710527i \(0.251543\pi\)
\(360\) 0 0
\(361\) 34.1738 1.79862
\(362\) 0 0
\(363\) −5.36940 −0.281821
\(364\) 0 0
\(365\) 6.46009 0.338137
\(366\) 0 0
\(367\) 23.0394 1.20265 0.601323 0.799006i \(-0.294641\pi\)
0.601323 + 0.799006i \(0.294641\pi\)
\(368\) 0 0
\(369\) 2.82840 0.147241
\(370\) 0 0
\(371\) −0.523070 −0.0271565
\(372\) 0 0
\(373\) 19.9479 1.03286 0.516432 0.856328i \(-0.327260\pi\)
0.516432 + 0.856328i \(0.327260\pi\)
\(374\) 0 0
\(375\) −12.1105 −0.625386
\(376\) 0 0
\(377\) −3.22411 −0.166050
\(378\) 0 0
\(379\) −5.94273 −0.305257 −0.152629 0.988284i \(-0.548774\pi\)
−0.152629 + 0.988284i \(0.548774\pi\)
\(380\) 0 0
\(381\) −13.6613 −0.699891
\(382\) 0 0
\(383\) 17.1706 0.877377 0.438688 0.898639i \(-0.355443\pi\)
0.438688 + 0.898639i \(0.355443\pi\)
\(384\) 0 0
\(385\) −0.856669 −0.0436599
\(386\) 0 0
\(387\) 9.02791 0.458914
\(388\) 0 0
\(389\) −9.89922 −0.501910 −0.250955 0.967999i \(-0.580745\pi\)
−0.250955 + 0.967999i \(0.580745\pi\)
\(390\) 0 0
\(391\) −1.22874 −0.0621400
\(392\) 0 0
\(393\) 0.920826 0.0464496
\(394\) 0 0
\(395\) 1.38770 0.0698226
\(396\) 0 0
\(397\) −6.53349 −0.327906 −0.163953 0.986468i \(-0.552425\pi\)
−0.163953 + 0.986468i \(0.552425\pi\)
\(398\) 0 0
\(399\) −1.53138 −0.0766648
\(400\) 0 0
\(401\) −28.3783 −1.41715 −0.708573 0.705638i \(-0.750661\pi\)
−0.708573 + 0.705638i \(0.750661\pi\)
\(402\) 0 0
\(403\) −11.8887 −0.592219
\(404\) 0 0
\(405\) 1.71910 0.0854229
\(406\) 0 0
\(407\) −18.1599 −0.900151
\(408\) 0 0
\(409\) −11.9632 −0.591543 −0.295771 0.955259i \(-0.595577\pi\)
−0.295771 + 0.955259i \(0.595577\pi\)
\(410\) 0 0
\(411\) −1.57814 −0.0778439
\(412\) 0 0
\(413\) −0.746865 −0.0367508
\(414\) 0 0
\(415\) 9.60042 0.471266
\(416\) 0 0
\(417\) 7.64986 0.374615
\(418\) 0 0
\(419\) 25.4630 1.24395 0.621974 0.783038i \(-0.286331\pi\)
0.621974 + 0.783038i \(0.286331\pi\)
\(420\) 0 0
\(421\) −26.3023 −1.28190 −0.640949 0.767584i \(-0.721459\pi\)
−0.640949 + 0.767584i \(0.721459\pi\)
\(422\) 0 0
\(423\) −5.43500 −0.264259
\(424\) 0 0
\(425\) 2.51238 0.121868
\(426\) 0 0
\(427\) −1.52737 −0.0739145
\(428\) 0 0
\(429\) 7.65045 0.369367
\(430\) 0 0
\(431\) 20.9906 1.01108 0.505540 0.862803i \(-0.331293\pi\)
0.505540 + 0.862803i \(0.331293\pi\)
\(432\) 0 0
\(433\) 12.3754 0.594722 0.297361 0.954765i \(-0.403894\pi\)
0.297361 + 0.954765i \(0.403894\pi\)
\(434\) 0 0
\(435\) 1.71910 0.0824247
\(436\) 0 0
\(437\) −7.29204 −0.348825
\(438\) 0 0
\(439\) 24.0738 1.14898 0.574490 0.818512i \(-0.305200\pi\)
0.574490 + 0.818512i \(0.305200\pi\)
\(440\) 0 0
\(441\) −6.95590 −0.331233
\(442\) 0 0
\(443\) 5.14360 0.244380 0.122190 0.992507i \(-0.461008\pi\)
0.122190 + 0.992507i \(0.461008\pi\)
\(444\) 0 0
\(445\) −19.3292 −0.916293
\(446\) 0 0
\(447\) 0.562591 0.0266097
\(448\) 0 0
\(449\) 18.0027 0.849601 0.424800 0.905287i \(-0.360344\pi\)
0.424800 + 0.905287i \(0.360344\pi\)
\(450\) 0 0
\(451\) −6.71148 −0.316031
\(452\) 0 0
\(453\) −4.59101 −0.215705
\(454\) 0 0
\(455\) −1.16398 −0.0545682
\(456\) 0 0
\(457\) 34.1329 1.59667 0.798334 0.602215i \(-0.205715\pi\)
0.798334 + 0.602215i \(0.205715\pi\)
\(458\) 0 0
\(459\) −1.22874 −0.0573527
\(460\) 0 0
\(461\) 10.0677 0.468899 0.234449 0.972128i \(-0.424671\pi\)
0.234449 + 0.972128i \(0.424671\pi\)
\(462\) 0 0
\(463\) −11.9720 −0.556387 −0.278194 0.960525i \(-0.589736\pi\)
−0.278194 + 0.960525i \(0.589736\pi\)
\(464\) 0 0
\(465\) 6.33909 0.293968
\(466\) 0 0
\(467\) −16.8685 −0.780582 −0.390291 0.920692i \(-0.627626\pi\)
−0.390291 + 0.920692i \(0.627626\pi\)
\(468\) 0 0
\(469\) 1.97617 0.0912508
\(470\) 0 0
\(471\) −17.6359 −0.812620
\(472\) 0 0
\(473\) −21.4222 −0.984995
\(474\) 0 0
\(475\) 14.9099 0.684113
\(476\) 0 0
\(477\) −2.49073 −0.114043
\(478\) 0 0
\(479\) 38.7594 1.77096 0.885480 0.464677i \(-0.153830\pi\)
0.885480 + 0.464677i \(0.153830\pi\)
\(480\) 0 0
\(481\) −24.6743 −1.12505
\(482\) 0 0
\(483\) 0.210007 0.00955565
\(484\) 0 0
\(485\) −19.9270 −0.904840
\(486\) 0 0
\(487\) −3.17969 −0.144085 −0.0720427 0.997402i \(-0.522952\pi\)
−0.0720427 + 0.997402i \(0.522952\pi\)
\(488\) 0 0
\(489\) −9.54677 −0.431720
\(490\) 0 0
\(491\) 1.43125 0.0645914 0.0322957 0.999478i \(-0.489718\pi\)
0.0322957 + 0.999478i \(0.489718\pi\)
\(492\) 0 0
\(493\) −1.22874 −0.0553397
\(494\) 0 0
\(495\) −4.07924 −0.183348
\(496\) 0 0
\(497\) −1.58239 −0.0709799
\(498\) 0 0
\(499\) 28.9140 1.29437 0.647184 0.762334i \(-0.275946\pi\)
0.647184 + 0.762334i \(0.275946\pi\)
\(500\) 0 0
\(501\) −18.8167 −0.840670
\(502\) 0 0
\(503\) 6.83555 0.304782 0.152391 0.988320i \(-0.451303\pi\)
0.152391 + 0.988320i \(0.451303\pi\)
\(504\) 0 0
\(505\) −2.65514 −0.118152
\(506\) 0 0
\(507\) −2.60511 −0.115697
\(508\) 0 0
\(509\) −16.3988 −0.726862 −0.363431 0.931621i \(-0.618395\pi\)
−0.363431 + 0.931621i \(0.618395\pi\)
\(510\) 0 0
\(511\) 0.789170 0.0349108
\(512\) 0 0
\(513\) −7.29204 −0.321951
\(514\) 0 0
\(515\) −25.3877 −1.11872
\(516\) 0 0
\(517\) 12.8966 0.567193
\(518\) 0 0
\(519\) 0.0827733 0.00363334
\(520\) 0 0
\(521\) 45.1845 1.97957 0.989784 0.142575i \(-0.0455382\pi\)
0.989784 + 0.142575i \(0.0455382\pi\)
\(522\) 0 0
\(523\) −8.82991 −0.386105 −0.193052 0.981188i \(-0.561839\pi\)
−0.193052 + 0.981188i \(0.561839\pi\)
\(524\) 0 0
\(525\) −0.429398 −0.0187404
\(526\) 0 0
\(527\) −4.53090 −0.197369
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −3.55638 −0.154334
\(532\) 0 0
\(533\) −9.11909 −0.394991
\(534\) 0 0
\(535\) −20.6730 −0.893774
\(536\) 0 0
\(537\) 9.20992 0.397437
\(538\) 0 0
\(539\) 16.5056 0.710945
\(540\) 0 0
\(541\) −15.9832 −0.687173 −0.343586 0.939121i \(-0.611642\pi\)
−0.343586 + 0.939121i \(0.611642\pi\)
\(542\) 0 0
\(543\) −9.17306 −0.393654
\(544\) 0 0
\(545\) −6.51925 −0.279254
\(546\) 0 0
\(547\) 26.8308 1.14720 0.573601 0.819135i \(-0.305546\pi\)
0.573601 + 0.819135i \(0.305546\pi\)
\(548\) 0 0
\(549\) −7.27294 −0.310402
\(550\) 0 0
\(551\) −7.29204 −0.310651
\(552\) 0 0
\(553\) 0.169522 0.00720881
\(554\) 0 0
\(555\) 13.1564 0.558458
\(556\) 0 0
\(557\) −3.96427 −0.167971 −0.0839857 0.996467i \(-0.526765\pi\)
−0.0839857 + 0.996467i \(0.526765\pi\)
\(558\) 0 0
\(559\) −29.1070 −1.23109
\(560\) 0 0
\(561\) 2.91566 0.123099
\(562\) 0 0
\(563\) −1.13810 −0.0479653 −0.0239827 0.999712i \(-0.507635\pi\)
−0.0239827 + 0.999712i \(0.507635\pi\)
\(564\) 0 0
\(565\) −26.1157 −1.09870
\(566\) 0 0
\(567\) 0.210007 0.00881946
\(568\) 0 0
\(569\) −19.6531 −0.823900 −0.411950 0.911206i \(-0.635152\pi\)
−0.411950 + 0.911206i \(0.635152\pi\)
\(570\) 0 0
\(571\) −10.0484 −0.420511 −0.210256 0.977646i \(-0.567430\pi\)
−0.210256 + 0.977646i \(0.567430\pi\)
\(572\) 0 0
\(573\) −1.71415 −0.0716095
\(574\) 0 0
\(575\) −2.04468 −0.0852692
\(576\) 0 0
\(577\) 23.9270 0.996093 0.498046 0.867150i \(-0.334051\pi\)
0.498046 + 0.867150i \(0.334051\pi\)
\(578\) 0 0
\(579\) 3.98986 0.165813
\(580\) 0 0
\(581\) 1.17279 0.0486557
\(582\) 0 0
\(583\) 5.91022 0.244776
\(584\) 0 0
\(585\) −5.54258 −0.229157
\(586\) 0 0
\(587\) −45.4351 −1.87531 −0.937654 0.347571i \(-0.887007\pi\)
−0.937654 + 0.347571i \(0.887007\pi\)
\(588\) 0 0
\(589\) −26.8889 −1.10794
\(590\) 0 0
\(591\) −3.34272 −0.137501
\(592\) 0 0
\(593\) 33.5765 1.37882 0.689411 0.724370i \(-0.257869\pi\)
0.689411 + 0.724370i \(0.257869\pi\)
\(594\) 0 0
\(595\) −0.443604 −0.0181860
\(596\) 0 0
\(597\) 18.4507 0.755136
\(598\) 0 0
\(599\) −10.5064 −0.429278 −0.214639 0.976693i \(-0.568858\pi\)
−0.214639 + 0.976693i \(0.568858\pi\)
\(600\) 0 0
\(601\) −9.26956 −0.378113 −0.189057 0.981966i \(-0.560543\pi\)
−0.189057 + 0.981966i \(0.560543\pi\)
\(602\) 0 0
\(603\) 9.41000 0.383205
\(604\) 0 0
\(605\) −9.23056 −0.375276
\(606\) 0 0
\(607\) 41.7857 1.69603 0.848014 0.529973i \(-0.177798\pi\)
0.848014 + 0.529973i \(0.177798\pi\)
\(608\) 0 0
\(609\) 0.210007 0.00850991
\(610\) 0 0
\(611\) 17.5230 0.708906
\(612\) 0 0
\(613\) −13.8443 −0.559168 −0.279584 0.960121i \(-0.590197\pi\)
−0.279584 + 0.960121i \(0.590197\pi\)
\(614\) 0 0
\(615\) 4.86232 0.196068
\(616\) 0 0
\(617\) −31.6630 −1.27470 −0.637352 0.770573i \(-0.719970\pi\)
−0.637352 + 0.770573i \(0.719970\pi\)
\(618\) 0 0
\(619\) −44.1516 −1.77460 −0.887301 0.461191i \(-0.847422\pi\)
−0.887301 + 0.461191i \(0.847422\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) −2.36127 −0.0946024
\(624\) 0 0
\(625\) −10.5959 −0.423834
\(626\) 0 0
\(627\) 17.3032 0.691023
\(628\) 0 0
\(629\) −9.40362 −0.374947
\(630\) 0 0
\(631\) 0.420214 0.0167284 0.00836422 0.999965i \(-0.497338\pi\)
0.00836422 + 0.999965i \(0.497338\pi\)
\(632\) 0 0
\(633\) 20.7086 0.823092
\(634\) 0 0
\(635\) −23.4852 −0.931983
\(636\) 0 0
\(637\) 22.4266 0.888574
\(638\) 0 0
\(639\) −7.53494 −0.298078
\(640\) 0 0
\(641\) −9.31380 −0.367873 −0.183937 0.982938i \(-0.558884\pi\)
−0.183937 + 0.982938i \(0.558884\pi\)
\(642\) 0 0
\(643\) 43.1468 1.70154 0.850772 0.525535i \(-0.176135\pi\)
0.850772 + 0.525535i \(0.176135\pi\)
\(644\) 0 0
\(645\) 15.5199 0.611096
\(646\) 0 0
\(647\) 13.0052 0.511287 0.255644 0.966771i \(-0.417713\pi\)
0.255644 + 0.966771i \(0.417713\pi\)
\(648\) 0 0
\(649\) 8.43890 0.331256
\(650\) 0 0
\(651\) 0.774388 0.0303506
\(652\) 0 0
\(653\) 24.4920 0.958444 0.479222 0.877694i \(-0.340919\pi\)
0.479222 + 0.877694i \(0.340919\pi\)
\(654\) 0 0
\(655\) 1.58300 0.0618528
\(656\) 0 0
\(657\) 3.75783 0.146607
\(658\) 0 0
\(659\) 5.15236 0.200707 0.100354 0.994952i \(-0.468003\pi\)
0.100354 + 0.994952i \(0.468003\pi\)
\(660\) 0 0
\(661\) −12.5643 −0.488693 −0.244347 0.969688i \(-0.578574\pi\)
−0.244347 + 0.969688i \(0.578574\pi\)
\(662\) 0 0
\(663\) 3.96159 0.153856
\(664\) 0 0
\(665\) −2.63260 −0.102088
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 0 0
\(669\) −12.1547 −0.469926
\(670\) 0 0
\(671\) 17.2579 0.666233
\(672\) 0 0
\(673\) −19.9920 −0.770633 −0.385317 0.922784i \(-0.625908\pi\)
−0.385317 + 0.922784i \(0.625908\pi\)
\(674\) 0 0
\(675\) −2.04468 −0.0786999
\(676\) 0 0
\(677\) 36.2945 1.39491 0.697456 0.716627i \(-0.254315\pi\)
0.697456 + 0.716627i \(0.254315\pi\)
\(678\) 0 0
\(679\) −2.43430 −0.0934199
\(680\) 0 0
\(681\) 12.9879 0.497696
\(682\) 0 0
\(683\) −26.0186 −0.995573 −0.497787 0.867300i \(-0.665854\pi\)
−0.497787 + 0.867300i \(0.665854\pi\)
\(684\) 0 0
\(685\) −2.71299 −0.103658
\(686\) 0 0
\(687\) 9.91961 0.378457
\(688\) 0 0
\(689\) 8.03038 0.305933
\(690\) 0 0
\(691\) −12.8459 −0.488679 −0.244340 0.969690i \(-0.578571\pi\)
−0.244340 + 0.969690i \(0.578571\pi\)
\(692\) 0 0
\(693\) −0.498323 −0.0189297
\(694\) 0 0
\(695\) 13.1509 0.498842
\(696\) 0 0
\(697\) −3.47537 −0.131639
\(698\) 0 0
\(699\) 13.0401 0.493222
\(700\) 0 0
\(701\) −23.7174 −0.895792 −0.447896 0.894086i \(-0.647827\pi\)
−0.447896 + 0.894086i \(0.647827\pi\)
\(702\) 0 0
\(703\) −55.8064 −2.10478
\(704\) 0 0
\(705\) −9.34332 −0.351890
\(706\) 0 0
\(707\) −0.324354 −0.0121986
\(708\) 0 0
\(709\) −14.4256 −0.541765 −0.270883 0.962612i \(-0.587316\pi\)
−0.270883 + 0.962612i \(0.587316\pi\)
\(710\) 0 0
\(711\) 0.807221 0.0302731
\(712\) 0 0
\(713\) 3.68744 0.138096
\(714\) 0 0
\(715\) 13.1519 0.491854
\(716\) 0 0
\(717\) −4.25253 −0.158814
\(718\) 0 0
\(719\) −17.6876 −0.659636 −0.329818 0.944044i \(-0.606987\pi\)
−0.329818 + 0.944044i \(0.606987\pi\)
\(720\) 0 0
\(721\) −3.10138 −0.115501
\(722\) 0 0
\(723\) −1.22996 −0.0457428
\(724\) 0 0
\(725\) −2.04468 −0.0759376
\(726\) 0 0
\(727\) 35.0547 1.30011 0.650053 0.759889i \(-0.274747\pi\)
0.650053 + 0.759889i \(0.274747\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −11.0930 −0.410288
\(732\) 0 0
\(733\) −1.31412 −0.0485383 −0.0242691 0.999705i \(-0.507726\pi\)
−0.0242691 + 0.999705i \(0.507726\pi\)
\(734\) 0 0
\(735\) −11.9579 −0.441074
\(736\) 0 0
\(737\) −22.3289 −0.822495
\(738\) 0 0
\(739\) −9.56395 −0.351816 −0.175908 0.984407i \(-0.556286\pi\)
−0.175908 + 0.984407i \(0.556286\pi\)
\(740\) 0 0
\(741\) 23.5103 0.863674
\(742\) 0 0
\(743\) −15.5554 −0.570673 −0.285336 0.958427i \(-0.592105\pi\)
−0.285336 + 0.958427i \(0.592105\pi\)
\(744\) 0 0
\(745\) 0.967153 0.0354337
\(746\) 0 0
\(747\) 5.58455 0.204328
\(748\) 0 0
\(749\) −2.52543 −0.0922773
\(750\) 0 0
\(751\) 27.3525 0.998106 0.499053 0.866572i \(-0.333681\pi\)
0.499053 + 0.866572i \(0.333681\pi\)
\(752\) 0 0
\(753\) 12.4225 0.452700
\(754\) 0 0
\(755\) −7.89243 −0.287235
\(756\) 0 0
\(757\) 17.2917 0.628479 0.314240 0.949344i \(-0.398250\pi\)
0.314240 + 0.949344i \(0.398250\pi\)
\(758\) 0 0
\(759\) −2.37289 −0.0861304
\(760\) 0 0
\(761\) 32.3174 1.17150 0.585752 0.810490i \(-0.300799\pi\)
0.585752 + 0.810490i \(0.300799\pi\)
\(762\) 0 0
\(763\) −0.796396 −0.0288315
\(764\) 0 0
\(765\) −2.11233 −0.0763715
\(766\) 0 0
\(767\) 11.4662 0.414020
\(768\) 0 0
\(769\) −5.88519 −0.212225 −0.106113 0.994354i \(-0.533840\pi\)
−0.106113 + 0.994354i \(0.533840\pi\)
\(770\) 0 0
\(771\) 3.16912 0.114133
\(772\) 0 0
\(773\) 19.0255 0.684298 0.342149 0.939646i \(-0.388845\pi\)
0.342149 + 0.939646i \(0.388845\pi\)
\(774\) 0 0
\(775\) −7.53964 −0.270832
\(776\) 0 0
\(777\) 1.60720 0.0576578
\(778\) 0 0
\(779\) −20.6248 −0.738961
\(780\) 0 0
\(781\) 17.8796 0.639781
\(782\) 0 0
\(783\) 1.00000 0.0357371
\(784\) 0 0
\(785\) −30.3180 −1.08209
\(786\) 0 0
\(787\) 18.6197 0.663720 0.331860 0.943329i \(-0.392324\pi\)
0.331860 + 0.943329i \(0.392324\pi\)
\(788\) 0 0
\(789\) −11.4038 −0.405987
\(790\) 0 0
\(791\) −3.19031 −0.113434
\(792\) 0 0
\(793\) 23.4488 0.832690
\(794\) 0 0
\(795\) −4.28182 −0.151860
\(796\) 0 0
\(797\) 20.6132 0.730158 0.365079 0.930977i \(-0.381042\pi\)
0.365079 + 0.930977i \(0.381042\pi\)
\(798\) 0 0
\(799\) 6.67819 0.236258
\(800\) 0 0
\(801\) −11.2438 −0.397280
\(802\) 0 0
\(803\) −8.91690 −0.314671
\(804\) 0 0
\(805\) 0.361024 0.0127244
\(806\) 0 0
\(807\) 3.50827 0.123497
\(808\) 0 0
\(809\) −22.9018 −0.805184 −0.402592 0.915379i \(-0.631891\pi\)
−0.402592 + 0.915379i \(0.631891\pi\)
\(810\) 0 0
\(811\) −21.5774 −0.757685 −0.378843 0.925461i \(-0.623678\pi\)
−0.378843 + 0.925461i \(0.623678\pi\)
\(812\) 0 0
\(813\) 2.74651 0.0963243
\(814\) 0 0
\(815\) −16.4119 −0.574883
\(816\) 0 0
\(817\) −65.8319 −2.30317
\(818\) 0 0
\(819\) −0.677086 −0.0236593
\(820\) 0 0
\(821\) 11.3416 0.395824 0.197912 0.980220i \(-0.436584\pi\)
0.197912 + 0.980220i \(0.436584\pi\)
\(822\) 0 0
\(823\) 4.53006 0.157908 0.0789540 0.996878i \(-0.474842\pi\)
0.0789540 + 0.996878i \(0.474842\pi\)
\(824\) 0 0
\(825\) 4.85180 0.168918
\(826\) 0 0
\(827\) 2.90044 0.100858 0.0504290 0.998728i \(-0.483941\pi\)
0.0504290 + 0.998728i \(0.483941\pi\)
\(828\) 0 0
\(829\) −5.31154 −0.184477 −0.0922387 0.995737i \(-0.529402\pi\)
−0.0922387 + 0.995737i \(0.529402\pi\)
\(830\) 0 0
\(831\) −26.2225 −0.909650
\(832\) 0 0
\(833\) 8.54699 0.296136
\(834\) 0 0
\(835\) −32.3479 −1.11945
\(836\) 0 0
\(837\) 3.68744 0.127457
\(838\) 0 0
\(839\) 52.2724 1.80464 0.902322 0.431063i \(-0.141861\pi\)
0.902322 + 0.431063i \(0.141861\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 13.9533 0.480576
\(844\) 0 0
\(845\) −4.47845 −0.154063
\(846\) 0 0
\(847\) −1.12761 −0.0387452
\(848\) 0 0
\(849\) 0.0948723 0.00325601
\(850\) 0 0
\(851\) 7.65306 0.262344
\(852\) 0 0
\(853\) 14.2670 0.488492 0.244246 0.969713i \(-0.421460\pi\)
0.244246 + 0.969713i \(0.421460\pi\)
\(854\) 0 0
\(855\) −12.5358 −0.428714
\(856\) 0 0
\(857\) 9.13021 0.311882 0.155941 0.987766i \(-0.450159\pi\)
0.155941 + 0.987766i \(0.450159\pi\)
\(858\) 0 0
\(859\) 16.4652 0.561785 0.280892 0.959739i \(-0.409370\pi\)
0.280892 + 0.959739i \(0.409370\pi\)
\(860\) 0 0
\(861\) 0.593984 0.0202429
\(862\) 0 0
\(863\) 15.6882 0.534032 0.267016 0.963692i \(-0.413962\pi\)
0.267016 + 0.963692i \(0.413962\pi\)
\(864\) 0 0
\(865\) 0.142296 0.00483820
\(866\) 0 0
\(867\) −15.4902 −0.526075
\(868\) 0 0
\(869\) −1.91544 −0.0649770
\(870\) 0 0
\(871\) −30.3389 −1.02799
\(872\) 0 0
\(873\) −11.5915 −0.392314
\(874\) 0 0
\(875\) −2.54330 −0.0859791
\(876\) 0 0
\(877\) −45.6806 −1.54252 −0.771262 0.636518i \(-0.780374\pi\)
−0.771262 + 0.636518i \(0.780374\pi\)
\(878\) 0 0
\(879\) −19.3283 −0.651928
\(880\) 0 0
\(881\) 58.8054 1.98120 0.990602 0.136777i \(-0.0436744\pi\)
0.990602 + 0.136777i \(0.0436744\pi\)
\(882\) 0 0
\(883\) −20.5660 −0.692099 −0.346050 0.938216i \(-0.612477\pi\)
−0.346050 + 0.938216i \(0.612477\pi\)
\(884\) 0 0
\(885\) −6.11379 −0.205513
\(886\) 0 0
\(887\) 12.0199 0.403587 0.201794 0.979428i \(-0.435323\pi\)
0.201794 + 0.979428i \(0.435323\pi\)
\(888\) 0 0
\(889\) −2.86897 −0.0962222
\(890\) 0 0
\(891\) −2.37289 −0.0794947
\(892\) 0 0
\(893\) 39.6322 1.32624
\(894\) 0 0
\(895\) 15.8328 0.529232
\(896\) 0 0
\(897\) −3.22411 −0.107650
\(898\) 0 0
\(899\) 3.68744 0.122983
\(900\) 0 0
\(901\) 3.06046 0.101959
\(902\) 0 0
\(903\) 1.89592 0.0630924
\(904\) 0 0
\(905\) −15.7694 −0.524194
\(906\) 0 0
\(907\) 0.278333 0.00924189 0.00462094 0.999989i \(-0.498529\pi\)
0.00462094 + 0.999989i \(0.498529\pi\)
\(908\) 0 0
\(909\) −1.54449 −0.0512275
\(910\) 0 0
\(911\) 40.1668 1.33079 0.665393 0.746493i \(-0.268264\pi\)
0.665393 + 0.746493i \(0.268264\pi\)
\(912\) 0 0
\(913\) −13.2515 −0.438561
\(914\) 0 0
\(915\) −12.5029 −0.413334
\(916\) 0 0
\(917\) 0.193380 0.00638597
\(918\) 0 0
\(919\) 11.1451 0.367644 0.183822 0.982960i \(-0.441153\pi\)
0.183822 + 0.982960i \(0.441153\pi\)
\(920\) 0 0
\(921\) −27.8115 −0.916421
\(922\) 0 0
\(923\) 24.2935 0.799630
\(924\) 0 0
\(925\) −15.6481 −0.514506
\(926\) 0 0
\(927\) −14.7680 −0.485045
\(928\) 0 0
\(929\) 22.1350 0.726227 0.363113 0.931745i \(-0.381714\pi\)
0.363113 + 0.931745i \(0.381714\pi\)
\(930\) 0 0
\(931\) 50.7227 1.66237
\(932\) 0 0
\(933\) 4.91082 0.160773
\(934\) 0 0
\(935\) 5.01232 0.163921
\(936\) 0 0
\(937\) −28.8017 −0.940909 −0.470454 0.882424i \(-0.655910\pi\)
−0.470454 + 0.882424i \(0.655910\pi\)
\(938\) 0 0
\(939\) 3.32210 0.108413
\(940\) 0 0
\(941\) −11.8130 −0.385092 −0.192546 0.981288i \(-0.561675\pi\)
−0.192546 + 0.981288i \(0.561675\pi\)
\(942\) 0 0
\(943\) 2.82840 0.0921055
\(944\) 0 0
\(945\) 0.361024 0.0117441
\(946\) 0 0
\(947\) −25.7370 −0.836340 −0.418170 0.908369i \(-0.637328\pi\)
−0.418170 + 0.908369i \(0.637328\pi\)
\(948\) 0 0
\(949\) −12.1157 −0.393291
\(950\) 0 0
\(951\) 11.0295 0.357655
\(952\) 0 0
\(953\) −43.0227 −1.39364 −0.696821 0.717245i \(-0.745403\pi\)
−0.696821 + 0.717245i \(0.745403\pi\)
\(954\) 0 0
\(955\) −2.94679 −0.0953560
\(956\) 0 0
\(957\) −2.37289 −0.0767046
\(958\) 0 0
\(959\) −0.331420 −0.0107021
\(960\) 0 0
\(961\) −17.4028 −0.561381
\(962\) 0 0
\(963\) −12.0255 −0.387516
\(964\) 0 0
\(965\) 6.85898 0.220798
\(966\) 0 0
\(967\) −45.1451 −1.45177 −0.725884 0.687817i \(-0.758569\pi\)
−0.725884 + 0.687817i \(0.758569\pi\)
\(968\) 0 0
\(969\) 8.96002 0.287837
\(970\) 0 0
\(971\) −13.2567 −0.425426 −0.212713 0.977115i \(-0.568230\pi\)
−0.212713 + 0.977115i \(0.568230\pi\)
\(972\) 0 0
\(973\) 1.60652 0.0515028
\(974\) 0 0
\(975\) 6.59228 0.211122
\(976\) 0 0
\(977\) 25.0117 0.800197 0.400098 0.916472i \(-0.368976\pi\)
0.400098 + 0.916472i \(0.368976\pi\)
\(978\) 0 0
\(979\) 26.6802 0.852704
\(980\) 0 0
\(981\) −3.79224 −0.121077
\(982\) 0 0
\(983\) 35.4337 1.13016 0.565080 0.825036i \(-0.308845\pi\)
0.565080 + 0.825036i \(0.308845\pi\)
\(984\) 0 0
\(985\) −5.74649 −0.183098
\(986\) 0 0
\(987\) −1.14139 −0.0363307
\(988\) 0 0
\(989\) 9.02791 0.287071
\(990\) 0 0
\(991\) −46.0130 −1.46165 −0.730825 0.682565i \(-0.760865\pi\)
−0.730825 + 0.682565i \(0.760865\pi\)
\(992\) 0 0
\(993\) −14.1235 −0.448194
\(994\) 0 0
\(995\) 31.7186 1.00555
\(996\) 0 0
\(997\) −34.7346 −1.10006 −0.550028 0.835146i \(-0.685383\pi\)
−0.550028 + 0.835146i \(0.685383\pi\)
\(998\) 0 0
\(999\) 7.65306 0.242132
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 \(a_p\))