Properties

Label 4012.2.a.g.1.10
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
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 1.10
Root \(-1.18842\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.18842 q^{3}\) \(+0.677556 q^{5}\) \(+1.46203 q^{7}\) \(-1.58766 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.18842 q^{3}\) \(+0.677556 q^{5}\) \(+1.46203 q^{7}\) \(-1.58766 q^{9}\) \(-2.15873 q^{11}\) \(+4.65583 q^{13}\) \(+0.805222 q^{15}\) \(-1.00000 q^{17}\) \(-6.39831 q^{19}\) \(+1.73751 q^{21}\) \(-8.06616 q^{23}\) \(-4.54092 q^{25}\) \(-5.45207 q^{27}\) \(-0.503272 q^{29}\) \(-6.46048 q^{31}\) \(-2.56548 q^{33}\) \(+0.990608 q^{35}\) \(-4.81150 q^{37}\) \(+5.53308 q^{39}\) \(+3.96183 q^{41}\) \(-3.76078 q^{43}\) \(-1.07573 q^{45}\) \(-5.61248 q^{47}\) \(-4.86246 q^{49}\) \(-1.18842 q^{51}\) \(+5.58471 q^{53}\) \(-1.46266 q^{55}\) \(-7.60389 q^{57}\) \(+1.00000 q^{59}\) \(-2.84854 q^{61}\) \(-2.32120 q^{63}\) \(+3.15458 q^{65}\) \(+3.63656 q^{67}\) \(-9.58599 q^{69}\) \(+6.38829 q^{71}\) \(+12.0069 q^{73}\) \(-5.39652 q^{75}\) \(-3.15614 q^{77}\) \(-10.7077 q^{79}\) \(-1.71638 q^{81}\) \(+1.34708 q^{83}\) \(-0.677556 q^{85}\) \(-0.598098 q^{87}\) \(+18.7751 q^{89}\) \(+6.80696 q^{91}\) \(-7.67776 q^{93}\) \(-4.33522 q^{95}\) \(+13.8516 q^{97}\) \(+3.42733 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 60q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 41q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 23q^{63} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 13q^{87} \) \(\mathstrut -\mathstrut 29q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.18842 0.686135 0.343067 0.939311i \(-0.388534\pi\)
0.343067 + 0.939311i \(0.388534\pi\)
\(4\) 0 0
\(5\) 0.677556 0.303012 0.151506 0.988456i \(-0.451588\pi\)
0.151506 + 0.988456i \(0.451588\pi\)
\(6\) 0 0
\(7\) 1.46203 0.552596 0.276298 0.961072i \(-0.410892\pi\)
0.276298 + 0.961072i \(0.410892\pi\)
\(8\) 0 0
\(9\) −1.58766 −0.529219
\(10\) 0 0
\(11\) −2.15873 −0.650883 −0.325442 0.945562i \(-0.605513\pi\)
−0.325442 + 0.945562i \(0.605513\pi\)
\(12\) 0 0
\(13\) 4.65583 1.29129 0.645647 0.763636i \(-0.276588\pi\)
0.645647 + 0.763636i \(0.276588\pi\)
\(14\) 0 0
\(15\) 0.805222 0.207907
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −6.39831 −1.46787 −0.733937 0.679218i \(-0.762319\pi\)
−0.733937 + 0.679218i \(0.762319\pi\)
\(20\) 0 0
\(21\) 1.73751 0.379155
\(22\) 0 0
\(23\) −8.06616 −1.68191 −0.840955 0.541105i \(-0.818006\pi\)
−0.840955 + 0.541105i \(0.818006\pi\)
\(24\) 0 0
\(25\) −4.54092 −0.908184
\(26\) 0 0
\(27\) −5.45207 −1.04925
\(28\) 0 0
\(29\) −0.503272 −0.0934552 −0.0467276 0.998908i \(-0.514879\pi\)
−0.0467276 + 0.998908i \(0.514879\pi\)
\(30\) 0 0
\(31\) −6.46048 −1.16034 −0.580168 0.814497i \(-0.697013\pi\)
−0.580168 + 0.814497i \(0.697013\pi\)
\(32\) 0 0
\(33\) −2.56548 −0.446594
\(34\) 0 0
\(35\) 0.990608 0.167443
\(36\) 0 0
\(37\) −4.81150 −0.791005 −0.395503 0.918465i \(-0.629430\pi\)
−0.395503 + 0.918465i \(0.629430\pi\)
\(38\) 0 0
\(39\) 5.53308 0.886002
\(40\) 0 0
\(41\) 3.96183 0.618735 0.309367 0.950943i \(-0.399883\pi\)
0.309367 + 0.950943i \(0.399883\pi\)
\(42\) 0 0
\(43\) −3.76078 −0.573514 −0.286757 0.958003i \(-0.592577\pi\)
−0.286757 + 0.958003i \(0.592577\pi\)
\(44\) 0 0
\(45\) −1.07573 −0.160360
\(46\) 0 0
\(47\) −5.61248 −0.818664 −0.409332 0.912386i \(-0.634238\pi\)
−0.409332 + 0.912386i \(0.634238\pi\)
\(48\) 0 0
\(49\) −4.86246 −0.694638
\(50\) 0 0
\(51\) −1.18842 −0.166412
\(52\) 0 0
\(53\) 5.58471 0.767119 0.383559 0.923516i \(-0.374698\pi\)
0.383559 + 0.923516i \(0.374698\pi\)
\(54\) 0 0
\(55\) −1.46266 −0.197226
\(56\) 0 0
\(57\) −7.60389 −1.00716
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) −2.84854 −0.364719 −0.182359 0.983232i \(-0.558373\pi\)
−0.182359 + 0.983232i \(0.558373\pi\)
\(62\) 0 0
\(63\) −2.32120 −0.292444
\(64\) 0 0
\(65\) 3.15458 0.391278
\(66\) 0 0
\(67\) 3.63656 0.444276 0.222138 0.975015i \(-0.428696\pi\)
0.222138 + 0.975015i \(0.428696\pi\)
\(68\) 0 0
\(69\) −9.58599 −1.15402
\(70\) 0 0
\(71\) 6.38829 0.758151 0.379075 0.925366i \(-0.376242\pi\)
0.379075 + 0.925366i \(0.376242\pi\)
\(72\) 0 0
\(73\) 12.0069 1.40530 0.702651 0.711535i \(-0.252000\pi\)
0.702651 + 0.711535i \(0.252000\pi\)
\(74\) 0 0
\(75\) −5.39652 −0.623136
\(76\) 0 0
\(77\) −3.15614 −0.359675
\(78\) 0 0
\(79\) −10.7077 −1.20470 −0.602352 0.798230i \(-0.705770\pi\)
−0.602352 + 0.798230i \(0.705770\pi\)
\(80\) 0 0
\(81\) −1.71638 −0.190709
\(82\) 0 0
\(83\) 1.34708 0.147862 0.0739308 0.997263i \(-0.476446\pi\)
0.0739308 + 0.997263i \(0.476446\pi\)
\(84\) 0 0
\(85\) −0.677556 −0.0734913
\(86\) 0 0
\(87\) −0.598098 −0.0641229
\(88\) 0 0
\(89\) 18.7751 1.99016 0.995079 0.0990883i \(-0.0315926\pi\)
0.995079 + 0.0990883i \(0.0315926\pi\)
\(90\) 0 0
\(91\) 6.80696 0.713564
\(92\) 0 0
\(93\) −7.67776 −0.796147
\(94\) 0 0
\(95\) −4.33522 −0.444784
\(96\) 0 0
\(97\) 13.8516 1.40642 0.703210 0.710982i \(-0.251749\pi\)
0.703210 + 0.710982i \(0.251749\pi\)
\(98\) 0 0
\(99\) 3.42733 0.344460
\(100\) 0 0
\(101\) −16.4356 −1.63541 −0.817703 0.575640i \(-0.804753\pi\)
−0.817703 + 0.575640i \(0.804753\pi\)
\(102\) 0 0
\(103\) 3.07384 0.302874 0.151437 0.988467i \(-0.451610\pi\)
0.151437 + 0.988467i \(0.451610\pi\)
\(104\) 0 0
\(105\) 1.17726 0.114889
\(106\) 0 0
\(107\) −0.798100 −0.0771552 −0.0385776 0.999256i \(-0.512283\pi\)
−0.0385776 + 0.999256i \(0.512283\pi\)
\(108\) 0 0
\(109\) 15.0629 1.44277 0.721384 0.692536i \(-0.243507\pi\)
0.721384 + 0.692536i \(0.243507\pi\)
\(110\) 0 0
\(111\) −5.71808 −0.542736
\(112\) 0 0
\(113\) −11.3690 −1.06951 −0.534754 0.845008i \(-0.679596\pi\)
−0.534754 + 0.845008i \(0.679596\pi\)
\(114\) 0 0
\(115\) −5.46528 −0.509640
\(116\) 0 0
\(117\) −7.39185 −0.683377
\(118\) 0 0
\(119\) −1.46203 −0.134024
\(120\) 0 0
\(121\) −6.33986 −0.576351
\(122\) 0 0
\(123\) 4.70833 0.424535
\(124\) 0 0
\(125\) −6.46451 −0.578203
\(126\) 0 0
\(127\) 4.22669 0.375058 0.187529 0.982259i \(-0.439952\pi\)
0.187529 + 0.982259i \(0.439952\pi\)
\(128\) 0 0
\(129\) −4.46939 −0.393508
\(130\) 0 0
\(131\) −13.1157 −1.14593 −0.572963 0.819581i \(-0.694206\pi\)
−0.572963 + 0.819581i \(0.694206\pi\)
\(132\) 0 0
\(133\) −9.35453 −0.811141
\(134\) 0 0
\(135\) −3.69408 −0.317936
\(136\) 0 0
\(137\) −5.39584 −0.460997 −0.230499 0.973073i \(-0.574036\pi\)
−0.230499 + 0.973073i \(0.574036\pi\)
\(138\) 0 0
\(139\) 13.0896 1.11024 0.555121 0.831770i \(-0.312672\pi\)
0.555121 + 0.831770i \(0.312672\pi\)
\(140\) 0 0
\(141\) −6.66998 −0.561714
\(142\) 0 0
\(143\) −10.0507 −0.840481
\(144\) 0 0
\(145\) −0.340995 −0.0283181
\(146\) 0 0
\(147\) −5.77865 −0.476615
\(148\) 0 0
\(149\) −16.1217 −1.32074 −0.660370 0.750940i \(-0.729601\pi\)
−0.660370 + 0.750940i \(0.729601\pi\)
\(150\) 0 0
\(151\) 8.37058 0.681188 0.340594 0.940210i \(-0.389372\pi\)
0.340594 + 0.940210i \(0.389372\pi\)
\(152\) 0 0
\(153\) 1.58766 0.128354
\(154\) 0 0
\(155\) −4.37733 −0.351596
\(156\) 0 0
\(157\) 4.75219 0.379266 0.189633 0.981855i \(-0.439270\pi\)
0.189633 + 0.981855i \(0.439270\pi\)
\(158\) 0 0
\(159\) 6.63698 0.526347
\(160\) 0 0
\(161\) −11.7930 −0.929417
\(162\) 0 0
\(163\) 8.94962 0.700988 0.350494 0.936565i \(-0.386014\pi\)
0.350494 + 0.936565i \(0.386014\pi\)
\(164\) 0 0
\(165\) −1.73826 −0.135323
\(166\) 0 0
\(167\) 0.900044 0.0696475 0.0348238 0.999393i \(-0.488913\pi\)
0.0348238 + 0.999393i \(0.488913\pi\)
\(168\) 0 0
\(169\) 8.67672 0.667440
\(170\) 0 0
\(171\) 10.1583 0.776827
\(172\) 0 0
\(173\) −12.7968 −0.972926 −0.486463 0.873701i \(-0.661713\pi\)
−0.486463 + 0.873701i \(0.661713\pi\)
\(174\) 0 0
\(175\) −6.63896 −0.501858
\(176\) 0 0
\(177\) 1.18842 0.0893272
\(178\) 0 0
\(179\) −2.46621 −0.184333 −0.0921666 0.995744i \(-0.529379\pi\)
−0.0921666 + 0.995744i \(0.529379\pi\)
\(180\) 0 0
\(181\) −12.0844 −0.898228 −0.449114 0.893474i \(-0.648260\pi\)
−0.449114 + 0.893474i \(0.648260\pi\)
\(182\) 0 0
\(183\) −3.38527 −0.250246
\(184\) 0 0
\(185\) −3.26006 −0.239684
\(186\) 0 0
\(187\) 2.15873 0.157862
\(188\) 0 0
\(189\) −7.97109 −0.579811
\(190\) 0 0
\(191\) −14.6034 −1.05666 −0.528331 0.849038i \(-0.677182\pi\)
−0.528331 + 0.849038i \(0.677182\pi\)
\(192\) 0 0
\(193\) −7.70959 −0.554948 −0.277474 0.960733i \(-0.589497\pi\)
−0.277474 + 0.960733i \(0.589497\pi\)
\(194\) 0 0
\(195\) 3.74897 0.268470
\(196\) 0 0
\(197\) −0.588856 −0.0419543 −0.0209771 0.999780i \(-0.506678\pi\)
−0.0209771 + 0.999780i \(0.506678\pi\)
\(198\) 0 0
\(199\) 6.65566 0.471807 0.235903 0.971776i \(-0.424195\pi\)
0.235903 + 0.971776i \(0.424195\pi\)
\(200\) 0 0
\(201\) 4.32176 0.304833
\(202\) 0 0
\(203\) −0.735799 −0.0516430
\(204\) 0 0
\(205\) 2.68437 0.187484
\(206\) 0 0
\(207\) 12.8063 0.890099
\(208\) 0 0
\(209\) 13.8123 0.955414
\(210\) 0 0
\(211\) −19.7552 −1.36000 −0.680002 0.733210i \(-0.738021\pi\)
−0.680002 + 0.733210i \(0.738021\pi\)
\(212\) 0 0
\(213\) 7.59198 0.520194
\(214\) 0 0
\(215\) −2.54814 −0.173782
\(216\) 0 0
\(217\) −9.44542 −0.641197
\(218\) 0 0
\(219\) 14.2693 0.964227
\(220\) 0 0
\(221\) −4.65583 −0.313185
\(222\) 0 0
\(223\) 25.4341 1.70319 0.851597 0.524197i \(-0.175634\pi\)
0.851597 + 0.524197i \(0.175634\pi\)
\(224\) 0 0
\(225\) 7.20942 0.480628
\(226\) 0 0
\(227\) 14.6147 0.970009 0.485004 0.874512i \(-0.338818\pi\)
0.485004 + 0.874512i \(0.338818\pi\)
\(228\) 0 0
\(229\) 7.64411 0.505137 0.252568 0.967579i \(-0.418725\pi\)
0.252568 + 0.967579i \(0.418725\pi\)
\(230\) 0 0
\(231\) −3.75082 −0.246786
\(232\) 0 0
\(233\) 26.3790 1.72815 0.864073 0.503367i \(-0.167906\pi\)
0.864073 + 0.503367i \(0.167906\pi\)
\(234\) 0 0
\(235\) −3.80277 −0.248065
\(236\) 0 0
\(237\) −12.7252 −0.826590
\(238\) 0 0
\(239\) −6.19929 −0.400999 −0.200499 0.979694i \(-0.564256\pi\)
−0.200499 + 0.979694i \(0.564256\pi\)
\(240\) 0 0
\(241\) 15.0051 0.966563 0.483281 0.875465i \(-0.339445\pi\)
0.483281 + 0.875465i \(0.339445\pi\)
\(242\) 0 0
\(243\) 14.3164 0.918399
\(244\) 0 0
\(245\) −3.29459 −0.210484
\(246\) 0 0
\(247\) −29.7894 −1.89546
\(248\) 0 0
\(249\) 1.60090 0.101453
\(250\) 0 0
\(251\) −2.06032 −0.130046 −0.0650232 0.997884i \(-0.520712\pi\)
−0.0650232 + 0.997884i \(0.520712\pi\)
\(252\) 0 0
\(253\) 17.4127 1.09473
\(254\) 0 0
\(255\) −0.805222 −0.0504249
\(256\) 0 0
\(257\) −24.1805 −1.50834 −0.754169 0.656680i \(-0.771960\pi\)
−0.754169 + 0.656680i \(0.771960\pi\)
\(258\) 0 0
\(259\) −7.03456 −0.437106
\(260\) 0 0
\(261\) 0.799022 0.0494582
\(262\) 0 0
\(263\) −10.5970 −0.653439 −0.326720 0.945121i \(-0.605943\pi\)
−0.326720 + 0.945121i \(0.605943\pi\)
\(264\) 0 0
\(265\) 3.78395 0.232446
\(266\) 0 0
\(267\) 22.3127 1.36552
\(268\) 0 0
\(269\) −9.38855 −0.572430 −0.286215 0.958165i \(-0.592397\pi\)
−0.286215 + 0.958165i \(0.592397\pi\)
\(270\) 0 0
\(271\) −3.59487 −0.218373 −0.109186 0.994021i \(-0.534825\pi\)
−0.109186 + 0.994021i \(0.534825\pi\)
\(272\) 0 0
\(273\) 8.08954 0.489601
\(274\) 0 0
\(275\) 9.80264 0.591121
\(276\) 0 0
\(277\) 15.4200 0.926497 0.463248 0.886228i \(-0.346684\pi\)
0.463248 + 0.886228i \(0.346684\pi\)
\(278\) 0 0
\(279\) 10.2570 0.614071
\(280\) 0 0
\(281\) 11.7653 0.701856 0.350928 0.936402i \(-0.385866\pi\)
0.350928 + 0.936402i \(0.385866\pi\)
\(282\) 0 0
\(283\) −5.99628 −0.356442 −0.178221 0.983991i \(-0.557034\pi\)
−0.178221 + 0.983991i \(0.557034\pi\)
\(284\) 0 0
\(285\) −5.15206 −0.305182
\(286\) 0 0
\(287\) 5.79233 0.341910
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 16.4616 0.964994
\(292\) 0 0
\(293\) −14.6820 −0.857731 −0.428865 0.903368i \(-0.641087\pi\)
−0.428865 + 0.903368i \(0.641087\pi\)
\(294\) 0 0
\(295\) 0.677556 0.0394488
\(296\) 0 0
\(297\) 11.7696 0.682939
\(298\) 0 0
\(299\) −37.5546 −2.17184
\(300\) 0 0
\(301\) −5.49838 −0.316922
\(302\) 0 0
\(303\) −19.5324 −1.12211
\(304\) 0 0
\(305\) −1.93005 −0.110514
\(306\) 0 0
\(307\) −15.6127 −0.891066 −0.445533 0.895265i \(-0.646986\pi\)
−0.445533 + 0.895265i \(0.646986\pi\)
\(308\) 0 0
\(309\) 3.65301 0.207813
\(310\) 0 0
\(311\) 3.87401 0.219675 0.109837 0.993950i \(-0.464967\pi\)
0.109837 + 0.993950i \(0.464967\pi\)
\(312\) 0 0
\(313\) −16.2306 −0.917408 −0.458704 0.888589i \(-0.651686\pi\)
−0.458704 + 0.888589i \(0.651686\pi\)
\(314\) 0 0
\(315\) −1.57275 −0.0886142
\(316\) 0 0
\(317\) 21.9739 1.23417 0.617087 0.786895i \(-0.288313\pi\)
0.617087 + 0.786895i \(0.288313\pi\)
\(318\) 0 0
\(319\) 1.08643 0.0608284
\(320\) 0 0
\(321\) −0.948478 −0.0529389
\(322\) 0 0
\(323\) 6.39831 0.356012
\(324\) 0 0
\(325\) −21.1417 −1.17273
\(326\) 0 0
\(327\) 17.9011 0.989933
\(328\) 0 0
\(329\) −8.20561 −0.452390
\(330\) 0 0
\(331\) −6.58838 −0.362130 −0.181065 0.983471i \(-0.557954\pi\)
−0.181065 + 0.983471i \(0.557954\pi\)
\(332\) 0 0
\(333\) 7.63900 0.418615
\(334\) 0 0
\(335\) 2.46397 0.134621
\(336\) 0 0
\(337\) −18.6130 −1.01391 −0.506956 0.861972i \(-0.669230\pi\)
−0.506956 + 0.861972i \(0.669230\pi\)
\(338\) 0 0
\(339\) −13.5112 −0.733827
\(340\) 0 0
\(341\) 13.9465 0.755243
\(342\) 0 0
\(343\) −17.3433 −0.936450
\(344\) 0 0
\(345\) −6.49505 −0.349682
\(346\) 0 0
\(347\) −14.0424 −0.753833 −0.376917 0.926247i \(-0.623016\pi\)
−0.376917 + 0.926247i \(0.623016\pi\)
\(348\) 0 0
\(349\) 8.50135 0.455067 0.227533 0.973770i \(-0.426934\pi\)
0.227533 + 0.973770i \(0.426934\pi\)
\(350\) 0 0
\(351\) −25.3839 −1.35489
\(352\) 0 0
\(353\) 9.77220 0.520122 0.260061 0.965592i \(-0.416257\pi\)
0.260061 + 0.965592i \(0.416257\pi\)
\(354\) 0 0
\(355\) 4.32843 0.229729
\(356\) 0 0
\(357\) −1.73751 −0.0919587
\(358\) 0 0
\(359\) −23.4908 −1.23980 −0.619899 0.784681i \(-0.712827\pi\)
−0.619899 + 0.784681i \(0.712827\pi\)
\(360\) 0 0
\(361\) 21.9384 1.15465
\(362\) 0 0
\(363\) −7.53443 −0.395455
\(364\) 0 0
\(365\) 8.13535 0.425824
\(366\) 0 0
\(367\) 31.7892 1.65938 0.829691 0.558223i \(-0.188517\pi\)
0.829691 + 0.558223i \(0.188517\pi\)
\(368\) 0 0
\(369\) −6.29003 −0.327446
\(370\) 0 0
\(371\) 8.16502 0.423907
\(372\) 0 0
\(373\) 25.4967 1.32017 0.660085 0.751191i \(-0.270520\pi\)
0.660085 + 0.751191i \(0.270520\pi\)
\(374\) 0 0
\(375\) −7.68255 −0.396725
\(376\) 0 0
\(377\) −2.34315 −0.120678
\(378\) 0 0
\(379\) 12.9453 0.664954 0.332477 0.943111i \(-0.392116\pi\)
0.332477 + 0.943111i \(0.392116\pi\)
\(380\) 0 0
\(381\) 5.02308 0.257340
\(382\) 0 0
\(383\) 14.5875 0.745386 0.372693 0.927955i \(-0.378434\pi\)
0.372693 + 0.927955i \(0.378434\pi\)
\(384\) 0 0
\(385\) −2.13846 −0.108986
\(386\) 0 0
\(387\) 5.97083 0.303514
\(388\) 0 0
\(389\) −2.90329 −0.147203 −0.0736014 0.997288i \(-0.523449\pi\)
−0.0736014 + 0.997288i \(0.523449\pi\)
\(390\) 0 0
\(391\) 8.06616 0.407923
\(392\) 0 0
\(393\) −15.5870 −0.786259
\(394\) 0 0
\(395\) −7.25504 −0.365040
\(396\) 0 0
\(397\) −13.2042 −0.662699 −0.331349 0.943508i \(-0.607504\pi\)
−0.331349 + 0.943508i \(0.607504\pi\)
\(398\) 0 0
\(399\) −11.1171 −0.556552
\(400\) 0 0
\(401\) −39.2650 −1.96080 −0.980401 0.197012i \(-0.936876\pi\)
−0.980401 + 0.197012i \(0.936876\pi\)
\(402\) 0 0
\(403\) −30.0789 −1.49833
\(404\) 0 0
\(405\) −1.16294 −0.0577871
\(406\) 0 0
\(407\) 10.3867 0.514852
\(408\) 0 0
\(409\) 20.2798 1.00277 0.501386 0.865224i \(-0.332824\pi\)
0.501386 + 0.865224i \(0.332824\pi\)
\(410\) 0 0
\(411\) −6.41252 −0.316306
\(412\) 0 0
\(413\) 1.46203 0.0719418
\(414\) 0 0
\(415\) 0.912725 0.0448039
\(416\) 0 0
\(417\) 15.5559 0.761776
\(418\) 0 0
\(419\) −13.2868 −0.649101 −0.324550 0.945868i \(-0.605213\pi\)
−0.324550 + 0.945868i \(0.605213\pi\)
\(420\) 0 0
\(421\) 12.3861 0.603661 0.301831 0.953362i \(-0.402402\pi\)
0.301831 + 0.953362i \(0.402402\pi\)
\(422\) 0 0
\(423\) 8.91068 0.433252
\(424\) 0 0
\(425\) 4.54092 0.220267
\(426\) 0 0
\(427\) −4.16466 −0.201542
\(428\) 0 0
\(429\) −11.9445 −0.576684
\(430\) 0 0
\(431\) −12.8438 −0.618665 −0.309332 0.950954i \(-0.600106\pi\)
−0.309332 + 0.950954i \(0.600106\pi\)
\(432\) 0 0
\(433\) −27.1939 −1.30686 −0.653428 0.756989i \(-0.726670\pi\)
−0.653428 + 0.756989i \(0.726670\pi\)
\(434\) 0 0
\(435\) −0.405245 −0.0194300
\(436\) 0 0
\(437\) 51.6098 2.46883
\(438\) 0 0
\(439\) −17.7534 −0.847321 −0.423661 0.905821i \(-0.639255\pi\)
−0.423661 + 0.905821i \(0.639255\pi\)
\(440\) 0 0
\(441\) 7.71992 0.367615
\(442\) 0 0
\(443\) −1.09413 −0.0519835 −0.0259918 0.999662i \(-0.508274\pi\)
−0.0259918 + 0.999662i \(0.508274\pi\)
\(444\) 0 0
\(445\) 12.7212 0.603042
\(446\) 0 0
\(447\) −19.1594 −0.906206
\(448\) 0 0
\(449\) −14.2020 −0.670232 −0.335116 0.942177i \(-0.608776\pi\)
−0.335116 + 0.942177i \(0.608776\pi\)
\(450\) 0 0
\(451\) −8.55255 −0.402724
\(452\) 0 0
\(453\) 9.94777 0.467387
\(454\) 0 0
\(455\) 4.61210 0.216219
\(456\) 0 0
\(457\) 4.21461 0.197151 0.0985755 0.995130i \(-0.468571\pi\)
0.0985755 + 0.995130i \(0.468571\pi\)
\(458\) 0 0
\(459\) 5.45207 0.254481
\(460\) 0 0
\(461\) −26.6055 −1.23914 −0.619572 0.784940i \(-0.712694\pi\)
−0.619572 + 0.784940i \(0.712694\pi\)
\(462\) 0 0
\(463\) −6.19016 −0.287681 −0.143841 0.989601i \(-0.545945\pi\)
−0.143841 + 0.989601i \(0.545945\pi\)
\(464\) 0 0
\(465\) −5.20211 −0.241242
\(466\) 0 0
\(467\) −6.82202 −0.315685 −0.157843 0.987464i \(-0.550454\pi\)
−0.157843 + 0.987464i \(0.550454\pi\)
\(468\) 0 0
\(469\) 5.31676 0.245505
\(470\) 0 0
\(471\) 5.64761 0.260228
\(472\) 0 0
\(473\) 8.11854 0.373291
\(474\) 0 0
\(475\) 29.0542 1.33310
\(476\) 0 0
\(477\) −8.86660 −0.405974
\(478\) 0 0
\(479\) −12.3300 −0.563373 −0.281686 0.959507i \(-0.590894\pi\)
−0.281686 + 0.959507i \(0.590894\pi\)
\(480\) 0 0
\(481\) −22.4015 −1.02142
\(482\) 0 0
\(483\) −14.0150 −0.637705
\(484\) 0 0
\(485\) 9.38526 0.426163
\(486\) 0 0
\(487\) −19.3105 −0.875042 −0.437521 0.899208i \(-0.644143\pi\)
−0.437521 + 0.899208i \(0.644143\pi\)
\(488\) 0 0
\(489\) 10.6359 0.480972
\(490\) 0 0
\(491\) −25.5729 −1.15409 −0.577044 0.816713i \(-0.695794\pi\)
−0.577044 + 0.816713i \(0.695794\pi\)
\(492\) 0 0
\(493\) 0.503272 0.0226662
\(494\) 0 0
\(495\) 2.32221 0.104375
\(496\) 0 0
\(497\) 9.33988 0.418951
\(498\) 0 0
\(499\) 5.84685 0.261741 0.130871 0.991399i \(-0.458223\pi\)
0.130871 + 0.991399i \(0.458223\pi\)
\(500\) 0 0
\(501\) 1.06963 0.0477876
\(502\) 0 0
\(503\) 10.4694 0.466809 0.233404 0.972380i \(-0.425013\pi\)
0.233404 + 0.972380i \(0.425013\pi\)
\(504\) 0 0
\(505\) −11.1361 −0.495548
\(506\) 0 0
\(507\) 10.3116 0.457954
\(508\) 0 0
\(509\) 17.7877 0.788427 0.394213 0.919019i \(-0.371017\pi\)
0.394213 + 0.919019i \(0.371017\pi\)
\(510\) 0 0
\(511\) 17.5545 0.776564
\(512\) 0 0
\(513\) 34.8840 1.54017
\(514\) 0 0
\(515\) 2.08270 0.0917747
\(516\) 0 0
\(517\) 12.1158 0.532854
\(518\) 0 0
\(519\) −15.2080 −0.667559
\(520\) 0 0
\(521\) 23.6032 1.03408 0.517038 0.855963i \(-0.327035\pi\)
0.517038 + 0.855963i \(0.327035\pi\)
\(522\) 0 0
\(523\) −18.5438 −0.810862 −0.405431 0.914126i \(-0.632878\pi\)
−0.405431 + 0.914126i \(0.632878\pi\)
\(524\) 0 0
\(525\) −7.88988 −0.344343
\(526\) 0 0
\(527\) 6.46048 0.281423
\(528\) 0 0
\(529\) 42.0629 1.82882
\(530\) 0 0
\(531\) −1.58766 −0.0688984
\(532\) 0 0
\(533\) 18.4456 0.798968
\(534\) 0 0
\(535\) −0.540757 −0.0233790
\(536\) 0 0
\(537\) −2.93090 −0.126478
\(538\) 0 0
\(539\) 10.4968 0.452128
\(540\) 0 0
\(541\) −23.3718 −1.00483 −0.502417 0.864626i \(-0.667556\pi\)
−0.502417 + 0.864626i \(0.667556\pi\)
\(542\) 0 0
\(543\) −14.3614 −0.616306
\(544\) 0 0
\(545\) 10.2060 0.437176
\(546\) 0 0
\(547\) −26.4644 −1.13153 −0.565767 0.824565i \(-0.691420\pi\)
−0.565767 + 0.824565i \(0.691420\pi\)
\(548\) 0 0
\(549\) 4.52251 0.193016
\(550\) 0 0
\(551\) 3.22009 0.137180
\(552\) 0 0
\(553\) −15.6549 −0.665715
\(554\) 0 0
\(555\) −3.87432 −0.164456
\(556\) 0 0
\(557\) −17.6498 −0.747847 −0.373923 0.927460i \(-0.621988\pi\)
−0.373923 + 0.927460i \(0.621988\pi\)
\(558\) 0 0
\(559\) −17.5096 −0.740575
\(560\) 0 0
\(561\) 2.56548 0.108315
\(562\) 0 0
\(563\) 27.4970 1.15886 0.579430 0.815022i \(-0.303275\pi\)
0.579430 + 0.815022i \(0.303275\pi\)
\(564\) 0 0
\(565\) −7.70315 −0.324074
\(566\) 0 0
\(567\) −2.50940 −0.105385
\(568\) 0 0
\(569\) −29.1172 −1.22066 −0.610328 0.792149i \(-0.708962\pi\)
−0.610328 + 0.792149i \(0.708962\pi\)
\(570\) 0 0
\(571\) 12.2631 0.513195 0.256598 0.966518i \(-0.417399\pi\)
0.256598 + 0.966518i \(0.417399\pi\)
\(572\) 0 0
\(573\) −17.3549 −0.725013
\(574\) 0 0
\(575\) 36.6278 1.52748
\(576\) 0 0
\(577\) 28.4697 1.18521 0.592604 0.805494i \(-0.298100\pi\)
0.592604 + 0.805494i \(0.298100\pi\)
\(578\) 0 0
\(579\) −9.16223 −0.380769
\(580\) 0 0
\(581\) 1.96948 0.0817077
\(582\) 0 0
\(583\) −12.0559 −0.499305
\(584\) 0 0
\(585\) −5.00840 −0.207072
\(586\) 0 0
\(587\) 33.0420 1.36379 0.681894 0.731451i \(-0.261157\pi\)
0.681894 + 0.731451i \(0.261157\pi\)
\(588\) 0 0
\(589\) 41.3362 1.70323
\(590\) 0 0
\(591\) −0.699809 −0.0287863
\(592\) 0 0
\(593\) 33.1496 1.36129 0.680645 0.732613i \(-0.261700\pi\)
0.680645 + 0.732613i \(0.261700\pi\)
\(594\) 0 0
\(595\) −0.990608 −0.0406110
\(596\) 0 0
\(597\) 7.90972 0.323723
\(598\) 0 0
\(599\) −21.3466 −0.872199 −0.436100 0.899898i \(-0.643640\pi\)
−0.436100 + 0.899898i \(0.643640\pi\)
\(600\) 0 0
\(601\) −31.4937 −1.28465 −0.642327 0.766431i \(-0.722031\pi\)
−0.642327 + 0.766431i \(0.722031\pi\)
\(602\) 0 0
\(603\) −5.77360 −0.235119
\(604\) 0 0
\(605\) −4.29561 −0.174642
\(606\) 0 0
\(607\) 32.8366 1.33280 0.666398 0.745596i \(-0.267835\pi\)
0.666398 + 0.745596i \(0.267835\pi\)
\(608\) 0 0
\(609\) −0.874438 −0.0354340
\(610\) 0 0
\(611\) −26.1307 −1.05714
\(612\) 0 0
\(613\) 47.3912 1.91411 0.957057 0.289900i \(-0.0936220\pi\)
0.957057 + 0.289900i \(0.0936220\pi\)
\(614\) 0 0
\(615\) 3.19016 0.128639
\(616\) 0 0
\(617\) 11.9072 0.479367 0.239684 0.970851i \(-0.422956\pi\)
0.239684 + 0.970851i \(0.422956\pi\)
\(618\) 0 0
\(619\) 7.47328 0.300376 0.150188 0.988657i \(-0.452012\pi\)
0.150188 + 0.988657i \(0.452012\pi\)
\(620\) 0 0
\(621\) 43.9772 1.76475
\(622\) 0 0
\(623\) 27.4498 1.09975
\(624\) 0 0
\(625\) 18.3245 0.732981
\(626\) 0 0
\(627\) 16.4148 0.655543
\(628\) 0 0
\(629\) 4.81150 0.191847
\(630\) 0 0
\(631\) 1.45088 0.0577586 0.0288793 0.999583i \(-0.490806\pi\)
0.0288793 + 0.999583i \(0.490806\pi\)
\(632\) 0 0
\(633\) −23.4775 −0.933146
\(634\) 0 0
\(635\) 2.86382 0.113647
\(636\) 0 0
\(637\) −22.6388 −0.896982
\(638\) 0 0
\(639\) −10.1424 −0.401228
\(640\) 0 0
\(641\) −40.8584 −1.61381 −0.806904 0.590682i \(-0.798859\pi\)
−0.806904 + 0.590682i \(0.798859\pi\)
\(642\) 0 0
\(643\) 20.7218 0.817187 0.408594 0.912716i \(-0.366019\pi\)
0.408594 + 0.912716i \(0.366019\pi\)
\(644\) 0 0
\(645\) −3.02826 −0.119238
\(646\) 0 0
\(647\) −14.3727 −0.565051 −0.282525 0.959260i \(-0.591172\pi\)
−0.282525 + 0.959260i \(0.591172\pi\)
\(648\) 0 0
\(649\) −2.15873 −0.0847378
\(650\) 0 0
\(651\) −11.2251 −0.439947
\(652\) 0 0
\(653\) 28.9443 1.13268 0.566339 0.824172i \(-0.308359\pi\)
0.566339 + 0.824172i \(0.308359\pi\)
\(654\) 0 0
\(655\) −8.88663 −0.347229
\(656\) 0 0
\(657\) −19.0628 −0.743712
\(658\) 0 0
\(659\) −38.5731 −1.50260 −0.751298 0.659964i \(-0.770572\pi\)
−0.751298 + 0.659964i \(0.770572\pi\)
\(660\) 0 0
\(661\) −10.1395 −0.394382 −0.197191 0.980365i \(-0.563182\pi\)
−0.197191 + 0.980365i \(0.563182\pi\)
\(662\) 0 0
\(663\) −5.53308 −0.214887
\(664\) 0 0
\(665\) −6.33822 −0.245786
\(666\) 0 0
\(667\) 4.05947 0.157183
\(668\) 0 0
\(669\) 30.2264 1.16862
\(670\) 0 0
\(671\) 6.14925 0.237389
\(672\) 0 0
\(673\) 32.1833 1.24058 0.620288 0.784374i \(-0.287016\pi\)
0.620288 + 0.784374i \(0.287016\pi\)
\(674\) 0 0
\(675\) 24.7574 0.952912
\(676\) 0 0
\(677\) 11.3291 0.435415 0.217707 0.976014i \(-0.430142\pi\)
0.217707 + 0.976014i \(0.430142\pi\)
\(678\) 0 0
\(679\) 20.2515 0.777182
\(680\) 0 0
\(681\) 17.3684 0.665557
\(682\) 0 0
\(683\) 2.24154 0.0857701 0.0428850 0.999080i \(-0.486345\pi\)
0.0428850 + 0.999080i \(0.486345\pi\)
\(684\) 0 0
\(685\) −3.65598 −0.139688
\(686\) 0 0
\(687\) 9.08442 0.346592
\(688\) 0 0
\(689\) 26.0014 0.990576
\(690\) 0 0
\(691\) −1.63967 −0.0623759 −0.0311880 0.999514i \(-0.509929\pi\)
−0.0311880 + 0.999514i \(0.509929\pi\)
\(692\) 0 0
\(693\) 5.01086 0.190347
\(694\) 0 0
\(695\) 8.86891 0.336417
\(696\) 0 0
\(697\) −3.96183 −0.150065
\(698\) 0 0
\(699\) 31.3493 1.18574
\(700\) 0 0
\(701\) −6.97462 −0.263428 −0.131714 0.991288i \(-0.542048\pi\)
−0.131714 + 0.991288i \(0.542048\pi\)
\(702\) 0 0
\(703\) 30.7855 1.16110
\(704\) 0 0
\(705\) −4.51929 −0.170206
\(706\) 0 0
\(707\) −24.0294 −0.903719
\(708\) 0 0
\(709\) −35.4365 −1.33085 −0.665423 0.746467i \(-0.731749\pi\)
−0.665423 + 0.746467i \(0.731749\pi\)
\(710\) 0 0
\(711\) 17.0001 0.637553
\(712\) 0 0
\(713\) 52.1112 1.95158
\(714\) 0 0
\(715\) −6.80991 −0.254676
\(716\) 0 0
\(717\) −7.36736 −0.275139
\(718\) 0 0
\(719\) −1.78953 −0.0667381 −0.0333691 0.999443i \(-0.510624\pi\)
−0.0333691 + 0.999443i \(0.510624\pi\)
\(720\) 0 0
\(721\) 4.49405 0.167367
\(722\) 0 0
\(723\) 17.8324 0.663192
\(724\) 0 0
\(725\) 2.28532 0.0848745
\(726\) 0 0
\(727\) −6.14617 −0.227949 −0.113974 0.993484i \(-0.536358\pi\)
−0.113974 + 0.993484i \(0.536358\pi\)
\(728\) 0 0
\(729\) 22.1631 0.820854
\(730\) 0 0
\(731\) 3.76078 0.139098
\(732\) 0 0
\(733\) −21.4431 −0.792019 −0.396010 0.918246i \(-0.629605\pi\)
−0.396010 + 0.918246i \(0.629605\pi\)
\(734\) 0 0
\(735\) −3.91536 −0.144420
\(736\) 0 0
\(737\) −7.85036 −0.289172
\(738\) 0 0
\(739\) −15.0414 −0.553306 −0.276653 0.960970i \(-0.589225\pi\)
−0.276653 + 0.960970i \(0.589225\pi\)
\(740\) 0 0
\(741\) −35.4024 −1.30054
\(742\) 0 0
\(743\) −48.1672 −1.76708 −0.883542 0.468351i \(-0.844848\pi\)
−0.883542 + 0.468351i \(0.844848\pi\)
\(744\) 0 0
\(745\) −10.9234 −0.400201
\(746\) 0 0
\(747\) −2.13871 −0.0782512
\(748\) 0 0
\(749\) −1.16685 −0.0426356
\(750\) 0 0
\(751\) 15.0633 0.549666 0.274833 0.961492i \(-0.411377\pi\)
0.274833 + 0.961492i \(0.411377\pi\)
\(752\) 0 0
\(753\) −2.44853 −0.0892294
\(754\) 0 0
\(755\) 5.67154 0.206408
\(756\) 0 0
\(757\) −4.64740 −0.168913 −0.0844564 0.996427i \(-0.526915\pi\)
−0.0844564 + 0.996427i \(0.526915\pi\)
\(758\) 0 0
\(759\) 20.6936 0.751130
\(760\) 0 0
\(761\) −24.2975 −0.880784 −0.440392 0.897806i \(-0.645161\pi\)
−0.440392 + 0.897806i \(0.645161\pi\)
\(762\) 0 0
\(763\) 22.0225 0.797267
\(764\) 0 0
\(765\) 1.07573 0.0388930
\(766\) 0 0
\(767\) 4.65583 0.168112
\(768\) 0 0
\(769\) 13.7888 0.497236 0.248618 0.968602i \(-0.420024\pi\)
0.248618 + 0.968602i \(0.420024\pi\)
\(770\) 0 0
\(771\) −28.7366 −1.03492
\(772\) 0 0
\(773\) 18.4329 0.662987 0.331493 0.943458i \(-0.392448\pi\)
0.331493 + 0.943458i \(0.392448\pi\)
\(774\) 0 0
\(775\) 29.3365 1.05380
\(776\) 0 0
\(777\) −8.36001 −0.299914
\(778\) 0 0
\(779\) −25.3491 −0.908224
\(780\) 0 0
\(781\) −13.7906 −0.493467
\(782\) 0 0
\(783\) 2.74387 0.0980579
\(784\) 0 0
\(785\) 3.21988 0.114922
\(786\) 0 0
\(787\) 12.7308 0.453805 0.226903 0.973917i \(-0.427140\pi\)
0.226903 + 0.973917i \(0.427140\pi\)
\(788\) 0 0
\(789\) −12.5937 −0.448347
\(790\) 0 0
\(791\) −16.6219 −0.591006
\(792\) 0 0
\(793\) −13.2623 −0.470959
\(794\) 0 0
\(795\) 4.49693 0.159490
\(796\) 0 0
\(797\) 16.5566 0.586463 0.293232 0.956041i \(-0.405269\pi\)
0.293232 + 0.956041i \(0.405269\pi\)
\(798\) 0 0
\(799\) 5.61248 0.198555
\(800\) 0 0
\(801\) −29.8084 −1.05323
\(802\) 0 0
\(803\) −25.9197 −0.914687
\(804\) 0 0
\(805\) −7.99040 −0.281625
\(806\) 0 0
\(807\) −11.1576 −0.392764
\(808\) 0 0
\(809\) 7.62197 0.267974 0.133987 0.990983i \(-0.457222\pi\)
0.133987 + 0.990983i \(0.457222\pi\)
\(810\) 0 0
\(811\) −56.0301 −1.96748 −0.983742 0.179590i \(-0.942523\pi\)
−0.983742 + 0.179590i \(0.942523\pi\)
\(812\) 0 0
\(813\) −4.27222 −0.149833
\(814\) 0 0
\(815\) 6.06387 0.212408
\(816\) 0 0
\(817\) 24.0627 0.841847
\(818\) 0 0
\(819\) −10.8071 −0.377631
\(820\) 0 0
\(821\) −2.86489 −0.0999853 −0.0499926 0.998750i \(-0.515920\pi\)
−0.0499926 + 0.998750i \(0.515920\pi\)
\(822\) 0 0
\(823\) −27.4404 −0.956513 −0.478256 0.878220i \(-0.658731\pi\)
−0.478256 + 0.878220i \(0.658731\pi\)
\(824\) 0 0
\(825\) 11.6497 0.405589
\(826\) 0 0
\(827\) −7.35460 −0.255745 −0.127872 0.991791i \(-0.540815\pi\)
−0.127872 + 0.991791i \(0.540815\pi\)
\(828\) 0 0
\(829\) −1.08547 −0.0377001 −0.0188500 0.999822i \(-0.506001\pi\)
−0.0188500 + 0.999822i \(0.506001\pi\)
\(830\) 0 0
\(831\) 18.3254 0.635702
\(832\) 0 0
\(833\) 4.86246 0.168474
\(834\) 0 0
\(835\) 0.609830 0.0211041
\(836\) 0 0
\(837\) 35.2229 1.21748
\(838\) 0 0
\(839\) −30.5467 −1.05459 −0.527294 0.849683i \(-0.676793\pi\)
−0.527294 + 0.849683i \(0.676793\pi\)
\(840\) 0 0
\(841\) −28.7467 −0.991266
\(842\) 0 0
\(843\) 13.9821 0.481568
\(844\) 0 0
\(845\) 5.87897 0.202243
\(846\) 0 0
\(847\) −9.26908 −0.318489
\(848\) 0 0
\(849\) −7.12610 −0.244567
\(850\) 0 0
\(851\) 38.8103 1.33040
\(852\) 0 0
\(853\) 14.9692 0.512537 0.256269 0.966606i \(-0.417507\pi\)
0.256269 + 0.966606i \(0.417507\pi\)
\(854\) 0 0
\(855\) 6.88284 0.235388
\(856\) 0 0
\(857\) 31.8766 1.08888 0.544442 0.838798i \(-0.316741\pi\)
0.544442 + 0.838798i \(0.316741\pi\)
\(858\) 0 0
\(859\) −0.868914 −0.0296470 −0.0148235 0.999890i \(-0.504719\pi\)
−0.0148235 + 0.999890i \(0.504719\pi\)
\(860\) 0 0
\(861\) 6.88372 0.234597
\(862\) 0 0
\(863\) 7.18049 0.244427 0.122213 0.992504i \(-0.461001\pi\)
0.122213 + 0.992504i \(0.461001\pi\)
\(864\) 0 0
\(865\) −8.67058 −0.294809
\(866\) 0 0
\(867\) 1.18842 0.0403609
\(868\) 0 0
\(869\) 23.1150 0.784122
\(870\) 0 0
\(871\) 16.9312 0.573691
\(872\) 0 0
\(873\) −21.9916 −0.744304
\(874\) 0 0
\(875\) −9.45131 −0.319513
\(876\) 0 0
\(877\) 37.2504 1.25786 0.628929 0.777463i \(-0.283494\pi\)
0.628929 + 0.777463i \(0.283494\pi\)
\(878\) 0 0
\(879\) −17.4484 −0.588519
\(880\) 0 0
\(881\) 11.8301 0.398568 0.199284 0.979942i \(-0.436138\pi\)
0.199284 + 0.979942i \(0.436138\pi\)
\(882\) 0 0
\(883\) −45.4087 −1.52812 −0.764062 0.645143i \(-0.776798\pi\)
−0.764062 + 0.645143i \(0.776798\pi\)
\(884\) 0 0
\(885\) 0.805222 0.0270672
\(886\) 0 0
\(887\) 1.62475 0.0545536 0.0272768 0.999628i \(-0.491316\pi\)
0.0272768 + 0.999628i \(0.491316\pi\)
\(888\) 0 0
\(889\) 6.17955 0.207255
\(890\) 0 0
\(891\) 3.70520 0.124129
\(892\) 0 0
\(893\) 35.9104 1.20170
\(894\) 0 0
\(895\) −1.67100 −0.0558553
\(896\) 0 0
\(897\) −44.6307 −1.49018
\(898\) 0 0
\(899\) 3.25137 0.108439
\(900\) 0 0
\(901\) −5.58471 −0.186054
\(902\) 0 0
\(903\) −6.53439 −0.217451
\(904\) 0 0
\(905\) −8.18788 −0.272174
\(906\) 0 0
\(907\) 24.8412 0.824839 0.412420 0.910994i \(-0.364684\pi\)
0.412420 + 0.910994i \(0.364684\pi\)
\(908\) 0 0
\(909\) 26.0941 0.865488
\(910\) 0 0
\(911\) −3.63895 −0.120564 −0.0602819 0.998181i \(-0.519200\pi\)
−0.0602819 + 0.998181i \(0.519200\pi\)
\(912\) 0 0
\(913\) −2.90800 −0.0962406
\(914\) 0 0
\(915\) −2.29371 −0.0758277
\(916\) 0 0
\(917\) −19.1756 −0.633234
\(918\) 0 0
\(919\) 37.8537 1.24868 0.624340 0.781153i \(-0.285368\pi\)
0.624340 + 0.781153i \(0.285368\pi\)
\(920\) 0 0
\(921\) −18.5545 −0.611392
\(922\) 0 0
\(923\) 29.7428 0.978996
\(924\) 0 0
\(925\) 21.8486 0.718378
\(926\) 0 0
\(927\) −4.88020 −0.160287
\(928\) 0 0
\(929\) 43.5268 1.42807 0.714034 0.700111i \(-0.246866\pi\)
0.714034 + 0.700111i \(0.246866\pi\)
\(930\) 0 0
\(931\) 31.1116 1.01964
\(932\) 0 0
\(933\) 4.60395 0.150727
\(934\) 0 0
\(935\) 1.46266 0.0478342
\(936\) 0 0
\(937\) −13.6024 −0.444370 −0.222185 0.975005i \(-0.571319\pi\)
−0.222185 + 0.975005i \(0.571319\pi\)
\(938\) 0 0
\(939\) −19.2888 −0.629466
\(940\) 0 0
\(941\) −29.5568 −0.963524 −0.481762 0.876302i \(-0.660003\pi\)
−0.481762 + 0.876302i \(0.660003\pi\)
\(942\) 0 0
\(943\) −31.9568 −1.04066
\(944\) 0 0
\(945\) −5.40086 −0.175690
\(946\) 0 0
\(947\) −18.0327 −0.585985 −0.292993 0.956115i \(-0.594651\pi\)
−0.292993 + 0.956115i \(0.594651\pi\)
\(948\) 0 0
\(949\) 55.9021 1.81466
\(950\) 0 0
\(951\) 26.1142 0.846810
\(952\) 0 0
\(953\) −43.6242 −1.41313 −0.706563 0.707650i \(-0.749755\pi\)
−0.706563 + 0.707650i \(0.749755\pi\)
\(954\) 0 0
\(955\) −9.89460 −0.320182
\(956\) 0 0
\(957\) 1.29114 0.0417365
\(958\) 0 0
\(959\) −7.88888 −0.254745
\(960\) 0 0
\(961\) 10.7377 0.346379
\(962\) 0 0
\(963\) 1.26711 0.0408320
\(964\) 0 0
\(965\) −5.22368 −0.168156
\(966\) 0 0
\(967\) 39.0870 1.25695 0.628476 0.777829i \(-0.283679\pi\)
0.628476 + 0.777829i \(0.283679\pi\)
\(968\) 0 0
\(969\) 7.60389 0.244272
\(970\) 0 0
\(971\) −21.9218 −0.703505 −0.351752 0.936093i \(-0.614414\pi\)
−0.351752 + 0.936093i \(0.614414\pi\)
\(972\) 0 0
\(973\) 19.1373 0.613515
\(974\) 0 0
\(975\) −25.1253 −0.804652
\(976\) 0 0
\(977\) 32.7035 1.04628 0.523140 0.852247i \(-0.324761\pi\)
0.523140 + 0.852247i \(0.324761\pi\)
\(978\) 0 0
\(979\) −40.5305 −1.29536
\(980\) 0 0
\(981\) −23.9148 −0.763540
\(982\) 0 0
\(983\) −39.0597 −1.24581 −0.622906 0.782297i \(-0.714048\pi\)
−0.622906 + 0.782297i \(0.714048\pi\)
\(984\) 0 0
\(985\) −0.398983 −0.0127127
\(986\) 0 0
\(987\) −9.75172 −0.310401
\(988\) 0 0
\(989\) 30.3351 0.964599
\(990\) 0 0
\(991\) 9.56585 0.303869 0.151935 0.988391i \(-0.451450\pi\)
0.151935 + 0.988391i \(0.451450\pi\)
\(992\) 0 0
\(993\) −7.82977 −0.248470
\(994\) 0 0
\(995\) 4.50958 0.142963
\(996\) 0 0
\(997\) 36.7431 1.16366 0.581832 0.813309i \(-0.302336\pi\)
0.581832 + 0.813309i \(0.302336\pi\)
\(998\) 0 0
\(999\) 26.2326 0.829962
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 \(a_p\))