Properties

Label 8046.2.a.l.1.5
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-1.12518\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.12518 q^{5} -0.686663 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.12518 q^{5} -0.686663 q^{7} -1.00000 q^{8} +1.12518 q^{10} +3.05448 q^{11} -3.99040 q^{13} +0.686663 q^{14} +1.00000 q^{16} +5.80043 q^{17} +8.32168 q^{19} -1.12518 q^{20} -3.05448 q^{22} -2.20462 q^{23} -3.73397 q^{25} +3.99040 q^{26} -0.686663 q^{28} +6.02040 q^{29} +8.16044 q^{31} -1.00000 q^{32} -5.80043 q^{34} +0.772621 q^{35} +4.59174 q^{37} -8.32168 q^{38} +1.12518 q^{40} +5.82690 q^{41} +0.944768 q^{43} +3.05448 q^{44} +2.20462 q^{46} -6.19531 q^{47} -6.52849 q^{49} +3.73397 q^{50} -3.99040 q^{52} -8.18515 q^{53} -3.43684 q^{55} +0.686663 q^{56} -6.02040 q^{58} +8.39608 q^{59} -14.1320 q^{61} -8.16044 q^{62} +1.00000 q^{64} +4.48992 q^{65} +6.33902 q^{67} +5.80043 q^{68} -0.772621 q^{70} +2.82097 q^{71} -3.33968 q^{73} -4.59174 q^{74} +8.32168 q^{76} -2.09740 q^{77} -8.49208 q^{79} -1.12518 q^{80} -5.82690 q^{82} +6.34293 q^{83} -6.52653 q^{85} -0.944768 q^{86} -3.05448 q^{88} +6.07267 q^{89} +2.74006 q^{91} -2.20462 q^{92} +6.19531 q^{94} -9.36339 q^{95} -11.5459 q^{97} +6.52849 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 12q^{2} + 12q^{4} + 5q^{5} - 6q^{7} - 12q^{8} + O(q^{10}) \) \( 12q - 12q^{2} + 12q^{4} + 5q^{5} - 6q^{7} - 12q^{8} - 5q^{10} + 10q^{11} - q^{13} + 6q^{14} + 12q^{16} + 6q^{17} - 10q^{19} + 5q^{20} - 10q^{22} + 15q^{23} + 7q^{25} + q^{26} - 6q^{28} + 33q^{29} - 6q^{31} - 12q^{32} - 6q^{34} + 16q^{35} - 13q^{37} + 10q^{38} - 5q^{40} + 20q^{41} - 11q^{43} + 10q^{44} - 15q^{46} + 15q^{47} + 2q^{49} - 7q^{50} - q^{52} + 4q^{53} - 17q^{55} + 6q^{56} - 33q^{58} + 10q^{59} - 12q^{61} + 6q^{62} + 12q^{64} + 40q^{65} - 19q^{67} + 6q^{68} - 16q^{70} + 47q^{71} - 2q^{73} + 13q^{74} - 10q^{76} - 6q^{77} - 15q^{79} + 5q^{80} - 20q^{82} + 18q^{83} - 25q^{85} + 11q^{86} - 10q^{88} + 24q^{89} - 3q^{91} + 15q^{92} - 15q^{94} - 3q^{95} - 25q^{97} - 2q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.12518 −0.503196 −0.251598 0.967832i \(-0.580956\pi\)
−0.251598 + 0.967832i \(0.580956\pi\)
\(6\) 0 0
\(7\) −0.686663 −0.259534 −0.129767 0.991544i \(-0.541423\pi\)
−0.129767 + 0.991544i \(0.541423\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.12518 0.355814
\(11\) 3.05448 0.920960 0.460480 0.887670i \(-0.347677\pi\)
0.460480 + 0.887670i \(0.347677\pi\)
\(12\) 0 0
\(13\) −3.99040 −1.10674 −0.553369 0.832936i \(-0.686658\pi\)
−0.553369 + 0.832936i \(0.686658\pi\)
\(14\) 0.686663 0.183519
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 5.80043 1.40681 0.703405 0.710789i \(-0.251662\pi\)
0.703405 + 0.710789i \(0.251662\pi\)
\(18\) 0 0
\(19\) 8.32168 1.90912 0.954562 0.298013i \(-0.0963240\pi\)
0.954562 + 0.298013i \(0.0963240\pi\)
\(20\) −1.12518 −0.251598
\(21\) 0 0
\(22\) −3.05448 −0.651217
\(23\) −2.20462 −0.459696 −0.229848 0.973227i \(-0.573823\pi\)
−0.229848 + 0.973227i \(0.573823\pi\)
\(24\) 0 0
\(25\) −3.73397 −0.746793
\(26\) 3.99040 0.782582
\(27\) 0 0
\(28\) −0.686663 −0.129767
\(29\) 6.02040 1.11796 0.558980 0.829181i \(-0.311193\pi\)
0.558980 + 0.829181i \(0.311193\pi\)
\(30\) 0 0
\(31\) 8.16044 1.46566 0.732829 0.680413i \(-0.238199\pi\)
0.732829 + 0.680413i \(0.238199\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −5.80043 −0.994765
\(35\) 0.772621 0.130597
\(36\) 0 0
\(37\) 4.59174 0.754877 0.377438 0.926035i \(-0.376805\pi\)
0.377438 + 0.926035i \(0.376805\pi\)
\(38\) −8.32168 −1.34995
\(39\) 0 0
\(40\) 1.12518 0.177907
\(41\) 5.82690 0.910009 0.455004 0.890489i \(-0.349638\pi\)
0.455004 + 0.890489i \(0.349638\pi\)
\(42\) 0 0
\(43\) 0.944768 0.144076 0.0720379 0.997402i \(-0.477050\pi\)
0.0720379 + 0.997402i \(0.477050\pi\)
\(44\) 3.05448 0.460480
\(45\) 0 0
\(46\) 2.20462 0.325054
\(47\) −6.19531 −0.903679 −0.451839 0.892099i \(-0.649232\pi\)
−0.451839 + 0.892099i \(0.649232\pi\)
\(48\) 0 0
\(49\) −6.52849 −0.932642
\(50\) 3.73397 0.528063
\(51\) 0 0
\(52\) −3.99040 −0.553369
\(53\) −8.18515 −1.12432 −0.562159 0.827029i \(-0.690029\pi\)
−0.562159 + 0.827029i \(0.690029\pi\)
\(54\) 0 0
\(55\) −3.43684 −0.463424
\(56\) 0.686663 0.0917593
\(57\) 0 0
\(58\) −6.02040 −0.790517
\(59\) 8.39608 1.09308 0.546538 0.837434i \(-0.315945\pi\)
0.546538 + 0.837434i \(0.315945\pi\)
\(60\) 0 0
\(61\) −14.1320 −1.80942 −0.904712 0.426024i \(-0.859914\pi\)
−0.904712 + 0.426024i \(0.859914\pi\)
\(62\) −8.16044 −1.03638
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 4.48992 0.556906
\(66\) 0 0
\(67\) 6.33902 0.774434 0.387217 0.921989i \(-0.373436\pi\)
0.387217 + 0.921989i \(0.373436\pi\)
\(68\) 5.80043 0.703405
\(69\) 0 0
\(70\) −0.772621 −0.0923459
\(71\) 2.82097 0.334787 0.167393 0.985890i \(-0.446465\pi\)
0.167393 + 0.985890i \(0.446465\pi\)
\(72\) 0 0
\(73\) −3.33968 −0.390880 −0.195440 0.980716i \(-0.562613\pi\)
−0.195440 + 0.980716i \(0.562613\pi\)
\(74\) −4.59174 −0.533779
\(75\) 0 0
\(76\) 8.32168 0.954562
\(77\) −2.09740 −0.239021
\(78\) 0 0
\(79\) −8.49208 −0.955433 −0.477717 0.878514i \(-0.658535\pi\)
−0.477717 + 0.878514i \(0.658535\pi\)
\(80\) −1.12518 −0.125799
\(81\) 0 0
\(82\) −5.82690 −0.643473
\(83\) 6.34293 0.696227 0.348113 0.937452i \(-0.386822\pi\)
0.348113 + 0.937452i \(0.386822\pi\)
\(84\) 0 0
\(85\) −6.52653 −0.707902
\(86\) −0.944768 −0.101877
\(87\) 0 0
\(88\) −3.05448 −0.325609
\(89\) 6.07267 0.643702 0.321851 0.946790i \(-0.395695\pi\)
0.321851 + 0.946790i \(0.395695\pi\)
\(90\) 0 0
\(91\) 2.74006 0.287236
\(92\) −2.20462 −0.229848
\(93\) 0 0
\(94\) 6.19531 0.638997
\(95\) −9.36339 −0.960664
\(96\) 0 0
\(97\) −11.5459 −1.17231 −0.586153 0.810200i \(-0.699358\pi\)
−0.586153 + 0.810200i \(0.699358\pi\)
\(98\) 6.52849 0.659477
\(99\) 0 0
\(100\) −3.73397 −0.373397
\(101\) −13.1430 −1.30778 −0.653891 0.756589i \(-0.726864\pi\)
−0.653891 + 0.756589i \(0.726864\pi\)
\(102\) 0 0
\(103\) −11.8728 −1.16986 −0.584932 0.811082i \(-0.698879\pi\)
−0.584932 + 0.811082i \(0.698879\pi\)
\(104\) 3.99040 0.391291
\(105\) 0 0
\(106\) 8.18515 0.795012
\(107\) 10.9151 1.05521 0.527603 0.849491i \(-0.323091\pi\)
0.527603 + 0.849491i \(0.323091\pi\)
\(108\) 0 0
\(109\) 2.92308 0.279980 0.139990 0.990153i \(-0.455293\pi\)
0.139990 + 0.990153i \(0.455293\pi\)
\(110\) 3.43684 0.327690
\(111\) 0 0
\(112\) −0.686663 −0.0648836
\(113\) 5.24148 0.493077 0.246539 0.969133i \(-0.420707\pi\)
0.246539 + 0.969133i \(0.420707\pi\)
\(114\) 0 0
\(115\) 2.48060 0.231317
\(116\) 6.02040 0.558980
\(117\) 0 0
\(118\) −8.39608 −0.772922
\(119\) −3.98294 −0.365116
\(120\) 0 0
\(121\) −1.67015 −0.151832
\(122\) 14.1320 1.27946
\(123\) 0 0
\(124\) 8.16044 0.732829
\(125\) 9.82730 0.878980
\(126\) 0 0
\(127\) −13.7317 −1.21849 −0.609247 0.792981i \(-0.708528\pi\)
−0.609247 + 0.792981i \(0.708528\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −4.48992 −0.393792
\(131\) 17.6560 1.54261 0.771307 0.636463i \(-0.219603\pi\)
0.771307 + 0.636463i \(0.219603\pi\)
\(132\) 0 0
\(133\) −5.71419 −0.495483
\(134\) −6.33902 −0.547608
\(135\) 0 0
\(136\) −5.80043 −0.497383
\(137\) 18.9694 1.62066 0.810332 0.585971i \(-0.199287\pi\)
0.810332 + 0.585971i \(0.199287\pi\)
\(138\) 0 0
\(139\) 8.88482 0.753601 0.376800 0.926294i \(-0.377024\pi\)
0.376800 + 0.926294i \(0.377024\pi\)
\(140\) 0.772621 0.0652984
\(141\) 0 0
\(142\) −2.82097 −0.236730
\(143\) −12.1886 −1.01926
\(144\) 0 0
\(145\) −6.77404 −0.562553
\(146\) 3.33968 0.276394
\(147\) 0 0
\(148\) 4.59174 0.377438
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) −15.2920 −1.24444 −0.622222 0.782841i \(-0.713770\pi\)
−0.622222 + 0.782841i \(0.713770\pi\)
\(152\) −8.32168 −0.674977
\(153\) 0 0
\(154\) 2.09740 0.169013
\(155\) −9.18198 −0.737514
\(156\) 0 0
\(157\) −6.18546 −0.493654 −0.246827 0.969060i \(-0.579388\pi\)
−0.246827 + 0.969060i \(0.579388\pi\)
\(158\) 8.49208 0.675593
\(159\) 0 0
\(160\) 1.12518 0.0889534
\(161\) 1.51383 0.119307
\(162\) 0 0
\(163\) 16.8203 1.31747 0.658733 0.752376i \(-0.271093\pi\)
0.658733 + 0.752376i \(0.271093\pi\)
\(164\) 5.82690 0.455004
\(165\) 0 0
\(166\) −6.34293 −0.492307
\(167\) −9.10633 −0.704669 −0.352334 0.935874i \(-0.614612\pi\)
−0.352334 + 0.935874i \(0.614612\pi\)
\(168\) 0 0
\(169\) 2.92329 0.224868
\(170\) 6.52653 0.500562
\(171\) 0 0
\(172\) 0.944768 0.0720379
\(173\) 19.5509 1.48643 0.743213 0.669055i \(-0.233301\pi\)
0.743213 + 0.669055i \(0.233301\pi\)
\(174\) 0 0
\(175\) 2.56398 0.193819
\(176\) 3.05448 0.230240
\(177\) 0 0
\(178\) −6.07267 −0.455166
\(179\) 11.9617 0.894063 0.447031 0.894518i \(-0.352481\pi\)
0.447031 + 0.894518i \(0.352481\pi\)
\(180\) 0 0
\(181\) 0.902790 0.0671039 0.0335519 0.999437i \(-0.489318\pi\)
0.0335519 + 0.999437i \(0.489318\pi\)
\(182\) −2.74006 −0.203107
\(183\) 0 0
\(184\) 2.20462 0.162527
\(185\) −5.16654 −0.379851
\(186\) 0 0
\(187\) 17.7173 1.29562
\(188\) −6.19531 −0.451839
\(189\) 0 0
\(190\) 9.36339 0.679292
\(191\) −10.3662 −0.750070 −0.375035 0.927011i \(-0.622369\pi\)
−0.375035 + 0.927011i \(0.622369\pi\)
\(192\) 0 0
\(193\) −17.1187 −1.23223 −0.616116 0.787656i \(-0.711295\pi\)
−0.616116 + 0.787656i \(0.711295\pi\)
\(194\) 11.5459 0.828945
\(195\) 0 0
\(196\) −6.52849 −0.466321
\(197\) −11.7114 −0.834405 −0.417202 0.908814i \(-0.636989\pi\)
−0.417202 + 0.908814i \(0.636989\pi\)
\(198\) 0 0
\(199\) 23.9115 1.69504 0.847520 0.530763i \(-0.178094\pi\)
0.847520 + 0.530763i \(0.178094\pi\)
\(200\) 3.73397 0.264031
\(201\) 0 0
\(202\) 13.1430 0.924741
\(203\) −4.13398 −0.290149
\(204\) 0 0
\(205\) −6.55632 −0.457913
\(206\) 11.8728 0.827219
\(207\) 0 0
\(208\) −3.99040 −0.276684
\(209\) 25.4184 1.75823
\(210\) 0 0
\(211\) −14.8387 −1.02154 −0.510769 0.859718i \(-0.670639\pi\)
−0.510769 + 0.859718i \(0.670639\pi\)
\(212\) −8.18515 −0.562159
\(213\) 0 0
\(214\) −10.9151 −0.746143
\(215\) −1.06304 −0.0724984
\(216\) 0 0
\(217\) −5.60348 −0.380389
\(218\) −2.92308 −0.197976
\(219\) 0 0
\(220\) −3.43684 −0.231712
\(221\) −23.1460 −1.55697
\(222\) 0 0
\(223\) 15.8699 1.06273 0.531365 0.847143i \(-0.321679\pi\)
0.531365 + 0.847143i \(0.321679\pi\)
\(224\) 0.686663 0.0458796
\(225\) 0 0
\(226\) −5.24148 −0.348658
\(227\) 15.2519 1.01230 0.506151 0.862445i \(-0.331068\pi\)
0.506151 + 0.862445i \(0.331068\pi\)
\(228\) 0 0
\(229\) 24.3514 1.60919 0.804594 0.593826i \(-0.202383\pi\)
0.804594 + 0.593826i \(0.202383\pi\)
\(230\) −2.48060 −0.163566
\(231\) 0 0
\(232\) −6.02040 −0.395258
\(233\) 7.46438 0.489008 0.244504 0.969648i \(-0.421375\pi\)
0.244504 + 0.969648i \(0.421375\pi\)
\(234\) 0 0
\(235\) 6.97085 0.454728
\(236\) 8.39608 0.546538
\(237\) 0 0
\(238\) 3.98294 0.258176
\(239\) 19.9977 1.29354 0.646772 0.762684i \(-0.276119\pi\)
0.646772 + 0.762684i \(0.276119\pi\)
\(240\) 0 0
\(241\) 12.9019 0.831081 0.415541 0.909575i \(-0.363592\pi\)
0.415541 + 0.909575i \(0.363592\pi\)
\(242\) 1.67015 0.107361
\(243\) 0 0
\(244\) −14.1320 −0.904712
\(245\) 7.34574 0.469302
\(246\) 0 0
\(247\) −33.2068 −2.11290
\(248\) −8.16044 −0.518189
\(249\) 0 0
\(250\) −9.82730 −0.621533
\(251\) −13.6343 −0.860589 −0.430295 0.902688i \(-0.641590\pi\)
−0.430295 + 0.902688i \(0.641590\pi\)
\(252\) 0 0
\(253\) −6.73398 −0.423361
\(254\) 13.7317 0.861605
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −26.4900 −1.65240 −0.826200 0.563377i \(-0.809502\pi\)
−0.826200 + 0.563377i \(0.809502\pi\)
\(258\) 0 0
\(259\) −3.15298 −0.195916
\(260\) 4.48992 0.278453
\(261\) 0 0
\(262\) −17.6560 −1.09079
\(263\) 4.98189 0.307196 0.153598 0.988133i \(-0.450914\pi\)
0.153598 + 0.988133i \(0.450914\pi\)
\(264\) 0 0
\(265\) 9.20978 0.565752
\(266\) 5.71419 0.350359
\(267\) 0 0
\(268\) 6.33902 0.387217
\(269\) 7.74980 0.472514 0.236257 0.971691i \(-0.424079\pi\)
0.236257 + 0.971691i \(0.424079\pi\)
\(270\) 0 0
\(271\) 20.0627 1.21872 0.609361 0.792893i \(-0.291426\pi\)
0.609361 + 0.792893i \(0.291426\pi\)
\(272\) 5.80043 0.351703
\(273\) 0 0
\(274\) −18.9694 −1.14598
\(275\) −11.4053 −0.687767
\(276\) 0 0
\(277\) 18.1869 1.09275 0.546373 0.837542i \(-0.316008\pi\)
0.546373 + 0.837542i \(0.316008\pi\)
\(278\) −8.88482 −0.532876
\(279\) 0 0
\(280\) −0.772621 −0.0461729
\(281\) 15.9505 0.951525 0.475763 0.879574i \(-0.342172\pi\)
0.475763 + 0.879574i \(0.342172\pi\)
\(282\) 0 0
\(283\) 1.04252 0.0619712 0.0309856 0.999520i \(-0.490135\pi\)
0.0309856 + 0.999520i \(0.490135\pi\)
\(284\) 2.82097 0.167393
\(285\) 0 0
\(286\) 12.1886 0.720727
\(287\) −4.00112 −0.236179
\(288\) 0 0
\(289\) 16.6450 0.979115
\(290\) 6.77404 0.397785
\(291\) 0 0
\(292\) −3.33968 −0.195440
\(293\) −1.65871 −0.0969029 −0.0484515 0.998826i \(-0.515429\pi\)
−0.0484515 + 0.998826i \(0.515429\pi\)
\(294\) 0 0
\(295\) −9.44711 −0.550032
\(296\) −4.59174 −0.266889
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) 8.79733 0.508762
\(300\) 0 0
\(301\) −0.648738 −0.0373926
\(302\) 15.2920 0.879955
\(303\) 0 0
\(304\) 8.32168 0.477281
\(305\) 15.9011 0.910495
\(306\) 0 0
\(307\) −30.3028 −1.72947 −0.864737 0.502225i \(-0.832515\pi\)
−0.864737 + 0.502225i \(0.832515\pi\)
\(308\) −2.09740 −0.119510
\(309\) 0 0
\(310\) 9.18198 0.521501
\(311\) 6.82658 0.387100 0.193550 0.981090i \(-0.438000\pi\)
0.193550 + 0.981090i \(0.438000\pi\)
\(312\) 0 0
\(313\) −3.07494 −0.173806 −0.0869030 0.996217i \(-0.527697\pi\)
−0.0869030 + 0.996217i \(0.527697\pi\)
\(314\) 6.18546 0.349066
\(315\) 0 0
\(316\) −8.49208 −0.477717
\(317\) −14.5491 −0.817161 −0.408581 0.912722i \(-0.633976\pi\)
−0.408581 + 0.912722i \(0.633976\pi\)
\(318\) 0 0
\(319\) 18.3892 1.02960
\(320\) −1.12518 −0.0628996
\(321\) 0 0
\(322\) −1.51383 −0.0843626
\(323\) 48.2693 2.68577
\(324\) 0 0
\(325\) 14.9000 0.826504
\(326\) −16.8203 −0.931590
\(327\) 0 0
\(328\) −5.82690 −0.321737
\(329\) 4.25409 0.234536
\(330\) 0 0
\(331\) 18.2660 1.00399 0.501994 0.864871i \(-0.332600\pi\)
0.501994 + 0.864871i \(0.332600\pi\)
\(332\) 6.34293 0.348113
\(333\) 0 0
\(334\) 9.10633 0.498276
\(335\) −7.13254 −0.389693
\(336\) 0 0
\(337\) 23.9834 1.30646 0.653228 0.757161i \(-0.273414\pi\)
0.653228 + 0.757161i \(0.273414\pi\)
\(338\) −2.92329 −0.159006
\(339\) 0 0
\(340\) −6.52653 −0.353951
\(341\) 24.9259 1.34981
\(342\) 0 0
\(343\) 9.28952 0.501587
\(344\) −0.944768 −0.0509385
\(345\) 0 0
\(346\) −19.5509 −1.05106
\(347\) −21.2095 −1.13859 −0.569293 0.822135i \(-0.692783\pi\)
−0.569293 + 0.822135i \(0.692783\pi\)
\(348\) 0 0
\(349\) 13.4739 0.721241 0.360620 0.932713i \(-0.382565\pi\)
0.360620 + 0.932713i \(0.382565\pi\)
\(350\) −2.56398 −0.137050
\(351\) 0 0
\(352\) −3.05448 −0.162804
\(353\) −17.1231 −0.911369 −0.455685 0.890141i \(-0.650605\pi\)
−0.455685 + 0.890141i \(0.650605\pi\)
\(354\) 0 0
\(355\) −3.17410 −0.168464
\(356\) 6.07267 0.321851
\(357\) 0 0
\(358\) −11.9617 −0.632198
\(359\) 33.0700 1.74537 0.872683 0.488288i \(-0.162378\pi\)
0.872683 + 0.488288i \(0.162378\pi\)
\(360\) 0 0
\(361\) 50.2503 2.64475
\(362\) −0.902790 −0.0474496
\(363\) 0 0
\(364\) 2.74006 0.143618
\(365\) 3.75775 0.196689
\(366\) 0 0
\(367\) 0.517529 0.0270148 0.0135074 0.999909i \(-0.495700\pi\)
0.0135074 + 0.999909i \(0.495700\pi\)
\(368\) −2.20462 −0.114924
\(369\) 0 0
\(370\) 5.16654 0.268595
\(371\) 5.62045 0.291799
\(372\) 0 0
\(373\) −24.3848 −1.26260 −0.631299 0.775540i \(-0.717478\pi\)
−0.631299 + 0.775540i \(0.717478\pi\)
\(374\) −17.7173 −0.916139
\(375\) 0 0
\(376\) 6.19531 0.319499
\(377\) −24.0238 −1.23729
\(378\) 0 0
\(379\) 10.9892 0.564479 0.282239 0.959344i \(-0.408923\pi\)
0.282239 + 0.959344i \(0.408923\pi\)
\(380\) −9.36339 −0.480332
\(381\) 0 0
\(382\) 10.3662 0.530380
\(383\) 25.8159 1.31913 0.659565 0.751648i \(-0.270741\pi\)
0.659565 + 0.751648i \(0.270741\pi\)
\(384\) 0 0
\(385\) 2.35995 0.120274
\(386\) 17.1187 0.871319
\(387\) 0 0
\(388\) −11.5459 −0.586153
\(389\) −37.0725 −1.87965 −0.939825 0.341656i \(-0.889012\pi\)
−0.939825 + 0.341656i \(0.889012\pi\)
\(390\) 0 0
\(391\) −12.7878 −0.646704
\(392\) 6.52849 0.329739
\(393\) 0 0
\(394\) 11.7114 0.590013
\(395\) 9.55513 0.480771
\(396\) 0 0
\(397\) −19.1725 −0.962242 −0.481121 0.876654i \(-0.659770\pi\)
−0.481121 + 0.876654i \(0.659770\pi\)
\(398\) −23.9115 −1.19857
\(399\) 0 0
\(400\) −3.73397 −0.186698
\(401\) 9.85673 0.492222 0.246111 0.969242i \(-0.420847\pi\)
0.246111 + 0.969242i \(0.420847\pi\)
\(402\) 0 0
\(403\) −32.5634 −1.62210
\(404\) −13.1430 −0.653891
\(405\) 0 0
\(406\) 4.13398 0.205166
\(407\) 14.0254 0.695212
\(408\) 0 0
\(409\) −8.27230 −0.409039 −0.204519 0.978863i \(-0.565563\pi\)
−0.204519 + 0.978863i \(0.565563\pi\)
\(410\) 6.55632 0.323794
\(411\) 0 0
\(412\) −11.8728 −0.584932
\(413\) −5.76528 −0.283691
\(414\) 0 0
\(415\) −7.13694 −0.350339
\(416\) 3.99040 0.195645
\(417\) 0 0
\(418\) −25.4184 −1.24325
\(419\) −5.77203 −0.281982 −0.140991 0.990011i \(-0.545029\pi\)
−0.140991 + 0.990011i \(0.545029\pi\)
\(420\) 0 0
\(421\) 8.50728 0.414619 0.207310 0.978275i \(-0.433529\pi\)
0.207310 + 0.978275i \(0.433529\pi\)
\(422\) 14.8387 0.722336
\(423\) 0 0
\(424\) 8.18515 0.397506
\(425\) −21.6586 −1.05060
\(426\) 0 0
\(427\) 9.70396 0.469608
\(428\) 10.9151 0.527603
\(429\) 0 0
\(430\) 1.06304 0.0512641
\(431\) −29.8564 −1.43813 −0.719067 0.694941i \(-0.755431\pi\)
−0.719067 + 0.694941i \(0.755431\pi\)
\(432\) 0 0
\(433\) 15.7016 0.754571 0.377286 0.926097i \(-0.376858\pi\)
0.377286 + 0.926097i \(0.376858\pi\)
\(434\) 5.60348 0.268975
\(435\) 0 0
\(436\) 2.92308 0.139990
\(437\) −18.3462 −0.877616
\(438\) 0 0
\(439\) 15.4229 0.736097 0.368048 0.929807i \(-0.380026\pi\)
0.368048 + 0.929807i \(0.380026\pi\)
\(440\) 3.43684 0.163845
\(441\) 0 0
\(442\) 23.1460 1.10094
\(443\) −5.88701 −0.279700 −0.139850 0.990173i \(-0.544662\pi\)
−0.139850 + 0.990173i \(0.544662\pi\)
\(444\) 0 0
\(445\) −6.83285 −0.323908
\(446\) −15.8699 −0.751463
\(447\) 0 0
\(448\) −0.686663 −0.0324418
\(449\) −23.1092 −1.09059 −0.545295 0.838244i \(-0.683582\pi\)
−0.545295 + 0.838244i \(0.683582\pi\)
\(450\) 0 0
\(451\) 17.7982 0.838082
\(452\) 5.24148 0.246539
\(453\) 0 0
\(454\) −15.2519 −0.715806
\(455\) −3.08307 −0.144536
\(456\) 0 0
\(457\) 16.5419 0.773798 0.386899 0.922122i \(-0.373546\pi\)
0.386899 + 0.922122i \(0.373546\pi\)
\(458\) −24.3514 −1.13787
\(459\) 0 0
\(460\) 2.48060 0.115659
\(461\) −3.97700 −0.185227 −0.0926137 0.995702i \(-0.529522\pi\)
−0.0926137 + 0.995702i \(0.529522\pi\)
\(462\) 0 0
\(463\) 18.7496 0.871366 0.435683 0.900100i \(-0.356507\pi\)
0.435683 + 0.900100i \(0.356507\pi\)
\(464\) 6.02040 0.279490
\(465\) 0 0
\(466\) −7.46438 −0.345781
\(467\) 9.33972 0.432191 0.216095 0.976372i \(-0.430668\pi\)
0.216095 + 0.976372i \(0.430668\pi\)
\(468\) 0 0
\(469\) −4.35277 −0.200992
\(470\) −6.97085 −0.321541
\(471\) 0 0
\(472\) −8.39608 −0.386461
\(473\) 2.88577 0.132688
\(474\) 0 0
\(475\) −31.0729 −1.42572
\(476\) −3.98294 −0.182558
\(477\) 0 0
\(478\) −19.9977 −0.914673
\(479\) −6.50916 −0.297411 −0.148705 0.988882i \(-0.547511\pi\)
−0.148705 + 0.988882i \(0.547511\pi\)
\(480\) 0 0
\(481\) −18.3229 −0.835451
\(482\) −12.9019 −0.587663
\(483\) 0 0
\(484\) −1.67015 −0.0759160
\(485\) 12.9912 0.589900
\(486\) 0 0
\(487\) 17.0058 0.770608 0.385304 0.922790i \(-0.374097\pi\)
0.385304 + 0.922790i \(0.374097\pi\)
\(488\) 14.1320 0.639728
\(489\) 0 0
\(490\) −7.34574 −0.331847
\(491\) 26.8032 1.20961 0.604807 0.796372i \(-0.293250\pi\)
0.604807 + 0.796372i \(0.293250\pi\)
\(492\) 0 0
\(493\) 34.9209 1.57276
\(494\) 33.2068 1.49405
\(495\) 0 0
\(496\) 8.16044 0.366415
\(497\) −1.93705 −0.0868887
\(498\) 0 0
\(499\) 21.4285 0.959272 0.479636 0.877467i \(-0.340769\pi\)
0.479636 + 0.877467i \(0.340769\pi\)
\(500\) 9.82730 0.439490
\(501\) 0 0
\(502\) 13.6343 0.608529
\(503\) −14.9635 −0.667189 −0.333594 0.942717i \(-0.608262\pi\)
−0.333594 + 0.942717i \(0.608262\pi\)
\(504\) 0 0
\(505\) 14.7883 0.658071
\(506\) 6.73398 0.299362
\(507\) 0 0
\(508\) −13.7317 −0.609247
\(509\) −5.63400 −0.249723 −0.124861 0.992174i \(-0.539849\pi\)
−0.124861 + 0.992174i \(0.539849\pi\)
\(510\) 0 0
\(511\) 2.29324 0.101447
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 26.4900 1.16842
\(515\) 13.3591 0.588671
\(516\) 0 0
\(517\) −18.9234 −0.832252
\(518\) 3.15298 0.138534
\(519\) 0 0
\(520\) −4.48992 −0.196896
\(521\) 4.52985 0.198456 0.0992281 0.995065i \(-0.468363\pi\)
0.0992281 + 0.995065i \(0.468363\pi\)
\(522\) 0 0
\(523\) −15.0316 −0.657285 −0.328643 0.944454i \(-0.606591\pi\)
−0.328643 + 0.944454i \(0.606591\pi\)
\(524\) 17.6560 0.771307
\(525\) 0 0
\(526\) −4.98189 −0.217221
\(527\) 47.3340 2.06190
\(528\) 0 0
\(529\) −18.1396 −0.788680
\(530\) −9.20978 −0.400047
\(531\) 0 0
\(532\) −5.71419 −0.247742
\(533\) −23.2517 −1.00714
\(534\) 0 0
\(535\) −12.2815 −0.530975
\(536\) −6.33902 −0.273804
\(537\) 0 0
\(538\) −7.74980 −0.334118
\(539\) −19.9412 −0.858926
\(540\) 0 0
\(541\) −13.2437 −0.569391 −0.284696 0.958618i \(-0.591893\pi\)
−0.284696 + 0.958618i \(0.591893\pi\)
\(542\) −20.0627 −0.861767
\(543\) 0 0
\(544\) −5.80043 −0.248691
\(545\) −3.28900 −0.140885
\(546\) 0 0
\(547\) −0.855180 −0.0365649 −0.0182824 0.999833i \(-0.505820\pi\)
−0.0182824 + 0.999833i \(0.505820\pi\)
\(548\) 18.9694 0.810332
\(549\) 0 0
\(550\) 11.4053 0.486325
\(551\) 50.0998 2.13432
\(552\) 0 0
\(553\) 5.83120 0.247968
\(554\) −18.1869 −0.772689
\(555\) 0 0
\(556\) 8.88482 0.376800
\(557\) 27.0002 1.14403 0.572017 0.820242i \(-0.306161\pi\)
0.572017 + 0.820242i \(0.306161\pi\)
\(558\) 0 0
\(559\) −3.77000 −0.159454
\(560\) 0.772621 0.0326492
\(561\) 0 0
\(562\) −15.9505 −0.672830
\(563\) −13.5674 −0.571799 −0.285900 0.958260i \(-0.592292\pi\)
−0.285900 + 0.958260i \(0.592292\pi\)
\(564\) 0 0
\(565\) −5.89762 −0.248115
\(566\) −1.04252 −0.0438202
\(567\) 0 0
\(568\) −2.82097 −0.118365
\(569\) 3.74436 0.156972 0.0784858 0.996915i \(-0.474991\pi\)
0.0784858 + 0.996915i \(0.474991\pi\)
\(570\) 0 0
\(571\) −17.6994 −0.740697 −0.370349 0.928893i \(-0.620762\pi\)
−0.370349 + 0.928893i \(0.620762\pi\)
\(572\) −12.1886 −0.509631
\(573\) 0 0
\(574\) 4.00112 0.167003
\(575\) 8.23199 0.343298
\(576\) 0 0
\(577\) −25.8371 −1.07561 −0.537805 0.843069i \(-0.680746\pi\)
−0.537805 + 0.843069i \(0.680746\pi\)
\(578\) −16.6450 −0.692339
\(579\) 0 0
\(580\) −6.77404 −0.281277
\(581\) −4.35546 −0.180695
\(582\) 0 0
\(583\) −25.0014 −1.03545
\(584\) 3.33968 0.138197
\(585\) 0 0
\(586\) 1.65871 0.0685207
\(587\) 18.4980 0.763495 0.381748 0.924267i \(-0.375322\pi\)
0.381748 + 0.924267i \(0.375322\pi\)
\(588\) 0 0
\(589\) 67.9086 2.79812
\(590\) 9.44711 0.388931
\(591\) 0 0
\(592\) 4.59174 0.188719
\(593\) 33.8650 1.39067 0.695335 0.718686i \(-0.255256\pi\)
0.695335 + 0.718686i \(0.255256\pi\)
\(594\) 0 0
\(595\) 4.48153 0.183725
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) −8.79733 −0.359749
\(599\) 3.73165 0.152471 0.0762354 0.997090i \(-0.475710\pi\)
0.0762354 + 0.997090i \(0.475710\pi\)
\(600\) 0 0
\(601\) −23.3136 −0.950980 −0.475490 0.879721i \(-0.657729\pi\)
−0.475490 + 0.879721i \(0.657729\pi\)
\(602\) 0.648738 0.0264406
\(603\) 0 0
\(604\) −15.2920 −0.622222
\(605\) 1.87922 0.0764013
\(606\) 0 0
\(607\) 6.50372 0.263978 0.131989 0.991251i \(-0.457864\pi\)
0.131989 + 0.991251i \(0.457864\pi\)
\(608\) −8.32168 −0.337489
\(609\) 0 0
\(610\) −15.9011 −0.643817
\(611\) 24.7218 1.00014
\(612\) 0 0
\(613\) 21.0805 0.851434 0.425717 0.904856i \(-0.360022\pi\)
0.425717 + 0.904856i \(0.360022\pi\)
\(614\) 30.3028 1.22292
\(615\) 0 0
\(616\) 2.09740 0.0845066
\(617\) 3.92176 0.157884 0.0789422 0.996879i \(-0.474846\pi\)
0.0789422 + 0.996879i \(0.474846\pi\)
\(618\) 0 0
\(619\) −23.6404 −0.950188 −0.475094 0.879935i \(-0.657586\pi\)
−0.475094 + 0.879935i \(0.657586\pi\)
\(620\) −9.18198 −0.368757
\(621\) 0 0
\(622\) −6.82658 −0.273721
\(623\) −4.16988 −0.167063
\(624\) 0 0
\(625\) 7.61234 0.304494
\(626\) 3.07494 0.122899
\(627\) 0 0
\(628\) −6.18546 −0.246827
\(629\) 26.6340 1.06197
\(630\) 0 0
\(631\) 3.61784 0.144024 0.0720120 0.997404i \(-0.477058\pi\)
0.0720120 + 0.997404i \(0.477058\pi\)
\(632\) 8.49208 0.337797
\(633\) 0 0
\(634\) 14.5491 0.577820
\(635\) 15.4507 0.613141
\(636\) 0 0
\(637\) 26.0513 1.03219
\(638\) −18.3892 −0.728034
\(639\) 0 0
\(640\) 1.12518 0.0444767
\(641\) 25.6454 1.01293 0.506467 0.862259i \(-0.330951\pi\)
0.506467 + 0.862259i \(0.330951\pi\)
\(642\) 0 0
\(643\) 41.2134 1.62530 0.812649 0.582754i \(-0.198025\pi\)
0.812649 + 0.582754i \(0.198025\pi\)
\(644\) 1.51383 0.0596534
\(645\) 0 0
\(646\) −48.2693 −1.89913
\(647\) 35.3255 1.38879 0.694394 0.719595i \(-0.255673\pi\)
0.694394 + 0.719595i \(0.255673\pi\)
\(648\) 0 0
\(649\) 25.6457 1.00668
\(650\) −14.9000 −0.584427
\(651\) 0 0
\(652\) 16.8203 0.658733
\(653\) −23.0974 −0.903872 −0.451936 0.892050i \(-0.649267\pi\)
−0.451936 + 0.892050i \(0.649267\pi\)
\(654\) 0 0
\(655\) −19.8662 −0.776238
\(656\) 5.82690 0.227502
\(657\) 0 0
\(658\) −4.25409 −0.165842
\(659\) −20.6520 −0.804487 −0.402244 0.915533i \(-0.631770\pi\)
−0.402244 + 0.915533i \(0.631770\pi\)
\(660\) 0 0
\(661\) 20.9399 0.814466 0.407233 0.913324i \(-0.366494\pi\)
0.407233 + 0.913324i \(0.366494\pi\)
\(662\) −18.2660 −0.709927
\(663\) 0 0
\(664\) −6.34293 −0.246153
\(665\) 6.42950 0.249325
\(666\) 0 0
\(667\) −13.2727 −0.513921
\(668\) −9.10633 −0.352334
\(669\) 0 0
\(670\) 7.13254 0.275554
\(671\) −43.1661 −1.66641
\(672\) 0 0
\(673\) 9.84995 0.379687 0.189844 0.981814i \(-0.439202\pi\)
0.189844 + 0.981814i \(0.439202\pi\)
\(674\) −23.9834 −0.923804
\(675\) 0 0
\(676\) 2.92329 0.112434
\(677\) 28.1520 1.08197 0.540985 0.841032i \(-0.318052\pi\)
0.540985 + 0.841032i \(0.318052\pi\)
\(678\) 0 0
\(679\) 7.92813 0.304254
\(680\) 6.52653 0.250281
\(681\) 0 0
\(682\) −24.9259 −0.954462
\(683\) −9.42277 −0.360552 −0.180276 0.983616i \(-0.557699\pi\)
−0.180276 + 0.983616i \(0.557699\pi\)
\(684\) 0 0
\(685\) −21.3440 −0.815512
\(686\) −9.28952 −0.354676
\(687\) 0 0
\(688\) 0.944768 0.0360189
\(689\) 32.6620 1.24432
\(690\) 0 0
\(691\) −51.7355 −1.96811 −0.984056 0.177856i \(-0.943084\pi\)
−0.984056 + 0.177856i \(0.943084\pi\)
\(692\) 19.5509 0.743213
\(693\) 0 0
\(694\) 21.2095 0.805101
\(695\) −9.99704 −0.379209
\(696\) 0 0
\(697\) 33.7985 1.28021
\(698\) −13.4739 −0.509994
\(699\) 0 0
\(700\) 2.56398 0.0969093
\(701\) 17.0599 0.644345 0.322172 0.946681i \(-0.395587\pi\)
0.322172 + 0.946681i \(0.395587\pi\)
\(702\) 0 0
\(703\) 38.2109 1.44115
\(704\) 3.05448 0.115120
\(705\) 0 0
\(706\) 17.1231 0.644435
\(707\) 9.02485 0.339414
\(708\) 0 0
\(709\) −37.2820 −1.40016 −0.700078 0.714066i \(-0.746851\pi\)
−0.700078 + 0.714066i \(0.746851\pi\)
\(710\) 3.17410 0.119122
\(711\) 0 0
\(712\) −6.07267 −0.227583
\(713\) −17.9907 −0.673757
\(714\) 0 0
\(715\) 13.7144 0.512889
\(716\) 11.9617 0.447031
\(717\) 0 0
\(718\) −33.0700 −1.23416
\(719\) 28.8178 1.07472 0.537362 0.843352i \(-0.319421\pi\)
0.537362 + 0.843352i \(0.319421\pi\)
\(720\) 0 0
\(721\) 8.15263 0.303620
\(722\) −50.2503 −1.87012
\(723\) 0 0
\(724\) 0.902790 0.0335519
\(725\) −22.4800 −0.834885
\(726\) 0 0
\(727\) 6.62094 0.245557 0.122779 0.992434i \(-0.460820\pi\)
0.122779 + 0.992434i \(0.460820\pi\)
\(728\) −2.74006 −0.101553
\(729\) 0 0
\(730\) −3.75775 −0.139080
\(731\) 5.48006 0.202687
\(732\) 0 0
\(733\) 27.7091 1.02346 0.511730 0.859146i \(-0.329005\pi\)
0.511730 + 0.859146i \(0.329005\pi\)
\(734\) −0.517529 −0.0191023
\(735\) 0 0
\(736\) 2.20462 0.0812635
\(737\) 19.3624 0.713223
\(738\) 0 0
\(739\) −22.1604 −0.815183 −0.407591 0.913164i \(-0.633631\pi\)
−0.407591 + 0.913164i \(0.633631\pi\)
\(740\) −5.16654 −0.189926
\(741\) 0 0
\(742\) −5.62045 −0.206333
\(743\) 16.1890 0.593917 0.296959 0.954890i \(-0.404028\pi\)
0.296959 + 0.954890i \(0.404028\pi\)
\(744\) 0 0
\(745\) −1.12518 −0.0412235
\(746\) 24.3848 0.892791
\(747\) 0 0
\(748\) 17.7173 0.647808
\(749\) −7.49502 −0.273862
\(750\) 0 0
\(751\) −46.6646 −1.70282 −0.851408 0.524503i \(-0.824251\pi\)
−0.851408 + 0.524503i \(0.824251\pi\)
\(752\) −6.19531 −0.225920
\(753\) 0 0
\(754\) 24.0238 0.874895
\(755\) 17.2063 0.626200
\(756\) 0 0
\(757\) 39.3659 1.43078 0.715389 0.698727i \(-0.246250\pi\)
0.715389 + 0.698727i \(0.246250\pi\)
\(758\) −10.9892 −0.399147
\(759\) 0 0
\(760\) 9.36339 0.339646
\(761\) −25.2105 −0.913879 −0.456940 0.889498i \(-0.651054\pi\)
−0.456940 + 0.889498i \(0.651054\pi\)
\(762\) 0 0
\(763\) −2.00717 −0.0726645
\(764\) −10.3662 −0.375035
\(765\) 0 0
\(766\) −25.8159 −0.932766
\(767\) −33.5037 −1.20975
\(768\) 0 0
\(769\) 23.2413 0.838103 0.419051 0.907963i \(-0.362363\pi\)
0.419051 + 0.907963i \(0.362363\pi\)
\(770\) −2.35995 −0.0850469
\(771\) 0 0
\(772\) −17.1187 −0.616116
\(773\) 17.1288 0.616080 0.308040 0.951373i \(-0.400327\pi\)
0.308040 + 0.951373i \(0.400327\pi\)
\(774\) 0 0
\(775\) −30.4708 −1.09454
\(776\) 11.5459 0.414473
\(777\) 0 0
\(778\) 37.0725 1.32911
\(779\) 48.4896 1.73732
\(780\) 0 0
\(781\) 8.61658 0.308326
\(782\) 12.7878 0.457289
\(783\) 0 0
\(784\) −6.52849 −0.233160
\(785\) 6.95977 0.248405
\(786\) 0 0
\(787\) −22.7947 −0.812542 −0.406271 0.913753i \(-0.633171\pi\)
−0.406271 + 0.913753i \(0.633171\pi\)
\(788\) −11.7114 −0.417202
\(789\) 0 0
\(790\) −9.55513 −0.339956
\(791\) −3.59914 −0.127971
\(792\) 0 0
\(793\) 56.3925 2.00256
\(794\) 19.1725 0.680408
\(795\) 0 0
\(796\) 23.9115 0.847520
\(797\) −24.3325 −0.861902 −0.430951 0.902375i \(-0.641822\pi\)
−0.430951 + 0.902375i \(0.641822\pi\)
\(798\) 0 0
\(799\) −35.9354 −1.27130
\(800\) 3.73397 0.132016
\(801\) 0 0
\(802\) −9.85673 −0.348053
\(803\) −10.2010 −0.359985
\(804\) 0 0
\(805\) −1.70334 −0.0600348
\(806\) 32.5634 1.14700
\(807\) 0 0
\(808\) 13.1430 0.462371
\(809\) −29.9622 −1.05341 −0.526707 0.850047i \(-0.676574\pi\)
−0.526707 + 0.850047i \(0.676574\pi\)
\(810\) 0 0
\(811\) 37.8887 1.33045 0.665226 0.746642i \(-0.268335\pi\)
0.665226 + 0.746642i \(0.268335\pi\)
\(812\) −4.13398 −0.145074
\(813\) 0 0
\(814\) −14.0254 −0.491589
\(815\) −18.9259 −0.662945
\(816\) 0 0
\(817\) 7.86205 0.275058
\(818\) 8.27230 0.289234
\(819\) 0 0
\(820\) −6.55632 −0.228957
\(821\) 42.2822 1.47566 0.737829 0.674988i \(-0.235851\pi\)
0.737829 + 0.674988i \(0.235851\pi\)
\(822\) 0 0
\(823\) −28.6134 −0.997399 −0.498699 0.866775i \(-0.666189\pi\)
−0.498699 + 0.866775i \(0.666189\pi\)
\(824\) 11.8728 0.413609
\(825\) 0 0
\(826\) 5.76528 0.200600
\(827\) −21.9207 −0.762259 −0.381130 0.924522i \(-0.624465\pi\)
−0.381130 + 0.924522i \(0.624465\pi\)
\(828\) 0 0
\(829\) 11.3236 0.393284 0.196642 0.980475i \(-0.436996\pi\)
0.196642 + 0.980475i \(0.436996\pi\)
\(830\) 7.13694 0.247727
\(831\) 0 0
\(832\) −3.99040 −0.138342
\(833\) −37.8681 −1.31205
\(834\) 0 0
\(835\) 10.2463 0.354587
\(836\) 25.4184 0.879114
\(837\) 0 0
\(838\) 5.77203 0.199392
\(839\) 43.3273 1.49583 0.747913 0.663797i \(-0.231056\pi\)
0.747913 + 0.663797i \(0.231056\pi\)
\(840\) 0 0
\(841\) 7.24516 0.249833
\(842\) −8.50728 −0.293180
\(843\) 0 0
\(844\) −14.8387 −0.510769
\(845\) −3.28923 −0.113153
\(846\) 0 0
\(847\) 1.14683 0.0394056
\(848\) −8.18515 −0.281079
\(849\) 0 0
\(850\) 21.6586 0.742884
\(851\) −10.1230 −0.347014
\(852\) 0 0
\(853\) 16.1588 0.553266 0.276633 0.960976i \(-0.410781\pi\)
0.276633 + 0.960976i \(0.410781\pi\)
\(854\) −9.70396 −0.332063
\(855\) 0 0
\(856\) −10.9151 −0.373071
\(857\) 11.2150 0.383098 0.191549 0.981483i \(-0.438649\pi\)
0.191549 + 0.981483i \(0.438649\pi\)
\(858\) 0 0
\(859\) 46.2975 1.57965 0.789825 0.613333i \(-0.210171\pi\)
0.789825 + 0.613333i \(0.210171\pi\)
\(860\) −1.06304 −0.0362492
\(861\) 0 0
\(862\) 29.8564 1.01691
\(863\) −12.4665 −0.424365 −0.212182 0.977230i \(-0.568057\pi\)
−0.212182 + 0.977230i \(0.568057\pi\)
\(864\) 0 0
\(865\) −21.9983 −0.747964
\(866\) −15.7016 −0.533562
\(867\) 0 0
\(868\) −5.60348 −0.190194
\(869\) −25.9389 −0.879916
\(870\) 0 0
\(871\) −25.2952 −0.857096
\(872\) −2.92308 −0.0989880
\(873\) 0 0
\(874\) 18.3462 0.620568
\(875\) −6.74804 −0.228126
\(876\) 0 0
\(877\) 58.2751 1.96781 0.983905 0.178695i \(-0.0571875\pi\)
0.983905 + 0.178695i \(0.0571875\pi\)
\(878\) −15.4229 −0.520499
\(879\) 0 0
\(880\) −3.43684 −0.115856
\(881\) −26.0826 −0.878745 −0.439372 0.898305i \(-0.644799\pi\)
−0.439372 + 0.898305i \(0.644799\pi\)
\(882\) 0 0
\(883\) 48.1927 1.62182 0.810908 0.585174i \(-0.198974\pi\)
0.810908 + 0.585174i \(0.198974\pi\)
\(884\) −23.1460 −0.778485
\(885\) 0 0
\(886\) 5.88701 0.197778
\(887\) −29.2074 −0.980689 −0.490345 0.871529i \(-0.663129\pi\)
−0.490345 + 0.871529i \(0.663129\pi\)
\(888\) 0 0
\(889\) 9.42907 0.316241
\(890\) 6.83285 0.229038
\(891\) 0 0
\(892\) 15.8699 0.531365
\(893\) −51.5554 −1.72523
\(894\) 0 0
\(895\) −13.4591 −0.449889
\(896\) 0.686663 0.0229398
\(897\) 0 0
\(898\) 23.1092 0.771163
\(899\) 49.1291 1.63855
\(900\) 0 0
\(901\) −47.4774 −1.58170
\(902\) −17.7982 −0.592614
\(903\) 0 0
\(904\) −5.24148 −0.174329
\(905\) −1.01580 −0.0337664
\(906\) 0 0
\(907\) −50.0879 −1.66314 −0.831571 0.555419i \(-0.812558\pi\)
−0.831571 + 0.555419i \(0.812558\pi\)
\(908\) 15.2519 0.506151
\(909\) 0 0
\(910\) 3.08307 0.102203
\(911\) 12.0650 0.399731 0.199866 0.979823i \(-0.435949\pi\)
0.199866 + 0.979823i \(0.435949\pi\)
\(912\) 0 0
\(913\) 19.3743 0.641197
\(914\) −16.5419 −0.547158
\(915\) 0 0
\(916\) 24.3514 0.804594
\(917\) −12.1237 −0.400361
\(918\) 0 0
\(919\) 18.0290 0.594721 0.297360 0.954765i \(-0.403894\pi\)
0.297360 + 0.954765i \(0.403894\pi\)
\(920\) −2.48060 −0.0817830
\(921\) 0 0
\(922\) 3.97700 0.130975
\(923\) −11.2568 −0.370521
\(924\) 0 0
\(925\) −17.1454 −0.563737
\(926\) −18.7496 −0.616149
\(927\) 0 0
\(928\) −6.02040 −0.197629
\(929\) 26.6010 0.872749 0.436375 0.899765i \(-0.356262\pi\)
0.436375 + 0.899765i \(0.356262\pi\)
\(930\) 0 0
\(931\) −54.3280 −1.78053
\(932\) 7.46438 0.244504
\(933\) 0 0
\(934\) −9.33972 −0.305605
\(935\) −19.9352 −0.651950
\(936\) 0 0
\(937\) 12.3300 0.402804 0.201402 0.979509i \(-0.435450\pi\)
0.201402 + 0.979509i \(0.435450\pi\)
\(938\) 4.35277 0.142123
\(939\) 0 0
\(940\) 6.97085 0.227364
\(941\) 47.7282 1.55589 0.777947 0.628330i \(-0.216261\pi\)
0.777947 + 0.628330i \(0.216261\pi\)
\(942\) 0 0
\(943\) −12.8461 −0.418327
\(944\) 8.39608 0.273269
\(945\) 0 0
\(946\) −2.88577 −0.0938246
\(947\) 20.7544 0.674427 0.337214 0.941428i \(-0.390516\pi\)
0.337214 + 0.941428i \(0.390516\pi\)
\(948\) 0 0
\(949\) 13.3267 0.432602
\(950\) 31.0729 1.00814
\(951\) 0 0
\(952\) 3.98294 0.129088
\(953\) −33.0722 −1.07131 −0.535657 0.844436i \(-0.679936\pi\)
−0.535657 + 0.844436i \(0.679936\pi\)
\(954\) 0 0
\(955\) 11.6638 0.377432
\(956\) 19.9977 0.646772
\(957\) 0 0
\(958\) 6.50916 0.210301
\(959\) −13.0256 −0.420618
\(960\) 0 0
\(961\) 35.5928 1.14816
\(962\) 18.3229 0.590753
\(963\) 0 0
\(964\) 12.9019 0.415541
\(965\) 19.2616 0.620054
\(966\) 0 0
\(967\) 18.9226 0.608511 0.304255 0.952590i \(-0.401592\pi\)
0.304255 + 0.952590i \(0.401592\pi\)
\(968\) 1.67015 0.0536807
\(969\) 0 0
\(970\) −12.9912 −0.417122
\(971\) 13.8653 0.444959 0.222480 0.974937i \(-0.428585\pi\)
0.222480 + 0.974937i \(0.428585\pi\)
\(972\) 0 0
\(973\) −6.10088 −0.195585
\(974\) −17.0058 −0.544902
\(975\) 0 0
\(976\) −14.1320 −0.452356
\(977\) 16.4738 0.527042 0.263521 0.964654i \(-0.415116\pi\)
0.263521 + 0.964654i \(0.415116\pi\)
\(978\) 0 0
\(979\) 18.5488 0.592824
\(980\) 7.34574 0.234651
\(981\) 0 0
\(982\) −26.8032 −0.855326
\(983\) −0.130489 −0.00416194 −0.00208097 0.999998i \(-0.500662\pi\)
−0.00208097 + 0.999998i \(0.500662\pi\)
\(984\) 0 0
\(985\) 13.1775 0.419870
\(986\) −34.9209 −1.11211
\(987\) 0 0
\(988\) −33.2068 −1.05645
\(989\) −2.08286 −0.0662310
\(990\) 0 0
\(991\) 9.54294 0.303142 0.151571 0.988446i \(-0.451567\pi\)
0.151571 + 0.988446i \(0.451567\pi\)
\(992\) −8.16044 −0.259094
\(993\) 0 0
\(994\) 1.93705 0.0614396
\(995\) −26.9048 −0.852938
\(996\) 0 0
\(997\) −35.1838 −1.11428 −0.557140 0.830418i \(-0.688101\pi\)
−0.557140 + 0.830418i \(0.688101\pi\)
\(998\) −21.4285 −0.678308
\(999\) 0 0
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 \(a_p\))