Properties

Label 2842.2.a.e.1.1
Level $2842$
Weight $2$
Character 2842.1
Self dual yes
Analytic conductor $22.693$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2842.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.6934842544\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 58)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2842.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{10} -3.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -8.00000 q^{17} -2.00000 q^{18} -1.00000 q^{20} -3.00000 q^{22} +4.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} +1.00000 q^{26} -5.00000 q^{27} -1.00000 q^{29} -1.00000 q^{30} +3.00000 q^{31} +1.00000 q^{32} -3.00000 q^{33} -8.00000 q^{34} -2.00000 q^{36} +8.00000 q^{37} +1.00000 q^{39} -1.00000 q^{40} -2.00000 q^{41} -11.0000 q^{43} -3.00000 q^{44} +2.00000 q^{45} +4.00000 q^{46} -13.0000 q^{47} +1.00000 q^{48} -4.00000 q^{50} -8.00000 q^{51} +1.00000 q^{52} -11.0000 q^{53} -5.00000 q^{54} +3.00000 q^{55} -1.00000 q^{58} -1.00000 q^{60} +8.00000 q^{61} +3.00000 q^{62} +1.00000 q^{64} -1.00000 q^{65} -3.00000 q^{66} -12.0000 q^{67} -8.00000 q^{68} +4.00000 q^{69} +2.00000 q^{71} -2.00000 q^{72} -4.00000 q^{73} +8.00000 q^{74} -4.00000 q^{75} +1.00000 q^{78} +15.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} -4.00000 q^{83} +8.00000 q^{85} -11.0000 q^{86} -1.00000 q^{87} -3.00000 q^{88} +10.0000 q^{89} +2.00000 q^{90} +4.00000 q^{92} +3.00000 q^{93} -13.0000 q^{94} +1.00000 q^{96} +2.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)

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
\(3\) 1.00000 0.577350 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) −1.00000 −0.316228
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −8.00000 −1.94029 −0.970143 0.242536i \(-0.922021\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) −2.00000 −0.471405
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −3.00000 −0.639602
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.00000 −0.800000
\(26\) 1.00000 0.196116
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) −1.00000 −0.182574
\(31\) 3.00000 0.538816 0.269408 0.963026i \(-0.413172\pi\)
0.269408 + 0.963026i \(0.413172\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.00000 −0.522233
\(34\) −8.00000 −1.37199
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) −1.00000 −0.158114
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) −11.0000 −1.67748 −0.838742 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) −3.00000 −0.452267
\(45\) 2.00000 0.298142
\(46\) 4.00000 0.589768
\(47\) −13.0000 −1.89624 −0.948122 0.317905i \(-0.897021\pi\)
−0.948122 + 0.317905i \(0.897021\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) −4.00000 −0.565685
\(51\) −8.00000 −1.12022
\(52\) 1.00000 0.138675
\(53\) −11.0000 −1.51097 −0.755483 0.655168i \(-0.772598\pi\)
−0.755483 + 0.655168i \(0.772598\pi\)
\(54\) −5.00000 −0.680414
\(55\) 3.00000 0.404520
\(56\) 0 0
\(57\) 0 0
\(58\) −1.00000 −0.131306
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −1.00000 −0.129099
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 3.00000 0.381000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) −3.00000 −0.369274
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) −8.00000 −0.970143
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −2.00000 −0.235702
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 8.00000 0.929981
\(75\) −4.00000 −0.461880
\(76\) 0 0
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) 15.0000 1.68763 0.843816 0.536633i \(-0.180304\pi\)
0.843816 + 0.536633i \(0.180304\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) −2.00000 −0.220863
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 8.00000 0.867722
\(86\) −11.0000 −1.18616
\(87\) −1.00000 −0.107211
\(88\) −3.00000 −0.319801
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) 4.00000 0.417029
\(93\) 3.00000 0.311086
\(94\) −13.0000 −1.34085
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) −4.00000 −0.400000
\(101\) 8.00000 0.796030 0.398015 0.917379i \(-0.369699\pi\)
0.398015 + 0.917379i \(0.369699\pi\)
\(102\) −8.00000 −0.792118
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) −11.0000 −1.06841
\(107\) −2.00000 −0.193347 −0.0966736 0.995316i \(-0.530820\pi\)
−0.0966736 + 0.995316i \(0.530820\pi\)
\(108\) −5.00000 −0.481125
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 3.00000 0.286039
\(111\) 8.00000 0.759326
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) −4.00000 −0.373002
\(116\) −1.00000 −0.0928477
\(117\) −2.00000 −0.184900
\(118\) 0 0
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) −2.00000 −0.181818
\(122\) 8.00000 0.724286
\(123\) −2.00000 −0.180334
\(124\) 3.00000 0.269408
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 1.00000 0.0883883
\(129\) −11.0000 −0.968496
\(130\) −1.00000 −0.0877058
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) −3.00000 −0.261116
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 5.00000 0.430331
\(136\) −8.00000 −0.685994
\(137\) −12.0000 −1.02523 −0.512615 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 4.00000 0.340503
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) −13.0000 −1.09480
\(142\) 2.00000 0.167836
\(143\) −3.00000 −0.250873
\(144\) −2.00000 −0.166667
\(145\) 1.00000 0.0830455
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) 15.0000 1.22885 0.614424 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) −4.00000 −0.326599
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 0 0
\(153\) 16.0000 1.29352
\(154\) 0 0
\(155\) −3.00000 −0.240966
\(156\) 1.00000 0.0800641
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 15.0000 1.19334
\(159\) −11.0000 −0.872357
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 9.00000 0.704934 0.352467 0.935824i \(-0.385343\pi\)
0.352467 + 0.935824i \(0.385343\pi\)
\(164\) −2.00000 −0.156174
\(165\) 3.00000 0.233550
\(166\) −4.00000 −0.310460
\(167\) 2.00000 0.154765 0.0773823 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 8.00000 0.613572
\(171\) 0 0
\(172\) −11.0000 −0.838742
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −1.00000 −0.0758098
\(175\) 0 0
\(176\) −3.00000 −0.226134
\(177\) 0 0
\(178\) 10.0000 0.749532
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 2.00000 0.149071
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 8.00000 0.591377
\(184\) 4.00000 0.294884
\(185\) −8.00000 −0.588172
\(186\) 3.00000 0.219971
\(187\) 24.0000 1.75505
\(188\) −13.0000 −0.948122
\(189\) 0 0
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 1.00000 0.0721688
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 2.00000 0.143592
\(195\) −1.00000 −0.0716115
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 6.00000 0.426401
\(199\) 10.0000 0.708881 0.354441 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) −4.00000 −0.282843
\(201\) −12.0000 −0.846415
\(202\) 8.00000 0.562878
\(203\) 0 0
\(204\) −8.00000 −0.560112
\(205\) 2.00000 0.139686
\(206\) −14.0000 −0.975426
\(207\) −8.00000 −0.556038
\(208\) 1.00000 0.0693375
\(209\) 0 0
\(210\) 0 0
\(211\) −3.00000 −0.206529 −0.103264 0.994654i \(-0.532929\pi\)
−0.103264 + 0.994654i \(0.532929\pi\)
\(212\) −11.0000 −0.755483
\(213\) 2.00000 0.137038
\(214\) −2.00000 −0.136717
\(215\) 11.0000 0.750194
\(216\) −5.00000 −0.340207
\(217\) 0 0
\(218\) 5.00000 0.338643
\(219\) −4.00000 −0.270295
\(220\) 3.00000 0.202260
\(221\) −8.00000 −0.538138
\(222\) 8.00000 0.536925
\(223\) 26.0000 1.74109 0.870544 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) 0 0
\(225\) 8.00000 0.533333
\(226\) −6.00000 −0.399114
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 0 0
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) −4.00000 −0.263752
\(231\) 0 0
\(232\) −1.00000 −0.0656532
\(233\) −1.00000 −0.0655122 −0.0327561 0.999463i \(-0.510428\pi\)
−0.0327561 + 0.999463i \(0.510428\pi\)
\(234\) −2.00000 −0.130744
\(235\) 13.0000 0.848026
\(236\) 0 0
\(237\) 15.0000 0.974355
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −17.0000 −1.09507 −0.547533 0.836784i \(-0.684433\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) −2.00000 −0.128565
\(243\) 16.0000 1.02640
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) 0 0
\(248\) 3.00000 0.190500
\(249\) −4.00000 −0.253490
\(250\) 9.00000 0.569210
\(251\) −27.0000 −1.70422 −0.852112 0.523359i \(-0.824679\pi\)
−0.852112 + 0.523359i \(0.824679\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 8.00000 0.501965
\(255\) 8.00000 0.500979
\(256\) 1.00000 0.0625000
\(257\) −13.0000 −0.810918 −0.405459 0.914113i \(-0.632888\pi\)
−0.405459 + 0.914113i \(0.632888\pi\)
\(258\) −11.0000 −0.684830
\(259\) 0 0
\(260\) −1.00000 −0.0620174
\(261\) 2.00000 0.123797
\(262\) −12.0000 −0.741362
\(263\) 9.00000 0.554964 0.277482 0.960731i \(-0.410500\pi\)
0.277482 + 0.960731i \(0.410500\pi\)
\(264\) −3.00000 −0.184637
\(265\) 11.0000 0.675725
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) −12.0000 −0.733017
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 5.00000 0.304290
\(271\) 13.0000 0.789694 0.394847 0.918747i \(-0.370798\pi\)
0.394847 + 0.918747i \(0.370798\pi\)
\(272\) −8.00000 −0.485071
\(273\) 0 0
\(274\) −12.0000 −0.724947
\(275\) 12.0000 0.723627
\(276\) 4.00000 0.240772
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 20.0000 1.19952
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) 27.0000 1.61068 0.805342 0.592810i \(-0.201981\pi\)
0.805342 + 0.592810i \(0.201981\pi\)
\(282\) −13.0000 −0.774139
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 2.00000 0.118678
\(285\) 0 0
\(286\) −3.00000 −0.177394
\(287\) 0 0
\(288\) −2.00000 −0.117851
\(289\) 47.0000 2.76471
\(290\) 1.00000 0.0587220
\(291\) 2.00000 0.117242
\(292\) −4.00000 −0.234082
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 8.00000 0.464991
\(297\) 15.0000 0.870388
\(298\) 15.0000 0.868927
\(299\) 4.00000 0.231326
\(300\) −4.00000 −0.230940
\(301\) 0 0
\(302\) 2.00000 0.115087
\(303\) 8.00000 0.459588
\(304\) 0 0
\(305\) −8.00000 −0.458079
\(306\) 16.0000 0.914659
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) 0 0
\(309\) −14.0000 −0.796432
\(310\) −3.00000 −0.170389
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 1.00000 0.0566139
\(313\) −9.00000 −0.508710 −0.254355 0.967111i \(-0.581863\pi\)
−0.254355 + 0.967111i \(0.581863\pi\)
\(314\) −18.0000 −1.01580
\(315\) 0 0
\(316\) 15.0000 0.843816
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) −11.0000 −0.616849
\(319\) 3.00000 0.167968
\(320\) −1.00000 −0.0559017
\(321\) −2.00000 −0.111629
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) −4.00000 −0.221880
\(326\) 9.00000 0.498464
\(327\) 5.00000 0.276501
\(328\) −2.00000 −0.110432
\(329\) 0 0
\(330\) 3.00000 0.165145
\(331\) −23.0000 −1.26419 −0.632097 0.774889i \(-0.717806\pi\)
−0.632097 + 0.774889i \(0.717806\pi\)
\(332\) −4.00000 −0.219529
\(333\) −16.0000 −0.876795
\(334\) 2.00000 0.109435
\(335\) 12.0000 0.655630
\(336\) 0 0
\(337\) −32.0000 −1.74315 −0.871576 0.490261i \(-0.836901\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) −12.0000 −0.652714
\(339\) −6.00000 −0.325875
\(340\) 8.00000 0.433861
\(341\) −9.00000 −0.487377
\(342\) 0 0
\(343\) 0 0
\(344\) −11.0000 −0.593080
\(345\) −4.00000 −0.215353
\(346\) 6.00000 0.322562
\(347\) −2.00000 −0.107366 −0.0536828 0.998558i \(-0.517096\pi\)
−0.0536828 + 0.998558i \(0.517096\pi\)
\(348\) −1.00000 −0.0536056
\(349\) 15.0000 0.802932 0.401466 0.915874i \(-0.368501\pi\)
0.401466 + 0.915874i \(0.368501\pi\)
\(350\) 0 0
\(351\) −5.00000 −0.266880
\(352\) −3.00000 −0.159901
\(353\) 26.0000 1.38384 0.691920 0.721974i \(-0.256765\pi\)
0.691920 + 0.721974i \(0.256765\pi\)
\(354\) 0 0
\(355\) −2.00000 −0.106149
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) −10.0000 −0.528516
\(359\) −25.0000 −1.31945 −0.659725 0.751507i \(-0.729327\pi\)
−0.659725 + 0.751507i \(0.729327\pi\)
\(360\) 2.00000 0.105409
\(361\) −19.0000 −1.00000
\(362\) −7.00000 −0.367912
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) 4.00000 0.209370
\(366\) 8.00000 0.418167
\(367\) 32.0000 1.67039 0.835193 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) 4.00000 0.208514
\(369\) 4.00000 0.208232
\(370\) −8.00000 −0.415900
\(371\) 0 0
\(372\) 3.00000 0.155543
\(373\) −21.0000 −1.08734 −0.543669 0.839299i \(-0.682965\pi\)
−0.543669 + 0.839299i \(0.682965\pi\)
\(374\) 24.0000 1.24101
\(375\) 9.00000 0.464758
\(376\) −13.0000 −0.670424
\(377\) −1.00000 −0.0515026
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) 8.00000 0.409852
\(382\) −8.00000 −0.409316
\(383\) −14.0000 −0.715367 −0.357683 0.933843i \(-0.616433\pi\)
−0.357683 + 0.933843i \(0.616433\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) 22.0000 1.11832
\(388\) 2.00000 0.101535
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) −1.00000 −0.0506370
\(391\) −32.0000 −1.61831
\(392\) 0 0
\(393\) −12.0000 −0.605320
\(394\) 18.0000 0.906827
\(395\) −15.0000 −0.754732
\(396\) 6.00000 0.301511
\(397\) 17.0000 0.853206 0.426603 0.904439i \(-0.359710\pi\)
0.426603 + 0.904439i \(0.359710\pi\)
\(398\) 10.0000 0.501255
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 27.0000 1.34832 0.674158 0.738587i \(-0.264507\pi\)
0.674158 + 0.738587i \(0.264507\pi\)
\(402\) −12.0000 −0.598506
\(403\) 3.00000 0.149441
\(404\) 8.00000 0.398015
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −24.0000 −1.18964
\(408\) −8.00000 −0.396059
\(409\) −30.0000 −1.48340 −0.741702 0.670729i \(-0.765981\pi\)
−0.741702 + 0.670729i \(0.765981\pi\)
\(410\) 2.00000 0.0987730
\(411\) −12.0000 −0.591916
\(412\) −14.0000 −0.689730
\(413\) 0 0
\(414\) −8.00000 −0.393179
\(415\) 4.00000 0.196352
\(416\) 1.00000 0.0490290
\(417\) 20.0000 0.979404
\(418\) 0 0
\(419\) 10.0000 0.488532 0.244266 0.969708i \(-0.421453\pi\)
0.244266 + 0.969708i \(0.421453\pi\)
\(420\) 0 0
\(421\) 32.0000 1.55958 0.779792 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) −3.00000 −0.146038
\(423\) 26.0000 1.26416
\(424\) −11.0000 −0.534207
\(425\) 32.0000 1.55223
\(426\) 2.00000 0.0969003
\(427\) 0 0
\(428\) −2.00000 −0.0966736
\(429\) −3.00000 −0.144841
\(430\) 11.0000 0.530467
\(431\) 32.0000 1.54139 0.770693 0.637207i \(-0.219910\pi\)
0.770693 + 0.637207i \(0.219910\pi\)
\(432\) −5.00000 −0.240563
\(433\) 16.0000 0.768911 0.384455 0.923144i \(-0.374389\pi\)
0.384455 + 0.923144i \(0.374389\pi\)
\(434\) 0 0
\(435\) 1.00000 0.0479463
\(436\) 5.00000 0.239457
\(437\) 0 0
\(438\) −4.00000 −0.191127
\(439\) −20.0000 −0.954548 −0.477274 0.878755i \(-0.658375\pi\)
−0.477274 + 0.878755i \(0.658375\pi\)
\(440\) 3.00000 0.143019
\(441\) 0 0
\(442\) −8.00000 −0.380521
\(443\) 4.00000 0.190046 0.0950229 0.995475i \(-0.469708\pi\)
0.0950229 + 0.995475i \(0.469708\pi\)
\(444\) 8.00000 0.379663
\(445\) −10.0000 −0.474045
\(446\) 26.0000 1.23114
\(447\) 15.0000 0.709476
\(448\) 0 0
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 8.00000 0.377124
\(451\) 6.00000 0.282529
\(452\) −6.00000 −0.282216
\(453\) 2.00000 0.0939682
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) 0 0
\(457\) −2.00000 −0.0935561 −0.0467780 0.998905i \(-0.514895\pi\)
−0.0467780 + 0.998905i \(0.514895\pi\)
\(458\) −10.0000 −0.467269
\(459\) 40.0000 1.86704
\(460\) −4.00000 −0.186501
\(461\) −2.00000 −0.0931493 −0.0465746 0.998915i \(-0.514831\pi\)
−0.0465746 + 0.998915i \(0.514831\pi\)
\(462\) 0 0
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) −1.00000 −0.0464238
\(465\) −3.00000 −0.139122
\(466\) −1.00000 −0.0463241
\(467\) 27.0000 1.24941 0.624705 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 13.0000 0.599645
\(471\) −18.0000 −0.829396
\(472\) 0 0
\(473\) 33.0000 1.51734
\(474\) 15.0000 0.688973
\(475\) 0 0
\(476\) 0 0
\(477\) 22.0000 1.00731
\(478\) 0 0
\(479\) 5.00000 0.228456 0.114228 0.993455i \(-0.463561\pi\)
0.114228 + 0.993455i \(0.463561\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 8.00000 0.364769
\(482\) −17.0000 −0.774329
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) −2.00000 −0.0908153
\(486\) 16.0000 0.725775
\(487\) −22.0000 −0.996915 −0.498458 0.866914i \(-0.666100\pi\)
−0.498458 + 0.866914i \(0.666100\pi\)
\(488\) 8.00000 0.362143
\(489\) 9.00000 0.406994
\(490\) 0 0
\(491\) −33.0000 −1.48927 −0.744635 0.667472i \(-0.767376\pi\)
−0.744635 + 0.667472i \(0.767376\pi\)
\(492\) −2.00000 −0.0901670
\(493\) 8.00000 0.360302
\(494\) 0 0
\(495\) −6.00000 −0.269680
\(496\) 3.00000 0.134704
\(497\) 0 0
\(498\) −4.00000 −0.179244
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 9.00000 0.402492
\(501\) 2.00000 0.0893534
\(502\) −27.0000 −1.20507
\(503\) −19.0000 −0.847168 −0.423584 0.905857i \(-0.639228\pi\)
−0.423584 + 0.905857i \(0.639228\pi\)
\(504\) 0 0
\(505\) −8.00000 −0.355995
\(506\) −12.0000 −0.533465
\(507\) −12.0000 −0.532939
\(508\) 8.00000 0.354943
\(509\) 15.0000 0.664863 0.332432 0.943127i \(-0.392131\pi\)
0.332432 + 0.943127i \(0.392131\pi\)
\(510\) 8.00000 0.354246
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −13.0000 −0.573405
\(515\) 14.0000 0.616914
\(516\) −11.0000 −0.484248
\(517\) 39.0000 1.71522
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) −1.00000 −0.0438529
\(521\) 13.0000 0.569540 0.284770 0.958596i \(-0.408083\pi\)
0.284770 + 0.958596i \(0.408083\pi\)
\(522\) 2.00000 0.0875376
\(523\) −24.0000 −1.04945 −0.524723 0.851273i \(-0.675831\pi\)
−0.524723 + 0.851273i \(0.675831\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 9.00000 0.392419
\(527\) −24.0000 −1.04546
\(528\) −3.00000 −0.130558
\(529\) −7.00000 −0.304348
\(530\) 11.0000 0.477809
\(531\) 0 0
\(532\) 0 0
\(533\) −2.00000 −0.0866296
\(534\) 10.0000 0.432742
\(535\) 2.00000 0.0864675
\(536\) −12.0000 −0.518321
\(537\) −10.0000 −0.431532
\(538\) 0 0
\(539\) 0 0
\(540\) 5.00000 0.215166
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) 13.0000 0.558398
\(543\) −7.00000 −0.300399
\(544\) −8.00000 −0.342997
\(545\) −5.00000 −0.214176
\(546\) 0 0
\(547\) 38.0000 1.62476 0.812381 0.583127i \(-0.198171\pi\)
0.812381 + 0.583127i \(0.198171\pi\)
\(548\) −12.0000 −0.512615
\(549\) −16.0000 −0.682863
\(550\) 12.0000 0.511682
\(551\) 0 0
\(552\) 4.00000 0.170251
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) −8.00000 −0.339581
\(556\) 20.0000 0.848189
\(557\) −2.00000 −0.0847427 −0.0423714 0.999102i \(-0.513491\pi\)
−0.0423714 + 0.999102i \(0.513491\pi\)
\(558\) −6.00000 −0.254000
\(559\) −11.0000 −0.465250
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) 27.0000 1.13893
\(563\) 11.0000 0.463595 0.231797 0.972764i \(-0.425539\pi\)
0.231797 + 0.972764i \(0.425539\pi\)
\(564\) −13.0000 −0.547399
\(565\) 6.00000 0.252422
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) 2.00000 0.0839181
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 0 0
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) −3.00000 −0.125436
\(573\) −8.00000 −0.334205
\(574\) 0 0
\(575\) −16.0000 −0.667246
\(576\) −2.00000 −0.0833333
\(577\) −8.00000 −0.333044 −0.166522 0.986038i \(-0.553254\pi\)
−0.166522 + 0.986038i \(0.553254\pi\)
\(578\) 47.0000 1.95494
\(579\) 14.0000 0.581820
\(580\) 1.00000 0.0415227
\(581\) 0 0
\(582\) 2.00000 0.0829027
\(583\) 33.0000 1.36672
\(584\) −4.00000 −0.165521
\(585\) 2.00000 0.0826898
\(586\) −14.0000 −0.578335
\(587\) −28.0000 −1.15568 −0.577842 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 18.0000 0.740421
\(592\) 8.00000 0.328798
\(593\) −39.0000 −1.60154 −0.800769 0.598973i \(-0.795576\pi\)
−0.800769 + 0.598973i \(0.795576\pi\)
\(594\) 15.0000 0.615457
\(595\) 0 0
\(596\) 15.0000 0.614424
\(597\) 10.0000 0.409273
\(598\) 4.00000 0.163572
\(599\) −5.00000 −0.204294 −0.102147 0.994769i \(-0.532571\pi\)
−0.102147 + 0.994769i \(0.532571\pi\)
\(600\) −4.00000 −0.163299
\(601\) −2.00000 −0.0815817 −0.0407909 0.999168i \(-0.512988\pi\)
−0.0407909 + 0.999168i \(0.512988\pi\)
\(602\) 0 0
\(603\) 24.0000 0.977356
\(604\) 2.00000 0.0813788
\(605\) 2.00000 0.0813116
\(606\) 8.00000 0.324978
\(607\) −3.00000 −0.121766 −0.0608831 0.998145i \(-0.519392\pi\)
−0.0608831 + 0.998145i \(0.519392\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −8.00000 −0.323911
\(611\) −13.0000 −0.525924
\(612\) 16.0000 0.646762
\(613\) −31.0000 −1.25208 −0.626039 0.779792i \(-0.715325\pi\)
−0.626039 + 0.779792i \(0.715325\pi\)
\(614\) 7.00000 0.282497
\(615\) 2.00000 0.0806478
\(616\) 0 0
\(617\) −12.0000 −0.483102 −0.241551 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) −14.0000 −0.563163
\(619\) 35.0000 1.40677 0.703384 0.710810i \(-0.251671\pi\)
0.703384 + 0.710810i \(0.251671\pi\)
\(620\) −3.00000 −0.120483
\(621\) −20.0000 −0.802572
\(622\) 8.00000 0.320771
\(623\) 0 0
\(624\) 1.00000 0.0400320
\(625\) 11.0000 0.440000
\(626\) −9.00000 −0.359712
\(627\) 0 0
\(628\) −18.0000 −0.718278
\(629\) −64.0000 −2.55185
\(630\) 0 0
\(631\) −38.0000 −1.51276 −0.756378 0.654135i \(-0.773033\pi\)
−0.756378 + 0.654135i \(0.773033\pi\)
\(632\) 15.0000 0.596668
\(633\) −3.00000 −0.119239
\(634\) −12.0000 −0.476581
\(635\) −8.00000 −0.317470
\(636\) −11.0000 −0.436178
\(637\) 0 0
\(638\) 3.00000 0.118771
\(639\) −4.00000 −0.158238
\(640\) −1.00000 −0.0395285
\(641\) −8.00000 −0.315981 −0.157991 0.987441i \(-0.550502\pi\)
−0.157991 + 0.987441i \(0.550502\pi\)
\(642\) −2.00000 −0.0789337
\(643\) −34.0000 −1.34083 −0.670415 0.741987i \(-0.733884\pi\)
−0.670415 + 0.741987i \(0.733884\pi\)
\(644\) 0 0
\(645\) 11.0000 0.433125
\(646\) 0 0
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) −4.00000 −0.156893
\(651\) 0 0
\(652\) 9.00000 0.352467
\(653\) −26.0000 −1.01746 −0.508729 0.860927i \(-0.669885\pi\)
−0.508729 + 0.860927i \(0.669885\pi\)
\(654\) 5.00000 0.195515
\(655\) 12.0000 0.468879
\(656\) −2.00000 −0.0780869
\(657\) 8.00000 0.312110
\(658\) 0 0
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) 3.00000 0.116775
\(661\) 18.0000 0.700119 0.350059 0.936727i \(-0.386161\pi\)
0.350059 + 0.936727i \(0.386161\pi\)
\(662\) −23.0000 −0.893920
\(663\) −8.00000 −0.310694
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) −16.0000 −0.619987
\(667\) −4.00000 −0.154881
\(668\) 2.00000 0.0773823
\(669\) 26.0000 1.00522
\(670\) 12.0000 0.463600
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) 9.00000 0.346925 0.173462 0.984841i \(-0.444505\pi\)
0.173462 + 0.984841i \(0.444505\pi\)
\(674\) −32.0000 −1.23259
\(675\) 20.0000 0.769800
\(676\) −12.0000 −0.461538
\(677\) −38.0000 −1.46046 −0.730229 0.683202i \(-0.760587\pi\)
−0.730229 + 0.683202i \(0.760587\pi\)
\(678\) −6.00000 −0.230429
\(679\) 0 0
\(680\) 8.00000 0.306786
\(681\) −18.0000 −0.689761
\(682\) −9.00000 −0.344628
\(683\) 24.0000 0.918334 0.459167 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) −11.0000 −0.419371
\(689\) −11.0000 −0.419067
\(690\) −4.00000 −0.152277
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −2.00000 −0.0759190
\(695\) −20.0000 −0.758643
\(696\) −1.00000 −0.0379049
\(697\) 16.0000 0.606043
\(698\) 15.0000 0.567758
\(699\) −1.00000 −0.0378235
\(700\) 0 0
\(701\) 27.0000 1.01978 0.509888 0.860241i \(-0.329687\pi\)
0.509888 + 0.860241i \(0.329687\pi\)
\(702\) −5.00000 −0.188713
\(703\) 0 0
\(704\) −3.00000 −0.113067
\(705\) 13.0000 0.489608
\(706\) 26.0000 0.978523
\(707\) 0 0
\(708\) 0 0
\(709\) 15.0000 0.563337 0.281668 0.959512i \(-0.409112\pi\)
0.281668 + 0.959512i \(0.409112\pi\)
\(710\) −2.00000 −0.0750587
\(711\) −30.0000 −1.12509
\(712\) 10.0000 0.374766
\(713\) 12.0000 0.449404
\(714\) 0 0
\(715\) 3.00000 0.112194
\(716\) −10.0000 −0.373718
\(717\) 0 0
\(718\) −25.0000 −0.932992
\(719\) 50.0000 1.86469 0.932343 0.361576i \(-0.117761\pi\)
0.932343 + 0.361576i \(0.117761\pi\)
\(720\) 2.00000 0.0745356
\(721\) 0 0
\(722\) −19.0000 −0.707107
\(723\) −17.0000 −0.632237
\(724\) −7.00000 −0.260153
\(725\) 4.00000 0.148556
\(726\) −2.00000 −0.0742270
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 4.00000 0.148047
\(731\) 88.0000 3.25480
\(732\) 8.00000 0.295689
\(733\) −24.0000 −0.886460 −0.443230 0.896408i \(-0.646168\pi\)
−0.443230 + 0.896408i \(0.646168\pi\)
\(734\) 32.0000 1.18114
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 36.0000 1.32608
\(738\) 4.00000 0.147242
\(739\) −5.00000 −0.183928 −0.0919640 0.995762i \(-0.529314\pi\)
−0.0919640 + 0.995762i \(0.529314\pi\)
\(740\) −8.00000 −0.294086
\(741\) 0 0
\(742\) 0 0
\(743\) 44.0000 1.61420 0.807102 0.590412i \(-0.201035\pi\)
0.807102 + 0.590412i \(0.201035\pi\)
\(744\) 3.00000 0.109985
\(745\) −15.0000 −0.549557
\(746\) −21.0000 −0.768865
\(747\) 8.00000 0.292705
\(748\) 24.0000 0.877527
\(749\) 0 0
\(750\) 9.00000 0.328634
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) −13.0000 −0.474061
\(753\) −27.0000 −0.983935
\(754\) −1.00000 −0.0364179
\(755\) −2.00000 −0.0727875
\(756\) 0 0
\(757\) 8.00000 0.290765 0.145382 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(758\) 20.0000 0.726433
\(759\) −12.0000 −0.435572
\(760\) 0 0
\(761\) −42.0000 −1.52250 −0.761249 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 8.00000 0.289809
\(763\) 0 0
\(764\) −8.00000 −0.289430
\(765\) −16.0000 −0.578481
\(766\) −14.0000 −0.505841
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 20.0000 0.721218 0.360609 0.932717i \(-0.382569\pi\)
0.360609 + 0.932717i \(0.382569\pi\)
\(770\) 0 0
\(771\) −13.0000 −0.468184
\(772\) 14.0000 0.503871
\(773\) −14.0000 −0.503545 −0.251773 0.967786i \(-0.581013\pi\)
−0.251773 + 0.967786i \(0.581013\pi\)
\(774\) 22.0000 0.790774
\(775\) −12.0000 −0.431053
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −1.00000 −0.0358057
\(781\) −6.00000 −0.214697
\(782\) −32.0000 −1.14432
\(783\) 5.00000 0.178685
\(784\) 0 0
\(785\) 18.0000 0.642448
\(786\) −12.0000 −0.428026
\(787\) 22.0000 0.784215 0.392108 0.919919i \(-0.371746\pi\)
0.392108 + 0.919919i \(0.371746\pi\)
\(788\) 18.0000 0.641223
\(789\) 9.00000 0.320408
\(790\) −15.0000 −0.533676
\(791\) 0 0
\(792\) 6.00000 0.213201
\(793\) 8.00000 0.284088
\(794\) 17.0000 0.603307
\(795\) 11.0000 0.390130
\(796\) 10.0000 0.354441
\(797\) 32.0000 1.13350 0.566749 0.823890i \(-0.308201\pi\)
0.566749 + 0.823890i \(0.308201\pi\)
\(798\) 0 0
\(799\) 104.000 3.67926
\(800\) −4.00000 −0.141421
\(801\) −20.0000 −0.706665
\(802\) 27.0000 0.953403
\(803\) 12.0000 0.423471
\(804\) −12.0000 −0.423207
\(805\) 0 0
\(806\) 3.00000 0.105670
\(807\) 0 0
\(808\) 8.00000 0.281439
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 18.0000 0.632065 0.316033 0.948748i \(-0.397649\pi\)
0.316033 + 0.948748i \(0.397649\pi\)
\(812\) 0 0
\(813\) 13.0000 0.455930
\(814\) −24.0000 −0.841200
\(815\) −9.00000 −0.315256
\(816\) −8.00000 −0.280056
\(817\) 0 0
\(818\) −30.0000 −1.04893
\(819\) 0 0
\(820\) 2.00000 0.0698430
\(821\) −33.0000 −1.15171 −0.575854 0.817553i \(-0.695330\pi\)
−0.575854 + 0.817553i \(0.695330\pi\)
\(822\) −12.0000 −0.418548
\(823\) −16.0000 −0.557725 −0.278862 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) −14.0000 −0.487713
\(825\) 12.0000 0.417786
\(826\) 0 0
\(827\) 13.0000 0.452054 0.226027 0.974121i \(-0.427426\pi\)
0.226027 + 0.974121i \(0.427426\pi\)
\(828\) −8.00000 −0.278019
\(829\) −40.0000 −1.38926 −0.694629 0.719368i \(-0.744431\pi\)
−0.694629 + 0.719368i \(0.744431\pi\)
\(830\) 4.00000 0.138842
\(831\) −2.00000 −0.0693792
\(832\) 1.00000 0.0346688
\(833\) 0 0
\(834\) 20.0000 0.692543
\(835\) −2.00000 −0.0692129
\(836\) 0 0
\(837\) −15.0000 −0.518476
\(838\) 10.0000 0.345444
\(839\) −45.0000 −1.55357 −0.776786 0.629764i \(-0.783151\pi\)
−0.776786 + 0.629764i \(0.783151\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 32.0000 1.10279
\(843\) 27.0000 0.929929
\(844\) −3.00000 −0.103264
\(845\) 12.0000 0.412813
\(846\) 26.0000 0.893898
\(847\) 0 0
\(848\) −11.0000 −0.377742
\(849\) −4.00000 −0.137280
\(850\) 32.0000 1.09759
\(851\) 32.0000 1.09695
\(852\) 2.00000 0.0685189
\(853\) −14.0000 −0.479351 −0.239675 0.970853i \(-0.577041\pi\)
−0.239675 + 0.970853i \(0.577041\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −2.00000 −0.0683586
\(857\) 27.0000 0.922302 0.461151 0.887322i \(-0.347437\pi\)
0.461151 + 0.887322i \(0.347437\pi\)
\(858\) −3.00000 −0.102418
\(859\) 25.0000 0.852989 0.426494 0.904490i \(-0.359748\pi\)
0.426494 + 0.904490i \(0.359748\pi\)
\(860\) 11.0000 0.375097
\(861\) 0 0
\(862\) 32.0000 1.08992
\(863\) −46.0000 −1.56586 −0.782929 0.622111i \(-0.786275\pi\)
−0.782929 + 0.622111i \(0.786275\pi\)
\(864\) −5.00000 −0.170103
\(865\) −6.00000 −0.204006
\(866\) 16.0000 0.543702
\(867\) 47.0000 1.59620
\(868\) 0 0
\(869\) −45.0000 −1.52652
\(870\) 1.00000 0.0339032
\(871\) −12.0000 −0.406604
\(872\) 5.00000 0.169321
\(873\) −4.00000 −0.135379
\(874\) 0 0
\(875\) 0 0
\(876\) −4.00000 −0.135147
\(877\) 13.0000 0.438979 0.219489 0.975615i \(-0.429561\pi\)
0.219489 + 0.975615i \(0.429561\pi\)
\(878\) −20.0000 −0.674967
\(879\) −14.0000 −0.472208
\(880\) 3.00000 0.101130
\(881\) −42.0000 −1.41502 −0.707508 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) 0 0
\(883\) −26.0000 −0.874970 −0.437485 0.899226i \(-0.644131\pi\)
−0.437485 + 0.899226i \(0.644131\pi\)
\(884\) −8.00000 −0.269069
\(885\) 0 0
\(886\) 4.00000 0.134383
\(887\) −33.0000 −1.10803 −0.554016 0.832506i \(-0.686905\pi\)
−0.554016 + 0.832506i \(0.686905\pi\)
\(888\) 8.00000 0.268462
\(889\) 0 0
\(890\) −10.0000 −0.335201
\(891\) −3.00000 −0.100504
\(892\) 26.0000 0.870544
\(893\) 0 0
\(894\) 15.0000 0.501675
\(895\) 10.0000 0.334263
\(896\) 0 0
\(897\) 4.00000 0.133556
\(898\) −10.0000 −0.333704
\(899\) −3.00000 −0.100056
\(900\) 8.00000 0.266667
\(901\) 88.0000 2.93171
\(902\) 6.00000 0.199778
\(903\) 0 0
\(904\) −6.00000 −0.199557
\(905\) 7.00000 0.232688
\(906\) 2.00000 0.0664455
\(907\) 28.0000 0.929725 0.464862 0.885383i \(-0.346104\pi\)
0.464862 + 0.885383i \(0.346104\pi\)
\(908\) −18.0000 −0.597351
\(909\) −16.0000 −0.530687
\(910\) 0 0
\(911\) −13.0000 −0.430709 −0.215355 0.976536i \(-0.569091\pi\)
−0.215355 + 0.976536i \(0.569091\pi\)
\(912\) 0 0
\(913\) 12.0000 0.397142
\(914\) −2.00000 −0.0661541
\(915\) −8.00000 −0.264472
\(916\) −10.0000 −0.330409
\(917\) 0 0
\(918\) 40.0000 1.32020
\(919\) 30.0000 0.989609 0.494804 0.869004i \(-0.335240\pi\)
0.494804 + 0.869004i \(0.335240\pi\)
\(920\) −4.00000 −0.131876
\(921\) 7.00000 0.230658
\(922\) −2.00000 −0.0658665
\(923\) 2.00000 0.0658308
\(924\) 0 0
\(925\) −32.0000 −1.05215
\(926\) 4.00000 0.131448
\(927\) 28.0000 0.919641
\(928\) −1.00000 −0.0328266
\(929\) 30.0000 0.984268 0.492134 0.870519i \(-0.336217\pi\)
0.492134 + 0.870519i \(0.336217\pi\)
\(930\) −3.00000 −0.0983739
\(931\) 0 0
\(932\) −1.00000 −0.0327561
\(933\) 8.00000 0.261908
\(934\) 27.0000 0.883467
\(935\) −24.0000 −0.784884
\(936\) −2.00000 −0.0653720
\(937\) 2.00000 0.0653372 0.0326686 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) 0 0
\(939\) −9.00000 −0.293704
\(940\) 13.0000 0.424013
\(941\) −37.0000 −1.20617 −0.603083 0.797679i \(-0.706061\pi\)
−0.603083 + 0.797679i \(0.706061\pi\)
\(942\) −18.0000 −0.586472
\(943\) −8.00000 −0.260516
\(944\) 0 0
\(945\) 0 0
\(946\) 33.0000 1.07292
\(947\) 33.0000 1.07236 0.536178 0.844105i \(-0.319868\pi\)
0.536178 + 0.844105i \(0.319868\pi\)
\(948\) 15.0000 0.487177
\(949\) −4.00000 −0.129845
\(950\) 0 0
\(951\) −12.0000 −0.389127
\(952\) 0 0
\(953\) −1.00000 −0.0323932 −0.0161966 0.999869i \(-0.505156\pi\)
−0.0161966 + 0.999869i \(0.505156\pi\)
\(954\) 22.0000 0.712276
\(955\) 8.00000 0.258874
\(956\) 0 0
\(957\) 3.00000 0.0969762
\(958\) 5.00000 0.161543
\(959\) 0 0
\(960\) −1.00000 −0.0322749
\(961\) −22.0000 −0.709677
\(962\) 8.00000 0.257930
\(963\) 4.00000 0.128898
\(964\) −17.0000 −0.547533
\(965\) −14.0000 −0.450676
\(966\) 0 0
\(967\) 13.0000 0.418052 0.209026 0.977910i \(-0.432971\pi\)
0.209026 + 0.977910i \(0.432971\pi\)
\(968\) −2.00000 −0.0642824
\(969\) 0 0
\(970\) −2.00000 −0.0642161
\(971\) 28.0000 0.898563 0.449281 0.893390i \(-0.351680\pi\)
0.449281 + 0.893390i \(0.351680\pi\)
\(972\) 16.0000 0.513200
\(973\) 0 0
\(974\) −22.0000 −0.704925
\(975\) −4.00000 −0.128103
\(976\) 8.00000 0.256074
\(977\) 13.0000 0.415907 0.207953 0.978139i \(-0.433320\pi\)
0.207953 + 0.978139i \(0.433320\pi\)
\(978\) 9.00000 0.287788
\(979\) −30.0000 −0.958804
\(980\) 0 0
\(981\) −10.0000 −0.319275
\(982\) −33.0000 −1.05307
\(983\) −49.0000 −1.56286 −0.781429 0.623995i \(-0.785509\pi\)
−0.781429 + 0.623995i \(0.785509\pi\)
\(984\) −2.00000 −0.0637577
\(985\) −18.0000 −0.573528
\(986\) 8.00000 0.254772
\(987\) 0 0
\(988\) 0 0
\(989\) −44.0000 −1.39912
\(990\) −6.00000 −0.190693
\(991\) 22.0000 0.698853 0.349427 0.936964i \(-0.386376\pi\)
0.349427 + 0.936964i \(0.386376\pi\)
\(992\) 3.00000 0.0952501
\(993\) −23.0000 −0.729883
\(994\) 0 0
\(995\) −10.0000 −0.317021
\(996\) −4.00000 −0.126745
\(997\) −8.00000 −0.253363 −0.126681 0.991943i \(-0.540433\pi\)
−0.126681 + 0.991943i \(0.540433\pi\)
\(998\) −20.0000 −0.633089
\(999\) −40.0000 −1.26554
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2842.2.a.e.1.1 1
7.6 odd 2 58.2.a.b.1.1 1
21.20 even 2 522.2.a.b.1.1 1
28.27 even 2 464.2.a.e.1.1 1
35.13 even 4 1450.2.b.b.349.1 2
35.27 even 4 1450.2.b.b.349.2 2
35.34 odd 2 1450.2.a.c.1.1 1
56.13 odd 2 1856.2.a.k.1.1 1
56.27 even 2 1856.2.a.f.1.1 1
77.76 even 2 7018.2.a.a.1.1 1
84.83 odd 2 4176.2.a.n.1.1 1
91.90 odd 2 9802.2.a.a.1.1 1
203.41 even 4 1682.2.b.a.1681.2 2
203.104 even 4 1682.2.b.a.1681.1 2
203.202 odd 2 1682.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
58.2.a.b.1.1 1 7.6 odd 2
464.2.a.e.1.1 1 28.27 even 2
522.2.a.b.1.1 1 21.20 even 2
1450.2.a.c.1.1 1 35.34 odd 2
1450.2.b.b.349.1 2 35.13 even 4
1450.2.b.b.349.2 2 35.27 even 4
1682.2.a.d.1.1 1 203.202 odd 2
1682.2.b.a.1681.1 2 203.104 even 4
1682.2.b.a.1681.2 2 203.41 even 4
1856.2.a.f.1.1 1 56.27 even 2
1856.2.a.k.1.1 1 56.13 odd 2
2842.2.a.e.1.1 1 1.1 even 1 trivial
4176.2.a.n.1.1 1 84.83 odd 2
7018.2.a.a.1.1 1 77.76 even 2
9802.2.a.a.1.1 1 91.90 odd 2