Properties

Label 1850.2.a.n.1.1
Level $1850$
Weight $2$
Character 1850.1
Self dual yes
Analytic conductor $14.772$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1850.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.7723243739\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1850.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +4.00000 q^{11} +2.00000 q^{12} -2.00000 q^{13} +1.00000 q^{16} +8.00000 q^{17} +1.00000 q^{18} -5.00000 q^{19} +4.00000 q^{22} +1.00000 q^{23} +2.00000 q^{24} -2.00000 q^{26} -4.00000 q^{27} +10.0000 q^{29} -4.00000 q^{31} +1.00000 q^{32} +8.00000 q^{33} +8.00000 q^{34} +1.00000 q^{36} +1.00000 q^{37} -5.00000 q^{38} -4.00000 q^{39} +7.00000 q^{41} -9.00000 q^{43} +4.00000 q^{44} +1.00000 q^{46} +6.00000 q^{47} +2.00000 q^{48} -7.00000 q^{49} +16.0000 q^{51} -2.00000 q^{52} -3.00000 q^{53} -4.00000 q^{54} -10.0000 q^{57} +10.0000 q^{58} -11.0000 q^{59} +2.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +8.00000 q^{66} +2.00000 q^{67} +8.00000 q^{68} +2.00000 q^{69} +14.0000 q^{71} +1.00000 q^{72} +3.00000 q^{73} +1.00000 q^{74} -5.00000 q^{76} -4.00000 q^{78} -11.0000 q^{79} -11.0000 q^{81} +7.00000 q^{82} +8.00000 q^{83} -9.00000 q^{86} +20.0000 q^{87} +4.00000 q^{88} -2.00000 q^{89} +1.00000 q^{92} -8.00000 q^{93} +6.00000 q^{94} +2.00000 q^{96} -8.00000 q^{97} -7.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)

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
\(3\) 2.00000 1.15470 0.577350 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 2.00000 0.816497
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 2.00000 0.577350
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 8.00000 1.94029 0.970143 0.242536i \(-0.0779791\pi\)
0.970143 + 0.242536i \(0.0779791\pi\)
\(18\) 1.00000 0.235702
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) 1.00000 0.208514 0.104257 0.994550i \(-0.466753\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(24\) 2.00000 0.408248
\(25\) 0 0
\(26\) −2.00000 −0.392232
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) 10.0000 1.85695 0.928477 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000 0.176777
\(33\) 8.00000 1.39262
\(34\) 8.00000 1.37199
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 1.00000 0.164399
\(38\) −5.00000 −0.811107
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) 7.00000 1.09322 0.546608 0.837389i \(-0.315919\pi\)
0.546608 + 0.837389i \(0.315919\pi\)
\(42\) 0 0
\(43\) −9.00000 −1.37249 −0.686244 0.727372i \(-0.740742\pi\)
−0.686244 + 0.727372i \(0.740742\pi\)
\(44\) 4.00000 0.603023
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 2.00000 0.288675
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 16.0000 2.24045
\(52\) −2.00000 −0.277350
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) −4.00000 −0.544331
\(55\) 0 0
\(56\) 0 0
\(57\) −10.0000 −1.32453
\(58\) 10.0000 1.31306
\(59\) −11.0000 −1.43208 −0.716039 0.698060i \(-0.754047\pi\)
−0.716039 + 0.698060i \(0.754047\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 8.00000 0.984732
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) 8.00000 0.970143
\(69\) 2.00000 0.240772
\(70\) 0 0
\(71\) 14.0000 1.66149 0.830747 0.556650i \(-0.187914\pi\)
0.830747 + 0.556650i \(0.187914\pi\)
\(72\) 1.00000 0.117851
\(73\) 3.00000 0.351123 0.175562 0.984468i \(-0.443826\pi\)
0.175562 + 0.984468i \(0.443826\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) −5.00000 −0.573539
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) 7.00000 0.773021
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −9.00000 −0.970495
\(87\) 20.0000 2.14423
\(88\) 4.00000 0.426401
\(89\) −2.00000 −0.212000 −0.106000 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.00000 0.104257
\(93\) −8.00000 −0.829561
\(94\) 6.00000 0.618853
\(95\) 0 0
\(96\) 2.00000 0.204124
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) −7.00000 −0.707107
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −9.00000 −0.895533 −0.447767 0.894150i \(-0.647781\pi\)
−0.447767 + 0.894150i \(0.647781\pi\)
\(102\) 16.0000 1.58424
\(103\) 17.0000 1.67506 0.837530 0.546392i \(-0.183999\pi\)
0.837530 + 0.546392i \(0.183999\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −3.00000 −0.291386
\(107\) −10.0000 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) −4.00000 −0.384900
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) −10.0000 −0.936586
\(115\) 0 0
\(116\) 10.0000 0.928477
\(117\) −2.00000 −0.184900
\(118\) −11.0000 −1.01263
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 2.00000 0.181071
\(123\) 14.0000 1.26234
\(124\) −4.00000 −0.359211
\(125\) 0 0
\(126\) 0 0
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) 1.00000 0.0883883
\(129\) −18.0000 −1.58481
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 8.00000 0.696311
\(133\) 0 0
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) 8.00000 0.685994
\(137\) −10.0000 −0.854358 −0.427179 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) 2.00000 0.170251
\(139\) −6.00000 −0.508913 −0.254457 0.967084i \(-0.581897\pi\)
−0.254457 + 0.967084i \(0.581897\pi\)
\(140\) 0 0
\(141\) 12.0000 1.01058
\(142\) 14.0000 1.17485
\(143\) −8.00000 −0.668994
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 3.00000 0.248282
\(147\) −14.0000 −1.15470
\(148\) 1.00000 0.0821995
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) −5.00000 −0.405554
\(153\) 8.00000 0.646762
\(154\) 0 0
\(155\) 0 0
\(156\) −4.00000 −0.320256
\(157\) 7.00000 0.558661 0.279330 0.960195i \(-0.409888\pi\)
0.279330 + 0.960195i \(0.409888\pi\)
\(158\) −11.0000 −0.875113
\(159\) −6.00000 −0.475831
\(160\) 0 0
\(161\) 0 0
\(162\) −11.0000 −0.864242
\(163\) −9.00000 −0.704934 −0.352467 0.935824i \(-0.614657\pi\)
−0.352467 + 0.935824i \(0.614657\pi\)
\(164\) 7.00000 0.546608
\(165\) 0 0
\(166\) 8.00000 0.620920
\(167\) 23.0000 1.77979 0.889897 0.456162i \(-0.150776\pi\)
0.889897 + 0.456162i \(0.150776\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −5.00000 −0.382360
\(172\) −9.00000 −0.686244
\(173\) −2.00000 −0.152057 −0.0760286 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) 20.0000 1.51620
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) −22.0000 −1.65362
\(178\) −2.00000 −0.149906
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 4.00000 0.295689
\(184\) 1.00000 0.0737210
\(185\) 0 0
\(186\) −8.00000 −0.586588
\(187\) 32.0000 2.34007
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) −19.0000 −1.37479 −0.687396 0.726283i \(-0.741246\pi\)
−0.687396 + 0.726283i \(0.741246\pi\)
\(192\) 2.00000 0.144338
\(193\) 20.0000 1.43963 0.719816 0.694165i \(-0.244226\pi\)
0.719816 + 0.694165i \(0.244226\pi\)
\(194\) −8.00000 −0.574367
\(195\) 0 0
\(196\) −7.00000 −0.500000
\(197\) 7.00000 0.498729 0.249365 0.968410i \(-0.419778\pi\)
0.249365 + 0.968410i \(0.419778\pi\)
\(198\) 4.00000 0.284268
\(199\) 1.00000 0.0708881 0.0354441 0.999372i \(-0.488715\pi\)
0.0354441 + 0.999372i \(0.488715\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) −9.00000 −0.633238
\(203\) 0 0
\(204\) 16.0000 1.12022
\(205\) 0 0
\(206\) 17.0000 1.18445
\(207\) 1.00000 0.0695048
\(208\) −2.00000 −0.138675
\(209\) −20.0000 −1.38343
\(210\) 0 0
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) −3.00000 −0.206041
\(213\) 28.0000 1.91853
\(214\) −10.0000 −0.683586
\(215\) 0 0
\(216\) −4.00000 −0.272166
\(217\) 0 0
\(218\) −16.0000 −1.08366
\(219\) 6.00000 0.405442
\(220\) 0 0
\(221\) −16.0000 −1.07628
\(222\) 2.00000 0.134231
\(223\) 6.00000 0.401790 0.200895 0.979613i \(-0.435615\pi\)
0.200895 + 0.979613i \(0.435615\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2.00000 −0.133038
\(227\) −7.00000 −0.464606 −0.232303 0.972643i \(-0.574626\pi\)
−0.232303 + 0.972643i \(0.574626\pi\)
\(228\) −10.0000 −0.662266
\(229\) −1.00000 −0.0660819 −0.0330409 0.999454i \(-0.510519\pi\)
−0.0330409 + 0.999454i \(0.510519\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 10.0000 0.656532
\(233\) −29.0000 −1.89985 −0.949927 0.312473i \(-0.898843\pi\)
−0.949927 + 0.312473i \(0.898843\pi\)
\(234\) −2.00000 −0.130744
\(235\) 0 0
\(236\) −11.0000 −0.716039
\(237\) −22.0000 −1.42905
\(238\) 0 0
\(239\) −13.0000 −0.840900 −0.420450 0.907316i \(-0.638128\pi\)
−0.420450 + 0.907316i \(0.638128\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 5.00000 0.321412
\(243\) −10.0000 −0.641500
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) 14.0000 0.892607
\(247\) 10.0000 0.636285
\(248\) −4.00000 −0.254000
\(249\) 16.0000 1.01396
\(250\) 0 0
\(251\) −21.0000 −1.32551 −0.662754 0.748837i \(-0.730613\pi\)
−0.662754 + 0.748837i \(0.730613\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 4.00000 0.250982
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 8.00000 0.499026 0.249513 0.968371i \(-0.419729\pi\)
0.249513 + 0.968371i \(0.419729\pi\)
\(258\) −18.0000 −1.12063
\(259\) 0 0
\(260\) 0 0
\(261\) 10.0000 0.618984
\(262\) −12.0000 −0.741362
\(263\) 14.0000 0.863277 0.431638 0.902047i \(-0.357936\pi\)
0.431638 + 0.902047i \(0.357936\pi\)
\(264\) 8.00000 0.492366
\(265\) 0 0
\(266\) 0 0
\(267\) −4.00000 −0.244796
\(268\) 2.00000 0.122169
\(269\) 31.0000 1.89010 0.945052 0.326921i \(-0.106011\pi\)
0.945052 + 0.326921i \(0.106011\pi\)
\(270\) 0 0
\(271\) −4.00000 −0.242983 −0.121491 0.992592i \(-0.538768\pi\)
−0.121491 + 0.992592i \(0.538768\pi\)
\(272\) 8.00000 0.485071
\(273\) 0 0
\(274\) −10.0000 −0.604122
\(275\) 0 0
\(276\) 2.00000 0.120386
\(277\) 10.0000 0.600842 0.300421 0.953807i \(-0.402873\pi\)
0.300421 + 0.953807i \(0.402873\pi\)
\(278\) −6.00000 −0.359856
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) 28.0000 1.67034 0.835170 0.549992i \(-0.185369\pi\)
0.835170 + 0.549992i \(0.185369\pi\)
\(282\) 12.0000 0.714590
\(283\) 3.00000 0.178331 0.0891657 0.996017i \(-0.471580\pi\)
0.0891657 + 0.996017i \(0.471580\pi\)
\(284\) 14.0000 0.830747
\(285\) 0 0
\(286\) −8.00000 −0.473050
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 47.0000 2.76471
\(290\) 0 0
\(291\) −16.0000 −0.937937
\(292\) 3.00000 0.175562
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) −14.0000 −0.816497
\(295\) 0 0
\(296\) 1.00000 0.0581238
\(297\) −16.0000 −0.928414
\(298\) 3.00000 0.173785
\(299\) −2.00000 −0.115663
\(300\) 0 0
\(301\) 0 0
\(302\) −8.00000 −0.460348
\(303\) −18.0000 −1.03407
\(304\) −5.00000 −0.286770
\(305\) 0 0
\(306\) 8.00000 0.457330
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 34.0000 1.93419
\(310\) 0 0
\(311\) 21.0000 1.19080 0.595400 0.803429i \(-0.296993\pi\)
0.595400 + 0.803429i \(0.296993\pi\)
\(312\) −4.00000 −0.226455
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 7.00000 0.395033
\(315\) 0 0
\(316\) −11.0000 −0.618798
\(317\) −27.0000 −1.51647 −0.758236 0.651981i \(-0.773938\pi\)
−0.758236 + 0.651981i \(0.773938\pi\)
\(318\) −6.00000 −0.336463
\(319\) 40.0000 2.23957
\(320\) 0 0
\(321\) −20.0000 −1.11629
\(322\) 0 0
\(323\) −40.0000 −2.22566
\(324\) −11.0000 −0.611111
\(325\) 0 0
\(326\) −9.00000 −0.498464
\(327\) −32.0000 −1.76960
\(328\) 7.00000 0.386510
\(329\) 0 0
\(330\) 0 0
\(331\) −24.0000 −1.31916 −0.659580 0.751635i \(-0.729266\pi\)
−0.659580 + 0.751635i \(0.729266\pi\)
\(332\) 8.00000 0.439057
\(333\) 1.00000 0.0547997
\(334\) 23.0000 1.25850
\(335\) 0 0
\(336\) 0 0
\(337\) −1.00000 −0.0544735 −0.0272367 0.999629i \(-0.508671\pi\)
−0.0272367 + 0.999629i \(0.508671\pi\)
\(338\) −9.00000 −0.489535
\(339\) −4.00000 −0.217250
\(340\) 0 0
\(341\) −16.0000 −0.866449
\(342\) −5.00000 −0.270369
\(343\) 0 0
\(344\) −9.00000 −0.485247
\(345\) 0 0
\(346\) −2.00000 −0.107521
\(347\) 33.0000 1.77153 0.885766 0.464131i \(-0.153633\pi\)
0.885766 + 0.464131i \(0.153633\pi\)
\(348\) 20.0000 1.07211
\(349\) −7.00000 −0.374701 −0.187351 0.982293i \(-0.559990\pi\)
−0.187351 + 0.982293i \(0.559990\pi\)
\(350\) 0 0
\(351\) 8.00000 0.427008
\(352\) 4.00000 0.213201
\(353\) −4.00000 −0.212899 −0.106449 0.994318i \(-0.533948\pi\)
−0.106449 + 0.994318i \(0.533948\pi\)
\(354\) −22.0000 −1.16929
\(355\) 0 0
\(356\) −2.00000 −0.106000
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −26.0000 −1.37223 −0.686114 0.727494i \(-0.740685\pi\)
−0.686114 + 0.727494i \(0.740685\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) −7.00000 −0.367912
\(363\) 10.0000 0.524864
\(364\) 0 0
\(365\) 0 0
\(366\) 4.00000 0.209083
\(367\) 14.0000 0.730794 0.365397 0.930852i \(-0.380933\pi\)
0.365397 + 0.930852i \(0.380933\pi\)
\(368\) 1.00000 0.0521286
\(369\) 7.00000 0.364405
\(370\) 0 0
\(371\) 0 0
\(372\) −8.00000 −0.414781
\(373\) 22.0000 1.13912 0.569558 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) 32.0000 1.65468
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) −20.0000 −1.03005
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 0 0
\(381\) 8.00000 0.409852
\(382\) −19.0000 −0.972125
\(383\) −29.0000 −1.48183 −0.740915 0.671598i \(-0.765608\pi\)
−0.740915 + 0.671598i \(0.765608\pi\)
\(384\) 2.00000 0.102062
\(385\) 0 0
\(386\) 20.0000 1.01797
\(387\) −9.00000 −0.457496
\(388\) −8.00000 −0.406138
\(389\) 32.0000 1.62246 0.811232 0.584724i \(-0.198797\pi\)
0.811232 + 0.584724i \(0.198797\pi\)
\(390\) 0 0
\(391\) 8.00000 0.404577
\(392\) −7.00000 −0.353553
\(393\) −24.0000 −1.21064
\(394\) 7.00000 0.352655
\(395\) 0 0
\(396\) 4.00000 0.201008
\(397\) −13.0000 −0.652451 −0.326226 0.945292i \(-0.605777\pi\)
−0.326226 + 0.945292i \(0.605777\pi\)
\(398\) 1.00000 0.0501255
\(399\) 0 0
\(400\) 0 0
\(401\) −2.00000 −0.0998752 −0.0499376 0.998752i \(-0.515902\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 4.00000 0.199502
\(403\) 8.00000 0.398508
\(404\) −9.00000 −0.447767
\(405\) 0 0
\(406\) 0 0
\(407\) 4.00000 0.198273
\(408\) 16.0000 0.792118
\(409\) 16.0000 0.791149 0.395575 0.918434i \(-0.370545\pi\)
0.395575 + 0.918434i \(0.370545\pi\)
\(410\) 0 0
\(411\) −20.0000 −0.986527
\(412\) 17.0000 0.837530
\(413\) 0 0
\(414\) 1.00000 0.0491473
\(415\) 0 0
\(416\) −2.00000 −0.0980581
\(417\) −12.0000 −0.587643
\(418\) −20.0000 −0.978232
\(419\) 8.00000 0.390826 0.195413 0.980721i \(-0.437395\pi\)
0.195413 + 0.980721i \(0.437395\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) −22.0000 −1.07094
\(423\) 6.00000 0.291730
\(424\) −3.00000 −0.145693
\(425\) 0 0
\(426\) 28.0000 1.35660
\(427\) 0 0
\(428\) −10.0000 −0.483368
\(429\) −16.0000 −0.772487
\(430\) 0 0
\(431\) −3.00000 −0.144505 −0.0722525 0.997386i \(-0.523019\pi\)
−0.0722525 + 0.997386i \(0.523019\pi\)
\(432\) −4.00000 −0.192450
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −16.0000 −0.766261
\(437\) −5.00000 −0.239182
\(438\) 6.00000 0.286691
\(439\) 3.00000 0.143182 0.0715911 0.997434i \(-0.477192\pi\)
0.0715911 + 0.997434i \(0.477192\pi\)
\(440\) 0 0
\(441\) −7.00000 −0.333333
\(442\) −16.0000 −0.761042
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) 6.00000 0.284108
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 28.0000 1.31847
\(452\) −2.00000 −0.0940721
\(453\) −16.0000 −0.751746
\(454\) −7.00000 −0.328526
\(455\) 0 0
\(456\) −10.0000 −0.468293
\(457\) −24.0000 −1.12267 −0.561336 0.827588i \(-0.689713\pi\)
−0.561336 + 0.827588i \(0.689713\pi\)
\(458\) −1.00000 −0.0467269
\(459\) −32.0000 −1.49363
\(460\) 0 0
\(461\) 24.0000 1.11779 0.558896 0.829238i \(-0.311225\pi\)
0.558896 + 0.829238i \(0.311225\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) 10.0000 0.464238
\(465\) 0 0
\(466\) −29.0000 −1.34340
\(467\) 36.0000 1.66588 0.832941 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) 14.0000 0.645086
\(472\) −11.0000 −0.506316
\(473\) −36.0000 −1.65528
\(474\) −22.0000 −1.01049
\(475\) 0 0
\(476\) 0 0
\(477\) −3.00000 −0.137361
\(478\) −13.0000 −0.594606
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) −2.00000 −0.0911922
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) −10.0000 −0.453609
\(487\) −24.0000 −1.08754 −0.543772 0.839233i \(-0.683004\pi\)
−0.543772 + 0.839233i \(0.683004\pi\)
\(488\) 2.00000 0.0905357
\(489\) −18.0000 −0.813988
\(490\) 0 0
\(491\) 34.0000 1.53440 0.767199 0.641409i \(-0.221650\pi\)
0.767199 + 0.641409i \(0.221650\pi\)
\(492\) 14.0000 0.631169
\(493\) 80.0000 3.60302
\(494\) 10.0000 0.449921
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 16.0000 0.716977
\(499\) −29.0000 −1.29822 −0.649109 0.760695i \(-0.724858\pi\)
−0.649109 + 0.760695i \(0.724858\pi\)
\(500\) 0 0
\(501\) 46.0000 2.05513
\(502\) −21.0000 −0.937276
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 4.00000 0.177822
\(507\) −18.0000 −0.799408
\(508\) 4.00000 0.177471
\(509\) −11.0000 −0.487566 −0.243783 0.969830i \(-0.578389\pi\)
−0.243783 + 0.969830i \(0.578389\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 20.0000 0.883022
\(514\) 8.00000 0.352865
\(515\) 0 0
\(516\) −18.0000 −0.792406
\(517\) 24.0000 1.05552
\(518\) 0 0
\(519\) −4.00000 −0.175581
\(520\) 0 0
\(521\) 15.0000 0.657162 0.328581 0.944476i \(-0.393430\pi\)
0.328581 + 0.944476i \(0.393430\pi\)
\(522\) 10.0000 0.437688
\(523\) −20.0000 −0.874539 −0.437269 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 14.0000 0.610429
\(527\) −32.0000 −1.39394
\(528\) 8.00000 0.348155
\(529\) −22.0000 −0.956522
\(530\) 0 0
\(531\) −11.0000 −0.477359
\(532\) 0 0
\(533\) −14.0000 −0.606407
\(534\) −4.00000 −0.173097
\(535\) 0 0
\(536\) 2.00000 0.0863868
\(537\) −24.0000 −1.03568
\(538\) 31.0000 1.33650
\(539\) −28.0000 −1.20605
\(540\) 0 0
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) −4.00000 −0.171815
\(543\) −14.0000 −0.600798
\(544\) 8.00000 0.342997
\(545\) 0 0
\(546\) 0 0
\(547\) −4.00000 −0.171028 −0.0855138 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) −10.0000 −0.427179
\(549\) 2.00000 0.0853579
\(550\) 0 0
\(551\) −50.0000 −2.13007
\(552\) 2.00000 0.0851257
\(553\) 0 0
\(554\) 10.0000 0.424859
\(555\) 0 0
\(556\) −6.00000 −0.254457
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) −4.00000 −0.169334
\(559\) 18.0000 0.761319
\(560\) 0 0
\(561\) 64.0000 2.70208
\(562\) 28.0000 1.18111
\(563\) 27.0000 1.13791 0.568957 0.822367i \(-0.307347\pi\)
0.568957 + 0.822367i \(0.307347\pi\)
\(564\) 12.0000 0.505291
\(565\) 0 0
\(566\) 3.00000 0.126099
\(567\) 0 0
\(568\) 14.0000 0.587427
\(569\) 44.0000 1.84458 0.922288 0.386503i \(-0.126317\pi\)
0.922288 + 0.386503i \(0.126317\pi\)
\(570\) 0 0
\(571\) −6.00000 −0.251092 −0.125546 0.992088i \(-0.540068\pi\)
−0.125546 + 0.992088i \(0.540068\pi\)
\(572\) −8.00000 −0.334497
\(573\) −38.0000 −1.58747
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −44.0000 −1.83174 −0.915872 0.401470i \(-0.868499\pi\)
−0.915872 + 0.401470i \(0.868499\pi\)
\(578\) 47.0000 1.95494
\(579\) 40.0000 1.66234
\(580\) 0 0
\(581\) 0 0
\(582\) −16.0000 −0.663221
\(583\) −12.0000 −0.496989
\(584\) 3.00000 0.124141
\(585\) 0 0
\(586\) 9.00000 0.371787
\(587\) 27.0000 1.11441 0.557205 0.830375i \(-0.311874\pi\)
0.557205 + 0.830375i \(0.311874\pi\)
\(588\) −14.0000 −0.577350
\(589\) 20.0000 0.824086
\(590\) 0 0
\(591\) 14.0000 0.575883
\(592\) 1.00000 0.0410997
\(593\) 31.0000 1.27302 0.636509 0.771270i \(-0.280378\pi\)
0.636509 + 0.771270i \(0.280378\pi\)
\(594\) −16.0000 −0.656488
\(595\) 0 0
\(596\) 3.00000 0.122885
\(597\) 2.00000 0.0818546
\(598\) −2.00000 −0.0817861
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −37.0000 −1.50926 −0.754631 0.656150i \(-0.772184\pi\)
−0.754631 + 0.656150i \(0.772184\pi\)
\(602\) 0 0
\(603\) 2.00000 0.0814463
\(604\) −8.00000 −0.325515
\(605\) 0 0
\(606\) −18.0000 −0.731200
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) −5.00000 −0.202777
\(609\) 0 0
\(610\) 0 0
\(611\) −12.0000 −0.485468
\(612\) 8.00000 0.323381
\(613\) 43.0000 1.73675 0.868377 0.495905i \(-0.165164\pi\)
0.868377 + 0.495905i \(0.165164\pi\)
\(614\) −12.0000 −0.484281
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 34.0000 1.36768
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) 0 0
\(621\) −4.00000 −0.160514
\(622\) 21.0000 0.842023
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 0 0
\(626\) −10.0000 −0.399680
\(627\) −40.0000 −1.59745
\(628\) 7.00000 0.279330
\(629\) 8.00000 0.318981
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) −11.0000 −0.437557
\(633\) −44.0000 −1.74884
\(634\) −27.0000 −1.07231
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) 14.0000 0.554700
\(638\) 40.0000 1.58362
\(639\) 14.0000 0.553831
\(640\) 0 0
\(641\) 11.0000 0.434474 0.217237 0.976119i \(-0.430296\pi\)
0.217237 + 0.976119i \(0.430296\pi\)
\(642\) −20.0000 −0.789337
\(643\) −28.0000 −1.10421 −0.552106 0.833774i \(-0.686176\pi\)
−0.552106 + 0.833774i \(0.686176\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −40.0000 −1.57378
\(647\) 7.00000 0.275198 0.137599 0.990488i \(-0.456061\pi\)
0.137599 + 0.990488i \(0.456061\pi\)
\(648\) −11.0000 −0.432121
\(649\) −44.0000 −1.72715
\(650\) 0 0
\(651\) 0 0
\(652\) −9.00000 −0.352467
\(653\) −30.0000 −1.17399 −0.586995 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) −32.0000 −1.25130
\(655\) 0 0
\(656\) 7.00000 0.273304
\(657\) 3.00000 0.117041
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 4.00000 0.155582 0.0777910 0.996970i \(-0.475213\pi\)
0.0777910 + 0.996970i \(0.475213\pi\)
\(662\) −24.0000 −0.932786
\(663\) −32.0000 −1.24278
\(664\) 8.00000 0.310460
\(665\) 0 0
\(666\) 1.00000 0.0387492
\(667\) 10.0000 0.387202
\(668\) 23.0000 0.889897
\(669\) 12.0000 0.463947
\(670\) 0 0
\(671\) 8.00000 0.308837
\(672\) 0 0
\(673\) 19.0000 0.732396 0.366198 0.930537i \(-0.380659\pi\)
0.366198 + 0.930537i \(0.380659\pi\)
\(674\) −1.00000 −0.0385186
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) −3.00000 −0.115299 −0.0576497 0.998337i \(-0.518361\pi\)
−0.0576497 + 0.998337i \(0.518361\pi\)
\(678\) −4.00000 −0.153619
\(679\) 0 0
\(680\) 0 0
\(681\) −14.0000 −0.536481
\(682\) −16.0000 −0.612672
\(683\) 16.0000 0.612223 0.306111 0.951996i \(-0.400972\pi\)
0.306111 + 0.951996i \(0.400972\pi\)
\(684\) −5.00000 −0.191180
\(685\) 0 0
\(686\) 0 0
\(687\) −2.00000 −0.0763048
\(688\) −9.00000 −0.343122
\(689\) 6.00000 0.228582
\(690\) 0 0
\(691\) 10.0000 0.380418 0.190209 0.981744i \(-0.439083\pi\)
0.190209 + 0.981744i \(0.439083\pi\)
\(692\) −2.00000 −0.0760286
\(693\) 0 0
\(694\) 33.0000 1.25266
\(695\) 0 0
\(696\) 20.0000 0.758098
\(697\) 56.0000 2.12115
\(698\) −7.00000 −0.264954
\(699\) −58.0000 −2.19376
\(700\) 0 0
\(701\) −10.0000 −0.377695 −0.188847 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) 8.00000 0.301941
\(703\) −5.00000 −0.188579
\(704\) 4.00000 0.150756
\(705\) 0 0
\(706\) −4.00000 −0.150542
\(707\) 0 0
\(708\) −22.0000 −0.826811
\(709\) 24.0000 0.901339 0.450669 0.892691i \(-0.351185\pi\)
0.450669 + 0.892691i \(0.351185\pi\)
\(710\) 0 0
\(711\) −11.0000 −0.412532
\(712\) −2.00000 −0.0749532
\(713\) −4.00000 −0.149801
\(714\) 0 0
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) −26.0000 −0.970988
\(718\) −26.0000 −0.970311
\(719\) 28.0000 1.04422 0.522112 0.852877i \(-0.325144\pi\)
0.522112 + 0.852877i \(0.325144\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 6.00000 0.223297
\(723\) 20.0000 0.743808
\(724\) −7.00000 −0.260153
\(725\) 0 0
\(726\) 10.0000 0.371135
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −72.0000 −2.66302
\(732\) 4.00000 0.147844
\(733\) 2.00000 0.0738717 0.0369358 0.999318i \(-0.488240\pi\)
0.0369358 + 0.999318i \(0.488240\pi\)
\(734\) 14.0000 0.516749
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) 8.00000 0.294684
\(738\) 7.00000 0.257674
\(739\) 18.0000 0.662141 0.331070 0.943606i \(-0.392590\pi\)
0.331070 + 0.943606i \(0.392590\pi\)
\(740\) 0 0
\(741\) 20.0000 0.734718
\(742\) 0 0
\(743\) −34.0000 −1.24734 −0.623670 0.781688i \(-0.714359\pi\)
−0.623670 + 0.781688i \(0.714359\pi\)
\(744\) −8.00000 −0.293294
\(745\) 0 0
\(746\) 22.0000 0.805477
\(747\) 8.00000 0.292705
\(748\) 32.0000 1.17004
\(749\) 0 0
\(750\) 0 0
\(751\) 26.0000 0.948753 0.474377 0.880322i \(-0.342673\pi\)
0.474377 + 0.880322i \(0.342673\pi\)
\(752\) 6.00000 0.218797
\(753\) −42.0000 −1.53057
\(754\) −20.0000 −0.728357
\(755\) 0 0
\(756\) 0 0
\(757\) −8.00000 −0.290765 −0.145382 0.989376i \(-0.546441\pi\)
−0.145382 + 0.989376i \(0.546441\pi\)
\(758\) 16.0000 0.581146
\(759\) 8.00000 0.290382
\(760\) 0 0
\(761\) 13.0000 0.471250 0.235625 0.971844i \(-0.424286\pi\)
0.235625 + 0.971844i \(0.424286\pi\)
\(762\) 8.00000 0.289809
\(763\) 0 0
\(764\) −19.0000 −0.687396
\(765\) 0 0
\(766\) −29.0000 −1.04781
\(767\) 22.0000 0.794374
\(768\) 2.00000 0.0721688
\(769\) −46.0000 −1.65880 −0.829401 0.558653i \(-0.811318\pi\)
−0.829401 + 0.558653i \(0.811318\pi\)
\(770\) 0 0
\(771\) 16.0000 0.576226
\(772\) 20.0000 0.719816
\(773\) 42.0000 1.51064 0.755318 0.655359i \(-0.227483\pi\)
0.755318 + 0.655359i \(0.227483\pi\)
\(774\) −9.00000 −0.323498
\(775\) 0 0
\(776\) −8.00000 −0.287183
\(777\) 0 0
\(778\) 32.0000 1.14726
\(779\) −35.0000 −1.25401
\(780\) 0 0
\(781\) 56.0000 2.00384
\(782\) 8.00000 0.286079
\(783\) −40.0000 −1.42948
\(784\) −7.00000 −0.250000
\(785\) 0 0
\(786\) −24.0000 −0.856052
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 7.00000 0.249365
\(789\) 28.0000 0.996826
\(790\) 0 0
\(791\) 0 0
\(792\) 4.00000 0.142134
\(793\) −4.00000 −0.142044
\(794\) −13.0000 −0.461353
\(795\) 0 0
\(796\) 1.00000 0.0354441
\(797\) 32.0000 1.13350 0.566749 0.823890i \(-0.308201\pi\)
0.566749 + 0.823890i \(0.308201\pi\)
\(798\) 0 0
\(799\) 48.0000 1.69812
\(800\) 0 0
\(801\) −2.00000 −0.0706665
\(802\) −2.00000 −0.0706225
\(803\) 12.0000 0.423471
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) 8.00000 0.281788
\(807\) 62.0000 2.18250
\(808\) −9.00000 −0.316619
\(809\) 8.00000 0.281265 0.140633 0.990062i \(-0.455086\pi\)
0.140633 + 0.990062i \(0.455086\pi\)
\(810\) 0 0
\(811\) 44.0000 1.54505 0.772524 0.634985i \(-0.218994\pi\)
0.772524 + 0.634985i \(0.218994\pi\)
\(812\) 0 0
\(813\) −8.00000 −0.280572
\(814\) 4.00000 0.140200
\(815\) 0 0
\(816\) 16.0000 0.560112
\(817\) 45.0000 1.57435
\(818\) 16.0000 0.559427
\(819\) 0 0
\(820\) 0 0
\(821\) 45.0000 1.57051 0.785255 0.619172i \(-0.212532\pi\)
0.785255 + 0.619172i \(0.212532\pi\)
\(822\) −20.0000 −0.697580
\(823\) 34.0000 1.18517 0.592583 0.805510i \(-0.298108\pi\)
0.592583 + 0.805510i \(0.298108\pi\)
\(824\) 17.0000 0.592223
\(825\) 0 0
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 1.00000 0.0347524
\(829\) −16.0000 −0.555703 −0.277851 0.960624i \(-0.589622\pi\)
−0.277851 + 0.960624i \(0.589622\pi\)
\(830\) 0 0
\(831\) 20.0000 0.693792
\(832\) −2.00000 −0.0693375
\(833\) −56.0000 −1.94029
\(834\) −12.0000 −0.415526
\(835\) 0 0
\(836\) −20.0000 −0.691714
\(837\) 16.0000 0.553041
\(838\) 8.00000 0.276355
\(839\) −6.00000 −0.207143 −0.103572 0.994622i \(-0.533027\pi\)
−0.103572 + 0.994622i \(0.533027\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) −26.0000 −0.896019
\(843\) 56.0000 1.92874
\(844\) −22.0000 −0.757271
\(845\) 0 0
\(846\) 6.00000 0.206284
\(847\) 0 0
\(848\) −3.00000 −0.103020
\(849\) 6.00000 0.205919
\(850\) 0 0
\(851\) 1.00000 0.0342796
\(852\) 28.0000 0.959264
\(853\) −30.0000 −1.02718 −0.513590 0.858036i \(-0.671685\pi\)
−0.513590 + 0.858036i \(0.671685\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −10.0000 −0.341793
\(857\) −6.00000 −0.204956 −0.102478 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) −16.0000 −0.546231
\(859\) 51.0000 1.74010 0.870049 0.492966i \(-0.164087\pi\)
0.870049 + 0.492966i \(0.164087\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −3.00000 −0.102180
\(863\) 6.00000 0.204242 0.102121 0.994772i \(-0.467437\pi\)
0.102121 + 0.994772i \(0.467437\pi\)
\(864\) −4.00000 −0.136083
\(865\) 0 0
\(866\) 26.0000 0.883516
\(867\) 94.0000 3.19241
\(868\) 0 0
\(869\) −44.0000 −1.49260
\(870\) 0 0
\(871\) −4.00000 −0.135535
\(872\) −16.0000 −0.541828
\(873\) −8.00000 −0.270759
\(874\) −5.00000 −0.169128
\(875\) 0 0
\(876\) 6.00000 0.202721
\(877\) 27.0000 0.911725 0.455863 0.890050i \(-0.349331\pi\)
0.455863 + 0.890050i \(0.349331\pi\)
\(878\) 3.00000 0.101245
\(879\) 18.0000 0.607125
\(880\) 0 0
\(881\) −15.0000 −0.505363 −0.252681 0.967550i \(-0.581312\pi\)
−0.252681 + 0.967550i \(0.581312\pi\)
\(882\) −7.00000 −0.235702
\(883\) 32.0000 1.07689 0.538443 0.842662i \(-0.319013\pi\)
0.538443 + 0.842662i \(0.319013\pi\)
\(884\) −16.0000 −0.538138
\(885\) 0 0
\(886\) 0 0
\(887\) 42.0000 1.41022 0.705111 0.709097i \(-0.250897\pi\)
0.705111 + 0.709097i \(0.250897\pi\)
\(888\) 2.00000 0.0671156
\(889\) 0 0
\(890\) 0 0
\(891\) −44.0000 −1.47406
\(892\) 6.00000 0.200895
\(893\) −30.0000 −1.00391
\(894\) 6.00000 0.200670
\(895\) 0 0
\(896\) 0 0
\(897\) −4.00000 −0.133556
\(898\) −30.0000 −1.00111
\(899\) −40.0000 −1.33407
\(900\) 0 0
\(901\) −24.0000 −0.799556
\(902\) 28.0000 0.932298
\(903\) 0 0
\(904\) −2.00000 −0.0665190
\(905\) 0 0
\(906\) −16.0000 −0.531564
\(907\) −3.00000 −0.0996134 −0.0498067 0.998759i \(-0.515861\pi\)
−0.0498067 + 0.998759i \(0.515861\pi\)
\(908\) −7.00000 −0.232303
\(909\) −9.00000 −0.298511
\(910\) 0 0
\(911\) 5.00000 0.165657 0.0828287 0.996564i \(-0.473605\pi\)
0.0828287 + 0.996564i \(0.473605\pi\)
\(912\) −10.0000 −0.331133
\(913\) 32.0000 1.05905
\(914\) −24.0000 −0.793849
\(915\) 0 0
\(916\) −1.00000 −0.0330409
\(917\) 0 0
\(918\) −32.0000 −1.05616
\(919\) 24.0000 0.791687 0.395843 0.918318i \(-0.370452\pi\)
0.395843 + 0.918318i \(0.370452\pi\)
\(920\) 0 0
\(921\) −24.0000 −0.790827
\(922\) 24.0000 0.790398
\(923\) −28.0000 −0.921631
\(924\) 0 0
\(925\) 0 0
\(926\) 24.0000 0.788689
\(927\) 17.0000 0.558353
\(928\) 10.0000 0.328266
\(929\) 34.0000 1.11550 0.557752 0.830008i \(-0.311664\pi\)
0.557752 + 0.830008i \(0.311664\pi\)
\(930\) 0 0
\(931\) 35.0000 1.14708
\(932\) −29.0000 −0.949927
\(933\) 42.0000 1.37502
\(934\) 36.0000 1.17796
\(935\) 0 0
\(936\) −2.00000 −0.0653720
\(937\) 38.0000 1.24141 0.620703 0.784046i \(-0.286847\pi\)
0.620703 + 0.784046i \(0.286847\pi\)
\(938\) 0 0
\(939\) −20.0000 −0.652675
\(940\) 0 0
\(941\) 6.00000 0.195594 0.0977972 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) 14.0000 0.456145
\(943\) 7.00000 0.227951
\(944\) −11.0000 −0.358020
\(945\) 0 0
\(946\) −36.0000 −1.17046
\(947\) −41.0000 −1.33232 −0.666160 0.745808i \(-0.732063\pi\)
−0.666160 + 0.745808i \(0.732063\pi\)
\(948\) −22.0000 −0.714527
\(949\) −6.00000 −0.194768
\(950\) 0 0
\(951\) −54.0000 −1.75107
\(952\) 0 0
\(953\) 41.0000 1.32812 0.664060 0.747679i \(-0.268832\pi\)
0.664060 + 0.747679i \(0.268832\pi\)
\(954\) −3.00000 −0.0971286
\(955\) 0 0
\(956\) −13.0000 −0.420450
\(957\) 80.0000 2.58603
\(958\) 24.0000 0.775405
\(959\) 0 0
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) −2.00000 −0.0644826
\(963\) −10.0000 −0.322245
\(964\) 10.0000 0.322078
\(965\) 0 0
\(966\) 0 0
\(967\) −13.0000 −0.418052 −0.209026 0.977910i \(-0.567029\pi\)
−0.209026 + 0.977910i \(0.567029\pi\)
\(968\) 5.00000 0.160706
\(969\) −80.0000 −2.56997
\(970\) 0 0
\(971\) 20.0000 0.641831 0.320915 0.947108i \(-0.396010\pi\)
0.320915 + 0.947108i \(0.396010\pi\)
\(972\) −10.0000 −0.320750
\(973\) 0 0
\(974\) −24.0000 −0.769010
\(975\) 0 0
\(976\) 2.00000 0.0640184
\(977\) 62.0000 1.98356 0.991778 0.127971i \(-0.0408466\pi\)
0.991778 + 0.127971i \(0.0408466\pi\)
\(978\) −18.0000 −0.575577
\(979\) −8.00000 −0.255681
\(980\) 0 0
\(981\) −16.0000 −0.510841
\(982\) 34.0000 1.08498
\(983\) −42.0000 −1.33959 −0.669796 0.742545i \(-0.733618\pi\)
−0.669796 + 0.742545i \(0.733618\pi\)
\(984\) 14.0000 0.446304
\(985\) 0 0
\(986\) 80.0000 2.54772
\(987\) 0 0
\(988\) 10.0000 0.318142
\(989\) −9.00000 −0.286183
\(990\) 0 0
\(991\) −23.0000 −0.730619 −0.365310 0.930886i \(-0.619037\pi\)
−0.365310 + 0.930886i \(0.619037\pi\)
\(992\) −4.00000 −0.127000
\(993\) −48.0000 −1.52323
\(994\) 0 0
\(995\) 0 0
\(996\) 16.0000 0.506979
\(997\) −60.0000 −1.90022 −0.950110 0.311916i \(-0.899029\pi\)
−0.950110 + 0.311916i \(0.899029\pi\)
\(998\) −29.0000 −0.917979
\(999\) −4.00000 −0.126554
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 1850.2.a.n.1.1 yes 1
5.2 odd 4 1850.2.b.h.149.2 2
5.3 odd 4 1850.2.b.h.149.1 2
5.4 even 2 1850.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1850.2.a.b.1.1 1 5.4 even 2
1850.2.a.n.1.1 yes 1 1.1 even 1 trivial
1850.2.b.h.149.1 2 5.3 odd 4
1850.2.b.h.149.2 2 5.2 odd 4