Properties

Label 1450.2.a.c.1.1
Level $1450$
Weight $2$
Character 1450.1
Self dual yes
Analytic conductor $11.578$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1450.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5783082931\)
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 \(\chi\) \(=\) 1450.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} -3.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} -8.00000 q^{17} +2.00000 q^{18} +2.00000 q^{21} +3.00000 q^{22} -4.00000 q^{23} -1.00000 q^{24} -1.00000 q^{26} -5.00000 q^{27} +2.00000 q^{28} -1.00000 q^{29} -3.00000 q^{31} -1.00000 q^{32} -3.00000 q^{33} +8.00000 q^{34} -2.00000 q^{36} -8.00000 q^{37} +1.00000 q^{39} +2.00000 q^{41} -2.00000 q^{42} +11.0000 q^{43} -3.00000 q^{44} +4.00000 q^{46} -13.0000 q^{47} +1.00000 q^{48} -3.00000 q^{49} -8.00000 q^{51} +1.00000 q^{52} +11.0000 q^{53} +5.00000 q^{54} -2.00000 q^{56} +1.00000 q^{58} -8.00000 q^{61} +3.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} +3.00000 q^{66} +12.0000 q^{67} -8.00000 q^{68} -4.00000 q^{69} +2.00000 q^{71} +2.00000 q^{72} -4.00000 q^{73} +8.00000 q^{74} -6.00000 q^{77} -1.00000 q^{78} +15.0000 q^{79} +1.00000 q^{81} -2.00000 q^{82} -4.00000 q^{83} +2.00000 q^{84} -11.0000 q^{86} -1.00000 q^{87} +3.00000 q^{88} -10.0000 q^{89} +2.00000 q^{91} -4.00000 q^{92} -3.00000 q^{93} +13.0000 q^{94} -1.00000 q^{96} +2.00000 q^{97} +3.00000 q^{98} +6.00000 q^{99} +O(q^{100})\)

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
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) −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 \(0.455716\pi\)
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) 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 \(0.5\pi\)
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) 3.00000 0.639602
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) −1.00000 −0.196116
\(27\) −5.00000 −0.962250
\(28\) 2.00000 0.377964
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) −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 \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) −2.00000 −0.308607
\(43\) 11.0000 1.67748 0.838742 0.544529i \(-0.183292\pi\)
0.838742 + 0.544529i \(0.183292\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) 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
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) −8.00000 −1.12022
\(52\) 1.00000 0.138675
\(53\) 11.0000 1.51097 0.755483 0.655168i \(-0.227402\pi\)
0.755483 + 0.655168i \(0.227402\pi\)
\(54\) 5.00000 0.680414
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) 0 0
\(58\) 1.00000 0.131306
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 3.00000 0.381000
\(63\) −4.00000 −0.503953
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.00000 0.369274
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) −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
\(75\) 0 0
\(76\) 0 0
\(77\) −6.00000 −0.683763
\(78\) −1.00000 −0.113228
\(79\) 15.0000 1.68763 0.843816 0.536633i \(-0.180304\pi\)
0.843816 + 0.536633i \(0.180304\pi\)
\(80\) 0 0
\(81\) 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 \(0.570452\pi\)
\(84\) 2.00000 0.218218
\(85\) 0 0
\(86\) −11.0000 −1.18616
\(87\) −1.00000 −0.107211
\(88\) 3.00000 0.319801
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) −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 \(0.467625\pi\)
\(98\) 3.00000 0.303046
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) −8.00000 −0.796030 −0.398015 0.917379i \(-0.630301\pi\)
−0.398015 + 0.917379i \(0.630301\pi\)
\(102\) 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 \(-0.469180\pi\)
0.0966736 + 0.995316i \(0.469180\pi\)
\(108\) −5.00000 −0.481125
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 0 0
\(111\) −8.00000 −0.759326
\(112\) 2.00000 0.188982
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.00000 −0.0928477
\(117\) −2.00000 −0.184900
\(118\) 0 0
\(119\) −16.0000 −1.46672
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 8.00000 0.724286
\(123\) 2.00000 0.180334
\(124\) −3.00000 −0.269408
\(125\) 0 0
\(126\) 4.00000 0.356348
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 11.0000 0.968496
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) −3.00000 −0.261116
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) 8.00000 0.685994
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 4.00000 0.340503
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) −13.0000 −1.09480
\(142\) −2.00000 −0.167836
\(143\) −3.00000 −0.250873
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) −3.00000 −0.247436
\(148\) −8.00000 −0.657596
\(149\) 15.0000 1.22885 0.614424 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) 0 0
\(151\) 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
\(154\) 6.00000 0.483494
\(155\) 0 0
\(156\) 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
\(160\) 0 0
\(161\) −8.00000 −0.630488
\(162\) −1.00000 −0.0785674
\(163\) −9.00000 −0.704934 −0.352467 0.935824i \(-0.614657\pi\)
−0.352467 + 0.935824i \(0.614657\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) 4.00000 0.310460
\(167\) 2.00000 0.154765 0.0773823 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) −2.00000 −0.154303
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 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 \(0.621917\pi\)
\(180\) 0 0
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) −2.00000 −0.148250
\(183\) −8.00000 −0.591377
\(184\) 4.00000 0.294884
\(185\) 0 0
\(186\) 3.00000 0.219971
\(187\) 24.0000 1.75505
\(188\) −13.0000 −0.948122
\(189\) −10.0000 −0.727393
\(190\) 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 \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) −6.00000 −0.426401
\(199\) −10.0000 −0.708881 −0.354441 0.935079i \(-0.615329\pi\)
−0.354441 + 0.935079i \(0.615329\pi\)
\(200\) 0 0
\(201\) 12.0000 0.846415
\(202\) 8.00000 0.562878
\(203\) −2.00000 −0.140372
\(204\) −8.00000 −0.560112
\(205\) 0 0
\(206\) 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
\(215\) 0 0
\(216\) 5.00000 0.340207
\(217\) −6.00000 −0.407307
\(218\) −5.00000 −0.338643
\(219\) −4.00000 −0.270295
\(220\) 0 0
\(221\) −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 \(0.163767\pi\)
\(224\) −2.00000 −0.133631
\(225\) 0 0
\(226\) −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 \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) −6.00000 −0.394771
\(232\) 1.00000 0.0656532
\(233\) 1.00000 0.0655122 0.0327561 0.999463i \(-0.489572\pi\)
0.0327561 + 0.999463i \(0.489572\pi\)
\(234\) 2.00000 0.130744
\(235\) 0 0
\(236\) 0 0
\(237\) 15.0000 0.974355
\(238\) 16.0000 1.03713
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 17.0000 1.09507 0.547533 0.836784i \(-0.315567\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 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
\(250\) 0 0
\(251\) 27.0000 1.70422 0.852112 0.523359i \(-0.175321\pi\)
0.852112 + 0.523359i \(0.175321\pi\)
\(252\) −4.00000 −0.251976
\(253\) 12.0000 0.754434
\(254\) 8.00000 0.501965
\(255\) 0 0
\(256\) 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
\(259\) −16.0000 −0.994192
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) −12.0000 −0.741362
\(263\) −9.00000 −0.554964 −0.277482 0.960731i \(-0.589500\pi\)
−0.277482 + 0.960731i \(0.589500\pi\)
\(264\) 3.00000 0.184637
\(265\) 0 0
\(266\) 0 0
\(267\) −10.0000 −0.611990
\(268\) 12.0000 0.733017
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) −13.0000 −0.789694 −0.394847 0.918747i \(-0.629202\pi\)
−0.394847 + 0.918747i \(0.629202\pi\)
\(272\) −8.00000 −0.485071
\(273\) 2.00000 0.121046
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) −4.00000 −0.240772
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) 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
\(287\) 4.00000 0.236113
\(288\) 2.00000 0.117851
\(289\) 47.0000 2.76471
\(290\) 0 0
\(291\) 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 \(0.634103\pi\)
\(294\) 3.00000 0.174964
\(295\) 0 0
\(296\) 8.00000 0.464991
\(297\) 15.0000 0.870388
\(298\) −15.0000 −0.868927
\(299\) −4.00000 −0.231326
\(300\) 0 0
\(301\) 22.0000 1.26806
\(302\) −2.00000 −0.115087
\(303\) −8.00000 −0.459588
\(304\) 0 0
\(305\) 0 0
\(306\) −16.0000 −0.914659
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) −6.00000 −0.341882
\(309\) −14.0000 −0.796432
\(310\) 0 0
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) −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 \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) −11.0000 −0.616849
\(319\) 3.00000 0.167968
\(320\) 0 0
\(321\) 2.00000 0.111629
\(322\) 8.00000 0.445823
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 9.00000 0.498464
\(327\) 5.00000 0.276501
\(328\) −2.00000 −0.110432
\(329\) −26.0000 −1.43343
\(330\) 0 0
\(331\) −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
\(335\) 0 0
\(336\) 2.00000 0.109109
\(337\) 32.0000 1.74315 0.871576 0.490261i \(-0.163099\pi\)
0.871576 + 0.490261i \(0.163099\pi\)
\(338\) 12.0000 0.652714
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) 9.00000 0.487377
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) −11.0000 −0.593080
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) 2.00000 0.107366 0.0536828 0.998558i \(-0.482904\pi\)
0.0536828 + 0.998558i \(0.482904\pi\)
\(348\) −1.00000 −0.0536056
\(349\) −15.0000 −0.802932 −0.401466 0.915874i \(-0.631499\pi\)
−0.401466 + 0.915874i \(0.631499\pi\)
\(350\) 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
\(355\) 0 0
\(356\) −10.0000 −0.529999
\(357\) −16.0000 −0.846810
\(358\) 10.0000 0.528516
\(359\) −25.0000 −1.31945 −0.659725 0.751507i \(-0.729327\pi\)
−0.659725 + 0.751507i \(0.729327\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) −7.00000 −0.367912
\(363\) −2.00000 −0.104973
\(364\) 2.00000 0.104828
\(365\) 0 0
\(366\) 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
\(370\) 0 0
\(371\) 22.0000 1.14218
\(372\) −3.00000 −0.155543
\(373\) 21.0000 1.08734 0.543669 0.839299i \(-0.317035\pi\)
0.543669 + 0.839299i \(0.317035\pi\)
\(374\) −24.0000 −1.24101
\(375\) 0 0
\(376\) 13.0000 0.670424
\(377\) −1.00000 −0.0515026
\(378\) 10.0000 0.514344
\(379\) 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 \(0.5\pi\)
\(390\) 0 0
\(391\) 32.0000 1.61831
\(392\) 3.00000 0.151523
\(393\) 12.0000 0.605320
\(394\) 18.0000 0.906827
\(395\) 0 0
\(396\) 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
\(400\) 0 0
\(401\) 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
\(405\) 0 0
\(406\) 2.00000 0.0992583
\(407\) 24.0000 1.18964
\(408\) 8.00000 0.396059
\(409\) 30.0000 1.48340 0.741702 0.670729i \(-0.234019\pi\)
0.741702 + 0.670729i \(0.234019\pi\)
\(410\) 0 0
\(411\) 12.0000 0.591916
\(412\) −14.0000 −0.689730
\(413\) 0 0
\(414\) −8.00000 −0.393179
\(415\) 0 0
\(416\) −1.00000 −0.0490290
\(417\) −20.0000 −0.979404
\(418\) 0 0
\(419\) −10.0000 −0.488532 −0.244266 0.969708i \(-0.578547\pi\)
−0.244266 + 0.969708i \(0.578547\pi\)
\(420\) 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
\(425\) 0 0
\(426\) −2.00000 −0.0969003
\(427\) −16.0000 −0.774294
\(428\) 2.00000 0.0966736
\(429\) −3.00000 −0.144841
\(430\) 0 0
\(431\) 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 \(0.374389\pi\)
\(434\) 6.00000 0.288009
\(435\) 0 0
\(436\) 5.00000 0.239457
\(437\) 0 0
\(438\) 4.00000 0.191127
\(439\) 20.0000 0.954548 0.477274 0.878755i \(-0.341625\pi\)
0.477274 + 0.878755i \(0.341625\pi\)
\(440\) 0 0
\(441\) 6.00000 0.285714
\(442\) 8.00000 0.380521
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) −8.00000 −0.379663
\(445\) 0 0
\(446\) −26.0000 −1.23114
\(447\) 15.0000 0.709476
\(448\) 2.00000 0.0944911
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 0 0
\(451\) −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 \(-0.485105\pi\)
0.0467780 + 0.998905i \(0.485105\pi\)
\(458\) −10.0000 −0.467269
\(459\) 40.0000 1.86704
\(460\) 0 0
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 6.00000 0.279145
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) −1.00000 −0.0464238
\(465\) 0 0
\(466\) −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
\(469\) 24.0000 1.10822
\(470\) 0 0
\(471\) −18.0000 −0.829396
\(472\) 0 0
\(473\) −33.0000 −1.51734
\(474\) −15.0000 −0.688973
\(475\) 0 0
\(476\) −16.0000 −0.733359
\(477\) −22.0000 −1.00731
\(478\) 0 0
\(479\) −5.00000 −0.228456 −0.114228 0.993455i \(-0.536439\pi\)
−0.114228 + 0.993455i \(0.536439\pi\)
\(480\) 0 0
\(481\) −8.00000 −0.364769
\(482\) −17.0000 −0.774329
\(483\) −8.00000 −0.364013
\(484\) −2.00000 −0.0909091
\(485\) 0 0
\(486\) −16.0000 −0.725775
\(487\) 22.0000 0.996915 0.498458 0.866914i \(-0.333900\pi\)
0.498458 + 0.866914i \(0.333900\pi\)
\(488\) 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
\(495\) 0 0
\(496\) −3.00000 −0.134704
\(497\) 4.00000 0.179425
\(498\) 4.00000 0.179244
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 0 0
\(501\) 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 \(0.639228\pi\)
\(504\) 4.00000 0.178174
\(505\) 0 0
\(506\) −12.0000 −0.533465
\(507\) −12.0000 −0.532939
\(508\) −8.00000 −0.354943
\(509\) −15.0000 −0.664863 −0.332432 0.943127i \(-0.607869\pi\)
−0.332432 + 0.943127i \(0.607869\pi\)
\(510\) 0 0
\(511\) −8.00000 −0.353899
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 13.0000 0.573405
\(515\) 0 0
\(516\) 11.0000 0.484248
\(517\) 39.0000 1.71522
\(518\) 16.0000 0.703000
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −13.0000 −0.569540 −0.284770 0.958596i \(-0.591917\pi\)
−0.284770 + 0.958596i \(0.591917\pi\)
\(522\) −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
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.00000 0.0866296
\(534\) 10.0000 0.432742
\(535\) 0 0
\(536\) −12.0000 −0.518321
\(537\) −10.0000 −0.431532
\(538\) 0 0
\(539\) 9.00000 0.387657
\(540\) 0 0
\(541\) −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
\(545\) 0 0
\(546\) −2.00000 −0.0855921
\(547\) −38.0000 −1.62476 −0.812381 0.583127i \(-0.801829\pi\)
−0.812381 + 0.583127i \(0.801829\pi\)
\(548\) 12.0000 0.512615
\(549\) 16.0000 0.682863
\(550\) 0 0
\(551\) 0 0
\(552\) 4.00000 0.170251
\(553\) 30.0000 1.27573
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) −20.0000 −0.848189
\(557\) 2.00000 0.0847427 0.0423714 0.999102i \(-0.486509\pi\)
0.0423714 + 0.999102i \(0.486509\pi\)
\(558\) −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
\(565\) 0 0
\(566\) 4.00000 0.168133
\(567\) 2.00000 0.0839921
\(568\) −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
\(574\) −4.00000 −0.166957
\(575\) 0 0
\(576\) −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
\(580\) 0 0
\(581\) −8.00000 −0.331896
\(582\) −2.00000 −0.0829027
\(583\) −33.0000 −1.36672
\(584\) 4.00000 0.165521
\(585\) 0 0
\(586\) 14.0000 0.578335
\(587\) −28.0000 −1.15568 −0.577842 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) −3.00000 −0.123718
\(589\) 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 \(0.532571\pi\)
\(600\) 0 0
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) −22.0000 −0.896653
\(603\) −24.0000 −0.977356
\(604\) 2.00000 0.0813788
\(605\) 0 0
\(606\) 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
\(609\) −2.00000 −0.0810441
\(610\) 0 0
\(611\) −13.0000 −0.525924
\(612\) 16.0000 0.646762
\(613\) 31.0000 1.25208 0.626039 0.779792i \(-0.284675\pi\)
0.626039 + 0.779792i \(0.284675\pi\)
\(614\) −7.00000 −0.282497
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) 12.0000 0.483102 0.241551 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) 14.0000 0.563163
\(619\) −35.0000 −1.40677 −0.703384 0.710810i \(-0.748329\pi\)
−0.703384 + 0.710810i \(0.748329\pi\)
\(620\) 0 0
\(621\) 20.0000 0.802572
\(622\) 8.00000 0.320771
\(623\) −20.0000 −0.801283
\(624\) 1.00000 0.0400320
\(625\) 0 0
\(626\) 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
\(635\) 0 0
\(636\) 11.0000 0.436178
\(637\) −3.00000 −0.118864
\(638\) −3.00000 −0.118771
\(639\) −4.00000 −0.158238
\(640\) 0 0
\(641\) −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 \(0.733884\pi\)
\(644\) −8.00000 −0.315244
\(645\) 0 0
\(646\) 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
\(650\) 0 0
\(651\) −6.00000 −0.235159
\(652\) −9.00000 −0.352467
\(653\) 26.0000 1.01746 0.508729 0.860927i \(-0.330115\pi\)
0.508729 + 0.860927i \(0.330115\pi\)
\(654\) −5.00000 −0.195515
\(655\) 0 0
\(656\) 2.00000 0.0780869
\(657\) 8.00000 0.312110
\(658\) 26.0000 1.01359
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) 0 0
\(661\) −18.0000 −0.700119 −0.350059 0.936727i \(-0.613839\pi\)
−0.350059 + 0.936727i \(0.613839\pi\)
\(662\) 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
\(670\) 0 0
\(671\) 24.0000 0.926510
\(672\) −2.00000 −0.0771517
\(673\) −9.00000 −0.346925 −0.173462 0.984841i \(-0.555495\pi\)
−0.173462 + 0.984841i \(0.555495\pi\)
\(674\) −32.0000 −1.23259
\(675\) 0 0
\(676\) −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
\(679\) 4.00000 0.153506
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) −9.00000 −0.344628
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 20.0000 0.763604
\(687\) 10.0000 0.381524
\(688\) 11.0000 0.419371
\(689\) 11.0000 0.419067
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 6.00000 0.228086
\(693\) 12.0000 0.455842
\(694\) −2.00000 −0.0759190
\(695\) 0 0
\(696\) 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
\(705\) 0 0
\(706\) −26.0000 −0.978523
\(707\) −16.0000 −0.601742
\(708\) 0 0
\(709\) 15.0000 0.563337 0.281668 0.959512i \(-0.409112\pi\)
0.281668 + 0.959512i \(0.409112\pi\)
\(710\) 0 0
\(711\) −30.0000 −1.12509
\(712\) 10.0000 0.374766
\(713\) 12.0000 0.449404
\(714\) 16.0000 0.598785
\(715\) 0 0
\(716\) −10.0000 −0.373718
\(717\) 0 0
\(718\) 25.0000 0.932992
\(719\) −50.0000 −1.86469 −0.932343 0.361576i \(-0.882239\pi\)
−0.932343 + 0.361576i \(0.882239\pi\)
\(720\) 0 0
\(721\) −28.0000 −1.04277
\(722\) 19.0000 0.707107
\(723\) 17.0000 0.632237
\(724\) 7.00000 0.260153
\(725\) 0 0
\(726\) 2.00000 0.0742270
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) −2.00000 −0.0741249
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −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 \(0.529314\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −22.0000 −0.807645
\(743\) −44.0000 −1.61420 −0.807102 0.590412i \(-0.798965\pi\)
−0.807102 + 0.590412i \(0.798965\pi\)
\(744\) 3.00000 0.109985
\(745\) 0 0
\(746\) −21.0000 −0.768865
\(747\) 8.00000 0.292705
\(748\) 24.0000 0.877527
\(749\) 4.00000 0.146157
\(750\) 0 0
\(751\) 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
\(755\) 0 0
\(756\) −10.0000 −0.363696
\(757\) −8.00000 −0.290765 −0.145382 0.989376i \(-0.546441\pi\)
−0.145382 + 0.989376i \(0.546441\pi\)
\(758\) −20.0000 −0.726433
\(759\) 12.0000 0.435572
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 8.00000 0.289809
\(763\) 10.0000 0.362024
\(764\) −8.00000 −0.289430
\(765\) 0 0
\(766\) 14.0000 0.505841
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −20.0000 −0.721218 −0.360609 0.932717i \(-0.617431\pi\)
−0.360609 + 0.932717i \(0.617431\pi\)
\(770\) 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
\(775\) 0 0
\(776\) −2.00000 −0.0717958
\(777\) −16.0000 −0.573997
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −6.00000 −0.214697
\(782\) −32.0000 −1.14432
\(783\) 5.00000 0.178685
\(784\) −3.00000 −0.107143
\(785\) 0 0
\(786\) −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
\(790\) 0 0
\(791\) 12.0000 0.426671
\(792\) −6.00000 −0.213201
\(793\) −8.00000 −0.284088
\(794\) −17.0000 −0.603307
\(795\) 0 0
\(796\) −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
\(800\) 0 0
\(801\) 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 \(0.5\pi\)
\(810\) 0 0
\(811\) −18.0000 −0.632065 −0.316033 0.948748i \(-0.602351\pi\)
−0.316033 + 0.948748i \(0.602351\pi\)
\(812\) −2.00000 −0.0701862
\(813\) −13.0000 −0.455930
\(814\) −24.0000 −0.841200
\(815\) 0 0
\(816\) −8.00000 −0.280056
\(817\) 0 0
\(818\) −30.0000 −1.04893
\(819\) −4.00000 −0.139771
\(820\) 0 0
\(821\) −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 \(-0.410043\pi\)
0.278862 + 0.960331i \(0.410043\pi\)
\(824\) 14.0000 0.487713
\(825\) 0 0
\(826\) 0 0
\(827\) −13.0000 −0.452054 −0.226027 0.974121i \(-0.572574\pi\)
−0.226027 + 0.974121i \(0.572574\pi\)
\(828\) 8.00000 0.278019
\(829\) 40.0000 1.38926 0.694629 0.719368i \(-0.255569\pi\)
0.694629 + 0.719368i \(0.255569\pi\)
\(830\) 0 0
\(831\) 2.00000 0.0693792
\(832\) 1.00000 0.0346688
\(833\) 24.0000 0.831551
\(834\) 20.0000 0.692543
\(835\) 0 0
\(836\) 0 0
\(837\) 15.0000 0.518476
\(838\) 10.0000 0.345444
\(839\) 45.0000 1.55357 0.776786 0.629764i \(-0.216849\pi\)
0.776786 + 0.629764i \(0.216849\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −32.0000 −1.10279
\(843\) 27.0000 0.929929
\(844\) −3.00000 −0.103264
\(845\) 0 0
\(846\) −26.0000 −0.893898
\(847\) −4.00000 −0.137442
\(848\) 11.0000 0.377742
\(849\) −4.00000 −0.137280
\(850\) 0 0
\(851\) 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 \(0.577041\pi\)
\(854\) 16.0000 0.547509
\(855\) 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 \(-0.640252\pi\)
−0.426494 + 0.904490i \(0.640252\pi\)
\(860\) 0 0
\(861\) 4.00000 0.136320
\(862\) −32.0000 −1.08992
\(863\) 46.0000 1.56586 0.782929 0.622111i \(-0.213725\pi\)
0.782929 + 0.622111i \(0.213725\pi\)
\(864\) 5.00000 0.170103
\(865\) 0 0
\(866\) −16.0000 −0.543702
\(867\) 47.0000 1.59620
\(868\) −6.00000 −0.203653
\(869\) −45.0000 −1.52652
\(870\) 0 0
\(871\) 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 \(-0.570439\pi\)
−0.219489 + 0.975615i \(0.570439\pi\)
\(878\) −20.0000 −0.674967
\(879\) −14.0000 −0.472208
\(880\) 0 0
\(881\) 42.0000 1.41502 0.707508 0.706705i \(-0.249819\pi\)
0.707508 + 0.706705i \(0.249819\pi\)
\(882\) −6.00000 −0.202031
\(883\) 26.0000 0.874970 0.437485 0.899226i \(-0.355869\pi\)
0.437485 + 0.899226i \(0.355869\pi\)
\(884\) −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
\(889\) −16.0000 −0.536623
\(890\) 0 0
\(891\) −3.00000 −0.100504
\(892\) 26.0000 0.870544
\(893\) 0 0
\(894\) −15.0000 −0.501675
\(895\) 0 0
\(896\) −2.00000 −0.0668153
\(897\) −4.00000 −0.133556
\(898\) 10.0000 0.333704
\(899\) 3.00000 0.100056
\(900\) 0 0
\(901\) −88.0000 −2.93171
\(902\) 6.00000 0.199778
\(903\) 22.0000 0.732114
\(904\) −6.00000 −0.199557
\(905\) 0 0
\(906\) −2.00000 −0.0664455
\(907\) −28.0000 −0.929725 −0.464862 0.885383i \(-0.653896\pi\)
−0.464862 + 0.885383i \(0.653896\pi\)
\(908\) −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
\(915\) 0 0
\(916\) 10.0000 0.330409
\(917\) 24.0000 0.792550
\(918\) −40.0000 −1.32020
\(919\) 30.0000 0.989609 0.494804 0.869004i \(-0.335240\pi\)
0.494804 + 0.869004i \(0.335240\pi\)
\(920\) 0 0
\(921\) 7.00000 0.230658
\(922\) −2.00000 −0.0658665
\(923\) 2.00000 0.0658308
\(924\) −6.00000 −0.197386
\(925\) 0 0
\(926\) 4.00000 0.131448
\(927\) 28.0000 0.919641
\(928\) 1.00000 0.0328266
\(929\) −30.0000 −0.984268 −0.492134 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 1.00000 0.0327561
\(933\) −8.00000 −0.261908
\(934\) −27.0000 −0.883467
\(935\) 0 0
\(936\) 2.00000 0.0653720
\(937\) 2.00000 0.0653372 0.0326686 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) −24.0000 −0.783628
\(939\) −9.00000 −0.293704
\(940\) 0 0
\(941\) 37.0000 1.20617 0.603083 0.797679i \(-0.293939\pi\)
0.603083 + 0.797679i \(0.293939\pi\)
\(942\) 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 \(-0.680132\pi\)
−0.536178 + 0.844105i \(0.680132\pi\)
\(948\) 15.0000 0.487177
\(949\) −4.00000 −0.129845
\(950\) 0 0
\(951\) 12.0000 0.389127
\(952\) 16.0000 0.518563
\(953\) 1.00000 0.0323932 0.0161966 0.999869i \(-0.494844\pi\)
0.0161966 + 0.999869i \(0.494844\pi\)
\(954\) 22.0000 0.712276
\(955\) 0 0
\(956\) 0 0
\(957\) 3.00000 0.0969762
\(958\) 5.00000 0.161543
\(959\) 24.0000 0.775000
\(960\) 0 0
\(961\) −22.0000 −0.709677
\(962\) 8.00000 0.257930
\(963\) −4.00000 −0.128898
\(964\) 17.0000 0.547533
\(965\) 0 0
\(966\) 8.00000 0.257396
\(967\) −13.0000 −0.418052 −0.209026 0.977910i \(-0.567029\pi\)
−0.209026 + 0.977910i \(0.567029\pi\)
\(968\) 2.00000 0.0642824
\(969\) 0 0
\(970\) 0 0
\(971\) −28.0000 −0.898563 −0.449281 0.893390i \(-0.648320\pi\)
−0.449281 + 0.893390i \(0.648320\pi\)
\(972\) 16.0000 0.513200
\(973\) −40.0000 −1.28234
\(974\) −22.0000 −0.704925
\(975\) 0 0
\(976\) −8.00000 −0.256074
\(977\) −13.0000 −0.415907 −0.207953 0.978139i \(-0.566680\pi\)
−0.207953 + 0.978139i \(0.566680\pi\)
\(978\) 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
\(985\) 0 0
\(986\) −8.00000 −0.254772
\(987\) −26.0000 −0.827589
\(988\) 0 0
\(989\) −44.0000 −1.39912
\(990\) 0 0
\(991\) 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
\(994\) −4.00000 −0.126872
\(995\) 0 0
\(996\) −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 1450.2.a.c.1.1 1
5.2 odd 4 1450.2.b.b.349.1 2
5.3 odd 4 1450.2.b.b.349.2 2
5.4 even 2 58.2.a.b.1.1 1
15.14 odd 2 522.2.a.b.1.1 1
20.19 odd 2 464.2.a.e.1.1 1
35.34 odd 2 2842.2.a.e.1.1 1
40.19 odd 2 1856.2.a.f.1.1 1
40.29 even 2 1856.2.a.k.1.1 1
55.54 odd 2 7018.2.a.a.1.1 1
60.59 even 2 4176.2.a.n.1.1 1
65.64 even 2 9802.2.a.a.1.1 1
145.99 odd 4 1682.2.b.a.1681.2 2
145.104 odd 4 1682.2.b.a.1681.1 2
145.144 even 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 5.4 even 2
464.2.a.e.1.1 1 20.19 odd 2
522.2.a.b.1.1 1 15.14 odd 2
1450.2.a.c.1.1 1 1.1 even 1 trivial
1450.2.b.b.349.1 2 5.2 odd 4
1450.2.b.b.349.2 2 5.3 odd 4
1682.2.a.d.1.1 1 145.144 even 2
1682.2.b.a.1681.1 2 145.104 odd 4
1682.2.b.a.1681.2 2 145.99 odd 4
1856.2.a.f.1.1 1 40.19 odd 2
1856.2.a.k.1.1 1 40.29 even 2
2842.2.a.e.1.1 1 35.34 odd 2
4176.2.a.n.1.1 1 60.59 even 2
7018.2.a.a.1.1 1 55.54 odd 2
9802.2.a.a.1.1 1 65.64 even 2