Properties

Label 950.2.a.a.1.1
Level $950$
Weight $2$
Character 950.1
Self dual yes
Analytic conductor $7.586$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 950.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} +2.00000 q^{18} +1.00000 q^{19} -1.00000 q^{21} -3.00000 q^{23} +1.00000 q^{24} -1.00000 q^{26} +5.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} +2.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} -2.00000 q^{36} +10.0000 q^{37} -1.00000 q^{38} -1.00000 q^{39} +6.00000 q^{41} +1.00000 q^{42} -2.00000 q^{43} +3.00000 q^{46} -1.00000 q^{48} -6.00000 q^{49} -3.00000 q^{51} +1.00000 q^{52} -3.00000 q^{53} -5.00000 q^{54} -1.00000 q^{56} -1.00000 q^{57} +3.00000 q^{58} +3.00000 q^{59} +8.00000 q^{61} -2.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +7.00000 q^{67} +3.00000 q^{68} +3.00000 q^{69} +12.0000 q^{71} +2.00000 q^{72} +13.0000 q^{73} -10.0000 q^{74} +1.00000 q^{76} +1.00000 q^{78} +14.0000 q^{79} +1.00000 q^{81} -6.00000 q^{82} -6.00000 q^{83} -1.00000 q^{84} +2.00000 q^{86} +3.00000 q^{87} +6.00000 q^{89} +1.00000 q^{91} -3.00000 q^{92} -2.00000 q^{93} +1.00000 q^{96} +10.0000 q^{97} +6.00000 q^{98} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 2.00000 0.471405
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 1.00000 0.204124
\(25\) 0 0
\(26\) −1.00000 −0.196116
\(27\) 5.00000 0.962250
\(28\) 1.00000 0.188982
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) −1.00000 −0.162221
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 1.00000 0.154303
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) −3.00000 −0.420084
\(52\) 1.00000 0.138675
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) −5.00000 −0.680414
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) −1.00000 −0.132453
\(58\) 3.00000 0.393919
\(59\) 3.00000 0.390567 0.195283 0.980747i \(-0.437437\pi\)
0.195283 + 0.980747i \(0.437437\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) −2.00000 −0.254000
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 7.00000 0.855186 0.427593 0.903971i \(-0.359362\pi\)
0.427593 + 0.903971i \(0.359362\pi\)
\(68\) 3.00000 0.363803
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 2.00000 0.235702
\(73\) 13.0000 1.52153 0.760767 0.649025i \(-0.224823\pi\)
0.760767 + 0.649025i \(0.224823\pi\)
\(74\) −10.0000 −1.16248
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) 14.0000 1.57512 0.787562 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −6.00000 −0.662589
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) 2.00000 0.215666
\(87\) 3.00000 0.321634
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) −3.00000 −0.312772
\(93\) −2.00000 −0.207390
\(94\) 0 0
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) 6.00000 0.606092
\(99\) 0 0
\(100\) 0 0
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 3.00000 0.297044
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) −15.0000 −1.45010 −0.725052 0.688694i \(-0.758184\pi\)
−0.725052 + 0.688694i \(0.758184\pi\)
\(108\) 5.00000 0.481125
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) 0 0
\(111\) −10.0000 −0.949158
\(112\) 1.00000 0.0944911
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 1.00000 0.0936586
\(115\) 0 0
\(116\) −3.00000 −0.278543
\(117\) −2.00000 −0.184900
\(118\) −3.00000 −0.276172
\(119\) 3.00000 0.275010
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) −8.00000 −0.724286
\(123\) −6.00000 −0.541002
\(124\) 2.00000 0.179605
\(125\) 0 0
\(126\) 2.00000 0.178174
\(127\) −2.00000 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.00000 0.176090
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 1.00000 0.0867110
\(134\) −7.00000 −0.604708
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) −3.00000 −0.255377
\(139\) 8.00000 0.678551 0.339276 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −12.0000 −1.00702
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) −13.0000 −1.07589
\(147\) 6.00000 0.494872
\(148\) 10.0000 0.821995
\(149\) −12.0000 −0.983078 −0.491539 0.870855i \(-0.663566\pi\)
−0.491539 + 0.870855i \(0.663566\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) −1.00000 −0.0800641
\(157\) 10.0000 0.798087 0.399043 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) −14.0000 −1.11378
\(159\) 3.00000 0.237915
\(160\) 0 0
\(161\) −3.00000 −0.236433
\(162\) −1.00000 −0.0785674
\(163\) 22.0000 1.72317 0.861586 0.507611i \(-0.169471\pi\)
0.861586 + 0.507611i \(0.169471\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 6.00000 0.465690
\(167\) −18.0000 −1.39288 −0.696441 0.717614i \(-0.745234\pi\)
−0.696441 + 0.717614i \(0.745234\pi\)
\(168\) 1.00000 0.0771517
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −2.00000 −0.152944
\(172\) −2.00000 −0.152499
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −3.00000 −0.227429
\(175\) 0 0
\(176\) 0 0
\(177\) −3.00000 −0.225494
\(178\) −6.00000 −0.449719
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −1.00000 −0.0741249
\(183\) −8.00000 −0.591377
\(184\) 3.00000 0.221163
\(185\) 0 0
\(186\) 2.00000 0.146647
\(187\) 0 0
\(188\) 0 0
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) −27.0000 −1.95365 −0.976826 0.214036i \(-0.931339\pi\)
−0.976826 + 0.214036i \(0.931339\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 22.0000 1.58359 0.791797 0.610784i \(-0.209146\pi\)
0.791797 + 0.610784i \(0.209146\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) −19.0000 −1.34687 −0.673437 0.739244i \(-0.735183\pi\)
−0.673437 + 0.739244i \(0.735183\pi\)
\(200\) 0 0
\(201\) −7.00000 −0.493742
\(202\) −12.0000 −0.844317
\(203\) −3.00000 −0.210559
\(204\) −3.00000 −0.210042
\(205\) 0 0
\(206\) 8.00000 0.557386
\(207\) 6.00000 0.417029
\(208\) 1.00000 0.0693375
\(209\) 0 0
\(210\) 0 0
\(211\) −25.0000 −1.72107 −0.860535 0.509390i \(-0.829871\pi\)
−0.860535 + 0.509390i \(0.829871\pi\)
\(212\) −3.00000 −0.206041
\(213\) −12.0000 −0.822226
\(214\) 15.0000 1.02538
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) 2.00000 0.135769
\(218\) −11.0000 −0.745014
\(219\) −13.0000 −0.878459
\(220\) 0 0
\(221\) 3.00000 0.201802
\(222\) 10.0000 0.671156
\(223\) −14.0000 −0.937509 −0.468755 0.883328i \(-0.655297\pi\)
−0.468755 + 0.883328i \(0.655297\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) −12.0000 −0.798228
\(227\) 15.0000 0.995585 0.497792 0.867296i \(-0.334144\pi\)
0.497792 + 0.867296i \(0.334144\pi\)
\(228\) −1.00000 −0.0662266
\(229\) 26.0000 1.71813 0.859064 0.511868i \(-0.171046\pi\)
0.859064 + 0.511868i \(0.171046\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 0.196960
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 2.00000 0.130744
\(235\) 0 0
\(236\) 3.00000 0.195283
\(237\) −14.0000 −0.909398
\(238\) −3.00000 −0.194461
\(239\) −15.0000 −0.970269 −0.485135 0.874439i \(-0.661229\pi\)
−0.485135 + 0.874439i \(0.661229\pi\)
\(240\) 0 0
\(241\) −4.00000 −0.257663 −0.128831 0.991667i \(-0.541123\pi\)
−0.128831 + 0.991667i \(0.541123\pi\)
\(242\) 11.0000 0.707107
\(243\) −16.0000 −1.02640
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) 1.00000 0.0636285
\(248\) −2.00000 −0.127000
\(249\) 6.00000 0.380235
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) 2.00000 0.125491
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) −2.00000 −0.124515
\(259\) 10.0000 0.621370
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −1.00000 −0.0613139
\(267\) −6.00000 −0.367194
\(268\) 7.00000 0.427593
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) −7.00000 −0.425220 −0.212610 0.977137i \(-0.568196\pi\)
−0.212610 + 0.977137i \(0.568196\pi\)
\(272\) 3.00000 0.181902
\(273\) −1.00000 −0.0605228
\(274\) 9.00000 0.543710
\(275\) 0 0
\(276\) 3.00000 0.180579
\(277\) −8.00000 −0.480673 −0.240337 0.970690i \(-0.577258\pi\)
−0.240337 + 0.970690i \(0.577258\pi\)
\(278\) −8.00000 −0.479808
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) −14.0000 −0.832214 −0.416107 0.909316i \(-0.636606\pi\)
−0.416107 + 0.909316i \(0.636606\pi\)
\(284\) 12.0000 0.712069
\(285\) 0 0
\(286\) 0 0
\(287\) 6.00000 0.354169
\(288\) 2.00000 0.117851
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −10.0000 −0.586210
\(292\) 13.0000 0.760767
\(293\) −21.0000 −1.22683 −0.613417 0.789760i \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) −6.00000 −0.349927
\(295\) 0 0
\(296\) −10.0000 −0.581238
\(297\) 0 0
\(298\) 12.0000 0.695141
\(299\) −3.00000 −0.173494
\(300\) 0 0
\(301\) −2.00000 −0.115278
\(302\) 10.0000 0.575435
\(303\) −12.0000 −0.689382
\(304\) 1.00000 0.0573539
\(305\) 0 0
\(306\) 6.00000 0.342997
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) −3.00000 −0.170114 −0.0850572 0.996376i \(-0.527107\pi\)
−0.0850572 + 0.996376i \(0.527107\pi\)
\(312\) 1.00000 0.0566139
\(313\) 1.00000 0.0565233 0.0282617 0.999601i \(-0.491003\pi\)
0.0282617 + 0.999601i \(0.491003\pi\)
\(314\) −10.0000 −0.564333
\(315\) 0 0
\(316\) 14.0000 0.787562
\(317\) −9.00000 −0.505490 −0.252745 0.967533i \(-0.581333\pi\)
−0.252745 + 0.967533i \(0.581333\pi\)
\(318\) −3.00000 −0.168232
\(319\) 0 0
\(320\) 0 0
\(321\) 15.0000 0.837218
\(322\) 3.00000 0.167183
\(323\) 3.00000 0.166924
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −22.0000 −1.21847
\(327\) −11.0000 −0.608301
\(328\) −6.00000 −0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) 5.00000 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) −6.00000 −0.329293
\(333\) −20.0000 −1.09599
\(334\) 18.0000 0.984916
\(335\) 0 0
\(336\) −1.00000 −0.0545545
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 12.0000 0.652714
\(339\) −12.0000 −0.651751
\(340\) 0 0
\(341\) 0 0
\(342\) 2.00000 0.108148
\(343\) −13.0000 −0.701934
\(344\) 2.00000 0.107833
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) 30.0000 1.61048 0.805242 0.592946i \(-0.202035\pi\)
0.805242 + 0.592946i \(0.202035\pi\)
\(348\) 3.00000 0.160817
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) 33.0000 1.75641 0.878206 0.478282i \(-0.158740\pi\)
0.878206 + 0.478282i \(0.158740\pi\)
\(354\) 3.00000 0.159448
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) −3.00000 −0.158777
\(358\) 0 0
\(359\) −33.0000 −1.74167 −0.870837 0.491572i \(-0.836422\pi\)
−0.870837 + 0.491572i \(0.836422\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −2.00000 −0.105118
\(363\) 11.0000 0.577350
\(364\) 1.00000 0.0524142
\(365\) 0 0
\(366\) 8.00000 0.418167
\(367\) 16.0000 0.835193 0.417597 0.908633i \(-0.362873\pi\)
0.417597 + 0.908633i \(0.362873\pi\)
\(368\) −3.00000 −0.156386
\(369\) −12.0000 −0.624695
\(370\) 0 0
\(371\) −3.00000 −0.155752
\(372\) −2.00000 −0.103695
\(373\) 31.0000 1.60512 0.802560 0.596572i \(-0.203471\pi\)
0.802560 + 0.596572i \(0.203471\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.00000 −0.154508
\(378\) −5.00000 −0.257172
\(379\) 35.0000 1.79783 0.898915 0.438124i \(-0.144357\pi\)
0.898915 + 0.438124i \(0.144357\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) 27.0000 1.38144
\(383\) 24.0000 1.22634 0.613171 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −22.0000 −1.11977
\(387\) 4.00000 0.203331
\(388\) 10.0000 0.507673
\(389\) −24.0000 −1.21685 −0.608424 0.793612i \(-0.708198\pi\)
−0.608424 + 0.793612i \(0.708198\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 6.00000 0.303046
\(393\) 0 0
\(394\) 6.00000 0.302276
\(395\) 0 0
\(396\) 0 0
\(397\) −8.00000 −0.401508 −0.200754 0.979642i \(-0.564339\pi\)
−0.200754 + 0.979642i \(0.564339\pi\)
\(398\) 19.0000 0.952384
\(399\) −1.00000 −0.0500626
\(400\) 0 0
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) 7.00000 0.349128
\(403\) 2.00000 0.0996271
\(404\) 12.0000 0.597022
\(405\) 0 0
\(406\) 3.00000 0.148888
\(407\) 0 0
\(408\) 3.00000 0.148522
\(409\) −22.0000 −1.08783 −0.543915 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) −8.00000 −0.394132
\(413\) 3.00000 0.147620
\(414\) −6.00000 −0.294884
\(415\) 0 0
\(416\) −1.00000 −0.0490290
\(417\) −8.00000 −0.391762
\(418\) 0 0
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 0 0
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) 25.0000 1.21698
\(423\) 0 0
\(424\) 3.00000 0.145693
\(425\) 0 0
\(426\) 12.0000 0.581402
\(427\) 8.00000 0.387147
\(428\) −15.0000 −0.725052
\(429\) 0 0
\(430\) 0 0
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 5.00000 0.240563
\(433\) 4.00000 0.192228 0.0961139 0.995370i \(-0.469359\pi\)
0.0961139 + 0.995370i \(0.469359\pi\)
\(434\) −2.00000 −0.0960031
\(435\) 0 0
\(436\) 11.0000 0.526804
\(437\) −3.00000 −0.143509
\(438\) 13.0000 0.621164
\(439\) 38.0000 1.81364 0.906821 0.421517i \(-0.138502\pi\)
0.906821 + 0.421517i \(0.138502\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) −3.00000 −0.142695
\(443\) 24.0000 1.14027 0.570137 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) −10.0000 −0.474579
\(445\) 0 0
\(446\) 14.0000 0.662919
\(447\) 12.0000 0.567581
\(448\) 1.00000 0.0472456
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 12.0000 0.564433
\(453\) 10.0000 0.469841
\(454\) −15.0000 −0.703985
\(455\) 0 0
\(456\) 1.00000 0.0468293
\(457\) −35.0000 −1.63723 −0.818615 0.574342i \(-0.805258\pi\)
−0.818615 + 0.574342i \(0.805258\pi\)
\(458\) −26.0000 −1.21490
\(459\) 15.0000 0.700140
\(460\) 0 0
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −3.00000 −0.139272
\(465\) 0 0
\(466\) −6.00000 −0.277945
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 7.00000 0.323230
\(470\) 0 0
\(471\) −10.0000 −0.460776
\(472\) −3.00000 −0.138086
\(473\) 0 0
\(474\) 14.0000 0.643041
\(475\) 0 0
\(476\) 3.00000 0.137505
\(477\) 6.00000 0.274721
\(478\) 15.0000 0.686084
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) 10.0000 0.455961
\(482\) 4.00000 0.182195
\(483\) 3.00000 0.136505
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 16.0000 0.725775
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) −8.00000 −0.362143
\(489\) −22.0000 −0.994874
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) −6.00000 −0.270501
\(493\) −9.00000 −0.405340
\(494\) −1.00000 −0.0449921
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 12.0000 0.538274
\(498\) −6.00000 −0.268866
\(499\) −10.0000 −0.447661 −0.223831 0.974628i \(-0.571856\pi\)
−0.223831 + 0.974628i \(0.571856\pi\)
\(500\) 0 0
\(501\) 18.0000 0.804181
\(502\) 0 0
\(503\) −39.0000 −1.73892 −0.869462 0.494000i \(-0.835534\pi\)
−0.869462 + 0.494000i \(0.835534\pi\)
\(504\) 2.00000 0.0890871
\(505\) 0 0
\(506\) 0 0
\(507\) 12.0000 0.532939
\(508\) −2.00000 −0.0887357
\(509\) 18.0000 0.797836 0.398918 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) 0 0
\(511\) 13.0000 0.575086
\(512\) −1.00000 −0.0441942
\(513\) 5.00000 0.220755
\(514\) 18.0000 0.793946
\(515\) 0 0
\(516\) 2.00000 0.0880451
\(517\) 0 0
\(518\) −10.0000 −0.439375
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) −6.00000 −0.262613
\(523\) −11.0000 −0.480996 −0.240498 0.970650i \(-0.577311\pi\)
−0.240498 + 0.970650i \(0.577311\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.00000 0.261364
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 1.00000 0.0433555
\(533\) 6.00000 0.259889
\(534\) 6.00000 0.259645
\(535\) 0 0
\(536\) −7.00000 −0.302354
\(537\) 0 0
\(538\) −18.0000 −0.776035
\(539\) 0 0
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 7.00000 0.300676
\(543\) −2.00000 −0.0858282
\(544\) −3.00000 −0.128624
\(545\) 0 0
\(546\) 1.00000 0.0427960
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) −9.00000 −0.384461
\(549\) −16.0000 −0.682863
\(550\) 0 0
\(551\) −3.00000 −0.127804
\(552\) −3.00000 −0.127688
\(553\) 14.0000 0.595341
\(554\) 8.00000 0.339887
\(555\) 0 0
\(556\) 8.00000 0.339276
\(557\) 12.0000 0.508456 0.254228 0.967144i \(-0.418179\pi\)
0.254228 + 0.967144i \(0.418179\pi\)
\(558\) 4.00000 0.169334
\(559\) −2.00000 −0.0845910
\(560\) 0 0
\(561\) 0 0
\(562\) −18.0000 −0.759284
\(563\) 12.0000 0.505740 0.252870 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 14.0000 0.588464
\(567\) 1.00000 0.0419961
\(568\) −12.0000 −0.503509
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) −22.0000 −0.920671 −0.460336 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) 0 0
\(573\) 27.0000 1.12794
\(574\) −6.00000 −0.250435
\(575\) 0 0
\(576\) −2.00000 −0.0833333
\(577\) 7.00000 0.291414 0.145707 0.989328i \(-0.453454\pi\)
0.145707 + 0.989328i \(0.453454\pi\)
\(578\) 8.00000 0.332756
\(579\) −22.0000 −0.914289
\(580\) 0 0
\(581\) −6.00000 −0.248922
\(582\) 10.0000 0.414513
\(583\) 0 0
\(584\) −13.0000 −0.537944
\(585\) 0 0
\(586\) 21.0000 0.867502
\(587\) −30.0000 −1.23823 −0.619116 0.785299i \(-0.712509\pi\)
−0.619116 + 0.785299i \(0.712509\pi\)
\(588\) 6.00000 0.247436
\(589\) 2.00000 0.0824086
\(590\) 0 0
\(591\) 6.00000 0.246807
\(592\) 10.0000 0.410997
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −12.0000 −0.491539
\(597\) 19.0000 0.777618
\(598\) 3.00000 0.122679
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 2.00000 0.0815139
\(603\) −14.0000 −0.570124
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) 12.0000 0.487467
\(607\) 10.0000 0.405887 0.202944 0.979190i \(-0.434949\pi\)
0.202944 + 0.979190i \(0.434949\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 3.00000 0.121566
\(610\) 0 0
\(611\) 0 0
\(612\) −6.00000 −0.242536
\(613\) 16.0000 0.646234 0.323117 0.946359i \(-0.395269\pi\)
0.323117 + 0.946359i \(0.395269\pi\)
\(614\) 20.0000 0.807134
\(615\) 0 0
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) −8.00000 −0.321807
\(619\) 44.0000 1.76851 0.884255 0.467005i \(-0.154667\pi\)
0.884255 + 0.467005i \(0.154667\pi\)
\(620\) 0 0
\(621\) −15.0000 −0.601929
\(622\) 3.00000 0.120289
\(623\) 6.00000 0.240385
\(624\) −1.00000 −0.0400320
\(625\) 0 0
\(626\) −1.00000 −0.0399680
\(627\) 0 0
\(628\) 10.0000 0.399043
\(629\) 30.0000 1.19618
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) −14.0000 −0.556890
\(633\) 25.0000 0.993661
\(634\) 9.00000 0.357436
\(635\) 0 0
\(636\) 3.00000 0.118958
\(637\) −6.00000 −0.237729
\(638\) 0 0
\(639\) −24.0000 −0.949425
\(640\) 0 0
\(641\) −12.0000 −0.473972 −0.236986 0.971513i \(-0.576159\pi\)
−0.236986 + 0.971513i \(0.576159\pi\)
\(642\) −15.0000 −0.592003
\(643\) −50.0000 −1.97181 −0.985904 0.167313i \(-0.946491\pi\)
−0.985904 + 0.167313i \(0.946491\pi\)
\(644\) −3.00000 −0.118217
\(645\) 0 0
\(646\) −3.00000 −0.118033
\(647\) 33.0000 1.29736 0.648682 0.761060i \(-0.275321\pi\)
0.648682 + 0.761060i \(0.275321\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) −2.00000 −0.0783862
\(652\) 22.0000 0.861586
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 11.0000 0.430134
\(655\) 0 0
\(656\) 6.00000 0.234261
\(657\) −26.0000 −1.01436
\(658\) 0 0
\(659\) 21.0000 0.818044 0.409022 0.912525i \(-0.365870\pi\)
0.409022 + 0.912525i \(0.365870\pi\)
\(660\) 0 0
\(661\) −49.0000 −1.90588 −0.952940 0.303160i \(-0.901958\pi\)
−0.952940 + 0.303160i \(0.901958\pi\)
\(662\) −5.00000 −0.194331
\(663\) −3.00000 −0.116510
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 20.0000 0.774984
\(667\) 9.00000 0.348481
\(668\) −18.0000 −0.696441
\(669\) 14.0000 0.541271
\(670\) 0 0
\(671\) 0 0
\(672\) 1.00000 0.0385758
\(673\) −20.0000 −0.770943 −0.385472 0.922720i \(-0.625961\pi\)
−0.385472 + 0.922720i \(0.625961\pi\)
\(674\) 2.00000 0.0770371
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 15.0000 0.576497 0.288248 0.957556i \(-0.406927\pi\)
0.288248 + 0.957556i \(0.406927\pi\)
\(678\) 12.0000 0.460857
\(679\) 10.0000 0.383765
\(680\) 0 0
\(681\) −15.0000 −0.574801
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 0 0
\(686\) 13.0000 0.496342
\(687\) −26.0000 −0.991962
\(688\) −2.00000 −0.0762493
\(689\) −3.00000 −0.114291
\(690\) 0 0
\(691\) −10.0000 −0.380418 −0.190209 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −30.0000 −1.13878
\(695\) 0 0
\(696\) −3.00000 −0.113715
\(697\) 18.0000 0.681799
\(698\) −14.0000 −0.529908
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) 48.0000 1.81293 0.906467 0.422276i \(-0.138769\pi\)
0.906467 + 0.422276i \(0.138769\pi\)
\(702\) −5.00000 −0.188713
\(703\) 10.0000 0.377157
\(704\) 0 0
\(705\) 0 0
\(706\) −33.0000 −1.24197
\(707\) 12.0000 0.451306
\(708\) −3.00000 −0.112747
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 0 0
\(711\) −28.0000 −1.05008
\(712\) −6.00000 −0.224860
\(713\) −6.00000 −0.224702
\(714\) 3.00000 0.112272
\(715\) 0 0
\(716\) 0 0
\(717\) 15.0000 0.560185
\(718\) 33.0000 1.23155
\(719\) 33.0000 1.23069 0.615346 0.788257i \(-0.289016\pi\)
0.615346 + 0.788257i \(0.289016\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) −1.00000 −0.0372161
\(723\) 4.00000 0.148762
\(724\) 2.00000 0.0743294
\(725\) 0 0
\(726\) −11.0000 −0.408248
\(727\) 13.0000 0.482143 0.241072 0.970507i \(-0.422501\pi\)
0.241072 + 0.970507i \(0.422501\pi\)
\(728\) −1.00000 −0.0370625
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −6.00000 −0.221918
\(732\) −8.00000 −0.295689
\(733\) 4.00000 0.147743 0.0738717 0.997268i \(-0.476464\pi\)
0.0738717 + 0.997268i \(0.476464\pi\)
\(734\) −16.0000 −0.590571
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) 0 0
\(738\) 12.0000 0.441726
\(739\) 2.00000 0.0735712 0.0367856 0.999323i \(-0.488288\pi\)
0.0367856 + 0.999323i \(0.488288\pi\)
\(740\) 0 0
\(741\) −1.00000 −0.0367359
\(742\) 3.00000 0.110133
\(743\) −18.0000 −0.660356 −0.330178 0.943919i \(-0.607109\pi\)
−0.330178 + 0.943919i \(0.607109\pi\)
\(744\) 2.00000 0.0733236
\(745\) 0 0
\(746\) −31.0000 −1.13499
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) −15.0000 −0.548088
\(750\) 0 0
\(751\) 2.00000 0.0729810 0.0364905 0.999334i \(-0.488382\pi\)
0.0364905 + 0.999334i \(0.488382\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 3.00000 0.109254
\(755\) 0 0
\(756\) 5.00000 0.181848
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −35.0000 −1.27126
\(759\) 0 0
\(760\) 0 0
\(761\) −21.0000 −0.761249 −0.380625 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) −2.00000 −0.0724524
\(763\) 11.0000 0.398227
\(764\) −27.0000 −0.976826
\(765\) 0 0
\(766\) −24.0000 −0.867155
\(767\) 3.00000 0.108324
\(768\) −1.00000 −0.0360844
\(769\) −55.0000 −1.98335 −0.991675 0.128763i \(-0.958899\pi\)
−0.991675 + 0.128763i \(0.958899\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 22.0000 0.791797
\(773\) −21.0000 −0.755318 −0.377659 0.925945i \(-0.623271\pi\)
−0.377659 + 0.925945i \(0.623271\pi\)
\(774\) −4.00000 −0.143777
\(775\) 0 0
\(776\) −10.0000 −0.358979
\(777\) −10.0000 −0.358748
\(778\) 24.0000 0.860442
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) 0 0
\(782\) 9.00000 0.321839
\(783\) −15.0000 −0.536056
\(784\) −6.00000 −0.214286
\(785\) 0 0
\(786\) 0 0
\(787\) −5.00000 −0.178231 −0.0891154 0.996021i \(-0.528404\pi\)
−0.0891154 + 0.996021i \(0.528404\pi\)
\(788\) −6.00000 −0.213741
\(789\) 0 0
\(790\) 0 0
\(791\) 12.0000 0.426671
\(792\) 0 0
\(793\) 8.00000 0.284088
\(794\) 8.00000 0.283909
\(795\) 0 0
\(796\) −19.0000 −0.673437
\(797\) 33.0000 1.16892 0.584460 0.811423i \(-0.301306\pi\)
0.584460 + 0.811423i \(0.301306\pi\)
\(798\) 1.00000 0.0353996
\(799\) 0 0
\(800\) 0 0
\(801\) −12.0000 −0.423999
\(802\) −6.00000 −0.211867
\(803\) 0 0
\(804\) −7.00000 −0.246871
\(805\) 0 0
\(806\) −2.00000 −0.0704470
\(807\) −18.0000 −0.633630
\(808\) −12.0000 −0.422159
\(809\) 33.0000 1.16022 0.580109 0.814539i \(-0.303010\pi\)
0.580109 + 0.814539i \(0.303010\pi\)
\(810\) 0 0
\(811\) −7.00000 −0.245803 −0.122902 0.992419i \(-0.539220\pi\)
−0.122902 + 0.992419i \(0.539220\pi\)
\(812\) −3.00000 −0.105279
\(813\) 7.00000 0.245501
\(814\) 0 0
\(815\) 0 0
\(816\) −3.00000 −0.105021
\(817\) −2.00000 −0.0699711
\(818\) 22.0000 0.769212
\(819\) −2.00000 −0.0698857
\(820\) 0 0
\(821\) −12.0000 −0.418803 −0.209401 0.977830i \(-0.567152\pi\)
−0.209401 + 0.977830i \(0.567152\pi\)
\(822\) −9.00000 −0.313911
\(823\) 31.0000 1.08059 0.540296 0.841475i \(-0.318312\pi\)
0.540296 + 0.841475i \(0.318312\pi\)
\(824\) 8.00000 0.278693
\(825\) 0 0
\(826\) −3.00000 −0.104383
\(827\) −33.0000 −1.14752 −0.573761 0.819023i \(-0.694516\pi\)
−0.573761 + 0.819023i \(0.694516\pi\)
\(828\) 6.00000 0.208514
\(829\) −13.0000 −0.451509 −0.225754 0.974184i \(-0.572485\pi\)
−0.225754 + 0.974184i \(0.572485\pi\)
\(830\) 0 0
\(831\) 8.00000 0.277517
\(832\) 1.00000 0.0346688
\(833\) −18.0000 −0.623663
\(834\) 8.00000 0.277017
\(835\) 0 0
\(836\) 0 0
\(837\) 10.0000 0.345651
\(838\) 30.0000 1.03633
\(839\) 36.0000 1.24286 0.621429 0.783470i \(-0.286552\pi\)
0.621429 + 0.783470i \(0.286552\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) −17.0000 −0.585859
\(843\) −18.0000 −0.619953
\(844\) −25.0000 −0.860535
\(845\) 0 0
\(846\) 0 0
\(847\) −11.0000 −0.377964
\(848\) −3.00000 −0.103020
\(849\) 14.0000 0.480479
\(850\) 0 0
\(851\) −30.0000 −1.02839
\(852\) −12.0000 −0.411113
\(853\) −50.0000 −1.71197 −0.855984 0.517003i \(-0.827048\pi\)
−0.855984 + 0.517003i \(0.827048\pi\)
\(854\) −8.00000 −0.273754
\(855\) 0 0
\(856\) 15.0000 0.512689
\(857\) −48.0000 −1.63965 −0.819824 0.572615i \(-0.805929\pi\)
−0.819824 + 0.572615i \(0.805929\pi\)
\(858\) 0 0
\(859\) −16.0000 −0.545913 −0.272956 0.962026i \(-0.588002\pi\)
−0.272956 + 0.962026i \(0.588002\pi\)
\(860\) 0 0
\(861\) −6.00000 −0.204479
\(862\) −24.0000 −0.817443
\(863\) 12.0000 0.408485 0.204242 0.978920i \(-0.434527\pi\)
0.204242 + 0.978920i \(0.434527\pi\)
\(864\) −5.00000 −0.170103
\(865\) 0 0
\(866\) −4.00000 −0.135926
\(867\) 8.00000 0.271694
\(868\) 2.00000 0.0678844
\(869\) 0 0
\(870\) 0 0
\(871\) 7.00000 0.237186
\(872\) −11.0000 −0.372507
\(873\) −20.0000 −0.676897
\(874\) 3.00000 0.101477
\(875\) 0 0
\(876\) −13.0000 −0.439229
\(877\) 31.0000 1.04680 0.523398 0.852088i \(-0.324664\pi\)
0.523398 + 0.852088i \(0.324664\pi\)
\(878\) −38.0000 −1.28244
\(879\) 21.0000 0.708312
\(880\) 0 0
\(881\) 42.0000 1.41502 0.707508 0.706705i \(-0.249819\pi\)
0.707508 + 0.706705i \(0.249819\pi\)
\(882\) −12.0000 −0.404061
\(883\) −38.0000 −1.27880 −0.639401 0.768874i \(-0.720818\pi\)
−0.639401 + 0.768874i \(0.720818\pi\)
\(884\) 3.00000 0.100901
\(885\) 0 0
\(886\) −24.0000 −0.806296
\(887\) −24.0000 −0.805841 −0.402921 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(888\) 10.0000 0.335578
\(889\) −2.00000 −0.0670778
\(890\) 0 0
\(891\) 0 0
\(892\) −14.0000 −0.468755
\(893\) 0 0
\(894\) −12.0000 −0.401340
\(895\) 0 0
\(896\) −1.00000 −0.0334077
\(897\) 3.00000 0.100167
\(898\) 30.0000 1.00111
\(899\) −6.00000 −0.200111
\(900\) 0 0
\(901\) −9.00000 −0.299833
\(902\) 0 0
\(903\) 2.00000 0.0665558
\(904\) −12.0000 −0.399114
\(905\) 0 0
\(906\) −10.0000 −0.332228
\(907\) −35.0000 −1.16216 −0.581078 0.813848i \(-0.697369\pi\)
−0.581078 + 0.813848i \(0.697369\pi\)
\(908\) 15.0000 0.497792
\(909\) −24.0000 −0.796030
\(910\) 0 0
\(911\) −36.0000 −1.19273 −0.596367 0.802712i \(-0.703390\pi\)
−0.596367 + 0.802712i \(0.703390\pi\)
\(912\) −1.00000 −0.0331133
\(913\) 0 0
\(914\) 35.0000 1.15770
\(915\) 0 0
\(916\) 26.0000 0.859064
\(917\) 0 0
\(918\) −15.0000 −0.495074
\(919\) −1.00000 −0.0329870 −0.0164935 0.999864i \(-0.505250\pi\)
−0.0164935 + 0.999864i \(0.505250\pi\)
\(920\) 0 0
\(921\) 20.0000 0.659022
\(922\) −6.00000 −0.197599
\(923\) 12.0000 0.394985
\(924\) 0 0
\(925\) 0 0
\(926\) −16.0000 −0.525793
\(927\) 16.0000 0.525509
\(928\) 3.00000 0.0984798
\(929\) 21.0000 0.688988 0.344494 0.938789i \(-0.388051\pi\)
0.344494 + 0.938789i \(0.388051\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) 6.00000 0.196537
\(933\) 3.00000 0.0982156
\(934\) 12.0000 0.392652
\(935\) 0 0
\(936\) 2.00000 0.0653720
\(937\) −47.0000 −1.53542 −0.767712 0.640796i \(-0.778605\pi\)
−0.767712 + 0.640796i \(0.778605\pi\)
\(938\) −7.00000 −0.228558
\(939\) −1.00000 −0.0326338
\(940\) 0 0
\(941\) 45.0000 1.46696 0.733479 0.679712i \(-0.237895\pi\)
0.733479 + 0.679712i \(0.237895\pi\)
\(942\) 10.0000 0.325818
\(943\) −18.0000 −0.586161
\(944\) 3.00000 0.0976417
\(945\) 0 0
\(946\) 0 0
\(947\) −24.0000 −0.779895 −0.389948 0.920837i \(-0.627507\pi\)
−0.389948 + 0.920837i \(0.627507\pi\)
\(948\) −14.0000 −0.454699
\(949\) 13.0000 0.421998
\(950\) 0 0
\(951\) 9.00000 0.291845
\(952\) −3.00000 −0.0972306
\(953\) 36.0000 1.16615 0.583077 0.812417i \(-0.301849\pi\)
0.583077 + 0.812417i \(0.301849\pi\)
\(954\) −6.00000 −0.194257
\(955\) 0 0
\(956\) −15.0000 −0.485135
\(957\) 0 0
\(958\) 24.0000 0.775405
\(959\) −9.00000 −0.290625
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) −10.0000 −0.322413
\(963\) 30.0000 0.966736
\(964\) −4.00000 −0.128831
\(965\) 0 0
\(966\) −3.00000 −0.0965234
\(967\) −44.0000 −1.41494 −0.707472 0.706741i \(-0.750165\pi\)
−0.707472 + 0.706741i \(0.750165\pi\)
\(968\) 11.0000 0.353553
\(969\) −3.00000 −0.0963739
\(970\) 0 0
\(971\) 12.0000 0.385098 0.192549 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) −16.0000 −0.513200
\(973\) 8.00000 0.256468
\(974\) 2.00000 0.0640841
\(975\) 0 0
\(976\) 8.00000 0.256074
\(977\) −6.00000 −0.191957 −0.0959785 0.995383i \(-0.530598\pi\)
−0.0959785 + 0.995383i \(0.530598\pi\)
\(978\) 22.0000 0.703482
\(979\) 0 0
\(980\) 0 0
\(981\) −22.0000 −0.702406
\(982\) −30.0000 −0.957338
\(983\) −54.0000 −1.72233 −0.861166 0.508323i \(-0.830265\pi\)
−0.861166 + 0.508323i \(0.830265\pi\)
\(984\) 6.00000 0.191273
\(985\) 0 0
\(986\) 9.00000 0.286618
\(987\) 0 0
\(988\) 1.00000 0.0318142
\(989\) 6.00000 0.190789
\(990\) 0 0
\(991\) 2.00000 0.0635321 0.0317660 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(992\) −2.00000 −0.0635001
\(993\) −5.00000 −0.158670
\(994\) −12.0000 −0.380617
\(995\) 0 0
\(996\) 6.00000 0.190117
\(997\) 46.0000 1.45683 0.728417 0.685134i \(-0.240256\pi\)
0.728417 + 0.685134i \(0.240256\pi\)
\(998\) 10.0000 0.316544
\(999\) 50.0000 1.58193
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 950.2.a.a.1.1 1
3.2 odd 2 8550.2.a.bd.1.1 1
4.3 odd 2 7600.2.a.m.1.1 1
5.2 odd 4 950.2.b.e.799.1 2
5.3 odd 4 950.2.b.e.799.2 2
5.4 even 2 190.2.a.c.1.1 1
15.14 odd 2 1710.2.a.d.1.1 1
20.19 odd 2 1520.2.a.d.1.1 1
35.34 odd 2 9310.2.a.o.1.1 1
40.19 odd 2 6080.2.a.p.1.1 1
40.29 even 2 6080.2.a.h.1.1 1
95.94 odd 2 3610.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.a.c.1.1 1 5.4 even 2
950.2.a.a.1.1 1 1.1 even 1 trivial
950.2.b.e.799.1 2 5.2 odd 4
950.2.b.e.799.2 2 5.3 odd 4
1520.2.a.d.1.1 1 20.19 odd 2
1710.2.a.d.1.1 1 15.14 odd 2
3610.2.a.b.1.1 1 95.94 odd 2
6080.2.a.h.1.1 1 40.29 even 2
6080.2.a.p.1.1 1 40.19 odd 2
7600.2.a.m.1.1 1 4.3 odd 2
8550.2.a.bd.1.1 1 3.2 odd 2
9310.2.a.o.1.1 1 35.34 odd 2