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Properties

Label 980.2.a.c.1.1
Level $980$
Weight $2$
Character 980.1
Self dual yes
Analytic conductor $7.825$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [980,2,Mod(1,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-1,0,-1,0,0,0,-2,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(7.82533939809\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 140)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 980.1

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} -1.00000 q^{5} -2.00000 q^{9} +3.00000 q^{11} +1.00000 q^{13} +1.00000 q^{15} +3.00000 q^{17} -2.00000 q^{19} -6.00000 q^{23} +1.00000 q^{25} +5.00000 q^{27} -9.00000 q^{29} -8.00000 q^{31} -3.00000 q^{33} -10.0000 q^{37} -1.00000 q^{39} +2.00000 q^{43} +2.00000 q^{45} +3.00000 q^{47} -3.00000 q^{51} -3.00000 q^{55} +2.00000 q^{57} -12.0000 q^{59} -8.00000 q^{61} -1.00000 q^{65} +8.00000 q^{67} +6.00000 q^{69} -14.0000 q^{73} -1.00000 q^{75} +5.00000 q^{79} +1.00000 q^{81} +12.0000 q^{83} -3.00000 q^{85} +9.00000 q^{87} -12.0000 q^{89} +8.00000 q^{93} +2.00000 q^{95} -17.0000 q^{97} -6.00000 q^{99} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350 −0.288675 − 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 − 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350 0.138675 − 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) 3.00000 0.727607 0.363803 − 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 − 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 − 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −9.00000 −1.67126 −0.835629 − 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) −8.00000 −1.43684 −0.718421 − 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 0 0
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −10.0000 −1.64399 −0.821995 − 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 − 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 0 0
\(45\) 2.00000 0.298142
\(46\) 0 0
\(47\) 3.00000 0.437595 0.218797 − 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −3.00000 −0.420084
\(52\) 0 0
\(53\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 0 0
\(59\) −12.0000 −1.56227 −0.781133 − 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 − 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 8.00000 0.977356 0.488678 − 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −14.0000 −1.63858 −0.819288 − 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 5.00000 0.562544 0.281272 − 0.959628i \(-0.409244\pi\)
0.281272 + 0.959628i \(0.409244\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 − 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 9.00000 0.964901
\(88\) 0 0
\(89\) −12.0000 −1.27200 −0.635999 − 0.771690i \(-0.719412\pi\)
−0.635999 + 0.771690i \(0.719412\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 8.00000 0.829561
\(94\) 0 0
\(95\) 2.00000 0.205196
\(96\) 0 0
\(97\) −17.0000 −1.72609 −0.863044 − 0.505128i \(-0.831445\pi\)
−0.863044 + 0.505128i \(0.831445\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 − 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) 7.00000 0.689730 0.344865 − 0.938652i \(-0.387925\pi\)
0.344865 + 0.938652i \(0.387925\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.00000 −0.580042 −0.290021 − 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 0 0
\(109\) −19.0000 −1.81987 −0.909935 − 0.414751i \(-0.863869\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) 0 0
\(111\) 10.0000 0.949158
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 − 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 6.00000 0.559503
\(116\) 0 0
\(117\) −2.00000 −0.184900
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 − 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 0 0
\(129\) −2.00000 −0.176090
\(130\) 0 0
\(131\) 18.0000 1.57267 0.786334 − 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −5.00000 −0.430331
\(136\) 0 0
\(137\) 12.0000 1.02523 0.512615 − 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 − 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 0 0
\(143\) 3.00000 0.250873
\(144\) 0 0
\(145\) 9.00000 0.747409
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 18.0000 1.47462 0.737309 − 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) −19.0000 −1.54620 −0.773099 − 0.634285i \(-0.781294\pi\)
−0.773099 + 0.634285i \(0.781294\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 8.00000 0.642575
\(156\) 0 0
\(157\) 22.0000 1.75579 0.877896 − 0.478852i \(-0.158947\pi\)
0.877896 + 0.478852i \(0.158947\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000 0.156652 0.0783260 − 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 0 0
\(165\) 3.00000 0.233550
\(166\) 0 0
\(167\) −9.00000 −0.696441 −0.348220 − 0.937413i \(-0.613214\pi\)
−0.348220 + 0.937413i \(0.613214\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 4.00000 0.305888
\(172\) 0 0
\(173\) 3.00000 0.228086 0.114043 − 0.993476i \(-0.463620\pi\)
0.114043 + 0.993476i \(0.463620\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 12.0000 0.901975
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 − 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −8.00000 −0.594635 −0.297318 − 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) 8.00000 0.591377
\(184\) 0 0
\(185\) 10.0000 0.735215
\(186\) 0 0
\(187\) 9.00000 0.658145
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.00000 0.217072 0.108536 − 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) 0 0
\(193\) −4.00000 −0.287926 −0.143963 − 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 0 0
\(195\) 1.00000 0.0716115
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 − 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) −20.0000 −1.41776 −0.708881 − 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) 0 0
\(201\) −8.00000 −0.564276
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 12.0000 0.834058
\(208\) 0 0
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 − 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.00000 −0.136399
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 14.0000 0.946032
\(220\) 0 0
\(221\) 3.00000 0.201802
\(222\) 0 0
\(223\) −17.0000 −1.13840 −0.569202 − 0.822198i \(-0.692748\pi\)
−0.569202 + 0.822198i \(0.692748\pi\)
\(224\) 0 0
\(225\) −2.00000 −0.133333
\(226\) 0 0
\(227\) 27.0000 1.79205 0.896026 − 0.444001i \(-0.146441\pi\)
0.896026 + 0.444001i \(0.146441\pi\)
\(228\) 0 0
\(229\) 16.0000 1.05731 0.528655 − 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 24.0000 1.57229 0.786146 − 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) 0 0
\(235\) −3.00000 −0.195698
\(236\) 0 0
\(237\) −5.00000 −0.324785
\(238\) 0 0
\(239\) 9.00000 0.582162 0.291081 − 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 − 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 0 0
\(243\) −16.0000 −1.02640
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.00000 −0.127257
\(248\) 0 0
\(249\) −12.0000 −0.760469
\(250\) 0 0
\(251\) −6.00000 −0.378717 −0.189358 − 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) 0 0
\(253\) −18.0000 −1.13165
\(254\) 0 0
\(255\) 3.00000 0.187867
\(256\) 0 0
\(257\) 6.00000 0.374270 0.187135 − 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 18.0000 1.11417
\(262\) 0 0
\(263\) −30.0000 −1.84988 −0.924940 − 0.380114i \(-0.875885\pi\)
−0.924940 + 0.380114i \(0.875885\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 12.0000 0.734388
\(268\) 0 0
\(269\) −18.0000 −1.09748 −0.548740 − 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 0 0
\(271\) 16.0000 0.971931 0.485965 − 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.00000 0.180907
\(276\) 0 0
\(277\) −22.0000 −1.32185 −0.660926 − 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 0 0
\(279\) 16.0000 0.957895
\(280\) 0 0
\(281\) −21.0000 −1.25275 −0.626377 − 0.779520i \(-0.715463\pi\)
−0.626377 + 0.779520i \(0.715463\pi\)
\(282\) 0 0
\(283\) −11.0000 −0.653882 −0.326941 − 0.945045i \(-0.606018\pi\)
−0.326941 + 0.945045i \(0.606018\pi\)
\(284\) 0 0
\(285\) −2.00000 −0.118470
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 17.0000 0.996558
\(292\) 0 0
\(293\) 15.0000 0.876309 0.438155 − 0.898900i \(-0.355632\pi\)
0.438155 + 0.898900i \(0.355632\pi\)
\(294\) 0 0
\(295\) 12.0000 0.698667
\(296\) 0 0
\(297\) 15.0000 0.870388
\(298\) 0 0
\(299\) −6.00000 −0.346989
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −6.00000 −0.344691
\(304\) 0 0
\(305\) 8.00000 0.458079
\(306\) 0 0
\(307\) 13.0000 0.741949 0.370975 − 0.928643i \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) 0 0
\(309\) −7.00000 −0.398216
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 − 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 0 0
\(313\) 13.0000 0.734803 0.367402 − 0.930062i \(-0.380247\pi\)
0.367402 + 0.930062i \(0.380247\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −18.0000 −1.01098 −0.505490 − 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 0 0
\(319\) −27.0000 −1.51171
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) −6.00000 −0.333849
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) 19.0000 1.05070
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 − 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 0 0
\(333\) 20.0000 1.09599
\(334\) 0 0
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 − 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) −24.0000 −1.29967
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −6.00000 −0.323029
\(346\) 0 0
\(347\) 30.0000 1.61048 0.805242 − 0.592946i \(-0.202035\pi\)
0.805242 + 0.592946i \(0.202035\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 − 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) 15.0000 0.798369 0.399185 − 0.916871i \(-0.369293\pi\)
0.399185 + 0.916871i \(0.369293\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) 14.0000 0.732793
\(366\) 0 0
\(367\) −5.00000 −0.260998 −0.130499 − 0.991448i \(-0.541658\pi\)
−0.130499 + 0.991448i \(0.541658\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −4.00000 −0.207112 −0.103556 − 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) −9.00000 −0.463524
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 − 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) −20.0000 −1.02463
\(382\) 0 0
\(383\) −36.0000 −1.83951 −0.919757 − 0.392488i \(-0.871614\pi\)
−0.919757 + 0.392488i \(0.871614\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4.00000 −0.203331
\(388\) 0 0
\(389\) 9.00000 0.456318 0.228159 − 0.973624i \(-0.426729\pi\)
0.228159 + 0.973624i \(0.426729\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) −18.0000 −0.907980
\(394\) 0 0
\(395\) −5.00000 −0.251577
\(396\) 0 0
\(397\) −5.00000 −0.250943 −0.125471 − 0.992097i \(-0.540044\pi\)
−0.125471 + 0.992097i \(0.540044\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −15.0000 −0.749064 −0.374532 − 0.927214i \(-0.622197\pi\)
−0.374532 + 0.927214i \(0.622197\pi\)
\(402\) 0 0
\(403\) −8.00000 −0.398508
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −30.0000 −1.48704
\(408\) 0 0
\(409\) −26.0000 −1.28562 −0.642809 − 0.766027i \(-0.722231\pi\)
−0.642809 + 0.766027i \(0.722231\pi\)
\(410\) 0 0
\(411\) −12.0000 −0.591916
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0 0
\(417\) 2.00000 0.0979404
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 − 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) 29.0000 1.41337 0.706687 − 0.707527i \(-0.250189\pi\)
0.706687 + 0.707527i \(0.250189\pi\)
\(422\) 0 0
\(423\) −6.00000 −0.291730
\(424\) 0 0
\(425\) 3.00000 0.145521
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −3.00000 −0.144841
\(430\) 0 0
\(431\) 15.0000 0.722525 0.361262 − 0.932464i \(-0.382346\pi\)
0.361262 + 0.932464i \(0.382346\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 − 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) −9.00000 −0.431517
\(436\) 0 0
\(437\) 12.0000 0.574038
\(438\) 0 0
\(439\) 10.0000 0.477274 0.238637 − 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.00000 −0.285069 −0.142534 − 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) 0 0
\(445\) 12.0000 0.568855
\(446\) 0 0
\(447\) −18.0000 −0.851371
\(448\) 0 0
\(449\) 15.0000 0.707894 0.353947 − 0.935266i \(-0.384839\pi\)
0.353947 + 0.935266i \(0.384839\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 19.0000 0.892698
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −28.0000 −1.30978 −0.654892 − 0.755722i \(-0.727286\pi\)
−0.654892 + 0.755722i \(0.727286\pi\)
\(458\) 0 0
\(459\) 15.0000 0.700140
\(460\) 0 0
\(461\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 − 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 0 0
\(465\) −8.00000 −0.370991
\(466\) 0 0
\(467\) −15.0000 −0.694117 −0.347059 − 0.937843i \(-0.612820\pi\)
−0.347059 + 0.937843i \(0.612820\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −22.0000 −1.01371
\(472\) 0 0
\(473\) 6.00000 0.275880
\(474\) 0 0
\(475\) −2.00000 −0.0917663
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.00000 −0.274147 −0.137073 − 0.990561i \(-0.543770\pi\)
−0.137073 + 0.990561i \(0.543770\pi\)
\(480\) 0 0
\(481\) −10.0000 −0.455961
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 17.0000 0.771930
\(486\) 0 0
\(487\) −10.0000 −0.453143 −0.226572 − 0.973995i \(-0.572752\pi\)
−0.226572 + 0.973995i \(0.572752\pi\)
\(488\) 0 0
\(489\) −2.00000 −0.0904431
\(490\) 0 0
\(491\) −15.0000 −0.676941 −0.338470 − 0.940977i \(-0.609909\pi\)
−0.338470 + 0.940977i \(0.609909\pi\)
\(492\) 0 0
\(493\) −27.0000 −1.21602
\(494\) 0 0
\(495\) 6.00000 0.269680
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −25.0000 −1.11915 −0.559577 − 0.828778i \(-0.689036\pi\)
−0.559577 + 0.828778i \(0.689036\pi\)
\(500\) 0 0
\(501\) 9.00000 0.402090
\(502\) 0 0
\(503\) 33.0000 1.47140 0.735699 − 0.677309i \(-0.236854\pi\)
0.735699 + 0.677309i \(0.236854\pi\)
\(504\) 0 0
\(505\) −6.00000 −0.266996
\(506\) 0 0
\(507\) 12.0000 0.532939
\(508\) 0 0
\(509\) −18.0000 −0.797836 −0.398918 − 0.916987i \(-0.630614\pi\)
−0.398918 + 0.916987i \(0.630614\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −10.0000 −0.441511
\(514\) 0 0
\(515\) −7.00000 −0.308457
\(516\) 0 0
\(517\) 9.00000 0.395820
\(518\) 0 0
\(519\) −3.00000 −0.131685
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 − 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) −20.0000 −0.874539 −0.437269 − 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −24.0000 −1.04546
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 24.0000 1.04151
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 6.00000 0.259403
\(536\) 0 0
\(537\) −12.0000 −0.517838
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −25.0000 −1.07483 −0.537417 − 0.843317i \(-0.680600\pi\)
−0.537417 + 0.843317i \(0.680600\pi\)
\(542\) 0 0
\(543\) 8.00000 0.343313
\(544\) 0 0
\(545\) 19.0000 0.813871
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 − 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 0 0
\(549\) 16.0000 0.682863
\(550\) 0 0
\(551\) 18.0000 0.766826
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −10.0000 −0.424476
\(556\) 0 0
\(557\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 2.00000 0.0845910
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) 0 0
\(563\) 12.0000 0.505740 0.252870 − 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 0 0
\(565\) 6.00000 0.252422
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 − 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 − 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) −3.00000 −0.125327
\(574\) 0 0
\(575\) −6.00000 −0.250217
\(576\) 0 0
\(577\) −47.0000 −1.95664 −0.978318 − 0.207109i \(-0.933594\pi\)
−0.978318 + 0.207109i \(0.933594\pi\)
\(578\) 0 0
\(579\) 4.00000 0.166234
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 2.00000 0.0826898
\(586\) 0 0
\(587\) 24.0000 0.990586 0.495293 − 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) −12.0000 −0.493614
\(592\) 0 0
\(593\) 33.0000 1.35515 0.677574 − 0.735455i \(-0.263031\pi\)
0.677574 + 0.735455i \(0.263031\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 20.0000 0.818546
\(598\) 0 0
\(599\) −9.00000 −0.367730 −0.183865 − 0.982952i \(-0.558861\pi\)
−0.183865 + 0.982952i \(0.558861\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 − 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) −16.0000 −0.651570
\(604\) 0 0
\(605\) 2.00000 0.0813116
\(606\) 0 0
\(607\) 1.00000 0.0405887 0.0202944 − 0.999794i \(-0.493540\pi\)
0.0202944 + 0.999794i \(0.493540\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3.00000 0.121367
\(612\) 0 0
\(613\) 2.00000 0.0807792 0.0403896 − 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 30.0000 1.20775 0.603877 − 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) 0 0
\(619\) 10.0000 0.401934 0.200967 − 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) 0 0
\(621\) −30.0000 −1.20386
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 6.00000 0.239617
\(628\) 0 0
\(629\) −30.0000 −1.19618
\(630\) 0 0
\(631\) −25.0000 −0.995234 −0.497617 − 0.867397i \(-0.665792\pi\)
−0.497617 + 0.867397i \(0.665792\pi\)
\(632\) 0 0
\(633\) −5.00000 −0.198732
\(634\) 0 0
\(635\) −20.0000 −0.793676
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −30.0000 −1.18493 −0.592464 − 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 0 0
\(643\) −41.0000 −1.61688 −0.808441 − 0.588577i \(-0.799688\pi\)
−0.808441 + 0.588577i \(0.799688\pi\)
\(644\) 0 0
\(645\) 2.00000 0.0787499
\(646\) 0 0
\(647\) −48.0000 −1.88707 −0.943537 − 0.331266i \(-0.892524\pi\)
−0.943537 + 0.331266i \(0.892524\pi\)
\(648\) 0 0
\(649\) −36.0000 −1.41312
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6.00000 −0.234798 −0.117399 − 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 0 0
\(655\) −18.0000 −0.703318
\(656\) 0 0
\(657\) 28.0000 1.09238
\(658\) 0 0
\(659\) −33.0000 −1.28550 −0.642749 − 0.766077i \(-0.722206\pi\)
−0.642749 + 0.766077i \(0.722206\pi\)
\(660\) 0 0
\(661\) −8.00000 −0.311164 −0.155582 − 0.987823i \(-0.549725\pi\)
−0.155582 + 0.987823i \(0.549725\pi\)
\(662\) 0 0
\(663\) −3.00000 −0.116510
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 54.0000 2.09089
\(668\) 0 0
\(669\) 17.0000 0.657258
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) 20.0000 0.770943 0.385472 − 0.922720i \(-0.374039\pi\)
0.385472 + 0.922720i \(0.374039\pi\)
\(674\) 0 0
\(675\) 5.00000 0.192450
\(676\) 0 0
\(677\) −15.0000 −0.576497 −0.288248 − 0.957556i \(-0.593073\pi\)
−0.288248 + 0.957556i \(0.593073\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −27.0000 −1.03464
\(682\) 0 0
\(683\) 24.0000 0.918334 0.459167 − 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) −16.0000 −0.610438
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 − 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.00000 0.0758643
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −24.0000 −0.907763
\(700\) 0 0
\(701\) 3.00000 0.113308 0.0566542 − 0.998394i \(-0.481957\pi\)
0.0566542 + 0.998394i \(0.481957\pi\)
\(702\) 0 0
\(703\) 20.0000 0.754314
\(704\) 0 0
\(705\) 3.00000 0.112987
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.00000 −0.0375558 −0.0187779 − 0.999824i \(-0.505978\pi\)
−0.0187779 + 0.999824i \(0.505978\pi\)
\(710\) 0 0
\(711\) −10.0000 −0.375029
\(712\) 0 0
\(713\) 48.0000 1.79761
\(714\) 0 0
\(715\) −3.00000 −0.112194
\(716\) 0 0
\(717\) −9.00000 −0.336111
\(718\) 0 0
\(719\) 18.0000 0.671287 0.335643 − 0.941989i \(-0.391046\pi\)
0.335643 + 0.941989i \(0.391046\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −10.0000 −0.371904
\(724\) 0 0
\(725\) −9.00000 −0.334252
\(726\) 0 0
\(727\) −32.0000 −1.18681 −0.593407 − 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 6.00000 0.221918
\(732\) 0 0
\(733\) 13.0000 0.480166 0.240083 − 0.970752i \(-0.422825\pi\)
0.240083 + 0.970752i \(0.422825\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24.0000 0.884051
\(738\) 0 0
\(739\) 11.0000 0.404642 0.202321 − 0.979319i \(-0.435152\pi\)
0.202321 + 0.979319i \(0.435152\pi\)
\(740\) 0 0
\(741\) 2.00000 0.0734718
\(742\) 0 0
\(743\) 48.0000 1.76095 0.880475 − 0.474093i \(-0.157224\pi\)
0.880475 + 0.474093i \(0.157224\pi\)
\(744\) 0 0
\(745\) −18.0000 −0.659469
\(746\) 0 0
\(747\) −24.0000 −0.878114
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 53.0000 1.93400 0.966999 − 0.254781i \(-0.0820034\pi\)
0.966999 + 0.254781i \(0.0820034\pi\)
\(752\) 0 0
\(753\) 6.00000 0.218652
\(754\) 0 0
\(755\) 19.0000 0.691481
\(756\) 0 0
\(757\) −16.0000 −0.581530 −0.290765 − 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) 0 0
\(759\) 18.0000 0.653359
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 − 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 6.00000 0.216930
\(766\) 0 0
\(767\) −12.0000 −0.433295
\(768\) 0 0
\(769\) −2.00000 −0.0721218 −0.0360609 − 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 0 0
\(773\) −15.0000 −0.539513 −0.269756 − 0.962929i \(-0.586943\pi\)
−0.269756 + 0.962929i \(0.586943\pi\)
\(774\) 0 0
\(775\) −8.00000 −0.287368
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −45.0000 −1.60817
\(784\) 0 0
\(785\) −22.0000 −0.785214
\(786\) 0 0
\(787\) −5.00000 −0.178231 −0.0891154 − 0.996021i \(-0.528404\pi\)
−0.0891154 + 0.996021i \(0.528404\pi\)
\(788\) 0 0
\(789\) 30.0000 1.06803
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −8.00000 −0.284088
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.00000 0.106265 0.0531327 − 0.998587i \(-0.483079\pi\)
0.0531327 + 0.998587i \(0.483079\pi\)
\(798\) 0 0
\(799\) 9.00000 0.318397
\(800\) 0 0
\(801\) 24.0000 0.847998
\(802\) 0 0
\(803\) −42.0000 −1.48215
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 18.0000 0.633630
\(808\) 0 0
\(809\) 9.00000 0.316423 0.158212 − 0.987405i \(-0.449427\pi\)
0.158212 + 0.987405i \(0.449427\pi\)
\(810\) 0 0
\(811\) 34.0000 1.19390 0.596951 − 0.802278i \(-0.296379\pi\)
0.596951 + 0.802278i \(0.296379\pi\)
\(812\) 0 0
\(813\) −16.0000 −0.561144
\(814\) 0 0
\(815\) −2.00000 −0.0700569
\(816\) 0 0
\(817\) −4.00000 −0.139942
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −15.0000 −0.523504 −0.261752 − 0.965135i \(-0.584300\pi\)
−0.261752 + 0.965135i \(0.584300\pi\)
\(822\) 0 0
\(823\) −40.0000 −1.39431 −0.697156 − 0.716919i \(-0.745552\pi\)
−0.697156 + 0.716919i \(0.745552\pi\)
\(824\) 0 0
\(825\) −3.00000 −0.104447
\(826\) 0 0
\(827\) −42.0000 −1.46048 −0.730242 − 0.683189i \(-0.760592\pi\)
−0.730242 + 0.683189i \(0.760592\pi\)
\(828\) 0 0
\(829\) 40.0000 1.38926 0.694629 − 0.719368i \(-0.255569\pi\)
0.694629 + 0.719368i \(0.255569\pi\)
\(830\) 0 0
\(831\) 22.0000 0.763172
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 9.00000 0.311458
\(836\) 0 0
\(837\) −40.0000 −1.38260
\(838\) 0 0
\(839\) −18.0000 −0.621429 −0.310715 − 0.950503i \(-0.600568\pi\)
−0.310715 + 0.950503i \(0.600568\pi\)
\(840\) 0 0
\(841\) 52.0000 1.79310
\(842\) 0 0
\(843\) 21.0000 0.723278
\(844\) 0 0
\(845\) 12.0000 0.412813
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 11.0000 0.377519
\(850\) 0 0
\(851\) 60.0000 2.05677
\(852\) 0 0
\(853\) 22.0000 0.753266 0.376633 − 0.926363i \(-0.377082\pi\)
0.376633 + 0.926363i \(0.377082\pi\)
\(854\) 0 0
\(855\) −4.00000 −0.136797
\(856\) 0 0
\(857\) −6.00000 −0.204956 −0.102478 − 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) 0 0
\(859\) 4.00000 0.136478 0.0682391 − 0.997669i \(-0.478262\pi\)
0.0682391 + 0.997669i \(0.478262\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 12.0000 0.408485 0.204242 − 0.978920i \(-0.434527\pi\)
0.204242 + 0.978920i \(0.434527\pi\)
\(864\) 0 0
\(865\) −3.00000 −0.102003
\(866\) 0 0
\(867\) 8.00000 0.271694
\(868\) 0 0
\(869\) 15.0000 0.508840
\(870\) 0 0
\(871\) 8.00000 0.271070
\(872\) 0 0
\(873\) 34.0000 1.15073
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −22.0000 −0.742887 −0.371444 − 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) 0 0
\(879\) −15.0000 −0.505937
\(880\) 0 0
\(881\) −48.0000 −1.61716 −0.808581 − 0.588386i \(-0.799764\pi\)
−0.808581 + 0.588386i \(0.799764\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 − 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 0 0
\(885\) −12.0000 −0.403376
\(886\) 0 0
\(887\) 48.0000 1.61168 0.805841 − 0.592132i \(-0.201714\pi\)
0.805841 + 0.592132i \(0.201714\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 3.00000 0.100504
\(892\) 0 0
\(893\) −6.00000 −0.200782
\(894\) 0 0
\(895\) −12.0000 −0.401116
\(896\) 0 0
\(897\) 6.00000 0.200334
\(898\) 0 0
\(899\) 72.0000 2.40133
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 8.00000 0.265929
\(906\) 0 0
\(907\) −22.0000 −0.730498 −0.365249 − 0.930910i \(-0.619016\pi\)
−0.365249 + 0.930910i \(0.619016\pi\)
\(908\) 0 0
\(909\) −12.0000 −0.398015
\(910\) 0 0
\(911\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 36.0000 1.19143
\(914\) 0 0
\(915\) −8.00000 −0.264472
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 41.0000 1.35247 0.676233 − 0.736688i \(-0.263611\pi\)
0.676233 + 0.736688i \(0.263611\pi\)
\(920\) 0 0
\(921\) −13.0000 −0.428365
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −10.0000 −0.328798
\(926\) 0 0
\(927\) −14.0000 −0.459820
\(928\) 0 0
\(929\) 24.0000 0.787414 0.393707 − 0.919236i \(-0.371192\pi\)
0.393707 + 0.919236i \(0.371192\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 18.0000 0.589294
\(934\) 0 0
\(935\) −9.00000 −0.294331
\(936\) 0 0
\(937\) 7.00000 0.228680 0.114340 − 0.993442i \(-0.463525\pi\)
0.114340 + 0.993442i \(0.463525\pi\)
\(938\) 0 0
\(939\) −13.0000 −0.424239
\(940\) 0 0
\(941\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 36.0000 1.16984 0.584921 − 0.811090i \(-0.301125\pi\)
0.584921 + 0.811090i \(0.301125\pi\)
\(948\) 0 0
\(949\) −14.0000 −0.454459
\(950\) 0 0
\(951\) 18.0000 0.583690
\(952\) 0 0
\(953\) 36.0000 1.16615 0.583077 − 0.812417i \(-0.301849\pi\)
0.583077 + 0.812417i \(0.301849\pi\)
\(954\) 0 0
\(955\) −3.00000 −0.0970777
\(956\) 0 0
\(957\) 27.0000 0.872786
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 0 0
\(963\) 12.0000 0.386695
\(964\) 0 0
\(965\) 4.00000 0.128765
\(966\) 0 0
\(967\) −34.0000 −1.09337 −0.546683 − 0.837340i \(-0.684110\pi\)
−0.546683 + 0.837340i \(0.684110\pi\)
\(968\) 0 0
\(969\) 6.00000 0.192748
\(970\) 0 0
\(971\) −36.0000 −1.15529 −0.577647 − 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −1.00000 −0.0320256
\(976\) 0 0
\(977\) −18.0000 −0.575871 −0.287936 − 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) 0 0
\(979\) −36.0000 −1.15056
\(980\) 0 0
\(981\) 38.0000 1.21325
\(982\) 0 0
\(983\) 33.0000 1.05254 0.526268 − 0.850319i \(-0.323591\pi\)
0.526268 + 0.850319i \(0.323591\pi\)
\(984\) 0 0
\(985\) −12.0000 −0.382352
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −12.0000 −0.381578
\(990\) 0 0
\(991\) −16.0000 −0.508257 −0.254128 − 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 0 0
\(993\) −20.0000 −0.634681
\(994\) 0 0
\(995\) 20.0000 0.634043
\(996\) 0 0
\(997\) −17.0000 −0.538395 −0.269198 − 0.963085i \(-0.586759\pi\)
−0.269198 + 0.963085i \(0.586759\pi\)
\(998\) 0 0
\(999\) −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 980.2.a.c.1.1 1
3.2 odd 2 8820.2.a.r.1.1 1
4.3 odd 2 3920.2.a.u.1.1 1
5.2 odd 4 4900.2.e.l.2549.2 2
5.3 odd 4 4900.2.e.l.2549.1 2
5.4 even 2 4900.2.a.p.1.1 1
7.2 even 3 980.2.i.h.361.1 2
7.3 odd 6 980.2.i.d.961.1 2
7.4 even 3 980.2.i.h.961.1 2
7.5 odd 6 980.2.i.d.361.1 2
7.6 odd 2 140.2.a.a.1.1 ✓ 1
21.20 even 2 1260.2.a.c.1.1 1
28.27 even 2 560.2.a.c.1.1 1
35.13 even 4 700.2.e.c.449.2 2
35.27 even 4 700.2.e.c.449.1 2
35.34 odd 2 700.2.a.d.1.1 1
56.13 odd 2 2240.2.a.g.1.1 1
56.27 even 2 2240.2.a.r.1.1 1
84.83 odd 2 5040.2.a.h.1.1 1
105.62 odd 4 6300.2.k.c.6049.2 2
105.83 odd 4 6300.2.k.c.6049.1 2
105.104 even 2 6300.2.a.d.1.1 1
140.27 odd 4 2800.2.g.j.449.2 2
140.83 odd 4 2800.2.g.j.449.1 2
140.139 even 2 2800.2.a.y.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.a.a.1.1 ✓ 1 7.6 odd 2
560.2.a.c.1.1 1 28.27 even 2
700.2.a.d.1.1 1 35.34 odd 2
700.2.e.c.449.1 2 35.27 even 4
700.2.e.c.449.2 2 35.13 even 4
980.2.a.c.1.1 1 1.1 even 1 trivial
980.2.i.d.361.1 2 7.5 odd 6
980.2.i.d.961.1 2 7.3 odd 6
980.2.i.h.361.1 2 7.2 even 3
980.2.i.h.961.1 2 7.4 even 3
1260.2.a.c.1.1 1 21.20 even 2
2240.2.a.g.1.1 1 56.13 odd 2
2240.2.a.r.1.1 1 56.27 even 2
2800.2.a.y.1.1 1 140.139 even 2
2800.2.g.j.449.1 2 140.83 odd 4
2800.2.g.j.449.2 2 140.27 odd 4
3920.2.a.u.1.1 1 4.3 odd 2
4900.2.a.p.1.1 1 5.4 even 2
4900.2.e.l.2549.1 2 5.3 odd 4
4900.2.e.l.2549.2 2 5.2 odd 4
5040.2.a.h.1.1 1 84.83 odd 2
6300.2.a.d.1.1 1 105.104 even 2
6300.2.k.c.6049.1 2 105.83 odd 4
6300.2.k.c.6049.2 2 105.62 odd 4
8820.2.a.r.1.1 1 3.2 odd 2