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Properties

Label 3332.2.a.f.1.1
Level $3332$
Weight $2$
Character 3332.1
Self dual yes
Analytic conductor $26.606$
Analytic rank $0$
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] = [3332,2,Mod(1,3332)] 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("3332.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3332, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3332.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,3,0,-4,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(26.6061539535\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 476)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 3332.1

$q$-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)
 
\(f(q)\) \(=\) \(q+3.00000 q^{3} -4.00000 q^{5} +6.00000 q^{9} +1.00000 q^{11} -3.00000 q^{13} -12.0000 q^{15} +1.00000 q^{17} +2.00000 q^{19} +4.00000 q^{23} +11.0000 q^{25} +9.00000 q^{27} -8.00000 q^{31} +3.00000 q^{33} +8.00000 q^{37} -9.00000 q^{39} +10.0000 q^{43} -24.0000 q^{45} +10.0000 q^{47} +3.00000 q^{51} +3.00000 q^{53} -4.00000 q^{55} +6.00000 q^{57} +14.0000 q^{59} +8.00000 q^{61} +12.0000 q^{65} -10.0000 q^{67} +12.0000 q^{69} -5.00000 q^{71} +16.0000 q^{73} +33.0000 q^{75} +11.0000 q^{79} +9.00000 q^{81} -12.0000 q^{83} -4.00000 q^{85} -9.00000 q^{89} -24.0000 q^{93} -8.00000 q^{95} -10.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)

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
\(3\) 3.00000 1.73205 0.866025 − 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) 0 0
\(5\) −4.00000 −1.78885 −0.894427 − 0.447214i \(-0.852416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 6.00000 2.00000
\(10\) 0 0
\(11\) 1.00000 0.301511 0.150756 − 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) 0 0
\(13\) −3.00000 −0.832050 −0.416025 − 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) 0 0
\(15\) −12.0000 −3.09839
\(16\) 0 0
\(17\) 1.00000 0.242536
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 − 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.00000 0.834058 0.417029 − 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 0 0
\(27\) 9.00000 1.73205
\(28\) 0 0
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 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
\(37\) 8.00000 1.31519 0.657596 − 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 0 0
\(39\) −9.00000 −1.44115
\(40\) 0 0
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 10.0000 1.52499 0.762493 − 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 0 0
\(45\) −24.0000 −3.57771
\(46\) 0 0
\(47\) 10.0000 1.45865 0.729325 − 0.684167i \(-0.239834\pi\)
0.729325 + 0.684167i \(0.239834\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 3.00000 0.420084
\(52\) 0 0
\(53\) 3.00000 0.412082 0.206041 − 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0 0
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) 6.00000 0.794719
\(58\) 0 0
\(59\) 14.0000 1.82264 0.911322 − 0.411693i \(-0.135063\pi\)
0.911322 + 0.411693i \(0.135063\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 − 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 12.0000 1.48842
\(66\) 0 0
\(67\) −10.0000 −1.22169 −0.610847 − 0.791748i \(-0.709171\pi\)
−0.610847 + 0.791748i \(0.709171\pi\)
\(68\) 0 0
\(69\) 12.0000 1.44463
\(70\) 0 0
\(71\) −5.00000 −0.593391 −0.296695 − 0.954972i \(-0.595885\pi\)
−0.296695 + 0.954972i \(0.595885\pi\)
\(72\) 0 0
\(73\) 16.0000 1.87266 0.936329 − 0.351123i \(-0.114200\pi\)
0.936329 + 0.351123i \(0.114200\pi\)
\(74\) 0 0
\(75\) 33.0000 3.81051
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 11.0000 1.23760 0.618798 − 0.785550i \(-0.287620\pi\)
0.618798 + 0.785550i \(0.287620\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 − 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −9.00000 −0.953998 −0.476999 − 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −24.0000 −2.48868
\(94\) 0 0
\(95\) −8.00000 −0.820783
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 − 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) −10.0000 −0.995037 −0.497519 − 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 − 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.00000 −0.290021 −0.145010 − 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) 8.00000 0.766261 0.383131 − 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(110\) 0 0
\(111\) 24.0000 2.27798
\(112\) 0 0
\(113\) −8.00000 −0.752577 −0.376288 − 0.926503i \(-0.622800\pi\)
−0.376288 + 0.926503i \(0.622800\pi\)
\(114\) 0 0
\(115\) −16.0000 −1.49201
\(116\) 0 0
\(117\) −18.0000 −1.66410
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 30.0000 2.64135
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 − 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −36.0000 −3.09839
\(136\) 0 0
\(137\) 17.0000 1.45241 0.726204 − 0.687479i \(-0.241283\pi\)
0.726204 + 0.687479i \(0.241283\pi\)
\(138\) 0 0
\(139\) 21.0000 1.78120 0.890598 − 0.454791i \(-0.150286\pi\)
0.890598 + 0.454791i \(0.150286\pi\)
\(140\) 0 0
\(141\) 30.0000 2.52646
\(142\) 0 0
\(143\) −3.00000 −0.250873
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −11.0000 −0.901155 −0.450578 − 0.892737i \(-0.648782\pi\)
−0.450578 + 0.892737i \(0.648782\pi\)
\(150\) 0 0
\(151\) 2.00000 0.162758 0.0813788 − 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 32.0000 2.57030
\(156\) 0 0
\(157\) −17.0000 −1.35675 −0.678374 − 0.734717i \(-0.737315\pi\)
−0.678374 + 0.734717i \(0.737315\pi\)
\(158\) 0 0
\(159\) 9.00000 0.713746
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 12.0000 0.939913 0.469956 − 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 0 0
\(165\) −12.0000 −0.934199
\(166\) 0 0
\(167\) −17.0000 −1.31550 −0.657750 − 0.753237i \(-0.728492\pi\)
−0.657750 + 0.753237i \(0.728492\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 12.0000 0.917663
\(172\) 0 0
\(173\) −6.00000 −0.456172 −0.228086 − 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 42.0000 3.15691
\(178\) 0 0
\(179\) 16.0000 1.19590 0.597948 − 0.801535i \(-0.295983\pi\)
0.597948 + 0.801535i \(0.295983\pi\)
\(180\) 0 0
\(181\) 6.00000 0.445976 0.222988 − 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 0 0
\(183\) 24.0000 1.77413
\(184\) 0 0
\(185\) −32.0000 −2.35269
\(186\) 0 0
\(187\) 1.00000 0.0731272
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 − 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 − 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 0 0
\(195\) 36.0000 2.57801
\(196\) 0 0
\(197\) −14.0000 −0.997459 −0.498729 − 0.866758i \(-0.666200\pi\)
−0.498729 + 0.866758i \(0.666200\pi\)
\(198\) 0 0
\(199\) 3.00000 0.212664 0.106332 − 0.994331i \(-0.466089\pi\)
0.106332 + 0.994331i \(0.466089\pi\)
\(200\) 0 0
\(201\) −30.0000 −2.11604
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 24.0000 1.66812
\(208\) 0 0
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 − 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 0 0
\(213\) −15.0000 −1.02778
\(214\) 0 0
\(215\) −40.0000 −2.72798
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 48.0000 3.24354
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) 6.00000 0.401790 0.200895 − 0.979613i \(-0.435615\pi\)
0.200895 + 0.979613i \(0.435615\pi\)
\(224\) 0 0
\(225\) 66.0000 4.40000
\(226\) 0 0
\(227\) 3.00000 0.199117 0.0995585 − 0.995032i \(-0.468257\pi\)
0.0995585 + 0.995032i \(0.468257\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 − 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −20.0000 −1.31024 −0.655122 − 0.755523i \(-0.727383\pi\)
−0.655122 + 0.755523i \(0.727383\pi\)
\(234\) 0 0
\(235\) −40.0000 −2.60931
\(236\) 0 0
\(237\) 33.0000 2.14358
\(238\) 0 0
\(239\) 2.00000 0.129369 0.0646846 − 0.997906i \(-0.479396\pi\)
0.0646846 + 0.997906i \(0.479396\pi\)
\(240\) 0 0
\(241\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.00000 −0.381771
\(248\) 0 0
\(249\) −36.0000 −2.28141
\(250\) 0 0
\(251\) −8.00000 −0.504956 −0.252478 − 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 0 0
\(255\) −12.0000 −0.751469
\(256\) 0 0
\(257\) −11.0000 −0.686161 −0.343081 − 0.939306i \(-0.611470\pi\)
−0.343081 + 0.939306i \(0.611470\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 12.0000 0.739952 0.369976 − 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) −27.0000 −1.65237
\(268\) 0 0
\(269\) 2.00000 0.121942 0.0609711 − 0.998140i \(-0.480580\pi\)
0.0609711 + 0.998140i \(0.480580\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 − 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 11.0000 0.663325
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 − 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 0 0
\(279\) −48.0000 −2.87368
\(280\) 0 0
\(281\) −3.00000 −0.178965 −0.0894825 − 0.995988i \(-0.528521\pi\)
−0.0894825 + 0.995988i \(0.528521\pi\)
\(282\) 0 0
\(283\) −19.0000 −1.12943 −0.564716 − 0.825285i \(-0.691014\pi\)
−0.564716 + 0.825285i \(0.691014\pi\)
\(284\) 0 0
\(285\) −24.0000 −1.42164
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −30.0000 −1.75863
\(292\) 0 0
\(293\) −1.00000 −0.0584206 −0.0292103 − 0.999573i \(-0.509299\pi\)
−0.0292103 + 0.999573i \(0.509299\pi\)
\(294\) 0 0
\(295\) −56.0000 −3.26045
\(296\) 0 0
\(297\) 9.00000 0.522233
\(298\) 0 0
\(299\) −12.0000 −0.693978
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −30.0000 −1.72345
\(304\) 0 0
\(305\) −32.0000 −1.83231
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 − 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) 12.0000 0.682656
\(310\) 0 0
\(311\) 9.00000 0.510343 0.255172 − 0.966896i \(-0.417868\pi\)
0.255172 + 0.966896i \(0.417868\pi\)
\(312\) 0 0
\(313\) 18.0000 1.01742 0.508710 − 0.860938i \(-0.330123\pi\)
0.508710 + 0.860938i \(0.330123\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.00000 0.336994 0.168497 − 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −9.00000 −0.502331
\(322\) 0 0
\(323\) 2.00000 0.111283
\(324\) 0 0
\(325\) −33.0000 −1.83051
\(326\) 0 0
\(327\) 24.0000 1.32720
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 10.0000 0.549650 0.274825 − 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(332\) 0 0
\(333\) 48.0000 2.63038
\(334\) 0 0
\(335\) 40.0000 2.18543
\(336\) 0 0
\(337\) −8.00000 −0.435788 −0.217894 − 0.975972i \(-0.569919\pi\)
−0.217894 + 0.975972i \(0.569919\pi\)
\(338\) 0 0
\(339\) −24.0000 −1.30350
\(340\) 0 0
\(341\) −8.00000 −0.433224
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −48.0000 −2.58423
\(346\) 0 0
\(347\) −4.00000 −0.214731 −0.107366 − 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) 0 0
\(349\) −30.0000 −1.60586 −0.802932 − 0.596071i \(-0.796728\pi\)
−0.802932 + 0.596071i \(0.796728\pi\)
\(350\) 0 0
\(351\) −27.0000 −1.44115
\(352\) 0 0
\(353\) −11.0000 −0.585471 −0.292735 − 0.956193i \(-0.594566\pi\)
−0.292735 + 0.956193i \(0.594566\pi\)
\(354\) 0 0
\(355\) 20.0000 1.06149
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.0000 −0.527780 −0.263890 − 0.964553i \(-0.585006\pi\)
−0.263890 + 0.964553i \(0.585006\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) −30.0000 −1.57459
\(364\) 0 0
\(365\) −64.0000 −3.34991
\(366\) 0 0
\(367\) −3.00000 −0.156599 −0.0782994 − 0.996930i \(-0.524949\pi\)
−0.0782994 + 0.996930i \(0.524949\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 7.00000 0.362446 0.181223 − 0.983442i \(-0.441994\pi\)
0.181223 + 0.983442i \(0.441994\pi\)
\(374\) 0 0
\(375\) −72.0000 −3.71806
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 13.0000 0.667765 0.333883 − 0.942615i \(-0.391641\pi\)
0.333883 + 0.942615i \(0.391641\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −34.0000 −1.73732 −0.868659 − 0.495410i \(-0.835018\pi\)
−0.868659 + 0.495410i \(0.835018\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 60.0000 3.04997
\(388\) 0 0
\(389\) −3.00000 −0.152106 −0.0760530 − 0.997104i \(-0.524232\pi\)
−0.0760530 + 0.997104i \(0.524232\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 0 0
\(393\) 36.0000 1.81596
\(394\) 0 0
\(395\) −44.0000 −2.21388
\(396\) 0 0
\(397\) −2.00000 −0.100377 −0.0501886 − 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −26.0000 −1.29838 −0.649189 − 0.760627i \(-0.724892\pi\)
−0.649189 + 0.760627i \(0.724892\pi\)
\(402\) 0 0
\(403\) 24.0000 1.19553
\(404\) 0 0
\(405\) −36.0000 −1.78885
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) −11.0000 −0.543915 −0.271957 − 0.962309i \(-0.587671\pi\)
−0.271957 + 0.962309i \(0.587671\pi\)
\(410\) 0 0
\(411\) 51.0000 2.51564
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 48.0000 2.35623
\(416\) 0 0
\(417\) 63.0000 3.08512
\(418\) 0 0
\(419\) −9.00000 −0.439679 −0.219839 − 0.975536i \(-0.570553\pi\)
−0.219839 + 0.975536i \(0.570553\pi\)
\(420\) 0 0
\(421\) 6.00000 0.292422 0.146211 − 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) 0 0
\(423\) 60.0000 2.91730
\(424\) 0 0
\(425\) 11.0000 0.533578
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −9.00000 −0.434524
\(430\) 0 0
\(431\) −19.0000 −0.915198 −0.457599 − 0.889159i \(-0.651290\pi\)
−0.457599 + 0.889159i \(0.651290\pi\)
\(432\) 0 0
\(433\) −6.00000 −0.288342 −0.144171 − 0.989553i \(-0.546051\pi\)
−0.144171 + 0.989553i \(0.546051\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.00000 0.382692
\(438\) 0 0
\(439\) 29.0000 1.38409 0.692047 − 0.721852i \(-0.256709\pi\)
0.692047 + 0.721852i \(0.256709\pi\)
\(440\) 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
\(445\) 36.0000 1.70656
\(446\) 0 0
\(447\) −33.0000 −1.56085
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 − 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 6.00000 0.281905
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −10.0000 −0.467780 −0.233890 − 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 0 0
\(459\) 9.00000 0.420084
\(460\) 0 0
\(461\) 17.0000 0.791769 0.395884 − 0.918300i \(-0.370438\pi\)
0.395884 + 0.918300i \(0.370438\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 − 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 0 0
\(465\) 96.0000 4.45189
\(466\) 0 0
\(467\) 36.0000 1.66588 0.832941 − 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −51.0000 −2.34996
\(472\) 0 0
\(473\) 10.0000 0.459800
\(474\) 0 0
\(475\) 22.0000 1.00943
\(476\) 0 0
\(477\) 18.0000 0.824163
\(478\) 0 0
\(479\) −24.0000 −1.09659 −0.548294 − 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) −24.0000 −1.09431
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 40.0000 1.81631
\(486\) 0 0
\(487\) 23.0000 1.04223 0.521115 − 0.853487i \(-0.325516\pi\)
0.521115 + 0.853487i \(0.325516\pi\)
\(488\) 0 0
\(489\) 36.0000 1.62798
\(490\) 0 0
\(491\) −26.0000 −1.17336 −0.586682 − 0.809818i \(-0.699566\pi\)
−0.586682 + 0.809818i \(0.699566\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −24.0000 −1.07872
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −5.00000 −0.223831 −0.111915 − 0.993718i \(-0.535699\pi\)
−0.111915 + 0.993718i \(0.535699\pi\)
\(500\) 0 0
\(501\) −51.0000 −2.27851
\(502\) 0 0
\(503\) −33.0000 −1.47140 −0.735699 − 0.677309i \(-0.763146\pi\)
−0.735699 + 0.677309i \(0.763146\pi\)
\(504\) 0 0
\(505\) 40.0000 1.77998
\(506\) 0 0
\(507\) −12.0000 −0.532939
\(508\) 0 0
\(509\) −38.0000 −1.68432 −0.842160 − 0.539227i \(-0.818716\pi\)
−0.842160 + 0.539227i \(0.818716\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 18.0000 0.794719
\(514\) 0 0
\(515\) −16.0000 −0.705044
\(516\) 0 0
\(517\) 10.0000 0.439799
\(518\) 0 0
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) −22.0000 −0.961993 −0.480996 − 0.876723i \(-0.659725\pi\)
−0.480996 + 0.876723i \(0.659725\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.00000 −0.348485
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 84.0000 3.64529
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 12.0000 0.518805
\(536\) 0 0
\(537\) 48.0000 2.07135
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 − 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 0 0
\(543\) 18.0000 0.772454
\(544\) 0 0
\(545\) −32.0000 −1.37073
\(546\) 0 0
\(547\) −1.00000 −0.0427569 −0.0213785 − 0.999771i \(-0.506805\pi\)
−0.0213785 + 0.999771i \(0.506805\pi\)
\(548\) 0 0
\(549\) 48.0000 2.04859
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −96.0000 −4.07497
\(556\) 0 0
\(557\) 15.0000 0.635570 0.317785 − 0.948163i \(-0.397061\pi\)
0.317785 + 0.948163i \(0.397061\pi\)
\(558\) 0 0
\(559\) −30.0000 −1.26886
\(560\) 0 0
\(561\) 3.00000 0.126660
\(562\) 0 0
\(563\) 2.00000 0.0842900 0.0421450 − 0.999112i \(-0.486581\pi\)
0.0421450 + 0.999112i \(0.486581\pi\)
\(564\) 0 0
\(565\) 32.0000 1.34625
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −15.0000 −0.628833 −0.314416 − 0.949285i \(-0.601809\pi\)
−0.314416 + 0.949285i \(0.601809\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 − 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 36.0000 1.50392
\(574\) 0 0
\(575\) 44.0000 1.83493
\(576\) 0 0
\(577\) 43.0000 1.79011 0.895057 − 0.445952i \(-0.147135\pi\)
0.895057 + 0.445952i \(0.147135\pi\)
\(578\) 0 0
\(579\) 42.0000 1.74546
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 3.00000 0.124247
\(584\) 0 0
\(585\) 72.0000 2.97683
\(586\) 0 0
\(587\) 10.0000 0.412744 0.206372 − 0.978474i \(-0.433834\pi\)
0.206372 + 0.978474i \(0.433834\pi\)
\(588\) 0 0
\(589\) −16.0000 −0.659269
\(590\) 0 0
\(591\) −42.0000 −1.72765
\(592\) 0 0
\(593\) −21.0000 −0.862367 −0.431183 − 0.902264i \(-0.641904\pi\)
−0.431183 + 0.902264i \(0.641904\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 9.00000 0.368345
\(598\) 0 0
\(599\) 30.0000 1.22577 0.612883 − 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 0 0
\(601\) 46.0000 1.87638 0.938190 − 0.346122i \(-0.112502\pi\)
0.938190 + 0.346122i \(0.112502\pi\)
\(602\) 0 0
\(603\) −60.0000 −2.44339
\(604\) 0 0
\(605\) 40.0000 1.62623
\(606\) 0 0
\(607\) −29.0000 −1.17707 −0.588537 − 0.808470i \(-0.700296\pi\)
−0.588537 + 0.808470i \(0.700296\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −30.0000 −1.21367
\(612\) 0 0
\(613\) 17.0000 0.686624 0.343312 − 0.939222i \(-0.388451\pi\)
0.343312 + 0.939222i \(0.388451\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −44.0000 −1.77137 −0.885687 − 0.464283i \(-0.846312\pi\)
−0.885687 + 0.464283i \(0.846312\pi\)
\(618\) 0 0
\(619\) 29.0000 1.16561 0.582804 − 0.812613i \(-0.301955\pi\)
0.582804 + 0.812613i \(0.301955\pi\)
\(620\) 0 0
\(621\) 36.0000 1.44463
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) 0 0
\(627\) 6.00000 0.239617
\(628\) 0 0
\(629\) 8.00000 0.318981
\(630\) 0 0
\(631\) −46.0000 −1.83123 −0.915616 − 0.402055i \(-0.868296\pi\)
−0.915616 + 0.402055i \(0.868296\pi\)
\(632\) 0 0
\(633\) 60.0000 2.38479
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −30.0000 −1.18678
\(640\) 0 0
\(641\) −26.0000 −1.02694 −0.513469 − 0.858108i \(-0.671640\pi\)
−0.513469 + 0.858108i \(0.671640\pi\)
\(642\) 0 0
\(643\) −27.0000 −1.06478 −0.532388 − 0.846500i \(-0.678705\pi\)
−0.532388 + 0.846500i \(0.678705\pi\)
\(644\) 0 0
\(645\) −120.000 −4.72500
\(646\) 0 0
\(647\) −28.0000 −1.10079 −0.550397 − 0.834903i \(-0.685524\pi\)
−0.550397 + 0.834903i \(0.685524\pi\)
\(648\) 0 0
\(649\) 14.0000 0.549548
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 46.0000 1.80012 0.900060 − 0.435767i \(-0.143523\pi\)
0.900060 + 0.435767i \(0.143523\pi\)
\(654\) 0 0
\(655\) −48.0000 −1.87552
\(656\) 0 0
\(657\) 96.0000 3.74532
\(658\) 0 0
\(659\) 2.00000 0.0779089 0.0389545 − 0.999241i \(-0.487597\pi\)
0.0389545 + 0.999241i \(0.487597\pi\)
\(660\) 0 0
\(661\) 30.0000 1.16686 0.583432 − 0.812162i \(-0.301709\pi\)
0.583432 + 0.812162i \(0.301709\pi\)
\(662\) 0 0
\(663\) −9.00000 −0.349531
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 18.0000 0.695920
\(670\) 0 0
\(671\) 8.00000 0.308837
\(672\) 0 0
\(673\) −44.0000 −1.69608 −0.848038 − 0.529936i \(-0.822216\pi\)
−0.848038 + 0.529936i \(0.822216\pi\)
\(674\) 0 0
\(675\) 99.0000 3.81051
\(676\) 0 0
\(677\) 48.0000 1.84479 0.922395 − 0.386248i \(-0.126229\pi\)
0.922395 + 0.386248i \(0.126229\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 9.00000 0.344881
\(682\) 0 0
\(683\) −9.00000 −0.344375 −0.172188 − 0.985064i \(-0.555084\pi\)
−0.172188 + 0.985064i \(0.555084\pi\)
\(684\) 0 0
\(685\) −68.0000 −2.59815
\(686\) 0 0
\(687\) 30.0000 1.14457
\(688\) 0 0
\(689\) −9.00000 −0.342873
\(690\) 0 0
\(691\) −16.0000 −0.608669 −0.304334 − 0.952565i \(-0.598434\pi\)
−0.304334 + 0.952565i \(0.598434\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −84.0000 −3.18630
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −60.0000 −2.26941
\(700\) 0 0
\(701\) 39.0000 1.47301 0.736505 − 0.676432i \(-0.236475\pi\)
0.736505 + 0.676432i \(0.236475\pi\)
\(702\) 0 0
\(703\) 16.0000 0.603451
\(704\) 0 0
\(705\) −120.000 −4.51946
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −2.00000 −0.0751116 −0.0375558 − 0.999295i \(-0.511957\pi\)
−0.0375558 + 0.999295i \(0.511957\pi\)
\(710\) 0 0
\(711\) 66.0000 2.47519
\(712\) 0 0
\(713\) −32.0000 −1.19841
\(714\) 0 0
\(715\) 12.0000 0.448775
\(716\) 0 0
\(717\) 6.00000 0.224074
\(718\) 0 0
\(719\) 15.0000 0.559406 0.279703 − 0.960087i \(-0.409764\pi\)
0.279703 + 0.960087i \(0.409764\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 14.0000 0.519231 0.259616 − 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 10.0000 0.369863
\(732\) 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
\(737\) −10.0000 −0.368355
\(738\) 0 0
\(739\) −34.0000 −1.25071 −0.625355 − 0.780340i \(-0.715046\pi\)
−0.625355 + 0.780340i \(0.715046\pi\)
\(740\) 0 0
\(741\) −18.0000 −0.661247
\(742\) 0 0
\(743\) −27.0000 −0.990534 −0.495267 − 0.868741i \(-0.664930\pi\)
−0.495267 + 0.868741i \(0.664930\pi\)
\(744\) 0 0
\(745\) 44.0000 1.61204
\(746\) 0 0
\(747\) −72.0000 −2.63434
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 23.0000 0.839282 0.419641 − 0.907690i \(-0.362156\pi\)
0.419641 + 0.907690i \(0.362156\pi\)
\(752\) 0 0
\(753\) −24.0000 −0.874609
\(754\) 0 0
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) 17.0000 0.617876 0.308938 − 0.951082i \(-0.400027\pi\)
0.308938 + 0.951082i \(0.400027\pi\)
\(758\) 0 0
\(759\) 12.0000 0.435572
\(760\) 0 0
\(761\) 27.0000 0.978749 0.489375 − 0.872074i \(-0.337225\pi\)
0.489375 + 0.872074i \(0.337225\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −24.0000 −0.867722
\(766\) 0 0
\(767\) −42.0000 −1.51653
\(768\) 0 0
\(769\) −25.0000 −0.901523 −0.450762 − 0.892644i \(-0.648848\pi\)
−0.450762 + 0.892644i \(0.648848\pi\)
\(770\) 0 0
\(771\) −33.0000 −1.18847
\(772\) 0 0
\(773\) −33.0000 −1.18693 −0.593464 − 0.804861i \(-0.702240\pi\)
−0.593464 + 0.804861i \(0.702240\pi\)
\(774\) 0 0
\(775\) −88.0000 −3.16105
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −5.00000 −0.178914
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 68.0000 2.42702
\(786\) 0 0
\(787\) 4.00000 0.142585 0.0712923 − 0.997455i \(-0.477288\pi\)
0.0712923 + 0.997455i \(0.477288\pi\)
\(788\) 0 0
\(789\) 36.0000 1.28163
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −24.0000 −0.852265
\(794\) 0 0
\(795\) −36.0000 −1.27679
\(796\) 0 0
\(797\) 37.0000 1.31061 0.655304 − 0.755366i \(-0.272541\pi\)
0.655304 + 0.755366i \(0.272541\pi\)
\(798\) 0 0
\(799\) 10.0000 0.353775
\(800\) 0 0
\(801\) −54.0000 −1.90800
\(802\) 0 0
\(803\) 16.0000 0.564628
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 6.00000 0.211210
\(808\) 0 0
\(809\) −42.0000 −1.47664 −0.738321 − 0.674450i \(-0.764381\pi\)
−0.738321 + 0.674450i \(0.764381\pi\)
\(810\) 0 0
\(811\) −5.00000 −0.175574 −0.0877869 − 0.996139i \(-0.527979\pi\)
−0.0877869 + 0.996139i \(0.527979\pi\)
\(812\) 0 0
\(813\) −24.0000 −0.841717
\(814\) 0 0
\(815\) −48.0000 −1.68137
\(816\) 0 0
\(817\) 20.0000 0.699711
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 24.0000 0.837606 0.418803 − 0.908077i \(-0.362450\pi\)
0.418803 + 0.908077i \(0.362450\pi\)
\(822\) 0 0
\(823\) −7.00000 −0.244005 −0.122002 − 0.992530i \(-0.538932\pi\)
−0.122002 + 0.992530i \(0.538932\pi\)
\(824\) 0 0
\(825\) 33.0000 1.14891
\(826\) 0 0
\(827\) −27.0000 −0.938882 −0.469441 − 0.882964i \(-0.655545\pi\)
−0.469441 + 0.882964i \(0.655545\pi\)
\(828\) 0 0
\(829\) −25.0000 −0.868286 −0.434143 − 0.900844i \(-0.642949\pi\)
−0.434143 + 0.900844i \(0.642949\pi\)
\(830\) 0 0
\(831\) 24.0000 0.832551
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 68.0000 2.35324
\(836\) 0 0
\(837\) −72.0000 −2.48868
\(838\) 0 0
\(839\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) −9.00000 −0.309976
\(844\) 0 0
\(845\) 16.0000 0.550417
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −57.0000 −1.95623
\(850\) 0 0
\(851\) 32.0000 1.09695
\(852\) 0 0
\(853\) −26.0000 −0.890223 −0.445112 − 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) 0 0
\(855\) −48.0000 −1.64157
\(856\) 0 0
\(857\) 2.00000 0.0683187 0.0341593 − 0.999416i \(-0.489125\pi\)
0.0341593 + 0.999416i \(0.489125\pi\)
\(858\) 0 0
\(859\) 20.0000 0.682391 0.341196 − 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 20.0000 0.680808 0.340404 − 0.940279i \(-0.389436\pi\)
0.340404 + 0.940279i \(0.389436\pi\)
\(864\) 0 0
\(865\) 24.0000 0.816024
\(866\) 0 0
\(867\) 3.00000 0.101885
\(868\) 0 0
\(869\) 11.0000 0.373149
\(870\) 0 0
\(871\) 30.0000 1.01651
\(872\) 0 0
\(873\) −60.0000 −2.03069
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 6.00000 0.202606 0.101303 − 0.994856i \(-0.467699\pi\)
0.101303 + 0.994856i \(0.467699\pi\)
\(878\) 0 0
\(879\) −3.00000 −0.101187
\(880\) 0 0
\(881\) 54.0000 1.81931 0.909653 − 0.415369i \(-0.136347\pi\)
0.909653 + 0.415369i \(0.136347\pi\)
\(882\) 0 0
\(883\) 34.0000 1.14419 0.572096 − 0.820187i \(-0.306131\pi\)
0.572096 + 0.820187i \(0.306131\pi\)
\(884\) 0 0
\(885\) −168.000 −5.64726
\(886\) 0 0
\(887\) 47.0000 1.57811 0.789053 − 0.614325i \(-0.210572\pi\)
0.789053 + 0.614325i \(0.210572\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 9.00000 0.301511
\(892\) 0 0
\(893\) 20.0000 0.669274
\(894\) 0 0
\(895\) −64.0000 −2.13928
\(896\) 0 0
\(897\) −36.0000 −1.20201
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 3.00000 0.0999445
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −24.0000 −0.797787
\(906\) 0 0
\(907\) 12.0000 0.398453 0.199227 − 0.979953i \(-0.436157\pi\)
0.199227 + 0.979953i \(0.436157\pi\)
\(908\) 0 0
\(909\) −60.0000 −1.99007
\(910\) 0 0
\(911\) 28.0000 0.927681 0.463841 − 0.885919i \(-0.346471\pi\)
0.463841 + 0.885919i \(0.346471\pi\)
\(912\) 0 0
\(913\) −12.0000 −0.397142
\(914\) 0 0
\(915\) −96.0000 −3.17366
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −4.00000 −0.131948 −0.0659739 − 0.997821i \(-0.521015\pi\)
−0.0659739 + 0.997821i \(0.521015\pi\)
\(920\) 0 0
\(921\) −12.0000 −0.395413
\(922\) 0 0
\(923\) 15.0000 0.493731
\(924\) 0 0
\(925\) 88.0000 2.89342
\(926\) 0 0
\(927\) 24.0000 0.788263
\(928\) 0 0
\(929\) 44.0000 1.44359 0.721797 − 0.692105i \(-0.243317\pi\)
0.721797 + 0.692105i \(0.243317\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 27.0000 0.883940
\(934\) 0 0
\(935\) −4.00000 −0.130814
\(936\) 0 0
\(937\) 22.0000 0.718709 0.359354 − 0.933201i \(-0.382997\pi\)
0.359354 + 0.933201i \(0.382997\pi\)
\(938\) 0 0
\(939\) 54.0000 1.76222
\(940\) 0 0
\(941\) 48.0000 1.56476 0.782378 − 0.622804i \(-0.214007\pi\)
0.782378 + 0.622804i \(0.214007\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 9.00000 0.292461 0.146230 − 0.989251i \(-0.453286\pi\)
0.146230 + 0.989251i \(0.453286\pi\)
\(948\) 0 0
\(949\) −48.0000 −1.55815
\(950\) 0 0
\(951\) 18.0000 0.583690
\(952\) 0 0
\(953\) −51.0000 −1.65205 −0.826026 − 0.563632i \(-0.809404\pi\)
−0.826026 + 0.563632i \(0.809404\pi\)
\(954\) 0 0
\(955\) −48.0000 −1.55324
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 0 0
\(963\) −18.0000 −0.580042
\(964\) 0 0
\(965\) −56.0000 −1.80270
\(966\) 0 0
\(967\) −22.0000 −0.707472 −0.353736 − 0.935345i \(-0.615089\pi\)
−0.353736 + 0.935345i \(0.615089\pi\)
\(968\) 0 0
\(969\) 6.00000 0.192748
\(970\) 0 0
\(971\) −6.00000 −0.192549 −0.0962746 − 0.995355i \(-0.530693\pi\)
−0.0962746 + 0.995355i \(0.530693\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −99.0000 −3.17054
\(976\) 0 0
\(977\) 34.0000 1.08776 0.543878 − 0.839164i \(-0.316955\pi\)
0.543878 + 0.839164i \(0.316955\pi\)
\(978\) 0 0
\(979\) −9.00000 −0.287641
\(980\) 0 0
\(981\) 48.0000 1.53252
\(982\) 0 0
\(983\) 37.0000 1.18012 0.590058 − 0.807361i \(-0.299105\pi\)
0.590058 + 0.807361i \(0.299105\pi\)
\(984\) 0 0
\(985\) 56.0000 1.78431
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 40.0000 1.27193
\(990\) 0 0
\(991\) 13.0000 0.412959 0.206479 − 0.978451i \(-0.433799\pi\)
0.206479 + 0.978451i \(0.433799\pi\)
\(992\) 0 0
\(993\) 30.0000 0.952021
\(994\) 0 0
\(995\) −12.0000 −0.380426
\(996\) 0 0
\(997\) 30.0000 0.950110 0.475055 − 0.879956i \(-0.342428\pi\)
0.475055 + 0.879956i \(0.342428\pi\)
\(998\) 0 0
\(999\) 72.0000 2.27798
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 3332.2.a.f.1.1 1
7.3 odd 6 476.2.i.c.205.1 yes 2
7.5 odd 6 476.2.i.c.137.1 ✓ 2
7.6 odd 2 3332.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
476.2.i.c.137.1 ✓ 2 7.5 odd 6
476.2.i.c.205.1 yes 2 7.3 odd 6
3332.2.a.a.1.1 1 7.6 odd 2
3332.2.a.f.1.1 1 1.1 even 1 trivial