Properties

Label 4864.2.a.i.1.1
Level $4864$
Weight $2$
Character 4864.1
Self dual yes
Analytic conductor $38.839$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4864,2,Mod(1,4864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4864, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4864.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4864 = 2^{8} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4864.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(38.8392355432\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 152)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 4864.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{7} -3.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{7} -3.00000 q^{9} -4.00000 q^{11} +2.00000 q^{13} +2.00000 q^{17} +1.00000 q^{19} -2.00000 q^{23} -5.00000 q^{25} +2.00000 q^{29} +8.00000 q^{31} -10.0000 q^{37} +6.00000 q^{41} +4.00000 q^{43} +2.00000 q^{47} -3.00000 q^{49} +2.00000 q^{53} -12.0000 q^{59} -8.00000 q^{61} -6.00000 q^{63} -4.00000 q^{67} -12.0000 q^{71} +10.0000 q^{73} -8.00000 q^{77} -4.00000 q^{79} +9.00000 q^{81} -4.00000 q^{83} -6.00000 q^{89} +4.00000 q^{91} -10.0000 q^{97} +12.0000 q^{99} +O(q^{100})\)

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
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 −0.417029 −0.208514 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 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
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 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
\(63\) −6.00000 −0.755929
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −8.00000 −0.911685
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) 12.0000 1.20605
\(100\) 0 0
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −18.0000 −1.72409 −0.862044 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −6.00000 −0.554700
\(118\) 0 0
\(119\) 4.00000 0.366679
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 2.00000 0.173422
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000 0.512615 0.256307 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −8.00000 −0.668994
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.00000 −0.327693 −0.163846 0.986486i \(-0.552390\pi\)
−0.163846 + 0.986486i \(0.552390\pi\)
\(150\) 0 0
\(151\) 12.0000 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −20.0000 −1.59617 −0.798087 0.602542i \(-0.794154\pi\)
−0.798087 + 0.602542i \(0.794154\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.00000 −0.315244
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −3.00000 −0.229416
\(172\) 0 0
\(173\) −22.0000 −1.67263 −0.836315 0.548250i \(-0.815294\pi\)
−0.836315 + 0.548250i \(0.815294\pi\)
\(174\) 0 0
\(175\) −10.0000 −0.755929
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 16.0000 1.19590 0.597948 0.801535i \(-0.295983\pi\)
0.597948 + 0.801535i \(0.295983\pi\)
\(180\) 0 0
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −8.00000 −0.585018
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 18.0000 1.30243 0.651217 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −24.0000 −1.70993 −0.854965 0.518686i \(-0.826421\pi\)
−0.854965 + 0.518686i \(0.826421\pi\)
\(198\) 0 0
\(199\) 22.0000 1.55954 0.779769 0.626067i \(-0.215336\pi\)
0.779769 + 0.626067i \(0.215336\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.00000 0.280745
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.00000 0.417029
\(208\) 0 0
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 16.0000 1.08615
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) 0 0
\(225\) 15.0000 1.00000
\(226\) 0 0
\(227\) −12.0000 −0.796468 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) 0 0
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.00000 0.127257
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −22.0000 −1.37232 −0.686161 0.727450i \(-0.740706\pi\)
−0.686161 + 0.727450i \(0.740706\pi\)
\(258\) 0 0
\(259\) −20.0000 −1.24274
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 0 0
\(263\) 6.00000 0.369976 0.184988 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) 30.0000 1.82237 0.911185 0.411997i \(-0.135169\pi\)
0.911185 + 0.411997i \(0.135169\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 20.0000 1.20605
\(276\) 0 0
\(277\) 28.0000 1.68236 0.841178 0.540758i \(-0.181862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 0 0
\(279\) −24.0000 −1.43684
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) 12.0000 0.713326 0.356663 0.934233i \(-0.383914\pi\)
0.356663 + 0.934233i \(0.383914\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 12.0000 0.708338
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −26.0000 −1.51894 −0.759468 0.650545i \(-0.774541\pi\)
−0.759468 + 0.650545i \(0.774541\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.00000 −0.231326
\(300\) 0 0
\(301\) 8.00000 0.461112
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 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
\(319\) −8.00000 −0.447914
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.00000 0.111283
\(324\) 0 0
\(325\) −10.0000 −0.554700
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.00000 0.220527
\(330\) 0 0
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) 0 0
\(333\) 30.0000 1.64399
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 26.0000 1.41631 0.708155 0.706057i \(-0.249528\pi\)
0.708155 + 0.706057i \(0.249528\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −32.0000 −1.73290
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) −4.00000 −0.214115 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 30.0000 1.59674 0.798369 0.602168i \(-0.205696\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −18.0000 −0.950004 −0.475002 0.879985i \(-0.657553\pi\)
−0.475002 + 0.879985i \(0.657553\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 2.00000 0.104399 0.0521996 0.998637i \(-0.483377\pi\)
0.0521996 + 0.998637i \(0.483377\pi\)
\(368\) 0 0
\(369\) −18.0000 −0.937043
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) −18.0000 −0.932005 −0.466002 0.884783i \(-0.654306\pi\)
−0.466002 + 0.884783i \(0.654306\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −12.0000 −0.609994
\(388\) 0 0
\(389\) 8.00000 0.405616 0.202808 0.979219i \(-0.434993\pi\)
0.202808 + 0.979219i \(0.434993\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −20.0000 −1.00377 −0.501886 0.864934i \(-0.667360\pi\)
−0.501886 + 0.864934i \(0.667360\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) 0 0
\(403\) 16.0000 0.797017
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 40.0000 1.98273
\(408\) 0 0
\(409\) 6.00000 0.296681 0.148340 0.988936i \(-0.452607\pi\)
0.148340 + 0.988936i \(0.452607\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −24.0000 −1.18096
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −28.0000 −1.36789 −0.683945 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) −6.00000 −0.291730
\(424\) 0 0
\(425\) −10.0000 −0.485071
\(426\) 0 0
\(427\) −16.0000 −0.774294
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.00000 −0.385346 −0.192673 0.981263i \(-0.561716\pi\)
−0.192673 + 0.981263i \(0.561716\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.00000 −0.0956730
\(438\) 0 0
\(439\) 20.0000 0.954548 0.477274 0.878755i \(-0.341625\pi\)
0.477274 + 0.878755i \(0.341625\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 0 0
\(443\) −28.0000 −1.33032 −0.665160 0.746701i \(-0.731637\pi\)
−0.665160 + 0.746701i \(0.731637\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 38.0000 1.79333 0.896665 0.442709i \(-0.145982\pi\)
0.896665 + 0.442709i \(0.145982\pi\)
\(450\) 0 0
\(451\) −24.0000 −1.13012
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −26.0000 −1.21623 −0.608114 0.793849i \(-0.708074\pi\)
−0.608114 + 0.793849i \(0.708074\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −36.0000 −1.67669 −0.838344 0.545142i \(-0.816476\pi\)
−0.838344 + 0.545142i \(0.816476\pi\)
\(462\) 0 0
\(463\) −34.0000 −1.58011 −0.790057 0.613033i \(-0.789949\pi\)
−0.790057 + 0.613033i \(0.789949\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) −8.00000 −0.369406
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −16.0000 −0.735681
\(474\) 0 0
\(475\) −5.00000 −0.229416
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) −42.0000 −1.91903 −0.959514 0.281659i \(-0.909115\pi\)
−0.959514 + 0.281659i \(0.909115\pi\)
\(480\) 0 0
\(481\) −20.0000 −0.911922
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 12.0000 0.543772 0.271886 0.962329i \(-0.412353\pi\)
0.271886 + 0.962329i \(0.412353\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) 4.00000 0.180151
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −24.0000 −1.07655
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −22.0000 −0.980932 −0.490466 0.871460i \(-0.663173\pi\)
−0.490466 + 0.871460i \(0.663173\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 14.0000 0.620539 0.310270 0.950649i \(-0.399581\pi\)
0.310270 + 0.950649i \(0.399581\pi\)
\(510\) 0 0
\(511\) 20.0000 0.884748
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −8.00000 −0.351840
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −2.00000 −0.0876216 −0.0438108 0.999040i \(-0.513950\pi\)
−0.0438108 + 0.999040i \(0.513950\pi\)
\(522\) 0 0
\(523\) 8.00000 0.349816 0.174908 0.984585i \(-0.444037\pi\)
0.174908 + 0.984585i \(0.444037\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16.0000 0.696971
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 0 0
\(531\) 36.0000 1.56227
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 12.0000 0.516877
\(540\) 0 0
\(541\) 16.0000 0.687894 0.343947 0.938989i \(-0.388236\pi\)
0.343947 + 0.938989i \(0.388236\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −32.0000 −1.36822 −0.684111 0.729378i \(-0.739809\pi\)
−0.684111 + 0.729378i \(0.739809\pi\)
\(548\) 0 0
\(549\) 24.0000 1.02430
\(550\) 0 0
\(551\) 2.00000 0.0852029
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12.0000 −0.508456 −0.254228 0.967144i \(-0.581821\pi\)
−0.254228 + 0.967144i \(0.581821\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −24.0000 −1.01148 −0.505740 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 18.0000 0.755929
\(568\) 0 0
\(569\) 30.0000 1.25767 0.628833 0.777541i \(-0.283533\pi\)
0.628833 + 0.777541i \(0.283533\pi\)
\(570\) 0 0
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 10.0000 0.417029
\(576\) 0 0
\(577\) −42.0000 −1.74848 −0.874241 0.485491i \(-0.838641\pi\)
−0.874241 + 0.485491i \(0.838641\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −8.00000 −0.331896
\(582\) 0 0
\(583\) −8.00000 −0.331326
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 36.0000 1.48588 0.742940 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) 0 0
\(589\) 8.00000 0.329634
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 40.0000 1.63436 0.817178 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4.00000 0.161823
\(612\) 0 0
\(613\) 36.0000 1.45403 0.727013 0.686624i \(-0.240908\pi\)
0.727013 + 0.686624i \(0.240908\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 26.0000 1.04672 0.523360 0.852111i \(-0.324678\pi\)
0.523360 + 0.852111i \(0.324678\pi\)
\(618\) 0 0
\(619\) 28.0000 1.12542 0.562708 0.826656i \(-0.309760\pi\)
0.562708 + 0.826656i \(0.309760\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −12.0000 −0.480770
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −20.0000 −0.797452
\(630\) 0 0
\(631\) −26.0000 −1.03504 −0.517522 0.855670i \(-0.673145\pi\)
−0.517522 + 0.855670i \(0.673145\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.00000 −0.237729
\(638\) 0 0
\(639\) 36.0000 1.42414
\(640\) 0 0
\(641\) 14.0000 0.552967 0.276483 0.961019i \(-0.410831\pi\)
0.276483 + 0.961019i \(0.410831\pi\)
\(642\) 0 0
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 22.0000 0.864909 0.432455 0.901656i \(-0.357648\pi\)
0.432455 + 0.901656i \(0.357648\pi\)
\(648\) 0 0
\(649\) 48.0000 1.88416
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 12.0000 0.469596 0.234798 0.972044i \(-0.424557\pi\)
0.234798 + 0.972044i \(0.424557\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −30.0000 −1.17041
\(658\) 0 0
\(659\) 32.0000 1.24654 0.623272 0.782006i \(-0.285803\pi\)
0.623272 + 0.782006i \(0.285803\pi\)
\(660\) 0 0
\(661\) 22.0000 0.855701 0.427850 0.903850i \(-0.359271\pi\)
0.427850 + 0.903850i \(0.359271\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4.00000 −0.154881
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 32.0000 1.23535
\(672\) 0 0
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 22.0000 0.845529 0.422764 0.906240i \(-0.361060\pi\)
0.422764 + 0.906240i \(0.361060\pi\)
\(678\) 0 0
\(679\) −20.0000 −0.767530
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4.00000 0.152388
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 0 0
\(693\) 24.0000 0.911685
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 12.0000 0.454532
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) 0 0
\(703\) −10.0000 −0.377157
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −24.0000 −0.902613
\(708\) 0 0
\(709\) 4.00000 0.150223 0.0751116 0.997175i \(-0.476069\pi\)
0.0751116 + 0.997175i \(0.476069\pi\)
\(710\) 0 0
\(711\) 12.0000 0.450035
\(712\) 0 0
\(713\) −16.0000 −0.599205
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2.00000 0.0745874 0.0372937 0.999304i \(-0.488126\pi\)
0.0372937 + 0.999304i \(0.488126\pi\)
\(720\) 0 0
\(721\) 16.0000 0.595871
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −10.0000 −0.371391
\(726\) 0 0
\(727\) −26.0000 −0.964287 −0.482143 0.876092i \(-0.660142\pi\)
−0.482143 + 0.876092i \(0.660142\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 8.00000 0.295891
\(732\) 0 0
\(733\) 24.0000 0.886460 0.443230 0.896408i \(-0.353832\pi\)
0.443230 + 0.896408i \(0.353832\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 16.0000 0.589368
\(738\) 0 0
\(739\) 4.00000 0.147142 0.0735712 0.997290i \(-0.476560\pi\)
0.0735712 + 0.997290i \(0.476560\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 44.0000 1.61420 0.807102 0.590412i \(-0.201035\pi\)
0.807102 + 0.590412i \(0.201035\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) 24.0000 0.876941
\(750\) 0 0
\(751\) 4.00000 0.145962 0.0729810 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 8.00000 0.290765 0.145382 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −42.0000 −1.52250 −0.761249 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 0 0
\(763\) −36.0000 −1.30329
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −24.0000 −0.866590
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 38.0000 1.36677 0.683383 0.730061i \(-0.260508\pi\)
0.683383 + 0.730061i \(0.260508\pi\)
\(774\) 0 0
\(775\) −40.0000 −1.43684
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) 48.0000 1.71758
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 20.0000 0.712923 0.356462 0.934310i \(-0.383983\pi\)
0.356462 + 0.934310i \(0.383983\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) −16.0000 −0.568177
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −6.00000 −0.212531 −0.106265 0.994338i \(-0.533889\pi\)
−0.106265 + 0.994338i \(0.533889\pi\)
\(798\) 0 0
\(799\) 4.00000 0.141510
\(800\) 0 0
\(801\) 18.0000 0.635999
\(802\) 0 0
\(803\) −40.0000 −1.41157
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 18.0000 0.632846 0.316423 0.948618i \(-0.397518\pi\)
0.316423 + 0.948618i \(0.397518\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 4.00000 0.139942
\(818\) 0 0
\(819\) −12.0000 −0.419314
\(820\) 0 0
\(821\) −28.0000 −0.977207 −0.488603 0.872506i \(-0.662493\pi\)
−0.488603 + 0.872506i \(0.662493\pi\)
\(822\) 0 0
\(823\) 30.0000 1.04573 0.522867 0.852414i \(-0.324862\pi\)
0.522867 + 0.852414i \(0.324862\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −40.0000 −1.39094 −0.695468 0.718557i \(-0.744803\pi\)
−0.695468 + 0.718557i \(0.744803\pi\)
\(828\) 0 0
\(829\) −2.00000 −0.0694629 −0.0347314 0.999397i \(-0.511058\pi\)
−0.0347314 + 0.999397i \(0.511058\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −6.00000 −0.207888
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 10.0000 0.343604
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 20.0000 0.685591
\(852\) 0 0
\(853\) 16.0000 0.547830 0.273915 0.961754i \(-0.411681\pi\)
0.273915 + 0.961754i \(0.411681\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 14.0000 0.478231 0.239115 0.970991i \(-0.423143\pi\)
0.239115 + 0.970991i \(0.423143\pi\)
\(858\) 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
\(863\) 4.00000 0.136162 0.0680808 0.997680i \(-0.478312\pi\)
0.0680808 + 0.997680i \(0.478312\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 16.0000 0.542763
\(870\) 0 0
\(871\) −8.00000 −0.271070
\(872\) 0 0
\(873\) 30.0000 1.01535
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 22.0000 0.742887 0.371444 0.928456i \(-0.378863\pi\)
0.371444 + 0.928456i \(0.378863\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 30.0000 1.01073 0.505363 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) 0 0
\(883\) 4.00000 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −12.0000 −0.402921 −0.201460 0.979497i \(-0.564569\pi\)
−0.201460 + 0.979497i \(0.564569\pi\)
\(888\) 0 0
\(889\) −24.0000 −0.804934
\(890\) 0 0
\(891\) −36.0000 −1.20605
\(892\) 0 0
\(893\) 2.00000 0.0669274
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 16.0000 0.533630
\(900\) 0 0
\(901\) 4.00000 0.133259
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 48.0000 1.59381 0.796907 0.604102i \(-0.206468\pi\)
0.796907 + 0.604102i \(0.206468\pi\)
\(908\) 0 0
\(909\) 36.0000 1.19404
\(910\) 0 0
\(911\) −36.0000 −1.19273 −0.596367 0.802712i \(-0.703390\pi\)
−0.596367 + 0.802712i \(0.703390\pi\)
\(912\) 0 0
\(913\) 16.0000 0.529523
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −24.0000 −0.792550
\(918\) 0 0
\(919\) −34.0000 −1.12156 −0.560778 0.827966i \(-0.689498\pi\)
−0.560778 + 0.827966i \(0.689498\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −24.0000 −0.789970
\(924\) 0 0
\(925\) 50.0000 1.64399
\(926\) 0 0
\(927\) −24.0000 −0.788263
\(928\) 0 0
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 0 0
\(931\) −3.00000 −0.0983210
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −26.0000 −0.849383 −0.424691 0.905338i \(-0.639617\pi\)
−0.424691 + 0.905338i \(0.639617\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −6.00000 −0.195594 −0.0977972 0.995206i \(-0.531180\pi\)
−0.0977972 + 0.995206i \(0.531180\pi\)
\(942\) 0 0
\(943\) −12.0000 −0.390774
\(944\) 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
\(949\) 20.0000 0.649227
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −26.0000 −0.842223 −0.421111 0.907009i \(-0.638360\pi\)
−0.421111 + 0.907009i \(0.638360\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 12.0000 0.387500
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 0 0
\(963\) −36.0000 −1.16008
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −2.00000 −0.0643157 −0.0321578 0.999483i \(-0.510238\pi\)
−0.0321578 + 0.999483i \(0.510238\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 20.0000 0.641831 0.320915 0.947108i \(-0.396010\pi\)
0.320915 + 0.947108i \(0.396010\pi\)
\(972\) 0 0
\(973\) 40.0000 1.28234
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 22.0000 0.703842 0.351921 0.936030i \(-0.385529\pi\)
0.351921 + 0.936030i \(0.385529\pi\)
\(978\) 0 0
\(979\) 24.0000 0.767043
\(980\) 0 0
\(981\) 54.0000 1.72409
\(982\) 0 0
\(983\) −8.00000 −0.255160 −0.127580 0.991828i \(-0.540721\pi\)
−0.127580 + 0.991828i \(0.540721\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −8.00000 −0.254385
\(990\) 0 0
\(991\) 56.0000 1.77890 0.889449 0.457034i \(-0.151088\pi\)
0.889449 + 0.457034i \(0.151088\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −28.0000 −0.886769 −0.443384 0.896332i \(-0.646222\pi\)
−0.443384 + 0.896332i \(0.646222\pi\)
\(998\) 0 0
\(999\) 0 0
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 4864.2.a.i.1.1 1
4.3 odd 2 4864.2.a.h.1.1 1
8.3 odd 2 4864.2.a.g.1.1 1
8.5 even 2 4864.2.a.j.1.1 1
16.3 odd 4 152.2.c.a.77.1 2
16.5 even 4 608.2.c.a.305.1 2
16.11 odd 4 152.2.c.a.77.2 yes 2
16.13 even 4 608.2.c.a.305.2 2
48.5 odd 4 5472.2.g.a.2737.2 2
48.11 even 4 1368.2.g.a.685.1 2
48.29 odd 4 5472.2.g.a.2737.1 2
48.35 even 4 1368.2.g.a.685.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.2.c.a.77.1 2 16.3 odd 4
152.2.c.a.77.2 yes 2 16.11 odd 4
608.2.c.a.305.1 2 16.5 even 4
608.2.c.a.305.2 2 16.13 even 4
1368.2.g.a.685.1 2 48.11 even 4
1368.2.g.a.685.2 2 48.35 even 4
4864.2.a.g.1.1 1 8.3 odd 2
4864.2.a.h.1.1 1 4.3 odd 2
4864.2.a.i.1.1 1 1.1 even 1 trivial
4864.2.a.j.1.1 1 8.5 even 2
5472.2.g.a.2737.1 2 48.29 odd 4
5472.2.g.a.2737.2 2 48.5 odd 4