↑

Properties

Label 8664.2.a.n.1.1
Level $8664$
Weight $2$
Character 8664.1
Self dual yes
Analytic conductor $69.182$
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] = [8664,2,Mod(1,8664)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8664, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("8664.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8664 = 2^{3} \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8664.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: \(69.1823883112\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 8664.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} +3.00000 q^{5} +1.00000 q^{7} +1.00000 q^{9} -3.00000 q^{11} +3.00000 q^{15} -7.00000 q^{17} +1.00000 q^{21} -4.00000 q^{23} +4.00000 q^{25} +1.00000 q^{27} -4.00000 q^{29} -4.00000 q^{31} -3.00000 q^{33} +3.00000 q^{35} +4.00000 q^{37} -12.0000 q^{41} +1.00000 q^{43} +3.00000 q^{45} -9.00000 q^{47} -6.00000 q^{49} -7.00000 q^{51} -12.0000 q^{53} -9.00000 q^{55} -8.00000 q^{59} -5.00000 q^{61} +1.00000 q^{63} +4.00000 q^{67} -4.00000 q^{69} +8.00000 q^{71} +5.00000 q^{73} +4.00000 q^{75} -3.00000 q^{77} +12.0000 q^{79} +1.00000 q^{81} -21.0000 q^{85} -4.00000 q^{87} +12.0000 q^{89} -4.00000 q^{93} +8.00000 q^{97} -3.00000 q^{99} +O(q^{100})\)

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
\(4\) 0 0
\(5\) 3.00000 1.34164 0.670820 − 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964 0.188982 − 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 − 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 0 0
\(17\) −7.00000 −1.69775 −0.848875 − 0.528594i \(-0.822719\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(18\) 0 0
\(19\) 0 0
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 − 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 − 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 − 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) 3.00000 0.507093
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 − 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −12.0000 −1.87409 −0.937043 − 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 − 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 0 0
\(45\) 3.00000 0.447214
\(46\) 0 0
\(47\) −9.00000 −1.31278 −0.656392 − 0.754420i \(-0.727918\pi\)
−0.656392 + 0.754420i \(0.727918\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) −7.00000 −0.980196
\(52\) 0 0
\(53\) −12.0000 −1.64833 −0.824163 − 0.566352i \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.00000 −1.04151 −0.520756 − 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 0 0
\(61\) −5.00000 −0.640184 −0.320092 − 0.947386i \(-0.603714\pi\)
−0.320092 + 0.947386i \(0.603714\pi\)
\(62\) 0 0
\(63\) 1.00000 0.125988
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 − 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 − 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) 5.00000 0.585206 0.292603 − 0.956234i \(-0.405479\pi\)
0.292603 + 0.956234i \(0.405479\pi\)
\(74\) 0 0
\(75\) 4.00000 0.461880
\(76\) 0 0
\(77\) −3.00000 −0.341882
\(78\) 0 0
\(79\) 12.0000 1.35011 0.675053 − 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −21.0000 −2.27777
\(86\) 0 0
\(87\) −4.00000 −0.428845
\(88\) 0 0
\(89\) 12.0000 1.27200 0.635999 − 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −4.00000 −0.414781
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 8.00000 0.812277 0.406138 − 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 0 0
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 − 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 − 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 3.00000 0.292770
\(106\) 0 0
\(107\) 8.00000 0.773389 0.386695 − 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) 0 0
\(109\) 4.00000 0.383131 0.191565 − 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) 4.00000 0.379663
\(112\) 0 0
\(113\) −12.0000 −1.12887 −0.564433 − 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 0 0
\(115\) −12.0000 −1.11901
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.00000 −0.641689
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) −12.0000 −1.08200
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) −20.0000 −1.77471 −0.887357 − 0.461084i \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 0 0
\(129\) 1.00000 0.0880451
\(130\) 0 0
\(131\) −1.00000 −0.0873704 −0.0436852 − 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 3.00000 0.258199
\(136\) 0 0
\(137\) 1.00000 0.0854358 0.0427179 − 0.999087i \(-0.486398\pi\)
0.0427179 + 0.999087i \(0.486398\pi\)
\(138\) 0 0
\(139\) −23.0000 −1.95083 −0.975417 − 0.220366i \(-0.929275\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) 0 0
\(141\) −9.00000 −0.757937
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −12.0000 −0.996546
\(146\) 0 0
\(147\) −6.00000 −0.494872
\(148\) 0 0
\(149\) 9.00000 0.737309 0.368654 − 0.929567i \(-0.379819\pi\)
0.368654 + 0.929567i \(0.379819\pi\)
\(150\) 0 0
\(151\) 16.0000 1.30206 0.651031 − 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 0 0
\(153\) −7.00000 −0.565916
\(154\) 0 0
\(155\) −12.0000 −0.963863
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 − 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) −12.0000 −0.951662
\(160\) 0 0
\(161\) −4.00000 −0.315244
\(162\) 0 0
\(163\) −8.00000 −0.626608 −0.313304 − 0.949653i \(-0.601436\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) 0 0
\(165\) −9.00000 −0.700649
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 − 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −24.0000 −1.82469 −0.912343 − 0.409426i \(-0.865729\pi\)
−0.912343 + 0.409426i \(0.865729\pi\)
\(174\) 0 0
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) −8.00000 −0.601317
\(178\) 0 0
\(179\) 20.0000 1.49487 0.747435 − 0.664335i \(-0.231285\pi\)
0.747435 + 0.664335i \(0.231285\pi\)
\(180\) 0 0
\(181\) −8.00000 −0.594635 −0.297318 − 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) −5.00000 −0.369611
\(184\) 0 0
\(185\) 12.0000 0.882258
\(186\) 0 0
\(187\) 21.0000 1.53567
\(188\) 0 0
\(189\) 1.00000 0.0727393
\(190\) 0 0
\(191\) −11.0000 −0.795932 −0.397966 − 0.917400i \(-0.630284\pi\)
−0.397966 + 0.917400i \(0.630284\pi\)
\(192\) 0 0
\(193\) 4.00000 0.287926 0.143963 − 0.989583i \(-0.454015\pi\)
0.143963 + 0.989583i \(0.454015\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.0000 −0.712470 −0.356235 − 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 0 0
\(199\) 21.0000 1.48865 0.744325 − 0.667817i \(-0.232771\pi\)
0.744325 + 0.667817i \(0.232771\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) 0 0
\(203\) −4.00000 −0.280745
\(204\) 0 0
\(205\) −36.0000 −2.51435
\(206\) 0 0
\(207\) −4.00000 −0.278019
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 24.0000 1.65223 0.826114 − 0.563503i \(-0.190547\pi\)
0.826114 + 0.563503i \(0.190547\pi\)
\(212\) 0 0
\(213\) 8.00000 0.548151
\(214\) 0 0
\(215\) 3.00000 0.204598
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) 0 0
\(219\) 5.00000 0.337869
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −4.00000 −0.267860 −0.133930 − 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) 0 0
\(225\) 4.00000 0.266667
\(226\) 0 0
\(227\) 24.0000 1.59294 0.796468 − 0.604681i \(-0.206699\pi\)
0.796468 + 0.604681i \(0.206699\pi\)
\(228\) 0 0
\(229\) −7.00000 −0.462573 −0.231287 − 0.972886i \(-0.574293\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 0 0
\(231\) −3.00000 −0.197386
\(232\) 0 0
\(233\) 23.0000 1.50678 0.753390 − 0.657574i \(-0.228417\pi\)
0.753390 + 0.657574i \(0.228417\pi\)
\(234\) 0 0
\(235\) −27.0000 −1.76129
\(236\) 0 0
\(237\) 12.0000 0.779484
\(238\) 0 0
\(239\) −15.0000 −0.970269 −0.485135 − 0.874439i \(-0.661229\pi\)
−0.485135 + 0.874439i \(0.661229\pi\)
\(240\) 0 0
\(241\) 20.0000 1.28831 0.644157 − 0.764894i \(-0.277208\pi\)
0.644157 + 0.764894i \(0.277208\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −18.0000 −1.14998
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 23.0000 1.45175 0.725874 − 0.687828i \(-0.241436\pi\)
0.725874 + 0.687828i \(0.241436\pi\)
\(252\) 0 0
\(253\) 12.0000 0.754434
\(254\) 0 0
\(255\) −21.0000 −1.31507
\(256\) 0 0
\(257\) 8.00000 0.499026 0.249513 − 0.968371i \(-0.419729\pi\)
0.249513 + 0.968371i \(0.419729\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) 0 0
\(261\) −4.00000 −0.247594
\(262\) 0 0
\(263\) 23.0000 1.41824 0.709120 − 0.705087i \(-0.249092\pi\)
0.709120 + 0.705087i \(0.249092\pi\)
\(264\) 0 0
\(265\) −36.0000 −2.21146
\(266\) 0 0
\(267\) 12.0000 0.734388
\(268\) 0 0
\(269\) −12.0000 −0.731653 −0.365826 − 0.930683i \(-0.619214\pi\)
−0.365826 + 0.930683i \(0.619214\pi\)
\(270\) 0 0
\(271\) 28.0000 1.70088 0.850439 − 0.526073i \(-0.176336\pi\)
0.850439 + 0.526073i \(0.176336\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −12.0000 −0.723627
\(276\) 0 0
\(277\) 13.0000 0.781094 0.390547 − 0.920583i \(-0.372286\pi\)
0.390547 + 0.920583i \(0.372286\pi\)
\(278\) 0 0
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) 16.0000 0.954480 0.477240 − 0.878773i \(-0.341637\pi\)
0.477240 + 0.878773i \(0.341637\pi\)
\(282\) 0 0
\(283\) 1.00000 0.0594438 0.0297219 − 0.999558i \(-0.490538\pi\)
0.0297219 + 0.999558i \(0.490538\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −12.0000 −0.708338
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) 0 0
\(291\) 8.00000 0.468968
\(292\) 0 0
\(293\) 24.0000 1.40209 0.701047 − 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) −24.0000 −1.39733
\(296\) 0 0
\(297\) −3.00000 −0.174078
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 1.00000 0.0576390
\(302\) 0 0
\(303\) −6.00000 −0.344691
\(304\) 0 0
\(305\) −15.0000 −0.858898
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 − 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) −33.0000 −1.87126 −0.935629 − 0.352985i \(-0.885167\pi\)
−0.935629 + 0.352985i \(0.885167\pi\)
\(312\) 0 0
\(313\) −22.0000 −1.24351 −0.621757 − 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 0 0
\(315\) 3.00000 0.169031
\(316\) 0 0
\(317\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) 0 0
\(321\) 8.00000 0.446516
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 4.00000 0.221201
\(328\) 0 0
\(329\) −9.00000 −0.496186
\(330\) 0 0
\(331\) −12.0000 −0.659580 −0.329790 − 0.944054i \(-0.606978\pi\)
−0.329790 + 0.944054i \(0.606978\pi\)
\(332\) 0 0
\(333\) 4.00000 0.219199
\(334\) 0 0
\(335\) 12.0000 0.655630
\(336\) 0 0
\(337\) −16.0000 −0.871576 −0.435788 − 0.900049i \(-0.643530\pi\)
−0.435788 + 0.900049i \(0.643530\pi\)
\(338\) 0 0
\(339\) −12.0000 −0.651751
\(340\) 0 0
\(341\) 12.0000 0.649836
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) −12.0000 −0.646058
\(346\) 0 0
\(347\) 3.00000 0.161048 0.0805242 − 0.996753i \(-0.474341\pi\)
0.0805242 + 0.996753i \(0.474341\pi\)
\(348\) 0 0
\(349\) −23.0000 −1.23116 −0.615581 − 0.788074i \(-0.711079\pi\)
−0.615581 + 0.788074i \(0.711079\pi\)
\(350\) 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
\(355\) 24.0000 1.27379
\(356\) 0 0
\(357\) −7.00000 −0.370479
\(358\) 0 0
\(359\) −19.0000 −1.00278 −0.501391 − 0.865221i \(-0.667178\pi\)
−0.501391 + 0.865221i \(0.667178\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) 15.0000 0.785136
\(366\) 0 0
\(367\) 4.00000 0.208798 0.104399 − 0.994535i \(-0.466708\pi\)
0.104399 + 0.994535i \(0.466708\pi\)
\(368\) 0 0
\(369\) −12.0000 −0.624695
\(370\) 0 0
\(371\) −12.0000 −0.623009
\(372\) 0 0
\(373\) −24.0000 −1.24267 −0.621336 − 0.783544i \(-0.713410\pi\)
−0.621336 + 0.783544i \(0.713410\pi\)
\(374\) 0 0
\(375\) −3.00000 −0.154919
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 − 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 0 0
\(381\) −20.0000 −1.02463
\(382\) 0 0
\(383\) 4.00000 0.204390 0.102195 − 0.994764i \(-0.467413\pi\)
0.102195 + 0.994764i \(0.467413\pi\)
\(384\) 0 0
\(385\) −9.00000 −0.458682
\(386\) 0 0
\(387\) 1.00000 0.0508329
\(388\) 0 0
\(389\) 11.0000 0.557722 0.278861 − 0.960331i \(-0.410043\pi\)
0.278861 + 0.960331i \(0.410043\pi\)
\(390\) 0 0
\(391\) 28.0000 1.41602
\(392\) 0 0
\(393\) −1.00000 −0.0504433
\(394\) 0 0
\(395\) 36.0000 1.81136
\(396\) 0 0
\(397\) −19.0000 −0.953583 −0.476791 − 0.879017i \(-0.658200\pi\)
−0.476791 + 0.879017i \(0.658200\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12.0000 −0.599251 −0.299626 − 0.954057i \(-0.596862\pi\)
−0.299626 + 0.954057i \(0.596862\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 3.00000 0.149071
\(406\) 0 0
\(407\) −12.0000 −0.594818
\(408\) 0 0
\(409\) 20.0000 0.988936 0.494468 − 0.869196i \(-0.335363\pi\)
0.494468 + 0.869196i \(0.335363\pi\)
\(410\) 0 0
\(411\) 1.00000 0.0493264
\(412\) 0 0
\(413\) −8.00000 −0.393654
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −23.0000 −1.12631
\(418\) 0 0
\(419\) −40.0000 −1.95413 −0.977064 − 0.212946i \(-0.931694\pi\)
−0.977064 + 0.212946i \(0.931694\pi\)
\(420\) 0 0
\(421\) 20.0000 0.974740 0.487370 − 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) 0 0
\(423\) −9.00000 −0.437595
\(424\) 0 0
\(425\) −28.0000 −1.35820
\(426\) 0 0
\(427\) −5.00000 −0.241967
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 − 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) −20.0000 −0.961139 −0.480569 − 0.876957i \(-0.659570\pi\)
−0.480569 + 0.876957i \(0.659570\pi\)
\(434\) 0 0
\(435\) −12.0000 −0.575356
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 28.0000 1.33637 0.668184 − 0.743996i \(-0.267072\pi\)
0.668184 + 0.743996i \(0.267072\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) 0 0
\(443\) −5.00000 −0.237557 −0.118779 − 0.992921i \(-0.537898\pi\)
−0.118779 + 0.992921i \(0.537898\pi\)
\(444\) 0 0
\(445\) 36.0000 1.70656
\(446\) 0 0
\(447\) 9.00000 0.425685
\(448\) 0 0
\(449\) 40.0000 1.88772 0.943858 − 0.330350i \(-0.107167\pi\)
0.943858 + 0.330350i \(0.107167\pi\)
\(450\) 0 0
\(451\) 36.0000 1.69517
\(452\) 0 0
\(453\) 16.0000 0.751746
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −25.0000 −1.16945 −0.584725 − 0.811231i \(-0.698798\pi\)
−0.584725 + 0.811231i \(0.698798\pi\)
\(458\) 0 0
\(459\) −7.00000 −0.326732
\(460\) 0 0
\(461\) 33.0000 1.53696 0.768482 − 0.639872i \(-0.221013\pi\)
0.768482 + 0.639872i \(0.221013\pi\)
\(462\) 0 0
\(463\) 3.00000 0.139422 0.0697109 − 0.997567i \(-0.477792\pi\)
0.0697109 + 0.997567i \(0.477792\pi\)
\(464\) 0 0
\(465\) −12.0000 −0.556487
\(466\) 0 0
\(467\) 27.0000 1.24941 0.624705 − 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) 0 0
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) 2.00000 0.0921551
\(472\) 0 0
\(473\) −3.00000 −0.137940
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) 0 0
\(479\) 28.0000 1.27935 0.639676 − 0.768644i \(-0.279068\pi\)
0.639676 + 0.768644i \(0.279068\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −4.00000 −0.182006
\(484\) 0 0
\(485\) 24.0000 1.08978
\(486\) 0 0
\(487\) −24.0000 −1.08754 −0.543772 − 0.839233i \(-0.683004\pi\)
−0.543772 + 0.839233i \(0.683004\pi\)
\(488\) 0 0
\(489\) −8.00000 −0.361773
\(490\) 0 0
\(491\) −8.00000 −0.361035 −0.180517 − 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(492\) 0 0
\(493\) 28.0000 1.26106
\(494\) 0 0
\(495\) −9.00000 −0.404520
\(496\) 0 0
\(497\) 8.00000 0.358849
\(498\) 0 0
\(499\) 15.0000 0.671492 0.335746 − 0.941953i \(-0.391012\pi\)
0.335746 + 0.941953i \(0.391012\pi\)
\(500\) 0 0
\(501\) 12.0000 0.536120
\(502\) 0 0
\(503\) −12.0000 −0.535054 −0.267527 − 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 0 0
\(507\) −13.0000 −0.577350
\(508\) 0 0
\(509\) −8.00000 −0.354594 −0.177297 − 0.984157i \(-0.556735\pi\)
−0.177297 + 0.984157i \(0.556735\pi\)
\(510\) 0 0
\(511\) 5.00000 0.221187
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 24.0000 1.05757
\(516\) 0 0
\(517\) 27.0000 1.18746
\(518\) 0 0
\(519\) −24.0000 −1.05348
\(520\) 0 0
\(521\) −20.0000 −0.876216 −0.438108 − 0.898922i \(-0.644351\pi\)
−0.438108 + 0.898922i \(0.644351\pi\)
\(522\) 0 0
\(523\) −32.0000 −1.39926 −0.699631 − 0.714504i \(-0.746652\pi\)
−0.699631 + 0.714504i \(0.746652\pi\)
\(524\) 0 0
\(525\) 4.00000 0.174574
\(526\) 0 0
\(527\) 28.0000 1.21970
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) −8.00000 −0.347170
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 24.0000 1.03761
\(536\) 0 0
\(537\) 20.0000 0.863064
\(538\) 0 0
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) −13.0000 −0.558914 −0.279457 − 0.960158i \(-0.590154\pi\)
−0.279457 + 0.960158i \(0.590154\pi\)
\(542\) 0 0
\(543\) −8.00000 −0.343313
\(544\) 0 0
\(545\) 12.0000 0.514024
\(546\) 0 0
\(547\) −16.0000 −0.684111 −0.342055 − 0.939680i \(-0.611123\pi\)
−0.342055 + 0.939680i \(0.611123\pi\)
\(548\) 0 0
\(549\) −5.00000 −0.213395
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 12.0000 0.510292
\(554\) 0 0
\(555\) 12.0000 0.509372
\(556\) 0 0
\(557\) −11.0000 −0.466085 −0.233042 − 0.972467i \(-0.574868\pi\)
−0.233042 + 0.972467i \(0.574868\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 21.0000 0.886621
\(562\) 0 0
\(563\) 28.0000 1.18006 0.590030 − 0.807382i \(-0.299116\pi\)
0.590030 + 0.807382i \(0.299116\pi\)
\(564\) 0 0
\(565\) −36.0000 −1.51453
\(566\) 0 0
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) −32.0000 −1.34151 −0.670755 − 0.741679i \(-0.734030\pi\)
−0.670755 + 0.741679i \(0.734030\pi\)
\(570\) 0 0
\(571\) −40.0000 −1.67395 −0.836974 − 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) 0 0
\(573\) −11.0000 −0.459532
\(574\) 0 0
\(575\) −16.0000 −0.667246
\(576\) 0 0
\(577\) −5.00000 −0.208153 −0.104076 − 0.994569i \(-0.533189\pi\)
−0.104076 + 0.994569i \(0.533189\pi\)
\(578\) 0 0
\(579\) 4.00000 0.166234
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 36.0000 1.49097
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7.00000 0.288921 0.144460 − 0.989511i \(-0.453855\pi\)
0.144460 + 0.989511i \(0.453855\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −10.0000 −0.411345
\(592\) 0 0
\(593\) −46.0000 −1.88899 −0.944497 − 0.328521i \(-0.893450\pi\)
−0.944497 + 0.328521i \(0.893450\pi\)
\(594\) 0 0
\(595\) −21.0000 −0.860916
\(596\) 0 0
\(597\) 21.0000 0.859473
\(598\) 0 0
\(599\) −20.0000 −0.817178 −0.408589 − 0.912719i \(-0.633979\pi\)
−0.408589 + 0.912719i \(0.633979\pi\)
\(600\) 0 0
\(601\) 32.0000 1.30531 0.652654 − 0.757656i \(-0.273656\pi\)
0.652654 + 0.757656i \(0.273656\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 0 0
\(605\) −6.00000 −0.243935
\(606\) 0 0
\(607\) −32.0000 −1.29884 −0.649420 − 0.760430i \(-0.724988\pi\)
−0.649420 + 0.760430i \(0.724988\pi\)
\(608\) 0 0
\(609\) −4.00000 −0.162088
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −11.0000 −0.444286 −0.222143 − 0.975014i \(-0.571305\pi\)
−0.222143 + 0.975014i \(0.571305\pi\)
\(614\) 0 0
\(615\) −36.0000 −1.45166
\(616\) 0 0
\(617\) −3.00000 −0.120775 −0.0603877 − 0.998175i \(-0.519234\pi\)
−0.0603877 + 0.998175i \(0.519234\pi\)
\(618\) 0 0
\(619\) −8.00000 −0.321547 −0.160774 − 0.986991i \(-0.551399\pi\)
−0.160774 + 0.986991i \(0.551399\pi\)
\(620\) 0 0
\(621\) −4.00000 −0.160514
\(622\) 0 0
\(623\) 12.0000 0.480770
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −28.0000 −1.11643
\(630\) 0 0
\(631\) −35.0000 −1.39333 −0.696664 − 0.717398i \(-0.745333\pi\)
−0.696664 + 0.717398i \(0.745333\pi\)
\(632\) 0 0
\(633\) 24.0000 0.953914
\(634\) 0 0
\(635\) −60.0000 −2.38103
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 8.00000 0.316475
\(640\) 0 0
\(641\) −40.0000 −1.57991 −0.789953 − 0.613168i \(-0.789895\pi\)
−0.789953 + 0.613168i \(0.789895\pi\)
\(642\) 0 0
\(643\) 41.0000 1.61688 0.808441 − 0.588577i \(-0.200312\pi\)
0.808441 + 0.588577i \(0.200312\pi\)
\(644\) 0 0
\(645\) 3.00000 0.118125
\(646\) 0 0
\(647\) −3.00000 −0.117942 −0.0589711 − 0.998260i \(-0.518782\pi\)
−0.0589711 + 0.998260i \(0.518782\pi\)
\(648\) 0 0
\(649\) 24.0000 0.942082
\(650\) 0 0
\(651\) −4.00000 −0.156772
\(652\) 0 0
\(653\) −3.00000 −0.117399 −0.0586995 − 0.998276i \(-0.518695\pi\)
−0.0586995 + 0.998276i \(0.518695\pi\)
\(654\) 0 0
\(655\) −3.00000 −0.117220
\(656\) 0 0
\(657\) 5.00000 0.195069
\(658\) 0 0
\(659\) −24.0000 −0.934907 −0.467454 − 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 0 0
\(661\) 32.0000 1.24466 0.622328 − 0.782757i \(-0.286187\pi\)
0.622328 + 0.782757i \(0.286187\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 16.0000 0.619522
\(668\) 0 0
\(669\) −4.00000 −0.154649
\(670\) 0 0
\(671\) 15.0000 0.579069
\(672\) 0 0
\(673\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 4.00000 0.153960
\(676\) 0 0
\(677\) −28.0000 −1.07613 −0.538064 − 0.842904i \(-0.680844\pi\)
−0.538064 + 0.842904i \(0.680844\pi\)
\(678\) 0 0
\(679\) 8.00000 0.307012
\(680\) 0 0
\(681\) 24.0000 0.919682
\(682\) 0 0
\(683\) −24.0000 −0.918334 −0.459167 − 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) 0 0
\(685\) 3.00000 0.114624
\(686\) 0 0
\(687\) −7.00000 −0.267067
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −29.0000 −1.10321 −0.551606 − 0.834105i \(-0.685985\pi\)
−0.551606 + 0.834105i \(0.685985\pi\)
\(692\) 0 0
\(693\) −3.00000 −0.113961
\(694\) 0 0
\(695\) −69.0000 −2.61732
\(696\) 0 0
\(697\) 84.0000 3.18173
\(698\) 0 0
\(699\) 23.0000 0.869940
\(700\) 0 0
\(701\) 2.00000 0.0755390 0.0377695 − 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −27.0000 −1.01688
\(706\) 0 0
\(707\) −6.00000 −0.225653
\(708\) 0 0
\(709\) −6.00000 −0.225335 −0.112667 − 0.993633i \(-0.535939\pi\)
−0.112667 + 0.993633i \(0.535939\pi\)
\(710\) 0 0
\(711\) 12.0000 0.450035
\(712\) 0 0
\(713\) 16.0000 0.599205
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −15.0000 −0.560185
\(718\) 0 0
\(719\) 21.0000 0.783168 0.391584 − 0.920142i \(-0.371927\pi\)
0.391584 + 0.920142i \(0.371927\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) 0 0
\(723\) 20.0000 0.743808
\(724\) 0 0
\(725\) −16.0000 −0.594225
\(726\) 0 0
\(727\) 39.0000 1.44643 0.723215 − 0.690623i \(-0.242664\pi\)
0.723215 + 0.690623i \(0.242664\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −7.00000 −0.258904
\(732\) 0 0
\(733\) −34.0000 −1.25582 −0.627909 − 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) 0 0
\(735\) −18.0000 −0.663940
\(736\) 0 0
\(737\) −12.0000 −0.442026
\(738\) 0 0
\(739\) −19.0000 −0.698926 −0.349463 − 0.936950i \(-0.613636\pi\)
−0.349463 + 0.936950i \(0.613636\pi\)
\(740\) 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
\(745\) 27.0000 0.989203
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8.00000 0.292314
\(750\) 0 0
\(751\) −8.00000 −0.291924 −0.145962 − 0.989290i \(-0.546628\pi\)
−0.145962 + 0.989290i \(0.546628\pi\)
\(752\) 0 0
\(753\) 23.0000 0.838167
\(754\) 0 0
\(755\) 48.0000 1.74690
\(756\) 0 0
\(757\) 7.00000 0.254419 0.127210 − 0.991876i \(-0.459398\pi\)
0.127210 + 0.991876i \(0.459398\pi\)
\(758\) 0 0
\(759\) 12.0000 0.435572
\(760\) 0 0
\(761\) 33.0000 1.19625 0.598125 − 0.801403i \(-0.295913\pi\)
0.598125 + 0.801403i \(0.295913\pi\)
\(762\) 0 0
\(763\) 4.00000 0.144810
\(764\) 0 0
\(765\) −21.0000 −0.759257
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 27.0000 0.973645 0.486822 − 0.873501i \(-0.338156\pi\)
0.486822 + 0.873501i \(0.338156\pi\)
\(770\) 0 0
\(771\) 8.00000 0.288113
\(772\) 0 0
\(773\) −32.0000 −1.15096 −0.575480 − 0.817816i \(-0.695185\pi\)
−0.575480 + 0.817816i \(0.695185\pi\)
\(774\) 0 0
\(775\) −16.0000 −0.574737
\(776\) 0 0
\(777\) 4.00000 0.143499
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −24.0000 −0.858788
\(782\) 0 0
\(783\) −4.00000 −0.142948
\(784\) 0 0
\(785\) 6.00000 0.214149
\(786\) 0 0
\(787\) 32.0000 1.14068 0.570338 − 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(788\) 0 0
\(789\) 23.0000 0.818822
\(790\) 0 0
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −36.0000 −1.27679
\(796\) 0 0
\(797\) 4.00000 0.141687 0.0708436 − 0.997487i \(-0.477431\pi\)
0.0708436 + 0.997487i \(0.477431\pi\)
\(798\) 0 0
\(799\) 63.0000 2.22878
\(800\) 0 0
\(801\) 12.0000 0.423999
\(802\) 0 0
\(803\) −15.0000 −0.529339
\(804\) 0 0
\(805\) −12.0000 −0.422944
\(806\) 0 0
\(807\) −12.0000 −0.422420
\(808\) 0 0
\(809\) −37.0000 −1.30085 −0.650425 − 0.759570i \(-0.725409\pi\)
−0.650425 + 0.759570i \(0.725409\pi\)
\(810\) 0 0
\(811\) −16.0000 −0.561836 −0.280918 − 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) 0 0
\(813\) 28.0000 0.982003
\(814\) 0 0
\(815\) −24.0000 −0.840683
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −23.0000 −0.802706 −0.401353 − 0.915924i \(-0.631460\pi\)
−0.401353 + 0.915924i \(0.631460\pi\)
\(822\) 0 0
\(823\) 21.0000 0.732014 0.366007 − 0.930612i \(-0.380725\pi\)
0.366007 + 0.930612i \(0.380725\pi\)
\(824\) 0 0
\(825\) −12.0000 −0.417786
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 − 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 0 0
\(829\) −56.0000 −1.94496 −0.972480 − 0.232986i \(-0.925151\pi\)
−0.972480 + 0.232986i \(0.925151\pi\)
\(830\) 0 0
\(831\) 13.0000 0.450965
\(832\) 0 0
\(833\) 42.0000 1.45521
\(834\) 0 0
\(835\) 36.0000 1.24583
\(836\) 0 0
\(837\) −4.00000 −0.138260
\(838\) 0 0
\(839\) −24.0000 −0.828572 −0.414286 − 0.910147i \(-0.635969\pi\)
−0.414286 + 0.910147i \(0.635969\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 0 0
\(843\) 16.0000 0.551069
\(844\) 0 0
\(845\) −39.0000 −1.34164
\(846\) 0 0
\(847\) −2.00000 −0.0687208
\(848\) 0 0
\(849\) 1.00000 0.0343199
\(850\) 0 0
\(851\) −16.0000 −0.548473
\(852\) 0 0
\(853\) 22.0000 0.753266 0.376633 − 0.926363i \(-0.377082\pi\)
0.376633 + 0.926363i \(0.377082\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −8.00000 −0.273275 −0.136637 − 0.990621i \(-0.543630\pi\)
−0.136637 + 0.990621i \(0.543630\pi\)
\(858\) 0 0
\(859\) −47.0000 −1.60362 −0.801810 − 0.597580i \(-0.796129\pi\)
−0.801810 + 0.597580i \(0.796129\pi\)
\(860\) 0 0
\(861\) −12.0000 −0.408959
\(862\) 0 0
\(863\) −44.0000 −1.49778 −0.748889 − 0.662696i \(-0.769412\pi\)
−0.748889 + 0.662696i \(0.769412\pi\)
\(864\) 0 0
\(865\) −72.0000 −2.44807
\(866\) 0 0
\(867\) 32.0000 1.08678
\(868\) 0 0
\(869\) −36.0000 −1.22122
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 8.00000 0.270759
\(874\) 0 0
\(875\) −3.00000 −0.101419
\(876\) 0 0
\(877\) 32.0000 1.08056 0.540282 − 0.841484i \(-0.318318\pi\)
0.540282 + 0.841484i \(0.318318\pi\)
\(878\) 0 0
\(879\) 24.0000 0.809500
\(880\) 0 0
\(881\) −27.0000 −0.909653 −0.454827 − 0.890580i \(-0.650299\pi\)
−0.454827 + 0.890580i \(0.650299\pi\)
\(882\) 0 0
\(883\) −51.0000 −1.71629 −0.858143 − 0.513410i \(-0.828382\pi\)
−0.858143 + 0.513410i \(0.828382\pi\)
\(884\) 0 0
\(885\) −24.0000 −0.806751
\(886\) 0 0
\(887\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) −20.0000 −0.670778
\(890\) 0 0
\(891\) −3.00000 −0.100504
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 60.0000 2.00558
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 16.0000 0.533630
\(900\) 0 0
\(901\) 84.0000 2.79845
\(902\) 0 0
\(903\) 1.00000 0.0332779
\(904\) 0 0
\(905\) −24.0000 −0.797787
\(906\) 0 0
\(907\) −12.0000 −0.398453 −0.199227 − 0.979953i \(-0.563843\pi\)
−0.199227 + 0.979953i \(0.563843\pi\)
\(908\) 0 0
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −15.0000 −0.495885
\(916\) 0 0
\(917\) −1.00000 −0.0330229
\(918\) 0 0
\(919\) 60.0000 1.97922 0.989609 − 0.143787i \(-0.0459280\pi\)
0.989609 + 0.143787i \(0.0459280\pi\)
\(920\) 0 0
\(921\) 12.0000 0.395413
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 16.0000 0.526077
\(926\) 0 0
\(927\) 8.00000 0.262754
\(928\) 0 0
\(929\) −30.0000 −0.984268 −0.492134 − 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −33.0000 −1.08037
\(934\) 0 0
\(935\) 63.0000 2.06032
\(936\) 0 0
\(937\) −23.0000 −0.751377 −0.375689 − 0.926746i \(-0.622594\pi\)
−0.375689 + 0.926746i \(0.622594\pi\)
\(938\) 0 0
\(939\) −22.0000 −0.717943
\(940\) 0 0
\(941\) 24.0000 0.782378 0.391189 − 0.920310i \(-0.372064\pi\)
0.391189 + 0.920310i \(0.372064\pi\)
\(942\) 0 0
\(943\) 48.0000 1.56310
\(944\) 0 0
\(945\) 3.00000 0.0975900
\(946\) 0 0
\(947\) 8.00000 0.259965 0.129983 − 0.991516i \(-0.458508\pi\)
0.129983 + 0.991516i \(0.458508\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −4.00000 −0.129573 −0.0647864 − 0.997899i \(-0.520637\pi\)
−0.0647864 + 0.997899i \(0.520637\pi\)
\(954\) 0 0
\(955\) −33.0000 −1.06785
\(956\) 0 0
\(957\) 12.0000 0.387905
\(958\) 0 0
\(959\) 1.00000 0.0322917
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 8.00000 0.257796
\(964\) 0 0
\(965\) 12.0000 0.386294
\(966\) 0 0
\(967\) −4.00000 −0.128631 −0.0643157 − 0.997930i \(-0.520486\pi\)
−0.0643157 + 0.997930i \(0.520486\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 16.0000 0.513464 0.256732 − 0.966483i \(-0.417354\pi\)
0.256732 + 0.966483i \(0.417354\pi\)
\(972\) 0 0
\(973\) −23.0000 −0.737346
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −60.0000 −1.91957 −0.959785 − 0.280736i \(-0.909421\pi\)
−0.959785 + 0.280736i \(0.909421\pi\)
\(978\) 0 0
\(979\) −36.0000 −1.15056
\(980\) 0 0
\(981\) 4.00000 0.127710
\(982\) 0 0
\(983\) −32.0000 −1.02064 −0.510321 − 0.859984i \(-0.670473\pi\)
−0.510321 + 0.859984i \(0.670473\pi\)
\(984\) 0 0
\(985\) −30.0000 −0.955879
\(986\) 0 0
\(987\) −9.00000 −0.286473
\(988\) 0 0
\(989\) −4.00000 −0.127193
\(990\) 0 0
\(991\) 4.00000 0.127064 0.0635321 − 0.997980i \(-0.479763\pi\)
0.0635321 + 0.997980i \(0.479763\pi\)
\(992\) 0 0
\(993\) −12.0000 −0.380808
\(994\) 0 0
\(995\) 63.0000 1.99723
\(996\) 0 0
\(997\) −3.00000 −0.0950110 −0.0475055 − 0.998871i \(-0.515127\pi\)
−0.0475055 + 0.998871i \(0.515127\pi\)
\(998\) 0 0
\(999\) 4.00000 0.126554
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 8664.2.a.n.1.1 yes 1
19.18 odd 2 8664.2.a.g.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8664.2.a.g.1.1 ✓ 1 19.18 odd 2
8664.2.a.n.1.1 yes 1 1.1 even 1 trivial