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Properties

Label 3264.2.a.p.1.1
Level $3264$
Weight $2$
Character 3264.1
Self dual yes
Analytic conductor $26.063$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3264,2,Mod(1,3264)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3264, 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("3264.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3264 = 2^{6} \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3264.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: \(26.0631712197\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 102)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 3264.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} +4.00000 q^{5} +2.00000 q^{7} +1.00000 q^{9} +6.00000 q^{13} -4.00000 q^{15} -1.00000 q^{17} +4.00000 q^{19} -2.00000 q^{21} -6.00000 q^{23} +11.0000 q^{25} -1.00000 q^{27} +4.00000 q^{29} +6.00000 q^{31} +8.00000 q^{35} +4.00000 q^{37} -6.00000 q^{39} -10.0000 q^{41} -4.00000 q^{43} +4.00000 q^{45} -4.00000 q^{47} -3.00000 q^{49} +1.00000 q^{51} +2.00000 q^{53} -4.00000 q^{57} +12.0000 q^{59} +4.00000 q^{61} +2.00000 q^{63} +24.0000 q^{65} -12.0000 q^{67} +6.00000 q^{69} +6.00000 q^{71} +2.00000 q^{73} -11.0000 q^{75} -10.0000 q^{79} +1.00000 q^{81} -12.0000 q^{83} -4.00000 q^{85} -4.00000 q^{87} -2.00000 q^{89} +12.0000 q^{91} -6.00000 q^{93} +16.0000 q^{95} +6.00000 q^{97} +O(q^{100})\)

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
\(5\) 4.00000 1.78885 0.894427 − 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) 0 0
\(7\) 2.00000 0.755929 0.377964 − 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 − 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) −4.00000 −1.03280
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 − 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 − 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 6.00000 1.07763 0.538816 − 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 8.00000 1.35225
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 − 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) −6.00000 −0.960769
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 − 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 − 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 4.00000 0.596285
\(46\) 0 0
\(47\) −4.00000 −0.583460 −0.291730 − 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) 1.00000 0.140028
\(52\) 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
\(57\) −4.00000 −0.529813
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 − 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) 4.00000 0.512148 0.256074 − 0.966657i \(-0.417571\pi\)
0.256074 + 0.966657i \(0.417571\pi\)
\(62\) 0 0
\(63\) 2.00000 0.251976
\(64\) 0 0
\(65\) 24.0000 2.97683
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 − 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 − 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 − 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) −11.0000 −1.27017
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 − 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 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
\(87\) −4.00000 −0.428845
\(88\) 0 0
\(89\) −2.00000 −0.212000 −0.106000 − 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 0 0
\(91\) 12.0000 1.25794
\(92\) 0 0
\(93\) −6.00000 −0.622171
\(94\) 0 0
\(95\) 16.0000 1.64157
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 − 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −14.0000 −1.39305 −0.696526 − 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) 0 0
\(103\) −4.00000 −0.394132 −0.197066 − 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 0 0
\(105\) −8.00000 −0.780720
\(106\) 0 0
\(107\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −16.0000 −1.53252 −0.766261 − 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 − 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) −24.0000 −2.23801
\(116\) 0 0
\(117\) 6.00000 0.554700
\(118\) 0 0
\(119\) −2.00000 −0.183340
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 10.0000 0.901670
\(124\) 0 0
\(125\) 24.0000 2.14663
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 − 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 4.00000 0.352180
\(130\) 0 0
\(131\) −16.0000 −1.39793 −0.698963 − 0.715158i \(-0.746355\pi\)
−0.698963 + 0.715158i \(0.746355\pi\)
\(132\) 0 0
\(133\) 8.00000 0.693688
\(134\) 0 0
\(135\) −4.00000 −0.344265
\(136\) 0 0
\(137\) −6.00000 −0.512615 −0.256307 − 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) 8.00000 0.678551 0.339276 − 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) 0 0
\(141\) 4.00000 0.336861
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 16.0000 1.32873
\(146\) 0 0
\(147\) 3.00000 0.247436
\(148\) 0 0
\(149\) 6.00000 0.491539 0.245770 − 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) 24.0000 1.95309 0.976546 − 0.215308i \(-0.0690756\pi\)
0.976546 + 0.215308i \(0.0690756\pi\)
\(152\) 0 0
\(153\) −1.00000 −0.0808452
\(154\) 0 0
\(155\) 24.0000 1.92773
\(156\) 0 0
\(157\) −6.00000 −0.478852 −0.239426 − 0.970915i \(-0.576959\pi\)
−0.239426 + 0.970915i \(0.576959\pi\)
\(158\) 0 0
\(159\) −2.00000 −0.158610
\(160\) 0 0
\(161\) −12.0000 −0.945732
\(162\) 0 0
\(163\) 12.0000 0.939913 0.469956 − 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.00000 0.154765 0.0773823 − 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 4.00000 0.305888
\(172\) 0 0
\(173\) 4.00000 0.304114 0.152057 − 0.988372i \(-0.451410\pi\)
0.152057 + 0.988372i \(0.451410\pi\)
\(174\) 0 0
\(175\) 22.0000 1.66304
\(176\) 0 0
\(177\) −12.0000 −0.901975
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 − 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 − 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 0 0
\(183\) −4.00000 −0.295689
\(184\) 0 0
\(185\) 16.0000 1.17634
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −2.00000 −0.145479
\(190\) 0 0
\(191\) 4.00000 0.289430 0.144715 − 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) 0 0
\(193\) 6.00000 0.431889 0.215945 − 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) 0 0
\(195\) −24.0000 −1.71868
\(196\) 0 0
\(197\) −8.00000 −0.569976 −0.284988 − 0.958531i \(-0.591990\pi\)
−0.284988 + 0.958531i \(0.591990\pi\)
\(198\) 0 0
\(199\) −14.0000 −0.992434 −0.496217 − 0.868199i \(-0.665278\pi\)
−0.496217 + 0.868199i \(0.665278\pi\)
\(200\) 0 0
\(201\) 12.0000 0.846415
\(202\) 0 0
\(203\) 8.00000 0.561490
\(204\) 0 0
\(205\) −40.0000 −2.79372
\(206\) 0 0
\(207\) −6.00000 −0.417029
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 − 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 0 0
\(213\) −6.00000 −0.411113
\(214\) 0 0
\(215\) −16.0000 −1.09119
\(216\) 0 0
\(217\) 12.0000 0.814613
\(218\) 0 0
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) −6.00000 −0.403604
\(222\) 0 0
\(223\) 4.00000 0.267860 0.133930 − 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 0 0
\(225\) 11.0000 0.733333
\(226\) 0 0
\(227\) 4.00000 0.265489 0.132745 − 0.991150i \(-0.457621\pi\)
0.132745 + 0.991150i \(0.457621\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 − 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 − 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −16.0000 −1.04372
\(236\) 0 0
\(237\) 10.0000 0.649570
\(238\) 0 0
\(239\) 20.0000 1.29369 0.646846 − 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) −18.0000 −1.15948 −0.579741 − 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −12.0000 −0.766652
\(246\) 0 0
\(247\) 24.0000 1.52708
\(248\) 0 0
\(249\) 12.0000 0.760469
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 − 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 4.00000 0.250490
\(256\) 0 0
\(257\) 18.0000 1.12281 0.561405 − 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) 8.00000 0.497096
\(260\) 0 0
\(261\) 4.00000 0.247594
\(262\) 0 0
\(263\) 12.0000 0.739952 0.369976 − 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) 8.00000 0.491436
\(266\) 0 0
\(267\) 2.00000 0.122398
\(268\) 0 0
\(269\) 12.0000 0.731653 0.365826 − 0.930683i \(-0.380786\pi\)
0.365826 + 0.930683i \(0.380786\pi\)
\(270\) 0 0
\(271\) 16.0000 0.971931 0.485965 − 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 0 0
\(273\) −12.0000 −0.726273
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 − 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 0 0
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 − 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 32.0000 1.90220 0.951101 − 0.308879i \(-0.0999539\pi\)
0.951101 + 0.308879i \(0.0999539\pi\)
\(284\) 0 0
\(285\) −16.0000 −0.947758
\(286\) 0 0
\(287\) −20.0000 −1.18056
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −6.00000 −0.351726
\(292\) 0 0
\(293\) −2.00000 −0.116841 −0.0584206 − 0.998292i \(-0.518606\pi\)
−0.0584206 + 0.998292i \(0.518606\pi\)
\(294\) 0 0
\(295\) 48.0000 2.79467
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −36.0000 −2.08193
\(300\) 0 0
\(301\) −8.00000 −0.461112
\(302\) 0 0
\(303\) 14.0000 0.804279
\(304\) 0 0
\(305\) 16.0000 0.916157
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 − 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) 0 0
\(311\) −30.0000 −1.70114 −0.850572 − 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) 0 0
\(313\) −26.0000 −1.46961 −0.734803 − 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 0 0
\(315\) 8.00000 0.450749
\(316\) 0 0
\(317\) 16.0000 0.898650 0.449325 − 0.893368i \(-0.351665\pi\)
0.449325 + 0.893368i \(0.351665\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) 0 0
\(325\) 66.0000 3.66102
\(326\) 0 0
\(327\) 16.0000 0.884802
\(328\) 0 0
\(329\) −8.00000 −0.441054
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 − 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 0 0
\(333\) 4.00000 0.219199
\(334\) 0 0
\(335\) −48.0000 −2.62252
\(336\) 0 0
\(337\) −6.00000 −0.326841 −0.163420 − 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) 0 0
\(339\) −2.00000 −0.108625
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 0 0
\(345\) 24.0000 1.29212
\(346\) 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 \(-0.203272\pi\)
0.802932 + 0.596071i \(0.203272\pi\)
\(350\) 0 0
\(351\) −6.00000 −0.320256
\(352\) 0 0
\(353\) 14.0000 0.745145 0.372572 − 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 0 0
\(355\) 24.0000 1.27379
\(356\) 0 0
\(357\) 2.00000 0.105851
\(358\) 0 0
\(359\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 8.00000 0.418739
\(366\) 0 0
\(367\) −10.0000 −0.521996 −0.260998 − 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) 0 0
\(369\) −10.0000 −0.520579
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) 14.0000 0.724893 0.362446 − 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 0 0
\(375\) −24.0000 −1.23935
\(376\) 0 0
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 − 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) 8.00000 0.409852
\(382\) 0 0
\(383\) −28.0000 −1.43073 −0.715367 − 0.698749i \(-0.753740\pi\)
−0.715367 + 0.698749i \(0.753740\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4.00000 −0.203331
\(388\) 0 0
\(389\) 14.0000 0.709828 0.354914 − 0.934899i \(-0.384510\pi\)
0.354914 + 0.934899i \(0.384510\pi\)
\(390\) 0 0
\(391\) 6.00000 0.303433
\(392\) 0 0
\(393\) 16.0000 0.807093
\(394\) 0 0
\(395\) −40.0000 −2.01262
\(396\) 0 0
\(397\) −20.0000 −1.00377 −0.501886 − 0.864934i \(-0.667360\pi\)
−0.501886 + 0.864934i \(0.667360\pi\)
\(398\) 0 0
\(399\) −8.00000 −0.400501
\(400\) 0 0
\(401\) 30.0000 1.49813 0.749064 − 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 0 0
\(403\) 36.0000 1.79329
\(404\) 0 0
\(405\) 4.00000 0.198762
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −26.0000 −1.28562 −0.642809 − 0.766027i \(-0.722231\pi\)
−0.642809 + 0.766027i \(0.722231\pi\)
\(410\) 0 0
\(411\) 6.00000 0.295958
\(412\) 0 0
\(413\) 24.0000 1.18096
\(414\) 0 0
\(415\) −48.0000 −2.35623
\(416\) 0 0
\(417\) −8.00000 −0.391762
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 − 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −34.0000 −1.65706 −0.828529 − 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) 0 0
\(423\) −4.00000 −0.194487
\(424\) 0 0
\(425\) −11.0000 −0.533578
\(426\) 0 0
\(427\) 8.00000 0.387147
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −14.0000 −0.674356 −0.337178 − 0.941441i \(-0.609472\pi\)
−0.337178 + 0.941441i \(0.609472\pi\)
\(432\) 0 0
\(433\) −18.0000 −0.865025 −0.432512 − 0.901628i \(-0.642373\pi\)
−0.432512 + 0.901628i \(0.642373\pi\)
\(434\) 0 0
\(435\) −16.0000 −0.767141
\(436\) 0 0
\(437\) −24.0000 −1.14808
\(438\) 0 0
\(439\) 10.0000 0.477274 0.238637 − 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) 12.0000 0.570137 0.285069 − 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 0 0
\(445\) −8.00000 −0.379236
\(446\) 0 0
\(447\) −6.00000 −0.283790
\(448\) 0 0
\(449\) −26.0000 −1.22702 −0.613508 − 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −24.0000 −1.12762
\(454\) 0 0
\(455\) 48.0000 2.25027
\(456\) 0 0
\(457\) 22.0000 1.02912 0.514558 − 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) 0 0
\(459\) 1.00000 0.0466760
\(460\) 0 0
\(461\) 10.0000 0.465746 0.232873 − 0.972507i \(-0.425187\pi\)
0.232873 + 0.972507i \(0.425187\pi\)
\(462\) 0 0
\(463\) 4.00000 0.185896 0.0929479 − 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) 0 0
\(465\) −24.0000 −1.11297
\(466\) 0 0
\(467\) −36.0000 −1.66588 −0.832941 − 0.553362i \(-0.813345\pi\)
−0.832941 + 0.553362i \(0.813345\pi\)
\(468\) 0 0
\(469\) −24.0000 −1.10822
\(470\) 0 0
\(471\) 6.00000 0.276465
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 44.0000 2.01886
\(476\) 0 0
\(477\) 2.00000 0.0915737
\(478\) 0 0
\(479\) −10.0000 −0.456912 −0.228456 − 0.973554i \(-0.573368\pi\)
−0.228456 + 0.973554i \(0.573368\pi\)
\(480\) 0 0
\(481\) 24.0000 1.09431
\(482\) 0 0
\(483\) 12.0000 0.546019
\(484\) 0 0
\(485\) 24.0000 1.08978
\(486\) 0 0
\(487\) 38.0000 1.72194 0.860972 − 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) 0 0
\(489\) −12.0000 −0.542659
\(490\) 0 0
\(491\) −20.0000 −0.902587 −0.451294 − 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 0 0
\(493\) −4.00000 −0.180151
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.0000 0.538274
\(498\) 0 0
\(499\) 32.0000 1.43252 0.716258 − 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) 0 0
\(501\) −2.00000 −0.0893534
\(502\) 0 0
\(503\) 26.0000 1.15928 0.579641 − 0.814872i \(-0.303193\pi\)
0.579641 + 0.814872i \(0.303193\pi\)
\(504\) 0 0
\(505\) −56.0000 −2.49197
\(506\) 0 0
\(507\) −23.0000 −1.02147
\(508\) 0 0
\(509\) −26.0000 −1.15243 −0.576215 − 0.817298i \(-0.695471\pi\)
−0.576215 + 0.817298i \(0.695471\pi\)
\(510\) 0 0
\(511\) 4.00000 0.176950
\(512\) 0 0
\(513\) −4.00000 −0.176604
\(514\) 0 0
\(515\) −16.0000 −0.705044
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −4.00000 −0.175581
\(520\) 0 0
\(521\) −10.0000 −0.438108 −0.219054 − 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) 0 0
\(523\) −20.0000 −0.874539 −0.437269 − 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 0 0
\(525\) −22.0000 −0.960159
\(526\) 0 0
\(527\) −6.00000 −0.261364
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) −60.0000 −2.59889
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 12.0000 0.517838
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 12.0000 0.515920 0.257960 − 0.966156i \(-0.416950\pi\)
0.257960 + 0.966156i \(0.416950\pi\)
\(542\) 0 0
\(543\) −20.0000 −0.858282
\(544\) 0 0
\(545\) −64.0000 −2.74146
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 − 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) 4.00000 0.170716
\(550\) 0 0
\(551\) 16.0000 0.681623
\(552\) 0 0
\(553\) −20.0000 −0.850487
\(554\) 0 0
\(555\) −16.0000 −0.679162
\(556\) 0 0
\(557\) −14.0000 −0.593199 −0.296600 − 0.955002i \(-0.595853\pi\)
−0.296600 + 0.955002i \(0.595853\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4.00000 −0.168580 −0.0842900 − 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) 0 0
\(565\) 8.00000 0.336563
\(566\) 0 0
\(567\) 2.00000 0.0839921
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 − 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) 44.0000 1.84134 0.920671 − 0.390339i \(-0.127642\pi\)
0.920671 + 0.390339i \(0.127642\pi\)
\(572\) 0 0
\(573\) −4.00000 −0.167102
\(574\) 0 0
\(575\) −66.0000 −2.75239
\(576\) 0 0
\(577\) −30.0000 −1.24892 −0.624458 − 0.781058i \(-0.714680\pi\)
−0.624458 + 0.781058i \(0.714680\pi\)
\(578\) 0 0
\(579\) −6.00000 −0.249351
\(580\) 0 0
\(581\) −24.0000 −0.995688
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 24.0000 0.992278
\(586\) 0 0
\(587\) 36.0000 1.48588 0.742940 − 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) 0 0
\(589\) 24.0000 0.988903
\(590\) 0 0
\(591\) 8.00000 0.329076
\(592\) 0 0
\(593\) −30.0000 −1.23195 −0.615976 − 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 0 0
\(595\) −8.00000 −0.327968
\(596\) 0 0
\(597\) 14.0000 0.572982
\(598\) 0 0
\(599\) 16.0000 0.653742 0.326871 − 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) −38.0000 −1.55005 −0.775026 − 0.631929i \(-0.782263\pi\)
−0.775026 + 0.631929i \(0.782263\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) 0 0
\(605\) −44.0000 −1.78885
\(606\) 0 0
\(607\) 38.0000 1.54237 0.771186 − 0.636610i \(-0.219664\pi\)
0.771186 + 0.636610i \(0.219664\pi\)
\(608\) 0 0
\(609\) −8.00000 −0.324176
\(610\) 0 0
\(611\) −24.0000 −0.970936
\(612\) 0 0
\(613\) −30.0000 −1.21169 −0.605844 − 0.795583i \(-0.707165\pi\)
−0.605844 + 0.795583i \(0.707165\pi\)
\(614\) 0 0
\(615\) 40.0000 1.61296
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 − 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 − 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 0 0
\(621\) 6.00000 0.240772
\(622\) 0 0
\(623\) −4.00000 −0.160257
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 − 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 0 0
\(633\) −8.00000 −0.317971
\(634\) 0 0
\(635\) −32.0000 −1.26988
\(636\) 0 0
\(637\) −18.0000 −0.713186
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) −2.00000 −0.0789953 −0.0394976 − 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) 0 0
\(643\) 4.00000 0.157745 0.0788723 − 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) 16.0000 0.629999
\(646\) 0 0
\(647\) −28.0000 −1.10079 −0.550397 − 0.834903i \(-0.685524\pi\)
−0.550397 + 0.834903i \(0.685524\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −12.0000 −0.470317
\(652\) 0 0
\(653\) −20.0000 −0.782660 −0.391330 − 0.920250i \(-0.627985\pi\)
−0.391330 + 0.920250i \(0.627985\pi\)
\(654\) 0 0
\(655\) −64.0000 −2.50069
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) 12.0000 0.467454 0.233727 − 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 − 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 0 0
\(663\) 6.00000 0.233021
\(664\) 0 0
\(665\) 32.0000 1.24091
\(666\) 0 0
\(667\) −24.0000 −0.929284
\(668\) 0 0
\(669\) −4.00000 −0.154649
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 − 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 0 0
\(675\) −11.0000 −0.423390
\(676\) 0 0
\(677\) −8.00000 −0.307465 −0.153732 − 0.988113i \(-0.549129\pi\)
−0.153732 + 0.988113i \(0.549129\pi\)
\(678\) 0 0
\(679\) 12.0000 0.460518
\(680\) 0 0
\(681\) −4.00000 −0.153280
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 − 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) −24.0000 −0.916993
\(686\) 0 0
\(687\) −2.00000 −0.0763048
\(688\) 0 0
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) 16.0000 0.608669 0.304334 − 0.952565i \(-0.401566\pi\)
0.304334 + 0.952565i \(0.401566\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 32.0000 1.21383
\(696\) 0 0
\(697\) 10.0000 0.378777
\(698\) 0 0
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 − 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 16.0000 0.603451
\(704\) 0 0
\(705\) 16.0000 0.602595
\(706\) 0 0
\(707\) −28.0000 −1.05305
\(708\) 0 0
\(709\) 16.0000 0.600893 0.300446 − 0.953799i \(-0.402864\pi\)
0.300446 + 0.953799i \(0.402864\pi\)
\(710\) 0 0
\(711\) −10.0000 −0.375029
\(712\) 0 0
\(713\) −36.0000 −1.34821
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −20.0000 −0.746914
\(718\) 0 0
\(719\) −42.0000 −1.56634 −0.783168 − 0.621810i \(-0.786397\pi\)
−0.783168 + 0.621810i \(0.786397\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 0 0
\(723\) 18.0000 0.669427
\(724\) 0 0
\(725\) 44.0000 1.63412
\(726\) 0 0
\(727\) 8.00000 0.296704 0.148352 − 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 4.00000 0.147945
\(732\) 0 0
\(733\) −18.0000 −0.664845 −0.332423 − 0.943131i \(-0.607866\pi\)
−0.332423 + 0.943131i \(0.607866\pi\)
\(734\) 0 0
\(735\) 12.0000 0.442627
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −12.0000 −0.441427 −0.220714 − 0.975339i \(-0.570839\pi\)
−0.220714 + 0.975339i \(0.570839\pi\)
\(740\) 0 0
\(741\) −24.0000 −0.881662
\(742\) 0 0
\(743\) −38.0000 −1.39408 −0.697042 − 0.717030i \(-0.745501\pi\)
−0.697042 + 0.717030i \(0.745501\pi\)
\(744\) 0 0
\(745\) 24.0000 0.879292
\(746\) 0 0
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 34.0000 1.24068 0.620339 − 0.784334i \(-0.286995\pi\)
0.620339 + 0.784334i \(0.286995\pi\)
\(752\) 0 0
\(753\) −12.0000 −0.437304
\(754\) 0 0
\(755\) 96.0000 3.49380
\(756\) 0 0
\(757\) −14.0000 −0.508839 −0.254419 − 0.967094i \(-0.581884\pi\)
−0.254419 + 0.967094i \(0.581884\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 10.0000 0.362500 0.181250 − 0.983437i \(-0.441986\pi\)
0.181250 + 0.983437i \(0.441986\pi\)
\(762\) 0 0
\(763\) −32.0000 −1.15848
\(764\) 0 0
\(765\) −4.00000 −0.144620
\(766\) 0 0
\(767\) 72.0000 2.59977
\(768\) 0 0
\(769\) 26.0000 0.937584 0.468792 − 0.883309i \(-0.344689\pi\)
0.468792 + 0.883309i \(0.344689\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 0 0
\(773\) −42.0000 −1.51064 −0.755318 − 0.655359i \(-0.772517\pi\)
−0.755318 + 0.655359i \(0.772517\pi\)
\(774\) 0 0
\(775\) 66.0000 2.37079
\(776\) 0 0
\(777\) −8.00000 −0.286998
\(778\) 0 0
\(779\) −40.0000 −1.43315
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −4.00000 −0.142948
\(784\) 0 0
\(785\) −24.0000 −0.856597
\(786\) 0 0
\(787\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) −12.0000 −0.427211
\(790\) 0 0
\(791\) 4.00000 0.142224
\(792\) 0 0
\(793\) 24.0000 0.852265
\(794\) 0 0
\(795\) −8.00000 −0.283731
\(796\) 0 0
\(797\) −46.0000 −1.62940 −0.814702 − 0.579880i \(-0.803099\pi\)
−0.814702 + 0.579880i \(0.803099\pi\)
\(798\) 0 0
\(799\) 4.00000 0.141510
\(800\) 0 0
\(801\) −2.00000 −0.0706665
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −48.0000 −1.69178
\(806\) 0 0
\(807\) −12.0000 −0.422420
\(808\) 0 0
\(809\) −26.0000 −0.914111 −0.457056 − 0.889438i \(-0.651096\pi\)
−0.457056 + 0.889438i \(0.651096\pi\)
\(810\) 0 0
\(811\) −12.0000 −0.421377 −0.210688 − 0.977553i \(-0.567571\pi\)
−0.210688 + 0.977553i \(0.567571\pi\)
\(812\) 0 0
\(813\) −16.0000 −0.561144
\(814\) 0 0
\(815\) 48.0000 1.68137
\(816\) 0 0
\(817\) −16.0000 −0.559769
\(818\) 0 0
\(819\) 12.0000 0.419314
\(820\) 0 0
\(821\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) −18.0000 −0.627441 −0.313720 − 0.949515i \(-0.601575\pi\)
−0.313720 + 0.949515i \(0.601575\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 16.0000 0.556375 0.278187 − 0.960527i \(-0.410266\pi\)
0.278187 + 0.960527i \(0.410266\pi\)
\(828\) 0 0
\(829\) −6.00000 −0.208389 −0.104194 − 0.994557i \(-0.533226\pi\)
−0.104194 + 0.994557i \(0.533226\pi\)
\(830\) 0 0
\(831\) −8.00000 −0.277517
\(832\) 0 0
\(833\) 3.00000 0.103944
\(834\) 0 0
\(835\) 8.00000 0.276851
\(836\) 0 0
\(837\) −6.00000 −0.207390
\(838\) 0 0
\(839\) 30.0000 1.03572 0.517858 − 0.855467i \(-0.326730\pi\)
0.517858 + 0.855467i \(0.326730\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 0 0
\(843\) 18.0000 0.619953
\(844\) 0 0
\(845\) 92.0000 3.16490
\(846\) 0 0
\(847\) −22.0000 −0.755929
\(848\) 0 0
\(849\) −32.0000 −1.09824
\(850\) 0 0
\(851\) −24.0000 −0.822709
\(852\) 0 0
\(853\) 16.0000 0.547830 0.273915 − 0.961754i \(-0.411681\pi\)
0.273915 + 0.961754i \(0.411681\pi\)
\(854\) 0 0
\(855\) 16.0000 0.547188
\(856\) 0 0
\(857\) −10.0000 −0.341593 −0.170797 − 0.985306i \(-0.554634\pi\)
−0.170797 + 0.985306i \(0.554634\pi\)
\(858\) 0 0
\(859\) 20.0000 0.682391 0.341196 − 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 0 0
\(861\) 20.0000 0.681598
\(862\) 0 0
\(863\) 48.0000 1.63394 0.816970 − 0.576681i \(-0.195652\pi\)
0.816970 + 0.576681i \(0.195652\pi\)
\(864\) 0 0
\(865\) 16.0000 0.544016
\(866\) 0 0
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −72.0000 −2.43963
\(872\) 0 0
\(873\) 6.00000 0.203069
\(874\) 0 0
\(875\) 48.0000 1.62270
\(876\) 0 0
\(877\) 24.0000 0.810422 0.405211 − 0.914223i \(-0.367198\pi\)
0.405211 + 0.914223i \(0.367198\pi\)
\(878\) 0 0
\(879\) 2.00000 0.0674583
\(880\) 0 0
\(881\) 50.0000 1.68454 0.842271 − 0.539054i \(-0.181218\pi\)
0.842271 + 0.539054i \(0.181218\pi\)
\(882\) 0 0
\(883\) −52.0000 −1.74994 −0.874970 − 0.484178i \(-0.839119\pi\)
−0.874970 + 0.484178i \(0.839119\pi\)
\(884\) 0 0
\(885\) −48.0000 −1.61350
\(886\) 0 0
\(887\) −18.0000 −0.604381 −0.302190 − 0.953248i \(-0.597718\pi\)
−0.302190 + 0.953248i \(0.597718\pi\)
\(888\) 0 0
\(889\) −16.0000 −0.536623
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −16.0000 −0.535420
\(894\) 0 0
\(895\) −48.0000 −1.60446
\(896\) 0 0
\(897\) 36.0000 1.20201
\(898\) 0 0
\(899\) 24.0000 0.800445
\(900\) 0 0
\(901\) −2.00000 −0.0666297
\(902\) 0 0
\(903\) 8.00000 0.266223
\(904\) 0 0
\(905\) 80.0000 2.65929
\(906\) 0 0
\(907\) 24.0000 0.796907 0.398453 − 0.917189i \(-0.369547\pi\)
0.398453 + 0.917189i \(0.369547\pi\)
\(908\) 0 0
\(909\) −14.0000 −0.464351
\(910\) 0 0
\(911\) −26.0000 −0.861418 −0.430709 − 0.902491i \(-0.641737\pi\)
−0.430709 + 0.902491i \(0.641737\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −16.0000 −0.528944
\(916\) 0 0
\(917\) −32.0000 −1.05673
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 − 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) 12.0000 0.395413
\(922\) 0 0
\(923\) 36.0000 1.18495
\(924\) 0 0
\(925\) 44.0000 1.44671
\(926\) 0 0
\(927\) −4.00000 −0.131377
\(928\) 0 0
\(929\) −34.0000 −1.11550 −0.557752 − 0.830008i \(-0.688336\pi\)
−0.557752 + 0.830008i \(0.688336\pi\)
\(930\) 0 0
\(931\) −12.0000 −0.393284
\(932\) 0 0
\(933\) 30.0000 0.982156
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 22.0000 0.718709 0.359354 − 0.933201i \(-0.382997\pi\)
0.359354 + 0.933201i \(0.382997\pi\)
\(938\) 0 0
\(939\) 26.0000 0.848478
\(940\) 0 0
\(941\) −48.0000 −1.56476 −0.782378 − 0.622804i \(-0.785993\pi\)
−0.782378 + 0.622804i \(0.785993\pi\)
\(942\) 0 0
\(943\) 60.0000 1.95387
\(944\) 0 0
\(945\) −8.00000 −0.260240
\(946\) 0 0
\(947\) −24.0000 −0.779895 −0.389948 − 0.920837i \(-0.627507\pi\)
−0.389948 + 0.920837i \(0.627507\pi\)
\(948\) 0 0
\(949\) 12.0000 0.389536
\(950\) 0 0
\(951\) −16.0000 −0.518836
\(952\) 0 0
\(953\) 22.0000 0.712650 0.356325 − 0.934362i \(-0.384030\pi\)
0.356325 + 0.934362i \(0.384030\pi\)
\(954\) 0 0
\(955\) 16.0000 0.517748
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −12.0000 −0.387500
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 24.0000 0.772587
\(966\) 0 0
\(967\) 44.0000 1.41494 0.707472 − 0.706741i \(-0.249835\pi\)
0.707472 + 0.706741i \(0.249835\pi\)
\(968\) 0 0
\(969\) 4.00000 0.128499
\(970\) 0 0
\(971\) 20.0000 0.641831 0.320915 − 0.947108i \(-0.396010\pi\)
0.320915 + 0.947108i \(0.396010\pi\)
\(972\) 0 0
\(973\) 16.0000 0.512936
\(974\) 0 0
\(975\) −66.0000 −2.11369
\(976\) 0 0
\(977\) 2.00000 0.0639857 0.0319928 − 0.999488i \(-0.489815\pi\)
0.0319928 + 0.999488i \(0.489815\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −16.0000 −0.510841
\(982\) 0 0
\(983\) 38.0000 1.21201 0.606006 − 0.795460i \(-0.292771\pi\)
0.606006 + 0.795460i \(0.292771\pi\)
\(984\) 0 0
\(985\) −32.0000 −1.01960
\(986\) 0 0
\(987\) 8.00000 0.254643
\(988\) 0 0
\(989\) 24.0000 0.763156
\(990\) 0 0
\(991\) 34.0000 1.08005 0.540023 − 0.841650i \(-0.318416\pi\)
0.540023 + 0.841650i \(0.318416\pi\)
\(992\) 0 0
\(993\) −20.0000 −0.634681
\(994\) 0 0
\(995\) −56.0000 −1.77532
\(996\) 0 0
\(997\) 20.0000 0.633406 0.316703 − 0.948525i \(-0.397424\pi\)
0.316703 + 0.948525i \(0.397424\pi\)
\(998\) 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 3264.2.a.p.1.1 1
3.2 odd 2 9792.2.a.b.1.1 1
4.3 odd 2 3264.2.a.bf.1.1 1
8.3 odd 2 102.2.a.a.1.1 ✓ 1
8.5 even 2 816.2.a.h.1.1 1
12.11 even 2 9792.2.a.a.1.1 1
24.5 odd 2 2448.2.a.t.1.1 1
24.11 even 2 306.2.a.d.1.1 1
40.3 even 4 2550.2.d.q.2449.2 2
40.19 odd 2 2550.2.a.be.1.1 1
40.27 even 4 2550.2.d.q.2449.1 2
56.27 even 2 4998.2.a.x.1.1 1
120.59 even 2 7650.2.a.z.1.1 1
136.19 odd 8 1734.2.f.g.1483.1 4
136.43 odd 8 1734.2.f.g.829.1 4
136.59 odd 8 1734.2.f.g.829.2 4
136.67 odd 2 1734.2.a.h.1.1 1
136.83 odd 8 1734.2.f.g.1483.2 4
136.115 odd 4 1734.2.b.d.577.1 2
136.123 odd 4 1734.2.b.d.577.2 2
408.203 even 2 5202.2.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
102.2.a.a.1.1 ✓ 1 8.3 odd 2
306.2.a.d.1.1 1 24.11 even 2
816.2.a.h.1.1 1 8.5 even 2
1734.2.a.h.1.1 1 136.67 odd 2
1734.2.b.d.577.1 2 136.115 odd 4
1734.2.b.d.577.2 2 136.123 odd 4
1734.2.f.g.829.1 4 136.43 odd 8
1734.2.f.g.829.2 4 136.59 odd 8
1734.2.f.g.1483.1 4 136.19 odd 8
1734.2.f.g.1483.2 4 136.83 odd 8
2448.2.a.t.1.1 1 24.5 odd 2
2550.2.a.be.1.1 1 40.19 odd 2
2550.2.d.q.2449.1 2 40.27 even 4
2550.2.d.q.2449.2 2 40.3 even 4
3264.2.a.p.1.1 1 1.1 even 1 trivial
3264.2.a.bf.1.1 1 4.3 odd 2
4998.2.a.x.1.1 1 56.27 even 2
5202.2.a.g.1.1 1 408.203 even 2
7650.2.a.z.1.1 1 120.59 even 2
9792.2.a.a.1.1 1 12.11 even 2
9792.2.a.b.1.1 1 3.2 odd 2