Properties

Label 8664.2.a.l.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

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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: no (minimal twist has level 456)
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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} +1.00000 q^{5} -3.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +1.00000 q^{5} -3.00000 q^{7} +1.00000 q^{9} -5.00000 q^{11} +2.00000 q^{13} +1.00000 q^{15} -1.00000 q^{17} -3.00000 q^{21} +4.00000 q^{23} -4.00000 q^{25} +1.00000 q^{27} +6.00000 q^{29} +10.0000 q^{31} -5.00000 q^{33} -3.00000 q^{35} +2.00000 q^{39} -11.0000 q^{43} +1.00000 q^{45} +9.00000 q^{47} +2.00000 q^{49} -1.00000 q^{51} -10.0000 q^{53} -5.00000 q^{55} -4.00000 q^{59} -5.00000 q^{61} -3.00000 q^{63} +2.00000 q^{65} +4.00000 q^{67} +4.00000 q^{69} -8.00000 q^{71} +13.0000 q^{73} -4.00000 q^{75} +15.0000 q^{77} -4.00000 q^{79} +1.00000 q^{81} -4.00000 q^{83} -1.00000 q^{85} +6.00000 q^{87} +6.00000 q^{89} -6.00000 q^{91} +10.0000 q^{93} -2.00000 q^{97} -5.00000 q^{99} +O(q^{100})\)

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
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 0 0
\(7\) −3.00000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.00000 −1.50756 −0.753778 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) −1.00000 −0.242536 −0.121268 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(18\) 0 0
\(19\) 0 0
\(20\) 0 0
\(21\) −3.00000 −0.654654
\(22\) 0 0
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 0 0
\(33\) −5.00000 −0.870388
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −11.0000 −1.67748 −0.838742 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 9.00000 1.31278 0.656392 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) 0 0
\(51\) −1.00000 −0.140028
\(52\) 0 0
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −5.00000 −0.640184 −0.320092 0.947386i \(-0.603714\pi\)
−0.320092 + 0.947386i \(0.603714\pi\)
\(62\) 0 0
\(63\) −3.00000 −0.377964
\(64\) 0 0
\(65\) 2.00000 0.248069
\(66\) 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 \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) 13.0000 1.52153 0.760767 0.649025i \(-0.224823\pi\)
0.760767 + 0.649025i \(0.224823\pi\)
\(74\) 0 0
\(75\) −4.00000 −0.461880
\(76\) 0 0
\(77\) 15.0000 1.70941
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) −1.00000 −0.108465
\(86\) 0 0
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 0 0
\(93\) 10.0000 1.03695
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) −5.00000 −0.502519
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) 0 0
\(105\) −3.00000 −0.292770
\(106\) 0 0
\(107\) −18.0000 −1.74013 −0.870063 0.492941i \(-0.835922\pi\)
−0.870063 + 0.492941i \(0.835922\pi\)
\(108\) 0 0
\(109\) 8.00000 0.766261 0.383131 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(110\) 0 0
\(111\) 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
\(115\) 4.00000 0.373002
\(116\) 0 0
\(117\) 2.00000 0.184900
\(118\) 0 0
\(119\) 3.00000 0.275010
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 0 0
\(129\) −11.0000 −0.968496
\(130\) 0 0
\(131\) −19.0000 −1.66004 −0.830019 0.557735i \(-0.811670\pi\)
−0.830019 + 0.557735i \(0.811670\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.00000 0.0860663
\(136\) 0 0
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) 0 0
\(139\) −15.0000 −1.27228 −0.636142 0.771572i \(-0.719471\pi\)
−0.636142 + 0.771572i \(0.719471\pi\)
\(140\) 0 0
\(141\) 9.00000 0.757937
\(142\) 0 0
\(143\) −10.0000 −0.836242
\(144\) 0 0
\(145\) 6.00000 0.498273
\(146\) 0 0
\(147\) 2.00000 0.164957
\(148\) 0 0
\(149\) −1.00000 −0.0819232 −0.0409616 0.999161i \(-0.513042\pi\)
−0.0409616 + 0.999161i \(0.513042\pi\)
\(150\) 0 0
\(151\) −20.0000 −1.62758 −0.813788 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 0 0
\(153\) −1.00000 −0.0808452
\(154\) 0 0
\(155\) 10.0000 0.803219
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 0 0
\(159\) −10.0000 −0.793052
\(160\) 0 0
\(161\) −12.0000 −0.945732
\(162\) 0 0
\(163\) −24.0000 −1.87983 −0.939913 0.341415i \(-0.889094\pi\)
−0.939913 + 0.341415i \(0.889094\pi\)
\(164\) 0 0
\(165\) −5.00000 −0.389249
\(166\) 0 0
\(167\) −18.0000 −1.39288 −0.696441 0.717614i \(-0.745234\pi\)
−0.696441 + 0.717614i \(0.745234\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 18.0000 1.36851 0.684257 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) 0 0
\(175\) 12.0000 0.907115
\(176\) 0 0
\(177\) −4.00000 −0.300658
\(178\) 0 0
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 0 0
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 0 0
\(183\) −5.00000 −0.369611
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 5.00000 0.365636
\(188\) 0 0
\(189\) −3.00000 −0.218218
\(190\) 0 0
\(191\) 15.0000 1.08536 0.542681 0.839939i \(-0.317409\pi\)
0.542681 + 0.839939i \(0.317409\pi\)
\(192\) 0 0
\(193\) 16.0000 1.15171 0.575853 0.817554i \(-0.304670\pi\)
0.575853 + 0.817554i \(0.304670\pi\)
\(194\) 0 0
\(195\) 2.00000 0.143223
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −11.0000 −0.779769 −0.389885 0.920864i \(-0.627485\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) 0 0
\(203\) −18.0000 −1.26335
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 4.00000 0.278019
\(208\) 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
\(213\) −8.00000 −0.548151
\(214\) 0 0
\(215\) −11.0000 −0.750194
\(216\) 0 0
\(217\) −30.0000 −2.03653
\(218\) 0 0
\(219\) 13.0000 0.878459
\(220\) 0 0
\(221\) −2.00000 −0.134535
\(222\) 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
\(227\) 6.00000 0.398234 0.199117 0.979976i \(-0.436193\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(228\) 0 0
\(229\) −11.0000 −0.726900 −0.363450 0.931614i \(-0.618401\pi\)
−0.363450 + 0.931614i \(0.618401\pi\)
\(230\) 0 0
\(231\) 15.0000 0.986928
\(232\) 0 0
\(233\) −23.0000 −1.50678 −0.753390 0.657574i \(-0.771583\pi\)
−0.753390 + 0.657574i \(0.771583\pi\)
\(234\) 0 0
\(235\) 9.00000 0.587095
\(236\) 0 0
\(237\) −4.00000 −0.259828
\(238\) 0 0
\(239\) 11.0000 0.711531 0.355765 0.934575i \(-0.384220\pi\)
0.355765 + 0.934575i \(0.384220\pi\)
\(240\) 0 0
\(241\) 12.0000 0.772988 0.386494 0.922292i \(-0.373686\pi\)
0.386494 + 0.922292i \(0.373686\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 2.00000 0.127775
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −4.00000 −0.253490
\(250\) 0 0
\(251\) −19.0000 −1.19927 −0.599635 0.800274i \(-0.704687\pi\)
−0.599635 + 0.800274i \(0.704687\pi\)
\(252\) 0 0
\(253\) −20.0000 −1.25739
\(254\) 0 0
\(255\) −1.00000 −0.0626224
\(256\) 0 0
\(257\) 16.0000 0.998053 0.499026 0.866587i \(-0.333691\pi\)
0.499026 + 0.866587i \(0.333691\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) −23.0000 −1.41824 −0.709120 0.705087i \(-0.750908\pi\)
−0.709120 + 0.705087i \(0.750908\pi\)
\(264\) 0 0
\(265\) −10.0000 −0.614295
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 0 0
\(269\) 22.0000 1.34136 0.670682 0.741745i \(-0.266002\pi\)
0.670682 + 0.741745i \(0.266002\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 0 0
\(273\) −6.00000 −0.363137
\(274\) 0 0
\(275\) 20.0000 1.20605
\(276\) 0 0
\(277\) 25.0000 1.50210 0.751052 0.660243i \(-0.229547\pi\)
0.751052 + 0.660243i \(0.229547\pi\)
\(278\) 0 0
\(279\) 10.0000 0.598684
\(280\) 0 0
\(281\) 22.0000 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) 0 0
\(283\) −7.00000 −0.416107 −0.208053 0.978117i \(-0.566713\pi\)
−0.208053 + 0.978117i \(0.566713\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 0 0
\(291\) −2.00000 −0.117242
\(292\) 0 0
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 0 0
\(297\) −5.00000 −0.290129
\(298\) 0 0
\(299\) 8.00000 0.462652
\(300\) 0 0
\(301\) 33.0000 1.90209
\(302\) 0 0
\(303\) −6.00000 −0.344691
\(304\) 0 0
\(305\) −5.00000 −0.286299
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) −10.0000 −0.568880
\(310\) 0 0
\(311\) −27.0000 −1.53103 −0.765515 0.643418i \(-0.777516\pi\)
−0.765515 + 0.643418i \(0.777516\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 0 0
\(315\) −3.00000 −0.169031
\(316\) 0 0
\(317\) −24.0000 −1.34797 −0.673987 0.738743i \(-0.735420\pi\)
−0.673987 + 0.738743i \(0.735420\pi\)
\(318\) 0 0
\(319\) −30.0000 −1.67968
\(320\) 0 0
\(321\) −18.0000 −1.00466
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −8.00000 −0.443760
\(326\) 0 0
\(327\) 8.00000 0.442401
\(328\) 0 0
\(329\) −27.0000 −1.48856
\(330\) 0 0
\(331\) −32.0000 −1.75888 −0.879440 0.476011i \(-0.842082\pi\)
−0.879440 + 0.476011i \(0.842082\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) −50.0000 −2.70765
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) 0 0
\(345\) 4.00000 0.215353
\(346\) 0 0
\(347\) 21.0000 1.12734 0.563670 0.826000i \(-0.309389\pi\)
0.563670 + 0.826000i \(0.309389\pi\)
\(348\) 0 0
\(349\) −27.0000 −1.44528 −0.722638 0.691226i \(-0.757071\pi\)
−0.722638 + 0.691226i \(0.757071\pi\)
\(350\) 0 0
\(351\) 2.00000 0.106752
\(352\) 0 0
\(353\) 14.0000 0.745145 0.372572 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 0 0
\(355\) −8.00000 −0.424596
\(356\) 0 0
\(357\) 3.00000 0.158777
\(358\) 0 0
\(359\) −21.0000 −1.10834 −0.554169 0.832404i \(-0.686964\pi\)
−0.554169 + 0.832404i \(0.686964\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 14.0000 0.734809
\(364\) 0 0
\(365\) 13.0000 0.680451
\(366\) 0 0
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 30.0000 1.55752
\(372\) 0 0
\(373\) 16.0000 0.828449 0.414224 0.910175i \(-0.364053\pi\)
0.414224 + 0.910175i \(0.364053\pi\)
\(374\) 0 0
\(375\) −9.00000 −0.464758
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) 34.0000 1.74646 0.873231 0.487306i \(-0.162020\pi\)
0.873231 + 0.487306i \(0.162020\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) 0 0
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 0 0
\(385\) 15.0000 0.764471
\(386\) 0 0
\(387\) −11.0000 −0.559161
\(388\) 0 0
\(389\) 25.0000 1.26755 0.633775 0.773517i \(-0.281504\pi\)
0.633775 + 0.773517i \(0.281504\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 0 0
\(393\) −19.0000 −0.958423
\(394\) 0 0
\(395\) −4.00000 −0.201262
\(396\) 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
\(401\) −24.0000 −1.19850 −0.599251 0.800561i \(-0.704535\pi\)
−0.599251 + 0.800561i \(0.704535\pi\)
\(402\) 0 0
\(403\) 20.0000 0.996271
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −18.0000 −0.890043 −0.445021 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) 0 0
\(411\) −9.00000 −0.443937
\(412\) 0 0
\(413\) 12.0000 0.590481
\(414\) 0 0
\(415\) −4.00000 −0.196352
\(416\) 0 0
\(417\) −15.0000 −0.734553
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 0 0
\(423\) 9.00000 0.437595
\(424\) 0 0
\(425\) 4.00000 0.194029
\(426\) 0 0
\(427\) 15.0000 0.725901
\(428\) 0 0
\(429\) −10.0000 −0.482805
\(430\) 0 0
\(431\) 10.0000 0.481683 0.240842 0.970564i \(-0.422577\pi\)
0.240842 + 0.970564i \(0.422577\pi\)
\(432\) 0 0
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 0 0
\(435\) 6.00000 0.287678
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 30.0000 1.43182 0.715911 0.698192i \(-0.246012\pi\)
0.715911 + 0.698192i \(0.246012\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 0 0
\(443\) −7.00000 −0.332580 −0.166290 0.986077i \(-0.553179\pi\)
−0.166290 + 0.986077i \(0.553179\pi\)
\(444\) 0 0
\(445\) 6.00000 0.284427
\(446\) 0 0
\(447\) −1.00000 −0.0472984
\(448\) 0 0
\(449\) 20.0000 0.943858 0.471929 0.881636i \(-0.343558\pi\)
0.471929 + 0.881636i \(0.343558\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −20.0000 −0.939682
\(454\) 0 0
\(455\) −6.00000 −0.281284
\(456\) 0 0
\(457\) 35.0000 1.63723 0.818615 0.574342i \(-0.194742\pi\)
0.818615 + 0.574342i \(0.194742\pi\)
\(458\) 0 0
\(459\) −1.00000 −0.0466760
\(460\) 0 0
\(461\) 7.00000 0.326023 0.163011 0.986624i \(-0.447879\pi\)
0.163011 + 0.986624i \(0.447879\pi\)
\(462\) 0 0
\(463\) −1.00000 −0.0464739 −0.0232370 0.999730i \(-0.507397\pi\)
−0.0232370 + 0.999730i \(0.507397\pi\)
\(464\) 0 0
\(465\) 10.0000 0.463739
\(466\) 0 0
\(467\) −15.0000 −0.694117 −0.347059 0.937843i \(-0.612820\pi\)
−0.347059 + 0.937843i \(0.612820\pi\)
\(468\) 0 0
\(469\) −12.0000 −0.554109
\(470\) 0 0
\(471\) −2.00000 −0.0921551
\(472\) 0 0
\(473\) 55.0000 2.52890
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) 0 0
\(479\) −16.0000 −0.731059 −0.365529 0.930800i \(-0.619112\pi\)
−0.365529 + 0.930800i \(0.619112\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −12.0000 −0.546019
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) 0 0
\(487\) −4.00000 −0.181257 −0.0906287 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(488\) 0 0
\(489\) −24.0000 −1.08532
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 0 0
\(493\) −6.00000 −0.270226
\(494\) 0 0
\(495\) −5.00000 −0.224733
\(496\) 0 0
\(497\) 24.0000 1.07655
\(498\) 0 0
\(499\) 39.0000 1.74588 0.872940 0.487828i \(-0.162211\pi\)
0.872940 + 0.487828i \(0.162211\pi\)
\(500\) 0 0
\(501\) −18.0000 −0.804181
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) −6.00000 −0.266996
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) 0 0
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 0 0
\(511\) −39.0000 −1.72526
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −10.0000 −0.440653
\(516\) 0 0
\(517\) −45.0000 −1.97910
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) −8.00000 −0.350486 −0.175243 0.984525i \(-0.556071\pi\)
−0.175243 + 0.984525i \(0.556071\pi\)
\(522\) 0 0
\(523\) 38.0000 1.66162 0.830812 0.556553i \(-0.187876\pi\)
0.830812 + 0.556553i \(0.187876\pi\)
\(524\) 0 0
\(525\) 12.0000 0.523723
\(526\) 0 0
\(527\) −10.0000 −0.435607
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −18.0000 −0.778208
\(536\) 0 0
\(537\) −6.00000 −0.258919
\(538\) 0 0
\(539\) −10.0000 −0.430730
\(540\) 0 0
\(541\) 15.0000 0.644900 0.322450 0.946586i \(-0.395494\pi\)
0.322450 + 0.946586i \(0.395494\pi\)
\(542\) 0 0
\(543\) −18.0000 −0.772454
\(544\) 0 0
\(545\) 8.00000 0.342682
\(546\) 0 0
\(547\) 10.0000 0.427569 0.213785 0.976881i \(-0.431421\pi\)
0.213785 + 0.976881i \(0.431421\pi\)
\(548\) 0 0
\(549\) −5.00000 −0.213395
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 12.0000 0.510292
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.00000 −0.211857 −0.105928 0.994374i \(-0.533781\pi\)
−0.105928 + 0.994374i \(0.533781\pi\)
\(558\) 0 0
\(559\) −22.0000 −0.930501
\(560\) 0 0
\(561\) 5.00000 0.211100
\(562\) 0 0
\(563\) 20.0000 0.842900 0.421450 0.906852i \(-0.361521\pi\)
0.421450 + 0.906852i \(0.361521\pi\)
\(564\) 0 0
\(565\) −6.00000 −0.252422
\(566\) 0 0
\(567\) −3.00000 −0.125988
\(568\) 0 0
\(569\) −34.0000 −1.42535 −0.712677 0.701492i \(-0.752517\pi\)
−0.712677 + 0.701492i \(0.752517\pi\)
\(570\) 0 0
\(571\) 24.0000 1.00437 0.502184 0.864761i \(-0.332530\pi\)
0.502184 + 0.864761i \(0.332530\pi\)
\(572\) 0 0
\(573\) 15.0000 0.626634
\(574\) 0 0
\(575\) −16.0000 −0.667246
\(576\) 0 0
\(577\) 35.0000 1.45707 0.728535 0.685009i \(-0.240202\pi\)
0.728535 + 0.685009i \(0.240202\pi\)
\(578\) 0 0
\(579\) 16.0000 0.664937
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) 0 0
\(583\) 50.0000 2.07079
\(584\) 0 0
\(585\) 2.00000 0.0826898
\(586\) 0 0
\(587\) −35.0000 −1.44460 −0.722302 0.691577i \(-0.756916\pi\)
−0.722302 + 0.691577i \(0.756916\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 6.00000 0.246807
\(592\) 0 0
\(593\) −14.0000 −0.574911 −0.287456 0.957794i \(-0.592809\pi\)
−0.287456 + 0.957794i \(0.592809\pi\)
\(594\) 0 0
\(595\) 3.00000 0.122988
\(596\) 0 0
\(597\) −11.0000 −0.450200
\(598\) 0 0
\(599\) −36.0000 −1.47092 −0.735460 0.677568i \(-0.763034\pi\)
−0.735460 + 0.677568i \(0.763034\pi\)
\(600\) 0 0
\(601\) 44.0000 1.79480 0.897399 0.441221i \(-0.145454\pi\)
0.897399 + 0.441221i \(0.145454\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 0 0
\(605\) 14.0000 0.569181
\(606\) 0 0
\(607\) 22.0000 0.892952 0.446476 0.894795i \(-0.352679\pi\)
0.446476 + 0.894795i \(0.352679\pi\)
\(608\) 0 0
\(609\) −18.0000 −0.729397
\(610\) 0 0
\(611\) 18.0000 0.728202
\(612\) 0 0
\(613\) 5.00000 0.201948 0.100974 0.994889i \(-0.467804\pi\)
0.100974 + 0.994889i \(0.467804\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 27.0000 1.08698 0.543490 0.839416i \(-0.317103\pi\)
0.543490 + 0.839416i \(0.317103\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 0 0
\(621\) 4.00000 0.160514
\(622\) 0 0
\(623\) −18.0000 −0.721155
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −47.0000 −1.87104 −0.935520 0.353273i \(-0.885069\pi\)
−0.935520 + 0.353273i \(0.885069\pi\)
\(632\) 0 0
\(633\) 8.00000 0.317971
\(634\) 0 0
\(635\) 2.00000 0.0793676
\(636\) 0 0
\(637\) 4.00000 0.158486
\(638\) 0 0
\(639\) −8.00000 −0.316475
\(640\) 0 0
\(641\) 26.0000 1.02694 0.513469 0.858108i \(-0.328360\pi\)
0.513469 + 0.858108i \(0.328360\pi\)
\(642\) 0 0
\(643\) 21.0000 0.828159 0.414080 0.910241i \(-0.364104\pi\)
0.414080 + 0.910241i \(0.364104\pi\)
\(644\) 0 0
\(645\) −11.0000 −0.433125
\(646\) 0 0
\(647\) −25.0000 −0.982851 −0.491426 0.870919i \(-0.663524\pi\)
−0.491426 + 0.870919i \(0.663524\pi\)
\(648\) 0 0
\(649\) 20.0000 0.785069
\(650\) 0 0
\(651\) −30.0000 −1.17579
\(652\) 0 0
\(653\) −9.00000 −0.352197 −0.176099 0.984373i \(-0.556348\pi\)
−0.176099 + 0.984373i \(0.556348\pi\)
\(654\) 0 0
\(655\) −19.0000 −0.742391
\(656\) 0 0
\(657\) 13.0000 0.507178
\(658\) 0 0
\(659\) −6.00000 −0.233727 −0.116863 0.993148i \(-0.537284\pi\)
−0.116863 + 0.993148i \(0.537284\pi\)
\(660\) 0 0
\(661\) 28.0000 1.08907 0.544537 0.838737i \(-0.316705\pi\)
0.544537 + 0.838737i \(0.316705\pi\)
\(662\) 0 0
\(663\) −2.00000 −0.0776736
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 24.0000 0.929284
\(668\) 0 0
\(669\) −4.00000 −0.154649
\(670\) 0 0
\(671\) 25.0000 0.965114
\(672\) 0 0
\(673\) 44.0000 1.69608 0.848038 0.529936i \(-0.177784\pi\)
0.848038 + 0.529936i \(0.177784\pi\)
\(674\) 0 0
\(675\) −4.00000 −0.153960
\(676\) 0 0
\(677\) 2.00000 0.0768662 0.0384331 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) 0 0
\(679\) 6.00000 0.230259
\(680\) 0 0
\(681\) 6.00000 0.229920
\(682\) 0 0
\(683\) −34.0000 −1.30097 −0.650487 0.759517i \(-0.725435\pi\)
−0.650487 + 0.759517i \(0.725435\pi\)
\(684\) 0 0
\(685\) −9.00000 −0.343872
\(686\) 0 0
\(687\) −11.0000 −0.419676
\(688\) 0 0
\(689\) −20.0000 −0.761939
\(690\) 0 0
\(691\) 35.0000 1.33146 0.665731 0.746191i \(-0.268120\pi\)
0.665731 + 0.746191i \(0.268120\pi\)
\(692\) 0 0
\(693\) 15.0000 0.569803
\(694\) 0 0
\(695\) −15.0000 −0.568982
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −23.0000 −0.869940
\(700\) 0 0
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 9.00000 0.338960
\(706\) 0 0
\(707\) 18.0000 0.676960
\(708\) 0 0
\(709\) −34.0000 −1.27690 −0.638448 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) 0 0
\(711\) −4.00000 −0.150012
\(712\) 0 0
\(713\) 40.0000 1.49801
\(714\) 0 0
\(715\) −10.0000 −0.373979
\(716\) 0 0
\(717\) 11.0000 0.410803
\(718\) 0 0
\(719\) −17.0000 −0.633993 −0.316997 0.948427i \(-0.602674\pi\)
−0.316997 + 0.948427i \(0.602674\pi\)
\(720\) 0 0
\(721\) 30.0000 1.11726
\(722\) 0 0
\(723\) 12.0000 0.446285
\(724\) 0 0
\(725\) −24.0000 −0.891338
\(726\) 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
\(731\) 11.0000 0.406850
\(732\) 0 0
\(733\) −46.0000 −1.69905 −0.849524 0.527549i \(-0.823111\pi\)
−0.849524 + 0.527549i \(0.823111\pi\)
\(734\) 0 0
\(735\) 2.00000 0.0737711
\(736\) 0 0
\(737\) −20.0000 −0.736709
\(738\) 0 0
\(739\) −7.00000 −0.257499 −0.128750 0.991677i \(-0.541096\pi\)
−0.128750 + 0.991677i \(0.541096\pi\)
\(740\) 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
\(745\) −1.00000 −0.0366372
\(746\) 0 0
\(747\) −4.00000 −0.146352
\(748\) 0 0
\(749\) 54.0000 1.97312
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) −19.0000 −0.692398
\(754\) 0 0
\(755\) −20.0000 −0.727875
\(756\) 0 0
\(757\) 35.0000 1.27210 0.636048 0.771649i \(-0.280568\pi\)
0.636048 + 0.771649i \(0.280568\pi\)
\(758\) 0 0
\(759\) −20.0000 −0.725954
\(760\) 0 0
\(761\) −1.00000 −0.0362500 −0.0181250 0.999836i \(-0.505770\pi\)
−0.0181250 + 0.999836i \(0.505770\pi\)
\(762\) 0 0
\(763\) −24.0000 −0.868858
\(764\) 0 0
\(765\) −1.00000 −0.0361551
\(766\) 0 0
\(767\) −8.00000 −0.288863
\(768\) 0 0
\(769\) −37.0000 −1.33425 −0.667127 0.744944i \(-0.732476\pi\)
−0.667127 + 0.744944i \(0.732476\pi\)
\(770\) 0 0
\(771\) 16.0000 0.576226
\(772\) 0 0
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 0 0
\(775\) −40.0000 −1.43684
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 40.0000 1.43131
\(782\) 0 0
\(783\) 6.00000 0.214423
\(784\) 0 0
\(785\) −2.00000 −0.0713831
\(786\) 0 0
\(787\) −16.0000 −0.570338 −0.285169 0.958477i \(-0.592050\pi\)
−0.285169 + 0.958477i \(0.592050\pi\)
\(788\) 0 0
\(789\) −23.0000 −0.818822
\(790\) 0 0
\(791\) 18.0000 0.640006
\(792\) 0 0
\(793\) −10.0000 −0.355110
\(794\) 0 0
\(795\) −10.0000 −0.354663
\(796\) 0 0
\(797\) −40.0000 −1.41687 −0.708436 0.705775i \(-0.750599\pi\)
−0.708436 + 0.705775i \(0.750599\pi\)
\(798\) 0 0
\(799\) −9.00000 −0.318397
\(800\) 0 0
\(801\) 6.00000 0.212000
\(802\) 0 0
\(803\) −65.0000 −2.29380
\(804\) 0 0
\(805\) −12.0000 −0.422944
\(806\) 0 0
\(807\) 22.0000 0.774437
\(808\) 0 0
\(809\) 17.0000 0.597688 0.298844 0.954302i \(-0.403399\pi\)
0.298844 + 0.954302i \(0.403399\pi\)
\(810\) 0 0
\(811\) 14.0000 0.491606 0.245803 0.969320i \(-0.420948\pi\)
0.245803 + 0.969320i \(0.420948\pi\)
\(812\) 0 0
\(813\) 20.0000 0.701431
\(814\) 0 0
\(815\) −24.0000 −0.840683
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) −6.00000 −0.209657
\(820\) 0 0
\(821\) −9.00000 −0.314102 −0.157051 0.987590i \(-0.550199\pi\)
−0.157051 + 0.987590i \(0.550199\pi\)
\(822\) 0 0
\(823\) 5.00000 0.174289 0.0871445 0.996196i \(-0.472226\pi\)
0.0871445 + 0.996196i \(0.472226\pi\)
\(824\) 0 0
\(825\) 20.0000 0.696311
\(826\) 0 0
\(827\) −32.0000 −1.11275 −0.556375 0.830932i \(-0.687808\pi\)
−0.556375 + 0.830932i \(0.687808\pi\)
\(828\) 0 0
\(829\) −4.00000 −0.138926 −0.0694629 0.997585i \(-0.522129\pi\)
−0.0694629 + 0.997585i \(0.522129\pi\)
\(830\) 0 0
\(831\) 25.0000 0.867240
\(832\) 0 0
\(833\) −2.00000 −0.0692959
\(834\) 0 0
\(835\) −18.0000 −0.622916
\(836\) 0 0
\(837\) 10.0000 0.345651
\(838\) 0 0
\(839\) −18.0000 −0.621429 −0.310715 0.950503i \(-0.600568\pi\)
−0.310715 + 0.950503i \(0.600568\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 22.0000 0.757720
\(844\) 0 0
\(845\) −9.00000 −0.309609
\(846\) 0 0
\(847\) −42.0000 −1.44314
\(848\) 0 0
\(849\) −7.00000 −0.240239
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 26.0000 0.890223 0.445112 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −12.0000 −0.409912 −0.204956 0.978771i \(-0.565705\pi\)
−0.204956 + 0.978771i \(0.565705\pi\)
\(858\) 0 0
\(859\) −15.0000 −0.511793 −0.255897 0.966704i \(-0.582371\pi\)
−0.255897 + 0.966704i \(0.582371\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −28.0000 −0.953131 −0.476566 0.879139i \(-0.658119\pi\)
−0.476566 + 0.879139i \(0.658119\pi\)
\(864\) 0 0
\(865\) 18.0000 0.612018
\(866\) 0 0
\(867\) −16.0000 −0.543388
\(868\) 0 0
\(869\) 20.0000 0.678454
\(870\) 0 0
\(871\) 8.00000 0.271070
\(872\) 0 0
\(873\) −2.00000 −0.0676897
\(874\) 0 0
\(875\) 27.0000 0.912767
\(876\) 0 0
\(877\) −18.0000 −0.607817 −0.303908 0.952701i \(-0.598292\pi\)
−0.303908 + 0.952701i \(0.598292\pi\)
\(878\) 0 0
\(879\) −12.0000 −0.404750
\(880\) 0 0
\(881\) −37.0000 −1.24656 −0.623281 0.781998i \(-0.714201\pi\)
−0.623281 + 0.781998i \(0.714201\pi\)
\(882\) 0 0
\(883\) −31.0000 −1.04323 −0.521617 0.853180i \(-0.674671\pi\)
−0.521617 + 0.853180i \(0.674671\pi\)
\(884\) 0 0
\(885\) −4.00000 −0.134459
\(886\) 0 0
\(887\) −56.0000 −1.88030 −0.940148 0.340766i \(-0.889313\pi\)
−0.940148 + 0.340766i \(0.889313\pi\)
\(888\) 0 0
\(889\) −6.00000 −0.201234
\(890\) 0 0
\(891\) −5.00000 −0.167506
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) −6.00000 −0.200558
\(896\) 0 0
\(897\) 8.00000 0.267112
\(898\) 0 0
\(899\) 60.0000 2.00111
\(900\) 0 0
\(901\) 10.0000 0.333148
\(902\) 0 0
\(903\) 33.0000 1.09817
\(904\) 0 0
\(905\) −18.0000 −0.598340
\(906\) 0 0
\(907\) −10.0000 −0.332045 −0.166022 0.986122i \(-0.553092\pi\)
−0.166022 + 0.986122i \(0.553092\pi\)
\(908\) 0 0
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) 50.0000 1.65657 0.828287 0.560304i \(-0.189316\pi\)
0.828287 + 0.560304i \(0.189316\pi\)
\(912\) 0 0
\(913\) 20.0000 0.661903
\(914\) 0 0
\(915\) −5.00000 −0.165295
\(916\) 0 0
\(917\) 57.0000 1.88231
\(918\) 0 0
\(919\) 16.0000 0.527791 0.263896 0.964551i \(-0.414993\pi\)
0.263896 + 0.964551i \(0.414993\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −16.0000 −0.526646
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −10.0000 −0.328443
\(928\) 0 0
\(929\) −34.0000 −1.11550 −0.557752 0.830008i \(-0.688336\pi\)
−0.557752 + 0.830008i \(0.688336\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −27.0000 −0.883940
\(934\) 0 0
\(935\) 5.00000 0.163517
\(936\) 0 0
\(937\) −3.00000 −0.0980057 −0.0490029 0.998799i \(-0.515604\pi\)
−0.0490029 + 0.998799i \(0.515604\pi\)
\(938\) 0 0
\(939\) 6.00000 0.195803
\(940\) 0 0
\(941\) −42.0000 −1.36916 −0.684580 0.728937i \(-0.740015\pi\)
−0.684580 + 0.728937i \(0.740015\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) −3.00000 −0.0975900
\(946\) 0 0
\(947\) −36.0000 −1.16984 −0.584921 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) 0 0
\(949\) 26.0000 0.843996
\(950\) 0 0
\(951\) −24.0000 −0.778253
\(952\) 0 0
\(953\) −12.0000 −0.388718 −0.194359 0.980930i \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(954\) 0 0
\(955\) 15.0000 0.485389
\(956\) 0 0
\(957\) −30.0000 −0.969762
\(958\) 0 0
\(959\) 27.0000 0.871875
\(960\) 0 0
\(961\) 69.0000 2.22581
\(962\) 0 0
\(963\) −18.0000 −0.580042
\(964\) 0 0
\(965\) 16.0000 0.515058
\(966\) 0 0
\(967\) 8.00000 0.257263 0.128631 0.991692i \(-0.458942\pi\)
0.128631 + 0.991692i \(0.458942\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 12.0000 0.385098 0.192549 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) 0 0
\(973\) 45.0000 1.44263
\(974\) 0 0
\(975\) −8.00000 −0.256205
\(976\) 0 0
\(977\) −30.0000 −0.959785 −0.479893 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 0 0
\(979\) −30.0000 −0.958804
\(980\) 0 0
\(981\) 8.00000 0.255420
\(982\) 0 0
\(983\) −12.0000 −0.382741 −0.191370 0.981518i \(-0.561293\pi\)
−0.191370 + 0.981518i \(0.561293\pi\)
\(984\) 0 0
\(985\) 6.00000 0.191176
\(986\) 0 0
\(987\) −27.0000 −0.859419
\(988\) 0 0
\(989\) −44.0000 −1.39912
\(990\) 0 0
\(991\) 32.0000 1.01651 0.508257 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) 0 0
\(993\) −32.0000 −1.01549
\(994\) 0 0
\(995\) −11.0000 −0.348723
\(996\) 0 0
\(997\) −35.0000 −1.10846 −0.554231 0.832363i \(-0.686987\pi\)
−0.554231 + 0.832363i \(0.686987\pi\)
\(998\) 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 8664.2.a.l.1.1 1
19.18 odd 2 456.2.a.a.1.1 1
57.56 even 2 1368.2.a.d.1.1 1
76.75 even 2 912.2.a.i.1.1 1
152.37 odd 2 3648.2.a.z.1.1 1
152.75 even 2 3648.2.a.g.1.1 1
228.227 odd 2 2736.2.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.2.a.a.1.1 1 19.18 odd 2
912.2.a.i.1.1 1 76.75 even 2
1368.2.a.d.1.1 1 57.56 even 2
2736.2.a.i.1.1 1 228.227 odd 2
3648.2.a.g.1.1 1 152.75 even 2
3648.2.a.z.1.1 1 152.37 odd 2
8664.2.a.l.1.1 1 1.1 even 1 trivial