Properties

Label 6080.2.a.x.1.1
Level $6080$
Weight $2$
Character 6080.1
Self dual yes
Analytic conductor $48.549$
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] = [6080,2,Mod(1,6080)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6080, 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("6080.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6080 = 2^{6} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6080.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: \(48.5490444289\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 6080.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{3} +1.00000 q^{5} -5.00000 q^{7} +6.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} +1.00000 q^{5} -5.00000 q^{7} +6.00000 q^{9} +4.00000 q^{11} +1.00000 q^{13} +3.00000 q^{15} -3.00000 q^{17} -1.00000 q^{19} -15.0000 q^{21} +7.00000 q^{23} +1.00000 q^{25} +9.00000 q^{27} +3.00000 q^{29} -2.00000 q^{31} +12.0000 q^{33} -5.00000 q^{35} +2.00000 q^{37} +3.00000 q^{39} -6.00000 q^{41} -6.00000 q^{43} +6.00000 q^{45} +18.0000 q^{49} -9.00000 q^{51} +13.0000 q^{53} +4.00000 q^{55} -3.00000 q^{57} +9.00000 q^{59} +12.0000 q^{61} -30.0000 q^{63} +1.00000 q^{65} +3.00000 q^{67} +21.0000 q^{69} +11.0000 q^{73} +3.00000 q^{75} -20.0000 q^{77} -2.00000 q^{79} +9.00000 q^{81} +10.0000 q^{83} -3.00000 q^{85} +9.00000 q^{87} +2.00000 q^{89} -5.00000 q^{91} -6.00000 q^{93} -1.00000 q^{95} -2.00000 q^{97} +24.0000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.00000 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −5.00000 −1.88982 −0.944911 0.327327i \(-0.893852\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) 0 0
\(9\) 6.00000 2.00000
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 0 0
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −15.0000 −3.27327
\(22\) 0 0
\(23\) 7.00000 1.45960 0.729800 0.683660i \(-0.239613\pi\)
0.729800 + 0.683660i \(0.239613\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 9.00000 1.73205
\(28\) 0 0
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0 0
\(33\) 12.0000 2.08893
\(34\) 0 0
\(35\) −5.00000 −0.845154
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 3.00000 0.480384
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 0 0
\(45\) 6.00000 0.894427
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 18.0000 2.57143
\(50\) 0 0
\(51\) −9.00000 −1.26025
\(52\) 0 0
\(53\) 13.0000 1.78569 0.892844 0.450367i \(-0.148707\pi\)
0.892844 + 0.450367i \(0.148707\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) −3.00000 −0.397360
\(58\) 0 0
\(59\) 9.00000 1.17170 0.585850 0.810419i \(-0.300761\pi\)
0.585850 + 0.810419i \(0.300761\pi\)
\(60\) 0 0
\(61\) 12.0000 1.53644 0.768221 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 0 0
\(63\) −30.0000 −3.77964
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 3.00000 0.366508 0.183254 0.983066i \(-0.441337\pi\)
0.183254 + 0.983066i \(0.441337\pi\)
\(68\) 0 0
\(69\) 21.0000 2.52810
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) 0 0
\(75\) 3.00000 0.346410
\(76\) 0 0
\(77\) −20.0000 −2.27921
\(78\) 0 0
\(79\) −2.00000 −0.225018 −0.112509 0.993651i \(-0.535889\pi\)
−0.112509 + 0.993651i \(0.535889\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 10.0000 1.09764 0.548821 0.835940i \(-0.315077\pi\)
0.548821 + 0.835940i \(0.315077\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 9.00000 0.964901
\(88\) 0 0
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 0 0
\(91\) −5.00000 −0.524142
\(92\) 0 0
\(93\) −6.00000 −0.622171
\(94\) 0 0
\(95\) −1.00000 −0.102598
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 24.0000 2.41209
\(100\) 0 0
\(101\) 8.00000 0.796030 0.398015 0.917379i \(-0.369699\pi\)
0.398015 + 0.917379i \(0.369699\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) −15.0000 −1.46385
\(106\) 0 0
\(107\) 13.0000 1.25676 0.628379 0.777908i \(-0.283719\pi\)
0.628379 + 0.777908i \(0.283719\pi\)
\(108\) 0 0
\(109\) −19.0000 −1.81987 −0.909935 0.414751i \(-0.863869\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 7.00000 0.652753
\(116\) 0 0
\(117\) 6.00000 0.554700
\(118\) 0 0
\(119\) 15.0000 1.37505
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) −18.0000 −1.62301
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −6.00000 −0.532414 −0.266207 0.963916i \(-0.585770\pi\)
−0.266207 + 0.963916i \(0.585770\pi\)
\(128\) 0 0
\(129\) −18.0000 −1.58481
\(130\) 0 0
\(131\) −16.0000 −1.39793 −0.698963 0.715158i \(-0.746355\pi\)
−0.698963 + 0.715158i \(0.746355\pi\)
\(132\) 0 0
\(133\) 5.00000 0.433555
\(134\) 0 0
\(135\) 9.00000 0.774597
\(136\) 0 0
\(137\) 9.00000 0.768922 0.384461 0.923141i \(-0.374387\pi\)
0.384461 + 0.923141i \(0.374387\pi\)
\(138\) 0 0
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.00000 0.334497
\(144\) 0 0
\(145\) 3.00000 0.249136
\(146\) 0 0
\(147\) 54.0000 4.45384
\(148\) 0 0
\(149\) 4.00000 0.327693 0.163846 0.986486i \(-0.447610\pi\)
0.163846 + 0.986486i \(0.447610\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 0 0
\(153\) −18.0000 −1.45521
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) 0 0
\(157\) −6.00000 −0.478852 −0.239426 0.970915i \(-0.576959\pi\)
−0.239426 + 0.970915i \(0.576959\pi\)
\(158\) 0 0
\(159\) 39.0000 3.09290
\(160\) 0 0
\(161\) −35.0000 −2.75839
\(162\) 0 0
\(163\) −22.0000 −1.72317 −0.861586 0.507611i \(-0.830529\pi\)
−0.861586 + 0.507611i \(0.830529\pi\)
\(164\) 0 0
\(165\) 12.0000 0.934199
\(166\) 0 0
\(167\) −2.00000 −0.154765 −0.0773823 0.997001i \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −6.00000 −0.458831
\(172\) 0 0
\(173\) 14.0000 1.06440 0.532200 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) 0 0
\(175\) −5.00000 −0.377964
\(176\) 0 0
\(177\) 27.0000 2.02944
\(178\) 0 0
\(179\) 8.00000 0.597948 0.298974 0.954261i \(-0.403356\pi\)
0.298974 + 0.954261i \(0.403356\pi\)
\(180\) 0 0
\(181\) −26.0000 −1.93256 −0.966282 0.257485i \(-0.917106\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 0 0
\(183\) 36.0000 2.66120
\(184\) 0 0
\(185\) 2.00000 0.147043
\(186\) 0 0
\(187\) −12.0000 −0.877527
\(188\) 0 0
\(189\) −45.0000 −3.27327
\(190\) 0 0
\(191\) 9.00000 0.651217 0.325609 0.945505i \(-0.394431\pi\)
0.325609 + 0.945505i \(0.394431\pi\)
\(192\) 0 0
\(193\) 10.0000 0.719816 0.359908 0.932988i \(-0.382808\pi\)
0.359908 + 0.932988i \(0.382808\pi\)
\(194\) 0 0
\(195\) 3.00000 0.214834
\(196\) 0 0
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 0 0
\(199\) −15.0000 −1.06332 −0.531661 0.846957i \(-0.678432\pi\)
−0.531661 + 0.846957i \(0.678432\pi\)
\(200\) 0 0
\(201\) 9.00000 0.634811
\(202\) 0 0
\(203\) −15.0000 −1.05279
\(204\) 0 0
\(205\) −6.00000 −0.419058
\(206\) 0 0
\(207\) 42.0000 2.91920
\(208\) 0 0
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6.00000 −0.409197
\(216\) 0 0
\(217\) 10.0000 0.678844
\(218\) 0 0
\(219\) 33.0000 2.22993
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) −2.00000 −0.133930 −0.0669650 0.997755i \(-0.521332\pi\)
−0.0669650 + 0.997755i \(0.521332\pi\)
\(224\) 0 0
\(225\) 6.00000 0.400000
\(226\) 0 0
\(227\) −5.00000 −0.331862 −0.165931 0.986137i \(-0.553063\pi\)
−0.165931 + 0.986137i \(0.553063\pi\)
\(228\) 0 0
\(229\) 6.00000 0.396491 0.198246 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) 0 0
\(231\) −60.0000 −3.94771
\(232\) 0 0
\(233\) 10.0000 0.655122 0.327561 0.944830i \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −6.00000 −0.389742
\(238\) 0 0
\(239\) −11.0000 −0.711531 −0.355765 0.934575i \(-0.615780\pi\)
−0.355765 + 0.934575i \(0.615780\pi\)
\(240\) 0 0
\(241\) −12.0000 −0.772988 −0.386494 0.922292i \(-0.626314\pi\)
−0.386494 + 0.922292i \(0.626314\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 18.0000 1.14998
\(246\) 0 0
\(247\) −1.00000 −0.0636285
\(248\) 0 0
\(249\) 30.0000 1.90117
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 28.0000 1.76034
\(254\) 0 0
\(255\) −9.00000 −0.563602
\(256\) 0 0
\(257\) 22.0000 1.37232 0.686161 0.727450i \(-0.259294\pi\)
0.686161 + 0.727450i \(0.259294\pi\)
\(258\) 0 0
\(259\) −10.0000 −0.621370
\(260\) 0 0
\(261\) 18.0000 1.11417
\(262\) 0 0
\(263\) 8.00000 0.493301 0.246651 0.969104i \(-0.420670\pi\)
0.246651 + 0.969104i \(0.420670\pi\)
\(264\) 0 0
\(265\) 13.0000 0.798584
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 0 0
\(269\) −2.00000 −0.121942 −0.0609711 0.998140i \(-0.519420\pi\)
−0.0609711 + 0.998140i \(0.519420\pi\)
\(270\) 0 0
\(271\) −27.0000 −1.64013 −0.820067 0.572268i \(-0.806064\pi\)
−0.820067 + 0.572268i \(0.806064\pi\)
\(272\) 0 0
\(273\) −15.0000 −0.907841
\(274\) 0 0
\(275\) 4.00000 0.241209
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 0 0
\(279\) −12.0000 −0.718421
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 2.00000 0.118888 0.0594438 0.998232i \(-0.481067\pi\)
0.0594438 + 0.998232i \(0.481067\pi\)
\(284\) 0 0
\(285\) −3.00000 −0.177705
\(286\) 0 0
\(287\) 30.0000 1.77084
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −6.00000 −0.351726
\(292\) 0 0
\(293\) 27.0000 1.57736 0.788678 0.614806i \(-0.210766\pi\)
0.788678 + 0.614806i \(0.210766\pi\)
\(294\) 0 0
\(295\) 9.00000 0.524000
\(296\) 0 0
\(297\) 36.0000 2.08893
\(298\) 0 0
\(299\) 7.00000 0.404820
\(300\) 0 0
\(301\) 30.0000 1.72917
\(302\) 0 0
\(303\) 24.0000 1.37876
\(304\) 0 0
\(305\) 12.0000 0.687118
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) 12.0000 0.682656
\(310\) 0 0
\(311\) 25.0000 1.41762 0.708810 0.705399i \(-0.249232\pi\)
0.708810 + 0.705399i \(0.249232\pi\)
\(312\) 0 0
\(313\) −1.00000 −0.0565233 −0.0282617 0.999601i \(-0.508997\pi\)
−0.0282617 + 0.999601i \(0.508997\pi\)
\(314\) 0 0
\(315\) −30.0000 −1.69031
\(316\) 0 0
\(317\) −9.00000 −0.505490 −0.252745 0.967533i \(-0.581333\pi\)
−0.252745 + 0.967533i \(0.581333\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) 0 0
\(321\) 39.0000 2.17677
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) −57.0000 −3.15211
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 7.00000 0.384755 0.192377 0.981321i \(-0.438380\pi\)
0.192377 + 0.981321i \(0.438380\pi\)
\(332\) 0 0
\(333\) 12.0000 0.657596
\(334\) 0 0
\(335\) 3.00000 0.163908
\(336\) 0 0
\(337\) 6.00000 0.326841 0.163420 0.986557i \(-0.447747\pi\)
0.163420 + 0.986557i \(0.447747\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −8.00000 −0.433224
\(342\) 0 0
\(343\) −55.0000 −2.96972
\(344\) 0 0
\(345\) 21.0000 1.13060
\(346\) 0 0
\(347\) 6.00000 0.322097 0.161048 0.986947i \(-0.448512\pi\)
0.161048 + 0.986947i \(0.448512\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 9.00000 0.480384
\(352\) 0 0
\(353\) 7.00000 0.372572 0.186286 0.982496i \(-0.440355\pi\)
0.186286 + 0.982496i \(0.440355\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 45.0000 2.38165
\(358\) 0 0
\(359\) −5.00000 −0.263890 −0.131945 0.991257i \(-0.542122\pi\)
−0.131945 + 0.991257i \(0.542122\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 15.0000 0.787296
\(364\) 0 0
\(365\) 11.0000 0.575766
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 0 0
\(369\) −36.0000 −1.87409
\(370\) 0 0
\(371\) −65.0000 −3.37463
\(372\) 0 0
\(373\) 23.0000 1.19089 0.595447 0.803394i \(-0.296975\pi\)
0.595447 + 0.803394i \(0.296975\pi\)
\(374\) 0 0
\(375\) 3.00000 0.154919
\(376\) 0 0
\(377\) 3.00000 0.154508
\(378\) 0 0
\(379\) 33.0000 1.69510 0.847548 0.530719i \(-0.178078\pi\)
0.847548 + 0.530719i \(0.178078\pi\)
\(380\) 0 0
\(381\) −18.0000 −0.922168
\(382\) 0 0
\(383\) −4.00000 −0.204390 −0.102195 0.994764i \(-0.532587\pi\)
−0.102195 + 0.994764i \(0.532587\pi\)
\(384\) 0 0
\(385\) −20.0000 −1.01929
\(386\) 0 0
\(387\) −36.0000 −1.82998
\(388\) 0 0
\(389\) 4.00000 0.202808 0.101404 0.994845i \(-0.467667\pi\)
0.101404 + 0.994845i \(0.467667\pi\)
\(390\) 0 0
\(391\) −21.0000 −1.06202
\(392\) 0 0
\(393\) −48.0000 −2.42128
\(394\) 0 0
\(395\) −2.00000 −0.100631
\(396\) 0 0
\(397\) 16.0000 0.803017 0.401508 0.915855i \(-0.368486\pi\)
0.401508 + 0.915855i \(0.368486\pi\)
\(398\) 0 0
\(399\) 15.0000 0.750939
\(400\) 0 0
\(401\) −6.00000 −0.299626 −0.149813 0.988714i \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) 0 0
\(403\) −2.00000 −0.0996271
\(404\) 0 0
\(405\) 9.00000 0.447214
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) 22.0000 1.08783 0.543915 0.839140i \(-0.316941\pi\)
0.543915 + 0.839140i \(0.316941\pi\)
\(410\) 0 0
\(411\) 27.0000 1.33181
\(412\) 0 0
\(413\) −45.0000 −2.21431
\(414\) 0 0
\(415\) 10.0000 0.490881
\(416\) 0 0
\(417\) −48.0000 −2.35057
\(418\) 0 0
\(419\) −14.0000 −0.683945 −0.341972 0.939710i \(-0.611095\pi\)
−0.341972 + 0.939710i \(0.611095\pi\)
\(420\) 0 0
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.00000 −0.145521
\(426\) 0 0
\(427\) −60.0000 −2.90360
\(428\) 0 0
\(429\) 12.0000 0.579365
\(430\) 0 0
\(431\) −36.0000 −1.73406 −0.867029 0.498257i \(-0.833974\pi\)
−0.867029 + 0.498257i \(0.833974\pi\)
\(432\) 0 0
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) 0 0
\(435\) 9.00000 0.431517
\(436\) 0 0
\(437\) −7.00000 −0.334855
\(438\) 0 0
\(439\) 26.0000 1.24091 0.620456 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 0 0
\(441\) 108.000 5.14286
\(442\) 0 0
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 0 0
\(445\) 2.00000 0.0948091
\(446\) 0 0
\(447\) 12.0000 0.567581
\(448\) 0 0
\(449\) −22.0000 −1.03824 −0.519122 0.854700i \(-0.673741\pi\)
−0.519122 + 0.854700i \(0.673741\pi\)
\(450\) 0 0
\(451\) −24.0000 −1.13012
\(452\) 0 0
\(453\) −30.0000 −1.40952
\(454\) 0 0
\(455\) −5.00000 −0.234404
\(456\) 0 0
\(457\) −29.0000 −1.35656 −0.678281 0.734802i \(-0.737275\pi\)
−0.678281 + 0.734802i \(0.737275\pi\)
\(458\) 0 0
\(459\) −27.0000 −1.26025
\(460\) 0 0
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 0 0
\(465\) −6.00000 −0.278243
\(466\) 0 0
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 0 0
\(469\) −15.0000 −0.692636
\(470\) 0 0
\(471\) −18.0000 −0.829396
\(472\) 0 0
\(473\) −24.0000 −1.10352
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 0 0
\(477\) 78.0000 3.57137
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 2.00000 0.0911922
\(482\) 0 0
\(483\) −105.000 −4.77767
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) 0 0
\(487\) −38.0000 −1.72194 −0.860972 0.508652i \(-0.830144\pi\)
−0.860972 + 0.508652i \(0.830144\pi\)
\(488\) 0 0
\(489\) −66.0000 −2.98462
\(490\) 0 0
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 0 0
\(493\) −9.00000 −0.405340
\(494\) 0 0
\(495\) 24.0000 1.07872
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −42.0000 −1.88018 −0.940089 0.340929i \(-0.889258\pi\)
−0.940089 + 0.340929i \(0.889258\pi\)
\(500\) 0 0
\(501\) −6.00000 −0.268060
\(502\) 0 0
\(503\) −21.0000 −0.936344 −0.468172 0.883637i \(-0.655087\pi\)
−0.468172 + 0.883637i \(0.655087\pi\)
\(504\) 0 0
\(505\) 8.00000 0.355995
\(506\) 0 0
\(507\) −36.0000 −1.59882
\(508\) 0 0
\(509\) −2.00000 −0.0886484 −0.0443242 0.999017i \(-0.514113\pi\)
−0.0443242 + 0.999017i \(0.514113\pi\)
\(510\) 0 0
\(511\) −55.0000 −2.43306
\(512\) 0 0
\(513\) −9.00000 −0.397360
\(514\) 0 0
\(515\) 4.00000 0.176261
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 42.0000 1.84360
\(520\) 0 0
\(521\) 24.0000 1.05146 0.525730 0.850652i \(-0.323792\pi\)
0.525730 + 0.850652i \(0.323792\pi\)
\(522\) 0 0
\(523\) 9.00000 0.393543 0.196771 0.980449i \(-0.436954\pi\)
0.196771 + 0.980449i \(0.436954\pi\)
\(524\) 0 0
\(525\) −15.0000 −0.654654
\(526\) 0 0
\(527\) 6.00000 0.261364
\(528\) 0 0
\(529\) 26.0000 1.13043
\(530\) 0 0
\(531\) 54.0000 2.34340
\(532\) 0 0
\(533\) −6.00000 −0.259889
\(534\) 0 0
\(535\) 13.0000 0.562039
\(536\) 0 0
\(537\) 24.0000 1.03568
\(538\) 0 0
\(539\) 72.0000 3.10126
\(540\) 0 0
\(541\) −16.0000 −0.687894 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(542\) 0 0
\(543\) −78.0000 −3.34730
\(544\) 0 0
\(545\) −19.0000 −0.813871
\(546\) 0 0
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) 0 0
\(549\) 72.0000 3.07289
\(550\) 0 0
\(551\) −3.00000 −0.127804
\(552\) 0 0
\(553\) 10.0000 0.425243
\(554\) 0 0
\(555\) 6.00000 0.254686
\(556\) 0 0
\(557\) −12.0000 −0.508456 −0.254228 0.967144i \(-0.581821\pi\)
−0.254228 + 0.967144i \(0.581821\pi\)
\(558\) 0 0
\(559\) −6.00000 −0.253773
\(560\) 0 0
\(561\) −36.0000 −1.51992
\(562\) 0 0
\(563\) −20.0000 −0.842900 −0.421450 0.906852i \(-0.638479\pi\)
−0.421450 + 0.906852i \(0.638479\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −45.0000 −1.88982
\(568\) 0 0
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) −6.00000 −0.251092 −0.125546 0.992088i \(-0.540068\pi\)
−0.125546 + 0.992088i \(0.540068\pi\)
\(572\) 0 0
\(573\) 27.0000 1.12794
\(574\) 0 0
\(575\) 7.00000 0.291920
\(576\) 0 0
\(577\) −7.00000 −0.291414 −0.145707 0.989328i \(-0.546546\pi\)
−0.145707 + 0.989328i \(0.546546\pi\)
\(578\) 0 0
\(579\) 30.0000 1.24676
\(580\) 0 0
\(581\) −50.0000 −2.07435
\(582\) 0 0
\(583\) 52.0000 2.15362
\(584\) 0 0
\(585\) 6.00000 0.248069
\(586\) 0 0
\(587\) −18.0000 −0.742940 −0.371470 0.928445i \(-0.621146\pi\)
−0.371470 + 0.928445i \(0.621146\pi\)
\(588\) 0 0
\(589\) 2.00000 0.0824086
\(590\) 0 0
\(591\) 66.0000 2.71488
\(592\) 0 0
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 15.0000 0.614940
\(596\) 0 0
\(597\) −45.0000 −1.84173
\(598\) 0 0
\(599\) −26.0000 −1.06233 −0.531166 0.847268i \(-0.678246\pi\)
−0.531166 + 0.847268i \(0.678246\pi\)
\(600\) 0 0
\(601\) 42.0000 1.71322 0.856608 0.515968i \(-0.172568\pi\)
0.856608 + 0.515968i \(0.172568\pi\)
\(602\) 0 0
\(603\) 18.0000 0.733017
\(604\) 0 0
\(605\) 5.00000 0.203279
\(606\) 0 0
\(607\) −26.0000 −1.05531 −0.527654 0.849460i \(-0.676928\pi\)
−0.527654 + 0.849460i \(0.676928\pi\)
\(608\) 0 0
\(609\) −45.0000 −1.82349
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 20.0000 0.807792 0.403896 0.914805i \(-0.367656\pi\)
0.403896 + 0.914805i \(0.367656\pi\)
\(614\) 0 0
\(615\) −18.0000 −0.725830
\(616\) 0 0
\(617\) 14.0000 0.563619 0.281809 0.959470i \(-0.409065\pi\)
0.281809 + 0.959470i \(0.409065\pi\)
\(618\) 0 0
\(619\) 24.0000 0.964641 0.482321 0.875995i \(-0.339794\pi\)
0.482321 + 0.875995i \(0.339794\pi\)
\(620\) 0 0
\(621\) 63.0000 2.52810
\(622\) 0 0
\(623\) −10.0000 −0.400642
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −12.0000 −0.479234
\(628\) 0 0
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) 15.0000 0.596196
\(634\) 0 0
\(635\) −6.00000 −0.238103
\(636\) 0 0
\(637\) 18.0000 0.713186
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.00000 0.315981 0.157991 0.987441i \(-0.449498\pi\)
0.157991 + 0.987441i \(0.449498\pi\)
\(642\) 0 0
\(643\) −26.0000 −1.02534 −0.512670 0.858586i \(-0.671344\pi\)
−0.512670 + 0.858586i \(0.671344\pi\)
\(644\) 0 0
\(645\) −18.0000 −0.708749
\(646\) 0 0
\(647\) −21.0000 −0.825595 −0.412798 0.910823i \(-0.635448\pi\)
−0.412798 + 0.910823i \(0.635448\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 0 0
\(651\) 30.0000 1.17579
\(652\) 0 0
\(653\) 16.0000 0.626128 0.313064 0.949732i \(-0.398644\pi\)
0.313064 + 0.949732i \(0.398644\pi\)
\(654\) 0 0
\(655\) −16.0000 −0.625172
\(656\) 0 0
\(657\) 66.0000 2.57491
\(658\) 0 0
\(659\) −33.0000 −1.28550 −0.642749 0.766077i \(-0.722206\pi\)
−0.642749 + 0.766077i \(0.722206\pi\)
\(660\) 0 0
\(661\) −15.0000 −0.583432 −0.291716 0.956505i \(-0.594226\pi\)
−0.291716 + 0.956505i \(0.594226\pi\)
\(662\) 0 0
\(663\) −9.00000 −0.349531
\(664\) 0 0
\(665\) 5.00000 0.193892
\(666\) 0 0
\(667\) 21.0000 0.813123
\(668\) 0 0
\(669\) −6.00000 −0.231973
\(670\) 0 0
\(671\) 48.0000 1.85302
\(672\) 0 0
\(673\) −44.0000 −1.69608 −0.848038 0.529936i \(-0.822216\pi\)
−0.848038 + 0.529936i \(0.822216\pi\)
\(674\) 0 0
\(675\) 9.00000 0.346410
\(676\) 0 0
\(677\) 39.0000 1.49889 0.749446 0.662066i \(-0.230320\pi\)
0.749446 + 0.662066i \(0.230320\pi\)
\(678\) 0 0
\(679\) 10.0000 0.383765
\(680\) 0 0
\(681\) −15.0000 −0.574801
\(682\) 0 0
\(683\) 44.0000 1.68361 0.841807 0.539779i \(-0.181492\pi\)
0.841807 + 0.539779i \(0.181492\pi\)
\(684\) 0 0
\(685\) 9.00000 0.343872
\(686\) 0 0
\(687\) 18.0000 0.686743
\(688\) 0 0
\(689\) 13.0000 0.495261
\(690\) 0 0
\(691\) 42.0000 1.59776 0.798878 0.601494i \(-0.205427\pi\)
0.798878 + 0.601494i \(0.205427\pi\)
\(692\) 0 0
\(693\) −120.000 −4.55842
\(694\) 0 0
\(695\) −16.0000 −0.606915
\(696\) 0 0
\(697\) 18.0000 0.681799
\(698\) 0 0
\(699\) 30.0000 1.13470
\(700\) 0 0
\(701\) −24.0000 −0.906467 −0.453234 0.891392i \(-0.649730\pi\)
−0.453234 + 0.891392i \(0.649730\pi\)
\(702\) 0 0
\(703\) −2.00000 −0.0754314
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −40.0000 −1.50435
\(708\) 0 0
\(709\) −2.00000 −0.0751116 −0.0375558 0.999295i \(-0.511957\pi\)
−0.0375558 + 0.999295i \(0.511957\pi\)
\(710\) 0 0
\(711\) −12.0000 −0.450035
\(712\) 0 0
\(713\) −14.0000 −0.524304
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) 0 0
\(717\) −33.0000 −1.23241
\(718\) 0 0
\(719\) −27.0000 −1.00693 −0.503465 0.864016i \(-0.667942\pi\)
−0.503465 + 0.864016i \(0.667942\pi\)
\(720\) 0 0
\(721\) −20.0000 −0.744839
\(722\) 0 0
\(723\) −36.0000 −1.33885
\(724\) 0 0
\(725\) 3.00000 0.111417
\(726\) 0 0
\(727\) 23.0000 0.853023 0.426511 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 18.0000 0.665754
\(732\) 0 0
\(733\) −36.0000 −1.32969 −0.664845 0.746981i \(-0.731502\pi\)
−0.664845 + 0.746981i \(0.731502\pi\)
\(734\) 0 0
\(735\) 54.0000 1.99182
\(736\) 0 0
\(737\) 12.0000 0.442026
\(738\) 0 0
\(739\) 10.0000 0.367856 0.183928 0.982940i \(-0.441119\pi\)
0.183928 + 0.982940i \(0.441119\pi\)
\(740\) 0 0
\(741\) −3.00000 −0.110208
\(742\) 0 0
\(743\) −18.0000 −0.660356 −0.330178 0.943919i \(-0.607109\pi\)
−0.330178 + 0.943919i \(0.607109\pi\)
\(744\) 0 0
\(745\) 4.00000 0.146549
\(746\) 0 0
\(747\) 60.0000 2.19529
\(748\) 0 0
\(749\) −65.0000 −2.37505
\(750\) 0 0
\(751\) −26.0000 −0.948753 −0.474377 0.880322i \(-0.657327\pi\)
−0.474377 + 0.880322i \(0.657327\pi\)
\(752\) 0 0
\(753\) 36.0000 1.31191
\(754\) 0 0
\(755\) −10.0000 −0.363937
\(756\) 0 0
\(757\) 6.00000 0.218074 0.109037 0.994038i \(-0.465223\pi\)
0.109037 + 0.994038i \(0.465223\pi\)
\(758\) 0 0
\(759\) 84.0000 3.04901
\(760\) 0 0
\(761\) 11.0000 0.398750 0.199375 0.979923i \(-0.436109\pi\)
0.199375 + 0.979923i \(0.436109\pi\)
\(762\) 0 0
\(763\) 95.0000 3.43923
\(764\) 0 0
\(765\) −18.0000 −0.650791
\(766\) 0 0
\(767\) 9.00000 0.324971
\(768\) 0 0
\(769\) −47.0000 −1.69486 −0.847432 0.530904i \(-0.821852\pi\)
−0.847432 + 0.530904i \(0.821852\pi\)
\(770\) 0 0
\(771\) 66.0000 2.37693
\(772\) 0 0
\(773\) 51.0000 1.83434 0.917171 0.398493i \(-0.130467\pi\)
0.917171 + 0.398493i \(0.130467\pi\)
\(774\) 0 0
\(775\) −2.00000 −0.0718421
\(776\) 0 0
\(777\) −30.0000 −1.07624
\(778\) 0 0
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 27.0000 0.964901
\(784\) 0 0
\(785\) −6.00000 −0.214149
\(786\) 0 0
\(787\) 39.0000 1.39020 0.695100 0.718913i \(-0.255360\pi\)
0.695100 + 0.718913i \(0.255360\pi\)
\(788\) 0 0
\(789\) 24.0000 0.854423
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 12.0000 0.426132
\(794\) 0 0
\(795\) 39.0000 1.38319
\(796\) 0 0
\(797\) −31.0000 −1.09808 −0.549038 0.835797i \(-0.685006\pi\)
−0.549038 + 0.835797i \(0.685006\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 12.0000 0.423999
\(802\) 0 0
\(803\) 44.0000 1.55273
\(804\) 0 0
\(805\) −35.0000 −1.23359
\(806\) 0 0
\(807\) −6.00000 −0.211210
\(808\) 0 0
\(809\) 25.0000 0.878953 0.439477 0.898254i \(-0.355164\pi\)
0.439477 + 0.898254i \(0.355164\pi\)
\(810\) 0 0
\(811\) −37.0000 −1.29925 −0.649623 0.760257i \(-0.725073\pi\)
−0.649623 + 0.760257i \(0.725073\pi\)
\(812\) 0 0
\(813\) −81.0000 −2.84079
\(814\) 0 0
\(815\) −22.0000 −0.770626
\(816\) 0 0
\(817\) 6.00000 0.209913
\(818\) 0 0
\(819\) −30.0000 −1.04828
\(820\) 0 0
\(821\) 52.0000 1.81481 0.907406 0.420255i \(-0.138059\pi\)
0.907406 + 0.420255i \(0.138059\pi\)
\(822\) 0 0
\(823\) −43.0000 −1.49889 −0.749443 0.662069i \(-0.769679\pi\)
−0.749443 + 0.662069i \(0.769679\pi\)
\(824\) 0 0
\(825\) 12.0000 0.417786
\(826\) 0 0
\(827\) 3.00000 0.104320 0.0521601 0.998639i \(-0.483389\pi\)
0.0521601 + 0.998639i \(0.483389\pi\)
\(828\) 0 0
\(829\) −35.0000 −1.21560 −0.607800 0.794090i \(-0.707948\pi\)
−0.607800 + 0.794090i \(0.707948\pi\)
\(830\) 0 0
\(831\) 24.0000 0.832551
\(832\) 0 0
\(833\) −54.0000 −1.87099
\(834\) 0 0
\(835\) −2.00000 −0.0692129
\(836\) 0 0
\(837\) −18.0000 −0.622171
\(838\) 0 0
\(839\) −4.00000 −0.138095 −0.0690477 0.997613i \(-0.521996\pi\)
−0.0690477 + 0.997613i \(0.521996\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) 0 0
\(843\) −54.0000 −1.85986
\(844\) 0 0
\(845\) −12.0000 −0.412813
\(846\) 0 0
\(847\) −25.0000 −0.859010
\(848\) 0 0
\(849\) 6.00000 0.205919
\(850\) 0 0
\(851\) 14.0000 0.479914
\(852\) 0 0
\(853\) −42.0000 −1.43805 −0.719026 0.694983i \(-0.755412\pi\)
−0.719026 + 0.694983i \(0.755412\pi\)
\(854\) 0 0
\(855\) −6.00000 −0.205196
\(856\) 0 0
\(857\) −40.0000 −1.36637 −0.683187 0.730243i \(-0.739407\pi\)
−0.683187 + 0.730243i \(0.739407\pi\)
\(858\) 0 0
\(859\) 28.0000 0.955348 0.477674 0.878537i \(-0.341480\pi\)
0.477674 + 0.878537i \(0.341480\pi\)
\(860\) 0 0
\(861\) 90.0000 3.06719
\(862\) 0 0
\(863\) 56.0000 1.90626 0.953131 0.302558i \(-0.0978405\pi\)
0.953131 + 0.302558i \(0.0978405\pi\)
\(864\) 0 0
\(865\) 14.0000 0.476014
\(866\) 0 0
\(867\) −24.0000 −0.815083
\(868\) 0 0
\(869\) −8.00000 −0.271381
\(870\) 0 0
\(871\) 3.00000 0.101651
\(872\) 0 0
\(873\) −12.0000 −0.406138
\(874\) 0 0
\(875\) −5.00000 −0.169031
\(876\) 0 0
\(877\) −33.0000 −1.11433 −0.557165 0.830402i \(-0.688111\pi\)
−0.557165 + 0.830402i \(0.688111\pi\)
\(878\) 0 0
\(879\) 81.0000 2.73206
\(880\) 0 0
\(881\) 10.0000 0.336909 0.168454 0.985709i \(-0.446122\pi\)
0.168454 + 0.985709i \(0.446122\pi\)
\(882\) 0 0
\(883\) −30.0000 −1.00958 −0.504790 0.863242i \(-0.668430\pi\)
−0.504790 + 0.863242i \(0.668430\pi\)
\(884\) 0 0
\(885\) 27.0000 0.907595
\(886\) 0 0
\(887\) −28.0000 −0.940148 −0.470074 0.882627i \(-0.655773\pi\)
−0.470074 + 0.882627i \(0.655773\pi\)
\(888\) 0 0
\(889\) 30.0000 1.00617
\(890\) 0 0
\(891\) 36.0000 1.20605
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 8.00000 0.267411
\(896\) 0 0
\(897\) 21.0000 0.701170
\(898\) 0 0
\(899\) −6.00000 −0.200111
\(900\) 0 0
\(901\) −39.0000 −1.29928
\(902\) 0 0
\(903\) 90.0000 2.99501
\(904\) 0 0
\(905\) −26.0000 −0.864269
\(906\) 0 0
\(907\) 1.00000 0.0332045 0.0166022 0.999862i \(-0.494715\pi\)
0.0166022 + 0.999862i \(0.494715\pi\)
\(908\) 0 0
\(909\) 48.0000 1.59206
\(910\) 0 0
\(911\) −12.0000 −0.397578 −0.198789 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) 0 0
\(913\) 40.0000 1.32381
\(914\) 0 0
\(915\) 36.0000 1.19012
\(916\) 0 0
\(917\) 80.0000 2.64183
\(918\) 0 0
\(919\) −5.00000 −0.164935 −0.0824674 0.996594i \(-0.526280\pi\)
−0.0824674 + 0.996594i \(0.526280\pi\)
\(920\) 0 0
\(921\) −12.0000 −0.395413
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 2.00000 0.0657596
\(926\) 0 0
\(927\) 24.0000 0.788263
\(928\) 0 0
\(929\) −3.00000 −0.0984268 −0.0492134 0.998788i \(-0.515671\pi\)
−0.0492134 + 0.998788i \(0.515671\pi\)
\(930\) 0 0
\(931\) −18.0000 −0.589926
\(932\) 0 0
\(933\) 75.0000 2.45539
\(934\) 0 0
\(935\) −12.0000 −0.392442
\(936\) 0 0
\(937\) 47.0000 1.53542 0.767712 0.640796i \(-0.221395\pi\)
0.767712 + 0.640796i \(0.221395\pi\)
\(938\) 0 0
\(939\) −3.00000 −0.0979013
\(940\) 0 0
\(941\) 51.0000 1.66255 0.831276 0.555860i \(-0.187611\pi\)
0.831276 + 0.555860i \(0.187611\pi\)
\(942\) 0 0
\(943\) −42.0000 −1.36771
\(944\) 0 0
\(945\) −45.0000 −1.46385
\(946\) 0 0
\(947\) 24.0000 0.779895 0.389948 0.920837i \(-0.372493\pi\)
0.389948 + 0.920837i \(0.372493\pi\)
\(948\) 0 0
\(949\) 11.0000 0.357075
\(950\) 0 0
\(951\) −27.0000 −0.875535
\(952\) 0 0
\(953\) −24.0000 −0.777436 −0.388718 0.921357i \(-0.627082\pi\)
−0.388718 + 0.921357i \(0.627082\pi\)
\(954\) 0 0
\(955\) 9.00000 0.291233
\(956\) 0 0
\(957\) 36.0000 1.16371
\(958\) 0 0
\(959\) −45.0000 −1.45313
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 78.0000 2.51351
\(964\) 0 0
\(965\) 10.0000 0.321911
\(966\) 0 0
\(967\) −44.0000 −1.41494 −0.707472 0.706741i \(-0.750165\pi\)
−0.707472 + 0.706741i \(0.750165\pi\)
\(968\) 0 0
\(969\) 9.00000 0.289122
\(970\) 0 0
\(971\) −28.0000 −0.898563 −0.449281 0.893390i \(-0.648320\pi\)
−0.449281 + 0.893390i \(0.648320\pi\)
\(972\) 0 0
\(973\) 80.0000 2.56468
\(974\) 0 0
\(975\) 3.00000 0.0960769
\(976\) 0 0
\(977\) −62.0000 −1.98356 −0.991778 0.127971i \(-0.959153\pi\)
−0.991778 + 0.127971i \(0.959153\pi\)
\(978\) 0 0
\(979\) 8.00000 0.255681
\(980\) 0 0
\(981\) −114.000 −3.63974
\(982\) 0 0
\(983\) −42.0000 −1.33959 −0.669796 0.742545i \(-0.733618\pi\)
−0.669796 + 0.742545i \(0.733618\pi\)
\(984\) 0 0
\(985\) 22.0000 0.700978
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −42.0000 −1.33552
\(990\) 0 0
\(991\) 30.0000 0.952981 0.476491 0.879180i \(-0.341909\pi\)
0.476491 + 0.879180i \(0.341909\pi\)
\(992\) 0 0
\(993\) 21.0000 0.666415
\(994\) 0 0
\(995\) −15.0000 −0.475532
\(996\) 0 0
\(997\) 50.0000 1.58352 0.791758 0.610835i \(-0.209166\pi\)
0.791758 + 0.610835i \(0.209166\pi\)
\(998\) 0 0
\(999\) 18.0000 0.569495
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 6080.2.a.x.1.1 1
4.3 odd 2 6080.2.a.b.1.1 1
8.3 odd 2 1520.2.a.j.1.1 1
8.5 even 2 190.2.a.b.1.1 1
24.5 odd 2 1710.2.a.g.1.1 1
40.13 odd 4 950.2.b.a.799.1 2
40.19 odd 2 7600.2.a.a.1.1 1
40.29 even 2 950.2.a.c.1.1 1
40.37 odd 4 950.2.b.a.799.2 2
56.13 odd 2 9310.2.a.u.1.1 1
120.29 odd 2 8550.2.a.bm.1.1 1
152.37 odd 2 3610.2.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.a.b.1.1 1 8.5 even 2
950.2.a.c.1.1 1 40.29 even 2
950.2.b.a.799.1 2 40.13 odd 4
950.2.b.a.799.2 2 40.37 odd 4
1520.2.a.j.1.1 1 8.3 odd 2
1710.2.a.g.1.1 1 24.5 odd 2
3610.2.a.e.1.1 1 152.37 odd 2
6080.2.a.b.1.1 1 4.3 odd 2
6080.2.a.x.1.1 1 1.1 even 1 trivial
7600.2.a.a.1.1 1 40.19 odd 2
8550.2.a.bm.1.1 1 120.29 odd 2
9310.2.a.u.1.1 1 56.13 odd 2