Properties

Label 1080.2.a.d.1.1
Level $1080$
Weight $2$
Character 1080.1
Self dual yes
Analytic conductor $8.624$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1080,2,Mod(1,1080)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1080, 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("1080.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1080.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: \(8.62384341830\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1080.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{5} +O(q^{10})\) \(q-1.00000 q^{5} -2.00000 q^{11} -3.00000 q^{17} -1.00000 q^{19} -3.00000 q^{23} +1.00000 q^{25} -4.00000 q^{29} -5.00000 q^{31} +10.0000 q^{37} -6.00000 q^{41} -6.00000 q^{43} -8.00000 q^{47} -7.00000 q^{49} -3.00000 q^{53} +2.00000 q^{55} +5.00000 q^{61} -2.00000 q^{67} -2.00000 q^{71} +6.00000 q^{73} -11.0000 q^{79} -9.00000 q^{83} +3.00000 q^{85} -10.0000 q^{89} +1.00000 q^{95} +8.00000 q^{97} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 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 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 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
\(45\) 0 0
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 5.00000 0.640184 0.320092 0.947386i \(-0.396286\pi\)
0.320092 + 0.947386i \(0.396286\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.00000 −0.244339 −0.122169 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −9.00000 −0.987878 −0.493939 0.869496i \(-0.664443\pi\)
−0.493939 + 0.869496i \(0.664443\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.00000 0.102598
\(96\) 0 0
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 0 0
\(103\) −12.0000 −1.18240 −0.591198 0.806527i \(-0.701345\pi\)
−0.591198 + 0.806527i \(0.701345\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) 9.00000 0.862044 0.431022 0.902342i \(-0.358153\pi\)
0.431022 + 0.902342i \(0.358153\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 3.00000 0.279751
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 22.0000 1.95218 0.976092 0.217357i \(-0.0697436\pi\)
0.976092 + 0.217357i \(0.0697436\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −10.0000 −0.873704 −0.436852 0.899533i \(-0.643907\pi\)
−0.436852 + 0.899533i \(0.643907\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 7.00000 0.598050 0.299025 0.954245i \(-0.403339\pi\)
0.299025 + 0.954245i \(0.403339\pi\)
\(138\) 0 0
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 4.00000 0.332182
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2.00000 −0.163846 −0.0819232 0.996639i \(-0.526106\pi\)
−0.0819232 + 0.996639i \(0.526106\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5.00000 0.401610
\(156\) 0 0
\(157\) 18.0000 1.43656 0.718278 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.00000 −0.156652 −0.0783260 0.996928i \(-0.524958\pi\)
−0.0783260 + 0.996928i \(0.524958\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 17.0000 1.31550 0.657750 0.753237i \(-0.271508\pi\)
0.657750 + 0.753237i \(0.271508\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 19.0000 1.44454 0.722272 0.691609i \(-0.243098\pi\)
0.722272 + 0.691609i \(0.243098\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 24.0000 1.79384 0.896922 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 0 0
\(181\) 17.0000 1.26360 0.631800 0.775131i \(-0.282316\pi\)
0.631800 + 0.775131i \(0.282316\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −10.0000 −0.735215
\(186\) 0 0
\(187\) 6.00000 0.438763
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 0 0
\(193\) −20.0000 −1.43963 −0.719816 0.694165i \(-0.755774\pi\)
−0.719816 + 0.694165i \(0.755774\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −5.00000 −0.356235 −0.178118 0.984009i \(-0.557001\pi\)
−0.178118 + 0.984009i \(0.557001\pi\)
\(198\) 0 0
\(199\) −12.0000 −0.850657 −0.425329 0.905039i \(-0.639842\pi\)
−0.425329 + 0.905039i \(0.639842\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 6.00000 0.419058
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −3.00000 −0.206529 −0.103264 0.994654i \(-0.532929\pi\)
−0.103264 + 0.994654i \(0.532929\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6.00000 0.409197
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 2.00000 0.133930 0.0669650 0.997755i \(-0.478668\pi\)
0.0669650 + 0.997755i \(0.478668\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −17.0000 −1.12833 −0.564165 0.825662i \(-0.690802\pi\)
−0.564165 + 0.825662i \(0.690802\pi\)
\(228\) 0 0
\(229\) −13.0000 −0.859064 −0.429532 0.903052i \(-0.641321\pi\)
−0.429532 + 0.903052i \(0.641321\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.0000 0.655122 0.327561 0.944830i \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) 0 0
\(235\) 8.00000 0.521862
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 30.0000 1.94054 0.970269 0.242028i \(-0.0778125\pi\)
0.970269 + 0.242028i \(0.0778125\pi\)
\(240\) 0 0
\(241\) −17.0000 −1.09507 −0.547533 0.836784i \(-0.684433\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 7.00000 0.447214
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 23.0000 1.43470 0.717350 0.696713i \(-0.245355\pi\)
0.717350 + 0.696713i \(0.245355\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −12.0000 −0.739952 −0.369976 0.929041i \(-0.620634\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(264\) 0 0
\(265\) 3.00000 0.184289
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 0 0
\(271\) 3.00000 0.182237 0.0911185 0.995840i \(-0.470956\pi\)
0.0911185 + 0.995840i \(0.470956\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.00000 −0.120605
\(276\) 0 0
\(277\) 22.0000 1.32185 0.660926 0.750451i \(-0.270164\pi\)
0.660926 + 0.750451i \(0.270164\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 28.0000 1.67034 0.835170 0.549992i \(-0.185369\pi\)
0.835170 + 0.549992i \(0.185369\pi\)
\(282\) 0 0
\(283\) 2.00000 0.118888 0.0594438 0.998232i \(-0.481067\pi\)
0.0594438 + 0.998232i \(0.481067\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 11.0000 0.642627 0.321313 0.946973i \(-0.395876\pi\)
0.321313 + 0.946973i \(0.395876\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −5.00000 −0.286299
\(306\) 0 0
\(307\) 26.0000 1.48390 0.741949 0.670456i \(-0.233902\pi\)
0.741949 + 0.670456i \(0.233902\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −20.0000 −1.13410 −0.567048 0.823685i \(-0.691915\pi\)
−0.567048 + 0.823685i \(0.691915\pi\)
\(312\) 0 0
\(313\) −20.0000 −1.13047 −0.565233 0.824931i \(-0.691214\pi\)
−0.565233 + 0.824931i \(0.691214\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −11.0000 −0.617822 −0.308911 0.951091i \(-0.599964\pi\)
−0.308911 + 0.951091i \(0.599964\pi\)
\(318\) 0 0
\(319\) 8.00000 0.447914
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.00000 0.109272
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 10.0000 0.541530
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) −7.00000 −0.374701 −0.187351 0.982293i \(-0.559990\pi\)
−0.187351 + 0.982293i \(0.559990\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.0000 0.532246 0.266123 0.963939i \(-0.414257\pi\)
0.266123 + 0.963939i \(0.414257\pi\)
\(354\) 0 0
\(355\) 2.00000 0.106149
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.00000 0.316668 0.158334 0.987386i \(-0.449388\pi\)
0.158334 + 0.987386i \(0.449388\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) 16.0000 0.835193 0.417597 0.908633i \(-0.362873\pi\)
0.417597 + 0.908633i \(0.362873\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.00000 −0.153293 −0.0766464 0.997058i \(-0.524421\pi\)
−0.0766464 + 0.997058i \(0.524421\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 0 0
\(391\) 9.00000 0.455150
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 11.0000 0.553470
\(396\) 0 0
\(397\) −4.00000 −0.200754 −0.100377 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −34.0000 −1.69788 −0.848939 0.528490i \(-0.822758\pi\)
−0.848939 + 0.528490i \(0.822758\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −20.0000 −0.991363
\(408\) 0 0
\(409\) −31.0000 −1.53285 −0.766426 0.642333i \(-0.777967\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 9.00000 0.441793
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.00000 0.293119 0.146560 0.989202i \(-0.453180\pi\)
0.146560 + 0.989202i \(0.453180\pi\)
\(420\) 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
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.00000 −0.385346 −0.192673 0.981263i \(-0.561716\pi\)
−0.192673 + 0.981263i \(0.561716\pi\)
\(432\) 0 0
\(433\) −24.0000 −1.15337 −0.576683 0.816968i \(-0.695653\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.00000 0.143509
\(438\) 0 0
\(439\) 7.00000 0.334092 0.167046 0.985949i \(-0.446577\pi\)
0.167046 + 0.985949i \(0.446577\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −29.0000 −1.37783 −0.688916 0.724841i \(-0.741913\pi\)
−0.688916 + 0.724841i \(0.741913\pi\)
\(444\) 0 0
\(445\) 10.0000 0.474045
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 0 0
\(451\) 12.0000 0.565058
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −16.0000 −0.748448 −0.374224 0.927338i \(-0.622091\pi\)
−0.374224 + 0.927338i \(0.622091\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 34.0000 1.58354 0.791769 0.610821i \(-0.209160\pi\)
0.791769 + 0.610821i \(0.209160\pi\)
\(462\) 0 0
\(463\) 14.0000 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.00000 0.323921 0.161961 0.986797i \(-0.448218\pi\)
0.161961 + 0.986797i \(0.448218\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 12.0000 0.551761
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −10.0000 −0.456912 −0.228456 0.973554i \(-0.573368\pi\)
−0.228456 + 0.973554i \(0.573368\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.00000 −0.363261
\(486\) 0 0
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −42.0000 −1.89543 −0.947717 0.319113i \(-0.896615\pi\)
−0.947717 + 0.319113i \(0.896615\pi\)
\(492\) 0 0
\(493\) 12.0000 0.540453
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 43.0000 1.92494 0.962472 0.271380i \(-0.0874801\pi\)
0.962472 + 0.271380i \(0.0874801\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −35.0000 −1.56057 −0.780286 0.625422i \(-0.784927\pi\)
−0.780286 + 0.625422i \(0.784927\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −28.0000 −1.24108 −0.620539 0.784176i \(-0.713086\pi\)
−0.620539 + 0.784176i \(0.713086\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 12.0000 0.528783
\(516\) 0 0
\(517\) 16.0000 0.703679
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 0 0
\(523\) −28.0000 −1.22435 −0.612177 0.790721i \(-0.709706\pi\)
−0.612177 + 0.790721i \(0.709706\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 15.0000 0.653410
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −4.00000 −0.172935
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 14.0000 0.603023
\(540\) 0 0
\(541\) −18.0000 −0.773880 −0.386940 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −9.00000 −0.385518
\(546\) 0 0
\(547\) 18.0000 0.769624 0.384812 0.922995i \(-0.374266\pi\)
0.384812 + 0.922995i \(0.374266\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.00000 0.170406
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18.0000 −0.762684 −0.381342 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −28.0000 −1.18006 −0.590030 0.807382i \(-0.700884\pi\)
−0.590030 + 0.807382i \(0.700884\pi\)
\(564\) 0 0
\(565\) −6.00000 −0.252422
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) −9.00000 −0.376638 −0.188319 0.982108i \(-0.560304\pi\)
−0.188319 + 0.982108i \(0.560304\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.00000 −0.125109
\(576\) 0 0
\(577\) −46.0000 −1.91501 −0.957503 0.288425i \(-0.906868\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 6.00000 0.248495
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −23.0000 −0.949312 −0.474656 0.880172i \(-0.657427\pi\)
−0.474656 + 0.880172i \(0.657427\pi\)
\(588\) 0 0
\(589\) 5.00000 0.206021
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 3.00000 0.123195 0.0615976 0.998101i \(-0.480380\pi\)
0.0615976 + 0.998101i \(0.480380\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 40.0000 1.63436 0.817178 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 0 0
\(601\) 17.0000 0.693444 0.346722 0.937968i \(-0.387295\pi\)
0.346722 + 0.937968i \(0.387295\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.00000 0.284590
\(606\) 0 0
\(607\) 10.0000 0.405887 0.202944 0.979190i \(-0.434949\pi\)
0.202944 + 0.979190i \(0.434949\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 16.0000 0.646234 0.323117 0.946359i \(-0.395269\pi\)
0.323117 + 0.946359i \(0.395269\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 25.0000 1.00646 0.503231 0.864152i \(-0.332144\pi\)
0.503231 + 0.864152i \(0.332144\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −30.0000 −1.19618
\(630\) 0 0
\(631\) −19.0000 −0.756378 −0.378189 0.925728i \(-0.623453\pi\)
−0.378189 + 0.925728i \(0.623453\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −22.0000 −0.873043
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 40.0000 1.57745 0.788723 0.614749i \(-0.210743\pi\)
0.788723 + 0.614749i \(0.210743\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −39.0000 −1.53325 −0.766624 0.642096i \(-0.778065\pi\)
−0.766624 + 0.642096i \(0.778065\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −11.0000 −0.430463 −0.215232 0.976563i \(-0.569051\pi\)
−0.215232 + 0.976563i \(0.569051\pi\)
\(654\) 0 0
\(655\) 10.0000 0.390732
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.00000 −0.155818 −0.0779089 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 0 0
\(661\) 6.00000 0.233373 0.116686 0.993169i \(-0.462773\pi\)
0.116686 + 0.993169i \(0.462773\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 12.0000 0.464642
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) −8.00000 −0.308377 −0.154189 0.988041i \(-0.549276\pi\)
−0.154189 + 0.988041i \(0.549276\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −50.0000 −1.92166 −0.960828 0.277145i \(-0.910612\pi\)
−0.960828 + 0.277145i \(0.910612\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 23.0000 0.880071 0.440035 0.897980i \(-0.354966\pi\)
0.440035 + 0.897980i \(0.354966\pi\)
\(684\) 0 0
\(685\) −7.00000 −0.267456
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 13.0000 0.494543 0.247272 0.968946i \(-0.420466\pi\)
0.247272 + 0.968946i \(0.420466\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 20.0000 0.758643
\(696\) 0 0
\(697\) 18.0000 0.681799
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) −10.0000 −0.377157
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 15.0000 0.561754
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −18.0000 −0.671287 −0.335643 0.941989i \(-0.608954\pi\)
−0.335643 + 0.941989i \(0.608954\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.00000 −0.148556
\(726\) 0 0
\(727\) −44.0000 −1.63187 −0.815935 0.578144i \(-0.803777\pi\)
−0.815935 + 0.578144i \(0.803777\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 18.0000 0.665754
\(732\) 0 0
\(733\) −8.00000 −0.295487 −0.147743 0.989026i \(-0.547201\pi\)
−0.147743 + 0.989026i \(0.547201\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.00000 0.147342
\(738\) 0 0
\(739\) −19.0000 −0.698926 −0.349463 0.936950i \(-0.613636\pi\)
−0.349463 + 0.936950i \(0.613636\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16.0000 0.586983 0.293492 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) 0 0
\(745\) 2.00000 0.0732743
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 53.0000 1.93400 0.966999 0.254781i \(-0.0820034\pi\)
0.966999 + 0.254781i \(0.0820034\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) −50.0000 −1.81728 −0.908640 0.417579i \(-0.862879\pi\)
−0.908640 + 0.417579i \(0.862879\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −44.0000 −1.59500 −0.797499 0.603320i \(-0.793844\pi\)
−0.797499 + 0.603320i \(0.793844\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 21.0000 0.757279 0.378640 0.925544i \(-0.376392\pi\)
0.378640 + 0.925544i \(0.376392\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3.00000 −0.107903 −0.0539513 0.998544i \(-0.517182\pi\)
−0.0539513 + 0.998544i \(0.517182\pi\)
\(774\) 0 0
\(775\) −5.00000 −0.179605
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −18.0000 −0.642448
\(786\) 0 0
\(787\) −38.0000 −1.35455 −0.677277 0.735728i \(-0.736840\pi\)
−0.677277 + 0.735728i \(0.736840\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 23.0000 0.814702 0.407351 0.913272i \(-0.366453\pi\)
0.407351 + 0.913272i \(0.366453\pi\)
\(798\) 0 0
\(799\) 24.0000 0.849059
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −12.0000 −0.423471
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 18.0000 0.632846 0.316423 0.948618i \(-0.397518\pi\)
0.316423 + 0.948618i \(0.397518\pi\)
\(810\) 0 0
\(811\) −52.0000 −1.82597 −0.912983 0.407997i \(-0.866228\pi\)
−0.912983 + 0.407997i \(0.866228\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2.00000 0.0700569
\(816\) 0 0
\(817\) 6.00000 0.209913
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 34.0000 1.18661 0.593304 0.804978i \(-0.297823\pi\)
0.593304 + 0.804978i \(0.297823\pi\)
\(822\) 0 0
\(823\) −6.00000 −0.209147 −0.104573 0.994517i \(-0.533348\pi\)
−0.104573 + 0.994517i \(0.533348\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 21.0000 0.730242 0.365121 0.930960i \(-0.381028\pi\)
0.365121 + 0.930960i \(0.381028\pi\)
\(828\) 0 0
\(829\) 34.0000 1.18087 0.590434 0.807086i \(-0.298956\pi\)
0.590434 + 0.807086i \(0.298956\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 21.0000 0.727607
\(834\) 0 0
\(835\) −17.0000 −0.588309
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 20.0000 0.690477 0.345238 0.938515i \(-0.387798\pi\)
0.345238 + 0.938515i \(0.387798\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 13.0000 0.447214
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −30.0000 −1.02839
\(852\) 0 0
\(853\) 8.00000 0.273915 0.136957 0.990577i \(-0.456268\pi\)
0.136957 + 0.990577i \(0.456268\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.00000 0.0341593 0.0170797 0.999854i \(-0.494563\pi\)
0.0170797 + 0.999854i \(0.494563\pi\)
\(858\) 0 0
\(859\) 37.0000 1.26242 0.631212 0.775610i \(-0.282558\pi\)
0.631212 + 0.775610i \(0.282558\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −23.0000 −0.782929 −0.391465 0.920193i \(-0.628031\pi\)
−0.391465 + 0.920193i \(0.628031\pi\)
\(864\) 0 0
\(865\) −19.0000 −0.646019
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 22.0000 0.746299
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 22.0000 0.742887 0.371444 0.928456i \(-0.378863\pi\)
0.371444 + 0.928456i \(0.378863\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 4.00000 0.134763 0.0673817 0.997727i \(-0.478535\pi\)
0.0673817 + 0.997727i \(0.478535\pi\)
\(882\) 0 0
\(883\) 16.0000 0.538443 0.269221 0.963078i \(-0.413234\pi\)
0.269221 + 0.963078i \(0.413234\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 33.0000 1.10803 0.554016 0.832506i \(-0.313095\pi\)
0.554016 + 0.832506i \(0.313095\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 8.00000 0.267710
\(894\) 0 0
\(895\) −24.0000 −0.802232
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 20.0000 0.667037
\(900\) 0 0
\(901\) 9.00000 0.299833
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −17.0000 −0.565099
\(906\) 0 0
\(907\) −44.0000 −1.46100 −0.730498 0.682915i \(-0.760712\pi\)
−0.730498 + 0.682915i \(0.760712\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 36.0000 1.19273 0.596367 0.802712i \(-0.296610\pi\)
0.596367 + 0.802712i \(0.296610\pi\)
\(912\) 0 0
\(913\) 18.0000 0.595713
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −40.0000 −1.31948 −0.659739 0.751495i \(-0.729333\pi\)
−0.659739 + 0.751495i \(0.729333\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 10.0000 0.328798
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −6.00000 −0.196854 −0.0984268 0.995144i \(-0.531381\pi\)
−0.0984268 + 0.995144i \(0.531381\pi\)
\(930\) 0 0
\(931\) 7.00000 0.229416
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −6.00000 −0.196221
\(936\) 0 0
\(937\) −12.0000 −0.392023 −0.196011 0.980602i \(-0.562799\pi\)
−0.196011 + 0.980602i \(0.562799\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −10.0000 −0.325991 −0.162995 0.986627i \(-0.552116\pi\)
−0.162995 + 0.986627i \(0.552116\pi\)
\(942\) 0 0
\(943\) 18.0000 0.586161
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.00000 0.0974869 0.0487435 0.998811i \(-0.484478\pi\)
0.0487435 + 0.998811i \(0.484478\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 26.0000 0.842223 0.421111 0.907009i \(-0.361640\pi\)
0.421111 + 0.907009i \(0.361640\pi\)
\(954\) 0 0
\(955\) −6.00000 −0.194155
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −6.00000 −0.193548
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 20.0000 0.643823
\(966\) 0 0
\(967\) −42.0000 −1.35063 −0.675314 0.737530i \(-0.735992\pi\)
−0.675314 + 0.737530i \(0.735992\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 6.00000 0.192549 0.0962746 0.995355i \(-0.469307\pi\)
0.0962746 + 0.995355i \(0.469307\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 50.0000 1.59964 0.799821 0.600239i \(-0.204928\pi\)
0.799821 + 0.600239i \(0.204928\pi\)
\(978\) 0 0
\(979\) 20.0000 0.639203
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −11.0000 −0.350846 −0.175423 0.984493i \(-0.556129\pi\)
−0.175423 + 0.984493i \(0.556129\pi\)
\(984\) 0 0
\(985\) 5.00000 0.159313
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 18.0000 0.572367
\(990\) 0 0
\(991\) 1.00000 0.0317660 0.0158830 0.999874i \(-0.494944\pi\)
0.0158830 + 0.999874i \(0.494944\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 12.0000 0.380426
\(996\) 0 0
\(997\) −18.0000 −0.570066 −0.285033 0.958518i \(-0.592005\pi\)
−0.285033 + 0.958518i \(0.592005\pi\)
\(998\) 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 1080.2.a.d.1.1 1
3.2 odd 2 1080.2.a.j.1.1 yes 1
4.3 odd 2 2160.2.a.f.1.1 1
5.2 odd 4 5400.2.f.j.649.1 2
5.3 odd 4 5400.2.f.j.649.2 2
5.4 even 2 5400.2.a.w.1.1 1
8.3 odd 2 8640.2.a.bs.1.1 1
8.5 even 2 8640.2.a.bt.1.1 1
9.2 odd 6 3240.2.q.e.1081.1 2
9.4 even 3 3240.2.q.s.2161.1 2
9.5 odd 6 3240.2.q.e.2161.1 2
9.7 even 3 3240.2.q.s.1081.1 2
12.11 even 2 2160.2.a.r.1.1 1
15.2 even 4 5400.2.f.r.649.2 2
15.8 even 4 5400.2.f.r.649.1 2
15.14 odd 2 5400.2.a.x.1.1 1
24.5 odd 2 8640.2.a.o.1.1 1
24.11 even 2 8640.2.a.p.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1080.2.a.d.1.1 1 1.1 even 1 trivial
1080.2.a.j.1.1 yes 1 3.2 odd 2
2160.2.a.f.1.1 1 4.3 odd 2
2160.2.a.r.1.1 1 12.11 even 2
3240.2.q.e.1081.1 2 9.2 odd 6
3240.2.q.e.2161.1 2 9.5 odd 6
3240.2.q.s.1081.1 2 9.7 even 3
3240.2.q.s.2161.1 2 9.4 even 3
5400.2.a.w.1.1 1 5.4 even 2
5400.2.a.x.1.1 1 15.14 odd 2
5400.2.f.j.649.1 2 5.2 odd 4
5400.2.f.j.649.2 2 5.3 odd 4
5400.2.f.r.649.1 2 15.8 even 4
5400.2.f.r.649.2 2 15.2 even 4
8640.2.a.o.1.1 1 24.5 odd 2
8640.2.a.p.1.1 1 24.11 even 2
8640.2.a.bs.1.1 1 8.3 odd 2
8640.2.a.bt.1.1 1 8.5 even 2