Properties

Label 2240.2.n.f.1119.4
Level $2240$
Weight $2$
Character 2240.1119
Analytic conductor $17.886$
Analytic rank $0$
Dimension $8$
CM discriminant -35
Inner twists $16$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2240,2,Mod(1119,2240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2240.1119");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.n (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(17.8864900528\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.384160000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 9x^{6} + 37x^{4} - 36x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 1119.4
Root \(-0.817582 + 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 2240.1119
Dual form 2240.2.n.f.1119.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.23607 q^{3} +2.23607i q^{5} +2.64575i q^{7} +2.00000 q^{9} +O(q^{10})\) \(q-2.23607 q^{3} +2.23607i q^{5} +2.64575i q^{7} +2.00000 q^{9} +5.91608 q^{11} -6.70820i q^{13} -5.00000i q^{15} -7.93725 q^{17} -5.91608i q^{21} -5.00000 q^{25} +2.23607 q^{27} -5.91608i q^{29} -13.2288 q^{33} -5.91608 q^{35} +15.0000i q^{39} +4.47214i q^{45} -7.93725i q^{47} -7.00000 q^{49} +17.7482 q^{51} +13.2288i q^{55} +5.29150i q^{63} +15.0000 q^{65} -12.0000i q^{71} +10.5830 q^{73} +11.1803 q^{75} +15.6525i q^{77} +1.00000i q^{79} -11.0000 q^{81} -8.94427 q^{83} -17.7482i q^{85} +13.2288i q^{87} +17.7482 q^{91} +18.5203 q^{97} +11.8322 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 16 q^{9} - 40 q^{25} - 56 q^{49} + 120 q^{65} - 88 q^{81}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).

\(n\) \(897\) \(1471\) \(1541\) \(1921\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

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
\(3\) −2.23607 −1.29099 −0.645497 0.763763i \(-0.723350\pi\)
−0.645497 + 0.763763i \(0.723350\pi\)
\(4\) 0 0
\(5\) 2.23607i 1.00000i
\(6\) 0 0
\(7\) 2.64575i 1.00000i
\(8\) 0 0
\(9\) 2.00000 0.666667
\(10\) 0 0
\(11\) 5.91608 1.78377 0.891883 0.452267i \(-0.149385\pi\)
0.891883 + 0.452267i \(0.149385\pi\)
\(12\) 0 0
\(13\) − 6.70820i − 1.86052i −0.366900 0.930261i \(-0.619581\pi\)
0.366900 0.930261i \(-0.380419\pi\)
\(14\) 0 0
\(15\) − 5.00000i − 1.29099i
\(16\) 0 0
\(17\) −7.93725 −1.92507 −0.962533 0.271163i \(-0.912592\pi\)
−0.962533 + 0.271163i \(0.912592\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) − 5.91608i − 1.29099i
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) 2.23607 0.430331
\(28\) 0 0
\(29\) − 5.91608i − 1.09859i −0.835629 0.549294i \(-0.814897\pi\)
0.835629 0.549294i \(-0.185103\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) −13.2288 −2.30283
\(34\) 0 0
\(35\) −5.91608 −1.00000
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 15.0000i 2.40192i
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 4.47214i 0.666667i
\(46\) 0 0
\(47\) − 7.93725i − 1.15777i −0.815410 0.578884i \(-0.803489\pi\)
0.815410 0.578884i \(-0.196511\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 17.7482 2.48525
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 13.2288i 1.78377i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 5.29150i 0.666667i
\(64\) 0 0
\(65\) 15.0000 1.86052
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) − 12.0000i − 1.42414i −0.702109 0.712069i \(-0.747758\pi\)
0.702109 0.712069i \(-0.252242\pi\)
\(72\) 0 0
\(73\) 10.5830 1.23865 0.619324 0.785136i \(-0.287407\pi\)
0.619324 + 0.785136i \(0.287407\pi\)
\(74\) 0 0
\(75\) 11.1803 1.29099
\(76\) 0 0
\(77\) 15.6525i 1.78377i
\(78\) 0 0
\(79\) 1.00000i 0.112509i 0.998416 + 0.0562544i \(0.0179158\pi\)
−0.998416 + 0.0562544i \(0.982084\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) 0 0
\(83\) −8.94427 −0.981761 −0.490881 0.871227i \(-0.663325\pi\)
−0.490881 + 0.871227i \(0.663325\pi\)
\(84\) 0 0
\(85\) − 17.7482i − 1.92507i
\(86\) 0 0
\(87\) 13.2288i 1.41827i
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 17.7482 1.86052
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 18.5203 1.88045 0.940224 0.340557i \(-0.110616\pi\)
0.940224 + 0.340557i \(0.110616\pi\)
\(98\) 0 0
\(99\) 11.8322 1.18918
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) − 2.64575i − 0.260694i −0.991468 0.130347i \(-0.958391\pi\)
0.991468 0.130347i \(-0.0416091\pi\)
\(104\) 0 0
\(105\) 13.2288 1.29099
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) − 17.7482i − 1.69997i −0.526804 0.849987i \(-0.676610\pi\)
0.526804 0.849987i \(-0.323390\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) − 13.4164i − 1.24035i
\(118\) 0 0
\(119\) − 21.0000i − 1.92507i
\(120\) 0 0
\(121\) 24.0000 2.18182
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 11.1803i − 1.00000i
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 5.00000i 0.430331i
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 17.7482i 1.49467i
\(142\) 0 0
\(143\) − 39.6863i − 3.31873i
\(144\) 0 0
\(145\) 13.2288 1.09859
\(146\) 0 0
\(147\) 15.6525 1.29099
\(148\) 0 0
\(149\) − 23.6643i − 1.93866i −0.245770 0.969328i \(-0.579041\pi\)
0.245770 0.969328i \(-0.420959\pi\)
\(150\) 0 0
\(151\) 17.0000i 1.38344i 0.722166 + 0.691720i \(0.243147\pi\)
−0.722166 + 0.691720i \(0.756853\pi\)
\(152\) 0 0
\(153\) −15.8745 −1.28338
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 13.4164i − 1.07075i −0.844616 0.535373i \(-0.820171\pi\)
0.844616 0.535373i \(-0.179829\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) − 29.5804i − 2.30283i
\(166\) 0 0
\(167\) − 7.93725i − 0.614203i −0.951677 0.307102i \(-0.900641\pi\)
0.951677 0.307102i \(-0.0993591\pi\)
\(168\) 0 0
\(169\) −32.0000 −2.46154
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 11.1803i 0.850026i 0.905187 + 0.425013i \(0.139730\pi\)
−0.905187 + 0.425013i \(0.860270\pi\)
\(174\) 0 0
\(175\) − 13.2288i − 1.00000i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 11.8322 0.884377 0.442189 0.896922i \(-0.354202\pi\)
0.442189 + 0.896922i \(0.354202\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −46.9574 −3.43387
\(188\) 0 0
\(189\) 5.91608i 0.430331i
\(190\) 0 0
\(191\) 27.0000i 1.95365i 0.214036 + 0.976826i \(0.431339\pi\)
−0.214036 + 0.976826i \(0.568661\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) −33.5410 −2.40192
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 15.6525 1.09859
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 17.7482 1.22184 0.610920 0.791693i \(-0.290800\pi\)
0.610920 + 0.791693i \(0.290800\pi\)
\(212\) 0 0
\(213\) 26.8328i 1.83855i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −23.6643 −1.59909
\(220\) 0 0
\(221\) 53.2447i 3.58163i
\(222\) 0 0
\(223\) − 29.1033i − 1.94890i −0.224607 0.974449i \(-0.572110\pi\)
0.224607 0.974449i \(-0.427890\pi\)
\(224\) 0 0
\(225\) −10.0000 −0.666667
\(226\) 0 0
\(227\) 29.0689 1.92937 0.964685 0.263407i \(-0.0848462\pi\)
0.964685 + 0.263407i \(0.0848462\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) − 35.0000i − 2.30283i
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 17.7482 1.15777
\(236\) 0 0
\(237\) − 2.23607i − 0.145248i
\(238\) 0 0
\(239\) 9.00000i 0.582162i 0.956698 + 0.291081i \(0.0940149\pi\)
−0.956698 + 0.291081i \(0.905985\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 17.8885 1.14755
\(244\) 0 0
\(245\) − 15.6525i − 1.00000i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 20.0000 1.26745
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 39.6863i 2.48525i
\(256\) 0 0
\(257\) 31.7490 1.98045 0.990225 0.139482i \(-0.0445438\pi\)
0.990225 + 0.139482i \(0.0445438\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) − 11.8322i − 0.732392i
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) −39.6863 −2.40192
\(274\) 0 0
\(275\) −29.5804 −1.78377
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −33.0000 −1.96861 −0.984307 0.176462i \(-0.943535\pi\)
−0.984307 + 0.176462i \(0.943535\pi\)
\(282\) 0 0
\(283\) 33.5410 1.99381 0.996903 0.0786368i \(-0.0250567\pi\)
0.996903 + 0.0786368i \(0.0250567\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 46.0000 2.70588
\(290\) 0 0
\(291\) −41.4126 −2.42765
\(292\) 0 0
\(293\) − 24.5967i − 1.43696i −0.695549 0.718479i \(-0.744839\pi\)
0.695549 0.718479i \(-0.255161\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 13.2288 0.767610
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −6.70820 −0.382857 −0.191429 0.981507i \(-0.561312\pi\)
−0.191429 + 0.981507i \(0.561312\pi\)
\(308\) 0 0
\(309\) 5.91608i 0.336554i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −29.1033 −1.64501 −0.822507 0.568755i \(-0.807425\pi\)
−0.822507 + 0.568755i \(0.807425\pi\)
\(314\) 0 0
\(315\) −11.8322 −0.666667
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) − 35.0000i − 1.95962i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 33.5410i 1.86052i
\(326\) 0 0
\(327\) 39.6863i 2.19466i
\(328\) 0 0
\(329\) 21.0000 1.15777
\(330\) 0 0
\(331\) 35.4965 1.95106 0.975531 0.219860i \(-0.0705600\pi\)
0.975531 + 0.219860i \(0.0705600\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) − 18.5203i − 1.00000i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) − 15.0000i − 0.800641i
\(352\) 0 0
\(353\) −23.8118 −1.26737 −0.633686 0.773590i \(-0.718459\pi\)
−0.633686 + 0.773590i \(0.718459\pi\)
\(354\) 0 0
\(355\) 26.8328 1.42414
\(356\) 0 0
\(357\) 46.9574i 2.48525i
\(358\) 0 0
\(359\) 36.0000i 1.90001i 0.312239 + 0.950004i \(0.398921\pi\)
−0.312239 + 0.950004i \(0.601079\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) −53.6656 −2.81672
\(364\) 0 0
\(365\) 23.6643i 1.23865i
\(366\) 0 0
\(367\) 18.5203i 0.966750i 0.875413 + 0.483375i \(0.160589\pi\)
−0.875413 + 0.483375i \(0.839411\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 25.0000i 1.29099i
\(376\) 0 0
\(377\) −39.6863 −2.04395
\(378\) 0 0
\(379\) −35.4965 −1.82333 −0.911666 0.410932i \(-0.865203\pi\)
−0.911666 + 0.410932i \(0.865203\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 15.8745i 0.811149i 0.914062 + 0.405575i \(0.132929\pi\)
−0.914062 + 0.405575i \(0.867071\pi\)
\(384\) 0 0
\(385\) −35.0000 −1.78377
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 5.91608i − 0.299957i −0.988689 0.149979i \(-0.952080\pi\)
0.988689 0.149979i \(-0.0479205\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.23607 −0.112509
\(396\) 0 0
\(397\) − 20.1246i − 1.01003i −0.863112 0.505013i \(-0.831488\pi\)
0.863112 0.505013i \(-0.168512\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −27.0000 −1.34832 −0.674158 0.738587i \(-0.735493\pi\)
−0.674158 + 0.738587i \(0.735493\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) − 24.5967i − 1.22222i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) − 20.0000i − 0.981761i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) − 17.7482i − 0.864996i −0.901635 0.432498i \(-0.857632\pi\)
0.901635 0.432498i \(-0.142368\pi\)
\(422\) 0 0
\(423\) − 15.8745i − 0.771845i
\(424\) 0 0
\(425\) 39.6863 1.92507
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 88.7412i 4.28447i
\(430\) 0 0
\(431\) 3.00000i 0.144505i 0.997386 + 0.0722525i \(0.0230187\pi\)
−0.997386 + 0.0722525i \(0.976981\pi\)
\(432\) 0 0
\(433\) −10.5830 −0.508587 −0.254293 0.967127i \(-0.581843\pi\)
−0.254293 + 0.967127i \(0.581843\pi\)
\(434\) 0 0
\(435\) −29.5804 −1.41827
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −14.0000 −0.666667
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 52.9150i 2.50279i
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) − 38.0132i − 1.78601i
\(454\) 0 0
\(455\) 39.6863i 1.86052i
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) −17.7482 −0.828417
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −42.4853 −1.96598 −0.982992 0.183646i \(-0.941210\pi\)
−0.982992 + 0.183646i \(0.941210\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 30.0000i 1.38233i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 41.4126i 1.88045i
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −29.5804 −1.33494 −0.667472 0.744635i \(-0.732624\pi\)
−0.667472 + 0.744635i \(0.732624\pi\)
\(492\) 0 0
\(493\) 46.9574i 2.11486i
\(494\) 0 0
\(495\) 26.4575i 1.18918i
\(496\) 0 0
\(497\) 31.7490 1.42414
\(498\) 0 0
\(499\) 17.7482 0.794520 0.397260 0.917706i \(-0.369961\pi\)
0.397260 + 0.917706i \(0.369961\pi\)
\(500\) 0 0
\(501\) 17.7482i 0.792933i
\(502\) 0 0
\(503\) − 23.8118i − 1.06171i −0.847461 0.530857i \(-0.821870\pi\)
0.847461 0.530857i \(-0.178130\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 71.5542 3.17783
\(508\) 0 0
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 28.0000i 1.23865i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.91608 0.260694
\(516\) 0 0
\(517\) − 46.9574i − 2.06519i
\(518\) 0 0
\(519\) − 25.0000i − 1.09738i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −26.8328 −1.17332 −0.586659 0.809834i \(-0.699557\pi\)
−0.586659 + 0.809834i \(0.699557\pi\)
\(524\) 0 0
\(525\) 29.5804i 1.29099i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −26.4575 −1.14173
\(538\) 0 0
\(539\) −41.4126 −1.78377
\(540\) 0 0
\(541\) − 17.7482i − 0.763056i −0.924357 0.381528i \(-0.875398\pi\)
0.924357 0.381528i \(-0.124602\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 39.6863 1.69997
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −2.64575 −0.112509
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 105.000 4.43310
\(562\) 0 0
\(563\) −44.7214 −1.88478 −0.942390 0.334515i \(-0.891427\pi\)
−0.942390 + 0.334515i \(0.891427\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 29.1033i − 1.22222i
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) −35.4965 −1.48548 −0.742741 0.669579i \(-0.766474\pi\)
−0.742741 + 0.669579i \(0.766474\pi\)
\(572\) 0 0
\(573\) − 60.3738i − 2.52215i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 34.3948 1.43187 0.715936 0.698165i \(-0.246000\pi\)
0.715936 + 0.698165i \(0.246000\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 23.6643i − 0.981761i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 30.0000 1.24035
\(586\) 0 0
\(587\) 8.94427 0.369170 0.184585 0.982817i \(-0.440906\pi\)
0.184585 + 0.982817i \(0.440906\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −23.8118 −0.977832 −0.488916 0.872331i \(-0.662608\pi\)
−0.488916 + 0.872331i \(0.662608\pi\)
\(594\) 0 0
\(595\) 46.9574 1.92507
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) − 39.0000i − 1.59350i −0.604311 0.796748i \(-0.706552\pi\)
0.604311 0.796748i \(-0.293448\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 53.6656i 2.18182i
\(606\) 0 0
\(607\) − 44.9778i − 1.82559i −0.408416 0.912796i \(-0.633919\pi\)
0.408416 0.912796i \(-0.366081\pi\)
\(608\) 0 0
\(609\) −35.0000 −1.41827
\(610\) 0 0
\(611\) −53.2447 −2.15405
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) − 47.0000i − 1.87104i −0.353273 0.935520i \(-0.614931\pi\)
0.353273 0.935520i \(-0.385069\pi\)
\(632\) 0 0
\(633\) −39.6863 −1.57739
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 46.9574i 1.86052i
\(638\) 0 0
\(639\) − 24.0000i − 0.949425i
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) −6.70820 −0.264546 −0.132273 0.991213i \(-0.542228\pi\)
−0.132273 + 0.991213i \(0.542228\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 47.6235i − 1.87227i −0.351636 0.936137i \(-0.614374\pi\)
0.351636 0.936137i \(-0.385626\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 21.1660 0.825765
\(658\) 0 0
\(659\) 5.91608 0.230458 0.115229 0.993339i \(-0.463240\pi\)
0.115229 + 0.993339i \(0.463240\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) − 119.059i − 4.62386i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 65.0769i 2.51602i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) −11.1803 −0.430331
\(676\) 0 0
\(677\) 51.4296i 1.97660i 0.152527 + 0.988299i \(0.451259\pi\)
−0.152527 + 0.988299i \(0.548741\pi\)
\(678\) 0 0
\(679\) 49.0000i 1.88045i
\(680\) 0 0
\(681\) −65.0000 −2.49081
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 31.3050i 1.18918i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 41.4126i 1.56413i 0.623196 + 0.782065i \(0.285834\pi\)
−0.623196 + 0.782065i \(0.714166\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −39.6863 −1.49467
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) − 53.2447i − 1.99965i −0.0187779 0.999824i \(-0.505978\pi\)
0.0187779 0.999824i \(-0.494022\pi\)
\(710\) 0 0
\(711\) 2.00000i 0.0750059i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 88.7412 3.31873
\(716\) 0 0
\(717\) − 20.1246i − 0.751567i
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 7.00000 0.260694
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 29.5804i 1.09859i
\(726\) 0 0
\(727\) − 5.29150i − 0.196251i −0.995174 0.0981255i \(-0.968715\pi\)
0.995174 0.0981255i \(-0.0312847\pi\)
\(728\) 0 0
\(729\) −7.00000 −0.259259
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) − 20.1246i − 0.743319i −0.928369 0.371660i \(-0.878789\pi\)
0.928369 0.371660i \(-0.121211\pi\)
\(734\) 0 0
\(735\) 35.0000i 1.29099i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 53.2447 1.95864 0.979319 0.202321i \(-0.0648484\pi\)
0.979319 + 0.202321i \(0.0648484\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 52.9150 1.93866
\(746\) 0 0
\(747\) −17.8885 −0.654508
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) − 13.0000i − 0.474377i −0.971464 0.237188i \(-0.923774\pi\)
0.971464 0.237188i \(-0.0762259\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −38.0132 −1.38344
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 46.9574 1.69997
\(764\) 0 0
\(765\) − 35.4965i − 1.28338i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) −70.9930 −2.55675
\(772\) 0 0
\(773\) − 2.23607i − 0.0804258i −0.999191 0.0402129i \(-0.987196\pi\)
0.999191 0.0402129i \(-0.0128036\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) − 70.9930i − 2.54033i
\(782\) 0 0
\(783\) − 13.2288i − 0.472757i
\(784\) 0 0
\(785\) 30.0000 1.07075
\(786\) 0 0
\(787\) 33.5410 1.19561 0.597804 0.801642i \(-0.296040\pi\)
0.597804 + 0.801642i \(0.296040\pi\)
\(788\) 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
\(797\) − 55.9017i − 1.98014i −0.140576 0.990070i \(-0.544895\pi\)
0.140576 0.990070i \(-0.455105\pi\)
\(798\) 0 0
\(799\) 63.0000i 2.22878i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 62.6099 2.20946
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 39.0000 1.37117 0.685583 0.727994i \(-0.259547\pi\)
0.685583 + 0.727994i \(0.259547\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 35.4965 1.24035
\(820\) 0 0
\(821\) − 5.91608i − 0.206473i −0.994657 0.103236i \(-0.967080\pi\)
0.994657 0.103236i \(-0.0329198\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 66.1438 2.30283
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 55.5608 1.92507
\(834\) 0 0
\(835\) 17.7482 0.614203
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −6.00000 −0.206897
\(842\) 0 0
\(843\) 73.7902 2.54147
\(844\) 0 0
\(845\) − 71.5542i − 2.46154i
\(846\) 0 0
\(847\) 63.4980i 2.18182i
\(848\) 0 0
\(849\) −75.0000 −2.57399
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 40.2492i 1.37811i 0.724710 + 0.689054i \(0.241974\pi\)
−0.724710 + 0.689054i \(0.758026\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −31.7490 −1.08453 −0.542263 0.840209i \(-0.682432\pi\)
−0.542263 + 0.840209i \(0.682432\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) −25.0000 −0.850026
\(866\) 0 0
\(867\) −102.859 −3.49328
\(868\) 0 0
\(869\) 5.91608i 0.200689i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 37.0405 1.25363
\(874\) 0 0
\(875\) 29.5804 1.00000
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 55.0000i 1.85510i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 47.6235i 1.59904i 0.600639 + 0.799521i \(0.294913\pi\)
−0.600639 + 0.799521i \(0.705087\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −65.0769 −2.18016
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 26.4575i 0.884377i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 12.0000i 0.397578i 0.980042 + 0.198789i \(0.0637008\pi\)
−0.980042 + 0.198789i \(0.936299\pi\)
\(912\) 0 0
\(913\) −52.9150 −1.75123
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) − 29.0000i − 0.956622i −0.878191 0.478311i \(-0.841249\pi\)
0.878191 0.478311i \(-0.158751\pi\)
\(920\) 0 0
\(921\) 15.0000 0.494267
\(922\) 0 0
\(923\) −80.4984 −2.64964
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) − 5.29150i − 0.173796i
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) − 105.000i − 3.43387i
\(936\) 0 0
\(937\) 60.8523 1.98796 0.993979 0.109574i \(-0.0349486\pi\)
0.993979 + 0.109574i \(0.0349486\pi\)
\(938\) 0 0
\(939\) 65.0769 2.12370
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) −13.2288 −0.430331
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) − 70.9930i − 2.30453i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) −60.3738 −1.95365
\(956\) 0 0
\(957\) 78.2624i 2.52986i
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) − 75.0000i − 2.40192i
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) − 35.4965i − 1.13332i
\(982\) 0 0
\(983\) 55.5608i 1.77211i 0.463577 + 0.886057i \(0.346566\pi\)
−0.463577 + 0.886057i \(0.653434\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −46.9574 −1.49467
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) − 52.0000i − 1.65183i −0.563791 0.825917i \(-0.690658\pi\)
0.563791 0.825917i \(-0.309342\pi\)
\(992\) 0 0
\(993\) −79.3725 −2.51881
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) − 60.3738i − 1.91206i −0.293271 0.956029i \(-0.594744\pi\)
0.293271 0.956029i \(-0.405256\pi\)
\(998\) 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 2240.2.n.f.1119.4 yes 8
4.3 odd 2 inner 2240.2.n.f.1119.7 yes 8
5.4 even 2 inner 2240.2.n.f.1119.5 yes 8
7.6 odd 2 inner 2240.2.n.f.1119.5 yes 8
8.3 odd 2 inner 2240.2.n.f.1119.1 8
8.5 even 2 inner 2240.2.n.f.1119.6 yes 8
20.19 odd 2 inner 2240.2.n.f.1119.2 yes 8
28.27 even 2 inner 2240.2.n.f.1119.2 yes 8
35.34 odd 2 CM 2240.2.n.f.1119.4 yes 8
40.19 odd 2 inner 2240.2.n.f.1119.8 yes 8
40.29 even 2 inner 2240.2.n.f.1119.3 yes 8
56.13 odd 2 inner 2240.2.n.f.1119.3 yes 8
56.27 even 2 inner 2240.2.n.f.1119.8 yes 8
140.139 even 2 inner 2240.2.n.f.1119.7 yes 8
280.69 odd 2 inner 2240.2.n.f.1119.6 yes 8
280.139 even 2 inner 2240.2.n.f.1119.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2240.2.n.f.1119.1 8 8.3 odd 2 inner
2240.2.n.f.1119.1 8 280.139 even 2 inner
2240.2.n.f.1119.2 yes 8 20.19 odd 2 inner
2240.2.n.f.1119.2 yes 8 28.27 even 2 inner
2240.2.n.f.1119.3 yes 8 40.29 even 2 inner
2240.2.n.f.1119.3 yes 8 56.13 odd 2 inner
2240.2.n.f.1119.4 yes 8 1.1 even 1 trivial
2240.2.n.f.1119.4 yes 8 35.34 odd 2 CM
2240.2.n.f.1119.5 yes 8 5.4 even 2 inner
2240.2.n.f.1119.5 yes 8 7.6 odd 2 inner
2240.2.n.f.1119.6 yes 8 8.5 even 2 inner
2240.2.n.f.1119.6 yes 8 280.69 odd 2 inner
2240.2.n.f.1119.7 yes 8 4.3 odd 2 inner
2240.2.n.f.1119.7 yes 8 140.139 even 2 inner
2240.2.n.f.1119.8 yes 8 40.19 odd 2 inner
2240.2.n.f.1119.8 yes 8 56.27 even 2 inner