Properties

Label 775.1.c.a.774.2
Level $775$
Weight $1$
Character 775.774
Analytic conductor $0.387$
Analytic rank $0$
Dimension $2$
Projective image $D_{3}$
CM discriminant -31
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [775,1,Mod(774,775)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(775, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("775.774");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 775.c (of order \(2\), degree \(1\), not 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: \(0.386775384791\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 31)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.31.1
Artin image: $C_4\times S_3$
Artin field: Galois closure of 12.0.1803751953125.3

Embedding invariants

Embedding label 774.2
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 775.774
Dual form 775.1.c.a.774.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -1.00000 q^{14} -1.00000 q^{16} -1.00000i q^{18} +1.00000 q^{19} +1.00000 q^{31} +1.00000i q^{38} -1.00000 q^{41} -2.00000i q^{47} -1.00000 q^{56} +1.00000 q^{59} +1.00000i q^{62} -1.00000i q^{63} -1.00000 q^{64} -2.00000i q^{67} -1.00000 q^{71} -1.00000i q^{72} +1.00000 q^{81} -1.00000i q^{82} +2.00000 q^{94} +1.00000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{9} - 2 q^{14} - 2 q^{16} + 2 q^{19} + 2 q^{31} - 2 q^{41} - 2 q^{56} + 2 q^{59} - 2 q^{64} - 2 q^{71} + 2 q^{81} + 4 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/775\mathbb{Z}\right)^\times\).

\(n\) \(251\) \(652\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(8\) 1.00000i 1.00000i
\(9\) −1.00000 −1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −1.00000 −1.00000
\(15\) 0 0
\(16\) −1.00000 −1.00000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) − 1.00000i − 1.00000i
\(19\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 1.00000 1.00000
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 1.00000i 1.00000i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 −1.00000
\(57\) 0 0
\(58\) 0 0
\(59\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 1.00000i 1.00000i
\(63\) − 1.00000i − 1.00000i
\(64\) −1.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) − 1.00000i − 1.00000i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 1.00000 1.00000
\(82\) − 1.00000i − 1.00000i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 2.00000 2.00000
\(95\) 0 0
\(96\) 0 0
\(97\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) 0 0
\(109\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) − 1.00000i − 1.00000i
\(113\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.00000i 1.00000i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 1.00000 1.00000
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) − 1.00000i − 1.00000i
\(129\) 0 0
\(130\) 0 0
\(131\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(132\) 0 0
\(133\) 1.00000i 1.00000i
\(134\) 2.00000 2.00000
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) − 1.00000i − 1.00000i
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 1.00000i 1.00000i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000i 1.00000i
\(163\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −1.00000 −1.00000
\(170\) 0 0
\(171\) −1.00000 −1.00000
\(172\) 0 0
\(173\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0 0
\(193\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(194\) −1.00000 −1.00000
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) − 1.00000i − 1.00000i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 1.00000 1.00000
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.00000 −1.00000
\(215\) 0 0
\(216\) 0 0
\(217\) 1.00000i 1.00000i
\(218\) 1.00000i 1.00000i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.00000 1.00000
\(227\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.00000i 1.00000i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 1.00000i 1.00000i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 2.00000i 2.00000i
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −1.00000 −1.00000
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) −1.00000 −1.00000
\(280\) 0 0
\(281\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) 0 0
\(283\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 1.00000i − 1.00000i
\(288\) 0 0
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) − 2.00000i − 2.00000i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.00000 −1.00000
\(305\) 0 0
\(306\) 0 0
\(307\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) −1.00000 −1.00000
\(315\) 0 0
\(316\) 0 0
\(317\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 1.00000 1.00000
\(327\) 0 0
\(328\) − 1.00000i − 1.00000i
\(329\) 2.00000 2.00000
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) − 1.00000i − 1.00000i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) − 1.00000i − 1.00000i
\(343\) 1.00000i 1.00000i
\(344\) 0 0
\(345\) 0 0
\(346\) −2.00000 −2.00000
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 1.00000 1.00000
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 2.00000 2.00000
\(377\) 0 0
\(378\) 0 0
\(379\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) − 1.00000i − 1.00000i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.00000 1.00000
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 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
\(413\) 1.00000i 1.00000i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(420\) 0 0
\(421\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) − 1.00000i − 1.00000i
\(423\) 2.00000i 2.00000i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) −1.00000 −1.00000
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) − 1.00000i − 1.00000i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 2.00000 2.00000
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 1.00000 1.00000
\(467\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(468\) 0 0
\(469\) 2.00000 2.00000
\(470\) 0 0
\(471\) 0 0
\(472\) 1.00000i 1.00000i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −1.00000 −1.00000
\(497\) − 1.00000i − 1.00000i
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(504\) 1.00000 1.00000
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) − 1.00000i − 1.00000i
\(513\) 0 0
\(514\) −1.00000 −1.00000
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −1.00000 −1.00000
\(530\) 0 0
\(531\) −1.00000 −1.00000
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 2.00000 2.00000
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) − 1.00000i − 1.00000i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) − 1.00000i − 1.00000i
\(563\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −2.00000 −2.00000
\(567\) 1.00000i 1.00000i
\(568\) − 1.00000i − 1.00000i
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 1.00000 1.00000
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(578\) − 1.00000i − 1.00000i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −2.00000 −2.00000
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 1.00000 1.00000
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 2.00000i 2.00000i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) −1.00000 −1.00000
\(615\) 0 0
\(616\) 0 0
\(617\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) − 1.00000i − 1.00000i
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −1.00000 −1.00000
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 1.00000 1.00000
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 1.00000i 1.00000i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.00000 1.00000
\(657\) 0 0
\(658\) 2.00000i 2.00000i
\(659\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(660\) 0 0
\(661\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) −1.00000 −1.00000
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.00000 −1.00000
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) − 2.00000i − 2.00000i
\(699\) 0 0
\(700\) 0 0
\(701\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 1.00000i − 1.00000i
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 1.00000i 1.00000i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 1.00000 1.00000
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(728\) 0 0
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) − 1.00000i − 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 1.00000i 1.00000i
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1.00000 1.00000
\(747\) 0 0
\(748\) 0 0
\(749\) −1.00000 −1.00000
\(750\) 0 0
\(751\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 2.00000i 2.00000i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) − 2.00000i − 2.00000i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 1.00000i 1.00000i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −1.00000 −1.00000
\(777\) 0 0
\(778\) 0 0
\(779\) −1.00000 −1.00000
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.00000 1.00000
\(792\) 0 0
\(793\) 0 0
\(794\) −1.00000 −1.00000
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) − 1.00000i − 1.00000i
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 1.00000 1.00000
\(825\) 0 0
\(826\) −1.00000 −1.00000
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 1.00000i 1.00000i
\(839\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) − 1.00000i − 1.00000i
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) −2.00000 −2.00000
\(847\) 1.00000i 1.00000i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.00000 −1.00000
\(857\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 2.00000i 2.00000i
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 1.00000i 1.00000i
\(873\) − 1.00000i − 1.00000i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(878\) 1.00000i 1.00000i
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.00000 1.00000
\(887\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 2.00000i − 2.00000i
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 1.00000
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 1.00000 1.00000
\(905\) 0 0
\(906\) 0 0
\(907\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(908\) 0 0
\(909\) 1.00000 1.00000
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.00000i 2.00000i
\(918\) 0 0
\(919\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1.00000i 1.00000i
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −1.00000 −1.00000
\(935\) 0 0
\(936\) 0 0
\(937\) − 2.00000i − 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(938\) 2.00000i 2.00000i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −1.00000 −1.00000
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 1.00000i 1.00000i
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) − 1.00000i − 1.00000i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 1.00000i 1.00000i
\(969\) 0 0
\(970\) 0 0
\(971\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −1.00000 −1.00000
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 1.00000 1.00000
\(995\) 0 0
\(996\) 0 0
\(997\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(998\) 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 775.1.c.a.774.2 2
5.2 odd 4 31.1.b.a.30.1 1
5.3 odd 4 775.1.d.b.526.1 1
5.4 even 2 inner 775.1.c.a.774.1 2
15.2 even 4 279.1.d.b.154.1 1
20.7 even 4 496.1.e.a.433.1 1
31.30 odd 2 CM 775.1.c.a.774.2 2
35.2 odd 12 1519.1.n.b.557.1 2
35.12 even 12 1519.1.n.a.557.1 2
35.17 even 12 1519.1.n.a.30.1 2
35.27 even 4 1519.1.c.a.1177.1 1
35.32 odd 12 1519.1.n.b.30.1 2
40.27 even 4 1984.1.e.b.1921.1 1
40.37 odd 4 1984.1.e.a.1921.1 1
45.2 even 12 2511.1.m.a.433.1 2
45.7 odd 12 2511.1.m.e.433.1 2
45.22 odd 12 2511.1.m.e.1270.1 2
45.32 even 12 2511.1.m.a.1270.1 2
55.2 even 20 3751.1.t.a.2138.1 4
55.7 even 20 3751.1.t.a.3657.1 4
55.17 even 20 3751.1.t.a.2665.1 4
55.27 odd 20 3751.1.t.c.2665.1 4
55.32 even 4 3751.1.d.b.1332.1 1
55.37 odd 20 3751.1.t.c.3657.1 4
55.42 odd 20 3751.1.t.c.2138.1 4
55.47 odd 20 3751.1.t.c.2913.1 4
55.52 even 20 3751.1.t.a.2913.1 4
155.2 odd 20 961.1.f.a.430.1 4
155.7 odd 60 961.1.h.a.726.1 8
155.12 even 60 961.1.h.a.414.1 8
155.17 even 60 961.1.h.a.145.1 8
155.22 even 60 961.1.h.a.229.1 8
155.27 even 20 961.1.f.a.573.1 4
155.37 even 12 961.1.e.a.522.1 2
155.42 even 60 961.1.h.a.623.1 8
155.47 odd 20 961.1.f.a.333.1 4
155.52 even 60 961.1.h.a.117.1 8
155.57 even 12 961.1.e.a.440.1 2
155.67 odd 12 961.1.e.a.440.1 2
155.72 odd 60 961.1.h.a.117.1 8
155.77 even 20 961.1.f.a.333.1 4
155.82 odd 60 961.1.h.a.623.1 8
155.87 odd 12 961.1.e.a.522.1 2
155.92 even 4 31.1.b.a.30.1 1
155.97 odd 20 961.1.f.a.573.1 4
155.102 odd 60 961.1.h.a.229.1 8
155.107 odd 60 961.1.h.a.145.1 8
155.112 odd 60 961.1.h.a.414.1 8
155.117 even 60 961.1.h.a.726.1 8
155.122 even 20 961.1.f.a.430.1 4
155.123 even 4 775.1.d.b.526.1 1
155.127 even 60 961.1.h.a.115.1 8
155.132 odd 20 961.1.f.a.587.1 4
155.137 even 60 961.1.h.a.513.1 8
155.142 odd 60 961.1.h.a.513.1 8
155.147 even 20 961.1.f.a.587.1 4
155.152 odd 60 961.1.h.a.115.1 8
155.154 odd 2 inner 775.1.c.a.774.1 2
465.92 odd 4 279.1.d.b.154.1 1
620.247 odd 4 496.1.e.a.433.1 1
1085.247 even 12 1519.1.n.b.557.1 2
1085.402 odd 12 1519.1.n.a.30.1 2
1085.557 even 12 1519.1.n.b.30.1 2
1085.712 odd 12 1519.1.n.a.557.1 2
1085.867 odd 4 1519.1.c.a.1177.1 1
1240.557 even 4 1984.1.e.a.1921.1 1
1240.867 odd 4 1984.1.e.b.1921.1 1
1395.92 odd 12 2511.1.m.a.433.1 2
1395.247 even 12 2511.1.m.e.1270.1 2
1395.1022 odd 12 2511.1.m.a.1270.1 2
1395.1177 even 12 2511.1.m.e.433.1 2
1705.92 even 20 3751.1.t.c.3657.1 4
1705.247 even 20 3751.1.t.c.2665.1 4
1705.402 odd 20 3751.1.t.a.2665.1 4
1705.557 odd 20 3751.1.t.a.3657.1 4
1705.712 odd 20 3751.1.t.a.2913.1 4
1705.867 even 20 3751.1.t.c.2138.1 4
1705.1022 odd 4 3751.1.d.b.1332.1 1
1705.1487 odd 20 3751.1.t.a.2138.1 4
1705.1642 even 20 3751.1.t.c.2913.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
31.1.b.a.30.1 1 5.2 odd 4
31.1.b.a.30.1 1 155.92 even 4
279.1.d.b.154.1 1 15.2 even 4
279.1.d.b.154.1 1 465.92 odd 4
496.1.e.a.433.1 1 20.7 even 4
496.1.e.a.433.1 1 620.247 odd 4
775.1.c.a.774.1 2 5.4 even 2 inner
775.1.c.a.774.1 2 155.154 odd 2 inner
775.1.c.a.774.2 2 1.1 even 1 trivial
775.1.c.a.774.2 2 31.30 odd 2 CM
775.1.d.b.526.1 1 5.3 odd 4
775.1.d.b.526.1 1 155.123 even 4
961.1.e.a.440.1 2 155.57 even 12
961.1.e.a.440.1 2 155.67 odd 12
961.1.e.a.522.1 2 155.37 even 12
961.1.e.a.522.1 2 155.87 odd 12
961.1.f.a.333.1 4 155.47 odd 20
961.1.f.a.333.1 4 155.77 even 20
961.1.f.a.430.1 4 155.2 odd 20
961.1.f.a.430.1 4 155.122 even 20
961.1.f.a.573.1 4 155.27 even 20
961.1.f.a.573.1 4 155.97 odd 20
961.1.f.a.587.1 4 155.132 odd 20
961.1.f.a.587.1 4 155.147 even 20
961.1.h.a.115.1 8 155.127 even 60
961.1.h.a.115.1 8 155.152 odd 60
961.1.h.a.117.1 8 155.52 even 60
961.1.h.a.117.1 8 155.72 odd 60
961.1.h.a.145.1 8 155.17 even 60
961.1.h.a.145.1 8 155.107 odd 60
961.1.h.a.229.1 8 155.22 even 60
961.1.h.a.229.1 8 155.102 odd 60
961.1.h.a.414.1 8 155.12 even 60
961.1.h.a.414.1 8 155.112 odd 60
961.1.h.a.513.1 8 155.137 even 60
961.1.h.a.513.1 8 155.142 odd 60
961.1.h.a.623.1 8 155.42 even 60
961.1.h.a.623.1 8 155.82 odd 60
961.1.h.a.726.1 8 155.7 odd 60
961.1.h.a.726.1 8 155.117 even 60
1519.1.c.a.1177.1 1 35.27 even 4
1519.1.c.a.1177.1 1 1085.867 odd 4
1519.1.n.a.30.1 2 35.17 even 12
1519.1.n.a.30.1 2 1085.402 odd 12
1519.1.n.a.557.1 2 35.12 even 12
1519.1.n.a.557.1 2 1085.712 odd 12
1519.1.n.b.30.1 2 35.32 odd 12
1519.1.n.b.30.1 2 1085.557 even 12
1519.1.n.b.557.1 2 35.2 odd 12
1519.1.n.b.557.1 2 1085.247 even 12
1984.1.e.a.1921.1 1 40.37 odd 4
1984.1.e.a.1921.1 1 1240.557 even 4
1984.1.e.b.1921.1 1 40.27 even 4
1984.1.e.b.1921.1 1 1240.867 odd 4
2511.1.m.a.433.1 2 45.2 even 12
2511.1.m.a.433.1 2 1395.92 odd 12
2511.1.m.a.1270.1 2 45.32 even 12
2511.1.m.a.1270.1 2 1395.1022 odd 12
2511.1.m.e.433.1 2 45.7 odd 12
2511.1.m.e.433.1 2 1395.1177 even 12
2511.1.m.e.1270.1 2 45.22 odd 12
2511.1.m.e.1270.1 2 1395.247 even 12
3751.1.d.b.1332.1 1 55.32 even 4
3751.1.d.b.1332.1 1 1705.1022 odd 4
3751.1.t.a.2138.1 4 55.2 even 20
3751.1.t.a.2138.1 4 1705.1487 odd 20
3751.1.t.a.2665.1 4 55.17 even 20
3751.1.t.a.2665.1 4 1705.402 odd 20
3751.1.t.a.2913.1 4 55.52 even 20
3751.1.t.a.2913.1 4 1705.712 odd 20
3751.1.t.a.3657.1 4 55.7 even 20
3751.1.t.a.3657.1 4 1705.557 odd 20
3751.1.t.c.2138.1 4 55.42 odd 20
3751.1.t.c.2138.1 4 1705.867 even 20
3751.1.t.c.2665.1 4 55.27 odd 20
3751.1.t.c.2665.1 4 1705.247 even 20
3751.1.t.c.2913.1 4 55.47 odd 20
3751.1.t.c.2913.1 4 1705.1642 even 20
3751.1.t.c.3657.1 4 55.37 odd 20
3751.1.t.c.3657.1 4 1705.92 even 20