Properties

Label 735.1.f.d.344.2
Level $735$
Weight $1$
Character 735.344
Self dual yes
Analytic conductor $0.367$
Analytic rank $0$
Dimension $2$
Projective image $D_{4}$
CM discriminant -15
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [735,1,Mod(344,735)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(735, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("735.344");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 735.f (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: yes
Analytic conductor: \(0.366812784285\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{4}\)
Projective field: Galois closure of 4.2.15435.1
Artin image: $D_8$
Artin field: Galois closure of 8.2.8338372875.2

Embedding invariants

Embedding label 344.2
Root \(-1.41421\) of defining polynomial
Character \(\chi\) \(=\) 735.344

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.41421 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.41421 q^{6} +1.00000 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.41421 q^{6} +1.00000 q^{9} -1.41421 q^{10} +1.00000 q^{12} -1.00000 q^{15} -1.00000 q^{16} +1.41421 q^{18} -1.41421 q^{19} -1.00000 q^{20} -1.41421 q^{23} +1.00000 q^{25} +1.00000 q^{27} -1.41421 q^{30} +1.41421 q^{31} -1.41421 q^{32} +1.00000 q^{36} -2.00000 q^{38} -1.00000 q^{45} -2.00000 q^{46} -1.00000 q^{48} +1.41421 q^{50} -1.41421 q^{53} +1.41421 q^{54} -1.41421 q^{57} -1.00000 q^{60} +1.41421 q^{61} +2.00000 q^{62} -1.00000 q^{64} -1.41421 q^{69} +1.00000 q^{75} -1.41421 q^{76} +1.00000 q^{80} +1.00000 q^{81} -1.41421 q^{90} -1.41421 q^{92} +1.41421 q^{93} +1.41421 q^{95} -1.41421 q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{9} + 2 q^{12} - 2 q^{15} - 2 q^{16} - 2 q^{20} + 2 q^{25} + 2 q^{27} + 2 q^{36} - 4 q^{38} - 2 q^{45} - 4 q^{46} - 2 q^{48} - 2 q^{60} + 4 q^{62} - 2 q^{64} + 2 q^{75} + 2 q^{80} + 2 q^{81}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) 1.00000 1.00000
\(4\) 1.00000 1.00000
\(5\) −1.00000 −1.00000
\(6\) 1.41421 1.41421
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 1.00000
\(10\) −1.41421 −1.41421
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.00000 1.00000
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) −1.00000 −1.00000
\(16\) −1.00000 −1.00000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 1.41421 1.41421
\(19\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(20\) −1.00000 −1.00000
\(21\) 0 0
\(22\) 0 0
\(23\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(24\) 0 0
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) 1.00000 1.00000
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) −1.41421 −1.41421
\(31\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(32\) −1.41421 −1.41421
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 1.00000
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −2.00000 −2.00000
\(39\) 0 0
\(40\) 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
\(45\) −1.00000 −1.00000
\(46\) −2.00000 −2.00000
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −1.00000 −1.00000
\(49\) 0 0
\(50\) 1.41421 1.41421
\(51\) 0 0
\(52\) 0 0
\(53\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(54\) 1.41421 1.41421
\(55\) 0 0
\(56\) 0 0
\(57\) −1.41421 −1.41421
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) −1.00000 −1.00000
\(61\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(62\) 2.00000 2.00000
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) −1.41421 −1.41421
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 1.00000 1.00000
\(76\) −1.41421 −1.41421
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 1.00000 1.00000
\(81\) 1.00000 1.00000
\(82\) 0 0
\(83\) 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 \(\pi\)
\(90\) −1.41421 −1.41421
\(91\) 0 0
\(92\) −1.41421 −1.41421
\(93\) 1.41421 1.41421
\(94\) 0 0
\(95\) 1.41421 1.41421
\(96\) −1.41421 −1.41421
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −2.00000 −2.00000
\(107\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(108\) 1.00000 1.00000
\(109\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(114\) −2.00000 −2.00000
\(115\) 1.41421 1.41421
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 2.00000 2.00000
\(123\) 0 0
\(124\) 1.41421 1.41421
\(125\) −1.00000 −1.00000
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 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
\(135\) −1.00000 −1.00000
\(136\) 0 0
\(137\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(138\) −2.00000 −2.00000
\(139\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 1.41421 1.41421
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.41421 −1.41421
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) −1.41421 −1.41421
\(160\) 1.41421 1.41421
\(161\) 0 0
\(162\) 1.41421 1.41421
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) −1.41421 −1.41421
\(172\) 0 0
\(173\) 0 0 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 \(\pi\)
\(180\) −1.00000 −1.00000
\(181\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(182\) 0 0
\(183\) 1.41421 1.41421
\(184\) 0 0
\(185\) 0 0
\(186\) 2.00000 2.00000
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 2.00000 2.00000
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −1.00000 −1.00000
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(198\) 0 0
\(199\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.41421 −1.41421
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(212\) −1.41421 −1.41421
\(213\) 0 0
\(214\) 2.00000 2.00000
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −2.82843 −2.82843
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 1.00000 1.00000
\(226\) 2.00000 2.00000
\(227\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(228\) −1.41421 −1.41421
\(229\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(230\) 2.00000 2.00000
\(231\) 0 0
\(232\) 0 0
\(233\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 1.00000 1.00000
\(241\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(242\) 1.41421 1.41421
\(243\) 1.00000 1.00000
\(244\) 1.41421 1.41421
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −1.41421 −1.41421
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(264\) 0 0
\(265\) 1.41421 1.41421
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) −1.41421 −1.41421
\(271\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 2.00000 2.00000
\(275\) 0 0
\(276\) −1.41421 −1.41421
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 2.00000 2.00000
\(279\) 1.41421 1.41421
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 1.41421 1.41421
\(286\) 0 0
\(287\) 0 0
\(288\) −1.41421 −1.41421
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 1.00000 1.00000
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.41421 1.41421
\(305\) −1.41421 −1.41421
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2.00000 −2.00000
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(318\) −2.00000 −2.00000
\(319\) 0 0
\(320\) 1.00000 1.00000
\(321\) 1.41421 1.41421
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) −2.00000 −2.00000
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −2.82843 −2.82843
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 1.41421 1.41421
\(339\) 1.41421 1.41421
\(340\) 0 0
\(341\) 0 0
\(342\) −2.00000 −2.00000
\(343\) 0 0
\(344\) 0 0
\(345\) 1.41421 1.41421
\(346\) 0 0
\(347\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(348\) 0 0
\(349\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) −2.00000 −2.00000
\(363\) 1.00000 1.00000
\(364\) 0 0
\(365\) 0 0
\(366\) 2.00000 2.00000
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 1.41421 1.41421
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 1.41421 1.41421
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −1.00000 −1.00000
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 1.41421 1.41421
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 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
\(394\) 2.00000 2.00000
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) −2.00000 −2.00000
\(399\) 0 0
\(400\) −1.00000 −1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.00000 −1.00000
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(410\) 0 0
\(411\) 1.41421 1.41421
\(412\) 0 0
\(413\) 0 0
\(414\) −2.00000 −2.00000
\(415\) 0 0
\(416\) 0 0
\(417\) 1.41421 1.41421
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) −2.82843 −2.82843
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 1.41421 1.41421
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −1.00000 −1.00000
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.00000 −2.00000
\(437\) 2.00000 2.00000
\(438\) 0 0
\(439\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 1.41421 1.41421
\(451\) 0 0
\(452\) 1.41421 1.41421
\(453\) 0 0
\(454\) −2.82843 −2.82843
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 2.00000 2.00000
\(459\) 0 0
\(460\) 1.41421 1.41421
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) −1.41421 −1.41421
\(466\) −2.00000 −2.00000
\(467\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.41421 −1.41421
\(476\) 0 0
\(477\) −1.41421 −1.41421
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 1.41421 1.41421
\(481\) 0 0
\(482\) −2.00000 −2.00000
\(483\) 0 0
\(484\) 1.00000 1.00000
\(485\) 0 0
\(486\) 1.41421 1.41421
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 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
\(496\) −1.41421 −1.41421
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −1.00000 −1.00000
\(501\) −2.00000 −2.00000
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 1.00000
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.41421 1.41421
\(513\) −1.41421 −1.41421
\(514\) 2.82843 2.82843
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 2.00000 2.00000
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 2.00000 2.00000
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −1.41421 −1.41421
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) −1.00000 −1.00000
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) −2.00000 −2.00000
\(543\) −1.41421 −1.41421
\(544\) 0 0
\(545\) 2.00000 2.00000
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 1.41421 1.41421
\(549\) 1.41421 1.41421
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 1.41421 1.41421
\(557\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(558\) 2.00000 2.00000
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) −1.41421 −1.41421
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 2.00000 2.00000
\(571\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.41421 −1.41421
\(576\) −1.00000 −1.00000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −1.41421 −1.41421
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 2.82843 2.82843
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) −2.00000 −2.00000
\(590\) 0 0
\(591\) 1.41421 1.41421
\(592\) 0 0
\(593\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1.41421 −1.41421
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.00000 −1.00000
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 2.00000 2.00000
\(609\) 0 0
\(610\) −2.00000 −2.00000
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(618\) 0 0
\(619\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(620\) −1.41421 −1.41421
\(621\) −1.41421 −1.41421
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) −2.00000 −2.00000
\(634\) −2.00000 −2.00000
\(635\) 0 0
\(636\) −1.41421 −1.41421
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 2.00000 2.00000
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(654\) −2.82843 −2.82843
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(662\) −2.82843 −2.82843
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −2.00000 −2.00000
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) 1.00000 1.00000
\(677\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(678\) 2.00000 2.00000
\(679\) 0 0
\(680\) 0 0
\(681\) −2.00000 −2.00000
\(682\) 0 0
\(683\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(684\) −1.41421 −1.41421
\(685\) −1.41421 −1.41421
\(686\) 0 0
\(687\) 1.41421 1.41421
\(688\) 0 0
\(689\) 0 0
\(690\) 2.00000 2.00000
\(691\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −2.00000 −2.00000
\(695\) −1.41421 −1.41421
\(696\) 0 0
\(697\) 0 0
\(698\) −2.00000 −2.00000
\(699\) −1.41421 −1.41421
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 2.82843 2.82843
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.00000 −2.00000
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 1.00000 1.00000
\(721\) 0 0
\(722\) 1.41421 1.41421
\(723\) −1.41421 −1.41421
\(724\) −1.41421 −1.41421
\(725\) 0 0
\(726\) 1.41421 1.41421
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 1.41421 1.41421
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 2.00000 2.00000
\(737\) 0 0
\(738\) 0 0
\(739\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) −1.41421 −1.41421
\(751\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.00000 1.00000
\(769\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(770\) 0 0
\(771\) 2.00000 2.00000
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 1.41421 1.41421
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 1.41421 1.41421
\(789\) 1.41421 1.41421
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 1.41421 1.41421
\(796\) −1.41421 −1.41421
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.41421 −1.41421
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) −1.41421 −1.41421
\(811\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(812\) 0 0
\(813\) −1.41421 −1.41421
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −2.00000 −2.00000
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 2.00000 2.00000
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(828\) −1.41421 −1.41421
\(829\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 2.00000 2.00000
\(835\) 2.00000 2.00000
\(836\) 0 0
\(837\) 1.41421 1.41421
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) −2.00000 −2.00000
\(845\) −1.00000 −1.00000
\(846\) 0 0
\(847\) 0 0
\(848\) 1.41421 1.41421
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 1.41421 1.41421
\(856\) 0 0
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(864\) −1.41421 −1.41421
\(865\) 0 0
\(866\) 0 0
\(867\) −1.00000 −1.00000
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 2.82843 2.82843
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 2.00000 2.00000
\(879\) 2.00000 2.00000
\(880\) 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
\(886\) 2.00000 2.00000
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 1.00000 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.41421 1.41421
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) −2.00000 −2.00000
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 1.41421 1.41421
\(913\) 0 0
\(914\) 0 0
\(915\) −1.41421 −1.41421
\(916\) 1.41421 1.41421
\(917\) 0 0
\(918\) 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
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) −2.00000 −2.00000
\(931\) 0 0
\(932\) −1.41421 −1.41421
\(933\) 0 0
\(934\) −2.82843 −2.82843
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −2.00000 −2.00000
\(951\) −1.41421 −1.41421
\(952\) 0 0
\(953\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(954\) −2.00000 −2.00000
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.00000 1.00000
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 1.41421 1.41421
\(964\) −1.41421 −1.41421
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 1.00000 1.00000
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −1.41421 −1.41421
\(977\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −2.00000 −2.00000
\(982\) 0 0
\(983\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(984\) 0 0
\(985\) −1.41421 −1.41421
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(992\) −2.00000 −2.00000
\(993\) −2.00000 −2.00000
\(994\) 0 0
\(995\) 1.41421 1.41421
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 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 735.1.f.d.344.2 yes 2
3.2 odd 2 735.1.f.c.344.1 2
5.2 odd 4 3675.1.c.f.1226.3 4
5.3 odd 4 3675.1.c.f.1226.2 4
5.4 even 2 735.1.f.c.344.1 2
7.2 even 3 735.1.o.c.704.1 4
7.3 odd 6 735.1.o.d.569.1 4
7.4 even 3 735.1.o.c.569.1 4
7.5 odd 6 735.1.o.d.704.1 4
7.6 odd 2 735.1.f.c.344.2 yes 2
15.2 even 4 3675.1.c.f.1226.2 4
15.8 even 4 3675.1.c.f.1226.3 4
15.14 odd 2 CM 735.1.f.d.344.2 yes 2
21.2 odd 6 735.1.o.d.704.2 4
21.5 even 6 735.1.o.c.704.2 4
21.11 odd 6 735.1.o.d.569.2 4
21.17 even 6 735.1.o.c.569.2 4
21.20 even 2 inner 735.1.f.d.344.1 yes 2
35.2 odd 12 3675.1.u.f.851.4 8
35.3 even 12 3675.1.u.f.1451.3 8
35.4 even 6 735.1.o.d.569.2 4
35.9 even 6 735.1.o.d.704.2 4
35.12 even 12 3675.1.u.f.851.3 8
35.13 even 4 3675.1.c.f.1226.1 4
35.17 even 12 3675.1.u.f.1451.2 8
35.18 odd 12 3675.1.u.f.1451.4 8
35.19 odd 6 735.1.o.c.704.2 4
35.23 odd 12 3675.1.u.f.851.1 8
35.24 odd 6 735.1.o.c.569.2 4
35.27 even 4 3675.1.c.f.1226.4 4
35.32 odd 12 3675.1.u.f.1451.1 8
35.33 even 12 3675.1.u.f.851.2 8
35.34 odd 2 inner 735.1.f.d.344.1 yes 2
105.2 even 12 3675.1.u.f.851.1 8
105.17 odd 12 3675.1.u.f.1451.3 8
105.23 even 12 3675.1.u.f.851.4 8
105.32 even 12 3675.1.u.f.1451.4 8
105.38 odd 12 3675.1.u.f.1451.2 8
105.44 odd 6 735.1.o.c.704.1 4
105.47 odd 12 3675.1.u.f.851.2 8
105.53 even 12 3675.1.u.f.1451.1 8
105.59 even 6 735.1.o.d.569.1 4
105.62 odd 4 3675.1.c.f.1226.1 4
105.68 odd 12 3675.1.u.f.851.3 8
105.74 odd 6 735.1.o.c.569.1 4
105.83 odd 4 3675.1.c.f.1226.4 4
105.89 even 6 735.1.o.d.704.1 4
105.104 even 2 735.1.f.c.344.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
735.1.f.c.344.1 2 3.2 odd 2
735.1.f.c.344.1 2 5.4 even 2
735.1.f.c.344.2 yes 2 7.6 odd 2
735.1.f.c.344.2 yes 2 105.104 even 2
735.1.f.d.344.1 yes 2 21.20 even 2 inner
735.1.f.d.344.1 yes 2 35.34 odd 2 inner
735.1.f.d.344.2 yes 2 1.1 even 1 trivial
735.1.f.d.344.2 yes 2 15.14 odd 2 CM
735.1.o.c.569.1 4 7.4 even 3
735.1.o.c.569.1 4 105.74 odd 6
735.1.o.c.569.2 4 21.17 even 6
735.1.o.c.569.2 4 35.24 odd 6
735.1.o.c.704.1 4 7.2 even 3
735.1.o.c.704.1 4 105.44 odd 6
735.1.o.c.704.2 4 21.5 even 6
735.1.o.c.704.2 4 35.19 odd 6
735.1.o.d.569.1 4 7.3 odd 6
735.1.o.d.569.1 4 105.59 even 6
735.1.o.d.569.2 4 21.11 odd 6
735.1.o.d.569.2 4 35.4 even 6
735.1.o.d.704.1 4 7.5 odd 6
735.1.o.d.704.1 4 105.89 even 6
735.1.o.d.704.2 4 21.2 odd 6
735.1.o.d.704.2 4 35.9 even 6
3675.1.c.f.1226.1 4 35.13 even 4
3675.1.c.f.1226.1 4 105.62 odd 4
3675.1.c.f.1226.2 4 5.3 odd 4
3675.1.c.f.1226.2 4 15.2 even 4
3675.1.c.f.1226.3 4 5.2 odd 4
3675.1.c.f.1226.3 4 15.8 even 4
3675.1.c.f.1226.4 4 35.27 even 4
3675.1.c.f.1226.4 4 105.83 odd 4
3675.1.u.f.851.1 8 35.23 odd 12
3675.1.u.f.851.1 8 105.2 even 12
3675.1.u.f.851.2 8 35.33 even 12
3675.1.u.f.851.2 8 105.47 odd 12
3675.1.u.f.851.3 8 35.12 even 12
3675.1.u.f.851.3 8 105.68 odd 12
3675.1.u.f.851.4 8 35.2 odd 12
3675.1.u.f.851.4 8 105.23 even 12
3675.1.u.f.1451.1 8 35.32 odd 12
3675.1.u.f.1451.1 8 105.53 even 12
3675.1.u.f.1451.2 8 35.17 even 12
3675.1.u.f.1451.2 8 105.38 odd 12
3675.1.u.f.1451.3 8 35.3 even 12
3675.1.u.f.1451.3 8 105.17 odd 12
3675.1.u.f.1451.4 8 35.18 odd 12
3675.1.u.f.1451.4 8 105.32 even 12