Properties

Label 2015.1.h.a.2014.4
Level $2015$
Weight $1$
Character 2015.2014
Analytic conductor $1.006$
Analytic rank $0$
Dimension $4$
Projective image $D_{4}$
CM discriminant -155
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2015,1,Mod(2014,2015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2015, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 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("2015.2014");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2015.h (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: \(1.00561600046\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{4}\)
Projective field: Galois closure of 4.2.130975.1

Embedding invariants

Embedding label 2014.4
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 2015.2014
Dual form 2015.1.h.a.2014.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.41421 q^{3} -1.00000 q^{4} +1.00000i q^{5} +1.00000 q^{9} +O(q^{10})\) \(q+1.41421 q^{3} -1.00000 q^{4} +1.00000i q^{5} +1.00000 q^{9} -1.41421 q^{12} +(0.707107 - 0.707107i) q^{13} +1.41421i q^{15} +1.00000 q^{16} +1.41421 q^{17} +2.00000i q^{19} -1.00000i q^{20} -1.41421 q^{23} -1.00000 q^{25} -1.00000i q^{31} -1.00000 q^{36} +1.41421i q^{37} +(1.00000 - 1.00000i) q^{39} +1.41421 q^{43} +1.00000i q^{45} +1.41421 q^{48} -1.00000 q^{49} +2.00000 q^{51} +(-0.707107 + 0.707107i) q^{52} +1.41421 q^{53} +2.82843i q^{57} -1.41421i q^{60} -1.00000 q^{64} +(0.707107 + 0.707107i) q^{65} -1.41421 q^{68} -2.00000 q^{69} -2.00000i q^{71} +1.41421i q^{73} -1.41421 q^{75} -2.00000i q^{76} +1.00000i q^{80} -1.00000 q^{81} -1.41421i q^{83} +1.41421i q^{85} +1.41421 q^{92} -1.41421i q^{93} -2.00000 q^{95} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} + 4 q^{9} + 4 q^{16} - 4 q^{25} - 4 q^{36} + 4 q^{39} - 4 q^{49} + 8 q^{51} - 4 q^{64} - 8 q^{69} - 4 q^{81} - 8 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2015\mathbb{Z}\right)^\times\).

\(n\) \(716\) \(807\) \(1861\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(4\) −1.00000 −1.00000
\(5\) 1.00000i 1.00000i
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 1.00000 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −1.41421 −1.41421
\(13\) 0.707107 0.707107i 0.707107 0.707107i
\(14\) 0 0
\(15\) 1.41421i 1.41421i
\(16\) 1.00000 1.00000
\(17\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(18\) 0 0
\(19\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 1.00000i 1.00000i
\(21\) 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
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 1.00000i 1.00000i
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −1.00000 −1.00000
\(37\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) 0 0
\(39\) 1.00000 1.00000i 1.00000 1.00000i
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(44\) 0 0
\(45\) 1.00000i 1.00000i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.41421 1.41421
\(49\) −1.00000 −1.00000
\(50\) 0 0
\(51\) 2.00000 2.00000
\(52\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(53\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.82843i 2.82843i
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 1.41421i 1.41421i
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) −1.41421 −1.41421
\(69\) −2.00000 −2.00000
\(70\) 0 0
\(71\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(72\) 0 0
\(73\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) 0 0
\(75\) −1.41421 −1.41421
\(76\) 2.00000i 2.00000i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 1.00000i 1.00000i
\(81\) −1.00000 −1.00000
\(82\) 0 0
\(83\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(84\) 0 0
\(85\) 1.41421i 1.41421i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.41421 1.41421
\(93\) 1.41421i 1.41421i
\(94\) 0 0
\(95\) −2.00000 −2.00000
\(96\) 0 0
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000 1.00000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(110\) 0 0
\(111\) 2.00000i 2.00000i
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 1.41421i 1.41421i
\(116\) 0 0
\(117\) 0.707107 0.707107i 0.707107 0.707107i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.00000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 1.00000i 1.00000i
\(125\) 1.00000i 1.00000i
\(126\) 0 0
\(127\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(128\) 0 0
\(129\) 2.00000 2.00000
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −1.41421 −1.41421
\(148\) 1.41421i 1.41421i
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 1.41421 1.41421
\(154\) 0 0
\(155\) 1.00000 1.00000
\(156\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 2.00000 2.00000
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(168\) 0 0
\(169\) 1.00000i 1.00000i
\(170\) 0 0
\(171\) 2.00000i 2.00000i
\(172\) −1.41421 −1.41421
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 1.00000i 1.00000i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.41421 −1.41421
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(192\) −1.41421 −1.41421
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(196\) 1.00000 1.00000
\(197\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) −2.00000 −2.00000
\(205\) 0 0
\(206\) 0 0
\(207\) −1.41421 −1.41421
\(208\) 0.707107 0.707107i 0.707107 0.707107i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) −1.41421 −1.41421
\(213\) 2.82843i 2.82843i
\(214\) 0 0
\(215\) 1.41421i 1.41421i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 2.00000i 2.00000i
\(220\) 0 0
\(221\) 1.00000 1.00000i 1.00000 1.00000i
\(222\) 0 0
\(223\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(224\) 0 0
\(225\) −1.00000 −1.00000
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 2.82843i 2.82843i
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 1.41421i 1.41421i
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) −1.41421 −1.41421
\(244\) 0 0
\(245\) 1.00000i 1.00000i
\(246\) 0 0
\(247\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(248\) 0 0
\(249\) 2.00000i 2.00000i
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 2.00000i 2.00000i
\(256\) 1.00000 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.707107 0.707107i −0.707107 0.707107i
\(261\) 0 0
\(262\) 0 0
\(263\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(264\) 0 0
\(265\) 1.41421i 1.41421i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 1.41421 1.41421
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 2.00000 2.00000
\(277\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(278\) 0 0
\(279\) 1.00000i 1.00000i
\(280\) 0 0
\(281\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 2.00000i 2.00000i
\(285\) −2.82843 −2.82843
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 1.41421i 1.41421i
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(300\) 1.41421 1.41421
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 2.00000i 2.00000i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(312\) 0 0
\(313\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.00000i 1.00000i
\(321\) 0 0
\(322\) 0 0
\(323\) 2.82843i 2.82843i
\(324\) 1.00000 1.00000
\(325\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(326\) 0 0
\(327\) 2.82843i 2.82843i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 1.41421i 1.41421i
\(333\) 1.41421i 1.41421i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 1.41421i 1.41421i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 2.00000i 2.00000i
\(346\) 0 0
\(347\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(354\) 0 0
\(355\) 2.00000 2.00000
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(360\) 0 0
\(361\) −3.00000 −3.00000
\(362\) 0 0
\(363\) −1.41421 −1.41421
\(364\) 0 0
\(365\) −1.41421 −1.41421
\(366\) 0 0
\(367\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(368\) −1.41421 −1.41421
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 1.41421i 1.41421i
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 1.41421i 1.41421i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 2.00000 2.00000
\(381\) −2.00000 −2.00000
\(382\) 0 0
\(383\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.41421 1.41421
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) −2.00000 −2.00000
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −1.00000 −1.00000
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) −0.707107 0.707107i −0.707107 0.707107i
\(404\) 0 0
\(405\) 1.00000i 1.00000i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 2.00000i 2.00000i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 1.41421 1.41421
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.41421 −1.41421
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.00000i 2.00000i
\(437\) 2.82843i 2.82843i
\(438\) 0 0
\(439\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −1.00000 −1.00000
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 2.00000i 2.00000i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 1.41421i 1.41421i
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(464\) 0 0
\(465\) 1.41421 1.41421
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 2.00000i 2.00000i
\(476\) 0 0
\(477\) 1.41421 1.41421
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(488\) 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
\(496\) 1.00000i 1.00000i
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 1.00000i 1.00000i
\(501\) 2.00000i 2.00000i
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.41421i 1.41421i
\(508\) 1.41421 1.41421
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) −2.00000 −2.00000
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.41421i 1.41421i
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.00000 2.00000
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 1.41421i 1.41421i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −2.00000 −2.00000
\(556\) 0 0
\(557\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(558\) 0 0
\(559\) 1.00000 1.00000i 1.00000 1.00000i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) −2.82843 −2.82843
\(574\) 0 0
\(575\) 1.41421 1.41421
\(576\) −1.00000 −1.00000
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(586\) 0 0
\(587\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(588\) 1.41421 1.41421
\(589\) 2.00000 2.00000
\(590\) 0 0
\(591\) 2.00000i 2.00000i
\(592\) 1.41421i 1.41421i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.00000i 1.00000i
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −1.41421 −1.41421
\(613\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) −1.00000 −1.00000
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 1.00000 1.00000i 1.00000 1.00000i
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.00000i 2.00000i
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.41421i 1.41421i
\(636\) −2.00000 −2.00000
\(637\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(638\) 0 0
\(639\) 2.00000i 2.00000i
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(644\) 0 0
\(645\) 2.00000i 2.00000i
\(646\) 0 0
\(647\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1.41421i 1.41421i
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) 1.41421 1.41421i 1.41421 1.41421i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.41421i 1.41421i
\(669\) 2.00000i 2.00000i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 1.00000i 1.00000i
\(677\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 2.00000i 2.00000i
\(685\) 1.41421 1.41421
\(686\) 0 0
\(687\) 0 0
\(688\) 1.41421 1.41421
\(689\) 1.00000 1.00000i 1.00000 1.00000i
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −2.82843 −2.82843
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 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
\(713\) 1.41421i 1.41421i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 1.00000i 1.00000i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) 2.00000 2.00000
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 1.41421i 1.41421i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 1.41421 1.41421
\(741\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(742\) 0 0
\(743\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.41421i 1.41421i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 2.00000 2.00000
\(765\) 1.41421i 1.41421i
\(766\) 0 0
\(767\) 0 0
\(768\) 1.41421 1.41421
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(774\) 0 0
\(775\) 1.00000i 1.00000i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −1.00000 1.00000i −1.00000 1.00000i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −1.00000 −1.00000
\(785\) 0 0
\(786\) 0 0
\(787\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(788\) 1.41421i 1.41421i
\(789\) −2.00000 −2.00000
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 2.00000i 2.00000i
\(796\) 0 0
\(797\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(798\) 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
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 2.00000 2.00000
\(817\) 2.82843i 2.82843i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(828\) 1.41421 1.41421
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 2.00000 2.00000
\(832\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(833\) −1.41421 −1.41421
\(834\) 0 0
\(835\) 1.41421 1.41421
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 2.82843i 2.82843i
\(844\) 0 0
\(845\) 1.00000 1.00000
\(846\) 0 0
\(847\) 0 0
\(848\) 1.41421 1.41421
\(849\) 0 0
\(850\) 0 0
\(851\) 2.00000i 2.00000i
\(852\) 2.82843i 2.82843i
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) −2.00000 −2.00000
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 1.41421i 1.41421i
\(861\) 0 0
\(862\) 0 0
\(863\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1.41421 1.41421
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 2.00000i 2.00000i
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(884\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 1.41421i 1.41421i
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(898\) 0 0
\(899\) 0 0
\(900\) 1.00000 1.00000
\(901\) 2.00000 2.00000
\(902\) 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
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 2.82843i 2.82843i
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.41421 1.41421i −1.41421 1.41421i
\(924\) 0 0
\(925\) 1.41421i 1.41421i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 2.00000i 2.00000i
\(932\) 0 0
\(933\) 2.82843 2.82843
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 2.00000 2.00000
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(948\) 0 0
\(949\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(954\) 0 0
\(955\) 2.00000i 2.00000i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.41421i 1.41421i
\(961\) −1.00000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(968\) 0 0
\(969\) 4.00000i 4.00000i
\(970\) 0 0
\(971\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(972\) 1.41421 1.41421
\(973\) 0 0
\(974\) 0 0
\(975\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(976\) 0 0
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 1.00000i 1.00000i
\(981\) 2.00000i 2.00000i
\(982\) 0 0
\(983\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(984\) 0 0
\(985\) 1.41421 1.41421
\(986\) 0 0
\(987\) 0 0
\(988\) −1.41421 1.41421i −1.41421 1.41421i
\(989\) −2.00000 −2.00000
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 2.00000i 2.00000i
\(997\) 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 2015.1.h.a.2014.4 yes 4
5.4 even 2 inner 2015.1.h.a.2014.2 yes 4
13.12 even 2 inner 2015.1.h.a.2014.3 yes 4
31.30 odd 2 inner 2015.1.h.a.2014.2 yes 4
65.64 even 2 inner 2015.1.h.a.2014.1 4
155.154 odd 2 CM 2015.1.h.a.2014.4 yes 4
403.402 odd 2 inner 2015.1.h.a.2014.1 4
2015.2014 odd 2 inner 2015.1.h.a.2014.3 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2015.1.h.a.2014.1 4 65.64 even 2 inner
2015.1.h.a.2014.1 4 403.402 odd 2 inner
2015.1.h.a.2014.2 yes 4 5.4 even 2 inner
2015.1.h.a.2014.2 yes 4 31.30 odd 2 inner
2015.1.h.a.2014.3 yes 4 13.12 even 2 inner
2015.1.h.a.2014.3 yes 4 2015.2014 odd 2 inner
2015.1.h.a.2014.4 yes 4 1.1 even 1 trivial
2015.1.h.a.2014.4 yes 4 155.154 odd 2 CM