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Properties

Label 3.25.b.a.2.1
Level $3$
Weight $25$
Character 3.2
Self dual yes
Analytic conductor $10.949$
Analytic rank $0$
Dimension $1$
CM discriminant -3
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3,25,Mod(2,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 25, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 25);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 25 \)
Character orbit: \([\chi]\) \(=\) 3.b (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: \(10.9490145677\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 2.1
Character \(\chi\) \(=\) 3.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+531441. q^{3} +1.67772e7 q^{4} -4.11971e9 q^{7} +2.82430e11 q^{9} +O(q^{10})\) \(q+531441. q^{3} +1.67772e7 q^{4} -4.11971e9 q^{7} +2.82430e11 q^{9} +8.91610e12 q^{12} +4.17184e13 q^{13} +2.81475e14 q^{16} -4.10669e15 q^{19} -2.18938e15 q^{21} +5.96046e16 q^{25} +1.50095e17 q^{27} -6.91173e16 q^{28} -1.29423e18 q^{31} +4.73838e18 q^{36} -5.17817e18 q^{37} +2.21709e19 q^{39} -7.98636e19 q^{43} +1.49587e20 q^{48} -1.74609e20 q^{49} +6.99918e20 q^{52} -2.18246e21 q^{57} +1.76759e20 q^{61} -1.16353e21 q^{63} +4.72237e21 q^{64} +6.44503e21 q^{67} -3.48923e22 q^{73} +3.16764e22 q^{75} -6.88988e22 q^{76} +7.92237e22 q^{79} +7.97664e22 q^{81} -3.67318e22 q^{84} -1.71868e23 q^{91} -6.87805e23 q^{93} +1.37708e24 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) 531441. 1.00000
\(4\) 1.67772e7 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) −4.11971e9 −0.297639 −0.148820 − 0.988864i \(-0.547547\pi\)
−0.148820 + 0.988864i \(0.547547\pi\)
\(8\) 0 0
\(9\) 2.82430e11 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 8.91610e12 1.00000
\(13\) 4.17184e13 1.79064 0.895318 − 0.445428i \(-0.146949\pi\)
0.895318 + 0.445428i \(0.146949\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.81475e14 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) −4.10669e15 −1.85545 −0.927723 − 0.373269i \(-0.878237\pi\)
−0.927723 + 0.373269i \(0.878237\pi\)
\(20\) 0 0
\(21\) −2.18938e15 −0.297639
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 5.96046e16 1.00000
\(26\) 0 0
\(27\) 1.50095e17 1.00000
\(28\) −6.91173e16 −0.297639
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −1.29423e18 −1.64312 −0.821561 − 0.570120i \(-0.806897\pi\)
−0.821561 + 0.570120i \(0.806897\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 4.73838e18 1.00000
\(37\) −5.17817e18 −0.786603 −0.393302 − 0.919409i \(-0.628667\pi\)
−0.393302 + 0.919409i \(0.628667\pi\)
\(38\) 0 0
\(39\) 2.21709e19 1.79064
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −7.98636e19 −1.99861 −0.999304 − 0.0373090i \(-0.988121\pi\)
−0.999304 + 0.0373090i \(0.988121\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 1.49587e20 1.00000
\(49\) −1.74609e20 −0.911411
\(50\) 0 0
\(51\) 0 0
\(52\) 6.99918e20 1.79064
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −2.18246e21 −1.85545
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 1.76759e20 0.0665924 0.0332962 − 0.999446i \(-0.489400\pi\)
0.0332962 + 0.999446i \(0.489400\pi\)
\(62\) 0 0
\(63\) −1.16353e21 −0.297639
\(64\) 4.72237e21 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 6.44503e21 0.787639 0.393820 − 0.919188i \(-0.371153\pi\)
0.393820 + 0.919188i \(0.371153\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −3.48923e22 −1.52354 −0.761771 − 0.647846i \(-0.775670\pi\)
−0.761771 + 0.647846i \(0.775670\pi\)
\(74\) 0 0
\(75\) 3.16764e22 1.00000
\(76\) −6.88988e22 −1.85545
\(77\) 0 0
\(78\) 0 0
\(79\) 7.92237e22 1.34069 0.670347 − 0.742047i \(-0.266145\pi\)
0.670347 + 0.742047i \(0.266145\pi\)
\(80\) 0 0
\(81\) 7.97664e22 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −3.67318e22 −0.297639
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −1.71868e23 −0.532963
\(92\) 0 0
\(93\) −6.87805e23 −1.64312
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.37708e24 1.98471 0.992357 − 0.123398i \(-0.0393792\pi\)
0.992357 + 0.123398i \(0.0393792\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000e24 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −1.60138e24 −1.12318 −0.561588 − 0.827417i \(-0.689809\pi\)
−0.561588 + 0.827417i \(0.689809\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 2.51817e24 1.00000
\(109\) −3.75771e24 −1.33600 −0.667999 − 0.744162i \(-0.732849\pi\)
−0.667999 + 0.744162i \(0.732849\pi\)
\(110\) 0 0
\(111\) −2.75189e24 −0.786603
\(112\) −1.15960e24 −0.297639
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.17825e25 1.79064
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 9.84973e24 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) −2.17135e25 −1.64312
\(125\) 0 0
\(126\) 0 0
\(127\) 1.70543e25 0.968698 0.484349 − 0.874875i \(-0.339057\pi\)
0.484349 + 0.874875i \(0.339057\pi\)
\(128\) 0 0
\(129\) −4.24428e25 −1.99861
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 1.69184e25 0.552254
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 6.04656e25 1.16233 0.581167 − 0.813784i \(-0.302596\pi\)
0.581167 + 0.813784i \(0.302596\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 7.94968e25 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −9.27945e25 −0.911411
\(148\) −8.68753e25 −0.786603
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −1.99383e26 −1.41895 −0.709473 − 0.704733i \(-0.751067\pi\)
−0.709473 + 0.704733i \(0.751067\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 3.71965e26 1.79064
\(157\) −4.00125e25 −0.178402 −0.0892009 − 0.996014i \(-0.528431\pi\)
−0.0892009 + 0.996014i \(0.528431\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1.43830e26 0.408881 0.204440 − 0.978879i \(-0.434463\pi\)
0.204440 + 0.978879i \(0.434463\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.19762e27 2.20638
\(170\) 0 0
\(171\) −1.15985e27 −1.85545
\(172\) −1.33989e27 −1.99861
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −2.45554e26 −0.297639
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 2.47135e27 1.99890 0.999451 − 0.0331431i \(-0.0105517\pi\)
0.999451 + 0.0331431i \(0.0105517\pi\)
\(182\) 0 0
\(183\) 9.39372e25 0.0665924
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −6.18346e26 −0.297639
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 2.50966e27 1.00000
\(193\) −8.41910e26 −0.315194 −0.157597 − 0.987504i \(-0.550375\pi\)
−0.157597 + 0.987504i \(0.550375\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −2.92946e27 −0.911411
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −7.57876e27 −1.96499 −0.982497 − 0.186280i \(-0.940357\pi\)
−0.982497 + 0.186280i \(0.940357\pi\)
\(200\) 0 0
\(201\) 3.42515e27 0.787639
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 1.17427e28 1.79064
\(209\) 0 0
\(210\) 0 0
\(211\) 2.15909e27 0.277256 0.138628 − 0.990345i \(-0.455731\pi\)
0.138628 + 0.990345i \(0.455731\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 5.33184e27 0.489058
\(218\) 0 0
\(219\) −1.85432e28 −1.52354
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.89129e28 −1.25055 −0.625274 − 0.780405i \(-0.715013\pi\)
−0.625274 + 0.780405i \(0.715013\pi\)
\(224\) 0 0
\(225\) 1.68341e28 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) −3.66156e28 −1.85545
\(229\) 3.23026e28 1.55315 0.776573 − 0.630028i \(-0.216957\pi\)
0.776573 + 0.630028i \(0.216957\pi\)
\(230\) 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
\(237\) 4.21027e28 1.34069
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 1.75967e28 0.458382 0.229191 − 0.973381i \(-0.426392\pi\)
0.229191 + 0.973381i \(0.426392\pi\)
\(242\) 0 0
\(243\) 4.23912e28 1.00000
\(244\) 2.96553e27 0.0665924
\(245\) 0 0
\(246\) 0 0
\(247\) −1.71324e29 −3.32243
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −1.95208e28 −0.297639
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 7.92282e28 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 2.13326e28 0.234124
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 1.08130e29 0.787639
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 2.34037e29 1.49160 0.745801 − 0.666169i \(-0.232067\pi\)
0.745801 + 0.666169i \(0.232067\pi\)
\(272\) 0 0
\(273\) −9.13375e28 −0.532963
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −3.62535e29 −1.77661 −0.888305 − 0.459253i \(-0.848117\pi\)
−0.888305 + 0.459253i \(0.848117\pi\)
\(278\) 0 0
\(279\) −3.65528e29 −1.64312
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 1.64843e29 0.624644 0.312322 − 0.949976i \(-0.398893\pi\)
0.312322 + 0.949976i \(0.398893\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 3.39449e29 1.00000
\(290\) 0 0
\(291\) 7.31836e29 1.98471
\(292\) −5.85395e29 −1.52354
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 5.31441e29 1.00000
\(301\) 3.29015e29 0.594864
\(302\) 0 0
\(303\) 0 0
\(304\) −1.15593e30 −1.85545
\(305\) 0 0
\(306\) 0 0
\(307\) 5.25259e29 0.749399 0.374699 − 0.927146i \(-0.377746\pi\)
0.374699 + 0.927146i \(0.377746\pi\)
\(308\) 0 0
\(309\) −8.51039e29 −1.12318
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −1.63172e30 −1.84550 −0.922748 − 0.385405i \(-0.874062\pi\)
−0.922748 + 0.385405i \(0.874062\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.32915e30 1.34069
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.33826e30 1.00000
\(325\) 2.48661e30 1.79064
\(326\) 0 0
\(327\) −1.99700e30 −1.33600
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 2.73339e30 1.58040 0.790199 − 0.612850i \(-0.209977\pi\)
0.790199 + 0.612850i \(0.209977\pi\)
\(332\) 0 0
\(333\) −1.46247e30 −0.786603
\(334\) 0 0
\(335\) 0 0
\(336\) −6.16257e29 −0.297639
\(337\) −4.25109e30 −1.98126 −0.990630 − 0.136575i \(-0.956390\pi\)
−0.990630 + 0.136575i \(0.956390\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.50860e30 0.568911
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −6.39094e30 −1.95731 −0.978655 − 0.205510i \(-0.934115\pi\)
−0.978655 + 0.205510i \(0.934115\pi\)
\(350\) 0 0
\(351\) 6.26170e30 1.79064
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 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
\(361\) 1.19661e31 2.44268
\(362\) 0 0
\(363\) 5.23455e30 1.00000
\(364\) −2.88346e30 −0.532963
\(365\) 0 0
\(366\) 0 0
\(367\) −9.63812e30 −1.61436 −0.807179 − 0.590307i \(-0.799007\pi\)
−0.807179 + 0.590307i \(0.799007\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −1.15395e31 −1.64312
\(373\) −5.43724e30 −0.749675 −0.374837 − 0.927091i \(-0.622301\pi\)
−0.374837 + 0.927091i \(0.622301\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 4.41715e30 0.502888 0.251444 − 0.967872i \(-0.419095\pi\)
0.251444 + 0.967872i \(0.419095\pi\)
\(380\) 0 0
\(381\) 9.06334e30 0.968698
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2.25558e31 −1.99861
\(388\) 2.31036e31 1.98471
\(389\) 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
\(397\) 2.52612e31 1.64804 0.824020 − 0.566561i \(-0.191726\pi\)
0.824020 + 0.566561i \(0.191726\pi\)
\(398\) 0 0
\(399\) 8.99111e30 0.552254
\(400\) 1.67772e31 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) −5.39930e31 −2.94223
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −2.24501e31 −1.02456 −0.512280 − 0.858818i \(-0.671199\pi\)
−0.512280 + 0.858818i \(0.671199\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −2.68667e31 −1.12318
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 3.21339e31 1.16233
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 3.28047e31 1.05816 0.529079 − 0.848572i \(-0.322537\pi\)
0.529079 + 0.848572i \(0.322537\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −7.28198e29 −0.0198205
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 4.22479e31 1.00000
\(433\) 3.51841e31 0.810012 0.405006 − 0.914314i \(-0.367269\pi\)
0.405006 + 0.914314i \(0.367269\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −6.30440e31 −1.33600
\(437\) 0 0
\(438\) 0 0
\(439\) 2.86721e31 0.559610 0.279805 − 0.960057i \(-0.409730\pi\)
0.279805 + 0.960057i \(0.409730\pi\)
\(440\) 0 0
\(441\) −4.93148e31 −0.911411
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −4.61691e31 −0.786603
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.94548e31 −0.297639
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −1.05961e32 −1.41895
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.35334e32 1.63084 0.815421 − 0.578868i \(-0.196505\pi\)
0.815421 + 0.578868i \(0.196505\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 1.10326e32 1.13685 0.568427 − 0.822734i \(-0.307552\pi\)
0.568427 + 0.822734i \(0.307552\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 1.97678e32 1.79064
\(469\) −2.65517e31 −0.234432
\(470\) 0 0
\(471\) −2.12643e31 −0.178402
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −2.44778e32 −1.85545
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) −2.16025e32 −1.40852
\(482\) 0 0
\(483\) 0 0
\(484\) 1.65251e32 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) −1.10217e32 −0.619299 −0.309649 − 0.950851i \(-0.600212\pi\)
−0.309649 + 0.950851i \(0.600212\pi\)
\(488\) 0 0
\(489\) 7.64369e31 0.408881
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −3.64292e32 −1.64312
\(497\) 0 0
\(498\) 0 0
\(499\) 4.53580e32 1.90304 0.951519 − 0.307591i \(-0.0995230\pi\)
0.951519 + 0.307591i \(0.0995230\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.36466e32 2.20638
\(508\) 2.86123e32 0.968698
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 1.43746e32 0.453466
\(512\) 0 0
\(513\) −6.16392e32 −1.85545
\(514\) 0 0
\(515\) 0 0
\(516\) −7.12072e32 −1.99861
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −3.96349e32 −0.946362 −0.473181 − 0.880965i \(-0.656894\pi\)
−0.473181 + 0.880965i \(0.656894\pi\)
\(524\) 0 0
\(525\) −1.30497e32 −0.297639
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 4.80251e32 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 2.83843e32 0.552254
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.13412e33 −1.80423 −0.902113 − 0.431501i \(-0.857984\pi\)
−0.902113 + 0.431501i \(0.857984\pi\)
\(542\) 0 0
\(543\) 1.31338e33 1.99890
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.25027e33 1.74243 0.871216 − 0.490900i \(-0.163332\pi\)
0.871216 + 0.490900i \(0.163332\pi\)
\(548\) 0 0
\(549\) 4.99221e31 0.0665924
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −3.26379e32 −0.399043
\(554\) 0 0
\(555\) 0 0
\(556\) 1.01444e33 1.16233
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) −3.33178e33 −3.57878
\(560\) 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
\(567\) −3.28615e32 −0.297639
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −7.99355e32 −0.665436 −0.332718 − 0.943026i \(-0.607966\pi\)
−0.332718 + 0.943026i \(0.607966\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.33374e33 1.00000
\(577\) 2.01354e33 1.47860 0.739299 − 0.673378i \(-0.235157\pi\)
0.739299 + 0.673378i \(0.235157\pi\)
\(578\) 0 0
\(579\) −4.47426e32 −0.315194
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −1.55683e33 −0.911411
\(589\) 5.31498e33 3.04873
\(590\) 0 0
\(591\) 0 0
\(592\) −1.45753e33 −0.786603
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.02766e33 −1.96499
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 2.93795e33 1.32297 0.661486 − 0.749958i \(-0.269926\pi\)
0.661486 + 0.749958i \(0.269926\pi\)
\(602\) 0 0
\(603\) 1.82027e33 0.787639
\(604\) −3.34510e33 −1.41895
\(605\) 0 0
\(606\) 0 0
\(607\) −4.11269e33 −1.64385 −0.821925 − 0.569596i \(-0.807100\pi\)
−0.821925 + 0.569596i \(0.807100\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 9.41107e32 0.334282 0.167141 − 0.985933i \(-0.446546\pi\)
0.167141 + 0.985933i \(0.446546\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −3.11156e33 −0.983309 −0.491654 − 0.870790i \(-0.663608\pi\)
−0.491654 + 0.870790i \(0.663608\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 6.24054e33 1.79064
\(625\) 3.55271e33 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) −6.71298e32 −0.178402
\(629\) 0 0
\(630\) 0 0
\(631\) 7.07640e33 1.77607 0.888034 − 0.459777i \(-0.152071\pi\)
0.888034 + 0.459777i \(0.152071\pi\)
\(632\) 0 0
\(633\) 1.14743e33 0.277256
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −7.28441e33 −1.63200
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) −9.82554e33 −1.96709 −0.983546 − 0.180656i \(-0.942178\pi\)
−0.983546 + 0.180656i \(0.942178\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 2.83356e33 0.489058
\(652\) 2.41306e33 0.408881
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −9.85460e33 −1.52354
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 6.19953e33 0.891130 0.445565 − 0.895250i \(-0.353003\pi\)
0.445565 + 0.895250i \(0.353003\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −1.00511e34 −1.25055
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.69050e34 1.95810 0.979048 − 0.203628i \(-0.0652733\pi\)
0.979048 + 0.203628i \(0.0652733\pi\)
\(674\) 0 0
\(675\) 8.94634e33 1.00000
\(676\) 2.00928e34 2.20638
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) −5.67317e33 −0.590729
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −1.94590e34 −1.85545
\(685\) 0 0
\(686\) 0 0
\(687\) 1.71669e34 1.55315
\(688\) −2.24796e34 −1.99861
\(689\) 0 0
\(690\) 0 0
\(691\) −2.05131e34 −1.73099 −0.865493 − 0.500920i \(-0.832995\pi\)
−0.865493 + 0.500920i \(0.832995\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −4.11971e33 −0.297639
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 2.12651e34 1.45950
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −2.25718e34 −1.39898 −0.699489 − 0.714643i \(-0.746589\pi\)
−0.699489 + 0.714643i \(0.746589\pi\)
\(710\) 0 0
\(711\) 2.23751e34 1.34069
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 6.59722e33 0.334301
\(722\) 0 0
\(723\) 9.35163e33 0.458382
\(724\) 4.14624e34 1.99890
\(725\) 0 0
\(726\) 0 0
\(727\) −2.66493e34 −1.22257 −0.611283 − 0.791412i \(-0.709346\pi\)
−0.611283 + 0.791412i \(0.709346\pi\)
\(728\) 0 0
\(729\) 2.25284e34 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 1.57600e33 0.0665924
\(733\) −4.80926e34 −1.99908 −0.999542 − 0.0302697i \(-0.990363\pi\)
−0.999542 + 0.0302697i \(0.990363\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 3.35698e34 1.26537 0.632683 − 0.774411i \(-0.281954\pi\)
0.632683 + 0.774411i \(0.281954\pi\)
\(740\) 0 0
\(741\) −9.10488e34 −3.32243
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 8.81053e33 0.273730 0.136865 − 0.990590i \(-0.456297\pi\)
0.136865 + 0.990590i \(0.456297\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1.03741e34 −0.297639
\(757\) 5.15522e34 1.45578 0.727892 − 0.685692i \(-0.240500\pi\)
0.727892 + 0.685692i \(0.240500\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 1.54807e34 0.397645
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 4.21051e34 1.00000
\(769\) 5.54394e34 1.29629 0.648145 − 0.761517i \(-0.275545\pi\)
0.648145 + 0.761517i \(0.275545\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.41249e34 −0.315194
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) −7.71419e34 −1.64312
\(776\) 0 0
\(777\) 1.13370e34 0.234124
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −4.91481e34 −0.911411
\(785\) 0 0
\(786\) 0 0
\(787\) 9.93108e33 0.175914 0.0879568 − 0.996124i \(-0.471966\pi\)
0.0879568 + 0.996124i \(0.471966\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 7.37412e33 0.119243
\(794\) 0 0
\(795\) 0 0
\(796\) −1.27150e35 −1.96499
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 5.74645e34 0.787639
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) −4.91832e34 −0.607529 −0.303764 − 0.952747i \(-0.598244\pi\)
−0.303764 + 0.952747i \(0.598244\pi\)
\(812\) 0 0
\(813\) 1.24377e35 1.49160
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 3.27975e35 3.70831
\(818\) 0 0
\(819\) −4.85405e34 −0.532963
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −9.65150e34 −0.999532 −0.499766 − 0.866161i \(-0.666581\pi\)
−0.499766 + 0.866161i \(0.666581\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −2.05772e35 −1.95313 −0.976565 − 0.215222i \(-0.930953\pi\)
−0.976565 + 0.215222i \(0.930953\pi\)
\(830\) 0 0
\(831\) −1.92666e35 −1.77661
\(832\) 1.97009e35 1.79064
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1.94256e35 −1.64312
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.25185e35 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 3.62235e34 0.277256
\(845\) 0 0
\(846\) 0 0
\(847\) −4.05780e34 −0.297639
\(848\) 0 0
\(849\) 8.76042e34 0.624644
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −2.84523e35 −1.91747 −0.958737 − 0.284294i \(-0.908241\pi\)
−0.958737 + 0.284294i \(0.908241\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 1.96615e35 1.21814 0.609072 − 0.793115i \(-0.291542\pi\)
0.609072 + 0.793115i \(0.291542\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1.80397e35 1.00000
\(868\) 8.94534e34 0.489058
\(869\) 0 0
\(870\) 0 0
\(871\) 2.68876e35 1.41037
\(872\) 0 0
\(873\) 3.88928e35 1.98471
\(874\) 0 0
\(875\) 0 0
\(876\) −3.11103e35 −1.52354
\(877\) −2.11959e35 −1.02390 −0.511950 − 0.859015i \(-0.671077\pi\)
−0.511950 + 0.859015i \(0.671077\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) −4.47127e35 −1.99023 −0.995113 − 0.0987404i \(-0.968519\pi\)
−0.995113 + 0.0987404i \(0.968519\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −7.02586e34 −0.288323
\(890\) 0 0
\(891\) 0 0
\(892\) −3.17306e35 −1.25055
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 2.82430e35 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) 1.74852e35 0.594864
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 9.37609e34 0.302506 0.151253 − 0.988495i \(-0.451669\pi\)
0.151253 + 0.988495i \(0.451669\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) −6.14308e35 −1.85545
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 5.41948e35 1.55315
\(917\) 0 0
\(918\) 0 0
\(919\) 6.69669e35 1.84533 0.922665 − 0.385603i \(-0.126007\pi\)
0.922665 + 0.385603i \(0.126007\pi\)
\(920\) 0 0
\(921\) 2.79144e35 0.749399
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −3.08643e35 −0.786603
\(926\) 0 0
\(927\) −4.52277e35 −1.12318
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 7.17065e35 1.69107
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −4.13765e35 −0.903397 −0.451698 − 0.892171i \(-0.649182\pi\)
−0.451698 + 0.892171i \(0.649182\pi\)
\(938\) 0 0
\(939\) −8.67162e35 −1.84550
\(940\) 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
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 7.06366e35 1.34069
\(949\) −1.45565e36 −2.72811
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 1.05461e36 1.69985
\(962\) 0 0
\(963\) 0 0
\(964\) 2.95224e35 0.458382
\(965\) 0 0
\(966\) 0 0
\(967\) −4.70559e33 −0.00703876 −0.00351938 − 0.999994i \(-0.501120\pi\)
−0.00351938 + 0.999994i \(0.501120\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 7.11206e35 1.00000
\(973\) −2.49101e35 −0.345956
\(974\) 0 0
\(975\) 1.32149e36 1.79064
\(976\) 4.97534e34 0.0665924
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −1.06129e36 −1.33600
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −2.87434e36 −3.32243
\(989\) 0 0
\(990\) 0 0
\(991\) 1.72522e36 1.92292 0.961460 − 0.274944i \(-0.0886594\pi\)
0.961460 + 0.274944i \(0.0886594\pi\)
\(992\) 0 0
\(993\) 1.45264e36 1.58040
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.50623e36 −1.56153 −0.780763 − 0.624827i \(-0.785169\pi\)
−0.780763 + 0.624827i \(0.785169\pi\)
\(998\) 0 0
\(999\) −7.77216e35 −0.786603
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 3.25.b.a.2.1 ✓ 1
3.2 odd 2 CM 3.25.b.a.2.1 ✓ 1
4.3 odd 2 48.25.e.a.17.1 1
12.11 even 2 48.25.e.a.17.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.25.b.a.2.1 ✓ 1 1.1 even 1 trivial
3.25.b.a.2.1 ✓ 1 3.2 odd 2 CM
48.25.e.a.17.1 1 4.3 odd 2
48.25.e.a.17.1 1 12.11 even 2