Properties

Label 75.13.c.a.26.1
Level $75$
Weight $13$
Character 75.26
Self dual yes
Analytic conductor $68.550$
Analytic rank $0$
Dimension $1$
CM discriminant -3
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,13,Mod(26,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 13, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.26");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 75.c (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: \(68.5495362957\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 3)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 26.1
Character \(\chi\) \(=\) 75.26

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-729.000 q^{3} +4096.00 q^{4} +153502. q^{7} +531441. q^{9} +O(q^{10})\) \(q-729.000 q^{3} +4096.00 q^{4} +153502. q^{7} +531441. q^{9} -2.98598e6 q^{12} +9.39758e6 q^{13} +1.67772e7 q^{16} +1.78870e7 q^{19} -1.11903e8 q^{21} -3.87420e8 q^{27} +6.28744e8 q^{28} -5.30188e8 q^{31} +2.17678e9 q^{36} -2.82626e9 q^{37} -6.85084e9 q^{39} +2.35885e8 q^{43} -1.22306e10 q^{48} +9.72158e9 q^{49} +3.84925e10 q^{52} -1.30396e10 q^{57} +7.40639e10 q^{61} +8.15773e10 q^{63} +6.87195e10 q^{64} +1.51031e11 q^{67} -1.04460e11 q^{73} +7.32650e10 q^{76} -4.44305e11 q^{79} +2.82430e11 q^{81} -4.58355e11 q^{84} +1.44255e12 q^{91} +3.86507e11 q^{93} +1.66276e12 q^{97} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) −729.000 −1.00000
\(4\) 4096.00 1.00000
\(5\) 0 0
\(6\) 0 0
\(7\) 153502. 1.30475 0.652373 0.757898i \(-0.273774\pi\)
0.652373 + 0.757898i \(0.273774\pi\)
\(8\) 0 0
\(9\) 531441. 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −2.98598e6 −1.00000
\(13\) 9.39758e6 1.94696 0.973478 0.228782i \(-0.0734743\pi\)
0.973478 + 0.228782i \(0.0734743\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.67772e7 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 1.78870e7 0.380203 0.190101 0.981764i \(-0.439118\pi\)
0.190101 + 0.981764i \(0.439118\pi\)
\(20\) 0 0
\(21\) −1.11903e8 −1.30475
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −3.87420e8 −1.00000
\(28\) 6.28744e8 1.30475
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −5.30188e8 −0.597392 −0.298696 0.954348i \(-0.596552\pi\)
−0.298696 + 0.954348i \(0.596552\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 2.17678e9 1.00000
\(37\) −2.82626e9 −1.10154 −0.550771 0.834656i \(-0.685666\pi\)
−0.550771 + 0.834656i \(0.685666\pi\)
\(38\) 0 0
\(39\) −6.85084e9 −1.94696
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 2.35885e8 0.0373155 0.0186578 0.999826i \(-0.494061\pi\)
0.0186578 + 0.999826i \(0.494061\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −1.22306e10 −1.00000
\(49\) 9.72158e9 0.702361
\(50\) 0 0
\(51\) 0 0
\(52\) 3.84925e10 1.94696
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.30396e10 −0.380203
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 7.40639e10 1.43756 0.718782 0.695235i \(-0.244700\pi\)
0.718782 + 0.695235i \(0.244700\pi\)
\(62\) 0 0
\(63\) 8.15773e10 1.30475
\(64\) 6.87195e10 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 1.51031e11 1.66962 0.834811 0.550536i \(-0.185577\pi\)
0.834811 + 0.550536i \(0.185577\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −1.04460e11 −0.690259 −0.345129 0.938555i \(-0.612165\pi\)
−0.345129 + 0.938555i \(0.612165\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 7.32650e10 0.380203
\(77\) 0 0
\(78\) 0 0
\(79\) −4.44305e11 −1.82776 −0.913878 0.405988i \(-0.866927\pi\)
−0.913878 + 0.405988i \(0.866927\pi\)
\(80\) 0 0
\(81\) 2.82430e11 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −4.58355e11 −1.30475
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 1.44255e12 2.54028
\(92\) 0 0
\(93\) 3.86507e11 0.597392
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.66276e12 1.99617 0.998087 0.0618173i \(-0.0196896\pi\)
0.998087 + 0.0618173i \(0.0196896\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 1.11810e12 0.936389 0.468194 0.883625i \(-0.344905\pi\)
0.468194 + 0.883625i \(0.344905\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −1.58687e12 −1.00000
\(109\) 1.36661e12 0.814863 0.407432 0.913236i \(-0.366424\pi\)
0.407432 + 0.913236i \(0.366424\pi\)
\(110\) 0 0
\(111\) 2.06034e12 1.10154
\(112\) 2.57534e12 1.30475
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 4.99426e12 1.94696
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 3.13843e12 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) −2.17165e12 −0.597392
\(125\) 0 0
\(126\) 0 0
\(127\) −7.22945e12 −1.72299 −0.861495 0.507765i \(-0.830472\pi\)
−0.861495 + 0.507765i \(0.830472\pi\)
\(128\) 0 0
\(129\) −1.71960e11 −0.0373155
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 2.74568e12 0.496068
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) −1.28260e13 −1.77830 −0.889148 0.457620i \(-0.848702\pi\)
−0.889148 + 0.457620i \(0.848702\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 8.91610e12 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −7.08703e12 −0.702361
\(148\) −1.15764e13 −1.10154
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) −9.03587e12 −0.762269 −0.381135 0.924520i \(-0.624467\pi\)
−0.381135 + 0.924520i \(0.624467\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −2.80610e13 −1.94696
\(157\) −2.02127e13 −1.34967 −0.674833 0.737971i \(-0.735784\pi\)
−0.674833 + 0.737971i \(0.735784\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.91094e13 1.55206 0.776028 0.630698i \(-0.217231\pi\)
0.776028 + 0.630698i \(0.217231\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 6.50165e13 2.79064
\(170\) 0 0
\(171\) 9.50586e12 0.380203
\(172\) 9.66185e11 0.0373155
\(173\) 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 \(\pi\)
\(180\) 0 0
\(181\) −7.03140e13 −1.99973 −0.999863 0.0165738i \(-0.994724\pi\)
−0.999863 + 0.0165738i \(0.994724\pi\)
\(182\) 0 0
\(183\) −5.39926e13 −1.43756
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −5.94698e13 −1.30475
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −5.00965e13 −1.00000
\(193\) −6.70840e13 −1.29800 −0.649000 0.760788i \(-0.724813\pi\)
−0.649000 + 0.760788i \(0.724813\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 3.98196e13 0.702361
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 1.16196e13 0.187100 0.0935501 0.995615i \(-0.470178\pi\)
0.0935501 + 0.995615i \(0.470178\pi\)
\(200\) 0 0
\(201\) −1.10102e14 −1.66962
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 1.57665e14 1.94696
\(209\) 0 0
\(210\) 0 0
\(211\) 1.33168e14 1.50906 0.754529 0.656267i \(-0.227865\pi\)
0.754529 + 0.656267i \(0.227865\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −8.13849e13 −0.779445
\(218\) 0 0
\(219\) 7.61512e13 0.690259
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.06464e14 0.865709 0.432854 0.901464i \(-0.357506\pi\)
0.432854 + 0.901464i \(0.357506\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) −5.34102e13 −0.380203
\(229\) −2.71844e14 −1.88498 −0.942489 0.334236i \(-0.891522\pi\)
−0.942489 + 0.334236i \(0.891522\pi\)
\(230\) 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
\(237\) 3.23898e14 1.82776
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 3.07204e14 1.56792 0.783961 0.620810i \(-0.213196\pi\)
0.783961 + 0.620810i \(0.213196\pi\)
\(242\) 0 0
\(243\) −2.05891e14 −1.00000
\(244\) 3.03366e14 1.43756
\(245\) 0 0
\(246\) 0 0
\(247\) 1.68094e14 0.740237
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 3.34140e14 1.30475
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 2.81475e14 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −4.33836e14 −1.43723
\(260\) 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
\(268\) 6.18624e14 1.66962
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 7.40164e14 1.86858 0.934291 0.356510i \(-0.116034\pi\)
0.934291 + 0.356510i \(0.116034\pi\)
\(272\) 0 0
\(273\) −1.05162e15 −2.54028
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 2.13506e14 0.472641 0.236320 0.971675i \(-0.424059\pi\)
0.236320 + 0.971675i \(0.424059\pi\)
\(278\) 0 0
\(279\) −2.81764e14 −0.597392
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 8.32250e14 1.62008 0.810038 0.586378i \(-0.199447\pi\)
0.810038 + 0.586378i \(0.199447\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 5.82622e14 1.00000
\(290\) 0 0
\(291\) −1.21215e15 −1.99617
\(292\) −4.27867e14 −0.690259
\(293\) 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
\(300\) 0 0
\(301\) 3.62088e13 0.0486873
\(302\) 0 0
\(303\) 0 0
\(304\) 3.00093e14 0.380203
\(305\) 0 0
\(306\) 0 0
\(307\) −1.38819e15 −1.65813 −0.829066 0.559151i \(-0.811127\pi\)
−0.829066 + 0.559151i \(0.811127\pi\)
\(308\) 0 0
\(309\) −8.15093e14 −0.936389
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 3.69604e14 0.393071 0.196535 0.980497i \(-0.437031\pi\)
0.196535 + 0.980497i \(0.437031\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −1.81987e15 −1.82776
\(317\) 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
\(324\) 1.15683e15 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) −9.96257e14 −0.814863
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 2.48848e15 1.89219 0.946097 0.323883i \(-0.104989\pi\)
0.946097 + 0.323883i \(0.104989\pi\)
\(332\) 0 0
\(333\) −1.50199e15 −1.10154
\(334\) 0 0
\(335\) 0 0
\(336\) −1.87742e15 −1.30475
\(337\) 2.00526e14 0.136896 0.0684482 0.997655i \(-0.478195\pi\)
0.0684482 + 0.997655i \(0.478195\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −6.32384e14 −0.388343
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −3.73350e14 −0.206616 −0.103308 0.994649i \(-0.532943\pi\)
−0.103308 + 0.994649i \(0.532943\pi\)
\(350\) 0 0
\(351\) −3.64082e15 −1.94696
\(352\) 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
\(361\) −1.89337e15 −0.855446
\(362\) 0 0
\(363\) −2.28791e15 −1.00000
\(364\) 5.90868e15 2.54028
\(365\) 0 0
\(366\) 0 0
\(367\) −1.51736e15 −0.621001 −0.310501 0.950573i \(-0.600497\pi\)
−0.310501 + 0.950573i \(0.600497\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 1.58313e15 0.597392
\(373\) 3.01137e15 1.11818 0.559090 0.829107i \(-0.311151\pi\)
0.559090 + 0.829107i \(0.311151\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −4.68874e15 −1.58205 −0.791026 0.611783i \(-0.790453\pi\)
−0.791026 + 0.611783i \(0.790453\pi\)
\(380\) 0 0
\(381\) 5.27027e15 1.72299
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.25359e14 0.0373155
\(388\) 6.81066e15 1.99617
\(389\) 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
\(397\) −7.47778e15 −1.90998 −0.954992 0.296631i \(-0.904137\pi\)
−0.954992 + 0.296631i \(0.904137\pi\)
\(398\) 0 0
\(399\) −2.00160e15 −0.496068
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) −4.98248e15 −1.16310
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −4.62317e15 −0.987643 −0.493822 0.869563i \(-0.664400\pi\)
−0.493822 + 0.869563i \(0.664400\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 4.57973e15 0.936389
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 9.35018e15 1.77830
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 9.73694e15 1.74876 0.874380 0.485242i \(-0.161269\pi\)
0.874380 + 0.485242i \(0.161269\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.13690e16 1.87566
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −6.49984e15 −1.00000
\(433\) −1.10479e16 −1.67631 −0.838155 0.545433i \(-0.816365\pi\)
−0.838155 + 0.545433i \(0.816365\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 5.59762e15 0.814863
\(437\) 0 0
\(438\) 0 0
\(439\) −1.14518e16 −1.59988 −0.799939 0.600081i \(-0.795135\pi\)
−0.799939 + 0.600081i \(0.795135\pi\)
\(440\) 0 0
\(441\) 5.16644e15 0.702361
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 8.43916e15 1.10154
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 1.05486e16 1.30475
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 6.58715e15 0.762269
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.73580e16 1.90548 0.952738 0.303792i \(-0.0982527\pi\)
0.952738 + 0.303792i \(0.0982527\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.74475e16 −1.77112 −0.885558 0.464528i \(-0.846224\pi\)
−0.885558 + 0.464528i \(0.846224\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 2.04565e16 1.94696
\(469\) 2.31836e16 2.17843
\(470\) 0 0
\(471\) 1.47351e16 1.34967
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) −2.65600e16 −2.14465
\(482\) 0 0
\(483\) 0 0
\(484\) 1.28550e16 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) −1.56756e16 −1.17503 −0.587516 0.809212i \(-0.699894\pi\)
−0.587516 + 0.809212i \(0.699894\pi\)
\(488\) 0 0
\(489\) −2.12208e16 −1.55206
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −8.89508e15 −0.597392
\(497\) 0 0
\(498\) 0 0
\(499\) −3.05003e16 −1.97561 −0.987805 0.155694i \(-0.950239\pi\)
−0.987805 + 0.155694i \(0.950239\pi\)
\(500\) 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
\(507\) −4.73970e16 −2.79064
\(508\) −2.96118e16 −1.72299
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −1.60348e16 −0.900612
\(512\) 0 0
\(513\) −6.92978e15 −0.380203
\(514\) 0 0
\(515\) 0 0
\(516\) −7.04349e14 −0.0373155
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 2.10066e16 1.02647 0.513234 0.858249i \(-0.328447\pi\)
0.513234 + 0.858249i \(0.328447\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 2.19146e16 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 1.12463e16 0.496068
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.10933e16 −0.442465 −0.221232 0.975221i \(-0.571008\pi\)
−0.221232 + 0.975221i \(0.571008\pi\)
\(542\) 0 0
\(543\) 5.12589e16 1.99973
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −5.18204e16 −1.93454 −0.967268 0.253756i \(-0.918334\pi\)
−0.967268 + 0.253756i \(0.918334\pi\)
\(548\) 0 0
\(549\) 3.93606e16 1.43756
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −6.82017e16 −2.38476
\(554\) 0 0
\(555\) 0 0
\(556\) −5.25355e16 −1.77830
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 2.21675e15 0.0726517
\(560\) 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
\(567\) 4.33535e16 1.30475
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −4.00393e16 −1.15523 −0.577617 0.816308i \(-0.696017\pi\)
−0.577617 + 0.816308i \(0.696017\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 3.65203e16 1.00000
\(577\) 6.88267e16 1.86510 0.932550 0.361041i \(-0.117579\pi\)
0.932550 + 0.361041i \(0.117579\pi\)
\(578\) 0 0
\(579\) 4.89042e16 1.29800
\(580\) 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 \(\pi\)
\(588\) −2.90285e16 −0.702361
\(589\) −9.48345e15 −0.227130
\(590\) 0 0
\(591\) 0 0
\(592\) −4.74167e16 −1.10154
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.47072e15 −0.187100
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 8.59034e16 1.82290 0.911451 0.411409i \(-0.134963\pi\)
0.911451 + 0.411409i \(0.134963\pi\)
\(602\) 0 0
\(603\) 8.02642e16 1.66962
\(604\) −3.70109e16 −0.762269
\(605\) 0 0
\(606\) 0 0
\(607\) −2.98503e16 −0.596784 −0.298392 0.954443i \(-0.596450\pi\)
−0.298392 + 0.954443i \(0.596450\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 8.10661e16 1.52784 0.763918 0.645313i \(-0.223273\pi\)
0.763918 + 0.645313i \(0.223273\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −5.67203e16 −1.00831 −0.504155 0.863613i \(-0.668196\pi\)
−0.504155 + 0.863613i \(0.668196\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −1.14938e17 −1.94696
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) −8.27912e16 −1.34967
\(629\) 0 0
\(630\) 0 0
\(631\) 1.22658e17 1.94321 0.971605 0.236607i \(-0.0760353\pi\)
0.971605 + 0.236607i \(0.0760353\pi\)
\(632\) 0 0
\(633\) −9.70796e16 −1.50906
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 9.13593e16 1.36747
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 1.28207e16 0.181404 0.0907019 0.995878i \(-0.471089\pi\)
0.0907019 + 0.995878i \(0.471089\pi\)
\(644\) 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
\(651\) 5.93296e16 0.779445
\(652\) 1.19232e17 1.55206
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −5.55142e16 −0.690259
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −1.41822e17 −1.70033 −0.850166 0.526514i \(-0.823499\pi\)
−0.850166 + 0.526514i \(0.823499\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −7.76119e16 −0.865709
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.84856e17 1.98950 0.994748 0.102351i \(-0.0326366\pi\)
0.994748 + 0.102351i \(0.0326366\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 2.66307e17 2.79064
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 2.55237e17 2.60450
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 3.89360e16 0.380203
\(685\) 0 0
\(686\) 0 0
\(687\) 1.98174e17 1.88498
\(688\) 3.95750e15 0.0373155
\(689\) 0 0
\(690\) 0 0
\(691\) −5.64619e16 −0.518665 −0.259333 0.965788i \(-0.583503\pi\)
−0.259333 + 0.965788i \(0.583503\pi\)
\(692\) 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
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −5.05532e16 −0.418809
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 9.84742e16 0.775256 0.387628 0.921816i \(-0.373295\pi\)
0.387628 + 0.921816i \(0.373295\pi\)
\(710\) 0 0
\(711\) −2.36122e17 −1.82776
\(712\) 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
\(721\) 1.71630e17 1.22175
\(722\) 0 0
\(723\) −2.23952e17 −1.56792
\(724\) −2.88006e17 −1.99973
\(725\) 0 0
\(726\) 0 0
\(727\) −1.30178e17 −0.881722 −0.440861 0.897575i \(-0.645327\pi\)
−0.440861 + 0.897575i \(0.645327\pi\)
\(728\) 0 0
\(729\) 1.50095e17 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) −2.21154e17 −1.43756
\(733\) −4.69550e15 −0.0302732 −0.0151366 0.999885i \(-0.504818\pi\)
−0.0151366 + 0.999885i \(0.504818\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −2.94329e17 −1.80703 −0.903516 0.428554i \(-0.859023\pi\)
−0.903516 + 0.428554i \(0.859023\pi\)
\(740\) 0 0
\(741\) −1.22541e17 −0.740237
\(742\) 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
\(751\) −2.70526e17 −1.50789 −0.753945 0.656938i \(-0.771851\pi\)
−0.753945 + 0.656938i \(0.771851\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −2.43588e17 −1.30475
\(757\) −3.49823e17 −1.85897 −0.929487 0.368855i \(-0.879750\pi\)
−0.929487 + 0.368855i \(0.879750\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 2.09777e17 1.06319
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −2.05195e17 −1.00000
\(769\) 3.75466e17 1.81557 0.907785 0.419437i \(-0.137772\pi\)
0.907785 + 0.419437i \(0.137772\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.74776e17 −1.29800
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 3.16267e17 1.43723
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.63101e17 0.702361
\(785\) 0 0
\(786\) 0 0
\(787\) −3.50485e17 −1.47510 −0.737549 0.675294i \(-0.764017\pi\)
−0.737549 + 0.675294i \(0.764017\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6.96021e17 2.79887
\(794\) 0 0
\(795\) 0 0
\(796\) 4.75941e16 0.187100
\(797\) 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
\(804\) −4.50977e17 −1.66962
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) −3.35752e17 −1.18003 −0.590015 0.807392i \(-0.700878\pi\)
−0.590015 + 0.807392i \(0.700878\pi\)
\(812\) 0 0
\(813\) −5.39580e17 −1.86858
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 4.21927e15 0.0141875
\(818\) 0 0
\(819\) 7.66629e17 2.54028
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −3.10814e17 −1.00023 −0.500117 0.865958i \(-0.666710\pi\)
−0.500117 + 0.865958i \(0.666710\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 7.02704e16 0.216494 0.108247 0.994124i \(-0.465476\pi\)
0.108247 + 0.994124i \(0.465476\pi\)
\(830\) 0 0
\(831\) −1.55646e17 −0.472641
\(832\) 6.45797e17 1.94696
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 2.05406e17 0.597392
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 3.53815e17 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 5.45457e17 1.50906
\(845\) 0 0
\(846\) 0 0
\(847\) 4.81755e17 1.30475
\(848\) 0 0
\(849\) −6.06710e17 −1.62008
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −1.10659e17 −0.287273 −0.143636 0.989631i \(-0.545880\pi\)
−0.143636 + 0.989631i \(0.545880\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −7.20712e17 −1.79392 −0.896959 0.442113i \(-0.854229\pi\)
−0.896959 + 0.442113i \(0.854229\pi\)
\(860\) 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
\(867\) −4.24732e17 −1.00000
\(868\) −3.33353e17 −0.779445
\(869\) 0 0
\(870\) 0 0
\(871\) 1.41933e18 3.25068
\(872\) 0 0
\(873\) 8.83658e17 1.99617
\(874\) 0 0
\(875\) 0 0
\(876\) 3.11915e17 0.690259
\(877\) −4.49516e17 −0.987978 −0.493989 0.869468i \(-0.664462\pi\)
−0.493989 + 0.869468i \(0.664462\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 4.68587e16 0.0988613 0.0494306 0.998778i \(-0.484259\pi\)
0.0494306 + 0.998778i \(0.484259\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −1.10974e18 −2.24806
\(890\) 0 0
\(891\) 0 0
\(892\) 4.36075e17 0.865709
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) −2.63962e16 −0.0486873
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 8.44781e17 1.51740 0.758701 0.651439i \(-0.225835\pi\)
0.758701 + 0.651439i \(0.225835\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) −2.18768e17 −0.380203
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −1.11347e18 −1.88498
\(917\) 0 0
\(918\) 0 0
\(919\) 1.18130e18 1.96095 0.980476 0.196641i \(-0.0630033\pi\)
0.980476 + 0.196641i \(0.0630033\pi\)
\(920\) 0 0
\(921\) 1.01199e18 1.65813
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 5.94203e17 0.936389
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 1.73889e17 0.267039
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −7.08700e17 −1.04719 −0.523594 0.851968i \(-0.675409\pi\)
−0.523594 + 0.851968i \(0.675409\pi\)
\(938\) 0 0
\(939\) −2.69441e17 −0.393071
\(940\) 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 \(\pi\)
\(948\) 1.32669e18 1.82776
\(949\) −9.81669e17 −1.34390
\(950\) 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
\(961\) −5.06564e17 −0.643122
\(962\) 0 0
\(963\) 0 0
\(964\) 1.25831e18 1.56792
\(965\) 0 0
\(966\) 0 0
\(967\) 1.15427e18 1.41172 0.705861 0.708350i \(-0.250560\pi\)
0.705861 + 0.708350i \(0.250560\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −8.43330e17 −1.00000
\(973\) −1.96882e18 −2.32022
\(974\) 0 0
\(975\) 0 0
\(976\) 1.24259e18 1.43756
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 7.26271e17 0.814863
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 6.88514e17 0.740237
\(989\) 0 0
\(990\) 0 0
\(991\) −1.87606e18 −1.98064 −0.990318 0.138816i \(-0.955670\pi\)
−0.990318 + 0.138816i \(0.955670\pi\)
\(992\) 0 0
\(993\) −1.81410e18 −1.89219
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 6.50344e17 0.662174 0.331087 0.943600i \(-0.392585\pi\)
0.331087 + 0.943600i \(0.392585\pi\)
\(998\) 0 0
\(999\) 1.09495e18 1.10154
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 75.13.c.a.26.1 1
3.2 odd 2 CM 75.13.c.a.26.1 1
5.2 odd 4 75.13.d.a.74.2 2
5.3 odd 4 75.13.d.a.74.1 2
5.4 even 2 3.13.b.a.2.1 1
15.2 even 4 75.13.d.a.74.2 2
15.8 even 4 75.13.d.a.74.1 2
15.14 odd 2 3.13.b.a.2.1 1
20.19 odd 2 48.13.e.a.17.1 1
40.19 odd 2 192.13.e.b.65.1 1
40.29 even 2 192.13.e.a.65.1 1
45.4 even 6 81.13.d.a.26.1 2
45.14 odd 6 81.13.d.a.26.1 2
45.29 odd 6 81.13.d.a.53.1 2
45.34 even 6 81.13.d.a.53.1 2
60.59 even 2 48.13.e.a.17.1 1
120.29 odd 2 192.13.e.a.65.1 1
120.59 even 2 192.13.e.b.65.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.13.b.a.2.1 1 5.4 even 2
3.13.b.a.2.1 1 15.14 odd 2
48.13.e.a.17.1 1 20.19 odd 2
48.13.e.a.17.1 1 60.59 even 2
75.13.c.a.26.1 1 1.1 even 1 trivial
75.13.c.a.26.1 1 3.2 odd 2 CM
75.13.d.a.74.1 2 5.3 odd 4
75.13.d.a.74.1 2 15.8 even 4
75.13.d.a.74.2 2 5.2 odd 4
75.13.d.a.74.2 2 15.2 even 4
81.13.d.a.26.1 2 45.4 even 6
81.13.d.a.26.1 2 45.14 odd 6
81.13.d.a.53.1 2 45.29 odd 6
81.13.d.a.53.1 2 45.34 even 6
192.13.e.a.65.1 1 40.29 even 2
192.13.e.a.65.1 1 120.29 odd 2
192.13.e.b.65.1 1 40.19 odd 2
192.13.e.b.65.1 1 120.59 even 2