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Properties

Label 4900.2.a.bj.1.4
Level $4900$
Weight $2$
Character 4900.1
Self dual yes
Analytic conductor $39.127$
Analytic rank $0$
Dimension $4$
CM discriminant -35
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4900,2,Mod(1,4900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4900, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4900.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4900.a (trivial)

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: \(39.1266969904\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{5}, \sqrt{21})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 13x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 980)
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

Embedding label 1.4
Root \(3.40932\) of defining polynomial
Character \(\chi\) \(=\) 4900.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.40932 q^{3} +8.62348 q^{9} +O(q^{10})\) \(q+3.40932 q^{3} +8.62348 q^{9} -3.62348 q^{11} -1.06281 q^{13} +5.75583 q^{17} +19.1722 q^{27} +9.62348 q^{29} -12.3536 q^{33} -3.62348 q^{39} -1.28369 q^{47} +19.6235 q^{51} -12.0000 q^{71} +13.4164 q^{73} -14.8704 q^{79} +39.4939 q^{81} -8.94427 q^{83} +32.8095 q^{87} +19.3931 q^{97} -31.2470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 14 q^{9} + 6 q^{11} + 18 q^{29} + 6 q^{39} + 58 q^{51} - 48 q^{71} + 2 q^{79} + 76 q^{81} - 84 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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
\(3\) 3.40932 1.96837 0.984186 − 0.177136i \(-0.0566831\pi\)
0.984186 + 0.177136i \(0.0566831\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 8.62348 2.87449
\(10\) 0 0
\(11\) −3.62348 −1.09252 −0.546259 − 0.837616i \(-0.683949\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0 0
\(13\) −1.06281 −0.294772 −0.147386 − 0.989079i \(-0.547086\pi\)
−0.147386 + 0.989079i \(0.547086\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.75583 1.39599 0.697997 − 0.716101i \(-0.254075\pi\)
0.697997 + 0.716101i \(0.254075\pi\)
\(18\) 0 0
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 19.1722 3.68970
\(28\) 0 0
\(29\) 9.62348 1.78703 0.893517 − 0.449029i \(-0.148230\pi\)
0.893517 + 0.449029i \(0.148230\pi\)
\(30\) 0 0
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) −12.3536 −2.15048
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) −3.62348 −0.580220
\(40\) 0 0
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.28369 −0.187246 −0.0936230 − 0.995608i \(-0.529845\pi\)
−0.0936230 + 0.995608i \(0.529845\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 19.6235 2.74784
\(52\) 0 0
\(53\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 − 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 13.4164 1.57027 0.785136 − 0.619324i \(-0.212593\pi\)
0.785136 + 0.619324i \(0.212593\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −14.8704 −1.67305 −0.836527 − 0.547926i \(-0.815418\pi\)
−0.836527 + 0.547926i \(0.815418\pi\)
\(80\) 0 0
\(81\) 39.4939 4.38821
\(82\) 0 0
\(83\) −8.94427 −0.981761 −0.490881 − 0.871227i \(-0.663325\pi\)
−0.490881 + 0.871227i \(0.663325\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 32.8095 3.51755
\(88\) 0 0
\(89\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 19.3931 1.96907 0.984536 − 0.175180i \(-0.0560509\pi\)
0.984536 + 0.175180i \(0.0560509\pi\)
\(98\) 0 0
\(99\) −31.2470 −3.14044
\(100\) 0 0
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 12.3536 1.21724 0.608618 − 0.793463i \(-0.291724\pi\)
0.608618 + 0.793463i \(0.291724\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 20.8704 1.99902 0.999512 − 0.0312328i \(-0.00994332\pi\)
0.999512 + 0.0312328i \(0.00994332\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −9.16515 −0.847319
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 2.12957 0.193598
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 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
\(137\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −4.37652 −0.368570
\(142\) 0 0
\(143\) 3.85108 0.322044
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 6.00000 0.491539 0.245770 − 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) −6.87043 −0.559107 −0.279554 − 0.960130i \(-0.590186\pi\)
−0.279554 + 0.960130i \(0.590186\pi\)
\(152\) 0 0
\(153\) 49.6353 4.01277
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −13.4164 −1.07075 −0.535373 − 0.844616i \(-0.679829\pi\)
−0.535373 + 0.844616i \(0.679829\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 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
\(167\) −19.1722 −1.48359 −0.741796 − 0.670625i \(-0.766026\pi\)
−0.741796 + 0.670625i \(0.766026\pi\)
\(168\) 0 0
\(169\) −11.8704 −0.913110
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −26.2118 −1.99284 −0.996422 − 0.0845218i \(-0.973064\pi\)
−0.996422 + 0.0845218i \(0.973064\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 24.0000 1.79384 0.896922 − 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 0 0
\(181\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −20.8561 −1.52515
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.37652 0.606104 0.303052 − 0.952974i \(-0.401994\pi\)
0.303052 + 0.952974i \(0.401994\pi\)
\(192\) 0 0
\(193\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −26.8704 −1.84984 −0.924918 − 0.380166i \(-0.875867\pi\)
−0.924918 + 0.380166i \(0.875867\pi\)
\(212\) 0 0
\(213\) −40.9119 −2.80323
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 45.7409 3.09088
\(220\) 0 0
\(221\) −6.11738 −0.411499
\(222\) 0 0
\(223\) −28.5583 −1.91240 −0.956202 − 0.292709i \(-0.905443\pi\)
−0.956202 + 0.292709i \(0.905443\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.66058 0.508450 0.254225 − 0.967145i \(-0.418180\pi\)
0.254225 + 0.967145i \(0.418180\pi\)
\(228\) 0 0
\(229\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −50.6981 −3.29319
\(238\) 0 0
\(239\) 30.1174 1.94813 0.974066 − 0.226266i \(-0.0726518\pi\)
0.974066 + 0.226266i \(0.0726518\pi\)
\(240\) 0 0
\(241\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) 77.1307 4.94794
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −30.4939 −1.93247
\(250\) 0 0
\(251\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.47214 0.278964 0.139482 − 0.990225i \(-0.455456\pi\)
0.139482 + 0.990225i \(0.455456\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 82.9878 5.13682
\(262\) 0 0
\(263\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 21.6235 1.28995 0.644974 − 0.764204i \(-0.276868\pi\)
0.644974 + 0.764204i \(0.276868\pi\)
\(282\) 0 0
\(283\) 14.4792 0.860700 0.430350 − 0.902662i \(-0.358390\pi\)
0.430350 + 0.902662i \(0.358390\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 16.1296 0.948798
\(290\) 0 0
\(291\) 66.1174 3.87587
\(292\) 0 0
\(293\) −8.32322 −0.486248 −0.243124 − 0.969995i \(-0.578172\pi\)
−0.243124 + 0.969995i \(0.578172\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −69.4701 −4.03107
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −26.4326 −1.50859 −0.754295 − 0.656535i \(-0.772021\pi\)
−0.754295 + 0.656535i \(0.772021\pi\)
\(308\) 0 0
\(309\) 42.1174 2.39597
\(310\) 0 0
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −15.1419 −0.855869 −0.427934 − 0.903810i \(-0.640759\pi\)
−0.427934 + 0.903810i \(0.640759\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) −34.8704 −1.95237
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 71.1540 3.93483
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 − 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) −20.3765 −1.08762
\(352\) 0 0
\(353\) −35.1560 −1.87117 −0.935583 − 0.353106i \(-0.885126\pi\)
−0.935583 + 0.353106i \(0.885126\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −36.0000 −1.90001 −0.950004 − 0.312239i \(-0.898921\pi\)
−0.950004 + 0.312239i \(0.898921\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) 7.26040 0.381072
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −32.8095 −1.71264 −0.856322 − 0.516443i \(-0.827256\pi\)
−0.856322 + 0.516443i \(0.827256\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −10.2280 −0.526767
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 − 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −35.7771 −1.82812 −0.914062 − 0.405575i \(-0.867071\pi\)
−0.914062 + 0.405575i \(0.867071\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 14.3765 0.728919 0.364459 − 0.931219i \(-0.381254\pi\)
0.364459 + 0.931219i \(0.381254\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −39.8490 −1.99997 −0.999983 − 0.00579782i \(-0.998154\pi\)
−0.999983 + 0.00579782i \(0.998154\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12.1174 −0.605113 −0.302556 − 0.953131i \(-0.597840\pi\)
−0.302556 + 0.953131i \(0.597840\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −3.12957 −0.152526 −0.0762630 − 0.997088i \(-0.524299\pi\)
−0.0762630 + 0.997088i \(0.524299\pi\)
\(422\) 0 0
\(423\) −11.0699 −0.538237
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 13.1296 0.633902
\(430\) 0 0
\(431\) 37.3643 1.79978 0.899888 − 0.436121i \(-0.143648\pi\)
0.899888 + 0.436121i \(0.143648\pi\)
\(432\) 0 0
\(433\) −40.2492 −1.93425 −0.967127 − 0.254293i \(-0.918157\pi\)
−0.967127 + 0.254293i \(0.918157\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 20.4559 0.967532
\(448\) 0 0
\(449\) −31.3643 −1.48017 −0.740087 − 0.672511i \(-0.765216\pi\)
−0.740087 + 0.672511i \(0.765216\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −23.4235 −1.10053
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 110.352 5.15080
\(460\) 0 0
\(461\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 28.1165 1.30108 0.650538 − 0.759473i \(-0.274543\pi\)
0.650538 + 0.759473i \(0.274543\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −45.7409 −2.10763
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 42.1174 1.90073 0.950365 − 0.311136i \(-0.100710\pi\)
0.950365 + 0.311136i \(0.100710\pi\)
\(492\) 0 0
\(493\) 55.3911 2.49469
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −5.12957 −0.229631 −0.114816 − 0.993387i \(-0.536628\pi\)
−0.114816 + 0.993387i \(0.536628\pi\)
\(500\) 0 0
\(501\) −65.3643 −2.92026
\(502\) 0 0
\(503\) −39.6282 −1.76693 −0.883466 − 0.468495i \(-0.844797\pi\)
−0.883466 + 0.468495i \(0.844797\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −40.4701 −1.79734
\(508\) 0 0
\(509\) 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
\(516\) 0 0
\(517\) 4.65143 0.204570
\(518\) 0 0
\(519\) −89.3643 −3.92266
\(520\) 0 0
\(521\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 26.8328 1.17332 0.586659 − 0.809834i \(-0.300443\pi\)
0.586659 + 0.809834i \(0.300443\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 81.8237 3.53095
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −36.8704 −1.58518 −0.792592 − 0.609753i \(-0.791269\pi\)
−0.792592 + 0.609753i \(0.791269\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −71.1052 −3.00206
\(562\) 0 0
\(563\) 44.7214 1.88478 0.942390 − 0.334515i \(-0.108573\pi\)
0.942390 + 0.334515i \(0.108573\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6.00000 0.251533 0.125767 − 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) 32.0000 1.33916 0.669579 − 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 0 0
\(573\) 28.5583 1.19304
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 13.0162 0.541873 0.270936 − 0.962597i \(-0.412667\pi\)
0.270936 + 0.962597i \(0.412667\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.94427 0.369170 0.184585 − 0.982817i \(-0.440906\pi\)
0.184585 + 0.982817i \(0.440906\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.621055 −0.0255037 −0.0127518 − 0.999919i \(-0.504059\pi\)
−0.0127518 + 0.999919i \(0.504059\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.11738 −0.249949 −0.124975 − 0.992160i \(-0.539885\pi\)
−0.124975 + 0.992160i \(0.539885\pi\)
\(600\) 0 0
\(601\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −49.0142 −1.98942 −0.994712 − 0.102699i \(-0.967252\pi\)
−0.994712 + 0.102699i \(0.967252\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.36433 0.0551948
\(612\) 0 0
\(613\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 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 \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 38.8704 1.54741 0.773704 − 0.633548i \(-0.218402\pi\)
0.773704 + 0.633548i \(0.218402\pi\)
\(632\) 0 0
\(633\) −91.6099 −3.64117
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −103.482 −4.09367
\(640\) 0 0
\(641\) 18.0000 0.710957 0.355479 − 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 0 0
\(643\) −46.8886 −1.84910 −0.924552 − 0.381055i \(-0.875561\pi\)
−0.924552 + 0.381055i \(0.875561\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.8885 0.703271 0.351636 − 0.936137i \(-0.385626\pi\)
0.351636 + 0.936137i \(0.385626\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 115.696 4.51373
\(658\) 0 0
\(659\) 20.3765 0.793757 0.396878 − 0.917871i \(-0.370093\pi\)
0.396878 + 0.917871i \(0.370093\pi\)
\(660\) 0 0
\(661\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) −20.8561 −0.809984
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −97.3643 −3.76432
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −32.5886 −1.25248 −0.626242 − 0.779629i \(-0.715408\pi\)
−0.626242 + 0.779629i \(0.715408\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 26.1174 1.00082
\(682\) 0 0
\(683\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 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
\(701\) −19.3643 −0.731381 −0.365690 − 0.930737i \(-0.619167\pi\)
−0.365690 + 0.930737i \(0.619167\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 46.6113 1.75052 0.875262 − 0.483650i \(-0.160689\pi\)
0.875262 + 0.483650i \(0.160689\pi\)
\(710\) 0 0
\(711\) −128.235 −4.80918
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 102.680 3.83465
\(718\) 0 0
\(719\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −53.6656 −1.99035 −0.995174 − 0.0981255i \(-0.968715\pi\)
−0.995174 + 0.0981255i \(0.968715\pi\)
\(728\) 0 0
\(729\) 144.482 5.35117
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −33.4722 −1.23632 −0.618161 − 0.786051i \(-0.712122\pi\)
−0.618161 + 0.786051i \(0.712122\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −40.6113 −1.49391 −0.746955 − 0.664875i \(-0.768485\pi\)
−0.746955 + 0.664875i \(0.768485\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −77.1307 −2.82207
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 52.6113 1.91981 0.959906 − 0.280321i \(-0.0904408\pi\)
0.959906 + 0.280321i \(0.0904408\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 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
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 15.2470 0.549106
\(772\) 0 0
\(773\) 49.2351 1.77086 0.885431 − 0.464770i \(-0.153863\pi\)
0.885431 + 0.464770i \(0.153863\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 43.4817 1.55590
\(782\) 0 0
\(783\) 184.504 6.59362
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 22.1814 0.790681 0.395340 − 0.918535i \(-0.370627\pi\)
0.395340 + 0.918535i \(0.370627\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −21.0770 −0.746585 −0.373293 − 0.927714i \(-0.621771\pi\)
−0.373293 + 0.927714i \(0.621771\pi\)
\(798\) 0 0
\(799\) −7.38872 −0.261394
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −48.6140 −1.71555
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 55.3643 1.94651 0.973253 − 0.229736i \(-0.0737862\pi\)
0.973253 + 0.229736i \(0.0737862\pi\)
\(810\) 0 0
\(811\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −33.6235 −1.17347 −0.586734 − 0.809780i \(-0.699586\pi\)
−0.586734 + 0.809780i \(0.699586\pi\)
\(822\) 0 0
\(823\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 63.6113 2.19349
\(842\) 0 0
\(843\) 73.7214 2.53910
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 49.3643 1.69418
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −40.2492 −1.37811 −0.689054 − 0.724710i \(-0.741974\pi\)
−0.689054 + 0.724710i \(0.741974\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 49.1935 1.68042 0.840209 − 0.542263i \(-0.182432\pi\)
0.840209 + 0.542263i \(0.182432\pi\)
\(858\) 0 0
\(859\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 54.9909 1.86759
\(868\) 0 0
\(869\) 53.8826 1.82784
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 167.236 5.66008
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) −28.3765 −0.957116
\(880\) 0 0
\(881\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 35.7771 1.20128 0.600639 − 0.799521i \(-0.294913\pi\)
0.600639 + 0.799521i \(0.294913\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −143.105 −4.79420
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −12.0000 −0.397578 −0.198789 − 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) 0 0
\(913\) 32.4093 1.07259
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 60.6113 1.99938 0.999691 − 0.0248659i \(-0.00791589\pi\)
0.999691 + 0.0248659i \(0.00791589\pi\)
\(920\) 0 0
\(921\) −90.1174 −2.96947
\(922\) 0 0
\(923\) 12.7538 0.419795
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 106.531 3.49893
\(928\) 0 0
\(929\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 56.0537 1.83120 0.915598 − 0.402096i \(-0.131718\pi\)
0.915598 + 0.402096i \(0.131718\pi\)
\(938\) 0 0
\(939\) −51.6235 −1.68467
\(940\) 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
\(947\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) −14.2591 −0.462872
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −118.885 −3.84299
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 179.976 5.74618
\(982\) 0 0
\(983\) −62.6515 −1.99827 −0.999136 − 0.0415592i \(-0.986767\pi\)
−0.999136 + 0.0415592i \(0.986767\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −52.0000 −1.65183 −0.825917 − 0.563791i \(-0.809342\pi\)
−0.825917 + 0.563791i \(0.809342\pi\)
\(992\) 0 0
\(993\) 27.2746 0.865532
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 46.2259 1.46399 0.731995 − 0.681310i \(-0.238589\pi\)
0.731995 + 0.681310i \(0.238589\pi\)
\(998\) 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 4900.2.a.bj.1.4 4
5.2 odd 4 980.2.e.d.589.1 ✓ 4
5.3 odd 4 980.2.e.d.589.4 yes 4
5.4 even 2 inner 4900.2.a.bj.1.1 4
7.6 odd 2 inner 4900.2.a.bj.1.1 4
35.2 odd 12 980.2.q.i.949.4 8
35.3 even 12 980.2.q.i.569.1 8
35.12 even 12 980.2.q.i.949.1 8
35.13 even 4 980.2.e.d.589.1 ✓ 4
35.17 even 12 980.2.q.i.569.4 8
35.18 odd 12 980.2.q.i.569.4 8
35.23 odd 12 980.2.q.i.949.1 8
35.27 even 4 980.2.e.d.589.4 yes 4
35.32 odd 12 980.2.q.i.569.1 8
35.33 even 12 980.2.q.i.949.4 8
35.34 odd 2 CM 4900.2.a.bj.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
980.2.e.d.589.1 ✓ 4 5.2 odd 4
980.2.e.d.589.1 ✓ 4 35.13 even 4
980.2.e.d.589.4 yes 4 5.3 odd 4
980.2.e.d.589.4 yes 4 35.27 even 4
980.2.q.i.569.1 8 35.3 even 12
980.2.q.i.569.1 8 35.32 odd 12
980.2.q.i.569.4 8 35.17 even 12
980.2.q.i.569.4 8 35.18 odd 12
980.2.q.i.949.1 8 35.12 even 12
980.2.q.i.949.1 8 35.23 odd 12
980.2.q.i.949.4 8 35.2 odd 12
980.2.q.i.949.4 8 35.33 even 12
4900.2.a.bj.1.1 4 5.4 even 2 inner
4900.2.a.bj.1.1 4 7.6 odd 2 inner
4900.2.a.bj.1.4 4 1.1 even 1 trivial
4900.2.a.bj.1.4 4 35.34 odd 2 CM