↑

Properties

Label 7.5.b.a.6.1
Level $7$
Weight $5$
Character 7.6
Self dual yes
Analytic conductor $0.724$
Analytic rank $0$
Dimension $1$
CM discriminant -7
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7,5,Mod(6,7)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7.6");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 7.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: \(0.723589741587\)
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 6.1
Character \(\chi\) \(=\) 7.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -15.0000 q^{4} +49.0000 q^{7} -31.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -15.0000 q^{4} +49.0000 q^{7} -31.0000 q^{8} +81.0000 q^{9} -206.000 q^{11} +49.0000 q^{14} +209.000 q^{16} +81.0000 q^{18} -206.000 q^{22} -734.000 q^{23} +625.000 q^{25} -735.000 q^{28} +1234.00 q^{29} +705.000 q^{32} -1215.00 q^{36} -1294.00 q^{37} -334.000 q^{43} +3090.00 q^{44} -734.000 q^{46} +2401.00 q^{49} +625.000 q^{50} -5582.00 q^{53} -1519.00 q^{56} +1234.00 q^{58} +3969.00 q^{63} -2639.00 q^{64} +4946.00 q^{67} +2914.00 q^{71} -2511.00 q^{72} -1294.00 q^{74} -10094.0 q^{77} -3646.00 q^{79} +6561.00 q^{81} -334.000 q^{86} +6386.00 q^{88} +11010.0 q^{92} +2401.00 q^{98} -16686.0 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.250000 0.125000 − 0.992157i \(-0.460107\pi\)
0.125000 + 0.992157i \(0.460107\pi\)
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) −15.0000 −0.937500
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) 49.0000 1.00000
\(8\) −31.0000 −0.484375
\(9\) 81.0000 1.00000
\(10\) 0 0
\(11\) −206.000 −1.70248 −0.851240 − 0.524777i \(-0.824149\pi\)
−0.851240 + 0.524777i \(0.824149\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 49.0000 0.250000
\(15\) 0 0
\(16\) 209.000 0.816406
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 81.0000 0.250000
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −206.000 −0.425620
\(23\) −734.000 −1.38752 −0.693762 − 0.720205i \(-0.744048\pi\)
−0.693762 + 0.720205i \(0.744048\pi\)
\(24\) 0 0
\(25\) 625.000 1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) −735.000 −0.937500
\(29\) 1234.00 1.46730 0.733650 − 0.679527i \(-0.237815\pi\)
0.733650 + 0.679527i \(0.237815\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 705.000 0.688477
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −1215.00 −0.937500
\(37\) −1294.00 −0.945215 −0.472608 − 0.881273i \(-0.656687\pi\)
−0.472608 + 0.881273i \(0.656687\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −334.000 −0.180638 −0.0903191 − 0.995913i \(-0.528789\pi\)
−0.0903191 + 0.995913i \(0.528789\pi\)
\(44\) 3090.00 1.59607
\(45\) 0 0
\(46\) −734.000 −0.346881
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 2401.00 1.00000
\(50\) 625.000 0.250000
\(51\) 0 0
\(52\) 0 0
\(53\) −5582.00 −1.98718 −0.993592 − 0.113026i \(-0.963946\pi\)
−0.993592 + 0.113026i \(0.963946\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1519.00 −0.484375
\(57\) 0 0
\(58\) 1234.00 0.366825
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 3969.00 1.00000
\(64\) −2639.00 −0.644287
\(65\) 0 0
\(66\) 0 0
\(67\) 4946.00 1.10180 0.550902 − 0.834570i \(-0.314284\pi\)
0.550902 + 0.834570i \(0.314284\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2914.00 0.578060 0.289030 − 0.957320i \(-0.406667\pi\)
0.289030 + 0.957320i \(0.406667\pi\)
\(72\) −2511.00 −0.484375
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) −1294.00 −0.236304
\(75\) 0 0
\(76\) 0 0
\(77\) −10094.0 −1.70248
\(78\) 0 0
\(79\) −3646.00 −0.584201 −0.292101 − 0.956388i \(-0.594354\pi\)
−0.292101 + 0.956388i \(0.594354\pi\)
\(80\) 0 0
\(81\) 6561.00 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −334.000 −0.0451595
\(87\) 0 0
\(88\) 6386.00 0.824638
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 11010.0 1.30080
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 2401.00 0.250000
\(99\) −16686.0 −1.70248
\(100\) −9375.00 −0.937500
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −5582.00 −0.496796
\(107\) 11698.0 1.02175 0.510874 − 0.859655i \(-0.329322\pi\)
0.510874 + 0.859655i \(0.329322\pi\)
\(108\) 0 0
\(109\) −12526.0 −1.05429 −0.527144 − 0.849776i \(-0.676737\pi\)
−0.527144 + 0.849776i \(0.676737\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 10241.0 0.816406
\(113\) 23746.0 1.85966 0.929830 − 0.367989i \(-0.119954\pi\)
0.929830 + 0.367989i \(0.119954\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −18510.0 −1.37559
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 27795.0 1.89844
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 3969.00 0.250000
\(127\) −32254.0 −1.99975 −0.999876 − 0.0157475i \(-0.994987\pi\)
−0.999876 + 0.0157475i \(0.994987\pi\)
\(128\) −13919.0 −0.849548
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4946.00 0.275451
\(135\) 0 0
\(136\) 0 0
\(137\) −7262.00 −0.386915 −0.193457 − 0.981109i \(-0.561970\pi\)
−0.193457 + 0.981109i \(0.561970\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2914.00 0.144515
\(143\) 0 0
\(144\) 16929.0 0.816406
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 19410.0 0.886140
\(149\) −9806.00 −0.441692 −0.220846 − 0.975309i \(-0.570882\pi\)
−0.220846 + 0.975309i \(0.570882\pi\)
\(150\) 0 0
\(151\) 29474.0 1.29266 0.646331 − 0.763057i \(-0.276302\pi\)
0.646331 + 0.763057i \(0.276302\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −10094.0 −0.425620
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) −3646.00 −0.146050
\(159\) 0 0
\(160\) 0 0
\(161\) −35966.0 −1.38752
\(162\) 6561.00 0.250000
\(163\) −47662.0 −1.79390 −0.896948 − 0.442137i \(-0.854221\pi\)
−0.896948 + 0.442137i \(0.854221\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 28561.0 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 5010.00 0.169348
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 30625.0 1.00000
\(176\) −43054.0 −1.38991
\(177\) 0 0
\(178\) 0 0
\(179\) 52882.0 1.65045 0.825224 − 0.564806i \(-0.191049\pi\)
0.825224 + 0.564806i \(0.191049\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 22754.0 0.672082
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 28162.0 0.771963 0.385982 − 0.922506i \(-0.373863\pi\)
0.385982 + 0.922506i \(0.373863\pi\)
\(192\) 0 0
\(193\) −70654.0 −1.89680 −0.948401 − 0.317073i \(-0.897300\pi\)
−0.948401 + 0.317073i \(0.897300\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −36015.0 −0.937500
\(197\) 1906.00 0.0491123 0.0245562 − 0.999698i \(-0.492183\pi\)
0.0245562 + 0.999698i \(0.492183\pi\)
\(198\) −16686.0 −0.425620
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −19375.0 −0.484375
\(201\) 0 0
\(202\) 0 0
\(203\) 60466.0 1.46730
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −59454.0 −1.38752
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −11758.0 −0.264100 −0.132050 − 0.991243i \(-0.542156\pi\)
−0.132050 + 0.991243i \(0.542156\pi\)
\(212\) 83730.0 1.86299
\(213\) 0 0
\(214\) 11698.0 0.255437
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −12526.0 −0.263572
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 34545.0 0.688477
\(225\) 50625.0 1.00000
\(226\) 23746.0 0.464915
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −38254.0 −0.710724
\(233\) −108254. −1.99403 −0.997016 − 0.0771956i \(-0.975403\pi\)
−0.997016 + 0.0771956i \(0.975403\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −64958.0 −1.13720 −0.568600 − 0.822614i \(-0.692515\pi\)
−0.568600 + 0.822614i \(0.692515\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 27795.0 0.474609
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −59535.0 −0.937500
\(253\) 151204. 2.36223
\(254\) −32254.0 −0.499938
\(255\) 0 0
\(256\) 28305.0 0.431900
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −63406.0 −0.945215
\(260\) 0 0
\(261\) 99954.0 1.46730
\(262\) 0 0
\(263\) 109666. 1.58548 0.792740 − 0.609561i \(-0.208654\pi\)
0.792740 + 0.609561i \(0.208654\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −74190.0 −1.03294
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −7262.00 −0.0967286
\(275\) −128750. −1.70248
\(276\) 0 0
\(277\) 52658.0 0.686285 0.343143 − 0.939283i \(-0.388509\pi\)
0.343143 + 0.939283i \(0.388509\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −144926. −1.83541 −0.917706 − 0.397260i \(-0.869961\pi\)
−0.917706 + 0.397260i \(0.869961\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) −43710.0 −0.541931
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 57105.0 0.688477
\(289\) 83521.0 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 40114.0 0.457839
\(297\) 0 0
\(298\) −9806.00 −0.110423
\(299\) 0 0
\(300\) 0 0
\(301\) −16366.0 −0.180638
\(302\) 29474.0 0.323166
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 151410. 1.59607
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 54690.0 0.547689
\(317\) 71506.0 0.711580 0.355790 − 0.934566i \(-0.384212\pi\)
0.355790 + 0.934566i \(0.384212\pi\)
\(318\) 0 0
\(319\) −254204. −2.49805
\(320\) 0 0
\(321\) 0 0
\(322\) −35966.0 −0.346881
\(323\) 0 0
\(324\) −98415.0 −0.937500
\(325\) 0 0
\(326\) −47662.0 −0.448474
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 182834. 1.66879 0.834394 − 0.551169i \(-0.185818\pi\)
0.834394 + 0.551169i \(0.185818\pi\)
\(332\) 0 0
\(333\) −104814. −0.945215
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −176062. −1.55026 −0.775132 − 0.631799i \(-0.782317\pi\)
−0.775132 + 0.631799i \(0.782317\pi\)
\(338\) 28561.0 0.250000
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 117649. 1.00000
\(344\) 10354.0 0.0874966
\(345\) 0 0
\(346\) 0 0
\(347\) 218866. 1.81769 0.908844 − 0.417136i \(-0.136966\pi\)
0.908844 + 0.417136i \(0.136966\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 30625.0 0.250000
\(351\) 0 0
\(352\) −145230. −1.17212
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 52882.0 0.412612
\(359\) 169954. 1.31869 0.659345 − 0.751841i \(-0.270834\pi\)
0.659345 + 0.751841i \(0.270834\pi\)
\(360\) 0 0
\(361\) 130321. 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) −153406. −1.13278
\(369\) 0 0
\(370\) 0 0
\(371\) −273518. −1.98718
\(372\) 0 0
\(373\) −209614. −1.50662 −0.753308 − 0.657668i \(-0.771543\pi\)
−0.753308 + 0.657668i \(0.771543\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 89714.0 0.624571 0.312285 − 0.949988i \(-0.398905\pi\)
0.312285 + 0.949988i \(0.398905\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 28162.0 0.192991
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −70654.0 −0.474201
\(387\) −27054.0 −0.180638
\(388\) 0 0
\(389\) 140914. 0.931226 0.465613 − 0.884989i \(-0.345834\pi\)
0.465613 + 0.884989i \(0.345834\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −74431.0 −0.484375
\(393\) 0 0
\(394\) 1906.00 0.0122781
\(395\) 0 0
\(396\) 250290. 1.59607
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 130625. 0.816406
\(401\) −196286. −1.22068 −0.610338 − 0.792141i \(-0.708966\pi\)
−0.610338 + 0.792141i \(0.708966\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 60466.0 0.366825
\(407\) 266564. 1.60921
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −59454.0 −0.346881
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −326926. −1.84453 −0.922264 − 0.386561i \(-0.873663\pi\)
−0.922264 + 0.386561i \(0.873663\pi\)
\(422\) −11758.0 −0.0660250
\(423\) 0 0
\(424\) 173042. 0.962542
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −175470. −0.957889
\(429\) 0 0
\(430\) 0 0
\(431\) −345278. −1.85872 −0.929361 − 0.369173i \(-0.879641\pi\)
−0.929361 + 0.369173i \(0.879641\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 187890. 0.988395
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 194481. 1.00000
\(442\) 0 0
\(443\) −156302. −0.796447 −0.398224 − 0.917288i \(-0.630373\pi\)
−0.398224 + 0.917288i \(0.630373\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −129311. −0.644287
\(449\) 396034. 1.96444 0.982222 − 0.187721i \(-0.0601102\pi\)
0.982222 + 0.187721i \(0.0601102\pi\)
\(450\) 50625.0 0.250000
\(451\) 0 0
\(452\) −356190. −1.74343
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 353186. 1.69111 0.845553 − 0.533891i \(-0.179271\pi\)
0.845553 + 0.533891i \(0.179271\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 25538.0 0.119131 0.0595655 − 0.998224i \(-0.481028\pi\)
0.0595655 + 0.998224i \(0.481028\pi\)
\(464\) 257906. 1.19791
\(465\) 0 0
\(466\) −108254. −0.498508
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 242354. 1.10180
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 68804.0 0.307533
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −452142. −1.98718
\(478\) −64958.0 −0.284300
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −416925. −1.77978
\(485\) 0 0
\(486\) 0 0
\(487\) −315934. −1.33210 −0.666052 − 0.745905i \(-0.732017\pi\)
−0.666052 + 0.745905i \(0.732017\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 427954. 1.77515 0.887573 − 0.460667i \(-0.152390\pi\)
0.887573 + 0.460667i \(0.152390\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 142786. 0.578060
\(498\) 0 0
\(499\) −409198. −1.64336 −0.821679 − 0.569950i \(-0.806963\pi\)
−0.821679 + 0.569950i \(0.806963\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) −123039. −0.484375
\(505\) 0 0
\(506\) 151204. 0.590558
\(507\) 0 0
\(508\) 483810. 1.87477
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 251009. 0.957523
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −63406.0 −0.236304
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 99954.0 0.366825
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 109666. 0.396370
\(527\) 0 0
\(528\) 0 0
\(529\) 258915. 0.925222
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −153326. −0.533687
\(537\) 0 0
\(538\) 0 0
\(539\) −494606. −1.70248
\(540\) 0 0
\(541\) −579886. −1.98129 −0.990645 − 0.136463i \(-0.956426\pi\)
−0.990645 + 0.136463i \(0.956426\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 110546. 0.369461 0.184730 − 0.982789i \(-0.440859\pi\)
0.184730 + 0.982789i \(0.440859\pi\)
\(548\) 108930. 0.362732
\(549\) 0 0
\(550\) −128750. −0.425620
\(551\) 0 0
\(552\) 0 0
\(553\) −178654. −0.584201
\(554\) 52658.0 0.171571
\(555\) 0 0
\(556\) 0 0
\(557\) 383506. 1.23612 0.618062 − 0.786130i \(-0.287918\pi\)
0.618062 + 0.786130i \(0.287918\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −144926. −0.458853
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 321489. 1.00000
\(568\) −90334.0 −0.279998
\(569\) −219806. −0.678914 −0.339457 − 0.940622i \(-0.610243\pi\)
−0.339457 + 0.940622i \(0.610243\pi\)
\(570\) 0 0
\(571\) 615794. 1.88870 0.944351 − 0.328941i \(-0.106692\pi\)
0.944351 + 0.328941i \(0.106692\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −458750. −1.38752
\(576\) −213759. −0.644287
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 83521.0 0.250000
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.14989e6 3.38314
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −270446. −0.771680
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 147090. 0.414086
\(597\) 0 0
\(598\) 0 0
\(599\) −687326. −1.91562 −0.957809 − 0.287404i \(-0.907208\pi\)
−0.957809 + 0.287404i \(0.907208\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) −16366.0 −0.0451595
\(603\) 400626. 1.10180
\(604\) −442110. −1.21187
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −704014. −1.87353 −0.936764 − 0.349961i \(-0.886195\pi\)
−0.936764 + 0.349961i \(0.886195\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 312914. 0.824638
\(617\) −450014. −1.18210 −0.591052 − 0.806633i \(-0.701287\pi\)
−0.591052 + 0.806633i \(0.701287\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 390625. 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 215714. 0.541776 0.270888 − 0.962611i \(-0.412683\pi\)
0.270888 + 0.962611i \(0.412683\pi\)
\(632\) 113026. 0.282972
\(633\) 0 0
\(634\) 71506.0 0.177895
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −254204. −0.624512
\(639\) 236034. 0.578060
\(640\) 0 0
\(641\) −126206. −0.307159 −0.153580 − 0.988136i \(-0.549080\pi\)
−0.153580 + 0.988136i \(0.549080\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 539490. 1.30080
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) −203391. −0.484375
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 714930. 1.68178
\(653\) 572818. 1.34335 0.671677 − 0.740844i \(-0.265574\pi\)
0.671677 + 0.740844i \(0.265574\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −486638. −1.12056 −0.560280 − 0.828303i \(-0.689307\pi\)
−0.560280 + 0.828303i \(0.689307\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 182834. 0.417197
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −104814. −0.236304
\(667\) −905756. −2.03591
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −706942. −1.56082 −0.780411 − 0.625266i \(-0.784990\pi\)
−0.780411 + 0.625266i \(0.784990\pi\)
\(674\) −176062. −0.387566
\(675\) 0 0
\(676\) −428415. −0.937500
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 857266. 1.83770 0.918849 − 0.394609i \(-0.129120\pi\)
0.918849 + 0.394609i \(0.129120\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 117649. 0.250000
\(687\) 0 0
\(688\) −69806.0 −0.147474
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) −817614. −1.70248
\(694\) 218866. 0.454422
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −459375. −0.937500
\(701\) 971602. 1.97721 0.988604 − 0.150539i \(-0.0481010\pi\)
0.988604 + 0.150539i \(0.0481010\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 543634. 1.09689
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 904562. 1.79948 0.899738 − 0.436431i \(-0.143758\pi\)
0.899738 + 0.436431i \(0.143758\pi\)
\(710\) 0 0
\(711\) −295326. −0.584201
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −793230. −1.54729
\(717\) 0 0
\(718\) 169954. 0.329672
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 130321. 0.250000
\(723\) 0 0
\(724\) 0 0
\(725\) 771250. 1.46730
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 531441. 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −517470. −0.955277
\(737\) −1.01888e6 −1.87580
\(738\) 0 0
\(739\) 410834. 0.752277 0.376138 − 0.926564i \(-0.377252\pi\)
0.376138 + 0.926564i \(0.377252\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −273518. −0.496796
\(743\) −1.09110e6 −1.97646 −0.988229 − 0.152980i \(-0.951113\pi\)
−0.988229 + 0.152980i \(0.951113\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −209614. −0.376654
\(747\) 0 0
\(748\) 0 0
\(749\) 573202. 1.02175
\(750\) 0 0
\(751\) −484798. −0.859569 −0.429785 − 0.902931i \(-0.641411\pi\)
−0.429785 + 0.902931i \(0.641411\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 819506. 1.43008 0.715040 − 0.699083i \(-0.246408\pi\)
0.715040 + 0.699083i \(0.246408\pi\)
\(758\) 89714.0 0.156143
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) −613774. −1.05429
\(764\) −422430. −0.723716
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.05981e6 1.77825
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −27054.0 −0.0451595
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 140914. 0.232806
\(779\) 0 0
\(780\) 0 0
\(781\) −600284. −0.984135
\(782\) 0 0
\(783\) 0 0
\(784\) 501809. 0.816406
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) −28590.0 −0.0460428
\(789\) 0 0
\(790\) 0 0
\(791\) 1.16355e6 1.85966
\(792\) 517266. 0.824638
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 440625. 0.688477
\(801\) 0 0
\(802\) −196286. −0.305169
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.27869e6 −1.95374 −0.976870 − 0.213833i \(-0.931405\pi\)
−0.976870 + 0.213833i \(0.931405\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −906990. −1.37559
\(813\) 0 0
\(814\) 266564. 0.402302
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −7118.00 −0.0105602 −0.00528009 − 0.999986i \(-0.501681\pi\)
−0.00528009 + 0.999986i \(0.501681\pi\)
\(822\) 0 0
\(823\) −967774. −1.42881 −0.714405 − 0.699733i \(-0.753302\pi\)
−0.714405 + 0.699733i \(0.753302\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.28833e6 −1.88372 −0.941862 − 0.335999i \(-0.890926\pi\)
−0.941862 + 0.335999i \(0.890926\pi\)
\(828\) 891810. 1.30080
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 815475. 1.15297
\(842\) −326926. −0.461132
\(843\) 0 0
\(844\) 176370. 0.247594
\(845\) 0 0
\(846\) 0 0
\(847\) 1.36196e6 1.89844
\(848\) −1.16664e6 −1.62235
\(849\) 0 0
\(850\) 0 0
\(851\) 949796. 1.31151
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −362638. −0.494909
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −345278. −0.464680
\(863\) 1.27271e6 1.70886 0.854430 − 0.519566i \(-0.173907\pi\)
0.854430 + 0.519566i \(0.173907\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 751076. 0.994591
\(870\) 0 0
\(871\) 0 0
\(872\) 388306. 0.510671
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −981742. −1.27643 −0.638217 − 0.769857i \(-0.720328\pi\)
−0.638217 + 0.769857i \(0.720328\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 194481. 0.250000
\(883\) 1.07151e6 1.37427 0.687137 − 0.726528i \(-0.258867\pi\)
0.687137 + 0.726528i \(0.258867\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −156302. −0.199112
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −1.58045e6 −1.99975
\(890\) 0 0
\(891\) −1.35157e6 −1.70248
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −682031. −0.849548
\(897\) 0 0
\(898\) 396034. 0.491111
\(899\) 0 0
\(900\) −759375. −0.937500
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −736126. −0.900773
\(905\) 0 0
\(906\) 0 0
\(907\) 1.54450e6 1.87747 0.938735 − 0.344641i \(-0.111999\pi\)
0.938735 + 0.344641i \(0.111999\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 792514. 0.954927 0.477464 − 0.878652i \(-0.341556\pi\)
0.477464 + 0.878652i \(0.341556\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 353186. 0.422777
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −1.47197e6 −1.74288 −0.871439 − 0.490505i \(-0.836812\pi\)
−0.871439 + 0.490505i \(0.836812\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −808750. −0.945215
\(926\) 25538.0 0.0297828
\(927\) 0 0
\(928\) 869970. 1.01020
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 1.62381e6 1.86940
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 242354. 0.275451
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 68804.0 0.0768832
\(947\) 438418. 0.488864 0.244432 − 0.969666i \(-0.421398\pi\)
0.244432 + 0.969666i \(0.421398\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 309346. 0.340611 0.170306 − 0.985391i \(-0.445525\pi\)
0.170306 + 0.985391i \(0.445525\pi\)
\(954\) −452142. −0.496796
\(955\) 0 0
\(956\) 974370. 1.06612
\(957\) 0 0
\(958\) 0 0
\(959\) −355838. −0.386915
\(960\) 0 0
\(961\) 923521. 1.00000
\(962\) 0 0
\(963\) 947538. 1.02175
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −1.75862e6 −1.88070 −0.940350 − 0.340208i \(-0.889502\pi\)
−0.940350 + 0.340208i \(0.889502\pi\)
\(968\) −861645. −0.919555
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −315934. −0.333026
\(975\) 0 0
\(976\) 0 0
\(977\) −1.88281e6 −1.97251 −0.986253 − 0.165243i \(-0.947159\pi\)
−0.986253 + 0.165243i \(0.947159\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −1.01461e6 −1.05429
\(982\) 427954. 0.443787
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 245156. 0.250640
\(990\) 0 0
\(991\) 12674.0 0.0129052 0.00645262 − 0.999979i \(-0.497946\pi\)
0.00645262 + 0.999979i \(0.497946\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 142786. 0.144515
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) −409198. −0.410840
\(999\) 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 7.5.b.a.6.1 ✓ 1
3.2 odd 2 63.5.d.a.55.1 1
4.3 odd 2 112.5.c.a.97.1 1
5.2 odd 4 175.5.c.a.174.2 2
5.3 odd 4 175.5.c.a.174.1 2
5.4 even 2 175.5.d.a.76.1 1
7.2 even 3 49.5.d.a.31.1 2
7.3 odd 6 49.5.d.a.19.1 2
7.4 even 3 49.5.d.a.19.1 2
7.5 odd 6 49.5.d.a.31.1 2
7.6 odd 2 CM 7.5.b.a.6.1 ✓ 1
8.3 odd 2 448.5.c.a.321.1 1
8.5 even 2 448.5.c.b.321.1 1
12.11 even 2 1008.5.f.a.433.1 1
21.20 even 2 63.5.d.a.55.1 1
28.27 even 2 112.5.c.a.97.1 1
35.13 even 4 175.5.c.a.174.1 2
35.27 even 4 175.5.c.a.174.2 2
35.34 odd 2 175.5.d.a.76.1 1
56.13 odd 2 448.5.c.b.321.1 1
56.27 even 2 448.5.c.a.321.1 1
84.83 odd 2 1008.5.f.a.433.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.5.b.a.6.1 ✓ 1 1.1 even 1 trivial
7.5.b.a.6.1 ✓ 1 7.6 odd 2 CM
49.5.d.a.19.1 2 7.3 odd 6
49.5.d.a.19.1 2 7.4 even 3
49.5.d.a.31.1 2 7.2 even 3
49.5.d.a.31.1 2 7.5 odd 6
63.5.d.a.55.1 1 3.2 odd 2
63.5.d.a.55.1 1 21.20 even 2
112.5.c.a.97.1 1 4.3 odd 2
112.5.c.a.97.1 1 28.27 even 2
175.5.c.a.174.1 2 5.3 odd 4
175.5.c.a.174.1 2 35.13 even 4
175.5.c.a.174.2 2 5.2 odd 4
175.5.c.a.174.2 2 35.27 even 4
175.5.d.a.76.1 1 5.4 even 2
175.5.d.a.76.1 1 35.34 odd 2
448.5.c.a.321.1 1 8.3 odd 2
448.5.c.a.321.1 1 56.27 even 2
448.5.c.b.321.1 1 8.5 even 2
448.5.c.b.321.1 1 56.13 odd 2
1008.5.f.a.433.1 1 12.11 even 2
1008.5.f.a.433.1 1 84.83 odd 2