Properties

Label 63.4.c.a.62.4
Level $63$
Weight $4$
Character 63.62
Analytic conductor $3.717$
Analytic rank $0$
Dimension $4$
CM discriminant -7
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{7})\)
Defining polynomial: \(x^{4} + 8 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 62.4
Root \(1.16372i\) of defining polynomial
Character \(\chi\) \(=\) 63.62
Dual form 63.4.c.a.62.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.40636i q^{2} -21.2288 q^{4} -18.5203 q^{7} -71.5195i q^{8} +O(q^{10})\) \(q+5.40636i q^{2} -21.2288 q^{4} -18.5203 q^{7} -71.5195i q^{8} +66.7915i q^{11} -100.127i q^{14} +216.830 q^{16} -361.099 q^{22} +125.124i q^{23} -125.000 q^{25} +393.162 q^{28} +69.7031i q^{29} +600.106i q^{32} +10.5830 q^{37} +534.442 q^{43} -1417.90i q^{44} -676.464 q^{46} +343.000 q^{49} -675.795i q^{50} +65.4772i q^{53} +1324.56i q^{56} -376.840 q^{58} -1509.75 q^{64} +740.000 q^{67} +205.717i q^{71} +57.2156i q^{74} -1237.00i q^{77} -1384.00 q^{79} +2889.39i q^{86} +4776.90 q^{88} -2656.22i q^{92} +1854.38i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 32q^{4} + O(q^{10}) \) \( 4q - 32q^{4} + 444q^{16} - 820q^{22} - 500q^{25} + 980q^{28} - 748q^{46} + 1372q^{49} + 260q^{58} - 3552q^{64} + 2960q^{67} - 5536q^{79} + 8260q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.40636i 1.91144i 0.294281 + 0.955719i \(0.404920\pi\)
−0.294281 + 0.955719i \(0.595080\pi\)
\(3\) 0 0
\(4\) −21.2288 −2.65359
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) −18.5203 −1.00000
\(8\) − 71.5195i − 3.16074i
\(9\) 0 0
\(10\) 0 0
\(11\) 66.7915i 1.83076i 0.402586 + 0.915382i \(0.368111\pi\)
−0.402586 + 0.915382i \(0.631889\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) − 100.127i − 1.91144i
\(15\) 0 0
\(16\) 216.830 3.38797
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −361.099 −3.49939
\(23\) 125.124i 1.13435i 0.823597 + 0.567176i \(0.191964\pi\)
−0.823597 + 0.567176i \(0.808036\pi\)
\(24\) 0 0
\(25\) −125.000 −1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) 393.162 2.65359
\(29\) 69.7031i 0.446329i 0.974781 + 0.223165i \(0.0716388\pi\)
−0.974781 + 0.223165i \(0.928361\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 600.106i 3.31515i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.5830 0.0470226 0.0235113 0.999724i \(-0.492515\pi\)
0.0235113 + 0.999724i \(0.492515\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 534.442 1.89539 0.947693 0.319183i \(-0.103408\pi\)
0.947693 + 0.319183i \(0.103408\pi\)
\(44\) − 1417.90i − 4.85811i
\(45\) 0 0
\(46\) −676.464 −2.16824
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 343.000 1.00000
\(50\) − 675.795i − 1.91144i
\(51\) 0 0
\(52\) 0 0
\(53\) 65.4772i 0.169698i 0.996394 + 0.0848489i \(0.0270408\pi\)
−0.996394 + 0.0848489i \(0.972959\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1324.56i 3.16074i
\(57\) 0 0
\(58\) −376.840 −0.853131
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1509.75 −2.94873
\(65\) 0 0
\(66\) 0 0
\(67\) 740.000 1.34933 0.674667 0.738122i \(-0.264287\pi\)
0.674667 + 0.738122i \(0.264287\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 205.717i 0.343861i 0.985109 + 0.171931i \(0.0550005\pi\)
−0.985109 + 0.171931i \(0.945000\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 57.2156i 0.0898807i
\(75\) 0 0
\(76\) 0 0
\(77\) − 1237.00i − 1.83076i
\(78\) 0 0
\(79\) −1384.00 −1.97104 −0.985520 0.169559i \(-0.945766\pi\)
−0.985520 + 0.169559i \(0.945766\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 2889.39i 3.62291i
\(87\) 0 0
\(88\) 4776.90 5.78658
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) − 2656.22i − 3.01011i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 1854.38i 1.91144i
\(99\) 0 0
\(100\) 2653.59 2.65359
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −353.994 −0.324367
\(107\) 2213.53i 1.99991i 0.00945193 + 0.999955i \(0.496991\pi\)
−0.00945193 + 0.999955i \(0.503009\pi\)
\(108\) 0 0
\(109\) −2275.35 −1.99944 −0.999718 0.0237260i \(-0.992447\pi\)
−0.999718 + 0.0237260i \(0.992447\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −4015.75 −3.38797
\(113\) − 2105.12i − 1.75251i −0.481849 0.876254i \(-0.660035\pi\)
0.481849 0.876254i \(-0.339965\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) − 1479.71i − 1.18438i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −3130.11 −2.35170
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2000.00 1.39741 0.698706 0.715409i \(-0.253760\pi\)
0.698706 + 0.715409i \(0.253760\pi\)
\(128\) − 3361.41i − 2.32117i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4000.71i 2.57917i
\(135\) 0 0
\(136\) 0 0
\(137\) 1645.34i 1.02606i 0.858370 + 0.513031i \(0.171478\pi\)
−0.858370 + 0.513031i \(0.828522\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1112.18 −0.657269
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −224.664 −0.124779
\(149\) − 3082.50i − 1.69482i −0.530941 0.847409i \(-0.678161\pi\)
0.530941 0.847409i \(-0.321839\pi\)
\(150\) 0 0
\(151\) 2248.89 1.21200 0.606000 0.795465i \(-0.292773\pi\)
0.606000 + 0.795465i \(0.292773\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 6687.65 3.49939
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) − 7482.41i − 3.76752i
\(159\) 0 0
\(160\) 0 0
\(161\) − 2317.32i − 1.13435i
\(162\) 0 0
\(163\) −1780.00 −0.855340 −0.427670 0.903935i \(-0.640665\pi\)
−0.427670 + 0.903935i \(0.640665\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 2197.00 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) −11345.5 −5.02959
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 2315.03 1.00000
\(176\) 14482.4i 6.20257i
\(177\) 0 0
\(178\) 0 0
\(179\) 4523.06i 1.88866i 0.329005 + 0.944328i \(0.393287\pi\)
−0.329005 + 0.944328i \(0.606713\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 8948.78 3.58539
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 503.386i − 0.190700i −0.995444 0.0953502i \(-0.969603\pi\)
0.995444 0.0953502i \(-0.0303971\pi\)
\(192\) 0 0
\(193\) 2772.75 1.03413 0.517064 0.855947i \(-0.327025\pi\)
0.517064 + 0.855947i \(0.327025\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −7281.46 −2.65359
\(197\) − 2021.80i − 0.731205i −0.930771 0.365603i \(-0.880863\pi\)
0.930771 0.365603i \(-0.119137\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 8939.93i 3.16074i
\(201\) 0 0
\(202\) 0 0
\(203\) − 1290.92i − 0.446329i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 1772.65 0.578363 0.289181 0.957274i \(-0.406617\pi\)
0.289181 + 0.957274i \(0.406617\pi\)
\(212\) − 1390.00i − 0.450309i
\(213\) 0 0
\(214\) −11967.2 −3.82270
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) − 12301.3i − 3.82180i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) − 11114.1i − 3.31515i
\(225\) 0 0
\(226\) 11381.1 3.34981
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4985.13 1.41073
\(233\) 7101.24i 1.99664i 0.0579219 + 0.998321i \(0.481553\pi\)
−0.0579219 + 0.998321i \(0.518447\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4897.58i 1.32551i 0.748834 + 0.662757i \(0.230614\pi\)
−0.748834 + 0.662757i \(0.769386\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) − 16922.5i − 4.49513i
\(243\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −8357.20 −2.07673
\(254\) 10812.7i 2.67107i
\(255\) 0 0
\(256\) 6095.01 1.48804
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) −196.000 −0.0470226
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 8164.84i 1.91432i 0.289561 + 0.957159i \(0.406491\pi\)
−0.289561 + 0.957159i \(0.593509\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −15709.3 −3.58059
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −8895.29 −1.96126
\(275\) − 8348.94i − 1.83076i
\(276\) 0 0
\(277\) 7310.00 1.58561 0.792807 0.609472i \(-0.208619\pi\)
0.792807 + 0.609472i \(0.208619\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2841.56i 0.603250i 0.953427 + 0.301625i \(0.0975291\pi\)
−0.953427 + 0.301625i \(0.902471\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) − 4367.12i − 0.912468i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −4913.00 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) − 756.891i − 0.148626i
\(297\) 0 0
\(298\) 16665.1 3.23954
\(299\) 0 0
\(300\) 0 0
\(301\) −9898.00 −1.89539
\(302\) 12158.3i 2.31666i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 26259.9i 4.85811i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 29380.6 5.23034
\(317\) − 11207.0i − 1.98565i −0.119593 0.992823i \(-0.538159\pi\)
0.119593 0.992823i \(-0.461841\pi\)
\(318\) 0 0
\(319\) −4655.58 −0.817124
\(320\) 0 0
\(321\) 0 0
\(322\) 12528.3 2.16824
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) − 9623.33i − 1.63493i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 5106.30 0.847938 0.423969 0.905677i \(-0.360636\pi\)
0.423969 + 0.905677i \(0.360636\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 11916.5 1.92621 0.963103 0.269135i \(-0.0867376\pi\)
0.963103 + 0.269135i \(0.0867376\pi\)
\(338\) 11877.8i 1.91144i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −6352.45 −1.00000
\(344\) − 38223.0i − 5.99083i
\(345\) 0 0
\(346\) 0 0
\(347\) − 5770.28i − 0.892694i −0.894860 0.446347i \(-0.852725\pi\)
0.894860 0.446347i \(-0.147275\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 12515.9i 1.91144i
\(351\) 0 0
\(352\) −40082.0 −6.06926
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −24453.3 −3.61005
\(359\) − 13456.9i − 1.97835i −0.146729 0.989177i \(-0.546875\pi\)
0.146729 0.989177i \(-0.453125\pi\)
\(360\) 0 0
\(361\) 6859.00 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 \(\pi\)
\(368\) 27130.6i 3.84315i
\(369\) 0 0
\(370\) 0 0
\(371\) − 1212.65i − 0.169698i
\(372\) 0 0
\(373\) 13970.0 1.93925 0.969624 0.244602i \(-0.0786573\pi\)
0.969624 + 0.244602i \(0.0786573\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −8704.52 −1.17974 −0.589870 0.807498i \(-0.700821\pi\)
−0.589870 + 0.807498i \(0.700821\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 2721.49 0.364512
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14990.5i 1.97667i
\(387\) 0 0
\(388\) 0 0
\(389\) − 451.891i − 0.0588992i −0.999566 0.0294496i \(-0.990625\pi\)
0.999566 0.0294496i \(-0.00937545\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) − 24531.2i − 3.16074i
\(393\) 0 0
\(394\) 10930.6 1.39765
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −27103.8 −3.38797
\(401\) 12429.8i 1.54791i 0.633239 + 0.773956i \(0.281725\pi\)
−0.633239 + 0.773956i \(0.718275\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 6979.18 0.853131
\(407\) 706.855i 0.0860873i
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 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
\(421\) −15262.0 −1.76680 −0.883402 0.468616i \(-0.844753\pi\)
−0.883402 + 0.468616i \(0.844753\pi\)
\(422\) 9583.61i 1.10550i
\(423\) 0 0
\(424\) 4682.89 0.536371
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) − 46990.6i − 5.30695i
\(429\) 0 0
\(430\) 0 0
\(431\) − 17180.8i − 1.92011i −0.279803 0.960057i \(-0.590269\pi\)
0.279803 0.960057i \(-0.409731\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 48302.8 5.30570
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 14264.3i − 1.52983i −0.644129 0.764917i \(-0.722780\pi\)
0.644129 0.764917i \(-0.277220\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 27961.0 2.94873
\(449\) 11421.0i 1.20043i 0.799841 + 0.600213i \(0.204917\pi\)
−0.799841 + 0.600213i \(0.795083\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 44689.2i 4.65045i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 17821.8 1.82422 0.912109 0.409947i \(-0.134453\pi\)
0.912109 + 0.409947i \(0.134453\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) −8440.00 −0.847171 −0.423585 0.905856i \(-0.639229\pi\)
−0.423585 + 0.905856i \(0.639229\pi\)
\(464\) 15113.7i 1.51215i
\(465\) 0 0
\(466\) −38391.9 −3.81646
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) −13705.0 −1.34933
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 35696.2i 3.47001i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −26478.1 −2.53364
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 66448.4 6.24045
\(485\) 0 0
\(486\) 0 0
\(487\) 3296.61 0.306742 0.153371 0.988169i \(-0.450987\pi\)
0.153371 + 0.988169i \(0.450987\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 19811.9i 1.82097i 0.413540 + 0.910486i \(0.364292\pi\)
−0.413540 + 0.910486i \(0.635708\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 3809.93i − 0.343861i
\(498\) 0 0
\(499\) −21086.6 −1.89172 −0.945859 0.324577i \(-0.894778\pi\)
−0.945859 + 0.324577i \(0.894778\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) − 45182.1i − 3.96954i
\(507\) 0 0
\(508\) −42457.5 −3.70816
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 6060.53i 0.523125i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) − 1059.65i − 0.0898807i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −44142.1 −3.65910
\(527\) 0 0
\(528\) 0 0
\(529\) −3488.94 −0.286754
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) − 52924.4i − 4.26490i
\(537\) 0 0
\(538\) 0 0
\(539\) 22909.5i 1.83076i
\(540\) 0 0
\(541\) 15878.0 1.26183 0.630914 0.775853i \(-0.282680\pi\)
0.630914 + 0.775853i \(0.282680\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 12980.0 1.01460 0.507299 0.861770i \(-0.330644\pi\)
0.507299 + 0.861770i \(0.330644\pi\)
\(548\) − 34928.5i − 2.72275i
\(549\) 0 0
\(550\) 45137.4 3.49939
\(551\) 0 0
\(552\) 0 0
\(553\) 25632.0 1.97104
\(554\) 39520.5i 3.03080i
\(555\) 0 0
\(556\) 0 0
\(557\) − 26141.0i − 1.98856i −0.106803 0.994280i \(-0.534061\pi\)
0.106803 0.994280i \(-0.465939\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −15362.5 −1.15308
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 14712.8 1.08686
\(569\) 21569.7i 1.58919i 0.607138 + 0.794596i \(0.292317\pi\)
−0.607138 + 0.794596i \(0.707683\pi\)
\(570\) 0 0
\(571\) 6788.00 0.497494 0.248747 0.968569i \(-0.419981\pi\)
0.248747 + 0.968569i \(0.419981\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) − 15640.5i − 1.13435i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) − 26561.5i − 1.91144i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −4373.32 −0.310677
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 2294.71 0.159311
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 65437.5i 4.49736i
\(597\) 0 0
\(598\) 0 0
\(599\) − 6359.56i − 0.433797i −0.976194 0.216899i \(-0.930406\pi\)
0.976194 0.216899i \(-0.0695941\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) − 53512.2i − 3.62291i
\(603\) 0 0
\(604\) −47741.1 −3.21616
\(605\) 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
\(613\) −15010.0 −0.988986 −0.494493 0.869182i \(-0.664646\pi\)
−0.494493 + 0.869182i \(0.664646\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −88469.3 −5.78658
\(617\) − 23368.2i − 1.52474i −0.647139 0.762372i \(-0.724035\pi\)
0.647139 0.762372i \(-0.275965\pi\)
\(618\) 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
\(625\) 15625.0 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 26192.0 1.65244 0.826218 0.563351i \(-0.190488\pi\)
0.826218 + 0.563351i \(0.190488\pi\)
\(632\) 98982.9i 6.22995i
\(633\) 0 0
\(634\) 60589.3 3.79544
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) − 25169.8i − 1.56188i
\(639\) 0 0
\(640\) 0 0
\(641\) 15798.1i 0.973458i 0.873553 + 0.486729i \(0.161810\pi\)
−0.873553 + 0.486729i \(0.838190\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 49193.9i 3.01011i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 37787.2 2.26972
\(653\) 5305.56i 0.317952i 0.987282 + 0.158976i \(0.0508192\pi\)
−0.987282 + 0.158976i \(0.949181\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 25166.1i − 1.48761i −0.668399 0.743803i \(-0.733020\pi\)
0.668399 0.743803i \(-0.266980\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 27606.5i 1.62078i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −8721.51 −0.506294
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −9609.37 −0.550392 −0.275196 0.961388i \(-0.588743\pi\)
−0.275196 + 0.961388i \(0.588743\pi\)
\(674\) 64424.7i 3.68182i
\(675\) 0 0
\(676\) −46639.6 −2.65359
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 16522.2i − 0.925627i −0.886456 0.462813i \(-0.846840\pi\)
0.886456 0.462813i \(-0.153160\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) − 34343.6i − 1.91144i
\(687\) 0 0
\(688\) 115883. 6.42151
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 31196.2 1.70633
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −49145.3 −2.65359
\(701\) − 29047.8i − 1.56508i −0.622602 0.782539i \(-0.713924\pi\)
0.622602 0.782539i \(-0.286076\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) − 100839.i − 5.39844i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −35611.8 −1.88636 −0.943180 0.332281i \(-0.892182\pi\)
−0.943180 + 0.332281i \(0.892182\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) − 96019.0i − 5.01173i
\(717\) 0 0
\(718\) 72753.0 3.78150
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 37082.2i 1.91144i
\(723\) 0 0
\(724\) 0 0
\(725\) − 8712.89i − 0.446329i
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −75087.5 −3.76055
\(737\) 49425.7i 2.47031i
\(738\) 0 0
\(739\) −25324.0 −1.26057 −0.630283 0.776365i \(-0.717061\pi\)
−0.630283 + 0.776365i \(0.717061\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 6556.05 0.324367
\(743\) 40237.0i 1.98675i 0.114933 + 0.993373i \(0.463335\pi\)
−0.114933 + 0.993373i \(0.536665\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 75526.9i 3.70675i
\(747\) 0 0
\(748\) 0 0
\(749\) − 40995.2i − 1.99991i
\(750\) 0 0
\(751\) −41088.5 −1.99646 −0.998230 0.0594732i \(-0.981058\pi\)
−0.998230 + 0.0594732i \(0.981058\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −22848.7 −1.09703 −0.548514 0.836141i \(-0.684806\pi\)
−0.548514 + 0.836141i \(0.684806\pi\)
\(758\) − 47059.8i − 2.25500i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 42140.0 1.99944
\(764\) 10686.3i 0.506041i
\(765\) 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
\(772\) −58862.0 −2.74416
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 2443.09 0.112582
\(779\) 0 0
\(780\) 0 0
\(781\) −13740.2 −0.629529
\(782\) 0 0
\(783\) 0 0
\(784\) 74372.7 3.38797
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 42920.3i 1.94032i
\(789\) 0 0
\(790\) 0 0
\(791\) 38987.4i 1.75251i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) − 75013.3i − 3.31515i
\(801\) 0 0
\(802\) −67199.8 −2.95874
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 45420.9i − 1.97393i −0.160920 0.986967i \(-0.551446\pi\)
0.160920 0.986967i \(-0.448554\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 27404.6i 1.18438i
\(813\) 0 0
\(814\) −3821.52 −0.164550
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 18176.6i 0.772678i 0.922357 + 0.386339i \(0.126261\pi\)
−0.922357 + 0.386339i \(0.873739\pi\)
\(822\) 0 0
\(823\) −46240.0 −1.95848 −0.979238 0.202716i \(-0.935023\pi\)
−0.979238 + 0.202716i \(0.935023\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 12090.1i 0.508359i 0.967157 + 0.254179i \(0.0818054\pi\)
−0.967157 + 0.254179i \(0.918195\pi\)
\(828\) 0 0
\(829\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 19530.5 0.800790
\(842\) − 82511.9i − 3.37714i
\(843\) 0 0
\(844\) −37631.2 −1.53474
\(845\) 0 0
\(846\) 0 0
\(847\) 57970.5 2.35170
\(848\) 14197.4i 0.574931i
\(849\) 0 0
\(850\) 0 0
\(851\) 1324.18i 0.0533401i
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 158311. 6.32120
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 92885.6 3.67018
\(863\) 18601.9i 0.733737i 0.930273 + 0.366868i \(0.119570\pi\)
−0.930273 + 0.366868i \(0.880430\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 92439.5i − 3.60851i
\(870\) 0 0
\(871\) 0 0
\(872\) 162732.i 6.31971i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −6550.00 −0.252198 −0.126099 0.992018i \(-0.540246\pi\)
−0.126099 + 0.992018i \(0.540246\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 43014.6 1.63936 0.819681 0.572820i \(-0.194150\pi\)
0.819681 + 0.572820i \(0.194150\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 77117.9 2.92418
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) −37040.5 −1.39741
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 62254.3i 2.32117i
\(897\) 0 0
\(898\) −61746.1 −2.29454
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −150557. −5.53923
\(905\) 0 0
\(906\) 0 0
\(907\) 14250.0 0.521680 0.260840 0.965382i \(-0.416000\pi\)
0.260840 + 0.965382i \(0.416000\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 54982.7i 1.99962i 0.0193736 + 0.999812i \(0.493833\pi\)
−0.0193736 + 0.999812i \(0.506167\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 96351.0i 3.48688i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 51301.1 1.84142 0.920711 0.390244i \(-0.127609\pi\)
0.920711 + 0.390244i \(0.127609\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −1322.88 −0.0470226
\(926\) − 45629.7i − 1.61931i
\(927\) 0 0
\(928\) −41829.3 −1.47965
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) − 150750.i − 5.29828i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) − 74094.2i − 2.57917i
\(939\) 0 0
\(940\) 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
\(946\) −192987. −6.63270
\(947\) − 12007.4i − 0.412025i −0.978549 0.206013i \(-0.933951\pi\)
0.978549 0.206013i \(-0.0660488\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 15373.4i 0.522553i 0.965264 + 0.261276i \(0.0841434\pi\)
−0.965264 + 0.261276i \(0.915857\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) − 103970.i − 3.51738i
\(957\) 0 0
\(958\) 0 0
\(959\) − 30472.1i − 1.02606i
\(960\) 0 0
\(961\) 29791.0 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 52040.0 1.73060 0.865302 0.501251i \(-0.167127\pi\)
0.865302 + 0.501251i \(0.167127\pi\)
\(968\) 223864.i 7.43312i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 17822.6i 0.586319i
\(975\) 0 0
\(976\) 0 0
\(977\) − 7584.55i − 0.248364i −0.992259 0.124182i \(-0.960369\pi\)
0.992259 0.124182i \(-0.0396306\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) −107110. −3.48068
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 66871.3i 2.15003i
\(990\) 0 0
\(991\) 24155.7 0.774300 0.387150 0.922017i \(-0.373460\pi\)
0.387150 + 0.922017i \(0.373460\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 20597.9 0.657269
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) − 114002.i − 3.61590i
\(999\) 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 63.4.c.a.62.4 yes 4
3.2 odd 2 inner 63.4.c.a.62.1 4
4.3 odd 2 1008.4.k.a.881.3 4
7.2 even 3 441.4.p.b.80.4 8
7.3 odd 6 441.4.p.b.215.1 8
7.4 even 3 441.4.p.b.215.1 8
7.5 odd 6 441.4.p.b.80.4 8
7.6 odd 2 CM 63.4.c.a.62.4 yes 4
12.11 even 2 1008.4.k.a.881.4 4
21.2 odd 6 441.4.p.b.80.1 8
21.5 even 6 441.4.p.b.80.1 8
21.11 odd 6 441.4.p.b.215.4 8
21.17 even 6 441.4.p.b.215.4 8
21.20 even 2 inner 63.4.c.a.62.1 4
28.27 even 2 1008.4.k.a.881.3 4
84.83 odd 2 1008.4.k.a.881.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.c.a.62.1 4 3.2 odd 2 inner
63.4.c.a.62.1 4 21.20 even 2 inner
63.4.c.a.62.4 yes 4 1.1 even 1 trivial
63.4.c.a.62.4 yes 4 7.6 odd 2 CM
441.4.p.b.80.1 8 21.2 odd 6
441.4.p.b.80.1 8 21.5 even 6
441.4.p.b.80.4 8 7.2 even 3
441.4.p.b.80.4 8 7.5 odd 6
441.4.p.b.215.1 8 7.3 odd 6
441.4.p.b.215.1 8 7.4 even 3
441.4.p.b.215.4 8 21.11 odd 6
441.4.p.b.215.4 8 21.17 even 6
1008.4.k.a.881.3 4 4.3 odd 2
1008.4.k.a.881.3 4 28.27 even 2
1008.4.k.a.881.4 4 12.11 even 2
1008.4.k.a.881.4 4 84.83 odd 2