Properties

Label 117.4.b.c.64.2
Level $117$
Weight $4$
Character 117.64
Analytic conductor $6.903$
Analytic rank $0$
Dimension $4$
CM discriminant -39
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.8112.1
Defining polynomial: \( x^{4} + 5x^{2} + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 64.2
Root \(-2.07431i\) of defining polynomial
Character \(\chi\) \(=\) 117.64
Dual form 117.4.b.c.64.3

$q$-expansion

\(f(q)\) \(=\) \(q-3.52058i q^{2} -4.39445 q^{4} -9.17304i q^{5} -12.6936i q^{8} +O(q^{10})\) \(q-3.52058i q^{2} -4.39445 q^{4} -9.17304i q^{5} -12.6936i q^{8} -32.2944 q^{10} -20.4780i q^{11} -46.8722 q^{13} -79.8444 q^{16} +40.3104i q^{20} -72.0942 q^{22} +40.8554 q^{25} +165.017i q^{26} +179.549i q^{32} -116.439 q^{40} -196.898i q^{41} +452.000 q^{43} +89.9894i q^{44} -640.490i q^{47} +343.000 q^{49} -143.834i q^{50} +205.977 q^{52} -187.845 q^{55} -579.506i q^{59} +944.654 q^{61} -6.63840 q^{64} +429.960i q^{65} +1190.09i q^{71} -418.244 q^{79} +732.416i q^{80} -693.193 q^{82} +94.6440i q^{83} -1591.30i q^{86} -259.939 q^{88} +1672.06i q^{89} -2254.89 q^{94} -1207.56i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 32 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 32 q^{4} + 116 q^{10} - 204 q^{16} + 476 q^{22} - 500 q^{25} - 884 q^{40} + 1808 q^{43} + 1372 q^{49} - 676 q^{52} - 3232 q^{55} + 1632 q^{64} + 2924 q^{82} - 2756 q^{88} - 5140 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) − 3.52058i − 1.24471i −0.782735 0.622356i \(-0.786176\pi\)
0.782735 0.622356i \(-0.213824\pi\)
\(3\) 0 0
\(4\) −4.39445 −0.549306
\(5\) − 9.17304i − 0.820462i −0.911982 0.410231i \(-0.865448\pi\)
0.911982 0.410231i \(-0.134552\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) − 12.6936i − 0.560984i
\(9\) 0 0
\(10\) −32.2944 −1.02124
\(11\) − 20.4780i − 0.561304i −0.959810 0.280652i \(-0.909449\pi\)
0.959810 0.280652i \(-0.0905506\pi\)
\(12\) 0 0
\(13\) −46.8722 −1.00000
\(14\) 0 0
\(15\) 0 0
\(16\) −79.8444 −1.24757
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 40.3104i 0.450685i
\(21\) 0 0
\(22\) −72.0942 −0.698661
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 40.8554 0.326843
\(26\) 165.017i 1.24471i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 179.549i 0.991879i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −116.439 −0.460266
\(41\) − 196.898i − 0.750006i −0.927024 0.375003i \(-0.877642\pi\)
0.927024 0.375003i \(-0.122358\pi\)
\(42\) 0 0
\(43\) 452.000 1.60301 0.801504 0.597989i \(-0.204033\pi\)
0.801504 + 0.597989i \(0.204033\pi\)
\(44\) 89.9894i 0.308327i
\(45\) 0 0
\(46\) 0 0
\(47\) − 640.490i − 1.98777i −0.110431 0.993884i \(-0.535223\pi\)
0.110431 0.993884i \(-0.464777\pi\)
\(48\) 0 0
\(49\) 343.000 1.00000
\(50\) − 143.834i − 0.406825i
\(51\) 0 0
\(52\) 205.977 0.549306
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) −187.845 −0.460528
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 579.506i − 1.27873i −0.768902 0.639367i \(-0.779197\pi\)
0.768902 0.639367i \(-0.220803\pi\)
\(60\) 0 0
\(61\) 944.654 1.98280 0.991398 0.130879i \(-0.0417798\pi\)
0.991398 + 0.130879i \(0.0417798\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −6.63840 −0.0129656
\(65\) 429.960i 0.820462i
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1190.09i 1.98926i 0.103474 + 0.994632i \(0.467004\pi\)
−0.103474 + 0.994632i \(0.532996\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −418.244 −0.595647 −0.297824 0.954621i \(-0.596261\pi\)
−0.297824 + 0.954621i \(0.596261\pi\)
\(80\) 732.416i 1.02358i
\(81\) 0 0
\(82\) −693.193 −0.933541
\(83\) 94.6440i 0.125163i 0.998040 + 0.0625815i \(0.0199333\pi\)
−0.998040 + 0.0625815i \(0.980067\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) − 1591.30i − 1.99528i
\(87\) 0 0
\(88\) −259.939 −0.314882
\(89\) 1672.06i 1.99143i 0.0924493 + 0.995717i \(0.470530\pi\)
−0.0924493 + 0.995717i \(0.529470\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −2254.89 −2.47420
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) − 1207.56i − 1.24471i
\(99\) 0 0
\(100\) −179.537 −0.179537
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 848.000 0.811223 0.405611 0.914046i \(-0.367059\pi\)
0.405611 + 0.914046i \(0.367059\pi\)
\(104\) 594.977i 0.560984i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 661.323i 0.573224i
\(111\) 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
\(117\) 0 0
\(118\) −2040.20 −1.59165
\(119\) 0 0
\(120\) 0 0
\(121\) 911.653 0.684938
\(122\) − 3325.73i − 2.46801i
\(123\) 0 0
\(124\) 0 0
\(125\) − 1521.40i − 1.08862i
\(126\) 0 0
\(127\) −2495.04 −1.74330 −0.871650 0.490129i \(-0.836950\pi\)
−0.871650 + 0.490129i \(0.836950\pi\)
\(128\) 1459.77i 1.00802i
\(129\) 0 0
\(130\) 1513.71 1.02124
\(131\) 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
\(137\) − 3018.79i − 1.88258i −0.337604 0.941288i \(-0.609616\pi\)
0.337604 0.941288i \(-0.390384\pi\)
\(138\) 0 0
\(139\) −340.000 −0.207471 −0.103735 0.994605i \(-0.533079\pi\)
−0.103735 + 0.994605i \(0.533079\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4189.80 2.47606
\(143\) 959.847i 0.561304i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2477.09i 1.36196i 0.732304 + 0.680978i \(0.238445\pi\)
−0.732304 + 0.680978i \(0.761555\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −934.000 −0.474785 −0.237393 0.971414i \(-0.576293\pi\)
−0.237393 + 0.971414i \(0.576293\pi\)
\(158\) 1472.46i 0.741409i
\(159\) 0 0
\(160\) 1647.01 0.813799
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 865.256i 0.411983i
\(165\) 0 0
\(166\) 333.201 0.155792
\(167\) 2446.51i 1.13363i 0.823845 + 0.566815i \(0.191825\pi\)
−0.823845 + 0.566815i \(0.808175\pi\)
\(168\) 0 0
\(169\) 2197.00 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) −1986.29 −0.880542
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1635.05i 0.700265i
\(177\) 0 0
\(178\) 5886.60 2.47876
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 4430.00 1.81922 0.909611 0.415460i \(-0.136379\pi\)
0.909611 + 0.415460i \(0.136379\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 2814.60i 1.09189i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1507.30 −0.549306
\(197\) − 3977.33i − 1.43844i −0.694782 0.719220i \(-0.744499\pi\)
0.694782 0.719220i \(-0.255501\pi\)
\(198\) 0 0
\(199\) −5610.24 −1.99849 −0.999244 0.0388706i \(-0.987624\pi\)
−0.999244 + 0.0388706i \(0.987624\pi\)
\(200\) − 518.602i − 0.183354i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −1806.15 −0.615351
\(206\) − 2985.45i − 1.00974i
\(207\) 0 0
\(208\) 3742.48 1.24757
\(209\) 0 0
\(210\) 0 0
\(211\) −5740.04 −1.87280 −0.936399 0.350937i \(-0.885863\pi\)
−0.936399 + 0.350937i \(0.885863\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) − 4146.21i − 1.31521i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 825.476 0.252971
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 6668.65i − 1.94984i −0.222554 0.974920i \(-0.571439\pi\)
0.222554 0.974920i \(-0.428561\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) −5875.24 −1.63089
\(236\) 2546.61i 0.702416i
\(237\) 0 0
\(238\) 0 0
\(239\) 6085.88i 1.64712i 0.567226 + 0.823562i \(0.308016\pi\)
−0.567226 + 0.823562i \(0.691984\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) − 3209.54i − 0.852550i
\(243\) 0 0
\(244\) −4151.24 −1.08916
\(245\) − 3146.35i − 0.820462i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −5356.19 −1.35502
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 8783.98i 2.16991i
\(255\) 0 0
\(256\) 5086.11 1.24173
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) − 1889.44i − 0.450685i
\(261\) 0 0
\(262\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −10627.9 −2.34326
\(275\) − 836.635i − 0.183458i
\(276\) 0 0
\(277\) 7634.00 1.65589 0.827947 0.560806i \(-0.189509\pi\)
0.827947 + 0.560806i \(0.189509\pi\)
\(278\) 1197.00i 0.258241i
\(279\) 0 0
\(280\) 0 0
\(281\) 8255.10i 1.75252i 0.481839 + 0.876260i \(0.339969\pi\)
−0.481839 + 0.876260i \(0.660031\pi\)
\(282\) 0 0
\(283\) 490.355 0.102999 0.0514993 0.998673i \(-0.483600\pi\)
0.0514993 + 0.998673i \(0.483600\pi\)
\(284\) − 5229.79i − 1.09272i
\(285\) 0 0
\(286\) 3379.21 0.698661
\(287\) 0 0
\(288\) 0 0
\(289\) −4913.00 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 9933.00i 1.98052i 0.139232 + 0.990260i \(0.455537\pi\)
−0.139232 + 0.990260i \(0.544463\pi\)
\(294\) 0 0
\(295\) −5315.83 −1.04915
\(296\) 0 0
\(297\) 0 0
\(298\) 8720.79 1.69524
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 8665.35i − 1.62681i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 6396.25 1.15507 0.577536 0.816365i \(-0.304014\pi\)
0.577536 + 0.816365i \(0.304014\pi\)
\(314\) 3288.22i 0.590971i
\(315\) 0 0
\(316\) 1837.95 0.327193
\(317\) 7133.53i 1.26391i 0.775006 + 0.631954i \(0.217747\pi\)
−0.775006 + 0.631954i \(0.782253\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 60.8943i 0.0106378i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −1914.98 −0.326843
\(326\) 0 0
\(327\) 0 0
\(328\) −2499.34 −0.420741
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) − 415.908i − 0.0687528i
\(333\) 0 0
\(334\) 8613.11 1.41104
\(335\) 0 0
\(336\) 0 0
\(337\) 10420.0 1.68432 0.842160 0.539228i \(-0.181284\pi\)
0.842160 + 0.539228i \(0.181284\pi\)
\(338\) − 7734.70i − 1.24471i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) − 5737.51i − 0.899262i
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 3676.81 0.556745
\(353\) − 7331.69i − 1.10546i −0.833361 0.552728i \(-0.813587\pi\)
0.833361 0.552728i \(-0.186413\pi\)
\(354\) 0 0
\(355\) 10916.7 1.63211
\(356\) − 7347.77i − 1.09391i
\(357\) 0 0
\(358\) 0 0
\(359\) 11077.3i 1.62852i 0.580502 + 0.814259i \(0.302857\pi\)
−0.580502 + 0.814259i \(0.697143\pi\)
\(360\) 0 0
\(361\) 6859.00 1.00000
\(362\) − 15596.1i − 2.26441i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −8296.00 −1.17997 −0.589983 0.807416i \(-0.700866\pi\)
−0.589983 + 0.807416i \(0.700866\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 6526.05 0.905914 0.452957 0.891532i \(-0.350369\pi\)
0.452957 + 0.891532i \(0.350369\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −8130.13 −1.11511
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) − 12702.2i − 1.69465i −0.531071 0.847327i \(-0.678210\pi\)
0.531071 0.847327i \(-0.321790\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) − 4353.91i − 0.560984i
\(393\) 0 0
\(394\) −14002.5 −1.79044
\(395\) 3836.57i 0.488706i
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 19751.3i 2.48754i
\(399\) 0 0
\(400\) −3262.07 −0.407759
\(401\) 15342.6i 1.91066i 0.295549 + 0.955328i \(0.404497\pi\)
−0.295549 + 0.955328i \(0.595503\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 6358.68i 0.765934i
\(411\) 0 0
\(412\) −3726.49 −0.445609
\(413\) 0 0
\(414\) 0 0
\(415\) 868.173 0.102691
\(416\) − 8415.87i − 0.991879i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 20208.2i 2.33109i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) −14597.1 −1.63705
\(431\) 320.305i 0.0357971i 0.999840 + 0.0178985i \(0.00569759\pi\)
−0.999840 + 0.0178985i \(0.994302\pi\)
\(432\) 0 0
\(433\) 36.0555 0.00400166 0.00200083 0.999998i \(-0.499363\pi\)
0.00200083 + 0.999998i \(0.499363\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −11320.0 −1.23069 −0.615346 0.788257i \(-0.710984\pi\)
−0.615346 + 0.788257i \(0.710984\pi\)
\(440\) 2384.43i 0.258349i
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 15337.8 1.63390
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 333.683i 0.0350723i 0.999846 + 0.0175361i \(0.00558221\pi\)
−0.999846 + 0.0175361i \(0.994418\pi\)
\(450\) 0 0
\(451\) −4032.06 −0.420981
\(452\) 0 0
\(453\) 0 0
\(454\) −23477.5 −2.42699
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 17433.8i − 1.76133i −0.473738 0.880666i \(-0.657095\pi\)
0.473738 0.880666i \(-0.342905\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 20684.2i 2.02998i
\(471\) 0 0
\(472\) −7356.03 −0.717349
\(473\) − 9256.04i − 0.899774i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 21425.8 2.05019
\(479\) − 5200.84i − 0.496101i −0.968747 0.248050i \(-0.920210\pi\)
0.968747 0.248050i \(-0.0797898\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −4006.21 −0.376241
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) − 11991.1i − 1.11232i
\(489\) 0 0
\(490\) −11077.0 −1.02124
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 6685.70i 0.597988i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 10964.3 0.957605
\(509\) − 22966.8i − 1.99997i −0.00508931 0.999987i \(-0.501620\pi\)
0.00508931 0.999987i \(-0.498380\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) − 6227.90i − 0.537572i
\(513\) 0 0
\(514\) 0 0
\(515\) − 7778.74i − 0.665577i
\(516\) 0 0
\(517\) −13115.9 −1.11574
\(518\) 0 0
\(519\) 0 0
\(520\) 5457.75 0.460266
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 16148.0 1.35010 0.675050 0.737772i \(-0.264122\pi\)
0.675050 + 0.737772i \(0.264122\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −12167.0 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 9229.02i 0.750006i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 7023.94i − 0.561304i
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 23996.0 1.87568 0.937838 0.347073i \(-0.112824\pi\)
0.937838 + 0.347073i \(0.112824\pi\)
\(548\) 13265.9i 1.03411i
\(549\) 0 0
\(550\) −2945.44 −0.228352
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) − 26876.1i − 2.06111i
\(555\) 0 0
\(556\) 1494.11 0.113965
\(557\) 22258.1i 1.69319i 0.532237 + 0.846595i \(0.321352\pi\)
−0.532237 + 0.846595i \(0.678648\pi\)
\(558\) 0 0
\(559\) −21186.2 −1.60301
\(560\) 0 0
\(561\) 0 0
\(562\) 29062.7 2.18138
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) − 1726.33i − 0.128203i
\(567\) 0 0
\(568\) 15106.6 1.11595
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 25411.9 1.86244 0.931222 0.364451i \(-0.118743\pi\)
0.931222 + 0.364451i \(0.118743\pi\)
\(572\) − 4218.00i − 0.308327i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 17296.6i 1.24471i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 34969.9 2.46517
\(587\) 19338.0i 1.35974i 0.733335 + 0.679868i \(0.237963\pi\)
−0.733335 + 0.679868i \(0.762037\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 18714.8i 1.30589i
\(591\) 0 0
\(592\) 0 0
\(593\) − 25958.2i − 1.79760i −0.438363 0.898798i \(-0.644442\pi\)
0.438363 0.898798i \(-0.355558\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) − 10885.5i − 0.748131i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 12626.6 0.856991 0.428495 0.903544i \(-0.359044\pi\)
0.428495 + 0.903544i \(0.359044\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 8362.63i − 0.561966i
\(606\) 0 0
\(607\) −25504.0 −1.70540 −0.852698 0.522404i \(-0.825035\pi\)
−0.852698 + 0.522404i \(0.825035\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −30507.0 −2.02491
\(611\) 30021.2i 1.98777i
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 29859.9i 1.94832i 0.225860 + 0.974160i \(0.427481\pi\)
−0.225860 + 0.974160i \(0.572519\pi\)
\(618\) 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
\(625\) −8848.92 −0.566331
\(626\) − 22518.5i − 1.43773i
\(627\) 0 0
\(628\) 4104.42 0.260803
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 5309.03i 0.334148i
\(633\) 0 0
\(634\) 25114.1 1.57320
\(635\) 22887.1i 1.43031i
\(636\) 0 0
\(637\) −16077.2 −1.00000
\(638\) 0 0
\(639\) 0 0
\(640\) 13390.5 0.827040
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) −11867.1 −0.717758
\(650\) 6741.83i 0.406825i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 15721.2i 0.935684i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1201.37 0.0702144
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) − 10751.0i − 0.622710i
\(669\) 0 0
\(670\) 0 0
\(671\) − 19344.6i − 1.11295i
\(672\) 0 0
\(673\) −25522.0 −1.46181 −0.730907 0.682477i \(-0.760903\pi\)
−0.730907 + 0.682477i \(0.760903\pi\)
\(674\) − 36684.5i − 2.09649i
\(675\) 0 0
\(676\) −9654.60 −0.549306
\(677\) 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
\(683\) − 32750.6i − 1.83480i −0.397968 0.917399i \(-0.630285\pi\)
0.397968 0.917399i \(-0.369715\pi\)
\(684\) 0 0
\(685\) −27691.5 −1.54458
\(686\) 0 0
\(687\) 0 0
\(688\) −36089.7 −1.99986
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3118.83i 0.170222i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 135.941i 0.00727765i
\(705\) 0 0
\(706\) −25811.8 −1.37597
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) − 38433.2i − 2.03151i
\(711\) 0 0
\(712\) 21224.4 1.11716
\(713\) 0 0
\(714\) 0 0
\(715\) 8804.71 0.460528
\(716\) 0 0
\(717\) 0 0
\(718\) 38998.5 2.02704
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) − 24147.6i − 1.24471i
\(723\) 0 0
\(724\) −19467.4 −0.999310
\(725\) 0 0
\(726\) 0 0
\(727\) −28455.0 −1.45163 −0.725817 0.687888i \(-0.758538\pi\)
−0.725817 + 0.687888i \(0.758538\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 29206.7i 1.46872i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) − 19936.4i − 0.984382i −0.870487 0.492191i \(-0.836196\pi\)
0.870487 0.492191i \(-0.163804\pi\)
\(744\) 0 0
\(745\) 22722.5 1.11743
\(746\) − 22975.4i − 1.12760i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 26120.0 1.26915 0.634575 0.772861i \(-0.281175\pi\)
0.634575 + 0.772861i \(0.281175\pi\)
\(752\) 51139.6i 2.47988i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −35009.9 −1.68092 −0.840460 0.541873i \(-0.817715\pi\)
−0.840460 + 0.541873i \(0.817715\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 28936.4i 1.37838i 0.724582 + 0.689189i \(0.242033\pi\)
−0.724582 + 0.689189i \(0.757967\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −44719.1 −2.10936
\(767\) 27162.7i 1.27873i
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 3484.00i − 0.162110i −0.996710 0.0810548i \(-0.974171\pi\)
0.996710 0.0810548i \(-0.0258289\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 24370.6 1.11658
\(782\) 0 0
\(783\) 0 0
\(784\) −27386.6 −1.24757
\(785\) 8567.62i 0.389543i
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 17478.2i 0.790144i
\(789\) 0 0
\(790\) 13506.9 0.608297
\(791\) 0 0
\(792\) 0 0
\(793\) −44278.0 −1.98280
\(794\) 0 0
\(795\) 0 0
\(796\) 24653.9 1.09778
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 7335.55i 0.324189i
\(801\) 0 0
\(802\) 54014.8 2.37821
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 7937.03 0.338016
\(821\) 33048.4i 1.40487i 0.711749 + 0.702433i \(0.247903\pi\)
−0.711749 + 0.702433i \(0.752097\pi\)
\(822\) 0 0
\(823\) 37352.0 1.58203 0.791014 0.611798i \(-0.209554\pi\)
0.791014 + 0.611798i \(0.209554\pi\)
\(824\) − 10764.2i − 0.455083i
\(825\) 0 0
\(826\) 0 0
\(827\) 31167.2i 1.31051i 0.755409 + 0.655253i \(0.227438\pi\)
−0.755409 + 0.655253i \(0.772562\pi\)
\(828\) 0 0
\(829\) −3079.14 −0.129002 −0.0645012 0.997918i \(-0.520546\pi\)
−0.0645012 + 0.997918i \(0.520546\pi\)
\(830\) − 3056.47i − 0.127821i
\(831\) 0 0
\(832\) 311.156 0.0129656
\(833\) 0 0
\(834\) 0 0
\(835\) 22441.9 0.930101
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) − 46872.5i − 1.92875i −0.264543 0.964374i \(-0.585221\pi\)
0.264543 0.964374i \(-0.414779\pi\)
\(840\) 0 0
\(841\) −24389.0 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 25224.3 1.02874
\(845\) − 20153.2i − 0.820462i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 43324.3 1.72085 0.860423 0.509581i \(-0.170200\pi\)
0.860423 + 0.509581i \(0.170200\pi\)
\(860\) 18220.3i 0.722451i
\(861\) 0 0
\(862\) 1127.66 0.0445571
\(863\) − 23594.8i − 0.930678i −0.885133 0.465339i \(-0.845932\pi\)
0.885133 0.465339i \(-0.154068\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) − 126.936i − 0.00498091i
\(867\) 0 0
\(868\) 0 0
\(869\) 8564.79i 0.334339i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 39852.9i 1.53186i
\(879\) 0 0
\(880\) 14998.4 0.574540
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 52410.3 1.99745 0.998724 0.0504988i \(-0.0160811\pi\)
0.998724 + 0.0504988i \(0.0160811\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) − 53998.0i − 2.03373i
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 1174.75 0.0436549
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 14195.2i 0.524000i
\(903\) 0 0
\(904\) 0 0
\(905\) − 40636.6i − 1.49260i
\(906\) 0 0
\(907\) 35017.1 1.28195 0.640973 0.767564i \(-0.278531\pi\)
0.640973 + 0.767564i \(0.278531\pi\)
\(908\) 29305.0i 1.07106i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 1938.12 0.0702545
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −36762.2 −1.31956 −0.659779 0.751460i \(-0.729350\pi\)
−0.659779 + 0.751460i \(0.729350\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −61377.1 −2.19235
\(923\) − 55782.1i − 1.98926i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 7352.53i − 0.259665i −0.991536 0.129832i \(-0.958556\pi\)
0.991536 0.129832i \(-0.0414439\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 13275.6 0.462856 0.231428 0.972852i \(-0.425660\pi\)
0.231428 + 0.972852i \(0.425660\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 25818.4 0.895856
\(941\) − 15462.1i − 0.535652i −0.963467 0.267826i \(-0.913695\pi\)
0.963467 0.267826i \(-0.0863052\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 46270.3i 1.59531i
\(945\) 0 0
\(946\) −32586.6 −1.11996
\(947\) − 56498.4i − 1.93870i −0.245678 0.969352i \(-0.579011\pi\)
0.245678 0.969352i \(-0.420989\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 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
\(956\) − 26744.1i − 0.904775i
\(957\) 0 0
\(958\) −18309.9 −0.617502
\(959\) 0 0
\(960\) 0 0
\(961\) 29791.0 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) − 11572.2i − 0.384239i
\(969\) 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
\(976\) −75425.4 −2.47368
\(977\) − 52089.2i − 1.70571i −0.522146 0.852856i \(-0.674868\pi\)
0.522146 0.852856i \(-0.325132\pi\)
\(978\) 0 0
\(979\) 34240.3 1.11780
\(980\) 13826.5i 0.450685i
\(981\) 0 0
\(982\) 0 0
\(983\) 60639.0i 1.96753i 0.179454 + 0.983766i \(0.442567\pi\)
−0.179454 + 0.983766i \(0.557433\pi\)
\(984\) 0 0
\(985\) −36484.2 −1.18019
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −23272.0 −0.745973 −0.372987 0.927837i \(-0.621666\pi\)
−0.372987 + 0.927837i \(0.621666\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 51462.9i 1.63968i
\(996\) 0 0
\(997\) −21634.0 −0.687217 −0.343609 0.939113i \(-0.611649\pi\)
−0.343609 + 0.939113i \(0.611649\pi\)
\(998\) 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 117.4.b.c.64.2 4
3.2 odd 2 inner 117.4.b.c.64.3 yes 4
13.5 odd 4 1521.4.a.y.1.2 4
13.8 odd 4 1521.4.a.y.1.3 4
13.12 even 2 inner 117.4.b.c.64.3 yes 4
39.5 even 4 1521.4.a.y.1.3 4
39.8 even 4 1521.4.a.y.1.2 4
39.38 odd 2 CM 117.4.b.c.64.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.4.b.c.64.2 4 1.1 even 1 trivial
117.4.b.c.64.2 4 39.38 odd 2 CM
117.4.b.c.64.3 yes 4 3.2 odd 2 inner
117.4.b.c.64.3 yes 4 13.12 even 2 inner
1521.4.a.y.1.2 4 13.5 odd 4
1521.4.a.y.1.2 4 39.8 even 4
1521.4.a.y.1.3 4 13.8 odd 4
1521.4.a.y.1.3 4 39.5 even 4