Properties

Label 117.4.b.c.64.1
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 64.1
Root \(-0.835000i\) of defining polynomial
Character \(\chi\) \(=\) 117.64
Dual form 117.4.b.c.64.4

$q$-expansion

\(f(q)\) \(=\) \(q-4.42782i q^{2} -11.6056 q^{4} +20.3925i q^{5} +15.9647i q^{8} +O(q^{10})\) \(q-4.42782i q^{2} -11.6056 q^{4} +20.3925i q^{5} +15.9647i q^{8} +90.2944 q^{10} +70.0332i q^{11} +46.8722 q^{13} -22.1556 q^{16} -236.667i q^{20} +310.094 q^{22} -290.855 q^{25} -207.541i q^{26} +225.819i q^{32} -325.561 q^{40} +486.739i q^{41} +452.000 q^{43} -812.774i q^{44} -71.1653i q^{47} +343.000 q^{49} +1287.85i q^{50} -543.977 q^{52} -1428.15 q^{55} -696.914i q^{59} -944.654 q^{61} +822.638 q^{64} +955.842i q^{65} +123.807i q^{71} +418.244 q^{79} -451.809i q^{80} +2155.19 q^{82} -1509.37i q^{83} -2001.37i q^{86} -1118.06 q^{88} +155.245i q^{89} -315.107 q^{94} -1518.74i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 32 q^{4}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) − 4.42782i − 1.56547i −0.622356 0.782735i \(-0.713824\pi\)
0.622356 0.782735i \(-0.286176\pi\)
\(3\) 0 0
\(4\) −11.6056 −1.45069
\(5\) 20.3925i 1.82396i 0.410231 + 0.911982i \(0.365448\pi\)
−0.410231 + 0.911982i \(0.634552\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 15.9647i 0.705547i
\(9\) 0 0
\(10\) 90.2944 2.85536
\(11\) 70.0332i 1.91962i 0.280652 + 0.959810i \(0.409449\pi\)
−0.280652 + 0.959810i \(0.590551\pi\)
\(12\) 0 0
\(13\) 46.8722 1.00000
\(14\) 0 0
\(15\) 0 0
\(16\) −22.1556 −0.346181
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) − 236.667i − 2.64601i
\(21\) 0 0
\(22\) 310.094 3.00510
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −290.855 −2.32684
\(26\) − 207.541i − 1.56547i
\(27\) 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 \(\pi\)
\(32\) 225.819i 1.24748i
\(33\) 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
\(40\) −325.561 −1.28689
\(41\) 486.739i 1.85405i 0.375003 + 0.927024i \(0.377642\pi\)
−0.375003 + 0.927024i \(0.622358\pi\)
\(42\) 0 0
\(43\) 452.000 1.60301 0.801504 0.597989i \(-0.204033\pi\)
0.801504 + 0.597989i \(0.204033\pi\)
\(44\) − 812.774i − 2.78478i
\(45\) 0 0
\(46\) 0 0
\(47\) − 71.1653i − 0.220862i −0.993884 0.110431i \(-0.964777\pi\)
0.993884 0.110431i \(-0.0352231\pi\)
\(48\) 0 0
\(49\) 343.000 1.00000
\(50\) 1287.85i 3.64260i
\(51\) 0 0
\(52\) −543.977 −1.45069
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) −1428.15 −3.50132
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 696.914i − 1.53780i −0.639367 0.768902i \(-0.720803\pi\)
0.639367 0.768902i \(-0.279197\pi\)
\(60\) 0 0
\(61\) −944.654 −1.98280 −0.991398 0.130879i \(-0.958220\pi\)
−0.991398 + 0.130879i \(0.958220\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 822.638 1.60672
\(65\) 955.842i 1.82396i
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 123.807i 0.206947i 0.994632 + 0.103474i \(0.0329957\pi\)
−0.994632 + 0.103474i \(0.967004\pi\)
\(72\) 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 \(-0.403739\pi\)
0.297824 + 0.954621i \(0.403739\pi\)
\(80\) − 451.809i − 0.631422i
\(81\) 0 0
\(82\) 2155.19 2.90245
\(83\) − 1509.37i − 1.99608i −0.0625815 0.998040i \(-0.519933\pi\)
0.0625815 0.998040i \(-0.480067\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) − 2001.37i − 2.50946i
\(87\) 0 0
\(88\) −1118.06 −1.35438
\(89\) 155.245i 0.184899i 0.995717 + 0.0924493i \(0.0294696\pi\)
−0.995717 + 0.0924493i \(0.970530\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −315.107 −0.345753
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) − 1518.74i − 1.56547i
\(99\) 0 0
\(100\) 3375.54 3.37554
\(101\) 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 \(0.367059\pi\)
\(104\) 748.301i 0.705547i
\(105\) 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 \(\pi\)
\(110\) 6323.61i 5.48120i
\(111\) 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
\(118\) −3085.80 −2.40738
\(119\) 0 0
\(120\) 0 0
\(121\) −3573.65 −2.68494
\(122\) 4182.76i 3.10401i
\(123\) 0 0
\(124\) 0 0
\(125\) − 3382.21i − 2.42011i
\(126\) 0 0
\(127\) 2495.04 1.74330 0.871650 0.490129i \(-0.163050\pi\)
0.871650 + 0.490129i \(0.163050\pi\)
\(128\) − 1835.94i − 1.26778i
\(129\) 0 0
\(130\) 4232.29 2.85536
\(131\) 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
\(137\) − 1082.73i − 0.675208i −0.941288 0.337604i \(-0.890384\pi\)
0.941288 0.337604i \(-0.109616\pi\)
\(138\) 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
\(142\) 548.197 0.323969
\(143\) 3282.61i 1.91962i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 2663.80i − 1.46461i −0.680978 0.732304i \(-0.738445\pi\)
0.680978 0.732304i \(-0.261555\pi\)
\(150\) 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 \(0.576293\pi\)
\(158\) − 1851.91i − 0.932467i
\(159\) 0 0
\(160\) −4605.01 −2.27536
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) − 5648.88i − 2.68966i
\(165\) 0 0
\(166\) −6683.20 −3.12480
\(167\) 3555.90i 1.64769i 0.566815 + 0.823845i \(0.308175\pi\)
−0.566815 + 0.823845i \(0.691825\pi\)
\(168\) 0 0
\(169\) 2197.00 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) −5245.71 −2.32547
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) − 1551.63i − 0.664536i
\(177\) 0 0
\(178\) 687.398 0.289453
\(179\) 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
\(188\) 825.912i 0.320403i
\(189\) 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
\(196\) −3980.70 −1.45069
\(197\) 3842.18i 1.38956i 0.719220 + 0.694782i \(0.244499\pi\)
−0.719220 + 0.694782i \(0.755501\pi\)
\(198\) 0 0
\(199\) 5610.24 1.99849 0.999244 0.0388706i \(-0.0123760\pi\)
0.999244 + 0.0388706i \(0.0123760\pi\)
\(200\) − 4643.42i − 1.64170i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −9925.85 −3.38171
\(206\) − 3754.79i − 1.26994i
\(207\) 0 0
\(208\) −1038.48 −0.346181
\(209\) 0 0
\(210\) 0 0
\(211\) 5740.04 1.87280 0.936399 0.350937i \(-0.114137\pi\)
0.936399 + 0.350937i \(0.114137\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 9217.42i 2.92383i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 16574.5 5.07934
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 1522.31i − 0.445107i −0.974920 0.222554i \(-0.928561\pi\)
0.974920 0.222554i \(-0.0714393\pi\)
\(228\) 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
\(235\) 1451.24 0.402845
\(236\) 8088.07i 2.23088i
\(237\) 0 0
\(238\) 0 0
\(239\) − 4191.63i − 1.13445i −0.823562 0.567226i \(-0.808016\pi\)
0.823562 0.567226i \(-0.191984\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 15823.5i 4.20319i
\(243\) 0 0
\(244\) 10963.2 2.87643
\(245\) 6994.64i 1.82396i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −14975.8 −3.78861
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) − 11047.6i − 2.72908i
\(255\) 0 0
\(256\) −1548.11 −0.377956
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) − 11093.1i − 2.64601i
\(261\) 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
\(274\) −4794.11 −1.05702
\(275\) − 20369.5i − 4.46665i
\(276\) 0 0
\(277\) 7634.00 1.65589 0.827947 0.560806i \(-0.189509\pi\)
0.827947 + 0.560806i \(0.189509\pi\)
\(278\) 1505.46i 0.324789i
\(279\) 0 0
\(280\) 0 0
\(281\) 4539.33i 0.963678i 0.876260 + 0.481839i \(0.160031\pi\)
−0.876260 + 0.481839i \(0.839969\pi\)
\(282\) 0 0
\(283\) −490.355 −0.102999 −0.0514993 0.998673i \(-0.516400\pi\)
−0.0514993 + 0.998673i \(0.516400\pi\)
\(284\) − 1436.85i − 0.300217i
\(285\) 0 0
\(286\) 14534.8 3.00510
\(287\) 0 0
\(288\) 0 0
\(289\) −4913.00 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 1396.60i − 0.278465i −0.990260 0.139232i \(-0.955537\pi\)
0.990260 0.139232i \(-0.0444635\pi\)
\(294\) 0 0
\(295\) 14211.8 2.80490
\(296\) 0 0
\(297\) 0 0
\(298\) −11794.8 −2.29280
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 19263.9i − 3.61655i
\(306\) 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 \(-0.695986\pi\)
−0.577536 + 0.816365i \(0.695986\pi\)
\(314\) 4135.58i 0.743262i
\(315\) 0 0
\(316\) −4853.95 −0.864102
\(317\) 8748.31i 1.55001i 0.631954 + 0.775006i \(0.282253\pi\)
−0.631954 + 0.775006i \(0.717747\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 16775.7i 2.93059i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −13633.0 −2.32684
\(326\) 0 0
\(327\) 0 0
\(328\) −7770.66 −1.30812
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 17517.0i 2.89570i
\(333\) 0 0
\(334\) 15744.9 2.57941
\(335\) 0 0
\(336\) 0 0
\(337\) −10420.0 −1.68432 −0.842160 0.539228i \(-0.818716\pi\)
−0.842160 + 0.539228i \(0.818716\pi\)
\(338\) − 9727.91i − 1.56547i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 7216.05i 1.13100i
\(345\) 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
\(352\) −15814.8 −2.39469
\(353\) 11054.2i 1.66672i 0.552728 + 0.833361i \(0.313587\pi\)
−0.552728 + 0.833361i \(0.686413\pi\)
\(354\) 0 0
\(355\) −2524.75 −0.377464
\(356\) − 1801.71i − 0.268231i
\(357\) 0 0
\(358\) 0 0
\(359\) 7897.23i 1.16100i 0.814259 + 0.580502i \(0.197143\pi\)
−0.814259 + 0.580502i \(0.802857\pi\)
\(360\) 0 0
\(361\) 6859.00 1.00000
\(362\) − 19615.2i − 2.84794i
\(363\) 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 \(-0.649631\pi\)
−0.452957 + 0.891532i \(0.649631\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1136.13 0.155829
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) − 7961.24i − 1.06214i −0.847327 0.531071i \(-0.821790\pi\)
0.847327 0.531071i \(-0.178210\pi\)
\(384\) 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
\(392\) 5475.90i 0.705547i
\(393\) 0 0
\(394\) 17012.5 2.17532
\(395\) 8529.05i 1.08644i
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) − 24841.1i − 3.12857i
\(399\) 0 0
\(400\) 6444.07 0.805509
\(401\) − 4746.53i − 0.591098i −0.955328 0.295549i \(-0.904497\pi\)
0.955328 0.295549i \(-0.0955026\pi\)
\(402\) 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 \(\pi\)
\(410\) 43949.8i 5.29397i
\(411\) 0 0
\(412\) −9841.51 −1.17684
\(413\) 0 0
\(414\) 0 0
\(415\) 30779.8 3.64078
\(416\) 10584.6i 1.24748i
\(417\) 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 \(\pi\)
\(422\) − 25415.8i − 2.93181i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 40813.1 4.57716
\(431\) − 17892.7i − 1.99968i −0.0178985 0.999840i \(-0.505698\pi\)
0.0178985 0.999840i \(-0.494302\pi\)
\(432\) 0 0
\(433\) −36.0555 −0.00400166 −0.00200083 0.999998i \(-0.500637\pi\)
−0.00200083 + 0.999998i \(0.500637\pi\)
\(434\) 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 \(0.710984\pi\)
\(440\) − 22800.1i − 2.47034i
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) −3165.84 −0.337248
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 19025.4i − 1.99969i −0.0175361 0.999846i \(-0.505582\pi\)
0.0175361 0.999846i \(-0.494418\pi\)
\(450\) 0 0
\(451\) −34087.9 −3.55906
\(452\) 0 0
\(453\) 0 0
\(454\) −6740.52 −0.696802
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 9378.19i − 0.947475i −0.880666 0.473738i \(-0.842905\pi\)
0.880666 0.473738i \(-0.157095\pi\)
\(462\) 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
\(470\) − 6425.82i − 0.630641i
\(471\) 0 0
\(472\) 11126.0 1.08499
\(473\) 31655.0i 3.07717i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −18559.8 −1.77595
\(479\) 20311.6i 1.93749i 0.248050 + 0.968747i \(0.420210\pi\)
−0.248050 + 0.968747i \(0.579790\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 41474.2 3.89502
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) − 15081.1i − 1.39896i
\(489\) 0 0
\(490\) 30971.0 2.85536
\(491\) 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 \(\pi\)
\(500\) 39252.4i 3.51084i
\(501\) 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
\(508\) −28956.3 −2.52900
\(509\) − 116.887i − 0.0101786i −0.999987 0.00508931i \(-0.998380\pi\)
0.999987 0.00508931i \(-0.00161998\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) − 7832.81i − 0.676102i
\(513\) 0 0
\(514\) 0 0
\(515\) 17292.9i 1.47964i
\(516\) 0 0
\(517\) 4983.93 0.423971
\(518\) 0 0
\(519\) 0 0
\(520\) −15259.7 −1.28689
\(521\) 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
\(533\) 22814.5i 1.85405i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 24021.4i 1.91962i
\(540\) 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 \(0.112824\pi\)
\(548\) 12565.6i 0.979520i
\(549\) 0 0
\(550\) −90192.6 −6.99241
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) − 33801.9i − 2.59225i
\(555\) 0 0
\(556\) 3945.89 0.300976
\(557\) − 13993.2i − 1.06447i −0.846595 0.532237i \(-0.821352\pi\)
0.846595 0.532237i \(-0.178648\pi\)
\(558\) 0 0
\(559\) 21186.2 1.60301
\(560\) 0 0
\(561\) 0 0
\(562\) 20099.3 1.50861
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 2171.20i 0.161241i
\(567\) 0 0
\(568\) −1976.55 −0.146011
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) −25411.9 −1.86244 −0.931222 0.364451i \(-0.881257\pi\)
−0.931222 + 0.364451i \(0.881257\pi\)
\(572\) − 38096.5i − 2.78478i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 21753.9i 1.56547i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −6183.88 −0.435928
\(587\) − 20858.8i − 1.46667i −0.679868 0.733335i \(-0.737963\pi\)
0.679868 0.733335i \(-0.262037\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) − 62927.4i − 4.39098i
\(591\) 0 0
\(592\) 0 0
\(593\) 12660.4i 0.876726i 0.898798 + 0.438363i \(0.144442\pi\)
−0.898798 + 0.438363i \(0.855558\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 30914.8i 2.12470i
\(597\) 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 \(-0.640956\pi\)
−0.428495 + 0.903544i \(0.640956\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 72875.8i − 4.89723i
\(606\) 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
\(610\) −85297.0 −5.66160
\(611\) − 3335.67i − 0.220862i
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 6923.04i − 0.451719i −0.974160 0.225860i \(-0.927481\pi\)
0.974160 0.225860i \(-0.0725191\pi\)
\(618\) 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
\(625\) 32614.9 2.08735
\(626\) 28321.4i 1.80823i
\(627\) 0 0
\(628\) 10839.6 0.688768
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 6677.15i 0.420257i
\(633\) 0 0
\(634\) 38735.9 2.42650
\(635\) 50880.2i 3.17972i
\(636\) 0 0
\(637\) 16077.2 1.00000
\(638\) 0 0
\(639\) 0 0
\(640\) 37439.5 2.31239
\(641\) 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
\(649\) 48807.1 2.95200
\(650\) 60364.5i 3.64260i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) − 10784.0i − 0.641836i
\(657\) 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
\(664\) 24096.6 1.40833
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) − 41268.2i − 2.39029i
\(669\) 0 0
\(670\) 0 0
\(671\) − 66157.2i − 3.80622i
\(672\) 0 0
\(673\) −25522.0 −1.46181 −0.730907 0.682477i \(-0.760903\pi\)
−0.730907 + 0.682477i \(0.760903\pi\)
\(674\) 46138.0i 2.63675i
\(675\) 0 0
\(676\) −25497.4 −1.45069
\(677\) 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
\(683\) 14207.2i 0.795936i 0.917399 + 0.397968i \(0.130285\pi\)
−0.917399 + 0.397968i \(0.869715\pi\)
\(684\) 0 0
\(685\) 22079.5 1.23155
\(686\) 0 0
\(687\) 0 0
\(688\) −10014.3 −0.554931
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) − 6933.46i − 0.378419i
\(696\) 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
\(704\) 57612.0i 3.08428i
\(705\) 0 0
\(706\) 48945.8 2.60920
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 11179.1i 0.590908i
\(711\) 0 0
\(712\) −2478.45 −0.130455
\(713\) 0 0
\(714\) 0 0
\(715\) −66940.7 −3.50132
\(716\) 0 0
\(717\) 0 0
\(718\) 34967.5 1.81751
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) − 30370.4i − 1.56547i
\(723\) 0 0
\(724\) −51412.6 −2.63914
\(725\) 0 0
\(726\) 0 0
\(727\) 28455.0 1.45163 0.725817 0.687888i \(-0.241462\pi\)
0.725817 + 0.687888i \(0.241462\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 36733.2i 1.84720i
\(735\) 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
\(743\) − 35259.5i − 1.74097i −0.492191 0.870487i \(-0.663804\pi\)
0.492191 0.870487i \(-0.336196\pi\)
\(744\) 0 0
\(745\) 54321.5 2.67139
\(746\) 28896.1i 1.41818i
\(747\) 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 \(0.281175\pi\)
\(752\) 1576.71i 0.0764583i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 35009.9 1.68092 0.840460 0.541873i \(-0.182285\pi\)
0.840460 + 0.541873i \(0.182285\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 30422.5i 1.44916i 0.689189 + 0.724582i \(0.257967\pi\)
−0.689189 + 0.724582i \(0.742033\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −35250.9 −1.66275
\(767\) − 32665.9i − 1.53780i
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 42841.8i 1.99342i 0.0810548 + 0.996710i \(0.474171\pi\)
−0.0810548 + 0.996710i \(0.525829\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −8670.64 −0.397260
\(782\) 0 0
\(783\) 0 0
\(784\) −7599.37 −0.346181
\(785\) − 19046.6i − 0.865991i
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) − 44590.6i − 2.01583i
\(789\) 0 0
\(790\) 37765.1 1.70079
\(791\) 0 0
\(792\) 0 0
\(793\) −44278.0 −1.98280
\(794\) 0 0
\(795\) 0 0
\(796\) −65109.9 −2.89920
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) − 65680.5i − 2.90270i
\(801\) 0 0
\(802\) −21016.8 −0.925346
\(803\) 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
\(820\) 115195. 4.90583
\(821\) 33486.7i 1.42350i 0.702433 + 0.711749i \(0.252097\pi\)
−0.702433 + 0.711749i \(0.747903\pi\)
\(822\) 0 0
\(823\) 37352.0 1.58203 0.791014 0.611798i \(-0.209554\pi\)
0.791014 + 0.611798i \(0.209554\pi\)
\(824\) 13538.1i 0.572356i
\(825\) 0 0
\(826\) 0 0
\(827\) − 35931.1i − 1.51082i −0.655253 0.755409i \(-0.727438\pi\)
0.655253 0.755409i \(-0.272562\pi\)
\(828\) 0 0
\(829\) 3079.14 0.129002 0.0645012 0.997918i \(-0.479454\pi\)
0.0645012 + 0.997918i \(0.479454\pi\)
\(830\) − 136287.i − 5.69952i
\(831\) 0 0
\(832\) 38558.8 1.60672
\(833\) 0 0
\(834\) 0 0
\(835\) −72513.9 −3.00533
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 12857.9i 0.529086i 0.964374 + 0.264543i \(0.0852210\pi\)
−0.964374 + 0.264543i \(0.914779\pi\)
\(840\) 0 0
\(841\) −24389.0 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) −66616.3 −2.71686
\(845\) 44802.4i 1.82396i
\(846\) 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 \(-0.829800\pi\)
−0.860423 + 0.509581i \(0.829800\pi\)
\(860\) − 106973.i − 4.24158i
\(861\) 0 0
\(862\) −79225.7 −3.13044
\(863\) 44880.2i 1.77027i 0.465339 + 0.885133i \(0.345932\pi\)
−0.465339 + 0.885133i \(0.654068\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 159.647i 0.00626447i
\(867\) 0 0
\(868\) 0 0
\(869\) 29291.0i 1.14342i
\(870\) 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 \(\pi\)
\(878\) 50122.9i 1.92661i
\(879\) 0 0
\(880\) 31641.6 1.21209
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) −52410.3 −1.99745 −0.998724 0.0504988i \(-0.983919\pi\)
−0.998724 + 0.0504988i \(0.983919\pi\)
\(884\) 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
\(890\) 14017.8i 0.527952i
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −84240.8 −3.13046
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 150935.i 5.57161i
\(903\) 0 0
\(904\) 0 0
\(905\) 90338.9i 3.31820i
\(906\) 0 0
\(907\) −35017.1 −1.28195 −0.640973 0.767564i \(-0.721469\pi\)
−0.640973 + 0.767564i \(0.721469\pi\)
\(908\) 17667.3i 0.645715i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 105706. 3.83171
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 36762.2 1.31956 0.659779 0.751460i \(-0.270650\pi\)
0.659779 + 0.751460i \(0.270650\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −41524.9 −1.48324
\(923\) 5803.12i 0.206947i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 56151.6i − 1.98307i −0.129832 0.991536i \(-0.541444\pi\)
0.129832 0.991536i \(-0.458556\pi\)
\(930\) 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 \(-0.574340\pi\)
−0.231428 + 0.972852i \(0.574340\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −16842.4 −0.584404
\(941\) − 55622.6i − 1.92693i −0.267826 0.963467i \(-0.586305\pi\)
0.267826 0.963467i \(-0.413695\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 15440.5i 0.532359i
\(945\) 0 0
\(946\) 140163. 4.81721
\(947\) − 14319.3i − 0.491356i −0.969352 0.245678i \(-0.920989\pi\)
0.969352 0.245678i \(-0.0790105\pi\)
\(948\) 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
\(956\) 48646.2i 1.64574i
\(957\) 0 0
\(958\) 89935.9 3.03309
\(959\) 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 \(\pi\)
\(968\) − 57052.4i − 1.89435i
\(969\) 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
\(976\) 20929.4 0.686407
\(977\) − 31890.7i − 1.04429i −0.852856 0.522146i \(-0.825132\pi\)
0.852856 0.522146i \(-0.174868\pi\)
\(978\) 0 0
\(979\) −10872.3 −0.354935
\(980\) − 81176.6i − 2.64601i
\(981\) 0 0
\(982\) 0 0
\(983\) − 11061.5i − 0.358908i −0.983766 0.179454i \(-0.942567\pi\)
0.983766 0.179454i \(-0.0574331\pi\)
\(984\) 0 0
\(985\) −78351.8 −2.53451
\(986\) 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
\(995\) 114407.i 3.64517i
\(996\) 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.64.1 4
3.2 odd 2 inner 117.4.b.c.64.4 yes 4
13.5 odd 4 1521.4.a.y.1.1 4
13.8 odd 4 1521.4.a.y.1.4 4
13.12 even 2 inner 117.4.b.c.64.4 yes 4
39.5 even 4 1521.4.a.y.1.4 4
39.8 even 4 1521.4.a.y.1.1 4
39.38 odd 2 CM 117.4.b.c.64.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.4.b.c.64.1 4 1.1 even 1 trivial
117.4.b.c.64.1 4 39.38 odd 2 CM
117.4.b.c.64.4 yes 4 3.2 odd 2 inner
117.4.b.c.64.4 yes 4 13.12 even 2 inner
1521.4.a.y.1.1 4 13.5 odd 4
1521.4.a.y.1.1 4 39.8 even 4
1521.4.a.y.1.4 4 13.8 odd 4
1521.4.a.y.1.4 4 39.5 even 4