Properties

Label 768.3.e.j.257.1
Level $768$
Weight $3$
Character 768.257
Analytic conductor $20.926$
Analytic rank $0$
Dimension $4$
CM discriminant -24
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [768,3,Mod(257,768)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(768, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("768.257");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 768.e (of order \(2\), degree \(1\), not 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: no
Analytic conductor: \(20.9264843029\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 384)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 257.1
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 768.257
Dual form 768.3.e.j.257.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.00000i q^{3} -9.79796i q^{5} -9.79796 q^{7} -9.00000 q^{9} +O(q^{10})\) \(q-3.00000i q^{3} -9.79796i q^{5} -9.79796 q^{7} -9.00000 q^{9} +10.0000i q^{11} -29.3939 q^{15} +29.3939i q^{21} -71.0000 q^{25} +27.0000i q^{27} -29.3939i q^{29} +48.9898 q^{31} +30.0000 q^{33} +96.0000i q^{35} +88.1816i q^{45} +47.0000 q^{49} -48.9898i q^{53} +97.9796 q^{55} -10.0000i q^{59} +88.1816 q^{63} +50.0000 q^{73} +213.000i q^{75} -97.9796i q^{77} -146.969 q^{79} +81.0000 q^{81} +134.000i q^{83} -88.1816 q^{87} -146.969i q^{93} -190.000 q^{97} -90.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 36 q^{9} - 284 q^{25} + 120 q^{33} + 188 q^{49} + 200 q^{73} + 324 q^{81} - 760 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) − 3.00000i − 1.00000i
\(4\) 0 0
\(5\) − 9.79796i − 1.95959i −0.200000 0.979796i \(-0.564094\pi\)
0.200000 0.979796i \(-0.435906\pi\)
\(6\) 0 0
\(7\) −9.79796 −1.39971 −0.699854 0.714286i \(-0.746752\pi\)
−0.699854 + 0.714286i \(0.746752\pi\)
\(8\) 0 0
\(9\) −9.00000 −1.00000
\(10\) 0 0
\(11\) 10.0000i 0.909091i 0.890724 + 0.454545i \(0.150198\pi\)
−0.890724 + 0.454545i \(0.849802\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) −29.3939 −1.95959
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 29.3939i 1.39971i
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) −71.0000 −2.84000
\(26\) 0 0
\(27\) 27.0000i 1.00000i
\(28\) 0 0
\(29\) − 29.3939i − 1.01358i −0.862069 0.506791i \(-0.830832\pi\)
0.862069 0.506791i \(-0.169168\pi\)
\(30\) 0 0
\(31\) 48.9898 1.58032 0.790158 0.612903i \(-0.209998\pi\)
0.790158 + 0.612903i \(0.209998\pi\)
\(32\) 0 0
\(33\) 30.0000 0.909091
\(34\) 0 0
\(35\) 96.0000i 2.74286i
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 88.1816i 1.95959i
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 47.0000 0.959184
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 48.9898i − 0.924336i −0.886792 0.462168i \(-0.847072\pi\)
0.886792 0.462168i \(-0.152928\pi\)
\(54\) 0 0
\(55\) 97.9796 1.78145
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 10.0000i − 0.169492i −0.996403 0.0847458i \(-0.972992\pi\)
0.996403 0.0847458i \(-0.0270078\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 88.1816 1.39971
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 50.0000 0.684932 0.342466 0.939530i \(-0.388738\pi\)
0.342466 + 0.939530i \(0.388738\pi\)
\(74\) 0 0
\(75\) 213.000i 2.84000i
\(76\) 0 0
\(77\) − 97.9796i − 1.27246i
\(78\) 0 0
\(79\) −146.969 −1.86037 −0.930186 0.367089i \(-0.880355\pi\)
−0.930186 + 0.367089i \(0.880355\pi\)
\(80\) 0 0
\(81\) 81.0000 1.00000
\(82\) 0 0
\(83\) 134.000i 1.61446i 0.590238 + 0.807229i \(0.299034\pi\)
−0.590238 + 0.807229i \(0.700966\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −88.1816 −1.01358
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) − 146.969i − 1.58032i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −190.000 −1.95876 −0.979381 0.202020i \(-0.935249\pi\)
−0.979381 + 0.202020i \(0.935249\pi\)
\(98\) 0 0
\(99\) − 90.0000i − 0.909091i
\(100\) 0 0
\(101\) 68.5857i 0.679066i 0.940594 + 0.339533i \(0.110269\pi\)
−0.940594 + 0.339533i \(0.889731\pi\)
\(102\) 0 0
\(103\) −205.757 −1.99764 −0.998821 0.0485437i \(-0.984542\pi\)
−0.998821 + 0.0485437i \(0.984542\pi\)
\(104\) 0 0
\(105\) 288.000 2.74286
\(106\) 0 0
\(107\) 86.0000i 0.803738i 0.915697 + 0.401869i \(0.131639\pi\)
−0.915697 + 0.401869i \(0.868361\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 21.0000 0.173554
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 450.706i 3.60565i
\(126\) 0 0
\(127\) −107.778 −0.848642 −0.424321 0.905512i \(-0.639487\pi\)
−0.424321 + 0.905512i \(0.639487\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 250.000i 1.90840i 0.299174 + 0.954198i \(0.403289\pi\)
−0.299174 + 0.954198i \(0.596711\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 264.545 1.95959
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −288.000 −1.98621
\(146\) 0 0
\(147\) − 141.000i − 0.959184i
\(148\) 0 0
\(149\) 68.5857i 0.460307i 0.973154 + 0.230153i \(0.0739228\pi\)
−0.973154 + 0.230153i \(0.926077\pi\)
\(150\) 0 0
\(151\) −48.9898 −0.324436 −0.162218 0.986755i \(-0.551865\pi\)
−0.162218 + 0.986755i \(0.551865\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 480.000i − 3.09677i
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) −146.969 −0.924336
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) − 293.939i − 1.78145i
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −169.000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 342.929i − 1.98225i −0.132948 0.991123i \(-0.542444\pi\)
0.132948 0.991123i \(-0.457556\pi\)
\(174\) 0 0
\(175\) 695.655 3.97517
\(176\) 0 0
\(177\) −30.0000 −0.169492
\(178\) 0 0
\(179\) − 230.000i − 1.28492i −0.766321 0.642458i \(-0.777915\pi\)
0.766321 0.642458i \(-0.222085\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) − 264.545i − 1.39971i
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) −290.000 −1.50259 −0.751295 0.659966i \(-0.770571\pi\)
−0.751295 + 0.659966i \(0.770571\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 342.929i 1.74075i 0.492386 + 0.870377i \(0.336125\pi\)
−0.492386 + 0.870377i \(0.663875\pi\)
\(198\) 0 0
\(199\) 342.929 1.72326 0.861630 0.507538i \(-0.169444\pi\)
0.861630 + 0.507538i \(0.169444\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 288.000i 1.41872i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −480.000 −2.21198
\(218\) 0 0
\(219\) − 150.000i − 0.684932i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −382.120 −1.71354 −0.856772 0.515695i \(-0.827534\pi\)
−0.856772 + 0.515695i \(0.827534\pi\)
\(224\) 0 0
\(225\) 639.000 2.84000
\(226\) 0 0
\(227\) − 346.000i − 1.52423i −0.647442 0.762115i \(-0.724161\pi\)
0.647442 0.762115i \(-0.275839\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) −293.939 −1.27246
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 440.908i 1.86037i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 382.000 1.58506 0.792531 0.609831i \(-0.208763\pi\)
0.792531 + 0.609831i \(0.208763\pi\)
\(242\) 0 0
\(243\) − 243.000i − 1.00000i
\(244\) 0 0
\(245\) − 460.504i − 1.87961i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 402.000 1.61446
\(250\) 0 0
\(251\) − 470.000i − 1.87251i −0.351321 0.936255i \(-0.614267\pi\)
0.351321 0.936255i \(-0.385733\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 264.545i 1.01358i
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) −480.000 −1.81132
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 323.333i 1.20198i 0.799257 + 0.600990i \(0.205227\pi\)
−0.799257 + 0.600990i \(0.794773\pi\)
\(270\) 0 0
\(271\) −538.888 −1.98852 −0.994258 0.107011i \(-0.965872\pi\)
−0.994258 + 0.107011i \(0.965872\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 710.000i − 2.58182i
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) −440.908 −1.58032
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 289.000 1.00000
\(290\) 0 0
\(291\) 570.000i 1.95876i
\(292\) 0 0
\(293\) − 440.908i − 1.50481i −0.658703 0.752403i \(-0.728895\pi\)
0.658703 0.752403i \(-0.271105\pi\)
\(294\) 0 0
\(295\) −97.9796 −0.332134
\(296\) 0 0
\(297\) −270.000 −0.909091
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 205.757 0.679066
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 617.271i 1.99764i
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 530.000 1.69329 0.846645 0.532158i \(-0.178619\pi\)
0.846645 + 0.532158i \(0.178619\pi\)
\(314\) 0 0
\(315\) − 864.000i − 2.74286i
\(316\) 0 0
\(317\) − 538.888i − 1.69996i −0.526814 0.849981i \(-0.676614\pi\)
0.526814 0.849981i \(-0.323386\pi\)
\(318\) 0 0
\(319\) 293.939 0.921438
\(320\) 0 0
\(321\) 258.000 0.803738
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 190.000 0.563798 0.281899 0.959444i \(-0.409036\pi\)
0.281899 + 0.959444i \(0.409036\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 489.898i 1.43665i
\(342\) 0 0
\(343\) 19.5959 0.0571310
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 106.000i 0.305476i 0.988267 + 0.152738i \(0.0488090\pi\)
−0.988267 + 0.152738i \(0.951191\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) −361.000 −1.00000
\(362\) 0 0
\(363\) − 63.0000i − 0.173554i
\(364\) 0 0
\(365\) − 489.898i − 1.34219i
\(366\) 0 0
\(367\) −186.161 −0.507251 −0.253626 0.967302i \(-0.581623\pi\)
−0.253626 + 0.967302i \(0.581623\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 480.000i 1.29380i
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 1352.12 3.60565
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 323.333i 0.848642i
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) −960.000 −2.49351
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 754.443i − 1.93944i −0.244216 0.969721i \(-0.578531\pi\)
0.244216 0.969721i \(-0.421469\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 750.000 1.90840
\(394\) 0 0
\(395\) 1440.00i 3.64557i
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) − 793.635i − 1.95959i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 718.000 1.75550 0.877751 0.479118i \(-0.159043\pi\)
0.877751 + 0.479118i \(0.159043\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 97.9796i 0.237239i
\(414\) 0 0
\(415\) 1312.93 3.16368
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 730.000i − 1.74224i −0.491067 0.871122i \(-0.663393\pi\)
0.491067 0.871122i \(-0.336607\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) −670.000 −1.54734 −0.773672 0.633586i \(-0.781582\pi\)
−0.773672 + 0.633586i \(0.781582\pi\)
\(434\) 0 0
\(435\) 864.000i 1.98621i
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −832.827 −1.89710 −0.948550 0.316629i \(-0.897449\pi\)
−0.948550 + 0.316629i \(0.897449\pi\)
\(440\) 0 0
\(441\) −423.000 −0.959184
\(442\) 0 0
\(443\) − 86.0000i − 0.194131i −0.995278 0.0970655i \(-0.969054\pi\)
0.995278 0.0970655i \(-0.0309456\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 205.757 0.460307
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 146.969i 0.324436i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −530.000 −1.15974 −0.579869 0.814710i \(-0.696896\pi\)
−0.579869 + 0.814710i \(0.696896\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 754.443i 1.63654i 0.574837 + 0.818268i \(0.305065\pi\)
−0.574837 + 0.818268i \(0.694935\pi\)
\(462\) 0 0
\(463\) −891.614 −1.92573 −0.962866 0.269978i \(-0.912983\pi\)
−0.962866 + 0.269978i \(0.912983\pi\)
\(464\) 0 0
\(465\) −1440.00 −3.09677
\(466\) 0 0
\(467\) − 634.000i − 1.35760i −0.734322 0.678801i \(-0.762500\pi\)
0.734322 0.678801i \(-0.237500\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 440.908i 0.924336i
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1861.61i 3.83838i
\(486\) 0 0
\(487\) −88.1816 −0.181071 −0.0905356 0.995893i \(-0.528858\pi\)
−0.0905356 + 0.995893i \(0.528858\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 470.000i 0.957230i 0.878025 + 0.478615i \(0.158861\pi\)
−0.878025 + 0.478615i \(0.841139\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −881.816 −1.78145
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 672.000 1.33069
\(506\) 0 0
\(507\) 507.000i 1.00000i
\(508\) 0 0
\(509\) 127.373i 0.250243i 0.992141 + 0.125121i \(0.0399320\pi\)
−0.992141 + 0.125121i \(0.960068\pi\)
\(510\) 0 0
\(511\) −489.898 −0.958704
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2016.00i 3.91456i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1028.79 −1.98225
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 0 0
\(525\) − 2086.97i − 3.97517i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 529.000 1.00000
\(530\) 0 0
\(531\) 90.0000i 0.169492i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 842.624 1.57500
\(536\) 0 0
\(537\) −690.000 −1.28492
\(538\) 0 0
\(539\) 470.000i 0.871985i
\(540\) 0 0
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 1440.00 2.60398
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 636.867i 1.14339i 0.820467 + 0.571694i \(0.193714\pi\)
−0.820467 + 0.571694i \(0.806286\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 326.000i 0.579041i 0.957172 + 0.289520i \(0.0934958\pi\)
−0.957172 + 0.289520i \(0.906504\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −793.635 −1.39971
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −290.000 −0.502600 −0.251300 0.967909i \(-0.580858\pi\)
−0.251300 + 0.967909i \(0.580858\pi\)
\(578\) 0 0
\(579\) 870.000i 1.50259i
\(580\) 0 0
\(581\) − 1312.93i − 2.25977i
\(582\) 0 0
\(583\) 489.898 0.840305
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 874.000i − 1.48893i −0.667663 0.744463i \(-0.732705\pi\)
0.667663 0.744463i \(-0.267295\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 1028.79 1.74075
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) − 1028.79i − 1.72326i
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −1198.00 −1.99334 −0.996672 0.0815138i \(-0.974025\pi\)
−0.996672 + 0.0815138i \(0.974025\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 205.757i − 0.340094i
\(606\) 0 0
\(607\) −969.998 −1.59802 −0.799010 0.601318i \(-0.794643\pi\)
−0.799010 + 0.601318i \(0.794643\pi\)
\(608\) 0 0
\(609\) 864.000 1.41872
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 2641.00 4.22560
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −244.949 −0.388192 −0.194096 0.980983i \(-0.562177\pi\)
−0.194096 + 0.980983i \(0.562177\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1056.00i 1.66299i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 100.000 0.154083
\(650\) 0 0
\(651\) 1440.00i 2.21198i
\(652\) 0 0
\(653\) 832.827i 1.27539i 0.770291 + 0.637693i \(0.220111\pi\)
−0.770291 + 0.637693i \(0.779889\pi\)
\(654\) 0 0
\(655\) 2449.49 3.73968
\(656\) 0 0
\(657\) −450.000 −0.684932
\(658\) 0 0
\(659\) 730.000i 1.10774i 0.832603 + 0.553869i \(0.186849\pi\)
−0.832603 + 0.553869i \(0.813151\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 1146.36i 1.71354i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −190.000 −0.282318 −0.141159 0.989987i \(-0.545083\pi\)
−0.141159 + 0.989987i \(0.545083\pi\)
\(674\) 0 0
\(675\) − 1917.00i − 2.84000i
\(676\) 0 0
\(677\) 146.969i 0.217089i 0.994092 + 0.108545i \(0.0346190\pi\)
−0.994092 + 0.108545i \(0.965381\pi\)
\(678\) 0 0
\(679\) 1861.61 2.74170
\(680\) 0 0
\(681\) −1038.00 −1.52423
\(682\) 0 0
\(683\) − 1334.00i − 1.95315i −0.215182 0.976574i \(-0.569035\pi\)
0.215182 0.976574i \(-0.430965\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 0 0
\(693\) 881.816i 1.27246i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 1401.11i − 1.99873i −0.0356633 0.999364i \(-0.511354\pi\)
0.0356633 0.999364i \(-0.488646\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 672.000i − 0.950495i
\(708\) 0 0
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 1322.72 1.86037
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 2016.00 2.79612
\(722\) 0 0
\(723\) − 1146.00i − 1.58506i
\(724\) 0 0
\(725\) 2086.97i 2.87857i
\(726\) 0 0
\(727\) 107.778 0.148250 0.0741249 0.997249i \(-0.476384\pi\)
0.0741249 + 0.997249i \(0.476384\pi\)
\(728\) 0 0
\(729\) −729.000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) −1381.51 −1.87961
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 672.000 0.902013
\(746\) 0 0
\(747\) − 1206.00i − 1.61446i
\(748\) 0 0
\(749\) − 842.624i − 1.12500i
\(750\) 0 0
\(751\) −538.888 −0.717560 −0.358780 0.933422i \(-0.616807\pi\)
−0.358780 + 0.933422i \(0.616807\pi\)
\(752\) 0 0
\(753\) −1410.00 −1.87251
\(754\) 0 0
\(755\) 480.000i 0.635762i
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 862.000 1.12094 0.560468 0.828176i \(-0.310621\pi\)
0.560468 + 0.828176i \(0.310621\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 1028.79i − 1.33090i −0.746442 0.665450i \(-0.768240\pi\)
0.746442 0.665450i \(-0.231760\pi\)
\(774\) 0 0
\(775\) −3478.28 −4.48810
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 793.635 1.01358
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 1440.00i 1.81132i
\(796\) 0 0
\(797\) − 930.806i − 1.16789i −0.811794 0.583944i \(-0.801509\pi\)
0.811794 0.583944i \(-0.198491\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 500.000i 0.622665i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 969.998 1.20198
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 1616.66i 1.98852i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 1499.09i − 1.82593i −0.408039 0.912965i \(-0.633787\pi\)
0.408039 0.912965i \(-0.366213\pi\)
\(822\) 0 0
\(823\) −1577.47 −1.91673 −0.958367 0.285541i \(-0.907827\pi\)
−0.958367 + 0.285541i \(0.907827\pi\)
\(824\) 0 0
\(825\) −2130.00 −2.58182
\(826\) 0 0
\(827\) − 1546.00i − 1.86941i −0.355428 0.934704i \(-0.615665\pi\)
0.355428 0.934704i \(-0.384335\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1322.72i 1.58032i
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) −23.0000 −0.0273484
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1655.86i 1.95959i
\(846\) 0 0
\(847\) −205.757 −0.242925
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) −3360.00 −3.88439
\(866\) 0 0
\(867\) − 867.000i − 1.00000i
\(868\) 0 0
\(869\) − 1469.69i − 1.69125i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 1710.00 1.95876
\(874\) 0 0
\(875\) − 4416.00i − 5.04686i
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) −1322.72 −1.50481
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 0 0
\(885\) 293.939i 0.332134i
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 1056.00 1.18785
\(890\) 0 0
\(891\) 810.000i 0.909091i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) −2253.53 −2.51791
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 1440.00i − 1.60178i
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) − 617.271i − 0.679066i
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) −1340.00 −1.46769
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 2449.49i − 2.67120i
\(918\) 0 0
\(919\) 1714.64 1.86577 0.932885 0.360174i \(-0.117283\pi\)
0.932885 + 0.360174i \(0.117283\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1851.81 1.99764
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1490.00 −1.59018 −0.795091 0.606491i \(-0.792577\pi\)
−0.795091 + 0.606491i \(0.792577\pi\)
\(938\) 0 0
\(939\) − 1590.00i − 1.69329i
\(940\) 0 0
\(941\) − 1832.22i − 1.94710i −0.228480 0.973549i \(-0.573376\pi\)
0.228480 0.973549i \(-0.426624\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) −2592.00 −2.74286
\(946\) 0 0
\(947\) 1306.00i 1.37909i 0.724242 + 0.689546i \(0.242190\pi\)
−0.724242 + 0.689546i \(0.757810\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −1616.66 −1.69996
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) − 881.816i − 0.921438i
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 1439.00 1.49740
\(962\) 0 0
\(963\) − 774.000i − 0.803738i
\(964\) 0 0
\(965\) 2841.41i 2.94446i
\(966\) 0 0
\(967\) 303.737 0.314102 0.157051 0.987590i \(-0.449801\pi\)
0.157051 + 0.987590i \(0.449801\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1930.00i 1.98764i 0.110996 + 0.993821i \(0.464596\pi\)
−0.110996 + 0.993821i \(0.535404\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 3360.00 3.41117
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1420.70 1.43361 0.716803 0.697275i \(-0.245605\pi\)
0.716803 + 0.697275i \(0.245605\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 3360.00i − 3.37688i
\(996\) 0 0
\(997\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 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 768.3.e.j.257.1 4
3.2 odd 2 inner 768.3.e.j.257.4 4
4.3 odd 2 inner 768.3.e.j.257.3 4
8.3 odd 2 inner 768.3.e.j.257.2 4
8.5 even 2 inner 768.3.e.j.257.4 4
12.11 even 2 inner 768.3.e.j.257.2 4
16.3 odd 4 384.3.h.a.65.1 2
16.5 even 4 384.3.h.a.65.2 yes 2
16.11 odd 4 384.3.h.d.65.2 yes 2
16.13 even 4 384.3.h.d.65.1 yes 2
24.5 odd 2 CM 768.3.e.j.257.1 4
24.11 even 2 inner 768.3.e.j.257.3 4
48.5 odd 4 384.3.h.d.65.1 yes 2
48.11 even 4 384.3.h.a.65.1 2
48.29 odd 4 384.3.h.a.65.2 yes 2
48.35 even 4 384.3.h.d.65.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
384.3.h.a.65.1 2 16.3 odd 4
384.3.h.a.65.1 2 48.11 even 4
384.3.h.a.65.2 yes 2 16.5 even 4
384.3.h.a.65.2 yes 2 48.29 odd 4
384.3.h.d.65.1 yes 2 16.13 even 4
384.3.h.d.65.1 yes 2 48.5 odd 4
384.3.h.d.65.2 yes 2 16.11 odd 4
384.3.h.d.65.2 yes 2 48.35 even 4
768.3.e.j.257.1 4 1.1 even 1 trivial
768.3.e.j.257.1 4 24.5 odd 2 CM
768.3.e.j.257.2 4 8.3 odd 2 inner
768.3.e.j.257.2 4 12.11 even 2 inner
768.3.e.j.257.3 4 4.3 odd 2 inner
768.3.e.j.257.3 4 24.11 even 2 inner
768.3.e.j.257.4 4 3.2 odd 2 inner
768.3.e.j.257.4 4 8.5 even 2 inner