Properties

Label 768.3.e.k.257.1
Level $768$
Weight $3$
Character 768.257
Analytic conductor $20.926$
Analytic rank $0$
Dimension $4$
CM discriminant -8
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: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) 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 \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 768.257
Dual form 768.3.e.k.257.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.82843 - 1.00000i) q^{3} +(7.00000 + 5.65685i) q^{9} +O(q^{10})\) \(q+(-2.82843 - 1.00000i) q^{3} +(7.00000 + 5.65685i) q^{9} +14.0000i q^{11} -33.9411i q^{17} -16.9706 q^{19} +25.0000 q^{25} +(-14.1421 - 23.0000i) q^{27} +(14.0000 - 39.5980i) q^{33} +67.8823i q^{41} -84.8528 q^{43} -49.0000 q^{49} +(-33.9411 + 96.0000i) q^{51} +(48.0000 + 16.9706i) q^{57} +82.0000i q^{59} -118.794 q^{67} -142.000 q^{73} +(-70.7107 - 25.0000i) q^{75} +(17.0000 + 79.1960i) q^{81} -158.000i q^{83} -101.823i q^{89} -94.0000 q^{97} +(-79.1960 + 98.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 28 q^{9} + 100 q^{25} + 56 q^{33} - 196 q^{49} + 192 q^{57} - 568 q^{73} + 68 q^{81} - 376 q^{97}+O(q^{100}) \) 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
\(3\) −2.82843 1.00000i −0.942809 0.333333i
\(4\) 0 0
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 7.00000 + 5.65685i 0.777778 + 0.628539i
\(10\) 0 0
\(11\) 14.0000i 1.27273i 0.771389 + 0.636364i \(0.219562\pi\)
−0.771389 + 0.636364i \(0.780438\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 33.9411i 1.99654i −0.0588235 0.998268i \(-0.518735\pi\)
0.0588235 0.998268i \(-0.481265\pi\)
\(18\) 0 0
\(19\) −16.9706 −0.893188 −0.446594 0.894737i \(-0.647363\pi\)
−0.446594 + 0.894737i \(0.647363\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 25.0000 1.00000
\(26\) 0 0
\(27\) −14.1421 23.0000i −0.523783 0.851852i
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 14.0000 39.5980i 0.424242 1.19994i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 67.8823i 1.65566i 0.560976 + 0.827832i \(0.310426\pi\)
−0.560976 + 0.827832i \(0.689574\pi\)
\(42\) 0 0
\(43\) −84.8528 −1.97332 −0.986661 0.162791i \(-0.947950\pi\)
−0.986661 + 0.162791i \(0.947950\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) −49.0000 −1.00000
\(50\) 0 0
\(51\) −33.9411 + 96.0000i −0.665512 + 1.88235i
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 48.0000 + 16.9706i 0.842105 + 0.297729i
\(58\) 0 0
\(59\) 82.0000i 1.38983i 0.719092 + 0.694915i \(0.244558\pi\)
−0.719092 + 0.694915i \(0.755442\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −118.794 −1.77304 −0.886522 0.462687i \(-0.846886\pi\)
−0.886522 + 0.462687i \(0.846886\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −142.000 −1.94521 −0.972603 0.232473i \(-0.925318\pi\)
−0.972603 + 0.232473i \(0.925318\pi\)
\(74\) 0 0
\(75\) −70.7107 25.0000i −0.942809 0.333333i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 17.0000 + 79.1960i 0.209877 + 0.977728i
\(82\) 0 0
\(83\) 158.000i 1.90361i −0.306697 0.951807i \(-0.599224\pi\)
0.306697 0.951807i \(-0.400776\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 101.823i 1.14408i −0.820225 0.572041i \(-0.806152\pi\)
0.820225 0.572041i \(-0.193848\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −94.0000 −0.969072 −0.484536 0.874771i \(-0.661012\pi\)
−0.484536 + 0.874771i \(0.661012\pi\)
\(98\) 0 0
\(99\) −79.1960 + 98.0000i −0.799959 + 0.989899i
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 178.000i 1.66355i 0.555112 + 0.831776i \(0.312675\pi\)
−0.555112 + 0.831776i \(0.687325\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 203.647i 1.80218i 0.433628 + 0.901092i \(0.357233\pi\)
−0.433628 + 0.901092i \(0.642767\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −75.0000 −0.619835
\(122\) 0 0
\(123\) 67.8823 192.000i 0.551888 1.56098i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 240.000 + 84.8528i 1.86047 + 0.657774i
\(130\) 0 0
\(131\) 62.0000i 0.473282i 0.971597 + 0.236641i \(0.0760466\pi\)
−0.971597 + 0.236641i \(0.923953\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 135.765i 0.990982i −0.868613 0.495491i \(-0.834988\pi\)
0.868613 0.495491i \(-0.165012\pi\)
\(138\) 0 0
\(139\) −186.676 −1.34299 −0.671497 0.741007i \(-0.734348\pi\)
−0.671497 + 0.741007i \(0.734348\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 138.593 + 49.0000i 0.942809 + 0.333333i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 192.000 237.588i 1.25490 1.55286i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 50.9117 0.312342 0.156171 0.987730i \(-0.450085\pi\)
0.156171 + 0.987730i \(0.450085\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −169.000 −1.00000
\(170\) 0 0
\(171\) −118.794 96.0000i −0.694701 0.561404i
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 82.0000 231.931i 0.463277 1.31034i
\(178\) 0 0
\(179\) 34.0000i 0.189944i −0.995480 0.0949721i \(-0.969724\pi\)
0.995480 0.0949721i \(-0.0302762\pi\)
\(180\) 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
\(187\) 475.176 2.54105
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) −98.0000 −0.507772 −0.253886 0.967234i \(-0.581709\pi\)
−0.253886 + 0.967234i \(0.581709\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 336.000 + 118.794i 1.67164 + 0.591015i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 237.588i 1.13678i
\(210\) 0 0
\(211\) 356.382 1.68901 0.844507 0.535545i \(-0.179894\pi\)
0.844507 + 0.535545i \(0.179894\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 401.637 + 142.000i 1.83396 + 0.648402i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 175.000 + 141.421i 0.777778 + 0.628539i
\(226\) 0 0
\(227\) 446.000i 1.96476i −0.186900 0.982379i \(-0.559844\pi\)
0.186900 0.982379i \(-0.440156\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 169.706i 0.728350i 0.931330 + 0.364175i \(0.118649\pi\)
−0.931330 + 0.364175i \(0.881351\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −194.000 −0.804979 −0.402490 0.915425i \(-0.631855\pi\)
−0.402490 + 0.915425i \(0.631855\pi\)
\(242\) 0 0
\(243\) 31.1127 241.000i 0.128036 0.991770i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −158.000 + 446.891i −0.634538 + 1.79474i
\(250\) 0 0
\(251\) 466.000i 1.85657i −0.371865 0.928287i \(-0.621282\pi\)
0.371865 0.928287i \(-0.378718\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 339.411i 1.32067i −0.750973 0.660333i \(-0.770415\pi\)
0.750973 0.660333i \(-0.229585\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −101.823 + 288.000i −0.381361 + 1.07865i
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 350.000i 1.27273i
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 509.117i 1.81180i 0.423488 + 0.905902i \(0.360806\pi\)
−0.423488 + 0.905902i \(0.639194\pi\)
\(282\) 0 0
\(283\) 560.029 1.97890 0.989450 0.144876i \(-0.0462784\pi\)
0.989450 + 0.144876i \(0.0462784\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −863.000 −2.98616
\(290\) 0 0
\(291\) 265.872 + 94.0000i 0.913650 + 0.323024i
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 322.000 197.990i 1.08418 0.666633i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 288.500 0.939738 0.469869 0.882736i \(-0.344301\pi\)
0.469869 + 0.882736i \(0.344301\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −526.000 −1.68051 −0.840256 0.542191i \(-0.817595\pi\)
−0.840256 + 0.542191i \(0.817595\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 178.000 503.460i 0.554517 1.56841i
\(322\) 0 0
\(323\) 576.000i 1.78328i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −661.852 −1.99955 −0.999776 0.0211480i \(-0.993268\pi\)
−0.999776 + 0.0211480i \(0.993268\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 478.000 1.41840 0.709199 0.705009i \(-0.249057\pi\)
0.709199 + 0.705009i \(0.249057\pi\)
\(338\) 0 0
\(339\) 203.647 576.000i 0.600728 1.69912i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 658.000i 1.89625i −0.317892 0.948127i \(-0.602975\pi\)
0.317892 0.948127i \(-0.397025\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 678.823i 1.92301i 0.274788 + 0.961505i \(0.411392\pi\)
−0.274788 + 0.961505i \(0.588608\pi\)
\(354\) 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
\(361\) −73.0000 −0.202216
\(362\) 0 0
\(363\) 212.132 + 75.0000i 0.584386 + 0.206612i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) −384.000 + 475.176i −1.04065 + 1.28774i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 322.441 0.850767 0.425383 0.905013i \(-0.360139\pi\)
0.425383 + 0.905013i \(0.360139\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −593.970 480.000i −1.53481 1.24031i
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 62.0000 175.362i 0.157761 0.446215i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 237.588i 0.592488i −0.955112 0.296244i \(-0.904266\pi\)
0.955112 0.296244i \(-0.0957342\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 334.000 0.816626 0.408313 0.912842i \(-0.366117\pi\)
0.408313 + 0.912842i \(0.366117\pi\)
\(410\) 0 0
\(411\) −135.765 + 384.000i −0.330327 + 0.934307i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 528.000 + 186.676i 1.26619 + 0.447665i
\(418\) 0 0
\(419\) 514.000i 1.22673i 0.789799 + 0.613365i \(0.210185\pi\)
−0.789799 + 0.613365i \(0.789815\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 848.528i 1.99654i
\(426\) 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
\(433\) 578.000 1.33487 0.667436 0.744667i \(-0.267392\pi\)
0.667436 + 0.744667i \(0.267392\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −343.000 277.186i −0.777778 0.628539i
\(442\) 0 0
\(443\) 878.000i 1.98194i 0.134079 + 0.990971i \(0.457192\pi\)
−0.134079 + 0.990971i \(0.542808\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 237.588i 0.529149i 0.964365 + 0.264574i \(0.0852315\pi\)
−0.964365 + 0.264574i \(0.914769\pi\)
\(450\) 0 0
\(451\) −950.352 −2.10721
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 238.000 0.520788 0.260394 0.965502i \(-0.416148\pi\)
0.260394 + 0.965502i \(0.416148\pi\)
\(458\) 0 0
\(459\) −780.646 + 480.000i −1.70075 + 1.04575i
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 34.0000i 0.0728051i 0.999337 + 0.0364026i \(0.0115899\pi\)
−0.999337 + 0.0364026i \(0.988410\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1187.94i 2.51150i
\(474\) 0 0
\(475\) −424.264 −0.893188
\(476\) 0 0
\(477\) 0 0
\(478\) 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
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) −144.000 50.9117i −0.294479 0.104114i
\(490\) 0 0
\(491\) 782.000i 1.59267i −0.604857 0.796334i \(-0.706770\pi\)
0.604857 0.796334i \(-0.293230\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −593.970 −1.19032 −0.595160 0.803607i \(-0.702911\pi\)
−0.595160 + 0.803607i \(0.702911\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 478.004 + 169.000i 0.942809 + 0.333333i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 240.000 + 390.323i 0.467836 + 0.760863i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 271.529i 0.521169i 0.965451 + 0.260584i \(0.0839152\pi\)
−0.965451 + 0.260584i \(0.916085\pi\)
\(522\) 0 0
\(523\) −967.322 −1.84956 −0.924782 0.380497i \(-0.875753\pi\)
−0.924782 + 0.380497i \(0.875753\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 529.000 1.00000
\(530\) 0 0
\(531\) −463.862 + 574.000i −0.873563 + 1.08098i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −34.0000 + 96.1665i −0.0633147 + 0.179081i
\(538\) 0 0
\(539\) 686.000i 1.27273i
\(540\) 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
\(547\) 390.323 0.713570 0.356785 0.934186i \(-0.383873\pi\)
0.356785 + 0.934186i \(0.383873\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −1344.00 475.176i −2.39572 0.847016i
\(562\) 0 0
\(563\) 226.000i 0.401421i 0.979651 + 0.200710i \(0.0643251\pi\)
−0.979651 + 0.200710i \(0.935675\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 950.352i 1.67021i 0.550088 + 0.835107i \(0.314594\pi\)
−0.550088 + 0.835107i \(0.685406\pi\)
\(570\) 0 0
\(571\) −933.381 −1.63464 −0.817321 0.576182i \(-0.804542\pi\)
−0.817321 + 0.576182i \(0.804542\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −2.00000 −0.00346620 −0.00173310 0.999998i \(-0.500552\pi\)
−0.00173310 + 0.999998i \(0.500552\pi\)
\(578\) 0 0
\(579\) 277.186 + 98.0000i 0.478732 + 0.169257i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1138.00i 1.93867i 0.245741 + 0.969336i \(0.420969\pi\)
−0.245741 + 0.969336i \(0.579031\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 814.587i 1.37367i 0.726813 + 0.686836i \(0.241001\pi\)
−0.726813 + 0.686836i \(0.758999\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 914.000 1.52080 0.760399 0.649456i \(-0.225003\pi\)
0.760399 + 0.649456i \(0.225003\pi\)
\(602\) 0 0
\(603\) −831.558 672.000i −1.37903 1.11443i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 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
\(617\) 1187.94i 1.92535i 0.270665 + 0.962674i \(0.412757\pi\)
−0.270665 + 0.962674i \(0.587243\pi\)
\(618\) 0 0
\(619\) 1103.09 1.78205 0.891023 0.453958i \(-0.149988\pi\)
0.891023 + 0.453958i \(0.149988\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000 1.00000
\(626\) 0 0
\(627\) −237.588 + 672.000i −0.378928 + 1.07177i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) −1008.00 356.382i −1.59242 0.563004i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1187.94i 1.85326i −0.375975 0.926630i \(-0.622692\pi\)
0.375975 0.926630i \(-0.377308\pi\)
\(642\) 0 0
\(643\) −424.264 −0.659820 −0.329910 0.944012i \(-0.607018\pi\)
−0.329910 + 0.944012i \(0.607018\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) −1148.00 −1.76888
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −994.000 803.273i −1.51294 1.22264i
\(658\) 0 0
\(659\) 994.000i 1.50835i −0.656676 0.754173i \(-0.728038\pi\)
0.656676 0.754173i \(-0.271962\pi\)
\(660\) 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
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1246.00 −1.85141 −0.925706 0.378244i \(-0.876528\pi\)
−0.925706 + 0.378244i \(0.876528\pi\)
\(674\) 0 0
\(675\) −353.553 575.000i −0.523783 0.851852i
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −446.000 + 1261.48i −0.654919 + 1.85239i
\(682\) 0 0
\(683\) 398.000i 0.582723i 0.956613 + 0.291362i \(0.0941083\pi\)
−0.956613 + 0.291362i \(0.905892\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −1170.97 −1.69460 −0.847300 0.531114i \(-0.821773\pi\)
−0.847300 + 0.531114i \(0.821773\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 2304.00 3.30560
\(698\) 0 0
\(699\) 169.706 480.000i 0.242783 0.686695i
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 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
\(721\) 0 0
\(722\) 0 0
\(723\) 548.715 + 194.000i 0.758942 + 0.268326i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −329.000 + 650.538i −0.451303 + 0.892371i
\(730\) 0 0
\(731\) 2880.00i 3.93981i
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1663.12i 2.25660i
\(738\) 0 0
\(739\) 1442.50 1.95196 0.975980 0.217862i \(-0.0699083\pi\)
0.975980 + 0.217862i \(0.0699083\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 893.783 1106.00i 1.19650 1.48059i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) −466.000 + 1318.05i −0.618858 + 1.75039i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 610.940i 0.802812i 0.915900 + 0.401406i \(0.131478\pi\)
−0.915900 + 0.401406i \(0.868522\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 1054.00 1.37061 0.685306 0.728256i \(-0.259669\pi\)
0.685306 + 0.728256i \(0.259669\pi\)
\(770\) 0 0
\(771\) −339.411 + 960.000i −0.440222 + 1.24514i
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1152.00i 1.47882i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 1272.79 1.61727 0.808635 0.588310i \(-0.200207\pi\)
0.808635 + 0.588310i \(0.200207\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 576.000 712.764i 0.719101 0.889842i
\(802\) 0 0
\(803\) 1988.00i 2.47572i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 339.411i 0.419544i −0.977750 0.209772i \(-0.932728\pi\)
0.977750 0.209772i \(-0.0672722\pi\)
\(810\) 0 0
\(811\) 1612.20 1.98792 0.993960 0.109741i \(-0.0350022\pi\)
0.993960 + 0.109741i \(0.0350022\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1440.00 1.76255
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 350.000 989.949i 0.424242 1.19994i
\(826\) 0 0
\(827\) 1262.00i 1.52600i −0.646400 0.762999i \(-0.723726\pi\)
0.646400 0.762999i \(-0.276274\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1663.12i 1.99654i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 841.000 1.00000
\(842\) 0 0
\(843\) 509.117 1440.00i 0.603935 1.70819i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −1584.00 560.029i −1.86572 0.659633i
\(850\) 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
\(857\) 1221.88i 1.42576i −0.701284 0.712882i \(-0.747389\pi\)
0.701284 0.712882i \(-0.252611\pi\)
\(858\) 0 0
\(859\) −492.146 −0.572929 −0.286465 0.958091i \(-0.592480\pi\)
−0.286465 + 0.958091i \(0.592480\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 2440.93 + 863.000i 2.81538 + 0.995386i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −658.000 531.744i −0.753723 0.609100i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1018.23i 1.15577i −0.816118 0.577885i \(-0.803878\pi\)
0.816118 0.577885i \(-0.196122\pi\)
\(882\) 0 0
\(883\) 118.794 0.134534 0.0672672 0.997735i \(-0.478572\pi\)
0.0672672 + 0.997735i \(0.478572\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1108.74 + 238.000i −1.24438 + 0.267116i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 593.970 0.654873 0.327436 0.944873i \(-0.393815\pi\)
0.327436 + 0.944873i \(0.393815\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 2212.00 2.42278
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) −816.000 288.500i −0.885993 0.313246i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1527.35i 1.64408i 0.569429 + 0.822040i \(0.307164\pi\)
−0.569429 + 0.822040i \(0.692836\pi\)
\(930\) 0 0
\(931\) 831.558 0.893188
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 718.000 0.766275 0.383138 0.923691i \(-0.374843\pi\)
0.383138 + 0.923691i \(0.374843\pi\)
\(938\) 0 0
\(939\) 1487.75 + 526.000i 1.58440 + 0.560170i
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 994.000i 1.04963i −0.851216 0.524815i \(-0.824134\pi\)
0.851216 0.524815i \(-0.175866\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1900.70i 1.99444i −0.0745016 0.997221i \(-0.523737\pi\)
0.0745016 0.997221i \(-0.476263\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −961.000 −1.00000
\(962\) 0 0
\(963\) −1006.92 + 1246.00i −1.04561 + 1.29387i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) 576.000 1629.17i 0.594427 1.68129i
\(970\) 0 0
\(971\) 974.000i 1.00309i 0.865132 + 0.501545i \(0.167235\pi\)
−0.865132 + 0.501545i \(0.832765\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 373.352i 0.382142i 0.981576 + 0.191071i \(0.0611960\pi\)
−0.981576 + 0.191071i \(0.938804\pi\)
\(978\) 0 0
\(979\) 1425.53 1.45611
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) 1872.00 + 661.852i 1.88520 + 0.666518i
\(994\) 0 0
\(995\) 0 0
\(996\) 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.k.257.1 4
3.2 odd 2 inner 768.3.e.k.257.2 4
4.3 odd 2 inner 768.3.e.k.257.4 4
8.3 odd 2 CM 768.3.e.k.257.1 4
8.5 even 2 inner 768.3.e.k.257.4 4
12.11 even 2 inner 768.3.e.k.257.3 4
16.3 odd 4 384.3.h.b.65.2 yes 2
16.5 even 4 384.3.h.b.65.2 yes 2
16.11 odd 4 384.3.h.c.65.1 yes 2
16.13 even 4 384.3.h.c.65.1 yes 2
24.5 odd 2 inner 768.3.e.k.257.3 4
24.11 even 2 inner 768.3.e.k.257.2 4
48.5 odd 4 384.3.h.c.65.2 yes 2
48.11 even 4 384.3.h.b.65.1 2
48.29 odd 4 384.3.h.b.65.1 2
48.35 even 4 384.3.h.c.65.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
384.3.h.b.65.1 2 48.11 even 4
384.3.h.b.65.1 2 48.29 odd 4
384.3.h.b.65.2 yes 2 16.3 odd 4
384.3.h.b.65.2 yes 2 16.5 even 4
384.3.h.c.65.1 yes 2 16.11 odd 4
384.3.h.c.65.1 yes 2 16.13 even 4
384.3.h.c.65.2 yes 2 48.5 odd 4
384.3.h.c.65.2 yes 2 48.35 even 4
768.3.e.k.257.1 4 1.1 even 1 trivial
768.3.e.k.257.1 4 8.3 odd 2 CM
768.3.e.k.257.2 4 3.2 odd 2 inner
768.3.e.k.257.2 4 24.11 even 2 inner
768.3.e.k.257.3 4 12.11 even 2 inner
768.3.e.k.257.3 4 24.5 odd 2 inner
768.3.e.k.257.4 4 4.3 odd 2 inner
768.3.e.k.257.4 4 8.5 even 2 inner