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Properties

Label 512.2.a.f.1.1
Level $512$
Weight $2$
Character 512.1
Self dual yes
Analytic conductor $4.088$
Analytic rank $0$
Dimension $2$
CM discriminant -8
Inner twists $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [512,2,Mod(1,512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("512.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 512 = 2^{9} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 512.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,4,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(4.08834058349\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

Embedding label 1.1
Root \(-1.41421\) of defining polynomial
Character \(\chi\) \(=\) 512.1

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.585786 q^{3} -2.65685 q^{9} +6.24264 q^{11} +5.65685 q^{17} +7.41421 q^{19} -5.00000 q^{25} -3.31371 q^{27} +3.65685 q^{33} -6.00000 q^{41} +13.0711 q^{43} -7.00000 q^{49} +3.31371 q^{51} +4.34315 q^{57} -14.2426 q^{59} -3.89949 q^{67} +16.9706 q^{73} -2.92893 q^{75} +6.02944 q^{81} -10.7279 q^{83} -5.65685 q^{89} -16.9706 q^{97} -16.5858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{3} + 6 q^{9} + 4 q^{11} + 12 q^{19} - 10 q^{25} + 16 q^{27} - 4 q^{33} - 12 q^{41} + 12 q^{43} - 14 q^{49} - 16 q^{51} + 20 q^{57} - 20 q^{59} + 12 q^{67} - 20 q^{75} + 46 q^{81} + 4 q^{83} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 0.585786 0.338204 0.169102 − 0.985599i \(-0.445913\pi\)
0.169102 + 0.985599i \(0.445913\pi\)
\(4\) 0 0
\(5\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) −2.65685 −0.885618
\(10\) 0 0
\(11\) 6.24264 1.88223 0.941113 − 0.338091i \(-0.109781\pi\)
0.941113 + 0.338091i \(0.109781\pi\)
\(12\) 0 0
\(13\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.65685 1.37199 0.685994 − 0.727607i \(-0.259367\pi\)
0.685994 + 0.727607i \(0.259367\pi\)
\(18\) 0 0
\(19\) 7.41421 1.70094 0.850469 − 0.526026i \(-0.176318\pi\)
0.850469 + 0.526026i \(0.176318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) −3.31371 −0.637723
\(28\) 0 0
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 3.65685 0.636577
\(34\) 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
\(41\) −6.00000 −0.937043 −0.468521 − 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 13.0711 1.99332 0.996660 − 0.0816682i \(-0.0260248\pi\)
0.996660 + 0.0816682i \(0.0260248\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 3.31371 0.464012
\(52\) 0 0
\(53\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.34315 0.575264
\(58\) 0 0
\(59\) −14.2426 −1.85423 −0.927117 − 0.374772i \(-0.877721\pi\)
−0.927117 + 0.374772i \(0.877721\pi\)
\(60\) 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
\(67\) −3.89949 −0.476399 −0.238200 − 0.971216i \(-0.576557\pi\)
−0.238200 + 0.971216i \(0.576557\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 16.9706 1.98625 0.993127 − 0.117041i \(-0.0373409\pi\)
0.993127 + 0.117041i \(0.0373409\pi\)
\(74\) 0 0
\(75\) −2.92893 −0.338204
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 6.02944 0.669937
\(82\) 0 0
\(83\) −10.7279 −1.17754 −0.588771 − 0.808300i \(-0.700388\pi\)
−0.588771 + 0.808300i \(0.700388\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.65685 −0.599625 −0.299813 − 0.953998i \(-0.596924\pi\)
−0.299813 + 0.953998i \(0.596924\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −16.9706 −1.72310 −0.861550 − 0.507673i \(-0.830506\pi\)
−0.861550 + 0.507673i \(0.830506\pi\)
\(98\) 0 0
\(99\) −16.5858 −1.66693
\(100\) 0 0
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −9.75736 −0.943280 −0.471640 − 0.881791i \(-0.656338\pi\)
−0.471640 + 0.881791i \(0.656338\pi\)
\(108\) 0 0
\(109\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −18.0000 −1.69330 −0.846649 − 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 27.9706 2.54278
\(122\) 0 0
\(123\) −3.51472 −0.316912
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 7.65685 0.674148
\(130\) 0 0
\(131\) 2.72792 0.238340 0.119170 − 0.992874i \(-0.461977\pi\)
0.119170 + 0.992874i \(0.461977\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000 0.512615 0.256307 − 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) −9.55635 −0.810559 −0.405279 − 0.914193i \(-0.632826\pi\)
−0.405279 + 0.914193i \(0.632826\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −4.10051 −0.338204
\(148\) 0 0
\(149\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −15.0294 −1.21506
\(154\) 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
\(163\) 16.5858 1.29910 0.649550 − 0.760319i \(-0.274958\pi\)
0.649550 + 0.760319i \(0.274958\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) −19.6985 −1.50638
\(172\) 0 0
\(173\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −8.34315 −0.627109
\(178\) 0 0
\(179\) −26.7279 −1.99774 −0.998869 − 0.0475398i \(-0.984862\pi\)
−0.998869 + 0.0475398i \(0.984862\pi\)
\(180\) 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
\(187\) 35.3137 2.58239
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) −16.9706 −1.22157 −0.610784 − 0.791797i \(-0.709146\pi\)
−0.610784 + 0.791797i \(0.709146\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) −2.28427 −0.161120
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 46.2843 3.20155
\(210\) 0 0
\(211\) 27.8995 1.92068 0.960340 − 0.278831i \(-0.0899469\pi\)
0.960340 + 0.278831i \(0.0899469\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 9.94113 0.671759
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 13.2843 0.885618
\(226\) 0 0
\(227\) 23.2132 1.54071 0.770357 − 0.637613i \(-0.220078\pi\)
0.770357 + 0.637613i \(0.220078\pi\)
\(228\) 0 0
\(229\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.65685 −0.370593 −0.185296 − 0.982683i \(-0.559325\pi\)
−0.185296 + 0.982683i \(0.559325\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −16.9706 −1.09317 −0.546585 − 0.837404i \(-0.684072\pi\)
−0.546585 + 0.837404i \(0.684072\pi\)
\(242\) 0 0
\(243\) 13.4731 0.864299
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −6.28427 −0.398250
\(250\) 0 0
\(251\) 17.7574 1.12083 0.560417 − 0.828210i \(-0.310641\pi\)
0.560417 + 0.828210i \(0.310641\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 30.0000 1.87135 0.935674 − 0.352865i \(-0.114792\pi\)
0.935674 + 0.352865i \(0.114792\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 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
\(267\) −3.31371 −0.202796
\(268\) 0 0
\(269\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −31.2132 −1.88223
\(276\) 0 0
\(277\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −28.2843 −1.68730 −0.843649 − 0.536895i \(-0.819597\pi\)
−0.843649 + 0.536895i \(0.819597\pi\)
\(282\) 0 0
\(283\) 33.5563 1.99472 0.997359 − 0.0726300i \(-0.0231392\pi\)
0.997359 + 0.0726300i \(0.0231392\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 15.0000 0.882353
\(290\) 0 0
\(291\) −9.94113 −0.582759
\(292\) 0 0
\(293\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −20.6863 −1.20034
\(298\) 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
\(307\) 30.0416 1.71457 0.857283 − 0.514845i \(-0.172151\pi\)
0.857283 + 0.514845i \(0.172151\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 − 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −5.71573 −0.319021
\(322\) 0 0
\(323\) 41.9411 2.33367
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.384776 −0.0211492 −0.0105746 − 0.999944i \(-0.503366\pi\)
−0.0105746 + 0.999944i \(0.503366\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 − 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) −10.5442 −0.572680
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −30.2426 −1.62351 −0.811755 − 0.583998i \(-0.801488\pi\)
−0.811755 + 0.583998i \(0.801488\pi\)
\(348\) 0 0
\(349\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −30.0000 −1.59674 −0.798369 − 0.602168i \(-0.794304\pi\)
−0.798369 + 0.602168i \(0.794304\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 35.9706 1.89319
\(362\) 0 0
\(363\) 16.3848 0.859978
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 15.9411 0.829862
\(370\) 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
\(379\) −20.8701 −1.07202 −0.536011 − 0.844211i \(-0.680070\pi\)
−0.536011 + 0.844211i \(0.680070\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −34.7279 −1.76532
\(388\) 0 0
\(389\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 1.59798 0.0806074
\(394\) 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
\(401\) −39.5980 −1.97743 −0.988714 − 0.149813i \(-0.952133\pi\)
−0.988714 + 0.149813i \(0.952133\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −22.0000 −1.08783 −0.543915 − 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 0 0
\(411\) 3.51472 0.173368
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −5.59798 −0.274134
\(418\) 0 0
\(419\) −13.2721 −0.648383 −0.324192 − 0.945991i \(-0.605092\pi\)
−0.324192 + 0.945991i \(0.605092\pi\)
\(420\) 0 0
\(421\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −28.2843 −1.37199
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −16.9706 −0.815553 −0.407777 − 0.913082i \(-0.633696\pi\)
−0.407777 + 0.913082i \(0.633696\pi\)
\(434\) 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
\(441\) 18.5980 0.885618
\(442\) 0 0
\(443\) −27.6985 −1.31599 −0.657997 − 0.753020i \(-0.728596\pi\)
−0.657997 + 0.753020i \(0.728596\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.65685 0.266963 0.133482 − 0.991051i \(-0.457384\pi\)
0.133482 + 0.991051i \(0.457384\pi\)
\(450\) 0 0
\(451\) −37.4558 −1.76373
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 26.0000 1.21623 0.608114 − 0.793849i \(-0.291926\pi\)
0.608114 + 0.793849i \(0.291926\pi\)
\(458\) 0 0
\(459\) −18.7452 −0.874949
\(460\) 0 0
\(461\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.786797 0.0364086 0.0182043 − 0.999834i \(-0.494205\pi\)
0.0182043 + 0.999834i \(0.494205\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 81.5980 3.75188
\(474\) 0 0
\(475\) −37.0711 −1.70094
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 9.71573 0.439360
\(490\) 0 0
\(491\) 19.6985 0.888980 0.444490 − 0.895784i \(-0.353385\pi\)
0.444490 + 0.895784i \(0.353385\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −20.1005 −0.899822 −0.449911 − 0.893073i \(-0.648544\pi\)
−0.449911 + 0.893073i \(0.648544\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −7.61522 −0.338204
\(508\) 0 0
\(509\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −24.5685 −1.08473
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 − 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) 44.8701 1.96203 0.981015 − 0.193930i \(-0.0621236\pi\)
0.981015 + 0.193930i \(0.0621236\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 37.8406 1.64214
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −15.6569 −0.675643
\(538\) 0 0
\(539\) −43.6985 −1.88223
\(540\) 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
\(547\) −26.5269 −1.13421 −0.567104 − 0.823646i \(-0.691936\pi\)
−0.567104 + 0.823646i \(0.691936\pi\)
\(548\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 20.6863 0.873376
\(562\) 0 0
\(563\) −47.2132 −1.98980 −0.994900 − 0.100870i \(-0.967837\pi\)
−0.994900 + 0.100870i \(0.967837\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −42.0000 −1.76073 −0.880366 − 0.474295i \(-0.842703\pi\)
−0.880366 + 0.474295i \(0.842703\pi\)
\(570\) 0 0
\(571\) −14.4437 −0.604448 −0.302224 − 0.953237i \(-0.597729\pi\)
−0.302224 + 0.953237i \(0.597729\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −34.0000 −1.41544 −0.707719 − 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) 0 0
\(579\) −9.94113 −0.413139
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 38.2426 1.57844 0.789221 − 0.614109i \(-0.210484\pi\)
0.789221 + 0.614109i \(0.210484\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 18.0000 0.739171 0.369586 − 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 16.9706 0.692244 0.346122 − 0.938190i \(-0.387498\pi\)
0.346122 + 0.938190i \(0.387498\pi\)
\(602\) 0 0
\(603\) 10.3604 0.421908
\(604\) 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
\(617\) 39.5980 1.59415 0.797077 − 0.603877i \(-0.206378\pi\)
0.797077 + 0.603877i \(0.206378\pi\)
\(618\) 0 0
\(619\) −48.3848 −1.94475 −0.972374 − 0.233428i \(-0.925006\pi\)
−0.972374 + 0.233428i \(0.925006\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 27.1127 1.08278
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 16.3431 0.649582
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 28.2843 1.11716 0.558581 − 0.829450i \(-0.311346\pi\)
0.558581 + 0.829450i \(0.311346\pi\)
\(642\) 0 0
\(643\) 41.3553 1.63090 0.815448 − 0.578831i \(-0.196491\pi\)
0.815448 + 0.578831i \(0.196491\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) −88.9117 −3.49009
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −45.0883 −1.75906
\(658\) 0 0
\(659\) 21.2721 0.828643 0.414321 − 0.910131i \(-0.364019\pi\)
0.414321 + 0.910131i \(0.364019\pi\)
\(660\) 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
\(673\) 50.9117 1.96250 0.981251 − 0.192736i \(-0.0617360\pi\)
0.981251 + 0.192736i \(0.0617360\pi\)
\(674\) 0 0
\(675\) 16.5685 0.637723
\(676\) 0 0
\(677\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 13.5980 0.521076
\(682\) 0 0
\(683\) 51.6985 1.97819 0.989094 − 0.147287i \(-0.0470541\pi\)
0.989094 + 0.147287i \(0.0470541\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 50.5269 1.92213 0.961067 − 0.276315i \(-0.0891133\pi\)
0.961067 + 0.276315i \(0.0891133\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −33.9411 −1.28561
\(698\) 0 0
\(699\) −3.31371 −0.125336
\(700\) 0 0
\(701\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −9.94113 −0.369714
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −10.1960 −0.377628
\(730\) 0 0
\(731\) 73.9411 2.73481
\(732\) 0 0
\(733\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −24.3431 −0.896691
\(738\) 0 0
\(739\) −54.0416 −1.98795 −0.993977 − 0.109591i \(-0.965046\pi\)
−0.993977 + 0.109591i \(0.965046\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 28.5025 1.04285
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 10.4020 0.379071
\(754\) 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
\(761\) −54.0000 −1.95750 −0.978749 − 0.205061i \(-0.934261\pi\)
−0.978749 + 0.205061i \(0.934261\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 50.9117 1.83592 0.917961 − 0.396670i \(-0.129834\pi\)
0.917961 + 0.396670i \(0.129834\pi\)
\(770\) 0 0
\(771\) 17.5736 0.632897
\(772\) 0 0
\(773\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −44.4853 −1.59385
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −17.3553 −0.618651 −0.309326 − 0.950956i \(-0.600103\pi\)
−0.309326 + 0.950956i \(0.600103\pi\)
\(788\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 15.0294 0.531039
\(802\) 0 0
\(803\) 105.941 3.73858
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −6.00000 −0.210949 −0.105474 − 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) 0 0
\(811\) −3.12994 −0.109907 −0.0549536 − 0.998489i \(-0.517501\pi\)
−0.0549536 + 0.998489i \(0.517501\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 96.9117 3.39051
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) −18.2843 −0.636577
\(826\) 0 0
\(827\) 24.1838 0.840952 0.420476 − 0.907304i \(-0.361863\pi\)
0.420476 + 0.907304i \(0.361863\pi\)
\(828\) 0 0
\(829\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −39.5980 −1.37199
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) −16.5685 −0.570651
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 19.6569 0.674621
\(850\) 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
\(857\) 54.0000 1.84460 0.922302 − 0.386469i \(-0.126305\pi\)
0.922302 + 0.386469i \(0.126305\pi\)
\(858\) 0 0
\(859\) 47.0122 1.60404 0.802018 − 0.597300i \(-0.203760\pi\)
0.802018 + 0.597300i \(0.203760\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 8.78680 0.298415
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 45.0883 1.52601
\(874\) 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
\(881\) −18.0000 −0.606435 −0.303218 − 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) −40.5858 −1.36582 −0.682910 − 0.730502i \(-0.739286\pi\)
−0.682910 + 0.730502i \(0.739286\pi\)
\(884\) 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
\(890\) 0 0
\(891\) 37.6396 1.26097
\(892\) 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
\(907\) −34.9289 −1.15980 −0.579898 − 0.814689i \(-0.696908\pi\)
−0.579898 + 0.814689i \(0.696908\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) −66.9706 −2.21640
\(914\) 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
\(921\) 17.5980 0.579873
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 28.2843 0.927977 0.463988 − 0.885841i \(-0.346418\pi\)
0.463988 + 0.885841i \(0.346418\pi\)
\(930\) 0 0
\(931\) −51.8995 −1.70094
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −50.9117 −1.66321 −0.831606 − 0.555366i \(-0.812578\pi\)
−0.831606 + 0.555366i \(0.812578\pi\)
\(938\) 0 0
\(939\) 5.85786 0.191164
\(940\) 0 0
\(941\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 16.7868 0.545498 0.272749 − 0.962085i \(-0.412067\pi\)
0.272749 + 0.962085i \(0.412067\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −42.0000 −1.36051 −0.680257 − 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 25.9239 0.835385
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) 24.5685 0.789255
\(970\) 0 0
\(971\) −16.1838 −0.519362 −0.259681 − 0.965694i \(-0.583617\pi\)
−0.259681 + 0.965694i \(0.583617\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −62.2254 −1.99077 −0.995383 − 0.0959785i \(-0.969402\pi\)
−0.995383 + 0.0959785i \(0.969402\pi\)
\(978\) 0 0
\(979\) −35.3137 −1.12863
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) −0.225397 −0.00715275
\(994\) 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 512.2.a.f.1.1 yes 2
3.2 odd 2 4608.2.a.i.1.1 2
4.3 odd 2 512.2.a.a.1.2 ✓ 2
8.3 odd 2 CM 512.2.a.f.1.1 yes 2
8.5 even 2 512.2.a.a.1.2 ✓ 2
12.11 even 2 4608.2.a.k.1.2 2
16.3 odd 4 512.2.b.c.257.2 4
16.5 even 4 512.2.b.c.257.2 4
16.11 odd 4 512.2.b.c.257.3 4
16.13 even 4 512.2.b.c.257.3 4
24.5 odd 2 4608.2.a.k.1.2 2
24.11 even 2 4608.2.a.i.1.1 2
32.3 odd 8 1024.2.e.o.257.1 4
32.5 even 8 1024.2.e.o.769.1 4
32.11 odd 8 1024.2.e.o.769.1 4
32.13 even 8 1024.2.e.o.257.1 4
32.19 odd 8 1024.2.e.g.257.2 4
32.21 even 8 1024.2.e.g.769.2 4
32.27 odd 8 1024.2.e.g.769.2 4
32.29 even 8 1024.2.e.g.257.2 4
48.5 odd 4 4608.2.d.k.2305.1 4
48.11 even 4 4608.2.d.k.2305.4 4
48.29 odd 4 4608.2.d.k.2305.4 4
48.35 even 4 4608.2.d.k.2305.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
512.2.a.a.1.2 ✓ 2 4.3 odd 2
512.2.a.a.1.2 ✓ 2 8.5 even 2
512.2.a.f.1.1 yes 2 1.1 even 1 trivial
512.2.a.f.1.1 yes 2 8.3 odd 2 CM
512.2.b.c.257.2 4 16.3 odd 4
512.2.b.c.257.2 4 16.5 even 4
512.2.b.c.257.3 4 16.11 odd 4
512.2.b.c.257.3 4 16.13 even 4
1024.2.e.g.257.2 4 32.19 odd 8
1024.2.e.g.257.2 4 32.29 even 8
1024.2.e.g.769.2 4 32.21 even 8
1024.2.e.g.769.2 4 32.27 odd 8
1024.2.e.o.257.1 4 32.3 odd 8
1024.2.e.o.257.1 4 32.13 even 8
1024.2.e.o.769.1 4 32.5 even 8
1024.2.e.o.769.1 4 32.11 odd 8
4608.2.a.i.1.1 2 3.2 odd 2
4608.2.a.i.1.1 2 24.11 even 2
4608.2.a.k.1.2 2 12.11 even 2
4608.2.a.k.1.2 2 24.5 odd 2
4608.2.d.k.2305.1 4 48.5 odd 4
4608.2.d.k.2305.1 4 48.35 even 4
4608.2.d.k.2305.4 4 48.11 even 4
4608.2.d.k.2305.4 4 48.29 odd 4