Properties

Label 640.2.f.d.449.2
Level $640$
Weight $2$
Character 640.449
Analytic conductor $5.110$
Analytic rank $0$
Dimension $4$
CM discriminant -40
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [640,2,Mod(449,640)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(640, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("640.449");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 640.f (of order \(2\), degree \(1\), 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: \(5.11042572936\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 6x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 449.2
Root \(2.28825i\) of defining polynomial
Character \(\chi\) \(=\) 640.449
Dual form 640.2.f.d.449.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.23607 q^{5} +2.82843i q^{7} -3.00000 q^{9} +O(q^{10})\) \(q-2.23607 q^{5} +2.82843i q^{7} -3.00000 q^{9} -6.32456i q^{11} +4.47214 q^{13} -6.32456i q^{19} -8.48528i q^{23} +5.00000 q^{25} -6.32456i q^{35} -4.47214 q^{37} -2.00000 q^{41} +6.70820 q^{45} +2.82843i q^{47} -1.00000 q^{49} -13.4164 q^{53} +14.1421i q^{55} -6.32456i q^{59} -8.48528i q^{63} -10.0000 q^{65} +17.8885 q^{77} +9.00000 q^{81} +14.0000 q^{89} +12.6491i q^{91} +14.1421i q^{95} +18.9737i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 12 q^{9} + 20 q^{25} - 8 q^{41} - 4 q^{49} - 40 q^{65} + 36 q^{81} + 56 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) −2.23607 −1.00000
\(6\) 0 0
\(7\) 2.82843i 1.06904i 0.845154 + 0.534522i \(0.179509\pi\)
−0.845154 + 0.534522i \(0.820491\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) − 6.32456i − 1.90693i −0.301511 0.953463i \(-0.597491\pi\)
0.301511 0.953463i \(-0.402509\pi\)
\(12\) 0 0
\(13\) 4.47214 1.24035 0.620174 0.784465i \(-0.287062\pi\)
0.620174 + 0.784465i \(0.287062\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) − 6.32456i − 1.45095i −0.688247 0.725476i \(-0.741620\pi\)
0.688247 0.725476i \(-0.258380\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 8.48528i − 1.76930i −0.466252 0.884652i \(-0.654396\pi\)
0.466252 0.884652i \(-0.345604\pi\)
\(24\) 0 0
\(25\) 5.00000 1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) 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
\(33\) 0 0
\(34\) 0 0
\(35\) − 6.32456i − 1.06904i
\(36\) 0 0
\(37\) −4.47214 −0.735215 −0.367607 0.929981i \(-0.619823\pi\)
−0.367607 + 0.929981i \(0.619823\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 6.70820 1.00000
\(46\) 0 0
\(47\) 2.82843i 0.412568i 0.978492 + 0.206284i \(0.0661372\pi\)
−0.978492 + 0.206284i \(0.933863\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −13.4164 −1.84289 −0.921443 0.388514i \(-0.872988\pi\)
−0.921443 + 0.388514i \(0.872988\pi\)
\(54\) 0 0
\(55\) 14.1421i 1.90693i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 6.32456i − 0.823387i −0.911322 0.411693i \(-0.864937\pi\)
0.911322 0.411693i \(-0.135063\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) − 8.48528i − 1.06904i
\(64\) 0 0
\(65\) −10.0000 −1.24035
\(66\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 17.8885 2.03859
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.0000 1.48400 0.741999 0.670402i \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) 0 0
\(91\) 12.6491i 1.32599i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 14.1421i 1.45095i
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 18.9737i 1.90693i
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) − 19.7990i − 1.95085i −0.220326 0.975426i \(-0.570712\pi\)
0.220326 0.975426i \(-0.429288\pi\)
\(104\) 0 0
\(105\) 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 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 18.9737i 1.76930i
\(116\) 0 0
\(117\) −13.4164 −1.24035
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −29.0000 −2.63636
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.1803 −1.00000
\(126\) 0 0
\(127\) 2.82843i 0.250982i 0.992095 + 0.125491i \(0.0400507\pi\)
−0.992095 + 0.125491i \(0.959949\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 6.32456i − 0.552579i −0.961074 0.276289i \(-0.910895\pi\)
0.961074 0.276289i \(-0.0891049\pi\)
\(132\) 0 0
\(133\) 17.8885 1.55113
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 18.9737i 1.60933i 0.593732 + 0.804663i \(0.297654\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 28.2843i − 2.36525i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 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
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −22.3607 −1.78458 −0.892288 0.451466i \(-0.850901\pi\)
−0.892288 + 0.451466i \(0.850901\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 24.0000 1.89146
\(162\) 0 0
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 25.4558i 1.96983i 0.173032 + 0.984916i \(0.444644\pi\)
−0.173032 + 0.984916i \(0.555356\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) 18.9737i 1.45095i
\(172\) 0 0
\(173\) 13.4164 1.02003 0.510015 0.860165i \(-0.329640\pi\)
0.510015 + 0.860165i \(0.329640\pi\)
\(174\) 0 0
\(175\) 14.1421i 1.06904i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 6.32456i − 0.472719i −0.971666 0.236360i \(-0.924046\pi\)
0.971666 0.236360i \(-0.0759544\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 10.0000 0.735215
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 22.3607 1.59313 0.796566 0.604551i \(-0.206648\pi\)
0.796566 + 0.604551i \(0.206648\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 4.47214 0.312348
\(206\) 0 0
\(207\) 25.4558i 1.76930i
\(208\) 0 0
\(209\) −40.0000 −2.76686
\(210\) 0 0
\(211\) 18.9737i 1.30620i 0.757271 + 0.653101i \(0.226532\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) − 19.7990i − 1.32584i −0.748691 0.662919i \(-0.769317\pi\)
0.748691 0.662919i \(-0.230683\pi\)
\(224\) 0 0
\(225\) −15.0000 −1.00000
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) − 6.32456i − 0.412568i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.23607 0.142857
\(246\) 0 0
\(247\) − 28.2843i − 1.79969i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 31.6228i − 1.99601i −0.0631194 0.998006i \(-0.520105\pi\)
0.0631194 0.998006i \(-0.479895\pi\)
\(252\) 0 0
\(253\) −53.6656 −3.37393
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) − 12.6491i − 0.785977i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) − 8.48528i − 0.523225i −0.965173 0.261612i \(-0.915746\pi\)
0.965173 0.261612i \(-0.0842542\pi\)
\(264\) 0 0
\(265\) 30.0000 1.84289
\(266\) 0 0
\(267\) 0 0
\(268\) 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
\(275\) − 31.6228i − 1.90693i
\(276\) 0 0
\(277\) 31.3050 1.88093 0.940466 0.339887i \(-0.110389\pi\)
0.940466 + 0.339887i \(0.110389\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 5.65685i − 0.333914i
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.47214 −0.261265 −0.130632 0.991431i \(-0.541701\pi\)
−0.130632 + 0.991431i \(0.541701\pi\)
\(294\) 0 0
\(295\) 14.1421i 0.823387i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 37.9473i − 2.19455i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 18.9737i 1.06904i
\(316\) 0 0
\(317\) −31.3050 −1.75826 −0.879131 0.476581i \(-0.841876\pi\)
−0.879131 + 0.476581i \(0.841876\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 22.3607 1.24035
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −8.00000 −0.441054
\(330\) 0 0
\(331\) − 31.6228i − 1.73814i −0.494685 0.869072i \(-0.664716\pi\)
0.494685 0.869072i \(-0.335284\pi\)
\(332\) 0 0
\(333\) 13.4164 0.735215
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 16.9706i 0.916324i
\(344\) 0 0
\(345\) 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
\(352\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −21.0000 −1.10526
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 31.1127i − 1.62407i −0.583609 0.812035i \(-0.698360\pi\)
0.583609 0.812035i \(-0.301640\pi\)
\(368\) 0 0
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) − 37.9473i − 1.97013i
\(372\) 0 0
\(373\) 31.3050 1.62091 0.810454 0.585802i \(-0.199220\pi\)
0.810454 + 0.585802i \(0.199220\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 18.9737i 0.974612i 0.873231 + 0.487306i \(0.162020\pi\)
−0.873231 + 0.487306i \(0.837980\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 36.7696i 1.87884i 0.342773 + 0.939418i \(0.388634\pi\)
−0.342773 + 0.939418i \(0.611366\pi\)
\(384\) 0 0
\(385\) −40.0000 −2.03859
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 4.47214 0.224450 0.112225 0.993683i \(-0.464202\pi\)
0.112225 + 0.993683i \(0.464202\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 38.0000 1.89763 0.948815 0.315833i \(-0.102284\pi\)
0.948815 + 0.315833i \(0.102284\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −20.1246 −1.00000
\(406\) 0 0
\(407\) 28.2843i 1.40200i
\(408\) 0 0
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 17.8885 0.880238
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 31.6228i − 1.54487i −0.635092 0.772437i \(-0.719038\pi\)
0.635092 0.772437i \(-0.280962\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) − 8.48528i − 0.412568i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −53.6656 −2.56718
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) −31.3050 −1.48400
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 34.0000 1.60456 0.802280 0.596948i \(-0.203620\pi\)
0.802280 + 0.596948i \(0.203620\pi\)
\(450\) 0 0
\(451\) 12.6491i 0.595623i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) − 28.2843i − 1.32599i
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 36.7696i 1.70883i 0.519594 + 0.854413i \(0.326083\pi\)
−0.519594 + 0.854413i \(0.673917\pi\)
\(464\) 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
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) − 31.6228i − 1.45095i
\(476\) 0 0
\(477\) 40.2492 1.84289
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −20.0000 −0.911922
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) − 31.1127i − 1.40985i −0.709281 0.704925i \(-0.750980\pi\)
0.709281 0.704925i \(-0.249020\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 44.2719i 1.99796i 0.0451294 + 0.998981i \(0.485630\pi\)
−0.0451294 + 0.998981i \(0.514370\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) − 42.4264i − 1.90693i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 44.2719i 1.98188i 0.134298 + 0.990941i \(0.457122\pi\)
−0.134298 + 0.990941i \(0.542878\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) − 19.7990i − 0.882793i −0.897312 0.441397i \(-0.854483\pi\)
0.897312 0.441397i \(-0.145517\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 44.2719i 1.95085i
\(516\) 0 0
\(517\) 17.8885 0.786737
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −38.0000 −1.66481 −0.832405 0.554168i \(-0.813037\pi\)
−0.832405 + 0.554168i \(0.813037\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −49.0000 −2.13043
\(530\) 0 0
\(531\) 18.9737i 0.823387i
\(532\) 0 0
\(533\) −8.94427 −0.387419
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 6.32456i 0.272418i
\(540\) 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
\(547\) 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
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 13.4164 0.568471 0.284236 0.958754i \(-0.408260\pi\)
0.284236 + 0.958754i \(0.408260\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 25.4558i 1.06904i
\(568\) 0 0
\(569\) 46.0000 1.92842 0.964210 0.265139i \(-0.0854179\pi\)
0.964210 + 0.265139i \(0.0854179\pi\)
\(570\) 0 0
\(571\) 44.2719i 1.85272i 0.376638 + 0.926360i \(0.377080\pi\)
−0.376638 + 0.926360i \(0.622920\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) − 42.4264i − 1.76930i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 84.8528i 3.51424i
\(584\) 0 0
\(585\) 30.0000 1.24035
\(586\) 0 0
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 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
\(601\) 42.0000 1.71322 0.856608 0.515968i \(-0.172568\pi\)
0.856608 + 0.515968i \(0.172568\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 64.8460 2.63636
\(606\) 0 0
\(607\) 2.82843i 0.114802i 0.998351 + 0.0574012i \(0.0182814\pi\)
−0.998351 + 0.0574012i \(0.981719\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.6491i 0.511728i
\(612\) 0 0
\(613\) −49.1935 −1.98691 −0.993453 0.114239i \(-0.963557\pi\)
−0.993453 + 0.114239i \(0.963557\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 18.9737i 0.762616i 0.924448 + 0.381308i \(0.124526\pi\)
−0.924448 + 0.381308i \(0.875474\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 39.5980i 1.58646i
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 6.32456i − 0.250982i
\(636\) 0 0
\(637\) −4.47214 −0.177192
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 31.1127i − 1.22317i −0.791180 0.611583i \(-0.790533\pi\)
0.791180 0.611583i \(-0.209467\pi\)
\(648\) 0 0
\(649\) −40.0000 −1.57014
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.47214 0.175008 0.0875041 0.996164i \(-0.472111\pi\)
0.0875041 + 0.996164i \(0.472111\pi\)
\(654\) 0 0
\(655\) 14.1421i 0.552579i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 44.2719i 1.72459i 0.506408 + 0.862294i \(0.330973\pi\)
−0.506408 + 0.862294i \(0.669027\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −40.0000 −1.55113
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −49.1935 −1.89066 −0.945330 0.326116i \(-0.894260\pi\)
−0.945330 + 0.326116i \(0.894260\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −60.0000 −2.28582
\(690\) 0 0
\(691\) − 31.6228i − 1.20299i −0.798878 0.601494i \(-0.794573\pi\)
0.798878 0.601494i \(-0.205427\pi\)
\(692\) 0 0
\(693\) −53.6656 −2.03859
\(694\) 0 0
\(695\) − 42.4264i − 1.60933i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 28.2843i 1.06676i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 63.2456i 2.36525i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 56.0000 2.08555
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 53.7401i − 1.99311i −0.0829312 0.996555i \(-0.526428\pi\)
0.0829312 0.996555i \(-0.473572\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 49.1935 1.81700 0.908502 0.417881i \(-0.137227\pi\)
0.908502 + 0.417881i \(0.137227\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) − 6.32456i − 0.232653i −0.993211 0.116326i \(-0.962888\pi\)
0.993211 0.116326i \(-0.0371118\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 36.7696i 1.34894i 0.738300 + 0.674472i \(0.235629\pi\)
−0.738300 + 0.674472i \(0.764371\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 31.3050 1.13780 0.568899 0.822407i \(-0.307370\pi\)
0.568899 + 0.822407i \(0.307370\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −22.0000 −0.797499 −0.398750 0.917060i \(-0.630556\pi\)
−0.398750 + 0.917060i \(0.630556\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) − 28.2843i − 1.02129i
\(768\) 0 0
\(769\) 54.0000 1.94729 0.973645 0.228069i \(-0.0732413\pi\)
0.973645 + 0.228069i \(0.0732413\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 22.3607 0.804258 0.402129 0.915583i \(-0.368270\pi\)
0.402129 + 0.915583i \(0.368270\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12.6491i 0.453201i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 50.0000 1.78458
\(786\) 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
\(795\) 0 0
\(796\) 0 0
\(797\) 40.2492 1.42570 0.712850 0.701316i \(-0.247404\pi\)
0.712850 + 0.701316i \(0.247404\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −42.0000 −1.48400
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −53.6656 −1.89146
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 26.0000 0.914111 0.457056 0.889438i \(-0.348904\pi\)
0.457056 + 0.889438i \(0.348904\pi\)
\(810\) 0 0
\(811\) − 56.9210i − 1.99877i −0.0351147 0.999383i \(-0.511180\pi\)
0.0351147 0.999383i \(-0.488820\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) − 37.9473i − 1.32599i
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 48.0833i 1.67608i 0.545611 + 0.838039i \(0.316298\pi\)
−0.545611 + 0.838039i \(0.683702\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) − 56.9210i − 1.96983i
\(836\) 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
\(843\) 0 0
\(844\) 0 0
\(845\) −15.6525 −0.538462
\(846\) 0 0
\(847\) − 82.0244i − 2.81839i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 37.9473i 1.30082i
\(852\) 0 0
\(853\) 58.1378 1.99060 0.995300 0.0968435i \(-0.0308746\pi\)
0.995300 + 0.0968435i \(0.0308746\pi\)
\(854\) 0 0
\(855\) − 42.4264i − 1.45095i
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) − 56.9210i − 1.94212i −0.238837 0.971060i \(-0.576766\pi\)
0.238837 0.971060i \(-0.423234\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) − 8.48528i − 0.288842i −0.989516 0.144421i \(-0.953868\pi\)
0.989516 0.144421i \(-0.0461320\pi\)
\(864\) 0 0
\(865\) −30.0000 −1.02003
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) − 31.6228i − 1.06904i
\(876\) 0 0
\(877\) −58.1378 −1.96317 −0.981586 0.191018i \(-0.938821\pi\)
−0.981586 + 0.191018i \(0.938821\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −58.0000 −1.95407 −0.977035 0.213080i \(-0.931651\pi\)
−0.977035 + 0.213080i \(0.931651\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 59.3970i 1.99436i 0.0750798 + 0.997178i \(0.476079\pi\)
−0.0750798 + 0.997178i \(0.523921\pi\)
\(888\) 0 0
\(889\) −8.00000 −0.268311
\(890\) 0 0
\(891\) − 56.9210i − 1.90693i
\(892\) 0 0
\(893\) 17.8885 0.598617
\(894\) 0 0
\(895\) 14.1421i 0.472719i
\(896\) 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
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 17.8885 0.590732
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −22.3607 −0.735215
\(926\) 0 0
\(927\) 59.3970i 1.95085i
\(928\) 0 0
\(929\) 34.0000 1.11550 0.557752 0.830008i \(-0.311664\pi\)
0.557752 + 0.830008i \(0.311664\pi\)
\(930\) 0 0
\(931\) 6.32456i 0.207279i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 16.9706i 0.552638i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 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
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 53.7401i − 1.72817i −0.503350 0.864083i \(-0.667899\pi\)
0.503350 0.864083i \(-0.332101\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 6.32456i − 0.202965i −0.994837 0.101482i \(-0.967641\pi\)
0.994837 0.101482i \(-0.0323585\pi\)
\(972\) 0 0
\(973\) −53.6656 −1.72044
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) − 88.5438i − 2.82987i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 48.0833i 1.53362i 0.641875 + 0.766809i \(0.278157\pi\)
−0.641875 + 0.766809i \(0.721843\pi\)
\(984\) 0 0
\(985\) −50.0000 −1.59313
\(986\) 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 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −49.1935 −1.55797 −0.778987 0.627040i \(-0.784266\pi\)
−0.778987 + 0.627040i \(0.784266\pi\)
\(998\) 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 640.2.f.d.449.2 yes 4
4.3 odd 2 inner 640.2.f.d.449.1 4
5.2 odd 4 3200.2.d.w.1601.1 4
5.3 odd 4 3200.2.d.w.1601.3 4
5.4 even 2 inner 640.2.f.d.449.3 yes 4
8.3 odd 2 inner 640.2.f.d.449.3 yes 4
8.5 even 2 inner 640.2.f.d.449.4 yes 4
16.3 odd 4 1280.2.c.l.769.4 4
16.5 even 4 1280.2.c.l.769.1 4
16.11 odd 4 1280.2.c.l.769.2 4
16.13 even 4 1280.2.c.l.769.3 4
20.3 even 4 3200.2.d.w.1601.2 4
20.7 even 4 3200.2.d.w.1601.4 4
20.19 odd 2 inner 640.2.f.d.449.4 yes 4
40.3 even 4 3200.2.d.w.1601.1 4
40.13 odd 4 3200.2.d.w.1601.4 4
40.19 odd 2 CM 640.2.f.d.449.2 yes 4
40.27 even 4 3200.2.d.w.1601.3 4
40.29 even 2 inner 640.2.f.d.449.1 4
40.37 odd 4 3200.2.d.w.1601.2 4
80.3 even 4 6400.2.a.cl.1.4 4
80.13 odd 4 6400.2.a.cl.1.1 4
80.19 odd 4 1280.2.c.l.769.1 4
80.27 even 4 6400.2.a.cl.1.1 4
80.29 even 4 1280.2.c.l.769.2 4
80.37 odd 4 6400.2.a.cl.1.4 4
80.43 even 4 6400.2.a.cl.1.3 4
80.53 odd 4 6400.2.a.cl.1.2 4
80.59 odd 4 1280.2.c.l.769.3 4
80.67 even 4 6400.2.a.cl.1.2 4
80.69 even 4 1280.2.c.l.769.4 4
80.77 odd 4 6400.2.a.cl.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.f.d.449.1 4 4.3 odd 2 inner
640.2.f.d.449.1 4 40.29 even 2 inner
640.2.f.d.449.2 yes 4 1.1 even 1 trivial
640.2.f.d.449.2 yes 4 40.19 odd 2 CM
640.2.f.d.449.3 yes 4 5.4 even 2 inner
640.2.f.d.449.3 yes 4 8.3 odd 2 inner
640.2.f.d.449.4 yes 4 8.5 even 2 inner
640.2.f.d.449.4 yes 4 20.19 odd 2 inner
1280.2.c.l.769.1 4 16.5 even 4
1280.2.c.l.769.1 4 80.19 odd 4
1280.2.c.l.769.2 4 16.11 odd 4
1280.2.c.l.769.2 4 80.29 even 4
1280.2.c.l.769.3 4 16.13 even 4
1280.2.c.l.769.3 4 80.59 odd 4
1280.2.c.l.769.4 4 16.3 odd 4
1280.2.c.l.769.4 4 80.69 even 4
3200.2.d.w.1601.1 4 5.2 odd 4
3200.2.d.w.1601.1 4 40.3 even 4
3200.2.d.w.1601.2 4 20.3 even 4
3200.2.d.w.1601.2 4 40.37 odd 4
3200.2.d.w.1601.3 4 5.3 odd 4
3200.2.d.w.1601.3 4 40.27 even 4
3200.2.d.w.1601.4 4 20.7 even 4
3200.2.d.w.1601.4 4 40.13 odd 4
6400.2.a.cl.1.1 4 80.13 odd 4
6400.2.a.cl.1.1 4 80.27 even 4
6400.2.a.cl.1.2 4 80.53 odd 4
6400.2.a.cl.1.2 4 80.67 even 4
6400.2.a.cl.1.3 4 80.43 even 4
6400.2.a.cl.1.3 4 80.77 odd 4
6400.2.a.cl.1.4 4 80.3 even 4
6400.2.a.cl.1.4 4 80.37 odd 4