Properties

Label 1600.2.a.z.1.1
Level $1600$
Weight $2$
Character 1600.1
Self dual yes
Analytic conductor $12.776$
Analytic rank $0$
Dimension $2$
CM discriminant -20
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1600,2,Mod(1,1600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1600, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1600.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.a (trivial)

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: yes
Analytic conductor: \(12.7760643234\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 160)
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 1600.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.23607 q^{3} +0.763932 q^{7} +7.47214 q^{9} +O(q^{10})\) \(q-3.23607 q^{3} +0.763932 q^{7} +7.47214 q^{9} -2.47214 q^{21} -5.70820 q^{23} -14.4721 q^{27} +6.00000 q^{29} -4.47214 q^{41} -11.2361 q^{43} +13.7082 q^{47} -6.41641 q^{49} +13.4164 q^{61} +5.70820 q^{63} +8.18034 q^{67} +18.4721 q^{69} +24.4164 q^{81} +17.7082 q^{83} -19.4164 q^{87} +6.00000 q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} + 6 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{3} + 6 q^{7} + 6 q^{9} + 4 q^{21} + 2 q^{23} - 20 q^{27} + 12 q^{29} - 18 q^{43} + 14 q^{47} + 14 q^{49} - 2 q^{63} - 6 q^{67} + 28 q^{69} + 22 q^{81} + 22 q^{83} - 12 q^{87} + 12 q^{89}+O(q^{100}) \) 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
\(3\) −3.23607 −1.86834 −0.934172 0.356822i \(-0.883860\pi\)
−0.934172 + 0.356822i \(0.883860\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.763932 0.288739 0.144370 0.989524i \(-0.453885\pi\)
0.144370 + 0.989524i \(0.453885\pi\)
\(8\) 0 0
\(9\) 7.47214 2.49071
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) −2.47214 −0.539464
\(22\) 0 0
\(23\) −5.70820 −1.19024 −0.595121 0.803636i \(-0.702896\pi\)
−0.595121 + 0.803636i \(0.702896\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −14.4721 −2.78516
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 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
\(41\) −4.47214 −0.698430 −0.349215 0.937043i \(-0.613552\pi\)
−0.349215 + 0.937043i \(0.613552\pi\)
\(42\) 0 0
\(43\) −11.2361 −1.71348 −0.856742 0.515745i \(-0.827515\pi\)
−0.856742 + 0.515745i \(0.827515\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 13.7082 1.99955 0.999774 0.0212814i \(-0.00677460\pi\)
0.999774 + 0.0212814i \(0.00677460\pi\)
\(48\) 0 0
\(49\) −6.41641 −0.916630
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 13.4164 1.71780 0.858898 0.512148i \(-0.171150\pi\)
0.858898 + 0.512148i \(0.171150\pi\)
\(62\) 0 0
\(63\) 5.70820 0.719166
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 8.18034 0.999388 0.499694 0.866202i \(-0.333446\pi\)
0.499694 + 0.866202i \(0.333446\pi\)
\(68\) 0 0
\(69\) 18.4721 2.22378
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 24.4164 2.71293
\(82\) 0 0
\(83\) 17.7082 1.94373 0.971864 0.235543i \(-0.0756868\pi\)
0.971864 + 0.235543i \(0.0756868\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −19.4164 −2.08166
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 18.0000 1.79107 0.895533 0.444994i \(-0.146794\pi\)
0.895533 + 0.444994i \(0.146794\pi\)
\(102\) 0 0
\(103\) 20.1803 1.98843 0.994214 0.107418i \(-0.0342582\pi\)
0.994214 + 0.107418i \(0.0342582\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.29180 0.608251 0.304125 0.952632i \(-0.401636\pi\)
0.304125 + 0.952632i \(0.401636\pi\)
\(108\) 0 0
\(109\) −13.4164 −1.28506 −0.642529 0.766261i \(-0.722115\pi\)
−0.642529 + 0.766261i \(0.722115\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 14.4721 1.30491
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 18.6525 1.65514 0.827570 0.561363i \(-0.189723\pi\)
0.827570 + 0.561363i \(0.189723\pi\)
\(128\) 0 0
\(129\) 36.3607 3.20138
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −44.3607 −3.73584
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 20.7639 1.71258
\(148\) 0 0
\(149\) 4.47214 0.366372 0.183186 0.983078i \(-0.441359\pi\)
0.183186 + 0.983078i \(0.441359\pi\)
\(150\) 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
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.36068 −0.343670
\(162\) 0 0
\(163\) 6.65248 0.521062 0.260531 0.965465i \(-0.416102\pi\)
0.260531 + 0.965465i \(0.416102\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −10.2918 −0.796403 −0.398202 0.917298i \(-0.630366\pi\)
−0.398202 + 0.917298i \(0.630366\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) −43.4164 −3.20943
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −11.0557 −0.804186
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 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
\(201\) −26.4721 −1.86720
\(202\) 0 0
\(203\) 4.58359 0.321705
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −42.6525 −2.96455
\(208\) 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
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 23.2361 1.55600 0.778001 0.628263i \(-0.216234\pi\)
0.778001 + 0.628263i \(0.216234\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.1246 0.871111 0.435556 0.900162i \(-0.356552\pi\)
0.435556 + 0.900162i \(0.356552\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) 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
\(241\) 13.4164 0.864227 0.432113 0.901819i \(-0.357768\pi\)
0.432113 + 0.901819i \(0.357768\pi\)
\(242\) 0 0
\(243\) −35.5967 −2.28353
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −57.3050 −3.63155
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 44.8328 2.77508
\(262\) 0 0
\(263\) 9.12461 0.562648 0.281324 0.959613i \(-0.409226\pi\)
0.281324 + 0.959613i \(0.409226\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −19.4164 −1.18826
\(268\) 0 0
\(269\) 22.3607 1.36335 0.681677 0.731653i \(-0.261251\pi\)
0.681677 + 0.731653i \(0.261251\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 31.3050 1.86750 0.933748 0.357930i \(-0.116517\pi\)
0.933748 + 0.357930i \(0.116517\pi\)
\(282\) 0 0
\(283\) −32.1803 −1.91292 −0.956461 0.291859i \(-0.905726\pi\)
−0.956461 + 0.291859i \(0.905726\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.41641 −0.201664
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −8.58359 −0.494750
\(302\) 0 0
\(303\) −58.2492 −3.34633
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −27.5967 −1.57503 −0.787515 0.616296i \(-0.788633\pi\)
−0.787515 + 0.616296i \(0.788633\pi\)
\(308\) 0 0
\(309\) −65.3050 −3.71507
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) 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
\(321\) −20.3607 −1.13642
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 43.4164 2.40093
\(328\) 0 0
\(329\) 10.4721 0.577348
\(330\) 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
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −10.2492 −0.553406
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 37.1246 1.99295 0.996477 0.0838690i \(-0.0267277\pi\)
0.996477 + 0.0838690i \(0.0267277\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 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
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) 35.5967 1.86834
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 24.7639 1.29267 0.646333 0.763055i \(-0.276302\pi\)
0.646333 + 0.763055i \(0.276302\pi\)
\(368\) 0 0
\(369\) −33.4164 −1.73959
\(370\) 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
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) −60.3607 −3.09237
\(382\) 0 0
\(383\) 1.12461 0.0574650 0.0287325 0.999587i \(-0.490853\pi\)
0.0287325 + 0.999587i \(0.490853\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −83.9574 −4.26780
\(388\) 0 0
\(389\) −31.3050 −1.58722 −0.793612 0.608424i \(-0.791802\pi\)
−0.793612 + 0.608424i \(0.791802\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 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
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 40.2492 1.99020 0.995098 0.0988936i \(-0.0315304\pi\)
0.995098 + 0.0988936i \(0.0315304\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −40.2492 −1.96163 −0.980814 0.194948i \(-0.937546\pi\)
−0.980814 + 0.194948i \(0.937546\pi\)
\(422\) 0 0
\(423\) 102.430 4.98030
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 10.2492 0.495995
\(428\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 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
\(441\) −47.9443 −2.28306
\(442\) 0 0
\(443\) −22.2918 −1.05912 −0.529558 0.848274i \(-0.677642\pi\)
−0.529558 + 0.848274i \(0.677642\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −14.4721 −0.684509
\(448\) 0 0
\(449\) 22.3607 1.05527 0.527633 0.849473i \(-0.323080\pi\)
0.527633 + 0.849473i \(0.323080\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 42.0000 1.95614 0.978068 0.208288i \(-0.0667892\pi\)
0.978068 + 0.208288i \(0.0667892\pi\)
\(462\) 0 0
\(463\) 38.0689 1.76921 0.884606 0.466340i \(-0.154428\pi\)
0.884606 + 0.466340i \(0.154428\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.87539 −0.133057 −0.0665285 0.997785i \(-0.521192\pi\)
−0.0665285 + 0.997785i \(0.521192\pi\)
\(468\) 0 0
\(469\) 6.24922 0.288562
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 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
\(483\) 14.1115 0.642093
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 42.6525 1.93277 0.966384 0.257103i \(-0.0827679\pi\)
0.966384 + 0.257103i \(0.0827679\pi\)
\(488\) 0 0
\(489\) −21.5279 −0.973524
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) 33.3050 1.48796
\(502\) 0 0
\(503\) −37.7082 −1.68133 −0.840663 0.541559i \(-0.817834\pi\)
−0.840663 + 0.541559i \(0.817834\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 42.0689 1.86834
\(508\) 0 0
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) 0 0
\(523\) 3.59675 0.157275 0.0786374 0.996903i \(-0.474943\pi\)
0.0786374 + 0.996903i \(0.474943\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 9.58359 0.416678
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −38.0000 −1.63375 −0.816874 0.576816i \(-0.804295\pi\)
−0.816874 + 0.576816i \(0.804295\pi\)
\(542\) 0 0
\(543\) −6.47214 −0.277746
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 35.2361 1.50659 0.753293 0.657685i \(-0.228464\pi\)
0.753293 + 0.657685i \(0.228464\pi\)
\(548\) 0 0
\(549\) 100.249 4.27853
\(550\) 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
\(561\) 0 0
\(562\) 0 0
\(563\) 32.5410 1.37144 0.685720 0.727865i \(-0.259487\pi\)
0.685720 + 0.727865i \(0.259487\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 18.6525 0.783330
\(568\) 0 0
\(569\) −31.3050 −1.31237 −0.656186 0.754599i \(-0.727831\pi\)
−0.656186 + 0.754599i \(0.727831\pi\)
\(570\) 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
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 13.5279 0.561230
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −40.5410 −1.67331 −0.836653 0.547733i \(-0.815491\pi\)
−0.836653 + 0.547733i \(0.815491\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 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
\(601\) −40.2492 −1.64180 −0.820900 0.571072i \(-0.806528\pi\)
−0.820900 + 0.571072i \(0.806528\pi\)
\(602\) 0 0
\(603\) 61.1246 2.48919
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −44.1803 −1.79322 −0.896612 0.442816i \(-0.853979\pi\)
−0.896612 + 0.442816i \(0.853979\pi\)
\(608\) 0 0
\(609\) −14.8328 −0.601056
\(610\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 82.6099 3.31502
\(622\) 0 0
\(623\) 4.58359 0.183638
\(624\) 0 0
\(625\) 0 0
\(626\) 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
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 49.1935 1.94303 0.971513 0.236986i \(-0.0761595\pi\)
0.971513 + 0.236986i \(0.0761595\pi\)
\(642\) 0 0
\(643\) −50.0689 −1.97452 −0.987262 0.159103i \(-0.949140\pi\)
−0.987262 + 0.159103i \(0.949140\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 20.5410 0.807551 0.403775 0.914858i \(-0.367698\pi\)
0.403775 + 0.914858i \(0.367698\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 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
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −40.2492 −1.56551 −0.782757 0.622328i \(-0.786187\pi\)
−0.782757 + 0.622328i \(0.786187\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −34.2492 −1.32614
\(668\) 0 0
\(669\) −75.1935 −2.90715
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −42.4721 −1.62754
\(682\) 0 0
\(683\) 10.8754 0.416135 0.208068 0.978114i \(-0.433283\pi\)
0.208068 + 0.978114i \(0.433283\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −45.3050 −1.72849
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −22.3607 −0.844551 −0.422276 0.906467i \(-0.638769\pi\)
−0.422276 + 0.906467i \(0.638769\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13.7508 0.517151
\(708\) 0 0
\(709\) 46.0000 1.72757 0.863783 0.503864i \(-0.168089\pi\)
0.863783 + 0.503864i \(0.168089\pi\)
\(710\) 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
\(721\) 15.4164 0.574137
\(722\) 0 0
\(723\) −43.4164 −1.61467
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −35.0132 −1.29857 −0.649283 0.760547i \(-0.724931\pi\)
−0.649283 + 0.760547i \(0.724931\pi\)
\(728\) 0 0
\(729\) 41.9443 1.55349
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 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
\(743\) −52.5410 −1.92754 −0.963772 0.266729i \(-0.914057\pi\)
−0.963772 + 0.266729i \(0.914057\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 132.318 4.84127
\(748\) 0 0
\(749\) 4.80650 0.175626
\(750\) 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
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 0 0
\(763\) −10.2492 −0.371047
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 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
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −86.8328 −3.10315
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 2.06888 0.0737477 0.0368739 0.999320i \(-0.488260\pi\)
0.0368739 + 0.999320i \(0.488260\pi\)
\(788\) 0 0
\(789\) −29.5279 −1.05122
\(790\) 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
\(801\) 44.8328 1.58409
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −72.3607 −2.54722
\(808\) 0 0
\(809\) 54.0000 1.89854 0.949269 0.314464i \(-0.101825\pi\)
0.949269 + 0.314464i \(0.101825\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 31.3050 1.09255 0.546275 0.837606i \(-0.316045\pi\)
0.546275 + 0.837606i \(0.316045\pi\)
\(822\) 0 0
\(823\) −27.8197 −0.969732 −0.484866 0.874588i \(-0.661132\pi\)
−0.484866 + 0.874588i \(0.661132\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −56.5410 −1.96612 −0.983062 0.183274i \(-0.941331\pi\)
−0.983062 + 0.183274i \(0.941331\pi\)
\(828\) 0 0
\(829\) −13.4164 −0.465971 −0.232986 0.972480i \(-0.574849\pi\)
−0.232986 + 0.972480i \(0.574849\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 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
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) −101.305 −3.48913
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −8.40325 −0.288739
\(848\) 0 0
\(849\) 104.138 3.57400
\(850\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 11.0557 0.376778
\(862\) 0 0
\(863\) 34.2918 1.16731 0.583653 0.812003i \(-0.301623\pi\)
0.583653 + 0.812003i \(0.301623\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 55.0132 1.86834
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −58.1378 −1.95871 −0.979356 0.202145i \(-0.935209\pi\)
−0.979356 + 0.202145i \(0.935209\pi\)
\(882\) 0 0
\(883\) 54.6525 1.83920 0.919601 0.392853i \(-0.128512\pi\)
0.919601 + 0.392853i \(0.128512\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −57.1246 −1.91806 −0.959028 0.283310i \(-0.908567\pi\)
−0.959028 + 0.283310i \(0.908567\pi\)
\(888\) 0 0
\(889\) 14.2492 0.477904
\(890\) 0 0
\(891\) 0 0
\(892\) 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
\(903\) 27.7771 0.924364
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −45.4853 −1.51031 −0.755157 0.655544i \(-0.772439\pi\)
−0.755157 + 0.655544i \(0.772439\pi\)
\(908\) 0 0
\(909\) 134.498 4.46103
\(910\) 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
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 89.3050 2.94270
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 150.790 4.95260
\(928\) 0 0
\(929\) −49.1935 −1.61399 −0.806993 0.590561i \(-0.798907\pi\)
−0.806993 + 0.590561i \(0.798907\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 42.0000 1.36916 0.684580 0.728937i \(-0.259985\pi\)
0.684580 + 0.728937i \(0.259985\pi\)
\(942\) 0 0
\(943\) 25.5279 0.831302
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −49.7082 −1.61530 −0.807650 0.589662i \(-0.799261\pi\)
−0.807650 + 0.589662i \(0.799261\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 47.0132 1.51498
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −62.0689 −1.99600 −0.998000 0.0632081i \(-0.979867\pi\)
−0.998000 + 0.0632081i \(0.979867\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −100.249 −3.20071
\(982\) 0 0
\(983\) −4.54102 −0.144836 −0.0724180 0.997374i \(-0.523072\pi\)
−0.0724180 + 0.997374i \(0.523072\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −33.8885 −1.07868
\(988\) 0 0
\(989\) 64.1378 2.03946
\(990\) 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
\(997\) 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 1600.2.a.z.1.1 2
4.3 odd 2 1600.2.a.bd.1.2 2
5.2 odd 4 320.2.c.d.129.4 4
5.3 odd 4 320.2.c.d.129.1 4
5.4 even 2 1600.2.a.bd.1.2 2
8.3 odd 2 800.2.a.j.1.1 2
8.5 even 2 800.2.a.n.1.2 2
15.2 even 4 2880.2.f.w.1729.4 4
15.8 even 4 2880.2.f.w.1729.3 4
20.3 even 4 320.2.c.d.129.4 4
20.7 even 4 320.2.c.d.129.1 4
20.19 odd 2 CM 1600.2.a.z.1.1 2
24.5 odd 2 7200.2.a.cr.1.1 2
24.11 even 2 7200.2.a.cb.1.2 2
40.3 even 4 160.2.c.b.129.1 4
40.13 odd 4 160.2.c.b.129.4 yes 4
40.19 odd 2 800.2.a.n.1.2 2
40.27 even 4 160.2.c.b.129.4 yes 4
40.29 even 2 800.2.a.j.1.1 2
40.37 odd 4 160.2.c.b.129.1 4
60.23 odd 4 2880.2.f.w.1729.4 4
60.47 odd 4 2880.2.f.w.1729.3 4
80.3 even 4 1280.2.f.g.129.2 4
80.13 odd 4 1280.2.f.h.129.4 4
80.27 even 4 1280.2.f.g.129.1 4
80.37 odd 4 1280.2.f.h.129.3 4
80.43 even 4 1280.2.f.h.129.3 4
80.53 odd 4 1280.2.f.g.129.1 4
80.67 even 4 1280.2.f.h.129.4 4
80.77 odd 4 1280.2.f.g.129.2 4
120.29 odd 2 7200.2.a.cb.1.2 2
120.53 even 4 1440.2.f.i.289.1 4
120.59 even 2 7200.2.a.cr.1.1 2
120.77 even 4 1440.2.f.i.289.2 4
120.83 odd 4 1440.2.f.i.289.2 4
120.107 odd 4 1440.2.f.i.289.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.c.b.129.1 4 40.3 even 4
160.2.c.b.129.1 4 40.37 odd 4
160.2.c.b.129.4 yes 4 40.13 odd 4
160.2.c.b.129.4 yes 4 40.27 even 4
320.2.c.d.129.1 4 5.3 odd 4
320.2.c.d.129.1 4 20.7 even 4
320.2.c.d.129.4 4 5.2 odd 4
320.2.c.d.129.4 4 20.3 even 4
800.2.a.j.1.1 2 8.3 odd 2
800.2.a.j.1.1 2 40.29 even 2
800.2.a.n.1.2 2 8.5 even 2
800.2.a.n.1.2 2 40.19 odd 2
1280.2.f.g.129.1 4 80.27 even 4
1280.2.f.g.129.1 4 80.53 odd 4
1280.2.f.g.129.2 4 80.3 even 4
1280.2.f.g.129.2 4 80.77 odd 4
1280.2.f.h.129.3 4 80.37 odd 4
1280.2.f.h.129.3 4 80.43 even 4
1280.2.f.h.129.4 4 80.13 odd 4
1280.2.f.h.129.4 4 80.67 even 4
1440.2.f.i.289.1 4 120.53 even 4
1440.2.f.i.289.1 4 120.107 odd 4
1440.2.f.i.289.2 4 120.77 even 4
1440.2.f.i.289.2 4 120.83 odd 4
1600.2.a.z.1.1 2 1.1 even 1 trivial
1600.2.a.z.1.1 2 20.19 odd 2 CM
1600.2.a.bd.1.2 2 4.3 odd 2
1600.2.a.bd.1.2 2 5.4 even 2
2880.2.f.w.1729.3 4 15.8 even 4
2880.2.f.w.1729.3 4 60.47 odd 4
2880.2.f.w.1729.4 4 15.2 even 4
2880.2.f.w.1729.4 4 60.23 odd 4
7200.2.a.cb.1.2 2 24.11 even 2
7200.2.a.cb.1.2 2 120.29 odd 2
7200.2.a.cr.1.1 2 24.5 odd 2
7200.2.a.cr.1.1 2 120.59 even 2