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Properties

Label 1600.3.b.f.1151.1
Level $1600$
Weight $3$
Character 1600.1151
Analytic conductor $43.597$
Analytic rank $0$
Dimension $2$
CM discriminant -20
Inner twists $4$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1600,3,Mod(1151,1600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1600, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1600.1151"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1600.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,0,0,0,0,0,0,-14,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(43.5968422976\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 1151.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1600.1151
Dual form 1600.3.b.f.1151.2

$q$-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)
 
\(f(q)\) \(=\) \(q-4.00000i q^{3} +4.00000i q^{7} -7.00000 q^{9} +16.0000 q^{21} +44.0000i q^{23} -8.00000i q^{27} -22.0000 q^{29} +62.0000 q^{41} +76.0000i q^{43} +4.00000i q^{47} +33.0000 q^{49} +58.0000 q^{61} -28.0000i q^{63} +116.000i q^{67} +176.000 q^{69} -95.0000 q^{81} +76.0000i q^{83} +88.0000i q^{87} +142.000 q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 14 q^{9} + 32 q^{21} - 44 q^{29} + 124 q^{41} + 66 q^{49} + 116 q^{61} + 352 q^{69} - 190 q^{81} + 284 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1151\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(3\) − 4.00000i − 1.33333i −0.745356 − 0.666667i \(-0.767720\pi\)
0.745356 − 0.666667i \(-0.232280\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.00000i 0.571429i 0.958315 + 0.285714i \(0.0922308\pi\)
−0.958315 + 0.285714i \(0.907769\pi\)
\(8\) 0 0
\(9\) −7.00000 −0.777778
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 16.0000 0.761905
\(22\) 0 0
\(23\) 44.0000i 1.91304i 0.291661 + 0.956522i \(0.405792\pi\)
−0.291661 + 0.956522i \(0.594208\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) − 8.00000i − 0.296296i
\(28\) 0 0
\(29\) −22.0000 −0.758621 −0.379310 − 0.925270i \(-0.623839\pi\)
−0.379310 + 0.925270i \(0.623839\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 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
\(41\) 62.0000 1.51220 0.756098 − 0.654459i \(-0.227104\pi\)
0.756098 + 0.654459i \(0.227104\pi\)
\(42\) 0 0
\(43\) 76.0000i 1.76744i 0.468014 + 0.883721i \(0.344970\pi\)
−0.468014 + 0.883721i \(0.655030\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.00000i 0.0851064i 0.999094 + 0.0425532i \(0.0135492\pi\)
−0.999094 + 0.0425532i \(0.986451\pi\)
\(48\) 0 0
\(49\) 33.0000 0.673469
\(50\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 58.0000 0.950820 0.475410 − 0.879764i \(-0.342300\pi\)
0.475410 + 0.879764i \(0.342300\pi\)
\(62\) 0 0
\(63\) − 28.0000i − 0.444444i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 116.000i 1.73134i 0.500612 + 0.865672i \(0.333108\pi\)
−0.500612 + 0.865672i \(0.666892\pi\)
\(68\) 0 0
\(69\) 176.000 2.55072
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) −95.0000 −1.17284
\(82\) 0 0
\(83\) 76.0000i 0.915663i 0.889039 + 0.457831i \(0.151374\pi\)
−0.889039 + 0.457831i \(0.848626\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 88.0000i 1.01149i
\(88\) 0 0
\(89\) 142.000 1.59551 0.797753 − 0.602985i \(-0.206022\pi\)
0.797753 + 0.602985i \(0.206022\pi\)
\(90\) 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
\(101\) −122.000 −1.20792 −0.603960 − 0.797014i \(-0.706411\pi\)
−0.603960 + 0.797014i \(0.706411\pi\)
\(102\) 0 0
\(103\) 44.0000i 0.427184i 0.976923 + 0.213592i \(0.0685164\pi\)
−0.976923 + 0.213592i \(0.931484\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 124.000i − 1.15888i −0.815015 − 0.579439i \(-0.803272\pi\)
0.815015 − 0.579439i \(-0.196728\pi\)
\(108\) 0 0
\(109\) 38.0000 0.348624 0.174312 − 0.984690i \(-0.444230\pi\)
0.174312 + 0.984690i \(0.444230\pi\)
\(110\) 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
\(121\) 121.000 1.00000
\(122\) 0 0
\(123\) − 248.000i − 2.01626i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) − 236.000i − 1.85827i −0.369744 − 0.929134i \(-0.620554\pi\)
0.369744 − 0.929134i \(-0.379446\pi\)
\(128\) 0 0
\(129\) 304.000 2.35659
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 16.0000 0.113475
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) − 132.000i − 0.897959i
\(148\) 0 0
\(149\) 278.000 1.86577 0.932886 − 0.360172i \(-0.117282\pi\)
0.932886 + 0.360172i \(0.117282\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 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
\(161\) −176.000 −1.09317
\(162\) 0 0
\(163\) − 164.000i − 1.00613i −0.864247 − 0.503067i \(-0.832205\pi\)
0.864247 − 0.503067i \(-0.167795\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 244.000i 1.46108i 0.682871 + 0.730539i \(0.260731\pi\)
−0.682871 + 0.730539i \(0.739269\pi\)
\(168\) 0 0
\(169\) −169.000 −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 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 358.000 1.97790 0.988950 − 0.148248i \(-0.0473633\pi\)
0.988950 + 0.148248i \(0.0473633\pi\)
\(182\) 0 0
\(183\) − 232.000i − 1.26776i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 32.0000 0.169312
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 464.000 2.30846
\(202\) 0 0
\(203\) − 88.0000i − 0.433498i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) − 308.000i − 1.48792i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 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
\(223\) − 436.000i − 1.95516i −0.210571 − 0.977578i \(-0.567532\pi\)
0.210571 − 0.977578i \(-0.432468\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 356.000i 1.56828i 0.620583 + 0.784141i \(0.286896\pi\)
−0.620583 + 0.784141i \(0.713104\pi\)
\(228\) 0 0
\(229\) −262.000 −1.14410 −0.572052 − 0.820217i \(-0.693853\pi\)
−0.572052 + 0.820217i \(0.693853\pi\)
\(230\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 302.000 1.25311 0.626556 − 0.779376i \(-0.284464\pi\)
0.626556 + 0.779376i \(0.284464\pi\)
\(242\) 0 0
\(243\) 308.000i 1.26749i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 304.000 1.22088
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 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
\(261\) 154.000 0.590038
\(262\) 0 0
\(263\) 284.000i 1.07985i 0.841714 + 0.539924i \(0.181547\pi\)
−0.841714 + 0.539924i \(0.818453\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) − 568.000i − 2.12734i
\(268\) 0 0
\(269\) 38.0000 0.141264 0.0706320 − 0.997502i \(-0.477498\pi\)
0.0706320 + 0.997502i \(0.477498\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 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
\(281\) −418.000 −1.48754 −0.743772 − 0.668433i \(-0.766965\pi\)
−0.743772 + 0.668433i \(0.766965\pi\)
\(282\) 0 0
\(283\) 316.000i 1.11661i 0.829637 + 0.558304i \(0.188548\pi\)
−0.829637 + 0.558304i \(0.811452\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 248.000i 0.864111i
\(288\) 0 0
\(289\) −289.000 −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
\(301\) −304.000 −1.00997
\(302\) 0 0
\(303\) 488.000i 1.61056i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 596.000i 1.94137i 0.240359 + 0.970684i \(0.422735\pi\)
−0.240359 + 0.970684i \(0.577265\pi\)
\(308\) 0 0
\(309\) 176.000 0.569579
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 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
\(321\) −496.000 −1.54517
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) − 152.000i − 0.464832i
\(328\) 0 0
\(329\) −16.0000 −0.0486322
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 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
\(343\) 328.000i 0.956268i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 116.000i 0.334294i 0.985932 + 0.167147i \(0.0534554\pi\)
−0.985932 + 0.167147i \(0.946545\pi\)
\(348\) 0 0
\(349\) −22.0000 −0.0630372 −0.0315186 − 0.999503i \(-0.510034\pi\)
−0.0315186 + 0.999503i \(0.510034\pi\)
\(350\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 361.000 1.00000
\(362\) 0 0
\(363\) − 484.000i − 1.33333i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 724.000i 1.97275i 0.164506 + 0.986376i \(0.447397\pi\)
−0.164506 + 0.986376i \(0.552603\pi\)
\(368\) 0 0
\(369\) −434.000 −1.17615
\(370\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) −944.000 −2.47769
\(382\) 0 0
\(383\) 44.0000i 0.114883i 0.998349 + 0.0574413i \(0.0182942\pi\)
−0.998349 + 0.0574413i \(0.981706\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) − 532.000i − 1.37468i
\(388\) 0 0
\(389\) −202.000 −0.519280 −0.259640 − 0.965705i \(-0.583604\pi\)
−0.259640 + 0.965705i \(0.583604\pi\)
\(390\) 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
\(401\) −478.000 −1.19202 −0.596010 − 0.802977i \(-0.703248\pi\)
−0.596010 + 0.802977i \(0.703248\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 802.000 1.96088 0.980440 − 0.196818i \(-0.0630607\pi\)
0.980440 + 0.196818i \(0.0630607\pi\)
\(410\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 778.000 1.84798 0.923990 − 0.382415i \(-0.124908\pi\)
0.923990 + 0.382415i \(0.124908\pi\)
\(422\) 0 0
\(423\) − 28.0000i − 0.0661939i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 232.000i 0.543326i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −231.000 −0.523810
\(442\) 0 0
\(443\) 796.000i 1.79684i 0.439138 + 0.898420i \(0.355284\pi\)
−0.439138 + 0.898420i \(0.644716\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) − 1112.00i − 2.48770i
\(448\) 0 0
\(449\) −398.000 −0.886414 −0.443207 − 0.896419i \(-0.646159\pi\)
−0.443207 + 0.896419i \(0.646159\pi\)
\(450\) 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
\(461\) −842.000 −1.82646 −0.913232 − 0.407440i \(-0.866422\pi\)
−0.913232 + 0.407440i \(0.866422\pi\)
\(462\) 0 0
\(463\) 764.000i 1.65011i 0.565054 + 0.825054i \(0.308855\pi\)
−0.565054 + 0.825054i \(0.691145\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 124.000i − 0.265525i −0.991148 − 0.132762i \(-0.957615\pi\)
0.991148 − 0.132762i \(-0.0423847\pi\)
\(468\) 0 0
\(469\) −464.000 −0.989339
\(470\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 704.000i 1.45756i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 484.000i 0.993840i 0.867796 + 0.496920i \(0.165536\pi\)
−0.867796 + 0.496920i \(0.834464\pi\)
\(488\) 0 0
\(489\) −656.000 −1.34151
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 976.000 1.94810
\(502\) 0 0
\(503\) − 916.000i − 1.82107i −0.413428 − 0.910537i \(-0.635669\pi\)
0.413428 − 0.910537i \(-0.364331\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 676.000i 1.33333i
\(508\) 0 0
\(509\) −982.000 −1.92927 −0.964637 − 0.263584i \(-0.915095\pi\)
−0.964637 + 0.263584i \(0.915095\pi\)
\(510\) 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
\(521\) 722.000 1.38580 0.692898 − 0.721035i \(-0.256333\pi\)
0.692898 + 0.721035i \(0.256333\pi\)
\(522\) 0 0
\(523\) − 164.000i − 0.313576i −0.987632 − 0.156788i \(-0.949886\pi\)
0.987632 − 0.156788i \(-0.0501139\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −1407.00 −2.65974
\(530\) 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
\(541\) −362.000 −0.669131 −0.334566 − 0.942372i \(-0.608590\pi\)
−0.334566 + 0.942372i \(0.608590\pi\)
\(542\) 0 0
\(543\) − 1432.00i − 2.63720i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 1084.00i − 1.98172i −0.134900 − 0.990859i \(-0.543071\pi\)
0.134900 − 0.990859i \(-0.456929\pi\)
\(548\) 0 0
\(549\) −406.000 −0.739526
\(550\) 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
\(563\) − 1124.00i − 1.99645i −0.0595755 − 0.998224i \(-0.518975\pi\)
0.0595755 − 0.998224i \(-0.481025\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 380.000i − 0.670194i
\(568\) 0 0
\(569\) −158.000 −0.277680 −0.138840 − 0.990315i \(-0.544337\pi\)
−0.138840 + 0.990315i \(0.544337\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 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
\(581\) −304.000 −0.523236
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1076.00i 1.83305i 0.399978 + 0.916525i \(0.369018\pi\)
−0.399978 + 0.916525i \(0.630982\pi\)
\(588\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −418.000 −0.695507 −0.347754 − 0.937586i \(-0.613055\pi\)
−0.347754 + 0.937586i \(0.613055\pi\)
\(602\) 0 0
\(603\) − 812.000i − 1.34660i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 964.000i 1.58814i 0.607827 + 0.794069i \(0.292041\pi\)
−0.607827 + 0.794069i \(0.707959\pi\)
\(608\) 0 0
\(609\) −352.000 −0.577997
\(610\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 352.000 0.566828
\(622\) 0 0
\(623\) 568.000i 0.911717i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 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
\(641\) −1138.00 −1.77535 −0.887676 − 0.460470i \(-0.847681\pi\)
−0.887676 + 0.460470i \(0.847681\pi\)
\(642\) 0 0
\(643\) − 404.000i − 0.628305i −0.949373 − 0.314152i \(-0.898280\pi\)
0.949373 − 0.314152i \(-0.101720\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 956.000i − 1.47759i −0.673931 − 0.738794i \(-0.735395\pi\)
0.673931 − 0.738794i \(-0.264605\pi\)
\(648\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 298.000 0.450832 0.225416 − 0.974263i \(-0.427626\pi\)
0.225416 + 0.974263i \(0.427626\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) − 968.000i − 1.45127i
\(668\) 0 0
\(669\) −1744.00 −2.60688
\(670\) 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
\(681\) 1424.00 2.09104
\(682\) 0 0
\(683\) 556.000i 0.814056i 0.913416 + 0.407028i \(0.133435\pi\)
−0.913416 + 0.407028i \(0.866565\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 1048.00i 1.52547i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 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
\(701\) −902.000 −1.28673 −0.643367 − 0.765558i \(-0.722463\pi\)
−0.643367 + 0.765558i \(0.722463\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 488.000i − 0.690240i
\(708\) 0 0
\(709\) 698.000 0.984485 0.492243 − 0.870458i \(-0.336177\pi\)
0.492243 + 0.870458i \(0.336177\pi\)
\(710\) 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
\(721\) −176.000 −0.244105
\(722\) 0 0
\(723\) − 1208.00i − 1.67082i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 1436.00i − 1.97524i −0.156863 − 0.987620i \(-0.550138\pi\)
0.156863 − 0.987620i \(-0.449862\pi\)
\(728\) 0 0
\(729\) 377.000 0.517147
\(730\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 764.000i 1.02826i 0.857711 + 0.514132i \(0.171886\pi\)
−0.857711 + 0.514132i \(0.828114\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) − 532.000i − 0.712182i
\(748\) 0 0
\(749\) 496.000 0.662216
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 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
\(761\) 242.000 0.318003 0.159001 − 0.987278i \(-0.449173\pi\)
0.159001 + 0.987278i \(0.449173\pi\)
\(762\) 0 0
\(763\) 152.000i 0.199214i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 1342.00 1.74512 0.872562 − 0.488504i \(-0.162457\pi\)
0.872562 + 0.488504i \(0.162457\pi\)
\(770\) 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
\(783\) 176.000i 0.224777i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 116.000i 0.147395i 0.997281 + 0.0736976i \(0.0234800\pi\)
−0.997281 + 0.0736976i \(0.976520\pi\)
\(788\) 0 0
\(789\) 1136.00 1.43980
\(790\) 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
\(801\) −994.000 −1.24095
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) − 152.000i − 0.188352i
\(808\) 0 0
\(809\) −1298.00 −1.60445 −0.802225 − 0.597022i \(-0.796351\pi\)
−0.802225 + 0.597022i \(0.796351\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 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
\(821\) −662.000 −0.806334 −0.403167 − 0.915126i \(-0.632091\pi\)
−0.403167 + 0.915126i \(0.632091\pi\)
\(822\) 0 0
\(823\) − 1396.00i − 1.69623i −0.529810 − 0.848117i \(-0.677737\pi\)
0.529810 − 0.848117i \(-0.322263\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 596.000i 0.720677i 0.932822 + 0.360339i \(0.117339\pi\)
−0.932822 + 0.360339i \(0.882661\pi\)
\(828\) 0 0
\(829\) 1478.00 1.78287 0.891435 − 0.453148i \(-0.149699\pi\)
0.891435 + 0.453148i \(0.149699\pi\)
\(830\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) −357.000 −0.424495
\(842\) 0 0
\(843\) 1672.00i 1.98339i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 484.000i 0.571429i
\(848\) 0 0
\(849\) 1264.00 1.48881
\(850\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 992.000 1.15215
\(862\) 0 0
\(863\) − 1636.00i − 1.89571i −0.318698 − 0.947856i \(-0.603246\pi\)
0.318698 − 0.947856i \(-0.396754\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1156.00i 1.33333i
\(868\) 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
\(881\) −1618.00 −1.83655 −0.918275 − 0.395944i \(-0.870417\pi\)
−0.918275 + 0.395944i \(0.870417\pi\)
\(882\) 0 0
\(883\) 1276.00i 1.44507i 0.691332 + 0.722537i \(0.257024\pi\)
−0.691332 + 0.722537i \(0.742976\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 964.000i 1.08681i 0.839471 + 0.543405i \(0.182865\pi\)
−0.839471 + 0.543405i \(0.817135\pi\)
\(888\) 0 0
\(889\) 944.000 1.06187
\(890\) 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
\(903\) 1216.00i 1.34662i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 1796.00i 1.98015i 0.140525 + 0.990077i \(0.455121\pi\)
−0.140525 + 0.990077i \(0.544879\pi\)
\(908\) 0 0
\(909\) 854.000 0.939494
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 2384.00 2.58849
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) − 308.000i − 0.332255i
\(928\) 0 0
\(929\) 562.000 0.604952 0.302476 − 0.953157i \(-0.402187\pi\)
0.302476 + 0.953157i \(0.402187\pi\)
\(930\) 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
\(941\) 118.000 0.125399 0.0626993 − 0.998032i \(-0.480029\pi\)
0.0626993 + 0.998032i \(0.480029\pi\)
\(942\) 0 0
\(943\) 2728.00i 2.89290i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 1804.00i − 1.90496i −0.304596 − 0.952482i \(-0.598522\pi\)
0.304596 − 0.952482i \(-0.401478\pi\)
\(948\) 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
\(961\) 961.000 1.00000
\(962\) 0 0
\(963\) 868.000i 0.901350i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 244.000i 0.252327i 0.992009 + 0.126163i \(0.0402664\pi\)
−0.992009 + 0.126163i \(0.959734\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 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
\(981\) −266.000 −0.271152
\(982\) 0 0
\(983\) 284.000i 0.288911i 0.989511 + 0.144456i \(0.0461431\pi\)
−0.989511 + 0.144456i \(0.953857\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 64.0000i 0.0648430i
\(988\) 0 0
\(989\) −3344.00 −3.38119
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 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 1600.3.b.f.1151.1 2
4.3 odd 2 inner 1600.3.b.f.1151.2 2
5.2 odd 4 320.3.h.a.319.1 1
5.3 odd 4 320.3.h.b.319.1 1
5.4 even 2 inner 1600.3.b.f.1151.2 2
8.3 odd 2 100.3.b.c.51.1 2
8.5 even 2 100.3.b.c.51.2 2
20.3 even 4 320.3.h.a.319.1 1
20.7 even 4 320.3.h.b.319.1 1
20.19 odd 2 CM 1600.3.b.f.1151.1 2
24.5 odd 2 900.3.c.h.451.1 2
24.11 even 2 900.3.c.h.451.2 2
40.3 even 4 20.3.d.a.19.1 ✓ 1
40.13 odd 4 20.3.d.b.19.1 yes 1
40.19 odd 2 100.3.b.c.51.2 2
40.27 even 4 20.3.d.b.19.1 yes 1
40.29 even 2 100.3.b.c.51.1 2
40.37 odd 4 20.3.d.a.19.1 ✓ 1
80.3 even 4 1280.3.e.c.639.1 2
80.13 odd 4 1280.3.e.b.639.2 2
80.27 even 4 1280.3.e.b.639.1 2
80.37 odd 4 1280.3.e.c.639.2 2
80.43 even 4 1280.3.e.c.639.2 2
80.53 odd 4 1280.3.e.b.639.1 2
80.67 even 4 1280.3.e.b.639.2 2
80.77 odd 4 1280.3.e.c.639.1 2
120.29 odd 2 900.3.c.h.451.2 2
120.53 even 4 180.3.f.a.19.1 1
120.59 even 2 900.3.c.h.451.1 2
120.77 even 4 180.3.f.b.19.1 1
120.83 odd 4 180.3.f.b.19.1 1
120.107 odd 4 180.3.f.a.19.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.3.d.a.19.1 ✓ 1 40.3 even 4
20.3.d.a.19.1 ✓ 1 40.37 odd 4
20.3.d.b.19.1 yes 1 40.13 odd 4
20.3.d.b.19.1 yes 1 40.27 even 4
100.3.b.c.51.1 2 8.3 odd 2
100.3.b.c.51.1 2 40.29 even 2
100.3.b.c.51.2 2 8.5 even 2
100.3.b.c.51.2 2 40.19 odd 2
180.3.f.a.19.1 1 120.53 even 4
180.3.f.a.19.1 1 120.107 odd 4
180.3.f.b.19.1 1 120.77 even 4
180.3.f.b.19.1 1 120.83 odd 4
320.3.h.a.319.1 1 5.2 odd 4
320.3.h.a.319.1 1 20.3 even 4
320.3.h.b.319.1 1 5.3 odd 4
320.3.h.b.319.1 1 20.7 even 4
900.3.c.h.451.1 2 24.5 odd 2
900.3.c.h.451.1 2 120.59 even 2
900.3.c.h.451.2 2 24.11 even 2
900.3.c.h.451.2 2 120.29 odd 2
1280.3.e.b.639.1 2 80.27 even 4
1280.3.e.b.639.1 2 80.53 odd 4
1280.3.e.b.639.2 2 80.13 odd 4
1280.3.e.b.639.2 2 80.67 even 4
1280.3.e.c.639.1 2 80.3 even 4
1280.3.e.c.639.1 2 80.77 odd 4
1280.3.e.c.639.2 2 80.37 odd 4
1280.3.e.c.639.2 2 80.43 even 4
1600.3.b.f.1151.1 2 1.1 even 1 trivial
1600.3.b.f.1151.1 2 20.19 odd 2 CM
1600.3.b.f.1151.2 2 4.3 odd 2 inner
1600.3.b.f.1151.2 2 5.4 even 2 inner