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Properties

Label 180.3.f.a.19.1
Level $180$
Weight $3$
Character 180.19
Self dual yes
Analytic conductor $4.905$
Analytic rank $0$
Dimension $1$
CM discriminant -20
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] = [180,3,Mod(19,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) 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("180.19"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 180.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-2,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(4.90464475849\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 19.1
Character \(\chi\) \(=\) 180.19

$q$-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)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} +4.00000 q^{7} -8.00000 q^{8} -10.0000 q^{10} -8.00000 q^{14} +16.0000 q^{16} +20.0000 q^{20} +44.0000 q^{23} +25.0000 q^{25} +16.0000 q^{28} +22.0000 q^{29} -32.0000 q^{32} +20.0000 q^{35} -40.0000 q^{40} -62.0000 q^{41} +76.0000 q^{43} -88.0000 q^{46} -4.00000 q^{47} -33.0000 q^{49} -50.0000 q^{50} -32.0000 q^{56} -44.0000 q^{58} -58.0000 q^{61} +64.0000 q^{64} -116.000 q^{67} -40.0000 q^{70} +80.0000 q^{80} +124.000 q^{82} -76.0000 q^{83} -152.000 q^{86} +142.000 q^{89} +176.000 q^{92} +8.00000 q^{94} +66.0000 q^{98} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(91\) \(101\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −1.00000
\(3\) 0 0
\(4\) 4.00000 1.00000
\(5\) 5.00000 1.00000
\(6\) 0 0
\(7\) 4.00000 0.571429 0.285714 − 0.958315i \(-0.407769\pi\)
0.285714 + 0.958315i \(0.407769\pi\)
\(8\) −8.00000 −1.00000
\(9\) 0 0
\(10\) −10.0000 −1.00000
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −8.00000 −0.571429
\(15\) 0 0
\(16\) 16.0000 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 20.0000 1.00000
\(21\) 0 0
\(22\) 0 0
\(23\) 44.0000 1.91304 0.956522 − 0.291661i \(-0.0942079\pi\)
0.956522 + 0.291661i \(0.0942079\pi\)
\(24\) 0 0
\(25\) 25.0000 1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) 16.0000 0.571429
\(29\) 22.0000 0.758621 0.379310 − 0.925270i \(-0.376161\pi\)
0.379310 + 0.925270i \(0.376161\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −32.0000 −1.00000
\(33\) 0 0
\(34\) 0 0
\(35\) 20.0000 0.571429
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −40.0000 −1.00000
\(41\) −62.0000 −1.51220 −0.756098 − 0.654459i \(-0.772896\pi\)
−0.756098 + 0.654459i \(0.772896\pi\)
\(42\) 0 0
\(43\) 76.0000 1.76744 0.883721 − 0.468014i \(-0.155030\pi\)
0.883721 + 0.468014i \(0.155030\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −88.0000 −1.91304
\(47\) −4.00000 −0.0851064 −0.0425532 − 0.999094i \(-0.513549\pi\)
−0.0425532 + 0.999094i \(0.513549\pi\)
\(48\) 0 0
\(49\) −33.0000 −0.673469
\(50\) −50.0000 −1.00000
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −32.0000 −0.571429
\(57\) 0 0
\(58\) −44.0000 −0.758621
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −58.0000 −0.950820 −0.475410 − 0.879764i \(-0.657700\pi\)
−0.475410 + 0.879764i \(0.657700\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 64.0000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −116.000 −1.73134 −0.865672 − 0.500612i \(-0.833108\pi\)
−0.865672 + 0.500612i \(0.833108\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −40.0000 −0.571429
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 80.0000 1.00000
\(81\) 0 0
\(82\) 124.000 1.51220
\(83\) −76.0000 −0.915663 −0.457831 − 0.889039i \(-0.651374\pi\)
−0.457831 + 0.889039i \(0.651374\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −152.000 −1.76744
\(87\) 0 0
\(88\) 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
\(92\) 176.000 1.91304
\(93\) 0 0
\(94\) 8.00000 0.0851064
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 66.0000 0.673469
\(99\) 0 0
\(100\) 100.000 1.00000
\(101\) −122.000 −1.20792 −0.603960 − 0.797014i \(-0.706411\pi\)
−0.603960 + 0.797014i \(0.706411\pi\)
\(102\) 0 0
\(103\) −44.0000 −0.427184 −0.213592 − 0.976923i \(-0.568516\pi\)
−0.213592 + 0.976923i \(0.568516\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −124.000 −1.15888 −0.579439 − 0.815015i \(-0.696728\pi\)
−0.579439 + 0.815015i \(0.696728\pi\)
\(108\) 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
\(112\) 64.0000 0.571429
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 220.000 1.91304
\(116\) 88.0000 0.758621
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 121.000 1.00000
\(122\) 116.000 0.950820
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 1.00000
\(126\) 0 0
\(127\) −236.000 −1.85827 −0.929134 − 0.369744i \(-0.879446\pi\)
−0.929134 + 0.369744i \(0.879446\pi\)
\(128\) −128.000 −1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 232.000 1.73134
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 80.0000 0.571429
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 110.000 0.758621
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −278.000 −1.86577 −0.932886 − 0.360172i \(-0.882718\pi\)
−0.932886 + 0.360172i \(0.882718\pi\)
\(150\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −160.000 −1.00000
\(161\) 176.000 1.09317
\(162\) 0 0
\(163\) −164.000 −1.00613 −0.503067 − 0.864247i \(-0.667795\pi\)
−0.503067 + 0.864247i \(0.667795\pi\)
\(164\) −248.000 −1.51220
\(165\) 0 0
\(166\) 152.000 0.915663
\(167\) −244.000 −1.46108 −0.730539 − 0.682871i \(-0.760731\pi\)
−0.730539 + 0.682871i \(0.760731\pi\)
\(168\) 0 0
\(169\) 169.000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 304.000 1.76744
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 100.000 0.571429
\(176\) 0 0
\(177\) 0 0
\(178\) −284.000 −1.59551
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −358.000 −1.97790 −0.988950 − 0.148248i \(-0.952637\pi\)
−0.988950 + 0.148248i \(0.952637\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −352.000 −1.91304
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −16.0000 −0.0851064
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −132.000 −0.673469
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −200.000 −1.00000
\(201\) 0 0
\(202\) 244.000 1.20792
\(203\) 88.0000 0.433498
\(204\) 0 0
\(205\) −310.000 −1.51220
\(206\) 88.0000 0.427184
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 248.000 1.15888
\(215\) 380.000 1.76744
\(216\) 0 0
\(217\) 0 0
\(218\) −76.0000 −0.348624
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 436.000 1.95516 0.977578 − 0.210571i \(-0.0675325\pi\)
0.977578 + 0.210571i \(0.0675325\pi\)
\(224\) −128.000 −0.571429
\(225\) 0 0
\(226\) 0 0
\(227\) 356.000 1.56828 0.784141 − 0.620583i \(-0.213104\pi\)
0.784141 + 0.620583i \(0.213104\pi\)
\(228\) 0 0
\(229\) −262.000 −1.14410 −0.572052 − 0.820217i \(-0.693853\pi\)
−0.572052 + 0.820217i \(0.693853\pi\)
\(230\) −440.000 −1.91304
\(231\) 0 0
\(232\) −176.000 −0.758621
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −20.0000 −0.0851064
\(236\) 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 \(0.284464\pi\)
\(242\) −242.000 −1.00000
\(243\) 0 0
\(244\) −232.000 −0.950820
\(245\) −165.000 −0.673469
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −250.000 −1.00000
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 472.000 1.85827
\(255\) 0 0
\(256\) 256.000 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 284.000 1.07985 0.539924 − 0.841714i \(-0.318453\pi\)
0.539924 + 0.841714i \(0.318453\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −464.000 −1.73134
\(269\) −38.0000 −0.141264 −0.0706320 − 0.997502i \(-0.522502\pi\)
−0.0706320 + 0.997502i \(0.522502\pi\)
\(270\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −160.000 −0.571429
\(281\) 418.000 1.48754 0.743772 − 0.668433i \(-0.233035\pi\)
0.743772 + 0.668433i \(0.233035\pi\)
\(282\) 0 0
\(283\) 316.000 1.11661 0.558304 − 0.829637i \(-0.311452\pi\)
0.558304 + 0.829637i \(0.311452\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −248.000 −0.864111
\(288\) 0 0
\(289\) 289.000 1.00000
\(290\) −220.000 −0.758621
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 556.000 1.86577
\(299\) 0 0
\(300\) 0 0
\(301\) 304.000 1.00997
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −290.000 −0.950820
\(306\) 0 0
\(307\) −596.000 −1.94137 −0.970684 − 0.240359i \(-0.922735\pi\)
−0.970684 + 0.240359i \(0.922735\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 320.000 1.00000
\(321\) 0 0
\(322\) −352.000 −1.09317
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 328.000 1.00613
\(327\) 0 0
\(328\) 496.000 1.51220
\(329\) −16.0000 −0.0486322
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −304.000 −0.915663
\(333\) 0 0
\(334\) 488.000 1.46108
\(335\) −580.000 −1.73134
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −338.000 −1.00000
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −328.000 −0.956268
\(344\) −608.000 −1.76744
\(345\) 0 0
\(346\) 0 0
\(347\) 116.000 0.334294 0.167147 − 0.985932i \(-0.446545\pi\)
0.167147 + 0.985932i \(0.446545\pi\)
\(348\) 0 0
\(349\) −22.0000 −0.0630372 −0.0315186 − 0.999503i \(-0.510034\pi\)
−0.0315186 + 0.999503i \(0.510034\pi\)
\(350\) −200.000 −0.571429
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 568.000 1.59551
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 361.000 1.00000
\(362\) 716.000 1.97790
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 724.000 1.97275 0.986376 − 0.164506i \(-0.0526031\pi\)
0.986376 + 0.164506i \(0.0526031\pi\)
\(368\) 704.000 1.91304
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 32.0000 0.0851064
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 44.0000 0.114883 0.0574413 − 0.998349i \(-0.481706\pi\)
0.0574413 + 0.998349i \(0.481706\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 202.000 0.519280 0.259640 − 0.965705i \(-0.416396\pi\)
0.259640 + 0.965705i \(0.416396\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 264.000 0.673469
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 400.000 1.00000
\(401\) 478.000 1.19202 0.596010 − 0.802977i \(-0.296752\pi\)
0.596010 + 0.802977i \(0.296752\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −488.000 −1.20792
\(405\) 0 0
\(406\) −176.000 −0.433498
\(407\) 0 0
\(408\) 0 0
\(409\) −802.000 −1.96088 −0.980440 − 0.196818i \(-0.936939\pi\)
−0.980440 + 0.196818i \(0.936939\pi\)
\(410\) 620.000 1.51220
\(411\) 0 0
\(412\) −176.000 −0.427184
\(413\) 0 0
\(414\) 0 0
\(415\) −380.000 −0.915663
\(416\) 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 \(-0.875092\pi\)
−0.923990 + 0.382415i \(0.875092\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −232.000 −0.543326
\(428\) −496.000 −1.15888
\(429\) 0 0
\(430\) −760.000 −1.76744
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 152.000 0.348624
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −796.000 −1.79684 −0.898420 − 0.439138i \(-0.855284\pi\)
−0.898420 + 0.439138i \(0.855284\pi\)
\(444\) 0 0
\(445\) 710.000 1.59551
\(446\) −872.000 −1.95516
\(447\) 0 0
\(448\) 256.000 0.571429
\(449\) −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
\(454\) −712.000 −1.56828
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 524.000 1.14410
\(459\) 0 0
\(460\) 880.000 1.91304
\(461\) −842.000 −1.82646 −0.913232 − 0.407440i \(-0.866422\pi\)
−0.913232 + 0.407440i \(0.866422\pi\)
\(462\) 0 0
\(463\) −764.000 −1.65011 −0.825054 − 0.565054i \(-0.808855\pi\)
−0.825054 + 0.565054i \(0.808855\pi\)
\(464\) 352.000 0.758621
\(465\) 0 0
\(466\) 0 0
\(467\) −124.000 −0.265525 −0.132762 − 0.991148i \(-0.542385\pi\)
−0.132762 + 0.991148i \(0.542385\pi\)
\(468\) 0 0
\(469\) −464.000 −0.989339
\(470\) 40.0000 0.0851064
\(471\) 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
\(482\) −604.000 −1.25311
\(483\) 0 0
\(484\) 484.000 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 484.000 0.993840 0.496920 − 0.867796i \(-0.334464\pi\)
0.496920 + 0.867796i \(0.334464\pi\)
\(488\) 464.000 0.950820
\(489\) 0 0
\(490\) 330.000 0.673469
\(491\) 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 \(\pi\)
\(500\) 500.000 1.00000
\(501\) 0 0
\(502\) 0 0
\(503\) −916.000 −1.82107 −0.910537 − 0.413428i \(-0.864331\pi\)
−0.910537 + 0.413428i \(0.864331\pi\)
\(504\) 0 0
\(505\) −610.000 −1.20792
\(506\) 0 0
\(507\) 0 0
\(508\) −944.000 −1.85827
\(509\) 982.000 1.92927 0.964637 − 0.263584i \(-0.0849045\pi\)
0.964637 + 0.263584i \(0.0849045\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) −220.000 −0.427184
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −722.000 −1.38580 −0.692898 − 0.721035i \(-0.743667\pi\)
−0.692898 + 0.721035i \(0.743667\pi\)
\(522\) 0 0
\(523\) −164.000 −0.313576 −0.156788 − 0.987632i \(-0.550114\pi\)
−0.156788 + 0.987632i \(0.550114\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −568.000 −1.07985
\(527\) 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
\(535\) −620.000 −1.15888
\(536\) 928.000 1.73134
\(537\) 0 0
\(538\) 76.0000 0.141264
\(539\) 0 0
\(540\) 0 0
\(541\) 362.000 0.669131 0.334566 − 0.942372i \(-0.391410\pi\)
0.334566 + 0.942372i \(0.391410\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 190.000 0.348624
\(546\) 0 0
\(547\) 1084.00 1.98172 0.990859 − 0.134900i \(-0.0430713\pi\)
0.990859 + 0.134900i \(0.0430713\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 320.000 0.571429
\(561\) 0 0
\(562\) −836.000 −1.48754
\(563\) 1124.00 1.99645 0.998224 − 0.0595755i \(-0.0189747\pi\)
0.998224 + 0.0595755i \(0.0189747\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −632.000 −1.11661
\(567\) 0 0
\(568\) 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
\(574\) 496.000 0.864111
\(575\) 1100.00 1.91304
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −578.000 −1.00000
\(579\) 0 0
\(580\) 440.000 0.758621
\(581\) −304.000 −0.523236
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1076.00 1.83305 0.916525 − 0.399978i \(-0.130982\pi\)
0.916525 + 0.399978i \(0.130982\pi\)
\(588\) 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
\(596\) −1112.00 −1.86577
\(597\) 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 \(0.613055\pi\)
\(602\) −608.000 −1.00997
\(603\) 0 0
\(604\) 0 0
\(605\) 605.000 1.00000
\(606\) 0 0
\(607\) 964.000 1.58814 0.794069 − 0.607827i \(-0.207959\pi\)
0.794069 + 0.607827i \(0.207959\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 580.000 0.950820
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 1192.00 1.94137
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 568.000 0.911717
\(624\) 0 0
\(625\) 625.000 1.00000
\(626\) 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
\(635\) −1180.00 −1.85827
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −640.000 −1.00000
\(641\) 1138.00 1.77535 0.887676 − 0.460470i \(-0.152319\pi\)
0.887676 + 0.460470i \(0.152319\pi\)
\(642\) 0 0
\(643\) −404.000 −0.628305 −0.314152 − 0.949373i \(-0.601720\pi\)
−0.314152 + 0.949373i \(0.601720\pi\)
\(644\) 704.000 1.09317
\(645\) 0 0
\(646\) 0 0
\(647\) 956.000 1.47759 0.738794 − 0.673931i \(-0.235395\pi\)
0.738794 + 0.673931i \(0.235395\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −656.000 −1.00613
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −992.000 −1.51220
\(657\) 0 0
\(658\) 32.0000 0.0486322
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −298.000 −0.450832 −0.225416 − 0.974263i \(-0.572374\pi\)
−0.225416 + 0.974263i \(0.572374\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 608.000 0.915663
\(665\) 0 0
\(666\) 0 0
\(667\) 968.000 1.45127
\(668\) −976.000 −1.46108
\(669\) 0 0
\(670\) 1160.00 1.73134
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 676.000 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −556.000 −0.814056 −0.407028 − 0.913416i \(-0.633435\pi\)
−0.407028 + 0.913416i \(0.633435\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 656.000 0.956268
\(687\) 0 0
\(688\) 1216.00 1.76744
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −232.000 −0.334294
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 44.0000 0.0630372
\(699\) 0 0
\(700\) 400.000 0.571429
\(701\) −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
\(707\) −488.000 −0.690240
\(708\) 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
\(712\) −1136.00 −1.59551
\(713\) 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
\(722\) −722.000 −1.00000
\(723\) 0 0
\(724\) −1432.00 −1.97790
\(725\) 550.000 0.758621
\(726\) 0 0
\(727\) −1436.00 −1.97524 −0.987620 − 0.156863i \(-0.949862\pi\)
−0.987620 + 0.156863i \(0.949862\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) −1448.00 −1.97275
\(735\) 0 0
\(736\) −1408.00 −1.91304
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 764.000 1.02826 0.514132 − 0.857711i \(-0.328114\pi\)
0.514132 + 0.857711i \(0.328114\pi\)
\(744\) 0 0
\(745\) −1390.00 −1.86577
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −496.000 −0.662216
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) −64.0000 −0.0851064
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −242.000 −0.318003 −0.159001 − 0.987278i \(-0.550827\pi\)
−0.159001 + 0.987278i \(0.550827\pi\)
\(762\) 0 0
\(763\) 152.000 0.199214
\(764\) 0 0
\(765\) 0 0
\(766\) −88.0000 −0.114883
\(767\) 0 0
\(768\) 0 0
\(769\) −1342.00 −1.74512 −0.872562 − 0.488504i \(-0.837543\pi\)
−0.872562 + 0.488504i \(0.837543\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −404.000 −0.519280
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −528.000 −0.673469
\(785\) 0 0
\(786\) 0 0
\(787\) −116.000 −0.147395 −0.0736976 − 0.997281i \(-0.523480\pi\)
−0.0736976 + 0.997281i \(0.523480\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −800.000 −1.00000
\(801\) 0 0
\(802\) −956.000 −1.19202
\(803\) 0 0
\(804\) 0 0
\(805\) 880.000 1.09317
\(806\) 0 0
\(807\) 0 0
\(808\) 976.000 1.20792
\(809\) −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 \(\pi\)
\(812\) 352.000 0.433498
\(813\) 0 0
\(814\) 0 0
\(815\) −820.000 −1.00613
\(816\) 0 0
\(817\) 0 0
\(818\) 1604.00 1.96088
\(819\) 0 0
\(820\) −1240.00 −1.51220
\(821\) −662.000 −0.806334 −0.403167 − 0.915126i \(-0.632091\pi\)
−0.403167 + 0.915126i \(0.632091\pi\)
\(822\) 0 0
\(823\) 1396.00 1.69623 0.848117 − 0.529810i \(-0.177737\pi\)
0.848117 + 0.529810i \(0.177737\pi\)
\(824\) 352.000 0.427184
\(825\) 0 0
\(826\) 0 0
\(827\) 596.000 0.720677 0.360339 − 0.932822i \(-0.382661\pi\)
0.360339 + 0.932822i \(0.382661\pi\)
\(828\) 0 0
\(829\) 1478.00 1.78287 0.891435 − 0.453148i \(-0.149699\pi\)
0.891435 + 0.453148i \(0.149699\pi\)
\(830\) 760.000 0.915663
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −1220.00 −1.46108
\(836\) 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
\(842\) 1556.00 1.84798
\(843\) 0 0
\(844\) 0 0
\(845\) 845.000 1.00000
\(846\) 0 0
\(847\) 484.000 0.571429
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 464.000 0.543326
\(855\) 0 0
\(856\) 992.000 1.15888
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 1520.00 1.76744
\(861\) 0 0
\(862\) 0 0
\(863\) −1636.00 −1.89571 −0.947856 − 0.318698i \(-0.896754\pi\)
−0.947856 + 0.318698i \(0.896754\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −304.000 −0.348624
\(873\) 0 0
\(874\) 0 0
\(875\) 500.000 0.571429
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1618.00 1.83655 0.918275 − 0.395944i \(-0.129583\pi\)
0.918275 + 0.395944i \(0.129583\pi\)
\(882\) 0 0
\(883\) 1276.00 1.44507 0.722537 − 0.691332i \(-0.242976\pi\)
0.722537 + 0.691332i \(0.242976\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1592.00 1.79684
\(887\) −964.000 −1.08681 −0.543405 − 0.839471i \(-0.682865\pi\)
−0.543405 + 0.839471i \(0.682865\pi\)
\(888\) 0 0
\(889\) −944.000 −1.06187
\(890\) −1420.00 −1.59551
\(891\) 0 0
\(892\) 1744.00 1.95516
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −512.000 −0.571429
\(897\) 0 0
\(898\) 796.000 0.886414
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1790.00 −1.97790
\(906\) 0 0
\(907\) −1796.00 −1.98015 −0.990077 − 0.140525i \(-0.955121\pi\)
−0.990077 + 0.140525i \(0.955121\pi\)
\(908\) 1424.00 1.56828
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −1048.00 −1.14410
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) −1760.00 −1.91304
\(921\) 0 0
\(922\) 1684.00 1.82646
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 1528.00 1.65011
\(927\) 0 0
\(928\) −704.000 −0.758621
\(929\) 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
\(934\) 248.000 0.265525
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 928.000 0.989339
\(939\) 0 0
\(940\) −80.0000 −0.0851064
\(941\) 118.000 0.125399 0.0626993 − 0.998032i \(-0.480029\pi\)
0.0626993 + 0.998032i \(0.480029\pi\)
\(942\) 0 0
\(943\) −2728.00 −2.89290
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1804.00 −1.90496 −0.952482 − 0.304596i \(-0.901478\pi\)
−0.952482 + 0.304596i \(0.901478\pi\)
\(948\) 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
\(961\) 961.000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 1208.00 1.25311
\(965\) 0 0
\(966\) 0 0
\(967\) 244.000 0.252327 0.126163 − 0.992009i \(-0.459734\pi\)
0.126163 + 0.992009i \(0.459734\pi\)
\(968\) −968.000 −1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −968.000 −0.993840
\(975\) 0 0
\(976\) −928.000 −0.950820
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −660.000 −0.673469
\(981\) 0 0
\(982\) 0 0
\(983\) 284.000 0.288911 0.144456 − 0.989511i \(-0.453857\pi\)
0.144456 + 0.989511i \(0.453857\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 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 180.3.f.a.19.1 1
3.2 odd 2 20.3.d.b.19.1 yes 1
4.3 odd 2 180.3.f.b.19.1 1
5.2 odd 4 900.3.c.h.451.1 2
5.3 odd 4 900.3.c.h.451.2 2
5.4 even 2 180.3.f.b.19.1 1
12.11 even 2 20.3.d.a.19.1 ✓ 1
15.2 even 4 100.3.b.c.51.2 2
15.8 even 4 100.3.b.c.51.1 2
15.14 odd 2 20.3.d.a.19.1 ✓ 1
20.3 even 4 900.3.c.h.451.1 2
20.7 even 4 900.3.c.h.451.2 2
20.19 odd 2 CM 180.3.f.a.19.1 1
24.5 odd 2 320.3.h.b.319.1 1
24.11 even 2 320.3.h.a.319.1 1
48.5 odd 4 1280.3.e.b.639.2 2
48.11 even 4 1280.3.e.c.639.1 2
48.29 odd 4 1280.3.e.b.639.1 2
48.35 even 4 1280.3.e.c.639.2 2
60.23 odd 4 100.3.b.c.51.2 2
60.47 odd 4 100.3.b.c.51.1 2
60.59 even 2 20.3.d.b.19.1 yes 1
120.29 odd 2 320.3.h.a.319.1 1
120.53 even 4 1600.3.b.f.1151.2 2
120.59 even 2 320.3.h.b.319.1 1
120.77 even 4 1600.3.b.f.1151.1 2
120.83 odd 4 1600.3.b.f.1151.1 2
120.107 odd 4 1600.3.b.f.1151.2 2
240.29 odd 4 1280.3.e.c.639.2 2
240.59 even 4 1280.3.e.b.639.2 2
240.149 odd 4 1280.3.e.c.639.1 2
240.179 even 4 1280.3.e.b.639.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.3.d.a.19.1 ✓ 1 12.11 even 2
20.3.d.a.19.1 ✓ 1 15.14 odd 2
20.3.d.b.19.1 yes 1 3.2 odd 2
20.3.d.b.19.1 yes 1 60.59 even 2
100.3.b.c.51.1 2 15.8 even 4
100.3.b.c.51.1 2 60.47 odd 4
100.3.b.c.51.2 2 15.2 even 4
100.3.b.c.51.2 2 60.23 odd 4
180.3.f.a.19.1 1 1.1 even 1 trivial
180.3.f.a.19.1 1 20.19 odd 2 CM
180.3.f.b.19.1 1 4.3 odd 2
180.3.f.b.19.1 1 5.4 even 2
320.3.h.a.319.1 1 24.11 even 2
320.3.h.a.319.1 1 120.29 odd 2
320.3.h.b.319.1 1 24.5 odd 2
320.3.h.b.319.1 1 120.59 even 2
900.3.c.h.451.1 2 5.2 odd 4
900.3.c.h.451.1 2 20.3 even 4
900.3.c.h.451.2 2 5.3 odd 4
900.3.c.h.451.2 2 20.7 even 4
1280.3.e.b.639.1 2 48.29 odd 4
1280.3.e.b.639.1 2 240.179 even 4
1280.3.e.b.639.2 2 48.5 odd 4
1280.3.e.b.639.2 2 240.59 even 4
1280.3.e.c.639.1 2 48.11 even 4
1280.3.e.c.639.1 2 240.149 odd 4
1280.3.e.c.639.2 2 48.35 even 4
1280.3.e.c.639.2 2 240.29 odd 4
1600.3.b.f.1151.1 2 120.77 even 4
1600.3.b.f.1151.1 2 120.83 odd 4
1600.3.b.f.1151.2 2 120.53 even 4
1600.3.b.f.1151.2 2 120.107 odd 4