Properties

Label 2183.1.d.a.2182.1
Level $2183$
Weight $1$
Character 2183.2182
Self dual yes
Analytic conductor $1.089$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -2183
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2183,1,Mod(2182,2183)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2183, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2183.2182");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2183 = 37 \cdot 59 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2183.d (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: yes
Analytic conductor: \(1.08945892258\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.2183.1
Artin image: $S_3$
Artin field: Galois closure of 3.1.2183.1

Embedding invariants

Embedding label 2182.1
Character \(\chi\) \(=\) 2183.2182

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.00000 q^{3} -2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.00000 q^{3} -2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +3.00000 q^{9} -1.00000 q^{13} +1.00000 q^{14} -1.00000 q^{16} -3.00000 q^{18} -2.00000 q^{21} +2.00000 q^{23} +2.00000 q^{24} +1.00000 q^{25} +1.00000 q^{26} +4.00000 q^{27} -1.00000 q^{31} +1.00000 q^{37} -2.00000 q^{39} -1.00000 q^{41} +2.00000 q^{42} +2.00000 q^{43} -2.00000 q^{46} -2.00000 q^{48} -1.00000 q^{50} -1.00000 q^{53} -4.00000 q^{54} -1.00000 q^{56} +1.00000 q^{59} -1.00000 q^{61} +1.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +4.00000 q^{69} -1.00000 q^{71} +3.00000 q^{72} -1.00000 q^{74} +2.00000 q^{75} +2.00000 q^{78} +5.00000 q^{81} +1.00000 q^{82} -2.00000 q^{86} -1.00000 q^{89} +1.00000 q^{91} -2.00000 q^{93} -1.00000 q^{97} +O(q^{100})\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2183\mathbb{Z}\right)^\times\).

\(n\) \(297\) \(1889\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(4\) 0 0
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) −2.00000 −2.00000
\(7\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 1.00000 1.00000
\(9\) 3.00000 3.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(14\) 1.00000 1.00000
\(15\) 0 0
\(16\) −1.00000 −1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) −3.00000 −3.00000
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) −2.00000 −2.00000
\(22\) 0 0
\(23\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(24\) 2.00000 2.00000
\(25\) 1.00000 1.00000
\(26\) 1.00000 1.00000
\(27\) 4.00000 4.00000
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.00000 1.00000
\(38\) 0 0
\(39\) −2.00000 −2.00000
\(40\) 0 0
\(41\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 2.00000 2.00000
\(43\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(44\) 0 0
\(45\) 0 0
\(46\) −2.00000 −2.00000
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −2.00000 −2.00000
\(49\) 0 0
\(50\) −1.00000 −1.00000
\(51\) 0 0
\(52\) 0 0
\(53\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) −4.00000 −4.00000
\(55\) 0 0
\(56\) −1.00000 −1.00000
\(57\) 0 0
\(58\) 0 0
\(59\) 1.00000 1.00000
\(60\) 0 0
\(61\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 1.00000 1.00000
\(63\) −3.00000 −3.00000
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 4.00000 4.00000
\(70\) 0 0
\(71\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) 3.00000 3.00000
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) −1.00000 −1.00000
\(75\) 2.00000 2.00000
\(76\) 0 0
\(77\) 0 0
\(78\) 2.00000 2.00000
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 5.00000 5.00000
\(82\) 1.00000 1.00000
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.00000 −2.00000
\(87\) 0 0
\(88\) 0 0
\(89\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) 0 0
\(91\) 1.00000 1.00000
\(92\) 0 0
\(93\) −2.00000 −2.00000
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) −1.00000 −1.00000
\(105\) 0 0
\(106\) 1.00000 1.00000
\(107\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 0 0
\(109\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(110\) 0 0
\(111\) 2.00000 2.00000
\(112\) 1.00000 1.00000
\(113\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −3.00000 −3.00000
\(118\) −1.00000 −1.00000
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 1.00000 1.00000
\(123\) −2.00000 −2.00000
\(124\) 0 0
\(125\) 0 0
\(126\) 3.00000 3.00000
\(127\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(128\) −1.00000 −1.00000
\(129\) 4.00000 4.00000
\(130\) 0 0
\(131\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) −4.00000 −4.00000
\(139\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.00000 1.00000
\(143\) 0 0
\(144\) −3.00000 −3.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −2.00000 −2.00000
\(151\) 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
\(159\) −2.00000 −2.00000
\(160\) 0 0
\(161\) −2.00000 −2.00000
\(162\) −5.00000 −5.00000
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) −2.00000 −2.00000
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −1.00000 −1.00000
\(176\) 0 0
\(177\) 2.00000 2.00000
\(178\) 1.00000 1.00000
\(179\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) 0 0
\(181\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(182\) −1.00000 −1.00000
\(183\) −2.00000 −2.00000
\(184\) 2.00000 2.00000
\(185\) 0 0
\(186\) 2.00000 2.00000
\(187\) 0 0
\(188\) 0 0
\(189\) −4.00000 −4.00000
\(190\) 0 0
\(191\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 2.00000 2.00000
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 1.00000 1.00000
\(195\) 0 0
\(196\) 0 0
\(197\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.00000 1.00000
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 1.00000 1.00000
\(207\) 6.00000 6.00000
\(208\) 1.00000 1.00000
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) −2.00000 −2.00000
\(214\) 1.00000 1.00000
\(215\) 0 0
\(216\) 4.00000 4.00000
\(217\) 1.00000 1.00000
\(218\) −2.00000 −2.00000
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) −2.00000 −2.00000
\(223\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(224\) 0 0
\(225\) 3.00000 3.00000
\(226\) 1.00000 1.00000
\(227\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 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 \(\pi\)
\(234\) 3.00000 3.00000
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −1.00000 −1.00000
\(243\) 6.00000 6.00000
\(244\) 0 0
\(245\) 0 0
\(246\) 2.00000 2.00000
\(247\) 0 0
\(248\) −1.00000 −1.00000
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.00000 1.00000
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) −4.00000 −4.00000
\(259\) −1.00000 −1.00000
\(260\) 0 0
\(261\) 0 0
\(262\) 1.00000 1.00000
\(263\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −2.00000 −2.00000
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(272\) 0 0
\(273\) 2.00000 2.00000
\(274\) 1.00000 1.00000
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 1.00000 1.00000
\(279\) −3.00000 −3.00000
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.00000 1.00000
\(288\) 0 0
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) −2.00000 −2.00000
\(292\) 0 0
\(293\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 1.00000
\(297\) 0 0
\(298\) 0 0
\(299\) −2.00000 −2.00000
\(300\) 0 0
\(301\) −2.00000 −2.00000
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) −2.00000 −2.00000
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) −2.00000 −2.00000
\(313\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) 2.00000 2.00000
\(319\) 0 0
\(320\) 0 0
\(321\) −2.00000 −2.00000
\(322\) 2.00000 2.00000
\(323\) 0 0
\(324\) 0 0
\(325\) −1.00000 −1.00000
\(326\) 0 0
\(327\) 4.00000 4.00000
\(328\) −1.00000 −1.00000
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 3.00000 3.00000
\(334\) 0 0
\(335\) 0 0
\(336\) 2.00000 2.00000
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) −2.00000 −2.00000
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 1.00000
\(344\) 2.00000 2.00000
\(345\) 0 0
\(346\) 0 0
\(347\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 1.00000 1.00000
\(351\) −4.00000 −4.00000
\(352\) 0 0
\(353\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(354\) −2.00000 −2.00000
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 1.00000 1.00000
\(359\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) −2.00000 −2.00000
\(363\) 2.00000 2.00000
\(364\) 0 0
\(365\) 0 0
\(366\) 2.00000 2.00000
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) −2.00000 −2.00000
\(369\) −3.00000 −3.00000
\(370\) 0 0
\(371\) 1.00000 1.00000
\(372\) 0 0
\(373\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 4.00000 4.00000
\(379\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(380\) 0 0
\(381\) −2.00000 −2.00000
\(382\) 1.00000 1.00000
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) −2.00000 −2.00000
\(385\) 0 0
\(386\) 0 0
\(387\) 6.00000 6.00000
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −2.00000 −2.00000
\(394\) −2.00000 −2.00000
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −1.00000 −1.00000
\(401\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0 0
\(403\) 1.00000 1.00000
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) −2.00000 −2.00000
\(412\) 0 0
\(413\) −1.00000 −1.00000
\(414\) −6.00000 −6.00000
\(415\) 0 0
\(416\) 0 0
\(417\) −2.00000 −2.00000
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −1.00000 −1.00000
\(425\) 0 0
\(426\) 2.00000 2.00000
\(427\) 1.00000 1.00000
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(432\) −4.00000 −4.00000
\(433\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(434\) −1.00000 −1.00000
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 1.00000 1.00000
\(447\) 0 0
\(448\) −1.00000 −1.00000
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) −3.00000 −3.00000
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 1.00000 1.00000
\(455\) 0 0
\(456\) 0 0
\(457\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.00000 1.00000
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −3.00000 −3.00000
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) −1.00000 −1.00000
\(482\) 0 0
\(483\) −4.00000 −4.00000
\(484\) 0 0
\(485\) 0 0
\(486\) −6.00000 −6.00000
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) −1.00000 −1.00000
\(489\) 0 0
\(490\) 0 0
\(491\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.00000 1.00000
\(497\) 1.00000 1.00000
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(504\) −3.00000 −3.00000
\(505\) 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
\(512\) 1.00000 1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 1.00000 1.00000
\(519\) 0 0
\(520\) 0 0
\(521\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) −2.00000 −2.00000
\(526\) 1.00000 1.00000
\(527\) 0 0
\(528\) 0 0
\(529\) 3.00000 3.00000
\(530\) 0 0
\(531\) 3.00000 3.00000
\(532\) 0 0
\(533\) 1.00000 1.00000
\(534\) 2.00000 2.00000
\(535\) 0 0
\(536\) 0 0
\(537\) −2.00000 −2.00000
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(542\) −2.00000 −2.00000
\(543\) 4.00000 4.00000
\(544\) 0 0
\(545\) 0 0
\(546\) −2.00000 −2.00000
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) −3.00000 −3.00000
\(550\) 0 0
\(551\) 0 0
\(552\) 4.00000 4.00000
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 3.00000 3.00000
\(559\) −2.00000 −2.00000
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.00000 1.00000
\(567\) −5.00000 −5.00000
\(568\) −1.00000 −1.00000
\(569\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) −2.00000 −2.00000
\(574\) −1.00000 −1.00000
\(575\) 2.00000 2.00000
\(576\) 3.00000 3.00000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −1.00000 −1.00000
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 2.00000 2.00000
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 1.00000 1.00000
\(587\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 4.00000 4.00000
\(592\) −1.00000 −1.00000
\(593\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 2.00000 2.00000
\(599\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 2.00000 2.00000
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 2.00000 2.00000
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 1.00000 1.00000
\(615\) 0 0
\(616\) 0 0
\(617\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) 2.00000 2.00000
\(619\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) 8.00000 8.00000
\(622\) 0 0
\(623\) 1.00000 1.00000
\(624\) 2.00000 2.00000
\(625\) 1.00000 1.00000
\(626\) 1.00000 1.00000
\(627\) 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
\(634\) 1.00000 1.00000
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −3.00000 −3.00000
\(640\) 0 0
\(641\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 2.00000 2.00000
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 5.00000 5.00000
\(649\) 0 0
\(650\) 1.00000 1.00000
\(651\) 2.00000 2.00000
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) −4.00000 −4.00000
\(655\) 0 0
\(656\) 1.00000 1.00000
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −3.00000 −3.00000
\(667\) 0 0
\(668\) 0 0
\(669\) −2.00000 −2.00000
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 4.00000 4.00000
\(676\) 0 0
\(677\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) 2.00000 2.00000
\(679\) 1.00000 1.00000
\(680\) 0 0
\(681\) −2.00000 −2.00000
\(682\) 0 0
\(683\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.00000 −1.00000
\(687\) 0 0
\(688\) −2.00000 −2.00000
\(689\) 1.00000 1.00000
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.00000 1.00000
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) 4.00000 4.00000
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −2.00000 −2.00000
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.00000 −1.00000
\(713\) −2.00000 −2.00000
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) −2.00000 −2.00000
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 1.00000 1.00000
\(722\) −1.00000 −1.00000
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −2.00000 −2.00000
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 1.00000 1.00000
\(729\) 7.00000 7.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 3.00000 3.00000
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.00000 −1.00000
\(743\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) −2.00000 −2.00000
\(745\) 0 0
\(746\) 1.00000 1.00000
\(747\) 0 0
\(748\) 0 0
\(749\) 1.00000 1.00000
\(750\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 1.00000 1.00000
\(759\) 0 0
\(760\) 0 0
\(761\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(762\) 2.00000 2.00000
\(763\) −2.00000 −2.00000
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.00000 −1.00000
\(768\) 0 0
\(769\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −6.00000 −6.00000
\(775\) −1.00000 −1.00000
\(776\) −1.00000 −1.00000
\(777\) −2.00000 −2.00000
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 2.00000 2.00000
\(787\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(788\) 0 0
\(789\) −2.00000 −2.00000
\(790\) 0 0
\(791\) 1.00000 1.00000
\(792\) 0 0
\(793\) 1.00000 1.00000
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −3.00000 −3.00000
\(802\) 1.00000 1.00000
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) −1.00000 −1.00000
\(807\) 0 0
\(808\) 0 0
\(809\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 4.00000 4.00000
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 1.00000 1.00000
\(819\) 3.00000 3.00000
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 2.00000 2.00000
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) −1.00000 −1.00000
\(825\) 0 0
\(826\) 1.00000 1.00000
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.00000 −1.00000
\(833\) 0 0
\(834\) 2.00000 2.00000
\(835\) 0 0
\(836\) 0 0
\(837\) −4.00000 −4.00000
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 1.00000 1.00000
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −1.00000 −1.00000
\(848\) 1.00000 1.00000
\(849\) −2.00000 −2.00000
\(850\) 0 0
\(851\) 2.00000 2.00000
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) −1.00000 −1.00000
\(855\) 0 0
\(856\) −1.00000 −1.00000
\(857\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(858\) 0 0
\(859\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(860\) 0 0
\(861\) 2.00000 2.00000
\(862\) −2.00000 −2.00000
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 1.00000 1.00000
\(867\) 2.00000 2.00000
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 2.00000 2.00000
\(873\) −3.00000 −3.00000
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(878\) 0 0
\(879\) −2.00000 −2.00000
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 2.00000 2.00000
\(889\) 1.00000 1.00000
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 1.00000
\(897\) −4.00000 −4.00000
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) −4.00000 −4.00000
\(904\) −1.00000 −1.00000
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −2.00000 −2.00000
\(915\) 0 0
\(916\) 0 0
\(917\) 1.00000 1.00000
\(918\) 0 0
\(919\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(920\) 0 0
\(921\) −2.00000 −2.00000
\(922\) 0 0
\(923\) 1.00000 1.00000
\(924\) 0 0
\(925\) 1.00000 1.00000
\(926\) 1.00000 1.00000
\(927\) −3.00000 −3.00000
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 1.00000 1.00000
\(935\) 0 0
\(936\) −3.00000 −3.00000
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) −2.00000 −2.00000
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) −2.00000 −2.00000
\(944\) −1.00000 −1.00000
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −2.00000 −2.00000
\(952\) 0 0
\(953\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(954\) 3.00000 3.00000
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1.00000 1.00000
\(960\) 0 0
\(961\) 0 0
\(962\) 1.00000 1.00000
\(963\) −3.00000 −3.00000
\(964\) 0 0
\(965\) 0 0
\(966\) 4.00000 4.00000
\(967\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(968\) 1.00000 1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(972\) 0 0
\(973\) 1.00000 1.00000
\(974\) 0 0
\(975\) −2.00000 −2.00000
\(976\) 1.00000 1.00000
\(977\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 6.00000 6.00000
\(982\) 1.00000 1.00000
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) −2.00000 −2.00000
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 4.00000 4.00000
\(990\) 0 0
\(991\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) −1.00000 −1.00000
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) 4.00000 4.00000
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 2183.1.d.a.2182.1 1
37.36 even 2 2183.1.d.b.2182.1 yes 1
59.58 odd 2 2183.1.d.b.2182.1 yes 1
2183.2182 odd 2 CM 2183.1.d.a.2182.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2183.1.d.a.2182.1 1 1.1 even 1 trivial
2183.1.d.a.2182.1 1 2183.2182 odd 2 CM
2183.1.d.b.2182.1 yes 1 37.36 even 2
2183.1.d.b.2182.1 yes 1 59.58 odd 2