Properties

Label 2583.1.f.b.2008.1
Level $2583$
Weight $1$
Character 2583.2008
Self dual yes
Analytic conductor $1.289$
Analytic rank $0$
Dimension $3$
Projective image $D_{7}$
CM discriminant -287
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] = [2583,1,Mod(2008,2583)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2583, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("2583.2008");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2583 = 3^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2583.f (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(1.28908492763\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 287)
Projective image: \(D_{7}\)
Projective field: Galois closure of 7.1.23639903.1
Artin image: $D_{14}$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{14} + \cdots)\)

Embedding invariants

Embedding label 2008.1
Root \(-1.24698\) of defining polynomial
Character \(\chi\) \(=\) 2583.2008

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.24698 q^{2} +0.554958 q^{4} +1.00000 q^{7} +0.554958 q^{8} +O(q^{10})\) \(q-1.24698 q^{2} +0.554958 q^{4} +1.00000 q^{7} +0.554958 q^{8} +1.24698 q^{13} -1.24698 q^{14} -1.24698 q^{16} +1.80194 q^{17} -1.80194 q^{19} +0.445042 q^{23} +1.00000 q^{25} -1.55496 q^{26} +0.554958 q^{28} +1.00000 q^{32} -2.24698 q^{34} +1.24698 q^{37} +2.24698 q^{38} -1.00000 q^{41} -1.80194 q^{43} -0.554958 q^{46} -1.24698 q^{47} +1.00000 q^{49} -1.24698 q^{50} +0.692021 q^{52} +0.554958 q^{56} +1.00000 q^{68} -1.55496 q^{74} -1.00000 q^{76} +1.24698 q^{82} +2.24698 q^{86} -1.24698 q^{89} +1.24698 q^{91} +0.246980 q^{92} +1.55496 q^{94} -0.445042 q^{97} -1.24698 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} + 2 q^{4} + 3 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} + 2 q^{4} + 3 q^{7} + 2 q^{8} - q^{13} + q^{14} + q^{16} + q^{17} - q^{19} + q^{23} + 3 q^{25} - 5 q^{26} + 2 q^{28} + 3 q^{32} - 2 q^{34} - q^{37} + 2 q^{38} - 3 q^{41} - q^{43} - 2 q^{46} + q^{47} + 3 q^{49} + q^{50} - 3 q^{52} + 2 q^{56} + 3 q^{68} - 5 q^{74} - 3 q^{76} - q^{82} + 2 q^{86} + q^{89} - q^{91} - 4 q^{92} + 5 q^{94} - q^{97} + q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2583\mathbb{Z}\right)^\times\).

\(n\) \(1072\) \(2215\) \(2297\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(3\) 0 0
\(4\) 0.554958 0.554958
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) 1.00000 1.00000
\(8\) 0.554958 0.554958
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(14\) −1.24698 −1.24698
\(15\) 0 0
\(16\) −1.24698 −1.24698
\(17\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(18\) 0 0
\(19\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(24\) 0 0
\(25\) 1.00000 1.00000
\(26\) −1.55496 −1.55496
\(27\) 0 0
\(28\) 0.554958 0.554958
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.00000 1.00000
\(33\) 0 0
\(34\) −2.24698 −2.24698
\(35\) 0 0
\(36\) 0 0
\(37\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(38\) 2.24698 2.24698
\(39\) 0 0
\(40\) 0 0
\(41\) −1.00000 −1.00000
\(42\) 0 0
\(43\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −0.554958 −0.554958
\(47\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(48\) 0 0
\(49\) 1.00000 1.00000
\(50\) −1.24698 −1.24698
\(51\) 0 0
\(52\) 0.692021 0.692021
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0.554958 0.554958
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 1.00000 1.00000
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) −1.55496 −1.55496
\(75\) 0 0
\(76\) −1.00000 −1.00000
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 1.24698 1.24698
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 2.24698 2.24698
\(87\) 0 0
\(88\) 0 0
\(89\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(90\) 0 0
\(91\) 1.24698 1.24698
\(92\) 0.246980 0.246980
\(93\) 0 0
\(94\) 1.55496 1.55496
\(95\) 0 0
\(96\) 0 0
\(97\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(98\) −1.24698 −1.24698
\(99\) 0 0
\(100\) 0.554958 0.554958
\(101\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0.692021 0.692021
\(105\) 0 0
\(106\) 0 0
\(107\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.24698 −1.24698
\(113\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.80194 1.80194
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(128\) −1.00000 −1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) −1.80194 −1.80194
\(134\) 0 0
\(135\) 0 0
\(136\) 1.00000 1.00000
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0.692021 0.692021
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) −1.00000 −1.00000
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.445042 0.445042
\(162\) 0 0
\(163\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(164\) −0.554958 −0.554958
\(165\) 0 0
\(166\) 0 0
\(167\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(168\) 0 0
\(169\) 0.554958 0.554958
\(170\) 0 0
\(171\) 0 0
\(172\) −1.00000 −1.00000
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 1.00000 1.00000
\(176\) 0 0
\(177\) 0 0
\(178\) 1.55496 1.55496
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(182\) −1.55496 −1.55496
\(183\) 0 0
\(184\) 0.246980 0.246980
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.692021 −0.692021
\(189\) 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 \(\pi\)
\(194\) 0.554958 0.554958
\(195\) 0 0
\(196\) 0.554958 0.554958
\(197\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(198\) 0 0
\(199\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(200\) 0.554958 0.554958
\(201\) 0 0
\(202\) −0.554958 −0.554958
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −1.55496 −1.55496
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −2.24698 −2.24698
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.24698 2.24698
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 1.00000 1.00000
\(225\) 0 0
\(226\) −0.554958 −0.554958
\(227\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) −2.24698 −2.24698
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −1.24698 −1.24698
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.24698 −2.24698
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −1.55496 −1.55496
\(255\) 0 0
\(256\) 1.24698 1.24698
\(257\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(258\) 0 0
\(259\) 1.24698 1.24698
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.24698 2.24698
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −2.24698 −2.24698
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.00000 −1.00000
\(288\) 0 0
\(289\) 2.24698 2.24698
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.692021 0.692021
\(297\) 0 0
\(298\) 0 0
\(299\) 0.554958 0.554958
\(300\) 0 0
\(301\) −1.80194 −1.80194
\(302\) 0 0
\(303\) 0 0
\(304\) 2.24698 2.24698
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(312\) 0 0
\(313\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(314\) 2.24698 2.24698
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) −0.554958 −0.554958
\(323\) −3.24698 −3.24698
\(324\) 0 0
\(325\) 1.24698 1.24698
\(326\) 0.554958 0.554958
\(327\) 0 0
\(328\) −0.554958 −0.554958
\(329\) −1.24698 −1.24698
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −2.24698 −2.24698
\(335\) 0 0
\(336\) 0 0
\(337\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(338\) −0.692021 −0.692021
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 1.00000
\(344\) −1.00000 −1.00000
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) −1.24698 −1.24698
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.692021 −0.692021
\(357\) 0 0
\(358\) 0 0
\(359\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(360\) 0 0
\(361\) 2.24698 2.24698
\(362\) 0.554958 0.554958
\(363\) 0 0
\(364\) 0.692021 0.692021
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) −0.554958 −0.554958
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −0.692021 −0.692021
\(377\) 0 0
\(378\) 0 0
\(379\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.246980 −0.246980
\(389\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(390\) 0 0
\(391\) 0.801938 0.801938
\(392\) 0.554958 0.554958
\(393\) 0 0
\(394\) −2.24698 −2.24698
\(395\) 0 0
\(396\) 0 0
\(397\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(398\) −1.55496 −1.55496
\(399\) 0 0
\(400\) −1.24698 −1.24698
\(401\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.246980 0.246980
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 1.24698 1.24698
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.80194 1.80194
\(426\) 0 0
\(427\) 0 0
\(428\) 1.00000 1.00000
\(429\) 0 0
\(430\) 0 0
\(431\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.801938 −0.801938
\(438\) 0 0
\(439\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −2.80194 −2.80194
\(443\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0.246980 0.246980
\(453\) 0 0
\(454\) 2.49396 2.49396
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0.554958 0.554958
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.80194 −1.80194
\(476\) 1.00000 1.00000
\(477\) 0 0
\(478\) 0 0
\(479\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(480\) 0 0
\(481\) 1.55496 1.55496
\(482\) 0 0
\(483\) 0 0
\(484\) 0.554958 0.554958
\(485\) 0 0
\(486\) 0 0
\(487\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 2.80194 2.80194
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0.692021 0.692021
\(509\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.554958 −0.554958
\(513\) 0 0
\(514\) −0.554958 −0.554958
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −1.55496 −1.55496
\(519\) 0 0
\(520\) 0 0
\(521\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.801938 −0.801938
\(530\) 0 0
\(531\) 0 0
\(532\) −1.00000 −1.00000
\(533\) −1.24698 −1.24698
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.80194 1.80194
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.554958 0.554958
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) −2.24698 −2.24698
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 1.24698 1.24698
\(575\) 0.445042 0.445042
\(576\) 0 0
\(577\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(578\) −2.80194 −2.80194
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 2.49396 2.49396
\(587\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.55496 −1.55496
\(593\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.692021 −0.692021
\(599\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(600\) 0 0
\(601\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(602\) 2.24698 2.24698
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) −1.80194 −1.80194
\(609\) 0 0
\(610\) 0 0
\(611\) −1.55496 −1.55496
\(612\) 0 0
\(613\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −2.24698 −2.24698
\(623\) −1.24698 −1.24698
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 2.24698 2.24698
\(627\) 0 0
\(628\) −1.00000 −1.00000
\(629\) 2.24698 2.24698
\(630\) 0 0
\(631\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.24698 1.24698
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(644\) 0.246980 0.246980
\(645\) 0 0
\(646\) 4.04892 4.04892
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −1.55496 −1.55496
\(651\) 0 0
\(652\) −0.246980 −0.246980
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.24698 1.24698
\(657\) 0 0
\(658\) 1.55496 1.55496
\(659\) 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
\(666\) 0 0
\(667\) 0 0
\(668\) 1.00000 1.00000
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0.554958 0.554958
\(675\) 0 0
\(676\) 0.307979 0.307979
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) −0.445042 −0.445042
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.24698 −1.24698
\(687\) 0 0
\(688\) 2.24698 2.24698
\(689\) 0 0
\(690\) 0 0
\(691\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −1.80194 −1.80194
\(698\) 0 0
\(699\) 0 0
\(700\) 0.554958 0.554958
\(701\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(702\) 0 0
\(703\) −2.24698 −2.24698
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0.445042 0.445042
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.692021 −0.692021
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 1.55496 1.55496
\(719\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −2.80194 −2.80194
\(723\) 0 0
\(724\) −0.246980 −0.246980
\(725\) 0 0
\(726\) 0 0
\(727\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(728\) 0.692021 0.692021
\(729\) 0 0
\(730\) 0 0
\(731\) −3.24698 −3.24698
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.445042 0.445042
\(737\) 0 0
\(738\) 0 0
\(739\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 2.24698 2.24698
\(747\) 0 0
\(748\) 0 0
\(749\) 1.80194 1.80194
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 1.55496 1.55496
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0.554958 0.554958
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −0.554958 −0.554958
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.246980 −0.246980
\(777\) 0 0
\(778\) 1.55496 1.55496
\(779\) 1.80194 1.80194
\(780\) 0 0
\(781\) 0 0
\(782\) −1.00000 −1.00000
\(783\) 0 0
\(784\) −1.24698 −1.24698
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 1.00000 1.00000
\(789\) 0 0
\(790\) 0 0
\(791\) 0.445042 0.445042
\(792\) 0 0
\(793\) 0 0
\(794\) −2.49396 −2.49396
\(795\) 0 0
\(796\) 0.692021 0.692021
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) −2.24698 −2.24698
\(800\) 1.00000 1.00000
\(801\) 0 0
\(802\) 1.55496 1.55496
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0.246980 0.246980
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 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
\(817\) 3.24698 3.24698
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 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
\(832\) 0 0
\(833\) 1.80194 1.80194
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 1.00000 1.00000
\(848\) 0 0
\(849\) 0 0
\(850\) −2.24698 −2.24698
\(851\) 0.554958 0.554958
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 1.00000 1.00000
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 2.49396 2.49396
\(863\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 1.00000 1.00000
\(875\) 0 0
\(876\) 0 0
\(877\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(878\) 0.554958 0.554958
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 1.24698 1.24698
\(885\) 0 0
\(886\) 1.55496 1.55496
\(887\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(888\) 0 0
\(889\) 1.24698 1.24698
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.24698 2.24698
\(894\) 0 0
\(895\) 0 0
\(896\) −1.00000 −1.00000
\(897\) 0 0
\(898\) −0.554958 −0.554958
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0.246980 0.246980
\(905\) 0 0
\(906\) 0 0
\(907\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(908\) −1.10992 −1.10992
\(909\) 0 0
\(910\) 0 0
\(911\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −0.246980 −0.246980
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.24698 1.24698
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(930\) 0 0
\(931\) −1.80194 −1.80194
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) −0.445042 −0.445042
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 2.24698 2.24698
\(951\) 0 0
\(952\) 1.00000 1.00000
\(953\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) −0.554958 −0.554958
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) −1.93900 −1.93900
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0.554958 0.554958
\(969\) 0 0
\(970\) 0 0
\(971\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 2.24698 2.24698
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) −0.554958 −0.554958
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −1.24698 −1.24698
\(989\) −0.801938 −0.801938
\(990\) 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
\(997\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(998\) 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 2583.1.f.b.2008.1 3
3.2 odd 2 287.1.d.a.286.3 3
7.6 odd 2 2583.1.f.a.2008.1 3
21.2 odd 6 2009.1.i.b.1844.1 6
21.5 even 6 2009.1.i.a.1844.1 6
21.11 odd 6 2009.1.i.b.901.1 6
21.17 even 6 2009.1.i.a.901.1 6
21.20 even 2 287.1.d.b.286.3 yes 3
41.40 even 2 2583.1.f.a.2008.1 3
123.122 odd 2 287.1.d.b.286.3 yes 3
287.286 odd 2 CM 2583.1.f.b.2008.1 3
861.122 even 6 2009.1.i.b.901.1 6
861.368 odd 6 2009.1.i.a.901.1 6
861.614 even 6 2009.1.i.b.1844.1 6
861.737 odd 6 2009.1.i.a.1844.1 6
861.860 even 2 287.1.d.a.286.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.1.d.a.286.3 3 3.2 odd 2
287.1.d.a.286.3 3 861.860 even 2
287.1.d.b.286.3 yes 3 21.20 even 2
287.1.d.b.286.3 yes 3 123.122 odd 2
2009.1.i.a.901.1 6 21.17 even 6
2009.1.i.a.901.1 6 861.368 odd 6
2009.1.i.a.1844.1 6 21.5 even 6
2009.1.i.a.1844.1 6 861.737 odd 6
2009.1.i.b.901.1 6 21.11 odd 6
2009.1.i.b.901.1 6 861.122 even 6
2009.1.i.b.1844.1 6 21.2 odd 6
2009.1.i.b.1844.1 6 861.614 even 6
2583.1.f.a.2008.1 3 7.6 odd 2
2583.1.f.a.2008.1 3 41.40 even 2
2583.1.f.b.2008.1 3 1.1 even 1 trivial
2583.1.f.b.2008.1 3 287.286 odd 2 CM