Properties

Label 3240.1.p.e.1459.1
Level $3240$
Weight $1$
Character 3240.1459
Self dual yes
Analytic conductor $1.617$
Analytic rank $0$
Dimension $2$
Projective image $D_{6}$
CM discriminant -40
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3240,1,Mod(1459,3240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3240, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3240.1459");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3240.p (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: \(1.61697064093\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{6}\)
Projective field: Galois closure of 6.2.251942400.1

Embedding invariants

Embedding label 1459.1
Root \(1.73205\) of defining polynomial
Character \(\chi\) \(=\) 3240.1459

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -1.73205 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -1.73205 q^{7} -1.00000 q^{8} -1.00000 q^{10} +1.73205 q^{13} +1.73205 q^{14} +1.00000 q^{16} +1.00000 q^{19} +1.00000 q^{20} -1.00000 q^{23} +1.00000 q^{25} -1.73205 q^{26} -1.73205 q^{28} -1.00000 q^{32} -1.73205 q^{35} -1.00000 q^{38} -1.00000 q^{40} -1.73205 q^{41} +1.00000 q^{46} +1.00000 q^{47} +2.00000 q^{49} -1.00000 q^{50} +1.73205 q^{52} +1.00000 q^{53} +1.73205 q^{56} +1.73205 q^{59} +1.00000 q^{64} +1.73205 q^{65} +1.73205 q^{70} +1.00000 q^{76} +1.00000 q^{80} +1.73205 q^{82} -3.00000 q^{91} -1.00000 q^{92} -1.00000 q^{94} +1.00000 q^{95} -2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 2 q^{8} - 2 q^{10} + 2 q^{16} + 2 q^{19} + 2 q^{20} - 2 q^{23} + 2 q^{25} - 2 q^{32} - 2 q^{38} - 2 q^{40} + 2 q^{46} + 2 q^{47} + 4 q^{49} - 2 q^{50} + 2 q^{53} + 2 q^{64} + 2 q^{76} + 2 q^{80} - 6 q^{91} - 2 q^{92} - 2 q^{94} + 2 q^{95} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times\).

\(n\) \(1297\) \(1621\) \(2431\) \(3161\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −1.00000
\(3\) 0 0
\(4\) 1.00000 1.00000
\(5\) 1.00000 1.00000
\(6\) 0 0
\(7\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(8\) −1.00000 −1.00000
\(9\) 0 0
\(10\) −1.00000 −1.00000
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(14\) 1.73205 1.73205
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) 1.00000 1.00000
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 0 0
\(25\) 1.00000 1.00000
\(26\) −1.73205 −1.73205
\(27\) 0 0
\(28\) −1.73205 −1.73205
\(29\) 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
\(34\) 0 0
\(35\) −1.73205 −1.73205
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) −1.00000 −1.00000
\(39\) 0 0
\(40\) −1.00000 −1.00000
\(41\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.00000 1.00000
\(47\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) 0 0
\(49\) 2.00000 2.00000
\(50\) −1.00000 −1.00000
\(51\) 0 0
\(52\) 1.73205 1.73205
\(53\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.73205 1.73205
\(57\) 0 0
\(58\) 0 0
\(59\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 1.73205 1.73205
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 1.73205 1.73205
\(71\) 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
\(76\) 1.00000 1.00000
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 1.00000 1.00000
\(81\) 0 0
\(82\) 1.73205 1.73205
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) −3.00000 −3.00000
\(92\) −1.00000 −1.00000
\(93\) 0 0
\(94\) −1.00000 −1.00000
\(95\) 1.00000 1.00000
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −2.00000 −2.00000
\(99\) 0 0
\(100\) 1.00000 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(104\) −1.73205 −1.73205
\(105\) 0 0
\(106\) −1.00000 −1.00000
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.73205 −1.73205
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) −1.00000 −1.00000
\(116\) 0 0
\(117\) 0 0
\(118\) −1.73205 −1.73205
\(119\) 0 0
\(120\) 0 0
\(121\) −1.00000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(128\) −1.00000 −1.00000
\(129\) 0 0
\(130\) −1.73205 −1.73205
\(131\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 0 0
\(133\) −1.73205 −1.73205
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) −1.73205 −1.73205
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 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
\(157\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −1.00000 −1.00000
\(161\) 1.73205 1.73205
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) −1.73205 −1.73205
\(165\) 0 0
\(166\) 0 0
\(167\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(168\) 0 0
\(169\) 2.00000 2.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0 0
\(175\) −1.73205 −1.73205
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 3.00000 3.00000
\(183\) 0 0
\(184\) 1.00000 1.00000
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 1.00000 1.00000
\(189\) 0 0
\(190\) −1.00000 −1.00000
\(191\) 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
\(196\) 2.00000 2.00000
\(197\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) 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
\(205\) −1.73205 −1.73205
\(206\) −1.73205 −1.73205
\(207\) 0 0
\(208\) 1.73205 1.73205
\(209\) 0 0
\(210\) 0 0
\(211\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 1.00000 1.00000
\(213\) 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
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 1.73205 1.73205
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 1.00000 1.00000
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 1.00000 1.00000
\(236\) 1.73205 1.73205
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(242\) 1.00000 1.00000
\(243\) 0 0
\(244\) 0 0
\(245\) 2.00000 2.00000
\(246\) 0 0
\(247\) 1.73205 1.73205
\(248\) 0 0
\(249\) 0 0
\(250\) −1.00000 −1.00000
\(251\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −1.73205 −1.73205
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.73205 1.73205
\(261\) 0 0
\(262\) −1.73205 −1.73205
\(263\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 1.00000 1.00000
\(266\) 1.73205 1.73205
\(267\) 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 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(278\) 1.00000 1.00000
\(279\) 0 0
\(280\) 1.73205 1.73205
\(281\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.00000 3.00000
\(288\) 0 0
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 0 0
\(295\) 1.73205 1.73205
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.73205 −1.73205
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.00000 1.00000
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 1.73205 1.73205
\(315\) 0 0
\(316\) 0 0
\(317\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.00000 1.00000
\(321\) 0 0
\(322\) −1.73205 −1.73205
\(323\) 0 0
\(324\) 0 0
\(325\) 1.73205 1.73205
\(326\) 0 0
\(327\) 0 0
\(328\) 1.73205 1.73205
\(329\) −1.73205 −1.73205
\(330\) 0 0
\(331\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −2.00000 −2.00000
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −2.00000 −2.00000
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.73205 −1.73205
\(344\) 0 0
\(345\) 0 0
\(346\) −1.00000 −1.00000
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 1.73205 1.73205
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 1.73205 1.73205
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 0 0
\(364\) −3.00000 −3.00000
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) −1.00000 −1.00000
\(369\) 0 0
\(370\) 0 0
\(371\) −1.73205 −1.73205
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −1.00000 −1.00000
\(377\) 0 0
\(378\) 0 0
\(379\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(380\) 1.00000 1.00000
\(381\) 0 0
\(382\) 0 0
\(383\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −2.00000 −2.00000
\(393\) 0 0
\(394\) 1.00000 1.00000
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 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 \(0.666667\pi\)
\(410\) 1.73205 1.73205
\(411\) 0 0
\(412\) 1.73205 1.73205
\(413\) −3.00000 −3.00000
\(414\) 0 0
\(415\) 0 0
\(416\) −1.73205 −1.73205
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 1.00000 1.00000
\(423\) 0 0
\(424\) −1.00000 −1.00000
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.00000 −1.00000
\(438\) 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
\(446\) 0 0
\(447\) 0 0
\(448\) −1.73205 −1.73205
\(449\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3.00000 −3.00000
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −1.00000 −1.00000
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1.00000 −1.00000
\(471\) 0 0
\(472\) −1.73205 −1.73205
\(473\) 0 0
\(474\) 0 0
\(475\) 1.00000 1.00000
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 2.00000 2.00000
\(483\) 0 0
\(484\) −1.00000 −1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −2.00000 −2.00000
\(491\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.73205 −1.73205
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) 1.00000 1.00000
\(501\) 0 0
\(502\) −1.73205 −1.73205
\(503\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 1.73205 1.73205
\(509\) 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
\(515\) 1.73205 1.73205
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −1.73205 −1.73205
\(521\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 1.73205 1.73205
\(525\) 0 0
\(526\) 1.00000 1.00000
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) −1.00000 −1.00000
\(531\) 0 0
\(532\) −1.73205 −1.73205
\(533\) −3.00000 −3.00000
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 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
\(554\) −1.73205 −1.73205
\(555\) 0 0
\(556\) −1.00000 −1.00000
\(557\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −1.73205 −1.73205
\(561\) 0 0
\(562\) 1.73205 1.73205
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(570\) 0 0
\(571\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −3.00000 −3.00000
\(575\) −1.00000 −1.00000
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −1.00000 −1.00000
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 1.00000 1.00000
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −1.73205 −1.73205
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 1.73205 1.73205
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.00000 −1.00000
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) −1.00000 −1.00000
\(609\) 0 0
\(610\) 0 0
\(611\) 1.73205 1.73205
\(612\) 0 0
\(613\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) −1.73205 −1.73205
\(629\) 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
\(635\) 1.73205 1.73205
\(636\) 0 0
\(637\) 3.46410 3.46410
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 −1.00000
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 1.73205 1.73205
\(645\) 0 0
\(646\) 0 0
\(647\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −1.73205 −1.73205
\(651\) 0 0
\(652\) 0 0
\(653\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(654\) 0 0
\(655\) 1.73205 1.73205
\(656\) −1.73205 −1.73205
\(657\) 0 0
\(658\) 1.73205 1.73205
\(659\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 2.00000 2.00000
\(663\) 0 0
\(664\) 0 0
\(665\) −1.73205 −1.73205
\(666\) 0 0
\(667\) 0 0
\(668\) 2.00000 2.00000
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 2.00000 2.00000
\(677\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.73205 1.73205
\(687\) 0 0
\(688\) 0 0
\(689\) 1.73205 1.73205
\(690\) 0 0
\(691\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(692\) 1.00000 1.00000
\(693\) 0 0
\(694\) 0 0
\(695\) −1.00000 −1.00000
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1.73205 −1.73205
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.73205 −1.73205
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) −3.00000 −3.00000
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(728\) 3.00000 3.00000
\(729\) 0 0
\(730\) 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
\(736\) 1.00000 1.00000
\(737\) 0 0
\(738\) 0 0
\(739\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.73205 1.73205
\(743\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 1.00000 1.00000
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(758\) 1.00000 1.00000
\(759\) 0 0
\(760\) −1.00000 −1.00000
\(761\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −1.00000 −1.00000
\(767\) 3.00000 3.00000
\(768\) 0 0
\(769\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.73205 −1.73205
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 2.00000 2.00000
\(785\) −1.73205 −1.73205
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) −1.00000 −1.00000
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.00000 −1.00000
\(801\) 0 0
\(802\) 1.73205 1.73205
\(803\) 0 0
\(804\) 0 0
\(805\) 1.73205 1.73205
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(810\) 0 0
\(811\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 1.00000 1.00000
\(819\) 0 0
\(820\) −1.73205 −1.73205
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) −1.73205 −1.73205
\(825\) 0 0
\(826\) 3.00000 3.00000
\(827\) 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
\(832\) 1.73205 1.73205
\(833\) 0 0
\(834\) 0 0
\(835\) 2.00000 2.00000
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) −1.00000 −1.00000
\(845\) 2.00000 2.00000
\(846\) 0 0
\(847\) 1.73205 1.73205
\(848\) 1.00000 1.00000
\(849\) 0 0
\(850\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(864\) 0 0
\(865\) 1.00000 1.00000
\(866\) 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
\(875\) −1.73205 −1.73205
\(876\) 0 0
\(877\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(888\) 0 0
\(889\) −3.00000 −3.00000
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.00000 1.00000
\(894\) 0 0
\(895\) −1.73205 −1.73205
\(896\) 1.73205 1.73205
\(897\) 0 0
\(898\) −1.73205 −1.73205
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 3.00000 3.00000
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3.00000 −3.00000
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 1.00000 1.00000
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 1.73205 1.73205
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 2.00000 2.00000
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 1.00000 1.00000
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 1.73205 1.73205
\(944\) 1.73205 1.73205
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −1.00000 −1.00000
\(951\) 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
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) −2.00000 −2.00000
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 1.00000 1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(972\) 0 0
\(973\) 1.73205 1.73205
\(974\) 1.73205 1.73205
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 2.00000 2.00000
\(981\) 0 0
\(982\) 1.73205 1.73205
\(983\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) −1.00000 −1.00000
\(986\) 0 0
\(987\) 0 0
\(988\) 1.73205 1.73205
\(989\) 0 0
\(990\) 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
\(997\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(998\) −1.00000 −1.00000
\(999\) 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 3240.1.p.e.1459.1 2
3.2 odd 2 3240.1.p.f.1459.1 yes 2
5.4 even 2 3240.1.p.f.1459.2 yes 2
8.3 odd 2 3240.1.p.f.1459.2 yes 2
9.2 odd 6 3240.1.z.k.2539.2 4
9.4 even 3 3240.1.z.l.379.2 4
9.5 odd 6 3240.1.z.k.379.2 4
9.7 even 3 3240.1.z.l.2539.2 4
15.14 odd 2 inner 3240.1.p.e.1459.2 yes 2
24.11 even 2 inner 3240.1.p.e.1459.2 yes 2
40.19 odd 2 CM 3240.1.p.e.1459.1 2
45.4 even 6 3240.1.z.k.379.1 4
45.14 odd 6 3240.1.z.l.379.1 4
45.29 odd 6 3240.1.z.l.2539.1 4
45.34 even 6 3240.1.z.k.2539.1 4
72.11 even 6 3240.1.z.l.2539.1 4
72.43 odd 6 3240.1.z.k.2539.1 4
72.59 even 6 3240.1.z.l.379.1 4
72.67 odd 6 3240.1.z.k.379.1 4
120.59 even 2 3240.1.p.f.1459.1 yes 2
360.59 even 6 3240.1.z.k.379.2 4
360.139 odd 6 3240.1.z.l.379.2 4
360.259 odd 6 3240.1.z.l.2539.2 4
360.299 even 6 3240.1.z.k.2539.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3240.1.p.e.1459.1 2 1.1 even 1 trivial
3240.1.p.e.1459.1 2 40.19 odd 2 CM
3240.1.p.e.1459.2 yes 2 15.14 odd 2 inner
3240.1.p.e.1459.2 yes 2 24.11 even 2 inner
3240.1.p.f.1459.1 yes 2 3.2 odd 2
3240.1.p.f.1459.1 yes 2 120.59 even 2
3240.1.p.f.1459.2 yes 2 5.4 even 2
3240.1.p.f.1459.2 yes 2 8.3 odd 2
3240.1.z.k.379.1 4 45.4 even 6
3240.1.z.k.379.1 4 72.67 odd 6
3240.1.z.k.379.2 4 9.5 odd 6
3240.1.z.k.379.2 4 360.59 even 6
3240.1.z.k.2539.1 4 45.34 even 6
3240.1.z.k.2539.1 4 72.43 odd 6
3240.1.z.k.2539.2 4 9.2 odd 6
3240.1.z.k.2539.2 4 360.299 even 6
3240.1.z.l.379.1 4 45.14 odd 6
3240.1.z.l.379.1 4 72.59 even 6
3240.1.z.l.379.2 4 9.4 even 3
3240.1.z.l.379.2 4 360.139 odd 6
3240.1.z.l.2539.1 4 45.29 odd 6
3240.1.z.l.2539.1 4 72.11 even 6
3240.1.z.l.2539.2 4 9.7 even 3
3240.1.z.l.2539.2 4 360.259 odd 6