Properties

Label 864.2.d.b.433.4
Level $864$
Weight $2$
Character 864.433
Analytic conductor $6.899$
Analytic rank $0$
Dimension $4$
CM discriminant -24
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [864,2,Mod(433,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.433");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.d (of order \(2\), degree \(1\), not 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: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 433.4
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 864.433
Dual form 864.2.d.b.433.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.41421i q^{5} -3.24264 q^{7} +O(q^{10})\) \(q+4.41421i q^{5} -3.24264 q^{7} -0.171573i q^{11} -14.4853 q^{25} -2.82843i q^{29} -9.24264 q^{31} -14.3137i q^{35} +3.51472 q^{49} -4.07107i q^{53} +0.757359 q^{55} +11.3137i q^{59} -15.4853 q^{73} +0.556349i q^{77} +10.0000 q^{79} +17.8284i q^{83} +15.9706 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{7} - 24 q^{25} - 20 q^{31} + 48 q^{49} + 20 q^{55} - 28 q^{73} + 40 q^{79} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 4.41421i 1.97410i 0.160424 + 0.987048i \(0.448714\pi\)
−0.160424 + 0.987048i \(0.551286\pi\)
\(6\) 0 0
\(7\) −3.24264 −1.22560 −0.612801 0.790237i \(-0.709957\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 0.171573i − 0.0517312i −0.999665 0.0258656i \(-0.991766\pi\)
0.999665 0.0258656i \(-0.00823419\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −14.4853 −2.89706
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 2.82843i − 0.525226i −0.964901 0.262613i \(-0.915416\pi\)
0.964901 0.262613i \(-0.0845842\pi\)
\(30\) 0 0
\(31\) −9.24264 −1.66003 −0.830014 0.557743i \(-0.811667\pi\)
−0.830014 + 0.557743i \(0.811667\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 14.3137i − 2.41946i
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 3.51472 0.502103
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 4.07107i − 0.559204i −0.960116 0.279602i \(-0.909797\pi\)
0.960116 0.279602i \(-0.0902025\pi\)
\(54\) 0 0
\(55\) 0.757359 0.102122
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 11.3137i 1.47292i 0.676481 + 0.736460i \(0.263504\pi\)
−0.676481 + 0.736460i \(0.736496\pi\)
\(60\) 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 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −15.4853 −1.81242 −0.906208 0.422833i \(-0.861036\pi\)
−0.906208 + 0.422833i \(0.861036\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.556349i 0.0634019i
\(78\) 0 0
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 17.8284i 1.95692i 0.206427 + 0.978462i \(0.433816\pi\)
−0.206427 + 0.978462i \(0.566184\pi\)
\(84\) 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
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 15.9706 1.62156 0.810782 0.585348i \(-0.199042\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 12.8995i 1.28355i 0.766894 + 0.641774i \(0.221801\pi\)
−0.766894 + 0.641774i \(0.778199\pi\)
\(102\) 0 0
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.34315i 0.903236i 0.892211 + 0.451618i \(0.149153\pi\)
−0.892211 + 0.451618i \(0.850847\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 10.9706 0.997324
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 41.8701i − 3.74497i
\(126\) 0 0
\(127\) −15.2426 −1.35257 −0.676283 0.736642i \(-0.736410\pi\)
−0.676283 + 0.736642i \(0.736410\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.31371i 0.726372i 0.931717 + 0.363186i \(0.118311\pi\)
−0.931717 + 0.363186i \(0.881689\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 12.4853 1.03685
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 22.4142i 1.83624i 0.396298 + 0.918122i \(0.370295\pi\)
−0.396298 + 0.918122i \(0.629705\pi\)
\(150\) 0 0
\(151\) 22.2132 1.80768 0.903842 0.427865i \(-0.140734\pi\)
0.903842 + 0.427865i \(0.140734\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 40.7990i − 3.27705i
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 5.10051i − 0.387784i −0.981023 0.193892i \(-0.937889\pi\)
0.981023 0.193892i \(-0.0621112\pi\)
\(174\) 0 0
\(175\) 46.9706 3.55064
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 26.6569i − 1.99243i −0.0869415 0.996213i \(-0.527709\pi\)
0.0869415 0.996213i \(-0.472291\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) −21.4853 −1.54654 −0.773272 0.634074i \(-0.781381\pi\)
−0.773272 + 0.634074i \(0.781381\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.9289i 0.992395i 0.868210 + 0.496198i \(0.165271\pi\)
−0.868210 + 0.496198i \(0.834729\pi\)
\(198\) 0 0
\(199\) 28.2132 1.99998 0.999990 0.00436292i \(-0.00138876\pi\)
0.999990 + 0.00436292i \(0.00138876\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.17157i 0.643718i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 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
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 29.9706 2.03453
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −26.0000 −1.74109 −0.870544 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 28.2843i 1.87729i 0.344881 + 0.938647i \(0.387919\pi\)
−0.344881 + 0.938647i \(0.612081\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 15.5147i 0.991199i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 5.65685i − 0.357057i −0.983935 0.178529i \(-0.942866\pi\)
0.983935 0.178529i \(-0.0571337\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 17.9706 1.10392
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 31.1127i 1.89697i 0.316815 + 0.948487i \(0.397387\pi\)
−0.316815 + 0.948487i \(0.602613\pi\)
\(270\) 0 0
\(271\) 10.2132 0.620408 0.310204 0.950670i \(-0.399603\pi\)
0.310204 + 0.950670i \(0.399603\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.48528i 0.149868i
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 14.1421i 0.826192i 0.910687 + 0.413096i \(0.135553\pi\)
−0.910687 + 0.413096i \(0.864447\pi\)
\(294\) 0 0
\(295\) −49.9411 −2.90768
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 8.51472 0.481280 0.240640 0.970614i \(-0.422643\pi\)
0.240640 + 0.970614i \(0.422643\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 30.5563i − 1.71622i −0.513470 0.858108i \(-0.671640\pi\)
0.513470 0.858108i \(-0.328360\pi\)
\(318\) 0 0
\(319\) −0.485281 −0.0271705
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.58579i 0.0858752i
\(342\) 0 0
\(343\) 11.3015 0.610224
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 35.1421i − 1.88653i −0.332043 0.943264i \(-0.607738\pi\)
0.332043 0.943264i \(-0.392262\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 68.3553i − 3.57788i
\(366\) 0 0
\(367\) 14.7574 0.770328 0.385164 0.922848i \(-0.374145\pi\)
0.385164 + 0.922848i \(0.374145\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 13.2010i 0.685362i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) −2.45584 −0.125161
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5.44365i 0.276004i 0.990432 + 0.138002i \(0.0440680\pi\)
−0.990432 + 0.138002i \(0.955932\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 44.1421i 2.22103i
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −28.9411 −1.43105 −0.715523 0.698589i \(-0.753812\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 36.6863i − 1.80521i
\(414\) 0 0
\(415\) −78.6985 −3.86316
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 39.5980i − 1.93449i −0.253849 0.967244i \(-0.581697\pi\)
0.253849 0.967244i \(-0.418303\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −40.9411 −1.96750 −0.983752 0.179530i \(-0.942542\pi\)
−0.983752 + 0.179530i \(0.942542\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 4.21320 0.201085 0.100543 0.994933i \(-0.467942\pi\)
0.100543 + 0.994933i \(0.467942\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 28.2843i 1.34383i 0.740630 + 0.671913i \(0.234527\pi\)
−0.740630 + 0.671913i \(0.765473\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −2.02944 −0.0949331 −0.0474665 0.998873i \(-0.515115\pi\)
−0.0474665 + 0.998873i \(0.515115\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 23.1005i − 1.07590i −0.842977 0.537949i \(-0.819199\pi\)
0.842977 0.537949i \(-0.180801\pi\)
\(462\) 0 0
\(463\) −16.6985 −0.776044 −0.388022 0.921650i \(-0.626842\pi\)
−0.388022 + 0.921650i \(0.626842\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 34.7990i 1.61031i 0.593068 + 0.805153i \(0.297917\pi\)
−0.593068 + 0.805153i \(0.702083\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 70.4975i 3.20113i
\(486\) 0 0
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 44.3137i 1.99985i 0.0122607 + 0.999925i \(0.496097\pi\)
−0.0122607 + 0.999925i \(0.503903\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) −56.9411 −2.53385
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 40.4142i 1.79133i 0.444731 + 0.895664i \(0.353299\pi\)
−0.444731 + 0.895664i \(0.646701\pi\)
\(510\) 0 0
\(511\) 50.2132 2.22130
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 61.7990i − 2.72319i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 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
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −41.2426 −1.78307
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 0.603030i − 0.0259744i
\(540\) 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
\(553\) −32.4264 −1.37891
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 31.9289i 1.35287i 0.736501 + 0.676436i \(0.236477\pi\)
−0.736501 + 0.676436i \(0.763523\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 18.8579i 0.794764i 0.917653 + 0.397382i \(0.130081\pi\)
−0.917653 + 0.397382i \(0.869919\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 38.0000 1.58196 0.790980 0.611842i \(-0.209571\pi\)
0.790980 + 0.611842i \(0.209571\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 57.8112i − 2.39841i
\(582\) 0 0
\(583\) −0.698485 −0.0289283
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 7.62742i − 0.314817i −0.987534 0.157409i \(-0.949686\pi\)
0.987534 0.157409i \(-0.0503140\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 41.4264 1.68982 0.844909 0.534910i \(-0.179654\pi\)
0.844909 + 0.534910i \(0.179654\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 48.4264i 1.96881i
\(606\) 0 0
\(607\) 22.0000 0.892952 0.446476 0.894795i \(-0.352679\pi\)
0.446476 + 0.894795i \(0.352679\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 112.397 4.49588
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 20.7574 0.826337 0.413169 0.910654i \(-0.364422\pi\)
0.413169 + 0.910654i \(0.364422\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 67.2843i − 2.67009i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 1.94113 0.0761958
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 39.0416i − 1.52782i −0.645325 0.763909i \(-0.723278\pi\)
0.645325 0.763909i \(-0.276722\pi\)
\(654\) 0 0
\(655\) −36.6985 −1.43393
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 43.6274i − 1.69948i −0.527200 0.849741i \(-0.676758\pi\)
0.527200 0.849741i \(-0.323242\pi\)
\(660\) 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
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −16.9411 −0.653032 −0.326516 0.945192i \(-0.605875\pi\)
−0.326516 + 0.945192i \(0.605875\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 2.82843i − 0.108705i −0.998522 0.0543526i \(-0.982690\pi\)
0.998522 0.0543526i \(-0.0173095\pi\)
\(678\) 0 0
\(679\) −51.7868 −1.98739
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 5.65685i − 0.216454i −0.994126 0.108227i \(-0.965483\pi\)
0.994126 0.108227i \(-0.0345173\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 14.6152i − 0.552009i −0.961156 0.276005i \(-0.910989\pi\)
0.961156 0.276005i \(-0.0890105\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 41.8284i − 1.57312i
\(708\) 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
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 45.3970 1.69067
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 40.9706i 1.52161i
\(726\) 0 0
\(727\) 47.6690 1.76795 0.883974 0.467537i \(-0.154858\pi\)
0.883974 + 0.467537i \(0.154858\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) −98.9411 −3.62492
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 30.2965i − 1.10701i
\(750\) 0 0
\(751\) 41.6690 1.52053 0.760263 0.649616i \(-0.225070\pi\)
0.760263 + 0.649616i \(0.225070\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 98.0538i 3.56854i
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 29.4264 1.06114 0.530572 0.847640i \(-0.321977\pi\)
0.530572 + 0.847640i \(0.321977\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 19.7990i − 0.712120i −0.934463 0.356060i \(-0.884120\pi\)
0.934463 0.356060i \(-0.115880\pi\)
\(774\) 0 0
\(775\) 133.882 4.80919
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 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
\(797\) 11.8701i 0.420459i 0.977652 + 0.210230i \(0.0674211\pi\)
−0.977652 + 0.210230i \(0.932579\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.65685i 0.0937584i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 48.0833i 1.67812i 0.544041 + 0.839059i \(0.316894\pi\)
−0.544041 + 0.839059i \(0.683106\pi\)
\(822\) 0 0
\(823\) −52.6985 −1.83695 −0.918477 0.395475i \(-0.870580\pi\)
−0.918477 + 0.395475i \(0.870580\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 56.5685i − 1.96708i −0.180688 0.983540i \(-0.557832\pi\)
0.180688 0.983540i \(-0.442168\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 21.0000 0.724138
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 57.3848i 1.97410i
\(846\) 0 0
\(847\) −35.5736 −1.22232
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 22.5147 0.765523
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 1.71573i − 0.0582021i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 135.770i 4.58985i
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 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
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 49.4264 1.65771
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 117.669 3.93324
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 26.1421i 0.871889i
\(900\) 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
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 3.05887 0.101234
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 26.9584i − 0.890244i
\(918\) 0 0
\(919\) −4.69848 −0.154989 −0.0774944 0.996993i \(-0.524692\pi\)
−0.0774944 + 0.996993i \(0.524692\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 45.9706 1.50179 0.750896 0.660420i \(-0.229622\pi\)
0.750896 + 0.660420i \(0.229622\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 57.0416i − 1.85950i −0.368186 0.929752i \(-0.620021\pi\)
0.368186 0.929752i \(-0.379979\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 7.28427i 0.236707i 0.992972 + 0.118354i \(0.0377616\pi\)
−0.992972 + 0.118354i \(0.962238\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 54.4264 1.75569
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) − 94.8406i − 3.05303i
\(966\) 0 0
\(967\) 26.7574 0.860459 0.430229 0.902720i \(-0.358433\pi\)
0.430229 + 0.902720i \(0.358433\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 34.1127i − 1.09473i −0.836894 0.547364i \(-0.815631\pi\)
0.836894 0.547364i \(-0.184369\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) −61.4853 −1.95908
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −7.78680 −0.247356 −0.123678 0.992322i \(-0.539469\pi\)
−0.123678 + 0.992322i \(0.539469\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 124.539i 3.94816i
\(996\) 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 864.2.d.b.433.4 4
3.2 odd 2 inner 864.2.d.b.433.1 4
4.3 odd 2 216.2.d.a.109.2 4
8.3 odd 2 216.2.d.a.109.3 yes 4
8.5 even 2 inner 864.2.d.b.433.1 4
9.2 odd 6 2592.2.r.o.433.4 8
9.4 even 3 2592.2.r.o.2161.4 8
9.5 odd 6 2592.2.r.o.2161.1 8
9.7 even 3 2592.2.r.o.433.1 8
12.11 even 2 216.2.d.a.109.3 yes 4
16.3 odd 4 6912.2.a.bz.1.2 2
16.5 even 4 6912.2.a.y.1.1 2
16.11 odd 4 6912.2.a.z.1.1 2
16.13 even 4 6912.2.a.by.1.2 2
24.5 odd 2 CM 864.2.d.b.433.4 4
24.11 even 2 216.2.d.a.109.2 4
36.7 odd 6 648.2.n.p.109.1 8
36.11 even 6 648.2.n.p.109.4 8
36.23 even 6 648.2.n.p.541.1 8
36.31 odd 6 648.2.n.p.541.4 8
48.5 odd 4 6912.2.a.by.1.2 2
48.11 even 4 6912.2.a.bz.1.2 2
48.29 odd 4 6912.2.a.y.1.1 2
48.35 even 4 6912.2.a.z.1.1 2
72.5 odd 6 2592.2.r.o.2161.4 8
72.11 even 6 648.2.n.p.109.1 8
72.13 even 6 2592.2.r.o.2161.1 8
72.29 odd 6 2592.2.r.o.433.1 8
72.43 odd 6 648.2.n.p.109.4 8
72.59 even 6 648.2.n.p.541.4 8
72.61 even 6 2592.2.r.o.433.4 8
72.67 odd 6 648.2.n.p.541.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.d.a.109.2 4 4.3 odd 2
216.2.d.a.109.2 4 24.11 even 2
216.2.d.a.109.3 yes 4 8.3 odd 2
216.2.d.a.109.3 yes 4 12.11 even 2
648.2.n.p.109.1 8 36.7 odd 6
648.2.n.p.109.1 8 72.11 even 6
648.2.n.p.109.4 8 36.11 even 6
648.2.n.p.109.4 8 72.43 odd 6
648.2.n.p.541.1 8 36.23 even 6
648.2.n.p.541.1 8 72.67 odd 6
648.2.n.p.541.4 8 36.31 odd 6
648.2.n.p.541.4 8 72.59 even 6
864.2.d.b.433.1 4 3.2 odd 2 inner
864.2.d.b.433.1 4 8.5 even 2 inner
864.2.d.b.433.4 4 1.1 even 1 trivial
864.2.d.b.433.4 4 24.5 odd 2 CM
2592.2.r.o.433.1 8 9.7 even 3
2592.2.r.o.433.1 8 72.29 odd 6
2592.2.r.o.433.4 8 9.2 odd 6
2592.2.r.o.433.4 8 72.61 even 6
2592.2.r.o.2161.1 8 9.5 odd 6
2592.2.r.o.2161.1 8 72.13 even 6
2592.2.r.o.2161.4 8 9.4 even 3
2592.2.r.o.2161.4 8 72.5 odd 6
6912.2.a.y.1.1 2 16.5 even 4
6912.2.a.y.1.1 2 48.29 odd 4
6912.2.a.z.1.1 2 16.11 odd 4
6912.2.a.z.1.1 2 48.35 even 4
6912.2.a.by.1.2 2 16.13 even 4
6912.2.a.by.1.2 2 48.5 odd 4
6912.2.a.bz.1.2 2 16.3 odd 4
6912.2.a.bz.1.2 2 48.11 even 4