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Properties

Label 6912.2.a.bz.1.2
Level $6912$
Weight $2$
Character 6912.1
Self dual yes
Analytic conductor $55.193$
Analytic rank $0$
Dimension $2$
CM discriminant -24
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6912,2,Mod(1,6912)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6912, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6912.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6912 = 2^{8} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6912.a (trivial)

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: \(55.1925978771\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 216)
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

Embedding label 1.2
Root \(1.41421\) of defining polynomial
Character \(\chi\) \(=\) 6912.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.41421 q^{5} -3.24264 q^{7} +O(q^{10})\) \(q+4.41421 q^{5} -3.24264 q^{7} +0.171573 q^{11} +14.4853 q^{25} +2.82843 q^{29} +9.24264 q^{31} -14.3137 q^{35} +3.51472 q^{49} -4.07107 q^{53} +0.757359 q^{55} -11.3137 q^{59} +15.4853 q^{73} -0.556349 q^{77} -10.0000 q^{79} +17.8284 q^{83} +15.9706 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{5} + 2 q^{7} + 6 q^{11} + 12 q^{25} + 10 q^{31} - 6 q^{35} + 24 q^{49} + 6 q^{53} + 10 q^{55} + 14 q^{73} + 30 q^{77} - 20 q^{79} + 30 q^{83} - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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
\(5\) 4.41421 1.97410 0.987048 − 0.160424i \(-0.0512862\pi\)
0.987048 + 0.160424i \(0.0512862\pi\)
\(6\) 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
\(11\) 0.171573 0.0517312 0.0258656 − 0.999665i \(-0.491766\pi\)
0.0258656 + 0.999665i \(0.491766\pi\)
\(12\) 0 0
\(13\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 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
\(29\) 2.82843 0.525226 0.262613 − 0.964901i \(-0.415416\pi\)
0.262613 + 0.964901i \(0.415416\pi\)
\(30\) 0 0
\(31\) 9.24264 1.66003 0.830014 − 0.557743i \(-0.188333\pi\)
0.830014 + 0.557743i \(0.188333\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −14.3137 −2.41946
\(36\) 0 0
\(37\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 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
\(53\) −4.07107 −0.559204 −0.279602 − 0.960116i \(-0.590203\pi\)
−0.279602 + 0.960116i \(0.590203\pi\)
\(54\) 0 0
\(55\) 0.757359 0.102122
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −11.3137 −1.47292 −0.736460 − 0.676481i \(-0.763504\pi\)
−0.736460 + 0.676481i \(0.763504\pi\)
\(60\) 0 0
\(61\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 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 \(-0.138964\pi\)
0.906208 + 0.422833i \(0.138964\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.556349 −0.0634019
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 − 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 17.8284 1.95692 0.978462 − 0.206427i \(-0.0661835\pi\)
0.978462 + 0.206427i \(0.0661835\pi\)
\(84\) 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
\(101\) 12.8995 1.28355 0.641774 − 0.766894i \(-0.278199\pi\)
0.641774 + 0.766894i \(0.278199\pi\)
\(102\) 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
\(107\) −9.34315 −0.903236 −0.451618 − 0.892211i \(-0.649153\pi\)
−0.451618 + 0.892211i \(0.649153\pi\)
\(108\) 0 0
\(109\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 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
\(125\) 41.8701 3.74497
\(126\) 0 0
\(127\) 15.2426 1.35257 0.676283 − 0.736642i \(-0.263590\pi\)
0.676283 + 0.736642i \(0.263590\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.31371 0.726372 0.363186 − 0.931717i \(-0.381689\pi\)
0.363186 + 0.931717i \(0.381689\pi\)
\(132\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 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
\(149\) 22.4142 1.83624 0.918122 − 0.396298i \(-0.129705\pi\)
0.918122 + 0.396298i \(0.129705\pi\)
\(150\) 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
\(155\) 40.7990 3.27705
\(156\) 0 0
\(157\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 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
\(173\) 5.10051 0.387784 0.193892 − 0.981023i \(-0.437889\pi\)
0.193892 + 0.981023i \(0.437889\pi\)
\(174\) 0 0
\(175\) −46.9706 −3.55064
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −26.6569 −1.99243 −0.996213 − 0.0869415i \(-0.972291\pi\)
−0.996213 + 0.0869415i \(0.972291\pi\)
\(180\) 0 0
\(181\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 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
\(197\) 13.9289 0.992395 0.496198 − 0.868210i \(-0.334729\pi\)
0.496198 + 0.868210i \(0.334729\pi\)
\(198\) 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
\(203\) −9.17157 −0.643718
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 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 \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 28.2843 1.87729 0.938647 − 0.344881i \(-0.112081\pi\)
0.938647 + 0.344881i \(0.112081\pi\)
\(228\) 0 0
\(229\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 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
\(245\) 15.5147 0.991199
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 5.65685 0.357057 0.178529 − 0.983935i \(-0.442866\pi\)
0.178529 + 0.983935i \(0.442866\pi\)
\(252\) 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
\(269\) −31.1127 −1.89697 −0.948487 − 0.316815i \(-0.897387\pi\)
−0.948487 + 0.316815i \(0.897387\pi\)
\(270\) 0 0
\(271\) −10.2132 −0.620408 −0.310204 − 0.950670i \(-0.600397\pi\)
−0.310204 + 0.950670i \(0.600397\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.48528 0.149868
\(276\) 0 0
\(277\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 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
\(293\) 14.1421 0.826192 0.413096 − 0.910687i \(-0.364447\pi\)
0.413096 + 0.910687i \(0.364447\pi\)
\(294\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 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 \(-0.577357\pi\)
−0.240640 + 0.970614i \(0.577357\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 30.5563 1.71622 0.858108 − 0.513470i \(-0.171640\pi\)
0.858108 + 0.513470i \(0.171640\pi\)
\(318\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 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
\(341\) 1.58579 0.0858752
\(342\) 0 0
\(343\) 11.3015 0.610224
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 35.1421 1.88653 0.943264 − 0.332043i \(-0.107738\pi\)
0.943264 + 0.332043i \(0.107738\pi\)
\(348\) 0 0
\(349\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 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
\(365\) 68.3553 3.57788
\(366\) 0 0
\(367\) −14.7574 −0.770328 −0.385164 − 0.922848i \(-0.625855\pi\)
−0.385164 + 0.922848i \(0.625855\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 13.2010 0.685362
\(372\) 0 0
\(373\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 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
\(389\) 5.44365 0.276004 0.138002 − 0.990432i \(-0.455932\pi\)
0.138002 + 0.990432i \(0.455932\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −44.1421 −2.22103
\(396\) 0 0
\(397\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 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 \(-0.246188\pi\)
0.715523 + 0.698589i \(0.246188\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 36.6863 1.80521
\(414\) 0 0
\(415\) 78.6985 3.86316
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −39.5980 −1.93449 −0.967244 − 0.253849i \(-0.918303\pi\)
−0.967244 + 0.253849i \(0.918303\pi\)
\(420\) 0 0
\(421\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 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
\(443\) −28.2843 −1.34383 −0.671913 − 0.740630i \(-0.734527\pi\)
−0.671913 + 0.740630i \(0.734527\pi\)
\(444\) 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 \(-0.484885\pi\)
0.0474665 + 0.998873i \(0.484885\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 23.1005 1.07590 0.537949 − 0.842977i \(-0.319199\pi\)
0.537949 + 0.842977i \(0.319199\pi\)
\(462\) 0 0
\(463\) 16.6985 0.776044 0.388022 − 0.921650i \(-0.373158\pi\)
0.388022 + 0.921650i \(0.373158\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 34.7990 1.61031 0.805153 − 0.593068i \(-0.202083\pi\)
0.805153 + 0.593068i \(0.202083\pi\)
\(468\) 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
\(485\) 70.4975 3.20113
\(486\) 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
\(491\) −44.3137 −1.99985 −0.999925 − 0.0122607i \(-0.996097\pi\)
−0.999925 + 0.0122607i \(0.996097\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 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
\(509\) −40.4142 −1.79133 −0.895664 − 0.444731i \(-0.853299\pi\)
−0.895664 + 0.444731i \(0.853299\pi\)
\(510\) 0 0
\(511\) −50.2132 −2.22130
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −61.7990 −2.72319
\(516\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 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
\(539\) 0.603030 0.0259744
\(540\) 0 0
\(541\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 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
\(557\) −31.9289 −1.35287 −0.676436 − 0.736501i \(-0.736477\pi\)
−0.676436 + 0.736501i \(0.736477\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 18.8579 0.794764 0.397382 − 0.917653i \(-0.369919\pi\)
0.397382 + 0.917653i \(0.369919\pi\)
\(564\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 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
\(581\) −57.8112 −2.39841
\(582\) 0 0
\(583\) −0.698485 −0.0289283
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7.62742 0.314817 0.157409 − 0.987534i \(-0.449686\pi\)
0.157409 + 0.987534i \(0.449686\pi\)
\(588\) 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 \(-0.820346\pi\)
−0.844909 + 0.534910i \(0.820346\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −48.4264 −1.96881
\(606\) 0 0
\(607\) −22.0000 −0.892952 −0.446476 − 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 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
\(635\) 67.2843 2.67009
\(636\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 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
\(653\) 39.0416 1.52782 0.763909 − 0.645325i \(-0.223278\pi\)
0.763909 + 0.645325i \(0.223278\pi\)
\(654\) 0 0
\(655\) 36.6985 1.43393
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −43.6274 −1.69948 −0.849741 − 0.527200i \(-0.823242\pi\)
−0.849741 + 0.527200i \(0.823242\pi\)
\(660\) 0 0
\(661\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 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
\(677\) −2.82843 −0.108705 −0.0543526 − 0.998522i \(-0.517310\pi\)
−0.0543526 + 0.998522i \(0.517310\pi\)
\(678\) 0 0
\(679\) −51.7868 −1.98739
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5.65685 0.216454 0.108227 − 0.994126i \(-0.465483\pi\)
0.108227 + 0.994126i \(0.465483\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 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
\(701\) 14.6152 0.552009 0.276005 − 0.961156i \(-0.410989\pi\)
0.276005 + 0.961156i \(0.410989\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −41.8284 −1.57312
\(708\) 0 0
\(709\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 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
\(725\) 40.9706 1.52161
\(726\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 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
\(749\) 30.2965 1.10701
\(750\) 0 0
\(751\) −41.6690 −1.52053 −0.760263 − 0.649616i \(-0.774930\pi\)
−0.760263 + 0.649616i \(0.774930\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 98.0538 3.56854
\(756\) 0 0
\(757\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 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
\(773\) −19.7990 −0.712120 −0.356060 − 0.934463i \(-0.615880\pi\)
−0.356060 + 0.934463i \(0.615880\pi\)
\(774\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 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
\(797\) −11.8701 −0.420459 −0.210230 − 0.977652i \(-0.567421\pi\)
−0.210230 + 0.977652i \(0.567421\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.65685 0.0937584
\(804\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 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
\(821\) 48.0833 1.67812 0.839059 − 0.544041i \(-0.183106\pi\)
0.839059 + 0.544041i \(0.183106\pi\)
\(822\) 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
\(827\) 56.5685 1.96708 0.983540 − 0.180688i \(-0.0578324\pi\)
0.983540 + 0.180688i \(0.0578324\pi\)
\(828\) 0 0
\(829\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 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
\(845\) −57.3848 −1.97410
\(846\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 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
\(869\) −1.71573 −0.0582021
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −135.770 −4.58985
\(876\) 0 0
\(877\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 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
\(899\) 26.1421 0.871889
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 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
\(917\) −26.9584 −0.890244
\(918\) 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 \(-0.770378\pi\)
−0.750896 + 0.660420i \(0.770378\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 57.0416 1.85950 0.929752 − 0.368186i \(-0.120021\pi\)
0.929752 + 0.368186i \(0.120021\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 7.28427 0.236707 0.118354 − 0.992972i \(-0.462238\pi\)
0.118354 + 0.992972i \(0.462238\pi\)
\(948\) 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
\(965\) −94.8406 −3.05303
\(966\) 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
\(971\) 34.1127 1.09473 0.547364 − 0.836894i \(-0.315631\pi\)
0.547364 + 0.836894i \(0.315631\pi\)
\(972\) 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 \(-0.460531\pi\)
0.123678 + 0.992322i \(0.460531\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 124.539 3.94816
\(996\) 0 0
\(997\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 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 6912.2.a.bz.1.2 2
3.2 odd 2 6912.2.a.z.1.1 2
4.3 odd 2 6912.2.a.by.1.2 2
8.3 odd 2 6912.2.a.y.1.1 2
8.5 even 2 6912.2.a.z.1.1 2
12.11 even 2 6912.2.a.y.1.1 2
16.3 odd 4 864.2.d.b.433.1 4
16.5 even 4 216.2.d.a.109.2 ✓ 4
16.11 odd 4 864.2.d.b.433.4 4
16.13 even 4 216.2.d.a.109.3 yes 4
24.5 odd 2 CM 6912.2.a.bz.1.2 2
24.11 even 2 6912.2.a.by.1.2 2
48.5 odd 4 216.2.d.a.109.3 yes 4
48.11 even 4 864.2.d.b.433.1 4
48.29 odd 4 216.2.d.a.109.2 ✓ 4
48.35 even 4 864.2.d.b.433.4 4
144.5 odd 12 648.2.n.p.541.1 8
144.11 even 12 2592.2.r.o.433.4 8
144.13 even 12 648.2.n.p.541.1 8
144.29 odd 12 648.2.n.p.109.1 8
144.43 odd 12 2592.2.r.o.433.1 8
144.59 even 12 2592.2.r.o.2161.1 8
144.61 even 12 648.2.n.p.109.4 8
144.67 odd 12 2592.2.r.o.2161.1 8
144.77 odd 12 648.2.n.p.541.4 8
144.83 even 12 2592.2.r.o.433.1 8
144.85 even 12 648.2.n.p.541.4 8
144.101 odd 12 648.2.n.p.109.4 8
144.115 odd 12 2592.2.r.o.433.4 8
144.131 even 12 2592.2.r.o.2161.4 8
144.133 even 12 648.2.n.p.109.1 8
144.139 odd 12 2592.2.r.o.2161.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.d.a.109.2 ✓ 4 16.5 even 4
216.2.d.a.109.2 ✓ 4 48.29 odd 4
216.2.d.a.109.3 yes 4 16.13 even 4
216.2.d.a.109.3 yes 4 48.5 odd 4
648.2.n.p.109.1 8 144.29 odd 12
648.2.n.p.109.1 8 144.133 even 12
648.2.n.p.109.4 8 144.61 even 12
648.2.n.p.109.4 8 144.101 odd 12
648.2.n.p.541.1 8 144.5 odd 12
648.2.n.p.541.1 8 144.13 even 12
648.2.n.p.541.4 8 144.77 odd 12
648.2.n.p.541.4 8 144.85 even 12
864.2.d.b.433.1 4 16.3 odd 4
864.2.d.b.433.1 4 48.11 even 4
864.2.d.b.433.4 4 16.11 odd 4
864.2.d.b.433.4 4 48.35 even 4
2592.2.r.o.433.1 8 144.43 odd 12
2592.2.r.o.433.1 8 144.83 even 12
2592.2.r.o.433.4 8 144.11 even 12
2592.2.r.o.433.4 8 144.115 odd 12
2592.2.r.o.2161.1 8 144.59 even 12
2592.2.r.o.2161.1 8 144.67 odd 12
2592.2.r.o.2161.4 8 144.131 even 12
2592.2.r.o.2161.4 8 144.139 odd 12
6912.2.a.y.1.1 2 8.3 odd 2
6912.2.a.y.1.1 2 12.11 even 2
6912.2.a.z.1.1 2 3.2 odd 2
6912.2.a.z.1.1 2 8.5 even 2
6912.2.a.by.1.2 2 4.3 odd 2
6912.2.a.by.1.2 2 24.11 even 2
6912.2.a.bz.1.2 2 1.1 even 1 trivial
6912.2.a.bz.1.2 2 24.5 odd 2 CM