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Properties

Label 704.2.g.a.351.3
Level $704$
Weight $2$
Character 704.351
Analytic conductor $5.621$
Analytic rank $0$
Dimension $4$
CM discriminant -88
Inner twists $8$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [704,2,Mod(351,704)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("704.351"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(704, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 704 = 2^{6} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 704.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,0,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.62146830230\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{11})\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 5x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 351.3
Root \(1.65831 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 704.351
Dual form 704.2.g.a.351.1

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.00000 q^{9} +3.31662i q^{11} -6.63325 q^{13} +6.63325i q^{19} +2.00000i q^{23} +5.00000 q^{25} -6.63325 q^{29} -6.00000i q^{31} +6.63325i q^{43} +10.0000i q^{47} -7.00000 q^{49} -6.63325 q^{61} -14.0000i q^{71} +9.00000 q^{81} +6.63325i q^{83} +2.00000 q^{89} -6.00000 q^{97} -9.94987i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 12 q^{9} + 20 q^{25} - 28 q^{49} + 36 q^{81} + 8 q^{89} - 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/704\mathbb{Z}\right)^\times\).

\(n\) \(133\) \(321\) \(639\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 3.31662i 1.00000i
\(12\) 0 0
\(13\) −6.63325 −1.83973 −0.919866 − 0.392232i \(-0.871703\pi\)
−0.919866 + 0.392232i \(0.871703\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 6.63325i 1.52177i 0.648886 + 0.760886i \(0.275235\pi\)
−0.648886 + 0.760886i \(0.724765\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.00000i 0.417029i 0.978019 + 0.208514i \(0.0668628\pi\)
−0.978019 + 0.208514i \(0.933137\pi\)
\(24\) 0 0
\(25\) 5.00000 1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.63325 −1.23176 −0.615882 − 0.787839i \(-0.711200\pi\)
−0.615882 + 0.787839i \(0.711200\pi\)
\(30\) 0 0
\(31\) − 6.00000i − 1.07763i −0.842424 − 0.538816i \(-0.818872\pi\)
0.842424 − 0.538816i \(-0.181128\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 6.63325i 1.01156i 0.862662 + 0.505781i \(0.168795\pi\)
−0.862662 + 0.505781i \(0.831205\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.0000i 1.45865i 0.684167 + 0.729325i \(0.260166\pi\)
−0.684167 + 0.729325i \(0.739834\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −6.63325 −0.849301 −0.424650 − 0.905357i \(-0.639603\pi\)
−0.424650 + 0.905357i \(0.639603\pi\)
\(62\) 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
\(71\) − 14.0000i − 1.66149i −0.556650 − 0.830747i \(-0.687914\pi\)
0.556650 − 0.830747i \(-0.312086\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 6.63325i 0.728094i 0.931381 + 0.364047i \(0.118605\pi\)
−0.931381 + 0.364047i \(0.881395\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.00000 0.212000 0.106000 − 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 − 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) − 9.94987i − 1.00000i
\(100\) 0 0
\(101\) 19.8997 1.98010 0.990050 − 0.140720i \(-0.0449416\pi\)
0.990050 + 0.140720i \(0.0449416\pi\)
\(102\) 0 0
\(103\) 18.0000i 1.77359i 0.462160 + 0.886796i \(0.347074\pi\)
−0.462160 + 0.886796i \(0.652926\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 19.8997i − 1.92378i −0.273434 − 0.961891i \(-0.588160\pi\)
0.273434 − 0.961891i \(-0.411840\pi\)
\(108\) 0 0
\(109\) −6.63325 −0.635350 −0.317675 − 0.948200i \(-0.602902\pi\)
−0.317675 + 0.948200i \(0.602902\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 − 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 19.8997 1.83973
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 19.8997i − 1.73865i −0.494242 − 0.869325i \(-0.664554\pi\)
0.494242 − 0.869325i \(-0.335446\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −14.0000 −1.19610 −0.598050 − 0.801459i \(-0.704058\pi\)
−0.598050 + 0.801459i \(0.704058\pi\)
\(138\) 0 0
\(139\) 6.63325i 0.562625i 0.959616 + 0.281312i \(0.0907697\pi\)
−0.959616 + 0.281312i \(0.909230\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 22.0000i − 1.83973i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 19.8997 1.63025 0.815125 − 0.579284i \(-0.196668\pi\)
0.815125 + 0.579284i \(0.196668\pi\)
\(150\) 0 0
\(151\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 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
\(169\) 31.0000 2.38462
\(170\) 0 0
\(171\) − 19.8997i − 1.52177i
\(172\) 0 0
\(173\) −6.63325 −0.504317 −0.252158 − 0.967686i \(-0.581140\pi\)
−0.252158 + 0.967686i \(0.581140\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 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
\(191\) 26.0000i 1.88129i 0.339387 + 0.940647i \(0.389781\pi\)
−0.339387 + 0.940647i \(0.610219\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 19.8997 1.41780 0.708899 − 0.705310i \(-0.249192\pi\)
0.708899 + 0.705310i \(0.249192\pi\)
\(198\) 0 0
\(199\) 2.00000i 0.141776i 0.997484 + 0.0708881i \(0.0225833\pi\)
−0.997484 + 0.0708881i \(0.977417\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) − 6.00000i − 0.417029i
\(208\) 0 0
\(209\) −22.0000 −1.52177
\(210\) 0 0
\(211\) 6.63325i 0.456652i 0.973585 + 0.228326i \(0.0733252\pi\)
−0.973585 + 0.228326i \(0.926675\pi\)
\(212\) 0 0
\(213\) 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
\(223\) 10.0000i 0.669650i 0.942280 + 0.334825i \(0.108677\pi\)
−0.942280 + 0.334825i \(0.891323\pi\)
\(224\) 0 0
\(225\) −15.0000 −1.00000
\(226\) 0 0
\(227\) − 19.8997i − 1.32079i −0.750917 − 0.660396i \(-0.770388\pi\)
0.750917 − 0.660396i \(-0.229612\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 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
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) − 44.0000i − 2.79965i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −6.63325 −0.417029
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 26.0000 1.62184 0.810918 − 0.585160i \(-0.198968\pi\)
0.810918 + 0.585160i \(0.198968\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 19.8997 1.23176
\(262\) 0 0
\(263\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 16.5831i 1.00000i
\(276\) 0 0
\(277\) −33.1662 −1.99277 −0.996383 − 0.0849719i \(-0.972920\pi\)
−0.996383 + 0.0849719i \(0.972920\pi\)
\(278\) 0 0
\(279\) 18.0000i 1.07763i
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 33.1662i 1.97153i 0.168133 + 0.985764i \(0.446226\pi\)
−0.168133 + 0.985764i \(0.553774\pi\)
\(284\) 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
\(293\) −33.1662 −1.93759 −0.968796 − 0.247858i \(-0.920273\pi\)
−0.968796 + 0.247858i \(0.920273\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 13.2665i − 0.767221i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 33.1662i 1.89290i 0.322854 + 0.946449i \(0.395358\pi\)
−0.322854 + 0.946449i \(0.604642\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 34.0000i 1.92796i 0.265969 + 0.963982i \(0.414308\pi\)
−0.265969 + 0.963982i \(0.585692\pi\)
\(312\) 0 0
\(313\) −30.0000 −1.69570 −0.847850 − 0.530236i \(-0.822103\pi\)
−0.847850 + 0.530236i \(0.822103\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) − 22.0000i − 1.23176i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −33.1662 −1.83973
\(326\) 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
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 19.8997 1.07763
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 33.1662i 1.78046i 0.455514 + 0.890229i \(0.349456\pi\)
−0.455514 + 0.890229i \(0.650544\pi\)
\(348\) 0 0
\(349\) −6.63325 −0.355070 −0.177535 − 0.984115i \(-0.556812\pi\)
−0.177535 + 0.984115i \(0.556812\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.00000 0.106449 0.0532246 − 0.998583i \(-0.483050\pi\)
0.0532246 + 0.998583i \(0.483050\pi\)
\(354\) 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
\(361\) −25.0000 −1.31579
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 26.0000i 1.35719i 0.734513 + 0.678594i \(0.237411\pi\)
−0.734513 + 0.678594i \(0.762589\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −33.1662 −1.71728 −0.858642 − 0.512576i \(-0.828691\pi\)
−0.858642 + 0.512576i \(0.828691\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 44.0000 2.26612
\(378\) 0 0
\(379\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) − 38.0000i − 1.94171i −0.239669 − 0.970855i \(-0.577039\pi\)
0.239669 − 0.970855i \(-0.422961\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) − 19.8997i − 1.01156i
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −14.0000 −0.699127 −0.349563 − 0.936913i \(-0.613670\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(402\) 0 0
\(403\) 39.7995i 1.98255i
\(404\) 0 0
\(405\) 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
\(416\) 0 0
\(417\) 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 \(\pi\)
\(422\) 0 0
\(423\) − 30.0000i − 1.45865i
\(424\) 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
\(433\) 18.0000 0.865025 0.432512 − 0.901628i \(-0.357627\pi\)
0.432512 + 0.901628i \(0.357627\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −13.2665 −0.634623
\(438\) 0 0
\(439\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 21.0000 1.00000
\(442\) 0 0
\(443\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −38.0000 −1.79333 −0.896665 − 0.442709i \(-0.854018\pi\)
−0.896665 + 0.442709i \(0.854018\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6.63325 −0.308941 −0.154471 − 0.987997i \(-0.549367\pi\)
−0.154471 + 0.987997i \(0.549367\pi\)
\(462\) 0 0
\(463\) 42.0000i 1.95191i 0.217982 + 0.975953i \(0.430053\pi\)
−0.217982 + 0.975953i \(0.569947\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −22.0000 −1.01156
\(474\) 0 0
\(475\) 33.1662i 1.52177i
\(476\) 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
\(485\) 0 0
\(486\) 0 0
\(487\) 34.0000i 1.54069i 0.637629 + 0.770344i \(0.279915\pi\)
−0.637629 + 0.770344i \(0.720085\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 19.8997i − 0.898063i −0.893516 − 0.449032i \(-0.851769\pi\)
0.893516 − 0.449032i \(-0.148231\pi\)
\(492\) 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
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −33.1662 −1.45865
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 26.0000 1.13908 0.569540 − 0.821963i \(-0.307121\pi\)
0.569540 + 0.821963i \(0.307121\pi\)
\(522\) 0 0
\(523\) 6.63325i 0.290052i 0.989428 + 0.145026i \(0.0463265\pi\)
−0.989428 + 0.145026i \(0.953673\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 19.0000 0.826087
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 23.2164i − 1.00000i
\(540\) 0 0
\(541\) 46.4327 1.99630 0.998150 − 0.0608018i \(-0.0193658\pi\)
0.998150 + 0.0608018i \(0.0193658\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 46.4327i − 1.98532i −0.120935 − 0.992660i \(-0.538589\pi\)
0.120935 − 0.992660i \(-0.461411\pi\)
\(548\) 0 0
\(549\) 19.8997 0.849301
\(550\) 0 0
\(551\) − 44.0000i − 1.87446i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 46.4327 1.96742 0.983709 − 0.179766i \(-0.0575342\pi\)
0.983709 + 0.179766i \(0.0575342\pi\)
\(558\) 0 0
\(559\) − 44.0000i − 1.86100i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 33.1662i 1.39779i 0.715224 + 0.698895i \(0.246325\pi\)
−0.715224 + 0.698895i \(0.753675\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) − 46.4327i − 1.94315i −0.236732 − 0.971575i \(-0.576076\pi\)
0.236732 − 0.971575i \(-0.423924\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 10.0000i 0.417029i
\(576\) 0 0
\(577\) −30.0000 −1.24892 −0.624458 − 0.781058i \(-0.714680\pi\)
−0.624458 + 0.781058i \(0.714680\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 39.7995 1.63991
\(590\) 0 0
\(591\) 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
\(598\) 0 0
\(599\) − 14.0000i − 0.572024i −0.958226 − 0.286012i \(-0.907670\pi\)
0.958226 − 0.286012i \(-0.0923298\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) − 66.3325i − 2.68353i
\(612\) 0 0
\(613\) −33.1662 −1.33957 −0.669786 − 0.742554i \(-0.733614\pi\)
−0.669786 + 0.742554i \(0.733614\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −46.0000 −1.85189 −0.925945 − 0.377658i \(-0.876729\pi\)
−0.925945 + 0.377658i \(0.876729\pi\)
\(618\) 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
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 18.0000i 0.716569i 0.933613 + 0.358284i \(0.116638\pi\)
−0.933613 + 0.358284i \(0.883362\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 46.4327 1.83973
\(638\) 0 0
\(639\) 42.0000i 1.66149i
\(640\) 0 0
\(641\) 34.0000 1.34292 0.671460 − 0.741041i \(-0.265668\pi\)
0.671460 + 0.741041i \(0.265668\pi\)
\(642\) 0 0
\(643\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 50.0000i 1.96570i 0.184399 + 0.982851i \(0.440966\pi\)
−0.184399 + 0.982851i \(0.559034\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6.63325i 0.258395i 0.991619 + 0.129197i \(0.0412401\pi\)
−0.991619 + 0.129197i \(0.958760\pi\)
\(660\) 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
\(667\) − 13.2665i − 0.513681i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) − 22.0000i − 0.849301i
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 19.8997 0.764809 0.382405 − 0.923995i \(-0.375096\pi\)
0.382405 + 0.923995i \(0.375096\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 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
\(701\) 46.4327 1.75374 0.876870 − 0.480727i \(-0.159627\pi\)
0.876870 + 0.480727i \(0.159627\pi\)
\(702\) 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
\(713\) 12.0000 0.449404
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 26.0000i 0.969636i 0.874615 + 0.484818i \(0.161114\pi\)
−0.874615 + 0.484818i \(0.838886\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −33.1662 −1.23176
\(726\) 0 0
\(727\) − 46.0000i − 1.70605i −0.521874 − 0.853023i \(-0.674767\pi\)
0.521874 − 0.853023i \(-0.325233\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −6.63325 −0.245005 −0.122502 − 0.992468i \(-0.539092\pi\)
−0.122502 + 0.992468i \(0.539092\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) − 46.4327i − 1.70806i −0.520227 − 0.854028i \(-0.674153\pi\)
0.520227 − 0.854028i \(-0.325847\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) − 19.8997i − 0.728094i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) − 54.0000i − 1.97049i −0.171156 − 0.985244i \(-0.554750\pi\)
0.171156 − 0.985244i \(-0.445250\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 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 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) − 30.0000i − 1.07763i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 46.4327 1.66149
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 33.1662i 1.18225i 0.806580 + 0.591125i \(0.201316\pi\)
−0.806580 + 0.591125i \(0.798684\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 44.0000 1.56249
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −6.00000 −0.212000
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 6.63325i 0.232925i 0.993195 + 0.116462i \(0.0371555\pi\)
−0.993195 + 0.116462i \(0.962845\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −44.0000 −1.53937
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 19.8997 0.694506 0.347253 − 0.937771i \(-0.387115\pi\)
0.347253 + 0.937771i \(0.387115\pi\)
\(822\) 0 0
\(823\) 50.0000i 1.74289i 0.490493 + 0.871445i \(0.336817\pi\)
−0.490493 + 0.871445i \(0.663183\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 46.4327i − 1.61462i −0.590124 − 0.807312i \(-0.700921\pi\)
0.590124 − 0.807312i \(-0.299079\pi\)
\(828\) 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
\(839\) 34.0000i 1.17381i 0.809656 + 0.586905i \(0.199654\pi\)
−0.809656 + 0.586905i \(0.800346\pi\)
\(840\) 0 0
\(841\) 15.0000 0.517241
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −33.1662 −1.13559 −0.567795 − 0.823170i \(-0.692204\pi\)
−0.567795 + 0.823170i \(0.692204\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 58.0000i 1.97434i 0.159664 + 0.987171i \(0.448959\pi\)
−0.159664 + 0.987171i \(0.551041\pi\)
\(864\) 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
\(873\) 18.0000 0.609208
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 46.4327 1.56792 0.783961 − 0.620810i \(-0.213196\pi\)
0.783961 + 0.620810i \(0.213196\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −46.0000 −1.54978 −0.774890 − 0.632096i \(-0.782195\pi\)
−0.774890 + 0.632096i \(0.782195\pi\)
\(882\) 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
\(889\) 0 0
\(890\) 0 0
\(891\) 29.8496i 1.00000i
\(892\) 0 0
\(893\) −66.3325 −2.21973
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 39.7995i 1.32739i
\(900\) 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
\(909\) −59.6992 −1.98010
\(910\) 0 0
\(911\) − 38.0000i − 1.25900i −0.777002 − 0.629498i \(-0.783261\pi\)
0.777002 − 0.629498i \(-0.216739\pi\)
\(912\) 0 0
\(913\) −22.0000 −0.728094
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 92.8655i 3.05670i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) − 54.0000i − 1.77359i
\(928\) 0 0
\(929\) 58.0000 1.90292 0.951459 − 0.307775i \(-0.0995844\pi\)
0.951459 + 0.307775i \(0.0995844\pi\)
\(930\) 0 0
\(931\) − 46.4327i − 1.52177i
\(932\) 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
\(940\) 0 0
\(941\) −59.6992 −1.94614 −0.973070 − 0.230510i \(-0.925960\pi\)
−0.973070 + 0.230510i \(0.925960\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 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
\(961\) −5.00000 −0.161290
\(962\) 0 0
\(963\) 59.6992i 1.92378i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 50.0000 1.59964 0.799821 − 0.600239i \(-0.204928\pi\)
0.799821 + 0.600239i \(0.204928\pi\)
\(978\) 0 0
\(979\) 6.63325i 0.212000i
\(980\) 0 0
\(981\) 19.8997 0.635350
\(982\) 0 0
\(983\) − 62.0000i − 1.97749i −0.149601 − 0.988746i \(-0.547799\pi\)
0.149601 − 0.988746i \(-0.452201\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −13.2665 −0.421850
\(990\) 0 0
\(991\) 42.0000i 1.33417i 0.744980 + 0.667087i \(0.232459\pi\)
−0.744980 + 0.667087i \(0.767541\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −33.1662 −1.05039 −0.525193 − 0.850983i \(-0.676007\pi\)
−0.525193 + 0.850983i \(0.676007\pi\)
\(998\) 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 704.2.g.a.351.3 yes 4
4.3 odd 2 inner 704.2.g.a.351.1 ✓ 4
8.3 odd 2 inner 704.2.g.a.351.4 yes 4
8.5 even 2 inner 704.2.g.a.351.2 yes 4
11.10 odd 2 inner 704.2.g.a.351.2 yes 4
16.3 odd 4 2816.2.e.e.2815.1 4
16.5 even 4 2816.2.e.e.2815.2 4
16.11 odd 4 2816.2.e.e.2815.4 4
16.13 even 4 2816.2.e.e.2815.3 4
44.43 even 2 inner 704.2.g.a.351.4 yes 4
88.21 odd 2 CM 704.2.g.a.351.3 yes 4
88.43 even 2 inner 704.2.g.a.351.1 ✓ 4
176.21 odd 4 2816.2.e.e.2815.3 4
176.43 even 4 2816.2.e.e.2815.1 4
176.109 odd 4 2816.2.e.e.2815.2 4
176.131 even 4 2816.2.e.e.2815.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
704.2.g.a.351.1 ✓ 4 4.3 odd 2 inner
704.2.g.a.351.1 ✓ 4 88.43 even 2 inner
704.2.g.a.351.2 yes 4 8.5 even 2 inner
704.2.g.a.351.2 yes 4 11.10 odd 2 inner
704.2.g.a.351.3 yes 4 1.1 even 1 trivial
704.2.g.a.351.3 yes 4 88.21 odd 2 CM
704.2.g.a.351.4 yes 4 8.3 odd 2 inner
704.2.g.a.351.4 yes 4 44.43 even 2 inner
2816.2.e.e.2815.1 4 16.3 odd 4
2816.2.e.e.2815.1 4 176.43 even 4
2816.2.e.e.2815.2 4 16.5 even 4
2816.2.e.e.2815.2 4 176.109 odd 4
2816.2.e.e.2815.3 4 16.13 even 4
2816.2.e.e.2815.3 4 176.21 odd 4
2816.2.e.e.2815.4 4 16.11 odd 4
2816.2.e.e.2815.4 4 176.131 even 4