Properties

Label 512.2.b.c.257.3
Level $512$
Weight $2$
Character 512.257
Analytic conductor $4.088$
Analytic rank $0$
Dimension $4$
CM discriminant -8
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [512,2,Mod(257,512)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(512, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("512.257");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 512 = 2^{9} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 512.b (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: \(4.08834058349\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 257.3
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 512.257
Dual form 512.2.b.c.257.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.585786i q^{3} +2.65685 q^{9} +O(q^{10})\) \(q+0.585786i q^{3} +2.65685 q^{9} -6.24264i q^{11} +5.65685 q^{17} +7.41421i q^{19} +5.00000 q^{25} +3.31371i q^{27} +3.65685 q^{33} +6.00000 q^{41} -13.0711i q^{43} -7.00000 q^{49} +3.31371i q^{51} -4.34315 q^{57} +14.2426i q^{59} -3.89949i q^{67} -16.9706 q^{73} +2.92893i q^{75} +6.02944 q^{81} -10.7279i q^{83} +5.65685 q^{89} -16.9706 q^{97} -16.5858i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 12 q^{9} + 20 q^{25} - 8 q^{33} + 24 q^{41} - 28 q^{49} - 40 q^{57} + 92 q^{81}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(511\)
\(\chi(n)\) \(-1\) \(1\)

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
\(3\) 0.585786i 0.338204i 0.985599 + 0.169102i \(0.0540867\pi\)
−0.985599 + 0.169102i \(0.945913\pi\)
\(4\) 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
\(9\) 2.65685 0.885618
\(10\) 0 0
\(11\) − 6.24264i − 1.88223i −0.338091 0.941113i \(-0.609781\pi\)
0.338091 0.941113i \(-0.390219\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.65685 1.37199 0.685994 0.727607i \(-0.259367\pi\)
0.685994 + 0.727607i \(0.259367\pi\)
\(18\) 0 0
\(19\) 7.41421i 1.70094i 0.526026 + 0.850469i \(0.323682\pi\)
−0.526026 + 0.850469i \(0.676318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 5.00000 1.00000
\(26\) 0 0
\(27\) 3.31371i 0.637723i
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 3.65685 0.636577
\(34\) 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
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) − 13.0711i − 1.99332i −0.0816682 0.996660i \(-0.526025\pi\)
0.0816682 0.996660i \(-0.473975\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 3.31371i 0.464012i
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −4.34315 −0.575264
\(58\) 0 0
\(59\) 14.2426i 1.85423i 0.374772 + 0.927117i \(0.377721\pi\)
−0.374772 + 0.927117i \(0.622279\pi\)
\(60\) 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
\(67\) − 3.89949i − 0.476399i −0.971216 0.238200i \(-0.923443\pi\)
0.971216 0.238200i \(-0.0765572\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −16.9706 −1.98625 −0.993127 0.117041i \(-0.962659\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(74\) 0 0
\(75\) 2.92893i 0.338204i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 6.02944 0.669937
\(82\) 0 0
\(83\) − 10.7279i − 1.17754i −0.808300 0.588771i \(-0.799612\pi\)
0.808300 0.588771i \(-0.200388\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.65685 0.599625 0.299813 0.953998i \(-0.403076\pi\)
0.299813 + 0.953998i \(0.403076\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −16.9706 −1.72310 −0.861550 0.507673i \(-0.830506\pi\)
−0.861550 + 0.507673i \(0.830506\pi\)
\(98\) 0 0
\(99\) − 16.5858i − 1.66693i
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.75736i 0.943280i 0.881791 + 0.471640i \(0.156338\pi\)
−0.881791 + 0.471640i \(0.843662\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −27.9706 −2.54278
\(122\) 0 0
\(123\) 3.51472i 0.316912i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 7.65685 0.674148
\(130\) 0 0
\(131\) 2.72792i 0.238340i 0.992874 + 0.119170i \(0.0380233\pi\)
−0.992874 + 0.119170i \(0.961977\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) 9.55635i 0.810559i 0.914193 + 0.405279i \(0.132826\pi\)
−0.914193 + 0.405279i \(0.867174\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) − 4.10051i − 0.338204i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 15.0294 1.21506
\(154\) 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
\(163\) 16.5858i 1.29910i 0.760319 + 0.649550i \(0.225042\pi\)
−0.760319 + 0.649550i \(0.774958\pi\)
\(164\) 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
\(171\) 19.6985i 1.50638i
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −8.34315 −0.627109
\(178\) 0 0
\(179\) − 26.7279i − 1.99774i −0.0475398 0.998869i \(-0.515138\pi\)
0.0475398 0.998869i \(-0.484862\pi\)
\(180\) 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
\(187\) − 35.3137i − 2.58239i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) −16.9706 −1.22157 −0.610784 0.791797i \(-0.709146\pi\)
−0.610784 + 0.791797i \(0.709146\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 2.28427 0.161120
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 46.2843 3.20155
\(210\) 0 0
\(211\) 27.8995i 1.92068i 0.278831 + 0.960340i \(0.410053\pi\)
−0.278831 + 0.960340i \(0.589947\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) − 9.94113i − 0.671759i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 13.2843 0.885618
\(226\) 0 0
\(227\) 23.2132i 1.54071i 0.637613 + 0.770357i \(0.279922\pi\)
−0.637613 + 0.770357i \(0.720078\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.65685 0.370593 0.185296 0.982683i \(-0.440675\pi\)
0.185296 + 0.982683i \(0.440675\pi\)
\(234\) 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
\(241\) −16.9706 −1.09317 −0.546585 0.837404i \(-0.684072\pi\)
−0.546585 + 0.837404i \(0.684072\pi\)
\(242\) 0 0
\(243\) 13.4731i 0.864299i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 6.28427 0.398250
\(250\) 0 0
\(251\) − 17.7574i − 1.12083i −0.828210 0.560417i \(-0.810641\pi\)
0.828210 0.560417i \(-0.189359\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 30.0000 1.87135 0.935674 0.352865i \(-0.114792\pi\)
0.935674 + 0.352865i \(0.114792\pi\)
\(258\) 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
\(265\) 0 0
\(266\) 0 0
\(267\) 3.31371i 0.202796i
\(268\) 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
\(275\) − 31.2132i − 1.88223i
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 28.2843 1.68730 0.843649 0.536895i \(-0.180403\pi\)
0.843649 + 0.536895i \(0.180403\pi\)
\(282\) 0 0
\(283\) − 33.5563i − 1.99472i −0.0726300 0.997359i \(-0.523139\pi\)
0.0726300 0.997359i \(-0.476861\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 15.0000 0.882353
\(290\) 0 0
\(291\) − 9.94113i − 0.582759i
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 20.6863 1.20034
\(298\) 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
\(307\) 30.0416i 1.71457i 0.514845 + 0.857283i \(0.327849\pi\)
−0.514845 + 0.857283i \(0.672151\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −5.71573 −0.319021
\(322\) 0 0
\(323\) 41.9411i 2.33367i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.384776i 0.0211492i 0.999944 + 0.0105746i \(0.00336607\pi\)
−0.999944 + 0.0105746i \(0.996634\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) − 10.5442i − 0.572680i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 30.2426i 1.62351i 0.583998 + 0.811755i \(0.301488\pi\)
−0.583998 + 0.811755i \(0.698512\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −30.0000 −1.59674 −0.798369 0.602168i \(-0.794304\pi\)
−0.798369 + 0.602168i \(0.794304\pi\)
\(354\) 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
\(361\) −35.9706 −1.89319
\(362\) 0 0
\(363\) − 16.3848i − 0.859978i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 15.9411 0.829862
\(370\) 0 0
\(371\) 0 0
\(372\) 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
\(379\) 20.8701i 1.07202i 0.844211 + 0.536011i \(0.180070\pi\)
−0.844211 + 0.536011i \(0.819930\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) − 34.7279i − 1.76532i
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −1.59798 −0.0806074
\(394\) 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
\(401\) −39.5980 −1.97743 −0.988714 0.149813i \(-0.952133\pi\)
−0.988714 + 0.149813i \(0.952133\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 22.0000 1.08783 0.543915 0.839140i \(-0.316941\pi\)
0.543915 + 0.839140i \(0.316941\pi\)
\(410\) 0 0
\(411\) − 3.51472i − 0.173368i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −5.59798 −0.274134
\(418\) 0 0
\(419\) − 13.2721i − 0.648383i −0.945991 0.324192i \(-0.894908\pi\)
0.945991 0.324192i \(-0.105092\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 28.2843 1.37199
\(426\) 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
\(433\) −16.9706 −0.815553 −0.407777 0.913082i \(-0.633696\pi\)
−0.407777 + 0.913082i \(0.633696\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −18.5980 −0.885618
\(442\) 0 0
\(443\) 27.6985i 1.31599i 0.753020 + 0.657997i \(0.228596\pi\)
−0.753020 + 0.657997i \(0.771404\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.65685 0.266963 0.133482 0.991051i \(-0.457384\pi\)
0.133482 + 0.991051i \(0.457384\pi\)
\(450\) 0 0
\(451\) − 37.4558i − 1.76373i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −26.0000 −1.21623 −0.608114 0.793849i \(-0.708074\pi\)
−0.608114 + 0.793849i \(0.708074\pi\)
\(458\) 0 0
\(459\) 18.7452i 0.874949i
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.786797i 0.0364086i 0.999834 + 0.0182043i \(0.00579493\pi\)
−0.999834 + 0.0182043i \(0.994205\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −81.5980 −3.75188
\(474\) 0 0
\(475\) 37.0711i 1.70094i
\(476\) 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
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) −9.71573 −0.439360
\(490\) 0 0
\(491\) − 19.6985i − 0.888980i −0.895784 0.444490i \(-0.853385\pi\)
0.895784 0.444490i \(-0.146615\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) − 20.1005i − 0.899822i −0.893073 0.449911i \(-0.851456\pi\)
0.893073 0.449911i \(-0.148544\pi\)
\(500\) 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
\(507\) 7.61522i 0.338204i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −24.5685 −1.08473
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 0 0
\(523\) − 44.8701i − 1.96203i −0.193930 0.981015i \(-0.562124\pi\)
0.193930 0.981015i \(-0.437876\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 37.8406i 1.64214i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 15.6569 0.675643
\(538\) 0 0
\(539\) 43.6985i 1.88223i
\(540\) 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
\(547\) − 26.5269i − 1.13421i −0.823646 0.567104i \(-0.808064\pi\)
0.823646 0.567104i \(-0.191936\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 20.6863 0.873376
\(562\) 0 0
\(563\) − 47.2132i − 1.98980i −0.100870 0.994900i \(-0.532163\pi\)
0.100870 0.994900i \(-0.467837\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 42.0000 1.76073 0.880366 0.474295i \(-0.157297\pi\)
0.880366 + 0.474295i \(0.157297\pi\)
\(570\) 0 0
\(571\) 14.4437i 0.604448i 0.953237 + 0.302224i \(0.0977291\pi\)
−0.953237 + 0.302224i \(0.902271\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) 0 0
\(579\) − 9.94113i − 0.413139i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 38.2426i − 1.57844i −0.614109 0.789221i \(-0.710484\pi\)
0.614109 0.789221i \(-0.289516\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 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
\(601\) −16.9706 −0.692244 −0.346122 0.938190i \(-0.612502\pi\)
−0.346122 + 0.938190i \(0.612502\pi\)
\(602\) 0 0
\(603\) − 10.3604i − 0.421908i
\(604\) 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
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −39.5980 −1.59415 −0.797077 0.603877i \(-0.793622\pi\)
−0.797077 + 0.603877i \(0.793622\pi\)
\(618\) 0 0
\(619\) 48.3848i 1.94475i 0.233428 + 0.972374i \(0.425006\pi\)
−0.233428 + 0.972374i \(0.574994\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 27.1127i 1.08278i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) −16.3431 −0.649582
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 28.2843 1.11716 0.558581 0.829450i \(-0.311346\pi\)
0.558581 + 0.829450i \(0.311346\pi\)
\(642\) 0 0
\(643\) 41.3553i 1.63090i 0.578831 + 0.815448i \(0.303509\pi\)
−0.578831 + 0.815448i \(0.696491\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 88.9117 3.49009
\(650\) 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
\(657\) −45.0883 −1.75906
\(658\) 0 0
\(659\) 21.2721i 0.828643i 0.910131 + 0.414321i \(0.135981\pi\)
−0.910131 + 0.414321i \(0.864019\pi\)
\(660\) 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
\(673\) 50.9117 1.96250 0.981251 0.192736i \(-0.0617360\pi\)
0.981251 + 0.192736i \(0.0617360\pi\)
\(674\) 0 0
\(675\) 16.5685i 0.637723i
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −13.5980 −0.521076
\(682\) 0 0
\(683\) − 51.6985i − 1.97819i −0.147287 0.989094i \(-0.547054\pi\)
0.147287 0.989094i \(-0.452946\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 50.5269i 1.92213i 0.276315 + 0.961067i \(0.410887\pi\)
−0.276315 + 0.961067i \(0.589113\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 33.9411 1.28561
\(698\) 0 0
\(699\) 3.31371i 0.125336i
\(700\) 0 0
\(701\) 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
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) − 9.94113i − 0.369714i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 10.1960 0.377628
\(730\) 0 0
\(731\) − 73.9411i − 2.73481i
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −24.3431 −0.896691
\(738\) 0 0
\(739\) − 54.0416i − 1.98795i −0.109591 0.993977i \(-0.534954\pi\)
0.109591 0.993977i \(-0.465046\pi\)
\(740\) 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
\(747\) − 28.5025i − 1.04285i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 10.4020 0.379071
\(754\) 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
\(761\) 54.0000 1.95750 0.978749 0.205061i \(-0.0657392\pi\)
0.978749 + 0.205061i \(0.0657392\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 50.9117 1.83592 0.917961 0.396670i \(-0.129834\pi\)
0.917961 + 0.396670i \(0.129834\pi\)
\(770\) 0 0
\(771\) 17.5736i 0.632897i
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 44.4853i 1.59385i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 17.3553i − 0.618651i −0.950956 0.309326i \(-0.899897\pi\)
0.950956 0.309326i \(-0.100103\pi\)
\(788\) 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
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 15.0294 0.531039
\(802\) 0 0
\(803\) 105.941i 3.73858i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 6.00000 0.210949 0.105474 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) 0 0
\(811\) 3.12994i 0.109907i 0.998489 + 0.0549536i \(0.0175011\pi\)
−0.998489 + 0.0549536i \(0.982499\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 96.9117 3.39051
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 18.2843 0.636577
\(826\) 0 0
\(827\) − 24.1838i − 0.840952i −0.907304 0.420476i \(-0.861863\pi\)
0.907304 0.420476i \(-0.138137\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −39.5980 −1.37199
\(834\) 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
\(841\) 29.0000 1.00000
\(842\) 0 0
\(843\) 16.5685i 0.570651i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 19.6569 0.674621
\(850\) 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
\(857\) −54.0000 −1.84460 −0.922302 0.386469i \(-0.873695\pi\)
−0.922302 + 0.386469i \(0.873695\pi\)
\(858\) 0 0
\(859\) − 47.0122i − 1.60404i −0.597300 0.802018i \(-0.703760\pi\)
0.597300 0.802018i \(-0.296240\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 8.78680i 0.298415i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −45.0883 −1.52601
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) − 40.5858i − 1.36582i −0.730502 0.682910i \(-0.760714\pi\)
0.730502 0.682910i \(-0.239286\pi\)
\(884\) 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
\(891\) − 37.6396i − 1.26097i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 34.9289i 1.15980i 0.814689 + 0.579898i \(0.196908\pi\)
−0.814689 + 0.579898i \(0.803092\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) −66.9706 −2.21640
\(914\) 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
\(921\) −17.5980 −0.579873
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 28.2843 0.927977 0.463988 0.885841i \(-0.346418\pi\)
0.463988 + 0.885841i \(0.346418\pi\)
\(930\) 0 0
\(931\) − 51.8995i − 1.70094i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 50.9117 1.66321 0.831606 0.555366i \(-0.187422\pi\)
0.831606 + 0.555366i \(0.187422\pi\)
\(938\) 0 0
\(939\) − 5.85786i − 0.191164i
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 16.7868i 0.545498i 0.962085 + 0.272749i \(0.0879328\pi\)
−0.962085 + 0.272749i \(0.912067\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 42.0000 1.36051 0.680257 0.732974i \(-0.261868\pi\)
0.680257 + 0.732974i \(0.261868\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 25.9239i 0.835385i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) −24.5685 −0.789255
\(970\) 0 0
\(971\) 16.1838i 0.519362i 0.965694 + 0.259681i \(0.0836174\pi\)
−0.965694 + 0.259681i \(0.916383\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −62.2254 −1.99077 −0.995383 0.0959785i \(-0.969402\pi\)
−0.995383 + 0.0959785i \(0.969402\pi\)
\(978\) 0 0
\(979\) − 35.3137i − 1.12863i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) −0.225397 −0.00715275
\(994\) 0 0
\(995\) 0 0
\(996\) 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 512.2.b.c.257.3 4
3.2 odd 2 4608.2.d.k.2305.4 4
4.3 odd 2 inner 512.2.b.c.257.2 4
8.3 odd 2 CM 512.2.b.c.257.3 4
8.5 even 2 inner 512.2.b.c.257.2 4
12.11 even 2 4608.2.d.k.2305.1 4
16.3 odd 4 512.2.a.f.1.1 yes 2
16.5 even 4 512.2.a.f.1.1 yes 2
16.11 odd 4 512.2.a.a.1.2 2
16.13 even 4 512.2.a.a.1.2 2
24.5 odd 2 4608.2.d.k.2305.1 4
24.11 even 2 4608.2.d.k.2305.4 4
32.3 odd 8 1024.2.e.g.769.2 4
32.5 even 8 1024.2.e.o.257.1 4
32.11 odd 8 1024.2.e.o.257.1 4
32.13 even 8 1024.2.e.g.769.2 4
32.19 odd 8 1024.2.e.o.769.1 4
32.21 even 8 1024.2.e.g.257.2 4
32.27 odd 8 1024.2.e.g.257.2 4
32.29 even 8 1024.2.e.o.769.1 4
48.5 odd 4 4608.2.a.i.1.1 2
48.11 even 4 4608.2.a.k.1.2 2
48.29 odd 4 4608.2.a.k.1.2 2
48.35 even 4 4608.2.a.i.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
512.2.a.a.1.2 2 16.11 odd 4
512.2.a.a.1.2 2 16.13 even 4
512.2.a.f.1.1 yes 2 16.3 odd 4
512.2.a.f.1.1 yes 2 16.5 even 4
512.2.b.c.257.2 4 4.3 odd 2 inner
512.2.b.c.257.2 4 8.5 even 2 inner
512.2.b.c.257.3 4 1.1 even 1 trivial
512.2.b.c.257.3 4 8.3 odd 2 CM
1024.2.e.g.257.2 4 32.21 even 8
1024.2.e.g.257.2 4 32.27 odd 8
1024.2.e.g.769.2 4 32.3 odd 8
1024.2.e.g.769.2 4 32.13 even 8
1024.2.e.o.257.1 4 32.5 even 8
1024.2.e.o.257.1 4 32.11 odd 8
1024.2.e.o.769.1 4 32.19 odd 8
1024.2.e.o.769.1 4 32.29 even 8
4608.2.a.i.1.1 2 48.5 odd 4
4608.2.a.i.1.1 2 48.35 even 4
4608.2.a.k.1.2 2 48.11 even 4
4608.2.a.k.1.2 2 48.29 odd 4
4608.2.d.k.2305.1 4 12.11 even 2
4608.2.d.k.2305.1 4 24.5 odd 2
4608.2.d.k.2305.4 4 3.2 odd 2
4608.2.d.k.2305.4 4 24.11 even 2