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Properties

Label 225.10.a.d.1.1
Level $225$
Weight $10$
Character 225.1
Self dual yes
Analytic conductor $115.883$
Analytic rank $1$
Dimension $1$
CM discriminant -3
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,10,Mod(1,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.1");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 225.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: \(115.883063137\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 9)
Fricke sign: \(+1\)
Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-512.000 q^{4} +12580.0 q^{7} -118370. q^{13} +262144. q^{16} -976696. q^{19} -6.44096e6 q^{28} +1.69123e6 q^{31} +1.53845e7 q^{37} +1.65771e7 q^{43} +1.17903e8 q^{49} +6.06054e7 q^{52} -1.17903e8 q^{61} -1.34218e8 q^{64} -1.12542e8 q^{67} -2.96368e8 q^{73} +5.00068e8 q^{76} -6.16732e8 q^{79} -1.48909e9 q^{91} -1.28893e9 q^{97} +O(q^{100})\)

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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 0 0
\(4\) −512.000 −1.00000
\(5\) 0 0
\(6\) 0 0
\(7\) 12580.0 1.98034 0.990169 − 0.139874i \(-0.0446697\pi\)
0.990169 + 0.139874i \(0.0446697\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −118370. −1.14947 −0.574734 − 0.818341i \(-0.694894\pi\)
−0.574734 + 0.818341i \(0.694894\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 262144. 1.00000
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) −976696. −1.71937 −0.859683 − 0.510828i \(-0.829339\pi\)
−0.859683 + 0.510828i \(0.829339\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) −6.44096e6 −1.98034
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 1.69123e6 0.328908 0.164454 − 0.986385i \(-0.447414\pi\)
0.164454 + 0.986385i \(0.447414\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.53845e7 1.34951 0.674754 − 0.738043i \(-0.264250\pi\)
0.674754 + 0.738043i \(0.264250\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 1.65771e7 0.739435 0.369717 − 0.929144i \(-0.379454\pi\)
0.369717 + 0.929144i \(0.379454\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 1.17903e8 2.92174
\(50\) 0 0
\(51\) 0 0
\(52\) 6.06054e7 1.14947
\(53\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 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
\(61\) −1.17903e8 −1.09029 −0.545143 − 0.838343i \(-0.683525\pi\)
−0.545143 + 0.838343i \(0.683525\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.34218e8 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.12542e8 −0.682306 −0.341153 − 0.940008i \(-0.610817\pi\)
−0.341153 + 0.940008i \(0.610817\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −2.96368e8 −1.22146 −0.610729 − 0.791839i \(-0.709124\pi\)
−0.610729 + 0.791839i \(0.709124\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 5.00068e8 1.71937
\(77\) 0 0
\(78\) 0 0
\(79\) −6.16732e8 −1.78145 −0.890727 − 0.454538i \(-0.849804\pi\)
−0.890727 + 0.454538i \(0.849804\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 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
\(91\) −1.48909e9 −2.27633
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.28893e9 −1.47828 −0.739139 − 0.673553i \(-0.764767\pi\)
−0.739139 + 0.673553i \(0.764767\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −6.22786e7 −0.0545219 −0.0272610 − 0.999628i \(-0.508679\pi\)
−0.0272610 + 0.999628i \(0.508679\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 2.24018e9 1.52007 0.760035 − 0.649882i \(-0.225182\pi\)
0.760035 + 0.649882i \(0.225182\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 3.29777e9 1.98034
\(113\) 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
\(121\) −2.35795e9 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) −8.65909e8 −0.328908
\(125\) 0 0
\(126\) 0 0
\(127\) 2.28028e9 0.777808 0.388904 − 0.921278i \(-0.372854\pi\)
0.388904 + 0.921278i \(0.372854\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −1.22868e10 −3.40493
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) −3.66070e9 −0.831760 −0.415880 − 0.909419i \(-0.636526\pi\)
−0.415880 + 0.909419i \(0.636526\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −7.87686e9 −1.34951
\(149\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) −1.27138e10 −1.99012 −0.995061 − 0.0992678i \(-0.968350\pi\)
−0.995061 + 0.0992678i \(0.968350\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1.23694e10 1.62480 0.812398 − 0.583103i \(-0.198162\pi\)
0.812398 + 0.583103i \(0.198162\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −4.86962e9 −0.540320 −0.270160 − 0.962815i \(-0.587077\pi\)
−0.270160 + 0.962815i \(0.587077\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 3.40696e9 0.321275
\(170\) 0 0
\(171\) 0 0
\(172\) −8.48746e9 −0.739435
\(173\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 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
\(181\) −2.01652e10 −1.39652 −0.698262 − 0.715842i \(-0.746043\pi\)
−0.698262 + 0.715842i \(0.746043\pi\)
\(182\) 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
\(193\) −2.32814e10 −1.20782 −0.603908 − 0.797054i \(-0.706391\pi\)
−0.603908 + 0.797054i \(0.706391\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −6.03662e10 −2.92174
\(197\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) −1.97601e10 −0.893205 −0.446602 − 0.894733i \(-0.647366\pi\)
−0.446602 + 0.894733i \(0.647366\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −3.10300e10 −1.14947
\(209\) 0 0
\(210\) 0 0
\(211\) 4.94819e10 1.71860 0.859301 − 0.511471i \(-0.170899\pi\)
0.859301 + 0.511471i \(0.170899\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 2.12756e10 0.651349
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −7.37390e10 −1.99676 −0.998378 − 0.0569257i \(-0.981870\pi\)
−0.998378 + 0.0569257i \(0.981870\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) −7.18214e10 −1.72581 −0.862907 − 0.505363i \(-0.831359\pi\)
−0.862907 + 0.505363i \(0.831359\pi\)
\(230\) 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
\(241\) −9.17994e10 −1.75293 −0.876463 − 0.481470i \(-0.840103\pi\)
−0.876463 + 0.481470i \(0.840103\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 6.03664e10 1.09029
\(245\) 0 0
\(246\) 0 0
\(247\) 1.15612e11 1.97635
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 6.87195e10 1.00000
\(257\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 1.93537e11 2.67248
\(260\) 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
\(267\) 0 0
\(268\) 5.76217e10 0.682306
\(269\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) −4.79471e10 −0.540009 −0.270004 − 0.962859i \(-0.587025\pi\)
−0.270004 + 0.962859i \(0.587025\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.91509e11 −1.95448 −0.977239 − 0.212142i \(-0.931956\pi\)
−0.977239 + 0.212142i \(0.931956\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 2.05159e11 1.90131 0.950653 − 0.310257i \(-0.100415\pi\)
0.950653 + 0.310257i \(0.100415\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.18588e11 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 1.51741e11 1.22146
\(293\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 2.08540e11 1.46433
\(302\) 0 0
\(303\) 0 0
\(304\) −2.56035e11 −1.71937
\(305\) 0 0
\(306\) 0 0
\(307\) −2.80963e11 −1.80520 −0.902601 − 0.430477i \(-0.858345\pi\)
−0.902601 + 0.430477i \(0.858345\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −8.21542e10 −0.483816 −0.241908 − 0.970299i \(-0.577773\pi\)
−0.241908 + 0.970299i \(0.577773\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 3.15767e11 1.78145
\(317\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 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
\(331\) −1.06948e11 −0.489717 −0.244858 − 0.969559i \(-0.578741\pi\)
−0.244858 + 0.969559i \(0.578741\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −4.46231e11 −1.88463 −0.942313 − 0.334734i \(-0.891354\pi\)
−0.942313 + 0.334734i \(0.891354\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 9.75569e11 3.80570
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) −1.71773e11 −0.619784 −0.309892 − 0.950772i \(-0.600293\pi\)
−0.309892 + 0.950772i \(0.600293\pi\)
\(350\) 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
\(361\) 6.31247e11 1.95622
\(362\) 0 0
\(363\) 0 0
\(364\) 7.62416e11 2.27633
\(365\) 0 0
\(366\) 0 0
\(367\) 5.61843e11 1.61666 0.808329 − 0.588732i \(-0.200372\pi\)
0.808329 + 0.588732i \(0.200372\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 3.90612e10 0.104485 0.0522427 − 0.998634i \(-0.483363\pi\)
0.0522427 + 0.998634i \(0.483363\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 7.69425e11 1.91553 0.957767 − 0.287546i \(-0.0928396\pi\)
0.957767 + 0.287546i \(0.0928396\pi\)
\(380\) 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
\(387\) 0 0
\(388\) 6.59931e11 1.47828
\(389\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 2.21693e11 0.447913 0.223957 − 0.974599i \(-0.428103\pi\)
0.223957 + 0.974599i \(0.428103\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) −2.00191e11 −0.378069
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.13182e12 −1.99997 −0.999986 − 0.00533967i \(-0.998300\pi\)
−0.999986 + 0.00533967i \(0.998300\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 3.18866e10 0.0545219
\(413\) 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
\(421\) 1.19719e12 1.85734 0.928672 − 0.370902i \(-0.120951\pi\)
0.928672 + 0.370902i \(0.120951\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.48322e12 −2.15914
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −6.13416e11 −0.838609 −0.419304 − 0.907846i \(-0.637726\pi\)
−0.419304 + 0.907846i \(0.637726\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.14697e12 −1.52007
\(437\) 0 0
\(438\) 0 0
\(439\) −4.63954e11 −0.596190 −0.298095 − 0.954536i \(-0.596351\pi\)
−0.298095 + 0.954536i \(0.596351\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 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
\(448\) −1.68846e12 −1.98034
\(449\) 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
\(457\) 1.58605e12 1.70096 0.850482 − 0.526004i \(-0.176310\pi\)
0.850482 + 0.526004i \(0.176310\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 1.84923e12 1.87015 0.935075 − 0.354451i \(-0.115332\pi\)
0.935075 + 0.354451i \(0.115332\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) −1.41578e12 −1.35120
\(470\) 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
\(481\) −1.82106e12 −1.55121
\(482\) 0 0
\(483\) 0 0
\(484\) 1.20727e12 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) −1.88740e12 −1.52049 −0.760244 − 0.649638i \(-0.774921\pi\)
−0.760244 + 0.649638i \(0.774921\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 4.43345e11 0.328908
\(497\) 0 0
\(498\) 0 0
\(499\) 2.17438e12 1.56994 0.784969 − 0.619535i \(-0.212679\pi\)
0.784969 + 0.619535i \(0.212679\pi\)
\(500\) 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
\(508\) −1.16751e12 −0.777808
\(509\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) −3.72831e12 −2.41890
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 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
\(523\) −3.42183e12 −1.99987 −0.999934 − 0.0115124i \(-0.996335\pi\)
−0.999934 + 0.0115124i \(0.996335\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −1.80115e12 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 6.29086e12 3.40493
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −8.90575e11 −0.446974 −0.223487 − 0.974707i \(-0.571744\pi\)
−0.223487 + 0.974707i \(0.571744\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 8.00832e11 0.382471 0.191236 − 0.981544i \(-0.438751\pi\)
0.191236 + 0.981544i \(0.438751\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −7.75849e12 −3.52788
\(554\) 0 0
\(555\) 0 0
\(556\) 1.87428e12 0.831760
\(557\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) −1.96223e12 −0.849956
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 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
\(571\) −3.51053e11 −0.138201 −0.0691003 − 0.997610i \(-0.522013\pi\)
−0.0691003 + 0.997610i \(0.522013\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −4.65164e12 −1.74709 −0.873544 − 0.486745i \(-0.838184\pi\)
−0.873544 + 0.486745i \(0.838184\pi\)
\(578\) 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
\(589\) −1.65182e12 −0.565513
\(590\) 0 0
\(591\) 0 0
\(592\) 4.03295e12 1.34951
\(593\) 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
\(601\) −6.07612e12 −1.89973 −0.949863 − 0.312667i \(-0.898778\pi\)
−0.949863 + 0.312667i \(0.898778\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 6.50947e12 1.99012
\(605\) 0 0
\(606\) 0 0
\(607\) 3.88646e12 1.16200 0.580998 − 0.813905i \(-0.302662\pi\)
0.580998 + 0.813905i \(0.302662\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 6.75823e12 1.93313 0.966564 − 0.256426i \(-0.0825451\pi\)
0.966564 + 0.256426i \(0.0825451\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 2.63266e10 0.00720753 0.00360376 − 0.999994i \(-0.498853\pi\)
0.00360376 + 0.999994i \(0.498853\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) −6.33311e12 −1.62480
\(629\) 0 0
\(630\) 0 0
\(631\) −1.41926e12 −0.356394 −0.178197 − 0.983995i \(-0.557026\pi\)
−0.178197 + 0.983995i \(0.557026\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.39562e13 −3.35845
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 8.21654e12 1.89557 0.947785 − 0.318910i \(-0.103317\pi\)
0.947785 + 0.318910i \(0.103317\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 2.49325e12 0.540320
\(653\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 9.15345e12 1.86500 0.932498 − 0.361174i \(-0.117624\pi\)
0.932498 + 0.361174i \(0.117624\pi\)
\(662\) 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
\(673\) 8.08227e12 1.51868 0.759339 − 0.650695i \(-0.225523\pi\)
0.759339 + 0.650695i \(0.225523\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −1.74436e12 −0.321275
\(677\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) −1.62147e13 −2.92749
\(680\) 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
\(688\) 4.34558e12 0.739435
\(689\) 0 0
\(690\) 0 0
\(691\) 1.17568e13 1.96173 0.980863 − 0.194699i \(-0.0623731\pi\)
0.980863 + 0.194699i \(0.0623731\pi\)
\(692\) 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
\(701\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) −1.50260e13 −2.32030
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 8.57856e12 1.27499 0.637494 − 0.770455i \(-0.279971\pi\)
0.637494 + 0.770455i \(0.279971\pi\)
\(710\) 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
\(721\) −7.83465e11 −0.107972
\(722\) 0 0
\(723\) 0 0
\(724\) 1.03246e13 1.39652
\(725\) 0 0
\(726\) 0 0
\(727\) −1.11736e13 −1.48350 −0.741752 − 0.670674i \(-0.766005\pi\)
−0.741752 + 0.670674i \(0.766005\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 1.43727e13 1.83895 0.919476 − 0.393147i \(-0.128614\pi\)
0.919476 + 0.393147i \(0.128614\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −7.10029e12 −0.875742 −0.437871 − 0.899038i \(-0.644267\pi\)
−0.437871 + 0.899038i \(0.644267\pi\)
\(740\) 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
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.69018e13 1.93889 0.969446 − 0.245306i \(-0.0788885\pi\)
0.969446 + 0.245306i \(0.0788885\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.73497e13 1.92026 0.960129 − 0.279557i \(-0.0901876\pi\)
0.960129 + 0.279557i \(0.0901876\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 2.81815e13 3.01025
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 6.18611e12 0.637895 0.318947 − 0.947772i \(-0.396671\pi\)
0.318947 + 0.947772i \(0.396671\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.19201e13 1.20782
\(773\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 3.09075e13 2.92174
\(785\) 0 0
\(786\) 0 0
\(787\) −1.82814e13 −1.69872 −0.849361 − 0.527812i \(-0.823013\pi\)
−0.849361 + 0.527812i \(0.823013\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 1.39562e13 1.25325
\(794\) 0 0
\(795\) 0 0
\(796\) 1.01172e13 0.893205
\(797\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) −1.98398e12 −0.161044 −0.0805218 − 0.996753i \(-0.525659\pi\)
−0.0805218 + 0.996753i \(0.525659\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −1.61908e13 −1.27136
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) −1.86110e13 −1.41407 −0.707035 − 0.707178i \(-0.749968\pi\)
−0.707035 + 0.707178i \(0.749968\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) −2.41982e13 −1.77946 −0.889730 − 0.456488i \(-0.849107\pi\)
−0.889730 + 0.456488i \(0.849107\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.58874e13 1.14947
\(833\) 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
\(841\) −1.45071e13 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) −2.53347e13 −1.71860
\(845\) 0 0
\(846\) 0 0
\(847\) −2.96630e13 −1.98034
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 1.48476e13 0.960255 0.480128 − 0.877199i \(-0.340590\pi\)
0.480128 + 0.877199i \(0.340590\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) −2.88491e13 −1.80785 −0.903927 − 0.427688i \(-0.859328\pi\)
−0.903927 + 0.427688i \(0.859328\pi\)
\(860\) 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
\(867\) 0 0
\(868\) −1.08931e13 −0.651349
\(869\) 0 0
\(870\) 0 0
\(871\) 1.33216e13 0.784288
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −2.46459e13 −1.40685 −0.703424 − 0.710771i \(-0.748346\pi\)
−0.703424 + 0.710771i \(0.748346\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) −3.38683e13 −1.87487 −0.937434 − 0.348163i \(-0.886806\pi\)
−0.937434 + 0.348163i \(0.886806\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 2.86860e13 1.54032
\(890\) 0 0
\(891\) 0 0
\(892\) 3.77544e13 1.99676
\(893\) 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
\(907\) 1.02147e13 0.501177 0.250588 − 0.968094i \(-0.419376\pi\)
0.250588 + 0.968094i \(0.419376\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 3.67725e13 1.72581
\(917\) 0 0
\(918\) 0 0
\(919\) −6.39629e12 −0.295807 −0.147903 − 0.989002i \(-0.547252\pi\)
−0.147903 + 0.989002i \(0.547252\pi\)
\(920\) 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
\(931\) −1.15155e14 −5.02354
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 3.40492e13 1.44304 0.721521 − 0.692392i \(-0.243443\pi\)
0.721521 + 0.692392i \(0.243443\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 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
\(949\) 3.50811e13 1.40403
\(950\) 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
\(961\) −2.35794e13 −0.891819
\(962\) 0 0
\(963\) 0 0
\(964\) 4.70013e13 1.75293
\(965\) 0 0
\(966\) 0 0
\(967\) −1.05389e13 −0.387591 −0.193796 − 0.981042i \(-0.562080\pi\)
−0.193796 + 0.981042i \(0.562080\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) −4.60517e13 −1.64717
\(974\) 0 0
\(975\) 0 0
\(976\) −3.09076e13 −1.09029
\(977\) 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
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −5.91931e13 −1.97635
\(989\) 0 0
\(990\) 0 0
\(991\) 3.82277e13 1.25906 0.629531 − 0.776976i \(-0.283247\pi\)
0.629531 + 0.776976i \(0.283247\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 6.17891e13 1.98054 0.990271 − 0.139155i \(-0.0444385\pi\)
0.990271 + 0.139155i \(0.0444385\pi\)
\(998\) 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 225.10.a.d.1.1 1
3.2 odd 2 CM 225.10.a.d.1.1 1
5.2 odd 4 225.10.b.f.199.2 2
5.3 odd 4 225.10.b.f.199.1 2
5.4 even 2 9.10.a.b.1.1 ✓ 1
15.2 even 4 225.10.b.f.199.2 2
15.8 even 4 225.10.b.f.199.1 2
15.14 odd 2 9.10.a.b.1.1 ✓ 1
20.19 odd 2 144.10.a.h.1.1 1
45.4 even 6 81.10.c.c.55.1 2
45.14 odd 6 81.10.c.c.55.1 2
45.29 odd 6 81.10.c.c.28.1 2
45.34 even 6 81.10.c.c.28.1 2
60.59 even 2 144.10.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9.10.a.b.1.1 ✓ 1 5.4 even 2
9.10.a.b.1.1 ✓ 1 15.14 odd 2
81.10.c.c.28.1 2 45.29 odd 6
81.10.c.c.28.1 2 45.34 even 6
81.10.c.c.55.1 2 45.4 even 6
81.10.c.c.55.1 2 45.14 odd 6
144.10.a.h.1.1 1 20.19 odd 2
144.10.a.h.1.1 1 60.59 even 2
225.10.a.d.1.1 1 1.1 even 1 trivial
225.10.a.d.1.1 1 3.2 odd 2 CM
225.10.b.f.199.1 2 5.3 odd 4
225.10.b.f.199.1 2 15.8 even 4
225.10.b.f.199.2 2 5.2 odd 4
225.10.b.f.199.2 2 15.2 even 4