Properties

Label 225.2.a.f.1.2
Level $225$
Weight $2$
Character 225.1
Self dual yes
Analytic conductor $1.797$
Analytic rank $0$
Dimension $2$
CM discriminant -15
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 45)
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 225.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.23607 q^{2} +3.00000 q^{4} +2.23607 q^{8} +O(q^{10})\) \(q+2.23607 q^{2} +3.00000 q^{4} +2.23607 q^{8} -1.00000 q^{16} -4.47214 q^{17} +4.00000 q^{19} -8.94427 q^{23} +8.00000 q^{31} -6.70820 q^{32} -10.0000 q^{34} +8.94427 q^{38} -20.0000 q^{46} +8.94427 q^{47} -7.00000 q^{49} +4.47214 q^{53} +2.00000 q^{61} +17.8885 q^{62} -13.0000 q^{64} -13.4164 q^{68} +12.0000 q^{76} +16.0000 q^{79} +17.8885 q^{83} -26.8328 q^{92} +20.0000 q^{94} -15.6525 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{4} - 2 q^{16} + 8 q^{19} + 16 q^{31} - 20 q^{34} - 40 q^{46} - 14 q^{49} + 4 q^{61} - 26 q^{64} + 24 q^{76} + 32 q^{79} + 40 q^{94}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.23607 1.58114 0.790569 0.612372i \(-0.209785\pi\)
0.790569 + 0.612372i \(0.209785\pi\)
\(3\) 0 0
\(4\) 3.00000 1.50000
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 2.23607 0.790569
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −4.47214 −1.08465 −0.542326 0.840168i \(-0.682456\pi\)
−0.542326 + 0.840168i \(0.682456\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −8.94427 −1.86501 −0.932505 0.361158i \(-0.882382\pi\)
−0.932505 + 0.361158i \(0.882382\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) −6.70820 −1.18585
\(33\) 0 0
\(34\) −10.0000 −1.71499
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 8.94427 1.45095
\(39\) 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
\(46\) −20.0000 −2.94884
\(47\) 8.94427 1.30466 0.652328 0.757937i \(-0.273792\pi\)
0.652328 + 0.757937i \(0.273792\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.47214 0.614295 0.307148 0.951662i \(-0.400625\pi\)
0.307148 + 0.951662i \(0.400625\pi\)
\(54\) 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
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 17.8885 2.27185
\(63\) 0 0
\(64\) −13.0000 −1.62500
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) −13.4164 −1.62698
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 12.0000 1.37649
\(77\) 0 0
\(78\) 0 0
\(79\) 16.0000 1.80014 0.900070 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 17.8885 1.96352 0.981761 0.190117i \(-0.0608868\pi\)
0.981761 + 0.190117i \(0.0608868\pi\)
\(84\) 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
\(92\) −26.8328 −2.79751
\(93\) 0 0
\(94\) 20.0000 2.06284
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) −15.6525 −1.58114
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 10.0000 0.971286
\(107\) −17.8885 −1.72935 −0.864675 0.502331i \(-0.832476\pi\)
−0.864675 + 0.502331i \(0.832476\pi\)
\(108\) 0 0
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 4.47214 0.420703 0.210352 0.977626i \(-0.432539\pi\)
0.210352 + 0.977626i \(0.432539\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 4.47214 0.404888
\(123\) 0 0
\(124\) 24.0000 2.15526
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) −15.6525 −1.38350
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −10.0000 −0.857493
\(137\) 22.3607 1.91040 0.955201 0.295958i \(-0.0956389\pi\)
0.955201 + 0.295958i \(0.0956389\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 8.94427 0.725476
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 35.7771 2.84627
\(159\) 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
\(166\) 40.0000 3.10460
\(167\) 8.94427 0.692129 0.346064 0.938211i \(-0.387518\pi\)
0.346064 + 0.938211i \(0.387518\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −22.3607 −1.70005 −0.850026 0.526742i \(-0.823414\pi\)
−0.850026 + 0.526742i \(0.823414\pi\)
\(174\) 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
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −20.0000 −1.47442
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 26.8328 1.95698
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −21.0000 −1.50000
\(197\) −4.47214 −0.318626 −0.159313 0.987228i \(-0.550928\pi\)
−0.159313 + 0.987228i \(0.550928\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −28.0000 −1.92760 −0.963800 0.266627i \(-0.914091\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) 13.4164 0.921443
\(213\) 0 0
\(214\) −40.0000 −2.73434
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −31.3050 −2.12024
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 10.0000 0.665190
\(227\) −17.8885 −1.18730 −0.593652 0.804722i \(-0.702314\pi\)
−0.593652 + 0.804722i \(0.702314\pi\)
\(228\) 0 0
\(229\) −26.0000 −1.71813 −0.859064 0.511868i \(-0.828954\pi\)
−0.859064 + 0.511868i \(0.828954\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −22.3607 −1.46490 −0.732448 0.680823i \(-0.761622\pi\)
−0.732448 + 0.680823i \(0.761622\pi\)
\(234\) 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
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) −24.5967 −1.58114
\(243\) 0 0
\(244\) 6.00000 0.384111
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 17.8885 1.13592
\(249\) 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
\(256\) −9.00000 −0.562500
\(257\) −31.3050 −1.95275 −0.976375 0.216085i \(-0.930671\pi\)
−0.976375 + 0.216085i \(0.930671\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −8.94427 −0.551527 −0.275764 0.961225i \(-0.588931\pi\)
−0.275764 + 0.961225i \(0.588931\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 32.0000 1.94386 0.971931 0.235267i \(-0.0755965\pi\)
0.971931 + 0.235267i \(0.0755965\pi\)
\(272\) 4.47214 0.271163
\(273\) 0 0
\(274\) 50.0000 3.02061
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 8.94427 0.536442
\(279\) 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
\(289\) 3.00000 0.176471
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 31.3050 1.82885 0.914427 0.404750i \(-0.132641\pi\)
0.914427 + 0.404750i \(0.132641\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 17.8885 1.02937
\(303\) 0 0
\(304\) −4.00000 −0.229416
\(305\) 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
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 48.0000 2.70021
\(317\) 22.3607 1.25590 0.627950 0.778253i \(-0.283894\pi\)
0.627950 + 0.778253i \(0.283894\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −17.8885 −0.995345
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) 53.6656 2.94528
\(333\) 0 0
\(334\) 20.0000 1.09435
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) −29.0689 −1.58114
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −50.0000 −2.68802
\(347\) 35.7771 1.92061 0.960307 0.278944i \(-0.0899844\pi\)
0.960307 + 0.278944i \(0.0899844\pi\)
\(348\) 0 0
\(349\) 34.0000 1.81998 0.909989 0.414632i \(-0.136090\pi\)
0.909989 + 0.414632i \(0.136090\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 31.3050 1.66619 0.833097 0.553127i \(-0.186565\pi\)
0.833097 + 0.553127i \(0.186565\pi\)
\(354\) 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
\(361\) −3.00000 −0.157895
\(362\) −49.1935 −2.58555
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 8.94427 0.466252
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 20.0000 1.03142
\(377\) 0 0
\(378\) 0 0
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8.94427 −0.457031 −0.228515 0.973540i \(-0.573387\pi\)
−0.228515 + 0.973540i \(0.573387\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 40.0000 2.02289
\(392\) −15.6525 −0.790569
\(393\) 0 0
\(394\) −10.0000 −0.503793
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 35.7771 1.79334
\(399\) 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
\(409\) −26.0000 −1.28562 −0.642809 0.766027i \(-0.722231\pi\)
−0.642809 + 0.766027i \(0.722231\pi\)
\(410\) 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
\(421\) 38.0000 1.85201 0.926003 0.377515i \(-0.123221\pi\)
0.926003 + 0.377515i \(0.123221\pi\)
\(422\) −62.6099 −3.04780
\(423\) 0 0
\(424\) 10.0000 0.485643
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −53.6656 −2.59403
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −42.0000 −2.01144
\(437\) −35.7771 −1.71145
\(438\) 0 0
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.8885 0.849910 0.424955 0.905214i \(-0.360290\pi\)
0.424955 + 0.905214i \(0.360290\pi\)
\(444\) 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
\(452\) 13.4164 0.631055
\(453\) 0 0
\(454\) −40.0000 −1.87729
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) −58.1378 −2.71660
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −50.0000 −2.31621
\(467\) 35.7771 1.65557 0.827783 0.561048i \(-0.189602\pi\)
0.827783 + 0.561048i \(0.189602\pi\)
\(468\) 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
\(482\) 4.47214 0.203700
\(483\) 0 0
\(484\) −33.0000 −1.50000
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 4.47214 0.202444
\(489\) 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
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) 0 0
\(499\) −44.0000 −1.96971 −0.984855 0.173379i \(-0.944532\pi\)
−0.984855 + 0.173379i \(0.944532\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 44.7214 1.99403 0.997013 0.0772283i \(-0.0246070\pi\)
0.997013 + 0.0772283i \(0.0246070\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11.1803 0.494106
\(513\) 0 0
\(514\) −70.0000 −3.08757
\(515\) 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
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −20.0000 −0.872041
\(527\) −35.7771 −1.55847
\(528\) 0 0
\(529\) 57.0000 2.47826
\(530\) 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
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 71.5542 3.07352
\(543\) 0 0
\(544\) 30.0000 1.28624
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 67.0820 2.86560
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 12.0000 0.508913
\(557\) 22.3607 0.947452 0.473726 0.880672i \(-0.342909\pi\)
0.473726 + 0.880672i \(0.342909\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −35.7771 −1.50782 −0.753912 0.656975i \(-0.771836\pi\)
−0.753912 + 0.656975i \(0.771836\pi\)
\(564\) 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
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 6.70820 0.279024
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 70.0000 2.89167
\(587\) −17.8885 −0.738339 −0.369170 0.929362i \(-0.620358\pi\)
−0.369170 + 0.929362i \(0.620358\pi\)
\(588\) 0 0
\(589\) 32.0000 1.31854
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 4.47214 0.183649 0.0918243 0.995775i \(-0.470730\pi\)
0.0918243 + 0.995775i \(0.470730\pi\)
\(594\) 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
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 24.0000 0.976546
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) −26.8328 −1.08821
\(609\) 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
\(617\) 49.1935 1.98046 0.990228 0.139459i \(-0.0445365\pi\)
0.990228 + 0.139459i \(0.0445365\pi\)
\(618\) 0 0
\(619\) −44.0000 −1.76851 −0.884255 0.467005i \(-0.845333\pi\)
−0.884255 + 0.467005i \(0.845333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 35.7771 1.42314
\(633\) 0 0
\(634\) 50.0000 1.98575
\(635\) 0 0
\(636\) 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
\(646\) −40.0000 −1.57378
\(647\) −44.7214 −1.75818 −0.879089 0.476658i \(-0.841848\pi\)
−0.879089 + 0.476658i \(0.841848\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −49.1935 −1.92509 −0.962545 0.271122i \(-0.912605\pi\)
−0.962545 + 0.271122i \(0.912605\pi\)
\(654\) 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
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) −62.6099 −2.43340
\(663\) 0 0
\(664\) 40.0000 1.55230
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 26.8328 1.03819
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −39.0000 −1.50000
\(677\) −31.3050 −1.20315 −0.601574 0.798817i \(-0.705459\pi\)
−0.601574 + 0.798817i \(0.705459\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −35.7771 −1.36897 −0.684486 0.729026i \(-0.739973\pi\)
−0.684486 + 0.729026i \(0.739973\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −52.0000 −1.97817 −0.989087 0.147335i \(-0.952930\pi\)
−0.989087 + 0.147335i \(0.952930\pi\)
\(692\) −67.0820 −2.55008
\(693\) 0 0
\(694\) 80.0000 3.03676
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 76.0263 2.87764
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 70.0000 2.63448
\(707\) 0 0
\(708\) 0 0
\(709\) −26.0000 −0.976450 −0.488225 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −71.5542 −2.67972
\(714\) 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
\(722\) −6.70820 −0.249653
\(723\) 0 0
\(724\) −66.0000 −2.45287
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 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
\(736\) 60.0000 2.21163
\(737\) 0 0
\(738\) 0 0
\(739\) 4.00000 0.147142 0.0735712 0.997290i \(-0.476560\pi\)
0.0735712 + 0.997290i \(0.476560\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 44.7214 1.64067 0.820334 0.571885i \(-0.193788\pi\)
0.820334 + 0.571885i \(0.193788\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) −8.94427 −0.326164
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 8.94427 0.324871
\(759\) 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
\(766\) −20.0000 −0.722629
\(767\) 0 0
\(768\) 0 0
\(769\) 46.0000 1.65880 0.829401 0.558653i \(-0.188682\pi\)
0.829401 + 0.558653i \(0.188682\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.47214 0.160852 0.0804258 0.996761i \(-0.474372\pi\)
0.0804258 + 0.996761i \(0.474372\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 89.4427 3.19847
\(783\) 0 0
\(784\) 7.00000 0.250000
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) −13.4164 −0.477940
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 48.0000 1.70131
\(797\) 49.1935 1.74252 0.871262 0.490819i \(-0.163302\pi\)
0.871262 + 0.490819i \(0.163302\pi\)
\(798\) 0 0
\(799\) −40.0000 −1.41510
\(800\) 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
\(811\) −52.0000 −1.82597 −0.912983 0.407997i \(-0.866228\pi\)
−0.912983 + 0.407997i \(0.866228\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −58.1378 −2.03274
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 35.7771 1.24409 0.622046 0.782981i \(-0.286302\pi\)
0.622046 + 0.782981i \(0.286302\pi\)
\(828\) 0 0
\(829\) 34.0000 1.18087 0.590434 0.807086i \(-0.298956\pi\)
0.590434 + 0.807086i \(0.298956\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 31.3050 1.08465
\(834\) 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
\(842\) 84.9706 2.92828
\(843\) 0 0
\(844\) −84.0000 −2.89140
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) −4.47214 −0.153574
\(849\) 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
\(856\) −40.0000 −1.36717
\(857\) −58.1378 −1.98595 −0.992974 0.118331i \(-0.962245\pi\)
−0.992974 + 0.118331i \(0.962245\pi\)
\(858\) 0 0
\(859\) −44.0000 −1.50126 −0.750630 0.660722i \(-0.770250\pi\)
−0.750630 + 0.660722i \(0.770250\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 44.7214 1.52233 0.761166 0.648557i \(-0.224627\pi\)
0.761166 + 0.648557i \(0.224627\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −31.3050 −1.06012
\(873\) 0 0
\(874\) −80.0000 −2.70604
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 35.7771 1.20742
\(879\) 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
\(886\) 40.0000 1.34383
\(887\) 8.94427 0.300319 0.150160 0.988662i \(-0.452021\pi\)
0.150160 + 0.988662i \(0.452021\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 35.7771 1.19723
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −20.0000 −0.666297
\(902\) 0 0
\(903\) 0 0
\(904\) 10.0000 0.332595
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) −53.6656 −1.78096
\(909\) 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
\(916\) −78.0000 −2.57719
\(917\) 0 0
\(918\) 0 0
\(919\) −56.0000 −1.84727 −0.923635 0.383274i \(-0.874797\pi\)
−0.923635 + 0.383274i \(0.874797\pi\)
\(920\) 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
\(931\) −28.0000 −0.917663
\(932\) −67.0820 −2.19735
\(933\) 0 0
\(934\) 80.0000 2.61768
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 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
\(947\) −17.8885 −0.581300 −0.290650 0.956830i \(-0.593871\pi\)
−0.290650 + 0.956830i \(0.593871\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 58.1378 1.88327 0.941634 0.336640i \(-0.109290\pi\)
0.941634 + 0.336640i \(0.109290\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 0 0
\(963\) 0 0
\(964\) 6.00000 0.193247
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) −24.5967 −0.790569
\(969\) 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
\(976\) −2.00000 −0.0640184
\(977\) −4.47214 −0.143076 −0.0715382 0.997438i \(-0.522791\pi\)
−0.0715382 + 0.997438i \(0.522791\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −62.6099 −1.99695 −0.998473 0.0552438i \(-0.982406\pi\)
−0.998473 + 0.0552438i \(0.982406\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 32.0000 1.01651 0.508257 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) −53.6656 −1.70389
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) −98.3870 −3.11439
\(999\) 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 225.2.a.f.1.2 2
3.2 odd 2 inner 225.2.a.f.1.1 2
4.3 odd 2 3600.2.a.bs.1.1 2
5.2 odd 4 45.2.b.a.19.2 yes 2
5.3 odd 4 45.2.b.a.19.1 2
5.4 even 2 inner 225.2.a.f.1.1 2
12.11 even 2 3600.2.a.bs.1.2 2
15.2 even 4 45.2.b.a.19.1 2
15.8 even 4 45.2.b.a.19.2 yes 2
15.14 odd 2 CM 225.2.a.f.1.2 2
20.3 even 4 720.2.f.d.289.2 2
20.7 even 4 720.2.f.d.289.1 2
20.19 odd 2 3600.2.a.bs.1.2 2
35.13 even 4 2205.2.d.a.1324.1 2
35.27 even 4 2205.2.d.a.1324.2 2
40.3 even 4 2880.2.f.j.1729.1 2
40.13 odd 4 2880.2.f.k.1729.1 2
40.27 even 4 2880.2.f.j.1729.2 2
40.37 odd 4 2880.2.f.k.1729.2 2
45.2 even 12 405.2.j.c.109.1 4
45.7 odd 12 405.2.j.c.109.2 4
45.13 odd 12 405.2.j.c.379.2 4
45.22 odd 12 405.2.j.c.379.1 4
45.23 even 12 405.2.j.c.379.1 4
45.32 even 12 405.2.j.c.379.2 4
45.38 even 12 405.2.j.c.109.2 4
45.43 odd 12 405.2.j.c.109.1 4
60.23 odd 4 720.2.f.d.289.1 2
60.47 odd 4 720.2.f.d.289.2 2
60.59 even 2 3600.2.a.bs.1.1 2
105.62 odd 4 2205.2.d.a.1324.1 2
105.83 odd 4 2205.2.d.a.1324.2 2
120.53 even 4 2880.2.f.k.1729.2 2
120.77 even 4 2880.2.f.k.1729.1 2
120.83 odd 4 2880.2.f.j.1729.2 2
120.107 odd 4 2880.2.f.j.1729.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.2.b.a.19.1 2 5.3 odd 4
45.2.b.a.19.1 2 15.2 even 4
45.2.b.a.19.2 yes 2 5.2 odd 4
45.2.b.a.19.2 yes 2 15.8 even 4
225.2.a.f.1.1 2 3.2 odd 2 inner
225.2.a.f.1.1 2 5.4 even 2 inner
225.2.a.f.1.2 2 1.1 even 1 trivial
225.2.a.f.1.2 2 15.14 odd 2 CM
405.2.j.c.109.1 4 45.2 even 12
405.2.j.c.109.1 4 45.43 odd 12
405.2.j.c.109.2 4 45.7 odd 12
405.2.j.c.109.2 4 45.38 even 12
405.2.j.c.379.1 4 45.22 odd 12
405.2.j.c.379.1 4 45.23 even 12
405.2.j.c.379.2 4 45.13 odd 12
405.2.j.c.379.2 4 45.32 even 12
720.2.f.d.289.1 2 20.7 even 4
720.2.f.d.289.1 2 60.23 odd 4
720.2.f.d.289.2 2 20.3 even 4
720.2.f.d.289.2 2 60.47 odd 4
2205.2.d.a.1324.1 2 35.13 even 4
2205.2.d.a.1324.1 2 105.62 odd 4
2205.2.d.a.1324.2 2 35.27 even 4
2205.2.d.a.1324.2 2 105.83 odd 4
2880.2.f.j.1729.1 2 40.3 even 4
2880.2.f.j.1729.1 2 120.107 odd 4
2880.2.f.j.1729.2 2 40.27 even 4
2880.2.f.j.1729.2 2 120.83 odd 4
2880.2.f.k.1729.1 2 40.13 odd 4
2880.2.f.k.1729.1 2 120.77 even 4
2880.2.f.k.1729.2 2 40.37 odd 4
2880.2.f.k.1729.2 2 120.53 even 4
3600.2.a.bs.1.1 2 4.3 odd 2
3600.2.a.bs.1.1 2 60.59 even 2
3600.2.a.bs.1.2 2 12.11 even 2
3600.2.a.bs.1.2 2 20.19 odd 2