Properties

Label 1225.2.b.c.99.2
Level $1225$
Weight $2$
Character 1225.99
Analytic conductor $9.782$
Analytic rank $0$
Dimension $2$
CM discriminant -7
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1225.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.78167424761\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 49)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 99.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1225.99
Dual form 1225.2.b.c.99.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000 q^{4} +3.00000i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000 q^{4} +3.00000i q^{8} +3.00000 q^{9} +4.00000 q^{11} -1.00000 q^{16} +3.00000i q^{18} +4.00000i q^{22} -8.00000i q^{23} -2.00000 q^{29} +5.00000i q^{32} +3.00000 q^{36} -6.00000i q^{37} +12.0000i q^{43} +4.00000 q^{44} +8.00000 q^{46} +10.0000i q^{53} -2.00000i q^{58} -7.00000 q^{64} +4.00000i q^{67} +16.0000 q^{71} +9.00000i q^{72} +6.00000 q^{74} -8.00000 q^{79} +9.00000 q^{81} -12.0000 q^{86} +12.0000i q^{88} -8.00000i q^{92} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{4} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{4} + 6 q^{9} + 8 q^{11} - 2 q^{16} - 4 q^{29} + 6 q^{36} + 8 q^{44} + 16 q^{46} - 14 q^{64} + 32 q^{71} + 12 q^{74} - 16 q^{79} + 18 q^{81} - 24 q^{86} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(1177\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i 0.935414 + 0.353553i \(0.115027\pi\)
−0.935414 + 0.353553i \(0.884973\pi\)
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 3.00000i 1.06066i
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 3.00000i 0.707107i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 4.00000i 0.852803i
\(23\) − 8.00000i − 1.66812i −0.551677 0.834058i \(-0.686012\pi\)
0.551677 0.834058i \(-0.313988\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 5.00000i 0.883883i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 3.00000 0.500000
\(37\) − 6.00000i − 0.986394i −0.869918 0.493197i \(-0.835828\pi\)
0.869918 0.493197i \(-0.164172\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 12.0000i 1.82998i 0.403473 + 0.914991i \(0.367803\pi\)
−0.403473 + 0.914991i \(0.632197\pi\)
\(44\) 4.00000 0.603023
\(45\) 0 0
\(46\) 8.00000 1.17954
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 10.0000i 1.37361i 0.726844 + 0.686803i \(0.240986\pi\)
−0.726844 + 0.686803i \(0.759014\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) − 2.00000i − 0.262613i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −7.00000 −0.875000
\(65\) 0 0
\(66\) 0 0
\(67\) 4.00000i 0.488678i 0.969690 + 0.244339i \(0.0785709\pi\)
−0.969690 + 0.244339i \(0.921429\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 16.0000 1.89885 0.949425 0.313993i \(-0.101667\pi\)
0.949425 + 0.313993i \(0.101667\pi\)
\(72\) 9.00000i 1.06066i
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −12.0000 −1.29399
\(87\) 0 0
\(88\) 12.0000i 1.27920i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) − 8.00000i − 0.834058i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 12.0000 1.20605
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −10.0000 −0.971286
\(107\) − 20.0000i − 1.93347i −0.255774 0.966736i \(-0.582330\pi\)
0.255774 0.966736i \(-0.417670\pi\)
\(108\) 0 0
\(109\) −18.0000 −1.72409 −0.862044 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 2.00000i − 0.188144i −0.995565 0.0940721i \(-0.970012\pi\)
0.995565 0.0940721i \(-0.0299884\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.00000 −0.185695
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 16.0000i 1.41977i 0.704317 + 0.709885i \(0.251253\pi\)
−0.704317 + 0.709885i \(0.748747\pi\)
\(128\) 3.00000i 0.265165i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 0 0
\(137\) − 10.0000i − 0.854358i −0.904167 0.427179i \(-0.859507\pi\)
0.904167 0.427179i \(-0.140493\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 16.0000i 1.34269i
\(143\) 0 0
\(144\) −3.00000 −0.250000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) − 6.00000i − 0.493197i
\(149\) −22.0000 −1.80231 −0.901155 0.433497i \(-0.857280\pi\)
−0.901155 + 0.433497i \(0.857280\pi\)
\(150\) 0 0
\(151\) −24.0000 −1.95309 −0.976546 0.215308i \(-0.930924\pi\)
−0.976546 + 0.215308i \(0.930924\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) − 8.00000i − 0.636446i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 9.00000i 0.707107i
\(163\) 20.0000i 1.56652i 0.621694 + 0.783260i \(0.286445\pi\)
−0.621694 + 0.783260i \(0.713555\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 12.0000i 0.914991i
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 0 0
\(178\) 0 0
\(179\) −4.00000 −0.298974 −0.149487 0.988764i \(-0.547762\pi\)
−0.149487 + 0.988764i \(0.547762\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 24.0000 1.76930
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) − 18.0000i − 1.29567i −0.761781 0.647834i \(-0.775675\pi\)
0.761781 0.647834i \(-0.224325\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 26.0000i − 1.85242i −0.377004 0.926212i \(-0.623046\pi\)
0.377004 0.926212i \(-0.376954\pi\)
\(198\) 12.0000i 0.852803i
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) − 24.0000i − 1.66812i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 10.0000i 0.686803i
\(213\) 0 0
\(214\) 20.0000 1.36717
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) − 18.0000i − 1.21911i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 2.00000 0.133038
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) − 6.00000i − 0.393919i
\(233\) − 22.0000i − 1.44127i −0.693316 0.720634i \(-0.743851\pi\)
0.693316 0.720634i \(-0.256149\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 5.00000i 0.321412i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) − 32.0000i − 2.01182i
\(254\) −16.0000 −1.00393
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 0 0
\(263\) − 32.0000i − 1.97320i −0.163144 0.986602i \(-0.552164\pi\)
0.163144 0.986602i \(-0.447836\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 4.00000i 0.244339i
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) 0 0
\(276\) 0 0
\(277\) − 10.0000i − 0.600842i −0.953807 0.300421i \(-0.902873\pi\)
0.953807 0.300421i \(-0.0971271\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −26.0000 −1.55103 −0.775515 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 16.0000 0.949425
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 15.0000i 0.883883i
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 18.0000 1.04623
\(297\) 0 0
\(298\) − 22.0000i − 1.27443i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) − 24.0000i − 1.38104i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) − 34.0000i − 1.90963i −0.297200 0.954815i \(-0.596053\pi\)
0.297200 0.954815i \(-0.403947\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 9.00000 0.500000
\(325\) 0 0
\(326\) −20.0000 −1.10770
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 36.0000 1.97874 0.989369 0.145424i \(-0.0464545\pi\)
0.989369 + 0.145424i \(0.0464545\pi\)
\(332\) 0 0
\(333\) − 18.0000i − 0.986394i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 30.0000i 1.63420i 0.576493 + 0.817102i \(0.304421\pi\)
−0.576493 + 0.817102i \(0.695579\pi\)
\(338\) 13.0000i 0.707107i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) −36.0000 −1.94099
\(345\) 0 0
\(346\) 0 0
\(347\) 4.00000i 0.214731i 0.994220 + 0.107366i \(0.0342415\pi\)
−0.994220 + 0.107366i \(0.965758\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 20.0000i 1.06600i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) − 4.00000i − 0.211407i
\(359\) −8.00000 −0.422224 −0.211112 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 8.00000i 0.417029i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) − 22.0000i − 1.13912i −0.821951 0.569558i \(-0.807114\pi\)
0.821951 0.569558i \(-0.192886\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 8.00000i 0.409316i
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 18.0000 0.916176
\(387\) 36.0000i 1.82998i
\(388\) 0 0
\(389\) 38.0000 1.92668 0.963338 0.268290i \(-0.0864585\pi\)
0.963338 + 0.268290i \(0.0864585\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 26.0000 1.30986
\(395\) 0 0
\(396\) 12.0000 0.603023
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −34.0000 −1.69788 −0.848939 0.528490i \(-0.822758\pi\)
−0.848939 + 0.528490i \(0.822758\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 24.0000i − 1.18964i
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 24.0000 1.17954
\(415\) 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
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) − 12.0000i − 0.584151i
\(423\) 0 0
\(424\) −30.0000 −1.45693
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) − 20.0000i − 0.966736i
\(429\) 0 0
\(430\) 0 0
\(431\) 32.0000 1.54139 0.770693 0.637207i \(-0.219910\pi\)
0.770693 + 0.637207i \(0.219910\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −18.0000 −0.862044
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 20.0000i 0.950229i 0.879924 + 0.475114i \(0.157593\pi\)
−0.879924 + 0.475114i \(0.842407\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) − 2.00000i − 0.0940721i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) − 6.00000i − 0.280668i −0.990104 0.140334i \(-0.955182\pi\)
0.990104 0.140334i \(-0.0448177\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 40.0000i 1.85896i 0.368875 + 0.929479i \(0.379743\pi\)
−0.368875 + 0.929479i \(0.620257\pi\)
\(464\) 2.00000 0.0928477
\(465\) 0 0
\(466\) 22.0000 1.01913
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 48.0000i 2.20704i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 30.0000i 1.37361i
\(478\) − 16.0000i − 0.731823i
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) 0 0
\(487\) − 24.0000i − 1.08754i −0.839233 0.543772i \(-0.816996\pi\)
0.839233 0.543772i \(-0.183004\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 44.0000 1.98569 0.992846 0.119401i \(-0.0380974\pi\)
0.992846 + 0.119401i \(0.0380974\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −36.0000 −1.61158 −0.805791 0.592200i \(-0.798259\pi\)
−0.805791 + 0.592200i \(0.798259\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 32.0000 1.42257
\(507\) 0 0
\(508\) 16.0000i 0.709885i
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) − 11.0000i − 0.486136i
\(513\) 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 \(0.5\pi\)
\(522\) − 6.00000i − 0.262613i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 32.0000 1.39527
\(527\) 0 0
\(528\) 0 0
\(529\) −41.0000 −1.78261
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −12.0000 −0.518321
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −34.0000 −1.46177 −0.730887 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 44.0000i 1.88130i 0.339372 + 0.940652i \(0.389785\pi\)
−0.339372 + 0.940652i \(0.610215\pi\)
\(548\) − 10.0000i − 0.427179i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 10.0000 0.424859
\(555\) 0 0
\(556\) 0 0
\(557\) 46.0000i 1.94908i 0.224208 + 0.974541i \(0.428020\pi\)
−0.224208 + 0.974541i \(0.571980\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) − 26.0000i − 1.09674i
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 48.0000i 2.01404i
\(569\) −22.0000 −0.922288 −0.461144 0.887325i \(-0.652561\pi\)
−0.461144 + 0.887325i \(0.652561\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −21.0000 −0.875000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 17.0000i 0.707107i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 40.0000i 1.65663i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 6.00000i 0.246598i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −22.0000 −0.901155
\(597\) 0 0
\(598\) 0 0
\(599\) −32.0000 −1.30748 −0.653742 0.756717i \(-0.726802\pi\)
−0.653742 + 0.756717i \(0.726802\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0 0
\(603\) 12.0000i 0.488678i
\(604\) −24.0000 −0.976546
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 38.0000i 1.53481i 0.641165 + 0.767403i \(0.278451\pi\)
−0.641165 + 0.767403i \(0.721549\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 26.0000i − 1.04672i −0.852111 0.523360i \(-0.824678\pi\)
0.852111 0.523360i \(-0.175322\pi\)
\(618\) 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
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) − 24.0000i − 0.954669i
\(633\) 0 0
\(634\) 34.0000 1.35031
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) − 8.00000i − 0.316723i
\(639\) 48.0000 1.89885
\(640\) 0 0
\(641\) 46.0000 1.81689 0.908445 0.418004i \(-0.137270\pi\)
0.908445 + 0.418004i \(0.137270\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 27.0000i 1.06066i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 20.0000i 0.783260i
\(653\) − 50.0000i − 1.95665i −0.207072 0.978326i \(-0.566394\pi\)
0.207072 0.978326i \(-0.433606\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −44.0000 −1.71400 −0.856998 0.515319i \(-0.827673\pi\)
−0.856998 + 0.515319i \(0.827673\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 36.0000i 1.39918i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 18.0000 0.697486
\(667\) 16.0000i 0.619522i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) − 30.0000i − 1.15642i −0.815890 0.578208i \(-0.803752\pi\)
0.815890 0.578208i \(-0.196248\pi\)
\(674\) −30.0000 −1.15556
\(675\) 0 0
\(676\) 13.0000 0.500000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 52.0000i 1.98972i 0.101237 + 0.994862i \(0.467720\pi\)
−0.101237 + 0.994862i \(0.532280\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) − 12.0000i − 0.457496i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −4.00000 −0.151838
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −28.0000 −1.05529
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) 0 0
\(711\) −24.0000 −0.900070
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −4.00000 −0.149487
\(717\) 0 0
\(718\) − 8.00000i − 0.298557i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) − 19.0000i − 0.707107i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 40.0000 1.47442
\(737\) 16.0000i 0.589368i
\(738\) 0 0
\(739\) 52.0000 1.91285 0.956425 0.291977i \(-0.0943129\pi\)
0.956425 + 0.291977i \(0.0943129\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 40.0000i 1.46746i 0.679442 + 0.733729i \(0.262222\pi\)
−0.679442 + 0.733729i \(0.737778\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 22.0000 0.805477
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −48.0000 −1.75154 −0.875772 0.482724i \(-0.839647\pi\)
−0.875772 + 0.482724i \(0.839647\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) − 54.0000i − 1.96266i −0.192323 0.981332i \(-0.561602\pi\)
0.192323 0.981332i \(-0.438398\pi\)
\(758\) 12.0000i 0.435860i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) − 18.0000i − 0.647834i
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −36.0000 −1.29399
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 38.0000i 1.36237i
\(779\) 0 0
\(780\) 0 0
\(781\) 64.0000 2.29010
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) − 26.0000i − 0.926212i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 36.0000i 1.27920i
\(793\) 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
\(801\) 0 0
\(802\) − 34.0000i − 1.20058i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 38.0000 1.33601 0.668004 0.744157i \(-0.267149\pi\)
0.668004 + 0.744157i \(0.267149\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 24.0000 0.841200
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 22.0000 0.767805 0.383903 0.923374i \(-0.374580\pi\)
0.383903 + 0.923374i \(0.374580\pi\)
\(822\) 0 0
\(823\) − 32.0000i − 1.11545i −0.830026 0.557725i \(-0.811674\pi\)
0.830026 0.557725i \(-0.188326\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 44.0000i 1.53003i 0.644013 + 0.765015i \(0.277268\pi\)
−0.644013 + 0.765015i \(0.722732\pi\)
\(828\) − 24.0000i − 0.834058i
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) − 26.0000i − 0.896019i
\(843\) 0 0
\(844\) −12.0000 −0.413057
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) − 10.0000i − 0.343401i
\(849\) 0 0
\(850\) 0 0
\(851\) −48.0000 −1.64542
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 60.0000 2.05076
\(857\) 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
\(862\) 32.0000i 1.08992i
\(863\) − 8.00000i − 0.272323i −0.990687 0.136162i \(-0.956523\pi\)
0.990687 0.136162i \(-0.0434766\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −32.0000 −1.08553
\(870\) 0 0
\(871\) 0 0
\(872\) − 54.0000i − 1.82867i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 50.0000i 1.68838i 0.536044 + 0.844190i \(0.319918\pi\)
−0.536044 + 0.844190i \(0.680082\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 12.0000i 0.403832i 0.979403 + 0.201916i \(0.0647168\pi\)
−0.979403 + 0.201916i \(0.935283\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −20.0000 −0.671913
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 36.0000 1.20605
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) − 2.00000i − 0.0667409i
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 6.00000 0.199557
\(905\) 0 0
\(906\) 0 0
\(907\) 60.0000i 1.99227i 0.0878507 + 0.996134i \(0.472000\pi\)
−0.0878507 + 0.996134i \(0.528000\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 16.0000 0.530104 0.265052 0.964234i \(-0.414611\pi\)
0.265052 + 0.964234i \(0.414611\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 6.00000 0.198462
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 48.0000 1.58337 0.791687 0.610927i \(-0.209203\pi\)
0.791687 + 0.610927i \(0.209203\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) −40.0000 −1.31448
\(927\) 0 0
\(928\) − 10.0000i − 0.328266i
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) − 22.0000i − 0.720634i
\(933\) 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
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) −48.0000 −1.56061
\(947\) − 20.0000i − 0.649913i −0.945729 0.324956i \(-0.894650\pi\)
0.945729 0.324956i \(-0.105350\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 58.0000i − 1.87880i −0.342817 0.939402i \(-0.611381\pi\)
0.342817 0.939402i \(-0.388619\pi\)
\(954\) −30.0000 −0.971286
\(955\) 0 0
\(956\) −16.0000 −0.517477
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) − 60.0000i − 1.93347i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 40.0000i − 1.28631i −0.765735 0.643157i \(-0.777624\pi\)
0.765735 0.643157i \(-0.222376\pi\)
\(968\) 15.0000i 0.482118i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 24.0000 0.769010
\(975\) 0 0
\(976\) 0 0
\(977\) 46.0000i 1.47167i 0.677161 + 0.735835i \(0.263210\pi\)
−0.677161 + 0.735835i \(0.736790\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −54.0000 −1.72409
\(982\) 44.0000i 1.40410i
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 96.0000 3.05262
\(990\) 0 0
\(991\) −24.0000 −0.762385 −0.381193 0.924496i \(-0.624487\pi\)
−0.381193 + 0.924496i \(0.624487\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) − 36.0000i − 1.13956i
\(999\) 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 1225.2.b.c.99.2 2
5.2 odd 4 1225.2.a.c.1.1 1
5.3 odd 4 49.2.a.a.1.1 1
5.4 even 2 inner 1225.2.b.c.99.1 2
7.6 odd 2 CM 1225.2.b.c.99.2 2
15.8 even 4 441.2.a.c.1.1 1
20.3 even 4 784.2.a.f.1.1 1
35.3 even 12 49.2.c.a.30.1 2
35.13 even 4 49.2.a.a.1.1 1
35.18 odd 12 49.2.c.a.30.1 2
35.23 odd 12 49.2.c.a.18.1 2
35.27 even 4 1225.2.a.c.1.1 1
35.33 even 12 49.2.c.a.18.1 2
35.34 odd 2 inner 1225.2.b.c.99.1 2
40.3 even 4 3136.2.a.o.1.1 1
40.13 odd 4 3136.2.a.n.1.1 1
55.43 even 4 5929.2.a.c.1.1 1
60.23 odd 4 7056.2.a.bg.1.1 1
65.38 odd 4 8281.2.a.d.1.1 1
105.23 even 12 441.2.e.d.361.1 2
105.38 odd 12 441.2.e.d.226.1 2
105.53 even 12 441.2.e.d.226.1 2
105.68 odd 12 441.2.e.d.361.1 2
105.83 odd 4 441.2.a.c.1.1 1
140.3 odd 12 784.2.i.f.177.1 2
140.23 even 12 784.2.i.f.753.1 2
140.83 odd 4 784.2.a.f.1.1 1
140.103 odd 12 784.2.i.f.753.1 2
140.123 even 12 784.2.i.f.177.1 2
280.13 even 4 3136.2.a.n.1.1 1
280.83 odd 4 3136.2.a.o.1.1 1
385.153 odd 4 5929.2.a.c.1.1 1
420.83 even 4 7056.2.a.bg.1.1 1
455.363 even 4 8281.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
49.2.a.a.1.1 1 5.3 odd 4
49.2.a.a.1.1 1 35.13 even 4
49.2.c.a.18.1 2 35.23 odd 12
49.2.c.a.18.1 2 35.33 even 12
49.2.c.a.30.1 2 35.3 even 12
49.2.c.a.30.1 2 35.18 odd 12
441.2.a.c.1.1 1 15.8 even 4
441.2.a.c.1.1 1 105.83 odd 4
441.2.e.d.226.1 2 105.38 odd 12
441.2.e.d.226.1 2 105.53 even 12
441.2.e.d.361.1 2 105.23 even 12
441.2.e.d.361.1 2 105.68 odd 12
784.2.a.f.1.1 1 20.3 even 4
784.2.a.f.1.1 1 140.83 odd 4
784.2.i.f.177.1 2 140.3 odd 12
784.2.i.f.177.1 2 140.123 even 12
784.2.i.f.753.1 2 140.23 even 12
784.2.i.f.753.1 2 140.103 odd 12
1225.2.a.c.1.1 1 5.2 odd 4
1225.2.a.c.1.1 1 35.27 even 4
1225.2.b.c.99.1 2 5.4 even 2 inner
1225.2.b.c.99.1 2 35.34 odd 2 inner
1225.2.b.c.99.2 2 1.1 even 1 trivial
1225.2.b.c.99.2 2 7.6 odd 2 CM
3136.2.a.n.1.1 1 40.13 odd 4
3136.2.a.n.1.1 1 280.13 even 4
3136.2.a.o.1.1 1 40.3 even 4
3136.2.a.o.1.1 1 280.83 odd 4
5929.2.a.c.1.1 1 55.43 even 4
5929.2.a.c.1.1 1 385.153 odd 4
7056.2.a.bg.1.1 1 60.23 odd 4
7056.2.a.bg.1.1 1 420.83 even 4
8281.2.a.d.1.1 1 65.38 odd 4
8281.2.a.d.1.1 1 455.363 even 4