Properties

Label 45.2.b.a.19.1
Level $45$
Weight $2$
Character 45.19
Analytic conductor $0.359$
Analytic rank $0$
Dimension $2$
CM discriminant -15
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.359326809096\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-5}) \)
Defining polynomial: \(x^{2} + 5\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 19.1
Root \(-2.23607i\) of defining polynomial
Character \(\chi\) \(=\) 45.19
Dual form 45.2.b.a.19.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.23607i q^{2} -3.00000 q^{4} +2.23607i q^{5} +2.23607i q^{8} +O(q^{10})\) \(q-2.23607i q^{2} -3.00000 q^{4} +2.23607i q^{5} +2.23607i q^{8} +5.00000 q^{10} -1.00000 q^{16} +4.47214i q^{17} -4.00000 q^{19} -6.70820i q^{20} -8.94427i q^{23} -5.00000 q^{25} +8.00000 q^{31} +6.70820i q^{32} +10.0000 q^{34} +8.94427i q^{38} -5.00000 q^{40} -20.0000 q^{46} -8.94427i q^{47} +7.00000 q^{49} +11.1803i q^{50} +4.47214i q^{53} +2.00000 q^{61} -17.8885i q^{62} +13.0000 q^{64} -13.4164i q^{68} +12.0000 q^{76} -16.0000 q^{79} -2.23607i q^{80} +17.8885i q^{83} -10.0000 q^{85} +26.8328i q^{92} -20.0000 q^{94} -8.94427i q^{95} -15.6525i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 6 q^{4} + O(q^{10}) \) \( 2 q - 6 q^{4} + 10 q^{10} - 2 q^{16} - 8 q^{19} - 10 q^{25} + 16 q^{31} + 20 q^{34} - 10 q^{40} - 40 q^{46} + 14 q^{49} + 4 q^{61} + 26 q^{64} + 24 q^{76} - 32 q^{79} - 20 q^{85} - 40 q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) − 2.23607i − 1.58114i −0.612372 0.790569i \(-0.709785\pi\)
0.612372 0.790569i \(-0.290215\pi\)
\(3\) 0 0
\(4\) −3.00000 −1.50000
\(5\) 2.23607i 1.00000i
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 2.23607i 0.790569i
\(9\) 0 0
\(10\) 5.00000 1.58114
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 4.47214i 1.08465i 0.840168 + 0.542326i \(0.182456\pi\)
−0.840168 + 0.542326i \(0.817544\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) − 6.70820i − 1.50000i
\(21\) 0 0
\(22\) 0 0
\(23\) − 8.94427i − 1.86501i −0.361158 0.932505i \(-0.617618\pi\)
0.361158 0.932505i \(-0.382382\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 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 \(0.244865\pi\)
\(32\) 6.70820i 1.18585i
\(33\) 0 0
\(34\) 10.0000 1.71499
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 8.94427i 1.45095i
\(39\) 0 0
\(40\) −5.00000 −0.790569
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −20.0000 −2.94884
\(47\) − 8.94427i − 1.30466i −0.757937 0.652328i \(-0.773792\pi\)
0.757937 0.652328i \(-0.226208\pi\)
\(48\) 0 0
\(49\) 7.00000 1.00000
\(50\) 11.1803i 1.58114i
\(51\) 0 0
\(52\) 0 0
\(53\) 4.47214i 0.614295i 0.951662 + 0.307148i \(0.0993745\pi\)
−0.951662 + 0.307148i \(0.900625\pi\)
\(54\) 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 \(0.459132\pi\)
\(62\) − 17.8885i − 2.27185i
\(63\) 0 0
\(64\) 13.0000 1.62500
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) − 13.4164i − 1.62698i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 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 \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) − 2.23607i − 0.250000i
\(81\) 0 0
\(82\) 0 0
\(83\) 17.8885i 1.96352i 0.190117 + 0.981761i \(0.439113\pi\)
−0.190117 + 0.981761i \(0.560887\pi\)
\(84\) 0 0
\(85\) −10.0000 −1.08465
\(86\) 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
\(92\) 26.8328i 2.79751i
\(93\) 0 0
\(94\) −20.0000 −2.06284
\(95\) − 8.94427i − 0.917663i
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) − 15.6525i − 1.58114i
\(99\) 0 0
\(100\) 15.0000 1.50000
\(101\) 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
\(107\) 17.8885i 1.72935i 0.502331 + 0.864675i \(0.332476\pi\)
−0.502331 + 0.864675i \(0.667524\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 4.47214i 0.420703i 0.977626 + 0.210352i \(0.0674609\pi\)
−0.977626 + 0.210352i \(0.932539\pi\)
\(114\) 0 0
\(115\) 20.0000 1.86501
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) − 4.47214i − 0.404888i
\(123\) 0 0
\(124\) −24.0000 −2.15526
\(125\) − 11.1803i − 1.00000i
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) − 15.6525i − 1.38350i
\(129\) 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
\(137\) − 22.3607i − 1.91040i −0.295958 0.955201i \(-0.595639\pi\)
0.295958 0.955201i \(-0.404361\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 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 \(0.394462\pi\)
\(152\) − 8.94427i − 0.725476i
\(153\) 0 0
\(154\) 0 0
\(155\) 17.8885i 1.43684i
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 35.7771i 2.84627i
\(159\) 0 0
\(160\) −15.0000 −1.18585
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 40.0000 3.10460
\(167\) − 8.94427i − 0.692129i −0.938211 0.346064i \(-0.887518\pi\)
0.938211 0.346064i \(-0.112482\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 22.3607i 1.71499i
\(171\) 0 0
\(172\) 0 0
\(173\) − 22.3607i − 1.70005i −0.526742 0.850026i \(-0.676586\pi\)
0.526742 0.850026i \(-0.323414\pi\)
\(174\) 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
\(188\) 26.8328i 1.95698i
\(189\) 0 0
\(190\) −20.0000 −1.45095
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −21.0000 −1.50000
\(197\) 4.47214i 0.318626i 0.987228 + 0.159313i \(0.0509280\pi\)
−0.987228 + 0.159313i \(0.949072\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) − 11.1803i − 0.790569i
\(201\) 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 \(0.914091\pi\)
\(212\) − 13.4164i − 0.921443i
\(213\) 0 0
\(214\) 40.0000 2.73434
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) − 31.3050i − 2.12024i
\(219\) 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
\(226\) 10.0000 0.665190
\(227\) 17.8885i 1.18730i 0.804722 + 0.593652i \(0.202314\pi\)
−0.804722 + 0.593652i \(0.797686\pi\)
\(228\) 0 0
\(229\) 26.0000 1.71813 0.859064 0.511868i \(-0.171046\pi\)
0.859064 + 0.511868i \(0.171046\pi\)
\(230\) − 44.7214i − 2.94884i
\(231\) 0 0
\(232\) 0 0
\(233\) − 22.3607i − 1.46490i −0.680823 0.732448i \(-0.738378\pi\)
0.680823 0.732448i \(-0.261622\pi\)
\(234\) 0 0
\(235\) 20.0000 1.30466
\(236\) 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 \(0.479482\pi\)
\(242\) 24.5967i 1.58114i
\(243\) 0 0
\(244\) −6.00000 −0.384111
\(245\) 15.6525i 1.00000i
\(246\) 0 0
\(247\) 0 0
\(248\) 17.8885i 1.13592i
\(249\) 0 0
\(250\) −25.0000 −1.58114
\(251\) 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
\(257\) 31.3050i 1.95275i 0.216085 + 0.976375i \(0.430671\pi\)
−0.216085 + 0.976375i \(0.569329\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) − 8.94427i − 0.551527i −0.961225 0.275764i \(-0.911069\pi\)
0.961225 0.275764i \(-0.0889307\pi\)
\(264\) 0 0
\(265\) −10.0000 −0.614295
\(266\) 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 \(0.0755965\pi\)
\(272\) − 4.47214i − 0.271163i
\(273\) 0 0
\(274\) −50.0000 −3.02061
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 8.94427i 0.536442i
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 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
\(293\) 31.3050i 1.82885i 0.404750 + 0.914427i \(0.367359\pi\)
−0.404750 + 0.914427i \(0.632641\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) − 17.8885i − 1.02937i
\(303\) 0 0
\(304\) 4.00000 0.229416
\(305\) 4.47214i 0.256074i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 40.0000 2.27185
\(311\) 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
\(316\) 48.0000 2.70021
\(317\) − 22.3607i − 1.25590i −0.778253 0.627950i \(-0.783894\pi\)
0.778253 0.627950i \(-0.216106\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 29.0689i 1.62500i
\(321\) 0 0
\(322\) 0 0
\(323\) − 17.8885i − 0.995345i
\(324\) 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 \(0.779499\pi\)
\(332\) − 53.6656i − 2.94528i
\(333\) 0 0
\(334\) −20.0000 −1.09435
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) − 29.0689i − 1.58114i
\(339\) 0 0
\(340\) 30.0000 1.62698
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −50.0000 −2.68802
\(347\) − 35.7771i − 1.92061i −0.278944 0.960307i \(-0.589984\pi\)
0.278944 0.960307i \(-0.410016\pi\)
\(348\) 0 0
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 31.3050i 1.66619i 0.553127 + 0.833097i \(0.313435\pi\)
−0.553127 + 0.833097i \(0.686565\pi\)
\(354\) 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
\(362\) 49.1935i 2.58555i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 8.94427i 0.466252i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 20.0000 1.03142
\(377\) 0 0
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 26.8328i 1.37649i
\(381\) 0 0
\(382\) 0 0
\(383\) − 8.94427i − 0.457031i −0.973540 0.228515i \(-0.926613\pi\)
0.973540 0.228515i \(-0.0733872\pi\)
\(384\) 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
\(392\) 15.6525i 0.790569i
\(393\) 0 0
\(394\) 10.0000 0.503793
\(395\) − 35.7771i − 1.80014i
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 35.7771i 1.79334i
\(399\) 0 0
\(400\) 5.00000 0.250000
\(401\) 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 \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −40.0000 −1.96352
\(416\) 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 \(0.123221\pi\)
\(422\) 62.6099i 3.04780i
\(423\) 0 0
\(424\) −10.0000 −0.485643
\(425\) − 22.3607i − 1.08465i
\(426\) 0 0
\(427\) 0 0
\(428\) − 53.6656i − 2.59403i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −42.0000 −2.01144
\(437\) 35.7771i 1.71145i
\(438\) 0 0
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.8885i 0.849910i 0.905214 + 0.424955i \(0.139710\pi\)
−0.905214 + 0.424955i \(0.860290\pi\)
\(444\) 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
\(452\) − 13.4164i − 0.631055i
\(453\) 0 0
\(454\) 40.0000 1.87729
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) − 58.1378i − 2.71660i
\(459\) 0 0
\(460\) −60.0000 −2.79751
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −50.0000 −2.31621
\(467\) − 35.7771i − 1.65557i −0.561048 0.827783i \(-0.689602\pi\)
0.561048 0.827783i \(-0.310398\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) − 44.7214i − 2.06284i
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 20.0000 0.917663
\(476\) 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
\(482\) − 4.47214i − 0.203700i
\(483\) 0 0
\(484\) 33.0000 1.50000
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 4.47214i 0.202444i
\(489\) 0 0
\(490\) 35.0000 1.58114
\(491\) 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 \(-0.0554684\pi\)
0.984855 + 0.173379i \(0.0554684\pi\)
\(500\) 33.5410i 1.50000i
\(501\) 0 0
\(502\) 0 0
\(503\) 44.7214i 1.99403i 0.0772283 + 0.997013i \(0.475393\pi\)
−0.0772283 + 0.997013i \(0.524607\pi\)
\(504\) 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
\(512\) − 11.1803i − 0.494106i
\(513\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −20.0000 −0.872041
\(527\) 35.7771i 1.55847i
\(528\) 0 0
\(529\) −57.0000 −2.47826
\(530\) 22.3607i 0.971286i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −40.0000 −1.72935
\(536\) 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 \(0.486311\pi\)
\(542\) − 71.5542i − 3.07352i
\(543\) 0 0
\(544\) −30.0000 −1.28624
\(545\) 31.3050i 1.34096i
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 67.0820i 2.86560i
\(549\) 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
\(557\) − 22.3607i − 0.947452i −0.880672 0.473726i \(-0.842909\pi\)
0.880672 0.473726i \(-0.157091\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 35.7771i − 1.50782i −0.656975 0.753912i \(-0.728164\pi\)
0.656975 0.753912i \(-0.271836\pi\)
\(564\) 0 0
\(565\) −10.0000 −0.420703
\(566\) 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
\(575\) 44.7214i 1.86501i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 6.70820i 0.279024i
\(579\) 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
\(587\) 17.8885i 0.738339i 0.929362 + 0.369170i \(0.120358\pi\)
−0.929362 + 0.369170i \(0.879642\pi\)
\(588\) 0 0
\(589\) −32.0000 −1.31854
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 4.47214i 0.183649i 0.995775 + 0.0918243i \(0.0292698\pi\)
−0.995775 + 0.0918243i \(0.970730\pi\)
\(594\) 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
\(605\) − 24.5967i − 1.00000i
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) − 26.8328i − 1.08821i
\(609\) 0 0
\(610\) 10.0000 0.404888
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 49.1935i − 1.98046i −0.139459 0.990228i \(-0.544536\pi\)
0.139459 0.990228i \(-0.455464\pi\)
\(618\) 0 0
\(619\) 44.0000 1.76851 0.884255 0.467005i \(-0.154667\pi\)
0.884255 + 0.467005i \(0.154667\pi\)
\(620\) − 53.6656i − 2.15526i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) − 35.7771i − 1.42314i
\(633\) 0 0
\(634\) −50.0000 −1.98575
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 35.0000 1.38350
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −40.0000 −1.57378
\(647\) 44.7214i 1.75818i 0.476658 + 0.879089i \(0.341848\pi\)
−0.476658 + 0.879089i \(0.658152\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 49.1935i − 1.92509i −0.271122 0.962545i \(-0.587395\pi\)
0.271122 0.962545i \(-0.412605\pi\)
\(654\) 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 \(0.640729\pi\)
\(662\) 62.6099i 2.43340i
\(663\) 0 0
\(664\) −40.0000 −1.55230
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 26.8328i 1.03819i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −39.0000 −1.50000
\(677\) 31.3050i 1.20315i 0.798817 + 0.601574i \(0.205459\pi\)
−0.798817 + 0.601574i \(0.794541\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) − 22.3607i − 0.857493i
\(681\) 0 0
\(682\) 0 0
\(683\) − 35.7771i − 1.36897i −0.729026 0.684486i \(-0.760027\pi\)
0.729026 0.684486i \(-0.239973\pi\)
\(684\) 0 0
\(685\) 50.0000 1.91040
\(686\) 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 \(0.952930\pi\)
\(692\) 67.0820i 2.55008i
\(693\) 0 0
\(694\) −80.0000 −3.03676
\(695\) − 8.94427i − 0.339276i
\(696\) 0 0
\(697\) 0 0
\(698\) 76.0263i 2.87764i
\(699\) 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 \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 71.5542i − 2.67972i
\(714\) 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
\(722\) 6.70820i 0.249653i
\(723\) 0 0
\(724\) 66.0000 2.45287
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 60.0000 2.21163
\(737\) 0 0
\(738\) 0 0
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 44.7214i 1.64067i 0.571885 + 0.820334i \(0.306212\pi\)
−0.571885 + 0.820334i \(0.693788\pi\)
\(744\) 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 \(0.453372\pi\)
\(752\) 8.94427i 0.326164i
\(753\) 0 0
\(754\) 0 0
\(755\) 17.8885i 0.651031i
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 8.94427i 0.324871i
\(759\) 0 0
\(760\) 20.0000 0.725476
\(761\) 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 \(-0.811318\pi\)
−0.829401 + 0.558653i \(0.811318\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.47214i 0.160852i 0.996761 + 0.0804258i \(0.0256280\pi\)
−0.996761 + 0.0804258i \(0.974372\pi\)
\(774\) 0 0
\(775\) −40.0000 −1.43684
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) − 89.4427i − 3.19847i
\(783\) 0 0
\(784\) −7.00000 −0.250000
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) − 13.4164i − 0.477940i
\(789\) 0 0
\(790\) −80.0000 −2.84627
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 48.0000 1.70131
\(797\) − 49.1935i − 1.74252i −0.490819 0.871262i \(-0.663302\pi\)
0.490819 0.871262i \(-0.336698\pi\)
\(798\) 0 0
\(799\) 40.0000 1.41510
\(800\) − 33.5410i − 1.18585i
\(801\) 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
\(818\) − 58.1378i − 2.03274i
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 35.7771i − 1.24409i −0.782981 0.622046i \(-0.786302\pi\)
0.782981 0.622046i \(-0.213698\pi\)
\(828\) 0 0
\(829\) −34.0000 −1.18087 −0.590434 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) 89.4427i 3.10460i
\(831\) 0 0
\(832\) 0 0
\(833\) 31.3050i 1.08465i
\(834\) 0 0
\(835\) 20.0000 0.692129
\(836\) 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
\(842\) − 84.9706i − 2.92828i
\(843\) 0 0
\(844\) 84.0000 2.89140
\(845\) 29.0689i 1.00000i
\(846\) 0 0
\(847\) 0 0
\(848\) − 4.47214i − 0.153574i
\(849\) 0 0
\(850\) −50.0000 −1.71499
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −40.0000 −1.36717
\(857\) 58.1378i 1.98595i 0.118331 + 0.992974i \(0.462245\pi\)
−0.118331 + 0.992974i \(0.537755\pi\)
\(858\) 0 0
\(859\) 44.0000 1.50126 0.750630 0.660722i \(-0.229750\pi\)
0.750630 + 0.660722i \(0.229750\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 44.7214i 1.52233i 0.648557 + 0.761166i \(0.275373\pi\)
−0.648557 + 0.761166i \(0.724627\pi\)
\(864\) 0 0
\(865\) 50.0000 1.70005
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 31.3050i 1.06012i
\(873\) 0 0
\(874\) 80.0000 2.70604
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 35.7771i 1.20742i
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 40.0000 1.34383
\(887\) − 8.94427i − 0.300319i −0.988662 0.150160i \(-0.952021\pi\)
0.988662 0.150160i \(-0.0479788\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 35.7771i 1.19723i
\(894\) 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
\(905\) − 49.1935i − 1.63525i
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) − 53.6656i − 1.78096i
\(909\) 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 \(-0.125203\pi\)
0.923635 + 0.383274i \(0.125203\pi\)
\(920\) 44.7214i 1.47442i
\(921\) 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
\(932\) 67.0820i 2.19735i
\(933\) 0 0
\(934\) −80.0000 −2.61768
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −60.0000 −1.95698
\(941\) 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
\(947\) 17.8885i 0.581300i 0.956830 + 0.290650i \(0.0938715\pi\)
−0.956830 + 0.290650i \(0.906129\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) − 44.7214i − 1.45095i
\(951\) 0 0
\(952\) 0 0
\(953\) 58.1378i 1.88327i 0.336640 + 0.941634i \(0.390710\pi\)
−0.336640 + 0.941634i \(0.609290\pi\)
\(954\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) − 24.5967i − 0.790569i
\(969\) 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
\(977\) 4.47214i 0.143076i 0.997438 + 0.0715382i \(0.0227908\pi\)
−0.997438 + 0.0715382i \(0.977209\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) − 46.9574i − 1.50000i
\(981\) 0 0
\(982\) 0 0
\(983\) − 62.6099i − 1.99695i −0.0552438 0.998473i \(-0.517594\pi\)
0.0552438 0.998473i \(-0.482406\pi\)
\(984\) 0 0
\(985\) −10.0000 −0.318626
\(986\) 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 \(0.330290\pi\)
\(992\) 53.6656i 1.70389i
\(993\) 0 0
\(994\) 0 0
\(995\) − 35.7771i − 1.13421i
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) − 98.3870i − 3.11439i
\(999\) 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 45.2.b.a.19.1 2
3.2 odd 2 inner 45.2.b.a.19.2 yes 2
4.3 odd 2 720.2.f.d.289.2 2
5.2 odd 4 225.2.a.f.1.2 2
5.3 odd 4 225.2.a.f.1.1 2
5.4 even 2 inner 45.2.b.a.19.2 yes 2
7.6 odd 2 2205.2.d.a.1324.1 2
8.3 odd 2 2880.2.f.j.1729.1 2
8.5 even 2 2880.2.f.k.1729.1 2
9.2 odd 6 405.2.j.c.109.2 4
9.4 even 3 405.2.j.c.379.2 4
9.5 odd 6 405.2.j.c.379.1 4
9.7 even 3 405.2.j.c.109.1 4
12.11 even 2 720.2.f.d.289.1 2
15.2 even 4 225.2.a.f.1.1 2
15.8 even 4 225.2.a.f.1.2 2
15.14 odd 2 CM 45.2.b.a.19.1 2
20.3 even 4 3600.2.a.bs.1.2 2
20.7 even 4 3600.2.a.bs.1.1 2
20.19 odd 2 720.2.f.d.289.1 2
21.20 even 2 2205.2.d.a.1324.2 2
24.5 odd 2 2880.2.f.k.1729.2 2
24.11 even 2 2880.2.f.j.1729.2 2
35.34 odd 2 2205.2.d.a.1324.2 2
40.19 odd 2 2880.2.f.j.1729.2 2
40.29 even 2 2880.2.f.k.1729.2 2
45.4 even 6 405.2.j.c.379.1 4
45.14 odd 6 405.2.j.c.379.2 4
45.29 odd 6 405.2.j.c.109.1 4
45.34 even 6 405.2.j.c.109.2 4
60.23 odd 4 3600.2.a.bs.1.1 2
60.47 odd 4 3600.2.a.bs.1.2 2
60.59 even 2 720.2.f.d.289.2 2
105.104 even 2 2205.2.d.a.1324.1 2
120.29 odd 2 2880.2.f.k.1729.1 2
120.59 even 2 2880.2.f.j.1729.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.2.b.a.19.1 2 1.1 even 1 trivial
45.2.b.a.19.1 2 15.14 odd 2 CM
45.2.b.a.19.2 yes 2 3.2 odd 2 inner
45.2.b.a.19.2 yes 2 5.4 even 2 inner
225.2.a.f.1.1 2 5.3 odd 4
225.2.a.f.1.1 2 15.2 even 4
225.2.a.f.1.2 2 5.2 odd 4
225.2.a.f.1.2 2 15.8 even 4
405.2.j.c.109.1 4 9.7 even 3
405.2.j.c.109.1 4 45.29 odd 6
405.2.j.c.109.2 4 9.2 odd 6
405.2.j.c.109.2 4 45.34 even 6
405.2.j.c.379.1 4 9.5 odd 6
405.2.j.c.379.1 4 45.4 even 6
405.2.j.c.379.2 4 9.4 even 3
405.2.j.c.379.2 4 45.14 odd 6
720.2.f.d.289.1 2 12.11 even 2
720.2.f.d.289.1 2 20.19 odd 2
720.2.f.d.289.2 2 4.3 odd 2
720.2.f.d.289.2 2 60.59 even 2
2205.2.d.a.1324.1 2 7.6 odd 2
2205.2.d.a.1324.1 2 105.104 even 2
2205.2.d.a.1324.2 2 21.20 even 2
2205.2.d.a.1324.2 2 35.34 odd 2
2880.2.f.j.1729.1 2 8.3 odd 2
2880.2.f.j.1729.1 2 120.59 even 2
2880.2.f.j.1729.2 2 24.11 even 2
2880.2.f.j.1729.2 2 40.19 odd 2
2880.2.f.k.1729.1 2 8.5 even 2
2880.2.f.k.1729.1 2 120.29 odd 2
2880.2.f.k.1729.2 2 24.5 odd 2
2880.2.f.k.1729.2 2 40.29 even 2
3600.2.a.bs.1.1 2 20.7 even 4
3600.2.a.bs.1.1 2 60.23 odd 4
3600.2.a.bs.1.2 2 20.3 even 4
3600.2.a.bs.1.2 2 60.47 odd 4