Properties

Label 175.5.d.c.76.1
Level $175$
Weight $5$
Character 175.76
Analytic conductor $18.090$
Analytic rank $0$
Dimension $2$
CM discriminant -35
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 175.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.0897435397\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 76.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 175.76
Dual form 175.5.d.c.76.2

$q$-expansion

\(f(q)\) \(=\) \(q-17.0000i q^{3} -16.0000 q^{4} -49.0000i q^{7} -208.000 q^{9} +O(q^{10})\) \(q-17.0000i q^{3} -16.0000 q^{4} -49.0000i q^{7} -208.000 q^{9} -73.0000 q^{11} +272.000i q^{12} +23.0000i q^{13} +256.000 q^{16} -263.000i q^{17} -833.000 q^{21} +2159.00i q^{27} +784.000i q^{28} +1153.00 q^{29} +1241.00i q^{33} +3328.00 q^{36} +391.000 q^{39} +1168.00 q^{44} +3457.00i q^{47} -4352.00i q^{48} -2401.00 q^{49} -4471.00 q^{51} -368.000i q^{52} +10192.0i q^{63} -4096.00 q^{64} +4208.00i q^{68} -10078.0 q^{71} -9502.00i q^{73} +3577.00i q^{77} -12167.0 q^{79} +19855.0 q^{81} -6382.00i q^{83} +13328.0 q^{84} -19601.0i q^{87} +1127.00 q^{91} -3383.00i q^{97} +15184.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 32 q^{4} - 416 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 32 q^{4} - 416 q^{9} - 146 q^{11} + 512 q^{16} - 1666 q^{21} + 2306 q^{29} + 6656 q^{36} + 782 q^{39} + 2336 q^{44} - 4802 q^{49} - 8942 q^{51} - 8192 q^{64} - 20156 q^{71} - 24334 q^{79} + 39710 q^{81} + 26656 q^{84} + 2254 q^{91} + 30368 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) − 17.0000i − 1.88889i −0.328671 0.944444i \(-0.606601\pi\)
0.328671 0.944444i \(-0.393399\pi\)
\(4\) −16.0000 −1.00000
\(5\) 0 0
\(6\) 0 0
\(7\) − 49.0000i − 1.00000i
\(8\) 0 0
\(9\) −208.000 −2.56790
\(10\) 0 0
\(11\) −73.0000 −0.603306 −0.301653 0.953418i \(-0.597538\pi\)
−0.301653 + 0.953418i \(0.597538\pi\)
\(12\) 272.000i 1.88889i
\(13\) 23.0000i 0.136095i 0.997682 + 0.0680473i \(0.0216769\pi\)
−0.997682 + 0.0680473i \(0.978323\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 256.000 1.00000
\(17\) − 263.000i − 0.910035i −0.890483 0.455017i \(-0.849633\pi\)
0.890483 0.455017i \(-0.150367\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) −833.000 −1.88889
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2159.00i 2.96159i
\(28\) 784.000i 1.00000i
\(29\) 1153.00 1.37099 0.685493 0.728079i \(-0.259587\pi\)
0.685493 + 0.728079i \(0.259587\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 1241.00i 1.13958i
\(34\) 0 0
\(35\) 0 0
\(36\) 3328.00 2.56790
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 391.000 0.257068
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 1168.00 0.603306
\(45\) 0 0
\(46\) 0 0
\(47\) 3457.00i 1.56496i 0.622675 + 0.782481i \(0.286046\pi\)
−0.622675 + 0.782481i \(0.713954\pi\)
\(48\) − 4352.00i − 1.88889i
\(49\) −2401.00 −1.00000
\(50\) 0 0
\(51\) −4471.00 −1.71895
\(52\) − 368.000i − 0.136095i
\(53\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 10192.0i 2.56790i
\(64\) −4096.00 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 4208.00i 0.910035i
\(69\) 0 0
\(70\) 0 0
\(71\) −10078.0 −1.99921 −0.999603 0.0281662i \(-0.991033\pi\)
−0.999603 + 0.0281662i \(0.991033\pi\)
\(72\) 0 0
\(73\) − 9502.00i − 1.78307i −0.452948 0.891537i \(-0.649628\pi\)
0.452948 0.891537i \(-0.350372\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3577.00i 0.603306i
\(78\) 0 0
\(79\) −12167.0 −1.94953 −0.974764 0.223239i \(-0.928337\pi\)
−0.974764 + 0.223239i \(0.928337\pi\)
\(80\) 0 0
\(81\) 19855.0 3.02622
\(82\) 0 0
\(83\) − 6382.00i − 0.926404i −0.886253 0.463202i \(-0.846700\pi\)
0.886253 0.463202i \(-0.153300\pi\)
\(84\) 13328.0 1.88889
\(85\) 0 0
\(86\) 0 0
\(87\) − 19601.0i − 2.58964i
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 1127.00 0.136095
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) − 3383.00i − 0.359549i −0.983708 0.179775i \(-0.942463\pi\)
0.983708 0.179775i \(-0.0575369\pi\)
\(98\) 0 0
\(99\) 15184.0 1.54923
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 18383.0i 1.73277i 0.499373 + 0.866387i \(0.333564\pi\)
−0.499373 + 0.866387i \(0.666436\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) − 34544.0i − 2.96159i
\(109\) 14353.0 1.20806 0.604032 0.796960i \(-0.293560\pi\)
0.604032 + 0.796960i \(0.293560\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) − 12544.0i − 1.00000i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −18448.0 −1.37099
\(117\) − 4784.00i − 0.349478i
\(118\) 0 0
\(119\) −12887.0 −0.910035
\(120\) 0 0
\(121\) −9312.00 −0.636022
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) − 19856.0i − 1.13958i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 58769.0 2.95604
\(142\) 0 0
\(143\) − 1679.00i − 0.0821067i
\(144\) −53248.0 −2.56790
\(145\) 0 0
\(146\) 0 0
\(147\) 40817.0i 1.88889i
\(148\) 0 0
\(149\) −24242.0 −1.09193 −0.545966 0.837807i \(-0.683837\pi\)
−0.545966 + 0.837807i \(0.683837\pi\)
\(150\) 0 0
\(151\) −45433.0 −1.99259 −0.996294 0.0860129i \(-0.972587\pi\)
−0.996294 + 0.0860129i \(0.972587\pi\)
\(152\) 0 0
\(153\) 54704.0i 2.33688i
\(154\) 0 0
\(155\) 0 0
\(156\) −6256.00 −0.257068
\(157\) 31342.0i 1.27153i 0.771882 + 0.635766i \(0.219316\pi\)
−0.771882 + 0.635766i \(0.780684\pi\)
\(158\) 0 0
\(159\) 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
\(166\) 0 0
\(167\) − 17663.0i − 0.633332i −0.948537 0.316666i \(-0.897437\pi\)
0.948537 0.316666i \(-0.102563\pi\)
\(168\) 0 0
\(169\) 28032.0 0.981478
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 11017.0i − 0.368105i −0.982916 0.184052i \(-0.941078\pi\)
0.982916 0.184052i \(-0.0589216\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −18688.0 −0.603306
\(177\) 0 0
\(178\) 0 0
\(179\) 16558.0 0.516775 0.258388 0.966041i \(-0.416809\pi\)
0.258388 + 0.966041i \(0.416809\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 19199.0i 0.549029i
\(188\) − 55312.0i − 1.56496i
\(189\) 105791. 2.96159
\(190\) 0 0
\(191\) 47447.0 1.30059 0.650297 0.759680i \(-0.274644\pi\)
0.650297 + 0.759680i \(0.274644\pi\)
\(192\) 69632.0i 1.88889i
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 38416.0 1.00000
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) − 56497.0i − 1.37099i
\(204\) 71536.0 1.71895
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 5888.00i 0.136095i
\(209\) 0 0
\(210\) 0 0
\(211\) −77593.0 −1.74284 −0.871420 0.490537i \(-0.836801\pi\)
−0.871420 + 0.490537i \(0.836801\pi\)
\(212\) 0 0
\(213\) 171326.i 3.77628i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −161534. −3.36803
\(220\) 0 0
\(221\) 6049.00 0.123851
\(222\) 0 0
\(223\) 61343.0i 1.23355i 0.787141 + 0.616773i \(0.211560\pi\)
−0.787141 + 0.616773i \(0.788440\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 49823.0i − 0.966892i −0.875374 0.483446i \(-0.839385\pi\)
0.875374 0.483446i \(-0.160615\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 60809.0 1.13958
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 206839.i 3.68244i
\(238\) 0 0
\(239\) −43367.0 −0.759213 −0.379606 0.925148i \(-0.623941\pi\)
−0.379606 + 0.925148i \(0.623941\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) − 162656.i − 2.75459i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −108494. −1.74988
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) − 163072.i − 2.56790i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 65536.0 1.00000
\(257\) − 111938.i − 1.69477i −0.530977 0.847386i \(-0.678175\pi\)
0.530977 0.847386i \(-0.321825\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −239824. −3.52056
\(262\) 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
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) − 67328.0i − 0.910035i
\(273\) − 19159.0i − 0.257068i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 119807. 1.51729 0.758647 0.651502i \(-0.225861\pi\)
0.758647 + 0.651502i \(0.225861\pi\)
\(282\) 0 0
\(283\) 152303.i 1.90167i 0.309695 + 0.950836i \(0.399773\pi\)
−0.309695 + 0.950836i \(0.600227\pi\)
\(284\) 161248. 1.99921
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 14352.0 0.171837
\(290\) 0 0
\(291\) −57511.0 −0.679149
\(292\) 152032.i 1.78307i
\(293\) − 171337.i − 1.99579i −0.0648123 0.997897i \(-0.520645\pi\)
0.0648123 0.997897i \(-0.479355\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) − 157607.i − 1.78675i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) − 135263.i − 1.43517i −0.696473 0.717583i \(-0.745248\pi\)
0.696473 0.717583i \(-0.254752\pi\)
\(308\) − 57232.0i − 0.603306i
\(309\) 312511. 3.27302
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) − 147097.i − 1.50146i −0.660606 0.750732i \(-0.729701\pi\)
0.660606 0.750732i \(-0.270299\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 194672. 1.94953
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) −84169.0 −0.827124
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −317680. −3.02622
\(325\) 0 0
\(326\) 0 0
\(327\) − 244001.i − 2.28190i
\(328\) 0 0
\(329\) 169393. 1.56496
\(330\) 0 0
\(331\) 138482. 1.26397 0.631986 0.774980i \(-0.282240\pi\)
0.631986 + 0.774980i \(0.282240\pi\)
\(332\) 102112.i 0.926404i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −213248. −1.88889
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 117649.i 1.00000i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 313616.i 2.58964i
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) −49657.0 −0.403057
\(352\) 0 0
\(353\) − 229897.i − 1.84495i −0.386060 0.922473i \(-0.626164\pi\)
0.386060 0.922473i \(-0.373836\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 219079.i 1.71895i
\(358\) 0 0
\(359\) −76322.0 −0.592190 −0.296095 0.955159i \(-0.595684\pi\)
−0.296095 + 0.955159i \(0.595684\pi\)
\(360\) 0 0
\(361\) 130321. 1.00000
\(362\) 0 0
\(363\) 158304.i 1.20138i
\(364\) −18032.0 −0.136095
\(365\) 0 0
\(366\) 0 0
\(367\) 116497.i 0.864933i 0.901650 + 0.432467i \(0.142357\pi\)
−0.901650 + 0.432467i \(0.857643\pi\)
\(368\) 0 0
\(369\) 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
\(376\) 0 0
\(377\) 26519.0i 0.186584i
\(378\) 0 0
\(379\) 35278.0 0.245598 0.122799 0.992432i \(-0.460813\pi\)
0.122799 + 0.992432i \(0.460813\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) − 29182.0i − 0.198938i −0.995041 0.0994689i \(-0.968286\pi\)
0.995041 0.0994689i \(-0.0317144\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 54128.0i 0.359549i
\(389\) −249407. −1.64820 −0.824099 0.566446i \(-0.808318\pi\)
−0.824099 + 0.566446i \(0.808318\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −242944. −1.54923
\(397\) 163897.i 1.03990i 0.854198 + 0.519948i \(0.174049\pi\)
−0.854198 + 0.519948i \(0.825951\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −316273. −1.96686 −0.983430 0.181289i \(-0.941973\pi\)
−0.983430 + 0.181289i \(0.941973\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) − 294128.i − 1.73277i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −76753.0 −0.433043 −0.216522 0.976278i \(-0.569471\pi\)
−0.216522 + 0.976278i \(0.569471\pi\)
\(422\) 0 0
\(423\) − 719056.i − 4.01867i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −28543.0 −0.155090
\(430\) 0 0
\(431\) 356087. 1.91691 0.958455 0.285245i \(-0.0920749\pi\)
0.958455 + 0.285245i \(0.0920749\pi\)
\(432\) 552704.i 2.96159i
\(433\) 193538.i 1.03226i 0.856509 + 0.516132i \(0.172628\pi\)
−0.856509 + 0.516132i \(0.827372\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −229648. −1.20806
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 499408. 2.56790
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 412114.i 2.06254i
\(448\) 200704.i 1.00000i
\(449\) −264287. −1.31094 −0.655470 0.755221i \(-0.727530\pi\)
−0.655470 + 0.755221i \(0.727530\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 772361.i 3.76378i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 567817. 2.69515
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 295168. 1.37099
\(465\) 0 0
\(466\) 0 0
\(467\) − 322463.i − 1.47858i −0.673385 0.739292i \(-0.735160\pi\)
0.673385 0.739292i \(-0.264840\pi\)
\(468\) 76544.0i 0.349478i
\(469\) 0 0
\(470\) 0 0
\(471\) 532814. 2.40178
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 206192. 0.910035
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 148992. 0.636022
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −470713. −1.95251 −0.976255 0.216625i \(-0.930495\pi\)
−0.976255 + 0.216625i \(0.930495\pi\)
\(492\) 0 0
\(493\) − 303239.i − 1.24765i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 493822.i 1.99921i
\(498\) 0 0
\(499\) 31513.0 0.126558 0.0632789 0.997996i \(-0.479844\pi\)
0.0632789 + 0.997996i \(0.479844\pi\)
\(500\) 0 0
\(501\) −300271. −1.19629
\(502\) 0 0
\(503\) − 313297.i − 1.23828i −0.785279 0.619142i \(-0.787481\pi\)
0.785279 0.619142i \(-0.212519\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) − 476544.i − 1.85390i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −465598. −1.78307
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) − 252361.i − 0.944150i
\(518\) 0 0
\(519\) −187289. −0.695309
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) − 440782.i − 1.61146i −0.592281 0.805732i \(-0.701772\pi\)
0.592281 0.805732i \(-0.298228\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 317696.i 1.13958i
\(529\) −279841. −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) − 281486.i − 0.976131i
\(538\) 0 0
\(539\) 175273. 0.603306
\(540\) 0 0
\(541\) 2927.00 0.0100006 0.00500032 0.999987i \(-0.498408\pi\)
0.00500032 + 0.999987i \(0.498408\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 596183.i 1.94953i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 326383. 1.03706
\(562\) 0 0
\(563\) 129938.i 0.409939i 0.978768 + 0.204970i \(0.0657095\pi\)
−0.978768 + 0.204970i \(0.934290\pi\)
\(564\) −940304. −2.95604
\(565\) 0 0
\(566\) 0 0
\(567\) − 972895.i − 3.02622i
\(568\) 0 0
\(569\) −566882. −1.75093 −0.875464 0.483284i \(-0.839444\pi\)
−0.875464 + 0.483284i \(0.839444\pi\)
\(570\) 0 0
\(571\) −638158. −1.95729 −0.978647 0.205549i \(-0.934102\pi\)
−0.978647 + 0.205549i \(0.934102\pi\)
\(572\) 26864.0i 0.0821067i
\(573\) − 806599.i − 2.45668i
\(574\) 0 0
\(575\) 0 0
\(576\) 851968. 2.56790
\(577\) 665017.i 1.99747i 0.0502441 + 0.998737i \(0.484000\pi\)
−0.0502441 + 0.998737i \(0.516000\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −312718. −0.926404
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 507698.i − 1.47343i −0.676204 0.736715i \(-0.736376\pi\)
0.676204 0.736715i \(-0.263624\pi\)
\(588\) − 653072.i − 1.88889i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 320137.i − 0.910388i −0.890392 0.455194i \(-0.849570\pi\)
0.890392 0.455194i \(-0.150430\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 387872. 1.09193
\(597\) 0 0
\(598\) 0 0
\(599\) 613273. 1.70923 0.854614 0.519263i \(-0.173794\pi\)
0.854614 + 0.519263i \(0.173794\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 726928. 1.99259
\(605\) 0 0
\(606\) 0 0
\(607\) 82417.0i 0.223686i 0.993726 + 0.111843i \(0.0356754\pi\)
−0.993726 + 0.111843i \(0.964325\pi\)
\(608\) 0 0
\(609\) −960449. −2.58964
\(610\) 0 0
\(611\) −79511.0 −0.212983
\(612\) − 875264.i − 2.33688i
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 100096. 0.257068
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) − 501472.i − 1.27153i
\(629\) 0 0
\(630\) 0 0
\(631\) 100487. 0.252378 0.126189 0.992006i \(-0.459725\pi\)
0.126189 + 0.992006i \(0.459725\pi\)
\(632\) 0 0
\(633\) 1.31908e6i 3.29203i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) − 55223.0i − 0.136095i
\(638\) 0 0
\(639\) 2.09622e6 5.13376
\(640\) 0 0
\(641\) 96002.0 0.233649 0.116825 0.993153i \(-0.462728\pi\)
0.116825 + 0.993153i \(0.462728\pi\)
\(642\) 0 0
\(643\) 713183.i 1.72496i 0.506091 + 0.862480i \(0.331090\pi\)
−0.506091 + 0.862480i \(0.668910\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 111458.i − 0.266258i −0.991099 0.133129i \(-0.957498\pi\)
0.991099 0.133129i \(-0.0425025\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1.97642e6i 4.57876i
\(658\) 0 0
\(659\) −777527. −1.79038 −0.895189 0.445687i \(-0.852959\pi\)
−0.895189 + 0.445687i \(0.852959\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) − 102833.i − 0.233941i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 282608.i 0.633332i
\(669\) 1.04283e6 2.33003
\(670\) 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
\(676\) −448512. −0.981478
\(677\) − 750023.i − 1.63643i −0.574913 0.818215i \(-0.694964\pi\)
0.574913 0.818215i \(-0.305036\pi\)
\(678\) 0 0
\(679\) −165767. −0.359549
\(680\) 0 0
\(681\) −846991. −1.82635
\(682\) 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
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 176272.i 0.368105i
\(693\) − 744016.i − 1.54923i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −884833. −1.80063 −0.900317 0.435235i \(-0.856665\pi\)
−0.900317 + 0.435235i \(0.856665\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 299008. 0.603306
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.00253e6 −1.99436 −0.997180 0.0750454i \(-0.976090\pi\)
−0.997180 + 0.0750454i \(0.976090\pi\)
\(710\) 0 0
\(711\) 2.53074e6 5.00619
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −264928. −0.516775
\(717\) 737239.i 1.43407i
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 900767. 1.73277
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 976418.i − 1.84743i −0.383086 0.923713i \(-0.625139\pi\)
0.383086 0.923713i \(-0.374861\pi\)
\(728\) 0 0
\(729\) −1.15690e6 −2.17691
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 51143.0i 0.0951871i 0.998867 + 0.0475936i \(0.0151552\pi\)
−0.998867 + 0.0475936i \(0.984845\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −749207. −1.37187 −0.685935 0.727663i \(-0.740607\pi\)
−0.685935 + 0.727663i \(0.740607\pi\)
\(740\) 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
\(747\) 1.32746e6i 2.37892i
\(748\) − 307184.i − 0.549029i
\(749\) 0 0
\(750\) 0 0
\(751\) 648887. 1.15051 0.575253 0.817975i \(-0.304903\pi\)
0.575253 + 0.817975i \(0.304903\pi\)
\(752\) 884992.i 1.56496i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1.69266e6 −2.96159
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) − 703297.i − 1.20806i
\(764\) −759152. −1.30059
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) − 1.11411e6i − 1.88889i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) −1.90295e6 −3.20124
\(772\) 0 0
\(773\) 1.17962e6i 1.97417i 0.160202 + 0.987084i \(0.448786\pi\)
−0.160202 + 0.987084i \(0.551214\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 735694. 1.20613
\(782\) 0 0
\(783\) 2.48933e6i 4.06030i
\(784\) −614656. −1.00000
\(785\) 0 0
\(786\) 0 0
\(787\) 1.03714e6i 1.67451i 0.546816 + 0.837253i \(0.315840\pi\)
−0.546816 + 0.837253i \(0.684160\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 1.07354e6i − 1.69006i −0.534717 0.845031i \(-0.679582\pi\)
0.534717 0.845031i \(-0.320418\pi\)
\(798\) 0 0
\(799\) 909191. 1.42417
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 693646.i 1.07574i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.29955e6 1.98562 0.992812 0.119685i \(-0.0381886\pi\)
0.992812 + 0.119685i \(0.0381886\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 903952.i 1.37099i
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) −1.14458e6 −1.71895
\(817\) 0 0
\(818\) 0 0
\(819\) −234416. −0.349478
\(820\) 0 0
\(821\) 1.23437e6 1.83129 0.915647 0.401984i \(-0.131679\pi\)
0.915647 + 0.401984i \(0.131679\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) − 94208.0i − 0.136095i
\(833\) 631463.i 0.910035i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 622128. 0.879605
\(842\) 0 0
\(843\) − 2.03672e6i − 2.86600i
\(844\) 1.24149e6 1.74284
\(845\) 0 0
\(846\) 0 0
\(847\) 456288.i 0.636022i
\(848\) 0 0
\(849\) 2.58915e6 3.59205
\(850\) 0 0
\(851\) 0 0
\(852\) − 2.74122e6i − 3.77628i
\(853\) − 1.44782e6i − 1.98984i −0.100692 0.994918i \(-0.532106\pi\)
0.100692 0.994918i \(-0.467894\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 970462.i 1.32135i 0.750673 + 0.660674i \(0.229729\pi\)
−0.750673 + 0.660674i \(0.770271\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 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
\(867\) − 243984.i − 0.324581i
\(868\) 0 0
\(869\) 888191. 1.17616
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 703664.i 0.923287i
\(874\) 0 0
\(875\) 0 0
\(876\) 2.58454e6 3.36803
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) −2.91273e6 −3.76983
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) −96784.0 −0.123851
\(885\) 0 0
\(886\) 0 0
\(887\) 1.32950e6i 1.68983i 0.534904 + 0.844913i \(0.320348\pi\)
−0.534904 + 0.844913i \(0.679652\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.44942e6 −1.82573
\(892\) − 981488.i − 1.23355i
\(893\) 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
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 797168.i 0.966892i
\(909\) 0 0
\(910\) 0 0
\(911\) 1.15584e6 1.39271 0.696357 0.717696i \(-0.254803\pi\)
0.696357 + 0.717696i \(0.254803\pi\)
\(912\) 0 0
\(913\) 465886.i 0.558905i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 695113. 0.823047 0.411523 0.911399i \(-0.364997\pi\)
0.411523 + 0.911399i \(0.364997\pi\)
\(920\) 0 0
\(921\) −2.29947e6 −2.71087
\(922\) 0 0
\(923\) − 231794.i − 0.272081i
\(924\) −972944. −1.13958
\(925\) 0 0
\(926\) 0 0
\(927\) − 3.82366e6i − 4.44959i
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) − 1.58930e6i − 1.81020i −0.425195 0.905102i \(-0.639794\pi\)
0.425195 0.905102i \(-0.360206\pi\)
\(938\) 0 0
\(939\) −2.50065e6 −2.83610
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) − 3.30942e6i − 3.68244i
\(949\) 218546. 0.242667
\(950\) 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
\(956\) 693872. 0.759213
\(957\) 1.43087e6i 1.56235i
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 923521. 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 2.60250e6i 2.75459i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −2.98542e6 −3.10219
\(982\) 0 0
\(983\) − 675937.i − 0.699518i −0.936840 0.349759i \(-0.886263\pi\)
0.936840 0.349759i \(-0.113737\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) − 2.87968e6i − 2.95604i
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −1.44288e6 −1.46920 −0.734602 0.678498i \(-0.762631\pi\)
−0.734602 + 0.678498i \(0.762631\pi\)
\(992\) 0 0
\(993\) − 2.35419e6i − 2.38750i
\(994\) 0 0
\(995\) 0 0
\(996\) 1.73590e6 1.74988
\(997\) − 737783.i − 0.742230i −0.928587 0.371115i \(-0.878976\pi\)
0.928587 0.371115i \(-0.121024\pi\)
\(998\) 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 175.5.d.c.76.1 2
5.2 odd 4 35.5.c.a.34.1 1
5.3 odd 4 35.5.c.b.34.1 yes 1
5.4 even 2 inner 175.5.d.c.76.2 2
7.6 odd 2 inner 175.5.d.c.76.2 2
15.2 even 4 315.5.e.a.244.1 1
15.8 even 4 315.5.e.b.244.1 1
20.3 even 4 560.5.p.a.209.1 1
20.7 even 4 560.5.p.b.209.1 1
35.13 even 4 35.5.c.a.34.1 1
35.27 even 4 35.5.c.b.34.1 yes 1
35.34 odd 2 CM 175.5.d.c.76.1 2
105.62 odd 4 315.5.e.b.244.1 1
105.83 odd 4 315.5.e.a.244.1 1
140.27 odd 4 560.5.p.a.209.1 1
140.83 odd 4 560.5.p.b.209.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.5.c.a.34.1 1 5.2 odd 4
35.5.c.a.34.1 1 35.13 even 4
35.5.c.b.34.1 yes 1 5.3 odd 4
35.5.c.b.34.1 yes 1 35.27 even 4
175.5.d.c.76.1 2 1.1 even 1 trivial
175.5.d.c.76.1 2 35.34 odd 2 CM
175.5.d.c.76.2 2 5.4 even 2 inner
175.5.d.c.76.2 2 7.6 odd 2 inner
315.5.e.a.244.1 1 15.2 even 4
315.5.e.a.244.1 1 105.83 odd 4
315.5.e.b.244.1 1 15.8 even 4
315.5.e.b.244.1 1 105.62 odd 4
560.5.p.a.209.1 1 20.3 even 4
560.5.p.a.209.1 1 140.27 odd 4
560.5.p.b.209.1 1 20.7 even 4
560.5.p.b.209.1 1 140.83 odd 4