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Properties

Label 3.175.b.a.2.1
Level $3$
Weight $175$
Character 3.2
Self dual yes
Analytic conductor $575.181$
Analytic rank $0$
Dimension $1$
CM discriminant -3
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3,175,Mod(2,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 175, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 175);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 175 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(575.181361704\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 2.1
Character \(\chi\) \(=\) 3.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.23258e41 q^{3} +2.39452e52 q^{4} +6.34208e72 q^{7} +1.04496e83 q^{9} +O(q^{10})\) \(q-3.23258e41 q^{3} +2.39452e52 q^{4} +6.34208e72 q^{7} +1.04496e83 q^{9} -7.74049e93 q^{12} -3.33900e96 q^{13} +5.73375e104 q^{16} -1.44617e111 q^{19} -2.05013e114 q^{21} +4.17619e121 q^{25} -3.37791e124 q^{27} +1.51863e125 q^{28} -5.08796e129 q^{31} +2.50217e135 q^{36} +9.80719e135 q^{37} +1.07936e138 q^{39} -1.27381e142 q^{43} -1.85348e146 q^{48} -1.07422e147 q^{49} -7.99532e148 q^{52} +4.67485e152 q^{57} -6.35015e154 q^{61} +6.62719e155 q^{63} +1.37296e157 q^{64} +1.21979e159 q^{67} +9.73521e161 q^{73} -1.34999e163 q^{75} -3.46288e163 q^{76} +5.44572e164 q^{79} +1.09193e166 q^{81} -4.90908e166 q^{84} -2.11762e169 q^{91} +1.64472e171 q^{93} -1.10421e173 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) −3.23258e41 −1.00000
\(4\) 2.39452e52 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) 6.34208e72 0.189977 0.0949887 − 0.995478i \(-0.469719\pi\)
0.0949887 + 0.995478i \(0.469719\pi\)
\(8\) 0 0
\(9\) 1.04496e83 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −7.74049e93 −1.00000
\(13\) −3.33900e96 −0.407892 −0.203946 − 0.978982i \(-0.565377\pi\)
−0.203946 + 0.978982i \(0.565377\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 5.73375e104 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) −1.44617e111 −0.810317 −0.405158 − 0.914247i \(-0.632784\pi\)
−0.405158 + 0.914247i \(0.632784\pi\)
\(20\) 0 0
\(21\) −2.05013e114 −0.189977
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 4.17619e121 1.00000
\(26\) 0 0
\(27\) −3.37791e124 −1.00000
\(28\) 1.51863e125 0.189977
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −5.08796e129 −0.907979 −0.453990 − 0.891007i \(-0.650000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 2.50217e135 1.00000
\(37\) 9.80719e135 0.361405 0.180703 − 0.983538i \(-0.442163\pi\)
0.180703 + 0.983538i \(0.442163\pi\)
\(38\) 0 0
\(39\) 1.07936e138 0.407892
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −1.27381e142 −0.984799 −0.492400 − 0.870369i \(-0.663880\pi\)
−0.492400 + 0.870369i \(0.663880\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −1.85348e146 −1.00000
\(49\) −1.07422e147 −0.963909
\(50\) 0 0
\(51\) 0 0
\(52\) −7.99532e148 −0.407892
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.67485e152 0.810317
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −6.35015e154 −0.301362 −0.150681 − 0.988582i \(-0.548147\pi\)
−0.150681 + 0.988582i \(0.548147\pi\)
\(62\) 0 0
\(63\) 6.62719e155 0.189977
\(64\) 1.37296e157 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 1.21979e159 1.65111 0.825554 − 0.564323i \(-0.190863\pi\)
0.825554 + 0.564323i \(0.190863\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 9.73521e161 0.757280 0.378640 − 0.925544i \(-0.376392\pi\)
0.378640 + 0.925544i \(0.376392\pi\)
\(74\) 0 0
\(75\) −1.34999e163 −1.00000
\(76\) −3.46288e163 −0.810317
\(77\) 0 0
\(78\) 0 0
\(79\) 5.44572e164 0.439034 0.219517 − 0.975609i \(-0.429552\pi\)
0.219517 + 0.975609i \(0.429552\pi\)
\(80\) 0 0
\(81\) 1.09193e166 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −4.90908e166 −0.189977
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −2.11762e169 −0.0774902
\(92\) 0 0
\(93\) 1.64472e171 0.907979
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.10421e173 −1.56282 −0.781411 − 0.624017i \(-0.785499\pi\)
−0.781411 + 0.624017i \(0.785499\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000e174 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −9.19177e172 −0.00702361 −0.00351181 − 0.999994i \(-0.501118\pi\)
−0.00351181 + 0.999994i \(0.501118\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −8.08848e176 −1.00000
\(109\) 1.99772e177 1.10772 0.553860 − 0.832610i \(-0.313154\pi\)
0.553860 + 0.832610i \(0.313154\pi\)
\(110\) 0 0
\(111\) −3.17025e177 −0.361405
\(112\) 3.63639e177 0.189977
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −3.48911e179 −0.407892
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.59341e181 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) −1.21832e182 −0.907979
\(125\) 0 0
\(126\) 0 0
\(127\) −2.81479e182 −0.262134 −0.131067 − 0.991374i \(-0.541840\pi\)
−0.131067 + 0.991374i \(0.541840\pi\)
\(128\) 0 0
\(129\) 4.11768e183 0.984799
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) −9.17169e183 −0.153942
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 3.16735e186 1.14395 0.571976 − 0.820270i \(-0.306177\pi\)
0.571976 + 0.820270i \(0.306177\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 5.99152e187 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 3.47251e188 0.963909
\(148\) 2.34835e188 0.361405
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 7.33778e189 1.97047 0.985236 − 0.171204i \(-0.0547656\pi\)
0.985236 + 0.171204i \(0.0547656\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 2.58455e190 0.407892
\(157\) 1.90581e191 1.72508 0.862539 − 0.505990i \(-0.168873\pi\)
0.862539 + 0.505990i \(0.168873\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.61822e192 −0.907160 −0.453580 − 0.891216i \(-0.649853\pi\)
−0.453580 + 0.891216i \(0.649853\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −5.58617e193 −0.833624
\(170\) 0 0
\(171\) −1.51118e194 −0.810317
\(172\) −3.05016e194 −0.984799
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 2.64857e194 0.189977
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 1.24649e196 0.476050 0.238025 − 0.971259i \(-0.423500\pi\)
0.238025 + 0.971259i \(0.423500\pi\)
\(182\) 0 0
\(183\) 2.05274e196 0.301362
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −2.14229e197 −0.189977
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −4.43820e198 −1.00000
\(193\) −1.39415e199 −1.99906 −0.999528 − 0.0307305i \(-0.990217\pi\)
−0.999528 + 0.0307305i \(0.990217\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −2.57226e199 −0.963909
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −1.68133e200 −1.68049 −0.840243 − 0.542210i \(-0.817588\pi\)
−0.840243 + 0.542210i \(0.817588\pi\)
\(200\) 0 0
\(201\) −3.94305e200 −1.65111
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −1.91450e201 −0.407892
\(209\) 0 0
\(210\) 0 0
\(211\) −1.88416e202 −1.15490 −0.577449 − 0.816427i \(-0.695952\pi\)
−0.577449 + 0.816427i \(0.695952\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −3.22682e202 −0.172496
\(218\) 0 0
\(219\) −3.14698e203 −0.757280
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 2.19145e204 1.09196 0.545982 − 0.837797i \(-0.316157\pi\)
0.545982 + 0.837797i \(0.316157\pi\)
\(224\) 0 0
\(225\) 4.36394e204 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 1.11940e205 0.810317
\(229\) 3.93745e205 1.94773 0.973864 − 0.227133i \(-0.0729351\pi\)
0.973864 + 0.227133i \(0.0729351\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.76037e206 −0.439034
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −3.29899e207 −1.91822 −0.959109 − 0.283036i \(-0.908658\pi\)
−0.959109 + 0.283036i \(0.908658\pi\)
\(242\) 0 0
\(243\) −3.52977e207 −1.00000
\(244\) −1.52056e207 −0.301362
\(245\) 0 0
\(246\) 0 0
\(247\) 4.82875e207 0.330521
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 1.58690e208 0.189977
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 3.28758e209 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 6.21979e208 0.0686588
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 2.92080e211 1.65111
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −5.05455e211 −1.08481 −0.542405 − 0.840117i \(-0.682486\pi\)
−0.542405 + 0.840117i \(0.682486\pi\)
\(272\) 0 0
\(273\) 6.84537e210 0.0774902
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −2.82306e212 −0.901529 −0.450764 − 0.892643i \(-0.648849\pi\)
−0.450764 + 0.892643i \(0.648849\pi\)
\(278\) 0 0
\(279\) −5.31669e212 −0.907979
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −1.34510e213 −0.665784 −0.332892 − 0.942965i \(-0.608024\pi\)
−0.332892 + 0.942965i \(0.608024\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.25347e214 1.00000
\(290\) 0 0
\(291\) 3.56943e214 1.56282
\(292\) 2.33112e214 0.757280
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −3.23258e215 −1.00000
\(301\) −8.07858e214 −0.187090
\(302\) 0 0
\(303\) 0 0
\(304\) −8.29195e215 −0.810317
\(305\) 0 0
\(306\) 0 0
\(307\) −3.27728e216 −1.36294 −0.681468 − 0.731848i \(-0.738658\pi\)
−0.681468 + 0.731848i \(0.738658\pi\)
\(308\) 0 0
\(309\) 2.97131e214 0.00702361
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 2.25802e217 1.74330 0.871648 − 0.490133i \(-0.163052\pi\)
0.871648 + 0.490133i \(0.163052\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.30399e217 0.439034
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 2.61466e218 1.00000
\(325\) −1.39443e218 −0.407892
\(326\) 0 0
\(327\) −6.45780e218 −1.10772
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.35415e218 −0.140216 −0.0701081 − 0.997539i \(-0.522334\pi\)
−0.0701081 + 0.997539i \(0.522334\pi\)
\(332\) 0 0
\(333\) 1.02481e219 0.361405
\(334\) 0 0
\(335\) 0 0
\(336\) −1.17549e219 −0.189977
\(337\) −3.30755e219 −0.412767 −0.206383 − 0.978471i \(-0.566169\pi\)
−0.206383 + 0.978471i \(0.566169\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.38807e220 −0.373098
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 2.20605e221 1.31160 0.655802 − 0.754933i \(-0.272331\pi\)
0.655802 + 0.754933i \(0.272331\pi\)
\(350\) 0 0
\(351\) 1.12788e221 0.407892
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) −1.09373e222 −0.343387
\(362\) 0 0
\(363\) −5.15082e222 −1.00000
\(364\) −5.07069e221 −0.0774902
\(365\) 0 0
\(366\) 0 0
\(367\) −2.12630e223 −1.59103 −0.795513 − 0.605937i \(-0.792798\pi\)
−0.795513 + 0.605937i \(0.792798\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 3.93833e223 0.907979
\(373\) 1.09498e224 1.99865 0.999326 − 0.0367030i \(-0.0116855\pi\)
0.999326 + 0.0367030i \(0.0116855\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 5.29010e223 0.240909 0.120454 − 0.992719i \(-0.461565\pi\)
0.120454 + 0.992719i \(0.461565\pi\)
\(380\) 0 0
\(381\) 9.09904e223 0.262134
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.33107e225 −0.984799
\(388\) −2.64405e225 −1.56282
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 8.42574e225 0.677383 0.338691 − 0.940898i \(-0.390016\pi\)
0.338691 + 0.940898i \(0.390016\pi\)
\(398\) 0 0
\(399\) 2.96482e225 0.153942
\(400\) 2.39452e226 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 1.69887e226 0.370357
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.35431e227 −0.816187 −0.408093 − 0.912940i \(-0.633806\pi\)
−0.408093 + 0.912940i \(0.633806\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −2.20099e225 −0.00702361
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.02387e228 −1.14395
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 1.99690e228 0.972329 0.486164 − 0.873867i \(-0.338396\pi\)
0.486164 + 0.873867i \(0.338396\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −4.02731e227 −0.0572520
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −1.93681e229 −1.00000
\(433\) 2.31709e229 0.978355 0.489178 − 0.872184i \(-0.337297\pi\)
0.489178 + 0.872184i \(0.337297\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 4.78360e229 1.10772
\(437\) 0 0
\(438\) 0 0
\(439\) 1.44930e229 0.184818 0.0924090 − 0.995721i \(-0.470543\pi\)
0.0924090 + 0.995721i \(0.470543\pi\)
\(440\) 0 0
\(441\) −1.12252e230 −0.963909
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −7.59124e229 −0.361405
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 8.70741e229 0.189977
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −2.37199e231 −1.97047
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 5.02876e231 1.94425 0.972123 − 0.234470i \(-0.0753354\pi\)
0.972123 + 0.234470i \(0.0753354\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 1.20781e232 1.50125 0.750623 − 0.660731i \(-0.229753\pi\)
0.750623 + 0.660731i \(0.229753\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −8.35476e231 −0.407892
\(469\) 7.73597e231 0.313673
\(470\) 0 0
\(471\) −6.16067e232 −1.72508
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −6.03947e232 −0.810317
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) −3.27462e232 −0.147414
\(482\) 0 0
\(483\) 0 0
\(484\) 3.81546e233 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 5.87439e233 0.899380 0.449690 − 0.893185i \(-0.351534\pi\)
0.449690 + 0.893185i \(0.351534\pi\)
\(488\) 0 0
\(489\) 8.46359e233 0.907160
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −2.91731e234 −0.907979
\(497\) 0 0
\(498\) 0 0
\(499\) −8.33315e234 −1.53483 −0.767417 − 0.641148i \(-0.778458\pi\)
−0.767417 + 0.641148i \(0.778458\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.80577e235 0.833624
\(508\) −6.74009e234 −0.262134
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 6.17414e234 0.143866
\(512\) 0 0
\(513\) 4.88501e235 0.810317
\(514\) 0 0
\(515\) 0 0
\(516\) 9.85989e235 0.984799
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −4.38977e236 −1.35767 −0.678837 − 0.734289i \(-0.737516\pi\)
−0.678837 + 0.734289i \(0.737516\pi\)
\(524\) 0 0
\(525\) −8.56173e235 −0.189977
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 8.72255e236 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) −2.19618e236 −0.153942
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 7.83891e237 1.27671 0.638357 − 0.769740i \(-0.279614\pi\)
0.638357 + 0.769740i \(0.279614\pi\)
\(542\) 0 0
\(543\) −4.02937e237 −0.476050
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 2.68403e238 1.67452 0.837261 − 0.546804i \(-0.184156\pi\)
0.837261 + 0.546804i \(0.184156\pi\)
\(548\) 0 0
\(549\) −6.63563e237 −0.301362
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 3.45372e237 0.0834066
\(554\) 0 0
\(555\) 0 0
\(556\) 7.58429e238 1.14395
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 4.25324e238 0.401691
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 6.92513e238 0.189977
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 1.28787e240 1.91660 0.958299 − 0.285767i \(-0.0922485\pi\)
0.958299 + 0.285767i \(0.0922485\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.43468e240 1.00000
\(577\) 2.66905e240 1.59979 0.799893 − 0.600143i \(-0.204890\pi\)
0.799893 + 0.600143i \(0.204890\pi\)
\(578\) 0 0
\(579\) 4.50671e240 1.99906
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 8.31502e240 0.963909
\(589\) 7.35803e240 0.735751
\(590\) 0 0
\(591\) 0 0
\(592\) 5.62319e240 0.361405
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 5.43503e241 1.68049
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 1.14585e242 1.98175 0.990875 − 0.134786i \(-0.0430346\pi\)
0.990875 + 0.134786i \(0.0430346\pi\)
\(602\) 0 0
\(603\) 1.27462e242 1.65111
\(604\) 1.75705e242 1.97047
\(605\) 0 0
\(606\) 0 0
\(607\) 2.45101e242 1.78619 0.893096 − 0.449865i \(-0.148528\pi\)
0.893096 + 0.449865i \(0.148528\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 4.38306e242 1.35742 0.678712 − 0.734404i \(-0.262538\pi\)
0.678712 + 0.734404i \(0.262538\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 8.42535e242 1.11815 0.559077 − 0.829116i \(-0.311156\pi\)
0.559077 + 0.829116i \(0.311156\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 6.18877e242 0.407892
\(625\) 1.74406e243 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 4.56350e243 1.72508
\(629\) 0 0
\(630\) 0 0
\(631\) 7.59735e243 1.89718 0.948588 − 0.316513i \(-0.102512\pi\)
0.948588 + 0.316513i \(0.102512\pi\)
\(632\) 0 0
\(633\) 6.09068e243 1.15490
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 3.58683e243 0.393170
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) −2.09079e244 −1.01381 −0.506905 − 0.862002i \(-0.669210\pi\)
−0.506905 + 0.862002i \(0.669210\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 1.04310e244 0.172496
\(652\) −6.26938e244 −0.907160
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1.01729e245 0.757280
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −4.47697e245 −1.96543 −0.982714 − 0.185128i \(-0.940730\pi\)
−0.982714 + 0.185128i \(0.940730\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −7.08403e245 −1.09196
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −2.17172e246 −1.99293 −0.996466 − 0.0839978i \(-0.973231\pi\)
−0.996466 + 0.0839978i \(0.973231\pi\)
\(674\) 0 0
\(675\) −1.41068e246 −1.00000
\(676\) −1.33762e246 −0.833624
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) −7.00296e245 −0.296901
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −3.61856e246 −0.810317
\(685\) 0 0
\(686\) 0 0
\(687\) −1.27281e247 −1.94773
\(688\) −7.30368e246 −0.984799
\(689\) 0 0
\(690\) 0 0
\(691\) −2.66135e246 −0.245760 −0.122880 − 0.992422i \(-0.539213\pi\)
−0.122880 + 0.992422i \(0.539213\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 6.34208e246 0.189977
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) −1.41828e247 −0.292853
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −5.49051e247 −0.541240 −0.270620 − 0.962686i \(-0.587229\pi\)
−0.270620 + 0.962686i \(0.587229\pi\)
\(710\) 0 0
\(711\) 5.69054e247 0.439034
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) −5.82949e245 −0.00133433
\(722\) 0 0
\(723\) 1.06642e249 1.91822
\(724\) 2.98475e248 0.476050
\(725\) 0 0
\(726\) 0 0
\(727\) 1.61918e249 1.80220 0.901099 − 0.433614i \(-0.142762\pi\)
0.901099 + 0.433614i \(0.142762\pi\)
\(728\) 0 0
\(729\) 1.14102e249 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 4.91533e248 0.301362
\(733\) 3.10078e249 1.68820 0.844101 − 0.536184i \(-0.180134\pi\)
0.844101 + 0.536184i \(0.180134\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1.03259e249 0.276606 0.138303 − 0.990390i \(-0.455835\pi\)
0.138303 + 0.990390i \(0.455835\pi\)
\(740\) 0 0
\(741\) −1.56093e249 −0.330521
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 2.49765e250 1.64762 0.823809 − 0.566867i \(-0.191845\pi\)
0.823809 + 0.566867i \(0.191845\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −5.12977e249 −0.189977
\(757\) 4.19746e250 1.38562 0.692811 − 0.721119i \(-0.256372\pi\)
0.692811 + 0.721119i \(0.256372\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 1.26697e250 0.210442
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1.06274e251 −1.00000
\(769\) −2.38018e251 −1.99995 −0.999974 − 0.00722406i \(-0.997700\pi\)
−0.999974 + 0.00722406i \(0.997700\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3.33834e251 −1.99906
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) −2.12483e251 −0.907979
\(776\) 0 0
\(777\) −2.01060e250 −0.0686588
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −6.15933e251 −0.963909
\(785\) 0 0
\(786\) 0 0
\(787\) −4.33565e251 −0.486690 −0.243345 − 0.969940i \(-0.578245\pi\)
−0.243345 + 0.969940i \(0.578245\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 2.12032e251 0.122923
\(794\) 0 0
\(795\) 0 0
\(796\) −4.02598e252 −1.68049
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) −9.44173e252 −1.65111
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 2.12045e253 1.74427 0.872136 − 0.489263i \(-0.162734\pi\)
0.872136 + 0.489263i \(0.162734\pi\)
\(812\) 0 0
\(813\) 1.63392e253 1.08481
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1.84214e253 0.798000
\(818\) 0 0
\(819\) −2.21282e252 −0.0774902
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 7.54838e253 1.73009 0.865044 − 0.501696i \(-0.167291\pi\)
0.865044 + 0.501696i \(0.167291\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 1.15864e254 1.41157 0.705787 − 0.708424i \(-0.250594\pi\)
0.705787 + 0.708424i \(0.250594\pi\)
\(830\) 0 0
\(831\) 9.12575e253 0.901529
\(832\) −4.58431e253 −0.407892
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.71866e254 0.907979
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 2.86584e254 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) −4.51166e254 −1.15490
\(845\) 0 0
\(846\) 0 0
\(847\) 1.01055e254 0.189977
\(848\) 0 0
\(849\) 4.34813e254 0.665784
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −5.17278e254 −0.526209 −0.263104 − 0.964767i \(-0.584746\pi\)
−0.263104 + 0.964767i \(0.584746\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −1.26473e255 −0.699186 −0.349593 − 0.936902i \(-0.613680\pi\)
−0.349593 + 0.936902i \(0.613680\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −4.05193e255 −1.00000
\(868\) −7.72670e254 −0.172496
\(869\) 0 0
\(870\) 0 0
\(871\) −4.07286e255 −0.673473
\(872\) 0 0
\(873\) −1.15385e256 −1.56282
\(874\) 0 0
\(875\) 0 0
\(876\) −7.53553e255 −0.757280
\(877\) −2.00398e256 −1.82360 −0.911798 − 0.410638i \(-0.865306\pi\)
−0.911798 + 0.410638i \(0.865306\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 2.71697e255 0.136617 0.0683083 − 0.997664i \(-0.478240\pi\)
0.0683083 + 0.997664i \(0.478240\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −1.78516e255 −0.0497994
\(890\) 0 0
\(891\) 0 0
\(892\) 5.24748e256 1.09196
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 1.04496e257 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) 2.61146e256 0.187090
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −3.11490e257 −1.51918 −0.759592 − 0.650400i \(-0.774601\pi\)
−0.759592 + 0.650400i \(0.774601\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 2.68044e257 0.810317
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 9.42832e257 1.94773
\(917\) 0 0
\(918\) 0 0
\(919\) 1.23954e258 1.92669 0.963344 − 0.268271i \(-0.0864521\pi\)
0.963344 + 0.268271i \(0.0864521\pi\)
\(920\) 0 0
\(921\) 1.05941e258 1.36294
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 4.09567e257 0.361405
\(926\) 0 0
\(927\) −9.60500e255 −0.00702361
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 1.55351e258 0.781071
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −4.20401e258 −1.20870 −0.604351 − 0.796718i \(-0.706567\pi\)
−0.604351 + 0.796718i \(0.706567\pi\)
\(938\) 0 0
\(939\) −7.29924e258 −1.74330
\(940\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) −4.21526e258 −0.439034
\(949\) −3.25059e258 −0.308888
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −5.51307e258 −0.175573
\(962\) 0 0
\(963\) 0 0
\(964\) −7.89951e259 −1.91822
\(965\) 0 0
\(966\) 0 0
\(967\) −9.86261e259 −1.82763 −0.913815 − 0.406130i \(-0.866878\pi\)
−0.913815 + 0.406130i \(0.866878\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −8.45211e259 −1.00000
\(973\) 2.00876e259 0.217325
\(974\) 0 0
\(975\) 4.50761e259 0.407892
\(976\) −3.64102e259 −0.301362
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 2.08753e260 1.10772
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 1.15626e260 0.330521
\(989\) 0 0
\(990\) 0 0
\(991\) 8.20726e260 1.80215 0.901074 − 0.433666i \(-0.142780\pi\)
0.901074 + 0.433666i \(0.142780\pi\)
\(992\) 0 0
\(993\) 7.60997e259 0.140216
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1.26689e261 1.64536 0.822680 − 0.568505i \(-0.192478\pi\)
0.822680 + 0.568505i \(0.192478\pi\)
\(998\) 0 0
\(999\) −3.31277e260 −0.361405
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 3.175.b.a.2.1 ✓ 1
3.2 odd 2 CM 3.175.b.a.2.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.175.b.a.2.1 ✓ 1 1.1 even 1 trivial
3.175.b.a.2.1 ✓ 1 3.2 odd 2 CM