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Properties

Label 75.15.c.b.26.1
Level $75$
Weight $15$
Character 75.26
Self dual yes
Analytic conductor $93.247$
Analytic rank $0$
Dimension $1$
CM discriminant -3
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,15,Mod(26,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.26");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 75.c (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: \(93.2467261139\)
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 26.1
Character \(\chi\) \(=\) 75.26

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2187.00 q^{3} +16384.0 q^{4} +72061.0 q^{7} +4.78297e6 q^{9} +O(q^{10})\) \(q+2187.00 q^{3} +16384.0 q^{4} +72061.0 q^{7} +4.78297e6 q^{9} +3.58318e7 q^{12} -3.33890e7 q^{13} +2.68435e8 q^{16} +6.90908e7 q^{19} +1.57597e8 q^{21} +1.04604e10 q^{27} +1.18065e9 q^{28} +5.47921e10 q^{31} +7.83642e10 q^{36} +1.11626e11 q^{37} -7.30217e10 q^{39} +3.75951e11 q^{43} +5.87068e11 q^{48} -6.73030e11 q^{49} -5.47045e11 q^{52} +1.51102e11 q^{57} -2.29209e12 q^{61} +3.44666e11 q^{63} +4.39805e12 q^{64} -4.34963e12 q^{67} -1.72784e13 q^{73} +1.13198e12 q^{76} +3.83831e13 q^{79} +2.28768e13 q^{81} +2.58208e12 q^{84} -2.40604e12 q^{91} +1.19830e14 q^{93} -1.45408e14 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(1\)

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 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) 2187.00 1.00000
\(4\) 16384.0 1.00000
\(5\) 0 0
\(6\) 0 0
\(7\) 72061.0 0.0875012 0.0437506 − 0.999042i \(-0.486069\pi\)
0.0437506 + 0.999042i \(0.486069\pi\)
\(8\) 0 0
\(9\) 4.78297e6 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 3.58318e7 1.00000
\(13\) −3.33890e7 −0.532108 −0.266054 − 0.963958i \(-0.585720\pi\)
−0.266054 + 0.963958i \(0.585720\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.68435e8 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 6.90908e7 0.0772939 0.0386469 − 0.999253i \(-0.487695\pi\)
0.0386469 + 0.999253i \(0.487695\pi\)
\(20\) 0 0
\(21\) 1.57597e8 0.0875012
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.04604e10 1.00000
\(28\) 1.18065e9 0.0875012
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 5.47921e10 1.99153 0.995764 − 0.0919510i \(-0.0293103\pi\)
0.995764 + 0.0919510i \(0.0293103\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 7.83642e10 1.00000
\(37\) 1.11626e11 1.17585 0.587927 − 0.808914i \(-0.299944\pi\)
0.587927 + 0.808914i \(0.299944\pi\)
\(38\) 0 0
\(39\) −7.30217e10 −0.532108
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 3.75951e11 1.38310 0.691548 − 0.722331i \(-0.256929\pi\)
0.691548 + 0.722331i \(0.256929\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 5.87068e11 1.00000
\(49\) −6.73030e11 −0.992344
\(50\) 0 0
\(51\) 0 0
\(52\) −5.47045e11 −0.532108
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.51102e11 0.0772939
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −2.29209e12 −0.729329 −0.364665 − 0.931139i \(-0.618816\pi\)
−0.364665 + 0.931139i \(0.618816\pi\)
\(62\) 0 0
\(63\) 3.44666e11 0.0875012
\(64\) 4.39805e12 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −4.34963e12 −0.717677 −0.358839 − 0.933400i \(-0.616827\pi\)
−0.358839 + 0.933400i \(0.616827\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −1.72784e13 −1.56403 −0.782014 − 0.623261i \(-0.785808\pi\)
−0.782014 + 0.623261i \(0.785808\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 1.13198e12 0.0772939
\(77\) 0 0
\(78\) 0 0
\(79\) 3.83831e13 1.99871 0.999357 − 0.0358548i \(-0.0114154\pi\)
0.999357 + 0.0358548i \(0.0114154\pi\)
\(80\) 0 0
\(81\) 2.28768e13 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 2.58208e12 0.0875012
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −2.40604e12 −0.0465601
\(92\) 0 0
\(93\) 1.19830e14 1.99153
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.45408e14 −1.79965 −0.899823 − 0.436255i \(-0.856305\pi\)
−0.899823 + 0.436255i \(0.856305\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 1.81555e14 1.47620 0.738102 − 0.674689i \(-0.235722\pi\)
0.738102 + 0.674689i \(0.235722\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 1.71382e14 1.00000
\(109\) 3.49727e14 1.91313 0.956564 − 0.291523i \(-0.0941618\pi\)
0.956564 + 0.291523i \(0.0941618\pi\)
\(110\) 0 0
\(111\) 2.44126e14 1.17585
\(112\) 1.93437e13 0.0875012
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.59699e14 −0.532108
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 3.79750e14 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 8.97714e14 1.99153
\(125\) 0 0
\(126\) 0 0
\(127\) −9.70570e14 −1.82138 −0.910690 − 0.413090i \(-0.864450\pi\)
−0.910690 + 0.413090i \(0.864450\pi\)
\(128\) 0 0
\(129\) 8.22205e14 1.38310
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 4.97875e12 0.00676331
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 1.05578e15 1.05310 0.526549 − 0.850144i \(-0.323485\pi\)
0.526549 + 0.850144i \(0.323485\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.28392e15 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −1.47192e15 −0.992344
\(148\) 1.82888e15 1.17585
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 1.15734e15 0.646580 0.323290 − 0.946300i \(-0.395211\pi\)
0.323290 + 0.946300i \(0.395211\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.19639e15 −0.532108
\(157\) −2.66451e15 −1.13324 −0.566618 − 0.823981i \(-0.691748\pi\)
−0.566618 + 0.823981i \(0.691748\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 5.88848e15 1.92615 0.963075 − 0.269232i \(-0.0867698\pi\)
0.963075 + 0.269232i \(0.0867698\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −2.82255e15 −0.716861
\(170\) 0 0
\(171\) 3.30459e14 0.0772939
\(172\) 6.15958e15 1.38310
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 1.08982e16 1.71239 0.856196 − 0.516652i \(-0.172822\pi\)
0.856196 + 0.516652i \(0.172822\pi\)
\(182\) 0 0
\(183\) −5.01281e15 −0.729329
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 7.53784e14 0.0875012
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 9.61853e15 1.00000
\(193\) −1.99346e16 −1.99851 −0.999256 − 0.0385736i \(-0.987719\pi\)
−0.999256 + 0.0385736i \(0.987719\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.10269e16 −0.992344
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −1.92800e16 −1.56004 −0.780021 − 0.625753i \(-0.784792\pi\)
−0.780021 + 0.625753i \(0.784792\pi\)
\(200\) 0 0
\(201\) −9.51265e15 −0.717677
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −8.96279e15 −0.532108
\(209\) 0 0
\(210\) 0 0
\(211\) −3.64059e16 −1.95521 −0.977606 − 0.210442i \(-0.932510\pi\)
−0.977606 + 0.210442i \(0.932510\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3.94837e15 0.174261
\(218\) 0 0
\(219\) −3.77880e16 −1.56403
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −3.87320e16 −1.41233 −0.706164 − 0.708048i \(-0.749576\pi\)
−0.706164 + 0.708048i \(0.749576\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 2.47565e15 0.0772939
\(229\) −3.99522e16 −1.20974 −0.604871 − 0.796323i \(-0.706775\pi\)
−0.604871 + 0.796323i \(0.706775\pi\)
\(230\) 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
\(237\) 8.39439e16 1.99871
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 2.40780e16 0.509918 0.254959 − 0.966952i \(-0.417938\pi\)
0.254959 + 0.966952i \(0.417938\pi\)
\(242\) 0 0
\(243\) 5.00315e16 1.00000
\(244\) −3.75537e16 −0.729329
\(245\) 0 0
\(246\) 0 0
\(247\) −2.30687e15 −0.0411287
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 5.64700e15 0.0875012
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 7.20576e16 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 8.04389e15 0.102889
\(260\) 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
\(268\) −7.12644e16 −0.717677
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 2.10731e16 0.196311 0.0981554 − 0.995171i \(-0.468706\pi\)
0.0981554 + 0.995171i \(0.468706\pi\)
\(272\) 0 0
\(273\) −5.26202e15 −0.0465601
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.28697e17 −1.02851 −0.514256 − 0.857637i \(-0.671932\pi\)
−0.514256 + 0.857637i \(0.671932\pi\)
\(278\) 0 0
\(279\) 2.62069e17 1.99153
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 1.94118e17 1.33524 0.667622 − 0.744501i \(-0.267312\pi\)
0.667622 + 0.744501i \(0.267312\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.68378e17 1.00000
\(290\) 0 0
\(291\) −3.18008e17 −1.79965
\(292\) −2.83090e17 −1.56403
\(293\) 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
\(300\) 0 0
\(301\) 2.70914e16 0.121023
\(302\) 0 0
\(303\) 0 0
\(304\) 1.85464e16 0.0772939
\(305\) 0 0
\(306\) 0 0
\(307\) −3.95714e17 −1.53962 −0.769808 − 0.638275i \(-0.779648\pi\)
−0.769808 + 0.638275i \(0.779648\pi\)
\(308\) 0 0
\(309\) 3.97060e17 1.47620
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 2.78369e17 0.945825 0.472912 − 0.881109i \(-0.343203\pi\)
0.472912 + 0.881109i \(0.343203\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 6.28869e17 1.99871
\(317\) 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
\(324\) 3.74813e17 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 7.64854e17 1.91313
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 6.86499e17 1.57704 0.788522 − 0.615007i \(-0.210847\pi\)
0.788522 + 0.615007i \(0.210847\pi\)
\(332\) 0 0
\(333\) 5.33904e17 1.17585
\(334\) 0 0
\(335\) 0 0
\(336\) 4.23047e16 0.0875012
\(337\) −3.30843e17 −0.670213 −0.335106 − 0.942180i \(-0.608772\pi\)
−0.335106 + 0.942180i \(0.608772\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −9.73727e16 −0.174332
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −7.77937e17 −1.23358 −0.616789 − 0.787129i \(-0.711567\pi\)
−0.616789 + 0.787129i \(0.711567\pi\)
\(350\) 0 0
\(351\) −3.49261e17 −0.532108
\(352\) 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
\(361\) −7.94233e17 −0.994026
\(362\) 0 0
\(363\) 8.30513e17 1.00000
\(364\) −3.94206e16 −0.0465601
\(365\) 0 0
\(366\) 0 0
\(367\) −1.63974e18 −1.82857 −0.914284 − 0.405073i \(-0.867246\pi\)
−0.914284 + 0.405073i \(0.867246\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 1.96330e18 1.99153
\(373\) −1.82585e18 −1.81762 −0.908812 − 0.417206i \(-0.863009\pi\)
−0.908812 + 0.417206i \(0.863009\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.56068e18 −1.38944 −0.694720 − 0.719280i \(-0.744472\pi\)
−0.694720 + 0.719280i \(0.744472\pi\)
\(380\) 0 0
\(381\) −2.12264e18 −1.82138
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.79816e18 1.38310
\(388\) −2.38237e18 −1.79965
\(389\) 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
\(397\) −2.38589e18 −1.53503 −0.767515 − 0.641031i \(-0.778507\pi\)
−0.767515 + 0.641031i \(0.778507\pi\)
\(398\) 0 0
\(399\) 1.08885e16 0.00676331
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) −1.82945e18 −1.05971
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −3.60890e18 −1.88500 −0.942501 − 0.334203i \(-0.891533\pi\)
−0.942501 + 0.334203i \(0.891533\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 2.97459e18 1.47620
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 2.30899e18 1.05310
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 3.16127e17 0.134861 0.0674305 − 0.997724i \(-0.478520\pi\)
0.0674305 + 0.997724i \(0.478520\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.65171e17 −0.0638172
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 2.80793e18 1.00000
\(433\) 8.49855e17 0.297803 0.148902 − 0.988852i \(-0.452426\pi\)
0.148902 + 0.988852i \(0.452426\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 5.72993e18 1.91313
\(437\) 0 0
\(438\) 0 0
\(439\) −6.12305e18 −1.94857 −0.974285 − 0.225319i \(-0.927657\pi\)
−0.974285 + 0.225319i \(0.927657\pi\)
\(440\) 0 0
\(441\) −3.21908e18 −0.992344
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 3.99976e18 1.17585
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 3.16928e17 0.0875012
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 2.53110e18 0.646580
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −8.21512e18 −1.97333 −0.986666 − 0.162756i \(-0.947962\pi\)
−0.986666 + 0.162756i \(0.947962\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 8.07617e18 1.77067 0.885337 − 0.464951i \(-0.153928\pi\)
0.885337 + 0.464951i \(0.153928\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −2.61650e18 −0.532108
\(469\) −3.13439e17 −0.0627976
\(470\) 0 0
\(471\) −5.82729e18 −1.13324
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) −3.72708e18 −0.625682
\(482\) 0 0
\(483\) 0 0
\(484\) 6.22182e18 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) −7.08110e18 −1.08993 −0.544964 − 0.838459i \(-0.683457\pi\)
−0.544964 + 0.838459i \(0.683457\pi\)
\(488\) 0 0
\(489\) 1.28781e19 1.92615
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.47081e19 1.99153
\(497\) 0 0
\(498\) 0 0
\(499\) 1.45193e19 1.88470 0.942349 − 0.334631i \(-0.108612\pi\)
0.942349 + 0.334631i \(0.108612\pi\)
\(500\) 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
\(507\) −6.17292e18 −0.716861
\(508\) −1.59018e19 −1.82138
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −1.24510e18 −0.136854
\(512\) 0 0
\(513\) 7.22714e17 0.0772939
\(514\) 0 0
\(515\) 0 0
\(516\) 1.34710e19 1.38310
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 1.99810e19 1.86683 0.933417 − 0.358793i \(-0.116812\pi\)
0.933417 + 0.358793i \(0.116812\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.15928e19 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 8.15719e16 0.00676331
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.36000e19 −1.00267 −0.501335 − 0.865253i \(-0.667157\pi\)
−0.501335 + 0.865253i \(0.667157\pi\)
\(542\) 0 0
\(543\) 2.38343e19 1.71239
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −6.51749e18 −0.444804 −0.222402 − 0.974955i \(-0.571390\pi\)
−0.222402 + 0.974955i \(0.571390\pi\)
\(548\) 0 0
\(549\) −1.09630e19 −0.729329
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 2.76593e18 0.174890
\(554\) 0 0
\(555\) 0 0
\(556\) 1.72979e19 1.05310
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) −1.25526e19 −0.735956
\(560\) 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
\(567\) 1.64852e18 0.0875012
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −3.28769e19 −1.66126 −0.830631 − 0.556823i \(-0.812020\pi\)
−0.830631 + 0.556823i \(0.812020\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 2.10357e19 1.00000
\(577\) 1.77893e19 0.835465 0.417732 − 0.908570i \(-0.362825\pi\)
0.417732 + 0.908570i \(0.362825\pi\)
\(578\) 0 0
\(579\) −4.35970e19 −1.99851
\(580\) 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 \(\pi\)
\(588\) −2.41159e19 −0.992344
\(589\) 3.78563e18 0.153933
\(590\) 0 0
\(591\) 0 0
\(592\) 2.99644e19 1.17585
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.21655e19 −1.56004
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −4.82150e19 −1.70240 −0.851198 − 0.524844i \(-0.824124\pi\)
−0.851198 + 0.524844i \(0.824124\pi\)
\(602\) 0 0
\(603\) −2.08042e19 −0.717677
\(604\) 1.89619e19 0.646580
\(605\) 0 0
\(606\) 0 0
\(607\) 5.51469e19 1.81635 0.908176 − 0.418588i \(-0.137475\pi\)
0.908176 + 0.418588i \(0.137475\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −6.22458e19 −1.91376 −0.956878 − 0.290491i \(-0.906181\pi\)
−0.956878 + 0.290491i \(0.906181\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −5.35981e19 −1.53927 −0.769636 − 0.638483i \(-0.779562\pi\)
−0.769636 + 0.638483i \(0.779562\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −1.96016e19 −0.532108
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) −4.36554e19 −1.13324
\(629\) 0 0
\(630\) 0 0
\(631\) 1.93152e19 0.484947 0.242474 − 0.970158i \(-0.422041\pi\)
0.242474 + 0.970158i \(0.422041\pi\)
\(632\) 0 0
\(633\) −7.96196e19 −1.95521
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 2.24718e19 0.528034
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 8.97867e19 1.97576 0.987882 − 0.155205i \(-0.0496038\pi\)
0.987882 + 0.155205i \(0.0496038\pi\)
\(644\) 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
\(651\) 8.63510e18 0.174261
\(652\) 9.64769e19 1.92615
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −8.26423e19 −1.56403
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −6.64598e19 −1.20545 −0.602725 − 0.797949i \(-0.705918\pi\)
−0.602725 + 0.797949i \(0.705918\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −8.47068e19 −1.41233
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.00073e20 1.60034 0.800170 − 0.599774i \(-0.204743\pi\)
0.800170 + 0.599774i \(0.204743\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −4.62447e19 −0.716861
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) −1.04783e19 −0.157471
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 5.41424e18 0.0772939
\(685\) 0 0
\(686\) 0 0
\(687\) −8.73756e19 −1.20974
\(688\) 1.00919e20 1.38310
\(689\) 0 0
\(690\) 0 0
\(691\) 8.09125e19 1.07565 0.537823 − 0.843058i \(-0.319247\pi\)
0.537823 + 0.843058i \(0.319247\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 7.71233e18 0.0908863
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.34674e20 1.49541 0.747704 − 0.664032i \(-0.231156\pi\)
0.747704 + 0.664032i \(0.231156\pi\)
\(710\) 0 0
\(711\) 1.83585e20 1.99871
\(712\) 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
\(721\) 1.30830e19 0.129170
\(722\) 0 0
\(723\) 5.26585e19 0.509918
\(724\) 1.78555e20 1.71239
\(725\) 0 0
\(726\) 0 0
\(727\) 5.74352e19 0.535103 0.267552 − 0.963544i \(-0.413785\pi\)
0.267552 + 0.963544i \(0.413785\pi\)
\(728\) 0 0
\(729\) 1.09419e20 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) −8.21299e19 −0.729329
\(733\) −1.63598e20 −1.43897 −0.719483 − 0.694510i \(-0.755621\pi\)
−0.719483 + 0.694510i \(0.755621\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1.21802e20 1.01191 0.505956 − 0.862559i \(-0.331140\pi\)
0.505956 + 0.862559i \(0.331140\pi\)
\(740\) 0 0
\(741\) −5.04513e18 −0.0411287
\(742\) 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
\(751\) −5.64342e19 −0.418854 −0.209427 − 0.977824i \(-0.567160\pi\)
−0.209427 + 0.977824i \(0.567160\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.23500e19 0.0875012
\(757\) −2.57679e20 −1.80887 −0.904436 − 0.426609i \(-0.859708\pi\)
−0.904436 + 0.426609i \(0.859708\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 2.52017e19 0.167401
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.57590e20 1.00000
\(769\) 2.72440e20 1.71311 0.856557 − 0.516052i \(-0.172599\pi\)
0.856557 + 0.516052i \(0.172599\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3.26609e20 −1.99851
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.75920e19 0.102889
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −1.80665e20 −0.992344
\(785\) 0 0
\(786\) 0 0
\(787\) 3.67789e20 1.96687 0.983434 − 0.181267i \(-0.0580197\pi\)
0.983434 + 0.181267i \(0.0580197\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 7.65307e19 0.388082
\(794\) 0 0
\(795\) 0 0
\(796\) −3.15884e20 −1.56004
\(797\) 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
\(804\) −1.55855e20 −0.717677
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 4.10527e20 1.77908 0.889541 − 0.456856i \(-0.151025\pi\)
0.889541 + 0.456856i \(0.151025\pi\)
\(812\) 0 0
\(813\) 4.60869e19 0.196311
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 2.59748e19 0.106905
\(818\) 0 0
\(819\) −1.15080e19 −0.0465601
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 1.75012e20 0.684337 0.342168 − 0.939639i \(-0.388839\pi\)
0.342168 + 0.939639i \(0.388839\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −4.98089e20 −1.85108 −0.925541 − 0.378648i \(-0.876389\pi\)
−0.925541 + 0.378648i \(0.876389\pi\)
\(830\) 0 0
\(831\) −2.81460e20 −1.02851
\(832\) −1.46846e20 −0.532108
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 5.73145e20 1.99153
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 2.97558e20 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) −5.96473e20 −1.95521
\(845\) 0 0
\(846\) 0 0
\(847\) 2.73652e19 0.0875012
\(848\) 0 0
\(849\) 4.24536e20 1.33524
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −5.97351e20 −1.81797 −0.908984 − 0.416831i \(-0.863141\pi\)
−0.908984 + 0.416831i \(0.863141\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −3.38702e20 −0.981445 −0.490723 − 0.871316i \(-0.663267\pi\)
−0.490723 + 0.871316i \(0.663267\pi\)
\(860\) 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
\(867\) 3.68242e20 1.00000
\(868\) 6.46902e19 0.174261
\(869\) 0 0
\(870\) 0 0
\(871\) 1.45230e20 0.381882
\(872\) 0 0
\(873\) −6.95483e20 −1.79965
\(874\) 0 0
\(875\) 0 0
\(876\) −6.19118e20 −1.56403
\(877\) 7.84775e20 1.96674 0.983372 − 0.181601i \(-0.0581281\pi\)
0.983372 + 0.181601i \(0.0581281\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) −5.56775e20 −1.33032 −0.665158 − 0.746703i \(-0.731636\pi\)
−0.665158 + 0.746703i \(0.731636\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −6.99402e19 −0.159373
\(890\) 0 0
\(891\) 0 0
\(892\) −6.34585e20 −1.41233
\(893\) 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
\(903\) 5.92489e19 0.121023
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −7.43690e20 −1.47279 −0.736395 − 0.676551i \(-0.763474\pi\)
−0.736395 + 0.676551i \(0.763474\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 4.05610e19 0.0772939
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −6.54578e20 −1.20974
\(917\) 0 0
\(918\) 0 0
\(919\) −1.07784e21 −1.94691 −0.973456 − 0.228872i \(-0.926496\pi\)
−0.973456 + 0.228872i \(0.926496\pi\)
\(920\) 0 0
\(921\) −8.65426e20 −1.53962
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 8.68370e20 1.47620
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −4.65002e19 −0.0767021
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −7.83676e20 −1.23583 −0.617916 − 0.786244i \(-0.712023\pi\)
−0.617916 + 0.786244i \(0.712023\pi\)
\(938\) 0 0
\(939\) 6.08793e20 0.945825
\(940\) 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 \(\pi\)
\(948\) 1.37534e21 1.99871
\(949\) 5.76910e20 0.832232
\(950\) 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
\(961\) 2.24523e21 2.96618
\(962\) 0 0
\(963\) 0 0
\(964\) 3.94493e20 0.509918
\(965\) 0 0
\(966\) 0 0
\(967\) −2.03183e20 −0.256981 −0.128491 − 0.991711i \(-0.541013\pi\)
−0.128491 + 0.991711i \(0.541013\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 8.19717e20 1.00000
\(973\) 7.60804e19 0.0921474
\(974\) 0 0
\(975\) 0 0
\(976\) −6.15280e20 −0.729329
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 1.67273e21 1.91313
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −3.77958e19 −0.0411287
\(989\) 0 0
\(990\) 0 0
\(991\) 1.45258e21 1.54748 0.773738 − 0.633506i \(-0.218385\pi\)
0.773738 + 0.633506i \(0.218385\pi\)
\(992\) 0 0
\(993\) 1.50137e21 1.57704
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.19373e21 −1.21911 −0.609553 − 0.792745i \(-0.708651\pi\)
−0.609553 + 0.792745i \(0.708651\pi\)
\(998\) 0 0
\(999\) 1.16765e21 1.17585
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 75.15.c.b.26.1 yes 1
3.2 odd 2 CM 75.15.c.b.26.1 yes 1
5.2 odd 4 75.15.d.a.74.1 2
5.3 odd 4 75.15.d.a.74.2 2
5.4 even 2 75.15.c.a.26.1 ✓ 1
15.2 even 4 75.15.d.a.74.1 2
15.8 even 4 75.15.d.a.74.2 2
15.14 odd 2 75.15.c.a.26.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.15.c.a.26.1 ✓ 1 5.4 even 2
75.15.c.a.26.1 ✓ 1 15.14 odd 2
75.15.c.b.26.1 yes 1 1.1 even 1 trivial
75.15.c.b.26.1 yes 1 3.2 odd 2 CM
75.15.d.a.74.1 2 5.2 odd 4
75.15.d.a.74.1 2 15.2 even 4
75.15.d.a.74.2 2 5.3 odd 4
75.15.d.a.74.2 2 15.8 even 4