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Properties

Label 75.17.c.a.26.1
Level $75$
Weight $17$
Character 75.26
Self dual yes
Analytic conductor $121.743$
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] = [75,17,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, 17, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.26");
 
S:= CuspForms(chi, 17);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 17 \)
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: \(121.743407892\)
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)
 
\(f(q)\) \(=\) \(q-6561.00 q^{3} +65536.0 q^{4} -6.72893e6 q^{7} +4.30467e7 q^{9} +O(q^{10})\) \(q-6561.00 q^{3} +65536.0 q^{4} -6.72893e6 q^{7} +4.30467e7 q^{9} -4.29982e8 q^{12} -1.55480e9 q^{13} +4.29497e9 q^{16} -9.01355e9 q^{19} +4.41485e10 q^{21} -2.82430e11 q^{27} -4.40987e11 q^{28} -2.02787e11 q^{31} +2.82111e12 q^{36} +6.77142e12 q^{37} +1.02011e13 q^{39} -2.33692e13 q^{43} -2.81793e13 q^{48} +1.20455e13 q^{49} -1.01896e14 q^{52} +5.91379e13 q^{57} -3.83320e14 q^{61} -2.89658e14 q^{63} +2.81475e14 q^{64} -2.03870e14 q^{67} +1.35147e15 q^{73} -5.90712e14 q^{76} -2.67750e15 q^{79} +1.85302e15 q^{81} +2.89332e15 q^{84} +1.04622e16 q^{91} +1.33049e15 q^{93} +8.92912e15 q^{97} +O(q^{100})\)

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 \(\pi\)
\(3\) −6561.00 −1.00000
\(4\) 65536.0 1.00000
\(5\) 0 0
\(6\) 0 0
\(7\) −6.72893e6 −1.16724 −0.583622 − 0.812026i \(-0.698365\pi\)
−0.583622 + 0.812026i \(0.698365\pi\)
\(8\) 0 0
\(9\) 4.30467e7 1.00000
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −4.29982e8 −1.00000
\(13\) −1.55480e9 −1.90602 −0.953012 − 0.302932i \(-0.902034\pi\)
−0.953012 + 0.302932i \(0.902034\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.29497e9 1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) −9.01355e9 −0.530722 −0.265361 − 0.964149i \(-0.585491\pi\)
−0.265361 + 0.964149i \(0.585491\pi\)
\(20\) 0 0
\(21\) 4.41485e10 1.16724
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.82430e11 −1.00000
\(28\) −4.40987e11 −1.16724
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −2.02787e11 −0.237764 −0.118882 − 0.992908i \(-0.537931\pi\)
−0.118882 + 0.992908i \(0.537931\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 2.82111e12 1.00000
\(37\) 6.77142e12 1.92782 0.963909 − 0.266230i \(-0.0857781\pi\)
0.963909 + 0.266230i \(0.0857781\pi\)
\(38\) 0 0
\(39\) 1.02011e13 1.90602
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −2.33692e13 −1.99938 −0.999691 − 0.0248759i \(-0.992081\pi\)
−0.999691 + 0.0248759i \(0.992081\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −2.81793e13 −1.00000
\(49\) 1.20455e13 0.362458
\(50\) 0 0
\(51\) 0 0
\(52\) −1.01896e14 −1.90602
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.91379e13 0.530722
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −3.83320e14 −1.99951 −0.999754 − 0.0221997i \(-0.992933\pi\)
−0.999754 + 0.0221997i \(0.992933\pi\)
\(62\) 0 0
\(63\) −2.89658e14 −1.16724
\(64\) 2.81475e14 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −2.03870e14 −0.502058 −0.251029 − 0.967980i \(-0.580769\pi\)
−0.251029 + 0.967980i \(0.580769\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 1.35147e15 1.67581 0.837905 − 0.545816i \(-0.183780\pi\)
0.837905 + 0.545816i \(0.183780\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −5.90712e14 −0.530722
\(77\) 0 0
\(78\) 0 0
\(79\) −2.67750e15 −1.76487 −0.882434 − 0.470436i \(-0.844097\pi\)
−0.882434 + 0.470436i \(0.844097\pi\)
\(80\) 0 0
\(81\) 1.85302e15 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 2.89332e15 1.16724
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 1.04622e16 2.22479
\(92\) 0 0
\(93\) 1.33049e15 0.237764
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 8.92912e15 1.13929 0.569645 − 0.821891i \(-0.307081\pi\)
0.569645 + 0.821891i \(0.307081\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 2.33597e16 1.84404 0.922018 − 0.387147i \(-0.126540\pi\)
0.922018 + 0.387147i \(0.126540\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −1.85093e16 −1.00000
\(109\) 3.37743e16 1.69502 0.847510 − 0.530779i \(-0.178101\pi\)
0.847510 + 0.530779i \(0.178101\pi\)
\(110\) 0 0
\(111\) −4.44273e16 −1.92782
\(112\) −2.89005e16 −1.16724
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −6.69291e16 −1.90602
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 4.59497e16 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) −1.32898e16 −0.237764
\(125\) 0 0
\(126\) 0 0
\(127\) −2.50994e16 −0.370880 −0.185440 − 0.982656i \(-0.559371\pi\)
−0.185440 + 0.982656i \(0.559371\pi\)
\(128\) 0 0
\(129\) 1.53325e17 1.99938
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 6.06515e16 0.619482
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 2.24585e17 1.61162 0.805809 − 0.592176i \(-0.201731\pi\)
0.805809 + 0.592176i \(0.201731\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.84884e17 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −7.90307e16 −0.362458
\(148\) 4.43772e17 1.92782
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 4.68743e17 1.73428 0.867140 − 0.498064i \(-0.165955\pi\)
0.867140 + 0.498064i \(0.165955\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 6.68537e17 1.90602
\(157\) −3.30441e17 −0.895151 −0.447576 − 0.894246i \(-0.647712\pi\)
−0.447576 + 0.894246i \(0.647712\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 9.87249e17 1.98119 0.990594 − 0.136831i \(-0.0436916\pi\)
0.990594 + 0.136831i \(0.0436916\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.75199e18 2.63293
\(170\) 0 0
\(171\) −3.88004e17 −0.530722
\(172\) −1.53152e18 −1.99938
\(173\) 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
\(181\) −1.10757e18 −0.961482 −0.480741 − 0.876863i \(-0.659632\pi\)
−0.480741 + 0.876863i \(0.659632\pi\)
\(182\) 0 0
\(183\) 2.51496e18 1.99951
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.90045e18 1.16724
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −1.84676e18 −1.00000
\(193\) −2.26556e18 −1.17684 −0.588420 − 0.808555i \(-0.700250\pi\)
−0.588420 + 0.808555i \(0.700250\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 7.89416e17 0.362458
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 4.88042e18 1.98442 0.992208 − 0.124592i \(-0.0397620\pi\)
0.992208 + 0.124592i \(0.0397620\pi\)
\(200\) 0 0
\(201\) 1.33759e18 0.502058
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −6.67783e18 −1.90602
\(209\) 0 0
\(210\) 0 0
\(211\) 3.28190e18 0.835344 0.417672 − 0.908598i \(-0.362846\pi\)
0.417672 + 0.908598i \(0.362846\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 1.36454e18 0.277529
\(218\) 0 0
\(219\) −8.86702e18 −1.67581
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.10118e19 1.80061 0.900307 − 0.435255i \(-0.143342\pi\)
0.900307 + 0.435255i \(0.143342\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 3.87566e18 0.530722
\(229\) −1.04595e18 −0.138302 −0.0691508 − 0.997606i \(-0.522029\pi\)
−0.0691508 + 0.997606i \(0.522029\pi\)
\(230\) 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
\(237\) 1.75671e19 1.76487
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −2.24898e19 −1.97628 −0.988140 − 0.153554i \(-0.950928\pi\)
−0.988140 + 0.153554i \(0.950928\pi\)
\(242\) 0 0
\(243\) −1.21577e19 −1.00000
\(244\) −2.51213e19 −1.99951
\(245\) 0 0
\(246\) 0 0
\(247\) 1.40143e19 1.01157
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −1.89830e19 −1.16724
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.84467e19 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −4.55644e19 −2.25023
\(260\) 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
\(268\) −1.33608e19 −0.502058
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −4.92587e19 −1.69328 −0.846640 − 0.532166i \(-0.821378\pi\)
−0.846640 + 0.532166i \(0.821378\pi\)
\(272\) 0 0
\(273\) −6.86422e19 −2.22479
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 5.16985e19 1.49156 0.745778 − 0.666195i \(-0.232078\pi\)
0.745778 + 0.666195i \(0.232078\pi\)
\(278\) 0 0
\(279\) −8.72931e18 −0.237764
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −5.52011e19 −1.34170 −0.670851 − 0.741592i \(-0.734071\pi\)
−0.670851 + 0.741592i \(0.734071\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.86612e19 1.00000
\(290\) 0 0
\(291\) −5.85839e19 −1.13929
\(292\) 8.85702e19 1.67581
\(293\) 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
\(301\) 1.57249e20 2.33376
\(302\) 0 0
\(303\) 0 0
\(304\) −3.87129e19 −0.530722
\(305\) 0 0
\(306\) 0 0
\(307\) −1.10946e20 −1.40606 −0.703028 − 0.711162i \(-0.748169\pi\)
−0.703028 + 0.711162i \(0.748169\pi\)
\(308\) 0 0
\(309\) −1.53263e20 −1.84404
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 1.30533e20 1.41699 0.708495 − 0.705716i \(-0.249375\pi\)
0.708495 + 0.705716i \(0.249375\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −1.75472e20 −1.76487
\(317\) 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
\(324\) 1.21440e20 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) −2.21593e20 −1.69502
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.41275e19 −0.167451 −0.0837255 − 0.996489i \(-0.526682\pi\)
−0.0837255 + 0.996489i \(0.526682\pi\)
\(332\) 0 0
\(333\) 2.91488e20 1.92782
\(334\) 0 0
\(335\) 0 0
\(336\) 1.89616e20 1.16724
\(337\) 1.91944e20 1.15381 0.576905 − 0.816811i \(-0.304260\pi\)
0.576905 + 0.816811i \(0.304260\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.42568e20 0.744167
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 4.35999e20 1.98099 0.990494 − 0.137553i \(-0.0439236\pi\)
0.990494 + 0.137553i \(0.0439236\pi\)
\(350\) 0 0
\(351\) 4.39122e20 1.90602
\(352\) 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
\(361\) −2.07197e20 −0.718334
\(362\) 0 0
\(363\) −3.01476e20 −1.00000
\(364\) 6.85648e20 2.22479
\(365\) 0 0
\(366\) 0 0
\(367\) −6.00738e20 −1.82539 −0.912697 − 0.408636i \(-0.866004\pi\)
−0.912697 + 0.408636i \(0.866004\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 8.71947e19 0.237764
\(373\) −1.98041e20 −0.528548 −0.264274 − 0.964448i \(-0.585132\pi\)
−0.264274 + 0.964448i \(0.585132\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 5.43958e20 1.27777 0.638884 − 0.769303i \(-0.279396\pi\)
0.638884 + 0.769303i \(0.279396\pi\)
\(380\) 0 0
\(381\) 1.64677e20 0.370880
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.00597e21 −1.99938
\(388\) 5.85179e20 1.13929
\(389\) 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
\(397\) 1.50247e20 0.243491 0.121745 − 0.992561i \(-0.461151\pi\)
0.121745 + 0.992561i \(0.461151\pi\)
\(398\) 0 0
\(399\) −3.97935e20 −0.619482
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 3.15294e20 0.453184
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 2.57296e20 0.328584 0.164292 − 0.986412i \(-0.447466\pi\)
0.164292 + 0.986412i \(0.447466\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.53090e21 1.84404
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.47350e21 −1.61162
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −1.83896e21 −1.86344 −0.931720 − 0.363178i \(-0.881692\pi\)
−0.931720 + 0.363178i \(0.881692\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 2.57933e21 2.33391
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −1.21303e21 −1.00000
\(433\) 2.37647e21 1.92322 0.961609 − 0.274424i \(-0.0884871\pi\)
0.961609 + 0.274424i \(0.0884871\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.21343e21 1.69502
\(437\) 0 0
\(438\) 0 0
\(439\) −2.70980e21 −1.96436 −0.982181 − 0.187937i \(-0.939820\pi\)
−0.982181 + 0.187937i \(0.939820\pi\)
\(440\) 0 0
\(441\) 5.18520e20 0.362458
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −2.91159e21 −1.92782
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.89402e21 −1.16724
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −3.07542e21 −1.73428
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 3.06189e21 1.60939 0.804693 − 0.593691i \(-0.202330\pi\)
0.804693 + 0.593691i \(0.202330\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −5.07863e20 −0.240491 −0.120245 − 0.992744i \(-0.538368\pi\)
−0.120245 + 0.992744i \(0.538368\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −4.38627e21 −1.90602
\(469\) 1.37182e21 0.586024
\(470\) 0 0
\(471\) 2.16802e21 0.895151
\(472\) 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
\(481\) −1.05282e22 −3.67447
\(482\) 0 0
\(483\) 0 0
\(484\) 3.01136e21 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 6.18907e21 1.95611 0.978055 − 0.208345i \(-0.0668078\pi\)
0.978055 + 0.208345i \(0.0668078\pi\)
\(488\) 0 0
\(489\) −6.47734e21 −1.98119
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −8.70963e20 −0.237764
\(497\) 0 0
\(498\) 0 0
\(499\) −5.13881e21 −1.33678 −0.668388 − 0.743813i \(-0.733015\pi\)
−0.668388 + 0.743813i \(0.733015\pi\)
\(500\) 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
\(507\) −1.14948e22 −2.63293
\(508\) −1.64491e21 −0.370880
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −9.09397e21 −1.95608
\(512\) 0 0
\(513\) 2.54569e21 0.530722
\(514\) 0 0
\(515\) 0 0
\(516\) 1.00483e22 1.99938
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −2.16931e21 −0.387533 −0.193766 − 0.981048i \(-0.562070\pi\)
−0.193766 + 0.981048i \(0.562070\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 6.13261e21 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 3.97486e21 0.619482
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.40316e22 1.91218 0.956091 − 0.293071i \(-0.0946772\pi\)
0.956091 + 0.293071i \(0.0946772\pi\)
\(542\) 0 0
\(543\) 7.26674e21 0.961482
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.22073e22 1.52307 0.761536 − 0.648122i \(-0.224445\pi\)
0.761536 + 0.648122i \(0.224445\pi\)
\(548\) 0 0
\(549\) −1.65007e22 −1.99951
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 1.80167e22 2.06003
\(554\) 0 0
\(555\) 0 0
\(556\) 1.47184e22 1.61162
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 3.63344e22 3.81087
\(560\) 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
\(567\) −1.24688e22 −1.16724
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −2.20252e22 −1.94909 −0.974543 − 0.224201i \(-0.928023\pi\)
−0.974543 + 0.224201i \(0.928023\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.21166e22 1.00000
\(577\) −2.16514e22 −1.76230 −0.881148 − 0.472841i \(-0.843229\pi\)
−0.881148 + 0.472841i \(0.843229\pi\)
\(578\) 0 0
\(579\) 1.48643e22 1.17684
\(580\) 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 \(\pi\)
\(588\) −5.17936e21 −0.362458
\(589\) 1.82783e21 0.126187
\(590\) 0 0
\(591\) 0 0
\(592\) 2.90830e22 1.92782
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −3.20204e22 −1.98442
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 1.42031e21 0.0834427 0.0417213 − 0.999129i \(-0.486716\pi\)
0.0417213 + 0.999129i \(0.486716\pi\)
\(602\) 0 0
\(603\) −8.77592e21 −0.502058
\(604\) 3.07196e22 1.73428
\(605\) 0 0
\(606\) 0 0
\(607\) −3.38912e22 −1.83898 −0.919492 − 0.393108i \(-0.871400\pi\)
−0.919492 + 0.393108i \(0.871400\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 3.96266e22 1.98748 0.993740 − 0.111719i \(-0.0356357\pi\)
0.993740 + 0.111719i \(0.0356357\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −4.06016e22 −1.88373 −0.941865 − 0.335993i \(-0.890928\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 4.38132e22 1.90602
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) −2.16558e22 −0.895151
\(629\) 0 0
\(630\) 0 0
\(631\) −3.74996e22 −1.49208 −0.746040 − 0.665901i \(-0.768047\pi\)
−0.746040 + 0.665901i \(0.768047\pi\)
\(632\) 0 0
\(633\) −2.15325e22 −0.835344
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.87284e22 −0.690853
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 2.28923e22 0.783433 0.391716 − 0.920086i \(-0.371881\pi\)
0.391716 + 0.920086i \(0.371881\pi\)
\(644\) 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
\(651\) −8.95274e21 −0.277529
\(652\) 6.47004e22 1.98119
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 5.81765e22 1.67581
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 5.38568e22 1.47784 0.738922 − 0.673791i \(-0.235335\pi\)
0.738922 + 0.673791i \(0.235335\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −7.22486e22 −1.80061
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 3.17578e22 0.754622 0.377311 − 0.926087i \(-0.376849\pi\)
0.377311 + 0.926087i \(0.376849\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 1.14819e23 2.63293
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) −6.00834e22 −1.32983
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −2.54282e22 −0.530722
\(685\) 0 0
\(686\) 0 0
\(687\) 6.86248e21 0.138302
\(688\) −1.00370e23 −1.99938
\(689\) 0 0
\(690\) 0 0
\(691\) −7.96831e22 −1.53300 −0.766500 − 0.642244i \(-0.778003\pi\)
−0.766500 + 0.642244i \(0.778003\pi\)
\(692\) 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
\(703\) −6.10346e22 −1.02314
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.11047e23 −1.73915 −0.869575 − 0.493801i \(-0.835607\pi\)
−0.869575 + 0.493801i \(0.835607\pi\)
\(710\) 0 0
\(711\) −1.15257e23 −1.76487
\(712\) 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
\(721\) −1.57186e23 −2.15244
\(722\) 0 0
\(723\) 1.47555e23 1.97628
\(724\) −7.25854e22 −0.961482
\(725\) 0 0
\(726\) 0 0
\(727\) −1.32720e22 −0.170083 −0.0850417 − 0.996377i \(-0.527102\pi\)
−0.0850417 + 0.996377i \(0.527102\pi\)
\(728\) 0 0
\(729\) 7.97664e22 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 1.64821e23 1.99951
\(733\) −1.66638e23 −1.99959 −0.999796 − 0.0201815i \(-0.993576\pi\)
−0.999796 + 0.0201815i \(0.993576\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1.18971e22 0.133748 0.0668739 − 0.997761i \(-0.478697\pi\)
0.0668739 + 0.997761i \(0.478697\pi\)
\(740\) 0 0
\(741\) −9.19478e22 −1.01157
\(742\) 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
\(751\) 8.47430e22 0.837499 0.418750 − 0.908102i \(-0.362468\pi\)
0.418750 + 0.908102i \(0.362468\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.24548e23 1.16724
\(757\) −1.88887e23 −1.75160 −0.875801 − 0.482672i \(-0.839666\pi\)
−0.875801 + 0.482672i \(0.839666\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) −2.27265e23 −1.97850
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1.21029e23 −1.00000
\(769\) 1.30797e22 0.106951 0.0534756 − 0.998569i \(-0.482970\pi\)
0.0534756 + 0.998569i \(0.482970\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.48476e23 −1.17684
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 2.98948e23 2.25023
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 5.17351e22 0.362458
\(785\) 0 0
\(786\) 0 0
\(787\) −1.31952e23 −0.896640 −0.448320 − 0.893873i \(-0.647977\pi\)
−0.448320 + 0.893873i \(0.647977\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 5.95987e23 3.81111
\(794\) 0 0
\(795\) 0 0
\(796\) 3.19843e23 1.98442
\(797\) 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
\(804\) 8.76602e22 0.502058
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 1.16968e23 0.625027 0.312514 − 0.949913i \(-0.398829\pi\)
0.312514 + 0.949913i \(0.398829\pi\)
\(812\) 0 0
\(813\) 3.23186e23 1.69328
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 2.10639e23 1.06112
\(818\) 0 0
\(819\) 4.50361e23 2.22479
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −7.31716e22 −0.347651 −0.173826 − 0.984776i \(-0.555613\pi\)
−0.173826 + 0.984776i \(0.555613\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −2.76418e23 −1.23917 −0.619583 − 0.784931i \(-0.712698\pi\)
−0.619583 + 0.784931i \(0.712698\pi\)
\(830\) 0 0
\(831\) −3.39194e23 −1.49156
\(832\) −4.37638e23 −1.90602
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 5.72730e22 0.237764
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 2.50246e23 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 2.15082e23 0.835344
\(845\) 0 0
\(846\) 0 0
\(847\) −3.09192e23 −1.16724
\(848\) 0 0
\(849\) 3.62175e23 1.34170
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 3.67842e23 1.31241 0.656205 − 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 5.15198e22 0.173792 0.0868958 − 0.996217i \(-0.472305\pi\)
0.0868958 + 0.996217i \(0.472305\pi\)
\(860\) 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
\(867\) −3.19266e23 −1.00000
\(868\) 8.94264e22 0.277529
\(869\) 0 0
\(870\) 0 0
\(871\) 3.16977e23 0.956935
\(872\) 0 0
\(873\) 3.84369e23 1.13929
\(874\) 0 0
\(875\) 0 0
\(876\) −5.81109e23 −1.67581
\(877\) −5.40275e23 −1.54390 −0.771949 − 0.635685i \(-0.780718\pi\)
−0.771949 + 0.635685i \(0.780718\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) −7.37515e23 −1.99565 −0.997827 − 0.0658866i \(-0.979012\pi\)
−0.997827 + 0.0658866i \(0.979012\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 1.68892e23 0.432907
\(890\) 0 0
\(891\) 0 0
\(892\) 7.21671e23 1.80061
\(893\) 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
\(903\) −1.03171e24 −2.33376
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −5.35809e23 −1.16991 −0.584953 − 0.811067i \(-0.698887\pi\)
−0.584953 + 0.811067i \(0.698887\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 2.53995e23 0.530722
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −6.85474e22 −0.138302
\(917\) 0 0
\(918\) 0 0
\(919\) 9.82317e23 1.93076 0.965378 − 0.260855i \(-0.0840044\pi\)
0.965378 + 0.260855i \(0.0840044\pi\)
\(920\) 0 0
\(921\) 7.27914e23 1.40606
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1.00556e24 1.84404
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −1.08573e23 −0.192364
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 1.13082e24 1.90317 0.951585 − 0.307387i \(-0.0994545\pi\)
0.951585 + 0.307387i \(0.0994545\pi\)
\(938\) 0 0
\(939\) −8.56429e23 −1.41699
\(940\) 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 \(\pi\)
\(948\) 1.15127e24 1.76487
\(949\) −2.10128e24 −3.19414
\(950\) 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
\(961\) −6.86301e23 −0.943468
\(962\) 0 0
\(963\) 0 0
\(964\) −1.47389e24 −1.97628
\(965\) 0 0
\(966\) 0 0
\(967\) −7.67665e23 −1.00406 −0.502031 − 0.864850i \(-0.667414\pi\)
−0.502031 + 0.864850i \(0.667414\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −7.96765e23 −1.00000
\(973\) −1.51122e24 −1.88115
\(974\) 0 0
\(975\) 0 0
\(976\) −1.64635e24 −1.99951
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 1.45387e24 1.69502
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 9.18441e23 1.01157
\(989\) 0 0
\(990\) 0 0
\(991\) −6.16773e23 −0.663034 −0.331517 − 0.943449i \(-0.607560\pi\)
−0.331517 + 0.943449i \(0.607560\pi\)
\(992\) 0 0
\(993\) 1.58300e23 0.167451
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1.61449e24 1.65376 0.826881 − 0.562377i \(-0.190113\pi\)
0.826881 + 0.562377i \(0.190113\pi\)
\(998\) 0 0
\(999\) −1.91245e24 −1.92782
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 75.17.c.a.26.1 ✓ 1
3.2 odd 2 CM 75.17.c.a.26.1 ✓ 1
5.2 odd 4 75.17.d.a.74.2 2
5.3 odd 4 75.17.d.a.74.1 2
5.4 even 2 75.17.c.b.26.1 yes 1
15.2 even 4 75.17.d.a.74.2 2
15.8 even 4 75.17.d.a.74.1 2
15.14 odd 2 75.17.c.b.26.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.17.c.a.26.1 ✓ 1 1.1 even 1 trivial
75.17.c.a.26.1 ✓ 1 3.2 odd 2 CM
75.17.c.b.26.1 yes 1 5.4 even 2
75.17.c.b.26.1 yes 1 15.14 odd 2
75.17.d.a.74.1 2 5.3 odd 4
75.17.d.a.74.1 2 15.8 even 4
75.17.d.a.74.2 2 5.2 odd 4
75.17.d.a.74.2 2 15.2 even 4