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Properties

Label 3575.1.h.a.2001.1
Level $3575$
Weight $1$
Character 3575.2001
Self dual yes
Analytic conductor $1.784$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -143
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] = [3575,1,Mod(2001,3575)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3575, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3575.2001");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3575 = 5^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3575.h (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: \(1.78415742016\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.3575.1
Artin image: $D_6$
Artin field: Galois closure of 6.0.702934375.1

Embedding invariants

Embedding label 2001.1
Character \(\chi\) \(=\) 3575.2001

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.00000 q^{3} +2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.00000 q^{3} +2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +3.00000 q^{9} -1.00000 q^{11} +1.00000 q^{13} +1.00000 q^{14} -1.00000 q^{16} -3.00000 q^{18} +1.00000 q^{19} +2.00000 q^{21} +1.00000 q^{22} +1.00000 q^{23} -2.00000 q^{24} -1.00000 q^{26} -4.00000 q^{27} +2.00000 q^{33} -1.00000 q^{38} -2.00000 q^{39} -2.00000 q^{41} -2.00000 q^{42} -1.00000 q^{46} +2.00000 q^{48} +1.00000 q^{53} +4.00000 q^{54} -1.00000 q^{56} -2.00000 q^{57} -3.00000 q^{63} +1.00000 q^{64} -2.00000 q^{66} -2.00000 q^{69} +3.00000 q^{72} -1.00000 q^{73} +1.00000 q^{77} +2.00000 q^{78} +5.00000 q^{81} +2.00000 q^{82} -1.00000 q^{83} -1.00000 q^{88} -1.00000 q^{91} -3.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3575\mathbb{Z}\right)^\times\).

\(n\) \(651\) \(1002\) \(1926\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 2.00000 2.00000
\(7\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 1.00000 1.00000
\(9\) 3.00000 3.00000
\(10\) 0 0
\(11\) −1.00000 −1.00000
\(12\) 0 0
\(13\) 1.00000 1.00000
\(14\) 1.00000 1.00000
\(15\) 0 0
\(16\) −1.00000 −1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) −3.00000 −3.00000
\(19\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) 0 0
\(21\) 2.00000 2.00000
\(22\) 1.00000 1.00000
\(23\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) −2.00000 −2.00000
\(25\) 0 0
\(26\) −1.00000 −1.00000
\(27\) −4.00000 −4.00000
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 2.00000 2.00000
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −1.00000 −1.00000
\(39\) −2.00000 −2.00000
\(40\) 0 0
\(41\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(42\) −2.00000 −2.00000
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −1.00000 −1.00000
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 2.00000 2.00000
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 4.00000 4.00000
\(55\) 0 0
\(56\) −1.00000 −1.00000
\(57\) −2.00000 −2.00000
\(58\) 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
\(63\) −3.00000 −3.00000
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −2.00000 −2.00000
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) −2.00000 −2.00000
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 3.00000 3.00000
\(73\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.00000 1.00000
\(78\) 2.00000 2.00000
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 5.00000 5.00000
\(82\) 2.00000 2.00000
\(83\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −1.00000 −1.00000
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −1.00000 −1.00000
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) −3.00000 −3.00000
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(104\) 1.00000 1.00000
\(105\) 0 0
\(106\) −1.00000 −1.00000
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000 1.00000
\(113\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(114\) 2.00000 2.00000
\(115\) 0 0
\(116\) 0 0
\(117\) 3.00000 3.00000
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 4.00000 4.00000
\(124\) 0 0
\(125\) 0 0
\(126\) 3.00000 3.00000
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −1.00000 −1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) −1.00000 −1.00000
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 2.00000 2.00000
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.00000 −1.00000
\(144\) −3.00000 −3.00000
\(145\) 0 0
\(146\) 1.00000 1.00000
\(147\) 0 0
\(148\) 0 0
\(149\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(152\) 1.00000 1.00000
\(153\) 0 0
\(154\) −1.00000 −1.00000
\(155\) 0 0
\(156\) 0 0
\(157\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(158\) 0 0
\(159\) −2.00000 −2.00000
\(160\) 0 0
\(161\) −1.00000 −1.00000
\(162\) −5.00000 −5.00000
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.00000 1.00000
\(167\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(168\) 2.00000 2.00000
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 3.00000 3.00000
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 1.00000
\(177\) 0 0
\(178\) 0 0
\(179\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) 0 0
\(181\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(182\) 1.00000 1.00000
\(183\) 0 0
\(184\) 1.00000 1.00000
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 4.00000 4.00000
\(190\) 0 0
\(191\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) −2.00000 −2.00000
\(193\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) 3.00000 3.00000
\(199\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −1.00000 −1.00000
\(207\) 3.00000 3.00000
\(208\) −1.00000 −1.00000
\(209\) −1.00000 −1.00000
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) −4.00000 −4.00000
\(217\) 0 0
\(218\) 2.00000 2.00000
\(219\) 2.00000 2.00000
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1.00000 −1.00000
\(227\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) −2.00000 −2.00000
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) −3.00000 −3.00000
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0 0
\(241\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) −1.00000 −1.00000
\(243\) −6.00000 −6.00000
\(244\) 0 0
\(245\) 0 0
\(246\) −4.00000 −4.00000
\(247\) 1.00000 1.00000
\(248\) 0 0
\(249\) 2.00000 2.00000
\(250\) 0 0
\(251\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(252\) 0 0
\(253\) −1.00000 −1.00000
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 2.00000 2.00000
\(265\) 0 0
\(266\) 1.00000 1.00000
\(267\) 0 0
\(268\) 0 0
\(269\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) 0 0
\(273\) 2.00000 2.00000
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 1.00000 1.00000
\(287\) 2.00000 2.00000
\(288\) 0 0
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 4.00000 4.00000
\(298\) −1.00000 −1.00000
\(299\) 1.00000 1.00000
\(300\) 0 0
\(301\) 0 0
\(302\) −1.00000 −1.00000
\(303\) 0 0
\(304\) −1.00000 −1.00000
\(305\) 0 0
\(306\) 0 0
\(307\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) −2.00000 −2.00000
\(310\) 0 0
\(311\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) −2.00000 −2.00000
\(313\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(314\) −1.00000 −1.00000
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 2.00000 2.00000
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 1.00000 1.00000
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 4.00000 4.00000
\(328\) −2.00000 −2.00000
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −2.00000 −2.00000
\(335\) 0 0
\(336\) −2.00000 −2.00000
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −1.00000 −1.00000
\(339\) −2.00000 −2.00000
\(340\) 0 0
\(341\) 0 0
\(342\) −3.00000 −3.00000
\(343\) 1.00000 1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) −4.00000 −4.00000
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 1.00000 1.00000
\(359\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) −2.00000 −2.00000
\(363\) −2.00000 −2.00000
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(368\) −1.00000 −1.00000
\(369\) −6.00000 −6.00000
\(370\) 0 0
\(371\) −1.00000 −1.00000
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) −4.00000 −4.00000
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.00000 1.00000
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 2.00000 2.00000
\(385\) 0 0
\(386\) −2.00000 −2.00000
\(387\) 0 0
\(388\) 0 0
\(389\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 1.00000 1.00000
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) −2.00000 −2.00000
\(399\) 2.00000 2.00000
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −3.00000 −3.00000
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 1.00000 1.00000
\(419\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 1.00000 1.00000
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 2.00000 2.00000
\(430\) 0 0
\(431\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 4.00000 4.00000
\(433\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.00000 1.00000
\(438\) −2.00000 −2.00000
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −2.00000 −2.00000
\(448\) −1.00000 −1.00000
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 2.00000 2.00000
\(452\) 0 0
\(453\) −2.00000 −2.00000
\(454\) 1.00000 1.00000
\(455\) 0 0
\(456\) −2.00000 −2.00000
\(457\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 2.00000 2.00000
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −2.00000 −2.00000
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 3.00000 3.00000
\(478\) −1.00000 −1.00000
\(479\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.00000 −1.00000
\(483\) 2.00000 2.00000
\(484\) 0 0
\(485\) 0 0
\(486\) 6.00000 6.00000
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.00000 −1.00000
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −2.00000 −2.00000
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) −4.00000 −4.00000
\(502\) 1.00000 1.00000
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) −3.00000 −3.00000
\(505\) 0 0
\(506\) 1.00000 1.00000
\(507\) −2.00000 −2.00000
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 1.00000 1.00000
\(512\) 1.00000 1.00000
\(513\) −4.00000 −4.00000
\(514\) 2.00000 2.00000
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −2.00000 −2.00000
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.00000 −2.00000
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.00000 2.00000
\(538\) 1.00000 1.00000
\(539\) 0 0
\(540\) 0 0
\(541\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(542\) −1.00000 −1.00000
\(543\) −4.00000 −4.00000
\(544\) 0 0
\(545\) 0 0
\(546\) −2.00000 −2.00000
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −2.00000 −2.00000
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.00000 −1.00000
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −5.00000 −5.00000
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 2.00000 2.00000
\(574\) −2.00000 −2.00000
\(575\) 0 0
\(576\) 3.00000 3.00000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −1.00000 −1.00000
\(579\) −4.00000 −4.00000
\(580\) 0 0
\(581\) 1.00000 1.00000
\(582\) 0 0
\(583\) −1.00000 −1.00000
\(584\) −1.00000 −1.00000
\(585\) 0 0
\(586\) 1.00000 1.00000
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 2.00000 2.00000
\(592\) 0 0
\(593\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) −4.00000 −4.00000
\(595\) 0 0
\(596\) 0 0
\(597\) −4.00000 −4.00000
\(598\) −1.00000 −1.00000
\(599\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(614\) 1.00000 1.00000
\(615\) 0 0
\(616\) 1.00000 1.00000
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 2.00000 2.00000
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) −4.00000 −4.00000
\(622\) 1.00000 1.00000
\(623\) 0 0
\(624\) 2.00000 2.00000
\(625\) 0 0
\(626\) −1.00000 −1.00000
\(627\) 2.00000 2.00000
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) 5.00000 5.00000
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(654\) −4.00000 −4.00000
\(655\) 0 0
\(656\) 2.00000 2.00000
\(657\) −3.00000 −3.00000
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.00000 −1.00000
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 2.00000 2.00000
\(679\) 0 0
\(680\) 0 0
\(681\) 2.00000 2.00000
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.00000 −1.00000
\(687\) 0 0
\(688\) 0 0
\(689\) 1.00000 1.00000
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 3.00000 3.00000
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 2.00000 2.00000
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 4.00000 4.00000
\(703\) 0 0
\(704\) −1.00000 −1.00000
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −2.00000 −2.00000
\(718\) −1.00000 −1.00000
\(719\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) 0 0
\(721\) −1.00000 −1.00000
\(722\) 0 0
\(723\) −2.00000 −2.00000
\(724\) 0 0
\(725\) 0 0
\(726\) 2.00000 2.00000
\(727\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(728\) −1.00000 −1.00000
\(729\) 7.00000 7.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(734\) −1.00000 −1.00000
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 6.00000 6.00000
\(739\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 0 0
\(741\) −2.00000 −2.00000
\(742\) 1.00000 1.00000
\(743\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −3.00000 −3.00000
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 0 0
\(753\) 2.00000 2.00000
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(758\) 0 0
\(759\) 2.00000 2.00000
\(760\) 0 0
\(761\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) 0 0
\(763\) 2.00000 2.00000
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(770\) 0 0
\(771\) 4.00000 4.00000
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 1.00000 1.00000
\(779\) −2.00000 −2.00000
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.00000 −1.00000
\(792\) −3.00000 −3.00000
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(798\) −2.00000 −2.00000
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.00000 1.00000
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 2.00000 2.00000
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(812\) 0 0
\(813\) −2.00000 −2.00000
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −1.00000 −1.00000
\(819\) −3.00000 −3.00000
\(820\) 0 0
\(821\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(822\) 0 0
\(823\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(824\) 1.00000 1.00000
\(825\) 0 0
\(826\) 0 0
\(827\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(828\) 0 0
\(829\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.00000 1.00000
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) −2.00000 −2.00000
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) −2.00000 −2.00000
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −1.00000 −1.00000
\(848\) −1.00000 −1.00000
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) −2.00000 −2.00000
\(859\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(860\) 0 0
\(861\) −4.00000 −4.00000
\(862\) −1.00000 −1.00000
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −1.00000 −1.00000
\(867\) −2.00000 −2.00000
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −2.00000 −2.00000
\(873\) 0 0
\(874\) −1.00000 −1.00000
\(875\) 0 0
\(876\) 0 0
\(877\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(878\) 0 0
\(879\) 2.00000 2.00000
\(880\) 0 0
\(881\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(882\) 0 0
\(883\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1.00000 −1.00000
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −5.00000 −5.00000
\(892\) 0 0
\(893\) 0 0
\(894\) 2.00000 2.00000
\(895\) 0 0
\(896\) 1.00000 1.00000
\(897\) −2.00000 −2.00000
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) −2.00000 −2.00000
\(903\) 0 0
\(904\) 1.00000 1.00000
\(905\) 0 0
\(906\) 2.00000 2.00000
\(907\) 1.00000 1.00000 0.500000 − 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(912\) 2.00000 2.00000
\(913\) 1.00000 1.00000
\(914\) 1.00000 1.00000
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 2.00000 2.00000
\(922\) −1.00000 −1.00000
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 3.00000 3.00000
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 2.00000 2.00000
\(934\) −1.00000 −1.00000
\(935\) 0 0
\(936\) 3.00000 3.00000
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) −2.00000 −2.00000
\(940\) 0 0
\(941\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(942\) 2.00000 2.00000
\(943\) −2.00000 −2.00000
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) −1.00000 −1.00000
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) −3.00000 −3.00000
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) −1.00000 −1.00000
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) −2.00000 −2.00000
\(967\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(968\) 1.00000 1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −6.00000 −6.00000
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 4.00000 4.00000
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −1.00000 −1.00000 −0.500000 − 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 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 3575.1.h.a.2001.1 ✓ 1
5.2 odd 4 3575.1.c.b.3574.1 2
5.3 odd 4 3575.1.c.b.3574.2 2
5.4 even 2 3575.1.h.d.2001.1 yes 1
11.10 odd 2 3575.1.h.c.2001.1 yes 1
13.12 even 2 3575.1.h.c.2001.1 yes 1
55.32 even 4 3575.1.c.a.3574.2 2
55.43 even 4 3575.1.c.a.3574.1 2
55.54 odd 2 3575.1.h.b.2001.1 yes 1
65.12 odd 4 3575.1.c.a.3574.2 2
65.38 odd 4 3575.1.c.a.3574.1 2
65.64 even 2 3575.1.h.b.2001.1 yes 1
143.142 odd 2 CM 3575.1.h.a.2001.1 ✓ 1
715.142 even 4 3575.1.c.b.3574.1 2
715.428 even 4 3575.1.c.b.3574.2 2
715.714 odd 2 3575.1.h.d.2001.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3575.1.c.a.3574.1 2 55.43 even 4
3575.1.c.a.3574.1 2 65.38 odd 4
3575.1.c.a.3574.2 2 55.32 even 4
3575.1.c.a.3574.2 2 65.12 odd 4
3575.1.c.b.3574.1 2 5.2 odd 4
3575.1.c.b.3574.1 2 715.142 even 4
3575.1.c.b.3574.2 2 5.3 odd 4
3575.1.c.b.3574.2 2 715.428 even 4
3575.1.h.a.2001.1 ✓ 1 1.1 even 1 trivial
3575.1.h.a.2001.1 ✓ 1 143.142 odd 2 CM
3575.1.h.b.2001.1 yes 1 55.54 odd 2
3575.1.h.b.2001.1 yes 1 65.64 even 2
3575.1.h.c.2001.1 yes 1 11.10 odd 2
3575.1.h.c.2001.1 yes 1 13.12 even 2
3575.1.h.d.2001.1 yes 1 5.4 even 2
3575.1.h.d.2001.1 yes 1 715.714 odd 2