Properties

Label 2400.2.m.a.1199.4
Level $2400$
Weight $2$
Character 2400.1199
Analytic conductor $19.164$
Analytic rank $0$
Dimension $4$
CM discriminant -8
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2400,2,Mod(1199,2400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2400, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2400.1199");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2400.m (of order \(2\), degree \(1\), not 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: no
Analytic conductor: \(19.1640964851\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 24)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 1199.4
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 2400.1199
Dual form 2400.2.m.a.1199.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.41421 + 1.00000i) q^{3} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(1.41421 + 1.00000i) q^{3} +(1.00000 + 2.82843i) q^{9} +2.82843i q^{11} +5.65685 q^{17} +2.00000 q^{19} +(-1.41421 + 5.00000i) q^{27} +(-2.82843 + 4.00000i) q^{33} -11.3137i q^{41} +10.0000i q^{43} -7.00000 q^{49} +(8.00000 + 5.65685i) q^{51} +(2.82843 + 2.00000i) q^{57} +14.1421i q^{59} +14.0000i q^{67} +2.00000i q^{73} +(-7.00000 + 5.65685i) q^{81} -2.82843 q^{83} -5.65685i q^{89} +10.0000i q^{97} +(-8.00000 + 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{9} + 8 q^{19} - 28 q^{49} + 32 q^{51} - 28 q^{81} - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1601\) \(1951\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.41421 + 1.00000i 0.816497 + 0.577350i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 1.00000 + 2.82843i 0.333333 + 0.942809i
\(10\) 0 0
\(11\) 2.82843i 0.852803i 0.904534 + 0.426401i \(0.140219\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.65685 1.37199 0.685994 0.727607i \(-0.259367\pi\)
0.685994 + 0.727607i \(0.259367\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.41421 + 5.00000i −0.272166 + 0.962250i
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) −2.82843 + 4.00000i −0.492366 + 0.696311i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 11.3137i 1.76690i −0.468521 0.883452i \(-0.655213\pi\)
0.468521 0.883452i \(-0.344787\pi\)
\(42\) 0 0
\(43\) 10.0000i 1.52499i 0.646997 + 0.762493i \(0.276025\pi\)
−0.646997 + 0.762493i \(0.723975\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 8.00000 + 5.65685i 1.12022 + 0.792118i
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.82843 + 2.00000i 0.374634 + 0.264906i
\(58\) 0 0
\(59\) 14.1421i 1.84115i 0.390567 + 0.920575i \(0.372279\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 14.0000i 1.71037i 0.518321 + 0.855186i \(0.326557\pi\)
−0.518321 + 0.855186i \(0.673443\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 2.00000i 0.234082i 0.993127 + 0.117041i \(0.0373409\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 0 0
\(83\) −2.82843 −0.310460 −0.155230 0.987878i \(-0.549612\pi\)
−0.155230 + 0.987878i \(0.549612\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.65685i 0.599625i −0.953998 0.299813i \(-0.903076\pi\)
0.953998 0.299813i \(-0.0969242\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 10.0000i 1.01535i 0.861550 + 0.507673i \(0.169494\pi\)
−0.861550 + 0.507673i \(0.830506\pi\)
\(98\) 0 0
\(99\) −8.00000 + 2.82843i −0.804030 + 0.284268i
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 19.7990 1.91404 0.957020 0.290021i \(-0.0936623\pi\)
0.957020 + 0.290021i \(0.0936623\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 11.3137 1.06430 0.532152 0.846649i \(-0.321383\pi\)
0.532152 + 0.846649i \(0.321383\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 3.00000 0.272727
\(122\) 0 0
\(123\) 11.3137 16.0000i 1.02012 1.44267i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) −10.0000 + 14.1421i −0.880451 + 1.24515i
\(130\) 0 0
\(131\) 14.1421i 1.23560i −0.786334 0.617802i \(-0.788023\pi\)
0.786334 0.617802i \(-0.211977\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 22.6274 1.93319 0.966595 0.256307i \(-0.0825059\pi\)
0.966595 + 0.256307i \(0.0825059\pi\)
\(138\) 0 0
\(139\) −22.0000 −1.86602 −0.933008 0.359856i \(-0.882826\pi\)
−0.933008 + 0.359856i \(0.882826\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −9.89949 7.00000i −0.816497 0.577350i
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 5.65685 + 16.0000i 0.457330 + 1.29352i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000i 0.156652i −0.996928 0.0783260i \(-0.975042\pi\)
0.996928 0.0783260i \(-0.0249575\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 2.00000 + 5.65685i 0.152944 + 0.432590i
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −14.1421 + 20.0000i −1.06299 + 1.50329i
\(178\) 0 0
\(179\) 19.7990i 1.47985i −0.672692 0.739923i \(-0.734862\pi\)
0.672692 0.739923i \(-0.265138\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 16.0000i 1.17004i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 22.0000i 1.58359i −0.610784 0.791797i \(-0.709146\pi\)
0.610784 0.791797i \(-0.290854\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) −14.0000 + 19.7990i −0.987484 + 1.39651i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5.65685i 0.391293i
\(210\) 0 0
\(211\) −14.0000 −0.963800 −0.481900 0.876226i \(-0.660053\pi\)
−0.481900 + 0.876226i \(0.660053\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −2.00000 + 2.82843i −0.135147 + 0.191127i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.82843 0.187729 0.0938647 0.995585i \(-0.470078\pi\)
0.0938647 + 0.995585i \(0.470078\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.65685 −0.370593 −0.185296 0.982683i \(-0.559325\pi\)
−0.185296 + 0.982683i \(0.559325\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 26.0000 1.67481 0.837404 0.546585i \(-0.184072\pi\)
0.837404 + 0.546585i \(0.184072\pi\)
\(242\) 0 0
\(243\) −15.5563 + 1.00000i −0.997940 + 0.0641500i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −4.00000 2.82843i −0.253490 0.179244i
\(250\) 0 0
\(251\) 31.1127i 1.96382i −0.189358 0.981908i \(-0.560641\pi\)
0.189358 0.981908i \(-0.439359\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −11.3137 −0.705730 −0.352865 0.935674i \(-0.614792\pi\)
−0.352865 + 0.935674i \(0.614792\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 5.65685 8.00000i 0.346194 0.489592i
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 28.2843i 1.68730i −0.536895 0.843649i \(-0.680403\pi\)
0.536895 0.843649i \(-0.319597\pi\)
\(282\) 0 0
\(283\) 22.0000i 1.30776i 0.756596 + 0.653882i \(0.226861\pi\)
−0.756596 + 0.653882i \(0.773139\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 15.0000 0.882353
\(290\) 0 0
\(291\) −10.0000 + 14.1421i −0.586210 + 0.829027i
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −14.1421 4.00000i −0.820610 0.232104i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 34.0000i 1.94048i −0.242140 0.970241i \(-0.577849\pi\)
0.242140 0.970241i \(-0.422151\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 10.0000i 0.565233i −0.959233 0.282617i \(-0.908798\pi\)
0.959233 0.282617i \(-0.0912024\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 28.0000 + 19.7990i 1.56281 + 1.10507i
\(322\) 0 0
\(323\) 11.3137 0.629512
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −26.0000 −1.42909 −0.714545 0.699590i \(-0.753366\pi\)
−0.714545 + 0.699590i \(0.753366\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 14.0000i 0.762629i −0.924445 0.381314i \(-0.875472\pi\)
0.924445 0.381314i \(-0.124528\pi\)
\(338\) 0 0
\(339\) 16.0000 + 11.3137i 0.869001 + 0.614476i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 36.7696 1.97389 0.986947 0.161048i \(-0.0514875\pi\)
0.986947 + 0.161048i \(0.0514875\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −22.6274 −1.20434 −0.602168 0.798369i \(-0.705696\pi\)
−0.602168 + 0.798369i \(0.705696\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 4.24264 + 3.00000i 0.222681 + 0.157459i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 32.0000 11.3137i 1.66585 0.588968i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 38.0000 1.95193 0.975964 0.217930i \(-0.0699304\pi\)
0.975964 + 0.217930i \(0.0699304\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −28.2843 + 10.0000i −1.43777 + 0.508329i
\(388\) 0 0
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 14.1421 20.0000i 0.713376 1.00887i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 39.5980i 1.97743i 0.149813 + 0.988714i \(0.452133\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 22.0000 1.08783 0.543915 0.839140i \(-0.316941\pi\)
0.543915 + 0.839140i \(0.316941\pi\)
\(410\) 0 0
\(411\) 32.0000 + 22.6274i 1.57844 + 1.11613i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −31.1127 22.0000i −1.52360 1.07734i
\(418\) 0 0
\(419\) 36.7696i 1.79631i −0.439679 0.898155i \(-0.644908\pi\)
0.439679 0.898155i \(-0.355092\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 38.0000i 1.82616i 0.407777 + 0.913082i \(0.366304\pi\)
−0.407777 + 0.913082i \(0.633696\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −7.00000 19.7990i −0.333333 0.942809i
\(442\) 0 0
\(443\) −2.82843 −0.134383 −0.0671913 0.997740i \(-0.521404\pi\)
−0.0671913 + 0.997740i \(0.521404\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.65685i 0.266963i −0.991051 0.133482i \(-0.957384\pi\)
0.991051 0.133482i \(-0.0426157\pi\)
\(450\) 0 0
\(451\) 32.0000 1.50682
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 26.0000i 1.21623i −0.793849 0.608114i \(-0.791926\pi\)
0.793849 0.608114i \(-0.208074\pi\)
\(458\) 0 0
\(459\) −8.00000 + 28.2843i −0.373408 + 1.32020i
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −31.1127 −1.43972 −0.719862 0.694117i \(-0.755795\pi\)
−0.719862 + 0.694117i \(0.755795\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −28.2843 −1.30051
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 2.00000 2.82843i 0.0904431 0.127906i
\(490\) 0 0
\(491\) 14.1421i 0.638226i −0.947717 0.319113i \(-0.896615\pi\)
0.947717 0.319113i \(-0.103385\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 14.0000 0.626726 0.313363 0.949633i \(-0.398544\pi\)
0.313363 + 0.949633i \(0.398544\pi\)
\(500\) 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
\(507\) −18.3848 13.0000i −0.816497 0.577350i
\(508\) 0 0
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2.82843 + 10.0000i −0.124878 + 0.441511i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 45.2548i 1.98265i −0.131432 0.991325i \(-0.541958\pi\)
0.131432 0.991325i \(-0.458042\pi\)
\(522\) 0 0
\(523\) 38.0000i 1.66162i −0.556553 0.830812i \(-0.687876\pi\)
0.556553 0.830812i \(-0.312124\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 23.0000 1.00000
\(530\) 0 0
\(531\) −40.0000 + 14.1421i −1.73585 + 0.613716i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 19.7990 28.0000i 0.854389 1.20829i
\(538\) 0 0
\(539\) 19.7990i 0.852803i
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 46.0000i 1.96682i −0.181402 0.983409i \(-0.558064\pi\)
0.181402 0.983409i \(-0.441936\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −16.0000 + 22.6274i −0.675521 + 0.955330i
\(562\) 0 0
\(563\) −36.7696 −1.54965 −0.774826 0.632175i \(-0.782163\pi\)
−0.774826 + 0.632175i \(0.782163\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22.6274i 0.948591i −0.880366 0.474295i \(-0.842703\pi\)
0.880366 0.474295i \(-0.157297\pi\)
\(570\) 0 0
\(571\) 22.0000 0.920671 0.460336 0.887745i \(-0.347729\pi\)
0.460336 + 0.887745i \(0.347729\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 34.0000i 1.41544i 0.706494 + 0.707719i \(0.250276\pi\)
−0.706494 + 0.707719i \(0.749724\pi\)
\(578\) 0 0
\(579\) 22.0000 31.1127i 0.914289 1.29300i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −48.0833 −1.98461 −0.992304 0.123823i \(-0.960484\pi\)
−0.992304 + 0.123823i \(0.960484\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 45.2548 1.85839 0.929197 0.369586i \(-0.120500\pi\)
0.929197 + 0.369586i \(0.120500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −46.0000 −1.87638 −0.938190 0.346122i \(-0.887498\pi\)
−0.938190 + 0.346122i \(0.887498\pi\)
\(602\) 0 0
\(603\) −39.5980 + 14.0000i −1.61255 + 0.570124i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 39.5980 1.59415 0.797077 0.603877i \(-0.206378\pi\)
0.797077 + 0.603877i \(0.206378\pi\)
\(618\) 0 0
\(619\) 26.0000 1.04503 0.522514 0.852631i \(-0.324994\pi\)
0.522514 + 0.852631i \(0.324994\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −5.65685 + 8.00000i −0.225913 + 0.319489i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) −19.7990 14.0000i −0.786939 0.556450i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 28.2843i 1.11716i −0.829450 0.558581i \(-0.811346\pi\)
0.829450 0.558581i \(-0.188654\pi\)
\(642\) 0 0
\(643\) 50.0000i 1.97181i −0.167313 0.985904i \(-0.553509\pi\)
0.167313 0.985904i \(-0.446491\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) −40.0000 −1.57014
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −5.65685 + 2.00000i −0.220695 + 0.0780274i
\(658\) 0 0
\(659\) 48.0833i 1.87306i 0.350590 + 0.936529i \(0.385981\pi\)
−0.350590 + 0.936529i \(0.614019\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 10.0000i 0.385472i −0.981251 0.192736i \(-0.938264\pi\)
0.981251 0.192736i \(-0.0617360\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 4.00000 + 2.82843i 0.153280 + 0.108386i
\(682\) 0 0
\(683\) 31.1127 1.19049 0.595247 0.803543i \(-0.297054\pi\)
0.595247 + 0.803543i \(0.297054\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 46.0000 1.74992 0.874961 0.484193i \(-0.160887\pi\)
0.874961 + 0.484193i \(0.160887\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 64.0000i 2.42417i
\(698\) 0 0
\(699\) −8.00000 5.65685i −0.302588 0.213962i
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 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
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 36.7696 + 26.0000i 1.36747 + 0.966950i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 0 0
\(731\) 56.5685i 2.09226i
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −39.5980 −1.45861
\(738\) 0 0
\(739\) −34.0000 −1.25071 −0.625355 0.780340i \(-0.715046\pi\)
−0.625355 + 0.780340i \(0.715046\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −2.82843 8.00000i −0.103487 0.292705i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 31.1127 44.0000i 1.13381 1.60345i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 11.3137i 0.410122i −0.978749 0.205061i \(-0.934261\pi\)
0.978749 0.205061i \(-0.0657392\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 22.0000 0.793340 0.396670 0.917961i \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) 0 0
\(771\) −16.0000 11.3137i −0.576226 0.407453i
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 22.6274i 0.810711i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 50.0000i 1.78231i 0.453701 + 0.891154i \(0.350103\pi\)
−0.453701 + 0.891154i \(0.649897\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 16.0000 5.65685i 0.565332 0.199875i
\(802\) 0 0
\(803\) −5.65685 −0.199626
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 56.5685i 1.98884i −0.105474 0.994422i \(-0.533636\pi\)
0.105474 0.994422i \(-0.466364\pi\)
\(810\) 0 0
\(811\) −38.0000 −1.33436 −0.667180 0.744896i \(-0.732499\pi\)
−0.667180 + 0.744896i \(0.732499\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 20.0000i 0.699711i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 19.7990 0.688478 0.344239 0.938882i \(-0.388137\pi\)
0.344239 + 0.938882i \(0.388137\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −39.5980 −1.37199
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) 28.2843 40.0000i 0.974162 1.37767i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −22.0000 + 31.1127i −0.755038 + 1.06779i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 22.6274 0.772938 0.386469 0.922302i \(-0.373695\pi\)
0.386469 + 0.922302i \(0.373695\pi\)
\(858\) 0 0
\(859\) −58.0000 −1.97893 −0.989467 0.144757i \(-0.953760\pi\)
−0.989467 + 0.144757i \(0.953760\pi\)
\(860\) 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
\(867\) 21.2132 + 15.0000i 0.720438 + 0.509427i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −28.2843 + 10.0000i −0.957278 + 0.338449i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 56.5685i 1.90584i 0.303218 + 0.952921i \(0.401939\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) 2.00000i 0.0673054i −0.999434 0.0336527i \(-0.989286\pi\)
0.999434 0.0336527i \(-0.0107140\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −16.0000 19.7990i −0.536020 0.663291i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 10.0000i 0.332045i −0.986122 0.166022i \(-0.946908\pi\)
0.986122 0.166022i \(-0.0530924\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 8.00000i 0.264761i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 34.0000 48.0833i 1.12034 1.58440i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 28.2843i 0.927977i 0.885841 + 0.463988i \(0.153582\pi\)
−0.885841 + 0.463988i \(0.846418\pi\)
\(930\) 0 0
\(931\) −14.0000 −0.458831
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 34.0000i 1.11073i 0.831606 + 0.555366i \(0.187422\pi\)
−0.831606 + 0.555366i \(0.812578\pi\)
\(938\) 0 0
\(939\) 10.0000 14.1421i 0.326338 0.461511i
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 53.7401 1.74632 0.873160 0.487435i \(-0.162067\pi\)
0.873160 + 0.487435i \(0.162067\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 45.2548 1.46595 0.732974 0.680257i \(-0.238132\pi\)
0.732974 + 0.680257i \(0.238132\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 31.0000 1.00000
\(962\) 0 0
\(963\) 19.7990 + 56.0000i 0.638014 + 1.80457i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) 16.0000 + 11.3137i 0.513994 + 0.363449i
\(970\) 0 0
\(971\) 31.1127i 0.998454i −0.866471 0.499227i \(-0.833617\pi\)
0.866471 0.499227i \(-0.166383\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −62.2254 −1.99077 −0.995383 0.0959785i \(-0.969402\pi\)
−0.995383 + 0.0959785i \(0.969402\pi\)
\(978\) 0 0
\(979\) 16.0000 0.511362
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) −36.7696 26.0000i −1.16685 0.825085i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 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 2400.2.m.a.1199.4 4
3.2 odd 2 inner 2400.2.m.a.1199.2 4
4.3 odd 2 600.2.m.a.299.1 4
5.2 odd 4 96.2.f.a.47.1 2
5.3 odd 4 2400.2.b.a.2351.2 2
5.4 even 2 inner 2400.2.m.a.1199.1 4
8.3 odd 2 CM 2400.2.m.a.1199.4 4
8.5 even 2 600.2.m.a.299.1 4
12.11 even 2 600.2.m.a.299.3 4
15.2 even 4 96.2.f.a.47.2 2
15.8 even 4 2400.2.b.a.2351.1 2
15.14 odd 2 inner 2400.2.m.a.1199.3 4
20.3 even 4 600.2.b.a.251.2 2
20.7 even 4 24.2.f.a.11.1 2
20.19 odd 2 600.2.m.a.299.4 4
24.5 odd 2 600.2.m.a.299.3 4
24.11 even 2 inner 2400.2.m.a.1199.2 4
40.3 even 4 2400.2.b.a.2351.2 2
40.13 odd 4 600.2.b.a.251.2 2
40.19 odd 2 inner 2400.2.m.a.1199.1 4
40.27 even 4 96.2.f.a.47.1 2
40.29 even 2 600.2.m.a.299.4 4
40.37 odd 4 24.2.f.a.11.1 2
45.2 even 12 2592.2.p.b.2159.1 4
45.7 odd 12 2592.2.p.b.2159.2 4
45.22 odd 12 2592.2.p.b.431.1 4
45.32 even 12 2592.2.p.b.431.2 4
60.23 odd 4 600.2.b.a.251.1 2
60.47 odd 4 24.2.f.a.11.2 yes 2
60.59 even 2 600.2.m.a.299.2 4
80.27 even 4 768.2.c.h.767.4 4
80.37 odd 4 768.2.c.h.767.1 4
80.67 even 4 768.2.c.h.767.1 4
80.77 odd 4 768.2.c.h.767.4 4
120.29 odd 2 600.2.m.a.299.2 4
120.53 even 4 600.2.b.a.251.1 2
120.59 even 2 inner 2400.2.m.a.1199.3 4
120.77 even 4 24.2.f.a.11.2 yes 2
120.83 odd 4 2400.2.b.a.2351.1 2
120.107 odd 4 96.2.f.a.47.2 2
180.7 even 12 648.2.l.b.539.1 4
180.47 odd 12 648.2.l.b.539.2 4
180.67 even 12 648.2.l.b.107.2 4
180.167 odd 12 648.2.l.b.107.1 4
240.77 even 4 768.2.c.h.767.2 4
240.107 odd 4 768.2.c.h.767.2 4
240.197 even 4 768.2.c.h.767.3 4
240.227 odd 4 768.2.c.h.767.3 4
360.67 even 12 2592.2.p.b.431.1 4
360.77 even 12 648.2.l.b.107.1 4
360.157 odd 12 648.2.l.b.107.2 4
360.187 even 12 2592.2.p.b.2159.2 4
360.227 odd 12 2592.2.p.b.2159.1 4
360.277 odd 12 648.2.l.b.539.1 4
360.317 even 12 648.2.l.b.539.2 4
360.347 odd 12 2592.2.p.b.431.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
24.2.f.a.11.1 2 20.7 even 4
24.2.f.a.11.1 2 40.37 odd 4
24.2.f.a.11.2 yes 2 60.47 odd 4
24.2.f.a.11.2 yes 2 120.77 even 4
96.2.f.a.47.1 2 5.2 odd 4
96.2.f.a.47.1 2 40.27 even 4
96.2.f.a.47.2 2 15.2 even 4
96.2.f.a.47.2 2 120.107 odd 4
600.2.b.a.251.1 2 60.23 odd 4
600.2.b.a.251.1 2 120.53 even 4
600.2.b.a.251.2 2 20.3 even 4
600.2.b.a.251.2 2 40.13 odd 4
600.2.m.a.299.1 4 4.3 odd 2
600.2.m.a.299.1 4 8.5 even 2
600.2.m.a.299.2 4 60.59 even 2
600.2.m.a.299.2 4 120.29 odd 2
600.2.m.a.299.3 4 12.11 even 2
600.2.m.a.299.3 4 24.5 odd 2
600.2.m.a.299.4 4 20.19 odd 2
600.2.m.a.299.4 4 40.29 even 2
648.2.l.b.107.1 4 180.167 odd 12
648.2.l.b.107.1 4 360.77 even 12
648.2.l.b.107.2 4 180.67 even 12
648.2.l.b.107.2 4 360.157 odd 12
648.2.l.b.539.1 4 180.7 even 12
648.2.l.b.539.1 4 360.277 odd 12
648.2.l.b.539.2 4 180.47 odd 12
648.2.l.b.539.2 4 360.317 even 12
768.2.c.h.767.1 4 80.37 odd 4
768.2.c.h.767.1 4 80.67 even 4
768.2.c.h.767.2 4 240.77 even 4
768.2.c.h.767.2 4 240.107 odd 4
768.2.c.h.767.3 4 240.197 even 4
768.2.c.h.767.3 4 240.227 odd 4
768.2.c.h.767.4 4 80.27 even 4
768.2.c.h.767.4 4 80.77 odd 4
2400.2.b.a.2351.1 2 15.8 even 4
2400.2.b.a.2351.1 2 120.83 odd 4
2400.2.b.a.2351.2 2 5.3 odd 4
2400.2.b.a.2351.2 2 40.3 even 4
2400.2.m.a.1199.1 4 5.4 even 2 inner
2400.2.m.a.1199.1 4 40.19 odd 2 inner
2400.2.m.a.1199.2 4 3.2 odd 2 inner
2400.2.m.a.1199.2 4 24.11 even 2 inner
2400.2.m.a.1199.3 4 15.14 odd 2 inner
2400.2.m.a.1199.3 4 120.59 even 2 inner
2400.2.m.a.1199.4 4 1.1 even 1 trivial
2400.2.m.a.1199.4 4 8.3 odd 2 CM
2592.2.p.b.431.1 4 45.22 odd 12
2592.2.p.b.431.1 4 360.67 even 12
2592.2.p.b.431.2 4 45.32 even 12
2592.2.p.b.431.2 4 360.347 odd 12
2592.2.p.b.2159.1 4 45.2 even 12
2592.2.p.b.2159.1 4 360.227 odd 12
2592.2.p.b.2159.2 4 45.7 odd 12
2592.2.p.b.2159.2 4 360.187 even 12