Properties

Label 1800.2.k.e.901.1
Level $1800$
Weight $2$
Character 1800.901
Analytic conductor $14.373$
Analytic rank $1$
Dimension $2$
CM discriminant -24
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1800,2,Mod(901,1800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1800.901");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.k (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: no
Analytic conductor: \(14.3730723638\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 901.1
Root \(1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 1800.901
Dual form 1800.2.k.e.901.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.41421i q^{2} -2.00000 q^{4} -2.00000 q^{7} +2.82843i q^{8} +O(q^{10})\) \(q-1.41421i q^{2} -2.00000 q^{4} -2.00000 q^{7} +2.82843i q^{8} -5.65685i q^{11} +2.82843i q^{14} +4.00000 q^{16} -8.00000 q^{22} +4.00000 q^{28} +2.82843i q^{29} -10.0000 q^{31} -5.65685i q^{32} +11.3137i q^{44} -3.00000 q^{49} +14.1421i q^{53} -5.65685i q^{56} +4.00000 q^{58} +11.3137i q^{59} +14.1421i q^{62} -8.00000 q^{64} -14.0000 q^{73} +11.3137i q^{77} -10.0000 q^{79} +5.65685i q^{83} +16.0000 q^{88} -2.00000 q^{97} +4.24264i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{4} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{4} - 4 q^{7} + 8 q^{16} - 16 q^{22} + 8 q^{28} - 20 q^{31} - 6 q^{49} + 8 q^{58} - 16 q^{64} - 28 q^{73} - 20 q^{79} + 32 q^{88} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1001\) \(1351\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) − 1.41421i − 1.00000i
\(3\) 0 0
\(4\) −2.00000 −1.00000
\(5\) 0 0
\(6\) 0 0
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 2.82843i 1.00000i
\(9\) 0 0
\(10\) 0 0
\(11\) − 5.65685i − 1.70561i −0.522233 0.852803i \(-0.674901\pi\)
0.522233 0.852803i \(-0.325099\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 2.82843i 0.755929i
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −8.00000 −1.70561
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 4.00000 0.755929
\(29\) 2.82843i 0.525226i 0.964901 + 0.262613i \(0.0845842\pi\)
−0.964901 + 0.262613i \(0.915416\pi\)
\(30\) 0 0
\(31\) −10.0000 −1.79605 −0.898027 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) − 5.65685i − 1.00000i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 11.3137i 1.70561i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 14.1421i 1.94257i 0.237915 + 0.971286i \(0.423536\pi\)
−0.237915 + 0.971286i \(0.576464\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) − 5.65685i − 0.755929i
\(57\) 0 0
\(58\) 4.00000 0.525226
\(59\) 11.3137i 1.47292i 0.676481 + 0.736460i \(0.263504\pi\)
−0.676481 + 0.736460i \(0.736496\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 14.1421i 1.79605i
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 11.3137i 1.28932i
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.65685i 0.620920i 0.950586 + 0.310460i \(0.100483\pi\)
−0.950586 + 0.310460i \(0.899517\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 16.0000 1.70561
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 4.24264i 0.428571i
\(99\) 0 0
\(100\) 0 0
\(101\) 19.7990i 1.97007i 0.172345 + 0.985037i \(0.444865\pi\)
−0.172345 + 0.985037i \(0.555135\pi\)
\(102\) 0 0
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 20.0000 1.94257
\(107\) − 11.3137i − 1.09374i −0.837218 0.546869i \(-0.815820\pi\)
0.837218 0.546869i \(-0.184180\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −8.00000 −0.755929
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) − 5.65685i − 0.525226i
\(117\) 0 0
\(118\) 16.0000 1.47292
\(119\) 0 0
\(120\) 0 0
\(121\) −21.0000 −1.90909
\(122\) 0 0
\(123\) 0 0
\(124\) 20.0000 1.79605
\(125\) 0 0
\(126\) 0 0
\(127\) 22.0000 1.95218 0.976092 0.217357i \(-0.0697436\pi\)
0.976092 + 0.217357i \(0.0697436\pi\)
\(128\) 11.3137i 1.00000i
\(129\) 0 0
\(130\) 0 0
\(131\) − 22.6274i − 1.97697i −0.151330 0.988483i \(-0.548356\pi\)
0.151330 0.988483i \(-0.451644\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 19.7990i 1.63858i
\(147\) 0 0
\(148\) 0 0
\(149\) 2.82843i 0.231714i 0.993266 + 0.115857i \(0.0369614\pi\)
−0.993266 + 0.115857i \(0.963039\pi\)
\(150\) 0 0
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 16.0000 1.28932
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 14.1421i 1.12509i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 8.00000 0.620920
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 19.7990i − 1.50529i −0.658427 0.752645i \(-0.728778\pi\)
0.658427 0.752645i \(-0.271222\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) − 22.6274i − 1.70561i
\(177\) 0 0
\(178\) 0 0
\(179\) 11.3137i 0.845626i 0.906217 + 0.422813i \(0.138957\pi\)
−0.906217 + 0.422813i \(0.861043\pi\)
\(180\) 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
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) −26.0000 −1.87152 −0.935760 0.352636i \(-0.885285\pi\)
−0.935760 + 0.352636i \(0.885285\pi\)
\(194\) 2.82843i 0.203069i
\(195\) 0 0
\(196\) 6.00000 0.428571
\(197\) 14.1421i 1.00759i 0.863825 + 0.503793i \(0.168062\pi\)
−0.863825 + 0.503793i \(0.831938\pi\)
\(198\) 0 0
\(199\) 14.0000 0.992434 0.496217 0.868199i \(-0.334722\pi\)
0.496217 + 0.868199i \(0.334722\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 28.0000 1.97007
\(203\) − 5.65685i − 0.397033i
\(204\) 0 0
\(205\) 0 0
\(206\) 19.7990i 1.37946i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) − 28.2843i − 1.94257i
\(213\) 0 0
\(214\) −16.0000 −1.09374
\(215\) 0 0
\(216\) 0 0
\(217\) 20.0000 1.35769
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −26.0000 −1.74109 −0.870544 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 11.3137i 0.755929i
\(225\) 0 0
\(226\) 0 0
\(227\) − 28.2843i − 1.87729i −0.344881 0.938647i \(-0.612081\pi\)
0.344881 0.938647i \(-0.387919\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −8.00000 −0.525226
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) − 22.6274i − 1.47292i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 29.6985i 1.90909i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) − 28.2843i − 1.79605i
\(249\) 0 0
\(250\) 0 0
\(251\) − 5.65685i − 0.357057i −0.983935 0.178529i \(-0.942866\pi\)
0.983935 0.178529i \(-0.0571337\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) − 31.1127i − 1.95218i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −32.0000 −1.97697
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 31.1127i − 1.89697i −0.316815 0.948487i \(-0.602613\pi\)
0.316815 0.948487i \(-0.397387\pi\)
\(270\) 0 0
\(271\) −22.0000 −1.33640 −0.668202 0.743980i \(-0.732936\pi\)
−0.668202 + 0.743980i \(0.732936\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 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
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 28.0000 1.63858
\(293\) 14.1421i 0.826192i 0.910687 + 0.413096i \(0.135553\pi\)
−0.910687 + 0.413096i \(0.864447\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 4.00000 0.231714
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) − 2.82843i − 0.162758i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) − 22.6274i − 1.28932i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 34.0000 1.92179 0.960897 0.276907i \(-0.0893093\pi\)
0.960897 + 0.276907i \(0.0893093\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 20.0000 1.12509
\(317\) 31.1127i 1.74746i 0.486408 + 0.873732i \(0.338307\pi\)
−0.486408 + 0.873732i \(0.661693\pi\)
\(318\) 0 0
\(319\) 16.0000 0.895828
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) − 11.3137i − 0.620920i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 22.0000 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(338\) − 18.3848i − 1.00000i
\(339\) 0 0
\(340\) 0 0
\(341\) 56.5685i 3.06336i
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) −28.0000 −1.50529
\(347\) − 28.2843i − 1.51838i −0.650870 0.759190i \(-0.725596\pi\)
0.650870 0.759190i \(-0.274404\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −32.0000 −1.70561
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 16.0000 0.845626
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −38.0000 −1.98358 −0.991792 0.127862i \(-0.959188\pi\)
−0.991792 + 0.127862i \(0.959188\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 28.2843i − 1.46845i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 36.7696i 1.87152i
\(387\) 0 0
\(388\) 4.00000 0.203069
\(389\) − 31.1127i − 1.57748i −0.614729 0.788738i \(-0.710735\pi\)
0.614729 0.788738i \(-0.289265\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) − 8.48528i − 0.428571i
\(393\) 0 0
\(394\) 20.0000 1.00759
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) − 19.7990i − 0.992434i
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) − 39.5980i − 1.97007i
\(405\) 0 0
\(406\) −8.00000 −0.397033
\(407\) 0 0
\(408\) 0 0
\(409\) −10.0000 −0.494468 −0.247234 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 28.0000 1.37946
\(413\) − 22.6274i − 1.11342i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 39.5980i − 1.93449i −0.253849 0.967244i \(-0.581697\pi\)
0.253849 0.967244i \(-0.418303\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −40.0000 −1.94257
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 22.6274i 1.09374i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) − 28.2843i − 1.35769i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −34.0000 −1.62273 −0.811366 0.584539i \(-0.801275\pi\)
−0.811366 + 0.584539i \(0.801275\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 28.2843i − 1.34383i −0.740630 0.671913i \(-0.765473\pi\)
0.740630 0.671913i \(-0.234527\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 36.7696i 1.74109i
\(447\) 0 0
\(448\) 16.0000 0.755929
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −40.0000 −1.87729
\(455\) 0 0
\(456\) 0 0
\(457\) −38.0000 −1.77757 −0.888783 0.458329i \(-0.848448\pi\)
−0.888783 + 0.458329i \(0.848448\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 19.7990i 0.922131i 0.887366 + 0.461065i \(0.152533\pi\)
−0.887366 + 0.461065i \(0.847467\pi\)
\(462\) 0 0
\(463\) −26.0000 −1.20832 −0.604161 0.796862i \(-0.706492\pi\)
−0.604161 + 0.796862i \(0.706492\pi\)
\(464\) 11.3137i 0.525226i
\(465\) 0 0
\(466\) 0 0
\(467\) 39.5980i 1.83238i 0.400749 + 0.916188i \(0.368750\pi\)
−0.400749 + 0.916188i \(0.631250\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −32.0000 −1.47292
\(473\) 0 0
\(474\) 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
\(482\) 14.1421i 0.644157i
\(483\) 0 0
\(484\) 42.0000 1.90909
\(485\) 0 0
\(486\) 0 0
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 22.6274i − 1.02116i −0.859830 0.510581i \(-0.829431\pi\)
0.859830 0.510581i \(-0.170569\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −40.0000 −1.79605
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −8.00000 −0.357057
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −44.0000 −1.95218
\(509\) 2.82843i 0.125368i 0.998033 + 0.0626839i \(0.0199660\pi\)
−0.998033 + 0.0626839i \(0.980034\pi\)
\(510\) 0 0
\(511\) 28.0000 1.23865
\(512\) − 22.6274i − 1.00000i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 45.2548i 1.97697i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −44.0000 −1.89697
\(539\) 16.9706i 0.730974i
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 31.1127i 1.33640i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 20.0000 0.850487
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14.1421i 0.599222i 0.954062 + 0.299611i \(0.0968568\pi\)
−0.954062 + 0.299611i \(0.903143\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 28.2843i − 1.19204i −0.802970 0.596020i \(-0.796748\pi\)
0.802970 0.596020i \(-0.203252\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −38.0000 −1.58196 −0.790980 0.611842i \(-0.790429\pi\)
−0.790980 + 0.611842i \(0.790429\pi\)
\(578\) 24.0416i 1.00000i
\(579\) 0 0
\(580\) 0 0
\(581\) − 11.3137i − 0.469372i
\(582\) 0 0
\(583\) 80.0000 3.31326
\(584\) − 39.5980i − 1.63858i
\(585\) 0 0
\(586\) 20.0000 0.826192
\(587\) − 45.2548i − 1.86787i −0.357447 0.933933i \(-0.616353\pi\)
0.357447 0.933933i \(-0.383647\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) − 5.65685i − 0.231714i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −4.00000 −0.162758
\(605\) 0 0
\(606\) 0 0
\(607\) 22.0000 0.892952 0.446476 0.894795i \(-0.352679\pi\)
0.446476 + 0.894795i \(0.352679\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −32.0000 −1.28932
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) − 48.0833i − 1.92179i
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 50.0000 1.99047 0.995234 0.0975126i \(-0.0310886\pi\)
0.995234 + 0.0975126i \(0.0310886\pi\)
\(632\) − 28.2843i − 1.12509i
\(633\) 0 0
\(634\) 44.0000 1.74746
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) − 22.6274i − 0.895828i
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 64.0000 2.51222
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 48.0833i 1.88164i 0.338902 + 0.940822i \(0.389945\pi\)
−0.338902 + 0.940822i \(0.610055\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 45.2548i 1.76288i 0.472298 + 0.881439i \(0.343425\pi\)
−0.472298 + 0.881439i \(0.656575\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −16.0000 −0.620920
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) − 31.1127i − 1.19842i
\(675\) 0 0
\(676\) −26.0000 −1.00000
\(677\) − 2.82843i − 0.108705i −0.998522 0.0543526i \(-0.982690\pi\)
0.998522 0.0543526i \(-0.0173095\pi\)
\(678\) 0 0
\(679\) 4.00000 0.153506
\(680\) 0 0
\(681\) 0 0
\(682\) 80.0000 3.06336
\(683\) 5.65685i 0.216454i 0.994126 + 0.108227i \(0.0345173\pi\)
−0.994126 + 0.108227i \(0.965483\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) − 28.2843i − 1.07990i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 39.5980i 1.50529i
\(693\) 0 0
\(694\) −40.0000 −1.51838
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 36.7696i 1.38877i 0.719605 + 0.694383i \(0.244323\pi\)
−0.719605 + 0.694383i \(0.755677\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 45.2548i 1.70561i
\(705\) 0 0
\(706\) 0 0
\(707\) − 39.5980i − 1.48924i
\(708\) 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
\(716\) − 22.6274i − 0.845626i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 28.0000 1.04277
\(722\) − 26.8701i − 1.00000i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −2.00000 −0.0741759 −0.0370879 0.999312i \(-0.511808\pi\)
−0.0370879 + 0.999312i \(0.511808\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 53.7401i 1.98358i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −40.0000 −1.46845
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 22.6274i 0.826788i
\(750\) 0 0
\(751\) −10.0000 −0.364905 −0.182453 0.983215i \(-0.558404\pi\)
−0.182453 + 0.983215i \(0.558404\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 26.0000 0.937584 0.468792 0.883309i \(-0.344689\pi\)
0.468792 + 0.883309i \(0.344689\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 52.0000 1.87152
\(773\) − 19.7990i − 0.712120i −0.934463 0.356060i \(-0.884120\pi\)
0.934463 0.356060i \(-0.115880\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) − 5.65685i − 0.203069i
\(777\) 0 0
\(778\) −44.0000 −1.57748
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −12.0000 −0.428571
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) − 28.2843i − 1.00759i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −28.0000 −0.992434
\(797\) − 53.7401i − 1.90357i −0.306762 0.951786i \(-0.599246\pi\)
0.306762 0.951786i \(-0.400754\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 79.1960i 2.79476i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −56.0000 −1.97007
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 11.3137i 0.397033i
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 14.1421i 0.494468i
\(819\) 0 0
\(820\) 0 0
\(821\) − 48.0833i − 1.67812i −0.544041 0.839059i \(-0.683106\pi\)
0.544041 0.839059i \(-0.316894\pi\)
\(822\) 0 0
\(823\) 46.0000 1.60346 0.801730 0.597687i \(-0.203913\pi\)
0.801730 + 0.597687i \(0.203913\pi\)
\(824\) − 39.5980i − 1.37946i
\(825\) 0 0
\(826\) −32.0000 −1.11342
\(827\) 56.5685i 1.96708i 0.180688 + 0.983540i \(0.442168\pi\)
−0.180688 + 0.983540i \(0.557832\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) −56.0000 −1.93449
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 21.0000 0.724138
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 42.0000 1.44314
\(848\) 56.5685i 1.94257i
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 32.0000 1.09374
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 19.7990i 0.672797i
\(867\) 0 0
\(868\) −40.0000 −1.35769
\(869\) 56.5685i 1.91896i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 48.0833i 1.62273i
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −40.0000 −1.34383
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) −44.0000 −1.47571
\(890\) 0 0
\(891\) 0 0
\(892\) 52.0000 1.74109
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) − 22.6274i − 0.755929i
\(897\) 0 0
\(898\) 0 0
\(899\) − 28.2843i − 0.943333i
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 56.5685i 1.87729i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 32.0000 1.05905
\(914\) 53.7401i 1.77757i
\(915\) 0 0
\(916\) 0 0
\(917\) 45.2548i 1.49445i
\(918\) 0 0
\(919\) 50.0000 1.64935 0.824674 0.565608i \(-0.191359\pi\)
0.824674 + 0.565608i \(0.191359\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 28.0000 0.922131
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 36.7696i 1.20832i
\(927\) 0 0
\(928\) 16.0000 0.525226
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 56.0000 1.83238
\(935\) 0 0
\(936\) 0 0
\(937\) 58.0000 1.89478 0.947389 0.320085i \(-0.103712\pi\)
0.947389 + 0.320085i \(0.103712\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 48.0833i − 1.56747i −0.621096 0.783735i \(-0.713312\pi\)
0.621096 0.783735i \(-0.286688\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 45.2548i 1.47292i
\(945\) 0 0
\(946\) 0 0
\(947\) 56.5685i 1.83823i 0.393989 + 0.919115i \(0.371095\pi\)
−0.393989 + 0.919115i \(0.628905\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 69.0000 2.22581
\(962\) 0 0
\(963\) 0 0
\(964\) 20.0000 0.644157
\(965\) 0 0
\(966\) 0 0
\(967\) −62.0000 −1.99379 −0.996893 0.0787703i \(-0.974901\pi\)
−0.996893 + 0.0787703i \(0.974901\pi\)
\(968\) − 59.3970i − 1.90909i
\(969\) 0 0
\(970\) 0 0
\(971\) 62.2254i 1.99691i 0.0555842 + 0.998454i \(0.482298\pi\)
−0.0555842 + 0.998454i \(0.517702\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 2.82843i 0.0906287i
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) −32.0000 −1.02116
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −58.0000 −1.84243 −0.921215 0.389053i \(-0.872802\pi\)
−0.921215 + 0.389053i \(0.872802\pi\)
\(992\) 56.5685i 1.79605i
\(993\) 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 1800.2.k.e.901.1 2
3.2 odd 2 inner 1800.2.k.e.901.2 2
4.3 odd 2 7200.2.k.h.3601.2 2
5.2 odd 4 1800.2.d.n.1549.3 4
5.3 odd 4 1800.2.d.n.1549.2 4
5.4 even 2 72.2.d.a.37.2 yes 2
8.3 odd 2 7200.2.k.h.3601.1 2
8.5 even 2 inner 1800.2.k.e.901.2 2
12.11 even 2 7200.2.k.h.3601.1 2
15.2 even 4 1800.2.d.n.1549.1 4
15.8 even 4 1800.2.d.n.1549.4 4
15.14 odd 2 72.2.d.a.37.1 2
20.3 even 4 7200.2.d.p.2449.2 4
20.7 even 4 7200.2.d.p.2449.4 4
20.19 odd 2 288.2.d.a.145.2 2
24.5 odd 2 CM 1800.2.k.e.901.1 2
24.11 even 2 7200.2.k.h.3601.2 2
40.3 even 4 7200.2.d.p.2449.1 4
40.13 odd 4 1800.2.d.n.1549.4 4
40.19 odd 2 288.2.d.a.145.1 2
40.27 even 4 7200.2.d.p.2449.3 4
40.29 even 2 72.2.d.a.37.1 2
40.37 odd 4 1800.2.d.n.1549.1 4
45.4 even 6 648.2.n.h.541.1 4
45.14 odd 6 648.2.n.h.541.2 4
45.29 odd 6 648.2.n.h.109.1 4
45.34 even 6 648.2.n.h.109.2 4
60.23 odd 4 7200.2.d.p.2449.1 4
60.47 odd 4 7200.2.d.p.2449.3 4
60.59 even 2 288.2.d.a.145.1 2
80.19 odd 4 2304.2.a.y.1.2 2
80.29 even 4 2304.2.a.q.1.2 2
80.59 odd 4 2304.2.a.y.1.1 2
80.69 even 4 2304.2.a.q.1.1 2
120.29 odd 2 72.2.d.a.37.2 yes 2
120.53 even 4 1800.2.d.n.1549.2 4
120.59 even 2 288.2.d.a.145.2 2
120.77 even 4 1800.2.d.n.1549.3 4
120.83 odd 4 7200.2.d.p.2449.2 4
120.107 odd 4 7200.2.d.p.2449.4 4
180.59 even 6 2592.2.r.i.2161.1 4
180.79 odd 6 2592.2.r.i.433.1 4
180.119 even 6 2592.2.r.i.433.2 4
180.139 odd 6 2592.2.r.i.2161.2 4
240.29 odd 4 2304.2.a.q.1.1 2
240.59 even 4 2304.2.a.y.1.2 2
240.149 odd 4 2304.2.a.q.1.2 2
240.179 even 4 2304.2.a.y.1.1 2
360.29 odd 6 648.2.n.h.109.2 4
360.59 even 6 2592.2.r.i.2161.2 4
360.139 odd 6 2592.2.r.i.2161.1 4
360.149 odd 6 648.2.n.h.541.1 4
360.229 even 6 648.2.n.h.541.2 4
360.259 odd 6 2592.2.r.i.433.2 4
360.299 even 6 2592.2.r.i.433.1 4
360.349 even 6 648.2.n.h.109.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.2.d.a.37.1 2 15.14 odd 2
72.2.d.a.37.1 2 40.29 even 2
72.2.d.a.37.2 yes 2 5.4 even 2
72.2.d.a.37.2 yes 2 120.29 odd 2
288.2.d.a.145.1 2 40.19 odd 2
288.2.d.a.145.1 2 60.59 even 2
288.2.d.a.145.2 2 20.19 odd 2
288.2.d.a.145.2 2 120.59 even 2
648.2.n.h.109.1 4 45.29 odd 6
648.2.n.h.109.1 4 360.349 even 6
648.2.n.h.109.2 4 45.34 even 6
648.2.n.h.109.2 4 360.29 odd 6
648.2.n.h.541.1 4 45.4 even 6
648.2.n.h.541.1 4 360.149 odd 6
648.2.n.h.541.2 4 45.14 odd 6
648.2.n.h.541.2 4 360.229 even 6
1800.2.d.n.1549.1 4 15.2 even 4
1800.2.d.n.1549.1 4 40.37 odd 4
1800.2.d.n.1549.2 4 5.3 odd 4
1800.2.d.n.1549.2 4 120.53 even 4
1800.2.d.n.1549.3 4 5.2 odd 4
1800.2.d.n.1549.3 4 120.77 even 4
1800.2.d.n.1549.4 4 15.8 even 4
1800.2.d.n.1549.4 4 40.13 odd 4
1800.2.k.e.901.1 2 1.1 even 1 trivial
1800.2.k.e.901.1 2 24.5 odd 2 CM
1800.2.k.e.901.2 2 3.2 odd 2 inner
1800.2.k.e.901.2 2 8.5 even 2 inner
2304.2.a.q.1.1 2 80.69 even 4
2304.2.a.q.1.1 2 240.29 odd 4
2304.2.a.q.1.2 2 80.29 even 4
2304.2.a.q.1.2 2 240.149 odd 4
2304.2.a.y.1.1 2 80.59 odd 4
2304.2.a.y.1.1 2 240.179 even 4
2304.2.a.y.1.2 2 80.19 odd 4
2304.2.a.y.1.2 2 240.59 even 4
2592.2.r.i.433.1 4 180.79 odd 6
2592.2.r.i.433.1 4 360.299 even 6
2592.2.r.i.433.2 4 180.119 even 6
2592.2.r.i.433.2 4 360.259 odd 6
2592.2.r.i.2161.1 4 180.59 even 6
2592.2.r.i.2161.1 4 360.139 odd 6
2592.2.r.i.2161.2 4 180.139 odd 6
2592.2.r.i.2161.2 4 360.59 even 6
7200.2.d.p.2449.1 4 40.3 even 4
7200.2.d.p.2449.1 4 60.23 odd 4
7200.2.d.p.2449.2 4 20.3 even 4
7200.2.d.p.2449.2 4 120.83 odd 4
7200.2.d.p.2449.3 4 40.27 even 4
7200.2.d.p.2449.3 4 60.47 odd 4
7200.2.d.p.2449.4 4 20.7 even 4
7200.2.d.p.2449.4 4 120.107 odd 4
7200.2.k.h.3601.1 2 8.3 odd 2
7200.2.k.h.3601.1 2 12.11 even 2
7200.2.k.h.3601.2 2 4.3 odd 2
7200.2.k.h.3601.2 2 24.11 even 2