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Properties

Label 675.2.a.j.1.2
Level $675$
Weight $2$
Character 675.1
Self dual yes
Analytic conductor $5.390$
Analytic rank $1$
Dimension $2$
CM discriminant -15
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [675,2,Mod(1,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("675.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.a (trivial)

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: \(5.38990213644\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 135)
Fricke sign: \(1\)
Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 675.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.381966 q^{2} -1.85410 q^{4} +1.47214 q^{8} +O(q^{10})\) \(q-0.381966 q^{2} -1.85410 q^{4} +1.47214 q^{8} +3.14590 q^{16} -8.23607 q^{17} +4.70820 q^{19} -7.47214 q^{23} -10.7082 q^{31} -4.14590 q^{32} +3.14590 q^{34} -1.79837 q^{38} +2.85410 q^{46} -8.94427 q^{47} -7.00000 q^{49} -9.76393 q^{53} +12.4164 q^{61} +4.09017 q^{62} -4.70820 q^{64} +15.2705 q^{68} -8.72949 q^{76} -1.29180 q^{79} +5.94427 q^{83} +13.8541 q^{92} +3.41641 q^{94} +2.67376 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{2} + 3 q^{4} - 6 q^{8} + 13 q^{16} - 12 q^{17} - 4 q^{19} - 6 q^{23} - 8 q^{31} - 15 q^{32} + 13 q^{34} + 21 q^{38} - q^{46} - 14 q^{49} - 24 q^{53} - 2 q^{61} - 3 q^{62} + 4 q^{64} - 3 q^{68} - 51 q^{76} - 16 q^{79} - 6 q^{83} + 21 q^{92} - 20 q^{94} + 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.381966 −0.270091 −0.135045 − 0.990839i \(-0.543118\pi\)
−0.135045 + 0.990839i \(0.543118\pi\)
\(3\) 0 0
\(4\) −1.85410 −0.927051
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 1.47214 0.520479
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 3.14590 0.786475
\(17\) −8.23607 −1.99754 −0.998770 − 0.0495842i \(-0.984210\pi\)
−0.998770 + 0.0495842i \(0.984210\pi\)
\(18\) 0 0
\(19\) 4.70820 1.08014 0.540068 − 0.841621i \(-0.318398\pi\)
0.540068 + 0.841621i \(0.318398\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.47214 −1.55805 −0.779024 − 0.626994i \(-0.784285\pi\)
−0.779024 + 0.626994i \(0.784285\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −10.7082 −1.92325 −0.961625 − 0.274367i \(-0.911532\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) −4.14590 −0.732898
\(33\) 0 0
\(34\) 3.14590 0.539517
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) −1.79837 −0.291735
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 2.85410 0.420814
\(47\) −8.94427 −1.30466 −0.652328 − 0.757937i \(-0.726208\pi\)
−0.652328 + 0.757937i \(0.726208\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −9.76393 −1.34118 −0.670590 − 0.741829i \(-0.733959\pi\)
−0.670590 + 0.741829i \(0.733959\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 12.4164 1.58976 0.794879 − 0.606768i \(-0.207534\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) 4.09017 0.519452
\(63\) 0 0
\(64\) −4.70820 −0.588525
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 15.2705 1.85182
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −8.72949 −1.00134
\(77\) 0 0
\(78\) 0 0
\(79\) −1.29180 −0.145338 −0.0726692 − 0.997356i \(-0.523152\pi\)
−0.0726692 + 0.997356i \(0.523152\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.94427 0.652469 0.326234 − 0.945289i \(-0.394220\pi\)
0.326234 + 0.945289i \(0.394220\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 13.8541 1.44439
\(93\) 0 0
\(94\) 3.41641 0.352376
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 2.67376 0.270091
\(99\) 0 0
\(100\) 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
\(106\) 3.72949 0.362240
\(107\) 17.8885 1.72935 0.864675 − 0.502331i \(-0.167524\pi\)
0.864675 + 0.502331i \(0.167524\pi\)
\(108\) 0 0
\(109\) −6.41641 −0.614580 −0.307290 − 0.951616i \(-0.599422\pi\)
−0.307290 + 0.951616i \(0.599422\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −4.47214 −0.420703 −0.210352 − 0.977626i \(-0.567461\pi\)
−0.210352 + 0.977626i \(0.567461\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) −4.74265 −0.429379
\(123\) 0 0
\(124\) 19.8541 1.78295
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 10.0902 0.891853
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −12.1246 −1.03968
\(137\) 5.18034 0.442586 0.221293 − 0.975207i \(-0.428972\pi\)
0.221293 + 0.975207i \(0.428972\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 − 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 − 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 6.93112 0.562188
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0.493422 0.0392546
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −2.27051 −0.176226
\(167\) 25.4721 1.97109 0.985547 − 0.169405i \(-0.0541846\pi\)
0.985547 + 0.169405i \(0.0541846\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −23.1803 −1.76237 −0.881184 − 0.472773i \(-0.843253\pi\)
−0.881184 + 0.472773i \(0.843253\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 24.4164 1.81486 0.907429 − 0.420206i \(-0.138042\pi\)
0.907429 + 0.420206i \(0.138042\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −11.0000 −0.810931
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 16.5836 1.20948
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 12.9787 0.927051
\(197\) −26.2361 −1.86924 −0.934621 − 0.355645i \(-0.884261\pi\)
−0.934621 + 0.355645i \(0.884261\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 − 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 7.29180 0.501988 0.250994 − 0.967989i \(-0.419243\pi\)
0.250994 + 0.967989i \(0.419243\pi\)
\(212\) 18.1033 1.24334
\(213\) 0 0
\(214\) −6.83282 −0.467082
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 2.45085 0.165992
\(219\) 0 0
\(220\) 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
\(226\) 1.70820 0.113628
\(227\) 12.0557 0.800167 0.400083 − 0.916479i \(-0.368981\pi\)
0.400083 + 0.916479i \(0.368981\pi\)
\(228\) 0 0
\(229\) −0.416408 −0.0275170 −0.0137585 − 0.999905i \(-0.504380\pi\)
−0.0137585 + 0.999905i \(0.504380\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 22.3607 1.46490 0.732448 − 0.680823i \(-0.238378\pi\)
0.732448 + 0.680823i \(0.238378\pi\)
\(234\) 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
\(241\) −27.8328 −1.79287 −0.896435 − 0.443176i \(-0.853852\pi\)
−0.896435 + 0.443176i \(0.853852\pi\)
\(242\) 4.20163 0.270091
\(243\) 0 0
\(244\) −23.0213 −1.47379
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −15.7639 −1.00101
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 5.56231 0.347644
\(257\) −21.6525 −1.35064 −0.675322 − 0.737523i \(-0.735995\pi\)
−0.675322 + 0.737523i \(0.735995\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 8.94427 0.551527 0.275764 − 0.961225i \(-0.411069\pi\)
0.275764 + 0.961225i \(0.411069\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) −22.7082 −1.37943 −0.689713 − 0.724083i \(-0.742263\pi\)
−0.689713 + 0.724083i \(0.742263\pi\)
\(272\) −25.9098 −1.57101
\(273\) 0 0
\(274\) −1.97871 −0.119538
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) −1.52786 −0.0916352
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 50.8328 2.99017
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3.65248 0.213380 0.106690 − 0.994292i \(-0.465975\pi\)
0.106690 + 0.994292i \(0.465975\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −3.05573 −0.175837
\(303\) 0 0
\(304\) 14.8115 0.849499
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 2.39512 0.134736
\(317\) −12.8197 −0.720024 −0.360012 − 0.932948i \(-0.617227\pi\)
−0.360012 + 0.932948i \(0.617227\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −38.7771 −2.15761
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −28.0000 −1.53902 −0.769510 − 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) −11.0213 −0.604872
\(333\) 0 0
\(334\) −9.72949 −0.532374
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 4.96556 0.270091
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 8.85410 0.475999
\(347\) −35.7771 −1.92061 −0.960307 − 0.278944i \(-0.910016\pi\)
−0.960307 + 0.278944i \(0.910016\pi\)
\(348\) 0 0
\(349\) −30.4164 −1.62815 −0.814076 − 0.580758i \(-0.802756\pi\)
−0.814076 + 0.580758i \(0.802756\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −31.3050 −1.66619 −0.833097 − 0.553127i \(-0.813435\pi\)
−0.833097 + 0.553127i \(0.813435\pi\)
\(354\) 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
\(361\) 3.16718 0.166694
\(362\) −9.32624 −0.490176
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) −23.5066 −1.22537
\(369\) 0 0
\(370\) 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
\(376\) −13.1672 −0.679046
\(377\) 0 0
\(378\) 0 0
\(379\) −35.5410 −1.82562 −0.912810 − 0.408385i \(-0.866092\pi\)
−0.912810 + 0.408385i \(0.866092\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 28.5279 1.45771 0.728853 − 0.684670i \(-0.240054\pi\)
0.728853 + 0.684670i \(0.240054\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 61.5410 3.11226
\(392\) −10.3050 −0.520479
\(393\) 0 0
\(394\) 10.0213 0.504865
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) −6.11146 −0.306340
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 39.8328 1.96961 0.984803 − 0.173675i \(-0.0555643\pi\)
0.984803 + 0.173675i \(0.0555643\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −5.58359 −0.272128 −0.136064 − 0.990700i \(-0.543445\pi\)
−0.136064 + 0.990700i \(0.543445\pi\)
\(422\) −2.78522 −0.135582
\(423\) 0 0
\(424\) −14.3738 −0.698055
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −33.1672 −1.60320
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 11.8967 0.569747
\(437\) −35.1803 −1.68290
\(438\) 0 0
\(439\) −41.5410 −1.98264 −0.991322 − 0.131453i \(-0.958036\pi\)
−0.991322 + 0.131453i \(0.958036\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 41.9443 1.99283 0.996416 − 0.0845852i \(-0.0269565\pi\)
0.996416 + 0.0845852i \(0.0269565\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 8.29180 0.390013
\(453\) 0 0
\(454\) −4.60488 −0.216118
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0.159054 0.00743209
\(459\) 0 0
\(460\) 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
\(466\) −8.54102 −0.395655
\(467\) 38.8885 1.79955 0.899774 − 0.436357i \(-0.143732\pi\)
0.899774 + 0.436357i \(0.143732\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 10.6312 0.484237
\(483\) 0 0
\(484\) 20.3951 0.927051
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 18.2786 0.827435
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −33.6869 −1.51259
\(497\) 0 0
\(498\) 0 0
\(499\) 28.7082 1.28516 0.642578 − 0.766220i \(-0.277865\pi\)
0.642578 + 0.766220i \(0.277865\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 19.3607 0.863250 0.431625 − 0.902053i \(-0.357940\pi\)
0.431625 + 0.902053i \(0.357940\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −22.3050 −0.985749
\(513\) 0 0
\(514\) 8.27051 0.364797
\(515\) 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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −3.41641 −0.148962
\(527\) 88.1935 3.84177
\(528\) 0 0
\(529\) 32.8328 1.42751
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 − 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 8.67376 0.372570
\(543\) 0 0
\(544\) 34.1459 1.46399
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) −9.60488 −0.410300
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −7.41641 −0.314526
\(557\) −22.3607 −0.947452 −0.473726 − 0.880672i \(-0.657091\pi\)
−0.473726 + 0.880672i \(0.657091\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 35.7771 1.50782 0.753912 − 0.656975i \(-0.228164\pi\)
0.753912 + 0.656975i \(0.228164\pi\)
\(564\) 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
\(571\) 47.5410 1.98953 0.994765 − 0.102190i \(-0.0325850\pi\)
0.994765 + 0.102190i \(0.0325850\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) −19.4164 −0.807616
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −1.39512 −0.0576319
\(587\) 30.0557 1.24053 0.620266 − 0.784391i \(-0.287025\pi\)
0.620266 + 0.784391i \(0.287025\pi\)
\(588\) 0 0
\(589\) −50.4164 −2.07737
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 44.2361 1.81656 0.908279 − 0.418365i \(-0.137397\pi\)
0.908279 + 0.418365i \(0.137397\pi\)
\(594\) 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
\(601\) −45.8328 −1.86956 −0.934780 − 0.355228i \(-0.884403\pi\)
−0.934780 + 0.355228i \(0.884403\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −14.8328 −0.603539
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) −19.5197 −0.791630
\(609\) 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
\(617\) 18.5967 0.748677 0.374338 − 0.927292i \(-0.377870\pi\)
0.374338 + 0.927292i \(0.377870\pi\)
\(618\) 0 0
\(619\) −44.0000 −1.76851 −0.884255 − 0.467005i \(-0.845333\pi\)
−0.884255 + 0.467005i \(0.845333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 17.5410 0.698297 0.349148 − 0.937067i \(-0.386471\pi\)
0.349148 + 0.937067i \(0.386471\pi\)
\(632\) −1.90170 −0.0756455
\(633\) 0 0
\(634\) 4.89667 0.194472
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 14.8115 0.582752
\(647\) −1.36068 −0.0534938 −0.0267469 − 0.999642i \(-0.508515\pi\)
−0.0267469 + 0.999642i \(0.508515\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −36.5967 −1.43214 −0.716071 − 0.698028i \(-0.754061\pi\)
−0.716071 + 0.698028i \(0.754061\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −22.0000 −0.855701 −0.427850 − 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) 10.6950 0.415675
\(663\) 0 0
\(664\) 8.75078 0.339596
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −47.2279 −1.82730
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 24.1033 0.927051
\(677\) 31.3050 1.20315 0.601574 − 0.798817i \(-0.294541\pi\)
0.601574 + 0.798817i \(0.294541\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 15.1115 0.578224 0.289112 − 0.957295i \(-0.406640\pi\)
0.289112 + 0.957295i \(0.406640\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 19.2918 0.733895 0.366947 − 0.930242i \(-0.380403\pi\)
0.366947 + 0.930242i \(0.380403\pi\)
\(692\) 42.9787 1.63381
\(693\) 0 0
\(694\) 13.6656 0.518740
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 11.6180 0.439749
\(699\) 0 0
\(700\) 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
\(706\) 11.9574 0.450024
\(707\) 0 0
\(708\) 0 0
\(709\) −26.0000 −0.976450 −0.488225 − 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 80.0132 2.99652
\(714\) 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
\(722\) −1.20976 −0.0450225
\(723\) 0 0
\(724\) −45.2705 −1.68247
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 30.9787 1.14189
\(737\) 0 0
\(738\) 0 0
\(739\) 44.9574 1.65379 0.826893 − 0.562360i \(-0.190106\pi\)
0.826893 + 0.562360i \(0.190106\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −44.7214 −1.64067 −0.820334 − 0.571885i \(-0.806212\pi\)
−0.820334 + 0.571885i \(0.806212\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −50.9574 −1.85946 −0.929731 − 0.368238i \(-0.879961\pi\)
−0.929731 + 0.368238i \(0.879961\pi\)
\(752\) −28.1378 −1.02608
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 13.5755 0.493083
\(759\) 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
\(766\) −10.8967 −0.393713
\(767\) 0 0
\(768\) 0 0
\(769\) 3.83282 0.138215 0.0691074 − 0.997609i \(-0.477985\pi\)
0.0691074 + 0.997609i \(0.477985\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −45.7639 −1.64601 −0.823007 − 0.568031i \(-0.807705\pi\)
−0.823007 + 0.568031i \(0.807705\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −23.5066 −0.840594
\(783\) 0 0
\(784\) −22.0213 −0.786475
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 48.6443 1.73288
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −29.6656 −1.05147
\(797\) 0.596748 0.0211379 0.0105689 − 0.999944i \(-0.496636\pi\)
0.0105689 + 0.999944i \(0.496636\pi\)
\(798\) 0 0
\(799\) 73.6656 2.60610
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) −52.0000 −1.82597 −0.912983 − 0.407997i \(-0.866228\pi\)
−0.912983 + 0.407997i \(0.866228\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −15.2148 −0.531972
\(819\) 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
\(827\) 56.8885 1.97821 0.989104 − 0.147217i \(-0.0470315\pi\)
0.989104 + 0.147217i \(0.0470315\pi\)
\(828\) 0 0
\(829\) 34.0000 1.18087 0.590434 − 0.807086i \(-0.298956\pi\)
0.590434 + 0.807086i \(0.298956\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 57.6525 1.99754
\(834\) 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
\(842\) 2.13274 0.0734992
\(843\) 0 0
\(844\) −13.5197 −0.465368
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) −30.7163 −1.05480
\(849\) 0 0
\(850\) 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
\(856\) 26.3344 0.900090
\(857\) −35.0689 −1.19793 −0.598965 − 0.800775i \(-0.704421\pi\)
−0.598965 + 0.800775i \(0.704421\pi\)
\(858\) 0 0
\(859\) −11.5410 −0.393775 −0.196887 − 0.980426i \(-0.563083\pi\)
−0.196887 + 0.980426i \(0.563083\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 55.3607 1.88450 0.942250 − 0.334911i \(-0.108706\pi\)
0.942250 + 0.334911i \(0.108706\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −9.44582 −0.319876
\(873\) 0 0
\(874\) 13.4377 0.454537
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 15.8673 0.535494
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −16.0213 −0.538246
\(887\) −46.5279 −1.56225 −0.781126 − 0.624373i \(-0.785355\pi\)
−0.781126 + 0.624373i \(0.785355\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −42.1115 −1.40921
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 80.4164 2.67906
\(902\) 0 0
\(903\) 0 0
\(904\) −6.58359 −0.218967
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) −22.3525 −0.741795
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0.772063 0.0255097
\(917\) 0 0
\(918\) 0 0
\(919\) −56.0000 −1.84727 −0.923635 − 0.383274i \(-0.874797\pi\)
−0.923635 + 0.383274i \(0.874797\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) −32.9574 −1.08014
\(932\) −41.4590 −1.35803
\(933\) 0 0
\(934\) −14.8541 −0.486041
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 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
\(947\) −59.9443 −1.94793 −0.973964 − 0.226705i \(-0.927205\pi\)
−0.973964 + 0.226705i \(0.927205\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −58.1378 −1.88327 −0.941634 − 0.336640i \(-0.890710\pi\)
−0.941634 + 0.336640i \(0.890710\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 83.6656 2.69889
\(962\) 0 0
\(963\) 0 0
\(964\) 51.6049 1.66208
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) −16.1935 −0.520479
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 39.0608 1.25030
\(977\) 4.47214 0.143076 0.0715382 − 0.997438i \(-0.477209\pi\)
0.0715382 + 0.997438i \(0.477209\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −34.3050 −1.09416 −0.547079 − 0.837081i \(-0.684260\pi\)
−0.547079 + 0.837081i \(0.684260\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −62.9574 −1.99991 −0.999954 − 0.00956046i \(-0.996957\pi\)
−0.999954 + 0.00956046i \(0.996957\pi\)
\(992\) 44.3951 1.40955
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) −10.9656 −0.347109
\(999\) 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 675.2.a.j.1.2 2
3.2 odd 2 675.2.a.q.1.1 2
5.2 odd 4 135.2.b.a.109.2 ✓ 4
5.3 odd 4 135.2.b.a.109.3 yes 4
5.4 even 2 675.2.a.q.1.1 2
15.2 even 4 135.2.b.a.109.3 yes 4
15.8 even 4 135.2.b.a.109.2 ✓ 4
15.14 odd 2 CM 675.2.a.j.1.2 2
20.3 even 4 2160.2.f.j.1729.2 4
20.7 even 4 2160.2.f.j.1729.3 4
45.2 even 12 405.2.j.h.109.3 8
45.7 odd 12 405.2.j.h.109.2 8
45.13 odd 12 405.2.j.h.379.2 8
45.22 odd 12 405.2.j.h.379.3 8
45.23 even 12 405.2.j.h.379.3 8
45.32 even 12 405.2.j.h.379.2 8
45.38 even 12 405.2.j.h.109.2 8
45.43 odd 12 405.2.j.h.109.3 8
60.23 odd 4 2160.2.f.j.1729.3 4
60.47 odd 4 2160.2.f.j.1729.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.2.b.a.109.2 ✓ 4 5.2 odd 4
135.2.b.a.109.2 ✓ 4 15.8 even 4
135.2.b.a.109.3 yes 4 5.3 odd 4
135.2.b.a.109.3 yes 4 15.2 even 4
405.2.j.h.109.2 8 45.7 odd 12
405.2.j.h.109.2 8 45.38 even 12
405.2.j.h.109.3 8 45.2 even 12
405.2.j.h.109.3 8 45.43 odd 12
405.2.j.h.379.2 8 45.13 odd 12
405.2.j.h.379.2 8 45.32 even 12
405.2.j.h.379.3 8 45.22 odd 12
405.2.j.h.379.3 8 45.23 even 12
675.2.a.j.1.2 2 1.1 even 1 trivial
675.2.a.j.1.2 2 15.14 odd 2 CM
675.2.a.q.1.1 2 3.2 odd 2
675.2.a.q.1.1 2 5.4 even 2
2160.2.f.j.1729.2 4 20.3 even 4
2160.2.f.j.1729.2 4 60.47 odd 4
2160.2.f.j.1729.3 4 20.7 even 4
2160.2.f.j.1729.3 4 60.23 odd 4