Properties

Label 1521.4.a.y.1.3
Level $1521$
Weight $4$
Character 1521.1
Self dual yes
Analytic conductor $89.742$
Analytic rank $1$
Dimension $4$
CM discriminant -39
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1521,4,Mod(1,1521)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1521.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.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: \(89.7419051187\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.8112.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 5x^{2} + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 117)
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

Embedding invariants

Embedding label 1.3
Root \(-2.07431\) of defining polynomial
Character \(\chi\) \(=\) 1521.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.52058 q^{2} +4.39445 q^{4} +9.17304 q^{5} -12.6936 q^{8} +O(q^{10})\) \(q+3.52058 q^{2} +4.39445 q^{4} +9.17304 q^{5} -12.6936 q^{8} +32.2944 q^{10} -20.4780 q^{11} -79.8444 q^{16} +40.3104 q^{20} -72.0942 q^{22} -40.8554 q^{25} -179.549 q^{32} -116.439 q^{40} +196.898 q^{41} -452.000 q^{43} -89.9894 q^{44} -640.490 q^{47} -343.000 q^{49} -143.834 q^{50} -187.845 q^{55} -579.506 q^{59} +944.654 q^{61} +6.63840 q^{64} -1190.09 q^{71} -418.244 q^{79} -732.416 q^{80} +693.193 q^{82} -94.6440 q^{83} -1591.30 q^{86} +259.939 q^{88} +1672.06 q^{89} -2254.89 q^{94} -1207.56 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 32 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 32 q^{4} - 116 q^{10} - 204 q^{16} + 476 q^{22} + 500 q^{25} - 884 q^{40} - 1808 q^{43} - 1372 q^{49} - 3232 q^{55} - 1632 q^{64} - 2924 q^{82} + 2756 q^{88} - 5140 q^{94}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.52058 1.24471 0.622356 0.782735i \(-0.286176\pi\)
0.622356 + 0.782735i \(0.286176\pi\)
\(3\) 0 0
\(4\) 4.39445 0.549306
\(5\) 9.17304 0.820462 0.410231 0.911982i \(-0.365448\pi\)
0.410231 + 0.911982i \(0.365448\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −12.6936 −0.560984
\(9\) 0 0
\(10\) 32.2944 1.02124
\(11\) −20.4780 −0.561304 −0.280652 0.959810i \(-0.590551\pi\)
−0.280652 + 0.959810i \(0.590551\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 0 0
\(15\) 0 0
\(16\) −79.8444 −1.24757
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 40.3104 0.450685
\(21\) 0 0
\(22\) −72.0942 −0.698661
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −40.8554 −0.326843
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −179.549 −0.991879
\(33\) 0 0
\(34\) 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
\(40\) −116.439 −0.460266
\(41\) 196.898 0.750006 0.375003 0.927024i \(-0.377642\pi\)
0.375003 + 0.927024i \(0.377642\pi\)
\(42\) 0 0
\(43\) −452.000 −1.60301 −0.801504 0.597989i \(-0.795967\pi\)
−0.801504 + 0.597989i \(0.795967\pi\)
\(44\) −89.9894 −0.308327
\(45\) 0 0
\(46\) 0 0
\(47\) −640.490 −1.98777 −0.993884 0.110431i \(-0.964777\pi\)
−0.993884 + 0.110431i \(0.964777\pi\)
\(48\) 0 0
\(49\) −343.000 −1.00000
\(50\) −143.834 −0.406825
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) −187.845 −0.460528
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −579.506 −1.27873 −0.639367 0.768902i \(-0.720803\pi\)
−0.639367 + 0.768902i \(0.720803\pi\)
\(60\) 0 0
\(61\) 944.654 1.98280 0.991398 0.130879i \(-0.0417798\pi\)
0.991398 + 0.130879i \(0.0417798\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 6.63840 0.0129656
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1190.09 −1.98926 −0.994632 0.103474i \(-0.967004\pi\)
−0.994632 + 0.103474i \(0.967004\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −418.244 −0.595647 −0.297824 0.954621i \(-0.596261\pi\)
−0.297824 + 0.954621i \(0.596261\pi\)
\(80\) −732.416 −1.02358
\(81\) 0 0
\(82\) 693.193 0.933541
\(83\) −94.6440 −0.125163 −0.0625815 0.998040i \(-0.519933\pi\)
−0.0625815 + 0.998040i \(0.519933\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1591.30 −1.99528
\(87\) 0 0
\(88\) 259.939 0.314882
\(89\) 1672.06 1.99143 0.995717 0.0924493i \(-0.0294696\pi\)
0.995717 + 0.0924493i \(0.0294696\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −2254.89 −2.47420
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) −1207.56 −1.24471
\(99\) 0 0
\(100\) −179.537 −0.179537
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −848.000 −0.811223 −0.405611 0.914046i \(-0.632941\pi\)
−0.405611 + 0.914046i \(0.632941\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) −661.323 −0.573224
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −2040.20 −1.59165
\(119\) 0 0
\(120\) 0 0
\(121\) −911.653 −0.684938
\(122\) 3325.73 2.46801
\(123\) 0 0
\(124\) 0 0
\(125\) −1521.40 −1.08862
\(126\) 0 0
\(127\) 2495.04 1.74330 0.871650 0.490129i \(-0.163050\pi\)
0.871650 + 0.490129i \(0.163050\pi\)
\(128\) 1459.77 1.00802
\(129\) 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
\(136\) 0 0
\(137\) −3018.79 −1.88258 −0.941288 0.337604i \(-0.890384\pi\)
−0.941288 + 0.337604i \(0.890384\pi\)
\(138\) 0 0
\(139\) −340.000 −0.207471 −0.103735 0.994605i \(-0.533079\pi\)
−0.103735 + 0.994605i \(0.533079\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4189.80 −2.47606
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2477.09 −1.36196 −0.680978 0.732304i \(-0.738445\pi\)
−0.680978 + 0.732304i \(0.738445\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −934.000 −0.474785 −0.237393 0.971414i \(-0.576293\pi\)
−0.237393 + 0.971414i \(0.576293\pi\)
\(158\) −1472.46 −0.741409
\(159\) 0 0
\(160\) −1647.01 −0.813799
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 865.256 0.411983
\(165\) 0 0
\(166\) −333.201 −0.155792
\(167\) 2446.51 1.13363 0.566815 0.823845i \(-0.308175\pi\)
0.566815 + 0.823845i \(0.308175\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) −1986.29 −0.880542
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1635.05 0.700265
\(177\) 0 0
\(178\) 5886.60 2.47876
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −4430.00 −1.81922 −0.909611 0.415460i \(-0.863621\pi\)
−0.909611 + 0.415460i \(0.863621\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −2814.60 −1.09189
\(189\) 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
\(196\) −1507.30 −0.549306
\(197\) 3977.33 1.43844 0.719220 0.694782i \(-0.244499\pi\)
0.719220 + 0.694782i \(0.244499\pi\)
\(198\) 0 0
\(199\) 5610.24 1.99849 0.999244 0.0388706i \(-0.0123760\pi\)
0.999244 + 0.0388706i \(0.0123760\pi\)
\(200\) 518.602 0.183354
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 1806.15 0.615351
\(206\) −2985.45 −1.00974
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −5740.04 −1.87280 −0.936399 0.350937i \(-0.885863\pi\)
−0.936399 + 0.350937i \(0.885863\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4146.21 −1.31521
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −825.476 −0.252971
\(221\) 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
\(227\) 6668.65 1.94984 0.974920 0.222554i \(-0.0714393\pi\)
0.974920 + 0.222554i \(0.0714393\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) −5875.24 −1.63089
\(236\) −2546.61 −0.702416
\(237\) 0 0
\(238\) 0 0
\(239\) −6085.88 −1.64712 −0.823562 0.567226i \(-0.808016\pi\)
−0.823562 + 0.567226i \(0.808016\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) −3209.54 −0.852550
\(243\) 0 0
\(244\) 4151.24 1.08916
\(245\) −3146.35 −0.820462
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −5356.19 −1.35502
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 8783.98 2.16991
\(255\) 0 0
\(256\) 5086.11 1.24173
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 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
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −10627.9 −2.34326
\(275\) 836.635 0.183458
\(276\) 0 0
\(277\) −7634.00 −1.65589 −0.827947 0.560806i \(-0.810491\pi\)
−0.827947 + 0.560806i \(0.810491\pi\)
\(278\) −1197.00 −0.258241
\(279\) 0 0
\(280\) 0 0
\(281\) 8255.10 1.75252 0.876260 0.481839i \(-0.160031\pi\)
0.876260 + 0.481839i \(0.160031\pi\)
\(282\) 0 0
\(283\) −490.355 −0.102999 −0.0514993 0.998673i \(-0.516400\pi\)
−0.0514993 + 0.998673i \(0.516400\pi\)
\(284\) −5229.79 −1.09272
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −4913.00 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 9933.00 1.98052 0.990260 0.139232i \(-0.0444635\pi\)
0.990260 + 0.139232i \(0.0444635\pi\)
\(294\) 0 0
\(295\) −5315.83 −1.04915
\(296\) 0 0
\(297\) 0 0
\(298\) −8720.79 −1.69524
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8665.35 1.62681
\(306\) 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
\(313\) 6396.25 1.15507 0.577536 0.816365i \(-0.304014\pi\)
0.577536 + 0.816365i \(0.304014\pi\)
\(314\) −3288.22 −0.590971
\(315\) 0 0
\(316\) −1837.95 −0.327193
\(317\) −7133.53 −1.26391 −0.631954 0.775006i \(-0.717747\pi\)
−0.631954 + 0.775006i \(0.717747\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 60.8943 0.0106378
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) −2499.34 −0.420741
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) −415.908 −0.0687528
\(333\) 0 0
\(334\) 8613.11 1.41104
\(335\) 0 0
\(336\) 0 0
\(337\) −10420.0 −1.68432 −0.842160 0.539228i \(-0.818716\pi\)
−0.842160 + 0.539228i \(0.818716\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 5737.51 0.899262
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 3676.81 0.556745
\(353\) 7331.69 1.10546 0.552728 0.833361i \(-0.313587\pi\)
0.552728 + 0.833361i \(0.313587\pi\)
\(354\) 0 0
\(355\) −10916.7 −1.63211
\(356\) 7347.77 1.09391
\(357\) 0 0
\(358\) 0 0
\(359\) 11077.3 1.62852 0.814259 0.580502i \(-0.197143\pi\)
0.814259 + 0.580502i \(0.197143\pi\)
\(360\) 0 0
\(361\) −6859.00 −1.00000
\(362\) −15596.1 −2.26441
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −8296.00 −1.17997 −0.589983 0.807416i \(-0.700866\pi\)
−0.589983 + 0.807416i \(0.700866\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 6526.05 0.905914 0.452957 0.891532i \(-0.350369\pi\)
0.452957 + 0.891532i \(0.350369\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 8130.13 1.11511
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12702.2 1.69465 0.847327 0.531071i \(-0.178210\pi\)
0.847327 + 0.531071i \(0.178210\pi\)
\(384\) 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
\(391\) 0 0
\(392\) 4353.91 0.560984
\(393\) 0 0
\(394\) 14002.5 1.79044
\(395\) −3836.57 −0.488706
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 19751.3 2.48754
\(399\) 0 0
\(400\) 3262.07 0.407759
\(401\) 15342.6 1.91066 0.955328 0.295549i \(-0.0955026\pi\)
0.955328 + 0.295549i \(0.0955026\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 6358.68 0.765934
\(411\) 0 0
\(412\) −3726.49 −0.445609
\(413\) 0 0
\(414\) 0 0
\(415\) −868.173 −0.102691
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) −20208.2 −2.33109
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) −14597.1 −1.63705
\(431\) −320.305 −0.0357971 −0.0178985 0.999840i \(-0.505698\pi\)
−0.0178985 + 0.999840i \(0.505698\pi\)
\(432\) 0 0
\(433\) −36.0555 −0.00400166 −0.00200083 0.999998i \(-0.500637\pi\)
−0.00200083 + 0.999998i \(0.500637\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 11320.0 1.23069 0.615346 0.788257i \(-0.289016\pi\)
0.615346 + 0.788257i \(0.289016\pi\)
\(440\) 2384.43 0.258349
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 15337.8 1.63390
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 333.683 0.0350723 0.0175361 0.999846i \(-0.494418\pi\)
0.0175361 + 0.999846i \(0.494418\pi\)
\(450\) 0 0
\(451\) −4032.06 −0.420981
\(452\) 0 0
\(453\) 0 0
\(454\) 23477.5 2.42699
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 17433.8 1.76133 0.880666 0.473738i \(-0.157095\pi\)
0.880666 + 0.473738i \(0.157095\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −20684.2 −2.02998
\(471\) 0 0
\(472\) 7356.03 0.717349
\(473\) 9256.04 0.899774
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −21425.8 −2.05019
\(479\) −5200.84 −0.496101 −0.248050 0.968747i \(-0.579790\pi\)
−0.248050 + 0.968747i \(0.579790\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −4006.21 −0.376241
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) −11991.1 −1.11232
\(489\) 0 0
\(490\) −11077.0 −1.02124
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −6685.70 −0.597988
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 10964.3 0.957605
\(509\) 22966.8 1.99997 0.999987 0.00508931i \(-0.00161998\pi\)
0.999987 + 0.00508931i \(0.00161998\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 6227.90 0.537572
\(513\) 0 0
\(514\) 0 0
\(515\) −7778.74 −0.665577
\(516\) 0 0
\(517\) 13115.9 1.11574
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 16148.0 1.35010 0.675050 0.737772i \(-0.264122\pi\)
0.675050 + 0.737772i \(0.264122\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −12167.0 −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
\(538\) 0 0
\(539\) 7023.94 0.561304
\(540\) 0 0
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 23996.0 1.87568 0.937838 0.347073i \(-0.112824\pi\)
0.937838 + 0.347073i \(0.112824\pi\)
\(548\) −13265.9 −1.03411
\(549\) 0 0
\(550\) 2945.44 0.228352
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −26876.1 −2.06111
\(555\) 0 0
\(556\) −1494.11 −0.113965
\(557\) 22258.1 1.69319 0.846595 0.532237i \(-0.178648\pi\)
0.846595 + 0.532237i \(0.178648\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 29062.7 2.18138
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1726.33 −0.128203
\(567\) 0 0
\(568\) 15106.6 1.11595
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) −25411.9 −1.86244 −0.931222 0.364451i \(-0.881257\pi\)
−0.931222 + 0.364451i \(0.881257\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) −17296.6 −1.24471
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 34969.9 2.46517
\(587\) −19338.0 −1.35974 −0.679868 0.733335i \(-0.737963\pi\)
−0.679868 + 0.733335i \(0.737963\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −18714.8 −1.30589
\(591\) 0 0
\(592\) 0 0
\(593\) −25958.2 −1.79760 −0.898798 0.438363i \(-0.855558\pi\)
−0.898798 + 0.438363i \(0.855558\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −10885.5 −0.748131
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 12626.6 0.856991 0.428495 0.903544i \(-0.359044\pi\)
0.428495 + 0.903544i \(0.359044\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −8362.63 −0.561966
\(606\) 0 0
\(607\) −25504.0 −1.70540 −0.852698 0.522404i \(-0.825035\pi\)
−0.852698 + 0.522404i \(0.825035\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 30507.0 2.02491
\(611\) 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
\(617\) −29859.9 −1.94832 −0.974160 0.225860i \(-0.927481\pi\)
−0.974160 + 0.225860i \(0.927481\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −8848.92 −0.566331
\(626\) 22518.5 1.43773
\(627\) 0 0
\(628\) −4104.42 −0.260803
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 5309.03 0.334148
\(633\) 0 0
\(634\) −25114.1 −1.57320
\(635\) 22887.1 1.43031
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 13390.5 0.827040
\(641\) 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
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 11867.1 0.717758
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −15721.2 −0.935684
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1201.37 0.0702144
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 10751.0 0.622710
\(669\) 0 0
\(670\) 0 0
\(671\) −19344.6 −1.11295
\(672\) 0 0
\(673\) 25522.0 1.46181 0.730907 0.682477i \(-0.239097\pi\)
0.730907 + 0.682477i \(0.239097\pi\)
\(674\) −36684.5 −2.09649
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −32750.6 −1.83480 −0.917399 0.397968i \(-0.869715\pi\)
−0.917399 + 0.397968i \(0.869715\pi\)
\(684\) 0 0
\(685\) −27691.5 −1.54458
\(686\) 0 0
\(687\) 0 0
\(688\) 36089.7 1.99986
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3118.83 −0.170222
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −135.941 −0.00727765
\(705\) 0 0
\(706\) 25811.8 1.37597
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) −38433.2 −2.03151
\(711\) 0 0
\(712\) −21224.4 −1.11716
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 38998.5 2.02704
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −24147.6 −1.24471
\(723\) 0 0
\(724\) −19467.4 −0.999310
\(725\) 0 0
\(726\) 0 0
\(727\) 28455.0 1.45163 0.725817 0.687888i \(-0.241462\pi\)
0.725817 + 0.687888i \(0.241462\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) −29206.7 −1.46872
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 19936.4 0.984382 0.492191 0.870487i \(-0.336196\pi\)
0.492191 + 0.870487i \(0.336196\pi\)
\(744\) 0 0
\(745\) −22722.5 −1.11743
\(746\) 22975.4 1.12760
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −26120.0 −1.26915 −0.634575 0.772861i \(-0.718825\pi\)
−0.634575 + 0.772861i \(0.718825\pi\)
\(752\) 51139.6 2.47988
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −35009.9 −1.68092 −0.840460 0.541873i \(-0.817715\pi\)
−0.840460 + 0.541873i \(0.817715\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 28936.4 1.37838 0.689189 0.724582i \(-0.257967\pi\)
0.689189 + 0.724582i \(0.257967\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 44719.1 2.10936
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 3484.00 0.162110 0.0810548 0.996710i \(-0.474171\pi\)
0.0810548 + 0.996710i \(0.474171\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 24370.6 1.11658
\(782\) 0 0
\(783\) 0 0
\(784\) 27386.6 1.24757
\(785\) −8567.62 −0.389543
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 17478.2 0.790144
\(789\) 0 0
\(790\) −13506.9 −0.608297
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 24653.9 1.09778
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 7335.55 0.324189
\(801\) 0 0
\(802\) 54014.8 2.37821
\(803\) 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
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 7937.03 0.338016
\(821\) −33048.4 −1.40487 −0.702433 0.711749i \(-0.747903\pi\)
−0.702433 + 0.711749i \(0.747903\pi\)
\(822\) 0 0
\(823\) −37352.0 −1.58203 −0.791014 0.611798i \(-0.790446\pi\)
−0.791014 + 0.611798i \(0.790446\pi\)
\(824\) 10764.2 0.455083
\(825\) 0 0
\(826\) 0 0
\(827\) 31167.2 1.31051 0.655253 0.755409i \(-0.272562\pi\)
0.655253 + 0.755409i \(0.272562\pi\)
\(828\) 0 0
\(829\) 3079.14 0.129002 0.0645012 0.997918i \(-0.479454\pi\)
0.0645012 + 0.997918i \(0.479454\pi\)
\(830\) −3056.47 −0.127821
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 22441.9 0.930101
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −46872.5 −1.92875 −0.964374 0.264543i \(-0.914779\pi\)
−0.964374 + 0.264543i \(0.914779\pi\)
\(840\) 0 0
\(841\) −24389.0 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) −25224.3 −1.02874
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 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
\(856\) 0 0
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 43324.3 1.72085 0.860423 0.509581i \(-0.170200\pi\)
0.860423 + 0.509581i \(0.170200\pi\)
\(860\) −18220.3 −0.722451
\(861\) 0 0
\(862\) −1127.66 −0.0445571
\(863\) 23594.8 0.930678 0.465339 0.885133i \(-0.345932\pi\)
0.465339 + 0.885133i \(0.345932\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −126.936 −0.00498091
\(867\) 0 0
\(868\) 0 0
\(869\) 8564.79 0.334339
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 39852.9 1.53186
\(879\) 0 0
\(880\) 14998.4 0.574540
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) −52410.3 −1.99745 −0.998724 0.0504988i \(-0.983919\pi\)
−0.998724 + 0.0504988i \(0.983919\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 53998.0 2.03373
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 1174.75 0.0436549
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) −14195.2 −0.524000
\(903\) 0 0
\(904\) 0 0
\(905\) −40636.6 −1.49260
\(906\) 0 0
\(907\) −35017.1 −1.28195 −0.640973 0.767564i \(-0.721469\pi\)
−0.640973 + 0.767564i \(0.721469\pi\)
\(908\) 29305.0 1.07106
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 1938.12 0.0702545
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −36762.2 −1.31956 −0.659779 0.751460i \(-0.729350\pi\)
−0.659779 + 0.751460i \(0.729350\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 61377.1 2.19235
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 7352.53 0.259665 0.129832 0.991536i \(-0.458556\pi\)
0.129832 + 0.991536i \(0.458556\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 13275.6 0.462856 0.231428 0.972852i \(-0.425660\pi\)
0.231428 + 0.972852i \(0.425660\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −25818.4 −0.895856
\(941\) 15462.1 0.535652 0.267826 0.963467i \(-0.413695\pi\)
0.267826 + 0.963467i \(0.413695\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 46270.3 1.59531
\(945\) 0 0
\(946\) 32586.6 1.11996
\(947\) −56498.4 −1.93870 −0.969352 0.245678i \(-0.920989\pi\)
−0.969352 + 0.245678i \(0.920989\pi\)
\(948\) 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
\(956\) −26744.1 −0.904775
\(957\) 0 0
\(958\) −18309.9 −0.617502
\(959\) 0 0
\(960\) 0 0
\(961\) −29791.0 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 11572.2 0.384239
\(969\) 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
\(976\) −75425.4 −2.47368
\(977\) 52089.2 1.70571 0.852856 0.522146i \(-0.174868\pi\)
0.852856 + 0.522146i \(0.174868\pi\)
\(978\) 0 0
\(979\) −34240.3 −1.11780
\(980\) −13826.5 −0.450685
\(981\) 0 0
\(982\) 0 0
\(983\) 60639.0 1.96753 0.983766 0.179454i \(-0.0574331\pi\)
0.983766 + 0.179454i \(0.0574331\pi\)
\(984\) 0 0
\(985\) 36484.2 1.18019
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −23272.0 −0.745973 −0.372987 0.927837i \(-0.621666\pi\)
−0.372987 + 0.927837i \(0.621666\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 51462.9 1.63968
\(996\) 0 0
\(997\) −21634.0 −0.687217 −0.343609 0.939113i \(-0.611649\pi\)
−0.343609 + 0.939113i \(0.611649\pi\)
\(998\) 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 1521.4.a.y.1.3 4
3.2 odd 2 inner 1521.4.a.y.1.2 4
13.5 odd 4 117.4.b.c.64.2 4
13.8 odd 4 117.4.b.c.64.3 yes 4
13.12 even 2 inner 1521.4.a.y.1.2 4
39.5 even 4 117.4.b.c.64.3 yes 4
39.8 even 4 117.4.b.c.64.2 4
39.38 odd 2 CM 1521.4.a.y.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.4.b.c.64.2 4 13.5 odd 4
117.4.b.c.64.2 4 39.8 even 4
117.4.b.c.64.3 yes 4 13.8 odd 4
117.4.b.c.64.3 yes 4 39.5 even 4
1521.4.a.y.1.2 4 3.2 odd 2 inner
1521.4.a.y.1.2 4 13.12 even 2 inner
1521.4.a.y.1.3 4 1.1 even 1 trivial
1521.4.a.y.1.3 4 39.38 odd 2 CM