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Properties

Label 1728.4.a.bb.1.1
Level $1728$
Weight $4$
Character 1728.1
Self dual yes
Analytic conductor $101.955$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1728,4,Mod(1,1728)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1728.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1728.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: \(101.955300490\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 54)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1728.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+12.0000 q^{5} +7.00000 q^{7} +O(q^{10})\) \(q+12.0000 q^{5} +7.00000 q^{7} -60.0000 q^{11} +79.0000 q^{13} +108.000 q^{17} +11.0000 q^{19} -132.000 q^{23} +19.0000 q^{25} +96.0000 q^{29} -20.0000 q^{31} +84.0000 q^{35} +169.000 q^{37} -192.000 q^{41} +488.000 q^{43} +204.000 q^{47} -294.000 q^{49} +360.000 q^{53} -720.000 q^{55} -156.000 q^{59} -83.0000 q^{61} +948.000 q^{65} +47.0000 q^{67} +216.000 q^{71} -511.000 q^{73} -420.000 q^{77} +529.000 q^{79} +1128.00 q^{83} +1296.00 q^{85} -36.0000 q^{89} +553.000 q^{91} +132.000 q^{95} +605.000 q^{97} +O(q^{100})\)

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 0
\(3\) 0 0
\(4\) 0 0
\(5\) 12.0000 1.07331 0.536656 − 0.843801i \(-0.319687\pi\)
0.536656 + 0.843801i \(0.319687\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964 0.188982 − 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −60.0000 −1.64461 −0.822304 − 0.569049i \(-0.807311\pi\)
−0.822304 + 0.569049i \(0.807311\pi\)
\(12\) 0 0
\(13\) 79.0000 1.68544 0.842718 − 0.538356i \(-0.180954\pi\)
0.842718 + 0.538356i \(0.180954\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 108.000 1.54081 0.770407 − 0.637552i \(-0.220053\pi\)
0.770407 + 0.637552i \(0.220053\pi\)
\(18\) 0 0
\(19\) 11.0000 0.132820 0.0664098 − 0.997792i \(-0.478846\pi\)
0.0664098 + 0.997792i \(0.478846\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −132.000 −1.19669 −0.598346 − 0.801238i \(-0.704175\pi\)
−0.598346 + 0.801238i \(0.704175\pi\)
\(24\) 0 0
\(25\) 19.0000 0.152000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 96.0000 0.614716 0.307358 − 0.951594i \(-0.400555\pi\)
0.307358 + 0.951594i \(0.400555\pi\)
\(30\) 0 0
\(31\) −20.0000 −0.115874 −0.0579372 − 0.998320i \(-0.518452\pi\)
−0.0579372 + 0.998320i \(0.518452\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 84.0000 0.405674
\(36\) 0 0
\(37\) 169.000 0.750903 0.375452 − 0.926842i \(-0.377488\pi\)
0.375452 + 0.926842i \(0.377488\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −192.000 −0.731350 −0.365675 − 0.930743i \(-0.619162\pi\)
−0.365675 + 0.930743i \(0.619162\pi\)
\(42\) 0 0
\(43\) 488.000 1.73068 0.865341 − 0.501184i \(-0.167102\pi\)
0.865341 + 0.501184i \(0.167102\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 204.000 0.633116 0.316558 − 0.948573i \(-0.397473\pi\)
0.316558 + 0.948573i \(0.397473\pi\)
\(48\) 0 0
\(49\) −294.000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 360.000 0.933015 0.466508 − 0.884517i \(-0.345512\pi\)
0.466508 + 0.884517i \(0.345512\pi\)
\(54\) 0 0
\(55\) −720.000 −1.76518
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −156.000 −0.344228 −0.172114 − 0.985077i \(-0.555060\pi\)
−0.172114 + 0.985077i \(0.555060\pi\)
\(60\) 0 0
\(61\) −83.0000 −0.174214 −0.0871071 − 0.996199i \(-0.527762\pi\)
−0.0871071 + 0.996199i \(0.527762\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 948.000 1.80900
\(66\) 0 0
\(67\) 47.0000 0.0857010 0.0428505 − 0.999081i \(-0.486356\pi\)
0.0428505 + 0.999081i \(0.486356\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 216.000 0.361049 0.180525 − 0.983570i \(-0.442220\pi\)
0.180525 + 0.983570i \(0.442220\pi\)
\(72\) 0 0
\(73\) −511.000 −0.819288 −0.409644 − 0.912245i \(-0.634347\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −420.000 −0.621603
\(78\) 0 0
\(79\) 529.000 0.753382 0.376691 − 0.926339i \(-0.377062\pi\)
0.376691 + 0.926339i \(0.377062\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1128.00 1.49174 0.745868 − 0.666094i \(-0.232035\pi\)
0.745868 + 0.666094i \(0.232035\pi\)
\(84\) 0 0
\(85\) 1296.00 1.65378
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −36.0000 −0.0428763 −0.0214382 − 0.999770i \(-0.506825\pi\)
−0.0214382 + 0.999770i \(0.506825\pi\)
\(90\) 0 0
\(91\) 553.000 0.637035
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 132.000 0.142557
\(96\) 0 0
\(97\) 605.000 0.633283 0.316641 − 0.948545i \(-0.397445\pi\)
0.316641 + 0.948545i \(0.397445\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1248.00 1.22951 0.614756 − 0.788718i \(-0.289255\pi\)
0.614756 + 0.788718i \(0.289255\pi\)
\(102\) 0 0
\(103\) −965.000 −0.923148 −0.461574 − 0.887102i \(-0.652715\pi\)
−0.461574 + 0.887102i \(0.652715\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1332.00 −1.20345 −0.601726 − 0.798703i \(-0.705520\pi\)
−0.601726 + 0.798703i \(0.705520\pi\)
\(108\) 0 0
\(109\) 1942.00 1.70651 0.853256 − 0.521492i \(-0.174624\pi\)
0.853256 + 0.521492i \(0.174624\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −516.000 −0.429568 −0.214784 − 0.976662i \(-0.568905\pi\)
−0.214784 + 0.976662i \(0.568905\pi\)
\(114\) 0 0
\(115\) −1584.00 −1.28442
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 756.000 0.582373
\(120\) 0 0
\(121\) 2269.00 1.70473
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1272.00 −0.910169
\(126\) 0 0
\(127\) 52.0000 0.0363327 0.0181664 − 0.999835i \(-0.494217\pi\)
0.0181664 + 0.999835i \(0.494217\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −48.0000 −0.0320136 −0.0160068 − 0.999872i \(-0.505095\pi\)
−0.0160068 + 0.999872i \(0.505095\pi\)
\(132\) 0 0
\(133\) 77.0000 0.0502011
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2364.00 −1.47423 −0.737117 − 0.675765i \(-0.763814\pi\)
−0.737117 + 0.675765i \(0.763814\pi\)
\(138\) 0 0
\(139\) 173.000 0.105566 0.0527830 − 0.998606i \(-0.483191\pi\)
0.0527830 + 0.998606i \(0.483191\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4740.00 −2.77188
\(144\) 0 0
\(145\) 1152.00 0.659782
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1608.00 −0.884111 −0.442055 − 0.896988i \(-0.645751\pi\)
−0.442055 + 0.896988i \(0.645751\pi\)
\(150\) 0 0
\(151\) 997.000 0.537316 0.268658 − 0.963236i \(-0.413420\pi\)
0.268658 + 0.963236i \(0.413420\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −240.000 −0.124369
\(156\) 0 0
\(157\) −614.000 −0.312118 −0.156059 − 0.987748i \(-0.549879\pi\)
−0.156059 + 0.987748i \(0.549879\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −924.000 −0.452307
\(162\) 0 0
\(163\) 2693.00 1.29406 0.647031 − 0.762464i \(-0.276011\pi\)
0.647031 + 0.762464i \(0.276011\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1164.00 0.539359 0.269680 − 0.962950i \(-0.413082\pi\)
0.269680 + 0.962950i \(0.413082\pi\)
\(168\) 0 0
\(169\) 4044.00 1.84069
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3648.00 −1.60319 −0.801596 − 0.597866i \(-0.796016\pi\)
−0.801596 + 0.597866i \(0.796016\pi\)
\(174\) 0 0
\(175\) 133.000 0.0574506
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1800.00 −0.751611 −0.375805 − 0.926699i \(-0.622634\pi\)
−0.375805 + 0.926699i \(0.622634\pi\)
\(180\) 0 0
\(181\) 547.000 0.224631 0.112315 − 0.993673i \(-0.464173\pi\)
0.112315 + 0.993673i \(0.464173\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2028.00 0.805954
\(186\) 0 0
\(187\) −6480.00 −2.53403
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3156.00 1.19560 0.597801 − 0.801644i \(-0.296041\pi\)
0.597801 + 0.801644i \(0.296041\pi\)
\(192\) 0 0
\(193\) 1127.00 0.420328 0.210164 − 0.977666i \(-0.432600\pi\)
0.210164 + 0.977666i \(0.432600\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1116.00 0.403613 0.201806 − 0.979425i \(-0.435319\pi\)
0.201806 + 0.979425i \(0.435319\pi\)
\(198\) 0 0
\(199\) 3283.00 1.16948 0.584738 − 0.811222i \(-0.301197\pi\)
0.584738 + 0.811222i \(0.301197\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 672.000 0.232341
\(204\) 0 0
\(205\) −2304.00 −0.784968
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −660.000 −0.218436
\(210\) 0 0
\(211\) −295.000 −0.0962495 −0.0481247 − 0.998841i \(-0.515324\pi\)
−0.0481247 + 0.998841i \(0.515324\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5856.00 1.85756
\(216\) 0 0
\(217\) −140.000 −0.0437964
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 8532.00 2.59694
\(222\) 0 0
\(223\) 2644.00 0.793970 0.396985 − 0.917825i \(-0.370056\pi\)
0.396985 + 0.917825i \(0.370056\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6024.00 1.76135 0.880676 − 0.473719i \(-0.157089\pi\)
0.880676 + 0.473719i \(0.157089\pi\)
\(228\) 0 0
\(229\) 4462.00 1.28759 0.643793 − 0.765200i \(-0.277360\pi\)
0.643793 + 0.765200i \(0.277360\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1008.00 0.283417 0.141709 − 0.989908i \(-0.454740\pi\)
0.141709 + 0.989908i \(0.454740\pi\)
\(234\) 0 0
\(235\) 2448.00 0.679532
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −5064.00 −1.37056 −0.685278 − 0.728281i \(-0.740319\pi\)
−0.685278 + 0.728281i \(0.740319\pi\)
\(240\) 0 0
\(241\) 6257.00 1.67240 0.836201 − 0.548423i \(-0.184772\pi\)
0.836201 + 0.548423i \(0.184772\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3528.00 −0.919982
\(246\) 0 0
\(247\) 869.000 0.223859
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2160.00 0.543179 0.271590 − 0.962413i \(-0.412451\pi\)
0.271590 + 0.962413i \(0.412451\pi\)
\(252\) 0 0
\(253\) 7920.00 1.96809
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 168.000 0.0407765 0.0203882 − 0.999792i \(-0.493510\pi\)
0.0203882 + 0.999792i \(0.493510\pi\)
\(258\) 0 0
\(259\) 1183.00 0.283815
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2424.00 −0.568328 −0.284164 − 0.958776i \(-0.591716\pi\)
−0.284164 + 0.958776i \(0.591716\pi\)
\(264\) 0 0
\(265\) 4320.00 1.00142
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −396.000 −0.0897567 −0.0448783 − 0.998992i \(-0.514290\pi\)
−0.0448783 + 0.998992i \(0.514290\pi\)
\(270\) 0 0
\(271\) −1811.00 −0.405942 −0.202971 − 0.979185i \(-0.565060\pi\)
−0.202971 + 0.979185i \(0.565060\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1140.00 −0.249980
\(276\) 0 0
\(277\) 3022.00 0.655503 0.327752 − 0.944764i \(-0.393709\pi\)
0.327752 + 0.944764i \(0.393709\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3072.00 0.652171 0.326086 − 0.945340i \(-0.394270\pi\)
0.326086 + 0.945340i \(0.394270\pi\)
\(282\) 0 0
\(283\) −8080.00 −1.69719 −0.848597 − 0.529039i \(-0.822552\pi\)
−0.848597 + 0.529039i \(0.822552\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1344.00 −0.276424
\(288\) 0 0
\(289\) 6751.00 1.37411
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4668.00 −0.930742 −0.465371 − 0.885116i \(-0.654079\pi\)
−0.465371 + 0.885116i \(0.654079\pi\)
\(294\) 0 0
\(295\) −1872.00 −0.369465
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −10428.0 −2.01695
\(300\) 0 0
\(301\) 3416.00 0.654136
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −996.000 −0.186986
\(306\) 0 0
\(307\) 6752.00 1.25523 0.627617 − 0.778522i \(-0.284030\pi\)
0.627617 + 0.778522i \(0.284030\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1812.00 0.330383 0.165191 − 0.986262i \(-0.447176\pi\)
0.165191 + 0.986262i \(0.447176\pi\)
\(312\) 0 0
\(313\) 6203.00 1.12017 0.560087 − 0.828434i \(-0.310768\pi\)
0.560087 + 0.828434i \(0.310768\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10968.0 1.94329 0.971647 − 0.236436i \(-0.0759793\pi\)
0.971647 + 0.236436i \(0.0759793\pi\)
\(318\) 0 0
\(319\) −5760.00 −1.01097
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1188.00 0.204650
\(324\) 0 0
\(325\) 1501.00 0.256186
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1428.00 0.239295
\(330\) 0 0
\(331\) 8165.00 1.35586 0.677929 − 0.735127i \(-0.262878\pi\)
0.677929 + 0.735127i \(0.262878\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 564.000 0.0919839
\(336\) 0 0
\(337\) −6523.00 −1.05439 −0.527197 − 0.849743i \(-0.676757\pi\)
−0.527197 + 0.849743i \(0.676757\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1200.00 0.190568
\(342\) 0 0
\(343\) −4459.00 −0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6168.00 −0.954224 −0.477112 − 0.878843i \(-0.658316\pi\)
−0.477112 + 0.878843i \(0.658316\pi\)
\(348\) 0 0
\(349\) 6001.00 0.920419 0.460209 − 0.887810i \(-0.347774\pi\)
0.460209 + 0.887810i \(0.347774\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 552.000 0.0832294 0.0416147 − 0.999134i \(-0.486750\pi\)
0.0416147 + 0.999134i \(0.486750\pi\)
\(354\) 0 0
\(355\) 2592.00 0.387519
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5004.00 −0.735657 −0.367829 − 0.929894i \(-0.619899\pi\)
−0.367829 + 0.929894i \(0.619899\pi\)
\(360\) 0 0
\(361\) −6738.00 −0.982359
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6132.00 −0.879352
\(366\) 0 0
\(367\) 4291.00 0.610323 0.305161 − 0.952301i \(-0.401290\pi\)
0.305161 + 0.952301i \(0.401290\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2520.00 0.352647
\(372\) 0 0
\(373\) 2833.00 0.393263 0.196632 − 0.980477i \(-0.437000\pi\)
0.196632 + 0.980477i \(0.437000\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 7584.00 1.03606
\(378\) 0 0
\(379\) −5137.00 −0.696227 −0.348113 − 0.937452i \(-0.613178\pi\)
−0.348113 + 0.937452i \(0.613178\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5088.00 0.678811 0.339406 − 0.940640i \(-0.389774\pi\)
0.339406 + 0.940640i \(0.389774\pi\)
\(384\) 0 0
\(385\) −5040.00 −0.667175
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 7980.00 1.04011 0.520054 − 0.854133i \(-0.325912\pi\)
0.520054 + 0.854133i \(0.325912\pi\)
\(390\) 0 0
\(391\) −14256.0 −1.84388
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6348.00 0.808614
\(396\) 0 0
\(397\) 1834.00 0.231853 0.115927 − 0.993258i \(-0.463016\pi\)
0.115927 + 0.993258i \(0.463016\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1464.00 0.182316 0.0911579 − 0.995836i \(-0.470943\pi\)
0.0911579 + 0.995836i \(0.470943\pi\)
\(402\) 0 0
\(403\) −1580.00 −0.195299
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10140.0 −1.23494
\(408\) 0 0
\(409\) −151.000 −0.0182554 −0.00912771 − 0.999958i \(-0.502905\pi\)
−0.00912771 + 0.999958i \(0.502905\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1092.00 −0.130106
\(414\) 0 0
\(415\) 13536.0 1.60110
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 11508.0 1.34177 0.670886 − 0.741560i \(-0.265914\pi\)
0.670886 + 0.741560i \(0.265914\pi\)
\(420\) 0 0
\(421\) 6271.00 0.725962 0.362981 − 0.931797i \(-0.381759\pi\)
0.362981 + 0.931797i \(0.381759\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2052.00 0.234204
\(426\) 0 0
\(427\) −581.000 −0.0658467
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 9468.00 1.05814 0.529069 − 0.848579i \(-0.322541\pi\)
0.529069 + 0.848579i \(0.322541\pi\)
\(432\) 0 0
\(433\) 3026.00 0.335844 0.167922 − 0.985800i \(-0.446294\pi\)
0.167922 + 0.985800i \(0.446294\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1452.00 −0.158944
\(438\) 0 0
\(439\) −11180.0 −1.21547 −0.607736 − 0.794139i \(-0.707922\pi\)
−0.607736 + 0.794139i \(0.707922\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 840.000 0.0900894 0.0450447 − 0.998985i \(-0.485657\pi\)
0.0450447 + 0.998985i \(0.485657\pi\)
\(444\) 0 0
\(445\) −432.000 −0.0460197
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −12780.0 −1.34326 −0.671632 − 0.740885i \(-0.734406\pi\)
−0.671632 + 0.740885i \(0.734406\pi\)
\(450\) 0 0
\(451\) 11520.0 1.20278
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6636.00 0.683737
\(456\) 0 0
\(457\) −15658.0 −1.60274 −0.801368 − 0.598172i \(-0.795894\pi\)
−0.801368 + 0.598172i \(0.795894\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −15564.0 −1.57242 −0.786212 − 0.617956i \(-0.787961\pi\)
−0.786212 + 0.617956i \(0.787961\pi\)
\(462\) 0 0
\(463\) 4183.00 0.419871 0.209936 − 0.977715i \(-0.432675\pi\)
0.209936 + 0.977715i \(0.432675\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −13932.0 −1.38051 −0.690253 − 0.723568i \(-0.742501\pi\)
−0.690253 + 0.723568i \(0.742501\pi\)
\(468\) 0 0
\(469\) 329.000 0.0323919
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −29280.0 −2.84629
\(474\) 0 0
\(475\) 209.000 0.0201886
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2712.00 −0.258694 −0.129347 − 0.991599i \(-0.541288\pi\)
−0.129347 + 0.991599i \(0.541288\pi\)
\(480\) 0 0
\(481\) 13351.0 1.26560
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7260.00 0.679711
\(486\) 0 0
\(487\) 9439.00 0.878279 0.439140 − 0.898419i \(-0.355283\pi\)
0.439140 + 0.898419i \(0.355283\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 11724.0 1.07759 0.538795 − 0.842437i \(-0.318880\pi\)
0.538795 + 0.842437i \(0.318880\pi\)
\(492\) 0 0
\(493\) 10368.0 0.947163
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1512.00 0.136464
\(498\) 0 0
\(499\) −11968.0 −1.07367 −0.536835 − 0.843687i \(-0.680380\pi\)
−0.536835 + 0.843687i \(0.680380\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 8892.00 0.788220 0.394110 − 0.919063i \(-0.371053\pi\)
0.394110 + 0.919063i \(0.371053\pi\)
\(504\) 0 0
\(505\) 14976.0 1.31965
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −6756.00 −0.588319 −0.294160 − 0.955756i \(-0.595040\pi\)
−0.294160 + 0.955756i \(0.595040\pi\)
\(510\) 0 0
\(511\) −3577.00 −0.309662
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −11580.0 −0.990827
\(516\) 0 0
\(517\) −12240.0 −1.04123
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6228.00 0.523711 0.261856 − 0.965107i \(-0.415666\pi\)
0.261856 + 0.965107i \(0.415666\pi\)
\(522\) 0 0
\(523\) 11639.0 0.973113 0.486556 − 0.873649i \(-0.338253\pi\)
0.486556 + 0.873649i \(0.338253\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2160.00 −0.178541
\(528\) 0 0
\(529\) 5257.00 0.432070
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −15168.0 −1.23264
\(534\) 0 0
\(535\) −15984.0 −1.29168
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 17640.0 1.40966
\(540\) 0 0
\(541\) −17705.0 −1.40702 −0.703510 − 0.710686i \(-0.748385\pi\)
−0.703510 + 0.710686i \(0.748385\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 23304.0 1.83162
\(546\) 0 0
\(547\) 3485.00 0.272409 0.136205 − 0.990681i \(-0.456510\pi\)
0.136205 + 0.990681i \(0.456510\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1056.00 0.0816463
\(552\) 0 0
\(553\) 3703.00 0.284751
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19116.0 −1.45417 −0.727083 − 0.686549i \(-0.759125\pi\)
−0.727083 + 0.686549i \(0.759125\pi\)
\(558\) 0 0
\(559\) 38552.0 2.91695
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −22368.0 −1.67442 −0.837210 − 0.546881i \(-0.815815\pi\)
−0.837210 + 0.546881i \(0.815815\pi\)
\(564\) 0 0
\(565\) −6192.00 −0.461061
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8340.00 −0.614466 −0.307233 − 0.951634i \(-0.599403\pi\)
−0.307233 + 0.951634i \(0.599403\pi\)
\(570\) 0 0
\(571\) −14677.0 −1.07568 −0.537840 − 0.843047i \(-0.680760\pi\)
−0.537840 + 0.843047i \(0.680760\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2508.00 −0.181897
\(576\) 0 0
\(577\) −10069.0 −0.726478 −0.363239 − 0.931696i \(-0.618329\pi\)
−0.363239 + 0.931696i \(0.618329\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7896.00 0.563823
\(582\) 0 0
\(583\) −21600.0 −1.53444
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1572.00 −0.110534 −0.0552669 − 0.998472i \(-0.517601\pi\)
−0.0552669 + 0.998472i \(0.517601\pi\)
\(588\) 0 0
\(589\) −220.000 −0.0153904
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1368.00 −0.0947336 −0.0473668 − 0.998878i \(-0.515083\pi\)
−0.0473668 + 0.998878i \(0.515083\pi\)
\(594\) 0 0
\(595\) 9072.00 0.625068
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −23712.0 −1.61744 −0.808720 − 0.588194i \(-0.799839\pi\)
−0.808720 + 0.588194i \(0.799839\pi\)
\(600\) 0 0
\(601\) −11014.0 −0.747538 −0.373769 − 0.927522i \(-0.621935\pi\)
−0.373769 + 0.927522i \(0.621935\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 27228.0 1.82971
\(606\) 0 0
\(607\) 6415.00 0.428957 0.214478 − 0.976729i \(-0.431195\pi\)
0.214478 + 0.976729i \(0.431195\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 16116.0 1.06708
\(612\) 0 0
\(613\) −15851.0 −1.04440 −0.522199 − 0.852824i \(-0.674888\pi\)
−0.522199 + 0.852824i \(0.674888\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5772.00 −0.376616 −0.188308 − 0.982110i \(-0.560300\pi\)
−0.188308 + 0.982110i \(0.560300\pi\)
\(618\) 0 0
\(619\) −27781.0 −1.80390 −0.901949 − 0.431843i \(-0.857863\pi\)
−0.901949 + 0.431843i \(0.857863\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −252.000 −0.0162057
\(624\) 0 0
\(625\) −17639.0 −1.12890
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 18252.0 1.15700
\(630\) 0 0
\(631\) 29869.0 1.88442 0.942208 − 0.335029i \(-0.108746\pi\)
0.942208 + 0.335029i \(0.108746\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 624.000 0.0389964
\(636\) 0 0
\(637\) −23226.0 −1.44466
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −3480.00 −0.214433 −0.107217 − 0.994236i \(-0.534194\pi\)
−0.107217 + 0.994236i \(0.534194\pi\)
\(642\) 0 0
\(643\) −7432.00 −0.455816 −0.227908 − 0.973683i \(-0.573188\pi\)
−0.227908 + 0.973683i \(0.573188\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −12960.0 −0.787496 −0.393748 − 0.919218i \(-0.628822\pi\)
−0.393748 + 0.919218i \(0.628822\pi\)
\(648\) 0 0
\(649\) 9360.00 0.566120
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 23592.0 1.41382 0.706911 − 0.707302i \(-0.250088\pi\)
0.706911 + 0.707302i \(0.250088\pi\)
\(654\) 0 0
\(655\) −576.000 −0.0343606
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −32280.0 −1.90812 −0.954059 − 0.299618i \(-0.903141\pi\)
−0.954059 + 0.299618i \(0.903141\pi\)
\(660\) 0 0
\(661\) −22619.0 −1.33098 −0.665490 − 0.746407i \(-0.731777\pi\)
−0.665490 + 0.746407i \(0.731777\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 924.000 0.0538815
\(666\) 0 0
\(667\) −12672.0 −0.735625
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4980.00 0.286514
\(672\) 0 0
\(673\) −19861.0 −1.13757 −0.568786 − 0.822486i \(-0.692587\pi\)
−0.568786 + 0.822486i \(0.692587\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −8292.00 −0.470735 −0.235367 − 0.971906i \(-0.575629\pi\)
−0.235367 + 0.971906i \(0.575629\pi\)
\(678\) 0 0
\(679\) 4235.00 0.239358
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −19728.0 −1.10523 −0.552614 − 0.833437i \(-0.686370\pi\)
−0.552614 + 0.833437i \(0.686370\pi\)
\(684\) 0 0
\(685\) −28368.0 −1.58231
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 28440.0 1.57254
\(690\) 0 0
\(691\) 27272.0 1.50141 0.750706 − 0.660636i \(-0.229713\pi\)
0.750706 + 0.660636i \(0.229713\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2076.00 0.113305
\(696\) 0 0
\(697\) −20736.0 −1.12688
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −21996.0 −1.18513 −0.592566 − 0.805522i \(-0.701885\pi\)
−0.592566 + 0.805522i \(0.701885\pi\)
\(702\) 0 0
\(703\) 1859.00 0.0997347
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8736.00 0.464712
\(708\) 0 0
\(709\) −2009.00 −0.106417 −0.0532084 − 0.998583i \(-0.516945\pi\)
−0.0532084 + 0.998583i \(0.516945\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2640.00 0.138666
\(714\) 0 0
\(715\) −56880.0 −2.97509
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 26280.0 1.36311 0.681557 − 0.731765i \(-0.261303\pi\)
0.681557 + 0.731765i \(0.261303\pi\)
\(720\) 0 0
\(721\) −6755.00 −0.348917
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1824.00 0.0934368
\(726\) 0 0
\(727\) −20900.0 −1.06621 −0.533107 − 0.846048i \(-0.678976\pi\)
−0.533107 + 0.846048i \(0.678976\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 52704.0 2.66666
\(732\) 0 0
\(733\) 17638.0 0.888778 0.444389 − 0.895834i \(-0.353421\pi\)
0.444389 + 0.895834i \(0.353421\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2820.00 −0.140944
\(738\) 0 0
\(739\) 30080.0 1.49731 0.748654 − 0.662961i \(-0.230700\pi\)
0.748654 + 0.662961i \(0.230700\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 15708.0 0.775600 0.387800 − 0.921744i \(-0.373235\pi\)
0.387800 + 0.921744i \(0.373235\pi\)
\(744\) 0 0
\(745\) −19296.0 −0.948927
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −9324.00 −0.454862
\(750\) 0 0
\(751\) −20423.0 −0.992338 −0.496169 − 0.868226i \(-0.665260\pi\)
−0.496169 + 0.868226i \(0.665260\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 11964.0 0.576708
\(756\) 0 0
\(757\) 4399.00 0.211208 0.105604 − 0.994408i \(-0.466322\pi\)
0.105604 + 0.994408i \(0.466322\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 20652.0 0.983751 0.491875 − 0.870666i \(-0.336312\pi\)
0.491875 + 0.870666i \(0.336312\pi\)
\(762\) 0 0
\(763\) 13594.0 0.645001
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12324.0 −0.580175
\(768\) 0 0
\(769\) 27407.0 1.28520 0.642602 − 0.766200i \(-0.277855\pi\)
0.642602 + 0.766200i \(0.277855\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 5976.00 0.278062 0.139031 − 0.990288i \(-0.455601\pi\)
0.139031 + 0.990288i \(0.455601\pi\)
\(774\) 0 0
\(775\) −380.000 −0.0176129
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2112.00 −0.0971377
\(780\) 0 0
\(781\) −12960.0 −0.593784
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7368.00 −0.335000
\(786\) 0 0
\(787\) 24131.0 1.09298 0.546491 − 0.837465i \(-0.315963\pi\)
0.546491 + 0.837465i \(0.315963\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3612.00 −0.162361
\(792\) 0 0
\(793\) −6557.00 −0.293627
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 912.000 0.0405329 0.0202664 − 0.999795i \(-0.493549\pi\)
0.0202664 + 0.999795i \(0.493549\pi\)
\(798\) 0 0
\(799\) 22032.0 0.975515
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 30660.0 1.34741
\(804\) 0 0
\(805\) −11088.0 −0.485467
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 12888.0 0.560096 0.280048 − 0.959986i \(-0.409650\pi\)
0.280048 + 0.959986i \(0.409650\pi\)
\(810\) 0 0
\(811\) −6856.00 −0.296852 −0.148426 − 0.988924i \(-0.547421\pi\)
−0.148426 + 0.988924i \(0.547421\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 32316.0 1.38893
\(816\) 0 0
\(817\) 5368.00 0.229868
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 636.000 0.0270360 0.0135180 − 0.999909i \(-0.495697\pi\)
0.0135180 + 0.999909i \(0.495697\pi\)
\(822\) 0 0
\(823\) −39827.0 −1.68686 −0.843428 − 0.537243i \(-0.819466\pi\)
−0.843428 + 0.537243i \(0.819466\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −38124.0 −1.60302 −0.801512 − 0.597978i \(-0.795971\pi\)
−0.801512 + 0.597978i \(0.795971\pi\)
\(828\) 0 0
\(829\) −18965.0 −0.794550 −0.397275 − 0.917700i \(-0.630044\pi\)
−0.397275 + 0.917700i \(0.630044\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −31752.0 −1.32070
\(834\) 0 0
\(835\) 13968.0 0.578901
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 27816.0 1.14459 0.572297 − 0.820046i \(-0.306052\pi\)
0.572297 + 0.820046i \(0.306052\pi\)
\(840\) 0 0
\(841\) −15173.0 −0.622125
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 48528.0 1.97564
\(846\) 0 0
\(847\) 15883.0 0.644329
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −22308.0 −0.898600
\(852\) 0 0
\(853\) 12337.0 0.495206 0.247603 − 0.968862i \(-0.420357\pi\)
0.247603 + 0.968862i \(0.420357\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 11352.0 0.452482 0.226241 − 0.974071i \(-0.427356\pi\)
0.226241 + 0.974071i \(0.427356\pi\)
\(858\) 0 0
\(859\) −2527.00 −0.100373 −0.0501863 − 0.998740i \(-0.515982\pi\)
−0.0501863 + 0.998740i \(0.515982\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −26388.0 −1.04086 −0.520428 − 0.853906i \(-0.674227\pi\)
−0.520428 + 0.853906i \(0.674227\pi\)
\(864\) 0 0
\(865\) −43776.0 −1.72073
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −31740.0 −1.23902
\(870\) 0 0
\(871\) 3713.00 0.144443
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8904.00 −0.344012
\(876\) 0 0
\(877\) −6383.00 −0.245768 −0.122884 − 0.992421i \(-0.539214\pi\)
−0.122884 + 0.992421i \(0.539214\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −28908.0 −1.10549 −0.552744 − 0.833351i \(-0.686419\pi\)
−0.552744 + 0.833351i \(0.686419\pi\)
\(882\) 0 0
\(883\) 36893.0 1.40606 0.703028 − 0.711162i \(-0.251831\pi\)
0.703028 + 0.711162i \(0.251831\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −45528.0 −1.72343 −0.861714 − 0.507394i \(-0.830609\pi\)
−0.861714 + 0.507394i \(0.830609\pi\)
\(888\) 0 0
\(889\) 364.000 0.0137325
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2244.00 0.0840903
\(894\) 0 0
\(895\) −21600.0 −0.806713
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1920.00 −0.0712298
\(900\) 0 0
\(901\) 38880.0 1.43760
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 6564.00 0.241099
\(906\) 0 0
\(907\) −31201.0 −1.14224 −0.571120 − 0.820866i \(-0.693491\pi\)
−0.571120 + 0.820866i \(0.693491\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 23856.0 0.867601 0.433801 − 0.901009i \(-0.357172\pi\)
0.433801 + 0.901009i \(0.357172\pi\)
\(912\) 0 0
\(913\) −67680.0 −2.45332
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −336.000 −0.0121000
\(918\) 0 0
\(919\) −23492.0 −0.843231 −0.421616 − 0.906775i \(-0.638537\pi\)
−0.421616 + 0.906775i \(0.638537\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 17064.0 0.608525
\(924\) 0 0
\(925\) 3211.00 0.114137
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 15096.0 0.533136 0.266568 − 0.963816i \(-0.414110\pi\)
0.266568 + 0.963816i \(0.414110\pi\)
\(930\) 0 0
\(931\) −3234.00 −0.113845
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −77760.0 −2.71981
\(936\) 0 0
\(937\) −14965.0 −0.521756 −0.260878 − 0.965372i \(-0.584012\pi\)
−0.260878 + 0.965372i \(0.584012\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 19524.0 0.676370 0.338185 − 0.941080i \(-0.390187\pi\)
0.338185 + 0.941080i \(0.390187\pi\)
\(942\) 0 0
\(943\) 25344.0 0.875201
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −11076.0 −0.380065 −0.190033 − 0.981778i \(-0.560859\pi\)
−0.190033 + 0.981778i \(0.560859\pi\)
\(948\) 0 0
\(949\) −40369.0 −1.38086
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 44748.0 1.52102 0.760509 − 0.649328i \(-0.224950\pi\)
0.760509 + 0.649328i \(0.224950\pi\)
\(954\) 0 0
\(955\) 37872.0 1.28326
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −16548.0 −0.557208
\(960\) 0 0
\(961\) −29391.0 −0.986573
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 13524.0 0.451143
\(966\) 0 0
\(967\) −41519.0 −1.38072 −0.690362 − 0.723464i \(-0.742549\pi\)
−0.690362 + 0.723464i \(0.742549\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −28404.0 −0.938752 −0.469376 − 0.882999i \(-0.655521\pi\)
−0.469376 + 0.882999i \(0.655521\pi\)
\(972\) 0 0
\(973\) 1211.00 0.0399002
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −43032.0 −1.40913 −0.704563 − 0.709642i \(-0.748857\pi\)
−0.704563 + 0.709642i \(0.748857\pi\)
\(978\) 0 0
\(979\) 2160.00 0.0705147
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 18132.0 0.588322 0.294161 − 0.955756i \(-0.404960\pi\)
0.294161 + 0.955756i \(0.404960\pi\)
\(984\) 0 0
\(985\) 13392.0 0.433203
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −64416.0 −2.07109
\(990\) 0 0
\(991\) 44467.0 1.42537 0.712685 − 0.701485i \(-0.247479\pi\)
0.712685 + 0.701485i \(0.247479\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 39396.0 1.25521
\(996\) 0 0
\(997\) −19550.0 −0.621018 −0.310509 − 0.950570i \(-0.600499\pi\)
−0.310509 + 0.950570i \(0.600499\pi\)
\(998\) 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 1728.4.a.bb.1.1 1
3.2 odd 2 1728.4.a.f.1.1 1
4.3 odd 2 1728.4.a.ba.1.1 1
8.3 odd 2 54.4.a.a.1.1 ✓ 1
8.5 even 2 432.4.a.b.1.1 1
12.11 even 2 1728.4.a.e.1.1 1
24.5 odd 2 432.4.a.m.1.1 1
24.11 even 2 54.4.a.d.1.1 yes 1
40.3 even 4 1350.4.c.a.649.2 2
40.19 odd 2 1350.4.a.v.1.1 1
40.27 even 4 1350.4.c.a.649.1 2
72.11 even 6 162.4.c.a.109.1 2
72.43 odd 6 162.4.c.h.109.1 2
72.59 even 6 162.4.c.a.55.1 2
72.67 odd 6 162.4.c.h.55.1 2
120.59 even 2 1350.4.a.h.1.1 1
120.83 odd 4 1350.4.c.t.649.1 2
120.107 odd 4 1350.4.c.t.649.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.4.a.a.1.1 ✓ 1 8.3 odd 2
54.4.a.d.1.1 yes 1 24.11 even 2
162.4.c.a.55.1 2 72.59 even 6
162.4.c.a.109.1 2 72.11 even 6
162.4.c.h.55.1 2 72.67 odd 6
162.4.c.h.109.1 2 72.43 odd 6
432.4.a.b.1.1 1 8.5 even 2
432.4.a.m.1.1 1 24.5 odd 2
1350.4.a.h.1.1 1 120.59 even 2
1350.4.a.v.1.1 1 40.19 odd 2
1350.4.c.a.649.1 2 40.27 even 4
1350.4.c.a.649.2 2 40.3 even 4
1350.4.c.t.649.1 2 120.83 odd 4
1350.4.c.t.649.2 2 120.107 odd 4
1728.4.a.e.1.1 1 12.11 even 2
1728.4.a.f.1.1 1 3.2 odd 2
1728.4.a.ba.1.1 1 4.3 odd 2
1728.4.a.bb.1.1 1 1.1 even 1 trivial