↑

Properties

Label 1872.4.a.n.1.1
Level $1872$
Weight $4$
Character 1872.1
Self dual yes
Analytic conductor $110.452$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1872,4,Mod(1,1872)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1872, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1872.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.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: \(110.451575531\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 52)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1872.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+13.0000 q^{5} +11.0000 q^{7} +O(q^{10})\) \(q+13.0000 q^{5} +11.0000 q^{7} -2.00000 q^{11} -13.0000 q^{13} +51.0000 q^{17} -150.000 q^{19} -4.00000 q^{23} +44.0000 q^{25} +118.000 q^{29} +116.000 q^{31} +143.000 q^{35} +63.0000 q^{37} +288.000 q^{41} +293.000 q^{43} -335.000 q^{47} -222.000 q^{49} +708.000 q^{53} -26.0000 q^{55} +566.000 q^{59} +904.000 q^{61} -169.000 q^{65} -382.000 q^{67} +7.00000 q^{71} +518.000 q^{73} -22.0000 q^{77} +100.000 q^{79} -1440.00 q^{83} +663.000 q^{85} -1254.00 q^{89} -143.000 q^{91} -1950.00 q^{95} +1262.00 q^{97} +O(q^{100})\)

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
\(5\) 13.0000 1.16276 0.581378 − 0.813634i \(-0.302514\pi\)
0.581378 + 0.813634i \(0.302514\pi\)
\(6\) 0 0
\(7\) 11.0000 0.593944 0.296972 − 0.954886i \(-0.404023\pi\)
0.296972 + 0.954886i \(0.404023\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.00000 −0.0548202 −0.0274101 − 0.999624i \(-0.508726\pi\)
−0.0274101 + 0.999624i \(0.508726\pi\)
\(12\) 0 0
\(13\) −13.0000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 51.0000 0.727607 0.363803 − 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) −150.000 −1.81118 −0.905588 − 0.424158i \(-0.860570\pi\)
−0.905588 + 0.424158i \(0.860570\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.00000 −0.0362634 −0.0181317 − 0.999836i \(-0.505772\pi\)
−0.0181317 + 0.999836i \(0.505772\pi\)
\(24\) 0 0
\(25\) 44.0000 0.352000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 118.000 0.755588 0.377794 − 0.925890i \(-0.376683\pi\)
0.377794 + 0.925890i \(0.376683\pi\)
\(30\) 0 0
\(31\) 116.000 0.672071 0.336036 − 0.941849i \(-0.390914\pi\)
0.336036 + 0.941849i \(0.390914\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 143.000 0.690612
\(36\) 0 0
\(37\) 63.0000 0.279923 0.139961 − 0.990157i \(-0.455302\pi\)
0.139961 + 0.990157i \(0.455302\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 288.000 1.09703 0.548513 − 0.836142i \(-0.315194\pi\)
0.548513 + 0.836142i \(0.315194\pi\)
\(42\) 0 0
\(43\) 293.000 1.03912 0.519559 − 0.854435i \(-0.326096\pi\)
0.519559 + 0.854435i \(0.326096\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −335.000 −1.03968 −0.519838 − 0.854265i \(-0.674008\pi\)
−0.519838 + 0.854265i \(0.674008\pi\)
\(48\) 0 0
\(49\) −222.000 −0.647230
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 708.000 1.83493 0.917465 − 0.397817i \(-0.130232\pi\)
0.917465 + 0.397817i \(0.130232\pi\)
\(54\) 0 0
\(55\) −26.0000 −0.0637425
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 566.000 1.24893 0.624465 − 0.781052i \(-0.285317\pi\)
0.624465 + 0.781052i \(0.285317\pi\)
\(60\) 0 0
\(61\) 904.000 1.89746 0.948732 − 0.316081i \(-0.102367\pi\)
0.948732 + 0.316081i \(0.102367\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −169.000 −0.322490
\(66\) 0 0
\(67\) −382.000 −0.696548 −0.348274 − 0.937393i \(-0.613232\pi\)
−0.348274 + 0.937393i \(0.613232\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.00000 0.0117007 0.00585033 − 0.999983i \(-0.498138\pi\)
0.00585033 + 0.999983i \(0.498138\pi\)
\(72\) 0 0
\(73\) 518.000 0.830511 0.415256 − 0.909705i \(-0.363692\pi\)
0.415256 + 0.909705i \(0.363692\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −22.0000 −0.0325602
\(78\) 0 0
\(79\) 100.000 0.142416 0.0712081 − 0.997461i \(-0.477315\pi\)
0.0712081 + 0.997461i \(0.477315\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1440.00 −1.90434 −0.952172 − 0.305563i \(-0.901155\pi\)
−0.952172 + 0.305563i \(0.901155\pi\)
\(84\) 0 0
\(85\) 663.000 0.846029
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1254.00 −1.49353 −0.746763 − 0.665091i \(-0.768393\pi\)
−0.746763 + 0.665091i \(0.768393\pi\)
\(90\) 0 0
\(91\) −143.000 −0.164730
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1950.00 −2.10596
\(96\) 0 0
\(97\) 1262.00 1.32100 0.660498 − 0.750827i \(-0.270345\pi\)
0.660498 + 0.750827i \(0.270345\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1772.00 1.74575 0.872874 − 0.487945i \(-0.162253\pi\)
0.872874 + 0.487945i \(0.162253\pi\)
\(102\) 0 0
\(103\) 1160.00 1.10969 0.554846 − 0.831953i \(-0.312777\pi\)
0.554846 + 0.831953i \(0.312777\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 500.000 0.451746 0.225873 − 0.974157i \(-0.427477\pi\)
0.225873 + 0.974157i \(0.427477\pi\)
\(108\) 0 0
\(109\) −329.000 −0.289105 −0.144553 − 0.989497i \(-0.546174\pi\)
−0.144553 + 0.989497i \(0.546174\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 766.000 0.637692 0.318846 − 0.947807i \(-0.396705\pi\)
0.318846 + 0.947807i \(0.396705\pi\)
\(114\) 0 0
\(115\) −52.0000 −0.0421654
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 561.000 0.432158
\(120\) 0 0
\(121\) −1327.00 −0.996995
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1053.00 −0.753465
\(126\) 0 0
\(127\) 2144.00 1.49803 0.749013 − 0.662556i \(-0.230528\pi\)
0.749013 + 0.662556i \(0.230528\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1847.00 1.23186 0.615928 − 0.787802i \(-0.288781\pi\)
0.615928 + 0.787802i \(0.288781\pi\)
\(132\) 0 0
\(133\) −1650.00 −1.07574
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 564.000 0.351721 0.175860 − 0.984415i \(-0.443729\pi\)
0.175860 + 0.984415i \(0.443729\pi\)
\(138\) 0 0
\(139\) −2719.00 −1.65916 −0.829578 − 0.558391i \(-0.811419\pi\)
−0.829578 + 0.558391i \(0.811419\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 26.0000 0.0152044
\(144\) 0 0
\(145\) 1534.00 0.878564
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1254.00 −0.689474 −0.344737 − 0.938699i \(-0.612032\pi\)
−0.344737 + 0.938699i \(0.612032\pi\)
\(150\) 0 0
\(151\) 1173.00 0.632168 0.316084 − 0.948731i \(-0.397632\pi\)
0.316084 + 0.948731i \(0.397632\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1508.00 0.781455
\(156\) 0 0
\(157\) −1714.00 −0.871287 −0.435644 − 0.900119i \(-0.643479\pi\)
−0.435644 + 0.900119i \(0.643479\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −44.0000 −0.0215384
\(162\) 0 0
\(163\) −2300.00 −1.10521 −0.552607 − 0.833442i \(-0.686367\pi\)
−0.552607 + 0.833442i \(0.686367\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1176.00 0.544920 0.272460 − 0.962167i \(-0.412163\pi\)
0.272460 + 0.962167i \(0.412163\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 844.000 0.370914 0.185457 − 0.982652i \(-0.440623\pi\)
0.185457 + 0.982652i \(0.440623\pi\)
\(174\) 0 0
\(175\) 484.000 0.209068
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1527.00 0.637616 0.318808 − 0.947819i \(-0.396717\pi\)
0.318808 + 0.947819i \(0.396717\pi\)
\(180\) 0 0
\(181\) −960.000 −0.394233 −0.197117 − 0.980380i \(-0.563158\pi\)
−0.197117 + 0.980380i \(0.563158\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 819.000 0.325482
\(186\) 0 0
\(187\) −102.000 −0.0398876
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −110.000 −0.0416718 −0.0208359 − 0.999783i \(-0.506633\pi\)
−0.0208359 + 0.999783i \(0.506633\pi\)
\(192\) 0 0
\(193\) −4096.00 −1.52765 −0.763825 − 0.645423i \(-0.776681\pi\)
−0.763825 + 0.645423i \(0.776681\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1635.00 0.591314 0.295657 − 0.955294i \(-0.404461\pi\)
0.295657 + 0.955294i \(0.404461\pi\)
\(198\) 0 0
\(199\) −2414.00 −0.859919 −0.429960 − 0.902848i \(-0.641472\pi\)
−0.429960 + 0.902848i \(0.641472\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1298.00 0.448777
\(204\) 0 0
\(205\) 3744.00 1.27557
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 300.000 0.0992892
\(210\) 0 0
\(211\) 3697.00 1.20622 0.603109 − 0.797659i \(-0.293928\pi\)
0.603109 + 0.797659i \(0.293928\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3809.00 1.20824
\(216\) 0 0
\(217\) 1276.00 0.399173
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −663.000 −0.201802
\(222\) 0 0
\(223\) 2841.00 0.853127 0.426564 − 0.904457i \(-0.359724\pi\)
0.426564 + 0.904457i \(0.359724\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2424.00 −0.708751 −0.354376 − 0.935103i \(-0.615307\pi\)
−0.354376 + 0.935103i \(0.615307\pi\)
\(228\) 0 0
\(229\) 429.000 0.123795 0.0618976 − 0.998083i \(-0.480285\pi\)
0.0618976 + 0.998083i \(0.480285\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 683.000 0.192038 0.0960189 − 0.995380i \(-0.469389\pi\)
0.0960189 + 0.995380i \(0.469389\pi\)
\(234\) 0 0
\(235\) −4355.00 −1.20889
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4053.00 1.09693 0.548466 − 0.836173i \(-0.315212\pi\)
0.548466 + 0.836173i \(0.315212\pi\)
\(240\) 0 0
\(241\) −4206.00 −1.12420 −0.562100 − 0.827069i \(-0.690006\pi\)
−0.562100 + 0.827069i \(0.690006\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2886.00 −0.752571
\(246\) 0 0
\(247\) 1950.00 0.502330
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6312.00 1.58729 0.793645 − 0.608381i \(-0.208181\pi\)
0.793645 + 0.608381i \(0.208181\pi\)
\(252\) 0 0
\(253\) 8.00000 0.00198797
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4065.00 −0.986645 −0.493322 − 0.869847i \(-0.664218\pi\)
−0.493322 + 0.869847i \(0.664218\pi\)
\(258\) 0 0
\(259\) 693.000 0.166258
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 7308.00 1.71342 0.856712 − 0.515795i \(-0.172503\pi\)
0.856712 + 0.515795i \(0.172503\pi\)
\(264\) 0 0
\(265\) 9204.00 2.13357
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4488.00 1.01724 0.508621 − 0.860990i \(-0.330155\pi\)
0.508621 + 0.860990i \(0.330155\pi\)
\(270\) 0 0
\(271\) 3935.00 0.882045 0.441023 − 0.897496i \(-0.354616\pi\)
0.441023 + 0.897496i \(0.354616\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −88.0000 −0.0192967
\(276\) 0 0
\(277\) −1140.00 −0.247278 −0.123639 − 0.992327i \(-0.539456\pi\)
−0.123639 + 0.992327i \(0.539456\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −838.000 −0.177904 −0.0889518 − 0.996036i \(-0.528352\pi\)
−0.0889518 + 0.996036i \(0.528352\pi\)
\(282\) 0 0
\(283\) 5972.00 1.25441 0.627206 − 0.778853i \(-0.284198\pi\)
0.627206 + 0.778853i \(0.284198\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3168.00 0.651572
\(288\) 0 0
\(289\) −2312.00 −0.470588
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 8093.00 1.61365 0.806823 − 0.590794i \(-0.201185\pi\)
0.806823 + 0.590794i \(0.201185\pi\)
\(294\) 0 0
\(295\) 7358.00 1.45220
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 52.0000 0.0100577
\(300\) 0 0
\(301\) 3223.00 0.617178
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 11752.0 2.20629
\(306\) 0 0
\(307\) −2894.00 −0.538011 −0.269005 − 0.963139i \(-0.586695\pi\)
−0.269005 + 0.963139i \(0.586695\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6006.00 −1.09508 −0.547539 − 0.836780i \(-0.684435\pi\)
−0.547539 + 0.836780i \(0.684435\pi\)
\(312\) 0 0
\(313\) 2063.00 0.372548 0.186274 − 0.982498i \(-0.440359\pi\)
0.186274 + 0.982498i \(0.440359\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5622.00 −0.996098 −0.498049 − 0.867149i \(-0.665950\pi\)
−0.498049 + 0.867149i \(0.665950\pi\)
\(318\) 0 0
\(319\) −236.000 −0.0414215
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −7650.00 −1.31782
\(324\) 0 0
\(325\) −572.000 −0.0976272
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3685.00 −0.617510
\(330\) 0 0
\(331\) 5188.00 0.861505 0.430753 − 0.902470i \(-0.358248\pi\)
0.430753 + 0.902470i \(0.358248\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −4966.00 −0.809915
\(336\) 0 0
\(337\) −5761.00 −0.931222 −0.465611 − 0.884990i \(-0.654165\pi\)
−0.465611 + 0.884990i \(0.654165\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −232.000 −0.0368431
\(342\) 0 0
\(343\) −6215.00 −0.978363
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4161.00 −0.643730 −0.321865 − 0.946786i \(-0.604310\pi\)
−0.321865 + 0.946786i \(0.604310\pi\)
\(348\) 0 0
\(349\) 6211.00 0.952628 0.476314 − 0.879275i \(-0.341973\pi\)
0.476314 + 0.879275i \(0.341973\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 332.000 0.0500583 0.0250291 − 0.999687i \(-0.492032\pi\)
0.0250291 + 0.999687i \(0.492032\pi\)
\(354\) 0 0
\(355\) 91.0000 0.0136050
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1296.00 0.190530 0.0952650 − 0.995452i \(-0.469630\pi\)
0.0952650 + 0.995452i \(0.469630\pi\)
\(360\) 0 0
\(361\) 15641.0 2.28036
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 6734.00 0.965681
\(366\) 0 0
\(367\) −11726.0 −1.66783 −0.833913 − 0.551896i \(-0.813905\pi\)
−0.833913 + 0.551896i \(0.813905\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 7788.00 1.08985
\(372\) 0 0
\(373\) 2780.00 0.385906 0.192953 − 0.981208i \(-0.438194\pi\)
0.192953 + 0.981208i \(0.438194\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1534.00 −0.209562
\(378\) 0 0
\(379\) 9920.00 1.34448 0.672238 − 0.740335i \(-0.265333\pi\)
0.672238 + 0.740335i \(0.265333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3033.00 −0.404645 −0.202323 − 0.979319i \(-0.564849\pi\)
−0.202323 + 0.979319i \(0.564849\pi\)
\(384\) 0 0
\(385\) −286.000 −0.0378595
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 12630.0 1.64619 0.823093 − 0.567906i \(-0.192246\pi\)
0.823093 + 0.567906i \(0.192246\pi\)
\(390\) 0 0
\(391\) −204.000 −0.0263855
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1300.00 0.165595
\(396\) 0 0
\(397\) 674.000 0.0852068 0.0426034 − 0.999092i \(-0.486435\pi\)
0.0426034 + 0.999092i \(0.486435\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3144.00 −0.391531 −0.195765 − 0.980651i \(-0.562719\pi\)
−0.195765 + 0.980651i \(0.562719\pi\)
\(402\) 0 0
\(403\) −1508.00 −0.186399
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −126.000 −0.0153454
\(408\) 0 0
\(409\) 1108.00 0.133954 0.0669769 − 0.997755i \(-0.478665\pi\)
0.0669769 + 0.997755i \(0.478665\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6226.00 0.741795
\(414\) 0 0
\(415\) −18720.0 −2.21429
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2277.00 0.265486 0.132743 − 0.991150i \(-0.457621\pi\)
0.132743 + 0.991150i \(0.457621\pi\)
\(420\) 0 0
\(421\) −8225.00 −0.952166 −0.476083 − 0.879400i \(-0.657944\pi\)
−0.476083 + 0.879400i \(0.657944\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2244.00 0.256118
\(426\) 0 0
\(427\) 9944.00 1.12699
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7005.00 0.782875 0.391437 − 0.920205i \(-0.371978\pi\)
0.391437 + 0.920205i \(0.371978\pi\)
\(432\) 0 0
\(433\) 5215.00 0.578792 0.289396 − 0.957209i \(-0.406546\pi\)
0.289396 + 0.957209i \(0.406546\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 600.000 0.0656794
\(438\) 0 0
\(439\) −4658.00 −0.506411 −0.253205 − 0.967413i \(-0.581485\pi\)
−0.253205 + 0.967413i \(0.581485\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8217.00 0.881267 0.440634 − 0.897687i \(-0.354754\pi\)
0.440634 + 0.897687i \(0.354754\pi\)
\(444\) 0 0
\(445\) −16302.0 −1.73660
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 16634.0 1.74835 0.874173 − 0.485615i \(-0.161404\pi\)
0.874173 + 0.485615i \(0.161404\pi\)
\(450\) 0 0
\(451\) −576.000 −0.0601392
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1859.00 −0.191541
\(456\) 0 0
\(457\) −9254.00 −0.947229 −0.473615 − 0.880732i \(-0.657051\pi\)
−0.473615 + 0.880732i \(0.657051\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −5295.00 −0.534952 −0.267476 − 0.963565i \(-0.586190\pi\)
−0.267476 + 0.963565i \(0.586190\pi\)
\(462\) 0 0
\(463\) 14984.0 1.50403 0.752015 − 0.659146i \(-0.229082\pi\)
0.752015 + 0.659146i \(0.229082\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9076.00 −0.899330 −0.449665 − 0.893197i \(-0.648457\pi\)
−0.449665 + 0.893197i \(0.648457\pi\)
\(468\) 0 0
\(469\) −4202.00 −0.413711
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −586.000 −0.0569647
\(474\) 0 0
\(475\) −6600.00 −0.637534
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4575.00 −0.436403 −0.218202 − 0.975904i \(-0.570019\pi\)
−0.218202 + 0.975904i \(0.570019\pi\)
\(480\) 0 0
\(481\) −819.000 −0.0776366
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 16406.0 1.53600
\(486\) 0 0
\(487\) −20504.0 −1.90785 −0.953927 − 0.300039i \(-0.903000\pi\)
−0.953927 + 0.300039i \(0.903000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −16949.0 −1.55784 −0.778918 − 0.627126i \(-0.784231\pi\)
−0.778918 + 0.627126i \(0.784231\pi\)
\(492\) 0 0
\(493\) 6018.00 0.549771
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 77.0000 0.00694954
\(498\) 0 0
\(499\) 11072.0 0.993288 0.496644 − 0.867954i \(-0.334565\pi\)
0.496644 + 0.867954i \(0.334565\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5194.00 0.460416 0.230208 − 0.973142i \(-0.426059\pi\)
0.230208 + 0.973142i \(0.426059\pi\)
\(504\) 0 0
\(505\) 23036.0 2.02988
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16186.0 −1.40949 −0.704746 − 0.709459i \(-0.748939\pi\)
−0.704746 + 0.709459i \(0.748939\pi\)
\(510\) 0 0
\(511\) 5698.00 0.493277
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 15080.0 1.29030
\(516\) 0 0
\(517\) 670.000 0.0569953
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −8055.00 −0.677343 −0.338672 − 0.940905i \(-0.609978\pi\)
−0.338672 + 0.940905i \(0.609978\pi\)
\(522\) 0 0
\(523\) −7092.00 −0.592947 −0.296474 − 0.955041i \(-0.595811\pi\)
−0.296474 + 0.955041i \(0.595811\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5916.00 0.489004
\(528\) 0 0
\(529\) −12151.0 −0.998685
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3744.00 −0.304260
\(534\) 0 0
\(535\) 6500.00 0.525270
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 444.000 0.0354813
\(540\) 0 0
\(541\) 11741.0 0.933059 0.466530 − 0.884506i \(-0.345504\pi\)
0.466530 + 0.884506i \(0.345504\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −4277.00 −0.336159
\(546\) 0 0
\(547\) −11605.0 −0.907119 −0.453559 − 0.891226i \(-0.649846\pi\)
−0.453559 + 0.891226i \(0.649846\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −17700.0 −1.36850
\(552\) 0 0
\(553\) 1100.00 0.0845873
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −13773.0 −1.04772 −0.523861 − 0.851804i \(-0.675509\pi\)
−0.523861 + 0.851804i \(0.675509\pi\)
\(558\) 0 0
\(559\) −3809.00 −0.288200
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4165.00 −0.311783 −0.155891 − 0.987774i \(-0.549825\pi\)
−0.155891 + 0.987774i \(0.549825\pi\)
\(564\) 0 0
\(565\) 9958.00 0.741480
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10505.0 0.773976 0.386988 − 0.922085i \(-0.373515\pi\)
0.386988 + 0.922085i \(0.373515\pi\)
\(570\) 0 0
\(571\) 3831.00 0.280775 0.140387 − 0.990097i \(-0.455165\pi\)
0.140387 + 0.990097i \(0.455165\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −176.000 −0.0127647
\(576\) 0 0
\(577\) −13566.0 −0.978787 −0.489393 − 0.872063i \(-0.662782\pi\)
−0.489393 + 0.872063i \(0.662782\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −15840.0 −1.13107
\(582\) 0 0
\(583\) −1416.00 −0.100591
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6932.00 0.487418 0.243709 − 0.969848i \(-0.421636\pi\)
0.243709 + 0.969848i \(0.421636\pi\)
\(588\) 0 0
\(589\) −17400.0 −1.21724
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −14762.0 −1.02226 −0.511132 − 0.859502i \(-0.670774\pi\)
−0.511132 + 0.859502i \(0.670774\pi\)
\(594\) 0 0
\(595\) 7293.00 0.502494
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −27962.0 −1.90734 −0.953670 − 0.300855i \(-0.902728\pi\)
−0.953670 + 0.300855i \(0.902728\pi\)
\(600\) 0 0
\(601\) 4165.00 0.282685 0.141343 − 0.989961i \(-0.454858\pi\)
0.141343 + 0.989961i \(0.454858\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −17251.0 −1.15926
\(606\) 0 0
\(607\) −8286.00 −0.554066 −0.277033 − 0.960860i \(-0.589351\pi\)
−0.277033 + 0.960860i \(0.589351\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4355.00 0.288354
\(612\) 0 0
\(613\) −1534.00 −0.101073 −0.0505364 − 0.998722i \(-0.516093\pi\)
−0.0505364 + 0.998722i \(0.516093\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21056.0 1.37388 0.686939 − 0.726715i \(-0.258954\pi\)
0.686939 + 0.726715i \(0.258954\pi\)
\(618\) 0 0
\(619\) 19916.0 1.29320 0.646601 − 0.762829i \(-0.276190\pi\)
0.646601 + 0.762829i \(0.276190\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −13794.0 −0.887071
\(624\) 0 0
\(625\) −19189.0 −1.22810
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3213.00 0.203674
\(630\) 0 0
\(631\) 2993.00 0.188826 0.0944132 − 0.995533i \(-0.469903\pi\)
0.0944132 + 0.995533i \(0.469903\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 27872.0 1.74184
\(636\) 0 0
\(637\) 2886.00 0.179509
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −5950.00 −0.366632 −0.183316 − 0.983054i \(-0.558683\pi\)
−0.183316 + 0.983054i \(0.558683\pi\)
\(642\) 0 0
\(643\) −5198.00 −0.318801 −0.159401 − 0.987214i \(-0.550956\pi\)
−0.159401 + 0.987214i \(0.550956\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −25982.0 −1.57876 −0.789380 − 0.613905i \(-0.789598\pi\)
−0.789380 + 0.613905i \(0.789598\pi\)
\(648\) 0 0
\(649\) −1132.00 −0.0684667
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −28824.0 −1.72737 −0.863683 − 0.504035i \(-0.831848\pi\)
−0.863683 + 0.504035i \(0.831848\pi\)
\(654\) 0 0
\(655\) 24011.0 1.43235
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 8220.00 0.485896 0.242948 − 0.970039i \(-0.421885\pi\)
0.242948 + 0.970039i \(0.421885\pi\)
\(660\) 0 0
\(661\) −8242.00 −0.484987 −0.242494 − 0.970153i \(-0.577965\pi\)
−0.242494 + 0.970153i \(0.577965\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −21450.0 −1.25082
\(666\) 0 0
\(667\) −472.000 −0.0274002
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1808.00 −0.104019
\(672\) 0 0
\(673\) 9013.00 0.516234 0.258117 − 0.966114i \(-0.416898\pi\)
0.258117 + 0.966114i \(0.416898\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 14100.0 0.800454 0.400227 − 0.916416i \(-0.368931\pi\)
0.400227 + 0.916416i \(0.368931\pi\)
\(678\) 0 0
\(679\) 13882.0 0.784598
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 32260.0 1.80731 0.903656 − 0.428258i \(-0.140873\pi\)
0.903656 + 0.428258i \(0.140873\pi\)
\(684\) 0 0
\(685\) 7332.00 0.408965
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9204.00 −0.508918
\(690\) 0 0
\(691\) 20840.0 1.14731 0.573655 − 0.819097i \(-0.305525\pi\)
0.573655 + 0.819097i \(0.305525\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −35347.0 −1.92919
\(696\) 0 0
\(697\) 14688.0 0.798203
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −15492.0 −0.834700 −0.417350 − 0.908746i \(-0.637041\pi\)
−0.417350 + 0.908746i \(0.637041\pi\)
\(702\) 0 0
\(703\) −9450.00 −0.506989
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 19492.0 1.03688
\(708\) 0 0
\(709\) −8770.00 −0.464548 −0.232274 − 0.972650i \(-0.574617\pi\)
−0.232274 + 0.972650i \(0.574617\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −464.000 −0.0243716
\(714\) 0 0
\(715\) 338.000 0.0176790
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 24626.0 1.27732 0.638661 − 0.769488i \(-0.279489\pi\)
0.638661 + 0.769488i \(0.279489\pi\)
\(720\) 0 0
\(721\) 12760.0 0.659095
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5192.00 0.265967
\(726\) 0 0
\(727\) −31162.0 −1.58973 −0.794866 − 0.606786i \(-0.792459\pi\)
−0.794866 + 0.606786i \(0.792459\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 14943.0 0.756070
\(732\) 0 0
\(733\) −21031.0 −1.05975 −0.529876 − 0.848075i \(-0.677761\pi\)
−0.529876 + 0.848075i \(0.677761\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 764.000 0.0381849
\(738\) 0 0
\(739\) −19116.0 −0.951547 −0.475774 − 0.879568i \(-0.657832\pi\)
−0.475774 + 0.879568i \(0.657832\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 25309.0 1.24966 0.624830 − 0.780761i \(-0.285168\pi\)
0.624830 + 0.780761i \(0.285168\pi\)
\(744\) 0 0
\(745\) −16302.0 −0.801690
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5500.00 0.268312
\(750\) 0 0
\(751\) 6552.00 0.318357 0.159178 − 0.987250i \(-0.449116\pi\)
0.159178 + 0.987250i \(0.449116\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 15249.0 0.735057
\(756\) 0 0
\(757\) 9684.00 0.464955 0.232478 − 0.972602i \(-0.425317\pi\)
0.232478 + 0.972602i \(0.425317\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −8118.00 −0.386698 −0.193349 − 0.981130i \(-0.561935\pi\)
−0.193349 + 0.981130i \(0.561935\pi\)
\(762\) 0 0
\(763\) −3619.00 −0.171712
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7358.00 −0.346391
\(768\) 0 0
\(769\) 768.000 0.0360140 0.0180070 − 0.999838i \(-0.494268\pi\)
0.0180070 + 0.999838i \(0.494268\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 11137.0 0.518202 0.259101 − 0.965850i \(-0.416574\pi\)
0.259101 + 0.965850i \(0.416574\pi\)
\(774\) 0 0
\(775\) 5104.00 0.236569
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −43200.0 −1.98691
\(780\) 0 0
\(781\) −14.0000 −0.000641433 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −22282.0 −1.01309
\(786\) 0 0
\(787\) 28000.0 1.26822 0.634112 − 0.773241i \(-0.281366\pi\)
0.634112 + 0.773241i \(0.281366\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8426.00 0.378754
\(792\) 0 0
\(793\) −11752.0 −0.526262
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 26082.0 1.15919 0.579593 − 0.814906i \(-0.303211\pi\)
0.579593 + 0.814906i \(0.303211\pi\)
\(798\) 0 0
\(799\) −17085.0 −0.756475
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1036.00 −0.0455288
\(804\) 0 0
\(805\) −572.000 −0.0250439
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 8409.00 0.365445 0.182722 − 0.983165i \(-0.441509\pi\)
0.182722 + 0.983165i \(0.441509\pi\)
\(810\) 0 0
\(811\) −41444.0 −1.79445 −0.897223 − 0.441578i \(-0.854419\pi\)
−0.897223 + 0.441578i \(0.854419\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −29900.0 −1.28509
\(816\) 0 0
\(817\) −43950.0 −1.88203
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −10715.0 −0.455489 −0.227744 − 0.973721i \(-0.573135\pi\)
−0.227744 + 0.973721i \(0.573135\pi\)
\(822\) 0 0
\(823\) −32622.0 −1.38169 −0.690845 − 0.723003i \(-0.742761\pi\)
−0.690845 + 0.723003i \(0.742761\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 26718.0 1.12343 0.561715 − 0.827331i \(-0.310142\pi\)
0.561715 + 0.827331i \(0.310142\pi\)
\(828\) 0 0
\(829\) 23266.0 0.974743 0.487371 − 0.873195i \(-0.337956\pi\)
0.487371 + 0.873195i \(0.337956\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −11322.0 −0.470929
\(834\) 0 0
\(835\) 15288.0 0.633608
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −44080.0 −1.81384 −0.906919 − 0.421304i \(-0.861572\pi\)
−0.906919 + 0.421304i \(0.861572\pi\)
\(840\) 0 0
\(841\) −10465.0 −0.429087
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2197.00 0.0894427
\(846\) 0 0
\(847\) −14597.0 −0.592159
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −252.000 −0.0101509
\(852\) 0 0
\(853\) −16787.0 −0.673829 −0.336914 − 0.941535i \(-0.609383\pi\)
−0.336914 + 0.941535i \(0.609383\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −28030.0 −1.11725 −0.558627 − 0.829419i \(-0.688672\pi\)
−0.558627 + 0.829419i \(0.688672\pi\)
\(858\) 0 0
\(859\) 1684.00 0.0668886 0.0334443 − 0.999441i \(-0.489352\pi\)
0.0334443 + 0.999441i \(0.489352\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −41135.0 −1.62254 −0.811270 − 0.584672i \(-0.801223\pi\)
−0.811270 + 0.584672i \(0.801223\pi\)
\(864\) 0 0
\(865\) 10972.0 0.431282
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −200.000 −0.00780729
\(870\) 0 0
\(871\) 4966.00 0.193188
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −11583.0 −0.447516
\(876\) 0 0
\(877\) −12483.0 −0.480640 −0.240320 − 0.970694i \(-0.577252\pi\)
−0.240320 + 0.970694i \(0.577252\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 22299.0 0.852750 0.426375 − 0.904547i \(-0.359790\pi\)
0.426375 + 0.904547i \(0.359790\pi\)
\(882\) 0 0
\(883\) 2663.00 0.101492 0.0507458 − 0.998712i \(-0.483840\pi\)
0.0507458 + 0.998712i \(0.483840\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 14488.0 0.548432 0.274216 − 0.961668i \(-0.411582\pi\)
0.274216 + 0.961668i \(0.411582\pi\)
\(888\) 0 0
\(889\) 23584.0 0.889744
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 50250.0 1.88304
\(894\) 0 0
\(895\) 19851.0 0.741392
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 13688.0 0.507809
\(900\) 0 0
\(901\) 36108.0 1.33511
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −12480.0 −0.458397
\(906\) 0 0
\(907\) −43863.0 −1.60579 −0.802893 − 0.596124i \(-0.796707\pi\)
−0.802893 + 0.596124i \(0.796707\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −8142.00 −0.296110 −0.148055 − 0.988979i \(-0.547301\pi\)
−0.148055 + 0.988979i \(0.547301\pi\)
\(912\) 0 0
\(913\) 2880.00 0.104397
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 20317.0 0.731654
\(918\) 0 0
\(919\) −18504.0 −0.664190 −0.332095 − 0.943246i \(-0.607755\pi\)
−0.332095 + 0.943246i \(0.607755\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −91.0000 −0.00324518
\(924\) 0 0
\(925\) 2772.00 0.0985328
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 26484.0 0.935320 0.467660 − 0.883909i \(-0.345097\pi\)
0.467660 + 0.883909i \(0.345097\pi\)
\(930\) 0 0
\(931\) 33300.0 1.17225
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1326.00 −0.0463795
\(936\) 0 0
\(937\) −4890.00 −0.170490 −0.0852451 − 0.996360i \(-0.527167\pi\)
−0.0852451 + 0.996360i \(0.527167\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −39709.0 −1.37564 −0.687820 − 0.725882i \(-0.741432\pi\)
−0.687820 + 0.725882i \(0.741432\pi\)
\(942\) 0 0
\(943\) −1152.00 −0.0397818
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 15582.0 0.534685 0.267343 − 0.963602i \(-0.413854\pi\)
0.267343 + 0.963602i \(0.413854\pi\)
\(948\) 0 0
\(949\) −6734.00 −0.230342
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −45887.0 −1.55973 −0.779867 − 0.625946i \(-0.784713\pi\)
−0.779867 + 0.625946i \(0.784713\pi\)
\(954\) 0 0
\(955\) −1430.00 −0.0484542
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 6204.00 0.208903
\(960\) 0 0
\(961\) −16335.0 −0.548320
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −53248.0 −1.77628
\(966\) 0 0
\(967\) −25139.0 −0.836004 −0.418002 − 0.908446i \(-0.637269\pi\)
−0.418002 + 0.908446i \(0.637269\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −36591.0 −1.20933 −0.604666 − 0.796479i \(-0.706693\pi\)
−0.604666 + 0.796479i \(0.706693\pi\)
\(972\) 0 0
\(973\) −29909.0 −0.985446
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 19182.0 0.628134 0.314067 − 0.949401i \(-0.398308\pi\)
0.314067 + 0.949401i \(0.398308\pi\)
\(978\) 0 0
\(979\) 2508.00 0.0818754
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −39835.0 −1.29251 −0.646256 − 0.763121i \(-0.723666\pi\)
−0.646256 + 0.763121i \(0.723666\pi\)
\(984\) 0 0
\(985\) 21255.0 0.687554
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1172.00 −0.0376819
\(990\) 0 0
\(991\) 28662.0 0.918747 0.459374 − 0.888243i \(-0.348074\pi\)
0.459374 + 0.888243i \(0.348074\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −31382.0 −0.999876
\(996\) 0 0
\(997\) 39182.0 1.24464 0.622320 − 0.782763i \(-0.286190\pi\)
0.622320 + 0.782763i \(0.286190\pi\)
\(998\) 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 1872.4.a.n.1.1 1
3.2 odd 2 208.4.a.f.1.1 1
4.3 odd 2 468.4.a.c.1.1 1
12.11 even 2 52.4.a.a.1.1 ✓ 1
24.5 odd 2 832.4.a.f.1.1 1
24.11 even 2 832.4.a.n.1.1 1
60.23 odd 4 1300.4.c.b.1249.1 2
60.47 odd 4 1300.4.c.b.1249.2 2
60.59 even 2 1300.4.a.d.1.1 1
156.11 odd 12 676.4.h.d.485.1 4
156.23 even 6 676.4.e.b.529.1 2
156.35 even 6 676.4.e.a.653.1 2
156.47 odd 4 676.4.d.a.337.1 2
156.59 odd 12 676.4.h.d.361.1 4
156.71 odd 12 676.4.h.d.361.2 4
156.83 odd 4 676.4.d.a.337.2 2
156.95 even 6 676.4.e.b.653.1 2
156.107 even 6 676.4.e.a.529.1 2
156.119 odd 12 676.4.h.d.485.2 4
156.155 even 2 676.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
52.4.a.a.1.1 ✓ 1 12.11 even 2
208.4.a.f.1.1 1 3.2 odd 2
468.4.a.c.1.1 1 4.3 odd 2
676.4.a.a.1.1 1 156.155 even 2
676.4.d.a.337.1 2 156.47 odd 4
676.4.d.a.337.2 2 156.83 odd 4
676.4.e.a.529.1 2 156.107 even 6
676.4.e.a.653.1 2 156.35 even 6
676.4.e.b.529.1 2 156.23 even 6
676.4.e.b.653.1 2 156.95 even 6
676.4.h.d.361.1 4 156.59 odd 12
676.4.h.d.361.2 4 156.71 odd 12
676.4.h.d.485.1 4 156.11 odd 12
676.4.h.d.485.2 4 156.119 odd 12
832.4.a.f.1.1 1 24.5 odd 2
832.4.a.n.1.1 1 24.11 even 2
1300.4.a.d.1.1 1 60.59 even 2
1300.4.c.b.1249.1 2 60.23 odd 4
1300.4.c.b.1249.2 2 60.47 odd 4
1872.4.a.n.1.1 1 1.1 even 1 trivial