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Properties

Label 1728.4.a.be.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 864)
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)
 
\(f(q)\) \(=\) \(q+19.0000 q^{5} -13.0000 q^{7} +O(q^{10})\) \(q+19.0000 q^{5} -13.0000 q^{7} +65.0000 q^{11} +56.0000 q^{13} -108.000 q^{17} +58.0000 q^{19} +66.0000 q^{23} +236.000 q^{25} +118.000 q^{29} +145.000 q^{31} -247.000 q^{35} -190.000 q^{37} -430.000 q^{41} +530.000 q^{43} +74.0000 q^{47} -174.000 q^{49} -295.000 q^{53} +1235.00 q^{55} +628.000 q^{59} -360.000 q^{61} +1064.00 q^{65} +146.000 q^{67} -388.000 q^{71} +753.000 q^{73} -845.000 q^{77} -1136.00 q^{79} +153.000 q^{83} -2052.00 q^{85} +850.000 q^{89} -728.000 q^{91} +1102.00 q^{95} +391.000 q^{97} +O(q^{100})\)

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
\(5\) 19.0000 1.69941 0.849706 − 0.527257i \(-0.176780\pi\)
0.849706 + 0.527257i \(0.176780\pi\)
\(6\) 0 0
\(7\) −13.0000 −0.701934 −0.350967 − 0.936388i \(-0.614147\pi\)
−0.350967 + 0.936388i \(0.614147\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 65.0000 1.78166 0.890829 − 0.454339i \(-0.150124\pi\)
0.890829 + 0.454339i \(0.150124\pi\)
\(12\) 0 0
\(13\) 56.0000 1.19474 0.597369 − 0.801966i \(-0.296213\pi\)
0.597369 + 0.801966i \(0.296213\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −108.000 −1.54081 −0.770407 − 0.637552i \(-0.779947\pi\)
−0.770407 + 0.637552i \(0.779947\pi\)
\(18\) 0 0
\(19\) 58.0000 0.700322 0.350161 − 0.936690i \(-0.386127\pi\)
0.350161 + 0.936690i \(0.386127\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 66.0000 0.598346 0.299173 − 0.954199i \(-0.403289\pi\)
0.299173 + 0.954199i \(0.403289\pi\)
\(24\) 0 0
\(25\) 236.000 1.88800
\(26\) 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
\(31\) 145.000 0.840089 0.420045 − 0.907503i \(-0.362014\pi\)
0.420045 + 0.907503i \(0.362014\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −247.000 −1.19287
\(36\) 0 0
\(37\) −190.000 −0.844211 −0.422106 − 0.906547i \(-0.638709\pi\)
−0.422106 + 0.906547i \(0.638709\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −430.000 −1.63792 −0.818960 − 0.573851i \(-0.805449\pi\)
−0.818960 + 0.573851i \(0.805449\pi\)
\(42\) 0 0
\(43\) 530.000 1.87963 0.939817 − 0.341679i \(-0.110996\pi\)
0.939817 + 0.341679i \(0.110996\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 74.0000 0.229660 0.114830 − 0.993385i \(-0.463368\pi\)
0.114830 + 0.993385i \(0.463368\pi\)
\(48\) 0 0
\(49\) −174.000 −0.507289
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −295.000 −0.764554 −0.382277 − 0.924048i \(-0.624860\pi\)
−0.382277 + 0.924048i \(0.624860\pi\)
\(54\) 0 0
\(55\) 1235.00 3.02777
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 628.000 1.38574 0.692870 − 0.721063i \(-0.256346\pi\)
0.692870 + 0.721063i \(0.256346\pi\)
\(60\) 0 0
\(61\) −360.000 −0.755627 −0.377814 − 0.925882i \(-0.623324\pi\)
−0.377814 + 0.925882i \(0.623324\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1064.00 2.03035
\(66\) 0 0
\(67\) 146.000 0.266220 0.133110 − 0.991101i \(-0.457504\pi\)
0.133110 + 0.991101i \(0.457504\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −388.000 −0.648551 −0.324276 − 0.945963i \(-0.605121\pi\)
−0.324276 + 0.945963i \(0.605121\pi\)
\(72\) 0 0
\(73\) 753.000 1.20729 0.603644 − 0.797254i \(-0.293715\pi\)
0.603644 + 0.797254i \(0.293715\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −845.000 −1.25061
\(78\) 0 0
\(79\) −1136.00 −1.61785 −0.808924 − 0.587913i \(-0.799950\pi\)
−0.808924 + 0.587913i \(0.799950\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 153.000 0.202337 0.101168 − 0.994869i \(-0.467742\pi\)
0.101168 + 0.994869i \(0.467742\pi\)
\(84\) 0 0
\(85\) −2052.00 −2.61848
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 850.000 1.01236 0.506179 − 0.862429i \(-0.331058\pi\)
0.506179 + 0.862429i \(0.331058\pi\)
\(90\) 0 0
\(91\) −728.000 −0.838628
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1102.00 1.19013
\(96\) 0 0
\(97\) 391.000 0.409279 0.204639 − 0.978837i \(-0.434398\pi\)
0.204639 + 0.978837i \(0.434398\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 597.000 0.588156 0.294078 − 0.955781i \(-0.404988\pi\)
0.294078 + 0.955781i \(0.404988\pi\)
\(102\) 0 0
\(103\) −252.000 −0.241071 −0.120535 − 0.992709i \(-0.538461\pi\)
−0.120535 + 0.992709i \(0.538461\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −395.000 −0.356879 −0.178440 − 0.983951i \(-0.557105\pi\)
−0.178440 + 0.983951i \(0.557105\pi\)
\(108\) 0 0
\(109\) −254.000 −0.223200 −0.111600 − 0.993753i \(-0.535598\pi\)
−0.111600 + 0.993753i \(0.535598\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −862.000 −0.717612 −0.358806 − 0.933412i \(-0.616816\pi\)
−0.358806 + 0.933412i \(0.616816\pi\)
\(114\) 0 0
\(115\) 1254.00 1.01684
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1404.00 1.08155
\(120\) 0 0
\(121\) 2894.00 2.17431
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2109.00 1.50908
\(126\) 0 0
\(127\) −1019.00 −0.711981 −0.355991 − 0.934490i \(-0.615857\pi\)
−0.355991 + 0.934490i \(0.615857\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2741.00 1.82811 0.914055 − 0.405591i \(-0.132934\pi\)
0.914055 + 0.405591i \(0.132934\pi\)
\(132\) 0 0
\(133\) −754.000 −0.491580
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −750.000 −0.467714 −0.233857 − 0.972271i \(-0.575135\pi\)
−0.233857 + 0.972271i \(0.575135\pi\)
\(138\) 0 0
\(139\) −3028.00 −1.84771 −0.923855 − 0.382743i \(-0.874979\pi\)
−0.923855 + 0.382743i \(0.874979\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3640.00 2.12862
\(144\) 0 0
\(145\) 2242.00 1.28405
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1677.00 −0.922048 −0.461024 − 0.887388i \(-0.652518\pi\)
−0.461024 + 0.887388i \(0.652518\pi\)
\(150\) 0 0
\(151\) 573.000 0.308808 0.154404 − 0.988008i \(-0.450654\pi\)
0.154404 + 0.988008i \(0.450654\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2755.00 1.42766
\(156\) 0 0
\(157\) 1564.00 0.795037 0.397518 − 0.917594i \(-0.369871\pi\)
0.397518 + 0.917594i \(0.369871\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −858.000 −0.419999
\(162\) 0 0
\(163\) 1072.00 0.515126 0.257563 − 0.966262i \(-0.417081\pi\)
0.257563 + 0.966262i \(0.417081\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3106.00 −1.43922 −0.719609 − 0.694379i \(-0.755679\pi\)
−0.719609 + 0.694379i \(0.755679\pi\)
\(168\) 0 0
\(169\) 939.000 0.427401
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4263.00 1.87347 0.936734 − 0.350043i \(-0.113833\pi\)
0.936734 + 0.350043i \(0.113833\pi\)
\(174\) 0 0
\(175\) −3068.00 −1.32525
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 723.000 0.301897 0.150948 − 0.988542i \(-0.451767\pi\)
0.150948 + 0.988542i \(0.451767\pi\)
\(180\) 0 0
\(181\) −3104.00 −1.27469 −0.637344 − 0.770579i \(-0.719967\pi\)
−0.637344 + 0.770579i \(0.719967\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3610.00 −1.43466
\(186\) 0 0
\(187\) −7020.00 −2.74520
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1776.00 −0.672811 −0.336405 − 0.941717i \(-0.609211\pi\)
−0.336405 + 0.941717i \(0.609211\pi\)
\(192\) 0 0
\(193\) 957.000 0.356924 0.178462 − 0.983947i \(-0.442888\pi\)
0.178462 + 0.983947i \(0.442888\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1007.00 −0.364192 −0.182096 − 0.983281i \(-0.558288\pi\)
−0.182096 + 0.983281i \(0.558288\pi\)
\(198\) 0 0
\(199\) −803.000 −0.286046 −0.143023 − 0.989719i \(-0.545682\pi\)
−0.143023 + 0.989719i \(0.545682\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1534.00 −0.530373
\(204\) 0 0
\(205\) −8170.00 −2.78350
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3770.00 1.24773
\(210\) 0 0
\(211\) 3274.00 1.06821 0.534103 − 0.845419i \(-0.320649\pi\)
0.534103 + 0.845419i \(0.320649\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 10070.0 3.19427
\(216\) 0 0
\(217\) −1885.00 −0.589687
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6048.00 −1.84087
\(222\) 0 0
\(223\) 1064.00 0.319510 0.159755 − 0.987157i \(-0.448930\pi\)
0.159755 + 0.987157i \(0.448930\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1644.00 0.480688 0.240344 − 0.970688i \(-0.422740\pi\)
0.240344 + 0.970688i \(0.422740\pi\)
\(228\) 0 0
\(229\) 3082.00 0.889364 0.444682 − 0.895689i \(-0.353317\pi\)
0.444682 + 0.895689i \(0.353317\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2766.00 0.777711 0.388856 − 0.921299i \(-0.372871\pi\)
0.388856 + 0.921299i \(0.372871\pi\)
\(234\) 0 0
\(235\) 1406.00 0.390286
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 798.000 0.215976 0.107988 − 0.994152i \(-0.465559\pi\)
0.107988 + 0.994152i \(0.465559\pi\)
\(240\) 0 0
\(241\) −3554.00 −0.949931 −0.474965 − 0.880005i \(-0.657539\pi\)
−0.474965 + 0.880005i \(0.657539\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3306.00 −0.862092
\(246\) 0 0
\(247\) 3248.00 0.836702
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2400.00 0.603532 0.301766 − 0.953382i \(-0.402424\pi\)
0.301766 + 0.953382i \(0.402424\pi\)
\(252\) 0 0
\(253\) 4290.00 1.06605
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1904.00 0.462133 0.231067 − 0.972938i \(-0.425778\pi\)
0.231067 + 0.972938i \(0.425778\pi\)
\(258\) 0 0
\(259\) 2470.00 0.592580
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6642.00 1.55727 0.778637 − 0.627474i \(-0.215911\pi\)
0.778637 + 0.627474i \(0.215911\pi\)
\(264\) 0 0
\(265\) −5605.00 −1.29929
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5034.00 −1.14100 −0.570499 − 0.821298i \(-0.693250\pi\)
−0.570499 + 0.821298i \(0.693250\pi\)
\(270\) 0 0
\(271\) −5973.00 −1.33887 −0.669435 − 0.742870i \(-0.733464\pi\)
−0.669435 + 0.742870i \(0.733464\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 15340.0 3.36377
\(276\) 0 0
\(277\) 5456.00 1.18346 0.591732 − 0.806135i \(-0.298445\pi\)
0.591732 + 0.806135i \(0.298445\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1908.00 0.405060 0.202530 − 0.979276i \(-0.435084\pi\)
0.202530 + 0.979276i \(0.435084\pi\)
\(282\) 0 0
\(283\) 6518.00 1.36910 0.684549 − 0.728967i \(-0.259999\pi\)
0.684549 + 0.728967i \(0.259999\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5590.00 1.14971
\(288\) 0 0
\(289\) 6751.00 1.37411
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4818.00 0.960650 0.480325 − 0.877090i \(-0.340519\pi\)
0.480325 + 0.877090i \(0.340519\pi\)
\(294\) 0 0
\(295\) 11932.0 2.35494
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3696.00 0.714867
\(300\) 0 0
\(301\) −6890.00 −1.31938
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −6840.00 −1.28412
\(306\) 0 0
\(307\) 8172.00 1.51922 0.759610 − 0.650379i \(-0.225390\pi\)
0.759610 + 0.650379i \(0.225390\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −8118.00 −1.48016 −0.740080 − 0.672519i \(-0.765212\pi\)
−0.740080 + 0.672519i \(0.765212\pi\)
\(312\) 0 0
\(313\) −4187.00 −0.756113 −0.378056 − 0.925783i \(-0.623407\pi\)
−0.378056 + 0.925783i \(0.623407\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3117.00 0.552265 0.276133 − 0.961120i \(-0.410947\pi\)
0.276133 + 0.961120i \(0.410947\pi\)
\(318\) 0 0
\(319\) 7670.00 1.34620
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −6264.00 −1.07907
\(324\) 0 0
\(325\) 13216.0 2.25567
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −962.000 −0.161206
\(330\) 0 0
\(331\) 1322.00 0.219528 0.109764 − 0.993958i \(-0.464991\pi\)
0.109764 + 0.993958i \(0.464991\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2774.00 0.452417
\(336\) 0 0
\(337\) 3362.00 0.543442 0.271721 − 0.962376i \(-0.412407\pi\)
0.271721 + 0.962376i \(0.412407\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 9425.00 1.49675
\(342\) 0 0
\(343\) 6721.00 1.05802
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3631.00 0.561736 0.280868 − 0.959746i \(-0.409378\pi\)
0.280868 + 0.959746i \(0.409378\pi\)
\(348\) 0 0
\(349\) 10454.0 1.60341 0.801705 − 0.597720i \(-0.203927\pi\)
0.801705 + 0.597720i \(0.203927\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 406.000 0.0612159 0.0306079 − 0.999531i \(-0.490256\pi\)
0.0306079 + 0.999531i \(0.490256\pi\)
\(354\) 0 0
\(355\) −7372.00 −1.10216
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4366.00 0.641863 0.320931 − 0.947102i \(-0.396004\pi\)
0.320931 + 0.947102i \(0.396004\pi\)
\(360\) 0 0
\(361\) −3495.00 −0.509549
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 14307.0 2.05168
\(366\) 0 0
\(367\) −9939.00 −1.41366 −0.706828 − 0.707386i \(-0.749874\pi\)
−0.706828 + 0.707386i \(0.749874\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3835.00 0.536667
\(372\) 0 0
\(373\) 5500.00 0.763483 0.381742 − 0.924269i \(-0.375324\pi\)
0.381742 + 0.924269i \(0.375324\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6608.00 0.902730
\(378\) 0 0
\(379\) −11060.0 −1.49898 −0.749491 − 0.662015i \(-0.769702\pi\)
−0.749491 + 0.662015i \(0.769702\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12668.0 1.69009 0.845045 − 0.534695i \(-0.179573\pi\)
0.845045 + 0.534695i \(0.179573\pi\)
\(384\) 0 0
\(385\) −16055.0 −2.12529
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −5925.00 −0.772261 −0.386130 − 0.922444i \(-0.626189\pi\)
−0.386130 + 0.922444i \(0.626189\pi\)
\(390\) 0 0
\(391\) −7128.00 −0.921940
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −21584.0 −2.74939
\(396\) 0 0
\(397\) 6296.00 0.795937 0.397969 − 0.917399i \(-0.369715\pi\)
0.397969 + 0.917399i \(0.369715\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 292.000 0.0363636 0.0181818 − 0.999835i \(-0.494212\pi\)
0.0181818 + 0.999835i \(0.494212\pi\)
\(402\) 0 0
\(403\) 8120.00 1.00369
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −12350.0 −1.50410
\(408\) 0 0
\(409\) −7649.00 −0.924740 −0.462370 − 0.886687i \(-0.653001\pi\)
−0.462370 + 0.886687i \(0.653001\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8164.00 −0.972698
\(414\) 0 0
\(415\) 2907.00 0.343853
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 15644.0 1.82401 0.912004 − 0.410181i \(-0.134535\pi\)
0.912004 + 0.410181i \(0.134535\pi\)
\(420\) 0 0
\(421\) −14192.0 −1.64294 −0.821468 − 0.570255i \(-0.806844\pi\)
−0.821468 + 0.570255i \(0.806844\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −25488.0 −2.90906
\(426\) 0 0
\(427\) 4680.00 0.530401
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 13158.0 1.47053 0.735265 − 0.677780i \(-0.237058\pi\)
0.735265 + 0.677780i \(0.237058\pi\)
\(432\) 0 0
\(433\) −7307.00 −0.810975 −0.405487 − 0.914101i \(-0.632898\pi\)
−0.405487 + 0.914101i \(0.632898\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3828.00 0.419034
\(438\) 0 0
\(439\) −11671.0 −1.26885 −0.634426 − 0.772983i \(-0.718764\pi\)
−0.634426 + 0.772983i \(0.718764\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9924.00 1.06434 0.532171 − 0.846637i \(-0.321376\pi\)
0.532171 + 0.846637i \(0.321376\pi\)
\(444\) 0 0
\(445\) 16150.0 1.72041
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3794.00 −0.398775 −0.199387 − 0.979921i \(-0.563895\pi\)
−0.199387 + 0.979921i \(0.563895\pi\)
\(450\) 0 0
\(451\) −27950.0 −2.91821
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −13832.0 −1.42517
\(456\) 0 0
\(457\) −4033.00 −0.412814 −0.206407 − 0.978466i \(-0.566177\pi\)
−0.206407 + 0.978466i \(0.566177\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16365.0 −1.65335 −0.826675 − 0.562680i \(-0.809770\pi\)
−0.826675 + 0.562680i \(0.809770\pi\)
\(462\) 0 0
\(463\) 2743.00 0.275330 0.137665 − 0.990479i \(-0.456040\pi\)
0.137665 + 0.990479i \(0.456040\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2551.00 −0.252776 −0.126388 − 0.991981i \(-0.540338\pi\)
−0.126388 + 0.991981i \(0.540338\pi\)
\(468\) 0 0
\(469\) −1898.00 −0.186869
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 34450.0 3.34886
\(474\) 0 0
\(475\) 13688.0 1.32221
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6906.00 0.658754 0.329377 − 0.944198i \(-0.393161\pi\)
0.329377 + 0.944198i \(0.393161\pi\)
\(480\) 0 0
\(481\) −10640.0 −1.00861
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7429.00 0.695533
\(486\) 0 0
\(487\) −10648.0 −0.990774 −0.495387 − 0.868672i \(-0.664974\pi\)
−0.495387 + 0.868672i \(0.664974\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 9899.00 0.909849 0.454924 − 0.890530i \(-0.349666\pi\)
0.454924 + 0.890530i \(0.349666\pi\)
\(492\) 0 0
\(493\) −12744.0 −1.16422
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5044.00 0.455240
\(498\) 0 0
\(499\) −2382.00 −0.213693 −0.106847 − 0.994276i \(-0.534075\pi\)
−0.106847 + 0.994276i \(0.534075\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −6450.00 −0.571752 −0.285876 − 0.958267i \(-0.592285\pi\)
−0.285876 + 0.958267i \(0.592285\pi\)
\(504\) 0 0
\(505\) 11343.0 0.999519
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4839.00 −0.421385 −0.210692 − 0.977552i \(-0.567572\pi\)
−0.210692 + 0.977552i \(0.567572\pi\)
\(510\) 0 0
\(511\) −9789.00 −0.847436
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4788.00 −0.409679
\(516\) 0 0
\(517\) 4810.00 0.409175
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7656.00 0.643792 0.321896 − 0.946775i \(-0.395680\pi\)
0.321896 + 0.946775i \(0.395680\pi\)
\(522\) 0 0
\(523\) 9756.00 0.815679 0.407839 − 0.913054i \(-0.366282\pi\)
0.407839 + 0.913054i \(0.366282\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −15660.0 −1.29442
\(528\) 0 0
\(529\) −7811.00 −0.641982
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −24080.0 −1.95689
\(534\) 0 0
\(535\) −7505.00 −0.606485
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −11310.0 −0.903815
\(540\) 0 0
\(541\) 12452.0 0.989562 0.494781 − 0.869018i \(-0.335248\pi\)
0.494781 + 0.869018i \(0.335248\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −4826.00 −0.379308
\(546\) 0 0
\(547\) −21708.0 −1.69683 −0.848416 − 0.529330i \(-0.822443\pi\)
−0.848416 + 0.529330i \(0.822443\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6844.00 0.529155
\(552\) 0 0
\(553\) 14768.0 1.13562
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18941.0 −1.44085 −0.720427 − 0.693531i \(-0.756054\pi\)
−0.720427 + 0.693531i \(0.756054\pi\)
\(558\) 0 0
\(559\) 29680.0 2.24567
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9561.00 −0.715716 −0.357858 − 0.933776i \(-0.616493\pi\)
−0.357858 + 0.933776i \(0.616493\pi\)
\(564\) 0 0
\(565\) −16378.0 −1.21952
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11932.0 −0.879113 −0.439557 − 0.898215i \(-0.644864\pi\)
−0.439557 + 0.898215i \(0.644864\pi\)
\(570\) 0 0
\(571\) −16016.0 −1.17382 −0.586908 − 0.809654i \(-0.699655\pi\)
−0.586908 + 0.809654i \(0.699655\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 15576.0 1.12968
\(576\) 0 0
\(577\) 15918.0 1.14848 0.574242 − 0.818686i \(-0.305297\pi\)
0.574242 + 0.818686i \(0.305297\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1989.00 −0.142027
\(582\) 0 0
\(583\) −19175.0 −1.36217
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19527.0 −1.37302 −0.686512 − 0.727118i \(-0.740859\pi\)
−0.686512 + 0.727118i \(0.740859\pi\)
\(588\) 0 0
\(589\) 8410.00 0.588333
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −14658.0 −1.01506 −0.507531 − 0.861633i \(-0.669442\pi\)
−0.507531 + 0.861633i \(0.669442\pi\)
\(594\) 0 0
\(595\) 26676.0 1.83800
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2086.00 −0.142290 −0.0711449 − 0.997466i \(-0.522665\pi\)
−0.0711449 + 0.997466i \(0.522665\pi\)
\(600\) 0 0
\(601\) −21125.0 −1.43379 −0.716894 − 0.697182i \(-0.754437\pi\)
−0.716894 + 0.697182i \(0.754437\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 54986.0 3.69504
\(606\) 0 0
\(607\) 184.000 0.0123037 0.00615184 − 0.999981i \(-0.498042\pi\)
0.00615184 + 0.999981i \(0.498042\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4144.00 0.274383
\(612\) 0 0
\(613\) 26658.0 1.75645 0.878227 − 0.478244i \(-0.158726\pi\)
0.878227 + 0.478244i \(0.158726\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4386.00 −0.286181 −0.143091 − 0.989710i \(-0.545704\pi\)
−0.143091 + 0.989710i \(0.545704\pi\)
\(618\) 0 0
\(619\) −15000.0 −0.973992 −0.486996 − 0.873404i \(-0.661907\pi\)
−0.486996 + 0.873404i \(0.661907\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −11050.0 −0.710608
\(624\) 0 0
\(625\) 10571.0 0.676544
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 20520.0 1.30077
\(630\) 0 0
\(631\) −19877.0 −1.25403 −0.627013 − 0.779008i \(-0.715723\pi\)
−0.627013 + 0.779008i \(0.715723\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −19361.0 −1.20995
\(636\) 0 0
\(637\) −9744.00 −0.606077
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 11146.0 0.686803 0.343401 − 0.939189i \(-0.388421\pi\)
0.343401 + 0.939189i \(0.388421\pi\)
\(642\) 0 0
\(643\) −23052.0 −1.41381 −0.706907 − 0.707307i \(-0.749910\pi\)
−0.706907 + 0.707307i \(0.749910\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −13896.0 −0.844371 −0.422186 − 0.906509i \(-0.638737\pi\)
−0.422186 + 0.906509i \(0.638737\pi\)
\(648\) 0 0
\(649\) 40820.0 2.46891
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7583.00 0.454434 0.227217 − 0.973844i \(-0.427037\pi\)
0.227217 + 0.973844i \(0.427037\pi\)
\(654\) 0 0
\(655\) 52079.0 3.10671
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 12591.0 0.744273 0.372136 − 0.928178i \(-0.378625\pi\)
0.372136 + 0.928178i \(0.378625\pi\)
\(660\) 0 0
\(661\) −30098.0 −1.77107 −0.885534 − 0.464574i \(-0.846208\pi\)
−0.885534 + 0.464574i \(0.846208\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −14326.0 −0.835396
\(666\) 0 0
\(667\) 7788.00 0.452103
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −23400.0 −1.34627
\(672\) 0 0
\(673\) 173.000 0.00990886 0.00495443 − 0.999988i \(-0.498423\pi\)
0.00495443 + 0.999988i \(0.498423\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −12934.0 −0.734260 −0.367130 − 0.930170i \(-0.619660\pi\)
−0.367130 + 0.930170i \(0.619660\pi\)
\(678\) 0 0
\(679\) −5083.00 −0.287287
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4164.00 −0.233281 −0.116641 − 0.993174i \(-0.537213\pi\)
−0.116641 + 0.993174i \(0.537213\pi\)
\(684\) 0 0
\(685\) −14250.0 −0.794839
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −16520.0 −0.913442
\(690\) 0 0
\(691\) 22660.0 1.24751 0.623753 − 0.781621i \(-0.285607\pi\)
0.623753 + 0.781621i \(0.285607\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −57532.0 −3.14002
\(696\) 0 0
\(697\) 46440.0 2.52373
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −27231.0 −1.46719 −0.733595 − 0.679587i \(-0.762159\pi\)
−0.733595 + 0.679587i \(0.762159\pi\)
\(702\) 0 0
\(703\) −11020.0 −0.591219
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7761.00 −0.412846
\(708\) 0 0
\(709\) −32140.0 −1.70246 −0.851229 − 0.524794i \(-0.824142\pi\)
−0.851229 + 0.524794i \(0.824142\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 9570.00 0.502664
\(714\) 0 0
\(715\) 69160.0 3.61739
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4028.00 0.208928 0.104464 − 0.994529i \(-0.466687\pi\)
0.104464 + 0.994529i \(0.466687\pi\)
\(720\) 0 0
\(721\) 3276.00 0.169216
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 27848.0 1.42655
\(726\) 0 0
\(727\) 27963.0 1.42653 0.713267 − 0.700892i \(-0.247215\pi\)
0.713267 + 0.700892i \(0.247215\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −57240.0 −2.89617
\(732\) 0 0
\(733\) −16142.0 −0.813395 −0.406697 − 0.913563i \(-0.633320\pi\)
−0.406697 + 0.913563i \(0.633320\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9490.00 0.474313
\(738\) 0 0
\(739\) 8404.00 0.418330 0.209165 − 0.977880i \(-0.432925\pi\)
0.209165 + 0.977880i \(0.432925\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −24912.0 −1.23006 −0.615029 − 0.788505i \(-0.710856\pi\)
−0.615029 + 0.788505i \(0.710856\pi\)
\(744\) 0 0
\(745\) −31863.0 −1.56694
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5135.00 0.250506
\(750\) 0 0
\(751\) 12685.0 0.616354 0.308177 − 0.951329i \(-0.400281\pi\)
0.308177 + 0.951329i \(0.400281\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 10887.0 0.524793
\(756\) 0 0
\(757\) 3702.00 0.177743 0.0888715 − 0.996043i \(-0.471674\pi\)
0.0888715 + 0.996043i \(0.471674\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −12024.0 −0.572759 −0.286380 − 0.958116i \(-0.592452\pi\)
−0.286380 + 0.958116i \(0.592452\pi\)
\(762\) 0 0
\(763\) 3302.00 0.156672
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 35168.0 1.65560
\(768\) 0 0
\(769\) −18215.0 −0.854161 −0.427080 − 0.904214i \(-0.640458\pi\)
−0.427080 + 0.904214i \(0.640458\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 24774.0 1.15273 0.576364 − 0.817193i \(-0.304471\pi\)
0.576364 + 0.817193i \(0.304471\pi\)
\(774\) 0 0
\(775\) 34220.0 1.58609
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −24940.0 −1.14707
\(780\) 0 0
\(781\) −25220.0 −1.15550
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 29716.0 1.35109
\(786\) 0 0
\(787\) −1152.00 −0.0521784 −0.0260892 − 0.999660i \(-0.508305\pi\)
−0.0260892 + 0.999660i \(0.508305\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 11206.0 0.503716
\(792\) 0 0
\(793\) −20160.0 −0.902778
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −30729.0 −1.36572 −0.682859 − 0.730550i \(-0.739264\pi\)
−0.682859 + 0.730550i \(0.739264\pi\)
\(798\) 0 0
\(799\) −7992.00 −0.353863
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 48945.0 2.15097
\(804\) 0 0
\(805\) −16302.0 −0.713752
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 27982.0 1.21606 0.608031 − 0.793913i \(-0.291959\pi\)
0.608031 + 0.793913i \(0.291959\pi\)
\(810\) 0 0
\(811\) 33394.0 1.44590 0.722948 − 0.690902i \(-0.242787\pi\)
0.722948 + 0.690902i \(0.242787\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 20368.0 0.875411
\(816\) 0 0
\(817\) 30740.0 1.31635
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −15650.0 −0.665273 −0.332636 − 0.943055i \(-0.607938\pi\)
−0.332636 + 0.943055i \(0.607938\pi\)
\(822\) 0 0
\(823\) −16555.0 −0.701180 −0.350590 − 0.936529i \(-0.614019\pi\)
−0.350590 + 0.936529i \(0.614019\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −27952.0 −1.17532 −0.587658 − 0.809109i \(-0.699950\pi\)
−0.587658 + 0.809109i \(0.699950\pi\)
\(828\) 0 0
\(829\) −31130.0 −1.30421 −0.652105 − 0.758129i \(-0.726114\pi\)
−0.652105 + 0.758129i \(0.726114\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 18792.0 0.781638
\(834\) 0 0
\(835\) −59014.0 −2.44582
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −10396.0 −0.427783 −0.213891 − 0.976857i \(-0.568614\pi\)
−0.213891 + 0.976857i \(0.568614\pi\)
\(840\) 0 0
\(841\) −10465.0 −0.429087
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 17841.0 0.726330
\(846\) 0 0
\(847\) −37622.0 −1.52622
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −12540.0 −0.505130
\(852\) 0 0
\(853\) 690.000 0.0276965 0.0138483 − 0.999904i \(-0.495592\pi\)
0.0138483 + 0.999904i \(0.495592\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −10436.0 −0.415971 −0.207985 − 0.978132i \(-0.566691\pi\)
−0.207985 + 0.978132i \(0.566691\pi\)
\(858\) 0 0
\(859\) −29584.0 −1.17508 −0.587540 − 0.809195i \(-0.699903\pi\)
−0.587540 + 0.809195i \(0.699903\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −30988.0 −1.22230 −0.611149 − 0.791515i \(-0.709293\pi\)
−0.611149 + 0.791515i \(0.709293\pi\)
\(864\) 0 0
\(865\) 80997.0 3.18379
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −73840.0 −2.88245
\(870\) 0 0
\(871\) 8176.00 0.318063
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −27417.0 −1.05927
\(876\) 0 0
\(877\) 24182.0 0.931092 0.465546 − 0.885024i \(-0.345858\pi\)
0.465546 + 0.885024i \(0.345858\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 13272.0 0.507543 0.253771 − 0.967264i \(-0.418329\pi\)
0.253771 + 0.967264i \(0.418329\pi\)
\(882\) 0 0
\(883\) −16606.0 −0.632884 −0.316442 − 0.948612i \(-0.602488\pi\)
−0.316442 + 0.948612i \(0.602488\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 20088.0 0.760416 0.380208 − 0.924901i \(-0.375852\pi\)
0.380208 + 0.924901i \(0.375852\pi\)
\(888\) 0 0
\(889\) 13247.0 0.499764
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4292.00 0.160836
\(894\) 0 0
\(895\) 13737.0 0.513047
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 17110.0 0.634761
\(900\) 0 0
\(901\) 31860.0 1.17804
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −58976.0 −2.16622
\(906\) 0 0
\(907\) 10234.0 0.374658 0.187329 − 0.982297i \(-0.440017\pi\)
0.187329 + 0.982297i \(0.440017\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −3966.00 −0.144236 −0.0721182 − 0.997396i \(-0.522976\pi\)
−0.0721182 + 0.997396i \(0.522976\pi\)
\(912\) 0 0
\(913\) 9945.00 0.360494
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −35633.0 −1.28321
\(918\) 0 0
\(919\) −24999.0 −0.897324 −0.448662 − 0.893701i \(-0.648099\pi\)
−0.448662 + 0.893701i \(0.648099\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −21728.0 −0.774849
\(924\) 0 0
\(925\) −44840.0 −1.59387
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 45444.0 1.60492 0.802459 − 0.596707i \(-0.203525\pi\)
0.802459 + 0.596707i \(0.203525\pi\)
\(930\) 0 0
\(931\) −10092.0 −0.355265
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −133380. −4.66523
\(936\) 0 0
\(937\) 5579.00 0.194512 0.0972561 − 0.995259i \(-0.468993\pi\)
0.0972561 + 0.995259i \(0.468993\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 9119.00 0.315910 0.157955 − 0.987446i \(-0.449510\pi\)
0.157955 + 0.987446i \(0.449510\pi\)
\(942\) 0 0
\(943\) −28380.0 −0.980042
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −7785.00 −0.267137 −0.133568 − 0.991040i \(-0.542644\pi\)
−0.133568 + 0.991040i \(0.542644\pi\)
\(948\) 0 0
\(949\) 42168.0 1.44239
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 31980.0 1.08702 0.543512 − 0.839401i \(-0.317094\pi\)
0.543512 + 0.839401i \(0.317094\pi\)
\(954\) 0 0
\(955\) −33744.0 −1.14338
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 9750.00 0.328304
\(960\) 0 0
\(961\) −8766.00 −0.294250
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 18183.0 0.606561
\(966\) 0 0
\(967\) 13395.0 0.445454 0.222727 − 0.974881i \(-0.428504\pi\)
0.222727 + 0.974881i \(0.428504\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −4615.00 −0.152526 −0.0762628 − 0.997088i \(-0.524299\pi\)
−0.0762628 + 0.997088i \(0.524299\pi\)
\(972\) 0 0
\(973\) 39364.0 1.29697
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −47782.0 −1.56467 −0.782335 − 0.622859i \(-0.785971\pi\)
−0.782335 + 0.622859i \(0.785971\pi\)
\(978\) 0 0
\(979\) 55250.0 1.80367
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −15798.0 −0.512592 −0.256296 − 0.966598i \(-0.582502\pi\)
−0.256296 + 0.966598i \(0.582502\pi\)
\(984\) 0 0
\(985\) −19133.0 −0.618912
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 34980.0 1.12467
\(990\) 0 0
\(991\) 13435.0 0.430653 0.215326 − 0.976542i \(-0.430918\pi\)
0.215326 + 0.976542i \(0.430918\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −15257.0 −0.486110
\(996\) 0 0
\(997\) −31536.0 −1.00176 −0.500880 − 0.865517i \(-0.666990\pi\)
−0.500880 + 0.865517i \(0.666990\pi\)
\(998\) 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.be.1.1 1
3.2 odd 2 1728.4.a.a.1.1 1
4.3 odd 2 1728.4.a.bf.1.1 1
8.3 odd 2 864.4.a.b.1.1 yes 1
8.5 even 2 864.4.a.a.1.1 ✓ 1
12.11 even 2 1728.4.a.b.1.1 1
24.5 odd 2 864.4.a.c.1.1 yes 1
24.11 even 2 864.4.a.d.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
864.4.a.a.1.1 ✓ 1 8.5 even 2
864.4.a.b.1.1 yes 1 8.3 odd 2
864.4.a.c.1.1 yes 1 24.5 odd 2
864.4.a.d.1.1 yes 1 24.11 even 2
1728.4.a.a.1.1 1 3.2 odd 2
1728.4.a.b.1.1 1 12.11 even 2
1728.4.a.be.1.1 1 1.1 even 1 trivial
1728.4.a.bf.1.1 1 4.3 odd 2