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Properties

Label 2160.4.a.k.1.1
Level $2160$
Weight $4$
Character 2160.1
Self dual yes
Analytic conductor $127.444$
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] = [2160,4,Mod(1,2160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2160, 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("2160.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.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: \(127.444125612\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 540)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2160.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.00000 q^{5} -17.0000 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} -17.0000 q^{7} +30.0000 q^{11} -61.0000 q^{13} -120.000 q^{17} +43.0000 q^{19} -90.0000 q^{23} +25.0000 q^{25} -90.0000 q^{29} -8.00000 q^{31} -85.0000 q^{35} +317.000 q^{37} -30.0000 q^{41} +220.000 q^{43} +180.000 q^{47} -54.0000 q^{49} -630.000 q^{53} +150.000 q^{55} +840.000 q^{59} +599.000 q^{61} -305.000 q^{65} -107.000 q^{67} +210.000 q^{71} -421.000 q^{73} -510.000 q^{77} -353.000 q^{79} +1350.00 q^{83} -600.000 q^{85} +1020.00 q^{89} +1037.00 q^{91} +215.000 q^{95} -997.000 q^{97} +O(q^{100})\)

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
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) −17.0000 −0.917914 −0.458957 − 0.888459i \(-0.651777\pi\)
−0.458957 + 0.888459i \(0.651777\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 30.0000 0.822304 0.411152 − 0.911567i \(-0.365127\pi\)
0.411152 + 0.911567i \(0.365127\pi\)
\(12\) 0 0
\(13\) −61.0000 −1.30141 −0.650706 − 0.759330i \(-0.725527\pi\)
−0.650706 + 0.759330i \(0.725527\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −120.000 −1.71202 −0.856008 − 0.516962i \(-0.827063\pi\)
−0.856008 + 0.516962i \(0.827063\pi\)
\(18\) 0 0
\(19\) 43.0000 0.519204 0.259602 − 0.965716i \(-0.416409\pi\)
0.259602 + 0.965716i \(0.416409\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −90.0000 −0.815926 −0.407963 − 0.912998i \(-0.633761\pi\)
−0.407963 + 0.912998i \(0.633761\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −90.0000 −0.576296 −0.288148 − 0.957586i \(-0.593039\pi\)
−0.288148 + 0.957586i \(0.593039\pi\)
\(30\) 0 0
\(31\) −8.00000 −0.0463498 −0.0231749 − 0.999731i \(-0.507377\pi\)
−0.0231749 + 0.999731i \(0.507377\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −85.0000 −0.410503
\(36\) 0 0
\(37\) 317.000 1.40850 0.704250 − 0.709952i \(-0.251284\pi\)
0.704250 + 0.709952i \(0.251284\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −30.0000 −0.114273 −0.0571367 − 0.998366i \(-0.518197\pi\)
−0.0571367 + 0.998366i \(0.518197\pi\)
\(42\) 0 0
\(43\) 220.000 0.780225 0.390113 − 0.920767i \(-0.372436\pi\)
0.390113 + 0.920767i \(0.372436\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 180.000 0.558632 0.279316 − 0.960199i \(-0.409892\pi\)
0.279316 + 0.960199i \(0.409892\pi\)
\(48\) 0 0
\(49\) −54.0000 −0.157434
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −630.000 −1.63278 −0.816388 − 0.577503i \(-0.804027\pi\)
−0.816388 + 0.577503i \(0.804027\pi\)
\(54\) 0 0
\(55\) 150.000 0.367745
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 840.000 1.85354 0.926769 − 0.375633i \(-0.122575\pi\)
0.926769 + 0.375633i \(0.122575\pi\)
\(60\) 0 0
\(61\) 599.000 1.25728 0.628640 − 0.777696i \(-0.283612\pi\)
0.628640 + 0.777696i \(0.283612\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −305.000 −0.582009
\(66\) 0 0
\(67\) −107.000 −0.195106 −0.0975532 − 0.995230i \(-0.531102\pi\)
−0.0975532 + 0.995230i \(0.531102\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 210.000 0.351020 0.175510 − 0.984478i \(-0.443843\pi\)
0.175510 + 0.984478i \(0.443843\pi\)
\(72\) 0 0
\(73\) −421.000 −0.674991 −0.337495 − 0.941327i \(-0.609580\pi\)
−0.337495 + 0.941327i \(0.609580\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −510.000 −0.754804
\(78\) 0 0
\(79\) −353.000 −0.502729 −0.251365 − 0.967892i \(-0.580879\pi\)
−0.251365 + 0.967892i \(0.580879\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1350.00 1.78532 0.892661 − 0.450728i \(-0.148836\pi\)
0.892661 + 0.450728i \(0.148836\pi\)
\(84\) 0 0
\(85\) −600.000 −0.765637
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1020.00 1.21483 0.607415 − 0.794385i \(-0.292207\pi\)
0.607415 + 0.794385i \(0.292207\pi\)
\(90\) 0 0
\(91\) 1037.00 1.19458
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 215.000 0.232195
\(96\) 0 0
\(97\) −997.000 −1.04361 −0.521804 − 0.853065i \(-0.674741\pi\)
−0.521804 + 0.853065i \(0.674741\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −960.000 −0.945778 −0.472889 − 0.881122i \(-0.656789\pi\)
−0.472889 + 0.881122i \(0.656789\pi\)
\(102\) 0 0
\(103\) −1181.00 −1.12978 −0.564890 − 0.825166i \(-0.691081\pi\)
−0.564890 + 0.825166i \(0.691081\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −330.000 −0.298152 −0.149076 − 0.988826i \(-0.547630\pi\)
−0.149076 + 0.988826i \(0.547630\pi\)
\(108\) 0 0
\(109\) 1454.00 1.27769 0.638844 − 0.769336i \(-0.279413\pi\)
0.638844 + 0.769336i \(0.279413\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1230.00 1.02397 0.511985 − 0.858994i \(-0.328910\pi\)
0.511985 + 0.858994i \(0.328910\pi\)
\(114\) 0 0
\(115\) −450.000 −0.364893
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2040.00 1.57148
\(120\) 0 0
\(121\) −431.000 −0.323817
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1280.00 −0.894344 −0.447172 − 0.894448i \(-0.647569\pi\)
−0.447172 + 0.894448i \(0.647569\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2220.00 1.48063 0.740314 − 0.672261i \(-0.234677\pi\)
0.740314 + 0.672261i \(0.234677\pi\)
\(132\) 0 0
\(133\) −731.000 −0.476585
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1170.00 −0.729634 −0.364817 − 0.931079i \(-0.618868\pi\)
−0.364817 + 0.931079i \(0.618868\pi\)
\(138\) 0 0
\(139\) 1393.00 0.850020 0.425010 − 0.905189i \(-0.360271\pi\)
0.425010 + 0.905189i \(0.360271\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1830.00 −1.07016
\(144\) 0 0
\(145\) −450.000 −0.257727
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1380.00 0.758752 0.379376 − 0.925243i \(-0.376139\pi\)
0.379376 + 0.925243i \(0.376139\pi\)
\(150\) 0 0
\(151\) 2659.00 1.43302 0.716511 − 0.697576i \(-0.245738\pi\)
0.716511 + 0.697576i \(0.245738\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −40.0000 −0.0207282
\(156\) 0 0
\(157\) 1850.00 0.940421 0.470210 − 0.882554i \(-0.344178\pi\)
0.470210 + 0.882554i \(0.344178\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1530.00 0.748950
\(162\) 0 0
\(163\) −1121.00 −0.538672 −0.269336 − 0.963046i \(-0.586804\pi\)
−0.269336 + 0.963046i \(0.586804\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −300.000 −0.139010 −0.0695051 − 0.997582i \(-0.522142\pi\)
−0.0695051 + 0.997582i \(0.522142\pi\)
\(168\) 0 0
\(169\) 1524.00 0.693673
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1620.00 −0.711944 −0.355972 − 0.934497i \(-0.615850\pi\)
−0.355972 + 0.934497i \(0.615850\pi\)
\(174\) 0 0
\(175\) −425.000 −0.183583
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 630.000 0.263064 0.131532 − 0.991312i \(-0.458010\pi\)
0.131532 + 0.991312i \(0.458010\pi\)
\(180\) 0 0
\(181\) −2299.00 −0.944107 −0.472053 − 0.881570i \(-0.656487\pi\)
−0.472053 + 0.881570i \(0.656487\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1585.00 0.629900
\(186\) 0 0
\(187\) −3600.00 −1.40780
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −900.000 −0.340951 −0.170476 − 0.985362i \(-0.554530\pi\)
−0.170476 + 0.985362i \(0.554530\pi\)
\(192\) 0 0
\(193\) 3461.00 1.29082 0.645410 − 0.763836i \(-0.276687\pi\)
0.645410 + 0.763836i \(0.276687\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4560.00 1.64917 0.824585 − 0.565738i \(-0.191409\pi\)
0.824585 + 0.565738i \(0.191409\pi\)
\(198\) 0 0
\(199\) 2077.00 0.739872 0.369936 − 0.929057i \(-0.379380\pi\)
0.369936 + 0.929057i \(0.379380\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1530.00 0.528990
\(204\) 0 0
\(205\) −150.000 −0.0511047
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1290.00 0.426943
\(210\) 0 0
\(211\) 4021.00 1.31193 0.655965 − 0.754792i \(-0.272262\pi\)
0.655965 + 0.754792i \(0.272262\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1100.00 0.348927
\(216\) 0 0
\(217\) 136.000 0.0425451
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 7320.00 2.22804
\(222\) 0 0
\(223\) −80.0000 −0.0240233 −0.0120117 − 0.999928i \(-0.503824\pi\)
−0.0120117 + 0.999928i \(0.503824\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3750.00 1.09646 0.548230 − 0.836328i \(-0.315302\pi\)
0.548230 + 0.836328i \(0.315302\pi\)
\(228\) 0 0
\(229\) −1234.00 −0.356092 −0.178046 − 0.984022i \(-0.556978\pi\)
−0.178046 + 0.984022i \(0.556978\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5880.00 1.65327 0.826634 − 0.562739i \(-0.190253\pi\)
0.826634 + 0.562739i \(0.190253\pi\)
\(234\) 0 0
\(235\) 900.000 0.249828
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −5130.00 −1.38842 −0.694209 − 0.719773i \(-0.744246\pi\)
−0.694209 + 0.719773i \(0.744246\pi\)
\(240\) 0 0
\(241\) −7231.00 −1.93274 −0.966369 − 0.257161i \(-0.917213\pi\)
−0.966369 + 0.257161i \(0.917213\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −270.000 −0.0704068
\(246\) 0 0
\(247\) −2623.00 −0.675698
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −7530.00 −1.89358 −0.946792 − 0.321847i \(-0.895696\pi\)
−0.946792 + 0.321847i \(0.895696\pi\)
\(252\) 0 0
\(253\) −2700.00 −0.670939
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4560.00 1.10679 0.553395 − 0.832919i \(-0.313332\pi\)
0.553395 + 0.832919i \(0.313332\pi\)
\(258\) 0 0
\(259\) −5389.00 −1.29288
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2100.00 0.492363 0.246182 − 0.969224i \(-0.420824\pi\)
0.246182 + 0.969224i \(0.420824\pi\)
\(264\) 0 0
\(265\) −3150.00 −0.730200
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3120.00 0.707174 0.353587 − 0.935402i \(-0.384962\pi\)
0.353587 + 0.935402i \(0.384962\pi\)
\(270\) 0 0
\(271\) −3449.00 −0.773106 −0.386553 − 0.922267i \(-0.626334\pi\)
−0.386553 + 0.922267i \(0.626334\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 750.000 0.164461
\(276\) 0 0
\(277\) 3770.00 0.817752 0.408876 − 0.912590i \(-0.365921\pi\)
0.408876 + 0.912590i \(0.365921\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6720.00 −1.42662 −0.713312 − 0.700846i \(-0.752806\pi\)
−0.713312 + 0.700846i \(0.752806\pi\)
\(282\) 0 0
\(283\) 100.000 0.0210049 0.0105024 − 0.999945i \(-0.496657\pi\)
0.0105024 + 0.999945i \(0.496657\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 510.000 0.104893
\(288\) 0 0
\(289\) 9487.00 1.93100
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 870.000 0.173467 0.0867337 − 0.996232i \(-0.472357\pi\)
0.0867337 + 0.996232i \(0.472357\pi\)
\(294\) 0 0
\(295\) 4200.00 0.828927
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5490.00 1.06186
\(300\) 0 0
\(301\) −3740.00 −0.716179
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2995.00 0.562273
\(306\) 0 0
\(307\) −3440.00 −0.639515 −0.319758 − 0.947499i \(-0.603601\pi\)
−0.319758 + 0.947499i \(0.603601\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5880.00 1.07210 0.536052 − 0.844185i \(-0.319915\pi\)
0.536052 + 0.844185i \(0.319915\pi\)
\(312\) 0 0
\(313\) 1841.00 0.332458 0.166229 − 0.986087i \(-0.446841\pi\)
0.166229 + 0.986087i \(0.446841\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3420.00 0.605951 0.302975 − 0.952998i \(-0.402020\pi\)
0.302975 + 0.952998i \(0.402020\pi\)
\(318\) 0 0
\(319\) −2700.00 −0.473890
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5160.00 −0.888886
\(324\) 0 0
\(325\) −1525.00 −0.260282
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3060.00 −0.512776
\(330\) 0 0
\(331\) 5641.00 0.936729 0.468365 − 0.883535i \(-0.344843\pi\)
0.468365 + 0.883535i \(0.344843\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −535.000 −0.0872542
\(336\) 0 0
\(337\) −1057.00 −0.170856 −0.0854280 − 0.996344i \(-0.527226\pi\)
−0.0854280 + 0.996344i \(0.527226\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −240.000 −0.0381136
\(342\) 0 0
\(343\) 6749.00 1.06242
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1290.00 0.199570 0.0997851 − 0.995009i \(-0.468184\pi\)
0.0997851 + 0.995009i \(0.468184\pi\)
\(348\) 0 0
\(349\) 3467.00 0.531760 0.265880 − 0.964006i \(-0.414337\pi\)
0.265880 + 0.964006i \(0.414337\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7740.00 1.16702 0.583511 − 0.812105i \(-0.301679\pi\)
0.583511 + 0.812105i \(0.301679\pi\)
\(354\) 0 0
\(355\) 1050.00 0.156981
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8130.00 −1.19522 −0.597611 − 0.801786i \(-0.703883\pi\)
−0.597611 + 0.801786i \(0.703883\pi\)
\(360\) 0 0
\(361\) −5010.00 −0.730427
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2105.00 −0.301865
\(366\) 0 0
\(367\) −12113.0 −1.72287 −0.861435 − 0.507867i \(-0.830434\pi\)
−0.861435 + 0.507867i \(0.830434\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 10710.0 1.49875
\(372\) 0 0
\(373\) 4349.00 0.603707 0.301853 − 0.953354i \(-0.402395\pi\)
0.301853 + 0.953354i \(0.402395\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5490.00 0.749998
\(378\) 0 0
\(379\) 7663.00 1.03858 0.519290 − 0.854598i \(-0.326196\pi\)
0.519290 + 0.854598i \(0.326196\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3960.00 0.528320 0.264160 − 0.964479i \(-0.414905\pi\)
0.264160 + 0.964479i \(0.414905\pi\)
\(384\) 0 0
\(385\) −2550.00 −0.337559
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1320.00 0.172048 0.0860240 − 0.996293i \(-0.472584\pi\)
0.0860240 + 0.996293i \(0.472584\pi\)
\(390\) 0 0
\(391\) 10800.0 1.39688
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1765.00 −0.224827
\(396\) 0 0
\(397\) 14390.0 1.81918 0.909589 − 0.415510i \(-0.136397\pi\)
0.909589 + 0.415510i \(0.136397\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8610.00 1.07223 0.536113 − 0.844146i \(-0.319892\pi\)
0.536113 + 0.844146i \(0.319892\pi\)
\(402\) 0 0
\(403\) 488.000 0.0603201
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9510.00 1.15821
\(408\) 0 0
\(409\) 7097.00 0.858005 0.429003 − 0.903303i \(-0.358865\pi\)
0.429003 + 0.903303i \(0.358865\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −14280.0 −1.70139
\(414\) 0 0
\(415\) 6750.00 0.798420
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 8880.00 1.03536 0.517681 − 0.855574i \(-0.326796\pi\)
0.517681 + 0.855574i \(0.326796\pi\)
\(420\) 0 0
\(421\) −5479.00 −0.634276 −0.317138 − 0.948379i \(-0.602722\pi\)
−0.317138 + 0.948379i \(0.602722\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3000.00 −0.342403
\(426\) 0 0
\(427\) −10183.0 −1.15407
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 12510.0 1.39811 0.699055 − 0.715068i \(-0.253604\pi\)
0.699055 + 0.715068i \(0.253604\pi\)
\(432\) 0 0
\(433\) −6790.00 −0.753595 −0.376797 − 0.926296i \(-0.622975\pi\)
−0.376797 + 0.926296i \(0.622975\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3870.00 −0.423632
\(438\) 0 0
\(439\) 11176.0 1.21504 0.607519 − 0.794305i \(-0.292165\pi\)
0.607519 + 0.794305i \(0.292165\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 13860.0 1.48648 0.743238 − 0.669028i \(-0.233289\pi\)
0.743238 + 0.669028i \(0.233289\pi\)
\(444\) 0 0
\(445\) 5100.00 0.543288
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4740.00 −0.498206 −0.249103 − 0.968477i \(-0.580136\pi\)
−0.249103 + 0.968477i \(0.580136\pi\)
\(450\) 0 0
\(451\) −900.000 −0.0939675
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5185.00 0.534234
\(456\) 0 0
\(457\) −1690.00 −0.172987 −0.0864933 − 0.996252i \(-0.527566\pi\)
−0.0864933 + 0.996252i \(0.527566\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14700.0 1.48514 0.742568 − 0.669771i \(-0.233608\pi\)
0.742568 + 0.669771i \(0.233608\pi\)
\(462\) 0 0
\(463\) 331.000 0.0332244 0.0166122 − 0.999862i \(-0.494712\pi\)
0.0166122 + 0.999862i \(0.494712\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8580.00 0.850182 0.425091 − 0.905151i \(-0.360242\pi\)
0.425091 + 0.905151i \(0.360242\pi\)
\(468\) 0 0
\(469\) 1819.00 0.179091
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6600.00 0.641582
\(474\) 0 0
\(475\) 1075.00 0.103841
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 14790.0 1.41080 0.705399 − 0.708810i \(-0.250768\pi\)
0.705399 + 0.708810i \(0.250768\pi\)
\(480\) 0 0
\(481\) −19337.0 −1.83304
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4985.00 −0.466716
\(486\) 0 0
\(487\) −13097.0 −1.21865 −0.609324 − 0.792921i \(-0.708559\pi\)
−0.609324 + 0.792921i \(0.708559\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1590.00 −0.146142 −0.0730710 − 0.997327i \(-0.523280\pi\)
−0.0730710 + 0.997327i \(0.523280\pi\)
\(492\) 0 0
\(493\) 10800.0 0.986628
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3570.00 −0.322206
\(498\) 0 0
\(499\) −17264.0 −1.54878 −0.774392 − 0.632707i \(-0.781944\pi\)
−0.774392 + 0.632707i \(0.781944\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 14730.0 1.30572 0.652861 − 0.757478i \(-0.273569\pi\)
0.652861 + 0.757478i \(0.273569\pi\)
\(504\) 0 0
\(505\) −4800.00 −0.422965
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 870.000 0.0757605 0.0378802 − 0.999282i \(-0.487939\pi\)
0.0378802 + 0.999282i \(0.487939\pi\)
\(510\) 0 0
\(511\) 7157.00 0.619583
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5905.00 −0.505253
\(516\) 0 0
\(517\) 5400.00 0.459365
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6990.00 −0.587788 −0.293894 − 0.955838i \(-0.594951\pi\)
−0.293894 + 0.955838i \(0.594951\pi\)
\(522\) 0 0
\(523\) −12119.0 −1.01324 −0.506622 − 0.862168i \(-0.669106\pi\)
−0.506622 + 0.862168i \(0.669106\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 960.000 0.0793515
\(528\) 0 0
\(529\) −4067.00 −0.334265
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1830.00 0.148717
\(534\) 0 0
\(535\) −1650.00 −0.133338
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1620.00 −0.129459
\(540\) 0 0
\(541\) −21511.0 −1.70948 −0.854741 − 0.519054i \(-0.826284\pi\)
−0.854741 + 0.519054i \(0.826284\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 7270.00 0.571399
\(546\) 0 0
\(547\) 10807.0 0.844742 0.422371 − 0.906423i \(-0.361198\pi\)
0.422371 + 0.906423i \(0.361198\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3870.00 −0.299215
\(552\) 0 0
\(553\) 6001.00 0.461462
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −20460.0 −1.55641 −0.778203 − 0.628013i \(-0.783868\pi\)
−0.778203 + 0.628013i \(0.783868\pi\)
\(558\) 0 0
\(559\) −13420.0 −1.01539
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4980.00 0.372792 0.186396 − 0.982475i \(-0.440319\pi\)
0.186396 + 0.982475i \(0.440319\pi\)
\(564\) 0 0
\(565\) 6150.00 0.457934
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 15840.0 1.16704 0.583521 − 0.812098i \(-0.301674\pi\)
0.583521 + 0.812098i \(0.301674\pi\)
\(570\) 0 0
\(571\) 24391.0 1.78762 0.893810 − 0.448445i \(-0.148022\pi\)
0.893810 + 0.448445i \(0.148022\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2250.00 −0.163185
\(576\) 0 0
\(577\) 7673.00 0.553607 0.276803 − 0.960927i \(-0.410725\pi\)
0.276803 + 0.960927i \(0.410725\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −22950.0 −1.63877
\(582\) 0 0
\(583\) −18900.0 −1.34264
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18930.0 −1.33105 −0.665524 − 0.746377i \(-0.731792\pi\)
−0.665524 + 0.746377i \(0.731792\pi\)
\(588\) 0 0
\(589\) −344.000 −0.0240650
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14190.0 0.982653 0.491327 − 0.870975i \(-0.336512\pi\)
0.491327 + 0.870975i \(0.336512\pi\)
\(594\) 0 0
\(595\) 10200.0 0.702789
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 12870.0 0.877886 0.438943 − 0.898515i \(-0.355353\pi\)
0.438943 + 0.898515i \(0.355353\pi\)
\(600\) 0 0
\(601\) 19598.0 1.33015 0.665074 − 0.746777i \(-0.268400\pi\)
0.665074 + 0.746777i \(0.268400\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2155.00 −0.144815
\(606\) 0 0
\(607\) 15163.0 1.01392 0.506958 − 0.861971i \(-0.330770\pi\)
0.506958 + 0.861971i \(0.330770\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −10980.0 −0.727010
\(612\) 0 0
\(613\) −29599.0 −1.95023 −0.975116 − 0.221695i \(-0.928841\pi\)
−0.975116 + 0.221695i \(0.928841\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −2490.00 −0.162469 −0.0812347 − 0.996695i \(-0.525886\pi\)
−0.0812347 + 0.996695i \(0.525886\pi\)
\(618\) 0 0
\(619\) −3713.00 −0.241095 −0.120548 − 0.992708i \(-0.538465\pi\)
−0.120548 + 0.992708i \(0.538465\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −17340.0 −1.11511
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −38040.0 −2.41137
\(630\) 0 0
\(631\) −19409.0 −1.22450 −0.612250 − 0.790664i \(-0.709736\pi\)
−0.612250 + 0.790664i \(0.709736\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6400.00 −0.399963
\(636\) 0 0
\(637\) 3294.00 0.204887
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6480.00 0.399290 0.199645 − 0.979868i \(-0.436021\pi\)
0.199645 + 0.979868i \(0.436021\pi\)
\(642\) 0 0
\(643\) −30260.0 −1.85589 −0.927945 − 0.372716i \(-0.878427\pi\)
−0.927945 + 0.372716i \(0.878427\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −21510.0 −1.30703 −0.653513 − 0.756916i \(-0.726705\pi\)
−0.653513 + 0.756916i \(0.726705\pi\)
\(648\) 0 0
\(649\) 25200.0 1.52417
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −540.000 −0.0323612 −0.0161806 − 0.999869i \(-0.505151\pi\)
−0.0161806 + 0.999869i \(0.505151\pi\)
\(654\) 0 0
\(655\) 11100.0 0.662157
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −29280.0 −1.73078 −0.865392 − 0.501095i \(-0.832931\pi\)
−0.865392 + 0.501095i \(0.832931\pi\)
\(660\) 0 0
\(661\) −21769.0 −1.28096 −0.640481 − 0.767974i \(-0.721265\pi\)
−0.640481 + 0.767974i \(0.721265\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3655.00 −0.213135
\(666\) 0 0
\(667\) 8100.00 0.470215
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 17970.0 1.03387
\(672\) 0 0
\(673\) −14551.0 −0.833432 −0.416716 − 0.909037i \(-0.636819\pi\)
−0.416716 + 0.909037i \(0.636819\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1500.00 −0.0851546 −0.0425773 − 0.999093i \(-0.513557\pi\)
−0.0425773 + 0.999093i \(0.513557\pi\)
\(678\) 0 0
\(679\) 16949.0 0.957942
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −16530.0 −0.926066 −0.463033 − 0.886341i \(-0.653239\pi\)
−0.463033 + 0.886341i \(0.653239\pi\)
\(684\) 0 0
\(685\) −5850.00 −0.326302
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 38430.0 2.12491
\(690\) 0 0
\(691\) 25972.0 1.42984 0.714921 − 0.699205i \(-0.246462\pi\)
0.714921 + 0.699205i \(0.246462\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6965.00 0.380140
\(696\) 0 0
\(697\) 3600.00 0.195638
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −10230.0 −0.551187 −0.275593 − 0.961274i \(-0.588874\pi\)
−0.275593 + 0.961274i \(0.588874\pi\)
\(702\) 0 0
\(703\) 13631.0 0.731299
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 16320.0 0.868143
\(708\) 0 0
\(709\) −14623.0 −0.774582 −0.387291 − 0.921958i \(-0.626589\pi\)
−0.387291 + 0.921958i \(0.626589\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 720.000 0.0378180
\(714\) 0 0
\(715\) −9150.00 −0.478588
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −6690.00 −0.347003 −0.173501 − 0.984834i \(-0.555508\pi\)
−0.173501 + 0.984834i \(0.555508\pi\)
\(720\) 0 0
\(721\) 20077.0 1.03704
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2250.00 −0.115259
\(726\) 0 0
\(727\) −11720.0 −0.597896 −0.298948 − 0.954269i \(-0.596636\pi\)
−0.298948 + 0.954269i \(0.596636\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −26400.0 −1.33576
\(732\) 0 0
\(733\) −4750.00 −0.239352 −0.119676 − 0.992813i \(-0.538186\pi\)
−0.119676 + 0.992813i \(0.538186\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3210.00 −0.160437
\(738\) 0 0
\(739\) 30724.0 1.52936 0.764682 − 0.644407i \(-0.222896\pi\)
0.764682 + 0.644407i \(0.222896\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −960.000 −0.0474011 −0.0237005 − 0.999719i \(-0.507545\pi\)
−0.0237005 + 0.999719i \(0.507545\pi\)
\(744\) 0 0
\(745\) 6900.00 0.339324
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5610.00 0.273678
\(750\) 0 0
\(751\) −22781.0 −1.10691 −0.553456 − 0.832879i \(-0.686691\pi\)
−0.553456 + 0.832879i \(0.686691\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 13295.0 0.640867
\(756\) 0 0
\(757\) 32387.0 1.55499 0.777494 − 0.628891i \(-0.216491\pi\)
0.777494 + 0.628891i \(0.216491\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 25290.0 1.20468 0.602340 − 0.798239i \(-0.294235\pi\)
0.602340 + 0.798239i \(0.294235\pi\)
\(762\) 0 0
\(763\) −24718.0 −1.17281
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −51240.0 −2.41222
\(768\) 0 0
\(769\) 16283.0 0.763563 0.381782 − 0.924253i \(-0.375311\pi\)
0.381782 + 0.924253i \(0.375311\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −31050.0 −1.44475 −0.722374 − 0.691502i \(-0.756949\pi\)
−0.722374 + 0.691502i \(0.756949\pi\)
\(774\) 0 0
\(775\) −200.000 −0.00926995
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1290.00 −0.0593313
\(780\) 0 0
\(781\) 6300.00 0.288645
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 9250.00 0.420569
\(786\) 0 0
\(787\) 5053.00 0.228869 0.114435 − 0.993431i \(-0.463494\pi\)
0.114435 + 0.993431i \(0.463494\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −20910.0 −0.939917
\(792\) 0 0
\(793\) −36539.0 −1.63624
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 43680.0 1.94131 0.970656 − 0.240474i \(-0.0773029\pi\)
0.970656 + 0.240474i \(0.0773029\pi\)
\(798\) 0 0
\(799\) −21600.0 −0.956387
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −12630.0 −0.555047
\(804\) 0 0
\(805\) 7650.00 0.334940
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1920.00 0.0834408 0.0417204 − 0.999129i \(-0.486716\pi\)
0.0417204 + 0.999129i \(0.486716\pi\)
\(810\) 0 0
\(811\) −37268.0 −1.61363 −0.806817 − 0.590802i \(-0.798811\pi\)
−0.806817 + 0.590802i \(0.798811\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −5605.00 −0.240901
\(816\) 0 0
\(817\) 9460.00 0.405096
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 5280.00 0.224450 0.112225 − 0.993683i \(-0.464202\pi\)
0.112225 + 0.993683i \(0.464202\pi\)
\(822\) 0 0
\(823\) −4511.00 −0.191061 −0.0955307 − 0.995426i \(-0.530455\pi\)
−0.0955307 + 0.995426i \(0.530455\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 10140.0 0.426363 0.213182 − 0.977013i \(-0.431617\pi\)
0.213182 + 0.977013i \(0.431617\pi\)
\(828\) 0 0
\(829\) −11923.0 −0.499521 −0.249760 − 0.968308i \(-0.580352\pi\)
−0.249760 + 0.968308i \(0.580352\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 6480.00 0.269530
\(834\) 0 0
\(835\) −1500.00 −0.0621672
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −21300.0 −0.876469 −0.438235 − 0.898861i \(-0.644396\pi\)
−0.438235 + 0.898861i \(0.644396\pi\)
\(840\) 0 0
\(841\) −16289.0 −0.667883
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 7620.00 0.310220
\(846\) 0 0
\(847\) 7327.00 0.297236
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −28530.0 −1.14923
\(852\) 0 0
\(853\) −40771.0 −1.63654 −0.818272 − 0.574831i \(-0.805068\pi\)
−0.818272 + 0.574831i \(0.805068\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 25170.0 1.00326 0.501628 − 0.865083i \(-0.332735\pi\)
0.501628 + 0.865083i \(0.332735\pi\)
\(858\) 0 0
\(859\) 42757.0 1.69831 0.849156 − 0.528142i \(-0.177111\pi\)
0.849156 + 0.528142i \(0.177111\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −15300.0 −0.603497 −0.301749 − 0.953388i \(-0.597570\pi\)
−0.301749 + 0.953388i \(0.597570\pi\)
\(864\) 0 0
\(865\) −8100.00 −0.318391
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −10590.0 −0.413396
\(870\) 0 0
\(871\) 6527.00 0.253914
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2125.00 −0.0821007
\(876\) 0 0
\(877\) −23743.0 −0.914189 −0.457095 − 0.889418i \(-0.651110\pi\)
−0.457095 + 0.889418i \(0.651110\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −27810.0 −1.06350 −0.531750 − 0.846902i \(-0.678465\pi\)
−0.531750 + 0.846902i \(0.678465\pi\)
\(882\) 0 0
\(883\) 42991.0 1.63846 0.819231 − 0.573463i \(-0.194400\pi\)
0.819231 + 0.573463i \(0.194400\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 45600.0 1.72615 0.863077 − 0.505073i \(-0.168534\pi\)
0.863077 + 0.505073i \(0.168534\pi\)
\(888\) 0 0
\(889\) 21760.0 0.820930
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 7740.00 0.290044
\(894\) 0 0
\(895\) 3150.00 0.117646
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 720.000 0.0267112
\(900\) 0 0
\(901\) 75600.0 2.79534
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −11495.0 −0.422217
\(906\) 0 0
\(907\) 4993.00 0.182789 0.0913946 − 0.995815i \(-0.470868\pi\)
0.0913946 + 0.995815i \(0.470868\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 4920.00 0.178932 0.0894659 − 0.995990i \(-0.471484\pi\)
0.0894659 + 0.995990i \(0.471484\pi\)
\(912\) 0 0
\(913\) 40500.0 1.46808
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −37740.0 −1.35909
\(918\) 0 0
\(919\) −5456.00 −0.195840 −0.0979199 − 0.995194i \(-0.531219\pi\)
−0.0979199 + 0.995194i \(0.531219\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −12810.0 −0.456822
\(924\) 0 0
\(925\) 7925.00 0.281700
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −14790.0 −0.522330 −0.261165 − 0.965294i \(-0.584107\pi\)
−0.261165 + 0.965294i \(0.584107\pi\)
\(930\) 0 0
\(931\) −2322.00 −0.0817406
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −18000.0 −0.629586
\(936\) 0 0
\(937\) −14023.0 −0.488913 −0.244456 − 0.969660i \(-0.578610\pi\)
−0.244456 + 0.969660i \(0.578610\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −35250.0 −1.22117 −0.610583 − 0.791952i \(-0.709065\pi\)
−0.610583 + 0.791952i \(0.709065\pi\)
\(942\) 0 0
\(943\) 2700.00 0.0932387
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 37920.0 1.30120 0.650599 − 0.759421i \(-0.274518\pi\)
0.650599 + 0.759421i \(0.274518\pi\)
\(948\) 0 0
\(949\) 25681.0 0.878441
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −49080.0 −1.66827 −0.834133 − 0.551564i \(-0.814031\pi\)
−0.834133 + 0.551564i \(0.814031\pi\)
\(954\) 0 0
\(955\) −4500.00 −0.152478
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 19890.0 0.669741
\(960\) 0 0
\(961\) −29727.0 −0.997852
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 17305.0 0.577272
\(966\) 0 0
\(967\) 33073.0 1.09985 0.549926 − 0.835214i \(-0.314656\pi\)
0.549926 + 0.835214i \(0.314656\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 6420.00 0.212181 0.106090 − 0.994356i \(-0.466167\pi\)
0.106090 + 0.994356i \(0.466167\pi\)
\(972\) 0 0
\(973\) −23681.0 −0.780245
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 25110.0 0.822252 0.411126 − 0.911579i \(-0.365136\pi\)
0.411126 + 0.911579i \(0.365136\pi\)
\(978\) 0 0
\(979\) 30600.0 0.998958
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −52410.0 −1.70053 −0.850264 − 0.526356i \(-0.823558\pi\)
−0.850264 + 0.526356i \(0.823558\pi\)
\(984\) 0 0
\(985\) 22800.0 0.737531
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −19800.0 −0.636606
\(990\) 0 0
\(991\) −52619.0 −1.68668 −0.843339 − 0.537382i \(-0.819413\pi\)
−0.843339 + 0.537382i \(0.819413\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 10385.0 0.330881
\(996\) 0 0
\(997\) −53890.0 −1.71185 −0.855924 − 0.517101i \(-0.827011\pi\)
−0.855924 + 0.517101i \(0.827011\pi\)
\(998\) 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 2160.4.a.k.1.1 1
3.2 odd 2 2160.4.a.a.1.1 1
4.3 odd 2 540.4.a.d.1.1 yes 1
12.11 even 2 540.4.a.b.1.1 ✓ 1
36.7 odd 6 1620.4.i.b.1081.1 2
36.11 even 6 1620.4.i.h.1081.1 2
36.23 even 6 1620.4.i.h.541.1 2
36.31 odd 6 1620.4.i.b.541.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
540.4.a.b.1.1 ✓ 1 12.11 even 2
540.4.a.d.1.1 yes 1 4.3 odd 2
1620.4.i.b.541.1 2 36.31 odd 6
1620.4.i.b.1081.1 2 36.7 odd 6
1620.4.i.h.541.1 2 36.23 even 6
1620.4.i.h.1081.1 2 36.11 even 6
2160.4.a.a.1.1 1 3.2 odd 2
2160.4.a.k.1.1 1 1.1 even 1 trivial