↑

Properties

Label 2160.4.a.f.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 $1$

Related objects

Downloads

Learn more

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 135)
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)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} +6.00000 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} +6.00000 q^{7} -47.0000 q^{11} -5.00000 q^{13} +131.000 q^{17} +56.0000 q^{19} +3.00000 q^{23} +25.0000 q^{25} +157.000 q^{29} -225.000 q^{31} -30.0000 q^{35} -70.0000 q^{37} -140.000 q^{41} -397.000 q^{43} -347.000 q^{47} -307.000 q^{49} -4.00000 q^{53} +235.000 q^{55} +748.000 q^{59} -338.000 q^{61} +25.0000 q^{65} -492.000 q^{67} +32.0000 q^{71} +970.000 q^{73} -282.000 q^{77} +1257.00 q^{79} -102.000 q^{83} -655.000 q^{85} +1488.00 q^{89} -30.0000 q^{91} -280.000 q^{95} +974.000 q^{97} +O(q^{100})\)

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
\(7\) 6.00000 0.323970 0.161985 − 0.986793i \(-0.448210\pi\)
0.161985 + 0.986793i \(0.448210\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −47.0000 −1.28828 −0.644138 − 0.764909i \(-0.722784\pi\)
−0.644138 + 0.764909i \(0.722784\pi\)
\(12\) 0 0
\(13\) −5.00000 −0.106673 −0.0533366 − 0.998577i \(-0.516986\pi\)
−0.0533366 + 0.998577i \(0.516986\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 131.000 1.86895 0.934475 − 0.356027i \(-0.115869\pi\)
0.934475 + 0.356027i \(0.115869\pi\)
\(18\) 0 0
\(19\) 56.0000 0.676173 0.338086 − 0.941115i \(-0.390220\pi\)
0.338086 + 0.941115i \(0.390220\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 0.0271975 0.0135988 − 0.999908i \(-0.495671\pi\)
0.0135988 + 0.999908i \(0.495671\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 157.000 1.00532 0.502658 − 0.864485i \(-0.332355\pi\)
0.502658 + 0.864485i \(0.332355\pi\)
\(30\) 0 0
\(31\) −225.000 −1.30359 −0.651793 − 0.758397i \(-0.725983\pi\)
−0.651793 + 0.758397i \(0.725983\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −30.0000 −0.144884
\(36\) 0 0
\(37\) −70.0000 −0.311025 −0.155513 − 0.987834i \(-0.549703\pi\)
−0.155513 + 0.987834i \(0.549703\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −140.000 −0.533276 −0.266638 − 0.963797i \(-0.585913\pi\)
−0.266638 + 0.963797i \(0.585913\pi\)
\(42\) 0 0
\(43\) −397.000 −1.40795 −0.703976 − 0.710224i \(-0.748594\pi\)
−0.703976 + 0.710224i \(0.748594\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −347.000 −1.07692 −0.538459 − 0.842652i \(-0.680993\pi\)
−0.538459 + 0.842652i \(0.680993\pi\)
\(48\) 0 0
\(49\) −307.000 −0.895044
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.00000 −0.0103668 −0.00518342 − 0.999987i \(-0.501650\pi\)
−0.00518342 + 0.999987i \(0.501650\pi\)
\(54\) 0 0
\(55\) 235.000 0.576134
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 748.000 1.65053 0.825265 − 0.564745i \(-0.191026\pi\)
0.825265 + 0.564745i \(0.191026\pi\)
\(60\) 0 0
\(61\) −338.000 −0.709450 −0.354725 − 0.934971i \(-0.615426\pi\)
−0.354725 + 0.934971i \(0.615426\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 25.0000 0.0477057
\(66\) 0 0
\(67\) −492.000 −0.897125 −0.448562 − 0.893751i \(-0.648064\pi\)
−0.448562 + 0.893751i \(0.648064\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 32.0000 0.0534888 0.0267444 − 0.999642i \(-0.491486\pi\)
0.0267444 + 0.999642i \(0.491486\pi\)
\(72\) 0 0
\(73\) 970.000 1.55520 0.777602 − 0.628757i \(-0.216436\pi\)
0.777602 + 0.628757i \(0.216436\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −282.000 −0.417362
\(78\) 0 0
\(79\) 1257.00 1.79017 0.895086 − 0.445894i \(-0.147114\pi\)
0.895086 + 0.445894i \(0.147114\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −102.000 −0.134891 −0.0674455 − 0.997723i \(-0.521485\pi\)
−0.0674455 + 0.997723i \(0.521485\pi\)
\(84\) 0 0
\(85\) −655.000 −0.835820
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1488.00 1.77222 0.886111 − 0.463474i \(-0.153397\pi\)
0.886111 + 0.463474i \(0.153397\pi\)
\(90\) 0 0
\(91\) −30.0000 −0.0345588
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −280.000 −0.302394
\(96\) 0 0
\(97\) 974.000 1.01953 0.509767 − 0.860313i \(-0.329732\pi\)
0.509767 + 0.860313i \(0.329732\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1335.00 1.31522 0.657611 − 0.753357i \(-0.271567\pi\)
0.657611 + 0.753357i \(0.271567\pi\)
\(102\) 0 0
\(103\) −686.000 −0.656248 −0.328124 − 0.944635i \(-0.606416\pi\)
−0.328124 + 0.944635i \(0.606416\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1098.00 −0.992034 −0.496017 − 0.868313i \(-0.665205\pi\)
−0.496017 + 0.868313i \(0.665205\pi\)
\(108\) 0 0
\(109\) −700.000 −0.615118 −0.307559 − 0.951529i \(-0.599512\pi\)
−0.307559 + 0.951529i \(0.599512\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1055.00 0.878284 0.439142 − 0.898418i \(-0.355283\pi\)
0.439142 + 0.898418i \(0.355283\pi\)
\(114\) 0 0
\(115\) −15.0000 −0.0121631
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 786.000 0.605483
\(120\) 0 0
\(121\) 878.000 0.659654
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1646.00 1.15007 0.575035 − 0.818129i \(-0.304988\pi\)
0.575035 + 0.818129i \(0.304988\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1833.00 −1.22252 −0.611259 − 0.791430i \(-0.709337\pi\)
−0.611259 + 0.791430i \(0.709337\pi\)
\(132\) 0 0
\(133\) 336.000 0.219059
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1098.00 −0.684733 −0.342367 − 0.939566i \(-0.611229\pi\)
−0.342367 + 0.939566i \(0.611229\pi\)
\(138\) 0 0
\(139\) 1042.00 0.635837 0.317918 − 0.948118i \(-0.397016\pi\)
0.317918 + 0.948118i \(0.397016\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 235.000 0.137424
\(144\) 0 0
\(145\) −785.000 −0.449591
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2941.00 1.61702 0.808510 − 0.588482i \(-0.200274\pi\)
0.808510 + 0.588482i \(0.200274\pi\)
\(150\) 0 0
\(151\) −511.000 −0.275395 −0.137697 − 0.990474i \(-0.543970\pi\)
−0.137697 + 0.990474i \(0.543970\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1125.00 0.582982
\(156\) 0 0
\(157\) −571.000 −0.290260 −0.145130 − 0.989413i \(-0.546360\pi\)
−0.145130 + 0.989413i \(0.546360\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 18.0000 0.00881117
\(162\) 0 0
\(163\) −713.000 −0.342616 −0.171308 − 0.985217i \(-0.554799\pi\)
−0.171308 + 0.985217i \(0.554799\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1596.00 0.739534 0.369767 − 0.929125i \(-0.379437\pi\)
0.369767 + 0.929125i \(0.379437\pi\)
\(168\) 0 0
\(169\) −2172.00 −0.988621
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4134.00 −1.81678 −0.908388 − 0.418129i \(-0.862686\pi\)
−0.908388 + 0.418129i \(0.862686\pi\)
\(174\) 0 0
\(175\) 150.000 0.0647939
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1828.00 0.763302 0.381651 − 0.924306i \(-0.375356\pi\)
0.381651 + 0.924306i \(0.375356\pi\)
\(180\) 0 0
\(181\) −520.000 −0.213543 −0.106772 − 0.994284i \(-0.534051\pi\)
−0.106772 + 0.994284i \(0.534051\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 350.000 0.139095
\(186\) 0 0
\(187\) −6157.00 −2.40772
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4826.00 1.82826 0.914129 − 0.405424i \(-0.132876\pi\)
0.914129 + 0.405424i \(0.132876\pi\)
\(192\) 0 0
\(193\) 1670.00 0.622846 0.311423 − 0.950271i \(-0.399194\pi\)
0.311423 + 0.950271i \(0.399194\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1380.00 0.499091 0.249546 − 0.968363i \(-0.419719\pi\)
0.249546 + 0.968363i \(0.419719\pi\)
\(198\) 0 0
\(199\) −4357.00 −1.55206 −0.776029 − 0.630697i \(-0.782769\pi\)
−0.776029 + 0.630697i \(0.782769\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 942.000 0.325692
\(204\) 0 0
\(205\) 700.000 0.238488
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2632.00 −0.871097
\(210\) 0 0
\(211\) 4162.00 1.35793 0.678967 − 0.734169i \(-0.262428\pi\)
0.678967 + 0.734169i \(0.262428\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1985.00 0.629655
\(216\) 0 0
\(217\) −1350.00 −0.422322
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −655.000 −0.199367
\(222\) 0 0
\(223\) 5956.00 1.78853 0.894267 − 0.447533i \(-0.147697\pi\)
0.894267 + 0.447533i \(0.147697\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4940.00 1.44440 0.722201 − 0.691683i \(-0.243130\pi\)
0.722201 + 0.691683i \(0.243130\pi\)
\(228\) 0 0
\(229\) 4344.00 1.25354 0.626768 − 0.779206i \(-0.284378\pi\)
0.626768 + 0.779206i \(0.284378\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5202.00 1.46264 0.731318 − 0.682036i \(-0.238905\pi\)
0.731318 + 0.682036i \(0.238905\pi\)
\(234\) 0 0
\(235\) 1735.00 0.481612
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1546.00 0.418420 0.209210 − 0.977871i \(-0.432911\pi\)
0.209210 + 0.977871i \(0.432911\pi\)
\(240\) 0 0
\(241\) −3659.00 −0.977995 −0.488998 − 0.872285i \(-0.662637\pi\)
−0.488998 + 0.872285i \(0.662637\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1535.00 0.400276
\(246\) 0 0
\(247\) −280.000 −0.0721294
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1221.00 0.307047 0.153524 − 0.988145i \(-0.450938\pi\)
0.153524 + 0.988145i \(0.450938\pi\)
\(252\) 0 0
\(253\) −141.000 −0.0350379
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6255.00 1.51820 0.759098 − 0.650977i \(-0.225640\pi\)
0.759098 + 0.650977i \(0.225640\pi\)
\(258\) 0 0
\(259\) −420.000 −0.100763
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 836.000 0.196007 0.0980037 − 0.995186i \(-0.468754\pi\)
0.0980037 + 0.995186i \(0.468754\pi\)
\(264\) 0 0
\(265\) 20.0000 0.00463619
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2231.00 0.505675 0.252837 − 0.967509i \(-0.418636\pi\)
0.252837 + 0.967509i \(0.418636\pi\)
\(270\) 0 0
\(271\) 4832.00 1.08311 0.541556 − 0.840665i \(-0.317836\pi\)
0.541556 + 0.840665i \(0.317836\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1175.00 −0.257655
\(276\) 0 0
\(277\) 6450.00 1.39907 0.699536 − 0.714597i \(-0.253390\pi\)
0.699536 + 0.714597i \(0.253390\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1050.00 0.222910 0.111455 − 0.993769i \(-0.464449\pi\)
0.111455 + 0.993769i \(0.464449\pi\)
\(282\) 0 0
\(283\) 1584.00 0.332717 0.166359 − 0.986065i \(-0.446799\pi\)
0.166359 + 0.986065i \(0.446799\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −840.000 −0.172765
\(288\) 0 0
\(289\) 12248.0 2.49298
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6594.00 −1.31476 −0.657382 − 0.753558i \(-0.728336\pi\)
−0.657382 + 0.753558i \(0.728336\pi\)
\(294\) 0 0
\(295\) −3740.00 −0.738140
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −15.0000 −0.00290125
\(300\) 0 0
\(301\) −2382.00 −0.456134
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1690.00 0.317276
\(306\) 0 0
\(307\) 4343.00 0.807388 0.403694 − 0.914894i \(-0.367726\pi\)
0.403694 + 0.914894i \(0.367726\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2124.00 −0.387270 −0.193635 − 0.981074i \(-0.562028\pi\)
−0.193635 + 0.981074i \(0.562028\pi\)
\(312\) 0 0
\(313\) −7516.00 −1.35728 −0.678641 − 0.734470i \(-0.737431\pi\)
−0.678641 + 0.734470i \(0.737431\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6880.00 1.21899 0.609494 − 0.792791i \(-0.291373\pi\)
0.609494 + 0.792791i \(0.291373\pi\)
\(318\) 0 0
\(319\) −7379.00 −1.29512
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 7336.00 1.26373
\(324\) 0 0
\(325\) −125.000 −0.0213346
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2082.00 −0.348889
\(330\) 0 0
\(331\) 4986.00 0.827962 0.413981 − 0.910286i \(-0.364138\pi\)
0.413981 + 0.910286i \(0.364138\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2460.00 0.401206
\(336\) 0 0
\(337\) 904.000 0.146125 0.0730623 − 0.997327i \(-0.476723\pi\)
0.0730623 + 0.997327i \(0.476723\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 10575.0 1.67938
\(342\) 0 0
\(343\) −3900.00 −0.613936
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 8860.00 1.37069 0.685345 − 0.728218i \(-0.259651\pi\)
0.685345 + 0.728218i \(0.259651\pi\)
\(348\) 0 0
\(349\) −4454.00 −0.683144 −0.341572 − 0.939856i \(-0.610959\pi\)
−0.341572 + 0.939856i \(0.610959\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8781.00 1.32398 0.661991 − 0.749512i \(-0.269712\pi\)
0.661991 + 0.749512i \(0.269712\pi\)
\(354\) 0 0
\(355\) −160.000 −0.0239209
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2928.00 0.430457 0.215228 − 0.976564i \(-0.430950\pi\)
0.215228 + 0.976564i \(0.430950\pi\)
\(360\) 0 0
\(361\) −3723.00 −0.542790
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4850.00 −0.695508
\(366\) 0 0
\(367\) −9102.00 −1.29461 −0.647303 − 0.762233i \(-0.724103\pi\)
−0.647303 + 0.762233i \(0.724103\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −24.0000 −0.00335854
\(372\) 0 0
\(373\) −8183.00 −1.13592 −0.567962 − 0.823055i \(-0.692268\pi\)
−0.567962 + 0.823055i \(0.692268\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −785.000 −0.107240
\(378\) 0 0
\(379\) −6136.00 −0.831623 −0.415812 − 0.909451i \(-0.636502\pi\)
−0.415812 + 0.909451i \(0.636502\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5643.00 0.752856 0.376428 − 0.926446i \(-0.377152\pi\)
0.376428 + 0.926446i \(0.377152\pi\)
\(384\) 0 0
\(385\) 1410.00 0.186650
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8991.00 −1.17188 −0.585941 − 0.810354i \(-0.699275\pi\)
−0.585941 + 0.810354i \(0.699275\pi\)
\(390\) 0 0
\(391\) 393.000 0.0508309
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6285.00 −0.800589
\(396\) 0 0
\(397\) −12449.0 −1.57380 −0.786898 − 0.617082i \(-0.788314\pi\)
−0.786898 + 0.617082i \(0.788314\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −8076.00 −1.00573 −0.502863 − 0.864366i \(-0.667720\pi\)
−0.502863 + 0.864366i \(0.667720\pi\)
\(402\) 0 0
\(403\) 1125.00 0.139058
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3290.00 0.400686
\(408\) 0 0
\(409\) −2833.00 −0.342501 −0.171250 − 0.985228i \(-0.554781\pi\)
−0.171250 + 0.985228i \(0.554781\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4488.00 0.534722
\(414\) 0 0
\(415\) 510.000 0.0603251
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4777.00 −0.556973 −0.278487 − 0.960440i \(-0.589833\pi\)
−0.278487 + 0.960440i \(0.589833\pi\)
\(420\) 0 0
\(421\) −6464.00 −0.748304 −0.374152 − 0.927367i \(-0.622066\pi\)
−0.374152 + 0.927367i \(0.622066\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3275.00 0.373790
\(426\) 0 0
\(427\) −2028.00 −0.229840
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10680.0 1.19359 0.596795 − 0.802394i \(-0.296440\pi\)
0.596795 + 0.802394i \(0.296440\pi\)
\(432\) 0 0
\(433\) 11566.0 1.28366 0.641832 − 0.766845i \(-0.278175\pi\)
0.641832 + 0.766845i \(0.278175\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 168.000 0.0183902
\(438\) 0 0
\(439\) 1448.00 0.157424 0.0787122 − 0.996897i \(-0.474919\pi\)
0.0787122 + 0.996897i \(0.474919\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2376.00 −0.254824 −0.127412 − 0.991850i \(-0.540667\pi\)
−0.127412 + 0.991850i \(0.540667\pi\)
\(444\) 0 0
\(445\) −7440.00 −0.792561
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14894.0 1.56546 0.782730 − 0.622362i \(-0.213827\pi\)
0.782730 + 0.622362i \(0.213827\pi\)
\(450\) 0 0
\(451\) 6580.00 0.687007
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 150.000 0.0154552
\(456\) 0 0
\(457\) 16204.0 1.65862 0.829312 − 0.558786i \(-0.188733\pi\)
0.829312 + 0.558786i \(0.188733\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5082.00 0.513432 0.256716 − 0.966487i \(-0.417359\pi\)
0.256716 + 0.966487i \(0.417359\pi\)
\(462\) 0 0
\(463\) 10326.0 1.03648 0.518240 − 0.855235i \(-0.326588\pi\)
0.518240 + 0.855235i \(0.326588\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4184.00 0.414588 0.207294 − 0.978279i \(-0.433534\pi\)
0.207294 + 0.978279i \(0.433534\pi\)
\(468\) 0 0
\(469\) −2952.00 −0.290641
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 18659.0 1.81383
\(474\) 0 0
\(475\) 1400.00 0.135235
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −15576.0 −1.48577 −0.742887 − 0.669417i \(-0.766544\pi\)
−0.742887 + 0.669417i \(0.766544\pi\)
\(480\) 0 0
\(481\) 350.000 0.0331780
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4870.00 −0.455949
\(486\) 0 0
\(487\) −10220.0 −0.950949 −0.475475 − 0.879729i \(-0.657724\pi\)
−0.475475 + 0.879729i \(0.657724\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2692.00 −0.247430 −0.123715 − 0.992318i \(-0.539481\pi\)
−0.123715 + 0.992318i \(0.539481\pi\)
\(492\) 0 0
\(493\) 20567.0 1.87889
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 192.000 0.0173287
\(498\) 0 0
\(499\) −5764.00 −0.517098 −0.258549 − 0.965998i \(-0.583244\pi\)
−0.258549 + 0.965998i \(0.583244\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2437.00 −0.216025 −0.108012 − 0.994150i \(-0.534449\pi\)
−0.108012 + 0.994150i \(0.534449\pi\)
\(504\) 0 0
\(505\) −6675.00 −0.588185
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5849.00 0.509337 0.254668 − 0.967028i \(-0.418034\pi\)
0.254668 + 0.967028i \(0.418034\pi\)
\(510\) 0 0
\(511\) 5820.00 0.503839
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3430.00 0.293483
\(516\) 0 0
\(517\) 16309.0 1.38737
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17032.0 1.43222 0.716109 − 0.697989i \(-0.245921\pi\)
0.716109 + 0.697989i \(0.245921\pi\)
\(522\) 0 0
\(523\) −4147.00 −0.346722 −0.173361 − 0.984858i \(-0.555463\pi\)
−0.173361 + 0.984858i \(0.555463\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −29475.0 −2.43634
\(528\) 0 0
\(529\) −12158.0 −0.999260
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 700.000 0.0568862
\(534\) 0 0
\(535\) 5490.00 0.443651
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 14429.0 1.15306
\(540\) 0 0
\(541\) −3942.00 −0.313271 −0.156636 − 0.987656i \(-0.550065\pi\)
−0.156636 + 0.987656i \(0.550065\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3500.00 0.275089
\(546\) 0 0
\(547\) 13751.0 1.07486 0.537432 − 0.843307i \(-0.319395\pi\)
0.537432 + 0.843307i \(0.319395\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 8792.00 0.679767
\(552\) 0 0
\(553\) 7542.00 0.579961
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7944.00 −0.604305 −0.302153 − 0.953260i \(-0.597705\pi\)
−0.302153 + 0.953260i \(0.597705\pi\)
\(558\) 0 0
\(559\) 1985.00 0.150191
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6702.00 −0.501697 −0.250849 − 0.968026i \(-0.580710\pi\)
−0.250849 + 0.968026i \(0.580710\pi\)
\(564\) 0 0
\(565\) −5275.00 −0.392780
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2760.00 0.203348 0.101674 − 0.994818i \(-0.467580\pi\)
0.101674 + 0.994818i \(0.467580\pi\)
\(570\) 0 0
\(571\) −8930.00 −0.654481 −0.327241 − 0.944941i \(-0.606119\pi\)
−0.327241 + 0.944941i \(0.606119\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 75.0000 0.00543951
\(576\) 0 0
\(577\) 6944.00 0.501010 0.250505 − 0.968115i \(-0.419403\pi\)
0.250505 + 0.968115i \(0.419403\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −612.000 −0.0437006
\(582\) 0 0
\(583\) 188.000 0.0133553
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −4206.00 −0.295741 −0.147871 − 0.989007i \(-0.547242\pi\)
−0.147871 + 0.989007i \(0.547242\pi\)
\(588\) 0 0
\(589\) −12600.0 −0.881450
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 6571.00 0.455040 0.227520 − 0.973773i \(-0.426938\pi\)
0.227520 + 0.973773i \(0.426938\pi\)
\(594\) 0 0
\(595\) −3930.00 −0.270780
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9490.00 −0.647330 −0.323665 − 0.946172i \(-0.604915\pi\)
−0.323665 + 0.946172i \(0.604915\pi\)
\(600\) 0 0
\(601\) 11861.0 0.805025 0.402513 − 0.915414i \(-0.368137\pi\)
0.402513 + 0.915414i \(0.368137\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4390.00 −0.295006
\(606\) 0 0
\(607\) 518.000 0.0346375 0.0173188 − 0.999850i \(-0.494487\pi\)
0.0173188 + 0.999850i \(0.494487\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1735.00 0.114878
\(612\) 0 0
\(613\) 15163.0 0.999067 0.499533 − 0.866295i \(-0.333505\pi\)
0.499533 + 0.866295i \(0.333505\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −19011.0 −1.24044 −0.620222 − 0.784426i \(-0.712958\pi\)
−0.620222 + 0.784426i \(0.712958\pi\)
\(618\) 0 0
\(619\) 7906.00 0.513359 0.256679 − 0.966497i \(-0.417372\pi\)
0.256679 + 0.966497i \(0.417372\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8928.00 0.574146
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −9170.00 −0.581291
\(630\) 0 0
\(631\) 3416.00 0.215513 0.107757 − 0.994177i \(-0.465633\pi\)
0.107757 + 0.994177i \(0.465633\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8230.00 −0.514327
\(636\) 0 0
\(637\) 1535.00 0.0954771
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −4830.00 −0.297619 −0.148809 − 0.988866i \(-0.547544\pi\)
−0.148809 + 0.988866i \(0.547544\pi\)
\(642\) 0 0
\(643\) −12549.0 −0.769649 −0.384824 − 0.922990i \(-0.625738\pi\)
−0.384824 + 0.922990i \(0.625738\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8164.00 0.496074 0.248037 − 0.968751i \(-0.420215\pi\)
0.248037 + 0.968751i \(0.420215\pi\)
\(648\) 0 0
\(649\) −35156.0 −2.12634
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −23768.0 −1.42437 −0.712185 − 0.701992i \(-0.752294\pi\)
−0.712185 + 0.701992i \(0.752294\pi\)
\(654\) 0 0
\(655\) 9165.00 0.546727
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 21472.0 1.26924 0.634621 − 0.772824i \(-0.281156\pi\)
0.634621 + 0.772824i \(0.281156\pi\)
\(660\) 0 0
\(661\) 12982.0 0.763905 0.381953 − 0.924182i \(-0.375252\pi\)
0.381953 + 0.924182i \(0.375252\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1680.00 −0.0979663
\(666\) 0 0
\(667\) 471.000 0.0273421
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15886.0 0.913968
\(672\) 0 0
\(673\) −6006.00 −0.344003 −0.172002 − 0.985097i \(-0.555023\pi\)
−0.172002 + 0.985097i \(0.555023\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1164.00 −0.0660800 −0.0330400 − 0.999454i \(-0.510519\pi\)
−0.0330400 + 0.999454i \(0.510519\pi\)
\(678\) 0 0
\(679\) 5844.00 0.330298
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 26496.0 1.48439 0.742197 − 0.670182i \(-0.233784\pi\)
0.742197 + 0.670182i \(0.233784\pi\)
\(684\) 0 0
\(685\) 5490.00 0.306222
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 20.0000 0.00110586
\(690\) 0 0
\(691\) −17110.0 −0.941961 −0.470981 − 0.882144i \(-0.656100\pi\)
−0.470981 + 0.882144i \(0.656100\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −5210.00 −0.284355
\(696\) 0 0
\(697\) −18340.0 −0.996667
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −30251.0 −1.62991 −0.814953 − 0.579527i \(-0.803237\pi\)
−0.814953 + 0.579527i \(0.803237\pi\)
\(702\) 0 0
\(703\) −3920.00 −0.210307
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8010.00 0.426092
\(708\) 0 0
\(709\) 18820.0 0.996897 0.498448 − 0.866919i \(-0.333903\pi\)
0.498448 + 0.866919i \(0.333903\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −675.000 −0.0354543
\(714\) 0 0
\(715\) −1175.00 −0.0614581
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 31890.0 1.65410 0.827049 − 0.562130i \(-0.190018\pi\)
0.827049 + 0.562130i \(0.190018\pi\)
\(720\) 0 0
\(721\) −4116.00 −0.212605
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3925.00 0.201063
\(726\) 0 0
\(727\) 11452.0 0.584224 0.292112 − 0.956384i \(-0.405642\pi\)
0.292112 + 0.956384i \(0.405642\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −52007.0 −2.63139
\(732\) 0 0
\(733\) 7094.00 0.357466 0.178733 − 0.983898i \(-0.442800\pi\)
0.178733 + 0.983898i \(0.442800\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 23124.0 1.15574
\(738\) 0 0
\(739\) 3200.00 0.159288 0.0796440 − 0.996823i \(-0.474622\pi\)
0.0796440 + 0.996823i \(0.474622\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −20831.0 −1.02855 −0.514277 − 0.857624i \(-0.671940\pi\)
−0.514277 + 0.857624i \(0.671940\pi\)
\(744\) 0 0
\(745\) −14705.0 −0.723154
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6588.00 −0.321389
\(750\) 0 0
\(751\) 15605.0 0.758235 0.379118 − 0.925349i \(-0.376228\pi\)
0.379118 + 0.925349i \(0.376228\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2555.00 0.123160
\(756\) 0 0
\(757\) 21349.0 1.02502 0.512512 − 0.858680i \(-0.328715\pi\)
0.512512 + 0.858680i \(0.328715\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3702.00 −0.176343 −0.0881717 − 0.996105i \(-0.528102\pi\)
−0.0881717 + 0.996105i \(0.528102\pi\)
\(762\) 0 0
\(763\) −4200.00 −0.199279
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3740.00 −0.176067
\(768\) 0 0
\(769\) −1393.00 −0.0653223 −0.0326612 − 0.999466i \(-0.510398\pi\)
−0.0326612 + 0.999466i \(0.510398\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6906.00 0.321334 0.160667 − 0.987009i \(-0.448635\pi\)
0.160667 + 0.987009i \(0.448635\pi\)
\(774\) 0 0
\(775\) −5625.00 −0.260717
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7840.00 −0.360587
\(780\) 0 0
\(781\) −1504.00 −0.0689083
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2855.00 0.129808
\(786\) 0 0
\(787\) −30493.0 −1.38114 −0.690571 − 0.723265i \(-0.742641\pi\)
−0.690571 + 0.723265i \(0.742641\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 6330.00 0.284537
\(792\) 0 0
\(793\) 1690.00 0.0756793
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −33488.0 −1.48834 −0.744169 − 0.667991i \(-0.767154\pi\)
−0.744169 + 0.667991i \(0.767154\pi\)
\(798\) 0 0
\(799\) −45457.0 −2.01271
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −45590.0 −2.00353
\(804\) 0 0
\(805\) −90.0000 −0.00394048
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 15304.0 0.665093 0.332546 − 0.943087i \(-0.392092\pi\)
0.332546 + 0.943087i \(0.392092\pi\)
\(810\) 0 0
\(811\) 40122.0 1.73721 0.868603 − 0.495509i \(-0.165018\pi\)
0.868603 + 0.495509i \(0.165018\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 3565.00 0.153223
\(816\) 0 0
\(817\) −22232.0 −0.952019
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −25098.0 −1.06690 −0.533451 − 0.845831i \(-0.679105\pi\)
−0.533451 + 0.845831i \(0.679105\pi\)
\(822\) 0 0
\(823\) 43492.0 1.84208 0.921042 − 0.389462i \(-0.127339\pi\)
0.921042 + 0.389462i \(0.127339\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 11206.0 0.471186 0.235593 − 0.971852i \(-0.424297\pi\)
0.235593 + 0.971852i \(0.424297\pi\)
\(828\) 0 0
\(829\) −23964.0 −1.00399 −0.501993 − 0.864872i \(-0.667400\pi\)
−0.501993 + 0.864872i \(0.667400\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −40217.0 −1.67279
\(834\) 0 0
\(835\) −7980.00 −0.330730
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −34606.0 −1.42399 −0.711997 − 0.702182i \(-0.752209\pi\)
−0.711997 + 0.702182i \(0.752209\pi\)
\(840\) 0 0
\(841\) 260.000 0.0106605
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 10860.0 0.442125
\(846\) 0 0
\(847\) 5268.00 0.213708
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −210.000 −0.00845912
\(852\) 0 0
\(853\) −18477.0 −0.741665 −0.370833 − 0.928700i \(-0.620928\pi\)
−0.370833 + 0.928700i \(0.620928\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 41342.0 1.64786 0.823930 − 0.566692i \(-0.191777\pi\)
0.823930 + 0.566692i \(0.191777\pi\)
\(858\) 0 0
\(859\) −21898.0 −0.869791 −0.434895 − 0.900481i \(-0.643215\pi\)
−0.434895 + 0.900481i \(0.643215\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −18487.0 −0.729206 −0.364603 − 0.931163i \(-0.618795\pi\)
−0.364603 + 0.931163i \(0.618795\pi\)
\(864\) 0 0
\(865\) 20670.0 0.812487
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −59079.0 −2.30623
\(870\) 0 0
\(871\) 2460.00 0.0956991
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −750.000 −0.0289767
\(876\) 0 0
\(877\) 7593.00 0.292357 0.146179 − 0.989258i \(-0.453303\pi\)
0.146179 + 0.989258i \(0.453303\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 3038.00 0.116178 0.0580890 − 0.998311i \(-0.481499\pi\)
0.0580890 + 0.998311i \(0.481499\pi\)
\(882\) 0 0
\(883\) 16732.0 0.637686 0.318843 − 0.947808i \(-0.396706\pi\)
0.318843 + 0.947808i \(0.396706\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −8031.00 −0.304007 −0.152004 − 0.988380i \(-0.548573\pi\)
−0.152004 + 0.988380i \(0.548573\pi\)
\(888\) 0 0
\(889\) 9876.00 0.372588
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −19432.0 −0.728183
\(894\) 0 0
\(895\) −9140.00 −0.341359
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −35325.0 −1.31052
\(900\) 0 0
\(901\) −524.000 −0.0193751
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2600.00 0.0954994
\(906\) 0 0
\(907\) 38487.0 1.40897 0.704487 − 0.709717i \(-0.251177\pi\)
0.704487 + 0.709717i \(0.251177\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −5120.00 −0.186205 −0.0931027 − 0.995657i \(-0.529679\pi\)
−0.0931027 + 0.995657i \(0.529679\pi\)
\(912\) 0 0
\(913\) 4794.00 0.173777
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −10998.0 −0.396059
\(918\) 0 0
\(919\) −28075.0 −1.00774 −0.503868 − 0.863781i \(-0.668090\pi\)
−0.503868 + 0.863781i \(0.668090\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −160.000 −0.00570581
\(924\) 0 0
\(925\) −1750.00 −0.0622050
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 12856.0 0.454028 0.227014 − 0.973892i \(-0.427104\pi\)
0.227014 + 0.973892i \(0.427104\pi\)
\(930\) 0 0
\(931\) −17192.0 −0.605204
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 30785.0 1.07677
\(936\) 0 0
\(937\) −1374.00 −0.0479046 −0.0239523 − 0.999713i \(-0.507625\pi\)
−0.0239523 + 0.999713i \(0.507625\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −8543.00 −0.295955 −0.147978 − 0.988991i \(-0.547276\pi\)
−0.147978 + 0.988991i \(0.547276\pi\)
\(942\) 0 0
\(943\) −420.000 −0.0145038
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 13506.0 0.463449 0.231724 − 0.972781i \(-0.425563\pi\)
0.231724 + 0.972781i \(0.425563\pi\)
\(948\) 0 0
\(949\) −4850.00 −0.165898
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −21775.0 −0.740148 −0.370074 − 0.929002i \(-0.620668\pi\)
−0.370074 + 0.929002i \(0.620668\pi\)
\(954\) 0 0
\(955\) −24130.0 −0.817621
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −6588.00 −0.221833
\(960\) 0 0
\(961\) 20834.0 0.699339
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −8350.00 −0.278545
\(966\) 0 0
\(967\) −3854.00 −0.128166 −0.0640829 − 0.997945i \(-0.520412\pi\)
−0.0640829 + 0.997945i \(0.520412\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 12933.0 0.427435 0.213718 − 0.976895i \(-0.431443\pi\)
0.213718 + 0.976895i \(0.431443\pi\)
\(972\) 0 0
\(973\) 6252.00 0.205992
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −17521.0 −0.573743 −0.286871 − 0.957969i \(-0.592615\pi\)
−0.286871 + 0.957969i \(0.592615\pi\)
\(978\) 0 0
\(979\) −69936.0 −2.28311
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −12573.0 −0.407952 −0.203976 − 0.978976i \(-0.565386\pi\)
−0.203976 + 0.978976i \(0.565386\pi\)
\(984\) 0 0
\(985\) −6900.00 −0.223200
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1191.00 −0.0382928
\(990\) 0 0
\(991\) −8945.00 −0.286728 −0.143364 − 0.989670i \(-0.545792\pi\)
−0.143364 + 0.989670i \(0.545792\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 21785.0 0.694101
\(996\) 0 0
\(997\) −58179.0 −1.84809 −0.924046 − 0.382282i \(-0.875138\pi\)
−0.924046 + 0.382282i \(0.875138\pi\)
\(998\) 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.f.1.1 1
3.2 odd 2 2160.4.a.p.1.1 1
4.3 odd 2 135.4.a.b.1.1 ✓ 1
12.11 even 2 135.4.a.c.1.1 yes 1
20.3 even 4 675.4.b.f.649.2 2
20.7 even 4 675.4.b.f.649.1 2
20.19 odd 2 675.4.a.h.1.1 1
36.7 odd 6 405.4.e.h.271.1 2
36.11 even 6 405.4.e.f.271.1 2
36.23 even 6 405.4.e.f.136.1 2
36.31 odd 6 405.4.e.h.136.1 2
60.23 odd 4 675.4.b.e.649.1 2
60.47 odd 4 675.4.b.e.649.2 2
60.59 even 2 675.4.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.4.a.b.1.1 ✓ 1 4.3 odd 2
135.4.a.c.1.1 yes 1 12.11 even 2
405.4.e.f.136.1 2 36.23 even 6
405.4.e.f.271.1 2 36.11 even 6
405.4.e.h.136.1 2 36.31 odd 6
405.4.e.h.271.1 2 36.7 odd 6
675.4.a.c.1.1 1 60.59 even 2
675.4.a.h.1.1 1 20.19 odd 2
675.4.b.e.649.1 2 60.23 odd 4
675.4.b.e.649.2 2 60.47 odd 4
675.4.b.f.649.1 2 20.7 even 4
675.4.b.f.649.2 2 20.3 even 4
2160.4.a.f.1.1 1 1.1 even 1 trivial
2160.4.a.p.1.1 1 3.2 odd 2