Properties

Label 2160.4.a.g.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 270)
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)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} +13.0000 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} +13.0000 q^{7} +30.0000 q^{11} -61.0000 q^{13} +12.0000 q^{17} +49.0000 q^{19} -18.0000 q^{23} +25.0000 q^{25} -186.000 q^{29} +160.000 q^{31} -65.0000 q^{35} -91.0000 q^{37} +378.000 q^{41} +268.000 q^{43} -144.000 q^{47} -174.000 q^{49} +570.000 q^{53} -150.000 q^{55} -204.000 q^{59} -877.000 q^{61} +305.000 q^{65} +187.000 q^{67} +606.000 q^{71} +431.000 q^{73} +390.000 q^{77} -1151.00 q^{79} -102.000 q^{83} -60.0000 q^{85} +984.000 q^{89} -793.000 q^{91} -245.000 q^{95} -265.000 q^{97} +O(q^{100})\)

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
\(7\) 13.0000 0.701934 0.350967 0.936388i \(-0.385853\pi\)
0.350967 + 0.936388i \(0.385853\pi\)
\(8\) 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
\(17\) 12.0000 0.171202 0.0856008 0.996330i \(-0.472719\pi\)
0.0856008 + 0.996330i \(0.472719\pi\)
\(18\) 0 0
\(19\) 49.0000 0.591651 0.295826 0.955242i \(-0.404405\pi\)
0.295826 + 0.955242i \(0.404405\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −18.0000 −0.163185 −0.0815926 0.996666i \(-0.526001\pi\)
−0.0815926 + 0.996666i \(0.526001\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −186.000 −1.19101 −0.595506 0.803351i \(-0.703048\pi\)
−0.595506 + 0.803351i \(0.703048\pi\)
\(30\) 0 0
\(31\) 160.000 0.926995 0.463498 0.886098i \(-0.346594\pi\)
0.463498 + 0.886098i \(0.346594\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −65.0000 −0.313914
\(36\) 0 0
\(37\) −91.0000 −0.404333 −0.202166 0.979351i \(-0.564798\pi\)
−0.202166 + 0.979351i \(0.564798\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 378.000 1.43985 0.719923 0.694054i \(-0.244177\pi\)
0.719923 + 0.694054i \(0.244177\pi\)
\(42\) 0 0
\(43\) 268.000 0.950456 0.475228 0.879863i \(-0.342366\pi\)
0.475228 + 0.879863i \(0.342366\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −144.000 −0.446906 −0.223453 0.974715i \(-0.571733\pi\)
−0.223453 + 0.974715i \(0.571733\pi\)
\(48\) 0 0
\(49\) −174.000 −0.507289
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 570.000 1.47727 0.738637 0.674103i \(-0.235470\pi\)
0.738637 + 0.674103i \(0.235470\pi\)
\(54\) 0 0
\(55\) −150.000 −0.367745
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −204.000 −0.450145 −0.225072 0.974342i \(-0.572262\pi\)
−0.225072 + 0.974342i \(0.572262\pi\)
\(60\) 0 0
\(61\) −877.000 −1.84079 −0.920396 0.390987i \(-0.872134\pi\)
−0.920396 + 0.390987i \(0.872134\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 305.000 0.582009
\(66\) 0 0
\(67\) 187.000 0.340980 0.170490 0.985359i \(-0.445465\pi\)
0.170490 + 0.985359i \(0.445465\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 606.000 1.01294 0.506472 0.862257i \(-0.330950\pi\)
0.506472 + 0.862257i \(0.330950\pi\)
\(72\) 0 0
\(73\) 431.000 0.691024 0.345512 0.938414i \(-0.387705\pi\)
0.345512 + 0.938414i \(0.387705\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 390.000 0.577203
\(78\) 0 0
\(79\) −1151.00 −1.63921 −0.819605 0.572929i \(-0.805807\pi\)
−0.819605 + 0.572929i \(0.805807\pi\)
\(80\) 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
\(85\) −60.0000 −0.0765637
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 984.000 1.17195 0.585976 0.810328i \(-0.300711\pi\)
0.585976 + 0.810328i \(0.300711\pi\)
\(90\) 0 0
\(91\) −793.000 −0.913505
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −245.000 −0.264594
\(96\) 0 0
\(97\) −265.000 −0.277388 −0.138694 0.990335i \(-0.544291\pi\)
−0.138694 + 0.990335i \(0.544291\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1248.00 −1.22951 −0.614756 0.788718i \(-0.710745\pi\)
−0.614756 + 0.788718i \(0.710745\pi\)
\(102\) 0 0
\(103\) 1225.00 1.17187 0.585936 0.810357i \(-0.300727\pi\)
0.585936 + 0.810357i \(0.300727\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 78.0000 0.0704724 0.0352362 0.999379i \(-0.488782\pi\)
0.0352362 + 0.999379i \(0.488782\pi\)
\(108\) 0 0
\(109\) 2198.00 1.93147 0.965735 0.259530i \(-0.0835678\pi\)
0.965735 + 0.259530i \(0.0835678\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1986.00 1.65334 0.826669 0.562689i \(-0.190233\pi\)
0.826669 + 0.562689i \(0.190233\pi\)
\(114\) 0 0
\(115\) 90.0000 0.0729786
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 156.000 0.120172
\(120\) 0 0
\(121\) −431.000 −0.323817
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −2792.00 −1.95079 −0.975393 0.220471i \(-0.929240\pi\)
−0.975393 + 0.220471i \(0.929240\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 708.000 0.472200 0.236100 0.971729i \(-0.424131\pi\)
0.236100 + 0.971729i \(0.424131\pi\)
\(132\) 0 0
\(133\) 637.000 0.415300
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1686.00 −1.05142 −0.525711 0.850663i \(-0.676201\pi\)
−0.525711 + 0.850663i \(0.676201\pi\)
\(138\) 0 0
\(139\) 307.000 0.187334 0.0936669 0.995604i \(-0.470141\pi\)
0.0936669 + 0.995604i \(0.470141\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1830.00 −1.07016
\(144\) 0 0
\(145\) 930.000 0.532637
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1812.00 −0.996274 −0.498137 0.867098i \(-0.665982\pi\)
−0.498137 + 0.867098i \(0.665982\pi\)
\(150\) 0 0
\(151\) −203.000 −0.109403 −0.0547017 0.998503i \(-0.517421\pi\)
−0.0547017 + 0.998503i \(0.517421\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −800.000 −0.414565
\(156\) 0 0
\(157\) −214.000 −0.108784 −0.0543919 0.998520i \(-0.517322\pi\)
−0.0543919 + 0.998520i \(0.517322\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −234.000 −0.114545
\(162\) 0 0
\(163\) 673.000 0.323395 0.161698 0.986840i \(-0.448303\pi\)
0.161698 + 0.986840i \(0.448303\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3696.00 1.71261 0.856303 0.516474i \(-0.172756\pi\)
0.856303 + 0.516474i \(0.172756\pi\)
\(168\) 0 0
\(169\) 1524.00 0.693673
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3132.00 1.37643 0.688213 0.725509i \(-0.258396\pi\)
0.688213 + 0.725509i \(0.258396\pi\)
\(174\) 0 0
\(175\) 325.000 0.140387
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −510.000 −0.212956 −0.106478 0.994315i \(-0.533957\pi\)
−0.106478 + 0.994315i \(0.533957\pi\)
\(180\) 0 0
\(181\) −1087.00 −0.446387 −0.223194 0.974774i \(-0.571648\pi\)
−0.223194 + 0.974774i \(0.571648\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 455.000 0.180823
\(186\) 0 0
\(187\) 360.000 0.140780
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4056.00 1.53655 0.768277 0.640117i \(-0.221114\pi\)
0.768277 + 0.640117i \(0.221114\pi\)
\(192\) 0 0
\(193\) 473.000 0.176411 0.0882054 0.996102i \(-0.471887\pi\)
0.0882054 + 0.996102i \(0.471887\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2556.00 0.924403 0.462202 0.886775i \(-0.347060\pi\)
0.462202 + 0.886775i \(0.347060\pi\)
\(198\) 0 0
\(199\) 2923.00 1.04124 0.520618 0.853790i \(-0.325702\pi\)
0.520618 + 0.853790i \(0.325702\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2418.00 −0.836011
\(204\) 0 0
\(205\) −1890.00 −0.643919
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1470.00 0.486517
\(210\) 0 0
\(211\) 3175.00 1.03591 0.517953 0.855409i \(-0.326694\pi\)
0.517953 + 0.855409i \(0.326694\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1340.00 −0.425057
\(216\) 0 0
\(217\) 2080.00 0.650689
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −732.000 −0.222804
\(222\) 0 0
\(223\) 2176.00 0.653434 0.326717 0.945122i \(-0.394058\pi\)
0.326717 + 0.945122i \(0.394058\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3834.00 1.12102 0.560510 0.828148i \(-0.310605\pi\)
0.560510 + 0.828148i \(0.310605\pi\)
\(228\) 0 0
\(229\) −3202.00 −0.923992 −0.461996 0.886882i \(-0.652867\pi\)
−0.461996 + 0.886882i \(0.652867\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4152.00 1.16741 0.583705 0.811966i \(-0.301602\pi\)
0.583705 + 0.811966i \(0.301602\pi\)
\(234\) 0 0
\(235\) 720.000 0.199862
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5466.00 1.47936 0.739678 0.672961i \(-0.234978\pi\)
0.739678 + 0.672961i \(0.234978\pi\)
\(240\) 0 0
\(241\) −943.000 −0.252050 −0.126025 0.992027i \(-0.540222\pi\)
−0.126025 + 0.992027i \(0.540222\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 870.000 0.226866
\(246\) 0 0
\(247\) −2989.00 −0.769982
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 7290.00 1.83323 0.916615 0.399771i \(-0.130910\pi\)
0.916615 + 0.399771i \(0.130910\pi\)
\(252\) 0 0
\(253\) −540.000 −0.134188
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 312.000 0.0757277 0.0378639 0.999283i \(-0.487945\pi\)
0.0378639 + 0.999283i \(0.487945\pi\)
\(258\) 0 0
\(259\) −1183.00 −0.283815
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 8004.00 1.87661 0.938304 0.345812i \(-0.112397\pi\)
0.938304 + 0.345812i \(0.112397\pi\)
\(264\) 0 0
\(265\) −2850.00 −0.660657
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −324.000 −0.0734373 −0.0367186 0.999326i \(-0.511691\pi\)
−0.0367186 + 0.999326i \(0.511691\pi\)
\(270\) 0 0
\(271\) 7849.00 1.75938 0.879692 0.475545i \(-0.157749\pi\)
0.879692 + 0.475545i \(0.157749\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 750.000 0.164461
\(276\) 0 0
\(277\) −5758.00 −1.24897 −0.624485 0.781037i \(-0.714691\pi\)
−0.624485 + 0.781037i \(0.714691\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2688.00 −0.570650 −0.285325 0.958431i \(-0.592102\pi\)
−0.285325 + 0.958431i \(0.592102\pi\)
\(282\) 0 0
\(283\) −3260.00 −0.684759 −0.342380 0.939562i \(-0.611233\pi\)
−0.342380 + 0.939562i \(0.611233\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4914.00 1.01068
\(288\) 0 0
\(289\) −4769.00 −0.970690
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5922.00 1.18077 0.590387 0.807120i \(-0.298975\pi\)
0.590387 + 0.807120i \(0.298975\pi\)
\(294\) 0 0
\(295\) 1020.00 0.201311
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1098.00 0.212371
\(300\) 0 0
\(301\) 3484.00 0.667158
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4385.00 0.823227
\(306\) 0 0
\(307\) −3728.00 −0.693056 −0.346528 0.938040i \(-0.612639\pi\)
−0.346528 + 0.938040i \(0.612639\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 732.000 0.133466 0.0667330 0.997771i \(-0.478742\pi\)
0.0667330 + 0.997771i \(0.478742\pi\)
\(312\) 0 0
\(313\) 5357.00 0.967398 0.483699 0.875234i \(-0.339293\pi\)
0.483699 + 0.875234i \(0.339293\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4572.00 −0.810060 −0.405030 0.914303i \(-0.632739\pi\)
−0.405030 + 0.914303i \(0.632739\pi\)
\(318\) 0 0
\(319\) −5580.00 −0.979373
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 588.000 0.101292
\(324\) 0 0
\(325\) −1525.00 −0.260282
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1872.00 −0.313698
\(330\) 0 0
\(331\) −845.000 −0.140318 −0.0701592 0.997536i \(-0.522351\pi\)
−0.0701592 + 0.997536i \(0.522351\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −935.000 −0.152491
\(336\) 0 0
\(337\) 8723.00 1.41001 0.705003 0.709204i \(-0.250946\pi\)
0.705003 + 0.709204i \(0.250946\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4800.00 0.762271
\(342\) 0 0
\(343\) −6721.00 −1.05802
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −9018.00 −1.39513 −0.697567 0.716519i \(-0.745734\pi\)
−0.697567 + 0.716519i \(0.745734\pi\)
\(348\) 0 0
\(349\) 5759.00 0.883301 0.441651 0.897187i \(-0.354393\pi\)
0.441651 + 0.897187i \(0.354393\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5772.00 −0.870291 −0.435145 0.900360i \(-0.643303\pi\)
−0.435145 + 0.900360i \(0.643303\pi\)
\(354\) 0 0
\(355\) −3030.00 −0.453002
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2046.00 0.300790 0.150395 0.988626i \(-0.451945\pi\)
0.150395 + 0.988626i \(0.451945\pi\)
\(360\) 0 0
\(361\) −4458.00 −0.649949
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2155.00 −0.309035
\(366\) 0 0
\(367\) 1069.00 0.152047 0.0760236 0.997106i \(-0.475778\pi\)
0.0760236 + 0.997106i \(0.475778\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 7410.00 1.03695
\(372\) 0 0
\(373\) 7133.00 0.990168 0.495084 0.868845i \(-0.335137\pi\)
0.495084 + 0.868845i \(0.335137\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 11346.0 1.55000
\(378\) 0 0
\(379\) 8557.00 1.15975 0.579873 0.814707i \(-0.303102\pi\)
0.579873 + 0.814707i \(0.303102\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −14328.0 −1.91156 −0.955779 0.294086i \(-0.904985\pi\)
−0.955779 + 0.294086i \(0.904985\pi\)
\(384\) 0 0
\(385\) −1950.00 −0.258133
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 13500.0 1.75958 0.879791 0.475361i \(-0.157683\pi\)
0.879791 + 0.475361i \(0.157683\pi\)
\(390\) 0 0
\(391\) −216.000 −0.0279376
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 5755.00 0.733077
\(396\) 0 0
\(397\) 1334.00 0.168644 0.0843218 0.996439i \(-0.473128\pi\)
0.0843218 + 0.996439i \(0.473128\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3474.00 0.432627 0.216313 0.976324i \(-0.430597\pi\)
0.216313 + 0.976324i \(0.430597\pi\)
\(402\) 0 0
\(403\) −9760.00 −1.20640
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2730.00 −0.332484
\(408\) 0 0
\(409\) 569.000 0.0687903 0.0343952 0.999408i \(-0.489050\pi\)
0.0343952 + 0.999408i \(0.489050\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2652.00 −0.315972
\(414\) 0 0
\(415\) 510.000 0.0603251
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9132.00 1.06474 0.532372 0.846511i \(-0.321301\pi\)
0.532372 + 0.846511i \(0.321301\pi\)
\(420\) 0 0
\(421\) −2971.00 −0.343937 −0.171969 0.985102i \(-0.555013\pi\)
−0.171969 + 0.985102i \(0.555013\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 300.000 0.0342403
\(426\) 0 0
\(427\) −11401.0 −1.29211
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12042.0 −1.34581 −0.672903 0.739730i \(-0.734953\pi\)
−0.672903 + 0.739730i \(0.734953\pi\)
\(432\) 0 0
\(433\) −8566.00 −0.950706 −0.475353 0.879795i \(-0.657680\pi\)
−0.475353 + 0.879795i \(0.657680\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −882.000 −0.0965487
\(438\) 0 0
\(439\) −7400.00 −0.804516 −0.402258 0.915526i \(-0.631775\pi\)
−0.402258 + 0.915526i \(0.631775\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2580.00 0.276703 0.138352 0.990383i \(-0.455820\pi\)
0.138352 + 0.990383i \(0.455820\pi\)
\(444\) 0 0
\(445\) −4920.00 −0.524113
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 13200.0 1.38741 0.693704 0.720260i \(-0.255977\pi\)
0.693704 + 0.720260i \(0.255977\pi\)
\(450\) 0 0
\(451\) 11340.0 1.18399
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3965.00 0.408532
\(456\) 0 0
\(457\) 18038.0 1.84635 0.923175 0.384380i \(-0.125585\pi\)
0.923175 + 0.384380i \(0.125585\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5544.00 0.560108 0.280054 0.959984i \(-0.409648\pi\)
0.280054 + 0.959984i \(0.409648\pi\)
\(462\) 0 0
\(463\) 17137.0 1.72014 0.860069 0.510178i \(-0.170420\pi\)
0.860069 + 0.510178i \(0.170420\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15888.0 1.57432 0.787162 0.616747i \(-0.211550\pi\)
0.787162 + 0.616747i \(0.211550\pi\)
\(468\) 0 0
\(469\) 2431.00 0.239346
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8040.00 0.781564
\(474\) 0 0
\(475\) 1225.00 0.118330
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3942.00 −0.376022 −0.188011 0.982167i \(-0.560204\pi\)
−0.188011 + 0.982167i \(0.560204\pi\)
\(480\) 0 0
\(481\) 5551.00 0.526203
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1325.00 0.124052
\(486\) 0 0
\(487\) −1379.00 −0.128313 −0.0641565 0.997940i \(-0.520436\pi\)
−0.0641565 + 0.997940i \(0.520436\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −14214.0 −1.30645 −0.653227 0.757162i \(-0.726585\pi\)
−0.653227 + 0.757162i \(0.726585\pi\)
\(492\) 0 0
\(493\) −2232.00 −0.203903
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7878.00 0.711019
\(498\) 0 0
\(499\) −9992.00 −0.896400 −0.448200 0.893933i \(-0.647935\pi\)
−0.448200 + 0.893933i \(0.647935\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 21258.0 1.88439 0.942194 0.335067i \(-0.108759\pi\)
0.942194 + 0.335067i \(0.108759\pi\)
\(504\) 0 0
\(505\) 6240.00 0.549854
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16614.0 −1.44676 −0.723382 0.690448i \(-0.757413\pi\)
−0.723382 + 0.690448i \(0.757413\pi\)
\(510\) 0 0
\(511\) 5603.00 0.485053
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6125.00 −0.524077
\(516\) 0 0
\(517\) −4320.00 −0.367492
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 11838.0 0.995455 0.497728 0.867333i \(-0.334168\pi\)
0.497728 + 0.867333i \(0.334168\pi\)
\(522\) 0 0
\(523\) −2201.00 −0.184021 −0.0920105 0.995758i \(-0.529329\pi\)
−0.0920105 + 0.995758i \(0.529329\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1920.00 0.158703
\(528\) 0 0
\(529\) −11843.0 −0.973371
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −23058.0 −1.87383
\(534\) 0 0
\(535\) −390.000 −0.0315162
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5220.00 −0.417145
\(540\) 0 0
\(541\) −10795.0 −0.857880 −0.428940 0.903333i \(-0.641113\pi\)
−0.428940 + 0.903333i \(0.641113\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −10990.0 −0.863780
\(546\) 0 0
\(547\) 14185.0 1.10879 0.554394 0.832254i \(-0.312950\pi\)
0.554394 + 0.832254i \(0.312950\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9114.00 −0.704663
\(552\) 0 0
\(553\) −14963.0 −1.15062
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3576.00 −0.272029 −0.136014 0.990707i \(-0.543429\pi\)
−0.136014 + 0.990707i \(0.543429\pi\)
\(558\) 0 0
\(559\) −16348.0 −1.23694
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9132.00 0.683602 0.341801 0.939772i \(-0.388963\pi\)
0.341801 + 0.939772i \(0.388963\pi\)
\(564\) 0 0
\(565\) −9930.00 −0.739395
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 25020.0 1.84340 0.921699 0.387907i \(-0.126802\pi\)
0.921699 + 0.387907i \(0.126802\pi\)
\(570\) 0 0
\(571\) 15997.0 1.17242 0.586212 0.810158i \(-0.300619\pi\)
0.586212 + 0.810158i \(0.300619\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −450.000 −0.0326370
\(576\) 0 0
\(577\) −5971.00 −0.430808 −0.215404 0.976525i \(-0.569107\pi\)
−0.215404 + 0.976525i \(0.569107\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1326.00 −0.0946846
\(582\) 0 0
\(583\) 17100.0 1.21477
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19242.0 −1.35299 −0.676493 0.736449i \(-0.736501\pi\)
−0.676493 + 0.736449i \(0.736501\pi\)
\(588\) 0 0
\(589\) 7840.00 0.548458
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8118.00 0.562169 0.281085 0.959683i \(-0.409306\pi\)
0.281085 + 0.959683i \(0.409306\pi\)
\(594\) 0 0
\(595\) −780.000 −0.0537427
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1902.00 −0.129739 −0.0648695 0.997894i \(-0.520663\pi\)
−0.0648695 + 0.997894i \(0.520663\pi\)
\(600\) 0 0
\(601\) −14074.0 −0.955225 −0.477613 0.878571i \(-0.658498\pi\)
−0.477613 + 0.878571i \(0.658498\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2155.00 0.144815
\(606\) 0 0
\(607\) 13825.0 0.924447 0.462224 0.886763i \(-0.347052\pi\)
0.462224 + 0.886763i \(0.347052\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8784.00 0.581608
\(612\) 0 0
\(613\) 15569.0 1.02582 0.512909 0.858443i \(-0.328568\pi\)
0.512909 + 0.858443i \(0.328568\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11922.0 0.777896 0.388948 0.921260i \(-0.372839\pi\)
0.388948 + 0.921260i \(0.372839\pi\)
\(618\) 0 0
\(619\) −6899.00 −0.447971 −0.223986 0.974592i \(-0.571907\pi\)
−0.223986 + 0.974592i \(0.571907\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12792.0 0.822633
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1092.00 −0.0692224
\(630\) 0 0
\(631\) −11711.0 −0.738839 −0.369420 0.929263i \(-0.620443\pi\)
−0.369420 + 0.929263i \(0.620443\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 13960.0 0.872418
\(636\) 0 0
\(637\) 10614.0 0.660192
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 9240.00 0.569357 0.284679 0.958623i \(-0.408113\pi\)
0.284679 + 0.958623i \(0.408113\pi\)
\(642\) 0 0
\(643\) 17908.0 1.09832 0.549162 0.835716i \(-0.314947\pi\)
0.549162 + 0.835716i \(0.314947\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7530.00 −0.457550 −0.228775 0.973479i \(-0.573472\pi\)
−0.228775 + 0.973479i \(0.573472\pi\)
\(648\) 0 0
\(649\) −6120.00 −0.370156
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −22788.0 −1.36564 −0.682820 0.730586i \(-0.739247\pi\)
−0.682820 + 0.730586i \(0.739247\pi\)
\(654\) 0 0
\(655\) −3540.00 −0.211174
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −16440.0 −0.971793 −0.485896 0.874016i \(-0.661507\pi\)
−0.485896 + 0.874016i \(0.661507\pi\)
\(660\) 0 0
\(661\) −12421.0 −0.730894 −0.365447 0.930832i \(-0.619084\pi\)
−0.365447 + 0.930832i \(0.619084\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3185.00 −0.185728
\(666\) 0 0
\(667\) 3348.00 0.194355
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −26310.0 −1.51369
\(672\) 0 0
\(673\) 6461.00 0.370064 0.185032 0.982732i \(-0.440761\pi\)
0.185032 + 0.982732i \(0.440761\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −912.000 −0.0517740 −0.0258870 0.999665i \(-0.508241\pi\)
−0.0258870 + 0.999665i \(0.508241\pi\)
\(678\) 0 0
\(679\) −3445.00 −0.194708
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 14442.0 0.809089 0.404544 0.914518i \(-0.367430\pi\)
0.404544 + 0.914518i \(0.367430\pi\)
\(684\) 0 0
\(685\) 8430.00 0.470210
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −34770.0 −1.92254
\(690\) 0 0
\(691\) −1892.00 −0.104161 −0.0520804 0.998643i \(-0.516585\pi\)
−0.0520804 + 0.998643i \(0.516585\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1535.00 −0.0837782
\(696\) 0 0
\(697\) 4536.00 0.246504
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −7914.00 −0.426402 −0.213201 0.977008i \(-0.568389\pi\)
−0.213201 + 0.977008i \(0.568389\pi\)
\(702\) 0 0
\(703\) −4459.00 −0.239224
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −16224.0 −0.863036
\(708\) 0 0
\(709\) −1291.00 −0.0683844 −0.0341922 0.999415i \(-0.510886\pi\)
−0.0341922 + 0.999415i \(0.510886\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2880.00 −0.151272
\(714\) 0 0
\(715\) 9150.00 0.478588
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 30210.0 1.56696 0.783479 0.621418i \(-0.213443\pi\)
0.783479 + 0.621418i \(0.213443\pi\)
\(720\) 0 0
\(721\) 15925.0 0.822577
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4650.00 −0.238202
\(726\) 0 0
\(727\) −15680.0 −0.799916 −0.399958 0.916533i \(-0.630975\pi\)
−0.399958 + 0.916533i \(0.630975\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3216.00 0.162720
\(732\) 0 0
\(733\) 13898.0 0.700320 0.350160 0.936690i \(-0.386127\pi\)
0.350160 + 0.936690i \(0.386127\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5610.00 0.280389
\(738\) 0 0
\(739\) −35300.0 −1.75715 −0.878573 0.477607i \(-0.841504\pi\)
−0.878573 + 0.477607i \(0.841504\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −28188.0 −1.39181 −0.695907 0.718132i \(-0.744997\pi\)
−0.695907 + 0.718132i \(0.744997\pi\)
\(744\) 0 0
\(745\) 9060.00 0.445547
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1014.00 0.0494670
\(750\) 0 0
\(751\) −25163.0 −1.22265 −0.611326 0.791379i \(-0.709363\pi\)
−0.611326 + 0.791379i \(0.709363\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1015.00 0.0489267
\(756\) 0 0
\(757\) 7979.00 0.383093 0.191547 0.981484i \(-0.438650\pi\)
0.191547 + 0.981484i \(0.438650\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 26622.0 1.26813 0.634065 0.773280i \(-0.281385\pi\)
0.634065 + 0.773280i \(0.281385\pi\)
\(762\) 0 0
\(763\) 28574.0 1.35576
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12444.0 0.585824
\(768\) 0 0
\(769\) −35413.0 −1.66063 −0.830316 0.557293i \(-0.811840\pi\)
−0.830316 + 0.557293i \(0.811840\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −33834.0 −1.57429 −0.787144 0.616769i \(-0.788441\pi\)
−0.787144 + 0.616769i \(0.788441\pi\)
\(774\) 0 0
\(775\) 4000.00 0.185399
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 18522.0 0.851886
\(780\) 0 0
\(781\) 18180.0 0.832947
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1070.00 0.0486496
\(786\) 0 0
\(787\) −13469.0 −0.610061 −0.305030 0.952343i \(-0.598667\pi\)
−0.305030 + 0.952343i \(0.598667\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 25818.0 1.16053
\(792\) 0 0
\(793\) 53497.0 2.39563
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −21168.0 −0.940789 −0.470395 0.882456i \(-0.655888\pi\)
−0.470395 + 0.882456i \(0.655888\pi\)
\(798\) 0 0
\(799\) −1728.00 −0.0765109
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 12930.0 0.568231
\(804\) 0 0
\(805\) 1170.00 0.0512262
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 408.000 0.0177312 0.00886558 0.999961i \(-0.497178\pi\)
0.00886558 + 0.999961i \(0.497178\pi\)
\(810\) 0 0
\(811\) 36916.0 1.59839 0.799196 0.601070i \(-0.205259\pi\)
0.799196 + 0.601070i \(0.205259\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −3365.00 −0.144627
\(816\) 0 0
\(817\) 13132.0 0.562338
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −24636.0 −1.04726 −0.523631 0.851945i \(-0.675423\pi\)
−0.523631 + 0.851945i \(0.675423\pi\)
\(822\) 0 0
\(823\) 18187.0 0.770303 0.385151 0.922853i \(-0.374149\pi\)
0.385151 + 0.922853i \(0.374149\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1464.00 −0.0615578 −0.0307789 0.999526i \(-0.509799\pi\)
−0.0307789 + 0.999526i \(0.509799\pi\)
\(828\) 0 0
\(829\) −12295.0 −0.515106 −0.257553 0.966264i \(-0.582916\pi\)
−0.257553 + 0.966264i \(0.582916\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2088.00 −0.0868486
\(834\) 0 0
\(835\) −18480.0 −0.765900
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −46884.0 −1.92922 −0.964610 0.263681i \(-0.915063\pi\)
−0.964610 + 0.263681i \(0.915063\pi\)
\(840\) 0 0
\(841\) 10207.0 0.418508
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −7620.00 −0.310220
\(846\) 0 0
\(847\) −5603.00 −0.227298
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1638.00 0.0659811
\(852\) 0 0
\(853\) 12197.0 0.489587 0.244793 0.969575i \(-0.421280\pi\)
0.244793 + 0.969575i \(0.421280\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −28182.0 −1.12331 −0.561656 0.827371i \(-0.689836\pi\)
−0.561656 + 0.827371i \(0.689836\pi\)
\(858\) 0 0
\(859\) −25433.0 −1.01020 −0.505101 0.863060i \(-0.668545\pi\)
−0.505101 + 0.863060i \(0.668545\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 16968.0 0.669290 0.334645 0.942344i \(-0.391384\pi\)
0.334645 + 0.942344i \(0.391384\pi\)
\(864\) 0 0
\(865\) −15660.0 −0.615556
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −34530.0 −1.34793
\(870\) 0 0
\(871\) −11407.0 −0.443756
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1625.00 −0.0627829
\(876\) 0 0
\(877\) −22423.0 −0.863365 −0.431682 0.902026i \(-0.642080\pi\)
−0.431682 + 0.902026i \(0.642080\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 8442.00 0.322836 0.161418 0.986886i \(-0.448393\pi\)
0.161418 + 0.986886i \(0.448393\pi\)
\(882\) 0 0
\(883\) −41207.0 −1.57047 −0.785236 0.619197i \(-0.787458\pi\)
−0.785236 + 0.619197i \(0.787458\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −8472.00 −0.320701 −0.160351 0.987060i \(-0.551262\pi\)
−0.160351 + 0.987060i \(0.551262\pi\)
\(888\) 0 0
\(889\) −36296.0 −1.36932
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −7056.00 −0.264412
\(894\) 0 0
\(895\) 2550.00 0.0952370
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −29760.0 −1.10406
\(900\) 0 0
\(901\) 6840.00 0.252912
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5435.00 0.199630
\(906\) 0 0
\(907\) 21799.0 0.798042 0.399021 0.916942i \(-0.369350\pi\)
0.399021 + 0.916942i \(0.369350\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −23544.0 −0.856254 −0.428127 0.903719i \(-0.640826\pi\)
−0.428127 + 0.903719i \(0.640826\pi\)
\(912\) 0 0
\(913\) −3060.00 −0.110921
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 9204.00 0.331453
\(918\) 0 0
\(919\) −11072.0 −0.397423 −0.198711 0.980058i \(-0.563676\pi\)
−0.198711 + 0.980058i \(0.563676\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −36966.0 −1.31826
\(924\) 0 0
\(925\) −2275.00 −0.0808665
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −21654.0 −0.764741 −0.382371 0.924009i \(-0.624892\pi\)
−0.382371 + 0.924009i \(0.624892\pi\)
\(930\) 0 0
\(931\) −8526.00 −0.300138
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1800.00 −0.0629586
\(936\) 0 0
\(937\) −42835.0 −1.49345 −0.746723 0.665135i \(-0.768374\pi\)
−0.746723 + 0.665135i \(0.768374\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −48534.0 −1.68136 −0.840682 0.541529i \(-0.817845\pi\)
−0.840682 + 0.541529i \(0.817845\pi\)
\(942\) 0 0
\(943\) −6804.00 −0.234962
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −14676.0 −0.503597 −0.251798 0.967780i \(-0.581022\pi\)
−0.251798 + 0.967780i \(0.581022\pi\)
\(948\) 0 0
\(949\) −26291.0 −0.899307
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 27372.0 0.930395 0.465197 0.885207i \(-0.345983\pi\)
0.465197 + 0.885207i \(0.345983\pi\)
\(954\) 0 0
\(955\) −20280.0 −0.687168
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −21918.0 −0.738028
\(960\) 0 0
\(961\) −4191.00 −0.140680
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −2365.00 −0.0788933
\(966\) 0 0
\(967\) −3581.00 −0.119087 −0.0595435 0.998226i \(-0.518965\pi\)
−0.0595435 + 0.998226i \(0.518965\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1824.00 0.0602832 0.0301416 0.999546i \(-0.490404\pi\)
0.0301416 + 0.999546i \(0.490404\pi\)
\(972\) 0 0
\(973\) 3991.00 0.131496
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −29778.0 −0.975110 −0.487555 0.873092i \(-0.662111\pi\)
−0.487555 + 0.873092i \(0.662111\pi\)
\(978\) 0 0
\(979\) 29520.0 0.963701
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −9402.00 −0.305063 −0.152532 0.988299i \(-0.548743\pi\)
−0.152532 + 0.988299i \(0.548743\pi\)
\(984\) 0 0
\(985\) −12780.0 −0.413406
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4824.00 −0.155100
\(990\) 0 0
\(991\) 24907.0 0.798382 0.399191 0.916868i \(-0.369291\pi\)
0.399191 + 0.916868i \(0.369291\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −14615.0 −0.465655
\(996\) 0 0
\(997\) 27830.0 0.884037 0.442019 0.897006i \(-0.354263\pi\)
0.442019 + 0.897006i \(0.354263\pi\)
\(998\) 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.g.1.1 1
3.2 odd 2 2160.4.a.q.1.1 1
4.3 odd 2 270.4.a.h.1.1 yes 1
12.11 even 2 270.4.a.d.1.1 1
20.3 even 4 1350.4.c.f.649.1 2
20.7 even 4 1350.4.c.f.649.2 2
20.19 odd 2 1350.4.a.i.1.1 1
36.7 odd 6 810.4.e.j.271.1 2
36.11 even 6 810.4.e.r.271.1 2
36.23 even 6 810.4.e.r.541.1 2
36.31 odd 6 810.4.e.j.541.1 2
60.23 odd 4 1350.4.c.o.649.2 2
60.47 odd 4 1350.4.c.o.649.1 2
60.59 even 2 1350.4.a.w.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.4.a.d.1.1 1 12.11 even 2
270.4.a.h.1.1 yes 1 4.3 odd 2
810.4.e.j.271.1 2 36.7 odd 6
810.4.e.j.541.1 2 36.31 odd 6
810.4.e.r.271.1 2 36.11 even 6
810.4.e.r.541.1 2 36.23 even 6
1350.4.a.i.1.1 1 20.19 odd 2
1350.4.a.w.1.1 1 60.59 even 2
1350.4.c.f.649.1 2 20.3 even 4
1350.4.c.f.649.2 2 20.7 even 4
1350.4.c.o.649.1 2 60.47 odd 4
1350.4.c.o.649.2 2 60.23 odd 4
2160.4.a.g.1.1 1 1.1 even 1 trivial
2160.4.a.q.1.1 1 3.2 odd 2