↑

Properties

Label 1800.4.a.k.1.1
Level $1800$
Weight $4$
Character 1800.1
Self dual yes
Analytic conductor $106.203$
Analytic rank $1$
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] = [1800,4,Mod(1,1800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1800, 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("1800.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.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: \(106.203438010\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 120)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1800.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-8.00000 q^{7} +O(q^{10})\) \(q-8.00000 q^{7} -20.0000 q^{11} -22.0000 q^{13} -14.0000 q^{17} +76.0000 q^{19} +56.0000 q^{23} +154.000 q^{29} +160.000 q^{31} +162.000 q^{37} +390.000 q^{41} -388.000 q^{43} -544.000 q^{47} -279.000 q^{49} -210.000 q^{53} +380.000 q^{59} -794.000 q^{61} +148.000 q^{67} +840.000 q^{71} -858.000 q^{73} +160.000 q^{77} +144.000 q^{79} +316.000 q^{83} -1098.00 q^{89} +176.000 q^{91} -994.000 q^{97} +O(q^{100})\)

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
\(5\) 0 0
\(6\) 0 0
\(7\) −8.00000 −0.431959 −0.215980 − 0.976398i \(-0.569295\pi\)
−0.215980 + 0.976398i \(0.569295\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −20.0000 −0.548202 −0.274101 − 0.961701i \(-0.588380\pi\)
−0.274101 + 0.961701i \(0.588380\pi\)
\(12\) 0 0
\(13\) −22.0000 −0.469362 −0.234681 − 0.972072i \(-0.575405\pi\)
−0.234681 + 0.972072i \(0.575405\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −14.0000 −0.199735 −0.0998676 − 0.995001i \(-0.531842\pi\)
−0.0998676 + 0.995001i \(0.531842\pi\)
\(18\) 0 0
\(19\) 76.0000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 56.0000 0.507687 0.253844 − 0.967245i \(-0.418305\pi\)
0.253844 + 0.967245i \(0.418305\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 154.000 0.986106 0.493053 − 0.869999i \(-0.335881\pi\)
0.493053 + 0.869999i \(0.335881\pi\)
\(30\) 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
\(35\) 0 0
\(36\) 0 0
\(37\) 162.000 0.719801 0.359900 − 0.932991i \(-0.382811\pi\)
0.359900 + 0.932991i \(0.382811\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 390.000 1.48556 0.742778 − 0.669538i \(-0.233508\pi\)
0.742778 + 0.669538i \(0.233508\pi\)
\(42\) 0 0
\(43\) −388.000 −1.37603 −0.688017 − 0.725695i \(-0.741518\pi\)
−0.688017 + 0.725695i \(0.741518\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −544.000 −1.68831 −0.844155 − 0.536099i \(-0.819897\pi\)
−0.844155 + 0.536099i \(0.819897\pi\)
\(48\) 0 0
\(49\) −279.000 −0.813411
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −210.000 −0.544259 −0.272129 − 0.962261i \(-0.587728\pi\)
−0.272129 + 0.962261i \(0.587728\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 380.000 0.838505 0.419252 − 0.907870i \(-0.362292\pi\)
0.419252 + 0.907870i \(0.362292\pi\)
\(60\) 0 0
\(61\) −794.000 −1.66658 −0.833289 − 0.552837i \(-0.813545\pi\)
−0.833289 + 0.552837i \(0.813545\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 148.000 0.269867 0.134933 − 0.990855i \(-0.456918\pi\)
0.134933 + 0.990855i \(0.456918\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 840.000 1.40408 0.702040 − 0.712138i \(-0.252273\pi\)
0.702040 + 0.712138i \(0.252273\pi\)
\(72\) 0 0
\(73\) −858.000 −1.37563 −0.687817 − 0.725884i \(-0.741431\pi\)
−0.687817 + 0.725884i \(0.741431\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 160.000 0.236801
\(78\) 0 0
\(79\) 144.000 0.205079 0.102540 − 0.994729i \(-0.467303\pi\)
0.102540 + 0.994729i \(0.467303\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 316.000 0.417898 0.208949 − 0.977927i \(-0.432996\pi\)
0.208949 + 0.977927i \(0.432996\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1098.00 −1.30773 −0.653864 − 0.756612i \(-0.726853\pi\)
−0.653864 + 0.756612i \(0.726853\pi\)
\(90\) 0 0
\(91\) 176.000 0.202745
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −994.000 −1.04047 −0.520234 − 0.854024i \(-0.674155\pi\)
−0.520234 + 0.854024i \(0.674155\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 834.000 0.821645 0.410822 − 0.911715i \(-0.365242\pi\)
0.410822 + 0.911715i \(0.365242\pi\)
\(102\) 0 0
\(103\) −1672.00 −1.59949 −0.799743 − 0.600343i \(-0.795031\pi\)
−0.799743 + 0.600343i \(0.795031\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −732.000 −0.661356 −0.330678 − 0.943744i \(-0.607277\pi\)
−0.330678 + 0.943744i \(0.607277\pi\)
\(108\) 0 0
\(109\) −970.000 −0.852378 −0.426189 − 0.904634i \(-0.640144\pi\)
−0.426189 + 0.904634i \(0.640144\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1938.00 1.61338 0.806689 − 0.590976i \(-0.201257\pi\)
0.806689 + 0.590976i \(0.201257\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 112.000 0.0862775
\(120\) 0 0
\(121\) −931.000 −0.699474
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 528.000 0.368917 0.184458 − 0.982840i \(-0.440947\pi\)
0.184458 + 0.982840i \(0.440947\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −636.000 −0.424180 −0.212090 − 0.977250i \(-0.568027\pi\)
−0.212090 + 0.977250i \(0.568027\pi\)
\(132\) 0 0
\(133\) −608.000 −0.396393
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1754.00 1.09383 0.546914 − 0.837189i \(-0.315803\pi\)
0.546914 + 0.837189i \(0.315803\pi\)
\(138\) 0 0
\(139\) −2508.00 −1.53040 −0.765201 − 0.643792i \(-0.777360\pi\)
−0.765201 + 0.643792i \(0.777360\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 440.000 0.257305
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1486.00 −0.817033 −0.408516 − 0.912751i \(-0.633954\pi\)
−0.408516 + 0.912751i \(0.633954\pi\)
\(150\) 0 0
\(151\) 2120.00 1.14254 0.571269 − 0.820763i \(-0.306451\pi\)
0.571269 + 0.820763i \(0.306451\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 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
\(161\) −448.000 −0.219300
\(162\) 0 0
\(163\) 1172.00 0.563179 0.281589 − 0.959535i \(-0.409138\pi\)
0.281589 + 0.959535i \(0.409138\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1656.00 −0.767336 −0.383668 − 0.923471i \(-0.625339\pi\)
−0.383668 + 0.923471i \(0.625339\pi\)
\(168\) 0 0
\(169\) −1713.00 −0.779700
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2666.00 −1.17163 −0.585816 − 0.810444i \(-0.699226\pi\)
−0.585816 + 0.810444i \(0.699226\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1132.00 −0.472680 −0.236340 − 0.971670i \(-0.575948\pi\)
−0.236340 + 0.971670i \(0.575948\pi\)
\(180\) 0 0
\(181\) −2866.00 −1.17695 −0.588475 − 0.808515i \(-0.700272\pi\)
−0.588475 + 0.808515i \(0.700272\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 280.000 0.109495
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1888.00 −0.715240 −0.357620 − 0.933867i \(-0.616412\pi\)
−0.357620 + 0.933867i \(0.616412\pi\)
\(192\) 0 0
\(193\) −1282.00 −0.478137 −0.239068 − 0.971003i \(-0.576842\pi\)
−0.239068 + 0.971003i \(0.576842\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 350.000 0.126581 0.0632905 − 0.997995i \(-0.479841\pi\)
0.0632905 + 0.997995i \(0.479841\pi\)
\(198\) 0 0
\(199\) −3400.00 −1.21115 −0.605577 − 0.795787i \(-0.707058\pi\)
−0.605577 + 0.795787i \(0.707058\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1232.00 −0.425958
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1520.00 −0.503065
\(210\) 0 0
\(211\) 4652.00 1.51781 0.758903 − 0.651204i \(-0.225736\pi\)
0.758903 + 0.651204i \(0.225736\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1280.00 −0.400424
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 308.000 0.0937481
\(222\) 0 0
\(223\) −4016.00 −1.20597 −0.602985 − 0.797753i \(-0.706022\pi\)
−0.602985 + 0.797753i \(0.706022\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2316.00 0.677173 0.338587 − 0.940935i \(-0.390051\pi\)
0.338587 + 0.940935i \(0.390051\pi\)
\(228\) 0 0
\(229\) 94.0000 0.0271253 0.0135627 − 0.999908i \(-0.495683\pi\)
0.0135627 + 0.999908i \(0.495683\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4230.00 −1.18934 −0.594671 − 0.803969i \(-0.702718\pi\)
−0.594671 + 0.803969i \(0.702718\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2064.00 −0.558615 −0.279308 − 0.960202i \(-0.590105\pi\)
−0.279308 + 0.960202i \(0.590105\pi\)
\(240\) 0 0
\(241\) 4562.00 1.21935 0.609677 − 0.792650i \(-0.291299\pi\)
0.609677 + 0.792650i \(0.291299\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1672.00 −0.430716
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2532.00 −0.636727 −0.318363 − 0.947969i \(-0.603133\pi\)
−0.318363 + 0.947969i \(0.603133\pi\)
\(252\) 0 0
\(253\) −1120.00 −0.278315
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3522.00 0.854850 0.427425 − 0.904051i \(-0.359421\pi\)
0.427425 + 0.904051i \(0.359421\pi\)
\(258\) 0 0
\(259\) −1296.00 −0.310925
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2232.00 −0.523312 −0.261656 − 0.965161i \(-0.584269\pi\)
−0.261656 + 0.965161i \(0.584269\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2806.00 −0.636003 −0.318002 − 0.948090i \(-0.603012\pi\)
−0.318002 + 0.948090i \(0.603012\pi\)
\(270\) 0 0
\(271\) 4848.00 1.08670 0.543349 − 0.839507i \(-0.317156\pi\)
0.543349 + 0.839507i \(0.317156\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −7790.00 −1.68973 −0.844866 − 0.534978i \(-0.820320\pi\)
−0.844866 + 0.534978i \(0.820320\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 118.000 0.0250509 0.0125254 − 0.999922i \(-0.496013\pi\)
0.0125254 + 0.999922i \(0.496013\pi\)
\(282\) 0 0
\(283\) 6508.00 1.36700 0.683499 − 0.729951i \(-0.260457\pi\)
0.683499 + 0.729951i \(0.260457\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3120.00 −0.641700
\(288\) 0 0
\(289\) −4717.00 −0.960106
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −8770.00 −1.74863 −0.874315 − 0.485358i \(-0.838689\pi\)
−0.874315 + 0.485358i \(0.838689\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1232.00 −0.238289
\(300\) 0 0
\(301\) 3104.00 0.594391
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4292.00 0.797907 0.398953 − 0.916971i \(-0.369374\pi\)
0.398953 + 0.916971i \(0.369374\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9464.00 1.72558 0.862788 − 0.505566i \(-0.168716\pi\)
0.862788 + 0.505566i \(0.168716\pi\)
\(312\) 0 0
\(313\) −9578.00 −1.72965 −0.864825 − 0.502073i \(-0.832571\pi\)
−0.864825 + 0.502073i \(0.832571\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −186.000 −0.0329552 −0.0164776 − 0.999864i \(-0.505245\pi\)
−0.0164776 + 0.999864i \(0.505245\pi\)
\(318\) 0 0
\(319\) −3080.00 −0.540586
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1064.00 −0.183290
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4352.00 0.729281
\(330\) 0 0
\(331\) −492.000 −0.0817002 −0.0408501 − 0.999165i \(-0.513007\pi\)
−0.0408501 + 0.999165i \(0.513007\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −2290.00 −0.370161 −0.185080 − 0.982723i \(-0.559255\pi\)
−0.185080 + 0.982723i \(0.559255\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3200.00 −0.508181
\(342\) 0 0
\(343\) 4976.00 0.783320
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6092.00 −0.942466 −0.471233 − 0.882009i \(-0.656191\pi\)
−0.471233 + 0.882009i \(0.656191\pi\)
\(348\) 0 0
\(349\) 5766.00 0.884375 0.442188 − 0.896923i \(-0.354203\pi\)
0.442188 + 0.896923i \(0.354203\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9374.00 −1.41339 −0.706696 − 0.707517i \(-0.749815\pi\)
−0.706696 + 0.707517i \(0.749815\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3528.00 0.518665 0.259332 − 0.965788i \(-0.416497\pi\)
0.259332 + 0.965788i \(0.416497\pi\)
\(360\) 0 0
\(361\) −1083.00 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −7616.00 −1.08325 −0.541624 − 0.840621i \(-0.682190\pi\)
−0.541624 + 0.840621i \(0.682190\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1680.00 0.235098
\(372\) 0 0
\(373\) −3406.00 −0.472804 −0.236402 − 0.971655i \(-0.575968\pi\)
−0.236402 + 0.971655i \(0.575968\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3388.00 −0.462841
\(378\) 0 0
\(379\) −12284.0 −1.66487 −0.832436 − 0.554121i \(-0.813055\pi\)
−0.832436 + 0.554121i \(0.813055\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5424.00 0.723638 0.361819 − 0.932248i \(-0.382156\pi\)
0.361819 + 0.932248i \(0.382156\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3486.00 −0.454363 −0.227182 − 0.973852i \(-0.572951\pi\)
−0.227182 + 0.973852i \(0.572951\pi\)
\(390\) 0 0
\(391\) −784.000 −0.101403
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 3626.00 0.458397 0.229199 − 0.973380i \(-0.426389\pi\)
0.229199 + 0.973380i \(0.426389\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5874.00 −0.731505 −0.365753 − 0.930712i \(-0.619188\pi\)
−0.365753 + 0.930712i \(0.619188\pi\)
\(402\) 0 0
\(403\) −3520.00 −0.435096
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3240.00 −0.394597
\(408\) 0 0
\(409\) −12662.0 −1.53080 −0.765398 − 0.643557i \(-0.777458\pi\)
−0.765398 + 0.643557i \(0.777458\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3040.00 −0.362200
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6396.00 −0.745740 −0.372870 − 0.927884i \(-0.621626\pi\)
−0.372870 + 0.927884i \(0.621626\pi\)
\(420\) 0 0
\(421\) 8286.00 0.959228 0.479614 − 0.877480i \(-0.340777\pi\)
0.479614 + 0.877480i \(0.340777\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 6352.00 0.719894
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4112.00 0.459555 0.229777 − 0.973243i \(-0.426200\pi\)
0.229777 + 0.973243i \(0.426200\pi\)
\(432\) 0 0
\(433\) −5330.00 −0.591555 −0.295778 − 0.955257i \(-0.595579\pi\)
−0.295778 + 0.955257i \(0.595579\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4256.00 0.465886
\(438\) 0 0
\(439\) 11272.0 1.22547 0.612737 − 0.790287i \(-0.290068\pi\)
0.612737 + 0.790287i \(0.290068\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14196.0 1.52251 0.761255 − 0.648452i \(-0.224583\pi\)
0.761255 + 0.648452i \(0.224583\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5886.00 0.618658 0.309329 − 0.950955i \(-0.399896\pi\)
0.309329 + 0.950955i \(0.399896\pi\)
\(450\) 0 0
\(451\) −7800.00 −0.814385
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 7526.00 0.770353 0.385177 − 0.922843i \(-0.374141\pi\)
0.385177 + 0.922843i \(0.374141\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8502.00 −0.858954 −0.429477 − 0.903078i \(-0.641302\pi\)
−0.429477 + 0.903078i \(0.641302\pi\)
\(462\) 0 0
\(463\) −12672.0 −1.27196 −0.635980 − 0.771705i \(-0.719404\pi\)
−0.635980 + 0.771705i \(0.719404\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 16540.0 1.63893 0.819465 − 0.573130i \(-0.194271\pi\)
0.819465 + 0.573130i \(0.194271\pi\)
\(468\) 0 0
\(469\) −1184.00 −0.116572
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7760.00 0.754345
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8864.00 −0.845525 −0.422763 − 0.906241i \(-0.638940\pi\)
−0.422763 + 0.906241i \(0.638940\pi\)
\(480\) 0 0
\(481\) −3564.00 −0.337847
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −3688.00 −0.343161 −0.171580 − 0.985170i \(-0.554887\pi\)
−0.171580 + 0.985170i \(0.554887\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 16140.0 1.48348 0.741739 − 0.670688i \(-0.234001\pi\)
0.741739 + 0.670688i \(0.234001\pi\)
\(492\) 0 0
\(493\) −2156.00 −0.196960
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6720.00 −0.606505
\(498\) 0 0
\(499\) 1580.00 0.141745 0.0708723 − 0.997485i \(-0.477422\pi\)
0.0708723 + 0.997485i \(0.477422\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 15000.0 1.32966 0.664828 − 0.746996i \(-0.268505\pi\)
0.664828 + 0.746996i \(0.268505\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −20486.0 −1.78394 −0.891971 − 0.452094i \(-0.850677\pi\)
−0.891971 + 0.452094i \(0.850677\pi\)
\(510\) 0 0
\(511\) 6864.00 0.594218
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 10880.0 0.925535
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7706.00 −0.647996 −0.323998 − 0.946058i \(-0.605027\pi\)
−0.323998 + 0.946058i \(0.605027\pi\)
\(522\) 0 0
\(523\) 3932.00 0.328746 0.164373 − 0.986398i \(-0.447440\pi\)
0.164373 + 0.986398i \(0.447440\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2240.00 −0.185154
\(528\) 0 0
\(529\) −9031.00 −0.742254
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −8580.00 −0.697263
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5580.00 0.445914
\(540\) 0 0
\(541\) −23930.0 −1.90172 −0.950860 − 0.309620i \(-0.899798\pi\)
−0.950860 + 0.309620i \(0.899798\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −11468.0 −0.896410 −0.448205 − 0.893931i \(-0.647937\pi\)
−0.448205 + 0.893931i \(0.647937\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 11704.0 0.904913
\(552\) 0 0
\(553\) −1152.00 −0.0885859
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −11498.0 −0.874660 −0.437330 − 0.899301i \(-0.644076\pi\)
−0.437330 + 0.899301i \(0.644076\pi\)
\(558\) 0 0
\(559\) 8536.00 0.645857
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 16988.0 1.27169 0.635843 − 0.771819i \(-0.280653\pi\)
0.635843 + 0.771819i \(0.280653\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 17366.0 1.27947 0.639737 − 0.768594i \(-0.279043\pi\)
0.639737 + 0.768594i \(0.279043\pi\)
\(570\) 0 0
\(571\) −24860.0 −1.82199 −0.910997 − 0.412413i \(-0.864686\pi\)
−0.910997 + 0.412413i \(0.864686\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 26302.0 1.89769 0.948845 − 0.315744i \(-0.102254\pi\)
0.948845 + 0.315744i \(0.102254\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2528.00 −0.180515
\(582\) 0 0
\(583\) 4200.00 0.298364
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7812.00 0.549294 0.274647 − 0.961545i \(-0.411439\pi\)
0.274647 + 0.961545i \(0.411439\pi\)
\(588\) 0 0
\(589\) 12160.0 0.850669
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7986.00 0.553028 0.276514 − 0.961010i \(-0.410821\pi\)
0.276514 + 0.961010i \(0.410821\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 21048.0 1.43572 0.717861 − 0.696186i \(-0.245121\pi\)
0.717861 + 0.696186i \(0.245121\pi\)
\(600\) 0 0
\(601\) 1738.00 0.117961 0.0589804 − 0.998259i \(-0.481215\pi\)
0.0589804 + 0.998259i \(0.481215\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −18576.0 −1.24214 −0.621068 − 0.783757i \(-0.713301\pi\)
−0.621068 + 0.783757i \(0.713301\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11968.0 0.792428
\(612\) 0 0
\(613\) 13602.0 0.896215 0.448107 − 0.893980i \(-0.352098\pi\)
0.448107 + 0.893980i \(0.352098\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 19578.0 1.27744 0.638720 − 0.769439i \(-0.279464\pi\)
0.638720 + 0.769439i \(0.279464\pi\)
\(618\) 0 0
\(619\) 12308.0 0.799193 0.399596 − 0.916691i \(-0.369150\pi\)
0.399596 + 0.916691i \(0.369150\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8784.00 0.564885
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2268.00 −0.143770
\(630\) 0 0
\(631\) −8600.00 −0.542568 −0.271284 − 0.962499i \(-0.587448\pi\)
−0.271284 + 0.962499i \(0.587448\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6138.00 0.381784
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −6978.00 −0.429976 −0.214988 − 0.976617i \(-0.568971\pi\)
−0.214988 + 0.976617i \(0.568971\pi\)
\(642\) 0 0
\(643\) 7668.00 0.470290 0.235145 − 0.971960i \(-0.424444\pi\)
0.235145 + 0.971960i \(0.424444\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15384.0 −0.934787 −0.467394 − 0.884049i \(-0.654807\pi\)
−0.467394 + 0.884049i \(0.654807\pi\)
\(648\) 0 0
\(649\) −7600.00 −0.459670
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2186.00 −0.131003 −0.0655014 − 0.997852i \(-0.520865\pi\)
−0.0655014 + 0.997852i \(0.520865\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1524.00 0.0900859 0.0450430 − 0.998985i \(-0.485658\pi\)
0.0450430 + 0.998985i \(0.485658\pi\)
\(660\) 0 0
\(661\) −4242.00 −0.249614 −0.124807 − 0.992181i \(-0.539831\pi\)
−0.124807 + 0.992181i \(0.539831\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 8624.00 0.500634
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15880.0 0.913622
\(672\) 0 0
\(673\) −24354.0 −1.39491 −0.697457 − 0.716626i \(-0.745685\pi\)
−0.697457 + 0.716626i \(0.745685\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −322.000 −0.0182799 −0.00913993 − 0.999958i \(-0.502909\pi\)
−0.00913993 + 0.999958i \(0.502909\pi\)
\(678\) 0 0
\(679\) 7952.00 0.449440
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −7932.00 −0.444377 −0.222189 − 0.975004i \(-0.571320\pi\)
−0.222189 + 0.975004i \(0.571320\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4620.00 0.255454
\(690\) 0 0
\(691\) 20684.0 1.13872 0.569361 − 0.822088i \(-0.307191\pi\)
0.569361 + 0.822088i \(0.307191\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −5460.00 −0.296718
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −25222.0 −1.35895 −0.679473 − 0.733700i \(-0.737792\pi\)
−0.679473 + 0.733700i \(0.737792\pi\)
\(702\) 0 0
\(703\) 12312.0 0.660535
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6672.00 −0.354917
\(708\) 0 0
\(709\) 23678.0 1.25423 0.627113 − 0.778928i \(-0.284236\pi\)
0.627113 + 0.778928i \(0.284236\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8960.00 0.470624
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −8432.00 −0.437358 −0.218679 − 0.975797i \(-0.570175\pi\)
−0.218679 + 0.975797i \(0.570175\pi\)
\(720\) 0 0
\(721\) 13376.0 0.690913
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −8312.00 −0.424037 −0.212019 − 0.977266i \(-0.568004\pi\)
−0.212019 + 0.977266i \(0.568004\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5432.00 0.274842
\(732\) 0 0
\(733\) 26298.0 1.32516 0.662578 − 0.748993i \(-0.269462\pi\)
0.662578 + 0.748993i \(0.269462\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2960.00 −0.147942
\(738\) 0 0
\(739\) 16956.0 0.844028 0.422014 − 0.906589i \(-0.361323\pi\)
0.422014 + 0.906589i \(0.361323\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −17880.0 −0.882845 −0.441422 − 0.897299i \(-0.645526\pi\)
−0.441422 + 0.897299i \(0.645526\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5856.00 0.285679
\(750\) 0 0
\(751\) 22032.0 1.07052 0.535259 − 0.844688i \(-0.320214\pi\)
0.535259 + 0.844688i \(0.320214\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −11534.0 −0.553779 −0.276889 − 0.960902i \(-0.589304\pi\)
−0.276889 + 0.960902i \(0.589304\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −38250.0 −1.82203 −0.911013 − 0.412378i \(-0.864698\pi\)
−0.911013 + 0.412378i \(0.864698\pi\)
\(762\) 0 0
\(763\) 7760.00 0.368192
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8360.00 −0.393562
\(768\) 0 0
\(769\) 19330.0 0.906447 0.453223 − 0.891397i \(-0.350274\pi\)
0.453223 + 0.891397i \(0.350274\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −40674.0 −1.89255 −0.946276 − 0.323361i \(-0.895187\pi\)
−0.946276 + 0.323361i \(0.895187\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 29640.0 1.36324
\(780\) 0 0
\(781\) −16800.0 −0.769720
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −7004.00 −0.317237 −0.158619 − 0.987340i \(-0.550704\pi\)
−0.158619 + 0.987340i \(0.550704\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −15504.0 −0.696914
\(792\) 0 0
\(793\) 17468.0 0.782228
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12198.0 0.542127 0.271064 − 0.962561i \(-0.412625\pi\)
0.271064 + 0.962561i \(0.412625\pi\)
\(798\) 0 0
\(799\) 7616.00 0.337215
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 17160.0 0.754126
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 25734.0 1.11837 0.559184 − 0.829044i \(-0.311115\pi\)
0.559184 + 0.829044i \(0.311115\pi\)
\(810\) 0 0
\(811\) 15668.0 0.678394 0.339197 − 0.940715i \(-0.389845\pi\)
0.339197 + 0.940715i \(0.389845\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −29488.0 −1.26274
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 34450.0 1.46445 0.732225 − 0.681063i \(-0.238482\pi\)
0.732225 + 0.681063i \(0.238482\pi\)
\(822\) 0 0
\(823\) 38792.0 1.64302 0.821509 − 0.570195i \(-0.193132\pi\)
0.821509 + 0.570195i \(0.193132\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −20460.0 −0.860295 −0.430147 − 0.902759i \(-0.641538\pi\)
−0.430147 + 0.902759i \(0.641538\pi\)
\(828\) 0 0
\(829\) 5542.00 0.232185 0.116093 − 0.993238i \(-0.462963\pi\)
0.116093 + 0.993238i \(0.462963\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3906.00 0.162467
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −25240.0 −1.03860 −0.519298 − 0.854593i \(-0.673806\pi\)
−0.519298 + 0.854593i \(0.673806\pi\)
\(840\) 0 0
\(841\) −673.000 −0.0275944
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 7448.00 0.302144
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 9072.00 0.365434
\(852\) 0 0
\(853\) 37330.0 1.49842 0.749212 − 0.662331i \(-0.230433\pi\)
0.749212 + 0.662331i \(0.230433\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3894.00 −0.155212 −0.0776059 − 0.996984i \(-0.524728\pi\)
−0.0776059 + 0.996984i \(0.524728\pi\)
\(858\) 0 0
\(859\) 20324.0 0.807271 0.403636 − 0.914920i \(-0.367746\pi\)
0.403636 + 0.914920i \(0.367746\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 6288.00 0.248026 0.124013 − 0.992281i \(-0.460424\pi\)
0.124013 + 0.992281i \(0.460424\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2880.00 −0.112425
\(870\) 0 0
\(871\) −3256.00 −0.126665
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 24650.0 0.949112 0.474556 − 0.880225i \(-0.342609\pi\)
0.474556 + 0.880225i \(0.342609\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −9426.00 −0.360465 −0.180233 − 0.983624i \(-0.557685\pi\)
−0.180233 + 0.983624i \(0.557685\pi\)
\(882\) 0 0
\(883\) 9316.00 0.355049 0.177525 − 0.984116i \(-0.443191\pi\)
0.177525 + 0.984116i \(0.443191\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 6968.00 0.263768 0.131884 − 0.991265i \(-0.457897\pi\)
0.131884 + 0.991265i \(0.457897\pi\)
\(888\) 0 0
\(889\) −4224.00 −0.159357
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −41344.0 −1.54930
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 24640.0 0.914116
\(900\) 0 0
\(901\) 2940.00 0.108708
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 35964.0 1.31661 0.658305 − 0.752751i \(-0.271274\pi\)
0.658305 + 0.752751i \(0.271274\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −47888.0 −1.74160 −0.870801 − 0.491635i \(-0.836399\pi\)
−0.870801 + 0.491635i \(0.836399\pi\)
\(912\) 0 0
\(913\) −6320.00 −0.229093
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 5088.00 0.183229
\(918\) 0 0
\(919\) −12760.0 −0.458013 −0.229006 − 0.973425i \(-0.573548\pi\)
−0.229006 + 0.973425i \(0.573548\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −18480.0 −0.659021
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 25054.0 0.884817 0.442409 − 0.896814i \(-0.354124\pi\)
0.442409 + 0.896814i \(0.354124\pi\)
\(930\) 0 0
\(931\) −21204.0 −0.746437
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −28282.0 −0.986054 −0.493027 − 0.870014i \(-0.664110\pi\)
−0.493027 + 0.870014i \(0.664110\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 30634.0 1.06125 0.530627 − 0.847605i \(-0.321957\pi\)
0.530627 + 0.847605i \(0.321957\pi\)
\(942\) 0 0
\(943\) 21840.0 0.754198
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 48572.0 1.66671 0.833357 − 0.552735i \(-0.186416\pi\)
0.833357 + 0.552735i \(0.186416\pi\)
\(948\) 0 0
\(949\) 18876.0 0.645670
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 12906.0 0.438685 0.219342 − 0.975648i \(-0.429609\pi\)
0.219342 + 0.975648i \(0.429609\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −14032.0 −0.472489
\(960\) 0 0
\(961\) −4191.00 −0.140680
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 5880.00 0.195541 0.0977705 − 0.995209i \(-0.468829\pi\)
0.0977705 + 0.995209i \(0.468829\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −55444.0 −1.83242 −0.916211 − 0.400695i \(-0.868769\pi\)
−0.916211 + 0.400695i \(0.868769\pi\)
\(972\) 0 0
\(973\) 20064.0 0.661071
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 32050.0 1.04951 0.524755 − 0.851254i \(-0.324157\pi\)
0.524755 + 0.851254i \(0.324157\pi\)
\(978\) 0 0
\(979\) 21960.0 0.716900
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 29880.0 0.969506 0.484753 − 0.874651i \(-0.338910\pi\)
0.484753 + 0.874651i \(0.338910\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −21728.0 −0.698595
\(990\) 0 0
\(991\) 5216.00 0.167196 0.0835982 − 0.996500i \(-0.473359\pi\)
0.0835982 + 0.996500i \(0.473359\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −6750.00 −0.214418 −0.107209 − 0.994237i \(-0.534191\pi\)
−0.107209 + 0.994237i \(0.534191\pi\)
\(998\) 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 1800.4.a.k.1.1 1
3.2 odd 2 600.4.a.d.1.1 1
5.2 odd 4 1800.4.f.h.649.1 2
5.3 odd 4 1800.4.f.h.649.2 2
5.4 even 2 360.4.a.e.1.1 1
12.11 even 2 1200.4.a.bf.1.1 1
15.2 even 4 600.4.f.g.49.2 2
15.8 even 4 600.4.f.g.49.1 2
15.14 odd 2 120.4.a.f.1.1 ✓ 1
20.19 odd 2 720.4.a.f.1.1 1
60.23 odd 4 1200.4.f.g.49.2 2
60.47 odd 4 1200.4.f.g.49.1 2
60.59 even 2 240.4.a.d.1.1 1
120.29 odd 2 960.4.a.g.1.1 1
120.59 even 2 960.4.a.v.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.a.f.1.1 ✓ 1 15.14 odd 2
240.4.a.d.1.1 1 60.59 even 2
360.4.a.e.1.1 1 5.4 even 2
600.4.a.d.1.1 1 3.2 odd 2
600.4.f.g.49.1 2 15.8 even 4
600.4.f.g.49.2 2 15.2 even 4
720.4.a.f.1.1 1 20.19 odd 2
960.4.a.g.1.1 1 120.29 odd 2
960.4.a.v.1.1 1 120.59 even 2
1200.4.a.bf.1.1 1 12.11 even 2
1200.4.f.g.49.1 2 60.47 odd 4
1200.4.f.g.49.2 2 60.23 odd 4
1800.4.a.k.1.1 1 1.1 even 1 trivial
1800.4.f.h.649.1 2 5.2 odd 4
1800.4.f.h.649.2 2 5.3 odd 4