↑

Properties

Label 1008.4.a.n.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
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] = [1008,4,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, 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("1008.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.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: \(59.4739252858\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+6.00000 q^{5} -7.00000 q^{7} +O(q^{10})\) \(q+6.00000 q^{5} -7.00000 q^{7} -30.0000 q^{11} +2.00000 q^{13} +66.0000 q^{17} +52.0000 q^{19} -114.000 q^{23} -89.0000 q^{25} +72.0000 q^{29} +196.000 q^{31} -42.0000 q^{35} -286.000 q^{37} -378.000 q^{41} -164.000 q^{43} +228.000 q^{47} +49.0000 q^{49} -348.000 q^{53} -180.000 q^{55} +348.000 q^{59} -106.000 q^{61} +12.0000 q^{65} -596.000 q^{67} -630.000 q^{71} -1042.00 q^{73} +210.000 q^{77} +88.0000 q^{79} +1440.00 q^{83} +396.000 q^{85} +1374.00 q^{89} -14.0000 q^{91} +312.000 q^{95} -34.0000 q^{97} +O(q^{100})\)

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
\(5\) 6.00000 0.536656 0.268328 − 0.963328i \(-0.413529\pi\)
0.268328 + 0.963328i \(0.413529\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −30.0000 −0.822304 −0.411152 − 0.911567i \(-0.634873\pi\)
−0.411152 + 0.911567i \(0.634873\pi\)
\(12\) 0 0
\(13\) 2.00000 0.0426692 0.0213346 − 0.999772i \(-0.493208\pi\)
0.0213346 + 0.999772i \(0.493208\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 66.0000 0.941609 0.470804 − 0.882238i \(-0.343964\pi\)
0.470804 + 0.882238i \(0.343964\pi\)
\(18\) 0 0
\(19\) 52.0000 0.627875 0.313937 − 0.949444i \(-0.398352\pi\)
0.313937 + 0.949444i \(0.398352\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −114.000 −1.03351 −0.516753 − 0.856134i \(-0.672859\pi\)
−0.516753 + 0.856134i \(0.672859\pi\)
\(24\) 0 0
\(25\) −89.0000 −0.712000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 72.0000 0.461037 0.230518 − 0.973068i \(-0.425958\pi\)
0.230518 + 0.973068i \(0.425958\pi\)
\(30\) 0 0
\(31\) 196.000 1.13557 0.567785 − 0.823177i \(-0.307801\pi\)
0.567785 + 0.823177i \(0.307801\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −42.0000 −0.202837
\(36\) 0 0
\(37\) −286.000 −1.27076 −0.635380 − 0.772200i \(-0.719156\pi\)
−0.635380 + 0.772200i \(0.719156\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −378.000 −1.43985 −0.719923 − 0.694054i \(-0.755823\pi\)
−0.719923 + 0.694054i \(0.755823\pi\)
\(42\) 0 0
\(43\) −164.000 −0.581622 −0.290811 − 0.956780i \(-0.593925\pi\)
−0.290811 + 0.956780i \(0.593925\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 228.000 0.707600 0.353800 − 0.935321i \(-0.384889\pi\)
0.353800 + 0.935321i \(0.384889\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −348.000 −0.901915 −0.450957 − 0.892546i \(-0.648917\pi\)
−0.450957 + 0.892546i \(0.648917\pi\)
\(54\) 0 0
\(55\) −180.000 −0.441294
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 348.000 0.767894 0.383947 − 0.923355i \(-0.374565\pi\)
0.383947 + 0.923355i \(0.374565\pi\)
\(60\) 0 0
\(61\) −106.000 −0.222490 −0.111245 − 0.993793i \(-0.535484\pi\)
−0.111245 + 0.993793i \(0.535484\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 12.0000 0.0228987
\(66\) 0 0
\(67\) −596.000 −1.08676 −0.543381 − 0.839487i \(-0.682856\pi\)
−0.543381 + 0.839487i \(0.682856\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −630.000 −1.05306 −0.526530 − 0.850157i \(-0.676507\pi\)
−0.526530 + 0.850157i \(0.676507\pi\)
\(72\) 0 0
\(73\) −1042.00 −1.67064 −0.835321 − 0.549762i \(-0.814718\pi\)
−0.835321 + 0.549762i \(0.814718\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 210.000 0.310802
\(78\) 0 0
\(79\) 88.0000 0.125326 0.0626631 − 0.998035i \(-0.480041\pi\)
0.0626631 + 0.998035i \(0.480041\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1440.00 1.90434 0.952172 − 0.305563i \(-0.0988446\pi\)
0.952172 + 0.305563i \(0.0988446\pi\)
\(84\) 0 0
\(85\) 396.000 0.505320
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1374.00 1.63645 0.818223 − 0.574901i \(-0.194959\pi\)
0.818223 + 0.574901i \(0.194959\pi\)
\(90\) 0 0
\(91\) −14.0000 −0.0161275
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 312.000 0.336953
\(96\) 0 0
\(97\) −34.0000 −0.0355895 −0.0177947 − 0.999842i \(-0.505665\pi\)
−0.0177947 + 0.999842i \(0.505665\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −438.000 −0.431511 −0.215756 − 0.976447i \(-0.569221\pi\)
−0.215756 + 0.976447i \(0.569221\pi\)
\(102\) 0 0
\(103\) −1676.00 −1.60331 −0.801656 − 0.597785i \(-0.796048\pi\)
−0.801656 + 0.597785i \(0.796048\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2022.00 −1.82686 −0.913430 − 0.406995i \(-0.866577\pi\)
−0.913430 + 0.406995i \(0.866577\pi\)
\(108\) 0 0
\(109\) −502.000 −0.441127 −0.220564 − 0.975373i \(-0.570790\pi\)
−0.220564 + 0.975373i \(0.570790\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2016.00 1.67831 0.839156 − 0.543890i \(-0.183049\pi\)
0.839156 + 0.543890i \(0.183049\pi\)
\(114\) 0 0
\(115\) −684.000 −0.554638
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −462.000 −0.355895
\(120\) 0 0
\(121\) −431.000 −0.323817
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1284.00 −0.918756
\(126\) 0 0
\(127\) −1784.00 −1.24649 −0.623246 − 0.782026i \(-0.714186\pi\)
−0.623246 + 0.782026i \(0.714186\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1608.00 −1.07246 −0.536228 − 0.844073i \(-0.680151\pi\)
−0.536228 + 0.844073i \(0.680151\pi\)
\(132\) 0 0
\(133\) −364.000 −0.237314
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2580.00 −1.60894 −0.804468 − 0.593996i \(-0.797550\pi\)
−0.804468 + 0.593996i \(0.797550\pi\)
\(138\) 0 0
\(139\) −2144.00 −1.30829 −0.654143 − 0.756371i \(-0.726970\pi\)
−0.654143 + 0.756371i \(0.726970\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −60.0000 −0.0350871
\(144\) 0 0
\(145\) 432.000 0.247418
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1500.00 0.824730 0.412365 − 0.911019i \(-0.364703\pi\)
0.412365 + 0.911019i \(0.364703\pi\)
\(150\) 0 0
\(151\) 1240.00 0.668277 0.334138 − 0.942524i \(-0.391555\pi\)
0.334138 + 0.942524i \(0.391555\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1176.00 0.609410
\(156\) 0 0
\(157\) 614.000 0.312118 0.156059 − 0.987748i \(-0.450121\pi\)
0.156059 + 0.987748i \(0.450121\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 798.000 0.390629
\(162\) 0 0
\(163\) −92.0000 −0.0442086 −0.0221043 − 0.999756i \(-0.507037\pi\)
−0.0221043 + 0.999756i \(0.507037\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3924.00 1.81825 0.909126 − 0.416520i \(-0.136750\pi\)
0.909126 + 0.416520i \(0.136750\pi\)
\(168\) 0 0
\(169\) −2193.00 −0.998179
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1902.00 −0.835875 −0.417938 − 0.908476i \(-0.637247\pi\)
−0.417938 + 0.908476i \(0.637247\pi\)
\(174\) 0 0
\(175\) 623.000 0.269111
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.00000 0.00250537 0.00125268 − 0.999999i \(-0.499601\pi\)
0.00125268 + 0.999999i \(0.499601\pi\)
\(180\) 0 0
\(181\) −2878.00 −1.18188 −0.590939 − 0.806716i \(-0.701243\pi\)
−0.590939 + 0.806716i \(0.701243\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1716.00 −0.681961
\(186\) 0 0
\(187\) −1980.00 −0.774288
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 354.000 0.134108 0.0670538 − 0.997749i \(-0.478640\pi\)
0.0670538 + 0.997749i \(0.478640\pi\)
\(192\) 0 0
\(193\) −4858.00 −1.81185 −0.905924 − 0.423441i \(-0.860822\pi\)
−0.905924 + 0.423441i \(0.860822\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −396.000 −0.143217 −0.0716087 − 0.997433i \(-0.522813\pi\)
−0.0716087 + 0.997433i \(0.522813\pi\)
\(198\) 0 0
\(199\) −1712.00 −0.609852 −0.304926 − 0.952376i \(-0.598632\pi\)
−0.304926 + 0.952376i \(0.598632\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −504.000 −0.174255
\(204\) 0 0
\(205\) −2268.00 −0.772702
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1560.00 −0.516304
\(210\) 0 0
\(211\) 772.000 0.251880 0.125940 − 0.992038i \(-0.459805\pi\)
0.125940 + 0.992038i \(0.459805\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −984.000 −0.312131
\(216\) 0 0
\(217\) −1372.00 −0.429205
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 132.000 0.0401777
\(222\) 0 0
\(223\) −776.000 −0.233026 −0.116513 − 0.993189i \(-0.537172\pi\)
−0.116513 + 0.993189i \(0.537172\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1788.00 0.522792 0.261396 − 0.965232i \(-0.415817\pi\)
0.261396 + 0.965232i \(0.415817\pi\)
\(228\) 0 0
\(229\) 5402.00 1.55884 0.779420 − 0.626502i \(-0.215514\pi\)
0.779420 + 0.626502i \(0.215514\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3012.00 0.846878 0.423439 − 0.905925i \(-0.360823\pi\)
0.423439 + 0.905925i \(0.360823\pi\)
\(234\) 0 0
\(235\) 1368.00 0.379738
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3546.00 −0.959714 −0.479857 − 0.877347i \(-0.659311\pi\)
−0.479857 + 0.877347i \(0.659311\pi\)
\(240\) 0 0
\(241\) −3562.00 −0.952069 −0.476034 − 0.879427i \(-0.657926\pi\)
−0.476034 + 0.879427i \(0.657926\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 294.000 0.0766652
\(246\) 0 0
\(247\) 104.000 0.0267909
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −3348.00 −0.841928 −0.420964 − 0.907077i \(-0.638308\pi\)
−0.420964 + 0.907077i \(0.638308\pi\)
\(252\) 0 0
\(253\) 3420.00 0.849856
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 366.000 0.0888344 0.0444172 − 0.999013i \(-0.485857\pi\)
0.0444172 + 0.999013i \(0.485857\pi\)
\(258\) 0 0
\(259\) 2002.00 0.480302
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4170.00 −0.977693 −0.488846 − 0.872370i \(-0.662582\pi\)
−0.488846 + 0.872370i \(0.662582\pi\)
\(264\) 0 0
\(265\) −2088.00 −0.484018
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6078.00 1.37763 0.688814 − 0.724938i \(-0.258131\pi\)
0.688814 + 0.724938i \(0.258131\pi\)
\(270\) 0 0
\(271\) −2468.00 −0.553212 −0.276606 − 0.960983i \(-0.589210\pi\)
−0.276606 + 0.960983i \(0.589210\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2670.00 0.585480
\(276\) 0 0
\(277\) −394.000 −0.0854627 −0.0427313 − 0.999087i \(-0.513606\pi\)
−0.0427313 + 0.999087i \(0.513606\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −396.000 −0.0840690 −0.0420345 − 0.999116i \(-0.513384\pi\)
−0.0420345 + 0.999116i \(0.513384\pi\)
\(282\) 0 0
\(283\) 1348.00 0.283146 0.141573 − 0.989928i \(-0.454784\pi\)
0.141573 + 0.989928i \(0.454784\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2646.00 0.544211
\(288\) 0 0
\(289\) −557.000 −0.113373
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7506.00 1.49660 0.748302 − 0.663358i \(-0.230869\pi\)
0.748302 + 0.663358i \(0.230869\pi\)
\(294\) 0 0
\(295\) 2088.00 0.412095
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −228.000 −0.0440989
\(300\) 0 0
\(301\) 1148.00 0.219833
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −636.000 −0.119401
\(306\) 0 0
\(307\) −1748.00 −0.324963 −0.162481 − 0.986712i \(-0.551950\pi\)
−0.162481 + 0.986712i \(0.551950\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1140.00 0.207857 0.103928 − 0.994585i \(-0.466859\pi\)
0.103928 + 0.994585i \(0.466859\pi\)
\(312\) 0 0
\(313\) 146.000 0.0263655 0.0131828 − 0.999913i \(-0.495804\pi\)
0.0131828 + 0.999913i \(0.495804\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8148.00 −1.44365 −0.721825 − 0.692075i \(-0.756697\pi\)
−0.721825 + 0.692075i \(0.756697\pi\)
\(318\) 0 0
\(319\) −2160.00 −0.379112
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3432.00 0.591212
\(324\) 0 0
\(325\) −178.000 −0.0303805
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1596.00 −0.267448
\(330\) 0 0
\(331\) 9700.00 1.61076 0.805378 − 0.592762i \(-0.201962\pi\)
0.805378 + 0.592762i \(0.201962\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3576.00 −0.583217
\(336\) 0 0
\(337\) 8174.00 1.32126 0.660632 − 0.750710i \(-0.270288\pi\)
0.660632 + 0.750710i \(0.270288\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5880.00 −0.933783
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4038.00 0.624701 0.312350 − 0.949967i \(-0.398884\pi\)
0.312350 + 0.949967i \(0.398884\pi\)
\(348\) 0 0
\(349\) 10766.0 1.65126 0.825631 − 0.564210i \(-0.190819\pi\)
0.825631 + 0.564210i \(0.190819\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3666.00 0.552752 0.276376 − 0.961050i \(-0.410866\pi\)
0.276376 + 0.961050i \(0.410866\pi\)
\(354\) 0 0
\(355\) −3780.00 −0.565131
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 5106.00 0.750653 0.375326 − 0.926893i \(-0.377531\pi\)
0.375326 + 0.926893i \(0.377531\pi\)
\(360\) 0 0
\(361\) −4155.00 −0.605773
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6252.00 −0.896561
\(366\) 0 0
\(367\) 5776.00 0.821539 0.410769 − 0.911739i \(-0.365260\pi\)
0.410769 + 0.911739i \(0.365260\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2436.00 0.340892
\(372\) 0 0
\(373\) 8462.00 1.17465 0.587327 − 0.809350i \(-0.300180\pi\)
0.587327 + 0.809350i \(0.300180\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 144.000 0.0196721
\(378\) 0 0
\(379\) −6860.00 −0.929748 −0.464874 − 0.885377i \(-0.653900\pi\)
−0.464874 + 0.885377i \(0.653900\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 696.000 0.0928562 0.0464281 − 0.998922i \(-0.485216\pi\)
0.0464281 + 0.998922i \(0.485216\pi\)
\(384\) 0 0
\(385\) 1260.00 0.166794
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11136.0 1.45146 0.725730 − 0.687980i \(-0.241502\pi\)
0.725730 + 0.687980i \(0.241502\pi\)
\(390\) 0 0
\(391\) −7524.00 −0.973159
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 528.000 0.0672571
\(396\) 0 0
\(397\) 10838.0 1.37014 0.685068 − 0.728480i \(-0.259773\pi\)
0.685068 + 0.728480i \(0.259773\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −8364.00 −1.04159 −0.520796 − 0.853681i \(-0.674365\pi\)
−0.520796 + 0.853681i \(0.674365\pi\)
\(402\) 0 0
\(403\) 392.000 0.0484539
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 8580.00 1.04495
\(408\) 0 0
\(409\) −1762.00 −0.213020 −0.106510 − 0.994312i \(-0.533968\pi\)
−0.106510 + 0.994312i \(0.533968\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2436.00 −0.290237
\(414\) 0 0
\(415\) 8640.00 1.02198
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −14580.0 −1.69995 −0.849976 − 0.526822i \(-0.823383\pi\)
−0.849976 + 0.526822i \(0.823383\pi\)
\(420\) 0 0
\(421\) 8534.00 0.987938 0.493969 − 0.869480i \(-0.335546\pi\)
0.493969 + 0.869480i \(0.335546\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5874.00 −0.670426
\(426\) 0 0
\(427\) 742.000 0.0840934
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5934.00 −0.663180 −0.331590 − 0.943424i \(-0.607585\pi\)
−0.331590 + 0.943424i \(0.607585\pi\)
\(432\) 0 0
\(433\) −14758.0 −1.63793 −0.818966 − 0.573843i \(-0.805452\pi\)
−0.818966 + 0.573843i \(0.805452\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5928.00 −0.648912
\(438\) 0 0
\(439\) 11392.0 1.23852 0.619260 − 0.785186i \(-0.287433\pi\)
0.619260 + 0.785186i \(0.287433\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −7026.00 −0.753533 −0.376767 − 0.926308i \(-0.622964\pi\)
−0.376767 + 0.926308i \(0.622964\pi\)
\(444\) 0 0
\(445\) 8244.00 0.878209
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3384.00 −0.355681 −0.177841 − 0.984059i \(-0.556911\pi\)
−0.177841 + 0.984059i \(0.556911\pi\)
\(450\) 0 0
\(451\) 11340.0 1.18399
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −84.0000 −0.00865490
\(456\) 0 0
\(457\) −4282.00 −0.438301 −0.219150 − 0.975691i \(-0.570329\pi\)
−0.219150 + 0.975691i \(0.570329\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 16650.0 1.68214 0.841071 − 0.540924i \(-0.181925\pi\)
0.841071 + 0.540924i \(0.181925\pi\)
\(462\) 0 0
\(463\) 9664.00 0.970031 0.485015 − 0.874506i \(-0.338814\pi\)
0.485015 + 0.874506i \(0.338814\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12324.0 1.22117 0.610585 − 0.791950i \(-0.290934\pi\)
0.610585 + 0.791950i \(0.290934\pi\)
\(468\) 0 0
\(469\) 4172.00 0.410757
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4920.00 0.478270
\(474\) 0 0
\(475\) −4628.00 −0.447047
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −18660.0 −1.77995 −0.889976 − 0.456007i \(-0.849279\pi\)
−0.889976 + 0.456007i \(0.849279\pi\)
\(480\) 0 0
\(481\) −572.000 −0.0542224
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −204.000 −0.0190993
\(486\) 0 0
\(487\) 3400.00 0.316363 0.158181 − 0.987410i \(-0.449437\pi\)
0.158181 + 0.987410i \(0.449437\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2970.00 −0.272982 −0.136491 − 0.990641i \(-0.543582\pi\)
−0.136491 + 0.990641i \(0.543582\pi\)
\(492\) 0 0
\(493\) 4752.00 0.434116
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4410.00 0.398019
\(498\) 0 0
\(499\) 988.000 0.0886352 0.0443176 − 0.999017i \(-0.485889\pi\)
0.0443176 + 0.999017i \(0.485889\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −5184.00 −0.459529 −0.229765 − 0.973246i \(-0.573796\pi\)
−0.229765 + 0.973246i \(0.573796\pi\)
\(504\) 0 0
\(505\) −2628.00 −0.231573
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 16854.0 1.46766 0.733831 − 0.679332i \(-0.237730\pi\)
0.733831 + 0.679332i \(0.237730\pi\)
\(510\) 0 0
\(511\) 7294.00 0.631443
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −10056.0 −0.860428
\(516\) 0 0
\(517\) −6840.00 −0.581862
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4398.00 −0.369827 −0.184914 − 0.982755i \(-0.559200\pi\)
−0.184914 + 0.982755i \(0.559200\pi\)
\(522\) 0 0
\(523\) 10672.0 0.892264 0.446132 − 0.894967i \(-0.352801\pi\)
0.446132 + 0.894967i \(0.352801\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12936.0 1.06926
\(528\) 0 0
\(529\) 829.000 0.0681351
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −756.000 −0.0614371
\(534\) 0 0
\(535\) −12132.0 −0.980396
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1470.00 −0.117472
\(540\) 0 0
\(541\) 20702.0 1.64519 0.822596 − 0.568627i \(-0.192525\pi\)
0.822596 + 0.568627i \(0.192525\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3012.00 −0.236734
\(546\) 0 0
\(547\) 22876.0 1.78813 0.894065 − 0.447937i \(-0.147841\pi\)
0.894065 + 0.447937i \(0.147841\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3744.00 0.289473
\(552\) 0 0
\(553\) −616.000 −0.0473689
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12876.0 −0.979486 −0.489743 − 0.871867i \(-0.662909\pi\)
−0.489743 + 0.871867i \(0.662909\pi\)
\(558\) 0 0
\(559\) −328.000 −0.0248174
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6900.00 0.516519 0.258260 − 0.966076i \(-0.416851\pi\)
0.258260 + 0.966076i \(0.416851\pi\)
\(564\) 0 0
\(565\) 12096.0 0.900677
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 14676.0 1.08128 0.540641 − 0.841253i \(-0.318182\pi\)
0.540641 + 0.841253i \(0.318182\pi\)
\(570\) 0 0
\(571\) −380.000 −0.0278503 −0.0139251 − 0.999903i \(-0.504433\pi\)
−0.0139251 + 0.999903i \(0.504433\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 10146.0 0.735856
\(576\) 0 0
\(577\) −11806.0 −0.851803 −0.425901 − 0.904770i \(-0.640043\pi\)
−0.425901 + 0.904770i \(0.640043\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −10080.0 −0.719774
\(582\) 0 0
\(583\) 10440.0 0.741648
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 19188.0 1.34919 0.674594 − 0.738189i \(-0.264319\pi\)
0.674594 + 0.738189i \(0.264319\pi\)
\(588\) 0 0
\(589\) 10192.0 0.712995
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 690.000 0.0477823 0.0238912 − 0.999715i \(-0.492394\pi\)
0.0238912 + 0.999715i \(0.492394\pi\)
\(594\) 0 0
\(595\) −2772.00 −0.190993
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 20490.0 1.39766 0.698830 − 0.715287i \(-0.253704\pi\)
0.698830 + 0.715287i \(0.253704\pi\)
\(600\) 0 0
\(601\) −11590.0 −0.786632 −0.393316 − 0.919403i \(-0.628672\pi\)
−0.393316 + 0.919403i \(0.628672\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2586.00 −0.173778
\(606\) 0 0
\(607\) 6424.00 0.429559 0.214779 − 0.976663i \(-0.431097\pi\)
0.214779 + 0.976663i \(0.431097\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 456.000 0.0301928
\(612\) 0 0
\(613\) −9682.00 −0.637932 −0.318966 − 0.947766i \(-0.603336\pi\)
−0.318966 + 0.947766i \(0.603336\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5076.00 0.331203 0.165601 − 0.986193i \(-0.447044\pi\)
0.165601 + 0.986193i \(0.447044\pi\)
\(618\) 0 0
\(619\) −22664.0 −1.47164 −0.735818 − 0.677179i \(-0.763202\pi\)
−0.735818 + 0.677179i \(0.763202\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −9618.00 −0.618519
\(624\) 0 0
\(625\) 3421.00 0.218944
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −18876.0 −1.19656
\(630\) 0 0
\(631\) 8584.00 0.541559 0.270779 − 0.962641i \(-0.412719\pi\)
0.270779 + 0.962641i \(0.412719\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −10704.0 −0.668937
\(636\) 0 0
\(637\) 98.0000 0.00609561
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 372.000 0.0229222 0.0114611 − 0.999934i \(-0.496352\pi\)
0.0114611 + 0.999934i \(0.496352\pi\)
\(642\) 0 0
\(643\) −3188.00 −0.195525 −0.0977624 − 0.995210i \(-0.531169\pi\)
−0.0977624 + 0.995210i \(0.531169\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12732.0 0.773642 0.386821 − 0.922155i \(-0.373573\pi\)
0.386821 + 0.922155i \(0.373573\pi\)
\(648\) 0 0
\(649\) −10440.0 −0.631442
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3576.00 −0.214303 −0.107151 − 0.994243i \(-0.534173\pi\)
−0.107151 + 0.994243i \(0.534173\pi\)
\(654\) 0 0
\(655\) −9648.00 −0.575540
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −11430.0 −0.675644 −0.337822 − 0.941210i \(-0.609690\pi\)
−0.337822 + 0.941210i \(0.609690\pi\)
\(660\) 0 0
\(661\) 22646.0 1.33257 0.666284 − 0.745698i \(-0.267884\pi\)
0.666284 + 0.745698i \(0.267884\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2184.00 −0.127356
\(666\) 0 0
\(667\) −8208.00 −0.476484
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3180.00 0.182955
\(672\) 0 0
\(673\) −13570.0 −0.777244 −0.388622 − 0.921397i \(-0.627049\pi\)
−0.388622 + 0.921397i \(0.627049\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2838.00 −0.161113 −0.0805563 − 0.996750i \(-0.525670\pi\)
−0.0805563 + 0.996750i \(0.525670\pi\)
\(678\) 0 0
\(679\) 238.000 0.0134515
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 6558.00 0.367401 0.183701 − 0.982982i \(-0.441192\pi\)
0.183701 + 0.982982i \(0.441192\pi\)
\(684\) 0 0
\(685\) −15480.0 −0.863446
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −696.000 −0.0384840
\(690\) 0 0
\(691\) 21832.0 1.20192 0.600961 − 0.799278i \(-0.294785\pi\)
0.600961 + 0.799278i \(0.294785\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −12864.0 −0.702100
\(696\) 0 0
\(697\) −24948.0 −1.35577
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 16200.0 0.872847 0.436423 − 0.899741i \(-0.356245\pi\)
0.436423 + 0.899741i \(0.356245\pi\)
\(702\) 0 0
\(703\) −14872.0 −0.797878
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3066.00 0.163096
\(708\) 0 0
\(709\) 36722.0 1.94517 0.972584 − 0.232553i \(-0.0747080\pi\)
0.972584 + 0.232553i \(0.0747080\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −22344.0 −1.17362
\(714\) 0 0
\(715\) −360.000 −0.0188297
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −13776.0 −0.714545 −0.357273 − 0.934000i \(-0.616293\pi\)
−0.357273 + 0.934000i \(0.616293\pi\)
\(720\) 0 0
\(721\) 11732.0 0.605995
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6408.00 −0.328258
\(726\) 0 0
\(727\) −34220.0 −1.74574 −0.872868 − 0.487957i \(-0.837742\pi\)
−0.872868 + 0.487957i \(0.837742\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −10824.0 −0.547661
\(732\) 0 0
\(733\) −13750.0 −0.692862 −0.346431 − 0.938075i \(-0.612607\pi\)
−0.346431 + 0.938075i \(0.612607\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 17880.0 0.893648
\(738\) 0 0
\(739\) −39836.0 −1.98294 −0.991469 − 0.130344i \(-0.958392\pi\)
−0.991469 + 0.130344i \(0.958392\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −34470.0 −1.70199 −0.850997 − 0.525170i \(-0.824002\pi\)
−0.850997 + 0.525170i \(0.824002\pi\)
\(744\) 0 0
\(745\) 9000.00 0.442597
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 14154.0 0.690489
\(750\) 0 0
\(751\) −5240.00 −0.254608 −0.127304 − 0.991864i \(-0.540632\pi\)
−0.127304 + 0.991864i \(0.540632\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 7440.00 0.358635
\(756\) 0 0
\(757\) 18578.0 0.891980 0.445990 − 0.895038i \(-0.352852\pi\)
0.445990 + 0.895038i \(0.352852\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 30534.0 1.45448 0.727238 − 0.686385i \(-0.240804\pi\)
0.727238 + 0.686385i \(0.240804\pi\)
\(762\) 0 0
\(763\) 3514.00 0.166730
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 696.000 0.0327655
\(768\) 0 0
\(769\) −39958.0 −1.87376 −0.936881 − 0.349650i \(-0.886301\pi\)
−0.936881 + 0.349650i \(0.886301\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3966.00 −0.184537 −0.0922685 − 0.995734i \(-0.529412\pi\)
−0.0922685 + 0.995734i \(0.529412\pi\)
\(774\) 0 0
\(775\) −17444.0 −0.808525
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −19656.0 −0.904043
\(780\) 0 0
\(781\) 18900.0 0.865935
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3684.00 0.167500
\(786\) 0 0
\(787\) 3760.00 0.170304 0.0851522 − 0.996368i \(-0.472862\pi\)
0.0851522 + 0.996368i \(0.472862\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −14112.0 −0.634343
\(792\) 0 0
\(793\) −212.000 −0.00949349
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −24102.0 −1.07119 −0.535594 − 0.844476i \(-0.679912\pi\)
−0.535594 + 0.844476i \(0.679912\pi\)
\(798\) 0 0
\(799\) 15048.0 0.666283
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 31260.0 1.37378
\(804\) 0 0
\(805\) 4788.00 0.209633
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 11712.0 0.508989 0.254494 − 0.967074i \(-0.418091\pi\)
0.254494 + 0.967074i \(0.418091\pi\)
\(810\) 0 0
\(811\) −37424.0 −1.62039 −0.810194 − 0.586162i \(-0.800638\pi\)
−0.810194 + 0.586162i \(0.800638\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −552.000 −0.0237248
\(816\) 0 0
\(817\) −8528.00 −0.365186
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 13452.0 0.571837 0.285918 − 0.958254i \(-0.407701\pi\)
0.285918 + 0.958254i \(0.407701\pi\)
\(822\) 0 0
\(823\) −20432.0 −0.865389 −0.432694 − 0.901541i \(-0.642437\pi\)
−0.432694 + 0.901541i \(0.642437\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −24390.0 −1.02554 −0.512771 − 0.858525i \(-0.671381\pi\)
−0.512771 + 0.858525i \(0.671381\pi\)
\(828\) 0 0
\(829\) −28510.0 −1.19444 −0.597221 − 0.802076i \(-0.703729\pi\)
−0.597221 + 0.802076i \(0.703729\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3234.00 0.134516
\(834\) 0 0
\(835\) 23544.0 0.975777
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 36972.0 1.52135 0.760677 − 0.649131i \(-0.224867\pi\)
0.760677 + 0.649131i \(0.224867\pi\)
\(840\) 0 0
\(841\) −19205.0 −0.787445
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −13158.0 −0.535679
\(846\) 0 0
\(847\) 3017.00 0.122391
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 32604.0 1.31334
\(852\) 0 0
\(853\) −14074.0 −0.564929 −0.282465 − 0.959278i \(-0.591152\pi\)
−0.282465 + 0.959278i \(0.591152\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −8826.00 −0.351797 −0.175899 − 0.984408i \(-0.556283\pi\)
−0.175899 + 0.984408i \(0.556283\pi\)
\(858\) 0 0
\(859\) 20500.0 0.814262 0.407131 − 0.913370i \(-0.366529\pi\)
0.407131 + 0.913370i \(0.366529\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −7674.00 −0.302695 −0.151348 − 0.988481i \(-0.548361\pi\)
−0.151348 + 0.988481i \(0.548361\pi\)
\(864\) 0 0
\(865\) −11412.0 −0.448578
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2640.00 −0.103056
\(870\) 0 0
\(871\) −1192.00 −0.0463713
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 8988.00 0.347257
\(876\) 0 0
\(877\) −8890.00 −0.342296 −0.171148 − 0.985245i \(-0.554748\pi\)
−0.171148 + 0.985245i \(0.554748\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 738.000 0.0282223 0.0141112 − 0.999900i \(-0.495508\pi\)
0.0141112 + 0.999900i \(0.495508\pi\)
\(882\) 0 0
\(883\) −20.0000 −0.000762235 0 −0.000381118 − 1.00000i \(-0.500121\pi\)
−0.000381118 1.00000i \(0.500121\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −39804.0 −1.50675 −0.753375 − 0.657591i \(-0.771576\pi\)
−0.753375 + 0.657591i \(0.771576\pi\)
\(888\) 0 0
\(889\) 12488.0 0.471129
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 11856.0 0.444284
\(894\) 0 0
\(895\) 36.0000 0.00134452
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 14112.0 0.523539
\(900\) 0 0
\(901\) −22968.0 −0.849251
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −17268.0 −0.634263
\(906\) 0 0
\(907\) −29180.0 −1.06825 −0.534127 − 0.845404i \(-0.679360\pi\)
−0.534127 + 0.845404i \(0.679360\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 48258.0 1.75506 0.877530 − 0.479523i \(-0.159190\pi\)
0.877530 + 0.479523i \(0.159190\pi\)
\(912\) 0 0
\(913\) −43200.0 −1.56595
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 11256.0 0.405350
\(918\) 0 0
\(919\) −25760.0 −0.924640 −0.462320 − 0.886713i \(-0.652983\pi\)
−0.462320 + 0.886713i \(0.652983\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1260.00 −0.0449333
\(924\) 0 0
\(925\) 25454.0 0.904781
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −44778.0 −1.58140 −0.790699 − 0.612205i \(-0.790283\pi\)
−0.790699 + 0.612205i \(0.790283\pi\)
\(930\) 0 0
\(931\) 2548.00 0.0896964
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −11880.0 −0.415527
\(936\) 0 0
\(937\) −44494.0 −1.55129 −0.775643 − 0.631171i \(-0.782574\pi\)
−0.775643 + 0.631171i \(0.782574\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −7458.00 −0.258368 −0.129184 − 0.991621i \(-0.541236\pi\)
−0.129184 + 0.991621i \(0.541236\pi\)
\(942\) 0 0
\(943\) 43092.0 1.48809
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −17790.0 −0.610451 −0.305226 − 0.952280i \(-0.598732\pi\)
−0.305226 + 0.952280i \(0.598732\pi\)
\(948\) 0 0
\(949\) −2084.00 −0.0712850
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −5832.00 −0.198234 −0.0991170 − 0.995076i \(-0.531602\pi\)
−0.0991170 + 0.995076i \(0.531602\pi\)
\(954\) 0 0
\(955\) 2124.00 0.0719697
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 18060.0 0.608121
\(960\) 0 0
\(961\) 8625.00 0.289517
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −29148.0 −0.972339
\(966\) 0 0
\(967\) 13264.0 0.441098 0.220549 − 0.975376i \(-0.429215\pi\)
0.220549 + 0.975376i \(0.429215\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −3984.00 −0.131671 −0.0658356 − 0.997830i \(-0.520971\pi\)
−0.0658356 + 0.997830i \(0.520971\pi\)
\(972\) 0 0
\(973\) 15008.0 0.494485
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −38940.0 −1.27513 −0.637564 − 0.770397i \(-0.720058\pi\)
−0.637564 + 0.770397i \(0.720058\pi\)
\(978\) 0 0
\(979\) −41220.0 −1.34566
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 8808.00 0.285790 0.142895 − 0.989738i \(-0.454359\pi\)
0.142895 + 0.989738i \(0.454359\pi\)
\(984\) 0 0
\(985\) −2376.00 −0.0768585
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 18696.0 0.601110
\(990\) 0 0
\(991\) −18488.0 −0.592624 −0.296312 − 0.955091i \(-0.595757\pi\)
−0.296312 + 0.955091i \(0.595757\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −10272.0 −0.327281
\(996\) 0 0
\(997\) −5002.00 −0.158892 −0.0794458 − 0.996839i \(-0.525315\pi\)
−0.0794458 + 0.996839i \(0.525315\pi\)
\(998\) 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 1008.4.a.n.1.1 1
3.2 odd 2 1008.4.a.g.1.1 1
4.3 odd 2 126.4.a.g.1.1 yes 1
12.11 even 2 126.4.a.b.1.1 ✓ 1
28.3 even 6 882.4.g.h.667.1 2
28.11 odd 6 882.4.g.e.667.1 2
28.19 even 6 882.4.g.h.361.1 2
28.23 odd 6 882.4.g.e.361.1 2
28.27 even 2 882.4.a.m.1.1 1
84.11 even 6 882.4.g.t.667.1 2
84.23 even 6 882.4.g.t.361.1 2
84.47 odd 6 882.4.g.q.361.1 2
84.59 odd 6 882.4.g.q.667.1 2
84.83 odd 2 882.4.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.4.a.b.1.1 ✓ 1 12.11 even 2
126.4.a.g.1.1 yes 1 4.3 odd 2
882.4.a.e.1.1 1 84.83 odd 2
882.4.a.m.1.1 1 28.27 even 2
882.4.g.e.361.1 2 28.23 odd 6
882.4.g.e.667.1 2 28.11 odd 6
882.4.g.h.361.1 2 28.19 even 6
882.4.g.h.667.1 2 28.3 even 6
882.4.g.q.361.1 2 84.47 odd 6
882.4.g.q.667.1 2 84.59 odd 6
882.4.g.t.361.1 2 84.23 even 6
882.4.g.t.667.1 2 84.11 even 6
1008.4.a.g.1.1 1 3.2 odd 2
1008.4.a.n.1.1 1 1.1 even 1 trivial