Properties

Label 3528.2.a.a.1.1
Level $3528$
Weight $2$
Character 3528.1
Self dual yes
Analytic conductor $28.171$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3528,2,Mod(1,3528)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3528, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3528.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.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: \(28.1712218331\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 504)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 3528.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000 q^{5} +O(q^{10})\) \(q-4.00000 q^{5} -3.00000 q^{13} +4.00000 q^{17} +7.00000 q^{19} -4.00000 q^{23} +11.0000 q^{25} +8.00000 q^{29} -5.00000 q^{31} +3.00000 q^{37} -8.00000 q^{41} +11.0000 q^{43} -4.00000 q^{47} -4.00000 q^{53} -12.0000 q^{59} -2.00000 q^{61} +12.0000 q^{65} -3.00000 q^{67} -12.0000 q^{71} +1.00000 q^{73} +1.00000 q^{79} -12.0000 q^{83} -16.0000 q^{85} -8.00000 q^{89} -28.0000 q^{95} -2.00000 q^{97} +O(q^{100})\)

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
\(5\) −4.00000 −1.78885 −0.894427 0.447214i \(-0.852416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) 7.00000 1.60591 0.802955 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 11.0000 1.67748 0.838742 0.544529i \(-0.183292\pi\)
0.838742 + 0.544529i \(0.183292\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −12.0000 −1.56227 −0.781133 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 12.0000 1.48842
\(66\) 0 0
\(67\) −3.00000 −0.366508 −0.183254 0.983066i \(-0.558663\pi\)
−0.183254 + 0.983066i \(0.558663\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 1.00000 0.117041 0.0585206 0.998286i \(-0.481362\pi\)
0.0585206 + 0.998286i \(0.481362\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.00000 0.112509 0.0562544 0.998416i \(-0.482084\pi\)
0.0562544 + 0.998416i \(0.482084\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) −16.0000 −1.73544
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −8.00000 −0.847998 −0.423999 0.905663i \(-0.639374\pi\)
−0.423999 + 0.905663i \(0.639374\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −28.0000 −2.87274
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 3.00000 0.295599 0.147799 0.989017i \(-0.452781\pi\)
0.147799 + 0.989017i \(0.452781\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −11.0000 −1.05361 −0.526804 0.849987i \(-0.676610\pi\)
−0.526804 + 0.849987i \(0.676610\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 0 0
\(115\) 16.0000 1.49201
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −16.0000 −1.36697 −0.683486 0.729964i \(-0.739537\pi\)
−0.683486 + 0.729964i \(0.739537\pi\)
\(138\) 0 0
\(139\) 15.0000 1.27228 0.636142 0.771572i \(-0.280529\pi\)
0.636142 + 0.771572i \(0.280529\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −32.0000 −2.65746
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 16.0000 1.31077 0.655386 0.755295i \(-0.272506\pi\)
0.655386 + 0.755295i \(0.272506\pi\)
\(150\) 0 0
\(151\) −20.0000 −1.62758 −0.813788 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 20.0000 1.60644
\(156\) 0 0
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −8.00000 −0.626608 −0.313304 0.949653i \(-0.601436\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4.00000 −0.304114 −0.152057 0.988372i \(-0.548590\pi\)
−0.152057 + 0.988372i \(0.548590\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 20.0000 1.49487 0.747435 0.664335i \(-0.231285\pi\)
0.747435 + 0.664335i \(0.231285\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −12.0000 −0.882258
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4.00000 0.289430 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) 0 0
\(193\) −9.00000 −0.647834 −0.323917 0.946085i \(-0.605000\pi\)
−0.323917 + 0.946085i \(0.605000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 32.0000 2.23498
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −44.0000 −3.00078
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) 0 0
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 8.00000 0.530979 0.265489 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) 0 0
\(229\) 5.00000 0.330409 0.165205 0.986259i \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −28.0000 −1.83434 −0.917170 0.398495i \(-0.869533\pi\)
−0.917170 + 0.398495i \(0.869533\pi\)
\(234\) 0 0
\(235\) 16.0000 1.04372
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 0 0
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −21.0000 −1.33620
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −12.0000 −0.748539 −0.374270 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 0 0
\(265\) 16.0000 0.982872
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 13.0000 0.781094 0.390547 0.920583i \(-0.372286\pi\)
0.390547 + 0.920583i \(0.372286\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 0 0
\(283\) −1.00000 −0.0594438 −0.0297219 0.999558i \(-0.509462\pi\)
−0.0297219 + 0.999558i \(0.509462\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) 48.0000 2.79467
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 12.0000 0.693978
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8.00000 0.458079
\(306\) 0 0
\(307\) −11.0000 −0.627803 −0.313902 0.949456i \(-0.601636\pi\)
−0.313902 + 0.949456i \(0.601636\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) −13.0000 −0.734803 −0.367402 0.930062i \(-0.619753\pi\)
−0.367402 + 0.930062i \(0.619753\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −24.0000 −1.34797 −0.673987 0.738743i \(-0.735420\pi\)
−0.673987 + 0.738743i \(0.735420\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 28.0000 1.55796
\(324\) 0 0
\(325\) −33.0000 −1.83051
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −7.00000 −0.384755 −0.192377 0.981321i \(-0.561620\pi\)
−0.192377 + 0.981321i \(0.561620\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 12.0000 0.655630
\(336\) 0 0
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −12.0000 −0.638696 −0.319348 0.947638i \(-0.603464\pi\)
−0.319348 + 0.947638i \(0.603464\pi\)
\(354\) 0 0
\(355\) 48.0000 2.54758
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4.00000 −0.209370
\(366\) 0 0
\(367\) 17.0000 0.887393 0.443696 0.896177i \(-0.353667\pi\)
0.443696 + 0.896177i \(0.353667\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −1.00000 −0.0517780 −0.0258890 0.999665i \(-0.508242\pi\)
−0.0258890 + 0.999665i \(0.508242\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −24.0000 −1.23606
\(378\) 0 0
\(379\) 21.0000 1.07870 0.539349 0.842082i \(-0.318670\pi\)
0.539349 + 0.842082i \(0.318670\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −12.0000 −0.613171 −0.306586 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4.00000 0.202808 0.101404 0.994845i \(-0.467667\pi\)
0.101404 + 0.994845i \(0.467667\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.00000 −0.201262
\(396\) 0 0
\(397\) 7.00000 0.351320 0.175660 0.984451i \(-0.443794\pi\)
0.175660 + 0.984451i \(0.443794\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 36.0000 1.79775 0.898877 0.438201i \(-0.144384\pi\)
0.898877 + 0.438201i \(0.144384\pi\)
\(402\) 0 0
\(403\) 15.0000 0.747203
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −15.0000 −0.741702 −0.370851 0.928692i \(-0.620934\pi\)
−0.370851 + 0.928692i \(0.620934\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 48.0000 2.35623
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −16.0000 −0.781651 −0.390826 0.920465i \(-0.627810\pi\)
−0.390826 + 0.920465i \(0.627810\pi\)
\(420\) 0 0
\(421\) 1.00000 0.0487370 0.0243685 0.999703i \(-0.492242\pi\)
0.0243685 + 0.999703i \(0.492242\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 44.0000 2.13431
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 0 0
\(433\) −5.00000 −0.240285 −0.120142 0.992757i \(-0.538335\pi\)
−0.120142 + 0.992757i \(0.538335\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −28.0000 −1.33942
\(438\) 0 0
\(439\) −12.0000 −0.572729 −0.286364 0.958121i \(-0.592447\pi\)
−0.286364 + 0.958121i \(0.592447\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 0 0
\(445\) 32.0000 1.51695
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −20.0000 −0.943858 −0.471929 0.881636i \(-0.656442\pi\)
−0.471929 + 0.881636i \(0.656442\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.00000 0.0467780 0.0233890 0.999726i \(-0.492554\pi\)
0.0233890 + 0.999726i \(0.492554\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 5.00000 0.232370 0.116185 0.993228i \(-0.462933\pi\)
0.116185 + 0.993228i \(0.462933\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 77.0000 3.53300
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4.00000 0.182765 0.0913823 0.995816i \(-0.470871\pi\)
0.0913823 + 0.995816i \(0.470871\pi\)
\(480\) 0 0
\(481\) −9.00000 −0.410365
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.00000 0.363261
\(486\) 0 0
\(487\) −35.0000 −1.58600 −0.793001 0.609221i \(-0.791482\pi\)
−0.793001 + 0.609221i \(0.791482\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) 32.0000 1.44121
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −29.0000 −1.29822 −0.649109 0.760695i \(-0.724858\pi\)
−0.649109 + 0.760695i \(0.724858\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 40.0000 1.78351 0.891756 0.452517i \(-0.149474\pi\)
0.891756 + 0.452517i \(0.149474\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 12.0000 0.531891 0.265945 0.963988i \(-0.414316\pi\)
0.265945 + 0.963988i \(0.414316\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −12.0000 −0.528783
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 24.0000 1.05146 0.525730 0.850652i \(-0.323792\pi\)
0.525730 + 0.850652i \(0.323792\pi\)
\(522\) 0 0
\(523\) 29.0000 1.26808 0.634041 0.773300i \(-0.281395\pi\)
0.634041 + 0.773300i \(0.281395\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −20.0000 −0.871214
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 24.0000 1.03956
\(534\) 0 0
\(535\) −48.0000 −2.07522
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −23.0000 −0.988847 −0.494424 0.869221i \(-0.664621\pi\)
−0.494424 + 0.869221i \(0.664621\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 44.0000 1.88475
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 56.0000 2.38568
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.00000 −0.338971 −0.169485 0.985533i \(-0.554211\pi\)
−0.169485 + 0.985533i \(0.554211\pi\)
\(558\) 0 0
\(559\) −33.0000 −1.39575
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −20.0000 −0.842900 −0.421450 0.906852i \(-0.638479\pi\)
−0.421450 + 0.906852i \(0.638479\pi\)
\(564\) 0 0
\(565\) −48.0000 −2.01938
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) −25.0000 −1.04622 −0.523109 0.852266i \(-0.675228\pi\)
−0.523109 + 0.852266i \(0.675228\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −44.0000 −1.83493
\(576\) 0 0
\(577\) 27.0000 1.12402 0.562012 0.827129i \(-0.310027\pi\)
0.562012 + 0.827129i \(0.310027\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 16.0000 0.660391 0.330195 0.943913i \(-0.392885\pi\)
0.330195 + 0.943913i \(0.392885\pi\)
\(588\) 0 0
\(589\) −35.0000 −1.44215
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −24.0000 −0.985562 −0.492781 0.870153i \(-0.664020\pi\)
−0.492781 + 0.870153i \(0.664020\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) −41.0000 −1.67242 −0.836212 0.548406i \(-0.815235\pi\)
−0.836212 + 0.548406i \(0.815235\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 44.0000 1.78885
\(606\) 0 0
\(607\) −35.0000 −1.42061 −0.710303 0.703896i \(-0.751442\pi\)
−0.710303 + 0.703896i \(0.751442\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) 0 0
\(613\) −26.0000 −1.05013 −0.525065 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 9.00000 0.361741 0.180870 0.983507i \(-0.442109\pi\)
0.180870 + 0.983507i \(0.442109\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −4.00000 −0.159237 −0.0796187 0.996825i \(-0.525370\pi\)
−0.0796187 + 0.996825i \(0.525370\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.00000 0.158735
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 28.0000 1.10593 0.552967 0.833203i \(-0.313496\pi\)
0.552967 + 0.833203i \(0.313496\pi\)
\(642\) 0 0
\(643\) 7.00000 0.276053 0.138027 0.990429i \(-0.455924\pi\)
0.138027 + 0.990429i \(0.455924\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −48.0000 −1.88707 −0.943537 0.331266i \(-0.892524\pi\)
−0.943537 + 0.331266i \(0.892524\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −16.0000 −0.626128 −0.313064 0.949732i \(-0.601356\pi\)
−0.313064 + 0.949732i \(0.601356\pi\)
\(654\) 0 0
\(655\) −32.0000 −1.25034
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.00000 −0.155818 −0.0779089 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 0 0
\(661\) 35.0000 1.36134 0.680671 0.732589i \(-0.261688\pi\)
0.680671 + 0.732589i \(0.261688\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −32.0000 −1.23904
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −29.0000 −1.11787 −0.558934 0.829212i \(-0.688789\pi\)
−0.558934 + 0.829212i \(0.688789\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 64.0000 2.44531
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) 17.0000 0.646710 0.323355 0.946278i \(-0.395189\pi\)
0.323355 + 0.946278i \(0.395189\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −60.0000 −2.27593
\(696\) 0 0
\(697\) −32.0000 −1.21209
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −20.0000 −0.755390 −0.377695 0.925930i \(-0.623283\pi\)
−0.377695 + 0.925930i \(0.623283\pi\)
\(702\) 0 0
\(703\) 21.0000 0.792030
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −38.0000 −1.42712 −0.713560 0.700594i \(-0.752918\pi\)
−0.713560 + 0.700594i \(0.752918\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 20.0000 0.749006
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 88.0000 3.26824
\(726\) 0 0
\(727\) 5.00000 0.185440 0.0927199 0.995692i \(-0.470444\pi\)
0.0927199 + 0.995692i \(0.470444\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 44.0000 1.62740
\(732\) 0 0
\(733\) −35.0000 −1.29275 −0.646377 0.763018i \(-0.723717\pi\)
−0.646377 + 0.763018i \(0.723717\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 19.0000 0.698926 0.349463 0.936950i \(-0.386364\pi\)
0.349463 + 0.936950i \(0.386364\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 8.00000 0.293492 0.146746 0.989174i \(-0.453120\pi\)
0.146746 + 0.989174i \(0.453120\pi\)
\(744\) 0 0
\(745\) −64.0000 −2.34478
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 11.0000 0.401396 0.200698 0.979653i \(-0.435679\pi\)
0.200698 + 0.979653i \(0.435679\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 80.0000 2.91150
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −12.0000 −0.435000 −0.217500 0.976060i \(-0.569790\pi\)
−0.217500 + 0.976060i \(0.569790\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 36.0000 1.29988
\(768\) 0 0
\(769\) 31.0000 1.11789 0.558944 0.829205i \(-0.311207\pi\)
0.558944 + 0.829205i \(0.311207\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −8.00000 −0.287740 −0.143870 0.989597i \(-0.545955\pi\)
−0.143870 + 0.989597i \(0.545955\pi\)
\(774\) 0 0
\(775\) −55.0000 −1.97566
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −56.0000 −2.00641
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 72.0000 2.56979
\(786\) 0 0
\(787\) 40.0000 1.42585 0.712923 0.701242i \(-0.247371\pi\)
0.712923 + 0.701242i \(0.247371\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6.00000 0.213066
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 0 0
\(799\) −16.0000 −0.566039
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −12.0000 −0.421898 −0.210949 0.977497i \(-0.567655\pi\)
−0.210949 + 0.977497i \(0.567655\pi\)
\(810\) 0 0
\(811\) 24.0000 0.842754 0.421377 0.906886i \(-0.361547\pi\)
0.421377 + 0.906886i \(0.361547\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 32.0000 1.12091
\(816\) 0 0
\(817\) 77.0000 2.69389
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 36.0000 1.25641 0.628204 0.778048i \(-0.283790\pi\)
0.628204 + 0.778048i \(0.283790\pi\)
\(822\) 0 0
\(823\) −4.00000 −0.139431 −0.0697156 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −36.0000 −1.25184 −0.625921 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) 0 0
\(829\) −19.0000 −0.659897 −0.329949 0.943999i \(-0.607031\pi\)
−0.329949 + 0.943999i \(0.607031\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 48.0000 1.66111
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 16.0000 0.550417
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −12.0000 −0.411355
\(852\) 0 0
\(853\) −17.0000 −0.582069 −0.291034 0.956713i \(-0.593999\pi\)
−0.291034 + 0.956713i \(0.593999\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 48.0000 1.63965 0.819824 0.572615i \(-0.194071\pi\)
0.819824 + 0.572615i \(0.194071\pi\)
\(858\) 0 0
\(859\) −8.00000 −0.272956 −0.136478 0.990643i \(-0.543578\pi\)
−0.136478 + 0.990643i \(0.543578\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 8.00000 0.272323 0.136162 0.990687i \(-0.456523\pi\)
0.136162 + 0.990687i \(0.456523\pi\)
\(864\) 0 0
\(865\) 16.0000 0.544016
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 9.00000 0.304953
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 14.0000 0.472746 0.236373 0.971662i \(-0.424041\pi\)
0.236373 + 0.971662i \(0.424041\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 28.0000 0.943344 0.471672 0.881774i \(-0.343651\pi\)
0.471672 + 0.881774i \(0.343651\pi\)
\(882\) 0 0
\(883\) −47.0000 −1.58168 −0.790838 0.612026i \(-0.790355\pi\)
−0.790838 + 0.612026i \(0.790355\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 24.0000 0.805841 0.402921 0.915235i \(-0.367995\pi\)
0.402921 + 0.915235i \(0.367995\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −28.0000 −0.936984
\(894\) 0 0
\(895\) −80.0000 −2.67411
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −40.0000 −1.33407
\(900\) 0 0
\(901\) −16.0000 −0.533037
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −20.0000 −0.664822
\(906\) 0 0
\(907\) 53.0000 1.75984 0.879918 0.475125i \(-0.157597\pi\)
0.879918 + 0.475125i \(0.157597\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 4.00000 0.132526 0.0662630 0.997802i \(-0.478892\pi\)
0.0662630 + 0.997802i \(0.478892\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −11.0000 −0.362857 −0.181428 0.983404i \(-0.558072\pi\)
−0.181428 + 0.983404i \(0.558072\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 36.0000 1.18495
\(924\) 0 0
\(925\) 33.0000 1.08503
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 28.0000 0.918650 0.459325 0.888268i \(-0.348091\pi\)
0.459325 + 0.888268i \(0.348091\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −45.0000 −1.47009 −0.735043 0.678021i \(-0.762838\pi\)
−0.735043 + 0.678021i \(0.762838\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 36.0000 1.17357 0.586783 0.809744i \(-0.300394\pi\)
0.586783 + 0.809744i \(0.300394\pi\)
\(942\) 0 0
\(943\) 32.0000 1.04206
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −8.00000 −0.259965 −0.129983 0.991516i \(-0.541492\pi\)
−0.129983 + 0.991516i \(0.541492\pi\)
\(948\) 0 0
\(949\) −3.00000 −0.0973841
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −20.0000 −0.647864 −0.323932 0.946080i \(-0.605005\pi\)
−0.323932 + 0.946080i \(0.605005\pi\)
\(954\) 0 0
\(955\) −16.0000 −0.517748
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −6.00000 −0.193548
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 36.0000 1.15888
\(966\) 0 0
\(967\) 57.0000 1.83300 0.916498 0.400039i \(-0.131003\pi\)
0.916498 + 0.400039i \(0.131003\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −20.0000 −0.641831 −0.320915 0.947108i \(-0.603990\pi\)
−0.320915 + 0.947108i \(0.603990\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 48.0000 1.53566 0.767828 0.640656i \(-0.221338\pi\)
0.767828 + 0.640656i \(0.221338\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −12.0000 −0.382741 −0.191370 0.981518i \(-0.561293\pi\)
−0.191370 + 0.981518i \(0.561293\pi\)
\(984\) 0 0
\(985\) 48.0000 1.52941
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −44.0000 −1.39912
\(990\) 0 0
\(991\) 3.00000 0.0952981 0.0476491 0.998864i \(-0.484827\pi\)
0.0476491 + 0.998864i \(0.484827\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −80.0000 −2.53617
\(996\) 0 0
\(997\) −29.0000 −0.918439 −0.459220 0.888323i \(-0.651871\pi\)
−0.459220 + 0.888323i \(0.651871\pi\)
\(998\) 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 3528.2.a.a.1.1 1
3.2 odd 2 3528.2.a.z.1.1 1
4.3 odd 2 7056.2.a.b.1.1 1
7.2 even 3 504.2.s.h.361.1 yes 2
7.3 odd 6 3528.2.s.b.3313.1 2
7.4 even 3 504.2.s.h.289.1 yes 2
7.5 odd 6 3528.2.s.b.361.1 2
7.6 odd 2 3528.2.a.ba.1.1 1
12.11 even 2 7056.2.a.cb.1.1 1
21.2 odd 6 504.2.s.a.361.1 yes 2
21.5 even 6 3528.2.s.bb.361.1 2
21.11 odd 6 504.2.s.a.289.1 2
21.17 even 6 3528.2.s.bb.3313.1 2
21.20 even 2 3528.2.a.c.1.1 1
28.11 odd 6 1008.2.s.q.289.1 2
28.23 odd 6 1008.2.s.q.865.1 2
28.27 even 2 7056.2.a.cc.1.1 1
84.11 even 6 1008.2.s.a.289.1 2
84.23 even 6 1008.2.s.a.865.1 2
84.83 odd 2 7056.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.s.a.289.1 2 21.11 odd 6
504.2.s.a.361.1 yes 2 21.2 odd 6
504.2.s.h.289.1 yes 2 7.4 even 3
504.2.s.h.361.1 yes 2 7.2 even 3
1008.2.s.a.289.1 2 84.11 even 6
1008.2.s.a.865.1 2 84.23 even 6
1008.2.s.q.289.1 2 28.11 odd 6
1008.2.s.q.865.1 2 28.23 odd 6
3528.2.a.a.1.1 1 1.1 even 1 trivial
3528.2.a.c.1.1 1 21.20 even 2
3528.2.a.z.1.1 1 3.2 odd 2
3528.2.a.ba.1.1 1 7.6 odd 2
3528.2.s.b.361.1 2 7.5 odd 6
3528.2.s.b.3313.1 2 7.3 odd 6
3528.2.s.bb.361.1 2 21.5 even 6
3528.2.s.bb.3313.1 2 21.17 even 6
7056.2.a.b.1.1 1 4.3 odd 2
7056.2.a.d.1.1 1 84.83 odd 2
7056.2.a.cb.1.1 1 12.11 even 2
7056.2.a.cc.1.1 1 28.27 even 2