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Properties

Label 1264.2.a.f.1.1
Level $1264$
Weight $2$
Character 1264.1
Self dual yes
Analytic conductor $10.093$
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] = [1264,2,Mod(1,1264)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1264, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1264.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1264 = 2^{4} \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1264.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: \(10.0930908155\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 158)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1264.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} +1.00000 q^{5} -3.00000 q^{7} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +1.00000 q^{5} -3.00000 q^{7} -2.00000 q^{9} -2.00000 q^{11} -1.00000 q^{13} +1.00000 q^{15} -2.00000 q^{17} -3.00000 q^{21} +6.00000 q^{23} -4.00000 q^{25} -5.00000 q^{27} -10.0000 q^{29} -2.00000 q^{31} -2.00000 q^{33} -3.00000 q^{35} -2.00000 q^{37} -1.00000 q^{39} +2.00000 q^{41} -4.00000 q^{43} -2.00000 q^{45} -3.00000 q^{47} +2.00000 q^{49} -2.00000 q^{51} +4.00000 q^{53} -2.00000 q^{55} -5.00000 q^{59} +12.0000 q^{61} +6.00000 q^{63} -1.00000 q^{65} -8.00000 q^{67} +6.00000 q^{69} +13.0000 q^{71} -6.00000 q^{73} -4.00000 q^{75} +6.00000 q^{77} +1.00000 q^{79} +1.00000 q^{81} +6.00000 q^{83} -2.00000 q^{85} -10.0000 q^{87} -15.0000 q^{89} +3.00000 q^{91} -2.00000 q^{93} +13.0000 q^{97} +4.00000 q^{99} +O(q^{100})\)

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
\(3\) 1.00000 0.577350 0.288675 − 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214 0.223607 − 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 0 0
\(7\) −3.00000 −1.13389 −0.566947 − 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 − 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 − 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 − 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) −3.00000 −0.654654
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 − 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) −10.0000 −1.85695 −0.928477 − 0.371391i \(-0.878881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 − 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0 0
\(33\) −2.00000 −0.348155
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 − 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 − 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 − 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) −2.00000 −0.298142
\(46\) 0 0
\(47\) −3.00000 −0.437595 −0.218797 − 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) 0 0
\(51\) −2.00000 −0.280056
\(52\) 0 0
\(53\) 4.00000 0.549442 0.274721 − 0.961524i \(-0.411414\pi\)
0.274721 + 0.961524i \(0.411414\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.00000 −0.650945 −0.325472 − 0.945552i \(-0.605523\pi\)
−0.325472 + 0.945552i \(0.605523\pi\)
\(60\) 0 0
\(61\) 12.0000 1.53644 0.768221 − 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 0 0
\(63\) 6.00000 0.755929
\(64\) 0 0
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) −8.00000 −0.977356 −0.488678 − 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 13.0000 1.54282 0.771408 − 0.636341i \(-0.219553\pi\)
0.771408 + 0.636341i \(0.219553\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 − 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 0 0
\(75\) −4.00000 −0.461880
\(76\) 0 0
\(77\) 6.00000 0.683763
\(78\) 0 0
\(79\) 1.00000 0.112509
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 6.00000 0.658586 0.329293 − 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) 0 0
\(87\) −10.0000 −1.07211
\(88\) 0 0
\(89\) −15.0000 −1.59000 −0.794998 − 0.606612i \(-0.792528\pi\)
−0.794998 + 0.606612i \(0.792528\pi\)
\(90\) 0 0
\(91\) 3.00000 0.314485
\(92\) 0 0
\(93\) −2.00000 −0.207390
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 13.0000 1.31995 0.659975 − 0.751288i \(-0.270567\pi\)
0.659975 + 0.751288i \(0.270567\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) 7.00000 0.696526 0.348263 − 0.937397i \(-0.386772\pi\)
0.348263 + 0.937397i \(0.386772\pi\)
\(102\) 0 0
\(103\) −19.0000 −1.87213 −0.936063 − 0.351833i \(-0.885559\pi\)
−0.936063 + 0.351833i \(0.885559\pi\)
\(104\) 0 0
\(105\) −3.00000 −0.292770
\(106\) 0 0
\(107\) −13.0000 −1.25676 −0.628379 − 0.777908i \(-0.716281\pi\)
−0.628379 + 0.777908i \(0.716281\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 − 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) −2.00000 −0.189832
\(112\) 0 0
\(113\) 4.00000 0.376288 0.188144 − 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) 0 0
\(115\) 6.00000 0.559503
\(116\) 0 0
\(117\) 2.00000 0.184900
\(118\) 0 0
\(119\) 6.00000 0.550019
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 2.00000 0.180334
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 7.00000 0.621150 0.310575 − 0.950549i \(-0.399478\pi\)
0.310575 + 0.950549i \(0.399478\pi\)
\(128\) 0 0
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) 18.0000 1.57267 0.786334 − 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −5.00000 −0.430331
\(136\) 0 0
\(137\) −12.0000 −1.02523 −0.512615 − 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 0 0
\(139\) 5.00000 0.424094 0.212047 − 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 0 0
\(143\) 2.00000 0.167248
\(144\) 0 0
\(145\) −10.0000 −0.830455
\(146\) 0 0
\(147\) 2.00000 0.164957
\(148\) 0 0
\(149\) −10.0000 −0.819232 −0.409616 − 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 0 0
\(151\) −2.00000 −0.162758 −0.0813788 − 0.996683i \(-0.525932\pi\)
−0.0813788 + 0.996683i \(0.525932\pi\)
\(152\) 0 0
\(153\) 4.00000 0.323381
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) 0 0
\(157\) 18.0000 1.43656 0.718278 − 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) 0 0
\(159\) 4.00000 0.317221
\(160\) 0 0
\(161\) −18.0000 −1.41860
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 − 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) −2.00000 −0.155700
\(166\) 0 0
\(167\) 2.00000 0.154765 0.0773823 − 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.00000 0.304114 0.152057 − 0.988372i \(-0.451410\pi\)
0.152057 + 0.988372i \(0.451410\pi\)
\(174\) 0 0
\(175\) 12.0000 0.907115
\(176\) 0 0
\(177\) −5.00000 −0.375823
\(178\) 0 0
\(179\) −20.0000 −1.49487 −0.747435 − 0.664335i \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) 0 0
\(181\) −18.0000 −1.33793 −0.668965 − 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 0 0
\(183\) 12.0000 0.887066
\(184\) 0 0
\(185\) −2.00000 −0.147043
\(186\) 0 0
\(187\) 4.00000 0.292509
\(188\) 0 0
\(189\) 15.0000 1.09109
\(190\) 0 0
\(191\) 3.00000 0.217072 0.108536 − 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 − 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 0 0
\(195\) −1.00000 −0.0716115
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 − 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −15.0000 −1.06332 −0.531661 − 0.846957i \(-0.678432\pi\)
−0.531661 + 0.846957i \(0.678432\pi\)
\(200\) 0 0
\(201\) −8.00000 −0.564276
\(202\) 0 0
\(203\) 30.0000 2.10559
\(204\) 0 0
\(205\) 2.00000 0.139686
\(206\) 0 0
\(207\) −12.0000 −0.834058
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 28.0000 1.92760 0.963800 − 0.266627i \(-0.0859092\pi\)
0.963800 + 0.266627i \(0.0859092\pi\)
\(212\) 0 0
\(213\) 13.0000 0.890745
\(214\) 0 0
\(215\) −4.00000 −0.272798
\(216\) 0 0
\(217\) 6.00000 0.407307
\(218\) 0 0
\(219\) −6.00000 −0.405442
\(220\) 0 0
\(221\) 2.00000 0.134535
\(222\) 0 0
\(223\) −14.0000 −0.937509 −0.468755 − 0.883328i \(-0.655297\pi\)
−0.468755 + 0.883328i \(0.655297\pi\)
\(224\) 0 0
\(225\) 8.00000 0.533333
\(226\) 0 0
\(227\) −8.00000 −0.530979 −0.265489 − 0.964114i \(-0.585534\pi\)
−0.265489 + 0.964114i \(0.585534\pi\)
\(228\) 0 0
\(229\) 20.0000 1.32164 0.660819 − 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) 0 0
\(231\) 6.00000 0.394771
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 − 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −3.00000 −0.195698
\(236\) 0 0
\(237\) 1.00000 0.0649570
\(238\) 0 0
\(239\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 17.0000 1.09507 0.547533 − 0.836784i \(-0.315567\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 0 0
\(243\) 16.0000 1.02640
\(244\) 0 0
\(245\) 2.00000 0.127775
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 6.00000 0.380235
\(250\) 0 0
\(251\) −27.0000 −1.70422 −0.852112 − 0.523359i \(-0.824679\pi\)
−0.852112 + 0.523359i \(0.824679\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) −2.00000 −0.125245
\(256\) 0 0
\(257\) −2.00000 −0.124757 −0.0623783 − 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 0 0
\(259\) 6.00000 0.372822
\(260\) 0 0
\(261\) 20.0000 1.23797
\(262\) 0 0
\(263\) 6.00000 0.369976 0.184988 − 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 0 0
\(267\) −15.0000 −0.917985
\(268\) 0 0
\(269\) 25.0000 1.52428 0.762138 − 0.647414i \(-0.224150\pi\)
0.762138 + 0.647414i \(0.224150\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 − 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 0 0
\(273\) 3.00000 0.181568
\(274\) 0 0
\(275\) 8.00000 0.482418
\(276\) 0 0
\(277\) −17.0000 −1.02143 −0.510716 − 0.859750i \(-0.670619\pi\)
−0.510716 + 0.859750i \(0.670619\pi\)
\(278\) 0 0
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) −33.0000 −1.96861 −0.984307 − 0.176462i \(-0.943535\pi\)
−0.984307 + 0.176462i \(0.943535\pi\)
\(282\) 0 0
\(283\) −4.00000 −0.237775 −0.118888 − 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.00000 −0.354169
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 13.0000 0.762073
\(292\) 0 0
\(293\) 24.0000 1.40209 0.701047 − 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) −5.00000 −0.291111
\(296\) 0 0
\(297\) 10.0000 0.580259
\(298\) 0 0
\(299\) −6.00000 −0.346989
\(300\) 0 0
\(301\) 12.0000 0.691669
\(302\) 0 0
\(303\) 7.00000 0.402139
\(304\) 0 0
\(305\) 12.0000 0.687118
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 − 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) −19.0000 −1.08087
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 − 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 0 0
\(313\) 14.0000 0.791327 0.395663 − 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) 0 0
\(315\) 6.00000 0.338062
\(316\) 0 0
\(317\) 3.00000 0.168497 0.0842484 − 0.996445i \(-0.473151\pi\)
0.0842484 + 0.996445i \(0.473151\pi\)
\(318\) 0 0
\(319\) 20.0000 1.11979
\(320\) 0 0
\(321\) −13.0000 −0.725589
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 4.00000 0.221880
\(326\) 0 0
\(327\) 10.0000 0.553001
\(328\) 0 0
\(329\) 9.00000 0.496186
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 − 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 0 0
\(333\) 4.00000 0.219199
\(334\) 0 0
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) 23.0000 1.25289 0.626445 − 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) 0 0
\(339\) 4.00000 0.217250
\(340\) 0 0
\(341\) 4.00000 0.216612
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) 0 0
\(345\) 6.00000 0.323029
\(346\) 0 0
\(347\) −18.0000 −0.966291 −0.483145 − 0.875540i \(-0.660506\pi\)
−0.483145 + 0.875540i \(0.660506\pi\)
\(348\) 0 0
\(349\) −20.0000 −1.07058 −0.535288 − 0.844670i \(-0.679797\pi\)
−0.535288 + 0.844670i \(0.679797\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) −36.0000 −1.91609 −0.958043 − 0.286623i \(-0.907467\pi\)
−0.958043 + 0.286623i \(0.907467\pi\)
\(354\) 0 0
\(355\) 13.0000 0.689968
\(356\) 0 0
\(357\) 6.00000 0.317554
\(358\) 0 0
\(359\) −25.0000 −1.31945 −0.659725 − 0.751507i \(-0.729327\pi\)
−0.659725 + 0.751507i \(0.729327\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) 22.0000 1.14839 0.574195 − 0.818718i \(-0.305315\pi\)
0.574195 + 0.818718i \(0.305315\pi\)
\(368\) 0 0
\(369\) −4.00000 −0.208232
\(370\) 0 0
\(371\) −12.0000 −0.623009
\(372\) 0 0
\(373\) 14.0000 0.724893 0.362446 − 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 0 0
\(375\) −9.00000 −0.464758
\(376\) 0 0
\(377\) 10.0000 0.515026
\(378\) 0 0
\(379\) 15.0000 0.770498 0.385249 − 0.922813i \(-0.374116\pi\)
0.385249 + 0.922813i \(0.374116\pi\)
\(380\) 0 0
\(381\) 7.00000 0.358621
\(382\) 0 0
\(383\) 6.00000 0.306586 0.153293 − 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 0 0
\(385\) 6.00000 0.305788
\(386\) 0 0
\(387\) 8.00000 0.406663
\(388\) 0 0
\(389\) −5.00000 −0.253510 −0.126755 − 0.991934i \(-0.540456\pi\)
−0.126755 + 0.991934i \(0.540456\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) 0 0
\(393\) 18.0000 0.907980
\(394\) 0 0
\(395\) 1.00000 0.0503155
\(396\) 0 0
\(397\) −37.0000 −1.85698 −0.928488 − 0.371361i \(-0.878891\pi\)
−0.928488 + 0.371361i \(0.878891\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.00000 0.0998752 0.0499376 − 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 0 0
\(403\) 2.00000 0.0996271
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 4.00000 0.198273
\(408\) 0 0
\(409\) −20.0000 −0.988936 −0.494468 − 0.869196i \(-0.664637\pi\)
−0.494468 + 0.869196i \(0.664637\pi\)
\(410\) 0 0
\(411\) −12.0000 −0.591916
\(412\) 0 0
\(413\) 15.0000 0.738102
\(414\) 0 0
\(415\) 6.00000 0.294528
\(416\) 0 0
\(417\) 5.00000 0.244851
\(418\) 0 0
\(419\) −25.0000 −1.22133 −0.610665 − 0.791889i \(-0.709098\pi\)
−0.610665 + 0.791889i \(0.709098\pi\)
\(420\) 0 0
\(421\) 7.00000 0.341159 0.170580 − 0.985344i \(-0.445436\pi\)
0.170580 + 0.985344i \(0.445436\pi\)
\(422\) 0 0
\(423\) 6.00000 0.291730
\(424\) 0 0
\(425\) 8.00000 0.388057
\(426\) 0 0
\(427\) −36.0000 −1.74216
\(428\) 0 0
\(429\) 2.00000 0.0965609
\(430\) 0 0
\(431\) −32.0000 −1.54139 −0.770693 − 0.637207i \(-0.780090\pi\)
−0.770693 + 0.637207i \(0.780090\pi\)
\(432\) 0 0
\(433\) −11.0000 −0.528626 −0.264313 − 0.964437i \(-0.585145\pi\)
−0.264313 + 0.964437i \(0.585145\pi\)
\(434\) 0 0
\(435\) −10.0000 −0.479463
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 40.0000 1.90910 0.954548 − 0.298057i \(-0.0963387\pi\)
0.954548 + 0.298057i \(0.0963387\pi\)
\(440\) 0 0
\(441\) −4.00000 −0.190476
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 − 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 0 0
\(445\) −15.0000 −0.711068
\(446\) 0 0
\(447\) −10.0000 −0.472984
\(448\) 0 0
\(449\) −10.0000 −0.471929 −0.235965 − 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 0 0
\(451\) −4.00000 −0.188353
\(452\) 0 0
\(453\) −2.00000 −0.0939682
\(454\) 0 0
\(455\) 3.00000 0.140642
\(456\) 0 0
\(457\) 23.0000 1.07589 0.537947 − 0.842978i \(-0.319200\pi\)
0.537947 + 0.842978i \(0.319200\pi\)
\(458\) 0 0
\(459\) 10.0000 0.466760
\(460\) 0 0
\(461\) −18.0000 −0.838344 −0.419172 − 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 31.0000 1.44069 0.720346 − 0.693615i \(-0.243983\pi\)
0.720346 + 0.693615i \(0.243983\pi\)
\(464\) 0 0
\(465\) −2.00000 −0.0927478
\(466\) 0 0
\(467\) 42.0000 1.94353 0.971764 − 0.235954i \(-0.0758216\pi\)
0.971764 + 0.235954i \(0.0758216\pi\)
\(468\) 0 0
\(469\) 24.0000 1.10822
\(470\) 0 0
\(471\) 18.0000 0.829396
\(472\) 0 0
\(473\) 8.00000 0.367840
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −8.00000 −0.366295
\(478\) 0 0
\(479\) 20.0000 0.913823 0.456912 − 0.889512i \(-0.348956\pi\)
0.456912 + 0.889512i \(0.348956\pi\)
\(480\) 0 0
\(481\) 2.00000 0.0911922
\(482\) 0 0
\(483\) −18.0000 −0.819028
\(484\) 0 0
\(485\) 13.0000 0.590300
\(486\) 0 0
\(487\) −38.0000 −1.72194 −0.860972 − 0.508652i \(-0.830144\pi\)
−0.860972 + 0.508652i \(0.830144\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 3.00000 0.135388 0.0676941 − 0.997706i \(-0.478436\pi\)
0.0676941 + 0.997706i \(0.478436\pi\)
\(492\) 0 0
\(493\) 20.0000 0.900755
\(494\) 0 0
\(495\) 4.00000 0.179787
\(496\) 0 0
\(497\) −39.0000 −1.74939
\(498\) 0 0
\(499\) 10.0000 0.447661 0.223831 − 0.974628i \(-0.428144\pi\)
0.223831 + 0.974628i \(0.428144\pi\)
\(500\) 0 0
\(501\) 2.00000 0.0893534
\(502\) 0 0
\(503\) −39.0000 −1.73892 −0.869462 − 0.494000i \(-0.835534\pi\)
−0.869462 + 0.494000i \(0.835534\pi\)
\(504\) 0 0
\(505\) 7.00000 0.311496
\(506\) 0 0
\(507\) −12.0000 −0.532939
\(508\) 0 0
\(509\) −20.0000 −0.886484 −0.443242 − 0.896402i \(-0.646172\pi\)
−0.443242 + 0.896402i \(0.646172\pi\)
\(510\) 0 0
\(511\) 18.0000 0.796273
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −19.0000 −0.837240
\(516\) 0 0
\(517\) 6.00000 0.263880
\(518\) 0 0
\(519\) 4.00000 0.175581
\(520\) 0 0
\(521\) 12.0000 0.525730 0.262865 − 0.964833i \(-0.415333\pi\)
0.262865 + 0.964833i \(0.415333\pi\)
\(522\) 0 0
\(523\) 26.0000 1.13690 0.568450 − 0.822718i \(-0.307543\pi\)
0.568450 + 0.822718i \(0.307543\pi\)
\(524\) 0 0
\(525\) 12.0000 0.523723
\(526\) 0 0
\(527\) 4.00000 0.174243
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 10.0000 0.433963
\(532\) 0 0
\(533\) −2.00000 −0.0866296
\(534\) 0 0
\(535\) −13.0000 −0.562039
\(536\) 0 0
\(537\) −20.0000 −0.863064
\(538\) 0 0
\(539\) −4.00000 −0.172292
\(540\) 0 0
\(541\) 7.00000 0.300954 0.150477 − 0.988614i \(-0.451919\pi\)
0.150477 + 0.988614i \(0.451919\pi\)
\(542\) 0 0
\(543\) −18.0000 −0.772454
\(544\) 0 0
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 − 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 0 0
\(549\) −24.0000 −1.02430
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −3.00000 −0.127573
\(554\) 0 0
\(555\) −2.00000 −0.0848953
\(556\) 0 0
\(557\) −7.00000 −0.296600 −0.148300 − 0.988942i \(-0.547380\pi\)
−0.148300 + 0.988942i \(0.547380\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) 4.00000 0.168880
\(562\) 0 0
\(563\) −14.0000 −0.590030 −0.295015 − 0.955493i \(-0.595325\pi\)
−0.295015 + 0.955493i \(0.595325\pi\)
\(564\) 0 0
\(565\) 4.00000 0.168281
\(566\) 0 0
\(567\) −3.00000 −0.125988
\(568\) 0 0
\(569\) −30.0000 −1.25767 −0.628833 − 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 0 0
\(571\) −22.0000 −0.920671 −0.460336 − 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) 0 0
\(573\) 3.00000 0.125327
\(574\) 0 0
\(575\) −24.0000 −1.00087
\(576\) 0 0
\(577\) −12.0000 −0.499567 −0.249783 − 0.968302i \(-0.580359\pi\)
−0.249783 + 0.968302i \(0.580359\pi\)
\(578\) 0 0
\(579\) 14.0000 0.581820
\(580\) 0 0
\(581\) −18.0000 −0.746766
\(582\) 0 0
\(583\) −8.00000 −0.331326
\(584\) 0 0
\(585\) 2.00000 0.0826898
\(586\) 0 0
\(587\) 7.00000 0.288921 0.144460 − 0.989511i \(-0.453855\pi\)
0.144460 + 0.989511i \(0.453855\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 18.0000 0.740421
\(592\) 0 0
\(593\) −21.0000 −0.862367 −0.431183 − 0.902264i \(-0.641904\pi\)
−0.431183 + 0.902264i \(0.641904\pi\)
\(594\) 0 0
\(595\) 6.00000 0.245976
\(596\) 0 0
\(597\) −15.0000 −0.613909
\(598\) 0 0
\(599\) −40.0000 −1.63436 −0.817178 − 0.576386i \(-0.804463\pi\)
−0.817178 + 0.576386i \(0.804463\pi\)
\(600\) 0 0
\(601\) 12.0000 0.489490 0.244745 − 0.969587i \(-0.421296\pi\)
0.244745 + 0.969587i \(0.421296\pi\)
\(602\) 0 0
\(603\) 16.0000 0.651570
\(604\) 0 0
\(605\) −7.00000 −0.284590
\(606\) 0 0
\(607\) −33.0000 −1.33943 −0.669714 − 0.742619i \(-0.733583\pi\)
−0.669714 + 0.742619i \(0.733583\pi\)
\(608\) 0 0
\(609\) 30.0000 1.21566
\(610\) 0 0
\(611\) 3.00000 0.121367
\(612\) 0 0
\(613\) 14.0000 0.565455 0.282727 − 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) 0 0
\(615\) 2.00000 0.0806478
\(616\) 0 0
\(617\) −27.0000 −1.08698 −0.543490 − 0.839416i \(-0.682897\pi\)
−0.543490 + 0.839416i \(0.682897\pi\)
\(618\) 0 0
\(619\) 35.0000 1.40677 0.703384 − 0.710810i \(-0.251671\pi\)
0.703384 + 0.710810i \(0.251671\pi\)
\(620\) 0 0
\(621\) −30.0000 −1.20386
\(622\) 0 0
\(623\) 45.0000 1.80289
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) −37.0000 −1.47295 −0.736473 − 0.676467i \(-0.763510\pi\)
−0.736473 + 0.676467i \(0.763510\pi\)
\(632\) 0 0
\(633\) 28.0000 1.11290
\(634\) 0 0
\(635\) 7.00000 0.277787
\(636\) 0 0
\(637\) −2.00000 −0.0792429
\(638\) 0 0
\(639\) −26.0000 −1.02854
\(640\) 0 0
\(641\) −33.0000 −1.30342 −0.651711 − 0.758468i \(-0.725948\pi\)
−0.651711 + 0.758468i \(0.725948\pi\)
\(642\) 0 0
\(643\) −4.00000 −0.157745 −0.0788723 − 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) 0 0
\(647\) 32.0000 1.25805 0.629025 − 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) 0 0
\(649\) 10.0000 0.392534
\(650\) 0 0
\(651\) 6.00000 0.235159
\(652\) 0 0
\(653\) −11.0000 −0.430463 −0.215232 − 0.976563i \(-0.569051\pi\)
−0.215232 + 0.976563i \(0.569051\pi\)
\(654\) 0 0
\(655\) 18.0000 0.703318
\(656\) 0 0
\(657\) 12.0000 0.468165
\(658\) 0 0
\(659\) −15.0000 −0.584317 −0.292159 − 0.956370i \(-0.594373\pi\)
−0.292159 + 0.956370i \(0.594373\pi\)
\(660\) 0 0
\(661\) 2.00000 0.0777910 0.0388955 − 0.999243i \(-0.487616\pi\)
0.0388955 + 0.999243i \(0.487616\pi\)
\(662\) 0 0
\(663\) 2.00000 0.0776736
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −60.0000 −2.32321
\(668\) 0 0
\(669\) −14.0000 −0.541271
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 − 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 0 0
\(675\) 20.0000 0.769800
\(676\) 0 0
\(677\) −27.0000 −1.03769 −0.518847 − 0.854867i \(-0.673639\pi\)
−0.518847 + 0.854867i \(0.673639\pi\)
\(678\) 0 0
\(679\) −39.0000 −1.49668
\(680\) 0 0
\(681\) −8.00000 −0.306561
\(682\) 0 0
\(683\) −4.00000 −0.153056 −0.0765279 − 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) 20.0000 0.763048
\(688\) 0 0
\(689\) −4.00000 −0.152388
\(690\) 0 0
\(691\) −17.0000 −0.646710 −0.323355 − 0.946278i \(-0.604811\pi\)
−0.323355 + 0.946278i \(0.604811\pi\)
\(692\) 0 0
\(693\) −12.0000 −0.455842
\(694\) 0 0
\(695\) 5.00000 0.189661
\(696\) 0 0
\(697\) −4.00000 −0.151511
\(698\) 0 0
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 − 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −3.00000 −0.112987
\(706\) 0 0
\(707\) −21.0000 −0.789786
\(708\) 0 0
\(709\) −50.0000 −1.87779 −0.938895 − 0.344204i \(-0.888149\pi\)
−0.938895 + 0.344204i \(0.888149\pi\)
\(710\) 0 0
\(711\) −2.00000 −0.0750059
\(712\) 0 0
\(713\) −12.0000 −0.449404
\(714\) 0 0
\(715\) 2.00000 0.0747958
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −30.0000 −1.11881 −0.559406 − 0.828894i \(-0.688971\pi\)
−0.559406 + 0.828894i \(0.688971\pi\)
\(720\) 0 0
\(721\) 57.0000 2.12279
\(722\) 0 0
\(723\) 17.0000 0.632237
\(724\) 0 0
\(725\) 40.0000 1.48556
\(726\) 0 0
\(727\) −18.0000 −0.667583 −0.333792 − 0.942647i \(-0.608328\pi\)
−0.333792 + 0.942647i \(0.608328\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 8.00000 0.295891
\(732\) 0 0
\(733\) 34.0000 1.25582 0.627909 − 0.778287i \(-0.283911\pi\)
0.627909 + 0.778287i \(0.283911\pi\)
\(734\) 0 0
\(735\) 2.00000 0.0737711
\(736\) 0 0
\(737\) 16.0000 0.589368
\(738\) 0 0
\(739\) 5.00000 0.183928 0.0919640 − 0.995762i \(-0.470686\pi\)
0.0919640 + 0.995762i \(0.470686\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 − 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) −10.0000 −0.366372
\(746\) 0 0
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) 39.0000 1.42503
\(750\) 0 0
\(751\) −42.0000 −1.53260 −0.766301 − 0.642482i \(-0.777905\pi\)
−0.766301 + 0.642482i \(0.777905\pi\)
\(752\) 0 0
\(753\) −27.0000 −0.983935
\(754\) 0 0
\(755\) −2.00000 −0.0727875
\(756\) 0 0
\(757\) −37.0000 −1.34479 −0.672394 − 0.740193i \(-0.734734\pi\)
−0.672394 + 0.740193i \(0.734734\pi\)
\(758\) 0 0
\(759\) −12.0000 −0.435572
\(760\) 0 0
\(761\) 22.0000 0.797499 0.398750 − 0.917060i \(-0.369444\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(762\) 0 0
\(763\) −30.0000 −1.08607
\(764\) 0 0
\(765\) 4.00000 0.144620
\(766\) 0 0
\(767\) 5.00000 0.180540
\(768\) 0 0
\(769\) −40.0000 −1.44244 −0.721218 − 0.692708i \(-0.756418\pi\)
−0.721218 + 0.692708i \(0.756418\pi\)
\(770\) 0 0
\(771\) −2.00000 −0.0720282
\(772\) 0 0
\(773\) 34.0000 1.22290 0.611448 − 0.791285i \(-0.290588\pi\)
0.611448 + 0.791285i \(0.290588\pi\)
\(774\) 0 0
\(775\) 8.00000 0.287368
\(776\) 0 0
\(777\) 6.00000 0.215249
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −26.0000 −0.930353
\(782\) 0 0
\(783\) 50.0000 1.78685
\(784\) 0 0
\(785\) 18.0000 0.642448
\(786\) 0 0
\(787\) −18.0000 −0.641631 −0.320815 − 0.947142i \(-0.603957\pi\)
−0.320815 + 0.947142i \(0.603957\pi\)
\(788\) 0 0
\(789\) 6.00000 0.213606
\(790\) 0 0
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) −12.0000 −0.426132
\(794\) 0 0
\(795\) 4.00000 0.141865
\(796\) 0 0
\(797\) −42.0000 −1.48772 −0.743858 − 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) 6.00000 0.212265
\(800\) 0 0
\(801\) 30.0000 1.06000
\(802\) 0 0
\(803\) 12.0000 0.423471
\(804\) 0 0
\(805\) −18.0000 −0.634417
\(806\) 0 0
\(807\) 25.0000 0.880042
\(808\) 0 0
\(809\) 15.0000 0.527372 0.263686 − 0.964609i \(-0.415062\pi\)
0.263686 + 0.964609i \(0.415062\pi\)
\(810\) 0 0
\(811\) −22.0000 −0.772524 −0.386262 − 0.922389i \(-0.626234\pi\)
−0.386262 + 0.922389i \(0.626234\pi\)
\(812\) 0 0
\(813\) 8.00000 0.280572
\(814\) 0 0
\(815\) −4.00000 −0.140114
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) −6.00000 −0.209657
\(820\) 0 0
\(821\) 42.0000 1.46581 0.732905 − 0.680331i \(-0.238164\pi\)
0.732905 + 0.680331i \(0.238164\pi\)
\(822\) 0 0
\(823\) 16.0000 0.557725 0.278862 − 0.960331i \(-0.410043\pi\)
0.278862 + 0.960331i \(0.410043\pi\)
\(824\) 0 0
\(825\) 8.00000 0.278524
\(826\) 0 0
\(827\) −23.0000 −0.799788 −0.399894 − 0.916561i \(-0.630953\pi\)
−0.399894 + 0.916561i \(0.630953\pi\)
\(828\) 0 0
\(829\) −20.0000 −0.694629 −0.347314 − 0.937749i \(-0.612906\pi\)
−0.347314 + 0.937749i \(0.612906\pi\)
\(830\) 0 0
\(831\) −17.0000 −0.589723
\(832\) 0 0
\(833\) −4.00000 −0.138592
\(834\) 0 0
\(835\) 2.00000 0.0692129
\(836\) 0 0
\(837\) 10.0000 0.345651
\(838\) 0 0
\(839\) −20.0000 −0.690477 −0.345238 − 0.938515i \(-0.612202\pi\)
−0.345238 + 0.938515i \(0.612202\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) 0 0
\(843\) −33.0000 −1.13658
\(844\) 0 0
\(845\) −12.0000 −0.412813
\(846\) 0 0
\(847\) 21.0000 0.721569
\(848\) 0 0
\(849\) −4.00000 −0.137280
\(850\) 0 0
\(851\) −12.0000 −0.411355
\(852\) 0 0
\(853\) −16.0000 −0.547830 −0.273915 − 0.961754i \(-0.588319\pi\)
−0.273915 + 0.961754i \(0.588319\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 33.0000 1.12726 0.563629 − 0.826028i \(-0.309405\pi\)
0.563629 + 0.826028i \(0.309405\pi\)
\(858\) 0 0
\(859\) 35.0000 1.19418 0.597092 − 0.802173i \(-0.296323\pi\)
0.597092 + 0.802173i \(0.296323\pi\)
\(860\) 0 0
\(861\) −6.00000 −0.204479
\(862\) 0 0
\(863\) 46.0000 1.56586 0.782929 − 0.622111i \(-0.213725\pi\)
0.782929 + 0.622111i \(0.213725\pi\)
\(864\) 0 0
\(865\) 4.00000 0.136004
\(866\) 0 0
\(867\) −13.0000 −0.441503
\(868\) 0 0
\(869\) −2.00000 −0.0678454
\(870\) 0 0
\(871\) 8.00000 0.271070
\(872\) 0 0
\(873\) −26.0000 −0.879967
\(874\) 0 0
\(875\) 27.0000 0.912767
\(876\) 0 0
\(877\) 58.0000 1.95852 0.979260 − 0.202606i \(-0.0649409\pi\)
0.979260 + 0.202606i \(0.0649409\pi\)
\(878\) 0 0
\(879\) 24.0000 0.809500
\(880\) 0 0
\(881\) 12.0000 0.404290 0.202145 − 0.979356i \(-0.435209\pi\)
0.202145 + 0.979356i \(0.435209\pi\)
\(882\) 0 0
\(883\) 1.00000 0.0336527 0.0168263 − 0.999858i \(-0.494644\pi\)
0.0168263 + 0.999858i \(0.494644\pi\)
\(884\) 0 0
\(885\) −5.00000 −0.168073
\(886\) 0 0
\(887\) 22.0000 0.738688 0.369344 − 0.929293i \(-0.379582\pi\)
0.369344 + 0.929293i \(0.379582\pi\)
\(888\) 0 0
\(889\) −21.0000 −0.704317
\(890\) 0 0
\(891\) −2.00000 −0.0670025
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) −20.0000 −0.668526
\(896\) 0 0
\(897\) −6.00000 −0.200334
\(898\) 0 0
\(899\) 20.0000 0.667037
\(900\) 0 0
\(901\) −8.00000 −0.266519
\(902\) 0 0
\(903\) 12.0000 0.399335
\(904\) 0 0
\(905\) −18.0000 −0.598340
\(906\) 0 0
\(907\) 12.0000 0.398453 0.199227 − 0.979953i \(-0.436157\pi\)
0.199227 + 0.979953i \(0.436157\pi\)
\(908\) 0 0
\(909\) −14.0000 −0.464351
\(910\) 0 0
\(911\) −12.0000 −0.397578 −0.198789 − 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) 0 0
\(913\) −12.0000 −0.397142
\(914\) 0 0
\(915\) 12.0000 0.396708
\(916\) 0 0
\(917\) −54.0000 −1.78324
\(918\) 0 0
\(919\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 12.0000 0.395413
\(922\) 0 0
\(923\) −13.0000 −0.427900
\(924\) 0 0
\(925\) 8.00000 0.263038
\(926\) 0 0
\(927\) 38.0000 1.24808
\(928\) 0 0
\(929\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −12.0000 −0.392862
\(934\) 0 0
\(935\) 4.00000 0.130814
\(936\) 0 0
\(937\) −12.0000 −0.392023 −0.196011 − 0.980602i \(-0.562799\pi\)
−0.196011 + 0.980602i \(0.562799\pi\)
\(938\) 0 0
\(939\) 14.0000 0.456873
\(940\) 0 0
\(941\) −38.0000 −1.23876 −0.619382 − 0.785090i \(-0.712617\pi\)
−0.619382 + 0.785090i \(0.712617\pi\)
\(942\) 0 0
\(943\) 12.0000 0.390774
\(944\) 0 0
\(945\) 15.0000 0.487950
\(946\) 0 0
\(947\) 32.0000 1.03986 0.519930 − 0.854209i \(-0.325958\pi\)
0.519930 + 0.854209i \(0.325958\pi\)
\(948\) 0 0
\(949\) 6.00000 0.194768
\(950\) 0 0
\(951\) 3.00000 0.0972817
\(952\) 0 0
\(953\) −31.0000 −1.00419 −0.502094 − 0.864813i \(-0.667437\pi\)
−0.502094 + 0.864813i \(0.667437\pi\)
\(954\) 0 0
\(955\) 3.00000 0.0970777
\(956\) 0 0
\(957\) 20.0000 0.646508
\(958\) 0 0
\(959\) 36.0000 1.16250
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 26.0000 0.837838
\(964\) 0 0
\(965\) 14.0000 0.450676
\(966\) 0 0
\(967\) 52.0000 1.67221 0.836104 − 0.548572i \(-0.184828\pi\)
0.836104 + 0.548572i \(0.184828\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −22.0000 −0.706014 −0.353007 − 0.935621i \(-0.614841\pi\)
−0.353007 + 0.935621i \(0.614841\pi\)
\(972\) 0 0
\(973\) −15.0000 −0.480878
\(974\) 0 0
\(975\) 4.00000 0.128103
\(976\) 0 0
\(977\) 58.0000 1.85558 0.927792 − 0.373097i \(-0.121704\pi\)
0.927792 + 0.373097i \(0.121704\pi\)
\(978\) 0 0
\(979\) 30.0000 0.958804
\(980\) 0 0
\(981\) −20.0000 −0.638551
\(982\) 0 0
\(983\) −24.0000 −0.765481 −0.382741 − 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) 0 0
\(985\) 18.0000 0.573528
\(986\) 0 0
\(987\) 9.00000 0.286473
\(988\) 0 0
\(989\) −24.0000 −0.763156
\(990\) 0 0
\(991\) 13.0000 0.412959 0.206479 − 0.978451i \(-0.433799\pi\)
0.206479 + 0.978451i \(0.433799\pi\)
\(992\) 0 0
\(993\) 28.0000 0.888553
\(994\) 0 0
\(995\) −15.0000 −0.475532
\(996\) 0 0
\(997\) −22.0000 −0.696747 −0.348373 − 0.937356i \(-0.613266\pi\)
−0.348373 + 0.937356i \(0.613266\pi\)
\(998\) 0 0
\(999\) 10.0000 0.316386
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 1264.2.a.f.1.1 1
4.3 odd 2 158.2.a.d.1.1 ✓ 1
8.3 odd 2 5056.2.a.m.1.1 1
8.5 even 2 5056.2.a.e.1.1 1
12.11 even 2 1422.2.a.a.1.1 1
20.19 odd 2 3950.2.a.d.1.1 1
28.27 even 2 7742.2.a.m.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
158.2.a.d.1.1 ✓ 1 4.3 odd 2
1264.2.a.f.1.1 1 1.1 even 1 trivial
1422.2.a.a.1.1 1 12.11 even 2
3950.2.a.d.1.1 1 20.19 odd 2
5056.2.a.e.1.1 1 8.5 even 2
5056.2.a.m.1.1 1 8.3 odd 2
7742.2.a.m.1.1 1 28.27 even 2