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Properties

Label 144.10.a.g.1.1
Level $144$
Weight $10$
Character 144.1
Self dual yes
Analytic conductor $74.165$
Analytic rank $0$
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] = [144,10,Mod(1,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.1");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 144.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: \(74.1651604076\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 18)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 144.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-384.000 q^{5} -5852.00 q^{7} +O(q^{10})\) \(q-384.000 q^{5} -5852.00 q^{7} +90624.0 q^{11} -102814. q^{13} -458496. q^{17} +128824. q^{19} -1.27488e6 q^{23} -1.80567e6 q^{25} +4.88486e6 q^{29} +7.72752e6 q^{31} +2.24717e6 q^{35} +3.12124e6 q^{37} -2.51866e7 q^{41} -1.02230e7 q^{43} +1.94304e7 q^{47} -6.10770e6 q^{49} +5.99351e7 q^{53} -3.47996e7 q^{55} -7.53347e7 q^{59} +2.07606e8 q^{61} +3.94806e7 q^{65} +1.78167e8 q^{67} +4.90291e6 q^{71} -4.20432e7 q^{73} -5.30332e8 q^{77} +3.64859e8 q^{79} +3.17941e8 q^{83} +1.76062e8 q^{85} +7.88009e8 q^{89} +6.01668e8 q^{91} -4.94684e7 q^{95} +6.31569e8 q^{97} +O(q^{100})\)

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
\(5\) −384.000 −0.274768 −0.137384 − 0.990518i \(-0.543869\pi\)
−0.137384 + 0.990518i \(0.543869\pi\)
\(6\) 0 0
\(7\) −5852.00 −0.921220 −0.460610 − 0.887603i \(-0.652369\pi\)
−0.460610 + 0.887603i \(0.652369\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 90624.0 1.86628 0.933139 − 0.359517i \(-0.117058\pi\)
0.933139 + 0.359517i \(0.117058\pi\)
\(12\) 0 0
\(13\) −102814. −0.998406 −0.499203 − 0.866485i \(-0.666374\pi\)
−0.499203 + 0.866485i \(0.666374\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −458496. −1.33142 −0.665711 − 0.746210i \(-0.731871\pi\)
−0.665711 + 0.746210i \(0.731871\pi\)
\(18\) 0 0
\(19\) 128824. 0.226780 0.113390 − 0.993551i \(-0.463829\pi\)
0.113390 + 0.993551i \(0.463829\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.27488e6 −0.949935 −0.474968 − 0.880003i \(-0.657540\pi\)
−0.474968 + 0.880003i \(0.657540\pi\)
\(24\) 0 0
\(25\) −1.80567e6 −0.924503
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.88486e6 1.28251 0.641256 − 0.767327i \(-0.278414\pi\)
0.641256 + 0.767327i \(0.278414\pi\)
\(30\) 0 0
\(31\) 7.72752e6 1.50284 0.751420 − 0.659824i \(-0.229369\pi\)
0.751420 + 0.659824i \(0.229369\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.24717e6 0.253122
\(36\) 0 0
\(37\) 3.12124e6 0.273791 0.136895 − 0.990585i \(-0.456288\pi\)
0.136895 + 0.990585i \(0.456288\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.51866e7 −1.39201 −0.696004 − 0.718038i \(-0.745040\pi\)
−0.696004 + 0.718038i \(0.745040\pi\)
\(42\) 0 0
\(43\) −1.02230e7 −0.456008 −0.228004 − 0.973660i \(-0.573220\pi\)
−0.228004 + 0.973660i \(0.573220\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.94304e7 0.580820 0.290410 − 0.956902i \(-0.406208\pi\)
0.290410 + 0.956902i \(0.406208\pi\)
\(48\) 0 0
\(49\) −6.10770e6 −0.151355
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.99351e7 1.04337 0.521687 − 0.853137i \(-0.325303\pi\)
0.521687 + 0.853137i \(0.325303\pi\)
\(54\) 0 0
\(55\) −3.47996e7 −0.512793
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7.53347e7 −0.809395 −0.404698 − 0.914451i \(-0.632623\pi\)
−0.404698 + 0.914451i \(0.632623\pi\)
\(60\) 0 0
\(61\) 2.07606e8 1.91980 0.959900 − 0.280344i \(-0.0904486\pi\)
0.959900 + 0.280344i \(0.0904486\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.94806e7 0.274330
\(66\) 0 0
\(67\) 1.78167e8 1.08017 0.540084 − 0.841611i \(-0.318393\pi\)
0.540084 + 0.841611i \(0.318393\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.90291e6 0.0228977 0.0114488 − 0.999934i \(-0.496356\pi\)
0.0114488 + 0.999934i \(0.496356\pi\)
\(72\) 0 0
\(73\) −4.20432e7 −0.173278 −0.0866389 − 0.996240i \(-0.527613\pi\)
−0.0866389 + 0.996240i \(0.527613\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −5.30332e8 −1.71925
\(78\) 0 0
\(79\) 3.64859e8 1.05391 0.526955 − 0.849893i \(-0.323334\pi\)
0.526955 + 0.849893i \(0.323334\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.17941e8 0.735352 0.367676 − 0.929954i \(-0.380153\pi\)
0.367676 + 0.929954i \(0.380153\pi\)
\(84\) 0 0
\(85\) 1.76062e8 0.365832
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.88009e8 1.33130 0.665651 − 0.746263i \(-0.268154\pi\)
0.665651 + 0.746263i \(0.268154\pi\)
\(90\) 0 0
\(91\) 6.01668e8 0.919751
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.94684e7 −0.0623120
\(96\) 0 0
\(97\) 6.31569e8 0.724350 0.362175 − 0.932110i \(-0.382034\pi\)
0.362175 + 0.932110i \(0.382034\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.68592e8 0.734936 0.367468 − 0.930036i \(-0.380225\pi\)
0.367468 + 0.930036i \(0.380225\pi\)
\(102\) 0 0
\(103\) 1.41060e9 1.23492 0.617458 − 0.786604i \(-0.288162\pi\)
0.617458 + 0.786604i \(0.288162\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.90538e9 −1.40525 −0.702627 − 0.711559i \(-0.747990\pi\)
−0.702627 + 0.711559i \(0.747990\pi\)
\(108\) 0 0
\(109\) 1.77990e9 1.20775 0.603873 − 0.797081i \(-0.293624\pi\)
0.603873 + 0.797081i \(0.293624\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.74893e9 −1.58603 −0.793014 − 0.609203i \(-0.791489\pi\)
−0.793014 + 0.609203i \(0.791489\pi\)
\(114\) 0 0
\(115\) 4.89554e8 0.261012
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.68312e9 1.22653
\(120\) 0 0
\(121\) 5.85476e9 2.48299
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.44338e9 0.528792
\(126\) 0 0
\(127\) 2.10461e9 0.717885 0.358942 − 0.933360i \(-0.383137\pi\)
0.358942 + 0.933360i \(0.383137\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.42082e9 1.01487 0.507434 − 0.861691i \(-0.330594\pi\)
0.507434 + 0.861691i \(0.330594\pi\)
\(132\) 0 0
\(133\) −7.53878e8 −0.208915
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.22889e7 0.0199572 0.00997858 − 0.999950i \(-0.496824\pi\)
0.00997858 + 0.999950i \(0.496824\pi\)
\(138\) 0 0
\(139\) 3.23773e9 0.735654 0.367827 − 0.929894i \(-0.380102\pi\)
0.367827 + 0.929894i \(0.380102\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −9.31742e9 −1.86330
\(144\) 0 0
\(145\) −1.87579e9 −0.352393
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.29370e8 −0.0215028 −0.0107514 − 0.999942i \(-0.503422\pi\)
−0.0107514 + 0.999942i \(0.503422\pi\)
\(150\) 0 0
\(151\) −1.00610e9 −0.157487 −0.0787436 − 0.996895i \(-0.525091\pi\)
−0.0787436 + 0.996895i \(0.525091\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.96737e9 −0.412932
\(156\) 0 0
\(157\) 1.64390e9 0.215937 0.107968 − 0.994154i \(-0.465565\pi\)
0.107968 + 0.994154i \(0.465565\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.46060e9 0.875099
\(162\) 0 0
\(163\) 9.72650e9 1.07923 0.539613 − 0.841913i \(-0.318571\pi\)
0.539613 + 0.841913i \(0.318571\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.42666e10 1.41937 0.709686 − 0.704518i \(-0.248837\pi\)
0.709686 + 0.704518i \(0.248837\pi\)
\(168\) 0 0
\(169\) −3.37808e7 −0.00318551
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.12395e10 −0.953981 −0.476991 − 0.878908i \(-0.658272\pi\)
−0.476991 + 0.878908i \(0.658272\pi\)
\(174\) 0 0
\(175\) 1.05668e10 0.851670
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.12310e10 0.817672 0.408836 − 0.912608i \(-0.365935\pi\)
0.408836 + 0.912608i \(0.365935\pi\)
\(180\) 0 0
\(181\) −2.00649e9 −0.138958 −0.0694791 − 0.997583i \(-0.522134\pi\)
−0.0694791 + 0.997583i \(0.522134\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.19856e9 −0.0752290
\(186\) 0 0
\(187\) −4.15507e10 −2.48480
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.73721e10 −0.944501 −0.472250 − 0.881465i \(-0.656558\pi\)
−0.472250 + 0.881465i \(0.656558\pi\)
\(192\) 0 0
\(193\) −1.77800e10 −0.922408 −0.461204 − 0.887294i \(-0.652582\pi\)
−0.461204 + 0.887294i \(0.652582\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4.44270e9 −0.210159 −0.105080 − 0.994464i \(-0.533510\pi\)
−0.105080 + 0.994464i \(0.533510\pi\)
\(198\) 0 0
\(199\) −2.20650e10 −0.997390 −0.498695 − 0.866777i \(-0.666187\pi\)
−0.498695 + 0.866777i \(0.666187\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.85862e10 −1.18148
\(204\) 0 0
\(205\) 9.67164e9 0.382479
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.16745e10 0.423235
\(210\) 0 0
\(211\) −2.21902e10 −0.770709 −0.385355 − 0.922769i \(-0.625921\pi\)
−0.385355 + 0.922769i \(0.625921\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.92565e9 0.125296
\(216\) 0 0
\(217\) −4.52215e10 −1.38445
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4.71398e10 1.32930
\(222\) 0 0
\(223\) −4.72556e9 −0.127962 −0.0639811 − 0.997951i \(-0.520380\pi\)
−0.0639811 + 0.997951i \(0.520380\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.64053e10 1.15998 0.579991 − 0.814623i \(-0.303056\pi\)
0.579991 + 0.814623i \(0.303056\pi\)
\(228\) 0 0
\(229\) −3.38127e10 −0.812495 −0.406248 − 0.913763i \(-0.633163\pi\)
−0.406248 + 0.913763i \(0.633163\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −7.74727e10 −1.72206 −0.861028 − 0.508558i \(-0.830179\pi\)
−0.861028 + 0.508558i \(0.830179\pi\)
\(234\) 0 0
\(235\) −7.46127e9 −0.159591
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.43839e10 0.285158 0.142579 − 0.989783i \(-0.454460\pi\)
0.142579 + 0.989783i \(0.454460\pi\)
\(240\) 0 0
\(241\) 1.89508e10 0.361868 0.180934 − 0.983495i \(-0.442088\pi\)
0.180934 + 0.983495i \(0.442088\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.34536e9 0.0415874
\(246\) 0 0
\(247\) −1.32449e10 −0.226419
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 8.18155e9 0.130108 0.0650539 − 0.997882i \(-0.479278\pi\)
0.0650539 + 0.997882i \(0.479278\pi\)
\(252\) 0 0
\(253\) −1.15535e11 −1.77284
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.30100e10 0.186028 0.0930139 − 0.995665i \(-0.470350\pi\)
0.0930139 + 0.995665i \(0.470350\pi\)
\(258\) 0 0
\(259\) −1.82655e10 −0.252222
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4.30171e10 −0.554421 −0.277211 − 0.960809i \(-0.589410\pi\)
−0.277211 + 0.960809i \(0.589410\pi\)
\(264\) 0 0
\(265\) −2.30151e10 −0.286686
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3.62974e10 −0.422660 −0.211330 − 0.977415i \(-0.567779\pi\)
−0.211330 + 0.977415i \(0.567779\pi\)
\(270\) 0 0
\(271\) 9.27601e10 1.04472 0.522359 − 0.852726i \(-0.325052\pi\)
0.522359 + 0.852726i \(0.325052\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.63637e11 −1.72538
\(276\) 0 0
\(277\) 5.70899e10 0.582640 0.291320 − 0.956626i \(-0.405906\pi\)
0.291320 + 0.956626i \(0.405906\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.95321e11 1.86883 0.934415 − 0.356186i \(-0.115923\pi\)
0.934415 + 0.356186i \(0.115923\pi\)
\(282\) 0 0
\(283\) −2.01364e11 −1.86613 −0.933067 − 0.359703i \(-0.882878\pi\)
−0.933067 + 0.359703i \(0.882878\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.47392e11 1.28234
\(288\) 0 0
\(289\) 9.16307e10 0.772682
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7.58592e10 −0.601318 −0.300659 − 0.953732i \(-0.597207\pi\)
−0.300659 + 0.953732i \(0.597207\pi\)
\(294\) 0 0
\(295\) 2.89285e10 0.222396
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.31076e11 0.948421
\(300\) 0 0
\(301\) 5.98253e10 0.420083
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −7.97207e10 −0.527499
\(306\) 0 0
\(307\) 5.44117e10 0.349599 0.174799 − 0.984604i \(-0.444072\pi\)
0.174799 + 0.984604i \(0.444072\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −7.17472e10 −0.434894 −0.217447 − 0.976072i \(-0.569773\pi\)
−0.217447 + 0.976072i \(0.569773\pi\)
\(312\) 0 0
\(313\) 2.05385e11 1.20954 0.604770 − 0.796400i \(-0.293265\pi\)
0.604770 + 0.796400i \(0.293265\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.38949e11 −1.32904 −0.664521 − 0.747270i \(-0.731364\pi\)
−0.664521 + 0.747270i \(0.731364\pi\)
\(318\) 0 0
\(319\) 4.42686e11 2.39352
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5.90653e10 −0.301940
\(324\) 0 0
\(325\) 1.85648e11 0.923029
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.13707e11 −0.535063
\(330\) 0 0
\(331\) −1.04864e11 −0.480176 −0.240088 − 0.970751i \(-0.577176\pi\)
−0.240088 + 0.970751i \(0.577176\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −6.84162e10 −0.296795
\(336\) 0 0
\(337\) −5.16500e10 −0.218140 −0.109070 − 0.994034i \(-0.534787\pi\)
−0.109070 + 0.994034i \(0.534787\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 7.00299e11 2.80472
\(342\) 0 0
\(343\) 2.71892e11 1.06065
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.17946e11 1.17726 0.588628 − 0.808404i \(-0.299668\pi\)
0.588628 + 0.808404i \(0.299668\pi\)
\(348\) 0 0
\(349\) 1.20631e11 0.435255 0.217628 − 0.976032i \(-0.430168\pi\)
0.217628 + 0.976032i \(0.430168\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 5.70133e10 0.195429 0.0977147 − 0.995214i \(-0.468847\pi\)
0.0977147 + 0.995214i \(0.468847\pi\)
\(354\) 0 0
\(355\) −1.88272e9 −0.00629155
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.86194e11 −0.909360 −0.454680 − 0.890655i \(-0.650246\pi\)
−0.454680 + 0.890655i \(0.650246\pi\)
\(360\) 0 0
\(361\) −3.06092e11 −0.948571
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.61446e10 0.0476112
\(366\) 0 0
\(367\) 3.63169e11 1.04499 0.522495 − 0.852643i \(-0.325001\pi\)
0.522495 + 0.852643i \(0.325001\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3.50740e11 −0.961176
\(372\) 0 0
\(373\) 1.32527e11 0.354500 0.177250 − 0.984166i \(-0.443280\pi\)
0.177250 + 0.984166i \(0.443280\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.02232e11 −1.28047
\(378\) 0 0
\(379\) −4.45768e10 −0.110977 −0.0554884 − 0.998459i \(-0.517672\pi\)
−0.0554884 + 0.998459i \(0.517672\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.73208e11 1.12372 0.561860 − 0.827233i \(-0.310086\pi\)
0.561860 + 0.827233i \(0.310086\pi\)
\(384\) 0 0
\(385\) 2.03647e11 0.472395
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7.51224e11 −1.66340 −0.831699 − 0.555227i \(-0.812631\pi\)
−0.831699 + 0.555227i \(0.812631\pi\)
\(390\) 0 0
\(391\) 5.84527e11 1.26476
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.40106e11 −0.289581
\(396\) 0 0
\(397\) 5.94202e11 1.20054 0.600271 − 0.799797i \(-0.295060\pi\)
0.600271 + 0.799797i \(0.295060\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.87626e11 0.555493 0.277747 − 0.960654i \(-0.410412\pi\)
0.277747 + 0.960654i \(0.410412\pi\)
\(402\) 0 0
\(403\) −7.94498e11 −1.50044
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.82859e11 0.510970
\(408\) 0 0
\(409\) 6.18770e11 1.09339 0.546694 − 0.837332i \(-0.315886\pi\)
0.546694 + 0.837332i \(0.315886\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4.40858e11 0.745631
\(414\) 0 0
\(415\) −1.22089e11 −0.202051
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.28112e11 0.995575 0.497787 − 0.867299i \(-0.334146\pi\)
0.497787 + 0.867299i \(0.334146\pi\)
\(420\) 0 0
\(421\) −9.91754e11 −1.53863 −0.769316 − 0.638869i \(-0.779403\pi\)
−0.769316 + 0.638869i \(0.779403\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8.27892e11 1.23090
\(426\) 0 0
\(427\) −1.21491e12 −1.76856
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.03397e12 −1.44332 −0.721659 − 0.692249i \(-0.756620\pi\)
−0.721659 + 0.692249i \(0.756620\pi\)
\(432\) 0 0
\(433\) −6.64087e11 −0.907882 −0.453941 − 0.891032i \(-0.649982\pi\)
−0.453941 + 0.891032i \(0.649982\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.64235e11 −0.215427
\(438\) 0 0
\(439\) 1.28096e12 1.64606 0.823031 − 0.567997i \(-0.192282\pi\)
0.823031 + 0.567997i \(0.192282\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5.41958e11 −0.668573 −0.334286 − 0.942472i \(-0.608495\pi\)
−0.334286 + 0.942472i \(0.608495\pi\)
\(444\) 0 0
\(445\) −3.02596e11 −0.365799
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.75228e11 0.319583 0.159792 − 0.987151i \(-0.448918\pi\)
0.159792 + 0.987151i \(0.448918\pi\)
\(450\) 0 0
\(451\) −2.28251e12 −2.59787
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.31040e11 −0.252718
\(456\) 0 0
\(457\) −3.32429e11 −0.356514 −0.178257 − 0.983984i \(-0.557046\pi\)
−0.178257 + 0.983984i \(0.557046\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6.98290e11 −0.720081 −0.360041 − 0.932937i \(-0.617237\pi\)
−0.360041 + 0.932937i \(0.617237\pi\)
\(462\) 0 0
\(463\) 5.45374e11 0.551544 0.275772 − 0.961223i \(-0.411067\pi\)
0.275772 + 0.961223i \(0.411067\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.11506e12 1.08485 0.542427 − 0.840103i \(-0.317506\pi\)
0.542427 + 0.840103i \(0.317506\pi\)
\(468\) 0 0
\(469\) −1.04263e12 −0.995071
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −9.26454e11 −0.851037
\(474\) 0 0
\(475\) −2.32614e11 −0.209659
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.82139e11 0.765645 0.382822 − 0.923822i \(-0.374952\pi\)
0.382822 + 0.923822i \(0.374952\pi\)
\(480\) 0 0
\(481\) −3.20907e11 −0.273355
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.42523e11 −0.199028
\(486\) 0 0
\(487\) 1.62147e11 0.130626 0.0653128 − 0.997865i \(-0.479195\pi\)
0.0653128 + 0.997865i \(0.479195\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.45587e12 −1.13046 −0.565231 − 0.824933i \(-0.691213\pi\)
−0.565231 + 0.824933i \(0.691213\pi\)
\(492\) 0 0
\(493\) −2.23969e12 −1.70756
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.86918e10 −0.0210938
\(498\) 0 0
\(499\) −3.00497e11 −0.216964 −0.108482 − 0.994098i \(-0.534599\pi\)
−0.108482 + 0.994098i \(0.534599\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2.40811e12 1.67734 0.838670 − 0.544640i \(-0.183334\pi\)
0.838670 + 0.544640i \(0.183334\pi\)
\(504\) 0 0
\(505\) −2.95139e11 −0.201937
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.76592e12 1.16611 0.583056 − 0.812432i \(-0.301857\pi\)
0.583056 + 0.812432i \(0.301857\pi\)
\(510\) 0 0
\(511\) 2.46037e11 0.159627
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5.41672e11 −0.339316
\(516\) 0 0
\(517\) 1.76086e12 1.08397
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.20224e12 −0.714863 −0.357432 − 0.933939i \(-0.616347\pi\)
−0.357432 + 0.933939i \(0.616347\pi\)
\(522\) 0 0
\(523\) −1.90882e12 −1.11560 −0.557799 − 0.829976i \(-0.688354\pi\)
−0.557799 + 0.829976i \(0.688354\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.54304e12 −2.00091
\(528\) 0 0
\(529\) −1.75834e11 −0.0976228
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.58953e12 1.38979
\(534\) 0 0
\(535\) 7.31666e11 0.386119
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.53504e11 −0.282470
\(540\) 0 0
\(541\) 1.82487e12 0.915891 0.457945 − 0.888980i \(-0.348586\pi\)
0.457945 + 0.888980i \(0.348586\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −6.83480e11 −0.331850
\(546\) 0 0
\(547\) −3.50888e12 −1.67581 −0.837907 − 0.545813i \(-0.816221\pi\)
−0.837907 + 0.545813i \(0.816221\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6.29288e11 0.290849
\(552\) 0 0
\(553\) −2.13516e12 −0.970882
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.43791e12 −1.07317 −0.536585 − 0.843846i \(-0.680286\pi\)
−0.536585 + 0.843846i \(0.680286\pi\)
\(558\) 0 0
\(559\) 1.05107e12 0.455281
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.30770e12 0.548555 0.274277 − 0.961651i \(-0.411561\pi\)
0.274277 + 0.961651i \(0.411561\pi\)
\(564\) 0 0
\(565\) 1.05559e12 0.435790
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.26094e12 0.504302 0.252151 − 0.967688i \(-0.418862\pi\)
0.252151 + 0.967688i \(0.418862\pi\)
\(570\) 0 0
\(571\) −1.54622e11 −0.0608706 −0.0304353 − 0.999537i \(-0.509689\pi\)
−0.0304353 + 0.999537i \(0.509689\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.30201e12 0.878218
\(576\) 0 0
\(577\) 1.36468e12 0.512556 0.256278 − 0.966603i \(-0.417504\pi\)
0.256278 + 0.966603i \(0.417504\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.86059e12 −0.677421
\(582\) 0 0
\(583\) 5.43156e12 1.94722
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.82740e12 0.982914 0.491457 − 0.870902i \(-0.336464\pi\)
0.491457 + 0.870902i \(0.336464\pi\)
\(588\) 0 0
\(589\) 9.95491e11 0.340815
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.54257e12 0.512271 0.256136 − 0.966641i \(-0.417551\pi\)
0.256136 + 0.966641i \(0.417551\pi\)
\(594\) 0 0
\(595\) −1.03032e12 −0.337012
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.48449e10 −0.0205805 −0.0102902 − 0.999947i \(-0.503276\pi\)
−0.0102902 + 0.999947i \(0.503276\pi\)
\(600\) 0 0
\(601\) 3.16163e12 0.988497 0.494249 − 0.869321i \(-0.335443\pi\)
0.494249 + 0.869321i \(0.335443\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.24823e12 −0.682246
\(606\) 0 0
\(607\) 2.74008e12 0.819246 0.409623 − 0.912255i \(-0.365660\pi\)
0.409623 + 0.912255i \(0.365660\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.99772e12 −0.579894
\(612\) 0 0
\(613\) 9.17903e11 0.262558 0.131279 − 0.991345i \(-0.458092\pi\)
0.131279 + 0.991345i \(0.458092\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.41762e12 1.50496 0.752481 − 0.658614i \(-0.228857\pi\)
0.752481 + 0.658614i \(0.228857\pi\)
\(618\) 0 0
\(619\) 5.98072e12 1.63736 0.818682 − 0.574247i \(-0.194705\pi\)
0.818682 + 0.574247i \(0.194705\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4.61143e12 −1.22642
\(624\) 0 0
\(625\) 2.97244e12 0.779207
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.43108e12 −0.364531
\(630\) 0 0
\(631\) 3.43035e12 0.861402 0.430701 − 0.902495i \(-0.358266\pi\)
0.430701 + 0.902495i \(0.358266\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.08170e11 −0.197252
\(636\) 0 0
\(637\) 6.27957e11 0.151113
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −4.91885e12 −1.15081 −0.575404 − 0.817870i \(-0.695155\pi\)
−0.575404 + 0.817870i \(0.695155\pi\)
\(642\) 0 0
\(643\) 3.29629e12 0.760460 0.380230 − 0.924892i \(-0.375845\pi\)
0.380230 + 0.924892i \(0.375845\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7.32018e12 −1.64230 −0.821151 − 0.570712i \(-0.806667\pi\)
−0.821151 + 0.570712i \(0.806667\pi\)
\(648\) 0 0
\(649\) −6.82713e12 −1.51056
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3.24958e12 0.699387 0.349693 − 0.936864i \(-0.386286\pi\)
0.349693 + 0.936864i \(0.386286\pi\)
\(654\) 0 0
\(655\) −1.31359e12 −0.278853
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.32956e12 −0.274615 −0.137307 − 0.990528i \(-0.543845\pi\)
−0.137307 + 0.990528i \(0.543845\pi\)
\(660\) 0 0
\(661\) 3.29879e11 0.0672123 0.0336061 − 0.999435i \(-0.489301\pi\)
0.0336061 + 0.999435i \(0.489301\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.89489e11 0.0574030
\(666\) 0 0
\(667\) −6.22762e12 −1.21830
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.88141e13 3.58288
\(672\) 0 0
\(673\) 8.54852e12 1.60629 0.803143 − 0.595786i \(-0.203159\pi\)
0.803143 + 0.595786i \(0.203159\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 5.35691e12 0.980089 0.490044 − 0.871697i \(-0.336981\pi\)
0.490044 + 0.871697i \(0.336981\pi\)
\(678\) 0 0
\(679\) −3.69594e12 −0.667285
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.45707e12 0.783711 0.391856 − 0.920027i \(-0.371833\pi\)
0.391856 + 0.920027i \(0.371833\pi\)
\(684\) 0 0
\(685\) −3.15989e10 −0.00548359
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6.16217e12 −1.04171
\(690\) 0 0
\(691\) 6.05385e12 1.01014 0.505068 − 0.863079i \(-0.331467\pi\)
0.505068 + 0.863079i \(0.331467\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.24329e12 −0.202134
\(696\) 0 0
\(697\) 1.15479e13 1.85335
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 3.35495e12 0.524753 0.262376 − 0.964966i \(-0.415494\pi\)
0.262376 + 0.964966i \(0.415494\pi\)
\(702\) 0 0
\(703\) 4.02090e11 0.0620904
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.49780e12 −0.677037
\(708\) 0 0
\(709\) −3.66296e12 −0.544408 −0.272204 − 0.962240i \(-0.587752\pi\)
−0.272204 + 0.962240i \(0.587752\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −9.85167e12 −1.42760
\(714\) 0 0
\(715\) 3.57789e12 0.511976
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.11959e13 −1.56235 −0.781177 − 0.624309i \(-0.785380\pi\)
−0.781177 + 0.624309i \(0.785380\pi\)
\(720\) 0 0
\(721\) −8.25486e12 −1.13763
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −8.82045e12 −1.18569
\(726\) 0 0
\(727\) −1.23989e13 −1.64618 −0.823091 − 0.567910i \(-0.807752\pi\)
−0.823091 + 0.567910i \(0.807752\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4.68723e12 0.607138
\(732\) 0 0
\(733\) 2.71674e12 0.347601 0.173800 − 0.984781i \(-0.444395\pi\)
0.173800 + 0.984781i \(0.444395\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.61462e13 2.01589
\(738\) 0 0
\(739\) 9.65750e10 0.0119115 0.00595573 − 0.999982i \(-0.498104\pi\)
0.00595573 + 0.999982i \(0.498104\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −9.15865e12 −1.10251 −0.551254 − 0.834338i \(-0.685850\pi\)
−0.551254 + 0.834338i \(0.685850\pi\)
\(744\) 0 0
\(745\) 4.96781e10 0.00590829
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.11503e13 1.29455
\(750\) 0 0
\(751\) 5.19463e12 0.595902 0.297951 − 0.954581i \(-0.403697\pi\)
0.297951 + 0.954581i \(0.403697\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.86343e11 0.0432724
\(756\) 0 0
\(757\) −8.50893e12 −0.941767 −0.470883 − 0.882195i \(-0.656065\pi\)
−0.470883 + 0.882195i \(0.656065\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.92236e12 0.315866 0.157933 − 0.987450i \(-0.449517\pi\)
0.157933 + 0.987450i \(0.449517\pi\)
\(762\) 0 0
\(763\) −1.04160e13 −1.11260
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7.74546e12 0.808105
\(768\) 0 0
\(769\) −1.41197e13 −1.45599 −0.727993 − 0.685584i \(-0.759547\pi\)
−0.727993 + 0.685584i \(0.759547\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −7.27237e12 −0.732602 −0.366301 − 0.930496i \(-0.619376\pi\)
−0.366301 + 0.930496i \(0.619376\pi\)
\(774\) 0 0
\(775\) −1.39534e13 −1.38938
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.24463e12 −0.315680
\(780\) 0 0
\(781\) 4.44321e11 0.0427334
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.31257e11 −0.0593325
\(786\) 0 0
\(787\) 1.42468e13 1.32383 0.661914 − 0.749580i \(-0.269744\pi\)
0.661914 + 0.749580i \(0.269744\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.60867e13 1.46108
\(792\) 0 0
\(793\) −2.13448e13 −1.91674
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.59547e13 −1.40064 −0.700320 − 0.713829i \(-0.746959\pi\)
−0.700320 + 0.713829i \(0.746959\pi\)
\(798\) 0 0
\(799\) −8.90876e12 −0.773316
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −3.81012e12 −0.323384
\(804\) 0 0
\(805\) −2.86487e12 −0.240449
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2.64541e12 −0.217132 −0.108566 − 0.994089i \(-0.534626\pi\)
−0.108566 + 0.994089i \(0.534626\pi\)
\(810\) 0 0
\(811\) 2.35878e12 0.191467 0.0957335 − 0.995407i \(-0.469480\pi\)
0.0957335 + 0.995407i \(0.469480\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −3.73497e12 −0.296537
\(816\) 0 0
\(817\) −1.31697e12 −0.103414
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2.90276e12 −0.222980 −0.111490 − 0.993766i \(-0.535562\pi\)
−0.111490 + 0.993766i \(0.535562\pi\)
\(822\) 0 0
\(823\) −5.05028e12 −0.383722 −0.191861 − 0.981422i \(-0.561452\pi\)
−0.191861 + 0.981422i \(0.561452\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3.12268e12 −0.232141 −0.116071 − 0.993241i \(-0.537030\pi\)
−0.116071 + 0.993241i \(0.537030\pi\)
\(828\) 0 0
\(829\) −7.82019e12 −0.575072 −0.287536 − 0.957770i \(-0.592836\pi\)
−0.287536 + 0.957770i \(0.592836\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.80036e12 0.201517
\(834\) 0 0
\(835\) −5.47838e12 −0.389998
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 6.08486e12 0.423957 0.211979 − 0.977274i \(-0.432009\pi\)
0.211979 + 0.977274i \(0.432009\pi\)
\(840\) 0 0
\(841\) 9.35475e12 0.644837
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.29718e10 0.000875277 0
\(846\) 0 0
\(847\) −3.42621e13 −2.28738
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −3.97920e12 −0.260084
\(852\) 0 0
\(853\) 3.96702e12 0.256563 0.128281 − 0.991738i \(-0.459054\pi\)
0.128281 + 0.991738i \(0.459054\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.34304e13 0.850501 0.425251 − 0.905076i \(-0.360186\pi\)
0.425251 + 0.905076i \(0.360186\pi\)
\(858\) 0 0
\(859\) 2.32727e13 1.45841 0.729203 − 0.684298i \(-0.239891\pi\)
0.729203 + 0.684298i \(0.239891\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −9.79865e12 −0.601336 −0.300668 − 0.953729i \(-0.597210\pi\)
−0.300668 + 0.953729i \(0.597210\pi\)
\(864\) 0 0
\(865\) 4.31597e12 0.262124
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 3.30650e13 1.96689
\(870\) 0 0
\(871\) −1.83181e13 −1.07845
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8.44664e12 −0.487133
\(876\) 0 0
\(877\) 3.06271e13 1.74827 0.874133 − 0.485686i \(-0.161430\pi\)
0.874133 + 0.485686i \(0.161430\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.56172e13 −0.873396 −0.436698 − 0.899608i \(-0.643852\pi\)
−0.436698 + 0.899608i \(0.643852\pi\)
\(882\) 0 0
\(883\) 2.45218e13 1.35747 0.678733 − 0.734385i \(-0.262529\pi\)
0.678733 + 0.734385i \(0.262529\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −6.59546e11 −0.0357758 −0.0178879 − 0.999840i \(-0.505694\pi\)
−0.0178879 + 0.999840i \(0.505694\pi\)
\(888\) 0 0
\(889\) −1.23162e13 −0.661329
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.50310e12 0.131719
\(894\) 0 0
\(895\) −4.31270e12 −0.224670
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3.77479e13 1.92741
\(900\) 0 0
\(901\) −2.74800e13 −1.38917
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 7.70494e11 0.0381813
\(906\) 0 0
\(907\) 1.59530e13 0.782725 0.391362 − 0.920237i \(-0.372004\pi\)
0.391362 + 0.920237i \(0.372004\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.55272e13 −1.22792 −0.613961 − 0.789337i \(-0.710425\pi\)
−0.613961 + 0.789337i \(0.710425\pi\)
\(912\) 0 0
\(913\) 2.88131e13 1.37237
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −2.00186e13 −0.934916
\(918\) 0 0
\(919\) −3.00938e13 −1.39174 −0.695868 − 0.718170i \(-0.744980\pi\)
−0.695868 + 0.718170i \(0.744980\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −5.04088e11 −0.0228612
\(924\) 0 0
\(925\) −5.63592e12 −0.253120
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −3.89454e13 −1.71548 −0.857741 − 0.514083i \(-0.828132\pi\)
−0.857741 + 0.514083i \(0.828132\pi\)
\(930\) 0 0
\(931\) −7.86819e11 −0.0343243
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.59555e13 0.682744
\(936\) 0 0
\(937\) −3.29655e12 −0.139711 −0.0698557 − 0.997557i \(-0.522254\pi\)
−0.0698557 + 0.997557i \(0.522254\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 7.63948e12 0.317622 0.158811 − 0.987309i \(-0.449234\pi\)
0.158811 + 0.987309i \(0.449234\pi\)
\(942\) 0 0
\(943\) 3.21098e13 1.32232
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.20965e12 0.170087 0.0850435 − 0.996377i \(-0.472897\pi\)
0.0850435 + 0.996377i \(0.472897\pi\)
\(948\) 0 0
\(949\) 4.32263e12 0.173002
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −1.30736e13 −0.513426 −0.256713 − 0.966488i \(-0.582640\pi\)
−0.256713 + 0.966488i \(0.582640\pi\)
\(954\) 0 0
\(955\) 6.67089e12 0.259519
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −4.81555e11 −0.0183849
\(960\) 0 0
\(961\) 3.32750e13 1.25853
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 6.82751e12 0.253448
\(966\) 0 0
\(967\) 4.07490e13 1.49864 0.749321 − 0.662207i \(-0.230380\pi\)
0.749321 + 0.662207i \(0.230380\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −3.75625e13 −1.35603 −0.678013 − 0.735050i \(-0.737159\pi\)
−0.678013 + 0.735050i \(0.737159\pi\)
\(972\) 0 0
\(973\) −1.89472e13 −0.677699
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 3.05558e13 1.07292 0.536461 − 0.843925i \(-0.319761\pi\)
0.536461 + 0.843925i \(0.319761\pi\)
\(978\) 0 0
\(979\) 7.14126e13 2.48458
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.22056e13 0.416935 0.208468 − 0.978029i \(-0.433152\pi\)
0.208468 + 0.978029i \(0.433152\pi\)
\(984\) 0 0
\(985\) 1.70600e12 0.0577451
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.30332e13 0.433178
\(990\) 0 0
\(991\) −2.58503e13 −0.851400 −0.425700 − 0.904864i \(-0.639972\pi\)
−0.425700 + 0.904864i \(0.639972\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 8.47296e12 0.274051
\(996\) 0 0
\(997\) 4.06864e13 1.30413 0.652065 − 0.758163i \(-0.273903\pi\)
0.652065 + 0.758163i \(0.273903\pi\)
\(998\) 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 144.10.a.g.1.1 1
3.2 odd 2 144.10.a.i.1.1 1
4.3 odd 2 18.10.a.b.1.1 ✓ 1
12.11 even 2 18.10.a.d.1.1 yes 1
36.7 odd 6 162.10.c.h.109.1 2
36.11 even 6 162.10.c.c.109.1 2
36.23 even 6 162.10.c.c.55.1 2
36.31 odd 6 162.10.c.h.55.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.10.a.b.1.1 ✓ 1 4.3 odd 2
18.10.a.d.1.1 yes 1 12.11 even 2
144.10.a.g.1.1 1 1.1 even 1 trivial
144.10.a.i.1.1 1 3.2 odd 2
162.10.c.c.55.1 2 36.23 even 6
162.10.c.c.109.1 2 36.11 even 6
162.10.c.h.55.1 2 36.31 odd 6
162.10.c.h.109.1 2 36.7 odd 6