Properties

Label 576.7.h.b.161.15
Level $576$
Weight $7$
Character 576.161
Analytic conductor $132.511$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [576,7,Mod(161,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.161");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 576.h (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(132.511152165\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 161.15
Character \(\chi\) \(=\) 576.161
Dual form 576.7.h.b.161.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-83.0572 q^{5} +37.1638 q^{7} +O(q^{10})\) \(q-83.0572 q^{5} +37.1638 q^{7} +1959.80 q^{11} -4306.41i q^{13} +7855.72i q^{17} -6114.84i q^{19} -15556.2i q^{23} -8726.51 q^{25} -1668.36 q^{29} +27871.2 q^{31} -3086.72 q^{35} +52355.1i q^{37} -51807.9i q^{41} +135857. i q^{43} +93610.2i q^{47} -116268. q^{49} +104925. q^{53} -162776. q^{55} +176394. q^{59} +926.866i q^{61} +357678. i q^{65} -163928. i q^{67} -610911. i q^{71} +333300. q^{73} +72833.8 q^{77} +605169. q^{79} -486745. q^{83} -652474. i q^{85} -826800. i q^{89} -160043. i q^{91} +507882. i q^{95} -1.11632e6 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 169888 q^{25} + 829792 q^{49} - 1493888 q^{73} - 15893248 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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
\(5\) −83.0572 −0.664457 −0.332229 0.943199i \(-0.607801\pi\)
−0.332229 + 0.943199i \(0.607801\pi\)
\(6\) 0 0
\(7\) 37.1638 0.108349 0.0541747 0.998531i \(-0.482747\pi\)
0.0541747 + 0.998531i \(0.482747\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1959.80 1.47243 0.736214 0.676748i \(-0.236612\pi\)
0.736214 + 0.676748i \(0.236612\pi\)
\(12\) 0 0
\(13\) − 4306.41i − 1.96013i −0.198675 0.980065i \(-0.563664\pi\)
0.198675 0.980065i \(-0.436336\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7855.72i 1.59897i 0.600688 + 0.799483i \(0.294893\pi\)
−0.600688 + 0.799483i \(0.705107\pi\)
\(18\) 0 0
\(19\) − 6114.84i − 0.891507i −0.895156 0.445753i \(-0.852936\pi\)
0.895156 0.445753i \(-0.147064\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 15556.2i − 1.27856i −0.768975 0.639279i \(-0.779233\pi\)
0.768975 0.639279i \(-0.220767\pi\)
\(24\) 0 0
\(25\) −8726.51 −0.558497
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1668.36 −0.0684061 −0.0342030 0.999415i \(-0.510889\pi\)
−0.0342030 + 0.999415i \(0.510889\pi\)
\(30\) 0 0
\(31\) 27871.2 0.935558 0.467779 0.883846i \(-0.345054\pi\)
0.467779 + 0.883846i \(0.345054\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3086.72 −0.0719935
\(36\) 0 0
\(37\) 52355.1i 1.03360i 0.856105 + 0.516802i \(0.172878\pi\)
−0.856105 + 0.516802i \(0.827122\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 51807.9i − 0.751699i −0.926681 0.375850i \(-0.877351\pi\)
0.926681 0.375850i \(-0.122649\pi\)
\(42\) 0 0
\(43\) 135857.i 1.70874i 0.519664 + 0.854371i \(0.326057\pi\)
−0.519664 + 0.854371i \(0.673943\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 93610.2i 0.901633i 0.892617 + 0.450816i \(0.148867\pi\)
−0.892617 + 0.450816i \(0.851133\pi\)
\(48\) 0 0
\(49\) −116268. −0.988260
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 104925. 0.704773 0.352387 0.935854i \(-0.385370\pi\)
0.352387 + 0.935854i \(0.385370\pi\)
\(54\) 0 0
\(55\) −162776. −0.978366
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 176394. 0.858870 0.429435 0.903098i \(-0.358713\pi\)
0.429435 + 0.903098i \(0.358713\pi\)
\(60\) 0 0
\(61\) 926.866i 0.00408345i 0.999998 + 0.00204173i \(0.000649902\pi\)
−0.999998 + 0.00204173i \(0.999350\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 357678.i 1.30242i
\(66\) 0 0
\(67\) − 163928.i − 0.545039i −0.962150 0.272520i \(-0.912143\pi\)
0.962150 0.272520i \(-0.0878570\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) − 610911.i − 1.70688i −0.521190 0.853441i \(-0.674512\pi\)
0.521190 0.853441i \(-0.325488\pi\)
\(72\) 0 0
\(73\) 333300. 0.856774 0.428387 0.903595i \(-0.359082\pi\)
0.428387 + 0.903595i \(0.359082\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 72833.8 0.159537
\(78\) 0 0
\(79\) 605169. 1.22743 0.613713 0.789529i \(-0.289675\pi\)
0.613713 + 0.789529i \(0.289675\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −486745. −0.851270 −0.425635 0.904895i \(-0.639949\pi\)
−0.425635 + 0.904895i \(0.639949\pi\)
\(84\) 0 0
\(85\) − 652474.i − 1.06245i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 826800.i − 1.17282i −0.810015 0.586409i \(-0.800541\pi\)
0.810015 0.586409i \(-0.199459\pi\)
\(90\) 0 0
\(91\) − 160043.i − 0.212379i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 507882.i 0.592368i
\(96\) 0 0
\(97\) −1.11632e6 −1.22313 −0.611565 0.791194i \(-0.709460\pi\)
−0.611565 + 0.791194i \(0.709460\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −153614. −0.149096 −0.0745481 0.997217i \(-0.523751\pi\)
−0.0745481 + 0.997217i \(0.523751\pi\)
\(102\) 0 0
\(103\) −1.73563e6 −1.58835 −0.794173 0.607692i \(-0.792096\pi\)
−0.794173 + 0.607692i \(0.792096\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.41074e6 −1.15159 −0.575793 0.817596i \(-0.695306\pi\)
−0.575793 + 0.817596i \(0.695306\pi\)
\(108\) 0 0
\(109\) − 121880.i − 0.0941137i −0.998892 0.0470568i \(-0.985016\pi\)
0.998892 0.0470568i \(-0.0149842\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 1.38095e6i − 0.957069i −0.878069 0.478534i \(-0.841168\pi\)
0.878069 0.478534i \(-0.158832\pi\)
\(114\) 0 0
\(115\) 1.29205e6i 0.849547i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 291949.i 0.173247i
\(120\) 0 0
\(121\) 2.06926e6 1.16805
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2.02257e6 1.03555
\(126\) 0 0
\(127\) −2.04249e6 −0.997124 −0.498562 0.866854i \(-0.666138\pi\)
−0.498562 + 0.866854i \(0.666138\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.55809e6 0.693072 0.346536 0.938037i \(-0.387358\pi\)
0.346536 + 0.938037i \(0.387358\pi\)
\(132\) 0 0
\(133\) − 227251.i − 0.0965942i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 227489.i 0.0884707i 0.999021 + 0.0442354i \(0.0140851\pi\)
−0.999021 + 0.0442354i \(0.985915\pi\)
\(138\) 0 0
\(139\) − 1.83311e6i − 0.682565i −0.939961 0.341282i \(-0.889139\pi\)
0.939961 0.341282i \(-0.110861\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 8.43971e6i − 2.88615i
\(144\) 0 0
\(145\) 138569. 0.0454529
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.77808e6 1.74673 0.873363 0.487070i \(-0.161935\pi\)
0.873363 + 0.487070i \(0.161935\pi\)
\(150\) 0 0
\(151\) 479414. 0.139245 0.0696226 0.997573i \(-0.477821\pi\)
0.0696226 + 0.997573i \(0.477821\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.31490e6 −0.621638
\(156\) 0 0
\(157\) − 5.54477e6i − 1.43280i −0.697692 0.716398i \(-0.745789\pi\)
0.697692 0.716398i \(-0.254211\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 578128.i − 0.138531i
\(162\) 0 0
\(163\) 1.96511e6i 0.453759i 0.973923 + 0.226879i \(0.0728523\pi\)
−0.973923 + 0.226879i \(0.927148\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.09517e6i 0.449852i 0.974376 + 0.224926i \(0.0722140\pi\)
−0.974376 + 0.224926i \(0.927786\pi\)
\(168\) 0 0
\(169\) −1.37183e7 −2.84211
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −964175. −0.186216 −0.0931081 0.995656i \(-0.529680\pi\)
−0.0931081 + 0.995656i \(0.529680\pi\)
\(174\) 0 0
\(175\) −324311. −0.0605128
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −7.77781e6 −1.35612 −0.678060 0.735007i \(-0.737179\pi\)
−0.678060 + 0.735007i \(0.737179\pi\)
\(180\) 0 0
\(181\) − 5.24935e6i − 0.885258i −0.896705 0.442629i \(-0.854046\pi\)
0.896705 0.442629i \(-0.145954\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 4.34847e6i − 0.686786i
\(186\) 0 0
\(187\) 1.53957e7i 2.35436i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 1.21395e7i − 1.74221i −0.491100 0.871103i \(-0.663405\pi\)
0.491100 0.871103i \(-0.336595\pi\)
\(192\) 0 0
\(193\) 2.06934e6 0.287846 0.143923 0.989589i \(-0.454028\pi\)
0.143923 + 0.989589i \(0.454028\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.58221e6 0.860940 0.430470 0.902605i \(-0.358348\pi\)
0.430470 + 0.902605i \(0.358348\pi\)
\(198\) 0 0
\(199\) −1.08503e7 −1.37683 −0.688416 0.725316i \(-0.741694\pi\)
−0.688416 + 0.725316i \(0.741694\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −62002.5 −0.00741176
\(204\) 0 0
\(205\) 4.30301e6i 0.499472i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 1.19839e7i − 1.31268i
\(210\) 0 0
\(211\) − 1.29771e6i − 0.138143i −0.997612 0.0690715i \(-0.977996\pi\)
0.997612 0.0690715i \(-0.0220036\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) − 1.12839e7i − 1.13539i
\(216\) 0 0
\(217\) 1.03580e6 0.101367
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.38299e7 3.13418
\(222\) 0 0
\(223\) −7.77428e6 −0.701044 −0.350522 0.936554i \(-0.613996\pi\)
−0.350522 + 0.936554i \(0.613996\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4.27506e6 −0.365481 −0.182740 0.983161i \(-0.558497\pi\)
−0.182740 + 0.983161i \(0.558497\pi\)
\(228\) 0 0
\(229\) − 8.38344e6i − 0.698097i −0.937105 0.349049i \(-0.886505\pi\)
0.937105 0.349049i \(-0.113495\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.76991e6i 0.377087i 0.982065 + 0.188544i \(0.0603767\pi\)
−0.982065 + 0.188544i \(0.939623\pi\)
\(234\) 0 0
\(235\) − 7.77500e6i − 0.599096i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) − 6.88451e6i − 0.504289i −0.967690 0.252144i \(-0.918864\pi\)
0.967690 0.252144i \(-0.0811358\pi\)
\(240\) 0 0
\(241\) 1.90446e6 0.136057 0.0680284 0.997683i \(-0.478329\pi\)
0.0680284 + 0.997683i \(0.478329\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 9.65688e6 0.656657
\(246\) 0 0
\(247\) −2.63330e7 −1.74747
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −7.61930e6 −0.481830 −0.240915 0.970546i \(-0.577447\pi\)
−0.240915 + 0.970546i \(0.577447\pi\)
\(252\) 0 0
\(253\) − 3.04871e7i − 1.88258i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 1.21558e7i − 0.716115i −0.933700 0.358058i \(-0.883439\pi\)
0.933700 0.358058i \(-0.116561\pi\)
\(258\) 0 0
\(259\) 1.94572e6i 0.111990i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) − 2.70043e7i − 1.48445i −0.670149 0.742226i \(-0.733770\pi\)
0.670149 0.742226i \(-0.266230\pi\)
\(264\) 0 0
\(265\) −8.71473e6 −0.468292
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.21804e7 −1.13949 −0.569747 0.821820i \(-0.692959\pi\)
−0.569747 + 0.821820i \(0.692959\pi\)
\(270\) 0 0
\(271\) 8.95677e6 0.450032 0.225016 0.974355i \(-0.427757\pi\)
0.225016 + 0.974355i \(0.427757\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.71022e7 −0.822346
\(276\) 0 0
\(277\) − 2.73042e7i − 1.28466i −0.766427 0.642332i \(-0.777967\pi\)
0.766427 0.642332i \(-0.222033\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 3.84445e7i − 1.73267i −0.499466 0.866334i \(-0.666470\pi\)
0.499466 0.866334i \(-0.333530\pi\)
\(282\) 0 0
\(283\) 2.02032e7i 0.891374i 0.895189 + 0.445687i \(0.147041\pi\)
−0.895189 + 0.445687i \(0.852959\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 1.92538e6i − 0.0814462i
\(288\) 0 0
\(289\) −3.75748e7 −1.55669
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.25402e7 0.498541 0.249270 0.968434i \(-0.419809\pi\)
0.249270 + 0.968434i \(0.419809\pi\)
\(294\) 0 0
\(295\) −1.46508e7 −0.570682
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6.69914e7 −2.50614
\(300\) 0 0
\(301\) 5.04896e6i 0.185141i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 76982.8i − 0.00271328i
\(306\) 0 0
\(307\) 8.56216e6i 0.295916i 0.988994 + 0.147958i \(0.0472700\pi\)
−0.988994 + 0.147958i \(0.952730\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) − 3.46955e7i − 1.15343i −0.816944 0.576716i \(-0.804334\pi\)
0.816944 0.576716i \(-0.195666\pi\)
\(312\) 0 0
\(313\) 3.49394e7 1.13942 0.569708 0.821847i \(-0.307056\pi\)
0.569708 + 0.821847i \(0.307056\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.33835e7 1.67583 0.837913 0.545804i \(-0.183776\pi\)
0.837913 + 0.545804i \(0.183776\pi\)
\(318\) 0 0
\(319\) −3.26965e6 −0.100723
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4.80365e7 1.42549
\(324\) 0 0
\(325\) 3.75799e7i 1.09473i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3.47891e6i 0.0976913i
\(330\) 0 0
\(331\) − 3.32801e7i − 0.917699i −0.888514 0.458850i \(-0.848262\pi\)
0.888514 0.458850i \(-0.151738\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.36154e7i 0.362155i
\(336\) 0 0
\(337\) −1.44209e7 −0.376792 −0.188396 0.982093i \(-0.560329\pi\)
−0.188396 + 0.982093i \(0.560329\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5.46220e7 1.37754
\(342\) 0 0
\(343\) −8.69325e6 −0.215427
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.05006e7 1.44801 0.724005 0.689795i \(-0.242299\pi\)
0.724005 + 0.689795i \(0.242299\pi\)
\(348\) 0 0
\(349\) − 2.78673e7i − 0.655569i −0.944753 0.327785i \(-0.893698\pi\)
0.944753 0.327785i \(-0.106302\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.20925e7i 0.729591i 0.931088 + 0.364796i \(0.118861\pi\)
−0.931088 + 0.364796i \(0.881139\pi\)
\(354\) 0 0
\(355\) 5.07406e7i 1.13415i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.17808e6i 0.198367i 0.995069 + 0.0991833i \(0.0316230\pi\)
−0.995069 + 0.0991833i \(0.968377\pi\)
\(360\) 0 0
\(361\) 9.65456e6 0.205216
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.76829e7 −0.569290
\(366\) 0 0
\(367\) −8.02971e7 −1.62443 −0.812216 0.583357i \(-0.801739\pi\)
−0.812216 + 0.583357i \(0.801739\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.89940e6 0.0763618
\(372\) 0 0
\(373\) − 2.61467e7i − 0.503837i −0.967748 0.251918i \(-0.918939\pi\)
0.967748 0.251918i \(-0.0810615\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 7.18462e6i 0.134085i
\(378\) 0 0
\(379\) 8.11681e7i 1.49097i 0.666524 + 0.745483i \(0.267781\pi\)
−0.666524 + 0.745483i \(0.732219\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) − 7.20532e7i − 1.28250i −0.767332 0.641250i \(-0.778416\pi\)
0.767332 0.641250i \(-0.221584\pi\)
\(384\) 0 0
\(385\) −6.04937e6 −0.106005
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8.30952e7 −1.41165 −0.705825 0.708386i \(-0.749423\pi\)
−0.705825 + 0.708386i \(0.749423\pi\)
\(390\) 0 0
\(391\) 1.22205e8 2.04437
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −5.02636e7 −0.815572
\(396\) 0 0
\(397\) 4.67473e7i 0.747111i 0.927608 + 0.373555i \(0.121861\pi\)
−0.927608 + 0.373555i \(0.878139\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.29945e7i 0.666775i 0.942790 + 0.333388i \(0.108192\pi\)
−0.942790 + 0.333388i \(0.891808\pi\)
\(402\) 0 0
\(403\) − 1.20025e8i − 1.83382i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.02606e8i 1.52191i
\(408\) 0 0
\(409\) −1.10094e8 −1.60914 −0.804571 0.593857i \(-0.797604\pi\)
−0.804571 + 0.593857i \(0.797604\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6.55547e6 0.0930580
\(414\) 0 0
\(415\) 4.04277e7 0.565633
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4.89084e7 −0.664877 −0.332439 0.943125i \(-0.607871\pi\)
−0.332439 + 0.943125i \(0.607871\pi\)
\(420\) 0 0
\(421\) 1.81777e7i 0.243608i 0.992554 + 0.121804i \(0.0388680\pi\)
−0.992554 + 0.121804i \(0.961132\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 6.85530e7i − 0.893017i
\(426\) 0 0
\(427\) 34445.9i 0 0.000442439i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.09271e7i 0.386285i 0.981171 + 0.193143i \(0.0618680\pi\)
−0.981171 + 0.193143i \(0.938132\pi\)
\(432\) 0 0
\(433\) 5.51429e7 0.679244 0.339622 0.940562i \(-0.389701\pi\)
0.339622 + 0.940562i \(0.389701\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −9.51238e7 −1.13984
\(438\) 0 0
\(439\) 1.34146e8 1.58557 0.792784 0.609503i \(-0.208631\pi\)
0.792784 + 0.609503i \(0.208631\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.59880e7 0.183900 0.0919501 0.995764i \(-0.470690\pi\)
0.0919501 + 0.995764i \(0.470690\pi\)
\(444\) 0 0
\(445\) 6.86717e7i 0.779287i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 7.72078e7i − 0.852947i −0.904500 0.426473i \(-0.859756\pi\)
0.904500 0.426473i \(-0.140244\pi\)
\(450\) 0 0
\(451\) − 1.01533e8i − 1.10682i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.32927e7i 0.141117i
\(456\) 0 0
\(457\) 1.09149e8 1.14359 0.571796 0.820396i \(-0.306247\pi\)
0.571796 + 0.820396i \(0.306247\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7.95186e7 −0.811645 −0.405822 0.913952i \(-0.633015\pi\)
−0.405822 + 0.913952i \(0.633015\pi\)
\(462\) 0 0
\(463\) −7.28884e7 −0.734371 −0.367185 0.930148i \(-0.619679\pi\)
−0.367185 + 0.930148i \(0.619679\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.96554e8 1.92988 0.964940 0.262470i \(-0.0845372\pi\)
0.964940 + 0.262470i \(0.0845372\pi\)
\(468\) 0 0
\(469\) − 6.09218e6i − 0.0590547i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.66253e8i 2.51600i
\(474\) 0 0
\(475\) 5.33612e7i 0.497903i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.05958e8i 1.87401i 0.349320 + 0.937004i \(0.386413\pi\)
−0.349320 + 0.937004i \(0.613587\pi\)
\(480\) 0 0
\(481\) 2.25463e8 2.02600
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 9.27182e7 0.812718
\(486\) 0 0
\(487\) −1.47902e8 −1.28052 −0.640262 0.768157i \(-0.721174\pi\)
−0.640262 + 0.768157i \(0.721174\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3.18634e7 0.269183 0.134592 0.990901i \(-0.457028\pi\)
0.134592 + 0.990901i \(0.457028\pi\)
\(492\) 0 0
\(493\) − 1.31061e7i − 0.109379i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 2.27038e7i − 0.184940i
\(498\) 0 0
\(499\) − 1.10011e8i − 0.885386i −0.896673 0.442693i \(-0.854023\pi\)
0.896673 0.442693i \(-0.145977\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3.58001e7i 0.281307i 0.990059 + 0.140653i \(0.0449203\pi\)
−0.990059 + 0.140653i \(0.955080\pi\)
\(504\) 0 0
\(505\) 1.27587e7 0.0990680
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2.16724e8 −1.64344 −0.821720 0.569892i \(-0.806985\pi\)
−0.821720 + 0.569892i \(0.806985\pi\)
\(510\) 0 0
\(511\) 1.23867e7 0.0928309
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.44156e8 1.05539
\(516\) 0 0
\(517\) 1.83457e8i 1.32759i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.01755e8i 0.719518i 0.933045 + 0.359759i \(0.117141\pi\)
−0.933045 + 0.359759i \(0.882859\pi\)
\(522\) 0 0
\(523\) − 1.10857e8i − 0.774920i −0.921887 0.387460i \(-0.873353\pi\)
0.921887 0.387460i \(-0.126647\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.18948e8i 1.49593i
\(528\) 0 0
\(529\) −9.39596e7 −0.634709
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.23106e8 −1.47343
\(534\) 0 0
\(535\) 1.17172e8 0.765179
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.27862e8 −1.45514
\(540\) 0 0
\(541\) 1.47693e8i 0.932756i 0.884586 + 0.466378i \(0.154441\pi\)
−0.884586 + 0.466378i \(0.845559\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.01230e7i 0.0625345i
\(546\) 0 0
\(547\) 8.41332e7i 0.514050i 0.966405 + 0.257025i \(0.0827423\pi\)
−0.966405 + 0.257025i \(0.917258\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.02017e7i 0.0609845i
\(552\) 0 0
\(553\) 2.24904e7 0.132991
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.09820e7 −0.295020 −0.147510 0.989061i \(-0.547126\pi\)
−0.147510 + 0.989061i \(0.547126\pi\)
\(558\) 0 0
\(559\) 5.85055e8 3.34936
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.51243e8 0.847521 0.423761 0.905774i \(-0.360710\pi\)
0.423761 + 0.905774i \(0.360710\pi\)
\(564\) 0 0
\(565\) 1.14698e8i 0.635931i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 1.34052e8i − 0.727671i −0.931463 0.363836i \(-0.881467\pi\)
0.931463 0.363836i \(-0.118533\pi\)
\(570\) 0 0
\(571\) − 8.15488e7i − 0.438035i −0.975721 0.219018i \(-0.929715\pi\)
0.975721 0.219018i \(-0.0702852\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.35751e8i 0.714070i
\(576\) 0 0
\(577\) 1.66709e6 0.00867826 0.00433913 0.999991i \(-0.498619\pi\)
0.00433913 + 0.999991i \(0.498619\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.80893e7 −0.0922346
\(582\) 0 0
\(583\) 2.05631e8 1.03773
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.33311e8 −0.659098 −0.329549 0.944138i \(-0.606897\pi\)
−0.329549 + 0.944138i \(0.606897\pi\)
\(588\) 0 0
\(589\) − 1.70428e8i − 0.834056i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.62556e8i 1.25910i 0.776962 + 0.629548i \(0.216760\pi\)
−0.776962 + 0.629548i \(0.783240\pi\)
\(594\) 0 0
\(595\) − 2.42484e7i − 0.115115i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) − 2.70406e7i − 0.125816i −0.998019 0.0629081i \(-0.979963\pi\)
0.998019 0.0629081i \(-0.0200375\pi\)
\(600\) 0 0
\(601\) −1.33675e8 −0.615782 −0.307891 0.951422i \(-0.599623\pi\)
−0.307891 + 0.951422i \(0.599623\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.71867e8 −0.776117
\(606\) 0 0
\(607\) −1.25106e8 −0.559387 −0.279693 0.960089i \(-0.590233\pi\)
−0.279693 + 0.960089i \(0.590233\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4.03124e8 1.76732
\(612\) 0 0
\(613\) − 1.23831e6i − 0.00537588i −0.999996 0.00268794i \(-0.999144\pi\)
0.999996 0.00268794i \(-0.000855599\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.35967e7i 0.185608i 0.995684 + 0.0928042i \(0.0295831\pi\)
−0.995684 + 0.0928042i \(0.970417\pi\)
\(618\) 0 0
\(619\) 3.54527e8i 1.49478i 0.664386 + 0.747390i \(0.268693\pi\)
−0.664386 + 0.747390i \(0.731307\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) − 3.07271e7i − 0.127074i
\(624\) 0 0
\(625\) −3.16370e7 −0.129585
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −4.11288e8 −1.65270
\(630\) 0 0
\(631\) −3.25768e8 −1.29664 −0.648322 0.761367i \(-0.724529\pi\)
−0.648322 + 0.761367i \(0.724529\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.69644e8 0.662547
\(636\) 0 0
\(637\) 5.00697e8i 1.93712i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.13127e8i 1.94828i 0.225954 + 0.974138i \(0.427450\pi\)
−0.225954 + 0.974138i \(0.572550\pi\)
\(642\) 0 0
\(643\) − 4.59513e8i − 1.72848i −0.503077 0.864242i \(-0.667799\pi\)
0.503077 0.864242i \(-0.332201\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.56031e8i 0.945323i 0.881244 + 0.472662i \(0.156707\pi\)
−0.881244 + 0.472662i \(0.843293\pi\)
\(648\) 0 0
\(649\) 3.45697e8 1.26462
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.52625e8 1.62555 0.812773 0.582580i \(-0.197957\pi\)
0.812773 + 0.582580i \(0.197957\pi\)
\(654\) 0 0
\(655\) −1.29410e8 −0.460516
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.27984e8 0.796613 0.398306 0.917252i \(-0.369598\pi\)
0.398306 + 0.917252i \(0.369598\pi\)
\(660\) 0 0
\(661\) − 1.28280e8i − 0.444177i −0.975027 0.222089i \(-0.928713\pi\)
0.975027 0.222089i \(-0.0712874\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.88748e7i 0.0641827i
\(666\) 0 0
\(667\) 2.59533e7i 0.0874611i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.81647e6i 0.00601259i
\(672\) 0 0
\(673\) −1.51573e8 −0.497253 −0.248627 0.968599i \(-0.579979\pi\)
−0.248627 + 0.968599i \(0.579979\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.60675e8 1.48467 0.742333 0.670031i \(-0.233719\pi\)
0.742333 + 0.670031i \(0.233719\pi\)
\(678\) 0 0
\(679\) −4.14867e7 −0.132525
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.03627e8 −0.325245 −0.162623 0.986688i \(-0.551995\pi\)
−0.162623 + 0.986688i \(0.551995\pi\)
\(684\) 0 0
\(685\) − 1.88946e7i − 0.0587850i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 4.51848e8i − 1.38145i
\(690\) 0 0
\(691\) − 5.59603e7i − 0.169608i −0.996398 0.0848039i \(-0.972974\pi\)
0.996398 0.0848039i \(-0.0270264\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.52253e8i 0.453535i
\(696\) 0 0
\(697\) 4.06988e8 1.20194
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −3.95564e8 −1.14832 −0.574159 0.818744i \(-0.694671\pi\)
−0.574159 + 0.818744i \(0.694671\pi\)
\(702\) 0 0
\(703\) 3.20144e8 0.921465
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.70888e6 −0.0161545
\(708\) 0 0
\(709\) 7.41424e7i 0.208031i 0.994576 + 0.104015i \(0.0331691\pi\)
−0.994576 + 0.104015i \(0.966831\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 4.33570e8i − 1.19616i
\(714\) 0 0
\(715\) 7.00978e8i 1.91772i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) − 5.26454e8i − 1.41636i −0.706032 0.708180i \(-0.749517\pi\)
0.706032 0.708180i \(-0.250483\pi\)
\(720\) 0 0
\(721\) −6.45026e7 −0.172096
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.45589e7 0.0382046
\(726\) 0 0
\(727\) 2.60552e8 0.678096 0.339048 0.940769i \(-0.389895\pi\)
0.339048 + 0.940769i \(0.389895\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.06725e9 −2.73222
\(732\) 0 0
\(733\) − 1.52419e8i − 0.387014i −0.981099 0.193507i \(-0.938014\pi\)
0.981099 0.193507i \(-0.0619861\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 3.21266e8i − 0.802531i
\(738\) 0 0
\(739\) − 7.15919e8i − 1.77391i −0.461860 0.886953i \(-0.652818\pi\)
0.461860 0.886953i \(-0.347182\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 4.70029e8i 1.14593i 0.819580 + 0.572965i \(0.194207\pi\)
−0.819580 + 0.572965i \(0.805793\pi\)
\(744\) 0 0
\(745\) −4.79911e8 −1.16062
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5.24286e7 −0.124774
\(750\) 0 0
\(751\) −2.67972e8 −0.632659 −0.316329 0.948649i \(-0.602450\pi\)
−0.316329 + 0.948649i \(0.602450\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3.98188e7 −0.0925225
\(756\) 0 0
\(757\) − 1.90775e8i − 0.439778i −0.975525 0.219889i \(-0.929431\pi\)
0.975525 0.219889i \(-0.0705695\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 1.63151e8i − 0.370200i −0.982720 0.185100i \(-0.940739\pi\)
0.982720 0.185100i \(-0.0592608\pi\)
\(762\) 0 0
\(763\) − 4.52953e6i − 0.0101972i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) − 7.59623e8i − 1.68350i
\(768\) 0 0
\(769\) −3.52840e8 −0.775888 −0.387944 0.921683i \(-0.626815\pi\)
−0.387944 + 0.921683i \(0.626815\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.92662e8 −0.417116 −0.208558 0.978010i \(-0.566877\pi\)
−0.208558 + 0.978010i \(0.566877\pi\)
\(774\) 0 0
\(775\) −2.43218e8 −0.522506
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.16797e8 −0.670145
\(780\) 0 0
\(781\) − 1.19727e9i − 2.51326i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4.60533e8i 0.952032i
\(786\) 0 0
\(787\) − 1.39654e8i − 0.286503i −0.989686 0.143252i \(-0.954244\pi\)
0.989686 0.143252i \(-0.0457558\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) − 5.13215e7i − 0.103698i
\(792\) 0 0
\(793\) 3.99146e6 0.00800410
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.74248e8 0.739239 0.369619 0.929183i \(-0.379488\pi\)
0.369619 + 0.929183i \(0.379488\pi\)
\(798\) 0 0
\(799\) −7.35376e8 −1.44168
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 6.53201e8 1.26154
\(804\) 0 0
\(805\) 4.80177e7i 0.0920479i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 8.07376e8i 1.52486i 0.647071 + 0.762430i \(0.275994\pi\)
−0.647071 + 0.762430i \(0.724006\pi\)
\(810\) 0 0
\(811\) 6.75232e8i 1.26587i 0.774204 + 0.632937i \(0.218151\pi\)
−0.774204 + 0.632937i \(0.781849\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) − 1.63217e8i − 0.301503i
\(816\) 0 0
\(817\) 8.30744e8 1.52335
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 4.61450e8 0.833865 0.416932 0.908938i \(-0.363105\pi\)
0.416932 + 0.908938i \(0.363105\pi\)
\(822\) 0 0
\(823\) −3.57228e8 −0.640835 −0.320418 0.947276i \(-0.603823\pi\)
−0.320418 + 0.947276i \(0.603823\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −7.57478e8 −1.33922 −0.669612 0.742711i \(-0.733540\pi\)
−0.669612 + 0.742711i \(0.733540\pi\)
\(828\) 0 0
\(829\) 1.96526e8i 0.344950i 0.985014 + 0.172475i \(0.0551764\pi\)
−0.985014 + 0.172475i \(0.944824\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 9.13368e8i − 1.58020i
\(834\) 0 0
\(835\) − 1.74019e8i − 0.298907i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) − 1.04024e9i − 1.76136i −0.473711 0.880680i \(-0.657086\pi\)
0.473711 0.880680i \(-0.342914\pi\)
\(840\) 0 0
\(841\) −5.92040e8 −0.995321
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.13941e9 1.88846
\(846\) 0 0
\(847\) 7.69018e7 0.126557
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 8.14447e8 1.32152
\(852\) 0 0
\(853\) − 6.97415e8i − 1.12368i −0.827244 0.561842i \(-0.810093\pi\)
0.827244 0.561842i \(-0.189907\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 5.24118e8i − 0.832696i −0.909205 0.416348i \(-0.863310\pi\)
0.909205 0.416348i \(-0.136690\pi\)
\(858\) 0 0
\(859\) 1.07319e8i 0.169315i 0.996410 + 0.0846575i \(0.0269796\pi\)
−0.996410 + 0.0846575i \(0.973020\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) − 2.28624e8i − 0.355705i −0.984057 0.177852i \(-0.943085\pi\)
0.984057 0.177852i \(-0.0569150\pi\)
\(864\) 0 0
\(865\) 8.00816e7 0.123733
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.18601e9 1.80730
\(870\) 0 0
\(871\) −7.05939e8 −1.06835
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 7.51664e7 0.112202
\(876\) 0 0
\(877\) 5.54337e8i 0.821818i 0.911676 + 0.410909i \(0.134789\pi\)
−0.911676 + 0.410909i \(0.865211\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 1.17732e9i − 1.72174i −0.508824 0.860870i \(-0.669920\pi\)
0.508824 0.860870i \(-0.330080\pi\)
\(882\) 0 0
\(883\) 7.67777e8i 1.11520i 0.830109 + 0.557600i \(0.188278\pi\)
−0.830109 + 0.557600i \(0.811722\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 6.89440e8i − 0.987929i −0.869482 0.493964i \(-0.835547\pi\)
0.869482 0.493964i \(-0.164453\pi\)
\(888\) 0 0
\(889\) −7.59069e7 −0.108038
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 5.72412e8 0.803811
\(894\) 0 0
\(895\) 6.46003e8 0.901084
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −4.64991e7 −0.0639978
\(900\) 0 0
\(901\) 8.24258e8i 1.12691i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 4.35996e8i 0.588216i
\(906\) 0 0
\(907\) 3.13153e8i 0.419696i 0.977734 + 0.209848i \(0.0672969\pi\)
−0.977734 + 0.209848i \(0.932703\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 7.81208e8i 1.03326i 0.856207 + 0.516632i \(0.172815\pi\)
−0.856207 + 0.516632i \(0.827185\pi\)
\(912\) 0 0
\(913\) −9.53924e8 −1.25343
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 5.79045e7 0.0750939
\(918\) 0 0
\(919\) −5.24800e8 −0.676157 −0.338078 0.941118i \(-0.609777\pi\)
−0.338078 + 0.941118i \(0.609777\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −2.63083e9 −3.34571
\(924\) 0 0
\(925\) − 4.56878e8i − 0.577264i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 6.73499e8i 0.840021i 0.907519 + 0.420010i \(0.137974\pi\)
−0.907519 + 0.420010i \(0.862026\pi\)
\(930\) 0 0
\(931\) 7.10960e8i 0.881041i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) − 1.27872e9i − 1.56437i
\(936\) 0 0
\(937\) −1.46278e9 −1.77812 −0.889060 0.457790i \(-0.848641\pi\)
−0.889060 + 0.457790i \(0.848641\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.46136e9 −1.75384 −0.876920 0.480637i \(-0.840405\pi\)
−0.876920 + 0.480637i \(0.840405\pi\)
\(942\) 0 0
\(943\) −8.05934e8 −0.961091
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 9.23223e8 1.08707 0.543534 0.839387i \(-0.317086\pi\)
0.543534 + 0.839387i \(0.317086\pi\)
\(948\) 0 0
\(949\) − 1.43532e9i − 1.67939i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 1.21757e9i − 1.40675i −0.710820 0.703374i \(-0.751676\pi\)
0.710820 0.703374i \(-0.248324\pi\)
\(954\) 0 0
\(955\) 1.00827e9i 1.15762i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 8.45438e6i 0.00958575i
\(960\) 0 0
\(961\) −1.10700e8 −0.124732
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.71874e8 −0.191261
\(966\) 0 0
\(967\) 1.22852e8 0.135863 0.0679317 0.997690i \(-0.478360\pi\)
0.0679317 + 0.997690i \(0.478360\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.16709e9 −1.27481 −0.637405 0.770529i \(-0.719992\pi\)
−0.637405 + 0.770529i \(0.719992\pi\)
\(972\) 0 0
\(973\) − 6.81253e7i − 0.0739554i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 3.31100e8i 0.355038i 0.984117 + 0.177519i \(0.0568071\pi\)
−0.984117 + 0.177519i \(0.943193\pi\)
\(978\) 0 0
\(979\) − 1.62037e9i − 1.72689i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) − 9.27161e8i − 0.976100i −0.872816 0.488050i \(-0.837708\pi\)
0.872816 0.488050i \(-0.162292\pi\)
\(984\) 0 0
\(985\) −5.46700e8 −0.572058
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 2.11342e9 2.18472
\(990\) 0 0
\(991\) 5.96968e8 0.613381 0.306691 0.951809i \(-0.400778\pi\)
0.306691 + 0.951809i \(0.400778\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 9.01192e8 0.914846
\(996\) 0 0
\(997\) − 1.50998e9i − 1.52365i −0.647782 0.761826i \(-0.724303\pi\)
0.647782 0.761826i \(-0.275697\pi\)
\(998\) 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 576.7.h.b.161.15 yes 32
3.2 odd 2 inner 576.7.h.b.161.17 yes 32
4.3 odd 2 inner 576.7.h.b.161.13 32
8.3 odd 2 inner 576.7.h.b.161.18 yes 32
8.5 even 2 inner 576.7.h.b.161.20 yes 32
12.11 even 2 inner 576.7.h.b.161.19 yes 32
24.5 odd 2 inner 576.7.h.b.161.14 yes 32
24.11 even 2 inner 576.7.h.b.161.16 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
576.7.h.b.161.13 32 4.3 odd 2 inner
576.7.h.b.161.14 yes 32 24.5 odd 2 inner
576.7.h.b.161.15 yes 32 1.1 even 1 trivial
576.7.h.b.161.16 yes 32 24.11 even 2 inner
576.7.h.b.161.17 yes 32 3.2 odd 2 inner
576.7.h.b.161.18 yes 32 8.3 odd 2 inner
576.7.h.b.161.19 yes 32 12.11 even 2 inner
576.7.h.b.161.20 yes 32 8.5 even 2 inner