Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,10,Mod(1,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.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: | \(13.9059675764\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.177113.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 118x + 136 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.15428\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.46285 | 0.153038 | 0.0765190 | − | 0.997068i | \(-0.475619\pi\) | ||||
0.0765190 | + | 0.997068i | \(0.475619\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −500.009 | −0.976579 | ||||||||
\(5\) | 1404.01 | 1.00463 | 0.502313 | − | 0.864686i | \(-0.332482\pi\) | ||||
0.502313 | + | 0.864686i | \(0.332482\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1665.57 | 0.262193 | 0.131097 | − | 0.991370i | \(-0.458150\pi\) | ||||
0.131097 | + | 0.991370i | \(0.458150\pi\) | |||||||
\(8\) | −3504.44 | −0.302492 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4861.88 | 0.153746 | ||||||||
\(11\) | −63618.6 | −1.31014 | −0.655069 | − | 0.755569i | \(-0.727360\pi\) | ||||
−0.655069 | + | 0.755569i | \(0.727360\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −111210. | −1.07993 | −0.539967 | − | 0.841686i | \(-0.681563\pi\) | ||||
−0.539967 | + | 0.841686i | \(0.681563\pi\) | |||||||
\(14\) | 5767.62 | 0.0401255 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 243869. | 0.930287 | ||||||||
\(17\) | −383783. | −1.11446 | −0.557231 | − | 0.830358i | \(-0.688136\pi\) | ||||
−0.557231 | + | 0.830358i | \(0.688136\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7441.82 | 0.0131005 | 0.00655025 | − | 0.999979i | \(-0.497915\pi\) | ||||
0.00655025 | + | 0.999979i | \(0.497915\pi\) | |||||||
\(20\) | −702017. | −0.981098 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −220302. | −0.200501 | ||||||||
\(23\) | −2.61722e6 | −1.95013 | −0.975067 | − | 0.221910i | \(-0.928771\pi\) | ||||
−0.975067 | + | 0.221910i | \(0.928771\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18115.8 | 0.00927531 | ||||||||
\(26\) | −385102. | −0.165271 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −832799. | −0.256053 | ||||||||
\(29\) | 579091. | 0.152039 | 0.0760196 | − | 0.997106i | \(-0.475779\pi\) | ||||
0.0760196 | + | 0.997106i | \(0.475779\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.51831e6 | 0.684237 | 0.342118 | − | 0.939657i | \(-0.388856\pi\) | ||||
0.342118 | + | 0.939657i | \(0.388856\pi\) | |||||||
\(32\) | 2.63875e6 | 0.444861 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.32898e6 | −0.170555 | ||||||||
\(35\) | 2.33847e6 | 0.263407 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.82783e6 | −0.862084 | −0.431042 | − | 0.902332i | \(-0.641854\pi\) | ||||
−0.431042 | + | 0.902332i | \(0.641854\pi\) | |||||||
\(38\) | 25769.9 | 0.00200487 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.92026e6 | −0.303891 | ||||||||
\(41\) | 1.77760e7 | 0.982441 | 0.491221 | − | 0.871035i | \(-0.336551\pi\) | ||||
0.491221 | + | 0.871035i | \(0.336551\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.91298e7 | 1.74542 | 0.872709 | − | 0.488240i | \(-0.162361\pi\) | ||||
0.872709 | + | 0.488240i | \(0.162361\pi\) | |||||||
\(44\) | 3.18098e7 | 1.27945 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.06304e6 | −0.298445 | ||||||||
\(47\) | 2.67867e7 | 0.800718 | 0.400359 | − | 0.916358i | \(-0.368885\pi\) | ||||
0.400359 | + | 0.916358i | \(0.368885\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.75795e7 | −0.931255 | ||||||||
\(50\) | 62732.5 | 0.00141947 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.56058e7 | 1.05464 | ||||||||
\(53\) | −6.04430e7 | −1.05222 | −0.526108 | − | 0.850418i | \(-0.676349\pi\) | ||||
−0.526108 | + | 0.850418i | \(0.676349\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.93210e7 | −1.31620 | ||||||||
\(56\) | −5.83689e6 | −0.0793113 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.00531e6 | 0.0232678 | ||||||||
\(59\) | −1.34817e8 | −1.44847 | −0.724237 | − | 0.689551i | \(-0.757808\pi\) | ||||
−0.724237 | + | 0.689551i | \(0.757808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.40769e8 | 1.30174 | 0.650869 | − | 0.759190i | \(-0.274405\pi\) | ||||
0.650869 | + | 0.759190i | \(0.274405\pi\) | |||||||
\(62\) | 1.21834e7 | 0.104714 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.15723e8 | −0.862206 | ||||||||
\(65\) | −1.56139e8 | −1.08493 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.31341e7 | 0.443387 | 0.221694 | − | 0.975116i | \(-0.428841\pi\) | ||||
0.221694 | + | 0.975116i | \(0.428841\pi\) | |||||||
\(68\) | 1.91895e8 | 1.08836 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.09780e6 | 0.0403112 | ||||||||
\(71\) | −2.72910e8 | −1.27455 | −0.637276 | − | 0.770636i | \(-0.719939\pi\) | ||||
−0.637276 | + | 0.770636i | \(0.719939\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.64531e8 | −1.09025 | −0.545123 | − | 0.838356i | \(-0.683517\pi\) | ||||
−0.545123 | + | 0.838356i | \(0.683517\pi\) | |||||||
\(74\) | −3.40323e7 | −0.131932 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.72097e6 | −0.0127937 | ||||||||
\(77\) | −1.05961e8 | −0.343509 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.44662e8 | 1.57328 | 0.786639 | − | 0.617413i | \(-0.211819\pi\) | ||||
0.786639 | + | 0.617413i | \(0.211819\pi\) | |||||||
\(80\) | 3.42394e8 | 0.934591 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.15557e7 | 0.150351 | ||||||||
\(83\) | 1.73988e8 | 0.402408 | 0.201204 | − | 0.979549i | \(-0.435515\pi\) | ||||
0.201204 | + | 0.979549i | \(0.435515\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.38834e8 | −1.11962 | ||||||||
\(86\) | 1.35501e8 | 0.267115 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.22947e8 | 0.396306 | ||||||||
\(89\) | 5.69208e8 | 0.961647 | 0.480823 | − | 0.876817i | \(-0.340338\pi\) | ||||
0.480823 | + | 0.876817i | \(0.340338\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.85227e8 | −0.283151 | ||||||||
\(92\) | 1.30863e9 | 1.90446 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.27586e7 | 0.122540 | ||||||||
\(95\) | 1.04484e7 | 0.0131611 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.86520e8 | −0.672682 | −0.336341 | − | 0.941740i | \(-0.609189\pi\) | ||||
−0.336341 | + | 0.941740i | \(0.609189\pi\) | |||||||
\(98\) | −1.30132e8 | −0.142517 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.05808e6 | −0.00905808 | ||||||||
\(101\) | −1.62439e9 | −1.55326 | −0.776629 | − | 0.629959i | \(-0.783072\pi\) | ||||
−0.776629 | + | 0.629959i | \(0.783072\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.92705e8 | 0.518885 | 0.259442 | − | 0.965759i | \(-0.416461\pi\) | ||||
0.259442 | + | 0.965759i | \(0.416461\pi\) | |||||||
\(104\) | 3.89727e8 | 0.326671 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.09305e8 | −0.161029 | ||||||||
\(107\) | −4.69405e8 | −0.346195 | −0.173098 | − | 0.984905i | \(-0.555378\pi\) | ||||
−0.173098 | + | 0.984905i | \(0.555378\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.10211e9 | 1.42639 | 0.713193 | − | 0.700968i | \(-0.247248\pi\) | ||||
0.713193 | + | 0.700968i | \(0.247248\pi\) | |||||||
\(110\) | −3.09306e8 | −0.201428 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.06181e8 | 0.243915 | ||||||||
\(113\) | −1.25356e9 | −0.723255 | −0.361628 | − | 0.932323i | \(-0.617779\pi\) | ||||
−0.361628 | + | 0.932323i | \(0.617779\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.67460e9 | −1.95916 | ||||||||
\(116\) | −2.89550e8 | −0.148478 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.66851e8 | −0.221671 | ||||||||
\(119\) | −6.39217e8 | −0.292204 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.68938e9 | 0.716460 | ||||||||
\(122\) | 4.87463e8 | 0.199215 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.75919e9 | −0.668212 | ||||||||
\(125\) | −2.71677e9 | −0.995309 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.81433e9 | 1.30107 | 0.650536 | − | 0.759476i | \(-0.274544\pi\) | ||||
0.650536 | + | 0.759476i | \(0.274544\pi\) | |||||||
\(128\) | −1.75178e9 | −0.576811 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.40687e8 | −0.166036 | ||||||||
\(131\) | −1.93974e9 | −0.575471 | −0.287735 | − | 0.957710i | \(-0.592902\pi\) | ||||
−0.287735 | + | 0.957710i | \(0.592902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.23949e7 | 0.00343486 | ||||||||
\(134\) | 2.53253e8 | 0.0678551 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.34494e9 | 0.337115 | ||||||||
\(137\) | 5.94264e9 | 1.44124 | 0.720621 | − | 0.693329i | \(-0.243857\pi\) | ||||
0.720621 | + | 0.693329i | \(0.243857\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.55150e9 | −1.26137 | −0.630687 | − | 0.776038i | \(-0.717227\pi\) | ||||
−0.630687 | + | 0.776038i | \(0.717227\pi\) | |||||||
\(140\) | −1.16926e9 | −0.257237 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.45049e8 | −0.195055 | ||||||||
\(143\) | 7.07500e9 | 1.41486 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.13049e8 | 0.152743 | ||||||||
\(146\) | −9.16033e8 | −0.166849 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.91400e9 | 0.841894 | ||||||||
\(149\) | 9.72401e9 | 1.61624 | 0.808122 | − | 0.589015i | \(-0.200484\pi\) | ||||
0.808122 | + | 0.589015i | \(0.200484\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.21852e9 | −0.503802 | −0.251901 | − | 0.967753i | \(-0.581056\pi\) | ||||
−0.251901 | + | 0.967753i | \(0.581056\pi\) | |||||||
\(152\) | −2.60794e7 | −0.00396279 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.66928e8 | −0.0525700 | ||||||||
\(155\) | 4.93974e9 | 0.687403 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.28576e9 | 0.168893 | 0.0844465 | − | 0.996428i | \(-0.473088\pi\) | ||||
0.0844465 | + | 0.996428i | \(0.473088\pi\) | |||||||
\(158\) | 1.88609e9 | 0.240771 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.70484e9 | 0.446919 | ||||||||
\(161\) | −4.35916e9 | −0.511312 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.38269e9 | 0.486291 | 0.243146 | − | 0.969990i | \(-0.421821\pi\) | ||||
0.243146 | + | 0.969990i | \(0.421821\pi\) | |||||||
\(164\) | −8.88815e9 | −0.959432 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.02494e8 | 0.0615837 | ||||||||
\(167\) | 1.53534e9 | 0.152750 | 0.0763750 | − | 0.997079i | \(-0.475665\pi\) | ||||
0.0763750 | + | 0.997079i | \(0.475665\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.76307e9 | 0.166257 | ||||||||
\(170\) | −1.86590e9 | −0.171344 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.95652e10 | −1.70454 | ||||||||
\(173\) | −7.58197e8 | −0.0643538 | −0.0321769 | − | 0.999482i | \(-0.510244\pi\) | ||||
−0.0321769 | + | 0.999482i | \(0.510244\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.01732e7 | 0.00243193 | ||||||||
\(176\) | −1.55146e10 | −1.21880 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.97108e9 | 0.147168 | ||||||||
\(179\) | 1.17238e10 | 0.853549 | 0.426774 | − | 0.904358i | \(-0.359650\pi\) | ||||
0.426774 | + | 0.904358i | \(0.359650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.83265e9 | −0.611698 | −0.305849 | − | 0.952080i | \(-0.598940\pi\) | ||||
−0.305849 | + | 0.952080i | \(0.598940\pi\) | |||||||
\(182\) | −6.41415e8 | −0.0433329 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.17188e9 | 0.589899 | ||||||||
\(185\) | −1.37984e10 | −0.866073 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.44157e10 | 1.46010 | ||||||||
\(188\) | −1.33936e10 | −0.781965 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.61812e7 | 0.00201415 | ||||||||
\(191\) | −3.14017e9 | −0.170727 | −0.0853636 | − | 0.996350i | \(-0.527205\pi\) | ||||
−0.0853636 | + | 0.996350i | \(0.527205\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.06350e10 | −1.58932 | −0.794658 | − | 0.607057i | \(-0.792350\pi\) | ||||
−0.794658 | + | 0.607057i | \(0.792350\pi\) | |||||||
\(194\) | −2.03103e9 | −0.102946 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.87901e10 | 0.909444 | ||||||||
\(197\) | −2.16444e10 | −1.02388 | −0.511939 | − | 0.859022i | \(-0.671073\pi\) | ||||
−0.511939 | + | 0.859022i | \(0.671073\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.61495e9 | −0.163404 | −0.0817021 | − | 0.996657i | \(-0.526036\pi\) | ||||
−0.0817021 | + | 0.996657i | \(0.526036\pi\) | |||||||
\(200\) | −6.34858e7 | −0.00280570 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.62501e9 | −0.237707 | ||||||||
\(203\) | 9.64516e8 | 0.0398637 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.49576e10 | 0.986987 | ||||||||
\(206\) | 2.05245e9 | 0.0794091 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.71206e10 | −1.00465 | ||||||||
\(209\) | −4.73438e8 | −0.0171635 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.18587e10 | −0.411877 | −0.205938 | − | 0.978565i | \(-0.566025\pi\) | ||||
−0.205938 | + | 0.978565i | \(0.566025\pi\) | |||||||
\(212\) | 3.02220e10 | 1.02757 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.62548e9 | −0.0529810 | ||||||||
\(215\) | 5.49386e10 | 1.75349 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.85999e9 | 0.179402 | ||||||||
\(218\) | 7.27931e9 | 0.218291 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.46613e10 | 1.28537 | ||||||||
\(221\) | 4.26803e10 | 1.20355 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.88757e10 | −0.511129 | −0.255565 | − | 0.966792i | \(-0.582261\pi\) | ||||
−0.255565 | + | 0.966792i | \(0.582261\pi\) | |||||||
\(224\) | 4.39503e9 | 0.116640 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.34089e9 | −0.110685 | ||||||||
\(227\) | −2.04771e9 | −0.0511862 | −0.0255931 | − | 0.999672i | \(-0.508147\pi\) | ||||
−0.0255931 | + | 0.999672i | \(0.508147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.13934e9 | 0.0514068 | 0.0257034 | − | 0.999670i | \(-0.491817\pi\) | ||||
0.0257034 | + | 0.999670i | \(0.491817\pi\) | |||||||
\(230\) | −1.27246e10 | −0.299825 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.02939e9 | −0.0459906 | ||||||||
\(233\) | −4.02632e10 | −0.894966 | −0.447483 | − | 0.894292i | \(-0.647679\pi\) | ||||
−0.447483 | + | 0.894292i | \(0.647679\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.76088e10 | 0.804423 | ||||||||
\(236\) | 6.74097e10 | 1.41455 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.21351e9 | −0.0447184 | ||||||||
\(239\) | −9.26326e9 | −0.183643 | −0.0918213 | − | 0.995776i | \(-0.529269\pi\) | ||||
−0.0918213 | + | 0.995776i | \(0.529269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.80952e10 | −1.49124 | −0.745620 | − | 0.666371i | \(-0.767847\pi\) | ||||
−0.745620 | + | 0.666371i | \(0.767847\pi\) | |||||||
\(242\) | 5.85006e9 | 0.109646 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.03859e10 | −1.27125 | ||||||||
\(245\) | −5.27619e10 | −0.935564 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.27602e8 | −0.0141477 | ||||||||
\(248\) | −1.23297e10 | −0.206976 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.40778e9 | −0.152320 | ||||||||
\(251\) | −1.54732e10 | −0.246064 | −0.123032 | − | 0.992403i | \(-0.539262\pi\) | ||||
−0.123032 | + | 0.992403i | \(0.539262\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.66504e11 | 2.55494 | ||||||||
\(254\) | 1.32085e10 | 0.199113 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.31842e10 | 0.773932 | ||||||||
\(257\) | −9.34772e10 | −1.33662 | −0.668308 | − | 0.743885i | \(-0.732981\pi\) | ||||
−0.668308 | + | 0.743885i | \(0.732981\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.63689e10 | −0.226033 | ||||||||
\(260\) | 7.80710e10 | 1.05952 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.71704e9 | −0.0880689 | ||||||||
\(263\) | −7.90979e9 | −0.101945 | −0.0509723 | − | 0.998700i | \(-0.516232\pi\) | ||||
−0.0509723 | + | 0.998700i | \(0.516232\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.48625e10 | −1.05708 | ||||||||
\(266\) | 4.29216e7 | 0.000525665 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.65677e10 | −0.433003 | ||||||||
\(269\) | −1.42705e11 | −1.66171 | −0.830853 | − | 0.556492i | \(-0.812147\pi\) | ||||
−0.830853 | + | 0.556492i | \(0.812147\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.60775e10 | 0.744203 | 0.372102 | − | 0.928192i | \(-0.378637\pi\) | ||||
0.372102 | + | 0.928192i | \(0.378637\pi\) | |||||||
\(272\) | −9.35927e10 | −1.03677 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.05785e10 | 0.220565 | ||||||||
\(275\) | −1.15250e9 | −0.0121519 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.30135e10 | −0.438981 | −0.219491 | − | 0.975615i | \(-0.570440\pi\) | ||||
−0.219491 | + | 0.975615i | \(0.570440\pi\) | |||||||
\(278\) | −1.92240e10 | −0.193038 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.19504e9 | −0.0796783 | ||||||||
\(281\) | −1.01031e11 | −0.966665 | −0.483333 | − | 0.875437i | \(-0.660574\pi\) | ||||
−0.483333 | + | 0.875437i | \(0.660574\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.17953e10 | −0.758036 | −0.379018 | − | 0.925389i | \(-0.623738\pi\) | ||||
−0.379018 | + | 0.925389i | \(0.623738\pi\) | |||||||
\(284\) | 1.36458e11 | 1.24470 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.44997e10 | 0.216528 | ||||||||
\(287\) | 2.96072e10 | 0.257590 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.87013e10 | 0.242025 | ||||||||
\(290\) | 2.81547e9 | 0.0233754 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.32268e11 | 1.06471 | ||||||||
\(293\) | −8.09103e10 | −0.641357 | −0.320678 | − | 0.947188i | \(-0.603911\pi\) | ||||
−0.320678 | + | 0.947188i | \(0.603911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.89284e11 | −1.45518 | ||||||||
\(296\) | 3.44410e10 | 0.260773 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.36728e10 | 0.247347 | ||||||||
\(299\) | 2.91060e11 | 2.10602 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.51734e10 | 0.457637 | ||||||||
\(302\) | −1.11453e10 | −0.0771008 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.81483e9 | 0.0121872 | ||||||||
\(305\) | 1.97641e11 | 1.30776 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.58062e10 | 0.487060 | 0.243530 | − | 0.969893i | \(-0.421695\pi\) | ||||
0.243530 | + | 0.969893i | \(0.421695\pi\) | |||||||
\(308\) | 5.29815e10 | 0.335464 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.71056e10 | 0.105199 | ||||||||
\(311\) | 1.77651e11 | 1.07683 | 0.538414 | − | 0.842680i | \(-0.319024\pi\) | ||||
0.538414 | + | 0.842680i | \(0.319024\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.37424e10 | 0.493169 | 0.246585 | − | 0.969121i | \(-0.420692\pi\) | ||||
0.246585 | + | 0.969121i | \(0.420692\pi\) | |||||||
\(314\) | 4.45240e9 | 0.0258470 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.72336e11 | −1.53643 | ||||||||
\(317\) | −5.30032e10 | −0.294805 | −0.147403 | − | 0.989077i | \(-0.547091\pi\) | ||||
−0.147403 | + | 0.989077i | \(0.547091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.68409e10 | −0.199192 | ||||||||
\(320\) | −1.62477e11 | −0.866195 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.50951e10 | −0.0782502 | ||||||||
\(323\) | −2.85604e9 | −0.0146000 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.01466e9 | −0.0100167 | ||||||||
\(326\) | 1.51766e10 | 0.0744210 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.22949e10 | −0.297180 | ||||||||
\(329\) | 4.46152e10 | 0.209943 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.21979e11 | 1.01645 | 0.508225 | − | 0.861225i | \(-0.330302\pi\) | ||||
0.508225 | + | 0.861225i | \(0.330302\pi\) | |||||||
\(332\) | −8.69953e10 | −0.392984 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.31667e9 | 0.0233765 | ||||||||
\(335\) | 1.02681e11 | 0.445439 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.13439e8 | −0.00132379 | −0.000661895 | − | 1.00000i | \(-0.500211\pi\) | ||||
−0.000661895 | 1.00000i | \(0.500211\pi\) | ||||||||
\(338\) | 6.10526e9 | 0.0254436 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.69422e11 | 1.09340 | ||||||||
\(341\) | −2.23830e11 | −0.896444 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.29803e11 | −0.506362 | ||||||||
\(344\) | −1.37128e11 | −0.527974 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.62552e9 | −0.00984858 | ||||||||
\(347\) | 2.96272e11 | 1.09700 | 0.548502 | − | 0.836149i | \(-0.315198\pi\) | ||||
0.548502 | + | 0.836149i | \(0.315198\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.21560e11 | 0.799424 | 0.399712 | − | 0.916641i | \(-0.369110\pi\) | ||||
0.399712 | + | 0.916641i | \(0.369110\pi\) | |||||||
\(350\) | 1.04485e8 | 0.000372177 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.67874e11 | −0.582829 | ||||||||
\(353\) | −3.81073e11 | −1.30624 | −0.653119 | − | 0.757255i | \(-0.726540\pi\) | ||||
−0.653119 | + | 0.757255i | \(0.726540\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.83169e11 | −1.28045 | ||||||||
\(356\) | −2.84609e11 | −0.939125 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.05977e10 | 0.130625 | ||||||||
\(359\) | 3.34181e11 | 1.06183 | 0.530917 | − | 0.847424i | \(-0.321847\pi\) | ||||
0.530917 | + | 0.847424i | \(0.321847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.22632e11 | −0.999828 | ||||||||
\(362\) | −3.05862e10 | −0.0936130 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.26153e10 | 0.276520 | ||||||||
\(365\) | −3.71404e11 | −1.09529 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.62773e11 | 1.33159 | 0.665795 | − | 0.746135i | \(-0.268092\pi\) | ||||
0.665795 | + | 0.746135i | \(0.268092\pi\) | |||||||
\(368\) | −6.38258e11 | −1.81418 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.77817e10 | −0.132542 | ||||||||
\(371\) | −1.00672e11 | −0.275884 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.32740e11 | −0.622559 | −0.311280 | − | 0.950318i | \(-0.600758\pi\) | ||||
−0.311280 | + | 0.950318i | \(0.600758\pi\) | |||||||
\(374\) | 8.45480e10 | 0.223450 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.38725e10 | −0.242211 | ||||||||
\(377\) | −6.44005e10 | −0.164192 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.92570e10 | 0.147524 | 0.0737621 | − | 0.997276i | \(-0.476499\pi\) | ||||
0.0737621 | + | 0.997276i | \(0.476499\pi\) | |||||||
\(380\) | −5.22428e9 | −0.0128529 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.08739e10 | −0.0261277 | ||||||||
\(383\) | 1.10580e11 | 0.262593 | 0.131296 | − | 0.991343i | \(-0.458086\pi\) | ||||
0.131296 | + | 0.991343i | \(0.458086\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.48770e11 | −0.345099 | ||||||||
\(386\) | −1.06085e11 | −0.243226 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.93265e11 | 0.656928 | ||||||||
\(389\) | 5.19724e11 | 1.15080 | 0.575400 | − | 0.817872i | \(-0.304846\pi\) | ||||
0.575400 | + | 0.817872i | \(0.304846\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.00444e12 | 2.17335 | ||||||||
\(392\) | 1.31695e11 | 0.281697 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.49515e10 | −0.156692 | ||||||||
\(395\) | 7.64711e11 | 1.58056 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.49123e11 | −0.907420 | −0.453710 | − | 0.891149i | \(-0.649900\pi\) | ||||
−0.453710 | + | 0.891149i | \(0.649900\pi\) | |||||||
\(398\) | −1.25180e10 | −0.0250071 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.41789e9 | 0.00862870 | ||||||||
\(401\) | −4.75290e11 | −0.917929 | −0.458964 | − | 0.888455i | \(-0.651779\pi\) | ||||
−0.458964 | + | 0.888455i | \(0.651779\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.91270e11 | −0.738930 | ||||||||
\(404\) | 8.12208e11 | 1.51688 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.33998e9 | 0.00610066 | ||||||||
\(407\) | 6.25232e11 | 1.12945 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.31939e11 | −0.763251 | −0.381626 | − | 0.924317i | \(-0.624636\pi\) | ||||
−0.381626 | + | 0.924317i | \(0.624636\pi\) | |||||||
\(410\) | 8.64247e10 | 0.151046 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.96358e11 | −0.506732 | ||||||||
\(413\) | −2.24547e11 | −0.379780 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.44280e11 | 0.404270 | ||||||||
\(416\) | −2.93455e11 | −0.480420 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.63945e9 | −0.00262666 | ||||||||
\(419\) | 9.04463e11 | 1.43360 | 0.716799 | − | 0.697280i | \(-0.245606\pi\) | ||||
0.716799 | + | 0.697280i | \(0.245606\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.53568e11 | 0.238250 | 0.119125 | − | 0.992879i | \(-0.461991\pi\) | ||||
0.119125 | + | 0.992879i | \(0.461991\pi\) | |||||||
\(422\) | −4.10651e10 | −0.0630328 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.11819e11 | 0.318286 | ||||||||
\(425\) | −6.95255e9 | −0.0103370 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.34461e11 | 0.341307 | ||||||||
\(428\) | 2.34707e11 | 0.338087 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.90244e11 | 0.268351 | ||||||||
\(431\) | −1.01001e12 | −1.40987 | −0.704933 | − | 0.709274i | \(-0.749023\pi\) | ||||
−0.704933 | + | 0.709274i | \(0.749023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.38892e12 | 1.89881 | 0.949407 | − | 0.314048i | \(-0.101685\pi\) | ||||
0.949407 | + | 0.314048i | \(0.101685\pi\) | |||||||
\(434\) | 2.02923e10 | 0.0274554 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.05107e12 | −1.39298 | ||||||||
\(437\) | −1.94769e10 | −0.0255477 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.13642e12 | −1.46032 | −0.730159 | − | 0.683277i | \(-0.760554\pi\) | ||||
−0.730159 | + | 0.683277i | \(0.760554\pi\) | |||||||
\(440\) | 3.13020e11 | 0.398139 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.47796e11 | 0.184188 | ||||||||
\(443\) | −9.02042e11 | −1.11278 | −0.556391 | − | 0.830921i | \(-0.687814\pi\) | ||||
−0.556391 | + | 0.830921i | \(0.687814\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.99172e11 | 0.966096 | ||||||||
\(446\) | −6.53637e10 | −0.0782222 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.92745e11 | −0.226065 | ||||||||
\(449\) | 4.28311e11 | 0.497337 | 0.248668 | − | 0.968589i | \(-0.420007\pi\) | ||||
0.248668 | + | 0.968589i | \(0.420007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.13088e12 | −1.28713 | ||||||||
\(452\) | 6.26790e11 | 0.706316 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.09093e9 | −0.00783343 | ||||||||
\(455\) | −2.60061e11 | −0.284462 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.75246e11 | −0.616922 | −0.308461 | − | 0.951237i | \(-0.599814\pi\) | ||||
−0.308461 | + | 0.951237i | \(0.599814\pi\) | |||||||
\(458\) | 7.40822e9 | 0.00786719 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.83733e12 | 1.91327 | ||||||||
\(461\) | −1.06514e12 | −1.09838 | −0.549192 | − | 0.835697i | \(-0.685064\pi\) | ||||
−0.549192 | + | 0.835697i | \(0.685064\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.91661e11 | −0.699486 | −0.349743 | − | 0.936846i | \(-0.613731\pi\) | ||||
−0.349743 | + | 0.936846i | \(0.613731\pi\) | |||||||
\(464\) | 1.41222e11 | 0.141440 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.39426e11 | −0.136964 | ||||||||
\(467\) | −1.39973e12 | −1.36181 | −0.680907 | − | 0.732370i | \(-0.738414\pi\) | ||||
−0.680907 | + | 0.732370i | \(0.738414\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.21810e11 | 0.116253 | ||||||||
\(470\) | 1.30234e11 | 0.123107 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.72458e11 | 0.438151 | ||||||||
\(473\) | −2.48938e12 | −2.28674 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.34815e8 | 0.000121511 0 | ||||||||
\(476\) | 3.19614e11 | 0.285361 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.20773e10 | −0.0281043 | ||||||||
\(479\) | 9.56803e11 | 0.830448 | 0.415224 | − | 0.909719i | \(-0.363703\pi\) | ||||
0.415224 | + | 0.909719i | \(0.363703\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.09295e12 | 0.930994 | ||||||||
\(482\) | −2.70432e11 | −0.228216 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.44702e11 | −0.699680 | ||||||||
\(485\) | −8.23479e11 | −0.675795 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.88361e11 | −0.232303 | −0.116152 | − | 0.993231i | \(-0.537056\pi\) | ||||
−0.116152 | + | 0.993231i | \(0.537056\pi\) | |||||||
\(488\) | −4.93317e11 | −0.393765 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.82707e11 | −0.143177 | ||||||||
\(491\) | 2.34624e11 | 0.182182 | 0.0910910 | − | 0.995843i | \(-0.470965\pi\) | ||||
0.0910910 | + | 0.995843i | \(0.470965\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.22245e11 | −0.169442 | ||||||||
\(494\) | −2.86586e9 | −0.00216513 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.58007e11 | 0.636536 | ||||||||
\(497\) | −4.54551e11 | −0.334179 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.52955e12 | 1.82638 | 0.913189 | − | 0.407536i | \(-0.133612\pi\) | ||||
0.913189 | + | 0.407536i | \(0.133612\pi\) | |||||||
\(500\) | 1.35841e12 | 0.971998 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.35814e10 | −0.0376571 | ||||||||
\(503\) | 3.09347e11 | 0.215471 | 0.107736 | − | 0.994180i | \(-0.465640\pi\) | ||||
0.107736 | + | 0.994180i | \(0.465640\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.28065e12 | −1.56044 | ||||||||
\(506\) | 5.76578e11 | 0.391003 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.90720e12 | −1.27060 | ||||||||
\(509\) | 2.54357e12 | 1.67963 | 0.839816 | − | 0.542871i | \(-0.182663\pi\) | ||||
0.839816 | + | 0.542871i | \(0.182663\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.40595e11 | −0.285855 | ||||||||
\(512\) | 1.08108e12 | 0.695252 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.23698e11 | −0.204553 | ||||||||
\(515\) | 8.32163e11 | 0.521286 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.70413e12 | −1.04905 | ||||||||
\(518\) | −5.66832e10 | −0.0345916 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.47180e11 | 0.328182 | ||||||||
\(521\) | 1.75471e12 | 1.04336 | 0.521682 | − | 0.853140i | \(-0.325305\pi\) | ||||
0.521682 | + | 0.853140i | \(0.325305\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.65849e11 | 0.564484 | 0.282242 | − | 0.959343i | \(-0.408922\pi\) | ||||
0.282242 | + | 0.959343i | \(0.408922\pi\) | |||||||
\(524\) | 9.69888e11 | 0.561993 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.73904e10 | −0.0156014 | ||||||||
\(527\) | −1.35027e12 | −0.762556 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.04867e12 | 2.80302 | ||||||||
\(530\) | −2.93866e11 | −0.161774 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.19754e9 | −0.00335442 | ||||||||
\(533\) | −1.97686e12 | −1.06097 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.59049e11 | −0.347797 | ||||||||
\(536\) | −2.56294e11 | −0.134121 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.94167e11 | −0.254304 | ||||||||
\(539\) | 2.39075e12 | 1.22007 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.09700e12 | −1.05247 | −0.526235 | − | 0.850339i | \(-0.676397\pi\) | ||||
−0.526235 | + | 0.850339i | \(0.676397\pi\) | |||||||
\(542\) | 2.28817e11 | 0.113891 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.01271e12 | −0.495780 | ||||||||
\(545\) | 2.95139e12 | 1.43299 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.50322e12 | 0.717926 | 0.358963 | − | 0.933352i | \(-0.383130\pi\) | ||||
0.358963 | + | 0.933352i | \(0.383130\pi\) | |||||||
\(548\) | −2.97137e12 | −1.40749 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.99095e9 | −0.00185971 | ||||||||
\(551\) | 4.30949e9 | 0.00199179 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.07173e11 | 0.412503 | ||||||||
\(554\) | −1.48949e11 | −0.0671808 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.77580e12 | 1.23183 | ||||||||
\(557\) | −4.83664e11 | −0.212910 | −0.106455 | − | 0.994318i | \(-0.533950\pi\) | ||||
−0.106455 | + | 0.994318i | \(0.533950\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.35161e12 | −1.88494 | ||||||||
\(560\) | 5.70282e11 | 0.245044 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.49855e11 | −0.147936 | ||||||||
\(563\) | −2.47754e12 | −1.03928 | −0.519641 | − | 0.854385i | \(-0.673934\pi\) | ||||
−0.519641 | + | 0.854385i | \(0.673934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.76001e12 | −0.726602 | ||||||||
\(566\) | −2.83245e11 | −0.116008 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.56398e11 | 0.385541 | ||||||||
\(569\) | 3.50996e12 | 1.40377 | 0.701886 | − | 0.712289i | \(-0.252342\pi\) | ||||
0.701886 | + | 0.712289i | \(0.252342\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.57255e11 | 0.101275 | 0.0506375 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506375 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(572\) | −3.53756e12 | −1.38172 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.02525e11 | 0.0394210 | ||||||||
\(575\) | −4.74131e10 | −0.0180881 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.55281e11 | 0.283673 | 0.141836 | − | 0.989890i | \(-0.454699\pi\) | ||||
0.141836 | + | 0.989890i | \(0.454699\pi\) | |||||||
\(578\) | 9.93883e10 | 0.0370390 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.06531e11 | −0.149165 | ||||||||
\(581\) | 2.89789e11 | 0.105509 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.84530e12 | 1.37855 | ||||||||
\(584\) | 9.27034e11 | 0.329790 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.80181e11 | −0.0981519 | ||||||||
\(587\) | −5.13111e12 | −1.78378 | −0.891888 | − | 0.452257i | \(-0.850619\pi\) | ||||
−0.891888 | + | 0.452257i | \(0.850619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.61826e10 | 0.00896384 | ||||||||
\(590\) | −6.55464e11 | −0.222697 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.39670e12 | −0.801986 | ||||||||
\(593\) | −1.98175e12 | −0.658116 | −0.329058 | − | 0.944310i | \(-0.606731\pi\) | ||||
−0.329058 | + | 0.944310i | \(0.606731\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.97466e11 | −0.293557 | ||||||||
\(596\) | −4.86209e12 | −1.57839 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.00790e12 | 0.322300 | ||||||||
\(599\) | −1.03251e12 | −0.327699 | −0.163850 | − | 0.986485i | \(-0.552391\pi\) | ||||
−0.163850 | + | 0.986485i | \(0.552391\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.06818e12 | −0.333971 | −0.166986 | − | 0.985959i | \(-0.553403\pi\) | ||||
−0.166986 | + | 0.985959i | \(0.553403\pi\) | |||||||
\(602\) | 2.25686e11 | 0.0700358 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.60929e12 | 0.492002 | ||||||||
\(605\) | 2.37190e12 | 0.719775 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.33870e12 | 0.998225 | 0.499112 | − | 0.866537i | \(-0.333660\pi\) | ||||
0.499112 | + | 0.866537i | \(0.333660\pi\) | |||||||
\(608\) | 1.96371e10 | 0.00582790 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.84403e11 | 0.200137 | ||||||||
\(611\) | −2.97894e12 | −0.864722 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.12503e12 | −1.17993 | −0.589964 | − | 0.807430i | \(-0.700858\pi\) | ||||
−0.589964 | + | 0.807430i | \(0.700858\pi\) | |||||||
\(614\) | 2.62506e11 | 0.0745386 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.71334e11 | 0.103909 | ||||||||
\(617\) | 4.32528e12 | 1.20152 | 0.600759 | − | 0.799430i | \(-0.294865\pi\) | ||||
0.600759 | + | 0.799430i | \(0.294865\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.31375e12 | −1.72854 | −0.864271 | − | 0.503027i | \(-0.832220\pi\) | ||||
−0.864271 | + | 0.503027i | \(0.832220\pi\) | |||||||
\(620\) | −2.46991e12 | −0.671303 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.15180e11 | 0.164796 | ||||||||
\(623\) | 9.48055e11 | 0.252137 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.84975e12 | −1.00919 | ||||||||
\(626\) | 2.89988e11 | 0.0754736 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.42891e11 | −0.164937 | ||||||||
\(629\) | 3.77175e12 | 0.960760 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.69921e12 | 1.68225 | 0.841127 | − | 0.540838i | \(-0.181893\pi\) | ||||
0.841127 | + | 0.540838i | \(0.181893\pi\) | |||||||
\(632\) | −1.90873e12 | −0.475903 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.83542e11 | −0.0451164 | ||||||||
\(635\) | 5.35535e12 | 1.30709 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.17920e12 | 1.00569 | ||||||||
\(638\) | −1.27575e11 | −0.0304840 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.45951e12 | −0.579480 | ||||||||
\(641\) | 7.06833e12 | 1.65370 | 0.826849 | − | 0.562425i | \(-0.190131\pi\) | ||||
0.826849 | + | 0.562425i | \(0.190131\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.70634e12 | 0.393656 | 0.196828 | − | 0.980438i | \(-0.436936\pi\) | ||||
0.196828 | + | 0.980438i | \(0.436936\pi\) | |||||||
\(644\) | 2.17962e12 | 0.499337 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.89005e9 | −0.00223436 | ||||||||
\(647\) | 3.85704e12 | 0.865336 | 0.432668 | − | 0.901553i | \(-0.357572\pi\) | ||||
0.432668 | + | 0.901553i | \(0.357572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.57687e12 | 1.89770 | ||||||||
\(650\) | −6.97646e9 | −0.00153294 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.19138e12 | −0.474902 | ||||||||
\(653\) | −4.62412e12 | −0.995221 | −0.497610 | − | 0.867401i | \(-0.665789\pi\) | ||||
−0.497610 | + | 0.867401i | \(0.665789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.72342e12 | −0.578133 | ||||||||
\(656\) | 4.33501e12 | 0.913952 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.54496e11 | 0.0321292 | ||||||||
\(659\) | 8.16802e11 | 0.168707 | 0.0843533 | − | 0.996436i | \(-0.473118\pi\) | ||||
0.0843533 | + | 0.996436i | \(0.473118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.14771e12 | −0.233843 | −0.116921 | − | 0.993141i | \(-0.537303\pi\) | ||||
−0.116921 | + | 0.993141i | \(0.537303\pi\) | |||||||
\(662\) | 7.68680e11 | 0.155555 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.09729e11 | −0.121725 | ||||||||
\(665\) | 1.74025e10 | 0.00345076 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.51561e12 | −0.296497 | ||||||||
\(668\) | −7.67684e11 | −0.149172 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.55569e11 | 0.0681691 | ||||||||
\(671\) | −8.95554e12 | −1.70546 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.17515e12 | −1.34823 | −0.674114 | − | 0.738627i | \(-0.735474\pi\) | ||||
−0.674114 | + | 0.738627i | \(0.735474\pi\) | |||||||
\(674\) | −1.08539e9 | −0.000202590 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.81552e11 | −0.162363 | ||||||||
\(677\) | 5.21004e12 | 0.953217 | 0.476609 | − | 0.879116i | \(-0.341866\pi\) | ||||
0.476609 | + | 0.879116i | \(0.341866\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.76890e11 | −0.176373 | ||||||||
\(680\) | 1.88831e12 | 0.338675 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.75090e11 | −0.137190 | ||||||||
\(683\) | −2.81291e12 | −0.494611 | −0.247305 | − | 0.968938i | \(-0.579545\pi\) | ||||
−0.247305 | + | 0.968938i | \(0.579545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.34352e12 | 1.44791 | ||||||||
\(686\) | −4.49489e11 | −0.0774926 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.54255e12 | 1.62374 | ||||||||
\(689\) | 6.72184e12 | 1.13632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.74991e12 | −1.29314 | −0.646570 | − | 0.762855i | \(-0.723797\pi\) | ||||
−0.646570 | + | 0.762855i | \(0.723797\pi\) | |||||||
\(692\) | 3.79105e11 | 0.0628466 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.02595e12 | 0.167883 | ||||||||
\(695\) | −7.79435e12 | −1.26721 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.82212e12 | −1.09489 | ||||||||
\(698\) | 7.67230e11 | 0.122342 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.50869e10 | −0.00237497 | ||||||||
\(701\) | −1.86576e12 | −0.291826 | −0.145913 | − | 0.989297i | \(-0.546612\pi\) | ||||
−0.145913 | + | 0.989297i | \(0.546612\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.31369e10 | −0.0112937 | ||||||||
\(704\) | 7.36215e12 | 1.12961 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.31960e12 | −0.199904 | ||||||||
\(707\) | −2.70553e12 | −0.407254 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.27617e11 | 0.0338295 | 0.0169148 | − | 0.999857i | \(-0.494616\pi\) | ||||
0.0169148 | + | 0.999857i | \(0.494616\pi\) | |||||||
\(710\) | −1.32686e12 | −0.195957 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.99475e12 | −0.290890 | ||||||||
\(713\) | −9.20818e12 | −1.33435 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.93336e12 | 1.42141 | ||||||||
\(716\) | −5.86198e12 | −0.833558 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.15722e12 | 0.162501 | ||||||||
\(719\) | −2.12785e12 | −0.296934 | −0.148467 | − | 0.988917i | \(-0.547434\pi\) | ||||
−0.148467 | + | 0.988917i | \(0.547434\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.87191e11 | 0.136048 | ||||||||
\(722\) | −1.11723e12 | −0.153012 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.41640e12 | 0.597372 | ||||||||
\(725\) | 1.04907e10 | 0.00141021 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.57756e12 | −0.209450 | −0.104725 | − | 0.994501i | \(-0.533396\pi\) | ||||
−0.104725 | + | 0.994501i | \(0.533396\pi\) | |||||||
\(728\) | 6.49118e11 | 0.0856510 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.28612e12 | −0.167621 | ||||||||
\(731\) | −1.50173e13 | −1.94520 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.60083e12 | −0.588665 | −0.294333 | − | 0.955703i | \(-0.595097\pi\) | ||||
−0.294333 | + | 0.955703i | \(0.595097\pi\) | |||||||
\(734\) | 1.60251e12 | 0.203784 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.90620e12 | −0.867538 | ||||||||
\(737\) | −4.65269e12 | −0.580899 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.25557e12 | −0.278199 | −0.139099 | − | 0.990278i | \(-0.544421\pi\) | ||||
−0.139099 | + | 0.990278i | \(0.544421\pi\) | |||||||
\(740\) | 6.89930e12 | 0.845789 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.48612e11 | −0.0422207 | ||||||||
\(743\) | −1.07745e13 | −1.29702 | −0.648508 | − | 0.761208i | \(-0.724607\pi\) | ||||
−0.648508 | + | 0.761208i | \(0.724607\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.36526e13 | 1.62372 | ||||||||
\(746\) | −8.05943e11 | −0.0952752 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.22081e13 | −1.42590 | ||||||||
\(749\) | −7.81827e11 | −0.0907700 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.32047e12 | −0.610338 | −0.305169 | − | 0.952298i | \(-0.598713\pi\) | ||||
−0.305169 | + | 0.952298i | \(0.598713\pi\) | |||||||
\(752\) | 6.53246e12 | 0.744897 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.23009e11 | −0.0251277 | ||||||||
\(755\) | −4.51883e12 | −0.506133 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.65829e12 | 0.958298 | 0.479149 | − | 0.877734i | \(-0.340945\pi\) | ||||
0.479149 | + | 0.877734i | \(0.340945\pi\) | |||||||
\(758\) | 2.05198e11 | 0.0225768 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.66157e10 | −0.00398113 | ||||||||
\(761\) | 7.04534e12 | 0.761502 | 0.380751 | − | 0.924678i | \(-0.375666\pi\) | ||||
0.380751 | + | 0.924678i | \(0.375666\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.50122e12 | 0.373989 | ||||||||
\(764\) | 1.57011e12 | 0.166729 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.82923e11 | 0.0401866 | ||||||||
\(767\) | 1.49929e13 | 1.56426 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.58271e12 | −0.678791 | −0.339395 | − | 0.940644i | \(-0.610222\pi\) | ||||
−0.339395 | + | 0.940644i | \(0.610222\pi\) | |||||||
\(770\) | −5.15170e11 | −0.0528132 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.53178e13 | 1.55209 | ||||||||
\(773\) | 1.34877e13 | 1.35872 | 0.679360 | − | 0.733805i | \(-0.262258\pi\) | ||||
0.679360 | + | 0.733805i | \(0.262258\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.37371e10 | 0.00634651 | ||||||||
\(776\) | 2.05542e12 | 0.203481 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.79973e12 | 0.176116 | ||||||||
\(779\) | 1.32286e11 | 0.0128705 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.73622e13 | 1.66984 | ||||||||
\(782\) | 3.47824e12 | 0.332605 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.16447e12 | −0.866334 | ||||||||
\(785\) | 1.80522e12 | 0.169674 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.23113e13 | −1.14398 | −0.571988 | − | 0.820262i | \(-0.693828\pi\) | ||||
−0.571988 | + | 0.820262i | \(0.693828\pi\) | |||||||
\(788\) | 1.08224e13 | 0.999899 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.64808e12 | 0.241885 | ||||||||
\(791\) | −2.08789e12 | −0.189633 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.56549e13 | −1.40579 | ||||||||
\(794\) | −1.55525e12 | −0.138870 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.80751e12 | 0.159577 | ||||||||
\(797\) | −1.13882e13 | −0.999753 | −0.499877 | − | 0.866097i | \(-0.666621\pi\) | ||||
−0.499877 | + | 0.866097i | \(0.666621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.02803e13 | −0.892370 | ||||||||
\(800\) | 4.78033e10 | 0.00412622 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.64586e12 | −0.140478 | ||||||||
\(803\) | 1.68291e13 | 1.42837 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.12030e12 | −0.513678 | ||||||||
\(806\) | −1.35491e12 | −0.113084 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.69256e12 | 0.469847 | ||||||||
\(809\) | 9.39455e12 | 0.771095 | 0.385547 | − | 0.922688i | \(-0.374013\pi\) | ||||
0.385547 | + | 0.922688i | \(0.374013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.85202e12 | 0.718536 | 0.359268 | − | 0.933234i | \(-0.383026\pi\) | ||||
0.359268 | + | 0.933234i | \(0.383026\pi\) | |||||||
\(812\) | −4.82266e11 | −0.0389300 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.16509e12 | 0.172849 | ||||||||
\(815\) | 6.15334e12 | 0.488541 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.91197e11 | 0.0228659 | ||||||||
\(818\) | −1.49574e12 | −0.116806 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.24790e13 | −0.963871 | ||||||||
\(821\) | −1.33940e13 | −1.02888 | −0.514441 | − | 0.857526i | \(-0.672000\pi\) | ||||
−0.514441 | + | 0.857526i | \(0.672000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.86595e13 | 1.41775 | 0.708876 | − | 0.705333i | \(-0.249203\pi\) | ||||
0.708876 | + | 0.705333i | \(0.249203\pi\) | |||||||
\(824\) | −2.07710e12 | −0.156958 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.77574e11 | −0.0581208 | ||||||||
\(827\) | −1.27791e13 | −0.950006 | −0.475003 | − | 0.879984i | \(-0.657553\pi\) | ||||
−0.475003 | + | 0.879984i | \(0.657553\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.09935e12 | −0.595600 | −0.297800 | − | 0.954628i | \(-0.596253\pi\) | ||||
−0.297800 | + | 0.954628i | \(0.596253\pi\) | |||||||
\(830\) | 8.45906e11 | 0.0618687 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.28695e13 | 0.931126 | ||||||||
\(833\) | 1.44224e13 | 1.03785 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.15563e12 | 0.153457 | ||||||||
\(836\) | 2.36723e11 | 0.0167615 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.13202e12 | 0.219395 | ||||||||
\(839\) | −1.17750e13 | −0.820409 | −0.410205 | − | 0.911994i | \(-0.634543\pi\) | ||||
−0.410205 | + | 0.911994i | \(0.634543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.41718e13 | −0.976884 | ||||||||
\(842\) | 5.31784e11 | 0.0364612 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.92947e12 | 0.402230 | ||||||||
\(845\) | 2.47537e12 | 0.167026 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.81377e12 | 0.187851 | ||||||||
\(848\) | −1.47402e13 | −0.978862 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.40756e10 | −0.00158195 | ||||||||
\(851\) | 2.57216e13 | 1.68118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.84220e11 | 0.0442512 | 0.0221256 | − | 0.999755i | \(-0.492957\pi\) | ||||
0.0221256 | + | 0.999755i | \(0.492957\pi\) | |||||||
\(854\) | 8.11904e11 | 0.0522329 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.64500e12 | 0.104721 | ||||||||
\(857\) | 1.15644e13 | 0.732337 | 0.366168 | − | 0.930549i | \(-0.380669\pi\) | ||||
0.366168 | + | 0.930549i | \(0.380669\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.50261e13 | 0.941623 | 0.470812 | − | 0.882234i | \(-0.343961\pi\) | ||||
0.470812 | + | 0.882234i | \(0.343961\pi\) | |||||||
\(860\) | −2.74698e13 | −1.71243 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.49752e12 | −0.215763 | ||||||||
\(863\) | −1.54066e13 | −0.945490 | −0.472745 | − | 0.881199i | \(-0.656737\pi\) | ||||
−0.472745 | + | 0.881199i | \(0.656737\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.06451e12 | −0.0646516 | ||||||||
\(866\) | 4.80964e12 | 0.290591 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.93005e12 | −0.175201 | ||||||||
\(869\) | −3.46506e13 | −2.06121 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.13322e12 | −0.478829 | ||||||||
\(872\) | −7.36673e12 | −0.431470 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.74455e10 | −0.00390977 | ||||||||
\(875\) | −4.52497e12 | −0.260963 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.57641e13 | −1.47068 | −0.735338 | − | 0.677700i | \(-0.762977\pi\) | ||||
−0.735338 | + | 0.677700i | \(0.762977\pi\) | |||||||
\(878\) | −3.93525e12 | −0.223484 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.17826e13 | −1.22444 | ||||||||
\(881\) | 8.67327e12 | 0.485055 | 0.242528 | − | 0.970144i | \(-0.422023\pi\) | ||||
0.242528 | + | 0.970144i | \(0.422023\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.27283e13 | 0.704607 | 0.352304 | − | 0.935886i | \(-0.385398\pi\) | ||||
0.352304 | + | 0.935886i | \(0.385398\pi\) | |||||||
\(884\) | −2.13405e13 | −1.17536 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.12364e12 | −0.170298 | ||||||||
\(887\) | −3.99323e12 | −0.216605 | −0.108302 | − | 0.994118i | \(-0.534541\pi\) | ||||
−0.108302 | + | 0.994118i | \(0.534541\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.35303e12 | 0.341132 | ||||||||
\(890\) | 2.76742e12 | 0.147849 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.43801e12 | 0.499159 | ||||||||
\(893\) | 1.99342e11 | 0.0104898 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.64603e13 | 0.857498 | ||||||||
\(896\) | −2.91770e12 | −0.151236 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.48318e12 | 0.0761114 | ||||||||
\(899\) | 2.03742e12 | 0.104031 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.31970e13 | 1.17265 | ||||||||
\(902\) | −3.91608e12 | −0.196980 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.39302e12 | 0.218779 | ||||||||
\(905\) | −1.24011e13 | −0.614529 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.79778e12 | −0.431659 | −0.215829 | − | 0.976431i | \(-0.569245\pi\) | ||||
−0.215829 | + | 0.976431i | \(0.569245\pi\) | |||||||
\(908\) | 1.02387e12 | 0.0499874 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9.00552e11 | −0.0435334 | ||||||||
\(911\) | 2.95612e13 | 1.42197 | 0.710983 | − | 0.703209i | \(-0.248250\pi\) | ||||
0.710983 | + | 0.703209i | \(0.248250\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.10688e13 | −0.527210 | ||||||||
\(914\) | −1.99199e12 | −0.0944125 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.06969e12 | −0.0502028 | ||||||||
\(917\) | −3.23078e12 | −0.150885 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.05646e13 | −0.488577 | −0.244288 | − | 0.969703i | \(-0.578554\pi\) | ||||
−0.244288 | + | 0.969703i | \(0.578554\pi\) | |||||||
\(920\) | 1.28774e13 | 0.592629 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.68843e12 | −0.168094 | ||||||||
\(923\) | 3.03503e13 | 1.37643 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.78039e11 | −0.00799610 | ||||||||
\(926\) | −2.39512e12 | −0.107048 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.52808e12 | 0.0676363 | ||||||||
\(929\) | 1.99951e13 | 0.880752 | 0.440376 | − | 0.897814i | \(-0.354845\pi\) | ||||
0.440376 | + | 0.897814i | \(0.354845\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.79660e11 | −0.0121999 | ||||||||
\(932\) | 2.01319e13 | 0.874005 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.84705e12 | −0.208409 | ||||||||
\(935\) | 3.42799e13 | 1.46685 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.60094e13 | 1.52612 | 0.763058 | − | 0.646330i | \(-0.223697\pi\) | ||||
0.763058 | + | 0.646330i | \(0.223697\pi\) | |||||||
\(938\) | 4.21810e11 | 0.0177912 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.88047e13 | −0.785583 | ||||||||
\(941\) | 2.20084e13 | 0.915028 | 0.457514 | − | 0.889202i | \(-0.348740\pi\) | ||||
0.457514 | + | 0.889202i | \(0.348740\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.65236e13 | −1.91589 | ||||||||
\(944\) | −3.28777e13 | −1.34750 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.62036e12 | −0.349958 | ||||||||
\(947\) | −2.27142e13 | −0.917746 | −0.458873 | − | 0.888502i | \(-0.651747\pi\) | ||||
−0.458873 | + | 0.888502i | \(0.651747\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.94184e13 | 1.17739 | ||||||||
\(950\) | 4.66844e8 | 1.85958e−5 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.24010e12 | 0.0883894 | ||||||||
\(953\) | 1.64449e13 | 0.645824 | 0.322912 | − | 0.946429i | \(-0.395338\pi\) | ||||
0.322912 | + | 0.946429i | \(0.395338\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.40882e12 | −0.171517 | ||||||||
\(956\) | 4.63171e12 | 0.179342 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.31327e12 | 0.127090 | ||||||||
\(959\) | 9.89789e12 | 0.377884 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.40611e13 | −0.531820 | ||||||||
\(962\) | 3.78472e12 | 0.142477 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.90483e13 | 1.45631 | ||||||||
\(965\) | −4.30118e13 | −1.59667 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.49306e13 | 0.916883 | 0.458442 | − | 0.888725i | \(-0.348408\pi\) | ||||
0.458442 | + | 0.888725i | \(0.348408\pi\) | |||||||
\(968\) | −5.92031e12 | −0.216723 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.85159e12 | −0.103422 | ||||||||
\(971\) | 4.38342e13 | 1.58244 | 0.791218 | − | 0.611534i | \(-0.209447\pi\) | ||||
0.791218 | + | 0.611534i | \(0.209447\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.24641e12 | −0.330724 | ||||||||
\(974\) | −9.98550e11 | −0.0355512 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.43293e13 | 1.21099 | ||||||||
\(977\) | −4.57358e12 | −0.160595 | −0.0802973 | − | 0.996771i | \(-0.525587\pi\) | ||||
−0.0802973 | + | 0.996771i | \(0.525587\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.62122e13 | −1.25989 | ||||||||
\(980\) | 2.63814e13 | 0.913652 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.12468e11 | 0.0278808 | ||||||||
\(983\) | 4.78406e13 | 1.63420 | 0.817101 | − | 0.576494i | \(-0.195580\pi\) | ||||
0.817101 | + | 0.576494i | \(0.195580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.03890e13 | −1.02862 | ||||||||
\(986\) | −7.69602e11 | −0.0259310 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.13808e11 | 0.0138163 | ||||||||
\(989\) | −1.02411e14 | −3.40380 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.94011e13 | −0.638993 | −0.319496 | − | 0.947588i | \(-0.603514\pi\) | ||||
−0.319496 | + | 0.947588i | \(0.603514\pi\) | |||||||
\(992\) | 9.28396e12 | 0.304390 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.57405e12 | −0.0511421 | ||||||||
\(995\) | −5.07542e12 | −0.164160 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.73855e13 | 1.51886 | 0.759429 | − | 0.650591i | \(-0.225479\pi\) | ||||
0.759429 | + | 0.650591i | \(0.225479\pi\) | |||||||
\(998\) | 8.75946e12 | 0.279505 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 27.10.a.c.1.2 | yes | 3 | |
3.2 | odd | 2 | 27.10.a.b.1.2 | ✓ | 3 | ||
9.2 | odd | 6 | 81.10.c.h.28.2 | 6 | |||
9.4 | even | 3 | 81.10.c.g.55.2 | 6 | |||
9.5 | odd | 6 | 81.10.c.h.55.2 | 6 | |||
9.7 | even | 3 | 81.10.c.g.28.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.10.a.b.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
27.10.a.c.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
81.10.c.g.28.2 | 6 | 9.7 | even | 3 | |||
81.10.c.g.55.2 | 6 | 9.4 | even | 3 | |||
81.10.c.h.28.2 | 6 | 9.2 | odd | 6 | |||
81.10.c.h.55.2 | 6 | 9.5 | odd | 6 |