Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,22,Mod(1,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.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: | \(125.764804929\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 11485586 x^{5} + 1293459480 x^{4} + 34165285911360 x^{3} + \cdots + 25\!\cdots\!88 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{17}\cdot 5^{7}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-997.261\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −915.261 | −0.632019 | −0.316009 | − | 0.948756i | \(-0.602343\pi\) | ||||
−0.316009 | + | 0.948756i | \(0.602343\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.25945e6 | −0.600552 | ||||||||
\(5\) | −9.76562e6 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.67247e8 | −1.29422 | −0.647110 | − | 0.762397i | \(-0.724022\pi\) | ||||
−0.647110 | + | 0.762397i | \(0.724022\pi\) | |||||||
\(8\) | 3.07217e9 | 1.01158 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.93809e9 | 0.282647 | ||||||||
\(11\) | 5.85592e10 | 0.680725 | 0.340363 | − | 0.940294i | \(-0.389450\pi\) | ||||
0.340363 | + | 0.940294i | \(0.389450\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.35652e11 | −1.68120 | −0.840602 | − | 0.541654i | \(-0.817798\pi\) | ||||
−0.840602 | + | 0.541654i | \(0.817798\pi\) | |||||||
\(14\) | 8.85283e11 | 0.817971 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.70575e11 | −0.0387843 | ||||||||
\(17\) | −2.88103e12 | −0.346604 | −0.173302 | − | 0.984869i | \(-0.555444\pi\) | ||||
−0.173302 | + | 0.984869i | \(0.555444\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.26372e13 | −0.472865 | −0.236432 | − | 0.971648i | \(-0.575978\pi\) | ||||
−0.236432 | + | 0.971648i | \(0.575978\pi\) | |||||||
\(20\) | 1.22993e13 | 0.268575 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.35969e13 | −0.430231 | ||||||||
\(23\) | 3.44241e14 | 1.73269 | 0.866343 | − | 0.499449i | \(-0.166464\pi\) | ||||
0.866343 | + | 0.499449i | \(0.166464\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.53674e13 | 0.200000 | ||||||||
\(26\) | 7.64839e14 | 1.06255 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.21820e15 | 0.777247 | ||||||||
\(29\) | −1.05067e15 | −0.463755 | −0.231878 | − | 0.972745i | \(-0.574487\pi\) | ||||
−0.231878 | + | 0.972745i | \(0.574487\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.70800e15 | 0.593405 | 0.296703 | − | 0.954970i | \(-0.404113\pi\) | ||||
0.296703 | + | 0.954970i | \(0.404113\pi\) | |||||||
\(32\) | −6.28668e15 | −0.987067 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.63689e15 | 0.219060 | ||||||||
\(35\) | 9.44577e15 | 0.578792 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.58723e15 | 0.122643 | 0.0613213 | − | 0.998118i | \(-0.480469\pi\) | ||||
0.0613213 | + | 0.998118i | \(0.480469\pi\) | |||||||
\(38\) | 1.15663e16 | 0.298859 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.00016e16 | −0.452392 | ||||||||
\(41\) | 8.22978e16 | 0.957542 | 0.478771 | − | 0.877940i | \(-0.341082\pi\) | ||||
0.478771 | + | 0.877940i | \(0.341082\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.16163e16 | 0.223097 | 0.111548 | − | 0.993759i | \(-0.464419\pi\) | ||||
0.111548 | + | 0.993759i | \(0.464419\pi\) | |||||||
\(44\) | −7.37523e16 | −0.408811 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.15070e17 | −1.09509 | ||||||||
\(47\) | 4.88337e17 | 1.35423 | 0.677115 | − | 0.735877i | \(-0.263230\pi\) | ||||
0.677115 | + | 0.735877i | \(0.263230\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.77020e17 | 0.675004 | ||||||||
\(50\) | −8.72861e16 | −0.126404 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.05246e18 | 1.00965 | ||||||||
\(53\) | 2.17151e17 | 0.170555 | 0.0852775 | − | 0.996357i | \(-0.472822\pi\) | ||||
0.0852775 | + | 0.996357i | \(0.472822\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.71867e17 | −0.304430 | ||||||||
\(56\) | −2.97154e18 | −1.30920 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.61640e17 | 0.293102 | ||||||||
\(59\) | −3.50397e18 | −0.892512 | −0.446256 | − | 0.894905i | \(-0.647243\pi\) | ||||
−0.446256 | + | 0.894905i | \(0.647243\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.82465e18 | −1.04546 | −0.522729 | − | 0.852499i | \(-0.675086\pi\) | ||||
−0.522729 | + | 0.852499i | \(0.675086\pi\) | |||||||
\(62\) | −2.47853e18 | −0.375043 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.11167e18 | 0.662629 | ||||||||
\(65\) | 8.16066e18 | 0.751857 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.95753e19 | 1.98218 | 0.991090 | − | 0.133191i | \(-0.0425223\pi\) | ||||
0.991090 | + | 0.133191i | \(0.0425223\pi\) | |||||||
\(68\) | 3.62851e18 | 0.208154 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.64534e18 | −0.365808 | ||||||||
\(71\) | 2.20469e19 | 0.803775 | 0.401887 | − | 0.915689i | \(-0.368354\pi\) | ||||
0.401887 | + | 0.915689i | \(0.368354\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.95169e19 | 1.07620 | 0.538100 | − | 0.842881i | \(-0.319142\pi\) | ||||
0.538100 | + | 0.842881i | \(0.319142\pi\) | |||||||
\(74\) | −3.28325e18 | −0.0775125 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.59159e19 | 0.283980 | ||||||||
\(77\) | −5.66412e19 | −0.881008 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.49205e19 | −0.177296 | −0.0886482 | − | 0.996063i | \(-0.528255\pi\) | ||||
−0.0886482 | + | 0.996063i | \(0.528255\pi\) | |||||||
\(80\) | 1.66577e18 | 0.0173449 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.53239e19 | −0.605184 | ||||||||
\(83\) | 8.63032e19 | 0.610530 | 0.305265 | − | 0.952267i | \(-0.401255\pi\) | ||||
0.305265 | + | 0.952267i | \(0.401255\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.81350e19 | 0.155006 | ||||||||
\(86\) | −2.89372e19 | −0.141001 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.79904e20 | 0.688607 | ||||||||
\(89\) | 8.04804e19 | 0.273587 | 0.136793 | − | 0.990600i | \(-0.456320\pi\) | ||||
0.136793 | + | 0.990600i | \(0.456320\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.08282e20 | 2.17585 | ||||||||
\(92\) | −4.33554e20 | −1.04057 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.46956e20 | −0.855899 | ||||||||
\(95\) | 1.23410e20 | 0.211471 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.75262e19 | −0.0792067 | −0.0396034 | − | 0.999215i | \(-0.512609\pi\) | ||||
−0.0396034 | + | 0.999215i | \(0.512609\pi\) | |||||||
\(98\) | −3.45072e20 | −0.426615 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.20110e20 | −0.120110 | ||||||||
\(101\) | 1.76126e21 | 1.58653 | 0.793266 | − | 0.608876i | \(-0.208379\pi\) | ||||
0.793266 | + | 0.608876i | \(0.208379\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.37927e21 | 1.01125 | 0.505624 | − | 0.862754i | \(-0.331262\pi\) | ||||
0.505624 | + | 0.862754i | \(0.331262\pi\) | |||||||
\(104\) | −2.56726e21 | −1.70067 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.98749e20 | −0.107794 | ||||||||
\(107\) | −2.14582e21 | −1.05454 | −0.527271 | − | 0.849697i | \(-0.676785\pi\) | ||||
−0.527271 | + | 0.849697i | \(0.676785\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.68807e21 | −1.89677 | −0.948387 | − | 0.317116i | \(-0.897285\pi\) | ||||
−0.948387 | + | 0.317116i | \(0.897285\pi\) | |||||||
\(110\) | 5.23407e20 | 0.192405 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.64988e20 | 0.0501954 | ||||||||
\(113\) | −6.02042e21 | −1.66841 | −0.834206 | − | 0.551453i | \(-0.814074\pi\) | ||||
−0.834206 | + | 0.551453i | \(0.814074\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.36173e21 | −0.774881 | ||||||||
\(116\) | 1.32327e21 | 0.278509 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.20705e21 | 0.564084 | ||||||||
\(119\) | 2.78666e21 | 0.448581 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.97107e21 | −0.536613 | ||||||||
\(122\) | 5.33107e21 | 0.660749 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.41059e21 | −0.356371 | ||||||||
\(125\) | −9.31323e20 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.44130e21 | 0.279758 | 0.139879 | − | 0.990169i | \(-0.455329\pi\) | ||||
0.139879 | + | 0.990169i | \(0.455329\pi\) | |||||||
\(128\) | 7.59035e21 | 0.568273 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.46913e21 | −0.475188 | ||||||||
\(131\) | −2.92284e22 | −1.71576 | −0.857880 | − | 0.513849i | \(-0.828219\pi\) | ||||
−0.857880 | + | 0.513849i | \(0.828219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.22233e22 | 0.611991 | ||||||||
\(134\) | −2.70691e22 | −1.25278 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.85099e21 | −0.350617 | ||||||||
\(137\) | −4.43501e22 | −1.62678 | −0.813390 | − | 0.581718i | \(-0.802381\pi\) | ||||
−0.813390 | + | 0.581718i | \(0.802381\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.52470e21 | −0.237047 | −0.118523 | − | 0.992951i | \(-0.537816\pi\) | ||||
−0.118523 | + | 0.992951i | \(0.537816\pi\) | |||||||
\(140\) | −1.18965e22 | −0.347595 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.01786e22 | −0.508001 | ||||||||
\(143\) | −4.89351e22 | −1.14444 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.02605e22 | 0.207398 | ||||||||
\(146\) | −3.61683e22 | −0.680178 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.51794e21 | −0.0736534 | ||||||||
\(149\) | −5.46937e21 | −0.0830771 | −0.0415385 | − | 0.999137i | \(-0.513226\pi\) | ||||
−0.0415385 | + | 0.999137i | \(0.513226\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.27229e23 | 1.68007 | 0.840037 | − | 0.542529i | \(-0.182533\pi\) | ||||
0.840037 | + | 0.542529i | \(0.182533\pi\) | |||||||
\(152\) | −3.88235e22 | −0.478340 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.18414e22 | 0.556813 | ||||||||
\(155\) | −2.64453e22 | −0.265379 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.51376e22 | −0.834461 | −0.417230 | − | 0.908801i | \(-0.636999\pi\) | ||||
−0.417230 | + | 0.908801i | \(0.636999\pi\) | |||||||
\(158\) | 1.36562e22 | 0.112055 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.13933e22 | 0.441430 | ||||||||
\(161\) | −3.32966e23 | −2.24248 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.39927e22 | −0.378582 | −0.189291 | − | 0.981921i | \(-0.560619\pi\) | ||||
−0.189291 | + | 0.981921i | \(0.560619\pi\) | |||||||
\(164\) | −1.03650e23 | −0.575054 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.89899e22 | −0.385866 | ||||||||
\(167\) | 1.65557e23 | 0.759319 | 0.379660 | − | 0.925126i | \(-0.376041\pi\) | ||||
0.379660 | + | 0.925126i | \(0.376041\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.51250e23 | 1.82644 | ||||||||
\(170\) | −2.57509e22 | −0.0979667 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.98192e22 | −0.133981 | ||||||||
\(173\) | −4.55954e23 | −1.44357 | −0.721784 | − | 0.692119i | \(-0.756677\pi\) | ||||
−0.721784 | + | 0.692119i | \(0.756677\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.22438e22 | −0.258844 | ||||||||
\(176\) | −9.98874e21 | −0.0264014 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.36605e22 | −0.172912 | ||||||||
\(179\) | −5.39064e23 | −1.19312 | −0.596559 | − | 0.802569i | \(-0.703466\pi\) | ||||
−0.596559 | + | 0.802569i | \(0.703466\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.81397e23 | −1.14511 | −0.572555 | − | 0.819866i | \(-0.694048\pi\) | ||||
−0.572555 | + | 0.819866i | \(0.694048\pi\) | |||||||
\(182\) | −7.39788e23 | −1.37517 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.05756e24 | 1.75275 | ||||||||
\(185\) | −3.50316e22 | −0.0548475 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.68711e23 | −0.235942 | ||||||||
\(188\) | −6.15036e23 | −0.813286 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.12952e23 | −0.133654 | ||||||||
\(191\) | 1.29385e24 | 1.44888 | 0.724440 | − | 0.689338i | \(-0.242098\pi\) | ||||
0.724440 | + | 0.689338i | \(0.242098\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.85192e23 | −0.286276 | −0.143138 | − | 0.989703i | \(-0.545719\pi\) | ||||
−0.143138 | + | 0.989703i | \(0.545719\pi\) | |||||||
\(194\) | 5.26514e22 | 0.0500601 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.74838e23 | −0.405375 | ||||||||
\(197\) | −9.53116e23 | −0.771348 | −0.385674 | − | 0.922635i | \(-0.626031\pi\) | ||||
−0.385674 | + | 0.922635i | \(0.626031\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.70629e24 | −1.24193 | −0.620965 | − | 0.783839i | \(-0.713259\pi\) | ||||
−0.620965 | + | 0.783839i | \(0.713259\pi\) | |||||||
\(200\) | 2.92985e23 | 0.202316 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.61201e24 | −1.00272 | ||||||||
\(203\) | 1.01626e24 | 0.600201 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.03689e23 | −0.428226 | ||||||||
\(206\) | −1.26239e24 | −0.639127 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.42541e23 | 0.0652043 | ||||||||
\(209\) | −7.40022e23 | −0.321891 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.10894e24 | 0.830037 | 0.415019 | − | 0.909813i | \(-0.363775\pi\) | ||||
0.415019 | + | 0.909813i | \(0.363775\pi\) | |||||||
\(212\) | −2.73490e23 | −0.102427 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.96399e24 | 0.666490 | ||||||||
\(215\) | −3.08753e23 | −0.0997718 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.61931e24 | −0.767997 | ||||||||
\(218\) | 4.29080e24 | 1.19880 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.20238e23 | 0.182826 | ||||||||
\(221\) | 2.40753e24 | 0.582712 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.71265e24 | 1.69825 | 0.849127 | − | 0.528189i | \(-0.177129\pi\) | ||||
0.849127 | + | 0.528189i | \(0.177129\pi\) | |||||||
\(224\) | 6.08077e24 | 1.27748 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.51026e24 | 1.05447 | ||||||||
\(227\) | 7.45871e24 | 1.36268 | 0.681338 | − | 0.731969i | \(-0.261399\pi\) | ||||
0.681338 | + | 0.731969i | \(0.261399\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.12934e24 | −1.18789 | −0.593946 | − | 0.804505i | \(-0.702431\pi\) | ||||
−0.593946 | + | 0.804505i | \(0.702431\pi\) | |||||||
\(230\) | 3.07686e24 | 0.489739 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.22784e24 | −0.469125 | ||||||||
\(233\) | −5.61256e23 | −0.0779694 | −0.0389847 | − | 0.999240i | \(-0.512412\pi\) | ||||
−0.0389847 | + | 0.999240i | \(0.512412\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.76892e24 | −0.605630 | ||||||||
\(236\) | 4.41307e24 | 0.536001 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.55052e24 | −0.283512 | ||||||||
\(239\) | −9.22281e23 | −0.0981037 | −0.0490518 | − | 0.998796i | \(-0.515620\pi\) | ||||
−0.0490518 | + | 0.998796i | \(0.515620\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.27261e24 | 0.221485 | 0.110743 | − | 0.993849i | \(-0.464677\pi\) | ||||
0.110743 | + | 0.993849i | \(0.464677\pi\) | |||||||
\(242\) | 3.63457e24 | 0.339150 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.33585e24 | 0.627852 | ||||||||
\(245\) | −3.68184e24 | −0.301871 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.05603e25 | 0.794982 | ||||||||
\(248\) | 8.31943e24 | 0.600276 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.52403e23 | 0.0565295 | ||||||||
\(251\) | 6.34616e23 | 0.0403586 | 0.0201793 | − | 0.999796i | \(-0.493576\pi\) | ||||
0.0201793 | + | 0.999796i | \(0.493576\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.01585e25 | 1.17948 | ||||||||
\(254\) | −3.14968e24 | −0.176812 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.97643e25 | −1.02179 | ||||||||
\(257\) | 3.08026e25 | 1.52859 | 0.764294 | − | 0.644868i | \(-0.223088\pi\) | ||||
0.764294 | + | 0.644868i | \(0.223088\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.46974e24 | −0.158727 | ||||||||
\(260\) | −1.02779e25 | −0.451530 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.67516e25 | 1.08439 | ||||||||
\(263\) | 1.89440e25 | 0.737797 | 0.368899 | − | 0.929470i | \(-0.379735\pi\) | ||||
0.368899 | + | 0.929470i | \(0.379735\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.12061e24 | −0.0762745 | ||||||||
\(266\) | −1.11875e25 | −0.386789 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.72486e25 | −1.19040 | ||||||||
\(269\) | 4.78265e25 | 1.46984 | 0.734919 | − | 0.678155i | \(-0.237220\pi\) | ||||
0.734919 | + | 0.678155i | \(0.237220\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.20632e25 | −0.627323 | −0.313661 | − | 0.949535i | \(-0.601556\pi\) | ||||
−0.313661 | + | 0.949535i | \(0.601556\pi\) | |||||||
\(272\) | 4.91431e23 | 0.0134428 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.05919e25 | 1.02816 | ||||||||
\(275\) | 5.58464e24 | 0.136145 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.34497e25 | −0.755709 | −0.377854 | − | 0.925865i | \(-0.623338\pi\) | ||||
−0.377854 | + | 0.925865i | \(0.623338\pi\) | |||||||
\(278\) | 6.88706e24 | 0.149818 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.90190e25 | 0.585494 | ||||||||
\(281\) | 6.54750e25 | 1.27250 | 0.636252 | − | 0.771481i | \(-0.280484\pi\) | ||||
0.636252 | + | 0.771481i | \(0.280484\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.97442e25 | −1.43861 | −0.719303 | − | 0.694697i | \(-0.755539\pi\) | ||||
−0.719303 | + | 0.694697i | \(0.755539\pi\) | |||||||
\(284\) | −2.77669e25 | −0.482709 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.47884e25 | 0.723306 | ||||||||
\(287\) | −7.96023e25 | −1.23927 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.07916e25 | −0.879866 | ||||||||
\(290\) | −9.39102e24 | −0.131079 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.97696e25 | −0.646315 | ||||||||
\(293\) | −5.34915e25 | −0.670154 | −0.335077 | − | 0.942191i | \(-0.608762\pi\) | ||||
−0.335077 | + | 0.942191i | \(0.608762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.42185e25 | 0.399144 | ||||||||
\(296\) | 1.10206e25 | 0.124063 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.00590e24 | 0.0525062 | ||||||||
\(299\) | −2.87665e26 | −2.91300 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.05808e25 | −0.288736 | ||||||||
\(302\) | −1.16448e26 | −1.06184 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.15559e24 | 0.0183397 | ||||||||
\(305\) | 5.68813e25 | 0.467543 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.45179e25 | 0.495139 | 0.247570 | − | 0.968870i | \(-0.420368\pi\) | ||||
0.247570 | + | 0.968870i | \(0.420368\pi\) | |||||||
\(308\) | 7.13367e25 | 0.529091 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.42044e25 | 0.167724 | ||||||||
\(311\) | −2.04121e26 | −1.36743 | −0.683713 | − | 0.729751i | \(-0.739636\pi\) | ||||
−0.683713 | + | 0.729751i | \(0.739636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.01579e25 | −0.314140 | −0.157070 | − | 0.987587i | \(-0.550205\pi\) | ||||
−0.157070 | + | 0.987587i | \(0.550205\pi\) | |||||||
\(314\) | 8.70757e25 | 0.527395 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.87917e25 | 0.106476 | ||||||||
\(317\) | 9.08402e25 | 0.497916 | 0.248958 | − | 0.968514i | \(-0.419912\pi\) | ||||
0.248958 | + | 0.968514i | \(0.419912\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.15266e25 | −0.315690 | ||||||||
\(320\) | −5.96843e25 | −0.296337 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.04751e26 | 1.41729 | ||||||||
\(323\) | 3.64080e25 | 0.163897 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.96940e25 | −0.336241 | ||||||||
\(326\) | 5.85700e25 | 0.239271 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.52832e26 | 0.968629 | ||||||||
\(329\) | −4.72343e26 | −1.75267 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.59672e26 | −0.555950 | −0.277975 | − | 0.960588i | \(-0.589663\pi\) | ||||
−0.277975 | + | 0.960588i | \(0.589663\pi\) | |||||||
\(332\) | −1.08695e26 | −0.366655 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.51528e26 | −0.479904 | ||||||||
\(335\) | −2.88821e26 | −0.886458 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.69981e26 | 0.778431 | 0.389215 | − | 0.921147i | \(-0.372746\pi\) | ||||
0.389215 | + | 0.921147i | \(0.372746\pi\) | |||||||
\(338\) | −4.13011e26 | −1.15435 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.54346e25 | −0.0930892 | ||||||||
\(341\) | 1.58578e26 | 0.403946 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.75580e26 | 0.420617 | ||||||||
\(344\) | 9.71307e25 | 0.225680 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.17317e26 | 0.912362 | ||||||||
\(347\) | −1.62844e26 | −0.345392 | −0.172696 | − | 0.984975i | \(-0.555248\pi\) | ||||
−0.172696 | + | 0.984975i | \(0.555248\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.04064e26 | 0.207794 | 0.103897 | − | 0.994588i | \(-0.466869\pi\) | ||||
0.103897 | + | 0.994588i | \(0.466869\pi\) | |||||||
\(350\) | 8.44272e25 | 0.163594 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.68143e26 | −0.671921 | ||||||||
\(353\) | 8.99929e26 | 1.59431 | 0.797157 | − | 0.603772i | \(-0.206336\pi\) | ||||
0.797157 | + | 0.603772i | \(0.206336\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.15302e26 | −0.359459 | ||||||||
\(356\) | −1.01361e26 | −0.164303 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.93384e26 | 0.754073 | ||||||||
\(359\) | −3.74893e26 | −0.556436 | −0.278218 | − | 0.960518i | \(-0.589744\pi\) | ||||
−0.278218 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.54512e26 | −0.776399 | ||||||||
\(362\) | 5.32130e26 | 0.723731 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.01799e27 | −1.30671 | ||||||||
\(365\) | −3.85907e26 | −0.481291 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.37842e26 | −0.633375 | −0.316688 | − | 0.948530i | \(-0.602571\pi\) | ||||
−0.316688 | + | 0.948530i | \(0.602571\pi\) | |||||||
\(368\) | −5.87189e25 | −0.0672010 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.20630e25 | 0.0346646 | ||||||||
\(371\) | −2.10038e26 | −0.220735 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.42062e26 | −0.637726 | −0.318863 | − | 0.947801i | \(-0.603301\pi\) | ||||
−0.318863 | + | 0.947801i | \(0.603301\pi\) | |||||||
\(374\) | 1.54414e26 | 0.149120 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.50025e27 | 1.36991 | ||||||||
\(377\) | 8.77997e26 | 0.779667 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.21546e26 | 0.690113 | 0.345056 | − | 0.938582i | \(-0.387860\pi\) | ||||
0.345056 | + | 0.938582i | \(0.387860\pi\) | |||||||
\(380\) | −1.55428e26 | −0.127000 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.18421e27 | −0.915719 | ||||||||
\(383\) | 2.13865e27 | 1.60899 | 0.804493 | − | 0.593962i | \(-0.202437\pi\) | ||||
0.804493 | + | 0.593962i | \(0.202437\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.53136e26 | 0.393999 | ||||||||
\(386\) | 2.61025e26 | 0.180932 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.24513e25 | 0.0475678 | ||||||||
\(389\) | −8.91956e26 | −0.569997 | −0.284999 | − | 0.958528i | \(-0.591993\pi\) | ||||
−0.284999 | + | 0.958528i | \(0.591993\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.91767e26 | −0.600556 | ||||||||
\(392\) | 1.15827e27 | 0.682819 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.72349e26 | 0.487506 | ||||||||
\(395\) | 1.45708e26 | 0.0792894 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.44289e26 | −0.280886 | −0.140443 | − | 0.990089i | \(-0.544853\pi\) | ||||
−0.140443 | + | 0.990089i | \(0.544853\pi\) | |||||||
\(398\) | 1.56170e27 | 0.784922 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.62673e25 | −0.00775686 | ||||||||
\(401\) | 3.58409e27 | 1.66481 | 0.832403 | − | 0.554171i | \(-0.186965\pi\) | ||||
0.832403 | + | 0.554171i | \(0.186965\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.26295e27 | −0.997635 | ||||||||
\(404\) | −2.21822e27 | −0.952795 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.30143e26 | −0.379338 | ||||||||
\(407\) | 2.10065e26 | 0.0834860 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.35423e27 | 1.64368 | 0.821840 | − | 0.569719i | \(-0.192948\pi\) | ||||
0.821840 | + | 0.569719i | \(0.192948\pi\) | |||||||
\(410\) | 7.35585e26 | 0.270647 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.73712e27 | −0.607307 | ||||||||
\(413\) | 3.38920e27 | 1.15511 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.42805e26 | −0.273037 | ||||||||
\(416\) | 5.25347e27 | 1.65946 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.77313e26 | 0.203441 | ||||||||
\(419\) | −2.45864e26 | −0.0720190 | −0.0360095 | − | 0.999351i | \(-0.511465\pi\) | ||||
−0.0360095 | + | 0.999351i | \(0.511465\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.28135e27 | −1.75021 | −0.875107 | − | 0.483929i | \(-0.839209\pi\) | ||||
−0.875107 | + | 0.483929i | \(0.839209\pi\) | |||||||
\(422\) | −1.93023e27 | −0.524599 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.67122e26 | 0.172530 | ||||||||
\(425\) | −2.74756e26 | −0.0693208 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.63387e27 | 1.35305 | ||||||||
\(428\) | 2.70255e27 | 0.633308 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.82590e26 | 0.0630576 | ||||||||
\(431\) | −1.82173e26 | −0.0396710 | −0.0198355 | − | 0.999803i | \(-0.506314\pi\) | ||||
−0.0198355 | + | 0.999803i | \(0.506314\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.57490e27 | 1.36385 | 0.681924 | − | 0.731423i | \(-0.261143\pi\) | ||||
0.681924 | + | 0.731423i | \(0.261143\pi\) | |||||||
\(434\) | 2.39735e27 | 0.485388 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.90438e27 | 1.13911 | ||||||||
\(437\) | −4.35023e27 | −0.819326 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.72073e27 | 0.847485 | 0.423742 | − | 0.905783i | \(-0.360716\pi\) | ||||
0.423742 | + | 0.905783i | \(0.360716\pi\) | |||||||
\(440\) | −1.75687e27 | −0.307955 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.20352e27 | −0.368285 | ||||||||
\(443\) | −8.10360e27 | −1.32263 | −0.661315 | − | 0.750108i | \(-0.730002\pi\) | ||||
−0.661315 | + | 0.750108i | \(0.730002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.85941e26 | −0.122352 | ||||||||
\(446\) | −7.05909e27 | −1.07333 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.91149e27 | −0.857587 | ||||||||
\(449\) | −1.19439e28 | −1.69262 | −0.846311 | − | 0.532690i | \(-0.821181\pi\) | ||||
−0.846311 | + | 0.532690i | \(0.821181\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.81929e27 | 0.651823 | ||||||||
\(452\) | 7.58242e27 | 1.00197 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.82667e27 | −0.861236 | ||||||||
\(455\) | −7.89338e27 | −0.973068 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.18815e26 | −0.0846247 | −0.0423124 | − | 0.999104i | \(-0.513472\pi\) | ||||
−0.0423124 | + | 0.999104i | \(0.513472\pi\) | |||||||
\(458\) | 6.52521e27 | 0.750770 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.23393e27 | 0.465357 | ||||||||
\(461\) | 3.30441e27 | 0.355005 | 0.177502 | − | 0.984120i | \(-0.443198\pi\) | ||||
0.177502 | + | 0.984120i | \(0.443198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.06575e28 | 1.09409 | 0.547046 | − | 0.837103i | \(-0.315752\pi\) | ||||
0.547046 | + | 0.837103i | \(0.315752\pi\) | |||||||
\(464\) | 1.79219e26 | 0.0179864 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.13696e26 | 0.0492781 | ||||||||
\(467\) | 2.56955e27 | 0.241007 | 0.120504 | − | 0.992713i | \(-0.461549\pi\) | ||||
0.120504 | + | 0.992713i | \(0.461549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.86066e28 | −2.56538 | ||||||||
\(470\) | 4.36480e27 | 0.382769 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.07648e28 | −0.902847 | ||||||||
\(473\) | 1.85143e27 | 0.151867 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.20517e27 | −0.0945729 | ||||||||
\(476\) | −3.50966e27 | −0.269397 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.44127e26 | 0.0620033 | ||||||||
\(479\) | −1.21419e28 | −0.872499 | −0.436249 | − | 0.899826i | \(-0.643693\pi\) | ||||
−0.436249 | + | 0.899826i | \(0.643693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.99768e27 | −0.206187 | ||||||||
\(482\) | −2.08003e27 | −0.139983 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.00137e27 | 0.322264 | ||||||||
\(485\) | 5.61779e26 | 0.0354223 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.63175e28 | 0.985372 | 0.492686 | − | 0.870207i | \(-0.336015\pi\) | ||||
0.492686 | + | 0.870207i | \(0.336015\pi\) | |||||||
\(488\) | −1.78943e28 | −1.05756 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.36984e27 | 0.190788 | ||||||||
\(491\) | −2.49249e28 | −1.38127 | −0.690634 | − | 0.723205i | \(-0.742668\pi\) | ||||
−0.690634 | + | 0.723205i | \(0.742668\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.02702e27 | 0.160739 | ||||||||
\(494\) | −9.66540e27 | −0.502443 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.61918e26 | −0.0230148 | ||||||||
\(497\) | −2.13248e28 | −1.04026 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.97808e27 | −0.279580 | −0.139790 | − | 0.990181i | \(-0.544643\pi\) | ||||
−0.139790 | + | 0.990181i | \(0.544643\pi\) | |||||||
\(500\) | 1.17295e27 | 0.0537150 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.80839e26 | −0.0255074 | ||||||||
\(503\) | 1.88655e28 | 0.811345 | 0.405672 | − | 0.914019i | \(-0.367037\pi\) | ||||
0.405672 | + | 0.914019i | \(0.367037\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.71998e28 | −0.709518 | ||||||||
\(506\) | −1.84502e28 | −0.745456 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.33414e27 | −0.168010 | ||||||||
\(509\) | −7.15931e27 | −0.271853 | −0.135927 | − | 0.990719i | \(-0.543401\pi\) | ||||
−0.135927 | + | 0.990719i | \(0.543401\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.82226e28 | −1.39284 | ||||||||
\(512\) | 2.17133e27 | 0.0775160 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.81925e28 | −0.966096 | ||||||||
\(515\) | −1.34694e28 | −0.452244 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.85966e28 | 0.921858 | ||||||||
\(518\) | 3.17572e27 | 0.100318 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.50709e28 | 0.760563 | ||||||||
\(521\) | −1.13976e26 | −0.00338858 | −0.00169429 | − | 0.999999i | \(-0.500539\pi\) | ||||
−0.00169429 | + | 0.999999i | \(0.500539\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.18787e28 | 0.910402 | 0.455201 | − | 0.890389i | \(-0.349567\pi\) | ||||
0.455201 | + | 0.890389i | \(0.349567\pi\) | |||||||
\(524\) | 3.68117e28 | 1.03040 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.73387e28 | −0.466301 | ||||||||
\(527\) | −7.80183e27 | −0.205677 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.90301e28 | 2.00220 | ||||||||
\(530\) | 1.94091e27 | 0.0482069 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.53946e28 | −0.367532 | ||||||||
\(533\) | −6.87723e28 | −1.60982 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.09553e28 | 0.471605 | ||||||||
\(536\) | 9.08601e28 | 2.00513 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.37737e28 | −0.928965 | ||||||||
\(539\) | 2.20780e28 | 0.459492 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.04081e28 | −0.208353 | −0.104176 | − | 0.994559i | \(-0.533221\pi\) | ||||
−0.104176 | + | 0.994559i | \(0.533221\pi\) | |||||||
\(542\) | 2.01936e28 | 0.396480 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.81121e28 | 0.342121 | ||||||||
\(545\) | 4.57819e28 | 0.848263 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.31815e28 | 0.413309 | 0.206654 | − | 0.978414i | \(-0.433742\pi\) | ||||
0.206654 | + | 0.978414i | \(0.433742\pi\) | |||||||
\(548\) | 5.58568e28 | 0.976967 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.11140e27 | −0.0860462 | ||||||||
\(551\) | 1.32775e28 | 0.219293 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.44318e28 | 0.229461 | ||||||||
\(554\) | 3.06152e28 | 0.477622 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.47698e27 | 0.142359 | ||||||||
\(557\) | −5.84547e28 | −0.861668 | −0.430834 | − | 0.902431i | \(-0.641781\pi\) | ||||
−0.430834 | + | 0.902431i | \(0.641781\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.64203e28 | −0.375071 | ||||||||
\(560\) | −1.61121e27 | −0.0224481 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.99267e28 | −0.804246 | ||||||||
\(563\) | −1.32370e28 | −0.174362 | −0.0871811 | − | 0.996192i | \(-0.527786\pi\) | ||||
−0.0871811 | + | 0.996192i | \(0.527786\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.87932e28 | 0.746136 | ||||||||
\(566\) | 7.29868e28 | 0.909225 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.77317e28 | 0.813082 | ||||||||
\(569\) | −6.62293e27 | −0.0780497 | −0.0390249 | − | 0.999238i | \(-0.512425\pi\) | ||||
−0.0390249 | + | 0.999238i | \(0.512425\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.96200e26 | −0.00904363 | −0.00452182 | − | 0.999990i | \(-0.501439\pi\) | ||||
−0.00452182 | + | 0.999990i | \(0.501439\pi\) | |||||||
\(572\) | 6.16313e28 | 0.687295 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.28568e28 | 0.783241 | ||||||||
\(575\) | 3.28294e28 | 0.346537 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.68060e29 | −1.71048 | −0.855242 | − | 0.518229i | \(-0.826591\pi\) | ||||
−0.855242 | + | 0.518229i | \(0.826591\pi\) | |||||||
\(578\) | 5.56402e28 | 0.556092 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.29226e28 | −0.124553 | ||||||||
\(581\) | −8.34765e28 | −0.790159 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.27162e28 | 0.116101 | ||||||||
\(584\) | 1.21403e29 | 1.08866 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.89586e28 | 0.423550 | ||||||||
\(587\) | 2.26546e29 | 1.92511 | 0.962555 | − | 0.271088i | \(-0.0873833\pi\) | ||||
0.962555 | + | 0.271088i | \(0.0873833\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.42215e28 | −0.280600 | ||||||||
\(590\) | −3.13188e28 | −0.252266 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.11893e26 | −0.00475661 | ||||||||
\(593\) | −1.73244e29 | −1.32307 | −0.661537 | − | 0.749913i | \(-0.730095\pi\) | ||||
−0.661537 | + | 0.749913i | \(0.730095\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.72135e28 | −0.200612 | ||||||||
\(596\) | 6.88839e27 | 0.0498921 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.63289e29 | 1.84107 | ||||||||
\(599\) | 2.58736e29 | 1.77777 | 0.888883 | − | 0.458134i | \(-0.151482\pi\) | ||||
0.888883 | + | 0.458134i | \(0.151482\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.10826e29 | −1.39876 | −0.699379 | − | 0.714751i | \(-0.746540\pi\) | ||||
−0.699379 | + | 0.714751i | \(0.746540\pi\) | |||||||
\(602\) | 2.79894e28 | 0.182486 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.60239e29 | −1.00897 | ||||||||
\(605\) | 3.87800e28 | 0.239981 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.56906e28 | −0.512214 | −0.256107 | − | 0.966648i | \(-0.582440\pi\) | ||||
−0.256107 | + | 0.966648i | \(0.582440\pi\) | |||||||
\(608\) | 7.94458e28 | 0.466749 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.20612e28 | −0.295496 | ||||||||
\(611\) | −4.08080e29 | −2.27674 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.13834e28 | 0.492643 | 0.246322 | − | 0.969188i | \(-0.420778\pi\) | ||||
0.246322 | + | 0.969188i | \(0.420778\pi\) | |||||||
\(614\) | −5.90507e28 | −0.312937 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.74011e29 | −0.891209 | ||||||||
\(617\) | −2.97590e29 | −1.49839 | −0.749195 | − | 0.662350i | \(-0.769559\pi\) | ||||
−0.749195 | + | 0.662350i | \(0.769559\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.94443e28 | 0.240638 | 0.120319 | − | 0.992735i | \(-0.461608\pi\) | ||||
0.120319 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(620\) | 3.33066e28 | 0.159374 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.86824e29 | 0.864239 | ||||||||
\(623\) | −7.78444e28 | −0.354081 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.09495e27 | 0.0400000 | ||||||||
\(626\) | 4.59076e28 | 0.198543 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.19821e29 | 0.501138 | ||||||||
\(629\) | −1.03349e28 | −0.0425084 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.44009e29 | −1.36855 | −0.684276 | − | 0.729223i | \(-0.739882\pi\) | ||||
−0.684276 | + | 0.729223i | \(0.739882\pi\) | |||||||
\(632\) | −4.58384e28 | −0.179349 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.31425e28 | −0.314692 | ||||||||
\(635\) | −3.36064e28 | −0.125112 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.15058e29 | −1.13482 | ||||||||
\(638\) | 5.63129e28 | 0.199522 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.41245e28 | −0.254139 | ||||||||
\(641\) | 1.38110e29 | 0.465818 | 0.232909 | − | 0.972499i | \(-0.425176\pi\) | ||||
0.232909 | + | 0.972499i | \(0.425176\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.35372e29 | 1.42117 | 0.710584 | − | 0.703613i | \(-0.248431\pi\) | ||||
0.710584 | + | 0.703613i | \(0.248431\pi\) | |||||||
\(644\) | 4.19354e29 | 1.34672 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.33228e28 | −0.103586 | ||||||||
\(647\) | −1.40465e29 | −0.429609 | −0.214804 | − | 0.976657i | \(-0.568911\pi\) | ||||
−0.214804 | + | 0.976657i | \(0.568911\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.05190e29 | −0.607556 | ||||||||
\(650\) | 7.29408e28 | 0.212510 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.05956e28 | 0.227359 | ||||||||
\(653\) | −4.87058e29 | −1.35205 | −0.676024 | − | 0.736880i | \(-0.736298\pi\) | ||||
−0.676024 | + | 0.736880i | \(0.736298\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.85434e29 | 0.767312 | ||||||||
\(656\) | −1.40380e28 | −0.0371376 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.32317e29 | 1.10772 | ||||||||
\(659\) | −6.21241e29 | −1.56662 | −0.783310 | − | 0.621632i | \(-0.786470\pi\) | ||||
−0.783310 | + | 0.621632i | \(0.786470\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.03932e29 | 1.47527 | 0.737637 | − | 0.675198i | \(-0.235942\pi\) | ||||
0.737637 | + | 0.675198i | \(0.235942\pi\) | |||||||
\(662\) | 1.46142e29 | 0.351370 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.65138e29 | 0.617599 | ||||||||
\(665\) | −1.19368e29 | −0.273690 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.61685e29 | −0.803543 | ||||||||
\(668\) | −2.08511e29 | −0.456011 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.64347e29 | 0.560258 | ||||||||
\(671\) | −3.41087e29 | −0.711669 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.02543e29 | 0.611827 | 0.305913 | − | 0.952059i | \(-0.401038\pi\) | ||||
0.305913 | + | 0.952059i | \(0.401038\pi\) | |||||||
\(674\) | −2.47103e29 | −0.491983 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.68326e29 | −1.09688 | ||||||||
\(677\) | −5.25623e29 | −0.998834 | −0.499417 | − | 0.866362i | \(-0.666452\pi\) | ||||
−0.499417 | + | 0.866362i | \(0.666452\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.56420e28 | 0.102511 | ||||||||
\(680\) | 8.64354e28 | 0.156801 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.45141e29 | −0.255301 | ||||||||
\(683\) | −9.04320e29 | −1.56641 | −0.783204 | − | 0.621765i | \(-0.786416\pi\) | ||||
−0.783204 | + | 0.621765i | \(0.786416\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.33107e29 | 0.727518 | ||||||||
\(686\) | −1.60701e29 | −0.265838 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.39296e27 | −0.00865264 | ||||||||
\(689\) | −1.81462e29 | −0.286738 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.14627e29 | −1.24865 | −0.624323 | − | 0.781166i | \(-0.714625\pi\) | ||||
−0.624323 | + | 0.781166i | \(0.714625\pi\) | |||||||
\(692\) | 5.74251e29 | 0.866938 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.49045e29 | 0.218294 | ||||||||
\(695\) | 7.34834e28 | 0.106011 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.37102e29 | −0.331888 | ||||||||
\(698\) | −9.52456e28 | −0.131330 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.16176e29 | 0.155449 | ||||||||
\(701\) | 3.91879e29 | 0.516551 | 0.258275 | − | 0.966071i | \(-0.416846\pi\) | ||||
0.258275 | + | 0.966071i | \(0.416846\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.53325e28 | −0.0579934 | ||||||||
\(704\) | 3.57894e29 | 0.451068 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.23670e29 | −1.00764 | ||||||||
\(707\) | −1.70357e30 | −2.05332 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.89513e29 | −0.338753 | −0.169376 | − | 0.985551i | \(-0.554175\pi\) | ||||
−0.169376 | + | 0.985551i | \(0.554175\pi\) | |||||||
\(710\) | 1.97057e29 | 0.227185 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.47249e29 | 0.276754 | ||||||||
\(713\) | 9.32205e29 | 1.02819 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.77882e29 | 0.511808 | ||||||||
\(716\) | 6.78924e29 | 0.716530 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.43125e29 | 0.351678 | ||||||||
\(719\) | −7.17610e29 | −0.724829 | −0.362414 | − | 0.932017i | \(-0.618047\pi\) | ||||
−0.362414 | + | 0.932017i | \(0.618047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.33409e30 | −1.30878 | ||||||||
\(722\) | 5.07523e29 | 0.490699 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.32240e29 | 0.687699 | ||||||||
\(725\) | −1.00200e29 | −0.0927510 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.02397e29 | 0.631643 | 0.315821 | − | 0.948819i | \(-0.397720\pi\) | ||||
0.315821 | + | 0.948819i | \(0.397720\pi\) | |||||||
\(728\) | 2.48318e30 | 2.20104 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.53206e29 | 0.304185 | ||||||||
\(731\) | −9.10875e28 | −0.0773261 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.24336e30 | 1.85057 | 0.925287 | − | 0.379268i | \(-0.123824\pi\) | ||||
0.925287 | + | 0.379268i | \(0.123824\pi\) | |||||||
\(734\) | 4.92266e29 | 0.400305 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.16413e30 | −1.71028 | ||||||||
\(737\) | 1.73190e30 | 1.34932 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.67883e30 | −1.27127 | −0.635637 | − | 0.771988i | \(-0.719263\pi\) | ||||
−0.635637 | + | 0.771988i | \(0.719263\pi\) | |||||||
\(740\) | 4.41205e28 | 0.0329388 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.92240e29 | 0.139509 | ||||||||
\(743\) | −1.09413e29 | −0.0782866 | −0.0391433 | − | 0.999234i | \(-0.512463\pi\) | ||||
−0.0391433 | + | 0.999234i | \(0.512463\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.34118e28 | 0.0371532 | ||||||||
\(746\) | 5.87654e29 | 0.403055 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.12482e29 | 0.141696 | ||||||||
\(749\) | 2.07554e30 | 1.36481 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.00380e29 | −0.383890 | −0.191945 | − | 0.981406i | \(-0.561480\pi\) | ||||
−0.191945 | + | 0.981406i | \(0.561480\pi\) | |||||||
\(752\) | −8.32982e28 | −0.0525228 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.03597e29 | −0.492764 | ||||||||
\(755\) | −1.24247e30 | −0.751352 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.10310e30 | −1.82511 | −0.912555 | − | 0.408954i | \(-0.865894\pi\) | ||||
−0.912555 | + | 0.408954i | \(0.865894\pi\) | |||||||
\(758\) | −7.51929e29 | −0.436164 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.79135e29 | 0.213920 | ||||||||
\(761\) | −2.20443e30 | −1.22675 | −0.613376 | − | 0.789791i | \(-0.710189\pi\) | ||||
−0.613376 | + | 0.789791i | \(0.710189\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.53452e30 | 2.45484 | ||||||||
\(764\) | −1.62953e30 | −0.870129 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.95742e30 | −1.01691 | ||||||||
\(767\) | 2.92810e30 | 1.50049 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.33161e30 | −0.663972 | −0.331986 | − | 0.943284i | \(-0.607719\pi\) | ||||
−0.331986 | + | 0.943284i | \(0.607719\pi\) | |||||||
\(770\) | −5.06264e29 | −0.249014 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.59184e29 | 0.171924 | ||||||||
\(773\) | 2.59159e30 | 1.22372 | 0.611858 | − | 0.790967i | \(-0.290422\pi\) | ||||
0.611858 | + | 0.790967i | \(0.290422\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.58255e29 | 0.118681 | ||||||||
\(776\) | −1.76730e29 | −0.0801239 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.16372e29 | 0.360249 | ||||||||
\(779\) | −1.04001e30 | −0.452788 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.29105e30 | 0.547150 | ||||||||
\(782\) | 9.07725e29 | 0.379563 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.43103e28 | −0.0261795 | ||||||||
\(785\) | 9.29078e29 | 0.373182 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.53600e30 | −0.600699 | −0.300350 | − | 0.953829i | \(-0.597103\pi\) | ||||
−0.300350 | + | 0.953829i | \(0.597103\pi\) | |||||||
\(788\) | 1.20040e30 | 0.463235 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.33361e29 | −0.0501124 | ||||||||
\(791\) | 5.82323e30 | 2.15929 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.86738e30 | 1.75763 | ||||||||
\(794\) | 4.98166e29 | 0.177525 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.14899e30 | 0.745844 | ||||||||
\(797\) | 4.14430e29 | 0.141951 | 0.0709755 | − | 0.997478i | \(-0.477389\pi\) | ||||
0.0709755 | + | 0.997478i | \(0.477389\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.40691e30 | −0.469381 | ||||||||
\(800\) | −5.99544e29 | −0.197413 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.28038e30 | −1.05219 | ||||||||
\(803\) | 2.31408e30 | 0.732596 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.25162e30 | 1.00287 | ||||||||
\(806\) | 2.07119e30 | 0.630524 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.41088e30 | 1.60490 | ||||||||
\(809\) | −5.69445e30 | −1.66722 | −0.833609 | − | 0.552355i | \(-0.813729\pi\) | ||||
−0.833609 | + | 0.552355i | \(0.813729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.82741e30 | −1.66248 | −0.831241 | − | 0.555913i | \(-0.812369\pi\) | ||||
−0.831241 | + | 0.555913i | \(0.812369\pi\) | |||||||
\(812\) | −1.27993e30 | −0.360452 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.92265e29 | −0.0527647 | ||||||||
\(815\) | 6.24929e29 | 0.169307 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.99541e29 | −0.105494 | ||||||||
\(818\) | −3.98526e30 | −1.03884 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.01221e30 | 0.257172 | ||||||||
\(821\) | −2.09582e30 | −0.525715 | −0.262857 | − | 0.964835i | \(-0.584665\pi\) | ||||
−0.262857 | + | 0.964835i | \(0.584665\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.51355e30 | 1.10362 | 0.551810 | − | 0.833970i | \(-0.313937\pi\) | ||||
0.551810 | + | 0.833970i | \(0.313937\pi\) | |||||||
\(824\) | 4.23734e30 | 1.02296 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.10200e30 | −0.730049 | ||||||||
\(827\) | −6.73591e30 | −1.56527 | −0.782634 | − | 0.622482i | \(-0.786124\pi\) | ||||
−0.782634 | + | 0.622482i | \(0.786124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.22443e30 | 1.18363 | 0.591816 | − | 0.806073i | \(-0.298411\pi\) | ||||
0.591816 | + | 0.806073i | \(0.298411\pi\) | |||||||
\(830\) | 7.71386e29 | 0.172565 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.10723e30 | −1.11401 | ||||||||
\(833\) | −1.08621e30 | −0.233959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.61677e30 | −0.339578 | ||||||||
\(836\) | 9.32021e29 | 0.193312 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.25029e29 | 0.0455174 | ||||||||
\(839\) | −5.77623e30 | −1.15384 | −0.576918 | − | 0.816802i | \(-0.695745\pi\) | ||||
−0.576918 | + | 0.816802i | \(0.695745\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.02893e30 | −0.784931 | ||||||||
\(842\) | 5.74908e30 | 1.10617 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.65610e30 | −0.498481 | ||||||||
\(845\) | −4.40673e30 | −0.816811 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.84101e30 | 0.694495 | ||||||||
\(848\) | −3.70405e28 | −0.00661485 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.51473e29 | 0.0438120 | ||||||||
\(851\) | 1.23487e30 | 0.212501 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.69670e30 | 0.956441 | 0.478221 | − | 0.878240i | \(-0.341282\pi\) | ||||
0.478221 | + | 0.878240i | \(0.341282\pi\) | |||||||
\(854\) | −5.15646e30 | −0.855153 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.59232e30 | −1.06675 | ||||||||
\(857\) | −4.61068e30 | −0.736998 | −0.368499 | − | 0.929628i | \(-0.620128\pi\) | ||||
−0.368499 | + | 0.929628i | \(0.620128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.02106e31 | 1.59266 | 0.796330 | − | 0.604862i | \(-0.206772\pi\) | ||||
0.796330 | + | 0.604862i | \(0.206772\pi\) | |||||||
\(860\) | 3.88859e29 | 0.0599182 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.66736e29 | 0.0250728 | ||||||||
\(863\) | 9.94622e30 | 1.47756 | 0.738779 | − | 0.673947i | \(-0.235403\pi\) | ||||
0.738779 | + | 0.673947i | \(0.235403\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.45268e30 | 0.645583 | ||||||||
\(866\) | −6.01774e30 | −0.861977 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.29889e30 | 0.461222 | ||||||||
\(869\) | −8.73735e29 | −0.120690 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.47146e31 | −3.33245 | ||||||||
\(872\) | −1.44025e31 | −1.91874 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.98159e30 | 0.517829 | ||||||||
\(875\) | 9.00819e29 | 0.115758 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.39556e31 | −1.75087 | −0.875435 | − | 0.483336i | \(-0.839425\pi\) | ||||
−0.875435 | + | 0.483336i | \(0.839425\pi\) | |||||||
\(878\) | −4.32070e30 | −0.535626 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.75463e28 | 0.0118071 | ||||||||
\(881\) | −6.73449e30 | −0.805486 | −0.402743 | − | 0.915313i | \(-0.631943\pi\) | ||||
−0.402743 | + | 0.915313i | \(0.631943\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.35750e30 | −0.625712 | −0.312856 | − | 0.949800i | \(-0.601286\pi\) | ||||
−0.312856 | + | 0.949800i | \(0.601286\pi\) | |||||||
\(884\) | −3.03217e30 | −0.349949 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.41690e30 | 0.835927 | ||||||||
\(887\) | 3.83803e30 | 0.427474 | 0.213737 | − | 0.976891i | \(-0.431436\pi\) | ||||
0.213737 | + | 0.976891i | \(0.431436\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.32858e30 | −0.362069 | ||||||||
\(890\) | 7.19341e29 | 0.0773285 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.71370e30 | −1.01989 | ||||||||
\(893\) | −6.17120e30 | −0.640367 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.26430e30 | 0.533579 | ||||||||
\(896\) | −7.34174e30 | −0.735470 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.09318e31 | 1.06977 | ||||||||
\(899\) | −2.84523e30 | −0.275195 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.25616e29 | −0.0591150 | ||||||||
\(902\) | −4.41091e30 | −0.411964 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.84957e31 | −1.68773 | ||||||||
\(905\) | 5.67770e30 | 0.512109 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.18425e30 | 0.721278 | 0.360639 | − | 0.932706i | \(-0.382559\pi\) | ||||
0.360639 | + | 0.932706i | \(0.382559\pi\) | |||||||
\(908\) | −9.39388e30 | −0.818358 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.22450e30 | 0.614997 | ||||||||
\(911\) | 1.35023e31 | 1.13623 | 0.568114 | − | 0.822950i | \(-0.307673\pi\) | ||||
0.568114 | + | 0.822950i | \(0.307673\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.05384e30 | 0.415603 | ||||||||
\(914\) | 6.57903e29 | 0.0534844 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.97905e30 | 0.713391 | ||||||||
\(917\) | 2.82711e31 | 2.22057 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.76946e30 | 0.519686 | 0.259843 | − | 0.965651i | \(-0.416329\pi\) | ||||
0.259843 | + | 0.965651i | \(0.416329\pi\) | |||||||
\(920\) | −1.03278e31 | −0.783853 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.02440e30 | −0.224370 | ||||||||
\(923\) | −1.84235e31 | −1.35131 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.42105e29 | 0.0245285 | ||||||||
\(926\) | −9.75436e30 | −0.691486 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.60525e30 | 0.457757 | ||||||||
\(929\) | 2.15858e31 | 1.47912 | 0.739561 | − | 0.673090i | \(-0.235033\pi\) | ||||
0.739561 | + | 0.673090i | \(0.235033\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.76447e30 | −0.319185 | ||||||||
\(932\) | 7.06874e29 | 0.0468247 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.35181e30 | −0.152321 | ||||||||
\(935\) | 1.64756e30 | 0.105516 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.93425e30 | 0.371621 | 0.185810 | − | 0.982586i | \(-0.440509\pi\) | ||||
0.185810 | + | 0.982586i | \(0.440509\pi\) | |||||||
\(938\) | 2.61825e31 | 1.62137 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.00621e30 | 0.363713 | ||||||||
\(941\) | −1.78030e30 | −0.106611 | −0.0533054 | − | 0.998578i | \(-0.516976\pi\) | ||||
−0.0533054 | + | 0.998578i | \(0.516976\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.83303e31 | 1.65912 | ||||||||
\(944\) | 5.97690e29 | 0.0346155 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.69454e30 | −0.0959830 | ||||||||
\(947\) | 1.38682e31 | 0.776866 | 0.388433 | − | 0.921477i | \(-0.373017\pi\) | ||||
0.388433 | + | 0.921477i | \(0.373017\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.30224e31 | −1.80931 | ||||||||
\(950\) | 1.10305e30 | 0.0597719 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.56109e30 | 0.453776 | ||||||||
\(953\) | 1.08134e31 | 0.566877 | 0.283438 | − | 0.958990i | \(-0.408525\pi\) | ||||
0.283438 | + | 0.958990i | \(0.408525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.26352e31 | −0.647959 | ||||||||
\(956\) | 1.16157e30 | 0.0589164 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.11130e31 | 0.551435 | ||||||||
\(959\) | 4.28975e31 | 2.10541 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.34922e31 | −0.647870 | ||||||||
\(962\) | 2.74366e30 | 0.130314 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.86223e30 | −0.133014 | ||||||||
\(965\) | 2.78507e30 | 0.128027 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.21987e30 | 0.234791 | 0.117396 | − | 0.993085i | \(-0.462545\pi\) | ||||
0.117396 | + | 0.993085i | \(0.462545\pi\) | |||||||
\(968\) | −1.21998e31 | −0.542827 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.14174e29 | −0.0223876 | ||||||||
\(971\) | 9.44324e30 | 0.406742 | 0.203371 | − | 0.979102i | \(-0.434810\pi\) | ||||
0.203371 | + | 0.979102i | \(0.434810\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.27824e30 | 0.306790 | ||||||||
\(974\) | −1.49348e31 | −0.622773 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.93540e29 | 0.0405473 | ||||||||
\(977\) | −3.14485e31 | −1.26972 | −0.634858 | − | 0.772628i | \(-0.718942\pi\) | ||||
−0.634858 | + | 0.772628i | \(0.718942\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.71286e30 | 0.186237 | ||||||||
\(980\) | 4.63709e30 | 0.181289 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.28128e31 | 0.872987 | ||||||||
\(983\) | −1.31474e31 | −0.497768 | −0.248884 | − | 0.968533i | \(-0.580064\pi\) | ||||
−0.248884 | + | 0.968533i | \(0.580064\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.30777e30 | 0.344957 | ||||||||
\(986\) | −2.77051e30 | −0.101590 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.33001e31 | −0.477428 | ||||||||
\(989\) | 1.08836e31 | 0.386556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.92159e31 | −1.01589 | −0.507944 | − | 0.861390i | \(-0.669594\pi\) | ||||
−0.507944 | + | 0.861390i | \(0.669594\pi\) | |||||||
\(992\) | −1.70243e31 | −0.585731 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.95177e31 | 0.657464 | ||||||||
\(995\) | 1.66630e31 | 0.555408 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.22592e30 | −0.0400095 | −0.0200047 | − | 0.999800i | \(-0.506368\pi\) | ||||
−0.0200047 | + | 0.999800i | \(0.506368\pi\) | |||||||
\(998\) | 5.47150e30 | 0.176700 | ||||||||
\(999\) | 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 | 45.22.a.i.1.3 | yes | 7 | |
3.2 | odd | 2 | 45.22.a.h.1.5 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.22.a.h.1.5 | ✓ | 7 | 3.2 | odd | 2 | ||
45.22.a.i.1.3 | yes | 7 | 1.1 | even | 1 | trivial |