Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,8,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(70.2866307339\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −14.0000 | −1.23744 | −0.618718 | − | 0.785613i | \(-0.712348\pi\) | ||||
−0.618718 | + | 0.785613i | \(0.712348\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 68.0000 | 0.531250 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1644.00 | 1.81158 | 0.905792 | − | 0.423722i | \(-0.139277\pi\) | ||||
0.905792 | + | 0.423722i | \(0.139277\pi\) | |||||||
\(8\) | 840.000 | 0.580049 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −172.000 | −0.0389631 | −0.0194816 | − | 0.999810i | \(-0.506202\pi\) | ||||
−0.0194816 | + | 0.999810i | \(0.506202\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3862.00 | −0.487540 | −0.243770 | − | 0.969833i | \(-0.578384\pi\) | ||||
−0.243770 | + | 0.969833i | \(0.578384\pi\) | |||||||
\(14\) | −23016.0 | −2.24172 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −20464.0 | −1.24902 | ||||||||
\(17\) | −12254.0 | −0.604932 | −0.302466 | − | 0.953160i | \(-0.597810\pi\) | ||||
−0.302466 | + | 0.953160i | \(0.597810\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −25940.0 | −0.867626 | −0.433813 | − | 0.901003i | \(-0.642832\pi\) | ||||
−0.433813 | + | 0.901003i | \(0.642832\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2408.00 | 0.0482144 | ||||||||
\(23\) | 12972.0 | 0.222310 | 0.111155 | − | 0.993803i | \(-0.464545\pi\) | ||||
0.111155 | + | 0.993803i | \(0.464545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 54068.0 | 0.603300 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 111792. | 0.962404 | ||||||||
\(29\) | 81610.0 | 0.621370 | 0.310685 | − | 0.950513i | \(-0.399442\pi\) | ||||
0.310685 | + | 0.950513i | \(0.399442\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −156888. | −0.945853 | −0.472927 | − | 0.881102i | \(-0.656802\pi\) | ||||
−0.472927 | + | 0.881102i | \(0.656802\pi\) | |||||||
\(32\) | 178976. | 0.965539 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 171556. | 0.748565 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −110126. | −0.357424 | −0.178712 | − | 0.983901i | \(-0.557193\pi\) | ||||
−0.178712 | + | 0.983901i | \(0.557193\pi\) | |||||||
\(38\) | 363160. | 1.07363 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −467882. | −1.06021 | −0.530106 | − | 0.847931i | \(-0.677848\pi\) | ||||
−0.530106 | + | 0.847931i | \(0.677848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 499208. | 0.957507 | 0.478753 | − | 0.877949i | \(-0.341089\pi\) | ||||
0.478753 | + | 0.877949i | \(0.341089\pi\) | |||||||
\(44\) | −11696.0 | −0.0206992 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −181608. | −0.275095 | ||||||||
\(47\) | −396884. | −0.557598 | −0.278799 | − | 0.960349i | \(-0.589936\pi\) | ||||
−0.278799 | + | 0.960349i | \(0.589936\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.87919e6 | 2.28184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −262616. | −0.259006 | ||||||||
\(53\) | −1.28050e6 | −1.18144 | −0.590722 | − | 0.806875i | \(-0.701157\pi\) | ||||
−0.590722 | + | 0.806875i | \(0.701157\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.38096e6 | 1.05081 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.14254e6 | −0.768906 | ||||||||
\(59\) | 1.33742e6 | 0.847785 | 0.423893 | − | 0.905712i | \(-0.360663\pi\) | ||||
0.423893 | + | 0.905712i | \(0.360663\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −923978. | −0.521203 | −0.260602 | − | 0.965446i | \(-0.583921\pi\) | ||||
−0.260602 | + | 0.965446i | \(0.583921\pi\) | |||||||
\(62\) | 2.19643e6 | 1.17043 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 113728. | 0.0542297 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 797304. | 0.323864 | 0.161932 | − | 0.986802i | \(-0.448228\pi\) | ||||
0.161932 | + | 0.986802i | \(0.448228\pi\) | |||||||
\(68\) | −833272. | −0.321370 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.10339e6 | −1.69221 | −0.846106 | − | 0.533015i | \(-0.821059\pi\) | ||||
−0.846106 | + | 0.533015i | \(0.821059\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.26748e6 | 1.28393 | 0.641965 | − | 0.766734i | \(-0.278119\pi\) | ||||
0.641965 | + | 0.766734i | \(0.278119\pi\) | |||||||
\(74\) | 1.54176e6 | 0.442290 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.76392e6 | −0.460926 | ||||||||
\(77\) | −282768. | −0.0705850 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −960.000 | −0.000219067 0 | −0.000109533 | − | 1.00000i | \(-0.500035\pi\) | ||||
−0.000109533 | 1.00000i | \(0.500035\pi\) | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.55035e6 | 1.31195 | ||||||||
\(83\) | 6.14083e6 | 1.17884 | 0.589419 | − | 0.807828i | \(-0.299357\pi\) | ||||
0.589419 | + | 0.807828i | \(0.299357\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.98891e6 | −1.18485 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −144480. | −0.0226005 | ||||||||
\(89\) | −2.01057e6 | −0.302311 | −0.151156 | − | 0.988510i | \(-0.548299\pi\) | ||||
−0.151156 | + | 0.988510i | \(0.548299\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.34913e6 | −0.883221 | ||||||||
\(92\) | 882096. | 0.118102 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.55638e6 | 0.689992 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.88193e6 | 0.543114 | 0.271557 | − | 0.962422i | \(-0.412461\pi\) | ||||
0.271557 | + | 0.962422i | \(0.412461\pi\) | |||||||
\(98\) | −2.63087e7 | −2.82363 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.72670e6 | −0.939379 | −0.469689 | − | 0.882832i | \(-0.655634\pi\) | ||||
−0.469689 | + | 0.882832i | \(0.655634\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.63151e7 | −1.47115 | −0.735577 | − | 0.677441i | \(-0.763089\pi\) | ||||
−0.735577 | + | 0.677441i | \(0.763089\pi\) | |||||||
\(104\) | −3.24408e6 | −0.282797 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.79270e7 | 1.46196 | ||||||||
\(107\) | −4.08974e6 | −0.322740 | −0.161370 | − | 0.986894i | \(-0.551591\pi\) | ||||
−0.161370 | + | 0.986894i | \(0.551591\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.68318e7 | −1.98453 | −0.992263 | − | 0.124158i | \(-0.960377\pi\) | ||||
−0.992263 | + | 0.124158i | \(0.960377\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.36428e7 | −2.26271 | ||||||||
\(113\) | −1.74810e7 | −1.13971 | −0.569853 | − | 0.821747i | \(-0.693000\pi\) | ||||
−0.569853 | + | 0.821747i | \(0.693000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.54948e6 | 0.330103 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.87239e7 | −1.04908 | ||||||||
\(119\) | −2.01456e7 | −1.09589 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.94576e7 | −0.998482 | ||||||||
\(122\) | 1.29357e7 | 0.644956 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.06684e7 | −0.502485 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.25018e7 | 0.541575 | 0.270787 | − | 0.962639i | \(-0.412716\pi\) | ||||
0.270787 | + | 0.962639i | \(0.412716\pi\) | |||||||
\(128\) | −2.45011e7 | −1.03264 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.75619e6 | 0.301439 | 0.150719 | − | 0.988577i | \(-0.451841\pi\) | ||||
0.150719 | + | 0.988577i | \(0.451841\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.26454e7 | −1.57178 | ||||||||
\(134\) | −1.11623e7 | −0.400761 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.02934e7 | −0.350890 | ||||||||
\(137\) | 3.61720e7 | 1.20185 | 0.600926 | − | 0.799305i | \(-0.294799\pi\) | ||||
0.600926 | + | 0.799305i | \(0.294799\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.09092e7 | 0.344542 | 0.172271 | − | 0.985050i | \(-0.444890\pi\) | ||||
0.172271 | + | 0.985050i | \(0.444890\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.14475e7 | 2.09401 | ||||||||
\(143\) | 664264. | 0.0189961 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.97447e7 | −1.58878 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.48857e6 | −0.189882 | ||||||||
\(149\) | 3.64580e7 | 0.902904 | 0.451452 | − | 0.892295i | \(-0.350906\pi\) | ||||
0.451452 | + | 0.892295i | \(0.350906\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.18955e6 | 0.169935 | 0.0849674 | − | 0.996384i | \(-0.472921\pi\) | ||||
0.0849674 | + | 0.996384i | \(0.472921\pi\) | |||||||
\(152\) | −2.17896e7 | −0.503265 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.95875e6 | 0.0873445 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.79932e7 | −1.81468 | −0.907341 | − | 0.420396i | \(-0.861891\pi\) | ||||
−0.907341 | + | 0.420396i | \(0.861891\pi\) | |||||||
\(158\) | 13440.0 | 0.000271081 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.13260e7 | 0.402734 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.48875e7 | 0.992697 | 0.496349 | − | 0.868123i | \(-0.334674\pi\) | ||||
0.496349 | + | 0.868123i | \(0.334674\pi\) | |||||||
\(164\) | −3.18160e7 | −0.563238 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.59716e7 | −1.45874 | ||||||||
\(167\) | 8.61460e6 | 0.143129 | 0.0715644 | − | 0.997436i | \(-0.477201\pi\) | ||||
0.0715644 | + | 0.997436i | \(0.477201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.78335e7 | −0.762304 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.39461e7 | 0.508676 | ||||||||
\(173\) | −5.12524e7 | −0.752580 | −0.376290 | − | 0.926502i | \(-0.622800\pi\) | ||||
−0.376290 | + | 0.926502i | \(0.622800\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.51981e6 | 0.0486659 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.81480e7 | 0.374091 | ||||||||
\(179\) | 5.01627e7 | 0.653725 | 0.326862 | − | 0.945072i | \(-0.394009\pi\) | ||||
0.326862 | + | 0.945072i | \(0.394009\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.90817e7 | 0.865940 | 0.432970 | − | 0.901408i | \(-0.357466\pi\) | ||||
0.432970 | + | 0.901408i | \(0.357466\pi\) | |||||||
\(182\) | 8.88878e7 | 1.09293 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.08965e7 | 0.128951 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.10769e6 | 0.0235701 | ||||||||
\(188\) | −2.69881e7 | −0.296224 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.54745e8 | −1.60695 | −0.803473 | − | 0.595342i | \(-0.797017\pi\) | ||||
−0.803473 | + | 0.595342i | \(0.797017\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.59406e7 | 0.159607 | 0.0798037 | − | 0.996811i | \(-0.474571\pi\) | ||||
0.0798037 | + | 0.996811i | \(0.474571\pi\) | |||||||
\(194\) | −6.83471e7 | −0.672069 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.27785e8 | 1.21223 | ||||||||
\(197\) | −1.68188e8 | −1.56734 | −0.783670 | − | 0.621177i | \(-0.786655\pi\) | ||||
−0.783670 | + | 0.621177i | \(0.786655\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.77773e8 | 1.59911 | 0.799556 | − | 0.600591i | \(-0.205068\pi\) | ||||
0.799556 | + | 0.600591i | \(0.205068\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.36174e8 | 1.16242 | ||||||||
\(203\) | 1.34167e8 | 1.12566 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.28411e8 | 1.82046 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.90320e7 | 0.608949 | ||||||||
\(209\) | 4.46168e6 | 0.0338054 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.61996e8 | −1.18718 | −0.593590 | − | 0.804767i | \(-0.702290\pi\) | ||||
−0.593590 | + | 0.804767i | \(0.702290\pi\) | |||||||
\(212\) | −8.70739e7 | −0.627642 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.72564e7 | 0.399370 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.57924e8 | −1.71349 | ||||||||
\(218\) | 3.75645e8 | 2.45572 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.73249e7 | 0.294929 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.75932e7 | −0.106237 | −0.0531187 | − | 0.998588i | \(-0.516916\pi\) | ||||
−0.0531187 | + | 0.998588i | \(0.516916\pi\) | |||||||
\(224\) | 2.94237e8 | 1.74916 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.44735e8 | 1.41031 | ||||||||
\(227\) | −2.03036e8 | −1.15208 | −0.576039 | − | 0.817422i | \(-0.695403\pi\) | ||||
−0.576039 | + | 0.817422i | \(0.695403\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.59559e8 | 0.878005 | 0.439003 | − | 0.898486i | \(-0.355332\pi\) | ||||
0.439003 | + | 0.898486i | \(0.355332\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.85524e7 | 0.360425 | ||||||||
\(233\) | −1.94985e7 | −0.100985 | −0.0504924 | − | 0.998724i | \(-0.516079\pi\) | ||||
−0.0504924 | + | 0.998724i | \(0.516079\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.09446e7 | 0.450386 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.82038e8 | 1.35609 | ||||||||
\(239\) | 1.60220e8 | 0.759146 | 0.379573 | − | 0.925162i | \(-0.376071\pi\) | ||||
0.379573 | + | 0.925162i | \(0.376071\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.78779e8 | −1.74311 | −0.871557 | − | 0.490294i | \(-0.836890\pi\) | ||||
−0.871557 | + | 0.490294i | \(0.836890\pi\) | |||||||
\(242\) | 2.72406e8 | 1.23556 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.28305e7 | −0.276889 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00180e8 | 0.423002 | ||||||||
\(248\) | −1.31786e8 | −0.548641 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.61304e8 | −0.643855 | −0.321927 | − | 0.946764i | \(-0.604331\pi\) | ||||
−0.321927 | + | 0.946764i | \(0.604331\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.23118e6 | −0.00866191 | ||||||||
\(254\) | −1.75025e8 | −0.670164 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.28458e8 | 1.22360 | ||||||||
\(257\) | 2.27387e8 | 0.835603 | 0.417801 | − | 0.908538i | \(-0.362801\pi\) | ||||
0.417801 | + | 0.908538i | \(0.362801\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.81047e8 | −0.647504 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.08587e8 | −0.373011 | ||||||||
\(263\) | 4.57728e8 | 1.55154 | 0.775768 | − | 0.631018i | \(-0.217363\pi\) | ||||
0.775768 | + | 0.631018i | \(0.217363\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.97035e8 | 1.94498 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.42167e7 | 0.172053 | ||||||||
\(269\) | −4.67286e8 | −1.46369 | −0.731847 | − | 0.681469i | \(-0.761341\pi\) | ||||
−0.731847 | + | 0.681469i | \(0.761341\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.45932e7 | −0.136106 | −0.0680528 | − | 0.997682i | \(-0.521679\pi\) | ||||
−0.0680528 | + | 0.997682i | \(0.521679\pi\) | |||||||
\(272\) | 2.50766e8 | 0.755574 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.06408e8 | −1.48722 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.16657e8 | −0.895179 | −0.447590 | − | 0.894239i | \(-0.647717\pi\) | ||||
−0.447590 | + | 0.894239i | \(0.647717\pi\) | |||||||
\(278\) | −1.52729e8 | −0.426349 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.25818e8 | 0.607136 | 0.303568 | − | 0.952810i | \(-0.401822\pi\) | ||||
0.303568 | + | 0.952810i | \(0.401822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.08210e7 | −0.0546072 | −0.0273036 | − | 0.999627i | \(-0.508692\pi\) | ||||
−0.0273036 | + | 0.999627i | \(0.508692\pi\) | |||||||
\(284\) | −3.47031e8 | −0.898987 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.29970e6 | −0.0235065 | ||||||||
\(287\) | −7.69198e8 | −1.92066 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.60178e8 | −0.634057 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.90189e8 | 0.682088 | ||||||||
\(293\) | −1.78825e8 | −0.415329 | −0.207665 | − | 0.978200i | \(-0.566586\pi\) | ||||
−0.207665 | + | 0.978200i | \(0.566586\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.25058e7 | −0.207323 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.10413e8 | −1.11729 | ||||||||
\(299\) | −5.00979e7 | −0.108385 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.20698e8 | 1.73461 | ||||||||
\(302\) | −1.00654e8 | −0.210284 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.30836e8 | 1.08368 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.55159e7 | 0.168680 | 0.0843398 | − | 0.996437i | \(-0.473122\pi\) | ||||
0.0843398 | + | 0.996437i | \(0.473122\pi\) | |||||||
\(308\) | −1.92282e7 | −0.0374983 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.84706e8 | 0.913728 | 0.456864 | − | 0.889537i | \(-0.348973\pi\) | ||||
0.456864 | + | 0.889537i | \(0.348973\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.70821e8 | −1.05219 | −0.526096 | − | 0.850425i | \(-0.676345\pi\) | ||||
−0.526096 | + | 0.850425i | \(0.676345\pi\) | |||||||
\(314\) | 1.23190e9 | 2.24555 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −65280.0 | −0.000116379 0 | ||||||||
\(317\) | −5.50191e8 | −0.970076 | −0.485038 | − | 0.874493i | \(-0.661194\pi\) | ||||
−0.485038 | + | 0.874493i | \(0.661194\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.40369e7 | −0.0242105 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.98564e8 | −0.498358 | ||||||||
\(323\) | 3.17869e8 | 0.524855 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.68425e8 | −1.22840 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.93021e8 | −0.614975 | ||||||||
\(329\) | −6.52477e8 | −1.01014 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.39839e8 | −1.42448 | −0.712238 | − | 0.701938i | \(-0.752319\pi\) | ||||
−0.712238 | + | 0.701938i | \(0.752319\pi\) | |||||||
\(332\) | 4.17577e8 | 0.626257 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.20604e8 | −0.177113 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.33632e8 | −0.759516 | −0.379758 | − | 0.925086i | \(-0.623993\pi\) | ||||
−0.379758 | + | 0.925086i | \(0.623993\pi\) | |||||||
\(338\) | 6.69669e8 | 0.943304 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.69847e7 | 0.0368534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.73549e9 | 2.32216 | ||||||||
\(344\) | 4.19335e8 | 0.555401 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.17533e8 | 0.931270 | ||||||||
\(347\) | 1.07934e9 | 1.38677 | 0.693385 | − | 0.720567i | \(-0.256118\pi\) | ||||
0.693385 | + | 0.720567i | \(0.256118\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.27217e8 | −0.537972 | −0.268986 | − | 0.963144i | \(-0.586689\pi\) | ||||
−0.268986 | + | 0.963144i | \(0.586689\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.07839e7 | −0.0376204 | ||||||||
\(353\) | −1.48966e9 | −1.80250 | −0.901250 | − | 0.433299i | \(-0.857350\pi\) | ||||
−0.901250 | + | 0.433299i | \(0.857350\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.36719e8 | −0.160603 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.02277e8 | −0.808943 | ||||||||
\(359\) | −8.41275e8 | −0.959638 | −0.479819 | − | 0.877367i | \(-0.659298\pi\) | ||||
−0.479819 | + | 0.877367i | \(0.659298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.20988e8 | −0.247226 | ||||||||
\(362\) | −9.67143e8 | −1.07155 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.31741e8 | −0.469211 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.50462e8 | 0.792496 | 0.396248 | − | 0.918143i | \(-0.370312\pi\) | ||||
0.396248 | + | 0.918143i | \(0.370312\pi\) | |||||||
\(368\) | −2.65459e8 | −0.277671 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.10514e9 | −2.14029 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.71074e8 | −0.170688 | −0.0853439 | − | 0.996352i | \(-0.527199\pi\) | ||||
−0.0853439 | + | 0.996352i | \(0.527199\pi\) | |||||||
\(374\) | −2.95076e7 | −0.0291665 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.33383e8 | −0.323434 | ||||||||
\(377\) | −3.15178e8 | −0.302943 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.66239e7 | 0.0439918 | 0.0219959 | − | 0.999758i | \(-0.492998\pi\) | ||||
0.0219959 | + | 0.999758i | \(0.492998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.16644e9 | 1.98849 | ||||||||
\(383\) | −4.42266e8 | −0.402242 | −0.201121 | − | 0.979566i | \(-0.564458\pi\) | ||||
−0.201121 | + | 0.979566i | \(0.564458\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.23168e8 | −0.197504 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.31972e8 | 0.288529 | ||||||||
\(389\) | 4.64033e8 | 0.399691 | 0.199846 | − | 0.979827i | \(-0.435956\pi\) | ||||
0.199846 | + | 0.979827i | \(0.435956\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.58959e8 | −0.134483 | ||||||||
\(392\) | 1.57852e9 | 1.32358 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.35463e9 | 1.93948 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.17792e8 | 0.254904 | 0.127452 | − | 0.991845i | \(-0.459320\pi\) | ||||
0.127452 | + | 0.991845i | \(0.459320\pi\) | |||||||
\(398\) | −2.48882e9 | −1.97880 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.19563e9 | 0.925958 | 0.462979 | − | 0.886369i | \(-0.346781\pi\) | ||||
0.462979 | + | 0.886369i | \(0.346781\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.05901e8 | 0.461142 | ||||||||
\(404\) | −6.61416e8 | −0.499045 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.87834e9 | −1.39294 | ||||||||
\(407\) | 1.89417e7 | 0.0139264 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.21305e9 | 1.59941 | 0.799704 | − | 0.600395i | \(-0.204990\pi\) | ||||
0.799704 | + | 0.600395i | \(0.204990\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.10942e9 | −0.781551 | ||||||||
\(413\) | 2.19872e9 | 1.53583 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.91205e8 | −0.470739 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.24635e7 | −0.0418321 | ||||||||
\(419\) | 8.02299e8 | 0.532828 | 0.266414 | − | 0.963859i | \(-0.414161\pi\) | ||||
0.266414 | + | 0.963859i | \(0.414161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.44713e7 | 0.0225149 | 0.0112575 | − | 0.999937i | \(-0.496417\pi\) | ||||
0.0112575 | + | 0.999937i | \(0.496417\pi\) | |||||||
\(422\) | 2.26795e9 | 1.46906 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.07562e9 | −0.685295 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.51902e9 | −0.944204 | ||||||||
\(428\) | −2.78103e8 | −0.171456 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.72692e9 | −1.03897 | −0.519485 | − | 0.854480i | \(-0.673876\pi\) | ||||
−0.519485 | + | 0.854480i | \(0.673876\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.88308e8 | −0.289059 | −0.144529 | − | 0.989501i | \(-0.546167\pi\) | ||||
−0.144529 | + | 0.989501i | \(0.546167\pi\) | |||||||
\(434\) | 3.61093e9 | 2.12034 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.82456e9 | −1.05428 | ||||||||
\(437\) | −3.36494e8 | −0.192882 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.88640e9 | −1.62828 | −0.814142 | − | 0.580665i | \(-0.802793\pi\) | ||||
−0.814142 | + | 0.580665i | \(0.802793\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.62549e8 | −0.364956 | ||||||||
\(443\) | 9.26583e8 | 0.506374 | 0.253187 | − | 0.967417i | \(-0.418521\pi\) | ||||
0.253187 | + | 0.967417i | \(0.418521\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.46304e8 | 0.131462 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.86969e8 | 0.0982418 | ||||||||
\(449\) | −1.35535e9 | −0.706627 | −0.353313 | − | 0.935505i | \(-0.614945\pi\) | ||||
−0.353313 | + | 0.935505i | \(0.614945\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.04757e7 | 0.0413092 | ||||||||
\(452\) | −1.18871e9 | −0.605469 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.84250e9 | 1.42563 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.63429e7 | −0.0227131 | −0.0113566 | − | 0.999936i | \(-0.503615\pi\) | ||||
−0.0113566 | + | 0.999936i | \(0.503615\pi\) | |||||||
\(458\) | −2.23383e9 | −1.08648 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.52117e8 | 0.0723144 | 0.0361572 | − | 0.999346i | \(-0.488488\pi\) | ||||
0.0361572 | + | 0.999346i | \(0.488488\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.63450e9 | −0.765337 | −0.382668 | − | 0.923886i | \(-0.624995\pi\) | ||||
−0.382668 | + | 0.923886i | \(0.624995\pi\) | |||||||
\(464\) | −1.67007e9 | −0.776106 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.72979e8 | 0.124962 | ||||||||
\(467\) | −1.11380e9 | −0.506057 | −0.253029 | − | 0.967459i | \(-0.581427\pi\) | ||||
−0.253029 | + | 0.967459i | \(0.581427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.31077e9 | 0.586706 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.12343e9 | 0.491756 | ||||||||
\(473\) | −8.58638e7 | −0.0373075 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.36990e9 | −0.582189 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.24309e9 | −0.939395 | ||||||||
\(479\) | −1.27745e9 | −0.531091 | −0.265546 | − | 0.964098i | \(-0.585552\pi\) | ||||
−0.265546 | + | 0.964098i | \(0.585552\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.25307e8 | 0.174259 | ||||||||
\(482\) | 5.30290e9 | 2.15699 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.32312e9 | −0.530443 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.79673e8 | −0.384352 | −0.192176 | − | 0.981360i | \(-0.561555\pi\) | ||||
−0.192176 | + | 0.981360i | \(0.561555\pi\) | |||||||
\(488\) | −7.76142e8 | −0.302323 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.92125e9 | 1.87625 | 0.938124 | − | 0.346298i | \(-0.112562\pi\) | ||||
0.938124 | + | 0.346298i | \(0.112562\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.00005e9 | −0.375887 | ||||||||
\(494\) | −1.40252e9 | −0.523439 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.21056e9 | 1.18139 | ||||||||
\(497\) | −8.38998e9 | −3.06559 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.65786e9 | −1.31788 | −0.658940 | − | 0.752196i | \(-0.728995\pi\) | ||||
−0.658940 | + | 0.752196i | \(0.728995\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.25826e9 | 0.796729 | ||||||||
\(503\) | −3.88358e9 | −1.36064 | −0.680322 | − | 0.732914i | \(-0.738160\pi\) | ||||
−0.680322 | + | 0.732914i | \(0.738160\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.12366e7 | 0.0107186 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.50120e8 | 0.287711 | ||||||||
\(509\) | −3.90072e9 | −1.31109 | −0.655545 | − | 0.755156i | \(-0.727561\pi\) | ||||
−0.655545 | + | 0.755156i | \(0.727561\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.01573e9 | 2.32595 | ||||||||
\(512\) | −1.46228e9 | −0.481487 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.18342e9 | −1.03401 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.82640e7 | 0.0217258 | ||||||||
\(518\) | 2.53466e9 | 0.801245 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.88399e9 | −0.893431 | −0.446716 | − | 0.894676i | \(-0.647406\pi\) | ||||
−0.446716 | + | 0.894676i | \(0.647406\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.77188e8 | −0.268125 | −0.134062 | − | 0.990973i | \(-0.542802\pi\) | ||||
−0.134062 | + | 0.990973i | \(0.542802\pi\) | |||||||
\(524\) | 5.27421e8 | 0.160139 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.40819e9 | −1.91993 | ||||||||
\(527\) | 1.92251e9 | 0.572177 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.23655e9 | −0.950578 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.89988e9 | −0.835007 | ||||||||
\(533\) | 1.80696e9 | 0.516896 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.69735e8 | 0.187857 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.54201e9 | 1.81123 | ||||||||
\(539\) | −3.23221e8 | −0.0889077 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.53485e8 | −0.177437 | −0.0887187 | − | 0.996057i | \(-0.528277\pi\) | ||||
−0.0887187 | + | 0.996057i | \(0.528277\pi\) | |||||||
\(542\) | 6.24305e8 | 0.168422 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.19317e9 | −0.584086 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.59299e9 | 1.19988 | 0.599942 | − | 0.800043i | \(-0.295190\pi\) | ||||
0.599942 | + | 0.800043i | \(0.295190\pi\) | |||||||
\(548\) | 2.45970e9 | 0.638484 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.11696e9 | −0.539117 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.57824e6 | −0.000396858 0 | ||||||||
\(554\) | 4.43320e9 | 1.10773 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.41827e8 | 0.183038 | ||||||||
\(557\) | 6.83164e9 | 1.67507 | 0.837533 | − | 0.546387i | \(-0.183997\pi\) | ||||
0.837533 | + | 0.546387i | \(0.183997\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.92794e9 | −0.466823 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.16145e9 | −0.751292 | ||||||||
\(563\) | 3.42509e9 | 0.808897 | 0.404449 | − | 0.914561i | \(-0.367463\pi\) | ||||
0.404449 | + | 0.914561i | \(0.367463\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.91494e8 | 0.0675729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.28685e9 | −0.981565 | ||||||||
\(569\) | 7.50930e9 | 1.70886 | 0.854430 | − | 0.519566i | \(-0.173906\pi\) | ||||
0.854430 | + | 0.519566i | \(0.173906\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.35841e8 | −0.0305355 | −0.0152677 | − | 0.999883i | \(-0.504860\pi\) | ||||
−0.0152677 | + | 0.999883i | \(0.504860\pi\) | |||||||
\(572\) | 4.51700e7 | 0.0100917 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.07688e10 | 2.37670 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.63775e9 | −0.354922 | −0.177461 | − | 0.984128i | \(-0.556788\pi\) | ||||
−0.177461 | + | 0.984128i | \(0.556788\pi\) | |||||||
\(578\) | 3.64249e9 | 0.784606 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.00955e10 | 2.13556 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.20246e8 | 0.0460328 | ||||||||
\(584\) | 3.58468e9 | 0.744742 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.50356e9 | 0.513944 | ||||||||
\(587\) | −5.97205e9 | −1.21868 | −0.609341 | − | 0.792909i | \(-0.708566\pi\) | ||||
−0.609341 | + | 0.792909i | \(0.708566\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.06967e9 | 0.820647 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.25362e9 | 0.446431 | ||||||||
\(593\) | 8.31347e9 | 1.63716 | 0.818579 | − | 0.574394i | \(-0.194762\pi\) | ||||
0.818579 | + | 0.574394i | \(0.194762\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.47915e9 | 0.479668 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.01370e8 | 0.134120 | ||||||||
\(599\) | −9.78368e9 | −1.85998 | −0.929990 | − | 0.367585i | \(-0.880185\pi\) | ||||
−0.929990 | + | 0.367585i | \(0.880185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.40159e9 | 1.01499 | 0.507494 | − | 0.861655i | \(-0.330572\pi\) | ||||
0.507494 | + | 0.861655i | \(0.330572\pi\) | |||||||
\(602\) | −1.14898e10 | −2.14646 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.88890e8 | 0.0902779 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.84439e9 | 0.516214 | 0.258107 | − | 0.966116i | \(-0.416901\pi\) | ||||
0.258107 | + | 0.966116i | \(0.416901\pi\) | |||||||
\(608\) | −4.64264e9 | −0.837726 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.53277e9 | 0.271851 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.02106e9 | 1.23109 | 0.615547 | − | 0.788101i | \(-0.288935\pi\) | ||||
0.615547 | + | 0.788101i | \(0.288935\pi\) | |||||||
\(614\) | −1.19722e9 | −0.208730 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.37525e8 | −0.0409428 | ||||||||
\(617\) | 3.35166e9 | 0.574462 | 0.287231 | − | 0.957861i | \(-0.407265\pi\) | ||||
0.287231 | + | 0.957861i | \(0.407265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.92362e9 | −0.664921 | −0.332461 | − | 0.943117i | \(-0.607879\pi\) | ||||
−0.332461 | + | 0.943117i | \(0.607879\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.78588e9 | −1.13068 | ||||||||
\(623\) | −3.30538e9 | −0.547662 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.99150e9 | 1.30202 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.98354e9 | −0.964049 | ||||||||
\(629\) | 1.34948e9 | 0.216217 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.81545e8 | −0.107992 | −0.0539960 | − | 0.998541i | \(-0.517196\pi\) | ||||
−0.0539960 | + | 0.998541i | \(0.517196\pi\) | |||||||
\(632\) | −806400. | −0.000127069 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.70267e9 | 1.20041 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.25744e9 | −1.11249 | ||||||||
\(638\) | 1.96517e8 | 0.0299590 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.65199e9 | −1.44748 | −0.723742 | − | 0.690071i | \(-0.757579\pi\) | ||||
−0.723742 | + | 0.690071i | \(0.757579\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.07826e9 | 0.753315 | 0.376657 | − | 0.926353i | \(-0.377073\pi\) | ||||
0.376657 | + | 0.926353i | \(0.377073\pi\) | |||||||
\(644\) | 1.45017e9 | 0.213952 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.45016e9 | −0.649474 | ||||||||
\(647\) | −2.08330e9 | −0.302404 | −0.151202 | − | 0.988503i | \(-0.548314\pi\) | ||||
−0.151202 | + | 0.988503i | \(0.548314\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.30036e8 | −0.0330324 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.73235e9 | 0.527370 | ||||||||
\(653\) | 6.84881e9 | 0.962540 | 0.481270 | − | 0.876572i | \(-0.340176\pi\) | ||||
0.481270 | + | 0.876572i | \(0.340176\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.57474e9 | 1.32423 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.13468e9 | 1.24998 | ||||||||
\(659\) | −6.99913e9 | −0.952676 | −0.476338 | − | 0.879262i | \(-0.658036\pi\) | ||||
−0.476338 | + | 0.879262i | \(0.658036\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.99594e9 | −0.268809 | −0.134404 | − | 0.990927i | \(-0.542912\pi\) | ||||
−0.134404 | + | 0.990927i | \(0.542912\pi\) | |||||||
\(662\) | 1.31577e10 | 1.76270 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.15830e9 | 0.683783 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.05864e9 | 0.138137 | ||||||||
\(668\) | 5.85793e8 | 0.0760372 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.58924e8 | 0.0203077 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.17939e10 | 1.49144 | 0.745718 | − | 0.666261i | \(-0.232106\pi\) | ||||
0.745718 | + | 0.666261i | \(0.232106\pi\) | |||||||
\(674\) | 7.47085e9 | 0.939853 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.25268e9 | −0.404974 | ||||||||
\(677\) | 7.80222e9 | 0.966402 | 0.483201 | − | 0.875509i | \(-0.339474\pi\) | ||||
0.483201 | + | 0.875509i | \(0.339474\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.02590e9 | 0.983897 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.77786e8 | −0.0456038 | ||||||||
\(683\) | 4.51153e9 | 0.541815 | 0.270908 | − | 0.962605i | \(-0.412676\pi\) | ||||
0.270908 | + | 0.962605i | \(0.412676\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.42968e10 | −2.87353 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.02158e10 | −1.19595 | ||||||||
\(689\) | 4.94528e9 | 0.576002 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.06331e10 | −1.22599 | −0.612997 | − | 0.790086i | \(-0.710036\pi\) | ||||
−0.612997 | + | 0.790086i | \(0.710036\pi\) | |||||||
\(692\) | −3.48516e9 | −0.399808 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.51107e10 | −1.71604 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.73343e9 | 0.641356 | ||||||||
\(698\) | 5.98104e9 | 0.665707 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.38514e9 | 0.480807 | 0.240403 | − | 0.970673i | \(-0.422720\pi\) | ||||
0.240403 | + | 0.970673i | \(0.422720\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.85667e9 | 0.310110 | ||||||||
\(704\) | −1.95612e7 | −0.00211296 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.08552e10 | 2.23048 | ||||||||
\(707\) | −1.59907e10 | −1.70176 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.98805e9 | −0.630992 | −0.315496 | − | 0.948927i | \(-0.602171\pi\) | ||||
−0.315496 | + | 0.948927i | \(0.602171\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.68888e9 | −0.175355 | ||||||||
\(713\) | −2.03515e9 | −0.210273 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.41106e9 | 0.347291 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.17779e10 | 1.18749 | ||||||||
\(719\) | 1.17768e10 | 1.18161 | 0.590807 | − | 0.806813i | \(-0.298809\pi\) | ||||
0.590807 | + | 0.806813i | \(0.298809\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.68219e10 | −2.66512 | ||||||||
\(722\) | 3.09383e9 | 0.305926 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.69755e9 | 0.460031 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.41051e9 | −0.811805 | −0.405902 | − | 0.913916i | \(-0.633043\pi\) | ||||
−0.405902 | + | 0.913916i | \(0.633043\pi\) | |||||||
\(728\) | −5.33327e9 | −0.512311 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.11729e9 | −0.579227 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.44084e10 | −1.35130 | −0.675650 | − | 0.737223i | \(-0.736137\pi\) | ||||
−0.675650 | + | 0.737223i | \(0.736137\pi\) | |||||||
\(734\) | −1.05065e10 | −0.980664 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.32168e9 | 0.214649 | ||||||||
\(737\) | −1.37136e8 | −0.0126187 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.21708e9 | 0.748966 | 0.374483 | − | 0.927234i | \(-0.377820\pi\) | ||||
0.374483 | + | 0.927234i | \(0.377820\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.94719e10 | 2.64847 | ||||||||
\(743\) | −1.72531e10 | −1.54314 | −0.771570 | − | 0.636144i | \(-0.780528\pi\) | ||||
−0.771570 | + | 0.636144i | \(0.780528\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.39503e9 | 0.211215 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.43323e8 | 0.0125216 | ||||||||
\(749\) | −6.72354e9 | −0.584671 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.58498e10 | 1.36548 | 0.682739 | − | 0.730662i | \(-0.260789\pi\) | ||||
0.682739 | + | 0.730662i | \(0.260789\pi\) | |||||||
\(752\) | 8.12183e9 | 0.696453 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.41249e9 | 0.374873 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.13856e9 | −0.598102 | −0.299051 | − | 0.954237i | \(-0.596670\pi\) | ||||
−0.299051 | + | 0.954237i | \(0.596670\pi\) | |||||||
\(758\) | −6.52735e8 | −0.0544371 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.59993e9 | 0.213853 | 0.106926 | − | 0.994267i | \(-0.465899\pi\) | ||||
0.106926 | + | 0.994267i | \(0.465899\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.41114e10 | −3.59514 | ||||||||
\(764\) | −1.05227e10 | −0.853690 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.19172e9 | 0.497749 | ||||||||
\(767\) | −5.16512e9 | −0.413329 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.96477e9 | −0.393692 | −0.196846 | − | 0.980434i | \(-0.563070\pi\) | ||||
−0.196846 | + | 0.980434i | \(0.563070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.08396e9 | 0.0847914 | ||||||||
\(773\) | −1.49681e10 | −1.16557 | −0.582786 | − | 0.812626i | \(-0.698037\pi\) | ||||
−0.582786 | + | 0.812626i | \(0.698037\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.10082e9 | 0.315032 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.49646e9 | −0.494593 | ||||||||
\(779\) | 1.21369e10 | 0.919867 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.77783e8 | 0.0659339 | ||||||||
\(782\) | 2.22542e9 | 0.166414 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.84558e10 | −2.85007 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.79990e9 | 0.716655 | 0.358328 | − | 0.933596i | \(-0.383347\pi\) | ||||
0.358328 | + | 0.933596i | \(0.383347\pi\) | |||||||
\(788\) | −1.14368e10 | −0.832650 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.87388e10 | −2.06467 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.56840e9 | 0.254108 | ||||||||
\(794\) | −4.44909e9 | −0.315428 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.20885e10 | 0.849529 | ||||||||
\(797\) | 3.93169e9 | 0.275090 | 0.137545 | − | 0.990495i | \(-0.456079\pi\) | ||||
0.137545 | + | 0.990495i | \(0.456079\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.86342e9 | 0.337309 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.67388e10 | −1.14581 | ||||||||
\(803\) | −7.34006e8 | −0.0500259 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.48262e9 | −0.570634 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.17043e9 | −0.544885 | ||||||||
\(809\) | −1.26324e10 | −0.838816 | −0.419408 | − | 0.907798i | \(-0.637762\pi\) | ||||
−0.419408 | + | 0.907798i | \(0.637762\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.16653e10 | 0.767934 | 0.383967 | − | 0.923347i | \(-0.374558\pi\) | ||||
0.383967 | + | 0.923347i | \(0.374558\pi\) | |||||||
\(812\) | 9.12335e9 | 0.598009 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.65183e8 | −0.0172330 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.29495e10 | −0.830758 | ||||||||
\(818\) | −3.09827e10 | −1.97917 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.17500e9 | 0.515569 | 0.257784 | − | 0.966202i | \(-0.417008\pi\) | ||||
0.257784 | + | 0.966202i | \(0.417008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.75211e10 | 1.09563 | 0.547813 | − | 0.836601i | \(-0.315460\pi\) | ||||
0.547813 | + | 0.836601i | \(0.315460\pi\) | |||||||
\(824\) | −1.37046e10 | −0.853341 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.07821e10 | −1.90050 | ||||||||
\(827\) | 1.22225e10 | 0.751437 | 0.375718 | − | 0.926734i | \(-0.377396\pi\) | ||||
0.375718 | + | 0.926734i | \(0.377396\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.06634e10 | −0.650063 | −0.325032 | − | 0.945703i | \(-0.605375\pi\) | ||||
−0.325032 | + | 0.945703i | \(0.605375\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.39218e8 | −0.0264392 | ||||||||
\(833\) | −2.30276e10 | −1.38036 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.03394e8 | 0.0179591 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.12322e10 | −0.659341 | ||||||||
\(839\) | 2.31400e9 | 0.135268 | 0.0676342 | − | 0.997710i | \(-0.478455\pi\) | ||||
0.0676342 | + | 0.997710i | \(0.478455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.05897e10 | −0.613899 | ||||||||
\(842\) | −4.82599e8 | −0.0278608 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.10158e10 | −0.630690 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.19883e10 | −1.80883 | ||||||||
\(848\) | 2.62041e10 | 1.47565 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.42855e9 | −0.0794590 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.22377e9 | 0.233012 | 0.116506 | − | 0.993190i | \(-0.462831\pi\) | ||||
0.116506 | + | 0.993190i | \(0.462831\pi\) | |||||||
\(854\) | 2.12663e10 | 1.16839 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.43538e9 | −0.187205 | ||||||||
\(857\) | −3.52104e9 | −0.191090 | −0.0955450 | − | 0.995425i | \(-0.530459\pi\) | ||||
−0.0955450 | + | 0.995425i | \(0.530459\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.44930e10 | 1.31846 | 0.659229 | − | 0.751943i | \(-0.270883\pi\) | ||||
0.659229 | + | 0.751943i | \(0.270883\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.41769e10 | 1.28566 | ||||||||
\(863\) | −5.40573e9 | −0.286297 | −0.143148 | − | 0.989701i | \(-0.545723\pi\) | ||||
−0.143148 | + | 0.989701i | \(0.545723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.83631e9 | 0.357692 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.75388e10 | −0.910293 | ||||||||
\(869\) | 165120. | 8.53553e−6 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.07919e9 | −0.157897 | ||||||||
\(872\) | −2.25387e10 | −1.15112 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.71091e9 | 0.238679 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.89155e10 | 1.44755 | 0.723773 | − | 0.690039i | \(-0.242406\pi\) | ||||
0.723773 | + | 0.690039i | \(0.242406\pi\) | |||||||
\(878\) | 4.04096e10 | 2.01490 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.80643e8 | −0.0384624 | −0.0192312 | − | 0.999815i | \(-0.506122\pi\) | ||||
−0.0192312 | + | 0.999815i | \(0.506122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.36907e10 | 0.669211 | 0.334605 | − | 0.942358i | \(-0.391397\pi\) | ||||
0.334605 | + | 0.942358i | \(0.391397\pi\) | |||||||
\(884\) | 3.21810e9 | 0.156681 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.29722e10 | −0.626606 | ||||||||
\(887\) | 3.58403e9 | 0.172441 | 0.0862203 | − | 0.996276i | \(-0.472521\pi\) | ||||
0.0862203 | + | 0.996276i | \(0.472521\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.05529e10 | 0.981108 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.19634e9 | −0.0564386 | ||||||||
\(893\) | 1.02952e10 | 0.483786 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.02798e10 | −1.87072 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.89749e10 | 0.874406 | ||||||||
\(899\) | −1.28036e10 | −0.587725 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.56912e10 | 0.714694 | ||||||||
\(902\) | −1.12666e9 | −0.0511175 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.46841e10 | −0.661085 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.01108e10 | 1.33998 | 0.669988 | − | 0.742372i | \(-0.266299\pi\) | ||||
0.669988 | + | 0.742372i | \(0.266299\pi\) | |||||||
\(908\) | −1.38064e10 | −0.612042 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.48800e10 | 1.09027 | 0.545137 | − | 0.838347i | \(-0.316477\pi\) | ||||
0.545137 | + | 0.838347i | \(0.316477\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.05622e9 | −0.0459312 | ||||||||
\(914\) | 6.48801e8 | 0.0281060 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.08500e10 | 0.466440 | ||||||||
\(917\) | 1.27512e10 | 0.546082 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.08420e10 | 0.460794 | 0.230397 | − | 0.973097i | \(-0.425997\pi\) | ||||
0.230397 | + | 0.973097i | \(0.425997\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.12964e9 | −0.0894846 | ||||||||
\(923\) | 1.97093e10 | 0.825021 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.28831e10 | 0.947056 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.46062e10 | 0.599957 | ||||||||
\(929\) | −1.07045e10 | −0.438038 | −0.219019 | − | 0.975721i | \(-0.570286\pi\) | ||||
−0.219019 | + | 0.975721i | \(0.570286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.87463e10 | −1.97978 | ||||||||
\(932\) | −1.32590e9 | −0.0536482 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.55933e10 | 0.626214 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.42787e10 | −1.36124 | −0.680621 | − | 0.732635i | \(-0.738290\pi\) | ||||
−0.680621 | + | 0.732635i | \(0.738290\pi\) | |||||||
\(938\) | −1.83507e10 | −0.726012 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.73695e9 | 0.146202 | 0.0731010 | − | 0.997325i | \(-0.476710\pi\) | ||||
0.0731010 | + | 0.997325i | \(0.476710\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.06937e9 | −0.235696 | ||||||||
\(944\) | −2.73690e10 | −1.05890 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.20209e9 | 0.0461657 | ||||||||
\(947\) | 3.32150e10 | 1.27089 | 0.635447 | − | 0.772145i | \(-0.280816\pi\) | ||||
0.635447 | + | 0.772145i | \(0.280816\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.64810e10 | −0.625968 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.69223e10 | −0.635667 | ||||||||
\(953\) | 4.69895e10 | 1.75864 | 0.879318 | − | 0.476235i | \(-0.157999\pi\) | ||||
0.879318 | + | 0.476235i | \(0.157999\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.08950e10 | 0.403296 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.78843e10 | 0.657192 | ||||||||
\(959\) | 5.94668e10 | 2.17726 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.89877e9 | −0.105361 | ||||||||
\(962\) | −5.95429e9 | −0.215634 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.57570e10 | −0.926030 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.42294e10 | 0.506050 | 0.253025 | − | 0.967460i | \(-0.418575\pi\) | ||||
0.253025 | + | 0.967460i | \(0.418575\pi\) | |||||||
\(968\) | −1.63444e10 | −0.579168 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.45474e8 | −0.0191208 | −0.00956041 | − | 0.999954i | \(-0.503043\pi\) | ||||
−0.00956041 | + | 0.999954i | \(0.503043\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.79348e10 | 0.624167 | ||||||||
\(974\) | 1.37154e10 | 0.475612 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.89083e10 | 0.650995 | ||||||||
\(977\) | −1.97916e10 | −0.678968 | −0.339484 | − | 0.940612i | \(-0.610252\pi\) | ||||
−0.339484 | + | 0.940612i | \(0.610252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.45818e8 | 0.0117790 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.88975e10 | −2.32174 | ||||||||
\(983\) | −4.71503e10 | −1.58324 | −0.791620 | − | 0.611013i | \(-0.790762\pi\) | ||||
−0.791620 | + | 0.611013i | \(0.790762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.40007e10 | 0.465136 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.81226e9 | 0.224720 | ||||||||
\(989\) | 6.47573e9 | 0.212864 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.87968e10 | 1.26631 | 0.633153 | − | 0.774027i | \(-0.281761\pi\) | ||||
0.633153 | + | 0.774027i | \(0.281761\pi\) | |||||||
\(992\) | −2.80792e10 | −0.913258 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.17460e11 | 3.79347 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.66394e10 | 1.81003 | 0.905015 | − | 0.425380i | \(-0.139860\pi\) | ||||
0.905015 | + | 0.425380i | \(0.139860\pi\) | |||||||
\(998\) | 5.12101e10 | 1.63079 | ||||||||
\(999\) | 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 | 225.8.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 25.8.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 225.8.b.b.199.1 | 2 | |||
5.3 | odd | 4 | 225.8.b.b.199.2 | 2 | |||
5.4 | even | 2 | 45.8.a.f.1.1 | 1 | |||
12.11 | even | 2 | 400.8.a.e.1.1 | 1 | |||
15.2 | even | 4 | 25.8.b.a.24.2 | 2 | |||
15.8 | even | 4 | 25.8.b.a.24.1 | 2 | |||
15.14 | odd | 2 | 5.8.a.a.1.1 | ✓ | 1 | ||
60.23 | odd | 4 | 400.8.c.e.49.1 | 2 | |||
60.47 | odd | 4 | 400.8.c.e.49.2 | 2 | |||
60.59 | even | 2 | 80.8.a.d.1.1 | 1 | |||
105.104 | even | 2 | 245.8.a.a.1.1 | 1 | |||
120.29 | odd | 2 | 320.8.a.h.1.1 | 1 | |||
120.59 | even | 2 | 320.8.a.a.1.1 | 1 | |||
165.164 | even | 2 | 605.8.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.8.a.a.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
25.8.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
25.8.b.a.24.1 | 2 | 15.8 | even | 4 | |||
25.8.b.a.24.2 | 2 | 15.2 | even | 4 | |||
45.8.a.f.1.1 | 1 | 5.4 | even | 2 | |||
80.8.a.d.1.1 | 1 | 60.59 | even | 2 | |||
225.8.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.8.b.b.199.1 | 2 | 5.2 | odd | 4 | |||
225.8.b.b.199.2 | 2 | 5.3 | odd | 4 | |||
245.8.a.a.1.1 | 1 | 105.104 | even | 2 | |||
320.8.a.a.1.1 | 1 | 120.59 | even | 2 | |||
320.8.a.h.1.1 | 1 | 120.29 | odd | 2 | |||
400.8.a.e.1.1 | 1 | 12.11 | even | 2 | |||
400.8.c.e.49.1 | 2 | 60.23 | odd | 4 | |||
400.8.c.e.49.2 | 2 | 60.47 | odd | 4 | |||
605.8.a.c.1.1 | 1 | 165.164 | even | 2 |