Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,18,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.6577669876\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7 x^{15} + 4022 x^{14} - 1102776 x^{13} - 373411968 x^{12} + 2100004864 x^{11} - 3763915816960 x^{10} + \cdots + 12\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{120}\cdot 3^{14}\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.4 | ||
Root | \(-136.895 - 127.099i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.18.b.a.5.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −257.790 | + | 254.197i | −0.712052 | + | 0.702127i | ||||
\(3\) | 4834.14i | 0.425391i | 0.977119 | + | 0.212696i | \(0.0682243\pi\) | ||||
−0.977119 | + | 0.212696i | \(0.931776\pi\) | |||||||
\(4\) | 1839.67 | − | 131059.i | 0.0140356 | − | 0.999901i | ||||
\(5\) | 524871.i | 0.600908i | 0.953796 | + | 0.300454i | \(0.0971381\pi\) | ||||
−0.953796 | + | 0.300454i | \(0.902862\pi\) | |||||||
\(6\) | −1.22882e6 | − | 1.24619e6i | −0.298679 | − | 0.302901i | ||||
\(7\) | 1.57495e7 | 1.03260 | 0.516302 | − | 0.856407i | \(-0.327308\pi\) | ||||
0.516302 | + | 0.856407i | \(0.327308\pi\) | |||||||
\(8\) | 3.28406e7 | + | 3.42534e7i | 0.692064 | + | 0.721836i | ||||
\(9\) | 1.05771e8 | 0.819042 | ||||||||
\(10\) | −1.33421e8 | − | 1.35307e8i | −0.421913 | − | 0.427877i | ||||
\(11\) | − | 2.44791e8i | − | 0.344316i | −0.985069 | − | 0.172158i | \(-0.944926\pi\) | ||
0.985069 | − | 0.172158i | \(-0.0550740\pi\) | |||||||
\(12\) | 6.33558e8 | + | 8.89324e6i | 0.425349 | + | 0.00597062i | ||||
\(13\) | 2.66178e9i | 0.905009i | 0.891762 | + | 0.452504i | \(0.149469\pi\) | ||||
−0.891762 | + | 0.452504i | \(0.850531\pi\) | |||||||
\(14\) | −4.06007e9 | + | 4.00348e9i | −0.735268 | + | 0.725019i | ||||
\(15\) | −2.53730e9 | −0.255621 | ||||||||
\(16\) | −1.71731e10 | − | 4.82212e8i | −0.999606 | − | 0.0280684i | ||||
\(17\) | −2.82837e10 | −0.983379 | −0.491689 | − | 0.870771i | \(-0.663620\pi\) | ||||
−0.491689 | + | 0.870771i | \(0.663620\pi\) | |||||||
\(18\) | −2.72668e10 | + | 2.68867e10i | −0.583201 | + | 0.575072i | ||||
\(19\) | 7.79642e10i | 1.05315i | 0.850129 | + | 0.526574i | \(0.176524\pi\) | ||||
−0.850129 | + | 0.526574i | \(0.823476\pi\) | |||||||
\(20\) | 6.87892e10 | + | 9.65592e8i | 0.600849 | + | 0.00843410i | ||||
\(21\) | 7.61353e10i | 0.439261i | ||||||||
\(22\) | 6.22252e10 | + | 6.31047e10i | 0.241754 | + | 0.245171i | ||||
\(23\) | −3.66576e11 | −0.976063 | −0.488031 | − | 0.872826i | \(-0.662285\pi\) | ||||
−0.488031 | + | 0.872826i | \(0.662285\pi\) | |||||||
\(24\) | −1.65586e11 | + | 1.58756e11i | −0.307063 | + | 0.294398i | ||||
\(25\) | 4.87450e11 | 0.638910 | ||||||||
\(26\) | −6.76615e11 | − | 6.86180e11i | −0.635431 | − | 0.644413i | ||||
\(27\) | 1.13559e12i | 0.773805i | ||||||||
\(28\) | 2.89740e10 | − | 2.06412e12i | 0.0144932 | − | 1.03250i | ||||
\(29\) | − | 2.78648e11i | − | 0.103436i | −0.998662 | − | 0.0517181i | \(-0.983530\pi\) | ||
0.998662 | − | 0.0517181i | \(-0.0164697\pi\) | |||||||
\(30\) | 6.54092e11 | − | 6.44975e11i | 0.182015 | − | 0.179478i | ||||
\(31\) | 3.68562e12 | 0.776133 | 0.388067 | − | 0.921631i | \(-0.373143\pi\) | ||||
0.388067 | + | 0.921631i | \(0.373143\pi\) | |||||||
\(32\) | 4.54964e12 | − | 4.24104e12i | 0.731479 | − | 0.681864i | ||||
\(33\) | 1.18335e12 | 0.146469 | ||||||||
\(34\) | 7.29127e12 | − | 7.18964e12i | 0.700216 | − | 0.690457i | ||||
\(35\) | 8.26647e12i | 0.620500i | ||||||||
\(36\) | 1.94585e11 | − | 1.38623e13i | 0.0114957 | − | 0.818962i | ||||
\(37\) | 3.50209e13i | 1.63913i | 0.572989 | + | 0.819563i | \(0.305784\pi\) | ||||
−0.572989 | + | 0.819563i | \(0.694216\pi\) | |||||||
\(38\) | −1.98183e13 | − | 2.00984e13i | −0.739444 | − | 0.749896i | ||||
\(39\) | −1.28674e13 | −0.384983 | ||||||||
\(40\) | −1.79786e13 | + | 1.72371e13i | −0.433757 | + | 0.415866i | ||||
\(41\) | −3.67533e13 | −0.718843 | −0.359422 | − | 0.933175i | \(-0.617026\pi\) | ||||
−0.359422 | + | 0.933175i | \(0.617026\pi\) | |||||||
\(42\) | −1.93534e13 | − | 1.96270e13i | −0.308417 | − | 0.312776i | ||||
\(43\) | 1.25028e14i | 1.63127i | 0.578565 | + | 0.815636i | \(0.303613\pi\) | ||||
−0.578565 | + | 0.815636i | \(0.696387\pi\) | |||||||
\(44\) | −3.20821e13 | − | 4.50335e11i | −0.344282 | − | 0.00483268i | ||||
\(45\) | 5.55163e13i | 0.492169i | ||||||||
\(46\) | 9.44998e13 | − | 9.31826e13i | 0.695007 | − | 0.685320i | ||||
\(47\) | 1.02087e14 | 0.625370 | 0.312685 | − | 0.949857i | \(-0.398772\pi\) | ||||
0.312685 | + | 0.949857i | \(0.398772\pi\) | |||||||
\(48\) | 2.33108e12 | − | 8.30172e13i | 0.0119401 | − | 0.425224i | ||||
\(49\) | 1.54166e13 | 0.0662709 | ||||||||
\(50\) | −1.25660e14 | + | 1.23908e14i | −0.454937 | + | 0.448596i | ||||
\(51\) | − | 1.36727e14i | − | 0.418321i | ||||||
\(52\) | 3.48850e14 | + | 4.89680e12i | 0.904920 | + | 0.0127023i | ||||
\(53\) | − | 4.67637e14i | − | 1.03173i | −0.856671 | − | 0.515863i | \(-0.827472\pi\) | ||
0.856671 | − | 0.515863i | \(-0.172528\pi\) | |||||||
\(54\) | −2.88665e14 | − | 2.92745e14i | −0.543309 | − | 0.550989i | ||||
\(55\) | 1.28484e14 | 0.206902 | ||||||||
\(56\) | 5.17223e14 | + | 5.39474e14i | 0.714628 | + | 0.745371i | ||||
\(57\) | −3.76890e14 | −0.448000 | ||||||||
\(58\) | 7.08315e13 | + | 7.18327e13i | 0.0726254 | + | 0.0736519i | ||||
\(59\) | − | 4.08479e13i | − | 0.0362183i | −0.999836 | − | 0.0181092i | \(-0.994235\pi\) | ||
0.999836 | − | 0.0181092i | \(-0.00576464\pi\) | |||||||
\(60\) | −4.66780e12 | + | 3.32536e14i | −0.00358779 | + | 0.255596i | ||||
\(61\) | − | 2.55846e15i | − | 1.70874i | −0.519669 | − | 0.854368i | \(-0.673945\pi\) | ||
0.519669 | − | 0.854368i | \(-0.326055\pi\) | |||||||
\(62\) | −9.50117e14 | + | 9.36874e14i | −0.552647 | + | 0.544944i | ||||
\(63\) | 1.66585e15 | 0.845746 | ||||||||
\(64\) | −9.47911e13 | + | 2.24980e15i | −0.0420957 | + | 0.999114i | ||||
\(65\) | −1.39709e15 | −0.543827 | ||||||||
\(66\) | −3.05057e14 | + | 3.00805e14i | −0.104294 | + | 0.102840i | ||||
\(67\) | 2.46686e15i | 0.742179i | 0.928597 | + | 0.371090i | \(0.121016\pi\) | ||||
−0.928597 | + | 0.371090i | \(0.878984\pi\) | |||||||
\(68\) | −5.20328e13 | + | 3.70684e15i | −0.0138023 | + | 0.983282i | ||||
\(69\) | − | 1.77208e15i | − | 0.415209i | ||||||
\(70\) | −2.10131e15 | − | 2.13101e15i | −0.435670 | − | 0.441828i | ||||
\(71\) | 1.09996e15 | 0.202153 | 0.101077 | − | 0.994879i | \(-0.467771\pi\) | ||||
0.101077 | + | 0.994879i | \(0.467771\pi\) | |||||||
\(72\) | 3.47359e15 | + | 3.62303e15i | 0.566829 | + | 0.591215i | ||||
\(73\) | −1.21919e16 | −1.76941 | −0.884703 | − | 0.466154i | \(-0.845639\pi\) | ||||
−0.884703 | + | 0.466154i | \(0.845639\pi\) | |||||||
\(74\) | −8.90221e15 | − | 9.02805e15i | −1.15087 | − | 1.16714i | ||||
\(75\) | 2.35640e15i | 0.271787i | ||||||||
\(76\) | 1.02179e16 | + | 1.43429e14i | 1.05304 | + | 0.0147816i | ||||
\(77\) | − | 3.85534e15i | − | 0.355542i | ||||||
\(78\) | 3.31709e15 | − | 3.27085e15i | 0.274128 | − | 0.270307i | ||||
\(79\) | 2.49946e16 | 1.85360 | 0.926801 | − | 0.375554i | \(-0.122547\pi\) | ||||
0.926801 | + | 0.375554i | \(0.122547\pi\) | |||||||
\(80\) | 2.53099e14 | − | 9.01367e15i | 0.0168665 | − | 0.600671i | ||||
\(81\) | 8.16969e15 | 0.489873 | ||||||||
\(82\) | 9.47466e15 | − | 9.34259e15i | 0.511854 | − | 0.504719i | ||||
\(83\) | 3.68875e16i | 1.79769i | 0.438262 | + | 0.898847i | \(0.355594\pi\) | ||||
−0.438262 | + | 0.898847i | \(0.644406\pi\) | |||||||
\(84\) | 9.97823e15 | + | 1.40064e14i | 0.439217 | + | 0.00616528i | ||||
\(85\) | − | 1.48453e16i | − | 0.590920i | ||||||
\(86\) | −3.17818e16 | − | 3.22311e16i | −1.14536 | − | 1.16155i | ||||
\(87\) | 1.34702e15 | 0.0440009 | ||||||||
\(88\) | 8.38492e15 | − | 8.03908e15i | 0.248540 | − | 0.238289i | ||||
\(89\) | −4.15487e16 | −1.11877 | −0.559387 | − | 0.828907i | \(-0.688963\pi\) | ||||
−0.559387 | + | 0.828907i | \(0.688963\pi\) | |||||||
\(90\) | −1.41121e16 | − | 1.43116e16i | −0.345565 | − | 0.350450i | ||||
\(91\) | 4.19217e16i | 0.934516i | ||||||||
\(92\) | −6.74381e14 | + | 4.80432e16i | −0.0136996 | + | 0.975967i | ||||
\(93\) | 1.78168e16i | 0.330160i | ||||||||
\(94\) | −2.63170e16 | + | 2.59501e16i | −0.445296 | + | 0.439089i | ||||
\(95\) | −4.09212e16 | −0.632845 | ||||||||
\(96\) | 2.05018e16 | + | 2.19936e16i | 0.290059 | + | 0.311165i | ||||
\(97\) | 7.13708e15 | 0.0924614 | 0.0462307 | − | 0.998931i | \(-0.485279\pi\) | ||||
0.0462307 | + | 0.998931i | \(0.485279\pi\) | |||||||
\(98\) | −3.97426e15 | + | 3.91886e15i | −0.0471883 | + | 0.0465305i | ||||
\(99\) | − | 2.58919e16i | − | 0.282010i | ||||||
\(100\) | 8.96748e14 | − | 6.38847e16i | 0.00896748 | − | 0.638847i | ||||
\(101\) | − | 2.76571e16i | − | 0.254141i | −0.991894 | − | 0.127070i | \(-0.959443\pi\) | ||
0.991894 | − | 0.127070i | \(-0.0405574\pi\) | |||||||
\(102\) | 3.47557e16 | + | 3.52470e16i | 0.293714 | + | 0.297866i | ||||
\(103\) | 1.40681e17 | 1.09426 | 0.547128 | − | 0.837049i | \(-0.315721\pi\) | ||||
0.547128 | + | 0.837049i | \(0.315721\pi\) | |||||||
\(104\) | −9.11748e16 | + | 8.74143e16i | −0.653268 | + | 0.626324i | ||||
\(105\) | −3.99613e16 | −0.263955 | ||||||||
\(106\) | 1.18872e17 | + | 1.20552e17i | 0.724402 | + | 0.734642i | ||||
\(107\) | − | 2.87686e17i | − | 1.61867i | −0.587350 | − | 0.809333i | \(-0.699829\pi\) | ||
0.587350 | − | 0.809333i | \(-0.300171\pi\) | |||||||
\(108\) | 1.48830e17 | + | 2.08912e15i | 0.773728 | + | 0.0108608i | ||||
\(109\) | − | 1.61873e17i | − | 0.778127i | −0.921211 | − | 0.389063i | \(-0.872799\pi\) | ||
0.921211 | − | 0.389063i | \(-0.127201\pi\) | |||||||
\(110\) | −3.31219e16 | + | 3.26602e16i | −0.147325 | + | 0.145272i | ||||
\(111\) | −1.69296e17 | −0.697270 | ||||||||
\(112\) | −2.70468e17 | − | 7.59460e15i | −1.03220 | − | 0.0289836i | ||||
\(113\) | 3.01267e17 | 1.06607 | 0.533033 | − | 0.846094i | \(-0.321052\pi\) | ||||
0.533033 | + | 0.846094i | \(0.321052\pi\) | |||||||
\(114\) | 9.71585e16 | − | 9.58043e16i | 0.318999 | − | 0.314553i | ||||
\(115\) | − | 1.92405e17i | − | 0.586524i | ||||||
\(116\) | −3.65193e16 | − | 5.12621e14i | −0.103426 | − | 0.00145179i | ||||
\(117\) | 2.81539e17i | 0.741241i | ||||||||
\(118\) | 1.03834e16 | + | 1.05302e16i | 0.0254298 | + | 0.0257893i | ||||
\(119\) | −4.45455e17 | −1.01544 | ||||||||
\(120\) | −8.33265e16 | − | 8.69112e16i | −0.176906 | − | 0.184516i | ||||
\(121\) | 4.45524e17 | 0.881446 | ||||||||
\(122\) | 6.50353e17 | + | 6.59546e17i | 1.19975 | + | 1.21671i | ||||
\(123\) | − | 1.77671e17i | − | 0.305790i | ||||||
\(124\) | 6.78034e15 | − | 4.83034e17i | 0.0108935 | − | 0.776057i | ||||
\(125\) | 6.56293e17i | 0.984834i | ||||||||
\(126\) | −4.29439e17 | + | 4.23453e17i | −0.602215 | + | 0.593821i | ||||
\(127\) | −3.10547e17 | −0.407189 | −0.203595 | − | 0.979055i | \(-0.565262\pi\) | ||||
−0.203595 | + | 0.979055i | \(0.565262\pi\) | |||||||
\(128\) | −5.47457e17 | − | 6.04073e17i | −0.671530 | − | 0.740977i | ||||
\(129\) | −6.04404e17 | −0.693929 | ||||||||
\(130\) | 3.60156e17 | − | 3.55136e17i | 0.387233 | − | 0.381835i | ||||
\(131\) | 1.23335e18i | 1.24246i | 0.783629 | + | 0.621229i | \(0.213366\pi\) | ||||
−0.783629 | + | 0.621229i | \(0.786634\pi\) | |||||||
\(132\) | 2.17698e15 | − | 1.55089e17i | 0.00205578 | − | 0.146455i | ||||
\(133\) | 1.22790e18i | 1.08749i | ||||||||
\(134\) | −6.27069e17 | − | 6.35933e17i | −0.521104 | − | 0.528470i | ||||
\(135\) | −5.96041e17 | −0.464985 | ||||||||
\(136\) | −9.28854e17 | − | 9.68814e17i | −0.680561 | − | 0.709838i | ||||
\(137\) | 1.77025e18 | 1.21873 | 0.609367 | − | 0.792888i | \(-0.291424\pi\) | ||||
0.609367 | + | 0.792888i | \(0.291424\pi\) | |||||||
\(138\) | 4.50458e17 | + | 4.56825e17i | 0.291529 | + | 0.295650i | ||||
\(139\) | − | 1.75424e18i | − | 1.06773i | −0.845569 | − | 0.533866i | \(-0.820739\pi\) | ||
0.845569 | − | 0.533866i | \(-0.179261\pi\) | |||||||
\(140\) | 1.08340e18 | + | 1.52076e16i | 0.620439 | + | 0.00870908i | ||||
\(141\) | 4.93501e17i | 0.266027i | ||||||||
\(142\) | −2.83559e17 | + | 2.79606e17i | −0.143944 | + | 0.141937i | ||||
\(143\) | 6.51579e17 | 0.311609 | ||||||||
\(144\) | −1.81642e18 | − | 5.10041e16i | −0.818720 | − | 0.0229892i | ||||
\(145\) | 1.46254e17 | 0.0621556 | ||||||||
\(146\) | 3.14296e18 | − | 3.09915e18i | 1.25991 | − | 1.24235i | ||||
\(147\) | 7.45261e16i | 0.0281910i | ||||||||
\(148\) | 4.58981e18 | + | 6.44270e16i | 1.63897 | + | 0.0230061i | ||||
\(149\) | − | 2.24173e18i | − | 0.755962i | −0.925813 | − | 0.377981i | \(-0.876618\pi\) | ||
0.925813 | − | 0.377981i | \(-0.123382\pi\) | |||||||
\(150\) | −5.98990e17 | − | 6.07457e17i | −0.190829 | − | 0.193526i | ||||
\(151\) | 1.48795e18 | 0.448006 | 0.224003 | − | 0.974589i | \(-0.428088\pi\) | ||||
0.224003 | + | 0.974589i | \(0.428088\pi\) | |||||||
\(152\) | −2.67054e18 | + | 2.56039e18i | −0.760201 | + | 0.728846i | ||||
\(153\) | −2.99160e18 | −0.805429 | ||||||||
\(154\) | 9.80016e17 | + | 9.93869e17i | 0.249636 | + | 0.253165i | ||||
\(155\) | 1.93448e18i | 0.466384i | ||||||||
\(156\) | −2.36718e16 | + | 1.68639e18i | −0.00540346 | + | 0.384945i | ||||
\(157\) | − | 5.36324e18i | − | 1.15953i | −0.814785 | − | 0.579763i | \(-0.803145\pi\) | ||
0.814785 | − | 0.579763i | \(-0.196855\pi\) | |||||||
\(158\) | −6.44337e18 | + | 6.35356e18i | −1.31986 | + | 1.30146i | ||||
\(159\) | 2.26062e18 | 0.438887 | ||||||||
\(160\) | 2.22600e18 | + | 2.38797e18i | 0.409737 | + | 0.439551i | ||||
\(161\) | −5.77340e18 | −1.00789 | ||||||||
\(162\) | −2.10607e18 | + | 2.07671e18i | −0.348815 | + | 0.343953i | ||||
\(163\) | − | 2.95894e18i | − | 0.465095i | −0.972585 | − | 0.232547i | \(-0.925294\pi\) | ||
0.972585 | − | 0.232547i | \(-0.0747061\pi\) | |||||||
\(164\) | −6.76141e16 | + | 4.81686e18i | −0.0100894 | + | 0.718772i | ||||
\(165\) | 6.21108e17i | 0.0880144i | ||||||||
\(166\) | −9.37670e18 | − | 9.50925e18i | −1.26221 | − | 1.28005i | ||||
\(167\) | −1.14232e18 | −0.146116 | −0.0730579 | − | 0.997328i | \(-0.523276\pi\) | ||||
−0.0730579 | + | 0.997328i | \(0.523276\pi\) | |||||||
\(168\) | −2.60789e18 | + | 2.50033e18i | −0.317074 | + | 0.303996i | ||||
\(169\) | 1.56537e18 | 0.180959 | ||||||||
\(170\) | 3.77364e18 | + | 3.82698e18i | 0.414901 | + | 0.420765i | ||||
\(171\) | 8.24637e18i | 0.862573i | ||||||||
\(172\) | 1.63861e19 | + | 2.30011e17i | 1.63111 | + | 0.0228959i | ||||
\(173\) | − | 1.13255e19i | − | 1.07316i | −0.843849 | − | 0.536581i | \(-0.819716\pi\) | ||
0.843849 | − | 0.536581i | \(-0.180284\pi\) | |||||||
\(174\) | −3.47249e17 | + | 3.42409e17i | −0.0313309 | + | 0.0308942i | ||||
\(175\) | 7.67709e18 | 0.659741 | ||||||||
\(176\) | −1.18041e17 | + | 4.20382e18i | −0.00966442 | + | 0.344181i | ||||
\(177\) | 1.97465e17 | 0.0154069 | ||||||||
\(178\) | 1.07108e19 | − | 1.05616e19i | 0.796625 | − | 0.785521i | ||||
\(179\) | 8.80447e18i | 0.624385i | 0.950019 | + | 0.312192i | \(0.101063\pi\) | ||||
−0.950019 | + | 0.312192i | \(0.898937\pi\) | |||||||
\(180\) | 7.27592e18 | + | 1.02132e17i | 0.492120 | + | 0.00690788i | ||||
\(181\) | − | 6.64994e18i | − | 0.429092i | −0.976714 | − | 0.214546i | \(-0.931173\pi\) | ||
0.976714 | − | 0.214546i | \(-0.0688271\pi\) | |||||||
\(182\) | −1.06564e19 | − | 1.08070e19i | −0.656149 | − | 0.665424i | ||||
\(183\) | 1.23679e19 | 0.726881 | ||||||||
\(184\) | −1.20386e19 | − | 1.25565e19i | −0.675498 | − | 0.704558i | ||||
\(185\) | −1.83815e19 | −0.984964 | ||||||||
\(186\) | −4.52898e18 | − | 4.59300e18i | −0.231814 | − | 0.235091i | ||||
\(187\) | 6.92360e18i | 0.338593i | ||||||||
\(188\) | 1.87806e17 | − | 1.33794e19i | 0.00877744 | − | 0.625309i | ||||
\(189\) | 1.78851e19i | 0.799034i | ||||||||
\(190\) | 1.05491e19 | − | 1.04020e19i | 0.450618 | − | 0.444337i | ||||
\(191\) | −1.48372e19 | −0.606135 | −0.303068 | − | 0.952969i | \(-0.598011\pi\) | ||||
−0.303068 | + | 0.952969i | \(0.598011\pi\) | |||||||
\(192\) | −1.08759e19 | − | 4.58234e17i | −0.425014 | − | 0.0179071i | ||||
\(193\) | 2.59123e19 | 0.968878 | 0.484439 | − | 0.874825i | \(-0.339024\pi\) | ||||
0.484439 | + | 0.874825i | \(0.339024\pi\) | |||||||
\(194\) | −1.83987e18 | + | 1.81422e18i | −0.0658373 | + | 0.0649197i | ||||
\(195\) | − | 6.75372e18i | − | 0.231339i | ||||||
\(196\) | 2.83615e16 | − | 2.02049e18i | 0.000930151 | − | 0.0662643i | ||||
\(197\) | 5.49419e19i | 1.72560i | 0.505543 | + | 0.862801i | \(0.331292\pi\) | ||||
−0.505543 | + | 0.862801i | \(0.668708\pi\) | |||||||
\(198\) | 6.58163e18 | + | 6.67467e18i | 0.198007 | + | 0.200805i | ||||
\(199\) | 7.58694e18 | 0.218683 | 0.109342 | − | 0.994004i | \(-0.465126\pi\) | ||||
0.109342 | + | 0.994004i | \(0.465126\pi\) | |||||||
\(200\) | 1.60081e19 | + | 1.66968e19i | 0.442166 | + | 0.461188i | ||||
\(201\) | −1.19251e19 | −0.315717 | ||||||||
\(202\) | 7.03035e18 | + | 7.12973e18i | 0.178439 | + | 0.180962i | ||||
\(203\) | − | 4.38857e18i | − | 0.106809i | ||||||
\(204\) | −1.79194e19 | − | 2.51534e17i | −0.418279 | − | 0.00587138i | ||||
\(205\) | − | 1.92908e19i | − | 0.431958i | ||||||
\(206\) | −3.62662e19 | + | 3.57607e19i | −0.779167 | + | 0.768307i | ||||
\(207\) | −3.87732e19 | −0.799437 | ||||||||
\(208\) | 1.28354e18 | − | 4.57109e19i | 0.0254022 | − | 0.904652i | ||||
\(209\) | 1.90849e19 | 0.362616 | ||||||||
\(210\) | 1.03016e19 | − | 1.01580e19i | 0.187950 | − | 0.185330i | ||||
\(211\) | − | 2.70658e19i | − | 0.474264i | −0.971477 | − | 0.237132i | \(-0.923793\pi\) | ||
0.971477 | − | 0.237132i | \(-0.0762074\pi\) | |||||||
\(212\) | −6.12881e19 | − | 8.60299e17i | −1.03162 | − | 0.0144809i | ||||
\(213\) | 5.31736e18i | 0.0859942i | ||||||||
\(214\) | 7.31290e19 | + | 7.41627e19i | 1.13651 | + | 1.15257i | ||||
\(215\) | −6.56238e19 | −0.980244 | ||||||||
\(216\) | −3.88980e19 | + | 3.72936e19i | −0.558560 | + | 0.535522i | ||||
\(217\) | 5.80467e19 | 0.801438 | ||||||||
\(218\) | 4.11477e19 | + | 4.17294e19i | 0.546344 | + | 0.554066i | ||||
\(219\) | − | 5.89374e19i | − | 0.752690i | ||||||
\(220\) | 2.36368e17 | − | 1.68390e19i | 0.00290400 | − | 0.206882i | ||||
\(221\) | − | 7.52849e19i | − | 0.889966i | ||||||
\(222\) | 4.36428e19 | − | 4.30345e19i | 0.496492 | − | 0.489572i | ||||
\(223\) | −6.99062e18 | −0.0765463 | −0.0382732 | − | 0.999267i | \(-0.512186\pi\) | ||||
−0.0382732 | + | 0.999267i | \(0.512186\pi\) | |||||||
\(224\) | 7.16545e19 | − | 6.67944e19i | 0.755328 | − | 0.704096i | ||||
\(225\) | 5.15582e19 | 0.523294 | ||||||||
\(226\) | −7.76636e19 | + | 7.65811e19i | −0.759094 | + | 0.748514i | ||||
\(227\) | − | 1.78757e20i | − | 1.68285i | −0.540377 | − | 0.841423i | \(-0.681719\pi\) | ||
0.540377 | − | 0.841423i | \(-0.318281\pi\) | |||||||
\(228\) | −6.93354e17 | + | 4.93948e19i | −0.00628795 | + | 0.447956i | ||||
\(229\) | 2.48507e19i | 0.217139i | 0.994089 | + | 0.108569i | \(0.0346269\pi\) | ||||
−0.994089 | + | 0.108569i | \(0.965373\pi\) | |||||||
\(230\) | 4.89089e19 | + | 4.96002e19i | 0.411814 | + | 0.417635i | ||||
\(231\) | 1.86372e19 | 0.151245 | ||||||||
\(232\) | 9.54463e18 | − | 9.15096e18i | 0.0746640 | − | 0.0715844i | ||||
\(233\) | 1.18068e20 | 0.890446 | 0.445223 | − | 0.895420i | \(-0.353124\pi\) | ||||
0.445223 | + | 0.895420i | \(0.353124\pi\) | |||||||
\(234\) | −7.15665e19 | − | 7.25781e19i | −0.520445 | − | 0.527802i | ||||
\(235\) | 5.35824e19i | 0.375790i | ||||||||
\(236\) | −5.35349e18 | − | 7.51469e16i | −0.0362147 | − | 0.000508345i | ||||
\(237\) | 1.20827e20i | 0.788506i | ||||||||
\(238\) | 1.14834e20 | − | 1.13233e20i | 0.723046 | − | 0.712968i | ||||
\(239\) | 1.23287e20 | 0.749092 | 0.374546 | − | 0.927208i | \(-0.377799\pi\) | ||||
0.374546 | + | 0.927208i | \(0.377799\pi\) | |||||||
\(240\) | 4.35733e19 | + | 1.22352e18i | 0.255520 | + | 0.00717487i | ||||
\(241\) | −2.67815e20 | −1.51597 | −0.757983 | − | 0.652275i | \(-0.773815\pi\) | ||||
−0.757983 | + | 0.652275i | \(0.773815\pi\) | |||||||
\(242\) | −1.14852e20 | + | 1.13251e20i | −0.627635 | + | 0.618887i | ||||
\(243\) | 1.86144e20i | 0.982192i | ||||||||
\(244\) | −3.35309e20 | − | 4.70673e18i | −1.70857 | − | 0.0239831i | ||||
\(245\) | 8.09174e18i | 0.0398227i | ||||||||
\(246\) | 4.51634e19 | + | 4.58018e19i | 0.214703 | + | 0.217738i | ||||
\(247\) | −2.07523e20 | −0.953109 | ||||||||
\(248\) | 1.21038e20 | + | 1.26245e20i | 0.537134 | + | 0.560241i | ||||
\(249\) | −1.78319e20 | −0.764723 | ||||||||
\(250\) | −1.66828e20 | − | 1.69186e20i | −0.691478 | − | 0.701253i | ||||
\(251\) | 1.11530e20i | 0.446854i | 0.974721 | + | 0.223427i | \(0.0717244\pi\) | ||||
−0.974721 | + | 0.223427i | \(0.928276\pi\) | |||||||
\(252\) | 3.06461e18 | − | 2.18324e20i | 0.0118706 | − | 0.845663i | ||||
\(253\) | 8.97346e19i | 0.336074i | ||||||||
\(254\) | 8.00561e19 | − | 7.89402e19i | 0.289940 | − | 0.285898i | ||||
\(255\) | 7.17643e19 | 0.251372 | ||||||||
\(256\) | 2.94683e20 | + | 1.65621e19i | 0.998424 | + | 0.0561147i | ||||
\(257\) | 2.70681e19 | 0.0887209 | 0.0443604 | − | 0.999016i | \(-0.485875\pi\) | ||||
0.0443604 | + | 0.999016i | \(0.485875\pi\) | |||||||
\(258\) | 1.55810e20 | − | 1.53638e20i | 0.494113 | − | 0.487226i | ||||
\(259\) | 5.51562e20i | 1.69257i | ||||||||
\(260\) | −2.57019e18 | + | 1.83101e20i | −0.00763293 | + | 0.543773i | ||||
\(261\) | − | 2.94729e19i | − | 0.0847186i | ||||||
\(262\) | −3.13515e20 | − | 3.17946e20i | −0.872363 | − | 0.884694i | ||||
\(263\) | 5.28511e20 | 1.42374 | 0.711869 | − | 0.702312i | \(-0.247849\pi\) | ||||
0.711869 | + | 0.702312i | \(0.247849\pi\) | |||||||
\(264\) | 3.88620e19 | + | 4.05339e19i | 0.101366 | + | 0.105727i | ||||
\(265\) | 2.45449e20 | 0.619972 | ||||||||
\(266\) | −3.12128e20 | − | 3.16540e20i | −0.763553 | − | 0.774346i | ||||
\(267\) | − | 2.00852e20i | − | 0.475916i | ||||||
\(268\) | 3.23305e20 | + | 4.53822e18i | 0.742106 | + | 0.0104169i | ||||
\(269\) | − | 7.69627e20i | − | 1.71153i | −0.517361 | − | 0.855767i | \(-0.673085\pi\) | ||
0.517361 | − | 0.855767i | \(-0.326915\pi\) | |||||||
\(270\) | 1.53654e20 | − | 1.51512e20i | 0.331094 | − | 0.326479i | ||||
\(271\) | −1.28273e18 | −0.00267853 | −0.00133927 | − | 0.999999i | \(-0.500426\pi\) | ||||
−0.00133927 | + | 0.999999i | \(0.500426\pi\) | |||||||
\(272\) | 4.85719e20 | + | 1.36387e19i | 0.982991 | + | 0.0276019i | ||||
\(273\) | −2.02655e20 | −0.397535 | ||||||||
\(274\) | −4.56352e20 | + | 4.49992e20i | −0.867802 | + | 0.855706i | ||||
\(275\) | − | 1.19323e20i | − | 0.219987i | ||||||
\(276\) | −2.32247e20 | − | 3.26005e18i | −0.415168 | − | 0.00582770i | ||||
\(277\) | 7.28964e19i | 0.126365i | 0.998002 | + | 0.0631827i | \(0.0201251\pi\) | ||||
−0.998002 | + | 0.0631827i | \(0.979875\pi\) | |||||||
\(278\) | 4.45922e20 | + | 4.52225e20i | 0.749684 | + | 0.760281i | ||||
\(279\) | 3.89833e20 | 0.635686 | ||||||||
\(280\) | −2.83155e20 | + | 2.71476e20i | −0.447899 | + | 0.429425i | ||||
\(281\) | −7.35344e20 | −1.12846 | −0.564231 | − | 0.825617i | \(-0.690827\pi\) | ||||
−0.564231 | + | 0.825617i | \(0.690827\pi\) | |||||||
\(282\) | −1.25447e20 | − | 1.27220e20i | −0.186785 | − | 0.189425i | ||||
\(283\) | 2.65211e19i | 0.0383184i | 0.999816 | + | 0.0191592i | \(0.00609894\pi\) | ||||
−0.999816 | + | 0.0191592i | \(0.993901\pi\) | |||||||
\(284\) | 2.02357e18 | − | 1.44160e20i | 0.00283734 | − | 0.202133i | ||||
\(285\) | − | 1.97819e20i | − | 0.269207i | ||||||
\(286\) | −1.67971e20 | + | 1.65629e20i | −0.221882 | + | 0.218789i | ||||
\(287\) | −5.78847e20 | −0.742280 | ||||||||
\(288\) | 4.81221e20 | − | 4.48580e20i | 0.599112 | − | 0.558476i | ||||
\(289\) | −2.72714e19 | −0.0329667 | ||||||||
\(290\) | −3.77029e19 | + | 3.71774e19i | −0.0442580 | + | 0.0436411i | ||||
\(291\) | 3.45016e19i | 0.0393323i | ||||||||
\(292\) | −2.24291e19 | + | 1.59786e21i | −0.0248347 | + | 1.76923i | ||||
\(293\) | − | 1.14055e21i | − | 1.22671i | −0.789809 | − | 0.613353i | \(-0.789820\pi\) | ||
0.789809 | − | 0.613353i | \(-0.210180\pi\) | |||||||
\(294\) | −1.89443e19 | − | 1.92121e19i | −0.0197937 | − | 0.0200735i | ||||
\(295\) | 2.14399e19 | 0.0217639 | ||||||||
\(296\) | −1.19958e21 | + | 1.15011e21i | −1.18318 | + | 1.13438i | ||||
\(297\) | 2.77983e20 | 0.266434 | ||||||||
\(298\) | 5.69841e20 | + | 5.77896e20i | 0.530781 | + | 0.538284i | ||||
\(299\) | − | 9.75744e20i | − | 0.883346i | ||||||
\(300\) | 3.08828e20 | + | 4.33500e18i | 0.271760 | + | 0.00381469i | ||||
\(301\) | 1.96914e21i | 1.68446i | ||||||||
\(302\) | −3.83578e20 | + | 3.78232e20i | −0.319003 | + | 0.314557i | ||||
\(303\) | 1.33698e20 | 0.108109 | ||||||||
\(304\) | 3.75952e19 | − | 1.33889e21i | 0.0295602 | − | 1.05273i | ||||
\(305\) | 1.34286e21 | 1.02679 | ||||||||
\(306\) | 7.71207e20 | − | 7.60457e20i | 0.573507 | − | 0.565513i | ||||
\(307\) | − | 4.88182e20i | − | 0.353107i | −0.984291 | − | 0.176553i | \(-0.943505\pi\) | ||
0.984291 | − | 0.176553i | \(-0.0564948\pi\) | |||||||
\(308\) | −5.05277e20 | − | 7.09256e18i | −0.355507 | − | 0.00499025i | ||||
\(309\) | 6.80072e20i | 0.465487i | ||||||||
\(310\) | −4.91738e20 | − | 4.98689e20i | −0.327461 | − | 0.332090i | ||||
\(311\) | −1.56774e21 | −1.01581 | −0.507904 | − | 0.861414i | \(-0.669580\pi\) | ||||
−0.507904 | + | 0.861414i | \(0.669580\pi\) | |||||||
\(312\) | −4.22573e20 | − | 4.40752e20i | −0.266433 | − | 0.277895i | ||||
\(313\) | −6.34156e20 | −0.389107 | −0.194554 | − | 0.980892i | \(-0.562326\pi\) | ||||
−0.194554 | + | 0.980892i | \(0.562326\pi\) | |||||||
\(314\) | 1.36332e21 | + | 1.38259e21i | 0.814135 | + | 0.825643i | ||||
\(315\) | 8.74355e20i | 0.508215i | ||||||||
\(316\) | 4.59819e19 | − | 3.27577e21i | 0.0260164 | − | 1.85342i | ||||
\(317\) | − | 2.83832e20i | − | 0.156335i | −0.996940 | − | 0.0781677i | \(-0.975093\pi\) | ||
0.996940 | − | 0.0781677i | \(-0.0249070\pi\) | |||||||
\(318\) | −5.82767e20 | + | 5.74644e20i | −0.312510 | + | 0.308154i | ||||
\(319\) | −6.82105e19 | −0.0356148 | ||||||||
\(320\) | −1.18086e21 | − | 4.97531e19i | −0.600375 | − | 0.0252956i | ||||
\(321\) | 1.39072e21 | 0.688566 | ||||||||
\(322\) | 1.48833e21 | − | 1.46758e21i | 0.717667 | − | 0.707664i | ||||
\(323\) | − | 2.20512e21i | − | 1.03564i | ||||||
\(324\) | 1.50296e19 | − | 1.07071e21i | 0.00687565 | − | 0.489824i | ||||
\(325\) | 1.29748e21i | 0.578219i | ||||||||
\(326\) | 7.52154e20 | + | 7.62786e20i | 0.326556 | + | 0.331172i | ||||
\(327\) | 7.82519e20 | 0.331008 | ||||||||
\(328\) | −1.20700e21 | − | 1.25893e21i | −0.497485 | − | 0.518887i | ||||
\(329\) | 1.60782e21 | 0.645760 | ||||||||
\(330\) | −1.57884e20 | − | 1.60116e20i | −0.0617973 | − | 0.0626708i | ||||
\(331\) | 2.11311e21i | 0.806089i | 0.915180 | + | 0.403045i | \(0.132048\pi\) | ||||
−0.915180 | + | 0.403045i | \(0.867952\pi\) | |||||||
\(332\) | 4.83445e21 | + | 6.78610e19i | 1.79752 | + | 0.0252317i | ||||
\(333\) | 3.70420e21i | 1.34251i | ||||||||
\(334\) | 2.94478e20 | − | 2.90374e20i | 0.104042 | − | 0.102592i | ||||
\(335\) | −1.29478e21 | −0.445981 | ||||||||
\(336\) | 3.67134e19 | − | 1.30748e21i | 0.0123294 | − | 0.439088i | ||||
\(337\) | 4.08155e20 | 0.133651 | 0.0668253 | − | 0.997765i | \(-0.478713\pi\) | ||||
0.0668253 | + | 0.997765i | \(0.478713\pi\) | |||||||
\(338\) | −4.03537e20 | + | 3.97912e20i | −0.128852 | + | 0.127056i | ||||
\(339\) | 1.45636e21i | 0.453495i | ||||||||
\(340\) | −1.94561e21 | − | 2.73105e19i | −0.590862 | − | 0.00829391i | ||||
\(341\) | − | 9.02207e20i | − | 0.267235i | ||||||
\(342\) | −2.09620e21 | − | 2.12583e21i | −0.605636 | − | 0.614197i | ||||
\(343\) | −3.42101e21 | −0.964172 | ||||||||
\(344\) | −4.28265e21 | + | 4.10600e21i | −1.17751 | + | 1.12894i | ||||
\(345\) | 9.30115e20 | 0.249502 | ||||||||
\(346\) | 2.87891e21 | + | 2.91960e21i | 0.753495 | + | 0.764146i | ||||
\(347\) | − | 3.05313e21i | − | 0.779732i | −0.920872 | − | 0.389866i | \(-0.872521\pi\) | ||
0.920872 | − | 0.389866i | \(-0.127479\pi\) | |||||||
\(348\) | 2.47808e18 | − | 1.76540e20i | 0.000617578 | − | 0.0439965i | ||||
\(349\) | − | 8.48728e20i | − | 0.206420i | −0.994660 | − | 0.103210i | \(-0.967089\pi\) | ||
0.994660 | − | 0.103210i | \(-0.0329114\pi\) | |||||||
\(350\) | −1.97908e21 | + | 1.95149e21i | −0.469770 | + | 0.463222i | ||||
\(351\) | −3.02270e21 | −0.700300 | ||||||||
\(352\) | −1.03817e21 | − | 1.11371e21i | −0.234777 | − | 0.251860i | ||||
\(353\) | −5.04249e21 | −1.11317 | −0.556583 | − | 0.830792i | \(-0.687888\pi\) | ||||
−0.556583 | + | 0.830792i | \(0.687888\pi\) | |||||||
\(354\) | −5.09045e19 | + | 5.01949e19i | −0.0109705 | + | 0.0108176i | ||||
\(355\) | 5.77337e20i | 0.121475i | ||||||||
\(356\) | −7.64360e19 | + | 5.44533e21i | −0.0157026 | + | 1.11866i | ||||
\(357\) | − | 2.15339e21i | − | 0.431959i | ||||||
\(358\) | −2.23807e21 | − | 2.26971e21i | −0.438397 | − | 0.444594i | ||||
\(359\) | 9.63686e21 | 1.84346 | 0.921728 | − | 0.387837i | \(-0.126778\pi\) | ||||
0.921728 | + | 0.387837i | \(0.126778\pi\) | |||||||
\(360\) | −1.90162e21 | + | 1.82319e21i | −0.355265 | + | 0.340612i | ||||
\(361\) | −5.98028e20 | −0.109121 | ||||||||
\(362\) | 1.69040e21 | + | 1.71429e21i | 0.301277 | + | 0.305536i | ||||
\(363\) | 2.15373e21i | 0.374959i | ||||||||
\(364\) | 5.49421e21 | + | 7.71222e19i | 0.934424 | + | 0.0131165i | ||||
\(365\) | − | 6.39919e21i | − | 1.06325i | ||||||
\(366\) | −3.18834e21 | + | 3.14390e21i | −0.517577 | + | 0.510363i | ||||
\(367\) | 8.52037e21 | 1.35144 | 0.675720 | − | 0.737158i | \(-0.263833\pi\) | ||||
0.675720 | + | 0.737158i | \(0.263833\pi\) | |||||||
\(368\) | 6.29525e21 | + | 1.76767e20i | 0.975678 | + | 0.0273965i | ||||
\(369\) | −3.88745e21 | −0.588763 | ||||||||
\(370\) | 4.73856e21 | − | 4.67251e21i | 0.701345 | − | 0.691570i | ||||
\(371\) | − | 7.36506e21i | − | 1.06536i | ||||||
\(372\) | 2.33505e21 | + | 3.27771e19i | 0.330128 | + | 0.00463399i | ||||
\(373\) | − | 5.97419e21i | − | 0.825569i | −0.910829 | − | 0.412785i | \(-0.864556\pi\) | ||
0.910829 | − | 0.412785i | \(-0.135444\pi\) | |||||||
\(374\) | −1.75996e21 | − | 1.78484e21i | −0.237735 | − | 0.241096i | ||||
\(375\) | −3.17261e21 | −0.418940 | ||||||||
\(376\) | 3.35259e21 | + | 3.49682e21i | 0.432796 | + | 0.451415i | ||||
\(377\) | 7.41698e20 | 0.0936107 | ||||||||
\(378\) | −4.54633e21 | − | 4.61060e21i | −0.561023 | − | 0.568953i | ||||
\(379\) | − | 1.72231e21i | − | 0.207816i | −0.994587 | − | 0.103908i | \(-0.966865\pi\) | ||
0.994587 | − | 0.103908i | \(-0.0331347\pi\) | |||||||
\(380\) | −7.52816e19 | + | 5.36309e21i | −0.00888235 | + | 0.632783i | ||||
\(381\) | − | 1.50123e21i | − | 0.173215i | ||||||
\(382\) | 3.82490e21 | − | 3.77158e21i | 0.431600 | − | 0.425584i | ||||
\(383\) | −5.14304e21 | −0.567584 | −0.283792 | − | 0.958886i | \(-0.591592\pi\) | ||||
−0.283792 | + | 0.958886i | \(0.591592\pi\) | |||||||
\(384\) | 2.92017e21 | − | 2.64649e21i | 0.315205 | − | 0.285663i | ||||
\(385\) | 2.02356e21 | 0.213648 | ||||||||
\(386\) | −6.67995e21 | + | 6.58684e21i | −0.689892 | + | 0.680275i | ||||
\(387\) | 1.32244e22i | 1.33608i | ||||||||
\(388\) | 1.31299e19 | − | 9.35379e20i | 0.00129775 | − | 0.0924523i | ||||
\(389\) | − | 1.71218e21i | − | 0.165569i | −0.996567 | − | 0.0827843i | \(-0.973619\pi\) | ||
0.996567 | − | 0.0827843i | \(-0.0263813\pi\) | |||||||
\(390\) | 1.71678e21 | + | 1.74104e21i | 0.162429 | + | 0.164725i | ||||
\(391\) | 1.03681e22 | 0.959839 | ||||||||
\(392\) | 5.06291e20 | + | 5.28072e20i | 0.0458636 | + | 0.0478367i | ||||
\(393\) | −5.96220e21 | −0.528530 | ||||||||
\(394\) | −1.39661e22 | − | 1.41635e22i | −1.21159 | − | 1.22872i | ||||
\(395\) | 1.31190e22i | 1.11384i | ||||||||
\(396\) | −3.39336e21 | − | 4.76325e19i | −0.281982 | − | 0.00395817i | ||||
\(397\) | 5.61976e21i | 0.457087i | 0.973534 | + | 0.228543i | \(0.0733962\pi\) | ||||
−0.973534 | + | 0.228543i | \(0.926604\pi\) | |||||||
\(398\) | −1.95584e21 | + | 1.92858e21i | −0.155714 | + | 0.153543i | ||||
\(399\) | −5.93583e21 | −0.462607 | ||||||||
\(400\) | −8.37102e21 | − | 2.35054e20i | −0.638658 | − | 0.0179332i | ||||
\(401\) | −1.00601e22 | −0.751410 | −0.375705 | − | 0.926739i | \(-0.622599\pi\) | ||||
−0.375705 | + | 0.926739i | \(0.622599\pi\) | |||||||
\(402\) | 3.07419e21 | − | 3.03134e21i | 0.224807 | − | 0.221673i | ||||
\(403\) | 9.81029e21i | 0.702407i | ||||||||
\(404\) | −3.62471e21 | − | 5.08800e19i | −0.254116 | − | 0.00356702i | ||||
\(405\) | 4.28804e21i | 0.294368i | ||||||||
\(406\) | 1.11556e21 | + | 1.13133e21i | 0.0749932 | + | 0.0760533i | ||||
\(407\) | 8.57280e21 | 0.564378 | ||||||||
\(408\) | 4.68338e21 | − | 4.49021e21i | 0.301959 | − | 0.289504i | ||||
\(409\) | 9.17274e21 | 0.579230 | 0.289615 | − | 0.957143i | \(-0.406473\pi\) | ||||
0.289615 | + | 0.957143i | \(0.406473\pi\) | |||||||
\(410\) | 4.90366e21 | + | 4.97297e21i | 0.303290 | + | 0.307577i | ||||
\(411\) | 8.55762e21i | 0.518439i | ||||||||
\(412\) | 2.58807e20 | − | 1.84375e22i | 0.0153585 | − | 1.09415i | ||||
\(413\) | − | 6.43335e20i | − | 0.0373992i | ||||||
\(414\) | 9.99537e21 | − | 9.85605e21i | 0.569240 | − | 0.561306i | ||||
\(415\) | −1.93612e22 | −1.08025 | ||||||||
\(416\) | 1.12887e22 | + | 1.21101e22i | 0.617093 | + | 0.661995i | ||||
\(417\) | 8.48023e21 | 0.454204 | ||||||||
\(418\) | −4.91991e21 | + | 4.85133e21i | −0.258202 | + | 0.254603i | ||||
\(419\) | − | 1.93790e22i | − | 0.996581i | −0.867010 | − | 0.498291i | \(-0.833961\pi\) | ||
0.867010 | − | 0.498291i | \(-0.166039\pi\) | |||||||
\(420\) | −7.35156e19 | + | 5.23729e21i | −0.00370477 | + | 0.263929i | ||||
\(421\) | 3.52568e22i | 1.74118i | 0.492006 | + | 0.870592i | \(0.336264\pi\) | ||||
−0.492006 | + | 0.870592i | \(0.663736\pi\) | |||||||
\(422\) | 6.88005e21 | + | 6.97730e21i | 0.332994 | + | 0.337701i | ||||
\(423\) | 1.07978e22 | 0.512205 | ||||||||
\(424\) | 1.60182e22 | − | 1.53575e22i | 0.744737 | − | 0.714019i | ||||
\(425\) | −1.37869e22 | −0.628290 | ||||||||
\(426\) | −1.35166e21 | − | 1.37076e21i | −0.0603788 | − | 0.0612323i | ||||
\(427\) | − | 4.02945e22i | − | 1.76445i | ||||||
\(428\) | −3.77039e22 | − | 5.29249e20i | −1.61851 | − | 0.0227189i | ||||
\(429\) | 3.14982e21i | 0.132556i | ||||||||
\(430\) | 1.69172e22 | − | 1.66814e22i | 0.697985 | − | 0.688256i | ||||
\(431\) | −1.08535e22 | −0.439048 | −0.219524 | − | 0.975607i | \(-0.570450\pi\) | ||||
−0.219524 | + | 0.975607i | \(0.570450\pi\) | |||||||
\(432\) | 5.47597e20 | − | 1.95017e22i | 0.0217195 | − | 0.773500i | ||||
\(433\) | 3.41436e22 | 1.32789 | 0.663945 | − | 0.747781i | \(-0.268881\pi\) | ||||
0.663945 | + | 0.747781i | \(0.268881\pi\) | |||||||
\(434\) | −1.49639e22 | + | 1.47553e22i | −0.570665 | + | 0.562711i | ||||
\(435\) | 7.07013e20i | 0.0264405i | ||||||||
\(436\) | −2.12150e22 | − | 2.97794e20i | −0.778050 | − | 0.0109215i | ||||
\(437\) | − | 2.85798e22i | − | 1.02794i | ||||||
\(438\) | 1.49817e22 | + | 1.51935e22i | 0.528484 | + | 0.535954i | ||||
\(439\) | −1.05534e22 | −0.365126 | −0.182563 | − | 0.983194i | \(-0.558439\pi\) | ||||
−0.182563 | + | 0.983194i | \(0.558439\pi\) | |||||||
\(440\) | 4.21948e21 | + | 4.40101e21i | 0.143190 | + | 0.149350i | ||||
\(441\) | 1.63064e21 | 0.0542786 | ||||||||
\(442\) | 1.91372e22 | + | 1.94077e22i | 0.624869 | + | 0.633702i | ||||
\(443\) | − | 2.27118e22i | − | 0.727478i | −0.931501 | − | 0.363739i | \(-0.881500\pi\) | ||
0.931501 | − | 0.363739i | \(-0.118500\pi\) | |||||||
\(444\) | −3.11449e20 | + | 2.21878e22i | −0.00978660 | + | 0.697201i | ||||
\(445\) | − | 2.18077e22i | − | 0.672280i | ||||||
\(446\) | 1.80211e21 | − | 1.77700e21i | 0.0545050 | − | 0.0537453i | ||||
\(447\) | 1.08368e22 | 0.321580 | ||||||||
\(448\) | −1.49291e21 | + | 3.54333e22i | −0.0434682 | + | 1.03169i | ||||
\(449\) | 2.63226e22 | 0.752029 | 0.376014 | − | 0.926614i | \(-0.377294\pi\) | ||||
0.376014 | + | 0.926614i | \(0.377294\pi\) | |||||||
\(450\) | −1.32912e22 | + | 1.31059e22i | −0.372613 | + | 0.367419i | ||||
\(451\) | 8.99689e21i | 0.247509i | ||||||||
\(452\) | 5.54232e20 | − | 3.94837e22i | 0.0149629 | − | 1.06596i | ||||
\(453\) | 7.19294e21i | 0.190578i | ||||||||
\(454\) | 4.54396e22 | + | 4.60819e22i | 1.18157 | + | 1.19827i | ||||
\(455\) | −2.20035e22 | −0.561558 | ||||||||
\(456\) | −1.23773e22 | − | 1.29098e22i | −0.310045 | − | 0.323383i | ||||
\(457\) | −7.36512e21 | −0.181089 | −0.0905445 | − | 0.995892i | \(-0.528861\pi\) | ||||
−0.0905445 | + | 0.995892i | \(0.528861\pi\) | |||||||
\(458\) | −6.31697e21 | − | 6.40627e21i | −0.152459 | − | 0.154614i | ||||
\(459\) | − | 3.21188e22i | − | 0.760943i | ||||||
\(460\) | −2.52165e22 | − | 3.53963e20i | −0.586466 | − | 0.00823221i | ||||
\(461\) | 3.04360e22i | 0.694912i | 0.937696 | + | 0.347456i | \(0.112954\pi\) | ||||
−0.937696 | + | 0.347456i | \(0.887046\pi\) | |||||||
\(462\) | −4.80450e21 | + | 4.73753e21i | −0.107694 | + | 0.106193i | ||||
\(463\) | −6.61609e22 | −1.45600 | −0.728002 | − | 0.685575i | \(-0.759551\pi\) | ||||
−0.728002 | + | 0.685575i | \(0.759551\pi\) | |||||||
\(464\) | −1.34367e20 | + | 4.78525e21i | −0.00290329 | + | 0.103395i | ||||
\(465\) | −9.35153e21 | −0.198396 | ||||||||
\(466\) | −3.04368e22 | + | 3.00126e22i | −0.634044 | + | 0.625206i | ||||
\(467\) | 6.69796e21i | 0.137009i | 0.997651 | + | 0.0685045i | \(0.0218228\pi\) | ||||
−0.997651 | + | 0.0685045i | \(0.978177\pi\) | |||||||
\(468\) | 3.68983e22 | + | 5.17940e20i | 0.741168 | + | 0.0104038i | ||||
\(469\) | 3.88519e22i | 0.766377i | ||||||||
\(470\) | −1.36205e22 | − | 1.38130e22i | −0.263852 | − | 0.267582i | ||||
\(471\) | 2.59267e22 | 0.493252 | ||||||||
\(472\) | 1.39918e21 | − | 1.34147e21i | 0.0261437 | − | 0.0250654i | ||||
\(473\) | 3.06058e22 | 0.561674 | ||||||||
\(474\) | −3.07140e22 | − | 3.11482e22i | −0.553631 | − | 0.561457i | ||||
\(475\) | 3.80036e22i | 0.672867i | ||||||||
\(476\) | −8.19491e20 | + | 5.83809e22i | −0.0142523 | + | 1.01534i | ||||
\(477\) | − | 4.94626e22i | − | 0.845027i | ||||||
\(478\) | −3.17822e22 | + | 3.13392e22i | −0.533392 | + | 0.525958i | ||||
\(479\) | 6.94574e20 | 0.0114516 | 0.00572581 | − | 0.999984i | \(-0.498177\pi\) | ||||
0.00572581 | + | 0.999984i | \(0.498177\pi\) | |||||||
\(480\) | −1.15438e22 | + | 1.07608e22i | −0.186981 | + | 0.174299i | ||||
\(481\) | −9.32177e22 | −1.48342 | ||||||||
\(482\) | 6.90400e22 | − | 6.80777e22i | 1.07945 | − | 1.06440i | ||||
\(483\) | − | 2.79094e22i | − | 0.428746i | ||||||
\(484\) | 8.19619e20 | − | 5.83900e22i | 0.0123716 | − | 0.881359i | ||||
\(485\) | 3.74605e21i | 0.0555608i | ||||||||
\(486\) | −4.73173e22 | − | 4.79862e22i | −0.689624 | − | 0.699372i | ||||
\(487\) | 9.69164e22 | 1.38804 | 0.694019 | − | 0.719957i | \(-0.255838\pi\) | ||||
0.694019 | + | 0.719957i | \(0.255838\pi\) | |||||||
\(488\) | 8.76359e22 | − | 8.40213e22i | 1.23343 | − | 1.18255i | ||||
\(489\) | 1.43039e22 | 0.197847 | ||||||||
\(490\) | −2.05690e21 | − | 2.08597e21i | −0.0279606 | − | 0.0283558i | ||||
\(491\) | 1.39521e23i | 1.86400i | 0.362455 | + | 0.932001i | \(0.381939\pi\) | ||||
−0.362455 | + | 0.932001i | \(0.618061\pi\) | |||||||
\(492\) | −2.32854e22 | − | 3.26856e20i | −0.305759 | − | 0.00429194i | ||||
\(493\) | 7.88120e21i | 0.101717i | ||||||||
\(494\) | 5.34974e22 | − | 5.27518e22i | 0.678663 | − | 0.669203i | ||||
\(495\) | 1.35899e22 | 0.169462 | ||||||||
\(496\) | −6.32935e22 | − | 1.77725e21i | −0.775827 | − | 0.0217848i | ||||
\(497\) | 1.73238e22 | 0.208744 | ||||||||
\(498\) | 4.59690e22 | − | 4.53283e22i | 0.544523 | − | 0.536933i | ||||
\(499\) | − | 8.18187e21i | − | 0.0952792i | −0.998865 | − | 0.0476396i | \(-0.984830\pi\) | ||
0.998865 | − | 0.0476396i | \(-0.0151699\pi\) | |||||||
\(500\) | 8.60132e22 | + | 1.20737e21i | 0.984737 | + | 0.0138227i | ||||
\(501\) | − | 5.52212e21i | − | 0.0621563i | ||||||
\(502\) | −2.83506e22 | − | 2.87514e22i | −0.313748 | − | 0.318183i | ||||
\(503\) | 1.78323e23 | 1.94034 | 0.970172 | − | 0.242419i | \(-0.0779408\pi\) | ||||
0.970172 | + | 0.242419i | \(0.0779408\pi\) | |||||||
\(504\) | 5.47074e22 | + | 5.70609e22i | 0.585310 | + | 0.610491i | ||||
\(505\) | 1.45164e22 | 0.152715 | ||||||||
\(506\) | −2.28103e22 | − | 2.31327e22i | −0.235967 | − | 0.239302i | ||||
\(507\) | 7.56721e21i | 0.0769783i | ||||||||
\(508\) | −5.71306e20 | + | 4.07001e22i | −0.00571514 | + | 0.407149i | ||||
\(509\) | − | 5.61580e22i | − | 0.552473i | −0.961090 | − | 0.276236i | \(-0.910913\pi\) | ||
0.961090 | − | 0.276236i | \(-0.0890872\pi\) | |||||||
\(510\) | −1.85001e22 | + | 1.82423e22i | −0.178990 | + | 0.176495i | ||||
\(511\) | −1.92017e23 | −1.82710 | ||||||||
\(512\) | −8.01764e22 | + | 7.06380e22i | −0.750330 | + | 0.661064i | ||||
\(513\) | −8.85357e22 | −0.814931 | ||||||||
\(514\) | −6.97789e21 | + | 6.88062e21i | −0.0631738 | + | 0.0622933i | ||||
\(515\) | 7.38394e22i | 0.657547i | ||||||||
\(516\) | −1.11191e21 | + | 7.92127e22i | −0.00973971 | + | 0.693861i | ||||
\(517\) | − | 2.49899e22i | − | 0.215325i | ||||||
\(518\) | −1.40205e23 | − | 1.42187e23i | −1.18840 | − | 1.20520i | ||||
\(519\) | 5.47490e22 | 0.456513 | ||||||||
\(520\) | −4.58812e22 | − | 4.78551e22i | −0.376363 | − | 0.392554i | ||||
\(521\) | −1.17899e23 | −0.951458 | −0.475729 | − | 0.879592i | \(-0.657816\pi\) | ||||
−0.475729 | + | 0.879592i | \(0.657816\pi\) | |||||||
\(522\) | 7.49193e21 | + | 7.59783e21i | 0.0594832 | + | 0.0603241i | ||||
\(523\) | − | 1.02181e21i | − | 0.00798187i | −0.999992 | − | 0.00399093i | \(-0.998730\pi\) | ||
0.999992 | − | 0.00399093i | \(-0.00127036\pi\) | |||||||
\(524\) | 1.61642e23 | + | 2.26897e21i | 1.24233 | + | 0.0174386i | ||||
\(525\) | 3.71121e22i | 0.280648i | ||||||||
\(526\) | −1.36245e23 | + | 1.34346e23i | −1.01378 | + | 0.999645i | ||||
\(527\) | −1.04243e23 | −0.763233 | ||||||||
\(528\) | −2.03219e22 | − | 5.70627e20i | −0.146411 | − | 0.00411116i | ||||
\(529\) | −6.67183e21 | −0.0473011 | ||||||||
\(530\) | −6.32744e22 | + | 6.23925e22i | −0.441452 | + | 0.435299i | ||||
\(531\) | − | 4.32054e21i | − | 0.0296643i | ||||||
\(532\) | 1.60927e23 | + | 2.25893e21i | 1.08738 | + | 0.0152635i | ||||
\(533\) | − | 9.78291e22i | − | 0.650559i | ||||||
\(534\) | 5.10560e22 | + | 5.17777e22i | 0.334154 | + | 0.338877i | ||||
\(535\) | 1.50998e23 | 0.972669 | ||||||||
\(536\) | −8.44984e22 | + | 8.10132e22i | −0.535732 | + | 0.513635i | ||||
\(537\) | −4.25620e22 | −0.265608 | ||||||||
\(538\) | 1.95637e23 | + | 1.98402e23i | 1.20171 | + | 1.21870i | ||||
\(539\) | − | 3.77385e21i | − | 0.0228181i | ||||||
\(540\) | −1.09652e21 | + | 7.81166e22i | −0.00652634 | + | 0.464939i | ||||
\(541\) | − | 3.93089e22i | − | 0.230311i | −0.993347 | − | 0.115155i | \(-0.963263\pi\) | ||
0.993347 | − | 0.115155i | \(-0.0367366\pi\) | |||||||
\(542\) | 3.30676e20 | − | 3.26067e20i | 0.00190726 | − | 0.00188067i | ||||
\(543\) | 3.21468e22 | 0.182532 | ||||||||
\(544\) | −1.28681e23 | + | 1.19952e23i | −0.719321 | + | 0.670531i | ||||
\(545\) | 8.49627e22 | 0.467582 | ||||||||
\(546\) | 5.22425e22 | − | 5.15144e22i | 0.283065 | − | 0.279120i | ||||
\(547\) | − | 2.63090e23i | − | 1.40350i | −0.712423 | − | 0.701750i | \(-0.752402\pi\) | ||
0.712423 | − | 0.701750i | \(-0.247598\pi\) | |||||||
\(548\) | 3.25668e21 | − | 2.32007e23i | 0.0171057 | − | 1.21861i | ||||
\(549\) | − | 2.70611e23i | − | 1.39953i | ||||||
\(550\) | 3.03316e22 | + | 3.07604e22i | 0.154459 | + | 0.156642i | ||||
\(551\) | 2.17245e22 | 0.108934 | ||||||||
\(552\) | 6.06998e22 | − | 5.81962e22i | 0.299713 | − | 0.287351i | ||||
\(553\) | 3.93653e23 | 1.91404 | ||||||||
\(554\) | −1.85300e22 | − | 1.87920e22i | −0.0887245 | − | 0.0899786i | ||||
\(555\) | − | 8.88585e22i | − | 0.418995i | ||||||
\(556\) | −2.29909e23 | − | 3.22722e21i | −1.06763 | − | 0.0149863i | ||||
\(557\) | 2.45492e23i | 1.12271i | 0.827574 | + | 0.561357i | \(0.189720\pi\) | ||||
−0.827574 | + | 0.561357i | \(0.810280\pi\) | |||||||
\(558\) | −1.00495e23 | + | 9.90944e22i | −0.452641 | + | 0.446332i | ||||
\(559\) | −3.32797e23 | −1.47632 | ||||||||
\(560\) | 3.98619e21 | − | 1.41961e23i | 0.0174164 | − | 0.620255i | ||||
\(561\) | −3.34697e22 | −0.144035 | ||||||||
\(562\) | 1.89565e23 | − | 1.86922e23i | 0.803523 | − | 0.792323i | ||||
\(563\) | 1.65751e23i | 0.692044i | 0.938226 | + | 0.346022i | \(0.112468\pi\) | ||||
−0.938226 | + | 0.346022i | \(0.887532\pi\) | |||||||
\(564\) | 6.46778e22 | + | 9.07881e20i | 0.266001 | + | 0.00373385i | ||||
\(565\) | 1.58126e23i | 0.640607i | ||||||||
\(566\) | −6.74160e21 | − | 6.83689e21i | −0.0269044 | − | 0.0272847i | ||||
\(567\) | 1.28669e23 | 0.505844 | ||||||||
\(568\) | 3.61233e22 | + | 3.76773e22i | 0.139903 | + | 0.145922i | ||||
\(569\) | −3.03432e23 | −1.15773 | −0.578866 | − | 0.815423i | \(-0.696504\pi\) | ||||
−0.578866 | + | 0.815423i | \(0.696504\pi\) | |||||||
\(570\) | 5.02849e22 | + | 5.09957e22i | 0.189017 | + | 0.191689i | ||||
\(571\) | − | 4.28152e23i | − | 1.58559i | −0.609489 | − | 0.792795i | \(-0.708625\pi\) | ||
0.609489 | − | 0.792795i | \(-0.291375\pi\) | |||||||
\(572\) | 1.19869e21 | − | 8.53953e22i | 0.00437362 | − | 0.311579i | ||||
\(573\) | − | 7.17253e22i | − | 0.257845i | ||||||
\(574\) | 1.49221e23 | − | 1.47141e23i | 0.528542 | − | 0.521175i | ||||
\(575\) | −1.78687e23 | −0.623616 | ||||||||
\(576\) | −1.00262e22 | + | 2.37965e23i | −0.0344782 | + | 0.818316i | ||||
\(577\) | 4.78622e23 | 1.62180 | 0.810902 | − | 0.585182i | \(-0.198977\pi\) | ||||
0.810902 | + | 0.585182i | \(0.198977\pi\) | |||||||
\(578\) | 7.03029e21 | − | 6.93230e21i | 0.0234740 | − | 0.0231468i | ||||
\(579\) | 1.25264e23i | 0.412152i | ||||||||
\(580\) | 2.69060e20 | − | 1.91679e22i | 0.000872391 | − | 0.0621495i | ||||
\(581\) | 5.80961e23i | 1.85631i | ||||||||
\(582\) | −8.77021e21 | − | 8.89418e21i | −0.0276163 | − | 0.0280066i | ||||
\(583\) | −1.14473e23 | −0.355240 | ||||||||
\(584\) | −4.00390e23 | − | 4.17615e23i | −1.22454 | − | 1.27722i | ||||
\(585\) | −1.47772e23 | −0.445417 | ||||||||
\(586\) | 2.89925e23 | + | 2.94023e23i | 0.861303 | + | 0.873478i | ||||
\(587\) | 3.65842e23i | 1.07120i | 0.844472 | + | 0.535599i | \(0.179914\pi\) | ||||
−0.844472 | + | 0.535599i | \(0.820086\pi\) | |||||||
\(588\) | 9.76732e21 | + | 1.37104e20i | 0.0281883 | + | 0.000395678i | ||||
\(589\) | 2.87346e23i | 0.817383i | ||||||||
\(590\) | −5.52700e21 | + | 5.44996e21i | −0.0154970 | + | 0.0152810i | ||||
\(591\) | −2.65597e23 | −0.734056 | ||||||||
\(592\) | 1.68875e22 | − | 6.01417e23i | 0.0460077 | − | 1.63848i | ||||
\(593\) | −6.50994e22 | −0.174828 | −0.0874142 | − | 0.996172i | \(-0.527860\pi\) | ||||
−0.0874142 | + | 0.996172i | \(0.527860\pi\) | |||||||
\(594\) | −7.16614e22 | + | 7.06626e22i | −0.189715 | + | 0.187070i | ||||
\(595\) | − | 2.33806e23i | − | 0.610186i | ||||||
\(596\) | −2.93799e23 | − | 4.12405e21i | −0.755888 | − | 0.0106104i | ||||
\(597\) | 3.66763e22i | 0.0930259i | ||||||||
\(598\) | 2.48031e23 | + | 2.51537e23i | 0.620221 | + | 0.628988i | ||||
\(599\) | 7.03579e23 | 1.73454 | 0.867271 | − | 0.497837i | \(-0.165872\pi\) | ||||
0.867271 | + | 0.497837i | \(0.165872\pi\) | |||||||
\(600\) | −8.07147e22 | + | 7.73855e22i | −0.196186 | + | 0.188094i | ||||
\(601\) | 1.22977e23 | 0.294707 | 0.147354 | − | 0.989084i | \(-0.452924\pi\) | ||||
0.147354 | + | 0.989084i | \(0.452924\pi\) | |||||||
\(602\) | −5.00548e23 | − | 5.07624e23i | −1.18270 | − | 1.19942i | ||||
\(603\) | 2.60923e23i | 0.607876i | ||||||||
\(604\) | 2.73734e21 | − | 1.95009e23i | 0.00628802 | − | 0.447961i | ||||
\(605\) | 2.33843e23i | 0.529668i | ||||||||
\(606\) | −3.44661e22 | + | 3.39857e22i | −0.0769794 | + | 0.0759065i | ||||
\(607\) | −5.67018e23 | −1.24880 | −0.624400 | − | 0.781105i | \(-0.714657\pi\) | ||||
−0.624400 | + | 0.781105i | \(0.714657\pi\) | |||||||
\(608\) | 3.30649e23 | + | 3.54709e23i | 0.718104 | + | 0.770356i | ||||
\(609\) | 2.12149e22 | 0.0454355 | ||||||||
\(610\) | −3.46177e23 | + | 3.41351e23i | −0.731129 | + | 0.720938i | ||||
\(611\) | 2.71732e23i | 0.565966i | ||||||||
\(612\) | −5.50358e21 | + | 3.92077e23i | −0.0113047 | + | 0.805349i | ||||
\(613\) | − | 3.36503e23i | − | 0.681672i | −0.940123 | − | 0.340836i | \(-0.889290\pi\) | ||
0.940123 | − | 0.340836i | \(-0.110710\pi\) | |||||||
\(614\) | 1.24094e23 | + | 1.25849e23i | 0.247926 | + | 0.251430i | ||||
\(615\) | 9.32543e22 | 0.183751 | ||||||||
\(616\) | 1.32058e23 | − | 1.26612e23i | 0.256643 | − | 0.246058i | ||||
\(617\) | −2.04462e22 | −0.0391912 | −0.0195956 | − | 0.999808i | \(-0.506238\pi\) | ||||
−0.0195956 | + | 0.999808i | \(0.506238\pi\) | |||||||
\(618\) | −1.72872e23 | − | 1.75316e23i | −0.326831 | − | 0.331451i | ||||
\(619\) | − | 5.34254e23i | − | 0.996270i | −0.867099 | − | 0.498135i | \(-0.834018\pi\) | ||
0.867099 | − | 0.498135i | \(-0.165982\pi\) | |||||||
\(620\) | 2.53531e23 | + | 3.55880e21i | 0.466338 | + | 0.00654598i | ||||
\(621\) | − | 4.16282e23i | − | 0.755282i | ||||||
\(622\) | 4.04149e23 | − | 3.98516e23i | 0.723308 | − | 0.713226i | ||||
\(623\) | −6.54371e23 | −1.15525 | ||||||||
\(624\) | 2.20973e23 | + | 6.20481e21i | 0.384831 | + | 0.0108059i | ||||
\(625\) | 2.74250e22 | 0.0471158 | ||||||||
\(626\) | 1.63479e23 | − | 1.61201e23i | 0.277064 | − | 0.273203i | ||||
\(627\) | 9.22592e22i | 0.154254i | ||||||||
\(628\) | −7.02902e23 | − | 9.86662e21i | −1.15941 | − | 0.0162746i | ||||
\(629\) | − | 9.90521e23i | − | 1.61188i | ||||||
\(630\) | −2.22258e23 | − | 2.25400e23i | −0.356832 | − | 0.361876i | ||||
\(631\) | 9.89627e23 | 1.56755 | 0.783776 | − | 0.621043i | \(-0.213291\pi\) | ||||
0.783776 | + | 0.621043i | \(0.213291\pi\) | |||||||
\(632\) | 8.20838e23 | + | 8.56151e23i | 1.28281 | + | 1.33800i | ||||
\(633\) | 1.30840e23 | 0.201748 | ||||||||
\(634\) | 7.21492e22 | + | 7.31691e22i | 0.109767 | + | 0.111319i | ||||
\(635\) | − | 1.62997e23i | − | 0.244683i | ||||||
\(636\) | 4.15881e21 | − | 2.96275e23i | 0.00616004 | − | 0.438844i | ||||
\(637\) | 4.10356e22i | 0.0599757i | ||||||||
\(638\) | 1.75840e22 | − | 1.73389e22i | 0.0253596 | − | 0.0250061i | ||||
\(639\) | 1.16344e23 | 0.165572 | ||||||||
\(640\) | 3.17061e23 | − | 2.87345e23i | 0.445259 | − | 0.403528i | ||||
\(641\) | −4.56767e23 | −0.632997 | −0.316498 | − | 0.948593i | \(-0.602507\pi\) | ||||
−0.316498 | + | 0.948593i | \(0.602507\pi\) | |||||||
\(642\) | −3.58513e23 | + | 3.53516e23i | −0.490295 | + | 0.483461i | ||||
\(643\) | − | 1.63786e23i | − | 0.221046i | −0.993874 | − | 0.110523i | \(-0.964747\pi\) | ||
0.993874 | − | 0.110523i | \(-0.0352526\pi\) | |||||||
\(644\) | −1.06212e22 | + | 7.56656e23i | −0.0141463 | + | 1.00779i | ||||
\(645\) | − | 3.17235e23i | − | 0.416987i | ||||||
\(646\) | 5.60534e23 | + | 5.68458e23i | 0.727153 | + | 0.737432i | ||||
\(647\) | 1.41349e24 | 1.80969 | 0.904846 | − | 0.425738i | \(-0.139986\pi\) | ||||
0.904846 | + | 0.425738i | \(0.139986\pi\) | |||||||
\(648\) | 2.68298e23 | + | 2.79840e23i | 0.339023 | + | 0.353608i | ||||
\(649\) | −9.99921e21 | −0.0124706 | ||||||||
\(650\) | −3.29816e23 | − | 3.34478e23i | −0.405983 | − | 0.411722i | ||||
\(651\) | 2.80606e23i | 0.340925i | ||||||||
\(652\) | −3.87796e23 | − | 5.44348e21i | −0.465049 | − | 0.00652788i | ||||
\(653\) | − | 8.79618e23i | − | 1.04119i | −0.853802 | − | 0.520597i | \(-0.825709\pi\) | ||
0.853802 | − | 0.520597i | \(-0.174291\pi\) | |||||||
\(654\) | −2.01726e23 | + | 1.98914e23i | −0.235695 | + | 0.232410i | ||||
\(655\) | −6.47352e23 | −0.746602 | ||||||||
\(656\) | 6.31169e23 | + | 1.77229e22i | 0.718560 | + | 0.0201768i | ||||
\(657\) | −1.28955e24 | −1.44922 | ||||||||
\(658\) | −4.14479e23 | + | 4.08702e23i | −0.459814 | + | 0.453405i | ||||
\(659\) | 4.40891e23i | 0.482843i | 0.970420 | + | 0.241421i | \(0.0776136\pi\) | ||||
−0.970420 | + | 0.241421i | \(0.922386\pi\) | |||||||
\(660\) | 8.14019e22 | + | 1.14264e21i | 0.0880058 | + | 0.00123533i | ||||
\(661\) | 7.35760e23i | 0.785278i | 0.919693 | + | 0.392639i | \(0.128438\pi\) | ||||
−0.919693 | + | 0.392639i | \(0.871562\pi\) | |||||||
\(662\) | −5.37145e23 | − | 5.44738e23i | −0.565977 | − | 0.573977i | ||||
\(663\) | 3.63938e23 | 0.378584 | ||||||||
\(664\) | −1.26352e24 | + | 1.21141e24i | −1.29764 | + | 1.24412i | ||||
\(665\) | −6.44488e23 | −0.653478 | ||||||||
\(666\) | −9.41598e23 | − | 9.54908e23i | −0.942615 | − | 0.955940i | ||||
\(667\) | 1.02146e23i | 0.100960i | ||||||||
\(668\) | −2.10149e21 | + | 1.49711e23i | −0.00205082 | + | 0.146101i | ||||
\(669\) | − | 3.37936e22i | − | 0.0325621i | ||||||
\(670\) | 3.33783e23 | − | 3.29130e23i | 0.317562 | − | 0.313135i | ||||
\(671\) | −6.26288e23 | −0.588346 | ||||||||
\(672\) | 3.22893e23 | + | 3.46388e23i | 0.299516 | + | 0.321310i | ||||
\(673\) | −3.52911e23 | −0.323249 | −0.161625 | − | 0.986852i | \(-0.551673\pi\) | ||||
−0.161625 | + | 0.986852i | \(0.551673\pi\) | |||||||
\(674\) | −1.05218e23 | + | 1.03752e23i | −0.0951662 | + | 0.0938397i | ||||
\(675\) | 5.53545e23i | 0.494391i | ||||||||
\(676\) | 2.87977e21 | − | 2.05156e23i | 0.00253986 | − | 0.180941i | ||||
\(677\) | 7.93301e23i | 0.690930i | 0.938432 | + | 0.345465i | \(0.112279\pi\) | ||||
−0.938432 | + | 0.345465i | \(0.887721\pi\) | |||||||
\(678\) | −3.70204e23 | − | 3.75437e23i | −0.318411 | − | 0.322912i | ||||
\(679\) | 1.12405e23 | 0.0954760 | ||||||||
\(680\) | 5.08502e23 | − | 4.87529e23i | 0.426547 | − | 0.408954i | ||||
\(681\) | 8.64138e23 | 0.715868 | ||||||||
\(682\) | 2.29338e23 | + | 2.32580e23i | 0.187633 | + | 0.190285i | ||||
\(683\) | 8.06966e23i | 0.652048i | 0.945362 | + | 0.326024i | \(0.105709\pi\) | ||||
−0.945362 | + | 0.326024i | \(0.894291\pi\) | |||||||
\(684\) | 1.08076e24 | + | 1.51706e22i | 0.862488 | + | 0.0121067i | ||||
\(685\) | 9.29152e23i | 0.732347i | ||||||||
\(686\) | 8.81904e23 | − | 8.69612e23i | 0.686541 | − | 0.676971i | ||||
\(687\) | −1.20132e23 | −0.0923688 | ||||||||
\(688\) | 6.02901e22 | − | 2.14712e24i | 0.0457872 | − | 1.63063i | ||||
\(689\) | 1.24474e24 | 0.933720 | ||||||||
\(690\) | −2.39774e23 | + | 2.36432e23i | −0.177658 | + | 0.175182i | ||||
\(691\) | − | 3.75773e23i | − | 0.275019i | −0.990500 | − | 0.137509i | \(-0.956090\pi\) | ||
0.990500 | − | 0.137509i | \(-0.0439097\pi\) | |||||||
\(692\) | −1.48431e24 | − | 2.08352e22i | −1.07306 | − | 0.0150625i | ||||
\(693\) | − | 4.07784e23i | − | 0.291204i | ||||||
\(694\) | 7.76098e23 | + | 7.87068e23i | 0.547471 | + | 0.555210i | ||||
\(695\) | 9.20749e23 | 0.641609 | ||||||||
\(696\) | 4.42370e22 | + | 4.61401e22i | 0.0304514 | + | 0.0317614i | ||||
\(697\) | 1.03952e24 | 0.706895 | ||||||||
\(698\) | 2.15744e23 | + | 2.18794e23i | 0.144933 | + | 0.146982i | ||||
\(699\) | 5.70758e23i | 0.378788i | ||||||||
\(700\) | 1.41233e22 | − | 1.00615e24i | 0.00925985 | − | 0.659676i | ||||
\(701\) | − | 1.69069e24i | − | 1.09512i | −0.836767 | − | 0.547559i | \(-0.815557\pi\) | ||
0.836767 | − | 0.547559i | \(-0.184443\pi\) | |||||||
\(702\) | 7.79222e23 | − | 7.68361e23i | 0.498650 | − | 0.491700i | ||||
\(703\) | −2.73038e24 | −1.72624 | ||||||||
\(704\) | 5.50732e23 | + | 2.32040e22i | 0.344011 | + | 0.0144942i | ||||
\(705\) | −2.59025e23 | −0.159858 | ||||||||
\(706\) | 1.29990e24 | − | 1.28179e24i | 0.792632 | − | 0.781584i | ||||
\(707\) | − | 4.35585e23i | − | 0.262427i | ||||||
\(708\) | 3.63270e20 | − | 2.58795e22i | 0.000216246 | − | 0.0154054i | ||||
\(709\) | 1.96311e24i | 1.15466i | 0.816512 | + | 0.577328i | \(0.195905\pi\) | ||||
−0.816512 | + | 0.577328i | \(0.804095\pi\) | |||||||
\(710\) | −1.46757e23 | − | 1.48832e23i | −0.0852911 | − | 0.0864968i | ||||
\(711\) | 2.64371e24 | 1.51818 | ||||||||
\(712\) | −1.36448e24 | − | 1.42318e24i | −0.774263 | − | 0.807571i | ||||
\(713\) | −1.35106e24 | −0.757555 | ||||||||
\(714\) | 5.47386e23 | + | 5.55123e23i | 0.303290 | + | 0.307578i | ||||
\(715\) | 3.41995e23i | 0.187248i | ||||||||
\(716\) | 1.15391e24 | + | 1.61973e22i | 0.624323 | + | 0.00876361i | ||||
\(717\) | 5.95987e23i | 0.318657i | ||||||||
\(718\) | −2.48429e24 | + | 2.44966e24i | −1.31264 | + | 1.29434i | ||||
\(719\) | −7.24919e23 | −0.378525 | −0.189262 | − | 0.981927i | \(-0.560610\pi\) | ||||
−0.189262 | + | 0.981927i | \(0.560610\pi\) | |||||||
\(720\) | 2.67706e22 | − | 9.53387e23i | 0.0138144 | − | 0.491975i | ||||
\(721\) | 2.21566e24 | 1.12993 | ||||||||
\(722\) | 1.54166e23 | − | 1.52017e23i | 0.0777001 | − | 0.0766171i | ||||
\(723\) | − | 1.29465e24i | − | 0.644878i | ||||||
\(724\) | −8.71536e23 | − | 1.22337e22i | −0.429049 | − | 0.00602256i | ||||
\(725\) | − | 1.35827e23i | − | 0.0660864i | ||||||
\(726\) | −5.47471e23 | − | 5.55210e23i | −0.263269 | − | 0.266991i | ||||
\(727\) | −3.57325e24 | −1.69832 | −0.849162 | − | 0.528132i | \(-0.822893\pi\) | ||||
−0.849162 | + | 0.528132i | \(0.822893\pi\) | |||||||
\(728\) | −1.43596e24 | + | 1.37673e24i | −0.674568 | + | 0.646744i | ||||
\(729\) | 1.55188e23 | 0.0720567 | ||||||||
\(730\) | 1.62665e24 | + | 1.64965e24i | 0.746537 | + | 0.757089i | ||||
\(731\) | − | 3.53627e24i | − | 1.60416i | ||||||
\(732\) | 2.27530e22 | − | 1.62093e24i | 0.0102022 | − | 0.726809i | ||||
\(733\) | 3.87913e24i | 1.71930i | 0.510887 | + | 0.859648i | \(0.329317\pi\) | ||||
−0.510887 | + | 0.859648i | \(0.670683\pi\) | |||||||
\(734\) | −2.19647e24 | + | 2.16585e24i | −0.962296 | + | 0.948883i | ||||
\(735\) | −3.91166e22 | −0.0169402 | ||||||||
\(736\) | −1.66779e24 | + | 1.55467e24i | −0.713969 | + | 0.665542i | ||||
\(737\) | 6.03865e23 | 0.255544 | ||||||||
\(738\) | 1.00215e24 | − | 9.88178e23i | 0.419230 | − | 0.413386i | ||||
\(739\) | − | 3.80051e24i | − | 1.57168i | −0.618430 | − | 0.785840i | \(-0.712231\pi\) | ||
0.618430 | − | 0.785840i | \(-0.287769\pi\) | |||||||
\(740\) | −3.38159e22 | + | 2.40906e24i | −0.0138246 | + | 0.984867i | ||||
\(741\) | − | 1.00320e24i | − | 0.405444i | ||||||
\(742\) | 1.87218e24 | + | 1.89864e24i | 0.748020 | + | 0.758594i | ||||
\(743\) | 9.34750e23 | 0.369224 | 0.184612 | − | 0.982811i | \(-0.440897\pi\) | ||||
0.184612 | + | 0.982811i | \(0.440897\pi\) | |||||||
\(744\) | −6.10286e23 | + | 5.85114e23i | −0.238322 | + | 0.228492i | ||||
\(745\) | 1.17662e24 | 0.454264 | ||||||||
\(746\) | 1.51862e24 | + | 1.54009e24i | 0.579655 | + | 0.587848i | ||||
\(747\) | 3.90164e24i | 1.47239i | ||||||||
\(748\) | 9.07401e23 | + | 1.27372e22i | 0.338560 | + | 0.00475236i | ||||
\(749\) | − | 4.53092e24i | − | 1.67144i | ||||||
\(750\) | 8.17869e23 | − | 8.06469e23i | 0.298307 | − | 0.294149i | ||||
\(751\) | −1.14251e24 | −0.412024 | −0.206012 | − | 0.978549i | \(-0.566049\pi\) | ||||
−0.206012 | + | 0.978549i | \(0.566049\pi\) | |||||||
\(752\) | −1.75314e24 | − | 4.92274e22i | −0.625124 | − | 0.0175532i | ||||
\(753\) | −5.39152e23 | −0.190088 | ||||||||
\(754\) | −1.91202e23 | + | 1.88537e23i | −0.0666557 | + | 0.0657266i | ||||
\(755\) | 7.80981e23i | 0.269210i | ||||||||
\(756\) | 2.34400e24 | + | 3.29027e22i | 0.798955 | + | 0.0112149i | ||||
\(757\) | 4.16361e24i | 1.40331i | 0.712515 | + | 0.701657i | \(0.247556\pi\) | ||||
−0.712515 | + | 0.701657i | \(0.752444\pi\) | |||||||
\(758\) | 4.37807e23 | + | 4.43995e23i | 0.145913 | + | 0.147976i | ||||
\(759\) | −4.33790e23 | −0.142963 | ||||||||
\(760\) | −1.34388e24 | − | 1.40169e24i | −0.437969 | − | 0.456811i | ||||
\(761\) | −2.67038e24 | −0.860606 | −0.430303 | − | 0.902685i | \(-0.641593\pi\) | ||||
−0.430303 | + | 0.902685i | \(0.641593\pi\) | |||||||
\(762\) | 3.81608e23 | + | 3.87002e23i | 0.121619 | + | 0.123338i | ||||
\(763\) | − | 2.54943e24i | − | 0.803496i | ||||||
\(764\) | −2.72957e22 | + | 1.94455e24i | −0.00850746 | + | 0.606075i | ||||
\(765\) | − | 1.57021e24i | − | 0.483988i | ||||||
\(766\) | 1.32582e24 | − | 1.30734e24i | 0.404149 | − | 0.398516i | ||||
\(767\) | 1.08728e23 | 0.0327779 | ||||||||
\(768\) | −8.00637e22 | + | 1.42454e24i | −0.0238707 | + | 0.424721i | ||||
\(769\) | 1.07347e24 | 0.316530 | 0.158265 | − | 0.987397i | \(-0.449410\pi\) | ||||
0.158265 | + | 0.987397i | \(0.449410\pi\) | |||||||
\(770\) | −5.21653e23 | + | 5.14382e23i | −0.152129 | + | 0.150008i | ||||
\(771\) | 1.30851e23i | 0.0377411i | ||||||||
\(772\) | 4.76702e22 | − | 3.39605e24i | 0.0135988 | − | 0.968783i | ||||
\(773\) | − | 5.44288e24i | − | 1.53569i | −0.640637 | − | 0.767844i | \(-0.721330\pi\) | ||
0.640637 | − | 0.767844i | \(-0.278670\pi\) | |||||||
\(774\) | −3.36161e24 | − | 3.40912e24i | −0.938099 | − | 0.951359i | ||||
\(775\) | 1.79655e24 | 0.495879 | ||||||||
\(776\) | 2.34386e23 | + | 2.44469e23i | 0.0639892 | + | 0.0667420i | ||||
\(777\) | −2.66633e24 | −0.720004 | ||||||||
\(778\) | 4.35231e23 | + | 4.41384e23i | 0.116250 | + | 0.117893i | ||||
\(779\) | − | 2.86544e24i | − | 0.757048i | ||||||
\(780\) | −8.85137e23 | − | 1.24246e22i | −0.231316 | − | 0.00324698i | ||||
\(781\) | − | 2.69260e23i | − | 0.0696046i | ||||||
\(782\) | −2.67281e24 | + | 2.63555e24i | −0.683455 | + | 0.673929i | ||||
\(783\) | 3.16431e23 | 0.0800394 | ||||||||
\(784\) | −2.64751e23 | − | 7.43408e21i | −0.0662447 | − | 0.00186012i | ||||
\(785\) | 2.81501e24 | 0.696768 | ||||||||
\(786\) | 1.53700e24 | − | 1.51557e24i | 0.376341 | − | 0.371095i | ||||
\(787\) | 7.33278e24i | 1.77617i | 0.459683 | + | 0.888083i | \(0.347963\pi\) | ||||
−0.459683 | + | 0.888083i | \(0.652037\pi\) | |||||||
\(788\) | 7.20064e24 | + | 1.01075e23i | 1.72543 | + | 0.0242199i | ||||
\(789\) | 2.55490e24i | 0.605646i | ||||||||
\(790\) | −3.33480e24 | − | 3.38194e24i | −0.782059 | − | 0.793114i | ||||
\(791\) | 4.74480e24 | 1.10082 | ||||||||
\(792\) | 8.86884e23 | − | 8.50304e23i | 0.203565 | − | 0.195169i | ||||
\(793\) | 6.81004e24 | 1.54642 | ||||||||
\(794\) | −1.42853e24 | − | 1.44872e24i | −0.320933 | − | 0.325469i | ||||
\(795\) | 1.18654e24i | 0.263730i | ||||||||
\(796\) | 1.39575e22 | − | 9.94337e23i | 0.00306935 | − | 0.218662i | ||||
\(797\) | 5.04426e24i | 1.09749i | 0.835989 | + | 0.548746i | \(0.184895\pi\) | ||||
−0.835989 | + | 0.548746i | \(0.815105\pi\) | |||||||
\(798\) | 1.53020e24 | − | 1.50887e24i | 0.329400 | − | 0.324809i | ||||
\(799\) | −2.88739e24 | −0.614976 | ||||||||
\(800\) | 2.21772e24 | − | 2.06729e24i | 0.467349 | − | 0.435650i | ||||
\(801\) | −4.39466e24 | −0.916323 | ||||||||
\(802\) | 2.59341e24 | − | 2.55726e24i | 0.535043 | − | 0.527585i | ||||
\(803\) | 2.98447e24i | 0.609236i | ||||||||
\(804\) | −2.19384e22 | + | 1.56290e24i | −0.00443127 | + | 0.315685i | ||||
\(805\) | − | 3.03029e24i | − | 0.605647i | ||||||
\(806\) | −2.49375e24 | − | 2.52900e24i | −0.493179 | − | 0.500150i | ||||
\(807\) | 3.72048e24 | 0.728072 | ||||||||
\(808\) | 9.47349e23 | − | 9.08275e23i | 0.183448 | − | 0.175882i | ||||
\(809\) | −6.54648e24 | −1.25443 | −0.627214 | − | 0.778847i | \(-0.715805\pi\) | ||||
−0.627214 | + | 0.778847i | \(0.715805\pi\) | |||||||
\(810\) | −1.09001e24 | − | 1.10541e24i | −0.206684 | − | 0.209605i | ||||
\(811\) | 1.96650e24i | 0.368992i | 0.982833 | + | 0.184496i | \(0.0590652\pi\) | ||||
−0.982833 | + | 0.184496i | \(0.940935\pi\) | |||||||
\(812\) | −5.75162e23 | − | 8.07353e21i | −0.106798 | − | 0.00149912i | ||||
\(813\) | − | 6.20091e21i | − | 0.00113943i | ||||||
\(814\) | −2.20998e24 | + | 2.17918e24i | −0.401866 | + | 0.396265i | ||||
\(815\) | 1.55306e24 | 0.279479 | ||||||||
\(816\) | −6.59316e22 | + | 2.34803e24i | −0.0117416 | + | 0.418156i | ||||
\(817\) | −9.74773e24 | −1.71797 | ||||||||
\(818\) | −2.36464e24 | + | 2.33168e24i | −0.412442 | + | 0.406693i | ||||
\(819\) | 4.43411e24i | 0.765408i | ||||||||
\(820\) | −2.52823e24 | − | 3.54887e22i | −0.431916 | − | 0.00606279i | ||||
\(821\) | − | 3.48398e24i | − | 0.589059i | −0.955642 | − | 0.294529i | \(-0.904837\pi\) | ||
0.955642 | − | 0.294529i | \(-0.0951629\pi\) | |||||||
\(822\) | −2.17532e24 | − | 2.20607e24i | −0.364010 | − | 0.369155i | ||||
\(823\) | −7.93327e23 | −0.131387 | −0.0656937 | − | 0.997840i | \(-0.520926\pi\) | ||||
−0.0656937 | + | 0.997840i | \(0.520926\pi\) | |||||||
\(824\) | 4.62005e24 | + | 4.81880e24i | 0.757295 | + | 0.789874i | ||||
\(825\) | 5.76825e23 | 0.0935806 | ||||||||
\(826\) | 1.63534e23 | + | 1.65846e23i | 0.0262590 | + | 0.0266301i | ||||
\(827\) | 8.23961e24i | 1.30951i | 0.755840 | + | 0.654756i | \(0.227229\pi\) | ||||
−0.755840 | + | 0.654756i | \(0.772771\pi\) | |||||||
\(828\) | −7.13301e22 | + | 5.08159e24i | −0.0112206 | + | 0.799358i | ||||
\(829\) | − | 2.42199e24i | − | 0.377102i | −0.982063 | − | 0.188551i | \(-0.939621\pi\) | ||
0.982063 | − | 0.188551i | \(-0.0603791\pi\) | |||||||
\(830\) | 4.99113e24 | − | 4.92156e24i | 0.769193 | − | 0.758471i | ||||
\(831\) | −3.52391e23 | −0.0537547 | ||||||||
\(832\) | −5.98847e24 | − | 2.52313e23i | −0.904207 | − | 0.0380970i | ||||
\(833\) | −4.36039e23 | −0.0651693 | ||||||||
\(834\) | −2.18612e24 | + | 2.15565e24i | −0.323417 | + | 0.318909i | ||||
\(835\) | − | 5.99570e23i | − | 0.0878021i | ||||||
\(836\) | 3.51100e22 | − | 2.50125e24i | 0.00508953 | − | 0.362580i | ||||
\(837\) | 4.18537e24i | 0.600575i | ||||||||
\(838\) | 4.92609e24 | + | 4.99572e24i | 0.699726 | + | 0.709617i | ||||
\(839\) | −3.72199e24 | −0.523358 | −0.261679 | − | 0.965155i | \(-0.584276\pi\) | ||||
−0.261679 | + | 0.965155i | \(0.584276\pi\) | |||||||
\(840\) | −1.31235e24 | − | 1.36881e24i | −0.182674 | − | 0.190532i | ||||
\(841\) | 7.17950e24 | 0.989301 | ||||||||
\(842\) | −8.96216e24 | − | 9.08885e24i | −1.22253 | − | 1.23981i | ||||
\(843\) | − | 3.55476e24i | − | 0.480038i | ||||||
\(844\) | −3.54722e24 | − | 4.97923e22i | −0.474217 | − | 0.00665658i | ||||
\(845\) | 8.21617e23i | 0.108740i | ||||||||
\(846\) | −2.78358e24 | + | 2.74478e24i | −0.364716 | + | 0.359633i | ||||
\(847\) | 7.01679e24 | 0.910185 | ||||||||
\(848\) | −2.25500e23 | + | 8.03078e24i | −0.0289589 | + | 1.03132i | ||||
\(849\) | −1.28207e23 | −0.0163003 | ||||||||
\(850\) | 3.55413e24 | − | 3.50459e24i | 0.447375 | − | 0.441140i | ||||
\(851\) | − | 1.28378e25i | − | 1.59989i | ||||||
\(852\) | 6.96888e23 | + | 9.78220e21i | 0.0859857 | + | 0.00120698i | ||||
\(853\) | − | 5.25914e24i | − | 0.642463i | −0.947001 | − | 0.321231i | \(-0.895903\pi\) | ||
0.947001 | − | 0.321231i | \(-0.104097\pi\) | |||||||
\(854\) | 1.02427e25 | + | 1.03875e25i | 1.23887 | + | 1.25638i | ||||
\(855\) | −4.32828e24 | −0.518327 | ||||||||
\(856\) | 9.85423e24 | − | 9.44779e24i | 1.16841 | − | 1.12022i | ||||
\(857\) | 1.85443e23 | 0.0217708 | 0.0108854 | − | 0.999941i | \(-0.496535\pi\) | ||||
0.0108854 | + | 0.999941i | \(0.496535\pi\) | |||||||
\(858\) | −8.00676e23 | − | 8.11994e23i | −0.0930711 | − | 0.0943867i | ||||
\(859\) | − | 1.65533e25i | − | 1.90521i | −0.304213 | − | 0.952604i | \(-0.598393\pi\) | ||
0.304213 | − | 0.952604i | \(-0.401607\pi\) | |||||||
\(860\) | −1.20726e23 | + | 8.60059e24i | −0.0137583 | + | 0.980148i | ||||
\(861\) | − | 2.79823e24i | − | 0.315759i | ||||||
\(862\) | 2.79792e24 | − | 2.75892e24i | 0.312625 | − | 0.308267i | ||||
\(863\) | 9.72354e24 | 1.07580 | 0.537901 | − | 0.843008i | \(-0.319217\pi\) | ||||
0.537901 | + | 0.843008i | \(0.319217\pi\) | |||||||
\(864\) | 4.81611e24 | + | 5.16654e24i | 0.527630 | + | 0.566022i | ||||
\(865\) | 5.94442e24 | 0.644871 | ||||||||
\(866\) | −8.80189e24 | + | 8.67920e24i | −0.945527 | + | 0.932347i | ||||
\(867\) | − | 1.31834e23i | − | 0.0140237i | ||||||
\(868\) | 1.06787e23 | − | 7.60755e24i | 0.0112487 | − | 0.801359i | ||||
\(869\) | − | 6.11846e24i | − | 0.638225i | ||||||
\(870\) | −1.79721e23 | − | 1.82261e23i | −0.0185646 | − | 0.0188270i | ||||
\(871\) | −6.56623e24 | −0.671679 | ||||||||
\(872\) | 5.54471e24 | − | 5.31602e24i | 0.561680 | − | 0.538513i | ||||
\(873\) | 7.54898e23 | 0.0757298 | ||||||||
\(874\) | 7.26491e24 | + | 7.36760e24i | 0.721744 | + | 0.731946i | ||||
\(875\) | 1.03363e25i | 1.01694i | ||||||||
\(876\) | −7.72429e24 | − | 1.08426e23i | −0.752616 | − | 0.0105645i | ||||
\(877\) | 3.35429e24i | 0.323671i | 0.986818 | + | 0.161836i | \(0.0517415\pi\) | ||||
−0.986818 | + | 0.161836i | \(0.948259\pi\) | |||||||
\(878\) | 2.72056e24 | − | 2.68264e24i | 0.259989 | − | 0.256365i | ||||
\(879\) | 5.51359e24 | 0.521830 | ||||||||
\(880\) | −2.20646e24 | − | 6.19564e22i | −0.206821 | − | 0.00580742i | ||||
\(881\) | 4.42293e24 | 0.410597 | 0.205298 | − | 0.978699i | \(-0.434184\pi\) | ||||
0.205298 | + | 0.978699i | \(0.434184\pi\) | |||||||
\(882\) | −4.20362e23 | + | 4.14503e23i | −0.0386492 | + | 0.0381105i | ||||
\(883\) | − | 5.46478e24i | − | 0.497630i | −0.968551 | − | 0.248815i | \(-0.919959\pi\) | ||
0.968551 | − | 0.248815i | \(-0.0800412\pi\) | |||||||
\(884\) | −9.86677e24 | − | 1.38500e23i | −0.889879 | − | 0.0124912i | ||||
\(885\) | 1.03644e23i | 0.00925815i | ||||||||
\(886\) | 5.77328e24 | + | 5.85488e24i | 0.510782 | + | 0.518002i | ||||
\(887\) | −2.15636e25 | −1.88960 | −0.944800 | − | 0.327646i | \(-0.893745\pi\) | ||||
−0.944800 | + | 0.327646i | \(0.893745\pi\) | |||||||
\(888\) | −5.55978e24 | − | 5.79896e24i | −0.482555 | − | 0.503315i | ||||
\(889\) | −4.89097e24 | −0.420465 | ||||||||
\(890\) | 5.54346e24 | + | 5.62182e24i | 0.472026 | + | 0.478698i | ||||
\(891\) | − | 1.99987e24i | − | 0.168671i | ||||||
\(892\) | −1.28605e22 | + | 9.16185e23i | −0.00107437 | + | 0.0765388i | ||||
\(893\) | 7.95910e24i | 0.658608i | ||||||||
\(894\) | −2.79363e24 | + | 2.75469e24i | −0.228981 | + | 0.225790i | ||||
\(895\) | −4.62121e24 | −0.375198 | ||||||||
\(896\) | −8.62219e24 | − | 9.51386e24i | −0.693425 | − | 0.765136i | ||||
\(897\) | 4.71688e24 | 0.375767 | ||||||||
\(898\) | −6.78570e24 | + | 6.69112e24i | −0.535483 | + | 0.528020i | ||||
\(899\) | − | 1.02699e24i | − | 0.0802803i | ||||||
\(900\) | 9.48502e22 | − | 6.75717e24i | 0.00734475 | − | 0.523243i | ||||
\(901\) | 1.32265e25i | 1.01458i | ||||||||
\(902\) | −2.28698e24 | − | 2.31931e24i | −0.173783 | − | 0.176240i | ||||
\(903\) | −9.51908e24 | −0.716554 | ||||||||
\(904\) | 9.89377e24 | + | 1.03194e25i | 0.737786 | + | 0.769526i | ||||
\(905\) | 3.49036e24 | 0.257844 | ||||||||
\(906\) | −1.82843e24 | − | 1.85427e24i | −0.133810 | − | 0.135701i | ||||
\(907\) | 2.01078e24i | 0.145781i | 0.997340 | + | 0.0728906i | \(0.0232224\pi\) | ||||
−0.997340 | + | 0.0728906i | \(0.976778\pi\) | |||||||
\(908\) | −2.34278e25 | − | 3.28855e23i | −1.68268 | − | 0.0236197i | ||||
\(909\) | − | 2.92532e24i | − | 0.208152i | ||||||
\(910\) | 5.67228e24 | − | 5.59322e24i | 0.399858 | − | 0.394285i | ||||
\(911\) | −7.02829e24 | −0.490844 | −0.245422 | − | 0.969416i | \(-0.578926\pi\) | ||||
−0.245422 | + | 0.969416i | \(0.578926\pi\) | |||||||
\(912\) | 6.47237e24 | + | 1.81741e23i | 0.447824 | + | 0.0125747i | ||||
\(913\) | 9.02974e24 | 0.618976 | ||||||||
\(914\) | 1.89866e24 | − | 1.87219e24i | 0.128945 | − | 0.127147i | ||||
\(915\) | 6.49158e24i | 0.436788i | ||||||||
\(916\) | 3.25691e24 | + | 4.57171e22i | 0.217117 | + | 0.00304767i | ||||
\(917\) | 1.94247e25i | 1.28297i | ||||||||
\(918\) | 8.16452e24 | + | 8.27993e24i | 0.534278 | + | 0.541831i | ||||
\(919\) | 3.84448e24 | 0.249262 | 0.124631 | − | 0.992203i | \(-0.460225\pi\) | ||||
0.124631 | + | 0.992203i | \(0.460225\pi\) | |||||||
\(920\) | 6.59054e24 | − | 6.31871e24i | 0.423374 | − | 0.405912i | ||||
\(921\) | 2.35994e24 | 0.150208 | ||||||||
\(922\) | −7.73675e24 | − | 7.84611e24i | −0.487916 | − | 0.494813i | ||||
\(923\) | 2.92784e24i | 0.182950i | ||||||||
\(924\) | 3.42864e22 | − | 2.44258e24i | 0.00212281 | − | 0.151230i | ||||
\(925\) | 1.70709e25i | 1.04725i | ||||||||
\(926\) | 1.70556e25 | − | 1.68179e25i | 1.03675 | − | 1.02230i | ||||
\(927\) | 1.48800e25 | 0.896242 | ||||||||
\(928\) | −1.18176e24 | − | 1.26775e24i | −0.0705294 | − | 0.0756614i | ||||
\(929\) | 9.60876e23 | 0.0568243 | 0.0284121 | − | 0.999596i | \(-0.490955\pi\) | ||||
0.0284121 | + | 0.999596i | \(0.490955\pi\) | |||||||
\(930\) | 2.41073e24 | − | 2.37713e24i | 0.141268 | − | 0.139299i | ||||
\(931\) | 1.20194e24i | 0.0697930i | ||||||||
\(932\) | 2.17207e23 | − | 1.54739e25i | 0.0124979 | − | 0.890358i | ||||
\(933\) | − | 7.57869e24i | − | 0.432116i | ||||||
\(934\) | −1.70260e24 | − | 1.72667e24i | −0.0961977 | − | 0.0975575i | ||||
\(935\) | −3.63400e24 | −0.203463 | ||||||||
\(936\) | −9.64368e24 | + | 9.24592e24i | −0.535054 | + | 0.512986i | ||||
\(937\) | 4.30409e24 | 0.236644 | 0.118322 | − | 0.992975i | \(-0.462249\pi\) | ||||
0.118322 | + | 0.992975i | \(0.462249\pi\) | |||||||
\(938\) | −9.87603e24 | − | 1.00156e25i | −0.538094 | − | 0.545700i | ||||
\(939\) | − | 3.06560e24i | − | 0.165523i | ||||||
\(940\) | 7.02246e24 | + | 9.85740e22i | 0.375753 | + | 0.00527443i | ||||
\(941\) | 3.71907e24i | 0.197207i | 0.995127 | + | 0.0986036i | \(0.0314376\pi\) | ||||
−0.995127 | + | 0.0986036i | \(0.968562\pi\) | |||||||
\(942\) | −6.68364e24 | + | 6.59048e24i | −0.351221 | + | 0.346326i | ||||
\(943\) | 1.34729e25 | 0.701636 | ||||||||
\(944\) | −1.96974e22 | + | 7.01486e23i | −0.00101659 | + | 0.0362040i | ||||
\(945\) | −9.38735e24 | −0.480145 | ||||||||
\(946\) | −7.88988e24 | + | 7.77991e24i | −0.399941 | + | 0.394366i | ||||
\(947\) | 8.59929e24i | 0.432004i | 0.976393 | + | 0.216002i | \(0.0693018\pi\) | ||||
−0.976393 | + | 0.216002i | \(0.930698\pi\) | |||||||
\(948\) | 1.58355e25 | + | 2.22283e23i | 0.788428 | + | 0.0110671i | ||||
\(949\) | − | 3.24521e25i | − | 1.60133i | ||||||
\(950\) | −9.66041e24 | − | 9.79696e24i | −0.472438 | − | 0.479116i | ||||
\(951\) | 1.37208e24 | 0.0665037 | ||||||||
\(952\) | −1.46290e25 | − | 1.52583e25i | −0.702750 | − | 0.732982i | ||||
\(953\) | −2.86348e25 | −1.36334 | −0.681671 | − | 0.731659i | \(-0.738747\pi\) | ||||
−0.681671 | + | 0.731659i | \(0.738747\pi\) | |||||||
\(954\) | 1.25732e25 | + | 1.27510e25i | 0.593316 | + | 0.601703i | ||||
\(955\) | − | 7.78764e24i | − | 0.364231i | ||||||
\(956\) | 2.26808e23 | − | 1.61579e25i | 0.0105140 | − | 0.749018i | ||||
\(957\) | − | 3.29739e23i | − | 0.0151502i | ||||||
\(958\) | −1.79055e23 | + | 1.76559e23i | −0.00815415 | + | 0.00804049i | ||||
\(959\) | 2.78805e25 | 1.25847 | ||||||||
\(960\) | 2.40514e23 | − | 5.70843e24i | 0.0107605 | − | 0.255394i | ||||
\(961\) | −8.96632e24 | −0.397617 | ||||||||
\(962\) | 2.40306e25 | − | 2.36957e25i | 1.05627 | − | 1.04155i | ||||
\(963\) | − | 3.04289e25i | − | 1.32576i | ||||||
\(964\) | −4.92691e23 | + | 3.50995e25i | −0.0212775 | + | 1.51582i | ||||
\(965\) | 1.36006e25i | 0.582206i | ||||||||
\(966\) | 7.09449e24 | + | 7.19478e24i | 0.301034 | + | 0.305289i | ||||
\(967\) | −2.59564e25 | −1.09174 | −0.545870 | − | 0.837870i | \(-0.683801\pi\) | ||||
−0.545870 | + | 0.837870i | \(0.683801\pi\) | |||||||
\(968\) | 1.46313e25 | + | 1.52607e25i | 0.610017 | + | 0.636260i | ||||
\(969\) | 1.06598e25 | 0.440554 | ||||||||
\(970\) | −9.52234e23 | − | 9.65694e23i | −0.0390107 | − | 0.0395622i | ||||
\(971\) | 3.57955e25i | 1.45367i | 0.686814 | + | 0.726833i | \(0.259009\pi\) | ||||
−0.686814 | + | 0.726833i | \(0.740991\pi\) | |||||||
\(972\) | 2.43959e25 | + | 3.42445e23i | 0.982095 | + | 0.0137856i | ||||
\(973\) | − | 2.76284e25i | − | 1.10254i | ||||||
\(974\) | −2.49841e25 | + | 2.46359e25i | −0.988355 | + | 0.974579i | ||||
\(975\) | −6.27221e24 | −0.245969 | ||||||||
\(976\) | −1.23372e24 | + | 4.39367e25i | −0.0479615 | + | 1.70806i | ||||
\(977\) | 2.92622e25 | 1.12773 | 0.563863 | − | 0.825869i | \(-0.309315\pi\) | ||||
0.563863 | + | 0.825869i | \(0.309315\pi\) | |||||||
\(978\) | −3.68741e24 | + | 3.63602e24i | −0.140877 | + | 0.138914i | ||||
\(979\) | 1.01707e25i | 0.385212i | ||||||||
\(980\) | 1.06050e24 | + | 1.48862e22i | 0.0398187 | + | 0.000558935i | ||||
\(981\) | − | 1.71216e25i | − | 0.637319i | ||||||
\(982\) | −3.54658e25 | − | 3.59671e25i | −1.30877 | − | 1.32727i | ||||
\(983\) | 8.30763e24 | 0.303929 | 0.151964 | − | 0.988386i | \(-0.451440\pi\) | ||||
0.151964 | + | 0.988386i | \(0.451440\pi\) | |||||||
\(984\) | 6.08583e24 | − | 5.83481e24i | 0.220730 | − | 0.211626i | ||||
\(985\) | −2.88374e25 | −1.03693 | ||||||||
\(986\) | −2.00338e24 | − | 2.03170e24i | −0.0714182 | − | 0.0724277i | ||||
\(987\) | 7.77240e24i | 0.274701i | ||||||||
\(988\) | −3.81775e23 | + | 2.71978e25i | −0.0133774 | + | 0.953015i | ||||
\(989\) | − | 4.58324e25i | − | 1.59222i | ||||||
\(990\) | −3.50334e24 | + | 3.45451e24i | −0.120666 | + | 0.118984i | ||||
\(991\) | 3.41708e25 | 1.16689 | 0.583443 | − | 0.812154i | \(-0.301705\pi\) | ||||
0.583443 | + | 0.812154i | \(0.301705\pi\) | |||||||
\(992\) | 1.67682e25 | − | 1.56309e25i | 0.567725 | − | 0.529217i | ||||
\(993\) | −1.02150e25 | −0.342903 | ||||||||
\(994\) | −4.46591e24 | + | 4.40366e24i | −0.148637 | + | 0.146565i | ||||
\(995\) | 3.98217e24i | 0.131408i | ||||||||
\(996\) | −3.28050e23 | + | 2.33704e25i | −0.0107333 | + | 0.764648i | ||||
\(997\) | 9.48702e24i | 0.307766i | 0.988089 | + | 0.153883i | \(0.0491779\pi\) | ||||
−0.988089 | + | 0.153883i | \(0.950822\pi\) | |||||||
\(998\) | 2.07981e24 | + | 2.10921e24i | 0.0668981 | + | 0.0678437i | ||||
\(999\) | −3.97695e25 | −1.26836 |
(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 | 8.18.b.a.5.4 | yes | 16 | |
3.2 | odd | 2 | 72.18.d.b.37.13 | 16 | |||
4.3 | odd | 2 | 32.18.b.a.17.6 | 16 | |||
8.3 | odd | 2 | 32.18.b.a.17.11 | 16 | |||
8.5 | even | 2 | inner | 8.18.b.a.5.3 | ✓ | 16 | |
24.5 | odd | 2 | 72.18.d.b.37.14 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.18.b.a.5.3 | ✓ | 16 | 8.5 | even | 2 | inner | |
8.18.b.a.5.4 | yes | 16 | 1.1 | even | 1 | trivial | |
32.18.b.a.17.6 | 16 | 4.3 | odd | 2 | |||
32.18.b.a.17.11 | 16 | 8.3 | odd | 2 | |||
72.18.d.b.37.13 | 16 | 3.2 | odd | 2 | |||
72.18.d.b.37.14 | 16 | 24.5 | odd | 2 |