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: | \( x^{16} - 7 x^{15} + 4022 x^{14} - 1102776 x^{13} - 373411968 x^{12} + 2100004864 x^{11} + \cdots + 12\!\cdots\!00 \) |
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 | 5.14 | ||
Root | \(156.321 - 75.9390i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.18.b.a.5.13 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 328.641 | + | 151.878i | 0.907752 | + | 0.419508i | ||||
\(3\) | − | 4248.51i | − | 0.373858i | −0.982373 | − | 0.186929i | \(-0.940147\pi\) | ||
0.982373 | − | 0.186929i | \(-0.0598534\pi\) | |||||||
\(4\) | 84938.1 | + | 99826.8i | 0.648026 | + | 0.761618i | ||||
\(5\) | 663971.i | 0.760158i | 0.924954 | + | 0.380079i | \(0.124103\pi\) | ||||
−0.924954 | + | 0.380079i | \(0.875897\pi\) | |||||||
\(6\) | 645256. | − | 1.39624e6i | 0.156836 | − | 0.339370i | ||||
\(7\) | −1.66742e7 | −1.09323 | −0.546615 | − | 0.837384i | \(-0.684084\pi\) | ||||
−0.546615 | + | 0.837384i | \(0.684084\pi\) | |||||||
\(8\) | 1.27527e7 | + | 4.57074e7i | 0.268742 | + | 0.963212i | ||||
\(9\) | 1.11090e8 | 0.860230 | ||||||||
\(10\) | −1.00843e8 | + | 2.18208e8i | −0.318892 | + | 0.690035i | ||||
\(11\) | 1.05479e9i | 1.48364i | 0.670600 | + | 0.741819i | \(0.266037\pi\) | ||||
−0.670600 | + | 0.741819i | \(0.733963\pi\) | |||||||
\(12\) | 4.24116e8 | − | 3.60861e8i | 0.284737 | − | 0.242270i | ||||
\(13\) | − | 9.19407e7i | − | 0.0312600i | −0.999878 | − | 0.0156300i | \(-0.995025\pi\) | ||
0.999878 | − | 0.0156300i | \(-0.00497539\pi\) | |||||||
\(14\) | −5.47982e9 | − | 2.53244e9i | −0.992381 | − | 0.458618i | ||||
\(15\) | 2.82089e9 | 0.284191 | ||||||||
\(16\) | −2.75091e9 | + | 1.69582e10i | −0.160124 | + | 0.987097i | ||||
\(17\) | −1.98326e10 | −0.689547 | −0.344773 | − | 0.938686i | \(-0.612044\pi\) | ||||
−0.344773 | + | 0.938686i | \(0.612044\pi\) | |||||||
\(18\) | 3.65088e10 | + | 1.68722e10i | 0.780876 | + | 0.360873i | ||||
\(19\) | 8.44846e10i | 1.14123i | 0.821219 | + | 0.570613i | \(0.193294\pi\) | ||||
−0.821219 | + | 0.570613i | \(0.806706\pi\) | |||||||
\(20\) | −6.62821e10 | + | 5.63964e10i | −0.578950 | + | 0.492602i | ||||
\(21\) | 7.08405e10i | 0.408712i | ||||||||
\(22\) | −1.60199e11 | + | 3.46647e11i | −0.622398 | + | 1.34677i | ||||
\(23\) | −2.72263e10 | −0.0724941 | −0.0362470 | − | 0.999343i | \(-0.511540\pi\) | ||||
−0.0362470 | + | 0.999343i | \(0.511540\pi\) | |||||||
\(24\) | 1.94189e11 | − | 5.41799e10i | 0.360104 | − | 0.100471i | ||||
\(25\) | 3.22082e11 | 0.422160 | ||||||||
\(26\) | 1.39638e10 | − | 3.02155e10i | 0.0131138 | − | 0.0283764i | ||||
\(27\) | − | 1.02062e12i | − | 0.695462i | ||||||
\(28\) | −1.41627e12 | − | 1.66453e12i | −0.708441 | − | 0.832623i | ||||
\(29\) | − | 3.75013e12i | − | 1.39208i | −0.718005 | − | 0.696038i | \(-0.754944\pi\) | ||
0.718005 | − | 0.696038i | \(-0.245056\pi\) | |||||||
\(30\) | 9.27061e11 | + | 4.28431e11i | 0.257975 | + | 0.119220i | ||||
\(31\) | 5.36921e12 | 1.13067 | 0.565336 | − | 0.824861i | \(-0.308747\pi\) | ||||
0.565336 | + | 0.824861i | \(0.308747\pi\) | |||||||
\(32\) | −3.47964e12 | + | 5.15536e12i | −0.559448 | + | 0.828866i | ||||
\(33\) | 4.48129e12 | 0.554669 | ||||||||
\(34\) | −6.51781e12 | − | 3.01214e12i | −0.625937 | − | 0.289270i | ||||
\(35\) | − | 1.10712e13i | − | 0.831027i | ||||||
\(36\) | 9.43580e12 | + | 1.10898e13i | 0.557452 | + | 0.655167i | ||||
\(37\) | − | 1.92294e13i | − | 0.900015i | −0.893025 | − | 0.450008i | \(-0.851421\pi\) | ||
0.893025 | − | 0.450008i | \(-0.148579\pi\) | |||||||
\(38\) | −1.28314e13 | + | 2.77651e13i | −0.478754 | + | 1.03595i | ||||
\(39\) | −3.90612e11 | −0.0116868 | ||||||||
\(40\) | −3.03484e13 | + | 8.46739e12i | −0.732194 | + | 0.204287i | ||||
\(41\) | 5.42400e13 | 1.06086 | 0.530429 | − | 0.847730i | \(-0.322031\pi\) | ||||
0.530429 | + | 0.847730i | \(0.322031\pi\) | |||||||
\(42\) | −1.07591e13 | + | 2.32811e13i | −0.171458 | + | 0.371009i | ||||
\(43\) | − | 3.96416e13i | − | 0.517213i | −0.965983 | − | 0.258607i | \(-0.916737\pi\) | ||
0.965983 | − | 0.258607i | \(-0.0832634\pi\) | |||||||
\(44\) | −1.05296e14 | + | 8.95918e13i | −1.12996 | + | 0.961436i | ||||
\(45\) | 7.37607e13i | 0.653911i | ||||||||
\(46\) | −8.94769e12 | − | 4.13508e12i | −0.0658066 | − | 0.0304118i | ||||
\(47\) | 4.48999e13 | 0.275051 | 0.137526 | − | 0.990498i | \(-0.456085\pi\) | ||||
0.137526 | + | 0.990498i | \(0.456085\pi\) | |||||||
\(48\) | 7.20471e13 | + | 1.16873e13i | 0.369034 | + | 0.0598636i | ||||
\(49\) | 4.53979e13 | 0.195150 | ||||||||
\(50\) | 1.05850e14 | + | 4.89172e13i | 0.383216 | + | 0.177099i | ||||
\(51\) | 8.42591e13i | 0.257792i | ||||||||
\(52\) | 9.17815e12 | − | 7.80927e12i | 0.0238082 | − | 0.0202573i | ||||
\(53\) | − | 7.81803e14i | − | 1.72485i | −0.506181 | − | 0.862427i | \(-0.668943\pi\) | ||
0.506181 | − | 0.862427i | \(-0.331057\pi\) | |||||||
\(54\) | 1.55010e14 | − | 3.35419e14i | 0.291752 | − | 0.631306i | ||||
\(55\) | −7.00349e14 | −1.12780 | ||||||||
\(56\) | −2.12640e14 | − | 7.62134e14i | −0.293797 | − | 1.05301i | ||||
\(57\) | 3.58934e14 | 0.426656 | ||||||||
\(58\) | 5.69562e14 | − | 1.23245e15i | 0.583987 | − | 1.26366i | ||||
\(59\) | 1.07092e15i | 0.949541i | 0.880110 | + | 0.474770i | \(0.157469\pi\) | ||||
−0.880110 | + | 0.474770i | \(0.842531\pi\) | |||||||
\(60\) | 2.39601e14 | + | 2.81600e14i | 0.184163 | + | 0.216445i | ||||
\(61\) | 1.92548e15i | 1.28599i | 0.765872 | + | 0.642993i | \(0.222308\pi\) | ||||
−0.765872 | + | 0.642993i | \(0.777692\pi\) | |||||||
\(62\) | 1.76454e15 | + | 8.15466e14i | 1.02637 | + | 0.474325i | ||||
\(63\) | −1.85234e15 | −0.940429 | ||||||||
\(64\) | −1.92654e15 | + | 1.16578e15i | −0.855555 | + | 0.517711i | ||||
\(65\) | 6.10460e13 | 0.0237626 | ||||||||
\(66\) | 1.47274e15 | + | 6.80609e14i | 0.503502 | + | 0.232688i | ||||
\(67\) | 3.68678e15i | 1.10920i | 0.832116 | + | 0.554602i | \(0.187129\pi\) | ||||
−0.832116 | + | 0.554602i | \(0.812871\pi\) | |||||||
\(68\) | −1.68454e15 | − | 1.97982e15i | −0.446845 | − | 0.525171i | ||||
\(69\) | 1.15671e14i | 0.0271025i | ||||||||
\(70\) | 1.68147e15 | − | 3.63844e15i | 0.348622 | − | 0.754366i | ||||
\(71\) | −1.02421e16 | −1.88232 | −0.941162 | − | 0.337957i | \(-0.890264\pi\) | ||||
−0.941162 | + | 0.337957i | \(0.890264\pi\) | |||||||
\(72\) | 1.41670e15 | + | 5.07765e15i | 0.231180 | + | 0.828584i | ||||
\(73\) | 1.25847e16 | 1.82641 | 0.913204 | − | 0.407502i | \(-0.133600\pi\) | ||||
0.913204 | + | 0.407502i | \(0.133600\pi\) | |||||||
\(74\) | 2.92052e15 | − | 6.31956e15i | 0.377564 | − | 0.816991i | ||||
\(75\) | − | 1.36837e15i | − | 0.157828i | ||||||
\(76\) | −8.43383e15 | + | 7.17596e15i | −0.869179 | + | 0.739545i | ||||
\(77\) | − | 1.75877e16i | − | 1.62196i | ||||||
\(78\) | −1.28371e14 | − | 5.93253e13i | −0.0106087 | − | 0.00490271i | ||||
\(79\) | 3.24102e15 | 0.240354 | 0.120177 | − | 0.992752i | \(-0.461654\pi\) | ||||
0.120177 | + | 0.992752i | \(0.461654\pi\) | |||||||
\(80\) | −1.12597e16 | − | 1.82652e15i | −0.750350 | − | 0.121720i | ||||
\(81\) | 1.00101e16 | 0.600227 | ||||||||
\(82\) | 1.78255e16 | + | 8.23787e15i | 0.962995 | + | 0.445038i | ||||
\(83\) | − | 4.28316e15i | − | 0.208737i | −0.994539 | − | 0.104369i | \(-0.966718\pi\) | ||
0.994539 | − | 0.104369i | \(-0.0332822\pi\) | |||||||
\(84\) | −7.07178e15 | + | 6.01706e15i | −0.311283 | + | 0.264856i | ||||
\(85\) | − | 1.31683e16i | − | 0.524165i | ||||||
\(86\) | 6.02070e15 | − | 1.30279e16i | 0.216975 | − | 0.469501i | ||||
\(87\) | −1.59325e16 | −0.520439 | ||||||||
\(88\) | −4.82117e16 | + | 1.34514e16i | −1.42906 | + | 0.398716i | ||||
\(89\) | 6.95255e16 | 1.87210 | 0.936050 | − | 0.351868i | \(-0.114453\pi\) | ||||
0.936050 | + | 0.351868i | \(0.114453\pi\) | |||||||
\(90\) | −1.12026e16 | + | 2.42408e16i | −0.274321 | + | 0.593589i | ||||
\(91\) | 1.53304e15i | 0.0341744i | ||||||||
\(92\) | −2.31255e15 | − | 2.71792e15i | −0.0469781 | − | 0.0552128i | ||||
\(93\) | − | 2.28112e16i | − | 0.422710i | ||||||
\(94\) | 1.47560e16 | + | 6.81931e15i | 0.249678 | + | 0.115386i | ||||
\(95\) | −5.60953e16 | −0.867513 | ||||||||
\(96\) | 2.19026e16 | + | 1.47833e16i | 0.309878 | + | 0.209154i | ||||
\(97\) | −7.74223e16 | −1.00301 | −0.501507 | − | 0.865154i | \(-0.667221\pi\) | ||||
−0.501507 | + | 0.865154i | \(0.667221\pi\) | |||||||
\(98\) | 1.49196e16 | + | 6.89495e15i | 0.177148 | + | 0.0818671i | ||||
\(99\) | 1.17177e17i | 1.27627i | ||||||||
\(100\) | 2.73571e16 | + | 3.21524e16i | 0.273571 | + | 0.321524i | ||||
\(101\) | 8.38662e16i | 0.770646i | 0.922782 | + | 0.385323i | \(0.125910\pi\) | ||||
−0.922782 | + | 0.385323i | \(0.874090\pi\) | |||||||
\(102\) | −1.27971e16 | + | 2.76910e16i | −0.108146 | + | 0.234012i | ||||
\(103\) | 8.10218e16 | 0.630210 | 0.315105 | − | 0.949057i | \(-0.397960\pi\) | ||||
0.315105 | + | 0.949057i | \(0.397960\pi\) | |||||||
\(104\) | 4.20238e15 | − | 1.17249e15i | 0.0301101 | − | 0.00840089i | ||||
\(105\) | −4.70360e16 | −0.310686 | ||||||||
\(106\) | 1.18739e17 | − | 2.56933e17i | 0.723590 | − | 1.56574i | ||||
\(107\) | − | 1.60731e17i | − | 0.904351i | −0.891929 | − | 0.452175i | \(-0.850648\pi\) | ||
0.891929 | − | 0.452175i | \(-0.149352\pi\) | |||||||
\(108\) | 1.01885e17 | − | 8.66897e16i | 0.529676 | − | 0.450677i | ||||
\(109\) | 1.05482e17i | 0.507053i | 0.967328 | + | 0.253526i | \(0.0815905\pi\) | ||||
−0.967328 | + | 0.253526i | \(0.918410\pi\) | |||||||
\(110\) | −2.30164e17 | − | 1.06368e17i | −1.02376 | − | 0.473121i | ||||
\(111\) | −8.16962e16 | −0.336478 | ||||||||
\(112\) | 4.58692e16 | − | 2.82764e17i | 0.175052 | − | 1.07912i | ||||
\(113\) | −1.30124e17 | −0.460458 | −0.230229 | − | 0.973136i | \(-0.573948\pi\) | ||||
−0.230229 | + | 0.973136i | \(0.573948\pi\) | |||||||
\(114\) | 1.17961e17 | + | 5.45142e16i | 0.387298 | + | 0.178986i | ||||
\(115\) | − | 1.80775e16i | − | 0.0551069i | ||||||
\(116\) | 3.74363e17 | − | 3.18529e17i | 1.06023 | − | 0.902102i | ||||
\(117\) | − | 1.02137e16i | − | 0.0268908i | ||||||
\(118\) | −1.62649e17 | + | 3.51947e17i | −0.398340 | + | 0.861947i | ||||
\(119\) | 3.30692e17 | 0.753833 | ||||||||
\(120\) | 3.59738e16 | + | 1.28936e17i | 0.0763741 | + | 0.273736i | ||||
\(121\) | −6.07133e17 | −1.20118 | ||||||||
\(122\) | −2.92439e17 | + | 6.32794e17i | −0.539481 | + | 1.16736i | ||||
\(123\) | − | 2.30439e17i | − | 0.396610i | ||||||
\(124\) | 4.56051e17 | + | 5.35991e17i | 0.732705 | + | 0.861139i | ||||
\(125\) | 7.20423e17i | 1.08107i | ||||||||
\(126\) | −6.08755e17 | − | 2.81330e17i | −0.853676 | − | 0.394517i | ||||
\(127\) | 1.12618e18 | 1.47664 | 0.738322 | − | 0.674448i | \(-0.235619\pi\) | ||||
0.738322 | + | 0.674448i | \(0.235619\pi\) | |||||||
\(128\) | −8.10197e17 | + | 9.05251e16i | −0.993816 | + | 0.111041i | ||||
\(129\) | −1.68418e17 | −0.193364 | ||||||||
\(130\) | 2.00622e16 | + | 9.27154e15i | 0.0215705 | + | 0.00996859i | ||||
\(131\) | 3.73512e17i | 0.376269i | 0.982143 | + | 0.188134i | \(0.0602440\pi\) | ||||
−0.982143 | + | 0.188134i | \(0.939756\pi\) | |||||||
\(132\) | 3.80632e17 | + | 4.47352e17i | 0.359440 | + | 0.422446i | ||||
\(133\) | − | 1.40871e18i | − | 1.24762i | ||||||
\(134\) | −5.59941e17 | + | 1.21163e18i | −0.465320 | + | 1.00688i | ||||
\(135\) | 6.77664e17 | 0.528661 | ||||||||
\(136\) | −2.52918e17 | − | 9.06497e17i | −0.185310 | − | 0.664180i | ||||
\(137\) | −3.64355e17 | −0.250842 | −0.125421 | − | 0.992104i | \(-0.540028\pi\) | ||||
−0.125421 | + | 0.992104i | \(0.540028\pi\) | |||||||
\(138\) | −1.75680e16 | + | 3.80144e16i | −0.0113697 | + | 0.0246023i | ||||
\(139\) | − | 2.51151e18i | − | 1.52866i | −0.644828 | − | 0.764328i | \(-0.723071\pi\) | ||
0.644828 | − | 0.764328i | \(-0.276929\pi\) | |||||||
\(140\) | 1.10520e18 | − | 9.40364e17i | 0.632925 | − | 0.538527i | ||||
\(141\) | − | 1.90758e17i | − | 0.102830i | ||||||
\(142\) | −3.36598e18 | − | 1.55555e18i | −1.70868 | − | 0.789649i | ||||
\(143\) | 9.69781e16 | 0.0463786 | ||||||||
\(144\) | −3.05599e17 | + | 1.88389e18i | −0.137743 | + | 0.849131i | ||||
\(145\) | 2.48998e18 | 1.05820 | ||||||||
\(146\) | 4.13585e18 | + | 1.91134e18i | 1.65793 | + | 0.766193i | ||||
\(147\) | − | 1.92874e17i | − | 0.0729585i | ||||||
\(148\) | 1.91960e18 | − | 1.63330e18i | 0.685468 | − | 0.583234i | ||||
\(149\) | 2.83942e18i | 0.957517i | 0.877947 | + | 0.478758i | \(0.158913\pi\) | ||||
−0.877947 | + | 0.478758i | \(0.841087\pi\) | |||||||
\(150\) | 2.07826e17 | − | 4.49703e17i | 0.0662100 | − | 0.143268i | ||||
\(151\) | −2.74195e18 | −0.825574 | −0.412787 | − | 0.910828i | \(-0.635445\pi\) | ||||
−0.412787 | + | 0.910828i | \(0.635445\pi\) | |||||||
\(152\) | −3.86157e18 | + | 1.07740e18i | −1.09924 | + | 0.306696i | ||||
\(153\) | −2.20321e18 | −0.593169 | ||||||||
\(154\) | 2.67119e18 | − | 5.78006e18i | 0.680423 | − | 1.47233i | ||||
\(155\) | 3.56500e18i | 0.859489i | ||||||||
\(156\) | −3.31778e16 | − | 3.89935e16i | −0.00757336 | − | 0.00890088i | ||||
\(157\) | − | 3.26134e18i | − | 0.705096i | −0.935794 | − | 0.352548i | \(-0.885315\pi\) | ||
0.935794 | − | 0.352548i | \(-0.114685\pi\) | |||||||
\(158\) | 1.06513e18 | + | 4.92239e17i | 0.218182 | + | 0.100830i | ||||
\(159\) | −3.32150e18 | −0.644850 | ||||||||
\(160\) | −3.42301e18 | − | 2.31038e18i | −0.630069 | − | 0.425269i | ||||
\(161\) | 4.53977e17 | 0.0792526 | ||||||||
\(162\) | 3.28973e18 | + | 1.52031e18i | 0.544857 | + | 0.251800i | ||||
\(163\) | 7.80461e18i | 1.22675i | 0.789791 | + | 0.613376i | \(0.210189\pi\) | ||||
−0.789791 | + | 0.613376i | \(0.789811\pi\) | |||||||
\(164\) | 4.60704e18 | + | 5.41461e18i | 0.687463 | + | 0.807968i | ||||
\(165\) | 2.97544e18i | 0.421636i | ||||||||
\(166\) | 6.50518e17 | − | 1.40762e18i | 0.0875670 | − | 0.189482i | ||||
\(167\) | −8.54007e18 | −1.09237 | −0.546187 | − | 0.837663i | \(-0.683921\pi\) | ||||
−0.546187 | + | 0.837663i | \(0.683921\pi\) | |||||||
\(168\) | −3.23794e18 | + | 9.03405e17i | −0.393677 | + | 0.109838i | ||||
\(169\) | 8.64196e18 | 0.999023 | ||||||||
\(170\) | 1.99997e18 | − | 4.32764e18i | 0.219891 | − | 0.475811i | ||||
\(171\) | 9.38542e18i | 0.981718i | ||||||||
\(172\) | 3.95730e18 | − | 3.36709e18i | 0.393919 | − | 0.335168i | ||||
\(173\) | 2.07391e18i | 0.196516i | 0.995161 | + | 0.0982581i | \(0.0313271\pi\) | ||||
−0.995161 | + | 0.0982581i | \(0.968673\pi\) | |||||||
\(174\) | −5.23607e18 | − | 2.41979e18i | −0.472429 | − | 0.218328i | ||||
\(175\) | −5.37046e18 | −0.461517 | ||||||||
\(176\) | −1.78873e19 | − | 2.90163e18i | −1.46449 | − | 0.237566i | ||||
\(177\) | 4.54981e18 | 0.354993 | ||||||||
\(178\) | 2.28489e19 | + | 1.05594e19i | 1.69940 | + | 0.785360i | ||||
\(179\) | − | 1.67289e19i | − | 1.18636i | −0.805071 | − | 0.593179i | \(-0.797873\pi\) | ||
0.805071 | − | 0.593179i | \(-0.202127\pi\) | |||||||
\(180\) | −7.36329e18 | + | 6.26509e18i | −0.498030 | + | 0.423752i | ||||
\(181\) | − | 3.02297e19i | − | 1.95059i | −0.220907 | − | 0.975295i | \(-0.570902\pi\) | ||
0.220907 | − | 0.975295i | \(-0.429098\pi\) | |||||||
\(182\) | −2.32835e17 | + | 5.03819e17i | −0.0143364 | + | 0.0310219i | ||||
\(183\) | 8.18045e18 | 0.480776 | ||||||||
\(184\) | −3.47208e17 | − | 1.24445e18i | −0.0194822 | − | 0.0698272i | ||||
\(185\) | 1.27677e19 | 0.684154 | ||||||||
\(186\) | 3.46452e18 | − | 7.49669e18i | 0.177330 | − | 0.383716i | ||||
\(187\) | − | 2.09192e19i | − | 1.02304i | ||||||
\(188\) | 3.81371e18 | + | 4.48221e18i | 0.178240 | + | 0.209484i | ||||
\(189\) | 1.70180e19i | 0.760299i | ||||||||
\(190\) | −1.84352e19 | − | 8.51965e18i | −0.787486 | − | 0.363928i | ||||
\(191\) | 1.22397e18 | 0.0500019 | 0.0250009 | − | 0.999687i | \(-0.492041\pi\) | ||||
0.0250009 | + | 0.999687i | \(0.492041\pi\) | |||||||
\(192\) | 4.95284e18 | + | 8.18493e18i | 0.193550 | + | 0.319856i | ||||
\(193\) | −6.70836e18 | −0.250830 | −0.125415 | − | 0.992104i | \(-0.540026\pi\) | ||||
−0.125415 | + | 0.992104i | \(0.540026\pi\) | |||||||
\(194\) | −2.54442e19 | − | 1.17588e19i | −0.910487 | − | 0.420772i | ||||
\(195\) | − | 2.59355e17i | − | 0.00888382i | ||||||
\(196\) | 3.85601e18 | + | 4.53193e18i | 0.126463 | + | 0.148630i | ||||
\(197\) | − | 1.35900e19i | − | 0.426832i | −0.976961 | − | 0.213416i | \(-0.931541\pi\) | ||
0.976961 | − | 0.213416i | \(-0.0684590\pi\) | |||||||
\(198\) | −1.77966e19 | + | 3.85091e19i | −0.535405 | + | 1.15854i | ||||
\(199\) | 2.94272e19 | 0.848198 | 0.424099 | − | 0.905616i | \(-0.360591\pi\) | ||||
0.424099 | + | 0.905616i | \(0.360591\pi\) | |||||||
\(200\) | 4.10741e18 | + | 1.47216e19i | 0.113452 | + | 0.406629i | ||||
\(201\) | 1.56633e19 | 0.414685 | ||||||||
\(202\) | −1.27374e19 | + | 2.75619e19i | −0.323292 | + | 0.699556i | ||||
\(203\) | 6.25303e19i | 1.52186i | ||||||||
\(204\) | −8.41131e18 | + | 7.15681e18i | −0.196339 | + | 0.167056i | ||||
\(205\) | 3.60138e19i | 0.806419i | ||||||||
\(206\) | 2.66271e19 | + | 1.23054e19i | 0.572074 | + | 0.264378i | ||||
\(207\) | −3.02458e18 | −0.0623616 | ||||||||
\(208\) | 1.55915e18 | + | 2.52921e17i | 0.0308567 | + | 0.00500548i | ||||
\(209\) | −8.91134e19 | −1.69317 | ||||||||
\(210\) | −1.54580e19 | − | 7.14374e18i | −0.282026 | − | 0.130335i | ||||
\(211\) | − | 7.34029e19i | − | 1.28621i | −0.765777 | − | 0.643106i | \(-0.777645\pi\) | ||
0.765777 | − | 0.643106i | \(-0.222355\pi\) | |||||||
\(212\) | 7.80449e19 | − | 6.64049e19i | 1.31368 | − | 1.11775i | ||||
\(213\) | 4.35138e19i | 0.703721i | ||||||||
\(214\) | 2.44115e19 | − | 5.28228e19i | 0.379382 | − | 0.820926i | ||||
\(215\) | 2.63209e19 | 0.393164 | ||||||||
\(216\) | 4.66500e19 | − | 1.30157e19i | 0.669877 | − | 0.186900i | ||||
\(217\) | −8.95273e19 | −1.23608 | ||||||||
\(218\) | −1.60204e19 | + | 3.46657e19i | −0.212713 | + | 0.460278i | ||||
\(219\) | − | 5.34662e19i | − | 0.682817i | ||||||
\(220\) | −5.94863e19 | − | 6.99136e19i | −0.730843 | − | 0.858952i | ||||
\(221\) | 1.82342e18i | 0.0215553i | ||||||||
\(222\) | −2.68487e19 | − | 1.24079e19i | −0.305438 | − | 0.141155i | ||||
\(223\) | 7.73683e19 | 0.847172 | 0.423586 | − | 0.905856i | \(-0.360771\pi\) | ||||
0.423586 | + | 0.905856i | \(0.360771\pi\) | |||||||
\(224\) | 5.80202e19 | − | 8.59614e19i | 0.611605 | − | 0.906140i | ||||
\(225\) | 3.57802e19 | 0.363155 | ||||||||
\(226\) | −4.27641e19 | − | 1.97630e19i | −0.417982 | − | 0.193166i | ||||
\(227\) | 1.21923e20i | 1.14780i | 0.818924 | + | 0.573902i | \(0.194571\pi\) | ||||
−0.818924 | + | 0.573902i | \(0.805429\pi\) | |||||||
\(228\) | 3.04872e19 | + | 3.58312e19i | 0.276485 | + | 0.324949i | ||||
\(229\) | 1.42038e19i | 0.124109i | 0.998073 | + | 0.0620543i | \(0.0197652\pi\) | ||||
−0.998073 | + | 0.0620543i | \(0.980235\pi\) | |||||||
\(230\) | 2.74557e18 | − | 5.94101e18i | 0.0231178 | − | 0.0500234i | ||||
\(231\) | −7.47218e19 | −0.606381 | ||||||||
\(232\) | 1.71409e20 | − | 4.78241e19i | 1.34087 | − | 0.374110i | ||||
\(233\) | −7.02873e19 | −0.530092 | −0.265046 | − | 0.964236i | \(-0.585387\pi\) | ||||
−0.265046 | + | 0.964236i | \(0.585387\pi\) | |||||||
\(234\) | 1.55124e18 | − | 3.35665e18i | 0.0112809 | − | 0.0244102i | ||||
\(235\) | 2.98122e19i | 0.209082i | ||||||||
\(236\) | −1.06906e20 | + | 9.09616e19i | −0.723187 | + | 0.615327i | ||||
\(237\) | − | 1.37695e19i | − | 0.0898581i | ||||||
\(238\) | 1.08679e20 | + | 5.02249e19i | 0.684293 | + | 0.316239i | ||||
\(239\) | 4.12244e19 | 0.250480 | 0.125240 | − | 0.992126i | \(-0.460030\pi\) | ||||
0.125240 | + | 0.992126i | \(0.460030\pi\) | |||||||
\(240\) | −7.76001e18 | + | 4.78372e19i | −0.0455058 | + | 0.280524i | ||||
\(241\) | 9.34265e19 | 0.528841 | 0.264420 | − | 0.964408i | \(-0.414819\pi\) | ||||
0.264420 | + | 0.964408i | \(0.414819\pi\) | |||||||
\(242\) | −1.99529e20 | − | 9.22102e19i | −1.09037 | − | 0.503904i | ||||
\(243\) | − | 1.74331e20i | − | 0.919861i | ||||||
\(244\) | −1.92215e20 | + | 1.63547e20i | −0.979430 | + | 0.833353i | ||||
\(245\) | 3.01429e19i | 0.148345i | ||||||||
\(246\) | 3.49987e19 | − | 7.57319e19i | 0.166381 | − | 0.360023i | ||||
\(247\) | 7.76758e18 | 0.0356748 | ||||||||
\(248\) | 6.84717e19 | + | 2.45413e20i | 0.303859 | + | 1.08908i | ||||
\(249\) | −1.81971e19 | −0.0780381 | ||||||||
\(250\) | −1.09416e20 | + | 2.36761e20i | −0.453516 | + | 0.981340i | ||||
\(251\) | − | 8.23914e19i | − | 0.330107i | −0.986285 | − | 0.165054i | \(-0.947220\pi\) | ||
0.986285 | − | 0.165054i | \(-0.0527797\pi\) | |||||||
\(252\) | −1.57334e20 | − | 1.84913e20i | −0.609423 | − | 0.716248i | ||||
\(253\) | − | 2.87180e19i | − | 0.107555i | ||||||
\(254\) | 3.70109e20 | + | 1.71042e20i | 1.34043 | + | 0.619464i | ||||
\(255\) | −5.59456e19 | −0.195963 | ||||||||
\(256\) | −2.80013e20 | − | 9.33009e19i | −0.948721 | − | 0.316116i | ||||
\(257\) | 3.96731e20 | 1.30036 | 0.650182 | − | 0.759779i | \(-0.274693\pi\) | ||||
0.650182 | + | 0.759779i | \(0.274693\pi\) | |||||||
\(258\) | −5.53491e19 | − | 2.55790e19i | −0.175527 | − | 0.0811178i | ||||
\(259\) | 3.20634e20i | 0.983923i | ||||||||
\(260\) | 5.18513e18 | + | 6.09402e18i | 0.0153988 | + | 0.0180980i | ||||
\(261\) | − | 4.16603e20i | − | 1.19751i | ||||||
\(262\) | −5.67282e19 | + | 1.22751e20i | −0.157848 | + | 0.341559i | ||||
\(263\) | −3.01079e20 | −0.811066 | −0.405533 | − | 0.914080i | \(-0.632914\pi\) | ||||
−0.405533 | + | 0.914080i | \(0.632914\pi\) | |||||||
\(264\) | 5.71483e19 | + | 2.04828e20i | 0.149063 | + | 0.534264i | ||||
\(265\) | 5.19094e20 | 1.31116 | ||||||||
\(266\) | 2.13952e20 | − | 4.62961e20i | 0.523387 | − | 1.13253i | ||||
\(267\) | − | 2.95380e20i | − | 0.699899i | ||||||
\(268\) | −3.68039e20 | + | 3.13148e20i | −0.844790 | + | 0.718793i | ||||
\(269\) | − | 7.99834e19i | − | 0.177871i | −0.996037 | − | 0.0889356i | \(-0.971653\pi\) | ||
0.996037 | − | 0.0889356i | \(-0.0283465\pi\) | |||||||
\(270\) | 2.22708e20 | + | 1.02922e20i | 0.479893 | + | 0.221777i | ||||
\(271\) | −3.82151e20 | −0.797986 | −0.398993 | − | 0.916954i | \(-0.630640\pi\) | ||||
−0.398993 | + | 0.916954i | \(0.630640\pi\) | |||||||
\(272\) | 5.45577e19 | − | 3.36325e20i | 0.110413 | − | 0.680650i | ||||
\(273\) | 6.51313e18 | 0.0127764 | ||||||||
\(274\) | −1.19742e20 | − | 5.53375e19i | −0.227702 | − | 0.105230i | ||||
\(275\) | 3.39729e20i | 0.626332i | ||||||||
\(276\) | −1.15471e19 | + | 9.82491e18i | −0.0206417 | + | 0.0175631i | ||||
\(277\) | − | 3.87625e20i | − | 0.671945i | −0.941872 | − | 0.335972i | \(-0.890935\pi\) | ||
0.941872 | − | 0.335972i | \(-0.109065\pi\) | |||||||
\(278\) | 3.81444e20 | − | 8.25387e20i | 0.641283 | − | 1.38764i | ||||
\(279\) | 5.96467e20 | 0.972638 | ||||||||
\(280\) | 5.06035e20 | − | 1.41187e20i | 0.800455 | − | 0.223332i | ||||
\(281\) | −5.68349e20 | −0.872190 | −0.436095 | − | 0.899901i | \(-0.643639\pi\) | ||||
−0.436095 | + | 0.899901i | \(0.643639\pi\) | |||||||
\(282\) | 2.89719e19 | − | 6.26909e19i | 0.0431380 | − | 0.0933441i | ||||
\(283\) | 4.50897e20i | 0.651467i | 0.945462 | + | 0.325734i | \(0.105611\pi\) | ||||
−0.945462 | + | 0.325734i | \(0.894389\pi\) | |||||||
\(284\) | −8.69947e20 | − | 1.02244e21i | −1.21979 | − | 1.43361i | ||||
\(285\) | 2.38322e20i | 0.324326i | ||||||||
\(286\) | 3.18710e19 | + | 1.47288e19i | 0.0421002 | + | 0.0194562i | ||||
\(287\) | −9.04408e20 | −1.15976 | ||||||||
\(288\) | −3.86554e20 | + | 5.72710e20i | −0.481254 | + | 0.713015i | ||||
\(289\) | −4.33908e20 | −0.524525 | ||||||||
\(290\) | 8.18309e20 | + | 3.78173e20i | 0.960581 | + | 0.443923i | ||||
\(291\) | 3.28930e20i | 0.374984i | ||||||||
\(292\) | 1.06892e21 | + | 1.25629e21i | 1.18356 | + | 1.39103i | ||||
\(293\) | 1.51002e21i | 1.62408i | 0.583602 | + | 0.812040i | \(0.301643\pi\) | ||||
−0.583602 | + | 0.812040i | \(0.698357\pi\) | |||||||
\(294\) | 2.92933e19 | − | 6.33863e19i | 0.0306067 | − | 0.0662282i | ||||
\(295\) | −7.11057e20 | −0.721801 | ||||||||
\(296\) | 8.78924e20 | − | 2.45225e20i | 0.866906 | − | 0.241872i | ||||
\(297\) | 1.07654e21 | 1.03181 | ||||||||
\(298\) | −4.31246e20 | + | 9.33150e20i | −0.401686 | + | 0.869187i | ||||
\(299\) | 2.50321e18i | 0.00226617i | ||||||||
\(300\) | 1.36600e20 | − | 1.16227e20i | 0.120204 | − | 0.102276i | ||||
\(301\) | 6.60992e20i | 0.565433i | ||||||||
\(302\) | −9.01119e20 | − | 4.16443e20i | −0.749416 | − | 0.346335i | ||||
\(303\) | 3.56307e20 | 0.288112 | ||||||||
\(304\) | −1.43271e21 | − | 2.32409e20i | −1.12650 | − | 0.182738i | ||||
\(305\) | −1.27847e21 | −0.977553 | ||||||||
\(306\) | −7.24065e20 | − | 3.34619e20i | −0.538450 | − | 0.248839i | ||||
\(307\) | − | 7.15201e20i | − | 0.517311i | −0.965970 | − | 0.258655i | \(-0.916721\pi\) | ||
0.965970 | − | 0.258655i | \(-0.0832794\pi\) | |||||||
\(308\) | 1.75573e21 | − | 1.49387e21i | 1.23531 | − | 1.05107i | ||||
\(309\) | − | 3.44222e20i | − | 0.235609i | ||||||
\(310\) | −5.41445e20 | + | 1.17161e21i | −0.360562 | + | 0.780202i | ||||
\(311\) | 1.55199e21 | 1.00560 | 0.502801 | − | 0.864402i | \(-0.332303\pi\) | ||||
0.502801 | + | 0.864402i | \(0.332303\pi\) | |||||||
\(312\) | −4.98134e18 | − | 1.78539e19i | −0.00314074 | − | 0.0112569i | ||||
\(313\) | −7.03438e20 | −0.431617 | −0.215809 | − | 0.976436i | \(-0.569239\pi\) | ||||
−0.215809 | + | 0.976436i | \(0.569239\pi\) | |||||||
\(314\) | 4.95325e20 | − | 1.07181e21i | 0.295793 | − | 0.640052i | ||||
\(315\) | − | 1.22990e21i | − | 0.714875i | ||||||
\(316\) | 2.75286e20 | + | 3.23540e20i | 0.155756 | + | 0.183058i | ||||
\(317\) | − | 2.05646e21i | − | 1.13270i | −0.824163 | − | 0.566352i | \(-0.808354\pi\) | ||
0.824163 | − | 0.566352i | \(-0.191646\pi\) | |||||||
\(318\) | −1.09158e21 | − | 5.04463e20i | −0.585364 | − | 0.270520i | ||||
\(319\) | 3.95559e21 | 2.06534 | ||||||||
\(320\) | −7.74046e20 | − | 1.27917e21i | −0.393543 | − | 0.650357i | ||||
\(321\) | −6.82867e20 | −0.338099 | ||||||||
\(322\) | 1.49195e20 | + | 6.89491e19i | 0.0719417 | + | 0.0332471i | ||||
\(323\) | − | 1.67555e21i | − | 0.786929i | ||||||
\(324\) | 8.50238e20 | + | 9.99275e20i | 0.388963 | + | 0.457143i | ||||
\(325\) | − | 2.96125e19i | − | 0.0131967i | ||||||
\(326\) | −1.18535e21 | + | 2.56492e21i | −0.514632 | + | 1.11359i | ||||
\(327\) | 4.48142e20 | 0.189566 | ||||||||
\(328\) | 6.91704e20 | + | 2.47917e21i | 0.285097 | + | 1.02183i | ||||
\(329\) | −7.48669e20 | −0.300694 | ||||||||
\(330\) | −4.51905e20 | + | 9.77853e20i | −0.176880 | + | 0.382741i | ||||
\(331\) | − | 7.03264e20i | − | 0.268275i | −0.990963 | − | 0.134138i | \(-0.957174\pi\) | ||
0.990963 | − | 0.134138i | \(-0.0428264\pi\) | |||||||
\(332\) | 4.27574e20 | − | 3.63803e20i | 0.158978 | − | 0.135267i | ||||
\(333\) | − | 2.13619e21i | − | 0.774221i | ||||||
\(334\) | −2.80662e21 | − | 1.29705e21i | −0.991605 | − | 0.458260i | ||||
\(335\) | −2.44791e21 | −0.843170 | ||||||||
\(336\) | −1.20133e21 | − | 1.94876e20i | −0.403439 | − | 0.0654446i | ||||
\(337\) | 8.84366e20 | 0.289586 | 0.144793 | − | 0.989462i | \(-0.453748\pi\) | ||||
0.144793 | + | 0.989462i | \(0.453748\pi\) | |||||||
\(338\) | 2.84011e21 | + | 1.31252e21i | 0.906865 | + | 0.419098i | ||||
\(339\) | 5.52833e20i | 0.172146i | ||||||||
\(340\) | 1.31455e21 | − | 1.11849e21i | 0.399213 | − | 0.339672i | ||||
\(341\) | 5.66339e21i | 1.67751i | ||||||||
\(342\) | −1.42544e21 | + | 3.08444e21i | −0.411838 | + | 0.891156i | ||||
\(343\) | 3.12195e21 | 0.879885 | ||||||||
\(344\) | 1.81192e21 | − | 5.05536e20i | 0.498186 | − | 0.138997i | ||||
\(345\) | −7.68024e19 | −0.0206022 | ||||||||
\(346\) | −3.14982e20 | + | 6.81573e20i | −0.0824401 | + | 0.178388i | ||||
\(347\) | 5.48605e21i | 1.40107i | 0.713620 | + | 0.700533i | \(0.247055\pi\) | ||||
−0.713620 | + | 0.700533i | \(0.752945\pi\) | |||||||
\(348\) | −1.35327e21 | − | 1.59049e21i | −0.337258 | − | 0.396375i | ||||
\(349\) | − | 2.09596e19i | − | 0.00509762i | −0.999997 | − | 0.00254881i | \(-0.999189\pi\) | ||
0.999997 | − | 0.00254881i | \(-0.000811312\pi\) | |||||||
\(350\) | −1.76495e21 | − | 8.15655e20i | −0.418943 | − | 0.193610i | ||||
\(351\) | −9.38368e19 | −0.0217402 | ||||||||
\(352\) | −5.43782e21 | − | 3.67029e21i | −1.22974 | − | 0.830018i | ||||
\(353\) | −8.34131e20 | −0.184141 | −0.0920703 | − | 0.995753i | \(-0.529348\pi\) | ||||
−0.0920703 | + | 0.995753i | \(0.529348\pi\) | |||||||
\(354\) | 1.49525e21 | + | 6.91016e20i | 0.322246 | + | 0.148922i | ||||
\(355\) | − | 6.80047e21i | − | 1.43086i | ||||||
\(356\) | 5.90536e21 | + | 6.94051e21i | 1.21317 | + | 1.42582i | ||||
\(357\) | − | 1.40495e21i | − | 0.281826i | ||||||
\(358\) | 2.54075e21 | − | 5.49780e21i | 0.497687 | − | 1.07692i | ||||
\(359\) | −7.98650e21 | −1.52775 | −0.763877 | − | 0.645361i | \(-0.776707\pi\) | ||||
−0.763877 | + | 0.645361i | \(0.776707\pi\) | |||||||
\(360\) | −3.37141e21 | + | 9.40645e20i | −0.629855 | + | 0.175733i | ||||
\(361\) | −1.65726e21 | −0.302398 | ||||||||
\(362\) | 4.59123e21 | − | 9.93473e21i | 0.818288 | − | 1.77065i | ||||
\(363\) | 2.57941e21i | 0.449071i | ||||||||
\(364\) | −1.53038e20 | + | 1.30213e20i | −0.0260278 | + | 0.0221459i | ||||
\(365\) | 8.35586e21i | 1.38836i | ||||||||
\(366\) | 2.68843e21 | + | 1.24243e21i | 0.436425 | + | 0.201689i | ||||
\(367\) | −4.95976e21 | −0.786682 | −0.393341 | − | 0.919393i | \(-0.628681\pi\) | ||||
−0.393341 | + | 0.919393i | \(0.628681\pi\) | |||||||
\(368\) | 7.48971e19 | − | 4.61709e20i | 0.0116080 | − | 0.0715587i | ||||
\(369\) | 6.02554e21 | 0.912581 | ||||||||
\(370\) | 4.19600e21 | + | 1.93914e21i | 0.621042 | + | 0.287008i | ||||
\(371\) | 1.30359e22i | 1.88566i | ||||||||
\(372\) | 2.27717e21 | − | 1.93754e21i | 0.321944 | − | 0.273927i | ||||
\(373\) | − | 1.32602e22i | − | 1.83243i | −0.400692 | − | 0.916213i | \(-0.631230\pi\) | ||
0.400692 | − | 0.916213i | \(-0.368770\pi\) | |||||||
\(374\) | 3.17717e21 | − | 6.87491e21i | 0.429172 | − | 0.928664i | ||||
\(375\) | 3.06073e21 | 0.404165 | ||||||||
\(376\) | 5.72593e20 | + | 2.05226e21i | 0.0739178 | + | 0.264933i | ||||
\(377\) | −3.44790e20 | −0.0435164 | ||||||||
\(378\) | −2.58467e21 | + | 5.59283e21i | −0.318951 | + | 0.690163i | ||||
\(379\) | − | 4.66066e21i | − | 0.562360i | −0.959655 | − | 0.281180i | \(-0.909274\pi\) | ||
0.959655 | − | 0.281180i | \(-0.0907258\pi\) | |||||||
\(380\) | −4.76463e21 | − | 5.59981e21i | −0.562171 | − | 0.660713i | ||||
\(381\) | − | 4.78459e21i | − | 0.552055i | ||||||
\(382\) | 4.02246e20 | + | 1.85894e20i | 0.0453893 | + | 0.0209762i | ||||
\(383\) | −9.41823e21 | −1.03939 | −0.519696 | − | 0.854351i | \(-0.673955\pi\) | ||||
−0.519696 | + | 0.854351i | \(0.673955\pi\) | |||||||
\(384\) | 3.84597e20 | + | 3.44213e21i | 0.0415136 | + | 0.371546i | ||||
\(385\) | 1.16778e22 | 1.23294 | ||||||||
\(386\) | −2.20464e21 | − | 1.01885e21i | −0.227691 | − | 0.105225i | ||||
\(387\) | − | 4.40380e21i | − | 0.444923i | ||||||
\(388\) | −6.57611e21 | − | 7.72882e21i | −0.649979 | − | 0.763913i | ||||
\(389\) | 2.84056e21i | 0.274683i | 0.990524 | + | 0.137342i | \(0.0438558\pi\) | ||||
−0.990524 | + | 0.137342i | \(0.956144\pi\) | |||||||
\(390\) | 3.93903e19 | − | 8.52346e19i | 0.00372683 | − | 0.00806431i | ||||
\(391\) | 5.39969e20 | 0.0499881 | ||||||||
\(392\) | 5.78944e20 | + | 2.07502e21i | 0.0524451 | + | 0.187971i | ||||
\(393\) | 1.58687e21 | 0.140671 | ||||||||
\(394\) | 2.06403e21 | − | 4.46624e21i | 0.179059 | − | 0.387458i | ||||
\(395\) | 2.15194e21i | 0.182707i | ||||||||
\(396\) | −1.16974e22 | + | 9.95278e21i | −0.972030 | + | 0.827056i | ||||
\(397\) | − | 6.92645e20i | − | 0.0563367i | −0.999603 | − | 0.0281683i | \(-0.991033\pi\) | ||
0.999603 | − | 0.0281683i | \(-0.00896745\pi\) | |||||||
\(398\) | 9.67098e21 | + | 4.46934e21i | 0.769953 | + | 0.355826i | ||||
\(399\) | −5.98493e21 | −0.466433 | ||||||||
\(400\) | −8.86019e20 | + | 5.46193e21i | −0.0675979 | + | 0.416713i | ||||
\(401\) | −4.47868e21 | −0.334521 | −0.167260 | − | 0.985913i | \(-0.553492\pi\) | ||||
−0.167260 | + | 0.985913i | \(0.553492\pi\) | |||||||
\(402\) | 5.14762e21 | + | 2.37892e21i | 0.376431 | + | 0.173963i | ||||
\(403\) | − | 4.93650e20i | − | 0.0353448i | ||||||
\(404\) | −8.37209e21 | + | 7.12343e21i | −0.586938 | + | 0.499399i | ||||
\(405\) | 6.64641e21i | 0.456267i | ||||||||
\(406\) | −9.49699e21 | + | 2.05500e22i | −0.638432 | + | 1.38147i | ||||
\(407\) | 2.02829e22 | 1.33530 | ||||||||
\(408\) | −3.85127e21 | + | 1.07453e21i | −0.248309 | + | 0.0692797i | ||||
\(409\) | 1.38245e22 | 0.872972 | 0.436486 | − | 0.899711i | \(-0.356223\pi\) | ||||
0.436486 | + | 0.899711i | \(0.356223\pi\) | |||||||
\(410\) | −5.46970e21 | + | 1.18356e22i | −0.338299 | + | 0.732028i | ||||
\(411\) | 1.54797e21i | 0.0937791i | ||||||||
\(412\) | 6.88184e21 | + | 8.08815e21i | 0.408393 | + | 0.479979i | ||||
\(413\) | − | 1.78567e22i | − | 1.03807i | ||||||
\(414\) | −9.94002e20 | − | 4.59367e20i | −0.0566088 | − | 0.0261612i | ||||
\(415\) | 2.84389e21 | 0.158673 | ||||||||
\(416\) | 4.73988e20 | + | 3.19921e20i | 0.0259104 | + | 0.0174884i | ||||
\(417\) | −1.06702e22 | −0.571500 | ||||||||
\(418\) | −2.92863e22 | − | 1.35344e22i | −1.53697 | − | 0.710297i | ||||
\(419\) | 4.06502e21i | 0.209047i | 0.994522 | + | 0.104523i | \(0.0333317\pi\) | ||||
−0.994522 | + | 0.104523i | \(0.966668\pi\) | |||||||
\(420\) | −3.99515e21 | − | 4.69546e21i | −0.201333 | − | 0.236624i | ||||
\(421\) | 8.16114e21i | 0.403045i | 0.979484 | + | 0.201522i | \(0.0645888\pi\) | ||||
−0.979484 | + | 0.201522i | \(0.935411\pi\) | |||||||
\(422\) | 1.11483e22 | − | 2.41232e22i | 0.539576 | − | 1.16756i | ||||
\(423\) | 4.98794e21 | 0.236607 | ||||||||
\(424\) | 3.57342e22 | − | 9.97007e21i | 1.66140 | − | 0.463541i | ||||
\(425\) | −6.38773e21 | −0.291099 | ||||||||
\(426\) | −6.60880e21 | + | 1.43004e22i | −0.295217 | + | 0.638804i | ||||
\(427\) | − | 3.21059e22i | − | 1.40588i | ||||||
\(428\) | 1.60452e22 | − | 1.36522e22i | 0.688770 | − | 0.586043i | ||||
\(429\) | − | 4.12013e20i | − | 0.0173390i | ||||||
\(430\) | 8.65013e21 | + | 3.99757e21i | 0.356895 | + | 0.164935i | ||||
\(431\) | −9.79174e21 | −0.396098 | −0.198049 | − | 0.980192i | \(-0.563461\pi\) | ||||
−0.198049 | + | 0.980192i | \(0.563461\pi\) | |||||||
\(432\) | 1.73079e22 | + | 2.80764e21i | 0.686488 | + | 0.111360i | ||||
\(433\) | −2.60425e22 | −1.01283 | −0.506414 | − | 0.862290i | \(-0.669029\pi\) | ||||
−0.506414 | + | 0.862290i | \(0.669029\pi\) | |||||||
\(434\) | −2.94223e22 | − | 1.35972e22i | −1.12206 | − | 0.518546i | ||||
\(435\) | − | 1.05787e22i | − | 0.395616i | ||||||
\(436\) | −1.05299e22 | + | 8.95944e21i | −0.386181 | + | 0.328584i | ||||
\(437\) | − | 2.30020e21i | − | 0.0827321i | ||||||
\(438\) | 8.12034e21 | − | 1.75712e22i | 0.286447 | − | 0.619828i | ||||
\(439\) | 2.68066e22 | 0.927455 | 0.463727 | − | 0.885978i | \(-0.346512\pi\) | ||||
0.463727 | + | 0.885978i | \(0.346512\pi\) | |||||||
\(440\) | −8.93131e21 | − | 3.20112e22i | −0.303087 | − | 1.08631i | ||||
\(441\) | 5.04327e21 | 0.167874 | ||||||||
\(442\) | −2.76938e20 | + | 5.99252e20i | −0.00904260 | + | 0.0195668i | ||||
\(443\) | − | 6.73832e21i | − | 0.215834i | −0.994160 | − | 0.107917i | \(-0.965582\pi\) | ||
0.994160 | − | 0.107917i | \(-0.0344181\pi\) | |||||||
\(444\) | −6.93912e21 | − | 8.15547e21i | −0.218046 | − | 0.256268i | ||||
\(445\) | 4.61629e22i | 1.42309i | ||||||||
\(446\) | 2.54264e22 | + | 1.17506e22i | 0.769022 | + | 0.355396i | ||||
\(447\) | 1.20633e22 | 0.357975 | ||||||||
\(448\) | 3.21235e22 | − | 1.94385e22i | 0.935318 | − | 0.565977i | ||||
\(449\) | −3.12876e22 | −0.893878 | −0.446939 | − | 0.894564i | \(-0.647486\pi\) | ||||
−0.446939 | + | 0.894564i | \(0.647486\pi\) | |||||||
\(450\) | 1.17589e22 | + | 5.43423e21i | 0.329654 | + | 0.152346i | ||||
\(451\) | 5.72118e22i | 1.57393i | ||||||||
\(452\) | −1.10525e22 | − | 1.29899e22i | −0.298389 | − | 0.350693i | ||||
\(453\) | 1.16492e22i | 0.308647i | ||||||||
\(454\) | −1.85175e22 | + | 4.00691e22i | −0.481512 | + | 1.04192i | ||||
\(455\) | −1.01789e21 | −0.0259779 | ||||||||
\(456\) | 4.57736e21 | + | 1.64060e22i | 0.114661 | + | 0.410961i | ||||
\(457\) | −5.48338e22 | −1.34822 | −0.674110 | − | 0.738631i | \(-0.735473\pi\) | ||||
−0.674110 | + | 0.738631i | \(0.735473\pi\) | |||||||
\(458\) | −2.15724e21 | + | 4.66794e21i | −0.0520645 | + | 0.112660i | ||||
\(459\) | 2.02416e22i | 0.479553i | ||||||||
\(460\) | 1.80462e21 | − | 1.53547e21i | 0.0419704 | − | 0.0357107i | ||||
\(461\) | 6.78571e22i | 1.54931i | 0.632386 | + | 0.774653i | \(0.282076\pi\) | ||||
−0.632386 | + | 0.774653i | \(0.717924\pi\) | |||||||
\(462\) | −2.45567e22 | − | 1.13486e22i | −0.550443 | − | 0.254382i | ||||
\(463\) | −1.64300e21 | −0.0361576 | −0.0180788 | − | 0.999837i | \(-0.505755\pi\) | ||||
−0.0180788 | + | 0.999837i | \(0.505755\pi\) | |||||||
\(464\) | 6.35954e22 | + | 1.03163e22i | 1.37411 | + | 0.222905i | ||||
\(465\) | 1.51460e22 | 0.321327 | ||||||||
\(466\) | −2.30993e22 | − | 1.06751e22i | −0.481192 | − | 0.222378i | ||||
\(467\) | − | 4.77673e22i | − | 0.977096i | −0.872537 | − | 0.488548i | \(-0.837527\pi\) | ||
0.872537 | − | 0.488548i | \(-0.162473\pi\) | |||||||
\(468\) | 1.01960e21 | − | 8.67534e20i | 0.0204805 | − | 0.0174260i | ||||
\(469\) | − | 6.14740e22i | − | 1.21261i | ||||||
\(470\) | −4.52782e21 | + | 9.79752e21i | −0.0877117 | + | 0.189795i | ||||
\(471\) | −1.38558e22 | −0.263606 | ||||||||
\(472\) | −4.89489e22 | + | 1.36570e22i | −0.914609 | + | 0.255182i | ||||
\(473\) | 4.18136e22 | 0.767357 | ||||||||
\(474\) | 2.09129e21 | − | 4.52523e21i | 0.0376962 | − | 0.0815689i | ||||
\(475\) | 2.72110e22i | 0.481780i | ||||||||
\(476\) | 2.80884e22 | + | 3.30120e22i | 0.488504 | + | 0.574133i | ||||
\(477\) | − | 8.68507e22i | − | 1.48377i | ||||||
\(478\) | 1.35480e22 | + | 6.26109e21i | 0.227373 | + | 0.105078i | ||||
\(479\) | −5.48658e22 | −0.904585 | −0.452293 | − | 0.891870i | \(-0.649394\pi\) | ||||
−0.452293 | + | 0.891870i | \(0.649394\pi\) | |||||||
\(480\) | −9.81568e21 | + | 1.45427e22i | −0.158990 | + | 0.235556i | ||||
\(481\) | −1.76796e21 | −0.0281345 | ||||||||
\(482\) | 3.07038e22 | + | 1.41894e22i | 0.480056 | + | 0.221853i | ||||
\(483\) | − | 1.92873e21i | − | 0.0296292i | ||||||
\(484\) | −5.15687e22 | − | 6.06081e22i | −0.778396 | − | 0.914840i | ||||
\(485\) | − | 5.14062e22i | − | 0.762448i | ||||||
\(486\) | 2.64771e22 | − | 5.72925e22i | 0.385889 | − | 0.835005i | ||||
\(487\) | 1.26074e23 | 1.80564 | 0.902818 | − | 0.430022i | \(-0.141494\pi\) | ||||
0.902818 | + | 0.430022i | \(0.141494\pi\) | |||||||
\(488\) | −8.80089e22 | + | 2.45550e22i | −1.23868 | + | 0.345599i | ||||
\(489\) | 3.31580e22 | 0.458630 | ||||||||
\(490\) | −4.57805e21 | + | 9.90620e21i | −0.0622320 | + | 0.134661i | ||||
\(491\) | − | 1.93871e22i | − | 0.259013i | −0.991579 | − | 0.129506i | \(-0.958661\pi\) | ||
0.991579 | − | 0.129506i | \(-0.0413393\pi\) | |||||||
\(492\) | 2.30040e22 | − | 1.95731e22i | 0.302065 | − | 0.257013i | ||||
\(493\) | 7.43748e22i | 0.959902i | ||||||||
\(494\) | 2.55275e21 | + | 1.17972e21i | 0.0323839 | + | 0.0149659i | ||||
\(495\) | −7.78020e22 | −0.970167 | ||||||||
\(496\) | −1.47702e22 | + | 9.10522e22i | −0.181048 | + | 1.11608i | ||||
\(497\) | 1.70779e23 | 2.05781 | ||||||||
\(498\) | −5.98030e21 | − | 2.76373e21i | −0.0708392 | − | 0.0327376i | ||||
\(499\) | − | 8.94608e22i | − | 1.04178i | −0.853622 | − | 0.520892i | \(-0.825599\pi\) | ||
0.853622 | − | 0.520892i | \(-0.174401\pi\) | |||||||
\(500\) | −7.19175e22 | + | 6.11913e22i | −0.823359 | + | 0.700559i | ||||
\(501\) | 3.62826e22i | 0.408393i | ||||||||
\(502\) | 1.25134e22 | − | 2.70772e22i | 0.138483 | − | 0.299655i | ||||
\(503\) | 3.84163e22 | 0.418011 | 0.209005 | − | 0.977914i | \(-0.432977\pi\) | ||||
0.209005 | + | 0.977914i | \(0.432977\pi\) | |||||||
\(504\) | −2.36223e22 | − | 8.46657e22i | −0.252733 | − | 0.905833i | ||||
\(505\) | −5.56847e22 | −0.585813 | ||||||||
\(506\) | 4.36164e21 | − | 9.43793e21i | 0.0451201 | − | 0.0976331i | ||||
\(507\) | − | 3.67155e22i | − | 0.373492i | ||||||
\(508\) | 9.56555e22 | + | 1.12423e23i | 0.956904 | + | 1.12464i | ||||
\(509\) | − | 1.79276e23i | − | 1.76369i | −0.471541 | − | 0.881844i | \(-0.656302\pi\) | ||
0.471541 | − | 0.881844i | \(-0.343698\pi\) | |||||||
\(510\) | −1.83860e22 | − | 8.49691e21i | −0.177886 | − | 0.0822080i | ||||
\(511\) | −2.09839e23 | −1.99668 | ||||||||
\(512\) | −7.78534e22 | − | 7.31903e22i | −0.728590 | − | 0.684950i | ||||
\(513\) | 8.62269e22 | 0.793679 | ||||||||
\(514\) | 1.30382e23 | + | 6.02547e22i | 1.18041 | + | 0.545513i | ||||
\(515\) | 5.37961e22i | 0.479059i | ||||||||
\(516\) | −1.43051e22 | − | 1.68126e22i | −0.125305 | − | 0.147270i | ||||
\(517\) | 4.73599e22i | 0.408076i | ||||||||
\(518\) | −4.86972e22 | + | 1.05373e23i | −0.412764 | + | 0.893158i | ||||
\(519\) | 8.81104e21 | 0.0734691 | ||||||||
\(520\) | 7.78498e20 | + | 2.79025e21i | 0.00638601 | + | 0.0228884i | ||||
\(521\) | 6.78107e22 | 0.547240 | 0.273620 | − | 0.961838i | \(-0.411779\pi\) | ||||
0.273620 | + | 0.961838i | \(0.411779\pi\) | |||||||
\(522\) | 6.32728e22 | − | 1.36913e23i | 0.502363 | − | 1.08704i | ||||
\(523\) | 2.09501e23i | 1.63652i | 0.574845 | + | 0.818262i | \(0.305062\pi\) | ||||
−0.574845 | + | 0.818262i | \(0.694938\pi\) | |||||||
\(524\) | −3.72865e22 | + | 3.17254e22i | −0.286573 | + | 0.243832i | ||||
\(525\) | 2.28165e22i | 0.172542i | ||||||||
\(526\) | −9.89468e22 | − | 4.57272e22i | −0.736246 | − | 0.340248i | ||||
\(527\) | −1.06485e23 | −0.779651 | ||||||||
\(528\) | −1.23276e22 | + | 7.59945e22i | −0.0888158 | + | 0.547512i | ||||
\(529\) | −1.40309e23 | −0.994745 | ||||||||
\(530\) | 1.70596e23 | + | 7.88390e22i | 1.19021 | + | 0.550043i | ||||
\(531\) | 1.18968e23i | 0.816824i | ||||||||
\(532\) | 1.40627e23 | − | 1.19653e23i | 0.950212 | − | 0.808492i | ||||
\(533\) | − | 4.98687e21i | − | 0.0331624i | ||||||
\(534\) | 4.48617e22 | − | 9.70740e22i | 0.293613 | − | 0.635334i | ||||
\(535\) | 1.06721e23 | 0.687450 | ||||||||
\(536\) | −1.68513e23 | + | 4.70162e22i | −1.06840 | + | 0.298090i | ||||
\(537\) | −7.10728e22 | −0.443529 | ||||||||
\(538\) | 1.21477e22 | − | 2.62858e22i | 0.0746184 | − | 0.161463i | ||||
\(539\) | 4.78852e22i | 0.289532i | ||||||||
\(540\) | 5.75595e22 | + | 6.76490e22i | 0.342586 | + | 0.402638i | ||||
\(541\) | 1.24185e23i | 0.727600i | 0.931477 | + | 0.363800i | \(0.118521\pi\) | ||||
−0.931477 | + | 0.363800i | \(0.881479\pi\) | |||||||
\(542\) | −1.25590e23 | − | 5.80403e22i | −0.724374 | − | 0.334762i | ||||
\(543\) | −1.28431e23 | −0.729243 | ||||||||
\(544\) | 6.90103e22 | − | 1.02244e23i | 0.385765 | − | 0.571542i | ||||
\(545\) | −7.00370e22 | −0.385440 | ||||||||
\(546\) | 2.14048e21 | + | 9.89202e20i | 0.0115978 | + | 0.00535979i | ||||
\(547\) | − | 1.22112e23i | − | 0.651429i | −0.945468 | − | 0.325714i | \(-0.894395\pi\) | ||
0.945468 | − | 0.325714i | \(-0.105605\pi\) | |||||||
\(548\) | −3.09476e22 | − | 3.63724e22i | −0.162552 | − | 0.191046i | ||||
\(549\) | 2.13903e23i | 1.10624i | ||||||||
\(550\) | −5.15974e22 | + | 1.11649e23i | −0.262751 | + | 0.568554i | ||||
\(551\) | 3.16828e23 | 1.58867 | ||||||||
\(552\) | −5.28704e21 | + | 1.47512e21i | −0.0261054 | + | 0.00728358i | ||||
\(553\) | −5.40413e22 | −0.262762 | ||||||||
\(554\) | 5.88717e22 | − | 1.27389e23i | 0.281886 | − | 0.609959i | ||||
\(555\) | − | 5.42439e22i | − | 0.255776i | ||||||
\(556\) | 2.50716e23 | − | 2.13323e23i | 1.16425 | − | 0.990609i | ||||
\(557\) | − | 2.07273e23i | − | 0.947924i | −0.880545 | − | 0.473962i | \(-0.842823\pi\) | ||
0.880545 | − | 0.473962i | \(-0.157177\pi\) | |||||||
\(558\) | 1.96024e23 | + | 9.05903e22i | 0.882913 | + | 0.408029i | ||||
\(559\) | −3.64468e21 | −0.0161681 | ||||||||
\(560\) | 1.87747e23 | + | 3.04558e22i | 0.820304 | + | 0.133067i | ||||
\(561\) | −8.88756e22 | −0.382471 | ||||||||
\(562\) | −1.86783e23 | − | 8.63197e22i | −0.791732 | − | 0.365891i | ||||
\(563\) | − | 1.43541e23i | − | 0.599314i | −0.954047 | − | 0.299657i | \(-0.903128\pi\) | ||
0.954047 | − | 0.299657i | \(-0.0968722\pi\) | |||||||
\(564\) | 1.90427e22 | − | 1.62026e22i | 0.0783172 | − | 0.0666365i | ||||
\(565\) | − | 8.63985e22i | − | 0.350021i | ||||||
\(566\) | −6.84813e22 | + | 1.48183e23i | −0.273296 | + | 0.591370i | ||||
\(567\) | −1.66910e23 | −0.656185 | ||||||||
\(568\) | −1.30614e23 | − | 4.68141e23i | −0.505860 | − | 1.81308i | ||||
\(569\) | 1.29010e23 | 0.492231 | 0.246116 | − | 0.969240i | \(-0.420846\pi\) | ||||
0.246116 | + | 0.969240i | \(0.420846\pi\) | |||||||
\(570\) | −3.61958e22 | + | 7.83223e22i | −0.136057 | + | 0.294408i | ||||
\(571\) | − | 2.64243e23i | − | 0.978579i | −0.872121 | − | 0.489290i | \(-0.837256\pi\) | ||
0.872121 | − | 0.489290i | \(-0.162744\pi\) | |||||||
\(572\) | 8.23713e21 | + | 9.68101e21i | 0.0300545 | + | 0.0353228i | ||||
\(573\) | − | 5.20005e21i | − | 0.0186936i | ||||||
\(574\) | −2.97226e23 | − | 1.37360e23i | −1.05277 | − | 0.486529i | ||||
\(575\) | −8.76912e21 | −0.0306041 | ||||||||
\(576\) | −2.14020e23 | + | 1.29507e23i | −0.735975 | + | 0.445351i | ||||
\(577\) | −9.70397e22 | −0.328818 | −0.164409 | − | 0.986392i | \(-0.552572\pi\) | ||||
−0.164409 | + | 0.986392i | \(0.552572\pi\) | |||||||
\(578\) | −1.42600e23 | − | 6.59011e22i | −0.476138 | − | 0.220042i | ||||
\(579\) | 2.85005e22i | 0.0937746i | ||||||||
\(580\) | 2.11494e23 | + | 2.48566e23i | 0.685740 | + | 0.805943i | ||||
\(581\) | 7.14182e22i | 0.228198i | ||||||||
\(582\) | −4.99573e22 | + | 1.08100e23i | −0.157309 | + | 0.340393i | ||||
\(583\) | 8.24637e23 | 2.55906 | ||||||||
\(584\) | 1.60488e23 | + | 5.75214e23i | 0.490833 | + | 1.75922i | ||||
\(585\) | 6.78161e21 | 0.0204413 | ||||||||
\(586\) | −2.29339e23 | + | 4.96254e23i | −0.681314 | + | 1.47426i | ||||
\(587\) | − | 3.02349e23i | − | 0.885288i | −0.896697 | − | 0.442644i | \(-0.854041\pi\) | ||
0.896697 | − | 0.442644i | \(-0.145959\pi\) | |||||||
\(588\) | 1.92540e22 | − | 1.63823e22i | 0.0555665 | − | 0.0472790i | ||||
\(589\) | 4.53616e23i | 1.29035i | ||||||||
\(590\) | −2.33683e23 | − | 1.07994e23i | −0.655216 | − | 0.302801i | ||||
\(591\) | −5.77374e22 | −0.159574 | ||||||||
\(592\) | 3.26095e23 | + | 5.28982e22i | 0.888402 | + | 0.144114i | ||||
\(593\) | −3.18008e23 | −0.854030 | −0.427015 | − | 0.904245i | \(-0.640435\pi\) | ||||
−0.427015 | + | 0.904245i | \(0.640435\pi\) | |||||||
\(594\) | 3.53796e23 | + | 1.63503e23i | 0.936630 | + | 0.432854i | ||||
\(595\) | 2.19570e23i | 0.573032i | ||||||||
\(596\) | −2.83450e23 | + | 2.41175e23i | −0.729262 | + | 0.620496i | ||||
\(597\) | − | 1.25022e23i | − | 0.317105i | ||||||
\(598\) | −3.80183e20 | + | 8.22657e20i | −0.000950675 | + | 0.00205712i | ||||
\(599\) | 3.24737e23 | 0.800578 | 0.400289 | − | 0.916389i | \(-0.368910\pi\) | ||||
0.400289 | + | 0.916389i | \(0.368910\pi\) | |||||||
\(600\) | 6.25447e22 | − | 1.74504e22i | 0.152022 | − | 0.0424150i | ||||
\(601\) | −3.78448e23 | −0.906929 | −0.453464 | − | 0.891274i | \(-0.649812\pi\) | ||||
−0.453464 | + | 0.891274i | \(0.649812\pi\) | |||||||
\(602\) | −1.00390e23 | + | 2.17229e23i | −0.237204 | + | 0.513273i | ||||
\(603\) | 4.09565e23i | 0.954171i | ||||||||
\(604\) | −2.32896e23 | − | 2.73721e23i | −0.534994 | − | 0.628772i | ||||
\(605\) | − | 4.03118e23i | − | 0.913087i | ||||||
\(606\) | 1.17097e23 | + | 5.41152e22i | 0.261534 | + | 0.120865i | ||||
\(607\) | −2.72859e23 | −0.600945 | −0.300472 | − | 0.953791i | \(-0.597144\pi\) | ||||
−0.300472 | + | 0.953791i | \(0.597144\pi\) | |||||||
\(608\) | −4.35548e23 | − | 2.93976e23i | −0.945924 | − | 0.638457i | ||||
\(609\) | 2.65661e23 | 0.568959 | ||||||||
\(610\) | −4.20156e23 | − | 1.94171e23i | −0.887375 | − | 0.410091i | ||||
\(611\) | − | 4.12813e21i | − | 0.00859811i | ||||||
\(612\) | −1.87136e23 | − | 2.19939e23i | −0.384389 | − | 0.451768i | ||||
\(613\) | − | 2.23929e23i | − | 0.453625i | −0.973938 | − | 0.226813i | \(-0.927169\pi\) | ||
0.973938 | − | 0.226813i | \(-0.0728305\pi\) | |||||||
\(614\) | 1.08623e23 | − | 2.35044e23i | 0.217016 | − | 0.469590i | ||||
\(615\) | 1.53005e23 | 0.301486 | ||||||||
\(616\) | 8.03891e23 | − | 2.24291e23i | 1.56229 | − | 0.435888i | ||||
\(617\) | 9.37688e23 | 1.79736 | 0.898679 | − | 0.438608i | \(-0.144528\pi\) | ||||
0.898679 | + | 0.438608i | \(0.144528\pi\) | |||||||
\(618\) | 5.22798e22 | − | 1.13126e23i | 0.0988398 | − | 0.213874i | ||||
\(619\) | − | 8.46873e23i | − | 1.57924i | −0.613597 | − | 0.789619i | \(-0.710278\pi\) | ||
0.613597 | − | 0.789619i | \(-0.289722\pi\) | |||||||
\(620\) | −3.55883e23 | + | 3.02804e23i | −0.654602 | + | 0.556971i | ||||
\(621\) | 2.77878e22i | 0.0504168i | ||||||||
\(622\) | 5.10048e23 | + | 2.35714e23i | 0.912837 | + | 0.421858i | ||||
\(623\) | −1.15928e24 | −2.04663 | ||||||||
\(624\) | 1.07454e21 | − | 6.62407e21i | 0.00187134 | − | 0.0115360i | ||||
\(625\) | −2.32610e23 | −0.399622 | ||||||||
\(626\) | −2.31179e23 | − | 1.06837e23i | −0.391801 | − | 0.181067i | ||||
\(627\) | 3.78600e23i | 0.633003i | ||||||||
\(628\) | 3.25569e23 | − | 2.77012e23i | 0.537014 | − | 0.456921i | ||||
\(629\) | 3.81368e23i | 0.620603i | ||||||||
\(630\) | 1.86795e23 | − | 4.04196e23i | 0.299896 | − | 0.648929i | ||||
\(631\) | 5.75474e23 | 0.911541 | 0.455771 | − | 0.890097i | \(-0.349364\pi\) | ||||
0.455771 | + | 0.890097i | \(0.349364\pi\) | |||||||
\(632\) | 4.13316e22 | + | 1.48139e23i | 0.0645932 | + | 0.231512i | ||||
\(633\) | −3.11853e23 | −0.480860 | ||||||||
\(634\) | 3.12331e23 | − | 6.75837e23i | 0.475178 | − | 1.02821i | ||||
\(635\) | 7.47750e23i | 1.12248i | ||||||||
\(636\) | −2.82122e23 | − | 3.31575e23i | −0.417880 | − | 0.491130i | ||||
\(637\) | − | 4.17392e21i | − | 0.00610041i | ||||||
\(638\) | 1.29997e24 | + | 6.00768e23i | 1.87481 | + | 0.866425i | ||||
\(639\) | −1.13780e24 | −1.61923 | ||||||||
\(640\) | −6.01060e22 | − | 5.37947e23i | −0.0844089 | − | 0.755457i | ||||
\(641\) | 4.70111e23 | 0.651489 | 0.325745 | − | 0.945458i | \(-0.394385\pi\) | ||||
0.325745 | + | 0.945458i | \(0.394385\pi\) | |||||||
\(642\) | −2.24418e23 | − | 1.03713e23i | −0.306910 | − | 0.141835i | ||||
\(643\) | − | 1.44971e23i | − | 0.195653i | −0.995203 | − | 0.0978266i | \(-0.968811\pi\) | ||
0.995203 | − | 0.0978266i | \(-0.0311891\pi\) | |||||||
\(644\) | 3.85599e22 | + | 4.53190e22i | 0.0513578 | + | 0.0603602i | ||||
\(645\) | − | 1.11825e23i | − | 0.146987i | ||||||
\(646\) | 2.54479e23 | − | 5.50655e23i | 0.330123 | − | 0.714336i | ||||
\(647\) | 1.43169e23 | 0.183300 | 0.0916502 | − | 0.995791i | \(-0.470786\pi\) | ||||
0.0916502 | + | 0.995791i | \(0.470786\pi\) | |||||||
\(648\) | 1.27655e23 | + | 4.57535e23i | 0.161306 | + | 0.578146i | ||||
\(649\) | −1.12959e24 | −1.40877 | ||||||||
\(650\) | 4.49749e21 | − | 9.73188e21i | 0.00553613 | − | 0.0119794i | ||||
\(651\) | 3.80358e23i | 0.462119i | ||||||||
\(652\) | −7.79109e23 | + | 6.62909e23i | −0.934316 | + | 0.794967i | ||||
\(653\) | − | 3.23785e23i | − | 0.383260i | −0.981467 | − | 0.191630i | \(-0.938623\pi\) | ||
0.981467 | − | 0.191630i | \(-0.0613774\pi\) | |||||||
\(654\) | 1.47278e23 | + | 6.80629e22i | 0.172079 | + | 0.0795243i | ||||
\(655\) | −2.48001e23 | −0.286024 | ||||||||
\(656\) | −1.49209e23 | + | 9.19813e23i | −0.169869 | + | 1.04717i | ||||
\(657\) | 1.39804e24 | 1.57113 | ||||||||
\(658\) | −2.46043e23 | − | 1.13706e23i | −0.272955 | − | 0.126143i | ||||
\(659\) | 8.58094e23i | 0.939742i | 0.882735 | + | 0.469871i | \(0.155700\pi\) | ||||
−0.882735 | + | 0.469871i | \(0.844300\pi\) | |||||||
\(660\) | −2.97029e23 | + | 2.52728e23i | −0.321126 | + | 0.273231i | ||||
\(661\) | 7.30451e23i | 0.779612i | 0.920897 | + | 0.389806i | \(0.127458\pi\) | ||||
−0.920897 | + | 0.389806i | \(0.872542\pi\) | |||||||
\(662\) | 1.06810e23 | − | 2.31121e23i | 0.112543 | − | 0.243527i | ||||
\(663\) | 7.74684e21 | 0.00805860 | ||||||||
\(664\) | 1.95772e23 | − | 5.46216e22i | 0.201058 | − | 0.0560965i | ||||
\(665\) | 9.35343e23 | 0.948390 | ||||||||
\(666\) | 3.24441e23 | − | 7.02041e23i | 0.324792 | − | 0.702800i | ||||
\(667\) | 1.02102e23i | 0.100917i | ||||||||
\(668\) | −7.25378e23 | − | 8.52528e23i | −0.707887 | − | 0.831972i | ||||
\(669\) | − | 3.28700e23i | − | 0.316722i | ||||||
\(670\) | −8.04485e23 | − | 3.71784e23i | −0.765389 | − | 0.353717i | ||||
\(671\) | −2.03098e24 | −1.90794 | ||||||||
\(672\) | −3.65208e23 | − | 2.46499e23i | −0.338768 | − | 0.228653i | ||||
\(673\) | −1.25481e23 | −0.114934 | −0.0574671 | − | 0.998347i | \(-0.518302\pi\) | ||||
−0.0574671 | + | 0.998347i | \(0.518302\pi\) | |||||||
\(674\) | 2.90639e23 | + | 1.34316e23i | 0.262872 | + | 0.121484i | ||||
\(675\) | − | 3.28724e23i | − | 0.293596i | ||||||
\(676\) | 7.34032e23 | + | 8.62699e23i | 0.647393 | + | 0.760874i | ||||
\(677\) | − | 3.68442e22i | − | 0.0320897i | −0.999871 | − | 0.0160448i | \(-0.994893\pi\) | ||
0.999871 | − | 0.0160448i | \(-0.00510745\pi\) | |||||||
\(678\) | −8.39633e22 | + | 1.81684e23i | −0.0722166 | + | 0.156266i | ||||
\(679\) | 1.29095e24 | 1.09652 | ||||||||
\(680\) | 6.01888e23 | − | 1.67930e23i | 0.504882 | − | 0.140865i | ||||
\(681\) | 5.17993e23 | 0.429115 | ||||||||
\(682\) | −8.60144e23 | + | 1.86122e24i | −0.703727 | + | 1.52276i | ||||
\(683\) | − | 3.46565e23i | − | 0.280033i | −0.990149 | − | 0.140016i | \(-0.955285\pi\) | ||
0.990149 | − | 0.140016i | \(-0.0447155\pi\) | |||||||
\(684\) | −9.36916e23 | + | 7.97180e23i | −0.747694 | + | 0.636179i | ||||
\(685\) | − | 2.41921e23i | − | 0.190679i | ||||||
\(686\) | 1.02600e24 | + | 4.74156e23i | 0.798717 | + | 0.369119i | ||||
\(687\) | 6.03449e22 | 0.0463990 | ||||||||
\(688\) | 6.72251e23 | + | 1.09051e23i | 0.510540 | + | 0.0828183i | ||||
\(689\) | −7.18795e22 | −0.0539190 | ||||||||
\(690\) | −2.52404e22 | − | 1.16646e22i | −0.0187016 | − | 0.00864277i | ||||
\(691\) | − | 1.64173e24i | − | 1.20154i | −0.799421 | − | 0.600771i | \(-0.794860\pi\) | ||
0.799421 | − | 0.600771i | \(-0.205140\pi\) | |||||||
\(692\) | −2.07032e23 | + | 1.76154e23i | −0.149670 | + | 0.127348i | ||||
\(693\) | − | 1.95383e24i | − | 1.39526i | ||||||
\(694\) | −8.33210e23 | + | 1.80294e24i | −0.587759 | + | 1.27182i | ||||
\(695\) | 1.66757e24 | 1.16202 | ||||||||
\(696\) | −2.03181e23 | − | 7.28233e23i | −0.139864 | − | 0.501293i | ||||
\(697\) | −1.07572e24 | −0.731511 | ||||||||
\(698\) | 3.18331e21 | − | 6.88820e21i | 0.00213849 | − | 0.00462737i | ||||
\(699\) | 2.98617e23i | 0.198179i | ||||||||
\(700\) | −4.56157e23 | − | 5.36116e23i | −0.299075 | − | 0.351500i | ||||
\(701\) | 1.08179e24i | 0.700709i | 0.936617 | + | 0.350355i | \(0.113939\pi\) | ||||
−0.936617 | + | 0.350355i | \(0.886061\pi\) | |||||||
\(702\) | −3.08386e22 | − | 1.42518e22i | −0.0197347 | − | 0.00912017i | ||||
\(703\) | 1.62458e24 | 1.02712 | ||||||||
\(704\) | −1.22965e24 | − | 2.03209e24i | −0.768096 | − | 1.26933i | ||||
\(705\) | 1.26658e23 | 0.0781670 | ||||||||
\(706\) | −2.74130e23 | − | 1.26686e23i | −0.167154 | − | 0.0772484i | ||||
\(707\) | − | 1.39840e24i | − | 0.842493i | ||||||
\(708\) | 3.86452e23 | + | 4.54192e23i | 0.230045 | + | 0.270369i | ||||
\(709\) | − | 1.54173e23i | − | 0.0906808i | −0.998972 | − | 0.0453404i | \(-0.985563\pi\) | ||
0.998972 | − | 0.0453404i | \(-0.0144372\pi\) | |||||||
\(710\) | 1.03284e24 | − | 2.23492e24i | 0.600258 | − | 1.29887i | ||||
\(711\) | 3.60045e23 | 0.206760 | ||||||||
\(712\) | 8.86635e23 | + | 3.17783e24i | 0.503112 | + | 1.80323i | ||||
\(713\) | −1.46184e23 | −0.0819669 | ||||||||
\(714\) | 2.13381e23 | − | 4.61725e23i | 0.118228 | − | 0.255828i | ||||
\(715\) | 6.43906e22i | 0.0352550i | ||||||||
\(716\) | 1.66999e24 | − | 1.42092e24i | 0.903552 | − | 0.768791i | ||||
\(717\) | − | 1.75143e23i | − | 0.0936438i | ||||||
\(718\) | −2.62469e24 | − | 1.21297e24i | −1.38682 | − | 0.640905i | ||||
\(719\) | −1.87407e24 | −0.978565 | −0.489283 | − | 0.872125i | \(-0.662741\pi\) | ||||
−0.489283 | + | 0.872125i | \(0.662741\pi\) | |||||||
\(720\) | −1.25085e24 | − | 2.02909e23i | −0.645474 | − | 0.104707i | ||||
\(721\) | −1.35097e24 | −0.688964 | ||||||||
\(722\) | −5.44644e23 | − | 2.51701e23i | −0.274502 | − | 0.126858i | ||||
\(723\) | − | 3.96924e23i | − | 0.197711i | ||||||
\(724\) | 3.01773e24 | − | 2.56765e24i | 1.48560 | − | 1.26403i | ||||
\(725\) | − | 1.20785e24i | − | 0.587679i | ||||||
\(726\) | −3.91756e23 | + | 8.47701e23i | −0.188389 | + | 0.407645i | ||||
\(727\) | 3.49121e24 | 1.65933 | 0.829667 | − | 0.558259i | \(-0.188531\pi\) | ||||
0.829667 | + | 0.558259i | \(0.188531\pi\) | |||||||
\(728\) | −7.00712e22 | + | 1.95503e22i | −0.0329172 | + | 0.00918410i | ||||
\(729\) | 5.52055e23 | 0.256329 | ||||||||
\(730\) | −1.26907e24 | + | 2.74608e24i | −0.582428 | + | 1.26029i | ||||
\(731\) | 7.86197e23i | 0.356643i | ||||||||
\(732\) | 6.94832e23 | + | 8.16628e23i | 0.311556 | + | 0.366168i | ||||
\(733\) | 4.17586e24i | 1.85081i | 0.378979 | + | 0.925405i | \(0.376275\pi\) | ||||
−0.378979 | + | 0.925405i | \(0.623725\pi\) | |||||||
\(734\) | −1.62998e24 | − | 7.53279e23i | −0.714112 | − | 0.330019i | ||||
\(735\) | 1.28063e23 | 0.0554600 | ||||||||
\(736\) | 9.47378e22 | − | 1.40361e23i | 0.0405566 | − | 0.0600878i | ||||
\(737\) | −3.88877e24 | −1.64566 | ||||||||
\(738\) | 1.98024e24 | + | 9.15147e23i | 0.828397 | + | 0.382835i | ||||
\(739\) | 3.77789e24i | 1.56233i | 0.624327 | + | 0.781163i | \(0.285373\pi\) | ||||
−0.624327 | + | 0.781163i | \(0.714627\pi\) | |||||||
\(740\) | 1.08447e24 | + | 1.27456e24i | 0.443350 | + | 0.521064i | ||||
\(741\) | − | 3.30007e22i | − | 0.0133373i | ||||||
\(742\) | −1.97987e24 | + | 4.28414e24i | −0.791050 | + | 1.71171i | ||||
\(743\) | −2.48774e24 | −0.982651 | −0.491326 | − | 0.870976i | \(-0.663487\pi\) | ||||
−0.491326 | + | 0.870976i | \(0.663487\pi\) | |||||||
\(744\) | 1.04264e24 | − | 2.90903e23i | 0.407160 | − | 0.113600i | ||||
\(745\) | −1.88529e24 | −0.727864 | ||||||||
\(746\) | 2.01394e24 | − | 4.35786e24i | 0.768717 | − | 1.66339i | ||||
\(747\) | − | 4.75817e23i | − | 0.179562i | ||||||
\(748\) | 2.08830e24 | − | 1.77684e24i | 0.779164 | − | 0.662955i | ||||
\(749\) | 2.68005e24i | 0.988663i | ||||||||
\(750\) | 1.00588e24 | + | 4.64857e23i | 0.366881 | + | 0.169550i | ||||
\(751\) | 1.46920e22 | 0.00529836 | 0.00264918 | − | 0.999996i | \(-0.499157\pi\) | ||||
0.00264918 | + | 0.999996i | \(0.499157\pi\) | |||||||
\(752\) | −1.23515e23 | + | 7.61421e23i | −0.0440423 | + | 0.271502i | ||||
\(753\) | −3.50041e23 | −0.123413 | ||||||||
\(754\) | −1.13312e23 | − | 5.23660e22i | −0.0395021 | − | 0.0182555i | ||||
\(755\) | − | 1.82058e24i | − | 0.627567i | ||||||
\(756\) | −1.69886e24 | + | 1.44548e24i | −0.579057 | + | 0.492694i | ||||
\(757\) | 4.58159e24i | 1.54419i | 0.635506 | + | 0.772096i | \(0.280792\pi\) | ||||
−0.635506 | + | 0.772096i | \(0.719208\pi\) | |||||||
\(758\) | 7.07853e23 | − | 1.53169e24i | 0.235914 | − | 0.510483i | ||||
\(759\) | −1.22009e23 | −0.0402102 | ||||||||
\(760\) | −7.15364e23 | − | 2.56397e24i | −0.233137 | − | 0.835599i | ||||
\(761\) | 2.36360e24 | 0.761736 | 0.380868 | − | 0.924629i | \(-0.375625\pi\) | ||||
0.380868 | + | 0.924629i | \(0.375625\pi\) | |||||||
\(762\) | 7.26674e23 | − | 1.57241e24i | 0.231591 | − | 0.501129i | ||||
\(763\) | − | 1.75883e24i | − | 0.554325i | ||||||
\(764\) | 1.03962e23 | + | 1.22185e23i | 0.0324025 | + | 0.0380823i | ||||
\(765\) | − | 1.46287e24i | − | 0.450902i | ||||||
\(766\) | −3.09522e24 | − | 1.43042e24i | −0.943510 | − | 0.436033i | ||||
\(767\) | 9.84609e22 | 0.0296827 | ||||||||
\(768\) | −3.96390e23 | + | 1.18964e24i | −0.118182 | + | 0.354687i | ||||
\(769\) | −9.13423e23 | −0.269338 | −0.134669 | − | 0.990891i | \(-0.542997\pi\) | ||||
−0.134669 | + | 0.990891i | \(0.542997\pi\) | |||||||
\(770\) | 3.83779e24 | + | 1.77359e24i | 1.11921 | + | 0.517229i | ||||
\(771\) | − | 1.68552e24i | − | 0.486151i | ||||||
\(772\) | −5.69795e23 | − | 6.69674e23i | −0.162544 | − | 0.191036i | ||||
\(773\) | − | 1.76234e24i | − | 0.497238i | −0.968601 | − | 0.248619i | \(-0.920023\pi\) | ||
0.968601 | − | 0.248619i | \(-0.0799766\pi\) | |||||||
\(774\) | 6.68841e23 | − | 1.44727e24i | 0.186649 | − | 0.403879i | ||||
\(775\) | 1.72933e24 | 0.477324 | ||||||||
\(776\) | −9.87341e23 | − | 3.53878e24i | −0.269552 | − | 0.966114i | ||||
\(777\) | 1.36222e24 | 0.367847 | ||||||||
\(778\) | −4.31418e23 | + | 9.33524e23i | −0.115232 | + | 0.249344i | ||||
\(779\) | 4.58244e24i | 1.21068i | ||||||||
\(780\) | 2.58905e22 | − | 2.20291e22i | 0.00676608 | − | 0.00575695i | ||||
\(781\) | − | 1.08033e25i | − | 2.79268i | ||||||
\(782\) | 1.77456e23 | + | 8.20094e22i | 0.0453767 | + | 0.0209704i | ||||
\(783\) | −3.82747e24 | −0.968136 | ||||||||
\(784\) | −1.24886e23 | + | 7.69867e23i | −0.0312482 | + | 0.192632i | ||||
\(785\) | 2.16543e24 | 0.535985 | ||||||||
\(786\) | 5.21511e23 | + | 2.41011e23i | 0.127694 | + | 0.0590126i | ||||
\(787\) | − | 3.12907e24i | − | 0.757933i | −0.925410 | − | 0.378966i | \(-0.876280\pi\) | ||
0.925410 | − | 0.378966i | \(-0.123720\pi\) | |||||||
\(788\) | 1.35665e24 | − | 1.15431e24i | 0.325083 | − | 0.276598i | ||||
\(789\) | 1.27914e24i | 0.303223i | ||||||||
\(790\) | −3.26832e23 | + | 7.07216e23i | −0.0766470 | + | 0.165852i | ||||
\(791\) | 2.16971e24 | 0.503387 | ||||||||
\(792\) | −5.35585e24 | + | 1.49432e24i | −1.22932 | + | 0.342988i | ||||
\(793\) | 1.77030e23 | 0.0402000 | ||||||||
\(794\) | 1.05198e23 | − | 2.27632e23i | 0.0236337 | − | 0.0511397i | ||||
\(795\) | − | 2.20538e24i | − | 0.490188i | ||||||
\(796\) | 2.49949e24 | + | 2.93762e24i | 0.549655 | + | 0.646003i | ||||
\(797\) | − | 1.77982e24i | − | 0.387241i | −0.981077 | − | 0.193620i | \(-0.937977\pi\) | ||
0.981077 | − | 0.193620i | \(-0.0620230\pi\) | |||||||
\(798\) | −1.96690e24 | − | 9.08980e23i | −0.423406 | − | 0.195672i | ||||
\(799\) | −8.90481e23 | −0.189661 | ||||||||
\(800\) | −1.12073e24 | + | 1.66045e24i | −0.236176 | + | 0.349914i | ||||
\(801\) | 7.72360e24 | 1.61044 | ||||||||
\(802\) | −1.47188e24 | − | 6.80214e23i | −0.303662 | − | 0.140334i | ||||
\(803\) | 1.32742e25i | 2.70973i | ||||||||
\(804\) | 1.33041e24 | + | 1.56362e24i | 0.268726 | + | 0.315831i | ||||
\(805\) | 3.01427e23i | 0.0602445i | ||||||||
\(806\) | 7.49745e22 | − | 1.62234e23i | 0.0148274 | − | 0.0320843i | ||||
\(807\) | −3.39811e23 | −0.0664985 | ||||||||
\(808\) | −3.83331e24 | + | 1.06952e24i | −0.742296 | + | 0.207105i | ||||
\(809\) | 2.82672e23 | 0.0541653 | 0.0270826 | − | 0.999633i | \(-0.491378\pi\) | ||||
0.0270826 | + | 0.999633i | \(0.491378\pi\) | |||||||
\(810\) | −1.00944e24 | + | 2.18428e24i | −0.191408 | + | 0.414177i | ||||
\(811\) | − | 9.40519e24i | − | 1.76478i | −0.470519 | − | 0.882390i | \(-0.655933\pi\) | ||
0.470519 | − | 0.882390i | \(-0.344067\pi\) | |||||||
\(812\) | −6.24220e24 | + | 5.31121e24i | −1.15908 | + | 0.986205i | ||||
\(813\) | 1.62357e24i | 0.298333i | ||||||||
\(814\) | 6.66580e24 | + | 3.08053e24i | 1.21212 | + | 0.560167i | ||||
\(815\) | −5.18203e24 | −0.932525 | ||||||||
\(816\) | −1.42888e24 | − | 2.31789e23i | −0.254466 | − | 0.0412787i | ||||
\(817\) | 3.34911e24 | 0.590258 | ||||||||
\(818\) | 4.54329e24 | + | 2.09963e24i | 0.792442 | + | 0.366219i | ||||
\(819\) | 1.70306e23i | 0.0293979i | ||||||||
\(820\) | −3.59514e24 | + | 3.05894e24i | −0.614183 | + | 0.522581i | ||||
\(821\) | − | 2.44785e24i | − | 0.413875i | −0.978354 | − | 0.206937i | \(-0.933650\pi\) | ||
0.978354 | − | 0.206937i | \(-0.0663496\pi\) | |||||||
\(822\) | −2.35102e23 | + | 5.08726e23i | −0.0393411 | + | 0.0851282i | ||||
\(823\) | 2.44893e24 | 0.405581 | 0.202791 | − | 0.979222i | \(-0.434999\pi\) | ||||
0.202791 | + | 0.979222i | \(0.434999\pi\) | |||||||
\(824\) | 1.03324e24 | + | 3.70330e24i | 0.169364 | + | 0.607026i | ||||
\(825\) | 1.44334e24 | 0.234159 | ||||||||
\(826\) | 2.71204e24 | − | 5.86844e24i | 0.435477 | − | 0.942306i | ||||
\(827\) | 3.39629e24i | 0.539769i | 0.962893 | + | 0.269885i | \(0.0869855\pi\) | ||||
−0.962893 | + | 0.269885i | \(0.913014\pi\) | |||||||
\(828\) | −2.56902e23 | − | 3.01934e23i | −0.0404119 | − | 0.0474957i | ||||
\(829\) | 3.76176e24i | 0.585703i | 0.956158 | + | 0.292851i | \(0.0946041\pi\) | ||||
−0.956158 | + | 0.292851i | \(0.905396\pi\) | |||||||
\(830\) | 9.34620e23 | + | 4.31925e23i | 0.144036 | + | 0.0665647i | ||||
\(831\) | −1.64683e24 | −0.251212 | ||||||||
\(832\) | 1.07183e23 | + | 1.77127e23i | 0.0161837 | + | 0.0267447i | ||||
\(833\) | −9.00359e23 | −0.134565 | ||||||||
\(834\) | −3.50667e24 | − | 1.62057e24i | −0.518780 | − | 0.239749i | ||||
\(835\) | − | 5.67036e24i | − | 0.830377i | ||||||
\(836\) | −7.56912e24 | − | 8.89591e24i | −1.09722 | − | 1.28955i | ||||
\(837\) | − | 5.47994e24i | − | 0.786338i | ||||||
\(838\) | −6.17387e23 | + | 1.33593e24i | −0.0876967 | + | 0.189762i | ||||
\(839\) | −1.26128e25 | −1.77352 | −0.886758 | − | 0.462234i | \(-0.847048\pi\) | ||||
−0.886758 | + | 0.462234i | \(0.847048\pi\) | |||||||
\(840\) | −5.99834e23 | − | 2.14990e24i | −0.0834944 | − | 0.299256i | ||||
\(841\) | −6.80632e24 | −0.937877 | ||||||||
\(842\) | −1.23950e24 | + | 2.68209e24i | −0.169080 | + | 0.365864i | ||||
\(843\) | 2.41464e24i | 0.326075i | ||||||||
\(844\) | 7.32758e24 | − | 6.23471e24i | 0.979602 | − | 0.833499i | ||||
\(845\) | 5.73801e24i | 0.759415i | ||||||||
\(846\) | 1.63924e24 | + | 7.57559e23i | 0.214781 | + | 0.0992586i | ||||
\(847\) | 1.01234e25 | 1.31317 | ||||||||
\(848\) | 1.32580e25 | + | 2.15067e24i | 1.70260 | + | 0.276190i | ||||
\(849\) | 1.91564e24 | 0.243556 | ||||||||
\(850\) | −2.09927e24 | − | 9.70156e23i | −0.264246 | − | 0.122118i | ||||
\(851\) | 5.23545e23i | 0.0652458i | ||||||||
\(852\) | −4.34385e24 | + | 3.69598e24i | −0.535967 | + | 0.456030i | ||||
\(853\) | 3.35040e24i | 0.409289i | 0.978836 | + | 0.204644i | \(0.0656038\pi\) | ||||
−0.978836 | + | 0.204644i | \(0.934396\pi\) | |||||||
\(854\) | 4.87618e24 | − | 1.05513e25i | 0.589777 | − | 1.27619i | ||||
\(855\) | −6.23164e24 | −0.746261 | ||||||||
\(856\) | 7.34659e24 | − | 2.04974e24i | 0.871082 | − | 0.243037i | ||||
\(857\) | 7.08522e24 | 0.831795 | 0.415897 | − | 0.909412i | \(-0.363468\pi\) | ||||
0.415897 | + | 0.909412i | \(0.363468\pi\) | |||||||
\(858\) | 6.25757e22 | − | 1.35404e23i | 0.00727384 | − | 0.0157395i | ||||
\(859\) | 8.34929e24i | 0.960966i | 0.877004 | + | 0.480483i | \(0.159539\pi\) | ||||
−0.877004 | + | 0.480483i | \(0.840461\pi\) | |||||||
\(860\) | 2.23565e24 | + | 2.62753e24i | 0.254781 | + | 0.299441i | ||||
\(861\) | 3.84239e24i | 0.433585i | ||||||||
\(862\) | −3.21797e24 | − | 1.48715e24i | −0.359559 | − | 0.166166i | ||||
\(863\) | 6.81718e24 | 0.754246 | 0.377123 | − | 0.926163i | \(-0.376913\pi\) | ||||
0.377123 | + | 0.926163i | \(0.376913\pi\) | |||||||
\(864\) | 5.26168e24 | + | 3.55140e24i | 0.576444 | + | 0.389074i | ||||
\(865\) | −1.37702e24 | −0.149383 | ||||||||
\(866\) | −8.55865e24 | − | 3.95529e24i | −0.919397 | − | 0.424890i | ||||
\(867\) | 1.84347e24i | 0.196098i | ||||||||
\(868\) | −7.60428e24 | − | 8.93722e24i | −0.801014 | − | 0.941423i | ||||
\(869\) | 3.41859e24i | 0.356598i | ||||||||
\(870\) | 1.60667e24 | − | 3.47660e24i | 0.165964 | − | 0.359121i | ||||
\(871\) | 3.38965e23 | 0.0346738 | ||||||||
\(872\) | −4.82131e24 | + | 1.34518e24i | −0.488400 | + | 0.136267i | ||||
\(873\) | −8.60087e24 | −0.862822 | ||||||||
\(874\) | 3.49351e23 | − | 7.55942e23i | 0.0347068 | − | 0.0751002i | ||||
\(875\) | − | 1.20125e25i | − | 1.18185i | ||||||
\(876\) | 5.33736e24 | − | 4.54132e24i | 0.520046 | − | 0.442483i | ||||
\(877\) | − | 1.56397e25i | − | 1.50914i | −0.656217 | − | 0.754572i | \(-0.727844\pi\) | ||
0.656217 | − | 0.754572i | \(-0.272156\pi\) | |||||||
\(878\) | 8.80974e24 | + | 4.07133e24i | 0.841899 | + | 0.389075i | ||||
\(879\) | 6.41533e24 | 0.607175 | ||||||||
\(880\) | 1.92660e24 | − | 1.18767e25i | 0.180588 | − | 1.11325i | ||||
\(881\) | −1.62905e25 | −1.51230 | −0.756152 | − | 0.654396i | \(-0.772923\pi\) | ||||
−0.756152 | + | 0.654396i | \(0.772923\pi\) | |||||||
\(882\) | 1.65743e24 | + | 7.65962e23i | 0.152388 | + | 0.0704246i | ||||
\(883\) | 4.63346e24i | 0.421929i | 0.977494 | + | 0.210964i | \(0.0676604\pi\) | ||||
−0.977494 | + | 0.210964i | \(0.932340\pi\) | |||||||
\(884\) | −1.82027e23 | + | 1.54878e23i | −0.0164169 | + | 0.0139684i | ||||
\(885\) | 3.02094e24i | 0.269851i | ||||||||
\(886\) | 1.02340e24 | − | 2.21449e24i | 0.0905441 | − | 0.195924i | ||||
\(887\) | −1.40637e24 | −0.123239 | −0.0616197 | − | 0.998100i | \(-0.519627\pi\) | ||||
−0.0616197 | + | 0.998100i | \(0.519627\pi\) | |||||||
\(888\) | −1.04184e24 | − | 3.73412e24i | −0.0904258 | − | 0.324099i | ||||
\(889\) | −1.87781e25 | −1.61431 | ||||||||
\(890\) | −7.01113e24 | + | 1.51710e25i | −0.596998 | + | 1.29181i | ||||
\(891\) | 1.05585e25i | 0.890519i | ||||||||
\(892\) | 6.57152e24 | + | 7.72343e24i | 0.548990 | + | 0.645222i | ||||
\(893\) | 3.79335e24i | 0.313896i | ||||||||
\(894\) | 3.96450e24 | + | 1.83215e24i | 0.324952 | + | 0.150173i | ||||
\(895\) | 1.11075e25 | 0.901820 | ||||||||
\(896\) | 1.35094e25 | − | 1.50943e24i | 1.08647 | − | 0.121394i | ||||
\(897\) | 1.06349e22 | 0.000847224 | ||||||||
\(898\) | −1.02824e25 | − | 4.75190e24i | −0.811419 | − | 0.374989i | ||||
\(899\) | − | 2.01352e25i | − | 1.57398i | ||||||
\(900\) | 3.03910e24 | + | 3.57182e24i | 0.235334 | + | 0.276585i | ||||
\(901\) | 1.55052e25i | 1.18937i | ||||||||
\(902\) | −8.68921e24 | + | 1.88021e25i | −0.660275 | + | 1.42874i | ||||
\(903\) | 2.80823e24 | 0.211392 | ||||||||
\(904\) | −1.65943e24 | − | 5.94763e24i | −0.123745 | − | 0.443519i | ||||
\(905\) | 2.00716e25 | 1.48276 | ||||||||
\(906\) | −1.76926e24 | + | 3.82842e24i | −0.129480 | + | 0.280175i | ||||
\(907\) | − | 8.93640e24i | − | 0.647889i | −0.946076 | − | 0.323945i | \(-0.894991\pi\) | ||
0.946076 | − | 0.323945i | \(-0.105009\pi\) | |||||||
\(908\) | −1.21712e25 | + | 1.03559e25i | −0.874188 | + | 0.743807i | ||||
\(909\) | 9.31672e24i | 0.662933i | ||||||||
\(910\) | −3.34521e23 | − | 1.54595e23i | −0.0235815 | − | 0.0108980i | ||||
\(911\) | 1.71271e25 | 1.19613 | 0.598064 | − | 0.801448i | \(-0.295937\pi\) | ||||
0.598064 | + | 0.801448i | \(0.295937\pi\) | |||||||
\(912\) | −9.87395e23 | + | 6.08687e24i | −0.0683179 | + | 0.421151i | ||||
\(913\) | 4.51783e24 | 0.309691 | ||||||||
\(914\) | −1.80207e25 | − | 8.32805e24i | −1.22385 | − | 0.565589i | ||||
\(915\) | 5.43158e24i | 0.365466i | ||||||||
\(916\) | −1.41792e24 | + | 1.20644e24i | −0.0945233 | + | 0.0804256i | ||||
\(917\) | − | 6.22800e24i | − | 0.411348i | ||||||
\(918\) | −3.07426e24 | + | 6.65222e24i | −0.201176 | + | 0.435315i | ||||
\(919\) | −1.92318e25 | −1.24692 | −0.623459 | − | 0.781856i | \(-0.714273\pi\) | ||||
−0.623459 | + | 0.781856i | \(0.714273\pi\) | |||||||
\(920\) | 8.26275e23 | − | 2.30536e23i | 0.0530797 | − | 0.0148096i | ||||
\(921\) | −3.03854e24 | −0.193401 | ||||||||
\(922\) | −1.03060e25 | + | 2.23006e25i | −0.649946 | + | 1.40639i | ||||
\(923\) | 9.41669e23i | 0.0588415i | ||||||||
\(924\) | −6.34673e24 | − | 7.45924e24i | −0.392951 | − | 0.461831i | ||||
\(925\) | − | 6.19343e24i | − | 0.379950i | ||||||
\(926\) | −5.39958e23 | − | 2.49536e23i | −0.0328221 | − | 0.0151684i | ||||
\(927\) | 9.00073e24 | 0.542126 | ||||||||
\(928\) | 1.93333e25 | + | 1.30491e25i | 1.15384 | + | 0.778794i | ||||
\(929\) | −1.01792e25 | −0.601979 | −0.300989 | − | 0.953627i | \(-0.597317\pi\) | ||||
−0.300989 | + | 0.953627i | \(0.597317\pi\) | |||||||
\(930\) | 4.97759e24 | + | 2.30034e24i | 0.291685 | + | 0.134799i | ||||
\(931\) | 3.83543e24i | 0.222711i | ||||||||
\(932\) | −5.97007e24 | − | 7.01656e24i | −0.343514 | − | 0.403728i | ||||
\(933\) | − | 6.59366e24i | − | 0.375952i | ||||||
\(934\) | 7.25480e24 | − | 1.56983e25i | 0.409899 | − | 0.886960i | ||||
\(935\) | 1.38897e25 | 0.777670 | ||||||||
\(936\) | 4.66843e23 | − | 1.30252e23i | 0.0259016 | − | 0.00722670i | ||||
\(937\) | 2.57324e25 | 1.41480 | 0.707399 | − | 0.706815i | \(-0.249869\pi\) | ||||
0.707399 | + | 0.706815i | \(0.249869\pi\) | |||||||
\(938\) | 9.33656e24 | − | 2.02029e25i | 0.508701 | − | 1.10075i | ||||
\(939\) | 2.98857e24i | 0.161364i | ||||||||
\(940\) | −2.97606e24 | + | 2.53219e24i | −0.159241 | + | 0.135491i | ||||
\(941\) | − | 1.64698e25i | − | 0.873327i | −0.899625 | − | 0.436663i | \(-0.856160\pi\) | ||
0.899625 | − | 0.436663i | \(-0.143840\pi\) | |||||||
\(942\) | −4.55360e24 | − | 2.10440e24i | −0.239289 | − | 0.110585i | ||||
\(943\) | −1.47676e24 | −0.0769058 | ||||||||
\(944\) | −1.81608e25 | − | 2.94599e24i | −0.937289 | − | 0.152044i | ||||
\(945\) | −1.12995e25 | −0.577947 | ||||||||
\(946\) | 1.37417e25 | + | 6.35057e24i | 0.696570 | + | 0.321912i | ||||
\(947\) | − | 3.53295e25i | − | 1.77485i | −0.460949 | − | 0.887427i | \(-0.652491\pi\) | ||
0.460949 | − | 0.887427i | \(-0.347509\pi\) | |||||||
\(948\) | 1.37457e24 | − | 1.16956e24i | 0.0684376 | − | 0.0582304i | ||||
\(949\) | − | 1.15705e24i | − | 0.0570936i | ||||||
\(950\) | −4.13275e24 | + | 8.94265e24i | −0.202110 | + | 0.437336i | ||||
\(951\) | −8.73690e24 | −0.423470 | ||||||||
\(952\) | 4.21721e24 | + | 1.51151e25i | 0.202587 | + | 0.726101i | ||||
\(953\) | −4.30929e24 | −0.205171 | −0.102585 | − | 0.994724i | \(-0.532712\pi\) | ||||
−0.102585 | + | 0.994724i | \(0.532712\pi\) | |||||||
\(954\) | 1.31907e25 | − | 2.85427e25i | 0.622454 | − | 1.34690i | ||||
\(955\) | 8.12679e23i | 0.0380093i | ||||||||
\(956\) | 3.50152e24 | + | 4.11530e24i | 0.162317 | + | 0.190770i | ||||
\(957\) | − | 1.68054e25i | − | 0.772142i | ||||||
\(958\) | −1.80311e25 | − | 8.33291e24i | −0.821139 | − | 0.379481i | ||||
\(959\) | 6.07532e24 | 0.274228 | ||||||||
\(960\) | −5.43455e24 | + | 3.28854e24i | −0.243141 | + | 0.147129i | ||||
\(961\) | 6.27834e24 | 0.278417 | ||||||||
\(962\) | −5.81025e23 | − | 2.68515e23i | −0.0255392 | − | 0.0118027i | ||||
\(963\) | − | 1.78556e25i | − | 0.777950i | ||||||
\(964\) | 7.93547e24 | + | 9.32646e24i | 0.342703 | + | 0.402775i | ||||
\(965\) | − | 4.45415e24i | − | 0.190670i | ||||||
\(966\) | 2.92931e23 | − | 6.33859e23i | 0.0124297 | − | 0.0268960i | ||||
\(967\) | −2.86774e25 | −1.20619 | −0.603094 | − | 0.797670i | \(-0.706066\pi\) | ||||
−0.603094 | + | 0.797670i | \(0.706066\pi\) | |||||||
\(968\) | −7.74256e24 | − | 2.77505e25i | −0.322808 | − | 1.15699i | ||||
\(969\) | −7.11859e24 | −0.294200 | ||||||||
\(970\) | 7.80747e24 | − | 1.68942e25i | 0.319853 | − | 0.692114i | ||||
\(971\) | 3.16457e25i | 1.28514i | 0.766225 | + | 0.642572i | \(0.222133\pi\) | ||||
−0.766225 | + | 0.642572i | \(0.777867\pi\) | |||||||
\(972\) | 1.74029e25 | − | 1.48074e25i | 0.700583 | − | 0.596094i | ||||
\(973\) | 4.18775e25i | 1.67117i | ||||||||
\(974\) | 4.14332e25 | + | 1.91479e25i | 1.63907 | + | 0.757479i | ||||
\(975\) | −1.25809e23 | −0.00493370 | ||||||||
\(976\) | −3.26527e25 | − | 5.29683e24i | −1.26939 | − | 0.205917i | ||||
\(977\) | 3.66143e25 | 1.41107 | 0.705533 | − | 0.708677i | \(-0.250708\pi\) | ||||
0.705533 | + | 0.708677i | \(0.250708\pi\) | |||||||
\(978\) | 1.08971e25 | + | 5.03597e24i | 0.416323 | + | 0.192399i | ||||
\(979\) | 7.33347e25i | 2.77752i | ||||||||
\(980\) | −3.00907e24 | + | 2.56028e24i | −0.112982 | + | 0.0961315i | ||||
\(981\) | 1.17180e25i | 0.436182i | ||||||||
\(982\) | 2.94448e24 | − | 6.37142e24i | 0.108658 | − | 0.235119i | ||||
\(983\) | −4.80762e25 | −1.75884 | −0.879418 | − | 0.476051i | \(-0.842068\pi\) | ||||
−0.879418 | + | 0.476051i | \(0.842068\pi\) | |||||||
\(984\) | 1.05328e25 | − | 2.93872e24i | 0.382019 | − | 0.106586i | ||||
\(985\) | 9.02337e24 | 0.324460 | ||||||||
\(986\) | −1.12959e25 | + | 2.44426e25i | −0.402687 | + | 0.871353i | ||||
\(987\) | 3.18073e24i | 0.112417i | ||||||||
\(988\) | 6.59763e23 | + | 7.75412e23i | 0.0231182 | + | 0.0271706i | ||||
\(989\) | 1.07930e24i | 0.0374949i | ||||||||
\(990\) | −2.55689e25 | − | 1.18164e25i | −0.880671 | − | 0.406993i | ||||
\(991\) | −2.82526e25 | −0.964789 | −0.482395 | − | 0.875954i | \(-0.660233\pi\) | ||||
−0.482395 | + | 0.875954i | \(0.660233\pi\) | |||||||
\(992\) | −1.86829e25 | + | 2.76802e25i | −0.632551 | + | 0.937174i | ||||
\(993\) | −2.98783e24 | −0.100297 | ||||||||
\(994\) | 5.61251e25 | + | 2.59376e25i | 1.86798 | + | 0.863268i | ||||
\(995\) | 1.95388e25i | 0.644765i | ||||||||
\(996\) | −1.54562e24 | − | 1.81655e24i | −0.0505707 | − | 0.0594352i | ||||
\(997\) | − | 2.70363e25i | − | 0.877078i | −0.898712 | − | 0.438539i | \(-0.855496\pi\) | ||
0.898712 | − | 0.438539i | \(-0.144504\pi\) | |||||||
\(998\) | 1.35871e25 | − | 2.94005e25i | 0.437037 | − | 0.945682i | ||||
\(999\) | −1.96259e25 | −0.625926 |
(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.5.14 | yes | 16 | |
3.2 | odd | 2 | 72.18.d.b.37.3 | 16 | |||
4.3 | odd | 2 | 32.18.b.a.17.10 | 16 | |||
8.3 | odd | 2 | 32.18.b.a.17.7 | 16 | |||
8.5 | even | 2 | inner | 8.18.b.a.5.13 | ✓ | 16 | |
24.5 | odd | 2 | 72.18.d.b.37.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.18.b.a.5.13 | ✓ | 16 | 8.5 | even | 2 | inner | |
8.18.b.a.5.14 | yes | 16 | 1.1 | even | 1 | trivial | |
32.18.b.a.17.7 | 16 | 8.3 | odd | 2 | |||
32.18.b.a.17.10 | 16 | 4.3 | odd | 2 | |||
72.18.d.b.37.3 | 16 | 3.2 | odd | 2 | |||
72.18.d.b.37.4 | 16 | 24.5 | odd | 2 |