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 | 5.11 | ||
Root | \(99.0623 + 145.965i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.18.b.a.5.12 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 214.125 | − | 291.929i | 0.591441 | − | 0.806348i | ||||
\(3\) | 1638.94i | 0.144223i | 0.997397 | + | 0.0721113i | \(0.0229737\pi\) | ||||
−0.997397 | + | 0.0721113i | \(0.977026\pi\) | |||||||
\(4\) | −39373.4 | − | 125018.i | −0.300395 | − | 0.953815i | ||||
\(5\) | 1.21254e6i | 1.38820i | 0.719879 | + | 0.694100i | \(0.244197\pi\) | ||||
−0.719879 | + | 0.694100i | \(0.755803\pi\) | |||||||
\(6\) | 478455. | + | 350938.i | 0.116294 | + | 0.0852991i | ||||
\(7\) | 1.76580e7 | 1.15773 | 0.578866 | − | 0.815423i | \(-0.303495\pi\) | ||||
0.578866 | + | 0.815423i | \(0.303495\pi\) | |||||||
\(8\) | −4.49273e7 | − | 1.52753e7i | −0.946773 | − | 0.321902i | ||||
\(9\) | 1.26454e8 | 0.979200 | ||||||||
\(10\) | 3.53976e8 | + | 2.59635e8i | 1.11937 | + | 0.821038i | ||||
\(11\) | 7.26817e8i | 1.02232i | 0.859485 | + | 0.511161i | \(0.170784\pi\) | ||||
−0.859485 | + | 0.511161i | \(0.829216\pi\) | |||||||
\(12\) | 2.04898e8 | − | 6.45307e7i | 0.137562 | − | 0.0433237i | ||||
\(13\) | − | 3.16645e9i | − | 1.07660i | −0.842753 | − | 0.538300i | \(-0.819067\pi\) | ||
0.842753 | − | 0.538300i | \(-0.180933\pi\) | |||||||
\(14\) | 3.78101e9 | − | 5.15488e9i | 0.684730 | − | 0.933535i | ||||
\(15\) | −1.98729e9 | −0.200210 | ||||||||
\(16\) | −1.40793e10 | + | 9.84479e9i | −0.819526 | + | 0.573042i | ||||
\(17\) | 4.56030e10 | 1.58554 | 0.792771 | − | 0.609520i | \(-0.208638\pi\) | ||||
0.792771 | + | 0.609520i | \(0.208638\pi\) | |||||||
\(18\) | 2.70769e10 | − | 3.69156e10i | 0.579139 | − | 0.789576i | ||||
\(19\) | − | 1.55789e10i | − | 0.210441i | −0.994449 | − | 0.105220i | \(-0.966445\pi\) | ||
0.994449 | − | 0.105220i | \(-0.0335548\pi\) | |||||||
\(20\) | 1.51590e11 | − | 4.77419e10i | 1.32408 | − | 0.417008i | ||||
\(21\) | 2.89404e10i | 0.166971i | ||||||||
\(22\) | 2.12179e11 | + | 1.55629e11i | 0.824347 | + | 0.604643i | ||||
\(23\) | 4.09250e11 | 1.08969 | 0.544843 | − | 0.838538i | \(-0.316589\pi\) | ||||
0.544843 | + | 0.838538i | \(0.316589\pi\) | |||||||
\(24\) | 2.50353e10 | − | 7.36333e10i | 0.0464256 | − | 0.136546i | ||||
\(25\) | −7.07318e11 | −0.927096 | ||||||||
\(26\) | −9.24380e11 | − | 6.78015e11i | −0.868115 | − | 0.636746i | ||||
\(27\) | 4.18904e11i | 0.285445i | ||||||||
\(28\) | −6.95255e11 | − | 2.20757e12i | −0.347777 | − | 1.10426i | ||||
\(29\) | 3.11338e12i | 1.15571i | 0.816139 | + | 0.577855i | \(0.196110\pi\) | ||||
−0.816139 | + | 0.577855i | \(0.803890\pi\) | |||||||
\(30\) | −4.25527e11 | + | 5.80147e11i | −0.118412 | + | 0.161439i | ||||
\(31\) | −6.57077e12 | −1.38370 | −0.691850 | − | 0.722041i | \(-0.743204\pi\) | ||||
−0.691850 | + | 0.722041i | \(0.743204\pi\) | |||||||
\(32\) | −1.40750e11 | + | 6.21818e12i | −0.0226295 | + | 0.999744i | ||||
\(33\) | −1.19121e12 | −0.147442 | ||||||||
\(34\) | 9.76472e12 | − | 1.33128e13i | 0.937754 | − | 1.27850i | ||||
\(35\) | 2.14111e13i | 1.60716i | ||||||||
\(36\) | −4.97892e12 | − | 1.58091e13i | −0.294147 | − | 0.933975i | ||||
\(37\) | 1.36898e13i | 0.640739i | 0.947293 | + | 0.320369i | \(0.103807\pi\) | ||||
−0.947293 | + | 0.320369i | \(0.896193\pi\) | |||||||
\(38\) | −4.54793e12 | − | 3.33582e12i | −0.169689 | − | 0.124463i | ||||
\(39\) | 5.18964e12 | 0.155270 | ||||||||
\(40\) | 1.85219e13 | − | 5.44763e13i | 0.446865 | − | 1.31431i | ||||
\(41\) | −2.81830e12 | −0.0551220 | −0.0275610 | − | 0.999620i | \(-0.508774\pi\) | ||||
−0.0275610 | + | 0.999620i | \(0.508774\pi\) | |||||||
\(42\) | 8.44856e12 | + | 6.19686e12i | 0.134637 | + | 0.0987535i | ||||
\(43\) | − | 1.36024e13i | − | 0.177474i | −0.996055 | − | 0.0887369i | \(-0.971717\pi\) | ||
0.996055 | − | 0.0887369i | \(-0.0282830\pi\) | |||||||
\(44\) | 9.08656e13 | − | 2.86173e13i | 0.975106 | − | 0.307100i | ||||
\(45\) | 1.53331e14i | 1.35932i | ||||||||
\(46\) | 8.76304e13 | − | 1.19472e14i | 0.644486 | − | 0.878667i | ||||
\(47\) | 6.84132e11 | 0.00419091 | 0.00209545 | − | 0.999998i | \(-0.499333\pi\) | ||||
0.00209545 | + | 0.999998i | \(0.499333\pi\) | |||||||
\(48\) | −1.61351e13 | − | 2.30752e13i | −0.0826456 | − | 0.118194i | ||||
\(49\) | 7.91743e13 | 0.340343 | ||||||||
\(50\) | −1.51454e14 | + | 2.06487e14i | −0.548323 | + | 0.747563i | ||||
\(51\) | 7.47407e13i | 0.228671i | ||||||||
\(52\) | −3.95865e14 | + | 1.24674e14i | −1.02688 | + | 0.323405i | ||||
\(53\) | − | 2.47869e14i | − | 0.546862i | −0.961892 | − | 0.273431i | \(-0.911841\pi\) | ||
0.961892 | − | 0.273431i | \(-0.0881585\pi\) | |||||||
\(54\) | 1.22290e14 | + | 8.96977e13i | 0.230168 | + | 0.168824i | ||||
\(55\) | −8.81297e14 | −1.41919 | ||||||||
\(56\) | −7.93327e14 | − | 2.69731e14i | −1.09611 | − | 0.372677i | ||||
\(57\) | 2.55329e13 | 0.0303503 | ||||||||
\(58\) | 9.08887e14 | + | 6.66651e14i | 0.931905 | + | 0.683535i | ||||
\(59\) | − | 2.03296e15i | − | 1.80255i | −0.433245 | − | 0.901276i | \(-0.642632\pi\) | ||
0.433245 | − | 0.901276i | \(-0.357368\pi\) | |||||||
\(60\) | 7.82462e13 | + | 2.48447e14i | 0.0601419 | + | 0.190963i | ||||
\(61\) | 8.92495e14i | 0.596077i | 0.954554 | + | 0.298038i | \(0.0963324\pi\) | ||||
−0.954554 | + | 0.298038i | \(0.903668\pi\) | |||||||
\(62\) | −1.40696e15 | + | 1.91820e15i | −0.818377 | + | 1.11574i | ||||
\(63\) | 2.23292e15 | 1.13365 | ||||||||
\(64\) | 1.78513e15 | + | 1.37255e15i | 0.792758 | + | 0.609537i | ||||
\(65\) | 3.83946e15 | 1.49454 | ||||||||
\(66\) | −2.55068e14 | + | 3.47750e14i | −0.0872031 | + | 0.118889i | ||||
\(67\) | − | 5.06693e15i | − | 1.52444i | −0.647321 | − | 0.762218i | \(-0.724111\pi\) | ||
0.647321 | − | 0.762218i | \(-0.275889\pi\) | |||||||
\(68\) | −1.79554e15 | − | 5.70121e15i | −0.476289 | − | 1.51231i | ||||
\(69\) | 6.70737e14i | 0.157157i | ||||||||
\(70\) | 6.25051e15 | + | 4.58463e15i | 1.29593 | + | 0.950542i | ||||
\(71\) | −6.85113e15 | −1.25912 | −0.629559 | − | 0.776953i | \(-0.716764\pi\) | ||||
−0.629559 | + | 0.776953i | \(0.716764\pi\) | |||||||
\(72\) | −5.68124e15 | − | 1.93162e15i | −0.927080 | − | 0.315207i | ||||
\(73\) | 1.37250e15 | 0.199191 | 0.0995954 | − | 0.995028i | \(-0.468245\pi\) | ||||
0.0995954 | + | 0.995028i | \(0.468245\pi\) | |||||||
\(74\) | 3.99644e15 | + | 2.93131e15i | 0.516659 | + | 0.378959i | ||||
\(75\) | − | 1.15925e15i | − | 0.133708i | ||||||
\(76\) | −1.94765e15 | + | 6.13392e14i | −0.200722 | + | 0.0632154i | ||||
\(77\) | 1.28341e16i | 1.18357i | ||||||||
\(78\) | 1.11123e15 | − | 1.51501e15i | 0.0918331 | − | 0.125202i | ||||
\(79\) | −1.78556e16 | −1.32417 | −0.662085 | − | 0.749429i | \(-0.730328\pi\) | ||||
−0.662085 | + | 0.749429i | \(0.730328\pi\) | |||||||
\(80\) | −1.19372e16 | − | 1.70718e16i | −0.795497 | − | 1.13766i | ||||
\(81\) | 1.56437e16 | 0.938032 | ||||||||
\(82\) | −6.03468e14 | + | 8.22745e14i | −0.0326014 | + | 0.0444475i | ||||
\(83\) | 1.48017e15i | 0.0721354i | 0.999349 | + | 0.0360677i | \(0.0114832\pi\) | ||||
−0.999349 | + | 0.0360677i | \(0.988517\pi\) | |||||||
\(84\) | 3.61809e15 | − | 1.13948e15i | 0.159259 | − | 0.0501573i | ||||
\(85\) | 5.52955e16i | 2.20105i | ||||||||
\(86\) | −3.97094e15 | − | 2.91261e15i | −0.143106 | − | 0.104965i | ||||
\(87\) | −5.10265e15 | −0.166680 | ||||||||
\(88\) | 1.11023e16 | − | 3.26540e16i | 0.329088 | − | 0.967906i | ||||
\(89\) | −3.78700e16 | −1.01972 | −0.509859 | − | 0.860258i | \(-0.670303\pi\) | ||||
−0.509859 | + | 0.860258i | \(0.670303\pi\) | |||||||
\(90\) | 4.47617e16 | + | 3.28319e16i | 1.09609 | + | 0.803960i | ||||
\(91\) | − | 5.59132e16i | − | 1.24642i | ||||||
\(92\) | −1.61135e16 | − | 5.11638e16i | −0.327336 | − | 1.03936i | ||||
\(93\) | − | 1.07691e16i | − | 0.199561i | ||||||
\(94\) | 1.46489e14 | − | 1.99718e14i | 0.00247868 | − | 0.00337933i | ||||
\(95\) | 1.88900e16 | 0.292134 | ||||||||
\(96\) | −1.01912e16 | − | 2.30681e14i | −0.144186 | − | 0.00326368i | ||||
\(97\) | 1.28098e17 | 1.65952 | 0.829760 | − | 0.558121i | \(-0.188477\pi\) | ||||
0.829760 | + | 0.558121i | \(0.188477\pi\) | |||||||
\(98\) | 1.69532e16 | − | 2.31133e16i | 0.201293 | − | 0.274435i | ||||
\(99\) | 9.19090e16i | 1.00106i | ||||||||
\(100\) | 2.78495e16 | + | 8.84278e16i | 0.278495 | + | 0.884278i | ||||
\(101\) | − | 6.82139e16i | − | 0.626818i | −0.949618 | − | 0.313409i | \(-0.898529\pi\) | ||
0.949618 | − | 0.313409i | \(-0.101471\pi\) | |||||||
\(102\) | 2.18190e16 | + | 1.60038e16i | 0.184388 | + | 0.135245i | ||||
\(103\) | −3.08715e16 | −0.240127 | −0.120063 | − | 0.992766i | \(-0.538310\pi\) | ||||
−0.120063 | + | 0.992766i | \(0.538310\pi\) | |||||||
\(104\) | −4.83684e16 | + | 1.42260e17i | −0.346560 | + | 1.01930i | ||||
\(105\) | −3.50915e16 | −0.231789 | ||||||||
\(106\) | −7.23603e16 | − | 5.30749e16i | −0.440961 | − | 0.323437i | ||||
\(107\) | − | 2.71861e17i | − | 1.52962i | −0.644253 | − | 0.764812i | \(-0.722832\pi\) | ||
0.644253 | − | 0.764812i | \(-0.277168\pi\) | |||||||
\(108\) | 5.23707e16 | − | 1.64937e16i | 0.272262 | − | 0.0857463i | ||||
\(109\) | − | 1.32808e17i | − | 0.638407i | −0.947686 | − | 0.319203i | \(-0.896585\pi\) | ||
0.947686 | − | 0.319203i | \(-0.103415\pi\) | |||||||
\(110\) | −1.88707e17 | + | 2.57276e17i | −0.839365 | + | 1.14436i | ||||
\(111\) | −2.24367e16 | −0.0924090 | ||||||||
\(112\) | −2.48613e17 | + | 1.73839e17i | −0.948791 | + | 0.663429i | ||||
\(113\) | −3.78953e17 | −1.34097 | −0.670484 | − | 0.741924i | \(-0.733913\pi\) | ||||
−0.670484 | + | 0.741924i | \(0.733913\pi\) | |||||||
\(114\) | 5.46721e15 | − | 7.45379e15i | 0.0179504 | − | 0.0244729i | ||||
\(115\) | 4.96232e17i | 1.51270i | ||||||||
\(116\) | 3.89230e17 | − | 1.22584e17i | 1.10233 | − | 0.347170i | ||||
\(117\) | − | 4.00411e17i | − | 1.05421i | ||||||
\(118\) | −5.93482e17 | − | 4.35308e17i | −1.45348 | − | 1.06610i | ||||
\(119\) | 8.05257e17 | 1.83563 | ||||||||
\(120\) | 8.92835e16 | + | 3.03563e16i | 0.189553 | + | 0.0644479i | ||||
\(121\) | −2.28165e16 | −0.0451413 | ||||||||
\(122\) | 2.60545e17 | + | 1.91105e17i | 0.480646 | + | 0.352544i | ||||
\(123\) | − | 4.61904e15i | − | 0.00794983i | ||||||
\(124\) | 2.58714e17 | + | 8.21468e17i | 0.415657 | + | 1.31979i | ||||
\(125\) | 6.74428e16i | 0.101205i | ||||||||
\(126\) | 4.78124e17 | − | 6.51856e17i | 0.670488 | − | 0.914117i | ||||
\(127\) | −2.56390e17 | −0.336179 | −0.168089 | − | 0.985772i | \(-0.553760\pi\) | ||||
−0.168089 | + | 0.985772i | \(0.553760\pi\) | |||||||
\(128\) | 7.82929e17 | − | 2.27234e17i | 0.960368 | − | 0.278734i | ||||
\(129\) | 2.22936e16 | 0.0255957 | ||||||||
\(130\) | 8.22122e17 | − | 1.12085e18i | 0.883930 | − | 1.20512i | ||||
\(131\) | 1.61862e18i | 1.63057i | 0.579060 | + | 0.815285i | \(0.303420\pi\) | ||||
−0.579060 | + | 0.815285i | \(0.696580\pi\) | |||||||
\(132\) | 4.69020e16 | + | 1.48923e17i | 0.0442908 | + | 0.140632i | ||||
\(133\) | − | 2.75092e17i | − | 0.243634i | ||||||
\(134\) | −1.47918e18 | − | 1.08495e18i | −1.22923 | − | 0.901614i | ||||
\(135\) | −5.07939e17 | −0.396255 | ||||||||
\(136\) | −2.04882e18 | − | 6.96598e17i | −1.50115 | − | 0.510389i | ||||
\(137\) | −3.32494e17 | −0.228907 | −0.114453 | − | 0.993429i | \(-0.536512\pi\) | ||||
−0.114453 | + | 0.993429i | \(0.536512\pi\) | |||||||
\(138\) | 1.95808e17 | + | 1.43621e17i | 0.126724 | + | 0.0929493i | ||||
\(139\) | 6.37994e17i | 0.388321i | 0.980970 | + | 0.194161i | \(0.0621983\pi\) | ||||
−0.980970 | + | 0.194161i | \(0.937802\pi\) | |||||||
\(140\) | 2.67678e18 | − | 8.43025e17i | 1.53294 | − | 0.482783i | ||||
\(141\) | 1.12125e15i | 0.000604423i | ||||||||
\(142\) | −1.46700e18 | + | 2.00005e18i | −0.744694 | + | 1.01529i | ||||
\(143\) | 2.30143e18 | 1.10063 | ||||||||
\(144\) | −1.78039e18 | + | 1.24491e18i | −0.802479 | + | 0.561123i | ||||
\(145\) | −3.77510e18 | −1.60436 | ||||||||
\(146\) | 2.93887e17 | − | 4.00674e17i | 0.117810 | − | 0.160617i | ||||
\(147\) | 1.29762e17i | 0.0490852i | ||||||||
\(148\) | 1.71147e18 | − | 5.39012e17i | 0.611146 | − | 0.192475i | ||||
\(149\) | 2.77142e18i | 0.934585i | 0.884103 | + | 0.467293i | \(0.154771\pi\) | ||||
−0.884103 | + | 0.467293i | \(0.845229\pi\) | |||||||
\(150\) | −3.38420e17 | − | 2.48225e17i | −0.107815 | − | 0.0790805i | ||||
\(151\) | −4.43299e18 | −1.33473 | −0.667364 | − | 0.744732i | \(-0.732577\pi\) | ||||
−0.667364 | + | 0.744732i | \(0.732577\pi\) | |||||||
\(152\) | −2.37971e17 | + | 6.99917e17i | −0.0677414 | + | 0.199240i | ||||
\(153\) | 5.76668e18 | 1.55256 | ||||||||
\(154\) | 3.74666e18 | + | 2.74810e18i | 0.954373 | + | 0.700014i | ||||
\(155\) | − | 7.96734e18i | − | 1.92085i | ||||||
\(156\) | −2.04333e17 | − | 6.48800e17i | −0.0466423 | − | 0.148099i | ||||
\(157\) | − | 3.50626e18i | − | 0.758048i | −0.925387 | − | 0.379024i | \(-0.876260\pi\) | ||
0.925387 | − | 0.379024i | \(-0.123740\pi\) | |||||||
\(158\) | −3.82332e18 | + | 5.21257e18i | −0.783169 | + | 1.06774i | ||||
\(159\) | 4.06244e17 | 0.0788698 | ||||||||
\(160\) | −7.53981e18 | − | 1.70665e17i | −1.38784 | − | 0.0314142i | ||||
\(161\) | 7.22653e18 | 1.26157 | ||||||||
\(162\) | 3.34971e18 | − | 4.56686e18i | 0.554791 | − | 0.756381i | ||||
\(163\) | − | 2.12490e18i | − | 0.333998i | −0.985957 | − | 0.166999i | \(-0.946592\pi\) | ||
0.985957 | − | 0.166999i | \(-0.0534076\pi\) | |||||||
\(164\) | 1.10966e17 | + | 3.52340e17i | 0.0165584 | + | 0.0525762i | ||||
\(165\) | − | 1.44439e18i | − | 0.204679i | ||||||
\(166\) | 4.32105e17 | + | 3.16941e17i | 0.0581662 | + | 0.0426638i | ||||
\(167\) | 3.81083e18 | 0.487450 | 0.243725 | − | 0.969844i | \(-0.421631\pi\) | ||||
0.243725 | + | 0.969844i | \(0.421631\pi\) | |||||||
\(168\) | 4.42073e17 | − | 1.30022e18i | 0.0537484 | − | 0.158084i | ||||
\(169\) | −1.37601e18 | −0.159069 | ||||||||
\(170\) | 1.61424e19 | + | 1.18401e19i | 1.77481 | + | 1.30179i | ||||
\(171\) | − | 1.97001e18i | − | 0.206064i | ||||||
\(172\) | −1.70055e18 | + | 5.35573e17i | −0.169277 | + | 0.0533122i | ||||
\(173\) | 8.51874e18i | 0.807204i | 0.914935 | + | 0.403602i | \(0.132242\pi\) | ||||
−0.914935 | + | 0.403602i | \(0.867758\pi\) | |||||||
\(174\) | −1.09260e18 | + | 1.48961e18i | −0.0985811 | + | 0.134402i | ||||
\(175\) | −1.24898e19 | −1.07333 | ||||||||
\(176\) | −7.15537e18 | − | 1.02331e19i | −0.585834 | − | 0.837819i | ||||
\(177\) | 3.33191e18 | 0.259969 | ||||||||
\(178\) | −8.10890e18 | + | 1.10554e19i | −0.603103 | + | 0.822248i | ||||
\(179\) | − | 1.98628e19i | − | 1.40860i | −0.709900 | − | 0.704302i | \(-0.751260\pi\) | ||
0.709900 | − | 0.704302i | \(-0.248740\pi\) | |||||||
\(180\) | 1.91692e19 | − | 6.03715e18i | 1.29654 | − | 0.408334i | ||||
\(181\) | 2.34430e19i | 1.51267i | 0.654182 | + | 0.756337i | \(0.273013\pi\) | ||||
−0.654182 | + | 0.756337i | \(0.726987\pi\) | |||||||
\(182\) | −1.63227e19 | − | 1.19724e19i | −1.00504 | − | 0.737181i | ||||
\(183\) | −1.46275e18 | −0.0859677 | ||||||||
\(184\) | −1.83865e19 | − | 6.25140e18i | −1.03169 | − | 0.350773i | ||||
\(185\) | −1.65994e19 | −0.889473 | ||||||||
\(186\) | −3.14382e18 | − | 2.30593e18i | −0.160915 | − | 0.118028i | ||||
\(187\) | 3.31451e19i | 1.62093i | ||||||||
\(188\) | −2.69366e16 | − | 8.55291e16i | −0.00125893 | − | 0.00399735i | ||||
\(189\) | 7.39701e18i | 0.330469i | ||||||||
\(190\) | 4.04482e18 | − | 5.51455e18i | 0.172780 | − | 0.235562i | ||||
\(191\) | −1.50710e19 | −0.615686 | −0.307843 | − | 0.951437i | \(-0.599607\pi\) | ||||
−0.307843 | + | 0.951437i | \(0.599607\pi\) | |||||||
\(192\) | −2.24954e18 | + | 2.92573e18i | −0.0879089 | + | 0.114334i | ||||
\(193\) | 9.30819e18 | 0.348039 | 0.174020 | − | 0.984742i | \(-0.444324\pi\) | ||||
0.174020 | + | 0.984742i | \(0.444324\pi\) | |||||||
\(194\) | 2.74289e19 | − | 3.73955e19i | 0.981508 | − | 1.33815i | ||||
\(195\) | 6.29265e18i | 0.215546i | ||||||||
\(196\) | −3.11736e18 | − | 9.89824e18i | −0.102237 | − | 0.324625i | ||||
\(197\) | − | 4.15016e19i | − | 1.30347i | −0.758445 | − | 0.651737i | \(-0.774041\pi\) | ||
0.758445 | − | 0.651737i | \(-0.225959\pi\) | |||||||
\(198\) | 2.68309e19 | + | 1.96800e19i | 0.807201 | + | 0.592066i | ||||
\(199\) | 1.63945e19 | 0.472550 | 0.236275 | − | 0.971686i | \(-0.424073\pi\) | ||||
0.236275 | + | 0.971686i | \(0.424073\pi\) | |||||||
\(200\) | 3.17779e19 | + | 1.08045e19i | 0.877750 | + | 0.298435i | ||||
\(201\) | 8.30440e18 | 0.219858 | ||||||||
\(202\) | −1.99136e19 | − | 1.46063e19i | −0.505433 | − | 0.370726i | ||||
\(203\) | 5.49760e19i | 1.33800i | ||||||||
\(204\) | 9.34396e18 | − | 2.94279e18i | 0.218110 | − | 0.0686915i | ||||
\(205\) | − | 3.41731e18i | − | 0.0765203i | ||||||
\(206\) | −6.61034e18 | + | 9.01228e18i | −0.142021 | + | 0.193626i | ||||
\(207\) | 5.17513e19 | 1.06702 | ||||||||
\(208\) | 3.11731e19 | + | 4.45816e19i | 0.616938 | + | 0.882302i | ||||
\(209\) | 1.13230e19 | 0.215138 | ||||||||
\(210\) | −7.51395e18 | + | 1.02442e19i | −0.137090 | + | 0.186903i | ||||
\(211\) | − | 7.37209e19i | − | 1.29178i | −0.763429 | − | 0.645892i | \(-0.776486\pi\) | ||
0.763429 | − | 0.645892i | \(-0.223514\pi\) | |||||||
\(212\) | −3.09882e19 | + | 9.75945e18i | −0.521605 | + | 0.164275i | ||||
\(213\) | − | 1.12286e19i | − | 0.181593i | ||||||
\(214\) | −7.93642e19 | − | 5.82121e19i | −1.23341 | − | 0.904683i | ||||
\(215\) | 1.64935e19 | 0.246369 | ||||||||
\(216\) | 6.39888e18 | − | 1.88203e19i | 0.0918855 | − | 0.270252i | ||||
\(217\) | −1.16027e20 | −1.60195 | ||||||||
\(218\) | −3.87704e19 | − | 2.84374e19i | −0.514778 | − | 0.377580i | ||||
\(219\) | 2.24946e18i | 0.0287278i | ||||||||
\(220\) | 3.46996e19 | + | 1.10178e20i | 0.426316 | + | 1.35364i | ||||
\(221\) | − | 1.44400e20i | − | 1.70699i | ||||||
\(222\) | −4.80425e18 | + | 6.54994e18i | −0.0546545 | + | 0.0745138i | ||||
\(223\) | 3.21618e19 | 0.352167 | 0.176083 | − | 0.984375i | \(-0.443657\pi\) | ||||
0.176083 | + | 0.984375i | \(0.443657\pi\) | |||||||
\(224\) | −2.48537e18 | + | 1.09801e20i | −0.0261988 | + | 1.15744i | ||||
\(225\) | −8.94433e19 | −0.907813 | ||||||||
\(226\) | −8.11430e19 | + | 1.10627e20i | −0.793103 | + | 1.08129i | ||||
\(227\) | 9.66411e19i | 0.909792i | 0.890545 | + | 0.454896i | \(0.150323\pi\) | ||||
−0.890545 | + | 0.454896i | \(0.849677\pi\) | |||||||
\(228\) | −1.00531e18 | − | 3.19208e18i | −0.00911708 | − | 0.0289486i | ||||
\(229\) | 3.07436e16i | 0.000268629i | 1.00000 | 0.000134314i | \(4.27536e-5\pi\) | |||||
−1.00000 | 0.000134314i | \(0.999957\pi\) | ||||||||
\(230\) | 1.44865e20 | + | 1.06256e20i | 1.21976 | + | 0.894674i | ||||
\(231\) | −2.10344e19 | −0.170698 | ||||||||
\(232\) | 4.75577e19 | − | 1.39876e20i | 0.372026 | − | 1.09420i | ||||
\(233\) | 2.21535e20 | 1.67077 | 0.835385 | − | 0.549666i | \(-0.185245\pi\) | ||||
0.835385 | + | 0.549666i | \(0.185245\pi\) | |||||||
\(234\) | −1.16892e20 | − | 8.57378e19i | −0.850058 | − | 0.623501i | ||||
\(235\) | 8.29539e17i | 0.00581781i | ||||||||
\(236\) | −2.54158e20 | + | 8.00447e19i | −1.71930 | + | 0.541478i | ||||
\(237\) | − | 2.92643e19i | − | 0.190975i | ||||||
\(238\) | 1.72425e20 | − | 2.35078e20i | 1.08567 | − | 1.48016i | ||||
\(239\) | −4.51465e18 | −0.0274310 | −0.0137155 | − | 0.999906i | \(-0.504366\pi\) | ||||
−0.0137155 | + | 0.999906i | \(0.504366\pi\) | |||||||
\(240\) | 2.79797e19 | − | 1.95644e19i | 0.164077 | − | 0.114729i | ||||
\(241\) | −1.81683e19 | −0.102842 | −0.0514209 | − | 0.998677i | \(-0.516375\pi\) | ||||
−0.0514209 | + | 0.998677i | \(0.516375\pi\) | |||||||
\(242\) | −4.88558e18 | + | 6.66082e18i | −0.0266984 | + | 0.0363996i | ||||
\(243\) | 7.97365e19i | 0.420731i | ||||||||
\(244\) | 1.11578e20 | − | 3.51405e19i | 0.568547 | − | 0.179059i | ||||
\(245\) | 9.60021e19i | 0.472464i | ||||||||
\(246\) | −1.34843e18 | − | 9.89049e17i | −0.00641033 | − | 0.00470186i | ||||
\(247\) | −4.93298e19 | −0.226561 | ||||||||
\(248\) | 2.95207e20 | + | 1.00370e20i | 1.31005 | + | 0.445416i | ||||
\(249\) | −2.42592e18 | −0.0104035 | ||||||||
\(250\) | 1.96885e19 | + | 1.44412e19i | 0.0816062 | + | 0.0598566i | ||||
\(251\) | − | 3.26192e20i | − | 1.30691i | −0.756964 | − | 0.653456i | \(-0.773318\pi\) | ||
0.756964 | − | 0.653456i | \(-0.226682\pi\) | |||||||
\(252\) | −8.79178e19 | − | 2.79157e20i | −0.340543 | − | 1.08129i | ||||
\(253\) | 2.97450e20i | 1.11401i | ||||||||
\(254\) | −5.48995e19 | + | 7.48479e19i | −0.198830 | + | 0.271077i | ||||
\(255\) | −9.06262e19 | −0.317441 | ||||||||
\(256\) | 1.01308e20 | − | 2.77216e20i | 0.343245 | − | 0.939246i | ||||
\(257\) | −1.22717e20 | −0.402228 | −0.201114 | − | 0.979568i | \(-0.564456\pi\) | ||||
−0.201114 | + | 0.979568i | \(0.564456\pi\) | |||||||
\(258\) | 4.77360e18 | − | 6.50815e18i | 0.0151384 | − | 0.0206391i | ||||
\(259\) | 2.41734e20i | 0.741804i | ||||||||
\(260\) | −1.51172e20 | − | 4.80003e20i | −0.448951 | − | 1.42551i | ||||
\(261\) | 3.93699e20i | 1.13167i | ||||||||
\(262\) | 4.72523e20 | + | 3.46587e20i | 1.31481 | + | 0.964386i | ||||
\(263\) | 3.35733e18 | 0.00904420 | 0.00452210 | − | 0.999990i | \(-0.498561\pi\) | ||||
0.00452210 | + | 0.999990i | \(0.498561\pi\) | |||||||
\(264\) | 5.35180e19 | + | 1.81961e19i | 0.139594 | + | 0.0474619i | ||||
\(265\) | 3.00552e20 | 0.759153 | ||||||||
\(266\) | −8.03073e19 | − | 5.89038e19i | −0.196454 | − | 0.144095i | ||||
\(267\) | − | 6.20668e19i | − | 0.147066i | ||||||
\(268\) | −6.33459e20 | + | 1.99502e20i | −1.45403 | + | 0.457933i | ||||
\(269\) | 2.42496e20i | 0.539275i | 0.962962 | + | 0.269637i | \(0.0869038\pi\) | ||||
−0.962962 | + | 0.269637i | \(0.913096\pi\) | |||||||
\(270\) | −1.08762e20 | + | 1.48282e20i | −0.234361 | + | 0.319519i | ||||
\(271\) | −2.38962e20 | −0.498988 | −0.249494 | − | 0.968376i | \(-0.580264\pi\) | ||||
−0.249494 | + | 0.968376i | \(0.580264\pi\) | |||||||
\(272\) | −6.42060e20 | + | 4.48952e20i | −1.29939 | + | 0.908582i | ||||
\(273\) | 9.16386e19 | 0.179761 | ||||||||
\(274\) | −7.11951e19 | + | 9.70647e19i | −0.135385 | + | 0.184579i | ||||
\(275\) | − | 5.14091e20i | − | 0.947791i | ||||||
\(276\) | 8.38545e19 | − | 2.64092e19i | 0.149899 | − | 0.0472093i | ||||
\(277\) | − | 5.05700e20i | − | 0.876628i | −0.898822 | − | 0.438314i | \(-0.855576\pi\) | ||
0.898822 | − | 0.438314i | \(-0.144424\pi\) | |||||||
\(278\) | 1.86249e20 | + | 1.36610e20i | 0.313122 | + | 0.229669i | ||||
\(279\) | −8.30901e20 | −1.35492 | ||||||||
\(280\) | 3.27060e20 | − | 9.61942e20i | 0.517349 | − | 1.52162i | ||||
\(281\) | −2.23986e20 | −0.343730 | −0.171865 | − | 0.985120i | \(-0.554979\pi\) | ||||
−0.171865 | + | 0.985120i | \(0.554979\pi\) | |||||||
\(282\) | 3.27327e17 | + | 2.40088e17i | 0.000487376 | + | 0.000357481i | ||||
\(283\) | − | 5.21843e20i | − | 0.753971i | −0.926219 | − | 0.376986i | \(-0.876961\pi\) | ||
0.926219 | − | 0.376986i | \(-0.123039\pi\) | |||||||
\(284\) | 2.69752e20 | + | 8.56518e20i | 0.378233 | + | 1.20097i | ||||
\(285\) | 3.09597e19i | 0.0421323i | ||||||||
\(286\) | 4.92793e20 | − | 6.71856e20i | 0.650959 | − | 0.887493i | ||||
\(287\) | −4.97656e19 | −0.0638165 | ||||||||
\(288\) | −1.77984e19 | + | 7.86314e20i | −0.0221588 | + | 0.978949i | ||||
\(289\) | 1.25239e21 | 1.51394 | ||||||||
\(290\) | −8.08342e20 | + | 1.10206e21i | −0.948882 | + | 1.29367i | ||||
\(291\) | 2.09945e20i | 0.239340i | ||||||||
\(292\) | −5.40401e19 | − | 1.71588e20i | −0.0598359 | − | 0.189991i | ||||
\(293\) | − | 4.94662e20i | − | 0.532027i | −0.963969 | − | 0.266014i | \(-0.914293\pi\) | ||
0.963969 | − | 0.266014i | \(-0.0857066\pi\) | |||||||
\(294\) | 3.78813e19 | + | 2.77852e19i | 0.0395797 | + | 0.0290310i | ||||
\(295\) | 2.46506e21 | 2.50230 | ||||||||
\(296\) | 2.09115e20 | − | 6.15044e20i | 0.206255 | − | 0.606634i | ||||
\(297\) | −3.04467e20 | −0.291817 | ||||||||
\(298\) | 8.09058e20 | + | 5.93429e20i | 0.753601 | + | 0.552752i | ||||
\(299\) | − | 1.29587e21i | − | 1.17316i | ||||||
\(300\) | −1.44928e20 | + | 4.56437e19i | −0.127533 | + | 0.0401653i | ||||
\(301\) | − | 2.40191e20i | − | 0.205467i | ||||||
\(302\) | −9.49212e20 | + | 1.29412e21i | −0.789413 | + | 1.07626i | ||||
\(303\) | 1.11799e20 | 0.0904012 | ||||||||
\(304\) | 1.53371e20 | + | 2.19340e20i | 0.120592 | + | 0.172462i | ||||
\(305\) | −1.08219e21 | −0.827473 | ||||||||
\(306\) | 1.23479e21 | − | 1.68346e21i | 0.918249 | − | 1.25191i | ||||
\(307\) | 1.86234e21i | 1.34705i | 0.739166 | + | 0.673523i | \(0.235220\pi\) | ||||
−0.739166 | + | 0.673523i | \(0.764780\pi\) | |||||||
\(308\) | 1.60450e21 | − | 5.05323e20i | 1.12891 | − | 0.355540i | ||||
\(309\) | − | 5.05965e19i | − | 0.0346317i | ||||||
\(310\) | −2.32590e21 | − | 1.70600e21i | −1.54888 | − | 1.13607i | ||||
\(311\) | −6.47522e20 | −0.419557 | −0.209779 | − | 0.977749i | \(-0.567274\pi\) | ||||
−0.209779 | + | 0.977749i | \(0.567274\pi\) | |||||||
\(312\) | −2.33157e20 | − | 7.92731e19i | −0.147005 | − | 0.0499818i | ||||
\(313\) | −1.62295e21 | −0.995817 | −0.497909 | − | 0.867230i | \(-0.665898\pi\) | ||||
−0.497909 | + | 0.867230i | \(0.665898\pi\) | |||||||
\(314\) | −1.02358e21 | − | 7.50775e20i | −0.611251 | − | 0.448341i | ||||
\(315\) | 2.70751e21i | 1.57373i | ||||||||
\(316\) | 7.03035e20 | + | 2.23228e21i | 0.397774 | + | 1.26301i | ||||
\(317\) | − | 2.11436e21i | − | 1.16460i | −0.812976 | − | 0.582298i | \(-0.802154\pi\) | ||
0.812976 | − | 0.582298i | \(-0.197846\pi\) | |||||||
\(318\) | 8.69867e19 | − | 1.18594e20i | 0.0466469 | − | 0.0635966i | ||||
\(319\) | −2.26286e21 | −1.18151 | ||||||||
\(320\) | −1.66428e21 | + | 2.16455e21i | −0.846158 | + | 1.10051i | ||||
\(321\) | 4.45565e20 | 0.220606 | ||||||||
\(322\) | 1.54738e21 | − | 2.10964e21i | 0.746142 | − | 1.01726i | ||||
\(323\) | − | 7.10443e20i | − | 0.333663i | ||||||
\(324\) | −6.15947e20 | − | 1.95576e21i | −0.281780 | − | 0.894709i | ||||
\(325\) | 2.23969e21i | 0.998113i | ||||||||
\(326\) | −6.20320e20 | − | 4.54993e20i | −0.269318 | − | 0.197540i | ||||
\(327\) | 2.17664e20 | 0.0920726 | ||||||||
\(328\) | 1.26619e20 | + | 4.30504e19i | 0.0521880 | + | 0.0177439i | ||||
\(329\) | 1.20804e19 | 0.00485195 | ||||||||
\(330\) | −4.21661e20 | − | 3.09280e20i | −0.165042 | − | 0.121055i | ||||
\(331\) | 4.36509e21i | 1.66516i | 0.553908 | + | 0.832578i | \(0.313136\pi\) | ||||
−0.553908 | + | 0.832578i | \(0.686864\pi\) | |||||||
\(332\) | 1.85049e20 | − | 5.82793e19i | 0.0688038 | − | 0.0216691i | ||||
\(333\) | 1.73112e21i | 0.627411i | ||||||||
\(334\) | 8.15993e20 | − | 1.11249e21i | 0.288298 | − | 0.393054i | ||||
\(335\) | 6.14386e21 | 2.11622 | ||||||||
\(336\) | −2.84913e20 | − | 4.07462e20i | −0.0956815 | − | 0.136837i | ||||
\(337\) | −2.59518e21 | −0.849792 | −0.424896 | − | 0.905242i | \(-0.639689\pi\) | ||||
−0.424896 | + | 0.905242i | \(0.639689\pi\) | |||||||
\(338\) | −2.94638e20 | + | 4.01698e20i | −0.0940799 | + | 0.128265i | ||||
\(339\) | − | 6.21082e20i | − | 0.193398i | ||||||
\(340\) | 6.91296e21 | − | 2.17717e21i | 2.09939 | − | 0.661183i | ||||
\(341\) | − | 4.77575e21i | − | 1.41459i | ||||||
\(342\) | −5.75104e20 | − | 4.21828e20i | −0.166159 | − | 0.121875i | ||||
\(343\) | −2.70973e21 | −0.763706 | ||||||||
\(344\) | −2.07781e20 | + | 6.11120e20i | −0.0571292 | + | 0.168027i | ||||
\(345\) | −8.13296e20 | −0.218166 | ||||||||
\(346\) | 2.48687e21 | + | 1.82407e21i | 0.650888 | + | 0.477414i | ||||
\(347\) | − | 7.40818e20i | − | 0.189195i | −0.995516 | − | 0.0945977i | \(-0.969844\pi\) | ||
0.995516 | − | 0.0945977i | \(-0.0301565\pi\) | |||||||
\(348\) | 2.00909e20 | + | 6.37925e20i | 0.0500697 | + | 0.158981i | ||||
\(349\) | 1.81507e20i | 0.0441446i | 0.999756 | + | 0.0220723i | \(0.00702640\pi\) | ||||
−0.999756 | + | 0.0220723i | \(0.992974\pi\) | |||||||
\(350\) | −2.67438e21 | + | 3.64615e21i | −0.634811 | + | 0.865477i | ||||
\(351\) | 1.32644e21 | 0.307310 | ||||||||
\(352\) | −4.51948e21 | − | 1.02300e20i | −1.02206 | − | 0.0231346i | ||||
\(353\) | 3.26526e21 | 0.720830 | 0.360415 | − | 0.932792i | \(-0.382635\pi\) | ||||
0.360415 | + | 0.932792i | \(0.382635\pi\) | |||||||
\(354\) | 7.13444e20 | − | 9.72683e20i | 0.153756 | − | 0.209625i | ||||
\(355\) | − | 8.30728e21i | − | 1.74791i | ||||||
\(356\) | 1.49107e21 | + | 4.73445e21i | 0.306318 | + | 0.972623i | ||||
\(357\) | 1.31977e21i | 0.264739i | ||||||||
\(358\) | −5.79852e21 | − | 4.25311e21i | −1.13583 | − | 0.833107i | ||||
\(359\) | 2.19419e21 | 0.419732 | 0.209866 | − | 0.977730i | \(-0.432697\pi\) | ||||
0.209866 | + | 0.977730i | \(0.432697\pi\) | |||||||
\(360\) | 2.34217e21 | − | 6.88875e21i | 0.437570 | − | 1.28697i | ||||
\(361\) | 5.23769e21 | 0.955715 | ||||||||
\(362\) | 6.84370e21 | + | 5.01972e21i | 1.21974 | + | 0.894658i | ||||
\(363\) | − | 3.73950e19i | − | 0.00651040i | ||||||
\(364\) | −6.99018e21 | + | 2.20149e21i | −1.18885 | + | 0.374417i | ||||
\(365\) | 1.66422e21i | 0.276516i | ||||||||
\(366\) | −3.13210e20 | + | 4.27019e20i | −0.0508448 | + | 0.0693199i | ||||
\(367\) | −1.08265e22 | −1.71723 | −0.858615 | − | 0.512621i | \(-0.828675\pi\) | ||||
−0.858615 | + | 0.512621i | \(0.828675\pi\) | |||||||
\(368\) | −5.76197e21 | + | 4.02898e21i | −0.893026 | + | 0.624437i | ||||
\(369\) | −3.56386e20 | −0.0539755 | ||||||||
\(370\) | −3.55434e21 | + | 4.84585e21i | −0.526071 | + | 0.717225i | ||||
\(371\) | − | 4.37687e21i | − | 0.633120i | ||||||
\(372\) | −1.34634e21 | + | 4.24017e20i | −0.190344 | + | 0.0599471i | ||||
\(373\) | − | 5.20618e20i | − | 0.0719439i | −0.999353 | − | 0.0359719i | \(-0.988547\pi\) | ||
0.999353 | − | 0.0359719i | \(-0.0114527\pi\) | |||||||
\(374\) | 9.67601e21 | + | 7.09717e21i | 1.30704 | + | 0.958686i | ||||
\(375\) | −1.10535e20 | −0.0145960 | ||||||||
\(376\) | −3.07362e19 | − | 1.04503e19i | −0.00396784 | − | 0.00134906i | ||||
\(377\) | 9.85837e21 | 1.24424 | ||||||||
\(378\) | 2.15940e21 | + | 1.58388e21i | 0.266473 | + | 0.195453i | ||||
\(379\) | 2.99720e21i | 0.361645i | 0.983516 | + | 0.180823i | \(0.0578760\pi\) | ||||
−0.983516 | + | 0.180823i | \(0.942124\pi\) | |||||||
\(380\) | −7.43764e20 | − | 2.36160e21i | −0.0877556 | − | 0.278642i | ||||
\(381\) | − | 4.20209e20i | − | 0.0484845i | ||||||
\(382\) | −3.22708e21 | + | 4.39968e21i | −0.364142 | + | 0.496458i | ||||
\(383\) | −1.22679e22 | −1.35388 | −0.676939 | − | 0.736039i | \(-0.736694\pi\) | ||||
−0.676939 | + | 0.736039i | \(0.736694\pi\) | |||||||
\(384\) | 3.72424e20 | + | 1.28318e21i | 0.0401997 | + | 0.138507i | ||||
\(385\) | −1.55619e22 | −1.64304 | ||||||||
\(386\) | 1.99311e21 | − | 2.71733e21i | 0.205845 | − | 0.280641i | ||||
\(387\) | − | 1.72008e21i | − | 0.173782i | ||||||
\(388\) | −5.04365e21 | − | 1.60146e22i | −0.498511 | − | 1.58287i | ||||
\(389\) | 1.60002e21i | 0.154722i | 0.997003 | + | 0.0773612i | \(0.0246495\pi\) | ||||
−0.997003 | + | 0.0773612i | \(0.975351\pi\) | |||||||
\(390\) | 1.83701e21 | + | 1.34741e21i | 0.173805 | + | 0.127483i | ||||
\(391\) | 1.86630e22 | 1.72774 | ||||||||
\(392\) | −3.55709e21 | − | 1.20941e21i | −0.322228 | − | 0.109557i | ||||
\(393\) | −2.65283e21 | −0.235165 | ||||||||
\(394\) | −1.21155e22 | − | 8.88652e21i | −1.05105 | − | 0.770928i | ||||
\(395\) | − | 2.16506e22i | − | 1.83821i | ||||||
\(396\) | 1.14903e22 | − | 3.61877e21i | 0.954823 | − | 0.300713i | ||||
\(397\) | 2.44521e22i | 1.98883i | 0.105546 | + | 0.994414i | \(0.466341\pi\) | ||||
−0.105546 | + | 0.994414i | \(0.533659\pi\) | |||||||
\(398\) | 3.51047e21 | − | 4.78604e21i | 0.279485 | − | 0.381040i | ||||
\(399\) | 4.50859e20 | 0.0351375 | ||||||||
\(400\) | 9.95858e21 | − | 6.96340e21i | 0.759779 | − | 0.531266i | ||||
\(401\) | 2.46119e22 | 1.83830 | 0.919152 | − | 0.393903i | \(-0.128875\pi\) | ||||
0.919152 | + | 0.393903i | \(0.128875\pi\) | |||||||
\(402\) | 1.77818e21 | − | 2.42430e21i | 0.130033 | − | 0.177282i | ||||
\(403\) | 2.08061e22i | 1.48969i | ||||||||
\(404\) | −8.52799e21 | + | 2.68581e21i | −0.597868 | + | 0.188293i | ||||
\(405\) | 1.89687e22i | 1.30218i | ||||||||
\(406\) | 1.60491e22 | + | 1.17717e22i | 1.07890 | + | 0.791350i | ||||
\(407\) | −9.94995e21 | −0.655041 | ||||||||
\(408\) | 1.14168e21 | − | 3.35790e21i | 0.0736097 | − | 0.216499i | ||||
\(409\) | −5.67464e21 | −0.358336 | −0.179168 | − | 0.983819i | \(-0.557341\pi\) | ||||
−0.179168 | + | 0.983819i | \(0.557341\pi\) | |||||||
\(410\) | −9.97613e20 | − | 7.31730e20i | −0.0617020 | − | 0.0452573i | ||||
\(411\) | − | 5.44938e20i | − | 0.0330135i | ||||||
\(412\) | 1.21551e21 | + | 3.85950e21i | 0.0721329 | + | 0.229037i | ||||
\(413\) | − | 3.58981e22i | − | 2.08687i | ||||||
\(414\) | 1.10812e22 | − | 1.51077e22i | 0.631080 | − | 0.860391i | ||||
\(415\) | −1.79477e21 | −0.100138 | ||||||||
\(416\) | 1.96896e22 | + | 4.45679e20i | 1.07632 | + | 0.0243629i | ||||
\(417\) | −1.04564e21 | −0.0560047 | ||||||||
\(418\) | 2.42453e21 | − | 3.30551e21i | 0.127242 | − | 0.173476i | ||||
\(419\) | 2.70146e22i | 1.38925i | 0.719374 | + | 0.694623i | \(0.244429\pi\) | ||||
−0.719374 | + | 0.694623i | \(0.755571\pi\) | |||||||
\(420\) | 1.38167e21 | + | 4.38708e21i | 0.0696283 | + | 0.221084i | ||||
\(421\) | − | 1.26169e22i | − | 0.623094i | −0.950231 | − | 0.311547i | \(-0.899153\pi\) | ||
0.950231 | − | 0.311547i | \(-0.100847\pi\) | |||||||
\(422\) | −2.15213e22 | − | 1.57855e22i | −1.04163 | − | 0.764014i | ||||
\(423\) | 8.65113e19 | 0.00410374 | ||||||||
\(424\) | −3.78627e21 | + | 1.11361e22i | −0.176036 | + | 0.517754i | ||||
\(425\) | −3.22558e22 | −1.46995 | ||||||||
\(426\) | −3.27796e21 | − | 2.40432e21i | −0.146427 | − | 0.107402i | ||||
\(427\) | 1.57597e22i | 0.690097i | ||||||||
\(428\) | −3.39876e22 | + | 1.07041e22i | −1.45898 | + | 0.459492i | ||||
\(429\) | 3.77192e21i | 0.158736i | ||||||||
\(430\) | 3.53166e21 | − | 4.81493e21i | 0.145713 | − | 0.198659i | ||||
\(431\) | 4.26128e21 | 0.172378 | 0.0861892 | − | 0.996279i | \(-0.472531\pi\) | ||||
0.0861892 | + | 0.996279i | \(0.472531\pi\) | |||||||
\(432\) | −4.12403e21 | − | 5.89790e21i | −0.163572 | − | 0.233930i | ||||
\(433\) | −1.62172e21 | −0.0630707 | −0.0315353 | − | 0.999503i | \(-0.510040\pi\) | ||||
−0.0315353 | + | 0.999503i | \(0.510040\pi\) | |||||||
\(434\) | −2.48442e22 | + | 3.38716e22i | −0.947462 | + | 1.29173i | ||||
\(435\) | − | 6.18718e21i | − | 0.231384i | ||||||
\(436\) | −1.66034e22 | + | 5.22908e21i | −0.608922 | + | 0.191774i | ||||
\(437\) | − | 6.37565e21i | − | 0.229315i | ||||||
\(438\) | 6.56682e20 | + | 4.81664e20i | 0.0231646 | + | 0.0169908i | ||||
\(439\) | 1.56475e22 | 0.541375 | 0.270687 | − | 0.962667i | \(-0.412749\pi\) | ||||
0.270687 | + | 0.962667i | \(0.412749\pi\) | |||||||
\(440\) | 3.95943e22 | + | 1.34620e22i | 1.34365 | + | 0.456839i | ||||
\(441\) | 1.00119e22 | 0.333264 | ||||||||
\(442\) | −4.21545e22 | − | 3.09195e22i | −1.37643 | − | 1.00959i | ||||
\(443\) | − | 3.08815e22i | − | 0.989161i | −0.869132 | − | 0.494581i | \(-0.835322\pi\) | ||
0.869132 | − | 0.494581i | \(-0.164678\pi\) | |||||||
\(444\) | 8.83409e20 | + | 2.80500e21i | 0.0277592 | + | 0.0881410i | ||||
\(445\) | − | 4.59190e22i | − | 1.41557i | ||||||
\(446\) | 6.88662e21 | − | 9.38896e21i | 0.208286 | − | 0.283969i | ||||
\(447\) | −4.54220e21 | −0.134788 | ||||||||
\(448\) | 3.15218e22 | + | 2.42366e22i | 0.917801 | + | 0.705680i | ||||
\(449\) | −1.44678e22 | −0.413340 | −0.206670 | − | 0.978411i | \(-0.566263\pi\) | ||||
−0.206670 | + | 0.978411i | \(0.566263\pi\) | |||||||
\(450\) | −1.91520e22 | + | 2.61111e22i | −0.536918 | + | 0.732013i | ||||
\(451\) | − | 2.04839e21i | − | 0.0563524i | ||||||
\(452\) | 1.49206e22 | + | 4.73761e22i | 0.402820 | + | 1.27903i | ||||
\(453\) | − | 7.26542e21i | − | 0.192498i | ||||||
\(454\) | 2.82124e22 | + | 2.06932e22i | 0.733609 | + | 0.538088i | ||||
\(455\) | 6.77971e22 | 1.73027 | ||||||||
\(456\) | −1.14712e21 | − | 3.90022e20i | −0.0287349 | − | 0.00976984i | ||||
\(457\) | −1.09366e22 | −0.268903 | −0.134452 | − | 0.990920i | \(-0.542927\pi\) | ||||
−0.134452 | + | 0.990920i | \(0.542927\pi\) | |||||||
\(458\) | 8.97495e18 | + | 6.58295e18i | 0.000216608 | + | 0.000158878i | ||||
\(459\) | 1.91033e22i | 0.452585i | ||||||||
\(460\) | 6.20382e22 | − | 1.95383e22i | 1.44284 | − | 0.454408i | ||||
\(461\) | 3.78938e22i | 0.865187i | 0.901589 | + | 0.432594i | \(0.142402\pi\) | ||||
−0.901589 | + | 0.432594i | \(0.857598\pi\) | |||||||
\(462\) | −4.50398e21 | + | 6.14056e21i | −0.100958 | + | 0.137642i | ||||
\(463\) | 5.34510e21 | 0.117630 | 0.0588149 | − | 0.998269i | \(-0.481268\pi\) | ||||
0.0588149 | + | 0.998269i | \(0.481268\pi\) | |||||||
\(464\) | −3.06506e22 | − | 4.38343e22i | −0.662271 | − | 0.947135i | ||||
\(465\) | 1.30580e22 | 0.277030 | ||||||||
\(466\) | 4.74360e22 | − | 6.46725e22i | 0.988162 | − | 1.34722i | ||||
\(467\) | 2.81699e21i | 0.0576224i | 0.999585 | + | 0.0288112i | \(0.00917216\pi\) | ||||
−0.999585 | + | 0.0288112i | \(0.990828\pi\) | |||||||
\(468\) | −5.00587e22 | + | 1.57655e22i | −1.00552 | + | 0.316679i | ||||
\(469\) | − | 8.94718e22i | − | 1.76489i | ||||||
\(470\) | 2.42167e20 | + | 1.77625e20i | 0.00469118 | + | 0.00344089i | ||||
\(471\) | 5.74655e21 | 0.109328 | ||||||||
\(472\) | −3.10541e22 | + | 9.13357e22i | −0.580246 | + | 1.70661i | ||||
\(473\) | 9.88647e21 | 0.181435 | ||||||||
\(474\) | −8.54310e21 | − | 6.26620e21i | −0.153992 | − | 0.112951i | ||||
\(475\) | 1.10192e22i | 0.195099i | ||||||||
\(476\) | −3.17057e22 | − | 1.00672e23i | −0.551415 | − | 1.75085i | ||||
\(477\) | − | 3.13441e22i | − | 0.535487i | ||||||
\(478\) | −9.66697e20 | + | 1.31796e21i | −0.0162238 | + | 0.0221190i | ||||
\(479\) | −9.05318e22 | −1.49262 | −0.746310 | − | 0.665598i | \(-0.768177\pi\) | ||||
−0.746310 | + | 0.665598i | \(0.768177\pi\) | |||||||
\(480\) | 2.79711e20 | − | 1.23573e22i | 0.00453063 | − | 0.200158i | ||||
\(481\) | 4.33480e22 | 0.689820 | ||||||||
\(482\) | −3.89028e21 | + | 5.30386e21i | −0.0608249 | + | 0.0829263i | ||||
\(483\) | 1.18439e22i | 0.181946i | ||||||||
\(484\) | 8.98364e20 | + | 2.85249e21i | 0.0135602 | + | 0.0430565i | ||||
\(485\) | 1.55324e23i | 2.30374i | ||||||||
\(486\) | 2.32774e22 | + | 1.70735e22i | 0.339255 | + | 0.248837i | ||||
\(487\) | −3.07462e22 | −0.440347 | −0.220173 | − | 0.975461i | \(-0.570662\pi\) | ||||
−0.220173 | + | 0.975461i | \(0.570662\pi\) | |||||||
\(488\) | 1.36331e22 | − | 4.00974e22i | 0.191879 | − | 0.564350i | ||||
\(489\) | 3.48259e21 | 0.0481700 | ||||||||
\(490\) | 2.80258e22 | + | 2.05564e22i | 0.380971 | + | 0.279435i | ||||
\(491\) | 1.94168e22i | 0.259409i | 0.991553 | + | 0.129704i | \(0.0414028\pi\) | ||||
−0.991553 | + | 0.129704i | \(0.958597\pi\) | |||||||
\(492\) | −5.77465e20 | + | 1.81867e20i | −0.00758267 | + | 0.00238809i | ||||
\(493\) | 1.41979e23i | 1.83243i | ||||||||
\(494\) | −1.05627e22 | + | 1.44008e22i | −0.133997 | + | 0.182687i | ||||
\(495\) | −1.11444e23 | −1.38967 | ||||||||
\(496\) | 9.25122e22 | − | 6.46879e22i | 1.13398 | − | 0.792919i | ||||
\(497\) | −1.20977e23 | −1.45772 | ||||||||
\(498\) | −5.19448e20 | + | 7.08196e20i | −0.00615308 | + | 0.00838888i | ||||
\(499\) | − | 7.79434e22i | − | 0.907664i | −0.891087 | − | 0.453832i | \(-0.850057\pi\) | ||
0.891087 | − | 0.453832i | \(-0.149943\pi\) | |||||||
\(500\) | 8.43159e21 | − | 2.65545e21i | 0.0965305 | − | 0.0304014i | ||||
\(501\) | 6.24573e21i | 0.0703012i | ||||||||
\(502\) | −9.52249e22 | − | 6.98457e22i | −1.05383 | − | 0.772962i | ||||
\(503\) | 1.18157e23 | 1.28568 | 0.642838 | − | 0.766002i | \(-0.277757\pi\) | ||||
0.642838 | + | 0.766002i | \(0.277757\pi\) | |||||||
\(504\) | −1.00319e23 | − | 3.41085e22i | −1.07331 | − | 0.364925i | ||||
\(505\) | 8.27122e22 | 0.870148 | ||||||||
\(506\) | 8.68343e22 | + | 6.36913e22i | 0.898280 | + | 0.658871i | ||||
\(507\) | − | 2.25521e21i | − | 0.0229413i | ||||||
\(508\) | 1.00950e22 | + | 3.20535e22i | 0.100986 | + | 0.320652i | ||||
\(509\) | − | 2.87932e21i | − | 0.0283262i | −0.999900 | − | 0.0141631i | \(-0.995492\pi\) | ||
0.999900 | − | 0.0141631i | \(-0.00450841\pi\) | |||||||
\(510\) | −1.94053e22 | + | 2.64564e22i | −0.187747 | + | 0.255968i | ||||
\(511\) | 2.42357e22 | 0.230610 | ||||||||
\(512\) | −5.92351e22 | − | 8.89336e22i | −0.554350 | − | 0.832284i | ||||
\(513\) | 6.52605e21 | 0.0600694 | ||||||||
\(514\) | −2.62767e22 | + | 3.58246e22i | −0.237894 | + | 0.324336i | ||||
\(515\) | − | 3.74329e22i | − | 0.333344i | ||||||
\(516\) | −8.77773e20 | − | 2.78711e21i | −0.00768882 | − | 0.0244136i | ||||
\(517\) | 4.97239e20i | 0.00428446i | ||||||||
\(518\) | 7.05691e22 | + | 5.17611e22i | 0.598152 | + | 0.438733i | ||||
\(519\) | −1.39617e22 | −0.116417 | ||||||||
\(520\) | −1.72497e23 | − | 5.86488e22i | −1.41499 | − | 0.481095i | ||||
\(521\) | 1.28391e23 | 1.03613 | 0.518066 | − | 0.855340i | \(-0.326652\pi\) | ||||
0.518066 | + | 0.855340i | \(0.326652\pi\) | |||||||
\(522\) | 1.14932e23 | + | 8.43007e22i | 0.912521 | + | 0.669317i | ||||
\(523\) | 1.89027e22i | 0.147659i | 0.997271 | + | 0.0738293i | \(0.0235220\pi\) | ||||
−0.997271 | + | 0.0738293i | \(0.976478\pi\) | |||||||
\(524\) | 2.02358e23 | − | 6.37306e22i | 1.55526 | − | 0.489815i | ||||
\(525\) | − | 2.04701e22i | − | 0.154798i | ||||||
\(526\) | 7.18887e20 | − | 9.80103e20i | 0.00534911 | − | 0.00729277i | ||||
\(527\) | −2.99647e23 | −2.19391 | ||||||||
\(528\) | 1.67715e22 | − | 1.17272e22i | 0.120832 | − | 0.0844904i | ||||
\(529\) | 2.64353e22 | 0.187418 | ||||||||
\(530\) | 6.43555e22 | − | 8.77399e22i | 0.448995 | − | 0.612142i | ||||
\(531\) | − | 2.57077e23i | − | 1.76506i | ||||||
\(532\) | −3.43915e22 | + | 1.08313e22i | −0.232382 | + | 0.0731865i | ||||
\(533\) | 8.92403e21i | 0.0593444i | ||||||||
\(534\) | −1.81191e22 | − | 1.32900e22i | −0.118587 | − | 0.0869811i | ||||
\(535\) | 3.29643e23 | 2.12342 | ||||||||
\(536\) | −7.73987e22 | + | 2.27644e23i | −0.490719 | + | 1.44329i | ||||
\(537\) | 3.25539e22 | 0.203152 | ||||||||
\(538\) | 7.07916e22 | + | 5.19243e22i | 0.434843 | + | 0.318949i | ||||
\(539\) | 5.75452e22i | 0.347940i | ||||||||
\(540\) | 1.99993e22 | + | 6.35017e22i | 0.119033 | + | 0.377954i | ||||
\(541\) | − | 3.25660e23i | − | 1.90804i | −0.299744 | − | 0.954020i | \(-0.596901\pi\) | ||
0.299744 | − | 0.954020i | \(-0.403099\pi\) | |||||||
\(542\) | −5.11676e22 | + | 6.97600e22i | −0.295122 | + | 0.402358i | ||||
\(543\) | −3.84218e22 | −0.218162 | ||||||||
\(544\) | −6.41863e21 | + | 2.83568e23i | −0.0358799 | + | 1.58514i | ||||
\(545\) | 1.61035e23 | 0.886236 | ||||||||
\(546\) | 1.96221e22 | − | 2.67520e22i | 0.106318 | − | 0.144950i | ||||
\(547\) | 4.90295e22i | 0.261556i | 0.991412 | + | 0.130778i | \(0.0417476\pi\) | ||||
−0.991412 | + | 0.130778i | \(0.958252\pi\) | |||||||
\(548\) | 1.30914e22 | + | 4.15679e22i | 0.0687625 | + | 0.218335i | ||||
\(549\) | 1.12860e23i | 0.583679i | ||||||||
\(550\) | −1.50078e23 | − | 1.10080e23i | −0.764249 | − | 0.560562i | ||||
\(551\) | 4.85029e22 | 0.243209 | ||||||||
\(552\) | 1.02457e22 | − | 3.01344e22i | 0.0505893 | − | 0.148792i | ||||
\(553\) | −3.15294e23 | −1.53303 | ||||||||
\(554\) | −1.47629e23 | − | 1.08283e23i | −0.706867 | − | 0.518473i | ||||
\(555\) | − | 2.72055e22i | − | 0.128282i | ||||||
\(556\) | 7.97611e22 | − | 2.51200e22i | 0.370387 | − | 0.116650i | ||||
\(557\) | 2.60011e23i | 1.18911i | 0.804054 | + | 0.594556i | \(0.202672\pi\) | ||||
−0.804054 | + | 0.594556i | \(0.797328\pi\) | |||||||
\(558\) | −1.77916e23 | + | 2.42564e23i | −0.801355 | + | 1.09254i | ||||
\(559\) | −4.30714e22 | −0.191068 | ||||||||
\(560\) | −2.10787e23 | − | 3.01454e23i | −0.920972 | − | 1.31711i | ||||
\(561\) | −5.43228e22 | −0.233775 | ||||||||
\(562\) | −4.79610e22 | + | 6.53882e22i | −0.203296 | + | 0.277166i | ||||
\(563\) | 1.80701e23i | 0.754467i | 0.926118 | + | 0.377233i | \(0.123125\pi\) | ||||
−0.926118 | + | 0.377233i | \(0.876875\pi\) | |||||||
\(564\) | 1.40177e20 | − | 4.41475e19i | 0.000576508 | − | 0.000181566i | ||||
\(565\) | − | 4.59496e23i | − | 1.86153i | ||||||
\(566\) | −1.52341e23 | − | 1.11739e23i | −0.607963 | − | 0.445930i | ||||
\(567\) | 2.76237e23 | 1.08599 | ||||||||
\(568\) | 3.07803e23 | + | 1.04653e23i | 1.19210 | + | 0.405313i | ||||
\(569\) | −3.54026e23 | −1.35077 | −0.675384 | − | 0.737467i | \(-0.736022\pi\) | ||||
−0.675384 | + | 0.737467i | \(0.736022\pi\) | |||||||
\(570\) | 9.03803e21 | + | 6.62923e21i | 0.0339733 | + | 0.0249188i | ||||
\(571\) | 1.77850e23i | 0.658637i | 0.944219 | + | 0.329318i | \(0.106819\pi\) | ||||
−0.944219 | + | 0.329318i | \(0.893181\pi\) | |||||||
\(572\) | −9.06152e22 | − | 2.87722e23i | −0.330624 | − | 1.04980i | ||||
\(573\) | − | 2.47006e22i | − | 0.0887958i | ||||||
\(574\) | −1.06560e22 | + | 1.45280e22i | −0.0377437 | + | 0.0514583i | ||||
\(575\) | −2.89470e23 | −1.01024 | ||||||||
\(576\) | 2.25737e23 | + | 1.73565e23i | 0.776268 | + | 0.596858i | ||||
\(577\) | −3.55869e23 | −1.20586 | −0.602928 | − | 0.797796i | \(-0.705999\pi\) | ||||
−0.602928 | + | 0.797796i | \(0.705999\pi\) | |||||||
\(578\) | 2.68168e23 | − | 3.65610e23i | 0.895407 | − | 1.22076i | ||||
\(579\) | 1.52556e22i | 0.0501951i | ||||||||
\(580\) | 1.48639e23 | + | 4.71958e23i | 0.481941 | + | 1.53026i | ||||
\(581\) | 2.61369e22i | 0.0835134i | ||||||||
\(582\) | 6.12891e22 | + | 4.49544e22i | 0.192991 | + | 0.141556i | ||||
\(583\) | 1.80156e23 | 0.559069 | ||||||||
\(584\) | −6.16629e22 | − | 2.09654e22i | −0.188588 | − | 0.0641200i | ||||
\(585\) | 4.85515e23 | 1.46345 | ||||||||
\(586\) | −1.44406e23 | − | 1.05919e23i | −0.428999 | − | 0.314663i | ||||
\(587\) | 2.22604e23i | 0.651791i | 0.945406 | + | 0.325896i | \(0.105666\pi\) | ||||
−0.945406 | + | 0.325896i | \(0.894334\pi\) | |||||||
\(588\) | 1.62226e22 | − | 5.10917e21i | 0.0468182 | − | 0.0147449i | ||||
\(589\) | 1.02365e23i | 0.291187i | ||||||||
\(590\) | 5.27829e23 | − | 7.19622e23i | 1.47996 | − | 2.01773i | ||||
\(591\) | 6.80188e22 | 0.187990 | ||||||||
\(592\) | −1.34773e23 | − | 1.92743e23i | −0.367170 | − | 0.525102i | ||||
\(593\) | 6.01922e23 | 1.61650 | 0.808250 | − | 0.588840i | \(-0.200415\pi\) | ||||
0.808250 | + | 0.588840i | \(0.200415\pi\) | |||||||
\(594\) | −6.51938e22 | + | 8.88828e22i | −0.172592 | + | 0.235306i | ||||
\(595\) | 9.76408e23i | 2.54822i | ||||||||
\(596\) | 3.46478e23 | − | 1.09120e23i | 0.891421 | − | 0.280745i | ||||
\(597\) | 2.68697e22i | 0.0681523i | ||||||||
\(598\) | −3.78302e23 | − | 2.77478e23i | −0.945974 | − | 0.693854i | ||||
\(599\) | 2.83674e23 | 0.699346 | 0.349673 | − | 0.936872i | \(-0.386293\pi\) | ||||
0.349673 | + | 0.936872i | \(0.386293\pi\) | |||||||
\(600\) | −1.77079e22 | + | 5.20822e22i | −0.0430410 | + | 0.126591i | ||||
\(601\) | −4.18303e23 | −1.00244 | −0.501220 | − | 0.865320i | \(-0.667115\pi\) | ||||
−0.501220 | + | 0.865320i | \(0.667115\pi\) | |||||||
\(602\) | −7.01189e22 | − | 5.14309e22i | −0.165678 | − | 0.121522i | ||||
\(603\) | − | 6.40734e23i | − | 1.49273i | ||||||
\(604\) | 1.74542e23 | + | 5.54205e23i | 0.400946 | + | 1.27308i | ||||
\(605\) | − | 2.76660e22i | − | 0.0626651i | ||||||
\(606\) | 2.39388e22 | − | 3.26373e22i | 0.0534670 | − | 0.0728949i | ||||
\(607\) | −2.31638e23 | −0.510159 | −0.255080 | − | 0.966920i | \(-0.582102\pi\) | ||||
−0.255080 | + | 0.966920i | \(0.582102\pi\) | |||||||
\(608\) | 9.68723e22 | + | 2.19273e21i | 0.210387 | + | 0.00476216i | ||||
\(609\) | −9.01026e22 | −0.192970 | ||||||||
\(610\) | −2.31723e23 | + | 3.15922e23i | −0.489402 | + | 0.667232i | ||||
\(611\) | − | 2.16627e21i | − | 0.00451193i | ||||||
\(612\) | −2.27054e23 | − | 7.20942e23i | −0.466382 | − | 1.48086i | ||||
\(613\) | − | 2.79613e23i | − | 0.566425i | −0.959057 | − | 0.283213i | \(-0.908600\pi\) | ||
0.959057 | − | 0.283213i | \(-0.0914002\pi\) | |||||||
\(614\) | 5.43671e23 | + | 3.98772e23i | 1.08619 | + | 0.796699i | ||||
\(615\) | 5.60078e21 | 0.0110360 | ||||||||
\(616\) | 1.96045e23 | − | 5.76604e23i | 0.380995 | − | 1.12058i | ||||
\(617\) | −1.73444e23 | −0.332457 | −0.166229 | − | 0.986087i | \(-0.553159\pi\) | ||||
−0.166229 | + | 0.986087i | \(0.553159\pi\) | |||||||
\(618\) | −1.47706e22 | − | 1.08340e22i | −0.0279252 | − | 0.0204826i | ||||
\(619\) | − | 6.77105e23i | − | 1.26266i | −0.775515 | − | 0.631329i | \(-0.782510\pi\) | ||
0.775515 | − | 0.631329i | \(-0.217490\pi\) | |||||||
\(620\) | −9.96064e23 | + | 3.13701e23i | −1.83214 | + | 0.577014i | ||||
\(621\) | 1.71436e23i | 0.311046i | ||||||||
\(622\) | −1.38650e23 | + | 1.89031e23i | −0.248143 | + | 0.338309i | ||||
\(623\) | −6.68708e23 | −1.18056 | ||||||||
\(624\) | −7.30667e22 | + | 5.10909e22i | −0.127248 | + | 0.0889763i | ||||
\(625\) | −6.21418e23 | −1.06759 | ||||||||
\(626\) | −3.47514e23 | + | 4.73788e23i | −0.588967 | + | 0.802975i | ||||
\(627\) | 1.85577e22i | 0.0310278i | ||||||||
\(628\) | −4.38347e23 | + | 1.38053e23i | −0.723037 | + | 0.227714i | ||||
\(629\) | 6.24294e23i | 1.01592i | ||||||||
\(630\) | 7.90403e23 | + | 5.79745e23i | 1.26898 | + | 0.930770i | ||||
\(631\) | 1.02867e24 | 1.62940 | 0.814698 | − | 0.579885i | \(-0.196903\pi\) | ||||
0.814698 | + | 0.579885i | \(0.196903\pi\) | |||||||
\(632\) | 8.02204e23 | + | 2.72749e23i | 1.25369 | + | 0.426253i | ||||
\(633\) | 1.20824e23 | 0.186304 | ||||||||
\(634\) | −6.17243e23 | − | 4.52736e23i | −0.939070 | − | 0.688790i | ||||
\(635\) | − | 3.10884e23i | − | 0.466683i | ||||||
\(636\) | −1.59952e22 | − | 5.07879e22i | −0.0236921 | − | 0.0752272i | ||||
\(637\) | − | 2.50702e23i | − | 0.366414i | ||||||
\(638\) | −4.84534e23 | + | 6.60595e23i | −0.698792 | + | 0.952707i | ||||
\(639\) | −8.66353e23 | −1.23293 | ||||||||
\(640\) | 2.75531e23 | + | 9.49335e23i | 0.386938 | + | 1.33318i | ||||
\(641\) | 7.31083e23 | 1.01315 | 0.506575 | − | 0.862196i | \(-0.330911\pi\) | ||||
0.506575 | + | 0.862196i | \(0.330911\pi\) | |||||||
\(642\) | 9.54063e22 | − | 1.30073e23i | 0.130476 | − | 0.177886i | ||||
\(643\) | − | 5.31860e23i | − | 0.717801i | −0.933376 | − | 0.358901i | \(-0.883152\pi\) | ||
0.933376 | − | 0.358901i | \(-0.116848\pi\) | |||||||
\(644\) | −2.84533e23 | − | 9.03449e23i | −0.378968 | − | 1.20330i | ||||
\(645\) | 2.70319e22i | 0.0355319i | ||||||||
\(646\) | −2.07399e23 | − | 1.52123e23i | −0.269048 | − | 0.197342i | ||||
\(647\) | 7.87216e23 | 1.00788 | 0.503939 | − | 0.863740i | \(-0.331884\pi\) | ||||
0.503939 | + | 0.863740i | \(0.331884\pi\) | |||||||
\(648\) | −7.02831e23 | − | 2.38962e23i | −0.888103 | − | 0.301955i | ||||
\(649\) | 1.47759e24 | 1.84279 | ||||||||
\(650\) | 6.53831e23 | + | 4.79573e23i | 0.804826 | + | 0.590325i | ||||
\(651\) | − | 1.90161e23i | − | 0.231038i | ||||||
\(652\) | −2.65651e23 | + | 8.36644e22i | −0.318572 | + | 0.100331i | ||||
\(653\) | − | 2.77252e22i | − | 0.0328180i | −0.999865 | − | 0.0164090i | \(-0.994777\pi\) | ||
0.999865 | − | 0.0164090i | \(-0.00522338\pi\) | |||||||
\(654\) | 4.66072e22 | − | 6.35425e22i | 0.0544555 | − | 0.0742426i | ||||
\(655\) | −1.96265e24 | −2.26356 | ||||||||
\(656\) | 3.96799e22 | − | 2.77456e22i | 0.0451739 | − | 0.0315872i | ||||
\(657\) | 1.73559e23 | 0.195048 | ||||||||
\(658\) | 2.58671e21 | − | 3.52662e21i | 0.00286964 | − | 0.00391236i | ||||
\(659\) | − | 1.48992e24i | − | 1.63169i | −0.578273 | − | 0.815843i | \(-0.696273\pi\) | ||
0.578273 | − | 0.815843i | \(-0.303727\pi\) | |||||||
\(660\) | −1.80576e23 | + | 5.68707e22i | −0.195225 | + | 0.0614844i | ||||
\(661\) | 2.01553e22i | 0.0215118i | 0.999942 | + | 0.0107559i | \(0.00342377\pi\) | ||||
−0.999942 | + | 0.0107559i | \(0.996576\pi\) | |||||||
\(662\) | 1.27430e24 | + | 9.34672e23i | 1.34270 | + | 0.984842i | ||||
\(663\) | 2.36663e23 | 0.246187 | ||||||||
\(664\) | 2.26100e22 | − | 6.65002e22i | 0.0232205 | − | 0.0682958i | ||||
\(665\) | 3.33560e23 | 0.338213 | ||||||||
\(666\) | 5.05366e23 | + | 3.70676e23i | 0.505912 | + | 0.371077i | ||||
\(667\) | 1.27415e24i | 1.25936i | ||||||||
\(668\) | −1.50045e23 | − | 4.76424e23i | −0.146427 | − | 0.464937i | ||||
\(669\) | 5.27113e22i | 0.0507904i | ||||||||
\(670\) | 1.31555e24 | − | 1.79357e24i | 1.25162 | − | 1.70641i | ||||
\(671\) | −6.48681e23 | −0.609382 | ||||||||
\(672\) | −1.79957e23 | − | 4.07337e21i | −0.166928 | − | 0.00377846i | ||||
\(673\) | −7.70622e23 | −0.705851 | −0.352926 | − | 0.935651i | \(-0.614813\pi\) | ||||
−0.352926 | + | 0.935651i | \(0.614813\pi\) | |||||||
\(674\) | −5.55691e23 | + | 7.57608e23i | −0.502602 | + | 0.685228i | ||||
\(675\) | − | 2.96299e23i | − | 0.264635i | ||||||
\(676\) | 5.41782e22 | + | 1.72027e23i | 0.0477835 | + | 0.151722i | ||||
\(677\) | 8.03721e23i | 0.700006i | 0.936749 | + | 0.350003i | \(0.113819\pi\) | ||||
−0.936749 | + | 0.350003i | \(0.886181\pi\) | |||||||
\(678\) | −1.81312e23 | − | 1.32989e23i | −0.155946 | − | 0.114383i | ||||
\(679\) | 2.26195e24 | 1.92128 | ||||||||
\(680\) | 8.44655e23 | − | 2.48428e24i | 0.708522 | − | 2.08389i | ||||
\(681\) | −1.58389e23 | −0.131212 | ||||||||
\(682\) | −1.39418e24 | − | 1.02261e24i | −1.14065 | − | 0.836645i | ||||
\(683\) | 3.12264e23i | 0.252317i | 0.992010 | + | 0.126158i | \(0.0402647\pi\) | ||||
−0.992010 | + | 0.126158i | \(0.959735\pi\) | |||||||
\(684\) | −2.46288e23 | + | 7.75659e22i | −0.196547 | + | 0.0619005i | ||||
\(685\) | − | 4.03163e23i | − | 0.317768i | ||||||
\(686\) | −5.80220e23 | + | 7.91049e23i | −0.451687 | + | 0.615813i | ||||
\(687\) | −5.03869e19 | −3.87423e−5 | ||||||||
\(688\) | 1.33913e23 | + | 1.91513e23i | 0.101700 | + | 0.145444i | ||||
\(689\) | −7.84867e23 | −0.588752 | ||||||||
\(690\) | −1.74147e23 | + | 2.37425e23i | −0.129032 | + | 0.175918i | ||||
\(691\) | 1.46577e24i | 1.07276i | 0.843977 | + | 0.536379i | \(0.180208\pi\) | ||||
−0.843977 | + | 0.536379i | \(0.819792\pi\) | |||||||
\(692\) | 1.06500e24 | − | 3.35411e23i | 0.769923 | − | 0.242480i | ||||
\(693\) | 1.62293e24i | 1.15896i | ||||||||
\(694\) | −2.16266e23 | − | 1.58627e23i | −0.152557 | − | 0.111898i | ||||
\(695\) | −7.73595e23 | −0.539067 | ||||||||
\(696\) | 2.29249e23 | + | 7.79444e22i | 0.157808 | + | 0.0536545i | ||||
\(697\) | −1.28523e23 | −0.0873982 | ||||||||
\(698\) | 5.29872e22 | + | 3.88651e22i | 0.0355959 | + | 0.0261089i | ||||
\(699\) | 3.63083e23i | 0.240963i | ||||||||
\(700\) | 4.91767e23 | + | 1.56146e24i | 0.322423 | + | 1.02376i | ||||
\(701\) | 2.04249e24i | 1.32299i | 0.749950 | + | 0.661495i | \(0.230078\pi\) | ||||
−0.749950 | + | 0.661495i | \(0.769922\pi\) | |||||||
\(702\) | 2.84024e23 | − | 3.87227e23i | 0.181756 | − | 0.247799i | ||||
\(703\) | 2.13271e23 | 0.134838 | ||||||||
\(704\) | −9.97597e23 | + | 1.29746e24i | −0.623143 | + | 0.810453i | ||||
\(705\) | −1.35957e21 | −0.000839060 | ||||||||
\(706\) | 6.99172e23 | − | 9.53225e23i | 0.426328 | − | 0.581240i | ||||
\(707\) | − | 1.20452e24i | − | 0.725687i | ||||||
\(708\) | −1.31189e23 | − | 4.16551e23i | −0.0780933 | − | 0.247962i | ||||
\(709\) | − | 2.96920e24i | − | 1.74641i | −0.487352 | − | 0.873206i | \(-0.662037\pi\) | ||
0.487352 | − | 0.873206i | \(-0.337963\pi\) | |||||||
\(710\) | −2.42514e24 | − | 1.77879e24i | −1.40942 | − | 1.03378i | ||||
\(711\) | −2.25791e24 | −1.29663 | ||||||||
\(712\) | 1.70140e24 | + | 5.78475e23i | 0.965442 | + | 0.328250i | ||||
\(713\) | −2.68909e24 | −1.50780 | ||||||||
\(714\) | 3.85280e23 | + | 2.82595e23i | 0.213472 | + | 0.156578i | ||||
\(715\) | 2.79058e24i | 1.52790i | ||||||||
\(716\) | −2.48321e24 | + | 7.82064e23i | −1.34355 | + | 0.423138i | ||||
\(717\) | − | 7.39925e21i | − | 0.00395617i | ||||||
\(718\) | 4.69831e23 | − | 6.40549e23i | 0.248247 | − | 0.338450i | ||||
\(719\) | 4.13376e23 | 0.215849 | 0.107924 | − | 0.994159i | \(-0.465580\pi\) | ||||
0.107924 | + | 0.994159i | \(0.465580\pi\) | |||||||
\(720\) | −1.50951e24 | − | 2.15880e24i | −0.778950 | − | 1.11400i | ||||
\(721\) | −5.45128e23 | −0.278003 | ||||||||
\(722\) | 1.12152e24 | − | 1.52903e24i | 0.565249 | − | 0.770639i | ||||
\(723\) | − | 2.97768e22i | − | 0.0148321i | ||||||
\(724\) | 2.93081e24 | − | 9.23030e23i | 1.44281 | − | 0.454400i | ||||
\(725\) | − | 2.20215e24i | − | 1.07146i | ||||||
\(726\) | −1.09167e22 | − | 8.00719e21i | −0.00524965 | − | 0.00385052i | ||||
\(727\) | 2.92465e24 | 1.39005 | 0.695027 | − | 0.718983i | \(-0.255392\pi\) | ||||
0.695027 | + | 0.718983i | \(0.255392\pi\) | |||||||
\(728\) | −8.54090e23 | + | 2.51203e24i | −0.401224 | + | 1.18007i | ||||
\(729\) | 1.88955e24 | 0.877353 | ||||||||
\(730\) | 4.85834e23 | + | 3.56350e23i | 0.222969 | + | 0.163543i | ||||
\(731\) | − | 6.20311e23i | − | 0.281392i | ||||||
\(732\) | 5.75933e22 | + | 1.82871e23i | 0.0258243 | + | 0.0819973i | ||||
\(733\) | − | 3.06846e24i | − | 1.35999i | −0.733216 | − | 0.679996i | \(-0.761982\pi\) | ||
0.733216 | − | 0.679996i | \(-0.238018\pi\) | |||||||
\(734\) | −2.31823e24 | + | 3.16059e24i | −1.01564 | + | 1.38469i | ||||
\(735\) | −1.57342e23 | −0.0681400 | ||||||||
\(736\) | −5.76020e22 | + | 2.54479e24i | −0.0246590 | + | 1.08941i | ||||
\(737\) | 3.68273e24 | 1.55846 | ||||||||
\(738\) | −7.63109e22 | + | 1.04039e23i | −0.0319233 | + | 0.0435230i | ||||
\(739\) | 3.06955e24i | 1.26939i | 0.772761 | + | 0.634697i | \(0.218875\pi\) | ||||
−0.772761 | + | 0.634697i | \(0.781125\pi\) | |||||||
\(740\) | 6.53574e23 | + | 2.07523e24i | 0.267193 | + | 0.848393i | ||||
\(741\) | − | 8.08486e22i | − | 0.0326752i | ||||||
\(742\) | −1.27774e24 | − | 9.37196e23i | −0.510515 | − | 0.374453i | ||||
\(743\) | 4.34334e24 | 1.71561 | 0.857805 | − | 0.513975i | \(-0.171828\pi\) | ||||
0.857805 | + | 0.513975i | \(0.171828\pi\) | |||||||
\(744\) | −1.64501e23 | + | 4.83828e23i | −0.0642391 | + | 0.188939i | ||||
\(745\) | −3.36046e24 | −1.29739 | ||||||||
\(746\) | −1.51984e23 | − | 1.11477e23i | −0.0580118 | − | 0.0425506i | ||||
\(747\) | 1.87174e23i | 0.0706350i | ||||||||
\(748\) | 4.14374e24 | − | 1.30503e24i | 1.54607 | − | 0.486920i | ||||
\(749\) | − | 4.80052e24i | − | 1.77090i | ||||||
\(750\) | −2.36682e22 | + | 3.22684e22i | −0.00863266 | + | 0.0117694i | ||||
\(751\) | 7.59956e23 | 0.274062 | 0.137031 | − | 0.990567i | \(-0.456244\pi\) | ||||
0.137031 | + | 0.990567i | \(0.456244\pi\) | |||||||
\(752\) | −9.63213e21 | + | 6.73514e21i | −0.00343456 | + | 0.00240157i | ||||
\(753\) | 5.34610e23 | 0.188486 | ||||||||
\(754\) | 2.11092e24 | − | 2.87795e24i | 0.735894 | − | 1.00329i | ||||
\(755\) | − | 5.37519e24i | − | 1.85287i | ||||||
\(756\) | 9.24762e23 | − | 2.91245e23i | 0.315206 | − | 0.0992712i | ||||
\(757\) | 2.36037e24i | 0.795544i | 0.917484 | + | 0.397772i | \(0.130217\pi\) | ||||
−0.917484 | + | 0.397772i | \(0.869783\pi\) | |||||||
\(758\) | 8.74971e23 | + | 6.41774e23i | 0.291612 | + | 0.213892i | ||||
\(759\) | −4.87503e23 | −0.160665 | ||||||||
\(760\) | −8.48679e23 | − | 2.88550e23i | −0.276584 | − | 0.0940386i | ||||
\(761\) | −3.99857e23 | −0.128865 | −0.0644326 | − | 0.997922i | \(-0.520524\pi\) | ||||
−0.0644326 | + | 0.997922i | \(0.520524\pi\) | |||||||
\(762\) | −1.22671e23 | − | 8.99771e22i | −0.0390954 | − | 0.0286758i | ||||
\(763\) | − | 2.34511e24i | − | 0.739104i | ||||||
\(764\) | 5.93398e23 | + | 1.88416e24i | 0.184949 | + | 0.587251i | ||||
\(765\) | 6.99234e24i | 2.15526i | ||||||||
\(766\) | −2.62685e24 | + | 3.58135e24i | −0.800739 | + | 1.09170i | ||||
\(767\) | −6.43729e24 | −1.94063 | ||||||||
\(768\) | 4.54342e23 | + | 1.66038e23i | 0.135460 | + | 0.0495036i | ||||
\(769\) | −3.40521e24 | −1.00408 | −0.502042 | − | 0.864843i | \(-0.667418\pi\) | ||||
−0.502042 | + | 0.864843i | \(0.667418\pi\) | |||||||
\(770\) | −3.33219e24 | + | 4.54298e24i | −0.971759 | + | 1.32486i | ||||
\(771\) | − | 2.01126e23i | − | 0.0580103i | ||||||
\(772\) | −3.66495e23 | − | 1.16370e24i | −0.104549 | − | 0.331965i | ||||
\(773\) | − | 9.20037e23i | − | 0.259585i | −0.991541 | − | 0.129793i | \(-0.958569\pi\) | ||
0.991541 | − | 0.129793i | \(-0.0414311\pi\) | |||||||
\(774\) | −5.02142e23 | − | 3.68311e23i | −0.140129 | − | 0.102782i | ||||
\(775\) | 4.64763e24 | 1.28282 | ||||||||
\(776\) | −5.75510e24 | − | 1.95673e24i | −1.57119 | − | 0.534203i | ||||
\(777\) | −3.96188e23 | −0.106985 | ||||||||
\(778\) | 4.67092e23 | + | 3.42603e23i | 0.124760 | + | 0.0915092i | ||||
\(779\) | 4.39060e22i | 0.0115999i | ||||||||
\(780\) | 7.86697e23 | − | 2.47763e23i | 0.205591 | − | 0.0647489i | ||||
\(781\) | − | 4.97952e24i | − | 1.28722i | ||||||
\(782\) | 3.99621e24 | − | 5.44828e24i | 1.02186 | − | 1.39316i | ||||
\(783\) | −1.30421e24 | −0.329892 | ||||||||
\(784\) | −1.11472e24 | + | 7.79454e23i | −0.278920 | + | 0.195031i | ||||
\(785\) | 4.25148e24 | 1.05232 | ||||||||
\(786\) | −5.68036e23 | + | 7.74438e23i | −0.139086 | + | 0.189625i | ||||
\(787\) | 7.43784e24i | 1.80161i | 0.434220 | + | 0.900807i | \(0.357024\pi\) | ||||
−0.434220 | + | 0.900807i | \(0.642976\pi\) | |||||||
\(788\) | −5.18847e24 | + | 1.63406e24i | −1.24327 | + | 0.391557i | ||||
\(789\) | 5.50247e21i | 0.00130438i | ||||||||
\(790\) | −6.32046e24 | − | 4.63593e24i | −1.48224 | − | 1.08719i | ||||
\(791\) | −6.69154e24 | −1.55248 | ||||||||
\(792\) | 1.40394e24 | − | 4.12923e24i | 0.322243 | − | 0.947774i | ||||
\(793\) | 2.82605e24 | 0.641737 | ||||||||
\(794\) | 7.13829e24 | + | 5.23580e24i | 1.60369 | + | 1.17628i | ||||
\(795\) | 4.92587e23i | 0.109487i | ||||||||
\(796\) | −6.45508e23 | − | 2.04962e24i | −0.141952 | − | 0.450725i | ||||
\(797\) | 6.58511e24i | 1.43274i | 0.697721 | + | 0.716369i | \(0.254197\pi\) | ||||
−0.697721 | + | 0.716369i | \(0.745803\pi\) | |||||||
\(798\) | 9.65400e22 | − | 1.31619e23i | 0.0207818 | − | 0.0283331i | ||||
\(799\) | 3.11985e22 | 0.00664486 | ||||||||
\(800\) | 9.95552e22 | − | 4.39824e24i | 0.0209797 | − | 0.926859i | ||||
\(801\) | −4.78881e24 | −0.998508 | ||||||||
\(802\) | 5.27000e24 | − | 7.18492e24i | 1.08725 | − | 1.48231i | ||||
\(803\) | 9.97560e23i | 0.203637i | ||||||||
\(804\) | −3.26972e23 | − | 1.03820e24i | −0.0660442 | − | 0.209704i | ||||
\(805\) | 8.76247e24i | 1.75130i | ||||||||
\(806\) | 6.07389e24 | + | 4.45509e24i | 1.20121 | + | 0.881066i | ||||
\(807\) | −3.97437e23 | −0.0777755 | ||||||||
\(808\) | −1.04199e24 | + | 3.06467e24i | −0.201774 | + | 0.593454i | ||||
\(809\) | 6.49816e24 | 1.24517 | 0.622584 | − | 0.782553i | \(-0.286083\pi\) | ||||
0.622584 | + | 0.782553i | \(0.286083\pi\) | |||||||
\(810\) | 5.53751e24 | + | 4.06166e24i | 1.05001 | + | 0.770160i | ||||
\(811\) | − | 5.42750e24i | − | 1.01841i | −0.860645 | − | 0.509205i | \(-0.829940\pi\) | ||
0.860645 | − | 0.509205i | \(-0.170060\pi\) | |||||||
\(812\) | 6.87302e24 | − | 2.16459e24i | 1.27621 | − | 0.401929i | ||||
\(813\) | − | 3.91645e23i | − | 0.0719653i | ||||||
\(814\) | −2.13053e24 | + | 2.90468e24i | −0.387418 | + | 0.528191i | ||||
\(815\) | 2.57653e24 | 0.463655 | ||||||||
\(816\) | −7.35807e23 | − | 1.05230e24i | −0.131038 | − | 0.187402i | ||||
\(817\) | −2.11910e23 | −0.0373477 | ||||||||
\(818\) | −1.21508e24 | + | 1.65659e24i | −0.211934 | + | 0.288943i | ||||
\(819\) | − | 7.07045e24i | − | 1.22049i | ||||||
\(820\) | −4.27227e23 | + | 1.34551e23i | −0.0729862 | + | 0.0229863i | ||||
\(821\) | 1.44666e24i | 0.244595i | 0.992493 | + | 0.122298i | \(0.0390263\pi\) | ||||
−0.992493 | + | 0.122298i | \(0.960974\pi\) | |||||||
\(822\) | −1.59083e23 | − | 1.16685e23i | −0.0266204 | − | 0.0195256i | ||||
\(823\) | −5.56998e24 | −0.922476 | −0.461238 | − | 0.887276i | \(-0.652595\pi\) | ||||
−0.461238 | + | 0.887276i | \(0.652595\pi\) | |||||||
\(824\) | 1.38697e24 | + | 4.71570e23i | 0.227346 | + | 0.0772974i | ||||
\(825\) | 8.42566e23 | 0.136693 | ||||||||
\(826\) | −1.04797e25 | − | 7.68666e24i | −1.68275 | − | 1.23426i | ||||
\(827\) | − | 5.21332e24i | − | 0.828548i | −0.910152 | − | 0.414274i | \(-0.864036\pi\) | ||
0.910152 | − | 0.414274i | \(-0.135964\pi\) | |||||||
\(828\) | −2.03762e24 | − | 6.46986e24i | −0.320528 | − | 1.01774i | ||||
\(829\) | 3.83347e24i | 0.596869i | 0.954430 | + | 0.298434i | \(0.0964644\pi\) | ||||
−0.954430 | + | 0.298434i | \(0.903536\pi\) | |||||||
\(830\) | −3.84304e23 | + | 5.23946e23i | −0.0592259 | + | 0.0807463i | ||||
\(831\) | 8.28814e23 | 0.126429 | ||||||||
\(832\) | 4.34613e24 | − | 5.65254e24i | 0.656228 | − | 0.853484i | ||||
\(833\) | 3.61058e24 | 0.539628 | ||||||||
\(834\) | −2.23896e23 | + | 3.05252e23i | −0.0331235 | + | 0.0451593i | ||||
\(835\) | 4.62079e24i | 0.676677i | ||||||||
\(836\) | −4.45824e23 | − | 1.41558e24i | −0.0646265 | − | 0.205202i | ||||
\(837\) | − | 2.75252e24i | − | 0.394971i | ||||||
\(838\) | 7.88634e24 | + | 5.78448e24i | 1.12022 | + | 0.821657i | ||||
\(839\) | 4.72339e24 | 0.664167 | 0.332083 | − | 0.943250i | \(-0.392248\pi\) | ||||
0.332083 | + | 0.943250i | \(0.392248\pi\) | |||||||
\(840\) | 1.57657e24 | + | 5.36032e23i | 0.219452 | + | 0.0746134i | ||||
\(841\) | −2.43599e24 | −0.335667 | ||||||||
\(842\) | −3.68323e24 | − | 2.70158e24i | −0.502430 | − | 0.368523i | ||||
\(843\) | − | 3.67101e23i | − | 0.0495737i | ||||||
\(844\) | −9.21648e24 | + | 2.90264e24i | −1.23212 | + | 0.388045i | ||||
\(845\) | − | 1.66847e24i | − | 0.220819i | ||||||
\(846\) | 1.85242e22 | − | 2.52552e22i | 0.00242712 | − | 0.00330904i | ||||
\(847\) | −4.02894e23 | −0.0522616 | ||||||||
\(848\) | 2.44022e24 | + | 3.48984e24i | 0.313375 | + | 0.448168i | ||||
\(849\) | 8.55270e23 | 0.108740 | ||||||||
\(850\) | −6.90677e24 | + | 9.41642e24i | −0.869389 | + | 1.18529i | ||||
\(851\) | 5.60253e24i | 0.698205i | ||||||||
\(852\) | −1.40378e24 | + | 4.42108e23i | −0.173206 | + | 0.0545497i | ||||
\(853\) | − | 7.83079e24i | − | 0.956619i | −0.878191 | − | 0.478309i | \(-0.841250\pi\) | ||
0.878191 | − | 0.478309i | \(-0.158750\pi\) | |||||||
\(854\) | 4.60071e24 | + | 3.37453e24i | 0.556459 | + | 0.408152i | ||||
\(855\) | 2.38872e24 | 0.286057 | ||||||||
\(856\) | −4.15275e24 | + | 1.22140e25i | −0.492390 | + | 1.44821i | ||||
\(857\) | −4.64085e24 | −0.544830 | −0.272415 | − | 0.962180i | \(-0.587822\pi\) | ||||
−0.272415 | + | 0.962180i | \(0.587822\pi\) | |||||||
\(858\) | 1.10113e24 | + | 8.07660e23i | 0.127996 | + | 0.0938829i | ||||
\(859\) | − | 6.90901e24i | − | 0.795195i | −0.917560 | − | 0.397598i | \(-0.869844\pi\) | ||
0.917560 | − | 0.397598i | \(-0.130156\pi\) | |||||||
\(860\) | −6.49404e23 | − | 2.06199e24i | −0.0740080 | − | 0.234990i | ||||
\(861\) | − | 8.15629e22i | − | 0.00920378i | ||||||
\(862\) | 9.12444e23 | − | 1.24399e24i | 0.101952 | − | 0.138997i | ||||
\(863\) | 4.17194e24 | 0.461579 | 0.230790 | − | 0.973004i | \(-0.425869\pi\) | ||||
0.230790 | + | 0.973004i | \(0.425869\pi\) | |||||||
\(864\) | −2.60482e24 | − | 5.89608e22i | −0.285372 | − | 0.00645947i | ||||
\(865\) | −1.03293e25 | −1.12056 | ||||||||
\(866\) | −3.47249e23 | + | 4.73426e23i | −0.0373026 | + | 0.0508569i | ||||
\(867\) | 2.05260e24i | 0.218344i | ||||||||
\(868\) | 4.56836e24 | + | 1.45055e25i | 0.481219 | + | 1.52797i | ||||
\(869\) | − | 1.29778e25i | − | 1.35373i | ||||||
\(870\) | −1.80622e24 | − | 1.32483e24i | −0.186576 | − | 0.136850i | ||||
\(871\) | −1.60442e25 | −1.64121 | ||||||||
\(872\) | −2.02867e24 | + | 5.96669e24i | −0.205505 | + | 0.604426i | ||||
\(873\) | 1.61985e25 | 1.62500 | ||||||||
\(874\) | −1.86124e24 | − | 1.36518e24i | −0.184908 | − | 0.135626i | ||||
\(875\) | 1.19090e24i | 0.117168i | ||||||||
\(876\) | 2.81223e23 | − | 8.85686e22i | 0.0274010 | − | 0.00862969i | ||||
\(877\) | − | 2.21294e24i | − | 0.213537i | −0.994284 | − | 0.106768i | \(-0.965950\pi\) | ||
0.994284 | − | 0.106768i | \(-0.0340504\pi\) | |||||||
\(878\) | 3.35052e24 | − | 4.56798e24i | 0.320191 | − | 0.436536i | ||||
\(879\) | 8.10723e23 | 0.0767303 | ||||||||
\(880\) | 1.24081e25 | − | 8.67618e24i | 1.16306 | − | 0.813254i | ||||
\(881\) | −1.30646e24 | −0.121283 | −0.0606415 | − | 0.998160i | \(-0.519315\pi\) | ||||
−0.0606415 | + | 0.998160i | \(0.519315\pi\) | |||||||
\(882\) | 2.14379e24 | − | 2.92277e24i | 0.197106 | − | 0.268727i | ||||
\(883\) | 2.46757e24i | 0.224700i | 0.993669 | + | 0.112350i | \(0.0358378\pi\) | ||||
−0.993669 | + | 0.112350i | \(0.964162\pi\) | |||||||
\(884\) | −1.80526e25 | + | 5.68551e24i | −1.62816 | + | 0.512773i | ||||
\(885\) | 4.04008e24i | 0.360888i | ||||||||
\(886\) | −9.01522e24 | − | 6.61249e24i | −0.797608 | − | 0.585031i | ||||
\(887\) | 2.19751e24 | 0.192567 | 0.0962833 | − | 0.995354i | \(-0.469305\pi\) | ||||
0.0962833 | + | 0.995354i | \(0.469305\pi\) | |||||||
\(888\) | 1.00802e24 | + | 3.42727e23i | 0.0874903 | + | 0.0297467i | ||||
\(889\) | −4.52734e24 | −0.389205 | ||||||||
\(890\) | −1.34051e25 | − | 9.83238e24i | −1.14144 | − | 0.837227i | ||||
\(891\) | 1.13701e25i | 0.958971i | ||||||||
\(892\) | −1.26632e24 | − | 4.02081e24i | −0.105789 | − | 0.335902i | ||||
\(893\) | − | 1.06580e22i | − | 0.000881939i | ||||||
\(894\) | −9.72596e23 | + | 1.32600e24i | −0.0797193 | + | 0.108686i | ||||
\(895\) | 2.40844e25 | 1.95542 | ||||||||
\(896\) | 1.38250e25 | − | 4.01251e24i | 1.11185 | − | 0.322699i | ||||
\(897\) | 2.12386e24 | 0.169196 | ||||||||
\(898\) | −3.09790e24 | + | 4.22356e24i | −0.244466 | + | 0.333296i | ||||
\(899\) | − | 2.04573e25i | − | 1.59916i | ||||||
\(900\) | 3.52168e24 | + | 1.11821e25i | 0.272702 | + | 0.865885i | ||||
\(901\) | − | 1.13036e25i | − | 0.867073i | ||||||
\(902\) | −5.97986e23 | − | 4.38611e23i | −0.0454397 | − | 0.0333291i | ||||
\(903\) | 3.93660e23 | 0.0296330 | ||||||||
\(904\) | 1.70253e25 | + | 5.78861e24i | 1.26959 | + | 0.431660i | ||||
\(905\) | −2.84256e25 | −2.09989 | ||||||||
\(906\) | −2.12099e24 | − | 1.55570e24i | −0.155220 | − | 0.113851i | ||||
\(907\) | 2.67764e25i | 1.94129i | 0.240512 | + | 0.970646i | \(0.422685\pi\) | ||||
−0.240512 | + | 0.970646i | \(0.577315\pi\) | |||||||
\(908\) | 1.20819e25 | − | 3.80508e24i | 0.867773 | − | 0.273297i | ||||
\(909\) | − | 8.62592e24i | − | 0.613780i | ||||||
\(910\) | 1.45170e25 | − | 1.97920e25i | 1.02335 | − | 1.39520i | ||||
\(911\) | 2.35546e25 | 1.64501 | 0.822506 | − | 0.568757i | \(-0.192576\pi\) | ||||
0.822506 | + | 0.568757i | \(0.192576\pi\) | |||||||
\(912\) | −3.59486e23 | + | 2.51366e23i | −0.0248729 | + | 0.0173920i | ||||
\(913\) | −1.07581e24 | −0.0737456 | ||||||||
\(914\) | −2.34180e24 | + | 3.19272e24i | −0.159040 | + | 0.216830i | ||||
\(915\) | − | 1.77364e24i | − | 0.119340i | ||||||
\(916\) | 3.84351e21 | − | 1.21048e21i | 0.000256222 | − | 8.06948e-5i | ||||
\(917\) | 2.85816e25i | 1.88776i | ||||||||
\(918\) | 5.57681e24 | + | 4.09048e24i | 0.364941 | + | 0.267677i | ||||
\(919\) | −5.71735e24 | −0.370692 | −0.185346 | − | 0.982673i | \(-0.559341\pi\) | ||||
−0.185346 | + | 0.982673i | \(0.559341\pi\) | |||||||
\(920\) | 7.58009e24 | − | 2.22944e25i | 0.486942 | − | 1.43219i | ||||
\(921\) | −3.05227e24 | −0.194274 | ||||||||
\(922\) | 1.10623e25 | + | 8.11399e24i | 0.697642 | + | 0.511707i | ||||
\(923\) | 2.16938e25i | 1.35557i | ||||||||
\(924\) | 8.28196e23 | + | 2.62969e24i | 0.0512768 | + | 0.162814i | ||||
\(925\) | − | 9.68302e24i | − | 0.594027i | ||||||
\(926\) | 1.14452e24 | − | 1.56039e24i | 0.0695711 | − | 0.0948505i | ||||
\(927\) | −3.90382e24 | −0.235132 | ||||||||
\(928\) | −1.93596e25 | − | 4.38209e23i | −1.15541 | − | 0.0261531i | ||||
\(929\) | 2.14170e25 | 1.26656 | 0.633278 | − | 0.773925i | \(-0.281709\pi\) | ||||
0.633278 | + | 0.773925i | \(0.281709\pi\) | |||||||
\(930\) | 2.79604e24 | − | 3.81202e24i | 0.163847 | − | 0.223383i | ||||
\(931\) | − | 1.23345e24i | − | 0.0716222i | ||||||
\(932\) | −8.72257e24 | − | 2.76959e25i | −0.501891 | − | 1.59360i | ||||
\(933\) | − | 1.06125e24i | − | 0.0605096i | ||||||
\(934\) | 8.22361e23 | + | 6.03186e23i | 0.0464637 | + | 0.0340803i | ||||
\(935\) | −4.01898e25 | −2.25018 | ||||||||
\(936\) | −6.11639e24 | + | 1.79894e25i | −0.339352 | + | 0.998095i | ||||
\(937\) | 1.03504e25 | 0.569076 | 0.284538 | − | 0.958665i | \(-0.408160\pi\) | ||||
0.284538 | + | 0.958665i | \(0.408160\pi\) | |||||||
\(938\) | −2.61194e25 | − | 1.91581e25i | −1.42311 | − | 1.04383i | ||||
\(939\) | − | 2.65993e24i | − | 0.143619i | ||||||
\(940\) | 1.03708e23 | − | 3.26617e22i | 0.00554912 | − | 0.00174764i | ||||
\(941\) | 1.49549e25i | 0.792997i | 0.918035 | + | 0.396498i | \(0.129775\pi\) | ||||
−0.918035 | + | 0.396498i | \(0.870225\pi\) | |||||||
\(942\) | 1.23048e24 | − | 1.67759e24i | 0.0646608 | − | 0.0881561i | ||||
\(943\) | −1.15339e24 | −0.0600657 | ||||||||
\(944\) | 2.00141e25 | + | 2.86228e25i | 1.03294 | + | 1.47724i | ||||
\(945\) | −8.96918e24 | −0.458757 | ||||||||
\(946\) | 2.11694e24 | − | 2.88615e24i | 0.107308 | − | 0.146300i | ||||
\(947\) | 2.05139e25i | 1.03056i | 0.857021 | + | 0.515281i | \(0.172312\pi\) | ||||
−0.857021 | + | 0.515281i | \(0.827688\pi\) | |||||||
\(948\) | −3.65857e24 | + | 1.15223e24i | −0.182155 | + | 0.0573680i | ||||
\(949\) | − | 4.34597e24i | − | 0.214449i | ||||||
\(950\) | 3.21683e24 | + | 2.35949e24i | 0.157318 | + | 0.115390i | ||||
\(951\) | 3.46531e24 | 0.167961 | ||||||||
\(952\) | −3.61781e25 | − | 1.23005e25i | −1.73793 | − | 0.590894i | ||||
\(953\) | −1.91249e25 | −0.910563 | −0.455281 | − | 0.890348i | \(-0.650461\pi\) | ||||
−0.455281 | + | 0.890348i | \(0.650461\pi\) | |||||||
\(954\) | −9.15025e24 | − | 6.71154e24i | −0.431789 | − | 0.316709i | ||||
\(955\) | − | 1.82743e25i | − | 0.854695i | ||||||
\(956\) | 1.77757e23 | + | 5.64414e23i | 0.00824014 | + | 0.0261641i | ||||
\(957\) | − | 3.70870e24i | − | 0.170400i | ||||||
\(958\) | −1.93851e25 | + | 2.64289e25i | −0.882797 | + | 1.20357i | ||||
\(959\) | −5.87117e24 | −0.265013 | ||||||||
\(960\) | −3.54757e24 | − | 2.72766e24i | −0.158718 | − | 0.122035i | ||||
\(961\) | 2.06250e25 | 0.914627 | ||||||||
\(962\) | 9.28186e24 | − | 1.26545e25i | 0.407988 | − | 0.556235i | ||||
\(963\) | − | 3.43779e25i | − | 1.49781i | ||||||
\(964\) | 7.15348e23 | + | 2.27137e24i | 0.0308932 | + | 0.0980921i | ||||
\(965\) | 1.12866e25i | 0.483148i | ||||||||
\(966\) | 3.45757e24 | + | 2.53606e24i | 0.146712 | + | 0.107610i | ||||
\(967\) | −8.63419e24 | −0.363159 | −0.181579 | − | 0.983376i | \(-0.558121\pi\) | ||||
−0.181579 | + | 0.983376i | \(0.558121\pi\) | |||||||
\(968\) | 1.02509e24 | + | 3.48529e23i | 0.0427386 | + | 0.0145311i | ||||
\(969\) | 1.16438e24 | 0.0481217 | ||||||||
\(970\) | 4.53436e25 | + | 3.32587e25i | 1.85762 | + | 1.36253i | ||||
\(971\) | − | 7.31893e24i | − | 0.297224i | −0.988896 | − | 0.148612i | \(-0.952519\pi\) | ||
0.988896 | − | 0.148612i | \(-0.0474806\pi\) | |||||||
\(972\) | 9.96854e24 | − | 3.13950e24i | 0.401299 | − | 0.126385i | ||||
\(973\) | 1.12657e25i | 0.449572i | ||||||||
\(974\) | −6.58351e24 | + | 8.97571e24i | −0.260439 | + | 0.355073i | ||||
\(975\) | −3.67073e24 | −0.143950 | ||||||||
\(976\) | −8.78643e24 | − | 1.25657e25i | −0.341577 | − | 0.488500i | ||||
\(977\) | −1.91796e25 | −0.739154 | −0.369577 | − | 0.929200i | \(-0.620497\pi\) | ||||
−0.369577 | + | 0.929200i | \(0.620497\pi\) | |||||||
\(978\) | 7.45707e23 | − | 1.01667e24i | 0.0284897 | − | 0.0388418i | ||||
\(979\) | − | 2.75246e25i | − | 1.04248i | ||||||
\(980\) | 1.20020e25 | − | 3.77993e24i | 0.450644 | − | 0.141926i | ||||
\(981\) | − | 1.67940e25i | − | 0.625128i | ||||||
\(982\) | 5.66832e24 | + | 4.15761e24i | 0.209174 | + | 0.153425i | ||||
\(983\) | 9.21150e24 | 0.336996 | 0.168498 | − | 0.985702i | \(-0.446108\pi\) | ||||
0.168498 | + | 0.985702i | \(0.446108\pi\) | |||||||
\(984\) | −7.05571e22 | + | 2.07521e23i | −0.00255907 | + | 0.00752669i | ||||
\(985\) | 5.03225e25 | 1.80948 | ||||||||
\(986\) | 4.14480e25 | + | 3.04013e25i | 1.47757 | + | 1.08377i | ||||
\(987\) | 1.97991e22i | 0.000699760i | ||||||||
\(988\) | 1.94228e24 | + | 6.16713e24i | 0.0680577 | + | 0.216097i | ||||
\(989\) | − | 5.56678e24i | − | 0.193391i | ||||||
\(990\) | −2.38628e25 | + | 3.25336e25i | −0.821906 | + | 1.12056i | ||||
\(991\) | 5.52241e25 | 1.88583 | 0.942915 | − | 0.333034i | \(-0.108073\pi\) | ||||
0.942915 | + | 0.333034i | \(0.108073\pi\) | |||||||
\(992\) | 9.24837e23 | − | 4.08583e25i | 0.0313124 | − | 1.38335i | ||||
\(993\) | −7.15413e24 | −0.240153 | ||||||||
\(994\) | −2.59042e25 | + | 3.53168e25i | −0.862156 | + | 1.17543i | ||||
\(995\) | 1.98790e25i | 0.655993i | ||||||||
\(996\) | 9.55165e22 | + | 3.03284e23i | 0.00312517 | + | 0.00992306i | ||||
\(997\) | 3.29322e25i | 1.06835i | 0.845375 | + | 0.534174i | \(0.179377\pi\) | ||||
−0.845375 | + | 0.534174i | \(0.820623\pi\) | |||||||
\(998\) | −2.27540e25 | − | 1.66896e25i | −0.731893 | − | 0.536830i | ||||
\(999\) | −5.73470e24 | −0.182896 |
(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.5.11 | ✓ | 16 | |
3.2 | odd | 2 | 72.18.d.b.37.6 | 16 | |||
4.3 | odd | 2 | 32.18.b.a.17.8 | 16 | |||
8.3 | odd | 2 | 32.18.b.a.17.9 | 16 | |||
8.5 | even | 2 | inner | 8.18.b.a.5.12 | yes | 16 | |
24.5 | odd | 2 | 72.18.d.b.37.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.18.b.a.5.11 | ✓ | 16 | 1.1 | even | 1 | trivial | |
8.18.b.a.5.12 | yes | 16 | 8.5 | even | 2 | inner | |
32.18.b.a.17.8 | 16 | 4.3 | odd | 2 | |||
32.18.b.a.17.9 | 16 | 8.3 | odd | 2 | |||
72.18.d.b.37.5 | 16 | 24.5 | odd | 2 | |||
72.18.d.b.37.6 | 16 | 3.2 | odd | 2 |