Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,39,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 39, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 39);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 39 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.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: | \(36.5853876134\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 9 x^{17} + \cdots + 98\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.13 | ||
Root | \(0.500000 - 2.95082e7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.39.b.a.3.14 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 383569. | − | 357425.i | 0.731599 | − | 0.681735i | ||||
\(3\) | 4.72132e8i | 0.406218i | 0.979156 | + | 0.203109i | \(0.0651046\pi\) | ||||
−0.979156 | + | 0.203109i | \(0.934895\pi\) | |||||||
\(4\) | 1.93720e10 | − | 2.74194e11i | 0.0704750 | − | 0.997514i | ||||
\(5\) | 2.09077e13 | 1.09616 | 0.548082 | − | 0.836425i | \(-0.315358\pi\) | ||||
0.548082 | + | 0.836425i | \(0.315358\pi\) | |||||||
\(6\) | 1.68752e14 | + | 1.81095e14i | 0.276933 | + | 0.297189i | ||||
\(7\) | − | 1.08901e16i | − | 0.955362i | −0.878533 | − | 0.477681i | \(-0.841477\pi\) | ||
0.878533 | − | 0.477681i | \(-0.158523\pi\) | |||||||
\(8\) | −9.05736e16 | − | 1.12096e17i | −0.628480 | − | 0.777825i | ||||
\(9\) | 1.12794e18 | 0.834987 | ||||||||
\(10\) | 8.01953e18 | − | 7.47293e18i | 0.801953 | − | 0.747293i | ||||
\(11\) | 5.05873e19i | 0.827143i | 0.910472 | + | 0.413572i | \(0.135719\pi\) | ||||
−0.910472 | + | 0.413572i | \(0.864281\pi\) | |||||||
\(12\) | 1.29456e20 | + | 9.14616e18i | 0.405208 | + | 0.0286283i | ||||
\(13\) | −7.96735e20 | −0.544992 | −0.272496 | − | 0.962157i | \(-0.587849\pi\) | ||||
−0.272496 | + | 0.962157i | \(0.587849\pi\) | |||||||
\(14\) | −3.89239e21 | − | 4.17709e21i | −0.651304 | − | 0.698942i | ||||
\(15\) | 9.87118e21i | 0.445282i | ||||||||
\(16\) | −7.48073e22 | − | 1.06234e22i | −0.990067 | − | 0.140600i | ||||
\(17\) | 3.83882e23 | 1.60572 | 0.802858 | − | 0.596170i | \(-0.203312\pi\) | ||||
0.802858 | + | 0.596170i | \(0.203312\pi\) | |||||||
\(18\) | 4.32644e23 | − | 4.03156e23i | 0.610876 | − | 0.569240i | ||||
\(19\) | − | 6.36661e23i | − | 0.321803i | −0.986970 | − | 0.160901i | \(-0.948560\pi\) | ||
0.986970 | − | 0.160901i | \(-0.0514401\pi\) | |||||||
\(20\) | 4.05024e23 | − | 5.73277e24i | 0.0772522 | − | 1.09344i | ||||
\(21\) | 5.14155e24 | 0.388086 | ||||||||
\(22\) | 1.80812e25 | + | 1.94037e25i | 0.563892 | + | 0.605137i | ||||
\(23\) | − | 1.18366e26i | − | 1.58635i | −0.608994 | − | 0.793175i | \(-0.708427\pi\) | ||
0.608994 | − | 0.793175i | \(-0.291573\pi\) | |||||||
\(24\) | 5.29243e25 | − | 4.27627e25i | 0.315967 | − | 0.255300i | ||||
\(25\) | 7.33327e25 | 0.201575 | ||||||||
\(26\) | −3.05603e26 | + | 2.84774e26i | −0.398716 | + | 0.371540i | ||||
\(27\) | 1.17032e27i | 0.745405i | ||||||||
\(28\) | −2.98600e27 | − | 2.10963e26i | −0.952987 | − | 0.0673292i | ||||
\(29\) | 1.59257e27 | 0.260937 | 0.130469 | − | 0.991452i | \(-0.458352\pi\) | ||||
0.130469 | + | 0.991452i | \(0.458352\pi\) | |||||||
\(30\) | 3.52821e27 | + | 3.78628e27i | 0.303564 | + | 0.325768i | ||||
\(31\) | − | 1.54910e28i | − | 0.714838i | −0.933944 | − | 0.357419i | \(-0.883657\pi\) | ||
0.933944 | − | 0.357419i | \(-0.116343\pi\) | |||||||
\(32\) | −3.24908e28 | + | 2.26632e28i | −0.820184 | + | 0.572100i | ||||
\(33\) | −2.38839e28 | −0.336001 | ||||||||
\(34\) | 1.47245e29 | − | 1.37209e29i | 1.17474 | − | 1.09467i | ||||
\(35\) | − | 2.27686e29i | − | 1.04723i | ||||||
\(36\) | 2.18506e28 | − | 3.09276e29i | 0.0588457 | − | 0.832910i | ||||
\(37\) | 4.02079e29 | 0.643396 | 0.321698 | − | 0.946842i | \(-0.395746\pi\) | ||||
0.321698 | + | 0.946842i | \(0.395746\pi\) | |||||||
\(38\) | −2.27559e29 | − | 2.44203e29i | −0.219384 | − | 0.235431i | ||||
\(39\) | − | 3.76164e29i | − | 0.221386i | ||||||
\(40\) | −1.89368e30 | − | 2.34368e30i | −0.688917 | − | 0.852624i | ||||
\(41\) | −5.97871e30 | −1.36055 | −0.680275 | − | 0.732957i | \(-0.738139\pi\) | ||||
−0.680275 | + | 0.732957i | \(0.738139\pi\) | |||||||
\(42\) | 1.97214e30 | − | 1.83772e30i | 0.283923 | − | 0.264572i | ||||
\(43\) | − | 1.62015e31i | − | 1.49160i | −0.666167 | − | 0.745802i | \(-0.732066\pi\) | ||
0.666167 | − | 0.745802i | \(-0.267934\pi\) | |||||||
\(44\) | 1.38708e31 | + | 9.79979e29i | 0.825086 | + | 0.0582929i | ||||
\(45\) | 2.35827e31 | 0.915282 | ||||||||
\(46\) | −4.23071e31 | − | 4.54016e31i | −1.08147 | − | 1.16057i | ||||
\(47\) | − | 7.30265e31i | − | 1.24057i | −0.784377 | − | 0.620284i | \(-0.787017\pi\) | ||
0.784377 | − | 0.620284i | \(-0.212983\pi\) | |||||||
\(48\) | 5.01565e30 | − | 3.53189e31i | 0.0571142 | − | 0.402183i | ||||
\(49\) | 1.13411e31 | 0.0872832 | ||||||||
\(50\) | 2.81281e31 | − | 2.62110e31i | 0.147472 | − | 0.137421i | ||||
\(51\) | 1.81243e32i | 0.652271i | ||||||||
\(52\) | −1.54344e31 | + | 2.18460e32i | −0.0384084 | + | 0.543637i | ||||
\(53\) | −3.06110e32 | −0.530439 | −0.265219 | − | 0.964188i | \(-0.585444\pi\) | ||||
−0.265219 | + | 0.964188i | \(0.585444\pi\) | |||||||
\(54\) | 4.18302e32 | + | 4.48898e32i | 0.508169 | + | 0.545338i | ||||
\(55\) | 1.05766e33i | 0.906685i | ||||||||
\(56\) | −1.22074e33 | + | 9.86353e32i | −0.743105 | + | 0.600426i | ||||
\(57\) | 3.00588e32 | 0.130722 | ||||||||
\(58\) | 6.10860e32 | − | 5.69225e32i | 0.190902 | − | 0.177890i | ||||
\(59\) | 5.23574e33i | 1.18247i | 0.806499 | + | 0.591235i | \(0.201359\pi\) | ||||
−0.806499 | + | 0.591235i | \(0.798641\pi\) | |||||||
\(60\) | 2.70662e33 | + | 1.91225e32i | 0.444175 | + | 0.0313813i | ||||
\(61\) | 8.85956e33 | 1.06205 | 0.531025 | − | 0.847356i | \(-0.321807\pi\) | ||||
0.531025 | + | 0.847356i | \(0.321807\pi\) | |||||||
\(62\) | −5.53688e33 | − | 5.94187e33i | −0.487330 | − | 0.522975i | ||||
\(63\) | − | 1.22834e34i | − | 0.797715i | ||||||
\(64\) | −4.36205e33 | + | 2.03060e34i | −0.210025 | + | 0.977696i | ||||
\(65\) | −1.66579e34 | −0.597401 | ||||||||
\(66\) | −9.16111e33 | + | 8.53671e33i | −0.245818 | + | 0.229063i | ||||
\(67\) | 2.65331e34i | 0.535016i | 0.963556 | + | 0.267508i | \(0.0862001\pi\) | ||||
−0.963556 | + | 0.267508i | \(0.913800\pi\) | |||||||
\(68\) | 7.43658e33 | − | 1.05258e35i | 0.113163 | − | 1.60172i | ||||
\(69\) | 5.58845e34 | 0.644404 | ||||||||
\(70\) | −8.13808e34 | − | 8.73332e34i | −0.713936 | − | 0.766155i | ||||
\(71\) | − | 4.15949e34i | − | 0.278696i | −0.990243 | − | 0.139348i | \(-0.955499\pi\) | ||
0.990243 | − | 0.139348i | \(-0.0445007\pi\) | |||||||
\(72\) | −1.02162e35 | − | 1.26438e35i | −0.524773 | − | 0.649474i | ||||
\(73\) | 1.69330e35 | 0.669268 | 0.334634 | − | 0.942348i | \(-0.391387\pi\) | ||||
0.334634 | + | 0.942348i | \(0.391387\pi\) | |||||||
\(74\) | 1.54225e35 | − | 1.43713e35i | 0.470708 | − | 0.438625i | ||||
\(75\) | 3.46227e34i | 0.0818837i | ||||||||
\(76\) | −1.74569e35 | − | 1.23334e34i | −0.321003 | − | 0.0226791i | ||||
\(77\) | 5.50900e35 | 0.790221 | ||||||||
\(78\) | −1.34451e35 | − | 1.44285e35i | −0.150927 | − | 0.161966i | ||||
\(79\) | 1.90317e36i | 1.67711i | 0.544816 | + | 0.838556i | \(0.316600\pi\) | ||||
−0.544816 | + | 0.838556i | \(0.683400\pi\) | |||||||
\(80\) | −1.56405e36 | − | 2.22111e35i | −1.08528 | − | 0.154120i | ||||
\(81\) | 9.71139e35 | 0.532189 | ||||||||
\(82\) | −2.29325e36 | + | 2.13694e36i | −0.995377 | + | 0.927534i | ||||
\(83\) | 5.71624e36i | 1.97073i | 0.170467 | + | 0.985363i | \(0.445472\pi\) | ||||
−0.170467 | + | 0.985363i | \(0.554528\pi\) | |||||||
\(84\) | 9.96023e34 | − | 1.40978e36i | 0.0273504 | − | 0.387121i | ||||
\(85\) | 8.02609e36 | 1.76013 | ||||||||
\(86\) | −5.79082e36 | − | 6.21438e36i | −1.01688 | − | 1.09126i | ||||
\(87\) | 7.51903e35i | 0.105998i | ||||||||
\(88\) | 5.67066e36 | − | 4.58187e36i | 0.643373 | − | 0.519843i | ||||
\(89\) | 1.56670e36 | 0.143409 | 0.0717046 | − | 0.997426i | \(-0.477156\pi\) | ||||
0.0717046 | + | 0.997426i | \(0.477156\pi\) | |||||||
\(90\) | 9.04557e36 | − | 8.42904e36i | 0.669620 | − | 0.623980i | ||||
\(91\) | 8.67651e36i | 0.520665i | ||||||||
\(92\) | −3.24553e37 | − | 2.29299e36i | −1.58240 | − | 0.111798i | ||||
\(93\) | 7.31380e36 | 0.290380 | ||||||||
\(94\) | −2.61015e37 | − | 2.80107e37i | −0.845739 | − | 0.907599i | ||||
\(95\) | − | 1.33111e37i | − | 0.352749i | ||||||
\(96\) | −1.07000e37 | − | 1.53400e37i | −0.232398 | − | 0.333174i | ||||
\(97\) | 7.60398e37 | 1.35637 | 0.678185 | − | 0.734891i | \(-0.262767\pi\) | ||||
0.678185 | + | 0.734891i | \(0.262767\pi\) | |||||||
\(98\) | 4.35010e36 | − | 4.05361e36i | 0.0638563 | − | 0.0595040i | ||||
\(99\) | 5.70596e37i | 0.690653i | ||||||||
\(100\) | 1.42060e36 | − | 2.01074e37i | 0.0142060 | − | 0.201074i | ||||
\(101\) | −1.38872e38 | −1.14950 | −0.574750 | − | 0.818329i | \(-0.694901\pi\) | ||||
−0.574750 | + | 0.818329i | \(0.694901\pi\) | |||||||
\(102\) | 6.47809e37 | + | 6.95192e37i | 0.444676 | + | 0.477201i | ||||
\(103\) | − | 2.02261e38i | − | 1.15346i | −0.816934 | − | 0.576732i | \(-0.804328\pi\) | ||
0.816934 | − | 0.576732i | \(-0.195672\pi\) | |||||||
\(104\) | 7.21632e37 | + | 8.93112e37i | 0.342517 | + | 0.423909i | ||||
\(105\) | 1.07498e38 | 0.425406 | ||||||||
\(106\) | −1.17414e38 | + | 1.09411e38i | −0.388069 | + | 0.361619i | ||||
\(107\) | 3.85604e38i | 1.06623i | 0.846044 | + | 0.533114i | \(0.178978\pi\) | ||||
−0.846044 | + | 0.533114i | \(0.821022\pi\) | |||||||
\(108\) | 3.20895e38 | + | 2.26714e37i | 0.743552 | + | 0.0525325i | ||||
\(109\) | −3.72464e38 | −0.724404 | −0.362202 | − | 0.932100i | \(-0.617975\pi\) | ||||
−0.362202 | + | 0.932100i | \(0.617975\pi\) | |||||||
\(110\) | 3.78036e38 | + | 4.05686e38i | 0.618118 | + | 0.663330i | ||||
\(111\) | 1.89834e38i | 0.261359i | ||||||||
\(112\) | −1.15690e38 | + | 8.14657e38i | −0.134324 | + | 0.945872i | ||||
\(113\) | −1.17442e39 | −1.15168 | −0.575841 | − | 0.817562i | \(-0.695325\pi\) | ||||
−0.575841 | + | 0.817562i | \(0.695325\pi\) | |||||||
\(114\) | 1.15296e38 | − | 1.07438e38i | 0.0956363 | − | 0.0891179i | ||||
\(115\) | − | 2.47476e39i | − | 1.73890i | ||||||
\(116\) | 3.08513e37 | − | 4.36674e38i | 0.0183896 | − | 0.260289i | ||||
\(117\) | −8.98672e38 | −0.455061 | ||||||||
\(118\) | 1.87139e39 | + | 2.00827e39i | 0.806131 | + | 0.865094i | ||||
\(119\) | − | 4.18051e39i | − | 1.53404i | ||||||
\(120\) | 1.10652e39 | − | 8.94068e38i | 0.346352 | − | 0.279851i | ||||
\(121\) | 1.18136e39 | 0.315834 | ||||||||
\(122\) | 3.39825e39 | − | 3.16663e39i | 0.776996 | − | 0.724037i | ||||
\(123\) | − | 2.82274e39i | − | 0.552680i | ||||||
\(124\) | −4.24755e39 | − | 3.00092e38i | −0.713060 | − | 0.0503782i | ||||
\(125\) | −6.07295e39 | −0.875204 | ||||||||
\(126\) | −4.39039e39 | − | 4.71152e39i | −0.543830 | − | 0.583607i | ||||
\(127\) | 1.45149e40i | 1.54719i | 0.633682 | + | 0.773593i | \(0.281543\pi\) | ||||
−0.633682 | + | 0.773593i | \(0.718457\pi\) | |||||||
\(128\) | 5.58472e39 | + | 9.34784e39i | 0.512875 | + | 0.858463i | ||||
\(129\) | 7.64923e39 | 0.605917 | ||||||||
\(130\) | −6.38944e39 | + | 5.95395e39i | −0.437058 | + | 0.407269i | ||||
\(131\) | 1.65764e39i | 0.0980247i | 0.998798 | + | 0.0490123i | \(0.0156074\pi\) | ||||
−0.998798 | + | 0.0490123i | \(0.984393\pi\) | |||||||
\(132\) | −4.62680e38 | + | 6.54883e39i | −0.0236797 | + | 0.335165i | ||||
\(133\) | −6.93328e39 | −0.307438 | ||||||||
\(134\) | 9.48360e39 | + | 1.01773e40i | 0.364739 | + | 0.391417i | ||||
\(135\) | 2.44686e40i | 0.817086i | ||||||||
\(136\) | −3.47696e40 | − | 4.30319e40i | −1.00916 | − | 1.24897i | ||||
\(137\) | 7.05321e40 | 1.78113 | 0.890566 | − | 0.454853i | \(-0.150308\pi\) | ||||
0.890566 | + | 0.454853i | \(0.150308\pi\) | |||||||
\(138\) | 2.14355e40 | − | 1.99745e40i | 0.471446 | − | 0.439313i | ||||
\(139\) | 4.86577e40i | 0.932976i | 0.884528 | + | 0.466488i | \(0.154481\pi\) | ||||
−0.884528 | + | 0.466488i | \(0.845519\pi\) | |||||||
\(140\) | −6.24302e40 | − | 4.41074e39i | −1.04463 | − | 0.0738038i | ||||
\(141\) | 3.44781e40 | 0.503942 | ||||||||
\(142\) | −1.48671e40 | − | 1.59545e40i | −0.189997 | − | 0.203894i | ||||
\(143\) | − | 4.03047e40i | − | 0.450787i | ||||||
\(144\) | −8.43784e40 | − | 1.19826e40i | −0.826692 | − | 0.117399i | ||||
\(145\) | 3.32969e40 | 0.286030 | ||||||||
\(146\) | 6.49498e40 | − | 6.05230e40i | 0.489636 | − | 0.456264i | ||||
\(147\) | 5.35451e39i | 0.0354560i | ||||||||
\(148\) | 7.78908e39 | − | 1.10248e41i | 0.0453433 | − | 0.641796i | ||||
\(149\) | −3.04583e41 | −1.56015 | −0.780075 | − | 0.625686i | \(-0.784819\pi\) | ||||
−0.780075 | + | 0.625686i | \(0.784819\pi\) | |||||||
\(150\) | 1.23750e40 | + | 1.32802e40i | 0.0558229 | + | 0.0599060i | ||||
\(151\) | 2.44695e40i | 0.0972888i | 0.998816 | + | 0.0486444i | \(0.0154901\pi\) | ||||
−0.998816 | + | 0.0486444i | \(0.984510\pi\) | |||||||
\(152\) | −7.13675e40 | + | 5.76647e40i | −0.250306 | + | 0.202247i | ||||
\(153\) | 4.32998e41 | 1.34075 | ||||||||
\(154\) | 2.11308e41 | − | 1.96906e41i | 0.578125 | − | 0.538721i | ||||
\(155\) | − | 3.23881e41i | − | 0.783580i | ||||||
\(156\) | −1.03142e41 | − | 7.28707e39i | −0.220835 | − | 0.0156022i | ||||
\(157\) | 2.74970e40 | 0.0521424 | 0.0260712 | − | 0.999660i | \(-0.491700\pi\) | ||||
0.0260712 | + | 0.999660i | \(0.491700\pi\) | |||||||
\(158\) | 6.80240e41 | + | 7.29995e41i | 1.14335 | + | 1.22697i | ||||
\(159\) | − | 1.44524e41i | − | 0.215474i | ||||||
\(160\) | −6.79307e41 | + | 4.73835e41i | −0.899056 | + | 0.627116i | ||||
\(161\) | −1.28902e42 | −1.51554 | ||||||||
\(162\) | 3.72499e41 | − | 3.47110e41i | 0.389349 | − | 0.362812i | ||||
\(163\) | 1.07391e42i | 0.998629i | 0.866421 | + | 0.499315i | \(0.166415\pi\) | ||||
−0.866421 | + | 0.499315i | \(0.833585\pi\) | |||||||
\(164\) | −1.15820e41 | + | 1.63933e42i | −0.0958848 | + | 1.35717i | ||||
\(165\) | −4.99357e41 | −0.368312 | ||||||||
\(166\) | 2.04313e42 | + | 2.19257e42i | 1.34351 | + | 1.44178i | ||||
\(167\) | − | 2.06172e42i | − | 1.20953i | −0.796405 | − | 0.604764i | \(-0.793267\pi\) | ||
0.796405 | − | 0.604764i | \(-0.206733\pi\) | |||||||
\(168\) | −4.65689e41 | − | 5.76350e41i | −0.243904 | − | 0.301863i | ||||
\(169\) | −1.50242e42 | −0.702983 | ||||||||
\(170\) | 3.07856e42 | − | 2.86873e42i | 1.28771 | − | 1.19994i | ||||
\(171\) | − | 7.18117e41i | − | 0.268701i | ||||||
\(172\) | −4.44235e42 | − | 3.13855e41i | −1.48790 | − | 0.105121i | ||||
\(173\) | 2.78835e42 | 0.836509 | 0.418255 | − | 0.908330i | \(-0.362642\pi\) | ||||
0.418255 | + | 0.908330i | \(0.362642\pi\) | |||||||
\(174\) | 2.68749e41 | + | 2.88406e41i | 0.0722622 | + | 0.0775477i | ||||
\(175\) | − | 7.98599e41i | − | 0.192578i | ||||||
\(176\) | 5.37410e41 | − | 3.78430e42i | 0.116296 | − | 0.818927i | ||||
\(177\) | −2.47196e42 | −0.480341 | ||||||||
\(178\) | 6.00939e41 | − | 5.59980e41i | 0.104918 | − | 0.0977670i | ||||
\(179\) | − | 4.60894e42i | − | 0.723425i | −0.932290 | − | 0.361713i | \(-0.882192\pi\) | ||
0.932290 | − | 0.361713i | \(-0.117808\pi\) | |||||||
\(180\) | 4.56844e41 | − | 6.46623e42i | 0.0645046 | − | 0.913006i | ||||
\(181\) | 2.68060e42 | 0.340674 | 0.170337 | − | 0.985386i | \(-0.445514\pi\) | ||||
0.170337 | + | 0.985386i | \(0.445514\pi\) | |||||||
\(182\) | 3.10120e42 | + | 3.32804e42i | 0.354956 | + | 0.380918i | ||||
\(183\) | 4.18288e42i | 0.431425i | ||||||||
\(184\) | −1.32684e43 | + | 1.07208e43i | −1.23390 | + | 0.996989i | ||||
\(185\) | 8.40653e42 | 0.705267 | ||||||||
\(186\) | 2.80535e42 | − | 2.61414e42i | 0.212442 | − | 0.197962i | ||||
\(187\) | 1.94196e43i | 1.32816i | ||||||||
\(188\) | −2.00234e43 | − | 1.41467e42i | −1.23748 | − | 0.0874291i | ||||
\(189\) | 1.27449e43 | 0.712132 | ||||||||
\(190\) | −4.75772e42 | − | 5.10572e42i | −0.240481 | − | 0.258071i | ||||
\(191\) | 3.38592e43i | 1.54897i | 0.632593 | + | 0.774484i | \(0.281991\pi\) | ||||
−0.632593 | + | 0.774484i | \(0.718009\pi\) | |||||||
\(192\) | −9.58709e42 | − | 2.05946e42i | −0.397158 | − | 0.0853160i | ||||
\(193\) | −5.60166e42 | −0.210246 | −0.105123 | − | 0.994459i | \(-0.533524\pi\) | ||||
−0.105123 | + | 0.994459i | \(0.533524\pi\) | |||||||
\(194\) | 2.91665e43 | − | 2.71786e43i | 0.992319 | − | 0.924684i | ||||
\(195\) | − | 7.86472e42i | − | 0.242675i | ||||||
\(196\) | 2.19701e41 | − | 3.10967e42i | 0.00615129 | − | 0.0870662i | ||||
\(197\) | 3.74560e43 | 0.952057 | 0.476029 | − | 0.879430i | \(-0.342076\pi\) | ||||
0.476029 | + | 0.879430i | \(0.342076\pi\) | |||||||
\(198\) | 2.03946e43 | + | 2.18863e43i | 0.470843 | + | 0.505282i | ||||
\(199\) | − | 1.44674e43i | − | 0.303517i | −0.988418 | − | 0.151759i | \(-0.951506\pi\) | ||
0.988418 | − | 0.151759i | \(-0.0484936\pi\) | |||||||
\(200\) | −6.64201e42 | − | 8.22034e42i | −0.126686 | − | 0.156791i | ||||
\(201\) | −1.25271e43 | −0.217333 | ||||||||
\(202\) | −5.32670e43 | + | 4.96364e43i | −0.840973 | + | 0.783654i | ||||
\(203\) | − | 1.73432e43i | − | 0.249290i | ||||||
\(204\) | 4.96959e43 | + | 3.51105e42i | 0.650650 | + | 0.0459689i | ||||
\(205\) | −1.25001e44 | −1.49138 | ||||||||
\(206\) | −7.22931e43 | − | 7.75808e43i | −0.786356 | − | 0.843873i | ||||
\(207\) | − | 1.33510e44i | − | 1.32458i | ||||||
\(208\) | 5.96016e43 | + | 8.46404e42i | 0.539579 | + | 0.0766257i | ||||
\(209\) | 3.22070e43 | 0.266177 | ||||||||
\(210\) | 4.12328e43 | − | 3.84225e43i | 0.311226 | − | 0.290014i | ||||
\(211\) | 6.54428e43i | 0.451331i | 0.974205 | + | 0.225666i | \(0.0724557\pi\) | ||||
−0.974205 | + | 0.225666i | \(0.927544\pi\) | |||||||
\(212\) | −5.92996e42 | + | 8.39335e43i | −0.0373827 | + | 0.529120i | ||||
\(213\) | 1.96383e43 | 0.113212 | ||||||||
\(214\) | 1.37825e44 | + | 1.47906e44i | 0.726885 | + | 0.780051i | ||||
\(215\) | − | 3.38735e44i | − | 1.63504i | ||||||
\(216\) | 1.31189e44 | − | 1.06000e44i | 0.579795 | − | 0.468473i | ||||
\(217\) | −1.68698e44 | −0.682929 | ||||||||
\(218\) | −1.42865e44 | + | 1.33128e44i | −0.529973 | + | 0.493851i | ||||
\(219\) | 7.99463e43i | 0.271869i | ||||||||
\(220\) | 2.90005e44 | + | 2.04891e43i | 0.904430 | + | 0.0638986i | ||||
\(221\) | −3.05853e44 | −0.875103 | ||||||||
\(222\) | 6.78516e43 | + | 7.28144e43i | 0.178178 | + | 0.191210i | ||||
\(223\) | 2.33526e44i | 0.563045i | 0.959555 | + | 0.281522i | \(0.0908394\pi\) | ||||
−0.959555 | + | 0.281522i | \(0.909161\pi\) | |||||||
\(224\) | 2.46804e44 | + | 3.53827e44i | 0.546563 | + | 0.783572i | ||||
\(225\) | 8.27151e43 | 0.168313 | ||||||||
\(226\) | −4.50470e44 | + | 4.19767e44i | −0.842569 | + | 0.785141i | ||||
\(227\) | 7.34501e44i | 1.26328i | 0.775260 | + | 0.631642i | \(0.217619\pi\) | ||||
−0.775260 | + | 0.631642i | \(0.782381\pi\) | |||||||
\(228\) | 5.82300e42 | − | 8.24196e43i | 0.00921265 | − | 0.130397i | ||||
\(229\) | 2.77326e44 | 0.403754 | 0.201877 | − | 0.979411i | \(-0.435296\pi\) | ||||
0.201877 | + | 0.979411i | \(0.435296\pi\) | |||||||
\(230\) | −8.84542e44 | − | 9.49241e44i | −1.18547 | − | 1.27218i | ||||
\(231\) | 2.60097e44i | 0.321002i | ||||||||
\(232\) | −1.44245e44 | − | 1.78521e44i | −0.163994 | − | 0.202964i | ||||
\(233\) | 1.17182e45 | 1.22772 | 0.613860 | − | 0.789415i | \(-0.289616\pi\) | ||||
0.613860 | + | 0.789415i | \(0.289616\pi\) | |||||||
\(234\) | −3.44703e44 | + | 3.21208e44i | −0.332923 | + | 0.310231i | ||||
\(235\) | − | 1.52681e45i | − | 1.35987i | ||||||
\(236\) | 1.43561e45 | + | 1.01427e44i | 1.17953 | + | 0.0833346i | ||||
\(237\) | −8.98546e44 | −0.681274 | ||||||||
\(238\) | −1.49422e45 | − | 1.60351e45i | −1.04581 | − | 1.12230i | ||||
\(239\) | − | 3.52214e44i | − | 0.227639i | −0.993501 | − | 0.113819i | \(-0.963692\pi\) | ||
0.993501 | − | 0.113819i | \(-0.0363085\pi\) | |||||||
\(240\) | 1.04866e44 | − | 7.38436e44i | 0.0626065 | − | 0.440859i | ||||
\(241\) | 2.19326e45 | 1.20995 | 0.604973 | − | 0.796246i | \(-0.293184\pi\) | ||||
0.604973 | + | 0.796246i | \(0.293184\pi\) | |||||||
\(242\) | 4.53132e44 | − | 4.22247e44i | 0.231064 | − | 0.215315i | ||||
\(243\) | 2.03943e45i | 0.961590i | ||||||||
\(244\) | 1.71628e44 | − | 2.42924e45i | 0.0748481 | − | 1.05941i | ||||
\(245\) | 2.37117e44 | 0.0956767 | ||||||||
\(246\) | −1.00892e45 | − | 1.08271e45i | −0.376781 | − | 0.404340i | ||||
\(247\) | 5.07250e44i | 0.175380i | ||||||||
\(248\) | −1.73649e45 | + | 1.40308e45i | −0.556019 | + | 0.449262i | ||||
\(249\) | −2.69882e45 | −0.800545 | ||||||||
\(250\) | −2.32939e45 | + | 2.17063e45i | −0.640299 | + | 0.596657i | ||||
\(251\) | 2.03962e45i | 0.519696i | 0.965650 | + | 0.259848i | \(0.0836724\pi\) | ||||
−0.965650 | + | 0.259848i | \(0.916328\pi\) | |||||||
\(252\) | −3.36804e45 | − | 2.37954e44i | −0.795731 | − | 0.0562190i | ||||
\(253\) | 5.98783e45 | 1.31214 | ||||||||
\(254\) | 5.18799e45 | + | 5.56745e45i | 1.05477 | + | 1.13192i | ||||
\(255\) | 3.78937e45i | 0.714996i | ||||||||
\(256\) | 5.48328e45 | + | 1.58942e45i | 0.960463 | + | 0.278406i | ||||
\(257\) | −8.53814e45 | −1.38878 | −0.694391 | − | 0.719598i | \(-0.744326\pi\) | ||||
−0.694391 | + | 0.719598i | \(0.744326\pi\) | |||||||
\(258\) | 2.93401e45 | − | 2.73403e45i | 0.443289 | − | 0.413075i | ||||
\(259\) | − | 4.37867e45i | − | 0.614676i | ||||||
\(260\) | −3.22697e44 | + | 4.56750e45i | −0.0421019 | + | 0.595916i | ||||
\(261\) | 1.79633e45 | 0.217879 | ||||||||
\(262\) | 5.92482e44 | + | 6.35818e44i | 0.0668268 | + | 0.0717148i | ||||
\(263\) | − | 1.31745e46i | − | 1.38221i | −0.722754 | − | 0.691105i | \(-0.757124\pi\) | ||
0.722754 | − | 0.691105i | \(-0.242876\pi\) | |||||||
\(264\) | 2.16325e45 | + | 2.67730e45i | 0.211170 | + | 0.261350i | ||||
\(265\) | −6.40004e45 | −0.581448 | ||||||||
\(266\) | −2.65939e45 | + | 2.47813e45i | −0.224922 | + | 0.209591i | ||||
\(267\) | 7.39691e44i | 0.0582554i | ||||||||
\(268\) | 7.27522e45 | + | 5.14000e44i | 0.533685 | + | 0.0377052i | ||||
\(269\) | −3.49902e45 | −0.239141 | −0.119570 | − | 0.992826i | \(-0.538152\pi\) | ||||
−0.119570 | + | 0.992826i | \(0.538152\pi\) | |||||||
\(270\) | 8.74571e45 | + | 9.38540e45i | 0.557036 | + | 0.597780i | ||||
\(271\) | − | 7.54533e45i | − | 0.447983i | −0.974591 | − | 0.223992i | \(-0.928091\pi\) | ||
0.974591 | − | 0.223992i | \(-0.0719088\pi\) | |||||||
\(272\) | −2.87172e46 | − | 4.07814e45i | −1.58977 | − | 0.225763i | ||||
\(273\) | −4.09646e45 | −0.211504 | ||||||||
\(274\) | 2.70539e46 | − | 2.52100e46i | 1.30308 | − | 1.21426i | ||||
\(275\) | 3.70971e45i | 0.166732i | ||||||||
\(276\) | 1.08260e45 | − | 1.53232e46i | 0.0454144 | − | 0.642802i | ||||
\(277\) | −1.89988e46 | −0.744063 | −0.372031 | − | 0.928220i | \(-0.621339\pi\) | ||||
−0.372031 | + | 0.928220i | \(0.621339\pi\) | |||||||
\(278\) | 1.73915e46 | + | 1.86636e46i | 0.636042 | + | 0.682564i | ||||
\(279\) | − | 1.74730e46i | − | 0.596880i | ||||||
\(280\) | −2.55228e46 | + | 2.06223e46i | −0.814565 | + | 0.658166i | ||||
\(281\) | 4.69370e45 | 0.139989 | 0.0699947 | − | 0.997547i | \(-0.477702\pi\) | ||||
0.0699947 | + | 0.997547i | \(0.477702\pi\) | |||||||
\(282\) | 1.32247e46 | − | 1.23234e46i | 0.368684 | − | 0.343555i | ||||
\(283\) | − | 2.58100e46i | − | 0.672738i | −0.941730 | − | 0.336369i | \(-0.890801\pi\) | ||
0.941730 | − | 0.336369i | \(-0.109199\pi\) | |||||||
\(284\) | −1.14051e46 | − | 8.05777e44i | −0.278003 | − | 0.0196411i | ||||
\(285\) | 6.28459e45 | 0.143293 | ||||||||
\(286\) | −1.44059e46 | − | 1.54596e46i | −0.307317 | − | 0.329795i | ||||
\(287\) | 6.51086e46i | 1.29982i | ||||||||
\(288\) | −3.66478e46 | + | 2.55628e46i | −0.684842 | + | 0.477696i | ||||
\(289\) | 9.02101e46 | 1.57832 | ||||||||
\(290\) | 1.27717e46 | − | 1.19012e46i | 0.209259 | − | 0.194997i | ||||
\(291\) | 3.59008e46i | 0.550982i | ||||||||
\(292\) | 3.28027e45 | − | 4.64294e46i | 0.0471667 | − | 0.667604i | ||||
\(293\) | 8.61122e46 | 1.16033 | 0.580163 | − | 0.814500i | \(-0.302989\pi\) | ||||
0.580163 | + | 0.814500i | \(0.302989\pi\) | |||||||
\(294\) | 1.91384e45 | + | 2.05382e45i | 0.0241716 | + | 0.0259396i | ||||
\(295\) | 1.09467e47i | 1.29618i | ||||||||
\(296\) | −3.64177e46 | − | 4.50716e46i | −0.404362 | − | 0.500450i | ||||
\(297\) | −5.92033e46 | −0.616557 | ||||||||
\(298\) | −1.16829e47 | + | 1.08866e47i | −1.14141 | + | 1.06361i | ||||
\(299\) | 9.43065e46i | 0.864548i | ||||||||
\(300\) | 9.49336e45 | + | 6.70713e44i | 0.0816801 | + | 0.00577075i | ||||
\(301\) | −1.76435e47 | −1.42502 | ||||||||
\(302\) | 8.74601e45 | + | 9.38573e45i | 0.0663251 | + | 0.0711764i | ||||
\(303\) | − | 6.55659e46i | − | 0.466948i | ||||||
\(304\) | −6.76351e45 | + | 4.76269e46i | −0.0452454 | + | 0.318606i | ||||
\(305\) | 1.85233e47 | 1.16418 | ||||||||
\(306\) | 1.66084e47 | − | 1.54764e47i | 0.980893 | − | 0.914037i | ||||
\(307\) | − | 2.32516e47i | − | 1.29070i | −0.763888 | − | 0.645348i | \(-0.776712\pi\) | ||
0.763888 | − | 0.645348i | \(-0.223288\pi\) | |||||||
\(308\) | 1.06720e46 | − | 1.51054e47i | 0.0556909 | − | 0.788256i | ||||
\(309\) | 9.54937e46 | 0.468558 | ||||||||
\(310\) | −1.15763e47 | − | 1.24231e47i | −0.534194 | − | 0.573266i | ||||
\(311\) | − | 2.89673e46i | − | 0.125736i | −0.998022 | − | 0.0628682i | \(-0.979975\pi\) | ||
0.998022 | − | 0.0628682i | \(-0.0200248\pi\) | |||||||
\(312\) | −4.21667e46 | + | 3.40705e46i | −0.172200 | + | 0.139137i | ||||
\(313\) | −7.03048e46 | −0.270174 | −0.135087 | − | 0.990834i | \(-0.543131\pi\) | ||||
−0.135087 | + | 0.990834i | \(0.543131\pi\) | |||||||
\(314\) | 1.05470e46 | − | 9.82811e45i | 0.0381474 | − | 0.0355473i | ||||
\(315\) | − | 2.56817e47i | − | 0.874426i | ||||||
\(316\) | 5.21838e47 | + | 3.68682e46i | 1.67294 | + | 0.118195i | ||||
\(317\) | −2.66860e47 | −0.805670 | −0.402835 | − | 0.915273i | \(-0.631975\pi\) | ||||
−0.402835 | + | 0.915273i | \(0.631975\pi\) | |||||||
\(318\) | −5.16566e46 | − | 5.54349e46i | −0.146896 | − | 0.157641i | ||||
\(319\) | 8.05638e46i | 0.215833i | ||||||||
\(320\) | −9.12003e46 | + | 4.24550e47i | −0.230222 | + | 1.07172i | ||||
\(321\) | −1.82056e47 | −0.433121 | ||||||||
\(322\) | −4.94426e47 | + | 4.60727e47i | −1.10877 | + | 1.03320i | ||||
\(323\) | − | 2.44403e47i | − | 0.516724i | ||||||
\(324\) | 1.88129e46 | − | 2.66281e47i | 0.0375061 | − | 0.530866i | ||||
\(325\) | −5.84268e46 | −0.109857 | ||||||||
\(326\) | 3.83844e47 | + | 4.11919e47i | 0.680800 | + | 0.730596i | ||||
\(327\) | − | 1.75852e47i | − | 0.294266i | ||||||
\(328\) | 5.41513e47 | + | 6.70192e47i | 0.855078 | + | 1.05827i | ||||
\(329\) | −7.95263e47 | −1.18519 | ||||||||
\(330\) | −1.91538e47 | + | 1.78483e47i | −0.269457 | + | 0.251091i | ||||
\(331\) | 8.32944e47i | 1.10633i | 0.833072 | + | 0.553164i | \(0.186580\pi\) | ||||
−0.833072 | + | 0.553164i | \(0.813420\pi\) | |||||||
\(332\) | 1.56736e48 | + | 1.10735e47i | 1.96583 | + | 0.138887i | ||||
\(333\) | 4.53522e47 | 0.537227 | ||||||||
\(334\) | −7.36910e47 | − | 7.90810e47i | −0.824578 | − | 0.884890i | ||||
\(335\) | 5.54745e47i | 0.586465i | ||||||||
\(336\) | −3.84626e47 | − | 5.46208e46i | −0.384231 | − | 0.0545647i | ||||
\(337\) | 1.74781e47 | 0.165016 | 0.0825078 | − | 0.996590i | \(-0.473707\pi\) | ||||
0.0825078 | + | 0.996590i | \(0.473707\pi\) | |||||||
\(338\) | −5.76283e47 | + | 5.37004e47i | −0.514302 | + | 0.479248i | ||||
\(339\) | − | 5.54480e47i | − | 0.467834i | ||||||
\(340\) | 1.55482e47 | − | 2.20071e48i | 0.124045 | − | 1.75575i | ||||
\(341\) | 7.83649e47 | 0.591273 | ||||||||
\(342\) | −2.56673e47 | − | 2.75447e47i | −0.183183 | − | 0.196581i | ||||
\(343\) | − | 1.53851e48i | − | 1.03875i | ||||||
\(344\) | −1.81613e48 | + | 1.46742e48i | −1.16021 | + | 0.937444i | ||||
\(345\) | 1.16841e48 | 0.706373 | ||||||||
\(346\) | 1.06952e48 | − | 9.96626e47i | 0.611990 | − | 0.570278i | ||||
\(347\) | 2.25920e48i | 1.22376i | 0.790952 | + | 0.611878i | \(0.209586\pi\) | ||||
−0.790952 | + | 0.611878i | \(0.790414\pi\) | |||||||
\(348\) | 2.06168e47 | + | 1.45659e46i | 0.105734 | + | 0.00747018i | ||||
\(349\) | −4.68675e47 | −0.227609 | −0.113804 | − | 0.993503i | \(-0.536304\pi\) | ||||
−0.113804 | + | 0.993503i | \(0.536304\pi\) | |||||||
\(350\) | −2.85439e47 | − | 3.06318e47i | −0.131287 | − | 0.140890i | ||||
\(351\) | − | 9.32434e47i | − | 0.406240i | ||||||
\(352\) | −1.14647e48 | − | 1.64362e48i | −0.473209 | − | 0.678409i | ||||
\(353\) | −1.08094e48 | −0.422749 | −0.211375 | − | 0.977405i | \(-0.567794\pi\) | ||||
−0.211375 | + | 0.977405i | \(0.567794\pi\) | |||||||
\(354\) | −9.48168e47 | + | 8.83542e47i | −0.351417 | + | 0.327465i | ||||
\(355\) | − | 8.69652e47i | − | 0.305497i | ||||||
\(356\) | 3.03502e46 | − | 4.29582e47i | 0.0101068 | − | 0.143053i | ||||
\(357\) | 1.97375e48 | 0.623155 | ||||||||
\(358\) | −1.64735e48 | − | 1.76785e48i | −0.493184 | − | 0.529257i | ||||
\(359\) | 4.37055e48i | 1.24091i | 0.784240 | + | 0.620457i | \(0.213053\pi\) | ||||
−0.784240 | + | 0.620457i | \(0.786947\pi\) | |||||||
\(360\) | −2.13597e48 | − | 2.64353e48i | −0.575237 | − | 0.711930i | ||||
\(361\) | 3.50881e48 | 0.896443 | ||||||||
\(362\) | 1.02819e48 | − | 9.58113e47i | 0.249237 | − | 0.232249i | ||||
\(363\) | 5.57757e47i | 0.128298i | ||||||||
\(364\) | 2.37905e48 | + | 1.68082e47i | 0.519370 | + | 0.0366939i | ||||
\(365\) | 3.54030e48 | 0.733628 | ||||||||
\(366\) | 1.49507e48 | + | 1.60442e48i | 0.294117 | + | 0.315630i | ||||
\(367\) | − | 3.55045e47i | − | 0.0663175i | −0.999450 | − | 0.0331588i | \(-0.989443\pi\) | ||
0.999450 | − | 0.0331588i | \(-0.0105567\pi\) | |||||||
\(368\) | −1.25745e48 | + | 8.85466e48i | −0.223040 | + | 1.57059i | ||||
\(369\) | −6.74364e48 | −1.13604 | ||||||||
\(370\) | 3.22448e48 | − | 3.00471e48i | 0.515973 | − | 0.480805i | ||||
\(371\) | 3.33356e48i | 0.506761i | ||||||||
\(372\) | 1.41683e47 | − | 2.00540e48i | 0.0204646 | − | 0.289658i | ||||
\(373\) | −6.83509e48 | −0.938159 | −0.469079 | − | 0.883156i | \(-0.655414\pi\) | ||||
−0.469079 | + | 0.883156i | \(0.655414\pi\) | |||||||
\(374\) | 6.94105e48 | + | 7.44875e48i | 0.905451 | + | 0.971679i | ||||
\(375\) | − | 2.86723e48i | − | 0.355524i | ||||||
\(376\) | −8.18601e48 | + | 6.61427e48i | −0.964946 | + | 0.779673i | ||||
\(377\) | −1.26886e48 | −0.142209 | ||||||||
\(378\) | 4.88853e48 | − | 4.55533e48i | 0.520995 | − | 0.485485i | ||||
\(379\) | − | 1.02030e49i | − | 1.03415i | −0.855941 | − | 0.517073i | \(-0.827021\pi\) | ||
0.855941 | − | 0.517073i | \(-0.172979\pi\) | |||||||
\(380\) | −3.64983e48 | − | 2.57863e47i | −0.351872 | − | 0.0248600i | ||||
\(381\) | −6.85294e48 | −0.628496 | ||||||||
\(382\) | 1.21021e49 | + | 1.29873e49i | 1.05599 | + | 1.13322i | ||||
\(383\) | 1.06014e49i | 0.880214i | 0.897945 | + | 0.440107i | \(0.145059\pi\) | ||||
−0.897945 | + | 0.440107i | \(0.854941\pi\) | |||||||
\(384\) | −4.41341e48 | + | 2.63672e48i | −0.348723 | + | 0.208339i | ||||
\(385\) | 1.15180e49 | 0.866212 | ||||||||
\(386\) | −2.14862e48 | + | 2.00218e48i | −0.153816 | + | 0.143332i | ||||
\(387\) | − | 1.82743e49i | − | 1.24547i | ||||||
\(388\) | 1.47305e48 | − | 2.08497e49i | 0.0955902 | − | 1.35300i | ||||
\(389\) | −1.15747e49 | −0.715264 | −0.357632 | − | 0.933863i | \(-0.616416\pi\) | ||||
−0.357632 | + | 0.933863i | \(0.616416\pi\) | |||||||
\(390\) | −2.81105e48 | − | 3.01666e48i | −0.165440 | − | 0.177541i | ||||
\(391\) | − | 4.54387e49i | − | 2.54723i | ||||||
\(392\) | −1.02721e48 | − | 1.27130e48i | −0.0548558 | − | 0.0678911i | ||||
\(393\) | −7.82624e47 | −0.0398194 | ||||||||
\(394\) | 1.43669e49 | − | 1.33877e49i | 0.696524 | − | 0.649051i | ||||
\(395\) | 3.97908e49i | 1.83839i | ||||||||
\(396\) | 1.56454e49 | + | 1.10536e48i | 0.688936 | + | 0.0486738i | ||||
\(397\) | −1.42293e49 | −0.597260 | −0.298630 | − | 0.954369i | \(-0.596530\pi\) | ||||
−0.298630 | + | 0.954369i | \(0.596530\pi\) | |||||||
\(398\) | −5.17103e48 | − | 5.54926e48i | −0.206918 | − | 0.222053i | ||||
\(399\) | − | 3.27343e48i | − | 0.124887i | ||||||
\(400\) | −5.48582e48 | − | 7.79043e47i | −0.199573 | − | 0.0283414i | ||||
\(401\) | 1.12813e49 | 0.391396 | 0.195698 | − | 0.980664i | \(-0.437303\pi\) | ||||
0.195698 | + | 0.980664i | \(0.437303\pi\) | |||||||
\(402\) | −4.80501e48 | + | 4.47751e48i | −0.159001 | + | 0.148164i | ||||
\(403\) | 1.23422e49i | 0.389581i | ||||||||
\(404\) | −2.69023e48 | + | 3.80779e49i | −0.0810110 | + | 1.14664i | ||||
\(405\) | 2.03043e49 | 0.583367 | ||||||||
\(406\) | −6.19890e48 | − | 6.65231e48i | −0.169949 | − | 0.182380i | ||||
\(407\) | 2.03401e49i | 0.532180i | ||||||||
\(408\) | 2.03167e49 | − | 1.64158e49i | 0.507353 | − | 0.409940i | ||||
\(409\) | 2.78981e48 | 0.0665016 | 0.0332508 | − | 0.999447i | \(-0.489414\pi\) | ||||
0.0332508 | + | 0.999447i | \(0.489414\pi\) | |||||||
\(410\) | −4.79464e49 | + | 4.46785e49i | −1.09110 | + | 1.01673i | ||||
\(411\) | 3.33005e49i | 0.723529i | ||||||||
\(412\) | −5.54587e49 | − | 3.91820e48i | −1.15060 | − | 0.0812904i | ||||
\(413\) | 5.70176e49 | 1.12969 | ||||||||
\(414\) | −4.77200e49 | − | 5.12104e49i | −0.903013 | − | 0.969062i | ||||
\(415\) | 1.19513e50i | 2.16024i | ||||||||
\(416\) | 2.58866e49 | − | 1.80566e49i | 0.446994 | − | 0.311790i | ||||
\(417\) | −2.29729e49 | −0.378992 | ||||||||
\(418\) | 1.23536e49 | − | 1.15116e49i | 0.194735 | − | 0.181462i | ||||
\(419\) | − | 3.56437e49i | − | 0.536928i | −0.963290 | − | 0.268464i | \(-0.913484\pi\) | ||
0.963290 | − | 0.268464i | \(-0.0865161\pi\) | |||||||
\(420\) | 2.08245e48 | − | 2.94753e49i | 0.0299805 | − | 0.424348i | ||||
\(421\) | 5.14183e49 | 0.707551 | 0.353776 | − | 0.935330i | \(-0.384898\pi\) | ||||
0.353776 | + | 0.935330i | \(0.384898\pi\) | |||||||
\(422\) | 2.33909e49 | + | 2.51018e49i | 0.307688 | + | 0.330194i | ||||
\(423\) | − | 8.23697e49i | − | 1.03586i | ||||||
\(424\) | 2.77254e49 | + | 3.43138e49i | 0.333370 | + | 0.412589i | ||||
\(425\) | 2.81511e49 | 0.323673 | ||||||||
\(426\) | 7.53262e48 | − | 7.01922e48i | 0.0828255 | − | 0.0771803i | ||||
\(427\) | − | 9.64813e49i | − | 1.01464i | ||||||
\(428\) | 1.05731e50 | + | 7.46994e48i | 1.06358 | + | 0.0751424i | ||||
\(429\) | 1.90291e49 | 0.183118 | ||||||||
\(430\) | −1.21072e50 | − | 1.29928e50i | −1.11467 | − | 1.19620i | ||||
\(431\) | 3.78128e48i | 0.0333097i | 0.999861 | + | 0.0166548i | \(0.00530165\pi\) | ||||
−0.999861 | + | 0.0166548i | \(0.994698\pi\) | |||||||
\(432\) | 1.24328e49 | − | 8.75484e49i | 0.104804 | − | 0.738001i | ||||
\(433\) | −1.94791e50 | −1.57145 | −0.785724 | − | 0.618578i | \(-0.787709\pi\) | ||||
−0.785724 | + | 0.618578i | \(0.787709\pi\) | |||||||
\(434\) | −6.47074e49 | + | 6.02970e49i | −0.499630 | + | 0.465577i | ||||
\(435\) | 1.57205e49i | 0.116191i | ||||||||
\(436\) | −7.21538e48 | + | 1.02128e50i | −0.0510524 | + | 0.722602i | ||||
\(437\) | −7.53591e49 | −0.510492 | ||||||||
\(438\) | 2.85748e49 | + | 3.06649e49i | 0.185343 | + | 0.198899i | ||||
\(439\) | 8.56681e49i | 0.532100i | 0.963959 | + | 0.266050i | \(0.0857186\pi\) | ||||
−0.963959 | + | 0.266050i | \(0.914281\pi\) | |||||||
\(440\) | 1.18560e50 | − | 9.57963e49i | 0.705242 | − | 0.569833i | ||||
\(441\) | 1.27921e49 | 0.0728803 | ||||||||
\(442\) | −1.17316e50 | + | 1.09320e50i | −0.640225 | + | 0.596588i | ||||
\(443\) | − | 1.27735e50i | − | 0.667787i | −0.942611 | − | 0.333893i | \(-0.891637\pi\) | ||
0.942611 | − | 0.333893i | \(-0.108363\pi\) | |||||||
\(444\) | 5.20515e49 | + | 3.67747e48i | 0.260709 | + | 0.0184193i | ||||
\(445\) | 3.27561e49 | 0.157200 | ||||||||
\(446\) | 8.34681e49 | + | 8.95733e49i | 0.383847 | + | 0.411923i | ||||
\(447\) | − | 1.43803e50i | − | 0.633762i | ||||||
\(448\) | 2.21133e50 | + | 4.75030e49i | 0.934054 | + | 0.200650i | ||||
\(449\) | −1.19966e50 | −0.485709 | −0.242855 | − | 0.970063i | \(-0.578084\pi\) | ||||
−0.242855 | + | 0.970063i | \(0.578084\pi\) | |||||||
\(450\) | 3.17269e49 | − | 2.95645e49i | 0.123138 | − | 0.114745i | ||||
\(451\) | − | 3.02447e50i | − | 1.12537i | ||||||
\(452\) | −2.27509e49 | + | 3.22019e50i | −0.0811648 | + | 1.14882i | ||||
\(453\) | −1.15528e49 | −0.0395205 | ||||||||
\(454\) | 2.62529e50 | + | 2.81731e50i | 0.861225 | + | 0.924218i | ||||
\(455\) | 1.81406e50i | 0.570734i | ||||||||
\(456\) | −2.72253e49 | − | 3.36949e49i | −0.0821563 | − | 0.101679i | ||||
\(457\) | 2.04703e50 | 0.592537 | 0.296269 | − | 0.955105i | \(-0.404258\pi\) | ||||
0.296269 | + | 0.955105i | \(0.404258\pi\) | |||||||
\(458\) | 1.06374e50 | − | 9.91233e49i | 0.295386 | − | 0.275253i | ||||
\(459\) | 4.49265e50i | 1.19691i | ||||||||
\(460\) | −6.78566e50 | − | 4.79411e49i | −1.73457 | − | 0.122549i | ||||
\(461\) | −5.51105e50 | −1.35181 | −0.675906 | − | 0.736988i | \(-0.736248\pi\) | ||||
−0.675906 | + | 0.736988i | \(0.736248\pi\) | |||||||
\(462\) | 9.29654e49 | + | 9.97652e49i | 0.218839 | + | 0.234845i | ||||
\(463\) | − | 1.39874e50i | − | 0.316007i | −0.987439 | − | 0.158004i | \(-0.949494\pi\) | ||
0.987439 | − | 0.158004i | \(-0.0505058\pi\) | |||||||
\(464\) | −1.19136e50 | − | 1.69185e49i | −0.258345 | − | 0.0366877i | ||||
\(465\) | 1.52915e50 | 0.318304 | ||||||||
\(466\) | 4.49474e50 | − | 4.18839e50i | 0.898198 | − | 0.836979i | ||||
\(467\) | 4.50874e50i | 0.865036i | 0.901625 | + | 0.432518i | \(0.142375\pi\) | ||||
−0.901625 | + | 0.432518i | \(0.857625\pi\) | |||||||
\(468\) | −1.74091e49 | + | 2.46411e50i | −0.0320705 | + | 0.453930i | ||||
\(469\) | 2.88947e50 | 0.511134 | ||||||||
\(470\) | −5.45722e50 | − | 5.85638e50i | −0.927069 | − | 0.994878i | ||||
\(471\) | 1.29822e49i | 0.0211812i | ||||||||
\(472\) | 5.86908e50 | − | 4.74220e50i | 0.919756 | − | 0.743159i | ||||
\(473\) | 8.19589e50 | 1.23377 | ||||||||
\(474\) | −3.44654e50 | + | 3.21163e50i | −0.498419 | + | 0.464448i | ||||
\(475\) | − | 4.66881e49i | − | 0.0648676i | ||||||
\(476\) | −1.14627e51 | − | 8.09849e49i | −1.53023 | − | 0.108112i | ||||
\(477\) | −3.45274e50 | −0.442909 | ||||||||
\(478\) | −1.25890e50 | − | 1.35098e50i | −0.155189 | − | 0.166540i | ||||
\(479\) | − | 4.76752e50i | − | 0.564830i | −0.959292 | − | 0.282415i | \(-0.908865\pi\) | ||
0.959292 | − | 0.282415i | \(-0.0911354\pi\) | |||||||
\(480\) | −2.23713e50 | − | 3.20723e50i | −0.254746 | − | 0.365213i | ||||
\(481\) | −3.20350e50 | −0.350646 | ||||||||
\(482\) | 8.41265e50 | − | 7.83926e50i | 0.885195 | − | 0.824862i | ||||
\(483\) | − | 6.08586e50i | − | 0.615639i | ||||||
\(484\) | 2.28853e49 | − | 3.23922e50i | 0.0222584 | − | 0.315049i | ||||
\(485\) | 1.58981e51 | 1.48680 | ||||||||
\(486\) | 7.28945e50 | + | 7.82262e50i | 0.655550 | + | 0.703499i | ||||
\(487\) | 5.31475e50i | 0.459655i | 0.973231 | + | 0.229828i | \(0.0738163\pi\) | ||||
−0.973231 | + | 0.229828i | \(0.926184\pi\) | |||||||
\(488\) | −8.02442e50 | − | 9.93125e50i | −0.667478 | − | 0.826090i | ||||
\(489\) | −5.07028e50 | −0.405662 | ||||||||
\(490\) | 9.09505e49 | − | 8.47515e49i | 0.0699970 | − | 0.0652261i | ||||
\(491\) | 2.92285e50i | 0.216400i | 0.994129 | + | 0.108200i | \(0.0345088\pi\) | ||||
−0.994129 | + | 0.108200i | \(0.965491\pi\) | |||||||
\(492\) | −7.73980e50 | − | 5.46822e49i | −0.551306 | − | 0.0389501i | ||||
\(493\) | 6.11359e50 | 0.418991 | ||||||||
\(494\) | 1.81304e50 | + | 1.94565e50i | 0.119563 | + | 0.128308i | ||||
\(495\) | 1.19298e51i | 0.757069i | ||||||||
\(496\) | −1.64567e50 | + | 1.15884e51i | −0.100506 | + | 0.707737i | ||||
\(497\) | −4.52971e50 | −0.266256 | ||||||||
\(498\) | −1.03518e51 | + | 9.64626e50i | −0.585679 | + | 0.545760i | ||||
\(499\) | 2.63381e51i | 1.43441i | 0.696860 | + | 0.717207i | \(0.254580\pi\) | ||||
−0.696860 | + | 0.717207i | \(0.745420\pi\) | |||||||
\(500\) | −1.17645e50 | + | 1.66517e51i | −0.0616801 | + | 0.873028i | ||||
\(501\) | 9.73402e50 | 0.491333 | ||||||||
\(502\) | 7.29013e50 | + | 7.82335e50i | 0.354295 | + | 0.380209i | ||||
\(503\) | − | 1.68584e51i | − | 0.788907i | −0.918916 | − | 0.394454i | \(-0.870934\pi\) | ||
0.918916 | − | 0.394454i | \(-0.129066\pi\) | |||||||
\(504\) | −1.37692e51 | + | 1.11255e51i | −0.620483 | + | 0.501348i | ||||
\(505\) | −2.90349e51 | −1.26004 | ||||||||
\(506\) | 2.29674e51 | − | 2.14020e51i | 0.959959 | − | 0.894530i | ||||
\(507\) | − | 7.09342e50i | − | 0.285565i | ||||||
\(508\) | 3.97990e51 | + | 2.81183e50i | 1.54334 | + | 0.109038i | ||||
\(509\) | −4.84627e51 | −1.81038 | −0.905190 | − | 0.425006i | \(-0.860272\pi\) | ||||
−0.905190 | + | 0.425006i | \(0.860272\pi\) | |||||||
\(510\) | 1.35442e51 | + | 1.45348e51i | 0.487438 | + | 0.523091i | ||||
\(511\) | − | 1.84402e51i | − | 0.639394i | ||||||
\(512\) | 2.67131e51 | − | 1.35021e51i | 0.892473 | − | 0.451100i | ||||
\(513\) | 7.45096e50 | 0.239874 | ||||||||
\(514\) | −3.27496e51 | + | 3.05175e51i | −1.01603 | + | 0.946781i | ||||
\(515\) | − | 4.22880e51i | − | 1.26439i | ||||||
\(516\) | 1.48181e50 | − | 2.09738e51i | 0.0427020 | − | 0.604411i | ||||
\(517\) | 3.69421e51 | 1.02613 | ||||||||
\(518\) | −1.56505e51 | − | 1.67952e51i | −0.419046 | − | 0.449696i | ||||
\(519\) | 1.31647e51i | 0.339805i | ||||||||
\(520\) | 1.50876e51 | + | 1.86729e51i | 0.375455 | + | 0.464674i | ||||
\(521\) | 3.73899e50 | 0.0897093 | 0.0448547 | − | 0.998994i | \(-0.485718\pi\) | ||||
0.0448547 | + | 0.998994i | \(0.485718\pi\) | |||||||
\(522\) | 6.89015e50 | − | 6.42053e50i | 0.159400 | − | 0.148536i | ||||
\(523\) | − | 4.26927e51i | − | 0.952404i | −0.879336 | − | 0.476202i | \(-0.842013\pi\) | ||
0.879336 | − | 0.476202i | \(-0.157987\pi\) | |||||||
\(524\) | 4.54515e50 | + | 3.21118e49i | 0.0977809 | + | 0.00690829i | ||||
\(525\) | 3.77044e50 | 0.0782285 | ||||||||
\(526\) | −4.70889e51 | − | 5.05332e51i | −0.942301 | − | 1.01122i | ||||
\(527\) | − | 5.94673e51i | − | 1.14783i | ||||||
\(528\) | 1.78669e51 | + | 2.53728e50i | 0.332663 | + | 0.0472416i | ||||
\(529\) | −8.44308e51 | −1.51650 | ||||||||
\(530\) | −2.45485e51 | + | 2.28754e51i | −0.425387 | + | 0.396393i | ||||
\(531\) | 5.90562e51i | 0.987347i | ||||||||
\(532\) | −1.34312e50 | + | 1.90107e51i | −0.0216667 | + | 0.306674i | ||||
\(533\) | 4.76345e51 | 0.741489 | ||||||||
\(534\) | 2.64384e50 | + | 2.83722e50i | 0.0397148 | + | 0.0426196i | ||||
\(535\) | 8.06208e51i | 1.16876i | ||||||||
\(536\) | 2.97426e51 | − | 2.40320e51i | 0.416149 | − | 0.336247i | ||||
\(537\) | 2.17603e51 | 0.293869 | ||||||||
\(538\) | −1.34212e51 | + | 1.25064e51i | −0.174955 | + | 0.163031i | ||||
\(539\) | 5.73717e50i | 0.0721957i | ||||||||
\(540\) | 6.70916e51 | + | 4.74007e50i | 0.815055 | + | 0.0575842i | ||||
\(541\) | 4.52519e51 | 0.530749 | 0.265374 | − | 0.964145i | \(-0.414504\pi\) | ||||
0.265374 | + | 0.964145i | \(0.414504\pi\) | |||||||
\(542\) | −2.69689e51 | − | 2.89415e51i | −0.305406 | − | 0.327744i | ||||
\(543\) | 1.26560e51i | 0.138388i | ||||||||
\(544\) | −1.24727e52 | + | 8.70002e51i | −1.31698 | + | 0.918631i | ||||
\(545\) | −7.78735e51 | −0.794065 | ||||||||
\(546\) | −1.57127e51 | + | 1.46418e51i | −0.154736 | + | 0.144189i | ||||
\(547\) | 1.30304e52i | 1.23936i | 0.784854 | + | 0.619681i | \(0.212738\pi\) | ||||
−0.784854 | + | 0.619681i | \(0.787262\pi\) | |||||||
\(548\) | 1.36635e51 | − | 1.93395e52i | 0.125525 | − | 1.77670i | ||||
\(549\) | 9.99308e51 | 0.886798 | ||||||||
\(550\) | 1.32594e51 | + | 1.42293e51i | 0.113667 | + | 0.121981i | ||||
\(551\) | − | 1.01393e51i | − | 0.0839704i | ||||||
\(552\) | −5.06165e51 | − | 6.26445e51i | −0.404995 | − | 0.501234i | ||||
\(553\) | 2.07256e52 | 1.60225 | ||||||||
\(554\) | −7.28733e51 | + | 6.79064e51i | −0.544356 | + | 0.507253i | ||||
\(555\) | 3.96899e51i | 0.286493i | ||||||||
\(556\) | 1.33417e52 | + | 9.42599e50i | 0.930656 | + | 0.0657515i | ||||
\(557\) | 7.16739e51 | 0.483184 | 0.241592 | − | 0.970378i | \(-0.422330\pi\) | ||||
0.241592 | + | 0.970378i | \(0.422330\pi\) | |||||||
\(558\) | −6.24529e51 | − | 6.70209e51i | −0.406914 | − | 0.436677i | ||||
\(559\) | 1.29083e52i | 0.812913i | ||||||||
\(560\) | −2.41880e51 | + | 1.70326e52i | −0.147241 | + | 1.03683i | ||||
\(561\) | −9.16861e51 | −0.539522 | ||||||||
\(562\) | 1.80036e51 | − | 1.67765e51i | 0.102416 | − | 0.0954356i | ||||
\(563\) | − | 2.88572e51i | − | 0.158706i | −0.996847 | − | 0.0793532i | \(-0.974715\pi\) | ||
0.996847 | − | 0.0793532i | \(-0.0252855\pi\) | |||||||
\(564\) | 6.67911e50 | − | 9.45371e51i | 0.0355153 | − | 0.502689i | ||||
\(565\) | −2.45543e52 | −1.26243 | ||||||||
\(566\) | −9.22516e51 | − | 9.89992e51i | −0.458629 | − | 0.492175i | ||||
\(567\) | − | 1.05758e52i | − | 0.508433i | ||||||
\(568\) | −4.66264e51 | + | 3.76739e51i | −0.216777 | + | 0.175155i | ||||
\(569\) | 9.00115e51 | 0.404730 | 0.202365 | − | 0.979310i | \(-0.435137\pi\) | ||||
0.202365 | + | 0.979310i | \(0.435137\pi\) | |||||||
\(570\) | 2.41057e51 | − | 2.24627e51i | 0.104833 | − | 0.0976878i | ||||
\(571\) | − | 4.31267e52i | − | 1.81410i | −0.421028 | − | 0.907048i | \(-0.638331\pi\) | ||
0.421028 | − | 0.907048i | \(-0.361669\pi\) | |||||||
\(572\) | −1.10513e52 | − | 7.80784e50i | −0.449666 | − | 0.0317692i | ||||
\(573\) | −1.59860e52 | −0.629220 | ||||||||
\(574\) | 2.32715e52 | + | 2.49736e52i | 0.886131 | + | 0.950945i | ||||
\(575\) | − | 8.68011e51i | − | 0.319769i | ||||||
\(576\) | −4.92014e51 | + | 2.29040e52i | −0.175368 | + | 0.816363i | ||||
\(577\) | −3.81069e52 | −1.31421 | −0.657103 | − | 0.753801i | \(-0.728218\pi\) | ||||
−0.657103 | + | 0.753801i | \(0.728218\pi\) | |||||||
\(578\) | 3.46018e52 | − | 3.22434e52i | 1.15470 | − | 1.07600i | ||||
\(579\) | − | 2.64472e51i | − | 0.0854058i | ||||||
\(580\) | 6.45029e50 | − | 9.12983e51i | 0.0201580 | − | 0.285319i | ||||
\(581\) | 6.22502e52 | 1.88276 | ||||||||
\(582\) | 1.28319e52 | + | 1.37704e52i | 0.375624 | + | 0.403098i | ||||
\(583\) | − | 1.54853e52i | − | 0.438749i | ||||||
\(584\) | −1.53368e52 | − | 1.89813e52i | −0.420622 | − | 0.520574i | ||||
\(585\) | −1.87891e52 | −0.498822 | ||||||||
\(586\) | 3.30300e52 | − | 3.07787e52i | 0.848894 | − | 0.791035i | ||||
\(587\) | 3.38931e52i | 0.843311i | 0.906756 | + | 0.421655i | \(0.138551\pi\) | ||||
−0.906756 | + | 0.421655i | \(0.861449\pi\) | |||||||
\(588\) | 1.46818e51 | + | 1.03728e50i | 0.0353679 | + | 0.00249877i | ||||
\(589\) | −9.86252e51 | −0.230037 | ||||||||
\(590\) | 3.91264e52 | + | 4.19882e52i | 0.883652 | + | 0.948285i | ||||
\(591\) | 1.76842e52i | 0.386743i | ||||||||
\(592\) | −3.00784e52 | − | 4.27144e51i | −0.637005 | − | 0.0904612i | ||||
\(593\) | −7.13251e52 | −1.46286 | −0.731430 | − | 0.681916i | \(-0.761147\pi\) | ||||
−0.731430 | + | 0.681916i | \(0.761147\pi\) | |||||||
\(594\) | −2.27085e52 | + | 2.11608e52i | −0.451073 | + | 0.420328i | ||||
\(595\) | − | 8.74047e52i | − | 1.68156i | ||||||
\(596\) | −5.90039e51 | + | 8.35150e52i | −0.109952 | + | 1.55627i | ||||
\(597\) | 6.83054e51 | 0.123294 | ||||||||
\(598\) | 3.37076e52 | + | 3.61730e52i | 0.589393 | + | 0.632503i | ||||
\(599\) | 8.06132e52i | 1.36552i | 0.730645 | + | 0.682758i | \(0.239220\pi\) | ||||
−0.730645 | + | 0.682758i | \(0.760780\pi\) | |||||||
\(600\) | 3.88109e51 | − | 3.13590e51i | 0.0636912 | − | 0.0514623i | ||||
\(601\) | 6.33670e50 | 0.0100751 | 0.00503753 | − | 0.999987i | \(-0.498396\pi\) | ||||
0.00503753 | + | 0.999987i | \(0.498396\pi\) | |||||||
\(602\) | −6.76750e52 | + | 6.30624e52i | −1.04255 | + | 0.971488i | ||||
\(603\) | 2.99278e52i | 0.446731i | ||||||||
\(604\) | 6.70939e51 | + | 4.74023e50i | 0.0970469 | + | 0.00685643i | ||||
\(605\) | 2.46994e52 | 0.346206 | ||||||||
\(606\) | −2.34349e52 | − | 2.51490e52i | −0.318335 | − | 0.341619i | ||||
\(607\) | − | 8.02934e51i | − | 0.105705i | −0.998602 | − | 0.0528524i | \(-0.983169\pi\) | ||
0.998602 | − | 0.0528524i | \(-0.0168313\pi\) | |||||||
\(608\) | 1.44288e52 | + | 2.06856e52i | 0.184103 | + | 0.263937i | ||||
\(609\) | 8.18828e51 | 0.101266 | ||||||||
\(610\) | 7.10495e52 | − | 6.62069e52i | 0.851715 | − | 0.793663i | ||||
\(611\) | 5.81828e52i | 0.676101i | ||||||||
\(612\) | 8.38804e51 | − | 1.18726e53i | 0.0944895 | − | 1.33742i | ||||
\(613\) | 1.75777e53 | 1.91961 | 0.959806 | − | 0.280663i | \(-0.0905542\pi\) | ||||
0.959806 | + | 0.280663i | \(0.0905542\pi\) | |||||||
\(614\) | −8.31072e52 | − | 8.91860e52i | −0.879913 | − | 0.944273i | ||||
\(615\) | − | 5.90169e52i | − | 0.605828i | ||||||
\(616\) | −4.98969e52 | − | 6.17539e52i | −0.496638 | − | 0.614654i | ||||
\(617\) | −9.81502e52 | −0.947268 | −0.473634 | − | 0.880722i | \(-0.657058\pi\) | ||||
−0.473634 | + | 0.880722i | \(0.657058\pi\) | |||||||
\(618\) | 3.66284e52 | − | 3.41319e52i | 0.342797 | − | 0.319432i | ||||
\(619\) | 1.47542e52i | 0.133904i | 0.997756 | + | 0.0669520i | \(0.0213274\pi\) | ||||
−0.997756 | + | 0.0669520i | \(0.978673\pi\) | |||||||
\(620\) | −8.88063e52 | − | 6.27423e51i | −0.781631 | − | 0.0552228i | ||||
\(621\) | 1.38526e53 | 1.18247 | ||||||||
\(622\) | −1.03537e52 | − | 1.11110e52i | −0.0857189 | − | 0.0919887i | ||||
\(623\) | − | 1.70615e52i | − | 0.137008i | ||||||
\(624\) | −3.99615e51 | + | 2.81398e52i | −0.0311268 | + | 0.219187i | ||||
\(625\) | −1.53650e53 | −1.16094 | ||||||||
\(626\) | −2.69667e52 | + | 2.51287e52i | −0.197659 | + | 0.184187i | ||||
\(627\) | 1.52059e52i | 0.108126i | ||||||||
\(628\) | 5.32672e50 | − | 7.53951e51i | 0.00367474 | − | 0.0520128i | ||||
\(629\) | 1.54351e53 | 1.03311 | ||||||||
\(630\) | −9.17929e52 | − | 9.85069e52i | −0.596127 | − | 0.639729i | ||||
\(631\) | − | 1.37006e53i | − | 0.863342i | −0.902031 | − | 0.431671i | \(-0.857924\pi\) | ||
0.902031 | − | 0.431671i | \(-0.142076\pi\) | |||||||
\(632\) | 2.13338e53 | − | 1.72377e53i | 1.30450 | − | 1.05403i | ||||
\(633\) | −3.08976e52 | −0.183339 | ||||||||
\(634\) | −1.02359e53 | + | 9.53825e52i | −0.589428 | + | 0.549254i | ||||
\(635\) | 3.03472e53i | 1.69597i | ||||||||
\(636\) | −3.96277e52 | − | 2.79973e51i | −0.214938 | − | 0.0151855i | ||||
\(637\) | −9.03588e51 | −0.0475687 | ||||||||
\(638\) | 2.87956e52 | + | 3.09018e52i | 0.147141 | + | 0.157903i | ||||
\(639\) | − | 4.69166e52i | − | 0.232708i | ||||||
\(640\) | 1.16763e53 | + | 1.95441e53i | 0.562195 | + | 0.941016i | ||||
\(641\) | −1.33117e53 | −0.622199 | −0.311100 | − | 0.950377i | \(-0.600697\pi\) | ||||
−0.311100 | + | 0.950377i | \(0.600697\pi\) | |||||||
\(642\) | −6.98310e52 | + | 6.50715e52i | −0.316871 | + | 0.295274i | ||||
\(643\) | − | 1.54720e51i | − | 0.00681614i | −0.999994 | − | 0.00340807i | \(-0.998915\pi\) | ||
0.999994 | − | 0.00340807i | \(-0.00108482\pi\) | |||||||
\(644\) | −2.49709e52 | + | 3.53441e53i | −0.106808 | + | 1.51177i | ||||
\(645\) | 1.59928e53 | 0.664185 | ||||||||
\(646\) | −8.73558e52 | − | 9.37453e52i | −0.352269 | − | 0.378035i | ||||
\(647\) | 1.34852e53i | 0.528052i | 0.964516 | + | 0.264026i | \(0.0850505\pi\) | ||||
−0.964516 | + | 0.264026i | \(0.914950\pi\) | |||||||
\(648\) | −8.79595e52 | − | 1.08861e53i | −0.334470 | − | 0.413950i | ||||
\(649\) | −2.64862e53 | −0.978072 | ||||||||
\(650\) | −2.24107e52 | + | 2.08832e52i | −0.0803714 | + | 0.0748934i | ||||
\(651\) | − | 7.96478e52i | − | 0.277418i | ||||||
\(652\) | 2.94461e53 | + | 2.08039e52i | 0.996146 | + | 0.0703784i | ||||
\(653\) | 2.32730e53 | 0.764719 | 0.382359 | − | 0.924014i | \(-0.375112\pi\) | ||||
0.382359 | + | 0.924014i | \(0.375112\pi\) | |||||||
\(654\) | −6.28540e52 | − | 6.74514e52i | −0.200611 | − | 0.215285i | ||||
\(655\) | 3.46574e52i | 0.107451i | ||||||||
\(656\) | 4.47251e53 | + | 6.35143e52i | 1.34703 | + | 0.191293i | ||||
\(657\) | 1.90995e53 | 0.558830 | ||||||||
\(658\) | −3.05038e53 | + | 2.84247e53i | −0.867086 | + | 0.807987i | ||||
\(659\) | − | 5.75603e53i | − | 1.58965i | −0.606842 | − | 0.794823i | \(-0.707564\pi\) | ||
0.606842 | − | 0.794823i | \(-0.292436\pi\) | |||||||
\(660\) | −9.67355e51 | + | 1.36921e53i | −0.0259568 | + | 0.367396i | ||||
\(661\) | −7.06863e53 | −1.84292 | −0.921462 | − | 0.388469i | \(-0.873004\pi\) | ||||
−0.921462 | + | 0.388469i | \(0.873004\pi\) | |||||||
\(662\) | 2.97715e53 | + | 3.19491e53i | 0.754223 | + | 0.809389i | ||||
\(663\) | − | 1.44403e53i | − | 0.355483i | ||||||
\(664\) | 6.40770e53 | − | 5.17740e53i | 1.53288 | − | 1.23856i | ||||
\(665\) | −1.44959e53 | −0.337003 | ||||||||
\(666\) | 1.73957e53 | − | 1.62100e53i | 0.393035 | − | 0.366246i | ||||
\(667\) | − | 1.88506e53i | − | 0.413938i | ||||||
\(668\) | −5.65311e53 | − | 3.99396e52i | −1.20652 | − | 0.0852416i | ||||
\(669\) | −1.10255e53 | −0.228719 | ||||||||
\(670\) | 1.98280e53 | + | 2.12783e53i | 0.399814 | + | 0.429057i | ||||
\(671\) | 4.48181e53i | 0.878468i | ||||||||
\(672\) | −1.67053e53 | + | 1.16524e53i | −0.318302 | + | 0.222024i | ||||
\(673\) | −7.44199e53 | −1.37849 | −0.689244 | − | 0.724529i | \(-0.742057\pi\) | ||||
−0.689244 | + | 0.724529i | \(0.742057\pi\) | |||||||
\(674\) | 6.70403e52 | − | 6.24710e52i | 0.120725 | − | 0.112497i | ||||
\(675\) | 8.58226e52i | 0.150255i | ||||||||
\(676\) | −2.91050e52 | + | 4.11956e53i | −0.0495428 | + | 0.701235i | ||||
\(677\) | 8.46471e53 | 1.40097 | 0.700483 | − | 0.713669i | \(-0.252968\pi\) | ||||
0.700483 | + | 0.713669i | \(0.252968\pi\) | |||||||
\(678\) | −1.98185e53 | − | 2.12681e53i | −0.318939 | − | 0.342267i | ||||
\(679\) | − | 8.28079e53i | − | 1.29582i | ||||||
\(680\) | −7.26951e53 | − | 8.99696e53i | −1.10621 | − | 1.36907i | ||||
\(681\) | −3.46781e53 | −0.513169 | ||||||||
\(682\) | 3.00583e53 | − | 2.80096e53i | 0.432575 | − | 0.403092i | ||||
\(683\) | 8.95780e52i | 0.125374i | 0.998033 | + | 0.0626871i | \(0.0199670\pi\) | ||||
−0.998033 | + | 0.0626871i | \(0.980033\pi\) | |||||||
\(684\) | −1.96904e53 | − | 1.39114e52i | −0.268033 | − | 0.0189367i | ||||
\(685\) | 1.47466e54 | 1.95241 | ||||||||
\(686\) | −5.49901e53 | − | 5.90123e53i | −0.708152 | − | 0.759948i | ||||
\(687\) | 1.30934e53i | 0.164012i | ||||||||
\(688\) | −1.72115e53 | + | 1.21199e54i | −0.209719 | + | 1.47679i | ||||
\(689\) | 2.43888e53 | 0.289085 | ||||||||
\(690\) | 4.48167e53 | − | 4.17621e53i | 0.516782 | − | 0.481559i | ||||
\(691\) | 2.09102e53i | 0.234572i | 0.993098 | + | 0.117286i | \(0.0374194\pi\) | ||||
−0.993098 | + | 0.117286i | \(0.962581\pi\) | |||||||
\(692\) | 5.40159e52 | − | 7.64549e53i | 0.0589530 | − | 0.834429i | ||||
\(693\) | 6.21383e53 | 0.659824 | ||||||||
\(694\) | 8.07496e53 | + | 8.66559e53i | 0.834277 | + | 0.895299i | ||||
\(695\) | 1.01732e54i | 1.02269i | ||||||||
\(696\) | 8.42856e52 | − | 6.81025e52i | 0.0824476 | − | 0.0666174i | ||||
\(697\) | −2.29512e54 | −2.18466 | ||||||||
\(698\) | −1.79769e53 | + | 1.67516e53i | −0.166518 | + | 0.155169i | ||||
\(699\) | 5.53254e53i | 0.498722i | ||||||||
\(700\) | −2.18971e53 | − | 1.54705e52i | −0.192099 | − | 0.0135719i | ||||
\(701\) | 1.33189e54 | 1.13717 | 0.568587 | − | 0.822623i | \(-0.307490\pi\) | ||||
0.568587 | + | 0.822623i | \(0.307490\pi\) | |||||||
\(702\) | −3.33276e53 | − | 3.57653e53i | −0.276948 | − | 0.297205i | ||||
\(703\) | − | 2.55988e53i | − | 0.207047i | ||||||
\(704\) | −1.02722e54 | − | 2.20664e53i | −0.808695 | − | 0.173721i | ||||
\(705\) | 7.20857e53 | 0.552403 | ||||||||
\(706\) | −4.14615e53 | + | 3.86356e53i | −0.309283 | + | 0.288203i | ||||
\(707\) | 1.51233e54i | 1.09819i | ||||||||
\(708\) | −4.78869e52 | + | 6.77798e53i | −0.0338521 | + | 0.479147i | ||||
\(709\) | 2.08719e54 | 1.43643 | 0.718213 | − | 0.695823i | \(-0.244960\pi\) | ||||
0.718213 | + | 0.695823i | \(0.244960\pi\) | |||||||
\(710\) | −3.10836e53 | − | 3.33571e53i | −0.208268 | − | 0.223501i | ||||
\(711\) | 2.14666e54i | 1.40037i | ||||||||
\(712\) | −1.41902e53 | − | 1.75622e53i | −0.0901298 | − | 0.111547i | ||||
\(713\) | −1.83361e54 | −1.13398 | ||||||||
\(714\) | 7.57069e53 | − | 7.05469e53i | 0.455900 | − | 0.424827i | ||||
\(715\) | − | 8.42678e53i | − | 0.494136i | ||||||
\(716\) | −1.26375e54 | − | 8.92846e52i | −0.721626 | − | 0.0509834i | ||||
\(717\) | 1.66291e53 | 0.0924710 | ||||||||
\(718\) | 1.56215e54 | + | 1.67641e54i | 0.845975 | + | 0.907852i | ||||
\(719\) | − | 1.57319e54i | − | 0.829721i | −0.909885 | − | 0.414861i | \(-0.863830\pi\) | ||
0.909885 | − | 0.414861i | \(-0.136170\pi\) | |||||||
\(720\) | −1.76416e54 | − | 2.50528e53i | −0.906190 | − | 0.128688i | ||||
\(721\) | −2.20263e54 | −1.10198 | ||||||||
\(722\) | 1.34587e54 | − | 1.25414e54i | 0.655837 | − | 0.611136i | ||||
\(723\) | 1.03551e54i | 0.491502i | ||||||||
\(724\) | 5.19286e52 | − | 7.35005e53i | 0.0240090 | − | 0.339827i | ||||
\(725\) | 1.16787e53 | 0.0525986 | ||||||||
\(726\) | 1.99356e53 | + | 2.13938e53i | 0.0874650 | + | 0.0938625i | ||||
\(727\) | − | 2.87479e54i | − | 1.22872i | −0.789027 | − | 0.614359i | \(-0.789415\pi\) | ||
0.789027 | − | 0.614359i | \(-0.210585\pi\) | |||||||
\(728\) | 9.72606e53 | − | 7.85862e53i | 0.404987 | − | 0.327228i | ||||
\(729\) | 3.48984e53 | 0.141574 | ||||||||
\(730\) | 1.35795e54 | − | 1.26539e54i | 0.536722 | − | 0.500140i | ||||
\(731\) | − | 6.21946e54i | − | 2.39509i | ||||||
\(732\) | 1.14692e54 | + | 8.10309e52i | 0.430352 | + | 0.0304047i | ||||
\(733\) | 7.86070e53 | 0.287399 | 0.143700 | − | 0.989621i | \(-0.454100\pi\) | ||||
0.143700 | + | 0.989621i | \(0.454100\pi\) | |||||||
\(734\) | −1.26902e53 | − | 1.36184e53i | −0.0452110 | − | 0.0485179i | ||||
\(735\) | 1.11950e53i | 0.0388656i | ||||||||
\(736\) | 2.68256e54 | + | 3.84581e54i | 0.907551 | + | 1.30110i | ||||
\(737\) | −1.34224e54 | −0.442534 | ||||||||
\(738\) | −2.58665e54 | + | 2.41035e54i | −0.831126 | + | 0.774478i | ||||
\(739\) | − | 3.69931e54i | − | 1.15845i | −0.815169 | − | 0.579224i | \(-0.803356\pi\) | ||
0.815169 | − | 0.579224i | \(-0.196644\pi\) | |||||||
\(740\) | 1.62851e53 | − | 2.30502e54i | 0.0497037 | − | 0.703514i | ||||
\(741\) | −2.39489e53 | −0.0712426 | ||||||||
\(742\) | 1.19150e54 | + | 1.27865e54i | 0.345477 | + | 0.370746i | ||||
\(743\) | 2.52661e54i | 0.714085i | 0.934088 | + | 0.357043i | \(0.116215\pi\) | ||||
−0.934088 | + | 0.357043i | \(0.883785\pi\) | |||||||
\(744\) | −6.62437e53 | − | 8.19851e53i | −0.182498 | − | 0.225865i | ||||
\(745\) | −6.36812e54 | −1.71018 | ||||||||
\(746\) | −2.62173e54 | + | 2.44303e54i | −0.686356 | + | 0.639575i | ||||
\(747\) | 6.44759e54i | 1.64553i | ||||||||
\(748\) | 5.32474e54 | + | 3.76197e53i | 1.32485 | + | 0.0936019i | ||||
\(749\) | 4.19926e54 | 1.01863 | ||||||||
\(750\) | −1.02482e54 | − | 1.09978e54i | −0.242373 | − | 0.260101i | ||||
\(751\) | 5.62779e52i | 0.0129771i | 0.999979 | + | 0.00648857i | \(0.00206539\pi\) | ||||
−0.999979 | + | 0.00648857i | \(0.997935\pi\) | |||||||
\(752\) | −7.75790e53 | + | 5.46291e54i | −0.174424 | + | 1.22825i | ||||
\(753\) | −9.62971e53 | −0.211110 | ||||||||
\(754\) | −4.86694e53 | + | 4.53521e53i | −0.104040 | + | 0.0969488i | ||||
\(755\) | 5.11600e53i | 0.106644i | ||||||||
\(756\) | 2.46894e53 | − | 3.49457e54i | 0.0501875 | − | 0.710361i | ||||
\(757\) | −6.65977e54 | −1.32019 | −0.660096 | − | 0.751181i | \(-0.729485\pi\) | ||||
−0.660096 | + | 0.751181i | \(0.729485\pi\) | |||||||
\(758\) | −3.64680e54 | − | 3.91354e54i | −0.705014 | − | 0.756581i | ||||
\(759\) | 2.82705e54i | 0.533014i | ||||||||
\(760\) | −1.49213e54 | + | 1.20563e54i | −0.274377 | + | 0.221696i | ||||
\(761\) | 3.83544e54 | 0.687870 | 0.343935 | − | 0.938993i | \(-0.388240\pi\) | ||||
0.343935 | + | 0.938993i | \(0.388240\pi\) | |||||||
\(762\) | −2.62857e54 | + | 2.44941e54i | −0.459807 | + | 0.428467i | ||||
\(763\) | 4.05616e54i | 0.692068i | ||||||||
\(764\) | 9.28400e54 | + | 6.55922e53i | 1.54512 | + | 0.109164i | ||||
\(765\) | 9.05297e54 | 1.46968 | ||||||||
\(766\) | 3.78922e54 | + | 4.06638e54i | 0.600073 | + | 0.643964i | ||||
\(767\) | − | 4.17150e54i | − | 0.644437i | ||||||
\(768\) | −7.50415e53 | + | 2.58883e54i | −0.113094 | + | 0.390158i | ||||
\(769\) | 1.07625e54 | 0.158239 | 0.0791194 | − | 0.996865i | \(-0.474789\pi\) | ||||
0.0791194 | + | 0.996865i | \(0.474789\pi\) | |||||||
\(770\) | 4.41795e54 | − | 4.11684e54i | 0.633720 | − | 0.590527i | ||||
\(771\) | − | 4.03113e54i | − | 0.564149i | ||||||
\(772\) | −1.08516e53 | + | 1.53594e54i | −0.0148171 | + | 0.209723i | ||||
\(773\) | 6.46623e53 | 0.0861471 | 0.0430735 | − | 0.999072i | \(-0.486285\pi\) | ||||
0.0430735 | + | 0.999072i | \(0.486285\pi\) | |||||||
\(774\) | −6.53171e54 | − | 7.00946e54i | −0.849080 | − | 0.911185i | ||||
\(775\) | − | 1.13600e54i | − | 0.144094i | ||||||
\(776\) | −6.88720e54 | − | 8.52379e54i | −0.852451 | − | 1.05502i | ||||
\(777\) | 2.06731e54 | 0.249693 | ||||||||
\(778\) | −4.43969e54 | + | 4.13708e54i | −0.523287 | + | 0.487621i | ||||
\(779\) | 3.80641e54i | 0.437829i | ||||||||
\(780\) | −2.15646e54 | − | 1.52356e53i | −0.242072 | − | 0.0171026i | ||||
\(781\) | 2.10417e54 | 0.230522 | ||||||||
\(782\) | −1.62409e55 | − | 1.74289e55i | −1.73653 | − | 1.86355i | ||||
\(783\) | 1.86381e54i | 0.194504i | ||||||||
\(784\) | −8.48399e53 | − | 1.20481e53i | −0.0864162 | − | 0.0122720i | ||||
\(785\) | 5.74897e53 | 0.0571567 | ||||||||
\(786\) | −3.00190e53 | + | 2.79730e53i | −0.0291319 | + | 0.0271463i | ||||
\(787\) | 3.54695e54i | 0.335996i | 0.985787 | + | 0.167998i | \(0.0537303\pi\) | ||||
−0.985787 | + | 0.167998i | \(0.946270\pi\) | |||||||
\(788\) | 7.25599e53 | − | 1.02702e55i | 0.0670963 | − | 0.949690i | ||||
\(789\) | 6.22009e54 | 0.561479 | ||||||||
\(790\) | 1.42222e55 | + | 1.52625e55i | 1.25329 | + | 1.34496i | ||||
\(791\) | 1.27895e55i | 1.10027i | ||||||||
\(792\) | 6.39618e54 | − | 5.16809e54i | 0.537208 | − | 0.434062i | ||||
\(793\) | −7.05873e54 | −0.578810 | ||||||||
\(794\) | −5.45791e54 | + | 5.08591e54i | −0.436955 | + | 0.407173i | ||||
\(795\) | − | 3.02166e54i | − | 0.236195i | ||||||
\(796\) | −3.96689e54 | − | 2.80264e53i | −0.302762 | − | 0.0213904i | ||||
\(797\) | 9.82426e54 | 0.732136 | 0.366068 | − | 0.930588i | \(-0.380704\pi\) | ||||
0.366068 | + | 0.930588i | \(0.380704\pi\) | |||||||
\(798\) | −1.17001e54 | − | 1.25558e54i | −0.0851399 | − | 0.0913673i | ||||
\(799\) | − | 2.80336e55i | − | 1.99200i | ||||||
\(800\) | −2.38264e54 | + | 1.66196e54i | −0.165329 | + | 0.115321i | ||||
\(801\) | 1.76715e54 | 0.119745 | ||||||||
\(802\) | 4.32716e54 | − | 4.03223e54i | 0.286345 | − | 0.266829i | ||||
\(803\) | 8.56597e54i | 0.553581i | ||||||||
\(804\) | −2.42676e53 | + | 3.43487e54i | −0.0153166 | + | 0.216793i | ||||
\(805\) | −2.69503e55 | −1.66128 | ||||||||
\(806\) | 4.41143e54 | + | 4.73410e54i | 0.265591 | + | 0.285017i | ||||
\(807\) | − | 1.65200e54i | − | 0.0971433i | ||||||
\(808\) | 1.25781e55 | + | 1.55671e55i | 0.722438 | + | 0.894110i | ||||
\(809\) | −2.21908e54 | −0.124495 | −0.0622475 | − | 0.998061i | \(-0.519827\pi\) | ||||
−0.0622475 | + | 0.998061i | \(0.519827\pi\) | |||||||
\(810\) | 7.78808e54 | − | 7.25726e54i | 0.426791 | − | 0.397701i | ||||
\(811\) | − | 5.68992e53i | − | 0.0304586i | −0.999884 | − | 0.0152293i | \(-0.995152\pi\) | ||
0.999884 | − | 0.0152293i | \(-0.00484782\pi\) | |||||||
\(812\) | −4.75541e54 | − | 3.35973e53i | −0.248670 | − | 0.0175687i | ||||
\(813\) | 3.56239e54 | 0.181979 | ||||||||
\(814\) | 7.27006e54 | + | 7.80182e54i | 0.362806 | + | 0.389343i | ||||
\(815\) | 2.24530e55i | 1.09466i | ||||||||
\(816\) | 1.92542e54 | − | 1.35583e55i | 0.0917091 | − | 0.645792i | ||||
\(817\) | −1.03148e55 | −0.480003 | ||||||||
\(818\) | 1.07008e54 | − | 9.97149e53i | 0.0486525 | − | 0.0453364i | ||||
\(819\) | 9.78661e54i | 0.434748i | ||||||||
\(820\) | −2.42152e54 | + | 3.42745e55i | −0.105105 | + | 1.48768i | ||||
\(821\) | 2.50665e55 | 1.06310 | 0.531550 | − | 0.847027i | \(-0.321610\pi\) | ||||
0.531550 | + | 0.847027i | \(0.321610\pi\) | |||||||
\(822\) | 1.19024e55 | + | 1.27730e55i | 0.493255 | + | 0.529333i | ||||
\(823\) | − | 2.89582e55i | − | 1.17267i | −0.810070 | − | 0.586333i | \(-0.800571\pi\) | ||
0.810070 | − | 0.586333i | \(-0.199429\pi\) | |||||||
\(824\) | −2.26727e55 | + | 1.83195e55i | −0.897193 | + | 0.724929i | ||||
\(825\) | −1.75147e54 | −0.0677295 | ||||||||
\(826\) | 2.18702e55 | − | 2.03796e55i | 0.826478 | − | 0.770147i | ||||
\(827\) | − | 8.07277e54i | − | 0.298138i | −0.988827 | − | 0.149069i | \(-0.952372\pi\) | ||
0.988827 | − | 0.149069i | \(-0.0476277\pi\) | |||||||
\(828\) | −3.66078e55 | − | 2.58637e54i | −1.32129 | − | 0.0933499i | ||||
\(829\) | −4.68868e55 | −1.65392 | −0.826959 | − | 0.562262i | \(-0.809931\pi\) | ||||
−0.826959 | + | 0.562262i | \(0.809931\pi\) | |||||||
\(830\) | 4.27170e55 | + | 4.58415e55i | 1.47271 | + | 1.58043i | ||||
\(831\) | − | 8.96992e54i | − | 0.302252i | ||||||
\(832\) | 3.47540e54 | − | 1.61785e55i | 0.114462 | − | 0.532837i | ||||
\(833\) | 4.35366e54 | 0.140152 | ||||||||
\(834\) | −8.81167e54 | + | 8.21108e54i | −0.277270 | + | 0.258372i | ||||
\(835\) | − | 4.31057e55i | − | 1.32584i | ||||||
\(836\) | 6.23915e53 | − | 8.83097e54i | 0.0187588 | − | 0.265515i | ||||
\(837\) | 1.81294e55 | 0.532844 | ||||||||
\(838\) | −1.27400e55 | − | 1.36718e55i | −0.366043 | − | 0.392817i | ||||
\(839\) | 4.12427e55i | 1.15843i | 0.815175 | + | 0.579215i | \(0.196641\pi\) | ||||
−0.815175 | + | 0.579215i | \(0.803359\pi\) | |||||||
\(840\) | −9.73646e54 | − | 1.20501e55i | −0.267359 | − | 0.330891i | ||||
\(841\) | −3.47135e55 | −0.931912 | ||||||||
\(842\) | 1.97225e55 | − | 1.83782e55i | 0.517644 | − | 0.482362i | ||||
\(843\) | 2.21604e54i | 0.0568662i | ||||||||
\(844\) | 1.79441e55 | + | 1.26776e54i | 0.450209 | + | 0.0318076i | ||||
\(845\) | −3.14122e55 | −0.770585 | ||||||||
\(846\) | −2.94410e55 | − | 3.15944e55i | −0.706181 | − | 0.757833i | ||||
\(847\) | − | 1.28651e55i | − | 0.301736i | ||||||
\(848\) | 2.28992e55 | + | 3.25193e54i | 0.525170 | + | 0.0745795i | ||||
\(849\) | 1.21857e55 | 0.273279 | ||||||||
\(850\) | 1.07979e55 | − | 1.00619e55i | 0.236799 | − | 0.220659i | ||||
\(851\) | − | 4.75925e55i | − | 1.02065i | ||||||
\(852\) | 3.80433e53 | − | 5.38470e54i | 0.00797859 | − | 0.112930i | ||||
\(853\) | 8.55540e55 | 1.75472 | 0.877362 | − | 0.479830i | \(-0.159302\pi\) | ||||
0.877362 | + | 0.479830i | \(0.159302\pi\) | |||||||
\(854\) | −3.44849e55 | − | 3.70072e55i | −0.691718 | − | 0.742312i | ||||
\(855\) | − | 1.50142e55i | − | 0.294540i | ||||||
\(856\) | 4.32249e55 | − | 3.49255e55i | 0.829339 | − | 0.670103i | ||||
\(857\) | 7.20266e55 | 1.35163 | 0.675814 | − | 0.737072i | \(-0.263792\pi\) | ||||
0.675814 | + | 0.737072i | \(0.263792\pi\) | |||||||
\(858\) | 7.29898e54 | − | 6.80150e54i | 0.133969 | − | 0.124838i | ||||
\(859\) | 4.54832e55i | 0.816546i | 0.912860 | + | 0.408273i | \(0.133869\pi\) | ||||
−0.912860 | + | 0.408273i | \(0.866131\pi\) | |||||||
\(860\) | −9.28792e55 | − | 6.56198e54i | −1.63098 | − | 0.115230i | ||||
\(861\) | −3.07398e55 | −0.528010 | ||||||||
\(862\) | 1.35153e54 | + | 1.45038e54i | 0.0227084 | + | 0.0243693i | ||||
\(863\) | 1.19707e56i | 1.96749i | 0.179564 | + | 0.983746i | \(0.442531\pi\) | ||||
−0.179564 | + | 0.983746i | \(0.557469\pi\) | |||||||
\(864\) | −2.65232e55 | − | 3.80246e55i | −0.426447 | − | 0.611369i | ||||
\(865\) | 5.82978e55 | 0.916951 | ||||||||
\(866\) | −7.47159e55 | + | 6.96234e55i | −1.14967 | + | 1.07131i | ||||
\(867\) | 4.25911e55i | 0.641144i | ||||||||
\(868\) | −3.26803e54 | + | 4.62561e55i | −0.0481295 | + | 0.681231i | ||||
\(869\) | −9.62761e55 | −1.38721 | ||||||||
\(870\) | 5.61892e54 | + | 6.02991e54i | 0.0792113 | + | 0.0850050i | ||||
\(871\) | − | 2.11398e55i | − | 0.291579i | ||||||
\(872\) | 3.37354e55 | + | 4.17519e55i | 0.455273 | + | 0.563460i | ||||
\(873\) | 8.57686e55 | 1.13255 | ||||||||
\(874\) | −2.89054e55 | + | 2.69353e55i | −0.373475 | + | 0.348020i | ||||
\(875\) | 6.61349e55i | 0.836137i | ||||||||
\(876\) | 2.19208e55 | + | 1.54872e54i | 0.271193 | + | 0.0191600i | ||||
\(877\) | −1.01372e56 | −1.22723 | −0.613614 | − | 0.789606i | \(-0.710285\pi\) | ||||
−0.613614 | + | 0.789606i | \(0.710285\pi\) | |||||||
\(878\) | 3.06200e55 | + | 3.28596e55i | 0.362751 | + | 0.389284i | ||||
\(879\) | 4.06563e55i | 0.471346i | ||||||||
\(880\) | 1.12360e55 | − | 7.91209e55i | 0.127479 | − | 0.897678i | ||||
\(881\) | 6.27766e55 | 0.697036 | 0.348518 | − | 0.937302i | \(-0.386685\pi\) | ||||
0.348518 | + | 0.937302i | \(0.386685\pi\) | |||||||
\(882\) | 4.90667e54 | − | 4.57224e54i | 0.0533192 | − | 0.0496850i | ||||
\(883\) | − | 1.03931e56i | − | 1.10533i | −0.833404 | − | 0.552665i | \(-0.813611\pi\) | ||
0.833404 | − | 0.552665i | \(-0.186389\pi\) | |||||||
\(884\) | −5.92499e54 | + | 8.38631e55i | −0.0616729 | + | 0.872927i | ||||
\(885\) | −5.16830e55 | −0.526533 | ||||||||
\(886\) | −4.56556e55 | − | 4.89950e55i | −0.455254 | − | 0.488552i | ||||
\(887\) | − | 1.42465e55i | − | 0.139046i | −0.997580 | − | 0.0695230i | \(-0.977852\pi\) | ||
0.997580 | − | 0.0695230i | \(-0.0221477\pi\) | |||||||
\(888\) | 2.12797e55 | − | 1.71940e55i | 0.203292 | − | 0.164259i | ||||
\(889\) | 1.58068e56 | 1.47812 | ||||||||
\(890\) | 1.25642e55 | − | 1.17079e55i | 0.115007 | − | 0.107169i | ||||
\(891\) | 4.91273e55i | 0.440197i | ||||||||
\(892\) | 6.40315e55 | + | 4.52387e54i | 0.561645 | + | 0.0396806i | ||||
\(893\) | −4.64931e55 | −0.399219 | ||||||||
\(894\) | −5.13990e55 | − | 5.51585e55i | −0.432058 | − | 0.463660i | ||||
\(895\) | − | 9.63622e55i | − | 0.792993i | ||||||
\(896\) | 1.01799e56 | − | 6.08180e55i | 0.820143 | − | 0.489982i | ||||
\(897\) | −4.45251e55 | −0.351195 | ||||||||
\(898\) | −4.60151e55 | + | 4.28788e55i | −0.355345 | + | 0.331125i | ||||
\(899\) | − | 2.46705e55i | − | 0.186528i | ||||||
\(900\) | 1.60236e54 | − | 2.26800e55i | 0.0118619 | − | 0.167894i | ||||
\(901\) | −1.17510e56 | −0.851734 | ||||||||
\(902\) | −1.08102e56 | − | 1.16009e56i | −0.767203 | − | 0.823319i | ||||
\(903\) | − | 8.33007e55i | − | 0.578870i | ||||||
\(904\) | 1.06371e56 | + | 1.31648e56i | 0.723809 | + | 0.895807i | ||||
\(905\) | 5.60450e55 | 0.373434 | ||||||||
\(906\) | −4.43130e54 | + | 4.12927e54i | −0.0289132 | + | 0.0269425i | ||||
\(907\) | − | 9.75834e55i | − | 0.623502i | −0.950164 | − | 0.311751i | \(-0.899085\pi\) | ||
0.950164 | − | 0.311751i | \(-0.100915\pi\) | |||||||
\(908\) | 2.01396e56 | + | 1.42288e55i | 1.26014 | + | 0.0890300i | ||||
\(909\) | −1.56640e56 | −0.959817 | ||||||||
\(910\) | 6.48389e55 | + | 6.95815e55i | 0.389090 | + | 0.417549i | ||||
\(911\) | − | 2.84255e56i | − | 1.67055i | −0.549832 | − | 0.835275i | \(-0.685308\pi\) | ||
0.549832 | − | 0.835275i | \(-0.314692\pi\) | |||||||
\(912\) | −2.24862e55 | − | 3.19327e54i | −0.129424 | − | 0.0183795i | ||||
\(913\) | −2.89169e56 | −1.63007 | ||||||||
\(914\) | 7.85175e55 | − | 7.31659e55i | 0.433500 | − | 0.403953i | ||||
\(915\) | 8.74543e55i | 0.472912i | ||||||||
\(916\) | 5.37237e54 | − | 7.60412e55i | 0.0284545 | − | 0.402750i | ||||
\(917\) | 1.80518e55 | 0.0936490 | ||||||||
\(918\) | 1.60579e56 | + | 1.72324e56i | 0.815975 | + | 0.875658i | ||||
\(919\) | 1.86426e56i | 0.927924i | 0.885855 | + | 0.463962i | \(0.153573\pi\) | ||||
−0.885855 | + | 0.463962i | \(0.846427\pi\) | |||||||
\(920\) | −2.77412e56 | + | 2.24148e56i | −1.35256 | + | 1.09286i | ||||
\(921\) | 1.09778e56 | 0.524305 | ||||||||
\(922\) | −2.11386e56 | + | 1.96979e56i | −0.988985 | + | 0.921578i | ||||
\(923\) | 3.31401e55i | 0.151887i | ||||||||
\(924\) | 7.13172e55 | + | 5.03861e54i | 0.320204 | + | 0.0226227i | ||||
\(925\) | 2.94855e55 | 0.129693 | ||||||||
\(926\) | −4.99944e55 | − | 5.36512e55i | −0.215433 | − | 0.231191i | ||||
\(927\) | − | 2.28138e56i | − | 0.963127i | ||||||
\(928\) | −5.17439e55 | + | 3.60928e55i | −0.214017 | + | 0.149282i | ||||
\(929\) | 1.83875e56 | 0.745118 | 0.372559 | − | 0.928009i | \(-0.378480\pi\) | ||||
0.372559 | + | 0.928009i | \(0.378480\pi\) | |||||||
\(930\) | 5.86532e55 | − | 5.46555e55i | 0.232871 | − | 0.216999i | ||||
\(931\) | − | 7.22045e54i | − | 0.0280880i | ||||||
\(932\) | 2.27006e55 | − | 3.21307e56i | 0.0865236 | − | 1.22467i | ||||
\(933\) | 1.36764e55 | 0.0510764 | ||||||||
\(934\) | 1.61154e56 | + | 1.72941e56i | 0.589725 | + | 0.632860i | ||||
\(935\) | 4.06018e56i | 1.45588i | ||||||||
\(936\) | 8.13959e55 | + | 1.00738e56i | 0.285997 | + | 0.353958i | ||||
\(937\) | 2.04279e56 | 0.703350 | 0.351675 | − | 0.936122i | \(-0.385612\pi\) | ||||
0.351675 | + | 0.936122i | \(0.385612\pi\) | |||||||
\(938\) | 1.10831e56 | − | 1.03277e56i | 0.373945 | − | 0.348458i | ||||
\(939\) | − | 3.31932e55i | − | 0.109749i | ||||||
\(940\) | −4.18644e56 | − | 2.95775e55i | −1.35649 | − | 0.0958367i | ||||
\(941\) | −1.06823e56 | −0.339205 | −0.169603 | − | 0.985513i | \(-0.554248\pi\) | ||||
−0.169603 | + | 0.985513i | \(0.554248\pi\) | |||||||
\(942\) | 4.64017e54 | + | 4.97956e54i | 0.0144400 | + | 0.0154962i | ||||
\(943\) | 7.07677e56i | 2.15831i | ||||||||
\(944\) | 5.56214e55 | − | 3.91672e56i | 0.166255 | − | 1.17072i | ||||
\(945\) | 2.66465e56 | 0.780613 | ||||||||
\(946\) | 3.14369e56 | − | 2.92942e56i | 0.902626 | − | 0.841104i | ||||
\(947\) | − | 3.52842e56i | − | 0.992958i | −0.868049 | − | 0.496479i | \(-0.834626\pi\) | ||
0.868049 | − | 0.496479i | \(-0.165374\pi\) | |||||||
\(948\) | −1.74067e55 | + | 2.46376e56i | −0.0480128 | + | 0.679580i | ||||
\(949\) | −1.34911e56 | −0.364746 | ||||||||
\(950\) | −1.66875e55 | − | 1.79081e55i | −0.0442225 | − | 0.0474571i | ||||
\(951\) | − | 1.25993e56i | − | 0.327278i | ||||||
\(952\) | −4.68620e56 | + | 3.78643e56i | −1.19322 | + | 0.964114i | ||||
\(953\) | −3.35786e55 | −0.0838102 | −0.0419051 | − | 0.999122i | \(-0.513343\pi\) | ||||
−0.0419051 | + | 0.999122i | \(0.513343\pi\) | |||||||
\(954\) | −1.32436e56 | + | 1.23410e56i | −0.324032 | + | 0.301947i | ||||
\(955\) | 7.07917e56i | 1.69792i | ||||||||
\(956\) | −9.65750e55 | − | 6.82309e54i | −0.227073 | − | 0.0160428i | ||||
\(957\) | −3.80367e55 | −0.0876752 | ||||||||
\(958\) | −1.70403e56 | − | 1.82867e56i | −0.385064 | − | 0.413229i | ||||
\(959\) | − | 7.68100e56i | − | 1.70163i | ||||||
\(960\) | −2.00444e56 | − | 4.30586e55i | −0.435350 | − | 0.0935203i | ||||
\(961\) | 2.29646e56 | 0.489007 | ||||||||
\(962\) | −1.22876e56 | + | 1.14501e56i | −0.256532 | + | 0.239047i | ||||
\(963\) | 4.34940e56i | 0.890286i | ||||||||
\(964\) | 4.24878e55 | − | 6.01379e56i | 0.0852709 | − | 1.20694i | ||||
\(965\) | −1.17118e56 | −0.230464 | ||||||||
\(966\) | −2.17524e56 | − | 2.33434e56i | −0.419703 | − | 0.450401i | ||||
\(967\) | − | 7.50504e55i | − | 0.141987i | −0.997477 | − | 0.0709937i | \(-0.977383\pi\) | ||
0.997477 | − | 0.0709937i | \(-0.0226170\pi\) | |||||||
\(968\) | −1.07000e56 | − | 1.32426e56i | −0.198496 | − | 0.245664i | ||||
\(969\) | 1.15390e56 | 0.209903 | ||||||||
\(970\) | 6.09803e56 | − | 5.68240e56i | 1.08774 | − | 1.01361i | ||||
\(971\) | − | 6.78010e56i | − | 1.18596i | −0.805216 | − | 0.592981i | \(-0.797951\pi\) | ||
0.805216 | − | 0.592981i | \(-0.202049\pi\) | |||||||
\(972\) | 5.59201e56 | + | 3.95080e55i | 0.959199 | + | 0.0677681i | ||||
\(973\) | 5.29886e56 | 0.891330 | ||||||||
\(974\) | 1.89963e56 | + | 2.03857e56i | 0.313363 | + | 0.336284i | ||||
\(975\) | − | 2.75852e55i | − | 0.0446260i | ||||||
\(976\) | −6.62760e56 | − | 9.41187e55i | −1.05150 | − | 0.149324i | ||||
\(977\) | 2.94582e56 | 0.458363 | 0.229181 | − | 0.973384i | \(-0.426395\pi\) | ||||
0.229181 | + | 0.973384i | \(0.426395\pi\) | |||||||
\(978\) | −1.94480e56 | + | 1.81225e56i | −0.296782 | + | 0.276554i | ||||
\(979\) | 7.92554e55i | 0.118620i | ||||||||
\(980\) | 4.59343e54 | − | 6.50160e55i | 0.00674282 | − | 0.0954388i | ||||
\(981\) | −4.20118e56 | −0.604867 | ||||||||
\(982\) | 1.04470e56 | + | 1.12111e56i | 0.147528 | + | 0.158318i | ||||
\(983\) | 4.91924e56i | 0.681368i | 0.940178 | + | 0.340684i | \(0.110659\pi\) | ||||
−0.940178 | + | 0.340684i | \(0.889341\pi\) | |||||||
\(984\) | −3.16419e56 | + | 2.55666e56i | −0.429889 | + | 0.347349i | ||||
\(985\) | 7.83118e56 | 1.04361 | ||||||||
\(986\) | 2.34498e56 | − | 2.18515e56i | 0.306534 | − | 0.285641i | ||||
\(987\) | − | 3.75469e56i | − | 0.481447i | ||||||
\(988\) | 1.39085e56 | + | 9.82647e54i | 0.174944 | + | 0.0123599i | ||||
\(989\) | −1.91771e57 | −2.36621 | ||||||||
\(990\) | 4.26403e56 | + | 4.57591e56i | 0.516121 | + | 0.553871i | ||||
\(991\) | − | 1.16876e57i | − | 1.38779i | −0.720074 | − | 0.693897i | \(-0.755892\pi\) | ||
0.720074 | − | 0.693897i | \(-0.244108\pi\) | |||||||
\(992\) | 3.51076e56 | + | 5.03316e56i | 0.408959 | + | 0.586298i | ||||
\(993\) | −3.93260e56 | −0.449411 | ||||||||
\(994\) | −1.73746e56 | + | 1.61903e56i | −0.194793 | + | 0.181516i | ||||
\(995\) | − | 3.02480e56i | − | 0.332705i | ||||||
\(996\) | −5.22816e55 | + | 7.40001e56i | −0.0564185 | + | 0.798555i | ||||
\(997\) | −3.67989e56 | −0.389608 | −0.194804 | − | 0.980842i | \(-0.562407\pi\) | ||||
−0.194804 | + | 0.980842i | \(0.562407\pi\) | |||||||
\(998\) | 9.41392e56 | + | 1.01025e57i | 0.977890 | + | 1.04942i | ||||
\(999\) | 4.70560e56i | 0.479591i |
(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 | 4.39.b.a.3.13 | ✓ | 18 | |
4.3 | odd | 2 | inner | 4.39.b.a.3.14 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.39.b.a.3.13 | ✓ | 18 | 1.1 | even | 1 | trivial | |
4.39.b.a.3.14 | yes | 18 | 4.3 | odd | 2 | inner |