Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,10,Mod(67,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.67");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.c (of order \(3\), degree \(2\), not 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: | \(50.4735119441\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{2305})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 577x^{2} + 576x + 331776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(-11.7526 - 20.3561i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.79 |
Dual form | 98.10.c.j.67.1 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | − | 13.8564i | 0.353553 | − | 0.612372i | ||||
\(3\) | −116.526 | − | 201.829i | −0.830572 | − | 1.43859i | −0.897585 | − | 0.440841i | \(-0.854680\pi\) |
0.0670131 | − | 0.997752i | \(-0.478653\pi\) | |||||||
\(4\) | −128.000 | − | 221.703i | −0.250000 | − | 0.433013i | ||||
\(5\) | 178.391 | − | 308.982i | 0.127646 | − | 0.221089i | −0.795118 | − | 0.606455i | \(-0.792591\pi\) |
0.922764 | + | 0.385365i | \(0.125925\pi\) | |||||||
\(6\) | −3728.83 | −1.17461 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | −17315.1 | + | 29990.7i | −0.879700 | + | 1.52369i | ||||
\(10\) | −2854.25 | − | 4943.71i | −0.0902593 | − | 0.156334i | ||||
\(11\) | −36440.5 | − | 63116.7i | −0.750442 | − | 1.29980i | −0.947609 | − | 0.319433i | \(-0.896508\pi\) |
0.197167 | − | 0.980370i | \(-0.436826\pi\) | |||||||
\(12\) | −29830.7 | + | 51668.2i | −0.415286 | + | 0.719297i | ||||
\(13\) | 39338.7 | 0.382010 | 0.191005 | − | 0.981589i | \(-0.438825\pi\) | ||||
0.191005 | + | 0.981589i | \(0.438825\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −83148.6 | −0.424077 | ||||||||
\(16\) | −32768.0 | + | 56755.8i | −0.125000 | + | 0.216506i | ||||
\(17\) | 255770. | + | 443007.i | 0.742728 | + | 1.28644i | 0.951249 | + | 0.308425i | \(0.0998019\pi\) |
−0.208520 | + | 0.978018i | \(0.566865\pi\) | |||||||
\(18\) | 277042. | + | 479851.i | 0.622042 | + | 1.07741i | ||||
\(19\) | −450184. | + | 779741.i | −0.792498 | + | 1.37265i | 0.131917 | + | 0.991261i | \(0.457887\pi\) |
−0.924416 | + | 0.381387i | \(0.875447\pi\) | |||||||
\(20\) | −91336.0 | −0.127646 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.16609e6 | −1.06128 | ||||||||
\(23\) | −191347. | + | 331423.i | −0.142576 | + | 0.246949i | −0.928466 | − | 0.371417i | \(-0.878872\pi\) |
0.785890 | + | 0.618366i | \(0.212205\pi\) | |||||||
\(24\) | 477291. | + | 826692.i | 0.293652 | + | 0.508619i | ||||
\(25\) | 912916. | + | 1.58122e6i | 0.467413 | + | 0.809583i | ||||
\(26\) | 314709. | − | 545092.i | 0.135061 | − | 0.233932i | ||||
\(27\) | 3.48349e6 | 1.26147 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.73360e6 | −1.24280 | −0.621399 | − | 0.783494i | \(-0.713435\pi\) | ||||
−0.621399 | + | 0.783494i | \(0.713435\pi\) | |||||||
\(30\) | −665189. | + | 1.15214e6i | −0.149934 | + | 0.259693i | ||||
\(31\) | 396942. | + | 687523.i | 0.0771968 | + | 0.133709i | 0.902039 | − | 0.431654i | \(-0.142070\pi\) |
−0.824843 | + | 0.565362i | \(0.808736\pi\) | |||||||
\(32\) | 524288. | + | 908093.i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −8.49253e6 | + | 1.47095e7i | −1.24659 | + | 2.15916i | ||||
\(34\) | 8.18465e6 | 1.05038 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8.86535e6 | 0.879700 | ||||||||
\(37\) | 8.61388e6 | − | 1.49197e7i | 0.755598 | − | 1.30873i | −0.189478 | − | 0.981885i | \(-0.560680\pi\) |
0.945076 | − | 0.326850i | \(-0.105987\pi\) | |||||||
\(38\) | 7.20294e6 | + | 1.24759e7i | 0.560381 | + | 0.970608i | ||||
\(39\) | −4.58398e6 | − | 7.93968e6i | −0.317287 | − | 0.549557i | ||||
\(40\) | −730688. | + | 1.26559e6i | −0.0451297 | + | 0.0781669i | ||||
\(41\) | −1.53558e7 | −0.848683 | −0.424342 | − | 0.905502i | \(-0.639494\pi\) | ||||
−0.424342 | + | 0.905502i | \(0.639494\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.87022e7 | 0.834229 | 0.417114 | − | 0.908854i | \(-0.363041\pi\) | ||||
0.417114 | + | 0.908854i | \(0.363041\pi\) | |||||||
\(44\) | −9.32876e6 | + | 1.61579e7i | −0.375221 | + | 0.649901i | ||||
\(45\) | 6.17772e6 | + | 1.07001e7i | 0.224580 | + | 0.388984i | ||||
\(46\) | 3.06155e6 | + | 5.30277e6i | 0.100817 | + | 0.174619i | ||||
\(47\) | 2.34470e7 | − | 4.06114e7i | 0.700885 | − | 1.21397i | −0.267271 | − | 0.963621i | \(-0.586122\pi\) |
0.968156 | − | 0.250347i | \(-0.0805448\pi\) | |||||||
\(48\) | 1.52733e7 | 0.415286 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.92133e7 | 0.661022 | ||||||||
\(51\) | 5.96078e7 | − | 1.03244e8i | 1.23378 | − | 2.13697i | ||||
\(52\) | −5.03535e6 | − | 8.72148e6i | −0.0955024 | − | 0.165415i | ||||
\(53\) | −1.03410e7 | − | 1.79111e7i | −0.180019 | − | 0.311803i | 0.761867 | − | 0.647733i | \(-0.224283\pi\) |
−0.941887 | + | 0.335930i | \(0.890949\pi\) | |||||||
\(54\) | 2.78679e7 | − | 4.82687e7i | 0.445998 | − | 0.772491i | ||||
\(55\) | −2.60026e7 | −0.383163 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.09832e8 | 2.63291 | ||||||||
\(58\) | −3.78688e7 | + | 6.55907e7i | −0.439396 | + | 0.761055i | ||||
\(59\) | 6.53112e6 | + | 1.13122e7i | 0.0701703 | + | 0.121539i | 0.898976 | − | 0.437998i | \(-0.144312\pi\) |
−0.828806 | + | 0.559537i | \(0.810979\pi\) | |||||||
\(60\) | 1.06430e7 | + | 1.84343e7i | 0.106019 | + | 0.183631i | ||||
\(61\) | −7.77439e7 | + | 1.34656e8i | −0.718922 | + | 1.24521i | 0.242505 | + | 0.970150i | \(0.422031\pi\) |
−0.961427 | + | 0.275059i | \(0.911302\pi\) | |||||||
\(62\) | 1.27021e7 | 0.109173 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | 7.01765e6 | − | 1.21549e7i | 0.0487620 | − | 0.0844583i | ||||
\(66\) | 1.35880e8 | + | 2.35352e8i | 0.881473 | + | 1.52676i | ||||
\(67\) | −1.22946e8 | − | 2.12949e8i | −0.745382 | − | 1.29104i | −0.950016 | − | 0.312201i | \(-0.898934\pi\) |
0.204634 | − | 0.978839i | \(-0.434400\pi\) | |||||||
\(68\) | 6.54772e7 | − | 1.13410e8i | 0.371364 | − | 0.643222i | ||||
\(69\) | 8.91877e7 | 0.473679 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.87608e8 | −1.81021 | −0.905107 | − | 0.425184i | \(-0.860210\pi\) | ||||
−0.905107 | + | 0.425184i | \(0.860210\pi\) | |||||||
\(72\) | 7.09228e7 | − | 1.22842e8i | 0.311021 | − | 0.538704i | ||||
\(73\) | 1.56238e8 | + | 2.70612e8i | 0.643922 | + | 1.11531i | 0.984549 | + | 0.175108i | \(0.0560274\pi\) |
−0.340627 | + | 0.940199i | \(0.610639\pi\) | |||||||
\(74\) | −1.37822e8 | − | 2.38715e8i | −0.534289 | − | 0.925415i | ||||
\(75\) | 2.12757e8 | − | 3.68506e8i | 0.776440 | − | 1.34483i | ||||
\(76\) | 2.30494e8 | 0.792498 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.46687e8 | −0.448711 | ||||||||
\(79\) | −1.20554e8 | + | 2.08805e8i | −0.348225 | + | 0.603143i | −0.985934 | − | 0.167134i | \(-0.946549\pi\) |
0.637710 | + | 0.770277i | \(0.279882\pi\) | |||||||
\(80\) | 1.16910e7 | + | 2.02494e7i | 0.0319115 | + | 0.0552723i | ||||
\(81\) | −6.51038e7 | − | 1.12763e8i | −0.168044 | − | 0.291061i | ||||
\(82\) | −1.22847e8 | + | 2.12776e8i | −0.300055 | + | 0.519710i | ||||
\(83\) | 2.00131e8 | 0.462875 | 0.231437 | − | 0.972850i | \(-0.425657\pi\) | ||||
0.231437 | + | 0.972850i | \(0.425657\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.82508e8 | 0.379225 | ||||||||
\(86\) | 1.49618e8 | − | 2.59146e8i | 0.294944 | − | 0.510859i | ||||
\(87\) | 5.51588e8 | + | 9.55378e8i | 1.03223 | + | 1.78788i | ||||
\(88\) | 1.49260e8 | + | 2.58526e8i | 0.265321 | + | 0.459550i | ||||
\(89\) | −3.50381e7 | + | 6.06878e7i | −0.0591951 | + | 0.102529i | −0.894104 | − | 0.447859i | \(-0.852187\pi\) |
0.834909 | + | 0.550388i | \(0.185520\pi\) | |||||||
\(90\) | 1.97687e8 | 0.317604 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.79698e7 | 0.142576 | ||||||||
\(93\) | 9.25081e7 | − | 1.60229e8i | 0.128235 | − | 0.222110i | ||||
\(94\) | −3.75152e8 | − | 6.49782e8i | −0.495601 | − | 0.858405i | ||||
\(95\) | 1.60617e8 | + | 2.78197e8i | 0.202318 | + | 0.350426i | ||||
\(96\) | 1.22186e8 | − | 2.11633e8i | 0.146826 | − | 0.254310i | ||||
\(97\) | 6.69566e8 | 0.767928 | 0.383964 | − | 0.923348i | \(-0.374559\pi\) | ||||
0.383964 | + | 0.923348i | \(0.374559\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.52389e9 | 2.64065 | ||||||||
\(100\) | 2.33707e8 | − | 4.04792e8i | 0.233707 | − | 0.404792i | ||||
\(101\) | 4.26449e8 | + | 7.38631e8i | 0.407775 | + | 0.706287i | 0.994640 | − | 0.103398i | \(-0.0329714\pi\) |
−0.586865 | + | 0.809685i | \(0.699638\pi\) | |||||||
\(102\) | −9.53725e8 | − | 1.65190e9i | −0.872413 | − | 1.51106i | ||||
\(103\) | 5.00991e8 | − | 8.67742e8i | 0.438594 | − | 0.759667i | −0.558987 | − | 0.829176i | \(-0.688810\pi\) |
0.997581 | + | 0.0695092i | \(0.0221433\pi\) | |||||||
\(104\) | −1.61131e8 | −0.135061 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.30911e8 | −0.254586 | ||||||||
\(107\) | −2.09153e8 | + | 3.62263e8i | −0.154254 | + | 0.267176i | −0.932787 | − | 0.360428i | \(-0.882631\pi\) |
0.778533 | + | 0.627603i | \(0.215964\pi\) | |||||||
\(108\) | −4.45887e8 | − | 7.72299e8i | −0.315368 | − | 0.546234i | ||||
\(109\) | −2.34533e8 | − | 4.06223e8i | −0.159142 | − | 0.275642i | 0.775418 | − | 0.631449i | \(-0.217539\pi\) |
−0.934559 | + | 0.355807i | \(0.884206\pi\) | |||||||
\(110\) | −2.08020e8 | + | 3.60302e8i | −0.135469 | + | 0.234639i | ||||
\(111\) | −4.01496e9 | −2.51032 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.03772e8 | 0.290657 | 0.145329 | − | 0.989383i | \(-0.453576\pi\) | ||||
0.145329 | + | 0.989383i | \(0.453576\pi\) | |||||||
\(114\) | 1.67866e9 | − | 2.90752e9i | 0.930874 | − | 1.61232i | ||||
\(115\) | 6.82691e7 | + | 1.18246e8i | 0.0363985 | + | 0.0630441i | ||||
\(116\) | 6.05901e8 | + | 1.04945e9i | 0.310700 | + | 0.538147i | ||||
\(117\) | −6.81154e8 | + | 1.17979e9i | −0.336054 | + | 0.582063i | ||||
\(118\) | 2.08996e8 | 0.0992358 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.40577e8 | 0.149934 | ||||||||
\(121\) | −1.47684e9 | + | 2.55796e9i | −0.626325 | + | 1.08483i | ||||
\(122\) | 1.24390e9 | + | 2.15450e9i | 0.508355 | + | 0.880496i | ||||
\(123\) | 1.78935e9 | + | 3.09925e9i | 0.704893 | + | 1.22091i | ||||
\(124\) | 1.01617e8 | − | 1.76006e8i | 0.0385984 | − | 0.0668544i | ||||
\(125\) | 1.34826e9 | 0.493945 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.45724e9 | 0.497065 | 0.248532 | − | 0.968624i | \(-0.420052\pi\) | ||||
0.248532 | + | 0.968624i | \(0.420052\pi\) | |||||||
\(128\) | 1.34218e8 | − | 2.32472e8i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −2.17930e9 | − | 3.77465e9i | −0.692887 | − | 1.20012i | ||||
\(130\) | −1.12282e8 | − | 1.94479e8i | −0.0344799 | − | 0.0597210i | ||||
\(131\) | −2.22230e9 | + | 3.84914e9i | −0.659299 | + | 1.14194i | 0.321498 | + | 0.946910i | \(0.395814\pi\) |
−0.980797 | + | 0.195030i | \(0.937520\pi\) | |||||||
\(132\) | 4.34817e9 | 1.24659 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.93428e9 | −1.05413 | ||||||||
\(135\) | 6.21422e8 | − | 1.07634e9i | 0.161022 | − | 0.278898i | ||||
\(136\) | −1.04764e9 | − | 1.81456e9i | −0.262594 | − | 0.454826i | ||||
\(137\) | 1.56628e9 | + | 2.71288e9i | 0.379864 | + | 0.657944i | 0.991042 | − | 0.133549i | \(-0.0426375\pi\) |
−0.611178 | + | 0.791493i | \(0.709304\pi\) | |||||||
\(138\) | 7.13502e8 | − | 1.23582e9i | 0.167471 | − | 0.290068i | ||||
\(139\) | 1.90826e9 | 0.433581 | 0.216790 | − | 0.976218i | \(-0.430441\pi\) | ||||
0.216790 | + | 0.976218i | \(0.430441\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.09287e10 | −2.32854 | ||||||||
\(142\) | −3.10086e9 | + | 5.37085e9i | −0.640007 | + | 1.10853i | ||||
\(143\) | −1.43352e9 | − | 2.48293e9i | −0.286676 | − | 0.496537i | ||||
\(144\) | −1.13476e9 | − | 1.96547e9i | −0.219925 | − | 0.380921i | ||||
\(145\) | −8.44430e8 | + | 1.46260e9i | −0.158638 | + | 0.274769i | ||||
\(146\) | 4.99961e9 | 0.910644 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.41031e9 | −0.755598 | ||||||||
\(149\) | −3.10948e9 | + | 5.38578e9i | −0.516832 | + | 0.895179i | 0.482977 | + | 0.875633i | \(0.339556\pi\) |
−0.999809 | + | 0.0195463i | \(0.993778\pi\) | |||||||
\(150\) | −3.40411e9 | − | 5.89609e9i | −0.549026 | − | 0.950941i | ||||
\(151\) | 1.21776e8 | + | 2.10922e8i | 0.0190619 | + | 0.0330162i | 0.875399 | − | 0.483401i | \(-0.160599\pi\) |
−0.856337 | + | 0.516417i | \(0.827265\pi\) | |||||||
\(152\) | 1.84395e9 | − | 3.19382e9i | 0.280191 | − | 0.485304i | ||||
\(153\) | −1.77148e10 | −2.61351 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.83243e8 | 0.0394154 | ||||||||
\(156\) | −1.17350e9 | + | 2.03256e9i | −0.158643 | + | 0.274778i | ||||
\(157\) | 2.82078e9 | + | 4.88574e9i | 0.370528 | + | 0.641774i | 0.989647 | − | 0.143524i | \(-0.0458433\pi\) |
−0.619119 | + | 0.785297i | \(0.712510\pi\) | |||||||
\(158\) | 1.92886e9 | + | 3.34089e9i | 0.246232 | + | 0.426486i | ||||
\(159\) | −2.40998e9 | + | 4.17421e9i | −0.299038 | + | 0.517950i | ||||
\(160\) | 3.74112e8 | 0.0451297 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.08332e9 | −0.237650 | ||||||||
\(163\) | −4.75790e8 | + | 8.24093e8i | −0.0527924 | + | 0.0914391i | −0.891214 | − | 0.453583i | \(-0.850145\pi\) |
0.838422 | + | 0.545022i | \(0.183479\pi\) | |||||||
\(164\) | 1.96554e9 | + | 3.40442e9i | 0.212171 | + | 0.367491i | ||||
\(165\) | 3.02997e9 | + | 5.24807e9i | 0.318245 | + | 0.551216i | ||||
\(166\) | 1.60105e9 | − | 2.77310e9i | 0.163651 | − | 0.283452i | ||||
\(167\) | −1.63986e10 | −1.63149 | −0.815743 | − | 0.578414i | \(-0.803672\pi\) | ||||
−0.815743 | + | 0.578414i | \(0.803672\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.05697e9 | −0.854069 | ||||||||
\(170\) | 1.46006e9 | − | 2.52891e9i | 0.134076 | − | 0.232227i | ||||
\(171\) | −1.55900e10 | − | 2.70026e10i | −1.39432 | − | 2.41504i | ||||
\(172\) | −2.39388e9 | − | 4.14633e9i | −0.208557 | − | 0.361232i | ||||
\(173\) | −9.36444e8 | + | 1.62197e9i | −0.0794830 | + | 0.137669i | −0.903027 | − | 0.429584i | \(-0.858660\pi\) |
0.823544 | + | 0.567252i | \(0.191994\pi\) | |||||||
\(174\) | 1.76508e10 | 1.45980 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.77633e9 | 0.375221 | ||||||||
\(177\) | 1.52209e9 | − | 2.63634e9i | 0.116563 | − | 0.201893i | ||||
\(178\) | 5.60610e8 | + | 9.71005e8i | 0.0418573 | + | 0.0724989i | ||||
\(179\) | −6.03931e9 | − | 1.04604e10i | −0.439692 | − | 0.761569i | 0.557973 | − | 0.829859i | \(-0.311579\pi\) |
−0.997666 | + | 0.0682895i | \(0.978246\pi\) | |||||||
\(180\) | 1.58150e9 | − | 2.73923e9i | 0.112290 | − | 0.194492i | ||||
\(181\) | −6.74447e9 | −0.467083 | −0.233541 | − | 0.972347i | \(-0.575031\pi\) | ||||
−0.233541 | + | 0.972347i | \(0.575031\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.62367e10 | 2.38847 | ||||||||
\(184\) | 7.83758e8 | − | 1.35751e9i | 0.0504083 | − | 0.0873097i | ||||
\(185\) | −3.07327e9 | − | 5.32306e9i | −0.192898 | − | 0.334109i | ||||
\(186\) | −1.48013e9 | − | 2.56366e9i | −0.0906758 | − | 0.157055i | ||||
\(187\) | 1.86408e10 | − | 3.22868e10i | 1.11475 | − | 1.93080i | ||||
\(188\) | −1.20049e10 | −0.700885 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.13975e9 | 0.286121 | ||||||||
\(191\) | −1.30308e10 | + | 2.25700e10i | −0.708468 | + | 1.22710i | 0.256957 | + | 0.966423i | \(0.417280\pi\) |
−0.965425 | + | 0.260680i | \(0.916053\pi\) | |||||||
\(192\) | −1.95498e9 | − | 3.38613e9i | −0.103822 | − | 0.179824i | ||||
\(193\) | 1.19542e10 | + | 2.07052e10i | 0.620170 | + | 1.07417i | 0.989454 | + | 0.144849i | \(0.0462698\pi\) |
−0.369284 | + | 0.929317i | \(0.620397\pi\) | |||||||
\(194\) | 5.35653e9 | − | 9.27778e9i | 0.271504 | − | 0.470258i | ||||
\(195\) | −3.27095e9 | −0.162001 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.91068e9 | 0.232297 | 0.116149 | − | 0.993232i | \(-0.462945\pi\) | ||||
0.116149 | + | 0.993232i | \(0.462945\pi\) | |||||||
\(198\) | 2.01911e10 | − | 3.49720e10i | 0.933612 | − | 1.61706i | ||||
\(199\) | 1.16907e10 | + | 2.02490e10i | 0.528449 | + | 0.915301i | 0.999450 | + | 0.0331679i | \(0.0105596\pi\) |
−0.471001 | + | 0.882133i | \(0.656107\pi\) | |||||||
\(200\) | −3.73930e9 | − | 6.47666e9i | −0.165255 | − | 0.286231i | ||||
\(201\) | −2.86529e10 | + | 4.96283e10i | −1.23819 | + | 2.14460i | ||||
\(202\) | 1.36464e10 | 0.576681 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.05192e10 | −1.23378 | ||||||||
\(205\) | −2.73933e9 | + | 4.74467e9i | −0.108331 | + | 0.187635i | ||||
\(206\) | −8.01586e9 | − | 1.38839e10i | −0.310133 | − | 0.537166i | ||||
\(207\) | −6.62640e9 | − | 1.14773e10i | −0.250848 | − | 0.434482i | ||||
\(208\) | −1.28905e9 | + | 2.23270e9i | −0.0477512 | + | 0.0827075i | ||||
\(209\) | 6.56196e10 | 2.37890 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.20831e10 | 0.766989 | 0.383494 | − | 0.923543i | \(-0.374721\pi\) | ||||
0.383494 | + | 0.923543i | \(0.374721\pi\) | |||||||
\(212\) | −2.64729e9 | + | 4.58523e9i | −0.0900097 | + | 0.155901i | ||||
\(213\) | 4.51664e10 | + | 7.82305e10i | 1.50351 | + | 2.60416i | ||||
\(214\) | 3.34644e9 | + | 5.79621e9i | 0.109074 | + | 0.188922i | ||||
\(215\) | 3.33630e9 | − | 5.77864e9i | 0.106486 | − | 0.184439i | ||||
\(216\) | −1.42684e10 | −0.445998 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.50505e9 | −0.225061 | ||||||||
\(219\) | 3.64116e10 | − | 6.30667e10i | 1.06965 | − | 1.85268i | ||||
\(220\) | 3.32833e9 | + | 5.76483e9i | 0.0957908 | + | 0.165915i | ||||
\(221\) | 1.00617e10 | + | 1.74273e10i | 0.283729 | + | 0.491434i | ||||
\(222\) | −3.21197e10 | + | 5.56330e10i | −0.887531 | + | 1.53725i | ||||
\(223\) | −3.22102e10 | −0.872211 | −0.436106 | − | 0.899895i | \(-0.643643\pi\) | ||||
−0.436106 | + | 0.899895i | \(0.643643\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.32291e10 | −1.64473 | ||||||||
\(226\) | 4.03018e9 | − | 6.98047e9i | 0.102763 | − | 0.177991i | ||||
\(227\) | 2.07667e10 | + | 3.59690e10i | 0.519101 | + | 0.899109i | 0.999754 | + | 0.0221980i | \(0.00706644\pi\) |
−0.480653 | + | 0.876911i | \(0.659600\pi\) | |||||||
\(228\) | −2.68586e10 | − | 4.65204e10i | −0.658227 | − | 1.14008i | ||||
\(229\) | 6.65363e9 | − | 1.15244e10i | 0.159882 | − | 0.276923i | −0.774944 | − | 0.632030i | \(-0.782222\pi\) |
0.934826 | + | 0.355106i | \(0.115555\pi\) | |||||||
\(230\) | 2.18461e9 | 0.0514753 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.93888e10 | 0.439396 | ||||||||
\(233\) | −4.01372e10 | + | 6.95197e10i | −0.892166 | + | 1.54528i | −0.0548936 | + | 0.998492i | \(0.517482\pi\) |
−0.837273 | + | 0.546785i | \(0.815851\pi\) | |||||||
\(234\) | 1.08985e10 | + | 1.88767e10i | 0.237626 | + | 0.411580i | ||||
\(235\) | −8.36545e9 | − | 1.44894e10i | −0.178930 | − | 0.309916i | ||||
\(236\) | 1.67197e9 | − | 2.89593e9i | 0.0350852 | − | 0.0607693i | ||||
\(237\) | 5.61907e10 | 1.15690 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.27858e10 | 1.24472 | 0.622359 | − | 0.782732i | \(-0.286174\pi\) | ||||
0.622359 | + | 0.782732i | \(0.286174\pi\) | |||||||
\(240\) | 2.72461e9 | − | 4.71917e9i | 0.0530096 | − | 0.0918153i | ||||
\(241\) | 4.23466e9 | + | 7.33464e9i | 0.0808615 | + | 0.140056i | 0.903620 | − | 0.428335i | \(-0.140900\pi\) |
−0.822759 | + | 0.568391i | \(0.807566\pi\) | |||||||
\(242\) | 2.36295e10 | + | 4.09274e10i | 0.442879 | + | 0.767088i | ||||
\(243\) | 1.91102e10 | − | 3.30999e10i | 0.351591 | − | 0.608973i | ||||
\(244\) | 3.98049e10 | 0.718922 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.72593e10 | 0.996869 | ||||||||
\(247\) | −1.77096e10 | + | 3.06740e10i | −0.302742 | + | 0.524365i | ||||
\(248\) | −1.62587e9 | − | 2.81610e9i | −0.0272932 | − | 0.0472732i | ||||
\(249\) | −2.33205e10 | − | 4.03923e10i | −0.384451 | − | 0.665889i | ||||
\(250\) | 1.07861e10 | − | 1.86821e10i | 0.174636 | − | 0.302479i | ||||
\(251\) | 9.73168e6 | 0.000154759 | 7.73795e−5 | − | 1.00000i | \(-0.499975\pi\) | ||||
7.73795e−5 | 1.00000i | \(0.499975\pi\) | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.78911e10 | 0.427980 | ||||||||
\(254\) | 1.16579e10 | − | 2.01921e10i | 0.175739 | − | 0.304389i | ||||
\(255\) | −2.12669e10 | − | 3.68354e10i | −0.314974 | − | 0.545550i | ||||
\(256\) | −2.14748e9 | − | 3.71955e9i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 8.63284e9 | − | 1.49525e10i | 0.123440 | − | 0.213804i | −0.797682 | − | 0.603078i | \(-0.793941\pi\) |
0.921122 | + | 0.389274i | \(0.127274\pi\) | |||||||
\(258\) | −6.97375e10 | −0.979890 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.59304e9 | −0.0487620 | ||||||||
\(261\) | 8.19629e10 | − | 1.41964e11i | 1.09329 | − | 1.89363i | ||||
\(262\) | 3.55569e10 | + | 6.15863e10i | 0.466195 | + | 0.807473i | ||||
\(263\) | 1.25707e10 | + | 2.17731e10i | 0.162016 | + | 0.280621i | 0.935592 | − | 0.353084i | \(-0.114867\pi\) |
−0.773575 | + | 0.633704i | \(0.781534\pi\) | |||||||
\(264\) | 3.47854e10 | − | 6.02501e10i | 0.440737 | − | 0.763378i | ||||
\(265\) | −7.37892e9 | −0.0919150 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.63314e10 | 0.196663 | ||||||||
\(268\) | −3.14743e10 | + | 5.45150e10i | −0.372691 | + | 0.645520i | ||||
\(269\) | −3.98552e10 | − | 6.90313e10i | −0.464087 | − | 0.803823i | 0.535072 | − | 0.844806i | \(-0.320284\pi\) |
−0.999160 | + | 0.0409831i | \(0.986951\pi\) | |||||||
\(270\) | −9.94276e9 | − | 1.72214e10i | −0.113860 | − | 0.197211i | ||||
\(271\) | 1.55347e10 | − | 2.69069e10i | 0.174961 | − | 0.303042i | −0.765187 | − | 0.643808i | \(-0.777353\pi\) |
0.940148 | + | 0.340767i | \(0.110687\pi\) | |||||||
\(272\) | −3.35243e10 | −0.371364 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.01211e10 | 0.537209 | ||||||||
\(275\) | 6.65342e10 | − | 1.15241e11i | 0.701532 | − | 1.21509i | ||||
\(276\) | −1.14160e10 | − | 1.97731e10i | −0.118420 | − | 0.205109i | ||||
\(277\) | −8.35497e10 | − | 1.44712e11i | −0.852679 | − | 1.47688i | −0.878781 | − | 0.477225i | \(-0.841643\pi\) |
0.0261018 | − | 0.999659i | \(-0.491691\pi\) | |||||||
\(278\) | 1.52660e10 | − | 2.64416e10i | 0.153294 | − | 0.265513i | ||||
\(279\) | −2.74924e10 | −0.271640 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.05809e10 | −0.675318 | −0.337659 | − | 0.941268i | \(-0.609635\pi\) | ||||
−0.337659 | + | 0.941268i | \(0.609635\pi\) | |||||||
\(282\) | −8.74299e10 | + | 1.51433e11i | −0.823264 | + | 1.42594i | ||||
\(283\) | 1.28894e10 | + | 2.23251e10i | 0.119452 | + | 0.206897i | 0.919551 | − | 0.392971i | \(-0.128553\pi\) |
−0.800099 | + | 0.599869i | \(0.795220\pi\) | |||||||
\(284\) | 4.96138e10 | + | 8.59336e10i | 0.452554 | + | 0.783846i | ||||
\(285\) | 3.74321e10 | − | 6.48344e10i | 0.336080 | − | 0.582108i | ||||
\(286\) | −4.58726e10 | −0.405421 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.63125e10 | −0.311021 | ||||||||
\(289\) | −7.15429e10 | + | 1.23916e11i | −0.603290 | + | 1.04493i | ||||
\(290\) | 1.35109e10 | + | 2.34015e10i | 0.112174 | + | 0.194291i | ||||
\(291\) | −7.80219e10 | − | 1.35138e11i | −0.637820 | − | 1.10474i | ||||
\(292\) | 3.99969e10 | − | 6.92767e10i | 0.321961 | − | 0.557653i | ||||
\(293\) | −4.21819e10 | −0.334365 | −0.167183 | − | 0.985926i | \(-0.553467\pi\) | ||||
−0.167183 | + | 0.985926i | \(0.553467\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.66036e9 | 0.0358278 | ||||||||
\(296\) | −3.52824e10 | + | 6.11110e10i | −0.267144 | + | 0.462708i | ||||
\(297\) | −1.26940e11 | − | 2.19867e11i | −0.946662 | − | 1.63967i | ||||
\(298\) | 4.97517e10 | + | 8.61724e10i | 0.365455 | + | 0.632987i | ||||
\(299\) | −7.52734e9 | + | 1.30377e10i | −0.0544655 | + | 0.0943370i | ||||
\(300\) | −1.08932e11 | −0.776440 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.89684e9 | 0.0269576 | ||||||||
\(303\) | 9.93848e10 | − | 1.72140e11i | 0.677373 | − | 1.17325i | ||||
\(304\) | −2.95032e10 | − | 5.11011e10i | −0.198125 | − | 0.343162i | ||||
\(305\) | 2.77376e10 | + | 4.80428e10i | 0.183535 | + | 0.317892i | ||||
\(306\) | −1.41718e11 | + | 2.45463e11i | −0.924016 | + | 1.60044i | ||||
\(307\) | 2.36528e11 | 1.51971 | 0.759855 | − | 0.650093i | \(-0.225270\pi\) | ||||
0.759855 | + | 0.650093i | \(0.225270\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.33514e11 | −1.45714 | ||||||||
\(310\) | 2.26594e9 | − | 3.92473e9i | 0.0139355 | − | 0.0241369i | ||||
\(311\) | −3.87665e10 | − | 6.71456e10i | −0.234982 | − | 0.407001i | 0.724285 | − | 0.689500i | \(-0.242170\pi\) |
−0.959268 | + | 0.282499i | \(0.908837\pi\) | |||||||
\(312\) | 1.87760e10 | + | 3.25209e10i | 0.112178 | + | 0.194298i | ||||
\(313\) | −1.19220e11 | + | 2.06495e11i | −0.702101 | + | 1.21607i | 0.265627 | + | 0.964076i | \(0.414421\pi\) |
−0.967728 | + | 0.251998i | \(0.918912\pi\) | |||||||
\(314\) | 9.02651e10 | 0.524006 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.17236e10 | 0.348225 | ||||||||
\(317\) | −8.22013e10 | + | 1.42377e11i | −0.457206 | + | 0.791904i | −0.998812 | − | 0.0487283i | \(-0.984483\pi\) |
0.541606 | + | 0.840632i | \(0.317817\pi\) | |||||||
\(318\) | 3.85597e10 | + | 6.67874e10i | 0.211452 | + | 0.366246i | ||||
\(319\) | 1.72495e11 | + | 2.98769e11i | 0.932647 | + | 1.61539i | ||||
\(320\) | 2.99290e9 | − | 5.18385e9i | 0.0159557 | − | 0.0276362i | ||||
\(321\) | 9.74869e10 | 0.512476 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.60574e11 | −2.35444 | ||||||||
\(324\) | −1.66666e10 | + | 2.88673e10i | −0.0840221 | + | 0.145531i | ||||
\(325\) | 3.59129e10 | + | 6.22030e10i | 0.178556 | + | 0.309269i | ||||
\(326\) | 7.61265e9 | + | 1.31855e10i | 0.0373299 | + | 0.0646572i | ||||
\(327\) | −5.46584e10 | + | 9.46711e10i | −0.264358 | + | 0.457881i | ||||
\(328\) | 6.28974e10 | 0.300055 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 9.69592e10 | 0.450066 | ||||||||
\(331\) | −2.83731e10 | + | 4.91436e10i | −0.129921 | + | 0.225030i | −0.923646 | − | 0.383247i | \(-0.874806\pi\) |
0.793725 | + | 0.608277i | \(0.208139\pi\) | |||||||
\(332\) | −2.56168e10 | − | 4.43696e10i | −0.115719 | − | 0.200431i | ||||
\(333\) | 2.98301e11 | + | 5.16672e11i | 1.32940 | + | 2.30259i | ||||
\(334\) | −1.31189e11 | + | 2.27226e11i | −0.576818 | + | 0.999077i | ||||
\(335\) | −8.77299e10 | −0.380580 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.03813e10 | 0.255016 | 0.127508 | − | 0.991838i | \(-0.459302\pi\) | ||||
0.127508 | + | 0.991838i | \(0.459302\pi\) | |||||||
\(338\) | −7.24558e10 | + | 1.25497e11i | −0.301959 | + | 0.523008i | ||||
\(339\) | −5.87026e10 | − | 1.01676e11i | −0.241412 | − | 0.418138i | ||||
\(340\) | −2.33610e10 | − | 4.04625e10i | −0.0948063 | − | 0.164209i | ||||
\(341\) | 2.89295e10 | − | 5.01073e10i | 0.115863 | − | 0.200681i | ||||
\(342\) | −4.98879e11 | −1.97187 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.66043e10 | −0.294944 | ||||||||
\(345\) | 1.59103e10 | − | 2.75574e10i | 0.0604632 | − | 0.104725i | ||||
\(346\) | 1.49831e10 | + | 2.59515e10i | 0.0562030 | + | 0.0973464i | ||||
\(347\) | −1.36982e11 | − | 2.37260e11i | −0.507201 | − | 0.878498i | −0.999965 | − | 0.00833542i | \(-0.997347\pi\) |
0.492764 | − | 0.870163i | \(-0.335987\pi\) | |||||||
\(348\) | 1.41206e11 | − | 2.44577e11i | 0.516117 | − | 0.893940i | ||||
\(349\) | −2.44394e11 | −0.881814 | −0.440907 | − | 0.897553i | \(-0.645343\pi\) | ||||
−0.440907 | + | 0.897553i | \(0.645343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.37036e11 | 0.481895 | ||||||||
\(352\) | 3.82106e10 | − | 6.61827e10i | 0.132661 | − | 0.229775i | ||||
\(353\) | −9.50389e10 | − | 1.64612e11i | −0.325773 | − | 0.564255i | 0.655896 | − | 0.754852i | \(-0.272291\pi\) |
−0.981668 | + | 0.190596i | \(0.938958\pi\) | |||||||
\(354\) | −2.43535e10 | − | 4.21814e10i | −0.0824225 | − | 0.142760i | ||||
\(355\) | −6.91456e10 | + | 1.19764e11i | −0.231067 | + | 0.400219i | ||||
\(356\) | 1.79395e10 | 0.0591951 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.93258e11 | −0.621819 | ||||||||
\(359\) | −2.37132e11 | + | 4.10724e11i | −0.753468 | + | 1.30504i | 0.192665 | + | 0.981265i | \(0.438287\pi\) |
−0.946133 | + | 0.323779i | \(0.895046\pi\) | |||||||
\(360\) | −2.53039e10 | − | 4.38277e10i | −0.0794011 | − | 0.137527i | ||||
\(361\) | −2.43987e11 | − | 4.22597e11i | −0.756108 | − | 1.30962i | ||||
\(362\) | −5.39557e10 | + | 9.34541e10i | −0.165139 | + | 0.286029i | ||||
\(363\) | 6.88362e11 | 2.08083 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.11486e11 | 0.328776 | ||||||||
\(366\) | 2.89894e11 | − | 5.02111e11i | 0.844450 | − | 1.46263i | ||||
\(367\) | 2.36860e11 | + | 4.10253e11i | 0.681544 | + | 1.18047i | 0.974509 | + | 0.224346i | \(0.0720247\pi\) |
−0.292965 | + | 0.956123i | \(0.594642\pi\) | |||||||
\(368\) | −1.25401e10 | − | 2.17201e10i | −0.0356440 | − | 0.0617373i | ||||
\(369\) | 2.65888e11 | − | 4.60532e11i | 0.746587 | − | 1.29313i | ||||
\(370\) | −9.83447e10 | −0.272799 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.73642e10 | −0.128235 | ||||||||
\(373\) | 2.92040e11 | − | 5.05828e11i | 0.781183 | − | 1.35305i | −0.150071 | − | 0.988675i | \(-0.547950\pi\) |
0.931253 | − | 0.364373i | \(-0.118717\pi\) | |||||||
\(374\) | −2.98252e11 | − | 5.16588e11i | −0.788246 | − | 1.36528i | ||||
\(375\) | −1.57108e11 | − | 2.72118e11i | −0.410257 | − | 0.710586i | ||||
\(376\) | −9.60389e10 | + | 1.66344e11i | −0.247800 | + | 0.429203i | ||||
\(377\) | −1.86213e11 | −0.474761 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.61076e11 | 1.39684 | 0.698418 | − | 0.715691i | \(-0.253888\pi\) | ||||
0.698418 | + | 0.715691i | \(0.253888\pi\) | |||||||
\(380\) | 4.11180e10 | − | 7.12184e10i | 0.101159 | − | 0.175213i | ||||
\(381\) | −1.69806e11 | − | 2.94112e11i | −0.412848 | − | 0.715074i | ||||
\(382\) | 2.08492e11 | + | 3.61120e11i | 0.500962 | + | 0.867692i | ||||
\(383\) | 4.42251e10 | − | 7.66001e10i | 0.105021 | − | 0.181901i | −0.808726 | − | 0.588185i | \(-0.799843\pi\) |
0.913747 | + | 0.406285i | \(0.133176\pi\) | |||||||
\(384\) | −6.25594e10 | −0.146826 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.82533e11 | 0.877053 | ||||||||
\(387\) | −3.23831e11 | + | 5.60893e11i | −0.733871 | + | 1.27110i | ||||
\(388\) | −8.57045e10 | − | 1.48444e11i | −0.191982 | − | 0.332523i | ||||
\(389\) | 2.11736e11 | + | 3.66737e11i | 0.468836 | + | 0.812048i | 0.999365 | − | 0.0356187i | \(-0.0113402\pi\) |
−0.530529 | + | 0.847667i | \(0.678007\pi\) | |||||||
\(390\) | −2.61676e10 | + | 4.53237e10i | −0.0572761 | + | 0.0992052i | ||||
\(391\) | −1.95764e11 | −0.423581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.03582e12 | 2.19038 | ||||||||
\(394\) | 3.92854e10 | − | 6.80444e10i | 0.0821294 | − | 0.142252i | ||||
\(395\) | 4.30114e10 | + | 7.44979e10i | 0.0888989 | + | 0.153977i | ||||
\(396\) | −3.23057e11 | − | 5.59552e11i | −0.660163 | − | 1.14344i | ||||
\(397\) | 1.81536e11 | − | 3.14430e11i | 0.366780 | − | 0.635281i | −0.622280 | − | 0.782795i | \(-0.713794\pi\) |
0.989060 | + | 0.147513i | \(0.0471269\pi\) | |||||||
\(398\) | 3.74104e11 | 0.747340 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.19658e11 | −0.233707 | ||||||||
\(401\) | 2.51584e11 | − | 4.35757e11i | 0.485885 | − | 0.841578i | −0.513983 | − | 0.857800i | \(-0.671831\pi\) |
0.999868 | + | 0.0162223i | \(0.00516395\pi\) | |||||||
\(402\) | 4.58446e11 | + | 7.94052e11i | 0.875530 | + | 1.51646i | ||||
\(403\) | 1.56152e10 | + | 2.70462e10i | 0.0294899 | + | 0.0510780i | ||||
\(404\) | 1.09171e11 | − | 1.89090e11i | 0.203888 | − | 0.353144i | ||||
\(405\) | −4.64556e10 | −0.0858007 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.25558e12 | −2.26813 | ||||||||
\(408\) | −2.44154e11 | + | 4.22886e11i | −0.436207 | + | 0.755532i | ||||
\(409\) | 3.96077e10 | + | 6.86026e10i | 0.0699882 | + | 0.121223i | 0.898896 | − | 0.438162i | \(-0.144370\pi\) |
−0.828908 | + | 0.559385i | \(0.811037\pi\) | |||||||
\(410\) | 4.38293e10 | + | 7.59147e10i | 0.0766016 | + | 0.132678i | ||||
\(411\) | 3.65026e11 | − | 6.32243e11i | 0.631009 | − | 1.09294i | ||||
\(412\) | −2.56508e11 | −0.438594 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.12045e11 | −0.354753 | ||||||||
\(415\) | 3.57015e10 | − | 6.18369e10i | 0.0590841 | − | 0.102337i | ||||
\(416\) | 2.06248e10 | + | 3.57232e10i | 0.0337652 | + | 0.0584831i | ||||
\(417\) | −2.22362e11 | − | 3.85141e11i | −0.360120 | − | 0.623746i | ||||
\(418\) | 5.24957e11 | − | 9.09252e11i | 0.841066 | − | 1.45677i | ||||
\(419\) | −3.38943e11 | −0.537234 | −0.268617 | − | 0.963247i | \(-0.586567\pi\) | ||||
−0.268617 | + | 0.963247i | \(0.586567\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.34126e11 | −0.983799 | −0.491899 | − | 0.870652i | \(-0.663697\pi\) | ||||
−0.491899 | + | 0.870652i | \(0.663697\pi\) | |||||||
\(422\) | 1.76665e11 | − | 3.05992e11i | 0.271171 | − | 0.469683i | ||||
\(423\) | 8.11976e11 | + | 1.40638e12i | 1.23314 | + | 2.13586i | ||||
\(424\) | 4.23566e10 | + | 7.33638e10i | 0.0636465 | + | 0.110239i | ||||
\(425\) | −4.66994e11 | + | 8.08857e11i | −0.694322 | + | 1.20260i | ||||
\(426\) | 1.44533e12 | 2.12629 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.07086e11 | 0.154254 | ||||||||
\(429\) | −3.34085e11 | + | 5.78651e11i | −0.476210 | + | 0.824820i | ||||
\(430\) | −5.33808e10 | − | 9.24583e10i | −0.0752969 | − | 0.130418i | ||||
\(431\) | −2.06806e11 | − | 3.58198e11i | −0.288679 | − | 0.500007i | 0.684816 | − | 0.728716i | \(-0.259883\pi\) |
−0.973495 | + | 0.228710i | \(0.926549\pi\) | |||||||
\(432\) | −1.14147e11 | + | 1.97709e11i | −0.157684 | + | 0.273117i | ||||
\(433\) | −8.78540e11 | −1.20106 | −0.600532 | − | 0.799601i | \(-0.705044\pi\) | ||||
−0.600532 | + | 0.799601i | \(0.705044\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.93592e11 | 0.527042 | ||||||||
\(436\) | −6.00404e10 | + | 1.03993e11i | −0.0795709 | + | 0.137821i | ||||
\(437\) | −1.72283e11 | − | 2.98402e11i | −0.225983 | − | 0.391414i | ||||
\(438\) | −5.82585e11 | − | 1.00907e12i | −0.756355 | − | 1.31005i | ||||
\(439\) | −7.13355e11 | + | 1.23557e12i | −0.916675 | + | 1.58773i | −0.112244 | + | 0.993681i | \(0.535804\pi\) |
−0.804431 | + | 0.594047i | \(0.797529\pi\) | |||||||
\(440\) | 1.06506e11 | 0.135469 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.21973e11 | 0.401254 | ||||||||
\(443\) | 5.83021e11 | − | 1.00982e12i | 0.719230 | − | 1.24574i | −0.242076 | − | 0.970257i | \(-0.577828\pi\) |
0.961305 | − | 0.275485i | \(-0.0888384\pi\) | |||||||
\(444\) | 5.13915e11 | + | 8.90128e11i | 0.627579 | + | 1.08700i | ||||
\(445\) | 1.25010e10 | + | 2.16523e10i | 0.0151120 | + | 0.0261748i | ||||
\(446\) | −2.57682e11 | + | 4.46318e11i | −0.308373 | + | 0.534118i | ||||
\(447\) | 1.44934e12 | 1.71707 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.47993e11 | 0.520191 | 0.260095 | − | 0.965583i | \(-0.416246\pi\) | ||||
0.260095 | + | 0.965583i | \(0.416246\pi\) | |||||||
\(450\) | −5.05832e11 | + | 8.76128e11i | −0.581501 | + | 1.00719i | ||||
\(451\) | 5.59573e11 | + | 9.69209e11i | 0.636887 | + | 1.10312i | ||||
\(452\) | −6.44828e10 | − | 1.11688e11i | −0.0726643 | − | 0.125858i | ||||
\(453\) | 2.83802e10 | − | 4.91559e10i | 0.0316645 | − | 0.0548446i | ||||
\(454\) | 6.64535e11 | 0.734119 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.59474e11 | −0.930874 | ||||||||
\(457\) | −2.69732e11 | + | 4.67190e11i | −0.289274 | + | 0.501038i | −0.973637 | − | 0.228104i | \(-0.926747\pi\) |
0.684362 | + | 0.729142i | \(0.260081\pi\) | |||||||
\(458\) | −1.06458e11 | − | 1.84391e11i | −0.113053 | − | 0.195814i | ||||
\(459\) | 8.90974e11 | + | 1.54321e12i | 0.936932 | + | 1.62281i | ||||
\(460\) | 1.74769e10 | − | 3.02709e10i | 0.0181993 | − | 0.0315221i | ||||
\(461\) | −4.24948e11 | −0.438209 | −0.219105 | − | 0.975701i | \(-0.570314\pi\) | ||||
−0.219105 | + | 0.975701i | \(0.570314\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.61716e11 | 0.871465 | 0.435732 | − | 0.900076i | \(-0.356489\pi\) | ||||
0.435732 | + | 0.900076i | \(0.356489\pi\) | |||||||
\(464\) | 1.55111e11 | − | 2.68659e11i | 0.155350 | − | 0.269074i | ||||
\(465\) | −3.30052e10 | − | 5.71666e10i | −0.0327374 | − | 0.0567028i | ||||
\(466\) | 6.42196e11 | + | 1.11232e12i | 0.630857 | + | 1.09268i | ||||
\(467\) | −3.32732e11 | + | 5.76308e11i | −0.323719 | + | 0.560698i | −0.981252 | − | 0.192728i | \(-0.938267\pi\) |
0.657533 | + | 0.753425i | \(0.271600\pi\) | |||||||
\(468\) | 3.48751e11 | 0.336054 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.67694e11 | −0.253046 | ||||||||
\(471\) | 6.57389e11 | − | 1.13863e12i | 0.615501 | − | 1.06608i | ||||
\(472\) | −2.67515e10 | − | 4.63349e10i | −0.0248090 | − | 0.0429704i | ||||
\(473\) | −6.81518e11 | − | 1.18042e12i | −0.626040 | − | 1.08433i | ||||
\(474\) | 4.49525e11 | − | 7.78601e11i | 0.409027 | − | 0.708455i | ||||
\(475\) | −1.64392e12 | −1.48170 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.16221e11 | 0.633453 | ||||||||
\(478\) | 5.02286e11 | − | 8.69986e11i | 0.440074 | − | 0.762231i | ||||
\(479\) | −4.28730e11 | − | 7.42582e11i | −0.372112 | − | 0.644517i | 0.617778 | − | 0.786352i | \(-0.288033\pi\) |
−0.989890 | + | 0.141835i | \(0.954700\pi\) | |||||||
\(480\) | −4.35938e10 | − | 7.55067e10i | −0.0374834 | − | 0.0649232i | ||||
\(481\) | 3.38858e11 | − | 5.86920e11i | 0.288646 | − | 0.499949i | ||||
\(482\) | 1.35509e11 | 0.114355 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.56143e11 | 0.626325 | ||||||||
\(485\) | 1.19444e11 | − | 2.06884e11i | 0.0980229 | − | 0.169781i | ||||
\(486\) | −3.05764e11 | − | 5.29598e11i | −0.248612 | − | 0.430609i | ||||
\(487\) | −1.01875e12 | − | 1.76453e12i | −0.820708 | − | 1.42151i | −0.905155 | − | 0.425081i | \(-0.860246\pi\) |
0.0844470 | − | 0.996428i | \(-0.473088\pi\) | |||||||
\(488\) | 3.18439e11 | − | 5.51552e11i | 0.254177 | − | 0.440248i | ||||
\(489\) | 2.21768e11 | 0.175392 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.85012e11 | 0.609550 | 0.304775 | − | 0.952424i | \(-0.401419\pi\) | ||||
0.304775 | + | 0.952424i | \(0.401419\pi\) | |||||||
\(492\) | 4.58074e11 | − | 7.93408e11i | 0.352446 | − | 0.610455i | ||||
\(493\) | −1.21071e12 | − | 2.09702e12i | −0.923061 | − | 1.59879i | ||||
\(494\) | 2.83354e11 | + | 4.90783e11i | 0.214071 | + | 0.370782i | ||||
\(495\) | 4.50238e11 | − | 7.79835e11i | 0.337069 | − | 0.583820i | ||||
\(496\) | −5.20280e10 | −0.0385984 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.46256e11 | −0.543696 | ||||||||
\(499\) | 1.30963e11 | − | 2.26835e11i | 0.0945578 | − | 0.163779i | −0.814866 | − | 0.579649i | \(-0.803190\pi\) |
0.909424 | + | 0.415870i | \(0.136523\pi\) | |||||||
\(500\) | −1.72577e11 | − | 2.98913e11i | −0.123486 | − | 0.213885i | ||||
\(501\) | 1.91087e12 | + | 3.30972e12i | 1.35507 | + | 2.34705i | ||||
\(502\) | 7.78534e7 | − | 1.34846e8i | 5.47156e−5 | − | 9.47702e-5i | ||||
\(503\) | 8.93639e11 | 0.622452 | 0.311226 | − | 0.950336i | \(-0.399260\pi\) | ||||
0.311226 | + | 0.950336i | \(0.399260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.04298e11 | 0.208203 | ||||||||
\(506\) | 2.23129e11 | − | 3.86471e11i | 0.151314 | − | 0.262083i | ||||
\(507\) | 1.05537e12 | + | 1.82796e12i | 0.709366 | + | 1.22866i | ||||
\(508\) | −1.86526e11 | − | 3.23073e11i | −0.124266 | − | 0.215235i | ||||
\(509\) | 2.60651e11 | − | 4.51462e11i | 0.172120 | − | 0.298120i | −0.767041 | − | 0.641598i | \(-0.778272\pi\) |
0.939161 | + | 0.343478i | \(0.111605\pi\) | |||||||
\(510\) | −6.80542e11 | −0.445440 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | −1.56821e12 | + | 2.71622e12i | −0.999715 | + | 1.73156i | ||||
\(514\) | −1.38125e11 | − | 2.39240e11i | −0.0872850 | − | 0.151182i | ||||
\(515\) | −1.78744e11 | − | 3.09594e11i | −0.111969 | − | 0.193937i | ||||
\(516\) | −5.57900e11 | + | 9.66311e11i | −0.346444 | + | 0.600058i | ||||
\(517\) | −3.41768e12 | −2.10389 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.36480e11 | 0.264066 | ||||||||
\(520\) | −2.87443e10 | + | 4.97866e10i | −0.0172400 | + | 0.0298605i | ||||
\(521\) | −1.20673e11 | − | 2.09012e11i | −0.0717530 | − | 0.124280i | 0.827917 | − | 0.560851i | \(-0.189526\pi\) |
−0.899670 | + | 0.436571i | \(0.856193\pi\) | |||||||
\(522\) | −1.31141e12 | − | 2.27142e12i | −0.773072 | − | 1.33900i | ||||
\(523\) | −1.13218e12 | + | 1.96099e12i | −0.661693 | + | 1.14609i | 0.318478 | + | 0.947930i | \(0.396828\pi\) |
−0.980171 | + | 0.198155i | \(0.936505\pi\) | |||||||
\(524\) | 1.13782e12 | 0.659299 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.02263e11 | 0.229126 | ||||||||
\(527\) | −2.03052e11 | + | 3.51696e11i | −0.114672 | + | 0.198619i | ||||
\(528\) | −5.56566e11 | − | 9.64001e11i | −0.311648 | − | 0.539790i | ||||
\(529\) | 8.27349e11 | + | 1.43301e12i | 0.459344 | + | 0.795607i | ||||
\(530\) | −5.90314e10 | + | 1.02245e11i | −0.0324969 | + | 0.0562862i | ||||
\(531\) | −4.52349e11 | −0.246915 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.04077e11 | −0.324205 | ||||||||
\(534\) | 1.30651e11 | − | 2.26295e11i | 0.0695310 | − | 0.120431i | ||||
\(535\) | 7.46217e10 | + | 1.29249e11i | 0.0393798 | + | 0.0682078i | ||||
\(536\) | 5.03588e11 | + | 8.72240e11i | 0.263532 | + | 0.456451i | ||||
\(537\) | −1.40747e12 | + | 2.43782e12i | −0.730392 | + | 1.26508i | ||||
\(538\) | −1.27537e12 | −0.656319 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.18168e11 | −0.161022 | ||||||||
\(541\) | −1.87065e12 | + | 3.24005e12i | −0.938867 | + | 1.62616i | −0.171277 | + | 0.985223i | \(0.554789\pi\) |
−0.767590 | + | 0.640942i | \(0.778544\pi\) | |||||||
\(542\) | −2.48555e11 | − | 4.30511e11i | −0.123716 | − | 0.214283i | ||||
\(543\) | 7.85906e11 | + | 1.36123e12i | 0.387946 | + | 0.671942i | ||||
\(544\) | −2.68195e11 | + | 4.64527e11i | −0.131297 | + | 0.227413i | ||||
\(545\) | −1.67354e11 | −0.0812553 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.37063e11 | −0.399775 | −0.199887 | − | 0.979819i | \(-0.564058\pi\) | ||||
−0.199887 | + | 0.979819i | \(0.564058\pi\) | |||||||
\(548\) | 4.00969e11 | − | 6.94498e11i | 0.189932 | − | 0.328972i | ||||
\(549\) | −2.69229e12 | − | 4.66318e12i | −1.26487 | − | 2.19082i | ||||
\(550\) | −1.06455e12 | − | 1.84385e12i | −0.496058 | − | 0.859198i | ||||
\(551\) | 2.13099e12 | − | 3.69098e12i | 0.984916 | − | 1.70592i | ||||
\(552\) | −3.65313e11 | −0.167471 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.67359e12 | −1.20587 | ||||||||
\(555\) | −7.16232e11 | + | 1.24055e12i | −0.320432 | + | 0.555004i | ||||
\(556\) | −2.44257e11 | − | 4.23065e11i | −0.108395 | − | 0.187746i | ||||
\(557\) | −8.22028e11 | − | 1.42379e12i | −0.361858 | − | 0.626756i | 0.626409 | − | 0.779495i | \(-0.284524\pi\) |
−0.988267 | + | 0.152738i | \(0.951191\pi\) | |||||||
\(558\) | −2.19939e11 | + | 3.80946e11i | −0.0960393 | + | 0.166345i | ||||
\(559\) | 7.35720e11 | 0.318683 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.68854e12 | −3.70352 | ||||||||
\(562\) | −5.64647e11 | + | 9.77997e11i | −0.238761 | + | 0.413546i | ||||
\(563\) | 6.32203e11 | + | 1.09501e12i | 0.265197 | + | 0.459335i | 0.967615 | − | 0.252429i | \(-0.0812296\pi\) |
−0.702418 | + | 0.711765i | \(0.747896\pi\) | |||||||
\(564\) | 1.39888e12 | + | 2.42293e12i | 0.582136 | + | 1.00829i | ||||
\(565\) | 8.98682e10 | − | 1.55656e11i | 0.0371012 | − | 0.0642612i | ||||
\(566\) | 4.12461e11 | 0.168931 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.58764e12 | 0.640007 | ||||||||
\(569\) | 2.93350e11 | − | 5.08097e11i | 0.117322 | − | 0.203208i | −0.801383 | − | 0.598151i | \(-0.795902\pi\) |
0.918706 | + | 0.394943i | \(0.129236\pi\) | |||||||
\(570\) | −5.98914e11 | − | 1.03735e12i | −0.237645 | − | 0.411612i | ||||
\(571\) | 2.89491e11 | + | 5.01413e11i | 0.113965 | + | 0.197394i | 0.917366 | − | 0.398046i | \(-0.130311\pi\) |
−0.803400 | + | 0.595439i | \(0.796978\pi\) | |||||||
\(572\) | −3.66981e11 | + | 6.35630e11i | −0.143338 | + | 0.248269i | ||||
\(573\) | 6.07370e12 | 2.35373 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.98736e11 | −0.266568 | ||||||||
\(576\) | −2.90500e11 | + | 5.03160e11i | −0.109963 | + | 0.190461i | ||||
\(577\) | 1.54947e12 | + | 2.68377e12i | 0.581960 | + | 1.00798i | 0.995247 | + | 0.0973829i | \(0.0310471\pi\) |
−0.413287 | + | 0.910601i | \(0.635620\pi\) | |||||||
\(578\) | 1.14469e12 | + | 1.98266e12i | 0.426591 | + | 0.738877i | ||||
\(579\) | 2.78594e12 | − | 4.82539e12i | 1.03019 | − | 1.78434i | ||||
\(580\) | 4.32348e11 | 0.158638 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.49670e12 | −0.902013 | ||||||||
\(583\) | −7.53659e11 | + | 1.30538e12i | −0.270188 | + | 0.467980i | ||||
\(584\) | −6.39950e11 | − | 1.10843e12i | −0.227661 | − | 0.394320i | ||||
\(585\) | 2.43023e11 | + | 4.20928e11i | 0.0857919 | + | 0.148596i | ||||
\(586\) | −3.37455e11 | + | 5.84489e11i | −0.118216 | + | 0.204756i | ||||
\(587\) | −1.61097e12 | −0.560035 | −0.280017 | − | 0.959995i | \(-0.590340\pi\) | ||||
−0.280017 | + | 0.959995i | \(0.590340\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.14787e11 | −0.244713 | ||||||||
\(590\) | 3.72829e10 | − | 6.45759e10i | 0.0126671 | − | 0.0219400i | ||||
\(591\) | −5.72222e11 | − | 9.91118e11i | −0.192939 | − | 0.334181i | ||||
\(592\) | 5.64519e11 | + | 9.77776e11i | 0.188900 | + | 0.327184i | ||||
\(593\) | −1.94134e12 | + | 3.36251e12i | −0.644698 | + | 1.11665i | 0.339673 | + | 0.940543i | \(0.389683\pi\) |
−0.984371 | + | 0.176106i | \(0.943650\pi\) | |||||||
\(594\) | −4.06208e12 | −1.33878 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.59205e12 | 0.516832 | ||||||||
\(597\) | 2.72455e12 | − | 4.71906e12i | 0.877830 | − | 1.52045i | ||||
\(598\) | 1.20437e11 | + | 2.08604e11i | 0.0385129 | + | 0.0667063i | ||||
\(599\) | −1.18137e12 | − | 2.04619e12i | −0.374942 | − | 0.649419i | 0.615376 | − | 0.788234i | \(-0.289004\pi\) |
−0.990318 | + | 0.138814i | \(0.955671\pi\) | |||||||
\(600\) | −8.71453e11 | + | 1.50940e12i | −0.274513 | + | 0.475471i | ||||
\(601\) | −1.88288e12 | −0.588692 | −0.294346 | − | 0.955699i | \(-0.595102\pi\) | ||||
−0.294346 | + | 0.955699i | \(0.595102\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.51533e12 | 2.62285 | ||||||||
\(604\) | 3.11747e10 | − | 5.39961e10i | 0.00953094 | − | 0.0165081i | ||||
\(605\) | 5.26909e11 | + | 9.12634e11i | 0.159896 | + | 0.276947i | ||||
\(606\) | −1.59016e12 | − | 2.75423e12i | −0.478975 | − | 0.829610i | ||||
\(607\) | −1.28351e12 | + | 2.22311e12i | −0.383753 | + | 0.664679i | −0.991595 | − | 0.129378i | \(-0.958702\pi\) |
0.607843 | + | 0.794057i | \(0.292035\pi\) | |||||||
\(608\) | −9.44103e11 | −0.280191 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.87602e11 | 0.259558 | ||||||||
\(611\) | 9.22373e11 | − | 1.59760e12i | 0.267745 | − | 0.463748i | ||||
\(612\) | 2.26749e12 | + | 3.92741e12i | 0.653378 | + | 1.13168i | ||||
\(613\) | 3.07070e12 | + | 5.31861e12i | 0.878345 | + | 1.52134i | 0.853156 | + | 0.521655i | \(0.174685\pi\) |
0.0251888 | + | 0.999683i | \(0.491981\pi\) | |||||||
\(614\) | 1.89223e12 | − | 3.27743e12i | 0.537299 | − | 0.930629i | ||||
\(615\) | 1.27682e12 | 0.359907 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.36828e12 | −1.21347 | −0.606733 | − | 0.794906i | \(-0.707520\pi\) | ||||
−0.606733 | + | 0.794906i | \(0.707520\pi\) | |||||||
\(618\) | −1.86811e12 | + | 3.23567e12i | −0.515175 | + | 0.892310i | ||||
\(619\) | −2.40713e12 | − | 4.16927e12i | −0.659009 | − | 1.14144i | −0.980872 | − | 0.194651i | \(-0.937642\pi\) |
0.321863 | − | 0.946786i | \(-0.395691\pi\) | |||||||
\(620\) | −3.62551e10 | − | 6.27956e10i | −0.00985386 | − | 0.0170674i | ||||
\(621\) | −6.66556e11 | + | 1.15451e12i | −0.179856 | + | 0.311520i | ||||
\(622\) | −1.24053e12 | −0.332315 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.00831e11 | 0.158643 | ||||||||
\(625\) | −1.54252e12 | + | 2.67173e12i | −0.404363 | + | 0.700377i | ||||
\(626\) | 1.90752e12 | + | 3.30392e12i | 0.496460 | + | 0.859894i | ||||
\(627\) | −7.64639e12 | − | 1.32439e13i | −1.97584 | − | 3.42226i | ||||
\(628\) | 7.22121e11 | − | 1.25075e12i | 0.185264 | − | 0.320887i | ||||
\(629\) | 8.81270e12 | 2.24482 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.12132e12 | 1.78825 | 0.894125 | − | 0.447818i | \(-0.147799\pi\) | ||||
0.894125 | + | 0.447818i | \(0.147799\pi\) | |||||||
\(632\) | 4.93789e11 | − | 8.55267e11i | 0.123116 | − | 0.213243i | ||||
\(633\) | −2.57326e12 | − | 4.45701e12i | −0.637039 | − | 1.10338i | ||||
\(634\) | 1.31522e12 | + | 2.27803e12i | 0.323294 | + | 0.559961i | ||||
\(635\) | 2.59957e11 | − | 4.50259e11i | 0.0634483 | − | 0.109896i | ||||
\(636\) | 1.23391e12 | 0.299038 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.51983e12 | 1.31896 | ||||||||
\(639\) | 6.71148e12 | − | 1.16246e13i | 1.59245 | − | 2.75820i | ||||
\(640\) | −4.78864e10 | − | 8.29416e10i | −0.0112824 | − | 0.0195417i | ||||
\(641\) | −9.29649e11 | − | 1.61020e12i | −0.217499 | − | 0.376720i | 0.736543 | − | 0.676390i | \(-0.236457\pi\) |
−0.954043 | + | 0.299670i | \(0.903123\pi\) | |||||||
\(642\) | 7.79895e11 | − | 1.35082e12i | 0.181188 | − | 0.313826i | ||||
\(643\) | −6.16271e12 | −1.42175 | −0.710874 | − | 0.703320i | \(-0.751700\pi\) | ||||
−0.710874 | + | 0.703320i | \(0.751700\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.55506e12 | −0.353777 | ||||||||
\(646\) | −3.68459e12 | + | 6.38190e12i | −0.832422 | + | 1.44180i | ||||
\(647\) | 1.81716e12 | + | 3.14742e12i | 0.407685 | + | 0.706131i | 0.994630 | − | 0.103496i | \(-0.0330029\pi\) |
−0.586945 | + | 0.809627i | \(0.699670\pi\) | |||||||
\(648\) | 2.66665e11 | + | 4.61877e11i | 0.0594126 | + | 0.102906i | ||||
\(649\) | 4.75994e11 | − | 8.24446e11i | 0.105317 | − | 0.182415i | ||||
\(650\) | 1.14921e12 | 0.252517 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.43605e11 | 0.0527924 | ||||||||
\(653\) | −3.34372e10 | + | 5.79149e10i | −0.00719649 | + | 0.0124647i | −0.869601 | − | 0.493755i | \(-0.835624\pi\) |
0.862405 | + | 0.506219i | \(0.168957\pi\) | |||||||
\(654\) | 8.74534e11 | + | 1.51474e12i | 0.186929 | + | 0.323771i | ||||
\(655\) | 7.92876e11 | + | 1.37330e12i | 0.168314 | + | 0.291528i | ||||
\(656\) | 5.03179e11 | − | 8.71532e11i | 0.106085 | − | 0.183745i | ||||
\(657\) | −1.08211e13 | −2.26583 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.97503e12 | 1.23411 | 0.617057 | − | 0.786918i | \(-0.288325\pi\) | ||||
0.617057 | + | 0.786918i | \(0.288325\pi\) | |||||||
\(660\) | 7.75673e11 | − | 1.34351e12i | 0.159122 | − | 0.275608i | ||||
\(661\) | 3.11074e12 | + | 5.38796e12i | 0.633807 | + | 1.09779i | 0.986767 | + | 0.162147i | \(0.0518420\pi\) |
−0.352960 | + | 0.935639i | \(0.614825\pi\) | |||||||
\(662\) | 4.53969e11 | + | 7.86298e11i | 0.0918683 | + | 0.159121i | ||||
\(663\) | 2.34489e12 | − | 4.06147e12i | 0.471315 | − | 0.816342i | ||||
\(664\) | −8.19738e11 | −0.163651 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.54563e12 | 1.88006 | ||||||||
\(667\) | 9.05761e11 | − | 1.56882e12i | 0.177193 | − | 0.306908i | ||||
\(668\) | 2.09902e12 | + | 3.63562e12i | 0.407872 | + | 0.706454i | ||||
\(669\) | 3.75333e12 | + | 6.50096e12i | 0.724434 | + | 1.25476i | ||||
\(670\) | −7.01839e11 | + | 1.21562e12i | −0.134555 | + | 0.233057i | ||||
\(671\) | 1.13321e13 | 2.15804 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.79437e12 | −0.900874 | −0.450437 | − | 0.892808i | \(-0.648732\pi\) | ||||
−0.450437 | + | 0.892808i | \(0.648732\pi\) | |||||||
\(674\) | 4.83050e11 | − | 8.36667e11i | 0.0901618 | − | 0.156165i | ||||
\(675\) | 3.18014e12 | + | 5.50816e12i | 0.589629 | + | 1.02127i | ||||
\(676\) | 1.15929e12 | + | 2.00795e12i | 0.213517 | + | 0.369823i | ||||
\(677\) | −2.10458e11 | + | 3.64523e11i | −0.0385049 | + | 0.0666924i | −0.884636 | − | 0.466283i | \(-0.845593\pi\) |
0.846131 | + | 0.532975i | \(0.178926\pi\) | |||||||
\(678\) | −1.87848e12 | −0.341408 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7.47553e11 | −0.134076 | ||||||||
\(681\) | 4.83973e12 | − | 8.38266e12i | 0.862301 | − | 1.49355i | ||||
\(682\) | −4.62872e11 | − | 8.01718e11i | −0.0819278 | − | 0.141903i | ||||
\(683\) | 1.15885e12 | + | 2.00719e12i | 0.203768 | + | 0.352936i | 0.949739 | − | 0.313042i | \(-0.101348\pi\) |
−0.745972 | + | 0.665978i | \(0.768015\pi\) | |||||||
\(684\) | −3.99103e12 | + | 6.91267e12i | −0.697161 | + | 1.20752i | ||||
\(685\) | 1.11764e12 | 0.193952 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.10128e12 | −0.531173 | ||||||||
\(688\) | −6.12834e11 | + | 1.06146e12i | −0.104279 | + | 0.180616i | ||||
\(689\) | −4.06800e11 | − | 7.04598e11i | −0.0687692 | − | 0.119112i | ||||
\(690\) | −2.54564e11 | − | 4.40918e11i | −0.0427539 | − | 0.0740520i | ||||
\(691\) | −1.21890e12 | + | 2.11120e12i | −0.203384 | + | 0.352272i | −0.949617 | − | 0.313413i | \(-0.898527\pi\) |
0.746232 | + | 0.665686i | \(0.231861\pi\) | |||||||
\(692\) | 4.79459e11 | 0.0794830 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.38342e12 | −0.717291 | ||||||||
\(695\) | 3.40415e11 | − | 5.89616e11i | 0.0553448 | − | 0.0958601i | ||||
\(696\) | −2.25930e12 | − | 3.91323e12i | −0.364950 | − | 0.632111i | ||||
\(697\) | −3.92756e12 | − | 6.80274e12i | −0.630341 | − | 1.09178i | ||||
\(698\) | −1.95516e12 | + | 3.38643e12i | −0.311768 | + | 0.539998i | ||||
\(699\) | 1.87081e13 | 2.96403 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.26491e12 | 0.197846 | 0.0989231 | − | 0.995095i | \(-0.468460\pi\) | ||||
0.0989231 | + | 0.995095i | \(0.468460\pi\) | |||||||
\(702\) | 1.09629e12 | − | 1.89883e12i | 0.170376 | − | 0.295099i | ||||
\(703\) | 7.75565e12 | + | 1.34332e13i | 1.19762 | + | 2.07434i | ||||
\(704\) | −6.11370e11 | − | 1.05892e12i | −0.0938052 | − | 0.162475i | ||||
\(705\) | −1.94959e12 | + | 3.37678e12i | −0.297229 | + | 0.514816i | ||||
\(706\) | −3.04124e12 | −0.460713 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.79311e11 | −0.116563 | ||||||||
\(709\) | −3.85471e12 | + | 6.67656e12i | −0.572907 | + | 0.992303i | 0.423359 | + | 0.905962i | \(0.360851\pi\) |
−0.996266 | + | 0.0863414i | \(0.972482\pi\) | |||||||
\(710\) | 1.10633e12 | + | 1.91622e12i | 0.163389 | + | 0.282998i | ||||
\(711\) | −4.17481e12 | − | 7.23099e12i | −0.612666 | − | 1.06117i | ||||
\(712\) | 1.43516e11 | − | 2.48577e11i | 0.0209286 | − | 0.0362495i | ||||
\(713\) | −3.03815e11 | −0.0440257 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.02291e12 | −0.146372 | ||||||||
\(716\) | −1.54606e12 | + | 2.67786e12i | −0.219846 | + | 0.380785i | ||||
\(717\) | −7.31618e12 | − | 1.26720e13i | −1.03383 | − | 1.79064i | ||||
\(718\) | 3.79411e12 | + | 6.57159e12i | 0.532782 | + | 0.922806i | ||||
\(719\) | 4.22559e12 | − | 7.31894e12i | 0.589668 | − | 1.02134i | −0.404607 | − | 0.914491i | \(-0.632592\pi\) |
0.994276 | − | 0.106845i | \(-0.0340749\pi\) | |||||||
\(720\) | −8.09726e11 | −0.112290 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.80757e12 | −1.06930 | ||||||||
\(723\) | 9.86896e11 | − | 1.70935e12i | 0.134323 | − | 0.232653i | ||||
\(724\) | 8.63292e11 | + | 1.49526e12i | 0.116771 | + | 0.202253i | ||||
\(725\) | −4.32138e12 | − | 7.48485e12i | −0.580900 | − | 1.00615i | ||||
\(726\) | 5.50690e12 | − | 9.53822e12i | 0.735685 | − | 1.27424i | ||||
\(727\) | −9.21867e12 | −1.22395 | −0.611974 | − | 0.790878i | \(-0.709624\pi\) | ||||
−0.611974 | + | 0.790878i | \(0.709624\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.14702e13 | −1.50417 | ||||||||
\(730\) | 8.91884e11 | − | 1.54479e12i | 0.116240 | − | 0.201334i | ||||
\(731\) | 4.78347e12 | + | 8.28522e12i | 0.619605 | + | 1.07319i | ||||
\(732\) | −4.63830e12 | − | 8.03377e12i | −0.597117 | − | 1.03424i | ||||
\(733\) | 2.52129e11 | − | 4.36701e11i | 0.0322593 | − | 0.0558748i | −0.849445 | − | 0.527677i | \(-0.823063\pi\) |
0.881704 | + | 0.471802i | \(0.156396\pi\) | |||||||
\(734\) | 7.57951e12 | 0.963849 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.01284e11 | −0.0504083 | ||||||||
\(737\) | −8.96044e12 | + | 1.55199e13i | −1.11873 | + | 1.93770i | ||||
\(738\) | −4.25421e12 | − | 7.36851e12i | −0.527916 | − | 0.914378i | ||||
\(739\) | 5.82376e12 | + | 1.00871e13i | 0.718296 | + | 1.24413i | 0.961674 | + | 0.274194i | \(0.0884112\pi\) |
−0.243378 | + | 0.969932i | \(0.578255\pi\) | |||||||
\(740\) | −7.86757e11 | + | 1.36270e12i | −0.0964491 | + | 0.167055i | ||||
\(741\) | 8.25453e12 | 1.00580 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.69366e12 | −0.324260 | −0.162130 | − | 0.986769i | \(-0.551836\pi\) | ||||
−0.162130 | + | 0.986769i | \(0.551836\pi\) | |||||||
\(744\) | −3.78913e11 | + | 6.56297e11i | −0.0453379 | + | 0.0785276i | ||||
\(745\) | 1.10940e12 | + | 1.92154e12i | 0.131943 | + | 0.228532i | ||||
\(746\) | −4.67264e12 | − | 8.09325e12i | −0.552380 | − | 0.956749i | ||||
\(747\) | −3.46530e12 | + | 6.00208e12i | −0.407191 | + | 0.705275i | ||||
\(748\) | −9.54408e12 | −1.11475 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5.02744e12 | −0.580191 | ||||||||
\(751\) | −4.10201e12 | + | 7.10489e12i | −0.470562 | + | 0.815037i | −0.999433 | − | 0.0336648i | \(-0.989282\pi\) |
0.528871 | + | 0.848702i | \(0.322615\pi\) | |||||||
\(752\) | 1.53662e12 | + | 2.66151e12i | 0.175221 | + | 0.303492i | ||||
\(753\) | −1.13399e9 | − | 1.96413e9i | −0.000128539 | − | 0.000222635i | ||||
\(754\) | −1.48971e12 | + | 2.58025e12i | −0.167853 | + | 0.290731i | ||||
\(755\) | 8.68949e10 | 0.00973269 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.42404e13 | 1.57613 | 0.788064 | − | 0.615594i | \(-0.211084\pi\) | ||||
0.788064 | + | 0.615594i | \(0.211084\pi\) | |||||||
\(758\) | 4.48861e12 | − | 7.77450e12i | 0.493856 | − | 0.855383i | ||||
\(759\) | −3.25004e12 | − | 5.62924e12i | −0.355468 | − | 0.615689i | ||||
\(760\) | −6.57888e11 | − | 1.13949e12i | −0.0715304 | − | 0.123894i | ||||
\(761\) | 5.97436e12 | − | 1.03479e13i | 0.645744 | − | 1.11846i | −0.338385 | − | 0.941008i | \(-0.609881\pi\) |
0.984129 | − | 0.177454i | \(-0.0567861\pi\) | |||||||
\(762\) | −5.43379e12 | −0.583856 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.67176e12 | 0.708468 | ||||||||
\(765\) | −3.16015e12 | + | 5.47354e12i | −0.333604 | + | 0.577819i | ||||
\(766\) | −7.07601e11 | − | 1.22560e12i | −0.0742607 | − | 0.128623i | ||||
\(767\) | 2.56925e11 | + | 4.45008e11i | 0.0268058 | + | 0.0464289i | ||||
\(768\) | −5.00476e11 | + | 8.66849e11i | −0.0519108 | + | 0.0899121i | ||||
\(769\) | −1.09236e13 | −1.12641 | −0.563206 | − | 0.826317i | \(-0.690432\pi\) | ||||
−0.563206 | + | 0.826317i | \(0.690432\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.02380e12 | −0.410102 | ||||||||
\(772\) | 3.06026e12 | − | 5.30053e12i | 0.310085 | − | 0.537083i | ||||
\(773\) | −8.69476e12 | − | 1.50598e13i | −0.875890 | − | 1.51709i | −0.855811 | − | 0.517288i | \(-0.826942\pi\) |
−0.0200787 | − | 0.999798i | \(-0.506392\pi\) | |||||||
\(774\) | 5.18130e12 | + | 8.97428e12i | 0.518925 | + | 0.898805i | ||||
\(775\) | −7.24749e11 | + | 1.25530e12i | −0.0721656 | + | 0.124994i | ||||
\(776\) | −2.74254e12 | −0.271504 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.77554e12 | 0.663034 | ||||||||
\(779\) | 6.91294e12 | − | 1.19736e13i | 0.672580 | − | 1.16494i | ||||
\(780\) | 4.18682e11 | + | 7.25179e11i | 0.0405004 | + | 0.0701487i | ||||
\(781\) | 1.41246e13 | + | 2.44645e13i | 1.35846 | + | 2.35292i | ||||
\(782\) | −1.56611e12 | + | 2.71258e12i | −0.149759 | + | 0.259389i | ||||
\(783\) | −1.64895e13 | −1.56776 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.01281e12 | 0.189186 | ||||||||
\(786\) | 8.28660e12 | − | 1.43528e13i | 0.774417 | − | 1.34133i | ||||
\(787\) | −4.34835e12 | − | 7.53156e12i | −0.404053 | − | 0.699840i | 0.590158 | − | 0.807288i | \(-0.299065\pi\) |
−0.994211 | + | 0.107448i | \(0.965732\pi\) | |||||||
\(788\) | −6.28567e11 | − | 1.08871e12i | −0.0580743 | − | 0.100588i | ||||
\(789\) | 2.92963e12 | − | 5.07427e12i | 0.269132 | − | 0.466151i | ||||
\(790\) | 1.37636e12 | 0.125722 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.03378e13 | −0.933612 | ||||||||
\(793\) | −3.05834e12 | + | 5.29720e12i | −0.274635 | + | 0.475682i | ||||
\(794\) | −2.90458e12 | − | 5.03087e12i | −0.259353 | − | 0.449212i | ||||
\(795\) | 8.59837e11 | + | 1.48928e12i | 0.0763421 | + | 0.132228i | ||||
\(796\) | 2.99283e12 | − | 5.18373e12i | 0.264225 | − | 0.457650i | ||||
\(797\) | 6.04620e12 | 0.530787 | 0.265393 | − | 0.964140i | \(-0.414498\pi\) | ||||
0.265393 | + | 0.964140i | \(0.414498\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.39882e13 | 2.08227 | ||||||||
\(800\) | −9.57262e11 | + | 1.65803e12i | −0.0826277 | + | 0.143115i | ||||
\(801\) | −1.21338e12 | − | 2.10164e12i | −0.104148 | − | 0.180390i | ||||
\(802\) | −4.02535e12 | − | 6.97211e12i | −0.343573 | − | 0.595085i | ||||
\(803\) | 1.13868e13 | − | 1.97225e13i | 0.966452 | − | 1.67394i | ||||
\(804\) | 1.46703e13 | 1.23819 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.99685e11 | 0.0417051 | ||||||||
\(807\) | −9.28834e12 | + | 1.60879e13i | −0.770916 | + | 1.33527i | ||||
\(808\) | −1.74673e12 | − | 3.02543e12i | −0.144170 | − | 0.249710i | ||||
\(809\) | −6.68109e12 | − | 1.15720e13i | −0.548377 | − | 0.949817i | −0.998386 | − | 0.0567926i | \(-0.981913\pi\) |
0.450009 | − | 0.893024i | \(-0.351421\pi\) | |||||||
\(810\) | −3.71645e11 | + | 6.43708e11i | −0.0303351 | + | 0.0525420i | ||||
\(811\) | 2.55667e11 | 0.0207530 | 0.0103765 | − | 0.999946i | \(-0.496697\pi\) | ||||
0.0103765 | + | 0.999946i | \(0.496697\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.24080e12 | −0.581271 | ||||||||
\(814\) | −1.00446e13 | + | 1.73978e13i | −0.801905 | + | 1.38894i | ||||
\(815\) | 1.69753e11 | + | 2.94021e11i | 0.0134775 | + | 0.0233437i | ||||
\(816\) | 3.90646e12 | + | 6.76618e12i | 0.308445 | + | 0.534242i | ||||
\(817\) | −8.41943e12 | + | 1.45829e13i | −0.661125 | + | 1.14510i | ||||
\(818\) | 1.26745e12 | 0.0989783 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.40254e12 | 0.108331 | ||||||||
\(821\) | 8.40243e12 | − | 1.45534e13i | 0.645447 | − | 1.11795i | −0.338751 | − | 0.940876i | \(-0.610004\pi\) |
0.984198 | − | 0.177071i | \(-0.0566623\pi\) | |||||||
\(822\) | −5.84041e12 | − | 1.01159e13i | −0.446191 | − | 0.772825i | ||||
\(823\) | 7.58134e11 | + | 1.31313e12i | 0.0576032 | + | 0.0997717i | 0.893389 | − | 0.449284i | \(-0.148321\pi\) |
−0.835786 | + | 0.549056i | \(0.814987\pi\) | |||||||
\(824\) | −2.05206e12 | + | 3.55427e12i | −0.155066 | + | 0.268583i | ||||
\(825\) | −3.10119e13 | −2.33069 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.47074e13 | −1.83676 | −0.918380 | − | 0.395699i | \(-0.870502\pi\) | ||||
−0.918380 | + | 0.395699i | \(0.870502\pi\) | |||||||
\(828\) | −1.69636e12 | + | 2.93818e12i | −0.125424 | + | 0.217241i | ||||
\(829\) | −9.77015e12 | − | 1.69224e13i | −0.718465 | − | 1.24442i | −0.961608 | − | 0.274428i | \(-0.911512\pi\) |
0.243142 | − | 0.969991i | \(-0.421822\pi\) | |||||||
\(830\) | −5.71225e11 | − | 9.89390e11i | −0.0417788 | − | 0.0723629i | ||||
\(831\) | −1.94714e13 | + | 3.37255e13i | −1.41642 | + | 2.45332i | ||||
\(832\) | 6.59993e11 | 0.0477512 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.11557e12 | −0.509287 | ||||||||
\(835\) | −2.92536e12 | + | 5.06688e12i | −0.208253 | + | 0.360704i | ||||
\(836\) | −8.39931e12 | − | 1.45480e13i | −0.594724 | − | 1.03009i | ||||
\(837\) | 1.38274e12 | + | 2.39498e12i | 0.0973817 | + | 0.168670i | ||||
\(838\) | −2.71154e12 | + | 4.69653e12i | −0.189941 | + | 0.328987i | ||||
\(839\) | −1.73255e13 | −1.20714 | −0.603569 | − | 0.797311i | \(-0.706255\pi\) | ||||
−0.603569 | + | 0.797311i | \(0.706255\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.89983e12 | 0.544547 | ||||||||
\(842\) | −5.07301e12 | + | 8.78671e12i | −0.347825 | + | 0.602451i | ||||
\(843\) | 8.22451e12 | + | 1.42453e13i | 0.560900 | + | 0.971508i | ||||
\(844\) | −2.82664e12 | − | 4.89588e12i | −0.191747 | − | 0.332116i | ||||
\(845\) | −1.61568e12 | + | 2.79844e12i | −0.109018 | + | 0.188825i | ||||
\(846\) | 2.59832e13 | 1.74392 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.35541e12 | 0.0900097 | ||||||||
\(849\) | 3.00390e12 | − | 5.20291e12i | 0.198427 | − | 0.343686i | ||||
\(850\) | 7.47190e12 | + | 1.29417e13i | 0.490960 | + | 0.850367i | ||||
\(851\) | 3.29648e12 | + | 5.70968e12i | 0.215461 | + | 0.373189i | ||||
\(852\) | 1.15626e13 | − | 2.00270e13i | 0.751757 | − | 1.30208i | ||||
\(853\) | −1.19537e12 | −0.0773096 | −0.0386548 | − | 0.999253i | \(-0.512307\pi\) | ||||
−0.0386548 | + | 0.999253i | \(0.512307\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.11244e13 | −0.711918 | ||||||||
\(856\) | 8.56689e11 | − | 1.48383e12i | 0.0545370 | − | 0.0944608i | ||||
\(857\) | 1.06769e13 | + | 1.84929e13i | 0.676132 | + | 1.17110i | 0.976137 | + | 0.217157i | \(0.0696785\pi\) |
−0.300004 | + | 0.953938i | \(0.596988\pi\) | |||||||
\(858\) | 5.34535e12 | + | 9.25842e12i | 0.336731 | + | 0.583236i | ||||
\(859\) | −5.31711e12 | + | 9.20950e12i | −0.333201 | + | 0.577121i | −0.983138 | − | 0.182867i | \(-0.941462\pi\) |
0.649937 | + | 0.759989i | \(0.274795\pi\) | |||||||
\(860\) | −1.70819e12 | −0.106486 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.61779e12 | −0.408254 | ||||||||
\(863\) | 7.07090e11 | − | 1.22472e12i | 0.0433936 | − | 0.0751600i | −0.843513 | − | 0.537109i | \(-0.819516\pi\) |
0.886906 | + | 0.461949i | \(0.152850\pi\) | |||||||
\(864\) | 1.82635e12 | + | 3.16334e12i | 0.111500 | + | 0.193123i | ||||
\(865\) | 3.34106e11 | + | 5.78688e11i | 0.0202914 | + | 0.0351457i | ||||
\(866\) | −7.02832e12 | + | 1.21734e13i | −0.424640 | + | 0.735498i | ||||
\(867\) | 3.33465e13 | 2.00430 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.75722e13 | 1.04529 | ||||||||
\(870\) | 3.14874e12 | − | 5.45378e12i | 0.186337 | − | 0.322746i | ||||
\(871\) | −4.83654e12 | − | 8.37714e12i | −0.284743 | − | 0.493190i | ||||
\(872\) | 9.60647e11 | + | 1.66389e12i | 0.0562651 | + | 0.0974541i | ||||
\(873\) | −1.15936e13 | + | 2.00808e13i | −0.675546 | + | 1.17008i | ||||
\(874\) | −5.51305e12 | −0.319588 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.86427e13 | −1.06965 | ||||||||
\(877\) | 7.78878e12 | − | 1.34906e13i | 0.444602 | − | 0.770073i | −0.553422 | − | 0.832901i | \(-0.686678\pi\) |
0.998024 | + | 0.0628273i | \(0.0200117\pi\) | |||||||
\(878\) | 1.14137e13 | + | 1.97691e13i | 0.648187 | + | 1.12269i | ||||
\(879\) | 4.91529e12 | + | 8.51352e12i | 0.277715 | + | 0.481016i | ||||
\(880\) | 8.52052e11 | − | 1.47580e12i | 0.0478954 | − | 0.0829573i | ||||
\(881\) | 1.55176e13 | 0.867825 | 0.433912 | − | 0.900955i | \(-0.357133\pi\) | ||||
0.433912 | + | 0.900955i | \(0.357133\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.94777e13 | −1.63181 | −0.815906 | − | 0.578185i | \(-0.803761\pi\) | ||||
−0.815906 | + | 0.578185i | \(0.803761\pi\) | |||||||
\(884\) | 2.57578e12 | − | 4.46139e12i | 0.141865 | − | 0.245717i | ||||
\(885\) | −5.43054e11 | − | 9.40596e11i | −0.0297576 | − | 0.0515417i | ||||
\(886\) | −9.32834e12 | − | 1.61572e13i | −0.508572 | − | 0.880873i | ||||
\(887\) | −3.15812e12 | + | 5.47002e12i | −0.171306 | + | 0.296710i | −0.938877 | − | 0.344254i | \(-0.888132\pi\) |
0.767571 | + | 0.640964i | \(0.221465\pi\) | |||||||
\(888\) | 1.64453e13 | 0.887531 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.00030e11 | 0.0213717 | ||||||||
\(891\) | −4.74482e12 | + | 8.21828e12i | −0.252215 | + | 0.436849i | ||||
\(892\) | 4.12291e12 | + | 7.14109e12i | 0.218053 | + | 0.377679i | ||||
\(893\) | 2.11109e13 | + | 3.65652e13i | 1.11090 | + | 1.92414i | ||||
\(894\) | 1.15947e13 | − | 2.00827e13i | 0.607074 | − | 1.05148i | ||||
\(895\) | −4.30943e12 | −0.224500 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.50852e12 | 0.180950 | ||||||||
\(898\) | 3.58394e12 | − | 6.20757e12i | 0.183915 | − | 0.318550i | ||||
\(899\) | −1.87896e12 | − | 3.25446e12i | −0.0959400 | − | 0.166173i | ||||
\(900\) | 8.09332e12 | + | 1.40180e13i | 0.411183 | + | 0.712190i | ||||
\(901\) | 5.28982e12 | − | 9.16224e12i | 0.267411 | − | 0.463170i | ||||
\(902\) | 1.79063e13 | 0.900694 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.06345e12 | −0.102763 | ||||||||
\(905\) | −1.20315e12 | + | 2.08392e12i | −0.0596212 | + | 0.103267i | ||||
\(906\) | −4.54083e11 | − | 7.86495e11i | −0.0223902 | − | 0.0387810i | ||||
\(907\) | −9.43632e12 | − | 1.63442e13i | −0.462988 | − | 0.801919i | 0.536120 | − | 0.844142i | \(-0.319889\pi\) |
−0.999108 | + | 0.0422226i | \(0.986556\pi\) | |||||||
\(908\) | 5.31628e12 | − | 9.20807e12i | 0.259550 | − | 0.449555i | ||||
\(909\) | −2.95361e13 | −1.43488 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.40579e13 | −1.15724 | −0.578622 | − | 0.815596i | \(-0.696409\pi\) | ||||
−0.578622 | + | 0.815596i | \(0.696409\pi\) | |||||||
\(912\) | −6.87579e12 | + | 1.19092e13i | −0.329114 | + | 0.570041i | ||||
\(913\) | −7.29288e12 | − | 1.26316e13i | −0.347360 | − | 0.601646i | ||||
\(914\) | 4.31571e12 | + | 7.47504e12i | 0.204548 | + | 0.354287i | ||||
\(915\) | 6.46429e12 | − | 1.11965e13i | 0.304878 | − | 0.528064i | ||||
\(916\) | −3.40666e12 | −0.159882 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.85112e13 | 1.32502 | ||||||||
\(919\) | −8.95336e12 | + | 1.55077e13i | −0.414063 | + | 0.717178i | −0.995330 | − | 0.0965354i | \(-0.969224\pi\) |
0.581267 | + | 0.813713i | \(0.302557\pi\) | |||||||
\(920\) | −2.79630e11 | − | 4.84334e11i | −0.0128688 | − | 0.0222895i | ||||
\(921\) | −2.75617e13 | − | 4.77383e13i | −1.26223 | − | 2.18624i | ||||
\(922\) | −3.39958e12 | + | 5.88825e12i | −0.154930 | + | 0.268347i | ||||
\(923\) | −1.52480e13 | −0.691519 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.14550e13 | 1.41271 | ||||||||
\(926\) | 6.89373e12 | − | 1.19403e13i | 0.308109 | − | 0.533661i | ||||
\(927\) | 1.73495e13 | + | 3.00502e13i | 0.771662 | + | 1.33656i | ||||
\(928\) | −2.48177e12 | − | 4.29855e12i | −0.109849 | − | 0.190264i | ||||
\(929\) | 5.90070e12 | − | 1.02203e13i | 0.259916 | − | 0.450187i | −0.706303 | − | 0.707909i | \(-0.749639\pi\) |
0.966219 | + | 0.257722i | \(0.0829719\pi\) | |||||||
\(930\) | −1.05617e12 | −0.0462976 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.05503e13 | 0.892166 | ||||||||
\(933\) | −9.03462e12 | + | 1.56484e13i | −0.390339 | + | 0.676088i | ||||
\(934\) | 5.32371e12 | + | 9.22093e12i | 0.228904 | + | 0.396473i | ||||
\(935\) | −6.65068e12 | − | 1.15193e13i | −0.284586 | − | 0.492918i | ||||
\(936\) | 2.79001e12 | − | 4.83243e12i | 0.118813 | − | 0.205790i | ||||
\(937\) | −2.93165e13 | −1.24246 | −0.621231 | − | 0.783627i | \(-0.713367\pi\) | ||||
−0.621231 | + | 0.783627i | \(0.713367\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.55689e13 | 2.33258 | ||||||||
\(940\) | −2.14155e12 | + | 3.70928e12i | −0.0894651 | + | 0.154958i | ||||
\(941\) | −2.28937e13 | − | 3.96531e13i | −0.951837 | − | 1.64863i | −0.741445 | − | 0.671014i | \(-0.765859\pi\) |
−0.210393 | − | 0.977617i | \(-0.567474\pi\) | |||||||
\(942\) | −1.05182e13 | − | 1.82181e13i | −0.435225 | − | 0.753832i | ||||
\(943\) | 2.93829e12 | − | 5.08927e12i | 0.121002 | − | 0.209582i | ||||
\(944\) | −8.56047e11 | −0.0350852 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.18086e13 | −0.885354 | ||||||||
\(947\) | 9.47480e12 | − | 1.64108e13i | 0.382820 | − | 0.663064i | −0.608644 | − | 0.793444i | \(-0.708286\pi\) |
0.991464 | + | 0.130379i | \(0.0416195\pi\) | |||||||
\(948\) | −7.19241e12 | − | 1.24576e13i | −0.289226 | − | 0.500953i | ||||
\(949\) | 6.14619e12 | + | 1.06455e13i | 0.245985 | + | 0.426058i | ||||
\(950\) | −1.31514e13 | + | 2.27788e13i | −0.523859 | + | 0.907350i | ||||
\(951\) | 3.83144e13 | 1.51897 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.44979e13 | 0.569362 | 0.284681 | − | 0.958622i | \(-0.408112\pi\) | ||||
0.284681 | + | 0.958622i | \(0.408112\pi\) | |||||||
\(954\) | 5.72977e12 | − | 9.92424e12i | 0.223959 | − | 0.387909i | ||||
\(955\) | 4.64914e12 | + | 8.05254e12i | 0.180866 | + | 0.313269i | ||||
\(956\) | −8.03658e12 | − | 1.39198e13i | −0.311179 | − | 0.538979i | ||||
\(957\) | 4.02002e13 | − | 6.96288e13i | 1.54926 | − | 2.68340i | ||||
\(958\) | −1.37194e13 | −0.526246 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.39500e12 | −0.0530096 | ||||||||
\(961\) | 1.29047e13 | − | 2.23516e13i | 0.488081 | − | 0.845382i | ||||
\(962\) | −5.42173e12 | − | 9.39072e12i | −0.204103 | − | 0.353518i | ||||
\(963\) | −7.24301e12 | − | 1.25453e13i | −0.271394 | − | 0.470069i | ||||
\(964\) | 1.08407e12 | − | 1.87767e12i | 0.0404307 | − | 0.0700281i | ||||
\(965\) | 8.53003e12 | 0.316649 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.84871e13 | 0.679909 | 0.339954 | − | 0.940442i | \(-0.389588\pi\) | ||||
0.339954 | + | 0.940442i | \(0.389588\pi\) | |||||||
\(968\) | 6.04914e12 | − | 1.04774e13i | 0.221439 | − | 0.383544i | ||||
\(969\) | 5.36689e13 | + | 9.29573e13i | 1.95554 | + | 3.38709i | ||||
\(970\) | −1.91111e12 | − | 3.31014e12i | −0.0693127 | − | 0.120053i | ||||
\(971\) | −2.24078e13 | + | 3.88114e13i | −0.808933 | + | 1.40111i | 0.104670 | + | 0.994507i | \(0.466621\pi\) |
−0.913603 | + | 0.406607i | \(0.866712\pi\) | |||||||
\(972\) | −9.78443e12 | −0.351591 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.26001e13 | −1.16066 | ||||||||
\(975\) | 8.36957e12 | − | 1.44965e13i | 0.296608 | − | 0.513740i | ||||
\(976\) | −5.09502e12 | − | 8.82484e12i | −0.179731 | − | 0.311302i | ||||
\(977\) | −1.23981e13 | − | 2.14742e13i | −0.435342 | − | 0.754035i | 0.561981 | − | 0.827150i | \(-0.310039\pi\) |
−0.997324 | + | 0.0731151i | \(0.976706\pi\) | |||||||
\(978\) | 1.77414e12 | − | 3.07291e12i | 0.0620103 | − | 0.107405i | ||||
\(979\) | 5.10723e12 | 0.177690 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.62439e13 | 0.559988 | ||||||||
\(982\) | 6.28010e12 | − | 1.08774e13i | 0.215509 | − | 0.373272i | ||||
\(983\) | −6.93158e12 | − | 1.20058e13i | −0.236778 | − | 0.410111i | 0.723010 | − | 0.690838i | \(-0.242758\pi\) |
−0.959788 | + | 0.280726i | \(0.909425\pi\) | |||||||
\(984\) | −7.32919e12 | − | 1.26945e13i | −0.249217 | − | 0.431657i | ||||
\(985\) | 8.76019e11 | − | 1.51731e12i | 0.0296518 | − | 0.0513584i | ||||
\(986\) | −3.87429e13 | −1.30541 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.06732e12 | 0.302742 | ||||||||
\(989\) | −3.57862e12 | + | 6.19835e12i | −0.118941 | + | 0.206012i | ||||
\(990\) | −7.20380e12 | − | 1.24774e13i | −0.238344 | − | 0.412823i | ||||
\(991\) | 3.32399e12 | + | 5.75732e12i | 0.109478 | + | 0.189622i | 0.915559 | − | 0.402184i | \(-0.131749\pi\) |
−0.806081 | + | 0.591806i | \(0.798415\pi\) | |||||||
\(992\) | −4.16224e11 | + | 7.20921e11i | −0.0136466 | + | 0.0236366i | ||||
\(993\) | 1.32248e13 | 0.431636 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.34208e12 | 0.269818 | ||||||||
\(996\) | −5.97005e12 | + | 1.03404e13i | −0.192225 | + | 0.332944i | ||||
\(997\) | 2.92310e13 | + | 5.06296e13i | 0.936949 | + | 1.62284i | 0.771122 | + | 0.636688i | \(0.219696\pi\) |
0.165827 | + | 0.986155i | \(0.446971\pi\) | |||||||
\(998\) | −2.09541e12 | − | 3.62936e12i | −0.0668625 | − | 0.115809i | ||||
\(999\) | 3.00064e13 | − | 5.19726e13i | 0.953167 | − | 1.65093i |
(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 | 98.10.c.j.79.1 | 4 | ||
7.2 | even | 3 | 14.10.a.c.1.2 | ✓ | 2 | ||
7.3 | odd | 6 | 98.10.c.h.67.2 | 4 | |||
7.4 | even | 3 | inner | 98.10.c.j.67.1 | 4 | ||
7.5 | odd | 6 | 98.10.a.e.1.1 | 2 | |||
7.6 | odd | 2 | 98.10.c.h.79.2 | 4 | |||
21.2 | odd | 6 | 126.10.a.o.1.1 | 2 | |||
28.23 | odd | 6 | 112.10.a.c.1.1 | 2 | |||
35.2 | odd | 12 | 350.10.c.j.99.1 | 4 | |||
35.9 | even | 6 | 350.10.a.j.1.1 | 2 | |||
35.23 | odd | 12 | 350.10.c.j.99.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.10.a.c.1.2 | ✓ | 2 | 7.2 | even | 3 | ||
98.10.a.e.1.1 | 2 | 7.5 | odd | 6 | |||
98.10.c.h.67.2 | 4 | 7.3 | odd | 6 | |||
98.10.c.h.79.2 | 4 | 7.6 | odd | 2 | |||
98.10.c.j.67.1 | 4 | 7.4 | even | 3 | inner | ||
98.10.c.j.79.1 | 4 | 1.1 | even | 1 | trivial | ||
112.10.a.c.1.1 | 2 | 28.23 | odd | 6 | |||
126.10.a.o.1.1 | 2 | 21.2 | odd | 6 | |||
350.10.a.j.1.1 | 2 | 35.9 | even | 6 | |||
350.10.c.j.99.1 | 4 | 35.2 | odd | 12 | |||
350.10.c.j.99.4 | 4 | 35.23 | odd | 12 |