Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,14,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.57847431615\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 5 x^{9} + 752 x^{8} + 708 x^{7} - 743866 x^{6} + 96647426 x^{5} + 2540283092 x^{4} - 180067834748 x^{3} + 15101451375489 x^{2} + \cdots + 31\!\cdots\!68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{48}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.4 | ||
Root | \(-17.5296 + 43.4857i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.14.b.b.5.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −25.0592 | + | 86.9715i | −0.276867 | + | 0.960908i | ||||
\(3\) | 1746.24i | 1.38298i | 0.722385 | + | 0.691491i | \(0.243046\pi\) | ||||
−0.722385 | + | 0.691491i | \(0.756954\pi\) | |||||||
\(4\) | −6936.08 | − | 4358.86i | −0.846689 | − | 0.532088i | ||||
\(5\) | 64905.5i | 1.85770i | 0.370453 | + | 0.928851i | \(0.379202\pi\) | ||||
−0.370453 | + | 0.928851i | \(0.620798\pi\) | |||||||
\(6\) | −151873. | − | 43759.4i | −1.32892 | − | 0.382902i | ||||
\(7\) | 201238. | 0.646505 | 0.323253 | − | 0.946313i | \(-0.395224\pi\) | ||||
0.323253 | + | 0.946313i | \(0.395224\pi\) | |||||||
\(8\) | 552909. | − | 494011.i | 0.745708 | − | 0.666273i | ||||
\(9\) | −1.45504e6 | −0.912638 | ||||||||
\(10\) | −5.64492e6 | − | 1.62648e6i | −1.78508 | − | 0.514337i | ||||
\(11\) | − | 1.75974e6i | − | 0.299500i | −0.988724 | − | 0.149750i | \(-0.952153\pi\) | ||
0.988724 | − | 0.149750i | \(-0.0478469\pi\) | |||||||
\(12\) | 7.61163e6 | − | 1.21121e7i | 0.735868 | − | 1.17096i | ||||
\(13\) | − | 1.36072e7i | − | 0.781875i | −0.920417 | − | 0.390937i | \(-0.872151\pi\) | ||
0.920417 | − | 0.390937i | \(-0.127849\pi\) | |||||||
\(14\) | −5.04285e6 | + | 1.75019e7i | −0.178996 | + | 0.621232i | ||||
\(15\) | −1.13341e8 | −2.56917 | ||||||||
\(16\) | 2.91095e7 | + | 6.04668e7i | 0.433765 | + | 0.901026i | ||||
\(17\) | 1.14077e8 | 1.14625 | 0.573126 | − | 0.819467i | \(-0.305731\pi\) | ||||
0.573126 | + | 0.819467i | \(0.305731\pi\) | |||||||
\(18\) | 3.64621e7 | − | 1.26547e8i | 0.252680 | − | 0.876962i | ||||
\(19\) | 2.75583e8i | 1.34386i | 0.740614 | + | 0.671931i | \(0.234535\pi\) | ||||
−0.740614 | + | 0.671931i | \(0.765465\pi\) | |||||||
\(20\) | 2.82914e8 | − | 4.50189e8i | 0.988461 | − | 1.57290i | ||||
\(21\) | 3.51410e8i | 0.894105i | ||||||||
\(22\) | 1.53048e8 | + | 4.40977e7i | 0.287792 | + | 0.0829218i | ||||
\(23\) | 1.08842e8 | 0.153308 | 0.0766541 | − | 0.997058i | \(-0.475576\pi\) | ||||
0.0766541 | + | 0.997058i | \(0.475576\pi\) | |||||||
\(24\) | 8.62664e8 | + | 9.65513e8i | 0.921443 | + | 1.03130i | ||||
\(25\) | −2.99201e9 | −2.45106 | ||||||||
\(26\) | 1.18344e9 | + | 3.40985e8i | 0.751310 | + | 0.216475i | ||||
\(27\) | 2.43222e8i | 0.120820i | ||||||||
\(28\) | −1.39580e9 | − | 8.77168e8i | −0.547389 | − | 0.343998i | ||||
\(29\) | − | 1.20078e9i | − | 0.374867i | −0.982277 | − | 0.187433i | \(-0.939983\pi\) | ||
0.982277 | − | 0.187433i | \(-0.0600169\pi\) | |||||||
\(30\) | 2.84022e9 | − | 9.85741e9i | 0.711318 | − | 2.46873i | ||||
\(31\) | −1.80300e9 | −0.364875 | −0.182437 | − | 0.983217i | \(-0.558399\pi\) | ||||
−0.182437 | + | 0.983217i | \(0.558399\pi\) | |||||||
\(32\) | −5.98835e9 | + | 1.01645e9i | −0.985899 | + | 0.167344i | ||||
\(33\) | 3.07294e9 | 0.414203 | ||||||||
\(34\) | −2.85867e9 | + | 9.92145e9i | −0.317360 | + | 1.10144i | ||||
\(35\) | 1.30614e10i | 1.20101i | ||||||||
\(36\) | 1.00923e10 | + | 6.34232e9i | 0.772721 | + | 0.485604i | ||||
\(37\) | − | 1.90075e10i | − | 1.21790i | −0.793207 | − | 0.608952i | \(-0.791590\pi\) | ||
0.793207 | − | 0.608952i | \(-0.208410\pi\) | |||||||
\(38\) | −2.39679e10 | − | 6.90588e9i | −1.29133 | − | 0.372071i | ||||
\(39\) | 2.37615e10 | 1.08132 | ||||||||
\(40\) | 3.20640e10 | + | 3.58868e10i | 1.23774 | + | 1.38530i | ||||
\(41\) | 2.47690e10 | 0.814355 | 0.407177 | − | 0.913349i | \(-0.366513\pi\) | ||||
0.407177 | + | 0.913349i | \(0.366513\pi\) | |||||||
\(42\) | −3.05626e10 | − | 8.80604e9i | −0.859153 | − | 0.247548i | ||||
\(43\) | 1.71033e10i | 0.412606i | 0.978488 | + | 0.206303i | \(0.0661432\pi\) | ||||
−0.978488 | + | 0.206303i | \(0.933857\pi\) | |||||||
\(44\) | −7.67048e9 | + | 1.22057e10i | −0.159360 | + | 0.253583i | ||||
\(45\) | − | 9.44400e10i | − | 1.69541i | ||||||
\(46\) | −2.72749e9 | + | 9.46614e9i | −0.0424460 | + | 0.147315i | ||||
\(47\) | 1.08638e10 | 0.147010 | 0.0735048 | − | 0.997295i | \(-0.476582\pi\) | ||||
0.0735048 | + | 0.997295i | \(0.476582\pi\) | |||||||
\(48\) | −1.05590e11 | + | 5.08322e10i | −1.24610 | + | 0.599889i | ||||
\(49\) | −5.63924e10 | −0.582031 | ||||||||
\(50\) | 7.49774e10 | − | 2.60220e11i | 0.678618 | − | 2.35524i | ||||
\(51\) | 1.99206e11i | 1.58525i | ||||||||
\(52\) | −5.93120e10 | + | 9.43806e10i | −0.416026 | + | 0.662005i | ||||
\(53\) | − | 8.06286e10i | − | 0.499684i | −0.968287 | − | 0.249842i | \(-0.919621\pi\) | ||
0.968287 | − | 0.249842i | \(-0.0803787\pi\) | |||||||
\(54\) | −2.11534e10 | − | 6.09493e9i | −0.116097 | − | 0.0334510i | ||||
\(55\) | 1.14217e11 | 0.556382 | ||||||||
\(56\) | 1.11266e11 | − | 9.94137e10i | 0.482104 | − | 0.430749i | ||||
\(57\) | −4.81235e11 | −1.85854 | ||||||||
\(58\) | 1.04434e11 | + | 3.00906e10i | 0.360213 | + | 0.103788i | ||||
\(59\) | − | 4.80718e10i | − | 0.148372i | −0.997244 | − | 0.0741861i | \(-0.976364\pi\) | ||
0.997244 | − | 0.0741861i | \(-0.0236359\pi\) | |||||||
\(60\) | 7.86140e11 | + | 4.94037e11i | 2.17529 | + | 1.36702i | ||||
\(61\) | 5.26856e10i | 0.130933i | 0.997855 | + | 0.0654663i | \(0.0208535\pi\) | ||||
−0.997855 | + | 0.0654663i | \(0.979147\pi\) | |||||||
\(62\) | 4.51816e10 | − | 1.56809e11i | 0.101022 | − | 0.350611i | ||||
\(63\) | −2.92809e11 | −0.590025 | ||||||||
\(64\) | 6.16612e10 | − | 5.46287e11i | 0.112161 | − | 0.993690i | ||||
\(65\) | 8.83182e11 | 1.45249 | ||||||||
\(66\) | −7.70053e10 | + | 2.67258e11i | −0.114679 | + | 0.398011i | ||||
\(67\) | 1.29726e12i | 1.75202i | 0.482293 | + | 0.876010i | \(0.339804\pi\) | ||||
−0.482293 | + | 0.876010i | \(0.660196\pi\) | |||||||
\(68\) | −7.91247e11 | − | 4.97246e11i | −0.970519 | − | 0.609907i | ||||
\(69\) | 1.90064e11i | 0.212022i | ||||||||
\(70\) | −1.13597e12 | − | 3.27308e11i | −1.15406 | − | 0.332522i | ||||
\(71\) | −1.26160e12 | −1.16881 | −0.584404 | − | 0.811463i | \(-0.698672\pi\) | ||||
−0.584404 | + | 0.811463i | \(0.698672\pi\) | |||||||
\(72\) | −8.04505e11 | + | 7.18806e11i | −0.680562 | + | 0.608066i | ||||
\(73\) | 6.89487e11 | 0.533246 | 0.266623 | − | 0.963801i | \(-0.414092\pi\) | ||||
0.266623 | + | 0.963801i | \(0.414092\pi\) | |||||||
\(74\) | 1.65311e12 | + | 4.76311e11i | 1.17029 | + | 0.337198i | ||||
\(75\) | − | 5.22478e12i | − | 3.38977i | ||||||
\(76\) | 1.20123e12 | − | 1.91147e12i | 0.715052 | − | 1.13783i | ||||
\(77\) | − | 3.54127e11i | − | 0.193628i | ||||||
\(78\) | −5.95443e11 | + | 2.06657e12i | −0.299382 | + | 1.03905i | ||||
\(79\) | 3.83954e12 | 1.77706 | 0.888531 | − | 0.458816i | \(-0.151726\pi\) | ||||
0.888531 | + | 0.458816i | \(0.151726\pi\) | |||||||
\(80\) | −3.92463e12 | + | 1.88936e12i | −1.67384 | + | 0.805806i | ||||
\(81\) | −2.74453e12 | −1.07973 | ||||||||
\(82\) | −6.20691e11 | + | 2.15420e12i | −0.225468 | + | 0.782520i | ||||
\(83\) | 9.29026e11i | 0.311903i | 0.987765 | + | 0.155952i | \(0.0498444\pi\) | ||||
−0.987765 | + | 0.155952i | \(0.950156\pi\) | |||||||
\(84\) | 1.53175e12 | − | 2.43741e12i | 0.475742 | − | 0.757029i | ||||
\(85\) | 7.40422e12i | 2.12940i | ||||||||
\(86\) | −1.48750e12 | − | 4.28595e11i | −0.396476 | − | 0.114237i | ||||
\(87\) | 2.09686e12 | 0.518434 | ||||||||
\(88\) | −8.69334e11 | − | 9.72978e11i | −0.199549 | − | 0.223340i | ||||
\(89\) | 6.60666e12 | 1.40912 | 0.704558 | − | 0.709647i | \(-0.251145\pi\) | ||||
0.704558 | + | 0.709647i | \(0.251145\pi\) | |||||||
\(90\) | 8.21359e12 | + | 2.36659e12i | 1.62913 | + | 0.469403i | ||||
\(91\) | − | 2.73828e12i | − | 0.505486i | ||||||
\(92\) | −7.54936e11 | − | 4.74427e11i | −0.129804 | − | 0.0815734i | ||||
\(93\) | − | 3.14847e12i | − | 0.504615i | ||||||
\(94\) | −2.72238e11 | + | 9.44840e11i | −0.0407021 | + | 0.141263i | ||||
\(95\) | −1.78869e13 | −2.49649 | ||||||||
\(96\) | −1.77496e12 | − | 1.04571e13i | −0.231433 | − | 1.36348i | ||||
\(97\) | 8.12199e11 | 0.0990025 | 0.0495013 | − | 0.998774i | \(-0.484237\pi\) | ||||
0.0495013 | + | 0.998774i | \(0.484237\pi\) | |||||||
\(98\) | 1.41315e12 | − | 4.90453e12i | 0.161145 | − | 0.559278i | ||||
\(99\) | 2.56050e12i | 0.273335i | ||||||||
\(100\) | 2.07528e13 | + | 1.30418e13i | 2.07528 | + | 1.30418i | ||||
\(101\) | 2.94586e12i | 0.276136i | 0.990423 | + | 0.138068i | \(0.0440893\pi\) | ||||
−0.990423 | + | 0.138068i | \(0.955911\pi\) | |||||||
\(102\) | −1.73252e13 | − | 4.99194e12i | −1.52328 | − | 0.438902i | ||||
\(103\) | −2.42353e12 | −0.199989 | −0.0999946 | − | 0.994988i | \(-0.531883\pi\) | ||||
−0.0999946 | + | 0.994988i | \(0.531883\pi\) | |||||||
\(104\) | −6.72212e12 | − | 7.52355e12i | −0.520942 | − | 0.583050i | ||||
\(105\) | −2.28084e13 | −1.66098 | ||||||||
\(106\) | 7.01238e12 | + | 2.02048e12i | 0.480151 | + | 0.138346i | ||||
\(107\) | 1.12502e13i | 0.724715i | 0.932039 | + | 0.362358i | \(0.118028\pi\) | ||||
−0.932039 | + | 0.362358i | \(0.881972\pi\) | |||||||
\(108\) | 1.06017e12 | − | 1.68701e12i | 0.0642867 | − | 0.102297i | ||||
\(109\) | − | 2.03236e13i | − | 1.16072i | −0.814359 | − | 0.580361i | \(-0.802911\pi\) | ||
0.814359 | − | 0.580361i | \(-0.197089\pi\) | |||||||
\(110\) | −2.86218e12 | + | 9.93362e12i | −0.154044 | + | 0.534632i | ||||
\(111\) | 3.31917e13 | 1.68434 | ||||||||
\(112\) | 5.85792e12 | + | 1.21682e13i | 0.280431 | + | 0.582518i | ||||
\(113\) | 5.93927e12 | 0.268363 | 0.134182 | − | 0.990957i | \(-0.457159\pi\) | ||||
0.134182 | + | 0.990957i | \(0.457159\pi\) | |||||||
\(114\) | 1.20593e13 | − | 4.18537e13i | 0.514567 | − | 1.78588i | ||||
\(115\) | 7.06443e12i | 0.284801i | ||||||||
\(116\) | −5.23404e12 | + | 8.32871e12i | −0.199462 | + | 0.317396i | ||||
\(117\) | 1.97990e13i | 0.713569i | ||||||||
\(118\) | 4.18088e12 | + | 1.20464e12i | 0.142572 | + | 0.0410794i | ||||
\(119\) | 2.29566e13 | 0.741058 | ||||||||
\(120\) | −6.26671e13 | + | 5.59916e13i | −1.91585 | + | 1.71177i | ||||
\(121\) | 3.14260e13 | 0.910300 | ||||||||
\(122\) | −4.58214e12 | − | 1.32026e12i | −0.125814 | − | 0.0362509i | ||||
\(123\) | 4.32527e13i | 1.12624i | ||||||||
\(124\) | 1.25057e13 | + | 7.85902e12i | 0.308936 | + | 0.194145i | ||||
\(125\) | − | 1.14968e14i | − | 2.69564i | ||||||
\(126\) | 7.33755e12 | − | 2.54660e13i | 0.163359 | − | 0.566960i | ||||
\(127\) | −2.04322e13 | −0.432106 | −0.216053 | − | 0.976382i | \(-0.569318\pi\) | ||||
−0.216053 | + | 0.976382i | \(0.569318\pi\) | |||||||
\(128\) | 4.59662e13 | + | 1.90523e13i | 0.923791 | + | 0.382897i | ||||
\(129\) | −2.98665e13 | −0.570626 | ||||||||
\(130\) | −2.21318e13 | + | 7.68116e13i | −0.402147 | + | 1.39571i | ||||
\(131\) | − | 8.08054e13i | − | 1.39694i | −0.715641 | − | 0.698469i | \(-0.753865\pi\) | ||
0.715641 | − | 0.698469i | \(-0.246135\pi\) | |||||||
\(132\) | −2.13141e13 | − | 1.33945e13i | −0.350701 | − | 0.220392i | ||||
\(133\) | 5.54577e13i | 0.868813i | ||||||||
\(134\) | −1.12824e14 | − | 3.25081e13i | −1.68353 | − | 0.485077i | ||||
\(135\) | −1.57864e13 | −0.224447 | ||||||||
\(136\) | 6.30742e13 | − | 5.63553e13i | 0.854769 | − | 0.763717i | ||||
\(137\) | −3.37588e12 | −0.0436218 | −0.0218109 | − | 0.999762i | \(-0.506943\pi\) | ||||
−0.0218109 | + | 0.999762i | \(0.506943\pi\) | |||||||
\(138\) | −1.65302e13 | − | 4.76285e12i | −0.203734 | − | 0.0587020i | ||||
\(139\) | 1.16370e14i | 1.36850i | 0.729249 | + | 0.684249i | \(0.239870\pi\) | ||||
−0.729249 | + | 0.684249i | \(0.760130\pi\) | |||||||
\(140\) | 5.69330e13 | − | 9.05951e13i | 0.639045 | − | 1.01689i | ||||
\(141\) | 1.89708e13i | 0.203311i | ||||||||
\(142\) | 3.16147e13 | − | 1.09723e14i | 0.323604 | − | 1.12312i | ||||
\(143\) | −2.39452e13 | −0.234172 | ||||||||
\(144\) | −4.23554e13 | − | 8.79817e13i | −0.395870 | − | 0.822311i | ||||
\(145\) | 7.79373e13 | 0.696391 | ||||||||
\(146\) | −1.72780e13 | + | 5.99657e13i | −0.147638 | + | 0.512400i | ||||
\(147\) | − | 9.84748e13i | − | 0.804938i | ||||||
\(148\) | −8.28510e13 | + | 1.31837e14i | −0.648032 | + | 1.03119i | ||||
\(149\) | 2.16755e14i | 1.62277i | 0.584509 | + | 0.811387i | \(0.301287\pi\) | ||||
−0.584509 | + | 0.811387i | \(0.698713\pi\) | |||||||
\(150\) | 4.54407e14 | + | 1.30929e14i | 3.25726 | + | 0.938516i | ||||
\(151\) | −1.68669e14 | −1.15793 | −0.578967 | − | 0.815351i | \(-0.696544\pi\) | ||||
−0.578967 | + | 0.815351i | \(0.696544\pi\) | |||||||
\(152\) | 1.36141e14 | + | 1.52372e14i | 0.895378 | + | 1.00213i | ||||
\(153\) | −1.65987e14 | −1.04611 | ||||||||
\(154\) | 3.07989e13 | + | 8.87412e12i | 0.186059 | + | 0.0536094i | ||||
\(155\) | − | 1.17024e14i | − | 0.677829i | ||||||
\(156\) | −1.64811e14 | − | 1.03573e14i | −0.915541 | − | 0.575356i | ||||
\(157\) | 2.89792e12i | 0.0154433i | 0.999970 | + | 0.00772163i | \(0.00245789\pi\) | ||||
−0.999970 | + | 0.00772163i | \(0.997542\pi\) | |||||||
\(158\) | −9.62156e13 | + | 3.33930e14i | −0.492010 | + | 1.70759i | ||||
\(159\) | 1.40797e14 | 0.691054 | ||||||||
\(160\) | −6.59729e13 | − | 3.88677e14i | −0.310875 | − | 1.83151i | ||||
\(161\) | 2.19031e13 | 0.0991145 | ||||||||
\(162\) | 6.87756e13 | − | 2.38696e14i | 0.298942 | − | 1.03752i | ||||
\(163\) | − | 1.11885e14i | − | 0.467252i | −0.972327 | − | 0.233626i | \(-0.924941\pi\) | ||
0.972327 | − | 0.233626i | \(-0.0750592\pi\) | |||||||
\(164\) | −1.71800e14 | − | 1.07965e14i | −0.689505 | − | 0.433308i | ||||
\(165\) | 1.99451e14i | 0.769466i | ||||||||
\(166\) | −8.07988e13 | − | 2.32806e13i | −0.299711 | − | 0.0863558i | ||||
\(167\) | 3.97953e14 | 1.41963 | 0.709814 | − | 0.704389i | \(-0.248779\pi\) | ||||
0.709814 | + | 0.704389i | \(0.248779\pi\) | |||||||
\(168\) | 1.73600e14 | + | 1.94298e14i | 0.595718 | + | 0.666741i | ||||
\(169\) | 1.17719e14 | 0.388672 | ||||||||
\(170\) | −6.43956e14 | − | 1.85543e14i | −2.04615 | − | 0.589560i | ||||
\(171\) | − | 4.00985e14i | − | 1.22646i | ||||||
\(172\) | 7.45510e13 | − | 1.18630e14i | 0.219543 | − | 0.349349i | ||||
\(173\) | − | 1.14455e14i | − | 0.324589i | −0.986742 | − | 0.162294i | \(-0.948111\pi\) | ||
0.986742 | − | 0.162294i | \(-0.0518894\pi\) | |||||||
\(174\) | −5.25454e13 | + | 1.82367e14i | −0.143537 | + | 0.498167i | ||||
\(175\) | −6.02106e14 | −1.58462 | ||||||||
\(176\) | 1.06406e14 | − | 5.12252e13i | 0.269857 | − | 0.129913i | ||||
\(177\) | 8.39451e13 | 0.205196 | ||||||||
\(178\) | −1.65557e14 | + | 5.74591e14i | −0.390138 | + | 1.35403i | ||||
\(179\) | 5.75190e14i | 1.30697i | 0.756938 | + | 0.653487i | \(0.226694\pi\) | ||||
−0.756938 | + | 0.653487i | \(0.773306\pi\) | |||||||
\(180\) | −4.11651e14 | + | 6.55043e14i | −0.902107 | + | 1.43549i | ||||
\(181\) | − | 6.03188e14i | − | 1.27509i | −0.770412 | − | 0.637546i | \(-0.779949\pi\) | ||
0.770412 | − | 0.637546i | \(-0.220051\pi\) | |||||||
\(182\) | 2.38153e14 | + | 6.86191e13i | 0.485726 | + | 0.139953i | ||||
\(183\) | −9.20018e13 | −0.181077 | ||||||||
\(184\) | 6.01797e13 | − | 5.37691e13i | 0.114323 | − | 0.102145i | ||||
\(185\) | 1.23369e15 | 2.26250 | ||||||||
\(186\) | 2.73827e14 | + | 7.88980e13i | 0.484889 | + | 0.139711i | ||||
\(187\) | − | 2.00746e14i | − | 0.343303i | ||||||
\(188\) | −7.53521e13 | − | 4.73538e13i | −0.124471 | − | 0.0782220i | ||||
\(189\) | 4.89454e13i | 0.0781106i | ||||||||
\(190\) | 4.48230e14 | − | 1.55565e15i | 0.691197 | − | 2.39890i | ||||
\(191\) | 4.64876e14 | 0.692820 | 0.346410 | − | 0.938083i | \(-0.387401\pi\) | ||||
0.346410 | + | 0.938083i | \(0.387401\pi\) | |||||||
\(192\) | 9.53949e14 | + | 1.07675e14i | 1.37426 | + | 0.155117i | ||||
\(193\) | −1.24010e15 | −1.72717 | −0.863583 | − | 0.504206i | \(-0.831785\pi\) | ||||
−0.863583 | + | 0.504206i | \(0.831785\pi\) | |||||||
\(194\) | −2.03530e13 | + | 7.06382e13i | −0.0274106 | + | 0.0951323i | ||||
\(195\) | 1.54225e15i | 2.00877i | ||||||||
\(196\) | 3.91142e14 | + | 2.45807e14i | 0.492799 | + | 0.309692i | ||||
\(197\) | − | 6.14978e14i | − | 0.749599i | −0.927106 | − | 0.374799i | \(-0.877712\pi\) | ||
0.927106 | − | 0.374799i | \(-0.122288\pi\) | |||||||
\(198\) | −2.22690e14 | − | 6.41639e13i | −0.262650 | − | 0.0756776i | ||||
\(199\) | 7.60323e14 | 0.867867 | 0.433933 | − | 0.900945i | \(-0.357125\pi\) | ||||
0.433933 | + | 0.900945i | \(0.357125\pi\) | |||||||
\(200\) | −1.65431e15 | + | 1.47809e15i | −1.82777 | + | 1.63307i | ||||
\(201\) | −2.26532e15 | −2.42301 | ||||||||
\(202\) | −2.56206e14 | − | 7.38209e13i | −0.265342 | − | 0.0764531i | ||||
\(203\) | − | 2.41643e14i | − | 0.242353i | ||||||
\(204\) | 8.68312e14 | − | 1.38171e15i | 0.843490 | − | 1.34221i | ||||
\(205\) | 1.60764e15i | 1.51283i | ||||||||
\(206\) | 6.07316e13 | − | 2.10778e14i | 0.0553704 | − | 0.192171i | ||||
\(207\) | −1.58369e14 | −0.139915 | ||||||||
\(208\) | 8.22785e14 | − | 3.96099e14i | 0.704490 | − | 0.339150i | ||||
\(209\) | 4.84956e14 | 0.402487 | ||||||||
\(210\) | 5.71560e14 | − | 1.98368e15i | 0.459871 | − | 1.59605i | ||||
\(211\) | − | 4.95425e13i | − | 0.0386493i | −0.999813 | − | 0.0193247i | \(-0.993848\pi\) | ||
0.999813 | − | 0.0193247i | \(-0.00615161\pi\) | |||||||
\(212\) | −3.51449e14 | + | 5.59246e14i | −0.265876 | + | 0.423077i | ||||
\(213\) | − | 2.20306e15i | − | 1.61644i | ||||||
\(214\) | −9.78450e14 | − | 2.81922e14i | −0.696385 | − | 0.200650i | ||||
\(215\) | −1.11010e15 | −0.766499 | ||||||||
\(216\) | 1.20154e14 | + | 1.34480e14i | 0.0804989 | + | 0.0900963i | ||||
\(217\) | −3.62831e14 | −0.235893 | ||||||||
\(218\) | 1.76757e15 | + | 5.09292e14i | 1.11535 | + | 0.321366i | ||||
\(219\) | 1.20401e15i | 0.737469i | ||||||||
\(220\) | −7.92218e14 | − | 4.97856e14i | −0.471083 | − | 0.296044i | ||||
\(221\) | − | 1.55227e15i | − | 0.896225i | ||||||
\(222\) | −8.31755e14 | + | 2.88673e15i | −0.466338 | + | 1.61850i | ||||
\(223\) | −1.52553e15 | −0.830691 | −0.415346 | − | 0.909664i | \(-0.636339\pi\) | ||||
−0.415346 | + | 0.909664i | \(0.636339\pi\) | |||||||
\(224\) | −1.20508e15 | + | 2.04547e14i | −0.637389 | + | 0.108189i | ||||
\(225\) | 4.35350e15 | 2.23693 | ||||||||
\(226\) | −1.48833e14 | + | 5.16547e14i | −0.0743010 | + | 0.257872i | ||||
\(227\) | − | 2.28161e15i | − | 1.10681i | −0.832912 | − | 0.553406i | \(-0.813328\pi\) | ||
0.832912 | − | 0.553406i | \(-0.186672\pi\) | |||||||
\(228\) | 3.33788e15 | + | 2.09764e15i | 1.57360 | + | 0.988904i | ||||
\(229\) | 1.55903e15i | 0.714371i | 0.934033 | + | 0.357185i | \(0.116264\pi\) | ||||
−0.934033 | + | 0.357185i | \(0.883736\pi\) | |||||||
\(230\) | −6.14404e14 | − | 1.77029e14i | −0.273667 | − | 0.0788520i | ||||
\(231\) | 6.18391e14 | 0.267785 | ||||||||
\(232\) | −5.93200e14 | − | 6.63923e14i | −0.249764 | − | 0.279541i | ||||
\(233\) | 2.57854e15 | 1.05575 | 0.527874 | − | 0.849323i | \(-0.322989\pi\) | ||||
0.527874 | + | 0.849323i | \(0.322989\pi\) | |||||||
\(234\) | −1.72195e15 | − | 4.96147e14i | −0.685674 | − | 0.197564i | ||||
\(235\) | 7.05119e14i | 0.273100i | ||||||||
\(236\) | −2.09539e14 | + | 3.33430e14i | −0.0789471 | + | 0.125625i | ||||
\(237\) | 6.70476e15i | 2.45765i | ||||||||
\(238\) | −5.75273e14 | + | 1.99657e15i | −0.205175 | + | 0.712089i | ||||
\(239\) | 4.22444e15 | 1.46616 | 0.733082 | − | 0.680140i | \(-0.238081\pi\) | ||||
0.733082 | + | 0.680140i | \(0.238081\pi\) | |||||||
\(240\) | −3.29929e15 | − | 6.85335e15i | −1.11442 | − | 2.31489i | ||||
\(241\) | −3.67088e15 | −1.20687 | −0.603433 | − | 0.797414i | \(-0.706201\pi\) | ||||
−0.603433 | + | 0.797414i | \(0.706201\pi\) | |||||||
\(242\) | −7.87509e14 | + | 2.73317e15i | −0.252032 | + | 0.874714i | ||||
\(243\) | − | 4.40484e15i | − | 1.37243i | ||||||
\(244\) | 2.29649e14 | − | 3.65431e14i | 0.0696677 | − | 0.110859i | ||||
\(245\) | − | 3.66017e15i | − | 1.08124i | ||||||
\(246\) | −3.76175e15 | − | 1.08388e15i | −1.08221 | − | 0.311818i | ||||
\(247\) | 3.74992e15 | 1.05073 | ||||||||
\(248\) | −9.96893e14 | + | 8.90701e14i | −0.272090 | + | 0.243106i | ||||
\(249\) | −1.62230e15 | −0.431357 | ||||||||
\(250\) | 9.99892e15 | + | 2.88100e15i | 2.59026 | + | 0.746333i | ||||
\(251\) | − | 3.43128e15i | − | 0.866119i | −0.901365 | − | 0.433059i | \(-0.857434\pi\) | ||
0.901365 | − | 0.433059i | \(-0.142566\pi\) | |||||||
\(252\) | 2.03095e15 | + | 1.27631e15i | 0.499568 | + | 0.313945i | ||||
\(253\) | − | 1.91534e14i | − | 0.0459158i | ||||||
\(254\) | 5.12012e14 | − | 1.77701e15i | 0.119636 | − | 0.415214i | ||||
\(255\) | −1.29296e16 | −2.94491 | ||||||||
\(256\) | −2.80888e15 | + | 3.52032e15i | −0.623696 | + | 0.781667i | ||||
\(257\) | −4.41136e15 | −0.955009 | −0.477504 | − | 0.878629i | \(-0.658459\pi\) | ||||
−0.477504 | + | 0.878629i | \(0.658459\pi\) | |||||||
\(258\) | 7.48430e14 | − | 2.59754e15i | 0.157988 | − | 0.548320i | ||||
\(259\) | − | 3.82502e15i | − | 0.787381i | ||||||
\(260\) | −6.12582e15 | − | 3.84967e15i | −1.22981 | − | 0.772853i | ||||
\(261\) | 1.74719e15i | 0.342118i | ||||||||
\(262\) | 7.02776e15 | + | 2.02491e15i | 1.34233 | + | 0.386766i | ||||
\(263\) | 4.10604e15 | 0.765086 | 0.382543 | − | 0.923938i | \(-0.375048\pi\) | ||||
0.382543 | + | 0.923938i | \(0.375048\pi\) | |||||||
\(264\) | 1.69906e15 | − | 1.51807e15i | 0.308875 | − | 0.275972i | ||||
\(265\) | 5.23323e15 | 0.928265 | ||||||||
\(266\) | −4.82324e15 | − | 1.38972e15i | −0.834850 | − | 0.240546i | ||||
\(267\) | 1.15368e16i | 1.94878i | ||||||||
\(268\) | 5.65456e15 | − | 8.99786e15i | 0.932229 | − | 1.48342i | ||||
\(269\) | 7.35764e15i | 1.18399i | 0.805941 | + | 0.591996i | \(0.201660\pi\) | ||||
−0.805941 | + | 0.591996i | \(0.798340\pi\) | |||||||
\(270\) | 3.95594e14 | − | 1.37297e15i | 0.0621421 | − | 0.215673i | ||||
\(271\) | −4.40071e15 | −0.674874 | −0.337437 | − | 0.941348i | \(-0.609560\pi\) | ||||
−0.337437 | + | 0.941348i | \(0.609560\pi\) | |||||||
\(272\) | 3.32072e15 | + | 6.89787e15i | 0.497204 | + | 1.03280i | ||||
\(273\) | 4.78171e15 | 0.699078 | ||||||||
\(274\) | 8.45968e13 | − | 2.93606e14i | 0.0120775 | − | 0.0419166i | ||||
\(275\) | 5.26518e15i | 0.734092i | ||||||||
\(276\) | 8.28465e14 | − | 1.31830e15i | 0.112814 | − | 0.179517i | ||||
\(277\) | 5.52444e15i | 0.734801i | 0.930063 | + | 0.367400i | \(0.119752\pi\) | ||||
−0.930063 | + | 0.367400i | \(0.880248\pi\) | |||||||
\(278\) | −1.01209e16 | − | 2.91613e15i | −1.31500 | − | 0.378892i | ||||
\(279\) | 2.62343e15 | 0.332999 | ||||||||
\(280\) | 6.45249e15 | + | 7.22178e15i | 0.800203 | + | 0.895606i | ||||
\(281\) | −9.11467e15 | −1.10446 | −0.552230 | − | 0.833692i | \(-0.686223\pi\) | ||||
−0.552230 | + | 0.833692i | \(0.686223\pi\) | |||||||
\(282\) | −1.64992e15 | − | 4.75393e14i | −0.195364 | − | 0.0562903i | ||||
\(283\) | − | 6.59039e14i | − | 0.0762604i | −0.999273 | − | 0.0381302i | \(-0.987860\pi\) | ||
0.999273 | − | 0.0381302i | \(-0.0121402\pi\) | |||||||
\(284\) | 8.75057e15 | + | 5.49915e15i | 0.989617 | + | 0.621908i | ||||
\(285\) | − | 3.12348e16i | − | 3.45261i | ||||||
\(286\) | 6.00046e14 | − | 2.08255e15i | 0.0648344 | − | 0.225017i | ||||
\(287\) | 4.98446e15 | 0.526485 | ||||||||
\(288\) | 8.71329e15 | − | 1.47897e15i | 0.899769 | − | 0.152724i | ||||
\(289\) | 3.10898e15 | 0.313894 | ||||||||
\(290\) | −1.95304e15 | + | 6.77832e15i | −0.192808 | + | 0.669168i | ||||
\(291\) | 1.41830e15i | 0.136919i | ||||||||
\(292\) | −4.78233e15 | − | 3.00538e15i | −0.451493 | − | 0.283734i | ||||
\(293\) | − | 1.53744e14i | − | 0.0141958i | −0.999975 | − | 0.00709789i | \(-0.997741\pi\) | ||
0.999975 | − | 0.00709789i | \(-0.00225935\pi\) | |||||||
\(294\) | 8.56450e15 | + | 2.46770e15i | 0.773471 | + | 0.222861i | ||||
\(295\) | 3.12012e15 | 0.275631 | ||||||||
\(296\) | −9.38991e15 | − | 1.05094e16i | −0.811456 | − | 0.908201i | ||||
\(297\) | 4.28008e14 | 0.0361855 | ||||||||
\(298\) | −1.88515e16 | − | 5.43170e15i | −1.55934 | − | 0.449293i | ||||
\(299\) | − | 1.48103e15i | − | 0.119868i | ||||||
\(300\) | −2.27741e16 | + | 3.62395e16i | −1.80366 | + | 2.87008i | ||||
\(301\) | 3.44183e15i | 0.266752i | ||||||||
\(302\) | 4.22669e15 | − | 1.46694e16i | 0.320594 | − | 1.11267i | ||||
\(303\) | −5.14419e15 | −0.381892 | ||||||||
\(304\) | −1.66636e16 | + | 8.02208e15i | −1.21085 | + | 0.582920i | ||||
\(305\) | −3.41958e15 | −0.243234 | ||||||||
\(306\) | 4.15948e15 | − | 1.44361e16i | 0.289634 | − | 1.00522i | ||||
\(307\) | 1.20014e16i | 0.818148i | 0.912501 | + | 0.409074i | \(0.134148\pi\) | ||||
−0.912501 | + | 0.409074i | \(0.865852\pi\) | |||||||
\(308\) | −1.54359e15 | + | 2.45625e15i | −0.103027 | + | 0.163943i | ||||
\(309\) | − | 4.23207e15i | − | 0.276581i | ||||||
\(310\) | 1.01778e16 | + | 2.93253e15i | 0.651331 | + | 0.187669i | ||||
\(311\) | 2.06212e16 | 1.29232 | 0.646162 | − | 0.763200i | \(-0.276373\pi\) | ||||
0.646162 | + | 0.763200i | \(0.276373\pi\) | |||||||
\(312\) | 1.31379e16 | − | 1.17384e16i | 0.806348 | − | 0.720453i | ||||
\(313\) | 1.11034e16 | 0.667448 | 0.333724 | − | 0.942671i | \(-0.391695\pi\) | ||||
0.333724 | + | 0.942671i | \(0.391695\pi\) | |||||||
\(314\) | −2.52036e14 | − | 7.26194e13i | −0.0148395 | − | 0.00427573i | ||||
\(315\) | − | 1.90049e16i | − | 1.09609i | ||||||
\(316\) | −2.66313e16 | − | 1.67360e16i | −1.50462 | − | 0.945554i | ||||
\(317\) | − | 2.68332e16i | − | 1.48521i | −0.669732 | − | 0.742603i | \(-0.733591\pi\) | ||
0.669732 | − | 0.742603i | \(-0.266409\pi\) | |||||||
\(318\) | −3.52825e15 | + | 1.22453e16i | −0.191330 | + | 0.664040i | ||||
\(319\) | −2.11307e15 | −0.112273 | ||||||||
\(320\) | 3.54570e16 | + | 4.00215e15i | 1.84598 | + | 0.208362i | ||||
\(321\) | −1.96457e16 | −1.00227 | ||||||||
\(322\) | −5.48873e14 | + | 1.90494e15i | −0.0274416 | + | 0.0952399i | ||||
\(323\) | 3.14377e16i | 1.54040i | ||||||||
\(324\) | 1.90363e16 | + | 1.19630e16i | 0.914195 | + | 0.574511i | ||||
\(325\) | 4.07130e16i | 1.91642i | ||||||||
\(326\) | 9.73078e15 | + | 2.80374e15i | 0.448986 | + | 0.129367i | ||||
\(327\) | 3.54899e16 | 1.60526 | ||||||||
\(328\) | 1.36950e16 | − | 1.22362e16i | 0.607271 | − | 0.542583i | ||||
\(329\) | 2.18621e15 | 0.0950424 | ||||||||
\(330\) | −1.73465e16 | − | 4.99806e15i | −0.739386 | − | 0.213040i | ||||
\(331\) | − | 3.59991e16i | − | 1.50456i | −0.658844 | − | 0.752280i | \(-0.728954\pi\) | ||
0.658844 | − | 0.752280i | \(-0.271046\pi\) | |||||||
\(332\) | 4.04950e15 | − | 6.44380e15i | 0.165960 | − | 0.264085i | ||||
\(333\) | 2.76566e16i | 1.11151i | ||||||||
\(334\) | −9.97236e15 | + | 3.46105e16i | −0.393048 | + | 1.36413i | ||||
\(335\) | −8.41989e16 | −3.25473 | ||||||||
\(336\) | −2.12486e16 | + | 1.02294e16i | −0.805612 | + | 0.387831i | ||||
\(337\) | 1.47079e16 | 0.546961 | 0.273480 | − | 0.961878i | \(-0.411825\pi\) | ||||
0.273480 | + | 0.961878i | \(0.411825\pi\) | |||||||
\(338\) | −2.94994e15 | + | 1.02382e16i | −0.107610 | + | 0.373478i | ||||
\(339\) | 1.03714e16i | 0.371141i | ||||||||
\(340\) | 3.22740e16 | − | 5.13562e16i | 1.13303 | − | 1.80294i | ||||
\(341\) | 3.17281e15i | 0.109280i | ||||||||
\(342\) | 3.48742e16 | + | 1.00483e16i | 1.17851 | + | 0.339566i | ||||
\(343\) | −3.08460e16 | −1.02279 | ||||||||
\(344\) | 8.44924e15 | + | 9.45658e15i | 0.274908 | + | 0.307684i | ||||
\(345\) | −1.23362e16 | −0.393874 | ||||||||
\(346\) | 9.95428e15 | + | 2.86813e15i | 0.311900 | + | 0.0898679i | ||||
\(347\) | 3.17052e15i | 0.0974964i | 0.998811 | + | 0.0487482i | \(0.0155232\pi\) | ||||
−0.998811 | + | 0.0487482i | \(0.984477\pi\) | |||||||
\(348\) | −1.45440e16 | − | 9.13991e15i | −0.438952 | − | 0.275852i | ||||
\(349\) | − | 2.58614e16i | − | 0.766101i | −0.923727 | − | 0.383051i | \(-0.874873\pi\) | ||
0.923727 | − | 0.383051i | \(-0.125127\pi\) | |||||||
\(350\) | 1.50883e16 | − | 5.23661e16i | 0.438730 | − | 1.52268i | ||||
\(351\) | 3.30957e15 | 0.0944659 | ||||||||
\(352\) | 1.78868e15 | + | 1.05380e16i | 0.0501195 | + | 0.295277i | ||||
\(353\) | 5.29307e16 | 1.45603 | 0.728017 | − | 0.685559i | \(-0.240442\pi\) | ||||
0.728017 | + | 0.685559i | \(0.240442\pi\) | |||||||
\(354\) | −2.10359e15 | + | 7.30083e15i | −0.0568121 | + | 0.197175i | ||||
\(355\) | − | 8.18848e16i | − | 2.17130i | ||||||
\(356\) | −4.58243e16 | − | 2.87975e16i | −1.19308 | − | 0.749773i | ||||
\(357\) | 4.00878e16i | 1.02487i | ||||||||
\(358\) | −5.00251e16 | − | 1.44138e16i | −1.25588 | − | 0.361858i | ||||
\(359\) | 1.99812e16 | 0.492614 | 0.246307 | − | 0.969192i | \(-0.420783\pi\) | ||||
0.246307 | + | 0.969192i | \(0.420783\pi\) | |||||||
\(360\) | −4.66545e16 | − | 5.22168e16i | −1.12961 | − | 1.26428i | ||||
\(361\) | −3.38931e16 | −0.805963 | ||||||||
\(362\) | 5.24601e16 | + | 1.51154e16i | 1.22525 | + | 0.353031i | ||||
\(363\) | 5.48774e16i | 1.25893i | ||||||||
\(364\) | −1.19358e16 | + | 1.89929e16i | −0.268963 | + | 0.427990i | ||||
\(365\) | 4.47514e16i | 0.990612i | ||||||||
\(366\) | 2.30549e15 | − | 8.00153e15i | 0.0501344 | − | 0.173999i | ||||
\(367\) | −6.18176e15 | −0.132063 | −0.0660317 | − | 0.997818i | \(-0.521034\pi\) | ||||
−0.0660317 | + | 0.997818i | \(0.521034\pi\) | |||||||
\(368\) | 3.16833e15 | + | 6.58132e15i | 0.0664997 | + | 0.138135i | ||||
\(369\) | −3.60399e16 | −0.743211 | ||||||||
\(370\) | −3.09152e16 | + | 1.07296e17i | −0.626413 | + | 2.17406i | ||||
\(371\) | − | 1.62255e16i | − | 0.323049i | ||||||
\(372\) | −1.37237e16 | + | 2.18380e16i | −0.268500 | + | 0.427252i | ||||
\(373\) | − | 2.71930e16i | − | 0.522817i | −0.965228 | − | 0.261408i | \(-0.915813\pi\) | ||
0.965228 | − | 0.261408i | \(-0.0841870\pi\) | |||||||
\(374\) | 1.74592e16 | + | 5.03053e15i | 0.329882 | + | 0.0950492i | ||||
\(375\) | 2.00762e17 | 3.72801 | ||||||||
\(376\) | 6.00669e15 | − | 5.36684e15i | 0.109626 | − | 0.0979484i | ||||
\(377\) | −1.63393e16 | −0.293099 | ||||||||
\(378\) | −4.25685e15 | − | 1.22653e15i | −0.0750571 | − | 0.0216263i | ||||
\(379\) | − | 7.60971e16i | − | 1.31890i | −0.751747 | − | 0.659452i | \(-0.770788\pi\) | ||
0.751747 | − | 0.659452i | \(-0.229212\pi\) | |||||||
\(380\) | 1.24065e17 | + | 7.79664e16i | 2.11375 | + | 1.32835i | ||||
\(381\) | − | 3.56795e16i | − | 0.597594i | ||||||
\(382\) | −1.16494e16 | + | 4.04310e16i | −0.191819 | + | 0.665737i | ||||
\(383\) | −1.01040e17 | −1.63568 | −0.817842 | − | 0.575443i | \(-0.804830\pi\) | ||||
−0.817842 | + | 0.575443i | \(0.804830\pi\) | |||||||
\(384\) | −3.32699e16 | + | 8.02681e16i | −0.529539 | + | 1.27759i | ||||
\(385\) | 2.29848e16 | 0.359704 | ||||||||
\(386\) | 3.10759e16 | − | 1.07853e17i | 0.478196 | − | 1.65965i | ||||
\(387\) | − | 2.48860e16i | − | 0.376560i | ||||||
\(388\) | −5.63348e15 | − | 3.54027e15i | −0.0838244 | − | 0.0526780i | ||||
\(389\) | − | 8.29495e16i | − | 1.21378i | −0.794784 | − | 0.606892i | \(-0.792416\pi\) | ||
0.794784 | − | 0.606892i | \(-0.207584\pi\) | |||||||
\(390\) | −1.34132e17 | − | 3.86475e16i | −1.93024 | − | 0.556162i | ||||
\(391\) | 1.24164e16 | 0.175730 | ||||||||
\(392\) | −3.11799e16 | + | 2.78585e16i | −0.434025 | + | 0.387791i | ||||
\(393\) | 1.41106e17 | 1.93194 | ||||||||
\(394\) | 5.34855e16 | + | 1.54108e16i | 0.720296 | + | 0.207539i | ||||
\(395\) | 2.49207e17i | 3.30125i | ||||||||
\(396\) | 1.11609e16 | − | 1.77598e16i | 0.145438 | − | 0.231430i | ||||
\(397\) | 8.74976e16i | 1.12165i | 0.827934 | + | 0.560826i | \(0.189516\pi\) | ||||
−0.827934 | + | 0.560826i | \(0.810484\pi\) | |||||||
\(398\) | −1.90531e16 | + | 6.61264e16i | −0.240284 | + | 0.833940i | ||||
\(399\) | −9.68427e16 | −1.20155 | ||||||||
\(400\) | −8.70960e16 | − | 1.80918e17i | −1.06318 | − | 2.20847i | ||||
\(401\) | −6.49955e16 | −0.780629 | −0.390315 | − | 0.920682i | \(-0.627634\pi\) | ||||
−0.390315 | + | 0.920682i | \(0.627634\pi\) | |||||||
\(402\) | 5.67671e16 | − | 1.97018e17i | 0.670853 | − | 2.32829i | ||||
\(403\) | 2.45337e16i | 0.285286i | ||||||||
\(404\) | 1.28406e16 | − | 2.04327e16i | 0.146929 | − | 0.233802i | ||||
\(405\) | − | 1.78135e17i | − | 2.00582i | ||||||
\(406\) | 2.10160e16 | + | 6.05536e15i | 0.232879 | + | 0.0670997i | ||||
\(407\) | −3.34483e16 | −0.364762 | ||||||||
\(408\) | 9.84101e16 | + | 1.10143e17i | 1.05621 | + | 1.18213i | ||||
\(409\) | 9.07398e16 | 0.958509 | 0.479255 | − | 0.877676i | \(-0.340907\pi\) | ||||
0.479255 | + | 0.877676i | \(0.340907\pi\) | |||||||
\(410\) | −1.39819e17 | − | 4.02862e16i | −1.45369 | − | 0.418853i | ||||
\(411\) | − | 5.89511e15i | − | 0.0603282i | ||||||
\(412\) | 1.68098e16 | + | 1.05638e16i | 0.169329 | + | 0.106412i | ||||
\(413\) | − | 9.67387e15i | − | 0.0959235i | ||||||
\(414\) | 3.96860e15 | − | 1.37736e16i | 0.0387378 | − | 0.134445i | ||||
\(415\) | −6.02988e16 | −0.579424 | ||||||||
\(416\) | 1.38310e16 | + | 8.14847e16i | 0.130842 | + | 0.770849i | ||||
\(417\) | −2.03210e17 | −1.89261 | ||||||||
\(418\) | −1.21526e16 | + | 4.21773e16i | −0.111435 | + | 0.386753i | ||||
\(419\) | − | 2.71651e16i | − | 0.245257i | −0.992453 | − | 0.122628i | \(-0.960868\pi\) | ||
0.992453 | − | 0.122628i | \(-0.0391323\pi\) | |||||||
\(420\) | 1.58201e17 | + | 9.94188e16i | 1.40633 | + | 0.883788i | ||||
\(421\) | 5.61455e16i | 0.491452i | 0.969339 | + | 0.245726i | \(0.0790264\pi\) | ||||
−0.969339 | + | 0.245726i | \(0.920974\pi\) | |||||||
\(422\) | 4.30878e15 | + | 1.24149e15i | 0.0371384 | + | 0.0107007i | ||||
\(423\) | −1.58073e16 | −0.134166 | ||||||||
\(424\) | −3.98314e16 | − | 4.45803e16i | −0.332926 | − | 0.372619i | ||||
\(425\) | −3.41320e17 | −2.80953 | ||||||||
\(426\) | 1.91604e17 | + | 5.52069e16i | 1.55325 | + | 0.447539i | ||||
\(427\) | 1.06023e16i | 0.0846486i | ||||||||
\(428\) | 4.90383e16 | − | 7.80326e16i | 0.385612 | − | 0.613608i | ||||
\(429\) | − | 4.18141e16i | − | 0.323855i | ||||||
\(430\) | 2.78181e16 | − | 9.65469e16i | 0.212218 | − | 0.736535i | ||||
\(431\) | 2.41184e17 | 1.81237 | 0.906183 | − | 0.422886i | \(-0.138983\pi\) | ||||
0.906183 | + | 0.422886i | \(0.138983\pi\) | |||||||
\(432\) | −1.47069e16 | + | 7.08006e15i | −0.108862 | + | 0.0524074i | ||||
\(433\) | 1.95363e17 | 1.42452 | 0.712262 | − | 0.701913i | \(-0.247671\pi\) | ||||
0.712262 | + | 0.701913i | \(0.247671\pi\) | |||||||
\(434\) | 9.09224e15 | − | 3.15559e16i | 0.0653112 | − | 0.226672i | ||||
\(435\) | 1.36097e17i | 0.963096i | ||||||||
\(436\) | −8.85878e16 | + | 1.40966e17i | −0.617607 | + | 0.982771i | ||||
\(437\) | 2.99950e16i | 0.206025i | ||||||||
\(438\) | −1.04715e17 | − | 3.01715e16i | −0.708640 | − | 0.204181i | ||||
\(439\) | 2.53786e17 | 1.69219 | 0.846093 | − | 0.533035i | \(-0.178948\pi\) | ||||
0.846093 | + | 0.533035i | \(0.178948\pi\) | |||||||
\(440\) | 6.31516e16 | − | 5.64245e16i | 0.414899 | − | 0.370702i | ||||
\(441\) | 8.20532e16 | 0.531184 | ||||||||
\(442\) | 1.35003e17 | + | 3.88986e16i | 0.861190 | + | 0.248135i | ||||
\(443\) | − | 2.11073e17i | − | 1.32681i | −0.748260 | − | 0.663406i | \(-0.769110\pi\) | ||
0.748260 | − | 0.663406i | \(-0.230890\pi\) | |||||||
\(444\) | −2.30220e17 | − | 1.44678e17i | −1.42611 | − | 0.896216i | ||||
\(445\) | 4.28808e17i | 2.61772i | ||||||||
\(446\) | 3.82285e16 | − | 1.32678e17i | 0.229991 | − | 0.798218i | ||||
\(447\) | −3.78507e17 | −2.24427 | ||||||||
\(448\) | 1.24086e16 | − | 1.09934e17i | 0.0725127 | − | 0.642426i | ||||
\(449\) | 1.85856e17 | 1.07047 | 0.535236 | − | 0.844703i | \(-0.320223\pi\) | ||||
0.535236 | + | 0.844703i | \(0.320223\pi\) | |||||||
\(450\) | −1.09095e17 | + | 3.78630e17i | −0.619332 | + | 2.14948i | ||||
\(451\) | − | 4.35871e16i | − | 0.243899i | ||||||
\(452\) | −4.11952e16 | − | 2.58885e16i | −0.227220 | − | 0.142793i | ||||
\(453\) | − | 2.94536e17i | − | 1.60140i | ||||||
\(454\) | 1.98435e17 | + | 5.71753e16i | 1.06354 | + | 0.306440i | ||||
\(455\) | 1.77730e17 | 0.939043 | ||||||||
\(456\) | −2.66079e17 | + | 2.37736e17i | −1.38592 | + | 1.23829i | ||||
\(457\) | 3.69775e16 | 0.189882 | 0.0949408 | − | 0.995483i | \(-0.469734\pi\) | ||||
0.0949408 | + | 0.995483i | \(0.469734\pi\) | |||||||
\(458\) | −1.35591e17 | − | 3.90680e16i | −0.686445 | − | 0.197786i | ||||
\(459\) | 2.77460e16i | 0.138490i | ||||||||
\(460\) | 3.07929e16 | − | 4.89994e16i | 0.151539 | − | 0.241138i | ||||
\(461\) | − | 2.06980e17i | − | 1.00432i | −0.864774 | − | 0.502161i | \(-0.832538\pi\) | ||
0.864774 | − | 0.502161i | \(-0.167462\pi\) | |||||||
\(462\) | −1.54964e16 | + | 5.37824e16i | −0.0741408 | + | 0.257316i | ||||
\(463\) | −3.70448e17 | −1.74764 | −0.873819 | − | 0.486252i | \(-0.838364\pi\) | ||||
−0.873819 | + | 0.486252i | \(0.838364\pi\) | |||||||
\(464\) | 7.26075e16 | − | 3.49541e16i | 0.337765 | − | 0.162604i | ||||
\(465\) | 2.04353e17 | 0.937425 | ||||||||
\(466\) | −6.46160e16 | + | 2.24259e17i | −0.292302 | + | 1.01448i | ||||
\(467\) | − | 2.35711e16i | − | 0.105153i | −0.998617 | − | 0.0525763i | \(-0.983257\pi\) | ||
0.998617 | − | 0.0525763i | \(-0.0167433\pi\) | |||||||
\(468\) | 8.63013e16 | − | 1.37328e17i | 0.379681 | − | 0.604171i | ||||
\(469\) | 2.61057e17i | 1.13269i | ||||||||
\(470\) | −6.13253e16 | − | 1.76697e16i | −0.262424 | − | 0.0756124i | ||||
\(471\) | −5.06047e15 | −0.0213577 | ||||||||
\(472\) | −2.37480e16 | − | 2.65794e16i | −0.0988564 | − | 0.110642i | ||||
\(473\) | 3.00975e16 | 0.123576 | ||||||||
\(474\) | −5.83123e17 | − | 1.68016e17i | −2.36157 | − | 0.680441i | ||||
\(475\) | − | 8.24549e17i | − | 3.29388i | ||||||
\(476\) | −1.59229e17 | − | 1.00065e17i | −0.627446 | − | 0.394308i | ||||
\(477\) | 1.17318e17i | 0.456031i | ||||||||
\(478\) | −1.05861e17 | + | 3.67406e17i | −0.405933 | + | 1.40885i | ||||
\(479\) | 1.66653e17 | 0.630424 | 0.315212 | − | 0.949021i | \(-0.397924\pi\) | ||||
0.315212 | + | 0.949021i | \(0.397924\pi\) | |||||||
\(480\) | 6.78723e17 | − | 1.15205e17i | 2.53294 | − | 0.429934i | ||||
\(481\) | −2.58639e17 | −0.952248 | ||||||||
\(482\) | 9.19890e16 | − | 3.19261e17i | 0.334141 | − | 1.15969i | ||||
\(483\) | 3.82481e16i | 0.137074i | ||||||||
\(484\) | −2.17973e17 | − | 1.36982e17i | −0.770741 | − | 0.484359i | ||||
\(485\) | 5.27162e16i | 0.183917i | ||||||||
\(486\) | 3.83095e17 | + | 1.10382e17i | 1.31878 | + | 0.379980i | ||||
\(487\) | 1.46517e17 | 0.497681 | 0.248841 | − | 0.968544i | \(-0.419950\pi\) | ||||
0.248841 | + | 0.968544i | \(0.419950\pi\) | |||||||
\(488\) | 2.60273e16 | + | 2.91303e16i | 0.0872369 | + | 0.0976375i | ||||
\(489\) | 1.95378e17 | 0.646201 | ||||||||
\(490\) | 3.18331e17 | + | 9.17209e16i | 1.03897 | + | 0.299360i | ||||
\(491\) | 4.34559e17i | 1.39965i | 0.714315 | + | 0.699825i | \(0.246739\pi\) | ||||
−0.714315 | + | 0.699825i | \(0.753261\pi\) | |||||||
\(492\) | 1.88533e17 | − | 3.00004e17i | 0.599258 | − | 0.953573i | ||||
\(493\) | − | 1.36982e17i | − | 0.429692i | ||||||
\(494\) | −9.39698e16 | + | 3.26136e17i | −0.290913 | + | 1.00966i | ||||
\(495\) | −1.66190e17 | −0.507776 | ||||||||
\(496\) | −5.24843e16 | − | 1.09021e17i | −0.158270 | − | 0.328762i | ||||
\(497\) | −2.53882e17 | −0.755640 | ||||||||
\(498\) | 4.06536e16 | − | 1.41094e17i | 0.119429 | − | 0.414494i | ||||
\(499\) | 4.52968e17i | 1.31345i | 0.754129 | + | 0.656726i | \(0.228059\pi\) | ||||
−0.754129 | + | 0.656726i | \(0.771941\pi\) | |||||||
\(500\) | −5.01129e17 | + | 7.97425e17i | −1.43431 | + | 2.28236i | ||||
\(501\) | 6.94922e17i | 1.96332i | ||||||||
\(502\) | 2.98424e17 | + | 8.59851e16i | 0.832261 | + | 0.239800i | ||||
\(503\) | −1.03763e17 | −0.285662 | −0.142831 | − | 0.989747i | \(-0.545620\pi\) | ||||
−0.142831 | + | 0.989747i | \(0.545620\pi\) | |||||||
\(504\) | −1.61897e17 | + | 1.44651e17i | −0.439987 | + | 0.393118i | ||||
\(505\) | −1.91203e17 | −0.512979 | ||||||||
\(506\) | 1.66580e16 | + | 4.79968e15i | 0.0441209 | + | 0.0127126i | ||||
\(507\) | 2.05566e17i | 0.537526i | ||||||||
\(508\) | 1.41719e17 | + | 8.90610e16i | 0.365859 | + | 0.229918i | ||||
\(509\) | − | 2.43253e17i | − | 0.620000i | −0.950737 | − | 0.310000i | \(-0.899671\pi\) | ||
0.950737 | − | 0.310000i | \(-0.100329\pi\) | |||||||
\(510\) | 3.24004e17 | − | 1.12450e18i | 0.815350 | − | 2.82979i | ||||
\(511\) | 1.38751e17 | 0.344746 | ||||||||
\(512\) | −2.35779e17 | − | 3.32508e17i | −0.578429 | − | 0.815733i | ||||
\(513\) | −6.70279e16 | −0.162365 | ||||||||
\(514\) | 1.10545e17 | − | 3.83663e17i | 0.264411 | − | 0.917676i | ||||
\(515\) | − | 1.57300e17i | − | 0.371520i | ||||||
\(516\) | 2.07157e17 | + | 1.30184e17i | 0.483143 | + | 0.303623i | ||||
\(517\) | − | 1.91175e16i | − | 0.0440294i | ||||||
\(518\) | 3.32668e17 | + | 9.58518e16i | 0.756601 | + | 0.218000i | ||||
\(519\) | 1.99865e17 | 0.448900 | ||||||||
\(520\) | 4.88319e17 | − | 4.36302e17i | 1.08313 | − | 0.967755i | ||||
\(521\) | 2.48301e17 | 0.543917 | 0.271959 | − | 0.962309i | \(-0.412329\pi\) | ||||
0.271959 | + | 0.962309i | \(0.412329\pi\) | |||||||
\(522\) | −1.51955e17 | − | 4.37830e16i | −0.328744 | − | 0.0947212i | ||||
\(523\) | − | 6.94419e16i | − | 0.148375i | −0.997244 | − | 0.0741875i | \(-0.976364\pi\) | ||
0.997244 | − | 0.0741875i | \(-0.0236363\pi\) | |||||||
\(524\) | −3.52220e17 | + | 5.60472e17i | −0.743293 | + | 1.18277i | ||||
\(525\) | − | 1.05142e18i | − | 2.19150i | ||||||
\(526\) | −1.02894e17 | + | 3.57108e17i | −0.211827 | + | 0.735178i | ||||
\(527\) | −2.05680e17 | −0.418238 | ||||||||
\(528\) | 8.94516e16 | + | 1.85811e17i | 0.179667 | + | 0.373208i | ||||
\(529\) | −4.92190e17 | −0.976497 | ||||||||
\(530\) | −1.31140e17 | + | 4.55142e17i | −0.257006 | + | 0.891977i | ||||
\(531\) | 6.99465e16i | 0.135410i | ||||||||
\(532\) | 2.41733e17 | − | 3.84659e17i | 0.462285 | − | 0.735615i | ||||
\(533\) | − | 3.37037e17i | − | 0.636724i | ||||||
\(534\) | −1.00337e18 | − | 2.89103e17i | −1.87260 | − | 0.539553i | ||||
\(535\) | −7.30202e17 | −1.34631 | ||||||||
\(536\) | 6.40859e17 | + | 7.17264e17i | 1.16732 | + | 1.30650i | ||||
\(537\) | −1.00442e18 | −1.80752 | ||||||||
\(538\) | −6.39904e17 | − | 1.84376e17i | −1.13771 | − | 0.327808i | ||||
\(539\) | 9.92362e16i | 0.174318i | ||||||||
\(540\) | 1.09496e17 | + | 6.88109e16i | 0.190037 | + | 0.119426i | ||||
\(541\) | 1.98249e17i | 0.339961i | 0.985447 | + | 0.169981i | \(0.0543705\pi\) | ||||
−0.985447 | + | 0.169981i | \(0.945629\pi\) | |||||||
\(542\) | 1.10278e17 | − | 3.82737e17i | 0.186850 | − | 0.648492i | ||||
\(543\) | 1.05331e18 | 1.76343 | ||||||||
\(544\) | −6.83133e17 | + | 1.15953e17i | −1.13009 | + | 0.191818i | ||||
\(545\) | 1.31911e18 | 2.15628 | ||||||||
\(546\) | −1.19826e17 | + | 4.15872e17i | −0.193552 | + | 0.671750i | ||||
\(547\) | − | 1.76150e17i | − | 0.281168i | −0.990069 | − | 0.140584i | \(-0.955102\pi\) | ||
0.990069 | − | 0.140584i | \(-0.0448980\pi\) | |||||||
\(548\) | 2.34154e16 | + | 1.47150e16i | 0.0369341 | + | 0.0232106i | ||||
\(549\) | − | 7.66596e16i | − | 0.119494i | ||||||
\(550\) | −4.57920e17 | − | 1.31941e17i | −0.705395 | − | 0.203246i | ||||
\(551\) | 3.30915e17 | 0.503769 | ||||||||
\(552\) | 9.38940e16 | + | 1.05088e17i | 0.141265 | + | 0.158107i | ||||
\(553\) | 7.72660e17 | 1.14888 | ||||||||
\(554\) | −4.80468e17 | − | 1.38438e17i | −0.706076 | − | 0.203442i | ||||
\(555\) | 2.15432e18i | 3.12900i | ||||||||
\(556\) | 5.07240e17 | − | 8.07150e17i | 0.728161 | − | 1.15869i | ||||
\(557\) | − | 8.23416e17i | − | 1.16832i | −0.811640 | − | 0.584158i | \(-0.801425\pi\) | ||
0.811640 | − | 0.584158i | \(-0.198575\pi\) | |||||||
\(558\) | −6.57410e16 | + | 2.28164e17i | −0.0921964 | + | 0.319981i | ||||
\(559\) | 2.32728e17 | 0.322606 | ||||||||
\(560\) | −7.89783e17 | + | 3.80211e17i | −1.08215 | + | 0.520958i | ||||
\(561\) | 3.50552e17 | 0.474781 | ||||||||
\(562\) | 2.28406e17 | − | 7.92716e17i | 0.305788 | − | 1.06128i | ||||
\(563\) | − | 6.70494e17i | − | 0.887341i | −0.896190 | − | 0.443670i | \(-0.853676\pi\) | ||
0.896190 | − | 0.443670i | \(-0.146324\pi\) | |||||||
\(564\) | 8.26912e16 | − | 1.31583e17i | 0.108180 | − | 0.172142i | ||||
\(565\) | 3.85491e17i | 0.498539i | ||||||||
\(566\) | 5.73176e16 | + | 1.65150e16i | 0.0732792 | + | 0.0211140i | ||||
\(567\) | −5.52303e17 | −0.698051 | ||||||||
\(568\) | −6.97551e17 | + | 6.23246e17i | −0.871589 | + | 0.778745i | ||||
\(569\) | 1.03780e18 | 1.28198 | 0.640991 | − | 0.767548i | \(-0.278524\pi\) | ||||
0.640991 | + | 0.767548i | \(0.278524\pi\) | |||||||
\(570\) | 2.71654e18 | + | 7.82717e17i | 3.31764 | + | 0.955913i | ||||
\(571\) | − | 1.11651e18i | − | 1.34812i | −0.738676 | − | 0.674061i | \(-0.764549\pi\) | ||
0.738676 | − | 0.674061i | \(-0.235451\pi\) | |||||||
\(572\) | 1.66086e17 | + | 1.04374e17i | 0.198271 | + | 0.124600i | ||||
\(573\) | 8.11787e17i | 0.958158i | ||||||||
\(574\) | −1.24906e17 | + | 4.33506e17i | −0.145766 | + | 0.505904i | ||||
\(575\) | −3.25657e17 | −0.375767 | ||||||||
\(576\) | −8.97195e16 | + | 7.94869e17i | −0.102362 | + | 0.906879i | ||||
\(577\) | −1.29130e18 | −1.45675 | −0.728373 | − | 0.685181i | \(-0.759723\pi\) | ||||
−0.728373 | + | 0.685181i | \(0.759723\pi\) | |||||||
\(578\) | −7.79085e16 | + | 2.70393e17i | −0.0869068 | + | 0.301623i | ||||
\(579\) | − | 2.16552e18i | − | 2.38864i | ||||||
\(580\) | −5.40579e17 | − | 3.39718e17i | −0.589627 | − | 0.370541i | ||||
\(581\) | 1.86955e17i | 0.201647i | ||||||||
\(582\) | −1.23351e17 | − | 3.55413e16i | −0.131566 | − | 0.0379083i | ||||
\(583\) | −1.41886e17 | −0.149656 | ||||||||
\(584\) | 3.81223e17 | − | 3.40614e17i | 0.397646 | − | 0.355287i | ||||
\(585\) | −1.28507e18 | −1.32560 | ||||||||
\(586\) | 1.33714e16 | + | 3.85270e15i | 0.0136408 | + | 0.00393034i | ||||
\(587\) | 1.10482e18i | 1.11466i | 0.830291 | + | 0.557331i | \(0.188174\pi\) | ||||
−0.830291 | + | 0.557331i | \(0.811826\pi\) | |||||||
\(588\) | −4.29238e17 | + | 6.83029e17i | −0.428298 | + | 0.681532i | ||||
\(589\) | − | 4.96876e17i | − | 0.490341i | ||||||
\(590\) | −7.81877e16 | + | 2.71362e17i | −0.0763133 | + | 0.264857i | ||||
\(591\) | 1.07390e18 | 1.03668 | ||||||||
\(592\) | 1.14932e18 | − | 5.53297e17i | 1.09736 | − | 0.528284i | ||||
\(593\) | −1.43752e18 | −1.35756 | −0.678779 | − | 0.734342i | \(-0.737491\pi\) | ||||
−0.678779 | + | 0.734342i | \(0.737491\pi\) | |||||||
\(594\) | −1.07255e16 | + | 3.72245e16i | −0.0100186 | + | 0.0347710i | ||||
\(595\) | 1.49001e18i | 1.37667i | ||||||||
\(596\) | 9.44805e17 | − | 1.50343e18i | 0.863459 | − | 1.37399i | ||||
\(597\) | 1.32771e18i | 1.20024i | ||||||||
\(598\) | 1.28808e17 | + | 3.71135e16i | 0.115182 | + | 0.0331874i | ||||
\(599\) | 6.32077e17 | 0.559107 | 0.279554 | − | 0.960130i | \(-0.409813\pi\) | ||||
0.279554 | + | 0.960130i | \(0.409813\pi\) | |||||||
\(600\) | −2.58110e18 | − | 2.88883e18i | −2.25851 | − | 2.52778i | ||||
\(601\) | 3.05117e17 | 0.264109 | 0.132054 | − | 0.991242i | \(-0.457843\pi\) | ||||
0.132054 | + | 0.991242i | \(0.457843\pi\) | |||||||
\(602\) | −2.99341e17 | − | 8.62494e16i | −0.256324 | − | 0.0738549i | ||||
\(603\) | − | 1.88756e18i | − | 1.59896i | ||||||
\(604\) | 1.16990e18 | + | 7.35203e17i | 0.980410 | + | 0.616123i | ||||
\(605\) | 2.03972e18i | 1.69107i | ||||||||
\(606\) | 1.28909e17 | − | 4.47398e17i | 0.105733 | − | 0.366963i | ||||
\(607\) | −1.57496e18 | −1.27804 | −0.639018 | − | 0.769192i | \(-0.720659\pi\) | ||||
−0.639018 | + | 0.769192i | \(0.720659\pi\) | |||||||
\(608\) | −2.80115e17 | − | 1.65029e18i | −0.224887 | − | 1.32491i | ||||
\(609\) | 4.21966e17 | 0.335170 | ||||||||
\(610\) | 8.56918e16 | − | 2.97406e17i | 0.0673435 | − | 0.233725i | ||||
\(611\) | − | 1.47826e17i | − | 0.114943i | ||||||
\(612\) | 1.15130e18 | + | 7.23513e17i | 0.885733 | + | 0.556624i | ||||
\(613\) | 1.32874e17i | 0.101146i | 0.998720 | + | 0.0505728i | \(0.0161047\pi\) | ||||
−0.998720 | + | 0.0505728i | \(0.983895\pi\) | |||||||
\(614\) | −1.04378e18 | − | 3.00744e17i | −0.786165 | − | 0.226518i | ||||
\(615\) | −2.80734e18 | −2.09221 | ||||||||
\(616\) | −1.74943e17 | − | 1.95800e17i | −0.129009 | − | 0.144390i | ||||
\(617\) | −1.56261e17 | −0.114024 | −0.0570121 | − | 0.998373i | \(-0.518157\pi\) | ||||
−0.0570121 | + | 0.998373i | \(0.518157\pi\) | |||||||
\(618\) | 3.68070e17 | + | 1.06052e17i | 0.265769 | + | 0.0765763i | ||||
\(619\) | − | 9.31102e17i | − | 0.665286i | −0.943053 | − | 0.332643i | \(-0.892060\pi\) | ||
0.943053 | − | 0.332643i | \(-0.107940\pi\) | |||||||
\(620\) | −5.10093e17 | + | 8.11690e17i | −0.360665 | + | 0.573910i | ||||
\(621\) | 2.64727e16i | 0.0185227i | ||||||||
\(622\) | −5.16750e17 | + | 1.79346e18i | −0.357802 | + | 1.24180i | ||||
\(623\) | 1.32951e18 | 0.911001 | ||||||||
\(624\) | 6.91684e17 | + | 1.43678e18i | 0.469038 | + | 0.974296i | ||||
\(625\) | 3.80967e18 | 2.55663 | ||||||||
\(626\) | −2.78242e17 | + | 9.65678e17i | −0.184794 | + | 0.641356i | ||||
\(627\) | 8.46851e17i | 0.556632i | ||||||||
\(628\) | 1.26316e16 | − | 2.01002e16i | 0.00821717 | − | 0.0130756i | ||||
\(629\) | − | 2.16831e18i | − | 1.39602i | ||||||
\(630\) | 1.65288e18 | + | 4.76247e17i | 1.05324 | + | 0.303472i | ||||
\(631\) | −1.97753e18 | −1.24719 | −0.623594 | − | 0.781748i | \(-0.714328\pi\) | ||||
−0.623594 | + | 0.781748i | \(0.714328\pi\) | |||||||
\(632\) | 2.12292e18 | − | 1.89678e18i | 1.32517 | − | 1.18401i | ||||
\(633\) | 8.65132e16 | 0.0534513 | ||||||||
\(634\) | 2.33372e18 | + | 6.72417e17i | 1.42715 | + | 0.411205i | ||||
\(635\) | − | 1.32616e18i | − | 0.802724i | ||||||
\(636\) | −9.76579e17 | − | 6.13715e17i | −0.585108 | − | 0.367702i | ||||
\(637\) | 7.67343e17i | 0.455075i | ||||||||
\(638\) | 5.29517e16 | − | 1.83777e17i | 0.0310846 | − | 0.107884i | ||||
\(639\) | 1.83568e18 | 1.06670 | ||||||||
\(640\) | −1.23660e18 | + | 2.98346e18i | −0.711308 | + | 1.71613i | ||||
\(641\) | 3.46004e17 | 0.197017 | 0.0985084 | − | 0.995136i | \(-0.468593\pi\) | ||||
0.0985084 | + | 0.995136i | \(0.468593\pi\) | |||||||
\(642\) | 4.92304e17 | − | 1.70861e18i | 0.277495 | − | 0.963087i | ||||
\(643\) | 3.31505e18i | 1.84977i | 0.380241 | + | 0.924887i | \(0.375841\pi\) | ||||
−0.380241 | + | 0.924887i | \(0.624159\pi\) | |||||||
\(644\) | −1.51922e17 | − | 9.54726e16i | −0.0839192 | − | 0.0527376i | ||||
\(645\) | − | 1.93850e18i | − | 1.06005i | ||||||
\(646\) | −2.73418e18 | − | 7.87803e17i | −1.48019 | − | 0.426487i | ||||
\(647\) | −1.25070e18 | −0.670309 | −0.335155 | − | 0.942163i | \(-0.608789\pi\) | ||||
−0.335155 | + | 0.942163i | \(0.608789\pi\) | |||||||
\(648\) | −1.51747e18 | + | 1.35583e18i | −0.805163 | + | 0.719395i | ||||
\(649\) | −8.45941e16 | −0.0444375 | ||||||||
\(650\) | −3.54087e18 | − | 1.02023e18i | −1.84150 | − | 0.530594i | ||||
\(651\) | − | 6.33591e17i | − | 0.326236i | ||||||
\(652\) | −4.87690e17 | + | 7.76041e17i | −0.248619 | + | 0.395617i | ||||
\(653\) | 3.28489e18i | 1.65800i | 0.559248 | + | 0.829000i | \(0.311090\pi\) | ||||
−0.559248 | + | 0.829000i | \(0.688910\pi\) | |||||||
\(654\) | −8.89348e17 | + | 3.08661e18i | −0.444443 | + | 1.54251i | ||||
\(655\) | 5.24471e18 | 2.59509 | ||||||||
\(656\) | 7.21013e17 | + | 1.49770e18i | 0.353239 | + | 0.733755i | ||||
\(657\) | −1.00323e18 | −0.486660 | ||||||||
\(658\) | −5.47845e16 | + | 1.90137e17i | −0.0263141 | + | 0.0913271i | ||||
\(659\) | − | 7.72337e17i | − | 0.367326i | −0.982989 | − | 0.183663i | \(-0.941204\pi\) | ||
0.982989 | − | 0.183663i | \(-0.0587955\pi\) | |||||||
\(660\) | 8.69378e17 | − | 1.38340e18i | 0.409424 | − | 0.651499i | ||||
\(661\) | − | 3.52021e18i | − | 1.64157i | −0.571238 | − | 0.820784i | \(-0.693537\pi\) | ||
0.571238 | − | 0.820784i | \(-0.306463\pi\) | |||||||
\(662\) | 3.13089e18 | + | 9.02107e17i | 1.44574 | + | 0.416563i | ||||
\(663\) | 2.71064e18 | 1.23946 | ||||||||
\(664\) | 4.58949e17 | + | 5.13667e17i | 0.207813 | + | 0.232589i | ||||
\(665\) | −3.59951e18 | −1.61400 | ||||||||
\(666\) | −2.40534e18 | − | 6.93052e17i | −1.06805 | − | 0.307739i | ||||
\(667\) | − | 1.30695e17i | − | 0.0574701i | ||||||
\(668\) | −2.76023e18 | − | 1.73462e18i | −1.20198 | − | 0.755367i | ||||
\(669\) | − | 2.66395e18i | − | 1.14883i | ||||||
\(670\) | 2.10995e18 | − | 7.32291e18i | 0.901129 | − | 3.12750i | ||||
\(671\) | 9.27131e16 | 0.0392143 | ||||||||
\(672\) | −3.57189e17 | − | 2.10436e18i | −0.149623 | − | 0.881497i | ||||
\(673\) | −3.14223e18 | −1.30359 | −0.651793 | − | 0.758397i | \(-0.725983\pi\) | ||||
−0.651793 | + | 0.758397i | \(0.725983\pi\) | |||||||
\(674\) | −3.68568e17 | + | 1.27917e18i | −0.151436 | + | 0.525579i | ||||
\(675\) | − | 7.27723e17i | − | 0.296136i | ||||||
\(676\) | −8.16508e17 | − | 5.13121e17i | −0.329084 | − | 0.206808i | ||||
\(677\) | 6.57394e17i | 0.262421i | 0.991354 | + | 0.131211i | \(0.0418865\pi\) | ||||
−0.991354 | + | 0.131211i | \(0.958114\pi\) | |||||||
\(678\) | −9.02016e17 | − | 2.59899e17i | −0.356633 | − | 0.102757i | ||||
\(679\) | 1.63445e17 | 0.0640057 | ||||||||
\(680\) | 3.65777e18 | + | 4.09386e18i | 1.41876 | + | 1.58791i | ||||
\(681\) | 3.98425e18 | 1.53070 | ||||||||
\(682\) | −2.75944e17 | − | 7.95080e16i | −0.105008 | − | 0.0302561i | ||||
\(683\) | 8.10111e17i | 0.305358i | 0.988276 | + | 0.152679i | \(0.0487901\pi\) | ||||
−0.988276 | + | 0.152679i | \(0.951210\pi\) | |||||||
\(684\) | −1.74784e18 | + | 2.78126e18i | −0.652584 | + | 1.03843i | ||||
\(685\) | − | 2.19113e17i | − | 0.0810364i | ||||||
\(686\) | 7.72975e17 | − | 2.68272e18i | 0.283177 | − | 0.982809i | ||||
\(687\) | −2.72244e18 | −0.987962 | ||||||||
\(688\) | −1.03418e18 | + | 4.97869e17i | −0.371769 | + | 0.178974i | ||||
\(689\) | −1.09713e18 | −0.390691 | ||||||||
\(690\) | 3.09135e17 | − | 1.07290e18i | 0.109051 | − | 0.378477i | ||||
\(691\) | 4.18606e18i | 1.46284i | 0.681925 | + | 0.731422i | \(0.261143\pi\) | ||||
−0.681925 | + | 0.731422i | \(0.738857\pi\) | |||||||
\(692\) | −4.98892e17 | + | 7.93865e17i | −0.172710 | + | 0.274826i | ||||
\(693\) | 5.15269e17i | 0.176713i | ||||||||
\(694\) | −2.75745e17 | − | 7.94505e16i | −0.0936851 | − | 0.0269936i | ||||
\(695\) | −7.55303e18 | −2.54226 | ||||||||
\(696\) | 1.15937e18 | − | 1.03587e18i | 0.386600 | − | 0.345418i | ||||
\(697\) | 2.82558e18 | 0.933456 | ||||||||
\(698\) | 2.24920e18 | + | 6.48064e17i | 0.736153 | + | 0.212108i | ||||
\(699\) | 4.50275e18i | 1.46008i | ||||||||
\(700\) | 4.17626e18 | + | 2.62450e18i | 1.34168 | + | 0.843158i | ||||
\(701\) | − | 2.70632e18i | − | 0.861414i | −0.902492 | − | 0.430707i | \(-0.858264\pi\) | ||
0.902492 | − | 0.430707i | \(-0.141736\pi\) | |||||||
\(702\) | −8.29350e16 | + | 2.87838e17i | −0.0261545 | + | 0.0907731i | ||||
\(703\) | 5.23814e18 | 1.63669 | ||||||||
\(704\) | −9.61325e17 | − | 1.08508e17i | −0.297610 | − | 0.0335922i | ||||
\(705\) | −1.23131e18 | −0.377692 | ||||||||
\(706\) | −1.32640e18 | + | 4.60346e18i | −0.403128 | + | 1.39912i | ||||
\(707\) | 5.92819e17i | 0.178524i | ||||||||
\(708\) | −5.82250e17 | − | 3.65905e17i | −0.173737 | − | 0.109182i | ||||
\(709\) | − | 3.11949e18i | − | 0.922322i | −0.887317 | − | 0.461161i | \(-0.847433\pi\) | ||
0.887317 | − | 0.461161i | \(-0.152567\pi\) | |||||||
\(710\) | 7.12165e18 | + | 2.05197e18i | 2.08642 | + | 0.601161i | ||||
\(711\) | −5.58668e18 | −1.62182 | ||||||||
\(712\) | 3.65288e18 | − | 3.26376e18i | 1.05079 | − | 0.938855i | ||||
\(713\) | −1.96242e17 | −0.0559383 | ||||||||
\(714\) | −3.48649e18 | − | 1.00457e18i | −0.984806 | − | 0.283753i | ||||
\(715\) | − | 1.55417e18i | − | 0.435021i | ||||||
\(716\) | 2.50718e18 | − | 3.98956e18i | 0.695425 | − | 1.10660i | ||||
\(717\) | 7.37690e18i | 2.02768i | ||||||||
\(718\) | −5.00711e17 | + | 1.73779e18i | −0.136389 | + | 0.473357i | ||||
\(719\) | −3.38700e17 | −0.0914276 | −0.0457138 | − | 0.998955i | \(-0.514556\pi\) | ||||
−0.0457138 | + | 0.998955i | \(0.514556\pi\) | |||||||
\(720\) | 5.71049e18 | − | 2.74910e18i | 1.52761 | − | 0.735410i | ||||
\(721\) | −4.87706e17 | −0.129294 | ||||||||
\(722\) | 8.49334e17 | − | 2.94774e18i | 0.223145 | − | 0.774456i | ||||
\(723\) | − | 6.41024e18i | − | 1.66907i | ||||||
\(724\) | −2.62921e18 | + | 4.18376e18i | −0.678461 | + | 1.07961i | ||||
\(725\) | 3.59276e18i | 0.918820i | ||||||||
\(726\) | −4.77277e18 | − | 1.37518e18i | −1.20971 | − | 0.348556i | ||||
\(727\) | 3.24412e18 | 0.814936 | 0.407468 | − | 0.913219i | \(-0.366412\pi\) | ||||
0.407468 | + | 0.913219i | \(0.366412\pi\) | |||||||
\(728\) | −1.35274e18 | − | 1.51402e18i | −0.336792 | − | 0.376945i | ||||
\(729\) | 3.31625e18 | 0.818311 | ||||||||
\(730\) | −3.89210e18 | − | 1.12143e18i | −0.951887 | − | 0.274268i | ||||
\(731\) | 1.95110e18i | 0.472950i | ||||||||
\(732\) | 6.38132e17 | + | 4.01023e17i | 0.153316 | + | 0.0963491i | ||||
\(733\) | − | 3.91150e18i | − | 0.931468i | −0.884925 | − | 0.465734i | \(-0.845790\pi\) | ||
0.884925 | − | 0.465734i | \(-0.154210\pi\) | |||||||
\(734\) | 1.54910e17 | − | 5.37637e17i | 0.0365640 | − | 0.126901i | ||||
\(735\) | 6.39155e18 | 1.49534 | ||||||||
\(736\) | −6.51783e17 | + | 1.10632e17i | −0.151146 | + | 0.0256551i | ||||
\(737\) | 2.28284e18 | 0.524730 | ||||||||
\(738\) | 9.03130e17 | − | 3.13444e18i | 0.205771 | − | 0.714158i | ||||
\(739\) | 3.74151e17i | 0.0845002i | 0.999107 | + | 0.0422501i | \(0.0134526\pi\) | ||||
−0.999107 | + | 0.0422501i | \(0.986547\pi\) | |||||||
\(740\) | −8.55696e18 | − | 5.37748e18i | −1.91564 | − | 1.20385i | ||||
\(741\) | 6.54827e18i | 1.45314i | ||||||||
\(742\) | 1.41116e18 | + | 4.06597e17i | 0.310420 | + | 0.0894415i | ||||
\(743\) | 1.22444e18 | 0.267000 | 0.133500 | − | 0.991049i | \(-0.457378\pi\) | ||||
0.133500 | + | 0.991049i | \(0.457378\pi\) | |||||||
\(744\) | −1.55538e18 | − | 1.74082e18i | −0.336211 | − | 0.376296i | ||||
\(745\) | −1.40686e19 | −3.01463 | ||||||||
\(746\) | 2.36502e18 | + | 6.81434e17i | 0.502379 | + | 0.144751i | ||||
\(747\) | − | 1.35177e18i | − | 0.284655i | ||||||
\(748\) | −8.75026e17 | + | 1.39239e18i | −0.182667 | + | 0.290671i | ||||
\(749\) | 2.26397e18i | 0.468532i | ||||||||
\(750\) | −5.03092e18 | + | 1.74605e19i | −1.03216 | + | 3.58228i | ||||
\(751\) | −7.11954e18 | −1.44808 | −0.724040 | − | 0.689758i | \(-0.757717\pi\) | ||||
−0.724040 | + | 0.689758i | \(0.757717\pi\) | |||||||
\(752\) | 3.16239e17 | + | 6.56899e17i | 0.0637676 | + | 0.132459i | ||||
\(753\) | 5.99185e18 | 1.19783 | ||||||||
\(754\) | 4.09449e17 | − | 1.42105e18i | 0.0811495 | − | 0.281641i | ||||
\(755\) | − | 1.09475e19i | − | 2.15110i | ||||||
\(756\) | 2.13346e17 | − | 3.39489e17i | 0.0415617 | − | 0.0661354i | ||||
\(757\) | − | 3.29155e18i | − | 0.635737i | −0.948135 | − | 0.317868i | \(-0.897033\pi\) | ||
0.948135 | − | 0.317868i | \(-0.102967\pi\) | |||||||
\(758\) | 6.61828e18 | + | 1.90693e18i | 1.26735 | + | 0.365161i | ||||
\(759\) | 3.34465e17 | 0.0635007 | ||||||||
\(760\) | −9.88981e18 | + | 8.83631e18i | −1.86166 | + | 1.66335i | ||||
\(761\) | 1.97090e18 | 0.367844 | 0.183922 | − | 0.982941i | \(-0.441121\pi\) | ||||
0.183922 | + | 0.982941i | \(0.441121\pi\) | |||||||
\(762\) | 3.10310e18 | + | 8.94098e17i | 0.574233 | + | 0.165454i | ||||
\(763\) | − | 4.08988e18i | − | 0.750413i | ||||||
\(764\) | −3.22442e18 | − | 2.02633e18i | −0.586603 | − | 0.368641i | ||||
\(765\) | − | 1.07734e19i | − | 1.94337i | ||||||
\(766\) | 2.53197e18 | − | 8.78756e18i | 0.452867 | − | 1.57174i | ||||
\(767\) | −6.54123e17 | −0.116009 | ||||||||
\(768\) | −6.14732e18 | − | 4.90498e18i | −1.08103 | − | 0.862560i | ||||
\(769\) | 5.34643e18 | 0.932272 | 0.466136 | − | 0.884713i | \(-0.345646\pi\) | ||||
0.466136 | + | 0.884713i | \(0.345646\pi\) | |||||||
\(770\) | −5.75979e17 | + | 1.99902e18i | −0.0995902 | + | 0.345643i | ||||
\(771\) | − | 7.70331e18i | − | 1.32076i | ||||||
\(772\) | 8.60143e18 | + | 5.40543e18i | 1.46237 | + | 0.919004i | ||||
\(773\) | 9.45579e18i | 1.59416i | 0.603876 | + | 0.797079i | \(0.293622\pi\) | ||||
−0.603876 | + | 0.797079i | \(0.706378\pi\) | |||||||
\(774\) | 2.16437e18 | + | 6.23623e17i | 0.361839 | + | 0.104257i | ||||
\(775\) | 5.39459e18 | 0.894329 | ||||||||
\(776\) | 4.49072e17 | − | 4.01236e17i | 0.0738270 | − | 0.0659627i | ||||
\(777\) | 6.67941e18 | 1.08893 | ||||||||
\(778\) | 7.21424e18 | + | 2.07865e18i | 1.16634 | + | 0.336057i | ||||
\(779\) | 6.82593e18i | 1.09438i | ||||||||
\(780\) | 6.72246e18 | − | 1.06972e19i | 1.06884 | − | 1.70080i | ||||
\(781\) | 2.22010e18i | 0.350058i | ||||||||
\(782\) | −3.11143e17 | + | 1.07987e18i | −0.0486538 | + | 0.168860i | ||||
\(783\) | 2.92056e17 | 0.0452913 | ||||||||
\(784\) | −1.64155e18 | − | 3.40987e18i | −0.252465 | − | 0.524425i | ||||
\(785\) | −1.88091e17 | −0.0286890 | ||||||||
\(786\) | −3.53599e18 | + | 1.22722e19i | −0.534890 | + | 1.85642i | ||||
\(787\) | 9.76299e18i | 1.46469i | 0.680932 | + | 0.732347i | \(0.261575\pi\) | ||||
−0.680932 | + | 0.732347i | \(0.738425\pi\) | |||||||
\(788\) | −2.68060e18 | + | 4.26553e18i | −0.398853 | + | 0.634677i | ||||
\(789\) | 7.17014e18i | 1.05810i | ||||||||
\(790\) | −2.16739e19 | − | 6.24492e18i | −3.17220 | − | 0.914009i | ||||
\(791\) | 1.19520e18 | 0.173498 | ||||||||
\(792\) | 1.26492e18 | + | 1.41572e18i | 0.182116 | + | 0.203828i | ||||
\(793\) | 7.16904e17 | 0.102373 | ||||||||
\(794\) | −7.60980e18 | − | 2.19262e18i | −1.07780 | − | 0.310549i | ||||
\(795\) | 9.13849e18i | 1.28377i | ||||||||
\(796\) | −5.27366e18 | − | 3.31414e18i | −0.734813 | − | 0.461781i | ||||
\(797\) | − | 2.77694e17i | − | 0.0383785i | −0.999816 | − | 0.0191892i | \(-0.993892\pi\) | ||
0.999816 | − | 0.0191892i | \(-0.00610850\pi\) | |||||||
\(798\) | 2.42680e18 | − | 8.42255e18i | 0.332671 | − | 1.15458i | ||||
\(799\) | 1.23931e18 | 0.168510 | ||||||||
\(800\) | 1.79172e19 | − | 3.04122e18i | 2.41650 | − | 0.410169i | ||||
\(801\) | −9.61295e18 | −1.28601 | ||||||||
\(802\) | 1.62873e18 | − | 5.65275e18i | 0.216131 | − | 0.750113i | ||||
\(803\) | − | 1.21332e18i | − | 0.159707i | ||||||
\(804\) | 1.57124e19 | + | 9.87423e18i | 2.05154 | + | 1.28926i | ||||
\(805\) | 1.42163e18i | 0.184125i | ||||||||
\(806\) | −2.13374e18 | − | 6.14795e17i | −0.274134 | − | 0.0789864i | ||||
\(807\) | −1.28482e19 | −1.63744 | ||||||||
\(808\) | 1.45529e18 | + | 1.62879e18i | 0.183982 | + | 0.205917i | ||||
\(809\) | 3.48686e18 | 0.437290 | 0.218645 | − | 0.975804i | \(-0.429836\pi\) | ||||
0.218645 | + | 0.975804i | \(0.429836\pi\) | |||||||
\(810\) | 1.54927e19 | + | 4.46391e18i | 1.92741 | + | 0.555345i | ||||
\(811\) | − | 1.02308e19i | − | 1.26262i | −0.775530 | − | 0.631310i | \(-0.782517\pi\) | ||
0.775530 | − | 0.631310i | \(-0.217483\pi\) | |||||||
\(812\) | −1.05329e18 | + | 1.67605e18i | −0.128953 | + | 0.205198i | ||||
\(813\) | − | 7.68471e18i | − | 0.933339i | ||||||
\(814\) | 8.38186e17 | − | 2.90905e18i | 0.100991 | − | 0.350503i | ||||
\(815\) | 7.26193e18 | 0.868015 | ||||||||
\(816\) | −1.20454e19 | + | 5.79878e18i | −1.42835 | + | 0.687624i | ||||
\(817\) | −4.71339e18 | −0.554485 | ||||||||
\(818\) | −2.27386e18 | + | 7.89177e18i | −0.265380 | + | 0.921039i | ||||
\(819\) | 3.98431e18i | 0.461326i | ||||||||
\(820\) | 7.00750e18 | − | 1.11507e19i | 0.804958 | − | 1.28090i | ||||
\(821\) | − | 9.37071e18i | − | 1.06793i | −0.845507 | − | 0.533964i | \(-0.820702\pi\) | ||
0.845507 | − | 0.533964i | \(-0.179298\pi\) | |||||||
\(822\) | 5.12707e17 | + | 1.47727e17i | 0.0579699 | + | 0.0167029i | ||||
\(823\) | −1.35722e19 | −1.52248 | −0.761240 | − | 0.648470i | \(-0.775409\pi\) | ||||
−0.761240 | + | 0.648470i | \(0.775409\pi\) | |||||||
\(824\) | −1.33999e18 | + | 1.19725e18i | −0.149134 | + | 0.133247i | ||||
\(825\) | −9.19428e18 | −1.01524 | ||||||||
\(826\) | 8.41351e17 | + | 2.42419e17i | 0.0921736 | + | 0.0265581i | ||||
\(827\) | 3.15313e18i | 0.342733i | 0.985207 | + | 0.171367i | \(0.0548183\pi\) | ||||
−0.985207 | + | 0.171367i | \(0.945182\pi\) | |||||||
\(828\) | 1.09846e18 | + | 6.90310e17i | 0.118464 | + | 0.0744470i | ||||
\(829\) | − | 1.29531e19i | − | 1.38601i | −0.720931 | − | 0.693007i | \(-0.756285\pi\) | ||
0.720931 | − | 0.693007i | \(-0.243715\pi\) | |||||||
\(830\) | 1.51104e18 | − | 5.24428e18i | 0.160423 | − | 0.556773i | ||||
\(831\) | −9.64701e18 | −1.01622 | ||||||||
\(832\) | −7.43344e18 | − | 8.39036e17i | −0.776941 | − | 0.0876959i | ||||
\(833\) | −6.43307e18 | −0.667154 | ||||||||
\(834\) | 5.09227e18 | − | 1.76735e19i | 0.524001 | − | 1.81862i | ||||
\(835\) | 2.58293e19i | 2.63725i | ||||||||
\(836\) | −3.36369e18 | − | 2.11386e18i | −0.340781 | − | 0.214158i | ||||
\(837\) | − | 4.38528e17i | − | 0.0440841i | ||||||
\(838\) | 2.36259e18 | + | 6.80736e17i | 0.235669 | + | 0.0679035i | ||||
\(839\) | 1.11182e19 | 1.10048 | 0.550242 | − | 0.835005i | \(-0.314536\pi\) | ||||
0.550242 | + | 0.835005i | \(0.314536\pi\) | |||||||
\(840\) | −1.26110e19 | + | 1.12676e19i | −1.23861 | + | 1.10667i | ||||
\(841\) | 8.81875e18 | 0.859475 | ||||||||
\(842\) | −4.88306e18 | − | 1.40696e18i | −0.472241 | − | 0.136067i | ||||
\(843\) | − | 1.59164e19i | − | 1.52745i | ||||||
\(844\) | −2.15949e17 | + | 3.43630e17i | −0.0205648 | + | 0.0327239i | ||||
\(845\) | 7.64061e18i | 0.722037i | ||||||||
\(846\) | 3.96116e17 | − | 1.37478e18i | 0.0371463 | − | 0.128922i | ||||
\(847\) | 6.32410e18 | 0.588514 | ||||||||
\(848\) | 4.87535e18 | − | 2.34705e18i | 0.450229 | − | 0.216746i | ||||
\(849\) | 1.15084e18 | 0.105467 | ||||||||
\(850\) | 8.55319e18 | − | 2.96851e19i | 0.777867 | − | 2.69970i | ||||
\(851\) | − | 2.06881e18i | − | 0.186715i | ||||||
\(852\) | −9.60285e18 | + | 1.52806e19i | −0.860088 | + | 1.36862i | ||||
\(853\) | − | 2.89593e18i | − | 0.257406i | −0.991683 | − | 0.128703i | \(-0.958919\pi\) | ||
0.991683 | − | 0.128703i | \(-0.0410814\pi\) | |||||||
\(854\) | −9.22100e17 | − | 2.65685e17i | −0.0813396 | − | 0.0234364i | ||||
\(855\) | 2.60261e19 | 2.27840 | ||||||||
\(856\) | 5.55775e18 | + | 6.22036e18i | 0.482858 | + | 0.540426i | ||||
\(857\) | −1.01399e19 | −0.874296 | −0.437148 | − | 0.899390i | \(-0.644011\pi\) | ||||
−0.437148 | + | 0.899390i | \(0.644011\pi\) | |||||||
\(858\) | 3.63664e18 | + | 1.04783e18i | 0.311195 | + | 0.0896648i | ||||
\(859\) | 1.44694e19i | 1.22884i | 0.788981 | + | 0.614418i | \(0.210609\pi\) | ||||
−0.788981 | + | 0.614418i | \(0.789391\pi\) | |||||||
\(860\) | 7.69973e18 | + | 4.83877e18i | 0.648986 | + | 0.407845i | ||||
\(861\) | 8.70408e18i | 0.728119i | ||||||||
\(862\) | −6.04386e18 | + | 2.09761e19i | −0.501785 | + | 1.74152i | ||||
\(863\) | −1.04390e19 | −0.860182 | −0.430091 | − | 0.902786i | \(-0.641519\pi\) | ||||
−0.430091 | + | 0.902786i | \(0.641519\pi\) | |||||||
\(864\) | −2.47222e17 | − | 1.45650e18i | −0.0202184 | − | 0.119116i | ||||
\(865\) | 7.42872e18 | 0.602989 | ||||||||
\(866\) | −4.89562e18 | + | 1.69910e19i | −0.394404 | + | 1.36884i | ||||
\(867\) | 5.42904e18i | 0.434109i | ||||||||
\(868\) | 2.51662e18 | + | 1.58153e18i | 0.199728 | + | 0.125516i | ||||
\(869\) | − | 6.75660e18i | − | 0.532231i | ||||||
\(870\) | −1.18366e19 | − | 3.41049e18i | −0.925447 | − | 0.266650i | ||||
\(871\) | 1.76520e19 | 1.36986 | ||||||||
\(872\) | −1.00401e19 | − | 1.12371e19i | −0.773358 | − | 0.865560i | ||||
\(873\) | −1.18178e18 | −0.0903535 | ||||||||
\(874\) | −2.60871e18 | − | 7.51649e17i | −0.197971 | − | 0.0570415i | ||||
\(875\) | − | 2.31359e19i | − | 1.74274i | ||||||
\(876\) | 5.24812e18 | − | 8.35111e18i | 0.392398 | − | 0.624407i | ||||
\(877\) | − | 5.07206e18i | − | 0.376432i | −0.982128 | − | 0.188216i | \(-0.939729\pi\) | ||
0.982128 | − | 0.188216i | \(-0.0602705\pi\) | |||||||
\(878\) | −6.35966e18 | + | 2.20721e19i | −0.468511 | + | 1.62604i | ||||
\(879\) | 2.68475e17 | 0.0196325 | ||||||||
\(880\) | 3.32480e18 | + | 6.90634e18i | 0.241339 | + | 0.501315i | ||||
\(881\) | 1.33390e19 | 0.961125 | 0.480562 | − | 0.876961i | \(-0.340433\pi\) | ||||
0.480562 | + | 0.876961i | \(0.340433\pi\) | |||||||
\(882\) | −2.05618e18 | + | 7.13629e18i | −0.147067 | + | 0.510419i | ||||
\(883\) | − | 3.37434e18i | − | 0.239577i | −0.992799 | − | 0.119788i | \(-0.961778\pi\) | ||
0.992799 | − | 0.119788i | \(-0.0382216\pi\) | |||||||
\(884\) | −6.76613e18 | + | 1.07667e19i | −0.476871 | + | 0.758824i | ||||
\(885\) | 5.44849e18i | 0.381193i | ||||||||
\(886\) | 1.83574e19 | + | 5.28932e18i | 1.27494 | + | 0.367351i | ||||
\(887\) | 9.03561e18 | 0.622951 | 0.311475 | − | 0.950254i | \(-0.399177\pi\) | ||||
0.311475 | + | 0.950254i | \(0.399177\pi\) | |||||||
\(888\) | 1.83520e19 | − | 1.63971e19i | 1.25603 | − | 1.12223i | ||||
\(889\) | −4.11172e18 | −0.279359 | ||||||||
\(890\) | −3.72941e19 | − | 1.07456e19i | −2.51539 | − | 0.724760i | ||||
\(891\) | 4.82967e18i | 0.323379i | ||||||||
\(892\) | 1.05812e19 | + | 6.64958e18i | 0.703337 | + | 0.442001i | ||||
\(893\) | 2.99388e18i | 0.197560i | ||||||||
\(894\) | 9.48506e18 | − | 3.29193e19i | 0.621364 | − | 2.15654i | ||||
\(895\) | −3.73330e19 | −2.42797 | ||||||||
\(896\) | 9.25013e18 | + | 3.83403e18i | 0.597236 | + | 0.247545i | ||||
\(897\) | 2.58624e18 | 0.165775 | ||||||||
\(898\) | −4.65739e18 | + | 1.61642e19i | −0.296379 | + | 1.02863i | ||||
\(899\) | 2.16500e18i | 0.136779i | ||||||||
\(900\) | −3.01962e19 | − | 1.89763e19i | −1.89398 | − | 1.19024i | ||||
\(901\) | − | 9.19786e18i | − | 0.572764i | ||||||
\(902\) | 3.79084e18 | + | 1.09226e18i | 0.234365 | + | 0.0675277i | ||||
\(903\) | −6.01027e18 | −0.368913 | ||||||||
\(904\) | 3.28387e18 | − | 2.93407e18i | 0.200121 | − | 0.178803i | ||||
\(905\) | 3.91502e19 | 2.36874 | ||||||||
\(906\) | 2.56162e19 | + | 7.38083e18i | 1.53880 | + | 0.443376i | ||||
\(907\) | − | 2.78144e19i | − | 1.65891i | −0.558577 | − | 0.829453i | \(-0.688652\pi\) | ||
0.558577 | − | 0.829453i | \(-0.311348\pi\) | |||||||
\(908\) | −9.94524e18 | + | 1.58254e19i | −0.588921 | + | 0.937125i | ||||
\(909\) | − | 4.28635e18i | − | 0.252013i | ||||||
\(910\) | −4.45375e18 | + | 1.54574e19i | −0.259990 | + | 0.902334i | ||||
\(911\) | −1.56079e19 | −0.904640 | −0.452320 | − | 0.891856i | \(-0.649404\pi\) | ||||
−0.452320 | + | 0.891856i | \(0.649404\pi\) | |||||||
\(912\) | −1.40085e19 | − | 2.90988e19i | −0.806167 | − | 1.67459i | ||||
\(913\) | 1.63485e18 | 0.0934151 | ||||||||
\(914\) | −9.26626e17 | + | 3.21599e18i | −0.0525720 | + | 0.182459i | ||||
\(915\) | − | 5.97142e18i | − | 0.336388i | ||||||
\(916\) | 6.79560e18 | − | 1.08136e19i | 0.380108 | − | 0.604850i | ||||
\(917\) | − | 1.62611e19i | − | 0.903127i | ||||||
\(918\) | −2.41311e18 | − | 6.95292e17i | −0.133076 | − | 0.0383433i | ||||
\(919\) | −1.84642e19 | −1.01107 | −0.505534 | − | 0.862807i | \(-0.668705\pi\) | ||||
−0.505534 | + | 0.862807i | \(0.668705\pi\) | |||||||
\(920\) | 3.48991e18 | + | 3.90599e18i | 0.189755 | + | 0.212378i | ||||
\(921\) | −2.09573e19 | −1.13148 | ||||||||
\(922\) | 1.80014e19 | + | 5.18676e18i | 0.965062 | + | 0.278064i | ||||
\(923\) | 1.71669e19i | 0.913861i | ||||||||
\(924\) | −4.28921e18 | − | 2.69548e18i | −0.226730 | − | 0.142485i | ||||
\(925\) | 5.68706e19i | 2.98515i | ||||||||
\(926\) | 9.28313e18 | − | 3.22184e19i | 0.483863 | − | 1.67932i | ||||
\(927\) | 3.52633e18 | 0.182518 | ||||||||
\(928\) | 1.22053e18 | + | 7.19070e18i | 0.0627316 | + | 0.369581i | ||||
\(929\) | −3.06640e19 | −1.56505 | −0.782523 | − | 0.622622i | \(-0.786067\pi\) | ||||
−0.782523 | + | 0.622622i | \(0.786067\pi\) | |||||||
\(930\) | −5.12091e18 | + | 1.77729e19i | −0.259542 | + | 0.900779i | ||||
\(931\) | − | 1.55408e19i | − | 0.782169i | ||||||
\(932\) | −1.78849e19 | − | 1.12395e19i | −0.893890 | − | 0.561750i | ||||
\(933\) | 3.60096e19i | 1.78726i | ||||||||
\(934\) | 2.05001e18 | + | 5.90672e17i | 0.101042 | + | 0.0291133i | ||||
\(935\) | 1.30295e19 | 0.637754 | ||||||||
\(936\) | 9.78095e18 | + | 1.09471e19i | 0.475431 | + | 0.532114i | ||||
\(937\) | −8.09512e18 | −0.390765 | −0.195383 | − | 0.980727i | \(-0.562595\pi\) | ||||
−0.195383 | + | 0.980727i | \(0.562595\pi\) | |||||||
\(938\) | −2.27045e19 | − | 6.54186e18i | −1.08841 | − | 0.313605i | ||||
\(939\) | 1.93892e19i | 0.923068i | ||||||||
\(940\) | 3.07352e18 | − | 4.89076e18i | 0.145313 | − | 0.231231i | ||||
\(941\) | 1.97554e19i | 0.927585i | 0.885944 | + | 0.463792i | \(0.153512\pi\) | ||||
−0.885944 | + | 0.463792i | \(0.846488\pi\) | |||||||
\(942\) | 1.26811e17 | − | 4.40117e17i | 0.00591326 | − | 0.0205228i | ||||
\(943\) | 2.69591e18 | 0.124847 | ||||||||
\(944\) | 2.90675e18 | − | 1.39935e18i | 0.133687 | − | 0.0643587i | ||||
\(945\) | −3.17682e18 | −0.145106 | ||||||||
\(946\) | −7.54217e17 | + | 2.61762e18i | −0.0342140 | + | 0.118745i | ||||
\(947\) | − | 3.83190e19i | − | 1.72639i | −0.504870 | − | 0.863195i | \(-0.668460\pi\) | ||
0.504870 | − | 0.863195i | \(-0.331540\pi\) | |||||||
\(948\) | 2.92252e19 | − | 4.65048e19i | 1.30768 | − | 2.08086i | ||||
\(949\) | − | 9.38199e18i | − | 0.416931i | ||||||
\(950\) | 7.17123e19 | + | 2.06625e19i | 3.16512 | + | 0.911968i | ||||
\(951\) | 4.68572e19 | 2.05401 | ||||||||
\(952\) | 1.26929e19 | − | 1.13408e19i | 0.552613 | − | 0.493747i | ||||
\(953\) | 1.84822e19 | 0.799191 | 0.399595 | − | 0.916692i | \(-0.369151\pi\) | ||||
0.399595 | + | 0.916692i | \(0.369151\pi\) | |||||||
\(954\) | −1.02033e19 | − | 2.93988e18i | −0.438204 | − | 0.126260i | ||||
\(955\) | 3.01730e19i | 1.28705i | ||||||||
\(956\) | −2.93010e19 | − | 1.84138e19i | −1.24139 | − | 0.780128i | ||||
\(957\) | − | 3.68993e18i | − | 0.155271i | ||||||
\(958\) | −4.17619e18 | + | 1.44941e19i | −0.174544 | + | 0.605780i | ||||
\(959\) | −6.79355e17 | −0.0282017 | ||||||||
\(960\) | −6.98872e18 | + | 6.19165e19i | −0.288161 | + | 2.55296i | ||||
\(961\) | −2.11668e19 | −0.866866 | ||||||||
\(962\) | 6.48126e18 | − | 2.24942e19i | 0.263646 | − | 0.915023i | ||||
\(963\) | − | 1.63696e19i | − | 0.661403i | ||||||
\(964\) | 2.54615e19 | + | 1.60008e19i | 1.02184 | + | 0.642159i | ||||
\(965\) | − | 8.04893e19i | − | 3.20856i | ||||||
\(966\) | −3.32649e18 | − | 9.58465e17i | −0.131715 | − | 0.0379512i | ||||
\(967\) | 3.63780e19 | 1.43076 | 0.715381 | − | 0.698735i | \(-0.246253\pi\) | ||||
0.715381 | + | 0.698735i | \(0.246253\pi\) | |||||||
\(968\) | 1.73757e19 | − | 1.55248e19i | 0.678818 | − | 0.606508i | ||||
\(969\) | −5.48979e19 | −2.13035 | ||||||||
\(970\) | −4.58480e18 | − | 1.32102e18i | −0.176728 | − | 0.0509207i | ||||
\(971\) | 1.07755e19i | 0.412582i | 0.978491 | + | 0.206291i | \(0.0661394\pi\) | ||||
−0.978491 | + | 0.206291i | \(0.933861\pi\) | |||||||
\(972\) | −1.92001e19 | + | 3.05523e19i | −0.730252 | + | 1.16202i | ||||
\(973\) | 2.34180e19i | 0.884741i | ||||||||
\(974\) | −3.67160e18 | + | 1.27428e19i | −0.137792 | + | 0.478226i | ||||
\(975\) | −7.10947e19 | −2.65037 | ||||||||
\(976\) | −3.18573e18 | + | 1.53365e18i | −0.117974 | + | 0.0567940i | ||||
\(977\) | 4.63072e19 | 1.70347 | 0.851733 | − | 0.523976i | \(-0.175552\pi\) | ||||
0.851733 | + | 0.523976i | \(0.175552\pi\) | |||||||
\(978\) | −4.89600e18 | + | 1.69923e19i | −0.178912 | + | 0.620940i | ||||
\(979\) | − | 1.16260e19i | − | 0.422030i | ||||||
\(980\) | −1.59542e19 | + | 2.53872e19i | −0.575315 | + | 0.915474i | ||||
\(981\) | 2.95717e19i | 1.05932i | ||||||||
\(982\) | −3.77943e19 | − | 1.08897e19i | −1.34493 | − | 0.387517i | ||||
\(983\) | −5.20948e19 | −1.84160 | −0.920802 | − | 0.390030i | \(-0.872465\pi\) | ||||
−0.920802 | + | 0.390030i | \(0.872465\pi\) | |||||||
\(984\) | 2.13673e19 | + | 2.39148e19i | 0.750382 | + | 0.839845i | ||||
\(985\) | 3.99154e19 | 1.39253 | ||||||||
\(986\) | 1.19135e19 | + | 3.43264e18i | 0.412894 | + | 0.118968i | ||||
\(987\) | 3.81764e18i | 0.131442i | ||||||||
\(988\) | −2.60097e19 | − | 1.63454e19i | −0.889643 | − | 0.559081i | ||||
\(989\) | 1.86156e18i | 0.0632558i | ||||||||
\(990\) | 4.16459e18 | − | 1.44538e19i | 0.140586 | − | 0.487926i | ||||
\(991\) | 3.18575e19 | 1.06840 | 0.534199 | − | 0.845358i | \(-0.320613\pi\) | ||||
0.534199 | + | 0.845358i | \(0.320613\pi\) | |||||||
\(992\) | 1.07970e19 | − | 1.83265e18i | 0.359730 | − | 0.0610595i | ||||
\(993\) | 6.28631e19 | 2.08078 | ||||||||
\(994\) | 6.36207e18 | − | 2.20805e19i | 0.209212 | − | 0.726101i | ||||
\(995\) | 4.93491e19i | 1.61224i | ||||||||
\(996\) | 1.12524e19 | + | 7.07140e18i | 0.365225 | + | 0.229520i | ||||
\(997\) | − | 4.12366e18i | − | 0.132973i | −0.997787 | − | 0.0664866i | \(-0.978821\pi\) | ||
0.997787 | − | 0.0664866i | \(-0.0211790\pi\) | |||||||
\(998\) | −3.93953e19 | − | 1.13510e19i | −1.26211 | − | 0.363652i | ||||
\(999\) | 4.62303e18 | 0.147147 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8.14.b.b.5.4 | yes | 10 | |
3.2 | odd | 2 | 72.14.d.c.37.7 | 10 | |||
4.3 | odd | 2 | 32.14.b.b.17.1 | 10 | |||
8.3 | odd | 2 | 32.14.b.b.17.10 | 10 | |||
8.5 | even | 2 | inner | 8.14.b.b.5.3 | ✓ | 10 | |
24.5 | odd | 2 | 72.14.d.c.37.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.14.b.b.5.3 | ✓ | 10 | 8.5 | even | 2 | inner | |
8.14.b.b.5.4 | yes | 10 | 1.1 | even | 1 | trivial | |
32.14.b.b.17.1 | 10 | 4.3 | odd | 2 | |||
32.14.b.b.17.10 | 10 | 8.3 | odd | 2 | |||
72.14.d.c.37.7 | 10 | 3.2 | odd | 2 | |||
72.14.d.c.37.8 | 10 | 24.5 | odd | 2 |