Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,17,Mod(3,8)]
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([1, 1]))
N = Newforms(chi, 17, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (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: | \(12.9859635085\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 7 x^{13} + 7894 x^{12} + 219192 x^{11} - 135772320 x^{10} + 11331786624 x^{9} - 652293490688 x^{8} + 465478371454976 x^{7} + \cdots + 27\!\cdots\!20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{91}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.14 | ||
Root | \(-137.581 - 24.7690i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.17.d.b.3.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 251.161 | + | 49.5380i | 0.981099 | + | 0.193508i | ||||
\(3\) | 6181.49 | 0.942157 | 0.471078 | − | 0.882091i | \(-0.343865\pi\) | ||||
0.471078 | + | 0.882091i | \(0.343865\pi\) | |||||||
\(4\) | 60628.0 | + | 24884.1i | 0.925109 | + | 0.379701i | ||||
\(5\) | − | 699404.i | − | 1.79048i | −0.445589 | − | 0.895238i | \(-0.647006\pi\) | ||
0.445589 | − | 0.895238i | \(-0.352994\pi\) | |||||||
\(6\) | 1.55255e6 | + | 306219.i | 0.924349 | + | 0.182315i | ||||
\(7\) | − | 4.65744e6i | − | 0.807911i | −0.914779 | − | 0.403955i | \(-0.867635\pi\) | ||
0.914779 | − | 0.403955i | \(-0.132365\pi\) | |||||||
\(8\) | 1.39947e7 | + | 9.25331e6i | 0.834148 | + | 0.551540i | ||||
\(9\) | −4.83590e6 | −0.112341 | ||||||||
\(10\) | 3.46471e7 | − | 1.75663e8i | 0.346471 | − | 1.75663i | ||||
\(11\) | −2.50802e7 | −0.117001 | −0.0585004 | − | 0.998287i | \(-0.518632\pi\) | ||||
−0.0585004 | + | 0.998287i | \(0.518632\pi\) | |||||||
\(12\) | 3.74771e8 | + | 1.53821e8i | 0.871598 | + | 0.357738i | ||||
\(13\) | 9.99771e8i | 1.22561i | 0.790233 | + | 0.612807i | \(0.209960\pi\) | ||||
−0.790233 | + | 0.612807i | \(0.790040\pi\) | |||||||
\(14\) | 2.30721e8 | − | 1.16977e9i | 0.156337 | − | 0.792640i | ||||
\(15\) | − | 4.32336e9i | − | 1.68691i | ||||||
\(16\) | 3.05653e9 | + | 3.01734e9i | 0.711655 | + | 0.702530i | ||||
\(17\) | 1.78097e9 | 0.255308 | 0.127654 | − | 0.991819i | \(-0.459255\pi\) | ||||
0.127654 | + | 0.991819i | \(0.459255\pi\) | |||||||
\(18\) | −1.21459e9 | − | 2.39561e8i | −0.110217 | − | 0.0217388i | ||||
\(19\) | 2.70321e10 | 1.59166 | 0.795832 | − | 0.605517i | \(-0.207034\pi\) | ||||
0.795832 | + | 0.605517i | \(0.207034\pi\) | |||||||
\(20\) | 1.74040e10 | − | 4.24035e10i | 0.679845 | − | 1.65639i | ||||
\(21\) | − | 2.87899e10i | − | 0.761178i | ||||||
\(22\) | −6.29917e9 | − | 1.24242e9i | −0.114789 | − | 0.0226406i | ||||
\(23\) | 7.64077e10i | 0.975696i | 0.872929 | + | 0.487848i | \(0.162218\pi\) | ||||
−0.872929 | + | 0.487848i | \(0.837782\pi\) | |||||||
\(24\) | 8.65080e10 | + | 5.71992e10i | 0.785899 | + | 0.519637i | ||||
\(25\) | −3.36579e11 | −2.20580 | ||||||||
\(26\) | −4.95267e10 | + | 2.51104e11i | −0.237166 | + | 1.20245i | ||||
\(27\) | −2.95986e11 | −1.04800 | ||||||||
\(28\) | 1.15896e11 | − | 2.82371e11i | 0.306764 | − | 0.747406i | ||||
\(29\) | 7.60372e11i | 1.51999i | 0.649926 | + | 0.759997i | \(0.274800\pi\) | ||||
−0.649926 | + | 0.759997i | \(0.725200\pi\) | |||||||
\(30\) | 2.14171e11 | − | 1.08586e12i | 0.326430 | − | 1.65502i | ||||
\(31\) | − | 2.35983e11i | − | 0.276686i | −0.990384 | − | 0.138343i | \(-0.955822\pi\) | ||
0.990384 | − | 0.138343i | \(-0.0441777\pi\) | |||||||
\(32\) | 6.18210e11 | + | 9.09254e11i | 0.562258 | + | 0.826962i | ||||
\(33\) | −1.55033e11 | −0.110233 | ||||||||
\(34\) | 4.47310e11 | + | 8.82257e10i | 0.250483 | + | 0.0494042i | ||||
\(35\) | −3.25744e12 | −1.44654 | ||||||||
\(36\) | −2.93191e11 | − | 1.20337e11i | −0.103928 | − | 0.0426559i | ||||
\(37\) | − | 2.42830e12i | − | 0.691336i | −0.938357 | − | 0.345668i | \(-0.887652\pi\) | ||
0.938357 | − | 0.345668i | \(-0.112348\pi\) | |||||||
\(38\) | 6.78943e12 | + | 1.33912e12i | 1.56158 | + | 0.308000i | ||||
\(39\) | 6.18007e12i | 1.15472i | ||||||||
\(40\) | 6.47180e12 | − | 9.78795e12i | 0.987519 | − | 1.49352i | ||||
\(41\) | 1.88090e12 | 0.235556 | 0.117778 | − | 0.993040i | \(-0.462423\pi\) | ||||
0.117778 | + | 0.993040i | \(0.462423\pi\) | |||||||
\(42\) | 1.42620e12 | − | 7.23092e12i | 0.147294 | − | 0.746791i | ||||
\(43\) | −9.47032e12 | −0.810246 | −0.405123 | − | 0.914262i | \(-0.632771\pi\) | ||||
−0.405123 | + | 0.914262i | \(0.632771\pi\) | |||||||
\(44\) | −1.52056e12 | − | 6.24097e11i | −0.108239 | − | 0.0444253i | ||||
\(45\) | 3.38225e12i | 0.201143i | ||||||||
\(46\) | −3.78509e12 | + | 1.91907e13i | −0.188805 | + | 0.957254i | ||||
\(47\) | − | 1.60529e13i | − | 0.674174i | −0.941474 | − | 0.337087i | \(-0.890558\pi\) | ||
0.941474 | − | 0.337087i | \(-0.109442\pi\) | |||||||
\(48\) | 1.88939e13 | + | 1.86517e13i | 0.670490 | + | 0.661893i | ||||
\(49\) | 1.15412e13 | 0.347281 | ||||||||
\(50\) | −8.45355e13 | − | 1.66734e13i | −2.16411 | − | 0.426840i | ||||
\(51\) | 1.10090e13 | 0.240540 | ||||||||
\(52\) | −2.48784e13 | + | 6.06141e13i | −0.465367 | + | 1.13383i | ||||
\(53\) | 1.92778e13i | 0.309635i | 0.987943 | + | 0.154817i | \(0.0494789\pi\) | ||||
−0.987943 | + | 0.154817i | \(0.950521\pi\) | |||||||
\(54\) | −7.43402e13 | − | 1.46626e13i | −1.02819 | − | 0.202796i | ||||
\(55\) | 1.75412e13i | 0.209487i | ||||||||
\(56\) | 4.30967e13 | − | 6.51795e13i | 0.445595 | − | 0.673917i | ||||
\(57\) | 1.67099e14 | 1.49960 | ||||||||
\(58\) | −3.76673e13 | + | 1.90976e14i | −0.294131 | + | 1.49126i | ||||
\(59\) | −3.49569e13 | −0.238076 | −0.119038 | − | 0.992890i | \(-0.537981\pi\) | ||||
−0.119038 | + | 0.992890i | \(0.537981\pi\) | |||||||
\(60\) | 1.07583e14 | − | 2.62117e14i | 0.640521 | − | 1.56057i | ||||
\(61\) | − | 3.45553e14i | − | 1.80250i | −0.433297 | − | 0.901251i | \(-0.642650\pi\) | ||
0.433297 | − | 0.901251i | \(-0.357350\pi\) | |||||||
\(62\) | 1.16901e13 | − | 5.92698e13i | 0.0535410 | − | 0.271456i | ||||
\(63\) | 2.25229e13i | 0.0907613i | ||||||||
\(64\) | 1.10228e14 | + | 2.58994e14i | 0.391607 | + | 0.920132i | ||||
\(65\) | 6.99244e14 | 2.19443 | ||||||||
\(66\) | −3.89382e13 | − | 7.68002e12i | −0.108150 | − | 0.0213310i | ||||
\(67\) | −6.70291e14 | −1.65069 | −0.825344 | − | 0.564630i | \(-0.809019\pi\) | ||||
−0.825344 | + | 0.564630i | \(0.809019\pi\) | |||||||
\(68\) | 1.07977e14 | + | 4.43178e13i | 0.236188 | + | 0.0969408i | ||||
\(69\) | 4.72314e14i | 0.919259i | ||||||||
\(70\) | −8.18142e14 | − | 1.61367e14i | −1.41920 | − | 0.279918i | ||||
\(71\) | 2.20461e14i | 0.341401i | 0.985323 | + | 0.170700i | \(0.0546030\pi\) | ||||
−0.985323 | + | 0.170700i | \(0.945397\pi\) | |||||||
\(72\) | −6.76769e13 | − | 4.47481e13i | −0.0937089 | − | 0.0619604i | ||||
\(73\) | 1.81005e14 | 0.224444 | 0.112222 | − | 0.993683i | \(-0.464203\pi\) | ||||
0.112222 | + | 0.993683i | \(0.464203\pi\) | |||||||
\(74\) | 1.20293e14 | − | 6.09895e14i | 0.133779 | − | 0.678268i | ||||
\(75\) | −2.08056e15 | −2.07821 | ||||||||
\(76\) | 1.63890e15 | + | 6.72670e14i | 1.47246 | + | 0.604356i | ||||
\(77\) | 1.16809e14i | 0.0945262i | ||||||||
\(78\) | −3.06149e14 | + | 1.55220e15i | −0.223448 | + | 1.13289i | ||||
\(79\) | 1.45789e14i | 0.0960965i | 0.998845 | + | 0.0480482i | \(0.0153001\pi\) | ||||
−0.998845 | + | 0.0480482i | \(0.984700\pi\) | |||||||
\(80\) | 2.11034e15 | − | 2.13775e15i | 1.25786 | − | 1.27420i | ||||
\(81\) | −1.62146e15 | −0.875039 | ||||||||
\(82\) | 4.72409e14 | + | 9.31760e13i | 0.231104 | + | 0.0455820i | ||||
\(83\) | −3.18974e14 | −0.141622 | −0.0708110 | − | 0.997490i | \(-0.522559\pi\) | ||||
−0.0708110 | + | 0.997490i | \(0.522559\pi\) | |||||||
\(84\) | 7.16411e14 | − | 1.74548e15i | 0.289020 | − | 0.704173i | ||||
\(85\) | − | 1.24562e15i | − | 0.457123i | ||||||
\(86\) | −2.37858e15 | − | 4.69141e14i | −0.794932 | − | 0.156789i | ||||
\(87\) | 4.70023e15i | 1.43207i | ||||||||
\(88\) | −3.50989e14 | − | 2.32075e14i | −0.0975961 | − | 0.0645307i | ||||
\(89\) | 2.96458e15 | 0.753083 | 0.376541 | − | 0.926400i | \(-0.377113\pi\) | ||||
0.376541 | + | 0.926400i | \(0.377113\pi\) | |||||||
\(90\) | −1.67550e14 | + | 8.49491e14i | −0.0389229 | + | 0.197342i | ||||
\(91\) | 4.65638e15 | 0.990186 | ||||||||
\(92\) | −1.90134e15 | + | 4.63244e15i | −0.370473 | + | 0.902625i | ||||
\(93\) | − | 1.45873e15i | − | 0.260682i | ||||||
\(94\) | 7.95231e14 | − | 4.03188e15i | 0.130458 | − | 0.661431i | ||||
\(95\) | − | 1.89064e16i | − | 2.84984i | ||||||
\(96\) | 3.82146e15 | + | 5.62054e15i | 0.529735 | + | 0.779127i | ||||
\(97\) | 7.93720e15 | 1.01273 | 0.506365 | − | 0.862319i | \(-0.330989\pi\) | ||||
0.506365 | + | 0.862319i | \(0.330989\pi\) | |||||||
\(98\) | 2.89869e15 | + | 5.71726e14i | 0.340717 | + | 0.0672016i | ||||
\(99\) | 1.21285e14 | 0.0131440 | ||||||||
\(100\) | −2.04061e16 | − | 8.37545e15i | −2.04061 | − | 0.837545i | ||||
\(101\) | 1.00307e16i | 0.926321i | 0.886274 | + | 0.463160i | \(0.153285\pi\) | ||||
−0.886274 | + | 0.463160i | \(0.846715\pi\) | |||||||
\(102\) | 2.76504e15 | + | 5.45366e14i | 0.235994 | + | 0.0465465i | ||||
\(103\) | 2.46355e16i | 1.94475i | 0.233429 | + | 0.972374i | \(0.425005\pi\) | ||||
−0.233429 | + | 0.972374i | \(0.574995\pi\) | |||||||
\(104\) | −9.25119e15 | + | 1.39915e16i | −0.675975 | + | 1.02234i | ||||
\(105\) | −2.01358e16 | −1.36287 | ||||||||
\(106\) | −9.54983e14 | + | 4.84183e15i | −0.0599168 | + | 0.303782i | ||||
\(107\) | 1.00547e16 | 0.585194 | 0.292597 | − | 0.956236i | \(-0.405481\pi\) | ||||
0.292597 | + | 0.956236i | \(0.405481\pi\) | |||||||
\(108\) | −1.79450e16 | − | 7.36534e15i | −0.969514 | − | 0.397926i | ||||
\(109\) | − | 1.73713e16i | − | 0.871806i | −0.899994 | − | 0.435903i | \(-0.856429\pi\) | ||
0.899994 | − | 0.435903i | \(-0.143571\pi\) | |||||||
\(110\) | −8.68956e14 | + | 4.40567e15i | −0.0405374 | + | 0.205528i | ||||
\(111\) | − | 1.50105e16i | − | 0.651346i | ||||||
\(112\) | 1.40531e16 | − | 1.42356e16i | 0.567581 | − | 0.574953i | ||||
\(113\) | −2.11437e16 | −0.795342 | −0.397671 | − | 0.917528i | \(-0.630181\pi\) | ||||
−0.397671 | + | 0.917528i | \(0.630181\pi\) | |||||||
\(114\) | 4.19688e16 | + | 8.27775e15i | 1.47125 | + | 0.290184i | ||||
\(115\) | 5.34399e16 | 1.74696 | ||||||||
\(116\) | −1.89211e16 | + | 4.60998e16i | −0.577143 | + | 1.40616i | ||||
\(117\) | − | 4.83479e15i | − | 0.137686i | ||||||
\(118\) | −8.77981e15 | − | 1.73169e15i | −0.233576 | − | 0.0460697i | ||||
\(119\) | − | 8.29476e15i | − | 0.206266i | ||||||
\(120\) | 4.00054e16 | − | 6.05041e16i | 0.930397 | − | 1.40713i | ||||
\(121\) | −4.53207e16 | −0.986311 | ||||||||
\(122\) | 1.71180e16 | − | 8.67895e16i | 0.348798 | − | 1.76843i | ||||
\(123\) | 1.16267e16 | 0.221931 | ||||||||
\(124\) | 5.87222e15 | − | 1.43072e16i | 0.105058 | − | 0.255965i | ||||
\(125\) | 1.28684e17i | 2.15896i | ||||||||
\(126\) | −1.11574e15 | + | 5.65689e15i | −0.0175630 | + | 0.0890458i | ||||
\(127\) | − | 6.32709e16i | − | 0.934920i | −0.884014 | − | 0.467460i | \(-0.845169\pi\) | ||
0.884014 | − | 0.467460i | \(-0.154831\pi\) | |||||||
\(128\) | 1.48548e16 | + | 7.05098e16i | 0.206152 | + | 0.978520i | ||||
\(129\) | −5.85407e16 | −0.763379 | ||||||||
\(130\) | 1.75623e17 | + | 3.46392e16i | 2.15295 | + | 0.424640i | ||||
\(131\) | −1.18988e17 | −1.37194 | −0.685968 | − | 0.727632i | \(-0.740621\pi\) | ||||
−0.685968 | + | 0.727632i | \(0.740621\pi\) | |||||||
\(132\) | −9.39933e15 | − | 3.85785e15i | −0.101978 | − | 0.0418556i | ||||
\(133\) | − | 1.25901e17i | − | 1.28592i | ||||||
\(134\) | −1.68351e17 | − | 3.32049e16i | −1.61949 | − | 0.319421i | ||||
\(135\) | 2.07014e17i | 1.87642i | ||||||||
\(136\) | 2.49241e16 | + | 1.64799e16i | 0.212965 | + | 0.140813i | ||||
\(137\) | 1.01693e16 | 0.0819460 | 0.0409730 | − | 0.999160i | \(-0.486954\pi\) | ||||
0.0409730 | + | 0.999160i | \(0.486954\pi\) | |||||||
\(138\) | −2.33975e16 | + | 1.18627e17i | −0.177884 | + | 0.901883i | ||||
\(139\) | −4.95907e16 | −0.355862 | −0.177931 | − | 0.984043i | \(-0.556940\pi\) | ||||
−0.177931 | + | 0.984043i | \(0.556940\pi\) | |||||||
\(140\) | −1.97492e17 | − | 8.10583e16i | −1.33821 | − | 0.549254i | ||||
\(141\) | − | 9.92311e16i | − | 0.635177i | ||||||
\(142\) | −1.09212e16 | + | 5.53712e16i | −0.0660637 | + | 0.334948i | ||||
\(143\) | − | 2.50744e16i | − | 0.143398i | ||||||
\(144\) | −1.47811e16 | − | 1.45916e16i | −0.0799478 | − | 0.0789227i | ||||
\(145\) | 5.31807e17 | 2.72151 | ||||||||
\(146\) | 4.54615e16 | + | 8.96665e15i | 0.220202 | + | 0.0434317i | ||||
\(147\) | 7.13415e16 | 0.327193 | ||||||||
\(148\) | 6.04260e16 | − | 1.47223e17i | 0.262501 | − | 0.639561i | ||||
\(149\) | 1.18135e17i | 0.486284i | 0.969991 | + | 0.243142i | \(0.0781781\pi\) | ||||
−0.969991 | + | 0.243142i | \(0.921822\pi\) | |||||||
\(150\) | −5.22556e17 | − | 1.03067e17i | −2.03893 | − | 0.402150i | ||||
\(151\) | − | 3.38113e17i | − | 1.25097i | −0.780237 | − | 0.625484i | \(-0.784902\pi\) | ||
0.780237 | − | 0.625484i | \(-0.215098\pi\) | |||||||
\(152\) | 3.78306e17 | + | 2.50137e17i | 1.32768 | + | 0.877867i | ||||
\(153\) | −8.61259e15 | −0.0286815 | ||||||||
\(154\) | −5.78651e15 | + | 2.93380e16i | −0.0182916 | + | 0.0927396i | ||||
\(155\) | −1.65048e17 | −0.495400 | ||||||||
\(156\) | −1.53785e17 | + | 3.74685e17i | −0.438448 | + | 1.06824i | ||||
\(157\) | − | 1.51106e17i | − | 0.409341i | −0.978831 | − | 0.204670i | \(-0.934388\pi\) | ||
0.978831 | − | 0.204670i | \(-0.0656122\pi\) | |||||||
\(158\) | −7.22209e15 | + | 3.66165e16i | −0.0185954 | + | 0.0942801i | ||||
\(159\) | 1.19165e17i | 0.291725i | ||||||||
\(160\) | 6.35936e17 | − | 4.32378e17i | 1.48065 | − | 1.00671i | ||||
\(161\) | 3.55865e17 | 0.788275 | ||||||||
\(162\) | −4.07249e17 | − | 8.03242e16i | −0.858499 | − | 0.169327i | ||||
\(163\) | −1.53662e16 | −0.0308365 | −0.0154183 | − | 0.999881i | \(-0.504908\pi\) | ||||
−0.0154183 | + | 0.999881i | \(0.504908\pi\) | |||||||
\(164\) | 1.14035e17 | + | 4.68044e16i | 0.217915 | + | 0.0894408i | ||||
\(165\) | 1.08431e17i | 0.197370i | ||||||||
\(166\) | −8.01140e16 | − | 1.58014e16i | −0.138945 | − | 0.0274050i | ||||
\(167\) | 4.82750e16i | 0.0797976i | 0.999204 | + | 0.0398988i | \(0.0127036\pi\) | ||||
−0.999204 | + | 0.0398988i | \(0.987296\pi\) | |||||||
\(168\) | 2.66402e17 | − | 4.02906e17i | 0.419820 | − | 0.634936i | ||||
\(169\) | −3.34125e17 | −0.502130 | ||||||||
\(170\) | 6.17055e16 | − | 3.12851e17i | 0.0884570 | − | 0.448483i | ||||
\(171\) | −1.30725e17 | −0.178809 | ||||||||
\(172\) | −5.74166e17 | − | 2.35660e17i | −0.749567 | − | 0.307651i | ||||
\(173\) | − | 5.34968e17i | − | 0.666744i | −0.942795 | − | 0.333372i | \(-0.891814\pi\) | ||
0.942795 | − | 0.333372i | \(-0.108186\pi\) | |||||||
\(174\) | −2.32840e17 | + | 1.18052e18i | −0.277117 | + | 1.40500i | ||||
\(175\) | 1.56760e18i | 1.78209i | ||||||||
\(176\) | −7.66584e16 | − | 7.56755e16i | −0.0832642 | − | 0.0821966i | ||||
\(177\) | −2.16086e17 | −0.224305 | ||||||||
\(178\) | 7.44587e17 | + | 1.46859e17i | 0.738849 | + | 0.145728i | ||||
\(179\) | −1.66428e18 | −1.57907 | −0.789536 | − | 0.613704i | \(-0.789679\pi\) | ||||
−0.789536 | + | 0.613704i | \(0.789679\pi\) | |||||||
\(180\) | −8.41642e16 | + | 2.05059e17i | −0.0763743 | + | 0.186080i | ||||
\(181\) | 8.37583e17i | 0.727108i | 0.931573 | + | 0.363554i | \(0.118437\pi\) | ||||
−0.931573 | + | 0.363554i | \(0.881563\pi\) | |||||||
\(182\) | 1.16950e18 | + | 2.30668e17i | 0.971471 | + | 0.191609i | ||||
\(183\) | − | 2.13603e18i | − | 1.69824i | ||||||
\(184\) | −7.07024e17 | + | 1.06930e18i | −0.538135 | + | 0.813875i | ||||
\(185\) | −1.69837e18 | −1.23782 | ||||||||
\(186\) | 7.22625e16 | − | 3.66376e17i | 0.0504440 | − | 0.255754i | ||||
\(187\) | −4.46670e16 | −0.0298713 | ||||||||
\(188\) | 3.99463e17 | − | 9.73257e17i | 0.255984 | − | 0.623684i | ||||
\(189\) | 1.37854e18i | 0.846690i | ||||||||
\(190\) | 9.36586e17 | − | 4.74856e18i | 0.551466 | − | 2.79597i | ||||
\(191\) | 1.41104e18i | 0.796659i | 0.917242 | + | 0.398329i | \(0.130410\pi\) | ||||
−0.917242 | + | 0.398329i | \(0.869590\pi\) | |||||||
\(192\) | 6.81371e17 | + | 1.60097e18i | 0.368955 | + | 0.866909i | ||||
\(193\) | 2.23870e18 | 1.16289 | 0.581444 | − | 0.813586i | \(-0.302488\pi\) | ||||
0.581444 | + | 0.813586i | \(0.302488\pi\) | |||||||
\(194\) | 1.99352e18 | + | 3.93193e17i | 0.993588 | + | 0.195971i | ||||
\(195\) | 4.32237e18 | 2.06750 | ||||||||
\(196\) | 6.99717e17 | + | 2.87191e17i | 0.321273 | + | 0.131863i | ||||
\(197\) | − | 1.68645e18i | − | 0.743436i | −0.928346 | − | 0.371718i | \(-0.878769\pi\) | ||
0.928346 | − | 0.371718i | \(-0.121231\pi\) | |||||||
\(198\) | 3.04622e16 | + | 6.00824e15i | 0.0128955 | + | 0.00254346i | ||||
\(199\) | − | 2.99452e18i | − | 1.21759i | −0.793326 | − | 0.608797i | \(-0.791652\pi\) | ||
0.793326 | − | 0.608797i | \(-0.208348\pi\) | |||||||
\(200\) | −4.71031e18 | − | 3.11447e18i | −1.83997 | − | 1.21659i | ||||
\(201\) | −4.14340e18 | −1.55521 | ||||||||
\(202\) | −4.96903e17 | + | 2.51933e18i | −0.179250 | + | 0.908812i | ||||
\(203\) | 3.54139e18 | 1.22802 | ||||||||
\(204\) | 6.67456e17 | + | 2.73950e17i | 0.222526 | + | 0.0913334i | ||||
\(205\) | − | 1.31551e18i | − | 0.421757i | ||||||
\(206\) | −1.22039e18 | + | 6.18748e18i | −0.376324 | + | 1.90799i | ||||
\(207\) | − | 3.69500e17i | − | 0.109610i | ||||||
\(208\) | −3.01665e18 | + | 3.05583e18i | −0.861030 | + | 0.872214i | ||||
\(209\) | −6.77971e17 | −0.186226 | ||||||||
\(210\) | −5.05734e18 | − | 9.97489e17i | −1.33711 | − | 0.263726i | ||||
\(211\) | 2.76684e18 | 0.704246 | 0.352123 | − | 0.935954i | \(-0.385460\pi\) | ||||
0.352123 | + | 0.935954i | \(0.385460\pi\) | |||||||
\(212\) | −4.79709e17 | + | 1.16877e18i | −0.117569 | + | 0.286446i | ||||
\(213\) | 1.36278e18i | 0.321653i | ||||||||
\(214\) | 2.52536e18 | + | 4.98091e17i | 0.574133 | + | 0.113240i | ||||
\(215\) | 6.62359e18i | 1.45073i | ||||||||
\(216\) | −4.14223e18 | − | 2.73885e18i | −0.874187 | − | 0.578014i | ||||
\(217\) | −1.09908e18 | −0.223538 | ||||||||
\(218\) | 8.60539e17 | − | 4.36299e18i | 0.168701 | − | 0.855327i | ||||
\(219\) | 1.11888e18 | 0.211462 | ||||||||
\(220\) | −4.36496e17 | + | 1.06349e18i | −0.0795425 | + | 0.193799i | ||||
\(221\) | 1.78056e18i | 0.312909i | ||||||||
\(222\) | 7.43592e17 | − | 3.77006e18i | 0.126041 | − | 0.639035i | ||||
\(223\) | − | 8.31324e18i | − | 1.35935i | −0.733513 | − | 0.679675i | \(-0.762121\pi\) | ||
0.733513 | − | 0.679675i | \(-0.237879\pi\) | |||||||
\(224\) | 4.23480e18 | − | 2.87928e18i | 0.668111 | − | 0.454254i | ||||
\(225\) | 1.62766e18 | 0.247802 | ||||||||
\(226\) | −5.31048e18 | − | 1.04742e18i | −0.780309 | − | 0.153905i | ||||
\(227\) | −9.98439e18 | −1.41617 | −0.708083 | − | 0.706129i | \(-0.750440\pi\) | ||||
−0.708083 | + | 0.706129i | \(0.750440\pi\) | |||||||
\(228\) | 1.01309e19 | + | 4.15810e18i | 1.38729 | + | 0.569398i | ||||
\(229\) | − | 5.03614e16i | − | 0.00665907i | −0.999994 | − | 0.00332954i | \(-0.998940\pi\) | ||
0.999994 | − | 0.00332954i | \(-0.00105983\pi\) | |||||||
\(230\) | 1.34220e19 | + | 2.64731e18i | 1.71394 | + | 0.338051i | ||||
\(231\) | 7.22057e17i | 0.0890585i | ||||||||
\(232\) | −7.03595e18 | + | 1.06412e19i | −0.838338 | + | 1.26790i | ||||
\(233\) | 6.71996e18 | 0.773605 | 0.386803 | − | 0.922162i | \(-0.373579\pi\) | ||||
0.386803 | + | 0.922162i | \(0.373579\pi\) | |||||||
\(234\) | 2.39506e17 | − | 1.21431e18i | 0.0266434 | − | 0.135084i | ||||
\(235\) | −1.12275e19 | −1.20709 | ||||||||
\(236\) | −2.11936e18 | − | 8.69869e17i | −0.220247 | − | 0.0903978i | ||||
\(237\) | 9.01192e17i | 0.0905379i | ||||||||
\(238\) | 4.10906e17 | − | 2.08332e18i | 0.0399142 | − | 0.202368i | ||||
\(239\) | − | 1.61742e18i | − | 0.151929i | −0.997111 | − | 0.0759643i | \(-0.975796\pi\) | ||
0.997111 | − | 0.0759643i | \(-0.0242035\pi\) | |||||||
\(240\) | 1.30451e19 | − | 1.32145e19i | 1.18510 | − | 1.20050i | ||||
\(241\) | 9.87362e18 | 0.867641 | 0.433821 | − | 0.900999i | \(-0.357165\pi\) | ||||
0.433821 | + | 0.900999i | \(0.357165\pi\) | |||||||
\(242\) | −1.13828e19 | − | 2.24510e18i | −0.967668 | − | 0.190859i | ||||
\(243\) | 2.71816e18 | 0.223576 | ||||||||
\(244\) | 8.59876e18 | − | 2.09502e19i | 0.684411 | − | 1.66751i | ||||
\(245\) | − | 8.07193e18i | − | 0.621797i | ||||||
\(246\) | 2.92019e18 | + | 5.75966e17i | 0.217736 | + | 0.0429454i | ||||
\(247\) | 2.70259e19i | 1.95077i | ||||||||
\(248\) | 2.18362e18 | − | 3.30251e18i | 0.152603 | − | 0.230797i | ||||
\(249\) | −1.97174e18 | −0.133430 | ||||||||
\(250\) | −6.37475e18 | + | 3.23204e19i | −0.417776 | + | 2.11815i | ||||
\(251\) | −1.58923e19 | −1.00878 | −0.504390 | − | 0.863476i | \(-0.668283\pi\) | ||||
−0.504390 | + | 0.863476i | \(0.668283\pi\) | |||||||
\(252\) | −5.60463e17 | + | 1.36552e18i | −0.0344621 | + | 0.0839641i | ||||
\(253\) | − | 1.91632e18i | − | 0.114157i | ||||||
\(254\) | 3.13432e18 | − | 1.58912e19i | 0.180914 | − | 0.917248i | ||||
\(255\) | − | 7.69977e18i | − | 0.430682i | ||||||
\(256\) | 2.38044e17 | + | 1.84452e19i | 0.0129044 | + | 0.999917i | ||||
\(257\) | −1.59897e19 | −0.840187 | −0.420093 | − | 0.907481i | \(-0.638003\pi\) | ||||
−0.420093 | + | 0.907481i | \(0.638003\pi\) | |||||||
\(258\) | −1.47032e19 | − | 2.89999e18i | −0.748950 | − | 0.147720i | ||||
\(259\) | −1.13097e19 | −0.558537 | ||||||||
\(260\) | 4.23938e19 | + | 1.74000e19i | 2.03009 | + | 0.833228i | ||||
\(261\) | − | 3.67708e18i | − | 0.170757i | ||||||
\(262\) | −2.98853e19 | − | 5.89445e18i | −1.34600 | − | 0.265481i | ||||
\(263\) | − | 1.53959e19i | − | 0.672602i | −0.941755 | − | 0.336301i | \(-0.890824\pi\) | ||
0.941755 | − | 0.336301i | \(-0.109176\pi\) | |||||||
\(264\) | −2.16964e18 | − | 1.43457e18i | −0.0919508 | − | 0.0607980i | ||||
\(265\) | 1.34830e19 | 0.554394 | ||||||||
\(266\) | 6.23687e18 | − | 3.16214e19i | 0.248836 | − | 1.26162i | ||||
\(267\) | 1.83255e19 | 0.709522 | ||||||||
\(268\) | −4.06384e19 | − | 1.66796e19i | −1.52707 | − | 0.626768i | ||||
\(269\) | 3.47917e19i | 1.26899i | 0.772927 | + | 0.634494i | \(0.218792\pi\) | ||||
−0.772927 | + | 0.634494i | \(0.781208\pi\) | |||||||
\(270\) | −1.02551e19 | + | 5.19939e19i | −0.363102 | + | 1.84095i | ||||
\(271\) | − | 1.10793e19i | − | 0.380854i | −0.981701 | − | 0.190427i | \(-0.939013\pi\) | ||
0.981701 | − | 0.190427i | \(-0.0609873\pi\) | |||||||
\(272\) | 5.44359e18 | + | 5.37379e18i | 0.181691 | + | 0.179362i | ||||
\(273\) | 2.87833e19 | 0.932911 | ||||||||
\(274\) | 2.55414e18 | + | 5.03769e17i | 0.0803971 | + | 0.0158572i | ||||
\(275\) | 8.44145e18 | 0.258081 | ||||||||
\(276\) | −1.17531e19 | + | 2.86354e19i | −0.349043 | + | 0.850415i | ||||
\(277\) | 1.03237e19i | 0.297850i | 0.988848 | + | 0.148925i | \(0.0475813\pi\) | ||||
−0.988848 | + | 0.148925i | \(0.952419\pi\) | |||||||
\(278\) | −1.24553e19 | − | 2.45663e18i | −0.349136 | − | 0.0688622i | ||||
\(279\) | 1.14119e18i | 0.0310831i | ||||||||
\(280\) | −4.55868e19 | − | 3.01421e19i | −1.20663 | − | 0.797827i | ||||
\(281\) | 3.43188e19 | 0.882840 | 0.441420 | − | 0.897301i | \(-0.354475\pi\) | ||||
0.441420 | + | 0.897301i | \(0.354475\pi\) | |||||||
\(282\) | 4.91571e18 | − | 2.49230e19i | 0.122912 | − | 0.623172i | ||||
\(283\) | 3.83778e19 | 0.932800 | 0.466400 | − | 0.884574i | \(-0.345551\pi\) | ||||
0.466400 | + | 0.884574i | \(0.345551\pi\) | |||||||
\(284\) | −5.48596e18 | + | 1.33661e19i | −0.129630 | + | 0.315833i | ||||
\(285\) | − | 1.16870e20i | − | 2.68499i | ||||||
\(286\) | 1.24214e18 | − | 6.29773e18i | 0.0277486 | − | 0.140687i | ||||
\(287\) | − | 8.76017e18i | − | 0.190308i | ||||||
\(288\) | −2.98960e18 | − | 4.39706e18i | −0.0631645 | − | 0.0929015i | ||||
\(289\) | −4.54893e19 | −0.934818 | ||||||||
\(290\) | 1.33569e20 | + | 2.63447e19i | 2.67007 | + | 0.526634i | ||||
\(291\) | 4.90637e19 | 0.954150 | ||||||||
\(292\) | 1.09740e19 | + | 4.50415e18i | 0.207635 | + | 0.0852217i | ||||
\(293\) | 2.69218e19i | 0.495636i | 0.968807 | + | 0.247818i | \(0.0797136\pi\) | ||||
−0.968807 | + | 0.247818i | \(0.920286\pi\) | |||||||
\(294\) | 1.79182e19 | + | 3.53412e18i | 0.321008 | + | 0.0633144i | ||||
\(295\) | 2.44490e19i | 0.426270i | ||||||||
\(296\) | 2.24698e19 | − | 3.39833e19i | 0.381299 | − | 0.576676i | ||||
\(297\) | 7.42338e18 | 0.122617 | ||||||||
\(298\) | −5.85219e18 | + | 2.96710e19i | −0.0940998 | + | 0.477092i | ||||
\(299\) | −7.63902e19 | −1.19583 | ||||||||
\(300\) | −1.26140e20 | − | 5.17728e19i | −1.92257 | − | 0.789099i | ||||
\(301\) | 4.41075e19i | 0.654607i | ||||||||
\(302\) | 1.67494e19 | − | 8.49208e19i | 0.242072 | − | 1.22732i | ||||
\(303\) | 6.20048e19i | 0.872739i | ||||||||
\(304\) | 8.26246e19 | + | 8.15652e19i | 1.13272 | + | 1.11819i | ||||
\(305\) | −2.41681e20 | −3.22734 | ||||||||
\(306\) | −2.16315e18 | − | 4.26651e17i | −0.0281394 | − | 0.00555011i | ||||
\(307\) | 3.17040e19 | 0.401797 | 0.200899 | − | 0.979612i | \(-0.435614\pi\) | ||||
0.200899 | + | 0.979612i | \(0.435614\pi\) | |||||||
\(308\) | −2.90670e18 | + | 7.08192e18i | −0.0358917 | + | 0.0874471i | ||||
\(309\) | 1.52284e20i | 1.83226i | ||||||||
\(310\) | −4.14536e19 | − | 8.17614e18i | −0.486036 | − | 0.0958638i | ||||
\(311\) | − | 1.11218e20i | − | 1.27084i | −0.772165 | − | 0.635422i | \(-0.780826\pi\) | ||
0.772165 | − | 0.635422i | \(-0.219174\pi\) | |||||||
\(312\) | −5.71861e19 | + | 8.64882e19i | −0.636875 | + | 0.963208i | ||||
\(313\) | −2.59112e19 | −0.281277 | −0.140638 | − | 0.990061i | \(-0.544915\pi\) | ||||
−0.140638 | + | 0.990061i | \(0.544915\pi\) | |||||||
\(314\) | 7.48550e18 | − | 3.79520e19i | 0.0792107 | − | 0.401603i | ||||
\(315\) | 1.57526e19 | 0.162506 | ||||||||
\(316\) | −3.62782e18 | + | 8.83888e18i | −0.0364879 | + | 0.0888997i | ||||
\(317\) | 9.95998e19i | 0.976752i | 0.872633 | + | 0.488376i | \(0.162411\pi\) | ||||
−0.872633 | + | 0.488376i | \(0.837589\pi\) | |||||||
\(318\) | −5.90322e18 | + | 2.99297e19i | −0.0564510 | + | 0.286211i | ||||
\(319\) | − | 1.90703e19i | − | 0.177841i | ||||||
\(320\) | 1.81142e20 | − | 7.70937e19i | 1.64747 | − | 0.701163i | ||||
\(321\) | 6.21532e19 | 0.551345 | ||||||||
\(322\) | 8.93794e19 | + | 1.76288e19i | 0.773376 | + | 0.152538i | ||||
\(323\) | 4.81434e19 | 0.406365 | ||||||||
\(324\) | −9.83061e19 | − | 4.03486e19i | −0.809507 | − | 0.332253i | ||||
\(325\) | − | 3.36502e20i | − | 2.70346i | ||||||
\(326\) | −3.85939e18 | − | 7.61211e17i | −0.0302537 | − | 0.00596711i | ||||
\(327\) | − | 1.07380e20i | − | 0.821377i | ||||||
\(328\) | 2.63226e19 | + | 1.74045e19i | 0.196489 | + | 0.129919i | ||||
\(329\) | −7.47657e19 | −0.544672 | ||||||||
\(330\) | −5.37144e18 | + | 2.72336e19i | −0.0381926 | + | 0.193639i | ||||
\(331\) | 1.21654e20 | 0.844311 | 0.422155 | − | 0.906524i | \(-0.361274\pi\) | ||||
0.422155 | + | 0.906524i | \(0.361274\pi\) | |||||||
\(332\) | −1.93388e19 | − | 7.93738e18i | −0.131016 | − | 0.0537740i | ||||
\(333\) | 1.17430e19i | 0.0776652i | ||||||||
\(334\) | −2.39145e18 | + | 1.21248e19i | −0.0154415 | + | 0.0782894i | ||||
\(335\) | 4.68805e20i | 2.95552i | ||||||||
\(336\) | 8.68691e19 | − | 8.79974e19i | 0.534750 | − | 0.541696i | ||||
\(337\) | 2.30463e20 | 1.38536 | 0.692680 | − | 0.721245i | \(-0.256430\pi\) | ||||
0.692680 | + | 0.721245i | \(0.256430\pi\) | |||||||
\(338\) | −8.39194e19 | − | 1.65519e19i | −0.492639 | − | 0.0971661i | ||||
\(339\) | −1.30700e20 | −0.749337 | ||||||||
\(340\) | 3.09960e19 | − | 7.55193e19i | 0.173570 | − | 0.422889i | ||||
\(341\) | 5.91850e18i | 0.0323725i | ||||||||
\(342\) | −3.28330e19 | − | 6.47585e18i | −0.175429 | − | 0.0346009i | ||||
\(343\) | − | 2.08533e20i | − | 1.08848i | ||||||
\(344\) | −1.32534e20 | − | 8.76318e19i | −0.675866 | − | 0.446883i | ||||
\(345\) | 3.30338e20 | 1.64591 | ||||||||
\(346\) | 2.65013e19 | − | 1.34363e20i | 0.129020 | − | 0.654142i | ||||
\(347\) | −3.36488e20 | −1.60079 | −0.800393 | − | 0.599476i | \(-0.795376\pi\) | ||||
−0.800393 | + | 0.599476i | \(0.795376\pi\) | |||||||
\(348\) | −1.16961e20 | + | 2.84965e20i | −0.543759 | + | 1.32482i | ||||
\(349\) | 5.21190e19i | 0.236806i | 0.992966 | + | 0.118403i | \(0.0377775\pi\) | ||||
−0.992966 | + | 0.118403i | \(0.962223\pi\) | |||||||
\(350\) | −7.76556e19 | + | 3.93719e20i | −0.344849 | + | 1.74841i | ||||
\(351\) | − | 2.95918e20i | − | 1.28444i | ||||||
\(352\) | −1.55048e19 | − | 2.28042e19i | −0.0657847 | − | 0.0967552i | ||||
\(353\) | −7.64010e18 | −0.0316885 | −0.0158442 | − | 0.999874i | \(-0.505044\pi\) | ||||
−0.0158442 | + | 0.999874i | \(0.505044\pi\) | |||||||
\(354\) | −5.42723e19 | − | 1.07045e19i | −0.220066 | − | 0.0434049i | ||||
\(355\) | 1.54191e20 | 0.611269 | ||||||||
\(356\) | 1.79736e20 | + | 7.37708e19i | 0.696684 | + | 0.285946i | ||||
\(357\) | − | 5.12740e19i | − | 0.194335i | ||||||
\(358\) | −4.18003e20 | − | 8.24452e19i | −1.54923 | − | 0.305563i | ||||
\(359\) | 1.32120e20i | 0.478865i | 0.970913 | + | 0.239432i | \(0.0769613\pi\) | ||||
−0.970913 | + | 0.239432i | \(0.923039\pi\) | |||||||
\(360\) | −3.12970e19 | + | 4.73336e19i | −0.110939 | + | 0.167783i | ||||
\(361\) | 4.42295e20 | 1.53340 | ||||||||
\(362\) | −4.14922e19 | + | 2.10368e20i | −0.140701 | + | 0.713365i | ||||
\(363\) | −2.80150e20 | −0.929259 | ||||||||
\(364\) | 2.82307e20 | + | 1.15870e20i | 0.916031 | + | 0.375975i | ||||
\(365\) | − | 1.26596e20i | − | 0.401862i | ||||||
\(366\) | 1.05815e20 | − | 5.36488e20i | 0.328623 | − | 1.66614i | ||||
\(367\) | − | 2.21954e20i | − | 0.674425i | −0.941429 | − | 0.337213i | \(-0.890516\pi\) | ||
0.941429 | − | 0.337213i | \(-0.109484\pi\) | |||||||
\(368\) | −2.30548e20 | + | 2.33543e20i | −0.685455 | + | 0.694359i | ||||
\(369\) | −9.09584e18 | −0.0264625 | ||||||||
\(370\) | −4.26564e20 | − | 8.41337e19i | −1.21442 | − | 0.239528i | ||||
\(371\) | 8.97851e19 | 0.250157 | ||||||||
\(372\) | 3.62991e19 | − | 8.84397e19i | 0.0989811 | − | 0.241159i | ||||
\(373\) | 5.49011e20i | 1.46525i | 0.680635 | + | 0.732623i | \(0.261704\pi\) | ||||
−0.680635 | + | 0.732623i | \(0.738296\pi\) | |||||||
\(374\) | −1.12186e19 | − | 2.21272e18i | −0.0293067 | − | 0.00578033i | ||||
\(375\) | 7.95459e20i | 2.03408i | ||||||||
\(376\) | 1.48543e20 | − | 2.24656e20i | 0.371834 | − | 0.562361i | ||||
\(377\) | −7.60198e20 | −1.86293 | ||||||||
\(378\) | −6.82901e19 | + | 3.46235e20i | −0.163841 | + | 0.830686i | ||||
\(379\) | −1.81621e20 | −0.426631 | −0.213316 | − | 0.976983i | \(-0.568426\pi\) | ||||
−0.213316 | + | 0.976983i | \(0.568426\pi\) | |||||||
\(380\) | 4.70468e20 | − | 1.14626e21i | 1.08209 | − | 2.63641i | ||||
\(381\) | − | 3.91108e20i | − | 0.880841i | ||||||
\(382\) | −6.99002e19 | + | 3.54399e20i | −0.154160 | + | 0.781601i | ||||
\(383\) | − | 1.94155e20i | − | 0.419333i | −0.977773 | − | 0.209666i | \(-0.932762\pi\) | ||
0.977773 | − | 0.209666i | \(-0.0672378\pi\) | |||||||
\(384\) | 9.18251e19 | + | 4.35856e20i | 0.194228 | + | 0.921919i | ||||
\(385\) | 8.16971e19 | 0.169247 | ||||||||
\(386\) | 5.62275e20 | + | 1.10901e20i | 1.14091 | + | 0.225028i | ||||
\(387\) | 4.57976e19 | 0.0910237 | ||||||||
\(388\) | 4.81216e20 | + | 1.97510e20i | 0.936886 | + | 0.384534i | ||||
\(389\) | − | 6.76602e20i | − | 1.29044i | −0.763998 | − | 0.645218i | \(-0.776766\pi\) | ||
0.763998 | − | 0.645218i | \(-0.223234\pi\) | |||||||
\(390\) | 1.08561e21 | + | 2.14122e20i | 2.02842 | + | 0.400077i | ||||
\(391\) | 1.36080e20i | 0.249103i | ||||||||
\(392\) | 1.61515e20 | + | 1.06794e20i | 0.289684 | + | 0.191539i | ||||
\(393\) | −7.35525e20 | −1.29258 | ||||||||
\(394\) | 8.35435e19 | − | 4.23571e20i | 0.143861 | − | 0.729384i | ||||
\(395\) | 1.01965e20 | 0.172058 | ||||||||
\(396\) | 7.35328e18 | + | 3.01807e18i | 0.0121596 | + | 0.00499078i | ||||
\(397\) | 5.08193e20i | 0.823578i | 0.911279 | + | 0.411789i | \(0.135096\pi\) | ||||
−0.911279 | + | 0.411789i | \(0.864904\pi\) | |||||||
\(398\) | 1.48343e20 | − | 7.52108e20i | 0.235614 | − | 1.19458i | ||||
\(399\) | − | 7.78254e20i | − | 1.21154i | ||||||
\(400\) | −1.02876e21 | − | 1.01557e21i | −1.56977 | − | 1.54964i | ||||
\(401\) | 6.93111e20 | 1.03669 | 0.518344 | − | 0.855172i | \(-0.326549\pi\) | ||||
0.518344 | + | 0.855172i | \(0.326549\pi\) | |||||||
\(402\) | −1.04066e21 | − | 2.05256e20i | −1.52581 | − | 0.300945i | ||||
\(403\) | 2.35929e20 | 0.339110 | ||||||||
\(404\) | −2.49605e20 | + | 6.08143e20i | −0.351725 | + | 0.856948i | ||||
\(405\) | 1.13406e21i | 1.56674i | ||||||||
\(406\) | 8.89460e20 | + | 1.75433e20i | 1.20481 | + | 0.237632i | ||||
\(407\) | 6.09022e19i | 0.0808869i | ||||||||
\(408\) | 1.54068e20 | + | 1.01870e20i | 0.200646 | + | 0.132668i | ||||
\(409\) | −1.79393e20 | −0.229097 | −0.114548 | − | 0.993418i | \(-0.536542\pi\) | ||||
−0.114548 | + | 0.993418i | \(0.536542\pi\) | |||||||
\(410\) | 6.51677e19 | − | 3.30405e20i | 0.0816134 | − | 0.413786i | ||||
\(411\) | 6.28616e19 | 0.0772060 | ||||||||
\(412\) | −6.13031e20 | + | 1.49360e21i | −0.738422 | + | 1.79910i | ||||
\(413\) | 1.62810e20i | 0.192344i | ||||||||
\(414\) | 1.83043e19 | − | 9.28042e19i | 0.0212105 | − | 0.107539i | ||||
\(415\) | 2.23092e20i | 0.253571i | ||||||||
\(416\) | −9.09046e20 | + | 6.18068e20i | −1.01354 | + | 0.689112i | ||||
\(417\) | −3.06545e20 | −0.335278 | ||||||||
\(418\) | −1.70280e20 | − | 3.35853e19i | −0.182706 | − | 0.0360362i | ||||
\(419\) | 1.13823e21 | 1.19817 | 0.599086 | − | 0.800685i | \(-0.295531\pi\) | ||||
0.599086 | + | 0.800685i | \(0.295531\pi\) | |||||||
\(420\) | −1.22079e21 | − | 5.01061e20i | −1.26080 | − | 0.517483i | ||||
\(421\) | − | 1.54426e21i | − | 1.56482i | −0.622765 | − | 0.782409i | \(-0.713991\pi\) | ||
0.622765 | − | 0.782409i | \(-0.286009\pi\) | |||||||
\(422\) | 6.94923e20 | + | 1.37064e20i | 0.690935 | + | 0.136277i | ||||
\(423\) | 7.76305e19i | 0.0757372i | ||||||||
\(424\) | −1.78383e20 | + | 2.69786e20i | −0.170776 | + | 0.258281i | ||||
\(425\) | −5.99436e20 | −0.563160 | ||||||||
\(426\) | −6.75092e19 | + | 3.42276e20i | −0.0622424 | + | 0.315573i | ||||
\(427\) | −1.60939e21 | −1.45626 | ||||||||
\(428\) | 6.09598e20 | + | 2.50203e20i | 0.541369 | + | 0.222199i | ||||
\(429\) | − | 1.54997e20i | − | 0.135103i | ||||||
\(430\) | −3.28119e20 | + | 1.66359e21i | −0.280727 | + | 1.42331i | ||||
\(431\) | − | 7.13757e20i | − | 0.599421i | −0.954030 | − | 0.299710i | \(-0.903110\pi\) | ||
0.954030 | − | 0.299710i | \(-0.0968901\pi\) | |||||||
\(432\) | −9.04691e20 | − | 8.93091e20i | −0.745813 | − | 0.736251i | ||||
\(433\) | −5.31329e20 | −0.429992 | −0.214996 | − | 0.976615i | \(-0.568974\pi\) | ||||
−0.214996 | + | 0.976615i | \(0.568974\pi\) | |||||||
\(434\) | −2.76046e20 | − | 5.44462e19i | −0.219312 | − | 0.0432563i | ||||
\(435\) | 3.28736e21 | 2.56409 | ||||||||
\(436\) | 4.32268e20 | − | 1.05318e21i | 0.331025 | − | 0.806515i | ||||
\(437\) | 2.06546e21i | 1.55298i | ||||||||
\(438\) | 2.81020e20 | + | 5.54272e19i | 0.207465 | + | 0.0409195i | ||||
\(439\) | 6.79982e20i | 0.492926i | 0.969152 | + | 0.246463i | \(0.0792683\pi\) | ||||
−0.969152 | + | 0.246463i | \(0.920732\pi\) | |||||||
\(440\) | −1.62314e20 | + | 2.45483e20i | −0.115541 | + | 0.174743i | ||||
\(441\) | −5.58119e19 | −0.0390138 | ||||||||
\(442\) | −8.82055e19 | + | 4.47208e20i | −0.0605505 | + | 0.306995i | ||||
\(443\) | 9.44712e20 | 0.636898 | 0.318449 | − | 0.947940i | \(-0.396838\pi\) | ||||
0.318449 | + | 0.947940i | \(0.396838\pi\) | |||||||
\(444\) | 3.73523e20 | − | 9.10057e20i | 0.247317 | − | 0.602567i | ||||
\(445\) | − | 2.07344e21i | − | 1.34838i | ||||||
\(446\) | 4.11821e20 | − | 2.08796e21i | 0.263045 | − | 1.33366i | ||||
\(447\) | 7.30253e20i | 0.458155i | ||||||||
\(448\) | 1.20625e21 | − | 5.13379e20i | 0.743385 | − | 0.316384i | ||||
\(449\) | 1.93362e21 | 1.17058 | 0.585288 | − | 0.810825i | \(-0.300981\pi\) | ||||
0.585288 | + | 0.810825i | \(0.300981\pi\) | |||||||
\(450\) | 4.08806e20 | + | 8.06312e19i | 0.243118 | + | 0.0479516i | ||||
\(451\) | −4.71732e19 | −0.0275603 | ||||||||
\(452\) | −1.28190e21 | − | 5.26142e20i | −0.735778 | − | 0.301992i | ||||
\(453\) | − | 2.09004e21i | − | 1.17861i | ||||||
\(454\) | −2.50769e21 | − | 4.94607e20i | −1.38940 | − | 0.274040i | ||||
\(455\) | − | 3.25669e21i | − | 1.77290i | ||||||
\(456\) | 2.33850e21 | + | 1.54622e21i | 1.25089 | + | 0.827088i | ||||
\(457\) | −7.52884e19 | −0.0395729 | −0.0197865 | − | 0.999804i | \(-0.506299\pi\) | ||||
−0.0197865 | + | 0.999804i | \(0.506299\pi\) | |||||||
\(458\) | 2.49480e18 | − | 1.26488e19i | 0.00128858 | − | 0.00653321i | ||||
\(459\) | −5.27142e20 | −0.267563 | ||||||||
\(460\) | 3.23995e21 | + | 1.32980e21i | 1.61613 | + | 0.663322i | ||||
\(461\) | 2.80291e21i | 1.37405i | 0.726636 | + | 0.687023i | \(0.241083\pi\) | ||||
−0.726636 | + | 0.687023i | \(0.758917\pi\) | |||||||
\(462\) | −3.57693e19 | + | 1.81353e20i | −0.0172335 | + | 0.0873752i | ||||
\(463\) | 1.79913e21i | 0.851950i | 0.904735 | + | 0.425975i | \(0.140069\pi\) | ||||
−0.904735 | + | 0.425975i | \(0.859931\pi\) | |||||||
\(464\) | −2.29430e21 | + | 2.32410e21i | −1.06784 | + | 1.08171i | ||||
\(465\) | −1.02024e21 | −0.466744 | ||||||||
\(466\) | 1.68779e21 | + | 3.32894e20i | 0.758983 | + | 0.149699i | ||||
\(467\) | −2.66105e21 | −1.17630 | −0.588150 | − | 0.808752i | \(-0.700143\pi\) | ||||
−0.588150 | + | 0.808752i | \(0.700143\pi\) | |||||||
\(468\) | 1.20309e20 | − | 2.93124e20i | 0.0522797 | − | 0.127375i | ||||
\(469\) | 3.12184e21i | 1.33361i | ||||||||
\(470\) | −2.81991e21 | − | 5.56188e20i | −1.18428 | − | 0.233582i | ||||
\(471\) | − | 9.34061e20i | − | 0.385663i | ||||||
\(472\) | −4.89210e20 | − | 3.23467e20i | −0.198591 | − | 0.131309i | ||||
\(473\) | 2.37517e20 | 0.0947995 | ||||||||
\(474\) | −4.46433e19 | + | 2.26344e20i | −0.0175198 | + | 0.0888266i | ||||
\(475\) | −9.09844e21 | −3.51090 | ||||||||
\(476\) | 2.06407e20 | − | 5.02895e20i | 0.0783195 | − | 0.190819i | ||||
\(477\) | − | 9.32254e19i | − | 0.0347846i | ||||||
\(478\) | 8.01238e19 | − | 4.06233e20i | 0.0293994 | − | 0.149057i | ||||
\(479\) | 3.29728e21i | 1.18979i | 0.803802 | + | 0.594897i | \(0.202807\pi\) | ||||
−0.803802 | + | 0.594897i | \(0.797193\pi\) | |||||||
\(480\) | 3.93103e21 | − | 2.67274e21i | 1.39501 | − | 0.948478i | ||||
\(481\) | 2.42775e21 | 0.847310 | ||||||||
\(482\) | 2.47987e21 | + | 4.89120e20i | 0.851242 | + | 0.167896i | ||||
\(483\) | 2.19977e21 | 0.742679 | ||||||||
\(484\) | −2.74770e21 | − | 1.12776e21i | −0.912445 | − | 0.374503i | ||||
\(485\) | − | 5.55131e21i | − | 1.81327i | ||||||
\(486\) | 6.82696e20 | + | 1.34652e20i | 0.219350 | + | 0.0432637i | ||||
\(487\) | 3.78361e21i | 1.19585i | 0.801554 | + | 0.597923i | \(0.204007\pi\) | ||||
−0.801554 | + | 0.597923i | \(0.795993\pi\) | |||||||
\(488\) | 3.19751e21 | − | 4.83590e21i | 0.994152 | − | 1.50355i | ||||
\(489\) | −9.49859e19 | −0.0290528 | ||||||||
\(490\) | 3.99868e20 | − | 2.02736e21i | 0.120323 | − | 0.610045i | ||||
\(491\) | −1.52093e21 | −0.450254 | −0.225127 | − | 0.974329i | \(-0.572280\pi\) | ||||
−0.225127 | + | 0.974329i | \(0.572280\pi\) | |||||||
\(492\) | 7.04906e20 | + | 2.89321e20i | 0.205310 | + | 0.0842673i | ||||
\(493\) | 1.35420e21i | 0.388067i | ||||||||
\(494\) | −1.33881e21 | + | 6.78787e21i | −0.377489 | + | 1.91389i | ||||
\(495\) | − | 8.48275e19i | − | 0.0235340i | ||||||
\(496\) | 7.12042e20 | − | 7.21290e20i | 0.194380 | − | 0.196905i | ||||
\(497\) | 1.02678e21 | 0.275821 | ||||||||
\(498\) | −4.95224e20 | − | 9.76759e19i | −0.130908 | − | 0.0258198i | ||||
\(499\) | −2.42572e20 | −0.0631010 | −0.0315505 | − | 0.999502i | \(-0.510044\pi\) | ||||
−0.0315505 | + | 0.999502i | \(0.510044\pi\) | |||||||
\(500\) | −3.20218e21 | + | 7.80185e21i | −0.819759 | + | 1.99727i | ||||
\(501\) | 2.98411e20i | 0.0751819i | ||||||||
\(502\) | −3.99152e21 | − | 7.87272e20i | −0.989712 | − | 0.195207i | ||||
\(503\) | − | 4.58027e21i | − | 1.11776i | −0.829250 | − | 0.558878i | \(-0.811232\pi\) | ||
0.829250 | − | 0.558878i | \(-0.188768\pi\) | |||||||
\(504\) | −2.08412e20 | + | 3.15202e20i | −0.0500585 | + | 0.0757084i | ||||
\(505\) | 7.01554e21 | 1.65855 | ||||||||
\(506\) | 9.49307e19 | − | 4.81305e20i | 0.0220903 | − | 0.112000i | ||||
\(507\) | −2.06539e21 | −0.473085 | ||||||||
\(508\) | 1.57444e21 | − | 3.83599e21i | 0.354990 | − | 0.864903i | ||||
\(509\) | − | 4.31209e21i | − | 0.957074i | −0.878067 | − | 0.478537i | \(-0.841167\pi\) | ||
0.878067 | − | 0.478537i | \(-0.158833\pi\) | |||||||
\(510\) | 3.81432e20 | − | 1.93388e21i | 0.0833403 | − | 0.422541i | ||||
\(511\) | − | 8.43022e20i | − | 0.181331i | ||||||
\(512\) | −8.53952e20 | + | 4.64451e21i | −0.180831 | + | 0.983514i | ||||
\(513\) | −8.00113e21 | −1.66806 | ||||||||
\(514\) | −4.01600e21 | − | 7.92099e20i | −0.824306 | − | 0.162583i | ||||
\(515\) | 1.72302e22 | 3.48202 | ||||||||
\(516\) | −3.54920e21 | − | 1.45673e21i | −0.706209 | − | 0.289856i | ||||
\(517\) | 4.02611e20i | 0.0788789i | ||||||||
\(518\) | −2.84055e21 | − | 5.60259e20i | −0.547980 | − | 0.108081i | ||||
\(519\) | − | 3.30690e21i | − | 0.628177i | ||||||
\(520\) | 9.78571e21 | + | 6.47032e21i | 1.83048 | + | 1.21032i | ||||
\(521\) | 6.59580e21 | 1.21497 | 0.607485 | − | 0.794331i | \(-0.292178\pi\) | ||||
0.607485 | + | 0.794331i | \(0.292178\pi\) | |||||||
\(522\) | 1.82155e20 | − | 9.23541e20i | 0.0330429 | − | 0.167530i | ||||
\(523\) | −1.51693e20 | −0.0270990 | −0.0135495 | − | 0.999908i | \(-0.504313\pi\) | ||||
−0.0135495 | + | 0.999908i | \(0.504313\pi\) | |||||||
\(524\) | −7.21402e21 | − | 2.96091e21i | −1.26919 | − | 0.520925i | ||||
\(525\) | 9.69008e21i | 1.67901i | ||||||||
\(526\) | 7.62681e20 | − | 3.86684e21i | 0.130154 | − | 0.659889i | ||||
\(527\) | − | 4.20279e20i | − | 0.0706403i | ||||||
\(528\) | −4.73863e20 | − | 4.67787e20i | −0.0784479 | − | 0.0774420i | ||||
\(529\) | 2.94471e20 | 0.0480173 | ||||||||
\(530\) | 3.38640e21 | + | 6.67919e20i | 0.543915 | + | 0.107280i | ||||
\(531\) | 1.69048e20 | 0.0267457 | ||||||||
\(532\) | 3.13292e21 | − | 7.63310e21i | 0.488266 | − | 1.18962i | ||||
\(533\) | 1.88047e21i | 0.288701i | ||||||||
\(534\) | 4.60266e21 | + | 9.07810e20i | 0.696111 | + | 0.137298i | ||||
\(535\) | − | 7.03232e21i | − | 1.04778i | ||||||
\(536\) | −9.38052e21 | − | 6.20241e21i | −1.37692 | − | 0.910421i | ||||
\(537\) | −1.02877e22 | −1.48773 | ||||||||
\(538\) | −1.72351e21 | + | 8.73834e21i | −0.245559 | + | 1.24500i | ||||
\(539\) | −2.89454e20 | −0.0406321 | ||||||||
\(540\) | −5.15135e21 | + | 1.25508e22i | −0.712477 | + | 1.73589i | ||||
\(541\) | − | 9.66048e21i | − | 1.31650i | −0.752800 | − | 0.658250i | \(-0.771297\pi\) | ||
0.752800 | − | 0.658250i | \(-0.228703\pi\) | |||||||
\(542\) | 5.48848e20 | − | 2.78270e21i | 0.0736983 | − | 0.373655i | ||||
\(543\) | 5.17751e21i | 0.685050i | ||||||||
\(544\) | 1.10101e21 | + | 1.61935e21i | 0.143549 | + | 0.211130i | ||||
\(545\) | −1.21495e22 | −1.56095 | ||||||||
\(546\) | 7.22926e21 | + | 1.42587e21i | 0.915278 | + | 0.180526i | ||||
\(547\) | 1.48555e21 | 0.185348 | 0.0926740 | − | 0.995697i | \(-0.470459\pi\) | ||||
0.0926740 | + | 0.995697i | \(0.470459\pi\) | |||||||
\(548\) | 6.16546e20 | + | 2.53054e20i | 0.0758090 | + | 0.0311150i | ||||
\(549\) | 1.67106e21i | 0.202494i | ||||||||
\(550\) | 2.12017e21 | + | 4.18173e20i | 0.253203 | + | 0.0499407i | ||||
\(551\) | 2.05545e22i | 2.41932i | ||||||||
\(552\) | −4.37046e21 | + | 6.60988e21i | −0.507008 | + | 0.766798i | ||||
\(553\) | 6.79003e20 | 0.0776373 | ||||||||
\(554\) | −5.11417e20 | + | 2.59292e21i | −0.0576364 | + | 0.292220i | ||||
\(555\) | −1.04984e22 | −1.16622 | ||||||||
\(556\) | −3.00659e21 | − | 1.23402e21i | −0.329212 | − | 0.135121i | ||||
\(557\) | − | 9.75638e21i | − | 1.05305i | −0.850161 | − | 0.526523i | \(-0.823495\pi\) | ||
0.850161 | − | 0.526523i | \(-0.176505\pi\) | |||||||
\(558\) | −5.65324e19 | + | 2.86623e20i | −0.00601483 | + | 0.0304956i | ||||
\(559\) | − | 9.46815e21i | − | 0.993049i | ||||||
\(560\) | −9.95646e21 | − | 9.82880e21i | −1.02944 | − | 1.01624i | ||||
\(561\) | −2.76109e20 | −0.0281434 | ||||||||
\(562\) | 8.61956e21 | + | 1.70009e21i | 0.866153 | + | 0.170837i | ||||
\(563\) | 1.86765e22 | 1.85025 | 0.925123 | − | 0.379668i | \(-0.123962\pi\) | ||||
0.925123 | + | 0.379668i | \(0.123962\pi\) | |||||||
\(564\) | 2.46927e21 | − | 6.01618e21i | 0.241177 | − | 0.587608i | ||||
\(565\) | 1.47880e22i | 1.42404i | ||||||||
\(566\) | 9.63901e21 | + | 1.90116e21i | 0.915168 | + | 0.180504i | ||||
\(567\) | 7.55188e21i | 0.706953i | ||||||||
\(568\) | −2.03999e21 | + | 3.08528e21i | −0.188296 | + | 0.284779i | ||||
\(569\) | −1.04130e21 | −0.0947711 | −0.0473856 | − | 0.998877i | \(-0.515089\pi\) | ||||
−0.0473856 | + | 0.998877i | \(0.515089\pi\) | |||||||
\(570\) | 5.78950e21 | − | 2.93531e22i | 0.519567 | − | 2.63424i | ||||
\(571\) | −1.77834e22 | −1.57371 | −0.786856 | − | 0.617137i | \(-0.788293\pi\) | ||||
−0.786856 | + | 0.617137i | \(0.788293\pi\) | |||||||
\(572\) | 6.23954e20 | − | 1.52021e21i | 0.0544483 | − | 0.132659i | ||||
\(573\) | 8.72233e21i | 0.750577i | ||||||||
\(574\) | 4.33962e20 | − | 2.20022e21i | 0.0368262 | − | 0.186711i | ||||
\(575\) | − | 2.57172e22i | − | 2.15219i | ||||||
\(576\) | −5.33050e20 | − | 1.25247e21i | −0.0439935 | − | 0.103368i | ||||
\(577\) | 8.34008e21 | 0.678834 | 0.339417 | − | 0.940636i | \(-0.389770\pi\) | ||||
0.339417 | + | 0.940636i | \(0.389770\pi\) | |||||||
\(578\) | −1.14252e22 | − | 2.25345e21i | −0.917148 | − | 0.180895i | ||||
\(579\) | 1.38385e22 | 1.09562 | ||||||||
\(580\) | 3.22424e22 | + | 1.32335e22i | 2.51770 | + | 1.03336i | ||||
\(581\) | 1.48560e21i | 0.114418i | ||||||||
\(582\) | 1.23229e22 | + | 2.43052e21i | 0.936115 | + | 0.184636i | ||||
\(583\) | − | 4.83490e20i | − | 0.0362275i | ||||||
\(584\) | 2.53311e21 | + | 1.67490e21i | 0.187220 | + | 0.123790i | ||||
\(585\) | −3.38148e21 | −0.246524 | ||||||||
\(586\) | −1.33365e21 | + | 6.76171e21i | −0.0959096 | + | 0.486268i | ||||
\(587\) | −9.67063e21 | −0.686041 | −0.343020 | − | 0.939328i | \(-0.611450\pi\) | ||||
−0.343020 | + | 0.939328i | \(0.611450\pi\) | |||||||
\(588\) | 4.32529e21 | + | 1.77527e21i | 0.302689 | + | 0.124235i | ||||
\(589\) | − | 6.37913e21i | − | 0.440392i | ||||||
\(590\) | −1.21115e21 | + | 6.14064e21i | −0.0824866 | + | 0.418213i | ||||
\(591\) | − | 1.04248e22i | − | 0.700434i | ||||||
\(592\) | 7.32702e21 | − | 7.42218e21i | 0.485684 | − | 0.491992i | ||||
\(593\) | −2.33346e22 | −1.52603 | −0.763016 | − | 0.646379i | \(-0.776282\pi\) | ||||
−0.763016 | + | 0.646379i | \(0.776282\pi\) | |||||||
\(594\) | 1.86447e21 | + | 3.67740e20i | 0.120299 | + | 0.0237273i | ||||
\(595\) | −5.80139e21 | −0.369315 | ||||||||
\(596\) | −2.93969e21 | + | 7.16231e21i | −0.184642 | + | 0.449866i | ||||
\(597\) | − | 1.85106e22i | − | 1.14716i | ||||||
\(598\) | −1.91863e22 | − | 3.78422e21i | −1.17322 | − | 0.231402i | ||||
\(599\) | 2.00138e22i | 1.20758i | 0.797144 | + | 0.603789i | \(0.206343\pi\) | ||||
−0.797144 | + | 0.603789i | \(0.793657\pi\) | |||||||
\(600\) | −2.91168e22 | − | 1.92520e22i | −1.73354 | − | 1.14622i | ||||
\(601\) | 1.72003e22 | 1.01051 | 0.505255 | − | 0.862970i | \(-0.331398\pi\) | ||||
0.505255 | + | 0.862970i | \(0.331398\pi\) | |||||||
\(602\) | −2.18500e21 | + | 1.10781e22i | −0.126672 | + | 0.642234i | ||||
\(603\) | 3.24146e21 | 0.185440 | ||||||||
\(604\) | 8.41362e21 | − | 2.04991e22i | 0.474993 | − | 1.15728i | ||||
\(605\) | 3.16975e22i | 1.76597i | ||||||||
\(606\) | −3.07160e21 | + | 1.55732e22i | −0.168882 | + | 0.856243i | ||||
\(607\) | 3.46685e22i | 1.88116i | 0.339570 | + | 0.940581i | \(0.389718\pi\) | ||||
−0.339570 | + | 0.940581i | \(0.610282\pi\) | |||||||
\(608\) | 1.67115e22 | + | 2.45791e22i | 0.894927 | + | 1.31625i | ||||
\(609\) | 2.18911e22 | 1.15699 | ||||||||
\(610\) | −6.07009e22 | − | 1.19724e22i | −3.16633 | − | 0.624515i | ||||
\(611\) | 1.60493e22 | 0.826277 | ||||||||
\(612\) | −5.22164e20 | − | 2.14316e20i | −0.0265336 | − | 0.0108904i | ||||
\(613\) | − | 2.69106e22i | − | 1.34971i | −0.737952 | − | 0.674853i | \(-0.764207\pi\) | ||
0.737952 | − | 0.674853i | \(-0.235793\pi\) | |||||||
\(614\) | 7.96282e21 | + | 1.57055e21i | 0.394203 | + | 0.0777510i | ||||
\(615\) | − | 8.13180e21i | − | 0.397361i | ||||||
\(616\) | −1.08087e21 | + | 1.63471e21i | −0.0521350 | + | 0.0788489i | ||||
\(617\) | −1.76570e21 | −0.0840689 | −0.0420345 | − | 0.999116i | \(-0.513384\pi\) | ||||
−0.0420345 | + | 0.999116i | \(0.513384\pi\) | |||||||
\(618\) | −7.54385e21 | + | 3.82478e22i | −0.354556 | + | 1.79763i | ||||
\(619\) | −1.74733e22 | −0.810682 | −0.405341 | − | 0.914166i | \(-0.632847\pi\) | ||||
−0.405341 | + | 0.914166i | \(0.632847\pi\) | |||||||
\(620\) | −1.00065e22 | − | 4.10706e21i | −0.458299 | − | 0.188104i | ||||
\(621\) | − | 2.26156e22i | − | 1.02253i | ||||||
\(622\) | 5.50953e21 | − | 2.79337e22i | 0.245918 | − | 1.24682i | ||||
\(623\) | − | 1.38074e22i | − | 0.608424i | ||||||
\(624\) | −1.86474e22 | + | 1.88896e22i | −0.811225 | + | 0.821762i | ||||
\(625\) | 3.86443e22 | 1.65976 | ||||||||
\(626\) | −6.50790e21 | − | 1.28359e21i | −0.275960 | − | 0.0544293i | ||||
\(627\) | −4.19087e21 | −0.175454 | ||||||||
\(628\) | 3.76014e21 | − | 9.16125e21i | 0.155427 | − | 0.378685i | ||||
\(629\) | − | 4.32473e21i | − | 0.176504i | ||||||
\(630\) | 3.95645e21 | + | 7.80355e20i | 0.159434 | + | 0.0314462i | ||||
\(631\) | − | 1.69094e22i | − | 0.672810i | −0.941717 | − | 0.336405i | \(-0.890789\pi\) | ||
0.941717 | − | 0.336405i | \(-0.109211\pi\) | |||||||
\(632\) | −1.34903e21 | + | 2.04027e21i | −0.0530010 | + | 0.0801587i | ||||
\(633\) | 1.71032e22 | 0.663510 | ||||||||
\(634\) | −4.93398e21 | + | 2.50156e22i | −0.189009 | + | 0.958290i | ||||
\(635\) | −4.42520e22 | −1.67395 | ||||||||
\(636\) | −2.96532e21 | + | 7.22475e21i | −0.110768 | + | 0.269877i | ||||
\(637\) | 1.15385e22i | 0.425632i | ||||||||
\(638\) | 9.44703e20 | − | 4.78971e21i | 0.0344136 | − | 0.174479i | ||||
\(639\) | − | 1.06613e21i | − | 0.0383532i | ||||||
\(640\) | 4.93149e22 | − | 1.03895e22i | 1.75202 | − | 0.369111i | ||||
\(641\) | 1.67907e22 | 0.589119 | 0.294560 | − | 0.955633i | \(-0.404827\pi\) | ||||
0.294560 | + | 0.955633i | \(0.404827\pi\) | |||||||
\(642\) | 1.56105e22 | + | 3.07895e21i | 0.540924 | + | 0.106690i | ||||
\(643\) | 1.76394e22 | 0.603665 | 0.301833 | − | 0.953361i | \(-0.402402\pi\) | ||||
0.301833 | + | 0.953361i | \(0.402402\pi\) | |||||||
\(644\) | 2.15753e22 | + | 8.85536e21i | 0.729241 | + | 0.299309i | ||||
\(645\) | 4.09436e22i | 1.36681i | ||||||||
\(646\) | 1.20918e22 | + | 2.38493e21i | 0.398684 | + | 0.0786349i | ||||
\(647\) | − | 5.24930e22i | − | 1.70949i | −0.519046 | − | 0.854747i | \(-0.673713\pi\) | ||
0.519046 | − | 0.854747i | \(-0.326287\pi\) | |||||||
\(648\) | −2.26919e22 | − | 1.50039e22i | −0.729912 | − | 0.482619i | ||||
\(649\) | 8.76724e20 | 0.0278551 | ||||||||
\(650\) | 1.66696e22 | − | 8.45162e22i | 0.523141 | − | 2.65236i | ||||
\(651\) | −6.79394e21 | −0.210607 | ||||||||
\(652\) | −9.31620e20 | − | 3.82373e20i | −0.0285271 | − | 0.0117086i | ||||
\(653\) | 1.05339e22i | 0.318628i | 0.987228 | + | 0.159314i | \(0.0509283\pi\) | ||||
−0.987228 | + | 0.159314i | \(0.949072\pi\) | |||||||
\(654\) | 5.31941e21 | − | 2.69698e22i | 0.158943 | − | 0.805852i | ||||
\(655\) | 8.32209e22i | 2.45642i | ||||||||
\(656\) | 5.74902e21 | + | 5.67531e21i | 0.167635 | + | 0.165485i | ||||
\(657\) | −8.75324e20 | −0.0252142 | ||||||||
\(658\) | −1.87782e22 | − | 3.70374e21i | −0.534377 | − | 0.105398i | ||||
\(659\) | −2.04422e21 | −0.0574704 | −0.0287352 | − | 0.999587i | \(-0.509148\pi\) | ||||
−0.0287352 | + | 0.999587i | \(0.509148\pi\) | |||||||
\(660\) | −2.69820e21 | + | 6.57393e21i | −0.0749415 | + | 0.182589i | ||||
\(661\) | − | 2.82087e22i | − | 0.774055i | −0.922068 | − | 0.387028i | \(-0.873502\pi\) | ||
0.922068 | − | 0.387028i | \(-0.126498\pi\) | |||||||
\(662\) | 3.05548e22 | + | 6.02650e21i | 0.828352 | + | 0.163381i | ||||
\(663\) | 1.10065e22i | 0.294810i | ||||||||
\(664\) | −4.46395e21 | − | 2.95157e21i | −0.118134 | − | 0.0781102i | ||||
\(665\) | −8.80555e22 | −2.30241 | ||||||||
\(666\) | −5.81727e20 | + | 2.94939e21i | −0.0150288 | + | 0.0761972i | ||||
\(667\) | −5.80983e22 | −1.48305 | ||||||||
\(668\) | −1.20128e21 | + | 2.92681e21i | −0.0302992 | + | 0.0738215i | ||||
\(669\) | − | 5.13882e22i | − | 1.28072i | ||||||
\(670\) | −2.32237e22 | + | 1.17746e23i | −0.571916 | + | 2.89965i | ||||
\(671\) | 8.66653e21i | 0.210894i | ||||||||
\(672\) | 2.61774e22 | − | 1.77982e22i | 0.629465 | − | 0.427979i | ||||
\(673\) | −4.51475e21 | −0.107279 | −0.0536393 | − | 0.998560i | \(-0.517082\pi\) | ||||
−0.0536393 | + | 0.998560i | \(0.517082\pi\) | |||||||
\(674\) | 5.78835e22 | + | 1.14167e22i | 1.35917 | + | 0.268078i | ||||
\(675\) | 9.96226e22 | 2.31168 | ||||||||
\(676\) | −2.02573e22 | − | 8.31440e21i | −0.464525 | − | 0.190659i | ||||
\(677\) | 4.53332e22i | 1.02732i | 0.857993 | + | 0.513662i | \(0.171711\pi\) | ||||
−0.857993 | + | 0.513662i | \(0.828289\pi\) | |||||||
\(678\) | −3.28267e22 | − | 6.47461e21i | −0.735173 | − | 0.145003i | ||||
\(679\) | − | 3.69671e22i | − | 0.818195i | ||||||
\(680\) | 1.15261e22 | − | 1.74320e22i | 0.252122 | − | 0.381309i | ||||
\(681\) | −6.17184e22 | −1.33425 | ||||||||
\(682\) | −2.93191e20 | + | 1.48650e21i | −0.00626434 | + | 0.0317606i | ||||
\(683\) | 7.32299e22 | 1.54640 | 0.773202 | − | 0.634160i | \(-0.218654\pi\) | ||||
0.773202 | + | 0.634160i | \(0.218654\pi\) | |||||||
\(684\) | −7.92558e21 | − | 3.25297e21i | −0.165418 | − | 0.0678939i | ||||
\(685\) | − | 7.11248e21i | − | 0.146722i | ||||||
\(686\) | 1.03303e22 | − | 5.23754e22i | 0.210630 | − | 1.06791i | ||||
\(687\) | − | 3.11308e20i | − | 0.00627389i | ||||||
\(688\) | −2.89464e22 | − | 2.85752e22i | −0.576616 | − | 0.569222i | ||||
\(689\) | −1.92734e22 | −0.379493 | ||||||||
\(690\) | 8.29682e22 | + | 1.63643e22i | 1.61480 | + | 0.318497i | ||||
\(691\) | −8.01612e22 | −1.54220 | −0.771099 | − | 0.636715i | \(-0.780293\pi\) | ||||
−0.771099 | + | 0.636715i | \(0.780293\pi\) | |||||||
\(692\) | 1.33122e22 | − | 3.24340e22i | 0.253163 | − | 0.616811i | ||||
\(693\) | − | 5.64879e20i | − | 0.0106192i | ||||||
\(694\) | −8.45127e22 | − | 1.66689e22i | −1.57053 | − | 0.309765i | ||||
\(695\) | 3.46840e22i | 0.637163i | ||||||||
\(696\) | −4.34927e22 | + | 6.57783e22i | −0.789845 | + | 1.19456i | ||||
\(697\) | 3.34982e21 | 0.0601394 | ||||||||
\(698\) | −2.58187e21 | + | 1.30903e22i | −0.0458239 | + | 0.232330i | ||||
\(699\) | 4.15394e22 | 0.728857 | ||||||||
\(700\) | −3.90082e22 | + | 9.50402e22i | −0.676661 | + | 1.64863i | ||||
\(701\) | 8.15142e22i | 1.39794i | 0.715150 | + | 0.698971i | \(0.246358\pi\) | ||||
−0.715150 | + | 0.698971i | \(0.753642\pi\) | |||||||
\(702\) | 1.46592e22 | − | 7.43232e22i | 0.248550 | − | 1.26016i | ||||
\(703\) | − | 6.56422e22i | − | 1.10037i | ||||||
\(704\) | −2.76453e21 | − | 6.49562e21i | −0.0458184 | − | 0.107656i | ||||
\(705\) | −6.94027e22 | −1.13727 | ||||||||
\(706\) | −1.91890e21 | − | 3.78476e20i | −0.0310895 | − | 0.00613198i | ||||
\(707\) | 4.67175e22 | 0.748384 | ||||||||
\(708\) | −1.31008e22 | − | 5.37709e21i | −0.207507 | − | 0.0851689i | ||||
\(709\) | 7.65528e22i | 1.19892i | 0.800403 | + | 0.599462i | \(0.204619\pi\) | ||||
−0.800403 | + | 0.599462i | \(0.795381\pi\) | |||||||
\(710\) | 3.87269e22 | + | 7.63833e21i | 0.599716 | + | 0.118286i | ||||
\(711\) | − | 7.05020e20i | − | 0.0107956i | ||||||
\(712\) | 4.14883e22 | + | 2.74321e22i | 0.628183 | + | 0.415355i | ||||
\(713\) | 1.80309e22 | 0.269962 | ||||||||
\(714\) | 2.54001e21 | − | 1.28780e22i | 0.0376054 | − | 0.190662i | ||||
\(715\) | −1.75372e22 | −0.256750 | ||||||||
\(716\) | −1.00902e23 | − | 4.14141e22i | −1.46081 | − | 0.599575i | ||||
\(717\) | − | 9.99807e21i | − | 0.143141i | ||||||
\(718\) | −6.54496e21 | + | 3.31834e22i | −0.0926641 | + | 0.469813i | ||||
\(719\) | 1.14958e21i | 0.0160956i | 0.999968 | + | 0.00804779i | \(0.00256172\pi\) | ||||
−0.999968 | + | 0.00804779i | \(0.997438\pi\) | |||||||
\(720\) | −1.02054e22 | + | 1.03380e22i | −0.141309 | + | 0.143145i | ||||
\(721\) | 1.14738e23 | 1.57118 | ||||||||
\(722\) | 1.11087e23 | + | 2.19104e22i | 1.50441 | + | 0.296725i | ||||
\(723\) | 6.10337e22 | 0.817454 | ||||||||
\(724\) | −2.08425e22 | + | 5.07809e22i | −0.276084 | + | 0.672655i | ||||
\(725\) | − | 2.55925e23i | − | 3.35281i | ||||||
\(726\) | −7.03627e22 | − | 1.38781e22i | −0.911695 | − | 0.179819i | ||||
\(727\) | − | 6.79227e22i | − | 0.870442i | −0.900324 | − | 0.435221i | \(-0.856670\pi\) | ||
0.900324 | − | 0.435221i | \(-0.143330\pi\) | |||||||
\(728\) | 6.51645e22 | + | 4.30869e22i | 0.825962 | + | 0.546127i | ||||
\(729\) | 8.66010e22 | 1.08568 | ||||||||
\(730\) | 6.27131e21 | − | 3.17960e22i | 0.0777635 | − | 0.394266i | ||||
\(731\) | −1.68663e22 | −0.206863 | ||||||||
\(732\) | 5.31532e22 | − | 1.29503e23i | 0.644823 | − | 1.57106i | ||||
\(733\) | − | 5.54834e22i | − | 0.665781i | −0.942966 | − | 0.332890i | \(-0.891976\pi\) | ||
0.942966 | − | 0.332890i | \(-0.108024\pi\) | |||||||
\(734\) | 1.09952e22 | − | 5.57462e22i | 0.130507 | − | 0.661678i | ||||
\(735\) | − | 4.98966e22i | − | 0.585831i | ||||||
\(736\) | −6.94740e22 | + | 4.72360e22i | −0.806863 | + | 0.548593i | ||||
\(737\) | 1.68110e22 | 0.193132 | ||||||||
\(738\) | −2.28452e21 | − | 4.50590e20i | −0.0259624 | − | 0.00512071i | ||||
\(739\) | 1.07018e23 | 1.20310 | 0.601548 | − | 0.798836i | \(-0.294551\pi\) | ||||
0.601548 | + | 0.798836i | \(0.294551\pi\) | |||||||
\(740\) | −1.02968e23 | − | 4.22622e22i | −1.14512 | − | 0.470001i | ||||
\(741\) | 1.67061e23i | 1.83793i | ||||||||
\(742\) | 2.25505e22 | + | 4.44778e21i | 0.245429 | + | 0.0484074i | ||||
\(743\) | 1.43921e23i | 1.54958i | 0.632217 | + | 0.774791i | \(0.282145\pi\) | ||||
−0.632217 | + | 0.774791i | \(0.717855\pi\) | |||||||
\(744\) | 1.34981e22 | − | 2.04144e22i | 0.143776 | − | 0.217447i | ||||
\(745\) | 8.26244e22 | 0.870679 | ||||||||
\(746\) | −2.71969e22 | + | 1.37890e23i | −0.283537 | + | 1.43755i | ||||
\(747\) | 1.54253e21 | 0.0159099 | ||||||||
\(748\) | −2.70807e21 | − | 1.11150e21i | −0.0276342 | − | 0.0113422i | ||||
\(749\) | − | 4.68293e22i | − | 0.472785i | ||||||
\(750\) | −3.94055e22 | + | 1.99788e23i | −0.393610 | + | 1.99563i | ||||
\(751\) | 8.40625e22i | 0.830774i | 0.909645 | + | 0.415387i | \(0.136354\pi\) | ||||
−0.909645 | + | 0.415387i | \(0.863646\pi\) | |||||||
\(752\) | 4.84372e22 | − | 4.90663e22i | 0.473627 | − | 0.479779i | ||||
\(753\) | −9.82379e22 | −0.950428 | ||||||||
\(754\) | −1.90932e23 | − | 3.76587e22i | −1.82771 | − | 0.360491i | ||||
\(755\) | −2.36478e23 | −2.23983 | ||||||||
\(756\) | −3.43036e22 | + | 8.35779e22i | −0.321489 | + | 0.783281i | ||||
\(757\) | 3.71747e22i | 0.344731i | 0.985033 | + | 0.172366i | \(0.0551410\pi\) | ||||
−0.985033 | + | 0.172366i | \(0.944859\pi\) | |||||||
\(758\) | −4.56162e22 | − | 8.99715e21i | −0.418567 | − | 0.0825565i | ||||
\(759\) | − | 1.18457e22i | − | 0.107554i | ||||||
\(760\) | 1.74947e23 | − | 2.64589e23i | 1.57180 | − | 2.37719i | ||||
\(761\) | −1.53461e23 | −1.36434 | −0.682168 | − | 0.731195i | \(-0.738963\pi\) | ||||
−0.682168 | + | 0.731195i | \(0.738963\pi\) | |||||||
\(762\) | 1.93747e22 | − | 9.82313e22i | 0.170450 | − | 0.864192i | ||||
\(763\) | −8.09057e22 | −0.704341 | ||||||||
\(764\) | −3.51124e22 | + | 8.55485e22i | −0.302492 | + | 0.736997i | ||||
\(765\) | 6.02369e21i | 0.0513536i | ||||||||
\(766\) | 9.61807e21 | − | 4.87643e22i | 0.0811442 | − | 0.411407i | ||||
\(767\) | − | 3.49489e22i | − | 0.291790i | ||||||
\(768\) | 1.47147e21 | + | 1.14019e23i | 0.0121580 | + | 0.942078i | ||||
\(769\) | 9.31513e22 | 0.761690 | 0.380845 | − | 0.924639i | \(-0.375633\pi\) | ||||
0.380845 | + | 0.924639i | \(0.375633\pi\) | |||||||
\(770\) | 2.05191e22 | + | 4.04711e21i | 0.166048 | + | 0.0327506i | ||||
\(771\) | −9.88403e22 | −0.791587 | ||||||||
\(772\) | 1.35728e23 | + | 5.57080e22i | 1.07580 | + | 0.441550i | ||||
\(773\) | 1.15903e23i | 0.909196i | 0.890697 | + | 0.454598i | \(0.150217\pi\) | ||||
−0.890697 | + | 0.454598i | \(0.849783\pi\) | |||||||
\(774\) | 1.15026e22 | + | 2.26872e21i | 0.0893033 | + | 0.0176138i | ||||
\(775\) | 7.94269e22i | 0.610315i | ||||||||
\(776\) | 1.11079e23 | + | 7.34454e22i | 0.844767 | + | 0.558561i | ||||
\(777\) | −6.99107e22 | −0.526230 | ||||||||
\(778\) | 3.35175e22 | − | 1.69936e23i | 0.249710 | − | 1.26605i | ||||
\(779\) | 5.08447e22 | 0.374926 | ||||||||
\(780\) | 2.62057e23 | + | 1.07558e23i | 1.91266 | + | 0.785031i | ||||
\(781\) | − | 5.52919e21i | − | 0.0399442i | ||||||
\(782\) | −6.74112e21 | + | 3.41780e22i | −0.0482035 | + | 0.244395i | ||||
\(783\) | − | 2.25059e23i | − | 1.59295i | ||||||
\(784\) | 3.52759e22 | + | 3.48236e22i | 0.247144 | + | 0.243975i | ||||
\(785\) | −1.05684e23 | −0.732914 | ||||||||
\(786\) | −1.84735e23 | − | 3.64365e22i | −1.26815 | − | 0.250124i | ||||
\(787\) | −2.21417e23 | −1.50457 | −0.752285 | − | 0.658838i | \(-0.771048\pi\) | ||||
−0.752285 | + | 0.658838i | \(0.771048\pi\) | |||||||
\(788\) | 4.19658e22 | − | 1.02246e23i | 0.282283 | − | 0.687760i | ||||
\(789\) | − | 9.51694e22i | − | 0.633696i | ||||||
\(790\) | 2.56097e22 | + | 5.05116e21i | 0.168806 | + | 0.0332947i | ||||
\(791\) | 9.84757e22i | 0.642565i | ||||||||
\(792\) | 1.69735e21 | + | 1.12229e21i | 0.0109640 | + | 0.00724943i | ||||
\(793\) | 3.45474e23 | 2.20917 | ||||||||
\(794\) | −2.51749e22 | + | 1.27638e23i | −0.159369 | + | 0.808011i | ||||
\(795\) | 8.33448e22 | 0.522326 | ||||||||
\(796\) | 7.45159e22 | − | 1.81552e23i | 0.462322 | − | 1.12641i | ||||
\(797\) | 1.86468e23i | 1.14535i | 0.819783 | + | 0.572674i | \(0.194094\pi\) | ||||
−0.819783 | + | 0.572674i | \(0.805906\pi\) | |||||||
\(798\) | 3.85532e22 | − | 1.95467e23i | 0.234443 | − | 1.18864i | ||||
\(799\) | − | 2.85898e22i | − | 0.172122i | ||||||
\(800\) | −2.08076e23 | − | 3.06036e23i | −1.24023 | − | 1.82411i | ||||
\(801\) | −1.43364e22 | −0.0846019 | ||||||||
\(802\) | 1.74083e23 | + | 3.43354e22i | 1.01709 | + | 0.200607i | ||||
\(803\) | −4.53964e21 | −0.0262602 | ||||||||
\(804\) | −2.51206e23 | − | 1.03105e23i | −1.43874 | − | 0.590514i | ||||
\(805\) | − | 2.48893e23i | − | 1.41139i | ||||||
\(806\) | 5.92562e22 | + | 1.16875e22i | 0.332701 | + | 0.0656206i | ||||
\(807\) | 2.15065e23i | 1.19559i | ||||||||
\(808\) | −9.28174e22 | + | 1.40377e23i | −0.510903 | + | 0.772689i | ||||
\(809\) | 3.28894e23 | 1.79254 | 0.896268 | − | 0.443514i | \(-0.146268\pi\) | ||||
0.896268 | + | 0.443514i | \(0.146268\pi\) | |||||||
\(810\) | −5.61791e22 | + | 2.84832e23i | −0.303176 | + | 1.53712i | ||||
\(811\) | 1.57001e23 | 0.838951 | 0.419476 | − | 0.907767i | \(-0.362214\pi\) | ||||
0.419476 | + | 0.907767i | \(0.362214\pi\) | |||||||
\(812\) | 2.14707e23 | + | 8.81242e22i | 1.13605 | + | 0.466280i | ||||
\(813\) | − | 6.84867e22i | − | 0.358824i | ||||||
\(814\) | −3.01698e21 | + | 1.52963e22i | −0.0156523 | + | 0.0793580i | ||||
\(815\) | 1.07472e22i | 0.0552120i | ||||||||
\(816\) | 3.36495e22 | + | 3.32180e22i | 0.171182 | + | 0.168987i | ||||
\(817\) | −2.56003e23 | −1.28964 | ||||||||
\(818\) | −4.50566e22 | − | 8.88678e21i | −0.224767 | − | 0.0443320i | ||||
\(819\) | −2.25178e22 | −0.111238 | ||||||||
\(820\) | 3.27352e22 | − | 7.97566e22i | 0.160142 | − | 0.390172i | ||||
\(821\) | − | 1.32878e23i | − | 0.643735i | −0.946785 | − | 0.321868i | \(-0.895689\pi\) | ||
0.946785 | − | 0.321868i | \(-0.104311\pi\) | |||||||
\(822\) | 1.57884e22 | + | 3.11404e21i | 0.0757467 | + | 0.0149400i | ||||
\(823\) | − | 1.08398e23i | − | 0.515018i | −0.966276 | − | 0.257509i | \(-0.917098\pi\) | ||
0.966276 | − | 0.257509i | \(-0.0829017\pi\) | |||||||
\(824\) | −2.27960e23 | + | 3.44766e23i | −1.07261 | + | 1.62221i | ||||
\(825\) | 5.21808e22 | 0.243153 | ||||||||
\(826\) | −8.06527e21 | + | 4.08915e22i | −0.0372202 | + | 0.188709i | ||||
\(827\) | −9.67193e22 | −0.442048 | −0.221024 | − | 0.975268i | \(-0.570940\pi\) | ||||
−0.221024 | + | 0.975268i | \(0.570940\pi\) | |||||||
\(828\) | 9.19467e21 | − | 2.24020e22i | 0.0416192 | − | 0.101402i | ||||
\(829\) | − | 1.48169e22i | − | 0.0664234i | −0.999448 | − | 0.0332117i | \(-0.989426\pi\) | ||
0.999448 | − | 0.0332117i | \(-0.0105736\pi\) | |||||||
\(830\) | −1.10515e22 | + | 5.60321e22i | −0.0490680 | + | 0.248778i | ||||
\(831\) | 6.38160e22i | 0.280622i | ||||||||
\(832\) | −2.58935e23 | + | 1.10202e23i | −1.12773 | + | 0.479959i | ||||
\(833\) | 2.05544e22 | 0.0886636 | ||||||||
\(834\) | −7.69921e22 | − | 1.51856e22i | −0.328941 | − | 0.0648790i | ||||
\(835\) | 3.37637e22 | 0.142876 | ||||||||
\(836\) | −4.11040e22 | − | 1.68707e22i | −0.172280 | − | 0.0707102i | ||||
\(837\) | 6.98477e22i | 0.289967i | ||||||||
\(838\) | 2.85880e23 | + | 5.63858e22i | 1.17552 | + | 0.231856i | ||||
\(839\) | − | 3.62220e23i | − | 1.47529i | −0.675191 | − | 0.737643i | \(-0.735939\pi\) | ||
0.675191 | − | 0.737643i | \(-0.264061\pi\) | |||||||
\(840\) | −2.81794e23 | − | 1.86323e23i | −1.13684 | − | 0.751678i | ||||
\(841\) | −3.27919e23 | −1.31038 | ||||||||
\(842\) | 7.64997e22 | − | 3.87859e23i | 0.302805 | − | 1.53524i | ||||
\(843\) | 2.12142e23 | 0.831774 | ||||||||
\(844\) | 1.67748e23 | + | 6.88503e22i | 0.651505 | + | 0.267403i | ||||
\(845\) | 2.33689e23i | 0.899051i | ||||||||
\(846\) | −3.84566e21 | + | 1.94978e22i | −0.0146558 | + | 0.0743057i | ||||
\(847\) | 2.11079e23i | 0.796851i | ||||||||
\(848\) | −5.81676e22 | + | 5.89231e22i | −0.217528 | + | 0.220353i | ||||
\(849\) | 2.37232e23 | 0.878843 | ||||||||
\(850\) | −1.50555e23 | − | 2.96949e22i | −0.552515 | − | 0.108976i | ||||
\(851\) | 1.85541e23 | 0.674533 | ||||||||
\(852\) | −3.39114e22 | + | 8.26223e22i | −0.122132 | + | 0.297564i | ||||
\(853\) | 3.18100e23i | 1.13494i | 0.823395 | + | 0.567469i | \(0.192077\pi\) | ||||
−0.823395 | + | 0.567469i | \(0.807923\pi\) | |||||||
\(854\) | −4.04217e23 | − | 7.97262e22i | −1.42874 | − | 0.281798i | ||||
\(855\) | 9.14295e22i | 0.320153i | ||||||||
\(856\) | 1.40713e23 | + | 9.30395e22i | 0.488139 | + | 0.322758i | ||||
\(857\) | −3.38794e23 | −1.16436 | −0.582182 | − | 0.813059i | \(-0.697801\pi\) | ||||
−0.582182 | + | 0.813059i | \(0.697801\pi\) | |||||||
\(858\) | 7.67826e21 | − | 3.89293e22i | 0.0261436 | − | 0.132550i | ||||
\(859\) | 5.84793e23 | 1.97268 | 0.986341 | − | 0.164717i | \(-0.0526711\pi\) | ||||
0.986341 | + | 0.164717i | \(0.0526711\pi\) | |||||||
\(860\) | −1.64822e23 | + | 4.01575e23i | −0.550842 | + | 1.34208i | ||||
\(861\) | − | 5.41509e22i | − | 0.179300i | ||||||
\(862\) | 3.53581e22 | − | 1.79268e23i | 0.115993 | − | 0.588091i | ||||
\(863\) | − | 1.38504e23i | − | 0.450170i | −0.974339 | − | 0.225085i | \(-0.927734\pi\) | ||
0.974339 | − | 0.225085i | \(-0.0722659\pi\) | |||||||
\(864\) | −1.82981e23 | − | 2.69126e23i | −0.589246 | − | 0.866655i | ||||
\(865\) | −3.74159e23 | −1.19379 | ||||||||
\(866\) | −1.33449e23 | − | 2.63210e22i | −0.421864 | − | 0.0832068i | ||||
\(867\) | −2.81192e23 | −0.880745 | ||||||||
\(868\) | −6.66349e22 | − | 2.73495e22i | −0.206797 | − | 0.0848774i | ||||
\(869\) | − | 3.65641e21i | − | 0.0112434i | ||||||
\(870\) | 8.25658e23 | + | 1.62849e23i | 2.51563 | + | 0.496172i | ||||
\(871\) | − | 6.70138e23i | − | 2.02311i | ||||||
\(872\) | 1.60742e23 | − | 2.43106e23i | 0.480836 | − | 0.727215i | ||||
\(873\) | −3.83835e22 | −0.113771 | ||||||||
\(874\) | −1.02319e23 | + | 5.18765e23i | −0.300514 | + | 1.52363i | ||||
\(875\) | 5.99338e23 | 1.74425 | ||||||||
\(876\) | 6.78356e22 | + | 2.78424e22i | 0.195625 | + | 0.0802922i | ||||
\(877\) | − | 3.04222e23i | − | 0.869348i | −0.900588 | − | 0.434674i | \(-0.856864\pi\) | ||
0.900588 | − | 0.434674i | \(-0.143136\pi\) | |||||||
\(878\) | −3.36850e22 | + | 1.70785e23i | −0.0953851 | + | 0.483609i | ||||
\(879\) | 1.66417e23i | 0.466967i | ||||||||
\(880\) | −5.29277e22 | + | 5.36152e22i | −0.147171 | + | 0.149083i | ||||
\(881\) | 1.55764e23 | 0.429201 | 0.214601 | − | 0.976702i | \(-0.431155\pi\) | ||||
0.214601 | + | 0.976702i | \(0.431155\pi\) | |||||||
\(882\) | −1.40178e22 | − | 2.76481e21i | −0.0382764 | − | 0.00754948i | ||||
\(883\) | −5.02093e23 | −1.35862 | −0.679310 | − | 0.733851i | \(-0.737721\pi\) | ||||
−0.679310 | + | 0.733851i | \(0.737721\pi\) | |||||||
\(884\) | −4.43076e22 | + | 1.07952e23i | −0.118812 | + | 0.289475i | ||||
\(885\) | 1.51131e23i | 0.401613i | ||||||||
\(886\) | 2.37275e23 | + | 4.67992e22i | 0.624860 | + | 0.123245i | ||||
\(887\) | 6.65140e22i | 0.173590i | 0.996226 | + | 0.0867948i | \(0.0276625\pi\) | ||||
−0.996226 | + | 0.0867948i | \(0.972338\pi\) | |||||||
\(888\) | 1.38897e23 | − | 2.10068e23i | 0.359244 | − | 0.543320i | ||||
\(889\) | −2.94681e23 | −0.755331 | ||||||||
\(890\) | 1.02714e23 | − | 5.20767e23i | 0.260922 | − | 1.32289i | ||||
\(891\) | 4.06666e22 | 0.102380 | ||||||||
\(892\) | 2.06867e23 | − | 5.04015e23i | 0.516146 | − | 1.25755i | ||||
\(893\) | − | 4.33945e23i | − | 1.07306i | ||||||
\(894\) | −3.61753e22 | + | 1.83411e23i | −0.0886567 | + | 0.449496i | ||||
\(895\) | 1.16400e24i | 2.82729i | ||||||||
\(896\) | 3.28395e23 | − | 6.91856e22i | 0.790557 | − | 0.166553i | ||||
\(897\) | −4.72205e23 | −1.12666 | ||||||||
\(898\) | 4.85650e23 | + | 9.57876e22i | 1.14845 | + | 0.226516i | ||||
\(899\) | 1.79435e23 | 0.420561 | ||||||||
\(900\) | 9.86818e22 | + | 4.05029e22i | 0.229244 | + | 0.0940905i | ||||
\(901\) | 3.43331e22i | 0.0790523i | ||||||||
\(902\) | −1.18481e22 | − | 2.33687e21i | −0.0270393 | − | 0.00533313i | ||||
\(903\) | 2.72650e23i | 0.616742i | ||||||||
\(904\) | −2.95900e23 | − | 1.95649e23i | −0.663433 | − | 0.438663i | ||||
\(905\) | 5.85809e23 | 1.30187 | ||||||||
\(906\) | 1.03537e23 | − | 5.24937e23i | 0.228070 | − | 1.15633i | ||||
\(907\) | −1.68108e23 | −0.367054 | −0.183527 | − | 0.983015i | \(-0.558751\pi\) | ||||
−0.183527 | + | 0.983015i | \(0.558751\pi\) | |||||||
\(908\) | −6.05333e23 | − | 2.48452e23i | −1.31011 | − | 0.537720i | ||||
\(909\) | − | 4.85076e22i | − | 0.104064i | ||||||
\(910\) | 1.61330e23 | − | 8.17955e23i | 0.343071 | − | 1.73939i | ||||
\(911\) | − | 5.30378e23i | − | 1.11799i | −0.829171 | − | 0.558996i | \(-0.811187\pi\) | ||
0.829171 | − | 0.558996i | \(-0.188813\pi\) | |||||||
\(912\) | 5.10743e23 | + | 5.04194e23i | 1.06720 | + | 1.05351i | ||||
\(913\) | 7.99993e21 | 0.0165699 | ||||||||
\(914\) | −1.89095e22 | − | 3.72964e21i | −0.0388250 | − | 0.00765768i | ||||
\(915\) | −1.49395e24 | −3.04066 | ||||||||
\(916\) | 1.25320e21 | − | 3.05331e21i | 0.00252846 | − | 0.00616037i | ||||
\(917\) | 5.54181e23i | 1.10840i | ||||||||
\(918\) | −1.32398e23 | − | 2.61136e22i | −0.262506 | − | 0.0517756i | ||||
\(919\) | − | 6.79014e23i | − | 1.33461i | −0.744784 | − | 0.667305i | \(-0.767448\pi\) | ||
0.744784 | − | 0.667305i | \(-0.232552\pi\) | |||||||
\(920\) | 7.47875e23 | + | 4.94496e23i | 1.45722 | + | 0.963518i | ||||
\(921\) | 1.95978e23 | 0.378556 | ||||||||
\(922\) | −1.38851e23 | + | 7.03982e23i | −0.265889 | + | 1.34807i | ||||
\(923\) | −2.20410e23 | −0.418425 | ||||||||
\(924\) | −1.79677e22 | + | 4.37768e22i | −0.0338156 | + | 0.0823889i | ||||
\(925\) | 8.17315e23i | 1.52495i | ||||||||
\(926\) | −8.91253e22 | + | 4.51871e23i | −0.164859 | + | 0.835847i | ||||
\(927\) | − | 1.19135e23i | − | 0.218474i | ||||||
\(928\) | −6.91371e23 | + | 4.70069e23i | −1.25698 | + | 0.854629i | ||||
\(929\) | 9.06740e23 | 1.63440 | 0.817198 | − | 0.576357i | \(-0.195526\pi\) | ||||
0.817198 | + | 0.576357i | \(0.195526\pi\) | |||||||
\(930\) | −2.56245e23 | − | 5.05407e22i | −0.457922 | − | 0.0903187i | ||||
\(931\) | 3.11982e23 | 0.552754 | ||||||||
\(932\) | 4.07418e23 | + | 1.67220e23i | 0.715670 | + | 0.293739i | ||||
\(933\) | − | 6.87494e23i | − | 1.19733i | ||||||
\(934\) | −6.68352e23 | − | 1.31823e23i | −1.15407 | − | 0.227623i | ||||
\(935\) | 3.12403e22i | 0.0534838i | ||||||||
\(936\) | 4.47378e22 | − | 6.76614e22i | 0.0759396 | − | 0.114851i | ||||
\(937\) | −9.57272e23 | −1.61108 | −0.805542 | − | 0.592538i | \(-0.798126\pi\) | ||||
−0.805542 | + | 0.592538i | \(0.798126\pi\) | |||||||
\(938\) | −1.54650e23 | + | 7.84086e23i | −0.258064 | + | 1.30840i | ||||
\(939\) | −1.60170e23 | −0.265007 | ||||||||
\(940\) | −6.80700e23 | − | 2.79386e23i | −1.11669 | − | 0.458334i | ||||
\(941\) | − | 2.45725e23i | − | 0.399698i | −0.979827 | − | 0.199849i | \(-0.935955\pi\) | ||
0.979827 | − | 0.199849i | \(-0.0640451\pi\) | |||||||
\(942\) | 4.62715e22 | − | 2.34600e23i | 0.0746288 | − | 0.378373i | ||||
\(943\) | 1.43715e23i | 0.229831i | ||||||||
\(944\) | −1.06847e23 | − | 1.05477e23i | −0.169428 | − | 0.167256i | ||||
\(945\) | 9.64155e23 | 1.51598 | ||||||||
\(946\) | 5.96552e22 | + | 1.17661e22i | 0.0930077 | + | 0.0183445i | ||||
\(947\) | −4.17834e23 | −0.645958 | −0.322979 | − | 0.946406i | \(-0.604684\pi\) | ||||
−0.322979 | + | 0.946406i | \(0.604684\pi\) | |||||||
\(948\) | −2.24253e22 | + | 5.46374e22i | −0.0343773 | + | 0.0837575i | ||||
\(949\) | 1.80964e23i | 0.275082i | ||||||||
\(950\) | −2.28518e24 | − | 4.50719e23i | −3.44454 | − | 0.679387i | ||||
\(951\) | 6.15675e23i | 0.920253i | ||||||||
\(952\) | 7.67540e22 | − | 1.16083e23i | 0.113764 | − | 0.172057i | ||||
\(953\) | 5.39088e23 | 0.792348 | 0.396174 | − | 0.918175i | \(-0.370338\pi\) | ||||
0.396174 | + | 0.918175i | \(0.370338\pi\) | |||||||
\(954\) | 4.61820e21 | − | 2.34146e22i | 0.00673110 | − | 0.0341271i | ||||
\(955\) | 9.86888e23 | 1.42640 | ||||||||
\(956\) | 4.02480e22 | − | 9.80609e22i | 0.0576874 | − | 0.140551i | ||||
\(957\) | − | 1.17883e23i | − | 0.167554i | ||||||
\(958\) | −1.63341e23 | + | 8.28149e23i | −0.230235 | + | 1.16730i | ||||
\(959\) | − | 4.73631e22i | − | 0.0662051i | ||||||
\(960\) | 1.11973e24 | − | 4.76554e23i | 1.55218 | − | 0.660605i | ||||
\(961\) | 6.71735e23 | 0.923445 | ||||||||
\(962\) | 6.09756e23 | + | 1.20266e23i | 0.831295 | + | 0.163961i | ||||
\(963\) | −4.86237e22 | −0.0657412 | ||||||||
\(964\) | 5.98618e23 | + | 2.45696e23i | 0.802663 | + | 0.329444i | ||||
\(965\) | − | 1.56576e24i | − | 2.08212i | ||||||
\(966\) | 5.52498e23 | + | 1.08972e23i | 0.728641 | + | 0.143714i | ||||
\(967\) | 7.48210e23i | 0.978614i | 0.872111 | + | 0.489307i | \(0.162750\pi\) | ||||
−0.872111 | + | 0.489307i | \(0.837250\pi\) | |||||||
\(968\) | −6.34249e23 | − | 4.19366e23i | −0.822730 | − | 0.543990i | ||||
\(969\) | 2.97598e23 | 0.382860 | ||||||||
\(970\) | 2.75001e23 | − | 1.39428e24i | 0.350882 | − | 1.77899i | ||||
\(971\) | 1.41552e24 | 1.79128 | 0.895640 | − | 0.444781i | \(-0.146718\pi\) | ||||
0.895640 | + | 0.444781i | \(0.146718\pi\) | |||||||
\(972\) | 1.64796e23 | + | 6.76389e22i | 0.206832 | + | 0.0848919i | ||||
\(973\) | 2.30966e23i | 0.287505i | ||||||||
\(974\) | −1.87433e23 | + | 9.50297e23i | −0.231406 | + | 1.17324i | ||||
\(975\) | − | 2.08008e24i | − | 2.54708i | ||||||
\(976\) | 1.04265e24 | − | 1.05619e24i | 1.26631 | − | 1.28276i | ||||
\(977\) | −3.64742e23 | −0.439369 | −0.219685 | − | 0.975571i | \(-0.570503\pi\) | ||||
−0.219685 | + | 0.975571i | \(0.570503\pi\) | |||||||
\(978\) | −2.38568e22 | − | 4.70542e21i | −0.0285037 | − | 0.00562195i | ||||
\(979\) | −7.43521e22 | −0.0881113 | ||||||||
\(980\) | 2.00863e23 | − | 4.89385e23i | 0.236097 | − | 0.575231i | ||||
\(981\) | 8.40058e22i | 0.0979393i | ||||||||
\(982\) | −3.81999e23 | − | 7.53439e22i | −0.441743 | − | 0.0871277i | ||||
\(983\) | 1.32002e24i | 1.51410i | 0.653359 | + | 0.757049i | \(0.273359\pi\) | ||||
−0.653359 | + | 0.757049i | \(0.726641\pi\) | |||||||
\(984\) | 1.62713e23 | + | 1.07586e23i | 0.185123 | + | 0.122404i | ||||
\(985\) | −1.17951e24 | −1.33110 | ||||||||
\(986\) | −6.70843e22 | + | 3.40122e23i | −0.0750941 | + | 0.380732i | ||||
\(987\) | −4.62163e23 | −0.513166 | ||||||||
\(988\) | −6.72516e23 | + | 1.63853e24i | −0.740708 | + | 1.80467i | ||||
\(989\) | − | 7.23606e23i | − | 0.790554i | ||||||
\(990\) | 4.20219e21 | − | 2.13054e22i | 0.00455401 | − | 0.0230891i | ||||
\(991\) | − | 7.48922e23i | − | 0.805095i | −0.915399 | − | 0.402548i | \(-0.868125\pi\) | ||
0.915399 | − | 0.402548i | \(-0.131875\pi\) | |||||||
\(992\) | 2.14569e23 | − | 1.45887e23i | 0.228809 | − | 0.155569i | ||||
\(993\) | 7.52003e23 | 0.795473 | ||||||||
\(994\) | 2.57888e23 | + | 5.08648e22i | 0.270608 | + | 0.0533736i | ||||
\(995\) | −2.09438e24 | −2.18007 | ||||||||
\(996\) | −1.19542e23 | − | 4.90648e22i | −0.123437 | − | 0.0506635i | ||||
\(997\) | 4.07882e23i | 0.417805i | 0.977937 | + | 0.208902i | \(0.0669891\pi\) | ||||
−0.977937 | + | 0.208902i | \(0.933011\pi\) | |||||||
\(998\) | −6.09247e22 | − | 1.20165e22i | −0.0619083 | − | 0.0122105i | ||||
\(999\) | 7.18743e23i | 0.724519i |
(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 | 8.17.d.b.3.14 | yes | 14 | |
3.2 | odd | 2 | 72.17.b.b.19.1 | 14 | |||
4.3 | odd | 2 | 32.17.d.b.15.3 | 14 | |||
8.3 | odd | 2 | inner | 8.17.d.b.3.13 | ✓ | 14 | |
8.5 | even | 2 | 32.17.d.b.15.4 | 14 | |||
24.11 | even | 2 | 72.17.b.b.19.2 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.17.d.b.3.13 | ✓ | 14 | 8.3 | odd | 2 | inner | |
8.17.d.b.3.14 | yes | 14 | 1.1 | even | 1 | trivial | |
32.17.d.b.15.3 | 14 | 4.3 | odd | 2 | |||
32.17.d.b.15.4 | 14 | 8.5 | even | 2 | |||
72.17.b.b.19.1 | 14 | 3.2 | odd | 2 | |||
72.17.b.b.19.2 | 14 | 24.11 | even | 2 |