Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,30,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (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: | \(111.883889004\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.8 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.30.c.a.20.7 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 21897.4i | 0.945058i | 0.881315 | + | 0.472529i | \(0.156659\pi\) | ||||
−0.881315 | + | 0.472529i | \(0.843341\pi\) | |||||||
\(3\) | −3.41396e6 | − | 7.54819e6i | −0.412098 | − | 0.911140i | ||||
\(4\) | 5.73727e7 | 0.106865 | ||||||||
\(5\) | −2.19660e10 | −1.60948 | −0.804742 | − | 0.593625i | \(-0.797696\pi\) | ||||
−0.804742 | + | 0.593625i | \(0.797696\pi\) | |||||||
\(6\) | 1.65286e11 | − | 7.47571e10i | 0.861080 | − | 0.389457i | ||||
\(7\) | 7.76630e11 | + | 1.61764e12i | 0.432805 | + | 0.901487i | ||||
\(8\) | 1.30124e13i | 1.04605i | ||||||||
\(9\) | −4.53201e13 | + | 5.15385e13i | −0.660351 | + | 0.750958i | ||||
\(10\) | − | 4.81000e14i | − | 1.52106i | ||||||
\(11\) | 2.40340e15i | 1.90824i | 0.299426 | + | 0.954120i | \(0.403205\pi\) | ||||
−0.299426 | + | 0.954120i | \(0.596795\pi\) | |||||||
\(12\) | −1.95868e14 | − | 4.33060e14i | −0.0440388 | − | 0.0973689i | ||||
\(13\) | − | 1.13407e16i | − | 0.798841i | −0.916768 | − | 0.399421i | \(-0.869211\pi\) | ||
0.916768 | − | 0.399421i | \(-0.130789\pi\) | |||||||
\(14\) | −3.54221e16 | + | 1.70062e16i | −0.851958 | + | 0.409026i | ||||
\(15\) | 7.49912e16 | + | 1.65804e17i | 0.663265 | + | 1.46646i | ||||
\(16\) | −2.54137e17 | −0.881715 | ||||||||
\(17\) | −2.64385e17 | −0.380827 | −0.190414 | − | 0.981704i | \(-0.560983\pi\) | ||||
−0.190414 | + | 0.981704i | \(0.560983\pi\) | |||||||
\(18\) | −1.12856e18 | − | 9.92395e17i | −0.709699 | − | 0.624070i | ||||
\(19\) | 3.62583e18i | 1.04107i | 0.853840 | + | 0.520535i | \(0.174267\pi\) | ||||
−0.853840 | + | 0.520535i | \(0.825733\pi\) | |||||||
\(20\) | −1.26025e18 | −0.171997 | ||||||||
\(21\) | 9.55886e18 | − | 1.13847e19i | 0.643023 | − | 0.765847i | ||||
\(22\) | −5.26284e19 | −1.80340 | ||||||||
\(23\) | 1.89636e19i | 0.341089i | 0.985350 | + | 0.170544i | \(0.0545526\pi\) | ||||
−0.985350 | + | 0.170544i | \(0.945447\pi\) | |||||||
\(24\) | 9.82203e19 | − | 4.44239e19i | 0.953099 | − | 0.431076i | ||||
\(25\) | 2.96242e20 | 1.59044 | ||||||||
\(26\) | 2.48332e20 | 0.754951 | ||||||||
\(27\) | 5.43744e20 | + | 1.66134e20i | 0.956356 | + | 0.292203i | ||||
\(28\) | 4.45574e19 | + | 9.28082e19i | 0.0462517 | + | 0.0963374i | ||||
\(29\) | 1.75722e21i | 1.09662i | 0.836276 | + | 0.548309i | \(0.184728\pi\) | ||||
−0.836276 | + | 0.548309i | \(0.815272\pi\) | |||||||
\(30\) | −3.63068e21 | + | 1.64212e21i | −1.38589 | + | 0.626824i | ||||
\(31\) | 5.25929e21i | 1.24791i | 0.781462 | + | 0.623953i | \(0.214475\pi\) | ||||
−0.781462 | + | 0.623953i | \(0.785525\pi\) | |||||||
\(32\) | 1.42104e21i | 0.212780i | ||||||||
\(33\) | 1.81414e22 | − | 8.20513e21i | 1.73867 | − | 0.786381i | ||||
\(34\) | − | 5.78936e21i | − | 0.359904i | ||||||
\(35\) | −1.70595e22 | − | 3.55331e22i | −0.696593 | − | 1.45093i | ||||
\(36\) | −2.60014e21 | + | 2.95690e21i | −0.0705683 | + | 0.0802510i | ||||
\(37\) | 7.21764e22 | 1.31665 | 0.658325 | − | 0.752734i | \(-0.271265\pi\) | ||||
0.658325 | + | 0.752734i | \(0.271265\pi\) | |||||||
\(38\) | −7.93963e22 | −0.983871 | ||||||||
\(39\) | −8.56016e22 | + | 3.87166e22i | −0.727856 | + | 0.329201i | ||||
\(40\) | − | 2.85831e23i | − | 1.68360i | ||||||
\(41\) | −6.20335e22 | −0.255423 | −0.127712 | − | 0.991811i | \(-0.540763\pi\) | ||||
−0.127712 | + | 0.991811i | \(0.540763\pi\) | |||||||
\(42\) | 2.49296e23 | + | 2.09315e23i | 0.723770 | + | 0.607694i | ||||
\(43\) | 4.32096e23 | 0.891841 | 0.445921 | − | 0.895072i | \(-0.352876\pi\) | ||||
0.445921 | + | 0.895072i | \(0.352876\pi\) | |||||||
\(44\) | 1.37890e23i | 0.203924i | ||||||||
\(45\) | 9.95503e23 | − | 1.13210e24i | 1.06282 | − | 1.20865i | ||||
\(46\) | −4.15254e23 | −0.322349 | ||||||||
\(47\) | 2.59257e24 | 1.47337 | 0.736684 | − | 0.676237i | \(-0.236391\pi\) | ||||
0.736684 | + | 0.676237i | \(0.236391\pi\) | |||||||
\(48\) | 8.67614e23 | + | 1.91828e24i | 0.363353 | + | 0.803365i | ||||
\(49\) | −2.01360e24 | + | 2.51261e24i | −0.625359 | + | 0.780337i | ||||
\(50\) | 6.48695e24i | 1.50306i | ||||||||
\(51\) | 9.02602e23 | + | 1.99563e24i | 0.156938 | + | 0.346987i | ||||
\(52\) | − | 6.50645e23i | − | 0.0853681i | ||||||
\(53\) | − | 2.18705e24i | − | 0.217700i | −0.994058 | − | 0.108850i | \(-0.965283\pi\) | ||
0.994058 | − | 0.108850i | \(-0.0347168\pi\) | |||||||
\(54\) | −3.63792e24 | + | 1.19066e25i | −0.276149 | + | 0.903812i | ||||
\(55\) | − | 5.27933e25i | − | 3.07128i | ||||||
\(56\) | −2.10494e25 | + | 1.01058e25i | −0.943003 | + | 0.452737i | ||||
\(57\) | 2.73684e25 | − | 1.23784e25i | 0.948560 | − | 0.429023i | ||||
\(58\) | −3.84786e25 | −1.03637 | ||||||||
\(59\) | −3.87703e25 | −0.814975 | −0.407488 | − | 0.913211i | \(-0.633595\pi\) | ||||
−0.407488 | + | 0.913211i | \(0.633595\pi\) | |||||||
\(60\) | 4.30245e24 | + | 9.51262e24i | 0.0708798 | + | 0.156714i | ||||
\(61\) | 1.06739e26i | 1.38369i | 0.722044 | + | 0.691847i | \(0.243203\pi\) | ||||
−0.722044 | + | 0.691847i | \(0.756797\pi\) | |||||||
\(62\) | −1.15165e26 | −1.17934 | ||||||||
\(63\) | −1.18568e26 | − | 3.32852e25i | −0.962782 | − | 0.270279i | ||||
\(64\) | −1.67556e26 | −1.08280 | ||||||||
\(65\) | 2.49110e26i | 1.28572i | ||||||||
\(66\) | 1.79671e26 | + | 3.97249e26i | 0.743176 | + | 1.64315i | ||||
\(67\) | −3.98782e26 | −1.32633 | −0.663164 | − | 0.748474i | \(-0.730787\pi\) | ||||
−0.663164 | + | 0.748474i | \(0.730787\pi\) | |||||||
\(68\) | −1.51685e25 | −0.0406971 | ||||||||
\(69\) | 1.43141e26 | − | 6.47410e25i | 0.310779 | − | 0.140562i | ||||
\(70\) | 7.78084e26 | − | 3.73559e26i | 1.37121 | − | 0.658321i | ||||
\(71\) | 9.94824e26i | 1.42725i | 0.700527 | + | 0.713625i | \(0.252948\pi\) | ||||
−0.700527 | + | 0.713625i | \(0.747052\pi\) | |||||||
\(72\) | −6.70640e26 | − | 5.89724e26i | −0.785540 | − | 0.690761i | ||||
\(73\) | 8.49053e25i | 0.0814242i | 0.999171 | + | 0.0407121i | \(0.0129626\pi\) | ||||
−0.999171 | + | 0.0407121i | \(0.987037\pi\) | |||||||
\(74\) | 1.58048e27i | 1.24431i | ||||||||
\(75\) | −1.01136e27 | − | 2.23610e27i | −0.655417 | − | 1.44911i | ||||
\(76\) | 2.08023e26i | 0.111254i | ||||||||
\(77\) | −3.88784e27 | + | 1.86656e27i | −1.72025 | + | 0.825896i | ||||
\(78\) | −8.47796e26 | − | 1.87446e27i | −0.311114 | − | 0.687866i | ||||
\(79\) | 1.57874e27 | 0.481635 | 0.240817 | − | 0.970570i | \(-0.422585\pi\) | ||||
0.240817 | + | 0.970570i | \(0.422585\pi\) | |||||||
\(80\) | 5.58238e27 | 1.41911 | ||||||||
\(81\) | −6.02305e26 | − | 4.67146e27i | −0.127874 | − | 0.991790i | ||||
\(82\) | − | 1.35838e27i | − | 0.241390i | ||||||
\(83\) | 3.67441e27 | 0.547715 | 0.273858 | − | 0.961770i | \(-0.411700\pi\) | ||||
0.273858 | + | 0.961770i | \(0.411700\pi\) | |||||||
\(84\) | 5.48417e26 | − | 6.53171e26i | 0.0687166 | − | 0.0818422i | ||||
\(85\) | 5.80750e27 | 0.612935 | ||||||||
\(86\) | 9.46180e27i | 0.842842i | ||||||||
\(87\) | 1.32638e28 | − | 5.99908e27i | 0.999172 | − | 0.451914i | ||||
\(88\) | −3.12741e28 | −1.99612 | ||||||||
\(89\) | −2.12846e28 | −1.15321 | −0.576607 | − | 0.817022i | \(-0.695623\pi\) | ||||
−0.576607 | + | 0.817022i | \(0.695623\pi\) | |||||||
\(90\) | 2.47900e28 | + | 2.17990e28i | 1.14225 | + | 1.00443i | ||||
\(91\) | 1.83451e28 | − | 8.80751e27i | 0.720145 | − | 0.345743i | ||||
\(92\) | 1.08799e27i | 0.0364504i | ||||||||
\(93\) | 3.96981e28 | − | 1.79550e28i | 1.13702 | − | 0.514260i | ||||
\(94\) | 5.67706e28i | 1.39242i | ||||||||
\(95\) | − | 7.96450e28i | − | 1.67558i | ||||||
\(96\) | 1.07263e28 | − | 4.85136e27i | 0.193872 | − | 0.0876862i | ||||
\(97\) | − | 7.01706e28i | − | 1.09135i | −0.837996 | − | 0.545676i | \(-0.816273\pi\) | ||
0.837996 | − | 0.545676i | \(-0.183727\pi\) | |||||||
\(98\) | −5.50198e28 | − | 4.40926e28i | −0.737464 | − | 0.591001i | ||||
\(99\) | −1.23868e29 | − | 1.08923e29i | −1.43301 | − | 1.26011i | ||||
\(100\) | 1.69962e28 | 0.169962 | ||||||||
\(101\) | −5.37882e28 | −0.465615 | −0.232808 | − | 0.972523i | \(-0.574791\pi\) | ||||
−0.232808 | + | 0.972523i | \(0.574791\pi\) | |||||||
\(102\) | −4.36993e28 | + | 1.97647e28i | −0.327923 | + | 0.148316i | ||||
\(103\) | 1.26950e27i | 0.00826978i | 0.999991 | + | 0.00413489i | \(0.00131618\pi\) | ||||
−0.999991 | + | 0.00413489i | \(0.998684\pi\) | |||||||
\(104\) | 1.47570e29 | 0.835629 | ||||||||
\(105\) | −2.09970e29 | + | 2.50077e29i | −1.03493 | + | 1.23262i | ||||
\(106\) | 4.78908e28 | 0.205739 | ||||||||
\(107\) | − | 3.07470e28i | − | 0.115276i | −0.998338 | − | 0.0576379i | \(-0.981643\pi\) | ||
0.998338 | − | 0.0576379i | \(-0.0183569\pi\) | |||||||
\(108\) | 3.11960e28 | + | 9.53158e27i | 0.102201 | + | 0.0312263i | ||||
\(109\) | −4.56998e29 | −1.30988 | −0.654938 | − | 0.755683i | \(-0.727305\pi\) | ||||
−0.654938 | + | 0.755683i | \(0.727305\pi\) | |||||||
\(110\) | 1.15604e30 | 2.90254 | ||||||||
\(111\) | −2.46407e29 | − | 5.44801e29i | −0.542589 | − | 1.19965i | ||||
\(112\) | −1.97370e29 | − | 4.11102e29i | −0.381611 | − | 0.794855i | ||||
\(113\) | − | 3.63848e29i | − | 0.618418i | −0.950994 | − | 0.309209i | \(-0.899936\pi\) | ||
0.950994 | − | 0.309209i | \(-0.100064\pi\) | |||||||
\(114\) | 2.71056e29 | + | 5.99299e29i | 0.405451 | + | 0.896444i | ||||
\(115\) | − | 4.16555e29i | − | 0.548977i | ||||||
\(116\) | 1.00816e29i | 0.117190i | ||||||||
\(117\) | 5.84482e29 | + | 5.13961e29i | 0.599896 | + | 0.527515i | ||||
\(118\) | − | 8.48970e29i | − | 0.770199i | ||||||
\(119\) | −2.05330e29 | − | 4.27680e29i | −0.164824 | − | 0.343311i | ||||
\(120\) | −2.15751e30 | + | 9.75817e29i | −1.53400 | + | 0.693810i | ||||
\(121\) | −4.19004e30 | −2.64138 | ||||||||
\(122\) | −2.33731e30 | −1.30767 | ||||||||
\(123\) | 2.11780e29 | + | 4.68241e29i | 0.105259 | + | 0.232726i | ||||
\(124\) | 3.01739e29i | 0.133358i | ||||||||
\(125\) | −2.41578e30 | −0.950302 | ||||||||
\(126\) | 7.28860e29 | − | 2.59633e30i | 0.255430 | − | 0.909885i | ||||
\(127\) | 4.56878e30 | 1.42773 | 0.713865 | − | 0.700283i | \(-0.246943\pi\) | ||||
0.713865 | + | 0.700283i | \(0.246943\pi\) | |||||||
\(128\) | − | 2.90613e30i | − | 0.810533i | ||||||
\(129\) | −1.47516e30 | − | 3.26154e30i | −0.367526 | − | 0.812592i | ||||
\(130\) | −5.45487e30 | −1.21508 | ||||||||
\(131\) | 3.50396e30 | 0.698433 | 0.349217 | − | 0.937042i | \(-0.386448\pi\) | ||||
0.349217 | + | 0.937042i | \(0.386448\pi\) | |||||||
\(132\) | 1.04082e30 | − | 4.70750e29i | 0.185803 | − | 0.0840366i | ||||
\(133\) | −5.86527e30 | + | 2.81593e30i | −0.938511 | + | 0.450580i | ||||
\(134\) | − | 8.73231e30i | − | 1.25346i | ||||||
\(135\) | −1.19439e31 | − | 3.64932e30i | −1.53924 | − | 0.470297i | ||||
\(136\) | − | 3.44029e30i | − | 0.398365i | ||||||
\(137\) | 7.58548e30i | 0.789832i | 0.918717 | + | 0.394916i | \(0.129226\pi\) | ||||
−0.918717 | + | 0.394916i | \(0.870774\pi\) | |||||||
\(138\) | 1.41766e30 | + | 3.13442e30i | 0.132839 | + | 0.293705i | ||||
\(139\) | 2.33968e30i | 0.197443i | 0.995115 | + | 0.0987214i | \(0.0314753\pi\) | ||||
−0.995115 | + | 0.0987214i | \(0.968525\pi\) | |||||||
\(140\) | −9.78749e29 | − | 2.03863e30i | −0.0744414 | − | 0.155054i | ||||
\(141\) | −8.85093e30 | − | 1.95692e31i | −0.607172 | − | 1.34244i | ||||
\(142\) | −2.17841e31 | −1.34884 | ||||||||
\(143\) | 2.72562e31 | 1.52438 | ||||||||
\(144\) | 1.15175e31 | − | 1.30978e31i | 0.582241 | − | 0.662130i | ||||
\(145\) | − | 3.85992e31i | − | 1.76499i | ||||||
\(146\) | −1.85921e30 | −0.0769506 | ||||||||
\(147\) | 2.58400e31 | + | 6.62106e30i | 0.968705 | + | 0.248214i | ||||
\(148\) | 4.14095e30 | 0.140704 | ||||||||
\(149\) | 1.50710e31i | 0.464452i | 0.972662 | + | 0.232226i | \(0.0746009\pi\) | ||||
−0.972662 | + | 0.232226i | \(0.925399\pi\) | |||||||
\(150\) | 4.89648e31 | − | 2.21462e31i | 1.36950 | − | 0.619407i | ||||
\(151\) | −2.61445e31 | −0.664070 | −0.332035 | − | 0.943267i | \(-0.607735\pi\) | ||||
−0.332035 | + | 0.943267i | \(0.607735\pi\) | |||||||
\(152\) | −4.71808e31 | −1.08901 | ||||||||
\(153\) | 1.19820e31 | − | 1.36260e31i | 0.251479 | − | 0.285985i | ||||
\(154\) | −4.08728e31 | − | 8.51337e31i | −0.780520 | − | 1.62574i | ||||
\(155\) | − | 1.15526e32i | − | 2.00849i | ||||||
\(156\) | −4.91120e30 | + | 2.22128e30i | −0.0777823 | + | 0.0351800i | ||||
\(157\) | 1.20234e32i | 1.73573i | 0.496796 | + | 0.867867i | \(0.334510\pi\) | ||||
−0.496796 | + | 0.867867i | \(0.665490\pi\) | |||||||
\(158\) | 3.45704e31i | 0.455173i | ||||||||
\(159\) | −1.65083e31 | + | 7.46650e30i | −0.198355 | + | 0.0897137i | ||||
\(160\) | − | 3.12145e31i | − | 0.342466i | ||||||
\(161\) | −3.06762e31 | + | 1.47277e31i | −0.307487 | + | 0.147625i | ||||
\(162\) | 1.02293e32 | − | 1.31889e31i | 0.937300 | − | 0.120849i | ||||
\(163\) | 2.51953e31 | 0.211154 | 0.105577 | − | 0.994411i | \(-0.466331\pi\) | ||||
0.105577 | + | 0.994411i | \(0.466331\pi\) | |||||||
\(164\) | −3.55903e30 | −0.0272958 | ||||||||
\(165\) | −3.98494e32 | + | 1.80234e32i | −2.79837 | + | 1.26567i | ||||
\(166\) | 8.04602e31i | 0.517623i | ||||||||
\(167\) | −4.27606e31 | −0.252148 | −0.126074 | − | 0.992021i | \(-0.540238\pi\) | ||||
−0.126074 | + | 0.992021i | \(0.540238\pi\) | |||||||
\(168\) | 1.48143e32 | + | 1.24384e32i | 0.801116 | + | 0.672635i | ||||
\(169\) | 7.29271e31 | 0.361853 | ||||||||
\(170\) | 1.27169e32i | 0.579260i | ||||||||
\(171\) | −1.86870e32 | − | 1.64323e32i | −0.781799 | − | 0.687471i | ||||
\(172\) | 2.47905e31 | 0.0953066 | ||||||||
\(173\) | −2.31530e32 | −0.818350 | −0.409175 | − | 0.912456i | \(-0.634183\pi\) | ||||
−0.409175 | + | 0.912456i | \(0.634183\pi\) | |||||||
\(174\) | 1.31365e32 | + | 2.90444e32i | 0.427085 | + | 0.944275i | ||||
\(175\) | 2.30071e32 | + | 4.79213e32i | 0.688351 | + | 1.43376i | ||||
\(176\) | − | 6.10794e32i | − | 1.68252i | ||||||
\(177\) | 1.32360e32 | + | 2.92645e32i | 0.335850 | + | 0.742556i | ||||
\(178\) | − | 4.66078e32i | − | 1.08985i | ||||||
\(179\) | 1.69293e32i | 0.364982i | 0.983208 | + | 0.182491i | \(0.0584160\pi\) | ||||
−0.983208 | + | 0.182491i | \(0.941584\pi\) | |||||||
\(180\) | 5.71147e31 | − | 6.49514e31i | 0.113579 | − | 0.129163i | ||||
\(181\) | 2.15005e32i | 0.394557i | 0.980347 | + | 0.197279i | \(0.0632104\pi\) | ||||
−0.980347 | + | 0.197279i | \(0.936790\pi\) | |||||||
\(182\) | 1.92862e32 | + | 4.01711e32i | 0.326747 | + | 0.680579i | ||||
\(183\) | 8.05685e32 | − | 3.64402e32i | 1.26074 | − | 0.570217i | ||||
\(184\) | −2.46762e32 | −0.356796 | ||||||||
\(185\) | −1.58543e33 | −2.11913 | ||||||||
\(186\) | 3.93169e32 | + | 8.69287e32i | 0.486006 | + | 1.07455i | ||||
\(187\) | − | 6.35425e32i | − | 0.726709i | ||||||
\(188\) | 1.48743e32 | 0.157451 | ||||||||
\(189\) | 1.53542e32 | + | 1.00861e33i | 0.150498 | + | 0.988610i | ||||
\(190\) | 1.74402e33 | 1.58353 | ||||||||
\(191\) | − | 2.23371e32i | − | 0.187950i | −0.995575 | − | 0.0939750i | \(-0.970043\pi\) | ||
0.995575 | − | 0.0939750i | \(-0.0299574\pi\) | |||||||
\(192\) | 5.72029e32 | + | 1.26474e33i | 0.446221 | + | 0.986586i | ||||
\(193\) | 1.36259e33 | 0.985793 | 0.492897 | − | 0.870088i | \(-0.335938\pi\) | ||||
0.492897 | + | 0.870088i | \(0.335938\pi\) | |||||||
\(194\) | 1.53656e33 | 1.03139 | ||||||||
\(195\) | 1.88033e33 | − | 8.50451e32i | 1.17147 | − | 0.529844i | ||||
\(196\) | −1.15525e32 | + | 1.44155e32i | −0.0668290 | + | 0.0833907i | ||||
\(197\) | − | 3.00287e33i | − | 1.61353i | −0.590875 | − | 0.806763i | \(-0.701217\pi\) | ||
0.590875 | − | 0.806763i | \(-0.298783\pi\) | |||||||
\(198\) | 2.38512e33 | − | 2.71239e33i | 1.19087 | − | 1.35427i | ||||
\(199\) | 2.91566e33i | 1.35322i | 0.736343 | + | 0.676608i | \(0.236551\pi\) | ||||
−0.736343 | + | 0.676608i | \(0.763449\pi\) | |||||||
\(200\) | 3.85483e33i | 1.66368i | ||||||||
\(201\) | 1.36143e33 | + | 3.01008e33i | 0.546577 | + | 1.20847i | ||||
\(202\) | − | 1.17782e33i | − | 0.440033i | ||||||
\(203\) | −2.84255e33 | + | 1.36471e33i | −0.988587 | + | 0.474622i | ||||
\(204\) | 5.17847e31 | + | 1.14495e32i | 0.0167712 | + | 0.0370807i | ||||
\(205\) | 1.36263e33 | 0.411100 | ||||||||
\(206\) | −2.77989e31 | −0.00781543 | ||||||||
\(207\) | −9.77356e32 | − | 8.59432e32i | −0.256143 | − | 0.225238i | ||||
\(208\) | 2.88209e33i | 0.704350i | ||||||||
\(209\) | −8.71432e33 | −1.98661 | ||||||||
\(210\) | −5.47605e33 | − | 4.59781e33i | −1.16490 | − | 0.978074i | ||||
\(211\) | 3.24786e33 | 0.644913 | 0.322457 | − | 0.946584i | \(-0.395491\pi\) | ||||
0.322457 | + | 0.946584i | \(0.395491\pi\) | |||||||
\(212\) | − | 1.25477e32i | − | 0.0232645i | ||||||
\(213\) | 7.50913e33 | − | 3.39629e33i | 1.30042 | − | 0.588167i | ||||
\(214\) | 6.73281e32 | 0.108942 | ||||||||
\(215\) | −9.49144e33 | −1.43540 | ||||||||
\(216\) | −2.16181e33 | + | 7.07542e33i | −0.305660 | + | 1.00040i | ||||
\(217\) | −8.50762e33 | + | 4.08452e33i | −1.12497 | + | 0.540101i | ||||
\(218\) | − | 1.00071e34i | − | 1.23791i | ||||||
\(219\) | 6.40882e32 | − | 2.89864e32i | 0.0741888 | − | 0.0335547i | ||||
\(220\) | − | 3.02889e33i | − | 0.328212i | ||||||
\(221\) | 2.99831e33i | 0.304221i | ||||||||
\(222\) | 1.19298e34 | − | 5.39569e33i | 1.13374 | − | 0.512778i | ||||
\(223\) | − | 3.14572e33i | − | 0.280091i | −0.990145 | − | 0.140045i | \(-0.955275\pi\) | ||
0.990145 | − | 0.140045i | \(-0.0447249\pi\) | |||||||
\(224\) | −2.29872e33 | + | 1.10362e33i | −0.191818 | + | 0.0920923i | ||||
\(225\) | −1.34257e34 | + | 1.52679e34i | −1.05025 | + | 1.19435i | ||||
\(226\) | 7.96734e33 | 0.584441 | ||||||||
\(227\) | 1.49046e34 | 1.02552 | 0.512761 | − | 0.858531i | \(-0.328623\pi\) | ||||
0.512761 | + | 0.858531i | \(0.328623\pi\) | |||||||
\(228\) | 1.57020e33 | − | 7.10184e32i | 0.101368 | − | 0.0458475i | ||||
\(229\) | − | 1.96703e34i | − | 1.19178i | −0.803065 | − | 0.595891i | \(-0.796799\pi\) | ||
0.803065 | − | 0.595891i | \(-0.203201\pi\) | |||||||
\(230\) | 9.12150e33 | 0.518815 | ||||||||
\(231\) | 2.73620e34 | + | 2.29738e34i | 1.46142 | + | 1.22704i | ||||
\(232\) | −2.28657e34 | −1.14712 | ||||||||
\(233\) | 1.34458e34i | 0.633763i | 0.948465 | + | 0.316882i | \(0.102636\pi\) | ||||
−0.948465 | + | 0.316882i | \(0.897364\pi\) | |||||||
\(234\) | −1.12544e34 | + | 1.27987e34i | −0.498533 | + | 0.566936i | ||||
\(235\) | −5.69484e34 | −2.37136 | ||||||||
\(236\) | −2.22435e33 | −0.0870923 | ||||||||
\(237\) | −5.38976e33 | − | 1.19166e34i | −0.198481 | − | 0.438836i | ||||
\(238\) | 9.36509e33 | − | 4.49619e33i | 0.324449 | − | 0.155768i | ||||
\(239\) | 5.26810e31i | 0.00171745i | 1.00000 | 0.000858726i | \(0.000273341\pi\) | |||||
−1.00000 | 0.000858726i | \(0.999727\pi\) | ||||||||
\(240\) | −1.90580e34 | − | 4.21369e34i | −0.584811 | − | 1.29300i | ||||
\(241\) | − | 2.27777e34i | − | 0.658057i | −0.944320 | − | 0.329028i | \(-0.893279\pi\) | ||
0.944320 | − | 0.329028i | \(-0.106721\pi\) | |||||||
\(242\) | − | 9.17512e34i | − | 2.49625i | ||||||
\(243\) | −3.32048e34 | + | 2.04945e34i | −0.850963 | + | 0.525226i | ||||
\(244\) | 6.12389e33i | 0.147868i | ||||||||
\(245\) | 4.42308e34 | − | 5.51921e34i | 1.00651 | − | 1.25594i | ||||
\(246\) | −1.02533e34 | + | 4.63744e33i | −0.219940 | + | 0.0994763i | ||||
\(247\) | 4.11193e34 | 0.831649 | ||||||||
\(248\) | −6.84360e34 | −1.30538 | ||||||||
\(249\) | −1.25443e34 | − | 2.77351e34i | −0.225712 | − | 0.499045i | ||||
\(250\) | − | 5.28994e34i | − | 0.898091i | ||||||
\(251\) | 3.42737e34 | 0.549151 | 0.274575 | − | 0.961566i | \(-0.411463\pi\) | ||||
0.274575 | + | 0.961566i | \(0.411463\pi\) | |||||||
\(252\) | −6.80254e33 | − | 1.90966e33i | −0.102888 | − | 0.0288834i | ||||
\(253\) | −4.55772e34 | −0.650879 | ||||||||
\(254\) | 1.00045e35i | 1.34929i | ||||||||
\(255\) | −1.98266e34 | − | 4.38361e34i | −0.252589 | − | 0.558470i | ||||
\(256\) | −2.63190e34 | −0.316803 | ||||||||
\(257\) | 5.24054e34 | 0.596137 | 0.298068 | − | 0.954545i | \(-0.403658\pi\) | ||||
0.298068 | + | 0.954545i | \(0.403658\pi\) | |||||||
\(258\) | 7.14195e34 | − | 3.23022e34i | 0.767947 | − | 0.347333i | ||||
\(259\) | 5.60544e34 | + | 1.16755e35i | 0.569853 | + | 1.18694i | ||||
\(260\) | 1.42921e34i | 0.137399i | ||||||||
\(261\) | −9.05645e34 | − | 7.96374e34i | −0.823513 | − | 0.724152i | ||||
\(262\) | 7.67277e34i | 0.660060i | ||||||||
\(263\) | − | 3.50044e34i | − | 0.284947i | −0.989799 | − | 0.142474i | \(-0.954494\pi\) | ||
0.989799 | − | 0.142474i | \(-0.0455056\pi\) | |||||||
\(264\) | 1.06769e35 | + | 2.36063e35i | 0.822596 | + | 1.81874i | ||||
\(265\) | 4.80408e34i | 0.350385i | ||||||||
\(266\) | −6.16616e34 | − | 1.28434e35i | −0.425825 | − | 0.886948i | ||||
\(267\) | 7.26647e34 | + | 1.60660e35i | 0.475237 | + | 1.05074i | ||||
\(268\) | −2.28792e34 | −0.141738 | ||||||||
\(269\) | −3.67604e34 | −0.215761 | −0.107880 | − | 0.994164i | \(-0.534406\pi\) | ||||
−0.107880 | + | 0.994164i | \(0.534406\pi\) | |||||||
\(270\) | 7.99107e34 | − | 2.61541e35i | 0.444458 | − | 1.45467i | ||||
\(271\) | − | 3.33205e35i | − | 1.75653i | −0.478171 | − | 0.878267i | \(-0.658700\pi\) | ||
0.478171 | − | 0.878267i | \(-0.341300\pi\) | |||||||
\(272\) | 6.71901e34 | 0.335781 | ||||||||
\(273\) | −1.29110e35 | − | 1.08404e35i | −0.611790 | − | 0.513673i | ||||
\(274\) | −1.66103e35 | −0.746437 | ||||||||
\(275\) | 7.11990e35i | 3.03494i | ||||||||
\(276\) | 8.21238e33 | − | 3.71437e33i | 0.0332114 | − | 0.0150211i | ||||
\(277\) | 3.53976e35 | 1.35837 | 0.679183 | − | 0.733969i | \(-0.262334\pi\) | ||||
0.679183 | + | 0.733969i | \(0.262334\pi\) | |||||||
\(278\) | −5.12330e34 | −0.186595 | ||||||||
\(279\) | −2.71056e35 | − | 2.38351e35i | −0.937125 | − | 0.824056i | ||||
\(280\) | 4.62371e35 | − | 2.21985e35i | 1.51775 | − | 0.728673i | ||||
\(281\) | 3.54541e35i | 1.10516i | 0.833460 | + | 0.552579i | \(0.186356\pi\) | ||||
−0.833460 | + | 0.552579i | \(0.813644\pi\) | |||||||
\(282\) | 4.28516e35 | − | 1.93813e35i | 1.26869 | − | 0.573813i | ||||
\(283\) | − | 4.63712e34i | − | 0.130420i | −0.997872 | − | 0.0652101i | \(-0.979228\pi\) | ||
0.997872 | − | 0.0652101i | \(-0.0207717\pi\) | |||||||
\(284\) | 5.70757e34i | 0.152523i | ||||||||
\(285\) | −6.01176e35 | + | 2.71905e35i | −1.52669 | + | 0.690505i | ||||
\(286\) | 5.96842e35i | 1.44063i | ||||||||
\(287\) | −4.81771e34 | − | 1.00348e35i | −0.110549 | − | 0.230261i | ||||
\(288\) | −7.32381e34 | − | 6.44015e34i | −0.159789 | − | 0.140509i | ||||
\(289\) | −4.12069e35 | −0.854971 | ||||||||
\(290\) | 8.45223e35 | 1.66802 | ||||||||
\(291\) | −5.29662e35 | + | 2.39560e35i | −0.994375 | + | 0.449744i | ||||
\(292\) | 4.87125e33i | 0.00870139i | ||||||||
\(293\) | 3.34930e35 | 0.569342 | 0.284671 | − | 0.958625i | \(-0.408116\pi\) | ||||
0.284671 | + | 0.958625i | \(0.408116\pi\) | |||||||
\(294\) | −1.44984e35 | + | 5.65831e35i | −0.234577 | + | 0.915483i | ||||
\(295\) | 8.51629e35 | 1.31169 | ||||||||
\(296\) | 9.39189e35i | 1.37728i | ||||||||
\(297\) | −3.99288e35 | + | 1.30684e36i | −0.557594 | + | 1.82496i | ||||
\(298\) | −3.30016e35 | −0.438934 | ||||||||
\(299\) | 2.15060e35 | 0.272476 | ||||||||
\(300\) | −5.80244e34 | − | 1.28291e35i | −0.0700411 | − | 0.154859i | ||||
\(301\) | 3.35579e35 | + | 6.98975e35i | 0.385994 | + | 0.803984i | ||||
\(302\) | − | 5.72497e35i | − | 0.627585i | ||||||
\(303\) | 1.83631e35 | + | 4.06004e35i | 0.191879 | + | 0.424240i | ||||
\(304\) | − | 9.21457e35i | − | 0.917927i | ||||||
\(305\) | − | 2.34463e36i | − | 2.22703i | ||||||
\(306\) | 2.98375e35 | + | 2.62375e35i | 0.270273 | + | 0.237663i | ||||
\(307\) | 8.52543e34i | 0.0736563i | 0.999322 | + | 0.0368281i | \(0.0117254\pi\) | ||||
−0.999322 | + | 0.0368281i | \(0.988275\pi\) | |||||||
\(308\) | −2.23056e35 | + | 1.07089e35i | −0.183835 | + | 0.0882593i | ||||
\(309\) | 9.58246e33 | − | 4.33404e33i | 0.00753493 | − | 0.00340796i | ||||
\(310\) | 2.52972e36 | 1.89814 | ||||||||
\(311\) | −8.00785e35 | −0.573443 | −0.286722 | − | 0.958014i | \(-0.592565\pi\) | ||||
−0.286722 | + | 0.958014i | \(0.592565\pi\) | |||||||
\(312\) | −5.03797e35 | − | 1.11388e36i | −0.344361 | − | 0.761375i | ||||
\(313\) | − | 3.66167e35i | − | 0.238938i | −0.992838 | − | 0.119469i | \(-0.961881\pi\) | ||
0.992838 | − | 0.119469i | \(-0.0381193\pi\) | |||||||
\(314\) | −2.63282e36 | −1.64037 | ||||||||
\(315\) | 2.60446e36 | + | 7.31143e35i | 1.54958 | + | 0.435010i | ||||
\(316\) | 9.05765e34 | 0.0514699 | ||||||||
\(317\) | − | 1.30822e36i | − | 0.710102i | −0.934847 | − | 0.355051i | \(-0.884463\pi\) | ||
0.934847 | − | 0.355051i | \(-0.115537\pi\) | |||||||
\(318\) | −1.63497e35 | − | 3.61489e35i | −0.0847847 | − | 0.187457i | ||||
\(319\) | −4.22331e36 | −2.09261 | ||||||||
\(320\) | 3.68054e36 | 1.74276 | ||||||||
\(321\) | −2.32084e35 | + | 1.04969e35i | −0.105032 | + | 0.0475049i | ||||
\(322\) | −3.22499e35 | − | 6.71731e35i | −0.139514 | − | 0.290593i | ||||
\(323\) | − | 9.58615e35i | − | 0.396468i | ||||||
\(324\) | −3.45559e34 | − | 2.68014e35i | −0.0136653 | − | 0.105988i | ||||
\(325\) | − | 3.35959e36i | − | 1.27051i | ||||||
\(326\) | 5.51712e35i | 0.199553i | ||||||||
\(327\) | 1.56017e36 | + | 3.44951e36i | 0.539797 | + | 1.19348i | ||||
\(328\) | − | 8.07206e35i | − | 0.267186i | ||||||
\(329\) | 2.01347e36 | + | 4.19383e36i | 0.637681 | + | 1.32822i | ||||
\(330\) | −3.94667e36 | − | 8.72600e36i | −1.19613 | − | 2.64462i | ||||
\(331\) | 4.26098e36 | 1.23596 | 0.617978 | − | 0.786195i | \(-0.287952\pi\) | ||||
0.617978 | + | 0.786195i | \(0.287952\pi\) | |||||||
\(332\) | 2.10811e35 | 0.0585316 | ||||||||
\(333\) | −3.27104e36 | + | 3.71986e36i | −0.869450 | + | 0.988748i | ||||
\(334\) | − | 9.36348e35i | − | 0.238294i | ||||||
\(335\) | 8.75966e36 | 2.13470 | ||||||||
\(336\) | −2.42926e36 | + | 2.89328e36i | −0.566963 | + | 0.675259i | ||||
\(337\) | −1.86913e36 | −0.417835 | −0.208918 | − | 0.977933i | \(-0.566994\pi\) | ||||
−0.208918 | + | 0.977933i | \(0.566994\pi\) | |||||||
\(338\) | 1.59692e36i | 0.341972i | ||||||||
\(339\) | −2.74639e36 | + | 1.24216e36i | −0.563466 | + | 0.254849i | ||||
\(340\) | 3.33192e35 | 0.0655013 | ||||||||
\(341\) | −1.26402e37 | −2.38130 | ||||||||
\(342\) | 3.59825e36 | − | 4.09197e36i | 0.649700 | − | 0.738846i | ||||
\(343\) | −5.62832e36 | − | 1.30590e36i | −0.974123 | − | 0.226019i | ||||
\(344\) | 5.62261e36i | 0.932912i | ||||||||
\(345\) | −3.14424e36 | + | 1.42210e36i | −0.500194 | + | 0.226232i | ||||
\(346\) | − | 5.06992e36i | − | 0.773388i | ||||||
\(347\) | − | 9.08226e36i | − | 1.32867i | −0.747436 | − | 0.664334i | \(-0.768715\pi\) | ||
0.747436 | − | 0.664334i | \(-0.231285\pi\) | |||||||
\(348\) | 7.60982e35 | − | 3.44183e35i | 0.106776 | − | 0.0482938i | ||||
\(349\) | 3.64732e36i | 0.490914i | 0.969407 | + | 0.245457i | \(0.0789381\pi\) | ||||
−0.969407 | + | 0.245457i | \(0.921062\pi\) | |||||||
\(350\) | −1.04935e37 | + | 5.03796e36i | −1.35499 | + | 0.650531i | ||||
\(351\) | 1.88408e36 | − | 6.16642e36i | 0.233424 | − | 0.763977i | ||||
\(352\) | −3.41532e36 | −0.406035 | ||||||||
\(353\) | −1.22050e37 | −1.39253 | −0.696263 | − | 0.717787i | \(-0.745155\pi\) | ||||
−0.696263 | + | 0.717787i | \(0.745155\pi\) | |||||||
\(354\) | −6.40819e36 | + | 2.89835e36i | −0.701759 | + | 0.317398i | ||||
\(355\) | − | 2.18523e37i | − | 2.29714i | ||||||
\(356\) | −1.22115e36 | −0.123238 | ||||||||
\(357\) | −2.52722e36 | + | 3.00995e36i | −0.244881 | + | 0.291655i | ||||
\(358\) | −3.70709e36 | −0.344929 | ||||||||
\(359\) | − | 1.78777e37i | − | 1.59751i | −0.601657 | − | 0.798754i | \(-0.705493\pi\) | ||
0.601657 | − | 0.798754i | \(-0.294507\pi\) | |||||||
\(360\) | 1.47313e37 | + | 1.29539e37i | 1.26431 | + | 1.11177i | ||||
\(361\) | −1.01679e36 | −0.0838257 | ||||||||
\(362\) | −4.70807e36 | −0.372880 | ||||||||
\(363\) | 1.43046e37 | + | 3.16272e37i | 1.08851 | + | 2.40666i | ||||
\(364\) | 1.05251e36 | − | 5.05311e35i | 0.0769583 | − | 0.0369478i | ||||
\(365\) | − | 1.86503e36i | − | 0.131051i | ||||||
\(366\) | 7.97948e36 | + | 1.76425e37i | 0.538888 | + | 1.19147i | ||||
\(367\) | 5.42324e36i | 0.352047i | 0.984386 | + | 0.176024i | \(0.0563235\pi\) | ||||
−0.984386 | + | 0.176024i | \(0.943676\pi\) | |||||||
\(368\) | − | 4.81935e36i | − | 0.300743i | ||||||
\(369\) | 2.81137e36 | − | 3.19712e36i | 0.168669 | − | 0.191812i | ||||
\(370\) | − | 3.47169e37i | − | 2.00270i | ||||||
\(371\) | 3.53785e36 | − | 1.69853e36i | 0.196254 | − | 0.0942217i | ||||
\(372\) | 2.27759e36 | − | 1.03013e36i | 0.121507 | − | 0.0549564i | ||||
\(373\) | −3.01156e36 | −0.154530 | −0.0772651 | − | 0.997011i | \(-0.524619\pi\) | ||||
−0.0772651 | + | 0.997011i | \(0.524619\pi\) | |||||||
\(374\) | 1.39142e37 | 0.686783 | ||||||||
\(375\) | 8.24737e36 | + | 1.82348e37i | 0.391618 | + | 0.865858i | ||||
\(376\) | 3.37356e37i | 1.54122i | ||||||||
\(377\) | 1.99281e37 | 0.876023 | ||||||||
\(378\) | −2.20859e37 | + | 3.36219e36i | −0.934294 | + | 0.142230i | ||||
\(379\) | 4.09990e37 | 1.66919 | 0.834594 | − | 0.550866i | \(-0.185702\pi\) | ||||
0.834594 | + | 0.550866i | \(0.185702\pi\) | |||||||
\(380\) | − | 4.56945e36i | − | 0.179061i | ||||||
\(381\) | −1.55976e37 | − | 3.44860e37i | −0.588365 | − | 1.30086i | ||||
\(382\) | 4.89125e36 | 0.177624 | ||||||||
\(383\) | 3.77532e37 | 1.31999 | 0.659996 | − | 0.751269i | \(-0.270558\pi\) | ||||
0.659996 | + | 0.751269i | \(0.270558\pi\) | |||||||
\(384\) | −2.19361e37 | + | 9.92143e36i | −0.738509 | + | 0.334019i | ||||
\(385\) | 8.54004e37 | − | 4.10008e37i | 2.76872 | − | 1.32927i | ||||
\(386\) | 2.98374e37i | 0.931632i | ||||||||
\(387\) | −1.95826e37 | + | 2.22696e37i | −0.588928 | + | 0.669735i | ||||
\(388\) | − | 4.02588e36i | − | 0.116627i | ||||||
\(389\) | − | 5.53900e37i | − | 1.54583i | −0.634509 | − | 0.772915i | \(-0.718798\pi\) | ||
0.634509 | − | 0.772915i | \(-0.281202\pi\) | |||||||
\(390\) | 1.86227e37 | + | 4.11744e37i | 0.500733 | + | 1.10711i | ||||
\(391\) | − | 5.01370e36i | − | 0.129896i | ||||||
\(392\) | −3.26952e37 | − | 2.62018e37i | −0.816273 | − | 0.654158i | ||||
\(393\) | −1.19624e37 | − | 2.64485e37i | −0.287823 | − | 0.636370i | ||||
\(394\) | 6.57552e37 | 1.52488 | ||||||||
\(395\) | −3.46787e37 | −0.775183 | ||||||||
\(396\) | −7.10663e36 | − | 6.24918e36i | −0.153138 | − | 0.134661i | ||||
\(397\) | 5.20498e37i | 1.08133i | 0.841239 | + | 0.540663i | \(0.181827\pi\) | ||||
−0.841239 | + | 0.540663i | \(0.818173\pi\) | |||||||
\(398\) | −6.38455e37 | −1.27887 | ||||||||
\(399\) | 4.12790e37 | + | 3.46588e37i | 0.797300 | + | 0.669431i | ||||
\(400\) | −7.52862e37 | −1.40231 | ||||||||
\(401\) | 6.29881e37i | 1.13153i | 0.824567 | + | 0.565764i | \(0.191419\pi\) | ||||
−0.824567 | + | 0.565764i | \(0.808581\pi\) | |||||||
\(402\) | −6.59131e37 | + | 2.98118e37i | −1.14207 | + | 0.516547i | ||||
\(403\) | 5.96439e37 | 0.996879 | ||||||||
\(404\) | −3.08597e36 | −0.0497579 | ||||||||
\(405\) | 1.32303e37 | + | 1.02613e38i | 0.205812 | + | 1.59627i | ||||
\(406\) | −2.98837e37 | − | 6.22445e37i | −0.448545 | − | 0.934272i | ||||
\(407\) | 1.73469e38i | 2.51248i | ||||||||
\(408\) | −2.59680e37 | + | 1.17450e37i | −0.362966 | + | 0.164165i | ||||
\(409\) | − | 3.88534e37i | − | 0.524133i | −0.965050 | − | 0.262066i | \(-0.915596\pi\) | ||
0.965050 | − | 0.262066i | \(-0.0844040\pi\) | |||||||
\(410\) | 2.98381e37i | 0.388513i | ||||||||
\(411\) | 5.72566e37 | − | 2.58965e37i | 0.719647 | − | 0.325488i | ||||
\(412\) | 7.28348e34i | 0.000883750i | ||||||||
\(413\) | −3.01101e37 | − | 6.27162e37i | −0.352726 | − | 0.734690i | ||||
\(414\) | 1.88194e37 | − | 2.14016e37i | 0.212863 | − | 0.242070i | ||||
\(415\) | −8.07122e37 | −0.881539 | ||||||||
\(416\) | 1.61155e37 | 0.169977 | ||||||||
\(417\) | 1.76603e37 | − | 7.98757e36i | 0.179898 | − | 0.0813658i | ||||
\(418\) | − | 1.90821e38i | − | 1.87746i | ||||||
\(419\) | 1.74807e38 | 1.66133 | 0.830664 | − | 0.556774i | \(-0.187961\pi\) | ||||
0.830664 | + | 0.556774i | \(0.187961\pi\) | |||||||
\(420\) | −1.20466e37 | + | 1.43476e37i | −0.110598 | + | 0.131724i | ||||
\(421\) | 1.75218e38 | 1.55413 | 0.777067 | − | 0.629418i | \(-0.216706\pi\) | ||||
0.777067 | + | 0.629418i | \(0.216706\pi\) | |||||||
\(422\) | 7.11198e37i | 0.609480i | ||||||||
\(423\) | −1.17495e38 | + | 1.33617e38i | −0.972939 | + | 1.10644i | ||||
\(424\) | 2.84588e37 | 0.227726 | ||||||||
\(425\) | −7.83221e37 | −0.605683 | ||||||||
\(426\) | 7.43701e37 | + | 1.64431e38i | 0.555852 | + | 1.22898i | ||||
\(427\) | −1.72665e38 | + | 8.28966e37i | −1.24738 | + | 0.598870i | ||||
\(428\) | − | 1.76404e36i | − | 0.0123189i | ||||||
\(429\) | −9.30517e37 | − | 2.05735e38i | −0.628194 | − | 1.38892i | ||||
\(430\) | − | 2.07838e38i | − | 1.35654i | ||||||
\(431\) | 2.27636e38i | 1.43655i | 0.695759 | + | 0.718275i | \(0.255068\pi\) | ||||
−0.695759 | + | 0.718275i | \(0.744932\pi\) | |||||||
\(432\) | −1.38185e38 | − | 4.22209e37i | −0.843234 | − | 0.257640i | ||||
\(433\) | − | 2.67289e38i | − | 1.57727i | −0.614861 | − | 0.788636i | \(-0.710788\pi\) | ||
0.614861 | − | 0.788636i | \(-0.289212\pi\) | |||||||
\(434\) | −8.94405e37 | − | 1.86295e38i | −0.510427 | − | 1.06316i | ||||
\(435\) | −2.91354e38 | + | 1.31776e38i | −1.60815 | + | 0.727348i | ||||
\(436\) | −2.62192e37 | −0.139980 | ||||||||
\(437\) | −6.87587e37 | −0.355097 | ||||||||
\(438\) | 6.34727e36 | + | 1.40337e37i | 0.0317112 | + | 0.0701127i | ||||
\(439\) | 1.23795e38i | 0.598368i | 0.954195 | + | 0.299184i | \(0.0967144\pi\) | ||||
−0.954195 | + | 0.299184i | \(0.903286\pi\) | |||||||
\(440\) | 6.86968e38 | 3.21272 | ||||||||
\(441\) | −3.82398e37 | − | 2.17650e38i | −0.173044 | − | 0.984914i | ||||
\(442\) | −6.56553e37 | −0.287506 | ||||||||
\(443\) | − | 2.63871e38i | − | 1.11825i | −0.829084 | − | 0.559124i | \(-0.811138\pi\) | ||
0.829084 | − | 0.559124i | \(-0.188862\pi\) | |||||||
\(444\) | −1.41371e37 | − | 3.12567e37i | −0.0579837 | − | 0.128201i | ||||
\(445\) | 4.67537e38 | 1.85608 | ||||||||
\(446\) | 6.88832e37 | 0.264702 | ||||||||
\(447\) | 1.13759e38 | − | 5.14518e37i | 0.423180 | − | 0.191400i | ||||
\(448\) | −1.30129e38 | − | 2.71045e38i | −0.468644 | − | 0.976134i | ||||
\(449\) | − | 3.98673e38i | − | 1.39010i | −0.718963 | − | 0.695048i | \(-0.755383\pi\) | ||
0.718963 | − | 0.695048i | \(-0.244617\pi\) | |||||||
\(450\) | −3.34328e38 | − | 2.93989e38i | −1.12873 | − | 0.992545i | ||||
\(451\) | − | 1.49092e38i | − | 0.487409i | ||||||
\(452\) | − | 2.08749e37i | − | 0.0660873i | ||||||
\(453\) | 8.92562e37 | + | 1.97344e38i | 0.273662 | + | 0.605061i | ||||
\(454\) | 3.26372e38i | 0.969178i | ||||||||
\(455\) | −4.02969e38 | + | 1.93466e38i | −1.15906 | + | 0.556467i | ||||
\(456\) | 1.61073e38 | + | 3.56130e38i | 0.448780 | + | 0.992242i | ||||
\(457\) | −2.56102e38 | −0.691239 | −0.345620 | − | 0.938375i | \(-0.612331\pi\) | ||||
−0.345620 | + | 0.938375i | \(0.612331\pi\) | |||||||
\(458\) | 4.30730e38 | 1.12630 | ||||||||
\(459\) | −1.43758e38 | − | 4.39235e37i | −0.364207 | − | 0.111279i | ||||
\(460\) | − | 2.38989e37i | − | 0.0586664i | ||||||
\(461\) | −4.38167e37 | −0.104226 | −0.0521130 | − | 0.998641i | \(-0.516596\pi\) | ||||
−0.0521130 | + | 0.998641i | \(0.516596\pi\) | |||||||
\(462\) | −5.03067e38 | + | 5.99159e38i | −1.15963 | + | 1.38113i | ||||
\(463\) | 1.24196e38 | 0.277448 | 0.138724 | − | 0.990331i | \(-0.455700\pi\) | ||||
0.138724 | + | 0.990331i | \(0.455700\pi\) | |||||||
\(464\) | − | 4.46575e38i | − | 0.966904i | ||||||
\(465\) | −8.72010e38 | + | 3.94400e38i | −1.83001 | + | 0.827693i | ||||
\(466\) | −2.94430e38 | −0.598943 | ||||||||
\(467\) | 4.25993e38 | 0.840054 | 0.420027 | − | 0.907512i | \(-0.362021\pi\) | ||||
0.420027 | + | 0.907512i | \(0.362021\pi\) | |||||||
\(468\) | 3.35333e37 | + | 2.94873e37i | 0.0641078 | + | 0.0563729i | ||||
\(469\) | −3.09706e38 | − | 6.45085e38i | −0.574042 | − | 1.19567i | ||||
\(470\) | − | 1.24703e39i | − | 2.24108i | ||||||
\(471\) | 9.07551e38 | − | 4.10475e38i | 1.58150 | − | 0.715293i | ||||
\(472\) | − | 5.04495e38i | − | 0.852506i | ||||||
\(473\) | 1.03850e39i | 1.70185i | ||||||||
\(474\) | 2.60944e38 | − | 1.18022e38i | 0.414726 | − | 0.187576i | ||||
\(475\) | 1.07412e39i | 1.65576i | ||||||||
\(476\) | −1.17803e37 | − | 2.45371e37i | −0.0176139 | − | 0.0366879i | ||||
\(477\) | 1.12717e38 | + | 9.91173e37i | 0.163483 | + | 0.143758i | ||||
\(478\) | −1.15358e36 | −0.00162309 | ||||||||
\(479\) | −9.45275e38 | −1.29031 | −0.645153 | − | 0.764053i | \(-0.723207\pi\) | ||||
−0.645153 | + | 0.764053i | \(0.723207\pi\) | |||||||
\(480\) | −2.35613e38 | + | 1.06565e38i | −0.312034 | + | 0.141129i | ||||
\(481\) | − | 8.18529e38i | − | 1.05179i | ||||||
\(482\) | 4.98774e38 | 0.621902 | ||||||||
\(483\) | 2.15895e38 | + | 1.81270e38i | 0.261222 | + | 0.219328i | ||||
\(484\) | −2.40394e38 | −0.282271 | ||||||||
\(485\) | 1.54137e39i | 1.75652i | ||||||||
\(486\) | −4.48777e38 | − | 7.27101e38i | −0.496369 | − | 0.804209i | ||||
\(487\) | −2.50491e38 | −0.268920 | −0.134460 | − | 0.990919i | \(-0.542930\pi\) | ||||
−0.134460 | + | 0.990919i | \(0.542930\pi\) | |||||||
\(488\) | −1.38893e39 | −1.44741 | ||||||||
\(489\) | −8.60157e37 | − | 1.90179e38i | −0.0870161 | − | 0.192391i | ||||
\(490\) | 1.20857e39 | + | 9.68541e38i | 1.18694 | + | 0.951206i | ||||
\(491\) | 7.94407e38i | 0.757463i | 0.925507 | + | 0.378732i | \(0.123640\pi\) | ||||
−0.925507 | + | 0.378732i | \(0.876360\pi\) | |||||||
\(492\) | 1.21504e37 | + | 2.68643e37i | 0.0112485 | + | 0.0248703i | ||||
\(493\) | − | 4.64583e38i | − | 0.417622i | ||||||
\(494\) | 9.00408e38i | 0.785957i | ||||||||
\(495\) | 2.72089e39 | + | 2.39260e39i | 2.30640 | + | 2.02812i | ||||
\(496\) | − | 1.33658e39i | − | 1.10030i | ||||||
\(497\) | −1.60927e39 | + | 7.72610e38i | −1.28665 | + | 0.617722i | ||||
\(498\) | 6.07329e38 | − | 2.74688e38i | 0.471627 | − | 0.213311i | ||||
\(499\) | 1.96619e39 | 1.48309 | 0.741546 | − | 0.670902i | \(-0.234093\pi\) | ||||
0.741546 | + | 0.670902i | \(0.234093\pi\) | |||||||
\(500\) | −1.38600e38 | −0.101554 | ||||||||
\(501\) | 1.45983e38 | + | 3.22765e38i | 0.103910 | + | 0.229742i | ||||
\(502\) | 7.50506e38i | 0.518980i | ||||||||
\(503\) | 1.11150e39 | 0.746748 | 0.373374 | − | 0.927681i | \(-0.378201\pi\) | ||||
0.373374 | + | 0.927681i | \(0.378201\pi\) | |||||||
\(504\) | 4.33120e38 | − | 1.54285e39i | 0.282726 | − | 1.00712i | ||||
\(505\) | 1.18151e39 | 0.749400 | ||||||||
\(506\) | − | 9.98024e38i | − | 0.615118i | ||||||
\(507\) | −2.48970e38 | − | 5.50468e38i | −0.149119 | − | 0.329698i | ||||
\(508\) | 2.62123e38 | 0.152574 | ||||||||
\(509\) | −8.58590e38 | −0.485711 | −0.242856 | − | 0.970062i | \(-0.578084\pi\) | ||||
−0.242856 | + | 0.970062i | \(0.578084\pi\) | |||||||
\(510\) | 9.59899e38 | − | 4.34152e38i | 0.527786 | − | 0.238712i | ||||
\(511\) | −1.37346e38 | + | 6.59400e37i | −0.0734029 | + | 0.0352408i | ||||
\(512\) | − | 2.13654e39i | − | 1.10993i | ||||||
\(513\) | −6.02375e38 | + | 1.97152e39i | −0.304204 | + | 0.995633i | ||||
\(514\) | 1.14754e39i | 0.563384i | ||||||||
\(515\) | − | 2.78860e37i | − | 0.0133101i | ||||||
\(516\) | −8.46338e37 | − | 1.87124e38i | −0.0392756 | − | 0.0868376i | ||||
\(517\) | 6.23099e39i | 2.81154i | ||||||||
\(518\) | −2.55664e39 | + | 1.22745e39i | −1.12173 | + | 0.538544i | ||||
\(519\) | 7.90435e38 | + | 1.74763e39i | 0.337240 | + | 0.745631i | ||||
\(520\) | −3.24152e39 | −1.34493 | ||||||||
\(521\) | 1.57313e39 | 0.634773 | 0.317386 | − | 0.948296i | \(-0.397195\pi\) | ||||
0.317386 | + | 0.948296i | \(0.397195\pi\) | |||||||
\(522\) | 1.74386e39 | − | 1.98313e39i | 0.684366 | − | 0.778268i | ||||
\(523\) | − | 6.19575e38i | − | 0.236494i | −0.992984 | − | 0.118247i | \(-0.962273\pi\) | ||
0.992984 | − | 0.118247i | \(-0.0377274\pi\) | |||||||
\(524\) | 2.01031e38 | 0.0746380 | ||||||||
\(525\) | 2.83174e39 | − | 3.37263e39i | 1.02269 | − | 1.21803i | ||||
\(526\) | 7.66507e38 | 0.269292 | ||||||||
\(527\) | − | 1.39048e39i | − | 0.475237i | ||||||
\(528\) | −4.61039e39 | + | 2.08523e39i | −1.53301 | + | 0.693364i | ||||
\(529\) | 2.73144e39 | 0.883659 | ||||||||
\(530\) | −1.05197e39 | −0.331134 | ||||||||
\(531\) | 1.75707e39 | − | 1.99816e39i | 0.538169 | − | 0.612012i | ||||
\(532\) | −3.36506e38 | + | 1.61557e38i | −0.100294 | + | 0.0481513i | ||||
\(533\) | 7.03502e38i | 0.204043i | ||||||||
\(534\) | −3.51804e39 | + | 1.59117e39i | −0.993009 | + | 0.449126i | ||||
\(535\) | 6.75390e38i | 0.185535i | ||||||||
\(536\) | − | 5.18912e39i | − | 1.38741i | ||||||
\(537\) | 1.27786e39 | − | 5.77961e38i | 0.332549 | − | 0.150408i | ||||
\(538\) | − | 8.04959e38i | − | 0.203906i | ||||||
\(539\) | −6.03882e39 | − | 4.83949e39i | −1.48907 | − | 1.19333i | ||||
\(540\) | −6.85253e38 | − | 2.09371e38i | −0.164491 | − | 0.0502582i | ||||
\(541\) | 3.88333e39 | 0.907495 | 0.453748 | − | 0.891130i | \(-0.350087\pi\) | ||||
0.453748 | + | 0.891130i | \(0.350087\pi\) | |||||||
\(542\) | 7.29633e39 | 1.66003 | ||||||||
\(543\) | 1.62290e39 | − | 7.34020e38i | 0.359497 | − | 0.162596i | ||||
\(544\) | − | 3.75701e38i | − | 0.0810324i | ||||||
\(545\) | 1.00384e40 | 2.10822 | ||||||||
\(546\) | 2.37377e39 | − | 2.82719e39i | 0.485451 | − | 0.578177i | ||||
\(547\) | −2.41811e39 | −0.481570 | −0.240785 | − | 0.970578i | \(-0.577405\pi\) | ||||
−0.240785 | + | 0.970578i | \(0.577405\pi\) | |||||||
\(548\) | 4.35199e38i | 0.0844053i | ||||||||
\(549\) | −5.50116e39 | − | 4.83741e39i | −1.03909 | − | 0.913723i | ||||
\(550\) | −1.55908e40 | −2.86819 | ||||||||
\(551\) | −6.37137e39 | −1.14166 | ||||||||
\(552\) | 8.42437e38 | + | 1.86261e39i | 0.147035 | + | 0.325091i | ||||
\(553\) | 1.22610e39 | + | 2.55383e39i | 0.208454 | + | 0.434188i | ||||
\(554\) | 7.75117e39i | 1.28374i | ||||||||
\(555\) | 5.41260e39 | + | 1.19671e40i | 0.873288 | + | 1.93082i | ||||
\(556\) | 1.34234e38i | 0.0210997i | ||||||||
\(557\) | − | 7.29364e39i | − | 1.11698i | −0.829513 | − | 0.558488i | \(-0.811382\pi\) | ||
0.829513 | − | 0.558488i | \(-0.188618\pi\) | |||||||
\(558\) | 5.21929e39 | − | 5.93543e39i | 0.778781 | − | 0.885638i | ||||
\(559\) | − | 4.90026e39i | − | 0.712440i | ||||||
\(560\) | 4.33545e39 | + | 9.03027e39i | 0.614197 | + | 1.27931i | ||||
\(561\) | −4.79631e39 | + | 2.16932e39i | −0.662134 | + | 0.299475i | ||||
\(562\) | −7.76354e39 | −1.04444 | ||||||||
\(563\) | −4.96577e39 | −0.651051 | −0.325525 | − | 0.945533i | \(-0.605541\pi\) | ||||
−0.325525 | + | 0.945533i | \(0.605541\pi\) | |||||||
\(564\) | −5.07801e38 | − | 1.12274e39i | −0.0648854 | − | 0.143460i | ||||
\(565\) | 7.99230e39i | 0.995335i | ||||||||
\(566\) | 1.01541e39 | 0.123255 | ||||||||
\(567\) | 7.08896e39 | − | 4.60231e39i | 0.838742 | − | 0.544529i | ||||
\(568\) | −1.29451e40 | −1.49298 | ||||||||
\(569\) | − | 3.34448e39i | − | 0.376011i | −0.982168 | − | 0.188006i | \(-0.939798\pi\) | ||
0.982168 | − | 0.188006i | \(-0.0602023\pi\) | |||||||
\(570\) | −5.95403e39 | − | 1.31642e40i | −0.652568 | − | 1.44281i | ||||
\(571\) | 4.89459e39 | 0.522989 | 0.261494 | − | 0.965205i | \(-0.415785\pi\) | ||||
0.261494 | + | 0.965205i | \(0.415785\pi\) | |||||||
\(572\) | 1.56376e39 | 0.162903 | ||||||||
\(573\) | −1.68605e39 | + | 7.62579e38i | −0.171249 | + | 0.0774538i | ||||
\(574\) | 2.19736e39 | − | 1.05496e39i | 0.217610 | − | 0.104475i | ||||
\(575\) | 5.61782e39i | 0.542481i | ||||||||
\(576\) | 7.59365e39 | − | 8.63558e39i | 0.715030 | − | 0.813140i | ||||
\(577\) | 3.45684e39i | 0.317417i | 0.987326 | + | 0.158708i | \(0.0507329\pi\) | ||||
−0.987326 | + | 0.158708i | \(0.949267\pi\) | |||||||
\(578\) | − | 9.02326e39i | − | 0.807997i | ||||||
\(579\) | −4.65185e39 | − | 1.02851e40i | −0.406243 | − | 0.898195i | ||||
\(580\) | − | 2.21454e39i | − | 0.188615i | ||||||
\(581\) | 2.85366e39 | + | 5.94386e39i | 0.237054 | + | 0.493759i | ||||
\(582\) | −5.24575e39 | − | 1.15982e40i | −0.425035 | − | 0.939742i | ||||
\(583\) | 5.25636e39 | 0.415424 | ||||||||
\(584\) | −1.10482e39 | −0.0851739 | ||||||||
\(585\) | −1.28387e40 | − | 1.12897e40i | −0.965523 | − | 0.849027i | ||||
\(586\) | 7.33410e39i | 0.538061i | ||||||||
\(587\) | −6.89040e39 | −0.493165 | −0.246583 | − | 0.969122i | \(-0.579308\pi\) | ||||
−0.246583 | + | 0.969122i | \(0.579308\pi\) | |||||||
\(588\) | 1.48251e39 | + | 3.79868e38i | 0.103521 | + | 0.0265254i | ||||
\(589\) | −1.90693e40 | −1.29916 | ||||||||
\(590\) | 1.86485e40i | 1.23962i | ||||||||
\(591\) | −2.26662e40 | + | 1.02517e40i | −1.47015 | + | 0.664931i | ||||
\(592\) | −1.83427e40 | −1.16091 | ||||||||
\(593\) | −3.60617e39 | −0.222717 | −0.111358 | − | 0.993780i | \(-0.535520\pi\) | ||||
−0.111358 | + | 0.993780i | \(0.535520\pi\) | |||||||
\(594\) | −2.86164e40 | − | 8.74339e39i | −1.72469 | − | 0.526959i | ||||
\(595\) | 4.51028e39 | + | 9.39443e39i | 0.265282 | + | 0.552554i | ||||
\(596\) | 8.64663e38i | 0.0496336i | ||||||||
\(597\) | 2.20080e40 | − | 9.95395e39i | 1.23297 | − | 0.557658i | ||||
\(598\) | 4.70927e39i | 0.257505i | ||||||||
\(599\) | 6.74977e39i | 0.360247i | 0.983644 | + | 0.180123i | \(0.0576497\pi\) | ||||
−0.983644 | + | 0.180123i | \(0.942350\pi\) | |||||||
\(600\) | 2.90970e40 | − | 1.31602e40i | 1.51585 | − | 0.685600i | ||||
\(601\) | 1.72976e40i | 0.879642i | 0.898086 | + | 0.439821i | \(0.144958\pi\) | ||||
−0.898086 | + | 0.439821i | \(0.855042\pi\) | |||||||
\(602\) | −1.53058e40 | + | 7.34832e39i | −0.759811 | + | 0.364787i | ||||
\(603\) | 1.80728e40 | − | 2.05526e40i | 0.875841 | − | 0.996016i | ||||
\(604\) | −1.49998e39 | −0.0709658 | ||||||||
\(605\) | 9.20386e40 | 4.25125 | ||||||||
\(606\) | −8.89045e39 | + | 4.02105e39i | −0.400932 | + | 0.181337i | ||||
\(607\) | 4.03223e40i | 1.77545i | 0.460371 | + | 0.887726i | \(0.347716\pi\) | ||||
−0.460371 | + | 0.887726i | \(0.652284\pi\) | |||||||
\(608\) | −5.15243e39 | −0.221519 | ||||||||
\(609\) | 2.00054e40 | + | 1.67970e40i | 0.839842 | + | 0.705150i | ||||
\(610\) | 5.13414e40 | 2.10468 | ||||||||
\(611\) | − | 2.94015e40i | − | 1.17699i | ||||||
\(612\) | 6.87438e38 | − | 7.81762e38i | 0.0268743 | − | 0.0305618i | ||||
\(613\) | 3.64404e40 | 1.39125 | 0.695627 | − | 0.718403i | \(-0.255127\pi\) | ||||
0.695627 | + | 0.718403i | \(0.255127\pi\) | |||||||
\(614\) | −1.86685e39 | −0.0696095 | ||||||||
\(615\) | −4.65197e39 | − | 1.02854e40i | −0.169413 | − | 0.374569i | ||||
\(616\) | −2.42884e40 | − | 5.05901e40i | −0.863930 | − | 1.79947i | ||||
\(617\) | 1.67933e40i | 0.583445i | 0.956503 | + | 0.291723i | \(0.0942284\pi\) | ||||
−0.956503 | + | 0.291723i | \(0.905772\pi\) | |||||||
\(618\) | 9.49043e37 | + | 2.09831e38i | 0.00322072 | + | 0.00712094i | ||||
\(619\) | 3.40129e40i | 1.12753i | 0.825935 | + | 0.563766i | \(0.190648\pi\) | ||||
−0.825935 | + | 0.563766i | \(0.809352\pi\) | |||||||
\(620\) | − | 6.62802e39i | − | 0.214637i | ||||||
\(621\) | −3.15051e39 | + | 1.03113e40i | −0.0996672 | + | 0.326202i | ||||
\(622\) | − | 1.75352e40i | − | 0.541937i | ||||||
\(623\) | −1.65302e40 | − | 3.44307e40i | −0.499117 | − | 1.03961i | ||||
\(624\) | 2.17545e40 | − | 9.83933e39i | 0.641761 | − | 0.290261i | ||||
\(625\) | −2.11437e39 | −0.0609425 | ||||||||
\(626\) | 8.01811e39 | 0.225811 | ||||||||
\(627\) | 2.97504e40 | + | 6.57774e40i | 0.818678 | + | 1.81008i | ||||
\(628\) | 6.89816e39i | 0.185489i | ||||||||
\(629\) | −1.90824e40 | −0.501416 | ||||||||
\(630\) | −1.60102e40 | + | 5.70310e40i | −0.411110 | + | 1.46445i | ||||
\(631\) | 2.25030e39 | 0.0564695 | 0.0282348 | − | 0.999601i | \(-0.491011\pi\) | ||||
0.0282348 | + | 0.999601i | \(0.491011\pi\) | |||||||
\(632\) | 2.05432e40i | 0.503815i | ||||||||
\(633\) | −1.10881e40 | − | 2.45155e40i | −0.265767 | − | 0.587606i | ||||
\(634\) | 2.86466e40 | 0.671088 | ||||||||
\(635\) | −1.00358e41 | −2.29791 | ||||||||
\(636\) | −9.47124e38 | + | 4.28373e38i | −0.0211972 | + | 0.00958725i | ||||
\(637\) | 2.84947e40 | + | 2.28356e40i | 0.623365 | + | 0.499563i | ||||
\(638\) | − | 9.24797e40i | − | 1.97764i | ||||||
\(639\) | −5.12717e40 | − | 4.50855e40i | −1.07180 | − | 0.942486i | ||||
\(640\) | 6.38362e40i | 1.30454i | ||||||||
\(641\) | 7.96830e40i | 1.59193i | 0.605342 | + | 0.795965i | \(0.293036\pi\) | ||||
−0.605342 | + | 0.795965i | \(0.706964\pi\) | |||||||
\(642\) | −2.29856e39 | − | 5.08206e39i | −0.0448949 | − | 0.0992617i | ||||
\(643\) | − | 5.54592e40i | − | 1.05905i | −0.848296 | − | 0.529523i | \(-0.822371\pi\) | ||
0.848296 | − | 0.529523i | \(-0.177629\pi\) | |||||||
\(644\) | −1.75998e39 | + | 8.44968e38i | −0.0328596 | + | 0.0157759i | ||||
\(645\) | 3.24034e40 | + | 7.16432e40i | 0.591527 | + | 1.30785i | ||||
\(646\) | 2.09912e40 | 0.374685 | ||||||||
\(647\) | −1.94441e40 | −0.339372 | −0.169686 | − | 0.985498i | \(-0.554275\pi\) | ||||
−0.169686 | + | 0.985498i | \(0.554275\pi\) | |||||||
\(648\) | 6.07870e40 | − | 7.83744e39i | 1.03746 | − | 0.133763i | ||||
\(649\) | − | 9.31806e40i | − | 1.55517i | ||||||
\(650\) | 7.35664e40 | 1.20070 | ||||||||
\(651\) | 5.98754e40 | + | 5.02728e40i | 0.955706 | + | 0.802432i | ||||
\(652\) | 1.44552e39 | 0.0225649 | ||||||||
\(653\) | 8.42089e40i | 1.28563i | 0.766020 | + | 0.642816i | \(0.222234\pi\) | ||||
−0.766020 | + | 0.642816i | \(0.777766\pi\) | |||||||
\(654\) | −7.55355e40 | + | 3.41638e40i | −1.12791 | + | 0.510140i | ||||
\(655\) | −7.69680e40 | −1.12412 | ||||||||
\(656\) | 1.57650e40 | 0.225211 | ||||||||
\(657\) | −4.37589e39 | − | 3.84792e39i | −0.0611461 | − | 0.0537685i | ||||
\(658\) | −9.18343e40 | + | 4.40898e40i | −1.25525 | + | 0.602646i | ||||
\(659\) | − | 2.47918e40i | − | 0.331489i | −0.986169 | − | 0.165745i | \(-0.946997\pi\) | ||
0.986169 | − | 0.165745i | \(-0.0530027\pi\) | |||||||
\(660\) | −2.28627e40 | + | 1.03405e40i | −0.299047 | + | 0.135256i | ||||
\(661\) | − | 4.90162e40i | − | 0.627218i | −0.949552 | − | 0.313609i | \(-0.898462\pi\) | ||
0.949552 | − | 0.313609i | \(-0.101538\pi\) | |||||||
\(662\) | 9.33045e40i | 1.16805i | ||||||||
\(663\) | 2.26318e40 | − | 1.02361e40i | 0.277187 | − | 0.125369i | ||||
\(664\) | 4.78129e40i | 0.572939i | ||||||||
\(665\) | 1.28837e41 | − | 6.18547e40i | 1.51052 | − | 0.725202i | ||||
\(666\) | −8.14555e40 | − | 7.16275e40i | −0.934424 | − | 0.821681i | ||||
\(667\) | −3.33232e40 | −0.374044 | ||||||||
\(668\) | −2.45329e39 | −0.0269458 | ||||||||
\(669\) | −2.37445e40 | + | 1.07394e40i | −0.255202 | + | 0.115425i | ||||
\(670\) | 1.91814e41i | 2.01742i | ||||||||
\(671\) | −2.56536e41 | −2.64042 | ||||||||
\(672\) | 1.61781e40 | + | 1.35835e40i | 0.162957 | + | 0.136822i | ||||
\(673\) | 3.96130e40 | 0.390499 | 0.195249 | − | 0.980754i | \(-0.437448\pi\) | ||||
0.195249 | + | 0.980754i | \(0.437448\pi\) | |||||||
\(674\) | − | 4.09291e40i | − | 0.394879i | ||||||
\(675\) | 1.61080e41 | + | 4.92161e40i | 1.52103 | + | 0.464732i | ||||
\(676\) | 4.18403e39 | 0.0386694 | ||||||||
\(677\) | −7.59452e40 | −0.687012 | −0.343506 | − | 0.939150i | \(-0.611615\pi\) | ||||
−0.343506 | + | 0.939150i | \(0.611615\pi\) | |||||||
\(678\) | −2.72002e40 | − | 6.01390e40i | −0.240847 | − | 0.532508i | ||||
\(679\) | 1.13511e41 | − | 5.44966e40i | 0.983841 | − | 0.472343i | ||||
\(680\) | 7.55696e40i | 0.641162i | ||||||||
\(681\) | −5.08837e40 | − | 1.12503e41i | −0.422616 | − | 0.934394i | ||||
\(682\) | − | 2.76788e41i | − | 2.25047i | ||||||
\(683\) | − | 1.13829e41i | − | 0.906054i | −0.891497 | − | 0.453027i | \(-0.850344\pi\) | ||
0.891497 | − | 0.453027i | \(-0.149656\pi\) | |||||||
\(684\) | −1.07212e40 | − | 9.42764e39i | −0.0835469 | − | 0.0734665i | ||||
\(685\) | − | 1.66623e41i | − | 1.27122i | ||||||
\(686\) | 2.85959e40 | − | 1.23246e41i | 0.213601 | − | 0.920603i | ||||
\(687\) | −1.48475e41 | + | 6.71537e40i | −1.08588 | + | 0.491131i | ||||
\(688\) | −1.09812e41 | −0.786350 | ||||||||
\(689\) | −2.48026e40 | −0.173908 | ||||||||
\(690\) | −3.11404e40 | − | 6.88508e40i | −0.213803 | − | 0.472713i | ||||
\(691\) | − | 1.08632e41i | − | 0.730338i | −0.930941 | − | 0.365169i | \(-0.881011\pi\) | ||
0.930941 | − | 0.365169i | \(-0.118989\pi\) | |||||||
\(692\) | −1.32835e40 | −0.0874529 | ||||||||
\(693\) | 7.99977e40 | − | 2.84966e41i | 0.515757 | − | 1.83722i | ||||
\(694\) | 1.98878e41 | 1.25567 | ||||||||
\(695\) | − | 5.13935e40i | − | 0.317781i | ||||||
\(696\) | 7.80626e40 | + | 1.72595e41i | 0.472725 | + | 1.04519i | ||||
\(697\) | 1.64008e40 | 0.0972722 | ||||||||
\(698\) | −7.98671e40 | −0.463943 | ||||||||
\(699\) | 1.01492e41 | − | 4.59036e40i | 0.577447 | − | 0.261173i | ||||
\(700\) | 1.31998e40 | + | 2.74937e40i | 0.0735605 | + | 0.153219i | ||||
\(701\) | 2.18266e41i | 1.19145i | 0.803189 | + | 0.595725i | \(0.203135\pi\) | ||||
−0.803189 | + | 0.595725i | \(0.796865\pi\) | |||||||
\(702\) | 1.35029e41 | + | 4.12565e40i | 0.722002 | + | 0.220599i | ||||
\(703\) | 2.61699e41i | 1.37072i | ||||||||
\(704\) | − | 4.02704e41i | − | 2.06625i | ||||||
\(705\) | 1.94420e41 | + | 4.29858e41i | 0.977233 | + | 2.16064i | ||||
\(706\) | − | 2.67258e41i | − | 1.31602i | ||||||
\(707\) | −4.17735e40 | − | 8.70098e40i | −0.201521 | − | 0.419746i | ||||
\(708\) | 7.59386e39 | + | 1.67899e40i | 0.0358906 | + | 0.0793532i | ||||
\(709\) | −1.65763e41 | −0.767568 | −0.383784 | − | 0.923423i | \(-0.625379\pi\) | ||||
−0.383784 | + | 0.923423i | \(0.625379\pi\) | |||||||
\(710\) | 4.78511e41 | 2.17093 | ||||||||
\(711\) | −7.15486e40 | + | 8.13659e40i | −0.318048 | + | 0.361687i | ||||
\(712\) | − | 2.76964e41i | − | 1.20632i | ||||||
\(713\) | −9.97350e40 | −0.425647 | ||||||||
\(714\) | −6.59102e40 | − | 5.53397e40i | −0.275631 | − | 0.231426i | ||||
\(715\) | −5.98711e41 | −2.45347 | ||||||||
\(716\) | 9.71282e39i | 0.0390038i | ||||||||
\(717\) | 3.97647e38 | − | 1.79851e38i | 0.00156484 | − | 0.000707758i | ||||
\(718\) | 3.91477e41 | 1.50974 | ||||||||
\(719\) | 1.69268e41 | 0.639745 | 0.319873 | − | 0.947461i | \(-0.396360\pi\) | ||||
0.319873 | + | 0.947461i | \(0.396360\pi\) | |||||||
\(720\) | −2.52994e41 | + | 2.87708e41i | −0.937107 | + | 1.06569i | ||||
\(721\) | −2.05360e39 | + | 9.85934e38i | −0.00745510 | + | 0.00357921i | ||||
\(722\) | − | 2.22651e40i | − | 0.0792201i | ||||||
\(723\) | −1.71931e41 | + | 7.77623e40i | −0.599581 | + | 0.271184i | ||||
\(724\) | 1.23354e40i | 0.0421643i | ||||||||
\(725\) | 5.20563e41i | 1.74410i | ||||||||
\(726\) | −6.92556e41 | + | 3.13235e41i | −2.27444 | + | 1.02870i | ||||
\(727\) | − | 8.07078e40i | − | 0.259816i | −0.991526 | − | 0.129908i | \(-0.958532\pi\) | ||
0.991526 | − | 0.129908i | \(-0.0414682\pi\) | |||||||
\(728\) | 1.14607e41 | + | 2.38714e41i | 0.361665 | + | 0.753309i | ||||
\(729\) | 2.68057e41 | + | 1.80669e41i | 0.829234 | + | 0.558901i | ||||
\(730\) | 4.08395e40 | 0.123851 | ||||||||
\(731\) | −1.14240e41 | −0.339637 | ||||||||
\(732\) | 4.62243e40 | − | 2.09067e40i | 0.134729 | − | 0.0609362i | ||||
\(733\) | − | 2.55511e41i | − | 0.730134i | −0.930981 | − | 0.365067i | \(-0.881046\pi\) | ||
0.930981 | − | 0.365067i | \(-0.118954\pi\) | |||||||
\(734\) | −1.18755e41 | −0.332705 | ||||||||
\(735\) | −5.67603e41 | − | 1.45438e41i | −1.55912 | − | 0.399496i | ||||
\(736\) | −2.69480e40 | −0.0725768 | ||||||||
\(737\) | − | 9.58434e41i | − | 2.53095i | ||||||
\(738\) | 7.00087e40 | + | 6.15617e40i | 0.181274 | + | 0.159402i | ||||
\(739\) | 9.41730e40 | 0.239101 | 0.119551 | − | 0.992828i | \(-0.461855\pi\) | ||||
0.119551 | + | 0.992828i | \(0.461855\pi\) | |||||||
\(740\) | −9.09603e40 | −0.226460 | ||||||||
\(741\) | −1.40380e41 | − | 3.10377e41i | −0.342721 | − | 0.757748i | ||||
\(742\) | 3.71934e40 | + | 7.74700e40i | 0.0890450 | + | 0.185471i | ||||
\(743\) | 4.06339e41i | 0.954005i | 0.878902 | + | 0.477003i | \(0.158277\pi\) | ||||
−0.878902 | + | 0.477003i | \(0.841723\pi\) | |||||||
\(744\) | 2.33638e41 | + | 5.16568e41i | 0.537943 | + | 1.18938i | ||||
\(745\) | − | 3.31050e41i | − | 0.747528i | ||||||
\(746\) | − | 6.59455e40i | − | 0.146040i | ||||||
\(747\) | −1.66525e41 | + | 1.89373e41i | −0.361684 | + | 0.411311i | ||||
\(748\) | − | 3.64560e40i | − | 0.0776598i | ||||||
\(749\) | 4.97375e40 | − | 2.38791e40i | 0.103920 | − | 0.0498920i | ||||
\(750\) | −3.99295e41 | + | 1.80596e41i | −0.818286 | + | 0.370102i | ||||
\(751\) | 8.78253e41 | 1.76539 | 0.882695 | − | 0.469947i | \(-0.155727\pi\) | ||||
0.882695 | + | 0.469947i | \(0.155727\pi\) | |||||||
\(752\) | −6.58867e41 | −1.29909 | ||||||||
\(753\) | −1.17009e41 | − | 2.58704e41i | −0.226304 | − | 0.500353i | ||||
\(754\) | 4.36374e41i | 0.827893i | ||||||||
\(755\) | 5.74290e41 | 1.06881 | ||||||||
\(756\) | 8.80914e39 | + | 5.78664e40i | 0.0160830 | + | 0.105648i | ||||
\(757\) | 5.89345e41 | 1.05555 | 0.527775 | − | 0.849384i | \(-0.323026\pi\) | ||||
0.527775 | + | 0.849384i | \(0.323026\pi\) | |||||||
\(758\) | 8.97774e41i | 1.57748i | ||||||||
\(759\) | 1.55599e41 | + | 3.44025e41i | 0.268226 | + | 0.593041i | ||||
\(760\) | 1.03637e42 | 1.75275 | ||||||||
\(761\) | 5.21591e41 | 0.865471 | 0.432736 | − | 0.901521i | \(-0.357548\pi\) | ||||
0.432736 | + | 0.901521i | \(0.357548\pi\) | |||||||
\(762\) | 7.55156e41 | − | 3.41548e41i | 1.22939 | − | 0.556039i | ||||
\(763\) | −3.54919e41 | − | 7.39257e41i | −0.566921 | − | 1.18084i | ||||
\(764\) | − | 1.28154e40i | − | 0.0200853i | ||||||
\(765\) | −2.63196e41 | + | 2.99310e41i | −0.404752 | + | 0.460288i | ||||
\(766\) | 8.26698e41i | 1.24747i | ||||||||
\(767\) | 4.39681e41i | 0.651036i | ||||||||
\(768\) | 8.98520e40 | + | 1.98661e41i | 0.130554 | + | 0.288652i | ||||
\(769\) | − | 3.60602e41i | − | 0.514157i | −0.966390 | − | 0.257079i | \(-0.917240\pi\) | ||
0.966390 | − | 0.257079i | \(-0.0827600\pi\) | |||||||
\(770\) | 8.97814e41 | + | 1.87005e42i | 1.25623 | + | 2.61660i | ||||
\(771\) | −1.78910e41 | − | 3.95566e41i | −0.245667 | − | 0.543164i | ||||
\(772\) | 7.81757e40 | 0.105347 | ||||||||
\(773\) | −1.32815e42 | −1.75648 | −0.878242 | − | 0.478216i | \(-0.841284\pi\) | ||||
−0.878242 | + | 0.478216i | \(0.841284\pi\) | |||||||
\(774\) | −4.87647e41 | − | 4.28810e41i | −0.632939 | − | 0.556571i | ||||
\(775\) | 1.55802e42i | 1.98472i | ||||||||
\(776\) | 9.13090e41 | 1.14161 | ||||||||
\(777\) | 6.89924e41 | − | 8.21707e41i | 0.846635 | − | 1.00835i | ||||
\(778\) | 1.21290e42 | 1.46090 | ||||||||
\(779\) | − | 2.24923e41i | − | 0.265913i | ||||||
\(780\) | 1.07880e41 | − | 4.87927e40i | 0.125189 | − | 0.0566217i | ||||
\(781\) | −2.39096e42 | −2.72354 | ||||||||
\(782\) | 1.09787e41 | 0.122759 | ||||||||
\(783\) | −2.91935e41 | + | 9.55477e41i | −0.320435 | + | 1.04876i | ||||
\(784\) | 5.11730e41 | − | 6.38548e41i | 0.551388 | − | 0.688035i | ||||
\(785\) | − | 2.64107e42i | − | 2.79364i | ||||||
\(786\) | 5.79156e41 | − | 2.61945e41i | 0.601407 | − | 0.272009i | ||||
\(787\) | − | 3.23407e41i | − | 0.329697i | −0.986319 | − | 0.164849i | \(-0.947286\pi\) | ||
0.986319 | − | 0.164849i | \(-0.0527136\pi\) | |||||||
\(788\) | − | 1.72283e41i | − | 0.172429i | ||||||
\(789\) | −2.64220e41 | + | 1.19504e41i | −0.259627 | + | 0.117426i | ||||
\(790\) | − | 7.59374e41i | − | 0.732593i | ||||||
\(791\) | 5.88574e41 | − | 2.82575e41i | 0.557496 | − | 0.267655i | ||||
\(792\) | 1.41735e42 | − | 1.61182e42i | 1.31814 | − | 1.49900i | ||||
\(793\) | 1.21049e42 | 1.10535 | ||||||||
\(794\) | −1.13976e42 | −1.02192 | ||||||||
\(795\) | 3.62621e41 | − | 1.64010e41i | 0.319249 | − | 0.144393i | ||||
\(796\) | 1.67279e41i | 0.144611i | ||||||||
\(797\) | −4.16632e41 | −0.353677 | −0.176839 | − | 0.984240i | \(-0.556587\pi\) | ||||
−0.176839 | + | 0.984240i | \(0.556587\pi\) | |||||||
\(798\) | −7.58938e41 | + | 9.03904e41i | −0.632651 | + | 0.753495i | ||||
\(799\) | −6.85437e41 | −0.561099 | ||||||||
\(800\) | 4.20971e41i | 0.338413i | ||||||||
\(801\) | 9.64618e41 | − | 1.09697e42i | 0.761525 | − | 0.866014i | ||||
\(802\) | −1.37928e42 | −1.06936 | ||||||||
\(803\) | −2.04062e41 | −0.155377 | ||||||||
\(804\) | 7.81087e40 | + | 1.72697e41i | 0.0584099 | + | 0.129143i | ||||
\(805\) | 6.73835e41 | − | 3.23509e41i | 0.494896 | − | 0.237600i | ||||
\(806\) | 1.30605e42i | 0.942109i | ||||||||
\(807\) | 1.25499e41 | + | 2.77475e41i | 0.0889145 | + | 0.196588i | ||||
\(808\) | − | 6.99915e41i | − | 0.487058i | ||||||
\(809\) | − | 1.03543e41i | − | 0.0707730i | −0.999374 | − | 0.0353865i | \(-0.988734\pi\) | ||
0.999374 | − | 0.0353865i | \(-0.0112662\pi\) | |||||||
\(810\) | −2.24697e42 | + | 2.89709e41i | −1.50857 | + | 0.194504i | ||||
\(811\) | − | 1.51069e41i | − | 0.0996263i | −0.998759 | − | 0.0498131i | \(-0.984137\pi\) | ||
0.998759 | − | 0.0498131i | \(-0.0158626\pi\) | |||||||
\(812\) | −1.63084e41 | + | 7.82971e40i | −0.105645 | + | 0.0507205i | ||||
\(813\) | −2.51509e42 | + | 1.13755e42i | −1.60045 | + | 0.723864i | ||||
\(814\) | −3.79853e42 | −2.37444 | ||||||||
\(815\) | −5.53441e41 | −0.339849 | ||||||||
\(816\) | −2.29384e41 | − | 5.07164e41i | −0.138375 | − | 0.305943i | ||||
\(817\) | 1.56670e42i | 0.928469i | ||||||||
\(818\) | 8.50791e41 | 0.495336 | ||||||||
\(819\) | −3.77476e41 | + | 1.34464e42i | −0.215910 | + | 0.769110i | ||||
\(820\) | 7.81778e40 | 0.0439322 | ||||||||
\(821\) | − | 2.56278e41i | − | 0.141493i | −0.997494 | − | 0.0707466i | \(-0.977462\pi\) | ||
0.997494 | − | 0.0707466i | \(-0.0225382\pi\) | |||||||
\(822\) | 5.67068e41 | + | 1.25377e42i | 0.307605 | + | 0.680108i | ||||
\(823\) | −1.96772e42 | −1.04873 | −0.524367 | − | 0.851492i | \(-0.675698\pi\) | ||||
−0.524367 | + | 0.851492i | \(0.675698\pi\) | |||||||
\(824\) | −1.65193e40 | −0.00865062 | ||||||||
\(825\) | 5.37424e42 | − | 2.43071e42i | 2.76525 | − | 1.25069i | ||||
\(826\) | 1.37333e42 | − | 6.59335e41i | 0.694325 | − | 0.333346i | ||||
\(827\) | − | 3.29125e42i | − | 1.63505i | −0.575892 | − | 0.817526i | \(-0.695345\pi\) | ||
0.575892 | − | 0.817526i | \(-0.304655\pi\) | |||||||
\(828\) | −5.60735e40 | − | 4.93079e40i | −0.0273727 | − | 0.0240701i | ||||
\(829\) | 1.78654e42i | 0.856982i | 0.903546 | + | 0.428491i | \(0.140955\pi\) | ||||
−0.903546 | + | 0.428491i | \(0.859045\pi\) | |||||||
\(830\) | − | 1.76739e42i | − | 0.833106i | ||||||
\(831\) | −1.20846e42 | − | 2.67188e42i | −0.559780 | − | 1.23766i | ||||
\(832\) | 1.90020e42i | 0.864989i | ||||||||
\(833\) | 5.32366e41 | − | 6.64298e41i | 0.238154 | − | 0.297174i | ||||
\(834\) | 1.74907e41 | + | 3.86716e41i | 0.0768954 | + | 0.170014i | ||||
\(835\) | 9.39281e41 | 0.405828 | ||||||||
\(836\) | −4.99964e41 | −0.212299 | ||||||||
\(837\) | −8.73749e41 | + | 2.85970e42i | −0.364643 | + | 1.19344i | ||||
\(838\) | 3.82783e42i | 1.57005i | ||||||||
\(839\) | 2.75094e42 | 1.10900 | 0.554502 | − | 0.832182i | \(-0.312909\pi\) | ||||
0.554502 | + | 0.832182i | \(0.312909\pi\) | |||||||
\(840\) | −3.25411e42 | − | 2.73222e42i | −1.28938 | − | 1.08260i | ||||
\(841\) | −5.20136e41 | −0.202570 | ||||||||
\(842\) | 3.83683e42i | 1.46875i | ||||||||
\(843\) | 2.67614e42 | − | 1.21039e42i | 1.00695 | − | 0.455434i | ||||
\(844\) | 1.86338e41 | 0.0689186 | ||||||||
\(845\) | −1.60192e42 | −0.582396 | ||||||||
\(846\) | −2.92587e42 | − | 2.57285e42i | −1.04565 | − | 0.919484i | ||||
\(847\) | −3.25411e42 | − | 6.77797e42i | −1.14320 | − | 2.38117i | ||||
\(848\) | 5.55810e41i | 0.191949i | ||||||||
\(849\) | −3.50019e41 | + | 1.58309e41i | −0.118831 | + | 0.0537459i | ||||
\(850\) | − | 1.71506e42i | − | 0.572405i | ||||||
\(851\) | 1.36872e42i | 0.449094i | ||||||||
\(852\) | 4.30819e41 | − | 1.94854e41i | 0.138970 | − | 0.0628545i | ||||
\(853\) | − | 4.01860e42i | − | 1.27442i | −0.770689 | − | 0.637212i | \(-0.780088\pi\) | ||
0.770689 | − | 0.637212i | \(-0.219912\pi\) | |||||||
\(854\) | −1.81522e42 | − | 3.78092e42i | −0.565967 | − | 1.17885i | ||||
\(855\) | 4.10479e42 | + | 3.60952e42i | 1.25829 | + | 1.10647i | ||||
\(856\) | 4.00093e41 | 0.120584 | ||||||||
\(857\) | −5.84887e42 | −1.73321 | −0.866603 | − | 0.498998i | \(-0.833701\pi\) | ||||
−0.866603 | + | 0.498998i | \(0.833701\pi\) | |||||||
\(858\) | 4.50508e42 | − | 2.03760e42i | 1.31261 | − | 0.593680i | ||||
\(859\) | 6.36561e42i | 1.82364i | 0.410589 | + | 0.911820i | \(0.365323\pi\) | ||||
−0.410589 | + | 0.911820i | \(0.634677\pi\) | |||||||
\(860\) | −5.44549e41 | −0.153394 | ||||||||
\(861\) | −5.92970e41 | + | 7.06234e41i | −0.164243 | + | 0.195615i | ||||
\(862\) | −4.98465e42 | −1.35762 | ||||||||
\(863\) | − | 1.37045e42i | − | 0.367035i | −0.983016 | − | 0.183517i | \(-0.941252\pi\) | ||
0.983016 | − | 0.183517i | \(-0.0587483\pi\) | |||||||
\(864\) | −2.36083e41 | + | 7.72680e41i | −0.0621750 | + | 0.203493i | ||||
\(865\) | 5.08580e42 | 1.31712 | ||||||||
\(866\) | 5.85295e42 | 1.49061 | ||||||||
\(867\) | 1.40679e42 | + | 3.11038e42i | 0.352332 | + | 0.778998i | ||||
\(868\) | −4.88105e41 | + | 2.34340e41i | −0.120220 | + | 0.0577178i | ||||
\(869\) | 3.79435e42i | 0.919074i | ||||||||
\(870\) | −2.88556e42 | − | 6.37991e42i | −0.687386 | − | 1.51980i | ||||
\(871\) | 4.52246e42i | 1.05952i | ||||||||
\(872\) | − | 5.94665e42i | − | 1.37020i | ||||||
\(873\) | 3.61649e42 | + | 3.18014e42i | 0.819560 | + | 0.720675i | ||||
\(874\) | − | 1.50564e42i | − | 0.335587i | ||||||
\(875\) | −1.87617e42 | − | 3.90785e42i | −0.411296 | − | 0.856686i | ||||
\(876\) | 3.67691e40 | − | 1.66302e40i | 0.00792818 | − | 0.00358583i | ||||
\(877\) | −3.50696e42 | −0.743766 | −0.371883 | − | 0.928280i | \(-0.621288\pi\) | ||||
−0.371883 | + | 0.928280i | \(0.621288\pi\) | |||||||
\(878\) | −2.71080e42 | −0.565492 | ||||||||
\(879\) | −1.14344e42 | − | 2.52811e42i | −0.234625 | − | 0.518750i | ||||
\(880\) | 1.34167e43i | 2.70799i | ||||||||
\(881\) | 3.81213e42 | 0.756864 | 0.378432 | − | 0.925629i | \(-0.376463\pi\) | ||||
0.378432 | + | 0.925629i | \(0.376463\pi\) | |||||||
\(882\) | 4.76597e42 | − | 8.37354e41i | 0.930801 | − | 0.163537i | ||||
\(883\) | −5.57603e42 | −1.07126 | −0.535630 | − | 0.844453i | \(-0.679926\pi\) | ||||
−0.535630 | + | 0.844453i | \(0.679926\pi\) | |||||||
\(884\) | 1.72021e41i | 0.0325105i | ||||||||
\(885\) | −2.90743e42 | − | 6.42826e42i | −0.540545 | − | 1.19513i | ||||
\(886\) | 5.77811e42 | 1.05681 | ||||||||
\(887\) | −7.14514e42 | −1.28564 | −0.642819 | − | 0.766018i | \(-0.722235\pi\) | ||||
−0.642819 | + | 0.766018i | \(0.722235\pi\) | |||||||
\(888\) | 7.08918e42 | − | 3.20636e42i | 1.25490 | − | 0.567576i | ||||
\(889\) | 3.54825e42 | + | 7.39063e42i | 0.617929 | + | 1.28708i | ||||
\(890\) | 1.02379e43i | 1.75410i | ||||||||
\(891\) | 1.12274e43 | − | 1.44758e42i | 1.89257 | − | 0.244015i | ||||
\(892\) | − | 1.80478e41i | − | 0.0299319i | ||||||
\(893\) | 9.40020e42i | 1.53388i | ||||||||
\(894\) | 1.12666e42 | + | 2.49102e42i | 0.180884 | + | 0.399930i | ||||
\(895\) | − | 3.71871e42i | − | 0.587432i | ||||||
\(896\) | 4.70107e42 | − | 2.25699e42i | 0.730686 | − | 0.350803i | ||||
\(897\) | −7.34207e41 | − | 1.62332e42i | −0.112287 | − | 0.248263i | ||||
\(898\) | 8.72993e42 | 1.31372 | ||||||||
\(899\) | −9.24172e42 | −1.36848 | ||||||||
\(900\) | −7.70270e41 | + | 8.75960e41i | −0.112235 | + | 0.127634i | ||||
\(901\) | 5.78224e41i | 0.0829061i | ||||||||
\(902\) | 3.26473e42 | 0.460630 | ||||||||
\(903\) | 4.13034e42 | − | 4.91929e42i | 0.573474 | − | 0.683014i | ||||
\(904\) | 4.73454e42 | 0.646898 | ||||||||
\(905\) | − | 4.72282e42i | − | 0.635034i | ||||||
\(906\) | −4.32132e42 | + | 1.95448e42i | −0.571818 | + | 0.258627i | ||||
\(907\) | 1.64542e42 | 0.214275 | 0.107137 | − | 0.994244i | \(-0.465832\pi\) | ||||
0.107137 | + | 0.994244i | \(0.465832\pi\) | |||||||
\(908\) | 8.55116e41 | 0.109592 | ||||||||
\(909\) | 2.43769e42 | − | 2.77216e42i | 0.307469 | − | 0.349657i | ||||
\(910\) | −4.23642e42 | − | 8.82400e42i | −0.525894 | − | 1.09538i | ||||
\(911\) | 4.57291e42i | 0.558696i | 0.960190 | + | 0.279348i | \(0.0901184\pi\) | ||||
−0.960190 | + | 0.279348i | \(0.909882\pi\) | |||||||
\(912\) | −6.95533e42 | + | 3.14582e42i | −0.836359 | + | 0.378276i | ||||
\(913\) | 8.83108e42i | 1.04517i | ||||||||
\(914\) | − | 5.60798e42i | − | 0.653261i | ||||||
\(915\) | −1.76977e43 | + | 8.00448e42i | −2.02914 | + | 0.917756i | ||||
\(916\) | − | 1.12854e42i | − | 0.127360i | ||||||
\(917\) | 2.72128e42 | + | 5.66813e42i | 0.302286 | + | 0.629629i | ||||
\(918\) | 9.61813e41 | − | 3.14793e42i | 0.105165 | − | 0.344196i | ||||
\(919\) | −5.81514e42 | −0.625872 | −0.312936 | − | 0.949774i | \(-0.601313\pi\) | ||||
−0.312936 | + | 0.949774i | \(0.601313\pi\) | |||||||
\(920\) | 5.42039e42 | 0.574258 | ||||||||
\(921\) | 6.43516e41 | − | 2.91055e41i | 0.0671112 | − | 0.0303536i | ||||
\(922\) | − | 9.59474e41i | − | 0.0984996i | ||||||
\(923\) | 1.12820e43 | 1.14015 | ||||||||
\(924\) | 1.56983e42 | + | 1.31807e42i | 0.156175 | + | 0.131128i | ||||
\(925\) | 2.13817e43 | 2.09405 | ||||||||
\(926\) | 2.71957e42i | 0.262205i | ||||||||
\(927\) | −6.54283e40 | − | 5.75340e40i | −0.00621026 | − | 0.00546096i | ||||
\(928\) | −2.49707e42 | −0.233338 | ||||||||
\(929\) | −1.50298e43 | −1.38269 | −0.691345 | − | 0.722525i | \(-0.742981\pi\) | ||||
−0.691345 | + | 0.722525i | \(0.742981\pi\) | |||||||
\(930\) | −8.63636e42 | − | 1.90948e43i | −0.782218 | − | 1.72947i | ||||
\(931\) | −9.11029e42 | − | 7.30095e42i | −0.812385 | − | 0.651042i | ||||
\(932\) | 7.71424e41i | 0.0677271i | ||||||||
\(933\) | 2.73385e42 | + | 6.04448e42i | 0.236315 | + | 0.522487i | ||||
\(934\) | 9.32815e42i | 0.793900i | ||||||||
\(935\) | 1.39578e43i | 1.16963i | ||||||||
\(936\) | −6.68787e42 | + | 7.60552e42i | −0.551808 | + | 0.627522i | ||||
\(937\) | 9.35203e42i | 0.759770i | 0.925034 | + | 0.379885i | \(0.124036\pi\) | ||||
−0.925034 | + | 0.379885i | \(0.875964\pi\) | |||||||
\(938\) | 1.41257e43 | − | 6.78177e42i | 1.12998 | − | 0.542503i | ||||
\(939\) | −2.76390e42 | + | 1.25008e42i | −0.217706 | + | 0.0984660i | ||||
\(940\) | −3.26728e42 | −0.253415 | ||||||||
\(941\) | 2.56054e43 | 1.95561 | 0.977805 | − | 0.209517i | \(-0.0671891\pi\) | ||||
0.977805 | + | 0.209517i | \(0.0671891\pi\) | |||||||
\(942\) | 8.98836e42 | + | 1.98731e43i | 0.675993 | + | 1.49461i | ||||
\(943\) | − | 1.17638e42i | − | 0.0871220i | ||||||
\(944\) | 9.85296e42 | 0.718576 | ||||||||
\(945\) | −3.37272e42 | − | 2.21551e43i | −0.242225 | − | 1.59115i | ||||
\(946\) | −2.27405e43 | −1.60834 | ||||||||
\(947\) | 3.74201e42i | 0.260634i | 0.991472 | + | 0.130317i | \(0.0415995\pi\) | ||||
−0.991472 | + | 0.130317i | \(0.958401\pi\) | |||||||
\(948\) | −3.09225e41 | − | 6.83689e41i | −0.0212106 | − | 0.0468962i | ||||
\(949\) | 9.62884e41 | 0.0650450 | ||||||||
\(950\) | −2.35206e43 | −1.56479 | ||||||||
\(951\) | −9.87468e42 | + | 4.46621e42i | −0.647002 | + | 0.292632i | ||||
\(952\) | 5.56515e42 | − | 2.67183e42i | 0.359121 | − | 0.172415i | ||||
\(953\) | − | 5.66163e42i | − | 0.359827i | −0.983682 | − | 0.179914i | \(-0.942418\pi\) | ||
0.983682 | − | 0.179914i | \(-0.0575818\pi\) | |||||||
\(954\) | −2.17042e42 | + | 2.46822e42i | −0.135860 | + | 0.154501i | ||||
\(955\) | 4.90657e42i | 0.302503i | ||||||||
\(956\) | 3.02245e39i | 0.000183535i | ||||||||
\(957\) | 1.44182e43 | + | 3.18784e43i | 0.862360 | + | 1.90666i | ||||
\(958\) | − | 2.06991e43i | − | 1.21942i | ||||||
\(959\) | −1.22706e43 | + | 5.89111e42i | −0.712023 | + | 0.341843i | ||||
\(960\) | −1.25652e43 | − | 2.77814e43i | −0.718186 | − | 1.58789i | ||||
\(961\) | −9.89819e42 | −0.557272 | ||||||||
\(962\) | 1.79237e43 | 0.994006 | ||||||||
\(963\) | 1.58465e42 | + | 1.39346e42i | 0.0865672 | + | 0.0761224i | ||||
\(964\) | − | 1.30682e42i | − | 0.0703232i | ||||||
\(965\) | −2.99308e43 | −1.58662 | ||||||||
\(966\) | −3.96936e42 | + | 4.72755e42i | −0.207277 | + | 0.246870i | ||||
\(967\) | 2.89678e43 | 1.49016 | 0.745079 | − | 0.666976i | \(-0.232412\pi\) | ||||
0.745079 | + | 0.666976i | \(0.232412\pi\) | |||||||
\(968\) | − | 5.45225e43i | − | 2.76302i | ||||||
\(969\) | −7.23581e42 | + | 3.27268e42i | −0.361237 | + | 0.163384i | ||||
\(970\) | −3.37521e43 | −1.66001 | ||||||||
\(971\) | 3.22888e41 | 0.0156449 | 0.00782245 | − | 0.999969i | \(-0.497510\pi\) | ||||
0.00782245 | + | 0.999969i | \(0.497510\pi\) | |||||||
\(972\) | −1.90505e42 | + | 1.17582e42i | −0.0909381 | + | 0.0561283i | ||||
\(973\) | −3.78475e42 | + | 1.81706e42i | −0.177992 | + | 0.0854543i | ||||
\(974\) | − | 5.48512e42i | − | 0.254145i | ||||||
\(975\) | −2.53588e43 | + | 1.14695e43i | −1.15761 | + | 0.523574i | ||||
\(976\) | − | 2.71263e43i | − | 1.22002i | ||||||
\(977\) | 2.36187e42i | 0.104661i | 0.998630 | + | 0.0523305i | \(0.0166649\pi\) | ||||
−0.998630 | + | 0.0523305i | \(0.983335\pi\) | |||||||
\(978\) | 4.16443e42 | − | 1.88352e42i | 0.181820 | − | 0.0822352i | ||||
\(979\) | − | 5.11554e43i | − | 2.20061i | ||||||
\(980\) | 2.53764e42 | − | 3.16652e42i | 0.107560 | − | 0.134216i | ||||
\(981\) | 2.07112e43 | − | 2.35530e43i | 0.864977 | − | 0.983661i | ||||
\(982\) | −1.73955e43 | −0.715847 | ||||||||
\(983\) | 2.18701e43 | 0.886799 | 0.443399 | − | 0.896324i | \(-0.353772\pi\) | ||||
0.443399 | + | 0.896324i | \(0.353772\pi\) | |||||||
\(984\) | −6.09295e42 | + | 2.75577e42i | −0.243444 | + | 0.110107i | ||||
\(985\) | 6.59612e43i | 2.59695i | ||||||||
\(986\) | 1.01732e43 | 0.394677 | ||||||||
\(987\) | 2.47820e43 | − | 2.95156e43i | 0.947409 | − | 1.12837i | ||||
\(988\) | 2.35913e42 | 0.0888741 | ||||||||
\(989\) | 8.19410e42i | 0.304197i | ||||||||
\(990\) | −5.23917e43 | + | 5.95804e43i | −1.91669 | + | 2.17968i | ||||
\(991\) | 4.77081e43 | 1.71998 | 0.859991 | − | 0.510310i | \(-0.170469\pi\) | ||||
0.859991 | + | 0.510310i | \(0.170469\pi\) | |||||||
\(992\) | −7.47364e42 | −0.265529 | ||||||||
\(993\) | −1.45468e43 | − | 3.21627e43i | −0.509335 | − | 1.12613i | ||||
\(994\) | −1.69182e43 | − | 3.52388e43i | −0.583783 | − | 1.21596i | ||||
\(995\) | − | 6.40455e43i | − | 2.17798i | ||||||
\(996\) | −7.19699e41 | − | 1.59124e42i | −0.0241207 | − | 0.0533304i | ||||
\(997\) | − | 5.29465e42i | − | 0.174887i | −0.996169 | − | 0.0874434i | \(-0.972130\pi\) | ||
0.996169 | − | 0.0874434i | \(-0.0278697\pi\) | |||||||
\(998\) | 4.30546e43i | 1.40161i | ||||||||
\(999\) | 3.92455e43 | + | 1.19910e43i | 1.25919 | + | 0.384729i |
(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 | 21.30.c.a.20.8 | yes | 76 | |
3.2 | odd | 2 | inner | 21.30.c.a.20.69 | yes | 76 | |
7.6 | odd | 2 | inner | 21.30.c.a.20.70 | yes | 76 | |
21.20 | even | 2 | inner | 21.30.c.a.20.7 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.30.c.a.20.7 | ✓ | 76 | 21.20 | even | 2 | inner | |
21.30.c.a.20.8 | yes | 76 | 1.1 | even | 1 | trivial | |
21.30.c.a.20.69 | yes | 76 | 3.2 | odd | 2 | inner | |
21.30.c.a.20.70 | yes | 76 | 7.6 | odd | 2 | inner |