Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,9,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.62951444024\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-39}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.2 | ||
Root | \(0.500000 - 3.12250i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.9.b.b.3.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.0000 | + | 12.4900i | −0.625000 | + | 0.780625i | ||||
\(3\) | 99.9200i | 1.23358i | 0.787128 | + | 0.616790i | \(0.211567\pi\) | ||||
−0.787128 | + | 0.616790i | \(0.788433\pi\) | |||||||
\(4\) | −56.0000 | − | 249.800i | −0.218750 | − | 0.975781i | ||||
\(5\) | 610.000 | 0.976000 | 0.488000 | − | 0.872844i | \(-0.337727\pi\) | ||||
0.488000 | + | 0.872844i | \(0.337727\pi\) | |||||||
\(6\) | −1248.00 | − | 999.200i | −0.962963 | − | 0.770987i | ||||
\(7\) | 1398.88i | 0.582624i | 0.956628 | + | 0.291312i | \(0.0940917\pi\) | ||||
−0.956628 | + | 0.291312i | \(0.905908\pi\) | |||||||
\(8\) | 3680.00 | + | 1798.56i | 0.898438 | + | 0.439101i | ||||
\(9\) | −3423.00 | −0.521719 | ||||||||
\(10\) | −6100.00 | + | 7618.90i | −0.610000 | + | 0.761890i | ||||
\(11\) | − | 18485.2i | − | 1.26256i | −0.775554 | − | 0.631282i | \(-0.782529\pi\) | ||
0.775554 | − | 0.631282i | \(-0.217471\pi\) | |||||||
\(12\) | 24960.0 | − | 5595.52i | 1.20370 | − | 0.269846i | ||||
\(13\) | −5470.00 | −0.191520 | −0.0957600 | − | 0.995404i | \(-0.530528\pi\) | ||||
−0.0957600 | + | 0.995404i | \(0.530528\pi\) | |||||||
\(14\) | −17472.0 | − | 13988.8i | −0.454810 | − | 0.364140i | ||||
\(15\) | 60951.2i | 1.20397i | ||||||||
\(16\) | −59264.0 | + | 27977.6i | −0.904297 | + | 0.426904i | ||||
\(17\) | 73090.0 | 0.875109 | 0.437555 | − | 0.899192i | \(-0.355845\pi\) | ||||
0.437555 | + | 0.899192i | \(0.355845\pi\) | |||||||
\(18\) | 34230.0 | − | 42753.3i | 0.326075 | − | 0.407267i | ||||
\(19\) | − | 19484.4i | − | 0.149511i | −0.997202 | − | 0.0747554i | \(-0.976182\pi\) | ||
0.997202 | − | 0.0747554i | \(-0.0238176\pi\) | |||||||
\(20\) | −34160.0 | − | 152378.i | −0.213500 | − | 0.952362i | ||||
\(21\) | −139776. | −0.718713 | ||||||||
\(22\) | 230880. | + | 184852.i | 0.985588 | + | 0.789102i | ||||
\(23\) | − | 237210.i | − | 0.847660i | −0.905742 | − | 0.423830i | \(-0.860685\pi\) | ||
0.905742 | − | 0.423830i | \(-0.139315\pi\) | |||||||
\(24\) | −179712. | + | 367705.i | −0.541667 | + | 1.10829i | ||||
\(25\) | −18525.0 | −0.0474240 | ||||||||
\(26\) | 54700.0 | − | 68320.3i | 0.119700 | − | 0.149505i | ||||
\(27\) | 313549.i | 0.589997i | ||||||||
\(28\) | 349440. | − | 78337.3i | 0.568513 | − | 0.127449i | ||||
\(29\) | −128222. | −0.181289 | −0.0906443 | − | 0.995883i | \(-0.528893\pi\) | ||||
−0.0906443 | + | 0.995883i | \(0.528893\pi\) | |||||||
\(30\) | −761280. | − | 609512.i | −0.939852 | − | 0.752484i | ||||
\(31\) | − | 67945.6i | − | 0.0735723i | −0.999323 | − | 0.0367862i | \(-0.988288\pi\) | ||
0.999323 | − | 0.0367862i | \(-0.0117120\pi\) | |||||||
\(32\) | 243200. | − | 1.01998e6i | 0.231934 | − | 0.972732i | ||||
\(33\) | 1.84704e6 | 1.55747 | ||||||||
\(34\) | −730900. | + | 912894.i | −0.546943 | + | 0.683132i | ||||
\(35\) | 853317.i | 0.568641i | ||||||||
\(36\) | 191688. | + | 855065.i | 0.114126 | + | 0.509084i | ||||
\(37\) | −3.47203e6 | −1.85258 | −0.926289 | − | 0.376813i | \(-0.877020\pi\) | ||||
−0.926289 | + | 0.376813i | \(0.877020\pi\) | |||||||
\(38\) | 243360. | + | 194844.i | 0.116712 | + | 0.0934442i | ||||
\(39\) | − | 546562.i | − | 0.236255i | ||||||
\(40\) | 2.24480e6 | + | 1.09712e6i | 0.876875 | + | 0.428563i | ||||
\(41\) | 2.14688e6 | 0.759754 | 0.379877 | − | 0.925037i | \(-0.375966\pi\) | ||||
0.379877 | + | 0.925037i | \(0.375966\pi\) | |||||||
\(42\) | 1.39776e6 | − | 1.74580e6i | 0.449196 | − | 0.561045i | ||||
\(43\) | − | 5.92815e6i | − | 1.73399i | −0.498321 | − | 0.866993i | \(-0.666050\pi\) | ||
0.498321 | − | 0.866993i | \(-0.333950\pi\) | |||||||
\(44\) | −4.61760e6 | + | 1.03517e6i | −1.23199 | + | 0.276186i | ||||
\(45\) | −2.08803e6 | −0.509198 | ||||||||
\(46\) | 2.96275e6 | + | 2.37210e6i | 0.661704 | + | 0.529787i | ||||
\(47\) | 7.62629e6i | 1.56287i | 0.623989 | + | 0.781433i | \(0.285511\pi\) | ||||
−0.623989 | + | 0.781433i | \(0.714489\pi\) | |||||||
\(48\) | −2.79552e6 | − | 5.92166e6i | −0.526620 | − | 1.11552i | ||||
\(49\) | 3.80794e6 | 0.660550 | ||||||||
\(50\) | 185250. | − | 231377.i | 0.0296400 | − | 0.0370203i | ||||
\(51\) | 7.30315e6i | 1.07952i | ||||||||
\(52\) | 306320. | + | 1.36641e6i | 0.0418950 | + | 0.186881i | ||||
\(53\) | 824290. | 0.104466 | 0.0522332 | − | 0.998635i | \(-0.483366\pi\) | ||||
0.0522332 | + | 0.998635i | \(0.483366\pi\) | |||||||
\(54\) | −3.91622e6 | − | 3.13549e6i | −0.460567 | − | 0.368748i | ||||
\(55\) | − | 1.12760e7i | − | 1.23226i | ||||||
\(56\) | −2.51597e6 | + | 5.14788e6i | −0.255831 | + | 0.523451i | ||||
\(57\) | 1.94688e6 | 0.184433 | ||||||||
\(58\) | 1.28222e6 | − | 1.60149e6i | 0.113305 | − | 0.141518i | ||||
\(59\) | − | 3.72552e6i | − | 0.307453i | −0.988113 | − | 0.153726i | \(-0.950873\pi\) | ||
0.988113 | − | 0.153726i | \(-0.0491274\pi\) | |||||||
\(60\) | 1.52256e7 | − | 3.41327e6i | 1.17481 | − | 0.263369i | ||||
\(61\) | −1.47461e7 | −1.06502 | −0.532509 | − | 0.846424i | \(-0.678751\pi\) | ||||
−0.532509 | + | 0.846424i | \(0.678751\pi\) | |||||||
\(62\) | 848640. | + | 679456.i | 0.0574324 | + | 0.0459827i | ||||
\(63\) | − | 4.78836e6i | − | 0.303966i | ||||||
\(64\) | 1.03076e7 | + | 1.32374e7i | 0.614380 | + | 0.789010i | ||||
\(65\) | −3.33670e6 | −0.186923 | ||||||||
\(66\) | −1.84704e7 | + | 2.30695e7i | −0.973421 | + | 1.21580i | ||||
\(67\) | 1.52567e7i | 0.757113i | 0.925578 | + | 0.378557i | \(0.123579\pi\) | ||||
−0.925578 | + | 0.378557i | \(0.876421\pi\) | |||||||
\(68\) | −4.09304e6 | − | 1.82579e7i | −0.191430 | − | 0.853915i | ||||
\(69\) | 2.37020e7 | 1.04566 | ||||||||
\(70\) | −1.06579e7 | − | 8.53317e6i | −0.443895 | − | 0.355400i | ||||
\(71\) | − | 1.19604e6i | − | 0.0470666i | −0.999723 | − | 0.0235333i | \(-0.992508\pi\) | ||
0.999723 | − | 0.0235333i | \(-0.00749158\pi\) | |||||||
\(72\) | −1.25966e7 | − | 6.15647e6i | −0.468732 | − | 0.229088i | ||||
\(73\) | −5.72563e6 | −0.201619 | −0.100810 | − | 0.994906i | \(-0.532143\pi\) | ||||
−0.100810 | + | 0.994906i | \(0.532143\pi\) | |||||||
\(74\) | 3.47203e7 | − | 4.33656e7i | 1.15786 | − | 1.44617i | ||||
\(75\) | − | 1.85102e6i | − | 0.0585013i | ||||||
\(76\) | −4.86720e6 | + | 1.09113e6i | −0.145890 | + | 0.0327055i | ||||
\(77\) | 2.58586e7 | 0.735600 | ||||||||
\(78\) | 6.82656e6 | + | 5.46562e6i | 0.184427 | + | 0.147659i | ||||
\(79\) | 3.59132e7i | 0.922032i | 0.887392 | + | 0.461016i | \(0.152515\pi\) | ||||
−0.887392 | + | 0.461016i | \(0.847485\pi\) | |||||||
\(80\) | −3.61510e7 | + | 1.70663e7i | −0.882594 | + | 0.416658i | ||||
\(81\) | −5.37881e7 | −1.24953 | ||||||||
\(82\) | −2.14688e7 | + | 2.68145e7i | −0.474846 | + | 0.593082i | ||||
\(83\) | − | 5.19603e7i | − | 1.09486i | −0.836851 | − | 0.547431i | \(-0.815606\pi\) | ||
0.836851 | − | 0.547431i | \(-0.184394\pi\) | |||||||
\(84\) | 7.82746e6 | + | 3.49160e7i | 0.157218 | + | 0.701306i | ||||
\(85\) | 4.45849e7 | 0.854107 | ||||||||
\(86\) | 7.40426e7 | + | 5.92815e7i | 1.35359 | + | 1.08374i | ||||
\(87\) | − | 1.28119e7i | − | 0.223634i | ||||||
\(88\) | 3.32467e7 | − | 6.80255e7i | 0.554393 | − | 1.13433i | ||||
\(89\) | −8.33242e7 | −1.32804 | −0.664020 | − | 0.747715i | \(-0.731151\pi\) | ||||
−0.664020 | + | 0.747715i | \(0.731151\pi\) | |||||||
\(90\) | 2.08803e7 | − | 2.60795e7i | 0.318249 | − | 0.397493i | ||||
\(91\) | − | 7.65187e6i | − | 0.111584i | ||||||
\(92\) | −5.92550e7 | + | 1.32838e7i | −0.827130 | + | 0.185426i | ||||
\(93\) | 6.78912e6 | 0.0907573 | ||||||||
\(94\) | −9.52524e7 | − | 7.62629e7i | −1.22001 | − | 0.976792i | ||||
\(95\) | − | 1.18855e7i | − | 0.145923i | ||||||
\(96\) | 1.01917e8 | + | 2.43005e7i | 1.19994 | + | 0.286109i | ||||
\(97\) | 1.20619e8 | 1.36248 | 0.681238 | − | 0.732062i | \(-0.261442\pi\) | ||||
0.681238 | + | 0.732062i | \(0.261442\pi\) | |||||||
\(98\) | −3.80794e7 | + | 4.75611e7i | −0.412844 | + | 0.515641i | ||||
\(99\) | 6.32748e7i | 0.658704i | ||||||||
\(100\) | 1.03740e6 | + | 4.62754e6i | 0.0103740 | + | 0.0462754i | ||||
\(101\) | 2.77246e7 | 0.266428 | 0.133214 | − | 0.991087i | \(-0.457470\pi\) | ||||
0.133214 | + | 0.991087i | \(0.457470\pi\) | |||||||
\(102\) | −9.12163e7 | − | 7.30315e7i | −0.842698 | − | 0.674698i | ||||
\(103\) | 1.04501e8i | 0.928477i | 0.885710 | + | 0.464238i | \(0.153672\pi\) | ||||
−0.885710 | + | 0.464238i | \(0.846328\pi\) | |||||||
\(104\) | −2.01296e7 | − | 9.83812e6i | −0.172069 | − | 0.0840967i | ||||
\(105\) | −8.52634e7 | −0.701464 | ||||||||
\(106\) | −8.24290e6 | + | 1.02954e7i | −0.0652915 | + | 0.0815490i | ||||
\(107\) | 1.00328e8i | 0.765394i | 0.923874 | + | 0.382697i | \(0.125005\pi\) | ||||
−0.923874 | + | 0.382697i | \(0.874995\pi\) | |||||||
\(108\) | 7.83245e7 | − | 1.75587e7i | 0.575708 | − | 0.129062i | ||||
\(109\) | −5.90716e7 | −0.418478 | −0.209239 | − | 0.977865i | \(-0.567099\pi\) | ||||
−0.209239 | + | 0.977865i | \(0.567099\pi\) | |||||||
\(110\) | 1.40837e8 | + | 1.12760e8i | 0.961934 | + | 0.770164i | ||||
\(111\) | − | 3.46925e8i | − | 2.28530i | ||||||
\(112\) | −3.91373e7 | − | 8.29032e7i | −0.248724 | − | 0.526865i | ||||
\(113\) | 5.50849e7 | 0.337846 | 0.168923 | − | 0.985629i | \(-0.445971\pi\) | ||||
0.168923 | + | 0.985629i | \(0.445971\pi\) | |||||||
\(114\) | −1.94688e7 | + | 2.43165e7i | −0.115271 | + | 0.143973i | ||||
\(115\) | − | 1.44698e8i | − | 0.827316i | ||||||
\(116\) | 7.18043e6 | + | 3.20298e7i | 0.0396569 | + | 0.176898i | ||||
\(117\) | 1.87238e7 | 0.0999196 | ||||||||
\(118\) | 4.65317e7 | + | 3.72552e7i | 0.240005 | + | 0.192158i | ||||
\(119\) | 1.02244e8i | 0.509859i | ||||||||
\(120\) | −1.09624e8 | + | 2.24300e8i | −0.528667 | + | 1.08170i | ||||
\(121\) | −1.27344e8 | −0.594067 | ||||||||
\(122\) | 1.47461e8 | − | 1.84178e8i | 0.665637 | − | 0.831380i | ||||
\(123\) | 2.14516e8i | 0.937217i | ||||||||
\(124\) | −1.69728e7 | + | 3.80495e6i | −0.0717905 | + | 0.0160939i | ||||
\(125\) | −2.49581e8 | −1.02229 | ||||||||
\(126\) | 5.98067e7 | + | 4.78836e7i | 0.237283 | + | 0.189979i | ||||
\(127\) | 2.57160e8i | 0.988529i | 0.869312 | + | 0.494264i | \(0.164562\pi\) | ||||
−0.869312 | + | 0.494264i | \(0.835438\pi\) | |||||||
\(128\) | −2.68411e8 | − | 3.63229e6i | −0.999908 | − | 0.0135313i | ||||
\(129\) | 5.92341e8 | 2.13901 | ||||||||
\(130\) | 3.33670e7 | − | 4.16754e7i | 0.116827 | − | 0.145917i | ||||
\(131\) | − | 3.12175e8i | − | 1.06002i | −0.847992 | − | 0.530009i | \(-0.822188\pi\) | ||
0.847992 | − | 0.530009i | \(-0.177812\pi\) | |||||||
\(132\) | −1.03434e8 | − | 4.61390e8i | −0.340697 | − | 1.51975i | ||||
\(133\) | 2.72563e7 | 0.0871085 | ||||||||
\(134\) | −1.90556e8 | − | 1.52567e8i | −0.591021 | − | 0.473196i | ||||
\(135\) | 1.91265e8i | 0.575838i | ||||||||
\(136\) | 2.68971e8 | + | 1.31457e8i | 0.786231 | + | 0.384262i | ||||
\(137\) | 2.21980e8 | 0.630132 | 0.315066 | − | 0.949070i | \(-0.397973\pi\) | ||||
0.315066 | + | 0.949070i | \(0.397973\pi\) | |||||||
\(138\) | −2.37020e8 | + | 2.96038e8i | −0.653535 | + | 0.816265i | ||||
\(139\) | − | 2.95030e8i | − | 0.790328i | −0.918611 | − | 0.395164i | \(-0.870688\pi\) | ||
0.918611 | − | 0.395164i | \(-0.129312\pi\) | |||||||
\(140\) | 2.13158e8 | − | 4.77857e7i | 0.554869 | − | 0.124390i | ||||
\(141\) | −7.62019e8 | −1.92792 | ||||||||
\(142\) | 1.49386e7 | + | 1.19604e7i | 0.0367414 | + | 0.0294166i | ||||
\(143\) | 1.01114e8i | 0.241806i | ||||||||
\(144\) | 2.02861e8 | − | 9.57673e7i | 0.471789 | − | 0.222724i | ||||
\(145\) | −7.82154e7 | −0.176938 | ||||||||
\(146\) | 5.72563e7 | − | 7.15131e7i | 0.126012 | − | 0.157389i | ||||
\(147\) | 3.80489e8i | 0.814841i | ||||||||
\(148\) | 1.94434e8 | + | 8.67313e8i | 0.405252 | + | 1.80771i | ||||
\(149\) | 4.03603e8 | 0.818859 | 0.409429 | − | 0.912342i | \(-0.365728\pi\) | ||||
0.409429 | + | 0.912342i | \(0.365728\pi\) | |||||||
\(150\) | 2.31192e7 | + | 1.85102e7i | 0.0456676 | + | 0.0365633i | ||||
\(151\) | − | 8.36985e8i | − | 1.60994i | −0.593316 | − | 0.804970i | \(-0.702181\pi\) | ||
0.593316 | − | 0.804970i | \(-0.297819\pi\) | |||||||
\(152\) | 3.50438e7 | − | 7.17026e7i | 0.0656504 | − | 0.134326i | ||||
\(153\) | −2.50187e8 | −0.456561 | ||||||||
\(154\) | −2.58586e8 | + | 3.22973e8i | −0.459750 | + | 0.574227i | ||||
\(155\) | − | 4.14468e7i | − | 0.0718066i | ||||||
\(156\) | −1.36531e8 | + | 3.06075e7i | −0.230533 | + | 0.0516808i | ||||
\(157\) | −2.71319e8 | −0.446561 | −0.223281 | − | 0.974754i | \(-0.571677\pi\) | ||||
−0.223281 | + | 0.974754i | \(0.571677\pi\) | |||||||
\(158\) | −4.48556e8 | − | 3.59132e8i | −0.719761 | − | 0.576270i | ||||
\(159\) | 8.23630e7i | 0.128868i | ||||||||
\(160\) | 1.48352e8 | − | 6.22190e8i | 0.226367 | − | 0.949386i | ||||
\(161\) | 3.31828e8 | 0.493867 | ||||||||
\(162\) | 5.37881e8 | − | 6.71813e8i | 0.780955 | − | 0.975413i | ||||
\(163\) | 5.78509e8i | 0.819520i | 0.912193 | + | 0.409760i | \(0.134388\pi\) | ||||
−0.912193 | + | 0.409760i | \(0.865612\pi\) | |||||||
\(164\) | −1.20225e8 | − | 5.36291e8i | −0.166196 | − | 0.741353i | ||||
\(165\) | 1.12669e9 | 1.52009 | ||||||||
\(166\) | 6.48984e8 | + | 5.19603e8i | 0.854676 | + | 0.684288i | ||||
\(167\) | 4.68118e8i | 0.601852i | 0.953647 | + | 0.300926i | \(0.0972958\pi\) | ||||
−0.953647 | + | 0.300926i | \(0.902704\pi\) | |||||||
\(168\) | −5.14376e8 | − | 2.51395e8i | −0.645719 | − | 0.315588i | ||||
\(169\) | −7.85810e8 | −0.963320 | ||||||||
\(170\) | −4.45849e8 | + | 5.56865e8i | −0.533817 | + | 0.666737i | ||||
\(171\) | 6.66951e7i | 0.0780026i | ||||||||
\(172\) | −1.48085e9 | + | 3.31976e8i | −1.69199 | + | 0.379309i | ||||
\(173\) | −2.06197e8 | −0.230196 | −0.115098 | − | 0.993354i | \(-0.536718\pi\) | ||||
−0.115098 | + | 0.993354i | \(0.536718\pi\) | |||||||
\(174\) | 1.60021e8 | + | 1.28119e8i | 0.174574 | + | 0.139771i | ||||
\(175\) | − | 2.59142e7i | − | 0.0276303i | ||||||
\(176\) | 5.17171e8 | + | 1.09551e9i | 0.538994 | + | 1.14173i | ||||
\(177\) | 3.72253e8 | 0.379268 | ||||||||
\(178\) | 8.33242e8 | − | 1.04072e9i | 0.830025 | − | 1.03670i | ||||
\(179\) | 1.41911e8i | 0.138230i | 0.997609 | + | 0.0691152i | \(0.0220176\pi\) | ||||
−0.997609 | + | 0.0691152i | \(0.977982\pi\) | |||||||
\(180\) | 1.16930e8 | + | 5.21590e8i | 0.111387 | + | 0.496866i | ||||
\(181\) | 4.82566e8 | 0.449616 | 0.224808 | − | 0.974403i | \(-0.427824\pi\) | ||||
0.224808 | + | 0.974403i | \(0.427824\pi\) | |||||||
\(182\) | 9.55718e7 | + | 7.65187e7i | 0.0871053 | + | 0.0697400i | ||||
\(183\) | − | 1.47343e9i | − | 1.31379i | ||||||
\(184\) | 4.26636e8 | − | 8.72933e8i | 0.372209 | − | 0.761569i | ||||
\(185\) | −2.11794e9 | −1.80812 | ||||||||
\(186\) | −6.78912e7 | + | 8.47961e7i | −0.0567233 | + | 0.0708474i | ||||
\(187\) | − | 1.35108e9i | − | 1.10488i | ||||||
\(188\) | 1.90505e9 | − | 4.27072e8i | 1.52502 | − | 0.341877i | ||||
\(189\) | −4.38617e8 | −0.343747 | ||||||||
\(190\) | 1.48450e8 | + | 1.18855e8i | 0.113911 | + | 0.0912016i | ||||
\(191\) | 9.92461e8i | 0.745727i | 0.927886 | + | 0.372864i | \(0.121624\pi\) | ||||
−0.927886 | + | 0.372864i | \(0.878376\pi\) | |||||||
\(192\) | −1.32268e9 | + | 1.02993e9i | −0.973307 | + | 0.757887i | ||||
\(193\) | 1.17593e9 | 0.847526 | 0.423763 | − | 0.905773i | \(-0.360709\pi\) | ||||
0.423763 | + | 0.905773i | \(0.360709\pi\) | |||||||
\(194\) | −1.20619e9 | + | 1.50653e9i | −0.851547 | + | 1.06358i | ||||
\(195\) | − | 3.33403e8i | − | 0.230585i | ||||||
\(196\) | −2.13244e8 | − | 9.51222e8i | −0.144495 | − | 0.644552i | ||||
\(197\) | 1.70538e9 | 1.13229 | 0.566144 | − | 0.824306i | \(-0.308435\pi\) | ||||
0.566144 | + | 0.824306i | \(0.308435\pi\) | |||||||
\(198\) | −7.90302e8 | − | 6.32748e8i | −0.514200 | − | 0.411690i | ||||
\(199\) | 2.49036e9i | 1.58800i | 0.607919 | + | 0.793999i | \(0.292004\pi\) | ||||
−0.607919 | + | 0.793999i | \(0.707996\pi\) | |||||||
\(200\) | −6.81720e7 | − | 3.33183e7i | −0.0426075 | − | 0.0208239i | ||||
\(201\) | −1.52445e9 | −0.933960 | ||||||||
\(202\) | −2.77246e8 | + | 3.46281e8i | −0.166518 | + | 0.207981i | ||||
\(203\) | − | 1.79367e8i | − | 0.105623i | ||||||
\(204\) | 1.82433e9 | − | 4.08976e8i | 1.05337 | − | 0.236144i | ||||
\(205\) | 1.30960e9 | 0.741519 | ||||||||
\(206\) | −1.30522e9 | − | 1.04501e9i | −0.724792 | − | 0.580298i | ||||
\(207\) | 8.11970e8i | 0.442241i | ||||||||
\(208\) | 3.24174e8 | − | 1.53037e8i | 0.173191 | − | 0.0817606i | ||||
\(209\) | −3.60173e8 | −0.188767 | ||||||||
\(210\) | 8.52634e8 | − | 1.06494e9i | 0.438415 | − | 0.547580i | ||||
\(211\) | 1.46774e9i | 0.740491i | 0.928934 | + | 0.370245i | \(0.120726\pi\) | ||||
−0.928934 | + | 0.370245i | \(0.879274\pi\) | |||||||
\(212\) | −4.61602e7 | − | 2.05908e8i | −0.0228520 | − | 0.101936i | ||||
\(213\) | 1.19508e8 | 0.0580604 | ||||||||
\(214\) | −1.25309e9 | − | 1.00328e9i | −0.597486 | − | 0.478371i | ||||
\(215\) | − | 3.61617e9i | − | 1.69237i | ||||||
\(216\) | −5.63936e8 | + | 1.15386e9i | −0.259069 | + | 0.530076i | ||||
\(217\) | 9.50477e7 | 0.0428650 | ||||||||
\(218\) | 5.90716e8 | − | 7.37804e8i | 0.261549 | − | 0.326674i | ||||
\(219\) | − | 5.72105e8i | − | 0.248713i | ||||||
\(220\) | −2.81674e9 | + | 6.31454e8i | −1.20242 | + | 0.269557i | ||||
\(221\) | −3.99802e8 | −0.167601 | ||||||||
\(222\) | 4.33309e9 | + | 3.46925e9i | 1.78396 | + | 1.42831i | ||||
\(223\) | − | 1.47920e9i | − | 0.598147i | −0.954230 | − | 0.299073i | \(-0.903322\pi\) | ||
0.954230 | − | 0.299073i | \(-0.0966776\pi\) | |||||||
\(224\) | 1.42683e9 | + | 3.40208e8i | 0.566737 | + | 0.135130i | ||||
\(225\) | 6.34111e7 | 0.0247420 | ||||||||
\(226\) | −5.50849e8 | + | 6.88011e8i | −0.211154 | + | 0.263731i | ||||
\(227\) | − | 7.50054e8i | − | 0.282481i | −0.989975 | − | 0.141241i | \(-0.954891\pi\) | ||
0.989975 | − | 0.141241i | \(-0.0451091\pi\) | |||||||
\(228\) | −1.09025e8 | − | 4.86330e8i | −0.0403448 | − | 0.179967i | ||||
\(229\) | −2.84784e9 | −1.03556 | −0.517778 | − | 0.855515i | \(-0.673241\pi\) | ||||
−0.517778 | + | 0.855515i | \(0.673241\pi\) | |||||||
\(230\) | 1.80728e9 | + | 1.44698e9i | 0.645823 | + | 0.517073i | ||||
\(231\) | 2.58379e9i | 0.907421i | ||||||||
\(232\) | −4.71857e8 | − | 2.30615e8i | −0.162876 | − | 0.0796041i | ||||
\(233\) | 2.20621e8 | 0.0748553 | 0.0374276 | − | 0.999299i | \(-0.488084\pi\) | ||||
0.0374276 | + | 0.999299i | \(0.488084\pi\) | |||||||
\(234\) | −1.87238e8 | + | 2.33860e8i | −0.0624498 | + | 0.0779997i | ||||
\(235\) | 4.65204e9i | 1.52536i | ||||||||
\(236\) | −9.30634e8 | + | 2.08629e8i | −0.300007 | + | 0.0672553i | ||||
\(237\) | −3.58845e9 | −1.13740 | ||||||||
\(238\) | −1.27703e9 | − | 1.02244e9i | −0.398009 | − | 0.318662i | ||||
\(239\) | − | 4.04493e9i | − | 1.23971i | −0.784717 | − | 0.619855i | \(-0.787192\pi\) | ||
0.784717 | − | 0.619855i | \(-0.212808\pi\) | |||||||
\(240\) | −1.70527e9 | − | 3.61221e9i | −0.513981 | − | 1.08875i | ||||
\(241\) | 6.17983e9 | 1.83193 | 0.915964 | − | 0.401260i | \(-0.131427\pi\) | ||||
0.915964 | + | 0.401260i | \(0.131427\pi\) | |||||||
\(242\) | 1.27344e9 | − | 1.59052e9i | 0.371292 | − | 0.463743i | ||||
\(243\) | − | 3.31731e9i | − | 0.951395i | ||||||
\(244\) | 8.25780e8 | + | 3.68357e9i | 0.232973 | + | 1.03922i | ||||
\(245\) | 2.32284e9 | 0.644696 | ||||||||
\(246\) | −2.67931e9 | − | 2.14516e9i | −0.731615 | − | 0.585760i | ||||
\(247\) | 1.06580e8i | 0.0286343i | ||||||||
\(248\) | 1.22204e8 | − | 2.50040e8i | 0.0323057 | − | 0.0661001i | ||||
\(249\) | 5.19187e9 | 1.35060 | ||||||||
\(250\) | 2.49582e9 | − | 3.11727e9i | 0.638929 | − | 0.798022i | ||||
\(251\) | 5.21367e9i | 1.31356i | 0.754084 | + | 0.656778i | \(0.228081\pi\) | ||||
−0.754084 | + | 0.656778i | \(0.771919\pi\) | |||||||
\(252\) | −1.19613e9 | + | 2.68148e8i | −0.296604 | + | 0.0664926i | ||||
\(253\) | −4.38487e9 | −1.07022 | ||||||||
\(254\) | −3.21193e9 | − | 2.57160e9i | −0.771670 | − | 0.617830i | ||||
\(255\) | 4.45492e9i | 1.05361i | ||||||||
\(256\) | 2.72948e9 | − | 3.31613e9i | 0.635506 | − | 0.772096i | ||||
\(257\) | −6.13693e9 | −1.40676 | −0.703378 | − | 0.710816i | \(-0.748326\pi\) | ||||
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(258\) | −5.92341e9 | + | 7.39833e9i | −1.33688 | + | 1.66976i | ||||
\(259\) | − | 4.85695e9i | − | 1.07936i | ||||||
\(260\) | 1.86855e8 | + | 8.33507e8i | 0.0408895 | + | 0.182396i | ||||
\(261\) | 4.38904e8 | 0.0945818 | ||||||||
\(262\) | 3.89907e9 | + | 3.12175e9i | 0.827477 | + | 0.662512i | ||||
\(263\) | 6.96916e9i | 1.45666i | 0.685228 | + | 0.728329i | \(0.259703\pi\) | ||||
−0.685228 | + | 0.728329i | \(0.740297\pi\) | |||||||
\(264\) | 6.79711e9 | + | 3.32201e9i | 1.39929 | + | 0.683889i | ||||
\(265\) | 5.02817e8 | 0.101959 | ||||||||
\(266\) | −2.72563e8 | + | 3.40431e8i | −0.0544428 | + | 0.0679991i | ||||
\(267\) | − | 8.32575e9i | − | 1.63824i | ||||||
\(268\) | 3.81112e9 | − | 8.54374e8i | 0.738777 | − | 0.165619i | ||||
\(269\) | 2.70720e9 | 0.517025 | 0.258513 | − | 0.966008i | \(-0.416768\pi\) | ||||
0.258513 | + | 0.966008i | \(0.416768\pi\) | |||||||
\(270\) | −2.38890e9 | − | 1.91265e9i | −0.449513 | − | 0.359898i | ||||
\(271\) | − | 7.99032e9i | − | 1.48145i | −0.671808 | − | 0.740725i | \(-0.734482\pi\) | ||
0.671808 | − | 0.740725i | \(-0.265518\pi\) | |||||||
\(272\) | −4.33161e9 | + | 2.04488e9i | −0.791359 | + | 0.373588i | ||||
\(273\) | 7.64575e8 | 0.137648 | ||||||||
\(274\) | −2.21980e9 | + | 2.77253e9i | −0.393832 | + | 0.491897i | ||||
\(275\) | 3.42438e8i | 0.0598758i | ||||||||
\(276\) | −1.32731e9 | − | 5.92076e9i | −0.228737 | − | 1.02033i | ||||
\(277\) | −8.22965e9 | −1.39786 | −0.698928 | − | 0.715192i | \(-0.746339\pi\) | ||||
−0.698928 | + | 0.715192i | \(0.746339\pi\) | |||||||
\(278\) | 3.68493e9 | + | 2.95030e9i | 0.616949 | + | 0.493955i | ||||
\(279\) | 2.32578e8i | 0.0383841i | ||||||||
\(280\) | −1.53474e9 | + | 3.14020e9i | −0.249691 | + | 0.510888i | ||||
\(281\) | 3.08105e9 | 0.494167 | 0.247083 | − | 0.968994i | \(-0.420528\pi\) | ||||
0.247083 | + | 0.968994i | \(0.420528\pi\) | |||||||
\(282\) | 7.62019e9 | − | 9.51761e9i | 1.20495 | − | 1.50498i | ||||
\(283\) | 1.17112e9i | 0.182582i | 0.995824 | + | 0.0912908i | \(0.0290993\pi\) | ||||
−0.995824 | + | 0.0912908i | \(0.970901\pi\) | |||||||
\(284\) | −2.98771e8 | + | 6.69784e7i | −0.0459267 | + | 0.0102958i | ||||
\(285\) | 1.18760e9 | 0.180007 | ||||||||
\(286\) | −1.26291e9 | − | 1.01114e9i | −0.188760 | − | 0.151129i | ||||
\(287\) | 3.00323e9i | 0.442650i | ||||||||
\(288\) | −8.32474e8 | + | 3.49140e9i | −0.121004 | + | 0.507493i | ||||
\(289\) | −1.63361e9 | −0.234184 | ||||||||
\(290\) | 7.82154e8 | − | 9.76910e8i | 0.110586 | − | 0.138122i | ||||
\(291\) | 1.20522e10i | 1.68072i | ||||||||
\(292\) | 3.20635e8 | + | 1.43026e9i | 0.0441042 | + | 0.196736i | ||||
\(293\) | 4.80980e9 | 0.652614 | 0.326307 | − | 0.945264i | \(-0.394196\pi\) | ||||
0.326307 | + | 0.945264i | \(0.394196\pi\) | |||||||
\(294\) | −4.75231e9 | − | 3.80489e9i | −0.636085 | − | 0.509275i | ||||
\(295\) | − | 2.27256e9i | − | 0.300074i | ||||||
\(296\) | −1.27771e10 | − | 6.24465e9i | −1.66443 | − | 0.813470i | ||||
\(297\) | 5.79601e9 | 0.744909 | ||||||||
\(298\) | −4.03603e9 | + | 5.04100e9i | −0.511787 | + | 0.639221i | ||||
\(299\) | 1.29754e9i | 0.162344i | ||||||||
\(300\) | −4.62384e8 | + | 1.03657e8i | −0.0570844 | + | 0.0127972i | ||||
\(301\) | 8.29277e9 | 1.01026 | ||||||||
\(302\) | 1.04539e10 | + | 8.36985e9i | 1.25676 | + | 1.00621i | ||||
\(303\) | 2.77025e9i | 0.328661i | ||||||||
\(304\) | 5.45126e8 | + | 1.15472e9i | 0.0638268 | + | 0.135202i | ||||
\(305\) | −8.99511e9 | −1.03946 | ||||||||
\(306\) | 2.50187e9 | − | 3.12484e9i | 0.285351 | − | 0.356403i | ||||
\(307\) | − | 3.49176e9i | − | 0.393089i | −0.980495 | − | 0.196545i | \(-0.937028\pi\) | ||
0.980495 | − | 0.196545i | \(-0.0629721\pi\) | |||||||
\(308\) | −1.44808e9 | − | 6.45947e9i | −0.160912 | − | 0.717784i | ||||
\(309\) | −1.04417e10 | −1.14535 | ||||||||
\(310\) | 5.17670e8 | + | 4.14468e8i | 0.0560540 | + | 0.0448791i | ||||
\(311\) | − | 1.29807e10i | − | 1.38757i | −0.720182 | − | 0.693785i | \(-0.755942\pi\) | ||
0.720182 | − | 0.693785i | \(-0.244058\pi\) | |||||||
\(312\) | 9.83025e8 | − | 2.01135e9i | 0.103740 | − | 0.212260i | ||||
\(313\) | −6.31165e9 | −0.657606 | −0.328803 | − | 0.944399i | \(-0.606645\pi\) | ||||
−0.328803 | + | 0.944399i | \(0.606645\pi\) | |||||||
\(314\) | 2.71319e9 | − | 3.38877e9i | 0.279101 | − | 0.348597i | ||||
\(315\) | − | 2.92090e9i | − | 0.296671i | ||||||
\(316\) | 8.97112e9 | − | 2.01114e9i | 0.899702 | − | 0.201695i | ||||
\(317\) | 1.65902e10 | 1.64291 | 0.821455 | − | 0.570273i | \(-0.193163\pi\) | ||||
0.821455 | + | 0.570273i | \(0.193163\pi\) | |||||||
\(318\) | −1.02871e9 | − | 8.23630e8i | −0.100597 | − | 0.0805423i | ||||
\(319\) | 2.37021e9i | 0.228888i | ||||||||
\(320\) | 6.28763e9 | + | 8.07481e9i | 0.599635 | + | 0.770074i | ||||
\(321\) | −1.00247e10 | −0.944175 | ||||||||
\(322\) | −3.31828e9 | + | 4.14453e9i | −0.308667 | + | 0.385525i | ||||
\(323\) | − | 1.42411e9i | − | 0.130838i | ||||||
\(324\) | 3.01213e9 | + | 1.34363e10i | 0.273334 | + | 1.21927i | ||||
\(325\) | 1.01332e8 | 0.00908264 | ||||||||
\(326\) | −7.22557e9 | − | 5.78509e9i | −0.639738 | − | 0.512200i | ||||
\(327\) | − | 5.90243e9i | − | 0.516226i | ||||||
\(328\) | 7.90053e9 | + | 3.86129e9i | 0.682591 | + | 0.333609i | ||||
\(329\) | −1.06683e10 | −0.910563 | ||||||||
\(330\) | −1.12669e10 | + | 1.40724e10i | −0.950059 | + | 1.18662i | ||||
\(331\) | 5.48640e9i | 0.457062i | 0.973537 | + | 0.228531i | \(0.0733922\pi\) | ||||
−0.973537 | + | 0.228531i | \(0.926608\pi\) | |||||||
\(332\) | −1.29797e10 | + | 2.90978e9i | −1.06834 | + | 0.239501i | ||||
\(333\) | 1.18848e10 | 0.966526 | ||||||||
\(334\) | −5.84680e9 | − | 4.68118e9i | −0.469821 | − | 0.376158i | ||||
\(335\) | 9.30657e9i | 0.738942i | ||||||||
\(336\) | 8.28368e9 | − | 3.91060e9i | 0.649930 | − | 0.306822i | ||||
\(337\) | −3.56226e8 | −0.0276189 | −0.0138095 | − | 0.999905i | \(-0.504396\pi\) | ||||
−0.0138095 | + | 0.999905i | \(0.504396\pi\) | |||||||
\(338\) | 7.85810e9 | − | 9.81476e9i | 0.602075 | − | 0.751992i | ||||
\(339\) | 5.50408e9i | 0.416760i | ||||||||
\(340\) | −2.49675e9 | − | 1.11373e10i | −0.186836 | − | 0.833421i | ||||
\(341\) | −1.25599e9 | −0.0928897 | ||||||||
\(342\) | −8.33021e8 | − | 6.66951e8i | −0.0608908 | − | 0.0487517i | ||||
\(343\) | 1.33911e10i | 0.967476i | ||||||||
\(344\) | 1.06621e10 | − | 2.18156e10i | 0.761396 | − | 1.55788i | ||||
\(345\) | 1.44582e10 | 1.02056 | ||||||||
\(346\) | 2.06197e9 | − | 2.57540e9i | 0.143872 | − | 0.179697i | ||||
\(347\) | − | 1.59731e10i | − | 1.10172i | −0.834599 | − | 0.550859i | \(-0.814300\pi\) | ||
0.834599 | − | 0.550859i | \(-0.185700\pi\) | |||||||
\(348\) | −3.20042e9 | + | 7.17469e8i | −0.218218 | + | 0.0489199i | ||||
\(349\) | 1.03634e10 | 0.698553 | 0.349277 | − | 0.937020i | \(-0.386427\pi\) | ||||
0.349277 | + | 0.937020i | \(0.386427\pi\) | |||||||
\(350\) | 3.23669e8 | + | 2.59142e8i | 0.0215689 | + | 0.0172690i | ||||
\(351\) | − | 1.71511e9i | − | 0.112996i | ||||||
\(352\) | −1.88546e10 | − | 4.49560e9i | −1.22814 | − | 0.292831i | ||||
\(353\) | −1.30979e10 | −0.843536 | −0.421768 | − | 0.906704i | \(-0.638590\pi\) | ||||
−0.421768 | + | 0.906704i | \(0.638590\pi\) | |||||||
\(354\) | −3.72253e9 | + | 4.64944e9i | −0.237042 | + | 0.296066i | ||||
\(355\) | − | 7.29586e8i | − | 0.0459370i | ||||||
\(356\) | 4.66616e9 | + | 2.08144e10i | 0.290509 | + | 1.29588i | ||||
\(357\) | −1.02162e10 | −0.628952 | ||||||||
\(358\) | −1.77247e9 | − | 1.41911e9i | −0.107906 | − | 0.0863940i | ||||
\(359\) | 3.31454e9i | 0.199547i | 0.995010 | + | 0.0997737i | \(0.0318119\pi\) | ||||
−0.995010 | + | 0.0997737i | \(0.968188\pi\) | |||||||
\(360\) | −7.68395e9 | − | 3.75545e9i | −0.457483 | − | 0.223590i | ||||
\(361\) | 1.66039e10 | 0.977647 | ||||||||
\(362\) | −4.82566e9 | + | 6.02724e9i | −0.281010 | + | 0.350982i | ||||
\(363\) | − | 1.27242e10i | − | 0.732829i | ||||||
\(364\) | −1.91144e9 | + | 4.28505e8i | −0.108882 | + | 0.0244090i | ||||
\(365\) | −3.49263e9 | −0.196780 | ||||||||
\(366\) | 1.84031e10 | + | 1.47343e10i | 1.02557 | + | 0.821116i | ||||
\(367\) | 1.96628e10i | 1.08388i | 0.840418 | + | 0.541939i | \(0.182309\pi\) | ||||
−0.840418 | + | 0.541939i | \(0.817691\pi\) | |||||||
\(368\) | 6.63656e9 | + | 1.40580e10i | 0.361870 | + | 0.766536i | ||||
\(369\) | −7.34878e9 | −0.396378 | ||||||||
\(370\) | 2.11794e10 | − | 2.64530e10i | 1.13007 | − | 1.41146i | ||||
\(371\) | 1.15308e9i | 0.0608646i | ||||||||
\(372\) | −3.80191e8 | − | 1.69592e9i | −0.0198532 | − | 0.0885593i | ||||
\(373\) | −2.10063e10 | −1.08521 | −0.542606 | − | 0.839987i | \(-0.682562\pi\) | ||||
−0.542606 | + | 0.839987i | \(0.682562\pi\) | |||||||
\(374\) | 1.68750e10 | + | 1.35108e10i | 0.862498 | + | 0.690551i | ||||
\(375\) | − | 2.49382e10i | − | 1.26107i | ||||||
\(376\) | −1.37163e10 | + | 2.80648e10i | −0.686257 | + | 1.40414i | ||||
\(377\) | 7.01374e8 | 0.0347204 | ||||||||
\(378\) | 4.38617e9 | − | 5.47833e9i | 0.214842 | − | 0.268337i | ||||
\(379\) | 3.04816e9i | 0.147734i | 0.997268 | + | 0.0738670i | \(0.0235340\pi\) | ||||
−0.997268 | + | 0.0738670i | \(0.976466\pi\) | |||||||
\(380\) | −2.96899e9 | + | 6.65587e8i | −0.142388 | + | 0.0319206i | ||||
\(381\) | −2.56955e10 | −1.21943 | ||||||||
\(382\) | −1.23958e10 | − | 9.92461e9i | −0.582133 | − | 0.466080i | ||||
\(383\) | − | 2.23357e10i | − | 1.03802i | −0.854770 | − | 0.519008i | \(-0.826302\pi\) | ||
0.854770 | − | 0.519008i | \(-0.173698\pi\) | |||||||
\(384\) | 3.62938e8 | − | 2.68196e10i | 0.0166920 | − | 1.23347i | ||||
\(385\) | 1.57737e10 | 0.717945 | ||||||||
\(386\) | −1.17593e10 | + | 1.46874e10i | −0.529704 | + | 0.661599i | ||||
\(387\) | 2.02921e10i | 0.904654i | ||||||||
\(388\) | −6.75466e9 | − | 3.01306e10i | −0.298042 | − | 1.32948i | ||||
\(389\) | 3.13680e10 | 1.36990 | 0.684948 | − | 0.728592i | \(-0.259825\pi\) | ||||
0.684948 | + | 0.728592i | \(0.259825\pi\) | |||||||
\(390\) | 4.16420e9 | + | 3.33403e9i | 0.180000 | + | 0.144116i | ||||
\(391\) | − | 1.73377e10i | − | 0.741795i | ||||||
\(392\) | 1.40132e10 | + | 6.84880e9i | 0.593463 | + | 0.290048i | ||||
\(393\) | 3.11926e10 | 1.30762 | ||||||||
\(394\) | −1.70538e10 | + | 2.13002e10i | −0.707680 | + | 0.883892i | ||||
\(395\) | 2.19071e10i | 0.899904i | ||||||||
\(396\) | 1.58060e10 | − | 3.54339e9i | 0.642751 | − | 0.144091i | ||||
\(397\) | 7.65788e9 | 0.308281 | 0.154140 | − | 0.988049i | \(-0.450739\pi\) | ||||
0.154140 | + | 0.988049i | \(0.450739\pi\) | |||||||
\(398\) | −3.11046e10 | − | 2.49036e10i | −1.23963 | − | 0.992499i | ||||
\(399\) | 2.72345e9i | 0.107455i | ||||||||
\(400\) | 1.09787e9 | − | 5.18285e8i | 0.0428854 | − | 0.0202455i | ||||
\(401\) | −3.26120e10 | −1.26125 | −0.630623 | − | 0.776089i | \(-0.717201\pi\) | ||||
−0.630623 | + | 0.776089i | \(0.717201\pi\) | |||||||
\(402\) | 1.52445e10 | − | 1.90403e10i | 0.583725 | − | 0.729072i | ||||
\(403\) | 3.71662e8i | 0.0140906i | ||||||||
\(404\) | −1.55258e9 | − | 6.92561e9i | −0.0582812 | − | 0.259976i | ||||
\(405\) | −3.28107e10 | −1.21954 | ||||||||
\(406\) | 2.24029e9 | + | 1.79367e9i | 0.0824520 | + | 0.0660144i | ||||
\(407\) | 6.41811e10i | 2.33900i | ||||||||
\(408\) | −1.31352e10 | + | 2.68756e10i | −0.474018 | + | 0.969879i | ||||
\(409\) | 2.26168e10 | 0.808236 | 0.404118 | − | 0.914707i | \(-0.367578\pi\) | ||||
0.404118 | + | 0.914707i | \(0.367578\pi\) | |||||||
\(410\) | −1.30960e10 | + | 1.63569e10i | −0.463450 | + | 0.578848i | ||||
\(411\) | 2.21802e10i | 0.777318i | ||||||||
\(412\) | 2.61043e10 | − | 5.85205e9i | 0.905990 | − | 0.203104i | ||||
\(413\) | 5.21155e9 | 0.179129 | ||||||||
\(414\) | −1.01415e10 | − | 8.11970e9i | −0.345224 | − | 0.276400i | ||||
\(415\) | − | 3.16958e10i | − | 1.06858i | ||||||
\(416\) | −1.33030e9 | + | 5.57931e9i | −0.0444199 | + | 0.186297i | ||||
\(417\) | 2.94794e10 | 0.974932 | ||||||||
\(418\) | 3.60173e9 | − | 4.49856e9i | 0.117979 | − | 0.147356i | ||||
\(419\) | − | 4.94503e10i | − | 1.60440i | −0.597054 | − | 0.802201i | \(-0.703662\pi\) | ||
0.597054 | − | 0.802201i | \(-0.296338\pi\) | |||||||
\(420\) | 4.77475e9 | + | 2.12988e10i | 0.153445 | + | 0.684475i | ||||
\(421\) | −3.34077e10 | −1.06345 | −0.531726 | − | 0.846916i | \(-0.678457\pi\) | ||||
−0.531726 | + | 0.846916i | \(0.678457\pi\) | |||||||
\(422\) | −1.83321e10 | − | 1.46774e10i | −0.578045 | − | 0.462807i | ||||
\(423\) | − | 2.61048e10i | − | 0.815378i | ||||||
\(424\) | 3.03339e9 | + | 1.48253e9i | 0.0938565 | + | 0.0458713i | ||||
\(425\) | −1.35399e9 | −0.0415012 | ||||||||
\(426\) | −1.19508e9 | + | 1.49266e9i | −0.0362878 | + | 0.0453234i | ||||
\(427\) | − | 2.06280e10i | − | 0.620505i | ||||||
\(428\) | 2.50618e10 | − | 5.61834e9i | 0.746857 | − | 0.167430i | ||||
\(429\) | −1.01033e10 | −0.298287 | ||||||||
\(430\) | 4.51660e10 | + | 3.61617e10i | 1.32111 | + | 1.05773i | ||||
\(431\) | − | 3.06956e10i | − | 0.889544i | −0.895644 | − | 0.444772i | \(-0.853285\pi\) | ||
0.895644 | − | 0.444772i | \(-0.146715\pi\) | |||||||
\(432\) | −8.77234e9 | − | 1.85822e10i | −0.251872 | − | 0.533533i | ||||
\(433\) | 2.88433e9 | 0.0820529 | 0.0410265 | − | 0.999158i | \(-0.486937\pi\) | ||||
0.0410265 | + | 0.999158i | \(0.486937\pi\) | |||||||
\(434\) | −9.50477e8 | + | 1.18715e9i | −0.0267906 | + | 0.0334615i | ||||
\(435\) | − | 7.81528e9i | − | 0.218267i | ||||||
\(436\) | 3.30801e9 | + | 1.47561e10i | 0.0915421 | + | 0.408343i | ||||
\(437\) | −4.62189e9 | −0.126734 | ||||||||
\(438\) | 7.14559e9 | + | 5.72105e9i | 0.194152 | + | 0.155446i | ||||
\(439\) | 6.92422e10i | 1.86429i | 0.362088 | + | 0.932144i | \(0.382064\pi\) | ||||
−0.362088 | + | 0.932144i | \(0.617936\pi\) | |||||||
\(440\) | 2.02805e10 | − | 4.14956e10i | 0.541088 | − | 1.10711i | ||||
\(441\) | −1.30346e10 | −0.344621 | ||||||||
\(442\) | 3.99802e9 | − | 4.99353e9i | 0.104751 | − | 0.130833i | ||||
\(443\) | 2.06609e10i | 0.536455i | 0.963356 | + | 0.268228i | \(0.0864379\pi\) | ||||
−0.963356 | + | 0.268228i | \(0.913562\pi\) | |||||||
\(444\) | −8.66619e10 | + | 1.94278e10i | −2.22996 | + | 0.499910i | ||||
\(445\) | −5.08278e10 | −1.29617 | ||||||||
\(446\) | 1.84752e10 | + | 1.47920e10i | 0.466928 | + | 0.373842i | ||||
\(447\) | 4.03280e10i | 1.01013i | ||||||||
\(448\) | −1.85175e10 | + | 1.44191e10i | −0.459696 | + | 0.357952i | ||||
\(449\) | 2.11092e10 | 0.519382 | 0.259691 | − | 0.965692i | \(-0.416379\pi\) | ||||
0.259691 | + | 0.965692i | \(0.416379\pi\) | |||||||
\(450\) | −6.34111e8 | + | 7.92004e8i | −0.0154638 | + | 0.0193142i | ||||
\(451\) | − | 3.96855e10i | − | 0.959237i | ||||||
\(452\) | −3.08476e9 | − | 1.37602e10i | −0.0739039 | − | 0.329664i | ||||
\(453\) | 8.36315e10 | 1.98599 | ||||||||
\(454\) | 9.36818e9 | + | 7.50054e9i | 0.220512 | + | 0.176551i | ||||
\(455\) | − | 4.66764e9i | − | 0.108906i | ||||||
\(456\) | 7.16452e9 | + | 3.50158e9i | 0.165702 | + | 0.0809850i | ||||
\(457\) | −2.06831e10 | −0.474188 | −0.237094 | − | 0.971487i | \(-0.576195\pi\) | ||||
−0.237094 | + | 0.971487i | \(0.576195\pi\) | |||||||
\(458\) | 2.84784e10 | − | 3.55695e10i | 0.647223 | − | 0.808381i | ||||
\(459\) | 2.29173e10i | 0.516312i | ||||||||
\(460\) | −3.61456e10 | + | 8.10309e9i | −0.807279 | + | 0.180975i | ||||
\(461\) | 7.65072e10 | 1.69394 | 0.846971 | − | 0.531640i | \(-0.178424\pi\) | ||||
0.846971 | + | 0.531640i | \(0.178424\pi\) | |||||||
\(462\) | −3.22715e10 | − | 2.58379e10i | −0.708355 | − | 0.567138i | ||||
\(463\) | 3.41303e9i | 0.0742704i | 0.999310 | + | 0.0371352i | \(0.0118232\pi\) | ||||
−0.999310 | + | 0.0371352i | \(0.988177\pi\) | |||||||
\(464\) | 7.59895e9 | − | 3.58734e9i | 0.163939 | − | 0.0773929i | ||||
\(465\) | 4.14136e9 | 0.0885791 | ||||||||
\(466\) | −2.20621e9 | + | 2.75555e9i | −0.0467845 | + | 0.0584339i | ||||
\(467\) | 1.92903e10i | 0.405576i | 0.979223 | + | 0.202788i | \(0.0650002\pi\) | ||||
−0.979223 | + | 0.202788i | \(0.935000\pi\) | |||||||
\(468\) | −1.04853e9 | − | 4.67721e9i | −0.0218574 | − | 0.0974997i | ||||
\(469\) | −2.13423e10 | −0.441112 | ||||||||
\(470\) | −5.81039e10 | − | 4.65204e10i | −1.19073 | − | 0.953349i | ||||
\(471\) | − | 2.71102e10i | − | 0.550869i | ||||||
\(472\) | 6.70056e9 | − | 1.37099e10i | 0.135003 | − | 0.276227i | ||||
\(473\) | −1.09583e11 | −2.18927 | ||||||||
\(474\) | 3.58845e10 | − | 4.48197e10i | 0.710875 | − | 0.887883i | ||||
\(475\) | 3.60948e8i | 0.00709040i | ||||||||
\(476\) | 2.55406e10 | − | 5.72567e9i | 0.497511 | − | 0.111532i | ||||
\(477\) | −2.82154e9 | −0.0545021 | ||||||||
\(478\) | 5.05212e10 | + | 4.04493e10i | 0.967748 | + | 0.774818i | ||||
\(479\) | − | 2.43887e10i | − | 0.463282i | −0.972801 | − | 0.231641i | \(-0.925590\pi\) | ||
0.972801 | − | 0.231641i | \(-0.0744095\pi\) | |||||||
\(480\) | 6.21692e10 | + | 1.48233e10i | 1.17114 | + | 0.279242i | ||||
\(481\) | 1.89920e10 | 0.354806 | ||||||||
\(482\) | −6.17983e10 | + | 7.71861e10i | −1.14496 | + | 1.43005i | ||||
\(483\) | 3.31563e10i | 0.609224i | ||||||||
\(484\) | 7.13124e9 | + | 3.18104e10i | 0.129952 | + | 0.579679i | ||||
\(485\) | 7.35776e10 | 1.32978 | ||||||||
\(486\) | 4.14332e10 | + | 3.31731e10i | 0.742683 | + | 0.594622i | ||||
\(487\) | − | 9.30801e10i | − | 1.65478i | −0.561626 | − | 0.827391i | \(-0.689824\pi\) | ||
0.561626 | − | 0.827391i | \(-0.310176\pi\) | |||||||
\(488\) | −5.42656e10 | − | 2.65217e10i | −0.956853 | − | 0.467651i | ||||
\(489\) | −5.78046e10 | −1.01094 | ||||||||
\(490\) | −2.32284e10 | + | 2.90123e10i | −0.402935 | + | 0.503266i | ||||
\(491\) | − | 2.12850e9i | − | 0.0366225i | −0.999832 | − | 0.0183113i | \(-0.994171\pi\) | ||
0.999832 | − | 0.0183113i | \(-0.00582898\pi\) | |||||||
\(492\) | 5.35862e10 | − | 1.20129e10i | 0.914518 | − | 0.205016i | ||||
\(493\) | −9.37175e9 | −0.158647 | ||||||||
\(494\) | −1.33118e9 | − | 1.06580e9i | −0.0223526 | − | 0.0178964i | ||||
\(495\) | 3.85976e10i | 0.642895i | ||||||||
\(496\) | 1.90095e9 | + | 4.02673e9i | 0.0314083 | + | 0.0665312i | ||||
\(497\) | 1.67312e9 | 0.0274221 | ||||||||
\(498\) | −5.19187e10 | + | 6.48464e10i | −0.844124 | + | 1.05431i | ||||
\(499\) | 1.04101e10i | 0.167901i | 0.996470 | + | 0.0839503i | \(0.0267537\pi\) | ||||
−0.996470 | + | 0.0839503i | \(0.973246\pi\) | |||||||
\(500\) | 1.39766e10 | + | 6.23454e10i | 0.223625 | + | 0.997527i | ||||
\(501\) | −4.67744e10 | −0.742433 | ||||||||
\(502\) | −6.51187e10 | − | 5.21367e10i | −1.02539 | − | 0.820973i | ||||
\(503\) | 3.93019e10i | 0.613962i | 0.951716 | + | 0.306981i | \(0.0993188\pi\) | ||||
−0.951716 | + | 0.306981i | \(0.900681\pi\) | |||||||
\(504\) | 8.61216e9 | − | 1.76212e10i | 0.133472 | − | 0.273094i | ||||
\(505\) | 1.69120e10 | 0.260034 | ||||||||
\(506\) | 4.38487e10 | − | 5.47670e10i | 0.668890 | − | 0.835444i | ||||
\(507\) | − | 7.85181e10i | − | 1.18833i | ||||||
\(508\) | 6.42387e10 | − | 1.44010e10i | 0.964587 | − | 0.216241i | ||||
\(509\) | −3.25113e10 | −0.484354 | −0.242177 | − | 0.970232i | \(-0.577861\pi\) | ||||
−0.242177 | + | 0.970232i | \(0.577861\pi\) | |||||||
\(510\) | −5.56420e10 | − | 4.45492e10i | −0.822473 | − | 0.658505i | ||||
\(511\) | − | 8.00947e9i | − | 0.117468i | ||||||
\(512\) | 1.41237e10 | + | 6.72524e10i | 0.205526 | + | 0.978652i | ||||
\(513\) | 6.10931e9 | 0.0882110 | ||||||||
\(514\) | 6.13693e10 | − | 7.66503e10i | 0.879223 | − | 1.09815i | ||||
\(515\) | 6.37455e10i | 0.906194i | ||||||||
\(516\) | −3.31711e10 | − | 1.47967e11i | −0.467908 | − | 2.08720i | ||||
\(517\) | 1.40973e11 | 1.97322 | ||||||||
\(518\) | 6.06633e10 | + | 4.85695e10i | 0.842572 | + | 0.674598i | ||||
\(519\) | − | 2.06032e10i | − | 0.283965i | ||||||
\(520\) | −1.22791e10 | − | 6.00125e9i | −0.167939 | − | 0.0820783i | ||||
\(521\) | 1.84550e9 | 0.0250475 | 0.0125237 | − | 0.999922i | \(-0.496013\pi\) | ||||
0.0125237 | + | 0.999922i | \(0.496013\pi\) | |||||||
\(522\) | −4.38904e9 | + | 5.48191e9i | −0.0591136 | + | 0.0738329i | ||||
\(523\) | 6.23770e10i | 0.833715i | 0.908972 | + | 0.416858i | \(0.136869\pi\) | ||||
−0.908972 | + | 0.416858i | \(0.863131\pi\) | |||||||
\(524\) | −7.79814e10 | + | 1.74818e10i | −1.03435 | + | 0.231879i | ||||
\(525\) | 2.58935e9 | 0.0340842 | ||||||||
\(526\) | −8.70448e10 | − | 6.96916e10i | −1.13710 | − | 0.910411i | ||||
\(527\) | − | 4.96614e9i | − | 0.0643838i | ||||||
\(528\) | −1.09463e11 | + | 5.16757e10i | −1.40842 | + | 0.664892i | ||||
\(529\) | 2.20424e10 | 0.281473 | ||||||||
\(530\) | −5.02817e9 | + | 6.28018e9i | −0.0637245 | + | 0.0795919i | ||||
\(531\) | 1.27524e10i | 0.160404i | ||||||||
\(532\) | −1.52635e9 | − | 6.80863e9i | −0.0190550 | − | 0.0849988i | ||||
\(533\) | −1.17434e10 | −0.145508 | ||||||||
\(534\) | 1.03989e11 | + | 8.32575e10i | 1.27885 | + | 1.02390i | ||||
\(535\) | 6.11998e10i | 0.747025i | ||||||||
\(536\) | −2.74400e10 | + | 5.61446e10i | −0.332449 | + | 0.680219i | ||||
\(537\) | −1.41797e10 | −0.170518 | ||||||||
\(538\) | −2.70720e10 | + | 3.38130e10i | −0.323141 | + | 0.403603i | ||||
\(539\) | − | 7.03905e10i | − | 0.833986i | ||||||
\(540\) | 4.77779e10 | − | 1.07108e10i | 0.561891 | − | 0.125964i | ||||
\(541\) | −7.45917e10 | −0.870766 | −0.435383 | − | 0.900245i | \(-0.643387\pi\) | ||||
−0.435383 | + | 0.900245i | \(0.643387\pi\) | |||||||
\(542\) | 9.97991e10 | + | 7.99032e10i | 1.15646 | + | 0.925907i | ||||
\(543\) | 4.82179e10i | 0.554638i | ||||||||
\(544\) | 1.77755e10 | − | 7.45506e10i | 0.202967 | − | 0.851246i | ||||
\(545\) | −3.60337e10 | −0.408435 | ||||||||
\(546\) | −7.64575e9 | + | 9.54954e9i | −0.0860299 | + | 0.107451i | ||||
\(547\) | 1.41531e9i | 0.0158089i | 0.999969 | + | 0.00790445i | \(0.00251609\pi\) | ||||
−0.999969 | + | 0.00790445i | \(0.997484\pi\) | |||||||
\(548\) | −1.24309e10 | − | 5.54506e10i | −0.137841 | − | 0.614871i | ||||
\(549\) | 5.04758e10 | 0.555641 | ||||||||
\(550\) | −4.27705e9 | − | 3.42438e9i | −0.0467405 | − | 0.0374224i | ||||
\(551\) | 2.49833e9i | 0.0271046i | ||||||||
\(552\) | 8.72234e10 | + | 4.26295e10i | 0.939457 | + | 0.459149i | ||||
\(553\) | −5.02383e10 | −0.537198 | ||||||||
\(554\) | 8.22965e10 | − | 1.02788e11i | 0.873660 | − | 1.09120i | ||||
\(555\) | − | 2.11624e11i | − | 2.23046i | ||||||
\(556\) | −7.36985e10 | + | 1.65217e10i | −0.771187 | + | 0.172884i | ||||
\(557\) | −1.37543e11 | −1.42895 | −0.714475 | − | 0.699661i | \(-0.753334\pi\) | ||||
−0.714475 | + | 0.699661i | \(0.753334\pi\) | |||||||
\(558\) | −2.90489e9 | − | 2.32578e9i | −0.0299636 | − | 0.0239901i | ||||
\(559\) | 3.24270e10i | 0.332093i | ||||||||
\(560\) | −2.38737e10 | − | 5.05710e10i | −0.242755 | − | 0.514220i | ||||
\(561\) | 1.35000e11 | 1.36296 | ||||||||
\(562\) | −3.08105e10 | + | 3.84823e10i | −0.308854 | + | 0.385759i | ||||
\(563\) | − | 1.06415e11i | − | 1.05918i | −0.848255 | − | 0.529589i | \(-0.822346\pi\) | ||
0.848255 | − | 0.529589i | \(-0.177654\pi\) | |||||||
\(564\) | 4.26731e10 | + | 1.90352e11i | 0.421733 | + | 1.88123i | ||||
\(565\) | 3.36018e10 | 0.329738 | ||||||||
\(566\) | −1.46273e10 | − | 1.17112e10i | −0.142528 | − | 0.114113i | ||||
\(567\) | − | 7.52431e10i | − | 0.728005i | ||||||
\(568\) | 2.15115e9 | − | 4.40143e9i | 0.0206670 | − | 0.0422864i | ||||
\(569\) | 4.02429e10 | 0.383919 | 0.191960 | − | 0.981403i | \(-0.438516\pi\) | ||||
0.191960 | + | 0.981403i | \(0.438516\pi\) | |||||||
\(570\) | −1.18760e10 | + | 1.48331e10i | −0.112504 | + | 0.140518i | ||||
\(571\) | 1.50341e11i | 1.41427i | 0.707077 | + | 0.707137i | \(0.250014\pi\) | ||||
−0.707077 | + | 0.707137i | \(0.749986\pi\) | |||||||
\(572\) | 2.52583e10 | − | 5.66238e9i | 0.235950 | − | 0.0528951i | ||||
\(573\) | −9.91667e10 | −0.919914 | ||||||||
\(574\) | −3.75103e10 | − | 3.00323e10i | −0.345544 | − | 0.276657i | ||||
\(575\) | 4.39432e9i | 0.0401994i | ||||||||
\(576\) | −3.52829e10 | − | 4.53116e10i | −0.320534 | − | 0.411642i | ||||
\(577\) | 4.96477e9 | 0.0447915 | 0.0223958 | − | 0.999749i | \(-0.492871\pi\) | ||||
0.0223958 | + | 0.999749i | \(0.492871\pi\) | |||||||
\(578\) | 1.63361e10 | − | 2.04038e10i | 0.146365 | − | 0.182810i | ||||
\(579\) | 1.17499e11i | 1.04549i | ||||||||
\(580\) | 4.38006e9 | + | 1.95382e10i | 0.0387051 | + | 0.172652i | ||||
\(581\) | 7.26862e10 | 0.637892 | ||||||||
\(582\) | −1.50533e11 | − | 1.20522e11i | −1.31201 | − | 1.05045i | ||||
\(583\) | − | 1.52372e10i | − | 0.131895i | ||||||
\(584\) | −2.10703e10 | − | 1.02979e10i | −0.181142 | − | 0.0885313i | ||||
\(585\) | 1.14215e10 | 0.0975216 | ||||||||
\(586\) | −4.80980e10 | + | 6.00743e10i | −0.407884 | + | 0.509446i | ||||
\(587\) | 1.53440e11i | 1.29237i | 0.763181 | + | 0.646185i | \(0.223637\pi\) | ||||
−0.763181 | + | 0.646185i | \(0.776363\pi\) | |||||||
\(588\) | 9.50461e10 | − | 2.13074e10i | 0.795106 | − | 0.178246i | ||||
\(589\) | −1.32388e9 | −0.0109999 | ||||||||
\(590\) | 2.83843e10 | + | 2.27256e10i | 0.234245 | + | 0.187546i | ||||
\(591\) | 1.70402e11i | 1.39677i | ||||||||
\(592\) | 2.05766e11 | − | 9.71390e10i | 1.67528 | − | 0.790873i | ||||
\(593\) | 2.06036e11 | 1.66619 | 0.833094 | − | 0.553131i | \(-0.186567\pi\) | ||||
0.833094 | + | 0.553131i | \(0.186567\pi\) | |||||||
\(594\) | −5.79601e10 | + | 7.23922e10i | −0.465568 | + | 0.581495i | ||||
\(595\) | 6.23689e10i | 0.497623i | ||||||||
\(596\) | −2.26017e10 | − | 1.00820e11i | −0.179125 | − | 0.799027i | ||||
\(597\) | −2.48837e11 | −1.95892 | ||||||||
\(598\) | −1.62063e10 | − | 1.29754e10i | −0.126730 | − | 0.101465i | ||||
\(599\) | − | 2.30634e11i | − | 1.79150i | −0.444558 | − | 0.895750i | \(-0.646639\pi\) | ||
0.444558 | − | 0.895750i | \(-0.353361\pi\) | |||||||
\(600\) | 3.32916e9 | − | 6.81174e9i | 0.0256880 | − | 0.0525598i | ||||
\(601\) | 1.01422e11 | 0.777382 | 0.388691 | − | 0.921368i | \(-0.372927\pi\) | ||||
0.388691 | + | 0.921368i | \(0.372927\pi\) | |||||||
\(602\) | −8.29277e10 | + | 1.03577e11i | −0.631413 | + | 0.788635i | ||||
\(603\) | − | 5.22236e10i | − | 0.395001i | ||||||
\(604\) | −2.09079e11 | + | 4.68711e10i | −1.57095 | + | 0.352174i | ||||
\(605\) | −7.76795e10 | −0.579809 | ||||||||
\(606\) | −3.46004e10 | − | 2.77025e10i | −0.256561 | − | 0.205413i | ||||
\(607\) | − | 1.97883e11i | − | 1.45765i | −0.684700 | − | 0.728825i | \(-0.740067\pi\) | ||
0.684700 | − | 0.728825i | \(-0.259933\pi\) | |||||||
\(608\) | −1.98738e10 | − | 4.73860e9i | −0.145434 | − | 0.0346766i | ||||
\(609\) | 1.79224e10 | 0.130294 | ||||||||
\(610\) | 8.99511e10 | − | 1.12349e11i | 0.649661 | − | 0.811427i | ||||
\(611\) | − | 4.17158e10i | − | 0.299320i | ||||||
\(612\) | 1.40105e10 | + | 6.24967e10i | 0.0998728 | + | 0.445504i | ||||
\(613\) | 1.27158e11 | 0.900538 | 0.450269 | − | 0.892893i | \(-0.351328\pi\) | ||||
0.450269 | + | 0.892893i | \(0.351328\pi\) | |||||||
\(614\) | 4.36121e10 | + | 3.49176e10i | 0.306855 | + | 0.245681i | ||||
\(615\) | 1.30855e11i | 0.914723i | ||||||||
\(616\) | 9.51595e10 | + | 4.65082e10i | 0.660890 | + | 0.323003i | ||||
\(617\) | −5.06702e10 | −0.349632 | −0.174816 | − | 0.984601i | \(-0.555933\pi\) | ||||
−0.174816 | + | 0.984601i | \(0.555933\pi\) | |||||||
\(618\) | 1.04417e11 | − | 1.30417e11i | 0.715844 | − | 0.894089i | ||||
\(619\) | − | 7.06748e10i | − | 0.481395i | −0.970600 | − | 0.240698i | \(-0.922624\pi\) | ||
0.970600 | − | 0.240698i | \(-0.0773762\pi\) | |||||||
\(620\) | −1.03534e10 | + | 2.32102e9i | −0.0700675 | + | 0.0157077i | ||||
\(621\) | 7.43769e10 | 0.500117 | ||||||||
\(622\) | 1.62128e11 | + | 1.29807e11i | 1.08317 | + | 0.867231i | ||||
\(623\) | − | 1.16561e11i | − | 0.773748i | ||||||
\(624\) | 1.52915e10 | + | 3.23915e10i | 0.100858 | + | 0.213645i | ||||
\(625\) | −1.45008e11 | −0.950327 | ||||||||
\(626\) | 6.31165e10 | − | 7.88325e10i | 0.411004 | − | 0.513343i | ||||
\(627\) | − | 3.59885e10i | − | 0.232859i | ||||||
\(628\) | 1.51938e10 | + | 6.77754e10i | 0.0976853 | + | 0.435746i | ||||
\(629\) | −2.53771e11 | −1.62121 | ||||||||
\(630\) | 3.64821e10 | + | 2.92090e10i | 0.231589 | + | 0.185419i | ||||
\(631\) | 1.65273e11i | 1.04252i | 0.853399 | + | 0.521259i | \(0.174537\pi\) | ||||
−0.853399 | + | 0.521259i | \(0.825463\pi\) | |||||||
\(632\) | −6.45921e10 | + | 1.32161e11i | −0.404866 | + | 0.828388i | ||||
\(633\) | −1.46657e11 | −0.913454 | ||||||||
\(634\) | −1.65902e11 | + | 2.07211e11i | −1.02682 | + | 1.28250i | ||||
\(635\) | 1.56868e11i | 0.964804i | ||||||||
\(636\) | 2.05743e10 | − | 4.61233e9i | 0.125747 | − | 0.0281898i | ||||
\(637\) | −2.08294e10 | −0.126508 | ||||||||
\(638\) | −2.96039e10 | − | 2.37021e10i | −0.178676 | − | 0.143055i | ||||
\(639\) | 4.09405e9i | 0.0245556i | ||||||||
\(640\) | −1.63731e11 | − | 2.21570e9i | −0.975911 | − | 0.0132066i | ||||
\(641\) | 1.12013e11 | 0.663490 | 0.331745 | − | 0.943369i | \(-0.392363\pi\) | ||||
0.331745 | + | 0.943369i | \(0.392363\pi\) | |||||||
\(642\) | 1.00247e11 | − | 1.25209e11i | 0.590109 | − | 0.737046i | ||||
\(643\) | − | 2.65913e11i | − | 1.55559i | −0.628518 | − | 0.777795i | \(-0.716338\pi\) | ||
0.628518 | − | 0.777795i | \(-0.283662\pi\) | |||||||
\(644\) | −1.85824e10 | − | 8.28907e10i | −0.108033 | − | 0.481906i | ||||
\(645\) | 3.61328e11 | 2.08767 | ||||||||
\(646\) | 1.77872e10 | + | 1.42411e10i | 0.102136 | + | 0.0817739i | ||||
\(647\) | 2.71996e11i | 1.55219i | 0.630614 | + | 0.776097i | \(0.282803\pi\) | ||||
−0.630614 | + | 0.776097i | \(0.717197\pi\) | |||||||
\(648\) | −1.97940e11 | − | 9.67411e10i | −1.12262 | − | 0.548670i | ||||
\(649\) | −6.88669e10 | −0.388179 | ||||||||
\(650\) | −1.01332e9 | + | 1.26563e9i | −0.00567665 | + | 0.00709013i | ||||
\(651\) | 9.49716e9i | 0.0528774i | ||||||||
\(652\) | 1.44511e11 | − | 3.23965e10i | 0.799672 | − | 0.179270i | ||||
\(653\) | 3.03789e11 | 1.67078 | 0.835391 | − | 0.549656i | \(-0.185241\pi\) | ||||
0.835391 | + | 0.549656i | \(0.185241\pi\) | |||||||
\(654\) | 7.37213e10 | + | 5.90243e10i | 0.402979 | + | 0.322641i | ||||
\(655\) | − | 1.90427e11i | − | 1.03458i | ||||||
\(656\) | −1.27233e11 | + | 6.00646e10i | −0.687043 | + | 0.324342i | ||||
\(657\) | 1.95988e10 | 0.105189 | ||||||||
\(658\) | 1.06683e11 | − | 1.33247e11i | 0.569102 | − | 0.710808i | ||||
\(659\) | 4.18575e10i | 0.221938i | 0.993824 | + | 0.110969i | \(0.0353954\pi\) | ||||
−0.993824 | + | 0.110969i | \(0.964605\pi\) | |||||||
\(660\) | −6.30949e10 | − | 2.81448e11i | −0.332520 | − | 1.48328i | ||||
\(661\) | −2.46529e11 | −1.29141 | −0.645703 | − | 0.763589i | \(-0.723435\pi\) | ||||
−0.645703 | + | 0.763589i | \(0.723435\pi\) | |||||||
\(662\) | −6.85251e10 | − | 5.48640e10i | −0.356794 | − | 0.285664i | ||||
\(663\) | − | 3.99482e10i | − | 0.206749i | ||||||
\(664\) | 9.34537e10 | − | 1.91214e11i | 0.480755 | − | 0.983665i | ||||
\(665\) | 1.66264e10 | 0.0850179 | ||||||||
\(666\) | −1.18848e11 | + | 1.48441e11i | −0.604079 | + | 0.754494i | ||||
\(667\) | 3.04155e10i | 0.153671i | ||||||||
\(668\) | 1.16936e11 | − | 2.62146e10i | 0.587276 | − | 0.131655i | ||||
\(669\) | 1.47802e11 | 0.737862 | ||||||||
\(670\) | −1.16239e11 | − | 9.30657e10i | −0.576837 | − | 0.461839i | ||||
\(671\) | 2.72584e11i | 1.34465i | ||||||||
\(672\) | −3.39935e10 | + | 1.42569e11i | −0.166694 | + | 0.699115i | ||||
\(673\) | −3.15336e11 | −1.53714 | −0.768569 | − | 0.639767i | \(-0.779031\pi\) | ||||
−0.768569 | + | 0.639767i | \(0.779031\pi\) | |||||||
\(674\) | 3.56226e9 | − | 4.44927e9i | 0.0172618 | − | 0.0215600i | ||||
\(675\) | − | 5.80849e9i | − | 0.0279800i | ||||||
\(676\) | 4.40053e10 | + | 1.96295e11i | 0.210726 | + | 0.939989i | ||||
\(677\) | −2.47236e10 | −0.117695 | −0.0588475 | − | 0.998267i | \(-0.518743\pi\) | ||||
−0.0588475 | + | 0.998267i | \(0.518743\pi\) | |||||||
\(678\) | −6.87460e10 | − | 5.50408e10i | −0.325333 | − | 0.260475i | ||||
\(679\) | 1.68731e11i | 0.793811i | ||||||||
\(680\) | 1.64072e11 | + | 8.01886e10i | 0.767361 | + | 0.375039i | ||||
\(681\) | 7.49454e10 | 0.348463 | ||||||||
\(682\) | 1.25599e10 | − | 1.56873e10i | 0.0580561 | − | 0.0725120i | ||||
\(683\) | 7.20843e10i | 0.331251i | 0.986189 | + | 0.165626i | \(0.0529644\pi\) | ||||
−0.986189 | + | 0.165626i | \(0.947036\pi\) | |||||||
\(684\) | 1.66604e10 | − | 3.73492e9i | 0.0761135 | − | 0.0170631i | ||||
\(685\) | 1.35408e11 | 0.615009 | ||||||||
\(686\) | −1.67255e11 | − | 1.33911e11i | −0.755235 | − | 0.604672i | ||||
\(687\) | − | 2.84556e11i | − | 1.27744i | ||||||
\(688\) | 1.65855e11 | + | 3.51326e11i | 0.740246 | + | 1.56804i | ||||
\(689\) | −4.50887e9 | −0.0200074 | ||||||||
\(690\) | −1.44582e11 | + | 1.80583e11i | −0.637850 | + | 0.796675i | ||||
\(691\) | − | 2.95424e11i | − | 1.29578i | −0.761732 | − | 0.647892i | \(-0.775651\pi\) | ||
0.761732 | − | 0.647892i | \(-0.224349\pi\) | |||||||
\(692\) | 1.15470e10 | + | 5.15080e10i | 0.0503554 | + | 0.224621i | ||||
\(693\) | −8.85139e10 | −0.383776 | ||||||||
\(694\) | 1.99503e11 | + | 1.59731e11i | 0.860028 | + | 0.688573i | ||||
\(695\) | − | 1.79968e11i | − | 0.771360i | ||||||
\(696\) | 2.30430e10 | − | 4.71479e10i | 0.0981980 | − | 0.200921i | ||||
\(697\) | 1.56916e11 | 0.664867 | ||||||||
\(698\) | −1.03634e11 | + | 1.29438e11i | −0.436596 | + | 0.545308i | ||||
\(699\) | 2.20444e10i | 0.0923400i | ||||||||
\(700\) | −6.47338e9 | + | 1.45120e9i | −0.0269612 | + | 0.00604414i | ||||
\(701\) | −2.87925e11 | −1.19236 | −0.596180 | − | 0.802851i | \(-0.703315\pi\) | ||||
−0.596180 | + | 0.802851i | \(0.703315\pi\) | |||||||
\(702\) | 2.14217e10 | + | 1.71511e10i | 0.0882077 | + | 0.0706227i | ||||
\(703\) | 6.76504e10i | 0.276980i | ||||||||
\(704\) | 2.44696e11 | − | 1.90538e11i | 0.996176 | − | 0.775694i | ||||
\(705\) | −4.64831e11 | −1.88165 | ||||||||
\(706\) | 1.30979e11 | − | 1.63593e11i | 0.527210 | − | 0.658485i | ||||
\(707\) | 3.87834e10i | 0.155227i | ||||||||
\(708\) | −2.08462e10 | − | 9.29889e10i | −0.0829648 | − | 0.370082i | ||||
\(709\) | 2.51685e11 | 0.996030 | 0.498015 | − | 0.867168i | \(-0.334062\pi\) | ||||
0.498015 | + | 0.867168i | \(0.334062\pi\) | |||||||
\(710\) | 9.11252e9 | + | 7.29586e9i | 0.0358596 | + | 0.0287106i | ||||
\(711\) | − | 1.22931e11i | − | 0.481042i | ||||||
\(712\) | −3.06633e11 | − | 1.49864e11i | −1.19316 | − | 0.583144i | ||||
\(713\) | −1.61174e10 | −0.0623643 | ||||||||
\(714\) | 1.02162e11 | − | 1.27601e11i | 0.393095 | − | 0.490976i | ||||
\(715\) | 6.16795e10i | 0.236003i | ||||||||
\(716\) | 3.54493e10 | − | 7.94701e9i | 0.134883 | − | 0.0302379i | ||||
\(717\) | 4.04170e11 | 1.52928 | ||||||||
\(718\) | −4.13986e10 | − | 3.31454e10i | −0.155772 | − | 0.124717i | ||||
\(719\) | − | 1.38856e11i | − | 0.519574i | −0.965666 | − | 0.259787i | \(-0.916348\pi\) | ||
0.965666 | − | 0.259787i | \(-0.0836524\pi\) | |||||||
\(720\) | 1.23745e11 | − | 5.84180e10i | 0.460466 | − | 0.217379i | ||||
\(721\) | −1.46184e11 | −0.540953 | ||||||||
\(722\) | −1.66039e11 | + | 2.07383e11i | −0.611029 | + | 0.763175i | ||||
\(723\) | 6.17489e11i | 2.25983i | ||||||||
\(724\) | −2.70237e10 | − | 1.20545e11i | −0.0983536 | − | 0.438727i | ||||
\(725\) | 2.37531e9 | 0.00859743 | ||||||||
\(726\) | 1.58925e11 | + | 1.27242e11i | 0.572064 | + | 0.458018i | ||||
\(727\) | − | 1.79083e11i | − | 0.641088i | −0.947234 | − | 0.320544i | \(-0.896134\pi\) | ||
0.947234 | − | 0.320544i | \(-0.103866\pi\) | |||||||
\(728\) | 1.37623e10 | − | 2.81589e10i | 0.0489967 | − | 0.100251i | ||||
\(729\) | −2.14381e10 | −0.0759061 | ||||||||
\(730\) | 3.49263e10 | − | 4.36230e10i | 0.122988 | − | 0.153612i | ||||
\(731\) | − | 4.33289e11i | − | 1.51743i | ||||||
\(732\) | −3.68062e11 | + | 8.25119e10i | −1.28197 | + | 0.287391i | ||||
\(733\) | 2.17618e11 | 0.753839 | 0.376920 | − | 0.926246i | \(-0.376983\pi\) | ||||
0.376920 | + | 0.926246i | \(0.376983\pi\) | |||||||
\(734\) | −2.45588e11 | − | 1.96628e11i | −0.846101 | − | 0.677423i | ||||
\(735\) | 2.32098e11i | 0.795285i | ||||||||
\(736\) | −2.41950e11 | − | 5.76895e10i | −0.824546 | − | 0.196601i | ||||
\(737\) | 2.82023e11 | 0.955904 | ||||||||
\(738\) | 7.34878e10 | − | 9.17862e10i | 0.247736 | − | 0.309423i | ||||
\(739\) | 4.84950e11i | 1.62599i | 0.582268 | + | 0.812997i | \(0.302166\pi\) | ||||
−0.582268 | + | 0.812997i | \(0.697834\pi\) | |||||||
\(740\) | 1.18605e11 | + | 5.29061e11i | 0.395525 | + | 1.76433i | ||||
\(741\) | −1.06494e10 | −0.0353227 | ||||||||
\(742\) | −1.44020e10 | − | 1.15308e10i | −0.0475124 | − | 0.0380404i | ||||
\(743\) | 2.03509e11i | 0.667771i | 0.942614 | + | 0.333886i | \(0.108360\pi\) | ||||
−0.942614 | + | 0.333886i | \(0.891640\pi\) | |||||||
\(744\) | 2.49840e10 | + | 1.22106e10i | 0.0815398 | + | 0.0398517i | ||||
\(745\) | 2.46198e11 | 0.799206 | ||||||||
\(746\) | 2.10063e11 | − | 2.62369e11i | 0.678258 | − | 0.847144i | ||||
\(747\) | 1.77860e11i | 0.571210i | ||||||||
\(748\) | −3.37500e11 | + | 7.56606e10i | −1.07812 | + | 0.241693i | ||||
\(749\) | −1.40346e11 | −0.445937 | ||||||||
\(750\) | 3.11478e11 | + | 2.49382e11i | 0.984423 | + | 0.788169i | ||||
\(751\) | 2.34693e11i | 0.737804i | 0.929468 | + | 0.368902i | \(0.120266\pi\) | ||||
−0.929468 | + | 0.368902i | \(0.879734\pi\) | |||||||
\(752\) | −2.13365e11 | − | 4.51965e11i | −0.667194 | − | 1.41330i | ||||
\(753\) | −5.20950e11 | −1.62038 | ||||||||
\(754\) | −7.01374e9 | + | 8.76016e9i | −0.0217002 | + | 0.0271036i | ||||
\(755\) | − | 5.10561e11i | − | 1.57130i | ||||||
\(756\) | 2.45626e10 | + | 1.09567e11i | 0.0751946 | + | 0.335421i | ||||
\(757\) | −3.84882e11 | −1.17204 | −0.586022 | − | 0.810295i | \(-0.699307\pi\) | ||||
−0.586022 | + | 0.810295i | \(0.699307\pi\) | |||||||
\(758\) | −3.80715e10 | − | 3.04816e10i | −0.115325 | − | 0.0923338i | ||||
\(759\) | − | 4.38136e11i | − | 1.32021i | ||||||
\(760\) | 2.13767e10 | − | 4.37386e10i | 0.0640748 | − | 0.131102i | ||||
\(761\) | 2.39209e11 | 0.713244 | 0.356622 | − | 0.934249i | \(-0.383928\pi\) | ||||
0.356622 | + | 0.934249i | \(0.383928\pi\) | |||||||
\(762\) | 2.56955e11 | − | 3.20936e11i | 0.762143 | − | 0.951916i | ||||
\(763\) | − | 8.26340e10i | − | 0.243815i | ||||||
\(764\) | 2.47917e11 | − | 5.55778e10i | 0.727666 | − | 0.163128i | ||||
\(765\) | −1.52614e11 | −0.445604 | ||||||||
\(766\) | 2.78972e11 | + | 2.23357e11i | 0.810301 | + | 0.648760i | ||||
\(767\) | 2.03786e10i | 0.0588833i | ||||||||
\(768\) | 3.31347e11 | + | 2.72729e11i | 0.952442 | + | 0.783947i | ||||
\(769\) | 2.08457e11 | 0.596089 | 0.298045 | − | 0.954552i | \(-0.403666\pi\) | ||||
0.298045 | + | 0.954552i | \(0.403666\pi\) | |||||||
\(770\) | −1.57737e11 | + | 1.97014e11i | −0.448716 | + | 0.560446i | ||||
\(771\) | − | 6.13202e11i | − | 1.73535i | ||||||
\(772\) | −6.58522e10 | − | 2.93748e11i | −0.185396 | − | 0.826999i | ||||
\(773\) | −5.54469e10 | −0.155296 | −0.0776478 | − | 0.996981i | \(-0.524741\pi\) | ||||
−0.0776478 | + | 0.996981i | \(0.524741\pi\) | |||||||
\(774\) | −2.53448e11 | − | 2.02921e11i | −0.706195 | − | 0.565409i | ||||
\(775\) | 1.25869e9i | 0.00348909i | ||||||||
\(776\) | 4.43878e11 | + | 2.16940e11i | 1.22410 | + | 0.598265i | ||||
\(777\) | 4.85306e11 | 1.33147 | ||||||||
\(778\) | −3.13680e11 | + | 3.91786e11i | −0.856185 | + | 1.06938i | ||||
\(779\) | − | 4.18307e10i | − | 0.113591i | ||||||
\(780\) | −8.32840e10 | + | 1.86706e10i | −0.225000 | + | 0.0504405i | ||||
\(781\) | −2.21091e10 | −0.0594246 | ||||||||
\(782\) | 2.16548e11 | + | 1.73377e11i | 0.579064 | + | 0.463622i | ||||
\(783\) | − | 4.02039e10i | − | 0.106960i | ||||||
\(784\) | −2.25674e11 | + | 1.06537e11i | −0.597333 | + | 0.281991i | ||||
\(785\) | −1.65504e11 | −0.435844 | ||||||||
\(786\) | −3.11926e11 | + | 3.89595e11i | −0.817261 | + | 1.02076i | ||||
\(787\) | 4.05908e11i | 1.05811i | 0.848589 | + | 0.529053i | \(0.177453\pi\) | ||||
−0.848589 | + | 0.529053i | \(0.822547\pi\) | |||||||
\(788\) | −9.55014e10 | − | 4.26005e11i | −0.247688 | − | 1.10487i | ||||
\(789\) | −6.96358e11 | −1.79690 | ||||||||
\(790\) | −2.73619e11 | − | 2.19071e11i | −0.702487 | − | 0.562440i | ||||
\(791\) | 7.70572e10i | 0.196837i | ||||||||
\(792\) | −1.13804e11 | + | 2.32851e11i | −0.289238 | + | 0.591804i | ||||
\(793\) | 8.06610e10 | 0.203972 | ||||||||
\(794\) | −7.65788e10 | + | 9.56469e10i | −0.192676 | + | 0.240652i | ||||
\(795\) | 5.02414e10i | 0.125775i | ||||||||
\(796\) | 6.22092e11 | − | 1.39460e11i | 1.54954 | − | 0.347375i | ||||
\(797\) | −3.09015e11 | −0.765855 | −0.382927 | − | 0.923778i | \(-0.625084\pi\) | ||||
−0.382927 | + | 0.923778i | \(0.625084\pi\) | |||||||
\(798\) | −3.40159e10 | − | 2.72345e10i | −0.0838823 | − | 0.0671596i | ||||
\(799\) | 5.57406e11i | 1.36768i | ||||||||
\(800\) | −4.50528e9 | + | 1.88952e10i | −0.0109992 | + | 0.0461308i | ||||
\(801\) | 2.85219e11 | 0.692864 | ||||||||
\(802\) | 3.26120e11 | − | 4.07324e11i | 0.788279 | − | 0.984560i | ||||
\(803\) | 1.05839e11i | 0.254557i | ||||||||
\(804\) | 8.53690e10 | + | 3.80807e11i | 0.204304 | + | 0.911340i | ||||
\(805\) | 2.02415e11 | 0.482014 | ||||||||
\(806\) | −4.64206e9 | − | 3.71662e9i | −0.0109994 | − | 0.00880660i | ||||
\(807\) | 2.70504e11i | 0.637792i | ||||||||
\(808\) | 1.02027e11 | + | 4.98644e10i | 0.239369 | + | 0.116989i | ||||
\(809\) | 4.77958e11 | 1.11582 | 0.557912 | − | 0.829900i | \(-0.311603\pi\) | ||||
0.557912 | + | 0.829900i | \(0.311603\pi\) | |||||||
\(810\) | 3.28107e11 | − | 4.09806e11i | 0.762212 | − | 0.952003i | ||||
\(811\) | − | 6.37503e11i | − | 1.47366i | −0.676075 | − | 0.736832i | \(-0.736321\pi\) | ||
0.676075 | − | 0.736832i | \(-0.263679\pi\) | |||||||
\(812\) | −4.48059e10 | + | 1.00446e10i | −0.103065 | + | 0.0231050i | ||||
\(813\) | 7.98393e11 | 1.82749 | ||||||||
\(814\) | −8.01622e11 | − | 6.41811e11i | −1.82588 | − | 1.46187i | ||||
\(815\) | 3.52890e11i | 0.799851i | ||||||||
\(816\) | −2.04325e11 | − | 4.32814e11i | −0.460850 | − | 0.976204i | ||||
\(817\) | −1.15506e11 | −0.259250 | ||||||||
\(818\) | −2.26168e11 | + | 2.82484e11i | −0.505148 | + | 0.630929i | ||||
\(819\) | 2.61924e10i | 0.0582155i | ||||||||
\(820\) | −7.33375e10 | − | 3.27137e11i | −0.162207 | − | 0.723561i | ||||
\(821\) | −8.43824e11 | −1.85729 | −0.928644 | − | 0.370973i | \(-0.879024\pi\) | ||||
−0.928644 | + | 0.370973i | \(0.879024\pi\) | |||||||
\(822\) | −2.77031e11 | − | 2.21802e11i | −0.606794 | − | 0.485824i | ||||
\(823\) | − | 2.60916e11i | − | 0.568723i | −0.958717 | − | 0.284362i | \(-0.908218\pi\) | ||
0.958717 | − | 0.284362i | \(-0.0917817\pi\) | |||||||
\(824\) | −1.87951e11 | + | 3.84563e11i | −0.407696 | + | 0.834179i | ||||
\(825\) | −3.42164e10 | −0.0738616 | ||||||||
\(826\) | −5.21155e10 | + | 6.50922e10i | −0.111956 | + | 0.139833i | ||||
\(827\) | 2.78675e11i | 0.595765i | 0.954602 | + | 0.297883i | \(0.0962804\pi\) | ||||
−0.954602 | + | 0.297883i | \(0.903720\pi\) | |||||||
\(828\) | 2.02830e11 | − | 4.54703e10i | 0.431530 | − | 0.0967401i | ||||
\(829\) | 4.75156e11 | 1.00605 | 0.503023 | − | 0.864273i | \(-0.332221\pi\) | ||||
0.503023 | + | 0.864273i | \(0.332221\pi\) | |||||||
\(830\) | 3.95880e11 | + | 3.16958e11i | 0.834164 | + | 0.667865i | ||||
\(831\) | − | 8.22306e11i | − | 1.72437i | ||||||
\(832\) | −5.63825e10 | − | 7.24086e10i | −0.117666 | − | 0.151111i | ||||
\(833\) | 2.78322e11 | 0.578053 | ||||||||
\(834\) | −2.94794e11 | + | 3.68198e11i | −0.609333 | + | 0.761056i | ||||
\(835\) | 2.85552e11i | 0.587408i | ||||||||
\(836\) | 2.01697e10 | + | 8.99711e10i | 0.0412928 | + | 0.184195i | ||||
\(837\) | 2.13043e10 | 0.0434075 | ||||||||
\(838\) | 6.17635e11 | + | 4.94503e11i | 1.25244 | + | 1.00275i | ||||
\(839\) | − | 3.35440e11i | − | 0.676966i | −0.940973 | − | 0.338483i | \(-0.890086\pi\) | ||
0.940973 | − | 0.338483i | \(-0.109914\pi\) | |||||||
\(840\) | −3.13769e11 | − | 1.53351e11i | −0.630221 | − | 0.308014i | ||||
\(841\) | −4.83806e11 | −0.967134 | ||||||||
\(842\) | 3.34077e11 | − | 4.17262e11i | 0.664658 | − | 0.830157i | ||||
\(843\) | 3.07858e11i | 0.609594i | ||||||||
\(844\) | 3.66642e11 | − | 8.21935e10i | 0.722557 | − | 0.161982i | ||||
\(845\) | −4.79344e11 | −0.940200 | ||||||||
\(846\) | 3.26049e11 | + | 2.61048e11i | 0.636504 | + | 0.509611i | ||||
\(847\) | − | 1.78138e11i | − | 0.346117i | ||||||
\(848\) | −4.88507e10 | + | 2.30616e10i | −0.0944686 | + | 0.0445971i | ||||
\(849\) | −1.17019e11 | −0.225229 | ||||||||
\(850\) | 1.35399e10 | − | 1.69114e10i | 0.0259382 | − | 0.0323968i | ||||
\(851\) | 8.23600e11i | 1.57036i | ||||||||
\(852\) | −6.69247e9 | − | 2.98532e10i | −0.0127007 | − | 0.0566543i | ||||
\(853\) | −9.75408e10 | −0.184243 | −0.0921213 | − | 0.995748i | \(-0.529365\pi\) | ||||
−0.0921213 | + | 0.995748i | \(0.529365\pi\) | |||||||
\(854\) | 2.57643e11 | + | 2.06280e11i | 0.484382 | + | 0.387816i | ||||
\(855\) | 4.06840e10i | 0.0761306i | ||||||||
\(856\) | −1.80445e11 | + | 3.69205e11i | −0.336086 | + | 0.687659i | ||||
\(857\) | −7.94769e10 | −0.147339 | −0.0736695 | − | 0.997283i | \(-0.523471\pi\) | ||||
−0.0736695 | + | 0.997283i | \(0.523471\pi\) | |||||||
\(858\) | 1.01033e11 | − | 1.26190e11i | 0.186429 | − | 0.232850i | ||||
\(859\) | − | 4.15618e11i | − | 0.763347i | −0.924297 | − | 0.381673i | \(-0.875348\pi\) | ||
0.924297 | − | 0.381673i | \(-0.124652\pi\) | |||||||
\(860\) | −9.03320e11 | + | 2.02506e11i | −1.65138 | + | 0.370206i | ||||
\(861\) | −3.00083e11 | −0.546045 | ||||||||
\(862\) | 3.83388e11 | + | 3.06956e11i | 0.694400 | + | 0.555965i | ||||
\(863\) | − | 4.80012e11i | − | 0.865383i | −0.901542 | − | 0.432692i | \(-0.857564\pi\) | ||
0.901542 | − | 0.432692i | \(-0.142436\pi\) | |||||||
\(864\) | 3.19815e11 | + | 7.62551e10i | 0.573909 | + | 0.136840i | ||||
\(865\) | −1.25780e11 | −0.224671 | ||||||||
\(866\) | −2.88433e10 | + | 3.60253e10i | −0.0512831 | + | 0.0640525i | ||||
\(867\) | − | 1.63230e11i | − | 0.288884i | ||||||
\(868\) | −5.32267e9 | − | 2.37429e10i | −0.00937671 | − | 0.0418268i | ||||
\(869\) | 6.63863e11 | 1.16412 | ||||||||
\(870\) | 9.76128e10 | + | 7.81528e10i | 0.170384 | + | 0.136417i | ||||
\(871\) | − | 8.34540e10i | − | 0.145002i | ||||||
\(872\) | −2.17383e11 | − | 1.06244e11i | −0.375976 | − | 0.183754i | ||||
\(873\) | −4.12879e11 | −0.710830 | ||||||||
\(874\) | 4.62189e10 | − | 5.77274e10i | 0.0792089 | − | 0.0989319i | ||||
\(875\) | − | 3.49134e11i | − | 0.595608i | ||||||
\(876\) | −1.42912e11 | + | 3.20379e10i | −0.242690 | + | 0.0544060i | ||||
\(877\) | 2.74155e11 | 0.463444 | 0.231722 | − | 0.972782i | \(-0.425564\pi\) | ||||
0.231722 | + | 0.972782i | \(0.425564\pi\) | |||||||
\(878\) | −8.64835e11 | − | 6.92422e11i | −1.45531 | − | 1.16518i | ||||
\(879\) | 4.80595e11i | 0.805051i | ||||||||
\(880\) | 3.15474e11 | + | 6.68259e11i | 0.526058 | + | 1.11433i | ||||
\(881\) | 8.01838e11 | 1.33101 | 0.665507 | − | 0.746391i | \(-0.268215\pi\) | ||||
0.665507 | + | 0.746391i | \(0.268215\pi\) | |||||||
\(882\) | 1.30346e11 | − | 1.62802e11i | 0.215388 | − | 0.269020i | ||||
\(883\) | − | 9.95008e11i | − | 1.63676i | −0.574681 | − | 0.818378i | \(-0.694874\pi\) | ||
0.574681 | − | 0.818378i | \(-0.305126\pi\) | |||||||
\(884\) | 2.23889e10 | + | 9.98706e10i | 0.0366627 | + | 0.163542i | ||||
\(885\) | 2.27075e11 | 0.370165 | ||||||||
\(886\) | −2.58054e11 | − | 2.06609e11i | −0.418770 | − | 0.335284i | ||||
\(887\) | 5.46038e11i | 0.882122i | 0.897477 | + | 0.441061i | \(0.145398\pi\) | ||||
−0.897477 | + | 0.441061i | \(0.854602\pi\) | |||||||
\(888\) | 6.23965e11 | − | 1.27668e12i | 1.00348 | − | 2.05320i | ||||
\(889\) | −3.59736e11 | −0.575940 | ||||||||
\(890\) | 5.08278e11 | − | 6.34839e11i | 0.810105 | − | 1.01182i | ||||
\(891\) | 9.94283e11i | 1.57761i | ||||||||
\(892\) | −3.69504e11 | + | 8.28353e10i | −0.583660 | + | 0.130845i | ||||
\(893\) | 1.48594e11 | 0.233665 | ||||||||
\(894\) | −5.03696e11 | − | 4.03280e11i | −0.788531 | − | 0.631330i | ||||
\(895\) | 8.65656e10i | 0.134913i | ||||||||
\(896\) | 5.08114e9 | − | 3.75474e11i | 0.00788368 | − | 0.582570i | ||||
\(897\) | −1.29650e11 | −0.200264 | ||||||||
\(898\) | −2.11092e11 | + | 2.63654e11i | −0.324614 | + | 0.405442i | ||||
\(899\) | 8.71212e9i | 0.0133378i | ||||||||
\(900\) | −3.55102e9 | − | 1.58401e10i | −0.00541232 | − | 0.0241428i | ||||
\(901\) | 6.02474e10 | 0.0914195 | ||||||||
\(902\) | 4.95672e11 | + | 3.96855e11i | 0.748804 | + | 0.599523i | ||||
\(903\) | 8.28613e11i | 1.24624i | ||||||||
\(904\) | 2.02713e11 | + | 9.90735e10i | 0.303534 | + | 0.148349i | ||||
\(905\) | 2.94365e11 | 0.438826 | ||||||||
\(906\) | −8.36315e11 | + | 1.04456e12i | −1.24124 | + | 1.55031i | ||||
\(907\) | 6.55018e11i | 0.967886i | 0.875100 | + | 0.483943i | \(0.160796\pi\) | ||||
−0.875100 | + | 0.483943i | \(0.839204\pi\) | |||||||
\(908\) | −1.87364e11 | + | 4.20030e10i | −0.275640 | + | 0.0617927i | ||||
\(909\) | −9.49014e10 | −0.139001 | ||||||||
\(910\) | 5.82988e10 | + | 4.66764e10i | 0.0850147 | + | 0.0680663i | ||||
\(911\) | − | 1.19425e11i | − | 0.173389i | −0.996235 | − | 0.0866943i | \(-0.972370\pi\) | ||
0.996235 | − | 0.0866943i | \(-0.0276304\pi\) | |||||||
\(912\) | −1.15380e11 | + | 5.44690e10i | −0.166783 | + | 0.0787354i | ||||
\(913\) | −9.60496e11 | −1.38233 | ||||||||
\(914\) | 2.06831e11 | − | 2.58332e11i | 0.296368 | − | 0.370163i | ||||
\(915\) | − | 8.98791e11i | − | 1.28225i | ||||||
\(916\) | 1.59479e11 | + | 7.11390e11i | 0.226528 | + | 1.01048i | ||||
\(917\) | 4.36696e11 | 0.617592 | ||||||||
\(918\) | −2.86237e11 | − | 2.29173e11i | −0.403046 | − | 0.322695i | ||||
\(919\) | 5.33989e10i | 0.0748635i | 0.999299 | + | 0.0374318i | \(0.0119177\pi\) | ||||
−0.999299 | + | 0.0374318i | \(0.988082\pi\) | |||||||
\(920\) | 2.60248e11 | − | 5.32489e11i | 0.363276 | − | 0.743292i | ||||
\(921\) | 3.48897e11 | 0.484907 | ||||||||
\(922\) | −7.65072e11 | + | 9.55574e11i | −1.05871 | + | 1.32233i | ||||
\(923\) | 6.54235e9i | 0.00901420i | ||||||||
\(924\) | 6.45430e11 | − | 1.44692e11i | 0.885444 | − | 0.198498i | ||||
\(925\) | 6.43194e10 | 0.0878567 | ||||||||
\(926\) | −4.26287e10 | − | 3.41303e10i | −0.0579773 | − | 0.0464190i | ||||
\(927\) | − | 3.57707e11i | − | 0.484404i | ||||||
\(928\) | −3.11836e10 | + | 1.30784e11i | −0.0420469 | + | 0.176345i | ||||
\(929\) | −6.30991e11 | −0.847150 | −0.423575 | − | 0.905861i | \(-0.639225\pi\) | ||||
−0.423575 | + | 0.905861i | \(0.639225\pi\) | |||||||
\(930\) | −4.14136e10 | + | 5.17256e10i | −0.0553620 | + | 0.0691471i | ||||
\(931\) | − | 7.41953e10i | − | 0.0987593i | ||||||
\(932\) | −1.23548e10 | − | 5.51110e10i | −0.0163746 | − | 0.0730423i | ||||
\(933\) | 1.29703e12 | 1.71168 | ||||||||
\(934\) | −2.40936e11 | − | 1.92903e11i | −0.316603 | − | 0.253485i | ||||
\(935\) | − | 8.24161e11i | − | 1.07836i | ||||||
\(936\) | 6.89036e10 | + | 3.36759e10i | 0.0897715 | + | 0.0438748i | ||||
\(937\) | −8.41436e11 | −1.09160 | −0.545799 | − | 0.837916i | \(-0.683774\pi\) | ||||
−0.545799 | + | 0.837916i | \(0.683774\pi\) | |||||||
\(938\) | 2.13423e11 | − | 2.66565e11i | 0.275695 | − | 0.344343i | ||||
\(939\) | − | 6.30660e11i | − | 0.811209i | ||||||
\(940\) | 1.16208e12 | − | 2.60514e11i | 1.48842 | − | 0.333672i | ||||
\(941\) | −4.52935e11 | −0.577666 | −0.288833 | − | 0.957379i | \(-0.593267\pi\) | ||||
−0.288833 | + | 0.957379i | \(0.593267\pi\) | |||||||
\(942\) | 3.38606e11 | + | 2.71102e11i | 0.430022 | + | 0.344293i | ||||
\(943\) | − | 5.09262e11i | − | 0.644013i | ||||||
\(944\) | 1.04231e11 | + | 2.20789e11i | 0.131253 | + | 0.278029i | ||||
\(945\) | −2.67556e11 | −0.335497 | ||||||||
\(946\) | 1.09583e12 | − | 1.36869e12i | 1.36829 | − | 1.70900i | ||||
\(947\) | − | 1.00309e12i | − | 1.24721i | −0.781739 | − | 0.623605i | \(-0.785667\pi\) | ||
0.781739 | − | 0.623605i | \(-0.214333\pi\) | |||||||
\(948\) | 2.00953e11 | + | 8.96394e11i | 0.248806 | + | 1.10985i | ||||
\(949\) | 3.13192e10 | 0.0386141 | ||||||||
\(950\) | −4.50824e9 | − | 3.60948e9i | −0.00553494 | − | 0.00443150i | ||||
\(951\) | 1.65769e12i | 2.02666i | ||||||||
\(952\) | −1.83892e11 | + | 3.76258e11i | −0.223880 | + | 0.458077i | ||||
\(953\) | −1.39040e12 | −1.68565 | −0.842826 | − | 0.538186i | \(-0.819110\pi\) | ||||
−0.842826 | + | 0.538186i | \(0.819110\pi\) | |||||||
\(954\) | 2.82154e10 | − | 3.52411e10i | 0.0340638 | − | 0.0425457i | ||||
\(955\) | 6.05401e11i | 0.727830i | ||||||||
\(956\) | −1.01042e12 | + | 2.26516e11i | −1.20968 | + | 0.271186i | ||||
\(957\) | −2.36831e11 | −0.282352 | ||||||||
\(958\) | 3.04614e11 | + | 2.43887e11i | 0.361650 | + | 0.289551i | ||||
\(959\) | 3.10523e11i | 0.367130i | ||||||||
\(960\) | −8.06835e11 | + | 6.28259e11i | −0.949948 | + | 0.739697i | ||||
\(961\) | 8.48274e11 | 0.994587 | ||||||||
\(962\) | −1.89920e11 | + | 2.37210e11i | −0.221754 | + | 0.276970i | ||||
\(963\) | − | 3.43421e11i | − | 0.399321i | ||||||
\(964\) | −3.46071e11 | − | 1.54372e12i | −0.400734 | − | 1.78756i | ||||
\(965\) | 7.17318e11 | 0.827185 | ||||||||
\(966\) | −4.14122e11 | − | 3.31563e11i | −0.475575 | − | 0.380765i | ||||
\(967\) | − | 9.01843e11i | − | 1.03140i | −0.856771 | − | 0.515698i | \(-0.827533\pi\) | ||
0.856771 | − | 0.515698i | \(-0.172467\pi\) | |||||||
\(968\) | −4.68624e11 | − | 2.29035e11i | −0.533732 | − | 0.260856i | ||||
\(969\) | 1.42297e11 | 0.161399 | ||||||||
\(970\) | −7.35776e11 | + | 9.18984e11i | −0.831110 | + | 1.03806i | ||||
\(971\) | 1.28411e12i | 1.44452i | 0.691621 | + | 0.722261i | \(0.256897\pi\) | ||||
−0.691621 | + | 0.722261i | \(0.743103\pi\) | |||||||
\(972\) | −8.28664e11 | + | 1.85769e11i | −0.928354 | + | 0.208118i | ||||
\(973\) | 4.12712e11 | 0.460464 | ||||||||
\(974\) | 1.16257e12 | + | 9.30801e11i | 1.29176 | + | 1.03424i | ||||
\(975\) | 1.01251e10i | 0.0112042i | ||||||||
\(976\) | 8.73912e11 | − | 4.12560e11i | 0.963093 | − | 0.454661i | ||||
\(977\) | 1.20120e12 | 1.31837 | 0.659183 | − | 0.751983i | \(-0.270902\pi\) | ||||
0.659183 | + | 0.751983i | \(0.270902\pi\) | |||||||
\(978\) | 5.78046e11 | − | 7.21979e11i | 0.631840 | − | 0.789167i | ||||
\(979\) | 1.54026e12i | 1.67674i | ||||||||
\(980\) | −1.30079e11 | − | 5.80246e11i | −0.141027 | − | 0.629082i | ||||
\(981\) | 2.02202e11 | 0.218328 | ||||||||
\(982\) | 2.65850e10 | + | 2.12850e10i | 0.0285884 | + | 0.0228891i | ||||
\(983\) | 3.77388e11i | 0.404179i | 0.979367 | + | 0.202090i | \(0.0647733\pi\) | ||||
−0.979367 | + | 0.202090i | \(0.935227\pi\) | |||||||
\(984\) | −3.85820e11 | + | 7.89420e11i | −0.411533 | + | 0.842031i | ||||
\(985\) | 1.04028e12 | 1.10511 | ||||||||
\(986\) | 9.37175e10 | − | 1.17053e11i | 0.0991546 | − | 0.123844i | ||||
\(987\) | − | 1.06597e12i | − | 1.12325i | ||||||
\(988\) | 2.66236e10 | − | 5.96846e9i | 0.0279408 | − | 0.00626375i | ||||
\(989\) | −1.40622e12 | −1.46983 | ||||||||
\(990\) | −4.82084e11 | − | 3.85976e11i | −0.501860 | − | 0.401809i | ||||
\(991\) | − | 3.35563e11i | − | 0.347920i | −0.984753 | − | 0.173960i | \(-0.944344\pi\) | ||
0.984753 | − | 0.173960i | \(-0.0556563\pi\) | |||||||
\(992\) | −6.93033e10 | − | 1.65244e10i | −0.0715661 | − | 0.0170639i | ||||
\(993\) | −5.48200e11 | −0.563822 | ||||||||
\(994\) | −1.67312e10 | + | 2.08972e10i | −0.0171388 | + | 0.0214064i | ||||
\(995\) | 1.51912e12i | 1.54989i | ||||||||
\(996\) | −2.90745e11 | − | 1.29693e12i | −0.295444 | − | 1.31789i | ||||
\(997\) | −1.03163e12 | −1.04410 | −0.522050 | − | 0.852915i | \(-0.674833\pi\) | ||||
−0.522050 | + | 0.852915i | \(0.674833\pi\) | |||||||
\(998\) | −1.30022e11 | − | 1.04101e11i | −0.131067 | − | 0.104938i | ||||
\(999\) | − | 1.08865e12i | − | 1.09302i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4.9.b.b.3.2 | yes | 2 | |
3.2 | odd | 2 | 36.9.d.b.19.1 | 2 | |||
4.3 | odd | 2 | inner | 4.9.b.b.3.1 | ✓ | 2 | |
5.2 | odd | 4 | 100.9.d.b.99.1 | 4 | |||
5.3 | odd | 4 | 100.9.d.b.99.4 | 4 | |||
5.4 | even | 2 | 100.9.b.c.51.1 | 2 | |||
8.3 | odd | 2 | 64.9.c.b.63.2 | 2 | |||
8.5 | even | 2 | 64.9.c.b.63.1 | 2 | |||
12.11 | even | 2 | 36.9.d.b.19.2 | 2 | |||
16.3 | odd | 4 | 256.9.d.e.127.3 | 4 | |||
16.5 | even | 4 | 256.9.d.e.127.4 | 4 | |||
16.11 | odd | 4 | 256.9.d.e.127.2 | 4 | |||
16.13 | even | 4 | 256.9.d.e.127.1 | 4 | |||
20.3 | even | 4 | 100.9.d.b.99.2 | 4 | |||
20.7 | even | 4 | 100.9.d.b.99.3 | 4 | |||
20.19 | odd | 2 | 100.9.b.c.51.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.9.b.b.3.1 | ✓ | 2 | 4.3 | odd | 2 | inner | |
4.9.b.b.3.2 | yes | 2 | 1.1 | even | 1 | trivial | |
36.9.d.b.19.1 | 2 | 3.2 | odd | 2 | |||
36.9.d.b.19.2 | 2 | 12.11 | even | 2 | |||
64.9.c.b.63.1 | 2 | 8.5 | even | 2 | |||
64.9.c.b.63.2 | 2 | 8.3 | odd | 2 | |||
100.9.b.c.51.1 | 2 | 5.4 | even | 2 | |||
100.9.b.c.51.2 | 2 | 20.19 | odd | 2 | |||
100.9.d.b.99.1 | 4 | 5.2 | odd | 4 | |||
100.9.d.b.99.2 | 4 | 20.3 | even | 4 | |||
100.9.d.b.99.3 | 4 | 20.7 | even | 4 | |||
100.9.d.b.99.4 | 4 | 5.3 | odd | 4 | |||
256.9.d.e.127.1 | 4 | 16.13 | even | 4 | |||
256.9.d.e.127.2 | 4 | 16.11 | odd | 4 | |||
256.9.d.e.127.3 | 4 | 16.3 | odd | 4 | |||
256.9.d.e.127.4 | 4 | 16.5 | even | 4 |