Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,9,Mod(19,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.19");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.n (of order \(6\), degree \(2\), 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: | \(51.3297048677\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 1771 x^{10} + 26038 x^{9} + 2442597 x^{8} + 26522276 x^{7} + 1175865280 x^{6} + 6901058684 x^{5} + 370996492174 x^{4} + \cdots + 36\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{10}\cdot 7^{3} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.6 | ||
Root | \(9.14374 + 15.8374i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.73 |
Dual form | 126.9.n.b.19.6 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.65685 | + | 9.79796i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −64.0000 | + | 110.851i | −0.250000 | + | 0.433013i | ||||
\(5\) | 758.365 | − | 437.842i | 1.21338 | − | 0.700547i | 0.249889 | − | 0.968274i | \(-0.419606\pi\) |
0.963495 | + | 0.267727i | \(0.0862725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 855.887 | + | 2243.27i | 0.356471 | + | 0.934306i | ||||
\(8\) | −1448.15 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8579.92 | + | 4953.62i | 0.857992 | + | 0.495362i | ||||
\(11\) | −6414.54 | + | 11110.3i | −0.438121 | + | 0.758849i | −0.997545 | − | 0.0700336i | \(-0.977689\pi\) |
0.559423 | + | 0.828882i | \(0.311023\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3065.53i | 0.107333i | 0.998559 | + | 0.0536664i | \(0.0170907\pi\) | ||||
−0.998559 | + | 0.0536664i | \(0.982909\pi\) | |||||||
\(14\) | −17137.8 | + | 21075.8i | −0.446112 | + | 0.548620i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8192.00 | − | 14189.0i | −0.125000 | − | 0.216506i | ||||
\(17\) | −62419.6 | − | 36038.0i | −0.747353 | − | 0.431484i | 0.0773839 | − | 0.997001i | \(-0.475343\pi\) |
−0.824737 | + | 0.565517i | \(0.808677\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 49079.6 | − | 28336.1i | 0.376605 | − | 0.217433i | −0.299735 | − | 0.954023i | \(-0.596898\pi\) |
0.676340 | + | 0.736589i | \(0.263565\pi\) | |||||||
\(20\) | 112088.i | 0.700547i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −145144. | −0.619597 | ||||||||
\(23\) | 249593. | + | 432307.i | 0.891908 | + | 1.54483i | 0.837585 | + | 0.546307i | \(0.183967\pi\) |
0.0543235 | + | 0.998523i | \(0.482700\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 188099. | − | 325797.i | 0.481534 | − | 0.834041i | ||||
\(26\) | −30035.9 | + | 17341.3i | −0.0657276 | + | 0.0379479i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −303446. | − | 48693.1i | −0.493684 | − | 0.0792200i | ||||
\(29\) | 88328.5 | 0.124885 | 0.0624423 | − | 0.998049i | \(-0.480111\pi\) | ||||
0.0624423 | + | 0.998049i | \(0.480111\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 501813. | + | 289722.i | 0.543370 | + | 0.313715i | 0.746444 | − | 0.665449i | \(-0.231760\pi\) |
−0.203074 | + | 0.979163i | \(0.565093\pi\) | |||||||
\(32\) | 92681.9 | − | 160530.i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 815447.i | − | 0.610211i | ||||||
\(35\) | 1.63127e6 | + | 1.32647e6i | 1.08706 | + | 0.883947i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 465050. | + | 805489.i | 0.248137 | + | 0.429787i | 0.963009 | − | 0.269469i | \(-0.0868482\pi\) |
−0.714872 | + | 0.699256i | \(0.753515\pi\) | |||||||
\(38\) | 555272. | + | 320587.i | 0.266300 | + | 0.153748i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.09823e6 | + | 634063.i | −0.428996 | + | 0.247681i | ||||
\(41\) | 1.42277e6i | 0.503499i | 0.967792 | + | 0.251749i | \(0.0810059\pi\) | ||||
−0.967792 | + | 0.251749i | \(0.918994\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.95457e6 | 0.864211 | 0.432106 | − | 0.901823i | \(-0.357771\pi\) | ||||
0.432106 | + | 0.901823i | \(0.357771\pi\) | |||||||
\(44\) | −821061. | − | 1.42212e6i | −0.219061 | − | 0.379424i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.82382e6 | + | 4.89099e6i | −0.630674 | + | 1.09236i | ||||
\(47\) | −6.92276e6 | + | 3.99685e6i | −1.41869 | + | 0.819081i | −0.996184 | − | 0.0872789i | \(-0.972183\pi\) |
−0.422506 | + | 0.906360i | \(0.638850\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.29971e6 | + | 3.83997e6i | −0.745857 | + | 0.666107i | ||||
\(50\) | 4.25620e6 | 0.680991 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −339818. | − | 196194.i | −0.0464764 | − | 0.0268332i | ||||
\(53\) | −1.04248e6 | + | 1.80563e6i | −0.132119 | + | 0.228837i | −0.924493 | − | 0.381199i | \(-0.875511\pi\) |
0.792374 | + | 0.610035i | \(0.208845\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.12342e7i | 1.22770i | ||||||||
\(56\) | −1.23946e6 | − | 3.24860e6i | −0.126032 | − | 0.330327i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 499661. | + | 865439.i | 0.0441534 | + | 0.0764759i | ||||
\(59\) | −7.60174e6 | − | 4.38887e6i | −0.627343 | − | 0.362197i | 0.152379 | − | 0.988322i | \(-0.451307\pi\) |
−0.779722 | + | 0.626125i | \(0.784640\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.25971e7 | + | 7.27293e6i | −0.909810 | + | 0.525279i | −0.880370 | − | 0.474287i | \(-0.842706\pi\) |
−0.0294401 | + | 0.999567i | \(0.509372\pi\) | |||||||
\(62\) | 6.55566e6i | 0.443660i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.09715e6 | 0.125000 | ||||||||
\(65\) | 1.34222e6 | + | 2.32479e6i | 0.0751917 | + | 0.130236i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.05740e6 | − | 1.22238e7i | 0.350224 | − | 0.606605i | −0.636065 | − | 0.771636i | \(-0.719439\pi\) |
0.986288 | + | 0.165030i | \(0.0527722\pi\) | |||||||
\(68\) | 7.98971e6 | − | 4.61286e6i | 0.373676 | − | 0.215742i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.76886e6 | + | 2.34868e7i | −0.156970 | + | 0.978209i | ||||
\(71\) | 3.34541e7 | 1.31649 | 0.658243 | − | 0.752806i | \(-0.271300\pi\) | ||||
0.658243 | + | 0.752806i | \(0.271300\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.12065e6 | + | 647007.i | 0.0394619 | + | 0.0227833i | 0.519601 | − | 0.854409i | \(-0.326081\pi\) |
−0.480139 | + | 0.877192i | \(0.659414\pi\) | |||||||
\(74\) | −5.26143e6 | + | 9.11307e6i | −0.175460 | + | 0.303905i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.25405e6i | 0.217433i | ||||||||
\(77\) | −3.04135e7 | − | 4.88037e6i | −0.865175 | − | 0.138832i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.69458e7 | + | 2.93509e7i | 0.435063 | + | 0.753552i | 0.997301 | − | 0.0734239i | \(-0.0233926\pi\) |
−0.562237 | + | 0.826976i | \(0.690059\pi\) | |||||||
\(80\) | −1.24251e7 | − | 7.17361e6i | −0.303346 | − | 0.175137i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.39402e7 | + | 8.04839e6i | −0.308329 | + | 0.178014i | ||||
\(83\) | 7.65808e6i | 0.161364i | 0.996740 | + | 0.0806821i | \(0.0257099\pi\) | ||||
−0.996740 | + | 0.0806821i | \(0.974290\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.31158e7 | −1.20910 | ||||||||
\(86\) | 1.67136e7 | + | 2.89487e7i | 0.305545 | + | 0.529219i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.28924e6 | − | 1.60894e7i | 0.154899 | − | 0.268294i | ||||
\(89\) | −8.82439e7 | + | 5.09476e7i | −1.40645 | + | 0.812015i | −0.995044 | − | 0.0994374i | \(-0.968296\pi\) |
−0.411407 | + | 0.911452i | \(0.634962\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.87681e6 | + | 2.62375e6i | −0.100282 | + | 0.0382610i | ||||
\(92\) | −6.38957e7 | −0.891908 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.83220e7 | − | 4.52192e7i | −1.00317 | − | 0.579178i | ||||
\(95\) | 2.48135e7 | − | 4.29782e7i | 0.304645 | − | 0.527660i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.91159e7i | − | 0.328884i | −0.986387 | − | 0.164442i | \(-0.947418\pi\) | ||
0.986387 | − | 0.164442i | \(-0.0525824\pi\) | |||||||
\(98\) | −6.19467e7 | − | 2.04063e7i | −0.671605 | − | 0.221238i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.40767e7 | + | 4.17020e7i | 0.240767 | + | 0.417020i | ||||
\(101\) | 3.14578e7 | + | 1.81622e7i | 0.302304 | + | 0.174535i | 0.643477 | − | 0.765465i | \(-0.277491\pi\) |
−0.341174 | + | 0.940000i | \(0.610824\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.41753e8 | + | 8.18412e7i | −1.25946 | + | 0.727149i | −0.972969 | − | 0.230935i | \(-0.925822\pi\) |
−0.286489 | + | 0.958083i | \(0.592488\pi\) | |||||||
\(104\) | − | 4.43936e6i | − | 0.0379479i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.35887e7 | −0.186844 | ||||||||
\(107\) | 1.00138e8 | + | 1.73443e8i | 0.763945 | + | 1.32319i | 0.940803 | + | 0.338954i | \(0.110073\pi\) |
−0.176858 | + | 0.984236i | \(0.556593\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.45243e7 | + | 1.29080e8i | −0.527949 | + | 0.914435i | 0.471520 | + | 0.881855i | \(0.343706\pi\) |
−0.999469 | + | 0.0325795i | \(0.989628\pi\) | |||||||
\(110\) | −1.10072e8 | + | 6.35503e7i | −0.751809 | + | 0.434057i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.48182e7 | − | 3.05210e7i | 0.157724 | − | 0.193967i | ||||
\(113\) | 2.00627e8 | 1.23048 | 0.615242 | − | 0.788338i | \(-0.289058\pi\) | ||||
0.615242 | + | 0.788338i | \(0.289058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.78564e8 | + | 2.18564e8i | 2.16445 | + | 1.24965i | ||||
\(116\) | −5.65302e6 | + | 9.79132e6i | −0.0312211 | + | 0.0540766i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 9.93088e7i | − | 0.512224i | ||||||
\(119\) | 2.74188e7 | − | 1.70869e8i | 0.136729 | − | 0.852068i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.48869e7 | + | 4.31053e7i | 0.116099 | + | 0.201090i | ||||
\(122\) | −1.42520e8 | − | 8.22838e7i | −0.643333 | − | 0.371428i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.42321e7 | + | 3.70844e7i | −0.271685 | + | 0.156857i | ||||
\(125\) | 1.26335e7i | 0.0517466i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.46459e6 | 0.0325380 | 0.0162690 | − | 0.999868i | \(-0.494821\pi\) | ||||
0.0162690 | + | 0.999868i | \(0.494821\pi\) | |||||||
\(128\) | 1.18633e7 | + | 2.05478e7i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.51855e7 | + | 2.63020e7i | −0.0531686 | + | 0.0920906i | ||||
\(131\) | 2.13575e8 | − | 1.23307e8i | 0.725212 | − | 0.418701i | −0.0914562 | − | 0.995809i | \(-0.529152\pi\) |
0.816668 | + | 0.577108i | \(0.195819\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.05572e8 | + | 8.58462e7i | 0.337398 | + | 0.274356i | ||||
\(134\) | 1.59691e8 | 0.495291 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.03933e7 | + | 5.21886e7i | 0.264229 | + | 0.152553i | ||||
\(137\) | 2.09994e8 | − | 3.63721e8i | 0.596109 | − | 1.03249i | −0.397280 | − | 0.917697i | \(-0.630046\pi\) |
0.993389 | − | 0.114794i | \(-0.0366207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.41408e8i | − | 1.71820i | −0.511804 | − | 0.859102i | \(-0.671023\pi\) | ||
0.511804 | − | 0.859102i | \(-0.328977\pi\) | |||||||
\(140\) | −2.51443e8 | + | 9.59343e7i | −0.654526 | + | 0.249725i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.89245e8 | + | 3.27782e8i | 0.465448 | + | 0.806179i | ||||
\(143\) | −3.40590e7 | − | 1.96640e7i | −0.0814493 | − | 0.0470248i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.69852e7 | − | 3.86739e7i | 0.151533 | − | 0.0874876i | ||||
\(146\) | 1.46401e7i | 0.0322205i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.19053e8 | −0.248137 | ||||||||
\(149\) | 1.15983e8 | + | 2.00889e8i | 0.235315 | + | 0.407578i | 0.959364 | − | 0.282170i | \(-0.0910544\pi\) |
−0.724049 | + | 0.689749i | \(0.757721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.83226e8 | − | 4.90561e8i | 0.544784 | − | 0.943594i | −0.453836 | − | 0.891085i | \(-0.649945\pi\) |
0.998620 | − | 0.0525090i | \(-0.0167218\pi\) | |||||||
\(152\) | −7.10748e7 | + | 4.10351e7i | −0.133150 | + | 0.0768742i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.24227e8 | − | 3.25598e8i | −0.220869 | − | 0.578894i | ||||
\(155\) | 5.07410e8 | 0.879088 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.98264e8 | − | 4.03143e8i | −1.14927 | − | 0.663530i | −0.200559 | − | 0.979682i | \(-0.564276\pi\) |
−0.948709 | + | 0.316152i | \(0.897609\pi\) | |||||||
\(158\) | −1.91719e8 | + | 3.32068e8i | −0.307636 | + | 0.532842i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.62320e8i | − | 0.247681i | ||||||
\(161\) | −7.56158e8 | + | 9.29909e8i | −1.12541 | + | 1.38400i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.01244e7 | − | 3.48565e7i | −0.0285084 | − | 0.0493780i | 0.851419 | − | 0.524486i | \(-0.175742\pi\) |
−0.879928 | + | 0.475108i | \(0.842409\pi\) | |||||||
\(164\) | −1.57716e8 | − | 9.10571e7i | −0.218021 | − | 0.125875i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.50335e7 | + | 4.33206e7i | −0.0988150 | + | 0.0570509i | ||||
\(167\) | − | 2.59671e6i | − | 0.00333854i | −0.999999 | − | 0.00166927i | \(-0.999469\pi\) | ||
0.999999 | − | 0.00166927i | \(-0.000531346\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.06333e8 | 0.988480 | ||||||||
\(170\) | −3.57037e8 | − | 6.18406e8i | −0.427482 | − | 0.740420i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.89092e8 | + | 3.27517e8i | −0.216053 | + | 0.374214i | ||||
\(173\) | 1.93829e8 | − | 1.11907e8i | 0.216388 | − | 0.124932i | −0.387889 | − | 0.921706i | \(-0.626795\pi\) |
0.604277 | + | 0.796774i | \(0.293462\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.91842e8 | + | 1.43111e8i | 0.950902 | + | 0.152588i | ||||
\(176\) | 2.10192e8 | 0.219061 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.98365e8 | − | 5.76406e8i | −0.994511 | − | 0.574181i | ||||
\(179\) | 6.89778e8 | − | 1.19473e9i | 0.671889 | − | 1.16375i | −0.305479 | − | 0.952199i | \(-0.598817\pi\) |
0.977368 | − | 0.211547i | \(-0.0678500\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.75868e9i | − | 1.63860i | −0.573368 | − | 0.819298i | \(-0.694364\pi\) | ||
0.573368 | − | 0.819298i | \(-0.305636\pi\) | |||||||
\(182\) | −6.46085e7 | − | 5.25366e7i | −0.0588849 | − | 0.0478824i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.61449e8 | − | 6.26047e8i | −0.315337 | − | 0.546180i | ||||
\(185\) | 7.05354e8 | + | 4.07237e8i | 0.602172 | + | 0.347664i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00786e8 | − | 4.62334e8i | 0.654862 | − | 0.378085i | ||||
\(188\) | − | 1.02319e9i | − | 0.819081i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.61465e8 | 0.430832 | ||||||||
\(191\) | −1.03184e9 | − | 1.78720e9i | −0.775316 | − | 1.34289i | −0.934617 | − | 0.355656i | \(-0.884257\pi\) |
0.159301 | − | 0.987230i | \(-0.449076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.13097e8 | − | 8.88711e8i | 0.369803 | − | 0.640518i | −0.619732 | − | 0.784814i | \(-0.712759\pi\) |
0.989535 | + | 0.144296i | \(0.0460918\pi\) | |||||||
\(194\) | 2.85276e8 | − | 1.64704e8i | 0.201400 | − | 0.116278i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.50484e8 | − | 7.22387e8i | −0.101968 | − | 0.489492i | ||||
\(197\) | 1.22831e9 | 0.815536 | 0.407768 | − | 0.913086i | \(-0.366307\pi\) | ||||
0.407768 | + | 0.913086i | \(0.366307\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.14905e9 | + | 1.24076e9i | 1.37036 | + | 0.791178i | 0.990973 | − | 0.134060i | \(-0.0428015\pi\) |
0.379387 | + | 0.925238i | \(0.376135\pi\) | |||||||
\(200\) | −2.72396e8 | + | 4.71805e8i | −0.170248 | + | 0.294878i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.10964e8i | 0.246830i | ||||||||
\(203\) | 7.55992e7 | + | 1.98145e8i | 0.0445178 | + | 0.116680i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.22948e8 | + | 1.07898e9i | 0.352725 | + | 0.610937i | ||||
\(206\) | −1.60375e9 | − | 9.25928e8i | −0.890572 | − | 0.514172i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.34967e7 | − | 2.51128e7i | 0.0232382 | − | 0.0134166i | ||||
\(209\) | 7.27052e8i | 0.381049i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.39729e9 | −1.71397 | −0.856984 | − | 0.515343i | \(-0.827665\pi\) | ||||
−0.856984 | + | 0.515343i | \(0.827665\pi\) | |||||||
\(212\) | −1.33438e8 | − | 2.31121e8i | −0.0660594 | − | 0.114418i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.13293e9 | + | 1.96229e9i | −0.540190 | + | 0.935637i | ||||
\(215\) | 2.24064e9 | − | 1.29363e9i | 1.04862 | − | 0.605421i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.20429e8 | + | 1.37367e9i | −0.0994100 | + | 0.619504i | ||||
\(218\) | −1.68629e9 | −0.746633 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.24533e9 | − | 7.18990e8i | −0.531610 | − | 0.306925i | ||||
\(221\) | 1.10476e8 | − | 1.91349e8i | 0.0463124 | − | 0.0802154i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.09206e8i | 0.0845971i | 0.999105 | + | 0.0422986i | \(0.0134681\pi\) | ||||
−0.999105 | + | 0.0422986i | \(0.986532\pi\) | |||||||
\(224\) | 4.39437e8 | + | 7.05151e7i | 0.174544 | + | 0.0280085i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.13492e9 | + | 1.96574e9i | 0.435042 | + | 0.753515i | ||||
\(227\) | −1.09121e9 | − | 6.30012e8i | −0.410966 | − | 0.237271i | 0.280239 | − | 0.959930i | \(-0.409586\pi\) |
−0.691205 | + | 0.722659i | \(0.742920\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.99386e9 | − | 1.72850e9i | 1.08865 | − | 0.628534i | 0.155435 | − | 0.987846i | \(-0.450322\pi\) |
0.933217 | + | 0.359312i | \(0.116989\pi\) | |||||||
\(230\) | 4.94554e9i | 1.76727i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.27913e8 | −0.0441534 | ||||||||
\(233\) | 9.17713e8 | + | 1.58953e9i | 0.311375 | + | 0.539316i | 0.978660 | − | 0.205485i | \(-0.0658773\pi\) |
−0.667286 | + | 0.744802i | \(0.732544\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.49998e9 | + | 6.06215e9i | −1.14761 | + | 1.98772i | ||||
\(236\) | 9.73023e8 | − | 5.61775e8i | 0.313672 | − | 0.181098i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.82927e9 | − | 6.97930e8i | 0.570124 | − | 0.217523i | ||||
\(239\) | −2.30067e9 | −0.705120 | −0.352560 | − | 0.935789i | \(-0.614689\pi\) | ||||
−0.352560 | + | 0.935789i | \(0.614689\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.26558e9 | − | 7.30684e8i | −0.375165 | − | 0.216602i | 0.300548 | − | 0.953767i | \(-0.402831\pi\) |
−0.675713 | + | 0.737165i | \(0.736164\pi\) | |||||||
\(242\) | −2.81563e8 | + | 4.87681e8i | −0.0820945 | + | 0.142192i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 1.86187e9i | − | 0.525279i | ||||||
\(245\) | −1.57945e9 | + | 4.79470e9i | −0.438371 | + | 1.33075i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.68652e7 | + | 1.50455e8i | 0.0233377 | + | 0.0404221i | ||||
\(248\) | −7.26703e8 | − | 4.19562e8i | −0.192110 | − | 0.110915i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.23782e8 | + | 7.14656e7i | −0.0316882 | + | 0.0182952i | ||||
\(251\) | 1.53360e9i | 0.386381i | 0.981161 | + | 0.193191i | \(0.0618836\pi\) | ||||
−0.981161 | + | 0.193191i | \(0.938116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.40408e9 | −1.56306 | ||||||||
\(254\) | 4.78830e7 | + | 8.29357e7i | 0.0115039 | + | 0.0199254i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.34218e8 | + | 2.32472e8i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2.50705e9 | − | 1.44744e9i | 0.574685 | − | 0.331795i | −0.184333 | − | 0.982864i | \(-0.559013\pi\) |
0.759018 | + | 0.651069i | \(0.225679\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.40890e9 | + | 1.73264e9i | −0.313099 | + | 0.385043i | ||||
\(260\) | −3.43608e8 | −0.0751917 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.41632e9 | + | 1.39506e9i | 0.512802 | + | 0.296066i | ||||
\(263\) | −2.71973e8 | + | 4.71071e8i | −0.0568464 | + | 0.0984609i | −0.893048 | − | 0.449961i | \(-0.851438\pi\) |
0.836202 | + | 0.548422i | \(0.184771\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.82577e9i | 0.370222i | ||||||||
\(266\) | −2.43912e8 | + | 1.52001e9i | −0.0487198 | + | 0.303613i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.03347e8 | + | 1.56464e9i | 0.175112 | + | 0.303303i | ||||
\(269\) | 6.55960e8 | + | 3.78719e8i | 0.125276 | + | 0.0723282i | 0.561328 | − | 0.827593i | \(-0.310290\pi\) |
−0.436052 | + | 0.899921i | \(0.643624\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.65727e9 | + | 1.53417e9i | −0.492672 | + | 0.284444i | −0.725682 | − | 0.688030i | \(-0.758476\pi\) |
0.233010 | + | 0.972474i | \(0.425142\pi\) | |||||||
\(272\) | 1.18089e9i | 0.215742i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.75163e9 | 0.843025 | ||||||||
\(275\) | 2.41314e9 | + | 4.17967e9i | 0.421940 | + | 0.730822i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.87053e9 | − | 4.97190e9i | 0.487576 | − | 0.844506i | −0.512322 | − | 0.858793i | \(-0.671215\pi\) |
0.999898 | + | 0.0142870i | \(0.00454786\pi\) | |||||||
\(278\) | 6.28448e9 | − | 3.62835e9i | 1.05218 | − | 0.607477i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.36234e9 | − | 1.92094e9i | −0.384335 | − | 0.312523i | ||||
\(281\) | −1.97804e9 | −0.317256 | −0.158628 | − | 0.987338i | \(-0.550707\pi\) | ||||
−0.158628 | + | 0.987338i | \(0.550707\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.52235e9 | + | 3.18833e9i | 0.860951 | + | 0.497070i | 0.864331 | − | 0.502924i | \(-0.167742\pi\) |
−0.00337979 | + | 0.999994i | \(0.501076\pi\) | |||||||
\(284\) | −2.14106e9 | + | 3.70843e9i | −0.329121 | + | 0.570055i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 4.44945e8i | − | 0.0665031i | ||||||
\(287\) | −3.19165e9 | + | 1.21773e9i | −0.470422 | + | 0.179483i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.90405e8 | − | 1.54223e9i | −0.127643 | − | 0.221084i | ||||
\(290\) | 7.57851e8 | + | 4.37546e8i | 0.107150 | + | 0.0618631i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.43443e8 | + | 8.28169e7i | −0.0197309 | + | 0.0113917i | ||||
\(293\) | − | 7.38690e9i | − | 1.00229i | −0.865364 | − | 0.501143i | \(-0.832913\pi\) | ||
0.865364 | − | 0.501143i | \(-0.167087\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.68653e9 | −1.01494 | ||||||||
\(296\) | −6.73464e8 | − | 1.16647e9i | −0.0877298 | − | 0.151953i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.31220e9 | + | 2.27280e9i | −0.166393 | + | 0.288201i | ||||
\(299\) | −1.32525e9 | + | 7.65134e8i | −0.165811 | + | 0.0957310i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.52878e9 | + | 6.62789e9i | 0.308066 | + | 0.807438i | ||||
\(302\) | 6.40866e9 | 0.770441 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.04120e8 | − | 4.64259e8i | −0.0941513 | − | 0.0543583i | ||||
\(305\) | −6.36879e9 | + | 1.10311e10i | −0.735966 | + | 1.27473i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.19092e9i | 0.246645i | 0.992367 | + | 0.123322i | \(0.0393549\pi\) | ||||
−0.992367 | + | 0.123322i | \(0.960645\pi\) | |||||||
\(308\) | 2.48746e9 | − | 3.05903e9i | 0.276410 | − | 0.339924i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.87035e9 | + | 4.97158e9i | 0.310805 | + | 0.538329i | ||||
\(311\) | −7.20343e9 | − | 4.15890e9i | −0.770013 | − | 0.444567i | 0.0628665 | − | 0.998022i | \(-0.479976\pi\) |
−0.832879 | + | 0.553455i | \(0.813309\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.36210e8 | − | 4.25051e8i | 0.0767051 | − | 0.0442857i | −0.461157 | − | 0.887319i | \(-0.652565\pi\) |
0.537862 | + | 0.843033i | \(0.319232\pi\) | |||||||
\(314\) | − | 9.12208e9i | − | 0.938373i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.33811e9 | −0.435063 | ||||||||
\(317\) | 2.14375e8 | + | 3.71309e8i | 0.0212294 | + | 0.0367704i | 0.876445 | − | 0.481502i | \(-0.159909\pi\) |
−0.855216 | + | 0.518272i | \(0.826575\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.66586e8 | + | 9.81356e8i | −0.0547146 | + | 0.0947685i | ||||
\(320\) | 1.59041e9 | − | 9.18222e8i | 0.151673 | − | 0.0875684i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.33887e10 | − | 2.14844e9i | −1.24542 | − | 0.199848i | ||||
\(323\) | −4.08471e9 | −0.375276 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.98741e8 | + | 5.76623e8i | 0.0895199 | + | 0.0516843i | ||||
\(326\) | 2.27682e8 | − | 3.94357e8i | 0.0201585 | − | 0.0349155i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 2.06039e9i | − | 0.178014i | ||||||
\(329\) | −1.48911e10 | − | 1.21087e10i | −1.27099 | − | 1.03351i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.98245e9 | − | 6.89781e9i | −0.331771 | − | 0.574645i | 0.651088 | − | 0.759002i | \(-0.274313\pi\) |
−0.982859 | + | 0.184358i | \(0.940980\pi\) | |||||||
\(332\) | −8.48908e8 | − | 4.90117e8i | −0.0698728 | − | 0.0403411i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.54424e7 | − | 1.46892e7i | 0.00204443 | − | 0.00118035i | ||||
\(335\) | − | 1.23601e10i | − | 0.981393i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.30470e10 | 1.01156 | 0.505779 | − | 0.862663i | \(-0.331205\pi\) | ||||
0.505779 | + | 0.862663i | \(0.331205\pi\) | |||||||
\(338\) | 4.56131e9 | + | 7.90042e9i | 0.349480 | + | 0.605318i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.03941e9 | − | 6.99647e9i | 0.302275 | − | 0.523556i | ||||
\(341\) | −6.43780e9 | + | 3.71687e9i | −0.476124 | + | 0.274890i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.22942e10 | − | 6.35884e9i | −0.888224 | − | 0.459411i | ||||
\(344\) | −4.27867e9 | −0.305545 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.19292e9 | + | 1.26608e9i | 0.153010 | + | 0.0883402i | ||||
\(347\) | 1.30853e10 | − | 2.26643e10i | 0.902535 | − | 1.56324i | 0.0783432 | − | 0.996926i | \(-0.475037\pi\) |
0.824192 | − | 0.566310i | \(-0.191630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 7.96331e9i | − | 0.536775i | −0.963311 | − | 0.268387i | \(-0.913509\pi\) | ||
0.963311 | − | 0.268387i | \(-0.0864907\pi\) | |||||||
\(350\) | 3.64282e9 | + | 9.54779e9i | 0.242754 | + | 0.636254i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.18902e9 | + | 2.05945e9i | 0.0774497 | + | 0.134147i | ||||
\(353\) | −2.48989e9 | − | 1.43754e9i | −0.160354 | − | 0.0925806i | 0.417675 | − | 0.908596i | \(-0.362845\pi\) |
−0.578030 | + | 0.816016i | \(0.696178\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.53704e10 | − | 1.46476e10i | 1.59740 | − | 0.922261i | ||||
\(356\) | − | 1.30426e10i | − | 0.812015i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.56079e10 | 0.950194 | ||||||||
\(359\) | 1.24261e10 | + | 2.15226e10i | 0.748094 | + | 1.29574i | 0.948735 | + | 0.316072i | \(0.102364\pi\) |
−0.200641 | + | 0.979665i | \(0.564302\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.88591e9 | + | 1.19267e10i | −0.405446 | + | 0.702252i | ||||
\(362\) | 1.72314e10 | − | 9.94858e9i | 1.00343 | − | 0.579331i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.49270e8 | − | 9.30223e8i | 0.00850290 | − | 0.0529885i | ||||
\(365\) | 1.13315e9 | 0.0638432 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.24815e8 | + | 1.29797e8i | 0.0123925 | + | 0.00715484i | 0.506183 | − | 0.862426i | \(-0.331056\pi\) |
−0.493791 | + | 0.869581i | \(0.664389\pi\) | |||||||
\(368\) | 4.08932e9 | − | 7.08292e9i | 0.222977 | − | 0.386208i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.21471e9i | 0.491671i | ||||||||
\(371\) | −4.94276e9 | − | 7.93150e8i | −0.260900 | − | 0.0418658i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.72152e10 | − | 2.98176e10i | −0.889359 | − | 1.54042i | −0.840634 | − | 0.541603i | \(-0.817818\pi\) |
−0.0487248 | − | 0.998812i | \(-0.515516\pi\) | |||||||
\(374\) | 9.05986e9 | + | 5.23071e9i | 0.463058 | + | 0.267346i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.00252e10 | − | 5.78806e9i | 0.501583 | − | 0.289589i | ||||
\(377\) | 2.70774e8i | 0.0134042i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.06189e10 | 1.48400 | 0.741998 | − | 0.670402i | \(-0.233878\pi\) | ||||
0.741998 | + | 0.670402i | \(0.233878\pi\) | |||||||
\(380\) | 3.17613e9 | + | 5.50121e9i | 0.152322 | + | 0.263830i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.16739e10 | − | 2.02198e10i | 0.548231 | − | 0.949564i | ||||
\(383\) | −1.73217e10 | + | 1.00007e10i | −0.804999 | + | 0.464766i | −0.845216 | − | 0.534425i | \(-0.820528\pi\) |
0.0402172 | + | 0.999191i | \(0.487195\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.52014e10 | + | 9.61522e9i | −1.14705 | + | 0.437640i | ||||
\(386\) | 1.16101e10 | 0.522980 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.22753e9 | + | 1.86342e9i | 0.142411 | + | 0.0822211i | ||||
\(389\) | −6.06521e9 | + | 1.05052e10i | −0.264879 | + | 0.458784i | −0.967532 | − | 0.252749i | \(-0.918665\pi\) |
0.702653 | + | 0.711533i | \(0.251999\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.59793e10i | − | 1.53938i | ||||||
\(392\) | 6.22665e9 | − | 5.56087e9i | 0.263700 | − | 0.235504i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.94837e9 | + | 1.20349e10i | 0.288335 | + | 0.499412i | ||||
\(395\) | 2.57021e10 | + | 1.48391e10i | 1.05580 | + | 0.609565i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.98646e9 | + | 3.45628e9i | −0.240995 | + | 0.139139i | −0.615634 | − | 0.788032i | \(-0.711100\pi\) |
0.374639 | + | 0.927171i | \(0.377767\pi\) | |||||||
\(398\) | 2.80751e10i | 1.11889i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.16363e9 | −0.240767 | ||||||||
\(401\) | 1.26426e10 | + | 2.18976e10i | 0.488944 | + | 0.846875i | 0.999919 | − | 0.0127200i | \(-0.00404901\pi\) |
−0.510975 | + | 0.859595i | \(0.670716\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.88152e8 | + | 1.53832e9i | −0.0336719 | + | 0.0583214i | ||||
\(404\) | −4.02660e9 | + | 2.32476e9i | −0.151152 | + | 0.0872676i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.51376e9 | + | 1.86159e9i | −0.0557125 | + | 0.0685142i | ||||
\(407\) | −1.19323e10 | −0.434857 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.79049e9 | + | 3.92049e9i | 0.242666 | + | 0.140103i | 0.616401 | − | 0.787432i | \(-0.288590\pi\) |
−0.373736 | + | 0.927535i | \(0.621923\pi\) | |||||||
\(410\) | −7.04785e9 | + | 1.22072e10i | −0.249414 | + | 0.431998i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 2.09514e10i | − | 0.727149i | ||||||
\(413\) | 3.33918e9 | − | 2.08091e10i | 0.114773 | − | 0.715244i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.35303e9 | + | 5.80762e9i | 0.113043 | + | 0.195797i | ||||
\(416\) | 4.92109e8 | + | 2.84119e8i | 0.0164319 | + | 0.00948696i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.12363e9 | + | 4.11283e9i | −0.233344 | + | 0.134721i | ||||
\(419\) | − | 4.39321e10i | − | 1.42536i | −0.701488 | − | 0.712682i | \(-0.747480\pi\) | ||
0.701488 | − | 0.712682i | \(-0.252520\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.72195e9 | 0.182144 | 0.0910721 | − | 0.995844i | \(-0.470971\pi\) | ||||
0.0910721 | + | 0.995844i | \(0.470971\pi\) | |||||||
\(422\) | −1.92180e10 | − | 3.32865e10i | −0.605979 | − | 1.04959i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.50967e9 | − | 2.61483e9i | 0.0467111 | − | 0.0809059i | ||||
\(425\) | −2.34821e10 | + | 1.35574e10i | −0.719751 | + | 0.415548i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.70968e10 | − | 2.20339e10i | −0.815093 | − | 0.662795i | ||||
\(428\) | −2.56352e10 | −0.763945 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.53499e10 | + | 1.46358e10i | 0.741486 | + | 0.428097i | ||||
\(431\) | 6.82833e9 | − | 1.18270e10i | 0.197882 | − | 0.342741i | −0.749960 | − | 0.661483i | \(-0.769927\pi\) |
0.947841 | + | 0.318743i | \(0.103261\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.05551e10i | 1.43818i | 0.694917 | + | 0.719090i | \(0.255441\pi\) | ||||
−0.694917 | + | 0.719090i | \(0.744559\pi\) | |||||||
\(434\) | −1.47061e10 | + | 5.61091e9i | −0.414514 | + | 0.158152i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.53912e9 | − | 1.65222e10i | −0.263975 | − | 0.457217i | ||||
\(437\) | 2.44998e10 | + | 1.41450e10i | 0.671795 | + | 0.387861i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.81030e10 | − | 2.19988e10i | 1.02589 | − | 0.592298i | 0.110086 | − | 0.993922i | \(-0.464887\pi\) |
0.915805 | + | 0.401624i | \(0.131554\pi\) | |||||||
\(440\) | − | 1.62689e10i | − | 0.434057i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.49978e9 | 0.0654956 | ||||||||
\(443\) | 2.48510e9 | + | 4.30432e9i | 0.0645252 | + | 0.111761i | 0.896483 | − | 0.443078i | \(-0.146113\pi\) |
−0.831958 | + | 0.554839i | \(0.812780\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.46140e10 | + | 7.72738e10i | −1.13771 | + | 1.97057i | ||||
\(446\) | −2.04980e9 | + | 1.18345e9i | −0.0518049 | + | 0.0299096i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.79493e9 | + | 4.70448e9i | 0.0445589 | + | 0.116788i | ||||
\(449\) | 1.19199e10 | 0.293284 | 0.146642 | − | 0.989190i | \(-0.453154\pi\) | ||||
0.146642 | + | 0.989190i | \(0.453154\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.58074e10 | − | 9.12639e9i | −0.382079 | − | 0.220594i | ||||
\(452\) | −1.28401e10 | + | 2.22398e10i | −0.307621 | + | 0.532816i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 1.42555e10i | − | 0.335552i | ||||||
\(455\) | −4.06634e9 | + | 5.00072e9i | −0.0948765 | + | 0.116677i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.45068e10 | + | 4.24470e10i | 0.561852 | + | 0.973155i | 0.997335 | + | 0.0729587i | \(0.0232441\pi\) |
−0.435483 | + | 0.900197i | \(0.643423\pi\) | |||||||
\(458\) | 3.38716e10 | + | 1.95558e10i | 0.769794 | + | 0.444441i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.84562e10 | + | 2.79762e10i | −1.08223 | + | 0.624824i | ||||
\(461\) | − | 5.59070e10i | − | 1.23784i | −0.785456 | − | 0.618918i | \(-0.787571\pi\) | ||
0.785456 | − | 0.618918i | \(-0.212429\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.00933e10 | 0.219638 | 0.109819 | − | 0.993952i | \(-0.464973\pi\) | ||||
0.109819 | + | 0.993952i | \(0.464973\pi\) | |||||||
\(464\) | −7.23587e8 | − | 1.25329e9i | −0.0156106 | − | 0.0270383i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.03827e10 | + | 1.79834e10i | −0.220175 | + | 0.381354i | ||||
\(467\) | 7.53687e10 | − | 4.35142e10i | 1.58461 | − | 0.914878i | 0.590442 | − | 0.807080i | \(-0.298954\pi\) |
0.994173 | − | 0.107797i | \(-0.0343798\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.34616e10 | + | 5.36948e9i | 0.691600 | + | 0.110979i | ||||
\(470\) | −7.91956e10 | −1.62297 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.10085e10 | + | 6.35576e9i | 0.221799 | + | 0.128056i | ||||
\(473\) | −1.89522e10 | + | 3.28261e10i | −0.378629 | + | 0.655806i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.13200e10i | − | 0.418806i | ||||||
\(476\) | 1.71862e10 | + | 1.39750e10i | 0.334774 | + | 0.272222i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.30146e10 | − | 2.25419e10i | −0.249298 | − | 0.431796i | ||||
\(479\) | −5.19458e10 | − | 2.99909e10i | −0.986752 | − | 0.569701i | −0.0824501 | − | 0.996595i | \(-0.526275\pi\) |
−0.904302 | + | 0.426894i | \(0.859608\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.46925e9 | + | 1.42562e9i | −0.0461302 | + | 0.0266333i | ||||
\(482\) | − | 1.65335e10i | − | 0.306321i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.37104e9 | −0.116099 | ||||||||
\(485\) | −1.27482e10 | − | 2.20805e10i | −0.230399 | − | 0.399063i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.90910e10 | + | 5.03871e10i | −0.517182 | + | 0.895785i | 0.482619 | + | 0.875830i | \(0.339686\pi\) |
−0.999801 | + | 0.0199548i | \(0.993648\pi\) | |||||||
\(488\) | 1.82425e10 | − | 1.05323e10i | 0.321666 | − | 0.185714i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.59130e10 | + | 1.16475e10i | −0.969903 | + | 0.202045i | ||||
\(491\) | 7.31652e10 | 1.25886 | 0.629432 | − | 0.777056i | \(-0.283288\pi\) | ||||
0.629432 | + | 0.777056i | \(0.283288\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.51343e9 | − | 3.18318e9i | −0.0933328 | − | 0.0538857i | ||||
\(494\) | −9.82768e8 | + | 1.70220e9i | −0.0165022 | + | 0.0285827i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 9.49361e9i | − | 0.156857i | ||||||
\(497\) | 2.86329e10 | + | 7.50466e10i | 0.469289 | + | 1.23000i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.13183e10 | − | 5.42448e10i | −0.505121 | − | 0.874895i | −0.999982 | − | 0.00592344i | \(-0.998115\pi\) |
0.494861 | − | 0.868972i | \(-0.335219\pi\) | |||||||
\(500\) | −1.40043e9 | − | 8.08541e8i | −0.0224069 | − | 0.0129367i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.50261e10 | + | 8.67533e9i | −0.236609 | + | 0.136606i | ||||
\(503\) | 1.86966e10i | 0.292072i | 0.989279 | + | 0.146036i | \(0.0466515\pi\) | ||||
−0.989279 | + | 0.146036i | \(0.953348\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.18087e10 | 0.489081 | ||||||||
\(506\) | −3.62270e10 | − | 6.27469e10i | −0.552624 | − | 0.957173i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.41734e8 | + | 9.38311e8i | −0.00813451 | + | 0.0140894i | ||||
\(509\) | −6.80948e10 | + | 3.93145e10i | −1.01448 | + | 0.585709i | −0.912500 | − | 0.409078i | \(-0.865851\pi\) |
−0.101978 | + | 0.994787i | \(0.532517\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.92262e8 | + | 3.06768e9i | −0.00721959 | + | 0.0449911i | ||||
\(512\) | −3.03700e9 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.83640e10 | + | 1.63760e10i | 0.406364 | + | 0.234614i | ||||
\(515\) | −7.16671e10 | + | 1.24131e11i | −1.01880 | + | 1.76462i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.02552e11i | − | 1.43543i | ||||||
\(518\) | −2.49463e10 | − | 4.00305e9i | −0.346487 | − | 0.0555997i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.94374e9 | − | 3.36666e9i | −0.0265843 | − | 0.0460453i | ||||
\(521\) | 2.52432e10 | + | 1.45742e10i | 0.342605 | + | 0.197803i | 0.661423 | − | 0.750013i | \(-0.269953\pi\) |
−0.318818 | + | 0.947816i | \(0.603286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.31017e9 | + | 3.06583e9i | −0.0709744 | + | 0.0409771i | −0.535067 | − | 0.844809i | \(-0.679714\pi\) |
0.464093 | + | 0.885787i | \(0.346380\pi\) | |||||||
\(524\) | 3.15667e10i | 0.418701i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.15405e9 | −0.0803930 | ||||||||
\(527\) | −2.08820e10 | − | 3.61687e10i | −0.270726 | − | 0.468911i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.54374e10 | + | 1.47982e11i | −1.09100 | + | 1.88967i | ||||
\(530\) | −1.78888e10 | + | 1.03281e10i | −0.226714 | + | 0.130893i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.62728e10 | + | 6.20864e9i | −0.203149 | + | 0.0775087i | ||||
\(533\) | −4.36154e9 | −0.0540419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.51882e11 | + | 8.76889e10i | 1.85392 | + | 1.07036i | ||||
\(536\) | −1.02202e10 | + | 1.77019e10i | −0.123823 | + | 0.214467i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.56942e9i | 0.102287i | ||||||||
\(539\) | −1.50826e10 | − | 7.24028e10i | −0.178698 | − | 0.857828i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.25770e10 | − | 1.08386e11i | −0.730509 | − | 1.26528i | −0.956666 | − | 0.291188i | \(-0.905950\pi\) |
0.226157 | − | 0.974091i | \(-0.427384\pi\) | |||||||
\(542\) | −3.00635e10 | − | 1.73572e10i | −0.348372 | − | 0.201132i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.15703e10 | + | 6.68014e9i | −0.132115 | + | 0.0762764i | ||||
\(545\) | 1.30520e11i | 1.47941i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.08478e9 | −0.0903064 | −0.0451532 | − | 0.998980i | \(-0.514378\pi\) | ||||
−0.0451532 | + | 0.998980i | \(0.514378\pi\) | |||||||
\(548\) | 2.68793e10 | + | 4.65563e10i | 0.298054 | + | 0.516245i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.73015e10 | + | 4.72876e10i | −0.298357 | + | 0.516769i | ||||
\(551\) | 4.33513e9 | − | 2.50289e9i | 0.0470322 | − | 0.0271541i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.13383e10 | + | 6.31350e10i | −0.548961 | + | 0.675102i | ||||
\(554\) | 6.49526e10 | 0.689537 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.11008e10 | + | 4.10501e10i | 0.744004 | + | 0.429551i | ||||
\(557\) | −2.26100e10 | + | 3.91616e10i | −0.234898 | + | 0.406855i | −0.959243 | − | 0.282583i | \(-0.908809\pi\) |
0.724345 | + | 0.689438i | \(0.242142\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.05731e9i | 0.0927582i | ||||||||
\(560\) | 5.45789e9 | − | 3.40125e10i | 0.0554974 | − | 0.345849i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.11895e10 | − | 1.93807e10i | −0.112167 | − | 0.194279i | ||||
\(563\) | 1.60535e11 | + | 9.26851e10i | 1.59785 | + | 0.922521i | 0.991900 | + | 0.127021i | \(0.0405414\pi\) |
0.605953 | + | 0.795500i | \(0.292792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.52149e11 | − | 8.78431e10i | 1.49305 | − | 0.862013i | ||||
\(566\) | 7.21437e10i | 0.702963i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.84467e10 | −0.465448 | ||||||||
\(569\) | −1.00436e11 | − | 1.73960e11i | −0.958164 | − | 1.65959i | −0.726957 | − | 0.686683i | \(-0.759066\pi\) |
−0.231207 | − | 0.972905i | \(-0.574267\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.50052e10 | − | 2.59897e10i | 0.141155 | − | 0.244488i | −0.786777 | − | 0.617238i | \(-0.788252\pi\) |
0.927932 | + | 0.372750i | \(0.121585\pi\) | |||||||
\(572\) | 4.35955e9 | − | 2.51699e9i | 0.0407247 | − | 0.0235124i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.99860e10 | − | 2.43831e10i | −0.276230 | − | 0.224617i | ||||
\(575\) | 1.87792e11 | 1.71794 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.61972e10 | + | 4.39925e10i | 0.687442 | + | 0.396895i | 0.802653 | − | 0.596446i | \(-0.203421\pi\) |
−0.115211 | + | 0.993341i | \(0.536754\pi\) | |||||||
\(578\) | 1.00738e10 | − | 1.74483e10i | 0.0902570 | − | 0.156330i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.90053e9i | 0.0874876i | ||||||||
\(581\) | −1.71791e10 | + | 6.55445e9i | −0.150764 | + | 0.0575217i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.33741e10 | − | 2.31646e10i | −0.115768 | − | 0.200516i | ||||
\(584\) | −1.62287e9 | − | 9.36966e8i | −0.0139519 | − | 0.00805513i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.23766e10 | − | 4.17866e10i | 0.613773 | − | 0.354362i | ||||
\(587\) | − | 4.35775e10i | − | 0.367037i | −0.983016 | − | 0.183519i | \(-0.941251\pi\) | ||
0.983016 | − | 0.183519i | \(-0.0587487\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.28384e10 | 0.272848 | ||||||||
\(590\) | −4.34816e10 | − | 7.53123e10i | −0.358837 | − | 0.621524i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.61937e9 | − | 1.31971e10i | 0.0620344 | − | 0.107447i | ||||
\(593\) | 1.49827e11 | − | 8.65027e10i | 1.21163 | − | 0.699537i | 0.248519 | − | 0.968627i | \(-0.420056\pi\) |
0.963115 | + | 0.269090i | \(0.0867227\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.40200e10 | − | 1.41586e11i | −0.431010 | − | 1.12967i | ||||
\(596\) | −2.96917e10 | −0.235315 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.49935e10 | − | 8.65650e9i | −0.117246 | − | 0.0676920i | ||||
\(599\) | 7.79310e10 | − | 1.34981e11i | 0.605345 | − | 1.04849i | −0.386652 | − | 0.922226i | \(-0.626368\pi\) |
0.991997 | − | 0.126263i | \(-0.0402983\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.42951e11i | − | 1.09569i | −0.836580 | − | 0.547845i | \(-0.815448\pi\) | ||
0.836580 | − | 0.547845i | \(-0.184552\pi\) | |||||||
\(602\) | −5.06349e10 | + | 6.22698e10i | −0.385535 | + | 0.474124i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.62529e10 | + | 6.27918e10i | 0.272392 | + | 0.471797i | ||||
\(605\) | 3.77467e10 | + | 2.17931e10i | 0.281746 | + | 0.162666i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.53187e11 | + | 8.84427e10i | −1.12841 | + | 0.651489i | −0.943535 | − | 0.331272i | \(-0.892522\pi\) |
−0.184877 | + | 0.982762i | \(0.559189\pi\) | |||||||
\(608\) | − | 1.05050e10i | − | 0.0768742i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.44109e11 | −1.04081 | ||||||||
\(611\) | −1.22525e10 | − | 2.12219e10i | −0.0879142 | − | 0.152272i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.87312e10 | + | 1.19046e11i | −0.486757 | + | 0.843088i | −0.999884 | − | 0.0152246i | \(-0.995154\pi\) |
0.513127 | + | 0.858313i | \(0.328487\pi\) | |||||||
\(614\) | −2.14665e10 | + | 1.23937e10i | −0.151039 | + | 0.0872022i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.40435e10 | + | 7.06753e9i | 0.305885 | + | 0.0490845i | ||||
\(617\) | 1.18079e10 | 0.0814761 | 0.0407381 | − | 0.999170i | \(-0.487029\pi\) | ||||
0.0407381 | + | 0.999170i | \(0.487029\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.06013e11 | + | 6.12069e10i | 0.722102 | + | 0.416906i | 0.815526 | − | 0.578721i | \(-0.196448\pi\) |
−0.0934240 | + | 0.995626i | \(0.529781\pi\) | |||||||
\(620\) | −3.24743e10 | + | 5.62471e10i | −0.219772 | + | 0.380656i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 9.41052e10i | − | 0.628713i | ||||||
\(623\) | −1.89816e11 | − | 1.54349e11i | −1.26003 | − | 1.02460i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.90076e10 | + | 1.36845e11i | 0.517784 | + | 0.896829i | ||||
\(626\) | 8.32926e9 | + | 4.80890e9i | 0.0542387 | + | 0.0313147i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.93778e10 | − | 5.16023e10i | 0.574634 | − | 0.331765i | ||||
\(629\) | − | 6.70378e10i | − | 0.428270i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.31617e10 | 0.398416 | 0.199208 | − | 0.979957i | \(-0.436163\pi\) | ||||
0.199208 | + | 0.979957i | \(0.436163\pi\) | |||||||
\(632\) | −2.45401e10 | − | 4.25047e10i | −0.153818 | − | 0.266421i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.42538e9 | + | 4.20088e9i | −0.0150114 | + | 0.0260006i | ||||
\(635\) | 6.41925e9 | − | 3.70616e9i | 0.0394811 | − | 0.0227944i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.17716e10 | − | 1.31809e10i | −0.0714950 | − | 0.0800548i | ||||
\(638\) | −1.28204e10 | −0.0773782 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.79934e10 | + | 1.03885e10i | 0.107249 | + | 0.0619202i | ||||
\(641\) | −1.41683e11 | + | 2.45402e11i | −0.839239 | + | 1.45360i | 0.0512925 | + | 0.998684i | \(0.483666\pi\) |
−0.890532 | + | 0.454921i | \(0.849667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.63523e11i | − | 0.956608i | −0.878194 | − | 0.478304i | \(-0.841252\pi\) | ||
0.878194 | − | 0.478304i | \(-0.158748\pi\) | |||||||
\(644\) | −5.46875e10 | − | 1.43335e11i | −0.317940 | − | 0.833316i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.31066e10 | − | 4.00218e10i | −0.132680 | − | 0.229809i | ||||
\(647\) | 7.92369e10 | + | 4.57474e10i | 0.452179 | + | 0.261066i | 0.708750 | − | 0.705460i | \(-0.249259\pi\) |
−0.256571 | + | 0.966525i | \(0.582593\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.75233e10 | − | 5.63051e10i | 0.549705 | − | 0.317372i | ||||
\(650\) | 1.30475e10i | 0.0730927i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.15185e9 | 0.0285084 | ||||||||
\(653\) | 7.72477e10 | + | 1.33797e11i | 0.424847 | + | 0.735857i | 0.996406 | − | 0.0847040i | \(-0.0269945\pi\) |
−0.571559 | + | 0.820561i | \(0.693661\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.07978e11 | − | 1.87024e11i | 0.586640 | − | 1.01609i | ||||
\(656\) | 2.01876e10 | − | 1.16553e10i | 0.109011 | − | 0.0629374i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.44041e10 | − | 2.14400e11i | 0.183530 | − | 1.14372i | ||||
\(659\) | 6.38574e9 | 0.0338586 | 0.0169293 | − | 0.999857i | \(-0.494611\pi\) | ||||
0.0169293 | + | 0.999857i | \(0.494611\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.84299e11 | + | 1.06405e11i | 0.965423 | + | 0.557387i | 0.897838 | − | 0.440326i | \(-0.145137\pi\) |
0.0675854 | + | 0.997713i | \(0.478470\pi\) | |||||||
\(662\) | 4.50563e10 | − | 7.80398e10i | 0.234598 | − | 0.406335i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1.10901e10i | − | 0.0570509i | ||||||
\(665\) | 1.17649e11 | + | 1.88788e10i | 0.601593 | + | 0.0965358i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.20461e10 | + | 3.81850e10i | 0.111386 | + | 0.192926i | ||||
\(668\) | 2.87848e8 | + | 1.66189e8i | 0.00144563 | + | 0.000834636i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.21104e11 | − | 6.99193e10i | 0.600978 | − | 0.346975i | ||||
\(671\) | − | 1.86610e11i | − | 0.920544i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.32635e11 | −1.62147 | −0.810734 | − | 0.585415i | \(-0.800932\pi\) | ||||
−0.810734 | + | 0.585415i | \(0.800932\pi\) | |||||||
\(674\) | 7.38049e10 | + | 1.27834e11i | 0.357639 | + | 0.619450i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.16053e10 | + | 8.93830e10i | −0.247120 | + | 0.428024i | ||||
\(677\) | −3.35630e11 | + | 1.93776e11i | −1.59774 | + | 0.922456i | −0.605819 | + | 0.795603i | \(0.707154\pi\) |
−0.991922 | + | 0.126853i | \(0.959512\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.53148e10 | − | 2.49199e10i | 0.307279 | − | 0.117238i | ||||
\(680\) | 9.14015e10 | 0.427482 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.28354e10 | − | 4.20515e10i | −0.336670 | − | 0.194377i | ||||
\(683\) | 1.26032e11 | − | 2.18293e11i | 0.579157 | − | 1.00313i | −0.416419 | − | 0.909173i | \(-0.636715\pi\) |
0.995576 | − | 0.0939571i | \(-0.0299517\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 3.67778e11i | − | 1.67041i | ||||||
\(686\) | −7.24267e9 | − | 1.56429e11i | −0.0327041 | − | 0.706350i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.42038e10 | − | 4.19222e10i | −0.108026 | − | 0.187107i | ||||
\(689\) | −5.53522e9 | − | 3.19576e9i | −0.0245617 | − | 0.0141807i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.42724e11 | + | 1.40137e11i | −1.06463 | + | 0.614666i | −0.926710 | − | 0.375777i | \(-0.877376\pi\) |
−0.137923 | + | 0.990443i | \(0.544043\pi\) | |||||||
\(692\) | 2.86482e10i | 0.124932i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.96085e11 | 1.27638 | ||||||||
\(695\) | −2.80835e11 | − | 4.86421e11i | −1.20368 | − | 2.08484i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.12737e10 | − | 8.88086e10i | 0.217252 | − | 0.376291i | ||||
\(698\) | 7.80242e10 | − | 4.50473e10i | 0.328706 | − | 0.189778i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.29420e10 | + | 8.97027e10i | −0.303798 | + | 0.373606i | ||||
\(701\) | 1.30623e11 | 0.540939 | 0.270469 | − | 0.962729i | \(-0.412821\pi\) | ||||
0.270469 | + | 0.962729i | \(0.412821\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.56489e10 | + | 2.63554e10i | 0.186900 | + | 0.107907i | ||||
\(704\) | −1.34523e10 | + | 2.33000e10i | −0.0547652 | + | 0.0948561i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 3.25277e10i | − | 0.130929i | ||||||
\(707\) | −1.38183e10 | + | 8.61132e10i | −0.0553067 | + | 0.344661i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.43526e11 | − | 2.48595e11i | −0.567997 | − | 0.983800i | −0.996764 | − | 0.0803847i | \(-0.974385\pi\) |
0.428767 | − | 0.903415i | \(-0.358948\pi\) | |||||||
\(710\) | 2.87034e11 | + | 1.65719e11i | 1.12953 | + | 0.652137i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.27791e11 | − | 7.37800e10i | 0.497255 | − | 0.287090i | ||||
\(713\) | 2.89250e11i | 1.11922i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.44388e10 | −0.131772 | ||||||||
\(716\) | 8.82916e10 | + | 1.52926e11i | 0.335944 | + | 0.581873i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.40585e11 | + | 2.43500e11i | −0.528982 | + | 0.916224i | ||||
\(719\) | −3.30933e10 | + | 1.91064e10i | −0.123830 | + | 0.0714931i | −0.560635 | − | 0.828063i | \(-0.689443\pi\) |
0.436806 | + | 0.899556i | \(0.356110\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.04917e11 | − | 2.47944e11i | −1.12834 | − | 0.917513i | ||||
\(722\) | −1.55810e11 | −0.573387 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.94952e11 | + | 1.12555e11i | 0.709533 | + | 0.409649i | ||||
\(725\) | 1.66145e10 | − | 2.87772e10i | 0.0601361 | − | 0.104159i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.60138e11i | − | 0.573268i | −0.958040 | − | 0.286634i | \(-0.907464\pi\) | ||
0.958040 | − | 0.286634i | \(-0.0925364\pi\) | |||||||
\(728\) | 9.95869e9 | − | 3.79959e9i | 0.0354549 | − | 0.0135273i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.41005e9 | + | 1.11025e10i | 0.0225720 | + | 0.0390958i | ||||
\(731\) | −1.84423e11 | − | 1.06477e11i | −0.645871 | − | 0.372894i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.36694e11 | + | 1.36655e11i | −0.819920 | + | 0.473381i | −0.850389 | − | 0.526154i | \(-0.823633\pi\) |
0.0304686 | + | 0.999536i | \(0.490300\pi\) | |||||||
\(734\) | 2.93697e9i | 0.0101185i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.25308e10 | 0.315337 | ||||||||
\(737\) | 9.05399e10 | + | 1.56820e11i | 0.306881 | + | 0.531534i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.04395e11 | + | 3.54022e11i | −0.685317 | + | 1.18700i | 0.288020 | + | 0.957624i | \(0.407003\pi\) |
−0.973337 | + | 0.229380i | \(0.926330\pi\) | |||||||
\(740\) | −9.02854e10 | + | 5.21263e10i | −0.301086 | + | 0.173832i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.01892e10 | − | 5.29157e10i | −0.0666046 | − | 0.174570i | ||||
\(743\) | 3.69962e10 | 0.121395 | 0.0606977 | − | 0.998156i | \(-0.480667\pi\) | ||||
0.0606977 | + | 0.998156i | \(0.480667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.75915e11 | + | 1.01565e11i | 0.571056 | + | 0.329699i | ||||
\(746\) | 1.94768e11 | − | 3.37348e11i | 0.628872 | − | 1.08924i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.18358e11i | 0.378085i | ||||||||
\(749\) | −3.03374e11 | + | 3.73083e11i | −0.963941 | + | 1.18544i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.71650e11 | + | 2.97307e11i | 0.539616 | + | 0.934642i | 0.998925 | + | 0.0463654i | \(0.0147639\pi\) |
−0.459309 | + | 0.888277i | \(0.651903\pi\) | |||||||
\(752\) | 1.13422e11 | + | 6.54845e10i | 0.354673 | + | 0.204770i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.65303e9 | + | 1.53173e9i | −0.00820837 | + | 0.00473910i | ||||
\(755\) | − | 4.96032e11i | − | 1.52659i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.19344e11 | 0.972468 | 0.486234 | − | 0.873829i | \(-0.338370\pi\) | ||||
0.486234 | + | 0.873829i | \(0.338370\pi\) | |||||||
\(758\) | 1.73207e11 | + | 3.00003e11i | 0.524672 | + | 0.908759i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.59338e10 | + | 6.22391e10i | −0.107708 | + | 0.186556i | ||||
\(761\) | −3.31461e11 | + | 1.91369e11i | −0.988312 | + | 0.570602i | −0.904769 | − | 0.425902i | \(-0.859957\pi\) |
−0.0835424 | + | 0.996504i | \(0.526623\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.53346e11 | − | 5.67003e10i | −1.04256 | − | 0.167297i | ||||
\(764\) | 2.64151e11 | 0.775316 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.95973e11 | − | 1.13145e11i | −0.569220 | − | 0.328639i | ||||
\(767\) | 1.34542e10 | − | 2.33034e10i | 0.0388756 | − | 0.0673345i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.74904e11i | 1.92991i | 0.262417 | + | 0.964955i | \(0.415480\pi\) | ||||
−0.262417 | + | 0.964955i | \(0.584520\pi\) | |||||||
\(770\) | −2.36770e11 | − | 1.92530e11i | −0.673541 | − | 0.547691i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.56764e10 | + | 1.13755e11i | 0.184902 | + | 0.320259i | ||||
\(773\) | −1.92323e10 | − | 1.11038e10i | −0.0538658 | − | 0.0310994i | 0.472825 | − | 0.881156i | \(-0.343234\pi\) |
−0.526691 | + | 0.850057i | \(0.676568\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.88781e11 | − | 1.08993e11i | 0.523301 | − | 0.302128i | ||||
\(776\) | 4.21643e10i | 0.116278i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.37240e11 | −0.374595 | ||||||||
\(779\) | 4.03157e10 | + | 6.98288e10i | 0.109477 | + | 0.189620i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.14593e11 | + | 3.71685e11i | −0.576781 | + | 0.999013i | ||||
\(782\) | 3.52523e11 | − | 2.03529e11i | 0.942672 | − | 0.544252i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.97085e10 | + | 2.95514e10i | 0.237448 | + | 0.0782194i | ||||
\(785\) | −7.06052e11 | −1.85934 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.20770e10 | + | 5.31607e10i | 0.240023 | + | 0.138577i | 0.615187 | − | 0.788381i | \(-0.289080\pi\) |
−0.375165 | + | 0.926958i | \(0.622414\pi\) | |||||||
\(788\) | −7.86118e10 | + | 1.36160e11i | −0.203884 | + | 0.353137i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.35771e11i | 0.862055i | ||||||||
\(791\) | 1.71714e11 | + | 4.50061e11i | 0.438632 | + | 1.14965i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.22954e10 | − | 3.86168e10i | −0.0563797 | − | 0.0976524i | ||||
\(794\) | −6.77291e10 | − | 3.91034e10i | −0.170409 | − | 0.0983858i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.75079e11 | + | 1.58817e11i | −0.685180 | + | 0.395589i | ||||
\(797\) | − | 4.77766e10i | − | 0.118408i | −0.998246 | − | 0.0592041i | \(-0.981144\pi\) | ||
0.998246 | − | 0.0592041i | \(-0.0188563\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.76155e11 | 1.41368 | ||||||||
\(800\) | −3.48668e10 | − | 6.03910e10i | −0.0851239 | − | 0.147439i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.43035e11 | + | 2.47743e11i | −0.345735 | + | 0.598831i | ||||
\(803\) | −1.43769e10 | + | 8.30050e9i | −0.0345782 | + | 0.0199637i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.66290e11 | + | 1.03629e12i | −0.395989 | + | 2.46773i | ||||
\(806\) | −2.00966e10 | −0.0476192 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.55558e10 | − | 2.63017e10i | −0.106880 | − | 0.0617075i | ||||
\(809\) | −4.04920e11 | + | 7.01341e11i | −0.945311 | + | 1.63733i | −0.190183 | + | 0.981749i | \(0.560908\pi\) |
−0.755128 | + | 0.655578i | \(0.772425\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.75704e11i | − | 0.868484i | −0.900796 | − | 0.434242i | \(-0.857016\pi\) | ||
0.900796 | − | 0.434242i | \(-0.142984\pi\) | |||||||
\(812\) | −2.68029e10 | − | 4.30099e9i | −0.0616536 | − | 0.00989336i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.74993e10 | − | 1.16912e11i | −0.153745 | − | 0.266295i | ||||
\(815\) | −3.05233e10 | − | 1.76226e10i | −0.0691833 | − | 0.0399430i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.45009e11 | − | 8.37209e10i | 0.325467 | − | 0.187908i | ||||
\(818\) | 8.87106e10i | 0.198136i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.59475e11 | −0.352725 | ||||||||
\(821\) | 1.38321e11 | + | 2.39579e11i | 0.304450 | + | 0.527323i | 0.977139 | − | 0.212603i | \(-0.0681940\pi\) |
−0.672689 | + | 0.739926i | \(0.734861\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.99482e11 | − | 3.45513e11i | 0.434814 | − | 0.753121i | −0.562466 | − | 0.826820i | \(-0.690147\pi\) |
0.997280 | + | 0.0736996i | \(0.0234806\pi\) | |||||||
\(824\) | 2.05281e11 | − | 1.18519e11i | 0.445286 | − | 0.257086i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.22776e11 | − | 8.49971e10i | 0.478574 | − | 0.182593i | ||||
\(827\) | 4.78161e11 | 1.02224 | 0.511119 | − | 0.859510i | \(-0.329231\pi\) | ||||
0.511119 | + | 0.859510i | \(0.329231\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.13580e11 | − | 2.38780e11i | −0.875671 | − | 0.505569i | −0.00644231 | − | 0.999979i | \(-0.502051\pi\) |
−0.869229 | + | 0.494410i | \(0.835384\pi\) | |||||||
\(830\) | −3.79352e10 | + | 6.57057e10i | −0.0799337 | + | 0.138449i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.42888e9i | 0.0134166i | ||||||||
\(833\) | 4.06772e11 | − | 8.47365e10i | 0.844832 | − | 0.175991i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.13695e9 | − | 1.96925e9i | −0.00233881 | − | 0.00405094i | ||||
\(836\) | −8.05946e10 | − | 4.65313e10i | −0.164999 | − | 0.0952622i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.30445e11 | − | 2.48517e11i | 0.872853 | − | 0.503942i | ||||
\(839\) | − | 4.93131e11i | − | 0.995209i | −0.867404 | − | 0.497604i | \(-0.834213\pi\) | ||
0.867404 | − | 0.497604i | \(-0.165787\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.92444e11 | −0.984404 | ||||||||
\(842\) | 3.23682e10 | + | 5.60634e10i | 0.0643977 | + | 0.111540i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.17427e11 | − | 3.76594e11i | 0.428492 | − | 0.742170i | ||||
\(845\) | 6.11495e11 | − | 3.53047e11i | 1.19941 | − | 0.692477i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.53965e10 | + | 9.27213e10i | −0.146493 | + | 0.180155i | ||||
\(848\) | 3.41600e10 | 0.0660594 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.65670e11 | − | 1.53385e11i | −0.508941 | − | 0.293837i | ||||
\(851\) | −2.32146e11 | + | 4.02088e11i | −0.442632 | + | 0.766661i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.24713e11i | 1.18001i | 0.807401 | + | 0.590004i | \(0.200874\pi\) | ||||
−0.807401 | + | 0.590004i | \(0.799126\pi\) | |||||||
\(854\) | 6.26039e10 | − | 3.90136e11i | 0.117698 | − | 0.733474i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.45015e11 | − | 2.51173e11i | −0.270095 | − | 0.467819i | ||||
\(857\) | 7.96567e10 | + | 4.59898e10i | 0.147672 | + | 0.0852587i | 0.572016 | − | 0.820243i | \(-0.306162\pi\) |
−0.424343 | + | 0.905501i | \(0.639495\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.04542e11 | + | 1.75827e11i | −0.559338 | + | 0.322934i | −0.752880 | − | 0.658158i | \(-0.771336\pi\) |
0.193541 | + | 0.981092i | \(0.438003\pi\) | |||||||
\(860\) | 3.31170e11i | 0.605421i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.54507e11 | 0.279847 | ||||||||
\(863\) | 1.79901e11 | + | 3.11598e11i | 0.324333 | + | 0.561762i | 0.981377 | − | 0.192091i | \(-0.0615268\pi\) |
−0.657044 | + | 0.753852i | \(0.728193\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.79953e10 | − | 1.69733e11i | 0.175041 | − | 0.303181i | ||||
\(866\) | −4.95336e11 | + | 2.85983e11i | −0.880701 | + | 0.508473i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.38166e11 | − | 1.12350e11i | −0.243401 | − | 0.197922i | ||||
\(869\) | −4.34797e11 | −0.762442 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.74724e10 | + | 2.16347e10i | 0.0651086 | + | 0.0375905i | ||||
\(872\) | 1.07923e11 | − | 1.86928e11i | 0.186658 | − | 0.323302i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.20064e11i | 0.548518i | ||||||||
\(875\) | −2.83402e10 | + | 1.08128e10i | −0.0483472 | + | 0.0184462i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.31314e11 | − | 9.20263e11i | −0.898158 | − | 1.55566i | −0.829847 | − | 0.557991i | \(-0.811572\pi\) |
−0.0683115 | − | 0.997664i | \(-0.521761\pi\) | |||||||
\(878\) | 4.31086e11 | + | 2.48888e11i | 0.725414 | + | 0.418818i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.59402e11 | − | 9.20307e10i | 0.265805 | − | 0.153462i | ||||
\(881\) | − | 3.25470e11i | − | 0.540266i | −0.962823 | − | 0.270133i | \(-0.912932\pi\) | ||
0.962823 | − | 0.270133i | \(-0.0870677\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.60107e11 | 0.756861 | 0.378431 | − | 0.925630i | \(-0.376464\pi\) | ||||
0.378431 | + | 0.925630i | \(0.376464\pi\) | |||||||
\(884\) | 1.41409e10 | + | 2.44927e10i | 0.0231562 | + | 0.0401077i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.81157e10 | + | 4.86979e10i | −0.0456262 | + | 0.0790269i | ||||
\(887\) | 4.83578e11 | − | 2.79194e11i | 0.781217 | − | 0.451036i | −0.0556445 | − | 0.998451i | \(-0.517721\pi\) |
0.836861 | + | 0.547415i | \(0.184388\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.24474e9 | + | 1.89884e10i | 0.0115989 | + | 0.0304005i | ||||
\(890\) | −1.00950e12 | −1.60896 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.31908e10 | − | 1.33892e10i | −0.0366316 | − | 0.0211493i | ||||
\(893\) | −2.26511e11 | + | 3.92328e11i | −0.356191 | + | 0.616941i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.20806e12i | − | 1.88276i | ||||||
\(896\) | −3.59406e10 | + | 4.41991e10i | −0.0557640 | + | 0.0685775i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.74293e10 | + | 1.16791e11i | 0.103691 | + | 0.179599i | ||||
\(899\) | 4.43244e10 | + | 2.55907e10i | 0.0678585 | + | 0.0391781i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.30143e11 | − | 7.51379e10i | 0.197479 | − | 0.114014i | ||||
\(902\) | − | 2.06507e11i | − | 0.311967i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.90539e11 | −0.435042 | ||||||||
\(905\) | −7.70023e11 | − | 1.33372e12i | −1.14791 | − | 1.98825i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.39788e11 | − | 4.15326e11i | 0.354323 | − | 0.613705i | −0.632679 | − | 0.774414i | \(-0.718045\pi\) |
0.987002 | + | 0.160709i | \(0.0513781\pi\) | |||||||
\(908\) | 1.39675e11 | − | 8.06415e10i | 0.205483 | − | 0.118636i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.19995e10 | − | 1.15535e10i | −0.104994 | − | 0.0168481i | ||||
\(911\) | −5.85058e11 | −0.849426 | −0.424713 | − | 0.905328i | \(-0.639625\pi\) | ||||
−0.424713 | + | 0.905328i | \(0.639625\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.50836e10 | − | 4.91230e10i | −0.122451 | − | 0.0706972i | ||||
\(914\) | −2.77263e11 | + | 4.80233e11i | −0.397289 | + | 0.688125i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.42497e11i | 0.628534i | ||||||||
\(917\) | 4.59408e11 | + | 3.73569e11i | 0.649712 | + | 0.528315i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.64889e11 | + | 1.15162e12i | 0.932152 | + | 1.61454i | 0.779635 | + | 0.626234i | \(0.215405\pi\) |
0.152517 | + | 0.988301i | \(0.451262\pi\) | |||||||
\(920\) | −5.48220e11 | − | 3.16515e11i | −0.765250 | − | 0.441817i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.47775e11 | − | 3.16258e11i | 0.758016 | − | 0.437641i | ||||
\(923\) | 1.02555e11i | 0.141302i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.49901e11 | 0.477946 | ||||||||
\(926\) | 5.70962e10 | + | 9.88936e10i | 0.0776539 | + | 0.134501i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.18645e9 | − | 1.41794e10i | 0.0110383 | − | 0.0191190i | ||||
\(929\) | 6.13628e11 | − | 3.54278e11i | 0.823839 | − | 0.475644i | −0.0278995 | − | 0.999611i | \(-0.508882\pi\) |
0.851739 | + | 0.523967i | \(0.175549\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.02218e11 | + | 3.10301e11i | −0.136060 | + | 0.413033i | ||||
\(932\) | −2.34934e11 | −0.311375 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.52700e11 | + | 4.92306e11i | 1.12049 | + | 0.646916i | ||||
\(935\) | 4.04859e11 | − | 7.01236e11i | 0.529733 | − | 0.917524i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.84697e11i | 0.369338i | 0.982801 | + | 0.184669i | \(0.0591213\pi\) | ||||
−0.982801 | + | 0.184669i | \(0.940879\pi\) | |||||||
\(938\) | 1.36677e11 | + | 3.58229e11i | 0.176557 | + | 0.462754i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.47998e11 | − | 7.75955e11i | −0.573805 | − | 0.993860i | ||||
\(941\) | −9.65681e11 | − | 5.57536e11i | −1.23162 | − | 0.711073i | −0.264249 | − | 0.964455i | \(-0.585124\pi\) |
−0.967366 | + | 0.253381i | \(0.918457\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.15072e11 | + | 3.55112e11i | −0.777820 | + | 0.449075i | ||||
\(944\) | 1.43814e11i | 0.181098i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.28839e11 | −0.535463 | ||||||||
\(947\) | 2.79065e11 | + | 4.83354e11i | 0.346981 | + | 0.600988i | 0.985712 | − | 0.168442i | \(-0.0538737\pi\) |
−0.638731 | + | 0.769430i | \(0.720540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.98342e9 | + | 3.43538e9i | −0.00244540 | + | 0.00423555i | ||||
\(950\) | 2.08892e11 | − | 1.20604e11i | 0.256465 | − | 0.148070i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.97066e10 | + | 2.47444e11i | −0.0483409 | + | 0.301252i | ||||
\(953\) | 8.07374e11 | 0.978821 | 0.489410 | − | 0.872054i | \(-0.337212\pi\) | ||||
0.489410 | + | 0.872054i | \(0.337212\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.56502e12 | − | 9.03566e11i | −1.88151 | − | 1.08629i | ||||
\(956\) | 1.47243e11 | − | 2.55032e11i | 0.176280 | − | 0.305326i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 6.78616e11i | − | 0.805680i | ||||||
\(959\) | 9.95656e11 | + | 1.59770e11i | 1.17716 | + | 0.188895i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.58568e11 | − | 4.47852e11i | −0.303166 | − | 0.525099i | ||||
\(962\) | −2.79364e10 | − | 1.61291e10i | −0.0326190 | − | 0.0188326i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.61995e11 | − | 9.35276e10i | 0.187582 | − | 0.108301i | ||||
\(965\) | − | 8.98622e11i | − | 1.03626i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.26699e10 | −0.0144899 | −0.00724495 | − | 0.999974i | \(-0.502306\pi\) | ||||
−0.00724495 | + | 0.999974i | \(0.502306\pi\) | |||||||
\(968\) | −3.60401e10 | − | 6.24232e10i | −0.0410472 | − | 0.0710959i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.44229e11 | − | 2.49812e11i | 0.162917 | − | 0.282180i | ||||
\(971\) | −3.00011e11 | + | 1.73212e11i | −0.337490 | + | 0.194850i | −0.659161 | − | 0.752001i | \(-0.729089\pi\) |
0.321672 | + | 0.946851i | \(0.395755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.43885e12 | − | 5.48973e11i | 1.60533 | − | 0.612490i | ||||
\(974\) | −6.58255e11 | −0.731405 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.06391e11 | + | 1.19160e11i | 0.227453 | + | 0.131320i | ||||
\(977\) | 3.56249e11 | − | 6.17041e11i | 0.390999 | − | 0.677230i | −0.601583 | − | 0.798810i | \(-0.705463\pi\) |
0.992582 | + | 0.121581i | \(0.0387963\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.30722e12i | − | 1.42304i | ||||||
\(980\) | −4.30413e11 | − | 4.81945e11i | −0.466639 | − | 0.522508i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.13885e11 | + | 7.16870e11i | 0.445076 | + | 0.770893i | ||||
\(983\) | −1.36181e12 | − | 7.86241e11i | −1.45849 | − | 0.842058i | −0.459549 | − | 0.888152i | \(-0.651989\pi\) |
−0.998937 | + | 0.0460947i | \(0.985322\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.31507e11 | − | 5.37806e11i | 0.989558 | − | 0.571321i | ||||
\(986\) | − | 7.20272e10i | − | 0.0762059i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.22375e10 | −0.0233377 | ||||||||
\(989\) | 7.37438e11 | + | 1.27728e12i | 0.770797 | + | 1.33506i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.68912e11 | − | 2.92564e11i | 0.175132 | − | 0.303338i | −0.765075 | − | 0.643941i | \(-0.777298\pi\) |
0.940207 | + | 0.340604i | \(0.110631\pi\) | |||||||
\(992\) | 9.30180e10 | − | 5.37040e10i | 0.0960551 | − | 0.0554574i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.73331e11 | + | 7.05072e11i | −0.587300 | + | 0.722251i | ||||
\(995\) | 2.17302e12 | 2.21703 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.01610e10 | − | 1.16400e10i | −0.0204048 | − | 0.0117807i | 0.489763 | − | 0.871856i | \(-0.337083\pi\) |
−0.510168 | + | 0.860075i | \(0.670417\pi\) | |||||||
\(998\) | 3.54326e11 | − | 6.13710e11i | 0.357175 | − | 0.618644i | ||||
\(999\) | 0 | 0 |
(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 | 126.9.n.b.73.6 | 12 | ||
3.2 | odd | 2 | 14.9.d.a.3.3 | ✓ | 12 | ||
7.5 | odd | 6 | inner | 126.9.n.b.19.6 | 12 | ||
12.11 | even | 2 | 112.9.s.c.17.2 | 12 | |||
21.2 | odd | 6 | 98.9.d.b.19.1 | 12 | |||
21.5 | even | 6 | 14.9.d.a.5.3 | yes | 12 | ||
21.11 | odd | 6 | 98.9.b.c.97.7 | 12 | |||
21.17 | even | 6 | 98.9.b.c.97.12 | 12 | |||
21.20 | even | 2 | 98.9.d.b.31.1 | 12 | |||
84.47 | odd | 6 | 112.9.s.c.33.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.9.d.a.3.3 | ✓ | 12 | 3.2 | odd | 2 | ||
14.9.d.a.5.3 | yes | 12 | 21.5 | even | 6 | ||
98.9.b.c.97.7 | 12 | 21.11 | odd | 6 | |||
98.9.b.c.97.12 | 12 | 21.17 | even | 6 | |||
98.9.d.b.19.1 | 12 | 21.2 | odd | 6 | |||
98.9.d.b.31.1 | 12 | 21.20 | even | 2 | |||
112.9.s.c.17.2 | 12 | 12.11 | even | 2 | |||
112.9.s.c.33.2 | 12 | 84.47 | odd | 6 | |||
126.9.n.b.19.6 | 12 | 7.5 | odd | 6 | inner | ||
126.9.n.b.73.6 | 12 | 1.1 | even | 1 | trivial |