Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,12,Mod(55,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.55");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.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: | \(64.5408271670\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.6 | ||
Character | \(\chi\) | \(=\) | 84.55 |
Dual form | 84.12.b.a.55.5 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −40.8700 | + | 19.4330i | −0.903108 | + | 0.429413i | ||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 1292.72 | − | 1588.45i | 0.631209 | − | 0.775613i | ||||
\(5\) | 1211.18i | 0.173330i | 0.996238 | + | 0.0866651i | \(0.0276210\pi\) | ||||
−0.996238 | + | 0.0866651i | \(0.972379\pi\) | |||||||
\(6\) | 9931.41 | − | 4722.22i | 0.521410 | − | 0.247922i | ||||
\(7\) | −25032.4 | − | 36752.0i | −0.562941 | − | 0.826497i | ||||
\(8\) | −21964.9 | + | 90041.5i | −0.236992 | + | 0.971512i | ||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −23536.9 | − | 49501.0i | −0.0744302 | − | 0.156536i | ||||
\(11\) | − | 495487.i | − | 0.927625i | −0.885934 | − | 0.463812i | \(-0.846481\pi\) | ||
0.885934 | − | 0.463812i | \(-0.153519\pi\) | |||||||
\(12\) | −314130. | + | 385994.i | −0.364429 | + | 0.447800i | ||||
\(13\) | 811.906i | 0.000606481i | 1.00000 | 0.000303241i | \(9.65245e-5\pi\) | |||||
−1.00000 | 0.000303241i | \(0.999903\pi\) | ||||||||
\(14\) | 1.73727e6 | + | 1.01560e6i | 0.863305 | + | 0.504683i | ||||
\(15\) | − | 294317.i | − | 0.100072i | ||||||
\(16\) | −852072. | − | 4.10684e6i | −0.203150 | − | 0.979148i | ||||
\(17\) | − | 4.23433e6i | − | 0.723296i | −0.932315 | − | 0.361648i | \(-0.882214\pi\) | ||
0.932315 | − | 0.361648i | \(-0.117786\pi\) | |||||||
\(18\) | −2.41333e6 | + | 1.14750e6i | −0.301036 | + | 0.143138i | ||||
\(19\) | −1.72662e7 | −1.59975 | −0.799876 | − | 0.600165i | \(-0.795102\pi\) | ||||
−0.799876 | + | 0.600165i | \(0.795102\pi\) | |||||||
\(20\) | 1.92391e6 | + | 1.56571e6i | 0.134437 | + | 0.109408i | ||||
\(21\) | 6.08286e6 | + | 8.93073e6i | 0.325014 | + | 0.477179i | ||||
\(22\) | 9.62880e6 | + | 2.02505e7i | 0.398334 | + | 0.837745i | ||||
\(23\) | − | 4.82401e7i | − | 1.56281i | −0.624026 | − | 0.781404i | \(-0.714504\pi\) | ||
0.624026 | − | 0.781404i | \(-0.285496\pi\) | |||||||
\(24\) | 5.33747e6 | − | 2.18801e7i | 0.136828 | − | 0.560902i | ||||
\(25\) | 4.73612e7 | 0.969957 | ||||||||
\(26\) | −15777.8 | − | 33182.6i | −0.000260431 | − | 0.000547718i | ||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | −9.07386e7 | − | 7.74713e6i | −0.996375 | − | 0.0850690i | ||||
\(29\) | −3.74837e7 | −0.339355 | −0.169677 | − | 0.985500i | \(-0.554273\pi\) | ||||
−0.169677 | + | 0.985500i | \(0.554273\pi\) | |||||||
\(30\) | 5.71946e6 | + | 1.20287e7i | 0.0429723 | + | 0.0903760i | ||||
\(31\) | 2.03149e8 | 1.27446 | 0.637230 | − | 0.770674i | \(-0.280080\pi\) | ||||
0.637230 | + | 0.770674i | \(0.280080\pi\) | |||||||
\(32\) | 1.14633e8 | + | 1.51288e8i | 0.603925 | + | 0.797041i | ||||
\(33\) | 1.20403e8i | 0.535564i | ||||||||
\(34\) | 8.22858e7 | + | 1.73057e8i | 0.310592 | + | 0.653214i | ||||
\(35\) | 4.45133e7 | − | 3.03187e7i | 0.143257 | − | 0.0975745i | ||||
\(36\) | 7.63336e7 | − | 9.37967e7i | 0.210403 | − | 0.258538i | ||||
\(37\) | 4.41964e8 | 1.04780 | 0.523899 | − | 0.851780i | \(-0.324477\pi\) | ||||
0.523899 | + | 0.851780i | \(0.324477\pi\) | |||||||
\(38\) | 7.05671e8 | − | 3.35535e8i | 1.44475 | − | 0.686954i | ||||
\(39\) | − | 197293.i | − | 0.000350152i | ||||||
\(40\) | −1.09057e8 | − | 2.66035e7i | −0.168392 | − | 0.0410779i | ||||
\(41\) | − | 5.82689e8i | − | 0.785463i | −0.919653 | − | 0.392732i | \(-0.871530\pi\) | ||
0.919653 | − | 0.392732i | \(-0.128470\pi\) | |||||||
\(42\) | −4.22158e8 | − | 2.46791e8i | −0.498429 | − | 0.291379i | ||||
\(43\) | 7.19229e8i | 0.746089i | 0.927813 | + | 0.373045i | \(0.121686\pi\) | ||||
−0.927813 | + | 0.373045i | \(0.878314\pi\) | |||||||
\(44\) | −7.87058e8 | − | 6.40524e8i | −0.719477 | − | 0.585525i | ||||
\(45\) | 7.15190e7i | 0.0577767i | ||||||||
\(46\) | 9.37451e8 | + | 1.97157e9i | 0.671089 | + | 1.41138i | ||||
\(47\) | 2.68659e9 | 1.70869 | 0.854345 | − | 0.519706i | \(-0.173958\pi\) | ||||
0.854345 | + | 0.519706i | \(0.173958\pi\) | |||||||
\(48\) | 2.07054e8 | + | 9.97963e8i | 0.117289 | + | 0.565311i | ||||
\(49\) | −7.24089e8 | + | 1.83998e9i | −0.366196 | + | 0.930538i | ||||
\(50\) | −1.93565e9 | + | 9.20370e8i | −0.875976 | + | 0.416512i | ||||
\(51\) | 1.02894e9i | 0.417595i | ||||||||
\(52\) | 1.28968e6 | + | 1.04956e6i | 0.000470394 | + | 0.000382816i | ||||
\(53\) | −3.24198e9 | −1.06486 | −0.532430 | − | 0.846474i | \(-0.678721\pi\) | ||||
−0.532430 | + | 0.846474i | \(0.678721\pi\) | |||||||
\(54\) | 5.86440e8 | − | 2.78842e8i | 0.173803 | − | 0.0826405i | ||||
\(55\) | 6.00124e8 | 0.160785 | ||||||||
\(56\) | 3.85904e9 | − | 1.44670e9i | 0.936364 | − | 0.351030i | ||||
\(57\) | 4.19569e9 | 0.923618 | ||||||||
\(58\) | 1.53196e9 | − | 7.28421e8i | 0.306474 | − | 0.145723i | ||||
\(59\) | −3.75912e9 | −0.684541 | −0.342271 | − | 0.939601i | \(-0.611196\pi\) | ||||
−0.342271 | + | 0.939601i | \(0.611196\pi\) | |||||||
\(60\) | −4.67509e8 | − | 3.80468e8i | −0.0776173 | − | 0.0631665i | ||||
\(61\) | − | 1.56573e9i | − | 0.237357i | −0.992933 | − | 0.118678i | \(-0.962134\pi\) | ||
0.992933 | − | 0.118678i | \(-0.0378658\pi\) | |||||||
\(62\) | −8.30272e9 | + | 3.94780e9i | −1.15098 | + | 0.547269i | ||||
\(63\) | −1.47814e9 | − | 2.17017e9i | −0.187647 | − | 0.275499i | ||||
\(64\) | −7.62502e9 | − | 3.95551e9i | −0.887669 | − | 0.460481i | ||||
\(65\) | −983365. | −0.000105121 | ||||||||
\(66\) | −2.33980e9 | − | 4.92088e9i | −0.229978 | − | 0.483673i | ||||
\(67\) | − | 1.21311e10i | − | 1.09771i | −0.835917 | − | 0.548857i | \(-0.815063\pi\) | ||
0.835917 | − | 0.548857i | \(-0.184937\pi\) | |||||||
\(68\) | −6.72604e9 | − | 5.47379e9i | −0.560997 | − | 0.456551i | ||||
\(69\) | 1.17224e10i | 0.902287i | ||||||||
\(70\) | −1.23008e9 | + | 2.10415e9i | −0.0874767 | + | 0.149637i | ||||
\(71\) | − | 1.57657e10i | − | 1.03703i | −0.855067 | − | 0.518517i | \(-0.826484\pi\) | ||
0.855067 | − | 0.518517i | \(-0.173516\pi\) | |||||||
\(72\) | −1.29701e9 | + | 5.31686e9i | −0.0789974 | + | 0.323837i | ||||
\(73\) | − | 4.84329e9i | − | 0.273442i | −0.990610 | − | 0.136721i | \(-0.956344\pi\) | ||
0.990610 | − | 0.136721i | \(-0.0436564\pi\) | |||||||
\(74\) | −1.80631e10 | + | 8.58870e9i | −0.946276 | + | 0.449938i | ||||
\(75\) | −1.15088e10 | −0.560005 | ||||||||
\(76\) | −2.23203e10 | + | 2.74266e10i | −1.00978 | + | 1.24079i | ||||
\(77\) | −1.82101e10 | + | 1.24032e10i | −0.766679 | + | 0.522197i | ||||
\(78\) | 3.83400e6 | + | 8.06337e6i | 0.000150360 | + | 0.000316225i | ||||
\(79\) | − | 2.24827e10i | − | 0.822054i | −0.911623 | − | 0.411027i | \(-0.865170\pi\) | ||
0.911623 | − | 0.411027i | \(-0.134830\pi\) | |||||||
\(80\) | 4.97413e9 | − | 1.03201e9i | 0.169716 | − | 0.0352120i | ||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 1.13234e10 | + | 2.38145e10i | 0.337288 | + | 0.709358i | ||||
\(83\) | −5.78633e10 | −1.61240 | −0.806202 | − | 0.591640i | \(-0.798481\pi\) | ||||
−0.806202 | + | 0.591640i | \(0.798481\pi\) | |||||||
\(84\) | 2.20495e10 | + | 1.88255e9i | 0.575257 | + | 0.0491146i | ||||
\(85\) | 5.12854e9 | 0.125369 | ||||||||
\(86\) | −1.39768e10 | − | 2.93949e10i | −0.320380 | − | 0.673799i | ||||
\(87\) | 9.10854e9 | 0.195926 | ||||||||
\(88\) | 4.46144e10 | + | 1.08833e10i | 0.901198 | + | 0.219840i | ||||
\(89\) | 6.72135e10i | 1.27589i | 0.770084 | + | 0.637943i | \(0.220214\pi\) | ||||
−0.770084 | + | 0.637943i | \(0.779786\pi\) | |||||||
\(90\) | −1.38983e9 | − | 2.92298e9i | −0.0248101 | − | 0.0521786i | ||||
\(91\) | 2.98391e7 | − | 2.03239e7i | 0.000501255 | − | 0.000341413i | ||||
\(92\) | −7.66273e10 | − | 6.23608e10i | −1.21213 | − | 0.986458i | ||||
\(93\) | −4.93653e10 | −0.735810 | ||||||||
\(94\) | −1.09801e11 | + | 5.22086e10i | −1.54313 | + | 0.733734i | ||||
\(95\) | − | 2.09125e10i | − | 0.277285i | ||||||
\(96\) | −2.78557e10 | − | 3.67631e10i | −0.348676 | − | 0.460172i | ||||
\(97\) | 1.16526e11i | 1.37777i | 0.724869 | + | 0.688887i | \(0.241900\pi\) | ||||
−0.724869 | + | 0.688887i | \(0.758100\pi\) | |||||||
\(98\) | −6.16276e9 | − | 8.92711e10i | −0.0688702 | − | 0.997626i | ||||
\(99\) | − | 2.92580e10i | − | 0.309208i | ||||||
\(100\) | 6.12246e10 | − | 7.52311e10i | 0.612246 | − | 0.752311i | ||||
\(101\) | − | 2.49783e10i | − | 0.236480i | −0.992985 | − | 0.118240i | \(-0.962275\pi\) | ||
0.992985 | − | 0.118240i | \(-0.0377253\pi\) | |||||||
\(102\) | −1.99954e10 | − | 4.20529e10i | −0.179321 | − | 0.377133i | ||||
\(103\) | −1.98339e11 | −1.68579 | −0.842894 | − | 0.538080i | \(-0.819150\pi\) | ||||
−0.842894 | + | 0.538080i | \(0.819150\pi\) | |||||||
\(104\) | −7.31052e7 | − | 1.78334e7i | −0.000589203 | − | 0.000143731i | ||||
\(105\) | −1.08167e10 | + | 7.36745e9i | −0.0827094 | + | 0.0563347i | ||||
\(106\) | 1.32500e11 | − | 6.30014e10i | 0.961684 | − | 0.457265i | ||||
\(107\) | 3.13969e10i | 0.216410i | 0.994129 | + | 0.108205i | \(0.0345102\pi\) | ||||
−0.994129 | + | 0.108205i | \(0.965490\pi\) | |||||||
\(108\) | −1.85491e10 | + | 2.27926e10i | −0.121476 | + | 0.149267i | ||||
\(109\) | −1.09821e11 | −0.683660 | −0.341830 | − | 0.939762i | \(-0.611047\pi\) | ||||
−0.341830 | + | 0.939762i | \(0.611047\pi\) | |||||||
\(110\) | −2.45271e10 | + | 1.16622e10i | −0.145207 | + | 0.0690433i | ||||
\(111\) | −1.07397e11 | −0.604947 | ||||||||
\(112\) | −1.29605e11 | + | 1.34119e11i | −0.694902 | + | 0.719105i | ||||
\(113\) | −2.62005e11 | −1.33776 | −0.668879 | − | 0.743371i | \(-0.733226\pi\) | ||||
−0.668879 | + | 0.743371i | \(0.733226\pi\) | |||||||
\(114\) | −1.71478e11 | + | 8.15350e10i | −0.834127 | + | 0.396613i | ||||
\(115\) | 5.84275e10 | 0.270882 | ||||||||
\(116\) | −4.84558e10 | + | 5.95412e10i | −0.214204 | + | 0.263208i | ||||
\(117\) | 4.79422e7i | 0.000202160i | ||||||||
\(118\) | 1.53635e11 | − | 7.30509e10i | 0.618215 | − | 0.293951i | ||||
\(119\) | −1.55620e11 | + | 1.05995e11i | −0.597802 | + | 0.407172i | ||||
\(120\) | 2.65008e10 | + | 6.46464e9i | 0.0972213 | + | 0.0237163i | ||||
\(121\) | 3.98046e10 | 0.139513 | ||||||||
\(122\) | 3.04268e10 | + | 6.39913e10i | 0.101924 | + | 0.214359i | ||||
\(123\) | 1.41593e11i | 0.453487i | ||||||||
\(124\) | 2.62615e11 | − | 3.22694e11i | 0.804451 | − | 0.988487i | ||||
\(125\) | 1.16503e11i | 0.341453i | ||||||||
\(126\) | 1.02584e11 | + | 5.99702e10i | 0.287768 | + | 0.168228i | ||||
\(127\) | − | 3.60186e11i | − | 0.967401i | −0.875234 | − | 0.483700i | \(-0.839292\pi\) | ||
0.875234 | − | 0.483700i | \(-0.160708\pi\) | |||||||
\(128\) | 3.88502e11 | + | 1.34845e10i | 0.999398 | + | 0.0346881i | ||||
\(129\) | − | 1.74773e11i | − | 0.430755i | ||||||
\(130\) | 4.01901e7 | − | 1.91097e7i | 9.49360e−5 | − | 4.51405e-5i | ||||
\(131\) | 1.40420e11 | 0.318007 | 0.159004 | − | 0.987278i | \(-0.449172\pi\) | ||||
0.159004 | + | 0.987278i | \(0.449172\pi\) | |||||||
\(132\) | 1.91255e11 | + | 1.55647e11i | 0.415390 | + | 0.338053i | ||||
\(133\) | 4.32214e11 | + | 6.34568e11i | 0.900565 | + | 1.32219i | ||||
\(134\) | 2.35744e11 | + | 4.95798e11i | 0.471372 | + | 0.991354i | ||||
\(135\) | − | 1.73791e10i | − | 0.0333574i | ||||||
\(136\) | 3.81266e11 | + | 9.30066e10i | 0.702690 | + | 0.171415i | ||||
\(137\) | 7.28759e10 | 0.129009 | 0.0645046 | − | 0.997917i | \(-0.479453\pi\) | ||||
0.0645046 | + | 0.997917i | \(0.479453\pi\) | |||||||
\(138\) | −2.27801e11 | − | 4.79093e11i | −0.387454 | − | 0.814863i | ||||
\(139\) | 2.66940e11 | 0.436348 | 0.218174 | − | 0.975910i | \(-0.429990\pi\) | ||||
0.218174 | + | 0.975910i | \(0.429990\pi\) | |||||||
\(140\) | 9.38317e9 | − | 1.09901e11i | 0.0147450 | − | 0.172702i | ||||
\(141\) | −6.52842e11 | −0.986513 | ||||||||
\(142\) | 3.06376e11 | + | 6.44346e11i | 0.445316 | + | 0.936554i | ||||
\(143\) | 4.02289e8 | 0.000562587 | ||||||||
\(144\) | −5.03140e10 | − | 2.42505e11i | −0.0677166 | − | 0.326383i | ||||
\(145\) | − | 4.53996e10i | − | 0.0588204i | ||||||
\(146\) | 9.41197e10 | + | 1.97945e11i | 0.117419 | + | 0.246948i | ||||
\(147\) | 1.75954e11 | − | 4.47114e11i | 0.211423 | − | 0.537246i | ||||
\(148\) | 5.71335e11 | − | 7.02040e11i | 0.661380 | − | 0.812686i | ||||
\(149\) | −3.79530e11 | −0.423371 | −0.211686 | − | 0.977338i | \(-0.567895\pi\) | ||||
−0.211686 | + | 0.977338i | \(0.567895\pi\) | |||||||
\(150\) | 4.70363e11 | − | 2.23650e11i | 0.505745 | − | 0.240473i | ||||
\(151\) | 1.15765e12i | 1.20007i | 0.799976 | + | 0.600033i | \(0.204846\pi\) | ||||
−0.799976 | + | 0.600033i | \(0.795154\pi\) | |||||||
\(152\) | 3.79251e11 | − | 1.55468e12i | 0.379129 | − | 1.55418i | ||||
\(153\) | − | 2.50033e11i | − | 0.241099i | ||||||
\(154\) | 5.03216e11 | − | 8.60796e11i | 0.468156 | − | 0.800823i | ||||
\(155\) | 2.46051e11i | 0.220902i | ||||||||
\(156\) | −3.13391e8 | − | 2.55044e8i | −0.000271582 | − | 0.000221019i | ||||
\(157\) | 1.90744e12i | 1.59589i | 0.602733 | + | 0.797943i | \(0.294078\pi\) | ||||
−0.602733 | + | 0.797943i | \(0.705922\pi\) | |||||||
\(158\) | 4.36907e11 | + | 9.18870e11i | 0.353000 | + | 0.742403i | ||||
\(159\) | 7.87801e11 | 0.614798 | ||||||||
\(160\) | −1.83238e11 | + | 1.38841e11i | −0.138151 | + | 0.104678i | ||||
\(161\) | −1.77292e12 | + | 1.20756e12i | −1.29166 | + | 0.879767i | ||||
\(162\) | −1.42505e11 | + | 6.77587e10i | −0.100345 | + | 0.0477125i | ||||
\(163\) | − | 1.28458e12i | − | 0.874435i | −0.899356 | − | 0.437218i | \(-0.855964\pi\) | ||
0.899356 | − | 0.437218i | \(-0.144036\pi\) | |||||||
\(164\) | −9.25575e11 | − | 7.53252e11i | −0.609215 | − | 0.495792i | ||||
\(165\) | −1.45830e11 | −0.0928294 | ||||||||
\(166\) | 2.36488e12 | − | 1.12446e12i | 1.45618 | − | 0.692387i | ||||
\(167\) | −1.10424e12 | −0.657843 | −0.328921 | − | 0.944357i | \(-0.606685\pi\) | ||||
−0.328921 | + | 0.944357i | \(0.606685\pi\) | |||||||
\(168\) | −9.37746e11 | + | 3.51548e11i | −0.540610 | + | 0.202667i | ||||
\(169\) | 1.79216e12 | 1.00000 | ||||||||
\(170\) | −2.09604e11 | + | 9.96630e10i | −0.113222 | + | 0.0538350i | ||||
\(171\) | −1.01955e12 | −0.533251 | ||||||||
\(172\) | 1.14246e12 | + | 9.29759e11i | 0.578676 | + | 0.470938i | ||||
\(173\) | − | 2.89632e12i | − | 1.42100i | −0.703698 | − | 0.710499i | \(-0.748469\pi\) | ||
0.703698 | − | 0.710499i | \(-0.251531\pi\) | |||||||
\(174\) | −3.72266e11 | + | 1.77006e11i | −0.176943 | + | 0.0841333i | ||||
\(175\) | −1.18556e12 | − | 1.74062e12i | −0.546028 | − | 0.801667i | ||||
\(176\) | −2.03489e12 | + | 4.22190e11i | −0.908281 | + | 0.188447i | ||||
\(177\) | 9.13465e11 | 0.395220 | ||||||||
\(178\) | −1.30616e12 | − | 2.74702e12i | −0.547882 | − | 1.15226i | ||||
\(179\) | − | 3.73432e12i | − | 1.51887i | −0.650584 | − | 0.759434i | \(-0.725476\pi\) | ||
0.650584 | − | 0.759434i | \(-0.274524\pi\) | |||||||
\(180\) | 1.13605e11 | + | 9.24538e10i | 0.0448123 | + | 0.0364692i | ||||
\(181\) | 3.30958e12i | 1.26631i | 0.774024 | + | 0.633156i | \(0.218241\pi\) | ||||
−0.774024 | + | 0.633156i | \(0.781759\pi\) | |||||||
\(182\) | −8.24572e8 | + | 1.41050e9i | −0.000306081 | + | 0.000523578i | ||||
\(183\) | 3.80471e11i | 0.137038i | ||||||||
\(184\) | 4.34362e12 | + | 1.05959e12i | 1.51829 | + | 0.370373i | ||||
\(185\) | 5.35299e11i | 0.181615i | ||||||||
\(186\) | 2.01756e12 | − | 9.59316e11i | 0.664516 | − | 0.315966i | ||||
\(187\) | −2.09805e12 | −0.670947 | ||||||||
\(188\) | 3.47300e12 | − | 4.26753e12i | 1.07854 | − | 1.32528i | ||||
\(189\) | 3.59187e11 | + | 5.27351e11i | 0.108338 | + | 0.159060i | ||||
\(190\) | 4.06393e11 | + | 8.54696e11i | 0.119070 | + | 0.250419i | ||||
\(191\) | 5.43520e12i | 1.54715i | 0.633706 | + | 0.773574i | \(0.281533\pi\) | ||||
−0.633706 | + | 0.773574i | \(0.718467\pi\) | |||||||
\(192\) | 1.85288e12 | + | 9.61188e11i | 0.512496 | + | 0.265859i | ||||
\(193\) | −3.03104e12 | −0.814755 | −0.407377 | − | 0.913260i | \(-0.633557\pi\) | ||||
−0.407377 | + | 0.913260i | \(0.633557\pi\) | |||||||
\(194\) | −2.26445e12 | − | 4.76242e12i | −0.591634 | − | 1.24428i | ||||
\(195\) | 2.38958e8 | 6.06919e−5 | ||||||||
\(196\) | 1.98668e12 | + | 3.52875e12i | 0.490591 | + | 0.871390i | ||||
\(197\) | −5.20245e12 | −1.24923 | −0.624617 | − | 0.780931i | \(-0.714745\pi\) | ||||
−0.624617 | + | 0.780931i | \(0.714745\pi\) | |||||||
\(198\) | 5.68571e11 | + | 1.19577e12i | 0.132778 | + | 0.279248i | ||||
\(199\) | 6.42699e12 | 1.45987 | 0.729937 | − | 0.683514i | \(-0.239549\pi\) | ||||
0.729937 | + | 0.683514i | \(0.239549\pi\) | |||||||
\(200\) | −1.04028e12 | + | 4.26447e12i | −0.229872 | + | 0.942324i | ||||
\(201\) | 2.94786e12i | 0.633765i | ||||||||
\(202\) | 4.85403e11 | + | 1.02086e12i | 0.101548 | + | 0.213567i | ||||
\(203\) | 9.38306e11 | + | 1.37760e12i | 0.191036 | + | 0.280476i | ||||
\(204\) | 1.63443e12 | + | 1.33013e12i | 0.323892 | + | 0.263590i | ||||
\(205\) | 7.05742e11 | 0.136144 | ||||||||
\(206\) | 8.10611e12 | − | 3.85432e12i | 1.52245 | − | 0.723899i | ||||
\(207\) | − | 2.84853e12i | − | 0.520936i | ||||||
\(208\) | 3.33437e9 | − | 6.91802e8i | 0.000593834 | − | 0.000123207i | ||||
\(209\) | 8.55519e12i | 1.48397i | ||||||||
\(210\) | 2.98908e11 | − | 5.11309e11i | 0.0505047 | − | 0.0863928i | ||||
\(211\) | − | 1.60347e11i | − | 0.0263940i | −0.999913 | − | 0.0131970i | \(-0.995799\pi\) | ||
0.999913 | − | 0.0131970i | \(-0.00420087\pi\) | |||||||
\(212\) | −4.19096e12 | + | 5.14973e12i | −0.672150 | + | 0.825919i | ||||
\(213\) | 3.83107e12i | 0.598732i | ||||||||
\(214\) | −6.10137e11 | − | 1.28319e12i | −0.0929290 | − | 0.195441i | ||||
\(215\) | −8.71116e11 | −0.129320 | ||||||||
\(216\) | 3.15172e11 | − | 1.29200e12i | 0.0456092 | − | 0.186967i | ||||
\(217\) | −5.08531e12 | − | 7.46614e12i | −0.717445 | − | 1.05334i | ||||
\(218\) | 4.48839e12 | − | 2.13416e12i | 0.617419 | − | 0.293573i | ||||
\(219\) | 1.17692e12i | 0.157872i | ||||||||
\(220\) | 7.75790e11 | − | 9.53270e11i | 0.101489 | − | 0.124707i | ||||
\(221\) | 3.43788e9 | 0.000438665 | ||||||||
\(222\) | 4.38933e12 | − | 2.08705e12i | 0.546332 | − | 0.259772i | ||||
\(223\) | −5.11461e12 | −0.621064 | −0.310532 | − | 0.950563i | \(-0.600507\pi\) | ||||
−0.310532 | + | 0.950563i | \(0.600507\pi\) | |||||||
\(224\) | 2.69063e12 | − | 8.00008e12i | 0.318779 | − | 0.947829i | ||||
\(225\) | 2.79663e12 | 0.323319 | ||||||||
\(226\) | 1.07081e13 | − | 5.09154e12i | 1.20814 | − | 0.574451i | ||||
\(227\) | −1.50549e13 | −1.65781 | −0.828905 | − | 0.559389i | \(-0.811036\pi\) | ||||
−0.828905 | + | 0.559389i | \(0.811036\pi\) | |||||||
\(228\) | 5.42384e12 | − | 6.66467e12i | 0.582996 | − | 0.716369i | ||||
\(229\) | − | 1.27546e12i | − | 0.133836i | −0.997758 | − | 0.0669179i | \(-0.978683\pi\) | ||
0.997758 | − | 0.0669179i | \(-0.0213166\pi\) | |||||||
\(230\) | −2.38793e12 | + | 1.13542e12i | −0.244635 | + | 0.116320i | ||||
\(231\) | 4.42506e12 | − | 3.01398e12i | 0.442642 | − | 0.301491i | ||||
\(232\) | 8.23326e11 | − | 3.37509e12i | 0.0804244 | − | 0.329687i | ||||
\(233\) | −1.09965e13 | −1.04905 | −0.524525 | − | 0.851395i | \(-0.675757\pi\) | ||||
−0.524525 | + | 0.851395i | \(0.675757\pi\) | |||||||
\(234\) | −9.31662e8 | − | 1.95940e9i | −8.68102e−5 | − | 0.000182573i | ||||
\(235\) | 3.25395e12i | 0.296168i | ||||||||
\(236\) | −4.85947e12 | + | 5.97119e12i | −0.432089 | + | 0.530939i | ||||
\(237\) | 5.46330e12i | 0.474613i | ||||||||
\(238\) | 4.30039e12 | − | 7.35619e12i | 0.365035 | − | 0.624425i | ||||
\(239\) | − | 2.76724e12i | − | 0.229540i | −0.993392 | − | 0.114770i | \(-0.963387\pi\) | ||
0.993392 | − | 0.114770i | \(-0.0366131\pi\) | |||||||
\(240\) | −1.20871e12 | + | 2.50779e11i | −0.0979855 | + | 0.0203296i | ||||
\(241\) | 2.15507e13i | 1.70753i | 0.520661 | + | 0.853764i | \(0.325686\pi\) | ||||
−0.520661 | + | 0.853764i | \(0.674314\pi\) | |||||||
\(242\) | −1.62681e12 | + | 7.73523e11i | −0.125995 | + | 0.0599085i | ||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | −2.48708e12 | − | 2.02404e12i | −0.184097 | − | 0.149822i | ||||
\(245\) | −2.22855e12 | − | 8.77003e11i | −0.161290 | − | 0.0634728i | ||||
\(246\) | −2.75159e12 | − | 5.78693e12i | −0.194733 | − | 0.409548i | ||||
\(247\) | − | 1.40186e10i | − | 0.000970220i | ||||||
\(248\) | −4.46215e12 | + | 1.82919e13i | −0.302037 | + | 1.23815i | ||||
\(249\) | 1.40608e13 | 0.930922 | ||||||||
\(250\) | −2.26400e12 | − | 4.76147e12i | −0.146624 | − | 0.308369i | ||||
\(251\) | −7.40890e12 | −0.469406 | −0.234703 | − | 0.972067i | \(-0.575412\pi\) | ||||
−0.234703 | + | 0.972067i | \(0.575412\pi\) | |||||||
\(252\) | −5.35802e12 | − | 4.57460e11i | −0.332125 | − | 0.0283563i | ||||
\(253\) | −2.39023e13 | −1.44970 | ||||||||
\(254\) | 6.99950e12 | + | 1.47208e13i | 0.415414 | + | 0.873668i | ||||
\(255\) | −1.24624e12 | −0.0723818 | ||||||||
\(256\) | −1.61401e13 | + | 6.99865e12i | −0.917460 | + | 0.397827i | ||||
\(257\) | − | 8.02831e12i | − | 0.446675i | −0.974741 | − | 0.223338i | \(-0.928305\pi\) | ||
0.974741 | − | 0.223338i | \(-0.0716952\pi\) | |||||||
\(258\) | 3.39636e12 | + | 7.14296e12i | 0.184972 | + | 0.389018i | ||||
\(259\) | −1.10634e13 | − | 1.62431e13i | −0.589848 | − | 0.866003i | ||||
\(260\) | −1.27121e9 | + | 1.56203e9i | −6.63536e−5 | + | 8.15335e-5i | ||||
\(261\) | −2.21338e12 | −0.113118 | ||||||||
\(262\) | −5.73897e12 | + | 2.72878e12i | −0.287195 | + | 0.136556i | ||||
\(263\) | 1.80266e13i | 0.883401i | 0.897163 | + | 0.441701i | \(0.145625\pi\) | ||||
−0.897163 | + | 0.441701i | \(0.854375\pi\) | |||||||
\(264\) | −1.08413e13 | − | 2.64465e12i | −0.520307 | − | 0.126925i | ||||
\(265\) | − | 3.92662e12i | − | 0.184572i | ||||||
\(266\) | −2.99962e13 | − | 1.75356e13i | −1.38107 | − | 0.807368i | ||||
\(267\) | − | 1.63329e13i | − | 0.736633i | ||||||
\(268\) | −1.92697e13 | − | 1.56821e13i | −0.851400 | − | 0.692887i | ||||
\(269\) | 2.45573e13i | 1.06302i | 0.847051 | + | 0.531511i | \(0.178376\pi\) | ||||
−0.847051 | + | 0.531511i | \(0.821624\pi\) | |||||||
\(270\) | 3.37729e11 | + | 7.10285e11i | 0.0143241 | + | 0.0301253i | ||||
\(271\) | −1.69197e13 | −0.703171 | −0.351586 | − | 0.936156i | \(-0.614357\pi\) | ||||
−0.351586 | + | 0.936156i | \(0.614357\pi\) | |||||||
\(272\) | −1.73897e13 | + | 3.60796e12i | −0.708213 | + | 0.146937i | ||||
\(273\) | −7.25091e9 | + | 4.93871e9i | −0.000289400 | + | 0.000197115i | ||||
\(274\) | −2.97844e12 | + | 1.41620e12i | −0.116509 | + | 0.0553982i | ||||
\(275\) | − | 2.34668e13i | − | 0.899756i | ||||||
\(276\) | 1.86204e13 | + | 1.51537e13i | 0.699825 | + | 0.569532i | ||||
\(277\) | 3.65497e12 | 0.134662 | 0.0673309 | − | 0.997731i | \(-0.478552\pi\) | ||||
0.0673309 | + | 0.997731i | \(0.478552\pi\) | |||||||
\(278\) | −1.09099e13 | + | 5.18746e12i | −0.394070 | + | 0.187373i | ||||
\(279\) | 1.19958e13 | 0.424820 | ||||||||
\(280\) | 1.75221e12 | + | 4.67399e12i | 0.0608440 | + | 0.162300i | ||||
\(281\) | −4.22188e12 | −0.143754 | −0.0718772 | − | 0.997413i | \(-0.522899\pi\) | ||||
−0.0718772 | + | 0.997413i | \(0.522899\pi\) | |||||||
\(282\) | 2.66817e13 | − | 1.26867e13i | 0.890928 | − | 0.423621i | ||||
\(283\) | −3.91328e12 | −0.128149 | −0.0640746 | − | 0.997945i | \(-0.520410\pi\) | ||||
−0.0640746 | + | 0.997945i | \(0.520410\pi\) | |||||||
\(284\) | −2.50431e13 | − | 2.03806e13i | −0.804337 | − | 0.654586i | ||||
\(285\) | 5.08175e12i | 0.160091i | ||||||||
\(286\) | −1.64415e10 | + | 7.81768e9i | −0.000508077 | + | 0.000241582i | ||||
\(287\) | −2.14150e13 | + | 1.45861e13i | −0.649183 | + | 0.442169i | ||||
\(288\) | 6.76893e12 | + | 8.93343e12i | 0.201308 | + | 0.265680i | ||||
\(289\) | 1.63423e13 | 0.476844 | ||||||||
\(290\) | 8.82250e11 | + | 1.85548e12i | 0.0252582 | + | 0.0531212i | ||||
\(291\) | − | 2.83158e13i | − | 0.795458i | ||||||
\(292\) | −7.69335e12 | − | 6.26100e12i | −0.212085 | − | 0.172599i | ||||
\(293\) | − | 5.17504e13i | − | 1.40004i | −0.714121 | − | 0.700022i | \(-0.753173\pi\) | ||
0.714121 | − | 0.700022i | \(-0.246827\pi\) | |||||||
\(294\) | 1.49755e12 | + | 2.16929e13i | 0.0397623 | + | 0.575979i | ||||
\(295\) | − | 4.55297e12i | − | 0.118652i | ||||||
\(296\) | −9.70770e12 | + | 3.97952e13i | −0.248320 | + | 1.01795i | ||||
\(297\) | 7.10969e12i | 0.178521i | ||||||||
\(298\) | 1.55114e13 | − | 7.37540e12i | 0.382350 | − | 0.181801i | ||||
\(299\) | 3.91664e10 | 0.000947813 | ||||||||
\(300\) | −1.48776e13 | + | 1.82811e13i | −0.353480 | + | 0.434347i | ||||
\(301\) | 2.64331e13 | − | 1.80040e13i | 0.616641 | − | 0.420004i | ||||
\(302\) | −2.24967e13 | − | 4.73133e13i | −0.515323 | − | 1.08379i | ||||
\(303\) | 6.06972e12i | 0.136532i | ||||||||
\(304\) | 1.47121e13 | + | 7.09097e13i | 0.324989 | + | 1.56639i | ||||
\(305\) | 1.89638e12 | 0.0411411 | ||||||||
\(306\) | 4.85889e12 | + | 1.02189e13i | 0.103531 | + | 0.217738i | ||||
\(307\) | 5.17255e13 | 1.08254 | 0.541269 | − | 0.840849i | \(-0.317944\pi\) | ||||
0.541269 | + | 0.840849i | \(0.317944\pi\) | |||||||
\(308\) | −3.83860e12 | + | 4.49598e13i | −0.0789121 | + | 0.924262i | ||||
\(309\) | 4.81963e13 | 0.973290 | ||||||||
\(310\) | −4.78150e12 | − | 1.00561e13i | −0.0948583 | − | 0.199499i | ||||
\(311\) | 8.23553e13 | 1.60513 | 0.802564 | − | 0.596567i | \(-0.203469\pi\) | ||||
0.802564 | + | 0.596567i | \(0.203469\pi\) | |||||||
\(312\) | 1.77646e10 | + | 4.33352e9i | 0.000340177 | + | 8.29833e-5i | ||||
\(313\) | − | 1.08163e13i | − | 0.203509i | −0.994810 | − | 0.101755i | \(-0.967554\pi\) | ||
0.994810 | − | 0.101755i | \(-0.0324456\pi\) | |||||||
\(314\) | −3.70672e13 | − | 7.79569e13i | −0.685294 | − | 1.44126i | ||||
\(315\) | 2.62847e12 | − | 1.79029e12i | 0.0477523 | − | 0.0325248i | ||||
\(316\) | −3.57128e13 | − | 2.90638e13i | −0.637595 | − | 0.518888i | ||||
\(317\) | 3.00106e13 | 0.526561 | 0.263281 | − | 0.964719i | \(-0.415195\pi\) | ||||
0.263281 | + | 0.964719i | \(0.415195\pi\) | |||||||
\(318\) | −3.21974e13 | + | 1.53093e13i | −0.555229 | + | 0.264002i | ||||
\(319\) | 1.85727e13i | 0.314794i | ||||||||
\(320\) | 4.79083e12 | − | 9.23528e12i | 0.0798153 | − | 0.153860i | ||||
\(321\) | − | 7.62945e12i | − | 0.124944i | ||||||
\(322\) | 4.89927e13 | − | 8.38063e13i | 0.788722 | − | 1.34918i | ||||
\(323\) | 7.31110e13i | 1.15709i | ||||||||
\(324\) | 4.50742e12 | − | 5.53860e12i | 0.0701344 | − | 0.0861792i | ||||
\(325\) | 3.84528e10i | 0.000588260i | ||||||||
\(326\) | 2.49632e13 | + | 5.25006e13i | 0.375494 | + | 0.789710i | ||||
\(327\) | 2.66866e13 | 0.394712 | ||||||||
\(328\) | 5.24662e13 | + | 1.27987e13i | 0.763086 | + | 0.186149i | ||||
\(329\) | −6.72517e13 | − | 9.87376e13i | −0.961891 | − | 1.41223i | ||||
\(330\) | 5.96008e12 | − | 2.83392e12i | 0.0838350 | − | 0.0398621i | ||||
\(331\) | 9.62657e13i | 1.33174i | 0.746070 | + | 0.665868i | \(0.231938\pi\) | ||||
−0.746070 | + | 0.665868i | \(0.768062\pi\) | |||||||
\(332\) | −7.48009e13 | + | 9.19133e13i | −1.01776 | + | 1.25060i | ||||
\(333\) | 2.60976e13 | 0.349266 | ||||||||
\(334\) | 4.51302e13 | − | 2.14587e13i | 0.594103 | − | 0.282486i | ||||
\(335\) | 1.46930e13 | 0.190267 | ||||||||
\(336\) | 3.14941e13 | − | 3.25910e13i | 0.401202 | − | 0.415175i | ||||
\(337\) | 1.08714e14 | 1.36245 | 0.681227 | − | 0.732073i | \(-0.261447\pi\) | ||||
0.681227 | + | 0.732073i | \(0.261447\pi\) | |||||||
\(338\) | −7.32456e13 | + | 3.48271e13i | −0.903108 | + | 0.429413i | ||||
\(339\) | 6.36671e13 | 0.772355 | ||||||||
\(340\) | 6.62975e12 | − | 8.14646e12i | 0.0791340 | − | 0.0972377i | ||||
\(341\) | − | 1.00658e14i | − | 1.18222i | ||||||
\(342\) | 4.16692e13 | − | 1.98130e13i | 0.481583 | − | 0.228985i | ||||
\(343\) | 8.57485e13 | − | 1.94473e13i | 0.975234 | − | 0.221177i | ||||
\(344\) | −6.47605e13 | − | 1.57978e13i | −0.724834 | − | 0.176817i | ||||
\(345\) | −1.41979e13 | −0.156394 | ||||||||
\(346\) | 5.62843e13 | + | 1.18373e14i | 0.610195 | + | 1.28331i | ||||
\(347\) | 1.09973e14i | 1.17347i | 0.809778 | + | 0.586736i | \(0.199588\pi\) | ||||
−0.809778 | + | 0.586736i | \(0.800412\pi\) | |||||||
\(348\) | 1.17748e13 | − | 1.44685e13i | 0.123671 | − | 0.151963i | ||||
\(349\) | − | 1.16282e14i | − | 1.20219i | −0.799177 | − | 0.601095i | \(-0.794731\pi\) | ||
0.799177 | − | 0.601095i | \(-0.205269\pi\) | |||||||
\(350\) | 8.22793e13 | + | 4.81000e13i | 0.837368 | + | 0.489520i | ||||
\(351\) | − | 1.16500e10i | − | 0.000116717i | ||||||
\(352\) | 7.49614e13 | − | 5.67989e13i | 0.739355 | − | 0.560216i | ||||
\(353\) | − | 5.22570e13i | − | 0.507439i | −0.967278 | − | 0.253719i | \(-0.918346\pi\) | ||
0.967278 | − | 0.253719i | \(-0.0816540\pi\) | |||||||
\(354\) | −3.73333e13 | + | 1.77514e13i | −0.356927 | + | 0.169713i | ||||
\(355\) | 1.90952e13 | 0.179749 | ||||||||
\(356\) | 1.06766e14 | + | 8.68880e13i | 0.989593 | + | 0.805351i | ||||
\(357\) | 3.78157e13 | − | 2.57569e13i | 0.345141 | − | 0.235081i | ||||
\(358\) | 7.25691e13 | + | 1.52622e14i | 0.652222 | + | 1.37170i | ||||
\(359\) | − | 1.30626e14i | − | 1.15614i | −0.815988 | − | 0.578069i | \(-0.803807\pi\) | ||
0.815988 | − | 0.578069i | \(-0.196193\pi\) | |||||||
\(360\) | −6.43968e12 | − | 1.57091e12i | −0.0561307 | − | 0.0136926i | ||||
\(361\) | 1.81633e14 | 1.55921 | ||||||||
\(362\) | −6.43151e13 | − | 1.35263e14i | −0.543771 | − | 1.14362i | ||||
\(363\) | −9.67252e12 | −0.0805477 | ||||||||
\(364\) | 6.28994e9 | − | 7.36712e10i | 5.15928e−5 | − | 0.000604283i | ||||
\(365\) | 5.86610e12 | 0.0473957 | ||||||||
\(366\) | −7.39370e12 | − | 1.55499e13i | −0.0588459 | − | 0.123760i | ||||
\(367\) | 1.51120e12 | 0.0118484 | 0.00592418 | − | 0.999982i | \(-0.498114\pi\) | ||||
0.00592418 | + | 0.999982i | \(0.498114\pi\) | |||||||
\(368\) | −1.98115e14 | + | 4.11041e13i | −1.53022 | + | 0.317484i | ||||
\(369\) | − | 3.44072e13i | − | 0.261821i | ||||||
\(370\) | −1.04025e13 | − | 2.18777e13i | −0.0779878 | − | 0.164018i | ||||
\(371\) | 8.11543e13 | + | 1.19149e14i | 0.599453 | + | 0.880104i | ||||
\(372\) | −6.38153e13 | + | 7.84145e13i | −0.464450 | + | 0.570703i | ||||
\(373\) | −1.23043e14 | −0.882385 | −0.441193 | − | 0.897412i | \(-0.645444\pi\) | ||||
−0.441193 | + | 0.897412i | \(0.645444\pi\) | |||||||
\(374\) | 8.57475e13 | − | 4.07715e13i | 0.605938 | − | 0.288113i | ||||
\(375\) | − | 2.83101e13i | − | 0.197138i | ||||||
\(376\) | −5.90107e13 | + | 2.41905e14i | −0.404946 | + | 1.66001i | ||||
\(377\) | − | 3.04333e10i | − | 0.000205812i | ||||||
\(378\) | −2.49280e13 | − | 1.45728e13i | −0.166143 | − | 0.0971263i | ||||
\(379\) | 2.06465e14i | 1.35622i | 0.734960 | + | 0.678111i | \(0.237201\pi\) | ||||
−0.734960 | + | 0.678111i | \(0.762799\pi\) | |||||||
\(380\) | −3.32186e13 | − | 2.70340e13i | −0.215066 | − | 0.175025i | ||||
\(381\) | 8.75252e13i | 0.558529i | ||||||||
\(382\) | −1.05622e14 | − | 2.22137e14i | −0.664365 | − | 1.39724i | ||||
\(383\) | −8.61224e13 | −0.533977 | −0.266989 | − | 0.963700i | \(-0.586029\pi\) | ||||
−0.266989 | + | 0.963700i | \(0.586029\pi\) | |||||||
\(384\) | −9.44060e13 | − | 3.27673e12i | −0.577003 | − | 0.0200272i | ||||
\(385\) | −1.50225e13 | − | 2.20557e13i | −0.0905125 | − | 0.132889i | ||||
\(386\) | 1.23879e14 | − | 5.89023e13i | 0.735812 | − | 0.349866i | ||||
\(387\) | 4.24697e13i | 0.248696i | ||||||||
\(388\) | 1.85096e14 | + | 1.50635e14i | 1.06862 | + | 0.869664i | ||||
\(389\) | 5.93145e13 | 0.337627 | 0.168814 | − | 0.985648i | \(-0.446006\pi\) | ||||
0.168814 | + | 0.985648i | \(0.446006\pi\) | |||||||
\(390\) | −9.76620e9 | + | 4.64367e9i | −5.48113e−5 | + | 2.60619e-5i | ||||
\(391\) | −2.04265e14 | −1.13037 | ||||||||
\(392\) | −1.49770e14 | − | 1.05613e14i | −0.817243 | − | 0.576294i | ||||
\(393\) | −3.41221e13 | −0.183602 | ||||||||
\(394\) | 2.12624e14 | − | 1.01099e14i | 1.12819 | − | 0.536437i | ||||
\(395\) | 2.72307e13 | 0.142487 | ||||||||
\(396\) | −4.64750e13 | − | 3.78223e13i | −0.239826 | − | 0.195175i | ||||
\(397\) | − | 2.29477e14i | − | 1.16786i | −0.811803 | − | 0.583932i | \(-0.801513\pi\) | ||
0.811803 | − | 0.583932i | \(-0.198487\pi\) | |||||||
\(398\) | −2.62671e14 | + | 1.24896e14i | −1.31842 | + | 0.626889i | ||||
\(399\) | −1.05028e14 | − | 1.54200e14i | −0.519942 | − | 0.763368i | ||||
\(400\) | −4.03551e13 | − | 1.94505e14i | −0.197047 | − | 0.949731i | ||||
\(401\) | −2.42600e13 | −0.116842 | −0.0584208 | − | 0.998292i | \(-0.518607\pi\) | ||||
−0.0584208 | + | 0.998292i | \(0.518607\pi\) | |||||||
\(402\) | −5.72857e13 | − | 1.20479e14i | −0.272147 | − | 0.572358i | ||||
\(403\) | 1.64938e11i | 0.000772936i | ||||||||
\(404\) | −3.96769e13 | − | 3.22898e13i | −0.183417 | − | 0.149269i | ||||
\(405\) | 4.22313e12i | 0.0192589i | ||||||||
\(406\) | −6.51195e13 | − | 3.80685e13i | −0.292966 | − | 0.171266i | ||||
\(407\) | − | 2.18987e14i | − | 0.971964i | ||||||
\(408\) | −9.26476e13 | − | 2.26006e13i | −0.405698 | − | 0.0989668i | ||||
\(409\) | 1.22760e14i | 0.530369i | 0.964198 | + | 0.265185i | \(0.0854329\pi\) | ||||
−0.964198 | + | 0.265185i | \(0.914567\pi\) | |||||||
\(410\) | −2.88437e13 | + | 1.37147e13i | −0.122953 | + | 0.0584622i | ||||
\(411\) | −1.77088e13 | −0.0744835 | ||||||||
\(412\) | −2.56396e14 | + | 3.15052e14i | −1.06408 | + | 1.30752i | ||||
\(413\) | 9.40995e13 | + | 1.38155e14i | 0.385356 | + | 0.565772i | ||||
\(414\) | 5.53555e13 | + | 1.16420e14i | 0.223696 | + | 0.470461i | ||||
\(415\) | − | 7.00830e13i | − | 0.279478i | ||||||
\(416\) | −1.22832e11 | + | 9.30708e10i | −0.000483390 | + | 0.000366269i | ||||
\(417\) | −6.48665e13 | −0.251926 | ||||||||
\(418\) | −1.66253e14 | − | 3.49651e14i | −0.637236 | − | 1.34019i | ||||
\(419\) | −1.00346e14 | −0.379599 | −0.189799 | − | 0.981823i | \(-0.560784\pi\) | ||||
−0.189799 | + | 0.981823i | \(0.560784\pi\) | |||||||
\(420\) | −2.28011e12 | + | 2.67059e13i | −0.00851305 | + | 0.0997094i | ||||
\(421\) | −1.50401e14 | −0.554243 | −0.277121 | − | 0.960835i | \(-0.589380\pi\) | ||||
−0.277121 | + | 0.960835i | \(0.589380\pi\) | |||||||
\(422\) | 3.11601e12 | + | 6.55336e12i | 0.0113339 | + | 0.0238367i | ||||
\(423\) | 1.58641e14 | 0.569564 | ||||||||
\(424\) | 7.12097e13 | − | 2.91913e14i | 0.252364 | − | 1.03452i | ||||
\(425\) | − | 2.00543e14i | − | 0.701565i | ||||||
\(426\) | −7.44493e13 | − | 1.56576e14i | −0.257103 | − | 0.540720i | ||||
\(427\) | −5.75435e13 | + | 3.91938e13i | −0.196175 | + | 0.133618i | ||||
\(428\) | 4.98726e13 | + | 4.05873e13i | 0.167850 | + | 0.136600i | ||||
\(429\) | −9.77561e10 | −0.000324810 | ||||||||
\(430\) | 3.56025e13 | − | 1.69284e13i | 0.116790 | − | 0.0555315i | ||||
\(431\) | − | 1.41120e14i | − | 0.457048i | −0.973538 | − | 0.228524i | \(-0.926610\pi\) | ||
0.973538 | − | 0.228524i | \(-0.0733900\pi\) | |||||||
\(432\) | 1.22263e13 | + | 5.89287e13i | 0.0390962 | + | 0.188437i | ||||
\(433\) | 2.43929e14i | 0.770158i | 0.922884 | + | 0.385079i | \(0.125826\pi\) | ||||
−0.922884 | + | 0.385079i | \(0.874174\pi\) | |||||||
\(434\) | 3.52926e14 | + | 2.06319e14i | 1.10025 | + | 0.643198i | ||||
\(435\) | 1.10321e13i | 0.0339600i | ||||||||
\(436\) | −1.41968e14 | + | 1.74446e14i | −0.431533 | + | 0.530256i | ||||
\(437\) | 8.32925e14i | 2.50010i | ||||||||
\(438\) | −2.28711e13 | − | 4.81007e13i | −0.0677921 | − | 0.142575i | ||||
\(439\) | −7.84321e13 | −0.229583 | −0.114791 | − | 0.993390i | \(-0.536620\pi\) | ||||
−0.114791 | + | 0.993390i | \(0.536620\pi\) | |||||||
\(440\) | −1.31817e13 | + | 5.40361e13i | −0.0381049 | + | 0.156205i | ||||
\(441\) | −4.27567e13 | + | 1.08649e14i | −0.122065 | + | 0.310179i | ||||
\(442\) | −1.40506e11 | + | 6.68083e10i | −0.000396162 | + | 0.000188368i | ||||
\(443\) | − | 4.58531e14i | − | 1.27688i | −0.769673 | − | 0.638438i | \(-0.779581\pi\) | ||
0.769673 | − | 0.638438i | \(-0.220419\pi\) | |||||||
\(444\) | −1.38834e14 | + | 1.70596e14i | −0.381848 | + | 0.469204i | ||||
\(445\) | −8.14078e13 | −0.221149 | ||||||||
\(446\) | 2.09034e14 | − | 9.93923e13i | 0.560888 | − | 0.266693i | ||||
\(447\) | 9.22257e13 | 0.244433 | ||||||||
\(448\) | 4.54996e13 | + | 3.79250e14i | 0.119118 | + | 0.992880i | ||||
\(449\) | 3.57670e14 | 0.924970 | 0.462485 | − | 0.886627i | \(-0.346958\pi\) | ||||
0.462485 | + | 0.886627i | \(0.346958\pi\) | |||||||
\(450\) | −1.14298e14 | + | 5.43469e13i | −0.291992 | + | 0.138837i | ||||
\(451\) | −2.88715e14 | −0.728615 | ||||||||
\(452\) | −3.38698e14 | + | 4.16183e14i | −0.844405 | + | 1.03758i | ||||
\(453\) | − | 2.81309e14i | − | 0.692858i | ||||||
\(454\) | 6.15293e14 | − | 2.92562e14i | 1.49718 | − | 0.711885i | ||||
\(455\) | 2.46159e10 | + | 3.61406e10i | 5.91771e−5 | + | 8.68826e-5i | ||||
\(456\) | −9.21580e13 | + | 3.77787e14i | −0.218890 | + | 0.897305i | ||||
\(457\) | −6.10405e14 | −1.43245 | −0.716224 | − | 0.697870i | \(-0.754131\pi\) | ||||
−0.716224 | + | 0.697870i | \(0.754131\pi\) | |||||||
\(458\) | 2.47861e13 | + | 5.21281e13i | 0.0574708 | + | 0.120868i | ||||
\(459\) | 6.07580e13i | 0.139198i | ||||||||
\(460\) | 7.55302e13 | − | 9.28095e13i | 0.170983 | − | 0.210099i | ||||
\(461\) | − | 6.56071e12i | − | 0.0146756i | −0.999973 | − | 0.00733780i | \(-0.997664\pi\) | ||
0.999973 | − | 0.00733780i | \(-0.00233571\pi\) | |||||||
\(462\) | −1.22282e14 | + | 2.09173e14i | −0.270290 | + | 0.462355i | ||||
\(463\) | 2.00722e14i | 0.438429i | 0.975677 | + | 0.219215i | \(0.0703495\pi\) | ||||
−0.975677 | + | 0.219215i | \(0.929651\pi\) | |||||||
\(464\) | 3.19388e13 | + | 1.53940e14i | 0.0689398 | + | 0.332278i | ||||
\(465\) | − | 5.97903e13i | − | 0.127538i | ||||||
\(466\) | 4.49426e14 | − | 2.13695e14i | 0.947406 | − | 0.450476i | ||||
\(467\) | 1.24443e14 | 0.259255 | 0.129628 | − | 0.991563i | \(-0.458622\pi\) | ||||
0.129628 | + | 0.991563i | \(0.458622\pi\) | |||||||
\(468\) | 7.61541e10 | + | 6.19757e10i | 0.000156798 | + | 0.000127605i | ||||
\(469\) | −4.45842e14 | + | 3.03670e14i | −0.907257 | + | 0.617947i | ||||
\(470\) | −6.32340e13 | − | 1.32989e14i | −0.127178 | − | 0.267471i | ||||
\(471\) | − | 4.63507e14i | − | 0.921385i | ||||||
\(472\) | 8.25686e13 | − | 3.38477e14i | 0.162231 | − | 0.665040i | ||||
\(473\) | 3.56368e14 | 0.692090 | ||||||||
\(474\) | −1.06168e14 | − | 2.23285e14i | −0.203805 | − | 0.428627i | ||||
\(475\) | −8.17749e14 | −1.55169 | ||||||||
\(476\) | −3.28039e13 | + | 3.84217e14i | −0.0615301 | + | 0.720674i | ||||
\(477\) | −1.91436e14 | −0.354954 | ||||||||
\(478\) | 5.37758e13 | + | 1.13097e14i | 0.0985675 | + | 0.207300i | ||||
\(479\) | 3.97194e14 | 0.719710 | 0.359855 | − | 0.933008i | \(-0.382826\pi\) | ||||
0.359855 | + | 0.933008i | \(0.382826\pi\) | |||||||
\(480\) | 4.45268e13 | − | 3.37383e13i | 0.0797617 | − | 0.0604361i | ||||
\(481\) | 3.58833e11i | 0.000635470i | ||||||||
\(482\) | −4.18795e14 | − | 8.80778e14i | −0.733234 | − | 1.54208i | ||||
\(483\) | 4.30820e14 | − | 2.93438e14i | 0.745738 | − | 0.507934i | ||||
\(484\) | 5.14561e13 | − | 6.32278e13i | 0.0880617 | − | 0.108208i | ||||
\(485\) | −1.41134e14 | −0.238810 | ||||||||
\(486\) | 3.46287e13 | − | 1.64654e13i | 0.0579344 | − | 0.0275468i | ||||
\(487\) | 6.65349e14i | 1.10063i | 0.834958 | + | 0.550313i | \(0.185492\pi\) | ||||
−0.834958 | + | 0.550313i | \(0.814508\pi\) | |||||||
\(488\) | 1.40980e14 | + | 3.43910e13i | 0.230595 | + | 0.0562517i | ||||
\(489\) | 3.12152e14i | 0.504855i | ||||||||
\(490\) | 1.08123e14 | − | 7.46421e12i | 0.172919 | − | 0.0119373i | ||||
\(491\) | − | 9.09612e14i | − | 1.43849i | −0.694754 | − | 0.719247i | \(-0.744487\pi\) | ||
0.694754 | − | 0.719247i | \(-0.255513\pi\) | |||||||
\(492\) | 2.24915e14 | + | 1.83040e14i | 0.351730 | + | 0.286245i | ||||
\(493\) | 1.58718e14i | 0.245454i | ||||||||
\(494\) | 2.72423e11 | + | 5.72939e11i | 0.000416625 | + | 0.000876213i | ||||
\(495\) | 3.54367e13 | 0.0535951 | ||||||||
\(496\) | −1.73098e14 | − | 8.34303e14i | −0.258906 | − | 1.24788i | ||||
\(497\) | −5.79422e14 | + | 3.94653e14i | −0.857106 | + | 0.583789i | ||||
\(498\) | −5.74665e14 | + | 2.73243e14i | −0.840724 | + | 0.399750i | ||||
\(499\) | 1.26979e15i | 1.83730i | 0.395076 | + | 0.918649i | \(0.370718\pi\) | ||||
−0.395076 | + | 0.918649i | \(0.629282\pi\) | |||||||
\(500\) | 1.85059e14 | + | 1.50605e14i | 0.264835 | + | 0.215528i | ||||
\(501\) | 2.68330e14 | 0.379806 | ||||||||
\(502\) | 3.02802e14 | − | 1.43977e14i | 0.423924 | − | 0.201569i | ||||
\(503\) | 2.46651e14 | 0.341554 | 0.170777 | − | 0.985310i | \(-0.445372\pi\) | ||||
0.170777 | + | 0.985310i | \(0.445372\pi\) | |||||||
\(504\) | 2.27872e14 | − | 8.54261e13i | 0.312121 | − | 0.117010i | ||||
\(505\) | 3.02532e13 | 0.0409892 | ||||||||
\(506\) | 9.76889e14 | − | 4.64494e14i | 1.30923 | − | 0.622519i | ||||
\(507\) | −4.35495e14 | −0.577350 | ||||||||
\(508\) | −5.72139e14 | − | 4.65618e14i | −0.750328 | − | 0.610632i | ||||
\(509\) | 1.25189e15i | 1.62412i | 0.583572 | + | 0.812061i | \(0.301655\pi\) | ||||
−0.583572 | + | 0.812061i | \(0.698345\pi\) | |||||||
\(510\) | 5.09337e13 | − | 2.42181e13i | 0.0653686 | − | 0.0310817i | ||||
\(511\) | −1.78001e14 | + | 1.21239e14i | −0.225999 | + | 0.153932i | ||||
\(512\) | 5.23643e14 | − | 5.99686e14i | 0.657734 | − | 0.753250i | ||||
\(513\) | 2.47752e14 | 0.307873 | ||||||||
\(514\) | 1.56014e14 | + | 3.28117e14i | 0.191808 | + | 0.403396i | ||||
\(515\) | − | 2.40224e14i | − | 0.292198i | ||||||
\(516\) | −2.77618e14 | − | 2.25931e14i | −0.334099 | − | 0.271896i | ||||
\(517\) | − | 1.33117e15i | − | 1.58502i | ||||||
\(518\) | 7.67813e14 | + | 4.48859e14i | 0.904570 | + | 0.528806i | ||||
\(519\) | 7.03806e14i | 0.820413i | ||||||||
\(520\) | 2.15995e10 | − | 8.85437e10i | 2.49130e−5 | − | 0.000102127i | ||||
\(521\) | − | 3.22040e14i | − | 0.367538i | −0.982969 | − | 0.183769i | \(-0.941170\pi\) | ||
0.982969 | − | 0.183769i | \(-0.0588298\pi\) | |||||||
\(522\) | 9.04607e13 | − | 4.30126e13i | 0.102158 | − | 0.0485744i | ||||
\(523\) | −1.50967e15 | −1.68702 | −0.843512 | − | 0.537110i | \(-0.819516\pi\) | ||||
−0.843512 | + | 0.537110i | \(0.819516\pi\) | |||||||
\(524\) | 1.81523e14 | − | 2.23051e14i | 0.200729 | − | 0.246651i | ||||
\(525\) | 2.88091e14 | + | 4.22970e14i | 0.315249 | + | 0.462842i | ||||
\(526\) | −3.50312e14 | − | 7.36749e14i | −0.379344 | − | 0.797807i | ||||
\(527\) | − | 8.60202e14i | − | 0.921811i | ||||||
\(528\) | 4.94477e14 | − | 1.02592e14i | 0.524397 | − | 0.108800i | ||||
\(529\) | −1.37430e15 | −1.44237 | ||||||||
\(530\) | 7.63061e13 | + | 1.60481e14i | 0.0792578 | + | 0.166689i | ||||
\(531\) | −2.21972e14 | −0.228180 | ||||||||
\(532\) | 1.56671e15 | + | 1.33764e14i | 1.59395 | + | 0.136089i | ||||
\(533\) | 4.73089e11 | 0.000476368 | ||||||||
\(534\) | 3.17397e14 | + | 6.67525e14i | 0.316320 | + | 0.665259i | ||||
\(535\) | −3.80274e13 | −0.0375103 | ||||||||
\(536\) | 1.09230e15 | + | 2.66458e14i | 1.06644 | + | 0.260150i | ||||
\(537\) | 9.07440e14i | 0.876919i | ||||||||
\(538\) | −4.77222e14 | − | 1.00366e15i | −0.456476 | − | 0.960024i | ||||
\(539\) | 9.11684e14 | + | 3.58777e14i | 0.863190 | + | 0.339692i | ||||
\(540\) | −2.76059e13 | − | 2.24663e13i | −0.0258724 | − | 0.0210555i | ||||
\(541\) | −6.30398e14 | −0.584830 | −0.292415 | − | 0.956291i | \(-0.594459\pi\) | ||||
−0.292415 | + | 0.956291i | \(0.594459\pi\) | |||||||
\(542\) | 6.91508e14 | − | 3.28800e14i | 0.635040 | − | 0.301951i | ||||
\(543\) | − | 8.04229e14i | − | 0.731106i | ||||||
\(544\) | 6.40605e14 | − | 4.85392e14i | 0.576496 | − | 0.436816i | ||||
\(545\) | − | 1.33013e14i | − | 0.118499i | ||||||
\(546\) | 2.00371e11 | − | 3.42752e11i | 0.000176716 | − | 0.000302288i | ||||
\(547\) | 5.63290e14i | 0.491815i | 0.969293 | + | 0.245907i | \(0.0790859\pi\) | ||||
−0.969293 | + | 0.245907i | \(0.920914\pi\) | |||||||
\(548\) | 9.42079e13 | − | 1.15760e14i | 0.0814318 | − | 0.100061i | ||||
\(549\) | − | 9.24546e13i | − | 0.0791189i | ||||||
\(550\) | 4.56031e14 | + | 9.59090e14i | 0.386367 | + | 0.812577i | ||||
\(551\) | 6.47203e14 | 0.542883 | ||||||||
\(552\) | −1.05550e15 | − | 2.57480e14i | −0.876582 | − | 0.213835i | ||||
\(553\) | −8.26285e14 | + | 5.62796e14i | −0.679425 | + | 0.462767i | ||||
\(554\) | −1.49379e14 | + | 7.10270e13i | −0.121614 | + | 0.0578255i | ||||
\(555\) | − | 1.30078e14i | − | 0.104855i | ||||||
\(556\) | 3.45078e14 | − | 4.24023e14i | 0.275427 | − | 0.338437i | ||||
\(557\) | 1.56348e15 | 1.23563 | 0.617814 | − | 0.786324i | \(-0.288019\pi\) | ||||
0.617814 | + | 0.786324i | \(0.288019\pi\) | |||||||
\(558\) | −4.90267e14 | + | 2.33114e14i | −0.383658 | + | 0.182423i | ||||
\(559\) | −5.83946e11 | −0.000452489 | ||||||||
\(560\) | −1.62443e14 | − | 1.56975e14i | −0.124643 | − | 0.120447i | ||||
\(561\) | 5.09827e14 | 0.387371 | ||||||||
\(562\) | 1.72548e14 | − | 8.20438e13i | 0.129826 | − | 0.0617300i | ||||
\(563\) | 3.59241e13 | 0.0267664 | 0.0133832 | − | 0.999910i | \(-0.495740\pi\) | ||||
0.0133832 | + | 0.999910i | \(0.495740\pi\) | |||||||
\(564\) | −8.43939e14 | + | 1.03701e15i | −0.622696 | + | 0.765152i | ||||
\(565\) | − | 3.17335e14i | − | 0.231874i | ||||||
\(566\) | 1.59936e14 | − | 7.60468e13i | 0.115733 | − | 0.0550289i | ||||
\(567\) | −8.72824e13 | − | 1.28146e14i | −0.0625489 | − | 0.0918330i | ||||
\(568\) | 1.41957e15 | + | 3.46293e14i | 1.00749 | + | 0.245769i | ||||
\(569\) | 9.67003e14 | 0.679689 | 0.339845 | − | 0.940482i | \(-0.389626\pi\) | ||||
0.339845 | + | 0.940482i | \(0.389626\pi\) | |||||||
\(570\) | −9.87536e13 | − | 2.07691e14i | −0.0687450 | − | 0.144579i | ||||
\(571\) | 1.15637e15i | 0.797254i | 0.917113 | + | 0.398627i | \(0.130513\pi\) | ||||
−0.917113 | + | 0.398627i | \(0.869487\pi\) | |||||||
\(572\) | 5.20045e11 | − | 6.39017e11i | 0.000355110 | − | 0.000436349i | ||||
\(573\) | − | 1.32075e15i | − | 0.893246i | ||||||
\(574\) | 5.91779e14 | − | 1.01229e15i | 0.396410 | − | 0.678094i | ||||
\(575\) | − | 2.28471e15i | − | 1.51586i | ||||||
\(576\) | −4.50250e14 | − | 2.33569e14i | −0.295890 | − | 0.153494i | ||||
\(577\) | − | 1.26741e15i | − | 0.824991i | −0.910960 | − | 0.412496i | \(-0.864657\pi\) | ||
0.910960 | − | 0.412496i | \(-0.135343\pi\) | |||||||
\(578\) | −6.67912e14 | + | 3.17581e14i | −0.430641 | + | 0.204763i | ||||
\(579\) | 7.36544e14 | 0.470399 | ||||||||
\(580\) | −7.21152e13 | − | 5.86888e13i | −0.0456218 | − | 0.0371280i | ||||
\(581\) | 1.44846e15 | + | 2.12659e15i | 0.907688 | + | 1.33265i | ||||
\(582\) | 5.50261e14 | + | 1.15727e15i | 0.341580 | + | 0.718385i | ||||
\(583\) | 1.60636e15i | 0.987791i | ||||||||
\(584\) | 4.36098e14 | + | 1.06382e14i | 0.265652 | + | 0.0648036i | ||||
\(585\) | −5.80667e10 | −3.50405e−5 | ||||||||
\(586\) | 1.00567e15 | + | 2.11504e15i | 0.601197 | + | 1.26439i | ||||
\(587\) | −1.16708e15 | −0.691181 | −0.345591 | − | 0.938385i | \(-0.612321\pi\) | ||||
−0.345591 | + | 0.938385i | \(0.612321\pi\) | |||||||
\(588\) | −4.82763e14 | − | 8.57487e14i | −0.283243 | − | 0.503097i | ||||
\(589\) | −3.50762e15 | −2.03882 | ||||||||
\(590\) | 8.84779e13 | + | 1.86080e14i | 0.0509505 | + | 0.107155i | ||||
\(591\) | 1.26420e15 | 0.721245 | ||||||||
\(592\) | −3.76586e14 | − | 1.81508e15i | −0.212860 | − | 1.02595i | ||||
\(593\) | 5.39604e14i | 0.302186i | 0.988520 | + | 0.151093i | \(0.0482793\pi\) | ||||
−0.988520 | + | 0.151093i | \(0.951721\pi\) | |||||||
\(594\) | −1.38163e14 | − | 2.90573e14i | −0.0766594 | − | 0.161224i | ||||
\(595\) | −1.28379e14 | − | 1.88484e14i | −0.0705752 | − | 0.103617i | ||||
\(596\) | −4.90624e14 | + | 6.02866e14i | −0.267236 | + | 0.328372i | ||||
\(597\) | −1.56176e15 | −0.842859 | ||||||||
\(598\) | −1.60073e12 | + | 7.61122e11i | −0.000855978 | + | 0.000407003i | ||||
\(599\) | 1.92745e15i | 1.02126i | 0.859801 | + | 0.510629i | \(0.170587\pi\) | ||||
−0.859801 | + | 0.510629i | \(0.829413\pi\) | |||||||
\(600\) | 2.52789e14 | − | 1.03627e15i | 0.132717 | − | 0.544051i | ||||
\(601\) | − | 3.03815e15i | − | 1.58052i | −0.612772 | − | 0.790260i | \(-0.709946\pi\) | ||
0.612772 | − | 0.790260i | \(-0.290054\pi\) | |||||||
\(602\) | −7.30449e14 | + | 1.24950e15i | −0.376538 | + | 0.644102i | ||||
\(603\) | − | 7.16329e14i | − | 0.365904i | ||||||
\(604\) | 1.83888e15 | + | 1.49652e15i | 0.930786 | + | 0.757492i | ||||
\(605\) | 4.82106e13i | 0.0241818i | ||||||||
\(606\) | −1.17953e14 | − | 2.48070e14i | −0.0586286 | − | 0.123303i | ||||
\(607\) | −1.95316e15 | −0.962055 | −0.481027 | − | 0.876706i | \(-0.659736\pi\) | ||||
−0.481027 | + | 0.876706i | \(0.659736\pi\) | |||||||
\(608\) | −1.97927e15 | − | 2.61218e15i | −0.966130 | − | 1.27507i | ||||
\(609\) | −2.28008e14 | − | 3.34757e14i | −0.110295 | − | 0.161933i | ||||
\(610\) | −7.75050e13 | + | 3.68523e13i | −0.0371549 | + | 0.0176665i | ||||
\(611\) | 2.18126e12i | 0.00103629i | ||||||||
\(612\) | −3.97166e14 | − | 3.23222e14i | −0.186999 | − | 0.152184i | ||||
\(613\) | 3.13686e15 | 1.46373 | 0.731867 | − | 0.681447i | \(-0.238649\pi\) | ||||
0.731867 | + | 0.681447i | \(0.238649\pi\) | |||||||
\(614\) | −2.11402e15 | + | 1.00518e15i | −0.977649 | + | 0.464856i | ||||
\(615\) | −1.71495e14 | −0.0786030 | ||||||||
\(616\) | −7.16820e14 | − | 1.91210e15i | −0.325624 | − | 0.868595i | ||||
\(617\) | 2.34841e15 | 1.05732 | 0.528660 | − | 0.848834i | \(-0.322695\pi\) | ||||
0.528660 | + | 0.848834i | \(0.322695\pi\) | |||||||
\(618\) | −1.96978e15 | + | 9.36599e14i | −0.878986 | + | 0.417943i | ||||
\(619\) | 2.71378e15 | 1.20026 | 0.600131 | − | 0.799902i | \(-0.295115\pi\) | ||||
0.600131 | + | 0.799902i | \(0.295115\pi\) | |||||||
\(620\) | 3.90840e14 | + | 3.18074e14i | 0.171335 | + | 0.139436i | ||||
\(621\) | 6.92193e14i | 0.300762i | ||||||||
\(622\) | −3.36586e15 | + | 1.60041e15i | −1.44960 | + | 0.689262i | ||||
\(623\) | 2.47023e15 | − | 1.68251e15i | 1.05452 | − | 0.718248i | ||||
\(624\) | −8.10252e11 | + | 1.68108e11i | −0.000342850 | + | 7.11333e-5i | ||||
\(625\) | 2.17145e15 | 0.910773 | ||||||||
\(626\) | 2.10193e14 | + | 4.42061e14i | 0.0873894 | + | 0.183791i | ||||
\(627\) | − | 2.07891e15i | − | 0.856770i | ||||||
\(628\) | 3.02987e15 | + | 2.46577e15i | 1.23779 | + | 1.00734i | ||||
\(629\) | − | 1.87142e15i | − | 0.757868i | ||||||
\(630\) | −7.26347e13 | + | 1.24248e14i | −0.0291589 | + | 0.0498789i | ||||
\(631\) | 2.86363e15i | 1.13961i | 0.821780 | + | 0.569805i | \(0.192981\pi\) | ||||
−0.821780 | + | 0.569805i | \(0.807019\pi\) | |||||||
\(632\) | 2.02438e15 | + | 4.93831e14i | 0.798634 | + | 0.194820i | ||||
\(633\) | 3.89642e13i | 0.0152386i | ||||||||
\(634\) | −1.22653e15 | + | 5.83197e14i | −0.475542 | + | 0.226112i | ||||
\(635\) | 4.36251e14 | 0.167680 | ||||||||
\(636\) | 1.01840e15 | − | 1.25139e15i | 0.388066 | − | 0.476845i | ||||
\(637\) | −1.49389e12 | − | 5.87892e11i | −0.000564353 | − | 0.000222091i | ||||
\(638\) | −3.60923e14 | − | 7.59066e14i | −0.135176 | − | 0.284293i | ||||
\(639\) | − | 9.30951e14i | − | 0.345678i | ||||||
\(640\) | −1.63322e13 | + | 4.70546e14i | −0.00601248 | + | 0.173226i | ||||
\(641\) | −4.03073e15 | −1.47117 | −0.735587 | − | 0.677430i | \(-0.763094\pi\) | ||||
−0.735587 | + | 0.677430i | \(0.763094\pi\) | |||||||
\(642\) | 1.48263e14 | + | 3.11816e14i | 0.0536526 | + | 0.112838i | ||||
\(643\) | −2.73534e15 | −0.981412 | −0.490706 | − | 0.871325i | \(-0.663261\pi\) | ||||
−0.490706 | + | 0.871325i | \(0.663261\pi\) | |||||||
\(644\) | −3.73722e14 | + | 4.37724e15i | −0.132947 | + | 1.55714i | ||||
\(645\) | 2.11681e14 | 0.0746628 | ||||||||
\(646\) | −1.42077e15 | − | 2.98805e15i | −0.496871 | − | 1.04498i | ||||
\(647\) | 1.24307e15 | 0.431046 | 0.215523 | − | 0.976499i | \(-0.430854\pi\) | ||||
0.215523 | + | 0.976499i | \(0.430854\pi\) | |||||||
\(648\) | −7.65869e13 | + | 3.13955e14i | −0.0263325 | + | 0.107946i | ||||
\(649\) | 1.86259e15i | 0.634997i | ||||||||
\(650\) | −7.47254e11 | − | 1.57157e12i | −0.000252607 | − | 0.000531263i | ||||
\(651\) | 1.23573e15 | + | 1.81427e15i | 0.414217 | + | 0.608145i | ||||
\(652\) | −2.04049e15 | − | 1.66059e15i | −0.678223 | − | 0.551952i | ||||
\(653\) | 5.49631e14 | 0.181154 | 0.0905772 | − | 0.995889i | \(-0.471129\pi\) | ||||
0.0905772 | + | 0.995889i | \(0.471129\pi\) | |||||||
\(654\) | −1.09068e15 | + | 5.18600e14i | −0.356467 | + | 0.169494i | ||||
\(655\) | 1.70074e14i | 0.0551203i | ||||||||
\(656\) | −2.39301e15 | + | 4.96493e14i | −0.769084 | + | 0.159567i | ||||
\(657\) | − | 2.85992e14i | − | 0.0911473i | ||||||
\(658\) | 4.66735e15 | + | 2.72850e15i | 1.47512 | + | 0.862347i | ||||
\(659\) | 8.09334e14i | 0.253664i | 0.991924 | + | 0.126832i | \(0.0404808\pi\) | ||||
−0.991924 | + | 0.126832i | \(0.959519\pi\) | |||||||
\(660\) | −1.88517e14 | + | 2.31645e14i | −0.0585948 | + | 0.0719997i | ||||
\(661\) | 1.42093e15i | 0.437992i | 0.975726 | + | 0.218996i | \(0.0702781\pi\) | ||||
−0.975726 | + | 0.218996i | \(0.929722\pi\) | |||||||
\(662\) | −1.87073e15 | − | 3.93438e15i | −0.571864 | − | 1.20270i | ||||
\(663\) | −8.35404e11 | −0.000253263 | ||||||||
\(664\) | 1.27096e15 | − | 5.21010e15i | 0.382127 | − | 1.56647i | ||||
\(665\) | −7.68577e14 | + | 5.23490e14i | −0.229176 | + | 0.156095i | ||||
\(666\) | −1.06661e15 | + | 5.07154e14i | −0.315425 | + | 0.149979i | ||||
\(667\) | 1.80822e15i | 0.530346i | ||||||||
\(668\) | −1.42747e15 | + | 1.75403e15i | −0.415236 | + | 0.510231i | ||||
\(669\) | 1.24285e15 | 0.358571 | ||||||||
\(670\) | −6.00502e14 | + | 2.85528e14i | −0.171831 | + | 0.0817030i | ||||
\(671\) | −7.75796e14 | −0.220178 | ||||||||
\(672\) | −6.53822e14 | + | 1.94402e15i | −0.184047 | + | 0.547229i | ||||
\(673\) | 2.59896e15 | 0.725633 | 0.362816 | − | 0.931861i | \(-0.381815\pi\) | ||||
0.362816 | + | 0.931861i | \(0.381815\pi\) | |||||||
\(674\) | −4.44315e15 | + | 2.11264e15i | −1.23044 | + | 0.585055i | ||||
\(675\) | −6.79581e14 | −0.186668 | ||||||||
\(676\) | 2.31675e15 | − | 2.84676e15i | 0.631209 | − | 0.775612i | ||||
\(677\) | − | 5.09684e15i | − | 1.37741i | −0.725042 | − | 0.688705i | \(-0.758180\pi\) | ||
0.725042 | − | 0.688705i | \(-0.241820\pi\) | |||||||
\(678\) | −2.60208e15 | + | 1.23724e15i | −0.697520 | + | 0.331659i | ||||
\(679\) | 4.28256e15 | − | 2.91692e15i | 1.13873 | − | 0.775605i | ||||
\(680\) | −1.12648e14 | + | 4.61782e14i | −0.0297115 | + | 0.121797i | ||||
\(681\) | 3.65833e15 | 0.957138 | ||||||||
\(682\) | 1.95608e15 | + | 4.11389e15i | 0.507661 | + | 1.06767i | ||||
\(683\) | − | 3.23473e15i | − | 0.832769i | −0.909189 | − | 0.416384i | \(-0.863297\pi\) | ||
0.909189 | − | 0.416384i | \(-0.136703\pi\) | |||||||
\(684\) | −1.31799e15 | + | 1.61951e15i | −0.336593 | + | 0.413596i | ||||
\(685\) | 8.82659e13i | 0.0223612i | ||||||||
\(686\) | −3.12662e15 | + | 2.46116e15i | −0.785765 | + | 0.618525i | ||||
\(687\) | 3.09937e14i | 0.0772701i | ||||||||
\(688\) | 2.95376e15 | − | 6.12835e14i | 0.730531 | − | 0.151568i | ||||
\(689\) | − | 2.63218e12i | − | 0.000645818i | ||||||
\(690\) | 5.80268e14 | − | 2.75908e14i | 0.141240 | − | 0.0671574i | ||||
\(691\) | −1.14923e15 | −0.277509 | −0.138755 | − | 0.990327i | \(-0.544310\pi\) | ||||
−0.138755 | + | 0.990327i | \(0.544310\pi\) | |||||||
\(692\) | −4.60068e15 | − | 3.74412e15i | −1.10214 | − | 0.896947i | ||||
\(693\) | −1.07529e15 | + | 7.32397e14i | −0.255560 | + | 0.174066i | ||||
\(694\) | −2.13710e15 | − | 4.49459e15i | −0.503904 | − | 1.05977i | ||||
\(695\) | 3.23313e14i | 0.0756323i | ||||||||
\(696\) | −2.00068e14 | + | 8.20147e14i | −0.0464331 | + | 0.190345i | ||||
\(697\) | −2.46730e15 | −0.568122 | ||||||||
\(698\) | 2.25971e15 | + | 4.75246e15i | 0.516236 | + | 1.08571i | ||||
\(699\) | 2.67215e15 | 0.605669 | ||||||||
\(700\) | −4.29749e15 | − | 3.66913e14i | −0.966441 | − | 0.0825133i | ||||
\(701\) | −1.26750e15 | −0.282812 | −0.141406 | − | 0.989952i | \(-0.545162\pi\) | ||||
−0.141406 | + | 0.989952i | \(0.545162\pi\) | |||||||
\(702\) | 2.26394e11 | + | 4.76134e11i | 5.01199e−5 | + | 0.000105408i | ||||
\(703\) | −7.63106e15 | −1.67622 | ||||||||
\(704\) | −1.95990e15 | + | 3.77810e15i | −0.427154 | + | 0.823424i | ||||
\(705\) | − | 7.90710e14i | − | 0.170992i | ||||||
\(706\) | 1.01551e15 | + | 2.13574e15i | 0.217901 | + | 0.458272i | ||||
\(707\) | −9.18001e14 | + | 6.25265e14i | −0.195450 | + | 0.133124i | ||||
\(708\) | 1.18085e15 | − | 1.45100e15i | 0.249467 | − | 0.306538i | ||||
\(709\) | 2.31841e15 | 0.486000 | 0.243000 | − | 0.970026i | \(-0.421869\pi\) | ||||
0.243000 | + | 0.970026i | \(0.421869\pi\) | |||||||
\(710\) | −7.80419e14 | + | 3.71076e14i | −0.162333 | + | 0.0771867i | ||||
\(711\) | − | 1.32758e15i | − | 0.274018i | ||||||
\(712\) | −6.05201e15 | − | 1.47634e15i | −1.23954 | − | 0.302375i | ||||
\(713\) | − | 9.79995e15i | − | 1.99173i | ||||||
\(714\) | −1.04499e15 | + | 1.78756e15i | −0.210753 | + | 0.360512i | ||||
\(715\) | 4.87244e11i | 9.75132e-5i | ||||||||
\(716\) | −5.93180e15 | − | 4.82742e15i | −1.17805 | − | 0.958724i | ||||
\(717\) | 6.72440e14i | 0.132525i | ||||||||
\(718\) | 2.53845e15 | + | 5.33868e15i | 0.496460 | + | 1.04412i | ||||
\(719\) | −5.67615e15 | −1.10165 | −0.550827 | − | 0.834620i | \(-0.685688\pi\) | ||||
−0.550827 | + | 0.834620i | \(0.685688\pi\) | |||||||
\(720\) | 2.93717e14 | − | 6.09394e13i | 0.0565719 | − | 0.0117373i | ||||
\(721\) | 4.96488e15 | + | 7.28934e15i | 0.948998 | + | 1.39330i | ||||
\(722\) | −7.42333e15 | + | 3.52967e15i | −1.40813 | + | 0.669544i | ||||
\(723\) | − | 5.23682e15i | − | 0.985841i | ||||||
\(724\) | 5.25712e15 | + | 4.27835e15i | 0.982168 | + | 0.799308i | ||||
\(725\) | −1.77527e15 | −0.329159 | ||||||||
\(726\) | 3.95316e14 | − | 1.87966e14i | 0.0727433 | − | 0.0345882i | ||||
\(727\) | −5.53672e15 | −1.01114 | −0.505572 | − | 0.862784i | \(-0.668719\pi\) | ||||
−0.505572 | + | 0.862784i | \(0.668719\pi\) | |||||||
\(728\) | 1.17458e12 | + | 3.13318e12i | 0.000212893 | + | 0.000567887i | ||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −2.39748e14 | + | 1.13996e14i | −0.0428035 | + | 0.0203523i | ||||
\(731\) | 3.04545e15 | 0.539643 | ||||||||
\(732\) | 6.04362e14 | + | 4.91842e14i | 0.106288 | + | 0.0864997i | ||||
\(733\) | − | 5.96837e15i | − | 1.04180i | −0.853618 | − | 0.520900i | \(-0.825597\pi\) | ||
0.853618 | − | 0.520900i | \(-0.174403\pi\) | |||||||
\(734\) | −6.17627e13 | + | 2.93671e13i | −0.0107003 | + | 0.00508783i | ||||
\(735\) | 5.41537e14 | + | 2.13112e14i | 0.0931210 | + | 0.0366460i | ||||
\(736\) | 7.29817e15 | − | 5.52989e15i | 1.24562 | − | 0.943818i | ||||
\(737\) | −6.01080e15 | −1.01827 | ||||||||
\(738\) | 6.68636e14 | + | 1.40622e15i | 0.112429 | + | 0.236453i | ||||
\(739\) | 4.23156e15i | 0.706246i | 0.935577 | + | 0.353123i | \(0.114880\pi\) | ||||
−0.935577 | + | 0.353123i | \(0.885120\pi\) | |||||||
\(740\) | 8.50298e14 | + | 6.91990e14i | 0.140863 | + | 0.114637i | ||||
\(741\) | 3.40651e12i | 0.000560157i | ||||||||
\(742\) | −5.63220e15 | − | 3.29255e15i | −0.919299 | − | 0.537417i | ||||
\(743\) | 1.66451e15i | 0.269680i | 0.990867 | + | 0.134840i | \(0.0430520\pi\) | ||||
−0.990867 | + | 0.134840i | \(0.956948\pi\) | |||||||
\(744\) | 1.08430e15 | − | 4.44493e15i | 0.174381 | − | 0.714848i | ||||
\(745\) | − | 4.59679e14i | − | 0.0733830i | ||||||
\(746\) | 5.02877e15 | − | 2.39110e15i | 0.796889 | − | 0.378908i | ||||
\(747\) | −3.41677e15 | −0.537468 | ||||||||
\(748\) | −2.71219e15 | + | 3.33266e15i | −0.423508 | + | 0.520395i | ||||
\(749\) | 1.15390e15 | − | 7.85939e14i | 0.178862 | − | 0.121826i | ||||
\(750\) | 5.50151e14 | + | 1.15704e15i | 0.0846535 | + | 0.178037i | ||||
\(751\) | 3.76217e15i | 0.574670i | 0.957830 | + | 0.287335i | \(0.0927693\pi\) | ||||
−0.957830 | + | 0.287335i | \(0.907231\pi\) | |||||||
\(752\) | −2.28917e15 | − | 1.10334e16i | −0.347120 | − | 1.67306i | ||||
\(753\) | 1.80036e15 | 0.271011 | ||||||||
\(754\) | 5.91410e11 | + | 1.24381e12i | 8.83784e−5 | + | 0.000185871i | ||||
\(755\) | −1.40213e15 | −0.208007 | ||||||||
\(756\) | 1.30200e15 | + | 1.11163e14i | 0.191752 | + | 0.0163715i | ||||
\(757\) | 1.95060e15 | 0.285195 | 0.142597 | − | 0.989781i | \(-0.454455\pi\) | ||||
0.142597 | + | 0.989781i | \(0.454455\pi\) | |||||||
\(758\) | −4.01223e15 | − | 8.43822e15i | −0.582379 | − | 1.22481i | ||||
\(759\) | 5.80827e15 | 0.836984 | ||||||||
\(760\) | 1.88300e15 | + | 4.59342e14i | 0.269386 | + | 0.0657145i | ||||
\(761\) | − | 7.62489e15i | − | 1.08297i | −0.840709 | − | 0.541487i | \(-0.817862\pi\) | ||
0.840709 | − | 0.541487i | \(-0.182138\pi\) | |||||||
\(762\) | −1.70088e15 | − | 3.57716e15i | −0.239840 | − | 0.504412i | ||||
\(763\) | 2.74908e15 | + | 4.03615e15i | 0.384860 | + | 0.565044i | ||||
\(764\) | 8.63356e15 | + | 7.02617e15i | 1.19999 | + | 0.976574i | ||||
\(765\) | 3.02835e14 | 0.0417896 | ||||||||
\(766\) | 3.51982e15 | − | 1.67362e15i | 0.482239 | − | 0.229297i | ||||
\(767\) | − | 3.05205e12i | − | 0.000415161i | ||||||
\(768\) | 3.92205e15 | − | 1.70067e15i | 0.529696 | − | 0.229686i | ||||
\(769\) | − | 9.15314e15i | − | 1.22737i | −0.789551 | − | 0.613685i | \(-0.789687\pi\) | ||
0.789551 | − | 0.613685i | \(-0.210313\pi\) | |||||||
\(770\) | 1.04258e15 | + | 6.09486e14i | 0.138807 | + | 0.0811456i | ||||
\(771\) | 1.95088e15i | 0.257888i | ||||||||
\(772\) | −3.91828e15 | + | 4.81468e15i | −0.514281 | + | 0.631934i | ||||
\(773\) | 9.67601e15i | 1.26098i | 0.776197 | + | 0.630491i | \(0.217146\pi\) | ||||
−0.776197 | + | 0.630491i | \(0.782854\pi\) | |||||||
\(774\) | −8.25315e14 | − | 1.73574e15i | −0.106793 | − | 0.224600i | ||||
\(775\) | 9.62139e15 | 1.23617 | ||||||||
\(776\) | −1.04922e16 | − | 2.55948e15i | −1.33852 | − | 0.326522i | ||||
\(777\) | 2.68841e15 | + | 3.94706e15i | 0.340549 | + | 0.499987i | ||||
\(778\) | −2.42418e15 | + | 1.15266e15i | −0.304914 | + | 0.144982i | ||||
\(779\) | 1.00608e16i | 1.25655i | ||||||||
\(780\) | 3.08905e11 | − | 3.79573e11i | 3.83093e−5 | − | 4.70734e-5i | ||||
\(781\) | −7.81171e15 | −0.961979 | ||||||||
\(782\) | 8.34830e15 | − | 3.96948e15i | 1.02085 | − | 0.485396i | ||||
\(783\) | 5.37850e14 | 0.0653088 | ||||||||
\(784\) | 8.17347e15 | + | 1.40593e15i | 0.985527 | + | 0.169521i | ||||
\(785\) | −2.31025e15 | −0.276615 | ||||||||
\(786\) | 1.39457e15 | − | 6.63095e14i | 0.165812 | − | 0.0788409i | ||||
\(787\) | 1.01634e16 | 1.19999 | 0.599994 | − | 0.800004i | \(-0.295169\pi\) | ||||
0.599994 | + | 0.800004i | \(0.295169\pi\) | |||||||
\(788\) | −6.72529e15 | + | 8.26385e15i | −0.788528 | + | 0.968921i | ||||
\(789\) | − | 4.38047e15i | − | 0.510032i | ||||||
\(790\) | −1.11292e15 | + | 5.29174e14i | −0.128681 | + | 0.0611856i | ||||
\(791\) | 6.55860e15 | + | 9.62919e15i | 0.753078 | + | 1.10565i | ||||
\(792\) | 2.63443e15 | + | 6.42649e14i | 0.300399 | + | 0.0732800i | ||||
\(793\) | 1.27122e12 | 0.000143952 | ||||||||
\(794\) | 4.45944e15 | + | 9.37875e15i | 0.501496 | + | 1.05471i | ||||
\(795\) | 9.54169e14i | 0.106563i | ||||||||
\(796\) | 8.30827e15 | − | 1.02090e16i | 0.921486 | − | 1.13230i | ||||
\(797\) | 1.11186e16i | 1.22470i | 0.790587 | + | 0.612350i | \(0.209776\pi\) | ||||
−0.790587 | + | 0.612350i | \(0.790224\pi\) | |||||||
\(798\) | 7.28907e15 | + | 4.26115e15i | 0.797363 | + | 0.466134i | ||||
\(799\) | − | 1.13759e16i | − | 1.23589i | ||||||
\(800\) | 5.42913e15 | + | 7.16520e15i | 0.585781 | + | 0.773095i | ||||
\(801\) | 3.96889e15i | 0.425295i | ||||||||
\(802\) | 9.91508e14 | − | 4.71445e14i | 0.105521 | − | 0.0501733i | ||||
\(803\) | −2.39979e15 | −0.253651 | ||||||||
\(804\) | 4.68254e15 | + | 3.81074e15i | 0.491556 | + | 0.400038i | ||||
\(805\) | −1.46258e15 | − | 2.14733e15i | −0.152490 | − | 0.223883i | ||||
\(806\) | −3.20524e12 | − | 6.74103e12i | −0.000331909 | − | 0.000698045i | ||||
\(807\) | − | 5.96742e15i | − | 0.613736i | ||||||
\(808\) | 2.24908e15 | + | 5.48645e14i | 0.229743 | + | 0.0560440i | ||||
\(809\) | 1.32449e16 | 1.34379 | 0.671896 | − | 0.740646i | \(-0.265480\pi\) | ||||
0.671896 | + | 0.740646i | \(0.265480\pi\) | |||||||
\(810\) | −8.20681e13 | − | 1.72599e14i | −0.00827002 | − | 0.0173929i | ||||
\(811\) | 8.19982e15 | 0.820710 | 0.410355 | − | 0.911926i | \(-0.365405\pi\) | ||||
0.410355 | + | 0.911926i | \(0.365405\pi\) | |||||||
\(812\) | 3.40122e15 | + | 2.90391e14i | 0.338124 | + | 0.0288686i | ||||
\(813\) | 4.11148e15 | 0.405976 | ||||||||
\(814\) | 4.25559e15 | + | 8.95002e15i | 0.417374 | + | 0.877788i | ||||
\(815\) | 1.55585e15 | 0.151566 | ||||||||
\(816\) | 4.22571e15 | − | 8.76733e14i | 0.408887 | − | 0.0848343i | ||||
\(817\) | − | 1.24184e16i | − | 1.19356i | ||||||
\(818\) | −2.38559e15 | − | 5.01720e15i | −0.227747 | − | 0.478981i | ||||
\(819\) | 1.76197e12 | − | 1.20011e12i | 0.000167085 | − | 0.000113804i | ||||
\(820\) | 9.12325e14 | − | 1.12104e15i | 0.0859356 | − | 0.105595i | ||||
\(821\) | 3.64874e15 | 0.341393 | 0.170697 | − | 0.985324i | \(-0.445398\pi\) | ||||
0.170697 | + | 0.985324i | \(0.445398\pi\) | |||||||
\(822\) | 7.23761e14 | − | 3.44136e14i | 0.0672667 | − | 0.0319842i | ||||
\(823\) | − | 2.77704e15i | − | 0.256380i | −0.991750 | − | 0.128190i | \(-0.959083\pi\) | ||
0.991750 | − | 0.128190i | \(-0.0409167\pi\) | |||||||
\(824\) | 4.35649e15 | − | 1.78587e16i | 0.399519 | − | 1.63776i | ||||
\(825\) | 5.70244e15i | 0.519474i | ||||||||
\(826\) | −6.53062e15 | − | 3.81776e15i | −0.590968 | − | 0.345476i | ||||
\(827\) | 1.15483e16i | 1.03810i | 0.854744 | + | 0.519050i | \(0.173714\pi\) | ||||
−0.854744 | + | 0.519050i | \(0.826286\pi\) | |||||||
\(828\) | −4.52476e15 | − | 3.68234e15i | −0.404044 | − | 0.328819i | ||||
\(829\) | 1.31645e13i | 0.00116776i | 1.00000 | 0.000583880i | \(0.000185855\pi\) | |||||
−1.00000 | 0.000583880i | \(0.999814\pi\) | ||||||||
\(830\) | 1.36192e15 | + | 2.86429e15i | 0.120012 | + | 0.252399i | ||||
\(831\) | −8.88157e14 | −0.0777471 | ||||||||
\(832\) | 3.21150e12 | − | 6.19080e12i | 0.000279273 | − | 0.000538355i | ||||
\(833\) | 7.79107e15 | + | 3.06603e15i | 0.673054 | + | 0.264868i | ||||
\(834\) | 2.65110e15 | − | 1.26055e15i | 0.227516 | − | 0.108180i | ||||
\(835\) | − | 1.33743e15i | − | 0.114024i | ||||||
\(836\) | 1.35895e16 | + | 1.10594e16i | 1.15099 | + | 0.936695i | ||||
\(837\) | −2.91497e15 | −0.245270 | ||||||||
\(838\) | 4.10116e15 | − | 1.95003e15i | 0.342819 | − | 0.163004i | ||||
\(839\) | 1.22372e15 | 0.101623 | 0.0508113 | − | 0.998708i | \(-0.483819\pi\) | ||||
0.0508113 | + | 0.998708i | \(0.483819\pi\) | |||||||
\(840\) | −4.25788e14 | − | 1.13578e15i | −0.0351283 | − | 0.0937040i | ||||
\(841\) | −1.07955e16 | −0.884838 | ||||||||
\(842\) | 6.14690e15 | − | 2.92275e15i | 0.500541 | − | 0.237999i | ||||
\(843\) | 1.02592e15 | 0.0829966 | ||||||||
\(844\) | −2.54703e14 | − | 2.07283e14i | −0.0204716 | − | 0.0166602i | ||||
\(845\) | 2.17063e15i | 0.173330i | ||||||||
\(846\) | −6.48364e15 | + | 3.08286e15i | −0.514378 | + | 0.244578i | ||||
\(847\) | −9.96403e14 | − | 1.46290e15i | −0.0785374 | − | 0.115307i | ||||
\(848\) | 2.76240e15 | + | 1.33143e16i | 0.216326 | + | 1.04266i | ||||
\(849\) | 9.50927e14 | 0.0739869 | ||||||||
\(850\) | 3.89715e15 | + | 8.19619e15i | 0.301261 | + | 0.633589i | ||||
\(851\) | − | 2.13204e16i | − | 1.63751i | ||||||
\(852\) | 6.08548e15 | + | 4.95249e15i | 0.464384 | + | 0.377925i | ||||
\(853\) | 1.85999e16i | 1.41024i | 0.709090 | + | 0.705118i | \(0.249106\pi\) | ||||
−0.709090 | + | 0.705118i | \(0.750894\pi\) | |||||||
\(854\) | 1.59015e15 | − | 2.72010e15i | 0.119790 | − | 0.204911i | ||||
\(855\) | − | 1.23486e15i | − | 0.0924284i | ||||||
\(856\) | −2.82703e15 | − | 6.89630e14i | −0.210244 | − | 0.0512874i | ||||
\(857\) | − | 4.77513e15i | − | 0.352851i | −0.984314 | − | 0.176425i | \(-0.943547\pi\) | ||
0.984314 | − | 0.176425i | \(-0.0564534\pi\) | |||||||
\(858\) | 3.99529e12 | − | 1.89970e12i | 0.000293338 | − | 0.000139477i | ||||
\(859\) | −2.45789e16 | −1.79309 | −0.896543 | − | 0.442958i | \(-0.853929\pi\) | ||||
−0.896543 | + | 0.442958i | \(0.853929\pi\) | |||||||
\(860\) | −1.12611e15 | + | 1.38373e15i | −0.0816278 | + | 0.100302i | ||||
\(861\) | 5.20384e15 | − | 3.54442e15i | 0.374806 | − | 0.255286i | ||||
\(862\) | 2.74238e15 | + | 5.76756e15i | 0.196262 | + | 0.412764i | ||||
\(863\) | − | 1.75527e16i | − | 1.24820i | −0.781345 | − | 0.624100i | \(-0.785466\pi\) | ||
0.781345 | − | 0.624100i | \(-0.214534\pi\) | |||||||
\(864\) | −1.64485e15 | − | 2.17082e15i | −0.116225 | − | 0.153391i | ||||
\(865\) | 3.50797e15 | 0.246302 | ||||||||
\(866\) | −4.74027e15 | − | 9.96938e15i | −0.330716 | − | 0.695536i | ||||
\(867\) | −3.97119e15 | −0.275306 | ||||||||
\(868\) | −1.84335e16 | − | 1.57382e15i | −1.26984 | − | 0.108417i | ||||
\(869\) | −1.11399e16 | −0.762557 | ||||||||
\(870\) | −2.14387e14 | − | 4.50882e14i | −0.0145828 | − | 0.0306695i | ||||
\(871\) | 9.84931e12 | 0.000665742 | ||||||||
\(872\) | 2.41221e15 | − | 9.88847e15i | 0.162022 | − | 0.664184i | ||||
\(873\) | 6.88074e15i | 0.459258i | ||||||||
\(874\) | −1.61862e16 | − | 3.40417e16i | −1.07358 | − | 2.25787i | ||||
\(875\) | 4.28170e15 | − | 2.91634e15i | 0.282210 | − | 0.192218i | ||||
\(876\) | 1.86948e15 | + | 1.52142e15i | 0.122447 | + | 0.0996501i | ||||
\(877\) | −3.59018e14 | −0.0233678 | −0.0116839 | − | 0.999932i | \(-0.503719\pi\) | ||||
−0.0116839 | + | 0.999932i | \(0.503719\pi\) | |||||||
\(878\) | 3.20552e15 | − | 1.52417e15i | 0.207338 | − | 0.0985857i | ||||
\(879\) | 1.25753e16i | 0.808316i | ||||||||
\(880\) | −5.11349e14 | − | 2.46462e15i | −0.0326635 | − | 0.157433i | ||||
\(881\) | 2.03463e15i | 0.129157i | 0.997913 | + | 0.0645786i | \(0.0205703\pi\) | ||||
−0.997913 | + | 0.0645786i | \(0.979430\pi\) | |||||||
\(882\) | −3.63905e14 | − | 5.27137e15i | −0.0229567 | − | 0.332542i | ||||
\(883\) | − | 2.71105e16i | − | 1.69963i | −0.527082 | − | 0.849815i | \(-0.676714\pi\) | ||
0.527082 | − | 0.849815i | \(-0.323286\pi\) | |||||||
\(884\) | 4.44420e12 | − | 5.46091e12i | 0.000276889 | − | 0.000340234i | ||||
\(885\) | 1.10637e15i | 0.0685036i | ||||||||
\(886\) | 8.91065e15 | + | 1.87402e16i | 0.548307 | + | 1.15316i | ||||
\(887\) | −2.71093e16 | −1.65782 | −0.828911 | − | 0.559381i | \(-0.811039\pi\) | ||||
−0.828911 | + | 0.559381i | \(0.811039\pi\) | |||||||
\(888\) | 2.35897e15 | − | 9.67022e15i | 0.143368 | − | 0.587713i | ||||
\(889\) | −1.32376e16 | + | 9.01631e15i | −0.799554 | + | 0.544589i | ||||
\(890\) | 3.32714e15 | − | 1.58200e15i | 0.199722 | − | 0.0949644i | ||||
\(891\) | − | 1.72766e15i | − | 0.103069i | ||||||
\(892\) | −6.61175e15 | + | 8.12433e15i | −0.392021 | + | 0.481705i | ||||
\(893\) | −4.63873e16 | −2.73348 | ||||||||
\(894\) | −3.76927e15 | + | 1.79222e15i | −0.220750 | + | 0.104963i | ||||
\(895\) | 4.52294e15 | 0.263266 | ||||||||
\(896\) | −9.22954e15 | − | 1.46158e16i | −0.533932 | − | 0.845527i | ||||
\(897\) | −9.51745e12 | −0.000547220 | ||||||||
\(898\) | −1.46180e16 | + | 6.95060e15i | −0.835348 | + | 0.397194i | ||||
\(899\) | −7.61479e15 | −0.432494 | ||||||||
\(900\) | 3.61525e15 | − | 4.44232e15i | 0.204082 | − | 0.250770i | ||||
\(901\) | 1.37276e16i | 0.770209i | ||||||||
\(902\) | 1.17998e16 | − | 5.61060e15i | 0.658018 | − | 0.312877i | ||||
\(903\) | −6.42324e15 | + | 4.37497e15i | −0.356018 | + | 0.242489i | ||||
\(904\) | 5.75491e15 | − | 2.35913e16i | 0.317038 | − | 1.29965i | ||||
\(905\) | −4.00850e15 | −0.219490 | ||||||||
\(906\) | 5.46669e15 | + | 1.14971e16i | 0.297522 | + | 0.625726i | ||||
\(907\) | 3.95568e15i | 0.213984i | 0.994260 | + | 0.106992i | \(0.0341219\pi\) | ||||
−0.994260 | + | 0.106992i | \(0.965878\pi\) | |||||||
\(908\) | −1.94617e16 | + | 2.39140e16i | −1.04643 | + | 1.28582i | ||||
\(909\) | − | 1.47494e15i | − | 0.0788268i | ||||||
\(910\) | −1.70837e12 | − | 9.98705e11i | −9.07518e−5 | − | 5.30530e-5i | ||||
\(911\) | 3.39057e16i | 1.79029i | 0.445780 | + | 0.895143i | \(0.352926\pi\) | ||||
−0.445780 | + | 0.895143i | \(0.647074\pi\) | |||||||
\(912\) | −3.57503e15 | − | 1.72311e16i | −0.187633 | − | 0.904358i | ||||
\(913\) | 2.86705e16i | 1.49571i | ||||||||
\(914\) | 2.49473e16 | − | 1.18620e16i | 1.29366 | − | 0.615112i | ||||
\(915\) | −4.60820e14 | −0.0237528 | ||||||||
\(916\) | −2.02601e15 | − | 1.64881e15i | −0.103805 | − | 0.0844784i | ||||
\(917\) | −3.51505e15 | − | 5.16072e15i | −0.179019 | − | 0.262832i | ||||
\(918\) | −1.18071e15 | − | 2.48318e15i | −0.0597735 | − | 0.125711i | ||||
\(919\) | 2.92165e16i | 1.47026i | 0.677928 | + | 0.735128i | \(0.262878\pi\) | ||||
−0.677928 | + | 0.735128i | \(0.737122\pi\) | |||||||
\(920\) | −1.28335e15 | + | 5.26090e15i | −0.0641968 | + | 0.263165i | ||||
\(921\) | −1.25693e16 | −0.625004 | ||||||||
\(922\) | 1.27494e14 | + | 2.68136e14i | 0.00630189 | + | 0.0132536i | ||||
\(923\) | 1.28003e13 | 0.000628942 | ||||||||
\(924\) | 9.32780e14 | − | 1.09252e16i | 0.0455599 | − | 0.533623i | ||||
\(925\) | 2.09319e16 | 1.01632 | ||||||||
\(926\) | −3.90063e15 | − | 8.20351e15i | −0.188267 | − | 0.395949i | ||||
\(927\) | −1.17117e16 | −0.561929 | ||||||||
\(928\) | −4.29685e15 | − | 5.67085e15i | −0.204945 | − | 0.270480i | ||||
\(929\) | 1.27705e15i | 0.0605511i | 0.999542 | + | 0.0302756i | \(0.00963849\pi\) | ||||
−0.999542 | + | 0.0302756i | \(0.990362\pi\) | |||||||
\(930\) | 1.16191e15 | + | 2.44363e15i | 0.0547665 | + | 0.115181i | ||||
\(931\) | 1.25023e16 | − | 3.17695e16i | 0.585823 | − | 1.48863i | ||||
\(932\) | −1.42153e16 | + | 1.74674e16i | −0.662170 | + | 0.813657i | ||||
\(933\) | −2.00123e16 | −0.926721 | ||||||||
\(934\) | −5.08598e15 | + | 2.41830e15i | −0.234135 | + | 0.111327i | ||||
\(935\) | − | 2.54112e15i | − | 0.116295i | ||||||
\(936\) | −4.31679e12 | − | 1.05305e12i | −0.000196401 | − | 4.79104e-5i | ||||
\(937\) | 4.83786e15i | 0.218819i | 0.993997 | + | 0.109410i | \(0.0348960\pi\) | ||||
−0.993997 | + | 0.109410i | \(0.965104\pi\) | |||||||
\(938\) | 1.23203e16 | − | 2.10751e16i | 0.553997 | − | 0.947661i | ||||
\(939\) | 2.62835e15i | 0.117496i | ||||||||
\(940\) | 5.16875e15 | + | 4.20643e15i | 0.229711 | + | 0.186944i | ||||
\(941\) | 4.15914e16i | 1.83764i | 0.394675 | + | 0.918821i | \(0.370857\pi\) | ||||
−0.394675 | + | 0.918821i | \(0.629143\pi\) | |||||||
\(942\) | 9.00733e15 | + | 1.89435e16i | 0.395655 | + | 0.832110i | ||||
\(943\) | −2.81090e16 | −1.22753 | ||||||||
\(944\) | 3.20304e15 | + | 1.54381e16i | 0.139064 | + | 0.670267i | ||||
\(945\) | −6.38717e14 | + | 4.35040e14i | −0.0275698 | + | 0.0187782i | ||||
\(946\) | −1.45648e16 | + | 6.92531e15i | −0.625033 | + | 0.297193i | ||||
\(947\) | − | 2.56071e16i | − | 1.09253i | −0.837611 | − | 0.546267i | \(-0.816048\pi\) | ||
0.837611 | − | 0.546267i | \(-0.183952\pi\) | |||||||
\(948\) | 8.67821e15 | + | 7.06250e15i | 0.368116 | + | 0.299580i | ||||
\(949\) | 3.93230e12 | 0.000165837 | ||||||||
\(950\) | 3.34214e16 | − | 1.58913e16i | 1.40134 | − | 0.666316i | ||||
\(951\) | −7.29258e15 | −0.304010 | ||||||||
\(952\) | −6.12580e15 | − | 1.63404e16i | −0.253898 | − | 0.677268i | ||||
\(953\) | 2.92620e15 | 0.120585 | 0.0602924 | − | 0.998181i | \(-0.480797\pi\) | ||||
0.0602924 | + | 0.998181i | \(0.480797\pi\) | |||||||
\(954\) | 7.82397e15 | − | 3.72017e15i | 0.320561 | − | 0.152422i | ||||
\(955\) | −6.58301e15 | −0.268167 | ||||||||
\(956\) | −4.39564e15 | − | 3.57726e15i | −0.178034 | − | 0.144888i | ||||
\(957\) | − | 4.51316e15i | − | 0.181746i | ||||||
\(958\) | −1.62333e16 | + | 7.71867e15i | −0.649976 | + | 0.309053i | ||||
\(959\) | −1.82426e15 | − | 2.67833e15i | −0.0726245 | − | 0.106626i | ||||
\(960\) | −1.16417e15 | + | 2.24417e15i | −0.0460814 | + | 0.0888310i | ||||
\(961\) | 1.58612e16 | 0.624248 | ||||||||
\(962\) | −6.97321e12 | − | 1.46655e13i | −0.000272879 | − | 0.000573898i | ||||
\(963\) | 1.85396e15i | 0.0721365i | ||||||||
\(964\) | 3.42323e16 | + | 2.78589e16i | 1.32438 | + | 1.07781i | ||||
\(965\) | − | 3.67114e15i | − | 0.141222i | ||||||
\(966\) | −1.19052e16 | + | 2.03649e16i | −0.455369 | + | 0.778949i | ||||
\(967\) | − | 3.14977e16i | − | 1.19794i | −0.800773 | − | 0.598968i | \(-0.795578\pi\) | ||
0.800773 | − | 0.598968i | \(-0.204422\pi\) | |||||||
\(968\) | −8.74304e14 | + | 3.58407e15i | −0.0330634 | + | 0.135538i | ||||
\(969\) | − | 1.77660e16i | − | 0.668048i | ||||||
\(970\) | 5.76815e15 | − | 2.74266e15i | 0.215671 | − | 0.102548i | ||||
\(971\) | −5.70074e15 | −0.211946 | −0.105973 | − | 0.994369i | \(-0.533796\pi\) | ||||
−0.105973 | + | 0.994369i | \(0.533796\pi\) | |||||||
\(972\) | −1.09530e15 | + | 1.34588e15i | −0.0404921 | + | 0.0497556i | ||||
\(973\) | −6.68215e15 | − | 9.81059e15i | −0.245638 | − | 0.360641i | ||||
\(974\) | −1.29297e16 | − | 2.71928e16i | −0.472623 | − | 0.993985i | ||||
\(975\) | − | 9.34403e12i | − | 0.000339632i | ||||||
\(976\) | −6.43019e15 | + | 1.33411e15i | −0.232407 | + | 0.0482190i | ||||
\(977\) | 6.89481e15 | 0.247800 | 0.123900 | − | 0.992295i | \(-0.460460\pi\) | ||||
0.123900 | + | 0.992295i | \(0.460460\pi\) | |||||||
\(978\) | −6.06605e15 | − | 1.27576e16i | −0.216791 | − | 0.455939i | ||||
\(979\) | 3.33034e16 | 1.18354 | ||||||||
\(980\) | −4.27396e15 | + | 2.40623e15i | −0.151038 | + | 0.0850341i | ||||
\(981\) | −6.48483e15 | −0.227887 | ||||||||
\(982\) | 1.76765e16 | + | 3.71759e16i | 0.617708 | + | 1.29912i | ||||
\(983\) | −4.76936e16 | −1.65736 | −0.828678 | − | 0.559725i | \(-0.810907\pi\) | ||||
−0.828678 | + | 0.559725i | \(0.810907\pi\) | |||||||
\(984\) | −1.27493e16 | − | 3.11009e15i | −0.440568 | − | 0.107473i | ||||
\(985\) | − | 6.30111e15i | − | 0.216530i | ||||||
\(986\) | −3.08438e15 | − | 6.48683e15i | −0.105401 | − | 0.221671i | ||||
\(987\) | 1.63422e16 | + | 2.39932e16i | 0.555348 | + | 0.815350i | ||||
\(988\) | −2.22678e13 | − | 1.81220e13i | −0.000752515 | − | 0.000612412i | ||||
\(989\) | 3.46957e16 | 1.16599 | ||||||||
\(990\) | −1.44830e15 | + | 6.88642e14i | −0.0484022 | + | 0.0230144i | ||||
\(991\) | − | 2.56370e16i | − | 0.852044i | −0.904713 | − | 0.426022i | \(-0.859915\pi\) | ||
0.904713 | − | 0.426022i | \(-0.140085\pi\) | |||||||
\(992\) | 2.32875e16 | + | 3.07341e16i | 0.769678 | + | 1.01580i | ||||
\(993\) | − | 2.33926e16i | − | 0.768878i | ||||||
\(994\) | 1.60117e16 | − | 2.73894e16i | 0.523373 | − | 0.895277i | ||||
\(995\) | 7.78424e15i | 0.253040i | ||||||||
\(996\) | 1.81766e16 | − | 2.23349e16i | 0.587607 | − | 0.722035i | ||||
\(997\) | 3.14188e16i | 1.01010i | 0.863089 | + | 0.505051i | \(0.168527\pi\) | ||||
−0.863089 | + | 0.505051i | \(0.831473\pi\) | |||||||
\(998\) | −2.46759e16 | − | 5.18964e16i | −0.788959 | − | 1.65928i | ||||
\(999\) | −6.34171e15 | −0.201649 |
(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 | 84.12.b.a.55.6 | yes | 44 | |
4.3 | odd | 2 | 84.12.b.b.55.5 | yes | 44 | ||
7.6 | odd | 2 | 84.12.b.b.55.6 | yes | 44 | ||
28.27 | even | 2 | inner | 84.12.b.a.55.5 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.b.a.55.5 | ✓ | 44 | 28.27 | even | 2 | inner | |
84.12.b.a.55.6 | yes | 44 | 1.1 | even | 1 | trivial | |
84.12.b.b.55.5 | yes | 44 | 4.3 | odd | 2 | ||
84.12.b.b.55.6 | yes | 44 | 7.6 | odd | 2 |