Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,8,Mod(2,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.2");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.e (of order \(4\), 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: | \(4.68577538226\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2.7 | ||
Character | \(\chi\) | \(=\) | 15.2 |
Dual form | 15.8.e.a.8.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.72123 | − | 1.72123i | 0.152136 | − | 0.152136i | −0.626935 | − | 0.779072i | \(-0.715691\pi\) |
0.779072 | + | 0.626935i | \(0.215691\pi\) | |||||||
\(3\) | 36.7583 | + | 28.9107i | 0.786014 | + | 0.618208i | ||||
\(4\) | 122.075i | 0.953709i | ||||||||
\(5\) | −270.133 | − | 71.7849i | −0.966458 | − | 0.256825i | ||||
\(6\) | 113.031 | − | 13.5074i | 0.213634 | − | 0.0255294i | ||||
\(7\) | 884.635 | + | 884.635i | 0.974812 | + | 0.974812i | 0.999690 | − | 0.0248787i | \(-0.00791994\pi\) |
−0.0248787 | + | 0.999690i | \(0.507920\pi\) | |||||||
\(8\) | 430.436 | + | 430.436i | 0.297230 | + | 0.297230i | ||||
\(9\) | 515.339 | + | 2125.42i | 0.235637 | + | 0.971841i | ||||
\(10\) | −588.519 | + | 341.403i | −0.186106 | + | 0.107961i | ||||
\(11\) | − | 3163.77i | − | 0.716689i | −0.933589 | − | 0.358345i | \(-0.883341\pi\) | ||
0.933589 | − | 0.358345i | \(-0.116659\pi\) | |||||||
\(12\) | −3529.27 | + | 4487.25i | −0.589591 | + | 0.749629i | ||||
\(13\) | 4367.37 | − | 4367.37i | 0.551339 | − | 0.551339i | −0.375488 | − | 0.926827i | \(-0.622525\pi\) |
0.926827 | + | 0.375488i | \(0.122525\pi\) | |||||||
\(14\) | 3045.32 | 0.296609 | ||||||||
\(15\) | −7854.27 | − | 10448.4i | −0.600878 | − | 0.799341i | ||||
\(16\) | −14143.8 | −0.863270 | ||||||||
\(17\) | 6264.66 | − | 6264.66i | 0.309262 | − | 0.309262i | −0.535361 | − | 0.844623i | \(-0.679825\pi\) |
0.844623 | + | 0.535361i | \(0.179825\pi\) | |||||||
\(18\) | 4545.34 | + | 2771.31i | 0.183702 | + | 0.112003i | ||||
\(19\) | − | 17030.1i | − | 0.569612i | −0.958585 | − | 0.284806i | \(-0.908071\pi\) | ||
0.958585 | − | 0.284806i | \(-0.0919292\pi\) | |||||||
\(20\) | 8763.12 | − | 32976.4i | 0.244937 | − | 0.921720i | ||||
\(21\) | 6942.19 | + | 58093.1i | 0.163579 | + | 1.36885i | ||||
\(22\) | −5445.58 | − | 5445.58i | −0.109035 | − | 0.109035i | ||||
\(23\) | −43591.1 | − | 43591.1i | −0.747051 | − | 0.747051i | 0.226873 | − | 0.973924i | \(-0.427150\pi\) |
−0.973924 | + | 0.226873i | \(0.927150\pi\) | |||||||
\(24\) | 3377.85 | + | 28266.3i | 0.0498771 | + | 0.417378i | ||||
\(25\) | 67818.9 | + | 38782.9i | 0.868082 | + | 0.496422i | ||||
\(26\) | − | 15034.5i | − | 0.167757i | ||||||
\(27\) | −42504.4 | + | 93025.4i | −0.415586 | + | 0.909554i | ||||
\(28\) | −107992. | + | 107992.i | −0.929687 | + | 0.929687i | ||||
\(29\) | 222298. | 1.69256 | 0.846278 | − | 0.532741i | \(-0.178838\pi\) | ||||
0.846278 | + | 0.532741i | \(0.178838\pi\) | |||||||
\(30\) | −31503.1 | − | 4465.15i | −0.213024 | − | 0.0301934i | ||||
\(31\) | 146894. | 0.885603 | 0.442801 | − | 0.896620i | \(-0.353985\pi\) | ||||
0.442801 | + | 0.896620i | \(0.353985\pi\) | |||||||
\(32\) | −79440.5 | + | 79440.5i | −0.428565 | + | 0.428565i | ||||
\(33\) | 91467.0 | − | 116295.i | 0.443063 | − | 0.563328i | ||||
\(34\) | − | 21565.8i | − | 0.0941001i | ||||||
\(35\) | −175466. | − | 302473.i | −0.691758 | − | 1.19247i | ||||
\(36\) | −259460. | + | 62909.8i | −0.926854 | + | 0.224729i | ||||
\(37\) | −234786. | − | 234786.i | −0.762019 | − | 0.762019i | 0.214668 | − | 0.976687i | \(-0.431133\pi\) |
−0.976687 | + | 0.214668i | \(0.931133\pi\) | |||||||
\(38\) | −29312.7 | − | 29312.7i | −0.0866588 | − | 0.0866588i | ||||
\(39\) | 286801. | − | 34273.0i | 0.774202 | − | 0.0925181i | ||||
\(40\) | −85376.2 | − | 147174.i | −0.210924 | − | 0.363597i | ||||
\(41\) | 471176.i | 1.06768i | 0.845587 | + | 0.533838i | \(0.179251\pi\) | ||||
−0.845587 | + | 0.533838i | \(0.820749\pi\) | |||||||
\(42\) | 111940. | + | 88042.3i | 0.233139 | + | 0.183366i | ||||
\(43\) | 297815. | − | 297815.i | 0.571225 | − | 0.571225i | −0.361245 | − | 0.932471i | \(-0.617648\pi\) |
0.932471 | + | 0.361245i | \(0.117648\pi\) | |||||||
\(44\) | 386217. | 0.683513 | ||||||||
\(45\) | 13362.6 | − | 611139.i | 0.0218599 | − | 0.999761i | ||||
\(46\) | −150060. | −0.227307 | ||||||||
\(47\) | −703959. | + | 703959.i | −0.989019 | + | 0.989019i | −0.999940 | − | 0.0109211i | \(-0.996524\pi\) |
0.0109211 | + | 0.999940i | \(0.496524\pi\) | |||||||
\(48\) | −519902. | − | 408908.i | −0.678542 | − | 0.533680i | ||||
\(49\) | 741614.i | 0.900516i | ||||||||
\(50\) | 183486. | − | 49977.4i | 0.207591 | − | 0.0565430i | ||||
\(51\) | 411394. | − | 49162.1i | 0.434273 | − | 0.0518961i | ||||
\(52\) | 533146. | + | 533146.i | 0.525817 | + | 0.525817i | ||||
\(53\) | −8798.09 | − | 8798.09i | −0.00811751 | − | 0.00811751i | 0.703036 | − | 0.711154i | \(-0.251827\pi\) |
−0.711154 | + | 0.703036i | \(0.751827\pi\) | |||||||
\(54\) | 86958.2 | + | 233278.i | 0.0751506 | + | 0.201602i | ||||
\(55\) | −227111. | + | 854640.i | −0.184064 | + | 0.692650i | ||||
\(56\) | 761557.i | 0.579487i | ||||||||
\(57\) | 492352. | − | 625996.i | 0.352139 | − | 0.447723i | ||||
\(58\) | 382626. | − | 382626.i | 0.257500 | − | 0.257500i | ||||
\(59\) | −37938.4 | −0.0240490 | −0.0120245 | − | 0.999928i | \(-0.503828\pi\) | ||||
−0.0120245 | + | 0.999928i | \(0.503828\pi\) | |||||||
\(60\) | 1.27549e6 | − | 958808.i | 0.762338 | − | 0.573063i | ||||
\(61\) | −250175. | −0.141120 | −0.0705602 | − | 0.997508i | \(-0.522479\pi\) | ||||
−0.0705602 | + | 0.997508i | \(0.522479\pi\) | |||||||
\(62\) | 252838. | − | 252838.i | 0.134732 | − | 0.134732i | ||||
\(63\) | −1.42433e6 | + | 2.33610e6i | −0.717660 | + | 1.17706i | ||||
\(64\) | − | 1.53694e6i | − | 0.732869i | ||||||
\(65\) | −1.49328e6 | + | 866261.i | −0.674443 | + | 0.391248i | ||||
\(66\) | −42734.3 | − | 357605.i | −0.0182967 | − | 0.153109i | ||||
\(67\) | −1.78739e6 | − | 1.78739e6i | −0.726034 | − | 0.726034i | 0.243794 | − | 0.969827i | \(-0.421608\pi\) |
−0.969827 | + | 0.243794i | \(0.921608\pi\) | |||||||
\(68\) | 764757. | + | 764757.i | 0.294946 | + | 0.294946i | ||||
\(69\) | −342082. | − | 2.86258e6i | −0.125360 | − | 1.04903i | ||||
\(70\) | −822641. | − | 218608.i | −0.286660 | − | 0.0761767i | ||||
\(71\) | − | 4.43696e6i | − | 1.47123i | −0.677399 | − | 0.735616i | \(-0.736893\pi\) | ||
0.677399 | − | 0.735616i | \(-0.263107\pi\) | |||||||
\(72\) | −693035. | + | 1.13668e6i | −0.218822 | + | 0.358899i | ||||
\(73\) | 560727. | − | 560727.i | 0.168703 | − | 0.168703i | −0.617706 | − | 0.786409i | \(-0.711938\pi\) |
0.786409 | + | 0.617706i | \(0.211938\pi\) | |||||||
\(74\) | −808240. | −0.231862 | ||||||||
\(75\) | 1.37166e6 | + | 3.38629e6i | 0.375433 | + | 0.926850i | ||||
\(76\) | 2.07894e6 | 0.543244 | ||||||||
\(77\) | 2.79878e6 | − | 2.79878e6i | 0.698637 | − | 0.698637i | ||||
\(78\) | 434658. | − | 552642.i | 0.103709 | − | 0.131860i | ||||
\(79\) | 4.39243e6i | 1.00233i | 0.865352 | + | 0.501165i | \(0.167095\pi\) | ||||
−0.865352 | + | 0.501165i | \(0.832905\pi\) | |||||||
\(80\) | 3.82071e6 | + | 1.01531e6i | 0.834314 | + | 0.221710i | ||||
\(81\) | −4.25182e6 | + | 2.19062e6i | −0.888950 | + | 0.458004i | ||||
\(82\) | 811001. | + | 811001.i | 0.162432 | + | 0.162432i | ||||
\(83\) | −263826. | − | 263826.i | −0.0506459 | − | 0.0506459i | 0.681330 | − | 0.731976i | \(-0.261402\pi\) |
−0.731976 | + | 0.681330i | \(0.761402\pi\) | |||||||
\(84\) | −7.09170e6 | + | 847466.i | −1.30549 | + | 0.156007i | ||||
\(85\) | −2.14200e6 | + | 1.24259e6i | −0.378315 | + | 0.219462i | ||||
\(86\) | − | 1.02522e6i | − | 0.173808i | ||||||
\(87\) | 8.17130e6 | + | 6.42681e6i | 1.33037 | + | 1.04635i | ||||
\(88\) | 1.36180e6 | − | 1.36180e6i | 0.213022 | − | 0.213022i | ||||
\(89\) | −9.13206e6 | −1.37310 | −0.686552 | − | 0.727080i | \(-0.740877\pi\) | ||||
−0.686552 | + | 0.727080i | \(0.740877\pi\) | |||||||
\(90\) | −1.02891e6 | − | 1.07491e6i | −0.148774 | − | 0.155426i | ||||
\(91\) | 7.72706e6 | 1.07490 | ||||||||
\(92\) | 5.32137e6 | − | 5.32137e6i | 0.712469 | − | 0.712469i | ||||
\(93\) | 5.39958e6 | + | 4.24682e6i | 0.696096 | + | 0.547487i | ||||
\(94\) | 2.42335e6i | 0.300932i | ||||||||
\(95\) | −1.22250e6 | + | 4.60039e6i | −0.146291 | + | 0.550506i | ||||
\(96\) | −5.21678e6 | + | 623411.i | −0.601801 | + | 0.0719159i | ||||
\(97\) | −8.07294e6 | − | 8.07294e6i | −0.898112 | − | 0.898112i | 0.0971567 | − | 0.995269i | \(-0.469025\pi\) |
−0.995269 | + | 0.0971567i | \(0.969025\pi\) | |||||||
\(98\) | 1.27649e6 | + | 1.27649e6i | 0.137001 | + | 0.137001i | ||||
\(99\) | 6.72434e6 | − | 1.63041e6i | 0.696508 | − | 0.168879i | ||||
\(100\) | −4.73442e6 | + | 8.27897e6i | −0.473442 | + | 0.827897i | ||||
\(101\) | − | 8.21700e6i | − | 0.793576i | −0.917910 | − | 0.396788i | \(-0.870125\pi\) | ||
0.917910 | − | 0.396788i | \(-0.129875\pi\) | |||||||
\(102\) | 623484. | − | 792722.i | 0.0581734 | − | 0.0739640i | ||||
\(103\) | 1.57945e6 | − | 1.57945e6i | 0.142421 | − | 0.142421i | −0.632301 | − | 0.774723i | \(-0.717889\pi\) |
0.774723 | + | 0.632301i | \(0.217889\pi\) | |||||||
\(104\) | 3.75975e6 | 0.327749 | ||||||||
\(105\) | 2.29489e6 | − | 1.61912e7i | 0.193463 | − | 1.36495i | ||||
\(106\) | −30287.0 | −0.00246994 | ||||||||
\(107\) | −1.00980e7 | + | 1.00980e7i | −0.796880 | + | 0.796880i | −0.982602 | − | 0.185722i | \(-0.940537\pi\) |
0.185722 | + | 0.982602i | \(0.440537\pi\) | |||||||
\(108\) | −1.13561e7 | − | 5.18871e6i | −0.867450 | − | 0.396348i | ||||
\(109\) | − | 1.32852e7i | − | 0.982600i | −0.870990 | − | 0.491300i | \(-0.836522\pi\) | ||
0.870990 | − | 0.491300i | \(-0.163478\pi\) | |||||||
\(110\) | 1.08012e6 | + | 1.86194e6i | 0.0773745 | + | 0.133380i | ||||
\(111\) | −1.84249e6 | − | 1.54181e7i | −0.127872 | − | 1.07004i | ||||
\(112\) | −1.25121e7 | − | 1.25121e7i | −0.841526 | − | 0.841526i | ||||
\(113\) | 4.24721e6 | + | 4.24721e6i | 0.276904 | + | 0.276904i | 0.831872 | − | 0.554968i | \(-0.187269\pi\) |
−0.554968 | + | 0.831872i | \(0.687269\pi\) | |||||||
\(114\) | −230032. | − | 1.92493e6i | −0.0145419 | − | 0.121688i | ||||
\(115\) | 8.64622e6 | + | 1.49046e7i | 0.530132 | + | 0.913855i | ||||
\(116\) | 2.71370e7i | 1.61421i | ||||||||
\(117\) | 1.15332e7 | + | 7.03181e6i | 0.665730 | + | 0.405898i | ||||
\(118\) | −65300.7 | + | 65300.7i | −0.00365873 | + | 0.00365873i | ||||
\(119\) | 1.10839e7 | 0.602944 | ||||||||
\(120\) | 1.11662e6 | − | 7.87814e6i | 0.0589890 | − | 0.416188i | ||||
\(121\) | 9.47771e6 | 0.486356 | ||||||||
\(122\) | −430609. | + | 430609.i | −0.0214696 | + | 0.0214696i | ||||
\(123\) | −1.36220e7 | + | 1.73196e7i | −0.660046 | + | 0.839208i | ||||
\(124\) | 1.79321e7i | 0.844607i | ||||||||
\(125\) | −1.55361e7 | − | 1.53449e7i | −0.711471 | − | 0.702716i | ||||
\(126\) | 1.56937e6 | + | 6.47256e6i | 0.0698921 | + | 0.288257i | ||||
\(127\) | 4.70330e6 | + | 4.70330e6i | 0.203746 | + | 0.203746i | 0.801603 | − | 0.597857i | \(-0.203981\pi\) |
−0.597857 | + | 0.801603i | \(0.703981\pi\) | |||||||
\(128\) | −1.28138e7 | − | 1.28138e7i | −0.540061 | − | 0.540061i | ||||
\(129\) | 1.95572e7 | − | 2.33711e6i | 0.802128 | − | 0.0958552i | ||||
\(130\) | −1.07925e6 | + | 4.06131e6i | −0.0430844 | + | 0.162131i | ||||
\(131\) | 1.91876e7i | 0.745711i | 0.927890 | + | 0.372855i | \(0.121621\pi\) | ||||
−0.927890 | + | 0.372855i | \(0.878379\pi\) | |||||||
\(132\) | 1.41967e7 | + | 1.11658e7i | 0.537251 | + | 0.422553i | ||||
\(133\) | 1.50654e7 | − | 1.50654e7i | 0.555265 | − | 0.555265i | ||||
\(134\) | −6.15300e6 | −0.220912 | ||||||||
\(135\) | 1.81597e7 | − | 2.20781e7i | 0.635243 | − | 0.772313i | ||||
\(136\) | 5.39307e6 | 0.183844 | ||||||||
\(137\) | −2.16166e7 | + | 2.16166e7i | −0.718232 | + | 0.718232i | −0.968243 | − | 0.250011i | \(-0.919566\pi\) |
0.250011 | + | 0.968243i | \(0.419566\pi\) | |||||||
\(138\) | −5.51596e6 | − | 4.33836e6i | −0.178667 | − | 0.140523i | ||||
\(139\) | 3.27651e7i | 1.03481i | 0.855742 | + | 0.517403i | \(0.173101\pi\) | ||||
−0.855742 | + | 0.517403i | \(0.826899\pi\) | |||||||
\(140\) | 3.69243e7 | − | 2.14199e7i | 1.13727 | − | 0.659736i | ||||
\(141\) | −4.62283e7 | + | 5.52433e6i | −1.38880 | + | 0.165964i | ||||
\(142\) | −7.63702e6 | − | 7.63702e6i | −0.223828 | − | 0.223828i | ||||
\(143\) | −1.38174e7 | − | 1.38174e7i | −0.395139 | − | 0.395139i | ||||
\(144\) | −7.28885e6 | − | 3.00615e7i | −0.203419 | − | 0.838961i | ||||
\(145\) | −6.00502e7 | − | 1.59577e7i | −1.63578 | − | 0.434691i | ||||
\(146\) | − | 1.93028e6i | − | 0.0513316i | ||||||
\(147\) | −2.14406e7 | + | 2.72604e7i | −0.556706 | + | 0.707819i | ||||
\(148\) | 2.86614e7 | − | 2.86614e7i | 0.726744 | − | 0.726744i | ||||
\(149\) | 7.48929e7 | 1.85476 | 0.927382 | − | 0.374116i | \(-0.122054\pi\) | ||||
0.927382 | + | 0.374116i | \(0.122054\pi\) | |||||||
\(150\) | 8.18951e6 | + | 3.46763e6i | 0.198125 | + | 0.0838907i | ||||
\(151\) | 1.02410e7 | 0.242060 | 0.121030 | − | 0.992649i | \(-0.461380\pi\) | ||||
0.121030 | + | 0.992649i | \(0.461380\pi\) | |||||||
\(152\) | 7.33036e6 | − | 7.33036e6i | 0.169306 | − | 0.169306i | ||||
\(153\) | 1.65434e7 | + | 1.00866e7i | 0.373427 | + | 0.227680i | ||||
\(154\) | − | 9.63469e6i | − | 0.212576i | ||||||
\(155\) | −3.96810e7 | − | 1.05448e7i | −0.855898 | − | 0.227445i | ||||
\(156\) | 4.18387e6 | + | 3.50112e7i | 0.0882353 | + | 0.738364i | ||||
\(157\) | −3.44091e7 | − | 3.44091e7i | −0.709618 | − | 0.709618i | 0.256837 | − | 0.966455i | \(-0.417320\pi\) |
−0.966455 | + | 0.256837i | \(0.917320\pi\) | |||||||
\(158\) | 7.56038e6 | + | 7.56038e6i | 0.152491 | + | 0.152491i | ||||
\(159\) | −69043.2 | − | 577762.i | −0.00136217 | − | 0.0113988i | ||||
\(160\) | 2.71621e7 | − | 1.57569e7i | 0.524257 | − | 0.304124i | ||||
\(161\) | − | 7.71244e7i | − | 1.45647i | ||||||
\(162\) | −3.54780e6 | + | 1.10889e7i | −0.0655626 | + | 0.204921i | ||||
\(163\) | −2.24266e7 | + | 2.24266e7i | −0.405608 | + | 0.405608i | −0.880204 | − | 0.474596i | \(-0.842594\pi\) |
0.474596 | + | 0.880204i | \(0.342594\pi\) | |||||||
\(164\) | −5.75186e7 | −1.01825 | ||||||||
\(165\) | −3.30565e7 | + | 2.48491e7i | −0.572879 | + | 0.430643i | ||||
\(166\) | −908209. | −0.0154102 | ||||||||
\(167\) | 4.14619e7 | − | 4.14619e7i | 0.688877 | − | 0.688877i | −0.273107 | − | 0.961984i | \(-0.588051\pi\) |
0.961984 | + | 0.273107i | \(0.0880512\pi\) | |||||||
\(168\) | −2.20172e7 | + | 2.79935e7i | −0.358244 | + | 0.455486i | ||||
\(169\) | 2.46006e7i | 0.392051i | ||||||||
\(170\) | −1.54810e6 | + | 5.82565e6i | −0.0241673 | + | 0.0909437i | ||||
\(171\) | 3.61960e7 | − | 8.77626e6i | 0.553572 | − | 0.134222i | ||||
\(172\) | 3.63557e7 | + | 3.63557e7i | 0.544783 | + | 0.544783i | ||||
\(173\) | 3.08157e7 | + | 3.08157e7i | 0.452492 | + | 0.452492i | 0.896181 | − | 0.443689i | \(-0.146331\pi\) |
−0.443689 | + | 0.896181i | \(0.646331\pi\) | |||||||
\(174\) | 2.51267e7 | − | 3.00267e6i | 0.361587 | − | 0.0432100i | ||||
\(175\) | 2.56862e7 | + | 9.43037e7i | 0.362298 | + | 1.33013i | ||||
\(176\) | 4.47478e7i | 0.618696i | ||||||||
\(177\) | −1.39455e6 | − | 1.09683e6i | −0.0189029 | − | 0.0148673i | ||||
\(178\) | −1.57184e7 | + | 1.57184e7i | −0.208899 | + | 0.208899i | ||||
\(179\) | −4.69726e7 | −0.612152 | −0.306076 | − | 0.952007i | \(-0.599016\pi\) | ||||
−0.306076 | + | 0.952007i | \(0.599016\pi\) | |||||||
\(180\) | 7.46046e7 | + | 1.63124e6i | 0.953481 | + | 0.0208480i | ||||
\(181\) | 4.21050e7 | 0.527787 | 0.263894 | − | 0.964552i | \(-0.414993\pi\) | ||||
0.263894 | + | 0.964552i | \(0.414993\pi\) | |||||||
\(182\) | 1.33000e7 | − | 1.33000e7i | 0.163532 | − | 0.163532i | ||||
\(183\) | −9.19601e6 | − | 7.23275e6i | −0.110923 | − | 0.0872418i | ||||
\(184\) | − | 3.75263e7i | − | 0.444093i | ||||||
\(185\) | 4.65694e7 | + | 8.02775e7i | 0.540753 | + | 0.932165i | ||||
\(186\) | 1.66036e7 | − | 1.98416e6i | 0.189194 | − | 0.0226089i | ||||
\(187\) | −1.98200e7 | − | 1.98200e7i | −0.221645 | − | 0.221645i | ||||
\(188\) | −8.59356e7 | − | 8.59356e7i | −0.943237 | − | 0.943237i | ||||
\(189\) | −1.19894e8 | + | 4.46926e7i | −1.29176 | + | 0.481526i | ||||
\(190\) | 5.81412e6 | + | 1.00225e7i | 0.0614959 | + | 0.106008i | ||||
\(191\) | − | 2.73525e7i | − | 0.284040i | −0.989864 | − | 0.142020i | \(-0.954640\pi\) | ||
0.989864 | − | 0.142020i | \(-0.0453598\pi\) | |||||||
\(192\) | 4.44340e7 | − | 5.64951e7i | 0.453066 | − | 0.576046i | ||||
\(193\) | 2.58245e7 | − | 2.58245e7i | 0.258572 | − | 0.258572i | −0.565901 | − | 0.824473i | \(-0.691472\pi\) |
0.824473 | + | 0.565901i | \(0.191472\pi\) | |||||||
\(194\) | −2.77907e7 | −0.273271 | ||||||||
\(195\) | −7.99347e7 | − | 1.13297e7i | −0.771995 | − | 0.109420i | ||||
\(196\) | −9.05323e7 | −0.858830 | ||||||||
\(197\) | −1.96188e7 | + | 1.96188e7i | −0.182827 | + | 0.182827i | −0.792587 | − | 0.609759i | \(-0.791266\pi\) |
0.609759 | + | 0.792587i | \(0.291266\pi\) | |||||||
\(198\) | 8.76780e6 | − | 1.43804e7i | 0.0802717 | − | 0.131657i | ||||
\(199\) | − | 1.42723e8i | − | 1.28383i | −0.766776 | − | 0.641915i | \(-0.778140\pi\) | ||
0.766776 | − | 0.641915i | \(-0.221860\pi\) | |||||||
\(200\) | 1.24981e7 | + | 4.58852e7i | 0.110469 | + | 0.405572i | ||||
\(201\) | −1.40266e7 | − | 1.17376e8i | −0.121833 | − | 1.01951i | ||||
\(202\) | −1.41433e7 | − | 1.41433e7i | −0.120732 | − | 0.120732i | ||||
\(203\) | 1.96653e8 | + | 1.96653e8i | 1.64992 | + | 1.64992i | ||||
\(204\) | 6.00145e6 | + | 5.02208e7i | 0.0494938 | + | 0.414170i | ||||
\(205\) | 3.38233e7 | − | 1.27280e8i | 0.274206 | − | 1.03186i | ||||
\(206\) | − | 5.43718e6i | − | 0.0433350i | ||||||
\(207\) | 7.01850e7 | − | 1.15113e8i | 0.549982 | − | 0.902048i | ||||
\(208\) | −6.17713e7 | + | 6.17713e7i | −0.475954 | + | 0.475954i | ||||
\(209\) | −5.38793e7 | −0.408235 | ||||||||
\(210\) | −2.39187e7 | − | 3.18188e7i | −0.178226 | − | 0.237092i | ||||
\(211\) | 2.35457e6 | 0.0172553 | 0.00862765 | − | 0.999963i | \(-0.497254\pi\) | ||||
0.00862765 | + | 0.999963i | \(0.497254\pi\) | |||||||
\(212\) | 1.07402e6 | − | 1.07402e6i | 0.00774174 | − | 0.00774174i | ||||
\(213\) | 1.28276e8 | − | 1.63095e8i | 0.909527 | − | 1.15641i | ||||
\(214\) | 3.47620e7i | 0.242469i | ||||||||
\(215\) | −1.01828e8 | + | 5.90712e7i | −0.698770 | + | 0.405360i | ||||
\(216\) | −5.83369e7 | + | 2.17460e7i | −0.393872 | + | 0.146822i | ||||
\(217\) | 1.29948e8 | + | 1.29948e8i | 0.863296 | + | 0.863296i | ||||
\(218\) | −2.28669e7 | − | 2.28669e7i | −0.149489 | − | 0.149489i | ||||
\(219\) | 3.68224e7 | − | 4.40032e6i | 0.236896 | − | 0.0283093i | ||||
\(220\) | −1.04330e8 | − | 2.77245e7i | −0.660587 | − | 0.175543i | ||||
\(221\) | − | 5.47202e7i | − | 0.341016i | ||||||
\(222\) | −2.97095e7 | − | 2.33668e7i | −0.182247 | − | 0.143339i | ||||
\(223\) | −7.49416e7 | + | 7.49416e7i | −0.452539 | + | 0.452539i | −0.896196 | − | 0.443658i | \(-0.853681\pi\) |
0.443658 | + | 0.896196i | \(0.353681\pi\) | |||||||
\(224\) | −1.40552e8 | −0.835541 | ||||||||
\(225\) | −4.74802e7 | + | 1.64130e8i | −0.277891 | + | 0.960613i | ||||
\(226\) | 1.46208e7 | 0.0842544 | ||||||||
\(227\) | −5.81623e7 | + | 5.81623e7i | −0.330028 | + | 0.330028i | −0.852597 | − | 0.522569i | \(-0.824974\pi\) |
0.522569 | + | 0.852597i | \(0.324974\pi\) | |||||||
\(228\) | 7.64183e7 | + | 6.01038e7i | 0.426998 | + | 0.335838i | ||||
\(229\) | 1.72092e8i | 0.946972i | 0.880801 | + | 0.473486i | \(0.157005\pi\) | ||||
−0.880801 | + | 0.473486i | \(0.842995\pi\) | |||||||
\(230\) | 4.05363e7 | + | 1.07721e7i | 0.219683 | + | 0.0583783i | ||||
\(231\) | 1.83793e8 | − | 2.19635e7i | 0.981042 | − | 0.117236i | ||||
\(232\) | 9.56851e7 | + | 9.56851e7i | 0.503079 | + | 0.503079i | ||||
\(233\) | −9.91208e7 | − | 9.91208e7i | −0.513356 | − | 0.513356i | 0.402197 | − | 0.915553i | \(-0.368247\pi\) |
−0.915553 | + | 0.402197i | \(0.868247\pi\) | |||||||
\(234\) | 3.19545e7 | − | 7.74785e6i | 0.163034 | − | 0.0395299i | ||||
\(235\) | 2.40696e8 | − | 1.39629e8i | 1.20985 | − | 0.701840i | ||||
\(236\) | − | 4.63132e6i | − | 0.0229358i | ||||||
\(237\) | −1.26988e8 | + | 1.61458e8i | −0.619648 | + | 0.787845i | ||||
\(238\) | 1.90779e7 | − | 1.90779e7i | 0.0917299 | − | 0.0917299i | ||||
\(239\) | 3.53439e8 | 1.67464 | 0.837320 | − | 0.546713i | \(-0.184121\pi\) | ||||
0.837320 | + | 0.546713i | \(0.184121\pi\) | |||||||
\(240\) | 1.11089e8 | + | 1.47781e8i | 0.518720 | + | 0.690047i | ||||
\(241\) | −1.60031e8 | −0.736453 | −0.368227 | − | 0.929736i | \(-0.620035\pi\) | ||||
−0.368227 | + | 0.929736i | \(0.620035\pi\) | |||||||
\(242\) | 1.63133e7 | − | 1.63133e7i | 0.0739925 | − | 0.0739925i | ||||
\(243\) | −2.19622e8 | − | 4.23999e7i | −0.981869 | − | 0.189559i | ||||
\(244\) | − | 3.05401e7i | − | 0.134588i | ||||||
\(245\) | 5.32366e7 | − | 2.00334e8i | 0.231275 | − | 0.870311i | ||||
\(246\) | 6.36434e6 | + | 5.32576e7i | 0.0272572 | + | 0.228091i | ||||
\(247\) | −7.43767e7 | − | 7.43767e7i | −0.314049 | − | 0.314049i | ||||
\(248\) | 6.32285e7 | + | 6.32285e7i | 0.263228 | + | 0.263228i | ||||
\(249\) | −2.07038e6 | − | 1.73252e7i | −0.00849869 | − | 0.0711181i | ||||
\(250\) | −5.31533e7 | + | 329046.i | −0.215149 | + | 0.00133189i | ||||
\(251\) | 2.02842e8i | 0.809655i | 0.914393 | + | 0.404828i | \(0.132669\pi\) | ||||
−0.914393 | + | 0.404828i | \(0.867331\pi\) | |||||||
\(252\) | −2.85179e8 | − | 1.73875e8i | −1.12258 | − | 0.684439i | ||||
\(253\) | −1.37912e8 | + | 1.37912e8i | −0.535404 | + | 0.535404i | ||||
\(254\) | 1.61909e7 | 0.0619944 | ||||||||
\(255\) | −1.14660e8 | − | 1.62516e7i | −0.433034 | − | 0.0613768i | ||||
\(256\) | 1.52617e8 | 0.568543 | ||||||||
\(257\) | 1.54186e8 | − | 1.54186e8i | 0.566602 | − | 0.566602i | −0.364573 | − | 0.931175i | \(-0.618785\pi\) |
0.931175 | + | 0.364573i | \(0.118785\pi\) | |||||||
\(258\) | 2.96398e7 | − | 3.76852e7i | 0.107450 | − | 0.136616i | ||||
\(259\) | − | 4.15399e8i | − | 1.48565i | ||||||
\(260\) | −1.05749e8 | − | 1.82292e8i | −0.373137 | − | 0.643223i | ||||
\(261\) | 1.14559e8 | + | 4.72477e8i | 0.398829 | + | 1.64490i | ||||
\(262\) | 3.30262e7 | + | 3.30262e7i | 0.113450 | + | 0.113450i | ||||
\(263\) | −3.22856e8 | − | 3.22856e8i | −1.09437 | − | 1.09437i | −0.995056 | − | 0.0993118i | \(-0.968336\pi\) |
−0.0993118 | − | 0.995056i | \(-0.531664\pi\) | |||||||
\(264\) | 8.94281e7 | − | 1.06868e7i | 0.299130 | − | 0.0357464i | ||||
\(265\) | 1.74509e6 | + | 3.00823e6i | 0.00576045 | + | 0.00993002i | ||||
\(266\) | − | 5.18620e7i | − | 0.168952i | ||||||
\(267\) | −3.35678e8 | − | 2.64014e8i | −1.07928 | − | 0.848864i | ||||
\(268\) | 2.18195e8 | − | 2.18195e8i | 0.692425 | − | 0.692425i | ||||
\(269\) | 6.12343e7 | 0.191806 | 0.0959030 | − | 0.995391i | \(-0.469426\pi\) | ||||
0.0959030 | + | 0.995391i | \(0.469426\pi\) | |||||||
\(270\) | −6.74448e6 | − | 6.92583e7i | −0.0208533 | − | 0.214141i | ||||
\(271\) | −6.33885e8 | −1.93472 | −0.967360 | − | 0.253407i | \(-0.918449\pi\) | ||||
−0.967360 | + | 0.253407i | \(0.918449\pi\) | |||||||
\(272\) | −8.86062e7 | + | 8.86062e7i | −0.266977 | + | 0.266977i | ||||
\(273\) | 2.84033e8 | + | 2.23395e8i | 0.844889 | + | 0.664514i | ||||
\(274\) | 7.44141e7i | 0.218539i | ||||||||
\(275\) | 1.22700e8 | − | 2.14564e8i | 0.355780 | − | 0.622145i | ||||
\(276\) | 3.49449e8 | − | 4.17596e7i | 1.00047 | − | 0.119557i | ||||
\(277\) | 3.46271e8 | + | 3.46271e8i | 0.978897 | + | 0.978897i | 0.999782 | − | 0.0208845i | \(-0.00664823\pi\) |
−0.0208845 | + | 0.999782i | \(0.506648\pi\) | |||||||
\(278\) | 5.63961e7 | + | 5.63961e7i | 0.157432 | + | 0.157432i | ||||
\(279\) | 7.57003e7 | + | 3.12211e8i | 0.208681 | + | 0.860665i | ||||
\(280\) | 5.46682e7 | − | 2.05722e8i | 0.148827 | − | 0.560050i | ||||
\(281\) | 2.07883e7i | 0.0558917i | 0.999609 | + | 0.0279458i | \(0.00889659\pi\) | ||||
−0.999609 | + | 0.0279458i | \(0.991103\pi\) | |||||||
\(282\) | −7.00608e7 | + | 8.90780e7i | −0.186039 | + | 0.236537i | ||||
\(283\) | −4.09164e7 | + | 4.09164e7i | −0.107311 | + | 0.107311i | −0.758724 | − | 0.651413i | \(-0.774177\pi\) |
0.651413 | + | 0.758724i | \(0.274177\pi\) | |||||||
\(284\) | 5.41640e8 | 1.40313 | ||||||||
\(285\) | −1.77938e8 | + | 1.33759e8i | −0.455314 | + | 0.342268i | ||||
\(286\) | −4.75657e7 | −0.120230 | ||||||||
\(287\) | −4.16818e8 | + | 4.16818e8i | −1.04078 | + | 1.04078i | ||||
\(288\) | −2.09783e8 | − | 1.27905e8i | −0.517483 | − | 0.315511i | ||||
\(289\) | 3.31847e8i | 0.808714i | ||||||||
\(290\) | −1.30827e8 | + | 7.58932e7i | −0.314995 | + | 0.182730i | ||||
\(291\) | −6.33526e7 | − | 5.30142e8i | −0.150709 | − | 1.26115i | ||||
\(292\) | 6.84506e7 | + | 6.84506e7i | 0.160893 | + | 0.160893i | ||||
\(293\) | −309871. | − | 309871.i | −0.000719688 | − | 0.000719688i | 0.706747 | − | 0.707467i | \(-0.250162\pi\) |
−0.707467 | + | 0.706747i | \(0.750162\pi\) | |||||||
\(294\) | 1.00173e7 | + | 8.38256e7i | 0.0229897 | + | 0.192380i | ||||
\(295\) | 1.02484e7 | + | 2.72340e6i | 0.0232423 | + | 0.00617639i | ||||
\(296\) | − | 2.02120e8i | − | 0.452991i | ||||||
\(297\) | 2.94311e8 | + | 1.34474e8i | 0.651868 | + | 0.297846i | ||||
\(298\) | 1.28908e8 | − | 1.28908e8i | 0.282177 | − | 0.282177i | ||||
\(299\) | −3.80757e8 | −0.823756 | ||||||||
\(300\) | −4.13380e8 | + | 1.67445e8i | −0.883945 | + | 0.358053i | ||||
\(301\) | 5.26916e8 | 1.11367 | ||||||||
\(302\) | 1.76271e7 | − | 1.76271e7i | 0.0368262 | − | 0.0368262i | ||||
\(303\) | 2.37560e8 | − | 3.02043e8i | 0.490595 | − | 0.623762i | ||||
\(304\) | 2.40870e8i | 0.491729i | ||||||||
\(305\) | 6.75807e7 | + | 1.79588e7i | 0.136387 | + | 0.0362433i | ||||
\(306\) | 4.58364e7 | − | 1.11137e7i | 0.0914503 | − | 0.0221735i | ||||
\(307\) | −5.93484e7 | − | 5.93484e7i | −0.117064 | − | 0.117064i | 0.646148 | − | 0.763212i | \(-0.276379\pi\) |
−0.763212 | + | 0.646148i | \(0.776379\pi\) | |||||||
\(308\) | 3.41661e8 | + | 3.41661e8i | 0.666297 | + | 0.666297i | ||||
\(309\) | 1.03721e8 | − | 1.23948e7i | 0.199991 | − | 0.0238992i | ||||
\(310\) | −8.64500e7 | + | 5.01501e7i | −0.164816 | + | 0.0956105i | ||||
\(311\) | 7.30350e8i | 1.37680i | 0.725333 | + | 0.688398i | \(0.241686\pi\) | ||||
−0.725333 | + | 0.688398i | \(0.758314\pi\) | |||||||
\(312\) | 1.38202e8 | + | 1.08697e8i | 0.257616 | + | 0.202617i | ||||
\(313\) | −5.06025e8 | + | 5.06025e8i | −0.932753 | + | 0.932753i | −0.997877 | − | 0.0651245i | \(-0.979256\pi\) |
0.0651245 | + | 0.997877i | \(0.479256\pi\) | |||||||
\(314\) | −1.18452e8 | −0.215918 | ||||||||
\(315\) | 5.52456e8 | − | 5.28814e8i | 0.995888 | − | 0.953270i | ||||
\(316\) | −5.36205e8 | −0.955930 | ||||||||
\(317\) | 4.82296e8 | − | 4.82296e8i | 0.850367 | − | 0.850367i | −0.139811 | − | 0.990178i | \(-0.544649\pi\) |
0.990178 | + | 0.139811i | \(0.0446495\pi\) | |||||||
\(318\) | −1.11330e6 | − | 875621.i | −0.00194141 | − | 0.00152694i | ||||
\(319\) | − | 7.03302e8i | − | 1.21304i | ||||||
\(320\) | −1.10329e8 | + | 4.15178e8i | −0.188219 | + | 0.708287i | ||||
\(321\) | −6.63126e8 | + | 7.92444e7i | −1.11900 | + | 0.133721i | ||||
\(322\) | −1.32749e8 | − | 1.32749e8i | −0.221582 | − | 0.221582i | ||||
\(323\) | −1.06688e8 | − | 1.06688e8i | −0.176159 | − | 0.176159i | ||||
\(324\) | −2.67419e8 | − | 5.19040e8i | −0.436802 | − | 0.847800i | ||||
\(325\) | 4.65570e8 | − | 1.26811e8i | 0.752303 | − | 0.204910i | ||||
\(326\) | 7.72026e7i | 0.123416i | ||||||||
\(327\) | 3.84086e8 | − | 4.88342e8i | 0.607451 | − | 0.772338i | ||||
\(328\) | −2.02811e8 | + | 2.02811e8i | −0.317346 | + | 0.317346i | ||||
\(329\) | −1.24549e9 | −1.92822 | ||||||||
\(330\) | −1.41267e7 | + | 9.96688e7i | −0.0216393 | + | 0.152672i | ||||
\(331\) | 7.63573e8 | 1.15732 | 0.578659 | − | 0.815570i | \(-0.303576\pi\) | ||||
0.578659 | + | 0.815570i | \(0.303576\pi\) | |||||||
\(332\) | 3.22065e7 | − | 3.22065e7i | 0.0483014 | − | 0.0483014i | ||||
\(333\) | 3.78023e8 | − | 6.20012e8i | 0.561001 | − | 0.920122i | ||||
\(334\) | − | 1.42731e8i | − | 0.209607i | ||||||
\(335\) | 3.54525e8 | + | 6.11140e8i | 0.515217 | + | 0.888145i | ||||
\(336\) | −9.81890e7 | − | 8.21657e8i | −0.141213 | − | 1.18169i | ||||
\(337\) | −6.74055e8 | − | 6.74055e8i | −0.959380 | − | 0.959380i | 0.0398266 | − | 0.999207i | \(-0.487319\pi\) |
−0.999207 | + | 0.0398266i | \(0.987319\pi\) | |||||||
\(338\) | 4.23433e7 | + | 4.23433e7i | 0.0596453 | + | 0.0596453i | ||||
\(339\) | 3.33301e7 | + | 2.78910e8i | 0.0464662 | + | 0.388835i | ||||
\(340\) | −1.51688e8 | − | 2.61484e8i | −0.209303 | − | 0.360802i | ||||
\(341\) | − | 4.64740e8i | − | 0.634702i | ||||||
\(342\) | 4.71957e7 | − | 7.74076e7i | 0.0637985 | − | 0.104639i | ||||
\(343\) | 7.24774e7 | − | 7.24774e7i | 0.0969780 | − | 0.0969780i | ||||
\(344\) | 2.56381e8 | 0.339571 | ||||||||
\(345\) | −1.13082e8 | + | 7.97835e8i | −0.148261 | + | 1.04603i | ||||
\(346\) | 1.06082e8 | 0.137681 | ||||||||
\(347\) | −1.10778e8 | + | 1.10778e8i | −0.142331 | + | 0.142331i | −0.774682 | − | 0.632351i | \(-0.782090\pi\) |
0.632351 | + | 0.774682i | \(0.282090\pi\) | |||||||
\(348\) | −7.84551e8 | + | 9.97509e8i | −0.997916 | + | 1.26879i | ||||
\(349\) | − | 5.70244e8i | − | 0.718078i | −0.933323 | − | 0.359039i | \(-0.883105\pi\) | ||
0.933323 | − | 0.359039i | \(-0.116895\pi\) | |||||||
\(350\) | 2.06530e8 | + | 1.18106e8i | 0.257481 | + | 0.147243i | ||||
\(351\) | 2.20644e8 | + | 5.91909e8i | 0.272344 | + | 0.730601i | ||||
\(352\) | 2.51332e8 | + | 2.51332e8i | 0.307148 | + | 0.307148i | ||||
\(353\) | −2.34804e7 | − | 2.34804e7i | −0.0284116 | − | 0.0284116i | 0.692758 | − | 0.721170i | \(-0.256395\pi\) |
−0.721170 | + | 0.692758i | \(0.756395\pi\) | |||||||
\(354\) | −4.28823e6 | + | 512448.i | −0.00513767 | + | 0.000613958i | ||||
\(355\) | −3.18506e8 | + | 1.19857e9i | −0.377850 | + | 1.42188i | ||||
\(356\) | − | 1.11479e9i | − | 1.30954i | ||||||
\(357\) | 4.07424e8 | + | 3.20443e8i | 0.473923 | + | 0.372745i | ||||
\(358\) | −8.08506e7 | + | 8.08506e7i | −0.0931306 | + | 0.0931306i | ||||
\(359\) | 5.24443e7 | 0.0598230 | 0.0299115 | − | 0.999553i | \(-0.490477\pi\) | ||||
0.0299115 | + | 0.999553i | \(0.490477\pi\) | |||||||
\(360\) | 2.68808e8 | − | 2.57304e8i | 0.303657 | − | 0.290662i | ||||
\(361\) | 6.03848e8 | 0.675542 | ||||||||
\(362\) | 7.24724e7 | − | 7.24724e7i | 0.0802957 | − | 0.0802957i | ||||
\(363\) | 3.48384e8 | + | 2.74008e8i | 0.382283 | + | 0.300669i | ||||
\(364\) | 9.43279e8i | 1.02514i | ||||||||
\(365\) | −1.91723e8 | + | 1.11219e8i | −0.206371 | + | 0.119717i | ||||
\(366\) | −2.82776e7 | + | 3.37921e6i | −0.0301481 | + | 0.00360273i | ||||
\(367\) | 3.20449e8 | + | 3.20449e8i | 0.338398 | + | 0.338398i | 0.855764 | − | 0.517366i | \(-0.173088\pi\) |
−0.517366 | + | 0.855764i | \(0.673088\pi\) | |||||||
\(368\) | 6.16544e8 | + | 6.16544e8i | 0.644907 | + | 0.644907i | ||||
\(369\) | −1.00144e9 | + | 2.42815e8i | −1.03761 | + | 0.251584i | ||||
\(370\) | 2.18332e8 | + | 5.80194e7i | 0.224085 | + | 0.0595480i | ||||
\(371\) | − | 1.55662e7i | − | 0.0158261i | ||||||
\(372\) | −5.18430e8 | + | 6.59152e8i | −0.522143 | + | 0.663873i | ||||
\(373\) | 8.34366e8 | − | 8.34366e8i | 0.832484 | − | 0.832484i | −0.155372 | − | 0.987856i | \(-0.549658\pi\) |
0.987856 | + | 0.155372i | \(0.0496576\pi\) | |||||||
\(374\) | −6.82294e7 | −0.0674405 | ||||||||
\(375\) | −1.27447e8 | − | 1.01321e9i | −0.124801 | − | 0.992182i | ||||
\(376\) | −6.06018e8 | −0.587933 | ||||||||
\(377\) | 9.70860e8 | − | 9.70860e8i | 0.933172 | − | 0.933172i | ||||
\(378\) | −1.29439e8 | + | 2.83292e8i | −0.123266 | + | 0.269782i | ||||
\(379\) | 1.26366e9i | 1.19232i | 0.802867 | + | 0.596158i | \(0.203307\pi\) | ||||
−0.802867 | + | 0.596158i | \(0.796693\pi\) | |||||||
\(380\) | −5.61592e8 | − | 1.49237e8i | −0.525023 | − | 0.139519i | ||||
\(381\) | 3.69092e7 | + | 3.08861e8i | 0.0341899 | + | 0.286105i | ||||
\(382\) | −4.70799e7 | − | 4.70799e7i | −0.0432129 | − | 0.0432129i | ||||
\(383\) | −4.54621e8 | − | 4.54621e8i | −0.413480 | − | 0.413480i | 0.469469 | − | 0.882949i | \(-0.344445\pi\) |
−0.882949 | + | 0.469469i | \(0.844445\pi\) | |||||||
\(384\) | −1.00557e8 | − | 8.41469e8i | −0.0906257 | − | 0.758366i | ||||
\(385\) | −9.56955e8 | + | 5.55134e8i | −0.854631 | + | 0.495776i | ||||
\(386\) | − | 8.88996e7i | − | 0.0786763i | ||||||
\(387\) | 7.86457e8 | + | 4.79506e8i | 0.689742 | + | 0.420538i | ||||
\(388\) | 9.85502e8 | − | 9.85502e8i | 0.856538 | − | 0.856538i | ||||
\(389\) | 1.48893e8 | 0.128248 | 0.0641239 | − | 0.997942i | \(-0.479575\pi\) | ||||
0.0641239 | + | 0.997942i | \(0.479575\pi\) | |||||||
\(390\) | −1.57087e8 | + | 1.18085e8i | −0.134095 | + | 0.100802i | ||||
\(391\) | −5.46167e8 | −0.462069 | ||||||||
\(392\) | −3.19217e8 | + | 3.19217e8i | −0.267661 | + | 0.267661i | ||||
\(393\) | −5.54727e8 | + | 7.05301e8i | −0.461004 | + | 0.586139i | ||||
\(394\) | 6.75369e7i | 0.0556294i | ||||||||
\(395\) | 3.15310e8 | − | 1.18654e9i | 0.257424 | − | 0.968709i | ||||
\(396\) | 1.99032e8 | + | 8.20872e8i | 0.161061 | + | 0.664266i | ||||
\(397\) | −1.39088e9 | − | 1.39088e9i | −1.11563 | − | 1.11563i | −0.992375 | − | 0.123259i | \(-0.960665\pi\) |
−0.123259 | − | 0.992375i | \(-0.539335\pi\) | |||||||
\(398\) | −2.45658e8 | − | 2.45658e8i | −0.195317 | − | 0.195317i | ||||
\(399\) | 9.89330e8 | − | 1.18226e8i | 0.779715 | − | 0.0931769i | ||||
\(400\) | −9.59217e8 | − | 5.48539e8i | −0.749389 | − | 0.428546i | ||||
\(401\) | − | 5.11604e8i | − | 0.396213i | −0.980181 | − | 0.198106i | \(-0.936521\pi\) | ||
0.980181 | − | 0.198106i | \(-0.0634792\pi\) | |||||||
\(402\) | −2.26174e8 | − | 1.77888e8i | −0.173640 | − | 0.136570i | ||||
\(403\) | 6.41542e8 | − | 6.41542e8i | 0.488267 | − | 0.488267i | ||||
\(404\) | 1.00309e9 | 0.756841 | ||||||||
\(405\) | 1.30581e9 | − | 2.86542e8i | 0.976760 | − | 0.214337i | ||||
\(406\) | 6.76969e8 | 0.502027 | ||||||||
\(407\) | −7.42809e8 | + | 7.42809e8i | −0.546131 | + | 0.546131i | ||||
\(408\) | 1.98240e8 | + | 1.55918e8i | 0.144504 | + | 0.113654i | ||||
\(409\) | − | 9.31820e8i | − | 0.673442i | −0.941604 | − | 0.336721i | \(-0.890682\pi\) | ||
0.941604 | − | 0.336721i | \(-0.109318\pi\) | |||||||
\(410\) | −1.60861e8 | − | 2.77296e8i | −0.115267 | − | 0.198701i | ||||
\(411\) | −1.41954e9 | + | 1.69636e8i | −1.00856 | + | 0.120524i | ||||
\(412\) | 1.92811e8 | + | 1.92811e8i | 0.135829 | + | 0.135829i | ||||
\(413\) | −3.35616e7 | − | 3.35616e7i | −0.0234433 | − | 0.0234433i | ||||
\(414\) | −7.73319e7 | − | 3.18941e8i | −0.0535621 | − | 0.220907i | ||||
\(415\) | 5.23294e7 | + | 9.02068e7i | 0.0359400 | + | 0.0619542i | ||||
\(416\) | 6.93892e8i | 0.472569i | ||||||||
\(417\) | −9.47262e8 | + | 1.20439e9i | −0.639726 | + | 0.813373i | ||||
\(418\) | −9.27386e7 | + | 9.27386e7i | −0.0621074 | + | 0.0621074i | ||||
\(419\) | 1.87062e8 | 0.124233 | 0.0621165 | − | 0.998069i | \(-0.480215\pi\) | ||||
0.0621165 | + | 0.998069i | \(0.480215\pi\) | |||||||
\(420\) | 1.97654e9 | + | 2.80148e8i | 1.30176 | + | 0.184508i | ||||
\(421\) | 2.80609e8 | 0.183280 | 0.0916400 | − | 0.995792i | \(-0.470789\pi\) | ||||
0.0916400 | + | 0.995792i | \(0.470789\pi\) | |||||||
\(422\) | 4.05275e6 | − | 4.05275e6i | 0.00262516 | − | 0.00262516i | ||||
\(423\) | −1.85898e9 | − | 1.13343e9i | −1.19422 | − | 0.728120i | ||||
\(424\) | − | 7.57402e6i | − | 0.00482554i | ||||||
\(425\) | 6.67824e8 | − | 1.81900e8i | 0.421989 | − | 0.114940i | ||||
\(426\) | −5.99316e7 | − | 5.01515e8i | −0.0375597 | − | 0.314304i | ||||
\(427\) | −2.21314e8 | − | 2.21314e8i | −0.137566 | − | 0.137566i | ||||
\(428\) | −1.23271e9 | − | 1.23271e9i | −0.759991 | − | 0.759991i | ||||
\(429\) | −1.08432e8 | − | 9.07373e8i | −0.0663067 | − | 0.554863i | ||||
\(430\) | −7.35950e7 | + | 2.76945e8i | −0.0446384 | + | 0.167979i | ||||
\(431\) | 2.93618e9i | 1.76650i | 0.468906 | + | 0.883248i | \(0.344648\pi\) | ||||
−0.468906 | + | 0.883248i | \(0.655352\pi\) | |||||||
\(432\) | 6.01174e8 | − | 1.31573e9i | 0.358763 | − | 0.785190i | ||||
\(433\) | −2.11328e9 | + | 2.11328e9i | −1.25098 | + | 1.25098i | −0.295695 | + | 0.955282i | \(0.595551\pi\) |
−0.955282 | + | 0.295695i | \(0.904449\pi\) | |||||||
\(434\) | 4.47339e8 | 0.262678 | ||||||||
\(435\) | −1.74599e9 | − | 2.32267e9i | −1.01702 | − | 1.35293i | ||||
\(436\) | 1.62179e9 | 0.937114 | ||||||||
\(437\) | −7.42360e8 | + | 7.42360e8i | −0.425529 | + | 0.425529i | ||||
\(438\) | 5.58058e7 | − | 7.09537e7i | 0.0317336 | − | 0.0403474i | ||||
\(439\) | 2.53076e9i | 1.42766i | 0.700318 | + | 0.713831i | \(0.253042\pi\) | ||||
−0.700318 | + | 0.713831i | \(0.746958\pi\) | |||||||
\(440\) | −4.65624e8 | + | 2.70111e8i | −0.260586 | + | 0.151167i | ||||
\(441\) | −1.57624e9 | + | 3.82182e8i | −0.875159 | + | 0.212195i | ||||
\(442\) | −9.41860e7 | − | 9.41860e7i | −0.0518810 | − | 0.0518810i | ||||
\(443\) | 1.47424e9 | + | 1.47424e9i | 0.805665 | + | 0.805665i | 0.983974 | − | 0.178309i | \(-0.0570628\pi\) |
−0.178309 | + | 0.983974i | \(0.557063\pi\) | |||||||
\(444\) | 1.88217e9 | − | 2.24921e8i | 1.02051 | − | 0.121952i | ||||
\(445\) | 2.46687e9 | + | 6.55543e8i | 1.32705 | + | 0.352648i | ||||
\(446\) | 2.57983e8i | 0.137695i | ||||||||
\(447\) | 2.75293e9 | + | 2.16521e9i | 1.45787 | + | 1.14663i | ||||
\(448\) | 1.35963e9 | − | 1.35963e9i | 0.714409 | − | 0.714409i | ||||
\(449\) | 2.67292e9 | 1.39355 | 0.696776 | − | 0.717289i | \(-0.254617\pi\) | ||||
0.696776 | + | 0.717289i | \(0.254617\pi\) | |||||||
\(450\) | 2.00780e8 | + | 3.64229e8i | 0.103867 | + | 0.188422i | ||||
\(451\) | 1.49069e9 | 0.765192 | ||||||||
\(452\) | −5.18477e8 | + | 5.18477e8i | −0.264086 | + | 0.264086i | ||||
\(453\) | 3.76442e8 | + | 2.96075e8i | 0.190263 | + | 0.149644i | ||||
\(454\) | 2.00221e8i | 0.100419i | ||||||||
\(455\) | −2.08733e9 | − | 5.54686e8i | −1.03885 | − | 0.276062i | ||||
\(456\) | 4.81377e8 | − | 5.75251e7i | 0.237743 | − | 0.0284106i | ||||
\(457\) | −1.29398e9 | − | 1.29398e9i | −0.634193 | − | 0.634193i | 0.314924 | − | 0.949117i | \(-0.398021\pi\) |
−0.949117 | + | 0.314924i | \(0.898021\pi\) | |||||||
\(458\) | 2.96210e8 | + | 2.96210e8i | 0.144069 | + | 0.144069i | ||||
\(459\) | 3.16497e8 | + | 8.49049e8i | 0.152766 | + | 0.409815i | ||||
\(460\) | −1.81947e9 | + | 1.05548e9i | −0.871552 | + | 0.505591i | ||||
\(461\) | − | 2.19571e9i | − | 1.04381i | −0.853003 | − | 0.521906i | \(-0.825221\pi\) | ||
0.853003 | − | 0.521906i | \(-0.174779\pi\) | |||||||
\(462\) | 2.78546e8 | − | 3.54154e8i | 0.131417 | − | 0.167088i | ||||
\(463\) | −8.89626e8 | + | 8.89626e8i | −0.416557 | + | 0.416557i | −0.884015 | − | 0.467458i | \(-0.845170\pi\) |
0.467458 | + | 0.884015i | \(0.345170\pi\) | |||||||
\(464\) | −3.14415e9 | −1.46113 | ||||||||
\(465\) | −1.15375e9 | − | 1.53482e9i | −0.532139 | − | 0.707898i | ||||
\(466\) | −3.41219e8 | −0.156200 | ||||||||
\(467\) | −1.96829e9 | + | 1.96829e9i | −0.894295 | + | 0.894295i | −0.994924 | − | 0.100629i | \(-0.967914\pi\) |
0.100629 | + | 0.994924i | \(0.467914\pi\) | |||||||
\(468\) | −8.58406e8 | + | 1.40791e9i | −0.387108 | + | 0.634912i | ||||
\(469\) | − | 3.16237e9i | − | 1.41549i | ||||||
\(470\) | 1.73960e8 | − | 6.54626e8i | 0.0772869 | − | 0.290838i | ||||
\(471\) | −2.70026e8 | − | 2.25961e9i | −0.119078 | − | 0.996462i | ||||
\(472\) | −1.63300e7 | − | 1.63300e7i | −0.00714810 | − | 0.00714810i | ||||
\(473\) | −9.42220e8 | − | 9.42220e8i | −0.409391 | − | 0.409391i | ||||
\(474\) | 5.93302e7 | + | 4.96482e8i | 0.0255889 | + | 0.214131i | ||||
\(475\) | 6.60477e8 | − | 1.15496e9i | 0.282768 | − | 0.494470i | ||||
\(476\) | 1.35306e9i | 0.575034i | ||||||||
\(477\) | 1.41656e7 | − | 2.32336e7i | 0.00597614 | − | 0.00980172i | ||||
\(478\) | 6.08349e8 | − | 6.08349e8i | 0.254774 | − | 0.254774i | ||||
\(479\) | 2.28503e9 | 0.949988 | 0.474994 | − | 0.879989i | \(-0.342450\pi\) | ||||
0.474994 | + | 0.879989i | \(0.342450\pi\) | |||||||
\(480\) | 1.45398e9 | + | 2.06082e8i | 0.600085 | + | 0.0850540i | ||||
\(481\) | −2.05079e9 | −0.840261 | ||||||||
\(482\) | −2.75450e8 | + | 2.75450e8i | −0.112041 | + | 0.112041i | ||||
\(483\) | 2.22972e9 | − | 2.83496e9i | 0.900401 | − | 1.14481i | ||||
\(484\) | 1.15699e9i | 0.463842i | ||||||||
\(485\) | 1.60125e9 | + | 2.76028e9i | 0.637330 | + | 1.09865i | ||||
\(486\) | −4.50999e8 | + | 3.05039e8i | −0.178217 | + | 0.120539i | ||||
\(487\) | −1.04806e8 | − | 1.04806e8i | −0.0411182 | − | 0.0411182i | 0.686249 | − | 0.727367i | \(-0.259256\pi\) |
−0.727367 | + | 0.686249i | \(0.759256\pi\) | |||||||
\(488\) | −1.07684e8 | − | 1.07684e8i | −0.0419453 | − | 0.0419453i | ||||
\(489\) | −1.47273e9 | + | 1.75993e8i | −0.569564 | + | 0.0680636i | ||||
\(490\) | −2.53189e8 | − | 4.36454e8i | −0.0972206 | − | 0.167591i | ||||
\(491\) | 6.21274e8i | 0.236864i | 0.992962 | + | 0.118432i | \(0.0377867\pi\) | ||||
−0.992962 | + | 0.118432i | \(0.962213\pi\) | |||||||
\(492\) | −2.11428e9 | − | 1.66291e9i | −0.800361 | − | 0.629492i | ||||
\(493\) | 1.39262e9 | − | 1.39262e9i | 0.523443 | − | 0.523443i | ||||
\(494\) | −2.56039e8 | −0.0955567 | ||||||||
\(495\) | −1.93351e9 | − | 4.22764e7i | −0.716518 | − | 0.0156668i | ||||
\(496\) | −2.07764e9 | −0.764514 | ||||||||
\(497\) | 3.92509e9 | − | 3.92509e9i | 1.43417 | − | 1.43417i | ||||
\(498\) | −3.33842e7 | − | 2.62570e7i | −0.0121126 | − | 0.00952669i | ||||
\(499\) | − | 1.04126e9i | − | 0.375151i | −0.982250 | − | 0.187575i | \(-0.939937\pi\) | ||
0.982250 | − | 0.187575i | \(-0.0600629\pi\) | |||||||
\(500\) | 1.87323e9 | − | 1.89657e9i | 0.670187 | − | 0.678536i | ||||
\(501\) | 2.72276e9 | − | 3.25373e8i | 0.967337 | − | 0.115598i | ||||
\(502\) | 3.49138e8 | + | 3.49138e8i | 0.123178 | + | 0.123178i | ||||
\(503\) | 8.74993e8 | + | 8.74993e8i | 0.306561 | + | 0.306561i | 0.843574 | − | 0.537013i | \(-0.180447\pi\) |
−0.537013 | + | 0.843574i | \(0.680447\pi\) | |||||||
\(504\) | −1.61862e9 | + | 3.92460e8i | −0.563170 | + | 0.136549i | ||||
\(505\) | −5.89856e8 | + | 2.21968e9i | −0.203810 | + | 0.766958i | ||||
\(506\) | 4.74757e8i | 0.162909i | ||||||||
\(507\) | −7.11222e8 | + | 9.04276e8i | −0.242369 | + | 0.308158i | ||||
\(508\) | −5.74154e8 | + | 5.74154e8i | −0.194315 | + | 0.194315i | ||||
\(509\) | −5.23513e9 | −1.75961 | −0.879803 | − | 0.475339i | \(-0.842325\pi\) | ||||
−0.879803 | + | 0.475339i | \(0.842325\pi\) | |||||||
\(510\) | −2.25329e8 | + | 1.69384e8i | −0.0752180 | + | 0.0565427i | ||||
\(511\) | 9.92077e8 | 0.328906 | ||||||||
\(512\) | 1.90286e9 | − | 1.90286e9i | 0.626557 | − | 0.626557i | ||||
\(513\) | 1.58423e9 | + | 7.23854e8i | 0.518093 | + | 0.236723i | ||||
\(514\) | − | 5.30778e8i | − | 0.172402i | ||||||
\(515\) | −5.40042e8 | + | 3.13281e8i | −0.174222 | + | 0.101067i | ||||
\(516\) | 2.85302e8 | + | 2.38744e9i | 0.0914179 | + | 0.764996i | ||||
\(517\) | 2.22717e9 | + | 2.22717e9i | 0.708820 | + | 0.708820i | ||||
\(518\) | −7.14997e8 | − | 7.14997e8i | −0.226022 | − | 0.226022i | ||||
\(519\) | 2.41827e8 | + | 2.02364e9i | 0.0759309 | + | 0.635399i | ||||
\(520\) | −1.01563e9 | − | 2.69893e8i | −0.316756 | − | 0.0841743i | ||||
\(521\) | − | 3.89754e9i | − | 1.20742i | −0.797203 | − | 0.603711i | \(-0.793688\pi\) | ||
0.797203 | − | 0.603711i | \(-0.206312\pi\) | |||||||
\(522\) | 1.01042e9 | + | 6.16058e8i | 0.310925 | + | 0.189572i | ||||
\(523\) | −1.14045e9 | + | 1.14045e9i | −0.348596 | + | 0.348596i | −0.859586 | − | 0.510991i | \(-0.829279\pi\) |
0.510991 | + | 0.859586i | \(0.329279\pi\) | |||||||
\(524\) | −2.34232e9 | −0.711191 | ||||||||
\(525\) | −1.78221e9 | + | 4.20904e9i | −0.537528 | + | 1.26948i | ||||
\(526\) | −1.11142e9 | −0.332987 | ||||||||
\(527\) | 9.20243e8 | − | 9.20243e8i | 0.273883 | − | 0.273883i | ||||
\(528\) | −1.29369e9 | + | 1.64485e9i | −0.382483 | + | 0.486304i | ||||
\(529\) | 3.95540e8i | 0.116170i | ||||||||
\(530\) | 8.18154e6 | + | 2.17415e6i | 0.00238709 | + | 0.000634343i | ||||
\(531\) | −1.95511e7 | − | 8.06349e7i | −0.00566684 | − | 0.0233718i | ||||
\(532\) | 1.83911e9 | + | 1.83911e9i | 0.529561 | + | 0.529561i | ||||
\(533\) | 2.05780e9 | + | 2.05780e9i | 0.588651 | + | 0.588651i | ||||
\(534\) | −1.03221e9 | + | 1.23350e8i | −0.293341 | + | 0.0350546i | ||||
\(535\) | 3.45269e9 | − | 2.00292e9i | 0.974810 | − | 0.565492i | ||||
\(536\) | − | 1.53871e9i | − | 0.431599i | ||||||
\(537\) | −1.72663e9 | − | 1.35801e9i | −0.481160 | − | 0.378437i | ||||
\(538\) | 1.05398e8 | − | 1.05398e8i | 0.0291807 | − | 0.0291807i | ||||
\(539\) | 2.34630e9 | 0.645390 | ||||||||
\(540\) | 2.69518e9 | + | 2.21684e9i | 0.736561 | + | 0.605837i | ||||
\(541\) | 5.67463e9 | 1.54080 | 0.770402 | − | 0.637559i | \(-0.220056\pi\) | ||||
0.770402 | + | 0.637559i | \(0.220056\pi\) | |||||||
\(542\) | −1.09106e9 | + | 1.09106e9i | −0.294341 | + | 0.294341i | ||||
\(543\) | 1.54771e9 | + | 1.21729e9i | 0.414848 | + | 0.326282i | ||||
\(544\) | 9.95336e8i | 0.265078i | ||||||||
\(545\) | −9.53679e8 | + | 3.58878e9i | −0.252357 | + | 0.949641i | ||||
\(546\) | 8.73399e8 | − | 1.04372e8i | 0.229635 | − | 0.0274417i | ||||
\(547\) | −1.60556e9 | − | 1.60556e9i | −0.419441 | − | 0.419441i | 0.465570 | − | 0.885011i | \(-0.345849\pi\) |
−0.885011 | + | 0.465570i | \(0.845849\pi\) | |||||||
\(548\) | −2.63884e9 | − | 2.63884e9i | −0.684984 | − | 0.684984i | ||||
\(549\) | −1.28925e8 | − | 5.31727e8i | −0.0332532 | − | 0.137147i | ||||
\(550\) | −1.58117e8 | − | 5.80508e8i | −0.0405238 | − | 0.148778i | ||||
\(551\) | − | 3.78576e9i | − | 0.964101i | ||||||
\(552\) | 1.08491e9 | − | 1.37940e9i | 0.274542 | − | 0.349063i | ||||
\(553\) | −3.88570e9 | + | 3.88570e9i | −0.977082 | + | 0.977082i | ||||
\(554\) | 1.19202e9 | 0.297852 | ||||||||
\(555\) | −6.09073e8 | + | 4.29722e9i | −0.151232 | + | 1.06699i | ||||
\(556\) | −3.99979e9 | −0.986904 | ||||||||
\(557\) | 8.47773e8 | − | 8.47773e8i | 0.207867 | − | 0.207867i | −0.595493 | − | 0.803360i | \(-0.703043\pi\) |
0.803360 | + | 0.595493i | \(0.203043\pi\) | |||||||
\(558\) | 6.67685e8 | + | 4.07090e8i | 0.162687 | + | 0.0991906i | ||||
\(559\) | − | 2.60134e9i | − | 0.629877i | ||||||
\(560\) | 2.48176e9 | + | 4.27811e9i | 0.597174 | + | 1.02942i | ||||
\(561\) | −1.55538e8 | − | 1.30156e9i | −0.0371934 | − | 0.311239i | ||||
\(562\) | 3.57814e7 | + | 3.57814e7i | 0.00850316 | + | 0.00850316i | ||||
\(563\) | 3.73177e8 | + | 3.73177e8i | 0.0881323 | + | 0.0881323i | 0.749799 | − | 0.661666i | \(-0.230150\pi\) |
−0.661666 | + | 0.749799i | \(0.730150\pi\) | |||||||
\(564\) | −6.74381e8 | − | 5.64330e9i | −0.158281 | − | 1.32451i | ||||
\(565\) | −8.42427e8 | − | 1.45220e9i | −0.196500 | − | 0.338732i | ||||
\(566\) | 1.40853e8i | 0.0326519i | ||||||||
\(567\) | −5.69921e9 | − | 1.82341e9i | −1.31303 | − | 0.420091i | ||||
\(568\) | 1.90982e9 | − | 1.90982e9i | 0.437295 | − | 0.437295i | ||||
\(569\) | −4.11594e9 | −0.936648 | −0.468324 | − | 0.883557i | \(-0.655142\pi\) | ||||
−0.468324 | + | 0.883557i | \(0.655142\pi\) | |||||||
\(570\) | −7.60418e7 | + | 5.36501e8i | −0.0171985 | + | 0.121341i | ||||
\(571\) | −2.99821e9 | −0.673962 | −0.336981 | − | 0.941512i | \(-0.609406\pi\) | ||||
−0.336981 | + | 0.941512i | \(0.609406\pi\) | |||||||
\(572\) | 1.68675e9 | − | 1.68675e9i | 0.376847 | − | 0.376847i | ||||
\(573\) | 7.90781e8 | − | 1.00543e9i | 0.175596 | − | 0.223260i | ||||
\(574\) | 1.43488e9i | 0.316682i | ||||||||
\(575\) | −1.26571e9 | − | 4.64689e9i | −0.277649 | − | 1.01935i | ||||
\(576\) | 3.26663e9 | − | 7.92043e8i | 0.712232 | − | 0.172691i | ||||
\(577\) | 1.54684e9 | + | 1.54684e9i | 0.335220 | + | 0.335220i | 0.854565 | − | 0.519345i | \(-0.173824\pi\) |
−0.519345 | + | 0.854565i | \(0.673824\pi\) | |||||||
\(578\) | 5.71184e8 | + | 5.71184e8i | 0.123035 | + | 0.123035i | ||||
\(579\) | 1.69587e9 | − | 2.02658e8i | 0.363092 | − | 0.0433899i | ||||
\(580\) | 1.94803e9 | − | 7.33061e9i | 0.414569 | − | 1.56006i | ||||
\(581\) | − | 4.66779e8i | − | 0.0987404i | ||||||
\(582\) | −1.02154e9 | − | 8.03451e8i | −0.214795 | − | 0.168939i | ||||
\(583\) | −2.78352e7 | + | 2.78352e7i | −0.00581773 | + | 0.00581773i | ||||
\(584\) | 4.82714e8 | 0.100287 | ||||||||
\(585\) | −2.61071e9 | − | 2.72743e9i | −0.539155 | − | 0.563259i | ||||
\(586\) | −1.06672e6 | −0.000218981 | ||||||||
\(587\) | −3.50513e9 | + | 3.50513e9i | −0.715271 | + | 0.715271i | −0.967633 | − | 0.252362i | \(-0.918793\pi\) |
0.252362 | + | 0.967633i | \(0.418793\pi\) | |||||||
\(588\) | −3.32781e9 | − | 2.61736e9i | −0.675053 | − | 0.530936i | ||||
\(589\) | − | 2.50162e9i | − | 0.504450i | ||||||
\(590\) | 2.23275e7 | − | 1.29523e7i | 0.00447566 | − | 0.00259635i | ||||
\(591\) | −1.28835e9 | + | 1.53959e8i | −0.256730 | + | 0.0306795i | ||||
\(592\) | 3.32077e9 | + | 3.32077e9i | 0.657828 | + | 0.657828i | ||||
\(593\) | 3.34493e9 | + | 3.34493e9i | 0.658712 | + | 0.658712i | 0.955075 | − | 0.296363i | \(-0.0957739\pi\) |
−0.296363 | + | 0.955075i | \(0.595774\pi\) | |||||||
\(594\) | 7.38038e8 | − | 2.75116e8i | 0.144486 | − | 0.0538596i | ||||
\(595\) | −2.99412e9 | − | 7.95655e8i | −0.582720 | − | 0.154851i | ||||
\(596\) | 9.14253e9i | 1.76890i | ||||||||
\(597\) | 4.12622e9 | − | 5.24624e9i | 0.793674 | − | 1.00911i | ||||
\(598\) | −6.55370e8 | + | 6.55370e8i | −0.125323 | + | 0.125323i | ||||
\(599\) | 4.84654e9 | 0.921378 | 0.460689 | − | 0.887562i | \(-0.347602\pi\) | ||||
0.460689 | + | 0.887562i | \(0.347602\pi\) | |||||||
\(600\) | −8.67167e8 | + | 2.04799e9i | −0.163898 | + | 0.387078i | ||||
\(601\) | −7.05160e9 | −1.32503 | −0.662517 | − | 0.749047i | \(-0.730512\pi\) | ||||
−0.662517 | + | 0.749047i | \(0.730512\pi\) | |||||||
\(602\) | 9.06942e8 | − | 9.06942e8i | 0.169431 | − | 0.169431i | ||||
\(603\) | 2.87783e9 | − | 4.72005e9i | 0.534509 | − | 0.876670i | ||||
\(604\) | 1.25017e9i | 0.230855i | ||||||||
\(605\) | −2.56024e9 | − | 6.80356e8i | −0.470043 | − | 0.124909i | ||||
\(606\) | −1.10990e8 | − | 9.28778e8i | −0.0202596 | − | 0.169534i | ||||
\(607\) | 2.33423e9 | + | 2.33423e9i | 0.423627 | + | 0.423627i | 0.886451 | − | 0.462823i | \(-0.153164\pi\) |
−0.462823 | + | 0.886451i | \(0.653164\pi\) | |||||||
\(608\) | 1.35288e9 | + | 1.35288e9i | 0.244116 | + | 0.244116i | ||||
\(609\) | 1.54324e9 | + | 1.29140e10i | 0.276868 | + | 2.31686i | ||||
\(610\) | 1.47233e8 | − | 8.54105e7i | 0.0262634 | − | 0.0152355i | ||||
\(611\) | 6.14890e9i | 1.09057i | ||||||||
\(612\) | −1.23132e9 | + | 2.01954e9i | −0.217140 | + | 0.356141i | ||||
\(613\) | −3.01299e8 | + | 3.01299e8i | −0.0528306 | + | 0.0528306i | −0.733029 | − | 0.680198i | \(-0.761894\pi\) |
0.680198 | + | 0.733029i | \(0.261894\pi\) | |||||||
\(614\) | −2.04304e8 | −0.0356195 | ||||||||
\(615\) | 4.92305e9 | − | 3.70074e9i | 0.853436 | − | 0.641543i | ||||
\(616\) | 2.40939e9 | 0.415313 | ||||||||
\(617\) | −5.38935e9 | + | 5.38935e9i | −0.923716 | + | 0.923716i | −0.997290 | − | 0.0735741i | \(-0.976559\pi\) |
0.0735741 | + | 0.997290i | \(0.476559\pi\) | |||||||
\(618\) | 1.57193e8 | − | 1.99861e8i | 0.0267901 | − | 0.0340619i | ||||
\(619\) | 1.22018e9i | 0.206779i | 0.994641 | + | 0.103390i | \(0.0329689\pi\) | ||||
−0.994641 | + | 0.103390i | \(0.967031\pi\) | |||||||
\(620\) | 1.28725e9 | − | 4.84405e9i | 0.216917 | − | 0.816277i | ||||
\(621\) | 5.90789e9 | − | 2.20227e9i | 0.989947 | − | 0.369019i | ||||
\(622\) | 1.25710e9 | + | 1.25710e9i | 0.209461 | + | 0.209461i | ||||
\(623\) | −8.07853e9 | − | 8.07853e9i | −1.33852 | − | 1.33852i | ||||
\(624\) | −4.05646e9 | + | 4.84751e8i | −0.668345 | + | 0.0798680i | ||||
\(625\) | 3.09528e9 | + | 5.26043e9i | 0.507131 | + | 0.861869i | ||||
\(626\) | 1.74197e9i | 0.283811i | ||||||||
\(627\) | −1.98051e9 | − | 1.55769e9i | −0.320879 | − | 0.252374i | ||||
\(628\) | 4.20048e9 | − | 4.20048e9i | 0.676769 | − | 0.676769i | ||||
\(629\) | −2.94171e9 | −0.471327 | ||||||||
\(630\) | 4.06934e7 | − | 1.86111e9i | 0.00648384 | − | 0.296538i | ||||
\(631\) | −1.39179e9 | −0.220532 | −0.110266 | − | 0.993902i | \(-0.535170\pi\) | ||||
−0.110266 | + | 0.993902i | \(0.535170\pi\) | |||||||
\(632\) | −1.89066e9 | + | 1.89066e9i | −0.297923 | + | 0.297923i | ||||
\(633\) | 8.65498e7 | + | 6.80723e7i | 0.0135629 | + | 0.0106674i | ||||
\(634\) | − | 1.66028e9i | − | 0.258744i | ||||||
\(635\) | −9.32891e8 | − | 1.60814e9i | −0.144585 | − | 0.249239i | ||||
\(636\) | 7.05301e7 | − | 8.42843e6i | 0.0108711 | − | 0.00129911i | ||||
\(637\) | 3.23890e9 | + | 3.23890e9i | 0.496489 | + | 0.496489i | ||||
\(638\) | −1.21054e9 | − | 1.21054e9i | −0.184547 | − | 0.184547i | ||||
\(639\) | 9.43038e9 | − | 2.28654e9i | 1.42980 | − | 0.346677i | ||||
\(640\) | 2.54160e9 | + | 4.38127e9i | 0.383245 | + | 0.660648i | ||||
\(641\) | − | 2.77059e9i | − | 0.415498i | −0.978182 | − | 0.207749i | \(-0.933386\pi\) | ||
0.978182 | − | 0.207749i | \(-0.0666137\pi\) | |||||||
\(642\) | −1.00499e9 | + | 1.27779e9i | −0.149896 | + | 0.190584i | ||||
\(643\) | −5.82699e9 | + | 5.82699e9i | −0.864383 | + | 0.864383i | −0.991844 | − | 0.127461i | \(-0.959317\pi\) |
0.127461 | + | 0.991844i | \(0.459317\pi\) | |||||||
\(644\) | 9.41494e9 | 1.38905 | ||||||||
\(645\) | −5.45083e9 | − | 7.72582e8i | −0.799841 | − | 0.113367i | ||||
\(646\) | −3.67268e8 | −0.0536005 | ||||||||
\(647\) | −5.05616e9 | + | 5.05616e9i | −0.733932 | + | 0.733932i | −0.971396 | − | 0.237465i | \(-0.923684\pi\) |
0.237465 | + | 0.971396i | \(0.423684\pi\) | |||||||
\(648\) | −2.77306e9 | − | 8.87215e8i | −0.400356 | − | 0.128090i | ||||
\(649\) | 1.20029e8i | 0.0172357i | ||||||||
\(650\) | 5.83082e8 | − | 1.01962e9i | 0.0832785 | − | 0.145627i | ||||
\(651\) | 1.01977e9 | + | 8.53354e9i | 0.144866 | + | 1.21226i | ||||
\(652\) | −2.73772e9 | − | 2.73772e9i | −0.386832 | − | 0.386832i | ||||
\(653\) | 4.26375e9 | + | 4.26375e9i | 0.599232 | + | 0.599232i | 0.940108 | − | 0.340876i | \(-0.110724\pi\) |
−0.340876 | + | 0.940108i | \(0.610724\pi\) | |||||||
\(654\) | −1.79449e8 | − | 1.50165e9i | −0.0250852 | − | 0.209916i | ||||
\(655\) | 1.37738e9 | − | 5.18320e9i | 0.191517 | − | 0.720698i | ||||
\(656\) | − | 6.66422e9i | − | 0.921692i | ||||||
\(657\) | 1.48074e9 | + | 9.02814e8i | 0.203705 | + | 0.124199i | ||||
\(658\) | −2.14378e9 | + | 2.14378e9i | −0.293352 | + | 0.293352i | ||||
\(659\) | 9.37824e9 | 1.27650 | 0.638252 | − | 0.769827i | \(-0.279658\pi\) | ||||
0.638252 | + | 0.769827i | \(0.279658\pi\) | |||||||
\(660\) | −3.03345e9 | − | 4.03536e9i | −0.410708 | − | 0.546360i | ||||
\(661\) | 7.09319e8 | 0.0955292 | 0.0477646 | − | 0.998859i | \(-0.484790\pi\) | ||||
0.0477646 | + | 0.998859i | \(0.484790\pi\) | |||||||
\(662\) | 1.31428e9 | − | 1.31428e9i | 0.176070 | − | 0.176070i | ||||
\(663\) | 1.58200e9 | − | 2.01142e9i | 0.210819 | − | 0.268044i | ||||
\(664\) | − | 2.27120e8i | − | 0.0301070i | ||||||
\(665\) | −5.15113e9 | + | 2.98820e9i | −0.679246 | + | 0.394034i | ||||
\(666\) | −4.16517e8 | − | 1.71785e9i | −0.0546353 | − | 0.225333i | ||||
\(667\) | −9.69023e9 | − | 9.69023e9i | −1.26443 | − | 1.26443i | ||||
\(668\) | 5.06145e9 | + | 5.06145e9i | 0.656988 | + | 0.656988i | ||||
\(669\) | −4.92134e9 | + | 5.88106e8i | −0.635465 | + | 0.0759388i | ||||
\(670\) | 1.66213e9 | + | 4.41692e8i | 0.213503 | + | 0.0567359i | ||||
\(671\) | 7.91498e8i | 0.101140i | ||||||||
\(672\) | −5.16643e9 | − | 4.06345e9i | −0.656747 | − | 0.516538i | ||||
\(673\) | 3.47585e9 | − | 3.47585e9i | 0.439550 | − | 0.439550i | −0.452310 | − | 0.891861i | \(-0.649400\pi\) |
0.891861 | + | 0.452310i | \(0.149400\pi\) | |||||||
\(674\) | −2.32040e9 | −0.291913 | ||||||||
\(675\) | −6.49040e9 | + | 4.66043e9i | −0.812285 | + | 0.583261i | ||||
\(676\) | −3.00312e9 | −0.373903 | ||||||||
\(677\) | 9.35828e9 | − | 9.35828e9i | 1.15914 | − | 1.15914i | 0.174478 | − | 0.984661i | \(-0.444176\pi\) |
0.984661 | − | 0.174478i | \(-0.0558239\pi\) | |||||||
\(678\) | 5.37436e8 | + | 4.22699e8i | 0.0662252 | + | 0.0520868i | ||||
\(679\) | − | 1.42832e10i | − | 1.75098i | ||||||
\(680\) | −1.45685e9 | − | 3.87141e8i | −0.177678 | − | 0.0472158i | ||||
\(681\) | −3.81946e9 | + | 4.56430e8i | −0.463433 | + | 0.0553808i | ||||
\(682\) | −7.99924e8 | − | 7.99924e8i | −0.0965613 | − | 0.0965613i | ||||
\(683\) | −6.79399e9 | − | 6.79399e9i | −0.815930 | − | 0.815930i | 0.169586 | − | 0.985515i | \(-0.445757\pi\) |
−0.985515 | + | 0.169586i | \(0.945757\pi\) | |||||||
\(684\) | 1.07136e9 | + | 4.41862e9i | 0.128009 | + | 0.527947i | ||||
\(685\) | 7.39110e9 | − | 4.28761e9i | 0.878601 | − | 0.509681i | ||||
\(686\) | − | 2.49500e8i | − | 0.0295078i | ||||||
\(687\) | −4.97531e9 | + | 6.32581e9i | −0.585426 | + | 0.744334i | ||||
\(688\) | −4.21224e9 | + | 4.21224e9i | −0.493122 | + | 0.493122i | ||||
\(689\) | −7.68491e7 | −0.00895100 | ||||||||
\(690\) | 1.17861e9 | + | 1.56790e9i | 0.136584 | + | 0.181696i | ||||
\(691\) | 1.04165e10 | 1.20101 | 0.600506 | − | 0.799620i | \(-0.294966\pi\) | ||||
0.600506 | + | 0.799620i | \(0.294966\pi\) | |||||||
\(692\) | −3.76182e9 | + | 3.76182e9i | −0.431545 | + | 0.431545i | ||||
\(693\) | 7.39090e9 | + | 4.50626e9i | 0.843589 | + | 0.514339i | ||||
\(694\) | 3.81347e8i | 0.0433075i | ||||||||
\(695\) | 2.35204e9 | − | 8.85093e9i | 0.265765 | − | 1.00010i | ||||
\(696\) | 7.50891e8 | + | 6.28355e9i | 0.0844198 | + | 0.706435i | ||||
\(697\) | 2.95176e9 | + | 2.95176e9i | 0.330191 | + | 0.330191i | ||||
\(698\) | −9.81519e8 | − | 9.81519e8i | −0.109246 | − | 0.109246i | ||||
\(699\) | −7.77852e8 | − | 6.50916e9i | −0.0861444 | − | 0.720867i | ||||
\(700\) | −1.15121e10 | + | 3.13563e9i | −1.26856 | + | 0.345527i | ||||
\(701\) | − | 6.11757e8i | − | 0.0670758i | −0.999437 | − | 0.0335379i | \(-0.989323\pi\) | ||
0.999437 | − | 0.0335379i | \(-0.0106774\pi\) | |||||||
\(702\) | 1.39859e9 | + | 6.39032e8i | 0.152584 | + | 0.0697176i | ||||
\(703\) | −3.99842e9 | + | 3.99842e9i | −0.434055 | + | 0.434055i | ||||
\(704\) | −4.86252e9 | −0.525239 | ||||||||
\(705\) | 1.28844e10 | + | 1.82618e9i | 1.38484 | + | 0.196283i | ||||
\(706\) | −8.08304e7 | −0.00864487 | ||||||||
\(707\) | 7.26904e9 | − | 7.26904e9i | 0.773587 | − | 0.773587i | ||||
\(708\) | 1.33895e8 | − | 1.70239e8i | 0.0141791 | − | 0.0180278i | ||||
\(709\) | 1.35614e10i | 1.42904i | 0.699616 | + | 0.714519i | \(0.253354\pi\) | ||||
−0.699616 | + | 0.714519i | \(0.746646\pi\) | |||||||
\(710\) | 1.51479e9 | + | 2.61123e9i | 0.158836 | + | 0.273805i | ||||
\(711\) | −9.33575e9 | + | 2.26359e9i | −0.974105 | + | 0.236186i | ||||
\(712\) | −3.93076e9 | − | 3.93076e9i | −0.408128 | − | 0.408128i | ||||
\(713\) | −6.40328e9 | − | 6.40328e9i | −0.661590 | − | 0.661590i | ||||
\(714\) | 1.25282e9 | − | 1.49714e8i | 0.128809 | − | 0.0153928i | ||||
\(715\) | 2.74065e9 | + | 4.72441e9i | 0.280403 | + | 0.483366i | ||||
\(716\) | − | 5.73417e9i | − | 0.583815i | ||||||
\(717\) | 1.29918e10 | + | 1.02182e10i | 1.31629 | + | 1.03528i | ||||
\(718\) | 9.02686e7 | − | 9.02686e7i | 0.00910126 | − | 0.00910126i | ||||
\(719\) | −9.45342e9 | −0.948501 | −0.474250 | − | 0.880390i | \(-0.657281\pi\) | ||||
−0.474250 | + | 0.880390i | \(0.657281\pi\) | |||||||
\(720\) | −1.88999e8 | + | 8.64384e9i | −0.0188710 | + | 0.863063i | ||||
\(721\) | 2.79447e9 | 0.277668 | ||||||||
\(722\) | 1.03936e9 | − | 1.03936e9i | 0.102775 | − | 0.102775i | ||||
\(723\) | −5.88247e9 | − | 4.62662e9i | −0.578863 | − | 0.455281i | ||||
\(724\) | 5.13996e9i | 0.503356i | ||||||||
\(725\) | 1.50760e10 | + | 8.62138e9i | 1.46928 | + | 0.840222i | ||||
\(726\) | 1.07128e9 | − | 1.28019e8i | 0.103902 | − | 0.0124164i | ||||
\(727\) | 1.02901e10 | + | 1.02901e10i | 0.993224 | + | 0.993224i | 0.999977 | − | 0.00675331i | \(-0.00214966\pi\) |
−0.00675331 | + | 0.999977i | \(0.502150\pi\) | |||||||
\(728\) | 3.32600e9 | + | 3.32600e9i | 0.319494 | + | 0.319494i | ||||
\(729\) | −6.84711e9 | − | 7.90798e9i | −0.654577 | − | 0.755995i | ||||
\(730\) | −1.38565e8 | + | 5.21432e8i | −0.0131833 | + | 0.0496099i | ||||
\(731\) | − | 3.73143e9i | − | 0.353317i | ||||||
\(732\) | 8.82937e8 | − | 1.12260e9i | 0.0832033 | − | 0.105788i | ||||
\(733\) | 9.43421e9 | − | 9.43421e9i | 0.884793 | − | 0.884793i | −0.109224 | − | 0.994017i | \(-0.534837\pi\) |
0.994017 | + | 0.109224i | \(0.0348366\pi\) | |||||||
\(734\) | 1.10313e9 | 0.102965 | ||||||||
\(735\) | 7.74870e9 | − | 5.82484e9i | 0.719819 | − | 0.541101i | ||||
\(736\) | 6.92579e9 | 0.640320 | ||||||||
\(737\) | −5.65489e9 | + | 5.65489e9i | −0.520341 | + | 0.520341i | ||||
\(738\) | −1.30577e9 | + | 2.14165e9i | −0.119583 | + | 0.196134i | ||||
\(739\) | 1.21933e10i | 1.11139i | 0.831386 | + | 0.555695i | \(0.187548\pi\) | ||||
−0.831386 | + | 0.555695i | \(0.812452\pi\) | |||||||
\(740\) | −9.79986e9 | + | 5.68494e9i | −0.889014 | + | 0.515721i | ||||
\(741\) | −5.83673e8 | − | 4.88424e9i | −0.0526994 | − | 0.440995i | ||||
\(742\) | −2.67930e7 | − | 2.67930e7i | −0.00240773 | − | 0.00240773i | ||||
\(743\) | 1.24919e10 | + | 1.24919e10i | 1.11729 | + | 1.11729i | 0.992137 | + | 0.125154i | \(0.0399425\pi\) |
0.125154 | + | 0.992137i | \(0.460057\pi\) | |||||||
\(744\) | 4.96187e8 | + | 4.15215e9i | 0.0441713 | + | 0.369631i | ||||
\(745\) | −2.02310e10 | − | 5.37617e9i | −1.79255 | − | 0.476350i | ||||
\(746\) | − | 2.87227e9i | − | 0.253302i | ||||||
\(747\) | 4.24780e8 | − | 6.96699e8i | 0.0372857 | − | 0.0611538i | ||||
\(748\) | 2.41952e9 | − | 2.41952e9i | 0.211385 | − | 0.211385i | ||||
\(749\) | −1.78661e10 | −1.55362 | ||||||||
\(750\) | −1.96334e9 | − | 1.52461e9i | −0.169934 | − | 0.131960i | ||||
\(751\) | −8.37358e9 | −0.721392 | −0.360696 | − | 0.932683i | \(-0.617461\pi\) | ||||
−0.360696 | + | 0.932683i | \(0.617461\pi\) | |||||||
\(752\) | 9.95666e9 | − | 9.95666e9i | 0.853790 | − | 0.853790i | ||||
\(753\) | −5.86432e9 | + | 7.45612e9i | −0.500536 | + | 0.636401i | ||||
\(754\) | − | 3.34214e9i | − | 0.283939i | ||||||
\(755\) | −2.76644e9 | − | 7.35150e8i | −0.233941 | − | 0.0621673i | ||||
\(756\) | −5.45584e9 | − | 1.46361e10i | −0.459236 | − | 1.23196i | ||||
\(757\) | −7.21696e9 | − | 7.21696e9i | −0.604670 | − | 0.604670i | 0.336878 | − | 0.941548i | \(-0.390629\pi\) |
−0.941548 | + | 0.336878i | \(0.890629\pi\) | |||||||
\(758\) | 2.17504e9 | + | 2.17504e9i | 0.181395 | + | 0.181395i | ||||
\(759\) | −9.05656e9 | + | 1.08227e9i | −0.751826 | + | 0.0898440i | ||||
\(760\) | −2.50638e9 | + | 1.45396e9i | −0.207109 | + | 0.120145i | ||||
\(761\) | 9.70805e9i | 0.798520i | 0.916838 | + | 0.399260i | \(0.130733\pi\) | ||||
−0.916838 | + | 0.399260i | \(0.869267\pi\) | |||||||
\(762\) | 5.95149e8 | + | 4.68091e8i | 0.0487285 | + | 0.0383255i | ||||
\(763\) | 1.17526e10 | − | 1.17526e10i | 0.957850 | − | 0.957850i | ||||
\(764\) | 3.33905e9 | 0.270892 | ||||||||
\(765\) | −3.74487e9 | − | 3.91229e9i | −0.302428 | − | 0.315949i | ||||
\(766\) | −1.56501e9 | −0.125811 | ||||||||
\(767\) | −1.65691e8 | + | 1.65691e8i | −0.0132591 | + | 0.0132591i | ||||
\(768\) | 5.60994e9 | + | 4.41227e9i | 0.446883 | + | 0.351478i | ||||
\(769\) | − | 8.37544e9i | − | 0.664149i | −0.943253 | − | 0.332075i | \(-0.892251\pi\) | ||
0.943253 | − | 0.332075i | \(-0.107749\pi\) | |||||||
\(770\) | −6.91625e8 | + | 2.60265e9i | −0.0545950 | + | 0.205446i | ||||
\(771\) | 1.01252e10 | − | 1.20998e9i | 0.795636 | − | 0.0950794i | ||||
\(772\) | 3.15252e9 | + | 3.15252e9i | 0.246602 | + | 0.246602i | ||||
\(773\) | −6.18804e8 | − | 6.18804e8i | −0.0481864 | − | 0.0481864i | 0.682603 | − | 0.730789i | \(-0.260848\pi\) |
−0.730789 | + | 0.682603i | \(0.760848\pi\) | |||||||
\(774\) | 2.17901e9 | − | 5.28334e8i | 0.168914 | − | 0.0409557i | ||||
\(775\) | 9.96220e9 | + | 5.69699e9i | 0.768775 | + | 0.439632i | ||||
\(776\) | − | 6.94976e9i | − | 0.533893i | ||||||
\(777\) | 1.20095e10 | − | 1.52694e10i | 0.918441 | − | 1.16774i | ||||
\(778\) | 2.56278e8 | − | 2.56278e8i | 0.0195112 | − | 0.0195112i | ||||
\(779\) | 8.02416e9 | 0.608161 | ||||||||
\(780\) | 1.38307e9 | − | 9.75801e9i | 0.104355 | − | 0.736258i | ||||
\(781\) | −1.40375e10 | −1.05442 | ||||||||
\(782\) | −9.40078e8 | + | 9.40078e8i | −0.0702975 | + | 0.0702975i | ||||
\(783\) | −9.44866e9 | + | 2.06794e10i | −0.703403 | + | 1.53947i | ||||
\(784\) | − | 1.04892e10i | − | 0.777388i | ||||||
\(785\) | 6.82499e9 | + | 1.17651e10i | 0.503568 | + | 0.868064i | ||||
\(786\) | 2.59174e8 | + | 2.16880e9i | 0.0190376 | + | 0.159309i | ||||
\(787\) | −1.30539e10 | − | 1.30539e10i | −0.954616 | − | 0.954616i | 0.0443978 | − | 0.999014i | \(-0.485863\pi\) |
−0.999014 | + | 0.0443978i | \(0.985863\pi\) | |||||||
\(788\) | −2.39496e9 | − | 2.39496e9i | −0.174364 | − | 0.174364i | ||||
\(789\) | −2.53362e9 | − | 2.12016e10i | −0.183642 | − | 1.53674i | ||||
\(790\) | −1.49959e9 | − | 2.58503e9i | −0.108212 | − | 0.186539i | ||||
\(791\) | 7.51446e9i | 0.539858i | ||||||||
\(792\) | 3.59618e9 | + | 2.19261e9i | 0.257219 | + | 0.156828i | ||||
\(793\) | −1.09261e9 | + | 1.09261e9i | −0.0778052 | + | 0.0778052i | ||||
\(794\) | −4.78803e9 | −0.339457 | ||||||||
\(795\) | −2.28237e7 | + | 1.61029e8i | −0.00161102 | + | 0.0113663i | ||||
\(796\) | 1.74228e10 | 1.22440 | ||||||||
\(797\) | −2.30188e9 | + | 2.30188e9i | −0.161056 | + | 0.161056i | −0.783035 | − | 0.621978i | \(-0.786329\pi\) |
0.621978 | + | 0.783035i | \(0.286329\pi\) | |||||||
\(798\) | 1.49937e9 | − | 1.90636e9i | 0.104448 | − | 0.132799i | ||||
\(799\) | 8.82013e9i | 0.611732i | ||||||||
\(800\) | −8.46850e9 | + | 2.30663e9i | −0.584779 | + | 0.159280i | ||||
\(801\) | −4.70610e9 | − | 1.94094e10i | −0.323555 | − | 1.33444i | ||||
\(802\) | −8.80587e8 | − | 8.80587e8i | −0.0602784 | − | 0.0602784i | ||||
\(803\) | −1.77401e9 | − | 1.77401e9i | −0.120907 | − | 0.120907i | ||||
\(804\) | 1.43286e10 | − | 1.71229e9i | 0.972318 | − | 0.116193i | ||||
\(805\) | −5.53636e9 | + | 2.08339e10i | −0.374058 | + | 1.40762i | ||||
\(806\) | − | 2.20848e9i | − | 0.148566i | ||||||
\(807\) | 2.25087e9 | + | 1.77033e9i | 0.150762 | + | 0.118576i | ||||
\(808\) | 3.53689e9 | − | 3.53689e9i | 0.235875 | − | 0.235875i | ||||
\(809\) | −1.09371e10 | −0.726243 | −0.363122 | − | 0.931742i | \(-0.618289\pi\) | ||||
−0.363122 | + | 0.931742i | \(0.618289\pi\) | |||||||
\(810\) | 1.75439e9 | − | 2.74080e9i | 0.115992 | − | 0.181209i | ||||
\(811\) | 8.81067e9 | 0.580011 | 0.290005 | − | 0.957025i | \(-0.406343\pi\) | ||||
0.290005 | + | 0.957025i | \(0.406343\pi\) | |||||||
\(812\) | −2.40063e10 | + | 2.40063e10i | −1.57355 | + | 1.57355i | ||||
\(813\) | −2.33005e10 | − | 1.83261e10i | −1.52072 | − | 1.19606i | ||||
\(814\) | 2.55709e9i | 0.166173i | ||||||||
\(815\) | 7.66806e9 | − | 4.44828e9i | 0.496174 | − | 0.287833i | ||||
\(816\) | −5.81868e9 | + | 6.95339e8i | −0.374894 | + | 0.0448003i | ||||
\(817\) | −5.07182e9 | − | 5.07182e9i | −0.325377 | − | 0.325377i | ||||
\(818\) | −1.60387e9 | − | 1.60387e9i | −0.102455 | − | 0.102455i | ||||
\(819\) | 3.98205e9 | + | 1.64232e10i | 0.253287 | + | 1.04463i | ||||
\(820\) | 1.55377e10 | + | 4.12897e9i | 0.984097 | + | 0.261513i | ||||
\(821\) | 6.77601e9i | 0.427339i | 0.976906 | + | 0.213670i | \(0.0685416\pi\) | ||||
−0.976906 | + | 0.213670i | \(0.931458\pi\) | |||||||
\(822\) | −2.15137e9 | + | 2.73533e9i | −0.135102 | + | 0.171775i | ||||
\(823\) | −1.05133e10 | + | 1.05133e10i | −0.657416 | + | 0.657416i | −0.954768 | − | 0.297352i | \(-0.903897\pi\) |
0.297352 | + | 0.954768i | \(0.403897\pi\) | |||||||
\(824\) | 1.35970e9 | 0.0846640 | ||||||||
\(825\) | 1.07134e10 | − | 4.33962e9i | 0.664263 | − | 0.269069i | ||||
\(826\) | −1.15534e8 | −0.00713315 | ||||||||
\(827\) | 1.82530e10 | − | 1.82530e10i | 1.12218 | − | 1.12218i | 0.130771 | − | 0.991413i | \(-0.458255\pi\) |
0.991413 | − | 0.130771i | \(-0.0417453\pi\) | |||||||
\(828\) | 1.40524e10 | + | 8.56782e9i | 0.860291 | + | 0.524523i | ||||
\(829\) | 8.82320e9i | 0.537880i | 0.963157 | + | 0.268940i | \(0.0866733\pi\) | ||||
−0.963157 | + | 0.268940i | \(0.913327\pi\) | |||||||
\(830\) | 2.45337e8 | + | 6.51956e7i | 0.0148933 | + | 0.00395772i | ||||
\(831\) | 2.71737e9 | + | 2.27393e10i | 0.164265 | + | 1.37459i | ||||
\(832\) | −6.71238e9 | − | 6.71238e9i | −0.404059 | − | 0.404059i | ||||
\(833\) | 4.64596e9 | + | 4.64596e9i | 0.278495 | + | 0.278495i | ||||
\(834\) | 4.42570e8 | + | 3.70348e9i | 0.0264180 | + | 0.221069i | ||||
\(835\) | −1.41766e10 | + | 8.22390e9i | −0.842692 | + | 0.488850i | ||||
\(836\) | − | 6.57731e9i | − | 0.389337i | ||||||
\(837\) | −6.24365e9 | + | 1.36649e10i | −0.368044 | + | 0.805503i | ||||
\(838\) | 3.21977e8 | − | 3.21977e8i | 0.0189004 | − | 0.0189004i | ||||
\(839\) | 1.27684e10 | 0.746399 | 0.373199 | − | 0.927751i | \(-0.378261\pi\) | ||||
0.373199 | + | 0.927751i | \(0.378261\pi\) | |||||||
\(840\) | 7.95707e9 | − | 5.98147e9i | 0.463208 | − | 0.348201i | ||||
\(841\) | 3.21667e10 | 1.86475 | ||||||||
\(842\) | 4.82993e8 | − | 4.82993e8i | 0.0278836 | − | 0.0278836i | ||||
\(843\) | −6.01005e8 | + | 7.64142e8i | −0.0345527 | + | 0.0439317i | ||||
\(844\) | 2.87433e8i | 0.0164565i | ||||||||
\(845\) | 1.76595e9 | − | 6.64545e9i | 0.100689 | − | 0.378901i | ||||
\(846\) | −5.15062e9 | + | 1.24884e9i | −0.292458 | + | 0.0709108i | ||||
\(847\) | 8.38431e9 | + | 8.38431e9i | 0.474106 | + | 0.474106i | ||||
\(848\) | 1.24439e8 | + | 1.24439e8i | 0.00700760 | + | 0.00700760i | ||||
\(849\) | −2.68694e9 | + | 3.21092e8i | −0.150689 | + | 0.0180075i | ||||
\(850\) | 8.36386e8 | − | 1.46257e9i | 0.0467133 | − | 0.0816865i | ||||
\(851\) | 2.04691e10i | 1.13853i | ||||||||
\(852\) | 1.99098e10 | + | 1.56592e10i | 1.10288 | + | 0.867425i | ||||
\(853\) | 1.08864e10 | − | 1.08864e10i | 0.600570 | − | 0.600570i | −0.339894 | − | 0.940464i | \(-0.610391\pi\) |
0.940464 | + | 0.339894i | \(0.110391\pi\) | |||||||
\(854\) | −7.61863e8 | −0.0418576 | ||||||||
\(855\) | −1.04078e10 | − | 2.27567e8i | −0.569476 | − | 0.0124517i | ||||
\(856\) | −8.69309e9 | −0.473714 | ||||||||
\(857\) | 1.08166e10 | − | 1.08166e10i | 0.587028 | − | 0.587028i | −0.349797 | − | 0.936826i | \(-0.613749\pi\) |
0.936826 | + | 0.349797i | \(0.113749\pi\) | |||||||
\(858\) | −1.74843e9 | − | 1.37516e9i | −0.0945025 | − | 0.0743272i | ||||
\(859\) | − | 2.68969e9i | − | 0.144786i | −0.997376 | − | 0.0723930i | \(-0.976936\pi\) | ||
0.997376 | − | 0.0723930i | \(-0.0230636\pi\) | |||||||
\(860\) | −7.21110e9 | − | 1.24307e10i | −0.386596 | − | 0.666424i | ||||
\(861\) | −2.73720e10 | + | 3.27099e9i | −1.46149 | + | 0.174650i | ||||
\(862\) | 5.05384e9 | + | 5.05384e9i | 0.268749 | + | 0.268749i | ||||
\(863\) | −2.24927e10 | − | 2.24927e10i | −1.19125 | − | 1.19125i | −0.976716 | − | 0.214537i | \(-0.931176\pi\) |
−0.214537 | − | 0.976716i | \(-0.568824\pi\) | |||||||
\(864\) | −4.01341e9 | − | 1.07666e10i | −0.211698 | − | 0.567909i | ||||
\(865\) | −6.11224e9 | − | 1.05364e10i | −0.321103 | − | 0.553526i | ||||
\(866\) | 7.27487e9i | 0.380639i | ||||||||
\(867\) | −9.59393e9 | + | 1.21981e10i | −0.499954 | + | 0.635661i | ||||
\(868\) | −1.58633e10 | + | 1.58633e10i | −0.823333 | + | 0.823333i | ||||
\(869\) | 1.38967e10 | 0.718359 | ||||||||
\(870\) | −7.00309e9 | − | 9.92595e8i | −0.360556 | − | 0.0511040i | ||||
\(871\) | −1.56124e10 | −0.800581 | ||||||||
\(872\) | 5.71844e9 | − | 5.71844e9i | 0.292059 | − | 0.292059i | ||||
\(873\) | 1.29981e10 | − | 2.13187e10i | 0.661194 | − | 1.08445i | ||||
\(874\) | 2.55554e9i | 0.129477i | ||||||||
\(875\) | −1.69115e8 | − | 2.73184e10i | −0.00853404 | − | 1.37857i | ||||
\(876\) | 5.37168e8 | + | 4.49508e9i | 0.0269989 | + | 0.225930i | ||||
\(877\) | −2.81331e10 | − | 2.81331e10i | −1.40838 | − | 1.40838i | −0.768361 | − | 0.640017i | \(-0.778927\pi\) |
−0.640017 | − | 0.768361i | \(-0.721073\pi\) | |||||||
\(878\) | 4.35602e9 | + | 4.35602e9i | 0.217200 | + | 0.217200i | ||||
\(879\) | −2.43172e6 | − | 2.03489e7i | −0.000120768 | − | 0.00101060i | ||||
\(880\) | 3.21222e9 | − | 1.20879e10i | 0.158897 | − | 0.597944i | ||||
\(881\) | 2.23778e9i | 0.110256i | 0.998479 | + | 0.0551280i | \(0.0175567\pi\) | ||||
−0.998479 | + | 0.0551280i | \(0.982443\pi\) | |||||||
\(882\) | −2.05524e9 | + | 3.37089e9i | −0.100861 | + | 0.165426i | ||||
\(883\) | 7.10936e9 | − | 7.10936e9i | 0.347510 | − | 0.347510i | −0.511671 | − | 0.859181i | \(-0.670973\pi\) |
0.859181 | + | 0.511671i | \(0.170973\pi\) | |||||||
\(884\) | 6.67996e9 | 0.325230 | ||||||||
\(885\) | 2.97979e8 | + | 3.96397e8i | 0.0144505 | + | 0.0192233i | ||||
\(886\) | 5.07500e9 | 0.245142 | ||||||||
\(887\) | −2.88502e10 | + | 2.88502e10i | −1.38809 | + | 1.38809i | −0.558747 | + | 0.829338i | \(0.688718\pi\) |
−0.829338 | + | 0.558747i | \(0.811282\pi\) | |||||||
\(888\) | 5.84345e9 | − | 7.42959e9i | 0.280042 | − | 0.356057i | ||||
\(889\) | 8.32140e9i | 0.397228i | ||||||||
\(890\) | 5.37439e9 | − | 3.11771e9i | 0.255543 | − | 0.148242i | ||||
\(891\) | 6.93062e9 | + | 1.34518e10i | 0.328247 | + | 0.637101i | ||||
\(892\) | −9.14847e9 | − | 9.14847e9i | −0.431590 | − | 0.431590i | ||||
\(893\) | 1.19885e10 | + | 1.19885e10i | 0.563357 | + | 0.563357i | ||||
\(894\) | 8.46524e9 | − | 1.01161e9i | 0.396240 | − | 0.0473511i | ||||
\(895\) | 1.26889e10 | + | 3.37192e9i | 0.591619 | + | 0.157216i | ||||
\(896\) | − | 2.26711e10i | − | 1.05292i | ||||||
\(897\) | −1.39960e10 | − | 1.10080e10i | −0.647484 | − | 0.509253i | ||||
\(898\) | 4.60070e9 | − | 4.60070e9i | 0.212010 | − | 0.212010i | ||||
\(899\) | 3.26543e10 | 1.49893 | ||||||||
\(900\) | −2.00361e10 | − | 5.79614e9i | −0.916145 | − | 0.265027i | ||||
\(901\) | −1.10234e8 | −0.00502088 | ||||||||
\(902\) | 2.56582e9 | − | 2.56582e9i | 0.116414 | − | 0.116414i | ||||
\(903\) | 1.93685e10 | + | 1.52335e10i | 0.875364 | + | 0.688483i | ||||
\(904\) | 3.65630e9i | 0.164609i | ||||||||
\(905\) | −1.13740e10 | − | 3.02250e9i | −0.510084 | − | 0.135549i | ||||
\(906\) | 1.15756e9 | − | 1.38329e8i | 0.0517122 | − | 0.00617967i | ||||
\(907\) | 2.32931e10 | + | 2.32931e10i | 1.03658 | + | 1.03658i | 0.999305 | + | 0.0372739i | \(0.0118674\pi\) |
0.0372739 | + | 0.999305i | \(0.488133\pi\) | |||||||
\(908\) | −7.10015e9 | − | 7.10015e9i | −0.314751 | − | 0.314751i | ||||
\(909\) | 1.74645e10 | − | 4.23454e9i | 0.771230 | − | 0.186996i | ||||
\(910\) | −4.54752e9 | + | 2.63804e9i | −0.200046 | + | 0.116048i | ||||
\(911\) | − | 3.14386e10i | − | 1.37768i | −0.724913 | − | 0.688840i | \(-0.758120\pi\) | ||
0.724913 | − | 0.688840i | \(-0.241880\pi\) | |||||||
\(912\) | −6.96374e9 | + | 8.85397e9i | −0.303991 | + | 0.386506i | ||||
\(913\) | −8.34685e8 | + | 8.34685e8i | −0.0362974 | + | 0.0362974i | ||||
\(914\) | −4.45448e9 | −0.192968 | ||||||||
\(915\) | 1.96495e9 | + | 2.61394e9i | 0.0847962 | + | 0.112803i | ||||
\(916\) | −2.10081e10 | −0.903136 | ||||||||
\(917\) | −1.69740e10 | + | 1.69740e10i | −0.726927 | + | 0.726927i | ||||
\(918\) | 2.00617e9 | + | 9.16643e8i | 0.0855891 | + | 0.0391067i | ||||
\(919\) | − | 2.30372e10i | − | 0.979095i | −0.871977 | − | 0.489548i | \(-0.837162\pi\) | ||
0.871977 | − | 0.489548i | \(-0.162838\pi\) | |||||||
\(920\) | −2.69382e9 | + | 1.01371e10i | −0.114054 | + | 0.429197i | ||||
\(921\) | −4.65738e8 | − | 3.89735e9i | −0.0196441 | − | 0.164385i | ||||
\(922\) | −3.77932e9 | − | 3.77932e9i | −0.158802 | − | 0.158802i | ||||
\(923\) | −1.93778e10 | − | 1.93778e10i | −0.811147 | − | 0.811147i | ||||
\(924\) | 2.68119e9 | + | 2.24365e10i | 0.111809 | + | 0.935629i | ||||
\(925\) | −6.81722e9 | − | 2.50286e10i | −0.283212 | − | 1.03978i | ||||
\(926\) | 3.06250e9i | 0.126747i | ||||||||
\(927\) | 4.17094e9 | + | 2.54304e9i | 0.171971 | + | 0.104851i | ||||
\(928\) | −1.76595e10 | + | 1.76595e10i | −0.725371 | + | 0.725371i | ||||
\(929\) | 7.81807e9 | 0.319923 | 0.159961 | − | 0.987123i | \(-0.448863\pi\) | ||||
0.159961 | + | 0.987123i | \(0.448863\pi\) | |||||||
\(930\) | −4.62763e9 | − | 6.55905e8i | −0.188655 | − | 0.0267393i | ||||
\(931\) | 1.26297e10 | 0.512945 | ||||||||
\(932\) | 1.21001e10 | − | 1.21001e10i | 0.489593 | − | 0.489593i | ||||
\(933\) | −2.11150e10 | + | 2.68464e10i | −0.851147 | + | 1.08218i | ||||
\(934\) | 6.77576e9i | 0.272110i | ||||||||
\(935\) | 3.93126e9 | + | 6.77681e9i | 0.157286 | + | 0.271134i | ||||
\(936\) | 1.93754e9 | + | 7.99102e9i | 0.0772300 | + | 0.318520i | ||||
\(937\) | 2.14206e10 | + | 2.14206e10i | 0.850634 | + | 0.850634i | 0.990211 | − | 0.139577i | \(-0.0445743\pi\) |
−0.139577 | + | 0.990211i | \(0.544574\pi\) | |||||||
\(938\) | −5.44316e9 | − | 5.44316e9i | −0.215348 | − | 0.215348i | ||||
\(939\) | −3.32301e10 | + | 3.97104e9i | −1.30979 | + | 0.156522i | ||||
\(940\) | 1.70452e10 | + | 2.93829e10i | 0.669351 | + | 1.15385i | ||||
\(941\) | 1.29439e10i | 0.506409i | 0.967413 | + | 0.253204i | \(0.0814845\pi\) | ||||
−0.967413 | + | 0.253204i | \(0.918515\pi\) | |||||||
\(942\) | −4.35408e9 | − | 3.42453e9i | −0.169714 | − | 0.133482i | ||||
\(943\) | 2.05391e10 | − | 2.05391e10i | 0.797608 | − | 0.797608i | ||||
\(944\) | 5.36594e8 | 0.0207608 | ||||||||
\(945\) | 3.55957e10 | − | 3.46637e9i | 1.37210 | − | 0.133617i | ||||
\(946\) | −3.24355e9 | −0.124567 | ||||||||
\(947\) | 1.02474e10 | − | 1.02474e10i | 0.392094 | − | 0.392094i | −0.483339 | − | 0.875433i | \(-0.660576\pi\) |
0.875433 | + | 0.483339i | \(0.160576\pi\) | |||||||
\(948\) | −1.97100e10 | − | 1.55021e10i | −0.751375 | − | 0.590964i | ||||
\(949\) | − | 4.89781e9i | − | 0.186025i | ||||||
\(950\) | −8.51120e8 | − | 3.12478e9i | −0.0322076 | − | 0.118246i | ||||
\(951\) | 3.16719e10 | − | 3.78483e9i | 1.19410 | − | 0.142697i | ||||
\(952\) | 4.77090e9 | + | 4.77090e9i | 0.179213 | + | 0.179213i | ||||
\(953\) | 3.48353e10 | + | 3.48353e10i | 1.30375 | + | 1.30375i | 0.925844 | + | 0.377906i | \(0.123356\pi\) |
0.377906 | + | 0.925844i | \(0.376644\pi\) | |||||||
\(954\) | −1.56081e7 | − | 6.43726e7i | −0.000582010 | − | 0.00240039i | ||||
\(955\) | −1.96349e9 | + | 7.38882e9i | −0.0729488 | + | 0.274513i | ||||
\(956\) | 4.31459e10i | 1.59712i | ||||||||
\(957\) | 2.03330e10 | − | 2.58521e10i | 0.749910 | − | 0.953465i | ||||
\(958\) | 3.93306e9 | − | 3.93306e9i | 0.144528 | − | 0.144528i | ||||
\(959\) | −3.82455e10 | −1.40028 | ||||||||
\(960\) | −1.60586e10 | + | 1.20715e10i | −0.585812 | + | 0.440365i | ||||
\(961\) | −5.93469e9 | −0.215708 | ||||||||
\(962\) | −3.52988e9 | + | 3.52988e9i | −0.127834 | + | 0.127834i | ||||
\(963\) | −2.66664e10 | − | 1.62586e10i | −0.962215 | − | 0.586666i | ||||
\(964\) | − | 1.95358e10i | − | 0.702362i | ||||||
\(965\) | −8.82985e9 | + | 5.12224e9i | −0.316306 | + | 0.183491i | ||||
\(966\) | −1.04175e9 | − | 8.71747e9i | −0.0371828 | − | 0.311150i | ||||
\(967\) | 5.74773e9 | + | 5.74773e9i | 0.204411 | + | 0.204411i | 0.801887 | − | 0.597476i | \(-0.203830\pi\) |
−0.597476 | + | 0.801887i | \(0.703830\pi\) | |||||||
\(968\) | 4.07954e9 | + | 4.07954e9i | 0.144560 | + | 0.144560i | ||||
\(969\) | −8.37234e8 | − | 7.00608e9i | −0.0295606 | − | 0.247367i | ||||
\(970\) | 7.50720e9 | + | 1.99495e9i | 0.264105 | + | 0.0701830i | ||||
\(971\) | − | 1.77158e9i | − | 0.0621003i | −0.999518 | − | 0.0310501i | \(-0.990115\pi\) | ||
0.999518 | − | 0.0310501i | \(-0.00988516\pi\) | |||||||
\(972\) | 5.17596e9 | − | 2.68103e10i | 0.180784 | − | 0.936418i | ||||
\(973\) | −2.89851e10 | + | 2.89851e10i | −1.00874 | + | 1.00874i | ||||
\(974\) | −3.60789e8 | −0.0125111 | ||||||||
\(975\) | 2.07797e10 | + | 8.79863e9i | 0.717999 | + | 0.304018i | ||||
\(976\) | 3.53843e9 | 0.121825 | ||||||||
\(977\) | 1.53673e10 | − | 1.53673e10i | 0.527190 | − | 0.527190i | −0.392543 | − | 0.919734i | \(-0.628405\pi\) |
0.919734 | + | 0.392543i | \(0.128405\pi\) | |||||||
\(978\) | −2.23198e9 | + | 2.83783e9i | −0.0762966 | + | 0.0970065i | ||||
\(979\) | 2.88918e10i | 0.984089i | ||||||||
\(980\) | 2.44558e10 | + | 6.49885e9i | 0.830023 | + | 0.220569i | ||||
\(981\) | 2.82367e10 | − | 6.84640e9i | 0.954931 | − | 0.231537i | ||||
\(982\) | 1.06935e9 | + | 1.06935e9i | 0.0360356 | + | 0.0360356i | ||||
\(983\) | 9.18416e9 | + | 9.18416e9i | 0.308391 | + | 0.308391i | 0.844285 | − | 0.535894i | \(-0.180025\pi\) |
−0.535894 | + | 0.844285i | \(0.680025\pi\) | |||||||
\(984\) | −1.33184e10 | + | 1.59156e9i | −0.445624 | + | 0.0532526i | ||||
\(985\) | 6.70802e9 | − | 3.89136e9i | 0.223649 | − | 0.129740i | ||||
\(986\) | − | 4.79405e9i | − | 0.159270i | ||||||
\(987\) | −4.57821e10 | − | 3.60081e10i | −1.51561 | − | 1.19204i | ||||
\(988\) | 9.07952e9 | − | 9.07952e9i | 0.299512 | − | 0.299512i | ||||
\(989\) | −2.59642e10 | −0.853469 | ||||||||
\(990\) | −3.40077e9 | + | 3.25524e9i | −0.111392 | + | 0.106625i | ||||
\(991\) | −4.39131e10 | −1.43330 | −0.716648 | − | 0.697435i | \(-0.754325\pi\) | ||||
−0.716648 | + | 0.697435i | \(0.754325\pi\) | |||||||
\(992\) | −1.16694e10 | + | 1.16694e10i | −0.379539 | + | 0.379539i | ||||
\(993\) | 2.80676e10 | + | 2.20755e10i | 0.909668 | + | 0.715463i | ||||
\(994\) | − | 1.35119e10i | − | 0.436380i | ||||||
\(995\) | −1.02453e10 | + | 3.85541e10i | −0.329720 | + | 1.24077i | ||||
\(996\) | 2.11497e9 | − | 2.52741e8i | 0.0678259 | − | 0.00810528i | ||||
\(997\) | 1.72444e10 | + | 1.72444e10i | 0.551082 | + | 0.551082i | 0.926753 | − | 0.375671i | \(-0.122588\pi\) |
−0.375671 | + | 0.926753i | \(0.622588\pi\) | |||||||
\(998\) | −1.79224e9 | − | 1.79224e9i | −0.0570741 | − | 0.0570741i | ||||
\(999\) | 3.18205e10 | − | 1.18616e10i | 1.00978 | − | 0.376413i |
(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 | 15.8.e.a.2.7 | yes | 24 | |
3.2 | odd | 2 | inner | 15.8.e.a.2.6 | ✓ | 24 | |
5.2 | odd | 4 | 75.8.e.d.68.7 | 24 | |||
5.3 | odd | 4 | inner | 15.8.e.a.8.6 | yes | 24 | |
5.4 | even | 2 | 75.8.e.d.32.6 | 24 | |||
15.2 | even | 4 | 75.8.e.d.68.6 | 24 | |||
15.8 | even | 4 | inner | 15.8.e.a.8.7 | yes | 24 | |
15.14 | odd | 2 | 75.8.e.d.32.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.8.e.a.2.6 | ✓ | 24 | 3.2 | odd | 2 | inner | |
15.8.e.a.2.7 | yes | 24 | 1.1 | even | 1 | trivial | |
15.8.e.a.8.6 | yes | 24 | 5.3 | odd | 4 | inner | |
15.8.e.a.8.7 | yes | 24 | 15.8 | even | 4 | inner | |
75.8.e.d.32.6 | 24 | 5.4 | even | 2 | |||
75.8.e.d.32.7 | 24 | 15.14 | odd | 2 | |||
75.8.e.d.68.6 | 24 | 15.2 | even | 4 | |||
75.8.e.d.68.7 | 24 | 5.2 | odd | 4 |