Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,35,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 35, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 35);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 35 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.2902616171\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 72626617369828 x^{14} - 508386321588656 x^{13} + \cdots + 10\!\cdots\!04 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{240}\cdot 3^{26}\cdot 5^{6}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.14 | ||
Root | \(0.500000 - 1.72842e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.35.b.a.3.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 114483. | + | 63824.3i | 0.873435 | + | 0.486940i | ||||
\(3\) | 8.29643e7i | 0.642436i | 0.947005 | + | 0.321218i | \(0.104092\pi\) | ||||
−0.947005 | + | 0.321218i | \(0.895908\pi\) | |||||||
\(4\) | 9.03280e9 | + | 1.46136e10i | 0.525778 | + | 0.850622i | ||||
\(5\) | 6.47366e11 | 0.848516 | 0.424258 | − | 0.905541i | \(-0.360535\pi\) | ||||
0.424258 | + | 0.905541i | \(0.360535\pi\) | |||||||
\(6\) | −5.29513e12 | + | 9.49799e12i | −0.312828 | + | 0.561126i | ||||
\(7\) | 1.29684e14i | 0.557470i | 0.960368 | + | 0.278735i | \(0.0899151\pi\) | ||||
−0.960368 | + | 0.278735i | \(0.910085\pi\) | |||||||
\(8\) | 1.01400e14 | + | 2.24952e15i | 0.0450307 | + | 0.998986i | ||||
\(9\) | 9.79411e15 | 0.587276 | ||||||||
\(10\) | 7.41124e16 | + | 4.13177e16i | 0.741124 | + | 0.413177i | ||||
\(11\) | − | 3.33547e16i | − | 0.0659906i | −0.999456 | − | 0.0329953i | \(-0.989495\pi\) | ||
0.999456 | − | 0.0329953i | \(-0.0105046\pi\) | |||||||
\(12\) | −1.21240e18 | + | 7.49399e17i | −0.546470 | + | 0.337779i | ||||
\(13\) | 8.70180e18 | 1.00594 | 0.502970 | − | 0.864304i | \(-0.332241\pi\) | ||||
0.502970 | + | 0.864304i | \(0.332241\pi\) | |||||||
\(14\) | −8.27701e18 | + | 1.48467e19i | −0.271455 | + | 0.486914i | ||||
\(15\) | 5.37083e19i | 0.545117i | ||||||||
\(16\) | −1.31965e20 | + | 2.64003e20i | −0.447115 | + | 0.894476i | ||||
\(17\) | −4.22830e20 | −0.511134 | −0.255567 | − | 0.966791i | \(-0.582262\pi\) | ||||
−0.255567 | + | 0.966791i | \(0.582262\pi\) | |||||||
\(18\) | 1.12126e21 | + | 6.25102e20i | 0.512948 | + | 0.285969i | ||||
\(19\) | 4.20554e21i | 0.767379i | 0.923462 | + | 0.383690i | \(0.125347\pi\) | ||||
−0.923462 | + | 0.383690i | \(0.874653\pi\) | |||||||
\(20\) | 5.84753e21 | + | 9.46034e21i | 0.446131 | + | 0.721766i | ||||
\(21\) | −1.07592e22 | −0.358138 | ||||||||
\(22\) | 2.12884e21 | − | 3.81855e21i | 0.0321335 | − | 0.0576385i | ||||
\(23\) | − | 2.57146e23i | − | 1.82308i | −0.411209 | − | 0.911541i | \(-0.634893\pi\) | ||
0.411209 | − | 0.911541i | \(-0.365107\pi\) | |||||||
\(24\) | −1.86629e23 | + | 8.41259e21i | −0.641784 | + | 0.0289293i | ||||
\(25\) | −1.62993e23 | −0.280020 | ||||||||
\(26\) | 9.96207e23 | + | 5.55386e23i | 0.878623 | + | 0.489833i | ||||
\(27\) | 2.19617e24i | 1.01972i | ||||||||
\(28\) | −1.89515e24 | + | 1.17141e24i | −0.474196 | + | 0.293105i | ||||
\(29\) | −4.39836e24 | −0.606072 | −0.303036 | − | 0.952979i | \(-0.598000\pi\) | ||||
−0.303036 | + | 0.952979i | \(0.598000\pi\) | |||||||
\(30\) | −3.42789e24 | + | 6.14868e24i | −0.265440 | + | 0.476124i | ||||
\(31\) | 3.47904e25i | 1.54281i | 0.636347 | + | 0.771403i | \(0.280445\pi\) | ||||
−0.636347 | + | 0.771403i | \(0.719555\pi\) | |||||||
\(32\) | −3.19575e25 | + | 2.18012e25i | −0.826083 | + | 0.563549i | ||||
\(33\) | 2.76725e24 | 0.0423947 | ||||||||
\(34\) | −4.84068e25 | − | 2.69868e25i | −0.446442 | − | 0.248892i | ||||
\(35\) | 8.39534e25i | 0.473022i | ||||||||
\(36\) | 8.84682e25 | + | 1.43127e26i | 0.308777 | + | 0.499550i | ||||
\(37\) | −5.87647e26 | −1.28732 | −0.643661 | − | 0.765311i | \(-0.722585\pi\) | ||||
−0.643661 | + | 0.765311i | \(0.722585\pi\) | |||||||
\(38\) | −2.68415e26 | + | 4.81462e26i | −0.373668 | + | 0.670256i | ||||
\(39\) | 7.21938e26i | 0.646252i | ||||||||
\(40\) | 6.56431e25 | + | 1.45626e27i | 0.0382093 | + | 0.847655i | ||||
\(41\) | 1.01906e27 | 0.389831 | 0.194915 | − | 0.980820i | \(-0.437557\pi\) | ||||
0.194915 | + | 0.980820i | \(0.437557\pi\) | |||||||
\(42\) | −1.23174e27 | − | 6.86696e26i | −0.312811 | − | 0.174392i | ||||
\(43\) | − | 2.83471e27i | − | 0.482552i | −0.970457 | − | 0.241276i | \(-0.922434\pi\) | ||
0.970457 | − | 0.241276i | \(-0.0775659\pi\) | |||||||
\(44\) | 4.87432e26 | − | 3.01287e26i | 0.0561330 | − | 0.0346964i | ||||
\(45\) | 6.34038e27 | 0.498313 | ||||||||
\(46\) | 1.64121e28 | − | 2.94388e28i | 0.887733 | − | 1.59234i | ||||
\(47\) | − | 2.29098e28i | − | 0.859722i | −0.902895 | − | 0.429861i | \(-0.858563\pi\) | ||
0.902895 | − | 0.429861i | \(-0.141437\pi\) | |||||||
\(48\) | −2.19028e28 | − | 1.09484e28i | −0.574644 | − | 0.287243i | ||||
\(49\) | 3.72989e28 | 0.689228 | ||||||||
\(50\) | −1.86599e28 | − | 1.04029e28i | −0.244580 | − | 0.136353i | ||||
\(51\) | − | 3.50798e28i | − | 0.328370i | ||||||
\(52\) | 7.86016e28 | + | 1.27164e29i | 0.528901 | + | 0.855674i | ||||
\(53\) | 1.06357e29 | 0.517698 | 0.258849 | − | 0.965918i | \(-0.416657\pi\) | ||||
0.258849 | + | 0.965918i | \(0.416657\pi\) | |||||||
\(54\) | −1.40169e29 | + | 2.51424e29i | −0.496544 | + | 0.890662i | ||||
\(55\) | − | 2.15927e28i | − | 0.0559941i | ||||||
\(56\) | −2.91727e29 | + | 1.31500e28i | −0.556904 | + | 0.0251033i | ||||
\(57\) | −3.48909e29 | −0.492992 | ||||||||
\(58\) | −5.03537e29 | − | 2.80722e29i | −0.529365 | − | 0.295121i | ||||
\(59\) | − | 4.19589e28i | − | 0.0329868i | −0.999864 | − | 0.0164934i | \(-0.994750\pi\) | ||
0.999864 | − | 0.0164934i | \(-0.00525025\pi\) | |||||||
\(60\) | −7.84870e29 | + | 4.85136e29i | −0.463689 | + | 0.286611i | ||||
\(61\) | 3.59417e30 | 1.60322 | 0.801608 | − | 0.597851i | \(-0.203978\pi\) | ||||
0.801608 | + | 0.597851i | \(0.203978\pi\) | |||||||
\(62\) | −2.22047e30 | + | 3.98291e30i | −0.751254 | + | 1.34754i | ||||
\(63\) | 1.27014e30i | 0.327389i | ||||||||
\(64\) | −5.05004e30 | + | 4.56202e29i | −0.995944 | + | 0.0899701i | ||||
\(65\) | 5.63325e30 | 0.853556 | ||||||||
\(66\) | 3.16803e29 | + | 1.76618e29i | 0.0370290 | + | 0.0206437i | ||||
\(67\) | − | 1.73917e31i | − | 1.57424i | −0.616803 | − | 0.787118i | \(-0.711572\pi\) | ||
0.616803 | − | 0.787118i | \(-0.288428\pi\) | |||||||
\(68\) | −3.81934e30 | − | 6.17906e30i | −0.268743 | − | 0.434781i | ||||
\(69\) | 2.13339e31 | 1.17121 | ||||||||
\(70\) | −5.35826e30 | + | 9.61122e30i | −0.230334 | + | 0.413154i | ||||
\(71\) | − | 4.95397e31i | − | 1.67325i | −0.547773 | − | 0.836627i | \(-0.684524\pi\) | ||
0.547773 | − | 0.836627i | \(-0.315476\pi\) | |||||||
\(72\) | 9.93125e29 | + | 2.20320e31i | 0.0264455 | + | 0.586680i | ||||
\(73\) | 8.07839e31 | 1.70152 | 0.850759 | − | 0.525557i | \(-0.176143\pi\) | ||||
0.850759 | + | 0.525557i | \(0.176143\pi\) | |||||||
\(74\) | −6.72755e31 | − | 3.75061e31i | −1.12439 | − | 0.626849i | ||||
\(75\) | − | 1.35226e31i | − | 0.179895i | ||||||
\(76\) | −6.14579e31 | + | 3.79878e31i | −0.652750 | + | 0.403471i | ||||
\(77\) | 4.32559e30 | 0.0367878 | ||||||||
\(78\) | −4.60772e31 | + | 8.26496e31i | −0.314686 | + | 0.564459i | ||||
\(79\) | 2.83994e32i | 1.56189i | 0.624602 | + | 0.780943i | \(0.285261\pi\) | ||||
−0.624602 | + | 0.780943i | \(0.714739\pi\) | |||||||
\(80\) | −8.54298e31 | + | 1.70907e32i | −0.379384 | + | 0.758978i | ||||
\(81\) | −1.88656e31 | −0.0678304 | ||||||||
\(82\) | 1.16665e32 | + | 6.50411e31i | 0.340492 | + | 0.189824i | ||||
\(83\) | − | 2.69083e32i | − | 0.639085i | −0.947572 | − | 0.319543i | \(-0.896471\pi\) | ||
0.947572 | − | 0.319543i | \(-0.103529\pi\) | |||||||
\(84\) | −9.71854e31 | − | 1.57230e32i | −0.188301 | − | 0.304640i | ||||
\(85\) | −2.73726e32 | −0.433705 | ||||||||
\(86\) | 1.80923e32 | − | 3.24525e32i | 0.234974 | − | 0.421478i | ||||
\(87\) | − | 3.64907e32i | − | 0.389363i | ||||||
\(88\) | 7.50320e31 | − | 3.38218e30i | 0.0659237 | − | 0.00297160i | ||||
\(89\) | −3.78316e32 | −0.274299 | −0.137150 | − | 0.990550i | \(-0.543794\pi\) | ||||
−0.137150 | + | 0.990550i | \(0.543794\pi\) | |||||||
\(90\) | 7.25865e32 | + | 4.04670e32i | 0.435244 | + | 0.242649i | ||||
\(91\) | 1.12849e33i | 0.560781i | ||||||||
\(92\) | 3.75782e33 | − | 2.32275e33i | 1.55075 | − | 0.958536i | ||||
\(93\) | −2.88636e33 | −0.991153 | ||||||||
\(94\) | 1.46220e33 | − | 2.62278e33i | 0.418633 | − | 0.750911i | ||||
\(95\) | 2.72252e33i | 0.651134i | ||||||||
\(96\) | −1.80872e33 | − | 2.65133e33i | −0.362044 | − | 0.530705i | ||||
\(97\) | 1.06366e33 | 0.178519 | 0.0892594 | − | 0.996008i | \(-0.471550\pi\) | ||||
0.0892594 | + | 0.996008i | \(0.471550\pi\) | |||||||
\(98\) | 4.27009e33 | + | 2.38057e33i | 0.601996 | + | 0.335613i | ||||
\(99\) | − | 3.26680e32i | − | 0.0387547i | ||||||
\(100\) | −1.47229e33 | − | 2.38191e33i | −0.147229 | − | 0.238191i | ||||
\(101\) | −1.65994e34 | −1.40162 | −0.700808 | − | 0.713350i | \(-0.747177\pi\) | ||||
−0.700808 | + | 0.713350i | \(0.747177\pi\) | |||||||
\(102\) | 2.23894e33 | − | 4.01604e33i | 0.159897 | − | 0.286810i | ||||
\(103\) | 9.46712e32i | 0.0572776i | 0.999590 | + | 0.0286388i | \(0.00911726\pi\) | ||||
−0.999590 | + | 0.0286388i | \(0.990883\pi\) | |||||||
\(104\) | 8.82364e32 | + | 1.95748e34i | 0.0452982 | + | 1.00492i | ||||
\(105\) | −6.96513e33 | −0.303886 | ||||||||
\(106\) | 1.21761e34 | + | 6.78816e33i | 0.452176 | + | 0.252088i | ||||
\(107\) | 4.09666e34i | 1.29690i | 0.761259 | + | 0.648448i | \(0.224582\pi\) | ||||
−0.761259 | + | 0.648448i | \(0.775418\pi\) | |||||||
\(108\) | −3.20939e34 | + | 1.98376e34i | −0.867399 | + | 0.536148i | ||||
\(109\) | 1.87027e34 | 0.432169 | 0.216084 | − | 0.976375i | \(-0.430671\pi\) | ||||
0.216084 | + | 0.976375i | \(0.430671\pi\) | |||||||
\(110\) | 1.37814e33 | − | 2.47200e33i | 0.0272658 | − | 0.0489072i | ||||
\(111\) | − | 4.87537e34i | − | 0.827021i | ||||||
\(112\) | −3.42371e34 | − | 1.71138e34i | −0.498643 | − | 0.249253i | ||||
\(113\) | 1.19952e35 | 1.50202 | 0.751010 | − | 0.660291i | \(-0.229567\pi\) | ||||
0.751010 | + | 0.660291i | \(0.229567\pi\) | |||||||
\(114\) | −3.99441e34 | − | 2.22689e34i | −0.430597 | − | 0.240058i | ||||
\(115\) | − | 1.66468e35i | − | 1.54691i | ||||||
\(116\) | −3.97295e34 | − | 6.42757e34i | −0.318660 | − | 0.515539i | ||||
\(117\) | 8.52264e34 | 0.590765 | ||||||||
\(118\) | 2.67800e33 | − | 4.80358e33i | 0.0160626 | − | 0.0288118i | ||||
\(119\) | − | 5.48345e34i | − | 0.284941i | ||||||
\(120\) | −1.20818e35 | + | 5.44603e33i | −0.544564 | + | 0.0245470i | ||||
\(121\) | 2.54364e35 | 0.995645 | ||||||||
\(122\) | 4.11471e35 | + | 2.29395e35i | 1.40030 | + | 0.780670i | ||||
\(123\) | 8.45460e34i | 0.250441i | ||||||||
\(124\) | −5.08413e35 | + | 3.14255e35i | −1.31234 | + | 0.811173i | ||||
\(125\) | −4.82333e35 | −1.08612 | ||||||||
\(126\) | −8.10660e34 | + | 1.45410e35i | −0.159419 | + | 0.285953i | ||||
\(127\) | − | 3.85585e34i | − | 0.0662914i | −0.999451 | − | 0.0331457i | \(-0.989447\pi\) | ||
0.999451 | − | 0.0331457i | \(-0.0105525\pi\) | |||||||
\(128\) | −6.07260e35 | − | 2.70088e35i | −0.913703 | − | 0.406383i | ||||
\(129\) | 2.35179e35 | 0.310009 | ||||||||
\(130\) | 6.44911e35 | + | 3.59538e35i | 0.745526 | + | 0.415631i | ||||
\(131\) | 8.06433e35i | 0.818382i | 0.912449 | + | 0.409191i | \(0.134189\pi\) | ||||
−0.912449 | + | 0.409191i | \(0.865811\pi\) | |||||||
\(132\) | 2.49960e34 | + | 4.04394e34i | 0.0222902 | + | 0.0360619i | ||||
\(133\) | −5.45393e35 | −0.427791 | ||||||||
\(134\) | 1.11001e36 | − | 1.99105e36i | 0.766559 | − | 1.37499i | ||||
\(135\) | 1.42173e36i | 0.865251i | ||||||||
\(136\) | −4.28751e34 | − | 9.51163e35i | −0.0230167 | − | 0.510615i | ||||
\(137\) | −3.19441e36 | −1.51405 | −0.757026 | − | 0.653385i | \(-0.773348\pi\) | ||||
−0.757026 | + | 0.653385i | \(0.773348\pi\) | |||||||
\(138\) | 2.44237e36 | + | 1.36162e36i | 1.02298 | + | 0.570311i | ||||
\(139\) | − | 1.92587e36i | − | 0.713469i | −0.934206 | − | 0.356735i | \(-0.883890\pi\) | ||
0.934206 | − | 0.356735i | \(-0.116110\pi\) | |||||||
\(140\) | −1.22686e36 | + | 7.58334e35i | −0.402363 | + | 0.248705i | ||||
\(141\) | 1.90070e36 | 0.552316 | ||||||||
\(142\) | 3.16184e36 | − | 5.67145e36i | 0.814775 | − | 1.46148i | ||||
\(143\) | − | 2.90246e35i | − | 0.0663826i | ||||||
\(144\) | −1.29248e36 | + | 2.58567e36i | −0.262580 | + | 0.525305i | ||||
\(145\) | −2.84735e36 | −0.514262 | ||||||||
\(146\) | 9.24838e36 | + | 5.15597e36i | 1.48616 | + | 0.828538i | ||||
\(147\) | 3.09448e36i | 0.442784i | ||||||||
\(148\) | −5.30809e36 | − | 8.58762e36i | −0.676845 | − | 1.09502i | ||||
\(149\) | 1.47472e36 | 0.167704 | 0.0838521 | − | 0.996478i | \(-0.473278\pi\) | ||||
0.0838521 | + | 0.996478i | \(0.473278\pi\) | |||||||
\(150\) | 8.63071e35 | − | 1.54811e36i | 0.0875982 | − | 0.157127i | ||||
\(151\) | − | 1.17710e37i | − | 1.06710i | −0.845769 | − | 0.533549i | \(-0.820858\pi\) | ||
0.845769 | − | 0.533549i | \(-0.179142\pi\) | |||||||
\(152\) | −9.46042e36 | + | 4.26442e35i | −0.766601 | + | 0.0345556i | ||||
\(153\) | −4.14125e36 | −0.300177 | ||||||||
\(154\) | 4.95206e35 | + | 2.76078e35i | 0.0321317 | + | 0.0179134i | ||||
\(155\) | 2.25222e37i | 1.30910i | ||||||||
\(156\) | −1.05501e37 | + | 6.52112e36i | −0.549716 | + | 0.339785i | ||||
\(157\) | 1.63675e37 | 0.765046 | 0.382523 | − | 0.923946i | \(-0.375055\pi\) | ||||
0.382523 | + | 0.923946i | \(0.375055\pi\) | |||||||
\(158\) | −1.81257e37 | + | 3.25125e37i | −0.760545 | + | 1.36421i | ||||
\(159\) | 8.82384e36i | 0.332588i | ||||||||
\(160\) | −2.06882e37 | + | 1.41134e37i | −0.700945 | + | 0.478180i | ||||
\(161\) | 3.33478e37 | 1.01631 | ||||||||
\(162\) | −2.15978e36 | − | 1.20408e36i | −0.0592455 | − | 0.0330294i | ||||
\(163\) | − | 3.99721e37i | − | 0.987569i | −0.869584 | − | 0.493785i | \(-0.835613\pi\) | ||
0.869584 | − | 0.493785i | \(-0.164387\pi\) | |||||||
\(164\) | 9.20500e36 | + | 1.48922e37i | 0.204964 | + | 0.331599i | ||||
\(165\) | 1.79143e36 | 0.0359726 | ||||||||
\(166\) | 1.71740e37 | − | 3.08054e37i | 0.311196 | − | 0.558199i | ||||
\(167\) | − | 9.71671e37i | − | 1.58979i | −0.606748 | − | 0.794894i | \(-0.707526\pi\) | ||
0.606748 | − | 0.794894i | \(-0.292474\pi\) | |||||||
\(168\) | −1.09098e36 | − | 2.42029e37i | −0.0161272 | − | 0.357775i | ||||
\(169\) | 8.91592e35 | 0.0119150 | ||||||||
\(170\) | −3.13370e37 | − | 1.74704e37i | −0.378813 | − | 0.211189i | ||||
\(171\) | 4.11895e37i | 0.450664i | ||||||||
\(172\) | 4.14252e37 | − | 2.56053e37i | 0.410469 | − | 0.253715i | ||||
\(173\) | 6.61410e37 | 0.593864 | 0.296932 | − | 0.954899i | \(-0.404037\pi\) | ||||
0.296932 | + | 0.954899i | \(0.404037\pi\) | |||||||
\(174\) | 2.32899e37 | − | 4.17756e37i | 0.189596 | − | 0.340083i | ||||
\(175\) | − | 2.11377e37i | − | 0.156103i | ||||||
\(176\) | 8.80575e36 | + | 4.40166e36i | 0.0590270 | + | 0.0295054i | ||||
\(177\) | 3.48109e36 | 0.0211919 | ||||||||
\(178\) | −4.33107e37 | − | 2.41458e37i | −0.239583 | − | 0.133568i | ||||
\(179\) | 2.38286e38i | 1.19839i | 0.800604 | + | 0.599194i | \(0.204512\pi\) | ||||
−0.800604 | + | 0.599194i | \(0.795488\pi\) | |||||||
\(180\) | 5.72714e37 | + | 9.26556e37i | 0.262002 | + | 0.423876i | ||||
\(181\) | −3.55657e38 | −1.48080 | −0.740399 | − | 0.672168i | \(-0.765363\pi\) | ||||
−0.740399 | + | 0.672168i | \(0.765363\pi\) | |||||||
\(182\) | −7.20249e37 | + | 1.29193e38i | −0.273067 | + | 0.489806i | ||||
\(183\) | 2.98188e38i | 1.02996i | ||||||||
\(184\) | 5.78454e38 | − | 2.60746e37i | 1.82123 | − | 0.0820947i | ||||
\(185\) | −3.80423e38 | −1.09231 | ||||||||
\(186\) | −3.30439e38 | − | 1.84220e38i | −0.865708 | − | 0.482633i | ||||
\(187\) | 1.41034e37i | 0.0337300i | ||||||||
\(188\) | 3.34794e38 | − | 2.06940e38i | 0.731298 | − | 0.452023i | ||||
\(189\) | −2.84809e38 | −0.568465 | ||||||||
\(190\) | −1.73763e38 | + | 3.11682e38i | −0.317063 | + | 0.568723i | ||||
\(191\) | − | 6.06399e38i | − | 1.01203i | −0.862526 | − | 0.506013i | \(-0.831119\pi\) | ||
0.862526 | − | 0.506013i | \(-0.168881\pi\) | |||||||
\(192\) | −3.78485e37 | − | 4.18973e38i | −0.0578000 | − | 0.639830i | ||||
\(193\) | 5.07300e38 | 0.709236 | 0.354618 | − | 0.935011i | \(-0.384611\pi\) | ||||
0.354618 | + | 0.935011i | \(0.384611\pi\) | |||||||
\(194\) | 1.21771e38 | + | 6.78874e37i | 0.155925 | + | 0.0869281i | ||||
\(195\) | 4.67359e38i | 0.548355i | ||||||||
\(196\) | 3.36913e38 | + | 5.45070e38i | 0.362381 | + | 0.586272i | ||||
\(197\) | 1.53316e38 | 0.151238 | 0.0756189 | − | 0.997137i | \(-0.475907\pi\) | ||||
0.0756189 | + | 0.997137i | \(0.475907\pi\) | |||||||
\(198\) | 2.08501e37 | − | 3.73993e37i | 0.0188712 | − | 0.0338497i | ||||
\(199\) | − | 1.08591e38i | − | 0.0902176i | −0.998982 | − | 0.0451088i | \(-0.985637\pi\) | ||
0.998982 | − | 0.0451088i | \(-0.0143634\pi\) | |||||||
\(200\) | −1.65275e37 | − | 3.66656e38i | −0.0126095 | − | 0.279736i | ||||
\(201\) | 1.44289e39 | 1.01135 | ||||||||
\(202\) | −1.90035e39 | − | 1.05944e39i | −1.22422 | − | 0.682503i | ||||
\(203\) | − | 5.70399e38i | − | 0.337867i | ||||||
\(204\) | 5.12641e38 | − | 3.16869e38i | 0.279319 | − | 0.172650i | ||||
\(205\) | 6.59708e38 | 0.330778 | ||||||||
\(206\) | −6.04232e37 | + | 1.08382e38i | −0.0278908 | + | 0.0500283i | ||||
\(207\) | − | 2.51852e39i | − | 1.07065i | ||||||
\(208\) | −1.14833e39 | + | 2.29730e39i | −0.449771 | + | 0.899789i | ||||
\(209\) | 1.40275e38 | 0.0506398 | ||||||||
\(210\) | −7.97388e38 | − | 4.44544e38i | −0.265425 | − | 0.147975i | ||||
\(211\) | 6.11765e38i | 0.187838i | 0.995580 | + | 0.0939189i | \(0.0299394\pi\) | ||||
−0.995580 | + | 0.0939189i | \(0.970061\pi\) | |||||||
\(212\) | 9.60702e38 | + | 1.55426e39i | 0.272194 | + | 0.440365i | ||||
\(213\) | 4.11003e39 | 1.07496 | ||||||||
\(214\) | −2.61466e39 | + | 4.68997e39i | −0.631512 | + | 1.13276i | ||||
\(215\) | − | 1.83509e39i | − | 0.409453i | ||||||
\(216\) | −4.94032e39 | + | 2.22692e38i | −1.01869 | + | 0.0459189i | ||||
\(217\) | −4.51178e39 | −0.860067 | ||||||||
\(218\) | 2.14114e39 | + | 1.19368e39i | 0.377471 | + | 0.210440i | ||||
\(219\) | 6.70218e39i | 1.09312i | ||||||||
\(220\) | 3.15547e38 | − | 1.95043e38i | 0.0476298 | − | 0.0294405i | ||||
\(221\) | −3.67938e39 | −0.514170 | ||||||||
\(222\) | 3.11167e39 | − | 5.58146e39i | 0.402710 | − | 0.722350i | ||||
\(223\) | 7.94706e39i | 0.952849i | 0.879215 | + | 0.476424i | \(0.158067\pi\) | ||||
−0.879215 | + | 0.476424i | \(0.841933\pi\) | |||||||
\(224\) | −2.82728e39 | − | 4.14440e39i | −0.314161 | − | 0.460516i | ||||
\(225\) | −1.59637e39 | −0.164449 | ||||||||
\(226\) | 1.37325e40 | + | 7.65588e39i | 1.31192 | + | 0.731394i | ||||
\(227\) | − | 1.05589e40i | − | 0.935796i | −0.883783 | − | 0.467898i | \(-0.845011\pi\) | ||
0.883783 | − | 0.467898i | \(-0.154989\pi\) | |||||||
\(228\) | −3.15163e39 | − | 5.09881e39i | −0.259204 | − | 0.419350i | ||||
\(229\) | 5.79914e39 | 0.442752 | 0.221376 | − | 0.975189i | \(-0.428945\pi\) | ||||
0.221376 | + | 0.975189i | \(0.428945\pi\) | |||||||
\(230\) | 1.06247e40 | − | 1.90577e40i | 0.753255 | − | 1.35113i | ||||
\(231\) | 3.58870e38i | 0.0236338i | ||||||||
\(232\) | −4.45994e38 | − | 9.89417e39i | −0.0272919 | − | 0.605458i | ||||
\(233\) | −5.75523e39 | −0.327350 | −0.163675 | − | 0.986514i | \(-0.552335\pi\) | ||||
−0.163675 | + | 0.986514i | \(0.552335\pi\) | |||||||
\(234\) | 9.75696e39 | + | 5.43951e39i | 0.515995 | + | 0.287667i | ||||
\(235\) | − | 1.48310e40i | − | 0.729488i | ||||||
\(236\) | 6.13170e38 | − | 3.79006e38i | 0.0280593 | − | 0.0173437i | ||||
\(237\) | −2.35614e40 | −1.00341 | ||||||||
\(238\) | 3.49977e39 | − | 6.27761e39i | 0.138750 | − | 0.248878i | ||||
\(239\) | 1.18884e40i | 0.438893i | 0.975625 | + | 0.219447i | \(0.0704251\pi\) | ||||
−0.975625 | + | 0.219447i | \(0.929575\pi\) | |||||||
\(240\) | −1.41791e40 | − | 7.08762e39i | −0.487594 | − | 0.243730i | ||||
\(241\) | −2.28994e40 | −0.733726 | −0.366863 | − | 0.930275i | \(-0.619568\pi\) | ||||
−0.366863 | + | 0.930275i | \(0.619568\pi\) | |||||||
\(242\) | 2.91203e40 | + | 1.62346e40i | 0.869632 | + | 0.484820i | ||||
\(243\) | 3.50608e40i | 0.976146i | ||||||||
\(244\) | 3.24654e40 | + | 5.25237e40i | 0.842935 | + | 1.36373i | ||||
\(245\) | 2.41461e40 | 0.584821 | ||||||||
\(246\) | −5.39608e39 | + | 9.67907e39i | −0.121950 | + | 0.218744i | ||||
\(247\) | 3.65957e40i | 0.771938i | ||||||||
\(248\) | −7.82616e40 | + | 3.52776e39i | −1.54124 | + | 0.0694736i | ||||
\(249\) | 2.23243e40 | 0.410571 | ||||||||
\(250\) | −5.52189e40 | − | 3.07846e40i | −0.948654 | − | 0.528875i | ||||
\(251\) | − | 5.78655e40i | − | 0.928895i | −0.885601 | − | 0.464447i | \(-0.846253\pi\) | ||
0.885601 | − | 0.464447i | \(-0.153747\pi\) | |||||||
\(252\) | −1.85613e40 | + | 1.14730e40i | −0.278484 | + | 0.172134i | ||||
\(253\) | −8.57703e39 | −0.120306 | ||||||||
\(254\) | 2.46097e39 | − | 4.41429e39i | 0.0322800 | − | 0.0579012i | ||||
\(255\) | − | 2.27095e40i | − | 0.278628i | ||||||
\(256\) | −5.22827e40 | − | 6.96783e40i | −0.600176 | − | 0.799868i | ||||
\(257\) | 1.57494e41 | 1.69201 | 0.846003 | − | 0.533178i | \(-0.179002\pi\) | ||||
0.846003 | + | 0.533178i | \(0.179002\pi\) | |||||||
\(258\) | 2.69240e40 | + | 1.50101e40i | 0.270773 | + | 0.150956i | ||||
\(259\) | − | 7.62086e40i | − | 0.717643i | ||||||
\(260\) | 5.08840e40 | + | 8.23219e40i | 0.448781 | + | 0.726054i | ||||
\(261\) | −4.30780e40 | −0.355932 | ||||||||
\(262\) | −5.14700e40 | + | 9.23228e40i | −0.398503 | + | 0.714804i | ||||
\(263\) | − | 3.05475e40i | − | 0.221681i | −0.993838 | − | 0.110840i | \(-0.964646\pi\) | ||
0.993838 | − | 0.110840i | \(-0.0353542\pi\) | |||||||
\(264\) | 2.80600e38 | + | 6.22498e39i | 0.00190906 | + | 0.0423517i | ||||
\(265\) | 6.88520e40 | 0.439275 | ||||||||
\(266\) | −6.24381e40 | − | 3.48093e40i | −0.373647 | − | 0.208309i | ||||
\(267\) | − | 3.13867e40i | − | 0.176220i | ||||||
\(268\) | 2.54154e41 | − | 1.57095e41i | 1.33908 | − | 0.827698i | ||||
\(269\) | 7.00941e40 | 0.346651 | 0.173325 | − | 0.984865i | \(-0.444549\pi\) | ||||
0.173325 | + | 0.984865i | \(0.444549\pi\) | |||||||
\(270\) | −9.07407e40 | + | 1.62763e41i | −0.421326 | + | 0.755741i | ||||
\(271\) | − | 6.84353e40i | − | 0.298402i | −0.988807 | − | 0.149201i | \(-0.952330\pi\) | ||
0.988807 | − | 0.149201i | \(-0.0476702\pi\) | |||||||
\(272\) | 5.57988e40 | − | 1.11628e41i | 0.228536 | − | 0.457197i | ||||
\(273\) | −9.36242e40 | −0.360266 | ||||||||
\(274\) | −3.65705e41 | − | 2.03881e41i | −1.32243 | − | 0.737253i | ||||
\(275\) | 5.43660e39i | 0.0184787i | ||||||||
\(276\) | 1.92705e41 | + | 3.11765e41i | 0.615798 | + | 0.996260i | ||||
\(277\) | −5.45252e40 | −0.163848 | −0.0819240 | − | 0.996639i | \(-0.526106\pi\) | ||||
−0.0819240 | + | 0.996639i | \(0.526106\pi\) | |||||||
\(278\) | 1.22917e41 | − | 2.20479e41i | 0.347417 | − | 0.623169i | ||||
\(279\) | 3.40741e41i | 0.906053i | ||||||||
\(280\) | −1.88854e41 | + | 8.51288e39i | −0.472542 | + | 0.0213005i | ||||
\(281\) | −5.70960e41 | −1.34461 | −0.672307 | − | 0.740272i | \(-0.734697\pi\) | ||||
−0.672307 | + | 0.740272i | \(0.734697\pi\) | |||||||
\(282\) | 2.17597e41 | + | 1.21311e41i | 0.482412 | + | 0.268945i | ||||
\(283\) | 5.84403e41i | 1.21995i | 0.792419 | + | 0.609977i | \(0.208821\pi\) | ||||
−0.792419 | + | 0.609977i | \(0.791179\pi\) | |||||||
\(284\) | 7.23953e41 | − | 4.47482e41i | 1.42331 | − | 0.879760i | ||||
\(285\) | −2.25872e41 | −0.418312 | ||||||||
\(286\) | 1.85248e40 | − | 3.32282e40i | 0.0323244 | − | 0.0579809i | ||||
\(287\) | 1.32157e41i | 0.217319i | ||||||||
\(288\) | −3.12996e41 | + | 2.13524e41i | −0.485139 | + | 0.330959i | ||||
\(289\) | −5.05541e41 | −0.738743 | ||||||||
\(290\) | −3.25973e41 | − | 1.81730e41i | −0.449175 | − | 0.250415i | ||||
\(291\) | 8.82459e40i | 0.114687i | ||||||||
\(292\) | 7.29705e41 | + | 1.18054e42i | 0.894620 | + | 1.44735i | ||||
\(293\) | 4.05544e41 | 0.469125 | 0.234563 | − | 0.972101i | \(-0.424634\pi\) | ||||
0.234563 | + | 0.972101i | \(0.424634\pi\) | |||||||
\(294\) | −1.97503e41 | + | 3.54265e41i | −0.215610 | + | 0.386744i | ||||
\(295\) | − | 2.71628e40i | − | 0.0279898i | ||||||
\(296\) | −5.95875e40 | − | 1.32192e42i | −0.0579690 | − | 1.28602i | ||||
\(297\) | 7.32527e40 | 0.0672921 | ||||||||
\(298\) | 1.68830e41 | + | 9.41231e40i | 0.146479 | + | 0.0816619i | ||||
\(299\) | − | 2.23763e42i | − | 1.83391i | ||||||
\(300\) | 1.97614e41 | − | 1.22147e41i | 0.153023 | − | 0.0945849i | ||||
\(301\) | 3.67617e41 | 0.269008 | ||||||||
\(302\) | 7.51274e41 | − | 1.34758e42i | 0.519613 | − | 0.932041i | ||||
\(303\) | − | 1.37716e42i | − | 0.900448i | ||||||
\(304\) | −1.11027e42 | − | 5.54984e41i | −0.686403 | − | 0.343107i | ||||
\(305\) | 2.32675e42 | 1.36035 | ||||||||
\(306\) | −4.74102e41 | − | 2.64312e41i | −0.262185 | − | 0.146168i | ||||
\(307\) | 3.09454e42i | 1.61899i | 0.587127 | + | 0.809495i | \(0.300259\pi\) | ||||
−0.587127 | + | 0.809495i | \(0.699741\pi\) | |||||||
\(308\) | 3.90722e40 | + | 6.32124e40i | 0.0193422 | + | 0.0312925i | ||||
\(309\) | −7.85433e40 | −0.0367972 | ||||||||
\(310\) | −1.43746e42 | + | 2.57840e42i | −0.637451 | + | 1.14341i | ||||
\(311\) | − | 1.35368e42i | − | 0.568317i | −0.958777 | − | 0.284158i | \(-0.908286\pi\) | ||
0.958777 | − | 0.284158i | \(-0.0917141\pi\) | |||||||
\(312\) | −1.62401e42 | + | 7.32047e40i | −0.645596 | + | 0.0291012i | ||||
\(313\) | 4.42782e41 | 0.166700 | 0.0833501 | − | 0.996520i | \(-0.473438\pi\) | ||||
0.0833501 | + | 0.996520i | \(0.473438\pi\) | |||||||
\(314\) | 1.87380e42 | + | 1.04464e42i | 0.668218 | + | 0.372532i | ||||
\(315\) | 8.22249e41i | 0.277795i | ||||||||
\(316\) | −4.15017e42 | + | 2.56526e42i | −1.32857 | + | 0.821205i | ||||
\(317\) | 2.55541e42 | 0.775270 | 0.387635 | − | 0.921813i | \(-0.373292\pi\) | ||||
0.387635 | + | 0.921813i | \(0.373292\pi\) | |||||||
\(318\) | −5.63175e41 | + | 1.01018e42i | −0.161951 | + | 0.290494i | ||||
\(319\) | 1.46706e41i | 0.0399951i | ||||||||
\(320\) | −3.26923e42 | + | 2.95330e41i | −0.845075 | + | 0.0763411i | ||||
\(321\) | −3.39876e42 | −0.833173 | ||||||||
\(322\) | 3.81775e42 | + | 2.12840e42i | 0.887684 | + | 0.494884i | ||||
\(323\) | − | 1.77823e42i | − | 0.392233i | ||||||
\(324\) | −1.70409e41 | − | 2.75693e41i | −0.0356637 | − | 0.0576980i | ||||
\(325\) | −1.41833e42 | −0.281684 | ||||||||
\(326\) | 2.55119e42 | − | 4.57612e42i | 0.480887 | − | 0.862578i | ||||
\(327\) | 1.55165e42i | 0.277641i | ||||||||
\(328\) | 1.03333e41 | + | 2.29240e42i | 0.0175544 | + | 0.389435i | ||||
\(329\) | 2.97105e42 | 0.479269 | ||||||||
\(330\) | 2.05088e41 | + | 1.14336e41i | 0.0314197 | + | 0.0175165i | ||||
\(331\) | 2.93715e42i | 0.427416i | 0.976898 | + | 0.213708i | \(0.0685541\pi\) | ||||
−0.976898 | + | 0.213708i | \(0.931446\pi\) | |||||||
\(332\) | 3.93226e42 | − | 2.43057e42i | 0.543620 | − | 0.336017i | ||||
\(333\) | −5.75548e42 | −0.756013 | ||||||||
\(334\) | 6.20162e42 | − | 1.11240e43i | 0.774132 | − | 1.38858i | ||||
\(335\) | − | 1.12588e43i | − | 1.33576i | ||||||
\(336\) | 1.41984e42 | − | 2.84045e42i | 0.160129 | − | 0.320346i | ||||
\(337\) | −6.07483e42 | −0.651368 | −0.325684 | − | 0.945479i | \(-0.605594\pi\) | ||||
−0.325684 | + | 0.945479i | \(0.605594\pi\) | |||||||
\(338\) | 1.02072e41 | + | 5.69052e40i | 0.0104069 | + | 0.00580187i | ||||
\(339\) | 9.95177e42i | 0.964951i | ||||||||
\(340\) | −2.47251e42 | − | 4.00012e42i | −0.228033 | − | 0.368919i | ||||
\(341\) | 1.16043e42 | 0.101811 | ||||||||
\(342\) | −2.62889e42 | + | 4.71549e42i | −0.219446 | + | 0.393626i | ||||
\(343\) | 1.18552e43i | 0.941693i | ||||||||
\(344\) | 6.37671e42 | − | 2.87440e41i | 0.482063 | − | 0.0217297i | ||||
\(345\) | 1.38109e43 | 0.993793 | ||||||||
\(346\) | 7.57201e42 | + | 4.22140e42i | 0.518702 | + | 0.289176i | ||||
\(347\) | − | 8.92154e42i | − | 0.581887i | −0.956740 | − | 0.290944i | \(-0.906031\pi\) | ||
0.956740 | − | 0.290944i | \(-0.0939692\pi\) | |||||||
\(348\) | 5.33259e42 | − | 3.29613e42i | 0.331200 | − | 0.204718i | ||||
\(349\) | −1.89322e43 | −1.11988 | −0.559938 | − | 0.828535i | \(-0.689175\pi\) | ||||
−0.559938 | + | 0.828535i | \(0.689175\pi\) | |||||||
\(350\) | 1.34910e42 | − | 2.41990e42i | 0.0760128 | − | 0.136346i | ||||
\(351\) | 1.91106e43i | 1.02578i | ||||||||
\(352\) | 7.27175e41 | + | 1.06594e42i | 0.0371889 | + | 0.0545137i | ||||
\(353\) | −2.28963e43 | −1.11582 | −0.557912 | − | 0.829900i | \(-0.688397\pi\) | ||||
−0.557912 | + | 0.829900i | \(0.688397\pi\) | |||||||
\(354\) | 3.98525e41 | + | 2.22178e41i | 0.0185098 | + | 0.0103192i | ||||
\(355\) | − | 3.20704e43i | − | 1.41978i | ||||||
\(356\) | −3.41725e42 | − | 5.52855e42i | −0.144221 | − | 0.233325i | ||||
\(357\) | 4.54930e42 | 0.183057 | ||||||||
\(358\) | −1.52084e43 | + | 2.72797e43i | −0.583544 | + | 1.04671i | ||||
\(359\) | − | 1.32335e42i | − | 0.0484248i | −0.999707 | − | 0.0242124i | \(-0.992292\pi\) | ||
0.999707 | − | 0.0242124i | \(-0.00770779\pi\) | |||||||
\(360\) | 6.42915e41 | + | 1.42628e43i | 0.0224394 | + | 0.497808i | ||||
\(361\) | 1.23481e43 | 0.411129 | ||||||||
\(362\) | −4.07167e43 | − | 2.26996e43i | −1.29338 | − | 0.721060i | ||||
\(363\) | 2.11031e43i | 0.639638i | ||||||||
\(364\) | −1.64912e43 | + | 1.01934e43i | −0.477013 | + | 0.294846i | ||||
\(365\) | 5.22968e43 | 1.44376 | ||||||||
\(366\) | −1.90316e43 | + | 3.41374e43i | −0.501531 | + | 0.899606i | ||||
\(367\) | 4.47029e41i | 0.0112464i | 0.999984 | + | 0.00562319i | \(0.00178993\pi\) | ||||
−0.999984 | + | 0.00562319i | \(0.998210\pi\) | |||||||
\(368\) | 6.78872e43 | + | 3.39343e43i | 1.63070 | + | 0.815128i | ||||
\(369\) | 9.98084e42 | 0.228938 | ||||||||
\(370\) | −4.35519e43 | − | 2.42802e43i | −0.954065 | − | 0.531891i | ||||
\(371\) | 1.37929e43i | 0.288601i | ||||||||
\(372\) | −2.60719e43 | − | 4.21801e43i | −0.521127 | − | 0.843097i | ||||
\(373\) | 5.76669e43 | 1.10123 | 0.550613 | − | 0.834761i | \(-0.314394\pi\) | ||||
0.550613 | + | 0.834761i | \(0.314394\pi\) | |||||||
\(374\) | −9.00139e41 | + | 1.61460e42i | −0.0164245 | + | 0.0294610i | ||||
\(375\) | − | 4.00164e43i | − | 0.697761i | ||||||
\(376\) | 5.15360e43 | − | 2.32306e42i | 0.858850 | − | 0.0387139i | ||||
\(377\) | −3.82736e43 | −0.609672 | ||||||||
\(378\) | −3.26058e43 | − | 1.81777e43i | −0.496517 | − | 0.276808i | ||||
\(379\) | − | 1.17062e44i | − | 1.70431i | −0.523288 | − | 0.852156i | \(-0.675295\pi\) | ||
0.523288 | − | 0.852156i | \(-0.324705\pi\) | |||||||
\(380\) | −3.97858e43 | + | 2.45920e43i | −0.553869 | + | 0.342352i | ||||
\(381\) | 3.19898e42 | 0.0425880 | ||||||||
\(382\) | 3.87030e43 | − | 6.94223e43i | 0.492796 | − | 0.883938i | ||||
\(383\) | 2.28376e43i | 0.278145i | 0.990282 | + | 0.139072i | \(0.0444121\pi\) | ||||
−0.990282 | + | 0.139072i | \(0.955588\pi\) | |||||||
\(384\) | 2.24076e43 | − | 5.03809e43i | 0.261075 | − | 0.586996i | ||||
\(385\) | 2.80024e42 | 0.0312150 | ||||||||
\(386\) | 5.80772e43 | + | 3.23781e43i | 0.619471 | + | 0.345356i | ||||
\(387\) | − | 2.77634e43i | − | 0.283391i | ||||||
\(388\) | 9.60784e42 | + | 1.55439e43i | 0.0938613 | + | 0.151852i | ||||
\(389\) | 9.45576e41 | 0.00884205 | 0.00442103 | − | 0.999990i | \(-0.498593\pi\) | ||||
0.00442103 | + | 0.999990i | \(0.498593\pi\) | |||||||
\(390\) | −2.98288e43 | + | 5.35046e43i | −0.267016 | + | 0.478953i | ||||
\(391\) | 1.08729e44i | 0.931838i | ||||||||
\(392\) | 3.78211e42 | + | 8.39045e43i | 0.0310364 | + | 0.688528i | ||||
\(393\) | −6.69051e43 | −0.525758 | ||||||||
\(394\) | 1.75520e43 | + | 9.78526e42i | 0.132096 | + | 0.0736438i | ||||
\(395\) | 1.83848e44i | 1.32529i | ||||||||
\(396\) | 4.77396e42 | − | 2.95084e42i | 0.0329656 | − | 0.0203764i | ||||
\(397\) | −1.93544e44 | −1.28039 | −0.640195 | − | 0.768213i | \(-0.721146\pi\) | ||||
−0.640195 | + | 0.768213i | \(0.721146\pi\) | |||||||
\(398\) | 6.93073e42 | − | 1.24318e43i | 0.0439306 | − | 0.0787992i | ||||
\(399\) | − | 4.52481e43i | − | 0.274828i | ||||||
\(400\) | 2.15094e43 | − | 4.30307e43i | 0.125201 | − | 0.250472i | ||||
\(401\) | −1.52086e44 | −0.848466 | −0.424233 | − | 0.905553i | \(-0.639456\pi\) | ||||
−0.424233 | + | 0.905553i | \(0.639456\pi\) | |||||||
\(402\) | 1.65186e44 | + | 9.20912e43i | 0.883344 | + | 0.492465i | ||||
\(403\) | 3.02739e44i | 1.55197i | ||||||||
\(404\) | −1.49939e44 | − | 2.42576e44i | −0.736938 | − | 1.19224i | ||||
\(405\) | −1.22129e43 | −0.0575552 | ||||||||
\(406\) | 3.64053e43 | − | 6.53009e43i | 0.164521 | − | 0.295105i | ||||
\(407\) | 1.96008e43i | 0.0849511i | ||||||||
\(408\) | 7.89126e43 | − | 3.55710e42i | 0.328037 | − | 0.0147868i | ||||
\(409\) | 1.14576e44 | 0.456876 | 0.228438 | − | 0.973558i | \(-0.426638\pi\) | ||||
0.228438 | + | 0.973558i | \(0.426638\pi\) | |||||||
\(410\) | 7.55253e43 | + | 4.21054e43i | 0.288913 | + | 0.161069i | ||||
\(411\) | − | 2.65022e44i | − | 0.972681i | ||||||
\(412\) | −1.38348e43 | + | 8.55146e42i | −0.0487216 | + | 0.0301153i | ||||
\(413\) | 5.44142e42 | 0.0183891 | ||||||||
\(414\) | 1.60742e44 | − | 2.88327e44i | 0.521344 | − | 0.935146i | ||||
\(415\) | − | 1.74195e44i | − | 0.542274i | ||||||
\(416\) | −2.78088e44 | + | 1.89710e44i | −0.830990 | + | 0.566896i | ||||
\(417\) | 1.59778e44 | 0.458358 | ||||||||
\(418\) | 1.60590e43 | + | 8.95292e42i | 0.0442306 | + | 0.0246586i | ||||
\(419\) | − | 5.13503e44i | − | 1.35801i | −0.734131 | − | 0.679007i | \(-0.762410\pi\) | ||
0.734131 | − | 0.679007i | \(-0.237590\pi\) | |||||||
\(420\) | −6.29146e43 | − | 1.01785e44i | −0.159777 | − | 0.258492i | ||||
\(421\) | 3.75101e44 | 0.914857 | 0.457428 | − | 0.889246i | \(-0.348771\pi\) | ||||
0.457428 | + | 0.889246i | \(0.348771\pi\) | |||||||
\(422\) | −3.90455e43 | + | 7.00367e43i | −0.0914658 | + | 0.164064i | ||||
\(423\) | − | 2.24381e44i | − | 0.504894i | ||||||
\(424\) | 1.07846e43 | + | 2.39252e44i | 0.0233123 | + | 0.517173i | ||||
\(425\) | 6.89185e43 | 0.143128 | ||||||||
\(426\) | 4.70528e44 | + | 2.62320e44i | 0.938906 | + | 0.523441i | ||||
\(427\) | 4.66108e44i | 0.893744i | ||||||||
\(428\) | −5.98668e44 | + | 3.70043e44i | −1.10317 | + | 0.681880i | ||||
\(429\) | 2.40801e43 | 0.0426465 | ||||||||
\(430\) | 1.17123e44 | − | 2.10087e44i | 0.199379 | − | 0.357631i | ||||
\(431\) | 5.86754e44i | 0.960158i | 0.877225 | + | 0.480079i | \(0.159392\pi\) | ||||
−0.877225 | + | 0.480079i | \(0.840608\pi\) | |||||||
\(432\) | −5.79796e44 | − | 2.89818e44i | −0.912118 | − | 0.455934i | ||||
\(433\) | −3.06479e44 | −0.463561 | −0.231781 | − | 0.972768i | \(-0.574455\pi\) | ||||
−0.231781 | + | 0.972768i | \(0.574455\pi\) | |||||||
\(434\) | −5.16522e44 | − | 2.87961e44i | −0.751213 | − | 0.418802i | ||||
\(435\) | − | 2.36228e44i | − | 0.330381i | ||||||
\(436\) | 1.68937e44 | + | 2.73313e44i | 0.227225 | + | 0.367612i | ||||
\(437\) | 1.08144e45 | 1.39900 | ||||||||
\(438\) | −4.27762e44 | + | 7.67285e44i | −0.532282 | + | 0.954766i | ||||
\(439\) | − | 1.33042e45i | − | 1.59255i | −0.604937 | − | 0.796273i | \(-0.706802\pi\) | ||
0.604937 | − | 0.796273i | \(-0.293198\pi\) | |||||||
\(440\) | 4.85732e43 | − | 2.18951e42i | 0.0559373 | − | 0.00252145i | ||||
\(441\) | 3.65310e44 | 0.404767 | ||||||||
\(442\) | −4.21226e44 | − | 2.34834e44i | −0.449094 | − | 0.250370i | ||||
\(443\) | 1.40788e45i | 1.44445i | 0.691656 | + | 0.722227i | \(0.256881\pi\) | ||||
−0.691656 | + | 0.722227i | \(0.743119\pi\) | |||||||
\(444\) | 7.12465e44 | − | 4.40382e44i | 0.703483 | − | 0.434830i | ||||
\(445\) | −2.44909e44 | −0.232748 | ||||||||
\(446\) | −5.07215e44 | + | 9.09803e44i | −0.463981 | + | 0.832252i | ||||
\(447\) | 1.22349e44i | 0.107739i | ||||||||
\(448\) | −5.91624e43 | − | 6.54911e44i | −0.0501556 | − | 0.555209i | ||||
\(449\) | −2.39263e45 | −1.95294 | −0.976468 | − | 0.215663i | \(-0.930809\pi\) | ||||
−0.976468 | + | 0.215663i | \(0.930809\pi\) | |||||||
\(450\) | −1.82758e44 | − | 1.01887e44i | −0.143636 | − | 0.0800770i | ||||
\(451\) | − | 3.39907e43i | − | 0.0257252i | ||||||
\(452\) | 1.08351e45 | + | 1.75293e45i | 0.789729 | + | 1.27765i | ||||
\(453\) | 9.76571e44 | 0.685542 | ||||||||
\(454\) | 6.73917e44 | − | 1.20882e45i | 0.455677 | − | 0.817357i | ||||
\(455\) | 7.30545e44i | 0.475832i | ||||||||
\(456\) | −3.53795e43 | − | 7.84877e44i | −0.0221998 | − | 0.492492i | ||||
\(457\) | −7.62339e44 | −0.460864 | −0.230432 | − | 0.973088i | \(-0.574014\pi\) | ||||
−0.230432 | + | 0.973088i | \(0.574014\pi\) | |||||||
\(458\) | 6.63902e44 | + | 3.70126e44i | 0.386715 | + | 0.215594i | ||||
\(459\) | − | 9.28608e44i | − | 0.521215i | ||||||
\(460\) | 2.43269e45 | − | 1.50367e45i | 1.31584 | − | 0.813334i | ||||
\(461\) | −4.08079e44 | −0.212730 | −0.106365 | − | 0.994327i | \(-0.533921\pi\) | ||||
−0.106365 | + | 0.994327i | \(0.533921\pi\) | |||||||
\(462\) | −2.29046e43 | + | 4.10844e43i | −0.0115082 | + | 0.0206426i | ||||
\(463\) | − | 4.89009e44i | − | 0.236832i | −0.992964 | − | 0.118416i | \(-0.962218\pi\) | ||
0.992964 | − | 0.118416i | \(-0.0377816\pi\) | |||||||
\(464\) | 5.80430e44 | − | 1.16118e45i | 0.270984 | − | 0.542118i | ||||
\(465\) | −1.86853e45 | −0.841010 | ||||||||
\(466\) | −6.58876e44 | − | 3.67323e44i | −0.285919 | − | 0.159400i | ||||
\(467\) | 1.85973e44i | 0.0778150i | 0.999243 | + | 0.0389075i | \(0.0123878\pi\) | ||||
−0.999243 | + | 0.0389075i | \(0.987612\pi\) | |||||||
\(468\) | 7.69833e44 | + | 1.24546e45i | 0.310611 | + | 0.502517i | ||||
\(469\) | 2.25543e45 | 0.877588 | ||||||||
\(470\) | 9.46581e44 | − | 1.69790e45i | 0.355217 | − | 0.637160i | ||||
\(471\) | 1.35792e45i | 0.491493i | ||||||||
\(472\) | 9.43873e43 | − | 4.25464e42i | 0.0329533 | − | 0.00148542i | ||||
\(473\) | −9.45509e43 | −0.0318439 | ||||||||
\(474\) | −2.69738e45 | − | 1.50379e45i | −0.876415 | − | 0.488602i | ||||
\(475\) | − | 6.85474e44i | − | 0.214882i | ||||||
\(476\) | 8.01328e44 | − | 4.95309e44i | 0.242377 | − | 0.149816i | ||||
\(477\) | 1.04167e45 | 0.304032 | ||||||||
\(478\) | −7.58768e44 | + | 1.36102e45i | −0.213715 | + | 0.383345i | ||||
\(479\) | − | 7.30451e44i | − | 0.198558i | −0.995060 | − | 0.0992790i | \(-0.968346\pi\) | ||
0.995060 | − | 0.0992790i | \(-0.0316536\pi\) | |||||||
\(480\) | −1.17091e45 | − | 1.71638e45i | −0.307200 | − | 0.450312i | ||||
\(481\) | −5.11358e45 | −1.29497 | ||||||||
\(482\) | −2.62159e45 | − | 1.46154e45i | −0.640862 | − | 0.357281i | ||||
\(483\) | 2.76668e45i | 0.652916i | ||||||||
\(484\) | 2.29762e45 | + | 3.71717e45i | 0.523488 | + | 0.846918i | ||||
\(485\) | 6.88579e44 | 0.151476 | ||||||||
\(486\) | −2.23773e45 | + | 4.01386e45i | −0.475325 | + | 0.852601i | ||||
\(487\) | 5.74351e45i | 1.17811i | 0.808094 | + | 0.589054i | \(0.200499\pi\) | ||||
−0.808094 | + | 0.589054i | \(0.799501\pi\) | |||||||
\(488\) | 3.64450e44 | + | 8.08515e45i | 0.0721939 | + | 1.60159i | ||||
\(489\) | 3.31625e45 | 0.634450 | ||||||||
\(490\) | 2.76431e45 | + | 1.54110e45i | 0.510803 | + | 0.284773i | ||||
\(491\) | − | 5.84413e45i | − | 1.04312i | −0.853215 | − | 0.521560i | \(-0.825350\pi\) | ||
0.853215 | − | 0.521560i | \(-0.174650\pi\) | |||||||
\(492\) | −1.23552e45 | + | 7.63686e44i | −0.213031 | + | 0.131677i | ||||
\(493\) | 1.85976e45 | 0.309784 | ||||||||
\(494\) | −2.33570e45 | + | 4.18958e45i | −0.375888 | + | 0.674237i | ||||
\(495\) | − | 2.11482e44i | − | 0.0328840i | ||||||
\(496\) | −9.18478e45 | − | 4.59112e45i | −1.38000 | − | 0.689812i | ||||
\(497\) | 6.42454e45 | 0.932788 | ||||||||
\(498\) | 2.55575e45 | + | 1.42483e45i | 0.358607 | + | 0.199924i | ||||
\(499\) | − | 8.01707e45i | − | 1.08719i | −0.839347 | − | 0.543596i | \(-0.817062\pi\) | ||
0.839347 | − | 0.543596i | \(-0.182938\pi\) | |||||||
\(500\) | −4.35682e45 | − | 7.04861e45i | −0.571057 | − | 0.923876i | ||||
\(501\) | 8.06140e45 | 1.02134 | ||||||||
\(502\) | 3.69322e45 | − | 6.62461e45i | 0.452316 | − | 0.811329i | ||||
\(503\) | − | 1.11697e46i | − | 1.32247i | −0.750178 | − | 0.661236i | \(-0.770032\pi\) | ||
0.750178 | − | 0.661236i | \(-0.229968\pi\) | |||||||
\(504\) | −2.85721e45 | + | 1.28793e44i | −0.327057 | + | 0.0147425i | ||||
\(505\) | −1.07459e46 | −1.18929 | ||||||||
\(506\) | −9.81924e44 | − | 5.47423e44i | −0.105080 | − | 0.0585820i | ||||
\(507\) | 7.39703e43i | 0.00765459i | ||||||||
\(508\) | 5.63478e44 | − | 3.48291e44i | 0.0563889 | − | 0.0348546i | ||||
\(509\) | 1.52847e46 | 1.47929 | 0.739647 | − | 0.672995i | \(-0.234992\pi\) | ||||
0.739647 | + | 0.672995i | \(0.234992\pi\) | |||||||
\(510\) | 1.44942e45 | − | 2.59985e45i | 0.135675 | − | 0.243363i | ||||
\(511\) | 1.04764e46i | 0.948544i | ||||||||
\(512\) | −1.53831e45 | − | 1.13139e46i | −0.134727 | − | 0.990883i | ||||
\(513\) | −9.23608e45 | −0.782515 | ||||||||
\(514\) | 1.80304e46 | + | 1.00520e46i | 1.47786 | + | 0.823906i | ||||
\(515\) | 6.12870e44i | 0.0486010i | ||||||||
\(516\) | 2.12433e45 | + | 3.43681e45i | 0.162996 | + | 0.263700i | ||||
\(517\) | −7.64151e44 | −0.0567336 | ||||||||
\(518\) | 4.86396e45 | − | 8.72459e45i | 0.349449 | − | 0.626814i | ||||
\(519\) | 5.48734e45i | 0.381520i | ||||||||
\(520\) | 5.71213e44 | + | 1.26721e46i | 0.0384362 | + | 0.852690i | ||||
\(521\) | −6.48428e45 | −0.422300 | −0.211150 | − | 0.977454i | \(-0.567721\pi\) | ||||
−0.211150 | + | 0.977454i | \(0.567721\pi\) | |||||||
\(522\) | −4.93169e45 | − | 2.74942e45i | −0.310883 | − | 0.173318i | ||||
\(523\) | 1.86380e46i | 1.13729i | 0.822583 | + | 0.568646i | \(0.192532\pi\) | ||||
−0.822583 | + | 0.568646i | \(0.807468\pi\) | |||||||
\(524\) | −1.17849e46 | + | 7.28434e45i | −0.696134 | + | 0.430287i | ||||
\(525\) | 1.75367e45 | 0.100286 | ||||||||
\(526\) | 1.94967e45 | − | 3.49717e45i | 0.107945 | − | 0.193624i | ||||
\(527\) | − | 1.47105e46i | − | 0.788580i | ||||||
\(528\) | −3.65181e44 | + | 7.30562e44i | −0.0189553 | + | 0.0379211i | ||||
\(529\) | −4.62289e46 | −2.32363 | ||||||||
\(530\) | 7.88238e45 | + | 4.39443e45i | 0.383679 | + | 0.213901i | ||||
\(531\) | − | 4.10950e44i | − | 0.0193724i | ||||||
\(532\) | −4.92642e45 | − | 7.97014e45i | −0.224923 | − | 0.363888i | ||||
\(533\) | 8.86770e45 | 0.392146 | ||||||||
\(534\) | 2.00324e45 | − | 3.59324e45i | 0.0858086 | − | 0.153917i | ||||
\(535\) | 2.65204e46i | 1.10044i | ||||||||
\(536\) | 3.91228e46 | − | 1.76352e45i | 1.57264 | − | 0.0708889i | ||||
\(537\) | −1.97693e46 | −0.769888 | ||||||||
\(538\) | 8.02457e45 | + | 4.47370e45i | 0.302777 | + | 0.168798i | ||||
\(539\) | − | 1.24410e45i | − | 0.0454825i | ||||||
\(540\) | −2.07765e46 | + | 1.28422e46i | −0.736002 | + | 0.454930i | ||||
\(541\) | 5.83524e45 | 0.200311 | 0.100156 | − | 0.994972i | \(-0.468066\pi\) | ||||
0.100156 | + | 0.994972i | \(0.468066\pi\) | |||||||
\(542\) | 4.36783e45 | − | 7.83467e45i | 0.145304 | − | 0.260635i | ||||
\(543\) | − | 2.95068e46i | − | 0.951318i | ||||||
\(544\) | 1.35126e46 | − | 9.21822e45i | 0.422239 | − | 0.288049i | ||||
\(545\) | 1.21075e46 | 0.366702 | ||||||||
\(546\) | −1.07184e46 | − | 5.97549e45i | −0.314669 | − | 0.175428i | ||||
\(547\) | 5.22326e46i | 1.48647i | 0.669029 | + | 0.743236i | \(0.266710\pi\) | ||||
−0.669029 | + | 0.743236i | \(0.733290\pi\) | |||||||
\(548\) | −2.88544e46 | − | 4.66817e46i | −0.796055 | − | 1.28789i | ||||
\(549\) | 3.52017e46 | 0.941530 | ||||||||
\(550\) | −3.46987e44 | + | 6.22398e44i | −0.00899803 | + | 0.0161400i | ||||
\(551\) | − | 1.84975e46i | − | 0.465088i | ||||||
\(552\) | 2.16326e45 | + | 4.79910e46i | 0.0527406 | + | 1.17003i | ||||
\(553\) | −3.68297e46 | −0.870704 | ||||||||
\(554\) | −6.24220e45 | − | 3.48003e45i | −0.143111 | − | 0.0797843i | ||||
\(555\) | − | 3.15615e46i | − | 0.701741i | ||||||
\(556\) | 2.81438e46 | − | 1.73960e46i | 0.606893 | − | 0.375126i | ||||
\(557\) | 9.34319e46 | 1.95415 | 0.977073 | − | 0.212906i | \(-0.0682929\pi\) | ||||
0.977073 | + | 0.212906i | \(0.0682929\pi\) | |||||||
\(558\) | −2.17476e46 | + | 3.90091e46i | −0.441194 | + | 0.791378i | ||||
\(559\) | − | 2.46670e46i | − | 0.485418i | ||||||
\(560\) | −2.21639e46 | − | 1.10789e46i | −0.423107 | − | 0.211495i | ||||
\(561\) | −1.17008e45 | −0.0216694 | ||||||||
\(562\) | −6.53651e46 | − | 3.64411e46i | −1.17443 | − | 0.654747i | ||||
\(563\) | − | 6.62861e46i | − | 1.15553i | −0.816204 | − | 0.577763i | \(-0.803926\pi\) | ||
0.816204 | − | 0.577763i | \(-0.196074\pi\) | |||||||
\(564\) | 1.71686e46 | + | 2.77760e46i | 0.290396 | + | 0.469812i | ||||
\(565\) | 7.76532e46 | 1.27449 | ||||||||
\(566\) | −3.72991e46 | + | 6.69042e46i | −0.594045 | + | 1.06555i | ||||
\(567\) | − | 2.44657e45i | − | 0.0378134i | ||||||
\(568\) | 1.11440e47 | − | 5.02334e45i | 1.67156 | − | 0.0753478i | ||||
\(569\) | −8.92896e46 | −1.29985 | −0.649923 | − | 0.760000i | \(-0.725199\pi\) | ||||
−0.649923 | + | 0.760000i | \(0.725199\pi\) | |||||||
\(570\) | −2.58585e46 | − | 1.44161e46i | −0.365368 | − | 0.203693i | ||||
\(571\) | − | 1.56228e46i | − | 0.214262i | −0.994245 | − | 0.107131i | \(-0.965834\pi\) | ||
0.994245 | − | 0.107131i | \(-0.0341664\pi\) | |||||||
\(572\) | 4.24154e45 | − | 2.62174e45i | 0.0564665 | − | 0.0349025i | ||||
\(573\) | 5.03095e46 | 0.650161 | ||||||||
\(574\) | −8.43481e45 | + | 1.51297e46i | −0.105821 | + | 0.189814i | ||||
\(575\) | 4.19130e46i | 0.510500i | ||||||||
\(576\) | −4.94606e46 | + | 4.46810e45i | −0.584895 | + | 0.0528373i | ||||
\(577\) | −8.63671e46 | −0.991652 | −0.495826 | − | 0.868422i | \(-0.665135\pi\) | ||||
−0.495826 | + | 0.868422i | \(0.665135\pi\) | |||||||
\(578\) | −5.78758e46 | − | 3.22658e46i | −0.645244 | − | 0.359724i | ||||
\(579\) | 4.20878e46i | 0.455638i | ||||||||
\(580\) | −2.57195e46 | − | 4.16099e46i | −0.270388 | − | 0.437443i | ||||
\(581\) | 3.48959e46 | 0.356271 | ||||||||
\(582\) | −5.63223e45 | + | 1.01027e46i | −0.0558457 | + | 0.100172i | ||||
\(583\) | − | 3.54751e45i | − | 0.0341632i | ||||||
\(584\) | 8.19150e45 | + | 1.81725e47i | 0.0766205 | + | 1.69979i | ||||
\(585\) | 5.51727e46 | 0.501273 | ||||||||
\(586\) | 4.64279e46 | + | 2.58836e46i | 0.409751 | + | 0.228436i | ||||
\(587\) | 1.78766e47i | 1.53263i | 0.642463 | + | 0.766316i | \(0.277912\pi\) | ||||
−0.642463 | + | 0.766316i | \(0.722088\pi\) | |||||||
\(588\) | −4.52213e46 | + | 2.79518e46i | −0.376642 | + | 0.232806i | ||||
\(589\) | −1.46312e47 | −1.18392 | ||||||||
\(590\) | 1.73365e45 | − | 3.10968e45i | 0.0136294 | − | 0.0244473i | ||||
\(591\) | 1.27197e46i | 0.0971606i | ||||||||
\(592\) | 7.75489e46 | − | 1.55140e47i | 0.575581 | − | 1.15148i | ||||
\(593\) | 5.04091e46 | 0.363563 | 0.181781 | − | 0.983339i | \(-0.441814\pi\) | ||||
0.181781 | + | 0.983339i | \(0.441814\pi\) | |||||||
\(594\) | 8.38619e45 | + | 4.67530e45i | 0.0587753 | + | 0.0327673i | ||||
\(595\) | − | 3.54980e46i | − | 0.241777i | ||||||
\(596\) | 1.33209e46 | + | 2.15510e46i | 0.0881751 | + | 0.142653i | ||||
\(597\) | 9.00917e45 | 0.0579590 | ||||||||
\(598\) | 1.42815e47 | − | 2.56170e47i | 0.893006 | − | 1.60180i | ||||
\(599\) | 1.86805e45i | 0.0113535i | 0.999984 | + | 0.00567677i | \(0.00180698\pi\) | ||||
−0.999984 | + | 0.00567677i | \(0.998193\pi\) | |||||||
\(600\) | 3.04193e46 | − | 1.37120e45i | 0.179713 | − | 0.00810081i | ||||
\(601\) | −3.30892e47 | −1.90029 | −0.950146 | − | 0.311804i | \(-0.899067\pi\) | ||||
−0.950146 | + | 0.311804i | \(0.899067\pi\) | |||||||
\(602\) | 4.20859e46 | + | 2.34629e46i | 0.234961 | + | 0.130991i | ||||
\(603\) | − | 1.70336e47i | − | 0.924511i | ||||||
\(604\) | 1.72016e47 | − | 1.06325e47i | 0.907697 | − | 0.561057i | ||||
\(605\) | 1.64667e47 | 0.844821 | ||||||||
\(606\) | 8.78960e46 | − | 1.57661e47i | 0.438465 | − | 0.786483i | ||||
\(607\) | 1.36309e46i | 0.0661177i | 0.999453 | + | 0.0330588i | \(0.0105249\pi\) | ||||
−0.999453 | + | 0.0330588i | \(0.989475\pi\) | |||||||
\(608\) | −9.16859e46 | − | 1.34399e47i | −0.432456 | − | 0.633919i | ||||
\(609\) | 4.73227e46 | 0.217058 | ||||||||
\(610\) | 2.66373e47 | + | 1.48503e47i | 1.18818 | + | 0.662411i | ||||
\(611\) | − | 1.99357e47i | − | 0.864829i | ||||||
\(612\) | −3.74070e46 | − | 6.05184e46i | −0.157826 | − | 0.255337i | ||||
\(613\) | −1.74577e47 | −0.716406 | −0.358203 | − | 0.933644i | \(-0.616610\pi\) | ||||
−0.358203 | + | 0.933644i | \(0.616610\pi\) | |||||||
\(614\) | −1.97507e47 | + | 3.54272e47i | −0.788352 | + | 1.41408i | ||||
\(615\) | 5.47322e46i | 0.212503i | ||||||||
\(616\) | 4.38616e44 | + | 9.73049e45i | 0.00165658 | + | 0.0367504i | ||||
\(617\) | −1.96130e47 | −0.720603 | −0.360302 | − | 0.932836i | \(-0.617326\pi\) | ||||
−0.360302 | + | 0.932836i | \(0.617326\pi\) | |||||||
\(618\) | −8.99186e45 | − | 5.01297e45i | −0.0321400 | − | 0.0179180i | ||||
\(619\) | 2.85150e47i | 0.991590i | 0.868440 | + | 0.495795i | \(0.165123\pi\) | ||||
−0.868440 | + | 0.495795i | \(0.834877\pi\) | |||||||
\(620\) | −3.29129e47 | + | 2.03438e47i | −1.11355 | + | 0.688293i | ||||
\(621\) | 5.64736e47 | 1.85904 | ||||||||
\(622\) | 8.63978e46 | − | 1.54974e47i | 0.276736 | − | 0.496388i | ||||
\(623\) | − | 4.90617e46i | − | 0.152914i | ||||||
\(624\) | −1.90594e47 | − | 9.52707e46i | −0.578057 | − | 0.288949i | ||||
\(625\) | −2.17372e47 | −0.641568 | ||||||||
\(626\) | 5.06910e46 | + | 2.82602e46i | 0.145602 | + | 0.0811731i | ||||
\(627\) | 1.16378e46i | 0.0325328i | ||||||||
\(628\) | 1.47844e47 | + | 2.39187e47i | 0.402244 | + | 0.650765i | ||||
\(629\) | 2.48475e47 | 0.657993 | ||||||||
\(630\) | −5.24794e46 | + | 9.41334e46i | −0.135269 | + | 0.242636i | ||||
\(631\) | 5.99210e47i | 1.50342i | 0.659494 | + | 0.751710i | \(0.270770\pi\) | ||||
−0.659494 | + | 0.751710i | \(0.729230\pi\) | |||||||
\(632\) | −6.38850e47 | + | 2.87971e46i | −1.56030 | + | 0.0703328i | ||||
\(633\) | −5.07547e46 | −0.120674 | ||||||||
\(634\) | 2.92550e47 | + | 1.63097e47i | 0.677148 | + | 0.377510i | ||||
\(635\) | − | 2.49615e46i | − | 0.0562493i | ||||||
\(636\) | −1.28948e47 | + | 7.97039e46i | −0.282907 | + | 0.174867i | ||||
\(637\) | 3.24567e47 | 0.693321 | ||||||||
\(638\) | −9.36341e45 | + | 1.67953e46i | −0.0194752 | + | 0.0349331i | ||||
\(639\) | − | 4.85198e47i | − | 0.982662i | ||||||
\(640\) | −3.93120e47 | − | 1.74846e47i | −0.775292 | − | 0.344822i | ||||
\(641\) | −1.67263e47 | −0.321228 | −0.160614 | − | 0.987017i | \(-0.551347\pi\) | ||||
−0.160614 | + | 0.987017i | \(0.551347\pi\) | |||||||
\(642\) | −3.89100e47 | − | 2.16923e47i | −0.727723 | − | 0.405706i | ||||
\(643\) | − | 7.59156e47i | − | 1.38275i | −0.722495 | − | 0.691376i | \(-0.757005\pi\) | ||
0.722495 | − | 0.691376i | \(-0.242995\pi\) | |||||||
\(644\) | 3.01224e47 | + | 4.87331e47i | 0.534355 | + | 0.864498i | ||||
\(645\) | 1.52247e47 | 0.263047 | ||||||||
\(646\) | 1.13494e47 | − | 2.03577e47i | 0.190994 | − | 0.342590i | ||||
\(647\) | − | 3.30834e47i | − | 0.542298i | −0.962537 | − | 0.271149i | \(-0.912596\pi\) | ||
0.962537 | − | 0.271149i | \(-0.0874035\pi\) | |||||||
\(648\) | −1.91297e45 | − | 4.24384e46i | −0.00305445 | − | 0.0677616i | ||||
\(649\) | −1.39953e45 | −0.00217682 | ||||||||
\(650\) | −1.62375e47 | − | 9.05242e46i | −0.246032 | − | 0.137163i | ||||
\(651\) | − | 3.74316e47i | − | 0.552538i | ||||||
\(652\) | 5.84135e47 | − | 3.61060e47i | 0.840048 | − | 0.519242i | ||||
\(653\) | 6.86204e47 | 0.961455 | 0.480727 | − | 0.876870i | \(-0.340373\pi\) | ||||
0.480727 | + | 0.876870i | \(0.340373\pi\) | |||||||
\(654\) | −9.90332e46 | + | 1.77638e47i | −0.135194 | + | 0.242501i | ||||
\(655\) | 5.22058e47i | 0.694411i | ||||||||
\(656\) | −1.34481e47 | + | 2.69036e47i | −0.174299 | + | 0.348695i | ||||
\(657\) | 7.91207e47 | 0.999261 | ||||||||
\(658\) | 3.40134e47 | + | 1.89625e47i | 0.418610 | + | 0.233375i | ||||
\(659\) | 4.54026e47i | 0.544538i | 0.962221 | + | 0.272269i | \(0.0877741\pi\) | ||||
−0.962221 | + | 0.272269i | \(0.912226\pi\) | |||||||
\(660\) | 1.61816e46 | + | 2.61791e46i | 0.0189136 | + | 0.0305991i | ||||
\(661\) | −1.17028e48 | −1.33311 | −0.666555 | − | 0.745455i | \(-0.732232\pi\) | ||||
−0.666555 | + | 0.745455i | \(0.732232\pi\) | |||||||
\(662\) | −1.87462e47 | + | 3.36254e47i | −0.208126 | + | 0.373320i | ||||
\(663\) | − | 3.05257e47i | − | 0.330321i | ||||||
\(664\) | 6.05306e47 | − | 2.72851e46i | 0.638437 | − | 0.0287785i | ||||
\(665\) | −3.53069e47 | −0.362987 | ||||||||
\(666\) | −6.58904e47 | − | 3.67339e47i | −0.660329 | − | 0.368133i | ||||
\(667\) | 1.13102e48i | 1.10492i | ||||||||
\(668\) | 1.41996e48 | − | 8.77690e47i | 1.35231 | − | 0.835875i | ||||
\(669\) | −6.59322e47 | −0.612144 | ||||||||
\(670\) | 7.18584e47 | − | 1.28894e48i | 0.650438 | − | 1.16670i | ||||
\(671\) | − | 1.19883e47i | − | 0.105797i | ||||||
\(672\) | 3.43837e47 | − | 2.34563e47i | 0.295852 | − | 0.201828i | ||||
\(673\) | −1.22899e48 | −1.03108 | −0.515540 | − | 0.856866i | \(-0.672408\pi\) | ||||
−0.515540 | + | 0.856866i | \(0.672408\pi\) | |||||||
\(674\) | −6.95465e47 | − | 3.87722e47i | −0.568927 | − | 0.317177i | ||||
\(675\) | − | 3.57961e47i | − | 0.285543i | ||||||
\(676\) | 8.05357e45 | + | 1.30293e46i | 0.00626462 | + | 0.0101351i | ||||
\(677\) | −1.23253e47 | −0.0934955 | −0.0467477 | − | 0.998907i | \(-0.514886\pi\) | ||||
−0.0467477 | + | 0.998907i | \(0.514886\pi\) | |||||||
\(678\) | −6.35164e47 | + | 1.13931e48i | −0.469874 | + | 0.842822i | ||||
\(679\) | 1.37940e47i | 0.0995189i | ||||||||
\(680\) | −2.77559e46 | − | 6.15751e47i | −0.0195300 | − | 0.433265i | ||||
\(681\) | 8.76015e47 | 0.601189 | ||||||||
\(682\) | 1.32849e47 | + | 7.40634e46i | 0.0889250 | + | 0.0495757i | ||||
\(683\) | 1.80253e48i | 1.17687i | 0.808543 | + | 0.588437i | \(0.200257\pi\) | ||||
−0.808543 | + | 0.588437i | \(0.799743\pi\) | |||||||
\(684\) | −6.01926e47 | + | 3.72056e47i | −0.383344 | + | 0.236949i | ||||
\(685\) | −2.06795e48 | −1.28470 | ||||||||
\(686\) | −7.56650e47 | + | 1.35722e48i | −0.458549 | + | 0.822508i | ||||
\(687\) | 4.81121e47i | 0.284440i | ||||||||
\(688\) | 7.48370e47 | + | 3.74082e47i | 0.431631 | + | 0.215756i | ||||
\(689\) | 9.25498e47 | 0.520773 | ||||||||
\(690\) | 1.58111e48 | + | 8.81468e47i | 0.868014 | + | 0.483918i | ||||
\(691\) | 7.77101e47i | 0.416246i | 0.978103 | + | 0.208123i | \(0.0667355\pi\) | ||||
−0.978103 | + | 0.208123i | \(0.933265\pi\) | |||||||
\(692\) | 5.97438e47 | + | 9.66556e47i | 0.312241 | + | 0.505154i | ||||
\(693\) | 4.23653e46 | 0.0216046 | ||||||||
\(694\) | 5.69411e47 | − | 1.02136e48i | 0.283344 | − | 0.508241i | ||||
\(695\) | − | 1.24674e48i | − | 0.605390i | ||||||
\(696\) | 8.20863e47 | − | 3.70016e46i | 0.388968 | − | 0.0175333i | ||||
\(697\) | −4.30891e47 | −0.199256 | ||||||||
\(698\) | −2.16742e48 | − | 1.20834e48i | −0.978139 | − | 0.545313i | ||||
\(699\) | − | 4.77479e47i | − | 0.210301i | ||||||
\(700\) | 3.08897e47 | − | 1.90933e47i | 0.132785 | − | 0.0820754i | ||||
\(701\) | −1.17801e48 | −0.494244 | −0.247122 | − | 0.968984i | \(-0.579485\pi\) | ||||
−0.247122 | + | 0.968984i | \(0.579485\pi\) | |||||||
\(702\) | −1.21972e48 | + | 2.18784e48i | −0.499494 | + | 0.895952i | ||||
\(703\) | − | 2.47137e48i | − | 0.987864i | ||||||
\(704\) | 1.52165e46 | + | 1.68443e47i | 0.00593718 | + | 0.0657230i | ||||
\(705\) | 1.23045e48 | 0.468649 | ||||||||
\(706\) | −2.62124e48 | − | 1.46134e48i | −0.974600 | − | 0.543340i | ||||
\(707\) | − | 2.15268e48i | − | 0.781358i | ||||||
\(708\) | 3.14440e46 | + | 5.08712e46i | 0.0111422 | + | 0.0180263i | ||||
\(709\) | 2.19394e48 | 0.758993 | 0.379497 | − | 0.925193i | \(-0.376097\pi\) | ||||
0.379497 | + | 0.925193i | \(0.376097\pi\) | |||||||
\(710\) | 2.04687e48 | − | 3.67151e48i | 0.691350 | − | 1.24009i | ||||
\(711\) | 2.78147e48i | 0.917258i | ||||||||
\(712\) | −3.83613e46 | − | 8.51029e47i | −0.0123519 | − | 0.274021i | ||||
\(713\) | 8.94622e48 | 2.81266 | ||||||||
\(714\) | 5.20818e47 | + | 2.90356e47i | 0.159888 | + | 0.0891377i | ||||
\(715\) | − | 1.87896e47i | − | 0.0563267i | ||||||
\(716\) | −3.48221e48 | + | 2.15239e48i | −1.01938 | + | 0.630086i | ||||
\(717\) | −9.86311e47 | −0.281961 | ||||||||
\(718\) | 8.44615e46 | − | 1.51500e47i | 0.0235800 | − | 0.0422959i | ||||
\(719\) | − | 7.14040e48i | − | 1.94685i | −0.229014 | − | 0.973423i | \(-0.573550\pi\) | ||
0.229014 | − | 0.973423i | \(-0.426450\pi\) | |||||||
\(720\) | −8.36709e47 | + | 1.67388e48i | −0.222803 | + | 0.445730i | ||||
\(721\) | −1.22774e47 | −0.0319305 | ||||||||
\(722\) | 1.41365e48 | + | 7.88109e47i | 0.359094 | + | 0.200195i | ||||
\(723\) | − | 1.89983e48i | − | 0.471372i | ||||||
\(724\) | −3.21258e48 | − | 5.19742e48i | −0.778571 | − | 1.25960i | ||||
\(725\) | 7.16903e47 | 0.169713 | ||||||||
\(726\) | −1.34689e48 | + | 2.41595e48i | −0.311466 | + | 0.558682i | ||||
\(727\) | 6.95703e48i | 1.57159i | 0.618488 | + | 0.785794i | \(0.287745\pi\) | ||||
−0.618488 | + | 0.785794i | \(0.712255\pi\) | |||||||
\(728\) | −2.53855e48 | + | 1.14429e47i | −0.560212 | + | 0.0252524i | ||||
\(729\) | −3.22342e48 | −0.694942 | ||||||||
\(730\) | 5.98709e48 | + | 3.33780e48i | 1.26103 | + | 0.703027i | ||||
\(731\) | 1.19860e48i | 0.246649i | ||||||||
\(732\) | −4.35759e48 | + | 2.69347e48i | −0.876109 | + | 0.541532i | ||||
\(733\) | −4.98745e48 | −0.979740 | −0.489870 | − | 0.871796i | \(-0.662956\pi\) | ||||
−0.489870 | + | 0.871796i | \(0.662956\pi\) | |||||||
\(734\) | −2.85313e46 | + | 5.11772e46i | −0.00547631 | + | 0.00982298i | ||||
\(735\) | 2.00326e48i | 0.375710i | ||||||||
\(736\) | 5.60610e48 | + | 8.21775e48i | 1.02740 | + | 1.50602i | ||||
\(737\) | −5.80095e47 | −0.103885 | ||||||||
\(738\) | 1.14263e48 | + | 6.37019e47i | 0.199963 | + | 0.111479i | ||||
\(739\) | 2.78662e48i | 0.476565i | 0.971196 | + | 0.238282i | \(0.0765844\pi\) | ||||
−0.971196 | + | 0.238282i | \(0.923416\pi\) | |||||||
\(740\) | −3.43628e48 | − | 5.55934e48i | −0.574314 | − | 0.929145i | ||||
\(741\) | −3.03614e48 | −0.495920 | ||||||||
\(742\) | −8.80319e47 | + | 1.57905e48i | −0.140532 | + | 0.252074i | ||||
\(743\) | 4.04892e48i | 0.631728i | 0.948805 | + | 0.315864i | \(0.102294\pi\) | ||||
−0.948805 | + | 0.315864i | \(0.897706\pi\) | |||||||
\(744\) | −2.92678e47 | − | 6.49292e48i | −0.0446323 | − | 0.990148i | ||||
\(745\) | 9.54686e47 | 0.142300 | ||||||||
\(746\) | 6.60187e48 | + | 3.68055e48i | 0.961849 | + | 0.536231i | ||||
\(747\) | − | 2.63543e48i | − | 0.375319i | ||||||
\(748\) | −2.06101e47 | + | 1.27393e47i | −0.0286915 | + | 0.0177345i | ||||
\(749\) | −5.31273e48 | −0.722981 | ||||||||
\(750\) | 2.55402e48 | − | 4.58120e48i | 0.339768 | − | 0.609449i | ||||
\(751\) | 2.00455e48i | 0.260698i | 0.991468 | + | 0.130349i | \(0.0416098\pi\) | ||||
−0.991468 | + | 0.130349i | \(0.958390\pi\) | |||||||
\(752\) | 6.04826e48 | + | 3.02330e48i | 0.769001 | + | 0.384395i | ||||
\(753\) | 4.80077e48 | 0.596755 | ||||||||
\(754\) | −4.38167e48 | − | 2.44279e48i | −0.532509 | − | 0.296874i | ||||
\(755\) | − | 7.62014e48i | − | 0.905450i | ||||||
\(756\) | −2.57262e48 | − | 4.16208e48i | −0.298886 | − | 0.483548i | ||||
\(757\) | −7.07325e48 | −0.803506 | −0.401753 | − | 0.915748i | \(-0.631599\pi\) | ||||
−0.401753 | + | 0.915748i | \(0.631599\pi\) | |||||||
\(758\) | 7.47139e48 | − | 1.34016e49i | 0.829898 | − | 1.48861i | ||||
\(759\) | − | 7.11587e47i | − | 0.0772891i | ||||||
\(760\) | −6.12436e48 | + | 2.76064e47i | −0.650473 | + | 0.0293210i | ||||
\(761\) | 2.19853e48 | 0.228346 | 0.114173 | − | 0.993461i | \(-0.463578\pi\) | ||||
0.114173 | + | 0.993461i | \(0.463578\pi\) | |||||||
\(762\) | 3.66228e47 | + | 2.04173e47i | 0.0371978 | + | 0.0207378i | ||||
\(763\) | 2.42545e48i | 0.240921i | ||||||||
\(764\) | 8.86166e48 | − | 5.47748e48i | 0.860851 | − | 0.532101i | ||||
\(765\) | −2.68090e48 | −0.254705 | ||||||||
\(766\) | −1.45759e48 | + | 2.61451e48i | −0.135440 | + | 0.242942i | ||||
\(767\) | − | 3.65118e47i | − | 0.0331827i | ||||||
\(768\) | 5.78081e48 | − | 4.33760e48i | 0.513864 | − | 0.385575i | ||||
\(769\) | 7.00757e48 | 0.609284 | 0.304642 | − | 0.952467i | \(-0.401463\pi\) | ||||
0.304642 | + | 0.952467i | \(0.401463\pi\) | |||||||
\(770\) | 3.20580e47 | + | 1.78723e47i | 0.0272643 | + | 0.0151998i | ||||
\(771\) | 1.30664e49i | 1.08701i | ||||||||
\(772\) | 4.58234e48 | + | 7.41347e48i | 0.372901 | + | 0.603291i | ||||
\(773\) | −1.07194e49 | −0.853331 | −0.426665 | − | 0.904410i | \(-0.640312\pi\) | ||||
−0.426665 | + | 0.904410i | \(0.640312\pi\) | |||||||
\(774\) | 1.77198e48 | − | 3.17844e48i | 0.137995 | − | 0.247524i | ||||
\(775\) | − | 5.67061e48i | − | 0.432017i | ||||||
\(776\) | 1.07855e47 | + | 2.39272e48i | 0.00803883 | + | 0.178338i | ||||
\(777\) | 6.32259e48 | 0.461039 | ||||||||
\(778\) | 1.08252e47 | + | 6.03507e46i | 0.00772296 | + | 0.00430555i | ||||
\(779\) | 4.28571e48i | 0.299148i | ||||||||
\(780\) | −6.82978e48 | + | 4.22156e48i | −0.466443 | + | 0.288313i | ||||
\(781\) | −1.65239e48 | −0.110419 | ||||||||
\(782\) | −6.93955e48 | + | 1.24476e49i | −0.453750 | + | 0.813901i | ||||
\(783\) | − | 9.65955e48i | − | 0.618026i | ||||||
\(784\) | −4.92215e48 | + | 9.84702e48i | −0.308164 | + | 0.616498i | ||||
\(785\) | 1.05958e49 | 0.649154 | ||||||||
\(786\) | −7.65949e48 | − | 4.27017e48i | −0.459216 | − | 0.256013i | ||||
\(787\) | − | 3.30427e49i | − | 1.93868i | −0.245732 | − | 0.969338i | \(-0.579028\pi\) | ||
0.245732 | − | 0.969338i | \(-0.420972\pi\) | |||||||
\(788\) | 1.38487e48 | + | 2.24049e48i | 0.0795175 | + | 0.128646i | ||||
\(789\) | 2.53435e48 | 0.142416 | ||||||||
\(790\) | −1.17340e49 | + | 2.10475e49i | −0.645335 | + | 1.15755i | ||||
\(791\) | 1.55560e49i | 0.837331i | ||||||||
\(792\) | 7.34872e47 | − | 3.31254e46i | 0.0387154 | − | 0.00174515i | ||||
\(793\) | 3.12758e49 | 1.61274 | ||||||||
\(794\) | −2.21575e49 | − | 1.23528e49i | −1.11834 | − | 0.623473i | ||||
\(795\) | 5.71226e48i | 0.282206i | ||||||||
\(796\) | 1.58690e48 | − | 9.80880e47i | 0.0767410 | − | 0.0474344i | ||||
\(797\) | −3.23366e49 | −1.53074 | −0.765372 | − | 0.643589i | \(-0.777445\pi\) | ||||
−0.765372 | + | 0.643589i | \(0.777445\pi\) | |||||||
\(798\) | 2.88793e48 | − | 5.18013e48i | 0.133825 | − | 0.240045i | ||||
\(799\) | 9.68696e48i | 0.439433i | ||||||||
\(800\) | 5.20886e48 | − | 3.55346e48i | 0.231320 | − | 0.157805i | ||||
\(801\) | −3.70527e48 | −0.161090 | ||||||||
\(802\) | −1.74112e49 | − | 9.70676e48i | −0.741080 | − | 0.413152i | ||||
\(803\) | − | 2.69453e48i | − | 0.112284i | ||||||
\(804\) | 1.30333e49 | + | 2.10857e49i | 0.531743 | + | 0.860272i | ||||
\(805\) | 2.15883e49 | 0.862358 | ||||||||
\(806\) | −1.93221e49 | + | 3.46585e49i | −0.755717 | + | 1.35554i | ||||
\(807\) | 5.81530e48i | 0.222701i | ||||||||
\(808\) | −1.68318e48 | − | 3.73406e49i | −0.0631157 | − | 1.40019i | ||||
\(809\) | 1.13694e49 | 0.417457 | 0.208729 | − | 0.977974i | \(-0.433067\pi\) | ||||
0.208729 | + | 0.977974i | \(0.433067\pi\) | |||||||
\(810\) | −1.39817e48 | − | 7.79481e47i | −0.0502707 | − | 0.0280260i | ||||
\(811\) | 1.72063e49i | 0.605807i | 0.953021 | + | 0.302903i | \(0.0979560\pi\) | ||||
−0.953021 | + | 0.302903i | \(0.902044\pi\) | |||||||
\(812\) | 8.33556e48 | − | 5.15229e48i | 0.287397 | − | 0.177643i | ||||
\(813\) | 5.67769e48 | 0.191704 | ||||||||
\(814\) | −1.25101e48 | + | 2.24396e48i | −0.0413661 | + | 0.0741993i | ||||
\(815\) | − | 2.58766e49i | − | 0.837968i | ||||||
\(816\) | 9.26117e48 | + | 4.62931e48i | 0.293720 | + | 0.146819i | ||||
\(817\) | 1.19215e49 | 0.370301 | ||||||||
\(818\) | 1.31170e49 | + | 7.31275e48i | 0.399052 | + | 0.222472i | ||||
\(819\) | 1.10525e49i | 0.329333i | ||||||||
\(820\) | 5.95901e48 | + | 9.64070e48i | 0.173916 | + | 0.281367i | ||||
\(821\) | −3.14575e49 | −0.899270 | −0.449635 | − | 0.893212i | \(-0.648446\pi\) | ||||
−0.449635 | + | 0.893212i | \(0.648446\pi\) | |||||||
\(822\) | 1.69148e49 | − | 3.03404e49i | 0.473638 | − | 0.849574i | ||||
\(823\) | − | 6.03104e49i | − | 1.65423i | −0.562036 | − | 0.827113i | \(-0.689982\pi\) | ||
0.562036 | − | 0.827113i | \(-0.310018\pi\) | |||||||
\(824\) | −2.12964e48 | + | 9.59967e46i | −0.0572195 | + | 0.00257925i | ||||
\(825\) | −4.51044e47 | −0.0118714 | ||||||||
\(826\) | 6.22950e47 | + | 3.47295e47i | 0.0160617 | + | 0.00895442i | ||||
\(827\) | 4.07466e49i | 1.02919i | 0.857432 | + | 0.514597i | \(0.172058\pi\) | ||||
−0.857432 | + | 0.514597i | \(0.827942\pi\) | |||||||
\(828\) | 3.68045e49 | − | 2.27492e49i | 0.910721 | − | 0.562926i | ||||
\(829\) | 1.59125e49 | 0.385755 | 0.192878 | − | 0.981223i | \(-0.438218\pi\) | ||||
0.192878 | + | 0.981223i | \(0.438218\pi\) | |||||||
\(830\) | 1.11179e49 | − | 1.99424e49i | 0.264055 | − | 0.473641i | ||||
\(831\) | − | 4.52364e48i | − | 0.105262i | ||||||
\(832\) | −4.39444e49 | + | 3.96978e48i | −1.00186 | + | 0.0905045i | ||||
\(833\) | −1.57711e49 | −0.352287 | ||||||||
\(834\) | 1.82919e49 | + | 1.01977e49i | 0.400346 | + | 0.223193i | ||||
\(835\) | − | 6.29027e49i | − | 1.34896i | ||||||
\(836\) | 1.26707e48 | + | 2.04991e48i | 0.0266253 | + | 0.0430753i | ||||
\(837\) | −7.64058e49 | −1.57323 | ||||||||
\(838\) | 3.27739e49 | − | 5.87873e49i | 0.661272 | − | 1.18614i | ||||
\(839\) | 9.09030e49i | 1.79732i | 0.438649 | + | 0.898658i | \(0.355457\pi\) | ||||
−0.438649 | + | 0.898658i | \(0.644543\pi\) | |||||||
\(840\) | −7.06265e47 | − | 1.56682e49i | −0.0136842 | − | 0.303578i | ||||
\(841\) | −3.33206e49 | −0.632676 | ||||||||
\(842\) | 4.29427e49 | + | 2.39406e49i | 0.799068 | + | 0.445481i | ||||
\(843\) | − | 4.73692e49i | − | 0.863829i | ||||||
\(844\) | −8.94008e48 | + | 5.52595e48i | −0.159779 | + | 0.0987610i | ||||
\(845\) | 5.77187e47 | 0.0101100 | ||||||||
\(846\) | 1.43210e49 | − | 2.56878e49i | 0.245853 | − | 0.440992i | ||||
\(847\) | 3.29871e49i | 0.555042i | ||||||||
\(848\) | −1.40354e49 | + | 2.80786e49i | −0.231471 | + | 0.463069i | ||||
\(849\) | −4.84846e49 | −0.783742 | ||||||||
\(850\) | 7.88999e48 | + | 4.39867e48i | 0.125013 | + | 0.0696947i | ||||
\(851\) | 1.51111e50i | 2.34689i | ||||||||
\(852\) | 3.71251e49 | + | 6.00622e49i | 0.565189 | + | 0.914383i | ||||
\(853\) | 1.02853e50 | 1.53491 | 0.767457 | − | 0.641100i | \(-0.221522\pi\) | ||||
0.767457 | + | 0.641100i | \(0.221522\pi\) | |||||||
\(854\) | −2.97490e49 | + | 5.33614e49i | −0.435200 | + | 0.780627i | ||||
\(855\) | 2.66647e49i | 0.382395i | ||||||||
\(856\) | −9.21549e49 | + | 4.15402e48i | −1.29558 | + | 0.0584002i | ||||
\(857\) | −4.17170e49 | −0.574961 | −0.287481 | − | 0.957786i | \(-0.592818\pi\) | ||||
−0.287481 | + | 0.957786i | \(0.592818\pi\) | |||||||
\(858\) | 2.75676e48 | + | 1.53689e48i | 0.0372490 | + | 0.0207663i | ||||
\(859\) | 5.60765e49i | 0.742844i | 0.928464 | + | 0.371422i | \(0.121130\pi\) | ||||
−0.928464 | + | 0.371422i | \(0.878870\pi\) | |||||||
\(860\) | 2.68173e49 | − | 1.65760e49i | 0.348290 | − | 0.215281i | ||||
\(861\) | −1.09643e49 | −0.139613 | ||||||||
\(862\) | −3.74492e49 | + | 6.71733e49i | −0.467540 | + | 0.838636i | ||||
\(863\) | − | 1.10970e50i | − | 1.35838i | −0.733962 | − | 0.679190i | \(-0.762331\pi\) | ||
0.733962 | − | 0.679190i | \(-0.237669\pi\) | |||||||
\(864\) | −4.78792e49 | − | 7.01842e49i | −0.574664 | − | 0.842376i | ||||
\(865\) | 4.28175e49 | 0.503903 | ||||||||
\(866\) | −3.50867e49 | − | 1.95608e49i | −0.404891 | − | 0.225727i | ||||
\(867\) | − | 4.19418e49i | − | 0.474595i | ||||||
\(868\) | −4.07540e49 | − | 6.59332e49i | −0.452204 | − | 0.731592i | ||||
\(869\) | 9.47256e48 | 0.103070 | ||||||||
\(870\) | 1.50771e49 | − | 2.70441e49i | 0.160876 | − | 0.288566i | ||||
\(871\) | − | 1.51339e50i | − | 1.58359i | ||||||
\(872\) | 1.89645e48 | + | 4.20720e49i | 0.0194609 | + | 0.431730i | ||||
\(873\) | 1.04176e49 | 0.104840 | ||||||||
\(874\) | 1.23806e50 | + | 6.90219e49i | 1.22193 | + | 0.681228i | ||||
\(875\) | − | 6.25511e49i | − | 0.605478i | ||||||
\(876\) | −9.79428e49 | + | 6.05394e49i | −0.929828 | + | 0.574736i | ||||
\(877\) | 1.99502e50 | 1.85761 | 0.928804 | − | 0.370570i | \(-0.120838\pi\) | ||||
0.928804 | + | 0.370570i | \(0.120838\pi\) | |||||||
\(878\) | 8.49131e49 | − | 1.52310e50i | 0.775475 | − | 1.39099i | ||||
\(879\) | 3.36457e49i | 0.301383i | ||||||||
\(880\) | 5.70055e48 | + | 2.84949e48i | 0.0500854 | + | 0.0250358i | ||||
\(881\) | −5.46277e49 | −0.470785 | −0.235392 | − | 0.971900i | \(-0.575637\pi\) | ||||
−0.235392 | + | 0.971900i | \(0.575637\pi\) | |||||||
\(882\) | 4.18217e49 | + | 2.33156e49i | 0.353538 | + | 0.197097i | ||||
\(883\) | − | 1.49088e50i | − | 1.23626i | −0.786075 | − | 0.618131i | \(-0.787890\pi\) | ||
0.786075 | − | 0.618131i | \(-0.212110\pi\) | |||||||
\(884\) | −3.32351e49 | − | 5.37689e49i | −0.270339 | − | 0.437364i | ||||
\(885\) | 2.25354e48 | 0.0179817 | ||||||||
\(886\) | −8.98572e49 | + | 1.61179e50i | −0.703363 | + | 1.26164i | ||||
\(887\) | 4.46950e49i | 0.343208i | 0.985166 | + | 0.171604i | \(0.0548950\pi\) | ||||
−0.985166 | + | 0.171604i | \(0.945105\pi\) | |||||||
\(888\) | 1.09672e50 | − | 4.94363e48i | 0.826183 | − | 0.0372414i | ||||
\(889\) | 5.00044e48 | 0.0369554 | ||||||||
\(890\) | −2.80379e49 | − | 1.56312e49i | −0.203290 | − | 0.113334i | ||||
\(891\) | 6.29256e47i | 0.00447617i | ||||||||
\(892\) | −1.16135e50 | + | 7.17842e49i | −0.810514 | + | 0.500987i | ||||
\(893\) | 9.63481e49 | 0.659733 | ||||||||
\(894\) | −7.80885e48 | + | 1.40069e49i | −0.0524625 | + | 0.0941031i | ||||
\(895\) | 1.54259e50i | 1.01685i | ||||||||
\(896\) | 3.50262e49 | − | 7.87522e49i | 0.226546 | − | 0.509362i | ||||
\(897\) | 1.85643e50 | 1.17817 | ||||||||
\(898\) | −2.73915e50 | − | 1.52708e50i | −1.70576 | − | 0.950964i | ||||
\(899\) | − | 1.53021e50i | − | 0.935052i | ||||||
\(900\) | −1.44197e49 | − | 2.33287e49i | −0.0864638 | − | 0.139884i | ||||
\(901\) | −4.49710e49 | −0.264613 | ||||||||
\(902\) | 2.16943e48 | − | 3.89135e48i | 0.0125266 | − | 0.0224693i | ||||
\(903\) | 3.04991e49i | 0.172820i | ||||||||
\(904\) | 1.21632e49 | + | 2.69835e50i | 0.0676370 | + | 1.50050i | ||||
\(905\) | −2.30241e50 | −1.25648 | ||||||||
\(906\) | 1.11801e50 | + | 6.23289e49i | 0.598777 | + | 0.333818i | ||||
\(907\) | 2.13798e50i | 1.12378i | 0.827213 | + | 0.561888i | \(0.189925\pi\) | ||||
−0.827213 | + | 0.561888i | \(0.810075\pi\) | |||||||
\(908\) | 1.54304e50 | − | 9.53768e49i | 0.796008 | − | 0.492021i | ||||
\(909\) | −1.62576e50 | −0.823135 | ||||||||
\(910\) | −4.66265e49 | + | 8.36349e49i | −0.231702 | + | 0.415608i | ||||
\(911\) | 1.58427e50i | 0.772710i | 0.922350 | + | 0.386355i | \(0.126266\pi\) | ||||
−0.922350 | + | 0.386355i | \(0.873734\pi\) | |||||||
\(912\) | 4.60438e49 | − | 9.21130e49i | 0.220424 | − | 0.440970i | ||||
\(913\) | −8.97520e48 | −0.0421736 | ||||||||
\(914\) | −8.72748e49 | − | 4.86557e49i | −0.402535 | − | 0.224413i | ||||
\(915\) | 1.93037e50i | 0.873940i | ||||||||
\(916\) | 5.23824e49 | + | 8.47461e49i | 0.232789 | + | 0.376614i | ||||
\(917\) | −1.04582e50 | −0.456223 | ||||||||
\(918\) | 5.92677e49 | − | 1.06310e50i | 0.253801 | − | 0.455247i | ||||
\(919\) | 3.60550e49i | 0.151566i | 0.997124 | + | 0.0757830i | \(0.0241456\pi\) | ||||
−0.997124 | + | 0.0757830i | \(0.975854\pi\) | |||||||
\(920\) | 3.74471e50 | − | 1.68798e49i | 1.54535 | − | 0.0696587i | ||||
\(921\) | −2.56737e50 | −1.04010 | ||||||||
\(922\) | −4.67180e49 | − | 2.60453e49i | −0.185806 | − | 0.103587i | ||||
\(923\) | − | 4.31085e50i | − | 1.68319i | ||||||
\(924\) | −5.24437e48 | + | 3.24160e48i | −0.0201034 | + | 0.0124261i | ||||
\(925\) | 9.57825e49 | 0.360476 | ||||||||
\(926\) | 3.12106e49 | − | 5.59831e49i | 0.115323 | − | 0.206857i | ||||
\(927\) | 9.27220e48i | 0.0336378i | ||||||||
\(928\) | 1.40561e50 | − | 9.58896e49i | 0.500666 | − | 0.341551i | ||||
\(929\) | −1.09796e50 | −0.383988 | −0.191994 | − | 0.981396i | \(-0.561495\pi\) | ||||
−0.191994 | + | 0.981396i | \(0.561495\pi\) | |||||||
\(930\) | −2.13915e50 | − | 1.19258e50i | −0.734567 | − | 0.409522i | ||||
\(931\) | 1.56862e50i | 0.528899i | ||||||||
\(932\) | −5.19858e49 | − | 8.41045e49i | −0.172113 | − | 0.278451i | ||||
\(933\) | 1.12307e50 | 0.365107 | ||||||||
\(934\) | −1.18696e49 | + | 2.12908e49i | −0.0378913 | + | 0.0679664i | ||||
\(935\) | 9.13007e48i | 0.0286205i | ||||||||
\(936\) | 8.64197e48 | + | 1.91718e50i | 0.0266026 | + | 0.590165i | ||||
\(937\) | −5.89876e50 | −1.78315 | −0.891575 | − | 0.452874i | \(-0.850399\pi\) | ||||
−0.891575 | + | 0.452874i | \(0.850399\pi\) | |||||||
\(938\) | 2.58208e50 | + | 1.43951e50i | 0.766517 | + | 0.427333i | ||||
\(939\) | 3.67351e49i | 0.107094i | ||||||||
\(940\) | 2.16735e50 | − | 1.33966e50i | 0.620518 | − | 0.383549i | ||||
\(941\) | 5.47279e50 | 1.53881 | 0.769405 | − | 0.638761i | \(-0.220553\pi\) | ||||
0.769405 | + | 0.638761i | \(0.220553\pi\) | |||||||
\(942\) | −8.66680e49 | + | 1.55458e50i | −0.239328 | + | 0.429287i | ||||
\(943\) | − | 2.62048e50i | − | 0.710694i | ||||||
\(944\) | 1.10773e49 | + | 5.53711e48i | 0.0295059 | + | 0.0147489i | ||||
\(945\) | −1.84376e50 | −0.482351 | ||||||||
\(946\) | −1.08245e49 | − | 6.03464e48i | −0.0278136 | − | 0.0155061i | ||||
\(947\) | 1.85227e50i | 0.467471i | 0.972300 | + | 0.233735i | \(0.0750949\pi\) | ||||
−0.972300 | + | 0.233735i | \(0.924905\pi\) | |||||||
\(948\) | −2.12825e50 | − | 3.44316e50i | −0.527572 | − | 0.853524i | ||||
\(949\) | 7.02965e50 | 1.71162 | ||||||||
\(950\) | 4.37499e49 | − | 7.84751e49i | 0.104635 | − | 0.187685i | ||||
\(951\) | 2.12008e50i | 0.498061i | ||||||||
\(952\) | 1.23351e50 | − | 5.56023e48i | 0.284652 | − | 0.0128311i | ||||
\(953\) | 3.27186e50 | 0.741677 | 0.370839 | − | 0.928697i | \(-0.379070\pi\) | ||||
0.370839 | + | 0.928697i | \(0.379070\pi\) | |||||||
\(954\) | 1.19254e50 | + | 6.64840e49i | 0.265552 | + | 0.148045i | ||||
\(955\) | − | 3.92562e50i | − | 0.858720i | ||||||
\(956\) | −1.73732e50 | + | 1.07385e50i | −0.373332 | + | 0.230760i | ||||
\(957\) | −1.21714e49 | −0.0256943 | ||||||||
\(958\) | 4.66205e49 | − | 8.36241e49i | 0.0966859 | − | 0.173428i | ||||
\(959\) | − | 4.14265e50i | − | 0.844038i | ||||||
\(960\) | −2.45019e49 | − | 2.71229e50i | −0.0490442 | − | 0.542906i | ||||
\(961\) | −7.01867e50 | −1.38025 | ||||||||
\(962\) | −5.85418e50 | − | 3.26371e50i | −1.13107 | − | 0.630572i | ||||
\(963\) | 4.01231e50i | 0.761637i | ||||||||
\(964\) | −2.06845e50 | − | 3.34642e50i | −0.385777 | − | 0.624123i | ||||
\(965\) | 3.28409e50 | 0.601798 | ||||||||
\(966\) | −1.76581e50 | + | 3.16737e50i | −0.317931 | + | 0.570280i | ||||
\(967\) | − | 2.96151e50i | − | 0.523918i | −0.965079 | − | 0.261959i | \(-0.915631\pi\) | ||
0.965079 | − | 0.261959i | \(-0.0843685\pi\) | |||||||
\(968\) | 2.57926e49 | + | 5.72196e50i | 0.0448346 | + | 0.994635i | ||||
\(969\) | 1.47529e50 | 0.251985 | ||||||||
\(970\) | 7.88305e49 | + | 4.39481e49i | 0.132305 | + | 0.0737599i | ||||
\(971\) | 8.75750e49i | 0.144429i | 0.997389 | + | 0.0722143i | \(0.0230066\pi\) | ||||
−0.997389 | + | 0.0722143i | \(0.976993\pi\) | |||||||
\(972\) | −5.12363e50 | + | 3.16697e50i | −0.830331 | + | 0.513236i | ||||
\(973\) | 2.49755e50 | 0.397738 | ||||||||
\(974\) | −3.66575e50 | + | 6.57533e50i | −0.573668 | + | 1.02900i | ||||
\(975\) | − | 1.17671e50i | − | 0.180964i | ||||||
\(976\) | −4.74305e50 | + | 9.48872e50i | −0.716822 | + | 1.43404i | ||||
\(977\) | 2.85606e50 | 0.424190 | 0.212095 | − | 0.977249i | \(-0.431971\pi\) | ||||
0.212095 | + | 0.977249i | \(0.431971\pi\) | |||||||
\(978\) | 3.79654e50 | + | 2.11658e50i | 0.554151 | + | 0.308939i | ||||
\(979\) | 1.26186e49i | 0.0181012i | ||||||||
\(980\) | 2.18106e50 | + | 3.52860e50i | 0.307486 | + | 0.497461i | ||||
\(981\) | 1.83176e50 | 0.253802 | ||||||||
\(982\) | 3.72997e50 | − | 6.69053e50i | 0.507938 | − | 0.911098i | ||||
\(983\) | − | 1.39848e50i | − | 0.187174i | −0.995611 | − | 0.0935869i | \(-0.970167\pi\) | ||
0.995611 | − | 0.0935869i | \(-0.0298333\pi\) | |||||||
\(984\) | −1.90187e50 | + | 8.57297e48i | −0.250187 | + | 0.0112776i | ||||
\(985\) | 9.92514e49 | 0.128328 | ||||||||
\(986\) | 2.12911e50 | + | 1.18698e50i | 0.270576 | + | 0.150846i | ||||
\(987\) | 2.46491e50i | 0.307900i | ||||||||
\(988\) | −5.34794e50 | + | 3.30562e50i | −0.656627 | + | 0.405868i | ||||
\(989\) | −7.28933e50 | −0.879732 | ||||||||
\(990\) | 1.34977e49 | − | 2.42110e49i | 0.0160125 | − | 0.0287220i | ||||
\(991\) | 1.13058e51i | 1.31841i | 0.751964 | + | 0.659205i | \(0.229107\pi\) | ||||
−0.751964 | + | 0.659205i | \(0.770893\pi\) | |||||||
\(992\) | −7.58475e50 | − | 1.11182e51i | −0.869446 | − | 1.27449i | ||||
\(993\) | −2.43679e50 | −0.274587 | ||||||||
\(994\) | 7.35499e50 | + | 4.10041e50i | 0.814730 | + | 0.454212i | ||||
\(995\) | − | 7.02981e49i | − | 0.0765511i | ||||||
\(996\) | 2.01651e50 | + | 3.26237e50i | 0.215869 | + | 0.349241i | ||||
\(997\) | 5.59246e49 | 0.0588552 | 0.0294276 | − | 0.999567i | \(-0.490632\pi\) | ||||
0.0294276 | + | 0.999567i | \(0.490632\pi\) | |||||||
\(998\) | 5.11683e50 | − | 9.17817e50i | 0.529398 | − | 0.949592i | ||||
\(999\) | − | 1.29057e51i | − | 1.31271i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4.35.b.a.3.14 | yes | 16 | |
4.3 | odd | 2 | inner | 4.35.b.a.3.13 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.35.b.a.3.13 | ✓ | 16 | 4.3 | odd | 2 | inner | |
4.35.b.a.3.14 | yes | 16 | 1.1 | even | 1 | trivial |