Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,33,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (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: | \(32.4333275711\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.9 | ||
Character | \(\chi\) | \(=\) | 5.3 |
Dual form | 5.33.c.a.2.9 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 24352.5 | − | 24352.5i | 0.371590 | − | 0.371590i | −0.496466 | − | 0.868056i | \(-0.665369\pi\) |
0.868056 | + | 0.496466i | \(0.165369\pi\) | |||||||
\(3\) | −2.67962e7 | − | 2.67962e7i | −0.622491 | − | 0.622491i | 0.323677 | − | 0.946168i | \(-0.395081\pi\) |
−0.946168 | + | 0.323677i | \(0.895081\pi\) | |||||||
\(4\) | 3.10888e9i | 0.723842i | ||||||||
\(5\) | −1.49880e11 | − | 2.86196e10i | −0.982253 | − | 0.187561i | ||||
\(6\) | −1.30511e12 | −0.462623 | ||||||||
\(7\) | 4.33877e13 | − | 4.33877e13i | 1.30556 | − | 1.30556i | 0.380979 | − | 0.924584i | \(-0.375587\pi\) |
0.924584 | − | 0.380979i | \(-0.124413\pi\) | |||||||
\(8\) | 1.80302e14 | + | 1.80302e14i | 0.640563 | + | 0.640563i | ||||
\(9\) | − | 4.16950e14i | − | 0.225011i | ||||||
\(10\) | −4.34691e15 | + | 2.95300e15i | −0.434691 | + | 0.295300i | ||||
\(11\) | 2.50521e16 | 0.545208 | 0.272604 | − | 0.962126i | \(-0.412115\pi\) | ||||
0.272604 | + | 0.962126i | \(0.412115\pi\) | |||||||
\(12\) | 8.33060e16 | − | 8.33060e16i | 0.450584 | − | 0.450584i | ||||
\(13\) | −7.52949e17 | − | 7.52949e17i | −1.13155 | − | 1.13155i | −0.989920 | − | 0.141626i | \(-0.954767\pi\) |
−0.141626 | − | 0.989920i | \(-0.545233\pi\) | |||||||
\(14\) | − | 2.11320e18i | − | 0.970269i | ||||||
\(15\) | 3.24931e18 | + | 4.78310e18i | 0.494688 | + | 0.728198i | ||||
\(16\) | −4.57088e18 | −0.247788 | ||||||||
\(17\) | −3.85049e19 | + | 3.85049e19i | −0.791287 | + | 0.791287i | −0.981703 | − | 0.190417i | \(-0.939016\pi\) |
0.190417 | + | 0.981703i | \(0.439016\pi\) | |||||||
\(18\) | −1.01538e19 | − | 1.01538e19i | −0.0836119 | − | 0.0836119i | ||||
\(19\) | 1.17007e20i | 0.405654i | 0.979215 | + | 0.202827i | \(0.0650129\pi\) | ||||
−0.979215 | + | 0.202827i | \(0.934987\pi\) | |||||||
\(20\) | 8.89746e19 | − | 4.65958e20i | 0.135765 | − | 0.710995i | ||||
\(21\) | −2.32525e21 | −1.62540 | ||||||||
\(22\) | 6.10083e20 | − | 6.10083e20i | 0.202594 | − | 0.202594i | ||||
\(23\) | 3.24732e21 | + | 3.24732e21i | 0.529518 | + | 0.529518i | 0.920428 | − | 0.390911i | \(-0.127840\pi\) |
−0.390911 | + | 0.920428i | \(0.627840\pi\) | |||||||
\(24\) | − | 9.66283e21i | − | 0.797488i | ||||||
\(25\) | 2.16449e22 | + | 8.57899e21i | 0.929642 | + | 0.368465i | ||||
\(26\) | −3.66725e22 | −0.840943 | ||||||||
\(27\) | −6.08265e22 | + | 6.08265e22i | −0.762558 | + | 0.762558i | ||||
\(28\) | 1.34887e23 | + | 1.34887e23i | 0.945021 | + | 0.945021i | ||||
\(29\) | − | 2.76596e23i | − | 1.10529i | −0.833415 | − | 0.552647i | \(-0.813618\pi\) | ||
0.833415 | − | 0.552647i | \(-0.186382\pi\) | |||||||
\(30\) | 1.95610e23 | + | 3.73517e22i | 0.454413 | + | 0.0867700i | ||||
\(31\) | −7.57486e23 | −1.04133 | −0.520664 | − | 0.853762i | \(-0.674316\pi\) | ||||
−0.520664 | + | 0.853762i | \(0.674316\pi\) | |||||||
\(32\) | −8.85705e23 | + | 8.85705e23i | −0.732638 | + | 0.732638i | ||||
\(33\) | −6.71302e23 | − | 6.71302e23i | −0.339387 | − | 0.339387i | ||||
\(34\) | 1.87539e24i | 0.588069i | ||||||||
\(35\) | −7.74468e24 | + | 5.26121e24i | −1.52727 | + | 1.03752i | ||||
\(36\) | 1.29625e24 | 0.162872 | ||||||||
\(37\) | −6.38692e24 | + | 6.38692e24i | −0.517683 | + | 0.517683i | −0.916870 | − | 0.399187i | \(-0.869293\pi\) |
0.399187 | + | 0.916870i | \(0.369293\pi\) | |||||||
\(38\) | 2.84943e24 | + | 2.84943e24i | 0.150737 | + | 0.150737i | ||||
\(39\) | 4.03523e25i | 1.40875i | ||||||||
\(40\) | −2.18635e25 | − | 3.21839e25i | −0.509050 | − | 0.749339i | ||||
\(41\) | −4.00127e25 | −0.627561 | −0.313781 | − | 0.949496i | \(-0.601596\pi\) | ||||
−0.313781 | + | 0.949496i | \(0.601596\pi\) | |||||||
\(42\) | −5.66257e25 | + | 5.66257e25i | −0.603983 | + | 0.603983i | ||||
\(43\) | −2.44781e24 | − | 2.44781e24i | −0.0179177 | − | 0.0179177i | 0.698091 | − | 0.716009i | \(-0.254033\pi\) |
−0.716009 | + | 0.698091i | \(0.754033\pi\) | |||||||
\(44\) | 7.78840e25i | 0.394644i | ||||||||
\(45\) | −1.19329e25 | + | 6.24925e25i | −0.0422033 | + | 0.221018i | ||||
\(46\) | 1.58161e26 | 0.393527 | ||||||||
\(47\) | −7.35501e26 | + | 7.35501e26i | −1.29723 | + | 1.29723i | −0.367017 | + | 0.930214i | \(0.619621\pi\) |
−0.930214 | + | 0.367017i | \(0.880379\pi\) | |||||||
\(48\) | 1.22482e26 | + | 1.22482e26i | 0.154246 | + | 0.154246i | ||||
\(49\) | − | 2.66055e27i | − | 2.40899i | ||||||
\(50\) | 7.36028e26 | − | 3.18188e26i | 0.482364 | − | 0.208528i | ||||
\(51\) | 2.06357e27 | 0.985137 | ||||||||
\(52\) | 2.34083e27 | − | 2.34083e27i | 0.819060 | − | 0.819060i | ||||
\(53\) | 4.27034e26 | + | 4.27034e26i | 0.110166 | + | 0.110166i | 0.760041 | − | 0.649875i | \(-0.225179\pi\) |
−0.649875 | + | 0.760041i | \(0.725179\pi\) | |||||||
\(54\) | 2.96256e27i | 0.566718i | ||||||||
\(55\) | −3.75481e27 | − | 7.16981e26i | −0.535532 | − | 0.102260i | ||||
\(56\) | 1.56458e28 | 1.67259 | ||||||||
\(57\) | 3.13535e27 | − | 3.13535e27i | 0.252516 | − | 0.252516i | ||||
\(58\) | −6.73582e27 | − | 6.73582e27i | −0.410717 | − | 0.410717i | ||||
\(59\) | − | 1.79592e28i | − | 0.833020i | −0.909131 | − | 0.416510i | \(-0.863253\pi\) | ||
0.909131 | − | 0.416510i | \(-0.136747\pi\) | |||||||
\(60\) | −1.48701e28 | + | 1.01017e28i | −0.527100 | + | 0.358076i | ||||
\(61\) | −1.42429e28 | −0.387544 | −0.193772 | − | 0.981047i | \(-0.562072\pi\) | ||||
−0.193772 | + | 0.981047i | \(0.562072\pi\) | |||||||
\(62\) | −1.84467e28 | + | 1.84467e28i | −0.386947 | + | 0.386947i | ||||
\(63\) | −1.80905e28 | − | 1.80905e28i | −0.293766 | − | 0.293766i | ||||
\(64\) | 2.35065e28i | 0.296694i | ||||||||
\(65\) | 9.13029e28 | + | 1.34401e29i | 0.899230 | + | 1.32370i | ||||
\(66\) | −3.26958e28 | −0.252225 | ||||||||
\(67\) | −1.58580e29 | + | 1.58580e29i | −0.961727 | + | 0.961727i | −0.999294 | − | 0.0375670i | \(-0.988039\pi\) |
0.0375670 | + | 0.999294i | \(0.488039\pi\) | |||||||
\(68\) | −1.19707e29 | − | 1.19707e29i | −0.572766 | − | 0.572766i | ||||
\(69\) | − | 1.74032e29i | − | 0.659239i | ||||||
\(70\) | −6.04788e28 | + | 3.16726e29i | −0.181985 | + | 0.953049i | ||||
\(71\) | 2.34998e29 | 0.563548 | 0.281774 | − | 0.959481i | \(-0.409077\pi\) | ||||
0.281774 | + | 0.959481i | \(0.409077\pi\) | |||||||
\(72\) | 7.51771e28 | − | 7.51771e28i | 0.144134 | − | 0.144134i | ||||
\(73\) | −1.18217e29 | − | 1.18217e29i | −0.181766 | − | 0.181766i | 0.610359 | − | 0.792125i | \(-0.291025\pi\) |
−0.792125 | + | 0.610359i | \(0.791025\pi\) | |||||||
\(74\) | 3.11075e29i | 0.384732i | ||||||||
\(75\) | −3.50117e29 | − | 8.09885e29i | −0.349327 | − | 0.808059i | ||||
\(76\) | −3.63762e29 | −0.293629 | ||||||||
\(77\) | 1.08695e30 | − | 1.08695e30i | 0.711803 | − | 0.711803i | ||||
\(78\) | 9.82681e29 | + | 9.82681e29i | 0.523479 | + | 0.523479i | ||||
\(79\) | − | 1.26158e30i | − | 0.548127i | −0.961712 | − | 0.274063i | \(-0.911632\pi\) | ||
0.961712 | − | 0.274063i | \(-0.0883678\pi\) | |||||||
\(80\) | 6.85083e29 | + | 1.30817e29i | 0.243391 | + | 0.0464754i | ||||
\(81\) | 2.48722e30 | 0.724359 | ||||||||
\(82\) | −9.74410e29 | + | 9.74410e29i | −0.233196 | + | 0.233196i | ||||
\(83\) | 7.76428e29 | + | 7.76428e29i | 0.153056 | + | 0.153056i | 0.779482 | − | 0.626425i | \(-0.215483\pi\) |
−0.626425 | + | 0.779482i | \(0.715483\pi\) | |||||||
\(84\) | − | 7.22891e30i | − | 1.17653i | ||||||
\(85\) | 6.87311e30 | − | 4.66912e30i | 0.925658 | − | 0.628829i | ||||
\(86\) | −1.19221e29 | −0.0133161 | ||||||||
\(87\) | −7.41172e30 | + | 7.41172e30i | −0.688035 | + | 0.688035i | ||||
\(88\) | 4.51696e30 | + | 4.51696e30i | 0.349240 | + | 0.349240i | ||||
\(89\) | 4.78198e30i | 0.308580i | 0.988026 | + | 0.154290i | \(0.0493090\pi\) | ||||
−0.988026 | + | 0.154290i | \(0.950691\pi\) | |||||||
\(90\) | 1.23125e30 | + | 1.81245e30i | 0.0664457 | + | 0.0978104i | ||||
\(91\) | −6.53375e31 | −2.95461 | ||||||||
\(92\) | −1.00955e31 | + | 1.00955e31i | −0.383287 | + | 0.383287i | ||||
\(93\) | 2.02977e31 | + | 2.02977e31i | 0.648217 | + | 0.648217i | ||||
\(94\) | 3.58226e31i | 0.964077i | ||||||||
\(95\) | 3.34870e30 | − | 1.75371e31i | 0.0760850 | − | 0.398455i | ||||
\(96\) | 4.74670e31 | 0.912121 | ||||||||
\(97\) | 1.96023e31 | − | 1.96023e31i | 0.319124 | − | 0.319124i | −0.529306 | − | 0.848431i | \(-0.677548\pi\) |
0.848431 | + | 0.529306i | \(0.177548\pi\) | |||||||
\(98\) | −6.47912e31 | − | 6.47912e31i | −0.895157 | − | 0.895157i | ||||
\(99\) | − | 1.04455e31i | − | 0.122678i | ||||||
\(100\) | −2.66710e31 | + | 6.72913e31i | −0.266710 | + | 0.672913i | ||||
\(101\) | −4.31365e31 | −0.367877 | −0.183939 | − | 0.982938i | \(-0.558885\pi\) | ||||
−0.183939 | + | 0.982938i | \(0.558885\pi\) | |||||||
\(102\) | 5.02532e31 | − | 5.02532e31i | 0.366067 | − | 0.366067i | ||||
\(103\) | 1.33235e32 | + | 1.33235e32i | 0.830273 | + | 0.830273i | 0.987554 | − | 0.157281i | \(-0.0502727\pi\) |
−0.157281 | + | 0.987554i | \(0.550273\pi\) | |||||||
\(104\) | − | 2.71517e32i | − | 1.44965i | ||||||
\(105\) | 3.48508e32 | + | 6.65476e31i | 1.59655 | + | 0.304862i | ||||
\(106\) | 2.07987e31 | 0.0818733 | ||||||||
\(107\) | −1.32243e32 | + | 1.32243e32i | −0.447951 | + | 0.447951i | −0.894673 | − | 0.446722i | \(-0.852591\pi\) |
0.446722 | + | 0.894673i | \(0.352591\pi\) | |||||||
\(108\) | −1.89102e32 | − | 1.89102e32i | −0.551971 | − | 0.551971i | ||||
\(109\) | − | 3.98070e32i | − | 1.00262i | −0.865269 | − | 0.501309i | \(-0.832852\pi\) | ||
0.865269 | − | 0.501309i | \(-0.167148\pi\) | |||||||
\(110\) | −1.08900e32 | + | 7.39789e31i | −0.236997 | + | 0.161000i | ||||
\(111\) | 3.42290e32 | 0.644506 | ||||||||
\(112\) | −1.98320e32 | + | 1.98320e32i | −0.323503 | + | 0.323503i | ||||
\(113\) | 4.64159e31 | + | 4.64159e31i | 0.0656768 | + | 0.0656768i | 0.739182 | − | 0.673505i | \(-0.235212\pi\) |
−0.673505 | + | 0.739182i | \(0.735212\pi\) | |||||||
\(114\) | − | 1.52708e32i | − | 0.187665i | ||||||
\(115\) | −3.93772e32 | − | 5.79646e32i | −0.420803 | − | 0.619437i | ||||
\(116\) | 8.59903e32 | 0.800058 | ||||||||
\(117\) | −3.13942e32 | + | 3.13942e32i | −0.254610 | + | 0.254610i | ||||
\(118\) | −4.37353e32 | − | 4.37353e32i | −0.309542 | − | 0.309542i | ||||
\(119\) | 3.34128e33i | 2.06615i | ||||||||
\(120\) | −2.76546e32 | + | 1.44826e33i | −0.149578 | + | 0.783335i | ||||
\(121\) | −1.48377e33 | −0.702749 | ||||||||
\(122\) | −3.46850e32 | + | 3.46850e32i | −0.144007 | + | 0.144007i | ||||
\(123\) | 1.07219e33 | + | 1.07219e33i | 0.390651 | + | 0.390651i | ||||
\(124\) | − | 2.35493e33i | − | 0.753756i | ||||||
\(125\) | −2.99861e33 | − | 1.90529e33i | −0.844034 | − | 0.536290i | ||||
\(126\) | −8.81099e32 | −0.218321 | ||||||||
\(127\) | 6.53773e32 | − | 6.53773e32i | 0.142747 | − | 0.142747i | −0.632122 | − | 0.774869i | \(-0.717816\pi\) |
0.774869 | + | 0.632122i | \(0.217816\pi\) | |||||||
\(128\) | −3.23163e33 | − | 3.23163e33i | −0.622389 | − | 0.622389i | ||||
\(129\) | 1.31184e32i | 0.0223072i | ||||||||
\(130\) | 5.49646e33 | + | 1.04955e33i | 0.826018 | + | 0.157728i | ||||
\(131\) | 2.38170e33 | 0.316626 | 0.158313 | − | 0.987389i | \(-0.449394\pi\) | ||||
0.158313 | + | 0.987389i | \(0.449394\pi\) | |||||||
\(132\) | 2.08699e33 | − | 2.08699e33i | 0.245662 | − | 0.245662i | ||||
\(133\) | 5.07668e33 | + | 5.07668e33i | 0.529607 | + | 0.529607i | ||||
\(134\) | 7.72365e33i | 0.714737i | ||||||||
\(135\) | 1.08575e34 | − | 7.37585e33i | 0.892051 | − | 0.605998i | ||||
\(136\) | −1.38851e34 | −1.01374 | ||||||||
\(137\) | 1.70613e34 | − | 1.70613e34i | 1.10785 | − | 1.10785i | 0.114422 | − | 0.993432i | \(-0.463498\pi\) |
0.993432 | − | 0.114422i | \(-0.0365017\pi\) | |||||||
\(138\) | −4.23811e33 | − | 4.23811e33i | −0.244967 | − | 0.244967i | ||||
\(139\) | 1.73904e34i | 0.895517i | 0.894154 | + | 0.447759i | \(0.147778\pi\) | ||||
−0.894154 | + | 0.447759i | \(0.852222\pi\) | |||||||
\(140\) | −1.63564e34 | − | 2.40772e34i | −0.751000 | − | 1.10550i | ||||
\(141\) | 3.94172e34 | 1.61503 | ||||||||
\(142\) | 5.72280e33 | − | 5.72280e33i | 0.209409 | − | 0.209409i | ||||
\(143\) | −1.88630e34 | − | 1.88630e34i | −0.616928 | − | 0.616928i | ||||
\(144\) | 1.90583e33i | 0.0557551i | ||||||||
\(145\) | −7.91606e33 | + | 4.14562e34i | −0.207310 | + | 1.08568i | ||||
\(146\) | −5.75775e33 | −0.135085 | ||||||||
\(147\) | −7.12927e34 | + | 7.12927e34i | −1.49957 | + | 1.49957i | ||||
\(148\) | −1.98561e34 | − | 1.98561e34i | −0.374721 | − | 0.374721i | ||||
\(149\) | 2.36243e34i | 0.400294i | 0.979766 | + | 0.200147i | \(0.0641419\pi\) | ||||
−0.979766 | + | 0.200147i | \(0.935858\pi\) | |||||||
\(150\) | −2.82490e34 | − | 1.11965e34i | −0.430073 | − | 0.170460i | ||||
\(151\) | 4.35905e34 | 0.596706 | 0.298353 | − | 0.954456i | \(-0.403563\pi\) | ||||
0.298353 | + | 0.954456i | \(0.403563\pi\) | |||||||
\(152\) | −2.10967e34 | + | 2.10967e34i | −0.259847 | + | 0.259847i | ||||
\(153\) | 1.60546e34 | + | 1.60546e34i | 0.178048 | + | 0.178048i | ||||
\(154\) | − | 5.29402e34i | − | 0.528998i | ||||||
\(155\) | 1.13532e35 | + | 2.16789e34i | 1.02285 | + | 0.195313i | ||||
\(156\) | −1.25450e35 | −1.01971 | ||||||||
\(157\) | −1.03876e35 | + | 1.03876e35i | −0.762292 | + | 0.762292i | −0.976736 | − | 0.214444i | \(-0.931206\pi\) |
0.214444 | + | 0.976736i | \(0.431206\pi\) | |||||||
\(158\) | −3.07226e34 | − | 3.07226e34i | −0.203678 | − | 0.203678i | ||||
\(159\) | − | 2.28857e34i | − | 0.137155i | ||||||
\(160\) | 1.58098e35 | − | 1.07401e35i | 0.857050 | − | 0.582222i | ||||
\(161\) | 2.81788e35 | 1.38264 | ||||||||
\(162\) | 6.05701e34 | − | 6.05701e34i | 0.269165 | − | 0.269165i | ||||
\(163\) | −9.01603e34 | − | 9.01603e34i | −0.363089 | − | 0.363089i | 0.501860 | − | 0.864949i | \(-0.332649\pi\) |
−0.864949 | + | 0.501860i | \(0.832649\pi\) | |||||||
\(164\) | − | 1.24394e35i | − | 0.454255i | ||||||
\(165\) | 8.14023e34 | + | 1.19827e35i | 0.269708 | + | 0.397019i | ||||
\(166\) | 3.78160e34 | 0.113749 | ||||||||
\(167\) | 9.95084e34 | − | 9.95084e34i | 0.271892 | − | 0.271892i | −0.557970 | − | 0.829861i | \(-0.688419\pi\) |
0.829861 | + | 0.557970i | \(0.188419\pi\) | |||||||
\(168\) | −4.19248e35 | − | 4.19248e35i | −1.04117 | − | 1.04117i | ||||
\(169\) | 6.91086e35i | 1.56079i | ||||||||
\(170\) | 5.36727e34 | − | 2.81083e35i | 0.110299 | − | 0.577632i | ||||
\(171\) | 4.87863e34 | 0.0912767 | ||||||||
\(172\) | 7.60993e33 | − | 7.60993e33i | 0.0129696 | − | 0.0129696i | ||||
\(173\) | −1.52907e35 | − | 1.52907e35i | −0.237514 | − | 0.237514i | 0.578306 | − | 0.815820i | \(-0.303714\pi\) |
−0.815820 | + | 0.578306i | \(0.803714\pi\) | |||||||
\(174\) | 3.60988e35i | 0.511334i | ||||||||
\(175\) | 1.31134e36 | − | 5.66900e35i | 1.69476 | − | 0.732652i | ||||
\(176\) | −1.14510e35 | −0.135096 | ||||||||
\(177\) | −4.81239e35 | + | 4.81239e35i | −0.518547 | + | 0.518547i | ||||
\(178\) | 1.16453e35 | + | 1.16453e35i | 0.114665 | + | 0.114665i | ||||
\(179\) | − | 5.23045e35i | − | 0.470859i | −0.971891 | − | 0.235430i | \(-0.924350\pi\) | ||
0.971891 | − | 0.235430i | \(-0.0756497\pi\) | |||||||
\(180\) | −1.94281e35 | − | 3.70980e34i | −0.159982 | − | 0.0305485i | ||||
\(181\) | −1.48698e36 | −1.12059 | −0.560295 | − | 0.828293i | \(-0.689312\pi\) | ||||
−0.560295 | + | 0.828293i | \(0.689312\pi\) | |||||||
\(182\) | −1.59113e36 | + | 1.59113e36i | −1.09790 | + | 1.09790i | ||||
\(183\) | 3.81655e35 | + | 3.81655e35i | 0.241242 | + | 0.241242i | ||||
\(184\) | 1.17100e36i | 0.678378i | ||||||||
\(185\) | 1.14006e36 | − | 7.74480e35i | 0.605593 | − | 0.411399i | ||||
\(186\) | 9.88602e35 | 0.481742 | ||||||||
\(187\) | −9.64632e35 | + | 9.64632e35i | −0.431416 | + | 0.431416i | ||||
\(188\) | −2.28658e36 | − | 2.28658e36i | −0.938990 | − | 0.938990i | ||||
\(189\) | 5.27824e36i | 1.99113i | ||||||||
\(190\) | −3.45523e35 | − | 5.08621e35i | −0.119790 | − | 0.176334i | ||||
\(191\) | 2.19182e36 | 0.698667 | 0.349333 | − | 0.936998i | \(-0.386408\pi\) | ||||
0.349333 | + | 0.936998i | \(0.386408\pi\) | |||||||
\(192\) | 6.29885e35 | − | 6.29885e35i | 0.184689 | − | 0.184689i | ||||
\(193\) | −4.67348e36 | − | 4.67348e36i | −1.26103 | − | 1.26103i | −0.950597 | − | 0.310429i | \(-0.899527\pi\) |
−0.310429 | − | 0.950597i | \(-0.600473\pi\) | |||||||
\(194\) | − | 9.54733e35i | − | 0.237167i | ||||||
\(195\) | 1.15487e36 | − | 6.04800e36i | 0.264227 | − | 1.38375i | ||||
\(196\) | 8.27133e36 | 1.74373 | ||||||||
\(197\) | −3.28347e35 | + | 3.28347e35i | −0.0638078 | + | 0.0638078i | −0.738291 | − | 0.674483i | \(-0.764367\pi\) |
0.674483 | + | 0.738291i | \(0.264367\pi\) | |||||||
\(198\) | −2.54374e35 | − | 2.54374e35i | −0.0455859 | − | 0.0455859i | ||||
\(199\) | 8.00529e35i | 0.132351i | 0.997808 | + | 0.0661756i | \(0.0210797\pi\) | ||||
−0.997808 | + | 0.0661756i | \(0.978920\pi\) | |||||||
\(200\) | 2.35581e36 | + | 5.44944e36i | 0.359469 | + | 0.831518i | ||||
\(201\) | 8.49868e36 | 1.19733 | ||||||||
\(202\) | −1.05048e36 | + | 1.05048e36i | −0.136700 | + | 0.136700i | ||||
\(203\) | −1.20009e37 | − | 1.20009e37i | −1.44303 | − | 1.44303i | ||||
\(204\) | 6.41538e36i | 0.713083i | ||||||||
\(205\) | 5.99710e36 | + | 1.14515e36i | 0.616424 | + | 0.117706i | ||||
\(206\) | 6.48920e36 | 0.617043 | ||||||||
\(207\) | 1.35397e36 | − | 1.35397e36i | 0.119147 | − | 0.119147i | ||||
\(208\) | 3.44164e36 | + | 3.44164e36i | 0.280384 | + | 0.280384i | ||||
\(209\) | 2.93129e36i | 0.221166i | ||||||||
\(210\) | 1.01077e37 | − | 6.86645e36i | 0.706548 | − | 0.479980i | ||||
\(211\) | −2.71957e37 | −1.76190 | −0.880950 | − | 0.473209i | \(-0.843096\pi\) | ||||
−0.880950 | + | 0.473209i | \(0.843096\pi\) | |||||||
\(212\) | −1.32759e36 | + | 1.32759e36i | −0.0797428 | + | 0.0797428i | ||||
\(213\) | −6.29705e36 | − | 6.29705e36i | −0.350803 | − | 0.350803i | ||||
\(214\) | 6.44088e36i | 0.332909i | ||||||||
\(215\) | 2.96822e35 | + | 4.36932e35i | 0.0142390 | + | 0.0209604i | ||||
\(216\) | −2.19343e37 | −0.976932 | ||||||||
\(217\) | −3.28656e37 | + | 3.28656e37i | −1.35952 | + | 1.35952i | ||||
\(218\) | −9.69401e36 | − | 9.69401e36i | −0.372563 | − | 0.372563i | ||||
\(219\) | 6.33551e36i | 0.226296i | ||||||||
\(220\) | 2.22901e36 | − | 1.16732e37i | 0.0740199 | − | 0.387640i | ||||
\(221\) | 5.79846e37 | 1.79075 | ||||||||
\(222\) | 8.33563e36 | − | 8.33563e36i | 0.239492 | − | 0.239492i | ||||
\(223\) | 4.02241e36 | + | 4.02241e36i | 0.107549 | + | 0.107549i | 0.758834 | − | 0.651284i | \(-0.225769\pi\) |
−0.651284 | + | 0.758834i | \(0.725769\pi\) | |||||||
\(224\) | 7.68574e37i | 1.91301i | ||||||||
\(225\) | 3.57701e36 | − | 9.02485e36i | 0.0829087 | − | 0.209180i | ||||
\(226\) | 2.26069e36 | 0.0488097 | ||||||||
\(227\) | −8.76357e36 | + | 8.76357e36i | −0.176306 | + | 0.176306i | −0.789743 | − | 0.613437i | \(-0.789786\pi\) |
0.613437 | + | 0.789743i | \(0.289786\pi\) | |||||||
\(228\) | 9.74742e36 | + | 9.74742e36i | 0.182781 | + | 0.182781i | ||||
\(229\) | − | 1.01590e38i | − | 1.77616i | −0.459688 | − | 0.888081i | \(-0.652039\pi\) | ||
0.459688 | − | 0.888081i | \(-0.347961\pi\) | |||||||
\(230\) | −2.37052e37 | − | 4.52650e36i | −0.386543 | − | 0.0738104i | ||||
\(231\) | −5.82525e37 | −0.886181 | ||||||||
\(232\) | 4.98709e37 | − | 4.98709e37i | 0.708010 | − | 0.708010i | ||||
\(233\) | −1.12534e37 | − | 1.12534e37i | −0.149139 | − | 0.149139i | 0.628594 | − | 0.777733i | \(-0.283631\pi\) |
−0.777733 | + | 0.628594i | \(0.783631\pi\) | |||||||
\(234\) | 1.52906e37i | 0.189221i | ||||||||
\(235\) | 1.31286e38 | − | 8.91871e37i | 1.51752 | − | 1.03090i | ||||
\(236\) | 5.58330e37 | 0.602974 | ||||||||
\(237\) | −3.38055e37 | + | 3.38055e37i | −0.341204 | + | 0.341204i | ||||
\(238\) | 8.13687e37 | + | 8.13687e37i | 0.767761 | + | 0.767761i | ||||
\(239\) | − | 1.37020e38i | − | 1.20897i | −0.796616 | − | 0.604486i | \(-0.793379\pi\) | ||
0.796616 | − | 0.604486i | \(-0.206621\pi\) | |||||||
\(240\) | −1.48522e37 | − | 2.18630e37i | −0.122578 | − | 0.180439i | ||||
\(241\) | −1.53875e38 | −1.18821 | −0.594107 | − | 0.804386i | \(-0.702495\pi\) | ||||
−0.594107 | + | 0.804386i | \(0.702495\pi\) | |||||||
\(242\) | −3.61335e37 | + | 3.61335e37i | −0.261134 | + | 0.261134i | ||||
\(243\) | 4.60648e37 | + | 4.60648e37i | 0.311651 | + | 0.311651i | ||||
\(244\) | − | 4.42793e37i | − | 0.280520i | ||||||
\(245\) | −7.61439e37 | + | 3.98764e38i | −0.451833 | + | 2.36624i | ||||
\(246\) | 5.22209e37 | 0.290324 | ||||||||
\(247\) | 8.81007e37 | − | 8.81007e37i | 0.459016 | − | 0.459016i | ||||
\(248\) | −1.36576e38 | − | 1.36576e38i | −0.667036 | − | 0.667036i | ||||
\(249\) | − | 4.16106e37i | − | 0.190552i | ||||||
\(250\) | −1.19422e38 | + | 2.66252e37i | −0.512915 | + | 0.114354i | ||||
\(251\) | 2.10544e38 | 0.848329 | 0.424164 | − | 0.905585i | \(-0.360568\pi\) | ||||
0.424164 | + | 0.905585i | \(0.360568\pi\) | |||||||
\(252\) | 5.62411e37 | − | 5.62411e37i | 0.212640 | − | 0.212640i | ||||
\(253\) | 8.13525e37 | + | 8.13525e37i | 0.288697 | + | 0.288697i | ||||
\(254\) | − | 3.18421e37i | − | 0.106087i | ||||||
\(255\) | −3.09288e38 | − | 5.90585e37i | −0.967654 | − | 0.184773i | ||||
\(256\) | −2.58357e38 | −0.759242 | ||||||||
\(257\) | 6.67731e37 | − | 6.67731e37i | 0.184362 | − | 0.184362i | −0.608891 | − | 0.793254i | \(-0.708385\pi\) |
0.793254 | + | 0.608891i | \(0.208385\pi\) | |||||||
\(258\) | 3.19466e36 | + | 3.19466e36i | 0.00828913 | + | 0.00828913i | ||||
\(259\) | 5.54227e38i | 1.35174i | ||||||||
\(260\) | −4.17836e38 | + | 2.83849e38i | −0.958148 | + | 0.650900i | ||||
\(261\) | −1.15327e38 | −0.248704 | ||||||||
\(262\) | 5.80005e37 | − | 5.80005e37i | 0.117655 | − | 0.117655i | ||||
\(263\) | 5.11526e38 | + | 5.11526e38i | 0.976283 | + | 0.976283i | 0.999725 | − | 0.0234420i | \(-0.00746252\pi\) |
−0.0234420 | + | 0.999725i | \(0.507463\pi\) | |||||||
\(264\) | − | 2.42075e38i | − | 0.434797i | ||||||
\(265\) | −5.17822e37 | − | 7.62253e37i | −0.0875481 | − | 0.128874i | ||||
\(266\) | 2.47260e38 | 0.393594 | ||||||||
\(267\) | 1.28139e38 | − | 1.28139e38i | 0.192088 | − | 0.192088i | ||||
\(268\) | −4.93006e38 | − | 4.93006e38i | −0.696138 | − | 0.696138i | ||||
\(269\) | − | 1.16830e39i | − | 1.55424i | −0.629351 | − | 0.777121i | \(-0.716679\pi\) | ||
0.629351 | − | 0.777121i | \(-0.283321\pi\) | |||||||
\(270\) | 8.47871e37 | − | 4.44028e38i | 0.106294 | − | 0.556660i | ||||
\(271\) | −8.98338e38 | −1.06153 | −0.530763 | − | 0.847520i | \(-0.678095\pi\) | ||||
−0.530763 | + | 0.847520i | \(0.678095\pi\) | |||||||
\(272\) | 1.76002e38 | − | 1.76002e38i | 0.196071 | − | 0.196071i | ||||
\(273\) | 1.75079e39 | + | 1.75079e39i | 1.83922 | + | 1.83922i | ||||
\(274\) | − | 8.30971e38i | − | 0.823336i | ||||||
\(275\) | 5.42251e38 | + | 2.14922e38i | 0.506848 | + | 0.200890i | ||||
\(276\) | 5.41043e38 | 0.477185 | ||||||||
\(277\) | 1.20101e39 | − | 1.20101e39i | 0.999699 | − | 0.999699i | −0.000301289 | − | 1.00000i | \(-0.500096\pi\) |
1.00000 | 0.000301289i | \(9.59033e-5\pi\) | ||||||||
\(278\) | 4.23501e38 | + | 4.23501e38i | 0.332765 | + | 0.332765i | ||||
\(279\) | 3.15834e38i | 0.234310i | ||||||||
\(280\) | −2.34499e39 | − | 4.47776e38i | −1.64291 | − | 0.313713i | ||||
\(281\) | −1.45156e37 | −0.00960578 | −0.00480289 | − | 0.999988i | \(-0.501529\pi\) | ||||
−0.00480289 | + | 0.999988i | \(0.501529\pi\) | |||||||
\(282\) | 9.59909e38 | − | 9.59909e38i | 0.600129 | − | 0.600129i | ||||
\(283\) | 1.31575e38 | + | 1.31575e38i | 0.0777302 | + | 0.0777302i | 0.744903 | − | 0.667173i | \(-0.232496\pi\) |
−0.667173 | + | 0.744903i | \(0.732496\pi\) | |||||||
\(284\) | 7.30580e38i | 0.407919i | ||||||||
\(285\) | −5.59659e38 | + | 3.80194e38i | −0.295397 | + | 0.200672i | ||||
\(286\) | −9.18724e38 | −0.458488 | ||||||||
\(287\) | −1.73606e39 | + | 1.73606e39i | −0.819320 | + | 0.819320i | ||||
\(288\) | 3.69295e38 | + | 3.69295e38i | 0.164852 | + | 0.164852i | ||||
\(289\) | − | 5.97351e38i | − | 0.252269i | ||||||
\(290\) | 8.16787e38 | + | 1.20234e39i | 0.326393 | + | 0.480462i | ||||
\(291\) | −1.05054e39 | −0.397304 | ||||||||
\(292\) | 3.67521e38 | − | 3.67521e38i | 0.131570 | − | 0.131570i | ||||
\(293\) | −2.56802e39 | − | 2.56802e39i | −0.870394 | − | 0.870394i | 0.122121 | − | 0.992515i | \(-0.461030\pi\) |
−0.992515 | + | 0.122121i | \(0.961030\pi\) | |||||||
\(294\) | 3.47231e39i | 1.11445i | ||||||||
\(295\) | −5.13985e38 | + | 2.69173e39i | −0.156242 | + | 0.818236i | ||||
\(296\) | −2.30315e39 | −0.663217 | ||||||||
\(297\) | −1.52384e39 | + | 1.52384e39i | −0.415752 | + | 0.415752i | ||||
\(298\) | 5.75312e38 | + | 5.75312e38i | 0.148745 | + | 0.148745i | ||||
\(299\) | − | 4.89014e39i | − | 1.19835i | ||||||
\(300\) | 2.51783e39 | − | 1.08847e39i | 0.584907 | − | 0.252858i | ||||
\(301\) | −2.12409e38 | −0.0467853 | ||||||||
\(302\) | 1.06154e39 | − | 1.06154e39i | 0.221730 | − | 0.221730i | ||||
\(303\) | 1.15589e39 | + | 1.15589e39i | 0.229000 | + | 0.229000i | ||||
\(304\) | − | 5.34827e38i | − | 0.100516i | ||||||
\(305\) | 2.13472e39 | + | 4.07625e38i | 0.380666 | + | 0.0726881i | ||||
\(306\) | 7.81943e38 | 0.132322 | ||||||||
\(307\) | −2.47399e39 | + | 2.47399e39i | −0.397361 | + | 0.397361i | −0.877301 | − | 0.479940i | \(-0.840658\pi\) |
0.479940 | + | 0.877301i | \(0.340658\pi\) | |||||||
\(308\) | 3.37921e39 | + | 3.37921e39i | 0.515233 | + | 0.515233i | ||||
\(309\) | − | 7.14035e39i | − | 1.03367i | ||||||
\(310\) | 3.29273e39 | − | 2.23685e39i | 0.452656 | − | 0.307504i | ||||
\(311\) | 1.10049e40 | 1.43688 | 0.718438 | − | 0.695591i | \(-0.244858\pi\) | ||||
0.718438 | + | 0.695591i | \(0.244858\pi\) | |||||||
\(312\) | −7.27562e39 | + | 7.27562e39i | −0.902395 | + | 0.902395i | ||||
\(313\) | −1.02390e40 | − | 1.02390e40i | −1.20656 | − | 1.20656i | −0.972134 | − | 0.234426i | \(-0.924679\pi\) |
−0.234426 | − | 0.972134i | \(-0.575321\pi\) | |||||||
\(314\) | 5.05930e39i | 0.566521i | ||||||||
\(315\) | 2.19366e39 | + | 3.22914e39i | 0.233454 | + | 0.343652i | ||||
\(316\) | 3.92209e39 | 0.396757 | ||||||||
\(317\) | 6.52521e39 | − | 6.52521e39i | 0.627547 | − | 0.627547i | −0.319903 | − | 0.947450i | \(-0.603650\pi\) |
0.947450 | + | 0.319903i | \(0.103650\pi\) | |||||||
\(318\) | −5.57326e38 | − | 5.57326e38i | −0.0509654 | − | 0.0509654i | ||||
\(319\) | − | 6.92933e39i | − | 0.602615i | ||||||
\(320\) | 6.72747e38 | − | 3.52316e39i | 0.0556483 | − | 0.291429i | ||||
\(321\) | 7.08719e39 | 0.557691 | ||||||||
\(322\) | 6.86225e39 | − | 6.86225e39i | 0.513774 | − | 0.513774i | ||||
\(323\) | −4.50537e39 | − | 4.50537e39i | −0.320989 | − | 0.320989i | ||||
\(324\) | 7.73246e39i | 0.524321i | ||||||||
\(325\) | −9.83797e39 | − | 2.27571e40i | −0.634997 | − | 1.46887i | ||||
\(326\) | −4.39126e39 | −0.269841 | ||||||||
\(327\) | −1.06667e40 | + | 1.06667e40i | −0.624120 | + | 0.624120i | ||||
\(328\) | −7.21438e39 | − | 7.21438e39i | −0.401992 | − | 0.401992i | ||||
\(329\) | 6.38233e40i | 3.38723i | ||||||||
\(330\) | 4.90044e39 | + | 9.35739e38i | 0.247749 | + | 0.0473077i | ||||
\(331\) | −1.86125e40 | −0.896512 | −0.448256 | − | 0.893905i | \(-0.647955\pi\) | ||||
−0.448256 | + | 0.893905i | \(0.647955\pi\) | |||||||
\(332\) | −2.41382e39 | + | 2.41382e39i | −0.110789 | + | 0.110789i | ||||
\(333\) | 2.66303e39 | + | 2.66303e39i | 0.116484 | + | 0.116484i | ||||
\(334\) | − | 4.84656e39i | − | 0.202065i | ||||||
\(335\) | 2.83065e40 | − | 1.92295e40i | 1.12504 | − | 0.764277i | ||||
\(336\) | 1.06284e40 | 0.402755 | ||||||||
\(337\) | −1.88141e40 | + | 1.88141e40i | −0.679838 | + | 0.679838i | −0.959963 | − | 0.280125i | \(-0.909624\pi\) |
0.280125 | + | 0.959963i | \(0.409624\pi\) | |||||||
\(338\) | 1.68297e40 | + | 1.68297e40i | 0.579975 | + | 0.579975i | ||||
\(339\) | − | 2.48754e39i | − | 0.0817664i | ||||||
\(340\) | 1.45157e40 | + | 2.13677e40i | 0.455173 | + | 0.670030i | ||||
\(341\) | −1.89767e40 | −0.567740 | ||||||||
\(342\) | 1.18807e39 | − | 1.18807e39i | 0.0339175 | − | 0.0339175i | ||||
\(343\) | −6.75167e40 | − | 6.75167e40i | −1.83952 | − | 1.83952i | ||||
\(344\) | − | 8.82691e38i | − | 0.0229548i | ||||||
\(345\) | −4.98071e39 | + | 2.60839e40i | −0.123648 | + | 0.647540i | ||||
\(346\) | −7.44734e39 | −0.176516 | ||||||||
\(347\) | 4.92168e39 | − | 4.92168e39i | 0.111389 | − | 0.111389i | −0.649216 | − | 0.760604i | \(-0.724903\pi\) |
0.760604 | + | 0.649216i | \(0.224903\pi\) | |||||||
\(348\) | −2.30421e40 | − | 2.30421e40i | −0.498029 | − | 0.498029i | ||||
\(349\) | 7.61296e39i | 0.157162i | 0.996908 | + | 0.0785808i | \(0.0250389\pi\) | ||||
−0.996908 | + | 0.0785808i | \(0.974961\pi\) | |||||||
\(350\) | 1.81291e40 | − | 4.57400e40i | 0.357510 | − | 0.902002i | ||||
\(351\) | 9.15986e40 | 1.72574 | ||||||||
\(352\) | −2.21888e40 | + | 2.21888e40i | −0.399440 | + | 0.399440i | ||||
\(353\) | 3.37734e40 | + | 3.37734e40i | 0.581005 | + | 0.581005i | 0.935179 | − | 0.354175i | \(-0.115238\pi\) |
−0.354175 | + | 0.935179i | \(0.615238\pi\) | |||||||
\(354\) | 2.34388e40i | 0.385374i | ||||||||
\(355\) | −3.52215e40 | − | 6.72554e39i | −0.553547 | − | 0.105700i | ||||
\(356\) | −1.48666e40 | −0.223363 | ||||||||
\(357\) | 8.95335e40 | − | 8.95335e40i | 1.28616 | − | 1.28616i | ||||
\(358\) | −1.27375e40 | − | 1.27375e40i | −0.174967 | − | 0.174967i | ||||
\(359\) | 5.02832e40i | 0.660559i | 0.943883 | + | 0.330280i | \(0.107143\pi\) | ||||
−0.943883 | + | 0.330280i | \(0.892857\pi\) | |||||||
\(360\) | −1.34191e40 | + | 9.11600e39i | −0.168610 | + | 0.114542i | ||||
\(361\) | 6.95077e40 | 0.835445 | ||||||||
\(362\) | −3.62116e40 | + | 3.62116e40i | −0.416400 | + | 0.416400i | ||||
\(363\) | 3.97593e40 | + | 3.97593e40i | 0.437454 | + | 0.437454i | ||||
\(364\) | − | 2.03126e41i | − | 2.13867i | ||||||
\(365\) | 1.43350e40 | + | 2.11016e40i | 0.144448 | + | 0.212633i | ||||
\(366\) | 1.85885e40 | 0.179286 | ||||||||
\(367\) | 8.72557e39 | − | 8.72557e39i | 0.0805632 | − | 0.0805632i | −0.665677 | − | 0.746240i | \(-0.731857\pi\) |
0.746240 | + | 0.665677i | \(0.231857\pi\) | |||||||
\(368\) | −1.48431e40 | − | 1.48431e40i | −0.131208 | − | 0.131208i | ||||
\(369\) | 1.66833e40i | 0.141208i | ||||||||
\(370\) | 8.90284e39 | − | 4.66240e40i | 0.0721607 | − | 0.377904i | ||||
\(371\) | 3.70560e40 | 0.287658 | ||||||||
\(372\) | −6.31031e40 | + | 6.31031e40i | −0.469206 | + | 0.469206i | ||||
\(373\) | −5.50332e40 | − | 5.50332e40i | −0.391998 | − | 0.391998i | 0.483401 | − | 0.875399i | \(-0.339401\pi\) |
−0.875399 | + | 0.483401i | \(0.839401\pi\) | |||||||
\(374\) | 4.69824e40i | 0.320620i | ||||||||
\(375\) | 2.92969e40 | + | 1.31406e41i | 0.191567 | + | 0.859239i | ||||
\(376\) | −2.65225e41 | −1.66192 | ||||||||
\(377\) | −2.08263e41 | + | 2.08263e41i | −1.25069 | + | 1.25069i | ||||
\(378\) | 1.28539e41 | + | 1.28539e41i | 0.739886 | + | 0.739886i | ||||
\(379\) | − | 3.09340e41i | − | 1.70690i | −0.521174 | − | 0.853451i | \(-0.674506\pi\) | ||
0.521174 | − | 0.853451i | \(-0.325494\pi\) | |||||||
\(380\) | 5.45206e40 | + | 1.04107e40i | 0.288418 | + | 0.0550734i | ||||
\(381\) | −3.50372e40 | −0.177717 | ||||||||
\(382\) | 5.33763e40 | − | 5.33763e40i | 0.259618 | − | 0.259618i | ||||
\(383\) | 1.77767e41 | + | 1.77767e41i | 0.829222 | + | 0.829222i | 0.987409 | − | 0.158187i | \(-0.0505649\pi\) |
−0.158187 | + | 0.987409i | \(0.550565\pi\) | |||||||
\(384\) | 1.73191e41i | 0.774863i | ||||||||
\(385\) | −1.94021e41 | + | 1.31804e41i | −0.832677 | + | 0.565664i | ||||
\(386\) | −2.27622e41 | −0.937169 | ||||||||
\(387\) | −1.02061e39 | + | 1.02061e39i | −0.00403168 | + | 0.00403168i | ||||
\(388\) | 6.09412e40 | + | 6.09412e40i | 0.230996 | + | 0.230996i | ||||
\(389\) | 7.04649e40i | 0.256318i | 0.991754 | + | 0.128159i | \(0.0409068\pi\) | ||||
−0.991754 | + | 0.128159i | \(0.959093\pi\) | |||||||
\(390\) | −1.19160e41 | − | 1.75408e41i | −0.416004 | − | 0.612373i | ||||
\(391\) | −2.50076e41 | −0.838000 | ||||||||
\(392\) | 4.79704e41 | − | 4.79704e41i | 1.54311 | − | 1.54311i | ||||
\(393\) | −6.38205e40 | − | 6.38205e40i | −0.197097 | − | 0.197097i | ||||
\(394\) | 1.59922e40i | 0.0474207i | ||||||||
\(395\) | −3.61058e40 | + | 1.89085e41i | −0.102807 | + | 0.538399i | ||||
\(396\) | 3.24738e40 | 0.0887993 | ||||||||
\(397\) | 3.88000e41 | − | 3.88000e41i | 1.01902 | − | 1.01902i | 0.0192058 | − | 0.999816i | \(-0.493886\pi\) |
0.999816 | − | 0.0192058i | \(-0.00611376\pi\) | |||||||
\(398\) | 1.94949e40 | + | 1.94949e40i | 0.0491804 | + | 0.0491804i | ||||
\(399\) | − | 2.72071e41i | − | 0.659351i | ||||||
\(400\) | −9.89363e40 | − | 3.92136e40i | −0.230354 | − | 0.0913012i | ||||
\(401\) | 8.07416e41 | 1.80629 | 0.903145 | − | 0.429336i | \(-0.141252\pi\) | ||||
0.903145 | + | 0.429336i | \(0.141252\pi\) | |||||||
\(402\) | 2.06964e41 | − | 2.06964e41i | 0.444917 | − | 0.444917i | ||||
\(403\) | 5.70349e41 | + | 5.70349e41i | 1.17831 | + | 1.17831i | ||||
\(404\) | − | 1.34106e41i | − | 0.266285i | ||||||
\(405\) | −3.72784e41 | − | 7.11831e40i | −0.711504 | − | 0.135862i | ||||
\(406\) | −5.84503e41 | −1.07243 | ||||||||
\(407\) | −1.60006e41 | + | 1.60006e41i | −0.282245 | + | 0.282245i | ||||
\(408\) | 3.72067e41 | + | 3.72067e41i | 0.631042 | + | 0.631042i | ||||
\(409\) | 1.84702e40i | 0.0301231i | 0.999887 | + | 0.0150616i | \(0.00479442\pi\) | ||||
−0.999887 | + | 0.0150616i | \(0.995206\pi\) | |||||||
\(410\) | 1.73932e41 | − | 1.18157e41i | 0.272795 | − | 0.185319i | ||||
\(411\) | −9.14355e41 | −1.37926 | ||||||||
\(412\) | −4.14210e41 | + | 4.14210e41i | −0.600986 | + | 0.600986i | ||||
\(413\) | −7.79209e41 | − | 7.79209e41i | −1.08756 | − | 1.08756i | ||||
\(414\) | − | 6.59453e40i | − | 0.0885480i | ||||||
\(415\) | −9.41499e40 | − | 1.38592e41i | −0.121633 | − | 0.179048i | ||||
\(416\) | 1.33378e42 | 1.65803 | ||||||||
\(417\) | 4.65997e41 | − | 4.65997e41i | 0.557451 | − | 0.557451i | ||||
\(418\) | 7.13843e40 | + | 7.13843e40i | 0.0821830 | + | 0.0821830i | ||||
\(419\) | − | 1.14625e42i | − | 1.27015i | −0.772450 | − | 0.635075i | \(-0.780969\pi\) | ||
0.772450 | − | 0.635075i | \(-0.219031\pi\) | |||||||
\(420\) | −2.06888e41 | + | 1.08347e42i | −0.220672 | + | 1.15565i | ||||
\(421\) | 6.28686e41 | 0.645536 | 0.322768 | − | 0.946478i | \(-0.395387\pi\) | ||||
0.322768 | + | 0.946478i | \(0.395387\pi\) | |||||||
\(422\) | −6.62285e41 | + | 6.62285e41i | −0.654705 | + | 0.654705i | ||||
\(423\) | 3.06667e41 | + | 3.06667e41i | 0.291891 | + | 0.291891i | ||||
\(424\) | 1.53990e41i | 0.141137i | ||||||||
\(425\) | −1.16377e42 | + | 5.03102e41i | −1.02717 | + | 0.444052i | ||||
\(426\) | −3.06698e41 | −0.260710 | ||||||||
\(427\) | −6.17966e41 | + | 6.17966e41i | −0.505962 | + | 0.505962i | ||||
\(428\) | −4.11126e41 | − | 4.11126e41i | −0.324246 | − | 0.324246i | ||||
\(429\) | 1.01091e42i | 0.768063i | ||||||||
\(430\) | 1.78688e40 | + | 3.41204e39i | 0.0130797 | + | 0.00249758i | ||||
\(431\) | −6.17023e41 | −0.435176 | −0.217588 | − | 0.976041i | \(-0.569819\pi\) | ||||
−0.217588 | + | 0.976041i | \(0.569819\pi\) | |||||||
\(432\) | 2.78031e41 | − | 2.78031e41i | 0.188953 | − | 0.188953i | ||||
\(433\) | −1.34665e41 | − | 1.34665e41i | −0.0881961 | − | 0.0881961i | 0.661632 | − | 0.749828i | \(-0.269864\pi\) |
−0.749828 | + | 0.661632i | \(0.769864\pi\) | |||||||
\(434\) | 1.60072e42i | 1.01037i | ||||||||
\(435\) | 1.32299e42 | − | 8.98747e41i | 0.804874 | − | 0.546776i | ||||
\(436\) | 1.23755e42 | 0.725736 | ||||||||
\(437\) | −3.79961e41 | + | 3.79961e41i | −0.214801 | + | 0.214801i | ||||
\(438\) | 1.54286e41 | + | 1.54286e41i | 0.0840892 | + | 0.0840892i | ||||
\(439\) | 4.39229e40i | 0.0230812i | 0.999933 | + | 0.0115406i | \(0.00367357\pi\) | ||||
−0.999933 | + | 0.0115406i | \(0.996326\pi\) | |||||||
\(440\) | −5.47728e41 | − | 8.06275e41i | −0.277538 | − | 0.408545i | ||||
\(441\) | −1.10932e42 | −0.542049 | ||||||||
\(442\) | 1.41207e42 | − | 1.41207e42i | 0.665427 | − | 0.665427i | ||||
\(443\) | −1.49466e42 | − | 1.49466e42i | −0.679332 | − | 0.679332i | 0.280517 | − | 0.959849i | \(-0.409494\pi\) |
−0.959849 | + | 0.280517i | \(0.909494\pi\) | |||||||
\(444\) | 1.06414e42i | 0.466520i | ||||||||
\(445\) | 1.36858e41 | − | 7.16723e41i | 0.0578776 | − | 0.303104i | ||||
\(446\) | 1.95912e41 | 0.0799287 | ||||||||
\(447\) | 6.33041e41 | − | 6.33041e41i | 0.249179 | − | 0.249179i | ||||
\(448\) | 1.01989e42 | + | 1.01989e42i | 0.387353 | + | 0.387353i | ||||
\(449\) | − | 2.13933e42i | − | 0.784036i | −0.919958 | − | 0.392018i | \(-0.871777\pi\) | ||
0.919958 | − | 0.392018i | \(-0.128223\pi\) | |||||||
\(450\) | −1.32669e41 | − | 3.06887e41i | −0.0469211 | − | 0.108537i | ||||
\(451\) | −1.00240e42 | −0.342151 | ||||||||
\(452\) | −1.44301e41 | + | 1.44301e41i | −0.0475396 | + | 0.0475396i | ||||
\(453\) | −1.16806e42 | − | 1.16806e42i | −0.371444 | − | 0.371444i | ||||
\(454\) | 4.26830e41i | 0.131027i | ||||||||
\(455\) | 9.79277e42 | + | 1.86993e42i | 2.90217 | + | 0.554170i | ||||
\(456\) | 1.13062e42 | 0.323504 | ||||||||
\(457\) | −1.54106e42 | + | 1.54106e42i | −0.425755 | + | 0.425755i | −0.887179 | − | 0.461424i | \(-0.847339\pi\) |
0.461424 | + | 0.887179i | \(0.347339\pi\) | |||||||
\(458\) | −2.47397e42 | − | 2.47397e42i | −0.660004 | − | 0.660004i | ||||
\(459\) | − | 4.68424e42i | − | 1.20680i | ||||||
\(460\) | 1.80205e42 | − | 1.22419e42i | 0.448374 | − | 0.304595i | ||||
\(461\) | −3.18592e41 | −0.0765632 | −0.0382816 | − | 0.999267i | \(-0.512188\pi\) | ||||
−0.0382816 | + | 0.999267i | \(0.512188\pi\) | |||||||
\(462\) | −1.41859e42 | + | 1.41859e42i | −0.329296 | + | 0.329296i | ||||
\(463\) | 2.12849e42 | + | 2.12849e42i | 0.477283 | + | 0.477283i | 0.904262 | − | 0.426979i | \(-0.140422\pi\) |
−0.426979 | + | 0.904262i | \(0.640422\pi\) | |||||||
\(464\) | 1.26429e42i | 0.273879i | ||||||||
\(465\) | −2.46131e42 | − | 3.62313e42i | −0.515133 | − | 0.758293i | ||||
\(466\) | −5.48100e41 | −0.110837 | ||||||||
\(467\) | −6.64052e42 | + | 6.64052e42i | −1.29757 | + | 1.29757i | −0.367581 | + | 0.929991i | \(0.619814\pi\) |
−0.929991 | + | 0.367581i | \(0.880186\pi\) | |||||||
\(468\) | −9.76008e41 | − | 9.76008e41i | −0.184298 | − | 0.184298i | ||||
\(469\) | 1.37608e43i | 2.51119i | ||||||||
\(470\) | 1.02523e42 | − | 5.36909e42i | 0.180823 | − | 0.946967i | ||||
\(471\) | 5.56697e42 | 0.949040 | ||||||||
\(472\) | 3.23809e42 | − | 3.23809e42i | 0.533601 | − | 0.533601i | ||||
\(473\) | −6.13228e40 | − | 6.13228e40i | −0.00976886 | − | 0.00976886i | ||||
\(474\) | 1.64650e42i | 0.253576i | ||||||||
\(475\) | −1.00381e42 | + | 2.53262e42i | −0.149469 | + | 0.377113i | ||||
\(476\) | −1.03876e43 | −1.49556 | ||||||||
\(477\) | 1.78052e41 | − | 1.78052e41i | 0.0247886 | − | 0.0247886i | ||||
\(478\) | −3.33677e42 | − | 3.33677e42i | −0.449242 | − | 0.449242i | ||||
\(479\) | 3.00551e41i | 0.0391337i | 0.999809 | + | 0.0195668i | \(0.00622872\pi\) | ||||
−0.999809 | + | 0.0195668i | \(0.993771\pi\) | |||||||
\(480\) | −7.11435e42 | − | 1.35849e42i | −0.895933 | − | 0.171078i | ||||
\(481\) | 9.61806e42 | 1.17156 | ||||||||
\(482\) | −3.74724e42 | + | 3.74724e42i | −0.441529 | + | 0.441529i | ||||
\(483\) | −7.55083e42 | − | 7.55083e42i | −0.860678 | − | 0.860678i | ||||
\(484\) | − | 4.61285e42i | − | 0.508679i | ||||||
\(485\) | −3.49901e42 | + | 2.37699e42i | −0.373316 | + | 0.253606i | ||||
\(486\) | 2.24359e42 | 0.231613 | ||||||||
\(487\) | −2.58335e42 | + | 2.58335e42i | −0.258060 | + | 0.258060i | −0.824265 | − | 0.566205i | \(-0.808411\pi\) |
0.566205 | + | 0.824265i | \(0.308411\pi\) | |||||||
\(488\) | −2.56802e42 | − | 2.56802e42i | −0.248246 | − | 0.248246i | ||||
\(489\) | 4.83190e42i | 0.452039i | ||||||||
\(490\) | 7.85661e42 | + | 1.15652e43i | 0.711374 | + | 1.04717i | ||||
\(491\) | 9.40886e42 | 0.824580 | 0.412290 | − | 0.911053i | \(-0.364729\pi\) | ||||
0.412290 | + | 0.911053i | \(0.364729\pi\) | |||||||
\(492\) | −3.33330e42 | + | 3.33330e42i | −0.282769 | + | 0.282769i | ||||
\(493\) | 1.06503e43 | + | 1.06503e43i | 0.874605 | + | 0.874605i | ||||
\(494\) | − | 4.29095e42i | − | 0.341132i | ||||||
\(495\) | −2.98945e41 | + | 1.56557e42i | −0.0230096 | + | 0.120501i | ||||
\(496\) | 3.46238e42 | 0.258029 | ||||||||
\(497\) | 1.01960e43 | − | 1.01960e43i | 0.735747 | − | 0.735747i | ||||
\(498\) | −1.01332e42 | − | 1.01332e42i | −0.0708074 | − | 0.0708074i | ||||
\(499\) | − | 1.78058e43i | − | 1.20491i | −0.798154 | − | 0.602453i | \(-0.794190\pi\) | ||
0.798154 | − | 0.602453i | \(-0.205810\pi\) | |||||||
\(500\) | 5.92330e42 | − | 9.32230e42i | 0.388189 | − | 0.610947i | ||||
\(501\) | −5.33289e42 | −0.338500 | ||||||||
\(502\) | 5.12729e42 | − | 5.12729e42i | 0.315231 | − | 0.315231i | ||||
\(503\) | −5.49096e42 | − | 5.49096e42i | −0.327009 | − | 0.327009i | 0.524439 | − | 0.851448i | \(-0.324275\pi\) |
−0.851448 | + | 0.524439i | \(0.824275\pi\) | |||||||
\(504\) | − | 6.52352e42i | − | 0.376351i | ||||||
\(505\) | 6.46530e42 | + | 1.23455e42i | 0.361349 | + | 0.0689995i | ||||
\(506\) | 3.96228e42 | 0.214554 | ||||||||
\(507\) | 1.85185e43 | − | 1.85185e43i | 0.971578 | − | 0.971578i | ||||
\(508\) | 2.03250e42 | + | 2.03250e42i | 0.103326 | + | 0.103326i | ||||
\(509\) | 2.47585e43i | 1.21966i | 0.792531 | + | 0.609831i | \(0.208763\pi\) | ||||
−0.792531 | + | 0.609831i | \(0.791237\pi\) | |||||||
\(510\) | −8.97016e42 | + | 6.09372e42i | −0.428230 | + | 0.290911i | ||||
\(511\) | −1.02583e43 | −0.474615 | ||||||||
\(512\) | 7.58811e42 | − | 7.58811e42i | 0.340263 | − | 0.340263i | ||||
\(513\) | −7.11716e42 | − | 7.11716e42i | −0.309335 | − | 0.309335i | ||||
\(514\) | − | 3.25219e42i | − | 0.137014i | ||||||
\(515\) | −1.61561e43 | − | 2.37823e43i | −0.659812 | − | 0.971266i | ||||
\(516\) | −4.07834e41 | −0.0161469 | ||||||||
\(517\) | −1.84259e43 | + | 1.84259e43i | −0.707260 | + | 0.707260i | ||||
\(518\) | 1.34968e43 | + | 1.34968e43i | 0.502292 | + | 0.502292i | ||||
\(519\) | 8.19464e42i | 0.295701i | ||||||||
\(520\) | −7.77070e42 | + | 4.06950e43i | −0.271898 | + | 1.42392i | ||||
\(521\) | −4.87360e43 | −1.65366 | −0.826831 | − | 0.562451i | \(-0.809858\pi\) | ||||
−0.826831 | + | 0.562451i | \(0.809858\pi\) | |||||||
\(522\) | −2.80850e42 | + | 2.80850e42i | −0.0924158 | + | 0.0924158i | ||||
\(523\) | 4.12764e43 | + | 4.12764e43i | 1.31727 | + | 1.31727i | 0.915929 | + | 0.401341i | \(0.131456\pi\) |
0.401341 | + | 0.915929i | \(0.368544\pi\) | |||||||
\(524\) | 7.40442e42i | 0.229187i | ||||||||
\(525\) | −5.03298e43 | − | 1.99483e43i | −1.51104 | − | 0.598903i | ||||
\(526\) | 2.49139e43 | 0.725554 | ||||||||
\(527\) | 2.91670e43 | − | 2.91670e43i | 0.823989 | − | 0.823989i | ||||
\(528\) | 3.06844e42 | + | 3.06844e42i | 0.0840959 | + | 0.0840959i | ||||
\(529\) | − | 1.65187e43i | − | 0.439222i | ||||||
\(530\) | −3.11731e42 | − | 5.95250e41i | −0.0804203 | − | 0.0153562i | ||||
\(531\) | −7.48810e42 | −0.187439 | ||||||||
\(532\) | −1.57828e43 | + | 1.57828e43i | −0.383352 | + | 0.383352i | ||||
\(533\) | 3.01275e43 | + | 3.01275e43i | 0.710114 | + | 0.710114i | ||||
\(534\) | − | 6.24101e42i | − | 0.142756i | ||||||
\(535\) | 2.36052e43 | − | 1.60358e43i | 0.524020 | − | 0.355983i | ||||
\(536\) | −5.71847e43 | −1.23209 | ||||||||
\(537\) | −1.40156e43 | + | 1.40156e43i | −0.293105 | + | 0.293105i | ||||
\(538\) | −2.84511e43 | − | 2.84511e43i | −0.577541 | − | 0.577541i | ||||
\(539\) | − | 6.66526e43i | − | 1.31340i | ||||||
\(540\) | 2.29306e43 | + | 3.37546e43i | 0.438647 | + | 0.645703i | ||||
\(541\) | −4.08446e43 | −0.758539 | −0.379270 | − | 0.925286i | \(-0.623825\pi\) | ||||
−0.379270 | + | 0.925286i | \(0.623825\pi\) | |||||||
\(542\) | −2.18768e43 | + | 2.18768e43i | −0.394453 | + | 0.394453i | ||||
\(543\) | 3.98453e43 | + | 3.98453e43i | 0.697557 | + | 0.697557i | ||||
\(544\) | − | 6.82081e43i | − | 1.15945i | ||||||
\(545\) | −1.13926e43 | + | 5.96627e43i | −0.188052 | + | 0.984824i | ||||
\(546\) | 8.52725e43 | 1.36687 | ||||||||
\(547\) | 2.40012e43 | − | 2.40012e43i | 0.373624 | − | 0.373624i | −0.495171 | − | 0.868795i | \(-0.664895\pi\) |
0.868795 | + | 0.495171i | \(0.164895\pi\) | |||||||
\(548\) | 5.30414e43 | + | 5.30414e43i | 0.801911 | + | 0.801911i | ||||
\(549\) | 5.93857e42i | 0.0872016i | ||||||||
\(550\) | 1.84391e43 | − | 7.97130e42i | 0.262988 | − | 0.113691i | ||||
\(551\) | 3.23638e43 | 0.448367 | ||||||||
\(552\) | 3.13783e43 | − | 3.13783e43i | 0.422284 | − | 0.422284i | ||||
\(553\) | −5.47370e43 | − | 5.47370e43i | −0.715614 | − | 0.715614i | ||||
\(554\) | − | 5.84951e43i | − | 0.742956i | ||||||
\(555\) | −5.13024e43 | − | 9.79619e42i | −0.633068 | − | 0.120884i | ||||
\(556\) | −5.40647e43 | −0.648213 | ||||||||
\(557\) | −9.45662e42 | + | 9.45662e42i | −0.110167 | + | 0.110167i | −0.760042 | − | 0.649874i | \(-0.774822\pi\) |
0.649874 | + | 0.760042i | \(0.274822\pi\) | |||||||
\(558\) | 7.69136e42 | + | 7.69136e42i | 0.0870674 | + | 0.0870674i | ||||
\(559\) | 3.68615e42i | 0.0405494i | ||||||||
\(560\) | 3.54000e43 | − | 2.40484e43i | 0.378438 | − | 0.257085i | ||||
\(561\) | 5.16969e43 | 0.537104 | ||||||||
\(562\) | −3.53491e41 | + | 3.53491e41i | −0.00356941 | + | 0.00356941i | ||||
\(563\) | −9.07140e43 | − | 9.07140e43i | −0.890307 | − | 0.890307i | 0.104244 | − | 0.994552i | \(-0.466758\pi\) |
−0.994552 | + | 0.104244i | \(0.966758\pi\) | |||||||
\(564\) | 1.22543e44i | 1.16902i | ||||||||
\(565\) | −5.62841e42 | − | 8.28522e42i | −0.0521928 | − | 0.0768296i | ||||
\(566\) | 6.40836e42 | 0.0577675 | ||||||||
\(567\) | 1.07915e44 | − | 1.07915e44i | 0.945696 | − | 0.945696i | ||||
\(568\) | 4.23707e43 | + | 4.23707e43i | 0.360988 | + | 0.360988i | ||||
\(569\) | − | 7.28203e43i | − | 0.603193i | −0.953436 | − | 0.301597i | \(-0.902480\pi\) | ||
0.953436 | − | 0.301597i | \(-0.0975195\pi\) | |||||||
\(570\) | −4.37042e42 | + | 2.28878e43i | −0.0351986 | + | 0.184334i | ||||
\(571\) | 3.37780e43 | 0.264519 | 0.132259 | − | 0.991215i | \(-0.457777\pi\) | ||||
0.132259 | + | 0.991215i | \(0.457777\pi\) | |||||||
\(572\) | 5.86427e43 | − | 5.86427e43i | 0.446558 | − | 0.446558i | ||||
\(573\) | −5.87323e43 | − | 5.87323e43i | −0.434913 | − | 0.434913i | ||||
\(574\) | 8.45548e43i | 0.608903i | ||||||||
\(575\) | 4.24293e43 | + | 9.81468e43i | 0.297153 | + | 0.687370i | ||||
\(576\) | 9.80105e42 | 0.0667595 | ||||||||
\(577\) | −1.73966e44 | + | 1.73966e44i | −1.15253 | + | 1.15253i | −0.166481 | + | 0.986045i | \(0.553240\pi\) |
−0.986045 | + | 0.166481i | \(0.946760\pi\) | |||||||
\(578\) | −1.45470e43 | − | 1.45470e43i | −0.0937407 | − | 0.0937407i | ||||
\(579\) | 2.50463e44i | 1.56995i | ||||||||
\(580\) | −1.28882e44 | − | 2.46100e43i | −0.785859 | − | 0.150060i | ||||
\(581\) | 6.73748e43 | 0.399650 | ||||||||
\(582\) | −2.55832e43 | + | 2.55832e43i | −0.147634 | + | 0.147634i | ||||
\(583\) | 1.06981e43 | + | 1.06981e43i | 0.0600634 | + | 0.0600634i | ||||
\(584\) | − | 4.26295e43i | − | 0.232865i | ||||||
\(585\) | 5.60385e43 | − | 3.80688e43i | 0.297847 | − | 0.202337i | ||||
\(586\) | −1.25075e44 | −0.646860 | ||||||||
\(587\) | −2.56273e44 | + | 2.56273e44i | −1.28971 | + | 1.28971i | −0.354753 | + | 0.934960i | \(0.615435\pi\) |
−0.934960 | + | 0.354753i | \(0.884565\pi\) | |||||||
\(588\) | −2.21640e44 | − | 2.21640e44i | −1.08545 | − | 1.08545i | ||||
\(589\) | − | 8.86315e43i | − | 0.422419i | ||||||
\(590\) | 5.30335e43 | + | 7.80672e43i | 0.245991 | + | 0.362107i | ||||
\(591\) | 1.75969e43 | 0.0794395 | ||||||||
\(592\) | 2.91939e43 | − | 2.91939e43i | 0.128276 | − | 0.128276i | ||||
\(593\) | 2.88770e44 | + | 2.88770e44i | 1.23503 | + | 1.23503i | 0.962009 | + | 0.273019i | \(0.0880222\pi\) |
0.273019 | + | 0.962009i | \(0.411978\pi\) | |||||||
\(594\) | 7.42185e43i | 0.308979i | ||||||||
\(595\) | 9.56260e43 | − | 5.00791e44i | 0.387529 | − | 2.02948i | ||||
\(596\) | −7.34450e43 | −0.289749 | ||||||||
\(597\) | 2.14511e43 | − | 2.14511e43i | 0.0823873 | − | 0.0823873i | ||||
\(598\) | −1.19087e44 | − | 1.19087e44i | −0.445294 | − | 0.445294i | ||||
\(599\) | 2.46189e43i | 0.0896272i | 0.998995 | + | 0.0448136i | \(0.0142694\pi\) | ||||
−0.998995 | + | 0.0448136i | \(0.985731\pi\) | |||||||
\(600\) | 8.28973e43 | − | 2.09151e44i | 0.293846 | − | 0.741378i | ||||
\(601\) | −2.45622e44 | −0.847766 | −0.423883 | − | 0.905717i | \(-0.639333\pi\) | ||||
−0.423883 | + | 0.905717i | \(0.639333\pi\) | |||||||
\(602\) | −5.17271e42 | + | 5.17271e42i | −0.0173850 | + | 0.0173850i | ||||
\(603\) | 6.61200e43 | + | 6.61200e43i | 0.216399 | + | 0.216399i | ||||
\(604\) | 1.35517e44i | 0.431921i | ||||||||
\(605\) | 2.22387e44 | + | 4.24648e43i | 0.690277 | + | 0.131808i | ||||
\(606\) | 5.62979e43 | 0.170188 | ||||||||
\(607\) | 4.17327e44 | − | 4.17327e44i | 1.22873 | − | 1.22873i | 0.264290 | − | 0.964443i | \(-0.414862\pi\) |
0.964443 | − | 0.264290i | \(-0.0851377\pi\) | |||||||
\(608\) | −1.03634e44 | − | 1.03634e44i | −0.297198 | − | 0.297198i | ||||
\(609\) | 6.43154e44i | 1.79655i | ||||||||
\(610\) | 6.19126e43 | − | 4.20592e43i | 0.168462 | − | 0.114441i | ||||
\(611\) | 1.10759e45 | 2.93575 | ||||||||
\(612\) | −4.99119e43 | + | 4.99119e43i | −0.128879 | + | 0.128879i | ||||
\(613\) | −5.37853e44 | − | 5.37853e44i | −1.35299 | − | 1.35299i | −0.882293 | − | 0.470701i | \(-0.844001\pi\) |
−0.470701 | − | 0.882293i | \(-0.655999\pi\) | |||||||
\(614\) | 1.20496e44i | 0.295311i | ||||||||
\(615\) | −1.30014e44 | − | 1.91385e44i | −0.310447 | − | 0.456989i | ||||
\(616\) | 3.91961e44 | 0.911909 | ||||||||
\(617\) | −4.60623e44 | + | 4.60623e44i | −1.04420 | + | 1.04420i | −0.0452218 | + | 0.998977i | \(0.514399\pi\) |
−0.998977 | + | 0.0452218i | \(0.985601\pi\) | |||||||
\(618\) | −1.73886e44 | − | 1.73886e44i | −0.384103 | − | 0.384103i | ||||
\(619\) | − | 4.15240e44i | − | 0.893817i | −0.894580 | − | 0.446909i | \(-0.852525\pi\) | ||
0.894580 | − | 0.446909i | \(-0.147475\pi\) | |||||||
\(620\) | −6.73970e43 | + | 3.52957e44i | −0.141375 | + | 0.740379i | ||||
\(621\) | −3.95047e44 | −0.807575 | ||||||||
\(622\) | 2.67997e44 | − | 2.67997e44i | 0.533929 | − | 0.533929i | ||||
\(623\) | 2.07479e44 | + | 2.07479e44i | 0.402871 | + | 0.402871i | ||||
\(624\) | − | 1.84446e44i | − | 0.349072i | ||||||
\(625\) | 3.94903e44 | + | 3.71383e44i | 0.728467 | + | 0.685081i | ||||
\(626\) | −4.98692e44 | −0.896691 | ||||||||
\(627\) | 7.85473e43 | − | 7.85473e43i | 0.137674 | − | 0.137674i | ||||
\(628\) | −3.22938e44 | − | 3.22938e44i | −0.551779 | − | 0.551779i | ||||
\(629\) | − | 4.91856e44i | − | 0.819271i | ||||||
\(630\) | 1.32059e44 | + | 2.52167e43i | 0.214447 | + | 0.0409486i | ||||
\(631\) | −1.70933e44 | −0.270618 | −0.135309 | − | 0.990803i | \(-0.543203\pi\) | ||||
−0.135309 | + | 0.990803i | \(0.543203\pi\) | |||||||
\(632\) | 2.27466e44 | − | 2.27466e44i | 0.351109 | − | 0.351109i | ||||
\(633\) | 7.28741e44 | + | 7.28741e44i | 1.09677 | + | 1.09677i | ||||
\(634\) | − | 3.17811e44i | − | 0.466381i | ||||||
\(635\) | −1.16698e44 | + | 7.92767e43i | −0.166988 | + | 0.113440i | ||||
\(636\) | 7.11489e43 | 0.0992783 | ||||||||
\(637\) | −2.00326e45 | + | 2.00326e45i | −2.72588 | + | 2.72588i | ||||
\(638\) | −1.68747e44 | − | 1.68747e44i | −0.223926 | − | 0.223926i | ||||
\(639\) | − | 9.79825e43i | − | 0.126805i | ||||||
\(640\) | 3.91869e44 | + | 5.76844e44i | 0.494608 | + | 0.728080i | ||||
\(641\) | −1.41918e45 | −1.74706 | −0.873530 | − | 0.486770i | \(-0.838175\pi\) | ||||
−0.873530 | + | 0.486770i | \(0.838175\pi\) | |||||||
\(642\) | 1.72591e44 | − | 1.72591e44i | 0.207232 | − | 0.207232i | ||||
\(643\) | −4.55857e44 | − | 4.55857e44i | −0.533892 | − | 0.533892i | 0.387836 | − | 0.921728i | \(-0.373223\pi\) |
−0.921728 | + | 0.387836i | \(0.873223\pi\) | |||||||
\(644\) | 8.76043e44i | 1.00081i | ||||||||
\(645\) | 3.75442e42 | − | 1.96618e43i | 0.00418396 | − | 0.0219113i | ||||
\(646\) | −2.19434e44 | −0.238553 | ||||||||
\(647\) | 1.10010e45 | − | 1.10010e45i | 1.16671 | − | 1.16671i | 0.183737 | − | 0.982975i | \(-0.441180\pi\) |
0.982975 | − | 0.183737i | \(-0.0588196\pi\) | |||||||
\(648\) | 4.48451e44 | + | 4.48451e44i | 0.463997 | + | 0.463997i | ||||
\(649\) | − | 4.49917e44i | − | 0.454169i | ||||||
\(650\) | −7.93772e44 | − | 3.14613e44i | −0.781775 | − | 0.309858i | ||||
\(651\) | 1.76134e45 | 1.69258 | ||||||||
\(652\) | 2.80297e44 | − | 2.80297e44i | 0.262819 | − | 0.262819i | ||||
\(653\) | 3.40447e44 | + | 3.40447e44i | 0.311486 | + | 0.311486i | 0.845485 | − | 0.533999i | \(-0.179312\pi\) |
−0.533999 | + | 0.845485i | \(0.679312\pi\) | |||||||
\(654\) | 5.19525e44i | 0.463833i | ||||||||
\(655\) | −3.56969e44 | − | 6.81633e43i | −0.311007 | − | 0.0593868i | ||||
\(656\) | 1.82893e44 | 0.155502 | ||||||||
\(657\) | −4.92905e43 | + | 4.92905e43i | −0.0408994 | + | 0.0408994i | ||||
\(658\) | 1.55426e45 | + | 1.55426e45i | 1.25866 | + | 1.25866i | ||||
\(659\) | − | 1.79663e45i | − | 1.42001i | −0.704197 | − | 0.710005i | \(-0.748693\pi\) | ||
0.704197 | − | 0.710005i | \(-0.251307\pi\) | |||||||
\(660\) | −3.72527e44 | + | 2.53070e44i | −0.287379 | + | 0.195226i | ||||
\(661\) | 1.36703e44 | 0.102933 | 0.0514664 | − | 0.998675i | \(-0.483611\pi\) | ||||
0.0514664 | + | 0.998675i | \(0.483611\pi\) | |||||||
\(662\) | −4.53261e44 | + | 4.53261e44i | −0.333135 | + | 0.333135i | ||||
\(663\) | −1.55376e45 | − | 1.55376e45i | −1.11473 | − | 1.11473i | ||||
\(664\) | 2.79983e44i | 0.196084i | ||||||||
\(665\) | −6.15600e44 | − | 9.06185e44i | −0.420874 | − | 0.619542i | ||||
\(666\) | 1.29703e44 | 0.0865690 | ||||||||
\(667\) | 8.98197e44 | − | 8.98197e44i | 0.585273 | − | 0.585273i | ||||
\(668\) | 3.09359e44 | + | 3.09359e44i | 0.196807 | + | 0.196807i | ||||
\(669\) | − | 2.15570e44i | − | 0.133897i | ||||||
\(670\) | 2.21048e44 | − | 1.15762e45i | 0.134057 | − | 0.702052i | ||||
\(671\) | −3.56815e44 | −0.211292 | ||||||||
\(672\) | 2.05948e45 | − | 2.05948e45i | 1.19083 | − | 1.19083i | ||||
\(673\) | 1.62702e45 | + | 1.62702e45i | 0.918656 | + | 0.918656i | 0.996932 | − | 0.0782760i | \(-0.0249415\pi\) |
−0.0782760 | + | 0.996932i | \(0.524942\pi\) | |||||||
\(674\) | 9.16343e44i | 0.505242i | ||||||||
\(675\) | −1.83841e45 | + | 7.94754e44i | −0.989881 | + | 0.427930i | ||||
\(676\) | −2.14850e45 | −1.12977 | ||||||||
\(677\) | 1.45909e45 | − | 1.45909e45i | 0.749313 | − | 0.749313i | −0.225037 | − | 0.974350i | \(-0.572250\pi\) |
0.974350 | + | 0.225037i | \(0.0722503\pi\) | |||||||
\(678\) | −6.05779e43 | − | 6.05779e43i | −0.0303836 | − | 0.0303836i | ||||
\(679\) | − | 1.70100e45i | − | 0.833274i | ||||||
\(680\) | 2.08109e45 | + | 3.97384e44i | 0.995746 | + | 0.190138i | ||||
\(681\) | 4.69660e44 | 0.219498 | ||||||||
\(682\) | −4.62130e44 | + | 4.62130e44i | −0.210967 | + | 0.210967i | ||||
\(683\) | 2.06851e45 | + | 2.06851e45i | 0.922414 | + | 0.922414i | 0.997200 | − | 0.0747859i | \(-0.0238273\pi\) |
−0.0747859 | + | 0.997200i | \(0.523827\pi\) | |||||||
\(684\) | 1.51670e44i | 0.0660699i | ||||||||
\(685\) | −3.04543e45 | + | 2.06886e45i | −1.29598 | + | 0.880403i | ||||
\(686\) | −3.28841e45 | −1.36710 | ||||||||
\(687\) | −2.72222e45 | + | 2.72222e45i | −1.10564 | + | 1.10564i | ||||
\(688\) | 1.11886e43 | + | 1.11886e43i | 0.00443979 | + | 0.00443979i | ||||
\(689\) | − | 6.43069e44i | − | 0.249316i | ||||||
\(690\) | 5.13915e44 | + | 7.56501e44i | 0.194673 | + | 0.286566i | ||||
\(691\) | 4.07782e45 | 1.50931 | 0.754656 | − | 0.656120i | \(-0.227804\pi\) | ||||
0.754656 | + | 0.656120i | \(0.227804\pi\) | |||||||
\(692\) | 4.75369e44 | − | 4.75369e44i | 0.171923 | − | 0.171923i | ||||
\(693\) | −4.53206e44 | − | 4.53206e44i | −0.160164 | − | 0.160164i | ||||
\(694\) | − | 2.39711e44i | − | 0.0827820i | ||||||
\(695\) | 4.97707e44 | − | 2.60648e45i | 0.167964 | − | 0.879624i | ||||
\(696\) | −2.67270e45 | −0.881459 | ||||||||
\(697\) | 1.54069e45 | − | 1.54069e45i | 0.496581 | − | 0.496581i | ||||
\(698\) | 1.85395e44 | + | 1.85395e44i | 0.0583997 | + | 0.0583997i | ||||
\(699\) | 6.03098e44i | 0.185675i | ||||||||
\(700\) | 1.76242e45 | + | 4.07681e45i | 0.530324 | + | 1.22674i | ||||
\(701\) | −2.35650e45 | −0.693073 | −0.346536 | − | 0.938037i | \(-0.612642\pi\) | ||||
−0.346536 | + | 0.938037i | \(0.612642\pi\) | |||||||
\(702\) | 2.23066e45 | − | 2.23066e45i | 0.641267 | − | 0.641267i | ||||
\(703\) | −7.47317e44 | − | 7.47317e44i | −0.210000 | − | 0.210000i | ||||
\(704\) | 5.88889e44i | 0.161760i | ||||||||
\(705\) | −5.90785e45 | − | 1.12810e45i | −1.58637 | − | 0.302916i | ||||
\(706\) | 1.64494e45 | 0.431791 | ||||||||
\(707\) | −1.87159e45 | + | 1.87159e45i | −0.480287 | + | 0.480287i | ||||
\(708\) | −1.49611e45 | − | 1.49611e45i | −0.375346 | − | 0.375346i | ||||
\(709\) | 5.86354e45i | 1.43820i | 0.694905 | + | 0.719102i | \(0.255447\pi\) | ||||
−0.694905 | + | 0.719102i | \(0.744553\pi\) | |||||||
\(710\) | −1.02152e45 | + | 6.93949e44i | −0.244969 | + | 0.166415i | ||||
\(711\) | −5.26015e44 | −0.123335 | ||||||||
\(712\) | −8.62202e44 | + | 8.62202e44i | −0.197665 | + | 0.197665i | ||||
\(713\) | −2.45980e45 | − | 2.45980e45i | −0.551401 | − | 0.551401i | ||||
\(714\) | − | 4.36074e45i | − | 0.955847i | ||||||
\(715\) | 2.28733e45 | + | 3.36704e45i | 0.490267 | + | 0.721691i | ||||
\(716\) | 1.62608e45 | 0.340827 | ||||||||
\(717\) | −3.67160e45 | + | 3.67160e45i | −0.752573 | + | 0.752573i | ||||
\(718\) | 1.22452e45 | + | 1.22452e45i | 0.245457 | + | 0.245457i | ||||
\(719\) | 1.65804e45i | 0.325038i | 0.986705 | + | 0.162519i | \(0.0519618\pi\) | ||||
−0.986705 | + | 0.162519i | \(0.948038\pi\) | |||||||
\(720\) | 5.45440e43 | − | 2.85646e44i | 0.0104575 | − | 0.0547656i | ||||
\(721\) | 1.15615e46 | 2.16795 | ||||||||
\(722\) | 1.69269e45 | − | 1.69269e45i | 0.310443 | − | 0.310443i | ||||
\(723\) | 4.12326e45 | + | 4.12326e45i | 0.739652 | + | 0.739652i | ||||
\(724\) | − | 4.62282e45i | − | 0.811130i | ||||||
\(725\) | 2.37292e45 | − | 5.98690e45i | 0.407262 | − | 1.02753i | ||||
\(726\) | 1.93648e45 | 0.325107 | ||||||||
\(727\) | 2.36251e43 | − | 2.36251e43i | 0.00387993 | − | 0.00387993i | −0.705164 | − | 0.709044i | \(-0.749127\pi\) |
0.709044 | + | 0.705164i | \(0.249127\pi\) | |||||||
\(728\) | −1.17805e46 | − | 1.17805e46i | −1.89261 | − | 1.89261i | ||||
\(729\) | − | 7.07759e45i | − | 1.11236i | ||||||
\(730\) | 8.62972e44 | + | 1.64784e44i | 0.132688 | + | 0.0253367i | ||||
\(731\) | 1.88505e44 | 0.0283560 | ||||||||
\(732\) | −1.18652e45 | + | 1.18652e45i | −0.174621 | + | 0.174621i | ||||
\(733\) | 4.55208e45 | + | 4.55208e45i | 0.655460 | + | 0.655460i | 0.954302 | − | 0.298843i | \(-0.0966006\pi\) |
−0.298843 | + | 0.954302i | \(0.596601\pi\) | |||||||
\(734\) | − | 4.24980e44i | − | 0.0598730i | ||||||
\(735\) | 1.27257e46 | − | 8.64497e45i | 1.75422 | − | 1.19170i | ||||
\(736\) | −5.75234e45 | −0.775889 | ||||||||
\(737\) | −3.97277e45 | + | 3.97277e45i | −0.524341 | + | 0.524341i | ||||
\(738\) | 4.06281e44 | + | 4.06281e44i | 0.0524716 | + | 0.0524716i | ||||
\(739\) | − | 2.32758e45i | − | 0.294167i | −0.989124 | − | 0.147084i | \(-0.953011\pi\) | ||
0.989124 | − | 0.147084i | \(-0.0469886\pi\) | |||||||
\(740\) | 2.40776e45 | + | 3.54431e45i | 0.297787 | + | 0.438353i | ||||
\(741\) | −4.72152e45 | −0.571467 | ||||||||
\(742\) | 9.02407e44 | − | 9.02407e44i | 0.106891 | − | 0.106891i | ||||
\(743\) | 1.08876e46 | + | 1.08876e46i | 1.26215 | + | 1.26215i | 0.950048 | + | 0.312104i | \(0.101034\pi\) |
0.312104 | + | 0.950048i | \(0.398966\pi\) | |||||||
\(744\) | 7.31946e45i | 0.830447i | ||||||||
\(745\) | 6.76117e44 | − | 3.54081e45i | 0.0750795 | − | 0.393190i | ||||
\(746\) | −2.68040e45 | −0.291325 | ||||||||
\(747\) | 3.23732e44 | − | 3.23732e44i | 0.0344394 | − | 0.0344394i | ||||
\(748\) | −2.99892e45 | − | 2.99892e45i | −0.312276 | − | 0.312276i | ||||
\(749\) | 1.14754e46i | 1.16966i | ||||||||
\(750\) | 3.91351e45 | + | 2.48661e45i | 0.390469 | + | 0.248100i | ||||
\(751\) | −5.61810e45 | −0.548719 | −0.274360 | − | 0.961627i | \(-0.588466\pi\) | ||||
−0.274360 | + | 0.961627i | \(0.588466\pi\) | |||||||
\(752\) | 3.36189e45 | − | 3.36189e45i | 0.321438 | − | 0.321438i | ||||
\(753\) | −5.64179e45 | − | 5.64179e45i | −0.528077 | − | 0.528077i | ||||
\(754\) | 1.01435e46i | 0.929489i | ||||||||
\(755\) | −6.53334e45 | − | 1.24754e45i | −0.586117 | − | 0.111919i | ||||
\(756\) | −1.64094e46 | −1.44127 | ||||||||
\(757\) | −9.88550e45 | + | 9.88550e45i | −0.850090 | + | 0.850090i | −0.990144 | − | 0.140054i | \(-0.955272\pi\) |
0.140054 | + | 0.990144i | \(0.455272\pi\) | |||||||
\(758\) | −7.53321e45 | − | 7.53321e45i | −0.634268 | − | 0.634268i | ||||
\(759\) | − | 4.35987e45i | − | 0.359422i | ||||||
\(760\) | 3.76575e45 | − | 2.55820e45i | 0.303973 | − | 0.206498i | ||||
\(761\) | 2.33867e46 | 1.84848 | 0.924240 | − | 0.381811i | \(-0.124700\pi\) | ||||
0.924240 | + | 0.381811i | \(0.124700\pi\) | |||||||
\(762\) | −8.53245e44 | + | 8.53245e44i | −0.0660381 | + | 0.0660381i | ||||
\(763\) | −1.72713e46 | − | 1.72713e46i | −1.30898 | − | 1.30898i | ||||
\(764\) | 6.81408e45i | 0.505724i | ||||||||
\(765\) | −1.94679e45 | − | 2.86575e45i | −0.141494 | − | 0.208283i | ||||
\(766\) | 8.65815e45 | 0.616261 | ||||||||
\(767\) | −1.35224e46 | + | 1.35224e46i | −0.942600 | + | 0.942600i | ||||
\(768\) | 6.92297e45 | + | 6.92297e45i | 0.472621 | + | 0.472621i | ||||
\(769\) | 2.13940e46i | 1.43044i | 0.698898 | + | 0.715221i | \(0.253674\pi\) | ||||
−0.698898 | + | 0.715221i | \(0.746326\pi\) | |||||||
\(770\) | −1.51512e45 | + | 7.93467e45i | −0.0992194 | + | 0.519610i | ||||
\(771\) | −3.57853e45 | −0.229527 | ||||||||
\(772\) | 1.45293e46 | − | 1.45293e46i | 0.912783 | − | 0.912783i | ||||
\(773\) | −1.42516e46 | − | 1.42516e46i | −0.876985 | − | 0.876985i | 0.116236 | − | 0.993222i | \(-0.462917\pi\) |
−0.993222 | + | 0.116236i | \(0.962917\pi\) | |||||||
\(774\) | 4.97090e43i | 0.00299626i | ||||||||
\(775\) | −1.63957e46 | − | 6.49847e45i | −0.968062 | − | 0.383693i | ||||
\(776\) | 7.06869e45 | 0.408838 | ||||||||
\(777\) | 1.48512e46 | − | 1.48512e46i | 0.841443 | − | 0.841443i | ||||
\(778\) | 1.71600e45 | + | 1.71600e45i | 0.0952452 | + | 0.0952452i | ||||
\(779\) | − | 4.68178e45i | − | 0.254573i | ||||||
\(780\) | 1.88025e46 | + | 3.59033e45i | 1.00162 | + | 0.191259i | ||||
\(781\) | 5.88721e45 | 0.307251 | ||||||||
\(782\) | −6.08999e45 | + | 6.08999e45i | −0.311393 | + | 0.311393i | ||||
\(783\) | 1.68244e46 | + | 1.68244e46i | 0.842851 | + | 0.842851i | ||||
\(784\) | 1.21611e46i | 0.596919i | ||||||||
\(785\) | 1.85418e46 | − | 1.25961e46i | 0.891740 | − | 0.605788i | ||||
\(786\) | −3.10838e45 | −0.146478 | ||||||||
\(787\) | −8.64458e45 | + | 8.64458e45i | −0.399161 | + | 0.399161i | −0.877937 | − | 0.478776i | \(-0.841081\pi\) |
0.478776 | + | 0.877937i | \(0.341081\pi\) | |||||||
\(788\) | −1.02079e45 | − | 1.02079e45i | −0.0461867 | − | 0.0461867i | ||||
\(789\) | − | 2.74139e46i | − | 1.21545i | ||||||
\(790\) | 3.72544e45 | + | 5.48397e45i | 0.161862 | + | 0.238266i | ||||
\(791\) | 4.02776e45 | 0.171490 | ||||||||
\(792\) | 1.88335e45 | − | 1.88335e45i | 0.0785828 | − | 0.0785828i | ||||
\(793\) | 1.07242e46 | + | 1.07242e46i | 0.438523 | + | 0.438523i | ||||
\(794\) | − | 1.88976e46i | − | 0.757317i | ||||||
\(795\) | −6.54980e44 | + | 3.43011e45i | −0.0257249 | + | 0.134721i | ||||
\(796\) | −2.48874e45 | −0.0958013 | ||||||||
\(797\) | 1.09776e45 | − | 1.09776e45i | 0.0414164 | − | 0.0414164i | −0.686095 | − | 0.727512i | \(-0.740677\pi\) |
0.727512 | + | 0.686095i | \(0.240677\pi\) | |||||||
\(798\) | −6.62563e45 | − | 6.62563e45i | −0.245008 | − | 0.245008i | ||||
\(799\) | − | 5.66408e46i | − | 2.05296i | ||||||
\(800\) | −2.67695e46 | + | 1.15725e46i | −0.951042 | + | 0.411139i | ||||
\(801\) | 1.99385e45 | 0.0694339 | ||||||||
\(802\) | 1.96626e46 | − | 1.96626e46i | 0.671200 | − | 0.671200i | ||||
\(803\) | −2.96158e45 | − | 2.96158e45i | −0.0991004 | − | 0.0991004i | ||||
\(804\) | 2.64213e46i | 0.866679i | ||||||||
\(805\) | −4.22343e46 | − | 8.06464e45i | −1.35810 | − | 0.259329i | ||||
\(806\) | 2.77789e46 | 0.875697 | ||||||||
\(807\) | −3.13060e46 | + | 3.13060e46i | −0.967501 | + | 0.967501i | ||||
\(808\) | −7.77762e45 | − | 7.77762e45i | −0.235649 | − | 0.235649i | ||||
\(809\) | 5.47578e45i | 0.162656i | 0.996687 | + | 0.0813279i | \(0.0259161\pi\) | ||||
−0.996687 | + | 0.0813279i | \(0.974084\pi\) | |||||||
\(810\) | −1.08117e46 | + | 7.34475e45i | −0.314873 | + | 0.213903i | ||||
\(811\) | 3.38115e46 | 0.965451 | 0.482725 | − | 0.875772i | \(-0.339647\pi\) | ||||
0.482725 | + | 0.875772i | \(0.339647\pi\) | |||||||
\(812\) | 3.73092e46 | − | 3.73092e46i | 1.04453 | − | 1.04453i | ||||
\(813\) | 2.40720e46 | + | 2.40720e46i | 0.660790 | + | 0.660790i | ||||
\(814\) | 7.79311e45i | 0.209759i | ||||||||
\(815\) | 1.09329e46 | + | 1.60936e46i | 0.288544 | + | 0.424747i | ||||
\(816\) | −9.43234e45 | −0.244105 | ||||||||
\(817\) | 2.86412e44 | − | 2.86412e44i | 0.00726838 | − | 0.00726838i | ||||
\(818\) | 4.49797e44 | + | 4.49797e44i | 0.0111934 | + | 0.0111934i | ||||
\(819\) | 2.72425e46i | 0.664820i | ||||||||
\(820\) | −3.56011e45 | + | 1.86442e46i | −0.0852005 | + | 0.446193i | ||||
\(821\) | −7.07861e46 | −1.66134 | −0.830668 | − | 0.556768i | \(-0.812041\pi\) | ||||
−0.830668 | + | 0.556768i | \(0.812041\pi\) | |||||||
\(822\) | −2.22668e46 | + | 2.22668e46i | −0.512519 | + | 0.512519i | ||||
\(823\) | 1.61126e45 | + | 1.61126e45i | 0.0363720 | + | 0.0363720i | 0.725059 | − | 0.688687i | \(-0.241813\pi\) |
−0.688687 | + | 0.725059i | \(0.741813\pi\) | |||||||
\(824\) | 4.80450e46i | 1.06368i | ||||||||
\(825\) | −8.77117e45 | − | 2.02894e46i | −0.190456 | − | 0.440560i | ||||
\(826\) | −3.79514e46 | −0.808253 | ||||||||
\(827\) | −6.47856e45 | + | 6.47856e45i | −0.135329 | + | 0.135329i | −0.771526 | − | 0.636197i | \(-0.780506\pi\) |
0.636197 | + | 0.771526i | \(0.280506\pi\) | |||||||
\(828\) | 4.20933e45 | + | 4.20933e45i | 0.0862438 | + | 0.0862438i | ||||
\(829\) | − | 5.29008e46i | − | 1.06314i | −0.847015 | − | 0.531569i | \(-0.821603\pi\) | ||
0.847015 | − | 0.531569i | \(-0.178397\pi\) | |||||||
\(830\) | −5.66785e45 | − | 1.08228e45i | −0.111730 | − | 0.0213348i | ||||
\(831\) | −6.43648e46 | −1.24461 | ||||||||
\(832\) | 1.76992e46 | − | 1.76992e46i | 0.335723 | − | 0.335723i | ||||
\(833\) | 1.02444e47 | + | 1.02444e47i | 1.90620 | + | 1.90620i | ||||
\(834\) | − | 2.26964e46i | − | 0.414287i | ||||||
\(835\) | −1.77622e46 | + | 1.20664e46i | −0.318063 | + | 0.216070i | ||||
\(836\) | −9.11301e45 | −0.160089 | ||||||||
\(837\) | 4.60752e46 | − | 4.60752e46i | 0.794073 | − | 0.794073i | ||||
\(838\) | −2.79141e46 | − | 2.79141e46i | −0.471975 | − | 0.471975i | ||||
\(839\) | − | 2.34805e46i | − | 0.389507i | −0.980852 | − | 0.194754i | \(-0.937609\pi\) | ||
0.980852 | − | 0.194754i | \(-0.0623907\pi\) | |||||||
\(840\) | 5.08381e46 | + | 7.48355e46i | 0.827410 | + | 1.21798i | ||||
\(841\) | −1.38821e46 | −0.221676 | ||||||||
\(842\) | 1.53101e46 | − | 1.53101e46i | 0.239875 | − | 0.239875i | ||||
\(843\) | 3.88961e44 | + | 3.88961e44i | 0.00597951 | + | 0.00597951i | ||||
\(844\) | − | 8.45481e46i | − | 1.27534i | ||||||
\(845\) | 1.97786e46 | − | 1.03580e47i | 0.292744 | − | 1.53309i | ||||
\(846\) | 1.49362e46 | 0.216928 | ||||||||
\(847\) | −6.43772e46 | + | 6.43772e46i | −0.917482 | + | 0.917482i | ||||
\(848\) | −1.95192e45 | − | 1.95192e45i | −0.0272979 | − | 0.0272979i | ||||
\(849\) | − | 7.05140e45i | − | 0.0967726i | ||||||
\(850\) | −1.60889e46 | + | 4.05926e46i | −0.216683 | + | 0.546693i | ||||
\(851\) | −4.14808e46 | −0.548245 | ||||||||
\(852\) | 1.95767e46 | − | 1.95767e46i | 0.253926 | − | 0.253926i | ||||
\(853\) | 9.73335e45 | + | 9.73335e45i | 0.123902 | + | 0.123902i | 0.766339 | − | 0.642437i | \(-0.222076\pi\) |
−0.642437 | + | 0.766339i | \(0.722076\pi\) | |||||||
\(854\) | 3.00981e46i | 0.376021i | ||||||||
\(855\) | −7.31208e45 | − | 1.39624e45i | −0.0896568 | − | 0.0171200i | ||||
\(856\) | −4.76873e46 | −0.573882 | ||||||||
\(857\) | 7.09163e46 | − | 7.09163e46i | 0.837632 | − | 0.837632i | −0.150915 | − | 0.988547i | \(-0.548222\pi\) |
0.988547 | + | 0.150915i | \(0.0482220\pi\) | |||||||
\(858\) | 2.46183e46 | + | 2.46183e46i | 0.285405 | + | 0.285405i | ||||
\(859\) | 5.67570e45i | 0.0645846i | 0.999478 | + | 0.0322923i | \(0.0102807\pi\) | ||||
−0.999478 | + | 0.0322923i | \(0.989719\pi\) | |||||||
\(860\) | −1.35837e45 | + | 9.22782e44i | −0.0151720 | + | 0.0103068i | ||||
\(861\) | 9.30394e46 | 1.02004 | ||||||||
\(862\) | −1.50261e46 | + | 1.50261e46i | −0.161707 | + | 0.161707i | ||||
\(863\) | 8.72119e46 | + | 8.72119e46i | 0.921304 | + | 0.921304i | 0.997122 | − | 0.0758173i | \(-0.0241566\pi\) |
−0.0758173 | + | 0.997122i | \(0.524157\pi\) | |||||||
\(864\) | − | 1.07749e47i | − | 1.11736i | ||||||
\(865\) | 1.85415e46 | + | 2.72938e46i | 0.188751 | + | 0.277847i | ||||
\(866\) | −6.55888e45 | −0.0655456 | ||||||||
\(867\) | −1.60067e46 | + | 1.60067e46i | −0.157035 | + | 0.157035i | ||||
\(868\) | −1.02175e47 | − | 1.02175e47i | −0.984076 | − | 0.984076i | ||||
\(869\) | − | 3.16053e46i | − | 0.298843i | ||||||
\(870\) | 1.03313e46 | − | 5.41049e46i | 0.0959064 | − | 0.502260i | ||||
\(871\) | 2.38806e47 | 2.17648 | ||||||||
\(872\) | 7.17729e46 | − | 7.17729e46i | 0.642239 | − | 0.642239i | ||||
\(873\) | −8.17320e45 | − | 8.17320e45i | −0.0718066 | − | 0.0718066i | ||||
\(874\) | 1.85060e46i | 0.159636i | ||||||||
\(875\) | −2.12769e47 | + | 4.74368e46i | −1.80210 | + | 0.401778i | ||||
\(876\) | −1.96963e46 | −0.163802 | ||||||||
\(877\) | −6.94834e46 | + | 6.94834e46i | −0.567397 | + | 0.567397i | −0.931399 | − | 0.364001i | \(-0.881410\pi\) |
0.364001 | + | 0.931399i | \(0.381410\pi\) | |||||||
\(878\) | 1.06963e45 | + | 1.06963e45i | 0.00857675 | + | 0.00857675i | ||||
\(879\) | 1.37626e47i | 1.08362i | ||||||||
\(880\) | 1.71628e46 | + | 3.27724e45i | 0.132698 | + | 0.0253387i | ||||
\(881\) | 1.40012e47 | 1.06304 | 0.531521 | − | 0.847045i | \(-0.321621\pi\) | ||||
0.531521 | + | 0.847045i | \(0.321621\pi\) | |||||||
\(882\) | −2.70147e46 | + | 2.70147e46i | −0.201420 | + | 0.201420i | ||||
\(883\) | −1.75045e47 | − | 1.75045e47i | −1.28168 | − | 1.28168i | −0.939712 | − | 0.341966i | \(-0.888907\pi\) |
−0.341966 | − | 0.939712i | \(-0.611093\pi\) | |||||||
\(884\) | 1.80267e47i | 1.29622i | ||||||||
\(885\) | 8.59008e46 | − | 5.83552e46i | 0.606604 | − | 0.412085i | ||||
\(886\) | −7.27974e46 | −0.504866 | ||||||||
\(887\) | −1.06668e47 | + | 1.06668e47i | −0.726538 | + | 0.726538i | −0.969928 | − | 0.243391i | \(-0.921740\pi\) |
0.243391 | + | 0.969928i | \(0.421740\pi\) | |||||||
\(888\) | 6.17157e46 | + | 6.17157e46i | 0.412846 | + | 0.412846i | ||||
\(889\) | − | 5.67314e46i | − | 0.372731i | ||||||
\(890\) | −1.41212e46 | − | 2.07869e46i | −0.0911236 | − | 0.134137i | ||||
\(891\) | 6.23102e46 | 0.394926 | ||||||||
\(892\) | −1.25052e46 | + | 1.25052e46i | −0.0778488 | + | 0.0778488i | ||||
\(893\) | −8.60591e46 | − | 8.60591e46i | −0.526227 | − | 0.526227i | ||||
\(894\) | − | 3.08323e46i | − | 0.185185i | ||||||
\(895\) | −1.49693e46 | + | 7.83940e46i | −0.0883149 | + | 0.462503i | ||||
\(896\) | −2.80426e47 | −1.62514 | ||||||||
\(897\) | −1.31037e47 | + | 1.31037e47i | −0.745960 | + | 0.745960i | ||||
\(898\) | −5.20980e46 | − | 5.20980e46i | −0.291340 | − | 0.291340i | ||||
\(899\) | 2.09518e47i | 1.15097i | ||||||||
\(900\) | 2.80571e46 | + | 1.11205e46i | 0.151413 | + | 0.0600128i | ||||
\(901\) | −3.28858e46 | −0.174346 | ||||||||
\(902\) | −2.44111e46 | + | 2.44111e46i | −0.127140 | + | 0.127140i | ||||
\(903\) | 5.69176e45 | + | 5.69176e45i | 0.0291234 | + | 0.0291234i | ||||
\(904\) | 1.67378e46i | 0.0841402i | ||||||||
\(905\) | 2.22868e47 | + | 4.25566e46i | 1.10070 | + | 0.210179i | ||||
\(906\) | −5.68904e46 | −0.276050 | ||||||||
\(907\) | 1.31265e47 | − | 1.31265e47i | 0.625794 | − | 0.625794i | −0.321213 | − | 0.947007i | \(-0.604090\pi\) |
0.947007 | + | 0.321213i | \(0.104090\pi\) | |||||||
\(908\) | −2.72448e46 | − | 2.72448e46i | −0.127618 | − | 0.127618i | ||||
\(909\) | 1.79858e46i | 0.0827765i | ||||||||
\(910\) | 2.84016e47 | − | 1.92941e47i | 1.28434 | − | 0.872495i | ||||
\(911\) | −5.01416e46 | −0.222794 | −0.111397 | − | 0.993776i | \(-0.535533\pi\) | ||||
−0.111397 | + | 0.993776i | \(0.535533\pi\) | |||||||
\(912\) | −1.43313e46 | + | 1.43313e46i | −0.0625704 | + | 0.0625704i | ||||
\(913\) | 1.94512e46 | + | 1.94512e46i | 0.0834476 | + | 0.0834476i | ||||
\(914\) | 7.50573e46i | 0.316413i | ||||||||
\(915\) | −4.62796e46 | − | 6.81252e46i | −0.191713 | − | 0.282208i | ||||
\(916\) | 3.15830e47 | 1.28566 | ||||||||
\(917\) | 1.03337e47 | − | 1.03337e47i | 0.413375 | − | 0.413375i | ||||
\(918\) | −1.14073e47 | − | 1.14073e47i | −0.448436 | − | 0.448436i | ||||
\(919\) | 2.00963e47i | 0.776369i | 0.921582 | + | 0.388185i | \(0.126898\pi\) | ||||
−0.921582 | + | 0.388185i | \(0.873102\pi\) | |||||||
\(920\) | 3.35135e46 | − | 1.75509e47i | 0.127237 | − | 0.666339i | ||||
\(921\) | 1.32587e47 | 0.494706 | ||||||||
\(922\) | −7.75852e45 | + | 7.75852e45i | −0.0284501 | + | 0.0284501i | ||||
\(923\) | −1.76942e47 | − | 1.76942e47i | −0.637680 | − | 0.637680i | ||||
\(924\) | − | 1.81100e47i | − | 0.641455i | ||||||
\(925\) | −1.93038e47 | + | 8.34510e46i | −0.672008 | + | 0.290512i | ||||
\(926\) | 1.03668e47 | 0.354707 | ||||||||
\(927\) | 5.55522e46 | − | 5.55522e46i | 0.186821 | − | 0.186821i | ||||
\(928\) | 2.44983e47 | + | 2.44983e47i | 0.809781 | + | 0.809781i | ||||
\(929\) | − | 4.97440e47i | − | 1.61618i | −0.589060 | − | 0.808089i | \(-0.700502\pi\) | ||
0.589060 | − | 0.808089i | \(-0.299498\pi\) | |||||||
\(930\) | −1.48172e47 | − | 2.82934e46i | −0.473192 | − | 0.0903561i | ||||
\(931\) | 3.11305e47 | 0.977216 | ||||||||
\(932\) | 3.49856e46 | − | 3.49856e46i | 0.107953 | − | 0.107953i | ||||
\(933\) | −2.94889e47 | − | 2.94889e47i | −0.894441 | − | 0.894441i | ||||
\(934\) | 3.23427e47i | 0.964330i | ||||||||
\(935\) | 1.72186e47 | − | 1.16972e47i | 0.504676 | − | 0.342842i | ||||
\(936\) | −1.13209e47 | −0.326188 | ||||||||
\(937\) | 1.57098e47 | − | 1.57098e47i | 0.444977 | − | 0.444977i | −0.448703 | − | 0.893681i | \(-0.648114\pi\) |
0.893681 | + | 0.448703i | \(0.148114\pi\) | |||||||
\(938\) | 3.35111e47 | + | 3.35111e47i | 0.933134 | + | 0.933134i | ||||
\(939\) | 5.48733e47i | 1.50214i | ||||||||
\(940\) | 2.77271e47 | + | 4.08153e47i | 0.746207 | + | 1.09844i | ||||
\(941\) | −6.33892e47 | −1.67719 | −0.838593 | − | 0.544759i | \(-0.816621\pi\) | ||||
−0.838593 | + | 0.544759i | \(0.816621\pi\) | |||||||
\(942\) | 1.35570e47 | − | 1.35570e47i | 0.352654 | − | 0.352654i | ||||
\(943\) | −1.29934e47 | − | 1.29934e47i | −0.332305 | − | 0.332305i | ||||
\(944\) | 8.20895e46i | 0.206412i | ||||||||
\(945\) | 1.51061e47 | − | 7.91103e47i | 0.373459 | − | 1.95580i | ||||
\(946\) | −2.98673e45 | −0.00726002 | ||||||||
\(947\) | −4.74807e47 | + | 4.74807e47i | −1.13480 | + | 1.13480i | −0.145426 | + | 0.989369i | \(0.546455\pi\) |
−0.989369 | + | 0.145426i | \(0.953545\pi\) | |||||||
\(948\) | −1.05097e47 | − | 1.05097e47i | −0.246977 | − | 0.246977i | ||||
\(949\) | 1.78022e47i | 0.411354i | ||||||||
\(950\) | 3.72304e46 | + | 8.61208e46i | 0.0845902 | + | 0.195673i | ||||
\(951\) | −3.49702e47 | −0.781285 | ||||||||
\(952\) | −6.02441e47 | + | 6.02441e47i | −1.32350 | + | 1.32350i | ||||
\(953\) | 2.21270e47 | + | 2.21270e47i | 0.478008 | + | 0.478008i | 0.904494 | − | 0.426486i | \(-0.140249\pi\) |
−0.426486 | + | 0.904494i | \(0.640249\pi\) | |||||||
\(954\) | − | 8.67202e45i | − | 0.0184224i | ||||||
\(955\) | −3.28509e47 | − | 6.27288e46i | −0.686267 | − | 0.131043i | ||||
\(956\) | 4.25977e47 | 0.875104 | ||||||||
\(957\) | −1.85679e47 | + | 1.85679e47i | −0.375122 | + | 0.375122i | ||||
\(958\) | 7.31919e45 | + | 7.31919e45i | 0.0145417 | + | 0.0145417i | ||||
\(959\) | − | 1.48050e48i | − | 2.89275i | ||||||
\(960\) | −1.12434e47 | + | 7.63801e46i | −0.216052 | + | 0.146771i | ||||
\(961\) | 4.46407e46 | 0.0843639 | ||||||||
\(962\) | 2.34224e47 | − | 2.34224e47i | 0.435342 | − | 0.435342i | ||||
\(963\) | 5.51386e46 | + | 5.51386e46i | 0.100794 | + | 0.100794i | ||||
\(964\) | − | 4.78378e47i | − | 0.860079i | ||||||
\(965\) | 5.66708e47 | + | 8.34214e47i | 1.00213 | + | 1.47517i | ||||
\(966\) | −3.67764e47 | −0.639639 | ||||||||
\(967\) | −5.48061e46 | + | 5.48061e46i | −0.0937573 | + | 0.0937573i | −0.752430 | − | 0.658672i | \(-0.771118\pi\) |
0.658672 | + | 0.752430i | \(0.271118\pi\) | |||||||
\(968\) | −2.67527e47 | − | 2.67527e47i | −0.450154 | − | 0.450154i | ||||
\(969\) | 2.41453e47i | 0.399625i | ||||||||
\(970\) | −2.73240e46 | + | 1.43095e47i | −0.0444833 | + | 0.232958i | ||||
\(971\) | 4.02019e47 | 0.643782 | 0.321891 | − | 0.946777i | \(-0.395682\pi\) | ||||
0.321891 | + | 0.946777i | \(0.395682\pi\) | |||||||
\(972\) | −1.43210e47 | + | 1.43210e47i | −0.225586 | + | 0.225586i | ||||
\(973\) | 7.54531e47 | + | 7.54531e47i | 1.16915 | + | 1.16915i | ||||
\(974\) | 1.25822e47i | 0.191785i | ||||||||
\(975\) | −3.46182e47 | + | 8.73422e47i | −0.519076 | + | 1.30964i | ||||
\(976\) | 6.51025e46 | 0.0960286 | ||||||||
\(977\) | −3.04071e47 | + | 3.04071e47i | −0.441226 | + | 0.441226i | −0.892424 | − | 0.451198i | \(-0.850997\pi\) |
0.451198 | + | 0.892424i | \(0.350997\pi\) | |||||||
\(978\) | 1.17669e47 | + | 1.17669e47i | 0.167973 | + | 0.167973i | ||||
\(979\) | 1.19799e47i | 0.168240i | ||||||||
\(980\) | −1.23971e48 | − | 2.36722e47i | −1.71278 | − | 0.327055i | ||||
\(981\) | −1.65975e47 | −0.225600 | ||||||||
\(982\) | 2.29129e47 | − | 2.29129e47i | 0.306406 | − | 0.306406i | ||||
\(983\) | −8.32725e47 | − | 8.32725e47i | −1.09558 | − | 1.09558i | −0.994921 | − | 0.100662i | \(-0.967904\pi\) |
−0.100662 | − | 0.994921i | \(-0.532096\pi\) | |||||||
\(984\) | 3.86636e47i | 0.500473i | ||||||||
\(985\) | 5.86098e46 | − | 3.98155e46i | 0.0746432 | − | 0.0507075i | ||||
\(986\) | 5.18724e47 | 0.649989 | ||||||||
\(987\) | 1.71022e48 | − | 1.71022e48i | 2.10852 | − | 2.10852i | ||||
\(988\) | 2.73894e47 | + | 2.73894e47i | 0.332255 | + | 0.332255i | ||||
\(989\) | − | 1.58976e46i | − | 0.0189755i | ||||||
\(990\) | 3.08455e46 | + | 4.54057e46i | 0.0362267 | + | 0.0533270i | ||||
\(991\) | −5.87247e46 | −0.0678644 | −0.0339322 | − | 0.999424i | \(-0.510803\pi\) | ||||
−0.0339322 | + | 0.999424i | \(0.510803\pi\) | |||||||
\(992\) | 6.70909e47 | − | 6.70909e47i | 0.762917 | − | 0.762917i | ||||
\(993\) | 4.98743e47 | + | 4.98743e47i | 0.558070 | + | 0.558070i | ||||
\(994\) | − | 4.96598e47i | − | 0.546793i | ||||||
\(995\) | 2.29108e46 | − | 1.19983e47i | 0.0248239 | − | 0.130002i | ||||
\(996\) | 1.29362e47 | 0.137930 | ||||||||
\(997\) | 5.40395e47 | − | 5.40395e47i | 0.567007 | − | 0.567007i | −0.364282 | − | 0.931289i | \(-0.618685\pi\) |
0.931289 | + | 0.364282i | \(0.118685\pi\) | |||||||
\(998\) | −4.33617e47 | − | 4.33617e47i | −0.447731 | − | 0.447731i | ||||
\(999\) | − | 7.76988e47i | − | 0.789527i |
(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 | 5.33.c.a.3.9 | yes | 30 | |
5.2 | odd | 4 | inner | 5.33.c.a.2.9 | ✓ | 30 | |
5.3 | odd | 4 | 25.33.c.b.7.7 | 30 | |||
5.4 | even | 2 | 25.33.c.b.18.7 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.33.c.a.2.9 | ✓ | 30 | 5.2 | odd | 4 | inner | |
5.33.c.a.3.9 | yes | 30 | 1.1 | even | 1 | trivial | |
25.33.c.b.7.7 | 30 | 5.3 | odd | 4 | |||
25.33.c.b.18.7 | 30 | 5.4 | even | 2 |