Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,39,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, 39, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 39);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 39 \) |
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: | \(36.5853876134\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 9 x^{17} + \cdots + 98\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.12 | ||
Root | \(0.500000 - 7.59483e7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.39.b.a.3.11 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 130787. | + | 507713.i | 0.249456 | + | 0.968386i | ||||
\(3\) | 1.21517e9i | 1.04552i | 0.852479 | + | 0.522762i | \(0.175098\pi\) | ||||
−0.852479 | + | 0.522762i | \(0.824902\pi\) | |||||||
\(4\) | −2.40667e11 | + | 1.32805e11i | −0.875543 | + | 0.483140i | ||||
\(5\) | −7.30752e12 | −0.383124 | −0.191562 | − | 0.981480i | \(-0.561355\pi\) | ||||
−0.191562 | + | 0.981480i | \(0.561355\pi\) | |||||||
\(6\) | −6.16959e14 | + | 1.58929e14i | −1.01247 | + | 0.260813i | ||||
\(7\) | − | 7.26783e15i | − | 0.637591i | −0.947824 | − | 0.318796i | \(-0.896722\pi\) | ||
0.947824 | − | 0.318796i | \(-0.103278\pi\) | |||||||
\(8\) | −9.89028e16 | − | 1.04821e17i | −0.686276 | − | 0.727341i | ||||
\(9\) | −1.25791e17 | −0.0931201 | ||||||||
\(10\) | −9.55728e17 | − | 3.71012e18i | −0.0955728 | − | 0.371012i | ||||
\(11\) | − | 4.95016e19i | − | 0.809390i | −0.914452 | − | 0.404695i | \(-0.867378\pi\) | ||
0.914452 | − | 0.404695i | \(-0.132622\pi\) | |||||||
\(12\) | −1.61380e20 | − | 2.92452e20i | −0.505135 | − | 0.915401i | ||||
\(13\) | 1.33417e21 | 0.912618 | 0.456309 | − | 0.889821i | \(-0.349171\pi\) | ||||
0.456309 | + | 0.889821i | \(0.349171\pi\) | |||||||
\(14\) | 3.68997e21 | − | 9.50538e20i | 0.617434 | − | 0.159051i | ||||
\(15\) | − | 8.87989e21i | − | 0.400566i | ||||||
\(16\) | 4.02837e22 | − | 6.39235e22i | 0.533151 | − | 0.846020i | ||||
\(17\) | −1.14555e22 | −0.0479165 | −0.0239582 | − | 0.999713i | \(-0.507627\pi\) | ||||
−0.0239582 | + | 0.999713i | \(0.507627\pi\) | |||||||
\(18\) | −1.64519e22 | − | 6.38660e22i | −0.0232294 | − | 0.0901762i | ||||
\(19\) | − | 5.70300e22i | − | 0.0288260i | −0.999896 | − | 0.0144130i | \(-0.995412\pi\) | ||
0.999896 | − | 0.0144130i | \(-0.00458797\pi\) | |||||||
\(20\) | 1.75868e24 | − | 9.70472e23i | 0.335442 | − | 0.185103i | ||||
\(21\) | 8.83167e24 | 0.666617 | ||||||||
\(22\) | 2.51326e25 | − | 6.47416e24i | 0.783802 | − | 0.201908i | ||||
\(23\) | − | 1.17299e26i | − | 1.57205i | −0.618195 | − | 0.786025i | \(-0.712136\pi\) | ||
0.618195 | − | 0.786025i | \(-0.287864\pi\) | |||||||
\(24\) | 1.27375e26 | − | 1.20184e26i | 0.760452 | − | 0.717518i | ||||
\(25\) | −3.10398e26 | −0.853216 | ||||||||
\(26\) | 1.74493e26 | + | 6.77378e26i | 0.227658 | + | 0.883766i | ||||
\(27\) | 1.48866e27i | 0.948165i | ||||||||
\(28\) | 9.65202e26 | + | 1.74913e27i | 0.308046 | + | 0.558238i | ||||
\(29\) | −1.11611e28 | −1.82871 | −0.914357 | − | 0.404908i | \(-0.867303\pi\) | ||||
−0.914357 | + | 0.404908i | \(0.867303\pi\) | |||||||
\(30\) | 4.50844e27 | − | 1.16137e27i | 0.387902 | − | 0.0999237i | ||||
\(31\) | − | 1.05042e28i | − | 0.484721i | −0.970186 | − | 0.242360i | \(-0.922078\pi\) | ||
0.970186 | − | 0.242360i | \(-0.0779217\pi\) | |||||||
\(32\) | 3.77234e28 | + | 1.20922e28i | 0.952272 | + | 0.305251i | ||||
\(33\) | 6.01529e28 | 0.846237 | ||||||||
\(34\) | −1.49823e27 | − | 5.81611e27i | −0.0119531 | − | 0.0464017i | ||||
\(35\) | 5.31098e28i | 0.244277i | ||||||||
\(36\) | 3.02739e28 | − | 1.67057e28i | 0.0815307 | − | 0.0449901i | ||||
\(37\) | 9.56044e29 | 1.52984 | 0.764918 | − | 0.644127i | \(-0.222779\pi\) | ||||
0.764918 | + | 0.644127i | \(0.222779\pi\) | |||||||
\(38\) | 2.89549e28 | − | 7.45878e27i | 0.0279147 | − | 0.00719084i | ||||
\(39\) | 1.62125e30i | 0.954164i | ||||||||
\(40\) | 7.22734e29 | + | 7.65980e29i | 0.262929 | + | 0.278662i | ||||
\(41\) | 5.59134e30 | 1.27240 | 0.636199 | − | 0.771525i | \(-0.280506\pi\) | ||||
0.636199 | + | 0.771525i | \(0.280506\pi\) | |||||||
\(42\) | 1.15507e30 | + | 4.48395e30i | 0.166292 | + | 0.645542i | ||||
\(43\) | 7.10284e30i | 0.653930i | 0.945036 | + | 0.326965i | \(0.106026\pi\) | ||||
−0.945036 | + | 0.326965i | \(0.893974\pi\) | |||||||
\(44\) | 6.57404e30 | + | 1.19134e31i | 0.391049 | + | 0.708656i | ||||
\(45\) | 9.19223e29 | 0.0356766 | ||||||||
\(46\) | 5.95544e31 | − | 1.53412e31i | 1.52235 | − | 0.392158i | ||||
\(47\) | − | 1.17187e31i | − | 0.199076i | −0.995034 | − | 0.0995380i | \(-0.968264\pi\) | ||
0.995034 | − | 0.0995380i | \(-0.0317365\pi\) | |||||||
\(48\) | 7.76780e31 | + | 4.89517e31i | 0.884534 | + | 0.557422i | ||||
\(49\) | 7.71134e31 | 0.593478 | ||||||||
\(50\) | −4.05960e31 | − | 1.57593e32i | −0.212840 | − | 0.826242i | ||||
\(51\) | − | 1.39204e31i | − | 0.0500978i | ||||||
\(52\) | −3.21092e32 | + | 1.77185e32i | −0.799036 | + | 0.440922i | ||||
\(53\) | −3.89822e32 | −0.675499 | −0.337749 | − | 0.941236i | \(-0.609666\pi\) | ||||
−0.337749 | + | 0.941236i | \(0.609666\pi\) | |||||||
\(54\) | −7.55812e32 | + | 1.94697e32i | −0.918189 | + | 0.236526i | ||||
\(55\) | 3.61734e32i | 0.310097i | ||||||||
\(56\) | −7.61821e32 | + | 7.18809e32i | −0.463746 | + | 0.437563i | ||||
\(57\) | 6.93013e31 | 0.0301383 | ||||||||
\(58\) | −1.45973e33 | − | 5.66665e33i | −0.456185 | − | 1.77090i | ||||
\(59\) | − | 6.64750e33i | − | 1.50131i | −0.660695 | − | 0.750654i | \(-0.729738\pi\) | ||
0.660695 | − | 0.750654i | \(-0.270262\pi\) | |||||||
\(60\) | 1.17929e33 | + | 2.13710e33i | 0.193529 | + | 0.350712i | ||||
\(61\) | −6.57417e33 | −0.788086 | −0.394043 | − | 0.919092i | \(-0.628924\pi\) | ||||
−0.394043 | + | 0.919092i | \(0.628924\pi\) | |||||||
\(62\) | 5.33313e33 | − | 1.37382e33i | 0.469397 | − | 0.120917i | ||||
\(63\) | 9.14232e32i | 0.0593726i | ||||||||
\(64\) | −1.20565e33 | + | 2.07342e34i | −0.0580501 | + | 0.998314i | ||||
\(65\) | −9.74950e33 | −0.349646 | ||||||||
\(66\) | 7.86722e33 | + | 3.05404e34i | 0.211099 | + | 0.819484i | ||||
\(67\) | − | 3.38641e33i | − | 0.0682838i | −0.999417 | − | 0.0341419i | \(-0.989130\pi\) | ||
0.999417 | − | 0.0341419i | \(-0.0108698\pi\) | |||||||
\(68\) | 2.75697e33 | − | 1.52134e33i | 0.0419529 | − | 0.0231504i | ||||
\(69\) | 1.42539e35 | 1.64362 | ||||||||
\(70\) | −2.69645e34 | + | 6.94607e33i | −0.236554 | + | 0.0609364i | ||||
\(71\) | − | 4.35113e34i | − | 0.291537i | −0.989319 | − | 0.145768i | \(-0.953435\pi\) | ||
0.989319 | − | 0.145768i | \(-0.0465655\pi\) | |||||||
\(72\) | 1.24411e34 | + | 1.31856e34i | 0.0639061 | + | 0.0677301i | ||||
\(73\) | 2.83225e35 | 1.11943 | 0.559715 | − | 0.828685i | \(-0.310911\pi\) | ||||
0.559715 | + | 0.828685i | \(0.310911\pi\) | |||||||
\(74\) | 1.25038e35 | + | 4.85396e35i | 0.381628 | + | 1.48147i | ||||
\(75\) | − | 3.77187e35i | − | 0.892057i | ||||||
\(76\) | 7.57385e33 | + | 1.37253e34i | 0.0139270 | + | 0.0252384i | ||||
\(77\) | −3.59769e35 | −0.516060 | ||||||||
\(78\) | −8.23131e35 | + | 2.12039e35i | −0.923999 | + | 0.238022i | ||||
\(79\) | − | 2.18449e36i | − | 1.92502i | −0.271252 | − | 0.962508i | \(-0.587438\pi\) | ||
0.271252 | − | 0.962508i | \(-0.412562\pi\) | |||||||
\(80\) | −2.94374e35 | + | 4.67122e35i | −0.204263 | + | 0.324131i | ||||
\(81\) | −1.97890e36 | −1.08445 | ||||||||
\(82\) | 7.31275e35 | + | 2.83880e36i | 0.317408 | + | 1.23217i | ||||
\(83\) | − | 1.82062e36i | − | 0.627677i | −0.949476 | − | 0.313839i | \(-0.898385\pi\) | ||
0.949476 | − | 0.313839i | \(-0.101615\pi\) | |||||||
\(84\) | −2.12549e36 | + | 1.17289e36i | −0.583651 | + | 0.322069i | ||||
\(85\) | 8.37113e34 | 0.0183580 | ||||||||
\(86\) | −3.60620e36 | + | 9.28959e35i | −0.633257 | + | 0.163127i | ||||
\(87\) | − | 1.35627e37i | − | 1.91196i | ||||||
\(88\) | −5.18880e36 | + | 4.89585e36i | −0.588703 | + | 0.555465i | ||||
\(89\) | 2.05963e37 | 1.88529 | 0.942646 | − | 0.333795i | \(-0.108329\pi\) | ||||
0.942646 | + | 0.333795i | \(0.108329\pi\) | |||||||
\(90\) | 1.20222e35 | + | 4.66702e35i | 0.00889976 | + | 0.0345487i | ||||
\(91\) | − | 9.69656e36i | − | 0.581877i | ||||||
\(92\) | 1.55779e37 | + | 2.82301e37i | 0.759521 | + | 1.37640i | ||||
\(93\) | 1.27644e37 | 0.506787 | ||||||||
\(94\) | 5.94972e36 | − | 1.53265e36i | 0.192782 | − | 0.0496608i | ||||
\(95\) | 4.16748e35i | 0.0110440i | ||||||||
\(96\) | −1.46941e37 | + | 4.58404e37i | −0.319147 | + | 0.995623i | ||||
\(97\) | −5.02029e37 | −0.895501 | −0.447750 | − | 0.894159i | \(-0.647775\pi\) | ||||
−0.447750 | + | 0.894159i | \(0.647775\pi\) | |||||||
\(98\) | 1.00854e37 | + | 3.91515e37i | 0.148047 | + | 0.574716i | ||||
\(99\) | 6.22688e36i | 0.0753705i | ||||||||
\(100\) | 7.47027e37 | − | 4.12223e37i | 0.747027 | − | 0.412223i | ||||
\(101\) | 6.20394e37 | 0.513525 | 0.256762 | − | 0.966475i | \(-0.417344\pi\) | ||||
0.256762 | + | 0.966475i | \(0.417344\pi\) | |||||||
\(102\) | 7.06758e36 | − | 1.82061e36i | 0.0485140 | − | 0.0124972i | ||||
\(103\) | − | 1.63183e38i | − | 0.930611i | −0.885150 | − | 0.465305i | \(-0.845945\pi\) | ||
0.885150 | − | 0.465305i | \(-0.154055\pi\) | |||||||
\(104\) | −1.31954e38 | − | 1.39849e38i | −0.626308 | − | 0.663784i | ||||
\(105\) | −6.45376e37 | −0.255397 | ||||||||
\(106\) | −5.09836e37 | − | 1.97918e38i | −0.168507 | − | 0.654143i | ||||
\(107\) | 2.75178e38i | 0.760889i | 0.924804 | + | 0.380444i | \(0.124229\pi\) | ||||
−0.924804 | + | 0.380444i | \(0.875771\pi\) | |||||||
\(108\) | −1.97701e38 | − | 3.58272e38i | −0.458096 | − | 0.830159i | ||||
\(109\) | −3.45759e38 | −0.672466 | −0.336233 | − | 0.941779i | \(-0.609153\pi\) | ||||
−0.336233 | + | 0.941779i | \(0.609153\pi\) | |||||||
\(110\) | −1.83657e38 | + | 4.73101e37i | −0.300294 | + | 0.0773557i | ||||
\(111\) | 1.16176e39i | 1.59948i | ||||||||
\(112\) | −4.64585e38 | − | 2.92776e38i | −0.539415 | − | 0.339932i | ||||
\(113\) | −3.27947e38 | −0.321598 | −0.160799 | − | 0.986987i | \(-0.551407\pi\) | ||||
−0.160799 | + | 0.986987i | \(0.551407\pi\) | |||||||
\(114\) | 9.06371e36 | + | 3.51852e37i | 0.00751820 | + | 0.0291855i | ||||
\(115\) | 8.57166e38i | 0.602290i | ||||||||
\(116\) | 2.68612e39 | − | 1.48225e39i | 1.60112 | − | 0.883526i | ||||
\(117\) | −1.67828e38 | −0.0849831 | ||||||||
\(118\) | 3.37502e39 | − | 8.69407e38i | 1.45385 | − | 0.374511i | ||||
\(119\) | 8.32567e37i | 0.0305511i | ||||||||
\(120\) | −9.30798e38 | + | 8.78246e38i | −0.291348 | + | 0.274899i | ||||
\(121\) | 1.29003e39 | 0.344887 | ||||||||
\(122\) | −8.59816e38 | − | 3.33779e39i | −0.196593 | − | 0.763172i | ||||
\(123\) | 6.79444e39i | 1.33032i | ||||||||
\(124\) | 1.39501e39 | + | 2.52802e39i | 0.234188 | + | 0.424394i | ||||
\(125\) | 4.92670e39 | 0.710012 | ||||||||
\(126\) | −4.64167e38 | + | 1.19570e38i | −0.0574956 | + | 0.0148109i | ||||
\(127\) | 3.39805e39i | 0.362208i | 0.983464 | + | 0.181104i | \(0.0579671\pi\) | ||||
−0.983464 | + | 0.181104i | \(0.942033\pi\) | |||||||
\(128\) | −1.06847e40 | + | 2.09963e39i | −0.981234 | + | 0.192821i | ||||
\(129\) | −8.63117e39 | −0.683699 | ||||||||
\(130\) | −1.27511e39 | − | 4.94995e39i | −0.0872215 | − | 0.338592i | ||||
\(131\) | − | 3.17297e40i | − | 1.87634i | −0.346173 | − | 0.938171i | \(-0.612519\pi\) | ||
0.346173 | − | 0.938171i | \(-0.387481\pi\) | |||||||
\(132\) | −1.44769e40 | + | 7.98859e39i | −0.740917 | + | 0.408851i | ||||
\(133\) | −4.14485e38 | −0.0183792 | ||||||||
\(134\) | 1.71932e39 | − | 4.42898e38i | 0.0661251 | − | 0.0170338i | ||||
\(135\) | − | 1.08784e40i | − | 0.363265i | ||||||
\(136\) | 1.13298e39 | + | 1.20078e39i | 0.0328839 | + | 0.0348516i | ||||
\(137\) | −1.96261e40 | −0.495613 | −0.247806 | − | 0.968810i | \(-0.579710\pi\) | ||||
−0.247806 | + | 0.968810i | \(0.579710\pi\) | |||||||
\(138\) | 1.86422e40 | + | 7.23688e40i | 0.410010 | + | 1.59165i | ||||
\(139\) | − | 5.67513e40i | − | 1.08817i | −0.839032 | − | 0.544083i | \(-0.816878\pi\) | ||
0.839032 | − | 0.544083i | \(-0.183122\pi\) | |||||||
\(140\) | −7.05323e39 | − | 1.27818e40i | −0.118020 | − | 0.213875i | ||||
\(141\) | 1.42402e40 | 0.208139 | ||||||||
\(142\) | 2.20913e40 | − | 5.69072e39i | 0.282320 | − | 0.0727258i | ||||
\(143\) | − | 6.60437e40i | − | 0.738664i | ||||||
\(144\) | −5.06735e39 | + | 8.04103e39i | −0.0496471 | + | 0.0787815i | ||||
\(145\) | 8.15601e40 | 0.700625 | ||||||||
\(146\) | 3.70421e40 | + | 1.43797e41i | 0.279249 | + | 1.08404i | ||||
\(147\) | 9.37061e40i | 0.620495i | ||||||||
\(148\) | −2.30089e41 | + | 1.26967e41i | −1.33944 | + | 0.739126i | ||||
\(149\) | 2.15975e41 | 1.10628 | 0.553139 | − | 0.833089i | \(-0.313430\pi\) | ||||
0.553139 | + | 0.833089i | \(0.313430\pi\) | |||||||
\(150\) | 1.91503e41 | − | 4.93312e40i | 0.863856 | − | 0.222529i | ||||
\(151\) | 8.25689e40i | 0.328288i | 0.986436 | + | 0.164144i | \(0.0524861\pi\) | ||||
−0.986436 | + | 0.164144i | \(0.947514\pi\) | |||||||
\(152\) | −5.97794e39 | + | 5.64043e39i | −0.0209664 | + | 0.0197826i | ||||
\(153\) | 1.44101e39 | 0.00446199 | ||||||||
\(154\) | −4.70531e40 | − | 1.82660e41i | −0.128735 | − | 0.499745i | ||||
\(155\) | 7.67598e40i | 0.185708i | ||||||||
\(156\) | −2.15310e41 | − | 3.90182e41i | −0.460995 | − | 0.835411i | ||||
\(157\) | −5.49352e41 | −1.04174 | −0.520868 | − | 0.853637i | \(-0.674392\pi\) | ||||
−0.520868 | + | 0.853637i | \(0.674392\pi\) | |||||||
\(158\) | 1.10909e42 | − | 2.85702e41i | 1.86416 | − | 0.480208i | ||||
\(159\) | − | 4.73700e41i | − | 0.706250i | ||||||
\(160\) | −2.75664e41 | − | 8.83641e40i | −0.364839 | − | 0.116949i | ||||
\(161\) | −8.52511e41 | −1.00232 | ||||||||
\(162\) | −2.58815e41 | − | 1.00471e42i | −0.270523 | − | 1.05017i | ||||
\(163\) | 1.84282e42i | 1.71364i | 0.515618 | + | 0.856819i | \(0.327562\pi\) | ||||
−0.515618 | + | 0.856819i | \(0.672438\pi\) | |||||||
\(164\) | −1.34565e42 | + | 7.42556e41i | −1.11404 | + | 0.614746i | ||||
\(165\) | −4.39569e41 | −0.324214 | ||||||||
\(166\) | 9.24355e41 | − | 2.38114e41i | 0.607834 | − | 0.156578i | ||||
\(167\) | 1.08923e42i | 0.639008i | 0.947585 | + | 0.319504i | \(0.103516\pi\) | ||||
−0.947585 | + | 0.319504i | \(0.896484\pi\) | |||||||
\(168\) | −8.73477e41 | − | 9.25743e41i | −0.457483 | − | 0.484858i | ||||
\(169\) | −3.57189e41 | −0.167129 | ||||||||
\(170\) | 1.09484e40 | + | 4.25013e40i | 0.00457951 | + | 0.0177776i | ||||
\(171\) | 7.17389e39i | 0.00268428i | ||||||||
\(172\) | −9.43289e41 | − | 1.70942e42i | −0.315940 | − | 0.572544i | ||||
\(173\) | 4.09054e42 | 1.22717 | 0.613584 | − | 0.789629i | \(-0.289727\pi\) | ||||
0.613584 | + | 0.789629i | \(0.289727\pi\) | |||||||
\(174\) | 6.88595e42 | − | 1.77382e42i | 1.85152 | − | 0.476952i | ||||
\(175\) | 2.25592e42i | 0.544003i | ||||||||
\(176\) | −3.16431e42 | − | 1.99411e42i | −0.684761 | − | 0.431527i | ||||
\(177\) | 8.07786e42 | 1.56965 | ||||||||
\(178\) | 2.69372e42 | + | 1.04570e43i | 0.470298 | + | 1.82569i | ||||
\(179\) | − | 3.65462e42i | − | 0.573634i | −0.957985 | − | 0.286817i | \(-0.907403\pi\) | ||
0.957985 | − | 0.286817i | \(-0.0925972\pi\) | |||||||
\(180\) | −2.21227e41 | + | 1.22077e41i | −0.0312364 | + | 0.0172368i | ||||
\(181\) | −1.33452e43 | −1.69603 | −0.848015 | − | 0.529972i | \(-0.822202\pi\) | ||||
−0.848015 | + | 0.529972i | \(0.822202\pi\) | |||||||
\(182\) | 4.92307e42 | − | 1.26818e42i | 0.563481 | − | 0.145153i | ||||
\(183\) | − | 7.98874e42i | − | 0.823963i | ||||||
\(184\) | −1.22954e43 | + | 1.16012e43i | −1.14342 | + | 1.07886i | ||||
\(185\) | −6.98631e42 | −0.586118 | ||||||||
\(186\) | 1.66942e42 | + | 6.48067e42i | 0.126421 | + | 0.490766i | ||||
\(187\) | 5.67066e41i | 0.0387831i | ||||||||
\(188\) | 1.55629e42 | + | 2.82030e42i | 0.0961816 | + | 0.174300i | ||||
\(189\) | 1.08193e43 | 0.604541 | ||||||||
\(190\) | −2.11588e41 | + | 5.45052e40i | −0.0106948 | + | 0.00275499i | ||||
\(191\) | − | 3.77753e43i | − | 1.72812i | −0.503387 | − | 0.864061i | \(-0.667913\pi\) | ||
0.503387 | − | 0.864061i | \(-0.332087\pi\) | |||||||
\(192\) | −2.51956e43 | − | 1.46508e42i | −1.04376 | − | 0.0606928i | ||||
\(193\) | 3.40504e42 | 0.127801 | 0.0639005 | − | 0.997956i | \(-0.479646\pi\) | ||||
0.0639005 | + | 0.997956i | \(0.479646\pi\) | |||||||
\(194\) | −6.56589e42 | − | 2.54887e43i | −0.223388 | − | 0.867190i | ||||
\(195\) | − | 1.18473e43i | − | 0.365563i | ||||||
\(196\) | −1.85587e43 | + | 1.02410e43i | −0.519615 | + | 0.286733i | ||||
\(197\) | 1.50175e43 | 0.381716 | 0.190858 | − | 0.981618i | \(-0.438873\pi\) | ||||
0.190858 | + | 0.981618i | \(0.438873\pi\) | |||||||
\(198\) | −3.16147e42 | + | 8.14395e41i | −0.0729878 | + | 0.0188017i | ||||
\(199\) | − | 3.32525e41i | − | 0.00697616i | −0.999994 | − | 0.00348808i | \(-0.998890\pi\) | ||
0.999994 | − | 0.00348808i | \(-0.00111029\pi\) | |||||||
\(200\) | 3.06992e43 | + | 3.25362e43i | 0.585542 | + | 0.620579i | ||||
\(201\) | 4.11507e42 | 0.0713924 | ||||||||
\(202\) | 8.11395e42 | + | 3.14982e43i | 0.128102 | + | 0.497290i | ||||
\(203\) | 8.11172e43i | 1.16597i | ||||||||
\(204\) | 1.84870e42 | + | 3.35019e42i | 0.0242043 | + | 0.0438628i | ||||
\(205\) | −4.08588e43 | −0.487486 | ||||||||
\(206\) | 8.28502e43 | − | 2.13422e43i | 0.901191 | − | 0.232147i | ||||
\(207\) | 1.47552e43i | 0.146389i | ||||||||
\(208\) | 5.37455e43 | − | 8.52851e43i | 0.486563 | − | 0.772093i | ||||
\(209\) | −2.82308e42 | −0.0233315 | ||||||||
\(210\) | −8.44068e42 | − | 3.27666e43i | −0.0637104 | − | 0.247323i | ||||
\(211\) | 1.86502e44i | 1.28622i | 0.765772 | + | 0.643112i | \(0.222357\pi\) | ||||
−0.765772 | + | 0.643112i | \(0.777643\pi\) | |||||||
\(212\) | 9.38174e43 | − | 5.17701e43i | 0.591428 | − | 0.326361i | ||||
\(213\) | 5.28737e43 | 0.304809 | ||||||||
\(214\) | −1.39711e44 | + | 3.59897e43i | −0.736834 | + | 0.189809i | ||||
\(215\) | − | 5.19041e43i | − | 0.250536i | ||||||
\(216\) | 1.56043e44 | − | 1.47233e44i | 0.689639 | − | 0.650703i | ||||
\(217\) | −7.63429e43 | −0.309054 | ||||||||
\(218\) | −4.52208e43 | − | 1.75546e44i | −0.167751 | − | 0.651206i | ||||
\(219\) | 3.44167e44i | 1.17039i | ||||||||
\(220\) | −4.80399e43 | − | 8.70575e43i | −0.149820 | − | 0.271503i | ||||
\(221\) | −1.52837e43 | −0.0437294 | ||||||||
\(222\) | −5.89840e44 | + | 1.51943e44i | −1.54891 | + | 0.399001i | ||||
\(223\) | − | 4.46316e44i | − | 1.07609i | −0.842915 | − | 0.538047i | \(-0.819162\pi\) | ||
0.842915 | − | 0.538047i | \(-0.180838\pi\) | |||||||
\(224\) | 8.78843e43 | − | 2.74167e44i | 0.194625 | − | 0.607160i | ||||
\(225\) | 3.90454e43 | 0.0794516 | ||||||||
\(226\) | −4.28912e43 | − | 1.66503e44i | −0.0802247 | − | 0.311431i | ||||
\(227\) | 2.49004e44i | 0.428267i | 0.976804 | + | 0.214134i | \(0.0686928\pi\) | ||||
−0.976804 | + | 0.214134i | \(0.931307\pi\) | |||||||
\(228\) | −1.66786e43 | + | 9.20353e42i | −0.0263874 | + | 0.0145610i | ||||
\(229\) | −6.19255e44 | −0.901562 | −0.450781 | − | 0.892635i | \(-0.648854\pi\) | ||||
−0.450781 | + | 0.892635i | \(0.648854\pi\) | |||||||
\(230\) | −4.35194e44 | + | 1.12106e44i | −0.583250 | + | 0.150245i | ||||
\(231\) | − | 4.37181e44i | − | 0.539553i | ||||||
\(232\) | 1.10387e45 | + | 1.16992e45i | 1.25500 | + | 1.33010i | ||||
\(233\) | −8.69248e44 | −0.910712 | −0.455356 | − | 0.890309i | \(-0.650488\pi\) | ||||
−0.455356 | + | 0.890309i | \(0.650488\pi\) | |||||||
\(234\) | −2.19497e43 | − | 8.52084e43i | −0.0211996 | − | 0.0822964i | ||||
\(235\) | 8.56344e43i | 0.0762709i | ||||||||
\(236\) | 8.82818e44 | + | 1.59984e45i | 0.725343 | + | 1.31446i | ||||
\(237\) | 2.65453e45 | 2.01265 | ||||||||
\(238\) | −4.22705e43 | + | 1.08889e43i | −0.0295853 | + | 0.00762117i | ||||
\(239\) | − | 2.46178e45i | − | 1.59107i | −0.605908 | − | 0.795534i | \(-0.707190\pi\) | ||
0.605908 | − | 0.795534i | \(-0.292810\pi\) | |||||||
\(240\) | −5.67633e44 | − | 3.57715e44i | −0.338887 | − | 0.213562i | ||||
\(241\) | 1.61182e45 | 0.889188 | 0.444594 | − | 0.895732i | \(-0.353348\pi\) | ||||
0.444594 | + | 0.895732i | \(0.353348\pi\) | |||||||
\(242\) | 1.68719e44 | + | 6.54964e44i | 0.0860343 | + | 0.333984i | ||||
\(243\) | − | 3.93750e44i | − | 0.185653i | ||||||
\(244\) | 1.58219e45 | − | 8.73079e44i | 0.690003 | − | 0.380756i | ||||
\(245\) | −5.63508e44 | −0.227376 | ||||||||
\(246\) | −3.44963e45 | + | 8.88625e44i | −1.28826 | + | 0.331857i | ||||
\(247\) | − | 7.60880e43i | − | 0.0263072i | ||||||
\(248\) | −1.10106e45 | + | 1.03890e45i | −0.352557 | + | 0.332652i | ||||
\(249\) | 2.21237e45 | 0.656252 | ||||||||
\(250\) | 6.44348e44 | + | 2.50135e45i | 0.177117 | + | 0.687566i | ||||
\(251\) | 3.21678e45i | 0.819635i | 0.912168 | + | 0.409817i | \(0.134408\pi\) | ||||
−0.912168 | + | 0.409817i | \(0.865592\pi\) | |||||||
\(252\) | −1.21414e44 | − | 2.20026e44i | −0.0286853 | − | 0.0519832i | ||||
\(253\) | −5.80650e45 | −1.27240 | ||||||||
\(254\) | −1.72523e45 | + | 4.44420e44i | −0.350758 | + | 0.0903552i | ||||
\(255\) | 1.01724e44i | 0.0191937i | ||||||||
\(256\) | −2.46343e45 | − | 5.15015e45i | −0.431500 | − | 0.902113i | ||||
\(257\) | −6.42474e45 | −1.04502 | −0.522512 | − | 0.852632i | \(-0.675005\pi\) | ||||
−0.522512 | + | 0.852632i | \(0.675005\pi\) | |||||||
\(258\) | −1.12885e45 | − | 4.38216e45i | −0.170553 | − | 0.662085i | ||||
\(259\) | − | 6.94837e45i | − | 0.975410i | ||||||
\(260\) | 2.34639e45 | − | 1.29478e45i | 0.306130 | − | 0.168928i | ||||
\(261\) | 1.40397e45 | 0.170290 | ||||||||
\(262\) | 1.61096e46 | − | 4.14984e45i | 1.81702 | − | 0.468065i | ||||
\(263\) | 3.42099e44i | 0.0358916i | 0.999839 | + | 0.0179458i | \(0.00571263\pi\) | ||||
−0.999839 | + | 0.0179458i | \(0.994287\pi\) | |||||||
\(264\) | −5.94929e45 | − | 6.30528e45i | −0.580752 | − | 0.615503i | ||||
\(265\) | 2.84863e45 | 0.258800 | ||||||||
\(266\) | −5.42092e43 | − | 2.10439e44i | −0.00458482 | − | 0.0177982i | ||||
\(267\) | 2.50280e46i | 1.97112i | ||||||||
\(268\) | 4.49730e44 | + | 8.14998e44i | 0.0329907 | + | 0.0597854i | ||||
\(269\) | −6.96422e45 | −0.475970 | −0.237985 | − | 0.971269i | \(-0.576487\pi\) | ||||
−0.237985 | + | 0.971269i | \(0.576487\pi\) | |||||||
\(270\) | 5.52311e45 | − | 1.42275e45i | 0.351781 | − | 0.0906188i | ||||
\(271\) | 1.11990e46i | 0.664912i | 0.943119 | + | 0.332456i | \(0.107877\pi\) | ||||
−0.943119 | + | 0.332456i | \(0.892123\pi\) | |||||||
\(272\) | −4.61471e44 | + | 7.32276e44i | −0.0255467 | + | 0.0405383i | ||||
\(273\) | 1.17830e46 | 0.608366 | ||||||||
\(274\) | −2.56684e45 | − | 9.96441e45i | −0.123634 | − | 0.479945i | ||||
\(275\) | 1.53652e46i | 0.690585i | ||||||||
\(276\) | −3.43044e46 | + | 1.89298e46i | −1.43906 | + | 0.794097i | ||||
\(277\) | 2.45032e46 | 0.959637 | 0.479819 | − | 0.877368i | \(-0.340702\pi\) | ||||
0.479819 | + | 0.877368i | \(0.340702\pi\) | |||||||
\(278\) | 2.88134e46 | − | 7.42234e45i | 1.05376 | − | 0.271450i | ||||
\(279\) | 1.32134e45i | 0.0451373i | ||||||||
\(280\) | 5.56702e45 | − | 5.25271e45i | 0.177672 | − | 0.167641i | ||||
\(281\) | −3.47809e45 | −0.103734 | −0.0518669 | − | 0.998654i | \(-0.516517\pi\) | ||||
−0.0518669 | + | 0.998654i | \(0.516517\pi\) | |||||||
\(282\) | 1.86243e45 | + | 7.22994e45i | 0.0519215 | + | 0.201559i | ||||
\(283\) | − | 4.65075e46i | − | 1.21222i | −0.795381 | − | 0.606109i | \(-0.792729\pi\) | ||
0.795381 | − | 0.606109i | \(-0.207271\pi\) | |||||||
\(284\) | 5.77850e45 | + | 1.04718e46i | 0.140853 | + | 0.255253i | ||||
\(285\) | −5.06420e44 | −0.0115467 | ||||||||
\(286\) | 3.35313e46 | − | 8.63767e45i | 0.715312 | − | 0.184265i | ||||
\(287\) | − | 4.06369e46i | − | 0.811269i | ||||||
\(288\) | −4.74528e45 | − | 1.52110e45i | −0.0886757 | − | 0.0284250i | ||||
\(289\) | −5.70244e46 | −0.997704 | ||||||||
\(290\) | 1.06670e46 | + | 4.14091e46i | 0.174775 | + | 0.678475i | ||||
\(291\) | − | 6.10052e46i | − | 0.936267i | ||||||
\(292\) | −6.81630e46 | + | 3.76136e46i | −0.980109 | + | 0.540842i | ||||
\(293\) | −6.29809e46 | −0.848641 | −0.424321 | − | 0.905512i | \(-0.639487\pi\) | ||||
−0.424321 | + | 0.905512i | \(0.639487\pi\) | |||||||
\(294\) | −4.75758e46 | + | 1.22555e46i | −0.600879 | + | 0.154787i | ||||
\(295\) | 4.85767e46i | 0.575188i | ||||||||
\(296\) | −9.45554e46 | − | 1.00213e47i | −1.04989 | − | 1.11271i | ||||
\(297\) | 7.36910e46 | 0.767435 | ||||||||
\(298\) | 2.82467e46 | + | 1.09653e47i | 0.275968 | + | 1.07130i | ||||
\(299\) | − | 1.56498e47i | − | 1.43468i | ||||||
\(300\) | 5.00922e46 | + | 9.07766e46i | 0.430989 | + | 0.781035i | ||||
\(301\) | 5.16222e46 | 0.416940 | ||||||||
\(302\) | −4.19213e46 | + | 1.07989e46i | −0.317909 | + | 0.0818935i | ||||
\(303\) | 7.53885e46i | 0.536902i | ||||||||
\(304\) | −3.64556e45 | − | 2.29738e45i | −0.0243874 | − | 0.0153686i | ||||
\(305\) | 4.80408e46 | 0.301935 | ||||||||
\(306\) | 1.88465e44 | + | 7.31618e44i | 0.00111307 | + | 0.00432093i | ||||
\(307\) | − | 4.16955e46i | − | 0.231452i | −0.993281 | − | 0.115726i | \(-0.963081\pi\) | ||
0.993281 | − | 0.115726i | \(-0.0369194\pi\) | |||||||
\(308\) | 8.65847e46 | − | 4.77790e46i | 0.451833 | − | 0.249329i | ||||
\(309\) | 1.98296e47 | 0.972976 | ||||||||
\(310\) | −3.89720e46 | + | 1.00392e46i | −0.179837 | + | 0.0463261i | ||||
\(311\) | 2.03179e47i | 0.881923i | 0.897526 | + | 0.440962i | \(0.145362\pi\) | ||||
−0.897526 | + | 0.440962i | \(0.854638\pi\) | |||||||
\(312\) | 1.69941e47 | − | 1.60346e47i | 0.694002 | − | 0.654820i | ||||
\(313\) | −8.98855e46 | −0.345420 | −0.172710 | − | 0.984973i | \(-0.555252\pi\) | ||||
−0.172710 | + | 0.984973i | \(0.555252\pi\) | |||||||
\(314\) | −7.18482e46 | − | 2.78913e47i | −0.259868 | − | 1.00880i | ||||
\(315\) | − | 6.68076e45i | − | 0.0227471i | ||||||
\(316\) | 2.90110e47 | + | 5.25735e47i | 0.930053 | + | 1.68543i | ||||
\(317\) | −5.01925e46 | −0.151535 | −0.0757675 | − | 0.997126i | \(-0.524141\pi\) | ||||
−0.0757675 | + | 0.997126i | \(0.524141\pi\) | |||||||
\(318\) | 2.40504e47 | − | 6.19539e46i | 0.683922 | − | 0.176179i | ||||
\(319\) | 5.52493e47i | 1.48014i | ||||||||
\(320\) | 8.81034e45 | − | 1.51515e47i | 0.0222404 | − | 0.382478i | ||||
\(321\) | −3.34388e47 | −0.795528 | ||||||||
\(322\) | −1.11497e47 | − | 4.32831e47i | −0.250036 | − | 0.970637i | ||||
\(323\) | 6.53308e44i | 0.00138124i | ||||||||
\(324\) | 4.76257e47 | − | 2.62807e47i | 0.949481 | − | 0.523941i | ||||
\(325\) | −4.14125e47 | −0.778660 | ||||||||
\(326\) | −9.35625e47 | + | 2.41017e47i | −1.65946 | + | 0.427478i | ||||
\(327\) | − | 4.20157e47i | − | 0.703079i | ||||||
\(328\) | −5.52999e47 | − | 5.86089e47i | −0.873216 | − | 0.925467i | ||||
\(329\) | −8.51693e46 | −0.126929 | ||||||||
\(330\) | −5.74899e46 | − | 2.23175e47i | −0.0808773 | − | 0.313964i | ||||
\(331\) | 9.10673e47i | 1.20957i | 0.796389 | + | 0.604784i | \(0.206741\pi\) | ||||
−0.796389 | + | 0.604784i | \(0.793259\pi\) | |||||||
\(332\) | 2.41787e47 | + | 4.38165e47i | 0.303256 | + | 0.549558i | ||||
\(333\) | −1.20262e47 | −0.142459 | ||||||||
\(334\) | −5.53016e47 | + | 1.42457e47i | −0.618806 | + | 0.159405i | ||||
\(335\) | 2.47462e46i | 0.0261612i | ||||||||
\(336\) | 3.55773e47 | − | 5.64551e47i | 0.355407 | − | 0.563971i | ||||
\(337\) | 1.64288e48 | 1.55109 | 0.775547 | − | 0.631289i | \(-0.217474\pi\) | ||||
0.775547 | + | 0.631289i | \(0.217474\pi\) | |||||||
\(338\) | −4.67157e46 | − | 1.81350e47i | −0.0416913 | − | 0.161845i | ||||
\(339\) | − | 3.98512e47i | − | 0.336238i | ||||||
\(340\) | −2.01466e46 | + | 1.11172e46i | −0.0160732 | + | 0.00886947i | ||||
\(341\) | −5.19976e47 | −0.392328 | ||||||||
\(342\) | −3.64228e45 | + | 9.38252e44i | −0.00259942 | + | 0.000669612i | ||||
\(343\) | − | 1.50479e48i | − | 1.01599i | ||||||
\(344\) | 7.44526e47 | − | 7.02491e47i | 0.475630 | − | 0.448777i | ||||
\(345\) | −1.04160e48 | −0.629709 | ||||||||
\(346\) | 5.34989e47 | + | 2.07682e48i | 0.306125 | + | 1.18837i | ||||
\(347\) | − | 1.70075e48i | − | 0.921258i | −0.887593 | − | 0.460629i | \(-0.847624\pi\) | ||
0.887593 | − | 0.460629i | \(-0.152376\pi\) | |||||||
\(348\) | 1.80119e48 | + | 3.26410e48i | 0.923747 | + | 1.67401i | ||||
\(349\) | 2.04634e48 | 0.993791 | 0.496896 | − | 0.867810i | \(-0.334473\pi\) | ||||
0.496896 | + | 0.867810i | \(0.334473\pi\) | |||||||
\(350\) | −1.14536e48 | + | 2.95045e47i | −0.526805 | + | 0.135705i | ||||
\(351\) | 1.98613e48i | 0.865312i | ||||||||
\(352\) | 5.98584e47 | − | 1.86737e48i | 0.247067 | − | 0.770760i | ||||
\(353\) | −8.30359e47 | −0.324748 | −0.162374 | − | 0.986729i | \(-0.551915\pi\) | ||||
−0.162374 | + | 0.986729i | \(0.551915\pi\) | |||||||
\(354\) | 1.05648e48 | + | 4.10123e48i | 0.391560 | + | 1.52003i | ||||
\(355\) | 3.17960e47i | 0.111695i | ||||||||
\(356\) | −4.95685e48 | + | 2.73528e48i | −1.65065 | + | 0.910860i | ||||
\(357\) | −1.01171e47 | −0.0319419 | ||||||||
\(358\) | 1.85550e48 | − | 4.77977e47i | 0.555499 | − | 0.143097i | ||||
\(359\) | − | 4.59767e48i | − | 1.30540i | −0.757617 | − | 0.652700i | \(-0.773636\pi\) | ||
0.757617 | − | 0.652700i | \(-0.226364\pi\) | |||||||
\(360\) | −9.09138e46 | − | 9.63538e46i | −0.0244840 | − | 0.0259490i | ||||
\(361\) | 3.91089e48 | 0.999169 | ||||||||
\(362\) | −1.74538e48 | − | 6.77556e48i | −0.423086 | − | 1.64241i | ||||
\(363\) | 1.56761e48i | 0.360588i | ||||||||
\(364\) | 1.28775e48 | + | 2.33365e48i | 0.281128 | + | 0.509458i | ||||
\(365\) | −2.06967e48 | −0.428881 | ||||||||
\(366\) | 4.05599e48 | − | 1.04482e48i | 0.797914 | − | 0.205543i | ||||
\(367\) | − | 6.04449e48i | − | 1.12903i | −0.825424 | − | 0.564513i | \(-0.809064\pi\) | ||
0.825424 | − | 0.564513i | \(-0.190936\pi\) | |||||||
\(368\) | −7.49817e48 | − | 4.72525e48i | −1.32999 | − | 0.838140i | ||||
\(369\) | −7.03343e47 | −0.118486 | ||||||||
\(370\) | −9.13718e47 | − | 3.54704e48i | −0.146211 | − | 0.567588i | ||||
\(371\) | 2.83316e48i | 0.430692i | ||||||||
\(372\) | −3.07198e48 | + | 1.69518e48i | −0.443714 | + | 0.244849i | ||||
\(373\) | 1.85397e48 | 0.254470 | 0.127235 | − | 0.991873i | \(-0.459390\pi\) | ||||
0.127235 | + | 0.991873i | \(0.459390\pi\) | |||||||
\(374\) | −2.87907e47 | + | 7.41649e46i | −0.0375571 | + | 0.00967470i | ||||
\(375\) | 5.98679e48i | 0.742334i | ||||||||
\(376\) | −1.22836e48 | + | 1.15901e48i | −0.144796 | + | 0.136621i | ||||
\(377\) | −1.48909e49 | −1.66892 | ||||||||
\(378\) | 1.41503e48 | + | 5.49311e48i | 0.150807 | + | 0.585429i | ||||
\(379\) | 1.44280e49i | 1.46238i | 0.682172 | + | 0.731192i | \(0.261036\pi\) | ||||
−0.682172 | + | 0.731192i | \(0.738964\pi\) | |||||||
\(380\) | −5.53460e46 | − | 1.00298e47i | −0.00533578 | − | 0.00966946i | ||||
\(381\) | −4.12921e48 | −0.378698 | ||||||||
\(382\) | 1.91790e49 | − | 4.94052e48i | 1.67349 | − | 0.431091i | ||||
\(383\) | 2.57290e48i | 0.213622i | 0.994279 | + | 0.106811i | \(0.0340640\pi\) | ||||
−0.994279 | + | 0.106811i | \(0.965936\pi\) | |||||||
\(384\) | −2.55142e48 | − | 1.29837e49i | −0.201599 | − | 1.02590i | ||||
\(385\) | 2.62902e48 | 0.197715 | ||||||||
\(386\) | 4.45336e47 | + | 1.72879e48i | 0.0318808 | + | 0.123761i | ||||
\(387\) | − | 8.93477e47i | − | 0.0608940i | ||||||
\(388\) | 1.20822e49 | − | 6.66718e48i | 0.784049 | − | 0.432652i | ||||
\(389\) | 4.82829e47 | 0.0298367 | 0.0149184 | − | 0.999889i | \(-0.495251\pi\) | ||||
0.0149184 | + | 0.999889i | \(0.495251\pi\) | |||||||
\(390\) | 6.01504e48 | − | 1.54948e48i | 0.354006 | − | 0.0911921i | ||||
\(391\) | 1.34372e48i | 0.0753271i | ||||||||
\(392\) | −7.62673e48 | − | 8.08310e48i | −0.407290 | − | 0.431661i | ||||
\(393\) | 3.85571e49 | 1.96176 | ||||||||
\(394\) | 1.96410e48 | + | 7.62459e48i | 0.0952214 | + | 0.369648i | ||||
\(395\) | 1.59632e49i | 0.737521i | ||||||||
\(396\) | −8.26958e47 | − | 1.49861e48i | −0.0364145 | − | 0.0659901i | ||||
\(397\) | 1.63366e49 | 0.685714 | 0.342857 | − | 0.939388i | \(-0.388605\pi\) | ||||
0.342857 | + | 0.939388i | \(0.388605\pi\) | |||||||
\(398\) | 1.68828e47 | − | 4.34900e46i | 0.00675562 | − | 0.00174025i | ||||
\(399\) | − | 5.03670e47i | − | 0.0192159i | ||||||
\(400\) | −1.25040e49 | + | 1.98417e49i | −0.454893 | + | 0.721838i | ||||
\(401\) | −3.91043e49 | −1.35669 | −0.678347 | − | 0.734742i | \(-0.737303\pi\) | ||||
−0.678347 | + | 0.734742i | \(0.737303\pi\) | |||||||
\(402\) | 5.38197e47 | + | 2.08927e48i | 0.0178093 | + | 0.0691354i | ||||
\(403\) | − | 1.40145e49i | − | 0.442365i | ||||||
\(404\) | −1.49309e49 | + | 8.23911e48i | −0.449613 | + | 0.248104i | ||||
\(405\) | 1.44609e49 | 0.415479 | ||||||||
\(406\) | −4.11843e49 | + | 1.06091e49i | −1.12911 | + | 0.290859i | ||||
\(407\) | − | 4.73257e49i | − | 1.23824i | ||||||
\(408\) | −1.45915e48 | + | 1.37677e48i | −0.0364382 | + | 0.0343809i | ||||
\(409\) | −4.46584e49 | −1.06454 | −0.532269 | − | 0.846576i | \(-0.678660\pi\) | ||||
−0.532269 | + | 0.846576i | \(0.678660\pi\) | |||||||
\(410\) | −5.34380e48 | − | 2.07446e49i | −0.121607 | − | 0.472075i | ||||
\(411\) | − | 2.38491e49i | − | 0.518175i | ||||||
\(412\) | 2.16715e49 | + | 3.92729e49i | 0.449616 | + | 0.814790i | ||||
\(413\) | −4.83129e49 | −0.957221 | ||||||||
\(414\) | −7.49143e48 | + | 1.92979e48i | −0.141762 | + | 0.0365178i | ||||
\(415\) | 1.33042e49i | 0.240478i | ||||||||
\(416\) | 5.03296e49 | + | 1.61331e49i | 0.869060 | + | 0.278577i | ||||
\(417\) | 6.89626e49 | 1.13770 | ||||||||
\(418\) | −3.69222e47 | − | 1.43331e48i | −0.00582020 | − | 0.0225939i | ||||
\(419\) | − | 1.14898e50i | − | 1.73080i | −0.501084 | − | 0.865399i | \(-0.667065\pi\) | ||
0.501084 | − | 0.865399i | \(-0.332935\pi\) | |||||||
\(420\) | 1.55321e49 | − | 8.57088e48i | 0.223611 | − | 0.123393i | ||||
\(421\) | −1.26109e49 | −0.173535 | −0.0867676 | − | 0.996229i | \(-0.527654\pi\) | ||||
−0.0867676 | + | 0.996229i | \(0.527654\pi\) | |||||||
\(422\) | −9.46895e49 | + | 2.43920e49i | −1.24556 | + | 0.320857i | ||||
\(423\) | 1.47411e48i | 0.0185380i | ||||||||
\(424\) | 3.85545e49 | + | 4.08615e49i | 0.463579 | + | 0.491318i | ||||
\(425\) | 3.55577e48 | 0.0408831 | ||||||||
\(426\) | 6.91520e48 | + | 2.68447e49i | 0.0760365 | + | 0.295173i | ||||
\(427\) | 4.77799e49i | 0.502477i | ||||||||
\(428\) | −3.65448e49 | − | 6.62263e49i | −0.367616 | − | 0.666191i | ||||
\(429\) | 8.02545e49 | 0.772291 | ||||||||
\(430\) | 2.63524e49 | − | 6.78838e48i | 0.242616 | − | 0.0624979i | ||||
\(431\) | 3.89274e49i | 0.342916i | 0.985191 | + | 0.171458i | \(0.0548477\pi\) | ||||
−0.985191 | + | 0.171458i | \(0.945152\pi\) | |||||||
\(432\) | 9.51603e49 | + | 5.99688e49i | 0.802166 | + | 0.505515i | ||||
\(433\) | 1.05308e50 | 0.849554 | 0.424777 | − | 0.905298i | \(-0.360352\pi\) | ||||
0.424777 | + | 0.905298i | \(0.360352\pi\) | |||||||
\(434\) | −9.98467e48 | − | 3.87603e49i | −0.0770954 | − | 0.299283i | ||||
\(435\) | 9.91095e49i | 0.732520i | ||||||||
\(436\) | 8.32129e49 | − | 4.59184e49i | 0.588773 | − | 0.324895i | ||||
\(437\) | −6.68958e48 | −0.0453160 | ||||||||
\(438\) | −1.74738e50 | + | 4.50126e49i | −1.13339 | + | 0.291962i | ||||
\(439\) | 2.51668e50i | 1.56316i | 0.623808 | + | 0.781578i | \(0.285585\pi\) | ||||
−0.623808 | + | 0.781578i | \(0.714415\pi\) | |||||||
\(440\) | 3.79172e49 | − | 3.57765e49i | 0.225546 | − | 0.212812i | ||||
\(441\) | −9.70021e48 | −0.0552647 | ||||||||
\(442\) | −1.99890e48 | − | 7.75971e48i | −0.0109086 | − | 0.0423470i | ||||
\(443\) | − | 1.36698e50i | − | 0.714648i | −0.933981 | − | 0.357324i | \(-0.883689\pi\) | ||
0.933981 | − | 0.357324i | \(-0.116311\pi\) | |||||||
\(444\) | −1.54287e50 | − | 2.79597e50i | −0.772774 | − | 1.40041i | ||||
\(445\) | −1.50508e50 | −0.722301 | ||||||||
\(446\) | 2.26601e50 | − | 5.83724e49i | 1.04207 | − | 0.268439i | ||||
\(447\) | 2.62447e50i | 1.15664i | ||||||||
\(448\) | 1.50692e50 | + | 8.76249e48i | 0.636516 | + | 0.0370122i | ||||
\(449\) | −3.22282e50 | −1.30484 | −0.652418 | − | 0.757860i | \(-0.726245\pi\) | ||||
−0.652418 | + | 0.757860i | \(0.726245\pi\) | |||||||
\(450\) | 5.10664e48 | + | 1.98239e49i | 0.0198197 | + | 0.0769398i | ||||
\(451\) | − | 2.76780e50i | − | 1.02987i | ||||||
\(452\) | 7.89262e49 | − | 4.35529e49i | 0.281573 | − | 0.155377i | ||||
\(453\) | −1.00335e50 | −0.343233 | ||||||||
\(454\) | −1.26423e50 | + | 3.25665e49i | −0.414728 | + | 0.106834i | ||||
\(455\) | 7.08578e49i | 0.222931i | ||||||||
\(456\) | −6.85409e48 | − | 7.26422e48i | −0.0206832 | − | 0.0219208i | ||||
\(457\) | −1.25133e50 | −0.362212 | −0.181106 | − | 0.983464i | \(-0.557968\pi\) | ||||
−0.181106 | + | 0.983464i | \(0.557968\pi\) | |||||||
\(458\) | −8.09906e49 | − | 3.14404e50i | −0.224900 | − | 0.873060i | ||||
\(459\) | − | 1.70533e49i | − | 0.0454327i | ||||||
\(460\) | −1.13836e50 | − | 2.06292e50i | −0.290991 | − | 0.527331i | ||||
\(461\) | 5.41554e50 | 1.32839 | 0.664193 | − | 0.747561i | \(-0.268775\pi\) | ||||
0.664193 | + | 0.747561i | \(0.268775\pi\) | |||||||
\(462\) | 2.21963e50 | − | 5.71777e49i | 0.522496 | − | 0.134595i | ||||
\(463\) | − | 2.68721e50i | − | 0.607104i | −0.952815 | − | 0.303552i | \(-0.901827\pi\) | ||
0.952815 | − | 0.303552i | \(-0.0981727\pi\) | |||||||
\(464\) | −4.49612e50 | + | 7.13458e50i | −0.974981 | + | 1.54713i | ||||
\(465\) | −9.32763e49 | −0.194163 | ||||||||
\(466\) | −1.13686e50 | − | 4.41329e50i | −0.227183 | − | 0.881921i | ||||
\(467\) | 6.79338e50i | 1.30336i | 0.758493 | + | 0.651681i | \(0.225936\pi\) | ||||
−0.758493 | + | 0.651681i | \(0.774064\pi\) | |||||||
\(468\) | 4.03907e49 | − | 2.22883e49i | 0.0744064 | − | 0.0410588i | ||||
\(469\) | −2.46118e49 | −0.0435372 | ||||||||
\(470\) | −4.34777e49 | + | 1.11999e49i | −0.0738596 | + | 0.0190263i | ||||
\(471\) | − | 6.67558e50i | − | 1.08916i | ||||||
\(472\) | −6.96797e50 | + | 6.57456e50i | −1.09196 | + | 1.03031i | ||||
\(473\) | 3.51602e50 | 0.529285 | ||||||||
\(474\) | 3.47178e50 | + | 1.34774e51i | 0.502069 | + | 1.94902i | ||||
\(475\) | 1.77020e49i | 0.0245948i | ||||||||
\(476\) | −1.10569e49 | − | 2.00372e49i | −0.0147605 | − | 0.0267488i | ||||
\(477\) | 4.90362e49 | 0.0629025 | ||||||||
\(478\) | 1.24988e51 | − | 3.21969e50i | 1.54077 | − | 0.396902i | ||||
\(479\) | 4.54455e49i | 0.0538413i | 0.999638 | + | 0.0269207i | \(0.00857015\pi\) | ||||
−0.999638 | + | 0.0269207i | \(0.991430\pi\) | |||||||
\(480\) | 1.07378e50 | − | 3.34979e50i | 0.122273 | − | 0.381447i | ||||
\(481\) | 1.27553e51 | 1.39616 | ||||||||
\(482\) | 2.10806e50 | + | 8.18344e50i | 0.221814 | + | 0.861077i | ||||
\(483\) | − | 1.03595e51i | − | 1.04795i | ||||||
\(484\) | −3.10468e50 | + | 1.71322e50i | −0.301964 | + | 0.166629i | ||||
\(485\) | 3.66859e50 | 0.343088 | ||||||||
\(486\) | 1.99912e50 | − | 5.14973e49i | 0.179783 | − | 0.0463122i | ||||
\(487\) | − | 1.48221e51i | − | 1.28191i | −0.767577 | − | 0.640957i | \(-0.778538\pi\) | ||
0.767577 | − | 0.640957i | \(-0.221462\pi\) | |||||||
\(488\) | 6.50203e50 | + | 6.89110e50i | 0.540845 | + | 0.573208i | ||||
\(489\) | −2.23935e51 | −1.79165 | ||||||||
\(490\) | −7.36995e49 | − | 2.86100e50i | −0.0567203 | − | 0.220187i | ||||
\(491\) | − | 6.80414e49i | − | 0.0503761i | −0.999683 | − | 0.0251881i | \(-0.991982\pi\) | ||
0.999683 | − | 0.0251881i | \(-0.00801846\pi\) | |||||||
\(492\) | −9.02333e50 | − | 1.63520e51i | −0.642732 | − | 1.16475i | ||||
\(493\) | 1.27856e50 | 0.0876256 | ||||||||
\(494\) | 3.86309e49 | − | 9.95132e48i | 0.0254755 | − | 0.00656249i | ||||
\(495\) | − | 4.55030e49i | − | 0.0288763i | ||||||
\(496\) | −6.71466e50 | − | 4.23149e50i | −0.410084 | − | 0.258429i | ||||
\(497\) | −3.16233e50 | −0.185881 | ||||||||
\(498\) | 2.89349e50 | + | 1.12325e51i | 0.163706 | + | 0.635505i | ||||
\(499\) | 3.16884e51i | 1.72580i | 0.505378 | + | 0.862898i | \(0.331353\pi\) | ||||
−0.505378 | + | 0.862898i | \(0.668647\pi\) | |||||||
\(500\) | −1.18570e51 | + | 6.54288e50i | −0.621646 | + | 0.343035i | ||||
\(501\) | −1.32360e51 | −0.668098 | ||||||||
\(502\) | −1.63320e51 | + | 4.20713e50i | −0.793723 | + | 0.204463i | ||||
\(503\) | 1.30008e51i | 0.608386i | 0.952610 | + | 0.304193i | \(0.0983867\pi\) | ||||
−0.952610 | + | 0.304193i | \(0.901613\pi\) | |||||||
\(504\) | 9.58306e49 | − | 9.04201e49i | 0.0431841 | − | 0.0407460i | ||||
\(505\) | −4.53354e50 | −0.196744 | ||||||||
\(506\) | −7.59414e50 | − | 2.94803e51i | −0.317409 | − | 1.23218i | ||||
\(507\) | − | 4.34046e50i | − | 0.174737i | ||||||
\(508\) | −4.51276e50 | − | 8.17799e50i | −0.174998 | − | 0.317129i | ||||
\(509\) | 2.56938e51 | 0.959821 | 0.479911 | − | 0.877317i | \(-0.340669\pi\) | ||||
0.479911 | + | 0.877317i | \(0.340669\pi\) | |||||||
\(510\) | −5.16464e49 | + | 1.33041e49i | −0.0185869 | + | 0.00478799i | ||||
\(511\) | − | 2.05843e51i | − | 0.713739i | ||||||
\(512\) | 2.29262e51 | − | 1.92429e51i | 0.765953 | − | 0.642897i | ||||
\(513\) | 8.48982e49 | 0.0273318 | ||||||||
\(514\) | −8.40272e50 | − | 3.26192e51i | −0.260688 | − | 1.01199i | ||||
\(515\) | 1.19246e51i | 0.356540i | ||||||||
\(516\) | 2.07724e51 | − | 1.14626e51i | 0.598608 | − | 0.330323i | ||||
\(517\) | −5.80093e50 | −0.161130 | ||||||||
\(518\) | 3.52778e51 | − | 9.08756e50i | 0.944574 | − | 0.243322i | ||||
\(519\) | 4.97071e51i | 1.28303i | ||||||||
\(520\) | 9.64253e50 | + | 1.02195e51i | 0.239954 | + | 0.254312i | ||||
\(521\) | 2.86439e51 | 0.687250 | 0.343625 | − | 0.939107i | \(-0.388345\pi\) | ||||
0.343625 | + | 0.939107i | \(0.388345\pi\) | |||||||
\(522\) | 1.83622e50 | + | 7.12816e50i | 0.0424800 | + | 0.164907i | ||||
\(523\) | 2.62713e51i | 0.586069i | 0.956102 | + | 0.293035i | \(0.0946651\pi\) | ||||
−0.956102 | + | 0.293035i | \(0.905335\pi\) | |||||||
\(524\) | 4.21385e51 | + | 7.63631e51i | 0.906536 | + | 1.64282i | ||||
\(525\) | −2.74133e51 | −0.568768 | ||||||||
\(526\) | −1.73688e50 | + | 4.47421e49i | −0.0347569 | + | 0.00895339i | ||||
\(527\) | 1.20331e50i | 0.0232261i | ||||||||
\(528\) | 2.42319e51 | − | 3.84518e51i | 0.451172 | − | 0.715933i | ||||
\(529\) | −8.19164e51 | −1.47134 | ||||||||
\(530\) | 3.72564e50 | + | 1.44629e51i | 0.0645593 | + | 0.250618i | ||||
\(531\) | 8.36199e50i | 0.139802i | ||||||||
\(532\) | 9.97529e49 | − | 5.50454e49i | 0.0160918 | − | 0.00887974i | ||||
\(533\) | 7.45982e51 | 1.16121 | ||||||||
\(534\) | −1.27071e52 | + | 3.27334e51i | −1.90880 | + | 0.491708i | ||||
\(535\) | − | 2.01086e51i | − | 0.291515i | ||||||
\(536\) | −3.54966e50 | + | 3.34925e50i | −0.0496656 | + | 0.0468616i | ||||
\(537\) | 4.44100e51 | 0.599748 | ||||||||
\(538\) | −9.10830e50 | − | 3.53583e51i | −0.118734 | − | 0.460922i | ||||
\(539\) | − | 3.81724e51i | − | 0.480355i | ||||||
\(540\) | 1.44470e51 | + | 2.61808e51i | 0.175508 | + | 0.318054i | ||||
\(541\) | −2.10965e50 | −0.0247436 | −0.0123718 | − | 0.999923i | \(-0.503938\pi\) | ||||
−0.0123718 | + | 0.999923i | \(0.503938\pi\) | |||||||
\(542\) | −5.68590e51 | + | 1.46469e51i | −0.643891 | + | 0.165867i | ||||
\(543\) | − | 1.62168e52i | − | 1.77324i | ||||||
\(544\) | −4.32141e50 | − | 1.38523e50i | −0.0456295 | − | 0.0146265i | ||||
\(545\) | 2.52664e51 | 0.257638 | ||||||||
\(546\) | 1.54106e51 | + | 5.98238e51i | 0.151761 | + | 0.589133i | ||||
\(547\) | − | 3.56277e51i | − | 0.338866i | −0.985542 | − | 0.169433i | \(-0.945806\pi\) | ||
0.985542 | − | 0.169433i | \(-0.0541937\pi\) | |||||||
\(548\) | 4.72336e51 | − | 2.60643e51i | 0.433930 | − | 0.239451i | ||||
\(549\) | 8.26974e50 | 0.0733867 | ||||||||
\(550\) | −7.80111e51 | + | 2.00957e51i | −0.668752 | + | 0.172271i | ||||
\(551\) | 6.36519e50i | 0.0527146i | ||||||||
\(552\) | −1.40975e52 | − | 1.49410e52i | −1.12797 | − | 1.19547i | ||||
\(553\) | −1.58765e52 | −1.22737 | ||||||||
\(554\) | 3.20470e51 | + | 1.24406e52i | 0.239388 | + | 0.929299i | ||||
\(555\) | − | 8.48956e51i | − | 0.612800i | ||||||
\(556\) | 7.53684e51 | + | 1.36582e52i | 0.525736 | + | 0.952735i | ||||
\(557\) | 1.02176e52 | 0.688809 | 0.344404 | − | 0.938821i | \(-0.388081\pi\) | ||||
0.344404 | + | 0.938821i | \(0.388081\pi\) | |||||||
\(558\) | −6.70863e50 | + | 1.72814e50i | −0.0437103 | + | 0.0112598i | ||||
\(559\) | 9.47642e51i | 0.596788i | ||||||||
\(560\) | 3.39496e51 | + | 2.13946e51i | 0.206663 | + | 0.130236i | ||||
\(561\) | −6.89083e50 | −0.0405487 | ||||||||
\(562\) | −4.54889e50 | − | 1.76587e51i | −0.0258771 | − | 0.100454i | ||||
\(563\) | − | 1.97371e52i | − | 1.08549i | −0.839899 | − | 0.542743i | \(-0.817386\pi\) | ||
0.839899 | − | 0.542743i | \(-0.182614\pi\) | |||||||
\(564\) | −3.42715e51 | + | 1.89116e51i | −0.182234 | + | 0.100560i | ||||
\(565\) | 2.39648e51 | 0.123212 | ||||||||
\(566\) | 2.36125e52 | − | 6.08258e51i | 1.17390 | − | 0.302396i | ||||
\(567\) | 1.43823e52i | 0.691435i | ||||||||
\(568\) | −4.56090e51 | + | 4.30339e51i | −0.212047 | + | 0.200075i | ||||
\(569\) | −3.96984e52 | −1.78501 | −0.892505 | − | 0.451038i | \(-0.851054\pi\) | ||||
−0.892505 | + | 0.451038i | \(0.851054\pi\) | |||||||
\(570\) | −6.62332e49 | − | 2.57116e50i | −0.00288040 | − | 0.0111817i | ||||
\(571\) | 9.79434e51i | 0.411992i | 0.978553 | + | 0.205996i | \(0.0660435\pi\) | ||||
−0.978553 | + | 0.205996i | \(0.933957\pi\) | |||||||
\(572\) | 8.77091e51 | + | 1.58946e52i | 0.356878 | + | 0.646732i | ||||
\(573\) | 4.59035e52 | 1.80679 | ||||||||
\(574\) | 2.06319e52 | − | 5.31478e51i | 0.785621 | − | 0.202376i | ||||
\(575\) | 3.64095e52i | 1.34130i | ||||||||
\(576\) | 1.51661e50 | − | 2.60818e51i | 0.00540564 | − | 0.0929631i | ||||
\(577\) | 2.89703e52 | 0.999107 | 0.499553 | − | 0.866283i | \(-0.333497\pi\) | ||||
0.499553 | + | 0.866283i | \(0.333497\pi\) | |||||||
\(578\) | −7.45805e51 | − | 2.89520e52i | −0.248884 | − | 0.966163i | ||||
\(579\) | 4.13772e51i | 0.133619i | ||||||||
\(580\) | −1.96289e52 | + | 1.08316e52i | −0.613427 | + | 0.338500i | ||||
\(581\) | −1.32320e52 | −0.400201 | ||||||||
\(582\) | 3.09731e52 | − | 7.97868e51i | 0.906668 | − | 0.233558i | ||||
\(583\) | 1.92968e52i | 0.546742i | ||||||||
\(584\) | −2.80117e52 | − | 2.96879e52i | −0.768238 | − | 0.814208i | ||||
\(585\) | 1.22640e51 | 0.0325591 | ||||||||
\(586\) | −8.23708e51 | − | 3.19762e52i | −0.211699 | − | 0.821812i | ||||
\(587\) | − | 2.04019e51i | − | 0.0507628i | −0.999678 | − | 0.0253814i | \(-0.991920\pi\) | ||
0.999678 | − | 0.0253814i | \(-0.00808002\pi\) | |||||||
\(588\) | −1.24446e52 | − | 2.25520e52i | −0.299786 | − | 0.543270i | ||||
\(589\) | −5.99056e50 | −0.0139726 | ||||||||
\(590\) | −2.46630e52 | + | 6.35320e51i | −0.557004 | + | 0.143484i | ||||
\(591\) | 1.82489e52i | 0.399093i | ||||||||
\(592\) | 3.85130e52 | − | 6.11136e52i | 0.815634 | − | 1.29427i | ||||
\(593\) | −4.25499e52 | −0.872688 | −0.436344 | − | 0.899780i | \(-0.643727\pi\) | ||||
−0.436344 | + | 0.899780i | \(0.643727\pi\) | |||||||
\(594\) | 9.63782e51 | + | 3.74139e52i | 0.191442 | + | 0.743174i | ||||
\(595\) | − | 6.08400e50i | − | 0.0117049i | ||||||
\(596\) | −5.19782e52 | + | 2.86825e52i | −0.968595 | + | 0.534488i | ||||
\(597\) | 4.04076e50 | 0.00729374 | ||||||||
\(598\) | 7.94559e52 | − | 2.04679e52i | 1.38932 | − | 0.357890i | ||||
\(599\) | − | 3.17123e52i | − | 0.537178i | −0.963255 | − | 0.268589i | \(-0.913443\pi\) | ||
0.963255 | − | 0.268589i | \(-0.0865573\pi\) | |||||||
\(600\) | −3.95371e52 | + | 3.73049e52i | −0.648830 | + | 0.612198i | ||||
\(601\) | −7.87931e52 | −1.25278 | −0.626388 | − | 0.779512i | \(-0.715467\pi\) | ||||
−0.626388 | + | 0.779512i | \(0.715467\pi\) | |||||||
\(602\) | 6.75152e51 | + | 2.62093e52i | 0.104008 | + | 0.403759i | ||||
\(603\) | 4.25981e50i | 0.00635860i | ||||||||
\(604\) | −1.09655e52 | − | 1.98717e52i | −0.158609 | − | 0.287430i | ||||
\(605\) | −9.42690e51 | −0.132135 | ||||||||
\(606\) | −3.82757e52 | + | 9.85984e51i | −0.519929 | + | 0.133934i | ||||
\(607\) | − | 1.64239e52i | − | 0.216217i | −0.994139 | − | 0.108109i | \(-0.965521\pi\) | ||
0.994139 | − | 0.108109i | \(-0.0344794\pi\) | |||||||
\(608\) | 6.89620e50 | − | 2.15136e51i | 0.00879917 | − | 0.0274502i | ||||
\(609\) | −9.85713e52 | −1.21905 | ||||||||
\(610\) | 6.28312e51 | + | 2.43910e52i | 0.0753196 | + | 0.292390i | ||||
\(611\) | − | 1.56347e52i | − | 0.181680i | ||||||
\(612\) | −3.46803e50 | + | 1.91372e50i | −0.00390666 | + | 0.00215577i | ||||
\(613\) | 1.37490e53 | 1.50149 | 0.750743 | − | 0.660594i | \(-0.229696\pi\) | ||||
0.750743 | + | 0.660594i | \(0.229696\pi\) | |||||||
\(614\) | 2.11694e52 | − | 5.45323e51i | 0.224135 | − | 0.0577371i | ||||
\(615\) | − | 4.96505e52i | − | 0.509678i | ||||||
\(616\) | 3.55822e52 | + | 3.77113e52i | 0.354160 | + | 0.375352i | ||||
\(617\) | 1.15288e53 | 1.11267 | 0.556335 | − | 0.830958i | \(-0.312207\pi\) | ||||
0.556335 | + | 0.830958i | \(0.312207\pi\) | |||||||
\(618\) | 2.59345e52 | + | 1.00677e53i | 0.242715 | + | 0.942216i | ||||
\(619\) | 2.79562e52i | 0.253721i | 0.991921 | + | 0.126860i | \(0.0404900\pi\) | ||||
−0.991921 | + | 0.126860i | \(0.959510\pi\) | |||||||
\(620\) | −1.01941e52 | − | 1.84736e52i | −0.0897232 | − | 0.162596i | ||||
\(621\) | 1.74619e53 | 1.49056 | ||||||||
\(622\) | −1.03156e53 | + | 2.65731e52i | −0.854042 | + | 0.220001i | ||||
\(623\) | − | 1.49690e53i | − | 1.20204i | ||||||
\(624\) | 1.03636e53 | + | 6.53101e52i | 0.807242 | + | 0.508713i | ||||
\(625\) | 7.69202e52 | 0.581193 | ||||||||
\(626\) | −1.17559e52 | − | 4.56360e52i | −0.0861672 | − | 0.334500i | ||||
\(627\) | − | 3.43052e51i | − | 0.0243937i | ||||||
\(628\) | 1.32211e53 | − | 7.29565e52i | 0.912084 | − | 0.503304i | ||||
\(629\) | −1.09520e52 | −0.0733044 | ||||||||
\(630\) | 3.39191e51 | − | 8.73757e50i | 0.0220279 | − | 0.00567440i | ||||
\(631\) | − | 1.04936e52i | − | 0.0661254i | −0.999453 | − | 0.0330627i | \(-0.989474\pi\) | ||
0.999453 | − | 0.0330627i | \(-0.0105261\pi\) | |||||||
\(632\) | −2.28980e53 | + | 2.16052e53i | −1.40014 | + | 1.32109i | ||||
\(633\) | −2.26632e53 | −1.34478 | ||||||||
\(634\) | −6.56453e51 | − | 2.54834e52i | −0.0378014 | − | 0.146744i | ||||
\(635\) | − | 2.48313e52i | − | 0.138771i | ||||||
\(636\) | 6.29096e52 | + | 1.14004e53i | 0.341218 | + | 0.618352i | ||||
\(637\) | 1.02883e53 | 0.541618 | ||||||||
\(638\) | −2.80508e53 | + | 7.22589e52i | −1.43335 | + | 0.369231i | ||||
\(639\) | 5.47335e51i | 0.0271480i | ||||||||
\(640\) | 7.80786e52 | − | 1.53431e52i | 0.375935 | − | 0.0738744i | ||||
\(641\) | −2.70023e53 | −1.26211 | −0.631056 | − | 0.775737i | \(-0.717378\pi\) | ||||
−0.631056 | + | 0.775737i | \(0.717378\pi\) | |||||||
\(642\) | −4.37336e52 | − | 1.69773e53i | −0.198449 | − | 0.770378i | ||||
\(643\) | 3.40744e53i | 1.50114i | 0.660793 | + | 0.750568i | \(0.270220\pi\) | ||||
−0.660793 | + | 0.750568i | \(0.729780\pi\) | |||||||
\(644\) | 2.05172e53 | − | 1.13217e53i | 0.877578 | − | 0.484263i | ||||
\(645\) | 6.30724e52 | 0.261942 | ||||||||
\(646\) | −3.31693e50 | + | 8.54442e49i | −0.00133758 | + | 0.000344560i | ||||
\(647\) | − | 2.23016e53i | − | 0.873283i | −0.899636 | − | 0.436641i | \(-0.856168\pi\) | ||
0.899636 | − | 0.436641i | \(-0.143832\pi\) | |||||||
\(648\) | 1.95719e53 | + | 2.07430e53i | 0.744231 | + | 0.788764i | ||||
\(649\) | −3.29062e53 | −1.21515 | ||||||||
\(650\) | −5.41622e52 | − | 2.10257e53i | −0.194242 | − | 0.754043i | ||||
\(651\) | − | 9.27698e52i | − | 0.323123i | ||||||
\(652\) | −2.44735e53 | − | 4.43507e53i | −0.827927 | − | 1.50036i | ||||
\(653\) | −9.12263e52 | −0.299757 | −0.149879 | − | 0.988704i | \(-0.547888\pi\) | ||||
−0.149879 | + | 0.988704i | \(0.547888\pi\) | |||||||
\(654\) | 2.13319e53 | − | 5.49510e52i | 0.680852 | − | 0.175388i | ||||
\(655\) | 2.31866e53i | 0.718872i | ||||||||
\(656\) | 2.25240e53 | − | 3.57418e53i | 0.678380 | − | 1.07647i | ||||
\(657\) | −3.56273e52 | −0.104241 | ||||||||
\(658\) | −1.11390e52 | − | 4.32416e52i | −0.0316633 | − | 0.122916i | ||||
\(659\) | − | 2.26086e53i | − | 0.624384i | −0.950019 | − | 0.312192i | \(-0.898937\pi\) | ||
0.950019 | − | 0.312192i | \(-0.101063\pi\) | |||||||
\(660\) | 1.05790e53 | − | 5.83767e52i | 0.283863 | − | 0.156641i | ||||
\(661\) | 5.08886e53 | 1.32676 | 0.663381 | − | 0.748282i | \(-0.269121\pi\) | ||||
0.663381 | + | 0.748282i | \(0.269121\pi\) | |||||||
\(662\) | −4.62361e53 | + | 1.19104e53i | −1.17133 | + | 0.301735i | ||||
\(663\) | − | 1.85723e52i | − | 0.0457202i | ||||||
\(664\) | −1.90839e53 | + | 1.80065e53i | −0.456536 | + | 0.430760i | ||||
\(665\) | 3.02885e51 | 0.00704153 | ||||||||
\(666\) | −1.57287e52 | − | 6.10587e52i | −0.0355372 | − | 0.137955i | ||||
\(667\) | 1.30919e54i | 2.87483i | ||||||||
\(668\) | −1.44655e53 | − | 2.62142e53i | −0.308730 | − | 0.559479i | ||||
\(669\) | 5.42351e53 | 1.12508 | ||||||||
\(670\) | −1.25640e52 | + | 3.23649e51i | −0.0253341 | + | 0.00652608i | ||||
\(671\) | 3.25432e53i | 0.637869i | ||||||||
\(672\) | 3.33160e53 | + | 1.06795e53i | 0.634800 | + | 0.203485i | ||||
\(673\) | −9.70945e53 | −1.79849 | −0.899246 | − | 0.437443i | \(-0.855884\pi\) | ||||
−0.899246 | + | 0.437443i | \(0.855884\pi\) | |||||||
\(674\) | 2.14868e53 | + | 8.34113e53i | 0.386931 | + | 1.50206i | ||||
\(675\) | − | 4.62077e53i | − | 0.808989i | ||||||
\(676\) | 8.59638e52 | − | 4.74364e52i | 0.146328 | − | 0.0807466i | ||||
\(677\) | 9.12822e53 | 1.51078 | 0.755391 | − | 0.655275i | \(-0.227447\pi\) | ||||
0.755391 | + | 0.655275i | \(0.227447\pi\) | |||||||
\(678\) | 2.02330e53 | − | 5.21202e52i | 0.325609 | − | 0.0838768i | ||||
\(679\) | 3.64866e53i | 0.570963i | ||||||||
\(680\) | −8.27929e51 | − | 8.77470e51i | −0.0125986 | − | 0.0133525i | ||||
\(681\) | −3.02582e53 | −0.447763 | ||||||||
\(682\) | −6.80061e52 | − | 2.63998e53i | −0.0978689 | − | 0.379925i | ||||
\(683\) | − | 5.74161e53i | − | 0.803601i | −0.915727 | − | 0.401801i | \(-0.868384\pi\) | ||
0.915727 | − | 0.401801i | \(-0.131616\pi\) | |||||||
\(684\) | −9.52725e50 | − | 1.72652e51i | −0.00129689 | − | 0.00235021i | ||||
\(685\) | 1.43418e53 | 0.189881 | ||||||||
\(686\) | 7.64003e53 | − | 1.96807e53i | 0.983868 | − | 0.253445i | ||||
\(687\) | − | 7.52502e53i | − | 0.942605i | ||||||
\(688\) | 4.54038e53 | + | 2.86129e53i | 0.553238 | + | 0.348643i | ||||
\(689\) | −5.20090e53 | −0.616472 | ||||||||
\(690\) | −1.36228e53 | − | 5.28836e53i | −0.157085 | − | 0.609801i | ||||
\(691\) | − | 1.18177e54i | − | 1.32572i | −0.748744 | − | 0.662860i | \(-0.769343\pi\) | ||
0.748744 | − | 0.662860i | \(-0.230657\pi\) | |||||||
\(692\) | −9.84459e53 | + | 5.43242e53i | −1.07444 | + | 0.592895i | ||||
\(693\) | 4.52559e52 | 0.0480556 | ||||||||
\(694\) | 8.63495e53 | − | 2.22436e53i | 0.892133 | − | 0.229814i | ||||
\(695\) | 4.14711e53i | 0.416903i | ||||||||
\(696\) | −1.42165e54 | + | 1.34139e54i | −1.39065 | + | 1.31214i | ||||
\(697\) | −6.40517e52 | −0.0609688 | ||||||||
\(698\) | 2.67635e53 | + | 1.03895e54i | 0.247908 | + | 0.962374i | ||||
\(699\) | − | 1.05629e54i | − | 0.952171i | ||||||
\(700\) | −2.99597e53 | − | 5.42927e53i | −0.262830 | − | 0.476298i | ||||
\(701\) | 4.63765e53 | 0.395964 | 0.197982 | − | 0.980206i | \(-0.436561\pi\) | ||||
0.197982 | + | 0.980206i | \(0.436561\pi\) | |||||||
\(702\) | −1.00838e54 | + | 2.59760e53i | −0.837956 | + | 0.215858i | ||||
\(703\) | − | 5.45232e52i | − | 0.0440991i | ||||||
\(704\) | 1.02637e54 | + | 5.96818e52i | 0.808025 | + | 0.0469852i | ||||
\(705\) | −1.04060e53 | −0.0797430 | ||||||||
\(706\) | −1.08600e53 | − | 4.21584e53i | −0.0810105 | − | 0.314481i | ||||
\(707\) | − | 4.50892e53i | − | 0.327419i | ||||||
\(708\) | −1.94408e54 | + | 1.07278e54i | −1.37430 | + | 0.758363i | ||||
\(709\) | −6.87957e53 | −0.473460 | −0.236730 | − | 0.971576i | \(-0.576076\pi\) | ||||
−0.236730 | + | 0.971576i | \(0.576076\pi\) | |||||||
\(710\) | −1.61432e53 | + | 4.15850e52i | −0.108164 | + | 0.0278630i | ||||
\(711\) | 2.74790e53i | 0.179258i | ||||||||
\(712\) | −2.03703e54 | − | 2.15892e54i | −1.29383 | − | 1.37125i | ||||
\(713\) | −1.23214e54 | −0.762005 | ||||||||
\(714\) | −1.32319e52 | − | 5.13660e52i | −0.00796812 | − | 0.0309321i | ||||
\(715\) | 4.82616e53i | 0.283000i | ||||||||
\(716\) | 4.85351e53 | + | 8.79549e53i | 0.277146 | + | 0.502241i | ||||
\(717\) | 2.99149e54 | 1.66350 | ||||||||
\(718\) | 2.33430e54 | − | 6.01316e53i | 1.26413 | − | 0.325640i | ||||
\(719\) | − | 1.88968e54i | − | 0.996642i | −0.866993 | − | 0.498321i | \(-0.833950\pi\) | ||
0.866993 | − | 0.498321i | \(-0.166050\pi\) | |||||||
\(720\) | 3.70298e52 | − | 5.87600e52i | 0.0190210 | − | 0.0301831i | ||||
\(721\) | −1.18599e54 | −0.593349 | ||||||||
\(722\) | 5.11494e53 | + | 1.98561e54i | 0.249249 | + | 0.967581i | ||||
\(723\) | 1.95864e54i | 0.929667i | ||||||||
\(724\) | 3.21177e54 | − | 1.77231e54i | 1.48495 | − | 0.819421i | ||||
\(725\) | 3.46439e54 | 1.56029 | ||||||||
\(726\) | −7.95894e53 | + | 2.05023e53i | −0.349188 | + | 0.0899510i | ||||
\(727\) | 3.93284e54i | 1.68094i | 0.541857 | + | 0.840471i | \(0.317721\pi\) | ||||
−0.541857 | + | 0.840471i | \(0.682279\pi\) | |||||||
\(728\) | −1.01640e54 | + | 9.59017e53i | −0.423223 | + | 0.399328i | ||||
\(729\) | −2.19473e54 | −0.890345 | ||||||||
\(730\) | −2.70686e53 | − | 1.05080e54i | −0.106987 | − | 0.415322i | ||||
\(731\) | − | 8.13666e52i | − | 0.0313340i | ||||||
\(732\) | 1.06094e54 | + | 1.92263e54i | 0.398090 | + | 0.721415i | ||||
\(733\) | −1.59209e54 | −0.582094 | −0.291047 | − | 0.956709i | \(-0.594004\pi\) | ||||
−0.291047 | + | 0.956709i | \(0.594004\pi\) | |||||||
\(734\) | 3.06887e54 | − | 7.90540e53i | 1.09333 | − | 0.281643i | ||||
\(735\) | − | 6.84759e53i | − | 0.237727i | ||||||
\(736\) | 1.41841e54 | − | 4.42492e54i | 0.479869 | − | 1.49702i | ||||
\(737\) | −1.67632e53 | −0.0552683 | ||||||||
\(738\) | −9.19881e52 | − | 3.57097e53i | −0.0295570 | − | 0.114740i | ||||
\(739\) | − | 2.11977e53i | − | 0.0663810i | −0.999449 | − | 0.0331905i | \(-0.989433\pi\) | ||
0.999449 | − | 0.0331905i | \(-0.0105668\pi\) | |||||||
\(740\) | 1.68138e54 | − | 9.27814e53i | 0.513171 | − | 0.283177i | ||||
\(741\) | 9.24600e52 | 0.0275048 | ||||||||
\(742\) | −1.43843e54 | + | 3.70540e53i | −0.417076 | + | 0.107439i | ||||
\(743\) | 2.29917e54i | 0.649807i | 0.945747 | + | 0.324903i | \(0.105332\pi\) | ||||
−0.945747 | + | 0.324903i | \(0.894668\pi\) | |||||||
\(744\) | −1.26244e54 | − | 1.33798e54i | −0.347796 | − | 0.368607i | ||||
\(745\) | −1.57824e54 | −0.423842 | ||||||||
\(746\) | 2.42476e53 | + | 9.41287e53i | 0.0634791 | + | 0.246425i | ||||
\(747\) | 2.29019e53i | 0.0584494i | ||||||||
\(748\) | −7.53089e52 | − | 1.36474e53i | −0.0187377 | − | 0.0339563i | ||||
\(749\) | 1.99994e54 | 0.485136 | ||||||||
\(750\) | −3.03957e54 | + | 7.82994e53i | −0.718866 | + | 0.185180i | ||||
\(751\) | 7.06622e54i | 1.62940i | 0.579882 | + | 0.814701i | \(0.303099\pi\) | ||||
−0.579882 | + | 0.814701i | \(0.696901\pi\) | |||||||
\(752\) | −7.49098e53 | − | 4.72072e53i | −0.168422 | − | 0.106138i | ||||
\(753\) | −3.90894e54 | −0.856948 | ||||||||
\(754\) | −1.94753e54 | − | 7.56030e54i | −0.416322 | − | 1.61616i | ||||
\(755\) | − | 6.03374e53i | − | 0.125775i | ||||||
\(756\) | −2.60386e54 | + | 1.43686e54i | −0.529302 | + | 0.292078i | ||||
\(757\) | 3.95297e54 | 0.783614 | 0.391807 | − | 0.920047i | \(-0.371850\pi\) | ||||
0.391807 | + | 0.920047i | \(0.371850\pi\) | |||||||
\(758\) | −7.32529e54 | + | 1.88700e54i | −1.41615 | + | 0.364801i | ||||
\(759\) | − | 7.05589e54i | − | 1.33033i | ||||||
\(760\) | 4.36839e52 | − | 4.12175e52i | 0.00803272 | − | 0.00757920i | ||||
\(761\) | −1.92105e54 | −0.344533 | −0.172266 | − | 0.985050i | \(-0.555109\pi\) | ||||
−0.172266 | + | 0.985050i | \(0.555109\pi\) | |||||||
\(762\) | −5.40047e53 | − | 2.09645e54i | −0.0944686 | − | 0.366725i | ||||
\(763\) | 2.51292e54i | 0.428758i | ||||||||
\(764\) | 5.01674e54 | + | 9.09129e54i | 0.834925 | + | 1.51304i | ||||
\(765\) | −1.05302e52 | −0.00170950 | ||||||||
\(766\) | −1.30630e54 | + | 3.36502e53i | −0.206869 | + | 0.0532895i | ||||
\(767\) | − | 8.86892e54i | − | 1.37012i | ||||||
\(768\) | 6.25832e54 | − | 2.99349e54i | 0.943181 | − | 0.451144i | ||||
\(769\) | −7.19087e54 | −1.05726 | −0.528629 | − | 0.848853i | \(-0.677294\pi\) | ||||
−0.528629 | + | 0.848853i | \(0.677294\pi\) | |||||||
\(770\) | 3.43842e53 | + | 1.33479e54i | 0.0493213 | + | 0.191465i | ||||
\(771\) | − | 7.80716e54i | − | 1.09260i | ||||||
\(772\) | −8.19483e53 | + | 4.52206e53i | −0.111895 | + | 0.0617458i | ||||
\(773\) | 5.65460e54 | 0.753341 | 0.376671 | − | 0.926347i | \(-0.377069\pi\) | ||||
0.376671 | + | 0.926347i | \(0.377069\pi\) | |||||||
\(774\) | 4.53630e53 | − | 1.16855e53i | 0.0589689 | − | 0.0151904i | ||||
\(775\) | 3.26049e54i | 0.413572i | ||||||||
\(776\) | 4.96521e54 | + | 5.26231e54i | 0.614561 | + | 0.651334i | ||||
\(777\) | 8.44346e54 | 1.01981 | ||||||||
\(778\) | 6.31478e52 | + | 2.45139e53i | 0.00744296 | + | 0.0288935i | ||||
\(779\) | − | 3.18874e53i | − | 0.0366782i | ||||||
\(780\) | 1.57338e54 | + | 2.85126e54i | 0.176618 | + | 0.320066i | ||||
\(781\) | −2.15388e54 | −0.235967 | ||||||||
\(782\) | −6.82226e53 | + | 1.75741e53i | −0.0729457 | + | 0.0187908i | ||||
\(783\) | − | 1.66151e55i | − | 1.73392i | ||||||
\(784\) | 3.10642e54 | − | 4.92936e54i | 0.316413 | − | 0.502094i | ||||
\(785\) | 4.01440e54 | 0.399114 | ||||||||
\(786\) | 5.04277e54 | + | 1.95759e55i | 0.489374 | + | 1.89974i | ||||
\(787\) | 1.74093e55i | 1.64915i | 0.565750 | + | 0.824577i | \(0.308587\pi\) | ||||
−0.565750 | + | 0.824577i | \(0.691413\pi\) | |||||||
\(788\) | −3.61423e54 | + | 1.99440e54i | −0.334208 | + | 0.184422i | ||||
\(789\) | −4.15709e53 | −0.0375255 | ||||||||
\(790\) | −8.10471e54 | + | 2.08777e54i | −0.714205 | + | 0.183979i | ||||
\(791\) | 2.38346e54i | 0.205048i | ||||||||
\(792\) | 6.52707e53 | − | 6.15856e53i | 0.0548201 | − | 0.0517250i | ||||
\(793\) | −8.77108e54 | −0.719222 | ||||||||
\(794\) | 2.13662e54 | + | 8.29433e54i | 0.171056 | + | 0.664036i | ||||
\(795\) | 3.46157e54i | 0.270581i | ||||||||
\(796\) | 4.41609e52 | + | 8.00280e52i | 0.00337046 | + | 0.00610793i | ||||
\(797\) | 1.50341e55 | 1.12039 | 0.560195 | − | 0.828361i | \(-0.310726\pi\) | ||||
0.560195 | + | 0.828361i | \(0.310726\pi\) | |||||||
\(798\) | 2.55720e53 | − | 6.58735e52i | 0.0186084 | − | 0.00479353i | ||||
\(799\) | 1.34243e53i | 0.00953902i | ||||||||
\(800\) | −1.17093e55 | − | 3.75340e54i | −0.812493 | − | 0.260445i | ||||
\(801\) | −2.59084e54 | −0.175559 | ||||||||
\(802\) | −5.11434e54 | − | 1.98538e55i | −0.338436 | − | 1.31380i | ||||
\(803\) | − | 1.40201e55i | − | 0.906056i | ||||||
\(804\) | −9.90363e53 | + | 5.46500e53i | −0.0625071 | + | 0.0344925i | ||||
\(805\) | 6.22974e54 | 0.384015 | ||||||||
\(806\) | 7.11533e54 | − | 1.83291e54i | 0.428380 | − | 0.110351i | ||||
\(807\) | − | 8.46273e54i | − | 0.497638i | ||||||
\(808\) | −6.13587e54 | − | 6.50302e54i | −0.352420 | − | 0.373508i | ||||
\(809\) | 3.16925e54 | 0.177801 | 0.0889006 | − | 0.996040i | \(-0.471665\pi\) | ||||
0.0889006 | + | 0.996040i | \(0.471665\pi\) | |||||||
\(810\) | 1.89129e54 | + | 7.34197e54i | 0.103644 | + | 0.402344i | ||||
\(811\) | 2.98626e55i | 1.59857i | 0.600954 | + | 0.799283i | \(0.294787\pi\) | ||||
−0.600954 | + | 0.799283i | \(0.705213\pi\) | |||||||
\(812\) | −1.07727e55 | − | 1.95223e55i | −0.563328 | − | 1.02086i | ||||
\(813\) | −1.36088e55 | −0.695181 | ||||||||
\(814\) | 2.40279e55 | − | 6.18959e54i | 1.19909 | − | 0.308886i | ||||
\(815\) | − | 1.34665e55i | − | 0.656536i | ||||||
\(816\) | −8.89841e53 | − | 5.60767e53i | −0.0423838 | − | 0.0267097i | ||||
\(817\) | 4.05075e53 | 0.0188502 | ||||||||
\(818\) | −5.84075e54 | − | 2.26737e55i | −0.265556 | − | 1.03088i | ||||
\(819\) | 1.21974e54i | 0.0541845i | ||||||||
\(820\) | 9.83338e54 | − | 5.42624e54i | 0.426815 | − | 0.235524i | ||||
\(821\) | −3.08324e55 | −1.30764 | −0.653818 | − | 0.756652i | \(-0.726834\pi\) | ||||
−0.653818 | + | 0.756652i | \(0.726834\pi\) | |||||||
\(822\) | 1.21085e55 | − | 3.11915e54i | 0.501793 | − | 0.129262i | ||||
\(823\) | 3.32552e55i | 1.34667i | 0.739336 | + | 0.673337i | \(0.235140\pi\) | ||||
−0.739336 | + | 0.673337i | \(0.764860\pi\) | |||||||
\(824\) | −1.71050e55 | + | 1.61393e55i | −0.676871 | + | 0.638656i | ||||
\(825\) | −1.86714e55 | −0.722023 | ||||||||
\(826\) | −6.31870e54 | − | 2.45291e55i | −0.238785 | − | 0.926960i | ||||
\(827\) | − | 6.70226e54i | − | 0.247524i | −0.992312 | − | 0.123762i | \(-0.960504\pi\) | ||
0.992312 | − | 0.123762i | \(-0.0394959\pi\) | |||||||
\(828\) | −1.95956e54 | − | 3.55111e54i | −0.0707267 | − | 0.128170i | ||||
\(829\) | −2.74877e55 | −0.969620 | −0.484810 | − | 0.874619i | \(-0.661111\pi\) | ||||
−0.484810 | + | 0.874619i | \(0.661111\pi\) | |||||||
\(830\) | −6.75474e54 | + | 1.74002e54i | −0.232876 | + | 0.0599889i | ||||
\(831\) | 2.97756e55i | 1.00332i | ||||||||
\(832\) | −1.60855e54 | + | 2.76630e55i | −0.0529776 | + | 0.911079i | ||||
\(833\) | −8.83374e53 | −0.0284374 | ||||||||
\(834\) | 9.01942e54 | + | 3.50132e55i | 0.283807 | + | 1.10174i | ||||
\(835\) | − | 7.95956e54i | − | 0.244819i | ||||||
\(836\) | 6.79422e53 | − | 3.74917e53i | 0.0204277 | − | 0.0112724i | ||||
\(837\) | 1.56372e55 | 0.459595 | ||||||||
\(838\) | 5.83353e55 | − | 1.50272e55i | 1.67608 | − | 0.431759i | ||||
\(839\) | 3.36217e55i | 0.944371i | 0.881499 | + | 0.472185i | \(0.156535\pi\) | ||||
−0.881499 | + | 0.472185i | \(0.843465\pi\) | |||||||
\(840\) | 6.38295e54 | + | 6.76488e54i | 0.175273 | + | 0.185761i | ||||
\(841\) | 8.73209e55 | 2.34420 | ||||||||
\(842\) | −1.64935e54 | − | 6.40274e54i | −0.0432895 | − | 0.168049i | ||||
\(843\) | − | 4.22647e54i | − | 0.108456i | ||||||
\(844\) | −2.47683e55 | − | 4.48849e55i | −0.621427 | − | 1.12614i | ||||
\(845\) | 2.61017e54 | 0.0640311 | ||||||||
\(846\) | −7.48424e53 | + | 1.92794e53i | −0.0179519 | + | 0.00462442i | ||||
\(847\) | − | 9.37571e54i | − | 0.219897i | ||||||
\(848\) | −1.57035e55 | + | 2.49188e55i | −0.360143 | + | 0.571485i | ||||
\(849\) | 5.65146e55 | 1.26740 | ||||||||
\(850\) | 4.65048e53 | + | 1.80531e54i | 0.0101986 | + | 0.0395906i | ||||
\(851\) | − | 1.12143e56i | − | 2.40498i | ||||||
\(852\) | −1.27250e55 | + | 7.02188e54i | −0.266873 | + | 0.147265i | ||||
\(853\) | 6.69387e54 | 0.137292 | 0.0686461 | − | 0.997641i | \(-0.478132\pi\) | ||||
0.0686461 | + | 0.997641i | \(0.478132\pi\) | |||||||
\(854\) | −2.42585e55 | + | 6.24900e54i | −0.486591 | + | 0.125346i | ||||
\(855\) | − | 5.24233e52i | − | 0.00102841i | ||||||
\(856\) | 2.88444e55 | − | 2.72158e55i | 0.553426 | − | 0.522180i | ||||
\(857\) | −6.80760e55 | −1.27749 | −0.638747 | − | 0.769417i | \(-0.720547\pi\) | ||||
−0.638747 | + | 0.769417i | \(0.720547\pi\) | |||||||
\(858\) | 1.04962e55 | + | 4.07463e55i | 0.192653 | + | 0.747876i | ||||
\(859\) | 9.19214e55i | 1.65024i | 0.564959 | + | 0.825119i | \(0.308892\pi\) | ||||
−0.564959 | + | 0.825119i | \(0.691108\pi\) | |||||||
\(860\) | 6.89310e54 | + | 1.24916e55i | 0.121044 | + | 0.219355i | ||||
\(861\) | 4.93809e55 | 0.848201 | ||||||||
\(862\) | −1.97640e55 | + | 5.09120e54i | −0.332075 | + | 0.0855425i | ||||
\(863\) | − | 4.40945e55i | − | 0.724734i | −0.932035 | − | 0.362367i | \(-0.881969\pi\) | ||
0.932035 | − | 0.362367i | \(-0.118031\pi\) | |||||||
\(864\) | −1.80012e55 | + | 5.61573e55i | −0.289428 | + | 0.902911i | ||||
\(865\) | −2.98917e55 | −0.470158 | ||||||||
\(866\) | 1.37729e55 | + | 5.34662e55i | 0.211927 | + | 0.822696i | ||||
\(867\) | − | 6.92945e55i | − | 1.04312i | ||||||
\(868\) | 1.83733e55 | − | 1.01387e55i | 0.270590 | − | 0.149316i | ||||
\(869\) | −1.08135e56 | −1.55809 | ||||||||
\(870\) | −5.03192e55 | + | 1.29622e55i | −0.709362 | + | 0.182732i | ||||
\(871\) | − | 4.51806e54i | − | 0.0623170i | ||||||
\(872\) | 3.41965e55 | + | 3.62428e55i | 0.461497 | + | 0.489112i | ||||
\(873\) | 6.31510e54 | 0.0833891 | ||||||||
\(874\) | −8.74910e53 | − | 3.39639e54i | −0.0113044 | − | 0.0438833i | ||||
\(875\) | − | 3.58064e55i | − | 0.452697i | ||||||
\(876\) | −4.57069e55 | − | 8.28298e55i | −0.565463 | − | 1.02473i | ||||
\(877\) | −7.01400e55 | −0.849129 | −0.424564 | − | 0.905398i | \(-0.639573\pi\) | ||||
−0.424564 | + | 0.905398i | \(0.639573\pi\) | |||||||
\(878\) | −1.27775e56 | + | 3.29149e55i | −1.51374 | + | 0.389939i | ||||
\(879\) | − | 7.65326e55i | − | 0.887274i | ||||||
\(880\) | 2.31233e55 | + | 1.45720e55i | 0.262348 | + | 0.165329i | ||||
\(881\) | 9.27731e55 | 1.03010 | 0.515051 | − | 0.857160i | \(-0.327773\pi\) | ||||
0.515051 | + | 0.857160i | \(0.327773\pi\) | |||||||
\(882\) | −1.26866e54 | − | 4.92493e54i | −0.0137861 | − | 0.0535176i | ||||
\(883\) | − | 1.16178e56i | − | 1.23558i | −0.786342 | − | 0.617792i | \(-0.788028\pi\) | ||
0.786342 | − | 0.617792i | \(-0.211972\pi\) | |||||||
\(884\) | 3.67828e54 | − | 2.02974e54i | 0.0382870 | − | 0.0211275i | ||||
\(885\) | −5.90291e55 | −0.601373 | ||||||||
\(886\) | 6.94035e55 | − | 1.78784e55i | 0.692055 | − | 0.178273i | ||||
\(887\) | 1.34404e56i | 1.31179i | 0.754853 | + | 0.655894i | \(0.227708\pi\) | ||||
−0.754853 | + | 0.655894i | \(0.772292\pi\) | |||||||
\(888\) | 1.21777e56 | − | 1.14901e56i | 1.16337 | − | 1.09769i | ||||
\(889\) | 2.46964e55 | 0.230941 | ||||||||
\(890\) | −1.96844e55 | − | 7.64147e55i | −0.180183 | − | 0.699466i | ||||
\(891\) | 9.79588e55i | 0.877742i | ||||||||
\(892\) | 5.92728e55 | + | 1.07414e56i | 0.519904 | + | 0.942166i | ||||
\(893\) | −6.68316e53 | −0.00573857 | ||||||||
\(894\) | −1.33248e56 | + | 3.43247e55i | −1.12007 | + | 0.288532i | ||||
\(895\) | 2.67062e55i | 0.219773i | ||||||||
\(896\) | 1.52598e55 | + | 7.76546e55i | 0.122941 | + | 0.625626i | ||||
\(897\) | 1.90172e56 | 1.49999 | ||||||||
\(898\) | −4.21503e55 | − | 1.63627e56i | −0.325500 | − | 1.26358i | ||||
\(899\) | 1.17239e56i | 0.886416i | ||||||||
\(900\) | −9.39696e54 | + | 5.18541e54i | −0.0695633 | + | 0.0383863i | ||||
\(901\) | 4.46561e54 | 0.0323675 | ||||||||
\(902\) | 1.40525e56 | − | 3.61993e55i | 0.997308 | − | 0.256907i | ||||
\(903\) | 6.27299e55i | 0.435921i | ||||||||
\(904\) | 3.24349e55 | + | 3.43757e55i | 0.220705 | + | 0.233911i | ||||
\(905\) | 9.75206e55 | 0.649790 | ||||||||
\(906\) | −1.31226e55 | − | 5.09416e55i | −0.0856216 | − | 0.332382i | ||||
\(907\) | 1.97114e56i | 1.25944i | 0.776820 | + | 0.629722i | \(0.216831\pi\) | ||||
−0.776820 | + | 0.629722i | \(0.783169\pi\) | |||||||
\(908\) | −3.30688e55 | − | 5.99271e55i | −0.206913 | − | 0.374966i | ||||
\(909\) | −7.80403e54 | −0.0478195 | ||||||||
\(910\) | −3.59754e55 | + | 9.26727e54i | −0.215883 | + | 0.0556116i | ||||
\(911\) | − | 1.01191e56i | − | 0.594692i | −0.954770 | − | 0.297346i | \(-0.903899\pi\) | ||
0.954770 | − | 0.297346i | \(-0.0961015\pi\) | |||||||
\(912\) | 2.79171e54 | − | 4.42998e54i | 0.0160683 | − | 0.0254976i | ||||
\(913\) | −9.01237e55 | −0.508036 | ||||||||
\(914\) | −1.63657e55 | − | 6.35314e55i | −0.0903560 | − | 0.350761i | ||||
\(915\) | 5.83779e55i | 0.315680i | ||||||||
\(916\) | 1.49035e56 | − | 8.22400e55i | 0.789356 | − | 0.435581i | ||||
\(917\) | −2.30606e56 | −1.19634 | ||||||||
\(918\) | 8.65821e54 | − | 2.23036e54i | 0.0439964 | − | 0.0113335i | ||||
\(919\) | 6.29072e55i | 0.313116i | 0.987669 | + | 0.156558i | \(0.0500399\pi\) | ||||
−0.987669 | + | 0.156558i | \(0.949960\pi\) | |||||||
\(920\) | 8.98489e55 | − | 8.47761e55i | 0.438071 | − | 0.413338i | ||||
\(921\) | 5.06672e55 | 0.241988 | ||||||||
\(922\) | 7.08283e55 | + | 2.74954e56i | 0.331375 | + | 1.28639i | ||||
\(923\) | − | 5.80517e55i | − | 0.266062i | ||||||
\(924\) | 5.80597e55 | + | 1.05215e56i | 0.260680 | + | 0.472402i | ||||
\(925\) | −2.96754e56 | −1.30528 | ||||||||
\(926\) | 1.36433e56 | − | 3.51453e55i | 0.587911 | − | 0.151446i | ||||
\(927\) | 2.05271e55i | 0.0866586i | ||||||||
\(928\) | −4.21035e56 | − | 1.34963e56i | −1.74143 | − | 0.558216i | ||||
\(929\) | 1.94099e56 | 0.786548 | 0.393274 | − | 0.919421i | \(-0.371342\pi\) | ||||
0.393274 | + | 0.919421i | \(0.371342\pi\) | |||||||
\(930\) | −1.21993e55 | − | 4.73576e55i | −0.0484351 | − | 0.188024i | ||||
\(931\) | − | 4.39778e54i | − | 0.0171076i | ||||||
\(932\) | 2.09200e56 | − | 1.15440e56i | 0.797368 | − | 0.440002i | ||||
\(933\) | −2.46897e56 | −0.922072 | ||||||||
\(934\) | −3.44909e56 | + | 8.88485e55i | −1.26216 | + | 0.325132i | ||||
\(935\) | − | 4.14384e54i | − | 0.0148588i | ||||||
\(936\) | 1.65986e55 | + | 1.75919e55i | 0.0583219 | + | 0.0618117i | ||||
\(937\) | 1.42702e56 | 0.491334 | 0.245667 | − | 0.969354i | \(-0.420993\pi\) | ||||
0.245667 | + | 0.969354i | \(0.420993\pi\) | |||||||
\(938\) | −3.21891e54 | − | 1.24958e55i | −0.0108606 | − | 0.0421608i | ||||
\(939\) | − | 1.09226e56i | − | 0.361145i | ||||||
\(940\) | −1.13726e55 | − | 2.06094e55i | −0.0368495 | − | 0.0667784i | ||||
\(941\) | 1.05206e56 | 0.334069 | 0.167035 | − | 0.985951i | \(-0.446581\pi\) | ||||
0.167035 | + | 0.985951i | \(0.446581\pi\) | |||||||
\(942\) | 3.38928e56 | − | 8.73079e55i | 1.05473 | − | 0.271698i | ||||
\(943\) | − | 6.55860e56i | − | 2.00027i | ||||||
\(944\) | −4.24931e56 | − | 2.67786e56i | −1.27014 | − | 0.800424i | ||||
\(945\) | −7.90624e55 | −0.231614 | ||||||||
\(946\) | 4.59849e55 | + | 1.78513e56i | 0.132033 | + | 0.512552i | ||||
\(947\) | − | 1.85655e56i | − | 0.522466i | −0.965276 | − | 0.261233i | \(-0.915871\pi\) | ||
0.965276 | − | 0.261233i | \(-0.0841290\pi\) | |||||||
\(948\) | −6.38858e56 | + | 3.52533e56i | −1.76216 | + | 0.972393i | ||||
\(949\) | 3.77871e56 | 1.02161 | ||||||||
\(950\) | −8.98754e54 | + | 2.31519e54i | −0.0238173 | + | 0.00613534i | ||||
\(951\) | − | 6.09925e55i | − | 0.158433i | ||||||
\(952\) | 8.72705e54 | − | 8.23433e54i | 0.0222211 | − | 0.0209665i | ||||
\(953\) | 5.16017e56 | 1.28795 | 0.643975 | − | 0.765046i | \(-0.277284\pi\) | ||||
0.643975 | + | 0.765046i | \(0.277284\pi\) | |||||||
\(954\) | 6.41331e54 | + | 2.48963e55i | 0.0156914 | + | 0.0609139i | ||||
\(955\) | 2.76044e56i | 0.662085i | ||||||||
\(956\) | 3.26936e56 | + | 5.92470e56i | 0.768709 | + | 1.39305i | ||||
\(957\) | −6.71374e56 | −1.54753 | ||||||||
\(958\) | −2.30733e55 | + | 5.94368e54i | −0.0521392 | + | 0.0134311i | ||||
\(959\) | 1.42639e56i | 0.315998i | ||||||||
\(960\) | 1.84117e56 | + | 1.07061e55i | 0.399890 | + | 0.0232529i | ||||
\(961\) | 3.59279e56 | 0.765046 | ||||||||
\(962\) | 1.66823e56 | + | 6.47603e56i | 0.348280 | + | 1.35202i | ||||
\(963\) | − | 3.46150e55i | − | 0.0708541i | ||||||
\(964\) | −3.87913e56 | + | 2.14057e56i | −0.778522 | + | 0.429602i | ||||
\(965\) | −2.48824e55 | −0.0489636 | ||||||||
\(966\) | 5.25964e56 | − | 1.35489e56i | 1.01482 | − | 0.261419i | ||||
\(967\) | − | 3.90929e56i | − | 0.739597i | −0.929112 | − | 0.369799i | \(-0.879427\pi\) | ||
0.929112 | − | 0.369799i | \(-0.120573\pi\) | |||||||
\(968\) | −1.27587e56 | − | 1.35222e56i | −0.236688 | − | 0.250851i | ||||
\(969\) | −7.93881e53 | −0.00144412 | ||||||||
\(970\) | 4.79803e55 | + | 1.86259e56i | 0.0855855 | + | 0.332242i | ||||
\(971\) | 8.16200e56i | 1.42768i | 0.700308 | + | 0.713841i | \(0.253046\pi\) | ||||
−0.700308 | + | 0.713841i | \(0.746954\pi\) | |||||||
\(972\) | 5.22917e55 | + | 9.47627e55i | 0.0896962 | + | 0.162547i | ||||
\(973\) | −4.12459e56 | −0.693804 | ||||||||
\(974\) | 7.52536e56 | − | 1.93853e56i | 1.24139 | − | 0.319781i | ||||
\(975\) | − | 5.03233e56i | − | 0.814108i | ||||||
\(976\) | −2.64832e56 | + | 4.20243e56i | −0.420169 | + | 0.666737i | ||||
\(977\) | 4.37423e56 | 0.680620 | 0.340310 | − | 0.940313i | \(-0.389468\pi\) | ||||
0.340310 | + | 0.940313i | \(0.389468\pi\) | |||||||
\(978\) | −2.92877e56 | − | 1.13695e57i | −0.446938 | − | 1.73501i | ||||
\(979\) | − | 1.01955e57i | − | 1.52594i | ||||||
\(980\) | 1.35618e56 | − | 7.48364e55i | 0.199077 | − | 0.109854i | ||||
\(981\) | 4.34935e55 | 0.0626201 | ||||||||
\(982\) | 3.45455e55 | − | 8.89893e54i | 0.0487835 | − | 0.0125667i | ||||
\(983\) | 1.32709e57i | 1.83816i | 0.394074 | + | 0.919079i | \(0.371066\pi\) | ||||
−0.394074 | + | 0.919079i | \(0.628934\pi\) | |||||||
\(984\) | 7.12199e56 | − | 6.71989e56i | 0.967597 | − | 0.912968i | ||||
\(985\) | −1.09741e56 | −0.146245 | ||||||||
\(986\) | 1.67220e55 | + | 6.49144e55i | 0.0218588 | + | 0.0848554i | ||||
\(987\) | − | 1.03495e56i | − | 0.132707i | ||||||
\(988\) | 1.01048e55 | + | 1.83119e55i | 0.0127100 | + | 0.0230330i | ||||
\(989\) | 8.33157e56 | 1.02801 | ||||||||
\(990\) | 2.31025e55 | − | 5.95120e54i | 0.0279634 | − | 0.00720338i | ||||
\(991\) | − | 6.86443e55i | − | 0.0815089i | −0.999169 | − | 0.0407545i | \(-0.987024\pi\) | ||
0.999169 | − | 0.0407545i | \(-0.0129761\pi\) | |||||||
\(992\) | 1.27019e56 | − | 3.96255e56i | 0.147961 | − | 0.461586i | ||||
\(993\) | −1.10662e57 | −1.26463 | ||||||||
\(994\) | −4.13592e55 | − | 1.60556e56i | −0.0463693 | − | 0.180005i | ||||
\(995\) | 2.42994e54i | 0.00267274i | ||||||||
\(996\) | −5.32446e56 | + | 2.93813e56i | −0.574576 | + | 0.317062i | ||||
\(997\) | −8.32531e56 | −0.881439 | −0.440719 | − | 0.897645i | \(-0.645277\pi\) | ||||
−0.440719 | + | 0.897645i | \(0.645277\pi\) | |||||||
\(998\) | −1.60886e57 | + | 4.14443e56i | −1.67124 | + | 0.430511i | ||||
\(999\) | 1.42322e57i | 1.45054i |
(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 | 4.39.b.a.3.12 | yes | 18 | |
4.3 | odd | 2 | inner | 4.39.b.a.3.11 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.39.b.a.3.11 | ✓ | 18 | 4.3 | odd | 2 | inner | |
4.39.b.a.3.12 | yes | 18 | 1.1 | even | 1 | trivial |