Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,19,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 19, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 19);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 19 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(12.3231682626\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 8797x^{4} + 1809980x^{3} + 107861490x^{2} - 7180095600x + 788142376800 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{31}\cdot 3^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.3 | ||
Root | \(-112.126 - 31.1763i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.19.b.a.5.6 |
$q$-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 \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 362.039i | − | 0.707107i | ||||||
\(3\) | 19502.4 | + | 2660.56i | 0.990822 | + | 0.135171i | ||||
\(4\) | −131072. | −0.500000 | ||||||||
\(5\) | − | 1.30525e6i | − | 0.668287i | −0.942522 | − | 0.334143i | \(-0.891553\pi\) | ||
0.942522 | − | 0.334143i | \(-0.108447\pi\) | |||||||
\(6\) | 963226. | − | 7.06061e6i | 0.0955800 | − | 0.700617i | ||||
\(7\) | 3.15845e7 | 0.782692 | 0.391346 | − | 0.920244i | \(-0.372009\pi\) | ||||
0.391346 | + | 0.920244i | \(0.372009\pi\) | |||||||
\(8\) | 4.74531e7i | 0.353553i | ||||||||
\(9\) | 3.73263e8 | + | 1.03774e8i | 0.963458 | + | 0.267860i | ||||
\(10\) | −4.72550e8 | −0.472550 | ||||||||
\(11\) | − | 3.81148e9i | − | 1.61644i | −0.588882 | − | 0.808219i | \(-0.700432\pi\) | ||
0.588882 | − | 0.808219i | \(-0.299568\pi\) | |||||||
\(12\) | −2.55621e9 | − | 3.48725e8i | −0.495411 | − | 0.0675853i | ||||
\(13\) | −5.50456e9 | −0.519078 | −0.259539 | − | 0.965733i | \(-0.583571\pi\) | ||||
−0.259539 | + | 0.965733i | \(0.583571\pi\) | |||||||
\(14\) | − | 1.14348e10i | − | 0.553447i | ||||||
\(15\) | 3.47269e9 | − | 2.54554e10i | 0.0903327 | − | 0.662154i | ||||
\(16\) | 1.71799e10 | 0.250000 | ||||||||
\(17\) | − | 1.95721e11i | − | 1.65043i | −0.564816 | − | 0.825217i | \(-0.691053\pi\) | ||
0.564816 | − | 0.825217i | \(-0.308947\pi\) | |||||||
\(18\) | 3.75704e10 | − | 1.35136e11i | 0.189406 | − | 0.681268i | ||||
\(19\) | −1.56485e11 | −0.484942 | −0.242471 | − | 0.970159i | \(-0.577958\pi\) | ||||
−0.242471 | + | 0.970159i | \(0.577958\pi\) | |||||||
\(20\) | 1.71081e11i | 0.334143i | ||||||||
\(21\) | 6.15971e11 | + | 8.40324e10i | 0.775509 | + | 0.105797i | ||||
\(22\) | −1.37990e12 | −1.14299 | ||||||||
\(23\) | 1.49039e12i | 0.827463i | 0.910399 | + | 0.413732i | \(0.135775\pi\) | ||||
−0.910399 | + | 0.413732i | \(0.864225\pi\) | |||||||
\(24\) | −1.26252e11 | + | 9.25448e11i | −0.0477900 | + | 0.350309i | ||||
\(25\) | 2.11102e12 | 0.553392 | ||||||||
\(26\) | 1.99286e12i | 0.367044i | ||||||||
\(27\) | 7.00342e12 | + | 3.01694e12i | 0.918409 | + | 0.395633i | ||||
\(28\) | −4.13984e12 | −0.391346 | ||||||||
\(29\) | 7.21871e12i | 0.497597i | 0.968555 | + | 0.248799i | \(0.0800357\pi\) | ||||
−0.968555 | + | 0.248799i | \(0.919964\pi\) | |||||||
\(30\) | −9.21584e12 | − | 1.25725e12i | −0.468213 | − | 0.0638749i | ||||
\(31\) | 3.81624e12 | 0.144338 | 0.0721690 | − | 0.997392i | \(-0.477008\pi\) | ||||
0.0721690 | + | 0.997392i | \(0.477008\pi\) | |||||||
\(32\) | − | 6.21978e12i | − | 0.176777i | ||||||
\(33\) | 1.01407e13 | − | 7.43328e13i | 0.218495 | − | 1.60160i | ||||
\(34\) | −7.08587e13 | −1.16703 | ||||||||
\(35\) | − | 4.12256e13i | − | 0.523063i | ||||||
\(36\) | −4.89244e13 | − | 1.36019e13i | −0.481729 | − | 0.133930i | ||||
\(37\) | 2.50324e14 | 1.92614 | 0.963068 | − | 0.269260i | \(-0.0867791\pi\) | ||||
0.963068 | + | 0.269260i | \(0.0867791\pi\) | |||||||
\(38\) | 5.66536e13i | 0.342906i | ||||||||
\(39\) | −1.07352e14 | − | 1.46452e13i | −0.514314 | − | 0.0701641i | ||||
\(40\) | 6.19381e13 | 0.236275 | ||||||||
\(41\) | 4.39043e14i | 1.34107i | 0.741876 | + | 0.670537i | \(0.233936\pi\) | ||||
−0.741876 | + | 0.670537i | \(0.766064\pi\) | |||||||
\(42\) | 3.04230e13 | − | 2.23005e14i | 0.0748098 | − | 0.548368i | ||||
\(43\) | −5.41174e14 | −1.07676 | −0.538382 | − | 0.842701i | \(-0.680964\pi\) | ||||
−0.538382 | + | 0.842701i | \(0.680964\pi\) | |||||||
\(44\) | 4.99578e14i | 0.808219i | ||||||||
\(45\) | 1.35451e14 | − | 4.87201e14i | 0.179007 | − | 0.643866i | ||||
\(46\) | 5.39578e14 | 0.585105 | ||||||||
\(47\) | 1.94037e15i | 1.73382i | 0.498464 | + | 0.866911i | \(0.333898\pi\) | ||||
−0.498464 | + | 0.866911i | \(0.666102\pi\) | |||||||
\(48\) | 3.35048e14 | + | 4.57081e13i | 0.247706 | + | 0.0337926i | ||||
\(49\) | −6.30835e14 | −0.387392 | ||||||||
\(50\) | − | 7.64273e14i | − | 0.391308i | ||||||
\(51\) | 5.20729e14 | − | 3.81703e15i | 0.223090 | − | 1.63529i | ||||
\(52\) | 7.21494e14 | 0.259539 | ||||||||
\(53\) | − | 1.53546e15i | − | 0.465325i | −0.972558 | − | 0.232663i | \(-0.925256\pi\) | ||
0.972558 | − | 0.232663i | \(-0.0747438\pi\) | |||||||
\(54\) | 1.09225e15 | − | 2.53551e15i | 0.279755 | − | 0.649413i | ||||
\(55\) | −4.97492e15 | −1.08024 | ||||||||
\(56\) | 1.49878e15i | 0.276724i | ||||||||
\(57\) | −3.05182e15 | − | 4.16338e14i | −0.480492 | − | 0.0655499i | ||||
\(58\) | 2.61345e15 | 0.351854 | ||||||||
\(59\) | 6.50072e15i | 0.750401i | 0.926944 | + | 0.375201i | \(0.122426\pi\) | ||||
−0.926944 | + | 0.375201i | \(0.877574\pi\) | |||||||
\(60\) | −4.55173e14 | + | 3.33649e15i | −0.0451664 | + | 0.331077i | ||||
\(61\) | 3.87413e15 | 0.331288 | 0.165644 | − | 0.986186i | \(-0.447030\pi\) | ||||
0.165644 | + | 0.986186i | \(0.447030\pi\) | |||||||
\(62\) | − | 1.38163e15i | − | 0.102062i | ||||||
\(63\) | 1.17893e16 | + | 3.27766e15i | 0.754091 | + | 0.209652i | ||||
\(64\) | −2.25180e15 | −0.125000 | ||||||||
\(65\) | 7.18482e15i | 0.346893i | ||||||||
\(66\) | −2.69113e16 | − | 3.67131e15i | −1.13250 | − | 0.154499i | ||||
\(67\) | 3.71114e16 | 1.36406 | 0.682032 | − | 0.731322i | \(-0.261097\pi\) | ||||
0.682032 | + | 0.731322i | \(0.261097\pi\) | |||||||
\(68\) | 2.56536e16i | 0.825217i | ||||||||
\(69\) | −3.96527e15 | + | 2.90661e16i | −0.111849 | + | 0.819869i | ||||
\(70\) | −1.49252e16 | −0.369862 | ||||||||
\(71\) | − | 6.33282e16i | − | 1.38125i | −0.723214 | − | 0.690624i | \(-0.757336\pi\) | ||
0.723214 | − | 0.690624i | \(-0.242664\pi\) | |||||||
\(72\) | −4.92442e15 | + | 1.77125e16i | −0.0947028 | + | 0.340634i | ||||
\(73\) | −5.51216e16 | −0.936302 | −0.468151 | − | 0.883648i | \(-0.655080\pi\) | ||||
−0.468151 | + | 0.883648i | \(0.655080\pi\) | |||||||
\(74\) | − | 9.06269e16i | − | 1.36198i | ||||||
\(75\) | 4.11700e16 | + | 5.61651e15i | 0.548314 | + | 0.0748024i | ||||
\(76\) | 2.05108e16 | 0.242471 | ||||||||
\(77\) | − | 1.20383e17i | − | 1.26517i | ||||||
\(78\) | −5.30214e15 | + | 3.88655e16i | −0.0496135 | + | 0.363675i | ||||
\(79\) | −7.16429e16 | −0.597763 | −0.298882 | − | 0.954290i | \(-0.596614\pi\) | ||||
−0.298882 | + | 0.954290i | \(0.596614\pi\) | |||||||
\(80\) | − | 2.24240e16i | − | 0.167072i | ||||||
\(81\) | 1.28556e17 | + | 7.74704e16i | 0.856502 | + | 0.516144i | ||||
\(82\) | 1.58951e17 | 0.948283 | ||||||||
\(83\) | 1.18877e17i | 0.635911i | 0.948106 | + | 0.317956i | \(0.102996\pi\) | ||||
−0.948106 | + | 0.317956i | \(0.897004\pi\) | |||||||
\(84\) | −8.07366e16 | − | 1.10143e16i | −0.387755 | − | 0.0528985i | ||||
\(85\) | −2.55465e17 | −1.10296 | ||||||||
\(86\) | 1.95926e17i | 0.761388i | ||||||||
\(87\) | −1.92058e16 | + | 1.40782e17i | −0.0672605 | + | 0.493030i | ||||
\(88\) | 1.80867e17 | 0.571497 | ||||||||
\(89\) | 9.49218e16i | 0.270929i | 0.990782 | + | 0.135465i | \(0.0432527\pi\) | ||||
−0.990782 | + | 0.135465i | \(0.956747\pi\) | |||||||
\(90\) | −1.76386e17 | − | 4.90386e16i | −0.455282 | − | 0.126577i | ||||
\(91\) | −1.73859e17 | −0.406278 | ||||||||
\(92\) | − | 1.95348e17i | − | 0.413732i | ||||||
\(93\) | 7.44258e16 | + | 1.01534e16i | 0.143013 | + | 0.0195103i | ||||
\(94\) | 7.02490e17 | 1.22600 | ||||||||
\(95\) | 2.04252e17i | 0.324081i | ||||||||
\(96\) | 1.65481e16 | − | 1.21300e17i | 0.0238950 | − | 0.175154i | ||||
\(97\) | −3.38927e17 | −0.445821 | −0.222910 | − | 0.974839i | \(-0.571556\pi\) | ||||
−0.222910 | + | 0.974839i | \(0.571556\pi\) | |||||||
\(98\) | 2.28387e17i | 0.273928i | ||||||||
\(99\) | 3.95534e17 | − | 1.42268e18i | 0.432979 | − | 1.55737i | ||||
\(100\) | −2.76696e17 | −0.276696 | ||||||||
\(101\) | − | 2.06526e17i | − | 0.188835i | −0.995533 | − | 0.0944176i | \(-0.969901\pi\) | ||
0.995533 | − | 0.0944176i | \(-0.0300989\pi\) | |||||||
\(102\) | −1.38191e18 | − | 1.88524e17i | −1.15632 | − | 0.157748i | ||||
\(103\) | 1.06701e18 | 0.817772 | 0.408886 | − | 0.912585i | \(-0.365917\pi\) | ||||
0.408886 | + | 0.912585i | \(0.365917\pi\) | |||||||
\(104\) | − | 2.61209e17i | − | 0.183522i | ||||||
\(105\) | 1.09683e17 | − | 8.03996e17i | 0.0707027 | − | 0.518263i | ||||
\(106\) | −5.55897e17 | −0.329035 | ||||||||
\(107\) | 8.00886e17i | 0.435629i | 0.975990 | + | 0.217814i | \(0.0698928\pi\) | ||||
−0.975990 | + | 0.217814i | \(0.930107\pi\) | |||||||
\(108\) | −9.17952e17 | − | 3.95436e17i | −0.459204 | − | 0.197816i | ||||
\(109\) | −2.27655e18 | −1.04819 | −0.524094 | − | 0.851660i | \(-0.675596\pi\) | ||||
−0.524094 | + | 0.851660i | \(0.675596\pi\) | |||||||
\(110\) | 1.80111e18i | 0.763848i | ||||||||
\(111\) | 4.88191e18 | + | 6.66002e17i | 1.90846 | + | 0.260357i | ||||
\(112\) | 5.42617e17 | 0.195673 | ||||||||
\(113\) | 5.22481e18i | 1.73926i | 0.493703 | + | 0.869630i | \(0.335643\pi\) | ||||
−0.493703 | + | 0.869630i | \(0.664357\pi\) | |||||||
\(114\) | −1.50730e17 | + | 1.10488e18i | −0.0463508 | + | 0.339759i | ||||
\(115\) | 1.94533e18 | 0.552983 | ||||||||
\(116\) | − | 9.46171e17i | − | 0.248799i | ||||||
\(117\) | −2.05465e18 | − | 5.71233e17i | −0.500110 | − | 0.139040i | ||||
\(118\) | 2.35351e18 | 0.530614 | ||||||||
\(119\) | − | 6.18176e18i | − | 1.29178i | ||||||
\(120\) | 1.20794e18 | + | 1.64790e17i | 0.234107 | + | 0.0319374i | ||||
\(121\) | −8.96744e18 | −1.61287 | ||||||||
\(122\) | − | 1.40258e18i | − | 0.234256i | ||||||
\(123\) | −1.16810e18 | + | 8.56238e18i | −0.181274 | + | 1.32877i | ||||
\(124\) | −5.00203e17 | −0.0721690 | ||||||||
\(125\) | − | 7.73454e18i | − | 1.03811i | ||||||
\(126\) | 1.18664e18 | − | 4.26819e18i | 0.148246 | − | 0.533223i | ||||
\(127\) | 1.03674e19 | 1.20625 | 0.603123 | − | 0.797648i | \(-0.293923\pi\) | ||||
0.603123 | + | 0.797648i | \(0.293923\pi\) | |||||||
\(128\) | 8.15239e17i | 0.0883883i | ||||||||
\(129\) | −1.05542e19 | − | 1.43983e18i | −1.06688 | − | 0.145547i | ||||
\(130\) | 2.60118e18 | 0.245290 | ||||||||
\(131\) | − | 7.19901e18i | − | 0.633623i | −0.948488 | − | 0.316812i | \(-0.897388\pi\) | ||
0.948488 | − | 0.316812i | \(-0.102612\pi\) | |||||||
\(132\) | −1.32916e18 | + | 9.74295e18i | −0.109247 | + | 0.800802i | ||||
\(133\) | −4.94249e18 | −0.379561 | ||||||||
\(134\) | − | 1.34358e19i | − | 0.964539i | ||||||
\(135\) | 3.93785e18 | − | 9.14119e18i | 0.264396 | − | 0.613761i | ||||
\(136\) | 9.28760e18 | 0.583516 | ||||||||
\(137\) | 3.99891e18i | 0.235210i | 0.993060 | + | 0.117605i | \(0.0375217\pi\) | ||||
−0.993060 | + | 0.117605i | \(0.962478\pi\) | |||||||
\(138\) | 1.05230e19 | + | 1.43558e18i | 0.579735 | + | 0.0790889i | ||||
\(139\) | 2.78138e18 | 0.143591 | 0.0717956 | − | 0.997419i | \(-0.477127\pi\) | ||||
0.0717956 | + | 0.997419i | \(0.477127\pi\) | |||||||
\(140\) | 5.40352e18i | 0.261532i | ||||||||
\(141\) | −5.16248e18 | + | 3.78418e19i | −0.234362 | + | 1.71791i | ||||
\(142\) | −2.29272e19 | −0.976690 | ||||||||
\(143\) | 2.09805e19i | 0.839057i | ||||||||
\(144\) | 6.41261e18 | + | 1.78283e18i | 0.240864 | + | 0.0669650i | ||||
\(145\) | 9.42221e18 | 0.332538 | ||||||||
\(146\) | 1.99561e19i | 0.662066i | ||||||||
\(147\) | −1.23028e19 | − | 1.67838e18i | −0.383837 | − | 0.0523641i | ||||
\(148\) | −3.28104e19 | −0.963068 | ||||||||
\(149\) | − | 1.35043e19i | − | 0.373074i | −0.982448 | − | 0.186537i | \(-0.940274\pi\) | ||
0.982448 | − | 0.186537i | \(-0.0597264\pi\) | |||||||
\(150\) | 2.03339e18 | − | 1.49051e19i | 0.0528933 | − | 0.387716i | ||||
\(151\) | 6.29355e19 | 1.54207 | 0.771034 | − | 0.636794i | \(-0.219740\pi\) | ||||
0.771034 | + | 0.636794i | \(0.219740\pi\) | |||||||
\(152\) | − | 7.42570e18i | − | 0.171453i | ||||||
\(153\) | 2.03109e19 | − | 7.30556e19i | 0.442085 | − | 1.59012i | ||||
\(154\) | −4.35835e19 | −0.894613 | ||||||||
\(155\) | − | 4.98115e18i | − | 0.0964593i | ||||||
\(156\) | 1.40708e19 | + | 1.91958e18i | 0.257157 | + | 0.0350820i | ||||
\(157\) | −1.52297e19 | −0.262781 | −0.131391 | − | 0.991331i | \(-0.541944\pi\) | ||||
−0.131391 | + | 0.991331i | \(0.541944\pi\) | |||||||
\(158\) | 2.59375e19i | 0.422683i | ||||||||
\(159\) | 4.08519e18 | − | 2.99451e19i | 0.0628983 | − | 0.461055i | ||||
\(160\) | −8.11835e18 | −0.118138 | ||||||||
\(161\) | 4.70731e19i | 0.647649i | ||||||||
\(162\) | 2.80473e19 | − | 4.65424e19i | 0.364969 | − | 0.605638i | ||||
\(163\) | 2.05524e19 | 0.253032 | 0.126516 | − | 0.991965i | \(-0.459621\pi\) | ||||
0.126516 | + | 0.991965i | \(0.459621\pi\) | |||||||
\(164\) | − | 5.75463e19i | − | 0.670537i | ||||||
\(165\) | −9.70227e19 | − | 1.32361e19i | −1.07033 | − | 0.146017i | ||||
\(166\) | 4.30382e19 | 0.449657 | ||||||||
\(167\) | 9.65270e18i | 0.0955434i | 0.998858 | + | 0.0477717i | \(0.0152120\pi\) | ||||
−0.998858 | + | 0.0477717i | \(0.984788\pi\) | |||||||
\(168\) | −3.98760e18 | + | 2.92298e19i | −0.0374049 | + | 0.274184i | ||||
\(169\) | −8.21552e19 | −0.730558 | ||||||||
\(170\) | 9.24882e19i | 0.779913i | ||||||||
\(171\) | −5.84101e19 | − | 1.62391e19i | −0.467221 | − | 0.129897i | ||||
\(172\) | 7.09328e19 | 0.538382 | ||||||||
\(173\) | 8.60111e19i | 0.619640i | 0.950795 | + | 0.309820i | \(0.100269\pi\) | ||||
−0.950795 | + | 0.309820i | \(0.899731\pi\) | |||||||
\(174\) | 5.09685e19 | + | 6.95326e18i | 0.348625 | + | 0.0475603i | ||||
\(175\) | 6.66756e19 | 0.433136 | ||||||||
\(176\) | − | 6.54807e19i | − | 0.404110i | ||||||
\(177\) | −1.72956e19 | + | 1.26779e20i | −0.101432 | + | 0.743514i | ||||
\(178\) | 3.43654e19 | 0.191576 | ||||||||
\(179\) | 1.49036e20i | 0.789977i | 0.918686 | + | 0.394988i | \(0.129251\pi\) | ||||
−0.918686 | + | 0.394988i | \(0.870749\pi\) | |||||||
\(180\) | −1.77539e19 | + | 6.38584e19i | −0.0895037 | + | 0.321933i | ||||
\(181\) | 2.50765e20 | 1.20271 | 0.601354 | − | 0.798983i | \(-0.294628\pi\) | ||||
0.601354 | + | 0.798983i | \(0.294628\pi\) | |||||||
\(182\) | 6.29436e19i | 0.287282i | ||||||||
\(183\) | 7.55547e19 | + | 1.03074e19i | 0.328248 | + | 0.0447804i | ||||
\(184\) | −7.07235e19 | −0.292552 | ||||||||
\(185\) | − | 3.26735e20i | − | 1.28721i | ||||||
\(186\) | 3.67591e18 | − | 2.69450e19i | 0.0137958 | − | 0.101126i | ||||
\(187\) | −7.45988e20 | −2.66782 | ||||||||
\(188\) | − | 2.54328e20i | − | 0.866911i | ||||||
\(189\) | 2.21199e20 | + | 9.52883e19i | 0.718832 | + | 0.309659i | ||||
\(190\) | 7.39470e19 | 0.229160 | ||||||||
\(191\) | − | 4.59540e20i | − | 1.35839i | −0.733959 | − | 0.679193i | \(-0.762330\pi\) | ||
0.733959 | − | 0.679193i | \(-0.237670\pi\) | |||||||
\(192\) | −4.39154e19 | − | 5.99105e18i | −0.123853 | − | 0.0168963i | ||||
\(193\) | 7.00243e19 | 0.188466 | 0.0942330 | − | 0.995550i | \(-0.469960\pi\) | ||||
0.0942330 | + | 0.995550i | \(0.469960\pi\) | |||||||
\(194\) | 1.22705e20i | 0.315243i | ||||||||
\(195\) | −1.91157e19 | + | 1.40121e20i | −0.0468897 | + | 0.343709i | ||||
\(196\) | 8.26848e19 | 0.193696 | ||||||||
\(197\) | − | 3.14404e20i | − | 0.703545i | −0.936086 | − | 0.351772i | \(-0.885579\pi\) | ||
0.936086 | − | 0.351772i | \(-0.114421\pi\) | |||||||
\(198\) | −5.15067e20 | − | 1.43199e20i | −1.10123 | − | 0.306162i | ||||
\(199\) | 1.46711e20 | 0.299768 | 0.149884 | − | 0.988704i | \(-0.452110\pi\) | ||||
0.149884 | + | 0.988704i | \(0.452110\pi\) | |||||||
\(200\) | 1.00175e20i | 0.195654i | ||||||||
\(201\) | 7.23761e20 | + | 9.87373e19i | 1.35154 | + | 0.184381i | ||||
\(202\) | −7.47705e19 | −0.133527 | ||||||||
\(203\) | 2.27999e20i | 0.389466i | ||||||||
\(204\) | −6.82530e19 | + | 5.00306e20i | −0.111545 | + | 0.817643i | ||||
\(205\) | 5.73061e20 | 0.896222 | ||||||||
\(206\) | − | 3.86298e20i | − | 0.578252i | ||||||
\(207\) | −1.54664e20 | + | 5.56307e20i | −0.221644 | + | 0.797226i | ||||
\(208\) | −9.45677e19 | −0.129769 | ||||||||
\(209\) | 5.96438e20i | 0.783879i | ||||||||
\(210\) | −2.91077e20 | − | 3.97095e19i | −0.366467 | − | 0.0499944i | ||||
\(211\) | −5.46493e20 | −0.659239 | −0.329619 | − | 0.944114i | \(-0.606920\pi\) | ||||
−0.329619 | + | 0.944114i | \(0.606920\pi\) | |||||||
\(212\) | 2.01256e20i | 0.232663i | ||||||||
\(213\) | 1.68488e20 | − | 1.23505e21i | 0.186704 | − | 1.36857i | ||||
\(214\) | 2.89952e20 | 0.308036 | ||||||||
\(215\) | 7.06366e20i | 0.719588i | ||||||||
\(216\) | −1.43163e20 | + | 3.32334e20i | −0.139877 | + | 0.324707i | ||||
\(217\) | 1.20534e20 | 0.112972 | ||||||||
\(218\) | 8.24200e20i | 0.741181i | ||||||||
\(219\) | −1.07500e21 | − | 1.46654e20i | −0.927709 | − | 0.126560i | ||||
\(220\) | 6.52073e20 | 0.540122 | ||||||||
\(221\) | 1.07736e21i | 0.856704i | ||||||||
\(222\) | 2.41119e20 | − | 1.76744e21i | 0.184100 | − | 1.34948i | ||||
\(223\) | −1.21601e21 | −0.891648 | −0.445824 | − | 0.895121i | \(-0.647089\pi\) | ||||
−0.445824 | + | 0.895121i | \(0.647089\pi\) | |||||||
\(224\) | − | 1.96448e20i | − | 0.138362i | ||||||
\(225\) | 7.87968e20 | + | 2.19070e20i | 0.533170 | + | 0.148232i | ||||
\(226\) | 1.89158e21 | 1.22984 | ||||||||
\(227\) | − | 1.82295e21i | − | 1.13905i | −0.821974 | − | 0.569524i | \(-0.807127\pi\) | ||
0.821974 | − | 0.569524i | \(-0.192873\pi\) | |||||||
\(228\) | 4.00009e20 | + | 5.45702e19i | 0.240246 | + | 0.0327749i | ||||
\(229\) | −1.70915e21 | −0.986872 | −0.493436 | − | 0.869782i | \(-0.664259\pi\) | ||||
−0.493436 | + | 0.869782i | \(0.664259\pi\) | |||||||
\(230\) | − | 7.04283e20i | − | 0.391018i | ||||||
\(231\) | 3.20288e20 | − | 2.34776e21i | 0.171014 | − | 1.25356i | ||||
\(232\) | −3.42551e20 | −0.175927 | ||||||||
\(233\) | − | 7.67655e20i | − | 0.379283i | −0.981853 | − | 0.189641i | \(-0.939267\pi\) | ||
0.981853 | − | 0.189641i | \(-0.0607325\pi\) | |||||||
\(234\) | −2.06808e20 | + | 7.43863e20i | −0.0983163 | + | 0.353631i | ||||
\(235\) | 2.53267e21 | 1.15869 | ||||||||
\(236\) | − | 8.52063e20i | − | 0.375201i | ||||||
\(237\) | −1.39721e21 | − | 1.90610e20i | −0.592277 | − | 0.0808000i | ||||
\(238\) | −2.23804e21 | −0.913428 | ||||||||
\(239\) | 2.79282e21i | 1.09765i | 0.835938 | + | 0.548823i | \(0.184924\pi\) | ||||
−0.835938 | + | 0.548823i | \(0.815076\pi\) | |||||||
\(240\) | 5.96604e19 | − | 4.37321e20i | 0.0225832 | − | 0.165538i | ||||
\(241\) | −2.42709e21 | −0.884979 | −0.442490 | − | 0.896774i | \(-0.645905\pi\) | ||||
−0.442490 | + | 0.896774i | \(0.645905\pi\) | |||||||
\(242\) | 3.24656e21i | 1.14047i | ||||||||
\(243\) | 2.30104e21 | + | 1.85289e21i | 0.778874 | + | 0.627180i | ||||
\(244\) | −5.07790e20 | −0.165644 | ||||||||
\(245\) | 8.23396e20i | 0.258889i | ||||||||
\(246\) | 3.09991e21 | + | 4.22898e20i | 0.939580 | + | 0.128180i | ||||
\(247\) | 8.61381e20 | 0.251723 | ||||||||
\(248\) | 1.81093e20i | 0.0510312i | ||||||||
\(249\) | −3.16281e20 | + | 2.31839e21i | −0.0859565 | + | 0.630075i | ||||
\(250\) | −2.80020e21 | −0.734056 | ||||||||
\(251\) | 6.90800e20i | 0.174698i | 0.996178 | + | 0.0873492i | \(0.0278396\pi\) | ||||
−0.996178 | + | 0.0873492i | \(0.972160\pi\) | |||||||
\(252\) | −1.54525e21 | − | 4.29610e20i | −0.377046 | − | 0.104826i | ||||
\(253\) | 5.68058e21 | 1.33754 | ||||||||
\(254\) | − | 3.75340e21i | − | 0.852945i | ||||||
\(255\) | −4.98217e21 | − | 6.79680e20i | −1.09284 | − | 0.149088i | ||||
\(256\) | 2.95148e20 | 0.0625000 | ||||||||
\(257\) | − | 4.00679e21i | − | 0.819216i | −0.912262 | − | 0.409608i | \(-0.865666\pi\) | ||
0.912262 | − | 0.409608i | \(-0.134334\pi\) | |||||||
\(258\) | −5.21273e20 | + | 3.82102e21i | −0.102917 | + | 0.754400i | ||||
\(259\) | 7.90635e21 | 1.50757 | ||||||||
\(260\) | − | 9.41729e20i | − | 0.173447i | ||||||
\(261\) | −7.49118e20 | + | 2.69448e21i | −0.133286 | + | 0.479414i | ||||
\(262\) | −2.60632e21 | −0.448039 | ||||||||
\(263\) | − | 3.40224e21i | − | 0.565149i | −0.959245 | − | 0.282575i | \(-0.908812\pi\) | ||
0.959245 | − | 0.282575i | \(-0.0911885\pi\) | |||||||
\(264\) | 3.52732e21 | + | 4.81207e20i | 0.566252 | + | 0.0772496i | ||||
\(265\) | −2.00416e21 | −0.310971 | ||||||||
\(266\) | 1.78937e21i | 0.268390i | ||||||||
\(267\) | −2.52545e20 | + | 1.85120e21i | −0.0366217 | + | 0.268443i | ||||
\(268\) | −4.86427e21 | −0.682032 | ||||||||
\(269\) | − | 8.26566e21i | − | 1.12075i | −0.828241 | − | 0.560373i | \(-0.810658\pi\) | ||
0.828241 | − | 0.560373i | \(-0.189342\pi\) | |||||||
\(270\) | −3.30947e21 | − | 1.42565e21i | −0.433994 | − | 0.186956i | ||||
\(271\) | −6.07257e20 | −0.0770280 | −0.0385140 | − | 0.999258i | \(-0.512262\pi\) | ||||
−0.0385140 | + | 0.999258i | \(0.512262\pi\) | |||||||
\(272\) | − | 3.36247e21i | − | 0.412608i | ||||||
\(273\) | −3.39065e21 | − | 4.62562e20i | −0.402550 | − | 0.0549169i | ||||
\(274\) | 1.44776e21 | 0.166319 | ||||||||
\(275\) | − | 8.04612e21i | − | 0.894525i | ||||||
\(276\) | 5.19736e20 | − | 3.80975e21i | 0.0559243 | − | 0.409934i | ||||
\(277\) | −7.76370e21 | −0.808632 | −0.404316 | − | 0.914619i | \(-0.632490\pi\) | ||||
−0.404316 | + | 0.914619i | \(0.632490\pi\) | |||||||
\(278\) | − | 1.00697e21i | − | 0.101534i | ||||||
\(279\) | 1.42446e21 | + | 3.96029e20i | 0.139064 | + | 0.0386624i | ||||
\(280\) | 1.95628e21 | 0.184931 | ||||||||
\(281\) | 1.12811e22i | 1.03274i | 0.856364 | + | 0.516372i | \(0.172718\pi\) | ||||
−0.856364 | + | 0.516372i | \(0.827282\pi\) | |||||||
\(282\) | 1.37002e22 | + | 1.86902e21i | 1.21474 | + | 0.165719i | ||||
\(283\) | 1.16922e22 | 1.00419 | 0.502096 | − | 0.864812i | \(-0.332562\pi\) | ||||
0.502096 | + | 0.864812i | \(0.332562\pi\) | |||||||
\(284\) | 8.30055e21i | 0.690624i | ||||||||
\(285\) | −5.43424e20 | + | 3.98339e21i | −0.0438061 | + | 0.321106i | ||||
\(286\) | 7.59576e21 | 0.593303 | ||||||||
\(287\) | 1.38670e22i | 1.04965i | ||||||||
\(288\) | 6.45454e20 | − | 2.32161e21i | 0.0473514 | − | 0.170317i | ||||
\(289\) | −2.42438e22 | −1.72393 | ||||||||
\(290\) | − | 3.41121e21i | − | 0.235140i | ||||||
\(291\) | −6.60987e21 | − | 9.01735e20i | −0.441729 | − | 0.0602618i | ||||
\(292\) | 7.22490e21 | 0.468151 | ||||||||
\(293\) | 2.56349e22i | 1.61073i | 0.592777 | + | 0.805367i | \(0.298032\pi\) | ||||
−0.592777 | + | 0.805367i | \(0.701968\pi\) | |||||||
\(294\) | −6.07637e20 | + | 4.45408e21i | −0.0370270 | + | 0.271414i | ||||
\(295\) | 8.48505e21 | 0.501483 | ||||||||
\(296\) | 1.18787e22i | 0.680992i | ||||||||
\(297\) | 1.14990e22 | − | 2.66934e22i | 0.639516 | − | 1.48455i | ||||
\(298\) | −4.88907e21 | −0.263803 | ||||||||
\(299\) | − | 8.20393e21i | − | 0.429518i | ||||||
\(300\) | −5.39623e21 | − | 7.36167e20i | −0.274157 | − | 0.0374012i | ||||
\(301\) | −1.70927e22 | −0.842776 | ||||||||
\(302\) | − | 2.27851e22i | − | 1.09041i | ||||||
\(303\) | 5.49476e20 | − | 4.02775e21i | 0.0255250 | − | 0.187102i | ||||
\(304\) | −2.68839e21 | −0.121236 | ||||||||
\(305\) | − | 5.05670e21i | − | 0.221395i | ||||||
\(306\) | −2.64490e22 | − | 7.35333e21i | −1.12439 | − | 0.312601i | ||||
\(307\) | 1.11726e22 | 0.461221 | 0.230610 | − | 0.973046i | \(-0.425928\pi\) | ||||
0.230610 | + | 0.973046i | \(0.425928\pi\) | |||||||
\(308\) | 1.57789e22i | 0.632587i | ||||||||
\(309\) | 2.08092e22 | + | 2.83884e21i | 0.810267 | + | 0.110539i | ||||
\(310\) | −1.80337e21 | −0.0682070 | ||||||||
\(311\) | 2.40165e21i | 0.0882403i | 0.999026 | + | 0.0441202i | \(0.0140484\pi\) | ||||
−0.999026 | + | 0.0441202i | \(0.985952\pi\) | |||||||
\(312\) | 6.94962e20 | − | 5.09419e21i | 0.0248067 | − | 0.181837i | ||||
\(313\) | 7.63802e21 | 0.264900 | 0.132450 | − | 0.991190i | \(-0.457716\pi\) | ||||
0.132450 | + | 0.991190i | \(0.457716\pi\) | |||||||
\(314\) | 5.51374e21i | 0.185815i | ||||||||
\(315\) | 4.27816e21 | − | 1.53880e22i | 0.140108 | − | 0.503949i | ||||
\(316\) | 9.39038e21 | 0.298882 | ||||||||
\(317\) | − | 5.61795e22i | − | 1.73798i | −0.494830 | − | 0.868990i | \(-0.664770\pi\) | ||
0.494830 | − | 0.868990i | \(-0.335230\pi\) | |||||||
\(318\) | −1.08413e22 | − | 1.47900e21i | −0.326015 | − | 0.0444758i | ||||
\(319\) | 2.75140e22 | 0.804335 | ||||||||
\(320\) | 2.93916e21i | 0.0835359i | ||||||||
\(321\) | −2.13081e21 | + | 1.56192e22i | −0.0588842 | + | 0.431631i | ||||
\(322\) | 1.70423e22 | 0.457957 | ||||||||
\(323\) | 3.06274e22i | 0.800365i | ||||||||
\(324\) | −1.68501e22 | − | 1.01542e22i | −0.428251 | − | 0.258072i | ||||
\(325\) | −1.16203e22 | −0.287254 | ||||||||
\(326\) | − | 7.44077e21i | − | 0.178920i | ||||||
\(327\) | −4.43981e22 | − | 6.05691e21i | −1.03857 | − | 0.141684i | ||||
\(328\) | −2.08340e22 | −0.474141 | ||||||||
\(329\) | 6.12856e22i | 1.35705i | ||||||||
\(330\) | −4.79198e21 | + | 3.51260e22i | −0.103250 | + | 0.756838i | ||||
\(331\) | −4.49114e22 | −0.941684 | −0.470842 | − | 0.882218i | \(-0.656050\pi\) | ||||
−0.470842 | + | 0.882218i | \(0.656050\pi\) | |||||||
\(332\) | − | 1.55815e22i | − | 0.317956i | ||||||
\(333\) | 9.34367e22 | + | 2.59772e22i | 1.85575 | + | 0.515935i | ||||
\(334\) | 3.49465e21 | 0.0675594 | ||||||||
\(335\) | − | 4.84396e22i | − | 0.911586i | ||||||
\(336\) | 1.05823e22 | + | 1.44367e21i | 0.193877 | + | 0.0264492i | ||||
\(337\) | 1.02040e22 | 0.182012 | 0.0910061 | − | 0.995850i | \(-0.470992\pi\) | ||||
0.0910061 | + | 0.995850i | \(0.470992\pi\) | |||||||
\(338\) | 2.97434e22i | 0.516583i | ||||||||
\(339\) | −1.39009e22 | + | 1.01896e23i | −0.235097 | + | 1.72330i | ||||
\(340\) | 3.34843e22 | 0.551482 | ||||||||
\(341\) | − | 1.45455e22i | − | 0.233314i | ||||||
\(342\) | −5.87919e21 | + | 2.11467e22i | −0.0918508 | + | 0.330375i | ||||
\(343\) | −7.13572e22 | −1.08590 | ||||||||
\(344\) | − | 2.56804e22i | − | 0.380694i | ||||||
\(345\) | 3.79384e22 | + | 5.17566e21i | 0.547908 | + | 0.0747470i | ||||
\(346\) | 3.11394e22 | 0.438152 | ||||||||
\(347\) | − | 6.29266e22i | − | 0.862718i | −0.902180 | − | 0.431359i | \(-0.858034\pi\) | ||
0.902180 | − | 0.431359i | \(-0.141966\pi\) | |||||||
\(348\) | 2.51735e21 | − | 1.84526e22i | 0.0336302 | − | 0.246515i | ||||
\(349\) | 4.44746e22 | 0.579006 | 0.289503 | − | 0.957177i | \(-0.406510\pi\) | ||||
0.289503 | + | 0.957177i | \(0.406510\pi\) | |||||||
\(350\) | − | 2.41391e22i | − | 0.306274i | ||||||
\(351\) | −3.85507e22 | − | 1.66069e22i | −0.476726 | − | 0.205364i | ||||
\(352\) | −2.37065e22 | −0.285749 | ||||||||
\(353\) | − | 1.05940e23i | − | 1.24476i | −0.782715 | − | 0.622380i | \(-0.786166\pi\) | ||
0.782715 | − | 0.622380i | \(-0.213834\pi\) | |||||||
\(354\) | 4.58990e22 | + | 6.26167e21i | 0.525744 | + | 0.0717233i | ||||
\(355\) | −8.26590e22 | −0.923070 | ||||||||
\(356\) | − | 1.24416e22i | − | 0.135465i | ||||||
\(357\) | 1.64469e22 | − | 1.20559e23i | 0.174611 | − | 1.27993i | ||||
\(358\) | 5.39568e22 | 0.558598 | ||||||||
\(359\) | 1.13366e23i | 1.14455i | 0.820063 | + | 0.572273i | \(0.193938\pi\) | ||||
−0.820063 | + | 0.572273i | \(0.806062\pi\) | |||||||
\(360\) | 2.31192e22 | + | 6.42759e21i | 0.227641 | + | 0.0632887i | ||||
\(361\) | −7.96398e22 | −0.764831 | ||||||||
\(362\) | − | 9.07867e22i | − | 0.850443i | ||||||
\(363\) | −1.74886e23 | − | 2.38584e22i | −1.59807 | − | 0.218013i | ||||
\(364\) | 2.27880e22 | 0.203139 | ||||||||
\(365\) | 7.19474e22i | 0.625719i | ||||||||
\(366\) | 3.73166e21 | − | 2.73537e22i | 0.0316645 | − | 0.232106i | ||||
\(367\) | 1.89333e23 | 1.56759 | 0.783795 | − | 0.621019i | \(-0.213281\pi\) | ||||
0.783795 | + | 0.621019i | \(0.213281\pi\) | |||||||
\(368\) | 2.56047e22i | 0.206866i | ||||||||
\(369\) | −4.55615e22 | + | 1.63879e23i | −0.359220 | + | 1.29207i | ||||
\(370\) | −1.18291e23 | −0.910196 | ||||||||
\(371\) | − | 4.84968e22i | − | 0.364207i | ||||||
\(372\) | −9.75513e21 | − | 1.33082e21i | −0.0715067 | − | 0.00975513i | ||||
\(373\) | 9.21191e22 | 0.659128 | 0.329564 | − | 0.944133i | \(-0.393098\pi\) | ||||
0.329564 | + | 0.944133i | \(0.393098\pi\) | |||||||
\(374\) | 2.70076e23i | 1.88644i | ||||||||
\(375\) | 2.05782e22 | − | 1.50842e23i | 0.140322 | − | 1.02858i | ||||
\(376\) | −9.20767e22 | −0.612998 | ||||||||
\(377\) | − | 3.97359e22i | − | 0.258292i | ||||||
\(378\) | 3.44981e22 | − | 8.00826e22i | 0.218962 | − | 0.508291i | ||||
\(379\) | 2.72704e23 | 1.69020 | 0.845102 | − | 0.534605i | \(-0.179540\pi\) | ||||
0.845102 | + | 0.534605i | \(0.179540\pi\) | |||||||
\(380\) | − | 2.67717e22i | − | 0.162040i | ||||||
\(381\) | 2.02189e23 | + | 2.75831e22i | 1.19518 | + | 0.163049i | ||||
\(382\) | −1.66371e23 | −0.960524 | ||||||||
\(383\) | 3.04293e23i | 1.71595i | 0.513696 | + | 0.857973i | \(0.328276\pi\) | ||||
−0.513696 | + | 0.857973i | \(0.671724\pi\) | |||||||
\(384\) | −2.16899e21 | + | 1.58991e22i | −0.0119475 | + | 0.0875772i | ||||
\(385\) | −1.57130e23 | −0.845499 | ||||||||
\(386\) | − | 2.53515e22i | − | 0.133266i | ||||||
\(387\) | −2.02000e23 | − | 5.61600e22i | −1.03742 | − | 0.288422i | ||||
\(388\) | 4.44238e22 | 0.222910 | ||||||||
\(389\) | 5.34134e22i | 0.261881i | 0.991390 | + | 0.130940i | \(0.0417997\pi\) | ||||
−0.991390 | + | 0.130940i | \(0.958200\pi\) | |||||||
\(390\) | 5.07292e22 | + | 6.92061e21i | 0.243039 | + | 0.0331560i | ||||
\(391\) | 2.91701e23 | 1.36567 | ||||||||
\(392\) | − | 2.99351e22i | − | 0.136964i | ||||||
\(393\) | 1.91534e22 | − | 1.40398e23i | 0.0856472 | − | 0.627808i | ||||
\(394\) | −1.13826e23 | −0.497481 | ||||||||
\(395\) | 9.35117e22i | 0.399477i | ||||||||
\(396\) | −5.18434e22 | + | 1.86474e23i | −0.216490 | + | 0.778685i | ||||
\(397\) | −2.54444e23 | −1.03867 | −0.519334 | − | 0.854571i | \(-0.673820\pi\) | ||||
−0.519334 | + | 0.854571i | \(0.673820\pi\) | |||||||
\(398\) | − | 5.31151e22i | − | 0.211968i | ||||||
\(399\) | −9.63902e22 | − | 1.31498e22i | −0.376077 | − | 0.0513054i | ||||
\(400\) | 3.62671e22 | 0.138348 | ||||||||
\(401\) | 1.36946e23i | 0.510799i | 0.966836 | + | 0.255400i | \(0.0822071\pi\) | ||||
−0.966836 | + | 0.255400i | \(0.917793\pi\) | |||||||
\(402\) | 3.57467e22 | − | 2.62029e23i | 0.130377 | − | 0.955687i | ||||
\(403\) | −2.10068e22 | −0.0749227 | ||||||||
\(404\) | 2.70698e22i | 0.0944176i | ||||||||
\(405\) | 1.01118e23 | − | 1.67798e23i | 0.344932 | − | 0.572389i | ||||
\(406\) | 8.25445e22 | 0.275394 | ||||||||
\(407\) | − | 9.54104e23i | − | 3.11348i | ||||||
\(408\) | 1.81130e23 | + | 2.47102e22i | 0.578161 | + | 0.0788742i | ||||
\(409\) | −3.94768e23 | −1.23263 | −0.616314 | − | 0.787501i | \(-0.711375\pi\) | ||||
−0.616314 | + | 0.787501i | \(0.711375\pi\) | |||||||
\(410\) | − | 2.07470e23i | − | 0.633725i | ||||||
\(411\) | −1.06393e22 | + | 7.79881e22i | −0.0317935 | + | 0.233052i | ||||
\(412\) | −1.39855e23 | −0.408886 | ||||||||
\(413\) | 2.05322e23i | 0.587333i | ||||||||
\(414\) | 2.01405e23 | + | 5.59944e22i | 0.563724 | + | 0.156726i | ||||
\(415\) | 1.55165e23 | 0.424971 | ||||||||
\(416\) | 3.42371e22i | 0.0917609i | ||||||||
\(417\) | 5.42435e22 | + | 7.40004e21i | 0.142273 | + | 0.0194093i | ||||
\(418\) | 2.15934e23 | 0.554286 | ||||||||
\(419\) | 3.47824e23i | 0.873843i | 0.899500 | + | 0.436922i | \(0.143931\pi\) | ||||
−0.899500 | + | 0.436922i | \(0.856069\pi\) | |||||||
\(420\) | −1.43764e22 | + | 1.05381e23i | −0.0353514 | + | 0.259131i | ||||
\(421\) | 2.83789e23 | 0.683056 | 0.341528 | − | 0.939872i | \(-0.389056\pi\) | ||||
0.341528 | + | 0.939872i | \(0.389056\pi\) | |||||||
\(422\) | 1.97852e23i | 0.466152i | ||||||||
\(423\) | −2.01361e23 | + | 7.24270e23i | −0.464421 | + | 1.67046i | ||||
\(424\) | 7.28625e22 | 0.164517 | ||||||||
\(425\) | − | 4.13173e23i | − | 0.913338i | ||||||
\(426\) | −4.47135e23 | − | 6.09993e22i | −0.967726 | − | 0.132020i | ||||
\(427\) | 1.22362e23 | 0.259297 | ||||||||
\(428\) | − | 1.04974e23i | − | 0.217814i | ||||||
\(429\) | −5.58199e22 | + | 4.09169e23i | −0.113416 | + | 0.831357i | ||||
\(430\) | 2.55732e23 | 0.508825 | ||||||||
\(431\) | 2.66986e23i | 0.520228i | 0.965578 | + | 0.260114i | \(0.0837601\pi\) | ||||
−0.965578 | + | 0.260114i | \(0.916240\pi\) | |||||||
\(432\) | 1.20318e23 | + | 5.18306e22i | 0.229602 | + | 0.0989082i | ||||
\(433\) | −9.50235e23 | −1.77599 | −0.887994 | − | 0.459856i | \(-0.847901\pi\) | ||||
−0.887994 | + | 0.459856i | \(0.847901\pi\) | |||||||
\(434\) | − | 4.36380e22i | − | 0.0798835i | ||||||
\(435\) | 1.83755e23 | + | 2.50684e22i | 0.329486 | + | 0.0449493i | ||||
\(436\) | 2.98392e23 | 0.524094 | ||||||||
\(437\) | − | 2.33223e23i | − | 0.401272i | ||||||
\(438\) | −5.30946e22 | + | 3.89192e23i | −0.0894918 | + | 0.655989i | ||||
\(439\) | −8.77998e22 | −0.144982 | −0.0724908 | − | 0.997369i | \(-0.523095\pi\) | ||||
−0.0724908 | + | 0.997369i | \(0.523095\pi\) | |||||||
\(440\) | − | 2.36076e23i | − | 0.381924i | ||||||
\(441\) | −2.35468e23 | − | 6.54646e22i | −0.373236 | − | 0.103767i | ||||
\(442\) | 3.90046e23 | 0.605781 | ||||||||
\(443\) | − | 5.17374e23i | − | 0.787356i | −0.919248 | − | 0.393678i | \(-0.871203\pi\) | ||
0.919248 | − | 0.393678i | \(-0.128797\pi\) | |||||||
\(444\) | −6.39881e23 | − | 8.72942e22i | −0.954229 | − | 0.130178i | ||||
\(445\) | 1.23897e23 | 0.181059 | ||||||||
\(446\) | 4.40243e23i | 0.630490i | ||||||||
\(447\) | 3.59290e22 | − | 2.63365e23i | 0.0504286 | − | 0.369650i | ||||
\(448\) | −7.11219e22 | −0.0978366 | ||||||||
\(449\) | 6.77346e23i | 0.913258i | 0.889657 | + | 0.456629i | \(0.150943\pi\) | ||||
−0.889657 | + | 0.456629i | \(0.849057\pi\) | |||||||
\(450\) | 7.93120e22 | − | 2.85275e23i | 0.104816 | − | 0.377008i | ||||
\(451\) | 1.67340e24 | 2.16776 | ||||||||
\(452\) | − | 6.84827e23i | − | 0.869630i | ||||||
\(453\) | 1.22739e24 | + | 1.67444e23i | 1.52791 | + | 0.208442i | ||||
\(454\) | −6.59979e23 | −0.805429 | ||||||||
\(455\) | 2.26929e23i | 0.271511i | ||||||||
\(456\) | 1.97565e22 | − | 1.44819e23i | 0.0231754 | − | 0.169879i | ||||
\(457\) | −1.62058e24 | −1.86391 | −0.931956 | − | 0.362571i | \(-0.881899\pi\) | ||||
−0.931956 | + | 0.362571i | \(0.881899\pi\) | |||||||
\(458\) | 6.18778e23i | 0.697824i | ||||||||
\(459\) | 5.90479e23 | − | 1.37072e24i | 0.652966 | − | 1.51577i | ||||
\(460\) | −2.54978e23 | −0.276491 | ||||||||
\(461\) | − | 1.38120e24i | − | 1.46876i | −0.678741 | − | 0.734378i | \(-0.737474\pi\) | ||
0.678741 | − | 0.734378i | \(-0.262526\pi\) | |||||||
\(462\) | −8.49980e23 | − | 1.15957e23i | −0.886403 | − | 0.120925i | ||||
\(463\) | −6.56869e23 | −0.671815 | −0.335908 | − | 0.941895i | \(-0.609043\pi\) | ||||
−0.335908 | + | 0.941895i | \(0.609043\pi\) | |||||||
\(464\) | 1.24017e23i | 0.124399i | ||||||||
\(465\) | 1.32526e22 | − | 9.71441e22i | 0.0130385 | − | 0.0955740i | ||||
\(466\) | −2.77921e23 | −0.268193 | ||||||||
\(467\) | − | 2.48434e23i | − | 0.235158i | −0.993064 | − | 0.117579i | \(-0.962487\pi\) | ||
0.993064 | − | 0.117579i | \(-0.0375133\pi\) | |||||||
\(468\) | 2.69307e23 | + | 7.48726e22i | 0.250055 | + | 0.0695201i | ||||
\(469\) | 1.17215e24 | 1.06764 | ||||||||
\(470\) | − | 9.16923e23i | − | 0.819318i | ||||||
\(471\) | −2.97015e23 | − | 4.05196e22i | −0.260370 | − | 0.0355203i | ||||
\(472\) | −3.08480e23 | −0.265307 | ||||||||
\(473\) | 2.06267e24i | 1.74052i | ||||||||
\(474\) | −6.90083e22 | + | 5.05842e23i | −0.0571342 | + | 0.418803i | ||||
\(475\) | −3.30343e23 | −0.268363 | ||||||||
\(476\) | 8.10255e23i | 0.645891i | ||||||||
\(477\) | 1.59342e23 | − | 5.73132e23i | 0.124642 | − | 0.448321i | ||||
\(478\) | 1.01111e24 | 0.776153 | ||||||||
\(479\) | 1.29607e24i | 0.976359i | 0.872743 | + | 0.488180i | \(0.162339\pi\) | ||||
−0.872743 | + | 0.488180i | \(0.837661\pi\) | |||||||
\(480\) | −1.58327e23 | − | 2.15994e22i | −0.117053 | − | 0.0159687i | ||||
\(481\) | −1.37792e24 | −0.999814 | ||||||||
\(482\) | 8.78701e23i | 0.625775i | ||||||||
\(483\) | −1.25241e23 | + | 9.18036e23i | −0.0875431 | + | 0.641705i | ||||
\(484\) | 1.17538e24 | 0.806436 | ||||||||
\(485\) | 4.42383e23i | 0.297936i | ||||||||
\(486\) | 6.70817e23 | − | 8.33064e23i | 0.443484 | − | 0.550747i | ||||
\(487\) | 9.72420e22 | 0.0631093 | 0.0315547 | − | 0.999502i | \(-0.489954\pi\) | ||||
0.0315547 | + | 0.999502i | \(0.489954\pi\) | |||||||
\(488\) | 1.83840e23i | 0.117128i | ||||||||
\(489\) | 4.00821e23 | + | 5.46810e22i | 0.250709 | + | 0.0342024i | ||||
\(490\) | 2.98101e23 | 0.183062 | ||||||||
\(491\) | 1.80548e24i | 1.08858i | 0.838898 | + | 0.544289i | \(0.183201\pi\) | ||||
−0.838898 | + | 0.544289i | \(0.816799\pi\) | |||||||
\(492\) | 1.53105e23 | − | 1.12229e24i | 0.0906369 | − | 0.664383i | ||||
\(493\) | 1.41286e24 | 0.821251 | ||||||||
\(494\) | − | 3.11853e23i | − | 0.177995i | ||||||
\(495\) | −1.85696e24 | − | 5.16270e23i | −1.04077 | − | 0.289354i | ||||
\(496\) | 6.55626e22 | 0.0360845 | ||||||||
\(497\) | − | 2.00019e24i | − | 1.08109i | ||||||
\(498\) | 8.39347e23 | + | 1.14506e23i | 0.445531 | + | 0.0607804i | ||||
\(499\) | −6.98251e23 | −0.364004 | −0.182002 | − | 0.983298i | \(-0.558258\pi\) | ||||
−0.182002 | + | 0.983298i | \(0.558258\pi\) | |||||||
\(500\) | 1.01378e24i | 0.519056i | ||||||||
\(501\) | −2.56816e22 | + | 1.88250e23i | −0.0129146 | + | 0.0946665i | ||||
\(502\) | 2.50096e23 | 0.123530 | ||||||||
\(503\) | − | 2.15858e24i | − | 1.04726i | −0.851945 | − | 0.523632i | \(-0.824577\pi\) | ||
0.851945 | − | 0.523632i | \(-0.175423\pi\) | |||||||
\(504\) | −1.55535e23 | + | 5.59440e23i | −0.0741232 | + | 0.266612i | ||||
\(505\) | −2.69568e23 | −0.126196 | ||||||||
\(506\) | − | 2.05659e24i | − | 0.945786i | ||||||
\(507\) | −1.60222e24 | − | 2.18579e23i | −0.723853 | − | 0.0987499i | ||||
\(508\) | −1.35887e24 | −0.603123 | ||||||||
\(509\) | − | 2.38712e23i | − | 0.104091i | −0.998645 | − | 0.0520456i | \(-0.983426\pi\) | ||
0.998645 | − | 0.0520456i | \(-0.0165741\pi\) | |||||||
\(510\) | −2.46071e23 | + | 1.80374e24i | −0.105421 | + | 0.772755i | ||||
\(511\) | −1.74099e24 | −0.732837 | ||||||||
\(512\) | − | 1.06855e23i | − | 0.0441942i | ||||||
\(513\) | −1.09593e24 | − | 4.72105e23i | −0.445375 | − | 0.191859i | ||||
\(514\) | −1.45061e24 | −0.579273 | ||||||||
\(515\) | − | 1.39271e24i | − | 0.546506i | ||||||
\(516\) | 1.38336e24 | + | 1.88721e23i | 0.533441 | + | 0.0727734i | ||||
\(517\) | 7.39568e24 | 2.80261 | ||||||||
\(518\) | − | 2.86240e24i | − | 1.06601i | ||||||
\(519\) | −2.28838e23 | + | 1.67742e24i | −0.0837571 | + | 0.613953i | ||||
\(520\) | −3.40942e23 | −0.122645 | ||||||||
\(521\) | − | 6.08131e23i | − | 0.215010i | −0.994205 | − | 0.107505i | \(-0.965714\pi\) | ||
0.994205 | − | 0.107505i | \(-0.0342861\pi\) | |||||||
\(522\) | 9.75506e23 | + | 2.71210e23i | 0.338997 | + | 0.0942477i | ||||
\(523\) | −3.17661e24 | −1.08505 | −0.542523 | − | 0.840041i | \(-0.682531\pi\) | ||||
−0.542523 | + | 0.840041i | \(0.682531\pi\) | |||||||
\(524\) | 9.43589e23i | 0.316812i | ||||||||
\(525\) | 1.30033e24 | + | 1.77395e23i | 0.429161 | + | 0.0585472i | ||||
\(526\) | −1.23174e24 | −0.399621 | ||||||||
\(527\) | − | 7.46921e23i | − | 0.238220i | ||||||
\(528\) | 1.74215e23 | − | 1.27703e24i | 0.0546237 | − | 0.400401i | ||||
\(529\) | 1.02290e24 | 0.315305 | ||||||||
\(530\) | 7.25584e23i | 0.219890i | ||||||||
\(531\) | −6.74609e23 | + | 2.42648e24i | −0.201002 | + | 0.722980i | ||||
\(532\) | 6.47822e23 | 0.189780 | ||||||||
\(533\) | − | 2.41674e24i | − | 0.696122i | ||||||
\(534\) | 6.70206e23 | + | 9.14312e22i | 0.189818 | + | 0.0258954i | ||||
\(535\) | 1.04535e24 | 0.291125 | ||||||||
\(536\) | 1.76105e24i | 0.482269i | ||||||||
\(537\) | −3.96520e23 | + | 2.90656e24i | −0.106782 | + | 0.782726i | ||||
\(538\) | −2.99249e24 | −0.792487 | ||||||||
\(539\) | 2.40441e24i | 0.626196i | ||||||||
\(540\) | −5.16142e23 | + | 1.19815e24i | −0.132198 | + | 0.306880i | ||||
\(541\) | 9.87736e23 | 0.248809 | 0.124404 | − | 0.992232i | \(-0.460298\pi\) | ||||
0.124404 | + | 0.992232i | \(0.460298\pi\) | |||||||
\(542\) | 2.19850e23i | 0.0544670i | ||||||||
\(543\) | 4.89051e24 | + | 6.67176e23i | 1.19167 | + | 0.162571i | ||||
\(544\) | −1.21734e24 | −0.291758 | ||||||||
\(545\) | 2.97147e24i | 0.700490i | ||||||||
\(546\) | −1.67465e23 | + | 1.22755e24i | −0.0388321 | + | 0.284646i | ||||
\(547\) | −6.90954e23 | −0.157603 | −0.0788013 | − | 0.996890i | \(-0.525109\pi\) | ||||
−0.0788013 | + | 0.996890i | \(0.525109\pi\) | |||||||
\(548\) | − | 5.24145e23i | − | 0.117605i | ||||||
\(549\) | 1.44607e24 | + | 4.02036e23i | 0.319182 | + | 0.0887388i | ||||
\(550\) | −2.91301e24 | −0.632525 | ||||||||
\(551\) | − | 1.12962e24i | − | 0.241306i | ||||||
\(552\) | −1.37928e24 | − | 1.88164e23i | −0.289867 | − | 0.0395445i | ||||
\(553\) | −2.26280e24 | −0.467865 | ||||||||
\(554\) | 2.81076e24i | 0.571789i | ||||||||
\(555\) | 8.69298e23 | − | 6.37210e24i | 0.173993 | − | 1.27540i | ||||
\(556\) | −3.64561e23 | −0.0717956 | ||||||||
\(557\) | 5.42846e24i | 1.05191i | 0.850512 | + | 0.525956i | \(0.176292\pi\) | ||||
−0.850512 | + | 0.525956i | \(0.823708\pi\) | |||||||
\(558\) | 1.43378e23 | − | 5.15711e23i | 0.0273384 | − | 0.0983329i | ||||
\(559\) | 2.97893e24 | 0.558925 | ||||||||
\(560\) | − | 7.08250e23i | − | 0.130766i | ||||||
\(561\) | −1.45485e25 | − | 1.98475e24i | −2.64334 | − | 0.360611i | ||||
\(562\) | 4.08418e24 | 0.730261 | ||||||||
\(563\) | − | 4.18442e24i | − | 0.736308i | −0.929765 | − | 0.368154i | \(-0.879990\pi\) | ||
0.929765 | − | 0.368154i | \(-0.120010\pi\) | |||||||
\(564\) | 6.76657e23 | − | 4.96000e24i | 0.117181 | − | 0.858954i | ||||
\(565\) | 6.81968e24 | 1.16233 | ||||||||
\(566\) | − | 4.23301e24i | − | 0.710071i | ||||||
\(567\) | 4.06038e24 | + | 2.44686e24i | 0.670378 | + | 0.403982i | ||||
\(568\) | 3.00512e24 | 0.488345 | ||||||||
\(569\) | − | 7.47092e24i | − | 1.19499i | −0.801873 | − | 0.597494i | \(-0.796163\pi\) | ||
0.801873 | − | 0.597494i | \(-0.203837\pi\) | |||||||
\(570\) | 1.44214e24 | + | 1.96740e23i | 0.227056 | + | 0.0309756i | ||||
\(571\) | −3.78796e23 | −0.0587057 | −0.0293528 | − | 0.999569i | \(-0.509345\pi\) | ||||
−0.0293528 | + | 0.999569i | \(0.509345\pi\) | |||||||
\(572\) | − | 2.74996e24i | − | 0.419529i | ||||||
\(573\) | 1.22264e24 | − | 8.96212e24i | 0.183614 | − | 1.34592i | ||||
\(574\) | 5.02037e24 | 0.742214 | ||||||||
\(575\) | 3.14624e24i | 0.457912i | ||||||||
\(576\) | −8.40514e23 | − | 2.33679e23i | −0.120432 | − | 0.0334825i | ||||
\(577\) | −1.36291e25 | −1.92258 | −0.961291 | − | 0.275534i | \(-0.911145\pi\) | ||||
−0.961291 | + | 0.275534i | \(0.911145\pi\) | |||||||
\(578\) | 8.77719e24i | 1.21900i | ||||||||
\(579\) | 1.36564e24 | + | 1.86304e23i | 0.186736 | + | 0.0254750i | ||||
\(580\) | −1.23499e24 | −0.166269 | ||||||||
\(581\) | 3.75468e24i | 0.497723i | ||||||||
\(582\) | −3.26463e23 | + | 2.39303e24i | −0.0426115 | + | 0.312350i | ||||
\(583\) | −5.85238e24 | −0.752169 | ||||||||
\(584\) | − | 2.61569e24i | − | 0.331033i | ||||||
\(585\) | −7.45601e23 | + | 2.68183e24i | −0.0929188 | + | 0.334217i | ||||
\(586\) | 9.28084e24 | 1.13896 | ||||||||
\(587\) | 1.35788e25i | 1.64104i | 0.571617 | + | 0.820520i | \(0.306316\pi\) | ||||
−0.571617 | + | 0.820520i | \(0.693684\pi\) | |||||||
\(588\) | 1.61255e24 | + | 2.19988e23i | 0.191919 | + | 0.0261820i | ||||
\(589\) | −5.97184e23 | −0.0699956 | ||||||||
\(590\) | − | 3.07192e24i | − | 0.354602i | ||||||
\(591\) | 8.36491e23 | − | 6.13161e24i | 0.0950985 | − | 0.697088i | ||||
\(592\) | 4.30053e24 | 0.481534 | ||||||||
\(593\) | 6.16432e24i | 0.679819i | 0.940458 | + | 0.339909i | \(0.110396\pi\) | ||||
−0.940458 | + | 0.339909i | \(0.889604\pi\) | |||||||
\(594\) | −9.66403e24 | − | 4.16308e24i | −1.04974 | − | 0.452206i | ||||
\(595\) | −8.06873e24 | −0.863281 | ||||||||
\(596\) | 1.77003e24i | 0.186537i | ||||||||
\(597\) | 2.86121e24 | + | 3.90334e23i | 0.297017 | + | 0.0405198i | ||||
\(598\) | −2.97014e24 | −0.303715 | ||||||||
\(599\) | − | 8.55875e24i | − | 0.862122i | −0.902323 | − | 0.431061i | \(-0.858139\pi\) | ||
0.902323 | − | 0.431061i | \(-0.141861\pi\) | |||||||
\(600\) | −2.66521e23 | + | 1.95364e24i | −0.0264466 | + | 0.193858i | ||||
\(601\) | 6.20429e24 | 0.606488 | 0.303244 | − | 0.952913i | \(-0.401930\pi\) | ||||
0.303244 | + | 0.952913i | \(0.401930\pi\) | |||||||
\(602\) | 6.18821e24i | 0.595932i | ||||||||
\(603\) | 1.38523e25 | + | 3.85122e24i | 1.31422 | + | 0.365378i | ||||
\(604\) | −8.24909e24 | −0.771034 | ||||||||
\(605\) | 1.17047e25i | 1.07786i | ||||||||
\(606\) | −1.45820e24 | − | 1.98932e23i | −0.132301 | − | 0.0180489i | ||||
\(607\) | 7.07816e24 | 0.632735 | 0.316368 | − | 0.948637i | \(-0.397537\pi\) | ||||
0.316368 | + | 0.948637i | \(0.397537\pi\) | |||||||
\(608\) | 9.73301e23i | 0.0857265i | ||||||||
\(609\) | −6.06606e23 | + | 4.44652e24i | −0.0526443 | + | 0.385891i | ||||
\(610\) | −1.83072e24 | −0.156550 | ||||||||
\(611\) | − | 1.06809e25i | − | 0.899988i | ||||||
\(612\) | −2.66219e24 | + | 9.57555e24i | −0.221043 | + | 0.795062i | ||||
\(613\) | −4.11449e24 | −0.336644 | −0.168322 | − | 0.985732i | \(-0.553835\pi\) | ||||
−0.168322 | + | 0.985732i | \(0.553835\pi\) | |||||||
\(614\) | − | 4.04491e24i | − | 0.326132i | ||||||
\(615\) | 1.11760e25 | + | 1.52466e24i | 0.887997 | + | 0.121143i | ||||
\(616\) | 5.71257e24 | 0.447307 | ||||||||
\(617\) | − | 9.81674e24i | − | 0.757532i | −0.925493 | − | 0.378766i | \(-0.876349\pi\) | ||
0.925493 | − | 0.378766i | \(-0.123651\pi\) | |||||||
\(618\) | 1.02777e24 | − | 7.53372e24i | 0.0781627 | − | 0.572945i | ||||
\(619\) | 3.40269e24 | 0.255039 | 0.127519 | − | 0.991836i | \(-0.459299\pi\) | ||||
0.127519 | + | 0.991836i | \(0.459299\pi\) | |||||||
\(620\) | 6.52889e23i | 0.0482296i | ||||||||
\(621\) | −4.49640e24 | + | 1.04378e25i | −0.327372 | + | 0.759949i | ||||
\(622\) | 8.69492e23 | 0.0623953 | ||||||||
\(623\) | 2.99805e24i | 0.212054i | ||||||||
\(624\) | −1.84429e24 | − | 2.51603e23i | −0.128579 | − | 0.0175410i | ||||
\(625\) | −2.04257e24 | −0.140364 | ||||||||
\(626\) | − | 2.76526e24i | − | 0.187312i | ||||||
\(627\) | −1.58686e24 | + | 1.16320e25i | −0.105957 | + | 0.776685i | ||||
\(628\) | 1.99619e24 | 0.131391 | ||||||||
\(629\) | − | 4.89937e25i | − | 3.17896i | ||||||
\(630\) | −5.57105e24 | − | 1.54886e24i | −0.356346 | − | 0.0990711i | ||||
\(631\) | −7.72031e24 | −0.486822 | −0.243411 | − | 0.969923i | \(-0.578266\pi\) | ||||
−0.243411 | + | 0.969923i | \(0.578266\pi\) | |||||||
\(632\) | − | 3.39968e24i | − | 0.211341i | ||||||
\(633\) | −1.06579e25 | − | 1.45398e24i | −0.653188 | − | 0.0891097i | ||||
\(634\) | −2.03392e25 | −1.22894 | ||||||||
\(635\) | − | 1.35320e25i | − | 0.806119i | ||||||
\(636\) | −5.35455e23 | + | 3.92497e24i | −0.0314491 | + | 0.230527i | ||||
\(637\) | 3.47247e24 | 0.201087 | ||||||||
\(638\) | − | 9.96112e24i | − | 0.568751i | ||||||
\(639\) | 6.57185e24 | − | 2.36381e25i | 0.369981 | − | 1.33077i | ||||
\(640\) | 1.06409e24 | 0.0590688 | ||||||||
\(641\) | 2.62444e25i | 1.43653i | 0.695770 | + | 0.718265i | \(0.255063\pi\) | ||||
−0.695770 | + | 0.718265i | \(0.744937\pi\) | |||||||
\(642\) | 5.65474e24 | + | 7.71434e23i | 0.305209 | + | 0.0416374i | ||||
\(643\) | 4.38088e23 | 0.0233164 | 0.0116582 | − | 0.999932i | \(-0.496289\pi\) | ||||
0.0116582 | + | 0.999932i | \(0.496289\pi\) | |||||||
\(644\) | − | 6.16996e24i | − | 0.323825i | ||||||
\(645\) | −1.87933e24 | + | 1.37758e25i | −0.0972671 | + | 0.712984i | ||||
\(646\) | 1.10883e25 | 0.565943 | ||||||||
\(647\) | 3.47092e25i | 1.74705i | 0.486776 | + | 0.873527i | \(0.338173\pi\) | ||||
−0.486776 | + | 0.873527i | \(0.661827\pi\) | |||||||
\(648\) | −3.67621e24 | + | 6.10040e24i | −0.182484 | + | 0.302819i | ||||
\(649\) | 2.47773e25 | 1.21298 | ||||||||
\(650\) | 4.20699e24i | 0.203119i | ||||||||
\(651\) | 2.35070e24 | + | 3.20688e23i | 0.111936 | + | 0.0152705i | ||||
\(652\) | −2.69385e24 | −0.126516 | ||||||||
\(653\) | − | 2.96983e24i | − | 0.137567i | −0.997632 | − | 0.0687833i | \(-0.978088\pi\) | ||
0.997632 | − | 0.0687833i | \(-0.0219117\pi\) | |||||||
\(654\) | −2.19283e24 | + | 1.60738e25i | −0.100186 | + | 0.734379i | ||||
\(655\) | −9.39650e24 | −0.423442 | ||||||||
\(656\) | 7.54271e24i | 0.335269i | ||||||||
\(657\) | −2.05749e25 | − | 5.72021e24i | −0.902088 | − | 0.250798i | ||||
\(658\) | 2.21878e25 | 0.959578 | ||||||||
\(659\) | − | 5.37440e24i | − | 0.229277i | −0.993407 | − | 0.114639i | \(-0.963429\pi\) | ||
0.993407 | − | 0.114639i | \(-0.0365710\pi\) | |||||||
\(660\) | 1.27170e25 | + | 1.73488e24i | 0.535165 | + | 0.0730086i | ||||
\(661\) | 3.04882e25 | 1.26566 | 0.632831 | − | 0.774290i | \(-0.281893\pi\) | ||||
0.632831 | + | 0.774290i | \(0.281893\pi\) | |||||||
\(662\) | 1.62597e25i | 0.665871i | ||||||||
\(663\) | −2.86638e24 | + | 2.10111e25i | −0.115801 | + | 0.848841i | ||||
\(664\) | −5.64111e24 | −0.224829 | ||||||||
\(665\) | 6.45118e24i | 0.253655i | ||||||||
\(666\) | 9.40476e24 | − | 3.38277e25i | 0.364821 | − | 1.31221i | ||||
\(667\) | −1.07587e25 | −0.411743 | ||||||||
\(668\) | − | 1.26520e24i | − | 0.0477717i | ||||||
\(669\) | −2.37151e25 | − | 3.23527e24i | −0.883464 | − | 0.120525i | ||||
\(670\) | −1.75370e25 | −0.644589 | ||||||||
\(671\) | − | 1.47662e25i | − | 0.535507i | ||||||
\(672\) | 5.22663e23 | − | 3.83121e24i | 0.0187024 | − | 0.137092i | ||||
\(673\) | −4.74754e25 | −1.67623 | −0.838114 | − | 0.545495i | \(-0.816342\pi\) | ||||
−0.838114 | + | 0.545495i | \(0.816342\pi\) | |||||||
\(674\) | − | 3.69423e24i | − | 0.128702i | ||||||
\(675\) | 1.47844e25 | + | 6.36883e24i | 0.508241 | + | 0.218940i | ||||
\(676\) | 1.07682e25 | 0.365279 | ||||||||
\(677\) | 5.46641e25i | 1.82980i | 0.403678 | + | 0.914901i | \(0.367732\pi\) | ||||
−0.403678 | + | 0.914901i | \(0.632268\pi\) | |||||||
\(678\) | 3.68904e25 | + | 5.03268e24i | 1.21856 | + | 0.166239i | ||||
\(679\) | −1.07048e25 | −0.348940 | ||||||||
\(680\) | − | 1.21226e25i | − | 0.389956i | ||||||
\(681\) | 4.85007e24 | − | 3.55518e25i | 0.153966 | − | 1.12859i | ||||
\(682\) | −5.26604e24 | −0.164978 | ||||||||
\(683\) | − | 1.33062e25i | − | 0.411404i | −0.978615 | − | 0.205702i | \(-0.934052\pi\) | ||
0.978615 | − | 0.205702i | \(-0.0659478\pi\) | |||||||
\(684\) | 7.65592e24 | + | 2.12850e24i | 0.233611 | + | 0.0649483i | ||||
\(685\) | 5.21956e24 | 0.157188 | ||||||||
\(686\) | 2.58341e25i | 0.767848i | ||||||||
\(687\) | −3.33324e25 | − | 4.54730e24i | −0.977814 | − | 0.133396i | ||||
\(688\) | −9.29730e24 | −0.269191 | ||||||||
\(689\) | 8.45205e24i | 0.241540i | ||||||||
\(690\) | 1.87379e24 | − | 1.37352e25i | 0.0528541 | − | 0.387429i | ||||
\(691\) | −2.30153e24 | −0.0640787 | −0.0320393 | − | 0.999487i | \(-0.510200\pi\) | ||||
−0.0320393 | + | 0.999487i | \(0.510200\pi\) | |||||||
\(692\) | − | 1.12736e25i | − | 0.309820i | ||||||
\(693\) | 1.24927e25 | − | 4.49347e25i | 0.338890 | − | 1.21894i | ||||
\(694\) | −2.27818e25 | −0.610034 | ||||||||
\(695\) | − | 3.63040e24i | − | 0.0959601i | ||||||
\(696\) | −6.68054e24 | − | 9.11377e23i | −0.174313 | − | 0.0237802i | ||||
\(697\) | 8.59302e25 | 2.21335 | ||||||||
\(698\) | − | 1.61015e25i | − | 0.409419i | ||||||
\(699\) | 2.04239e24 | − | 1.49711e25i | 0.0512678 | − | 0.375802i | ||||
\(700\) | −8.73930e24 | −0.216568 | ||||||||
\(701\) | − | 4.35484e25i | − | 1.06539i | −0.846306 | − | 0.532697i | \(-0.821178\pi\) | ||
0.846306 | − | 0.532697i | \(-0.178822\pi\) | |||||||
\(702\) | −6.01234e24 | + | 1.39569e25i | −0.145214 | + | 0.337096i | ||||
\(703\) | −3.91719e25 | −0.934064 | ||||||||
\(704\) | 8.58268e24i | 0.202055i | ||||||||
\(705\) | 4.93930e25 | + | 6.73832e24i | 1.14806 | + | 0.156621i | ||||
\(706\) | −3.83542e25 | −0.880179 | ||||||||
\(707\) | − | 6.52302e24i | − | 0.147800i | ||||||
\(708\) | 2.26697e24 | − | 1.66172e25i | 0.0507161 | − | 0.371757i | ||||
\(709\) | 3.77583e25 | 0.834059 | 0.417030 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417030 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(710\) | 2.99257e25i | 0.652709i | ||||||||
\(711\) | −2.67417e25 | − | 7.43470e24i | −0.575920 | − | 0.160117i | ||||
\(712\) | −4.50434e24 | −0.0957880 | ||||||||
\(713\) | 5.68768e24i | 0.119434i | ||||||||
\(714\) | −4.36470e25 | − | 5.95443e24i | −0.905045 | − | 0.123469i | ||||
\(715\) | 2.73848e25 | 0.560731 | ||||||||
\(716\) | − | 1.95345e25i | − | 0.394988i | ||||||
\(717\) | −7.43048e24 | + | 5.44666e25i | −0.148369 | + | 1.08757i | ||||
\(718\) | 4.10429e25 | 0.809316 | ||||||||
\(719\) | 5.42700e25i | 1.05682i | 0.848990 | + | 0.528408i | \(0.177211\pi\) | ||||
−0.848990 | + | 0.528408i | \(0.822789\pi\) | |||||||
\(720\) | 2.32704e24 | − | 8.37005e24i | 0.0447518 | − | 0.160967i | ||||
\(721\) | 3.37009e25 | 0.640064 | ||||||||
\(722\) | 2.88327e25i | 0.540817i | ||||||||
\(723\) | −4.73340e25 | − | 6.45743e24i | −0.876857 | − | 0.119623i | ||||
\(724\) | −3.28683e25 | −0.601354 | ||||||||
\(725\) | 1.52389e25i | 0.275367i | ||||||||
\(726\) | −8.63767e24 | + | 6.33156e25i | −0.154158 | + | 1.13001i | ||||
\(727\) | −3.54138e25 | −0.624257 | −0.312128 | − | 0.950040i | \(-0.601042\pi\) | ||||
−0.312128 | + | 0.950040i | \(0.601042\pi\) | |||||||
\(728\) | − | 8.25014e24i | − | 0.143641i | ||||||
\(729\) | 3.99459e25 | + | 4.22577e25i | 0.686949 | + | 0.726705i | ||||
\(730\) | 2.60477e25 | 0.442450 | ||||||||
\(731\) | 1.05919e26i | 1.77713i | ||||||||
\(732\) | −9.90310e24 | − | 1.35101e24i | −0.164124 | − | 0.0223902i | ||||
\(733\) | −7.56671e25 | −1.23872 | −0.619358 | − | 0.785109i | \(-0.712607\pi\) | ||||
−0.619358 | + | 0.785109i | \(0.712607\pi\) | |||||||
\(734\) | − | 6.85460e25i | − | 1.10845i | ||||||
\(735\) | −2.19070e24 | + | 1.60582e25i | −0.0349942 | + | 0.256513i | ||||
\(736\) | 9.26988e24 | 0.146276 | ||||||||
\(737\) | − | 1.41449e26i | − | 2.20492i | ||||||
\(738\) | 5.93305e25 | + | 1.64950e25i | 0.913630 | + | 0.254007i | ||||
\(739\) | 5.97970e25 | 0.909660 | 0.454830 | − | 0.890578i | \(-0.349700\pi\) | ||||
0.454830 | + | 0.890578i | \(0.349700\pi\) | |||||||
\(740\) | 4.28258e25i | 0.643606i | ||||||||
\(741\) | 1.67990e25 | + | 2.29176e24i | 0.249413 | + | 0.0340255i | ||||
\(742\) | −1.75577e25 | −0.257533 | ||||||||
\(743\) | − | 1.08144e26i | − | 1.56713i | −0.621311 | − | 0.783564i | \(-0.713399\pi\) | ||
0.621311 | − | 0.783564i | \(-0.286601\pi\) | |||||||
\(744\) | −4.81808e23 | + | 3.53174e24i | −0.00689792 | + | 0.0505629i | ||||
\(745\) | −1.76264e25 | −0.249321 | ||||||||
\(746\) | − | 3.33507e25i | − | 0.466074i | ||||||
\(747\) | −1.23364e25 | + | 4.43726e25i | −0.170335 | + | 0.612674i | ||||
\(748\) | 9.77781e25 | 1.33391 | ||||||||
\(749\) | 2.52956e25i | 0.340963i | ||||||||
\(750\) | −5.46105e25 | − | 7.45011e24i | −0.727319 | − | 0.0992228i | ||||
\(751\) | 1.63334e25 | 0.214940 | 0.107470 | − | 0.994208i | \(-0.465725\pi\) | ||||
0.107470 | + | 0.994208i | \(0.465725\pi\) | |||||||
\(752\) | 3.33353e25i | 0.433455i | ||||||||
\(753\) | −1.83792e24 | + | 1.34722e25i | −0.0236141 | + | 0.173095i | ||||
\(754\) | −1.43859e25 | −0.182640 | ||||||||
\(755\) | − | 8.21465e25i | − | 1.03054i | ||||||
\(756\) | −2.89930e25 | − | 1.24896e25i | −0.359416 | − | 0.154829i | ||||
\(757\) | −9.00151e25 | −1.10269 | −0.551344 | − | 0.834278i | \(-0.685885\pi\) | ||||
−0.551344 | + | 0.834278i | \(0.685885\pi\) | |||||||
\(758\) | − | 9.87295e25i | − | 1.19515i | ||||||
\(759\) | 1.10785e26 | + | 1.51135e25i | 1.32527 | + | 0.180796i | ||||
\(760\) | −9.69238e24 | −0.114580 | ||||||||
\(761\) | − | 1.56524e25i | − | 0.182860i | −0.995811 | − | 0.0914302i | \(-0.970856\pi\) | ||
0.995811 | − | 0.0914302i | \(-0.0291438\pi\) | |||||||
\(762\) | 9.98614e24 | − | 7.32001e25i | 0.115293 | − | 0.845117i | ||||
\(763\) | −7.19037e25 | −0.820409 | ||||||||
\(764\) | 6.02329e25i | 0.679193i | ||||||||
\(765\) | −9.53557e25 | − | 2.65107e25i | −1.06266 | − | 0.295440i | ||||
\(766\) | 1.10166e26 | 1.21336 | ||||||||
\(767\) | − | 3.57836e25i | − | 0.389517i | ||||||
\(768\) | 5.75608e24 | + | 7.85259e23i | 0.0619264 | + | 0.00844816i | ||||
\(769\) | −4.92978e25 | −0.524192 | −0.262096 | − | 0.965042i | \(-0.584414\pi\) | ||||
−0.262096 | + | 0.965042i | \(0.584414\pi\) | |||||||
\(770\) | 5.68872e25i | 0.597858i | ||||||||
\(771\) | 1.06603e25 | − | 7.81418e25i | 0.110734 | − | 0.811697i | ||||
\(772\) | −9.17822e24 | −0.0942330 | ||||||||
\(773\) | 1.44380e26i | 1.46518i | 0.680670 | + | 0.732590i | \(0.261689\pi\) | ||||
−0.680670 | + | 0.732590i | \(0.738311\pi\) | |||||||
\(774\) | −2.03321e25 | + | 7.31319e25i | −0.203945 | + | 0.733565i | ||||
\(775\) | 8.05619e24 | 0.0798756 | ||||||||
\(776\) | − | 1.60831e25i | − | 0.157621i | ||||||
\(777\) | 1.54192e26 | + | 2.10353e25i | 1.49374 | + | 0.203779i | ||||
\(778\) | 1.93377e25 | 0.185178 | ||||||||
\(779\) | − | 6.87037e25i | − | 0.650343i | ||||||
\(780\) | 2.50553e24 | − | 1.83659e25i | 0.0234449 | − | 0.171855i | ||||
\(781\) | −2.41374e26 | −2.23270 | ||||||||
\(782\) | − | 1.05607e26i | − | 0.965677i | ||||||
\(783\) | −2.17784e25 | + | 5.05557e25i | −0.196866 | + | 0.456998i | ||||
\(784\) | −1.08377e25 | −0.0968481 | ||||||||
\(785\) | 1.98785e25i | 0.175613i | ||||||||
\(786\) | −5.08294e25 | − | 6.93428e24i | −0.443927 | − | 0.0605617i | ||||
\(787\) | 9.40272e25 | 0.811860 | 0.405930 | − | 0.913904i | \(-0.366948\pi\) | ||||
0.405930 | + | 0.913904i | \(0.366948\pi\) | |||||||
\(788\) | 4.12095e25i | 0.351772i | ||||||||
\(789\) | 9.05187e24 | − | 6.63517e25i | 0.0763915 | − | 0.559963i | ||||
\(790\) | 3.38549e25 | 0.282473 | ||||||||
\(791\) | 1.65023e26i | 1.36131i | ||||||||
\(792\) | 6.75108e25 | + | 1.87693e25i | 0.550613 | + | 0.153081i | ||||
\(793\) | −2.13254e25 | −0.171964 | ||||||||
\(794\) | 9.21184e25i | 0.734450i | ||||||||
\(795\) | −3.90858e25 | − | 5.33219e24i | −0.308117 | − | 0.0420341i | ||||
\(796\) | −1.92297e25 | −0.149884 | ||||||||
\(797\) | − | 1.37212e25i | − | 0.105746i | −0.998601 | − | 0.0528732i | \(-0.983162\pi\) | ||
0.998601 | − | 0.0528732i | \(-0.0168379\pi\) | |||||||
\(798\) | −4.76074e24 | + | 3.48970e25i | −0.0362784 | + | 0.265927i | ||||
\(799\) | 3.79772e26 | 2.86156 | ||||||||
\(800\) | − | 1.31301e25i | − | 0.0978269i | ||||||
\(801\) | −9.85046e24 | + | 3.54308e25i | −0.0725711 | + | 0.261029i | ||||
\(802\) | 4.95798e25 | 0.361190 | ||||||||
\(803\) | 2.10095e26i | 1.51347i | ||||||||
\(804\) | −9.48648e25 | − | 1.29417e25i | −0.675772 | − | 0.0921906i | ||||
\(805\) | 6.14421e25 | 0.432816 | ||||||||
\(806\) | 7.60526e24i | 0.0529784i | ||||||||
\(807\) | 2.19913e25 | − | 1.61200e26i | 0.151492 | − | 1.11046i | ||||
\(808\) | 9.80032e24 | 0.0667634 | ||||||||
\(809\) | 1.50535e26i | 1.01415i | 0.861903 | + | 0.507074i | \(0.169273\pi\) | ||||
−0.861903 | + | 0.507074i | \(0.830727\pi\) | |||||||
\(810\) | −6.07493e25 | − | 3.66087e25i | −0.404740 | − | 0.243904i | ||||
\(811\) | −1.38926e26 | −0.915367 | −0.457683 | − | 0.889115i | \(-0.651321\pi\) | ||||
−0.457683 | + | 0.889115i | \(0.651321\pi\) | |||||||
\(812\) | − | 2.98843e25i | − | 0.194733i | ||||||
\(813\) | −1.18429e25 | − | 1.61564e24i | −0.0763211 | − | 0.0104119i | ||||
\(814\) | −3.45422e26 | −2.20156 | ||||||||
\(815\) | − | 2.68260e25i | − | 0.169098i | ||||||
\(816\) | 8.94606e24 | − | 6.55761e25i | 0.0557725 | − | 0.408822i | ||||
\(817\) | 8.46855e25 | 0.522169 | ||||||||
\(818\) | 1.42921e26i | 0.871599i | ||||||||
\(819\) | −6.48951e25 | − | 1.80421e25i | −0.391432 | − | 0.108826i | ||||
\(820\) | −7.51122e25 | −0.448111 | ||||||||
\(821\) | − | 3.07155e26i | − | 1.81246i | −0.422782 | − | 0.906231i | \(-0.638946\pi\) | ||
0.422782 | − | 0.906231i | \(-0.361054\pi\) | |||||||
\(822\) | 2.82347e25 | + | 3.85185e24i | 0.164792 | + | 0.0224814i | ||||
\(823\) | 2.44832e26 | 1.41342 | 0.706708 | − | 0.707505i | \(-0.250179\pi\) | ||||
0.706708 | + | 0.707505i | \(0.250179\pi\) | |||||||
\(824\) | 5.06328e25i | 0.289126i | ||||||||
\(825\) | 2.14072e25 | − | 1.56918e26i | 0.120913 | − | 0.886315i | ||||
\(826\) | 7.43344e25 | 0.415307 | ||||||||
\(827\) | − | 2.20127e26i | − | 1.21653i | −0.793732 | − | 0.608267i | \(-0.791865\pi\) | ||
0.793732 | − | 0.608267i | \(-0.208135\pi\) | |||||||
\(828\) | 2.02721e25 | − | 7.29163e25i | 0.110822 | − | 0.398613i | ||||
\(829\) | −2.47819e26 | −1.34012 | −0.670061 | − | 0.742306i | \(-0.733732\pi\) | ||||
−0.670061 | + | 0.742306i | \(0.733732\pi\) | |||||||
\(830\) | − | 5.61756e25i | − | 0.300500i | ||||||
\(831\) | −1.51410e26 | − | 2.06558e25i | −0.801210 | − | 0.109303i | ||||
\(832\) | 1.23952e25 | 0.0648847 | ||||||||
\(833\) | 1.23468e26i | 0.639366i | ||||||||
\(834\) | 2.67910e24 | − | 1.96383e25i | 0.0137244 | − | 0.100602i | ||||
\(835\) | 1.25992e25 | 0.0638504 | ||||||||
\(836\) | − | 7.81764e25i | − | 0.391940i | ||||||
\(837\) | 2.67267e25 | + | 1.15134e25i | 0.132561 | + | 0.0571049i | ||||
\(838\) | 1.25926e26 | 0.617900 | ||||||||
\(839\) | − | 1.51315e26i | − | 0.734557i | −0.930111 | − | 0.367278i | \(-0.880290\pi\) | ||
0.930111 | − | 0.367278i | \(-0.119710\pi\) | |||||||
\(840\) | 3.81521e25 | + | 5.20481e24i | 0.183234 | + | 0.0249972i | ||||
\(841\) | 1.58347e26 | 0.752397 | ||||||||
\(842\) | − | 1.02742e26i | − | 0.482993i | ||||||
\(843\) | −3.00139e25 | + | 2.20007e26i | −0.139597 | + | 1.02327i | ||||
\(844\) | 7.16300e25 | 0.329619 | ||||||||
\(845\) | 1.07233e26i | 0.488222i | ||||||||
\(846\) | 2.62214e26 | + | 7.29005e25i | 1.18120 | + | 0.328395i | ||||
\(847\) | −2.83232e26 | −1.26238 | ||||||||
\(848\) | − | 2.63791e25i | − | 0.116331i | ||||||
\(849\) | 2.28025e26 | + | 3.11077e25i | 0.994976 | + | 0.135737i | ||||
\(850\) | −1.49585e26 | −0.645827 | ||||||||
\(851\) | 3.73080e26i | 1.59381i | ||||||||
\(852\) | −2.20841e25 | + | 1.61880e26i | −0.0933520 | + | 0.684286i | ||||
\(853\) | −3.47086e26 | −1.45176 | −0.725881 | − | 0.687821i | \(-0.758568\pi\) | ||||
−0.725881 | + | 0.687821i | \(0.758568\pi\) | |||||||
\(854\) | − | 4.42999e25i | − | 0.183350i | ||||||
\(855\) | −2.11961e25 | + | 7.62396e25i | −0.0868082 | + | 0.312238i | ||||
\(856\) | −3.80045e25 | −0.154018 | ||||||||
\(857\) | − | 3.05940e26i | − | 1.22690i | −0.789733 | − | 0.613451i | \(-0.789781\pi\) | ||
0.789733 | − | 0.613451i | \(-0.210219\pi\) | |||||||
\(858\) | 1.48135e26 | + | 2.02090e25i | 0.587858 | + | 0.0801971i | ||||
\(859\) | 4.26960e26 | 1.67667 | 0.838336 | − | 0.545153i | \(-0.183529\pi\) | ||||
0.838336 | + | 0.545153i | \(0.183529\pi\) | |||||||
\(860\) | − | 9.25848e25i | − | 0.359794i | ||||||
\(861\) | −3.68939e25 | + | 2.70438e26i | −0.141882 | + | 1.04002i | ||||
\(862\) | 9.66594e25 | 0.367857 | ||||||||
\(863\) | − | 2.75377e26i | − | 1.03712i | −0.855040 | − | 0.518562i | \(-0.826468\pi\) | ||
0.855040 | − | 0.518562i | \(-0.173532\pi\) | |||||||
\(864\) | 1.87647e25 | − | 4.35597e25i | 0.0699387 | − | 0.162353i | ||||
\(865\) | 1.12266e26 | 0.414098 | ||||||||
\(866\) | 3.44022e26i | 1.25581i | ||||||||
\(867\) | −4.72811e26 | − | 6.45021e25i | −1.70811 | − | 0.233025i | ||||
\(868\) | −1.57986e25 | −0.0564862 | ||||||||
\(869\) | 2.73065e26i | 0.966247i | ||||||||
\(870\) | 9.07572e24 | − | 6.65265e25i | 0.0317840 | − | 0.232982i | ||||
\(871\) | −2.04282e26 | −0.708055 | ||||||||
\(872\) | − | 1.08030e26i | − | 0.370590i | ||||||
\(873\) | −1.26509e26 | − | 3.51719e25i | −0.429529 | − | 0.119417i | ||||
\(874\) | −8.44358e25 | −0.283742 | ||||||||
\(875\) | − | 2.44291e26i | − | 0.812522i | ||||||
\(876\) | 1.40903e26 | + | 1.92223e25i | 0.463855 | + | 0.0632802i | ||||
\(877\) | −3.39070e25 | −0.110482 | −0.0552411 | − | 0.998473i | \(-0.517593\pi\) | ||||
−0.0552411 | + | 0.998473i | \(0.517593\pi\) | |||||||
\(878\) | 3.17869e25i | 0.102517i | ||||||||
\(879\) | −6.82033e25 | + | 4.99942e26i | −0.217724 | + | 1.59595i | ||||
\(880\) | −8.54685e25 | −0.270061 | ||||||||
\(881\) | 2.34511e26i | 0.733466i | 0.930326 | + | 0.366733i | \(0.119524\pi\) | ||||
−0.930326 | + | 0.366733i | \(0.880476\pi\) | |||||||
\(882\) | −2.37007e25 | + | 8.52484e25i | −0.0733743 | + | 0.263918i | ||||
\(883\) | 1.50498e26 | 0.461194 | 0.230597 | − | 0.973049i | \(-0.425932\pi\) | ||||
0.230597 | + | 0.973049i | \(0.425932\pi\) | |||||||
\(884\) | − | 1.41212e26i | − | 0.428352i | ||||||
\(885\) | 1.65479e26 | + | 2.25750e25i | 0.496881 | + | 0.0677858i | ||||
\(886\) | −1.87309e26 | −0.556745 | ||||||||
\(887\) | 6.20499e25i | 0.182570i | 0.995825 | + | 0.0912848i | \(0.0290974\pi\) | ||||
−0.995825 | + | 0.0912848i | \(0.970903\pi\) | |||||||
\(888\) | −3.16039e25 | + | 2.31662e26i | −0.0920500 | + | 0.674742i | ||||
\(889\) | 3.27449e26 | 0.944120 | ||||||||
\(890\) | − | 4.48553e25i | − | 0.128028i | ||||||
\(891\) | 2.95277e26 | − | 4.89990e26i | 0.834314 | − | 1.38448i | ||||
\(892\) | 1.59385e26 | 0.445824 | ||||||||
\(893\) | − | 3.03639e26i | − | 0.840803i | ||||||
\(894\) | −9.53484e25 | − | 1.30077e25i | −0.261382 | − | 0.0356584i | ||||
\(895\) | 1.94529e26 | 0.527931 | ||||||||
\(896\) | 2.57489e25i | 0.0691809i | ||||||||
\(897\) | 2.18271e25 | − | 1.59996e26i | 0.0580582 | − | 0.425576i | ||||
\(898\) | 2.45226e26 | 0.645771 | ||||||||
\(899\) | 2.75484e25i | 0.0718222i | ||||||||
\(900\) | −1.03281e26 | − | 2.87140e25i | −0.266585 | − | 0.0741159i | ||||
\(901\) | −3.00523e26 | −0.767988 | ||||||||
\(902\) | − | 6.05837e26i | − | 1.53284i | ||||||
\(903\) | −3.33348e26 | − | 4.54762e25i | −0.835041 | − | 0.113918i | ||||
\(904\) | −2.47934e26 | −0.614922 | ||||||||
\(905\) | − | 3.27311e26i | − | 0.803754i | ||||||
\(906\) | 6.06212e25 | − | 4.44363e26i | 0.147391 | − | 1.08040i | ||||
\(907\) | −1.76420e26 | −0.424699 | −0.212349 | − | 0.977194i | \(-0.568112\pi\) | ||||
−0.212349 | + | 0.977194i | \(0.568112\pi\) | |||||||
\(908\) | 2.38938e26i | 0.569524i | ||||||||
\(909\) | 2.14322e25 | − | 7.70887e25i | 0.0505814 | − | 0.181935i | ||||
\(910\) | 8.21569e25 | 0.191987 | ||||||||
\(911\) | − | 4.89283e25i | − | 0.113213i | −0.998397 | − | 0.0566063i | \(-0.981972\pi\) | ||
0.998397 | − | 0.0566063i | \(-0.0180280\pi\) | |||||||
\(912\) | −5.24299e25 | − | 7.15263e24i | −0.120123 | − | 0.0163875i | ||||
\(913\) | 4.53099e26 | 1.02791 | ||||||||
\(914\) | 5.86714e26i | 1.31798i | ||||||||
\(915\) | 1.34537e25 | − | 9.86176e25i | 0.0299261 | − | 0.219364i | ||||
\(916\) | 2.24022e26 | 0.493436 | ||||||||
\(917\) | − | 2.27377e26i | − | 0.495932i | ||||||
\(918\) | −4.96253e26 | − | 2.13776e26i | −1.07181 | − | 0.461716i | ||||
\(919\) | −5.67137e26 | −1.21296 | −0.606482 | − | 0.795097i | \(-0.707420\pi\) | ||||
−0.606482 | + | 0.795097i | \(0.707420\pi\) | |||||||
\(920\) | 9.23118e25i | 0.195509i | ||||||||
\(921\) | 2.17892e26 | + | 2.97254e25i | 0.456988 | + | 0.0623435i | ||||
\(922\) | −5.00049e26 | −1.03857 | ||||||||
\(923\) | 3.48594e26i | 0.716976i | ||||||||
\(924\) | −4.19807e25 | + | 3.07726e26i | −0.0855071 | + | 0.626781i | ||||
\(925\) | 5.28440e26 | 1.06591 | ||||||||
\(926\) | 2.37812e26i | 0.475045i | ||||||||
\(927\) | 3.98275e26 | + | 1.10728e26i | 0.787889 | + | 0.219048i | ||||
\(928\) | 4.48988e25 | 0.0879636 | ||||||||
\(929\) | 1.93301e26i | 0.375053i | 0.982260 | + | 0.187527i | \(0.0600471\pi\) | ||||
−0.982260 | + | 0.187527i | \(0.939953\pi\) | |||||||
\(930\) | −3.51699e25 | − | 4.79797e24i | −0.0675810 | − | 0.00921958i | ||||
\(931\) | 9.87162e25 | 0.187863 | ||||||||
\(932\) | 1.00618e26i | 0.189641i | ||||||||
\(933\) | −6.38975e24 | + | 4.68379e25i | −0.0119275 | + | 0.0874305i | ||||
\(934\) | −8.99429e25 | −0.166282 | ||||||||
\(935\) | 9.73699e26i | 1.78287i | ||||||||
\(936\) | 2.71068e25 | − | 9.74996e25i | 0.0491581 | − | 0.176815i | ||||
\(937\) | −3.34473e25 | −0.0600765 | −0.0300383 | − | 0.999549i | \(-0.509563\pi\) | ||||
−0.0300383 | + | 0.999549i | \(0.509563\pi\) | |||||||
\(938\) | − | 4.24362e26i | − | 0.754937i | ||||||
\(939\) | 1.48959e26 | + | 2.03214e25i | 0.262469 | + | 0.0358067i | ||||
\(940\) | −3.31962e26 | −0.579345 | ||||||||
\(941\) | 7.15034e26i | 1.23600i | 0.786176 | + | 0.618002i | \(0.212058\pi\) | ||||
−0.786176 | + | 0.618002i | \(0.787942\pi\) | |||||||
\(942\) | −1.46697e25 | + | 1.07531e26i | −0.0251166 | + | 0.184109i | ||||
\(943\) | −6.54345e26 | −1.10969 | ||||||||
\(944\) | 1.11682e26i | 0.187600i | ||||||||
\(945\) | 1.24375e26 | − | 2.88720e26i | 0.206941 | − | 0.480386i | ||||
\(946\) | 7.46767e26 | 1.23074 | ||||||||
\(947\) | − | 2.50281e26i | − | 0.408581i | −0.978910 | − | 0.204291i | \(-0.934511\pi\) | ||
0.978910 | − | 0.204291i | \(-0.0654888\pi\) | |||||||
\(948\) | 1.83134e26 | + | 2.49837e25i | 0.296139 | + | 0.0404000i | ||||
\(949\) | 3.03420e26 | 0.486014 | ||||||||
\(950\) | 1.19597e26i | 0.189762i | ||||||||
\(951\) | 1.49469e26 | − | 1.09563e27i | 0.234924 | − | 1.72203i | ||||
\(952\) | 2.93344e26 | 0.456714 | ||||||||
\(953\) | 1.23347e26i | 0.190236i | 0.995466 | + | 0.0951180i | \(0.0303229\pi\) | ||||
−0.995466 | + | 0.0951180i | \(0.969677\pi\) | |||||||
\(954\) | −2.07496e26 | − | 5.76879e25i | −0.317011 | − | 0.0881352i | ||||
\(955\) | −5.99814e26 | −0.907792 | ||||||||
\(956\) | − | 3.66061e26i | − | 0.548823i | ||||||
\(957\) | 5.36587e26 | + | 7.32026e25i | 0.796953 | + | 0.108722i | ||||
\(958\) | 4.69228e26 | 0.690390 | ||||||||
\(959\) | 1.26303e26i | 0.184097i | ||||||||
\(960\) | −7.81981e24 | + | 5.73205e25i | −0.0112916 | + | 0.0827692i | ||||
\(961\) | −6.84490e26 | −0.979167 | ||||||||
\(962\) | 4.98861e26i | 0.706975i | ||||||||
\(963\) | −8.31115e25 | + | 2.98941e26i | −0.116688 | + | 0.419710i | ||||
\(964\) | 3.18124e26 | 0.442490 | ||||||||
\(965\) | − | 9.13991e25i | − | 0.125949i | ||||||
\(966\) | 3.32365e26 | + | 4.53420e25i | 0.453754 | + | 0.0619023i | ||||
\(967\) | −1.07798e27 | −1.45805 | −0.729027 | − | 0.684485i | \(-0.760027\pi\) | ||||
−0.729027 | + | 0.684485i | \(0.760027\pi\) | |||||||
\(968\) | − | 4.25533e26i | − | 0.570237i | ||||||
\(969\) | −8.14862e25 | + | 5.97307e26i | −0.108186 | + | 0.793019i | ||||
\(970\) | 1.60160e26 | 0.210673 | ||||||||
\(971\) | − | 1.59421e26i | − | 0.207765i | −0.994590 | − | 0.103882i | \(-0.966873\pi\) | ||
0.994590 | − | 0.103882i | \(-0.0331265\pi\) | |||||||
\(972\) | −3.01602e26 | − | 2.42862e26i | −0.389437 | − | 0.313590i | ||||
\(973\) | 8.78485e25 | 0.112388 | ||||||||
\(974\) | − | 3.52054e25i | − | 0.0446250i | ||||||
\(975\) | −2.26623e26 | − | 3.09164e25i | −0.284618 | − | 0.0388283i | ||||
\(976\) | 6.65571e25 | 0.0828220 | ||||||||
\(977\) | − | 9.18709e26i | − | 1.13273i | −0.824154 | − | 0.566366i | \(-0.808349\pi\) | ||
0.824154 | − | 0.566366i | \(-0.191651\pi\) | |||||||
\(978\) | 1.97966e25 | − | 1.45113e26i | 0.0241848 | − | 0.177278i | ||||
\(979\) | 3.61792e26 | 0.437940 | ||||||||
\(980\) | − | 1.07924e26i | − | 0.129445i | ||||||
\(981\) | −8.49753e26 | − | 2.36248e26i | −1.00988 | − | 0.280768i | ||||
\(982\) | 6.53654e26 | 0.769741 | ||||||||
\(983\) | − | 1.27925e27i | − | 1.49270i | −0.665552 | − | 0.746351i | \(-0.731804\pi\) | ||
0.665552 | − | 0.746351i | \(-0.268196\pi\) | |||||||
\(984\) | −4.06312e26 | − | 5.54301e25i | −0.469790 | − | 0.0640899i | ||||
\(985\) | −4.10375e26 | −0.470170 | ||||||||
\(986\) | − | 5.11509e26i | − | 0.580712i | ||||||
\(987\) | −1.63054e26 | + | 1.19521e27i | −0.183433 | + | 1.34459i | ||||
\(988\) | −1.12903e26 | −0.125861 | ||||||||
\(989\) | − | 8.06559e26i | − | 0.890983i | ||||||
\(990\) | −1.86910e26 | + | 6.72290e26i | −0.204604 | + | 0.735936i | ||||
\(991\) | 1.34771e27 | 1.46195 | 0.730975 | − | 0.682404i | \(-0.239065\pi\) | ||||
0.730975 | + | 0.682404i | \(0.239065\pi\) | |||||||
\(992\) | − | 2.37362e25i | − | 0.0255156i | ||||||
\(993\) | −8.75879e26 | − | 1.19490e26i | −0.933041 | − | 0.127288i | ||||
\(994\) | −7.24145e26 | −0.764448 | ||||||||
\(995\) | − | 1.91494e26i | − | 0.200331i | ||||||
\(996\) | 4.14556e25 | − | 3.03876e26i | 0.0429782 | − | 0.315038i | ||||
\(997\) | −4.03504e25 | −0.0414564 | −0.0207282 | − | 0.999785i | \(-0.506598\pi\) | ||||
−0.0207282 | + | 0.999785i | \(0.506598\pi\) | |||||||
\(998\) | 2.52794e26i | 0.257390i | ||||||||
\(999\) | 1.75312e27 | + | 7.55211e26i | 1.76898 | + | 0.762042i |
(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 | 6.19.b.a.5.3 | ✓ | 6 | |
3.2 | odd | 2 | inner | 6.19.b.a.5.6 | yes | 6 | |
4.3 | odd | 2 | 48.19.e.d.17.1 | 6 | |||
12.11 | even | 2 | 48.19.e.d.17.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.19.b.a.5.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
6.19.b.a.5.6 | yes | 6 | 3.2 | odd | 2 | inner | |
48.19.e.d.17.1 | 6 | 4.3 | odd | 2 | |||
48.19.e.d.17.2 | 6 | 12.11 | even | 2 |