Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(7,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.7");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.5533957546\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 192 x^{9} + 27713 x^{8} - 24384 x^{7} + 18432 x^{6} - 2072064 x^{5} + 128589064 x^{4} - 223046400 x^{3} + 184320000 x^{2} + 558720000 x + 846810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{18}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.3 | ||
Root | \(8.37625 - 8.37625i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.43 |
Dual form | 75.9.f.d.7.3 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.10647 | + | 3.10647i | −0.194154 | + | 0.194154i | −0.797488 | − | 0.603334i | \(-0.793838\pi\) |
0.603334 | + | 0.797488i | \(0.293838\pi\) | |||||||
\(3\) | −33.0681 | − | 33.0681i | −0.408248 | − | 0.408248i | ||||
\(4\) | 236.700i | 0.924608i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 205.450 | 0.158526 | ||||||||
\(7\) | 974.502 | − | 974.502i | 0.405873 | − | 0.405873i | −0.474424 | − | 0.880297i | \(-0.657343\pi\) |
0.880297 | + | 0.474424i | \(0.157343\pi\) | |||||||
\(8\) | −1530.56 | − | 1530.56i | −0.373671 | − | 0.373671i | ||||
\(9\) | 2187.00i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4996.30 | −0.341254 | −0.170627 | − | 0.985336i | \(-0.554579\pi\) | ||||
−0.170627 | + | 0.985336i | \(0.554579\pi\) | |||||||
\(12\) | 7827.21 | − | 7827.21i | 0.377470 | − | 0.377470i | ||||
\(13\) | −14944.9 | − | 14944.9i | −0.523261 | − | 0.523261i | 0.395294 | − | 0.918555i | \(-0.370643\pi\) |
−0.918555 | + | 0.395294i | \(0.870643\pi\) | |||||||
\(14\) | 6054.51i | 0.157604i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −51085.9 | −0.779509 | ||||||||
\(17\) | 11795.2 | − | 11795.2i | 0.141225 | − | 0.141225i | −0.632960 | − | 0.774185i | \(-0.718160\pi\) |
0.774185 | + | 0.632960i | \(0.218160\pi\) | |||||||
\(18\) | −6793.84 | − | 6793.84i | −0.0647181 | − | 0.0647181i | ||||
\(19\) | 52539.8i | 0.403157i | 0.979472 | + | 0.201578i | \(0.0646070\pi\) | ||||
−0.979472 | + | 0.201578i | \(0.935393\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −64449.9 | −0.331394 | ||||||||
\(22\) | 15520.8 | − | 15520.8i | 0.0662559 | − | 0.0662559i | ||||
\(23\) | 245594. | + | 245594.i | 0.877620 | + | 0.877620i | 0.993288 | − | 0.115668i | \(-0.0369008\pi\) |
−0.115668 | + | 0.993288i | \(0.536901\pi\) | |||||||
\(24\) | 101225.i | 0.305101i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 92851.4 | 0.203187 | ||||||||
\(27\) | 72320.0 | − | 72320.0i | 0.136083 | − | 0.136083i | ||||
\(28\) | 230664. | + | 230664.i | 0.375274 | + | 0.375274i | ||||
\(29\) | − | 1.02151e6i | − | 1.44428i | −0.691749 | − | 0.722138i | \(-0.743159\pi\) | ||
0.691749 | − | 0.722138i | \(-0.256841\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −165534. | −0.179242 | −0.0896211 | − | 0.995976i | \(-0.528566\pi\) | ||||
−0.0896211 | + | 0.995976i | \(0.528566\pi\) | |||||||
\(32\) | 550519. | − | 550519.i | 0.525016 | − | 0.525016i | ||||
\(33\) | 165218. | + | 165218.i | 0.139316 | + | 0.139316i | ||||
\(34\) | 73282.9i | 0.0548387i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −517662. | −0.308203 | ||||||||
\(37\) | 2.47866e6 | − | 2.47866e6i | 1.32255 | − | 1.32255i | 0.410837 | − | 0.911709i | \(-0.365236\pi\) |
0.911709 | − | 0.410837i | \(-0.134764\pi\) | |||||||
\(38\) | −163213. | − | 163213.i | −0.0782745 | − | 0.0782745i | ||||
\(39\) | 988397.i | 0.427241i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.10533e6 | 1.09894 | 0.549468 | − | 0.835515i | \(-0.314830\pi\) | ||||
0.549468 | + | 0.835515i | \(0.314830\pi\) | |||||||
\(42\) | 200211. | − | 200211.i | 0.0643415 | − | 0.0643415i | ||||
\(43\) | 1.63711e6 | + | 1.63711e6i | 0.478854 | + | 0.478854i | 0.904765 | − | 0.425911i | \(-0.140046\pi\) |
−0.425911 | + | 0.904765i | \(0.640046\pi\) | |||||||
\(44\) | − | 1.18262e6i | − | 0.315526i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.52586e6 | −0.340787 | ||||||||
\(47\) | 5.87036e6 | − | 5.87036e6i | 1.20302 | − | 1.20302i | 0.229779 | − | 0.973243i | \(-0.426200\pi\) |
0.973243 | − | 0.229779i | \(-0.0738004\pi\) | |||||||
\(48\) | 1.68931e6 | + | 1.68931e6i | 0.318233 | + | 0.318233i | ||||
\(49\) | 3.86549e6i | 0.670534i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −780091. | −0.115309 | ||||||||
\(52\) | 3.53744e6 | − | 3.53744e6i | 0.483812 | − | 0.483812i | ||||
\(53\) | 8.41070e6 | + | 8.41070e6i | 1.06593 | + | 1.06593i | 0.997667 | + | 0.0682627i | \(0.0217456\pi\) |
0.0682627 | + | 0.997667i | \(0.478254\pi\) | |||||||
\(54\) | 449319.i | 0.0528421i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.98306e6 | −0.303326 | ||||||||
\(57\) | 1.73739e6 | − | 1.73739e6i | 0.164588 | − | 0.164588i | ||||
\(58\) | 3.17328e6 | + | 3.17328e6i | 0.280412 | + | 0.280412i | ||||
\(59\) | 9.42589e6i | 0.777883i | 0.921262 | + | 0.388942i | \(0.127159\pi\) | ||||
−0.921262 | + | 0.388942i | \(0.872841\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.74107e6 | 0.270194 | 0.135097 | − | 0.990832i | \(-0.456865\pi\) | ||||
0.135097 | + | 0.990832i | \(0.456865\pi\) | |||||||
\(62\) | 514226. | − | 514226.i | 0.0348006 | − | 0.0348006i | ||||
\(63\) | 2.13123e6 | + | 2.13123e6i | 0.135291 | + | 0.135291i | ||||
\(64\) | − | 9.65765e6i | − | 0.575641i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.02649e6 | −0.0540977 | ||||||||
\(67\) | 1.23693e7 | − | 1.23693e7i | 0.613827 | − | 0.613827i | −0.330114 | − | 0.943941i | \(-0.607087\pi\) |
0.943941 | + | 0.330114i | \(0.107087\pi\) | |||||||
\(68\) | 2.79193e6 | + | 2.79193e6i | 0.130577 | + | 0.130577i | ||||
\(69\) | − | 1.62427e7i | − | 0.716574i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.38777e7 | 0.546116 | 0.273058 | − | 0.961998i | \(-0.411965\pi\) | ||||
0.273058 | + | 0.961998i | \(0.411965\pi\) | |||||||
\(72\) | 3.34732e6 | − | 3.34732e6i | 0.124557 | − | 0.124557i | ||||
\(73\) | −2.14552e7 | − | 2.14552e7i | −0.755511 | − | 0.755511i | 0.219991 | − | 0.975502i | \(-0.429397\pi\) |
−0.975502 | + | 0.219991i | \(0.929397\pi\) | |||||||
\(74\) | 1.53998e7i | 0.513556i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.24361e7 | −0.372762 | ||||||||
\(77\) | −4.86890e6 | + | 4.86890e6i | −0.138506 | + | 0.138506i | ||||
\(78\) | −3.07042e6 | − | 3.07042e6i | −0.0829506 | − | 0.0829506i | ||||
\(79\) | − | 4.04271e7i | − | 1.03792i | −0.854798 | − | 0.518961i | \(-0.826319\pi\) | ||
0.854798 | − | 0.518961i | \(-0.173681\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.78297e6 | −0.111111 | ||||||||
\(82\) | −9.64661e6 | + | 9.64661e6i | −0.213363 | + | 0.213363i | ||||
\(83\) | −1.85669e7 | − | 1.85669e7i | −0.391225 | − | 0.391225i | 0.483899 | − | 0.875124i | \(-0.339220\pi\) |
−0.875124 | + | 0.483899i | \(0.839220\pi\) | |||||||
\(84\) | − | 1.52553e7i | − | 0.306410i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.01712e7 | −0.185943 | ||||||||
\(87\) | −3.37794e7 | + | 3.37794e7i | −0.589623 | + | 0.589623i | ||||
\(88\) | 7.64712e6 | + | 7.64712e6i | 0.127517 | + | 0.127517i | ||||
\(89\) | 5.33621e7i | 0.850497i | 0.905077 | + | 0.425248i | \(0.139813\pi\) | ||||
−0.905077 | + | 0.425248i | \(0.860187\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.91276e7 | −0.424755 | ||||||||
\(92\) | −5.81321e7 | + | 5.81321e7i | −0.811455 | + | 0.811455i | ||||
\(93\) | 5.47390e6 | + | 5.47390e6i | 0.0731753 | + | 0.0731753i | ||||
\(94\) | 3.64722e7i | 0.467143i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.64092e7 | −0.428673 | ||||||||
\(97\) | −8.55969e7 | + | 8.55969e7i | −0.966877 | + | 0.966877i | −0.999469 | − | 0.0325916i | \(-0.989624\pi\) |
0.0325916 | + | 0.999469i | \(0.489624\pi\) | |||||||
\(98\) | −1.20080e7 | − | 1.20080e7i | −0.130187 | − | 0.130187i | ||||
\(99\) | − | 1.09269e7i | − | 0.113751i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.76856e8 | 1.69955 | 0.849774 | − | 0.527147i | \(-0.176738\pi\) | ||||
0.849774 | + | 0.527147i | \(0.176738\pi\) | |||||||
\(102\) | 2.42333e6 | − | 2.42333e6i | 0.0223878 | − | 0.0223878i | ||||
\(103\) | −7.41794e7 | − | 7.41794e7i | −0.659074 | − | 0.659074i | 0.296087 | − | 0.955161i | \(-0.404318\pi\) |
−0.955161 | + | 0.296087i | \(0.904318\pi\) | |||||||
\(104\) | 4.57479e7i | 0.391055i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.22551e7 | −0.413910 | ||||||||
\(107\) | −4.71593e7 | + | 4.71593e7i | −0.359776 | + | 0.359776i | −0.863730 | − | 0.503955i | \(-0.831878\pi\) |
0.503955 | + | 0.863730i | \(0.331878\pi\) | |||||||
\(108\) | 1.71181e7 | + | 1.71181e7i | 0.125823 | + | 0.125823i | ||||
\(109\) | − | 1.75445e7i | − | 0.124290i | −0.998067 | − | 0.0621449i | \(-0.980206\pi\) | ||
0.998067 | − | 0.0621449i | \(-0.0197941\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.63929e8 | −1.07985 | ||||||||
\(112\) | −4.97833e7 | + | 4.97833e7i | −0.316382 | + | 0.316382i | ||||
\(113\) | −1.15312e8 | − | 1.15312e8i | −0.707229 | − | 0.707229i | 0.258722 | − | 0.965952i | \(-0.416699\pi\) |
−0.965952 | + | 0.258722i | \(0.916699\pi\) | |||||||
\(114\) | 1.07943e7i | 0.0639109i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.41791e8 | 1.33539 | ||||||||
\(117\) | 3.26844e7 | − | 3.26844e7i | 0.174420 | − | 0.174420i | ||||
\(118\) | −2.92812e7 | − | 2.92812e7i | −0.151029 | − | 0.151029i | ||||
\(119\) | − | 2.29889e7i | − | 0.114639i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.89396e8 | −0.883546 | ||||||||
\(122\) | −1.16215e7 | + | 1.16215e7i | −0.0524594 | + | 0.0524594i | ||||
\(123\) | −1.02687e8 | − | 1.02687e8i | −0.448639 | − | 0.448639i | ||||
\(124\) | − | 3.91819e7i | − | 0.165729i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.32412e7 | −0.0525347 | ||||||||
\(127\) | 1.05771e8 | − | 1.05771e8i | 0.406585 | − | 0.406585i | −0.473961 | − | 0.880546i | \(-0.657176\pi\) |
0.880546 | + | 0.473961i | \(0.157176\pi\) | |||||||
\(128\) | 1.70934e8 | + | 1.70934e8i | 0.636779 | + | 0.636779i | ||||
\(129\) | − | 1.08272e8i | − | 0.390983i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.98885e8 | 1.69401 | 0.847004 | − | 0.531587i | \(-0.178404\pi\) | ||||
0.847004 | + | 0.531587i | \(0.178404\pi\) | |||||||
\(132\) | −3.91071e7 | + | 3.91071e7i | −0.128813 | + | 0.128813i | ||||
\(133\) | 5.12001e7 | + | 5.12001e7i | 0.163630 | + | 0.163630i | ||||
\(134\) | 7.68496e7i | 0.238354i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.61065e7 | −0.105543 | ||||||||
\(137\) | 1.96007e8 | − | 1.96007e8i | 0.556403 | − | 0.556403i | −0.371879 | − | 0.928281i | \(-0.621286\pi\) |
0.928281 | + | 0.371879i | \(0.121286\pi\) | |||||||
\(138\) | 5.04573e7 | + | 5.04573e7i | 0.139126 | + | 0.139126i | ||||
\(139\) | − | 3.18232e8i | − | 0.852480i | −0.904610 | − | 0.426240i | \(-0.859838\pi\) | ||
0.904610 | − | 0.426240i | \(-0.140162\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.88244e8 | −0.982263 | ||||||||
\(142\) | −4.31107e7 | + | 4.31107e7i | −0.106031 | + | 0.106031i | ||||
\(143\) | 7.46690e7 | + | 7.46690e7i | 0.178565 | + | 0.178565i | ||||
\(144\) | − | 1.11725e8i | − | 0.259836i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.33300e8 | 0.293371 | ||||||||
\(147\) | 1.27825e8 | − | 1.27825e8i | 0.273744 | − | 0.273744i | ||||
\(148\) | 5.86699e8 | + | 5.86699e8i | 1.22284 | + | 1.22284i | ||||
\(149\) | 7.86775e8i | 1.59627i | 0.602481 | + | 0.798134i | \(0.294179\pi\) | ||||
−0.602481 | + | 0.798134i | \(0.705821\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.06754e8 | −1.35944 | −0.679721 | − | 0.733471i | \(-0.737899\pi\) | ||||
−0.679721 | + | 0.733471i | \(0.737899\pi\) | |||||||
\(152\) | 8.04150e7 | − | 8.04150e7i | 0.150648 | − | 0.150648i | ||||
\(153\) | 2.57961e7 | + | 2.57961e7i | 0.0470749 | + | 0.0470749i | ||||
\(154\) | − | 3.02502e7i | − | 0.0537830i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.33953e8 | −0.395031 | ||||||||
\(157\) | 7.32328e8 | − | 7.32328e8i | 1.20533 | − | 1.20533i | 0.232811 | − | 0.972522i | \(-0.425208\pi\) |
0.972522 | − | 0.232811i | \(-0.0747922\pi\) | |||||||
\(158\) | 1.25586e8 | + | 1.25586e8i | 0.201517 | + | 0.201517i | ||||
\(159\) | − | 5.56252e8i | − | 0.870328i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.78664e8 | 0.712405 | ||||||||
\(162\) | 1.48581e7 | − | 1.48581e7i | 0.0215727 | − | 0.0215727i | ||||
\(163\) | 3.22135e7 | + | 3.22135e7i | 0.0456339 | + | 0.0456339i | 0.729555 | − | 0.683922i | \(-0.239727\pi\) |
−0.683922 | + | 0.729555i | \(0.739727\pi\) | |||||||
\(164\) | 7.35031e8i | 1.01609i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.15355e8 | 0.151916 | ||||||||
\(167\) | 7.92458e8 | − | 7.92458e8i | 1.01885 | − | 1.01885i | 0.0190311 | − | 0.999819i | \(-0.493942\pi\) |
0.999819 | − | 0.0190311i | \(-0.00605815\pi\) | |||||||
\(168\) | 9.86441e7 | + | 9.86441e7i | 0.123832 | + | 0.123832i | ||||
\(169\) | − | 3.69033e8i | − | 0.452395i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.14904e8 | −0.134386 | ||||||||
\(172\) | −3.87503e8 | + | 3.87503e8i | −0.442752 | + | 0.442752i | ||||
\(173\) | −6.76294e8 | − | 6.76294e8i | −0.755008 | − | 0.755008i | 0.220402 | − | 0.975409i | \(-0.429263\pi\) |
−0.975409 | + | 0.220402i | \(0.929263\pi\) | |||||||
\(174\) | − | 2.09869e8i | − | 0.228956i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.55241e8 | 0.266011 | ||||||||
\(177\) | 3.11697e8 | − | 3.11697e8i | 0.317570 | − | 0.317570i | ||||
\(178\) | −1.65767e8 | − | 1.65767e8i | −0.165127 | − | 0.165127i | ||||
\(179\) | 8.49985e8i | 0.827940i | 0.910290 | + | 0.413970i | \(0.135858\pi\) | ||||
−0.910290 | + | 0.413970i | \(0.864142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.37723e8 | 0.128319 | 0.0641596 | − | 0.997940i | \(-0.479563\pi\) | ||||
0.0641596 | + | 0.997940i | \(0.479563\pi\) | |||||||
\(182\) | 9.04839e7 | − | 9.04839e7i | 0.0824680 | − | 0.0824680i | ||||
\(183\) | −1.23710e8 | − | 1.23710e8i | −0.110306 | − | 0.110306i | ||||
\(184\) | − | 7.51791e8i | − | 0.655882i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.40090e7 | −0.0284146 | ||||||||
\(187\) | −5.89325e7 | + | 5.89325e7i | −0.0481935 | + | 0.0481935i | ||||
\(188\) | 1.38951e9 | + | 1.38951e9i | 1.11232 | + | 1.11232i | ||||
\(189\) | − | 1.40952e8i | − | 0.110465i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.83102e9 | 1.37581 | 0.687905 | − | 0.725800i | \(-0.258530\pi\) | ||||
0.687905 | + | 0.725800i | \(0.258530\pi\) | |||||||
\(192\) | −3.19360e8 | + | 3.19360e8i | −0.235004 | + | 0.235004i | ||||
\(193\) | −4.47959e8 | − | 4.47959e8i | −0.322856 | − | 0.322856i | 0.527006 | − | 0.849862i | \(-0.323315\pi\) |
−0.849862 | + | 0.527006i | \(0.823315\pi\) | |||||||
\(194\) | − | 5.31808e8i | − | 0.375446i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.14961e8 | −0.619981 | ||||||||
\(197\) | −1.01717e9 | + | 1.01717e9i | −0.675351 | + | 0.675351i | −0.958945 | − | 0.283594i | \(-0.908473\pi\) |
0.283594 | + | 0.958945i | \(0.408473\pi\) | |||||||
\(198\) | 3.39441e7 | + | 3.39441e7i | 0.0220853 | + | 0.0220853i | ||||
\(199\) | 4.81408e8i | 0.306973i | 0.988151 | + | 0.153487i | \(0.0490502\pi\) | ||||
−0.988151 | + | 0.153487i | \(0.950950\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.18059e8 | −0.501187 | ||||||||
\(202\) | −5.49396e8 | + | 5.49396e8i | −0.329974 | + | 0.329974i | ||||
\(203\) | −9.95463e8 | − | 9.95463e8i | −0.586193 | − | 0.586193i | ||||
\(204\) | − | 1.84647e8i | − | 0.106616i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.60871e8 | 0.255924 | ||||||||
\(207\) | −5.37114e8 | + | 5.37114e8i | −0.292540 | + | 0.292540i | ||||
\(208\) | 7.63472e8 | + | 7.63472e8i | 0.407887 | + | 0.407887i | ||||
\(209\) | − | 2.62505e8i | − | 0.137579i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.57618e7 | 0.0281324 | 0.0140662 | − | 0.999901i | \(-0.495522\pi\) | ||||
0.0140662 | + | 0.999901i | \(0.495522\pi\) | |||||||
\(212\) | −1.99081e9 | + | 1.99081e9i | −0.985568 | + | 0.985568i | ||||
\(213\) | −4.58910e8 | − | 4.58910e8i | −0.222951 | − | 0.222951i | ||||
\(214\) | − | 2.92997e8i | − | 0.139704i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.21379e8 | −0.101700 | ||||||||
\(217\) | −1.61313e8 | + | 1.61313e8i | −0.0727496 | + | 0.0727496i | ||||
\(218\) | 5.45015e7 | + | 5.45015e7i | 0.0241314 | + | 0.0241314i | ||||
\(219\) | 1.41897e9i | 0.616872i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.52556e8 | −0.147795 | ||||||||
\(222\) | 5.09241e8 | − | 5.09241e8i | 0.209658 | − | 0.209658i | ||||
\(223\) | −3.04995e9 | − | 3.04995e9i | −1.23331 | − | 1.23331i | −0.962684 | − | 0.270629i | \(-0.912768\pi\) |
−0.270629 | − | 0.962684i | \(-0.587232\pi\) | |||||||
\(224\) | − | 1.07296e9i | − | 0.426180i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.16425e8 | 0.274623 | ||||||||
\(227\) | −6.19777e8 | + | 6.19777e8i | −0.233417 | + | 0.233417i | −0.814117 | − | 0.580701i | \(-0.802779\pi\) |
0.580701 | + | 0.814117i | \(0.302779\pi\) | |||||||
\(228\) | 4.11240e8 | + | 4.11240e8i | 0.152179 | + | 0.152179i | ||||
\(229\) | 3.01662e9i | 1.09693i | 0.836173 | + | 0.548465i | \(0.184788\pi\) | ||||
−0.836173 | + | 0.548465i | \(0.815212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.22011e8 | 0.113090 | ||||||||
\(232\) | −1.56348e9 | + | 1.56348e9i | −0.539684 | + | 0.539684i | ||||
\(233\) | −2.53460e9 | − | 2.53460e9i | −0.859974 | − | 0.859974i | 0.131361 | − | 0.991335i | \(-0.458065\pi\) |
−0.991335 | + | 0.131361i | \(0.958065\pi\) | |||||||
\(234\) | 2.03066e8i | 0.0677289i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.23111e9 | −0.719238 | ||||||||
\(237\) | −1.33685e9 | + | 1.33685e9i | −0.423730 | + | 0.423730i | ||||
\(238\) | 7.14143e7 | + | 7.14143e7i | 0.0222576 | + | 0.0222576i | ||||
\(239\) | − | 2.93731e9i | − | 0.900240i | −0.892968 | − | 0.450120i | \(-0.851381\pi\) | ||
0.892968 | − | 0.450120i | \(-0.148619\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.48664e9 | −0.737132 | −0.368566 | − | 0.929602i | \(-0.620151\pi\) | ||||
−0.368566 | + | 0.929602i | \(0.620151\pi\) | |||||||
\(242\) | 5.88352e8 | − | 5.88352e8i | 0.171544 | − | 0.171544i | ||||
\(243\) | 1.58164e8 | + | 1.58164e8i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 8.85510e8i | 0.249824i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.37990e8 | 0.174210 | ||||||||
\(247\) | 7.85200e8 | − | 7.85200e8i | 0.210956 | − | 0.210956i | ||||
\(248\) | 2.53359e8 | + | 2.53359e8i | 0.0669776 | + | 0.0669776i | ||||
\(249\) | 1.22794e9i | 0.319434i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.67826e9 | −0.674772 | −0.337386 | − | 0.941366i | \(-0.609543\pi\) | ||||
−0.337386 | + | 0.941366i | \(0.609543\pi\) | |||||||
\(252\) | −5.04463e8 | + | 5.04463e8i | −0.125091 | + | 0.125091i | ||||
\(253\) | −1.22706e9 | − | 1.22706e9i | −0.299492 | − | 0.299492i | ||||
\(254\) | 6.57147e8i | 0.157880i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.41036e9 | 0.328374 | ||||||||
\(257\) | 1.40231e9 | − | 1.40231e9i | 0.321449 | − | 0.321449i | −0.527874 | − | 0.849323i | \(-0.677011\pi\) |
0.849323 | + | 0.527874i | \(0.177011\pi\) | |||||||
\(258\) | 3.36344e8 | + | 3.36344e8i | 0.0759109 | + | 0.0759109i | ||||
\(259\) | − | 4.83092e9i | − | 1.07357i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.23404e9 | 0.481426 | ||||||||
\(262\) | −1.54977e9 | + | 1.54977e9i | −0.328899 | + | 0.328899i | ||||
\(263\) | 3.19839e9 | + | 3.19839e9i | 0.668510 | + | 0.668510i | 0.957371 | − | 0.288861i | \(-0.0932766\pi\) |
−0.288861 | + | 0.957371i | \(0.593277\pi\) | |||||||
\(264\) | − | 5.05751e8i | − | 0.104117i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.18103e8 | −0.0635391 | ||||||||
\(267\) | 1.76458e9 | − | 1.76458e9i | 0.347214 | − | 0.347214i | ||||
\(268\) | 2.92781e9 | + | 2.92781e9i | 0.567549 | + | 0.567549i | ||||
\(269\) | − | 2.77450e9i | − | 0.529877i | −0.964265 | − | 0.264939i | \(-0.914648\pi\) | ||
0.964265 | − | 0.264939i | \(-0.0853517\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.95720e9 | 1.84612 | 0.923060 | − | 0.384656i | \(-0.125680\pi\) | ||||
0.923060 | + | 0.384656i | \(0.125680\pi\) | |||||||
\(272\) | −6.02569e8 | + | 6.02569e8i | −0.110086 | + | 0.110086i | ||||
\(273\) | 9.63194e8 | + | 9.63194e8i | 0.173406 | + | 0.173406i | ||||
\(274\) | 1.21778e9i | 0.216056i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.84464e9 | 0.662550 | ||||||||
\(277\) | 2.87012e9 | − | 2.87012e9i | 0.487508 | − | 0.487508i | −0.420011 | − | 0.907519i | \(-0.637974\pi\) |
0.907519 | + | 0.420011i | \(0.137974\pi\) | |||||||
\(278\) | 9.88577e8 | + | 9.88577e8i | 0.165513 | + | 0.165513i | ||||
\(279\) | − | 3.62023e8i | − | 0.0597474i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.02942e10 | −1.65108 | −0.825540 | − | 0.564344i | \(-0.809129\pi\) | ||||
−0.825540 | + | 0.564344i | \(0.809129\pi\) | |||||||
\(282\) | 1.20607e9 | − | 1.20607e9i | 0.190711 | − | 0.190711i | ||||
\(283\) | 3.13540e9 | + | 3.13540e9i | 0.488818 | + | 0.488818i | 0.907933 | − | 0.419115i | \(-0.137660\pi\) |
−0.419115 | + | 0.907933i | \(0.637660\pi\) | |||||||
\(284\) | 3.28486e9i | 0.504944i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.63914e8 | −0.0693383 | ||||||||
\(287\) | 3.02615e9 | − | 3.02615e9i | 0.446029 | − | 0.446029i | ||||
\(288\) | 1.20398e9 | + | 1.20398e9i | 0.175005 | + | 0.175005i | ||||
\(289\) | 6.69750e9i | 0.960111i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.66106e9 | 0.789452 | ||||||||
\(292\) | 5.07844e9 | − | 5.07844e9i | 0.698552 | − | 0.698552i | ||||
\(293\) | 2.31877e9 | + | 2.31877e9i | 0.314620 | + | 0.314620i | 0.846697 | − | 0.532076i | \(-0.178588\pi\) |
−0.532076 | + | 0.846697i | \(0.678588\pi\) | |||||||
\(294\) | 7.94166e8i | 0.106297i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.58747e9 | −0.988393 | ||||||||
\(297\) | −3.61332e8 | + | 3.61332e8i | −0.0464388 | + | 0.0464388i | ||||
\(298\) | −2.44409e9 | − | 2.44409e9i | −0.309922 | − | 0.309922i | ||||
\(299\) | − | 7.34074e9i | − | 0.918449i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.19073e9 | 0.388708 | ||||||||
\(302\) | 2.19551e9 | − | 2.19551e9i | 0.263941 | − | 0.263941i | ||||
\(303\) | −5.84828e9 | − | 5.84828e9i | −0.693838 | − | 0.693838i | ||||
\(304\) | − | 2.68404e9i | − | 0.314264i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.60270e8 | −0.0182796 | ||||||||
\(307\) | 7.65906e9 | − | 7.65906e9i | 0.862228 | − | 0.862228i | −0.129368 | − | 0.991597i | \(-0.541295\pi\) |
0.991597 | + | 0.129368i | \(0.0412950\pi\) | |||||||
\(308\) | −1.15247e9 | − | 1.15247e9i | −0.128064 | − | 0.128064i | ||||
\(309\) | 4.90594e9i | 0.538132i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.30214e9 | −0.994355 | −0.497178 | − | 0.867649i | \(-0.665630\pi\) | ||||
−0.497178 | + | 0.867649i | \(0.665630\pi\) | |||||||
\(312\) | 1.51280e9 | − | 1.51280e9i | 0.159647 | − | 0.159647i | ||||
\(313\) | 6.96927e9 | + | 6.96927e9i | 0.726122 | + | 0.726122i | 0.969845 | − | 0.243723i | \(-0.0783686\pi\) |
−0.243723 | + | 0.969845i | \(0.578369\pi\) | |||||||
\(314\) | 4.54990e9i | 0.468041i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.56909e9 | 0.959671 | ||||||||
\(317\) | 5.65467e9 | − | 5.65467e9i | 0.559977 | − | 0.559977i | −0.369324 | − | 0.929301i | \(-0.620411\pi\) |
0.929301 | + | 0.369324i | \(0.120411\pi\) | |||||||
\(318\) | 1.72798e9 | + | 1.72798e9i | 0.168978 | + | 0.168978i | ||||
\(319\) | 5.10377e9i | 0.492865i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.11894e9 | 0.293756 | ||||||||
\(322\) | −1.48695e9 | + | 1.48695e9i | −0.138316 | + | 0.138316i | ||||
\(323\) | 6.19718e8 | + | 6.19718e8i | 0.0569356 | + | 0.0569356i | ||||
\(324\) | − | 1.13213e9i | − | 0.102734i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.00140e8 | −0.0177200 | ||||||||
\(327\) | −5.80164e8 | + | 5.80164e8i | −0.0507411 | + | 0.0507411i | ||||
\(328\) | −4.75288e9 | − | 4.75288e9i | −0.410640 | − | 0.410640i | ||||
\(329\) | − | 1.14414e10i | − | 0.976549i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.43122e10 | −1.19232 | −0.596160 | − | 0.802865i | \(-0.703308\pi\) | ||||
−0.596160 | + | 0.802865i | \(0.703308\pi\) | |||||||
\(332\) | 4.39477e9 | − | 4.39477e9i | 0.361730 | − | 0.361730i | ||||
\(333\) | 5.42084e9 | + | 5.42084e9i | 0.440849 | + | 0.440849i | ||||
\(334\) | 4.92349e9i | 0.395628i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.29248e9 | 0.258325 | ||||||||
\(337\) | −1.43343e10 | + | 1.43343e10i | −1.11136 | + | 1.11136i | −0.118399 | + | 0.992966i | \(0.537776\pi\) |
−0.992966 | + | 0.118399i | \(0.962224\pi\) | |||||||
\(338\) | 1.14639e9 | + | 1.14639e9i | 0.0878345 | + | 0.0878345i | ||||
\(339\) | 7.62629e9i | 0.577450i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.27058e8 | 0.0611672 | ||||||||
\(342\) | 3.56947e8 | − | 3.56947e8i | 0.0260915 | − | 0.0260915i | ||||
\(343\) | 9.38474e9 | + | 9.38474e9i | 0.678025 | + | 0.678025i | ||||
\(344\) | − | 5.01137e9i | − | 0.357868i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.20177e9 | 0.293176 | ||||||||
\(347\) | −1.41952e10 | + | 1.41952e10i | −0.979092 | + | 0.979092i | −0.999786 | − | 0.0206935i | \(-0.993413\pi\) |
0.0206935 | + | 0.999786i | \(0.493413\pi\) | |||||||
\(348\) | −7.99557e9 | − | 7.99557e9i | −0.545171 | − | 0.545171i | ||||
\(349\) | − | 1.42593e9i | − | 0.0961159i | −0.998845 | − | 0.0480579i | \(-0.984697\pi\) | ||
0.998845 | − | 0.0480579i | \(-0.0153032\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.16162e9 | −0.142414 | ||||||||
\(352\) | −2.75056e9 | + | 2.75056e9i | −0.179164 | + | 0.179164i | ||||
\(353\) | −6.11946e9 | − | 6.11946e9i | −0.394107 | − | 0.394107i | 0.482041 | − | 0.876149i | \(-0.339896\pi\) |
−0.876149 | + | 0.482041i | \(0.839896\pi\) | |||||||
\(354\) | 1.93655e9i | 0.123315i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.26308e10 | −0.786376 | ||||||||
\(357\) | −7.60200e8 | + | 7.60200e8i | −0.0468010 | + | 0.0468010i | ||||
\(358\) | −2.64045e9 | − | 2.64045e9i | −0.160748 | − | 0.160748i | ||||
\(359\) | − | 2.72763e10i | − | 1.64213i | −0.570833 | − | 0.821066i | \(-0.693380\pi\) | ||
0.570833 | − | 0.821066i | \(-0.306620\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.42231e10 | 0.837465 | ||||||||
\(362\) | −4.27831e8 | + | 4.27831e8i | −0.0249137 | + | 0.0249137i | ||||
\(363\) | 6.26296e9 | + | 6.26296e9i | 0.360706 | + | 0.360706i | ||||
\(364\) | − | 6.89449e9i | − | 0.392732i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.68603e8 | 0.0428329 | ||||||||
\(367\) | −4.35880e9 | + | 4.35880e9i | −0.240271 | + | 0.240271i | −0.816962 | − | 0.576691i | \(-0.804344\pi\) |
0.576691 | + | 0.816962i | \(0.304344\pi\) | |||||||
\(368\) | −1.25464e10 | − | 1.25464e10i | −0.684113 | − | 0.684113i | ||||
\(369\) | 6.79136e9i | 0.366312i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.63925e10 | 0.865265 | ||||||||
\(372\) | −1.29567e9 | + | 1.29567e9i | −0.0676585 | + | 0.0676585i | ||||
\(373\) | −8.61815e9 | − | 8.61815e9i | −0.445224 | − | 0.445224i | 0.448539 | − | 0.893763i | \(-0.351945\pi\) |
−0.893763 | + | 0.448539i | \(0.851945\pi\) | |||||||
\(374\) | − | 3.66144e8i | − | 0.0187139i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.79698e10 | −0.899068 | ||||||||
\(377\) | −1.52663e10 | + | 1.52663e10i | −0.755734 | + | 0.755734i | ||||
\(378\) | 4.37862e8 | + | 4.37862e8i | 0.0214472 | + | 0.0214472i | ||||
\(379\) | 1.62972e10i | 0.789873i | 0.918708 | + | 0.394936i | \(0.129233\pi\) | ||||
−0.918708 | + | 0.394936i | \(0.870767\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.99528e9 | −0.331975 | ||||||||
\(382\) | −5.68799e9 | + | 5.68799e9i | −0.267119 | + | 0.267119i | ||||
\(383\) | 9.04711e8 | + | 9.04711e8i | 0.0420450 | + | 0.0420450i | 0.727817 | − | 0.685772i | \(-0.240535\pi\) |
−0.685772 | + | 0.727817i | \(0.740535\pi\) | |||||||
\(384\) | − | 1.13049e10i | − | 0.519928i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.78314e9 | 0.125368 | ||||||||
\(387\) | −3.58035e9 | + | 3.58035e9i | −0.159618 | + | 0.159618i | ||||
\(388\) | −2.02608e10 | − | 2.02608e10i | −0.893983 | − | 0.893983i | ||||
\(389\) | 1.38210e10i | 0.603591i | 0.953373 | + | 0.301795i | \(0.0975860\pi\) | ||||
−0.953373 | + | 0.301795i | \(0.902414\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.79367e9 | 0.247883 | ||||||||
\(392\) | 5.91635e9 | − | 5.91635e9i | 0.250559 | − | 0.250559i | ||||
\(393\) | −1.64972e10 | − | 1.64972e10i | −0.691576 | − | 0.691576i | ||||
\(394\) | − | 6.31962e9i | − | 0.262244i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.58640e9 | 0.105175 | ||||||||
\(397\) | −1.18087e10 | + | 1.18087e10i | −0.475378 | + | 0.475378i | −0.903650 | − | 0.428272i | \(-0.859122\pi\) |
0.428272 | + | 0.903650i | \(0.359122\pi\) | |||||||
\(398\) | −1.49548e9 | − | 1.49548e9i | −0.0596002 | − | 0.0596002i | ||||
\(399\) | − | 3.38618e9i | − | 0.133604i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.44172e10 | 0.944319 | 0.472160 | − | 0.881513i | \(-0.343475\pi\) | ||||
0.472160 | + | 0.881513i | \(0.343475\pi\) | |||||||
\(402\) | 2.54127e9 | − | 2.54127e9i | 0.0973076 | − | 0.0973076i | ||||
\(403\) | 2.47388e9 | + | 2.47388e9i | 0.0937905 | + | 0.0937905i | ||||
\(404\) | 4.18617e10i | 1.57142i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.18474e9 | 0.227624 | ||||||||
\(407\) | −1.23842e10 | + | 1.23842e10i | −0.451324 | + | 0.451324i | ||||
\(408\) | 1.19397e9 | + | 1.19397e9i | 0.0430877 | + | 0.0430877i | ||||
\(409\) | 1.20856e9i | 0.0431894i | 0.999767 | + | 0.0215947i | \(0.00687433\pi\) | ||||
−0.999767 | + | 0.0215947i | \(0.993126\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.29632e10 | −0.454301 | ||||||||
\(412\) | 1.75582e10 | − | 1.75582e10i | 0.609385 | − | 0.609385i | ||||
\(413\) | 9.18555e9 | + | 9.18555e9i | 0.315722 | + | 0.315722i | ||||
\(414\) | − | 3.33706e9i | − | 0.113596i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.64549e10 | −0.549441 | ||||||||
\(417\) | −1.05233e10 | + | 1.05233e10i | −0.348024 | + | 0.348024i | ||||
\(418\) | 8.15462e8 | + | 8.15462e8i | 0.0267115 | + | 0.0267115i | ||||
\(419\) | 2.99061e10i | 0.970296i | 0.874432 | + | 0.485148i | \(0.161234\pi\) | ||||
−0.874432 | + | 0.485148i | \(0.838766\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.13382e10 | −0.997574 | −0.498787 | − | 0.866725i | \(-0.666221\pi\) | ||||
−0.498787 | + | 0.866725i | \(0.666221\pi\) | |||||||
\(422\) | −1.73222e8 | + | 1.73222e8i | −0.00546203 | + | 0.00546203i | ||||
\(423\) | 1.28385e10 | + | 1.28385e10i | 0.401007 | + | 0.401007i | ||||
\(424\) | − | 2.57461e10i | − | 0.796614i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.85118e9 | 0.0865737 | ||||||||
\(427\) | 3.64568e9 | − | 3.64568e9i | 0.109665 | − | 0.109665i | ||||
\(428\) | −1.11626e10 | − | 1.11626e10i | −0.332652 | − | 0.332652i | ||||
\(429\) | − | 4.93833e9i | − | 0.145798i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.97968e10 | 0.573701 | 0.286850 | − | 0.957975i | \(-0.407392\pi\) | ||||
0.286850 | + | 0.957975i | \(0.407392\pi\) | |||||||
\(432\) | −3.69453e9 | + | 3.69453e9i | −0.106078 | + | 0.106078i | ||||
\(433\) | 2.04786e10 | + | 2.04786e10i | 0.582570 | + | 0.582570i | 0.935609 | − | 0.353039i | \(-0.114852\pi\) |
−0.353039 | + | 0.935609i | \(0.614852\pi\) | |||||||
\(434\) | − | 1.00223e9i | − | 0.0282493i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.15278e9 | 0.114919 | ||||||||
\(437\) | −1.29035e10 | + | 1.29035e10i | −0.353818 | + | 0.353818i | ||||
\(438\) | −4.40797e9 | − | 4.40797e9i | −0.119768 | − | 0.119768i | ||||
\(439\) | − | 1.52813e10i | − | 0.411435i | −0.978611 | − | 0.205717i | \(-0.934047\pi\) | ||
0.978611 | − | 0.205717i | \(-0.0659528\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.45384e9 | −0.223511 | ||||||||
\(442\) | 1.09520e9 | − | 1.09520e9i | 0.0286950 | − | 0.0286950i | ||||
\(443\) | 4.19068e10 | + | 4.19068e10i | 1.08810 | + | 1.08810i | 0.995724 | + | 0.0923778i | \(0.0294468\pi\) |
0.0923778 | + | 0.995724i | \(0.470553\pi\) | |||||||
\(444\) | − | 3.88021e10i | − | 0.998442i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.89491e10 | 0.478906 | ||||||||
\(447\) | 2.60172e10 | − | 2.60172e10i | 0.651673 | − | 0.651673i | ||||
\(448\) | −9.41140e9 | − | 9.41140e9i | −0.233637 | − | 0.233637i | ||||
\(449\) | 3.76958e9i | 0.0927487i | 0.998924 | + | 0.0463743i | \(0.0147667\pi\) | ||||
−0.998924 | + | 0.0463743i | \(0.985233\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.55152e10 | −0.375017 | ||||||||
\(452\) | 2.72943e10 | − | 2.72943e10i | 0.653910 | − | 0.653910i | ||||
\(453\) | 2.33710e10 | + | 2.33710e10i | 0.554990 | + | 0.554990i | ||||
\(454\) | − | 3.85063e9i | − | 0.0906377i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.31835e9 | −0.123003 | ||||||||
\(457\) | 1.58058e10 | − | 1.58058e10i | 0.362370 | − | 0.362370i | −0.502315 | − | 0.864685i | \(-0.667518\pi\) |
0.864685 | + | 0.502315i | \(0.167518\pi\) | |||||||
\(458\) | −9.37104e9 | − | 9.37104e9i | −0.212974 | − | 0.212974i | ||||
\(459\) | − | 1.70606e9i | − | 0.0384365i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.93819e10 | 1.31477 | 0.657386 | − | 0.753554i | \(-0.271662\pi\) | ||||
0.657386 | + | 0.753554i | \(0.271662\pi\) | |||||||
\(462\) | −1.00032e9 | + | 1.00032e9i | −0.0219568 | + | 0.0219568i | ||||
\(463\) | 3.75293e9 | + | 3.75293e9i | 0.0816670 | + | 0.0816670i | 0.746760 | − | 0.665093i | \(-0.231608\pi\) |
−0.665093 | + | 0.746760i | \(0.731608\pi\) | |||||||
\(464\) | 5.21847e10i | 1.12583i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.57473e10 | 0.333935 | ||||||||
\(467\) | 6.17134e10 | − | 6.17134e10i | 1.29751 | − | 1.29751i | 0.367484 | − | 0.930030i | \(-0.380219\pi\) |
0.930030 | − | 0.367484i | \(-0.119781\pi\) | |||||||
\(468\) | 7.73639e9 | + | 7.73639e9i | 0.161271 | + | 0.161271i | ||||
\(469\) | − | 2.41078e10i | − | 0.498272i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.84334e10 | −0.984150 | ||||||||
\(472\) | 1.44269e10 | − | 1.44269e10i | 0.290672 | − | 0.290672i | ||||
\(473\) | −8.17948e9 | − | 8.17948e9i | −0.163411 | − | 0.163411i | ||||
\(474\) | − | 8.30575e9i | − | 0.164538i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.44147e9 | 0.105996 | ||||||||
\(477\) | −1.83942e10 | + | 1.83942e10i | −0.355310 | + | 0.355310i | ||||
\(478\) | 9.12466e9 | + | 9.12466e9i | 0.174785 | + | 0.174785i | ||||
\(479\) | − | 2.65972e9i | − | 0.0505235i | −0.999681 | − | 0.0252617i | \(-0.991958\pi\) | ||
0.999681 | − | 0.0252617i | \(-0.00804191\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.40866e10 | −1.38407 | ||||||||
\(482\) | 7.72467e9 | − | 7.72467e9i | 0.143117 | − | 0.143117i | ||||
\(483\) | −1.58285e10 | − | 1.58285e10i | −0.290838 | − | 0.290838i | ||||
\(484\) | − | 4.48299e10i | − | 0.816934i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.82661e8 | −0.0176140 | ||||||||
\(487\) | 4.38176e10 | − | 4.38176e10i | 0.778991 | − | 0.778991i | −0.200668 | − | 0.979659i | \(-0.564311\pi\) |
0.979659 | + | 0.200668i | \(0.0643114\pi\) | |||||||
\(488\) | −5.72591e9 | − | 5.72591e9i | −0.100964 | − | 0.100964i | ||||
\(489\) | − | 2.13048e9i | − | 0.0372599i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.09667e10 | 1.04898 | 0.524490 | − | 0.851417i | \(-0.324256\pi\) | ||||
0.524490 | + | 0.851417i | \(0.324256\pi\) | |||||||
\(492\) | 2.43061e10 | − | 2.43061e10i | 0.414815 | − | 0.414815i | ||||
\(493\) | −1.20489e10 | − | 1.20489e10i | −0.203967 | − | 0.203967i | ||||
\(494\) | 4.87839e9i | 0.0819161i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.45645e9 | 0.139721 | ||||||||
\(497\) | 1.35239e10 | − | 1.35239e10i | 0.221654 | − | 0.221654i | ||||
\(498\) | −3.81456e9 | − | 3.81456e9i | −0.0620194 | − | 0.0620194i | ||||
\(499\) | 6.14633e10i | 0.991319i | 0.868517 | + | 0.495660i | \(0.165074\pi\) | ||||
−0.868517 | + | 0.495660i | \(0.834926\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.24102e10 | −0.831888 | ||||||||
\(502\) | 8.31992e9 | − | 8.31992e9i | 0.131010 | − | 0.131010i | ||||
\(503\) | 4.56188e10 | + | 4.56188e10i | 0.712642 | + | 0.712642i | 0.967087 | − | 0.254445i | \(-0.0818927\pi\) |
−0.254445 | + | 0.967087i | \(0.581893\pi\) | |||||||
\(504\) | − | 6.52395e9i | − | 0.101109i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.62366e9 | 0.116295 | ||||||||
\(507\) | −1.22032e10 | + | 1.22032e10i | −0.184690 | + | 0.184690i | ||||
\(508\) | 2.50359e10 | + | 2.50359e10i | 0.375931 | + | 0.375931i | ||||
\(509\) | − | 9.24908e10i | − | 1.37793i | −0.724794 | − | 0.688966i | \(-0.758065\pi\) | ||
0.724794 | − | 0.688966i | \(-0.241935\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.18162e10 | −0.613284 | ||||||||
\(512\) | −4.81403e10 | + | 4.81403e10i | −0.700534 | + | 0.700534i | ||||
\(513\) | 3.79967e9 | + | 3.79967e9i | 0.0548627 | + | 0.0548627i | ||||
\(514\) | 8.71248e9i | 0.124821i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.56280e10 | 0.361506 | ||||||||
\(517\) | −2.93301e10 | + | 2.93301e10i | −0.410536 | + | 0.410536i | ||||
\(518\) | 1.50071e10 | + | 1.50071e10i | 0.208438 | + | 0.208438i | ||||
\(519\) | 4.47276e10i | 0.616461i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.59534e10 | 1.16657 | 0.583287 | − | 0.812266i | \(-0.301766\pi\) | ||||
0.583287 | + | 0.812266i | \(0.301766\pi\) | |||||||
\(522\) | −6.93997e9 | + | 6.93997e9i | −0.0934708 | + | 0.0934708i | ||||
\(523\) | 1.53299e10 | + | 1.53299e10i | 0.204896 | + | 0.204896i | 0.802094 | − | 0.597198i | \(-0.203719\pi\) |
−0.597198 | + | 0.802094i | \(0.703719\pi\) | |||||||
\(524\) | 1.18086e11i | 1.56629i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.98714e10 | −0.259588 | ||||||||
\(527\) | −1.95251e9 | + | 1.95251e9i | −0.0253134 | + | 0.0253134i | ||||
\(528\) | −8.44032e9 | − | 8.44032e9i | −0.108598 | − | 0.108598i | ||||
\(529\) | 4.23220e10i | 0.540435i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.06144e10 | −0.259294 | ||||||||
\(532\) | −1.21190e10 | + | 1.21190e10i | −0.151294 | + | 0.151294i | ||||
\(533\) | −4.64088e10 | − | 4.64088e10i | −0.575031 | − | 0.575031i | ||||
\(534\) | 1.09632e10i | 0.134826i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.78638e10 | −0.458738 | ||||||||
\(537\) | 2.81074e10 | − | 2.81074e10i | 0.338005 | − | 0.338005i | ||||
\(538\) | 8.61889e9 | + | 8.61889e9i | 0.102878 | + | 0.102878i | ||||
\(539\) | − | 1.93132e10i | − | 0.228822i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.92085e9 | −0.0224236 | −0.0112118 | − | 0.999937i | \(-0.503569\pi\) | ||||
−0.0112118 | + | 0.999937i | \(0.503569\pi\) | |||||||
\(542\) | −3.09317e10 | + | 3.09317e10i | −0.358432 | + | 0.358432i | ||||
\(543\) | −4.55423e9 | − | 4.55423e9i | −0.0523861 | − | 0.0523861i | ||||
\(544\) | − | 1.29870e10i | − | 0.148290i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.98426e9 | −0.0673349 | ||||||||
\(547\) | −4.24260e10 | + | 4.24260e10i | −0.473896 | + | 0.473896i | −0.903173 | − | 0.429277i | \(-0.858768\pi\) |
0.429277 | + | 0.903173i | \(0.358768\pi\) | |||||||
\(548\) | 4.63948e10 | + | 4.63948e10i | 0.514454 | + | 0.514454i | ||||
\(549\) | 8.18172e9i | 0.0900648i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.36699e10 | 0.582270 | ||||||||
\(552\) | −2.48603e10 | + | 2.48603e10i | −0.267763 | + | 0.267763i | ||||
\(553\) | −3.93963e10 | − | 3.93963e10i | −0.421265 | − | 0.421265i | ||||
\(554\) | 1.78319e10i | 0.189303i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.53254e10 | 0.788210 | ||||||||
\(557\) | −7.68174e10 | + | 7.68174e10i | −0.798066 | + | 0.798066i | −0.982790 | − | 0.184725i | \(-0.940861\pi\) |
0.184725 | + | 0.982790i | \(0.440861\pi\) | |||||||
\(558\) | 1.12461e9 | + | 1.12461e9i | 0.0116002 | + | 0.0116002i | ||||
\(559\) | − | 4.89327e10i | − | 0.501132i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.89757e9 | 0.0393498 | ||||||||
\(562\) | 3.19786e10 | − | 3.19786e10i | 0.320564 | − | 0.320564i | ||||
\(563\) | −1.20218e11 | − | 1.20218e11i | −1.19657 | − | 1.19657i | −0.975188 | − | 0.221377i | \(-0.928945\pi\) |
−0.221377 | − | 0.975188i | \(-0.571055\pi\) | |||||||
\(564\) | − | 9.18972e10i | − | 0.908209i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.94800e10 | −0.189812 | ||||||||
\(567\) | −4.66101e9 | + | 4.66101e9i | −0.0450970 | + | 0.0450970i | ||||
\(568\) | −2.12406e10 | − | 2.12406e10i | −0.204068 | − | 0.204068i | ||||
\(569\) | − | 1.12597e11i | − | 1.07418i | −0.843525 | − | 0.537090i | \(-0.819523\pi\) | ||
0.843525 | − | 0.537090i | \(-0.180477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.88582e9 | −0.0741827 | −0.0370913 | − | 0.999312i | \(-0.511809\pi\) | ||||
−0.0370913 | + | 0.999312i | \(0.511809\pi\) | |||||||
\(572\) | −1.76741e10 | + | 1.76741e10i | −0.165103 | + | 0.165103i | ||||
\(573\) | −6.05483e10 | − | 6.05483e10i | −0.561672 | − | 0.561672i | ||||
\(574\) | 1.88013e10i | 0.173197i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.11213e10 | 0.191880 | ||||||||
\(577\) | −1.35022e11 | + | 1.35022e11i | −1.21815 | + | 1.21815i | −0.249872 | + | 0.968279i | \(0.580389\pi\) |
−0.968279 | + | 0.249872i | \(0.919611\pi\) | |||||||
\(578\) | −2.08056e10 | − | 2.08056e10i | −0.186410 | − | 0.186410i | ||||
\(579\) | 2.96263e10i | 0.263611i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.61869e10 | −0.317575 | ||||||||
\(582\) | −1.75859e10 | + | 1.75859e10i | −0.153275 | + | 0.153275i | ||||
\(583\) | −4.20224e10 | − | 4.20224e10i | −0.363753 | − | 0.363753i | ||||
\(584\) | 6.56767e10i | 0.564625i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.44064e10 | −0.122170 | ||||||||
\(587\) | 1.24270e11 | − | 1.24270e11i | 1.04668 | − | 1.04668i | 0.0478229 | − | 0.998856i | \(-0.484772\pi\) |
0.998856 | − | 0.0478229i | \(-0.0152283\pi\) | |||||||
\(588\) | 3.02560e10 | + | 3.02560e10i | 0.253106 | + | 0.253106i | ||||
\(589\) | − | 8.69712e9i | − | 0.0722627i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.72719e10 | 0.551422 | ||||||||
\(592\) | −1.26625e11 | + | 1.26625e11i | −1.03094 | + | 1.03094i | ||||
\(593\) | −6.87856e10 | − | 6.87856e10i | −0.556261 | − | 0.556261i | 0.371980 | − | 0.928241i | \(-0.378679\pi\) |
−0.928241 | + | 0.371980i | \(0.878679\pi\) | |||||||
\(594\) | − | 2.24493e9i | − | 0.0180326i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.86229e11 | −1.47592 | ||||||||
\(597\) | 1.59192e10 | − | 1.59192e10i | 0.125321 | − | 0.125321i | ||||
\(598\) | 2.28038e10 | + | 2.28038e10i | 0.178321 | + | 0.178321i | ||||
\(599\) | − | 4.22834e10i | − | 0.328445i | −0.986423 | − | 0.164222i | \(-0.947489\pi\) | ||
0.986423 | − | 0.164222i | \(-0.0525115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.67538e11 | 1.28415 | 0.642075 | − | 0.766642i | \(-0.278074\pi\) | ||||
0.642075 | + | 0.766642i | \(0.278074\pi\) | |||||||
\(602\) | −9.91189e9 | + | 9.91189e9i | −0.0754693 | + | 0.0754693i | ||||
\(603\) | 2.70517e10 | + | 2.70517e10i | 0.204609 | + | 0.204609i | ||||
\(604\) | − | 1.67288e11i | − | 1.25695i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.63350e10 | 0.269423 | ||||||||
\(607\) | 7.21743e10 | − | 7.21743e10i | 0.531653 | − | 0.531653i | −0.389411 | − | 0.921064i | \(-0.627322\pi\) |
0.921064 | + | 0.389411i | \(0.127322\pi\) | |||||||
\(608\) | 2.89241e10 | + | 2.89241e10i | 0.211664 | + | 0.211664i | ||||
\(609\) | 6.58361e10i | 0.478625i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.75464e11 | −1.25899 | ||||||||
\(612\) | −6.10594e9 | + | 6.10594e9i | −0.0435258 | + | 0.0435258i | ||||
\(613\) | −1.16637e11 | − | 1.16637e11i | −0.826024 | − | 0.826024i | 0.160940 | − | 0.986964i | \(-0.448548\pi\) |
−0.986964 | + | 0.160940i | \(0.948548\pi\) | |||||||
\(614\) | 4.75853e10i | 0.334810i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.49043e10 | 0.103511 | ||||||||
\(617\) | −1.32769e11 | + | 1.32769e11i | −0.916126 | + | 0.916126i | −0.996745 | − | 0.0806194i | \(-0.974310\pi\) |
0.0806194 | + | 0.996745i | \(0.474310\pi\) | |||||||
\(618\) | −1.52401e10 | − | 1.52401e10i | −0.104480 | − | 0.104480i | ||||
\(619\) | 2.20817e11i | 1.50408i | 0.659118 | + | 0.752040i | \(0.270930\pi\) | ||||
−0.659118 | + | 0.752040i | \(0.729070\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.55227e10 | 0.238858 | ||||||||
\(622\) | 2.88968e10 | − | 2.88968e10i | 0.193058 | − | 0.193058i | ||||
\(623\) | 5.20014e10 | + | 5.20014e10i | 0.345194 | + | 0.345194i | ||||
\(624\) | − | 5.04931e10i | − | 0.333038i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.32996e10 | −0.281959 | ||||||||
\(627\) | −8.68053e9 | + | 8.68053e9i | −0.0561663 | + | 0.0561663i | ||||
\(628\) | 1.73342e11 | + | 1.73342e11i | 1.11446 | + | 1.11446i | ||||
\(629\) | − | 5.84728e10i | − | 0.373552i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.85541e10 | −0.369352 | −0.184676 | − | 0.982800i | \(-0.559123\pi\) | ||||
−0.184676 | + | 0.982800i | \(0.559123\pi\) | |||||||
\(632\) | −6.18760e10 | + | 6.18760e10i | −0.387841 | + | 0.387841i | ||||
\(633\) | −1.84394e9 | − | 1.84394e9i | −0.0114850 | − | 0.0114850i | ||||
\(634\) | 3.51321e10i | 0.217444i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.31665e11 | 0.804713 | ||||||||
\(637\) | 5.77693e10 | − | 5.77693e10i | 0.350864 | − | 0.350864i | ||||
\(638\) | −1.58547e10 | − | 1.58547e10i | −0.0956919 | − | 0.0956919i | ||||
\(639\) | 3.03506e10i | 0.182039i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.71973e10 | −0.575734 | −0.287867 | − | 0.957670i | \(-0.592946\pi\) | ||||
−0.287867 | + | 0.957670i | \(0.592946\pi\) | |||||||
\(642\) | −9.68887e9 | + | 9.68887e9i | −0.0570339 | + | 0.0570339i | ||||
\(643\) | 1.13687e11 | + | 1.13687e11i | 0.665071 | + | 0.665071i | 0.956571 | − | 0.291500i | \(-0.0941543\pi\) |
−0.291500 | + | 0.956571i | \(0.594154\pi\) | |||||||
\(644\) | 1.13300e11i | 0.658696i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.85027e9 | −0.0221086 | ||||||||
\(647\) | 1.17592e11 | − | 1.17592e11i | 0.671061 | − | 0.671061i | −0.286899 | − | 0.957961i | \(-0.592625\pi\) |
0.957961 | + | 0.286899i | \(0.0926246\pi\) | |||||||
\(648\) | 7.32060e9 | + | 7.32060e9i | 0.0415190 | + | 0.0415190i | ||||
\(649\) | − | 4.70946e10i | − | 0.265456i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.06686e10 | 0.0593998 | ||||||||
\(652\) | −7.62492e9 | + | 7.62492e9i | −0.0421935 | + | 0.0421935i | ||||
\(653\) | 2.53561e10 | + | 2.53561e10i | 0.139454 | + | 0.139454i | 0.773387 | − | 0.633934i | \(-0.218561\pi\) |
−0.633934 | + | 0.773387i | \(0.718561\pi\) | |||||||
\(654\) | − | 3.60452e9i | − | 0.0197032i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.58639e11 | −0.856631 | ||||||||
\(657\) | 4.69225e10 | − | 4.69225e10i | 0.251837 | − | 0.251837i | ||||
\(658\) | 3.55422e10 | + | 3.55422e10i | 0.189601 | + | 0.189601i | ||||
\(659\) | − | 2.75271e11i | − | 1.45955i | −0.683689 | − | 0.729774i | \(-0.739625\pi\) | ||
0.683689 | − | 0.729774i | \(-0.260375\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.27595e10 | 0.328756 | 0.164378 | − | 0.986397i | \(-0.447438\pi\) | ||||
0.164378 | + | 0.986397i | \(0.447438\pi\) | |||||||
\(662\) | 4.44602e10 | − | 4.44602e10i | 0.231494 | − | 0.231494i | ||||
\(663\) | 1.16584e10 | + | 1.16584e10i | 0.0603369 | + | 0.0603369i | ||||
\(664\) | 5.68353e10i | 0.292379i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.36793e10 | −0.171185 | ||||||||
\(667\) | 2.50877e11 | − | 2.50877e11i | 1.26753 | − | 1.26753i | ||||
\(668\) | 1.87575e11 | + | 1.87575e11i | 0.942037 | + | 0.942037i | ||||
\(669\) | 2.01712e11i | 1.00700i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.86915e10 | −0.0922050 | ||||||||
\(672\) | −3.54809e10 | + | 3.54809e10i | −0.173987 | + | 0.173987i | ||||
\(673\) | −2.01482e11 | − | 2.01482e11i | −0.982147 | − | 0.982147i | 0.0176962 | − | 0.999843i | \(-0.494367\pi\) |
−0.999843 | + | 0.0176962i | \(0.994367\pi\) | |||||||
\(674\) | − | 8.90580e10i | − | 0.431552i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.73500e10 | 0.418289 | ||||||||
\(677\) | 4.34668e10 | − | 4.34668e10i | 0.206920 | − | 0.206920i | −0.596037 | − | 0.802957i | \(-0.703259\pi\) |
0.802957 | + | 0.596037i | \(0.203259\pi\) | |||||||
\(678\) | −2.36908e10 | − | 2.36908e10i | −0.112114 | − | 0.112114i | ||||
\(679\) | 1.66829e11i | 0.784859i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.09897e10 | 0.190584 | ||||||||
\(682\) | −2.56923e9 | + | 2.56923e9i | −0.0118759 | + | 0.0118759i | ||||
\(683\) | 1.33784e10 | + | 1.33784e10i | 0.0614780 | + | 0.0614780i | 0.737177 | − | 0.675699i | \(-0.236158\pi\) |
−0.675699 | + | 0.737177i | \(0.736158\pi\) | |||||||
\(684\) | − | 2.71979e10i | − | 0.124254i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.83068e10 | −0.263283 | ||||||||
\(687\) | 9.97540e10 | − | 9.97540e10i | 0.447820 | − | 0.447820i | ||||
\(688\) | −8.36331e10 | − | 8.36331e10i | −0.373271 | − | 0.373271i | ||||
\(689\) | − | 2.51394e11i | − | 1.11552i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.54479e11 | 1.11619 | 0.558097 | − | 0.829775i | \(-0.311532\pi\) | ||||
0.558097 | + | 0.829775i | \(0.311532\pi\) | |||||||
\(692\) | 1.60079e11 | − | 1.60079e11i | 0.698086 | − | 0.698086i | ||||
\(693\) | −1.06483e10 | − | 1.06483e10i | −0.0461686 | − | 0.0461686i | ||||
\(694\) | − | 8.81938e10i | − | 0.380190i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.03402e11 | 0.440650 | ||||||||
\(697\) | 3.66281e10 | − | 3.66281e10i | 0.155197 | − | 0.155197i | ||||
\(698\) | 4.42959e9 | + | 4.42959e9i | 0.0186613 | + | 0.0186613i | ||||
\(699\) | 1.67629e11i | 0.702166i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.18657e11 | 0.491384 | 0.245692 | − | 0.969348i | \(-0.420985\pi\) | ||||
0.245692 | + | 0.969348i | \(0.420985\pi\) | |||||||
\(702\) | 6.71501e9 | − | 6.71501e9i | 0.0276502 | − | 0.0276502i | ||||
\(703\) | 1.30228e11 | + | 1.30228e11i | 0.533193 | + | 0.533193i | ||||
\(704\) | 4.82525e10i | 0.196440i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.80198e10 | 0.153035 | ||||||||
\(707\) | 1.72346e11 | − | 1.72346e11i | 0.689801 | − | 0.689801i | ||||
\(708\) | 7.37785e10 | + | 7.37785e10i | 0.293627 | + | 0.293627i | ||||
\(709\) | 3.20598e11i | 1.26875i | 0.773025 | + | 0.634375i | \(0.218743\pi\) | ||||
−0.773025 | + | 0.634375i | \(0.781257\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.84141e10 | 0.345974 | ||||||||
\(712\) | 8.16736e10 | − | 8.16736e10i | 0.317806 | − | 0.317806i | ||||
\(713\) | −4.06542e10 | − | 4.06542e10i | −0.157307 | − | 0.157307i | ||||
\(714\) | − | 4.72307e9i | − | 0.0181732i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.01191e11 | −0.765520 | ||||||||
\(717\) | −9.71313e10 | + | 9.71313e10i | −0.367521 | + | 0.367521i | ||||
\(718\) | 8.47330e10 | + | 8.47330e10i | 0.318827 | + | 0.318827i | ||||
\(719\) | − | 4.23512e11i | − | 1.58471i | −0.610059 | − | 0.792356i | \(-0.708854\pi\) | ||
0.610059 | − | 0.792356i | \(-0.291146\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.44576e11 | −0.535001 | ||||||||
\(722\) | −4.41837e10 | + | 4.41837e10i | −0.162597 | + | 0.162597i | ||||
\(723\) | 8.22286e10 | + | 8.22286e10i | 0.300933 | + | 0.300933i | ||||
\(724\) | 3.25990e10i | 0.118645i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.89114e10 | −0.140065 | ||||||||
\(727\) | 9.00351e10 | − | 9.00351e10i | 0.322310 | − | 0.322310i | −0.527342 | − | 0.849653i | \(-0.676811\pi\) |
0.849653 | + | 0.527342i | \(0.176811\pi\) | |||||||
\(728\) | 4.45814e10 | + | 4.45814e10i | 0.158719 | + | 0.158719i | ||||
\(729\) | − | 1.04604e10i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.86201e10 | 0.135252 | ||||||||
\(732\) | 2.92821e10 | − | 2.92821e10i | 0.101990 | − | 0.101990i | ||||
\(733\) | −1.38110e10 | − | 1.38110e10i | −0.0478421 | − | 0.0478421i | 0.682781 | − | 0.730623i | \(-0.260770\pi\) |
−0.730623 | + | 0.682781i | \(0.760770\pi\) | |||||||
\(734\) | − | 2.70809e10i | − | 0.0932994i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.70408e11 | 0.921529 | ||||||||
\(737\) | −6.18007e10 | + | 6.18007e10i | −0.209471 | + | 0.209471i | ||||
\(738\) | −2.10971e10 | − | 2.10971e10i | −0.0711210 | − | 0.0711210i | ||||
\(739\) | − | 3.81206e11i | − | 1.27815i | −0.769144 | − | 0.639075i | \(-0.779317\pi\) | ||
0.769144 | − | 0.639075i | \(-0.220683\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.19301e10 | −0.172245 | ||||||||
\(742\) | −5.09227e10 | + | 5.09227e10i | −0.167995 | + | 0.167995i | ||||
\(743\) | 1.18224e11 | + | 1.18224e11i | 0.387927 | + | 0.387927i | 0.873947 | − | 0.486020i | \(-0.161552\pi\) |
−0.486020 | + | 0.873947i | \(0.661552\pi\) | |||||||
\(744\) | − | 1.67562e10i | − | 0.0546870i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.35440e10 | 0.172884 | ||||||||
\(747\) | 4.06058e10 | − | 4.06058e10i | 0.130408 | − | 0.130408i | ||||
\(748\) | −1.39493e10 | − | 1.39493e10i | −0.0445601 | − | 0.0445601i | ||||
\(749\) | 9.19135e10i | 0.292047i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.45619e11 | −1.40089 | −0.700445 | − | 0.713707i | \(-0.747015\pi\) | ||||
−0.700445 | + | 0.713707i | \(0.747015\pi\) | |||||||
\(752\) | −2.99893e11 | + | 2.99893e11i | −0.937766 | + | 0.937766i | ||||
\(753\) | 8.85649e10 | + | 8.85649e10i | 0.275475 | + | 0.275475i | ||||
\(754\) | − | 9.48486e10i | − | 0.293458i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.33633e10 | 0.102137 | ||||||||
\(757\) | −4.26149e11 | + | 4.26149e11i | −1.29771 | + | 1.29771i | −0.367808 | + | 0.929902i | \(0.619892\pi\) |
−0.929902 | + | 0.367808i | \(0.880108\pi\) | |||||||
\(758\) | −5.06268e10 | − | 5.06268e10i | −0.153357 | − | 0.153357i | ||||
\(759\) | 8.11533e10i | 0.244534i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.56636e11 | −0.765207 | −0.382603 | − | 0.923913i | \(-0.624972\pi\) | ||||
−0.382603 | + | 0.923913i | \(0.624972\pi\) | |||||||
\(762\) | 2.17306e10 | − | 2.17306e10i | 0.0644543 | − | 0.0644543i | ||||
\(763\) | −1.70972e10 | − | 1.70972e10i | −0.0504459 | − | 0.0504459i | ||||
\(764\) | 4.33401e11i | 1.27209i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.62091e9 | −0.0163264 | ||||||||
\(767\) | 1.40869e11 | − | 1.40869e11i | 0.407036 | − | 0.407036i | ||||
\(768\) | −4.66379e10 | − | 4.66379e10i | −0.134058 | − | 0.134058i | ||||
\(769\) | 5.23066e11i | 1.49572i | 0.663855 | + | 0.747861i | \(0.268919\pi\) | ||||
−0.663855 | + | 0.747861i | \(0.731081\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.27437e10 | −0.262462 | ||||||||
\(772\) | 1.06032e11 | − | 1.06032e11i | 0.298516 | − | 0.298516i | ||||
\(773\) | −2.31264e11 | − | 2.31264e11i | −0.647723 | − | 0.647723i | 0.304719 | − | 0.952442i | \(-0.401437\pi\) |
−0.952442 | + | 0.304719i | \(0.901437\pi\) | |||||||
\(774\) | − | 2.22445e10i | − | 0.0619810i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.62022e11 | 0.722587 | ||||||||
\(777\) | −1.59750e11 | + | 1.59750e11i | −0.438284 | + | 0.438284i | ||||
\(778\) | −4.29346e10 | − | 4.29346e10i | −0.117190 | − | 0.117190i | ||||
\(779\) | 1.63153e11i | 0.443044i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.93373e10 | −0.186364 | ||||||||
\(782\) | −1.79979e10 | + | 1.79979e10i | −0.0481275 | + | 0.0481275i | ||||
\(783\) | −7.38755e10 | − | 7.38755e10i | −0.196541 | − | 0.196541i | ||||
\(784\) | − | 1.97472e11i | − | 0.522687i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.02496e11 | 0.268545 | ||||||||
\(787\) | 9.83798e9 | − | 9.83798e9i | 0.0256453 | − | 0.0256453i | −0.694168 | − | 0.719813i | \(-0.744227\pi\) |
0.719813 | + | 0.694168i | \(0.244227\pi\) | |||||||
\(788\) | −2.40764e11 | − | 2.40764e11i | −0.624435 | − | 0.624435i | ||||
\(789\) | − | 2.11529e11i | − | 0.545836i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.24743e11 | −0.574091 | ||||||||
\(792\) | −1.67242e10 | + | 1.67242e10i | −0.0425056 | + | 0.0425056i | ||||
\(793\) | −5.59098e10 | − | 5.59098e10i | −0.141382 | − | 0.141382i | ||||
\(794\) | − | 7.33665e10i | − | 0.184593i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.13949e11 | −0.283830 | ||||||||
\(797\) | −5.12588e11 | + | 5.12588e11i | −1.27038 | + | 1.27038i | −0.324497 | + | 0.945887i | \(0.605195\pi\) |
−0.945887 | + | 0.324497i | \(0.894805\pi\) | |||||||
\(798\) | 1.05191e10 | + | 1.05191e10i | 0.0259397 | + | 0.0259397i | ||||
\(799\) | − | 1.38484e11i | − | 0.339793i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.16703e11 | −0.283499 | ||||||||
\(802\) | −7.58513e10 | + | 7.58513e10i | −0.183344 | + | 0.183344i | ||||
\(803\) | 1.07197e11 | + | 1.07197e11i | 0.257821 | + | 0.257821i | ||||
\(804\) | − | 1.93634e11i | − | 0.463402i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.53701e10 | −0.0364196 | ||||||||
\(807\) | −9.17474e10 | + | 9.17474e10i | −0.216322 | + | 0.216322i | ||||
\(808\) | −2.70687e11 | − | 2.70687e11i | −0.635071 | − | 0.635071i | ||||
\(809\) | 2.69111e11i | 0.628258i | 0.949380 | + | 0.314129i | \(0.101712\pi\) | ||||
−0.949380 | + | 0.314129i | \(0.898288\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.11333e11 | 1.18201 | 0.591004 | − | 0.806669i | \(-0.298732\pi\) | ||||
0.591004 | + | 0.806669i | \(0.298732\pi\) | |||||||
\(812\) | 2.35626e11 | − | 2.35626e11i | 0.541999 | − | 0.541999i | ||||
\(813\) | −3.29266e11 | − | 3.29266e11i | −0.753675 | − | 0.753675i | ||||
\(814\) | − | 7.69419e10i | − | 0.175253i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.98517e10 | 0.0898847 | ||||||||
\(817\) | −8.60132e10 | + | 8.60132e10i | −0.193053 | + | 0.193053i | ||||
\(818\) | −3.75437e9 | − | 3.75437e9i | −0.00838539 | − | 0.00838539i | ||||
\(819\) | − | 6.37020e10i | − | 0.141585i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.54755e11 | 0.340623 | 0.170311 | − | 0.985390i | \(-0.445523\pi\) | ||||
0.170311 | + | 0.985390i | \(0.445523\pi\) | |||||||
\(822\) | 4.02696e10 | − | 4.02696e10i | 0.0882044 | − | 0.0882044i | ||||
\(823\) | −9.01212e10 | − | 9.01212e10i | −0.196439 | − | 0.196439i | 0.602033 | − | 0.798471i | \(-0.294358\pi\) |
−0.798471 | + | 0.602033i | \(0.794358\pi\) | |||||||
\(824\) | 2.27071e11i | 0.492553i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.70692e10 | −0.122598 | ||||||||
\(827\) | −2.24761e11 | + | 2.24761e11i | −0.480506 | + | 0.480506i | −0.905293 | − | 0.424787i | \(-0.860349\pi\) |
0.424787 | + | 0.905293i | \(0.360349\pi\) | |||||||
\(828\) | −1.27135e11 | − | 1.27135e11i | −0.270485 | − | 0.270485i | ||||
\(829\) | − | 7.91622e11i | − | 1.67610i | −0.545594 | − | 0.838050i | \(-0.683696\pi\) | ||
0.545594 | − | 0.838050i | \(-0.316304\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.89819e11 | −0.398048 | ||||||||
\(832\) | −1.44332e11 | + | 1.44332e11i | −0.301211 | + | 0.301211i | ||||
\(833\) | 4.55944e10 | + | 4.55944e10i | 0.0946959 | + | 0.0946959i | ||||
\(834\) | − | 6.53807e10i | − | 0.135140i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.21348e10 | 0.127207 | ||||||||
\(837\) | −1.19714e10 | + | 1.19714e10i | −0.0243918 | + | 0.0243918i | ||||
\(838\) | −9.29024e10 | − | 9.29024e10i | −0.188387 | − | 0.188387i | ||||
\(839\) | 3.46532e11i | 0.699352i | 0.936871 | + | 0.349676i | \(0.113708\pi\) | ||||
−0.936871 | + | 0.349676i | \(0.886292\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.43235e11 | −1.08593 | ||||||||
\(842\) | 9.73510e10 | − | 9.73510e10i | 0.193683 | − | 0.193683i | ||||
\(843\) | 3.40410e11 | + | 3.40410e11i | 0.674051 | + | 0.674051i | ||||
\(844\) | 1.31988e10i | 0.0260115i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.97647e10 | −0.155714 | ||||||||
\(847\) | −1.84567e11 | + | 1.84567e11i | −0.358608 | + | 0.358608i | ||||
\(848\) | −4.29668e11 | − | 4.29668e11i | −0.830902 | − | 0.830902i | ||||
\(849\) | − | 2.07363e11i | − | 0.399118i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.21749e12 | 2.32139 | ||||||||
\(852\) | 1.08624e11 | − | 1.08624e11i | 0.206142 | − | 0.206142i | ||||
\(853\) | 2.32474e11 | + | 2.32474e11i | 0.439114 | + | 0.439114i | 0.891714 | − | 0.452600i | \(-0.149503\pi\) |
−0.452600 | + | 0.891714i | \(0.649503\pi\) | |||||||
\(854\) | 2.26504e10i | 0.0425837i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.44360e11 | 0.268875 | ||||||||
\(857\) | −3.14575e11 | + | 3.14575e11i | −0.583177 | + | 0.583177i | −0.935775 | − | 0.352598i | \(-0.885298\pi\) |
0.352598 | + | 0.935775i | \(0.385298\pi\) | |||||||
\(858\) | 1.53408e10 | + | 1.53408e10i | 0.0283072 | + | 0.0283072i | ||||
\(859\) | 4.37243e11i | 0.803063i | 0.915845 | + | 0.401532i | \(0.131522\pi\) | ||||
−0.915845 | + | 0.401532i | \(0.868478\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.00138e11 | −0.364181 | ||||||||
\(862\) | −6.14980e10 | + | 6.14980e10i | −0.111386 | + | 0.111386i | ||||
\(863\) | 2.88466e11 | + | 2.88466e11i | 0.520057 | + | 0.520057i | 0.917588 | − | 0.397532i | \(-0.130133\pi\) |
−0.397532 | + | 0.917588i | \(0.630133\pi\) | |||||||
\(864\) | − | 7.96270e10i | − | 0.142891i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.27232e11 | −0.226217 | ||||||||
\(867\) | 2.21474e11 | − | 2.21474e11i | 0.391964 | − | 0.391964i | ||||
\(868\) | −3.81828e10 | − | 3.81828e10i | −0.0672649 | − | 0.0672649i | ||||
\(869\) | 2.01986e11i | 0.354195i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.69715e11 | −0.642383 | ||||||||
\(872\) | −2.68529e10 | + | 2.68529e10i | −0.0464435 | + | 0.0464435i | ||||
\(873\) | −1.87201e11 | − | 1.87201e11i | −0.322292 | − | 0.322292i | ||||
\(874\) | − | 8.01683e10i | − | 0.137391i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.35869e11 | −0.570365 | ||||||||
\(877\) | −6.00399e11 | + | 6.00399e11i | −1.01494 | + | 1.01494i | −0.0150556 | + | 0.999887i | \(0.504793\pi\) |
−0.999887 | + | 0.0150556i | \(0.995207\pi\) | |||||||
\(878\) | 4.74707e10 | + | 4.74707e10i | 0.0798818 | + | 0.0798818i | ||||
\(879\) | − | 1.53355e11i | − | 0.256887i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.08213e12 | 1.79629 | 0.898147 | − | 0.439694i | \(-0.144913\pi\) | ||||
0.898147 | + | 0.439694i | \(0.144913\pi\) | |||||||
\(882\) | 2.62616e10 | − | 2.62616e10i | 0.0433956 | − | 0.0433956i | ||||
\(883\) | 7.01877e11 | + | 7.01877e11i | 1.15456 | + | 1.15456i | 0.985627 | + | 0.168938i | \(0.0540338\pi\) |
0.168938 | + | 0.985627i | \(0.445966\pi\) | |||||||
\(884\) | − | 8.34499e10i | − | 0.136652i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.60364e11 | −0.422519 | ||||||||
\(887\) | 4.78658e11 | − | 4.78658e11i | 0.773270 | − | 0.773270i | −0.205407 | − | 0.978677i | \(-0.565852\pi\) |
0.978677 | + | 0.205407i | \(0.0658518\pi\) | |||||||
\(888\) | 2.50903e11 | + | 2.50903e11i | 0.403510 | + | 0.403510i | ||||
\(889\) | − | 2.06148e11i | − | 0.330044i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.38972e10 | 0.0379171 | ||||||||
\(892\) | 7.21922e11 | − | 7.21922e11i | 1.14033 | − | 1.14033i | ||||
\(893\) | 3.08428e11 | + | 3.08428e11i | 0.485006 | + | 0.485006i | ||||
\(894\) | 1.61643e11i | 0.253050i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.33151e11 | 0.516903 | ||||||||
\(897\) | −2.42744e11 | + | 2.42744e11i | −0.374955 | + | 0.374955i | ||||
\(898\) | −1.17101e10 | − | 1.17101e10i | −0.0180075 | − | 0.0180075i | ||||
\(899\) | 1.69095e11i | 0.258875i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.98412e11 | 0.301071 | ||||||||
\(902\) | 4.81974e10 | − | 4.81974e10i | 0.0728110 | − | 0.0728110i | ||||
\(903\) | −1.05511e11 | − | 1.05511e11i | −0.158689 | − | 0.158689i | ||||
\(904\) | 3.52982e11i | 0.528542i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.45203e11 | −0.215507 | ||||||||
\(907\) | 5.94503e11 | − | 5.94503e11i | 0.878465 | − | 0.878465i | −0.114911 | − | 0.993376i | \(-0.536658\pi\) |
0.993376 | + | 0.114911i | \(0.0366582\pi\) | |||||||
\(908\) | −1.46701e11 | − | 1.46701e11i | −0.215819 | − | 0.215819i | ||||
\(909\) | 3.86783e11i | 0.566516i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.94927e10 | 0.0283008 | 0.0141504 | − | 0.999900i | \(-0.495496\pi\) | ||||
0.0141504 | + | 0.999900i | \(0.495496\pi\) | |||||||
\(912\) | −8.87562e10 | + | 8.87562e10i | −0.128298 | + | 0.128298i | ||||
\(913\) | 9.27657e10 | + | 9.27657e10i | 0.133507 | + | 0.133507i | ||||
\(914\) | 9.82006e10i | 0.140711i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.14034e11 | −1.01423 | ||||||||
\(917\) | 4.86164e11 | − | 4.86164e11i | 0.687552 | − | 0.687552i | ||||
\(918\) | 5.29982e9 | + | 5.29982e9i | 0.00746260 | + | 0.00746260i | ||||
\(919\) | − | 5.36385e11i | − | 0.751995i | −0.926621 | − | 0.375997i | \(-0.877300\pi\) | ||
0.926621 | − | 0.375997i | \(-0.122700\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.06542e11 | −0.704006 | ||||||||
\(922\) | −1.84468e11 | + | 1.84468e11i | −0.255268 | + | 0.255268i | ||||
\(923\) | −2.07401e11 | − | 2.07401e11i | −0.285761 | − | 0.285761i | ||||
\(924\) | 7.62199e10i | 0.104564i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.33167e10 | −0.0317120 | ||||||||
\(927\) | 1.62230e11 | − | 1.62230e11i | 0.219691 | − | 0.219691i | ||||
\(928\) | −5.62360e11 | − | 5.62360e11i | −0.758268 | − | 0.758268i | ||||
\(929\) | 2.91516e11i | 0.391381i | 0.980666 | + | 0.195691i | \(0.0626948\pi\) | ||||
−0.980666 | + | 0.195691i | \(0.937305\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.03092e11 | −0.270330 | ||||||||
\(932\) | 5.99939e11 | − | 5.99939e11i | 0.795139 | − | 0.795139i | ||||
\(933\) | 3.07604e11 | + | 3.07604e11i | 0.405944 | + | 0.405944i | ||||
\(934\) | 3.83421e11i | 0.503835i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.00051e11 | −0.130352 | ||||||||
\(937\) | 3.52799e11 | − | 3.52799e11i | 0.457688 | − | 0.457688i | −0.440208 | − | 0.897896i | \(-0.645095\pi\) |
0.897896 | + | 0.440208i | \(0.145095\pi\) | |||||||
\(938\) | 7.48901e10 | + | 7.48901e10i | 0.0967415 | + | 0.0967415i | ||||
\(939\) | − | 4.60921e11i | − | 0.592876i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.96719e9 | −0.00250893 | −0.00125446 | − | 0.999999i | \(-0.500399\pi\) | ||||
−0.00125446 | + | 0.999999i | \(0.500399\pi\) | |||||||
\(942\) | 1.50457e11 | − | 1.50457e11i | 0.191077 | − | 0.191077i | ||||
\(943\) | 7.62651e11 | + | 7.62651e11i | 0.964449 | + | 0.964449i | ||||
\(944\) | − | 4.81530e11i | − | 0.606367i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.08186e10 | 0.0634538 | ||||||||
\(947\) | 2.52474e11 | − | 2.52474e11i | 0.313918 | − | 0.313918i | −0.532507 | − | 0.846426i | \(-0.678750\pi\) |
0.846426 | + | 0.532507i | \(0.178750\pi\) | |||||||
\(948\) | −3.16432e11 | − | 3.16432e11i | −0.391784 | − | 0.391784i | ||||
\(949\) | 6.41290e11i | 0.790659i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.73978e11 | −0.457219 | ||||||||
\(952\) | −3.51858e10 | + | 3.51858e10i | −0.0428371 | + | 0.0428371i | ||||
\(953\) | 1.39641e11 | + | 1.39641e11i | 0.169294 | + | 0.169294i | 0.786669 | − | 0.617375i | \(-0.211804\pi\) |
−0.617375 | + | 0.786669i | \(0.711804\pi\) | |||||||
\(954\) | − | 1.14282e11i | − | 0.137970i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.95260e11 | 0.832369 | ||||||||
\(957\) | 1.68772e11 | − | 1.68772e11i | 0.201211 | − | 0.201211i | ||||
\(958\) | 8.26232e9 | + | 8.26232e9i | 0.00980934 | + | 0.00980934i | ||||
\(959\) | − | 3.82018e11i | − | 0.451658i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.25490e11 | −0.967872 | ||||||||
\(962\) | 2.30148e11 | − | 2.30148e11i | 0.268724 | − | 0.268724i | ||||
\(963\) | −1.03137e11 | − | 1.03137e11i | −0.119925 | − | 0.119925i | ||||
\(964\) | − | 5.88587e11i | − | 0.681558i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.83415e10 | 0.112935 | ||||||||
\(967\) | 1.22373e12 | − | 1.22373e12i | 1.39953 | − | 1.39953i | 0.598124 | − | 0.801403i | \(-0.295913\pi\) |
0.801403 | − | 0.598124i | \(-0.204087\pi\) | |||||||
\(968\) | 2.89881e11 | + | 2.89881e11i | 0.330155 | + | 0.330155i | ||||
\(969\) | − | 4.09858e10i | − | 0.0464877i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.85260e11 | 0.208403 | 0.104202 | − | 0.994556i | \(-0.466771\pi\) | ||||
0.104202 | + | 0.994556i | \(0.466771\pi\) | |||||||
\(972\) | −3.74373e10 | + | 3.74373e10i | −0.0419411 | + | 0.0419411i | ||||
\(973\) | −3.10117e11 | − | 3.10117e11i | −0.345999 | − | 0.345999i | ||||
\(974\) | 2.72236e11i | 0.302489i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.91116e11 | −0.210619 | ||||||||
\(977\) | −8.96530e11 | + | 8.96530e11i | −0.983981 | + | 0.983981i | −0.999874 | − | 0.0158927i | \(-0.994941\pi\) |
0.0158927 | + | 0.999874i | \(0.494941\pi\) | |||||||
\(978\) | 6.61826e9 | + | 6.61826e9i | 0.00723417 | + | 0.00723417i | ||||
\(979\) | − | 2.66613e11i | − | 0.290235i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.83699e10 | 0.0414299 | ||||||||
\(982\) | −1.89391e11 | + | 1.89391e11i | −0.203664 | + | 0.203664i | ||||
\(983\) | 7.43264e11 | + | 7.43264e11i | 0.796029 | + | 0.796029i | 0.982467 | − | 0.186438i | \(-0.0596944\pi\) |
−0.186438 | + | 0.982467i | \(0.559694\pi\) | |||||||
\(984\) | 3.14338e11i | 0.335286i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.48592e10 | 0.0792022 | ||||||||
\(987\) | −3.78344e11 | + | 3.78344e11i | −0.398674 | + | 0.398674i | ||||
\(988\) | 1.85857e11 | + | 1.85857e11i | 0.195052 | + | 0.195052i | ||||
\(989\) | 8.04128e11i | 0.840504i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.69152e12 | 1.75381 | 0.876904 | − | 0.480665i | \(-0.159605\pi\) | ||||
0.876904 | + | 0.480665i | \(0.159605\pi\) | |||||||
\(992\) | −9.11296e10 | + | 9.11296e10i | −0.0941050 | + | 0.0941050i | ||||
\(993\) | 4.73276e11 | + | 4.73276e11i | 0.486763 | + | 0.486763i | ||||
\(994\) | 8.40229e10i | 0.0860701i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.90654e11 | −0.295351 | ||||||||
\(997\) | −6.16013e11 | + | 6.16013e11i | −0.623461 | + | 0.623461i | −0.946415 | − | 0.322953i | \(-0.895324\pi\) |
0.322953 | + | 0.946415i | \(0.395324\pi\) | |||||||
\(998\) | −1.90934e11 | − | 1.90934e11i | −0.192469 | − | 0.192469i | ||||
\(999\) | − | 3.58514e11i | − | 0.359951i |
(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 | 75.9.f.d.43.3 | yes | 12 | |
5.2 | odd | 4 | inner | 75.9.f.d.7.3 | ✓ | 12 | |
5.3 | odd | 4 | inner | 75.9.f.d.7.4 | yes | 12 | |
5.4 | even | 2 | inner | 75.9.f.d.43.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.9.f.d.7.3 | ✓ | 12 | 5.2 | odd | 4 | inner | |
75.9.f.d.7.4 | yes | 12 | 5.3 | odd | 4 | inner | |
75.9.f.d.43.3 | yes | 12 | 1.1 | even | 1 | trivial | |
75.9.f.d.43.4 | yes | 12 | 5.4 | even | 2 | inner |