Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(74,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.74");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.d (of order \(2\), degree \(1\), not 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: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 943 x^{18} + 318815 x^{16} + 48938090 x^{14} + 3842259173 x^{12} + 159675554657 x^{10} + 3390679484573 x^{8} + 32981662033730 x^{6} + \cdots + 336685801 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{28}\cdot 3^{22}\cdot 5^{32} \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 74.17 | ||
Root | \(2.23448i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.74 |
Dual form | 75.9.d.c.74.18 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 23.7888 | 1.48680 | 0.743399 | − | 0.668848i | \(-0.233212\pi\) | ||||
0.743399 | + | 0.668848i | \(0.233212\pi\) | |||||||
\(3\) | −10.0775 | − | 80.3707i | −0.124414 | − | 0.992230i | ||||
\(4\) | 309.906 | 1.21057 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −239.732 | − | 1911.92i | −0.184978 | − | 1.47525i | ||||
\(7\) | 692.753i | 0.288527i | 0.989539 | + | 0.144263i | \(0.0460813\pi\) | ||||
−0.989539 | + | 0.144263i | \(0.953919\pi\) | |||||||
\(8\) | 1282.36 | 0.313077 | ||||||||
\(9\) | −6357.89 | + | 1619.88i | −0.969042 | + | 0.246895i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 15881.8i | − | 1.08475i | −0.840137 | − | 0.542374i | \(-0.817525\pi\) | ||
0.840137 | − | 0.542374i | \(-0.182475\pi\) | |||||||
\(12\) | −3123.09 | − | 24907.4i | −0.150612 | − | 1.20117i | ||||
\(13\) | − | 48870.9i | − | 1.71110i | −0.517716 | − | 0.855552i | \(-0.673218\pi\) | ||
0.517716 | − | 0.855552i | \(-0.326782\pi\) | |||||||
\(14\) | 16479.8i | 0.428982i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −48830.2 | −0.745089 | ||||||||
\(17\) | −41025.6 | −0.491201 | −0.245600 | − | 0.969371i | \(-0.578985\pi\) | ||||
−0.245600 | + | 0.969371i | \(0.578985\pi\) | |||||||
\(18\) | −151246. | + | 38534.9i | −1.44077 | + | 0.367083i | ||||
\(19\) | 108213. | 0.830356 | 0.415178 | − | 0.909740i | \(-0.363719\pi\) | ||||
0.415178 | + | 0.909740i | \(0.363719\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 55677.0 | − | 6981.24i | 0.286285 | − | 0.0358968i | ||||
\(22\) | − | 377809.i | − | 1.61280i | ||||||
\(23\) | −433886. | −1.55047 | −0.775237 | − | 0.631671i | \(-0.782369\pi\) | ||||
−0.775237 | + | 0.631671i | \(0.782369\pi\) | |||||||
\(24\) | −12923.0 | − | 103064.i | −0.0389511 | − | 0.310644i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 1.16258e6i | − | 2.54407i | ||||||
\(27\) | 194262. | + | 494663.i | 0.365539 | + | 0.930796i | ||||
\(28\) | 214688.i | 0.349282i | ||||||||
\(29\) | 377879.i | 0.534270i | 0.963659 | + | 0.267135i | \(0.0860770\pi\) | ||||
−0.963659 | + | 0.267135i | \(0.913923\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −408921. | −0.442784 | −0.221392 | − | 0.975185i | \(-0.571060\pi\) | ||||
−0.221392 | + | 0.975185i | \(0.571060\pi\) | |||||||
\(32\) | −1.48989e6 | −1.42087 | ||||||||
\(33\) | −1.27643e6 | + | 160049.i | −1.07632 | + | 0.134958i | ||||
\(34\) | −975949. | −0.730317 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.97035e6 | + | 502009.i | −1.17309 | + | 0.298883i | ||||
\(37\) | − | 2.31002e6i | − | 1.23256i | −0.787526 | − | 0.616282i | \(-0.788638\pi\) | ||
0.787526 | − | 0.616282i | \(-0.211362\pi\) | |||||||
\(38\) | 2.57425e6 | 1.23457 | ||||||||
\(39\) | −3.92778e6 | + | 492497.i | −1.69781 | + | 0.212885i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.15170e6i | 0.761460i | 0.924686 | + | 0.380730i | \(0.124327\pi\) | ||||
−0.924686 | + | 0.380730i | \(0.875673\pi\) | |||||||
\(42\) | 1.32449e6 | − | 166075.i | 0.425649 | − | 0.0533713i | ||||
\(43\) | − | 2.42811e6i | − | 0.710223i | −0.934824 | − | 0.355111i | \(-0.884443\pi\) | ||
0.934824 | − | 0.355111i | \(-0.115557\pi\) | |||||||
\(44\) | − | 4.92187e6i | − | 1.31317i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.03216e7 | −2.30524 | ||||||||
\(47\) | 8.18110e6 | 1.67656 | 0.838282 | − | 0.545237i | \(-0.183560\pi\) | ||||
0.838282 | + | 0.545237i | \(0.183560\pi\) | |||||||
\(48\) | 492087. | + | 3.92451e6i | 0.0926994 | + | 0.739300i | ||||
\(49\) | 5.28489e6 | 0.916752 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 413437. | + | 3.29725e6i | 0.0611122 | + | 0.487385i | ||||
\(52\) | − | 1.51454e7i | − | 2.07141i | ||||||
\(53\) | 1.36324e7 | 1.72770 | 0.863850 | − | 0.503748i | \(-0.168046\pi\) | ||||
0.863850 | + | 0.503748i | \(0.168046\pi\) | |||||||
\(54\) | 4.62126e6 | + | 1.17674e7i | 0.543482 | + | 1.38391i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 888360.i | 0.0903310i | ||||||||
\(57\) | −1.09052e6 | − | 8.69714e6i | −0.103308 | − | 0.823904i | ||||
\(58\) | 8.98929e6i | 0.794353i | ||||||||
\(59\) | − | 1.23667e7i | − | 1.02057i | −0.860004 | − | 0.510287i | \(-0.829539\pi\) | ||
0.860004 | − | 0.510287i | \(-0.170461\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.15129e6 | −0.0831509 | −0.0415755 | − | 0.999135i | \(-0.513238\pi\) | ||||
−0.0415755 | + | 0.999135i | \(0.513238\pi\) | |||||||
\(62\) | −9.72773e6 | −0.658331 | ||||||||
\(63\) | −1.12217e6 | − | 4.40445e6i | −0.0712357 | − | 0.279595i | ||||
\(64\) | −2.29423e7 | −1.36746 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.03647e7 | + | 3.80738e6i | −1.60027 | + | 0.200655i | ||||
\(67\) | 1.55586e7i | 0.772096i | 0.922479 | + | 0.386048i | \(0.126160\pi\) | ||||
−0.922479 | + | 0.386048i | \(0.873840\pi\) | |||||||
\(68\) | −1.27141e7 | −0.594634 | ||||||||
\(69\) | 4.37250e6 | + | 3.48717e7i | 0.192900 | + | 1.53843i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.52525e7i | − | 0.993735i | −0.867826 | − | 0.496868i | \(-0.834483\pi\) | ||
0.867826 | − | 0.496868i | \(-0.165517\pi\) | |||||||
\(72\) | −8.15311e6 | + | 2.07727e6i | −0.303384 | + | 0.0772969i | ||||
\(73\) | − | 2.29182e7i | − | 0.807030i | −0.914973 | − | 0.403515i | \(-0.867788\pi\) | ||
0.914973 | − | 0.403515i | \(-0.132212\pi\) | |||||||
\(74\) | − | 5.49526e7i | − | 1.83257i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.35358e7 | 1.00520 | ||||||||
\(77\) | 1.10022e7 | 0.312979 | ||||||||
\(78\) | −9.34372e7 | + | 1.17159e7i | −2.52430 | + | 0.316518i | ||||
\(79\) | −4.49938e7 | −1.15517 | −0.577583 | − | 0.816332i | \(-0.696004\pi\) | ||||
−0.577583 | + | 0.816332i | \(0.696004\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.77987e7 | − | 2.05980e7i | 0.878086 | − | 0.478503i | ||||
\(82\) | 5.11864e7i | 1.13214i | ||||||||
\(83\) | 2.12119e7 | 0.446957 | 0.223479 | − | 0.974709i | \(-0.428259\pi\) | ||||
0.223479 | + | 0.974709i | \(0.428259\pi\) | |||||||
\(84\) | 1.72547e7 | − | 2.16353e6i | 0.346569 | − | 0.0434556i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 5.77618e7i | − | 1.05596i | ||||||
\(87\) | 3.03704e7 | − | 3.80809e6i | 0.530119 | − | 0.0664707i | ||||
\(88\) | − | 2.03662e7i | − | 0.339609i | ||||||
\(89\) | 4.87898e7i | 0.777622i | 0.921317 | + | 0.388811i | \(0.127114\pi\) | ||||
−0.921317 | + | 0.388811i | \(0.872886\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.38555e7 | 0.493700 | ||||||||
\(92\) | −1.34464e8 | −1.87696 | ||||||||
\(93\) | 4.12091e6 | + | 3.28652e7i | 0.0550885 | + | 0.439344i | ||||
\(94\) | 1.94618e8 | 2.49271 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.50145e7 | + | 1.19744e8i | 0.176777 | + | 1.40983i | ||||
\(97\) | − | 2.91619e7i | − | 0.329404i | −0.986343 | − | 0.164702i | \(-0.947334\pi\) | ||
0.986343 | − | 0.164702i | \(-0.0526662\pi\) | |||||||
\(98\) | 1.25721e8 | 1.36303 | ||||||||
\(99\) | 2.57265e7 | + | 1.00975e8i | 0.267818 | + | 1.05117i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.31995e7i | 0.607335i | 0.952778 | + | 0.303667i | \(0.0982111\pi\) | ||||
−0.952778 | + | 0.303667i | \(0.901789\pi\) | |||||||
\(102\) | 9.83515e6 | + | 7.84377e7i | 0.0908616 | + | 0.724643i | ||||
\(103\) | − | 6.94350e7i | − | 0.616921i | −0.951237 | − | 0.308461i | \(-0.900186\pi\) | ||
0.951237 | − | 0.308461i | \(-0.0998138\pi\) | |||||||
\(104\) | − | 6.26701e7i | − | 0.535707i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.24298e8 | 2.56874 | ||||||||
\(107\) | 2.16211e8 | 1.64946 | 0.824732 | − | 0.565523i | \(-0.191326\pi\) | ||||
0.824732 | + | 0.565523i | \(0.191326\pi\) | |||||||
\(108\) | 6.02031e7 | + | 1.53299e8i | 0.442510 | + | 1.12679i | ||||
\(109\) | −7.00475e7 | −0.496234 | −0.248117 | − | 0.968730i | \(-0.579812\pi\) | ||||
−0.248117 | + | 0.968730i | \(0.579812\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.85658e8 | + | 2.32793e7i | −1.22299 | + | 0.153348i | ||||
\(112\) | − | 3.38272e7i | − | 0.214978i | ||||||
\(113\) | 4.56013e7 | 0.279681 | 0.139841 | − | 0.990174i | \(-0.455341\pi\) | ||||
0.139841 | + | 0.990174i | \(0.455341\pi\) | |||||||
\(114\) | −2.59421e7 | − | 2.06894e8i | −0.153598 | − | 1.22498i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.17107e8i | 0.646772i | ||||||||
\(117\) | 7.91647e7 | + | 3.10715e8i | 0.422462 | + | 1.65813i | ||||
\(118\) | − | 2.94188e8i | − | 1.51739i | ||||||
\(119\) | − | 2.84206e7i | − | 0.141725i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.78728e7 | −0.176679 | ||||||||
\(122\) | −2.73879e7 | −0.123629 | ||||||||
\(123\) | 1.72934e8 | − | 2.16839e7i | 0.755544 | − | 0.0947362i | ||||
\(124\) | −1.26727e8 | −0.536022 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.66951e7 | − | 1.04776e8i | −0.105913 | − | 0.415701i | ||||
\(127\) | − | 1.07871e7i | − | 0.0414660i | −0.999785 | − | 0.0207330i | \(-0.993400\pi\) | ||
0.999785 | − | 0.0207330i | \(-0.00659998\pi\) | |||||||
\(128\) | −1.64355e8 | −0.612271 | ||||||||
\(129\) | −1.95149e8 | + | 2.44694e7i | −0.704705 | + | 0.0883616i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.88284e8i | 0.978894i | 0.872033 | + | 0.489447i | \(0.162801\pi\) | ||||
−0.872033 | + | 0.489447i | \(0.837199\pi\) | |||||||
\(132\) | −3.95574e8 | + | 4.96003e7i | −1.30296 | + | 0.163376i | ||||
\(133\) | 7.49648e7i | 0.239580i | ||||||||
\(134\) | 3.70120e8i | 1.14795i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.26097e7 | −0.153784 | ||||||||
\(137\) | −7.39800e7 | −0.210006 | −0.105003 | − | 0.994472i | \(-0.533485\pi\) | ||||
−0.105003 | + | 0.994472i | \(0.533485\pi\) | |||||||
\(138\) | 1.04016e8 | + | 8.29555e8i | 0.286804 | + | 2.28733i | ||||
\(139\) | 4.00966e7 | 0.107411 | 0.0537054 | − | 0.998557i | \(-0.482897\pi\) | ||||
0.0537054 | + | 0.998557i | \(0.482897\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.24452e7 | − | 6.57520e8i | −0.208588 | − | 1.66354i | ||||
\(142\) | − | 6.00726e8i | − | 1.47748i | ||||||
\(143\) | −7.76158e8 | −1.85612 | ||||||||
\(144\) | 3.10457e8 | − | 7.90987e7i | 0.722023 | − | 0.183958i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 5.45197e8i | − | 1.19989i | ||||||
\(147\) | −5.32587e7 | − | 4.24750e8i | −0.114057 | − | 0.909629i | ||||
\(148\) | − | 7.15890e8i | − | 1.49211i | ||||||
\(149\) | 1.80649e8i | 0.366515i | 0.983065 | + | 0.183257i | \(0.0586641\pi\) | ||||
−0.983065 | + | 0.183257i | \(0.941336\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.33011e7 | −0.0832898 | −0.0416449 | − | 0.999132i | \(-0.513260\pi\) | ||||
−0.0416449 | + | 0.999132i | \(0.513260\pi\) | |||||||
\(152\) | 1.38768e8 | 0.259965 | ||||||||
\(153\) | 2.60836e8 | − | 6.64563e7i | 0.475995 | − | 0.121275i | ||||
\(154\) | 2.61728e8 | 0.465337 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.21724e9 | + | 1.52628e8i | −2.05532 | + | 0.257713i | ||||
\(157\) | − | 9.98639e7i | − | 0.164365i | −0.996617 | − | 0.0821826i | \(-0.973811\pi\) | ||
0.996617 | − | 0.0821826i | \(-0.0261891\pi\) | |||||||
\(158\) | −1.07035e9 | −1.71750 | ||||||||
\(159\) | −1.37381e8 | − | 1.09564e9i | −0.214950 | − | 1.71428i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.00576e8i | − | 0.447353i | ||||||
\(162\) | 8.99186e8 | − | 4.90000e8i | 1.30554 | − | 0.711437i | ||||
\(163\) | − | 4.15495e8i | − | 0.588594i | −0.955714 | − | 0.294297i | \(-0.904915\pi\) | ||
0.955714 | − | 0.294297i | \(-0.0950854\pi\) | |||||||
\(164\) | 6.66826e8i | 0.921801i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.04604e8 | 0.664536 | ||||||||
\(167\) | −2.00570e8 | −0.257869 | −0.128935 | − | 0.991653i | \(-0.541156\pi\) | ||||
−0.128935 | + | 0.991653i | \(0.541156\pi\) | |||||||
\(168\) | 7.13981e7 | − | 8.95247e6i | 0.0896292 | − | 0.0112384i | ||||
\(169\) | −1.57263e9 | −1.92788 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.88005e8 | + | 1.75291e8i | −0.804650 | + | 0.205010i | ||||
\(172\) | − | 7.52487e8i | − | 0.859775i | ||||||
\(173\) | 1.07943e9 | 1.20507 | 0.602534 | − | 0.798093i | \(-0.294158\pi\) | ||||
0.602534 | + | 0.798093i | \(0.294158\pi\) | |||||||
\(174\) | 7.22475e8 | − | 9.05898e7i | 0.788181 | − | 0.0988285i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.75511e8i | 0.808234i | ||||||||
\(177\) | −9.93918e8 | + | 1.24626e8i | −1.01265 | + | 0.126974i | ||||
\(178\) | 1.16065e9i | 1.15617i | ||||||||
\(179\) | 4.03427e8i | 0.392964i | 0.980507 | + | 0.196482i | \(0.0629517\pi\) | ||||
−0.980507 | + | 0.196482i | \(0.937048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.48830e8 | −0.884045 | −0.442022 | − | 0.897004i | \(-0.645739\pi\) | ||||
−0.442022 | + | 0.897004i | \(0.645739\pi\) | |||||||
\(182\) | 8.05380e8 | 0.734032 | ||||||||
\(183\) | 1.16022e7 | + | 9.25303e7i | 0.0103451 | + | 0.0825049i | ||||
\(184\) | −5.56399e8 | −0.485417 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.80314e7 | + | 7.81824e8i | 0.0819056 | + | 0.653216i | ||||
\(187\) | 6.51560e8i | 0.532830i | ||||||||
\(188\) | 2.53537e9 | 2.02960 | ||||||||
\(189\) | −3.42680e8 | + | 1.34576e8i | −0.268560 | + | 0.105468i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.09216e9i | 0.820643i | 0.911941 | + | 0.410322i | \(0.134584\pi\) | ||||
−0.911941 | + | 0.410322i | \(0.865416\pi\) | |||||||
\(192\) | 2.31201e8 | + | 1.84388e9i | 0.170132 | + | 1.35684i | ||||
\(193\) | − | 2.66289e9i | − | 1.91921i | −0.281342 | − | 0.959607i | \(-0.590780\pi\) | ||
0.281342 | − | 0.959607i | \(-0.409220\pi\) | |||||||
\(194\) | − | 6.93725e8i | − | 0.489757i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.63782e9 | 1.10979 | ||||||||
\(197\) | −2.31610e9 | −1.53777 | −0.768886 | − | 0.639386i | \(-0.779189\pi\) | ||||
−0.768886 | + | 0.639386i | \(0.779189\pi\) | |||||||
\(198\) | 6.12003e8 | + | 2.40207e9i | 0.398192 | + | 1.56287i | ||||
\(199\) | 9.37508e8 | 0.597809 | 0.298905 | − | 0.954283i | \(-0.403379\pi\) | ||||
0.298905 | + | 0.954283i | \(0.403379\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.25046e9 | − | 1.56792e8i | 0.766097 | − | 0.0960595i | ||||
\(202\) | 1.50344e9i | 0.902984i | ||||||||
\(203\) | −2.61777e8 | −0.154151 | ||||||||
\(204\) | 1.28127e8 | + | 1.02184e9i | 0.0739807 | + | 0.590014i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 1.65177e9i | − | 0.917238i | ||||||
\(207\) | 2.75860e9 | − | 7.02841e8i | 1.50247 | − | 0.382803i | ||||
\(208\) | 2.38637e9i | 1.27493i | ||||||||
\(209\) | − | 1.71861e9i | − | 0.900727i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.14693e9 | 1.08315 | 0.541575 | − | 0.840652i | \(-0.317828\pi\) | ||||
0.541575 | + | 0.840652i | \(0.317828\pi\) | |||||||
\(212\) | 4.22476e9 | 2.09150 | ||||||||
\(213\) | −2.02956e9 | + | 2.54483e8i | −0.986014 | + | 0.123634i | ||||
\(214\) | 5.14340e9 | 2.45242 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.49114e8 | + | 6.34337e8i | 0.114442 | + | 0.291411i | ||||
\(217\) | − | 2.83281e8i | − | 0.127755i | ||||||
\(218\) | −1.66634e9 | −0.737800 | ||||||||
\(219\) | −1.84195e9 | + | 2.30959e8i | −0.800759 | + | 0.100406i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00496e9i | 0.840496i | ||||||||
\(222\) | −4.41658e9 | + | 5.53787e8i | −1.81834 | + | 0.227998i | ||||
\(223\) | − | 3.70772e9i | − | 1.49929i | −0.661838 | − | 0.749647i | \(-0.730223\pi\) | ||
0.661838 | − | 0.749647i | \(-0.269777\pi\) | |||||||
\(224\) | − | 1.03213e9i | − | 0.409960i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.08480e9 | 0.415830 | ||||||||
\(227\) | −3.97024e9 | −1.49525 | −0.747624 | − | 0.664122i | \(-0.768806\pi\) | ||||
−0.747624 | + | 0.664122i | \(0.768806\pi\) | |||||||
\(228\) | −3.37958e8 | − | 2.69530e9i | −0.125061 | − | 0.997395i | ||||
\(229\) | −2.84129e9 | −1.03317 | −0.516587 | − | 0.856235i | \(-0.672798\pi\) | ||||
−0.516587 | + | 0.856235i | \(0.672798\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.10875e8 | − | 8.84252e8i | −0.0389390 | − | 0.310547i | ||||
\(232\) | 4.84578e8i | 0.167268i | ||||||||
\(233\) | −3.80946e8 | −0.129253 | −0.0646264 | − | 0.997910i | \(-0.520586\pi\) | ||||
−0.0646264 | + | 0.997910i | \(0.520586\pi\) | |||||||
\(234\) | 1.88323e9 | + | 7.39154e9i | 0.628117 | + | 2.46531i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 3.83251e9i | − | 1.23548i | ||||||
\(237\) | 4.53426e8 | + | 3.61618e9i | 0.143719 | + | 1.14619i | ||||
\(238\) | − | 6.76092e8i | − | 0.210716i | ||||||
\(239\) | − | 3.08542e9i | − | 0.945633i | −0.881161 | − | 0.472817i | \(-0.843237\pi\) | ||
0.881161 | − | 0.472817i | \(-0.156763\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.83623e9 | −0.544326 | −0.272163 | − | 0.962251i | \(-0.587739\pi\) | ||||
−0.272163 | + | 0.962251i | \(0.587739\pi\) | |||||||
\(242\) | −9.00948e8 | −0.262687 | ||||||||
\(243\) | −2.03639e9 | − | 2.83033e9i | −0.584031 | − | 0.811731i | ||||
\(244\) | −3.56793e8 | −0.100660 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.11389e9 | − | 5.15833e8i | 1.12334 | − | 0.140854i | ||||
\(247\) | − | 5.28845e9i | − | 1.42083i | ||||||
\(248\) | −5.24384e8 | −0.138625 | ||||||||
\(249\) | −2.13763e8 | − | 1.70481e9i | −0.0556077 | − | 0.443485i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4.14381e9i | − | 1.04401i | −0.852942 | − | 0.522005i | \(-0.825184\pi\) | ||
0.852942 | − | 0.522005i | \(-0.174816\pi\) | |||||||
\(252\) | −3.47769e8 | − | 1.36497e9i | −0.0862359 | − | 0.338469i | ||||
\(253\) | 6.89089e9i | 1.68187i | ||||||||
\(254\) | − | 2.56613e8i | − | 0.0616515i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.96340e9 | 0.457141 | ||||||||
\(257\) | 1.12642e9 | 0.258207 | 0.129104 | − | 0.991631i | \(-0.458790\pi\) | ||||
0.129104 | + | 0.991631i | \(0.458790\pi\) | |||||||
\(258\) | −4.64235e9 | + | 5.82096e8i | −1.04775 | + | 0.131376i | ||||
\(259\) | 1.60028e9 | 0.355628 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.12117e8 | − | 2.40251e9i | −0.131908 | − | 0.517731i | ||||
\(262\) | 6.85793e9i | 1.45542i | ||||||||
\(263\) | 6.91865e9 | 1.44610 | 0.723050 | − | 0.690796i | \(-0.242740\pi\) | ||||
0.723050 | + | 0.690796i | \(0.242740\pi\) | |||||||
\(264\) | −1.63685e9 | + | 2.05241e8i | −0.336971 | + | 0.0422521i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.78332e9i | 0.356207i | ||||||||
\(267\) | 3.92127e9 | − | 4.91680e8i | 0.771581 | − | 0.0967470i | ||||
\(268\) | 4.82171e9i | 0.934677i | ||||||||
\(269\) | 1.04065e9i | 0.198744i | 0.995050 | + | 0.0993720i | \(0.0316834\pi\) | ||||
−0.995050 | + | 0.0993720i | \(0.968317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.30357e9 | −0.797906 | −0.398953 | − | 0.916971i | \(-0.630626\pi\) | ||||
−0.398953 | + | 0.916971i | \(0.630626\pi\) | |||||||
\(272\) | 2.00329e9 | 0.365988 | ||||||||
\(273\) | −3.41179e8 | − | 2.72099e9i | −0.0614231 | − | 0.489864i | ||||
\(274\) | −1.75989e9 | −0.312237 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.35506e9 | + | 1.08070e10i | 0.233520 | + | 1.86237i | ||||
\(277\) | 1.01360e10i | 1.72166i | 0.508889 | + | 0.860832i | \(0.330056\pi\) | ||||
−0.508889 | + | 0.860832i | \(0.669944\pi\) | |||||||
\(278\) | 9.53848e8 | 0.159698 | ||||||||
\(279\) | 2.59987e9 | − | 6.62400e8i | 0.429077 | − | 0.109321i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.82598e9i | 1.41559i | 0.706418 | + | 0.707795i | \(0.250310\pi\) | ||||
−0.706418 | + | 0.707795i | \(0.749690\pi\) | |||||||
\(282\) | −1.96127e9 | − | 1.56416e10i | −0.310128 | − | 2.47335i | ||||
\(283\) | 1.58051e9i | 0.246405i | 0.992382 | + | 0.123203i | \(0.0393165\pi\) | ||||
−0.992382 | + | 0.123203i | \(0.960683\pi\) | |||||||
\(284\) | − | 7.82590e9i | − | 1.20299i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.84638e10 | −2.75967 | ||||||||
\(287\) | −1.49060e9 | −0.219702 | ||||||||
\(288\) | 9.47258e9 | − | 2.41344e9i | 1.37689 | − | 0.350806i | ||||
\(289\) | −5.29266e9 | −0.758722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.34376e9 | + | 2.93880e8i | −0.326844 | + | 0.0409824i | ||||
\(292\) | − | 7.10250e9i | − | 0.976967i | ||||||
\(293\) | 7.30987e8 | 0.0991835 | 0.0495917 | − | 0.998770i | \(-0.484208\pi\) | ||||
0.0495917 | + | 0.998770i | \(0.484208\pi\) | |||||||
\(294\) | −1.26696e9 | − | 1.01043e10i | −0.169579 | − | 1.35244i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 2.96228e9i | − | 0.385887i | ||||||
\(297\) | 7.85614e9 | − | 3.08523e9i | 1.00968 | − | 0.396517i | ||||
\(298\) | 4.29743e9i | 0.544934i | ||||||||
\(299\) | 2.12044e10i | 2.65302i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.68208e9 | 0.204918 | ||||||||
\(302\) | −1.03008e9 | −0.123835 | ||||||||
\(303\) | 5.07938e9 | − | 6.36894e8i | 0.602616 | − | 0.0755609i | ||||
\(304\) | −5.28405e9 | −0.618689 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.20497e9 | − | 1.58092e9i | 0.707708 | − | 0.180311i | ||||
\(307\) | − | 8.05460e9i | − | 0.906757i | −0.891318 | − | 0.453378i | \(-0.850219\pi\) | ||
0.891318 | − | 0.453378i | \(-0.149781\pi\) | |||||||
\(308\) | 3.40964e9 | 0.378884 | ||||||||
\(309\) | −5.58054e9 | + | 6.99733e8i | −0.612128 | + | 0.0767536i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.28173e9i | 0.243906i | 0.992536 | + | 0.121953i | \(0.0389157\pi\) | ||||
−0.992536 | + | 0.121953i | \(0.961084\pi\) | |||||||
\(312\) | −5.03684e9 | + | 6.31560e8i | −0.531545 | + | 0.0666494i | ||||
\(313\) | 3.40795e9i | 0.355072i | 0.984114 | + | 0.177536i | \(0.0568126\pi\) | ||||
−0.984114 | + | 0.177536i | \(0.943187\pi\) | |||||||
\(314\) | − | 2.37564e9i | − | 0.244378i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.39439e10 | −1.39841 | ||||||||
\(317\) | 2.80342e9 | 0.277620 | 0.138810 | − | 0.990319i | \(-0.455672\pi\) | ||||
0.138810 | + | 0.990319i | \(0.455672\pi\) | |||||||
\(318\) | −3.26812e9 | − | 2.60640e10i | −0.319587 | − | 2.54879i | ||||
\(319\) | 6.00140e9 | 0.579549 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.17887e9 | − | 1.73770e10i | −0.205216 | − | 1.63665i | ||||
\(322\) | − | 7.15034e9i | − | 0.665125i | ||||||
\(323\) | −4.43950e9 | −0.407872 | ||||||||
\(324\) | 1.17141e10 | − | 6.38344e9i | 1.06299 | − | 0.579261i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 9.88412e9i | − | 0.875120i | ||||||
\(327\) | 7.05906e8 | + | 5.62976e9i | 0.0617384 | + | 0.492379i | ||||
\(328\) | 2.75926e9i | 0.238395i | ||||||||
\(329\) | 5.66748e9i | 0.483734i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.85817e9 | −0.321417 | −0.160709 | − | 0.987002i | \(-0.551378\pi\) | ||||
−0.160709 | + | 0.987002i | \(0.551378\pi\) | |||||||
\(332\) | 6.57368e9 | 0.541074 | ||||||||
\(333\) | 3.74195e9 | + | 1.46869e10i | 0.304313 | + | 1.19441i | ||||
\(334\) | −4.77131e9 | −0.383400 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.71872e9 | + | 3.40895e8i | −0.213308 | + | 0.0267463i | ||||
\(337\) | − | 4.33270e9i | − | 0.335922i | −0.985794 | − | 0.167961i | \(-0.946282\pi\) | ||
0.985794 | − | 0.167961i | \(-0.0537183\pi\) | |||||||
\(338\) | −3.74110e10 | −2.86637 | ||||||||
\(339\) | −4.59548e8 | − | 3.66500e9i | −0.0347962 | − | 0.277508i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.49440e9i | 0.480310i | ||||||||
\(342\) | −1.63668e10 | + | 4.16997e9i | −1.19635 | + | 0.304809i | ||||
\(343\) | 7.65471e9i | 0.553035i | ||||||||
\(344\) | − | 3.11372e9i | − | 0.222354i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.56784e10 | 1.79169 | ||||||||
\(347\) | 1.49997e9 | 0.103458 | 0.0517291 | − | 0.998661i | \(-0.483527\pi\) | ||||
0.0517291 | + | 0.998661i | \(0.483527\pi\) | |||||||
\(348\) | 9.41198e9 | − | 1.18015e9i | 0.641747 | − | 0.0804675i | ||||
\(349\) | 1.91502e10 | 1.29084 | 0.645418 | − | 0.763830i | \(-0.276683\pi\) | ||||
0.645418 | + | 0.763830i | \(0.276683\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.41746e10 | − | 9.49376e9i | 1.59269 | − | 0.625475i | ||||
\(352\) | 2.36622e10i | 1.54129i | ||||||||
\(353\) | −2.74321e10 | −1.76669 | −0.883345 | − | 0.468723i | \(-0.844714\pi\) | ||||
−0.883345 | + | 0.468723i | \(0.844714\pi\) | |||||||
\(354\) | −2.36441e10 | + | 2.96469e9i | −1.50560 | + | 0.188784i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.51202e10i | 0.941367i | ||||||||
\(357\) | −2.28418e9 | + | 2.86410e8i | −0.140624 | + | 0.0176325i | ||||
\(358\) | 9.59704e9i | 0.584258i | ||||||||
\(359\) | 7.34907e9i | 0.442440i | 0.975224 | + | 0.221220i | \(0.0710039\pi\) | ||||
−0.975224 | + | 0.221220i | \(0.928996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.27355e9 | −0.310509 | ||||||||
\(362\) | −2.25715e10 | −1.31440 | ||||||||
\(363\) | 3.81664e8 | + | 3.04386e9i | 0.0219814 | + | 0.175307i | ||||
\(364\) | 1.04920e10 | 0.597659 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.76002e8 | + | 2.20118e9i | 0.0153811 | + | 0.122668i | ||||
\(367\) | 6.53522e9i | 0.360243i | 0.983644 | + | 0.180122i | \(0.0576492\pi\) | ||||
−0.983644 | + | 0.180122i | \(0.942351\pi\) | |||||||
\(368\) | 2.11867e10 | 1.15524 | ||||||||
\(369\) | −3.48549e9 | − | 1.36803e10i | −0.188000 | − | 0.737887i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.44388e9i | 0.498488i | ||||||||
\(372\) | 1.27710e9 | + | 1.01851e10i | 0.0666886 | + | 0.531857i | ||||
\(373\) | − | 3.22724e10i | − | 1.66723i | −0.552346 | − | 0.833615i | \(-0.686267\pi\) | ||
0.552346 | − | 0.833615i | \(-0.313733\pi\) | |||||||
\(374\) | 1.54998e10i | 0.792210i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.04911e10 | 0.524893 | ||||||||
\(377\) | 1.84673e10 | 0.914193 | ||||||||
\(378\) | −8.15193e9 | + | 3.20139e9i | −0.399294 | + | 0.156809i | ||||
\(379\) | 2.00937e10 | 0.973875 | 0.486938 | − | 0.873437i | \(-0.338114\pi\) | ||||
0.486938 | + | 0.873437i | \(0.338114\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.66970e8 | + | 1.08708e8i | −0.0411438 | + | 0.00515894i | ||||
\(382\) | 2.59813e10i | 1.22013i | ||||||||
\(383\) | 2.64566e10 | 1.22953 | 0.614765 | − | 0.788711i | \(-0.289251\pi\) | ||||
0.614765 | + | 0.788711i | \(0.289251\pi\) | |||||||
\(384\) | 1.65630e9 | + | 1.32093e10i | 0.0761751 | + | 0.607514i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 6.33469e10i | − | 2.85349i | ||||||
\(387\) | 3.93324e9 | + | 1.54377e10i | 0.175350 | + | 0.688236i | ||||
\(388\) | − | 9.03744e9i | − | 0.398766i | ||||||
\(389\) | − | 2.69010e10i | − | 1.17482i | −0.809291 | − | 0.587408i | \(-0.800149\pi\) | ||
0.809291 | − | 0.587408i | \(-0.199851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.78004e10 | 0.761594 | ||||||||
\(392\) | 6.77715e9 | 0.287014 | ||||||||
\(393\) | 2.31696e10 | − | 2.90519e9i | 0.971288 | − | 0.121788i | ||||
\(394\) | −5.50971e10 | −2.28636 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.97281e9 | + | 3.12927e10i | 0.324213 | + | 1.27251i | ||||
\(397\) | − | 2.18233e10i | − | 0.878533i | −0.898357 | − | 0.439266i | \(-0.855238\pi\) | ||
0.898357 | − | 0.439266i | \(-0.144762\pi\) | |||||||
\(398\) | 2.23022e10 | 0.888822 | ||||||||
\(399\) | 6.02497e9 | − | 7.55460e8i | 0.237719 | − | 0.0298071i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.86361e10i | 1.49422i | 0.664698 | + | 0.747112i | \(0.268560\pi\) | ||||
−0.664698 | + | 0.747112i | \(0.731440\pi\) | |||||||
\(402\) | 2.97468e10 | − | 3.72990e9i | 1.13903 | − | 0.142821i | ||||
\(403\) | 1.99843e10i | 0.757651i | ||||||||
\(404\) | 1.95859e10i | 0.735222i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.22736e9 | −0.229192 | ||||||||
\(407\) | −3.66873e10 | −1.33702 | ||||||||
\(408\) | 5.30175e8 | + | 4.22827e9i | 0.0191328 | + | 0.152589i | ||||
\(409\) | 1.02245e10 | 0.365385 | 0.182692 | − | 0.983170i | \(-0.441519\pi\) | ||||
0.182692 | + | 0.983170i | \(0.441519\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.45535e8 | + | 5.94582e9i | 0.0261277 | + | 0.208375i | ||||
\(412\) | − | 2.15183e10i | − | 0.746827i | ||||||
\(413\) | 8.56705e9 | 0.294463 | ||||||||
\(414\) | 6.56237e10 | − | 1.67197e10i | 2.23388 | − | 0.569152i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.28124e10i | 2.43126i | ||||||||
\(417\) | −4.04074e8 | − | 3.22259e9i | −0.0133634 | − | 0.106576i | ||||
\(418\) | − | 4.08838e10i | − | 1.33920i | ||||||
\(419\) | − | 3.03535e10i | − | 0.984812i | −0.870366 | − | 0.492406i | \(-0.836118\pi\) | ||
0.870366 | − | 0.492406i | \(-0.163882\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.94064e10 | 1.25441 | 0.627203 | − | 0.778856i | \(-0.284200\pi\) | ||||
0.627203 | + | 0.778856i | \(0.284200\pi\) | |||||||
\(422\) | 5.10729e10 | 1.61043 | ||||||||
\(423\) | −5.20145e10 | + | 1.32524e10i | −1.62466 | + | 0.413934i | ||||
\(424\) | 1.74817e10 | 0.540903 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.82807e10 | + | 6.05383e9i | −1.46600 | + | 0.183820i | ||||
\(427\) | − | 7.97563e8i | − | 0.0239913i | ||||||
\(428\) | 6.70052e10 | 1.99679 | ||||||||
\(429\) | 7.82175e9 | + | 6.23803e10i | 0.230927 | + | 1.84170i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.00931e10i | − | 0.582288i | −0.956679 | − | 0.291144i | \(-0.905964\pi\) | ||
0.956679 | − | 0.291144i | \(-0.0940358\pi\) | |||||||
\(432\) | −9.48585e9 | − | 2.41545e10i | −0.272359 | − | 0.693526i | ||||
\(433\) | 4.76129e10i | 1.35448i | 0.735761 | + | 0.677241i | \(0.236824\pi\) | ||||
−0.735761 | + | 0.677241i | \(0.763176\pi\) | |||||||
\(434\) | − | 6.73891e9i | − | 0.189946i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.17082e10 | −0.600727 | ||||||||
\(437\) | −4.69520e10 | −1.28744 | ||||||||
\(438\) | −4.38178e10 | + | 5.49423e9i | −1.19057 | + | 0.149283i | ||||
\(439\) | 2.80845e10 | 0.756151 | 0.378076 | − | 0.925775i | \(-0.376586\pi\) | ||||
0.378076 | + | 0.925775i | \(0.376586\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.36008e10 | + | 8.56087e9i | −0.888372 | + | 0.226341i | ||||
\(442\) | 4.76955e10i | 1.24965i | ||||||||
\(443\) | −3.22901e9 | −0.0838407 | −0.0419204 | − | 0.999121i | \(-0.513348\pi\) | ||||
−0.0419204 | + | 0.999121i | \(0.513348\pi\) | |||||||
\(444\) | −5.75366e10 | + | 7.21440e9i | −1.48051 | + | 0.185639i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 8.82020e10i | − | 2.22915i | ||||||
\(447\) | 1.45189e10 | − | 1.82050e9i | 0.363667 | − | 0.0455995i | ||||
\(448\) | − | 1.58933e10i | − | 0.394551i | ||||||
\(449\) | − | 4.21051e10i | − | 1.03598i | −0.855388 | − | 0.517988i | \(-0.826681\pi\) | ||
0.855388 | − | 0.517988i | \(-0.173319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.41729e10 | 0.825993 | ||||||||
\(452\) | 1.41321e10 | 0.338574 | ||||||||
\(453\) | 4.36368e8 | + | 3.48014e9i | 0.0103624 | + | 0.0826426i | ||||
\(454\) | −9.44472e10 | −2.22313 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.39844e9 | − | 1.11529e10i | −0.0323433 | − | 0.257945i | ||||
\(457\) | − | 4.14329e10i | − | 0.949905i | −0.880011 | − | 0.474952i | \(-0.842465\pi\) | ||
0.880011 | − | 0.474952i | \(-0.157535\pi\) | |||||||
\(458\) | −6.75908e10 | −1.53612 | ||||||||
\(459\) | −7.96972e9 | − | 2.02939e10i | −0.179553 | − | 0.457208i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.44199e10i | − | 1.64773i | −0.566789 | − | 0.823863i | \(-0.691814\pi\) | ||
0.566789 | − | 0.823863i | \(-0.308186\pi\) | |||||||
\(462\) | −2.63757e9 | − | 2.10353e10i | −0.0578944 | − | 0.461722i | ||||
\(463\) | − | 4.57191e10i | − | 0.994887i | −0.867496 | − | 0.497444i | \(-0.834272\pi\) | ||
0.867496 | − | 0.497444i | \(-0.165728\pi\) | |||||||
\(464\) | − | 1.84519e10i | − | 0.398079i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.06225e9 | −0.192173 | ||||||||
\(467\) | 2.76952e9 | 0.0582286 | 0.0291143 | − | 0.999576i | \(-0.490731\pi\) | ||||
0.0291143 | + | 0.999576i | \(0.490731\pi\) | |||||||
\(468\) | 2.45336e10 | + | 9.62926e10i | 0.511421 | + | 2.00729i | ||||
\(469\) | −1.07783e10 | −0.222771 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.02613e9 | + | 1.00638e9i | −0.163088 | + | 0.0204493i | ||||
\(472\) | − | 1.58586e10i | − | 0.319518i | ||||||
\(473\) | −3.85628e10 | −0.770413 | ||||||||
\(474\) | 1.07865e10 | + | 8.60245e10i | 0.213681 | + | 1.70415i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 8.80772e9i | − | 0.171568i | ||||||
\(477\) | −8.66732e10 | + | 2.20828e10i | −1.67422 | + | 0.426560i | ||||
\(478\) | − | 7.33984e10i | − | 1.40597i | ||||||
\(479\) | 3.82055e10i | 0.725744i | 0.931839 | + | 0.362872i | \(0.118204\pi\) | ||||
−0.931839 | + | 0.362872i | \(0.881796\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.12893e11 | −2.10905 | ||||||||
\(482\) | −4.36817e10 | −0.809303 | ||||||||
\(483\) | −2.41575e10 | + | 3.02906e9i | −0.443878 | + | 0.0556570i | ||||
\(484\) | −1.17370e10 | −0.213883 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.84432e10 | − | 6.73302e10i | −0.868336 | − | 1.20688i | ||||
\(487\) | − | 2.79097e10i | − | 0.496179i | −0.968737 | − | 0.248090i | \(-0.920197\pi\) | ||
0.968737 | − | 0.248090i | \(-0.0798028\pi\) | |||||||
\(488\) | −1.47638e9 | −0.0260326 | ||||||||
\(489\) | −3.33936e10 | + | 4.18716e9i | −0.584021 | + | 0.0732292i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.62482e10i | 0.623677i | 0.950135 | + | 0.311839i | \(0.100945\pi\) | ||||
−0.950135 | + | 0.311839i | \(0.899055\pi\) | |||||||
\(492\) | 5.35933e10 | − | 6.71996e9i | 0.914639 | − | 0.114685i | ||||
\(493\) | − | 1.55027e10i | − | 0.262434i | ||||||
\(494\) | − | 1.25806e11i | − | 2.11248i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.99677e10 | 0.329914 | ||||||||
\(497\) | 1.74937e10 | 0.286719 | ||||||||
\(498\) | −5.08516e9 | − | 4.05554e10i | −0.0826775 | − | 0.659373i | ||||
\(499\) | 1.31298e10 | 0.211765 | 0.105883 | − | 0.994379i | \(-0.466233\pi\) | ||||
0.105883 | + | 0.994379i | \(0.466233\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.02125e9 | + | 1.61199e10i | 0.0320825 | + | 0.255866i | ||||
\(502\) | − | 9.85762e10i | − | 1.55223i | ||||||
\(503\) | −1.84778e10 | −0.288654 | −0.144327 | − | 0.989530i | \(-0.546102\pi\) | ||||
−0.144327 | + | 0.989530i | \(0.546102\pi\) | |||||||
\(504\) | −1.43903e9 | − | 5.64809e9i | −0.0223022 | − | 0.0875346i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.63926e11i | 2.50061i | ||||||||
\(507\) | 1.58482e10 | + | 1.26393e11i | 0.239855 | + | 1.91290i | ||||
\(508\) | − | 3.34300e9i | − | 0.0501975i | ||||||
\(509\) | 7.39108e10i | 1.10112i | 0.834794 | + | 0.550562i | \(0.185587\pi\) | ||||
−0.834794 | + | 0.550562i | \(0.814413\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.58767e10 | 0.232850 | ||||||||
\(512\) | 8.87820e10 | 1.29195 | ||||||||
\(513\) | 2.10217e10 | + | 5.35289e10i | 0.303527 | + | 0.772892i | ||||
\(514\) | 2.67962e10 | 0.383902 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.04778e10 | + | 7.58320e9i | −0.853095 | + | 0.106968i | ||||
\(517\) | − | 1.29931e11i | − | 1.81865i | ||||||
\(518\) | 3.80686e10 | 0.528747 | ||||||||
\(519\) | −1.08780e10 | − | 8.67548e10i | −0.149927 | − | 1.19571i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.94911e10i | − | 1.07887i | −0.842029 | − | 0.539433i | \(-0.818639\pi\) | ||
0.842029 | − | 0.539433i | \(-0.181361\pi\) | |||||||
\(522\) | −1.45615e10 | − | 5.71529e10i | −0.196121 | − | 0.769761i | ||||
\(523\) | 3.03522e10i | 0.405680i | 0.979212 | + | 0.202840i | \(0.0650171\pi\) | ||||
−0.979212 | + | 0.202840i | \(0.934983\pi\) | |||||||
\(524\) | 8.93410e10i | 1.18502i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.64586e11 | 2.15006 | ||||||||
\(527\) | 1.67762e10 | 0.217496 | ||||||||
\(528\) | 6.23283e10 | − | 7.81523e9i | 0.801955 | − | 0.100556i | ||||
\(529\) | 1.09946e11 | 1.40397 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.00325e10 | + | 7.86259e10i | 0.251974 | + | 0.988980i | ||||
\(532\) | 2.32320e10i | 0.290029i | ||||||||
\(533\) | 1.05156e11 | 1.30294 | ||||||||
\(534\) | 9.32821e10 | − | 1.16965e10i | 1.14719 | − | 0.143843i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.99518e10i | 0.241725i | ||||||||
\(537\) | 3.24237e10 | − | 4.06555e9i | 0.389911 | − | 0.0488902i | ||||
\(538\) | 2.47557e10i | 0.295492i | ||||||||
\(539\) | − | 8.39336e10i | − | 0.994446i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.53261e10 | −0.412389 | −0.206195 | − | 0.978511i | \(-0.566108\pi\) | ||||
−0.206195 | + | 0.978511i | \(0.566108\pi\) | |||||||
\(542\) | −1.02377e11 | −1.18633 | ||||||||
\(543\) | 9.56187e9 | + | 7.62581e10i | 0.109987 | + | 0.877176i | ||||
\(544\) | 6.11238e10 | 0.697935 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.11624e9 | − | 6.47289e10i | −0.0913239 | − | 0.728329i | ||||
\(547\) | 1.62586e11i | 1.81607i | 0.418891 | + | 0.908036i | \(0.362419\pi\) | ||||
−0.418891 | + | 0.908036i | \(0.637581\pi\) | |||||||
\(548\) | −2.29269e10 | −0.254227 | ||||||||
\(549\) | 7.31980e9 | − | 1.86495e9i | 0.0805768 | − | 0.0205295i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.08914e10i | 0.443635i | ||||||||
\(552\) | 5.60712e9 | + | 4.47181e10i | 0.0603926 | + | 0.481645i | ||||
\(553\) | − | 3.11696e10i | − | 0.333296i | ||||||
\(554\) | 2.41124e11i | 2.55977i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.24262e10 | 0.130028 | ||||||||
\(557\) | 1.81639e11 | 1.88707 | 0.943535 | − | 0.331273i | \(-0.107478\pi\) | ||||
0.943535 | + | 0.331273i | \(0.107478\pi\) | |||||||
\(558\) | 6.18478e10 | − | 1.57577e10i | 0.637951 | − | 0.162538i | ||||
\(559\) | −1.18664e11 | −1.21527 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.23663e10 | − | 6.56612e9i | 0.528690 | − | 0.0662914i | ||||
\(562\) | 2.09959e11i | 2.10470i | ||||||||
\(563\) | 6.38376e10 | 0.635394 | 0.317697 | − | 0.948192i | \(-0.397090\pi\) | ||||
0.317697 | + | 0.948192i | \(0.397090\pi\) | |||||||
\(564\) | −2.55503e10 | − | 2.03770e11i | −0.252510 | − | 2.01383i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.75983e10i | 0.366355i | ||||||||
\(567\) | 1.42693e10 | + | 2.61852e10i | 0.138061 | + | 0.253352i | ||||
\(568\) | − | 3.23828e10i | − | 0.311115i | ||||||
\(569\) | 1.31605e10i | 0.125552i | 0.998028 | + | 0.0627760i | \(0.0199954\pi\) | ||||
−0.998028 | + | 0.0627760i | \(0.980005\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.09445e10 | 0.667382 | 0.333691 | − | 0.942683i | \(-0.391706\pi\) | ||||
0.333691 | + | 0.942683i | \(0.391706\pi\) | |||||||
\(572\) | −2.40536e11 | −2.24696 | ||||||||
\(573\) | 8.77780e10 | − | 1.10063e10i | 0.814267 | − | 0.102099i | ||||
\(574\) | −3.54596e10 | −0.326652 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.45864e11 | − | 3.71636e10i | 1.32513 | − | 0.337620i | ||||
\(577\) | − | 1.05284e11i | − | 0.949859i | −0.880024 | − | 0.474929i | \(-0.842474\pi\) | ||
0.880024 | − | 0.474929i | \(-0.157526\pi\) | |||||||
\(578\) | −1.25906e11 | −1.12807 | ||||||||
\(579\) | −2.14018e11 | + | 2.68353e10i | −1.90430 | + | 0.238777i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.46946e10i | 0.128959i | ||||||||
\(582\) | −5.57552e10 | + | 6.99104e9i | −0.485952 | + | 0.0609326i | ||||
\(583\) | − | 2.16507e11i | − | 1.87412i | ||||||
\(584\) | − | 2.93895e10i | − | 0.252662i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.73893e10 | 0.147466 | ||||||||
\(587\) | −3.67507e10 | −0.309538 | −0.154769 | − | 0.987951i | \(-0.549463\pi\) | ||||
−0.154769 | + | 0.987951i | \(0.549463\pi\) | |||||||
\(588\) | −1.65052e10 | − | 1.31633e11i | −0.138074 | − | 1.10117i | ||||
\(589\) | −4.42505e10 | −0.367669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.33405e10 | + | 1.86146e11i | 0.191320 | + | 1.52582i | ||||
\(592\) | 1.12799e11i | 0.918370i | ||||||||
\(593\) | −2.06347e11 | −1.66870 | −0.834351 | − | 0.551234i | \(-0.814157\pi\) | ||||
−0.834351 | + | 0.551234i | \(0.814157\pi\) | |||||||
\(594\) | 1.86888e11 | − | 7.33940e10i | 1.50119 | − | 0.589542i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.59843e10i | 0.443692i | ||||||||
\(597\) | −9.44776e9 | − | 7.53481e10i | −0.0743758 | − | 0.593164i | ||||
\(598\) | 5.04427e11i | 3.94451i | ||||||||
\(599\) | 1.66792e11i | 1.29559i | 0.761813 | + | 0.647797i | \(0.224310\pi\) | ||||
−0.761813 | + | 0.647797i | \(0.775690\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.53051e11 | −1.17311 | −0.586555 | − | 0.809909i | \(-0.699516\pi\) | ||||
−0.586555 | + | 0.809909i | \(0.699516\pi\) | |||||||
\(602\) | 4.00147e10 | 0.304673 | ||||||||
\(603\) | −2.52030e10 | − | 9.89199e10i | −0.190626 | − | 0.748194i | ||||
\(604\) | −1.34193e10 | −0.100828 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.20832e11 | − | 1.51509e10i | 0.895969 | − | 0.112344i | ||||
\(607\) | 2.06970e11i | 1.52459i | 0.647233 | + | 0.762293i | \(0.275926\pi\) | ||||
−0.647233 | + | 0.762293i | \(0.724074\pi\) | |||||||
\(608\) | −1.61226e11 | −1.17983 | ||||||||
\(609\) | 2.63807e9 | + | 2.10392e10i | 0.0191786 | + | 0.152954i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.99817e11i | − | 2.86878i | ||||||
\(612\) | 8.08347e10 | − | 2.05952e10i | 0.576225 | − | 0.146812i | ||||
\(613\) | − | 1.06596e11i | − | 0.754913i | −0.926027 | − | 0.377457i | \(-0.876799\pi\) | ||
0.926027 | − | 0.377457i | \(-0.123201\pi\) | |||||||
\(614\) | − | 1.91609e11i | − | 1.34816i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.41088e10 | 0.0979865 | ||||||||
\(617\) | 1.06362e11 | 0.733914 | 0.366957 | − | 0.930238i | \(-0.380400\pi\) | ||||
0.366957 | + | 0.930238i | \(0.380400\pi\) | |||||||
\(618\) | −1.32754e11 | + | 1.66458e10i | −0.910111 | + | 0.114117i | ||||
\(619\) | 1.57576e11 | 1.07332 | 0.536659 | − | 0.843799i | \(-0.319686\pi\) | ||||
0.536659 | + | 0.843799i | \(0.319686\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.42877e10 | − | 2.14627e11i | −0.566758 | − | 1.44317i | ||||
\(622\) | 5.42795e10i | 0.362639i | ||||||||
\(623\) | −3.37993e10 | −0.224365 | ||||||||
\(624\) | 1.91794e11 | − | 2.40487e10i | 1.26502 | − | 0.158618i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.10711e10i | 0.527920i | ||||||||
\(627\) | −1.38126e11 | + | 1.73194e10i | −0.893729 | + | 0.112063i | ||||
\(628\) | − | 3.09484e10i | − | 0.198976i | ||||||
\(629\) | 9.47701e10i | 0.605436i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.74992e11 | 1.73461 | 0.867306 | − | 0.497775i | \(-0.165850\pi\) | ||||
0.867306 | + | 0.497775i | \(0.165850\pi\) | |||||||
\(632\) | −5.76983e10 | −0.361655 | ||||||||
\(633\) | −2.16358e10 | − | 1.72550e11i | −0.134759 | − | 1.07473i | ||||
\(634\) | 6.66900e10 | 0.412766 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.25752e10 | − | 3.39547e11i | −0.260212 | − | 2.07525i | ||||
\(637\) | − | 2.58277e11i | − | 1.56866i | ||||||
\(638\) | 1.42766e11 | 0.861673 | ||||||||
\(639\) | 4.09059e10 | + | 1.60552e11i | 0.245348 | + | 0.962971i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.88263e11i | 1.70749i | 0.520695 | + | 0.853743i | \(0.325673\pi\) | ||||
−0.520695 | + | 0.853743i | \(0.674327\pi\) | |||||||
\(642\) | −5.18328e10 | − | 4.13379e11i | −0.305116 | − | 2.43337i | ||||
\(643\) | 2.34011e11i | 1.36896i | 0.729030 | + | 0.684481i | \(0.239971\pi\) | ||||
−0.729030 | + | 0.684481i | \(0.760029\pi\) | |||||||
\(644\) | − | 9.31503e10i | − | 0.541553i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.05610e11 | −0.606423 | ||||||||
\(647\) | 1.59734e11 | 0.911551 | 0.455775 | − | 0.890095i | \(-0.349362\pi\) | ||||
0.455775 | + | 0.890095i | \(0.349362\pi\) | |||||||
\(648\) | 4.84716e10 | − | 2.64140e10i | 0.274908 | − | 0.149808i | ||||
\(649\) | −1.96405e11 | −1.10707 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.27675e10 | + | 2.85477e9i | −0.126763 | + | 0.0158945i | ||||
\(652\) | − | 1.28765e11i | − | 0.712534i | ||||||
\(653\) | 1.20294e11 | 0.661596 | 0.330798 | − | 0.943702i | \(-0.392682\pi\) | ||||
0.330798 | + | 0.943702i | \(0.392682\pi\) | |||||||
\(654\) | 1.67926e10 | + | 1.33925e11i | 0.0917926 | + | 0.732068i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1.05068e11i | − | 0.567356i | ||||||
\(657\) | 3.71247e10 | + | 1.45711e11i | 0.199251 | + | 0.782046i | ||||
\(658\) | 1.34822e11i | 0.719215i | ||||||||
\(659\) | 9.51290e10i | 0.504396i | 0.967676 | + | 0.252198i | \(0.0811534\pi\) | ||||
−0.967676 | + | 0.252198i | \(0.918847\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.37799e11 | −1.76951 | −0.884755 | − | 0.466056i | \(-0.845674\pi\) | ||||
−0.884755 | + | 0.466056i | \(0.845674\pi\) | |||||||
\(662\) | −9.17811e10 | −0.477882 | ||||||||
\(663\) | 1.61140e11 | − | 2.02050e10i | 0.833966 | − | 0.104569i | ||||
\(664\) | 2.72013e10 | 0.139932 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.90164e10 | + | 3.49383e11i | 0.452453 | + | 1.77584i | ||||
\(667\) | − | 1.63957e11i | − | 0.828372i | ||||||
\(668\) | −6.21578e10 | −0.312169 | ||||||||
\(669\) | −2.97992e11 | + | 3.73646e10i | −1.48765 | + | 0.186533i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.82846e10i | 0.0901978i | ||||||||
\(672\) | −8.29529e10 | + | 1.04013e10i | −0.406775 | + | 0.0510048i | ||||
\(673\) | − | 1.01484e11i | − | 0.494693i | −0.968927 | − | 0.247347i | \(-0.920441\pi\) | ||
0.968927 | − | 0.247347i | \(-0.0795586\pi\) | |||||||
\(674\) | − | 1.03070e11i | − | 0.499449i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.87368e11 | −2.33384 | ||||||||
\(677\) | −1.58724e11 | −0.755595 | −0.377797 | − | 0.925888i | \(-0.623318\pi\) | ||||
−0.377797 | + | 0.925888i | \(0.623318\pi\) | |||||||
\(678\) | −1.09321e10 | − | 8.71860e10i | −0.0517350 | − | 0.412599i | ||||
\(679\) | 2.02020e10 | 0.0950418 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.00102e10 | + | 3.19091e11i | 0.186030 | + | 1.48363i | ||||
\(682\) | 1.54494e11i | 0.714124i | ||||||||
\(683\) | 1.30156e11 | 0.598110 | 0.299055 | − | 0.954236i | \(-0.403329\pi\) | ||||
0.299055 | + | 0.954236i | \(0.403329\pi\) | |||||||
\(684\) | −2.13217e11 | + | 5.43238e10i | −0.974086 | + | 0.248180i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.82096e11i | 0.822251i | ||||||||
\(687\) | 2.86332e10 | + | 2.28356e11i | 0.128541 | + | 1.02515i | ||||
\(688\) | 1.18565e11i | 0.529179i | ||||||||
\(689\) | − | 6.66227e11i | − | 2.95628i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.27036e9 | −0.00995823 | −0.00497912 | − | 0.999988i | \(-0.501585\pi\) | ||||
−0.00497912 | + | 0.999988i | \(0.501585\pi\) | |||||||
\(692\) | 3.34523e11 | 1.45882 | ||||||||
\(693\) | −6.99506e10 | + | 1.78221e10i | −0.303290 | + | 0.0772729i | ||||
\(694\) | 3.56825e10 | 0.153821 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.89459e10 | − | 4.88335e9i | 0.165968 | − | 0.0208104i | ||||
\(697\) | − | 8.82750e10i | − | 0.374030i | ||||||
\(698\) | 4.55559e11 | 1.91921 | ||||||||
\(699\) | 3.83900e9 | + | 3.06169e10i | 0.0160808 | + | 0.128249i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.75263e11i | − | 1.13993i | −0.821671 | − | 0.569963i | \(-0.806958\pi\) | ||
0.821671 | − | 0.569963i | \(-0.193042\pi\) | |||||||
\(702\) | 5.75085e11 | − | 2.25845e11i | 2.36801 | − | 0.929955i | ||||
\(703\) | − | 2.49974e11i | − | 1.02347i | ||||||
\(704\) | 3.64364e11i | 1.48336i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.52577e11 | −2.62671 | ||||||||
\(707\) | −4.37816e10 | −0.175232 | ||||||||
\(708\) | −3.08021e11 | + | 3.86222e10i | −1.22588 | + | 0.153711i | ||||
\(709\) | −1.38692e11 | −0.548865 | −0.274433 | − | 0.961606i | \(-0.588490\pi\) | ||||
−0.274433 | + | 0.961606i | \(0.588490\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.86065e11 | − | 7.28843e10i | 1.11940 | − | 0.285204i | ||||
\(712\) | 6.25661e10i | 0.243455i | ||||||||
\(713\) | 1.77425e11 | 0.686525 | ||||||||
\(714\) | −5.43379e10 | + | 6.81333e9i | −0.209079 | + | 0.0262160i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.25024e11i | 0.475711i | ||||||||
\(717\) | −2.47977e11 | + | 3.10934e10i | −0.938286 | + | 0.117650i | ||||
\(718\) | 1.74825e11i | 0.657820i | ||||||||
\(719\) | − | 5.06730e11i | − | 1.89610i | −0.318125 | − | 0.948049i | \(-0.603053\pi\) | ||
0.318125 | − | 0.948049i | \(-0.396947\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.81013e10 | 0.177998 | ||||||||
\(722\) | −1.25451e11 | −0.461664 | ||||||||
\(723\) | 1.85047e10 | + | 1.47579e11i | 0.0677217 | + | 0.540097i | ||||
\(724\) | −2.94048e11 | −1.07020 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.07933e9 | + | 7.24098e10i | 0.0326819 | + | 0.260646i | ||||
\(727\) | − | 2.19798e11i | − | 0.786840i | −0.919359 | − | 0.393420i | \(-0.871292\pi\) | ||
0.919359 | − | 0.393420i | \(-0.128708\pi\) | |||||||
\(728\) | 4.34149e10 | 0.154566 | ||||||||
\(729\) | −2.06954e11 | + | 1.92189e11i | −0.732763 | + | 0.680484i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.96147e10i | 0.348862i | ||||||||
\(732\) | 3.59559e9 | + | 2.86757e10i | 0.0125235 | + | 0.0998780i | ||||
\(733\) | 3.34443e11i | 1.15853i | 0.815140 | + | 0.579263i | \(0.196660\pi\) | ||||
−0.815140 | + | 0.579263i | \(0.803340\pi\) | |||||||
\(734\) | 1.55465e11i | 0.535609i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.46444e11 | 2.20303 | ||||||||
\(737\) | 2.47099e11 | 0.837530 | ||||||||
\(738\) | −8.29156e10 | − | 3.25437e11i | −0.279519 | − | 1.09709i | ||||
\(739\) | 4.18860e11 | 1.40440 | 0.702201 | − | 0.711979i | \(-0.252201\pi\) | ||||
0.702201 | + | 0.711979i | \(0.252201\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.25037e11 | + | 5.32945e10i | −1.40979 | + | 0.176771i | ||||
\(742\) | 2.24658e11i | 0.741152i | ||||||||
\(743\) | −1.94993e11 | −0.639830 | −0.319915 | − | 0.947446i | \(-0.603654\pi\) | ||||
−0.319915 | + | 0.947446i | \(0.603654\pi\) | |||||||
\(744\) | 5.28450e9 | + | 4.21451e10i | 0.0172469 | + | 0.137548i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 7.67721e11i | − | 2.47884i | ||||||
\(747\) | −1.34863e11 | + | 3.43606e10i | −0.433121 | + | 0.110351i | ||||
\(748\) | 2.01923e11i | 0.645028i | ||||||||
\(749\) | 1.49781e11i | 0.475915i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.13581e10 | 0.0671433 | 0.0335717 | − | 0.999436i | \(-0.489312\pi\) | ||||
0.0335717 | + | 0.999436i | \(0.489312\pi\) | |||||||
\(752\) | −3.99484e11 | −1.24919 | ||||||||
\(753\) | −3.33041e11 | + | 4.17594e10i | −1.03590 | + | 0.129889i | ||||
\(754\) | 4.39314e11 | 1.35922 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.06199e11 | + | 4.17059e10i | −0.325111 | + | 0.127676i | ||||
\(757\) | 9.33494e10i | 0.284268i | 0.989847 | + | 0.142134i | \(0.0453964\pi\) | ||||
−0.989847 | + | 0.142134i | \(0.954604\pi\) | |||||||
\(758\) | 4.78005e11 | 1.44796 | ||||||||
\(759\) | 5.53826e11 | − | 6.94432e10i | 1.66881 | − | 0.209248i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.19545e10i | 0.214546i | 0.994230 | + | 0.107273i | \(0.0342118\pi\) | ||||
−0.994230 | + | 0.107273i | \(0.965788\pi\) | |||||||
\(762\) | −2.06242e10 | + | 2.58603e9i | −0.0611725 | + | 0.00767031i | ||||
\(763\) | − | 4.85256e10i | − | 0.143177i | ||||||
\(764\) | 3.38468e11i | 0.993447i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.29370e11 | 1.82806 | ||||||||
\(767\) | −6.04370e11 | −1.74631 | ||||||||
\(768\) | −1.97863e10 | − | 1.57800e11i | −0.0568747 | − | 0.453589i | ||||
\(769\) | 1.60418e11 | 0.458720 | 0.229360 | − | 0.973342i | \(-0.426337\pi\) | ||||
0.229360 | + | 0.973342i | \(0.426337\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.13515e10 | − | 9.05313e10i | −0.0321246 | − | 0.256201i | ||||
\(772\) | − | 8.25245e11i | − | 2.32335i | ||||||
\(773\) | −3.72166e11 | −1.04236 | −0.521181 | − | 0.853446i | \(-0.674508\pi\) | ||||
−0.521181 | + | 0.853446i | \(0.674508\pi\) | |||||||
\(774\) | 9.35669e10 | + | 3.67243e11i | 0.260710 | + | 1.02327i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 3.73961e10i | − | 0.103129i | ||||||
\(777\) | −1.61268e10 | − | 1.28615e11i | −0.0442451 | − | 0.352865i | ||||
\(778\) | − | 6.39941e11i | − | 1.74671i | ||||||
\(779\) | 2.32842e11i | 0.632283i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.01055e11 | −1.07795 | ||||||||
\(782\) | 4.23451e11 | 1.13234 | ||||||||
\(783\) | −1.86923e11 | + | 7.34077e10i | −0.497297 | + | 0.195296i | ||||
\(784\) | −2.58062e11 | −0.683062 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.51176e11 | − | 6.91110e10i | 1.44411 | − | 0.181074i | ||||
\(787\) | 5.18916e11i | 1.35269i | 0.736585 | + | 0.676345i | \(0.236437\pi\) | ||||
−0.736585 | + | 0.676345i | \(0.763563\pi\) | |||||||
\(788\) | −7.17773e11 | −1.86158 | ||||||||
\(789\) | −6.97229e10 | − | 5.56056e11i | −0.179915 | − | 1.43486i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.15904e10i | 0.0806956i | ||||||||
\(792\) | 3.29907e10 | + | 1.29486e11i | 0.0838477 | + | 0.329096i | ||||
\(793\) | 5.62648e10i | 0.142280i | ||||||||
\(794\) | − | 5.19149e11i | − | 1.30620i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.90539e11 | 0.723690 | ||||||||
\(797\) | 1.05184e11 | 0.260686 | 0.130343 | − | 0.991469i | \(-0.458392\pi\) | ||||
0.130343 | + | 0.991469i | \(0.458392\pi\) | |||||||
\(798\) | 1.43327e11 | − | 1.79715e10i | 0.353440 | − | 0.0443172i | ||||
\(799\) | −3.35634e11 | −0.823530 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.90333e10 | − | 3.10200e11i | −0.191991 | − | 0.753549i | ||||
\(802\) | 9.19105e11i | 2.22161i | ||||||||
\(803\) | −3.63983e11 | −0.875424 | ||||||||
\(804\) | 3.87524e11 | − | 4.85909e10i | 0.927415 | − | 0.116287i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.75402e11i | 1.12647i | ||||||||
\(807\) | 8.36375e10 | − | 1.04871e10i | 0.197200 | − | 0.0247265i | ||||
\(808\) | 8.10446e10i | 0.190142i | ||||||||
\(809\) | − | 1.09572e10i | − | 0.0255804i | −0.999918 | − | 0.0127902i | \(-0.995929\pi\) | ||
0.999918 | − | 0.0127902i | \(-0.00407135\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.31782e11 | 0.304630 | 0.152315 | − | 0.988332i | \(-0.451327\pi\) | ||||
0.152315 | + | 0.988332i | \(0.451327\pi\) | |||||||
\(812\) | −8.11263e10 | −0.186611 | ||||||||
\(813\) | 4.33694e10 | + | 3.45881e11i | 0.0992706 | + | 0.791707i | ||||
\(814\) | −8.72747e11 | −1.98788 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.01882e10 | − | 1.61005e11i | −0.0455341 | − | 0.363145i | ||||
\(817\) | − | 2.62753e11i | − | 0.589738i | ||||||
\(818\) | 2.43229e11 | 0.543254 | ||||||||
\(819\) | −2.15249e11 | + | 5.48416e10i | −0.478416 | + | 0.121892i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 3.65371e10i | − | 0.0804194i | −0.999191 | − | 0.0402097i | \(-0.987197\pi\) | ||
0.999191 | − | 0.0402097i | \(-0.0128026\pi\) | |||||||
\(822\) | 1.77354e10 | + | 1.41444e11i | 0.0388466 | + | 0.309811i | ||||
\(823\) | − | 4.11792e11i | − | 0.897591i | −0.893635 | − | 0.448795i | \(-0.851853\pi\) | ||
0.893635 | − | 0.448795i | \(-0.148147\pi\) | |||||||
\(824\) | − | 8.90408e10i | − | 0.193144i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.03800e11 | 0.437808 | ||||||||
\(827\) | 1.78687e11 | 0.382007 | 0.191004 | − | 0.981589i | \(-0.438826\pi\) | ||||
0.191004 | + | 0.981589i | \(0.438826\pi\) | |||||||
\(828\) | 8.54907e11 | − | 2.17815e11i | 1.81885 | − | 0.463411i | ||||
\(829\) | 3.65541e11 | 0.773960 | 0.386980 | − | 0.922088i | \(-0.373518\pi\) | ||||
0.386980 | + | 0.922088i | \(0.373518\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.14639e11 | − | 1.02146e11i | 1.70829 | − | 0.214199i | ||||
\(832\) | 1.12121e12i | 2.33988i | ||||||||
\(833\) | −2.16816e11 | −0.450310 | ||||||||
\(834\) | −9.61243e9 | − | 7.66614e10i | −0.0198687 | − | 0.158457i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 5.32609e11i | − | 1.09039i | ||||||
\(837\) | −7.94378e10 | − | 2.02278e11i | −0.161855 | − | 0.412142i | ||||
\(838\) | − | 7.22074e11i | − | 1.46422i | ||||||
\(839\) | 5.20766e11i | 1.05098i | 0.850799 | + | 0.525491i | \(0.176118\pi\) | ||||
−0.850799 | + | 0.525491i | \(0.823882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.57454e11 | 0.714555 | ||||||||
\(842\) | 9.37429e11 | 1.86505 | ||||||||
\(843\) | 7.09349e11 | − | 8.89440e10i | 1.40459 | − | 0.176119i | ||||
\(844\) | 6.65348e11 | 1.31123 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.23736e12 | + | 3.15257e11i | −2.41554 | + | 0.615437i | ||||
\(847\) | − | 2.62365e10i | − | 0.0509768i | ||||||
\(848\) | −6.65672e11 | −1.28729 | ||||||||
\(849\) | 1.27026e11 | − | 1.59276e10i | 0.244491 | − | 0.0306563i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.00229e12i | 1.91106i | ||||||||
\(852\) | −6.28973e11 | + | 7.88657e10i | −1.19364 | + | 0.149668i | ||||
\(853\) | 5.21152e11i | 0.984392i | 0.870484 | + | 0.492196i | \(0.163806\pi\) | ||||
−0.870484 | + | 0.492196i | \(0.836194\pi\) | |||||||
\(854\) | − | 1.89731e10i | − | 0.0356702i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.77261e11 | 0.516409 | ||||||||
\(857\) | −8.67435e11 | −1.60810 | −0.804051 | − | 0.594560i | \(-0.797326\pi\) | ||||
−0.804051 | + | 0.594560i | \(0.797326\pi\) | |||||||
\(858\) | 1.86070e11 | + | 1.48395e12i | 0.343342 | + | 2.73823i | ||||
\(859\) | 6.24921e11 | 1.14776 | 0.573882 | − | 0.818938i | \(-0.305437\pi\) | ||||
0.573882 | + | 0.818938i | \(0.305437\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.50216e10 | + | 1.19801e11i | 0.0273340 | + | 0.217995i | ||||
\(862\) | − | 4.77990e11i | − | 0.865745i | ||||||
\(863\) | 8.65555e11 | 1.56046 | 0.780228 | − | 0.625495i | \(-0.215103\pi\) | ||||
0.780228 | + | 0.625495i | \(0.215103\pi\) | |||||||
\(864\) | −2.89430e11 | − | 7.36996e11i | −0.519384 | − | 1.32254i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.13265e12i | 2.01384i | ||||||||
\(867\) | 5.33369e10 | + | 4.25374e11i | 0.0943955 | + | 0.752827i | ||||
\(868\) | − | 8.77906e10i | − | 0.154657i | ||||||
\(869\) | 7.14583e11i | 1.25306i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.60363e11 | 1.32114 | ||||||||
\(872\) | −8.98262e10 | −0.155359 | ||||||||
\(873\) | 4.72386e10 | + | 1.85408e11i | 0.0813280 | + | 0.319206i | ||||
\(874\) | −1.11693e12 | −1.91417 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.70833e11 | + | 7.15756e10i | −0.969376 | + | 0.121548i | ||||
\(877\) | − | 3.45290e10i | − | 0.0583694i | −0.999574 | − | 0.0291847i | \(-0.990709\pi\) | ||
0.999574 | − | 0.0291847i | \(-0.00929110\pi\) | |||||||
\(878\) | 6.68096e11 | 1.12424 | ||||||||
\(879\) | −7.36654e9 | − | 5.87499e10i | −0.0123398 | − | 0.0984129i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 5.74904e10i | − | 0.0954316i | −0.998861 | − | 0.0477158i | \(-0.984806\pi\) | ||
0.998861 | − | 0.0477158i | \(-0.0151942\pi\) | |||||||
\(882\) | −7.99321e11 | + | 2.03653e11i | −1.32083 | + | 0.336524i | ||||
\(883\) | 7.36663e11i | 1.21179i | 0.795546 | + | 0.605893i | \(0.207184\pi\) | ||||
−0.795546 | + | 0.605893i | \(0.792816\pi\) | |||||||
\(884\) | 6.21348e11i | 1.01748i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.68143e10 | −0.124654 | ||||||||
\(887\) | 1.56687e11 | 0.253126 | 0.126563 | − | 0.991959i | \(-0.459605\pi\) | ||||
0.126563 | + | 0.991959i | \(0.459605\pi\) | |||||||
\(888\) | −2.38081e11 | + | 2.98525e10i | −0.382889 | + | 0.0480097i | ||||
\(889\) | 7.47283e9 | 0.0119640 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.27133e11 | − | 6.00312e11i | −0.519055 | − | 0.952503i | ||||
\(892\) | − | 1.14904e12i | − | 1.81500i | ||||||
\(893\) | 8.85300e11 | 1.39214 | ||||||||
\(894\) | 3.45387e11 | − | 4.33074e10i | 0.540700 | − | 0.0677973i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.13858e11i | − | 0.176657i | ||||||
\(897\) | 1.70421e12 | − | 2.13688e11i | 2.63241 | − | 0.330073i | ||||
\(898\) | − | 1.00163e12i | − | 1.54029i | ||||||
\(899\) | − | 1.54523e11i | − | 0.236567i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.59277e11 | −0.848648 | ||||||||
\(902\) | 8.12933e11 | 1.22809 | ||||||||
\(903\) | −1.69512e10 | − | 1.35190e11i | −0.0254947 | − | 0.203326i | ||||
\(904\) | 5.84773e10 | 0.0875616 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.03807e10 | + | 8.27883e10i | 0.0154068 | + | 0.122873i | ||||
\(907\) | − | 5.78430e11i | − | 0.854716i | −0.904083 | − | 0.427358i | \(-0.859444\pi\) | ||
0.904083 | − | 0.427358i | \(-0.140556\pi\) | |||||||
\(908\) | −1.23040e12 | −1.81010 | ||||||||
\(909\) | −1.02375e11 | − | 4.01815e11i | −0.149948 | − | 0.588533i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 8.17142e10i | − | 0.118638i | −0.998239 | − | 0.0593190i | \(-0.981107\pi\) | ||
0.998239 | − | 0.0593190i | \(-0.0188929\pi\) | |||||||
\(912\) | 5.32501e10 | + | 4.24682e11i | 0.0769735 | + | 0.613882i | ||||
\(913\) | − | 3.36882e11i | − | 0.484836i | ||||||
\(914\) | − | 9.85637e11i | − | 1.41232i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.80533e11 | −1.25073 | ||||||||
\(917\) | −1.99710e11 | −0.282437 | ||||||||
\(918\) | −1.89590e11 | − | 4.82766e11i | −0.266959 | − | 0.679776i | ||||
\(919\) | 8.52245e11 | 1.19482 | 0.597410 | − | 0.801936i | \(-0.296197\pi\) | ||||
0.597410 | + | 0.801936i | \(0.296197\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.47354e11 | + | 8.11705e10i | −0.899711 | + | 0.112813i | ||||
\(922\) | − | 1.77036e12i | − | 2.44984i | ||||||
\(923\) | −1.23411e12 | −1.70038 | ||||||||
\(924\) | −3.43607e10 | − | 2.74035e11i | −0.0471384 | − | 0.375940i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 1.08760e12i | − | 1.47920i | ||||||
\(927\) | 1.12476e11 | + | 4.41460e11i | 0.152314 | + | 0.597823i | ||||
\(928\) | − | 5.63000e11i | − | 0.759131i | ||||||
\(929\) | 4.58591e11i | 0.615691i | 0.951436 | + | 0.307845i | \(0.0996079\pi\) | ||||
−0.951436 | + | 0.307845i | \(0.900392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.71893e11 | 0.761231 | ||||||||
\(932\) | −1.18058e11 | −0.156470 | ||||||||
\(933\) | 1.83384e11 | − | 2.29942e10i | 0.242011 | − | 0.0303453i | ||||
\(934\) | 6.58834e10 | 0.0865742 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.01518e11 | + | 3.98450e11i | 0.132263 | + | 0.519123i | ||||
\(937\) | 1.32495e11i | 0.171886i | 0.996300 | + | 0.0859432i | \(0.0273904\pi\) | ||||
−0.996300 | + | 0.0859432i | \(0.972610\pi\) | |||||||
\(938\) | −2.56402e11 | −0.331215 | ||||||||
\(939\) | 2.73899e11 | − | 3.43437e10i | 0.352313 | − | 0.0441759i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 7.82786e11i | − | 0.998354i | −0.866500 | − | 0.499177i | \(-0.833636\pi\) | ||
0.866500 | − | 0.499177i | \(-0.166364\pi\) | |||||||
\(942\) | −1.90932e11 | + | 2.39406e10i | −0.242479 | + | 0.0304040i | ||||
\(943\) | − | 9.33594e11i | − | 1.18062i | ||||||
\(944\) | 6.03867e11i | 0.760419i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.17362e11 | −1.14545 | ||||||||
\(947\) | 7.18981e11 | 0.893959 | 0.446980 | − | 0.894544i | \(-0.352500\pi\) | ||||
0.446980 | + | 0.894544i | \(0.352500\pi\) | |||||||
\(948\) | 1.40520e11 | + | 1.12068e12i | 0.173982 | + | 1.38754i | ||||
\(949\) | −1.12003e12 | −1.38091 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.82516e10 | − | 2.25313e11i | −0.0345398 | − | 0.275463i | ||||
\(952\) | − | 3.64455e10i | − | 0.0443707i | ||||||
\(953\) | 3.21954e11 | 0.390321 | 0.195160 | − | 0.980771i | \(-0.437477\pi\) | ||||
0.195160 | + | 0.980771i | \(0.437477\pi\) | |||||||
\(954\) | −2.06185e12 | + | 5.25322e11i | −2.48922 | + | 0.634209i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 9.56191e11i | − | 1.14476i | ||||||
\(957\) | −6.04793e10 | − | 4.82337e11i | −0.0721040 | − | 0.575046i | ||||
\(958\) | 9.08862e11i | 1.07904i | ||||||||
\(959\) | − | 5.12499e10i | − | 0.0605924i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.85675e11 | −0.803942 | ||||||||
\(962\) | −2.68558e12 | −3.13573 | ||||||||
\(963\) | −1.37465e12 | + | 3.50235e11i | −1.59840 | + | 0.407244i | ||||
\(964\) | −5.69059e11 | −0.658945 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.74677e11 | + | 7.20577e10i | −0.659957 | + | 0.0827507i | ||||
\(967\) | − | 4.20589e11i | − | 0.481008i | −0.970648 | − | 0.240504i | \(-0.922687\pi\) | ||
0.970648 | − | 0.240504i | \(-0.0773127\pi\) | |||||||
\(968\) | −4.85666e10 | −0.0553142 | ||||||||
\(969\) | 4.47391e10 | + | 3.56805e11i | 0.0507449 | + | 0.404703i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.93768e11i | 1.00542i | 0.864455 | + | 0.502710i | \(0.167664\pi\) | ||||
−0.864455 | + | 0.502710i | \(0.832336\pi\) | |||||||
\(972\) | −6.31090e11 | − | 8.77137e11i | −0.707011 | − | 0.982658i | ||||
\(973\) | 2.77770e10i | 0.0309909i | ||||||||
\(974\) | − | 6.63937e11i | − | 0.737719i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.62179e10 | 0.0619548 | ||||||||
\(977\) | −8.04509e11 | −0.882983 | −0.441492 | − | 0.897265i | \(-0.645551\pi\) | ||||
−0.441492 | + | 0.897265i | \(0.645551\pi\) | |||||||
\(978\) | −7.94394e11 | + | 9.96075e10i | −0.868321 | + | 0.108877i | ||||
\(979\) | 7.74869e11 | 0.843525 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.45354e11 | − | 1.13468e11i | 0.480872 | − | 0.122518i | ||||
\(982\) | 8.62300e11i | 0.927283i | ||||||||
\(983\) | 7.12126e11 | 0.762681 | 0.381340 | − | 0.924435i | \(-0.375463\pi\) | ||||
0.381340 | + | 0.924435i | \(0.375463\pi\) | |||||||
\(984\) | 2.21764e11 | − | 2.78066e10i | 0.236543 | − | 0.0296597i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 3.68791e11i | − | 0.390187i | ||||||
\(987\) | 4.55499e11 | − | 5.71142e10i | 0.479975 | − | 0.0601832i | ||||
\(988\) | − | 1.63892e12i | − | 1.72001i | ||||||
\(989\) | 1.05352e12i | 1.10118i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.20276e12 | 1.24705 | 0.623526 | − | 0.781803i | \(-0.285700\pi\) | ||||
0.623526 | + | 0.781803i | \(0.285700\pi\) | |||||||
\(992\) | 6.09249e11 | 0.629141 | ||||||||
\(993\) | 3.88808e10 | + | 3.10083e11i | 0.0399887 | + | 0.318920i | ||||
\(994\) | 4.16155e11 | 0.426294 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.62465e10 | − | 5.28331e11i | −0.0673171 | − | 0.536870i | ||||
\(997\) | − | 2.28898e11i | − | 0.231665i | −0.993269 | − | 0.115833i | \(-0.963046\pi\) | ||
0.993269 | − | 0.115833i | \(-0.0369536\pi\) | |||||||
\(998\) | 3.12341e11 | 0.314852 | ||||||||
\(999\) | 1.14268e12 | − | 4.48750e11i | 1.14727 | − | 0.450550i |
(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.d.c.74.17 | 20 | ||
3.2 | odd | 2 | inner | 75.9.d.c.74.3 | 20 | ||
5.2 | odd | 4 | 15.9.c.a.11.9 | yes | 10 | ||
5.3 | odd | 4 | 75.9.c.g.26.2 | 10 | |||
5.4 | even | 2 | inner | 75.9.d.c.74.4 | 20 | ||
15.2 | even | 4 | 15.9.c.a.11.2 | ✓ | 10 | ||
15.8 | even | 4 | 75.9.c.g.26.9 | 10 | |||
15.14 | odd | 2 | inner | 75.9.d.c.74.18 | 20 | ||
20.7 | even | 4 | 240.9.l.b.161.9 | 10 | |||
60.47 | odd | 4 | 240.9.l.b.161.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.9.c.a.11.2 | ✓ | 10 | 15.2 | even | 4 | ||
15.9.c.a.11.9 | yes | 10 | 5.2 | odd | 4 | ||
75.9.c.g.26.2 | 10 | 5.3 | odd | 4 | |||
75.9.c.g.26.9 | 10 | 15.8 | even | 4 | |||
75.9.d.c.74.3 | 20 | 3.2 | odd | 2 | inner | ||
75.9.d.c.74.4 | 20 | 5.4 | even | 2 | inner | ||
75.9.d.c.74.17 | 20 | 1.1 | even | 1 | trivial | ||
75.9.d.c.74.18 | 20 | 15.14 | odd | 2 | inner | ||
240.9.l.b.161.9 | 10 | 20.7 | even | 4 | |||
240.9.l.b.161.10 | 10 | 60.47 | odd | 4 |