Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,69,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 69, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 69);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 69 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(87.8517980619\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.6 | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.69.b.a.2.17 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.98633e10i | − | 1.15619i | −0.815968 | − | 0.578097i | \(-0.803795\pi\) | ||
0.815968 | − | 0.578097i | \(-0.196205\pi\) | |||||||
\(3\) | −1.52299e16 | + | 6.79538e15i | −0.913220 | + | 0.407466i | ||||
\(4\) | −9.94018e19 | −0.336786 | ||||||||
\(5\) | − | 1.15188e23i | − | 0.197891i | −0.995093 | − | 0.0989453i | \(-0.968453\pi\) | ||
0.995093 | − | 0.0989453i | \(-0.0315469\pi\) | |||||||
\(6\) | 1.34979e26 | + | 3.02517e26i | 0.471110 | + | 1.05586i | ||||
\(7\) | −6.02651e28 | −1.11361 | −0.556804 | − | 0.830644i | \(-0.687972\pi\) | ||||
−0.556804 | + | 0.830644i | \(0.687972\pi\) | |||||||
\(8\) | − | 3.88816e30i | − | 0.766804i | ||||||
\(9\) | 1.85774e32 | − | 2.06987e32i | 0.667943 | − | 0.744212i | ||||
\(10\) | −2.28800e33 | −0.228800 | ||||||||
\(11\) | − | 2.49072e35i | − | 0.974931i | −0.873142 | − | 0.487466i | \(-0.837921\pi\) | ||
0.873142 | − | 0.487466i | \(-0.162079\pi\) | |||||||
\(12\) | 1.51388e36 | − | 6.75473e35i | 0.307560 | − | 0.137229i | ||||
\(13\) | 6.80608e37 | 0.909543 | 0.454772 | − | 0.890608i | \(-0.349721\pi\) | ||||
0.454772 | + | 0.890608i | \(0.349721\pi\) | |||||||
\(14\) | 1.19706e39i | 1.28755i | ||||||||
\(15\) | 7.82743e38 | + | 1.75430e39i | 0.0806337 | + | 0.180718i | ||||
\(16\) | −1.06570e41 | −1.22336 | ||||||||
\(17\) | 5.64414e41i | 0.824773i | 0.911009 | + | 0.412386i | \(0.135305\pi\) | ||||
−0.911009 | + | 0.412386i | \(0.864695\pi\) | |||||||
\(18\) | −4.11143e42 | − | 3.69008e42i | −0.860454 | − | 0.772273i | ||||
\(19\) | 3.74530e43 | 1.24699 | 0.623497 | − | 0.781825i | \(-0.285711\pi\) | ||||
0.623497 | + | 0.781825i | \(0.285711\pi\) | |||||||
\(20\) | 1.14498e43i | 0.0666469i | ||||||||
\(21\) | 9.17833e44 | − | 4.09524e44i | 1.01697 | − | 0.453757i | ||||
\(22\) | −4.94739e45 | −1.12721 | ||||||||
\(23\) | 9.44969e45i | 0.474976i | 0.971391 | + | 0.237488i | \(0.0763240\pi\) | ||||
−0.971391 | + | 0.237488i | \(0.923676\pi\) | |||||||
\(24\) | 2.64215e46 | + | 5.92164e46i | 0.312446 | + | 0.700261i | ||||
\(25\) | 3.25545e47 | 0.960839 | ||||||||
\(26\) | − | 1.35191e48i | − | 1.05161i | ||||||
\(27\) | −1.42278e48 | + | 4.41480e48i | −0.306739 | + | 0.951794i | ||||
\(28\) | 5.99045e48 | 0.375048 | ||||||||
\(29\) | 4.04571e49i | 0.768180i | 0.923296 | + | 0.384090i | \(0.125485\pi\) | ||||
−0.923296 | + | 0.384090i | \(0.874515\pi\) | |||||||
\(30\) | 3.48461e49 | − | 1.55478e49i | 0.208945 | − | 0.0932282i | ||||
\(31\) | 3.19261e50 | 0.627840 | 0.313920 | − | 0.949449i | \(-0.398358\pi\) | ||||
0.313920 | + | 0.949449i | \(0.398358\pi\) | |||||||
\(32\) | 9.69243e50i | 0.647640i | ||||||||
\(33\) | 1.69254e51 | + | 3.79336e51i | 0.397251 | + | 0.890327i | ||||
\(34\) | 1.12111e52 | 0.953598 | ||||||||
\(35\) | 6.94178e51i | 0.220373i | ||||||||
\(36\) | −1.84663e52 | + | 2.05748e52i | −0.224954 | + | 0.250640i | ||||
\(37\) | 5.63328e52 | 0.270335 | 0.135168 | − | 0.990823i | \(-0.456843\pi\) | ||||
0.135168 | + | 0.990823i | \(0.456843\pi\) | |||||||
\(38\) | − | 7.43940e53i | − | 1.44177i | ||||||
\(39\) | −1.03656e54 | + | 4.62499e53i | −0.830613 | + | 0.370608i | ||||
\(40\) | −4.47867e53 | −0.151743 | ||||||||
\(41\) | − | 5.48217e54i | − | 0.802235i | −0.916027 | − | 0.401117i | \(-0.868622\pi\) | ||
0.916027 | − | 0.401117i | \(-0.131378\pi\) | |||||||
\(42\) | −8.13449e54 | − | 1.82312e55i | −0.524631 | − | 1.17581i | ||||
\(43\) | 5.73328e55 | 1.66141 | 0.830703 | − | 0.556716i | \(-0.187939\pi\) | ||||
0.830703 | + | 0.556716i | \(0.187939\pi\) | |||||||
\(44\) | 2.47582e55i | 0.328344i | ||||||||
\(45\) | −2.38423e55 | − | 2.13988e55i | −0.147273 | − | 0.132180i | ||||
\(46\) | 1.87702e56 | 0.549164 | ||||||||
\(47\) | − | 1.10405e57i | − | 1.55475i | −0.629038 | − | 0.777375i | \(-0.716551\pi\) | ||
0.629038 | − | 0.777375i | \(-0.283449\pi\) | |||||||
\(48\) | 1.62305e57 | − | 7.24182e56i | 1.11720 | − | 0.498478i | ||||
\(49\) | 7.03232e56 | 0.240122 | ||||||||
\(50\) | − | 6.46639e57i | − | 1.11092i | ||||||
\(51\) | −3.83541e57 | − | 8.59599e57i | −0.336067 | − | 0.753199i | ||||
\(52\) | −6.76537e57 | −0.306322 | ||||||||
\(53\) | − | 5.86838e58i | − | 1.39040i | −0.718818 | − | 0.695198i | \(-0.755316\pi\) | ||
0.718818 | − | 0.695198i | \(-0.244684\pi\) | |||||||
\(54\) | 8.76923e58 | + | 2.82610e58i | 1.10046 | + | 0.354650i | ||||
\(55\) | −2.86900e58 | −0.192930 | ||||||||
\(56\) | 2.34320e59i | 0.853919i | ||||||||
\(57\) | −5.70408e59 | + | 2.54508e59i | −1.13878 | + | 0.508108i | ||||
\(58\) | 8.03611e59 | 0.888166 | ||||||||
\(59\) | 2.64517e60i | 1.63487i | 0.576017 | + | 0.817437i | \(0.304606\pi\) | ||||
−0.576017 | + | 0.817437i | \(0.695394\pi\) | |||||||
\(60\) | −7.78060e58 | − | 1.74380e59i | −0.0271563 | − | 0.0608633i | ||||
\(61\) | −3.65756e60 | −0.727741 | −0.363870 | − | 0.931450i | \(-0.618545\pi\) | ||||
−0.363870 | + | 0.931450i | \(0.618545\pi\) | |||||||
\(62\) | − | 6.34158e60i | − | 0.725905i | ||||||
\(63\) | −1.11957e61 | + | 1.24741e61i | −0.743827 | + | 0.828760i | ||||
\(64\) | −1.22015e61 | −0.474564 | ||||||||
\(65\) | − | 7.83976e60i | − | 0.179990i | ||||||
\(66\) | 7.53485e61 | − | 3.36194e61i | 1.02939 | − | 0.459300i | ||||
\(67\) | 1.10141e62 | 0.902410 | 0.451205 | − | 0.892420i | \(-0.350994\pi\) | ||||
0.451205 | + | 0.892420i | \(0.350994\pi\) | |||||||
\(68\) | − | 5.61037e61i | − | 0.277772i | ||||||
\(69\) | −6.42143e61 | − | 1.43918e62i | −0.193536 | − | 0.433757i | ||||
\(70\) | 1.37887e62 | 0.254794 | ||||||||
\(71\) | − | 2.24430e62i | − | 0.256033i | −0.991772 | − | 0.128017i | \(-0.959139\pi\) | ||
0.991772 | − | 0.128017i | \(-0.0408611\pi\) | |||||||
\(72\) | −8.04796e62 | − | 7.22319e62i | −0.570665 | − | 0.512182i | ||||
\(73\) | 6.26092e62 | 0.277754 | 0.138877 | − | 0.990310i | \(-0.455651\pi\) | ||||
0.138877 | + | 0.990310i | \(0.455651\pi\) | |||||||
\(74\) | − | 1.11895e63i | − | 0.312560i | ||||||
\(75\) | −4.95803e63 | + | 2.21220e63i | −0.877458 | + | 0.391509i | ||||
\(76\) | −3.72290e63 | −0.419971 | ||||||||
\(77\) | 1.50104e64i | 1.08569i | ||||||||
\(78\) | 9.18675e63 | + | 2.05895e64i | 0.428495 | + | 0.960351i | ||||
\(79\) | −3.84819e63 | −0.116395 | −0.0581977 | − | 0.998305i | \(-0.518535\pi\) | ||||
−0.0581977 | + | 0.998305i | \(0.518535\pi\) | |||||||
\(80\) | 1.22755e64i | 0.242092i | ||||||||
\(81\) | −8.33144e63 | − | 7.69054e64i | −0.107703 | − | 0.994183i | ||||
\(82\) | −1.08894e65 | −0.927540 | ||||||||
\(83\) | − | 1.42586e65i | − | 0.804309i | −0.915572 | − | 0.402155i | \(-0.868261\pi\) | ||
0.915572 | − | 0.402155i | \(-0.131739\pi\) | |||||||
\(84\) | −9.12343e64 | + | 4.07074e64i | −0.342501 | + | 0.152819i | ||||
\(85\) | 6.50134e64 | 0.163215 | ||||||||
\(86\) | − | 1.13882e66i | − | 1.92091i | ||||||
\(87\) | −2.74922e65 | − | 6.16160e65i | −0.313007 | − | 0.701518i | ||||
\(88\) | −9.68432e65 | −0.747581 | ||||||||
\(89\) | 1.80918e66i | 0.951089i | 0.879692 | + | 0.475544i | \(0.157749\pi\) | ||||
−0.879692 | + | 0.475544i | \(0.842251\pi\) | |||||||
\(90\) | −4.25051e65 | + | 4.73585e65i | −0.152826 | + | 0.170276i | ||||
\(91\) | −4.10169e66 | −1.01287 | ||||||||
\(92\) | − | 9.39316e65i | − | 0.159965i | ||||||
\(93\) | −4.86233e66 | + | 2.16950e66i | −0.573356 | + | 0.255823i | ||||
\(94\) | −2.19300e67 | −1.79759 | ||||||||
\(95\) | − | 4.31412e66i | − | 0.246769i | ||||||
\(96\) | −6.58638e66 | − | 1.47615e67i | −0.263891 | − | 0.591438i | ||||
\(97\) | −5.21425e67 | −1.46877 | −0.734384 | − | 0.678734i | \(-0.762529\pi\) | ||||
−0.734384 | + | 0.678734i | \(0.762529\pi\) | |||||||
\(98\) | − | 1.39685e67i | − | 0.277628i | ||||||
\(99\) | −5.15546e67 | − | 4.62711e67i | −0.725556 | − | 0.651199i | ||||
\(100\) | −3.23598e67 | −0.323598 | ||||||||
\(101\) | − | 2.16565e68i | − | 1.54405i | −0.635591 | − | 0.772026i | \(-0.719243\pi\) | ||
0.635591 | − | 0.772026i | \(-0.280757\pi\) | |||||||
\(102\) | −1.70744e68 | + | 7.61837e67i | −0.870845 | + | 0.388558i | ||||
\(103\) | 2.15308e68 | 0.788125 | 0.394062 | − | 0.919084i | \(-0.371069\pi\) | ||||
0.394062 | + | 0.919084i | \(0.371069\pi\) | |||||||
\(104\) | − | 2.64631e68i | − | 0.697441i | ||||||
\(105\) | −4.71720e67 | − | 1.05723e68i | −0.0897943 | − | 0.201249i | ||||
\(106\) | −1.16565e69 | −1.60757 | ||||||||
\(107\) | 6.73705e68i | 0.675182i | 0.941293 | + | 0.337591i | \(0.109612\pi\) | ||||
−0.941293 | + | 0.337591i | \(0.890388\pi\) | |||||||
\(108\) | 1.41426e68 | − | 4.38839e68i | 0.103305 | − | 0.320551i | ||||
\(109\) | −1.91053e69 | −1.02012 | −0.510061 | − | 0.860138i | \(-0.670377\pi\) | ||||
−0.510061 | + | 0.860138i | \(0.670377\pi\) | |||||||
\(110\) | 5.69878e68i | 0.223064i | ||||||||
\(111\) | −8.57946e68 | + | 3.82803e68i | −0.246876 | + | 0.110152i | ||||
\(112\) | 6.42244e69 | 1.36234 | ||||||||
\(113\) | 3.71019e69i | 0.581739i | 0.956763 | + | 0.290870i | \(0.0939446\pi\) | ||||
−0.956763 | + | 0.290870i | \(0.906055\pi\) | |||||||
\(114\) | 5.05536e69 | + | 1.13302e70i | 0.587471 | + | 1.31665i | ||||
\(115\) | 1.08849e69 | 0.0939932 | ||||||||
\(116\) | − | 4.02151e69i | − | 0.258713i | ||||||
\(117\) | 1.26439e70 | − | 1.40877e70i | 0.607523 | − | 0.676893i | ||||
\(118\) | 5.25417e70 | 1.89023 | ||||||||
\(119\) | − | 3.40144e70i | − | 0.918473i | ||||||
\(120\) | 6.82099e69 | − | 3.04343e69i | 0.138575 | − | 0.0618302i | ||||
\(121\) | 3.23138e69 | 0.0495091 | ||||||||
\(122\) | 7.26511e70i | 0.841410i | ||||||||
\(123\) | 3.72534e70 | + | 8.34932e70i | 0.326883 | + | 0.732617i | ||||
\(124\) | −3.17351e70 | −0.211448 | ||||||||
\(125\) | − | 7.65258e70i | − | 0.388032i | ||||||
\(126\) | 2.47776e71 | + | 2.22383e71i | 0.958208 | + | 0.860009i | ||||
\(127\) | 3.65635e71 | 1.08074 | 0.540370 | − | 0.841427i | \(-0.318284\pi\) | ||||
0.540370 | + | 0.841427i | \(0.318284\pi\) | |||||||
\(128\) | 5.28432e71i | 1.19633i | ||||||||
\(129\) | −8.73175e71 | + | 3.89598e71i | −1.51723 | + | 0.676966i | ||||
\(130\) | −1.55723e71 | −0.208104 | ||||||||
\(131\) | − | 1.67473e72i | − | 1.72473i | −0.506287 | − | 0.862365i | \(-0.668982\pi\) | ||
0.506287 | − | 0.862365i | \(-0.331018\pi\) | |||||||
\(132\) | −1.68242e71 | − | 3.77066e71i | −0.133789 | − | 0.299850i | ||||
\(133\) | −2.25711e72 | −1.38866 | ||||||||
\(134\) | − | 2.18775e72i | − | 1.04336i | ||||||
\(135\) | 5.08530e71 | + | 1.63886e71i | 0.188351 | + | 0.0607007i | ||||
\(136\) | 2.19453e72 | 0.632439 | ||||||||
\(137\) | − | 6.45507e72i | − | 1.45011i | −0.688689 | − | 0.725057i | \(-0.741814\pi\) | ||
0.688689 | − | 0.725057i | \(-0.258186\pi\) | |||||||
\(138\) | −2.85869e72 | + | 1.27551e72i | −0.501508 | + | 0.223766i | ||||
\(139\) | −1.33816e73 | −1.83656 | −0.918280 | − | 0.395931i | \(-0.870422\pi\) | ||||
−0.918280 | + | 0.395931i | \(0.870422\pi\) | |||||||
\(140\) | − | 6.90026e71i | − | 0.0742185i | ||||||
\(141\) | 7.50242e72 | + | 1.68146e73i | 0.633507 | + | 1.41983i | ||||
\(142\) | −4.45791e72 | −0.296025 | ||||||||
\(143\) | − | 1.69521e73i | − | 0.886742i | ||||||
\(144\) | −1.97979e73 | + | 2.20585e73i | −0.817136 | + | 0.910440i | ||||
\(145\) | 4.66015e72 | 0.152016 | ||||||||
\(146\) | − | 1.24362e73i | − | 0.321138i | ||||||
\(147\) | −1.07102e73 | + | 4.77873e72i | −0.219284 | + | 0.0978415i | ||||
\(148\) | −5.59958e72 | −0.0910453 | ||||||||
\(149\) | − | 3.03729e73i | − | 0.392783i | −0.980526 | − | 0.196391i | \(-0.937078\pi\) | ||
0.980526 | − | 0.196391i | \(-0.0629223\pi\) | |||||||
\(150\) | 4.39416e73 | + | 9.84828e73i | 0.452661 | + | 1.01451i | ||||
\(151\) | 1.78959e74 | 1.47074 | 0.735372 | − | 0.677663i | \(-0.237007\pi\) | ||||
0.735372 | + | 0.677663i | \(0.237007\pi\) | |||||||
\(152\) | − | 1.45623e74i | − | 0.956201i | ||||||
\(153\) | 1.16826e74 | + | 1.04853e74i | 0.613806 | + | 0.550901i | ||||
\(154\) | 2.98155e74 | 1.25527 | ||||||||
\(155\) | − | 3.67749e73i | − | 0.124244i | ||||||
\(156\) | 1.03036e74 | − | 4.59733e73i | 0.279739 | − | 0.124816i | ||||
\(157\) | −2.32870e74 | −0.508775 | −0.254388 | − | 0.967102i | \(-0.581874\pi\) | ||||
−0.254388 | + | 0.967102i | \(0.581874\pi\) | |||||||
\(158\) | 7.64377e73i | 0.134576i | ||||||||
\(159\) | 3.98779e74 | + | 8.93751e74i | 0.566539 | + | 1.26974i | ||||
\(160\) | 1.11645e74 | 0.128162 | ||||||||
\(161\) | − | 5.69486e74i | − | 0.528936i | ||||||
\(162\) | −1.52759e75 | + | 1.65490e74i | −1.14947 | + | 0.124526i | ||||
\(163\) | 9.31786e73 | 0.0568771 | 0.0284386 | − | 0.999596i | \(-0.490947\pi\) | ||||
0.0284386 | + | 0.999596i | \(0.490947\pi\) | |||||||
\(164\) | 5.44938e74i | 0.270182i | ||||||||
\(165\) | 4.36947e74 | − | 1.94960e74i | 0.176187 | − | 0.0786123i | ||||
\(166\) | −2.83223e75 | −0.929938 | ||||||||
\(167\) | 2.53201e75i | 0.677807i | 0.940821 | + | 0.338903i | \(0.110056\pi\) | ||||
−0.940821 | + | 0.338903i | \(0.889944\pi\) | |||||||
\(168\) | −1.59229e75 | − | 3.56868e75i | −0.347943 | − | 0.779816i | ||||
\(169\) | −9.67206e74 | −0.172731 | ||||||||
\(170\) | − | 1.29138e75i | − | 0.188708i | ||||||
\(171\) | 6.95780e75 | − | 7.75228e75i | 0.832922 | − | 0.928029i | ||||
\(172\) | −5.69898e75 | −0.559539 | ||||||||
\(173\) | − | 2.27373e76i | − | 1.83304i | −0.399991 | − | 0.916519i | \(-0.630987\pi\) | ||
0.399991 | − | 0.916519i | \(-0.369013\pi\) | |||||||
\(174\) | −1.22389e76 | + | 5.46084e75i | −0.811091 | + | 0.361897i | ||||
\(175\) | −1.96190e76 | −1.07000 | ||||||||
\(176\) | 2.65436e76i | 1.19269i | ||||||||
\(177\) | −1.79749e76 | − | 4.02857e76i | −0.666156 | − | 1.49300i | ||||
\(178\) | 3.59362e76 | 1.09964 | ||||||||
\(179\) | 7.05084e76i | 1.78335i | 0.452672 | + | 0.891677i | \(0.350471\pi\) | ||||
−0.452672 | + | 0.891677i | \(0.649529\pi\) | |||||||
\(180\) | 2.36996e75 | + | 2.12708e75i | 0.0495994 | + | 0.0445163i | ||||
\(181\) | 1.24635e76 | 0.216057 | 0.108028 | − | 0.994148i | \(-0.465546\pi\) | ||||
0.108028 | + | 0.994148i | \(0.465546\pi\) | |||||||
\(182\) | 8.14730e76i | 1.17108i | ||||||||
\(183\) | 5.57044e76 | − | 2.48545e76i | 0.664588 | − | 0.296529i | ||||
\(184\) | 3.67419e76 | 0.364213 | ||||||||
\(185\) | − | 6.48884e75i | − | 0.0534969i | ||||||
\(186\) | 4.30934e76 | + | 9.65818e76i | 0.295781 | + | 0.662911i | ||||
\(187\) | 1.40580e77 | 0.804096 | ||||||||
\(188\) | 1.09744e77i | 0.523618i | ||||||||
\(189\) | 8.57437e76 | − | 2.66058e77i | 0.341586 | − | 1.05992i | ||||
\(190\) | −8.56926e76 | −0.285313 | ||||||||
\(191\) | − | 7.15809e77i | − | 1.99371i | −0.0792288 | − | 0.996856i | \(-0.525246\pi\) | ||
0.0792288 | − | 0.996856i | \(-0.474754\pi\) | |||||||
\(192\) | 1.85828e77 | − | 8.29139e76i | 0.433381 | − | 0.193368i | ||||
\(193\) | 1.71789e77 | 0.335775 | 0.167887 | − | 0.985806i | \(-0.446306\pi\) | ||||
0.167887 | + | 0.985806i | \(0.446306\pi\) | |||||||
\(194\) | 1.03572e78i | 1.69818i | ||||||||
\(195\) | 5.32741e76 | + | 1.19399e77i | 0.0733398 | + | 0.164371i | ||||
\(196\) | −6.99025e76 | −0.0808698 | ||||||||
\(197\) | 7.28159e76i | 0.0708557i | 0.999372 | + | 0.0354278i | \(0.0112794\pi\) | ||||
−0.999372 | + | 0.0354278i | \(0.988721\pi\) | |||||||
\(198\) | −9.19096e77 | + | 1.02404e78i | −0.752913 | + | 0.838884i | ||||
\(199\) | 4.42225e77 | 0.305238 | 0.152619 | − | 0.988285i | \(-0.451229\pi\) | ||||
0.152619 | + | 0.988285i | \(0.451229\pi\) | |||||||
\(200\) | − | 1.26577e78i | − | 0.736776i | ||||||
\(201\) | −1.67743e78 | + | 7.48447e77i | −0.824099 | + | 0.367701i | ||||
\(202\) | −4.30170e78 | −1.78523 | ||||||||
\(203\) | − | 2.43815e78i | − | 0.855451i | ||||||
\(204\) | 3.81246e77 | + | 8.54457e77i | 0.113183 | + | 0.253667i | ||||
\(205\) | −6.31478e77 | −0.158755 | ||||||||
\(206\) | − | 4.27673e78i | − | 0.911225i | ||||||
\(207\) | 1.95596e78 | + | 1.75551e78i | 0.353483 | + | 0.317257i | ||||
\(208\) | −7.25323e78 | −1.11270 | ||||||||
\(209\) | − | 9.32851e78i | − | 1.21573i | ||||||
\(210\) | −2.10000e78 | + | 9.36991e77i | −0.232683 | + | 0.103820i | ||||
\(211\) | 1.65840e79 | 1.56346 | 0.781728 | − | 0.623619i | \(-0.214338\pi\) | ||||
0.781728 | + | 0.623619i | \(0.214338\pi\) | |||||||
\(212\) | 5.83328e78i | 0.468267i | ||||||||
\(213\) | 1.52509e78 | + | 3.41805e78i | 0.104325 | + | 0.233815i | ||||
\(214\) | 1.33820e79 | 0.780642 | ||||||||
\(215\) | − | 6.60402e78i | − | 0.328777i | ||||||
\(216\) | 1.71654e79 | + | 5.53198e78i | 0.729839 | + | 0.235208i | ||||
\(217\) | −1.92403e79 | −0.699167 | ||||||||
\(218\) | 3.79493e79i | 1.17946i | ||||||||
\(219\) | −9.53535e78 | + | 4.25453e78i | −0.253651 | + | 0.113175i | ||||
\(220\) | 2.85184e78 | 0.0649761 | ||||||||
\(221\) | 3.84145e79i | 0.750166i | ||||||||
\(222\) | 7.60372e78 | + | 1.70416e79i | 0.127358 | + | 0.285437i | ||||
\(223\) | 4.05994e79 | 0.583652 | 0.291826 | − | 0.956471i | \(-0.405737\pi\) | ||||
0.291826 | + | 0.956471i | \(0.405737\pi\) | |||||||
\(224\) | − | 5.84115e79i | − | 0.721217i | ||||||
\(225\) | 6.04778e79 | − | 6.73834e79i | 0.641786 | − | 0.715068i | ||||
\(226\) | 7.36964e79 | 0.672604 | ||||||||
\(227\) | 1.68370e80i | 1.32247i | 0.750181 | + | 0.661233i | \(0.229966\pi\) | ||||
−0.750181 | + | 0.661233i | \(0.770034\pi\) | |||||||
\(228\) | 5.66996e79 | − | 2.52985e79i | 0.383526 | − | 0.171124i | ||||
\(229\) | −2.25334e80 | −1.31347 | −0.656736 | − | 0.754120i | \(-0.728064\pi\) | ||||
−0.656736 | + | 0.754120i | \(0.728064\pi\) | |||||||
\(230\) | − | 2.16209e79i | − | 0.108674i | ||||||
\(231\) | −1.02001e80 | − | 2.28607e80i | −0.442382 | − | 0.991475i | ||||
\(232\) | 1.57304e80 | 0.589044 | ||||||||
\(233\) | − | 1.00818e80i | − | 0.326163i | −0.986613 | − | 0.163082i | \(-0.947857\pi\) | ||
0.986613 | − | 0.163082i | \(-0.0521434\pi\) | |||||||
\(234\) | −2.79827e80 | − | 2.51150e80i | −0.782620 | − | 0.702415i | ||||
\(235\) | −1.27172e80 | −0.307670 | ||||||||
\(236\) | − | 2.62934e80i | − | 0.550604i | ||||||
\(237\) | 5.86078e79 | − | 2.61499e79i | 0.106295 | − | 0.0474271i | ||||
\(238\) | −6.75638e80 | −1.06193 | ||||||||
\(239\) | 1.04423e81i | 1.42320i | 0.702583 | + | 0.711602i | \(0.252030\pi\) | ||||
−0.702583 | + | 0.711602i | \(0.747970\pi\) | |||||||
\(240\) | −8.34168e79 | − | 1.86955e80i | −0.0986441 | − | 0.221083i | ||||
\(241\) | −1.76780e81 | −1.81491 | −0.907453 | − | 0.420154i | \(-0.861976\pi\) | ||||
−0.907453 | + | 0.420154i | \(0.861976\pi\) | |||||||
\(242\) | − | 6.41858e79i | − | 0.0572422i | ||||||
\(243\) | 6.49489e80 | + | 1.11465e81i | 0.503452 | + | 0.864023i | ||||
\(244\) | 3.63568e80 | 0.245093 | ||||||||
\(245\) | − | 8.10036e79i | − | 0.0475179i | ||||||
\(246\) | 1.65845e81 | − | 7.39975e80i | 0.847048 | − | 0.377941i | ||||
\(247\) | 2.54909e81 | 1.13420 | ||||||||
\(248\) | − | 1.24134e81i | − | 0.481430i | ||||||
\(249\) | 9.68929e80 | + | 2.17158e81i | 0.327728 | + | 0.734511i | ||||
\(250\) | −1.52005e81 | −0.448640 | ||||||||
\(251\) | − | 4.93576e80i | − | 0.127189i | −0.997976 | − | 0.0635943i | \(-0.979744\pi\) | ||
0.997976 | − | 0.0635943i | \(-0.0202564\pi\) | |||||||
\(252\) | 1.11287e81 | − | 1.23994e81i | 0.250511 | − | 0.279115i | ||||
\(253\) | 2.35366e81 | 0.463068 | ||||||||
\(254\) | − | 7.26271e81i | − | 1.24955i | ||||||
\(255\) | −9.90151e80 | + | 4.41791e80i | −0.149051 | + | 0.0665044i | ||||
\(256\) | 6.89514e81 | 0.908624 | ||||||||
\(257\) | 9.31605e80i | 0.107524i | 0.998554 | + | 0.0537621i | \(0.0171212\pi\) | ||||
−0.998554 | + | 0.0537621i | \(0.982879\pi\) | |||||||
\(258\) | 7.73869e81 | + | 1.73441e82i | 0.782704 | + | 1.75421i | ||||
\(259\) | −3.39490e81 | −0.301048 | ||||||||
\(260\) | 7.79286e80i | 0.0606182i | ||||||||
\(261\) | 8.37408e81 | + | 7.51588e81i | 0.571689 | + | 0.513101i | ||||
\(262\) | −3.32656e82 | −1.99412 | ||||||||
\(263\) | − | 6.01550e79i | − | 0.00316793i | −0.999999 | − | 0.00158397i | \(-0.999496\pi\) | ||
0.999999 | − | 0.00158397i | \(-0.000504192\pi\) | |||||||
\(264\) | 1.47492e82 | − | 6.58087e81i | 0.682707 | − | 0.304614i | ||||
\(265\) | −6.75964e81 | −0.275147 | ||||||||
\(266\) | 4.48336e82i | 1.60557i | ||||||||
\(267\) | −1.22941e82 | − | 2.75537e82i | −0.387536 | − | 0.868554i | ||||
\(268\) | −1.09482e82 | −0.303919 | ||||||||
\(269\) | − | 6.04892e82i | − | 1.47945i | −0.672910 | − | 0.739725i | \(-0.734956\pi\) | ||
0.672910 | − | 0.739725i | \(-0.265044\pi\) | |||||||
\(270\) | 3.25531e81 | − | 1.01011e82i | 0.0701818 | − | 0.217771i | ||||
\(271\) | −6.91155e82 | −1.31407 | −0.657036 | − | 0.753859i | \(-0.728190\pi\) | ||||
−0.657036 | + | 0.753859i | \(0.728190\pi\) | |||||||
\(272\) | − | 6.01494e82i | − | 1.00899i | ||||||
\(273\) | 6.24685e82 | − | 2.78725e82i | 0.924977 | − | 0.412712i | ||||
\(274\) | −1.28219e83 | −1.67661 | ||||||||
\(275\) | − | 8.10842e82i | − | 0.936752i | ||||||
\(276\) | 6.38301e81 | + | 1.43057e82i | 0.0651804 | + | 0.146084i | ||||
\(277\) | 6.09620e82 | 0.550487 | 0.275243 | − | 0.961375i | \(-0.411242\pi\) | ||||
0.275243 | + | 0.961375i | \(0.411242\pi\) | |||||||
\(278\) | 2.65803e83i | 2.12342i | ||||||||
\(279\) | 5.93105e82 | − | 6.60828e82i | 0.419361 | − | 0.467246i | ||||
\(280\) | 2.69908e82 | 0.168983 | ||||||||
\(281\) | 2.16955e83i | 1.20325i | 0.798779 | + | 0.601625i | \(0.205480\pi\) | ||||
−0.798779 | + | 0.601625i | \(0.794520\pi\) | |||||||
\(282\) | 3.33993e83 | − | 1.49023e83i | 1.64160 | − | 0.732458i | ||||
\(283\) | −2.16587e83 | −0.943831 | −0.471915 | − | 0.881644i | \(-0.656437\pi\) | ||||
−0.471915 | + | 0.881644i | \(0.656437\pi\) | |||||||
\(284\) | 2.23087e82i | 0.0862286i | ||||||||
\(285\) | 2.93161e82 | + | 6.57039e82i | 0.100550 | + | 0.225354i | ||||
\(286\) | −3.36723e83 | −1.02525 | ||||||||
\(287\) | 3.30383e83i | 0.893375i | ||||||||
\(288\) | 2.00620e83 | + | 1.80060e83i | 0.481981 | + | 0.432587i | ||||
\(289\) | 1.49740e83 | 0.319750 | ||||||||
\(290\) | − | 9.25659e82i | − | 0.175760i | ||||||
\(291\) | 7.94128e83 | − | 3.54328e83i | 1.34131 | − | 0.598472i | ||||
\(292\) | −6.22347e82 | −0.0935439 | ||||||||
\(293\) | − | 6.78020e83i | − | 0.907285i | −0.891184 | − | 0.453642i | \(-0.850124\pi\) | ||
0.891184 | − | 0.453642i | \(-0.149876\pi\) | |||||||
\(294\) | 9.49212e82 | + | 2.12739e83i | 0.113124 | + | 0.253535i | ||||
\(295\) | 3.04690e83 | 0.323526 | ||||||||
\(296\) | − | 2.19031e83i | − | 0.207294i | ||||||
\(297\) | 1.09960e84 | + | 3.54374e83i | 0.927933 | + | 0.299049i | ||||
\(298\) | −6.03304e83 | −0.454133 | ||||||||
\(299\) | 6.43154e83i | 0.432011i | ||||||||
\(300\) | 4.92837e83 | − | 2.19897e83i | 0.295516 | − | 0.131855i | ||||
\(301\) | −3.45516e84 | −1.85015 | ||||||||
\(302\) | − | 3.55471e84i | − | 1.70047i | ||||||
\(303\) | 1.47164e84 | + | 3.29828e84i | 0.629149 | + | 1.41006i | ||||
\(304\) | −3.99136e84 | −1.52553 | ||||||||
\(305\) | 4.21305e83i | 0.144013i | ||||||||
\(306\) | 2.08273e84 | − | 2.32055e84i | 0.636949 | − | 0.709679i | ||||
\(307\) | −5.81498e84 | −1.59164 | −0.795818 | − | 0.605536i | \(-0.792959\pi\) | ||||
−0.795818 | + | 0.605536i | \(0.792959\pi\) | |||||||
\(308\) | − | 1.49206e84i | − | 0.365646i | ||||||
\(309\) | −3.27913e84 | + | 1.46310e84i | −0.719732 | + | 0.321134i | ||||
\(310\) | −7.30470e83 | −0.143650 | ||||||||
\(311\) | − | 2.63993e83i | − | 0.0465307i | −0.999729 | − | 0.0232653i | \(-0.992594\pi\) | ||
0.999729 | − | 0.0232653i | \(-0.00740625\pi\) | |||||||
\(312\) | 1.79827e84 | + | 4.03032e84i | 0.284183 | + | 0.636918i | ||||
\(313\) | 2.89450e84 | 0.410266 | 0.205133 | − | 0.978734i | \(-0.434237\pi\) | ||||
0.205133 | + | 0.978734i | \(0.434237\pi\) | |||||||
\(314\) | 4.62557e84i | 0.588243i | ||||||||
\(315\) | 1.43686e84 | + | 1.28960e84i | 0.164004 | + | 0.147196i | ||||
\(316\) | 3.82517e83 | 0.0392004 | ||||||||
\(317\) | − | 1.18721e85i | − | 1.09273i | −0.837549 | − | 0.546363i | \(-0.816012\pi\) | ||
0.837549 | − | 0.546363i | \(-0.183988\pi\) | |||||||
\(318\) | 1.77528e85 | − | 7.92105e84i | 1.46807 | − | 0.655030i | ||||
\(319\) | 1.00767e85 | 0.748923 | ||||||||
\(320\) | 1.40546e84i | 0.0939117i | ||||||||
\(321\) | −4.57808e84 | − | 1.02605e85i | −0.275114 | − | 0.616590i | ||||
\(322\) | −1.13119e85 | −0.611554 | ||||||||
\(323\) | 2.11390e85i | 1.02849i | ||||||||
\(324\) | 8.28160e83 | + | 7.64454e84i | 0.0362730 | + | 0.334827i | ||||
\(325\) | 2.21569e85 | 0.873925 | ||||||||
\(326\) | − | 1.85083e84i | − | 0.0657610i | ||||||
\(327\) | 2.90972e85 | − | 1.29828e85i | 0.931596 | − | 0.415665i | ||||
\(328\) | −2.13156e85 | −0.615157 | ||||||||
\(329\) | 6.65355e85i | 1.73138i | ||||||||
\(330\) | −3.87253e84 | − | 8.67920e84i | −0.0908911 | − | 0.203707i | ||||
\(331\) | −1.68286e85 | −0.356365 | −0.178183 | − | 0.983997i | \(-0.557022\pi\) | ||||
−0.178183 | + | 0.983997i | \(0.557022\pi\) | |||||||
\(332\) | 1.41733e85i | 0.270880i | ||||||||
\(333\) | 1.04652e85 | − | 1.16601e85i | 0.180569 | − | 0.201187i | ||||
\(334\) | 5.02941e85 | 0.783677 | ||||||||
\(335\) | − | 1.26868e85i | − | 0.178579i | ||||||
\(336\) | −9.78133e85 | + | 4.36429e85i | −1.24412 | + | 0.555109i | ||||
\(337\) | 1.09475e84 | 0.0125863 | 0.00629314 | − | 0.999980i | \(-0.497997\pi\) | ||||
0.00629314 | + | 0.999980i | \(0.497997\pi\) | |||||||
\(338\) | 1.92119e85i | 0.199711i | ||||||||
\(339\) | −2.52121e85 | − | 5.65059e85i | −0.237039 | − | 0.531256i | ||||
\(340\) | −6.46245e84 | −0.0549685 | ||||||||
\(341\) | − | 7.95191e85i | − | 0.612101i | ||||||
\(342\) | −1.53986e86 | − | 1.38205e86i | −1.07298 | − | 0.963020i | ||||
\(343\) | 1.34115e86 | 0.846206 | ||||||||
\(344\) | − | 2.22919e86i | − | 1.27397i | ||||||
\(345\) | −1.65776e85 | + | 7.39668e84i | −0.0858365 | + | 0.0382990i | ||||
\(346\) | −4.51637e86 | −2.11935 | ||||||||
\(347\) | − | 2.29793e86i | − | 0.977540i | −0.872413 | − | 0.488770i | \(-0.837446\pi\) | ||
0.872413 | − | 0.488770i | \(-0.162554\pi\) | |||||||
\(348\) | 2.73277e85 | + | 6.12474e85i | 0.105417 | + | 0.236262i | ||||
\(349\) | 4.51770e86 | 1.58071 | 0.790357 | − | 0.612646i | \(-0.209895\pi\) | ||||
0.790357 | + | 0.612646i | \(0.209895\pi\) | |||||||
\(350\) | 3.89697e86i | 1.23713i | ||||||||
\(351\) | −9.68353e85 | + | 3.00475e86i | −0.278992 | + | 0.865698i | ||||
\(352\) | 2.41412e86 | 0.631404 | ||||||||
\(353\) | 3.93415e85i | 0.0934353i | 0.998908 | + | 0.0467177i | \(0.0148761\pi\) | ||||
−0.998908 | + | 0.0467177i | \(0.985124\pi\) | |||||||
\(354\) | −8.00207e86 | + | 3.57041e86i | −1.72620 | + | 0.770206i | ||||
\(355\) | −2.58515e85 | −0.0506666 | ||||||||
\(356\) | − | 1.79836e86i | − | 0.320314i | ||||||
\(357\) | 2.31141e86 | + | 5.18038e86i | 0.374246 | + | 0.838768i | ||||
\(358\) | 1.40053e87 | 2.06190 | ||||||||
\(359\) | − | 6.87613e85i | − | 0.0920732i | −0.998940 | − | 0.0460366i | \(-0.985341\pi\) | ||
0.998940 | − | 0.0460366i | \(-0.0146591\pi\) | |||||||
\(360\) | −8.32021e85 | + | 9.27025e85i | −0.101356 | + | 0.112929i | ||||
\(361\) | 5.00651e86 | 0.554996 | ||||||||
\(362\) | − | 2.47566e86i | − | 0.249804i | ||||||
\(363\) | −4.92137e85 | + | 2.19584e85i | −0.0452128 | + | 0.0201733i | ||||
\(364\) | 4.07715e86 | 0.341122 | ||||||||
\(365\) | − | 7.21180e85i | − | 0.0549650i | ||||||
\(366\) | −4.93692e86 | − | 1.10647e87i | −0.342846 | − | 0.768393i | ||||
\(367\) | 8.37135e86 | 0.529846 | 0.264923 | − | 0.964270i | \(-0.414653\pi\) | ||||
0.264923 | + | 0.964270i | \(0.414653\pi\) | |||||||
\(368\) | − | 1.00705e87i | − | 0.581067i | ||||||
\(369\) | −1.13474e87 | − | 1.01845e87i | −0.597033 | − | 0.535847i | ||||
\(370\) | −1.28890e86 | −0.0618528 | ||||||||
\(371\) | 3.53658e87i | 1.54836i | ||||||||
\(372\) | 4.83325e86 | − | 2.15652e86i | 0.193098 | − | 0.0861577i | ||||
\(373\) | 2.98517e87 | 1.08860 | 0.544300 | − | 0.838890i | \(-0.316795\pi\) | ||||
0.544300 | + | 0.838890i | \(0.316795\pi\) | |||||||
\(374\) | − | 2.79237e87i | − | 0.929692i | ||||||
\(375\) | 5.20022e86 | + | 1.16548e87i | 0.158110 | + | 0.354359i | ||||
\(376\) | −4.29271e87 | −1.19219 | ||||||||
\(377\) | 2.75355e87i | 0.698693i | ||||||||
\(378\) | −5.28478e87 | − | 1.70315e87i | −1.22548 | − | 0.394940i | ||||
\(379\) | 5.25133e87 | 1.11310 | 0.556552 | − | 0.830813i | \(-0.312124\pi\) | ||||
0.556552 | + | 0.830813i | \(0.312124\pi\) | |||||||
\(380\) | 4.28832e86i | 0.0831083i | ||||||||
\(381\) | −5.56861e87 | + | 2.48463e87i | −0.986955 | + | 0.440365i | ||||
\(382\) | −1.42183e88 | −2.30512 | ||||||||
\(383\) | 7.02219e87i | 1.04163i | 0.853669 | + | 0.520816i | \(0.174372\pi\) | ||||
−0.853669 | + | 0.520816i | \(0.825628\pi\) | |||||||
\(384\) | −3.59090e87 | − | 8.04799e87i | −0.487463 | − | 1.09251i | ||||
\(385\) | 1.72900e87 | 0.214848 | ||||||||
\(386\) | − | 3.41230e87i | − | 0.388221i | ||||||
\(387\) | 1.06509e88 | − | 1.18671e88i | 1.10972 | − | 1.23644i | ||||
\(388\) | 5.18306e87 | 0.494661 | ||||||||
\(389\) | − | 3.59519e87i | − | 0.314366i | −0.987570 | − | 0.157183i | \(-0.949759\pi\) | ||
0.987570 | − | 0.157183i | \(-0.0502412\pi\) | |||||||
\(390\) | 2.37166e87 | − | 1.05820e87i | 0.190044 | − | 0.0847951i | ||||
\(391\) | −5.33354e87 | −0.391747 | ||||||||
\(392\) | − | 2.73428e87i | − | 0.184127i | ||||||
\(393\) | 1.13804e88 | + | 2.55061e88i | 0.702768 | + | 1.57506i | ||||
\(394\) | 1.44636e87 | 0.0819229 | ||||||||
\(395\) | 4.43264e86i | 0.0230336i | ||||||||
\(396\) | 5.12462e87 | + | 4.59943e87i | 0.244357 | + | 0.219315i | ||||
\(397\) | 2.41590e88 | 1.05731 | 0.528653 | − | 0.848838i | \(-0.322697\pi\) | ||||
0.528653 | + | 0.848838i | \(0.322697\pi\) | |||||||
\(398\) | − | 8.78404e87i | − | 0.352915i | ||||||
\(399\) | 3.43757e88 | − | 1.53379e88i | 1.26816 | − | 0.565833i | ||||
\(400\) | −3.46933e88 | −1.17545 | ||||||||
\(401\) | 2.69778e87i | 0.0839648i | 0.999118 | + | 0.0419824i | \(0.0133673\pi\) | ||||
−0.999118 | + | 0.0419824i | \(0.986633\pi\) | |||||||
\(402\) | 1.48666e88 | + | 3.33193e88i | 0.425134 | + | 0.952819i | ||||
\(403\) | 2.17292e88 | 0.571047 | ||||||||
\(404\) | 2.15270e88i | 0.520016i | ||||||||
\(405\) | −8.85855e87 | + | 9.59677e86i | −0.196740 | + | 0.0213135i | ||||
\(406\) | −4.84297e88 | −0.989068 | ||||||||
\(407\) | − | 1.40309e88i | − | 0.263558i | ||||||
\(408\) | −3.34226e88 | + | 1.49127e88i | −0.577556 | + | 0.257697i | ||||
\(409\) | −1.10706e88 | −0.176027 | −0.0880134 | − | 0.996119i | \(-0.528052\pi\) | ||||
−0.0880134 | + | 0.996119i | \(0.528052\pi\) | |||||||
\(410\) | 1.25432e88i | 0.183551i | ||||||||
\(411\) | 4.38647e88 | + | 9.83104e88i | 0.590871 | + | 1.32427i | ||||
\(412\) | −2.14020e88 | −0.265430 | ||||||||
\(413\) | − | 1.59411e89i | − | 1.82061i | ||||||
\(414\) | 3.48701e88 | − | 3.88518e88i | 0.366811 | − | 0.408695i | ||||
\(415\) | −1.64242e88 | −0.159165 | ||||||||
\(416\) | 6.59675e88i | 0.589056i | ||||||||
\(417\) | 2.03801e89 | − | 9.09331e88i | 1.67718 | − | 0.748335i | ||||
\(418\) | −1.85295e89 | −1.40563 | ||||||||
\(419\) | 6.64029e88i | 0.464419i | 0.972666 | + | 0.232210i | \(0.0745955\pi\) | ||||
−0.972666 | + | 0.232210i | \(0.925404\pi\) | |||||||
\(420\) | 4.68899e87 | + | 1.05091e88i | 0.0302415 | + | 0.0677778i | ||||
\(421\) | −1.62399e89 | −0.966035 | −0.483017 | − | 0.875611i | \(-0.660459\pi\) | ||||
−0.483017 | + | 0.875611i | \(0.660459\pi\) | |||||||
\(422\) | − | 3.29413e89i | − | 1.80766i | ||||||
\(423\) | −2.28523e89 | − | 2.05103e89i | −1.15706 | − | 1.03848i | ||||
\(424\) | −2.28172e89 | −1.06616 | ||||||||
\(425\) | 1.83742e89i | 0.792474i | ||||||||
\(426\) | 6.78937e88 | − | 3.02932e88i | 0.270336 | − | 0.120620i | ||||
\(427\) | 2.20423e89 | 0.810418 | ||||||||
\(428\) | − | 6.69674e88i | − | 0.227392i | ||||||
\(429\) | 1.15196e89 | + | 2.58179e89i | 0.361317 | + | 0.809791i | ||||
\(430\) | −1.31178e89 | −0.380130 | ||||||||
\(431\) | 7.30357e89i | 1.95573i | 0.209246 | + | 0.977863i | \(0.432899\pi\) | ||||
−0.209246 | + | 0.977863i | \(0.567101\pi\) | |||||||
\(432\) | 1.51625e89 | − | 4.70484e89i | 0.375252 | − | 1.16439i | ||||
\(433\) | 1.20039e89 | 0.274621 | 0.137310 | − | 0.990528i | \(-0.456154\pi\) | ||||
0.137310 | + | 0.990528i | \(0.456154\pi\) | |||||||
\(434\) | 3.82175e89i | 0.808373i | ||||||||
\(435\) | −7.09739e88 | + | 3.16675e88i | −0.138824 | + | 0.0619412i | ||||
\(436\) | 1.89910e89 | 0.343563 | ||||||||
\(437\) | 3.53920e89i | 0.592292i | ||||||||
\(438\) | 8.45090e88 | + | 1.89403e89i | 0.130853 | + | 0.293270i | ||||
\(439\) | 4.92290e89 | 0.705387 | 0.352694 | − | 0.935739i | \(-0.385266\pi\) | ||||
0.352694 | + | 0.935739i | \(0.385266\pi\) | |||||||
\(440\) | 1.11551e89i | 0.147939i | ||||||||
\(441\) | 1.30642e89 | − | 1.45560e89i | 0.160388 | − | 0.178702i | ||||
\(442\) | 7.63037e89 | 0.867338 | ||||||||
\(443\) | − | 8.30618e89i | − | 0.874328i | −0.899382 | − | 0.437164i | \(-0.855983\pi\) | ||
0.899382 | − | 0.437164i | \(-0.144017\pi\) | |||||||
\(444\) | 8.52814e88 | − | 3.80513e88i | 0.0831444 | − | 0.0370978i | ||||
\(445\) | 2.08395e89 | 0.188212 | ||||||||
\(446\) | − | 8.06437e89i | − | 0.674816i | ||||||
\(447\) | 2.06395e89 | + | 4.62577e89i | 0.160046 | + | 0.358697i | ||||
\(448\) | 7.35325e89 | 0.528478 | ||||||||
\(449\) | − | 9.67234e89i | − | 0.644401i | −0.946671 | − | 0.322200i | \(-0.895578\pi\) | ||
0.946671 | − | 0.322200i | \(-0.104422\pi\) | |||||||
\(450\) | −1.33846e90 | − | 1.20129e90i | −0.826758 | − | 0.742030i | ||||
\(451\) | −1.36546e90 | −0.782124 | ||||||||
\(452\) | − | 3.68799e89i | − | 0.195922i | ||||||
\(453\) | −2.72553e90 | + | 1.21609e90i | −1.34311 | + | 0.599278i | ||||
\(454\) | 3.34437e90 | 1.52903 | ||||||||
\(455\) | 4.72463e89i | 0.200438i | ||||||||
\(456\) | 9.89566e89 | + | 2.21784e90i | 0.389619 | + | 0.873222i | ||||
\(457\) | −2.44890e90 | −0.894994 | −0.447497 | − | 0.894285i | \(-0.647684\pi\) | ||||
−0.447497 | + | 0.894285i | \(0.647684\pi\) | |||||||
\(458\) | 4.47588e90i | 1.51863i | ||||||||
\(459\) | −2.49177e90 | − | 8.03034e89i | −0.785013 | − | 0.252990i | ||||
\(460\) | −1.08198e89 | −0.0316556 | ||||||||
\(461\) | − | 5.49886e90i | − | 1.49431i | −0.664648 | − | 0.747156i | \(-0.731419\pi\) | ||
0.664648 | − | 0.747156i | \(-0.268581\pi\) | |||||||
\(462\) | −4.54088e90 | + | 2.02607e90i | −1.14634 | + | 0.511480i | ||||
\(463\) | 1.91790e90 | 0.449854 | 0.224927 | − | 0.974376i | \(-0.427786\pi\) | ||||
0.224927 | + | 0.974376i | \(0.427786\pi\) | |||||||
\(464\) | − | 4.31151e90i | − | 0.939762i | ||||||
\(465\) | 2.49900e89 | + | 5.60080e89i | 0.0506250 | + | 0.113462i | ||||
\(466\) | −2.00257e90 | −0.377109 | ||||||||
\(467\) | 4.58814e89i | 0.0803273i | 0.999193 | + | 0.0401636i | \(0.0127879\pi\) | ||||
−0.999193 | + | 0.0401636i | \(0.987212\pi\) | |||||||
\(468\) | −1.25683e90 | + | 1.40034e90i | −0.204606 | + | 0.227968i | ||||
\(469\) | −6.63763e90 | −1.00493 | ||||||||
\(470\) | 2.52606e90i | 0.355727i | ||||||||
\(471\) | 3.54660e90 | − | 1.58244e90i | 0.464624 | − | 0.207308i | ||||
\(472\) | 1.02848e91 | 1.25363 | ||||||||
\(473\) | − | 1.42800e91i | − | 1.61976i | ||||||
\(474\) | −5.19423e89 | − | 1.16414e90i | −0.0548350 | − | 0.122897i | ||||
\(475\) | 1.21927e91 | 1.19816 | ||||||||
\(476\) | 3.38109e90i | 0.309329i | ||||||||
\(477\) | −1.21468e91 | − | 1.09019e91i | −1.03475 | − | 0.928706i | ||||
\(478\) | 2.07418e91 | 1.64550 | ||||||||
\(479\) | 1.28875e91i | 0.952270i | 0.879372 | + | 0.476135i | \(0.157963\pi\) | ||||
−0.879372 | + | 0.476135i | \(0.842037\pi\) | |||||||
\(480\) | −1.70034e90 | + | 7.58668e89i | −0.117040 | + | 0.0522216i | ||||
\(481\) | 3.83406e90 | 0.245882 | ||||||||
\(482\) | 3.51143e91i | 2.09838i | ||||||||
\(483\) | 3.86988e90 | + | 8.67324e90i | 0.215523 | + | 0.483036i | ||||
\(484\) | −3.21205e89 | −0.0166740 | ||||||||
\(485\) | 6.00617e90i | 0.290655i | ||||||||
\(486\) | 2.21406e91 | − | 1.29010e91i | 0.998979 | − | 0.582089i | ||||
\(487\) | −1.73033e91 | −0.728021 | −0.364011 | − | 0.931395i | \(-0.618593\pi\) | ||||
−0.364011 | + | 0.931395i | \(0.618593\pi\) | |||||||
\(488\) | 1.42212e91i | 0.558035i | ||||||||
\(489\) | −1.41910e90 | + | 6.33184e89i | −0.0519414 | + | 0.0231755i | ||||
\(490\) | −1.60900e90 | −0.0549399 | ||||||||
\(491\) | − | 5.25722e90i | − | 0.167489i | −0.996487 | − | 0.0837444i | \(-0.973312\pi\) | ||
0.996487 | − | 0.0837444i | \(-0.0266879\pi\) | |||||||
\(492\) | −3.70306e90 | − | 8.29937e90i | −0.110090 | − | 0.246736i | ||||
\(493\) | −2.28346e91 | −0.633574 | ||||||||
\(494\) | − | 5.06332e91i | − | 1.31135i | ||||||
\(495\) | −5.32986e90 | + | 5.93844e90i | −0.128866 | + | 0.143581i | ||||
\(496\) | −3.40236e91 | −0.768075 | ||||||||
\(497\) | 1.35253e91i | 0.285121i | ||||||||
\(498\) | 4.31347e91 | − | 1.92461e91i | 0.849238 | − | 0.378918i | ||||
\(499\) | −4.47706e91 | −0.823330 | −0.411665 | − | 0.911335i | \(-0.635053\pi\) | ||||
−0.411665 | + | 0.911335i | \(0.635053\pi\) | |||||||
\(500\) | 7.60680e90i | 0.130684i | ||||||||
\(501\) | −1.72060e91 | − | 3.85624e91i | −0.276183 | − | 0.618987i | ||||
\(502\) | −9.80404e90 | −0.147055 | ||||||||
\(503\) | − | 3.53315e91i | − | 0.495280i | −0.968852 | − | 0.247640i | \(-0.920345\pi\) | ||
0.968852 | − | 0.247640i | \(-0.0796551\pi\) | |||||||
\(504\) | 4.85011e91 | + | 4.35306e91i | 0.635497 | + | 0.570370i | ||||
\(505\) | −2.49456e91 | −0.305554 | ||||||||
\(506\) | − | 4.67513e91i | − | 0.535397i | ||||||
\(507\) | 1.47305e91 | − | 6.57253e90i | 0.157742 | − | 0.0703821i | ||||
\(508\) | −3.63448e91 | −0.363979 | ||||||||
\(509\) | − | 7.41101e91i | − | 0.694181i | −0.937832 | − | 0.347091i | \(-0.887170\pi\) | ||
0.937832 | − | 0.347091i | \(-0.112830\pi\) | |||||||
\(510\) | 8.77541e90 | + | 1.96676e91i | 0.0768921 | + | 0.172332i | ||||
\(511\) | −3.77315e91 | −0.309309 | ||||||||
\(512\) | 1.90055e91i | 0.145781i | ||||||||
\(513\) | −5.32873e91 | + | 1.65348e92i | −0.382502 | + | 1.18688i | ||||
\(514\) | 1.85047e91 | 0.124319 | ||||||||
\(515\) | − | 2.48008e91i | − | 0.155962i | ||||||
\(516\) | 8.67952e91 | − | 3.87268e91i | 0.510982 | − | 0.227993i | ||||
\(517\) | −2.74987e92 | −1.51577 | ||||||||
\(518\) | 6.74339e91i | 0.348070i | ||||||||
\(519\) | 1.54509e92 | + | 3.46288e92i | 0.746900 | + | 1.67397i | ||||
\(520\) | −3.04822e91 | −0.138017 | ||||||||
\(521\) | − | 9.12033e91i | − | 0.386837i | −0.981116 | − | 0.193418i | \(-0.938042\pi\) | ||
0.981116 | − | 0.193418i | \(-0.0619575\pi\) | |||||||
\(522\) | 1.49290e92 | − | 1.66337e92i | 0.593244 | − | 0.660984i | ||||
\(523\) | 3.06182e92 | 1.14004 | 0.570022 | − | 0.821629i | \(-0.306935\pi\) | ||||
0.570022 | + | 0.821629i | \(0.306935\pi\) | |||||||
\(524\) | 1.66471e92i | 0.580865i | ||||||||
\(525\) | 2.98796e92 | − | 1.33318e92i | 0.977144 | − | 0.435988i | ||||
\(526\) | −1.19487e90 | −0.00366275 | ||||||||
\(527\) | 1.80195e92i | 0.517825i | ||||||||
\(528\) | −1.80374e92 | − | 4.04257e92i | −0.485982 | − | 1.08919i | ||||
\(529\) | 3.06519e92 | 0.774398 | ||||||||
\(530\) | 1.34269e92i | 0.318123i | ||||||||
\(531\) | 5.47514e92 | + | 4.91403e92i | 1.21669 | + | 1.09200i | ||||
\(532\) | 2.24361e92 | 0.467683 | ||||||||
\(533\) | − | 3.73121e92i | − | 0.729667i | ||||||
\(534\) | −5.47306e92 | + | 2.44200e92i | −1.00422 | + | 0.448067i | ||||
\(535\) | 7.76024e91 | 0.133612 | ||||||||
\(536\) | − | 4.28244e92i | − | 0.691972i | ||||||
\(537\) | −4.79131e92 | − | 1.07384e93i | −0.726656 | − | 1.62860i | ||||
\(538\) | −1.20151e93 | −1.71053 | ||||||||
\(539\) | − | 1.75156e92i | − | 0.234102i | ||||||
\(540\) | −5.05488e91 | − | 1.62906e91i | −0.0634341 | − | 0.0204432i | ||||
\(541\) | 5.55105e91 | 0.0654136 | 0.0327068 | − | 0.999465i | \(-0.489587\pi\) | ||||
0.0327068 | + | 0.999465i | \(0.489587\pi\) | |||||||
\(542\) | 1.37286e93i | 1.51932i | ||||||||
\(543\) | −1.89818e92 | + | 8.46941e91i | −0.197308 | + | 0.0880357i | ||||
\(544\) | −5.47054e92 | −0.534156 | ||||||||
\(545\) | 2.20069e92i | 0.201873i | ||||||||
\(546\) | −5.53640e92 | − | 1.24083e93i | −0.477175 | − | 1.06945i | ||||
\(547\) | 1.49648e93 | 1.21200 | 0.605999 | − | 0.795465i | \(-0.292773\pi\) | ||||
0.605999 | + | 0.795465i | \(0.292773\pi\) | |||||||
\(548\) | 6.41646e92i | 0.488378i | ||||||||
\(549\) | −6.79479e92 | + | 7.57065e92i | −0.486090 | + | 0.541594i | ||||
\(550\) | −1.61060e93 | −1.08307 | ||||||||
\(551\) | 1.51524e93i | 0.957917i | ||||||||
\(552\) | −5.59577e92 | + | 2.49675e92i | −0.332607 | + | 0.148404i | ||||
\(553\) | 2.31912e92 | 0.129619 | ||||||||
\(554\) | − | 1.21090e93i | − | 0.636470i | ||||||
\(555\) | 4.40941e91 | + | 9.88247e91i | 0.0217981 | + | 0.0488544i | ||||
\(556\) | 1.33016e93 | 0.618528 | ||||||||
\(557\) | − | 2.73968e93i | − | 1.19846i | −0.800578 | − | 0.599228i | \(-0.795474\pi\) | ||
0.800578 | − | 0.599228i | \(-0.204526\pi\) | |||||||
\(558\) | −1.31262e93 | − | 1.17810e93i | −0.540227 | − | 0.484863i | ||||
\(559\) | 3.90212e93 | 1.51112 | ||||||||
\(560\) | − | 7.39784e92i | − | 0.269595i | ||||||
\(561\) | −2.14102e93 | + | 9.55293e92i | −0.734317 | + | 0.327642i | ||||
\(562\) | 4.30944e93 | 1.39119 | ||||||||
\(563\) | − | 2.77015e93i | − | 0.841818i | −0.907103 | − | 0.420909i | \(-0.861711\pi\) | ||
0.907103 | − | 0.420909i | \(-0.138289\pi\) | |||||||
\(564\) | −7.45754e92 | − | 1.67140e93i | −0.213357 | − | 0.478179i | ||||
\(565\) | 4.27367e92 | 0.115121 | ||||||||
\(566\) | 4.30213e93i | 1.09125i | ||||||||
\(567\) | 5.02095e92 | + | 4.63471e93i | 0.119939 | + | 1.10713i | ||||
\(568\) | −8.72619e92 | −0.196328 | ||||||||
\(569\) | − | 4.21480e93i | − | 0.893222i | −0.894728 | − | 0.446611i | \(-0.852631\pi\) | ||
0.894728 | − | 0.446611i | \(-0.147369\pi\) | |||||||
\(570\) | 1.30509e93 | − | 5.82314e92i | 0.260553 | − | 0.116255i | ||||
\(571\) | −1.40508e93 | −0.264285 | −0.132142 | − | 0.991231i | \(-0.542186\pi\) | ||||
−0.132142 | + | 0.991231i | \(0.542186\pi\) | |||||||
\(572\) | 1.68507e93i | 0.298643i | ||||||||
\(573\) | 4.86419e93 | + | 1.09017e94i | 0.812370 | + | 1.82070i | ||||
\(574\) | 6.56250e93 | 1.03292 | ||||||||
\(575\) | 3.07630e93i | 0.456375i | ||||||||
\(576\) | −2.26672e93 | + | 2.52555e93i | −0.316982 | + | 0.353176i | ||||
\(577\) | 4.64687e93 | 0.612608 | 0.306304 | − | 0.951934i | \(-0.400908\pi\) | ||||
0.306304 | + | 0.951934i | \(0.400908\pi\) | |||||||
\(578\) | − | 2.97433e93i | − | 0.369694i | ||||||
\(579\) | −2.61634e93 | + | 1.16737e93i | −0.306636 | + | 0.136817i | ||||
\(580\) | −4.63228e92 | −0.0511968 | ||||||||
\(581\) | 8.59298e93i | 0.895685i | ||||||||
\(582\) | −7.03812e93 | − | 1.57740e94i | −0.691951 | − | 1.55081i | ||||
\(583\) | −1.46165e94 | −1.35554 | ||||||||
\(584\) | − | 2.43435e93i | − | 0.212983i | ||||||
\(585\) | −1.62272e93 | − | 1.45642e93i | −0.133951 | − | 0.120223i | ||||
\(586\) | −1.34677e94 | −1.04900 | ||||||||
\(587\) | − | 1.01821e94i | − | 0.748416i | −0.927345 | − | 0.374208i | \(-0.877915\pi\) | ||
0.927345 | − | 0.374208i | \(-0.122085\pi\) | |||||||
\(588\) | 1.06461e93 | − | 4.75014e92i | 0.0738520 | − | 0.0329517i | ||||
\(589\) | 1.19573e94 | 0.782913 | ||||||||
\(590\) | − | 6.05214e93i | − | 0.374060i | ||||||
\(591\) | −4.94812e92 | − | 1.10898e93i | −0.0288713 | − | 0.0647068i | ||||
\(592\) | −6.00338e93 | −0.330718 | ||||||||
\(593\) | − | 1.93681e94i | − | 1.00746i | −0.863861 | − | 0.503731i | \(-0.831960\pi\) | ||
0.863861 | − | 0.503731i | \(-0.168040\pi\) | |||||||
\(594\) | 7.03903e93 | − | 2.18417e94i | 0.345759 | − | 1.07287i | ||||
\(595\) | −3.91804e93 | −0.181757 | ||||||||
\(596\) | 3.01912e93i | 0.132284i | ||||||||
\(597\) | −6.73506e93 | + | 3.00509e93i | −0.278750 | + | 0.124374i | ||||
\(598\) | 1.27751e94 | 0.499489 | ||||||||
\(599\) | 1.66298e94i | 0.614291i | 0.951663 | + | 0.307145i | \(0.0993738\pi\) | ||||
−0.951663 | + | 0.307145i | \(0.900626\pi\) | |||||||
\(600\) | 8.60139e93 | + | 1.92776e94i | 0.300211 | + | 0.672839i | ||||
\(601\) | −5.90854e94 | −1.94871 | −0.974356 | − | 0.225010i | \(-0.927759\pi\) | ||||
−0.974356 | + | 0.225010i | \(0.927759\pi\) | |||||||
\(602\) | 6.86309e94i | 2.13914i | ||||||||
\(603\) | 2.04613e94 | − | 2.27976e94i | 0.602759 | − | 0.671585i | ||||
\(604\) | −1.77888e94 | −0.495327 | ||||||||
\(605\) | − | 3.72214e92i | − | 0.00979739i | ||||||
\(606\) | 6.55146e94 | − | 2.92317e94i | 1.63030 | − | 0.727418i | ||||
\(607\) | −1.06612e94 | −0.250837 | −0.125419 | − | 0.992104i | \(-0.540027\pi\) | ||||
−0.125419 | + | 0.992104i | \(0.540027\pi\) | |||||||
\(608\) | 3.63011e94i | 0.807604i | ||||||||
\(609\) | 1.65682e94 | + | 3.71329e94i | 0.348567 | + | 0.781216i | ||||
\(610\) | 8.36850e93 | 0.166507 | ||||||||
\(611\) | − | 7.51424e94i | − | 1.41411i | ||||||
\(612\) | −1.16127e94 | − | 1.04226e94i | −0.206721 | − | 0.185536i | ||||
\(613\) | 1.72386e94 | 0.290300 | 0.145150 | − | 0.989410i | \(-0.453634\pi\) | ||||
0.145150 | + | 0.989410i | \(0.453634\pi\) | |||||||
\(614\) | 1.15505e95i | 1.84024i | ||||||||
\(615\) | 9.61737e93 | − | 4.29113e93i | 0.144978 | − | 0.0646871i | ||||
\(616\) | 5.83626e94 | 0.832512 | ||||||||
\(617\) | − | 1.07332e95i | − | 1.44888i | −0.689336 | − | 0.724442i | \(-0.742098\pi\) | ||
0.689336 | − | 0.724442i | \(-0.257902\pi\) | |||||||
\(618\) | 2.90620e94 | + | 6.51343e94i | 0.371293 | + | 0.832150i | ||||
\(619\) | −5.31537e94 | −0.642764 | −0.321382 | − | 0.946950i | \(-0.604147\pi\) | ||||
−0.321382 | + | 0.946950i | \(0.604147\pi\) | |||||||
\(620\) | 3.65549e93i | 0.0418435i | ||||||||
\(621\) | −4.17185e94 | − | 1.34448e94i | −0.452079 | − | 0.145693i | ||||
\(622\) | −5.24377e93 | −0.0537985 | ||||||||
\(623\) | − | 1.09030e95i | − | 1.05914i | ||||||
\(624\) | 1.10466e95 | − | 4.92885e94i | 1.01614 | − | 0.453387i | ||||
\(625\) | 1.01484e95 | 0.884051 | ||||||||
\(626\) | − | 5.74942e94i | − | 0.474348i | ||||||
\(627\) | 6.33908e94 | + | 1.42073e95i | 0.495370 | + | 1.11023i | ||||
\(628\) | 2.31477e94 | 0.171349 | ||||||||
\(629\) | 3.17950e94i | 0.222965i | ||||||||
\(630\) | 2.56157e94 | − | 2.85407e94i | 0.170188 | − | 0.189620i | ||||
\(631\) | −2.13438e95 | −1.34361 | −0.671806 | − | 0.740728i | \(-0.734481\pi\) | ||||
−0.671806 | + | 0.740728i | \(0.734481\pi\) | |||||||
\(632\) | 1.49624e94i | 0.0892525i | ||||||||
\(633\) | −2.52573e95 | + | 1.12695e95i | −1.42778 | + | 0.637055i | ||||
\(634\) | −2.35818e95 | −1.26340 | ||||||||
\(635\) | − | 4.21166e94i | − | 0.213869i | ||||||
\(636\) | −3.96393e94 | − | 8.88405e94i | −0.190803 | − | 0.427631i | ||||
\(637\) | 4.78626e94 | 0.218401 | ||||||||
\(638\) | − | 2.00157e95i | − | 0.865901i | ||||||
\(639\) | −4.64540e94 | − | 4.16932e94i | −0.190543 | − | 0.171016i | ||||
\(640\) | 6.08688e94 | 0.236742 | ||||||||
\(641\) | 1.92445e95i | 0.709796i | 0.934905 | + | 0.354898i | \(0.115484\pi\) | ||||
−0.934905 | + | 0.354898i | \(0.884516\pi\) | |||||||
\(642\) | −2.03807e95 | + | 9.09356e94i | −0.712898 | + | 0.318085i | ||||
\(643\) | −4.13132e95 | −1.37062 | −0.685309 | − | 0.728253i | \(-0.740333\pi\) | ||||
−0.685309 | + | 0.728253i | \(0.740333\pi\) | |||||||
\(644\) | 5.66080e94i | 0.178139i | ||||||||
\(645\) | 4.48768e94 | + | 1.00579e95i | 0.133965 | + | 0.300246i | ||||
\(646\) | 4.19890e95 | 1.18913 | ||||||||
\(647\) | − | 1.23705e95i | − | 0.332385i | −0.986093 | − | 0.166192i | \(-0.946853\pi\) | ||
0.986093 | − | 0.166192i | \(-0.0531472\pi\) | |||||||
\(648\) | −2.99021e95 | + | 3.23940e94i | −0.762344 | + | 0.0825874i | ||||
\(649\) | 6.58837e95 | 1.59389 | ||||||||
\(650\) | − | 4.40108e95i | − | 1.01043i | ||||||
\(651\) | 2.93029e95 | − | 1.30745e95i | 0.638494 | − | 0.284887i | ||||
\(652\) | −9.26212e93 | −0.0191554 | ||||||||
\(653\) | 6.46490e95i | 1.26915i | 0.772860 | + | 0.634576i | \(0.218825\pi\) | ||||
−0.772860 | + | 0.634576i | \(0.781175\pi\) | |||||||
\(654\) | −2.57880e95 | − | 5.77966e95i | −0.480589 | − | 1.07711i | ||||
\(655\) | −1.92908e95 | −0.341308 | ||||||||
\(656\) | 5.84234e95i | 0.981423i | ||||||||
\(657\) | 1.16312e95 | − | 1.29593e95i | 0.185524 | − | 0.206708i | ||||
\(658\) | 1.32161e96 | 2.00181 | ||||||||
\(659\) | − | 5.84076e94i | − | 0.0840167i | −0.999117 | − | 0.0420084i | \(-0.986624\pi\) | ||
0.999117 | − | 0.0420084i | \(-0.0133756\pi\) | |||||||
\(660\) | −4.34333e94 | + | 1.93793e94i | −0.0593375 | + | 0.0264755i | ||||
\(661\) | 1.15780e96 | 1.50240 | 0.751199 | − | 0.660076i | \(-0.229476\pi\) | ||||
0.751199 | + | 0.660076i | \(0.229476\pi\) | |||||||
\(662\) | 3.34270e95i | 0.412028i | ||||||||
\(663\) | −2.61041e95 | − | 5.85050e95i | −0.305667 | − | 0.685067i | ||||
\(664\) | −5.54399e95 | −0.616747 | ||||||||
\(665\) | 2.59991e95i | 0.274803i | ||||||||
\(666\) | −2.31609e95 | − | 2.07873e95i | −0.232611 | − | 0.208773i | ||||
\(667\) | −3.82307e95 | −0.364867 | ||||||||
\(668\) | − | 2.51687e95i | − | 0.228276i | ||||||
\(669\) | −6.18326e95 | + | 2.75888e95i | −0.533003 | + | 0.237818i | ||||
\(670\) | −2.52002e95 | −0.206472 | ||||||||
\(671\) | 9.10996e95i | 0.709497i | ||||||||
\(672\) | 3.96928e95 | + | 8.89604e95i | 0.293871 | + | 0.658630i | ||||
\(673\) | 9.16629e94 | 0.0645181 | 0.0322590 | − | 0.999480i | \(-0.489730\pi\) | ||||
0.0322590 | + | 0.999480i | \(0.489730\pi\) | |||||||
\(674\) | − | 2.17453e94i | − | 0.0145522i | ||||||
\(675\) | −4.63178e95 | + | 1.43722e96i | −0.294727 | + | 0.914521i | ||||
\(676\) | 9.61420e94 | 0.0581735 | ||||||||
\(677\) | 3.10703e95i | 0.178785i | 0.995996 | + | 0.0893925i | \(0.0284926\pi\) | ||||
−0.995996 | + | 0.0893925i | \(0.971507\pi\) | |||||||
\(678\) | −1.12239e96 | + | 5.00795e95i | −0.614236 | + | 0.274063i | ||||
\(679\) | 3.14237e96 | 1.63563 | ||||||||
\(680\) | − | 2.52782e95i | − | 0.125154i | ||||||
\(681\) | −1.14413e96 | − | 2.56426e96i | −0.538859 | − | 1.20770i | ||||
\(682\) | −1.57951e96 | −0.707707 | ||||||||
\(683\) | − | 2.61309e96i | − | 1.11391i | −0.830543 | − | 0.556954i | \(-0.811970\pi\) | ||
0.830543 | − | 0.556954i | \(-0.188030\pi\) | |||||||
\(684\) | −6.91618e95 | + | 7.70590e95i | −0.280517 | + | 0.312547i | ||||
\(685\) | −7.43544e95 | −0.286964 | ||||||||
\(686\) | − | 2.66396e96i | − | 0.978379i | ||||||
\(687\) | 3.43183e96 | − | 1.53123e96i | 1.19949 | − | 0.535195i | ||||
\(688\) | −6.10994e96 | −2.03250 | ||||||||
\(689\) | − | 3.99407e96i | − | 1.26463i | ||||||
\(690\) | 1.46922e95 | + | 3.29285e95i | 0.0442811 | + | 0.0992438i | ||||
\(691\) | −1.35230e96 | −0.387989 | −0.193995 | − | 0.981003i | \(-0.562144\pi\) | ||||
−0.193995 | + | 0.981003i | \(0.562144\pi\) | |||||||
\(692\) | 2.26013e96i | 0.617342i | ||||||||
\(693\) | 3.10694e96 | + | 2.78853e96i | 0.807984 | + | 0.725180i | ||||
\(694\) | −4.56444e96 | −1.13023 | ||||||||
\(695\) | 1.54139e96i | 0.363438i | ||||||||
\(696\) | −2.39573e96 | + | 1.06894e96i | −0.537927 | + | 0.240015i | ||||
\(697\) | 3.09421e96 | 0.661661 | ||||||||
\(698\) | − | 8.97364e96i | − | 1.82761i | ||||||
\(699\) | 6.85094e95 | + | 1.53545e96i | 0.132900 | + | 0.297859i | ||||
\(700\) | 1.95016e96 | 0.360361 | ||||||||
\(701\) | 7.12654e96i | 1.25449i | 0.778824 | + | 0.627243i | \(0.215817\pi\) | ||||
−0.778824 | + | 0.627243i | \(0.784183\pi\) | |||||||
\(702\) | 5.96841e96 | + | 1.92347e96i | 1.00091 | + | 0.322569i | ||||
\(703\) | 2.10984e96 | 0.337107 | ||||||||
\(704\) | 3.03906e96i | 0.462667i | ||||||||
\(705\) | 1.93683e96 | − | 8.64185e95i | 0.280971 | − | 0.125365i | ||||
\(706\) | 7.81451e95 | 0.108029 | ||||||||
\(707\) | 1.30513e97i | 1.71947i | ||||||||
\(708\) | 1.78674e96 | + | 4.00447e96i | 0.224352 | + | 0.502822i | ||||
\(709\) | −4.24428e96 | −0.507963 | −0.253981 | − | 0.967209i | \(-0.581740\pi\) | ||||
−0.253981 | + | 0.967209i | \(0.581740\pi\) | |||||||
\(710\) | 5.13496e95i | 0.0585805i | ||||||||
\(711\) | −7.14894e95 | + | 7.96524e95i | −0.0777455 | + | 0.0866229i | ||||
\(712\) | 7.03437e96 | 0.729299 | ||||||||
\(713\) | 3.01692e96i | 0.298209i | ||||||||
\(714\) | 1.02899e97 | − | 4.59122e96i | 0.969780 | − | 0.432702i | ||||
\(715\) | −1.95267e96 | −0.175478 | ||||||||
\(716\) | − | 7.00866e96i | − | 0.600609i | ||||||
\(717\) | −7.09593e96 | − | 1.59035e97i | −0.579907 | − | 1.29970i | ||||
\(718\) | −1.36583e96 | −0.106454 | ||||||||
\(719\) | − | 1.01354e97i | − | 0.753457i | −0.926324 | − | 0.376728i | \(-0.877049\pi\) | ||
0.926324 | − | 0.376728i | \(-0.122951\pi\) | |||||||
\(720\) | 2.54087e96 | + | 2.28047e96i | 0.180168 | + | 0.161704i | ||||
\(721\) | −1.29756e97 | −0.877662 | ||||||||
\(722\) | − | 9.94457e96i | − | 0.641684i | ||||||
\(723\) | 2.69235e97 | − | 1.20129e97i | 1.65741 | − | 0.739512i | ||||
\(724\) | −1.23889e96 | −0.0727650 | ||||||||
\(725\) | 1.31706e97i | 0.738098i | ||||||||
\(726\) | 4.36167e95 | + | 9.77546e95i | 0.0233242 | + | 0.0522747i | ||||
\(727\) | −1.36739e97 | −0.697784 | −0.348892 | − | 0.937163i | \(-0.613442\pi\) | ||||
−0.348892 | + | 0.937163i | \(0.613442\pi\) | |||||||
\(728\) | 1.59480e97i | 0.776676i | ||||||||
\(729\) | −1.74662e97 | − | 1.25625e97i | −0.811823 | − | 0.583904i | ||||
\(730\) | −1.43250e96 | −0.0635502 | ||||||||
\(731\) | 3.23594e97i | 1.37028i | ||||||||
\(732\) | −5.53712e96 | + | 2.47058e96i | −0.223824 | + | 0.0998671i | ||||
\(733\) | 3.50164e96 | 0.135125 | 0.0675626 | − | 0.997715i | \(-0.478478\pi\) | ||||
0.0675626 | + | 0.997715i | \(0.478478\pi\) | |||||||
\(734\) | − | 1.66283e97i | − | 0.612605i | ||||||
\(735\) | 5.50450e95 | + | 1.23368e96i | 0.0193619 | + | 0.0433943i | ||||
\(736\) | −9.15905e96 | −0.307613 | ||||||||
\(737\) | − | 2.74330e97i | − | 0.879788i | ||||||
\(738\) | −2.02297e97 | + | 2.25396e97i | −0.619544 | + | 0.690286i | ||||
\(739\) | −5.53437e97 | −1.61867 | −0.809333 | − | 0.587351i | \(-0.800171\pi\) | ||||
−0.809333 | + | 0.587351i | \(0.800171\pi\) | |||||||
\(740\) | 6.45002e95i | 0.0180170i | ||||||||
\(741\) | −3.88224e97 | + | 1.73220e97i | −1.03577 | + | 0.462146i | ||||
\(742\) | 7.02481e97 | 1.79020 | ||||||||
\(743\) | 8.05221e96i | 0.196018i | 0.995186 | + | 0.0980088i | \(0.0312473\pi\) | ||||
−0.995186 | + | 0.0980088i | \(0.968753\pi\) | |||||||
\(744\) | 8.43537e96 | + | 1.89055e97i | 0.196166 | + | 0.439652i | ||||
\(745\) | −3.49857e96 | −0.0777280 | ||||||||
\(746\) | − | 5.92952e97i | − | 1.25863i | ||||||
\(747\) | −2.95135e97 | − | 2.64888e97i | −0.598577 | − | 0.537233i | ||||
\(748\) | −1.39739e97 | −0.270809 | ||||||||
\(749\) | − | 4.06008e97i | − | 0.751888i | ||||||
\(750\) | 2.31503e97 | − | 1.03293e97i | 0.409707 | − | 0.182806i | ||||
\(751\) | 4.73700e97 | 0.801208 | 0.400604 | − | 0.916251i | \(-0.368800\pi\) | ||||
0.400604 | + | 0.916251i | \(0.368800\pi\) | |||||||
\(752\) | 1.17658e98i | 1.90202i | ||||||||
\(753\) | 3.35404e96 | + | 7.51714e96i | 0.0518250 | + | 0.116151i | ||||
\(754\) | 5.46944e97 | 0.807825 | ||||||||
\(755\) | − | 2.06138e97i | − | 0.291047i | ||||||
\(756\) | −8.52307e96 | + | 2.64466e97i | −0.115042 | + | 0.356968i | ||||
\(757\) | 1.29124e98 | 1.66628 | 0.833140 | − | 0.553063i | \(-0.186541\pi\) | ||||
0.833140 | + | 0.553063i | \(0.186541\pi\) | |||||||
\(758\) | − | 1.04309e98i | − | 1.28697i | ||||||
\(759\) | −3.58460e97 | + | 1.59940e97i | −0.422884 | + | 0.188685i | ||||
\(760\) | −1.67740e97 | −0.189223 | ||||||||
\(761\) | − | 1.17233e98i | − | 1.26465i | −0.774704 | − | 0.632324i | \(-0.782101\pi\) | ||
0.774704 | − | 0.632324i | \(-0.217899\pi\) | |||||||
\(762\) | 4.93529e97 | + | 1.10611e98i | 0.509148 | + | 1.14111i | ||||
\(763\) | 1.15138e98 | 1.13602 | ||||||||
\(764\) | 7.11527e97i | 0.671455i | ||||||||
\(765\) | 1.20778e97 | − | 1.34569e97i | 0.109018 | − | 0.121466i | ||||
\(766\) | 1.39484e98 | 1.20433 | ||||||||
\(767\) | 1.80032e98i | 1.48699i | ||||||||
\(768\) | −1.05013e98 | + | 4.68551e97i | −0.829774 | + | 0.370233i | ||||
\(769\) | −2.34147e98 | −1.77008 | −0.885041 | − | 0.465513i | \(-0.845870\pi\) | ||||
−0.885041 | + | 0.465513i | \(0.845870\pi\) | |||||||
\(770\) | − | 3.43437e97i | − | 0.248406i | ||||||
\(771\) | −6.33061e96 | − | 1.41883e97i | −0.0438124 | − | 0.0981932i | ||||
\(772\) | −1.70762e97 | −0.113084 | ||||||||
\(773\) | 3.80988e97i | 0.241440i | 0.992687 | + | 0.120720i | \(0.0385203\pi\) | ||||
−0.992687 | + | 0.120720i | \(0.961480\pi\) | |||||||
\(774\) | −2.35720e98 | − | 2.11563e98i | −1.42956 | − | 1.28306i | ||||
\(775\) | 1.03934e98 | 0.603253 | ||||||||
\(776\) | 2.02738e98i | 1.12626i | ||||||||
\(777\) | 5.17042e97 | − | 2.30696e97i | 0.274923 | − | 0.122667i | ||||
\(778\) | −7.14122e97 | −0.363468 | ||||||||
\(779\) | − | 2.05324e98i | − | 1.00038i | ||||||
\(780\) | −5.29554e96 | − | 1.18685e97i | −0.0246998 | − | 0.0553578i | ||||
\(781\) | −5.58992e97 | −0.249615 | ||||||||
\(782\) | 1.05941e98i | 0.452936i | ||||||||
\(783\) | −1.78610e98 | − | 5.75614e97i | −0.731149 | − | 0.235630i | ||||
\(784\) | −7.49433e97 | −0.293756 | ||||||||
\(785\) | 2.68237e97i | 0.100682i | ||||||||
\(786\) | 5.06634e98 | − | 2.26053e98i | 1.82107 | − | 0.812537i | ||||
\(787\) | −2.79285e98 | −0.961405 | −0.480703 | − | 0.876884i | \(-0.659618\pi\) | ||||
−0.480703 | + | 0.876884i | \(0.659618\pi\) | |||||||
\(788\) | − | 7.23803e96i | − | 0.0238632i | ||||||
\(789\) | 4.08776e95 | + | 9.16157e95i | 0.00129082 | + | 0.00289302i | ||||
\(790\) | 8.80467e96 | 0.0266313 | ||||||||
\(791\) | − | 2.23595e98i | − | 0.647830i | ||||||
\(792\) | −1.79910e98 | + | 2.00452e98i | −0.499342 | + | 0.556359i | ||||
\(793\) | −2.48936e98 | −0.661912 | ||||||||
\(794\) | − | 4.79876e98i | − | 1.22245i | ||||||
\(795\) | 1.02949e98 | − | 4.59343e97i | 0.251269 | − | 0.112113i | ||||
\(796\) | −4.39579e97 | −0.102800 | ||||||||
\(797\) | 6.14826e98i | 1.37775i | 0.724882 | + | 0.688873i | \(0.241894\pi\) | ||||
−0.724882 | + | 0.688873i | \(0.758106\pi\) | |||||||
\(798\) | −3.04661e98 | − | 6.82813e98i | −0.654213 | − | 1.46623i | ||||
\(799\) | 6.23139e98 | 1.28231 | ||||||||
\(800\) | 3.15532e98i | 0.622278i | ||||||||
\(801\) | 3.74475e98 | + | 3.36098e98i | 0.707812 | + | 0.635273i | ||||
\(802\) | 5.35867e97 | 0.0970796 | ||||||||
\(803\) | − | 1.55942e98i | − | 0.270791i | ||||||
\(804\) | 1.66740e98 | − | 7.43970e97i | 0.277545 | − | 0.123837i | ||||
\(805\) | −6.55977e97 | −0.104672 | ||||||||
\(806\) | − | 4.31613e98i | − | 0.660242i | ||||||
\(807\) | 4.11047e98 | + | 9.21247e98i | 0.602825 | + | 1.35106i | ||||
\(808\) | −8.42040e98 | −1.18399 | ||||||||
\(809\) | 9.14482e98i | 1.23289i | 0.787397 | + | 0.616447i | \(0.211428\pi\) | ||||
−0.787397 | + | 0.616447i | \(0.788572\pi\) | |||||||
\(810\) | 1.90623e97 | + | 1.75960e98i | 0.0246425 | + | 0.227469i | ||||
\(811\) | −7.70599e98 | −0.955255 | −0.477628 | − | 0.878562i | \(-0.658503\pi\) | ||||
−0.477628 | + | 0.878562i | \(0.658503\pi\) | |||||||
\(812\) | 2.42357e98i | 0.288104i | ||||||||
\(813\) | 1.05262e99 | − | 4.69666e98i | 1.20004 | − | 0.535440i | ||||
\(814\) | −2.78700e98 | −0.304725 | ||||||||
\(815\) | − | 1.07330e97i | − | 0.0112555i | ||||||
\(816\) | 4.08738e98 | + | 9.16073e98i | 0.411131 | + | 0.921435i | ||||
\(817\) | 2.14729e99 | 2.07176 | ||||||||
\(818\) | 2.19899e98i | 0.203521i | ||||||||
\(819\) | −7.61987e98 | + | 8.48995e98i | −0.676543 | + | 0.753793i | ||||
\(820\) | 6.27700e97 | 0.0534664 | ||||||||
\(821\) | − | 1.60428e99i | − | 1.31103i | −0.755181 | − | 0.655516i | \(-0.772451\pi\) | ||
0.755181 | − | 0.655516i | \(-0.227549\pi\) | |||||||
\(822\) | 1.95277e99 | − | 8.71296e98i | 1.53112 | − | 0.683162i | ||||
\(823\) | 6.91361e98 | 0.520128 | 0.260064 | − | 0.965591i | \(-0.416256\pi\) | ||||
0.260064 | + | 0.965591i | \(0.416256\pi\) | |||||||
\(824\) | − | 8.37152e98i | − | 0.604337i | ||||||
\(825\) | 5.50998e98 | + | 1.23491e99i | 0.381694 | + | 0.855461i | ||||
\(826\) | −3.16643e99 | −2.10498 | ||||||||
\(827\) | − | 2.56124e99i | − | 1.63404i | −0.576608 | − | 0.817021i | \(-0.695624\pi\) | ||
0.576608 | − | 0.817021i | \(-0.304376\pi\) | |||||||
\(828\) | −1.94426e98 | − | 1.74501e98i | −0.119048 | − | 0.106848i | ||||
\(829\) | −1.50521e99 | −0.884594 | −0.442297 | − | 0.896869i | \(-0.645836\pi\) | ||||
−0.442297 | + | 0.896869i | \(0.645836\pi\) | |||||||
\(830\) | 3.26238e98i | 0.184026i | ||||||||
\(831\) | −9.28447e98 | + | 4.14260e98i | −0.502716 | + | 0.224304i | ||||
\(832\) | −8.30445e98 | −0.431636 | ||||||||
\(833\) | 3.96914e98i | 0.198046i | ||||||||
\(834\) | −1.80623e99 | − | 4.04816e99i | −0.865222 | − | 1.93915i | ||||
\(835\) | 2.91656e98 | 0.134132 | ||||||||
\(836\) | 9.27271e98i | 0.409443i | ||||||||
\(837\) | −4.54237e98 | + | 1.40947e99i | −0.192583 | + | 0.597574i | ||||
\(838\) | 1.31898e99 | 0.536959 | ||||||||
\(839\) | − | 7.75975e98i | − | 0.303348i | −0.988431 | − | 0.151674i | \(-0.951534\pi\) | ||
0.988431 | − | 0.151674i | \(-0.0484664\pi\) | |||||||
\(840\) | −4.11068e98 | + | 1.83412e98i | −0.154318 | + | 0.0688546i | ||||
\(841\) | 1.13695e99 | 0.409899 | ||||||||
\(842\) | 3.22578e99i | 1.11692i | ||||||||
\(843\) | −1.47429e99 | − | 3.30422e99i | −0.490283 | − | 1.09883i | ||||
\(844\) | −1.64848e99 | −0.526551 | ||||||||
\(845\) | 1.11410e98i | 0.0341819i | ||||||||
\(846\) | −4.07402e99 | + | 4.53921e99i | −1.20069 | + | 1.33779i | ||||
\(847\) | −1.94739e98 | −0.0551337 | ||||||||
\(848\) | 6.25392e99i | 1.70096i | ||||||||
\(849\) | 3.29861e99 | − | 1.47179e99i | 0.861926 | − | 0.384579i | ||||
\(850\) | 3.64972e99 | 0.916254 | ||||||||
\(851\) | 5.32328e98i | 0.128403i | ||||||||
\(852\) | −1.51596e98 | − | 3.39761e98i | −0.0351352 | − | 0.0787457i | ||||
\(853\) | −2.93055e99 | −0.652653 | −0.326327 | − | 0.945257i | \(-0.605811\pi\) | ||||
−0.326327 | + | 0.945257i | \(0.605811\pi\) | |||||||
\(854\) | − | 4.37832e99i | − | 0.937001i | ||||||
\(855\) | −8.92965e98 | − | 8.01452e98i | −0.183648 | − | 0.164827i | ||||
\(856\) | 2.61947e99 | 0.517733 | ||||||||
\(857\) | 4.95199e98i | 0.0940658i | 0.998893 | + | 0.0470329i | \(0.0149766\pi\) | ||||
−0.998893 | + | 0.0470329i | \(0.985023\pi\) | |||||||
\(858\) | 5.12828e99 | − | 2.28816e99i | 0.936276 | − | 0.417753i | ||||
\(859\) | 1.22694e99 | 0.215306 | 0.107653 | − | 0.994189i | \(-0.465667\pi\) | ||||
0.107653 | + | 0.994189i | \(0.465667\pi\) | |||||||
\(860\) | 6.56452e98i | 0.110727i | ||||||||
\(861\) | −2.24508e99 | − | 5.03172e99i | −0.364020 | − | 0.815848i | ||||
\(862\) | 1.45073e100 | 2.26120 | ||||||||
\(863\) | − | 1.73452e99i | − | 0.259903i | −0.991520 | − | 0.129952i | \(-0.958518\pi\) | ||
0.991520 | − | 0.129952i | \(-0.0414822\pi\) | |||||||
\(864\) | −4.27901e99 | − | 1.37902e99i | −0.616420 | − | 0.198656i | ||||
\(865\) | −2.61905e99 | −0.362741 | ||||||||
\(866\) | − | 2.38436e99i | − | 0.317515i | ||||||
\(867\) | −2.28053e99 | + | 1.01754e99i | −0.292003 | + | 0.130287i | ||||
\(868\) | 1.91252e99 | 0.235470 | ||||||||
\(869\) | 9.58478e98i | 0.113478i | ||||||||
\(870\) | 6.29021e98 | + | 1.40977e99i | 0.0716161 | + | 0.160507i | ||||
\(871\) | 7.49626e99 | 0.820781 | ||||||||
\(872\) | 7.42843e99i | 0.782234i | ||||||||
\(873\) | −9.68673e99 | + | 1.07928e100i | −0.981054 | + | 1.09307i | ||||
\(874\) | 7.03001e99 | 0.684805 | ||||||||
\(875\) | 4.61183e99i | 0.432115i | ||||||||
\(876\) | 9.47830e98 | − | 4.22908e98i | 0.0854262 | − | 0.0381159i | ||||
\(877\) | 4.46587e99 | 0.387187 | 0.193593 | − | 0.981082i | \(-0.437986\pi\) | ||||
0.193593 | + | 0.981082i | \(0.437986\pi\) | |||||||
\(878\) | − | 9.77850e99i | − | 0.815565i | ||||||
\(879\) | 4.60741e99 | + | 1.03262e100i | 0.369687 | + | 0.828551i | ||||
\(880\) | 3.05749e99 | 0.236023 | ||||||||
\(881\) | − | 1.45906e99i | − | 0.108365i | −0.998531 | − | 0.0541827i | \(-0.982745\pi\) | ||
0.998531 | − | 0.0541827i | \(-0.0172553\pi\) | |||||||
\(882\) | −2.89129e99 | − | 2.59498e99i | −0.206614 | − | 0.185440i | ||||
\(883\) | −1.59495e100 | −1.09668 | −0.548342 | − | 0.836254i | \(-0.684741\pi\) | ||||
−0.548342 | + | 0.836254i | \(0.684741\pi\) | |||||||
\(884\) | − | 3.81847e99i | − | 0.252646i | ||||||
\(885\) | −4.64041e99 | + | 2.07049e99i | −0.295451 | + | 0.131826i | ||||
\(886\) | −1.64988e100 | −1.01089 | ||||||||
\(887\) | 9.58087e99i | 0.564939i | 0.959276 | + | 0.282470i | \(0.0911536\pi\) | ||||
−0.959276 | + | 0.282470i | \(0.908846\pi\) | |||||||
\(888\) | 1.48840e99 | + | 3.33583e99i | 0.0844653 | + | 0.189305i | ||||
\(889\) | −2.20350e100 | −1.20352 | ||||||||
\(890\) | − | 4.13940e99i | − | 0.217609i | ||||||
\(891\) | −1.91550e100 | + | 2.07513e99i | −0.969260 | + | 0.105003i | ||||
\(892\) | −4.03565e99 | −0.196566 | ||||||||
\(893\) | − | 4.13499e100i | − | 1.93876i | ||||||
\(894\) | 9.18829e99 | − | 4.09968e99i | 0.414724 | − | 0.185044i | ||||
\(895\) | 8.12168e99 | 0.352909 | ||||||||
\(896\) | − | 3.18460e100i | − | 1.33224i | ||||||
\(897\) | −4.37048e99 | − | 9.79520e99i | −0.176030 | − | 0.394521i | ||||
\(898\) | −1.92124e100 | −0.745053 | ||||||||
\(899\) | 1.29164e100i | 0.482294i | ||||||||
\(900\) | −6.01160e99 | + | 6.69803e99i | −0.216145 | + | 0.240825i | ||||
\(901\) | 3.31219e100 | 1.14676 | ||||||||
\(902\) | 2.71224e100i | 0.904287i | ||||||||
\(903\) | 5.26220e100 | − | 2.34792e100i | 1.68960 | − | 0.753874i | ||||
\(904\) | 1.44258e100 | 0.446080 | ||||||||
\(905\) | − | 1.43564e99i | − | 0.0427556i | ||||||
\(906\) | 2.41556e100 | + | 5.41380e100i | 0.692882 | + | 1.55290i | ||||
\(907\) | −3.84144e100 | −1.06132 | −0.530660 | − | 0.847585i | \(-0.678056\pi\) | ||||
−0.530660 | + | 0.847585i | \(0.678056\pi\) | |||||||
\(908\) | − | 1.67362e100i | − | 0.445388i | ||||||
\(909\) | −4.48261e100 | − | 4.02322e100i | −1.14910 | − | 1.03134i | ||||
\(910\) | 9.38467e99 | 0.231746 | ||||||||
\(911\) | 2.38974e100i | 0.568494i | 0.958751 | + | 0.284247i | \(0.0917435\pi\) | ||||
−0.958751 | + | 0.284247i | \(0.908256\pi\) | |||||||
\(912\) | 6.07882e100 | − | 2.71228e100i | 1.39314 | − | 0.621599i | ||||
\(913\) | −3.55143e100 | −0.784146 | ||||||||
\(914\) | 4.86432e100i | 1.03479i | ||||||||
\(915\) | −2.86293e99 | − | 6.41645e99i | −0.0586804 | − | 0.131516i | ||||
\(916\) | 2.23986e100 | 0.442360 | ||||||||
\(917\) | 1.00928e101i | 1.92067i | ||||||||
\(918\) | −1.59509e100 | + | 4.94948e100i | −0.292505 | + | 0.907628i | ||||
\(919\) | 3.79080e100 | 0.669889 | 0.334945 | − | 0.942238i | \(-0.391282\pi\) | ||||
0.334945 | + | 0.942238i | \(0.391282\pi\) | |||||||
\(920\) | − | 4.23221e99i | − | 0.0720744i | ||||||
\(921\) | 8.85619e100 | − | 3.95150e100i | 1.45351 | − | 0.648537i | ||||
\(922\) | −1.09225e101 | −1.72772 | ||||||||
\(923\) | − | 1.52749e100i | − | 0.232874i | ||||||
\(924\) | 1.01391e100 | + | 2.27239e100i | 0.148988 | + | 0.333915i | ||||
\(925\) | 1.83389e100 | 0.259749 | ||||||||
\(926\) | − | 3.80957e100i | − | 0.520119i | ||||||
\(927\) | 3.99987e100 | − | 4.45659e100i | 0.526423 | − | 0.586532i | ||||
\(928\) | −3.92128e100 | −0.497504 | ||||||||
\(929\) | − | 8.14244e99i | − | 0.0995911i | −0.998759 | − | 0.0497955i | \(-0.984143\pi\) | ||
0.998759 | − | 0.0497955i | \(-0.0158570\pi\) | |||||||
\(930\) | 1.11250e100 | − | 4.96382e99i | 0.131184 | − | 0.0585324i | ||||
\(931\) | 2.63382e100 | 0.299431 | ||||||||
\(932\) | 1.00215e100i | 0.109847i | ||||||||
\(933\) | 1.79393e99 | + | 4.02060e99i | 0.0189597 | + | 0.0424928i | ||||
\(934\) | 9.11355e99 | 0.0928739 | ||||||||
\(935\) | − | 1.61930e100i | − | 0.159123i | ||||||
\(936\) | −5.47751e100 | − | 4.91616e100i | −0.519044 | − | 0.465851i | ||||
\(937\) | 6.42060e100 | 0.586718 | 0.293359 | − | 0.956002i | \(-0.405227\pi\) | ||||
0.293359 | + | 0.956002i | \(0.405227\pi\) | |||||||
\(938\) | 1.31845e101i | 1.16190i | ||||||||
\(939\) | −4.40831e100 | + | 1.96692e100i | −0.374664 | + | 0.167170i | ||||
\(940\) | 1.26412e100 | 0.103619 | ||||||||
\(941\) | 3.98299e100i | 0.314892i | 0.987528 | + | 0.157446i | \(0.0503261\pi\) | ||||
−0.987528 | + | 0.157446i | \(0.949674\pi\) | |||||||
\(942\) | −3.14325e100 | − | 7.04471e100i | −0.239689 | − | 0.537196i | ||||
\(943\) | 5.18048e100 | 0.381042 | ||||||||
\(944\) | − | 2.81895e101i | − | 2.00004i | ||||||
\(945\) | −3.06466e100 | − | 9.87660e99i | −0.209749 | − | 0.0675968i | ||||
\(946\) | −2.83648e101 | −1.87275 | ||||||||
\(947\) | − | 1.23420e101i | − | 0.786114i | −0.919514 | − | 0.393057i | \(-0.871418\pi\) | ||
0.919514 | − | 0.393057i | \(-0.128582\pi\) | |||||||
\(948\) | −5.82572e99 | + | 2.59935e99i | −0.0357986 | + | 0.0159728i | ||||
\(949\) | 4.26123e100 | 0.252630 | ||||||||
\(950\) | − | 2.42186e101i | − | 1.38531i | ||||||
\(951\) | 8.06752e100 | + | 1.80811e101i | 0.445248 | + | 0.997900i | ||||
\(952\) | −1.32253e101 | −0.704289 | ||||||||
\(953\) | 1.06228e101i | 0.545858i | 0.962034 | + | 0.272929i | \(0.0879924\pi\) | ||||
−0.962034 | + | 0.272929i | \(0.912008\pi\) | |||||||
\(954\) | −2.16548e101 | + | 2.41274e101i | −1.07377 | + | 1.19637i | ||||
\(955\) | −8.24523e100 | −0.394537 | ||||||||
\(956\) | − | 1.03798e101i | − | 0.479316i | ||||||
\(957\) | −1.53468e101 | + | 6.84753e100i | −0.683932 | + | 0.305160i | ||||
\(958\) | 2.55987e101 | 1.10101 | ||||||||
\(959\) | 3.89015e101i | 1.61486i | ||||||||
\(960\) | −9.55064e99 | − | 2.14051e100i | −0.0382658 | − | 0.0857621i | ||||
\(961\) | −1.56652e101 | −0.605817 | ||||||||
\(962\) | − | 7.61570e100i | − | 0.284287i | ||||||
\(963\) | 1.39448e101 | + | 1.25157e101i | 0.502479 | + | 0.450984i | ||||
\(964\) | 1.75723e101 | 0.611235 | ||||||||
\(965\) | − | 1.97880e100i | − | 0.0664467i | ||||||
\(966\) | 1.72279e101 | − | 7.68684e100i | 0.558483 | − | 0.249187i | ||||
\(967\) | 2.02776e101 | 0.634624 | 0.317312 | − | 0.948321i | \(-0.397220\pi\) | ||||
0.317312 | + | 0.948321i | \(0.397220\pi\) | |||||||
\(968\) | − | 1.25641e100i | − | 0.0379638i | ||||||
\(969\) | −1.43648e101 | − | 3.21946e101i | −0.419073 | − | 0.939236i | ||||
\(970\) | 1.19302e101 | 0.336054 | ||||||||
\(971\) | 1.25298e101i | 0.340794i | 0.985375 | + | 0.170397i | \(0.0545050\pi\) | ||||
−0.985375 | + | 0.170397i | \(0.945495\pi\) | |||||||
\(972\) | −6.45604e100 | − | 1.10798e101i | −0.169556 | − | 0.290991i | ||||
\(973\) | 8.06444e101 | 2.04521 | ||||||||
\(974\) | 3.43700e101i | 0.841735i | ||||||||
\(975\) | −3.37448e101 | + | 1.50564e101i | −0.798086 | + | 0.356094i | ||||
\(976\) | 3.89785e101 | 0.890290 | ||||||||
\(977\) | − | 3.46871e101i | − | 0.765160i | −0.923922 | − | 0.382580i | \(-0.875036\pi\) | ||
0.923922 | − | 0.382580i | \(-0.124964\pi\) | |||||||
\(978\) | 1.25771e100 | + | 2.81881e100i | 0.0267954 | + | 0.0600543i | ||||
\(979\) | 4.50616e101 | 0.927246 | ||||||||
\(980\) | 8.05190e99i | 0.0160034i | ||||||||
\(981\) | −3.54926e101 | + | 3.95453e101i | −0.681384 | + | 0.759187i | ||||
\(982\) | −1.04426e101 | −0.193650 | ||||||||
\(983\) | − | 7.15686e101i | − | 1.28204i | −0.767523 | − | 0.641022i | \(-0.778511\pi\) | ||
0.767523 | − | 0.641022i | \(-0.221489\pi\) | |||||||
\(984\) | 3.24635e101 | − | 1.44847e101i | 0.561774 | − | 0.250655i | ||||
\(985\) | 8.38748e99 | 0.0140217 | ||||||||
\(986\) | 4.53569e101i | 0.732535i | ||||||||
\(987\) | −4.52134e101 | − | 1.01333e102i | −0.705478 | − | 1.58113i | ||||
\(988\) | −2.53384e101 | −0.381982 | ||||||||
\(989\) | 5.41777e101i | 0.789127i | ||||||||
\(990\) | 1.17957e101 | + | 1.05868e101i | 0.166007 | + | 0.148994i | ||||
\(991\) | −9.37374e101 | −1.27470 | −0.637351 | − | 0.770574i | \(-0.719970\pi\) | ||||
−0.637351 | + | 0.770574i | \(0.719970\pi\) | |||||||
\(992\) | 3.09442e101i | 0.406614i | ||||||||
\(993\) | 2.56298e101 | − | 1.14357e101i | 0.325440 | − | 0.145207i | ||||
\(994\) | 2.68656e101 | 0.329655 | ||||||||
\(995\) | − | 5.09388e100i | − | 0.0604037i | ||||||
\(996\) | −9.63132e100 | − | 2.15859e101i | −0.110374 | − | 0.247373i | ||||
\(997\) | −1.91051e100 | −0.0211599 | −0.0105800 | − | 0.999944i | \(-0.503368\pi\) | ||||
−0.0105800 | + | 0.999944i | \(0.503368\pi\) | |||||||
\(998\) | 8.89290e101i | 0.951930i | ||||||||
\(999\) | −8.01490e100 | + | 2.48698e101i | −0.0829223 | + | 0.257304i |
(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 | 3.69.b.a.2.6 | ✓ | 22 | |
3.2 | odd | 2 | inner | 3.69.b.a.2.17 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.69.b.a.2.6 | ✓ | 22 | 1.1 | even | 1 | trivial | |
3.69.b.a.2.17 | yes | 22 | 3.2 | odd | 2 | inner |