Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,11,Mod(149,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.149");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.b (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: | \(95.3035879011\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3421020160000.10 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 967x^{4} + 194481 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 6) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.2 | ||
Root | \(-3.61315 + 3.61315i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.149 |
Dual form | 150.11.b.a.149.1 |
$q$-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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −22.6274 | −0.707107 | ||||||||
\(3\) | −137.627 | + | 200.269i | −0.566368 | + | 0.824153i | ||||
\(4\) | 512.000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3114.15 | − | 4531.57i | 0.400483 | − | 0.582764i | ||||
\(7\) | − | 23226.5i | − | 1.38196i | −0.722876 | − | 0.690978i | \(-0.757180\pi\) | ||
0.722876 | − | 0.690978i | \(-0.242820\pi\) | |||||||
\(8\) | −11585.2 | −0.353553 | ||||||||
\(9\) | −21166.4 | − | 55125.0i | −0.358455 | − | 0.933547i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 62442.7i | 0.387720i | 0.981029 | + | 0.193860i | \(0.0621007\pi\) | ||||
−0.981029 | + | 0.193860i | \(0.937899\pi\) | |||||||
\(12\) | −70465.2 | + | 102538.i | −0.283184 | + | 0.412076i | ||||
\(13\) | 170161.i | 0.458292i | 0.973392 | + | 0.229146i | \(0.0735933\pi\) | ||||
−0.973392 | + | 0.229146i | \(0.926407\pi\) | |||||||
\(14\) | 525556.i | 0.977190i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 262144. | 0.250000 | ||||||||
\(17\) | 2.66626e6 | 1.87784 | 0.938919 | − | 0.344139i | \(-0.111829\pi\) | ||||
0.938919 | + | 0.344139i | \(0.111829\pi\) | |||||||
\(18\) | 478941. | + | 1.24734e6i | 0.253466 | + | 0.660117i | ||||
\(19\) | −766825. | −0.309691 | −0.154845 | − | 0.987939i | \(-0.549488\pi\) | ||||
−0.154845 | + | 0.987939i | \(0.549488\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.65156e6 | + | 3.19661e6i | 1.13894 | + | 0.782695i | ||||
\(22\) | − | 1.41292e6i | − | 0.274159i | ||||||
\(23\) | 1.40327e6 | 0.218022 | 0.109011 | − | 0.994041i | \(-0.465232\pi\) | ||||
0.109011 | + | 0.994041i | \(0.465232\pi\) | |||||||
\(24\) | 1.59445e6 | − | 2.32016e6i | 0.200241 | − | 0.291382i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 3.85029e6i | − | 0.324061i | ||||||
\(27\) | 1.39529e7 | + | 3.34774e6i | 0.972402 | + | 0.233310i | ||||
\(28\) | − | 1.18920e7i | − | 0.690978i | ||||||
\(29\) | − | 4.83245e6i | − | 0.235601i | −0.993037 | − | 0.117801i | \(-0.962416\pi\) | ||
0.993037 | − | 0.117801i | \(-0.0375844\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.18297e7 | −1.46109 | −0.730544 | − | 0.682865i | \(-0.760734\pi\) | ||||
−0.730544 | + | 0.682865i | \(0.760734\pi\) | |||||||
\(32\) | −5.93164e6 | −0.176777 | ||||||||
\(33\) | −1.25053e7 | − | 8.59382e6i | −0.319540 | − | 0.219592i | ||||
\(34\) | −6.03306e7 | −1.32783 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.08372e7 | − | 2.82240e7i | −0.179227 | − | 0.466774i | ||||
\(37\) | 5.01619e7i | 0.723378i | 0.932299 | + | 0.361689i | \(0.117800\pi\) | ||||
−0.932299 | + | 0.361689i | \(0.882200\pi\) | |||||||
\(38\) | 1.73513e7 | 0.218985 | ||||||||
\(39\) | −3.40779e7 | − | 2.34188e7i | −0.377702 | − | 0.259562i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.49239e8i | − | 1.28814i | −0.764967 | − | 0.644069i | \(-0.777245\pi\) | ||
0.764967 | − | 0.644069i | \(-0.222755\pi\) | |||||||
\(42\) | −1.05253e8 | − | 7.23310e7i | −0.805354 | − | 0.553449i | ||||
\(43\) | 1.98719e8i | 1.35175i | 0.737015 | + | 0.675876i | \(0.236235\pi\) | ||||
−0.737015 | + | 0.675876i | \(0.763765\pi\) | |||||||
\(44\) | 3.19706e7i | 0.193860i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.17523e7 | −0.154165 | ||||||||
\(47\) | 1.55059e8 | 0.676093 | 0.338047 | − | 0.941129i | \(-0.390234\pi\) | ||||
0.338047 | + | 0.941129i | \(0.390234\pi\) | |||||||
\(48\) | −3.60782e7 | + | 5.24993e7i | −0.141592 | + | 0.206038i | ||||
\(49\) | −2.56996e8 | −0.909802 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.66951e8 | + | 5.33970e8i | −1.06355 | + | 1.54762i | ||||
\(52\) | 8.71222e7i | 0.229146i | ||||||||
\(53\) | 4.21541e7 | 0.100800 | 0.0503999 | − | 0.998729i | \(-0.483950\pi\) | ||||
0.0503999 | + | 0.998729i | \(0.483950\pi\) | |||||||
\(54\) | −3.15718e8 | − | 7.57507e7i | −0.687592 | − | 0.164975i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.69085e8i | 0.488595i | ||||||||
\(57\) | 1.05536e8 | − | 1.53571e8i | 0.175399 | − | 0.255233i | ||||
\(58\) | 1.09346e8i | 0.166595i | ||||||||
\(59\) | − | 2.92026e8i | − | 0.408471i | −0.978922 | − | 0.204236i | \(-0.934529\pi\) | ||
0.978922 | − | 0.204236i | \(-0.0654708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.30727e8 | −0.628379 | −0.314190 | − | 0.949360i | \(-0.601733\pi\) | ||||
−0.314190 | + | 0.949360i | \(0.601733\pi\) | |||||||
\(62\) | 9.46499e8 | 1.03315 | ||||||||
\(63\) | −1.28036e9 | + | 4.91622e8i | −1.29012 | + | 0.495369i | ||||
\(64\) | 1.34218e8 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.82963e8 | + | 1.94456e8i | 0.225949 | + | 0.155275i | ||||
\(67\) | 5.22093e8i | 0.386700i | 0.981130 | + | 0.193350i | \(0.0619353\pi\) | ||||
−0.981130 | + | 0.193350i | \(0.938065\pi\) | |||||||
\(68\) | 1.36513e9 | 0.938919 | ||||||||
\(69\) | −1.93128e8 | + | 2.81031e8i | −0.123481 | + | 0.179684i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.71364e8i | 0.316681i | 0.987385 | + | 0.158340i | \(0.0506143\pi\) | ||||
−0.987385 | + | 0.158340i | \(0.949386\pi\) | |||||||
\(72\) | 2.45218e8 | + | 6.38636e8i | 0.126733 | + | 0.330059i | ||||
\(73\) | − | 2.18588e9i | − | 1.05441i | −0.849737 | − | 0.527207i | \(-0.823239\pi\) | ||
0.849737 | − | 0.527207i | \(-0.176761\pi\) | |||||||
\(74\) | − | 1.13503e9i | − | 0.511506i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.92615e8 | −0.154845 | ||||||||
\(77\) | 1.45033e9 | 0.535812 | ||||||||
\(78\) | 7.71095e8 | + | 5.29906e8i | 0.267076 | + | 0.183538i | ||||
\(79\) | −1.96592e9 | −0.638897 | −0.319449 | − | 0.947604i | \(-0.603498\pi\) | ||||
−0.319449 | + | 0.947604i | \(0.603498\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.59075e9 | + | 2.33360e9i | −0.743020 | + | 0.669269i | ||||
\(82\) | 3.37689e9i | 0.910851i | ||||||||
\(83\) | −2.18558e9 | −0.554850 | −0.277425 | − | 0.960747i | \(-0.589481\pi\) | ||||
−0.277425 | + | 0.960747i | \(0.589481\pi\) | |||||||
\(84\) | 2.38160e9 | + | 1.63666e9i | 0.569471 | + | 0.391348i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 4.49650e9i | − | 0.955833i | ||||||
\(87\) | 9.67791e8 | + | 6.65078e8i | 0.194171 | + | 0.133437i | ||||
\(88\) | − | 7.23413e8i | − | 0.137080i | ||||||
\(89\) | 2.38742e8i | 0.0427542i | 0.999771 | + | 0.0213771i | \(0.00680506\pi\) | ||||
−0.999771 | + | 0.0213771i | \(0.993195\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.95224e9 | 0.633339 | ||||||||
\(92\) | 7.18473e8 | 0.109011 | ||||||||
\(93\) | 5.75692e9 | − | 8.37720e9i | 0.827514 | − | 1.20416i | ||||
\(94\) | −3.50858e9 | −0.478070 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.16356e8 | − | 1.18792e9i | 0.100121 | − | 0.145691i | ||||
\(97\) | − | 8.84112e9i | − | 1.02955i | −0.857324 | − | 0.514776i | \(-0.827875\pi\) | ||
0.857324 | − | 0.514776i | \(-0.172125\pi\) | |||||||
\(98\) | 5.81517e9 | 0.643327 | ||||||||
\(99\) | 3.44215e9 | − | 1.32169e9i | 0.361955 | − | 0.138980i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.67928e10i | 1.59778i | 0.601477 | + | 0.798890i | \(0.294579\pi\) | ||||
−0.601477 | + | 0.798890i | \(0.705421\pi\) | |||||||
\(102\) | 8.30314e9 | − | 1.20824e10i | 0.752041 | − | 1.09434i | ||||
\(103\) | − | 8.36865e9i | − | 0.721887i | −0.932588 | − | 0.360944i | \(-0.882455\pi\) | ||
0.932588 | − | 0.360944i | \(-0.117545\pi\) | |||||||
\(104\) | − | 1.97135e9i | − | 0.162031i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.53837e8 | −0.0712763 | ||||||||
\(107\) | 1.43555e10 | 1.02353 | 0.511764 | − | 0.859126i | \(-0.328992\pi\) | ||||
0.511764 | + | 0.859126i | \(0.328992\pi\) | |||||||
\(108\) | 7.14389e9 | + | 1.71404e9i | 0.486201 | + | 0.116655i | ||||
\(109\) | 4.72564e9 | 0.307134 | 0.153567 | − | 0.988138i | \(-0.450924\pi\) | ||||
0.153567 | + | 0.988138i | \(0.450924\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00459e10 | − | 6.90365e9i | −0.596174 | − | 0.409698i | ||||
\(112\) | − | 6.08870e9i | − | 0.345489i | ||||||
\(113\) | −1.32158e10 | −0.717303 | −0.358651 | − | 0.933472i | \(-0.616763\pi\) | ||||
−0.358651 | + | 0.933472i | \(0.616763\pi\) | |||||||
\(114\) | −2.38801e9 | + | 3.47492e9i | −0.124026 | + | 0.180477i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 2.47422e9i | − | 0.117801i | ||||||
\(117\) | 9.38011e9 | − | 3.60169e9i | 0.427837 | − | 0.164277i | ||||
\(118\) | 6.60779e9i | 0.288833i | ||||||||
\(119\) | − | 6.19280e10i | − | 2.59509i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.20383e10 | 0.849673 | ||||||||
\(122\) | 1.20090e10 | 0.444331 | ||||||||
\(123\) | 2.98879e10 | + | 2.05393e10i | 1.06162 | + | 0.729560i | ||||
\(124\) | −2.14168e10 | −0.730544 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.89713e10 | − | 1.11241e10i | 0.912253 | − | 0.350279i | ||||
\(127\) | − | 3.17814e10i | − | 0.961953i | −0.876733 | − | 0.480976i | \(-0.840282\pi\) | ||
0.876733 | − | 0.480976i | \(-0.159718\pi\) | |||||||
\(128\) | −3.03700e9 | −0.0883883 | ||||||||
\(129\) | −3.97973e10 | − | 2.73492e10i | −1.11405 | − | 0.765589i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5.01094e10i | − | 1.29886i | −0.760421 | − | 0.649430i | \(-0.775007\pi\) | ||
0.760421 | − | 0.649430i | \(-0.224993\pi\) | |||||||
\(132\) | −6.40273e9 | − | 4.40004e9i | −0.159770 | − | 0.109796i | ||||
\(133\) | 1.78107e10i | 0.427979i | ||||||||
\(134\) | − | 1.18136e10i | − | 0.273438i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.08893e10 | −0.663916 | ||||||||
\(137\) | 2.74744e10 | 0.569279 | 0.284639 | − | 0.958635i | \(-0.408126\pi\) | ||||
0.284639 | + | 0.958635i | \(0.408126\pi\) | |||||||
\(138\) | 4.36999e9 | − | 6.35900e9i | 0.0873142 | − | 0.127056i | ||||
\(139\) | −6.32488e10 | −1.21893 | −0.609464 | − | 0.792814i | \(-0.708615\pi\) | ||||
−0.609464 | + | 0.792814i | \(0.708615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.13403e10 | + | 3.10534e10i | −0.382917 | + | 0.557204i | ||||
\(142\) | − | 1.29285e10i | − | 0.223927i | ||||||
\(143\) | −1.06253e10 | −0.177689 | ||||||||
\(144\) | −5.54864e9 | − | 1.44507e10i | −0.0896137 | − | 0.233387i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.94607e10i | 0.745583i | ||||||||
\(147\) | 3.53697e10 | − | 5.14684e10i | 0.515282 | − | 0.749815i | ||||
\(148\) | 2.56829e10i | 0.361689i | ||||||||
\(149\) | − | 3.38479e10i | − | 0.460893i | −0.973085 | − | 0.230446i | \(-0.925981\pi\) | ||
0.973085 | − | 0.230446i | \(-0.0740186\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.22386e11 | 1.55901 | 0.779503 | − | 0.626399i | \(-0.215472\pi\) | ||||
0.779503 | + | 0.626399i | \(0.215472\pi\) | |||||||
\(152\) | 8.88385e9 | 0.109492 | ||||||||
\(153\) | −5.64351e10 | − | 1.46978e11i | −0.673120 | − | 1.75305i | ||||
\(154\) | −3.28171e10 | −0.378876 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.74479e10 | − | 1.19904e10i | −0.188851 | − | 0.129781i | ||||
\(157\) | − | 1.58971e11i | − | 1.66656i | −0.552853 | − | 0.833279i | \(-0.686461\pi\) | ||
0.552853 | − | 0.833279i | \(-0.313539\pi\) | |||||||
\(158\) | 4.44838e10 | 0.451769 | ||||||||
\(159\) | −5.80155e9 | + | 8.44215e9i | −0.0570898 | + | 0.0830745i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.25930e10i | − | 0.301297i | ||||||
\(162\) | 5.86220e10 | − | 5.28033e10i | 0.525395 | − | 0.473245i | ||||
\(163\) | 9.20831e10i | 0.800280i | 0.916454 | + | 0.400140i | \(0.131038\pi\) | ||||
−0.916454 | + | 0.400140i | \(0.868962\pi\) | |||||||
\(164\) | − | 7.64102e10i | − | 0.644069i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.94540e10 | 0.392338 | ||||||||
\(167\) | 2.12416e11 | 1.63533 | 0.817663 | − | 0.575697i | \(-0.195269\pi\) | ||||
0.817663 | + | 0.575697i | \(0.195269\pi\) | |||||||
\(168\) | −5.38894e10 | − | 3.70334e10i | −0.402677 | − | 0.276725i | ||||
\(169\) | 1.08904e11 | 0.789968 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.62309e10 | + | 4.22713e10i | 0.111010 | + | 0.289111i | ||||
\(172\) | 1.01744e11i | 0.675876i | ||||||||
\(173\) | 3.04132e11 | 1.96260 | 0.981300 | − | 0.192482i | \(-0.0616538\pi\) | ||||
0.981300 | + | 0.192482i | \(0.0616538\pi\) | |||||||
\(174\) | −2.18986e10 | − | 1.50490e10i | −0.137300 | − | 0.0943542i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.63690e10i | 0.0969300i | ||||||||
\(177\) | 5.84837e10 | + | 4.01908e10i | 0.336642 | + | 0.231345i | ||||
\(178\) | − | 5.40212e9i | − | 0.0302318i | ||||||
\(179\) | − | 7.07114e9i | − | 0.0384791i | −0.999815 | − | 0.0192395i | \(-0.993875\pi\) | ||
0.999815 | − | 0.0192395i | \(-0.00612451\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.27309e11 | −0.655337 | −0.327669 | − | 0.944793i | \(-0.606263\pi\) | ||||
−0.327669 | + | 0.944793i | \(0.606263\pi\) | |||||||
\(182\) | −8.94290e10 | −0.447838 | ||||||||
\(183\) | 7.30425e10 | − | 1.06288e11i | 0.355894 | − | 0.517880i | ||||
\(184\) | −1.62572e10 | −0.0770825 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.30264e11 | + | 1.89554e11i | −0.585141 | + | 0.851470i | ||||
\(187\) | 1.66488e11i | 0.728075i | ||||||||
\(188\) | 7.93900e10 | 0.338047 | ||||||||
\(189\) | 7.77563e10 | − | 3.24078e11i | 0.322424 | − | 1.34382i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.06460e11i | − | 0.812209i | −0.913827 | − | 0.406105i | \(-0.866887\pi\) | ||
0.913827 | − | 0.406105i | \(-0.133113\pi\) | |||||||
\(192\) | −1.84720e10 | + | 2.68797e10i | −0.0707960 | + | 0.103019i | ||||
\(193\) | − | 3.11606e11i | − | 1.16364i | −0.813317 | − | 0.581821i | \(-0.802340\pi\) | ||
0.813317 | − | 0.581821i | \(-0.197660\pi\) | |||||||
\(194\) | 2.00052e11i | 0.728004i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.31582e11 | −0.454901 | ||||||||
\(197\) | 1.51694e11 | 0.511255 | 0.255628 | − | 0.966775i | \(-0.417718\pi\) | ||||
0.255628 | + | 0.966775i | \(0.417718\pi\) | |||||||
\(198\) | −7.78870e10 | + | 2.99063e10i | −0.255941 | + | 0.0982737i | ||||
\(199\) | 1.11692e11 | 0.357895 | 0.178947 | − | 0.983859i | \(-0.442731\pi\) | ||||
0.178947 | + | 0.983859i | \(0.442731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.04559e11 | − | 7.18543e10i | −0.318700 | − | 0.219014i | ||||
\(202\) | − | 3.79978e11i | − | 1.12980i | ||||||
\(203\) | −1.12241e11 | −0.325591 | ||||||||
\(204\) | −1.87879e11 | + | 2.73392e11i | −0.531773 | + | 0.773812i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.89361e11i | 0.510451i | ||||||||
\(207\) | −2.97021e10 | − | 7.73551e10i | −0.0781512 | − | 0.203534i | ||||
\(208\) | 4.46066e10i | 0.114573i | ||||||||
\(209\) | − | 4.78826e10i | − | 0.120073i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.53066e11 | 0.365987 | 0.182994 | − | 0.983114i | \(-0.441421\pi\) | ||||
0.182994 | + | 0.983114i | \(0.441421\pi\) | |||||||
\(212\) | 2.15829e10 | 0.0503999 | ||||||||
\(213\) | −1.14427e11 | − | 7.86354e10i | −0.260993 | − | 0.179358i | ||||
\(214\) | −3.24828e11 | −0.723744 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.61648e11 | − | 3.87843e10i | −0.343796 | − | 0.0824874i | ||||
\(217\) | 9.71560e11i | 2.01916i | ||||||||
\(218\) | −1.06929e11 | −0.217177 | ||||||||
\(219\) | 4.37763e11 | + | 3.00836e11i | 0.868998 | + | 0.597186i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.53693e11i | 0.860598i | ||||||||
\(222\) | 2.27312e11 | + | 1.56212e11i | 0.421559 | + | 0.289700i | ||||
\(223\) | 6.05759e11i | 1.09844i | 0.835678 | + | 0.549219i | \(0.185075\pi\) | ||||
−0.835678 | + | 0.549219i | \(0.814925\pi\) | |||||||
\(224\) | 1.37771e11i | 0.244298i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.99040e11 | 0.507210 | ||||||||
\(227\) | −6.70588e11 | −1.11257 | −0.556284 | − | 0.830992i | \(-0.687773\pi\) | ||||
−0.556284 | + | 0.830992i | \(0.687773\pi\) | |||||||
\(228\) | 5.40345e10 | − | 7.86286e10i | 0.0876995 | − | 0.127616i | ||||
\(229\) | −3.53356e11 | −0.561094 | −0.280547 | − | 0.959840i | \(-0.590516\pi\) | ||||
−0.280547 | + | 0.959840i | \(0.590516\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.99605e11 | + | 2.90456e11i | −0.303467 | + | 0.441591i | ||||
\(232\) | 5.59851e10i | 0.0832976i | ||||||||
\(233\) | −1.12390e12 | −1.63662 | −0.818309 | − | 0.574779i | \(-0.805088\pi\) | ||||
−0.818309 | + | 0.574779i | \(0.805088\pi\) | |||||||
\(234\) | −2.12248e11 | + | 8.14969e10i | −0.302527 | + | 0.116161i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 1.49517e11i | − | 0.204236i | ||||||
\(237\) | 2.70565e11 | − | 3.93714e11i | 0.361851 | − | 0.526549i | ||||
\(238\) | 1.40127e12i | 1.83500i | ||||||||
\(239\) | 2.64603e11i | 0.339317i | 0.985503 | + | 0.169658i | \(0.0542665\pi\) | ||||
−0.985503 | + | 0.169658i | \(0.945734\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.86768e11 | 1.09075 | 0.545375 | − | 0.838192i | \(-0.316387\pi\) | ||||
0.545375 | + | 0.838192i | \(0.316387\pi\) | |||||||
\(242\) | −4.98671e11 | −0.600810 | ||||||||
\(243\) | −1.10789e11 | − | 8.40014e11i | −0.130757 | − | 0.991414i | ||||
\(244\) | −2.71732e11 | −0.314190 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.76286e11 | − | 4.64752e11i | −0.750680 | − | 0.515877i | ||||
\(247\) | − | 1.30483e11i | − | 0.141929i | ||||||
\(248\) | 4.84607e11 | 0.516573 | ||||||||
\(249\) | 3.00795e11 | − | 4.37704e11i | 0.314249 | − | 0.457281i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 8.59494e11i | − | 0.862729i | −0.902178 | − | 0.431364i | \(-0.858032\pi\) | ||
0.902178 | − | 0.431364i | \(-0.141968\pi\) | |||||||
\(252\) | −6.55546e11 | + | 2.51710e11i | −0.645060 | + | 0.247684i | ||||
\(253\) | 8.76237e10i | 0.0845316i | ||||||||
\(254\) | 7.19130e11i | 0.680203i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.87195e10 | 0.0625000 | ||||||||
\(257\) | −2.17900e12 | −1.94353 | −0.971764 | − | 0.235954i | \(-0.924179\pi\) | ||||
−0.971764 | + | 0.235954i | \(0.924179\pi\) | |||||||
\(258\) | 9.00510e11 | + | 6.18841e11i | 0.787753 | + | 0.541353i | ||||
\(259\) | 1.16509e12 | 0.999677 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.66389e11 | + | 1.02286e11i | −0.219945 | + | 0.0844524i | ||||
\(262\) | 1.13385e12i | 0.918433i | ||||||||
\(263\) | −1.37942e12 | −1.09627 | −0.548134 | − | 0.836391i | \(-0.684661\pi\) | ||||
−0.548134 | + | 0.836391i | \(0.684661\pi\) | |||||||
\(264\) | 1.44877e11 | + | 9.95615e10i | 0.112975 | + | 0.0776375i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 4.03010e11i | − | 0.302627i | ||||||
\(267\) | −4.78126e10 | − | 3.28574e10i | −0.0352360 | − | 0.0242146i | ||||
\(268\) | 2.67312e11i | 0.193350i | ||||||||
\(269\) | − | 1.18129e12i | − | 0.838680i | −0.907829 | − | 0.419340i | \(-0.862262\pi\) | ||
0.907829 | − | 0.419340i | \(-0.137738\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.42251e12 | −0.973213 | −0.486606 | − | 0.873621i | \(-0.661765\pi\) | ||||
−0.486606 | + | 0.873621i | \(0.661765\pi\) | |||||||
\(272\) | 6.98944e11 | 0.469459 | ||||||||
\(273\) | −5.43937e11 | + | 7.91511e11i | −0.358703 | + | 0.521968i | ||||
\(274\) | −6.21674e11 | −0.402541 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.88815e10 | + | 1.43888e11i | −0.0617404 | + | 0.0898418i | ||||
\(277\) | 5.29960e11i | 0.324971i | 0.986711 | + | 0.162485i | \(0.0519510\pi\) | ||||
−0.986711 | + | 0.162485i | \(0.948049\pi\) | |||||||
\(278\) | 1.43116e12 | 0.861913 | ||||||||
\(279\) | 8.85385e11 | + | 2.30587e12i | 0.523734 | + | 1.36400i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.28441e12i | − | 1.30389i | −0.758265 | − | 0.651946i | \(-0.773953\pi\) | ||
0.758265 | − | 0.651946i | \(-0.226047\pi\) | |||||||
\(282\) | 4.82876e11 | − | 7.02659e11i | 0.270764 | − | 0.394003i | ||||
\(283\) | − | 2.31274e12i | − | 1.27408i | −0.770833 | − | 0.637038i | \(-0.780160\pi\) | ||
0.770833 | − | 0.637038i | \(-0.219840\pi\) | |||||||
\(284\) | 2.92539e11i | 0.158340i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.40423e11 | 0.125645 | ||||||||
\(287\) | −3.46630e12 | −1.78015 | ||||||||
\(288\) | 1.25551e11 | + | 3.26982e11i | 0.0633665 | + | 0.165029i | ||||
\(289\) | 5.09295e12 | 2.52627 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.77060e12 | + | 1.21678e12i | 0.848509 | + | 0.583106i | ||||
\(292\) | − | 1.11917e12i | − | 0.527207i | ||||||
\(293\) | 1.05989e12 | 0.490822 | 0.245411 | − | 0.969419i | \(-0.421077\pi\) | ||||
0.245411 | + | 0.969419i | \(0.421077\pi\) | |||||||
\(294\) | −8.00326e11 | + | 1.16460e12i | −0.364360 | + | 0.530199i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 5.81138e11i | − | 0.255753i | ||||||
\(297\) | −2.09042e11 | + | 8.71257e11i | −0.0904588 | + | 0.377020i | ||||
\(298\) | 7.65890e11i | 0.325900i | ||||||||
\(299\) | 2.38781e11i | 0.0999179i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.61555e12 | 1.86806 | ||||||||
\(302\) | −2.76928e12 | −1.10238 | ||||||||
\(303\) | −3.36308e12 | − | 2.31115e12i | −1.31681 | − | 0.904931i | ||||
\(304\) | −2.01019e11 | −0.0774227 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.27698e12 | + | 3.32573e12i | 0.475968 | + | 1.23959i | ||||
\(307\) | 6.89209e11i | 0.252731i | 0.991984 | + | 0.126366i | \(0.0403313\pi\) | ||||
−0.991984 | + | 0.126366i | \(0.959669\pi\) | |||||||
\(308\) | 7.42567e11 | 0.267906 | ||||||||
\(309\) | 1.67598e12 | + | 1.15176e12i | 0.594945 | + | 0.408854i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.95674e12i | − | 0.672559i | −0.941762 | − | 0.336280i | \(-0.890831\pi\) | ||
0.941762 | − | 0.336280i | \(-0.109169\pi\) | |||||||
\(312\) | 3.94801e11 | + | 2.71312e11i | 0.133538 | + | 0.0917690i | ||||
\(313\) | 2.48821e11i | 0.0828256i | 0.999142 | + | 0.0414128i | \(0.0131859\pi\) | ||||
−0.999142 | + | 0.0414128i | \(0.986814\pi\) | |||||||
\(314\) | 3.59711e12i | 1.17843i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.00655e12 | −0.319449 | ||||||||
\(317\) | 4.63675e12 | 1.44850 | 0.724249 | − | 0.689539i | \(-0.242187\pi\) | ||||
0.724249 | + | 0.689539i | \(0.242187\pi\) | |||||||
\(318\) | 1.31274e11 | − | 1.91024e11i | 0.0403686 | − | 0.0587425i | ||||
\(319\) | 3.01751e11 | 0.0913473 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.97571e12 | + | 2.87497e12i | −0.579694 | + | 0.843544i | ||||
\(322\) | 7.37496e11i | 0.213049i | ||||||||
\(323\) | −2.04456e12 | −0.581549 | ||||||||
\(324\) | −1.32646e12 | + | 1.19480e12i | −0.371510 | + | 0.334634i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 2.08360e12i | − | 0.565883i | ||||||
\(327\) | −6.50378e11 | + | 9.46400e11i | −0.173951 | + | 0.253125i | ||||
\(328\) | 1.72897e12i | 0.455426i | ||||||||
\(329\) | − | 3.60147e12i | − | 0.934331i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.41443e12 | −0.355994 | −0.177997 | − | 0.984031i | \(-0.556962\pi\) | ||||
−0.177997 | + | 0.984031i | \(0.556962\pi\) | |||||||
\(332\) | −1.11902e12 | −0.277425 | ||||||||
\(333\) | 2.76518e12 | − | 1.06175e12i | 0.675308 | − | 0.259298i | ||||
\(334\) | −4.80642e12 | −1.15635 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.21938e12 | + | 8.37971e11i | 0.284736 | + | 0.195674i | ||||
\(337\) | 8.67755e11i | 0.199640i | 0.995006 | + | 0.0998201i | \(0.0318267\pi\) | ||||
−0.995006 | + | 0.0998201i | \(0.968173\pi\) | |||||||
\(338\) | −2.46421e12 | −0.558592 | ||||||||
\(339\) | 1.81886e12 | − | 2.64672e12i | 0.406257 | − | 0.591167i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.61196e12i | − | 0.566493i | ||||||
\(342\) | −3.67264e11 | − | 9.56490e11i | −0.0784961 | − | 0.204432i | ||||
\(343\) | − | 5.91785e11i | − | 0.124650i | ||||||
\(344\) | − | 2.30221e12i | − | 0.477917i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.88173e12 | −1.38777 | ||||||||
\(347\) | −5.20712e12 | −1.03502 | −0.517512 | − | 0.855676i | \(-0.673142\pi\) | ||||
−0.517512 | + | 0.855676i | \(0.673142\pi\) | |||||||
\(348\) | 4.95509e11 | + | 3.40520e11i | 0.0970857 | + | 0.0667185i | ||||
\(349\) | −1.11953e12 | −0.216226 | −0.108113 | − | 0.994139i | \(-0.534481\pi\) | ||||
−0.108113 | + | 0.994139i | \(0.534481\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.69653e11 | + | 2.37424e12i | −0.106924 | + | 0.445644i | ||||
\(352\) | − | 3.70388e11i | − | 0.0685398i | ||||||
\(353\) | 3.73952e12 | 0.682248 | 0.341124 | − | 0.940018i | \(-0.389192\pi\) | ||||
0.341124 | + | 0.940018i | \(0.389192\pi\) | |||||||
\(354\) | −1.32334e12 | − | 9.09413e11i | −0.238042 | − | 0.163586i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.22236e11i | 0.0213771i | ||||||||
\(357\) | 1.24023e13 | + | 8.52299e12i | 2.13875 | + | 1.46977i | ||||
\(358\) | 1.60002e11i | 0.0272088i | ||||||||
\(359\) | − | 3.54489e12i | − | 0.594471i | −0.954804 | − | 0.297235i | \(-0.903935\pi\) | ||
0.954804 | − | 0.297235i | \(-0.0960646\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.54305e12 | −0.904092 | ||||||||
\(362\) | 2.88066e12 | 0.463393 | ||||||||
\(363\) | −3.03308e12 | + | 4.41360e12i | −0.481228 | + | 0.700260i | ||||
\(364\) | 2.02355e12 | 0.316670 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.65276e12 | + | 2.40503e12i | −0.251655 | + | 0.366197i | ||||
\(367\) | − | 1.01161e13i | − | 1.51944i | −0.650248 | − | 0.759722i | \(-0.725335\pi\) | ||
0.650248 | − | 0.759722i | \(-0.274665\pi\) | |||||||
\(368\) | 3.67858e11 | 0.0545056 | ||||||||
\(369\) | −8.22679e12 | + | 3.15885e12i | −1.20254 | + | 0.461739i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 9.79093e11i | − | 0.139301i | ||||||
\(372\) | 2.94754e12 | − | 4.28913e12i | 0.413757 | − | 0.602080i | ||||
\(373\) | − | 3.81055e12i | − | 0.527769i | −0.964554 | − | 0.263885i | \(-0.914996\pi\) | ||
0.964554 | − | 0.263885i | \(-0.0850038\pi\) | |||||||
\(374\) | − | 3.76720e12i | − | 0.514827i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.79639e12 | −0.239035 | ||||||||
\(377\) | 8.22293e11 | 0.107974 | ||||||||
\(378\) | −1.75943e12 | + | 7.33304e12i | −0.227988 | + | 0.950222i | ||||
\(379\) | −1.11052e13 | −1.42014 | −0.710069 | − | 0.704132i | \(-0.751336\pi\) | ||||
−0.710069 | + | 0.704132i | \(0.751336\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.36482e12 | + | 4.37399e12i | 0.792796 | + | 0.544819i | ||||
\(382\) | 4.67165e12i | 0.574319i | ||||||||
\(383\) | 4.29169e12 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(384\) | 4.17974e11 | − | 6.08217e11i | 0.0500603 | − | 0.0728455i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.05084e12i | 0.822820i | ||||||||
\(387\) | 1.09544e13 | − | 4.20617e12i | 1.26192 | − | 0.484542i | ||||
\(388\) | − | 4.52665e12i | − | 0.514776i | ||||||
\(389\) | − | 1.50554e13i | − | 1.69023i | −0.534588 | − | 0.845113i | \(-0.679533\pi\) | ||
0.534588 | − | 0.845113i | \(-0.320467\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.74148e12 | 0.409411 | ||||||||
\(392\) | 2.97736e12 | 0.321663 | ||||||||
\(393\) | 1.00354e13 | + | 6.89642e12i | 1.07046 | + | 0.735633i | ||||
\(394\) | −3.43245e12 | −0.361512 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.76238e12 | − | 6.76703e11i | 0.180977 | − | 0.0694900i | ||||
\(397\) | − | 1.11669e13i | − | 1.13235i | −0.824286 | − | 0.566174i | \(-0.808423\pi\) | ||
0.824286 | − | 0.566174i | \(-0.191577\pi\) | |||||||
\(398\) | −2.52729e12 | −0.253070 | ||||||||
\(399\) | −3.56693e12 | − | 2.45124e12i | −0.352720 | − | 0.242394i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.15685e13i | − | 1.11572i | −0.829935 | − | 0.557861i | \(-0.811622\pi\) | ||
0.829935 | − | 0.557861i | \(-0.188378\pi\) | |||||||
\(402\) | 2.36590e12 | + | 1.62588e12i | 0.225355 | + | 0.154867i | ||||
\(403\) | − | 7.11777e12i | − | 0.669605i | ||||||
\(404\) | 8.59793e12i | 0.798890i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.53973e12 | 0.230227 | ||||||||
\(407\) | −3.13224e12 | −0.280468 | ||||||||
\(408\) | 4.25121e12 | − | 6.18616e12i | 0.376021 | − | 0.547168i | ||||
\(409\) | 1.07411e13 | 0.938498 | 0.469249 | − | 0.883066i | \(-0.344525\pi\) | ||||
0.469249 | + | 0.883066i | \(0.344525\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.78123e12 | + | 5.50227e12i | −0.322421 | + | 0.469172i | ||||
\(412\) | − | 4.28475e12i | − | 0.360944i | ||||||
\(413\) | −6.78275e12 | −0.564489 | ||||||||
\(414\) | 6.72082e11 | + | 1.75035e12i | 0.0552612 | + | 0.143920i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 1.00933e12i | − | 0.0810153i | ||||||
\(417\) | 8.70477e12 | − | 1.26668e13i | 0.690362 | − | 1.00458i | ||||
\(418\) | 1.08346e12i | 0.0849047i | ||||||||
\(419\) | 8.81717e12i | 0.682746i | 0.939928 | + | 0.341373i | \(0.110892\pi\) | ||||
−0.939928 | + | 0.341373i | \(0.889108\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.69741e12 | −0.430792 | −0.215396 | − | 0.976527i | \(-0.569104\pi\) | ||||
−0.215396 | + | 0.976527i | \(0.569104\pi\) | |||||||
\(422\) | −3.46348e12 | −0.258792 | ||||||||
\(423\) | −3.28203e12 | − | 8.54761e12i | −0.242349 | − | 0.631165i | ||||
\(424\) | −4.88365e11 | −0.0356381 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.58918e12 | + | 1.77932e12i | 0.184550 | + | 0.126825i | ||||
\(427\) | 1.23269e13i | 0.868392i | ||||||||
\(428\) | 7.35003e12 | 0.511764 | ||||||||
\(429\) | 1.46233e12 | − | 2.12792e12i | 0.100637 | − | 0.146443i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.80323e13i | − | 1.21245i | −0.795293 | − | 0.606226i | \(-0.792683\pi\) | ||
0.795293 | − | 0.606226i | \(-0.207317\pi\) | |||||||
\(432\) | 3.65767e12 | + | 8.77590e11i | 0.243101 | + | 0.0583274i | ||||
\(433\) | − | 2.06339e13i | − | 1.35563i | −0.735232 | − | 0.677816i | \(-0.762927\pi\) | ||
0.735232 | − | 0.677816i | \(-0.237073\pi\) | |||||||
\(434\) | − | 2.19839e13i | − | 1.42776i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.41953e12 | 0.153567 | ||||||||
\(437\) | −1.07606e12 | −0.0675195 | ||||||||
\(438\) | −9.90545e12 | − | 6.80715e12i | −0.614474 | − | 0.422275i | ||||
\(439\) | −1.95313e13 | −1.19787 | −0.598935 | − | 0.800798i | \(-0.704409\pi\) | ||||
−0.598935 | + | 0.800798i | \(0.704409\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.43969e12 | + | 1.41669e13i | 0.326123 | + | 0.849343i | ||||
\(442\) | − | 1.02659e13i | − | 0.608535i | ||||||
\(443\) | 2.97469e13 | 1.74351 | 0.871753 | − | 0.489946i | \(-0.162984\pi\) | ||||
0.871753 | + | 0.489946i | \(0.162984\pi\) | |||||||
\(444\) | −5.14349e12 | − | 3.53467e12i | −0.298087 | − | 0.204849i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 1.37068e13i | − | 0.776713i | ||||||
\(447\) | 6.77868e12 | + | 4.65839e12i | 0.379846 | + | 0.261035i | ||||
\(448\) | − | 3.11741e12i | − | 0.172744i | ||||||
\(449\) | − | 1.37505e13i | − | 0.753509i | −0.926313 | − | 0.376754i | \(-0.877040\pi\) | ||
0.926313 | − | 0.376754i | \(-0.122960\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.31887e12 | 0.499437 | ||||||||
\(452\) | −6.76651e12 | −0.358651 | ||||||||
\(453\) | −1.68437e13 | + | 2.45102e13i | −0.882971 | + | 1.28486i | ||||
\(454\) | 1.51737e13 | 0.786704 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.22266e12 | + | 1.77916e12i | −0.0620129 | + | 0.0902383i | ||||
\(457\) | 4.10224e11i | 0.0205798i | 0.999947 | + | 0.0102899i | \(0.00327543\pi\) | ||||
−0.999947 | + | 0.0102899i | \(0.996725\pi\) | |||||||
\(458\) | 7.99554e12 | 0.396753 | ||||||||
\(459\) | 3.72021e13 | + | 8.92594e12i | 1.82601 | + | 0.438118i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.10914e11i | 0.0101298i | 0.999987 | + | 0.00506490i | \(0.00161221\pi\) | ||||
−0.999987 | + | 0.00506490i | \(0.998388\pi\) | |||||||
\(462\) | 4.51654e12 | − | 6.57226e12i | 0.214583 | − | 0.312252i | ||||
\(463\) | 1.96738e13i | 0.924660i | 0.886708 | + | 0.462330i | \(0.152987\pi\) | ||||
−0.886708 | + | 0.462330i | \(0.847013\pi\) | |||||||
\(464\) | − | 1.26680e12i | − | 0.0589003i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.54309e13 | 1.15726 | ||||||||
\(467\) | −1.21902e13 | −0.548815 | −0.274407 | − | 0.961614i | \(-0.588482\pi\) | ||||
−0.274407 | + | 0.961614i | \(0.588482\pi\) | |||||||
\(468\) | 4.80261e12 | − | 1.84406e12i | 0.213919 | − | 0.0821385i | ||||
\(469\) | 1.21264e13 | 0.534402 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.18370e13 | + | 2.18788e13i | 1.37350 | + | 0.943885i | ||||
\(472\) | 3.38319e12i | 0.144416i | ||||||||
\(473\) | −1.24085e13 | −0.524101 | ||||||||
\(474\) | −6.12218e12 | + | 8.90872e12i | −0.255867 | + | 0.372326i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 3.17071e13i | − | 1.29754i | ||||||
\(477\) | −8.92250e11 | − | 2.32374e12i | −0.0361322 | − | 0.0941014i | ||||
\(478\) | − | 5.98729e12i | − | 0.239933i | ||||||
\(479\) | 5.00886e12i | 0.198637i | 0.995056 | + | 0.0993187i | \(0.0316663\pi\) | ||||
−0.995056 | + | 0.0993187i | \(0.968334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.53558e12 | −0.331518 | ||||||||
\(482\) | −2.00653e13 | −0.771276 | ||||||||
\(483\) | 6.52737e12 | + | 4.48569e12i | 0.248315 | + | 0.170645i | ||||
\(484\) | 1.12836e13 | 0.424837 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.50686e12 | + | 1.90074e13i | 0.0924590 | + | 0.701036i | ||||
\(487\) | − | 4.17000e13i | − | 1.52227i | −0.648595 | − | 0.761134i | \(-0.724643\pi\) | ||
0.648595 | − | 0.761134i | \(-0.275357\pi\) | |||||||
\(488\) | 6.14859e12 | 0.222166 | ||||||||
\(489\) | −1.84414e13 | − | 1.26732e13i | −0.659553 | − | 0.453253i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.10340e12i | 0.0737081i | 0.999321 | + | 0.0368540i | \(0.0117337\pi\) | ||||
−0.999321 | + | 0.0368540i | \(0.988266\pi\) | |||||||
\(492\) | 1.53026e13 | + | 1.05161e13i | 0.530811 | + | 0.364780i | ||||
\(493\) | − | 1.28846e13i | − | 0.442421i | ||||||
\(494\) | 2.95250e12i | 0.100359i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.09654e13 | −0.365272 | ||||||||
\(497\) | 1.32708e13 | 0.437639 | ||||||||
\(498\) | −6.80622e12 | + | 9.90410e12i | −0.222208 | + | 0.323347i | ||||
\(499\) | −2.74482e13 | −0.887179 | −0.443589 | − | 0.896230i | \(-0.646295\pi\) | ||||
−0.443589 | + | 0.896230i | \(0.646295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.92342e13 | + | 4.25403e13i | −0.926197 | + | 1.34776i | ||||
\(502\) | 1.94481e13i | 0.610041i | ||||||||
\(503\) | −2.26985e13 | −0.704949 | −0.352474 | − | 0.935822i | \(-0.614660\pi\) | ||||
−0.352474 | + | 0.935822i | \(0.614660\pi\) | |||||||
\(504\) | 1.48333e13 | − | 5.69556e12i | 0.456127 | − | 0.175139i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 1.98270e12i | − | 0.0597729i | ||||||
\(507\) | −1.49882e13 | + | 2.18101e13i | −0.447413 | + | 0.651055i | ||||
\(508\) | − | 1.62721e13i | − | 0.480976i | ||||||
\(509\) | 4.21460e13i | 1.23358i | 0.787127 | + | 0.616791i | \(0.211567\pi\) | ||||
−0.787127 | + | 0.616791i | \(0.788433\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.07703e13 | −1.45715 | ||||||||
\(512\) | −1.55494e12 | −0.0441942 | ||||||||
\(513\) | −1.06994e13 | − | 2.56713e12i | −0.301144 | − | 0.0722539i | ||||
\(514\) | 4.93051e13 | 1.37428 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.03762e13 | − | 1.40028e13i | −0.557025 | − | 0.382795i | ||||
\(517\) | 9.68227e12i | 0.262135i | ||||||||
\(518\) | −2.63629e13 | −0.706878 | ||||||||
\(519\) | −4.18569e13 | + | 6.09083e13i | −1.11155 | + | 1.61748i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6.54420e13i | − | 1.70478i | −0.522907 | − | 0.852390i | \(-0.675152\pi\) | ||
0.522907 | − | 0.852390i | \(-0.324848\pi\) | |||||||
\(522\) | 6.02770e12 | − | 2.31446e12i | 0.155525 | − | 0.0597169i | ||||
\(523\) | 6.14531e13i | 1.57049i | 0.619185 | + | 0.785245i | \(0.287463\pi\) | ||||
−0.619185 | + | 0.785245i | \(0.712537\pi\) | |||||||
\(524\) | − | 2.56560e13i | − | 0.649430i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.12126e13 | 0.775178 | ||||||||
\(527\) | −1.11529e14 | −2.74369 | ||||||||
\(528\) | −3.27820e12 | − | 2.25282e12i | −0.0798851 | − | 0.0548980i | ||||
\(529\) | −3.94574e13 | −0.952466 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.60979e13 | + | 6.18114e12i | −0.381327 | + | 0.146418i | ||||
\(532\) | 9.11907e12i | 0.213990i | ||||||||
\(533\) | 2.53946e13 | 0.590343 | ||||||||
\(534\) | 1.08188e12 | + | 7.43479e11i | 0.0249156 | + | 0.0171223i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 6.04857e12i | − | 0.136719i | ||||||
\(537\) | 1.41613e12 | + | 9.73183e11i | 0.0317126 | + | 0.0217933i | ||||
\(538\) | 2.67296e13i | 0.593036i | ||||||||
\(539\) | − | 1.60475e13i | − | 0.352748i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.50207e13 | 0.324118 | 0.162059 | − | 0.986781i | \(-0.448187\pi\) | ||||
0.162059 | + | 0.986781i | \(0.448187\pi\) | |||||||
\(542\) | 3.21877e13 | 0.688166 | ||||||||
\(543\) | 1.75211e13 | − | 2.54960e13i | 0.371162 | − | 0.540098i | ||||
\(544\) | −1.58153e13 | −0.331958 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.23079e13 | − | 1.79099e13i | 0.253641 | − | 0.369087i | ||||
\(547\) | 7.15097e13i | 1.46025i | 0.683312 | + | 0.730127i | \(0.260539\pi\) | ||||
−0.683312 | + | 0.730127i | \(0.739461\pi\) | |||||||
\(548\) | 1.40669e13 | 0.284639 | ||||||||
\(549\) | 1.12336e13 | + | 2.92563e13i | 0.225245 | + | 0.586621i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.70565e12i | 0.0729636i | ||||||||
\(552\) | 2.23743e12 | − | 3.25581e12i | 0.0436571 | − | 0.0635278i | ||||
\(553\) | 4.56616e13i | 0.882928i | ||||||||
\(554\) | − | 1.19916e13i | − | 0.229789i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.23834e13 | −0.609464 | ||||||||
\(557\) | −7.34107e13 | −1.36925 | −0.684626 | − | 0.728895i | \(-0.740034\pi\) | ||||
−0.684626 | + | 0.728895i | \(0.740034\pi\) | |||||||
\(558\) | −2.00340e13 | − | 5.21758e13i | −0.370336 | − | 0.964490i | ||||
\(559\) | −3.38141e13 | −0.619497 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.33425e13 | − | 2.29134e13i | −0.600045 | − | 0.412358i | ||||
\(562\) | 5.16902e13i | 0.921991i | ||||||||
\(563\) | −4.77347e13 | −0.843902 | −0.421951 | − | 0.906619i | \(-0.638655\pi\) | ||||
−0.421951 | + | 0.906619i | \(0.638655\pi\) | |||||||
\(564\) | −1.09262e13 | + | 1.58994e13i | −0.191459 | + | 0.278602i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.23314e13i | 0.900907i | ||||||||
\(567\) | 5.42013e13 | + | 6.01742e13i | 0.924900 | + | 1.02682i | ||||
\(568\) | − | 6.61939e12i | − | 0.111963i | ||||||
\(569\) | 1.90951e13i | 0.320156i | 0.987104 | + | 0.160078i | \(0.0511745\pi\) | ||||
−0.987104 | + | 0.160078i | \(0.948825\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.09448e13 | −0.345060 | −0.172530 | − | 0.985004i | \(-0.555194\pi\) | ||||
−0.172530 | + | 0.985004i | \(0.555194\pi\) | |||||||
\(572\) | −5.44014e12 | −0.0888444 | ||||||||
\(573\) | 4.13475e13 | + | 2.84145e13i | 0.669385 | + | 0.460009i | ||||
\(574\) | 7.84334e13 | 1.25876 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.84091e12 | − | 7.39876e12i | −0.0448069 | − | 0.116693i | ||||
\(577\) | 3.56688e13i | 0.557711i | 0.960333 | + | 0.278855i | \(0.0899550\pi\) | ||||
−0.960333 | + | 0.278855i | \(0.910045\pi\) | |||||||
\(578\) | −1.15240e14 | −1.78635 | ||||||||
\(579\) | 6.24051e13 | + | 4.28856e13i | 0.959019 | + | 0.659050i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.07634e13i | 0.766778i | ||||||||
\(582\) | −4.00642e13 | − | 2.75326e13i | −0.599986 | − | 0.412318i | ||||
\(583\) | 2.63221e12i | 0.0390821i | ||||||||
\(584\) | 2.53239e13i | 0.372792i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.39826e13 | −0.347064 | ||||||||
\(587\) | 1.29418e14 | 1.85697 | 0.928483 | − | 0.371375i | \(-0.121114\pi\) | ||||
0.928483 | + | 0.371375i | \(0.121114\pi\) | |||||||
\(588\) | 1.81093e13 | − | 2.63518e13i | 0.257641 | − | 0.374908i | ||||
\(589\) | 3.20761e13 | 0.452486 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.08773e13 | + | 3.03797e13i | −0.289559 | + | 0.421352i | ||||
\(592\) | 1.31496e13i | 0.180845i | ||||||||
\(593\) | 3.96596e13 | 0.540848 | 0.270424 | − | 0.962741i | \(-0.412836\pi\) | ||||
0.270424 | + | 0.962741i | \(0.412836\pi\) | |||||||
\(594\) | 4.73007e12 | − | 1.97143e13i | 0.0639640 | − | 0.266593i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 1.73301e13i | − | 0.230446i | ||||||
\(597\) | −1.53718e13 | + | 2.23684e13i | −0.202700 | + | 0.294960i | ||||
\(598\) | − | 5.40299e12i | − | 0.0706526i | ||||||
\(599\) | 4.57555e13i | 0.593347i | 0.954979 | + | 0.296674i | \(0.0958774\pi\) | ||||
−0.954979 | + | 0.296674i | \(0.904123\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.06033e14 | 1.35229 | 0.676143 | − | 0.736770i | \(-0.263650\pi\) | ||||
0.676143 | + | 0.736770i | \(0.263650\pi\) | |||||||
\(602\) | −1.04438e14 | −1.32092 | ||||||||
\(603\) | 2.87804e13 | − | 1.10508e13i | 0.361003 | − | 0.138614i | ||||
\(604\) | 6.26617e13 | 0.779503 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.60979e13 | + | 5.22954e13i | 0.931128 | + | 0.639883i | ||||
\(607\) | − | 9.55067e13i | − | 1.15902i | −0.814966 | − | 0.579509i | \(-0.803244\pi\) | ||
0.814966 | − | 0.579509i | \(-0.196756\pi\) | |||||||
\(608\) | 4.54853e12 | 0.0547461 | ||||||||
\(609\) | 1.54475e13 | − | 2.24784e13i | 0.184404 | − | 0.268336i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.63849e13i | 0.309848i | ||||||||
\(612\) | −2.88948e13 | − | 7.52526e13i | −0.336560 | − | 0.876525i | ||||
\(613\) | 5.18411e13i | 0.598924i | 0.954108 | + | 0.299462i | \(0.0968072\pi\) | ||||
−0.954108 | + | 0.299462i | \(0.903193\pi\) | |||||||
\(614\) | − | 1.55950e13i | − | 0.178708i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.68024e13 | −0.189438 | ||||||||
\(617\) | −8.05443e13 | −0.900760 | −0.450380 | − | 0.892837i | \(-0.648711\pi\) | ||||
−0.450380 | + | 0.892837i | \(0.648711\pi\) | |||||||
\(618\) | −3.79231e13 | − | 2.60612e13i | −0.420690 | − | 0.289103i | ||||
\(619\) | 5.14946e13 | 0.566642 | 0.283321 | − | 0.959025i | \(-0.408564\pi\) | ||||
0.283321 | + | 0.959025i | \(0.408564\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.95797e13 | + | 4.69777e12i | 0.212005 | + | 0.0508667i | ||||
\(622\) | 4.42759e13i | 0.475571i | ||||||||
\(623\) | 5.54515e12 | 0.0590844 | ||||||||
\(624\) | −8.93332e12 | − | 6.13909e12i | −0.0944256 | − | 0.0648905i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 5.63017e12i | − | 0.0585665i | ||||||
\(627\) | 9.58941e12 | + | 6.58996e12i | 0.0989587 | + | 0.0680057i | ||||
\(628\) | − | 8.13933e13i | − | 0.833279i | ||||||
\(629\) | 1.33745e14i | 1.35839i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.02922e13 | −0.102887 | −0.0514435 | − | 0.998676i | \(-0.516382\pi\) | ||||
−0.0514435 | + | 0.998676i | \(0.516382\pi\) | |||||||
\(632\) | 2.27757e13 | 0.225884 | ||||||||
\(633\) | −2.10660e13 | + | 3.06543e13i | −0.207283 | + | 0.301629i | ||||
\(634\) | −1.04918e14 | −1.02424 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.97040e12 | + | 4.32238e12i | −0.0285449 | + | 0.0415372i | ||||
\(637\) | − | 4.37307e13i | − | 0.416955i | ||||||
\(638\) | −6.82785e12 | −0.0645923 | ||||||||
\(639\) | 3.14965e13 | − | 1.20937e13i | 0.295636 | − | 0.113516i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.62451e13i | − | 0.427342i | −0.976906 | − | 0.213671i | \(-0.931458\pi\) | ||
0.976906 | − | 0.213671i | \(-0.0685420\pi\) | |||||||
\(642\) | 4.47053e13 | − | 6.50531e13i | 0.409906 | − | 0.596476i | ||||
\(643\) | − | 2.73102e13i | − | 0.248468i | −0.992253 | − | 0.124234i | \(-0.960353\pi\) | ||
0.992253 | − | 0.124234i | \(-0.0396474\pi\) | |||||||
\(644\) | − | 1.66876e13i | − | 0.150649i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.62630e13 | 0.411217 | ||||||||
\(647\) | −1.34984e13 | −0.119059 | −0.0595293 | − | 0.998227i | \(-0.518960\pi\) | ||||
−0.0595293 | + | 0.998227i | \(0.518960\pi\) | |||||||
\(648\) | 3.00145e13 | − | 2.70353e13i | 0.262697 | − | 0.236622i | ||||
\(649\) | 1.82349e13 | 0.158372 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.94573e14 | − | 1.33713e14i | −1.66410 | − | 1.14359i | ||||
\(652\) | 4.71466e13i | 0.400140i | ||||||||
\(653\) | 8.41840e13 | 0.709029 | 0.354514 | − | 0.935051i | \(-0.384646\pi\) | ||||
0.354514 | + | 0.935051i | \(0.384646\pi\) | |||||||
\(654\) | 1.47164e13 | − | 2.14146e13i | 0.123002 | − | 0.178987i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 3.91220e13i | − | 0.322034i | ||||||
\(657\) | −1.20496e14 | + | 4.62671e13i | −0.984345 | + | 0.377960i | ||||
\(658\) | 8.14920e13i | 0.660672i | ||||||||
\(659\) | − | 1.65464e14i | − | 1.33130i | −0.746264 | − | 0.665650i | \(-0.768154\pi\) | ||
0.746264 | − | 0.665650i | \(-0.231846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.01681e14 | 1.59830 | 0.799148 | − | 0.601135i | \(-0.205284\pi\) | ||||
0.799148 | + | 0.601135i | \(0.205284\pi\) | |||||||
\(662\) | 3.20050e13 | 0.251726 | ||||||||
\(663\) | −9.08606e13 | − | 6.24405e13i | −0.709264 | − | 0.487415i | ||||
\(664\) | 2.53204e13 | 0.196169 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.25688e13 | + | 2.40246e13i | −0.477515 | + | 0.183352i | ||||
\(667\) | − | 6.78122e12i | − | 0.0513664i | ||||||
\(668\) | 1.08757e14 | 0.817663 | ||||||||
\(669\) | −1.21315e14 | − | 8.33691e13i | −0.905281 | − | 0.622120i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.31400e13i | − | 0.243635i | ||||||
\(672\) | −2.75914e13 | − | 1.89611e13i | −0.201338 | − | 0.138362i | ||||
\(673\) | − | 6.04368e12i | − | 0.0437750i | −0.999760 | − | 0.0218875i | \(-0.993032\pi\) | ||
0.999760 | − | 0.0218875i | \(-0.00696757\pi\) | |||||||
\(674\) | − | 1.96351e13i | − | 0.141167i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.57588e13 | 0.394984 | ||||||||
\(677\) | 1.21474e14 | 0.854164 | 0.427082 | − | 0.904213i | \(-0.359542\pi\) | ||||
0.427082 | + | 0.904213i | \(0.359542\pi\) | |||||||
\(678\) | −4.11561e13 | + | 5.98885e13i | −0.287267 | + | 0.418018i | ||||
\(679\) | −2.05349e14 | −1.42280 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.22913e13 | − | 1.34298e14i | 0.630123 | − | 0.916926i | ||||
\(682\) | 5.91019e13i | 0.400571i | ||||||||
\(683\) | 1.51629e14 | 1.02019 | 0.510094 | − | 0.860119i | \(-0.329611\pi\) | ||||
0.510094 | + | 0.860119i | \(0.329611\pi\) | |||||||
\(684\) | 8.31024e12 | + | 2.16429e13i | 0.0555051 | + | 0.144556i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.33906e13i | 0.0881410i | ||||||||
\(687\) | 4.86315e13 | − | 7.07663e13i | 0.317785 | − | 0.462427i | ||||
\(688\) | 5.20930e13i | 0.337938i | ||||||||
\(689\) | 7.17296e12i | 0.0461958i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.62249e13 | 0.420369 | 0.210185 | − | 0.977662i | \(-0.432593\pi\) | ||||
0.210185 | + | 0.977662i | \(0.432593\pi\) | |||||||
\(692\) | 1.55716e14 | 0.981300 | ||||||||
\(693\) | −3.06982e13 | − | 7.99493e13i | −0.192064 | − | 0.500205i | ||||
\(694\) | 1.17824e14 | 0.731873 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.12121e13 | − | 7.70509e12i | −0.0686500 | − | 0.0471771i | ||||
\(697\) | − | 3.97909e14i | − | 2.41891i | ||||||
\(698\) | 2.53321e13 | 0.152895 | ||||||||
\(699\) | 1.54679e14 | − | 2.25082e14i | 0.926928 | − | 1.34882i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5.78990e13i | − | 0.342043i | −0.985267 | − | 0.171022i | \(-0.945293\pi\) | ||
0.985267 | − | 0.171022i | \(-0.0547068\pi\) | |||||||
\(702\) | 1.28898e13 | − | 5.37228e13i | 0.0756066 | − | 0.315118i | ||||
\(703\) | − | 3.84654e13i | − | 0.224024i | ||||||
\(704\) | 8.38091e12i | 0.0484650i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.46157e13 | −0.482422 | ||||||||
\(707\) | 3.90039e14 | 2.20806 | ||||||||
\(708\) | 2.99437e13 | + | 2.05777e13i | 0.168321 | + | 0.115672i | ||||
\(709\) | −2.70077e14 | −1.50750 | −0.753750 | − | 0.657162i | \(-0.771757\pi\) | ||||
−0.753750 | + | 0.657162i | \(0.771757\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.16115e13 | + | 1.08372e14i | 0.229016 | + | 0.596441i | ||||
\(712\) | − | 2.76588e12i | − | 0.0151159i | ||||||
\(713\) | −5.86983e13 | −0.318550 | ||||||||
\(714\) | −2.80631e14 | − | 1.92853e14i | −1.51232 | − | 1.03929i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 3.62043e12i | − | 0.0192395i | ||||||
\(717\) | −5.29918e13 | − | 3.64166e13i | −0.279649 | − | 0.192178i | ||||
\(718\) | 8.02117e13i | 0.420354i | ||||||||
\(719\) | − | 1.48102e14i | − | 0.770755i | −0.922759 | − | 0.385377i | \(-0.874071\pi\) | ||
0.922759 | − | 0.385377i | \(-0.125929\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.94375e14 | −0.997616 | ||||||||
\(722\) | 1.25425e14 | 0.639289 | ||||||||
\(723\) | −1.22044e14 | + | 1.77592e14i | −0.617765 | + | 0.898944i | ||||
\(724\) | −6.51820e13 | −0.327669 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.86307e13 | − | 9.98683e13i | 0.340279 | − | 0.495159i | ||||
\(727\) | 5.21602e13i | 0.256842i | 0.991720 | + | 0.128421i | \(0.0409910\pi\) | ||||
−0.991720 | + | 0.128421i | \(0.959009\pi\) | |||||||
\(728\) | −4.57876e13 | −0.223919 | ||||||||
\(729\) | 1.83476e14 | + | 9.34214e13i | 0.891133 | + | 0.453742i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.29837e14i | 2.53837i | ||||||||
\(732\) | 3.73978e13 | − | 5.44195e13i | 0.177947 | − | 0.258940i | ||||
\(733\) | − | 3.21782e14i | − | 1.52069i | −0.649518 | − | 0.760346i | \(-0.725029\pi\) | ||
0.649518 | − | 0.760346i | \(-0.274971\pi\) | |||||||
\(734\) | 2.28902e14i | 1.07441i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.32367e12 | −0.0385413 | ||||||||
\(737\) | −3.26009e13 | −0.149931 | ||||||||
\(738\) | 1.86151e14 | − | 7.14765e13i | 0.850322 | − | 0.326499i | ||||
\(739\) | −1.66542e14 | −0.755617 | −0.377809 | − | 0.925884i | \(-0.623322\pi\) | ||||
−0.377809 | + | 0.925884i | \(0.623322\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.61318e13 | + | 1.79581e13i | 0.116971 | + | 0.0803839i | ||||
\(742\) | 2.21543e13i | 0.0985007i | ||||||||
\(743\) | −1.13631e14 | −0.501825 | −0.250912 | − | 0.968010i | \(-0.580731\pi\) | ||||
−0.250912 | + | 0.968010i | \(0.580731\pi\) | |||||||
\(744\) | −6.66953e13 | + | 9.70519e13i | −0.292570 | + | 0.425735i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.62230e13i | 0.373189i | ||||||||
\(747\) | 4.62608e13 | + | 1.20480e14i | 0.198889 | + | 0.517979i | ||||
\(748\) | 8.52421e13i | 0.364037i | ||||||||
\(749\) | − | 3.33429e14i | − | 1.41447i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.64956e14 | −0.690508 | −0.345254 | − | 0.938509i | \(-0.612207\pi\) | ||||
−0.345254 | + | 0.938509i | \(0.612207\pi\) | |||||||
\(752\) | 4.06477e13 | 0.169023 | ||||||||
\(753\) | 1.72130e14 | + | 1.18290e14i | 0.711020 | + | 0.488622i | ||||
\(754\) | −1.86064e13 | −0.0763493 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.98112e13 | − | 1.65928e14i | 0.161212 | − | 0.671909i | ||||
\(757\) | − | 2.67990e14i | − | 1.07805i | −0.842289 | − | 0.539026i | \(-0.818793\pi\) | ||
0.842289 | − | 0.539026i | \(-0.181207\pi\) | |||||||
\(758\) | 2.51282e14 | 1.00419 | ||||||||
\(759\) | −1.75483e13 | − | 1.20594e13i | −0.0696669 | − | 0.0478760i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.29795e14i | 0.508550i | 0.967132 | + | 0.254275i | \(0.0818368\pi\) | ||||
−0.967132 | + | 0.254275i | \(0.918163\pi\) | |||||||
\(762\) | −1.44020e14 | − | 9.89720e13i | −0.560591 | − | 0.385245i | ||||
\(763\) | − | 1.09760e14i | − | 0.424446i | ||||||
\(764\) | − | 1.05707e14i | − | 0.406105i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.71099e13 | −0.368230 | ||||||||
\(767\) | 4.96913e13 | 0.187199 | ||||||||
\(768\) | −9.45768e12 | + | 1.37624e13i | −0.0353980 | + | 0.0515095i | ||||
\(769\) | 2.19185e14 | 0.815041 | 0.407521 | − | 0.913196i | \(-0.366393\pi\) | ||||
0.407521 | + | 0.913196i | \(0.366393\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.99890e14 | − | 4.36386e14i | 1.10075 | − | 1.60176i | ||||
\(772\) | − | 1.59542e14i | − | 0.581821i | ||||||
\(773\) | −4.05042e14 | −1.46758 | −0.733792 | − | 0.679374i | \(-0.762251\pi\) | ||||
−0.733792 | + | 0.679374i | \(0.762251\pi\) | |||||||
\(774\) | −2.47870e14 | + | 9.51747e13i | −0.892315 | + | 0.342623i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.02426e14i | 0.364002i | ||||||||
\(777\) | −1.60348e14 | + | 2.33331e14i | −0.566185 | + | 0.823886i | ||||
\(778\) | 3.40665e14i | 1.19517i | ||||||||
\(779\) | 1.14440e14i | 0.398925i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.56775e13 | −0.122783 | ||||||||
\(782\) | −8.46599e13 | −0.289497 | ||||||||
\(783\) | 1.61778e13 | − | 6.74268e13i | 0.0549681 | − | 0.229099i | ||||
\(784\) | −6.73701e13 | −0.227450 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.27074e14 | − | 1.56048e14i | −0.756929 | − | 0.520171i | ||||
\(787\) | 4.98729e14i | 1.65193i | 0.563724 | + | 0.825963i | \(0.309368\pi\) | ||||
−0.563724 | + | 0.825963i | \(0.690632\pi\) | |||||||
\(788\) | 7.76674e13 | 0.255628 | ||||||||
\(789\) | 1.89845e14 | − | 2.76254e14i | 0.620890 | − | 0.903491i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.06958e14i | 0.991280i | ||||||||
\(792\) | −3.98782e13 | + | 1.53121e13i | −0.127970 | + | 0.0491369i | ||||
\(793\) | − | 9.03088e13i | − | 0.287981i | ||||||
\(794\) | 2.52678e14i | 0.800690i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.71861e13 | 0.178947 | ||||||||
\(797\) | 1.48672e14 | 0.462314 | 0.231157 | − | 0.972917i | \(-0.425749\pi\) | ||||
0.231157 | + | 0.972917i | \(0.425749\pi\) | |||||||
\(798\) | 8.07104e13 | + | 5.54652e13i | 0.249411 | + | 0.171398i | ||||
\(799\) | 4.13427e14 | 1.26959 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.31607e13 | − | 5.05331e12i | 0.0399131 | − | 0.0153255i | ||||
\(802\) | 2.61766e14i | 0.788934i | ||||||||
\(803\) | 1.36492e14 | 0.408817 | ||||||||
\(804\) | −5.35343e13 | − | 3.67894e13i | −0.159350 | − | 0.109507i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.61057e14i | 0.473482i | ||||||||
\(807\) | 2.36576e14 | + | 1.62578e14i | 0.691200 | + | 0.475001i | ||||
\(808\) | − | 1.94549e14i | − | 0.564901i | ||||||
\(809\) | 1.32296e14i | 0.381772i | 0.981612 | + | 0.190886i | \(0.0611361\pi\) | ||||
−0.981612 | + | 0.190886i | \(0.938864\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.75449e14 | −1.07016 | −0.535078 | − | 0.844803i | \(-0.679718\pi\) | ||||
−0.535078 | + | 0.844803i | \(0.679718\pi\) | |||||||
\(812\) | −5.74675e13 | −0.162795 | ||||||||
\(813\) | 1.95776e14 | − | 2.84884e14i | 0.551197 | − | 0.802076i | ||||
\(814\) | 7.08746e13 | 0.198321 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −9.61939e13 | + | 1.39977e14i | −0.265887 | + | 0.386906i | ||||
\(817\) | − | 1.52383e14i | − | 0.418625i | ||||||
\(818\) | −2.43044e14 | −0.663618 | ||||||||
\(819\) | −8.36547e13 | − | 2.17867e14i | −0.227023 | − | 0.591252i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 4.64480e12i | − | 0.0124524i | −0.999981 | − | 0.00622618i | \(-0.998018\pi\) | ||
0.999981 | − | 0.00622618i | \(-0.00198187\pi\) | |||||||
\(822\) | 8.55594e13 | − | 1.24502e14i | 0.227986 | − | 0.331755i | ||||
\(823\) | − | 6.38146e14i | − | 1.69013i | −0.534661 | − | 0.845067i | \(-0.679561\pi\) | ||
0.534661 | − | 0.845067i | \(-0.320439\pi\) | |||||||
\(824\) | 9.69528e13i | 0.255226i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.53476e14 | 0.399154 | ||||||||
\(827\) | 5.33624e14 | 1.37946 | 0.689728 | − | 0.724068i | \(-0.257730\pi\) | ||||
0.689728 | + | 0.724068i | \(0.257730\pi\) | |||||||
\(828\) | −1.52075e13 | − | 3.96058e13i | −0.0390756 | − | 0.101767i | ||||
\(829\) | 8.63626e13 | 0.220573 | 0.110287 | − | 0.993900i | \(-0.464823\pi\) | ||||
0.110287 | + | 0.993900i | \(0.464823\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.06135e14 | − | 7.29370e13i | −0.267825 | − | 0.184053i | ||||
\(832\) | 2.28386e13i | 0.0572865i | ||||||||
\(833\) | −6.85220e14 | −1.70846 | ||||||||
\(834\) | −1.96966e14 | + | 2.86616e14i | −0.488160 | + | 0.710347i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 2.45159e13i | − | 0.0600367i | ||||||
\(837\) | −5.83647e14 | − | 1.40035e14i | −1.42077 | − | 0.340886i | ||||
\(838\) | − | 1.99510e14i | − | 0.482774i | ||||||
\(839\) | 4.28770e14i | 1.03137i | 0.856778 | + | 0.515685i | \(0.172462\pi\) | ||||
−0.856778 | + | 0.515685i | \(0.827538\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.97355e14 | 0.944492 | ||||||||
\(842\) | 1.28918e14 | 0.304616 | ||||||||
\(843\) | 4.57496e14 | + | 3.14397e14i | 1.07461 | + | 0.738483i | ||||
\(844\) | 7.83697e13 | 0.182994 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.42639e13 | + | 1.93410e14i | 0.171367 | + | 0.446301i | ||||
\(847\) | − | 5.11874e14i | − | 1.17421i | ||||||
\(848\) | 1.10504e13 | 0.0252000 | ||||||||
\(849\) | 4.63171e14 | + | 3.18297e14i | 1.05003 | + | 0.721595i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.03905e13i | 0.157713i | ||||||||
\(852\) | −5.85864e13 | − | 4.02613e13i | −0.130497 | − | 0.0896789i | ||||
\(853\) | 8.99493e10i | 0.000199183i | 1.00000 | 9.95916e-5i | \(3.17010e-5\pi\) | |||||
−1.00000 | 9.95916e-5i | \(0.999968\pi\) | ||||||||
\(854\) | − | 2.78927e14i | − | 0.614046i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.66312e14 | −0.361872 | ||||||||
\(857\) | 1.45265e14 | 0.314238 | 0.157119 | − | 0.987580i | \(-0.449779\pi\) | ||||
0.157119 | + | 0.987580i | \(0.449779\pi\) | |||||||
\(858\) | −3.30887e13 | + | 4.81492e13i | −0.0711613 | + | 0.103551i | ||||
\(859\) | 3.53555e14 | 0.755947 | 0.377974 | − | 0.925816i | \(-0.376621\pi\) | ||||
0.377974 | + | 0.925816i | \(0.376621\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.77058e14 | − | 6.94192e14i | 1.00822 | − | 1.46711i | ||||
\(862\) | 4.08024e14i | 0.857333i | ||||||||
\(863\) | 5.16372e14 | 1.07872 | 0.539360 | − | 0.842075i | \(-0.318666\pi\) | ||||
0.539360 | + | 0.842075i | \(0.318666\pi\) | |||||||
\(864\) | −8.27637e13 | − | 1.98576e13i | −0.171898 | − | 0.0412437i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.66892e14i | 0.958576i | ||||||||
\(867\) | −7.00930e14 | + | 1.01996e15i | −1.43080 | + | 2.08204i | ||||
\(868\) | 4.97439e14i | 1.00958i | ||||||||
\(869\) | − | 1.22757e14i | − | 0.247713i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.88397e13 | −0.177221 | ||||||||
\(872\) | −5.47477e13 | −0.108588 | ||||||||
\(873\) | −4.87367e14 | + | 1.87135e14i | −0.961136 | + | 0.369048i | ||||
\(874\) | 2.43485e13 | 0.0477435 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.24135e14 | + | 1.54028e14i | 0.434499 | + | 0.298593i | ||||
\(877\) | 3.23487e13i | 0.0623532i | 0.999514 | + | 0.0311766i | \(0.00992543\pi\) | ||||
−0.999514 | + | 0.0311766i | \(0.990075\pi\) | |||||||
\(878\) | 4.41944e14 | 0.847022 | ||||||||
\(879\) | −1.45870e14 | + | 2.12264e14i | −0.277986 | + | 0.404512i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.45484e14i | − | 0.650950i | −0.945551 | − | 0.325475i | \(-0.894476\pi\) | ||
0.945551 | − | 0.325475i | \(-0.105524\pi\) | |||||||
\(882\) | −1.23086e14 | − | 3.20561e14i | −0.230604 | − | 0.600576i | ||||
\(883\) | 1.94069e14i | 0.361537i | 0.983526 | + | 0.180769i | \(0.0578585\pi\) | ||||
−0.983526 | + | 0.180769i | \(0.942141\pi\) | |||||||
\(884\) | 2.32291e14i | 0.430299i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.73096e14 | −1.23284 | ||||||||
\(887\) | −2.06383e14 | −0.375885 | −0.187943 | − | 0.982180i | \(-0.560182\pi\) | ||||
−0.187943 | + | 0.982180i | \(0.560182\pi\) | |||||||
\(888\) | 1.16384e14 | + | 7.99804e13i | 0.210779 | + | 0.144850i | ||||
\(889\) | −7.38171e14 | −1.32938 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.45716e14 | − | 1.61773e14i | −0.259489 | − | 0.288084i | ||||
\(892\) | 3.10149e14i | 0.549219i | ||||||||
\(893\) | −1.18903e14 | −0.209380 | ||||||||
\(894\) | −1.53384e14 | − | 1.05407e14i | −0.268592 | − | 0.184579i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.05390e13i | 0.122149i | ||||||||
\(897\) | −4.78204e13 | − | 3.28628e13i | −0.0823476 | − | 0.0565903i | ||||
\(898\) | 3.11139e14i | 0.532811i | ||||||||
\(899\) | 2.02140e14i | 0.344234i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.12394e14 | 0.189286 | ||||||||
\(902\) | −2.10862e14 | −0.353155 | ||||||||
\(903\) | −6.35227e14 | + | 9.24353e14i | −1.05801 | + | 1.53957i | ||||
\(904\) | 1.53109e14 | 0.253605 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.81129e14 | − | 5.54602e14i | 0.624354 | − | 0.908532i | ||||
\(907\) | − | 3.53646e14i | − | 0.576145i | −0.957609 | − | 0.288073i | \(-0.906986\pi\) | ||
0.957609 | − | 0.288073i | \(-0.0930144\pi\) | |||||||
\(908\) | −3.43341e14 | −0.556284 | ||||||||
\(909\) | 9.25705e14 | − | 3.55444e14i | 1.49160 | − | 0.572732i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.57044e14i | − | 0.728394i | −0.931322 | − | 0.364197i | \(-0.881344\pi\) | ||
0.931322 | − | 0.364197i | \(-0.118656\pi\) | |||||||
\(912\) | 2.76657e13 | − | 4.02578e13i | 0.0438497 | − | 0.0638081i | ||||
\(913\) | − | 1.36473e14i | − | 0.215126i | ||||||
\(914\) | − | 9.28232e12i | − | 0.0145521i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.80918e14 | −0.280547 | ||||||||
\(917\) | −1.16387e15 | −1.79497 | ||||||||
\(918\) | −8.41788e14 | − | 2.01971e14i | −1.29119 | − | 0.309796i | ||||
\(919\) | −4.85254e14 | −0.740273 | −0.370136 | − | 0.928977i | \(-0.620689\pi\) | ||||
−0.370136 | + | 0.928977i | \(0.620689\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.38027e14 | − | 9.48541e13i | −0.208289 | − | 0.143139i | ||||
\(922\) | − | 4.77244e12i | − | 0.00716285i | ||||||
\(923\) | −9.72237e13 | −0.145132 | ||||||||
\(924\) | −1.02198e14 | + | 1.48713e14i | −0.151733 | + | 0.220795i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 4.45166e14i | − | 0.653834i | ||||||
\(927\) | −4.61322e14 | + | 1.77134e14i | −0.673916 | + | 0.258764i | ||||
\(928\) | 2.86644e13i | 0.0416488i | ||||||||
\(929\) | 8.16207e14i | 1.17957i | 0.807562 | + | 0.589783i | \(0.200787\pi\) | ||||
−0.807562 | + | 0.589783i | \(0.799213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.97071e14 | 0.281757 | ||||||||
\(932\) | −5.75436e14 | −0.818309 | ||||||||
\(933\) | 3.91874e14 | + | 2.69301e14i | 0.554292 | + | 0.380916i | ||||
\(934\) | 2.75832e14 | 0.388071 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.08671e14 | + | 4.17264e13i | −0.151263 | + | 0.0580807i | ||||
\(937\) | − | 6.90133e14i | − | 0.955510i | −0.878493 | − | 0.477755i | \(-0.841451\pi\) | ||
0.878493 | − | 0.477755i | \(-0.158549\pi\) | |||||||
\(938\) | −2.74389e14 | −0.377879 | ||||||||
\(939\) | −4.98311e13 | − | 3.42445e13i | −0.0682609 | − | 0.0469098i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.26481e14i | − | 0.171426i | −0.996320 | − | 0.0857129i | \(-0.972683\pi\) | ||
0.996320 | − | 0.0857129i | \(-0.0273168\pi\) | |||||||
\(942\) | −7.20390e14 | − | 4.95061e14i | −0.971210 | − | 0.667428i | ||||
\(943\) | − | 2.09422e14i | − | 0.280843i | ||||||
\(944\) | − | 7.65528e13i | − | 0.102118i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.80773e14 | 0.370596 | ||||||||
\(947\) | −3.05743e14 | −0.401427 | −0.200713 | − | 0.979650i | \(-0.564326\pi\) | ||||
−0.200713 | + | 0.979650i | \(0.564326\pi\) | |||||||
\(948\) | 1.38529e14 | − | 2.01581e14i | 0.180925 | − | 0.263274i | ||||
\(949\) | 3.71950e14 | 0.483230 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.38144e14 | + | 9.28598e14i | −0.820382 | + | 1.19378i | ||||
\(952\) | 7.17450e14i | 0.917502i | ||||||||
\(953\) | 7.71039e14 | 0.980870 | 0.490435 | − | 0.871478i | \(-0.336838\pi\) | ||||
0.490435 | + | 0.871478i | \(0.336838\pi\) | |||||||
\(954\) | 2.01893e13 | + | 5.25803e13i | 0.0255493 | + | 0.0665398i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.35477e14i | 0.169658i | ||||||||
\(957\) | −4.15292e13 | + | 6.04315e13i | −0.0517362 | + | 0.0752841i | ||||
\(958\) | − | 1.13338e14i | − | 0.140458i | ||||||
\(959\) | − | 6.38134e14i | − | 0.786718i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.30098e14 | 1.13478 | ||||||||
\(962\) | 1.93138e14 | 0.234419 | ||||||||
\(963\) | −3.03855e14 | − | 7.91348e14i | −0.366889 | − | 0.955512i | ||||
\(964\) | 4.54025e14 | 0.545375 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.47698e14 | − | 1.01500e14i | −0.175585 | − | 0.120664i | ||||
\(967\) | 1.27364e15i | 1.50631i | 0.657845 | + | 0.753154i | \(0.271468\pi\) | ||||
−0.657845 | + | 0.753154i | \(0.728532\pi\) | |||||||
\(968\) | −2.55319e14 | −0.300405 | ||||||||
\(969\) | 2.81387e14 | − | 4.09461e14i | 0.329371 | − | 0.479285i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.71364e14i | 0.546085i | 0.962002 | + | 0.273043i | \(0.0880300\pi\) | ||||
−0.962002 | + | 0.273043i | \(0.911970\pi\) | |||||||
\(972\) | −5.67238e13 | − | 4.30087e14i | −0.0653784 | − | 0.495707i | ||||
\(973\) | 1.46905e15i | 1.68451i | ||||||||
\(974\) | 9.43563e14i | 1.07641i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.39127e14 | −0.157095 | ||||||||
\(977\) | 1.09733e15 | 1.23272 | 0.616360 | − | 0.787465i | \(-0.288607\pi\) | ||||
0.616360 | + | 0.787465i | \(0.288607\pi\) | |||||||
\(978\) | 4.17281e14 | + | 2.86761e14i | 0.466374 | + | 0.320498i | ||||
\(979\) | −1.49077e13 | −0.0165767 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.00025e14 | − | 2.60501e14i | −0.110094 | − | 0.286724i | ||||
\(982\) | − | 4.75946e13i | − | 0.0521195i | ||||||
\(983\) | −1.52240e15 | −1.65867 | −0.829336 | − | 0.558751i | \(-0.811281\pi\) | ||||
−0.829336 | + | 0.558751i | \(0.811281\pi\) | |||||||
\(984\) | −3.46258e14 | − | 2.37953e14i | −0.375340 | − | 0.257938i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.91545e14i | 0.312839i | ||||||||
\(987\) | 7.21264e14 | + | 4.95661e14i | 0.770031 | + | 0.529175i | ||||
\(988\) | − | 6.68075e13i | − | 0.0709644i | ||||||
\(989\) | 2.78856e14i | 0.294712i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.79461e14 | 0.397008 | 0.198504 | − | 0.980100i | \(-0.436392\pi\) | ||||
0.198504 | + | 0.980100i | \(0.436392\pi\) | |||||||
\(992\) | 2.48119e14 | 0.258286 | ||||||||
\(993\) | 1.94665e14 | − | 2.83267e14i | 0.201623 | − | 0.293393i | ||||
\(994\) | −3.00284e14 | −0.309457 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.54007e14 | − | 2.24104e14i | 0.157125 | − | 0.228641i | ||||
\(997\) | 3.25337e13i | 0.0330262i | 0.999864 | + | 0.0165131i | \(0.00525652\pi\) | ||||
−0.999864 | + | 0.0165131i | \(0.994743\pi\) | |||||||
\(998\) | 6.21082e14 | 0.627330 | ||||||||
\(999\) | −1.67929e14 | + | 6.99905e14i | −0.168771 | + | 0.703415i |
(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 | 150.11.b.a.149.2 | 8 | ||
3.2 | odd | 2 | inner | 150.11.b.a.149.8 | 8 | ||
5.2 | odd | 4 | 150.11.d.a.101.2 | 4 | |||
5.3 | odd | 4 | 6.11.b.a.5.3 | yes | 4 | ||
5.4 | even | 2 | inner | 150.11.b.a.149.7 | 8 | ||
15.2 | even | 4 | 150.11.d.a.101.4 | 4 | |||
15.8 | even | 4 | 6.11.b.a.5.1 | ✓ | 4 | ||
15.14 | odd | 2 | inner | 150.11.b.a.149.1 | 8 | ||
20.3 | even | 4 | 48.11.e.d.17.4 | 4 | |||
40.3 | even | 4 | 192.11.e.h.65.1 | 4 | |||
40.13 | odd | 4 | 192.11.e.g.65.4 | 4 | |||
45.13 | odd | 12 | 162.11.d.d.107.1 | 8 | |||
45.23 | even | 12 | 162.11.d.d.107.4 | 8 | |||
45.38 | even | 12 | 162.11.d.d.53.1 | 8 | |||
45.43 | odd | 12 | 162.11.d.d.53.4 | 8 | |||
60.23 | odd | 4 | 48.11.e.d.17.3 | 4 | |||
120.53 | even | 4 | 192.11.e.g.65.3 | 4 | |||
120.83 | odd | 4 | 192.11.e.h.65.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.11.b.a.5.1 | ✓ | 4 | 15.8 | even | 4 | ||
6.11.b.a.5.3 | yes | 4 | 5.3 | odd | 4 | ||
48.11.e.d.17.3 | 4 | 60.23 | odd | 4 | |||
48.11.e.d.17.4 | 4 | 20.3 | even | 4 | |||
150.11.b.a.149.1 | 8 | 15.14 | odd | 2 | inner | ||
150.11.b.a.149.2 | 8 | 1.1 | even | 1 | trivial | ||
150.11.b.a.149.7 | 8 | 5.4 | even | 2 | inner | ||
150.11.b.a.149.8 | 8 | 3.2 | odd | 2 | inner | ||
150.11.d.a.101.2 | 4 | 5.2 | odd | 4 | |||
150.11.d.a.101.4 | 4 | 15.2 | even | 4 | |||
162.11.d.d.53.1 | 8 | 45.38 | even | 12 | |||
162.11.d.d.53.4 | 8 | 45.43 | odd | 12 | |||
162.11.d.d.107.1 | 8 | 45.13 | odd | 12 | |||
162.11.d.d.107.4 | 8 | 45.23 | even | 12 | |||
192.11.e.g.65.3 | 4 | 120.53 | even | 4 | |||
192.11.e.g.65.4 | 4 | 40.13 | odd | 4 | |||
192.11.e.h.65.1 | 4 | 40.3 | even | 4 | |||
192.11.e.h.65.2 | 4 | 120.83 | odd | 4 |