Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,11,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.81214351604\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{85})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 37x^{2} + 38x + 531 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.3 | ||
Root | \(-4.10977 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.11.b.a.5.1 |
$q$-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 \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 22.6274i | 0.707107i | ||||||||
\(3\) | −200.269 | − | 137.627i | −0.824153 | − | 0.566368i | ||||
\(4\) | −512.000 | −0.500000 | ||||||||
\(5\) | − | 3630.47i | − | 1.16175i | −0.813992 | − | 0.580876i | \(-0.802710\pi\) | ||
0.813992 | − | 0.580876i | \(-0.197290\pi\) | |||||||
\(6\) | 3114.15 | − | 4531.57i | 0.400483 | − | 0.582764i | ||||
\(7\) | −23226.5 | −1.38196 | −0.690978 | − | 0.722876i | \(-0.742820\pi\) | ||||
−0.690978 | + | 0.722876i | \(0.742820\pi\) | |||||||
\(8\) | − | 11585.2i | − | 0.353553i | ||||||
\(9\) | 21166.4 | + | 55125.0i | 0.358455 | + | 0.933547i | ||||
\(10\) | 82148.2 | 0.821482 | ||||||||
\(11\) | 62442.7i | 0.387720i | 0.981029 | + | 0.193860i | \(0.0621007\pi\) | ||||
−0.981029 | + | 0.193860i | \(0.937899\pi\) | |||||||
\(12\) | 102538. | + | 70465.2i | 0.412076 | + | 0.283184i | ||||
\(13\) | −170161. | −0.458292 | −0.229146 | − | 0.973392i | \(-0.573593\pi\) | ||||
−0.229146 | + | 0.973392i | \(0.573593\pi\) | |||||||
\(14\) | − | 525556.i | − | 0.977190i | ||||||
\(15\) | −499653. | + | 727072.i | −0.657979 | + | 0.957460i | ||||
\(16\) | 262144. | 0.250000 | ||||||||
\(17\) | − | 2.66626e6i | − | 1.87784i | −0.344139 | − | 0.938919i | \(-0.611829\pi\) | ||
0.344139 | − | 0.938919i | \(-0.388171\pi\) | |||||||
\(18\) | −1.24734e6 | + | 478941.i | −0.660117 | + | 0.253466i | ||||
\(19\) | 766825. | 0.309691 | 0.154845 | − | 0.987939i | \(-0.450512\pi\) | ||||
0.154845 | + | 0.987939i | \(0.450512\pi\) | |||||||
\(20\) | 1.85880e6i | 0.580876i | ||||||||
\(21\) | 4.65156e6 | + | 3.19661e6i | 1.13894 | + | 0.782695i | ||||
\(22\) | −1.41292e6 | −0.274159 | ||||||||
\(23\) | 1.40327e6i | 0.218022i | 0.994041 | + | 0.109011i | \(0.0347684\pi\) | ||||
−0.994041 | + | 0.109011i | \(0.965232\pi\) | |||||||
\(24\) | −1.59445e6 | + | 2.32016e6i | −0.200241 | + | 0.291382i | ||||
\(25\) | −3.41471e6 | −0.349667 | ||||||||
\(26\) | − | 3.85029e6i | − | 0.324061i | ||||||
\(27\) | 3.34774e6 | − | 1.39529e7i | 0.233310 | − | 0.972402i | ||||
\(28\) | 1.18920e7 | 0.690978 | ||||||||
\(29\) | 4.83245e6i | 0.235601i | 0.993037 | + | 0.117801i | \(0.0375844\pi\) | ||||
−0.993037 | + | 0.117801i | \(0.962416\pi\) | |||||||
\(30\) | −1.64518e7 | − | 1.13058e7i | −0.677027 | − | 0.465261i | ||||
\(31\) | −4.18297e7 | −1.46109 | −0.730544 | − | 0.682865i | \(-0.760734\pi\) | ||||
−0.730544 | + | 0.682865i | \(0.760734\pi\) | |||||||
\(32\) | 5.93164e6i | 0.176777i | ||||||||
\(33\) | 8.59382e6 | − | 1.25053e7i | 0.219592 | − | 0.319540i | ||||
\(34\) | 6.03306e7 | 1.32783 | ||||||||
\(35\) | 8.43233e7i | 1.60549i | ||||||||
\(36\) | −1.08372e7 | − | 2.82240e7i | −0.179227 | − | 0.466774i | ||||
\(37\) | 5.01619e7 | 0.723378 | 0.361689 | − | 0.932299i | \(-0.382200\pi\) | ||||
0.361689 | + | 0.932299i | \(0.382200\pi\) | |||||||
\(38\) | 1.73513e7i | 0.218985i | ||||||||
\(39\) | 3.40779e7 | + | 2.34188e7i | 0.377702 | + | 0.259562i | ||||
\(40\) | −4.20599e7 | −0.410741 | ||||||||
\(41\) | − | 1.49239e8i | − | 1.28814i | −0.764967 | − | 0.644069i | \(-0.777245\pi\) | ||
0.764967 | − | 0.644069i | \(-0.222755\pi\) | |||||||
\(42\) | −7.23310e7 | + | 1.05253e8i | −0.553449 | + | 0.805354i | ||||
\(43\) | −1.98719e8 | −1.35175 | −0.675876 | − | 0.737015i | \(-0.736235\pi\) | ||||
−0.675876 | + | 0.737015i | \(0.736235\pi\) | |||||||
\(44\) | − | 3.19706e7i | − | 0.193860i | ||||||
\(45\) | 2.00130e8 | − | 7.68440e7i | 1.08455 | − | 0.416435i | ||||
\(46\) | −3.17523e7 | −0.154165 | ||||||||
\(47\) | − | 1.55059e8i | − | 0.676093i | −0.941129 | − | 0.338047i | \(-0.890234\pi\) | ||
0.941129 | − | 0.338047i | \(-0.109766\pi\) | |||||||
\(48\) | −5.24993e7 | − | 3.60782e7i | −0.206038 | − | 0.141592i | ||||
\(49\) | 2.56996e8 | 0.909802 | ||||||||
\(50\) | − | 7.72661e7i | − | 0.247252i | ||||||
\(51\) | −3.66951e8 | + | 5.33970e8i | −1.06355 | + | 1.54762i | ||||
\(52\) | 8.71222e7 | 0.229146 | ||||||||
\(53\) | 4.21541e7i | 0.100800i | 0.998729 | + | 0.0503999i | \(0.0160496\pi\) | ||||
−0.998729 | + | 0.0503999i | \(0.983950\pi\) | |||||||
\(54\) | 3.15718e8 | + | 7.57507e7i | 0.687592 | + | 0.164975i | ||||
\(55\) | 2.26696e8 | 0.450434 | ||||||||
\(56\) | 2.69085e8i | 0.488595i | ||||||||
\(57\) | −1.53571e8 | − | 1.05536e8i | −0.255233 | − | 0.175399i | ||||
\(58\) | −1.09346e8 | −0.166595 | ||||||||
\(59\) | 2.92026e8i | 0.408471i | 0.978922 | + | 0.204236i | \(0.0654708\pi\) | ||||
−0.978922 | + | 0.204236i | \(0.934529\pi\) | |||||||
\(60\) | 2.55822e8 | − | 3.72261e8i | 0.328989 | − | 0.478730i | ||||
\(61\) | −5.30727e8 | −0.628379 | −0.314190 | − | 0.949360i | \(-0.601733\pi\) | ||||
−0.314190 | + | 0.949360i | \(0.601733\pi\) | |||||||
\(62\) | − | 9.46499e8i | − | 1.03315i | ||||||
\(63\) | −4.91622e8 | − | 1.28036e9i | −0.495369 | − | 1.29012i | ||||
\(64\) | −1.34218e8 | −0.125000 | ||||||||
\(65\) | 6.17764e8i | 0.532421i | ||||||||
\(66\) | 2.82963e8 | + | 1.94456e8i | 0.225949 | + | 0.155275i | ||||
\(67\) | 5.22093e8 | 0.386700 | 0.193350 | − | 0.981130i | \(-0.438065\pi\) | ||||
0.193350 | + | 0.981130i | \(0.438065\pi\) | |||||||
\(68\) | 1.36513e9i | 0.938919i | ||||||||
\(69\) | 1.93128e8 | − | 2.81031e8i | 0.123481 | − | 0.179684i | ||||
\(70\) | −1.90802e9 | −1.13525 | ||||||||
\(71\) | 5.71364e8i | 0.316681i | 0.987385 | + | 0.158340i | \(0.0506143\pi\) | ||||
−0.987385 | + | 0.158340i | \(0.949386\pi\) | |||||||
\(72\) | 6.38636e8 | − | 2.45218e8i | 0.330059 | − | 0.126733i | ||||
\(73\) | 2.18588e9 | 1.05441 | 0.527207 | − | 0.849737i | \(-0.323239\pi\) | ||||
0.527207 | + | 0.849737i | \(0.323239\pi\) | |||||||
\(74\) | 1.13503e9i | 0.511506i | ||||||||
\(75\) | 6.83861e8 | + | 4.69958e8i | 0.288179 | + | 0.198040i | ||||
\(76\) | −3.92615e8 | −0.154845 | ||||||||
\(77\) | − | 1.45033e9i | − | 0.535812i | ||||||
\(78\) | −5.29906e8 | + | 7.71095e8i | −0.183538 | + | 0.267076i | ||||
\(79\) | 1.96592e9 | 0.638897 | 0.319449 | − | 0.947604i | \(-0.396502\pi\) | ||||
0.319449 | + | 0.947604i | \(0.396502\pi\) | |||||||
\(80\) | − | 9.51707e8i | − | 0.290438i | ||||||
\(81\) | −2.59075e9 | + | 2.33360e9i | −0.743020 | + | 0.669269i | ||||
\(82\) | 3.37689e9 | 0.910851 | ||||||||
\(83\) | − | 2.18558e9i | − | 0.554850i | −0.960747 | − | 0.277425i | \(-0.910519\pi\) | ||
0.960747 | − | 0.277425i | \(-0.0894810\pi\) | |||||||
\(84\) | −2.38160e9 | − | 1.63666e9i | −0.569471 | − | 0.391348i | ||||
\(85\) | −9.67979e9 | −2.18158 | ||||||||
\(86\) | − | 4.49650e9i | − | 0.955833i | ||||||
\(87\) | 6.65078e8 | − | 9.67791e8i | 0.133437 | − | 0.194171i | ||||
\(88\) | 7.23413e8 | 0.137080 | ||||||||
\(89\) | − | 2.38742e8i | − | 0.0427542i | −0.999771 | − | 0.0213771i | \(-0.993195\pi\) | ||
0.999771 | − | 0.0213771i | \(-0.00680506\pi\) | |||||||
\(90\) | 1.73878e9 | + | 4.52842e9i | 0.294464 | + | 0.766892i | ||||
\(91\) | 3.95224e9 | 0.633339 | ||||||||
\(92\) | − | 7.18473e8i | − | 0.109011i | ||||||
\(93\) | 8.37720e9 | + | 5.75692e9i | 1.20416 | + | 0.827514i | ||||
\(94\) | 3.50858e9 | 0.478070 | ||||||||
\(95\) | − | 2.78394e9i | − | 0.359784i | ||||||
\(96\) | 8.16356e8 | − | 1.18792e9i | 0.100121 | − | 0.145691i | ||||
\(97\) | −8.84112e9 | −1.02955 | −0.514776 | − | 0.857324i | \(-0.672125\pi\) | ||||
−0.514776 | + | 0.857324i | \(0.672125\pi\) | |||||||
\(98\) | 5.81517e9i | 0.643327i | ||||||||
\(99\) | −3.44215e9 | + | 1.32169e9i | −0.361955 | + | 0.138980i | ||||
\(100\) | 1.74833e9 | 0.174833 | ||||||||
\(101\) | 1.67928e10i | 1.59778i | 0.601477 | + | 0.798890i | \(0.294579\pi\) | ||||
−0.601477 | + | 0.798890i | \(0.705421\pi\) | |||||||
\(102\) | −1.20824e10 | − | 8.30314e9i | −1.09434 | − | 0.752041i | ||||
\(103\) | 8.36865e9 | 0.721887 | 0.360944 | − | 0.932588i | \(-0.382455\pi\) | ||||
0.360944 | + | 0.932588i | \(0.382455\pi\) | |||||||
\(104\) | 1.97135e9i | 0.162031i | ||||||||
\(105\) | 1.16052e10 | − | 1.68873e10i | 0.909297 | − | 1.32317i | ||||
\(106\) | −9.53837e8 | −0.0712763 | ||||||||
\(107\) | − | 1.43555e10i | − | 1.02353i | −0.859126 | − | 0.511764i | \(-0.828992\pi\) | ||
0.859126 | − | 0.511764i | \(-0.171008\pi\) | |||||||
\(108\) | −1.71404e9 | + | 7.14389e9i | −0.116655 | + | 0.486201i | ||||
\(109\) | −4.72564e9 | −0.307134 | −0.153567 | − | 0.988138i | \(-0.549076\pi\) | ||||
−0.153567 | + | 0.988138i | \(0.549076\pi\) | |||||||
\(110\) | 5.12956e9i | 0.318505i | ||||||||
\(111\) | −1.00459e10 | − | 6.90365e9i | −0.596174 | − | 0.409698i | ||||
\(112\) | −6.08870e9 | −0.345489 | ||||||||
\(113\) | − | 1.32158e10i | − | 0.717303i | −0.933472 | − | 0.358651i | \(-0.883237\pi\) | ||
0.933472 | − | 0.358651i | \(-0.116763\pi\) | |||||||
\(114\) | 2.38801e9 | − | 3.47492e9i | 0.124026 | − | 0.180477i | ||||
\(115\) | 5.09452e9 | 0.253288 | ||||||||
\(116\) | − | 2.47422e9i | − | 0.117801i | ||||||
\(117\) | −3.60169e9 | − | 9.38011e9i | −0.164277 | − | 0.427837i | ||||
\(118\) | −6.60779e9 | −0.288833 | ||||||||
\(119\) | 6.19280e10i | 2.59509i | ||||||||
\(120\) | 8.42330e9 | + | 5.78859e9i | 0.338513 | + | 0.232631i | ||||
\(121\) | 2.20383e10 | 0.849673 | ||||||||
\(122\) | − | 1.20090e10i | − | 0.444331i | ||||||
\(123\) | −2.05393e10 | + | 2.98879e10i | −0.729560 | + | 1.06162i | ||||
\(124\) | 2.14168e10 | 0.730544 | ||||||||
\(125\) | − | 2.30568e10i | − | 0.755526i | ||||||
\(126\) | 2.89713e10 | − | 1.11241e10i | 0.912253 | − | 0.350279i | ||||
\(127\) | −3.17814e10 | −0.961953 | −0.480976 | − | 0.876733i | \(-0.659718\pi\) | ||||
−0.480976 | + | 0.876733i | \(0.659718\pi\) | |||||||
\(128\) | − | 3.03700e9i | − | 0.0883883i | ||||||
\(129\) | 3.97973e10 | + | 2.73492e10i | 1.11405 | + | 0.765589i | ||||
\(130\) | −1.39784e10 | −0.376479 | ||||||||
\(131\) | − | 5.01094e10i | − | 1.29886i | −0.760421 | − | 0.649430i | \(-0.775007\pi\) | ||
0.760421 | − | 0.649430i | \(-0.224993\pi\) | |||||||
\(132\) | −4.40004e9 | + | 6.40273e9i | −0.109796 | + | 0.159770i | ||||
\(133\) | −1.78107e10 | −0.427979 | ||||||||
\(134\) | 1.18136e10i | 0.273438i | ||||||||
\(135\) | −5.06557e10 | − | 1.21539e10i | −1.12969 | − | 0.271048i | ||||
\(136\) | −3.08893e10 | −0.663916 | ||||||||
\(137\) | − | 2.74744e10i | − | 0.569279i | −0.958635 | − | 0.284639i | \(-0.908126\pi\) | ||
0.958635 | − | 0.284639i | \(-0.0918738\pi\) | |||||||
\(138\) | 6.35900e9 | + | 4.36999e9i | 0.127056 | + | 0.0873142i | ||||
\(139\) | 6.32488e10 | 1.21893 | 0.609464 | − | 0.792814i | \(-0.291385\pi\) | ||||
0.609464 | + | 0.792814i | \(0.291385\pi\) | |||||||
\(140\) | − | 4.31735e10i | − | 0.802745i | ||||||
\(141\) | −2.13403e10 | + | 3.10534e10i | −0.382917 | + | 0.557204i | ||||
\(142\) | −1.29285e10 | −0.223927 | ||||||||
\(143\) | − | 1.06253e10i | − | 0.177689i | ||||||
\(144\) | 5.54864e9 | + | 1.44507e10i | 0.0896137 | + | 0.233387i | ||||
\(145\) | 1.75441e10 | 0.273710 | ||||||||
\(146\) | 4.94607e10i | 0.745583i | ||||||||
\(147\) | −5.14684e10 | − | 3.53697e10i | −0.749815 | − | 0.515282i | ||||
\(148\) | −2.56829e10 | −0.361689 | ||||||||
\(149\) | 3.38479e10i | 0.460893i | 0.973085 | + | 0.230446i | \(0.0740186\pi\) | ||||
−0.973085 | + | 0.230446i | \(0.925981\pi\) | |||||||
\(150\) | −1.06339e10 | + | 1.54740e10i | −0.140035 | + | 0.203773i | ||||
\(151\) | 1.22386e11 | 1.55901 | 0.779503 | − | 0.626399i | \(-0.215472\pi\) | ||||
0.779503 | + | 0.626399i | \(0.215472\pi\) | |||||||
\(152\) | − | 8.88385e9i | − | 0.109492i | ||||||
\(153\) | 1.46978e11 | − | 5.64351e10i | 1.75305 | − | 0.673120i | ||||
\(154\) | 3.28171e10 | 0.378876 | ||||||||
\(155\) | 1.51862e11i | 1.69742i | ||||||||
\(156\) | −1.74479e10 | − | 1.19904e10i | −0.188851 | − | 0.129781i | ||||
\(157\) | −1.58971e11 | −1.66656 | −0.833279 | − | 0.552853i | \(-0.813539\pi\) | ||||
−0.833279 | + | 0.552853i | \(0.813539\pi\) | |||||||
\(158\) | 4.44838e10i | 0.451769i | ||||||||
\(159\) | 5.80155e9 | − | 8.44215e9i | 0.0570898 | − | 0.0830745i | ||||
\(160\) | 2.15347e10 | 0.205371 | ||||||||
\(161\) | − | 3.25930e10i | − | 0.301297i | ||||||
\(162\) | −5.28033e10 | − | 5.86220e10i | −0.473245 | − | 0.525395i | ||||
\(163\) | −9.20831e10 | −0.800280 | −0.400140 | − | 0.916454i | \(-0.631038\pi\) | ||||
−0.400140 | + | 0.916454i | \(0.631038\pi\) | |||||||
\(164\) | 7.64102e10i | 0.644069i | ||||||||
\(165\) | −4.54003e10 | − | 3.11996e10i | −0.371226 | − | 0.255111i | ||||
\(166\) | 4.94540e10 | 0.392338 | ||||||||
\(167\) | − | 2.12416e11i | − | 1.63533i | −0.575697 | − | 0.817663i | \(-0.695269\pi\) | ||
0.575697 | − | 0.817663i | \(-0.304731\pi\) | |||||||
\(168\) | 3.70334e10 | − | 5.38894e10i | 0.276725 | − | 0.402677i | ||||
\(169\) | −1.08904e11 | −0.789968 | ||||||||
\(170\) | − | 2.19029e11i | − | 1.54261i | ||||||
\(171\) | 1.62309e10 | + | 4.22713e10i | 0.111010 | + | 0.289111i | ||||
\(172\) | 1.01744e11 | 0.675876 | ||||||||
\(173\) | 3.04132e11i | 1.96260i | 0.192482 | + | 0.981300i | \(0.438346\pi\) | ||||
−0.192482 | + | 0.981300i | \(0.561654\pi\) | |||||||
\(174\) | 2.18986e10 | + | 1.50490e10i | 0.137300 | + | 0.0943542i | ||||
\(175\) | 7.93119e10 | 0.483224 | ||||||||
\(176\) | 1.63690e10i | 0.0969300i | ||||||||
\(177\) | 4.01908e10 | − | 5.84837e10i | 0.231345 | − | 0.336642i | ||||
\(178\) | 5.40212e9 | 0.0302318 | ||||||||
\(179\) | 7.07114e9i | 0.0384791i | 0.999815 | + | 0.0192395i | \(0.00612451\pi\) | ||||
−0.999815 | + | 0.0192395i | \(0.993875\pi\) | |||||||
\(180\) | −1.02467e11 | + | 3.93442e10i | −0.542275 | + | 0.208218i | ||||
\(181\) | −1.27309e11 | −0.655337 | −0.327669 | − | 0.944793i | \(-0.606263\pi\) | ||||
−0.327669 | + | 0.944793i | \(0.606263\pi\) | |||||||
\(182\) | 8.94290e10i | 0.447838i | ||||||||
\(183\) | 1.06288e11 | + | 7.30425e10i | 0.517880 | + | 0.355894i | ||||
\(184\) | 1.62572e10 | 0.0770825 | ||||||||
\(185\) | − | 1.82111e11i | − | 0.840386i | ||||||
\(186\) | −1.30264e11 | + | 1.89554e11i | −0.585141 | + | 0.851470i | ||||
\(187\) | 1.66488e11 | 0.728075 | ||||||||
\(188\) | 7.93900e10i | 0.338047i | ||||||||
\(189\) | −7.77563e10 | + | 3.24078e11i | −0.322424 | + | 1.34382i | ||||
\(190\) | 6.29934e10 | 0.254406 | ||||||||
\(191\) | − | 2.06460e11i | − | 0.812209i | −0.913827 | − | 0.406105i | \(-0.866887\pi\) | ||
0.913827 | − | 0.406105i | \(-0.133113\pi\) | |||||||
\(192\) | 2.68797e10 | + | 1.84720e10i | 0.103019 | + | 0.0707960i | ||||
\(193\) | 3.11606e11 | 1.16364 | 0.581821 | − | 0.813317i | \(-0.302340\pi\) | ||||
0.581821 | + | 0.813317i | \(0.302340\pi\) | |||||||
\(194\) | − | 2.00052e11i | − | 0.728004i | ||||||
\(195\) | 8.50212e10 | − | 1.23719e11i | 0.301546 | − | 0.438796i | ||||
\(196\) | −1.31582e11 | −0.454901 | ||||||||
\(197\) | − | 1.51694e11i | − | 0.511255i | −0.966775 | − | 0.255628i | \(-0.917718\pi\) | ||
0.966775 | − | 0.255628i | \(-0.0822821\pi\) | |||||||
\(198\) | −2.99063e10 | − | 7.78870e10i | −0.0982737 | − | 0.255941i | ||||
\(199\) | −1.11692e11 | −0.357895 | −0.178947 | − | 0.983859i | \(-0.557269\pi\) | ||||
−0.178947 | + | 0.983859i | \(0.557269\pi\) | |||||||
\(200\) | 3.95603e10i | 0.123626i | ||||||||
\(201\) | −1.04559e11 | − | 7.18543e10i | −0.318700 | − | 0.219014i | ||||
\(202\) | −3.79978e11 | −1.12980 | ||||||||
\(203\) | − | 1.12241e11i | − | 0.325591i | ||||||
\(204\) | 1.87879e11 | − | 2.73392e11i | 0.531773 | − | 0.773812i | ||||
\(205\) | −5.41807e11 | −1.49650 | ||||||||
\(206\) | 1.89361e11i | 0.510451i | ||||||||
\(207\) | −7.73551e10 | + | 2.97021e10i | −0.203534 | + | 0.0781512i | ||||
\(208\) | −4.46066e10 | −0.114573 | ||||||||
\(209\) | 4.78826e10i | 0.120073i | ||||||||
\(210\) | 3.82117e11 | + | 2.62596e11i | 0.935621 | + | 0.642970i | ||||
\(211\) | 1.53066e11 | 0.365987 | 0.182994 | − | 0.983114i | \(-0.441421\pi\) | ||||
0.182994 | + | 0.983114i | \(0.441421\pi\) | |||||||
\(212\) | − | 2.15829e10i | − | 0.0503999i | ||||||
\(213\) | 7.86354e10 | − | 1.14427e11i | 0.179358 | − | 0.260993i | ||||
\(214\) | 3.24828e11 | 0.723744 | ||||||||
\(215\) | 7.21444e11i | 1.57040i | ||||||||
\(216\) | −1.61648e11 | − | 3.87843e10i | −0.343796 | − | 0.0824874i | ||||
\(217\) | 9.71560e11 | 2.01916 | ||||||||
\(218\) | − | 1.06929e11i | − | 0.217177i | ||||||
\(219\) | −4.37763e11 | − | 3.00836e11i | −0.868998 | − | 0.597186i | ||||
\(220\) | −1.16069e11 | −0.225217 | ||||||||
\(221\) | 4.53693e11i | 0.860598i | ||||||||
\(222\) | 1.56212e11 | − | 2.27312e11i | 0.289700 | − | 0.421559i | ||||
\(223\) | −6.05759e11 | −1.09844 | −0.549219 | − | 0.835678i | \(-0.685075\pi\) | ||||
−0.549219 | + | 0.835678i | \(0.685075\pi\) | |||||||
\(224\) | − | 1.37771e11i | − | 0.244298i | ||||||
\(225\) | −7.22772e10 | − | 1.88236e11i | −0.125340 | − | 0.326430i | ||||
\(226\) | 2.99040e11 | 0.507210 | ||||||||
\(227\) | 6.70588e11i | 1.11257i | 0.830992 | + | 0.556284i | \(0.187773\pi\) | ||||
−0.830992 | + | 0.556284i | \(0.812227\pi\) | |||||||
\(228\) | 7.86286e10 | + | 5.40345e10i | 0.127616 | + | 0.0876995i | ||||
\(229\) | 3.53356e11 | 0.561094 | 0.280547 | − | 0.959840i | \(-0.409484\pi\) | ||||
0.280547 | + | 0.959840i | \(0.409484\pi\) | |||||||
\(230\) | 1.15276e11i | 0.179102i | ||||||||
\(231\) | −1.99605e11 | + | 2.90456e11i | −0.303467 | + | 0.441591i | ||||
\(232\) | 5.59851e10 | 0.0832976 | ||||||||
\(233\) | − | 1.12390e12i | − | 1.63662i | −0.574779 | − | 0.818309i | \(-0.694912\pi\) | ||
0.574779 | − | 0.818309i | \(-0.305088\pi\) | |||||||
\(234\) | 2.12248e11 | − | 8.14969e10i | 0.302527 | − | 0.116161i | ||||
\(235\) | −5.62936e11 | −0.785452 | ||||||||
\(236\) | − | 1.49517e11i | − | 0.204236i | ||||||
\(237\) | −3.93714e11 | − | 2.70565e11i | −0.526549 | − | 0.361851i | ||||
\(238\) | −1.40127e12 | −1.83500 | ||||||||
\(239\) | − | 2.64603e11i | − | 0.339317i | −0.985503 | − | 0.169658i | \(-0.945734\pi\) | ||
0.985503 | − | 0.169658i | \(-0.0542665\pi\) | |||||||
\(240\) | −1.30981e11 | + | 1.90597e11i | −0.164495 | + | 0.239365i | ||||
\(241\) | 8.86768e11 | 1.09075 | 0.545375 | − | 0.838192i | \(-0.316387\pi\) | ||||
0.545375 | + | 0.838192i | \(0.316387\pi\) | |||||||
\(242\) | 4.98671e11i | 0.600810i | ||||||||
\(243\) | 8.40014e11 | − | 1.10789e11i | 0.991414 | − | 0.130757i | ||||
\(244\) | 2.71732e11 | 0.314190 | ||||||||
\(245\) | − | 9.33019e11i | − | 1.05696i | ||||||
\(246\) | −6.76286e11 | − | 4.64752e11i | −0.750680 | − | 0.515877i | ||||
\(247\) | −1.30483e11 | −0.141929 | ||||||||
\(248\) | 4.84607e11i | 0.516573i | ||||||||
\(249\) | −3.00795e11 | + | 4.37704e11i | −0.314249 | + | 0.457281i | ||||
\(250\) | 5.21716e11 | 0.534237 | ||||||||
\(251\) | − | 8.59494e11i | − | 0.862729i | −0.902178 | − | 0.431364i | \(-0.858032\pi\) | ||
0.902178 | − | 0.431364i | \(-0.141968\pi\) | |||||||
\(252\) | 2.51710e11 | + | 6.55546e11i | 0.247684 | + | 0.645060i | ||||
\(253\) | −8.76237e10 | −0.0845316 | ||||||||
\(254\) | − | 7.19130e11i | − | 0.680203i | ||||||
\(255\) | 1.93856e12 | + | 1.33220e12i | 1.79796 | + | 1.23558i | ||||
\(256\) | 6.87195e10 | 0.0625000 | ||||||||
\(257\) | 2.17900e12i | 1.94353i | 0.235954 | + | 0.971764i | \(0.424179\pi\) | ||||
−0.235954 | + | 0.971764i | \(0.575821\pi\) | |||||||
\(258\) | −6.18841e11 | + | 9.00510e11i | −0.541353 | + | 0.787753i | ||||
\(259\) | −1.16509e12 | −0.999677 | ||||||||
\(260\) | − | 3.16295e11i | − | 0.266211i | ||||||
\(261\) | −2.66389e11 | + | 1.02286e11i | −0.219945 | + | 0.0844524i | ||||
\(262\) | 1.13385e12 | 0.918433 | ||||||||
\(263\) | − | 1.37942e12i | − | 1.09627i | −0.836391 | − | 0.548134i | \(-0.815339\pi\) | ||
0.836391 | − | 0.548134i | \(-0.184661\pi\) | |||||||
\(264\) | −1.44877e11 | − | 9.95615e10i | −0.112975 | − | 0.0776375i | ||||
\(265\) | 1.53039e11 | 0.117104 | ||||||||
\(266\) | − | 4.03010e11i | − | 0.302627i | ||||||
\(267\) | −3.28574e10 | + | 4.78126e10i | −0.0242146 | + | 0.0352360i | ||||
\(268\) | −2.67312e11 | −0.193350 | ||||||||
\(269\) | 1.18129e12i | 0.838680i | 0.907829 | + | 0.419340i | \(0.137738\pi\) | ||||
−0.907829 | + | 0.419340i | \(0.862262\pi\) | |||||||
\(270\) | 2.75011e11 | − | 1.14621e12i | 0.191660 | − | 0.798812i | ||||
\(271\) | −1.42251e12 | −0.973213 | −0.486606 | − | 0.873621i | \(-0.661765\pi\) | ||||
−0.486606 | + | 0.873621i | \(0.661765\pi\) | |||||||
\(272\) | − | 6.98944e11i | − | 0.469459i | ||||||
\(273\) | −7.91511e11 | − | 5.43937e11i | −0.521968 | − | 0.358703i | ||||
\(274\) | 6.21674e11 | 0.402541 | ||||||||
\(275\) | − | 2.13224e11i | − | 0.135573i | ||||||
\(276\) | −9.88815e10 | + | 1.43888e11i | −0.0617404 | + | 0.0898418i | ||||
\(277\) | 5.29960e11 | 0.324971 | 0.162485 | − | 0.986711i | \(-0.448049\pi\) | ||||
0.162485 | + | 0.986711i | \(0.448049\pi\) | |||||||
\(278\) | 1.43116e12i | 0.861913i | ||||||||
\(279\) | −8.85385e11 | − | 2.30587e12i | −0.523734 | − | 1.36400i | ||||
\(280\) | 9.76905e11 | 0.567626 | ||||||||
\(281\) | − | 2.28441e12i | − | 1.30389i | −0.758265 | − | 0.651946i | \(-0.773953\pi\) | ||
0.758265 | − | 0.651946i | \(-0.226047\pi\) | |||||||
\(282\) | −7.02659e11 | − | 4.82876e11i | −0.394003 | − | 0.270764i | ||||
\(283\) | 2.31274e12 | 1.27408 | 0.637038 | − | 0.770833i | \(-0.280160\pi\) | ||||
0.637038 | + | 0.770833i | \(0.280160\pi\) | |||||||
\(284\) | − | 2.92539e11i | − | 0.158340i | ||||||
\(285\) | −3.83146e11 | + | 5.57537e11i | −0.203770 | + | 0.296517i | ||||
\(286\) | 2.40423e11 | 0.125645 | ||||||||
\(287\) | 3.46630e12i | 1.78015i | ||||||||
\(288\) | −3.26982e11 | + | 1.25551e11i | −0.165029 | + | 0.0633665i | ||||
\(289\) | −5.09295e12 | −2.52627 | ||||||||
\(290\) | 3.96978e11i | 0.193542i | ||||||||
\(291\) | 1.77060e12 | + | 1.21678e12i | 0.848509 | + | 0.583106i | ||||
\(292\) | −1.11917e12 | −0.527207 | ||||||||
\(293\) | 1.05989e12i | 0.490822i | 0.969419 | + | 0.245411i | \(0.0789229\pi\) | ||||
−0.969419 | + | 0.245411i | \(0.921077\pi\) | |||||||
\(294\) | 8.00326e11 | − | 1.16460e12i | 0.364360 | − | 0.530199i | ||||
\(295\) | 1.06019e12 | 0.474542 | ||||||||
\(296\) | − | 5.81138e11i | − | 0.255753i | ||||||
\(297\) | 8.71257e11 | + | 2.09042e11i | 0.377020 | + | 0.0904588i | ||||
\(298\) | −7.65890e11 | −0.325900 | ||||||||
\(299\) | − | 2.38781e11i | − | 0.0999179i | ||||||
\(300\) | −3.50137e11 | − | 2.40618e11i | −0.144089 | − | 0.0990200i | ||||
\(301\) | 4.61555e12 | 1.86806 | ||||||||
\(302\) | 2.76928e12i | 1.10238i | ||||||||
\(303\) | 2.31115e12 | − | 3.36308e12i | 0.904931 | − | 1.31681i | ||||
\(304\) | 2.01019e11 | 0.0774227 | ||||||||
\(305\) | 1.92679e12i | 0.730020i | ||||||||
\(306\) | 1.27698e12 | + | 3.32573e12i | 0.475968 | + | 1.23959i | ||||
\(307\) | 6.89209e11 | 0.252731 | 0.126366 | − | 0.991984i | \(-0.459669\pi\) | ||||
0.126366 | + | 0.991984i | \(0.459669\pi\) | |||||||
\(308\) | 7.42567e11i | 0.267906i | ||||||||
\(309\) | −1.67598e12 | − | 1.15176e12i | −0.594945 | − | 0.408854i | ||||
\(310\) | −3.43624e12 | −1.20026 | ||||||||
\(311\) | − | 1.95674e12i | − | 0.672559i | −0.941762 | − | 0.336280i | \(-0.890831\pi\) | ||
0.941762 | − | 0.336280i | \(-0.109169\pi\) | |||||||
\(312\) | 2.71312e11 | − | 3.94801e11i | 0.0917690 | − | 0.133538i | ||||
\(313\) | −2.48821e11 | −0.0828256 | −0.0414128 | − | 0.999142i | \(-0.513186\pi\) | ||||
−0.0414128 | + | 0.999142i | \(0.513186\pi\) | |||||||
\(314\) | − | 3.59711e12i | − | 1.17843i | ||||||
\(315\) | −4.64832e12 | + | 1.78482e12i | −1.49880 | + | 0.575495i | ||||
\(316\) | −1.00655e12 | −0.319449 | ||||||||
\(317\) | − | 4.63675e12i | − | 1.44850i | −0.689539 | − | 0.724249i | \(-0.742187\pi\) | ||
0.689539 | − | 0.724249i | \(-0.257813\pi\) | |||||||
\(318\) | 1.91024e11 | + | 1.31274e11i | 0.0587425 | + | 0.0403686i | ||||
\(319\) | −3.01751e11 | −0.0913473 | ||||||||
\(320\) | 4.87274e11i | 0.145219i | ||||||||
\(321\) | −1.97571e12 | + | 2.87497e12i | −0.579694 | + | 0.843544i | ||||
\(322\) | 7.37496e11 | 0.213049 | ||||||||
\(323\) | − | 2.04456e12i | − | 0.581549i | ||||||
\(324\) | 1.32646e12 | − | 1.19480e12i | 0.371510 | − | 0.334634i | ||||
\(325\) | 5.81050e11 | 0.160249 | ||||||||
\(326\) | − | 2.08360e12i | − | 0.565883i | ||||||
\(327\) | 9.46400e11 | + | 6.50378e11i | 0.253125 | + | 0.173951i | ||||
\(328\) | −1.72897e12 | −0.455426 | ||||||||
\(329\) | 3.60147e12i | 0.934331i | ||||||||
\(330\) | 7.05967e11 | − | 1.02729e12i | 0.180391 | − | 0.262497i | ||||
\(331\) | −1.41443e12 | −0.355994 | −0.177997 | − | 0.984031i | \(-0.556962\pi\) | ||||
−0.177997 | + | 0.984031i | \(0.556962\pi\) | |||||||
\(332\) | 1.11902e12i | 0.277425i | ||||||||
\(333\) | 1.06175e12 | + | 2.76518e12i | 0.259298 | + | 0.675308i | ||||
\(334\) | 4.80642e12 | 1.15635 | ||||||||
\(335\) | − | 1.89545e12i | − | 0.449249i | ||||||
\(336\) | 1.21938e12 | + | 8.37971e11i | 0.284736 | + | 0.195674i | ||||
\(337\) | 8.67755e11 | 0.199640 | 0.0998201 | − | 0.995006i | \(-0.468173\pi\) | ||||
0.0998201 | + | 0.995006i | \(0.468173\pi\) | |||||||
\(338\) | − | 2.46421e12i | − | 0.558592i | ||||||
\(339\) | −1.81886e12 | + | 2.64672e12i | −0.406257 | + | 0.591167i | ||||
\(340\) | 4.95605e12 | 1.09079 | ||||||||
\(341\) | − | 2.61196e12i | − | 0.566493i | ||||||
\(342\) | −9.56490e11 | + | 3.67264e11i | −0.204432 | + | 0.0784961i | ||||
\(343\) | 5.91785e11 | 0.124650 | ||||||||
\(344\) | 2.30221e12i | 0.477917i | ||||||||
\(345\) | −1.02028e12 | − | 7.01146e11i | −0.208748 | − | 0.143454i | ||||
\(346\) | −6.88173e12 | −1.38777 | ||||||||
\(347\) | 5.20712e12i | 1.03502i | 0.855676 | + | 0.517512i | \(0.173142\pi\) | ||||
−0.855676 | + | 0.517512i | \(0.826858\pi\) | |||||||
\(348\) | −3.40520e11 | + | 4.95509e11i | −0.0667185 | + | 0.0970857i | ||||
\(349\) | 1.11953e12 | 0.216226 | 0.108113 | − | 0.994139i | \(-0.465519\pi\) | ||||
0.108113 | + | 0.994139i | \(0.465519\pi\) | |||||||
\(350\) | 1.79462e12i | 0.341691i | ||||||||
\(351\) | −5.69653e11 | + | 2.37424e12i | −0.106924 | + | 0.445644i | ||||
\(352\) | −3.70388e11 | −0.0685398 | ||||||||
\(353\) | 3.73952e12i | 0.682248i | 0.940018 | + | 0.341124i | \(0.110808\pi\) | ||||
−0.940018 | + | 0.341124i | \(0.889192\pi\) | |||||||
\(354\) | 1.32334e12 | + | 9.09413e11i | 0.238042 | + | 0.163586i | ||||
\(355\) | 2.07432e12 | 0.367904 | ||||||||
\(356\) | 1.22236e11i | 0.0213771i | ||||||||
\(357\) | 8.52299e12 | − | 1.24023e13i | 1.46977 | − | 2.13875i | ||||
\(358\) | −1.60002e11 | −0.0272088 | ||||||||
\(359\) | 3.54489e12i | 0.594471i | 0.954804 | + | 0.297235i | \(0.0960646\pi\) | ||||
−0.954804 | + | 0.297235i | \(0.903935\pi\) | |||||||
\(360\) | −8.90257e11 | − | 2.31855e12i | −0.147232 | − | 0.383446i | ||||
\(361\) | −5.54305e12 | −0.904092 | ||||||||
\(362\) | − | 2.88066e12i | − | 0.463393i | ||||||
\(363\) | −4.41360e12 | − | 3.03308e12i | −0.700260 | − | 0.481228i | ||||
\(364\) | −2.02355e12 | −0.316670 | ||||||||
\(365\) | − | 7.93577e12i | − | 1.22497i | ||||||
\(366\) | −1.65276e12 | + | 2.40503e12i | −0.251655 | + | 0.366197i | ||||
\(367\) | −1.01161e13 | −1.51944 | −0.759722 | − | 0.650248i | \(-0.774665\pi\) | ||||
−0.759722 | + | 0.650248i | \(0.774665\pi\) | |||||||
\(368\) | 3.67858e11i | 0.0545056i | ||||||||
\(369\) | 8.22679e12 | − | 3.15885e12i | 1.20254 | − | 0.461739i | ||||
\(370\) | 4.12071e12 | 0.594242 | ||||||||
\(371\) | − | 9.79093e11i | − | 0.139301i | ||||||
\(372\) | −4.28913e12 | − | 2.94754e12i | −0.602080 | − | 0.413757i | ||||
\(373\) | 3.81055e12 | 0.527769 | 0.263885 | − | 0.964554i | \(-0.414996\pi\) | ||||
0.263885 | + | 0.964554i | \(0.414996\pi\) | |||||||
\(374\) | 3.76720e12i | 0.514827i | ||||||||
\(375\) | −3.17325e12 | + | 4.61757e12i | −0.427906 | + | 0.622669i | ||||
\(376\) | −1.79639e12 | −0.239035 | ||||||||
\(377\) | − | 8.22293e11i | − | 0.107974i | ||||||
\(378\) | −7.33304e12 | − | 1.75943e12i | −0.950222 | − | 0.227988i | ||||
\(379\) | 1.11052e13 | 1.42014 | 0.710069 | − | 0.704132i | \(-0.248664\pi\) | ||||
0.710069 | + | 0.704132i | \(0.248664\pi\) | |||||||
\(380\) | 1.42538e12i | 0.179892i | ||||||||
\(381\) | 6.36482e12 | + | 4.37399e12i | 0.792796 | + | 0.544819i | ||||
\(382\) | 4.67165e12 | 0.574319 | ||||||||
\(383\) | 4.29169e12i | 0.520756i | 0.965507 | + | 0.260378i | \(0.0838472\pi\) | ||||
−0.965507 | + | 0.260378i | \(0.916153\pi\) | |||||||
\(384\) | −4.17974e11 | + | 6.08217e11i | −0.0500603 | + | 0.0728455i | ||||
\(385\) | −5.26537e12 | −0.622480 | ||||||||
\(386\) | 7.05084e12i | 0.822820i | ||||||||
\(387\) | −4.20617e12 | − | 1.09544e13i | −0.484542 | − | 1.26192i | ||||
\(388\) | 4.52665e12 | 0.514776 | ||||||||
\(389\) | 1.50554e13i | 1.69023i | 0.534588 | + | 0.845113i | \(0.320467\pi\) | ||||
−0.534588 | + | 0.845113i | \(0.679533\pi\) | |||||||
\(390\) | 2.79944e12 | + | 1.92381e12i | 0.310276 | + | 0.213225i | ||||
\(391\) | 3.74148e12 | 0.409411 | ||||||||
\(392\) | − | 2.97736e12i | − | 0.321663i | ||||||
\(393\) | −6.89642e12 | + | 1.00354e13i | −0.735633 | + | 1.07046i | ||||
\(394\) | 3.43245e12 | 0.361512 | ||||||||
\(395\) | − | 7.13723e12i | − | 0.742240i | ||||||
\(396\) | 1.76238e12 | − | 6.76703e11i | 0.180977 | − | 0.0694900i | ||||
\(397\) | −1.11669e13 | −1.13235 | −0.566174 | − | 0.824286i | \(-0.691577\pi\) | ||||
−0.566174 | + | 0.824286i | \(0.691577\pi\) | |||||||
\(398\) | − | 2.52729e12i | − | 0.253070i | ||||||
\(399\) | 3.56693e12 | + | 2.45124e12i | 0.352720 | + | 0.242394i | ||||
\(400\) | −8.95146e11 | −0.0874166 | ||||||||
\(401\) | − | 1.15685e13i | − | 1.11572i | −0.829935 | − | 0.557861i | \(-0.811622\pi\) | ||
0.829935 | − | 0.557861i | \(-0.188378\pi\) | |||||||
\(402\) | 1.62588e12 | − | 2.36590e12i | 0.154867 | − | 0.225355i | ||||
\(403\) | 7.11777e12 | 0.669605 | ||||||||
\(404\) | − | 8.59793e12i | − | 0.798890i | ||||||
\(405\) | 8.47206e12 | + | 9.40565e12i | 0.777524 | + | 0.863205i | ||||
\(406\) | 2.53973e12 | 0.230227 | ||||||||
\(407\) | 3.13224e12i | 0.280468i | ||||||||
\(408\) | 6.18616e12 | + | 4.25121e12i | 0.547168 | + | 0.376021i | ||||
\(409\) | −1.07411e13 | −0.938498 | −0.469249 | − | 0.883066i | \(-0.655475\pi\) | ||||
−0.469249 | + | 0.883066i | \(0.655475\pi\) | |||||||
\(410\) | − | 1.22597e13i | − | 1.05818i | ||||||
\(411\) | −3.78123e12 | + | 5.50227e12i | −0.322421 | + | 0.469172i | ||||
\(412\) | −4.28475e12 | −0.360944 | ||||||||
\(413\) | − | 6.78275e12i | − | 0.564489i | ||||||
\(414\) | −6.72082e11 | − | 1.75035e12i | −0.0552612 | − | 0.143920i | ||||
\(415\) | −7.93468e12 | −0.644598 | ||||||||
\(416\) | − | 1.00933e12i | − | 0.0810153i | ||||||
\(417\) | −1.26668e13 | − | 8.70477e12i | −1.00458 | − | 0.690362i | ||||
\(418\) | −1.08346e12 | −0.0849047 | ||||||||
\(419\) | − | 8.81717e12i | − | 0.682746i | −0.939928 | − | 0.341373i | \(-0.889108\pi\) | ||
0.939928 | − | 0.341373i | \(-0.110892\pi\) | |||||||
\(420\) | −5.94186e12 | + | 8.64632e12i | −0.454649 | + | 0.661584i | ||||
\(421\) | −5.69741e12 | −0.430792 | −0.215396 | − | 0.976527i | \(-0.569104\pi\) | ||||
−0.215396 | + | 0.976527i | \(0.569104\pi\) | |||||||
\(422\) | 3.46348e12i | 0.258792i | ||||||||
\(423\) | 8.54761e12 | − | 3.28203e12i | 0.631165 | − | 0.242349i | ||||
\(424\) | 4.88365e11 | 0.0356381 | ||||||||
\(425\) | 9.10451e12i | 0.656617i | ||||||||
\(426\) | 2.58918e12 | + | 1.77932e12i | 0.184550 | + | 0.126825i | ||||
\(427\) | 1.23269e13 | 0.868392 | ||||||||
\(428\) | 7.35003e12i | 0.511764i | ||||||||
\(429\) | −1.46233e12 | + | 2.12792e12i | −0.100637 | + | 0.146443i | ||||
\(430\) | −1.63244e13 | −1.11044 | ||||||||
\(431\) | − | 1.80323e13i | − | 1.21245i | −0.795293 | − | 0.606226i | \(-0.792683\pi\) | ||
0.795293 | − | 0.606226i | \(-0.207317\pi\) | |||||||
\(432\) | 8.77590e11 | − | 3.65767e12i | 0.0583274 | − | 0.243101i | ||||
\(433\) | 2.06339e13 | 1.35563 | 0.677816 | − | 0.735232i | \(-0.262927\pi\) | ||||
0.677816 | + | 0.735232i | \(0.262927\pi\) | |||||||
\(434\) | 2.19839e13i | 1.42776i | ||||||||
\(435\) | −3.51354e12 | − | 2.41455e12i | −0.225579 | − | 0.155021i | ||||
\(436\) | 2.41953e12 | 0.153567 | ||||||||
\(437\) | 1.07606e12i | 0.0675195i | ||||||||
\(438\) | 6.80715e12 | − | 9.90545e12i | 0.422275 | − | 0.614474i | ||||
\(439\) | 1.95313e13 | 1.19787 | 0.598935 | − | 0.800798i | \(-0.295591\pi\) | ||||
0.598935 | + | 0.800798i | \(0.295591\pi\) | |||||||
\(440\) | − | 2.62633e12i | − | 0.159253i | ||||||
\(441\) | 5.43969e12 | + | 1.41669e13i | 0.326123 | + | 0.849343i | ||||
\(442\) | −1.02659e13 | −0.608535 | ||||||||
\(443\) | 2.97469e13i | 1.74351i | 0.489946 | + | 0.871753i | \(0.337016\pi\) | ||||
−0.489946 | + | 0.871753i | \(0.662984\pi\) | |||||||
\(444\) | 5.14349e12 | + | 3.53467e12i | 0.298087 | + | 0.204849i | ||||
\(445\) | −8.66747e11 | −0.0496698 | ||||||||
\(446\) | − | 1.37068e13i | − | 0.776713i | ||||||
\(447\) | 4.65839e12 | − | 6.77868e12i | 0.261035 | − | 0.379846i | ||||
\(448\) | 3.11741e12 | 0.172744 | ||||||||
\(449\) | 1.37505e13i | 0.753509i | 0.926313 | + | 0.376754i | \(0.122960\pi\) | ||||
−0.926313 | + | 0.376754i | \(0.877040\pi\) | |||||||
\(450\) | 4.25930e12 | − | 1.63545e12i | 0.230821 | − | 0.0886285i | ||||
\(451\) | 9.31887e12 | 0.499437 | ||||||||
\(452\) | 6.76651e12i | 0.358651i | ||||||||
\(453\) | −2.45102e13 | − | 1.68437e13i | −1.28486 | − | 0.882971i | ||||
\(454\) | −1.51737e13 | −0.786704 | ||||||||
\(455\) | − | 1.43485e13i | − | 0.735783i | ||||||
\(456\) | −1.22266e12 | + | 1.77916e12i | −0.0620129 | + | 0.0902383i | ||||
\(457\) | 4.10224e11 | 0.0205798 | 0.0102899 | − | 0.999947i | \(-0.496725\pi\) | ||||
0.0102899 | + | 0.999947i | \(0.496725\pi\) | |||||||
\(458\) | 7.99554e12i | 0.396753i | ||||||||
\(459\) | −3.72021e13 | − | 8.92594e12i | −1.82601 | − | 0.438118i | ||||
\(460\) | −2.60840e12 | −0.126644 | ||||||||
\(461\) | 2.10914e11i | 0.0101298i | 0.999987 | + | 0.00506490i | \(0.00161221\pi\) | ||||
−0.999987 | + | 0.00506490i | \(0.998388\pi\) | |||||||
\(462\) | −6.57226e12 | − | 4.51654e12i | −0.312252 | − | 0.214583i | ||||
\(463\) | −1.96738e13 | −0.924660 | −0.462330 | − | 0.886708i | \(-0.652987\pi\) | ||||
−0.462330 | + | 0.886708i | \(0.652987\pi\) | |||||||
\(464\) | 1.26680e12i | 0.0589003i | ||||||||
\(465\) | 2.09003e13 | − | 3.04132e13i | 0.961365 | − | 1.39893i | ||||
\(466\) | 2.54309e13 | 1.15726 | ||||||||
\(467\) | 1.21902e13i | 0.548815i | 0.961614 | + | 0.274407i | \(0.0884817\pi\) | ||||
−0.961614 | + | 0.274407i | \(0.911518\pi\) | |||||||
\(468\) | 1.84406e12 | + | 4.80261e12i | 0.0821385 | + | 0.213919i | ||||
\(469\) | −1.21264e13 | −0.534402 | ||||||||
\(470\) | − | 1.27378e13i | − | 0.555399i | ||||||
\(471\) | 3.18370e13 | + | 2.18788e13i | 1.37350 | + | 0.943885i | ||||
\(472\) | 3.38319e12 | 0.144416 | ||||||||
\(473\) | − | 1.24085e13i | − | 0.524101i | ||||||
\(474\) | 6.12218e12 | − | 8.90872e12i | 0.255867 | − | 0.372326i | ||||
\(475\) | −2.61849e12 | −0.108289 | ||||||||
\(476\) | − | 3.17071e13i | − | 1.29754i | ||||||
\(477\) | −2.32374e12 | + | 8.92250e11i | −0.0941014 | + | 0.0361322i | ||||
\(478\) | 5.98729e12 | 0.239933 | ||||||||
\(479\) | − | 5.00886e12i | − | 0.198637i | −0.995056 | − | 0.0993187i | \(-0.968334\pi\) | ||
0.995056 | − | 0.0993187i | \(-0.0316663\pi\) | |||||||
\(480\) | −4.31273e12 | − | 2.96376e12i | −0.169257 | − | 0.116315i | ||||
\(481\) | −8.53558e12 | −0.331518 | ||||||||
\(482\) | 2.00653e13i | 0.771276i | ||||||||
\(483\) | −4.48569e12 | + | 6.52737e12i | −0.170645 | + | 0.248315i | ||||
\(484\) | −1.12836e13 | −0.424837 | ||||||||
\(485\) | 3.20975e13i | 1.19608i | ||||||||
\(486\) | 2.50686e12 | + | 1.90074e13i | 0.0924590 | + | 0.701036i | ||||
\(487\) | −4.17000e13 | −1.52227 | −0.761134 | − | 0.648595i | \(-0.775357\pi\) | ||||
−0.761134 | + | 0.648595i | \(0.775357\pi\) | |||||||
\(488\) | 6.14859e12i | 0.222166i | ||||||||
\(489\) | 1.84414e13 | + | 1.26732e13i | 0.659553 | + | 0.453253i | ||||
\(490\) | 2.11118e13 | 0.747386 | ||||||||
\(491\) | 2.10340e12i | 0.0737081i | 0.999321 | + | 0.0368540i | \(0.0117337\pi\) | ||||
−0.999321 | + | 0.0368540i | \(0.988266\pi\) | |||||||
\(492\) | 1.05161e13 | − | 1.53026e13i | 0.364780 | − | 0.530811i | ||||
\(493\) | 1.28846e13 | 0.442421 | ||||||||
\(494\) | − | 2.95250e12i | − | 0.100359i | ||||||
\(495\) | 4.79835e12 | + | 1.24966e13i | 0.161460 | + | 0.420501i | ||||
\(496\) | −1.09654e13 | −0.365272 | ||||||||
\(497\) | − | 1.32708e13i | − | 0.437639i | ||||||
\(498\) | −9.90410e12 | − | 6.80622e12i | −0.323347 | − | 0.222208i | ||||
\(499\) | 2.74482e13 | 0.887179 | 0.443589 | − | 0.896230i | \(-0.353705\pi\) | ||||
0.443589 | + | 0.896230i | \(0.353705\pi\) | |||||||
\(500\) | 1.18051e13i | 0.377763i | ||||||||
\(501\) | −2.92342e13 | + | 4.25403e13i | −0.926197 | + | 1.34776i | ||||
\(502\) | 1.94481e13 | 0.610041 | ||||||||
\(503\) | − | 2.26985e13i | − | 0.704949i | −0.935822 | − | 0.352474i | \(-0.885340\pi\) | ||
0.935822 | − | 0.352474i | \(-0.114660\pi\) | |||||||
\(504\) | −1.48333e13 | + | 5.69556e12i | −0.456127 | + | 0.175139i | ||||
\(505\) | 6.09659e13 | 1.85622 | ||||||||
\(506\) | − | 1.98270e12i | − | 0.0597729i | ||||||
\(507\) | 2.18101e13 | + | 1.49882e13i | 0.651055 | + | 0.447413i | ||||
\(508\) | 1.62721e13 | 0.480976 | ||||||||
\(509\) | − | 4.21460e13i | − | 1.23358i | −0.787127 | − | 0.616791i | \(-0.788433\pi\) | ||
0.787127 | − | 0.616791i | \(-0.211567\pi\) | |||||||
\(510\) | −3.01443e13 | + | 4.38647e13i | −0.873685 | + | 1.27135i | ||||
\(511\) | −5.07703e13 | −1.45715 | ||||||||
\(512\) | 1.55494e12i | 0.0441942i | ||||||||
\(513\) | 2.56713e12 | − | 1.06994e13i | 0.0722539 | − | 0.301144i | ||||
\(514\) | −4.93051e13 | −1.37428 | ||||||||
\(515\) | − | 3.03822e13i | − | 0.838653i | ||||||
\(516\) | −2.03762e13 | − | 1.40028e13i | −0.557025 | − | 0.382795i | ||||
\(517\) | 9.68227e12 | 0.262135 | ||||||||
\(518\) | − | 2.63629e13i | − | 0.706878i | ||||||
\(519\) | 4.18569e13 | − | 6.09083e13i | 1.11155 | − | 1.61748i | ||||
\(520\) | 7.15694e12 | 0.188239 | ||||||||
\(521\) | − | 6.54420e13i | − | 1.70478i | −0.522907 | − | 0.852390i | \(-0.675152\pi\) | ||
0.522907 | − | 0.852390i | \(-0.324848\pi\) | |||||||
\(522\) | −2.31446e12 | − | 6.02770e12i | −0.0597169 | − | 0.155525i | ||||
\(523\) | −6.14531e13 | −1.57049 | −0.785245 | − | 0.619185i | \(-0.787463\pi\) | ||||
−0.785245 | + | 0.619185i | \(0.787463\pi\) | |||||||
\(524\) | 2.56560e13i | 0.649430i | ||||||||
\(525\) | −1.58837e13 | − | 1.09155e13i | −0.398250 | − | 0.273682i | ||||
\(526\) | 3.12126e13 | 0.775178 | ||||||||
\(527\) | 1.11529e14i | 2.74369i | ||||||||
\(528\) | 2.25282e12 | − | 3.27820e12i | 0.0548980 | − | 0.0798851i | ||||
\(529\) | 3.94574e13 | 0.952466 | ||||||||
\(530\) | 3.46288e12i | 0.0828053i | ||||||||
\(531\) | −1.60979e13 | + | 6.18114e12i | −0.381327 | + | 0.146418i | ||||
\(532\) | 9.11907e12 | 0.213990 | ||||||||
\(533\) | 2.53946e13i | 0.590343i | ||||||||
\(534\) | −1.08188e12 | − | 7.43479e11i | −0.0249156 | − | 0.0171223i | ||||
\(535\) | −5.21173e13 | −1.18909 | ||||||||
\(536\) | − | 6.04857e12i | − | 0.136719i | ||||||
\(537\) | 9.73183e11 | − | 1.41613e12i | 0.0217933 | − | 0.0317126i | ||||
\(538\) | −2.67296e13 | −0.593036 | ||||||||
\(539\) | 1.60475e13i | 0.352748i | ||||||||
\(540\) | 2.59357e13 | + | 6.22278e12i | 0.564845 | + | 0.135524i | ||||
\(541\) | 1.50207e13 | 0.324118 | 0.162059 | − | 0.986781i | \(-0.448187\pi\) | ||||
0.162059 | + | 0.986781i | \(0.448187\pi\) | |||||||
\(542\) | − | 3.21877e13i | − | 0.688166i | ||||||
\(543\) | 2.54960e13 | + | 1.75211e13i | 0.540098 | + | 0.371162i | ||||
\(544\) | 1.58153e13 | 0.331958 | ||||||||
\(545\) | 1.71563e13i | 0.356814i | ||||||||
\(546\) | 1.23079e13 | − | 1.79099e13i | 0.253641 | − | 0.369087i | ||||
\(547\) | 7.15097e13 | 1.46025 | 0.730127 | − | 0.683312i | \(-0.239461\pi\) | ||||
0.730127 | + | 0.683312i | \(0.239461\pi\) | |||||||
\(548\) | 1.40669e13i | 0.284639i | ||||||||
\(549\) | −1.12336e13 | − | 2.92563e13i | −0.225245 | − | 0.586621i | ||||
\(550\) | 4.82470e12 | 0.0958644 | ||||||||
\(551\) | 3.70565e12i | 0.0729636i | ||||||||
\(552\) | −3.25581e12 | − | 2.23743e12i | −0.0635278 | − | 0.0436571i | ||||
\(553\) | −4.56616e13 | −0.882928 | ||||||||
\(554\) | 1.19916e13i | 0.229789i | ||||||||
\(555\) | −2.50635e13 | + | 3.64713e13i | −0.475967 | + | 0.692606i | ||||
\(556\) | −3.23834e13 | −0.609464 | ||||||||
\(557\) | 7.34107e13i | 1.36925i | 0.728895 | + | 0.684626i | \(0.240034\pi\) | ||||
−0.728895 | + | 0.684626i | \(0.759966\pi\) | |||||||
\(558\) | 5.21758e13 | − | 2.00340e13i | 0.964490 | − | 0.370336i | ||||
\(559\) | 3.38141e13 | 0.619497 | ||||||||
\(560\) | 2.21048e13i | 0.401372i | ||||||||
\(561\) | −3.33425e13 | − | 2.29134e13i | −0.600045 | − | 0.412358i | ||||
\(562\) | 5.16902e13 | 0.921991 | ||||||||
\(563\) | − | 4.77347e13i | − | 0.843902i | −0.906619 | − | 0.421951i | \(-0.861345\pi\) | ||
0.906619 | − | 0.421951i | \(-0.138655\pi\) | |||||||
\(564\) | 1.09262e13 | − | 1.58994e13i | 0.191459 | − | 0.278602i | ||||
\(565\) | −4.79797e13 | −0.833327 | ||||||||
\(566\) | 5.23314e13i | 0.900907i | ||||||||
\(567\) | 6.01742e13 | − | 5.42013e13i | 1.02682 | − | 0.924900i | ||||
\(568\) | 6.61939e12 | 0.111963 | ||||||||
\(569\) | − | 1.90951e13i | − | 0.320156i | −0.987104 | − | 0.160078i | \(-0.948825\pi\) | ||
0.987104 | − | 0.160078i | \(-0.0511745\pi\) | |||||||
\(570\) | −1.26156e13 | − | 8.66961e12i | −0.209669 | − | 0.144087i | ||||
\(571\) | −2.09448e13 | −0.345060 | −0.172530 | − | 0.985004i | \(-0.555194\pi\) | ||||
−0.172530 | + | 0.985004i | \(0.555194\pi\) | |||||||
\(572\) | 5.44014e12i | 0.0888444i | ||||||||
\(573\) | −2.84145e13 | + | 4.13475e13i | −0.460009 | + | 0.669385i | ||||
\(574\) | −7.84334e13 | −1.25876 | ||||||||
\(575\) | − | 4.79175e12i | − | 0.0762351i | ||||||
\(576\) | −2.84091e12 | − | 7.39876e12i | −0.0448069 | − | 0.116693i | ||||
\(577\) | 3.56688e13 | 0.557711 | 0.278855 | − | 0.960333i | \(-0.410045\pi\) | ||||
0.278855 | + | 0.960333i | \(0.410045\pi\) | |||||||
\(578\) | − | 1.15240e14i | − | 1.78635i | ||||||
\(579\) | −6.24051e13 | − | 4.28856e13i | −0.959019 | − | 0.659050i | ||||
\(580\) | −8.98258e12 | −0.136855 | ||||||||
\(581\) | 5.07634e13i | 0.766778i | ||||||||
\(582\) | −2.75326e13 | + | 4.00642e13i | −0.412318 | + | 0.599986i | ||||
\(583\) | −2.63221e12 | −0.0390821 | ||||||||
\(584\) | − | 2.53239e13i | − | 0.372792i | ||||||
\(585\) | −3.40542e13 | + | 1.30758e13i | −0.497040 | + | 0.190849i | ||||
\(586\) | −2.39826e13 | −0.347064 | ||||||||
\(587\) | − | 1.29418e14i | − | 1.85697i | −0.371375 | − | 0.928483i | \(-0.621114\pi\) | ||
0.371375 | − | 0.928483i | \(-0.378886\pi\) | |||||||
\(588\) | 2.63518e13 | + | 1.81093e13i | 0.374908 | + | 0.257641i | ||||
\(589\) | −3.20761e13 | −0.452486 | ||||||||
\(590\) | 2.39894e13i | 0.335552i | ||||||||
\(591\) | −2.08773e13 | + | 3.03797e13i | −0.289559 | + | 0.421352i | ||||
\(592\) | 1.31496e13 | 0.180845 | ||||||||
\(593\) | 3.96596e13i | 0.540848i | 0.962741 | + | 0.270424i | \(0.0871639\pi\) | ||||
−0.962741 | + | 0.270424i | \(0.912836\pi\) | |||||||
\(594\) | −4.73007e12 | + | 1.97143e13i | −0.0639640 | + | 0.266593i | ||||
\(595\) | 2.24828e14 | 3.01485 | ||||||||
\(596\) | − | 1.73301e13i | − | 0.230446i | ||||||
\(597\) | 2.23684e13 | + | 1.53718e13i | 0.294960 | + | 0.202700i | ||||
\(598\) | 5.40299e12 | 0.0706526 | ||||||||
\(599\) | − | 4.57555e13i | − | 0.593347i | −0.954979 | − | 0.296674i | \(-0.904123\pi\) | ||
0.954979 | − | 0.296674i | \(-0.0958774\pi\) | |||||||
\(600\) | 5.44458e12 | − | 7.92270e12i | 0.0700177 | − | 0.101887i | ||||
\(601\) | 1.06033e14 | 1.35229 | 0.676143 | − | 0.736770i | \(-0.263650\pi\) | ||||
0.676143 | + | 0.736770i | \(0.263650\pi\) | |||||||
\(602\) | 1.04438e14i | 1.32092i | ||||||||
\(603\) | 1.10508e13 | + | 2.87804e13i | 0.138614 | + | 0.361003i | ||||
\(604\) | −6.26617e13 | −0.779503 | ||||||||
\(605\) | − | 8.00096e13i | − | 0.987109i | ||||||
\(606\) | 7.60979e13 | + | 5.22954e13i | 0.931128 | + | 0.639883i | ||||
\(607\) | −9.55067e13 | −1.15902 | −0.579509 | − | 0.814966i | \(-0.696756\pi\) | ||||
−0.579509 | + | 0.814966i | \(0.696756\pi\) | |||||||
\(608\) | 4.54853e12i | 0.0547461i | ||||||||
\(609\) | −1.54475e13 | + | 2.24784e13i | −0.184404 | + | 0.268336i | ||||
\(610\) | −4.35983e13 | −0.516202 | ||||||||
\(611\) | 2.63849e13i | 0.309848i | ||||||||
\(612\) | −7.52526e13 | + | 2.88948e13i | −0.876525 | + | 0.336560i | ||||
\(613\) | −5.18411e13 | −0.598924 | −0.299462 | − | 0.954108i | \(-0.596807\pi\) | ||||
−0.299462 | + | 0.954108i | \(0.596807\pi\) | |||||||
\(614\) | 1.55950e13i | 0.178708i | ||||||||
\(615\) | 1.08507e14 | + | 7.45675e13i | 1.23334 | + | 0.847567i | ||||
\(616\) | −1.68024e13 | −0.189438 | ||||||||
\(617\) | 8.05443e13i | 0.900760i | 0.892837 | + | 0.450380i | \(0.148711\pi\) | ||||
−0.892837 | + | 0.450380i | \(0.851289\pi\) | |||||||
\(618\) | 2.60612e13 | − | 3.79231e13i | 0.289103 | − | 0.420690i | ||||
\(619\) | −5.14946e13 | −0.566642 | −0.283321 | − | 0.959025i | \(-0.591436\pi\) | ||||
−0.283321 | + | 0.959025i | \(0.591436\pi\) | |||||||
\(620\) | − | 7.77532e13i | − | 0.848711i | ||||||
\(621\) | 1.95797e13 | + | 4.69777e12i | 0.212005 | + | 0.0508667i | ||||
\(622\) | 4.42759e13 | 0.475571 | ||||||||
\(623\) | 5.54515e12i | 0.0590844i | ||||||||
\(624\) | 8.93332e12 | + | 6.13909e12i | 0.0944256 | + | 0.0648905i | ||||
\(625\) | −1.17054e14 | −1.22740 | ||||||||
\(626\) | − | 5.63017e12i | − | 0.0585665i | ||||||
\(627\) | 6.58996e12 | − | 9.58941e12i | 0.0680057 | − | 0.0989587i | ||||
\(628\) | 8.13933e13 | 0.833279 | ||||||||
\(629\) | − | 1.33745e14i | − | 1.35839i | ||||||
\(630\) | −4.03859e13 | − | 1.05180e14i | −0.406937 | − | 1.05981i | ||||
\(631\) | −1.02922e13 | −0.102887 | −0.0514435 | − | 0.998676i | \(-0.516382\pi\) | ||||
−0.0514435 | + | 0.998676i | \(0.516382\pi\) | |||||||
\(632\) | − | 2.27757e13i | − | 0.225884i | ||||||
\(633\) | −3.06543e13 | − | 2.10660e13i | −0.301629 | − | 0.207283i | ||||
\(634\) | 1.04918e14 | 1.02424 | ||||||||
\(635\) | 1.15381e14i | 1.11755i | ||||||||
\(636\) | −2.97040e12 | + | 4.32238e12i | −0.0285449 | + | 0.0415372i | ||||
\(637\) | −4.37307e13 | −0.416955 | ||||||||
\(638\) | − | 6.82785e12i | − | 0.0645923i | ||||||
\(639\) | −3.14965e13 | + | 1.20937e13i | −0.295636 | + | 0.113516i | ||||
\(640\) | −1.10257e13 | −0.102685 | ||||||||
\(641\) | − | 4.62451e13i | − | 0.427342i | −0.976906 | − | 0.213671i | \(-0.931458\pi\) | ||
0.976906 | − | 0.213671i | \(-0.0685420\pi\) | |||||||
\(642\) | −6.50531e13 | − | 4.47053e13i | −0.596476 | − | 0.409906i | ||||
\(643\) | 2.73102e13 | 0.248468 | 0.124234 | − | 0.992253i | \(-0.460353\pi\) | ||||
0.124234 | + | 0.992253i | \(0.460353\pi\) | |||||||
\(644\) | 1.66876e13i | 0.150649i | ||||||||
\(645\) | 9.92905e13 | − | 1.44483e14i | 0.889424 | − | 1.29425i | ||||
\(646\) | 4.62630e13 | 0.411217 | ||||||||
\(647\) | 1.34984e13i | 0.119059i | 0.998227 | + | 0.0595293i | \(0.0189600\pi\) | ||||
−0.998227 | + | 0.0595293i | \(0.981040\pi\) | |||||||
\(648\) | 2.70353e13 | + | 3.00145e13i | 0.236622 | + | 0.262697i | ||||
\(649\) | −1.82349e13 | −0.158372 | ||||||||
\(650\) | 1.31476e13i | 0.113313i | ||||||||
\(651\) | −1.94573e14 | − | 1.33713e14i | −1.66410 | − | 1.14359i | ||||
\(652\) | 4.71466e13 | 0.400140 | ||||||||
\(653\) | 8.41840e13i | 0.709029i | 0.935051 | + | 0.354514i | \(0.115354\pi\) | ||||
−0.935051 | + | 0.354514i | \(0.884646\pi\) | |||||||
\(654\) | −1.47164e13 | + | 2.14146e13i | −0.123002 | + | 0.178987i | ||||
\(655\) | −1.81921e14 | −1.50895 | ||||||||
\(656\) | − | 3.91220e13i | − | 0.322034i | ||||||
\(657\) | 4.62671e13 | + | 1.20496e14i | 0.377960 | + | 0.984345i | ||||
\(658\) | −8.14920e13 | −0.660672 | ||||||||
\(659\) | 1.65464e14i | 1.33130i | 0.746264 | + | 0.665650i | \(0.231846\pi\) | ||||
−0.746264 | + | 0.665650i | \(0.768154\pi\) | |||||||
\(660\) | 2.32449e13 | + | 1.59742e13i | 0.185613 | + | 0.127556i | ||||
\(661\) | 2.01681e14 | 1.59830 | 0.799148 | − | 0.601135i | \(-0.205284\pi\) | ||||
0.799148 | + | 0.601135i | \(0.205284\pi\) | |||||||
\(662\) | − | 3.20050e13i | − | 0.251726i | ||||||
\(663\) | 6.24405e13 | − | 9.08606e13i | 0.487415 | − | 0.709264i | ||||
\(664\) | −2.53204e13 | −0.196169 | ||||||||
\(665\) | 6.46612e13i | 0.497205i | ||||||||
\(666\) | −6.25688e13 | + | 2.40246e13i | −0.477515 | + | 0.183352i | ||||
\(667\) | −6.78122e12 | −0.0513664 | ||||||||
\(668\) | 1.08757e14i | 0.817663i | ||||||||
\(669\) | 1.21315e14 | + | 8.33691e13i | 0.905281 | + | 0.622120i | ||||
\(670\) | 4.28890e13 | 0.317667 | ||||||||
\(671\) | − | 3.31400e13i | − | 0.243635i | ||||||
\(672\) | −1.89611e13 | + | 2.75914e13i | −0.138362 | + | 0.201338i | ||||
\(673\) | 6.04368e12 | 0.0437750 | 0.0218875 | − | 0.999760i | \(-0.493032\pi\) | ||||
0.0218875 | + | 0.999760i | \(0.493032\pi\) | |||||||
\(674\) | 1.96351e13i | 0.141167i | ||||||||
\(675\) | −1.14316e13 | + | 4.76452e13i | −0.0815806 | + | 0.340017i | ||||
\(676\) | 5.57588e13 | 0.394984 | ||||||||
\(677\) | − | 1.21474e14i | − | 0.854164i | −0.904213 | − | 0.427082i | \(-0.859542\pi\) | ||
0.904213 | − | 0.427082i | \(-0.140458\pi\) | |||||||
\(678\) | −5.98885e13 | − | 4.11561e13i | −0.418018 | − | 0.287267i | ||||
\(679\) | 2.05349e14 | 1.42280 | ||||||||
\(680\) | 1.12143e14i | 0.771305i | ||||||||
\(681\) | 9.22913e13 | − | 1.34298e14i | 0.630123 | − | 0.916926i | ||||
\(682\) | 5.91019e13 | 0.400571 | ||||||||
\(683\) | 1.51629e14i | 1.02019i | 0.860119 | + | 0.510094i | \(0.170389\pi\) | ||||
−0.860119 | + | 0.510094i | \(0.829611\pi\) | |||||||
\(684\) | −8.31024e12 | − | 2.16429e13i | −0.0555051 | − | 0.144556i | ||||
\(685\) | −9.97450e13 | −0.661360 | ||||||||
\(686\) | 1.33906e13i | 0.0881410i | ||||||||
\(687\) | −7.07663e13 | − | 4.86315e13i | −0.462427 | − | 0.317785i | ||||
\(688\) | −5.20930e13 | −0.337938 | ||||||||
\(689\) | − | 7.17296e12i | − | 0.0461958i | ||||||
\(690\) | 1.58651e13 | − | 2.30862e13i | 0.101437 | − | 0.147607i | ||||
\(691\) | 6.62249e13 | 0.420369 | 0.210185 | − | 0.977662i | \(-0.432593\pi\) | ||||
0.210185 | + | 0.977662i | \(0.432593\pi\) | |||||||
\(692\) | − | 1.55716e14i | − | 0.981300i | ||||||
\(693\) | 7.99493e13 | − | 3.06982e13i | 0.500205 | − | 0.192064i | ||||
\(694\) | −1.17824e14 | −0.731873 | ||||||||
\(695\) | − | 2.29623e14i | − | 1.41609i | ||||||
\(696\) | −1.12121e13 | − | 7.70509e12i | −0.0686500 | − | 0.0471771i | ||||
\(697\) | −3.97909e14 | −2.41891 | ||||||||
\(698\) | 2.53321e13i | 0.152895i | ||||||||
\(699\) | −1.54679e14 | + | 2.25082e14i | −0.926928 | + | 1.34882i | ||||
\(700\) | −4.06077e13 | −0.241612 | ||||||||
\(701\) | − | 5.78990e13i | − | 0.342043i | −0.985267 | − | 0.171022i | \(-0.945293\pi\) | ||
0.985267 | − | 0.171022i | \(-0.0547068\pi\) | |||||||
\(702\) | −5.37228e13 | − | 1.28898e13i | −0.315118 | − | 0.0756066i | ||||
\(703\) | 3.84654e13 | 0.224024 | ||||||||
\(704\) | − | 8.38091e12i | − | 0.0484650i | ||||||
\(705\) | 1.12739e14 | + | 7.74754e13i | 0.647332 | + | 0.444855i | ||||
\(706\) | −8.46157e13 | −0.482422 | ||||||||
\(707\) | − | 3.90039e14i | − | 2.20806i | ||||||
\(708\) | −2.05777e13 | + | 2.99437e13i | −0.115672 | + | 0.168321i | ||||
\(709\) | 2.70077e14 | 1.50750 | 0.753750 | − | 0.657162i | \(-0.228243\pi\) | ||||
0.753750 | + | 0.657162i | \(0.228243\pi\) | |||||||
\(710\) | 4.69366e13i | 0.260148i | ||||||||
\(711\) | 4.16115e13 | + | 1.08372e14i | 0.229016 | + | 0.596441i | ||||
\(712\) | −2.76588e12 | −0.0151159 | ||||||||
\(713\) | − | 5.86983e13i | − | 0.318550i | ||||||
\(714\) | 2.80631e14 | + | 1.92853e14i | 1.51232 | + | 1.03929i | ||||
\(715\) | −3.85748e13 | −0.206430 | ||||||||
\(716\) | − | 3.62043e12i | − | 0.0192395i | ||||||
\(717\) | −3.64166e13 | + | 5.29918e13i | −0.192178 | + | 0.279649i | ||||
\(718\) | −8.02117e13 | −0.420354 | ||||||||
\(719\) | 1.48102e14i | 0.770755i | 0.922759 | + | 0.385377i | \(0.125929\pi\) | ||||
−0.922759 | + | 0.385377i | \(0.874071\pi\) | |||||||
\(720\) | 5.24629e13 | − | 2.01442e13i | 0.271137 | − | 0.104109i | ||||
\(721\) | −1.94375e14 | −0.997616 | ||||||||
\(722\) | − | 1.25425e14i | − | 0.639289i | ||||||
\(723\) | −1.77592e14 | − | 1.22044e14i | −0.898944 | − | 0.617765i | ||||
\(724\) | 6.51820e13 | 0.327669 | ||||||||
\(725\) | − | 1.65014e13i | − | 0.0823819i | ||||||
\(726\) | 6.86307e13 | − | 9.98683e13i | 0.340279 | − | 0.495159i | ||||
\(727\) | 5.21602e13 | 0.256842 | 0.128421 | − | 0.991720i | \(-0.459009\pi\) | ||||
0.128421 | + | 0.991720i | \(0.459009\pi\) | |||||||
\(728\) | − | 4.57876e13i | − | 0.223919i | ||||||
\(729\) | −1.83476e14 | − | 9.34214e13i | −0.891133 | − | 0.453742i | ||||
\(730\) | 1.79566e14 | 0.866183 | ||||||||
\(731\) | 5.29837e14i | 2.53837i | ||||||||
\(732\) | −5.44195e13 | − | 3.73978e13i | −0.258940 | − | 0.177947i | ||||
\(733\) | 3.21782e14 | 1.52069 | 0.760346 | − | 0.649518i | \(-0.225029\pi\) | ||||
0.760346 | + | 0.649518i | \(0.225029\pi\) | |||||||
\(734\) | − | 2.28902e14i | − | 1.07441i | ||||||
\(735\) | −1.28409e14 | + | 1.86855e14i | −0.598630 | + | 0.871099i | ||||
\(736\) | −8.32367e12 | −0.0385413 | ||||||||
\(737\) | 3.26009e13i | 0.149931i | ||||||||
\(738\) | 7.14765e13 | + | 1.86151e14i | 0.326499 | + | 0.850322i | ||||
\(739\) | 1.66542e14 | 0.755617 | 0.377809 | − | 0.925884i | \(-0.376678\pi\) | ||||
0.377809 | + | 0.925884i | \(0.376678\pi\) | |||||||
\(740\) | 9.32411e13i | 0.420193i | ||||||||
\(741\) | 2.61318e13 | + | 1.79581e13i | 0.116971 | + | 0.0803839i | ||||
\(742\) | 2.21543e13 | 0.0985007 | ||||||||
\(743\) | − | 1.13631e14i | − | 0.501825i | −0.968010 | − | 0.250912i | \(-0.919269\pi\) | ||
0.968010 | − | 0.250912i | \(-0.0807306\pi\) | |||||||
\(744\) | 6.66953e13 | − | 9.70519e13i | 0.292570 | − | 0.425735i | ||||
\(745\) | 1.22884e14 | 0.535443 | ||||||||
\(746\) | 8.62230e13i | 0.373189i | ||||||||
\(747\) | 1.20480e14 | − | 4.62608e13i | 0.517979 | − | 0.198889i | ||||
\(748\) | −8.52421e13 | −0.364037 | ||||||||
\(749\) | 3.33429e14i | 1.41447i | ||||||||
\(750\) | −1.04484e14 | − | 7.18025e13i | −0.440293 | − | 0.302575i | ||||
\(751\) | −1.64956e14 | −0.690508 | −0.345254 | − | 0.938509i | \(-0.612207\pi\) | ||||
−0.345254 | + | 0.938509i | \(0.612207\pi\) | |||||||
\(752\) | − | 4.06477e13i | − | 0.169023i | ||||||
\(753\) | −1.18290e14 | + | 1.72130e14i | −0.488622 | + | 0.711020i | ||||
\(754\) | 1.86064e13 | 0.0763493 | ||||||||
\(755\) | − | 4.44320e14i | − | 1.81118i | ||||||
\(756\) | 3.98112e13 | − | 1.65928e14i | 0.161212 | − | 0.671909i | ||||
\(757\) | −2.67990e14 | −1.07805 | −0.539026 | − | 0.842289i | \(-0.681207\pi\) | ||||
−0.539026 | + | 0.842289i | \(0.681207\pi\) | |||||||
\(758\) | 2.51282e14i | 1.00419i | ||||||||
\(759\) | 1.75483e13 | + | 1.20594e13i | 0.0696669 | + | 0.0478760i | ||||
\(760\) | −3.22526e13 | −0.127203 | ||||||||
\(761\) | 1.29795e14i | 0.508550i | 0.967132 | + | 0.254275i | \(0.0818368\pi\) | ||||
−0.967132 | + | 0.254275i | \(0.918163\pi\) | |||||||
\(762\) | −9.89720e13 | + | 1.44020e14i | −0.385245 | + | 0.560591i | ||||
\(763\) | 1.09760e14 | 0.424446 | ||||||||
\(764\) | 1.05707e14i | 0.406105i | ||||||||
\(765\) | −2.04886e14 | − | 5.33599e14i | −0.781998 | − | 2.03661i | ||||
\(766\) | −9.71099e13 | −0.368230 | ||||||||
\(767\) | − | 4.96913e13i | − | 0.187199i | ||||||
\(768\) | −1.37624e13 | − | 9.45768e12i | −0.0515095 | − | 0.0353980i | ||||
\(769\) | −2.19185e14 | −0.815041 | −0.407521 | − | 0.913196i | \(-0.633607\pi\) | ||||
−0.407521 | + | 0.913196i | \(0.633607\pi\) | |||||||
\(770\) | − | 1.19142e14i | − | 0.440160i | ||||||
\(771\) | 2.99890e14 | − | 4.36386e14i | 1.10075 | − | 1.60176i | ||||
\(772\) | −1.59542e14 | −0.581821 | ||||||||
\(773\) | − | 4.05042e14i | − | 1.46758i | −0.679374 | − | 0.733792i | \(-0.737749\pi\) | ||
0.679374 | − | 0.733792i | \(-0.262251\pi\) | |||||||
\(774\) | 2.47870e14 | − | 9.51747e13i | 0.892315 | − | 0.342623i | ||||
\(775\) | 1.42837e14 | 0.510894 | ||||||||
\(776\) | 1.02426e14i | 0.364002i | ||||||||
\(777\) | 2.33331e14 | + | 1.60348e14i | 0.823886 | + | 0.566185i | ||||
\(778\) | −3.40665e14 | −1.19517 | ||||||||
\(779\) | − | 1.14440e14i | − | 0.398925i | ||||||
\(780\) | −4.35308e13 | + | 6.33441e13i | −0.150773 | + | 0.219398i | ||||
\(781\) | −3.56775e13 | −0.122783 | ||||||||
\(782\) | 8.46599e13i | 0.289497i | ||||||||
\(783\) | 6.74268e13 | + | 1.61778e13i | 0.229099 | + | 0.0549681i | ||||
\(784\) | 6.73701e13 | 0.227450 | ||||||||
\(785\) | 5.77141e14i | 1.93613i | ||||||||
\(786\) | −2.27074e14 | − | 1.56048e14i | −0.756929 | − | 0.520171i | ||||
\(787\) | 4.98729e14 | 1.65193 | 0.825963 | − | 0.563724i | \(-0.190632\pi\) | ||||
0.825963 | + | 0.563724i | \(0.190632\pi\) | |||||||
\(788\) | 7.76674e13i | 0.255628i | ||||||||
\(789\) | −1.89845e14 | + | 2.76254e14i | −0.620890 | + | 0.903491i | ||||
\(790\) | 1.61497e14 | 0.524843 | ||||||||
\(791\) | 3.06958e14i | 0.991280i | ||||||||
\(792\) | 1.53121e13 | + | 3.98782e13i | 0.0491369 | + | 0.127970i | ||||
\(793\) | 9.03088e13 | 0.287981 | ||||||||
\(794\) | − | 2.52678e14i | − | 0.800690i | ||||||
\(795\) | −3.06490e13 | − | 2.10624e13i | −0.0965119 | − | 0.0663242i | ||||
\(796\) | 5.71861e13 | 0.178947 | ||||||||
\(797\) | − | 1.48672e14i | − | 0.462314i | −0.972917 | − | 0.231157i | \(-0.925749\pi\) | ||
0.972917 | − | 0.231157i | \(-0.0742510\pi\) | |||||||
\(798\) | −5.54652e13 | + | 8.07104e13i | −0.171398 | + | 0.249411i | ||||
\(799\) | −4.13427e14 | −1.26959 | ||||||||
\(800\) | − | 2.02549e13i | − | 0.0618129i | ||||||
\(801\) | 1.31607e13 | − | 5.05331e12i | 0.0399131 | − | 0.0153255i | ||||
\(802\) | 2.61766e14 | 0.788934 | ||||||||
\(803\) | 1.36492e14i | 0.408817i | ||||||||
\(804\) | 5.35343e13 | + | 3.67894e13i | 0.159350 | + | 0.109507i | ||||
\(805\) | −1.18328e14 | −0.350033 | ||||||||
\(806\) | 1.61057e14i | 0.473482i | ||||||||
\(807\) | 1.62578e14 | − | 2.36576e14i | 0.475001 | − | 0.691200i | ||||
\(808\) | 1.94549e14 | 0.564901 | ||||||||
\(809\) | − | 1.32296e14i | − | 0.381772i | −0.981612 | − | 0.190886i | \(-0.938864\pi\) | ||
0.981612 | − | 0.190886i | \(-0.0611361\pi\) | |||||||
\(810\) | −2.12826e14 | + | 1.91701e14i | −0.610378 | + | 0.549793i | ||||
\(811\) | −3.75449e14 | −1.07016 | −0.535078 | − | 0.844803i | \(-0.679718\pi\) | ||||
−0.535078 | + | 0.844803i | \(0.679718\pi\) | |||||||
\(812\) | 5.74675e13i | 0.162795i | ||||||||
\(813\) | 2.84884e14 | + | 1.95776e14i | 0.802076 | + | 0.551197i | ||||
\(814\) | −7.08746e13 | −0.198321 | ||||||||
\(815\) | 3.34305e14i | 0.929726i | ||||||||
\(816\) | −9.61939e13 | + | 1.39977e14i | −0.265887 | + | 0.386906i | ||||
\(817\) | −1.52383e14 | −0.418625 | ||||||||
\(818\) | − | 2.43044e14i | − | 0.663618i | ||||||
\(819\) | 8.36547e13 | + | 2.17867e14i | 0.227023 | + | 0.591252i | ||||
\(820\) | 2.77405e14 | 0.748248 | ||||||||
\(821\) | − | 4.64480e12i | − | 0.0124524i | −0.999981 | − | 0.00622618i | \(-0.998018\pi\) | ||
0.999981 | − | 0.00622618i | \(-0.00198187\pi\) | |||||||
\(822\) | −1.24502e14 | − | 8.55594e13i | −0.331755 | − | 0.227986i | ||||
\(823\) | 6.38146e14 | 1.69013 | 0.845067 | − | 0.534661i | \(-0.179561\pi\) | ||||
0.845067 | + | 0.534661i | \(0.179561\pi\) | |||||||
\(824\) | − | 9.69528e13i | − | 0.255226i | ||||||
\(825\) | −2.93454e13 | + | 4.27021e13i | −0.0767840 | + | 0.111733i | ||||
\(826\) | 1.53476e14 | 0.399154 | ||||||||
\(827\) | − | 5.33624e14i | − | 1.37946i | −0.724068 | − | 0.689728i | \(-0.757730\pi\) | ||
0.724068 | − | 0.689728i | \(-0.242270\pi\) | |||||||
\(828\) | 3.96058e13 | − | 1.52075e13i | 0.101767 | − | 0.0390756i | ||||
\(829\) | −8.63626e13 | −0.220573 | −0.110287 | − | 0.993900i | \(-0.535177\pi\) | ||||
−0.110287 | + | 0.993900i | \(0.535177\pi\) | |||||||
\(830\) | − | 1.79541e14i | − | 0.455800i | ||||||
\(831\) | −1.06135e14 | − | 7.29370e13i | −0.267825 | − | 0.184053i | ||||
\(832\) | 2.28386e13 | 0.0572865 | ||||||||
\(833\) | − | 6.85220e14i | − | 1.70846i | ||||||
\(834\) | 1.96966e14 | − | 2.86616e14i | 0.488160 | − | 0.710347i | ||||
\(835\) | −7.71170e14 | −1.89984 | ||||||||
\(836\) | − | 2.45159e13i | − | 0.0600367i | ||||||
\(837\) | −1.40035e14 | + | 5.83647e14i | −0.340886 | + | 1.42077i | ||||
\(838\) | 1.99510e14 | 0.482774 | ||||||||
\(839\) | − | 4.28770e14i | − | 1.03137i | −0.856778 | − | 0.515685i | \(-0.827538\pi\) | ||
0.856778 | − | 0.515685i | \(-0.172462\pi\) | |||||||
\(840\) | −1.95644e14 | − | 1.34449e14i | −0.467811 | − | 0.321485i | ||||
\(841\) | 3.97355e14 | 0.944492 | ||||||||
\(842\) | − | 1.28918e14i | − | 0.304616i | ||||||
\(843\) | −3.14397e14 | + | 4.57496e14i | −0.738483 | + | 1.07461i | ||||
\(844\) | −7.83697e13 | −0.182994 | ||||||||
\(845\) | 3.95373e14i | 0.917747i | ||||||||
\(846\) | 7.42639e13 | + | 1.93410e14i | 0.171367 | + | 0.446301i | ||||
\(847\) | −5.11874e14 | −1.17421 | ||||||||
\(848\) | 1.10504e13i | 0.0252000i | ||||||||
\(849\) | −4.63171e14 | − | 3.18297e14i | −1.05003 | − | 0.721595i | ||||
\(850\) | −2.06012e14 | −0.464298 | ||||||||
\(851\) | 7.03905e13i | 0.157713i | ||||||||
\(852\) | −4.02613e13 | + | 5.85864e13i | −0.0896789 | + | 0.130497i | ||||
\(853\) | −8.99493e10 | −0.000199183 | −9.95916e−5 | − | 1.00000i | \(-0.500032\pi\) | ||||
−9.95916e−5 | 1.00000i | \(0.500032\pi\) | ||||||||
\(854\) | 2.78927e14i | 0.614046i | ||||||||
\(855\) | 1.53465e14 | − | 5.89260e13i | 0.335875 | − | 0.128966i | ||||
\(856\) | −1.66312e14 | −0.361872 | ||||||||
\(857\) | − | 1.45265e14i | − | 0.314238i | −0.987580 | − | 0.157119i | \(-0.949779\pi\) | ||
0.987580 | − | 0.157119i | \(-0.0502205\pi\) | |||||||
\(858\) | −4.81492e13 | − | 3.30887e13i | −0.103551 | − | 0.0711613i | ||||
\(859\) | −3.53555e14 | −0.755947 | −0.377974 | − | 0.925816i | \(-0.623379\pi\) | ||||
−0.377974 | + | 0.925816i | \(0.623379\pi\) | |||||||
\(860\) | − | 3.69379e14i | − | 0.785200i | ||||||
\(861\) | 4.77058e14 | − | 6.94192e14i | 1.00822 | − | 1.46711i | ||||
\(862\) | 4.08024e14 | 0.857333 | ||||||||
\(863\) | 5.16372e14i | 1.07872i | 0.842075 | + | 0.539360i | \(0.181334\pi\) | ||||
−0.842075 | + | 0.539360i | \(0.818666\pi\) | |||||||
\(864\) | 8.27637e13 | + | 1.98576e13i | 0.171898 | + | 0.0412437i | ||||
\(865\) | 1.10414e15 | 2.28005 | ||||||||
\(866\) | 4.66892e14i | 0.958576i | ||||||||
\(867\) | 1.01996e15 | + | 7.00930e14i | 2.08204 | + | 1.43080i | ||||
\(868\) | −4.97439e14 | −1.00958 | ||||||||
\(869\) | 1.22757e14i | 0.247713i | ||||||||
\(870\) | 5.46350e13 | − | 7.95023e13i | 0.109616 | − | 0.159508i | ||||
\(871\) | −8.88397e13 | −0.177221 | ||||||||
\(872\) | 5.47477e13i | 0.108588i | ||||||||
\(873\) | −1.87135e14 | − | 4.87367e14i | −0.369048 | − | 0.961136i | ||||
\(874\) | −2.43485e13 | −0.0477435 | ||||||||
\(875\) | 5.35530e14i | 1.04410i | ||||||||
\(876\) | 2.24135e14 | + | 1.54028e14i | 0.434499 | + | 0.298593i | ||||
\(877\) | 3.23487e13 | 0.0623532 | 0.0311766 | − | 0.999514i | \(-0.490075\pi\) | ||||
0.0311766 | + | 0.999514i | \(0.490075\pi\) | |||||||
\(878\) | 4.41944e14i | 0.847022i | ||||||||
\(879\) | 1.45870e14 | − | 2.12264e14i | 0.277986 | − | 0.404512i | ||||
\(880\) | 5.94271e13 | 0.112609 | ||||||||
\(881\) | − | 3.45484e14i | − | 0.650950i | −0.945551 | − | 0.325475i | \(-0.894476\pi\) | ||
0.945551 | − | 0.325475i | \(-0.105524\pi\) | |||||||
\(882\) | −3.20561e14 | + | 1.23086e14i | −0.600576 | + | 0.230604i | ||||
\(883\) | −1.94069e14 | −0.361537 | −0.180769 | − | 0.983526i | \(-0.557859\pi\) | ||||
−0.180769 | + | 0.983526i | \(0.557859\pi\) | |||||||
\(884\) | − | 2.32291e14i | − | 0.430299i | ||||||
\(885\) | −2.12324e14 | − | 1.45911e14i | −0.391095 | − | 0.268765i | ||||
\(886\) | −6.73096e14 | −1.23284 | ||||||||
\(887\) | 2.06383e14i | 0.375885i | 0.982180 | + | 0.187943i | \(0.0601819\pi\) | ||||
−0.982180 | + | 0.187943i | \(0.939818\pi\) | |||||||
\(888\) | −7.99804e13 | + | 1.16384e14i | −0.144850 | + | 0.210779i | ||||
\(889\) | 7.38171e14 | 1.32938 | ||||||||
\(890\) | − | 1.96122e13i | − | 0.0351218i | ||||||
\(891\) | −1.45716e14 | − | 1.61773e14i | −0.259489 | − | 0.288084i | ||||
\(892\) | 3.10149e14 | 0.549219 | ||||||||
\(893\) | − | 1.18903e14i | − | 0.209380i | ||||||
\(894\) | 1.53384e14 | + | 1.05407e14i | 0.268592 | + | 0.184579i | ||||
\(895\) | 2.56716e13 | 0.0447031 | ||||||||
\(896\) | 7.05390e13i | 0.122149i | ||||||||
\(897\) | −3.28628e13 | + | 4.78204e13i | −0.0565903 | + | 0.0823476i | ||||
\(898\) | −3.11139e14 | −0.532811 | ||||||||
\(899\) | − | 2.02140e14i | − | 0.344234i | ||||||
\(900\) | 3.70059e13 | + | 9.63769e13i | 0.0626698 | + | 0.163215i | ||||
\(901\) | 1.12394e14 | 0.189286 | ||||||||
\(902\) | 2.10862e14i | 0.353155i | ||||||||
\(903\) | −9.24353e14 | − | 6.35227e14i | −1.53957 | − | 1.05801i | ||||
\(904\) | −1.53109e14 | −0.253605 | ||||||||
\(905\) | 4.62190e14i | 0.761339i | ||||||||
\(906\) | 3.81129e14 | − | 5.54602e14i | 0.624354 | − | 0.908532i | ||||
\(907\) | −3.53646e14 | −0.576145 | −0.288073 | − | 0.957609i | \(-0.593014\pi\) | ||||
−0.288073 | + | 0.957609i | \(0.593014\pi\) | |||||||
\(908\) | − | 3.43341e14i | − | 0.556284i | ||||||
\(909\) | −9.25705e14 | + | 3.55444e14i | −1.49160 | + | 0.572732i | ||||
\(910\) | 3.24670e14 | 0.520277 | ||||||||
\(911\) | − | 4.57044e14i | − | 0.728394i | −0.931322 | − | 0.364197i | \(-0.881344\pi\) | ||
0.931322 | − | 0.364197i | \(-0.118656\pi\) | |||||||
\(912\) | −4.02578e13 | − | 2.76657e13i | −0.0638081 | − | 0.0438497i | ||||
\(913\) | 1.36473e14 | 0.215126 | ||||||||
\(914\) | 9.28232e12i | 0.0145521i | ||||||||
\(915\) | 2.65179e14 | − | 3.85876e14i | 0.413460 | − | 0.601648i | ||||
\(916\) | −1.80918e14 | −0.280547 | ||||||||
\(917\) | 1.16387e15i | 1.79497i | ||||||||
\(918\) | 2.01971e14 | − | 8.41788e14i | 0.309796 | − | 1.29119i | ||||
\(919\) | 4.85254e14 | 0.740273 | 0.370136 | − | 0.928977i | \(-0.379311\pi\) | ||||
0.370136 | + | 0.928977i | \(0.379311\pi\) | |||||||
\(920\) | − | 5.90213e13i | − | 0.0895508i | ||||||
\(921\) | −1.38027e14 | − | 9.48541e13i | −0.208289 | − | 0.143139i | ||||
\(922\) | −4.77244e12 | −0.00716285 | ||||||||
\(923\) | − | 9.72237e13i | − | 0.145132i | ||||||
\(924\) | 1.02198e14 | − | 1.48713e14i | 0.151733 | − | 0.220795i | ||||
\(925\) | −1.71288e14 | −0.252941 | ||||||||
\(926\) | − | 4.45166e14i | − | 0.653834i | ||||||
\(927\) | 1.77134e14 | + | 4.61322e14i | 0.258764 | + | 0.673916i | ||||
\(928\) | −2.86644e13 | −0.0416488 | ||||||||
\(929\) | − | 8.16207e14i | − | 1.17957i | −0.807562 | − | 0.589783i | \(-0.799213\pi\) | ||
0.807562 | − | 0.589783i | \(-0.200787\pi\) | |||||||
\(930\) | 6.88172e14 | + | 4.72921e14i | 0.989196 | + | 0.679788i | ||||
\(931\) | 1.97071e14 | 0.281757 | ||||||||
\(932\) | 5.75436e14i | 0.818309i | ||||||||
\(933\) | −2.69301e14 | + | 3.91874e14i | −0.380916 | + | 0.554292i | ||||
\(934\) | −2.75832e14 | −0.388071 | ||||||||
\(935\) | − | 6.04432e14i | − | 0.845842i | ||||||
\(936\) | −1.08671e14 | + | 4.17264e13i | −0.151263 | + | 0.0580807i | ||||
\(937\) | −6.90133e14 | −0.955510 | −0.477755 | − | 0.878493i | \(-0.658549\pi\) | ||||
−0.477755 | + | 0.878493i | \(0.658549\pi\) | |||||||
\(938\) | − | 2.74389e14i | − | 0.377879i | ||||||
\(939\) | 4.98311e13 | + | 3.42445e13i | 0.0682609 | + | 0.0469098i | ||||
\(940\) | 2.88223e14 | 0.392726 | ||||||||
\(941\) | − | 1.26481e14i | − | 0.171426i | −0.996320 | − | 0.0857129i | \(-0.972683\pi\) | ||
0.996320 | − | 0.0857129i | \(-0.0273168\pi\) | |||||||
\(942\) | −4.95061e14 | + | 7.20390e14i | −0.667428 | + | 0.971210i | ||||
\(943\) | 2.09422e14 | 0.280843 | ||||||||
\(944\) | 7.65528e13i | 0.102118i | ||||||||
\(945\) | 1.17656e15 | + | 2.82292e14i | 1.56118 | + | 0.374576i | ||||
\(946\) | 2.80773e14 | 0.370596 | ||||||||
\(947\) | 3.05743e14i | 0.401427i | 0.979650 | + | 0.200713i | \(0.0643260\pi\) | ||||
−0.979650 | + | 0.200713i | \(0.935674\pi\) | |||||||
\(948\) | 2.01581e14 | + | 1.38529e14i | 0.263274 | + | 0.180925i | ||||
\(949\) | −3.71950e14 | −0.483230 | ||||||||
\(950\) | − | 5.92496e13i | − | 0.0765716i | ||||||
\(951\) | −6.38144e14 | + | 9.28598e14i | −0.820382 | + | 1.19378i | ||||
\(952\) | 7.17450e14 | 0.917502 | ||||||||
\(953\) | 7.71039e14i | 0.980870i | 0.871478 | + | 0.490435i | \(0.163162\pi\) | ||||
−0.871478 | + | 0.490435i | \(0.836838\pi\) | |||||||
\(954\) | −2.01893e13 | − | 5.25803e13i | −0.0255493 | − | 0.0665398i | ||||
\(955\) | −7.49546e14 | −0.943586 | ||||||||
\(956\) | 1.35477e14i | 0.169658i | ||||||||
\(957\) | 6.04315e13 | + | 4.15292e13i | 0.0752841 | + | 0.0517362i | ||||
\(958\) | 1.13338e14 | 0.140458 | ||||||||
\(959\) | 6.38134e14i | 0.786718i | ||||||||
\(960\) | 6.70622e13 | − | 9.75859e13i | 0.0822473 | − | 0.119683i | ||||
\(961\) | 9.30098e14 | 1.13478 | ||||||||
\(962\) | − | 1.93138e14i | − | 0.234419i | ||||||
\(963\) | 7.91348e14 | − | 3.03855e14i | 0.955512 | − | 0.366889i | ||||
\(964\) | −4.54025e14 | −0.545375 | ||||||||
\(965\) | − | 1.13128e15i | − | 1.35186i | ||||||
\(966\) | −1.47698e14 | − | 1.01500e14i | −0.175585 | − | 0.120664i | ||||
\(967\) | 1.27364e15 | 1.50631 | 0.753154 | − | 0.657845i | \(-0.228532\pi\) | ||||
0.753154 | + | 0.657845i | \(0.228532\pi\) | |||||||
\(968\) | − | 2.55319e14i | − | 0.300405i | ||||||
\(969\) | −2.81387e14 | + | 4.09461e14i | −0.329371 | + | 0.479285i | ||||
\(970\) | −7.26283e14 | −0.845760 | ||||||||
\(971\) | 4.71364e14i | 0.546085i | 0.962002 | + | 0.273043i | \(0.0880300\pi\) | ||||
−0.962002 | + | 0.273043i | \(0.911970\pi\) | |||||||
\(972\) | −4.30087e14 | + | 5.67238e13i | −0.495707 | + | 0.0653784i | ||||
\(973\) | −1.46905e15 | −1.68451 | ||||||||
\(974\) | − | 9.43563e14i | − | 1.07641i | ||||||
\(975\) | −1.16366e14 | − | 7.99683e13i | −0.132070 | − | 0.0907601i | ||||
\(976\) | −1.39127e14 | −0.157095 | ||||||||
\(977\) | − | 1.09733e15i | − | 1.23272i | −0.787465 | − | 0.616360i | \(-0.788607\pi\) | ||
0.787465 | − | 0.616360i | \(-0.211393\pi\) | |||||||
\(978\) | −2.86761e14 | + | 4.17281e14i | −0.320498 | + | 0.466374i | ||||
\(979\) | 1.49077e13 | 0.0165767 | ||||||||
\(980\) | 4.77706e14i | 0.528482i | ||||||||
\(981\) | −1.00025e14 | − | 2.60501e14i | −0.110094 | − | 0.286724i | ||||
\(982\) | −4.75946e13 | −0.0521195 | ||||||||
\(983\) | − | 1.52240e15i | − | 1.65867i | −0.558751 | − | 0.829336i | \(-0.688719\pi\) | ||
0.558751 | − | 0.829336i | \(-0.311281\pi\) | |||||||
\(984\) | 3.46258e14 | + | 2.37953e14i | 0.375340 | + | 0.257938i | ||||
\(985\) | −5.50722e14 | −0.593952 | ||||||||
\(986\) | 2.91545e14i | 0.312839i | ||||||||
\(987\) | 4.95661e14 | − | 7.21264e14i | 0.529175 | − | 0.770031i | ||||
\(988\) | 6.68075e13 | 0.0709644 | ||||||||
\(989\) | − | 2.78856e14i | − | 0.294712i | ||||||
\(990\) | −2.82767e14 | + | 1.08574e14i | −0.297339 | + | 0.114170i | ||||
\(991\) | 3.79461e14 | 0.397008 | 0.198504 | − | 0.980100i | \(-0.436392\pi\) | ||||
0.198504 | + | 0.980100i | \(0.436392\pi\) | |||||||
\(992\) | − | 2.48119e14i | − | 0.258286i | ||||||
\(993\) | 2.83267e14 | + | 1.94665e14i | 0.293393 | + | 0.201623i | ||||
\(994\) | 3.00284e14 | 0.309457 | ||||||||
\(995\) | 4.05493e14i | 0.415785i | ||||||||
\(996\) | 1.54007e14 | − | 2.24104e14i | 0.157125 | − | 0.228641i | ||||
\(997\) | 3.25337e13 | 0.0330262 | 0.0165131 | − | 0.999864i | \(-0.494743\pi\) | ||||
0.0165131 | + | 0.999864i | \(0.494743\pi\) | |||||||
\(998\) | 6.21082e14i | 0.627330i | ||||||||
\(999\) | 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 | 6.11.b.a.5.3 | yes | 4 | |
3.2 | odd | 2 | inner | 6.11.b.a.5.1 | ✓ | 4 | |
4.3 | odd | 2 | 48.11.e.d.17.4 | 4 | |||
5.2 | odd | 4 | 150.11.b.a.149.2 | 8 | |||
5.3 | odd | 4 | 150.11.b.a.149.7 | 8 | |||
5.4 | even | 2 | 150.11.d.a.101.2 | 4 | |||
8.3 | odd | 2 | 192.11.e.h.65.1 | 4 | |||
8.5 | even | 2 | 192.11.e.g.65.4 | 4 | |||
9.2 | odd | 6 | 162.11.d.d.53.1 | 8 | |||
9.4 | even | 3 | 162.11.d.d.107.1 | 8 | |||
9.5 | odd | 6 | 162.11.d.d.107.4 | 8 | |||
9.7 | even | 3 | 162.11.d.d.53.4 | 8 | |||
12.11 | even | 2 | 48.11.e.d.17.3 | 4 | |||
15.2 | even | 4 | 150.11.b.a.149.8 | 8 | |||
15.8 | even | 4 | 150.11.b.a.149.1 | 8 | |||
15.14 | odd | 2 | 150.11.d.a.101.4 | 4 | |||
24.5 | odd | 2 | 192.11.e.g.65.3 | 4 | |||
24.11 | even | 2 | 192.11.e.h.65.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.11.b.a.5.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
6.11.b.a.5.3 | yes | 4 | 1.1 | even | 1 | trivial | |
48.11.e.d.17.3 | 4 | 12.11 | even | 2 | |||
48.11.e.d.17.4 | 4 | 4.3 | odd | 2 | |||
150.11.b.a.149.1 | 8 | 15.8 | even | 4 | |||
150.11.b.a.149.2 | 8 | 5.2 | odd | 4 | |||
150.11.b.a.149.7 | 8 | 5.3 | odd | 4 | |||
150.11.b.a.149.8 | 8 | 15.2 | even | 4 | |||
150.11.d.a.101.2 | 4 | 5.4 | even | 2 | |||
150.11.d.a.101.4 | 4 | 15.14 | odd | 2 | |||
162.11.d.d.53.1 | 8 | 9.2 | odd | 6 | |||
162.11.d.d.53.4 | 8 | 9.7 | even | 3 | |||
162.11.d.d.107.1 | 8 | 9.4 | even | 3 | |||
162.11.d.d.107.4 | 8 | 9.5 | odd | 6 | |||
192.11.e.g.65.3 | 4 | 24.5 | odd | 2 | |||
192.11.e.g.65.4 | 4 | 8.5 | even | 2 | |||
192.11.e.h.65.1 | 4 | 8.3 | odd | 2 | |||
192.11.e.h.65.2 | 4 | 24.11 | even | 2 |