Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,33,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.4333275711\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.10 | ||
Character | \(\chi\) | \(=\) | 5.3 |
Dual form | 5.33.c.a.2.10 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 25524.4 | − | 25524.4i | 0.389471 | − | 0.389471i | −0.485028 | − | 0.874499i | \(-0.661191\pi\) |
0.874499 | + | 0.485028i | \(0.161191\pi\) | |||||||
\(3\) | 3.82280e7 | + | 3.82280e7i | 0.888058 | + | 0.888058i | 0.994336 | − | 0.106278i | \(-0.0338934\pi\) |
−0.106278 | + | 0.994336i | \(0.533893\pi\) | |||||||
\(4\) | 2.99198e9i | 0.696625i | ||||||||
\(5\) | −1.26030e11 | + | 8.60210e10i | −0.825948 | + | 0.563747i | ||||
\(6\) | 1.95149e12 | 0.691745 | ||||||||
\(7\) | −1.22489e13 | + | 1.22489e13i | −0.368578 | + | 0.368578i | −0.866958 | − | 0.498381i | \(-0.833928\pi\) |
0.498381 | + | 0.866958i | \(0.333928\pi\) | |||||||
\(8\) | 1.85995e14 | + | 1.85995e14i | 0.660786 | + | 0.660786i | ||||
\(9\) | 1.06974e15i | 0.577295i | ||||||||
\(10\) | −1.02119e15 | + | 5.41245e15i | −0.102119 | + | 0.541245i | ||||
\(11\) | −6.03478e16 | −1.31334 | −0.656672 | − | 0.754176i | \(-0.728036\pi\) | ||||
−0.656672 | + | 0.754176i | \(0.728036\pi\) | |||||||
\(12\) | −1.14377e17 | + | 1.14377e17i | −0.618644 | + | 0.618644i | ||||
\(13\) | 1.61811e17 | + | 1.61811e17i | 0.243173 | + | 0.243173i | 0.818161 | − | 0.574989i | \(-0.194993\pi\) |
−0.574989 | + | 0.818161i | \(0.694993\pi\) | |||||||
\(14\) | 6.25291e17i | 0.287100i | ||||||||
\(15\) | −8.10627e18 | − | 1.52945e18i | −1.23413 | − | 0.232849i | ||||
\(16\) | −3.35568e18 | −0.181912 | ||||||||
\(17\) | 3.87016e19 | − | 3.87016e19i | 0.795328 | − | 0.795328i | −0.187027 | − | 0.982355i | \(-0.559885\pi\) |
0.982355 | + | 0.187027i | \(0.0598852\pi\) | |||||||
\(18\) | 2.73044e19 | + | 2.73044e19i | 0.224839 | + | 0.224839i | ||||
\(19\) | − | 2.45952e20i | − | 0.852693i | −0.904560 | − | 0.426346i | \(-0.859800\pi\) | ||
0.904560 | − | 0.426346i | \(-0.140200\pi\) | |||||||
\(20\) | −2.57373e20 | − | 3.77078e20i | −0.392720 | − | 0.575376i | ||||
\(21\) | −9.36503e20 | −0.654637 | ||||||||
\(22\) | −1.54034e21 | + | 1.54034e21i | −0.511509 | + | 0.511509i | ||||
\(23\) | −9.22936e19 | − | 9.22936e19i | −0.0150496 | − | 0.0150496i | 0.699542 | − | 0.714592i | \(-0.253387\pi\) |
−0.714592 | + | 0.699542i | \(0.753387\pi\) | |||||||
\(24\) | 1.42204e22i | 1.17363i | ||||||||
\(25\) | 8.48385e21 | − | 2.16824e22i | 0.364379 | − | 0.931251i | ||||
\(26\) | 8.26026e21 | 0.189417 | ||||||||
\(27\) | 2.99433e22 | − | 2.99433e22i | 0.375387 | − | 0.375387i | ||||
\(28\) | −3.66485e22 | − | 3.66485e22i | −0.256760 | − | 0.256760i | ||||
\(29\) | 1.82230e23i | 0.728202i | 0.931359 | + | 0.364101i | \(0.118624\pi\) | ||||
−0.931359 | + | 0.364101i | \(0.881376\pi\) | |||||||
\(30\) | −2.45945e23 | + | 1.67869e23i | −0.571345 | + | 0.389969i | ||||
\(31\) | −3.83738e23 | −0.527530 | −0.263765 | − | 0.964587i | \(-0.584964\pi\) | ||||
−0.263765 | + | 0.964587i | \(0.584964\pi\) | |||||||
\(32\) | −8.84493e23 | + | 8.84493e23i | −0.731635 | + | 0.731635i | ||||
\(33\) | −2.30698e24 | − | 2.30698e24i | −1.16633 | − | 1.16633i | ||||
\(34\) | − | 1.97567e24i | − | 0.619514i | ||||||
\(35\) | 4.90062e23 | − | 2.59739e24i | 0.0966413 | − | 0.512210i | ||||
\(36\) | −3.20064e24 | −0.402158 | ||||||||
\(37\) | −1.31159e25 | + | 1.31159e25i | −1.06309 | + | 1.06309i | −0.0652199 | + | 0.997871i | \(0.520775\pi\) |
−0.997871 | + | 0.0652199i | \(0.979225\pi\) | |||||||
\(38\) | −6.27776e24 | − | 6.27776e24i | −0.332099 | − | 0.332099i | ||||
\(39\) | 1.23714e25i | 0.431903i | ||||||||
\(40\) | −3.94403e25 | − | 7.44139e24i | −0.918290 | − | 0.173258i | ||||
\(41\) | −1.00429e26 | −1.57513 | −0.787567 | − | 0.616230i | \(-0.788659\pi\) | ||||
−0.787567 | + | 0.616230i | \(0.788659\pi\) | |||||||
\(42\) | −2.39036e25 | + | 2.39036e25i | −0.254962 | + | 0.254962i | ||||
\(43\) | 7.50109e25 | + | 7.50109e25i | 0.549072 | + | 0.549072i | 0.926172 | − | 0.377101i | \(-0.123079\pi\) |
−0.377101 | + | 0.926172i | \(0.623079\pi\) | |||||||
\(44\) | − | 1.80560e26i | − | 0.914909i | ||||||
\(45\) | −9.20200e25 | − | 1.34819e26i | −0.325448 | − | 0.476815i | ||||
\(46\) | −4.71147e24 | −0.0117228 | ||||||||
\(47\) | −3.79204e24 | + | 3.79204e24i | −0.00668817 | + | 0.00668817i | −0.710443 | − | 0.703755i | \(-0.751505\pi\) |
0.703755 | + | 0.710443i | \(0.251505\pi\) | |||||||
\(48\) | −1.28281e26 | − | 1.28281e26i | −0.161548 | − | 0.161548i | ||||
\(49\) | 8.04356e26i | 0.728301i | ||||||||
\(50\) | −3.36884e26 | − | 7.69974e26i | −0.220780 | − | 0.504610i | ||||
\(51\) | 2.95897e27 | 1.41259 | ||||||||
\(52\) | −4.84136e26 | + | 4.84136e26i | −0.169400 | + | 0.169400i | ||||
\(53\) | 5.28931e27 | + | 5.28931e27i | 1.36454 | + | 1.36454i | 0.868037 | + | 0.496500i | \(0.165382\pi\) |
0.496500 | + | 0.868037i | \(0.334618\pi\) | |||||||
\(54\) | − | 1.52857e27i | − | 0.292404i | ||||||
\(55\) | 7.60561e27 | − | 5.19118e27i | 1.08475 | − | 0.740394i | ||||
\(56\) | −4.55646e27 | −0.487102 | ||||||||
\(57\) | 9.40225e27 | − | 9.40225e27i | 0.757241 | − | 0.757241i | ||||
\(58\) | 4.65131e27 | + | 4.65131e27i | 0.283614 | + | 0.283614i | ||||
\(59\) | 2.33154e28i | 1.08146i | 0.841197 | + | 0.540729i | \(0.181852\pi\) | ||||
−0.841197 | + | 0.540729i | \(0.818148\pi\) | |||||||
\(60\) | 4.57609e27 | − | 2.42538e28i | 0.162209 | − | 0.859726i | ||||
\(61\) | −6.44243e28 | −1.75296 | −0.876481 | − | 0.481437i | \(-0.840115\pi\) | ||||
−0.876481 | + | 0.481437i | \(0.840115\pi\) | |||||||
\(62\) | −9.79466e27 | + | 9.79466e27i | −0.205458 | + | 0.205458i | ||||
\(63\) | −1.31031e28 | − | 1.31031e28i | −0.212778 | − | 0.212778i | ||||
\(64\) | 3.07397e28i | 0.387989i | ||||||||
\(65\) | −3.43122e28 | − | 6.47385e27i | −0.337936 | − | 0.0637601i | ||||
\(66\) | −1.17768e29 | −0.908500 | ||||||||
\(67\) | 1.20462e29 | − | 1.20462e29i | 0.730555 | − | 0.730555i | −0.240175 | − | 0.970730i | \(-0.577205\pi\) |
0.970730 | + | 0.240175i | \(0.0772048\pi\) | |||||||
\(68\) | 1.15794e29 | + | 1.15794e29i | 0.554045 | + | 0.554045i | ||||
\(69\) | − | 7.05640e27i | − | 0.0267299i | ||||||
\(70\) | −5.37881e28 | − | 7.88052e28i | −0.161852 | − | 0.237130i | ||||
\(71\) | −7.66986e29 | −1.83931 | −0.919653 | − | 0.392733i | \(-0.871530\pi\) | ||||
−0.919653 | + | 0.392733i | \(0.871530\pi\) | |||||||
\(72\) | −1.98966e29 | + | 1.98966e29i | −0.381468 | + | 0.381468i | ||||
\(73\) | −5.26426e28 | − | 5.26426e28i | −0.0809416 | − | 0.0809416i | 0.665477 | − | 0.746418i | \(-0.268228\pi\) |
−0.746418 | + | 0.665477i | \(0.768228\pi\) | |||||||
\(74\) | 6.69550e29i | 0.828086i | ||||||||
\(75\) | 1.15319e30 | − | 5.04553e29i | 1.15059 | − | 0.503415i | ||||
\(76\) | 7.35884e29 | 0.594007 | ||||||||
\(77\) | 7.39195e29 | − | 7.39195e29i | 0.484069 | − | 0.484069i | ||||
\(78\) | 3.15773e29 | + | 3.15773e29i | 0.168214 | + | 0.168214i | ||||
\(79\) | − | 2.15502e30i | − | 0.936308i | −0.883647 | − | 0.468154i | \(-0.844919\pi\) | ||
0.883647 | − | 0.468154i | \(-0.155081\pi\) | |||||||
\(80\) | 4.22914e29 | − | 2.88658e29i | 0.150249 | − | 0.102552i | ||||
\(81\) | 4.27159e30 | 1.24403 | ||||||||
\(82\) | −2.56338e30 | + | 2.56338e30i | −0.613468 | + | 0.613468i | ||||
\(83\) | 4.04853e30 | + | 4.04853e30i | 0.798084 | + | 0.798084i | 0.982793 | − | 0.184710i | \(-0.0591344\pi\) |
−0.184710 | + | 0.982793i | \(0.559134\pi\) | |||||||
\(84\) | − | 2.80200e30i | − | 0.456036i | ||||||
\(85\) | −1.54840e30 | + | 8.20669e30i | −0.208535 | + | 1.10526i | ||||
\(86\) | 3.82921e30 | 0.427695 | ||||||||
\(87\) | −6.96629e30 | + | 6.96629e30i | −0.646686 | + | 0.646686i | ||||
\(88\) | −1.12244e31 | − | 1.12244e31i | −0.867839 | − | 0.867839i | ||||
\(89\) | − | 2.02304e31i | − | 1.30547i | −0.757588 | − | 0.652733i | \(-0.773622\pi\) | ||
0.757588 | − | 0.652733i | \(-0.226378\pi\) | |||||||
\(90\) | −5.78991e30 | − | 1.09241e30i | −0.312458 | − | 0.0589530i | ||||
\(91\) | −3.96402e30 | −0.179256 | ||||||||
\(92\) | 2.76141e29 | − | 2.76141e29i | 0.0104840 | − | 0.0104840i | ||||
\(93\) | −1.46695e31 | − | 1.46695e31i | −0.468477 | − | 0.468477i | ||||
\(94\) | 1.93579e29i | 0.00520969i | ||||||||
\(95\) | 2.11570e31 | + | 3.09972e31i | 0.480703 | + | 0.704280i | ||||
\(96\) | −6.76248e31 | −1.29947 | ||||||||
\(97\) | −5.39171e31 | + | 5.39171e31i | −0.877766 | + | 0.877766i | −0.993303 | − | 0.115537i | \(-0.963141\pi\) |
0.115537 | + | 0.993303i | \(0.463141\pi\) | |||||||
\(98\) | 2.05307e31 | + | 2.05307e31i | 0.283652 | + | 0.283652i | ||||
\(99\) | − | 6.45564e31i | − | 0.758187i | ||||||
\(100\) | 6.48733e31 | + | 2.53835e31i | 0.648733 | + | 0.253835i | ||||
\(101\) | 2.58425e31 | 0.220390 | 0.110195 | − | 0.993910i | \(-0.464852\pi\) | ||||
0.110195 | + | 0.993910i | \(0.464852\pi\) | |||||||
\(102\) | 7.55258e31 | − | 7.55258e31i | 0.550164 | − | 0.550164i | ||||
\(103\) | 2.27845e31 | + | 2.27845e31i | 0.141985 | + | 0.141985i | 0.774527 | − | 0.632541i | \(-0.217988\pi\) |
−0.632541 | + | 0.774527i | \(0.717988\pi\) | |||||||
\(104\) | 6.01921e31i | 0.321370i | ||||||||
\(105\) | 1.18027e32 | − | 8.05589e31i | 0.540696 | − | 0.369049i | ||||
\(106\) | 2.70013e32 | 1.06289 | ||||||||
\(107\) | 6.98821e31 | − | 6.98821e31i | 0.236715 | − | 0.236715i | −0.578773 | − | 0.815488i | \(-0.696468\pi\) |
0.815488 | + | 0.578773i | \(0.196468\pi\) | |||||||
\(108\) | 8.95897e31 | + | 8.95897e31i | 0.261504 | + | 0.261504i | ||||
\(109\) | 1.90698e32i | 0.480312i | 0.970734 | + | 0.240156i | \(0.0771985\pi\) | ||||
−0.970734 | + | 0.240156i | \(0.922801\pi\) | |||||||
\(110\) | 6.16269e31 | − | 3.26630e32i | 0.134118 | − | 0.710842i | ||||
\(111\) | −1.00279e33 | −1.88817 | ||||||||
\(112\) | 4.11034e31 | − | 4.11034e31i | 0.0670485 | − | 0.0670485i | ||||
\(113\) | 5.72067e32 | + | 5.72067e32i | 0.809453 | + | 0.809453i | 0.984551 | − | 0.175098i | \(-0.0560242\pi\) |
−0.175098 | + | 0.984551i | \(0.556024\pi\) | |||||||
\(114\) | − | 4.79973e32i | − | 0.589846i | ||||||
\(115\) | 1.95709e31 | + | 3.69254e30i | 0.0209144 | + | 0.00394603i | ||||
\(116\) | −5.45229e32 | −0.507284 | ||||||||
\(117\) | −1.73096e32 | + | 1.73096e32i | −0.140382 | + | 0.140382i | ||||
\(118\) | 5.95110e32 | + | 5.95110e32i | 0.421197 | + | 0.421197i | ||||
\(119\) | 9.48105e32i | 0.586280i | ||||||||
\(120\) | −1.22325e33 | − | 1.79219e33i | −0.661632 | − | 0.969359i | ||||
\(121\) | 1.53048e33 | 0.724873 | ||||||||
\(122\) | −1.64439e33 | + | 1.64439e33i | −0.682727 | + | 0.682727i | ||||
\(123\) | −3.83920e33 | − | 3.83920e33i | −1.39881 | − | 1.39881i | ||||
\(124\) | − | 1.14814e33i | − | 0.367491i | ||||||
\(125\) | 7.95922e32 | + | 3.46241e33i | 0.224032 | + | 0.974582i | ||||
\(126\) | −6.68898e32 | −0.165742 | ||||||||
\(127\) | −3.47065e32 | + | 3.47065e32i | −0.0757795 | + | 0.0757795i | −0.743981 | − | 0.668201i | \(-0.767065\pi\) |
0.668201 | + | 0.743981i | \(0.267065\pi\) | |||||||
\(128\) | −3.01426e33 | − | 3.01426e33i | −0.580525 | − | 0.580525i | ||||
\(129\) | 5.73503e33i | 0.975215i | ||||||||
\(130\) | −1.04104e33 | + | 7.10555e32i | −0.156449 | + | 0.106784i | ||||
\(131\) | 9.01964e33 | 1.19908 | 0.599540 | − | 0.800344i | \(-0.295350\pi\) | ||||
0.599540 | + | 0.800344i | \(0.295350\pi\) | |||||||
\(132\) | 6.90243e33 | − | 6.90243e33i | 0.812492 | − | 0.812492i | ||||
\(133\) | 3.01264e33 | + | 3.01264e33i | 0.314283 | + | 0.314283i | ||||
\(134\) | − | 6.14942e33i | − | 0.569059i | ||||||
\(135\) | −1.19799e33 | + | 6.34949e33i | −0.0984267 | + | 0.521673i | ||||
\(136\) | 1.43966e34 | 1.05108 | ||||||||
\(137\) | 8.97738e33 | − | 8.97738e33i | 0.582935 | − | 0.582935i | −0.352773 | − | 0.935709i | \(-0.614761\pi\) |
0.935709 | + | 0.352773i | \(0.114761\pi\) | |||||||
\(138\) | −1.80110e32 | − | 1.80110e32i | −0.0104105 | − | 0.0104105i | ||||
\(139\) | 1.59798e34i | 0.822876i | 0.911438 | + | 0.411438i | \(0.134973\pi\) | ||||
−0.911438 | + | 0.411438i | \(0.865027\pi\) | |||||||
\(140\) | 7.77134e33 | + | 1.46626e33i | 0.356818 | + | 0.0673227i | ||||
\(141\) | −2.89924e32 | −0.0118790 | ||||||||
\(142\) | −1.95768e34 | + | 1.95768e34i | −0.716356 | + | 0.716356i | ||||
\(143\) | −9.76496e33 | − | 9.76496e33i | −0.319370 | − | 0.319370i | ||||
\(144\) | − | 3.58970e33i | − | 0.105017i | ||||||
\(145\) | −1.56756e34 | − | 2.29664e34i | −0.410522 | − | 0.601457i | ||||
\(146\) | −2.68734e33 | −0.0630488 | ||||||||
\(147\) | −3.07489e34 | + | 3.07489e34i | −0.646774 | + | 0.646774i | ||||
\(148\) | −3.92425e34 | − | 3.92425e34i | −0.740576 | − | 0.740576i | ||||
\(149\) | 2.71186e34i | 0.459502i | 0.973249 | + | 0.229751i | \(0.0737912\pi\) | ||||
−0.973249 | + | 0.229751i | \(0.926209\pi\) | |||||||
\(150\) | 1.65562e34 | − | 4.23129e34i | 0.252057 | − | 0.644188i | ||||
\(151\) | −6.27427e34 | −0.858879 | −0.429440 | − | 0.903096i | \(-0.641289\pi\) | ||||
−0.429440 | + | 0.903096i | \(0.641289\pi\) | |||||||
\(152\) | 4.57458e34 | − | 4.57458e34i | 0.563447 | − | 0.563447i | ||||
\(153\) | 4.14006e34 | + | 4.14006e34i | 0.459138 | + | 0.459138i | ||||
\(154\) | − | 3.77350e34i | − | 0.377062i | ||||||
\(155\) | 4.83623e34 | − | 3.30095e34i | 0.435712 | − | 0.297394i | ||||
\(156\) | −3.70151e34 | −0.300875 | ||||||||
\(157\) | −1.47429e35 | + | 1.47429e35i | −1.08190 | + | 1.08190i | −0.0855710 | + | 0.996332i | \(0.527271\pi\) |
−0.996332 | + | 0.0855710i | \(0.972729\pi\) | |||||||
\(158\) | −5.50056e34 | − | 5.50056e34i | −0.364665 | − | 0.364665i | ||||
\(159\) | 4.04400e35i | 2.42358i | ||||||||
\(160\) | 3.53873e34 | − | 1.87557e35i | 0.191835 | − | 1.01675i | ||||
\(161\) | 2.26099e33 | 0.0110939 | ||||||||
\(162\) | 1.09030e35 | − | 1.09030e35i | 0.484512 | − | 0.484512i | ||||
\(163\) | 9.35744e34 | + | 9.35744e34i | 0.376839 | + | 0.376839i | 0.869960 | − | 0.493122i | \(-0.164144\pi\) |
−0.493122 | + | 0.869960i | \(0.664144\pi\) | |||||||
\(164\) | − | 3.00482e35i | − | 1.09728i | ||||||
\(165\) | 4.89196e35 | + | 9.22990e34i | 1.62084 | + | 0.305811i | ||||
\(166\) | 2.06672e35 | 0.621660 | ||||||||
\(167\) | −1.02297e34 | + | 1.02297e34i | −0.0279511 | + | 0.0279511i | −0.720944 | − | 0.692993i | \(-0.756292\pi\) |
0.692993 | + | 0.720944i | \(0.256292\pi\) | |||||||
\(168\) | −1.74185e35 | − | 1.74185e35i | −0.432575 | − | 0.432575i | ||||
\(169\) | − | 3.90413e35i | − | 0.881734i | ||||||
\(170\) | 1.69949e35 | + | 2.48992e35i | 0.349249 | + | 0.511686i | ||||
\(171\) | 2.63104e35 | 0.492255 | ||||||||
\(172\) | −2.24431e35 | + | 2.24431e35i | −0.382497 | + | 0.382497i | ||||
\(173\) | −5.46385e35 | − | 5.46385e35i | −0.848713 | − | 0.848713i | 0.141259 | − | 0.989973i | \(-0.454885\pi\) |
−0.989973 | + | 0.141259i | \(0.954885\pi\) | |||||||
\(174\) | 3.55620e35i | 0.503731i | ||||||||
\(175\) | 1.61667e35 | + | 3.69503e35i | 0.208936 | + | 0.477540i | ||||
\(176\) | 2.02508e35 | 0.238912 | ||||||||
\(177\) | −8.91300e35 | + | 8.91300e35i | −0.960398 | + | 0.960398i | ||||
\(178\) | −5.16369e35 | − | 5.16369e35i | −0.508441 | − | 0.508441i | ||||
\(179\) | 1.42175e36i | 1.27990i | 0.768418 | + | 0.639948i | \(0.221044\pi\) | ||||
−0.768418 | + | 0.639948i | \(0.778956\pi\) | |||||||
\(180\) | 4.03375e35 | − | 2.75322e35i | 0.332161 | − | 0.226715i | ||||
\(181\) | 1.21808e36 | 0.917952 | 0.458976 | − | 0.888449i | \(-0.348216\pi\) | ||||
0.458976 | + | 0.888449i | \(0.348216\pi\) | |||||||
\(182\) | −1.01179e35 | + | 1.01179e35i | −0.0698150 | + | 0.0698150i | ||||
\(183\) | −2.46281e36 | − | 2.46281e36i | −1.55673 | − | 1.55673i | ||||
\(184\) | − | 3.43322e34i | − | 0.0198892i | ||||||
\(185\) | 5.24749e35 | − | 2.78123e36i | 0.278743 | − | 1.47737i | ||||
\(186\) | −7.48860e35 | −0.364917 | ||||||||
\(187\) | −2.33556e36 | + | 2.33556e36i | −1.04454 | + | 1.04454i | ||||
\(188\) | −1.13457e34 | − | 1.13457e34i | −0.00465915 | − | 0.00465915i | ||||
\(189\) | 7.33545e35i | 0.276718i | ||||||||
\(190\) | 1.33120e36 | + | 2.51165e35i | 0.461516 | + | 0.0870765i | ||||
\(191\) | 3.06927e36 | 0.978366 | 0.489183 | − | 0.872181i | \(-0.337295\pi\) | ||||
0.489183 | + | 0.872181i | \(0.337295\pi\) | |||||||
\(192\) | −1.17512e36 | + | 1.17512e36i | −0.344557 | + | 0.344557i | ||||
\(193\) | 1.46007e34 | + | 1.46007e34i | 0.00393965 | + | 0.00393965i | 0.709074 | − | 0.705134i | \(-0.249113\pi\) |
−0.705134 | + | 0.709074i | \(0.749113\pi\) | |||||||
\(194\) | 2.75240e36i | 0.683728i | ||||||||
\(195\) | −1.06420e36 | − | 1.55917e36i | −0.243484 | − | 0.356730i | ||||
\(196\) | −2.40662e36 | −0.507353 | ||||||||
\(197\) | 4.81103e36 | − | 4.81103e36i | 0.934929 | − | 0.934929i | −0.0630793 | − | 0.998009i | \(-0.520092\pi\) |
0.998009 | + | 0.0630793i | \(0.0200921\pi\) | |||||||
\(198\) | −1.64776e36 | − | 1.64776e36i | −0.295292 | − | 0.295292i | ||||
\(199\) | 7.23484e36i | 1.19613i | 0.801447 | + | 0.598066i | \(0.204064\pi\) | ||||
−0.801447 | + | 0.598066i | \(0.795936\pi\) | |||||||
\(200\) | 5.61076e36 | − | 2.45485e36i | 0.856134 | − | 0.374581i | ||||
\(201\) | 9.21003e36 | 1.29755 | ||||||||
\(202\) | 6.59613e35 | − | 6.59613e35i | 0.0858356 | − | 0.0858356i | ||||
\(203\) | −2.23212e36 | − | 2.23212e36i | −0.268399 | − | 0.268399i | ||||
\(204\) | 8.85318e36i | 0.984049i | ||||||||
\(205\) | 1.26570e37 | − | 8.63900e36i | 1.30098 | − | 0.887977i | ||||
\(206\) | 1.16312e36 | 0.110598 | ||||||||
\(207\) | 9.87301e34 | − | 9.87301e34i | 0.00868808 | − | 0.00868808i | ||||
\(208\) | −5.42986e35 | − | 5.42986e35i | −0.0442360 | − | 0.0442360i | ||||
\(209\) | 1.48427e37i | 1.11988i | ||||||||
\(210\) | 9.56352e35 | − | 5.06878e36i | 0.0668511 | − | 0.354319i | ||||
\(211\) | −1.91789e37 | −1.24253 | −0.621263 | − | 0.783602i | \(-0.713380\pi\) | ||||
−0.621263 | + | 0.783602i | \(0.713380\pi\) | |||||||
\(212\) | −1.58255e37 | + | 1.58255e37i | −0.950571 | + | 0.950571i | ||||
\(213\) | −2.93203e37 | − | 2.93203e37i | −1.63341 | − | 1.63341i | ||||
\(214\) | − | 3.56739e36i | − | 0.184387i | ||||||
\(215\) | −1.59061e37 | − | 3.00108e36i | −0.763042 | − | 0.143967i | ||||
\(216\) | 1.11386e37 | 0.496101 | ||||||||
\(217\) | 4.70037e36 | − | 4.70037e36i | 0.194436 | − | 0.194436i | ||||
\(218\) | 4.86745e36 | + | 4.86745e36i | 0.187067 | + | 0.187067i | ||||
\(219\) | − | 4.02485e36i | − | 0.143762i | ||||||
\(220\) | 1.55319e37 | + | 2.27558e37i | 0.515777 | + | 0.755666i | ||||
\(221\) | 1.25247e37 | 0.386804 | ||||||||
\(222\) | −2.55955e37 | + | 2.55955e37i | −0.735388 | + | 0.735388i | ||||
\(223\) | −2.91044e37 | − | 2.91044e37i | −0.778180 | − | 0.778180i | 0.201341 | − | 0.979521i | \(-0.435470\pi\) |
−0.979521 | + | 0.201341i | \(0.935470\pi\) | |||||||
\(224\) | − | 2.16681e37i | − | 0.539328i | ||||||
\(225\) | 2.31945e37 | + | 9.07551e36i | 0.537606 | + | 0.210354i | ||||
\(226\) | 2.92033e37 | 0.630517 | ||||||||
\(227\) | −1.82430e37 | + | 1.82430e37i | −0.367014 | + | 0.367014i | −0.866387 | − | 0.499373i | \(-0.833564\pi\) |
0.499373 | + | 0.866387i | \(0.333564\pi\) | |||||||
\(228\) | 2.81314e37 | + | 2.81314e37i | 0.527513 | + | 0.527513i | ||||
\(229\) | − | 5.31018e37i | − | 0.928414i | −0.885727 | − | 0.464207i | \(-0.846339\pi\) | ||
0.885727 | − | 0.464207i | \(-0.153661\pi\) | |||||||
\(230\) | 5.93785e35 | − | 4.05285e35i | 0.00968241 | − | 0.00660869i | ||||
\(231\) | 5.65159e37 | 0.859763 | ||||||||
\(232\) | −3.38938e37 | + | 3.38938e37i | −0.481186 | + | 0.481186i | ||||
\(233\) | 1.79434e37 | + | 1.79434e37i | 0.237799 | + | 0.237799i | 0.815938 | − | 0.578139i | \(-0.196221\pi\) |
−0.578139 | + | 0.815938i | \(0.696221\pi\) | |||||||
\(234\) | 8.83632e36i | 0.109350i | ||||||||
\(235\) | 1.51714e35 | − | 8.04104e35i | 0.00175364 | − | 0.00929451i | ||||
\(236\) | −6.97591e37 | −0.753371 | ||||||||
\(237\) | 8.23823e37 | − | 8.23823e37i | 0.831496 | − | 0.831496i | ||||
\(238\) | 2.41998e37 | + | 2.41998e37i | 0.228339 | + | 0.228339i | ||||
\(239\) | 5.12367e37i | 0.452080i | 0.974118 | + | 0.226040i | \(0.0725779\pi\) | ||||
−0.974118 | + | 0.226040i | \(0.927422\pi\) | |||||||
\(240\) | 2.72020e37 | + | 5.13234e36i | 0.224502 | + | 0.0423580i | ||||
\(241\) | 6.19512e37 | 0.478384 | 0.239192 | − | 0.970972i | \(-0.423117\pi\) | ||||
0.239192 | + | 0.970972i | \(0.423117\pi\) | |||||||
\(242\) | 3.90645e37 | − | 3.90645e37i | 0.282317 | − | 0.282317i | ||||
\(243\) | 1.07809e38 | + | 1.07809e38i | 0.729380 | + | 0.729380i | ||||
\(244\) | − | 1.92756e38i | − | 1.22116i | ||||||
\(245\) | −6.91915e37 | − | 1.01373e38i | −0.410578 | − | 0.601539i | ||||
\(246\) | −1.95986e38 | −1.08959 | ||||||||
\(247\) | 3.97978e37 | − | 3.97978e37i | 0.207352 | − | 0.207352i | ||||
\(248\) | −7.13732e37 | − | 7.13732e37i | −0.348584 | − | 0.348584i | ||||
\(249\) | 3.09535e38i | 1.41749i | ||||||||
\(250\) | 1.08691e38 | + | 6.80604e37i | 0.466825 | + | 0.292317i | ||||
\(251\) | −2.36998e38 | −0.954915 | −0.477457 | − | 0.878655i | \(-0.658441\pi\) | ||||
−0.477457 | + | 0.878655i | \(0.658441\pi\) | |||||||
\(252\) | 3.92043e37 | − | 3.92043e37i | 0.148226 | − | 0.148226i | ||||
\(253\) | 5.56972e36 | + | 5.56972e36i | 0.0197654 | + | 0.0197654i | ||||
\(254\) | 1.77172e37i | 0.0590278i | ||||||||
\(255\) | −3.72918e38 | + | 2.54533e38i | −1.16673 | + | 0.796346i | ||||
\(256\) | −2.85900e38 | −0.840184 | ||||||||
\(257\) | −5.30335e37 | + | 5.30335e37i | −0.146427 | + | 0.146427i | −0.776520 | − | 0.630093i | \(-0.783017\pi\) |
0.630093 | + | 0.776520i | \(0.283017\pi\) | |||||||
\(258\) | 1.46383e38 | + | 1.46383e38i | 0.379818 | + | 0.379818i | ||||
\(259\) | − | 3.21311e38i | − | 0.783663i | ||||||
\(260\) | 1.93696e37 | − | 1.02661e38i | 0.0444169 | − | 0.235415i | ||||
\(261\) | −1.94939e38 | −0.420387 | ||||||||
\(262\) | 2.30220e38 | − | 2.30220e38i | 0.467007 | − | 0.467007i | ||||
\(263\) | 4.90685e38 | + | 4.90685e38i | 0.936506 | + | 0.936506i | 0.998101 | − | 0.0615952i | \(-0.0196188\pi\) |
−0.0615952 | + | 0.998101i | \(0.519619\pi\) | |||||||
\(264\) | − | 8.58171e38i | − | 1.54138i | ||||||
\(265\) | −1.12160e39 | − | 2.11618e38i | −1.89629 | − | 0.357782i | ||||
\(266\) | 1.53792e38 | 0.244808 | ||||||||
\(267\) | 7.73369e38 | − | 7.73369e38i | 1.15933 | − | 1.15933i | ||||
\(268\) | 3.60420e38 | + | 3.60420e38i | 0.508923 | + | 0.508923i | ||||
\(269\) | 9.02803e38i | 1.20104i | 0.799611 | + | 0.600519i | \(0.205039\pi\) | ||||
−0.799611 | + | 0.600519i | \(0.794961\pi\) | |||||||
\(270\) | 1.31489e38 | + | 1.92644e38i | 0.164842 | + | 0.241511i | ||||
\(271\) | 1.34673e39 | 1.59138 | 0.795689 | − | 0.605706i | \(-0.207109\pi\) | ||||
0.795689 | + | 0.605706i | \(0.207109\pi\) | |||||||
\(272\) | −1.29870e38 | + | 1.29870e38i | −0.144679 | + | 0.144679i | ||||
\(273\) | −1.51537e38 | − | 1.51537e38i | −0.159190 | − | 0.159190i | ||||
\(274\) | − | 4.58284e38i | − | 0.454073i | ||||||
\(275\) | −5.11982e38 | + | 1.30848e39i | −0.478555 | + | 1.22305i | ||||
\(276\) | 2.11126e37 | 0.0186207 | ||||||||
\(277\) | −5.46248e38 | + | 5.46248e38i | −0.454688 | + | 0.454688i | −0.896907 | − | 0.442219i | \(-0.854191\pi\) |
0.442219 | + | 0.896907i | \(0.354191\pi\) | |||||||
\(278\) | 4.07874e38 | + | 4.07874e38i | 0.320486 | + | 0.320486i | ||||
\(279\) | − | 4.10499e38i | − | 0.304540i | ||||||
\(280\) | 5.74249e38 | − | 3.91951e38i | 0.402320 | − | 0.274602i | ||||
\(281\) | 1.38640e39 | 0.917463 | 0.458731 | − | 0.888575i | \(-0.348304\pi\) | ||||
0.458731 | + | 0.888575i | \(0.348304\pi\) | |||||||
\(282\) | −7.40013e36 | + | 7.40013e36i | −0.00462651 | + | 0.00462651i | ||||
\(283\) | 3.63813e37 | + | 3.63813e37i | 0.0214929 | + | 0.0214929i | 0.717772 | − | 0.696279i | \(-0.245162\pi\) |
−0.696279 | + | 0.717772i | \(0.745162\pi\) | |||||||
\(284\) | − | 2.29481e39i | − | 1.28131i | ||||||
\(285\) | −3.76171e38 | + | 1.99375e39i | −0.198549 | + | 1.05233i | ||||
\(286\) | −4.98489e38 | −0.248770 | ||||||||
\(287\) | 1.23015e39 | − | 1.23015e39i | 0.580559 | − | 0.580559i | ||||
\(288\) | −9.46176e38 | − | 9.46176e38i | −0.422369 | − | 0.422369i | ||||
\(289\) | − | 6.27714e38i | − | 0.265092i | ||||||
\(290\) | −9.86312e38 | − | 1.86092e38i | −0.394136 | − | 0.0743636i | ||||
\(291\) | −4.12228e39 | −1.55901 | ||||||||
\(292\) | 1.57506e38 | − | 1.57506e38i | 0.0563860 | − | 0.0563860i | ||||
\(293\) | 1.32517e39 | + | 1.32517e39i | 0.449149 | + | 0.449149i | 0.895072 | − | 0.445922i | \(-0.147124\pi\) |
−0.445922 | + | 0.895072i | \(0.647124\pi\) | |||||||
\(294\) | 1.56969e39i | 0.503799i | ||||||||
\(295\) | −2.00561e39 | − | 2.93843e39i | −0.609669 | − | 0.893228i | ||||
\(296\) | −4.87897e39 | −1.40495 | ||||||||
\(297\) | −1.80701e39 | + | 1.80701e39i | −0.493012 | + | 0.493012i | ||||
\(298\) | 6.92186e38 | + | 6.92186e38i | 0.178963 | + | 0.178963i | ||||
\(299\) | − | 2.98683e37i | − | 0.00731933i | ||||||
\(300\) | 1.50961e39 | + | 3.45034e39i | 0.350692 | + | 0.801533i | ||||
\(301\) | −1.83760e39 | −0.404751 | ||||||||
\(302\) | −1.60147e39 | + | 1.60147e39i | −0.334508 | + | 0.334508i | ||||
\(303\) | 9.87907e38 | + | 9.87907e38i | 0.195719 | + | 0.195719i | ||||
\(304\) | 8.25335e38i | 0.155115i | ||||||||
\(305\) | 8.11937e39 | − | 5.54184e39i | 1.44785 | − | 0.988227i | ||||
\(306\) | 2.11345e39 | 0.357642 | ||||||||
\(307\) | 7.05755e39 | − | 7.05755e39i | 1.13355 | − | 1.13355i | 0.143966 | − | 0.989583i | \(-0.454014\pi\) |
0.989583 | − | 0.143966i | \(-0.0459856\pi\) | |||||||
\(308\) | 2.21166e39 | + | 2.21166e39i | 0.337215 | + | 0.337215i | ||||
\(309\) | 1.74201e39i | 0.252183i | ||||||||
\(310\) | 3.91871e38 | − | 2.07696e39i | 0.0538711 | − | 0.285523i | ||||
\(311\) | 5.74069e39 | 0.749545 | 0.374773 | − | 0.927117i | \(-0.377721\pi\) | ||||
0.374773 | + | 0.927117i | \(0.377721\pi\) | |||||||
\(312\) | −2.30102e39 | + | 2.30102e39i | −0.285396 | + | 0.285396i | ||||
\(313\) | −8.73997e39 | − | 8.73997e39i | −1.02991 | − | 1.02991i | −0.999539 | − | 0.0303741i | \(-0.990330\pi\) |
−0.0303741 | − | 0.999539i | \(-0.509670\pi\) | |||||||
\(314\) | 7.52606e39i | 0.842739i | ||||||||
\(315\) | 2.77853e39 | + | 5.24239e38i | 0.295696 | + | 0.0557905i | ||||
\(316\) | 6.44780e39 | 0.652256 | ||||||||
\(317\) | −9.63203e39 | + | 9.63203e39i | −0.926338 | + | 0.926338i | −0.997467 | − | 0.0711291i | \(-0.977340\pi\) |
0.0711291 | + | 0.997467i | \(0.477340\pi\) | |||||||
\(318\) | 1.03220e40 | + | 1.03220e40i | 0.943912 | + | 0.943912i | ||||
\(319\) | − | 1.09972e40i | − | 0.956380i | ||||||
\(320\) | −2.64426e39 | − | 3.87411e39i | −0.218728 | − | 0.320459i | ||||
\(321\) | 5.34291e39 | 0.420433 | ||||||||
\(322\) | 5.77104e37 | − | 5.77104e37i | 0.00432076 | − | 0.00432076i | ||||
\(323\) | −9.51873e39 | − | 9.51873e39i | −0.678170 | − | 0.678170i | ||||
\(324\) | 1.27805e40i | 0.866619i | ||||||||
\(325\) | 4.88124e39 | − | 2.13567e39i | 0.315062 | − | 0.137848i | ||||
\(326\) | 4.77685e39 | 0.293535 | ||||||||
\(327\) | −7.29002e39 | + | 7.29002e39i | −0.426545 | + | 0.426545i | ||||
\(328\) | −1.86793e40 | − | 1.86793e40i | −1.04083 | − | 1.04083i | ||||
\(329\) | − | 9.28967e37i | − | 0.00493022i | ||||||
\(330\) | 1.48423e40 | − | 1.01305e40i | 0.750373 | − | 0.512164i | ||||
\(331\) | 4.22090e39 | 0.203309 | 0.101655 | − | 0.994820i | \(-0.467586\pi\) | ||||
0.101655 | + | 0.994820i | \(0.467586\pi\) | |||||||
\(332\) | −1.21131e40 | + | 1.21131e40i | −0.555965 | + | 0.555965i | ||||
\(333\) | −1.40306e40 | − | 1.40306e40i | −0.613717 | − | 0.613717i | ||||
\(334\) | 5.22212e38i | 0.0217723i | ||||||||
\(335\) | −4.81951e39 | + | 2.55440e40i | −0.191552 | + | 1.01525i | ||||
\(336\) | 3.14260e39 | 0.119086 | ||||||||
\(337\) | 1.22132e40 | − | 1.22132e40i | 0.441318 | − | 0.441318i | −0.451137 | − | 0.892455i | \(-0.648981\pi\) |
0.892455 | + | 0.451137i | \(0.148981\pi\) | |||||||
\(338\) | −9.96505e39 | − | 9.96505e39i | −0.343410 | − | 0.343410i | ||||
\(339\) | 4.37379e40i | 1.43768i | ||||||||
\(340\) | −2.45543e40 | − | 4.63278e39i | −0.769953 | − | 0.145271i | ||||
\(341\) | 2.31577e40 | 0.692829 | ||||||||
\(342\) | 6.71557e39 | − | 6.71557e39i | 0.191719 | − | 0.191719i | ||||
\(343\) | −2.33805e40 | − | 2.33805e40i | −0.637013 | − | 0.637013i | ||||
\(344\) | 2.79032e40i | 0.725637i | ||||||||
\(345\) | 6.06998e38 | + | 8.89315e38i | 0.0150689 | + | 0.0220775i | ||||
\(346\) | −2.78922e40 | −0.661098 | ||||||||
\(347\) | −3.70278e40 | + | 3.70278e40i | −0.838023 | + | 0.838023i | −0.988599 | − | 0.150575i | \(-0.951887\pi\) |
0.150575 | + | 0.988599i | \(0.451887\pi\) | |||||||
\(348\) | −2.08430e40 | − | 2.08430e40i | −0.450498 | − | 0.450498i | ||||
\(349\) | − | 6.84855e40i | − | 1.41381i | −0.707307 | − | 0.706907i | \(-0.750090\pi\) | ||
0.707307 | − | 0.706907i | \(-0.249910\pi\) | |||||||
\(350\) | 1.35578e40 | + | 5.30488e39i | 0.267362 | + | 0.104613i | ||||
\(351\) | 9.69032e39 | 0.182568 | ||||||||
\(352\) | 5.33772e40 | − | 5.33772e40i | 0.960889 | − | 0.960889i | ||||
\(353\) | 1.81046e40 | + | 1.81046e40i | 0.311454 | + | 0.311454i | 0.845473 | − | 0.534018i | \(-0.179319\pi\) |
−0.534018 | + | 0.845473i | \(0.679319\pi\) | |||||||
\(354\) | 4.54997e40i | 0.748094i | ||||||||
\(355\) | 9.66629e40 | − | 6.59769e40i | 1.51917 | − | 1.03690i | ||||
\(356\) | 6.05291e40 | 0.909420 | ||||||||
\(357\) | −3.62441e40 | + | 3.62441e40i | −0.520651 | + | 0.520651i | ||||
\(358\) | 3.62893e40 | + | 3.62893e40i | 0.498482 | + | 0.498482i | ||||
\(359\) | 7.67945e40i | 1.00883i | 0.863461 | + | 0.504416i | \(0.168292\pi\) | ||||
−0.863461 | + | 0.504416i | \(0.831708\pi\) | |||||||
\(360\) | 7.96035e39 | − | 4.21908e40i | 0.100021 | − | 0.530124i | ||||
\(361\) | 2.27061e40 | 0.272915 | ||||||||
\(362\) | 3.10908e40 | − | 3.10908e40i | 0.357515 | − | 0.357515i | ||||
\(363\) | 5.85072e40 | + | 5.85072e40i | 0.643730 | + | 0.643730i | ||||
\(364\) | − | 1.18603e40i | − | 0.124874i | ||||||
\(365\) | 1.11629e40 | + | 2.10616e39i | 0.112484 | + | 0.0212229i | ||||
\(366\) | −1.25723e41 | −1.21260 | ||||||||
\(367\) | −5.02195e40 | + | 5.02195e40i | −0.463677 | + | 0.463677i | −0.899859 | − | 0.436181i | \(-0.856331\pi\) |
0.436181 | + | 0.899859i | \(0.356331\pi\) | |||||||
\(368\) | 3.09707e38 | + | 3.09707e38i | 0.00273770 | + | 0.00273770i | ||||
\(369\) | − | 1.07433e41i | − | 0.909316i | ||||||
\(370\) | −5.75953e40 | − | 8.43831e40i | −0.466831 | − | 0.683955i | ||||
\(371\) | −1.29577e41 | −1.00588 | ||||||||
\(372\) | 4.38909e40 | − | 4.38909e40i | 0.326353 | − | 0.326353i | ||||
\(373\) | 8.76062e40 | + | 8.76062e40i | 0.624013 | + | 0.624013i | 0.946555 | − | 0.322542i | \(-0.104537\pi\) |
−0.322542 | + | 0.946555i | \(0.604537\pi\) | |||||||
\(374\) | 1.19227e41i | 0.813635i | ||||||||
\(375\) | −1.01934e41 | + | 1.62787e41i | −0.666532 | + | 1.06444i | ||||
\(376\) | −1.41060e39 | −0.00883889 | ||||||||
\(377\) | −2.94869e40 | + | 2.94869e40i | −0.177079 | + | 0.177079i | ||||
\(378\) | 1.87233e40 | + | 1.87233e40i | 0.107774 | + | 0.107774i | ||||
\(379\) | − | 3.34210e41i | − | 1.84413i | −0.387033 | − | 0.922066i | \(-0.626500\pi\) | ||
0.387033 | − | 0.922066i | \(-0.373500\pi\) | |||||||
\(380\) | −9.27431e40 | + | 6.33014e40i | −0.490619 | + | 0.334870i | ||||
\(381\) | −2.65352e40 | −0.134593 | ||||||||
\(382\) | 7.83412e40 | − | 7.83412e40i | 0.381045 | − | 0.381045i | ||||
\(383\) | −1.18599e41 | − | 1.18599e41i | −0.553223 | − | 0.553223i | 0.374147 | − | 0.927369i | \(-0.377936\pi\) |
−0.927369 | + | 0.374147i | \(0.877936\pi\) | |||||||
\(384\) | − | 2.30458e41i | − | 1.03108i | ||||||
\(385\) | −2.95742e40 | + | 1.56747e41i | −0.126923 | + | 0.672708i | ||||
\(386\) | 7.45348e38 | 0.00306875 | ||||||||
\(387\) | −8.02421e40 | + | 8.02421e40i | −0.316976 | + | 0.316976i | ||||
\(388\) | −1.61319e41 | − | 1.61319e41i | −0.611474 | − | 0.611474i | ||||
\(389\) | 1.16963e41i | 0.425456i | 0.977111 | + | 0.212728i | \(0.0682349\pi\) | ||||
−0.977111 | + | 0.212728i | \(0.931765\pi\) | |||||||
\(390\) | −6.69599e40 | − | 1.26337e40i | −0.233766 | − | 0.0441058i | ||||
\(391\) | −7.14382e39 | −0.0239388 | ||||||||
\(392\) | −1.49606e41 | + | 1.49606e41i | −0.481251 | + | 0.481251i | ||||
\(393\) | 3.44803e41 | + | 3.44803e41i | 1.06485 | + | 1.06485i | ||||
\(394\) | − | 2.45597e41i | − | 0.728255i | ||||||
\(395\) | 1.85377e41 | + | 2.71597e41i | 0.527841 | + | 0.773341i | ||||
\(396\) | 1.93152e41 | 0.528172 | ||||||||
\(397\) | 2.38763e41 | − | 2.38763e41i | 0.627074 | − | 0.627074i | −0.320257 | − | 0.947331i | \(-0.603769\pi\) |
0.947331 | + | 0.320257i | \(0.103769\pi\) | |||||||
\(398\) | 1.84664e41 | + | 1.84664e41i | 0.465859 | + | 0.465859i | ||||
\(399\) | 2.30335e41i | 0.558204i | ||||||||
\(400\) | −2.84691e40 | + | 7.27590e40i | −0.0662847 | + | 0.169405i | ||||
\(401\) | −4.39823e40 | −0.0983938 | −0.0491969 | − | 0.998789i | \(-0.515666\pi\) | ||||
−0.0491969 | + | 0.998789i | \(0.515666\pi\) | |||||||
\(402\) | 2.35080e41 | − | 2.35080e41i | 0.505358 | − | 0.505358i | ||||
\(403\) | −6.20931e40 | − | 6.20931e40i | −0.128281 | − | 0.128281i | ||||
\(404\) | 7.73203e40i | 0.153529i | ||||||||
\(405\) | −5.38347e41 | + | 3.67446e41i | −1.02750 | + | 0.701316i | ||||
\(406\) | −1.13947e41 | −0.209067 | ||||||||
\(407\) | 7.91516e41 | − | 7.91516e41i | 1.39620 | − | 1.39620i | ||||
\(408\) | 5.50352e41 | + | 5.50352e41i | 0.933422 | + | 0.933422i | ||||
\(409\) | − | 6.56453e41i | − | 1.07061i | −0.844660 | − | 0.535304i | \(-0.820197\pi\) | ||
0.844660 | − | 0.535304i | \(-0.179803\pi\) | |||||||
\(410\) | 1.02558e41 | − | 5.43567e41i | 0.160852 | − | 0.852534i | ||||
\(411\) | 6.86374e41 | 1.03536 | ||||||||
\(412\) | −6.81708e40 | + | 6.81708e40i | −0.0989106 | + | 0.0989106i | ||||
\(413\) | −2.85588e41 | − | 2.85588e41i | −0.398601 | − | 0.398601i | ||||
\(414\) | − | 5.04004e39i | − | 0.00676751i | ||||||
\(415\) | −8.58494e41 | − | 1.61976e41i | −1.10909 | − | 0.209258i | ||||
\(416\) | −2.86242e41 | −0.355828 | ||||||||
\(417\) | −6.10875e41 | + | 6.10875e41i | −0.730762 | + | 0.730762i | ||||
\(418\) | 3.78849e41 | + | 3.78849e41i | 0.436160 | + | 0.436160i | ||||
\(419\) | − | 1.28771e41i | − | 0.142690i | −0.997452 | − | 0.0713450i | \(-0.977271\pi\) | ||
0.997452 | − | 0.0713450i | \(-0.0227291\pi\) | |||||||
\(420\) | 2.41031e41 | + | 3.53135e41i | 0.257089 | + | 0.376662i | ||||
\(421\) | −1.05429e42 | −1.08254 | −0.541272 | − | 0.840848i | \(-0.682057\pi\) | ||||
−0.541272 | + | 0.840848i | \(0.682057\pi\) | |||||||
\(422\) | −4.89530e41 | + | 4.89530e41i | −0.483927 | + | 0.483927i | ||||
\(423\) | −4.05649e39 | − | 4.05649e39i | −0.00386104 | − | 0.00386104i | ||||
\(424\) | 1.96757e42i | 1.80333i | ||||||||
\(425\) | −5.10804e41 | − | 1.16748e42i | −0.450849 | − | 1.03045i | ||||
\(426\) | −1.49677e42 | −1.27233 | ||||||||
\(427\) | 7.89128e41 | − | 7.89128e41i | 0.646102 | − | 0.646102i | ||||
\(428\) | 2.09086e41 | + | 2.09086e41i | 0.164902 | + | 0.164902i | ||||
\(429\) | − | 7.46590e41i | − | 0.567238i | ||||||
\(430\) | −4.82594e41 | + | 3.29392e41i | −0.353253 | + | 0.241112i | ||||
\(431\) | 1.73817e42 | 1.22590 | 0.612951 | − | 0.790121i | \(-0.289982\pi\) | ||||
0.612951 | + | 0.790121i | \(0.289982\pi\) | |||||||
\(432\) | −1.00480e41 | + | 1.00480e41i | −0.0682872 | + | 0.0682872i | ||||
\(433\) | −3.37670e41 | − | 3.37670e41i | −0.221150 | − | 0.221150i | 0.587833 | − | 0.808982i | \(-0.299981\pi\) |
−0.808982 | + | 0.587833i | \(0.799981\pi\) | |||||||
\(434\) | − | 2.39948e41i | − | 0.151454i | ||||||
\(435\) | 2.78712e41 | − | 1.47721e42i | 0.169561 | − | 0.898696i | ||||
\(436\) | −5.70566e41 | −0.334597 | ||||||||
\(437\) | −2.26998e40 | + | 2.26998e40i | −0.0128327 | + | 0.0128327i | ||||
\(438\) | −1.02732e41 | − | 1.02732e41i | −0.0559910 | − | 0.0559910i | ||||
\(439\) | 1.88083e42i | 0.988363i | 0.869359 | + | 0.494182i | \(0.164532\pi\) | ||||
−0.869359 | + | 0.494182i | \(0.835468\pi\) | |||||||
\(440\) | 2.38013e42 | + | 4.49072e41i | 1.20603 | + | 0.227548i | ||||
\(441\) | −8.60451e41 | −0.420445 | ||||||||
\(442\) | 3.19685e41 | − | 3.19685e41i | 0.150649 | − | 0.150649i | ||||
\(443\) | −1.07059e42 | − | 1.07059e42i | −0.486590 | − | 0.486590i | 0.420639 | − | 0.907228i | \(-0.361806\pi\) |
−0.907228 | + | 0.420639i | \(0.861806\pi\) | |||||||
\(444\) | − | 3.00033e42i | − | 1.31535i | ||||||
\(445\) | 1.74024e42 | + | 2.54963e42i | 0.735952 | + | 1.07825i | ||||
\(446\) | −1.48574e42 | −0.606157 | ||||||||
\(447\) | −1.03669e42 | + | 1.03669e42i | −0.408065 | + | 0.408065i | ||||
\(448\) | −3.76528e41 | − | 3.76528e41i | −0.143004 | − | 0.143004i | ||||
\(449\) | 2.36463e42i | 0.866607i | 0.901248 | + | 0.433304i | \(0.142652\pi\) | ||||
−0.901248 | + | 0.433304i | \(0.857348\pi\) | |||||||
\(450\) | 8.23671e41 | − | 3.60378e41i | 0.291309 | − | 0.127455i | ||||
\(451\) | 6.06067e42 | 2.06869 | ||||||||
\(452\) | −1.71161e42 | + | 1.71161e42i | −0.563885 | + | 0.563885i | ||||
\(453\) | −2.39853e42 | − | 2.39853e42i | −0.762735 | − | 0.762735i | ||||
\(454\) | 9.31281e41i | 0.285882i | ||||||||
\(455\) | 4.99584e41 | − | 3.40989e41i | 0.148056 | − | 0.101055i | ||||
\(456\) | 3.49754e42 | 1.00075 | ||||||||
\(457\) | −5.36646e41 | + | 5.36646e41i | −0.148262 | + | 0.148262i | −0.777341 | − | 0.629079i | \(-0.783432\pi\) |
0.629079 | + | 0.777341i | \(0.283432\pi\) | |||||||
\(458\) | −1.35539e42 | − | 1.35539e42i | −0.361590 | − | 0.361590i | ||||
\(459\) | − | 2.31770e42i | − | 0.597111i | ||||||
\(460\) | −1.10480e40 | + | 5.85558e40i | −0.00274890 | + | 0.0145695i | ||||
\(461\) | 4.09470e42 | 0.984027 | 0.492014 | − | 0.870587i | \(-0.336261\pi\) | ||||
0.492014 | + | 0.870587i | \(0.336261\pi\) | |||||||
\(462\) | 1.44253e42 | − | 1.44253e42i | 0.334853 | − | 0.334853i | ||||
\(463\) | 1.54711e42 | + | 1.54711e42i | 0.346918 | + | 0.346918i | 0.858960 | − | 0.512043i | \(-0.171111\pi\) |
−0.512043 | + | 0.858960i | \(0.671111\pi\) | |||||||
\(464\) | − | 6.11505e41i | − | 0.132468i | ||||||
\(465\) | 3.11068e42 | + | 5.86908e41i | 0.651041 | + | 0.122835i | ||||
\(466\) | 9.15989e41 | 0.185232 | ||||||||
\(467\) | −1.55016e42 | + | 1.55016e42i | −0.302904 | + | 0.302904i | −0.842149 | − | 0.539245i | \(-0.818710\pi\) |
0.539245 | + | 0.842149i | \(0.318710\pi\) | |||||||
\(468\) | −5.17900e41 | − | 5.17900e41i | −0.0977939 | − | 0.0977939i | ||||
\(469\) | 2.95105e42i | 0.538532i | ||||||||
\(470\) | −1.66518e40 | − | 2.43966e40i | −0.00293695 | − | 0.00430293i | ||||
\(471\) | −1.12718e43 | −1.92159 | ||||||||
\(472\) | −4.33653e42 | + | 4.33653e42i | −0.714613 | + | 0.714613i | ||||
\(473\) | −4.52674e42 | − | 4.52674e42i | −0.721120 | − | 0.721120i | ||||
\(474\) | − | 4.20551e42i | − | 0.647687i | ||||||
\(475\) | −5.33282e42 | − | 2.08662e42i | −0.794071 | − | 0.310703i | ||||
\(476\) | −2.83671e42 | −0.408417 | ||||||||
\(477\) | −5.65818e42 | + | 5.65818e42i | −0.787740 | + | 0.787740i | ||||
\(478\) | 1.30778e42 | + | 1.30778e42i | 0.176072 | + | 0.176072i | ||||
\(479\) | 7.32607e42i | 0.953900i | 0.878930 | + | 0.476950i | \(0.158258\pi\) | ||||
−0.878930 | + | 0.476950i | \(0.841742\pi\) | |||||||
\(480\) | 8.52272e42 | − | 5.81715e42i | 1.07329 | − | 0.732572i | ||||
\(481\) | −4.24460e42 | −0.517030 | ||||||||
\(482\) | 1.58126e42 | − | 1.58126e42i | 0.186317 | − | 0.186317i | ||||
\(483\) | 8.64332e40 | + | 8.64332e40i | 0.00985205 | + | 0.00985205i | ||||
\(484\) | 4.57917e42i | 0.504965i | ||||||||
\(485\) | 2.15715e42 | − | 1.14331e43i | 0.230151 | − | 1.21983i | ||||
\(486\) | 5.50350e42 | 0.568145 | ||||||||
\(487\) | −2.12024e42 | + | 2.12024e42i | −0.211798 | + | 0.211798i | −0.805031 | − | 0.593233i | \(-0.797851\pi\) |
0.593233 | + | 0.805031i | \(0.297851\pi\) | |||||||
\(488\) | −1.19826e43 | − | 1.19826e43i | −1.15833 | − | 1.15833i | ||||
\(489\) | 7.15432e42i | 0.669309i | ||||||||
\(490\) | −4.35354e42 | − | 8.21404e41i | −0.394190 | − | 0.0743737i | ||||
\(491\) | 8.11842e42 | 0.711488 | 0.355744 | − | 0.934583i | \(-0.384228\pi\) | ||||
0.355744 | + | 0.934583i | \(0.384228\pi\) | |||||||
\(492\) | 1.14868e43 | − | 1.14868e43i | 0.974446 | − | 0.974446i | ||||
\(493\) | 7.05259e42 | + | 7.05259e42i | 0.579159 | + | 0.579159i | ||||
\(494\) | − | 2.03163e42i | − | 0.161515i | ||||||
\(495\) | 5.55320e42 | + | 8.13602e42i | 0.427426 | + | 0.626223i | ||||
\(496\) | 1.28770e42 | 0.0959638 | ||||||||
\(497\) | 9.39474e42 | − | 9.39474e42i | 0.677927 | − | 0.677927i | ||||
\(498\) | 7.90067e42 | + | 7.90067e42i | 0.552071 | + | 0.552071i | ||||
\(499\) | 1.37353e43i | 0.929455i | 0.885454 | + | 0.464727i | \(0.153848\pi\) | ||||
−0.885454 | + | 0.464727i | \(0.846152\pi\) | |||||||
\(500\) | −1.03595e43 | + | 2.38138e42i | −0.678918 | + | 0.156066i | ||||
\(501\) | −7.82121e41 | −0.0496444 | ||||||||
\(502\) | −6.04921e42 | + | 6.04921e42i | −0.371911 | + | 0.371911i | ||||
\(503\) | 1.55558e43 | + | 1.55558e43i | 0.926411 | + | 0.926411i | 0.997472 | − | 0.0710610i | \(-0.0226385\pi\) |
−0.0710610 | + | 0.997472i | \(0.522639\pi\) | |||||||
\(504\) | − | 4.87423e42i | − | 0.281201i | ||||||
\(505\) | −3.25692e42 | + | 2.22300e42i | −0.182031 | + | 0.124244i | ||||
\(506\) | 2.84327e41 | 0.0153961 | ||||||||
\(507\) | 1.49247e43 | − | 1.49247e43i | 0.783031 | − | 0.783031i | ||||
\(508\) | −1.03841e42 | − | 1.03841e42i | −0.0527899 | − | 0.0527899i | ||||
\(509\) | − | 1.49333e43i | − | 0.735650i | −0.929895 | − | 0.367825i | \(-0.880103\pi\) | ||
0.929895 | − | 0.367825i | \(-0.119897\pi\) | |||||||
\(510\) | −3.02168e42 | + | 1.60153e43i | −0.144253 | + | 0.764560i | ||||
\(511\) | 1.28963e42 | 0.0596665 | ||||||||
\(512\) | 5.64872e42 | − | 5.64872e42i | 0.253297 | − | 0.253297i | ||||
\(513\) | −7.36461e42 | − | 7.36461e42i | −0.320090 | − | 0.320090i | ||||
\(514\) | 2.70729e42i | 0.114058i | ||||||||
\(515\) | −4.83146e42 | − | 9.11577e41i | −0.197316 | − | 0.0372287i | ||||
\(516\) | −1.71591e43 | −0.679359 | ||||||||
\(517\) | 2.28841e41 | − | 2.28841e41i | 0.00878387 | − | 0.00878387i | ||||
\(518\) | −8.20125e42 | − | 8.20125e42i | −0.305214 | − | 0.305214i | ||||
\(519\) | − | 4.17744e43i | − | 1.50741i | ||||||
\(520\) | −5.17778e42 | − | 7.58598e42i | −0.181172 | − | 0.265435i | ||||
\(521\) | −8.58493e42 | −0.291295 | −0.145647 | − | 0.989337i | \(-0.546527\pi\) | ||||
−0.145647 | + | 0.989337i | \(0.546527\pi\) | |||||||
\(522\) | −4.97568e42 | + | 4.97568e42i | −0.163729 | + | 0.163729i | ||||
\(523\) | 1.07427e43 | + | 1.07427e43i | 0.342837 | + | 0.342837i | 0.857433 | − | 0.514596i | \(-0.172058\pi\) |
−0.514596 | + | 0.857433i | \(0.672058\pi\) | |||||||
\(524\) | 2.69866e43i | 0.835310i | ||||||||
\(525\) | −7.94515e42 | + | 2.03056e43i | −0.238536 | + | 0.609631i | ||||
\(526\) | 2.50488e43 | 0.729483 | ||||||||
\(527\) | −1.48513e43 | + | 1.48513e43i | −0.419559 | + | 0.419559i | ||||
\(528\) | 7.74146e42 | + | 7.74146e42i | 0.212168 | + | 0.212168i | ||||
\(529\) | − | 3.75919e43i | − | 0.999547i | ||||||
\(530\) | −3.40296e43 | + | 2.32267e43i | −0.877895 | + | 0.599203i | ||||
\(531\) | −2.49414e43 | −0.624321 | ||||||||
\(532\) | −9.01377e42 | + | 9.01377e42i | −0.218938 | + | 0.218938i | ||||
\(533\) | −1.62505e43 | − | 1.62505e43i | −0.383030 | − | 0.383030i | ||||
\(534\) | − | 3.94795e43i | − | 0.903050i | ||||||
\(535\) | −2.79589e42 | + | 1.48185e43i | −0.0620668 | + | 0.328962i | ||||
\(536\) | 4.48105e43 | 0.965480 | ||||||||
\(537\) | −5.43507e43 | + | 5.43507e43i | −1.13662 | + | 1.13662i | ||||
\(538\) | 2.30435e43 | + | 2.30435e43i | 0.467769 | + | 0.467769i | ||||
\(539\) | − | 4.85411e43i | − | 0.956510i | ||||||
\(540\) | −1.89976e43 | − | 3.58436e42i | −0.363410 | − | 0.0685665i | ||||
\(541\) | −6.33794e43 | −1.17704 | −0.588521 | − | 0.808482i | \(-0.700290\pi\) | ||||
−0.588521 | + | 0.808482i | \(0.700290\pi\) | |||||||
\(542\) | 3.43745e43 | − | 3.43745e43i | 0.619795 | − | 0.619795i | ||||
\(543\) | 4.65649e43 | + | 4.65649e43i | 0.815195 | + | 0.815195i | ||||
\(544\) | 6.84625e43i | 1.16378i | ||||||||
\(545\) | −1.64041e43 | − | 2.40336e43i | −0.270774 | − | 0.396712i | ||||
\(546\) | −7.73575e42 | −0.124000 | ||||||||
\(547\) | 8.25783e43 | − | 8.25783e43i | 1.28549 | − | 1.28549i | 0.347993 | − | 0.937497i | \(-0.386863\pi\) |
0.937497 | − | 0.347993i | \(-0.113137\pi\) | |||||||
\(548\) | 2.68602e43 | + | 2.68602e43i | 0.406087 | + | 0.406087i | ||||
\(549\) | − | 6.89172e43i | − | 1.01198i | ||||||
\(550\) | 2.03302e43 | + | 4.64662e43i | 0.289960 | + | 0.662726i | ||||
\(551\) | 4.48198e43 | 0.620933 | ||||||||
\(552\) | 1.31245e42 | − | 1.31245e42i | 0.0176628 | − | 0.0176628i | ||||
\(553\) | 2.63967e43 | + | 2.63967e43i | 0.345102 | + | 0.345102i | ||||
\(554\) | 2.78853e43i | 0.354176i | ||||||||
\(555\) | 1.26381e44 | − | 8.62609e43i | 1.55953 | − | 1.06445i | ||||
\(556\) | −4.78113e43 | −0.573236 | ||||||||
\(557\) | 3.60283e43 | − | 3.60283e43i | 0.419721 | − | 0.419721i | −0.465387 | − | 0.885107i | \(-0.654085\pi\) |
0.885107 | + | 0.465387i | \(0.154085\pi\) | |||||||
\(558\) | −1.04777e43 | − | 1.04777e43i | −0.118610 | − | 0.118610i | ||||
\(559\) | 2.42752e43i | 0.267039i | ||||||||
\(560\) | −1.64449e42 | + | 8.71599e42i | −0.0175802 | + | 0.0931769i | ||||
\(561\) | −1.78567e44 | −1.85522 | ||||||||
\(562\) | 3.53870e43 | − | 3.53870e43i | 0.357325 | − | 0.357325i | ||||
\(563\) | 9.28636e43 | + | 9.28636e43i | 0.911405 | + | 0.911405i | 0.996383 | − | 0.0849781i | \(-0.0270820\pi\) |
−0.0849781 | + | 0.996383i | \(0.527082\pi\) | |||||||
\(564\) | − | 8.67448e41i | − | 0.00827518i | ||||||
\(565\) | −1.21307e44 | − | 2.28876e43i | −1.12489 | − | 0.212239i | ||||
\(566\) | 1.85722e42 | 0.0167417 | ||||||||
\(567\) | −5.23223e43 | + | 5.23223e43i | −0.458520 | + | 0.458520i | ||||
\(568\) | −1.42655e44 | − | 1.42655e44i | −1.21539 | − | 1.21539i | ||||
\(569\) | 1.45469e44i | 1.20496i | 0.798134 | + | 0.602480i | \(0.205821\pi\) | ||||
−0.798134 | + | 0.602480i | \(0.794179\pi\) | |||||||
\(570\) | 4.12877e43 | + | 6.04908e43i | 0.332524 | + | 0.487182i | ||||
\(571\) | 1.95688e44 | 1.53245 | 0.766227 | − | 0.642570i | \(-0.222132\pi\) | ||||
0.766227 | + | 0.642570i | \(0.222132\pi\) | |||||||
\(572\) | 2.92166e43 | − | 2.92166e43i | 0.222481 | − | 0.222481i | ||||
\(573\) | 1.17332e44 | + | 1.17332e44i | 0.868846 | + | 0.868846i | ||||
\(574\) | − | 6.27973e43i | − | 0.452221i | ||||||
\(575\) | −2.78415e42 | + | 1.21814e42i | −0.0194988 | + | 0.00853122i | ||||
\(576\) | −3.28834e43 | −0.223984 | ||||||||
\(577\) | −6.66021e43 | + | 6.66021e43i | −0.441240 | + | 0.441240i | −0.892429 | − | 0.451188i | \(-0.851000\pi\) |
0.451188 | + | 0.892429i | \(0.351000\pi\) | |||||||
\(578\) | −1.60220e43 | − | 1.60220e43i | −0.103246 | − | 0.103246i | ||||
\(579\) | 1.11631e42i | 0.00699727i | ||||||||
\(580\) | 6.87150e43 | − | 4.69011e43i | 0.418990 | − | 0.285980i | ||||
\(581\) | −9.91803e43 | −0.588311 | ||||||||
\(582\) | −1.05219e44 | + | 1.05219e44i | −0.607190 | + | 0.607190i | ||||
\(583\) | −3.19198e44 | − | 3.19198e44i | −1.79211 | − | 1.79211i | ||||
\(584\) | − | 1.95825e43i | − | 0.106970i | ||||||
\(585\) | 6.92533e42 | − | 3.67051e43i | 0.0368084 | − | 0.195089i | ||||
\(586\) | 6.76484e43 | 0.349861 | ||||||||
\(587\) | −1.58074e43 | + | 1.58074e43i | −0.0795519 | + | 0.0795519i | −0.745763 | − | 0.666211i | \(-0.767915\pi\) |
0.666211 | + | 0.745763i | \(0.267915\pi\) | |||||||
\(588\) | −9.20002e43 | − | 9.20002e43i | −0.450559 | − | 0.450559i | ||||
\(589\) | 9.43810e43i | 0.449821i | ||||||||
\(590\) | −1.26193e44 | − | 2.38095e43i | −0.585335 | − | 0.110438i | ||||
\(591\) | 3.67832e44 | 1.66054 | ||||||||
\(592\) | 4.40127e43 | − | 4.40127e43i | 0.193388 | − | 0.193388i | ||||
\(593\) | −2.31682e44 | − | 2.31682e44i | −0.990872 | − | 0.990872i | 0.00908685 | − | 0.999959i | \(-0.497108\pi\) |
−0.999959 | + | 0.00908685i | \(0.997108\pi\) | |||||||
\(594\) | 9.22456e43i | 0.384028i | ||||||||
\(595\) | −8.15569e43 | − | 1.19489e44i | −0.330513 | − | 0.484236i | ||||
\(596\) | −8.11385e43 | −0.320101 | ||||||||
\(597\) | −2.76573e44 | + | 2.76573e44i | −1.06224 | + | 1.06224i | ||||
\(598\) | −7.62369e41 | − | 7.62369e41i | −0.00285067 | − | 0.00285067i | ||||
\(599\) | 4.34699e44i | 1.58256i | 0.611454 | + | 0.791280i | \(0.290585\pi\) | ||||
−0.611454 | + | 0.791280i | \(0.709415\pi\) | |||||||
\(600\) | 3.08332e44 | + | 1.20644e44i | 1.09295 | + | 0.427647i | ||||
\(601\) | 3.47776e44 | 1.20035 | 0.600174 | − | 0.799869i | \(-0.295098\pi\) | ||||
0.600174 | + | 0.799869i | \(0.295098\pi\) | |||||||
\(602\) | −4.69036e43 | + | 4.69036e43i | −0.157639 | + | 0.157639i | ||||
\(603\) | 1.28863e44 | + | 1.28863e44i | 0.421745 | + | 0.421745i | ||||
\(604\) | − | 1.87725e44i | − | 0.598317i | ||||||
\(605\) | −1.92886e44 | + | 1.31653e44i | −0.598707 | + | 0.408645i | ||||
\(606\) | 5.04314e43 | 0.152454 | ||||||||
\(607\) | 3.58025e44 | − | 3.58025e44i | 1.05413 | − | 1.05413i | 0.0556819 | − | 0.998449i | \(-0.482267\pi\) |
0.998449 | − | 0.0556819i | \(-0.0177333\pi\) | |||||||
\(608\) | 2.17543e44 | + | 2.17543e44i | 0.623860 | + | 0.623860i | ||||
\(609\) | − | 1.70659e44i | − | 0.476708i | ||||||
\(610\) | 6.57898e43 | − | 3.48694e44i | 0.179011 | − | 0.948782i | ||||
\(611\) | −1.22719e42 | −0.00325276 | ||||||||
\(612\) | −1.23870e44 | + | 1.23870e44i | −0.319847 | + | 0.319847i | ||||
\(613\) | −1.77316e44 | − | 1.77316e44i | −0.446046 | − | 0.446046i | 0.447992 | − | 0.894038i | \(-0.352139\pi\) |
−0.894038 | + | 0.447992i | \(0.852139\pi\) | |||||||
\(614\) | − | 3.60279e44i | − | 0.882968i | ||||||
\(615\) | 8.14104e44 | + | 1.53601e44i | 1.94392 | + | 0.366769i | ||||
\(616\) | 2.74973e44 | 0.639732 | ||||||||
\(617\) | −7.20277e43 | + | 7.20277e43i | −0.163282 | + | 0.163282i | −0.784019 | − | 0.620737i | \(-0.786833\pi\) |
0.620737 | + | 0.784019i | \(0.286833\pi\) | |||||||
\(618\) | 4.44637e43 | + | 4.44637e43i | 0.0982178 | + | 0.0982178i | ||||
\(619\) | 2.62343e44i | 0.564701i | 0.959311 | + | 0.282351i | \(0.0911141\pi\) | ||||
−0.959311 | + | 0.282351i | \(0.908886\pi\) | |||||||
\(620\) | 9.87638e43 | + | 1.44699e44i | 0.207172 | + | 0.303528i | ||||
\(621\) | −5.52714e42 | −0.0112989 | ||||||||
\(622\) | 1.46527e44 | − | 1.46527e44i | 0.291926 | − | 0.291926i | ||||
\(623\) | 2.47801e44 | + | 2.47801e44i | 0.481165 | + | 0.481165i | ||||
\(624\) | − | 4.15146e43i | − | 0.0785682i | ||||||
\(625\) | −3.98150e44 | − | 3.67900e44i | −0.734456 | − | 0.678656i | ||||
\(626\) | −4.46164e44 | −0.802242 | ||||||||
\(627\) | −5.67405e44 | + | 5.67405e44i | −0.994518 | + | 0.994518i | ||||
\(628\) | −4.41105e44 | − | 4.41105e44i | −0.753681 | − | 0.753681i | ||||
\(629\) | 1.01521e45i | 1.69101i | ||||||||
\(630\) | 8.43010e43 | − | 5.75393e43i | 0.136894 | − | 0.0934363i | ||||
\(631\) | −2.95807e44 | −0.468315 | −0.234158 | − | 0.972199i | \(-0.575233\pi\) | ||||
−0.234158 | + | 0.972199i | \(0.575233\pi\) | |||||||
\(632\) | 4.00823e44 | − | 4.00823e44i | 0.618699 | − | 0.618699i | ||||
\(633\) | −7.33172e44 | − | 7.33172e44i | −1.10343 | − | 1.10343i | ||||
\(634\) | 4.91703e44i | 0.721563i | ||||||||
\(635\) | 1.38856e43 | − | 7.35954e43i | 0.0198694 | − | 0.105310i | ||||
\(636\) | −1.20996e45 | −1.68832 | ||||||||
\(637\) | −1.30154e44 | + | 1.30154e44i | −0.177103 | + | 0.177103i | ||||
\(638\) | −2.80696e44 | − | 2.80696e44i | −0.372482 | − | 0.372482i | ||||
\(639\) | − | 8.20475e44i | − | 1.06182i | ||||||
\(640\) | 6.39175e44 | + | 1.20596e44i | 0.806752 | + | 0.152214i | ||||
\(641\) | −1.20869e44 | −0.148794 | −0.0743970 | − | 0.997229i | \(-0.523703\pi\) | ||||
−0.0743970 | + | 0.997229i | \(0.523703\pi\) | |||||||
\(642\) | 1.36374e44 | − | 1.36374e44i | 0.163747 | − | 0.163747i | ||||
\(643\) | 1.10766e45 | + | 1.10766e45i | 1.29727 | + | 1.29727i | 0.930191 | + | 0.367076i | \(0.119641\pi\) |
0.367076 | + | 0.930191i | \(0.380359\pi\) | |||||||
\(644\) | 6.76485e42i | 0.00772830i | ||||||||
\(645\) | −4.93333e44 | − | 7.22784e44i | −0.549775 | − | 0.805477i | ||||
\(646\) | −4.85919e44 | −0.528255 | ||||||||
\(647\) | 1.38258e44 | − | 1.38258e44i | 0.146629 | − | 0.146629i | −0.629981 | − | 0.776610i | \(-0.716937\pi\) |
0.776610 | + | 0.629981i | \(0.216937\pi\) | |||||||
\(648\) | 7.94493e44 | + | 7.94493e44i | 0.822034 | + | 0.822034i | ||||
\(649\) | − | 1.40703e45i | − | 1.42033i | ||||||
\(650\) | 7.00788e43 | − | 1.79102e44i | 0.0690197 | − | 0.176395i | ||||
\(651\) | 3.59371e44 | 0.345341 | ||||||||
\(652\) | −2.79973e44 | + | 2.79973e44i | −0.262515 | + | 0.262515i | ||||
\(653\) | 5.22925e44 | + | 5.22925e44i | 0.478441 | + | 0.478441i | 0.904633 | − | 0.426192i | \(-0.140145\pi\) |
−0.426192 | + | 0.904633i | \(0.640145\pi\) | |||||||
\(654\) | 3.72146e44i | 0.332253i | ||||||||
\(655\) | −1.13674e45 | + | 7.75878e44i | −0.990378 | + | 0.675978i | ||||
\(656\) | 3.37007e44 | 0.286535 | ||||||||
\(657\) | 5.63139e43 | − | 5.63139e43i | 0.0467272 | − | 0.0467272i | ||||
\(658\) | −2.37113e42 | − | 2.37113e42i | −0.00192018 | − | 0.00192018i | ||||
\(659\) | − | 1.28026e45i | − | 1.01189i | −0.862567 | − | 0.505943i | \(-0.831144\pi\) | ||
0.862567 | − | 0.505943i | \(-0.168856\pi\) | |||||||
\(660\) | −2.76157e44 | + | 1.46366e45i | −0.213036 | + | 1.12912i | ||||
\(661\) | 7.17962e44 | 0.540602 | 0.270301 | − | 0.962776i | \(-0.412877\pi\) | ||||
0.270301 | + | 0.962776i | \(0.412877\pi\) | |||||||
\(662\) | 1.07736e44 | − | 1.07736e44i | 0.0791830 | − | 0.0791830i | ||||
\(663\) | 4.78794e44 | + | 4.78794e44i | 0.343505 | + | 0.343505i | ||||
\(664\) | 1.50601e45i | 1.05472i | ||||||||
\(665\) | −6.38833e44 | − | 1.20532e44i | −0.436758 | − | 0.0824053i | ||||
\(666\) | −7.16243e44 | −0.478050 | ||||||||
\(667\) | 1.68187e43 | − | 1.68187e43i | 0.0109592 | − | 0.0109592i | ||||
\(668\) | −3.06070e43 | − | 3.06070e43i | −0.0194714 | − | 0.0194714i | ||||
\(669\) | − | 2.22520e45i | − | 1.38214i | ||||||
\(670\) | 5.28979e44 | + | 7.75009e44i | 0.320805 | + | 0.470013i | ||||
\(671\) | 3.88787e45 | 2.30224 | ||||||||
\(672\) | 8.28330e44 | − | 8.28330e44i | 0.478955 | − | 0.478955i | ||||
\(673\) | −1.17159e45 | − | 1.17159e45i | −0.661509 | − | 0.661509i | 0.294227 | − | 0.955736i | \(-0.404938\pi\) |
−0.955736 | + | 0.294227i | \(0.904938\pi\) | |||||||
\(674\) | − | 6.23469e44i | − | 0.343761i | ||||||
\(675\) | −3.95207e44 | − | 9.03276e44i | −0.212796 | − | 0.486362i | ||||
\(676\) | 1.16811e45 | 0.614238 | ||||||||
\(677\) | 3.70142e43 | − | 3.70142e43i | 0.0190086 | − | 0.0190086i | −0.697539 | − | 0.716547i | \(-0.745721\pi\) |
0.716547 | + | 0.697539i | \(0.245721\pi\) | |||||||
\(678\) | 1.11638e45 | + | 1.11638e45i | 0.559936 | + | 0.559936i | ||||
\(679\) | − | 1.32085e45i | − | 0.647049i | ||||||
\(680\) | −1.81439e45 | + | 1.23841e45i | −0.868139 | + | 0.592544i | ||||
\(681\) | −1.39479e45 | −0.651859 | ||||||||
\(682\) | 5.91086e44 | − | 5.91086e44i | 0.269837 | − | 0.269837i | ||||
\(683\) | 4.65304e44 | + | 4.65304e44i | 0.207494 | + | 0.207494i | 0.803201 | − | 0.595707i | \(-0.203128\pi\) |
−0.595707 | + | 0.803201i | \(0.703128\pi\) | |||||||
\(684\) | 7.87203e44i | 0.342917i | ||||||||
\(685\) | −3.59173e44 | + | 1.90366e45i | −0.152846 | + | 0.810102i | ||||
\(686\) | −1.19355e45 | −0.496196 | ||||||||
\(687\) | 2.02998e45 | − | 2.02998e45i | 0.824486 | − | 0.824486i | ||||
\(688\) | −2.51712e44 | − | 2.51712e44i | −0.0998825 | − | 0.0998825i | ||||
\(689\) | 1.71174e45i | 0.663637i | ||||||||
\(690\) | 3.81924e43 | + | 7.20596e42i | 0.0144674 | + | 0.00272965i | ||||
\(691\) | −2.71789e45 | −1.00596 | −0.502982 | − | 0.864297i | \(-0.667764\pi\) | ||||
−0.502982 | + | 0.864297i | \(0.667764\pi\) | |||||||
\(692\) | 1.63477e45 | − | 1.63477e45i | 0.591235 | − | 0.591235i | ||||
\(693\) | 7.90746e44 | + | 7.90746e44i | 0.279451 | + | 0.279451i | ||||
\(694\) | 1.89022e45i | 0.652771i | ||||||||
\(695\) | −1.37460e45 | − | 2.01393e45i | −0.463894 | − | 0.679652i | ||||
\(696\) | −2.59139e45 | −0.854642 | ||||||||
\(697\) | −3.88676e45 | + | 3.88676e45i | −1.25275 | + | 1.25275i | ||||
\(698\) | −1.74805e45 | − | 1.74805e45i | −0.550639 | − | 0.550639i | ||||
\(699\) | 1.37188e45i | 0.422359i | ||||||||
\(700\) | −1.10555e45 | + | 4.83706e44i | −0.332666 | + | 0.145550i | ||||
\(701\) | −2.04201e45 | −0.600578 | −0.300289 | − | 0.953848i | \(-0.597083\pi\) | ||||
−0.300289 | + | 0.953848i | \(0.597083\pi\) | |||||||
\(702\) | 2.47339e44 | − | 2.47339e44i | 0.0711048 | − | 0.0711048i | ||||
\(703\) | 3.22588e45 | + | 3.22588e45i | 0.906490 | + | 0.906490i | ||||
\(704\) | − | 1.85507e45i | − | 0.509564i | ||||||
\(705\) | 3.65390e43 | − | 2.49396e43i | 0.00981140 | − | 0.00669673i | ||||
\(706\) | 9.24218e44 | 0.242605 | ||||||||
\(707\) | −3.16542e44 | + | 3.16542e44i | −0.0812309 | + | 0.0812309i | ||||
\(708\) | −2.66675e45 | − | 2.66675e45i | −0.669038 | − | 0.669038i | ||||
\(709\) | − | 2.09336e45i | − | 0.513458i | −0.966483 | − | 0.256729i | \(-0.917355\pi\) | ||
0.966483 | − | 0.256729i | \(-0.0826447\pi\) | |||||||
\(710\) | 7.83242e44 | − | 4.15128e45i | 0.187829 | − | 0.995515i | ||||
\(711\) | 2.30531e45 | 0.540526 | ||||||||
\(712\) | 3.76276e45 | − | 3.76276e45i | 0.862633 | − | 0.862633i | ||||
\(713\) | 3.54165e43 | + | 3.54165e43i | 0.00793914 | + | 0.00793914i | ||||
\(714\) | 1.85022e45i | 0.405556i | ||||||||
\(715\) | 2.07066e45 | + | 3.90683e44i | 0.443826 | + | 0.0837390i | ||||
\(716\) | −4.25385e45 | −0.891608 | ||||||||
\(717\) | −1.95868e45 | + | 1.95868e45i | −0.401473 | + | 0.401473i | ||||
\(718\) | 1.96013e45 | + | 1.96013e45i | 0.392911 | + | 0.392911i | ||||
\(719\) | − | 4.97562e45i | − | 0.975404i | −0.873010 | − | 0.487702i | \(-0.837835\pi\) | ||
0.873010 | − | 0.487702i | \(-0.162165\pi\) | |||||||
\(720\) | 3.08789e44 | + | 4.52408e44i | 0.0592028 | + | 0.0867382i | ||||
\(721\) | −5.58170e44 | −0.104665 | ||||||||
\(722\) | 5.79558e44 | − | 5.79558e44i | 0.106292 | − | 0.106292i | ||||
\(723\) | 2.36827e45 | + | 2.36827e45i | 0.424833 | + | 0.424833i | ||||
\(724\) | 3.64448e45i | 0.639468i | ||||||||
\(725\) | 3.95118e45 | + | 1.54601e45i | 0.678139 | + | 0.265341i | ||||
\(726\) | 2.98672e45 | 0.501428 | ||||||||
\(727\) | −5.33936e45 | + | 5.33936e45i | −0.876877 | + | 0.876877i | −0.993210 | − | 0.116334i | \(-0.962886\pi\) |
0.116334 | + | 0.993210i | \(0.462886\pi\) | |||||||
\(728\) | −7.37287e44 | − | 7.37287e44i | −0.118450 | − | 0.118450i | ||||
\(729\) | 3.27289e44i | 0.0514388i | ||||||||
\(730\) | 3.38684e44 | − | 2.31167e44i | 0.0520750 | − | 0.0355436i | ||||
\(731\) | 5.80608e45 | 0.873384 | ||||||||
\(732\) | 7.36869e45 | − | 7.36869e45i | 1.08446 | − | 1.08446i | ||||
\(733\) | 3.57603e45 | + | 3.57603e45i | 0.514917 | + | 0.514917i | 0.916029 | − | 0.401112i | \(-0.131376\pi\) |
−0.401112 | + | 0.916029i | \(0.631376\pi\) | |||||||
\(734\) | 2.56364e45i | 0.361177i | ||||||||
\(735\) | 1.23022e45 | − | 6.52032e45i | 0.169585 | − | 0.898818i | ||||
\(736\) | 1.63266e44 | 0.0220217 | ||||||||
\(737\) | −7.26961e45 | + | 7.26961e45i | −0.959470 | + | 0.959470i | ||||
\(738\) | −2.74215e45 | − | 2.74215e45i | −0.354152 | − | 0.354152i | ||||
\(739\) | 5.00870e45i | 0.633016i | 0.948590 | + | 0.316508i | \(0.102510\pi\) | ||||
−0.948590 | + | 0.316508i | \(0.897490\pi\) | |||||||
\(740\) | 8.32140e45 | + | 1.57004e45i | 1.02917 | + | 0.194179i | ||||
\(741\) | 3.04278e45 | 0.368281 | ||||||||
\(742\) | −3.30736e45 | + | 3.30736e45i | −0.391759 | + | 0.391759i | ||||
\(743\) | −5.33609e45 | − | 5.33609e45i | −0.618589 | − | 0.618589i | 0.326580 | − | 0.945169i | \(-0.394104\pi\) |
−0.945169 | + | 0.326580i | \(0.894104\pi\) | |||||||
\(744\) | − | 5.45691e45i | − | 0.619127i | ||||||
\(745\) | −2.33277e45 | − | 3.41775e45i | −0.259043 | − | 0.379525i | ||||
\(746\) | 4.47218e45 | 0.486070 | ||||||||
\(747\) | −4.33088e45 | + | 4.33088e45i | −0.460730 | + | 0.460730i | ||||
\(748\) | −6.98794e45 | − | 6.98794e45i | −0.727652 | − | 0.727652i | ||||
\(749\) | 1.71196e45i | 0.174496i | ||||||||
\(750\) | 1.55323e45 | + | 6.75686e45i | 0.154973 | + | 0.674162i | ||||
\(751\) | 1.08028e46 | 1.05511 | 0.527554 | − | 0.849522i | \(-0.323109\pi\) | ||||
0.527554 | + | 0.849522i | \(0.323109\pi\) | |||||||
\(752\) | 1.27249e43 | − | 1.27249e43i | 0.00121665 | − | 0.00121665i | ||||
\(753\) | −9.05995e45 | − | 9.05995e45i | −0.848020 | − | 0.848020i | ||||
\(754\) | 1.50527e45i | 0.137934i | ||||||||
\(755\) | 7.90744e45 | − | 5.39719e45i | 0.709389 | − | 0.484190i | ||||
\(756\) | −2.19475e45 | −0.192769 | ||||||||
\(757\) | −5.34983e45 | + | 5.34983e45i | −0.460051 | + | 0.460051i | −0.898672 | − | 0.438621i | \(-0.855467\pi\) |
0.438621 | + | 0.898672i | \(0.355467\pi\) | |||||||
\(758\) | −8.53049e45 | − | 8.53049e45i | −0.718235 | − | 0.718235i | ||||
\(759\) | 4.25838e44i | 0.0351056i | ||||||||
\(760\) | −1.83023e45 | + | 9.70041e45i | −0.147736 | + | 0.783020i | ||||
\(761\) | −1.07252e46 | −0.847715 | −0.423858 | − | 0.905729i | \(-0.639324\pi\) | ||||
−0.423858 | + | 0.905729i | \(0.639324\pi\) | |||||||
\(762\) | −6.77295e44 | + | 6.77295e44i | −0.0524201 | + | 0.0524201i | ||||
\(763\) | −2.33585e45 | − | 2.33585e45i | −0.177032 | − | 0.177032i | ||||
\(764\) | 9.18320e45i | 0.681554i | ||||||||
\(765\) | −8.77902e45 | − | 1.65638e45i | −0.638062 | − | 0.120386i | ||||
\(766\) | −6.05432e45 | −0.430928 | ||||||||
\(767\) | −3.77269e45 | + | 3.77269e45i | −0.262982 | + | 0.262982i | ||||
\(768\) | −1.09294e46 | − | 1.09294e46i | −0.746132 | − | 0.746132i | ||||
\(769\) | − | 1.99842e46i | − | 1.33618i | −0.744080 | − | 0.668091i | \(-0.767112\pi\) | ||
0.744080 | − | 0.668091i | \(-0.232888\pi\) | |||||||
\(770\) | 3.24600e45 | + | 4.75572e45i | 0.212567 | + | 0.311433i | ||||
\(771\) | −4.05473e45 | −0.260071 | ||||||||
\(772\) | −4.36851e43 | + | 4.36851e43i | −0.00274446 | + | 0.00274446i | ||||
\(773\) | 1.45259e46 | + | 1.45259e46i | 0.893863 | + | 0.893863i | 0.994884 | − | 0.101021i | \(-0.0322110\pi\) |
−0.101021 | + | 0.994884i | \(0.532211\pi\) | |||||||
\(774\) | 4.09625e45i | 0.246906i | ||||||||
\(775\) | −3.25557e45 | + | 8.32034e45i | −0.192221 | + | 0.491263i | ||||
\(776\) | −2.00566e46 | −1.16003 | ||||||||
\(777\) | 1.22831e46 | − | 1.22831e46i | 0.695938 | − | 0.695938i | ||||
\(778\) | 2.98541e45 | + | 2.98541e45i | 0.165703 | + | 0.165703i | ||||
\(779\) | 2.47007e46i | 1.34310i | ||||||||
\(780\) | 4.66500e45 | − | 3.18408e45i | 0.248507 | − | 0.169617i | ||||
\(781\) | 4.62859e46 | 2.41564 | ||||||||
\(782\) | −1.82341e44 | + | 1.82341e44i | −0.00932346 | + | 0.00932346i | ||||
\(783\) | 5.45656e45 | + | 5.45656e45i | 0.273358 | + | 0.273358i | ||||
\(784\) | − | 2.69916e45i | − | 0.132486i | ||||||
\(785\) | 5.89843e45 | − | 3.12624e46i | 0.283676 | − | 1.50351i | ||||
\(786\) | 1.76017e46 | 0.829459 | ||||||||
\(787\) | 1.06227e46 | − | 1.06227e46i | 0.490502 | − | 0.490502i | −0.417962 | − | 0.908464i | \(-0.637256\pi\) |
0.908464 | + | 0.417962i | \(0.137256\pi\) | |||||||
\(788\) | 1.43945e46 | + | 1.43945e46i | 0.651295 | + | 0.651295i | ||||
\(789\) | 3.75158e46i | 1.66334i | ||||||||
\(790\) | 1.16640e46 | + | 2.20070e45i | 0.506772 | + | 0.0956153i | ||||
\(791\) | −1.40144e46 | −0.596693 | ||||||||
\(792\) | 1.20071e46 | − | 1.20071e46i | 0.500999 | − | 0.500999i | ||||
\(793\) | −1.04246e46 | − | 1.04246e46i | −0.426273 | − | 0.426273i | ||||
\(794\) | − | 1.21885e46i | − | 0.488454i | ||||||
\(795\) | −3.47868e46 | − | 5.09663e46i | −1.36628 | − | 2.00175i | ||||
\(796\) | −2.16465e46 | −0.833256 | ||||||||
\(797\) | 2.35170e45 | − | 2.35170e45i | 0.0887256 | − | 0.0887256i | −0.661351 | − | 0.750077i | \(-0.730017\pi\) |
0.750077 | + | 0.661351i | \(0.230017\pi\) | |||||||
\(798\) | 5.87914e45 | + | 5.87914e45i | 0.217404 | + | 0.217404i | ||||
\(799\) | 2.93516e44i | 0.0106386i | ||||||||
\(800\) | 1.16740e46 | + | 2.66818e46i | 0.414743 | + | 0.947928i | ||||
\(801\) | 2.16413e46 | 0.753638 | ||||||||
\(802\) | −1.12262e45 | + | 1.12262e45i | −0.0383215 | + | 0.0383215i | ||||
\(803\) | 3.17687e45 | + | 3.17687e45i | 0.106304 | + | 0.106304i | ||||
\(804\) | 2.75562e46i | 0.903906i | ||||||||
\(805\) | −2.84952e44 | + | 1.94493e44i | −0.00916300 | + | 0.00625416i | ||||
\(806\) | −3.16977e45 | −0.0999234 | ||||||||
\(807\) | −3.45123e46 | + | 3.45123e46i | −1.06659 | + | 1.06659i | ||||
\(808\) | 4.80657e45 | + | 4.80657e45i | 0.145631 | + | 0.145631i | ||||
\(809\) | − | 5.77586e46i | − | 1.71570i | −0.513903 | − | 0.857849i | \(-0.671801\pi\) | ||
0.513903 | − | 0.857849i | \(-0.328199\pi\) | |||||||
\(810\) | −4.36213e45 | + | 2.31198e46i | −0.127039 | + | 0.673323i | ||||
\(811\) | −5.81027e46 | −1.65906 | −0.829531 | − | 0.558460i | \(-0.811392\pi\) | ||||
−0.829531 | + | 0.558460i | \(0.811392\pi\) | |||||||
\(812\) | 6.67846e45 | − | 6.67846e45i | 0.186973 | − | 0.186973i | ||||
\(813\) | 5.14829e46 | + | 5.14829e46i | 1.41324 | + | 1.41324i | ||||
\(814\) | − | 4.04059e46i | − | 1.08756i | ||||||
\(815\) | −1.98425e46 | − | 3.74378e45i | −0.523690 | − | 0.0988073i | ||||
\(816\) | −9.92934e45 | −0.256967 | ||||||||
\(817\) | 1.84491e46 | − | 1.84491e46i | 0.468189 | − | 0.468189i | ||||
\(818\) | −1.67555e46 | − | 1.67555e46i | −0.416970 | − | 0.416970i | ||||
\(819\) | − | 4.24047e45i | − | 0.103484i | ||||||
\(820\) | 2.58477e46 | + | 3.78696e46i | 0.618587 | + | 0.906293i | ||||
\(821\) | 5.18726e46 | 1.21744 | 0.608720 | − | 0.793385i | \(-0.291683\pi\) | ||||
0.608720 | + | 0.793385i | \(0.291683\pi\) | |||||||
\(822\) | 1.75193e46 | − | 1.75193e46i | 0.403243 | − | 0.403243i | ||||
\(823\) | −4.00836e46 | − | 4.00836e46i | −0.904836 | − | 0.904836i | 0.0910136 | − | 0.995850i | \(-0.470989\pi\) |
−0.995850 | + | 0.0910136i | \(0.970989\pi\) | |||||||
\(824\) | 8.47559e45i | 0.187644i | ||||||||
\(825\) | −6.95928e46 | + | 3.04487e46i | −1.51113 | + | 0.661158i | ||||
\(826\) | −1.45789e46 | −0.310487 | ||||||||
\(827\) | 7.27694e45 | − | 7.27694e45i | 0.152006 | − | 0.152006i | −0.627007 | − | 0.779013i | \(-0.715720\pi\) |
0.779013 | + | 0.627007i | \(0.215720\pi\) | |||||||
\(828\) | 2.95399e44 | + | 2.95399e44i | 0.00605234 | + | 0.00605234i | ||||
\(829\) | − | 7.48241e46i | − | 1.50373i | −0.659319 | − | 0.751863i | \(-0.729155\pi\) | ||
0.659319 | − | 0.751863i | \(-0.270845\pi\) | |||||||
\(830\) | −2.60468e46 | + | 1.77782e46i | −0.513459 | + | 0.350459i | ||||
\(831\) | −4.17640e46 | −0.807580 | ||||||||
\(832\) | −4.97403e45 | + | 4.97403e45i | −0.0943485 | + | 0.0943485i | ||||
\(833\) | 3.11299e46 | + | 3.11299e46i | 0.579238 | + | 0.579238i | ||||
\(834\) | 3.11844e46i | 0.569221i | ||||||||
\(835\) | 4.09276e44 | − | 2.16921e45i | 0.00732879 | − | 0.0388435i | ||||
\(836\) | −4.44090e46 | −0.780136 | ||||||||
\(837\) | −1.14904e46 | + | 1.14904e46i | −0.198028 | + | 0.198028i | ||||
\(838\) | −3.28679e45 | − | 3.28679e45i | −0.0555736 | − | 0.0555736i | ||||
\(839\) | 4.40031e45i | 0.0729948i | 0.999334 | + | 0.0364974i | \(0.0116201\pi\) | ||||
−0.999334 | + | 0.0364974i | \(0.988380\pi\) | |||||||
\(840\) | 3.69359e46 | + | 6.96889e45i | 0.601147 | + | 0.113421i | ||||
\(841\) | 2.94155e46 | 0.469721 | ||||||||
\(842\) | −2.69100e46 | + | 2.69100e46i | −0.421619 | + | 0.421619i | ||||
\(843\) | 5.29994e46 | + | 5.29994e46i | 0.814760 | + | 0.814760i | ||||
\(844\) | − | 5.73830e46i | − | 0.865574i | ||||||
\(845\) | 3.35837e46 | + | 4.92037e46i | 0.497075 | + | 0.728266i | ||||
\(846\) | −2.07079e44 | −0.00300753 | ||||||||
\(847\) | −1.87467e46 | + | 1.87467e46i | −0.267172 | + | 0.267172i | ||||
\(848\) | −1.77492e46 | − | 1.77492e46i | −0.248225 | − | 0.248225i | ||||
\(849\) | 2.78157e45i | 0.0381739i | ||||||||
\(850\) | −4.28371e46 | − | 1.67613e46i | −0.576923 | − | 0.225738i | ||||
\(851\) | 2.42103e45 | 0.0319983 | ||||||||
\(852\) | 8.77259e46 | − | 8.77259e46i | 1.13787 | − | 1.13787i | ||||
\(853\) | −3.53006e45 | − | 3.53006e45i | −0.0449363 | − | 0.0449363i | 0.684282 | − | 0.729218i | \(-0.260116\pi\) |
−0.729218 | + | 0.684282i | \(0.760116\pi\) | |||||||
\(854\) | − | 4.02839e46i | − | 0.503276i | ||||||
\(855\) | −3.31589e46 | + | 2.26325e46i | −0.406577 | + | 0.277507i | ||||
\(856\) | 2.59954e46 | 0.312836 | ||||||||
\(857\) | 2.43894e45 | − | 2.43894e45i | 0.0288076 | − | 0.0288076i | −0.692556 | − | 0.721364i | \(-0.743516\pi\) |
0.721364 | + | 0.692556i | \(0.243516\pi\) | |||||||
\(858\) | −1.90562e46 | − | 1.90562e46i | −0.220923 | − | 0.220923i | ||||
\(859\) | − | 9.26407e46i | − | 1.05417i | −0.849812 | − | 0.527086i | \(-0.823285\pi\) | ||
0.849812 | − | 0.527086i | \(-0.176715\pi\) | |||||||
\(860\) | 8.97919e45 | − | 4.75908e46i | 0.100291 | − | 0.531554i | ||||
\(861\) | 9.40520e46 | 1.03114 | ||||||||
\(862\) | 4.43657e46 | − | 4.43657e46i | 0.477453 | − | 0.477453i | ||||
\(863\) | 1.04331e47 | + | 1.04331e47i | 1.10215 | + | 1.10215i | 0.994151 | + | 0.107998i | \(0.0344439\pi\) |
0.107998 | + | 0.994151i | \(0.465556\pi\) | |||||||
\(864\) | 5.29692e46i | 0.549292i | ||||||||
\(865\) | 1.15861e47 | + | 2.18601e46i | 1.17945 | + | 0.222533i | ||||
\(866\) | −1.72376e46 | −0.172263 | ||||||||
\(867\) | 2.39962e46 | − | 2.39962e46i | 0.235417 | − | 0.235417i | ||||
\(868\) | 1.40634e46 | + | 1.40634e46i | 0.135449 | + | 0.135449i | ||||
\(869\) | 1.30051e47i | 1.22970i | ||||||||
\(870\) | −3.05908e46 | − | 4.48187e46i | −0.283977 | − | 0.416055i | ||||
\(871\) | 3.89842e46 | 0.355302 | ||||||||
\(872\) | −3.54689e46 | + | 3.54689e46i | −0.317383 | + | 0.317383i | ||||
\(873\) | −5.76772e46 | − | 5.76772e46i | −0.506730 | − | 0.506730i | ||||
\(874\) | 1.15880e45i | 0.00999594i | ||||||||
\(875\) | −5.21599e46 | − | 3.26616e46i | −0.441782 | − | 0.276636i | ||||
\(876\) | 1.20423e46 | 0.100148 | ||||||||
\(877\) | −1.55142e47 | + | 1.55142e47i | −1.26688 | + | 1.26688i | −0.319195 | + | 0.947689i | \(0.603412\pi\) |
−0.947689 | + | 0.319195i | \(0.896588\pi\) | |||||||
\(878\) | 4.80069e46 | + | 4.80069e46i | 0.384939 | + | 0.384939i | ||||
\(879\) | 1.01317e47i | 0.797742i | ||||||||
\(880\) | −2.55220e46 | + | 1.74199e46i | −0.197329 | + | 0.134686i | ||||
\(881\) | −1.72836e47 | −1.31226 | −0.656129 | − | 0.754649i | \(-0.727807\pi\) | ||||
−0.656129 | + | 0.754649i | \(0.727807\pi\) | |||||||
\(882\) | −2.19625e46 | + | 2.19625e46i | −0.163751 | + | 0.163751i | ||||
\(883\) | 4.39802e45 | + | 4.39802e45i | 0.0322022 | + | 0.0322022i | 0.723025 | − | 0.690822i | \(-0.242751\pi\) |
−0.690822 | + | 0.723025i | \(0.742751\pi\) | |||||||
\(884\) | 3.74737e46i | 0.269458i | ||||||||
\(885\) | 3.56597e46 | − | 1.89001e47i | 0.251817 | − | 1.33466i | ||||
\(886\) | −5.46521e46 | −0.379025 | ||||||||
\(887\) | 2.61672e46 | − | 2.61672e46i | 0.178229 | − | 0.178229i | −0.612354 | − | 0.790583i | \(-0.709777\pi\) |
0.790583 | + | 0.612354i | \(0.209777\pi\) | |||||||
\(888\) | −1.86513e47 | − | 1.86513e47i | −1.24768 | − | 1.24768i | ||||
\(889\) | − | 8.50235e45i | − | 0.0558613i | ||||||
\(890\) | 1.09496e47 | + | 2.06592e46i | 0.706577 | + | 0.133313i | ||||
\(891\) | −2.57781e47 | −1.63383 | ||||||||
\(892\) | 8.70797e46 | − | 8.70797e46i | 0.542100 | − | 0.542100i | ||||
\(893\) | 9.32659e44 | + | 9.32659e44i | 0.00570295 | + | 0.00570295i | ||||
\(894\) | 5.29217e46i | 0.317858i | ||||||||
\(895\) | −1.22300e47 | − | 1.79183e47i | −0.721538 | − | 1.05713i | ||||
\(896\) | 7.38427e46 | 0.427937 | ||||||||
\(897\) | 1.14181e45 | − | 1.14181e45i | 0.00649999 | − | 0.00649999i | ||||
\(898\) | 6.03557e46 | + | 6.03557e46i | 0.337518 | + | 0.337518i | ||||
\(899\) | − | 6.99285e46i | − | 0.384149i | ||||||
\(900\) | −2.71538e46 | + | 6.93975e46i | −0.146538 | + | 0.374510i | ||||
\(901\) | 4.09410e47 | 2.17051 | ||||||||
\(902\) | 1.54695e47 | − | 1.54695e47i | 0.805695 | − | 0.805695i | ||||
\(903\) | −7.02479e46 | − | 7.02479e46i | −0.359442 | − | 0.359442i | ||||
\(904\) | 2.12803e47i | 1.06975i | ||||||||
\(905\) | −1.53515e47 | + | 1.04781e47i | −0.758180 | + | 0.517493i | ||||
\(906\) | −1.22442e47 | −0.594126 | ||||||||
\(907\) | −2.13404e47 | + | 2.13404e47i | −1.01739 | + | 1.01739i | −0.0175404 | + | 0.999846i | \(0.505584\pi\) |
−0.999846 | + | 0.0175404i | \(0.994416\pi\) | |||||||
\(908\) | −5.45827e46 | − | 5.45827e46i | −0.255671 | − | 0.255671i | ||||
\(909\) | 2.76447e46i | 0.127230i | ||||||||
\(910\) | 4.04804e45 | − | 2.14551e46i | 0.0183055 | − | 0.0970216i | ||||
\(911\) | −9.63664e46 | −0.428185 | −0.214092 | − | 0.976813i | \(-0.568679\pi\) | ||||
−0.214092 | + | 0.976813i | \(0.568679\pi\) | |||||||
\(912\) | −3.15509e46 | + | 3.15509e46i | −0.137751 | + | 0.137751i | ||||
\(913\) | −2.44320e47 | − | 2.44320e47i | −1.04816 | − | 1.04816i | ||||
\(914\) | 2.73951e46i | 0.115487i | ||||||||
\(915\) | 5.22241e47 | + | 9.85337e46i | 2.16338 | + | 0.408176i | ||||
\(916\) | 1.58880e47 | 0.646756 | ||||||||
\(917\) | −1.10481e47 | + | 1.10481e47i | −0.441954 | + | 0.441954i | ||||
\(918\) | −5.91579e46 | − | 5.91579e46i | −0.232557 | − | 0.232557i | ||||
\(919\) | 1.63060e47i | 0.629941i | 0.949101 | + | 0.314971i | \(0.101995\pi\) | ||||
−0.949101 | + | 0.314971i | \(0.898005\pi\) | |||||||
\(920\) | 2.95329e45 | + | 4.32688e45i | 0.0112125 | + | 0.0164274i | ||||
\(921\) | 5.39592e47 | 2.01331 | ||||||||
\(922\) | 1.04515e47 | − | 1.04515e47i | 0.383250 | − | 0.383250i | ||||
\(923\) | −1.24107e47 | − | 1.24107e47i | −0.447269 | − | 0.447269i | ||||
\(924\) | 1.69095e47i | 0.598933i | ||||||||
\(925\) | 1.73110e47 | + | 3.95657e47i | 0.602636 | + | 1.37737i | ||||
\(926\) | 7.89781e46 | 0.270228 | ||||||||
\(927\) | −2.43735e46 | + | 2.43735e46i | −0.0819675 | + | 0.0819675i | ||||
\(928\) | −1.61181e47 | − | 1.61181e47i | −0.532778 | − | 0.532778i | ||||
\(929\) | − | 2.28965e47i | − | 0.743906i | −0.928252 | − | 0.371953i | \(-0.878688\pi\) | ||
0.928252 | − | 0.371953i | \(-0.121312\pi\) | |||||||
\(930\) | 9.43785e46 | − | 6.44177e46i | 0.301402 | − | 0.205721i | ||||
\(931\) | 1.97833e47 | 0.621017 | ||||||||
\(932\) | −5.36864e46 | + | 5.36864e46i | −0.165657 | + | 0.165657i | ||||
\(933\) | 2.19455e47 | + | 2.19455e47i | 0.665640 | + | 0.665640i | ||||
\(934\) | 7.91335e46i | 0.235945i | ||||||||
\(935\) | 9.34424e46 | − | 4.95256e47i | 0.273879 | − | 1.45159i | ||||
\(936\) | −6.43898e46 | −0.185525 | ||||||||
\(937\) | −5.70765e46 | + | 5.70765e46i | −0.161668 | + | 0.161668i | −0.783305 | − | 0.621637i | \(-0.786468\pi\) |
0.621637 | + | 0.783305i | \(0.286468\pi\) | |||||||
\(938\) | 7.53237e46 | + | 7.53237e46i | 0.209742 | + | 0.209742i | ||||
\(939\) | − | 6.68223e47i | − | 1.82924i | ||||||
\(940\) | 2.40586e45 | + | 4.53927e44i | 0.00647479 | + | 0.00122163i | ||||
\(941\) | 1.76199e47 | 0.466198 | 0.233099 | − | 0.972453i | \(-0.425113\pi\) | ||||
0.233099 | + | 0.972453i | \(0.425113\pi\) | |||||||
\(942\) | −2.87706e47 | + | 2.87706e47i | −0.748401 | + | 0.748401i | ||||
\(943\) | 9.26895e45 | + | 9.26895e45i | 0.0237052 | + | 0.0237052i | ||||
\(944\) | − | 7.82388e46i | − | 0.196730i | ||||||
\(945\) | −6.31002e46 | − | 9.24484e46i | −0.155999 | − | 0.228555i | ||||
\(946\) | −2.31084e47 | −0.561710 | ||||||||
\(947\) | 2.42014e46 | − | 2.42014e46i | 0.0578417 | − | 0.0578417i | −0.677594 | − | 0.735436i | \(-0.736977\pi\) |
0.735436 | + | 0.677594i | \(0.236977\pi\) | |||||||
\(948\) | 2.46486e47 | + | 2.46486e47i | 0.579241 | + | 0.579241i | ||||
\(949\) | − | 1.70363e46i | − | 0.0393656i | ||||||
\(950\) | −1.89376e47 | + | 8.28572e46i | −0.430277 | + | 0.188258i | ||||
\(951\) | −7.36426e47 | −1.64528 | ||||||||
\(952\) | −1.76342e47 | + | 1.76342e47i | −0.387405 | + | 0.387405i | ||||
\(953\) | −2.51593e47 | − | 2.51593e47i | −0.543517 | − | 0.543517i | 0.381041 | − | 0.924558i | \(-0.375566\pi\) |
−0.924558 | + | 0.381041i | \(0.875566\pi\) | |||||||
\(954\) | 2.88843e47i | 0.613603i | ||||||||
\(955\) | −3.86819e47 | + | 2.64022e47i | −0.808079 | + | 0.551551i | ||||
\(956\) | −1.53299e47 | −0.314930 | ||||||||
\(957\) | 4.20400e47 | − | 4.20400e47i | 0.849321 | − | 0.849321i | ||||
\(958\) | 1.86993e47 | + | 1.86993e47i | 0.371516 | + | 0.371516i | ||||
\(959\) | 2.19926e47i | 0.429714i | ||||||||
\(960\) | 4.70148e46 | − | 2.49184e47i | 0.0903431 | − | 0.478829i | ||||
\(961\) | −3.81890e47 | −0.721712 | ||||||||
\(962\) | −1.08341e47 | + | 1.08341e47i | −0.201368 | + | 0.201368i | ||||
\(963\) | 7.47557e46 | + | 7.47557e46i | 0.136654 | + | 0.136654i | ||||
\(964\) | 1.85357e47i | 0.333255i | ||||||||
\(965\) | −3.09609e45 | − | 5.84155e44i | −0.00547491 | − | 0.00103298i | ||||
\(966\) | 4.41230e45 | 0.00767417 | ||||||||
\(967\) | −4.34892e46 | + | 4.34892e46i | −0.0743975 | + | 0.0743975i | −0.743326 | − | 0.668929i | \(-0.766753\pi\) |
0.668929 | + | 0.743326i | \(0.266753\pi\) | |||||||
\(968\) | 2.84661e47 | + | 2.84661e47i | 0.478986 | + | 0.478986i | ||||
\(969\) | − | 7.27764e47i | − | 1.20451i | ||||||
\(970\) | −2.36764e47 | − | 3.46884e47i | −0.385450 | − | 0.564724i | ||||
\(971\) | −3.34580e47 | −0.535786 | −0.267893 | − | 0.963449i | \(-0.586327\pi\) | ||||
−0.267893 | + | 0.963449i | \(0.586327\pi\) | |||||||
\(972\) | −3.22562e47 | + | 3.22562e47i | −0.508105 | + | 0.508105i | ||||
\(973\) | −1.95735e47 | − | 1.95735e47i | −0.303294 | − | 0.303294i | ||||
\(974\) | 1.08235e47i | 0.164978i | ||||||||
\(975\) | 2.68242e47 | + | 1.04958e47i | 0.402210 | + | 0.157376i | ||||
\(976\) | 2.16187e47 | 0.318884 | ||||||||
\(977\) | 7.67559e47 | − | 7.67559e47i | 1.11378 | − | 1.11378i | 0.121144 | − | 0.992635i | \(-0.461344\pi\) |
0.992635 | − | 0.121144i | \(-0.0386561\pi\) | |||||||
\(978\) | 1.82609e47 | + | 1.82609e47i | 0.260676 | + | 0.260676i | ||||
\(979\) | 1.22086e48i | 1.71453i | ||||||||
\(980\) | 3.03305e47 | − | 2.07020e47i | 0.419047 | − | 0.286019i | ||||
\(981\) | −2.03997e47 | −0.277281 | ||||||||
\(982\) | 2.07217e47 | − | 2.07217e47i | 0.277104 | − | 0.277104i | ||||
\(983\) | 1.98440e47 | + | 1.98440e47i | 0.261080 | + | 0.261080i | 0.825493 | − | 0.564413i | \(-0.190897\pi\) |
−0.564413 | + | 0.825493i | \(0.690897\pi\) | |||||||
\(984\) | − | 1.42814e48i | − | 1.84863i | ||||||
\(985\) | −1.92483e47 | + | 1.02018e48i | −0.245139 | + | 1.29927i | ||||
\(986\) | 3.60026e47 | 0.451131 | ||||||||
\(987\) | 3.55126e45 | − | 3.55126e45i | 0.00437832 | − | 0.00437832i | ||||
\(988\) | 1.19074e47 | + | 1.19074e47i | 0.144446 | + | 0.144446i | ||||
\(989\) | − | 1.38460e46i | − | 0.0165267i | ||||||
\(990\) | 3.49409e47 | + | 6.59247e46i | 0.410365 | + | 0.0774256i | ||||
\(991\) | 1.63311e46 | 0.0188729 | 0.00943643 | − | 0.999955i | \(-0.496996\pi\) | ||||
0.00943643 | + | 0.999955i | \(0.496996\pi\) | |||||||
\(992\) | 3.39413e47 | − | 3.39413e47i | 0.385960 | − | 0.385960i | ||||
\(993\) | 1.61356e47 | + | 1.61356e47i | 0.180550 | + | 0.180550i | ||||
\(994\) | − | 4.79590e47i | − | 0.528065i | ||||||
\(995\) | −6.22347e47 | − | 9.11803e47i | −0.674316 | − | 0.987943i | ||||
\(996\) | −9.26122e47 | −0.987459 | ||||||||
\(997\) | 1.60500e47 | − | 1.60500e47i | 0.168404 | − | 0.168404i | −0.617874 | − | 0.786277i | \(-0.712006\pi\) |
0.786277 | + | 0.617874i | \(0.212006\pi\) | |||||||
\(998\) | 3.50584e47 | + | 3.50584e47i | 0.361995 | + | 0.361995i | ||||
\(999\) | 7.85466e47i | 0.798141i |
(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 | 5.33.c.a.3.10 | yes | 30 | |
5.2 | odd | 4 | inner | 5.33.c.a.2.10 | ✓ | 30 | |
5.3 | odd | 4 | 25.33.c.b.7.6 | 30 | |||
5.4 | even | 2 | 25.33.c.b.18.6 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.33.c.a.2.10 | ✓ | 30 | 5.2 | odd | 4 | inner | |
5.33.c.a.3.10 | yes | 30 | 1.1 | even | 1 | trivial | |
25.33.c.b.7.6 | 30 | 5.3 | odd | 4 | |||
25.33.c.b.18.6 | 30 | 5.4 | even | 2 |