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 | 2.4 | ||
Character | \(\chi\) | \(=\) | 5.2 |
Dual form | 5.33.c.a.3.4 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −42029.2 | − | 42029.2i | −0.641314 | − | 0.641314i | 0.309564 | − | 0.950878i | \(-0.399817\pi\) |
−0.950878 | + | 0.309564i | \(0.899817\pi\) | |||||||
\(3\) | −2.23370e7 | + | 2.23370e7i | −0.518900 | + | 0.518900i | −0.917239 | − | 0.398338i | \(-0.869587\pi\) |
0.398338 | + | 0.917239i | \(0.369587\pi\) | |||||||
\(4\) | − | 7.62067e8i | − | 0.177433i | ||||||
\(5\) | −7.62027e10 | + | 1.32198e11i | −0.499402 | + | 0.866370i | ||||
\(6\) | 1.87761e12 | 0.665556 | ||||||||
\(7\) | −2.39791e13 | − | 2.39791e13i | −0.721547 | − | 0.721547i | 0.247373 | − | 0.968920i | \(-0.420433\pi\) |
−0.968920 | + | 0.247373i | \(0.920433\pi\) | |||||||
\(8\) | −2.12543e14 | + | 2.12543e14i | −0.755104 | + | 0.755104i | ||||
\(9\) | 8.55140e14i | 0.461485i | ||||||||
\(10\) | 8.75889e15 | − | 2.35342e15i | 0.875889 | − | 0.235342i | ||||
\(11\) | −3.17226e16 | −0.690377 | −0.345188 | − | 0.938533i | \(-0.612185\pi\) | ||||
−0.345188 | + | 0.938533i | \(0.612185\pi\) | |||||||
\(12\) | 1.70223e16 | + | 1.70223e16i | 0.0920698 | + | 0.0920698i | ||||
\(13\) | −5.32549e17 | + | 5.32549e17i | −0.800324 | + | 0.800324i | −0.983146 | − | 0.182822i | \(-0.941477\pi\) |
0.182822 | + | 0.983146i | \(0.441477\pi\) | |||||||
\(14\) | 2.01564e18i | 0.925476i | ||||||||
\(15\) | −1.25076e18 | − | 4.65503e18i | −0.190420 | − | 0.708700i | ||||
\(16\) | 1.45929e19 | 0.791085 | ||||||||
\(17\) | 4.10053e19 | + | 4.10053e19i | 0.842669 | + | 0.842669i | 0.989205 | − | 0.146536i | \(-0.0468124\pi\) |
−0.146536 | + | 0.989205i | \(0.546812\pi\) | |||||||
\(18\) | 3.59408e19 | − | 3.59408e19i | 0.295957 | − | 0.295957i | ||||
\(19\) | 2.22048e20i | 0.769821i | 0.922954 | + | 0.384911i | \(0.125768\pi\) | ||||
−0.922954 | + | 0.384911i | \(0.874232\pi\) | |||||||
\(20\) | 1.00743e20 | + | 5.80716e19i | 0.153722 | + | 0.0886102i | ||||
\(21\) | 1.07124e21 | 0.748822 | ||||||||
\(22\) | 1.33328e21 | + | 1.33328e21i | 0.442748 | + | 0.442748i | ||||
\(23\) | −6.22444e21 | + | 6.22444e21i | −1.01497 | + | 1.01497i | −0.0150872 | + | 0.999886i | \(0.504803\pi\) |
−0.999886 | + | 0.0150872i | \(0.995197\pi\) | |||||||
\(24\) | − | 9.49513e21i | − | 0.783648i | ||||||
\(25\) | −1.16694e22 | − | 2.01476e22i | −0.501195 | − | 0.865334i | ||||
\(26\) | 4.47652e22 | 1.02652 | ||||||||
\(27\) | −6.04921e22 | − | 6.04921e22i | −0.758365 | − | 0.758365i | ||||
\(28\) | −1.82737e22 | + | 1.82737e22i | −0.128026 | + | 0.128026i | ||||
\(29\) | − | 3.25507e23i | − | 1.30075i | −0.759615 | − | 0.650373i | \(-0.774613\pi\) | ||
0.759615 | − | 0.650373i | \(-0.225387\pi\) | |||||||
\(30\) | −1.43079e23 | + | 2.48215e23i | −0.332380 | + | 0.576618i | ||||
\(31\) | 1.21168e22 | 0.0166572 | 0.00832861 | − | 0.999965i | \(-0.497349\pi\) | ||||
0.00832861 | + | 0.999965i | \(0.497349\pi\) | |||||||
\(32\) | 2.99536e23 | + | 2.99536e23i | 0.247770 | + | 0.247770i | ||||
\(33\) | 7.08587e23 | − | 7.08587e23i | 0.358237 | − | 0.358237i | ||||
\(34\) | − | 3.44684e24i | − | 1.08083i | ||||||
\(35\) | 4.99726e24 | − | 1.34271e24i | 0.985469 | − | 0.264785i | ||||
\(36\) | 6.51674e23 | 0.0818824 | ||||||||
\(37\) | −1.53437e25 | − | 1.53437e25i | −1.24366 | − | 1.24366i | −0.958472 | − | 0.285187i | \(-0.907944\pi\) |
−0.285187 | − | 0.958472i | \(-0.592056\pi\) | |||||||
\(38\) | 9.33250e24 | − | 9.33250e24i | 0.493697 | − | 0.493697i | ||||
\(39\) | − | 2.37911e25i | − | 0.830577i | ||||||
\(40\) | −1.19013e25 | − | 4.42940e25i | −0.277099 | − | 1.03130i | ||||
\(41\) | −2.70283e25 | −0.423913 | −0.211957 | − | 0.977279i | \(-0.567984\pi\) | ||||
−0.211957 | + | 0.977279i | \(0.567984\pi\) | |||||||
\(42\) | −4.50234e25 | − | 4.50234e25i | −0.480230 | − | 0.480230i | ||||
\(43\) | 9.54673e25 | − | 9.54673e25i | 0.698811 | − | 0.698811i | −0.265343 | − | 0.964154i | \(-0.585485\pi\) |
0.964154 | + | 0.265343i | \(0.0854853\pi\) | |||||||
\(44\) | 2.41748e25i | 0.122495i | ||||||||
\(45\) | −1.13048e26 | − | 6.51640e25i | −0.399817 | − | 0.230466i | ||||
\(46\) | 5.23216e26 | 1.30183 | ||||||||
\(47\) | 2.53838e26 | + | 2.53838e26i | 0.447704 | + | 0.447704i | 0.894591 | − | 0.446887i | \(-0.147467\pi\) |
−0.446887 | + | 0.894591i | \(0.647467\pi\) | |||||||
\(48\) | −3.25962e26 | + | 3.25962e26i | −0.410494 | + | 0.410494i | ||||
\(49\) | 4.55683e25i | 0.0412597i | ||||||||
\(50\) | −3.56335e26 | + | 1.33724e27i | −0.233528 | + | 0.876375i | ||||
\(51\) | −1.83187e27 | −0.874523 | ||||||||
\(52\) | 4.05838e26 | + | 4.05838e26i | 0.142004 | + | 0.142004i | ||||
\(53\) | −1.49223e27 | + | 1.49223e27i | −0.384966 | + | 0.384966i | −0.872888 | − | 0.487921i | \(-0.837755\pi\) |
0.487921 | + | 0.872888i | \(0.337755\pi\) | |||||||
\(54\) | 5.08486e27i | 0.972700i | ||||||||
\(55\) | 2.41735e27 | − | 4.19366e27i | 0.344776 | − | 0.598122i | ||||
\(56\) | 1.01932e28 | 1.08969 | ||||||||
\(57\) | −4.95988e27 | − | 4.95988e27i | −0.399460 | − | 0.399460i | ||||
\(58\) | −1.36808e28 | + | 1.36808e28i | −0.834186 | + | 0.834186i | ||||
\(59\) | 2.48663e28i | 1.15340i | 0.816958 | + | 0.576698i | \(0.195659\pi\) | ||||
−0.816958 | + | 0.576698i | \(0.804341\pi\) | |||||||
\(60\) | −3.54744e27 | + | 9.53160e26i | −0.125746 | + | 0.0337867i | ||||
\(61\) | 3.17251e28 | 0.863229 | 0.431615 | − | 0.902058i | \(-0.357944\pi\) | ||||
0.431615 | + | 0.902058i | \(0.357944\pi\) | |||||||
\(62\) | −5.09261e26 | − | 5.09261e26i | −0.0106825 | − | 0.0106825i | ||||
\(63\) | 2.05055e28 | − | 2.05055e28i | 0.332983 | − | 0.332983i | ||||
\(64\) | − | 8.78547e28i | − | 1.10888i | ||||||
\(65\) | −2.98200e28 | − | 1.10983e29i | −0.293694 | − | 1.09306i | ||||
\(66\) | −5.95627e28 | −0.459485 | ||||||||
\(67\) | −3.16482e27 | − | 3.16482e27i | −0.0191934 | − | 0.0191934i | 0.697445 | − | 0.716638i | \(-0.254320\pi\) |
−0.716638 | + | 0.697445i | \(0.754320\pi\) | |||||||
\(68\) | 3.12488e28 | − | 3.12488e28i | 0.149517 | − | 0.149517i | ||||
\(69\) | − | 2.78070e29i | − | 1.05334i | ||||||
\(70\) | −2.66463e29 | − | 1.53598e29i | −0.801805 | − | 0.462185i | ||||
\(71\) | 4.69621e29 | 1.12620 | 0.563098 | − | 0.826390i | \(-0.309609\pi\) | ||||
0.563098 | + | 0.826390i | \(0.309609\pi\) | |||||||
\(72\) | −1.81754e29 | − | 1.81754e29i | −0.348469 | − | 0.348469i | ||||
\(73\) | −3.04177e29 | + | 3.04177e29i | −0.467692 | + | 0.467692i | −0.901166 | − | 0.433474i | \(-0.857288\pi\) |
0.433474 | + | 0.901166i | \(0.357288\pi\) | |||||||
\(74\) | 1.28976e30i | 1.59515i | ||||||||
\(75\) | 7.10695e29 | + | 1.89379e29i | 0.709093 | + | 0.188952i | ||||
\(76\) | 1.69216e29 | 0.136591 | ||||||||
\(77\) | 7.60681e29 | + | 7.60681e29i | 0.498139 | + | 0.498139i | ||||
\(78\) | −9.99918e29 | + | 9.99918e29i | −0.532661 | + | 0.532661i | ||||
\(79\) | − | 1.79248e30i | − | 0.778791i | −0.921071 | − | 0.389395i | \(-0.872684\pi\) | ||
0.921071 | − | 0.389395i | \(-0.127316\pi\) | |||||||
\(80\) | −1.11202e30 | + | 1.92915e30i | −0.395070 | + | 0.685373i | ||||
\(81\) | 1.11783e30 | 0.325547 | ||||||||
\(82\) | 1.13598e30 | + | 1.13598e30i | 0.271861 | + | 0.271861i | ||||
\(83\) | −4.68812e29 | + | 4.68812e29i | −0.0924165 | + | 0.0924165i | −0.751804 | − | 0.659387i | \(-0.770816\pi\) |
0.659387 | + | 0.751804i | \(0.270816\pi\) | |||||||
\(84\) | − | 8.16358e29i | − | 0.132865i | ||||||
\(85\) | −8.54552e30 | + | 2.29609e30i | −1.15089 | + | 0.309233i | ||||
\(86\) | −8.02482e30 | −0.896314 | ||||||||
\(87\) | 7.27084e30 | + | 7.27084e30i | 0.674957 | + | 0.674957i | ||||
\(88\) | 6.74242e30 | − | 6.74242e30i | 0.521306 | − | 0.521306i | ||||
\(89\) | − | 2.97738e31i | − | 1.92130i | −0.277765 | − | 0.960649i | \(-0.589594\pi\) | ||
0.277765 | − | 0.960649i | \(-0.410406\pi\) | |||||||
\(90\) | 2.01250e30 | + | 7.49008e30i | 0.108607 | + | 0.404209i | ||||
\(91\) | 2.55401e31 | 1.15494 | ||||||||
\(92\) | 4.74344e30 | + | 4.74344e30i | 0.180089 | + | 0.180089i | ||||
\(93\) | −2.70654e29 | + | 2.70654e29i | −0.00864344 | + | 0.00864344i | ||||
\(94\) | − | 2.13372e31i | − | 0.574237i | ||||||
\(95\) | −2.93543e31 | − | 1.69207e31i | −0.666950 | − | 0.384450i | ||||
\(96\) | −1.33814e31 | −0.257136 | ||||||||
\(97\) | −1.89647e31 | − | 1.89647e31i | −0.308743 | − | 0.308743i | 0.535679 | − | 0.844422i | \(-0.320056\pi\) |
−0.844422 | + | 0.535679i | \(0.820056\pi\) | |||||||
\(98\) | 1.91520e30 | − | 1.91520e30i | 0.0264604 | − | 0.0264604i | ||||
\(99\) | − | 2.71273e31i | − | 0.318598i | ||||||
\(100\) | −1.53538e31 | + | 8.89283e30i | −0.153538 | + | 0.0889283i | ||||
\(101\) | 2.42812e31 | 0.207075 | 0.103538 | − | 0.994626i | \(-0.466984\pi\) | ||||
0.103538 | + | 0.994626i | \(0.466984\pi\) | |||||||
\(102\) | 7.69919e31 | + | 7.69919e31i | 0.560844 | + | 0.560844i | ||||
\(103\) | −1.53297e32 | + | 1.53297e32i | −0.955297 | + | 0.955297i | −0.999043 | − | 0.0437452i | \(-0.986071\pi\) |
0.0437452 | + | 0.999043i | \(0.486071\pi\) | |||||||
\(104\) | − | 2.26379e32i | − | 1.20866i | ||||||
\(105\) | −8.16315e31 | + | 1.41616e32i | −0.373963 | + | 0.648757i | ||||
\(106\) | 1.25434e32 | 0.493768 | ||||||||
\(107\) | 3.13053e32 | + | 3.13053e32i | 1.06042 | + | 1.06042i | 0.998053 | + | 0.0623638i | \(0.0198639\pi\) |
0.0623638 | + | 0.998053i | \(0.480136\pi\) | |||||||
\(108\) | −4.60990e31 | + | 4.60990e31i | −0.134559 | + | 0.134559i | ||||
\(109\) | 4.40291e32i | 1.10896i | 0.832197 | + | 0.554480i | \(0.187083\pi\) | ||||
−0.832197 | + | 0.554480i | \(0.812917\pi\) | |||||||
\(110\) | −2.77855e32 | + | 7.46566e31i | −0.604694 | + | 0.162475i | ||||
\(111\) | 6.85461e32 | 1.29067 | ||||||||
\(112\) | −3.49926e32 | − | 3.49926e32i | −0.570805 | − | 0.570805i | ||||
\(113\) | −3.62769e32 | + | 3.62769e32i | −0.513304 | + | 0.513304i | −0.915537 | − | 0.402233i | \(-0.868234\pi\) |
0.402233 | + | 0.915537i | \(0.368234\pi\) | |||||||
\(114\) | 4.16920e32i | 0.512359i | ||||||||
\(115\) | −3.48537e32 | − | 1.29717e33i | −0.372463 | − | 1.38622i | ||||
\(116\) | −2.48058e32 | −0.230795 | ||||||||
\(117\) | −4.55404e32 | − | 4.55404e32i | −0.369337 | − | 0.369337i | ||||
\(118\) | 1.04511e33 | − | 1.04511e33i | 0.739689 | − | 0.739689i | ||||
\(119\) | − | 1.96654e33i | − | 1.21605i | ||||||
\(120\) | 1.25523e33 | + | 7.23554e32i | 0.678929 | + | 0.391355i | ||||
\(121\) | −1.10505e33 | −0.523380 | ||||||||
\(122\) | −1.33338e33 | − | 1.33338e33i | −0.553601 | − | 0.553601i | ||||
\(123\) | 6.03730e32 | − | 6.03730e32i | 0.219969 | − | 0.219969i | ||||
\(124\) | − | 9.23385e30i | − | 0.00295553i | ||||||
\(125\) | 3.55271e33 | − | 7.35668e30i | 0.999998 | − | 0.00207072i | ||||
\(126\) | −1.72366e33 | −0.427093 | ||||||||
\(127\) | 1.06536e33 | + | 1.06536e33i | 0.232616 | + | 0.232616i | 0.813784 | − | 0.581168i | \(-0.197404\pi\) |
−0.581168 | + | 0.813784i | \(0.697404\pi\) | |||||||
\(128\) | −2.40596e33 | + | 2.40596e33i | −0.463372 | + | 0.463372i | ||||
\(129\) | 4.26490e33i | 0.725226i | ||||||||
\(130\) | −3.41123e33 | + | 5.91785e33i | −0.512646 | + | 0.889345i | ||||
\(131\) | 3.24991e33 | 0.432047 | 0.216023 | − | 0.976388i | \(-0.430691\pi\) | ||||
0.216023 | + | 0.976388i | \(0.430691\pi\) | |||||||
\(132\) | −5.39991e32 | − | 5.39991e32i | −0.0635629 | − | 0.0635629i | ||||
\(133\) | 5.32452e33 | − | 5.32452e33i | 0.555462 | − | 0.555462i | ||||
\(134\) | 2.66029e32i | 0.0246180i | ||||||||
\(135\) | 1.26066e34 | − | 3.38725e33i | 1.03575 | − | 0.278296i | ||||
\(136\) | −1.74308e34 | −1.27261 | ||||||||
\(137\) | 2.72630e33 | + | 2.72630e33i | 0.177029 | + | 0.177029i | 0.790059 | − | 0.613030i | \(-0.210050\pi\) |
−0.613030 | + | 0.790059i | \(0.710050\pi\) | |||||||
\(138\) | −1.16870e34 | + | 1.16870e34i | −0.675522 | + | 0.675522i | ||||
\(139\) | 2.06077e34i | 1.06119i | 0.847626 | + | 0.530594i | \(0.178031\pi\) | ||||
−0.847626 | + | 0.530594i | \(0.821969\pi\) | |||||||
\(140\) | −1.02323e33 | − | 3.80824e33i | −0.0469814 | − | 0.174854i | ||||
\(141\) | −1.13399e34 | −0.464627 | ||||||||
\(142\) | −1.97378e34 | − | 1.97378e34i | −0.722245 | − | 0.722245i | ||||
\(143\) | 1.68939e34 | − | 1.68939e34i | 0.552525 | − | 0.552525i | ||||
\(144\) | 1.24790e34i | 0.365074i | ||||||||
\(145\) | 4.30312e34 | + | 2.48045e34i | 1.12693 | + | 0.649595i | ||||
\(146\) | 2.55686e34 | 0.599875 | ||||||||
\(147\) | −1.01786e33 | − | 1.01786e33i | −0.0214097 | − | 0.0214097i | ||||
\(148\) | −1.16929e34 | + | 1.16929e34i | −0.220666 | + | 0.220666i | ||||
\(149\) | − | 8.61495e34i | − | 1.45973i | −0.683591 | − | 0.729865i | \(-0.739583\pi\) | ||
0.683591 | − | 0.729865i | \(-0.260417\pi\) | |||||||
\(150\) | −2.19105e34 | − | 3.78294e34i | −0.333574 | − | 0.575929i | ||||
\(151\) | 7.13058e34 | 0.976098 | 0.488049 | − | 0.872816i | \(-0.337709\pi\) | ||||
0.488049 | + | 0.872816i | \(0.337709\pi\) | |||||||
\(152\) | −4.71948e34 | − | 4.71948e34i | −0.581295 | − | 0.581295i | ||||
\(153\) | −3.50653e34 | + | 3.50653e34i | −0.388879 | + | 0.388879i | ||||
\(154\) | − | 6.39415e34i | − | 0.638927i | ||||||
\(155\) | −9.23337e32 | + | 1.60182e33i | −0.00831865 | + | 0.0144313i | ||||
\(156\) | −1.81304e34 | −0.147371 | ||||||||
\(157\) | −1.43355e34 | − | 1.43355e34i | −0.105201 | − | 0.105201i | 0.652547 | − | 0.757748i | \(-0.273700\pi\) |
−0.757748 | + | 0.652547i | \(0.773700\pi\) | |||||||
\(158\) | −7.53364e34 | + | 7.53364e34i | −0.499449 | + | 0.499449i | ||||
\(159\) | − | 6.66639e34i | − | 0.399518i | ||||||
\(160\) | −6.24233e34 | + | 1.67725e34i | −0.338397 | + | 0.0909237i | ||||
\(161\) | 2.98513e35 | 1.46470 | ||||||||
\(162\) | −4.69813e34 | − | 4.69813e34i | −0.208778 | − | 0.208778i | ||||
\(163\) | −2.71331e35 | + | 2.71331e35i | −1.09269 | + | 1.09269i | −0.0974522 | + | 0.995240i | \(0.531069\pi\) |
−0.995240 | + | 0.0974522i | \(0.968931\pi\) | |||||||
\(164\) | 2.05974e34i | 0.0752160i | ||||||||
\(165\) | 3.96773e34 | + | 1.47670e35i | 0.131462 | + | 0.489270i | ||||
\(166\) | 3.94076e34 | 0.118536 | ||||||||
\(167\) | 3.89137e35 | + | 3.89137e35i | 1.06326 | + | 1.06326i | 0.997859 | + | 0.0654007i | \(0.0208326\pi\) |
0.0654007 | + | 0.997859i | \(0.479167\pi\) | |||||||
\(168\) | −2.27685e35 | + | 2.27685e35i | −0.565438 | + | 0.565438i | ||||
\(169\) | − | 1.24438e35i | − | 0.281038i | ||||||
\(170\) | 4.55664e35 | + | 2.62658e35i | 0.936400 | + | 0.539770i | ||||
\(171\) | −1.89882e35 | −0.355261 | ||||||||
\(172\) | −7.27525e34 | − | 7.27525e34i | −0.123992 | − | 0.123992i | ||||
\(173\) | 4.75765e35 | − | 4.75765e35i | 0.739018 | − | 0.739018i | −0.233370 | − | 0.972388i | \(-0.574975\pi\) |
0.972388 | + | 0.233370i | \(0.0749754\pi\) | |||||||
\(174\) | − | 6.11174e35i | − | 0.865719i | ||||||
\(175\) | −2.03302e35 | + | 7.62943e35i | −0.262744 | + | 0.986015i | ||||
\(176\) | −4.62927e35 | −0.546147 | ||||||||
\(177\) | −5.55437e35 | − | 5.55437e35i | −0.598497 | − | 0.598497i | ||||
\(178\) | −1.25137e36 | + | 1.25137e36i | −1.23216 | + | 1.23216i | ||||
\(179\) | − | 1.99998e36i | − | 1.80044i | −0.435440 | − | 0.900218i | \(-0.643407\pi\) | ||
0.435440 | − | 0.900218i | \(-0.356593\pi\) | |||||||
\(180\) | −4.96593e34 | + | 8.61498e34i | −0.0408922 | + | 0.0709405i | ||||
\(181\) | 2.34543e36 | 1.76752 | 0.883762 | − | 0.467936i | \(-0.155002\pi\) | ||||
0.883762 | + | 0.467936i | \(0.155002\pi\) | |||||||
\(182\) | −1.07343e36 | − | 1.07343e36i | −0.740681 | − | 0.740681i | ||||
\(183\) | −7.08643e35 | + | 7.08643e35i | −0.447930 | + | 0.447930i | ||||
\(184\) | − | 2.64592e36i | − | 1.53282i | ||||||
\(185\) | 3.19762e36 | − | 8.59167e35i | 1.69856 | − | 0.456383i | ||||
\(186\) | 2.27507e34 | 0.0110863 | ||||||||
\(187\) | −1.30080e36 | − | 1.30080e36i | −0.581760 | − | 0.581760i | ||||
\(188\) | 1.93441e35 | − | 1.93441e35i | 0.0794372 | − | 0.0794372i | ||||
\(189\) | 2.90109e36i | 1.09439i | ||||||||
\(190\) | 5.22573e35 | + | 1.94490e36i | 0.181171 | + | 0.674278i | ||||
\(191\) | −9.51069e35 | −0.303164 | −0.151582 | − | 0.988445i | \(-0.548437\pi\) | ||||
−0.151582 | + | 0.988445i | \(0.548437\pi\) | |||||||
\(192\) | 1.96241e36 | + | 1.96241e36i | 0.575399 | + | 0.575399i | ||||
\(193\) | −2.25391e36 | + | 2.25391e36i | −0.608163 | + | 0.608163i | −0.942466 | − | 0.334303i | \(-0.891499\pi\) |
0.334303 | + | 0.942466i | \(0.391499\pi\) | |||||||
\(194\) | 1.59414e36i | 0.396003i | ||||||||
\(195\) | 3.14512e36 | + | 1.81294e36i | 0.719588 | + | 0.414792i | ||||
\(196\) | 3.47261e34 | 0.00732081 | ||||||||
\(197\) | −7.15338e36 | − | 7.15338e36i | −1.39012 | − | 1.39012i | −0.825034 | − | 0.565083i | \(-0.808844\pi\) |
−0.565083 | − | 0.825034i | \(-0.691156\pi\) | |||||||
\(198\) | −1.14014e36 | + | 1.14014e36i | −0.204322 | + | 0.204322i | ||||
\(199\) | 2.07919e36i | 0.343753i | 0.985119 | + | 0.171876i | \(0.0549829\pi\) | ||||
−0.985119 | + | 0.171876i | \(0.945017\pi\) | |||||||
\(200\) | 6.76248e36 | + | 1.80200e36i | 1.03187 | + | 0.274963i | ||||
\(201\) | 1.41385e35 | 0.0199189 | ||||||||
\(202\) | −1.02052e36 | − | 1.02052e36i | −0.132800 | − | 0.132800i | ||||
\(203\) | −7.80537e36 | + | 7.80537e36i | −0.938549 | + | 0.938549i | ||||
\(204\) | 1.39601e36i | 0.155169i | ||||||||
\(205\) | 2.05963e36 | − | 3.57308e36i | 0.211703 | − | 0.367266i | ||||
\(206\) | 1.28859e37 | 1.22529 | ||||||||
\(207\) | −5.32277e36 | − | 5.32277e36i | −0.468395 | − | 0.468395i | ||||
\(208\) | −7.77146e36 | + | 7.77146e36i | −0.633125 | + | 0.633125i | ||||
\(209\) | − | 7.04396e36i | − | 0.531467i | ||||||
\(210\) | 9.38288e36 | − | 2.52108e36i | 0.655885 | − | 0.176229i | ||||
\(211\) | −6.09709e36 | −0.395006 | −0.197503 | − | 0.980302i | \(-0.563283\pi\) | ||||
−0.197503 | + | 0.980302i | \(0.563283\pi\) | |||||||
\(212\) | 1.13718e36 | + | 1.13718e36i | 0.0683055 | + | 0.0683055i | ||||
\(213\) | −1.04899e37 | + | 1.04899e37i | −0.584383 | + | 0.584383i | ||||
\(214\) | − | 2.63147e37i | − | 1.36012i | ||||||
\(215\) | 5.34568e36 | + | 1.98954e37i | 0.256441 | + | 0.954416i | ||||
\(216\) | 2.57143e37 | 1.14529 | ||||||||
\(217\) | −2.90551e35 | − | 2.90551e35i | −0.0120190 | − | 0.0120190i | ||||
\(218\) | 1.85051e37 | − | 1.85051e37i | 0.711192 | − | 0.711192i | ||||
\(219\) | − | 1.35888e37i | − | 0.485371i | ||||||
\(220\) | −3.19585e36 | − | 1.84218e36i | −0.106126 | − | 0.0611744i | ||||
\(221\) | −4.36747e37 | −1.34882 | ||||||||
\(222\) | −2.88094e37 | − | 2.88094e37i | −0.827725 | − | 0.827725i | ||||
\(223\) | 1.87440e36 | − | 1.87440e36i | 0.0501170 | − | 0.0501170i | −0.681604 | − | 0.731721i | \(-0.738717\pi\) |
0.731721 | + | 0.681604i | \(0.238717\pi\) | |||||||
\(224\) | − | 1.43652e37i | − | 0.357555i | ||||||
\(225\) | 1.72291e37 | − | 9.97894e36i | 0.399339 | − | 0.231294i | ||||
\(226\) | 3.04937e37 | 0.658378 | ||||||||
\(227\) | 1.09568e37 | + | 1.09568e37i | 0.220429 | + | 0.220429i | 0.808679 | − | 0.588250i | \(-0.200183\pi\) |
−0.588250 | + | 0.808679i | \(0.700183\pi\) | |||||||
\(228\) | −3.77976e36 | + | 3.77976e36i | −0.0708773 | + | 0.0708773i | ||||
\(229\) | − | 3.80575e37i | − | 0.665384i | −0.943035 | − | 0.332692i | \(-0.892043\pi\) | ||
0.943035 | − | 0.332692i | \(-0.107957\pi\) | |||||||
\(230\) | −3.98705e37 | + | 6.91679e37i | −0.650138 | + | 1.12787i | ||||
\(231\) | −3.39826e37 | −0.516969 | ||||||||
\(232\) | 6.91842e37 | + | 6.91842e37i | 0.982198 | + | 0.982198i | ||||
\(233\) | −2.53746e37 | + | 2.53746e37i | −0.336283 | + | 0.336283i | −0.854966 | − | 0.518684i | \(-0.826422\pi\) |
0.518684 | + | 0.854966i | \(0.326422\pi\) | |||||||
\(234\) | 3.82805e37i | 0.473723i | ||||||||
\(235\) | −5.28999e37 | + | 1.42136e37i | −0.611461 | + | 0.164293i | ||||
\(236\) | 1.89498e37 | 0.204650 | ||||||||
\(237\) | 4.00385e37 | + | 4.00385e37i | 0.404115 | + | 0.404115i | ||||
\(238\) | −8.26521e37 | + | 8.26521e37i | −0.779871 | + | 0.779871i | ||||
\(239\) | 5.62465e37i | 0.496283i | 0.968724 | + | 0.248141i | \(0.0798197\pi\) | ||||
−0.968724 | + | 0.248141i | \(0.920180\pi\) | |||||||
\(240\) | −1.82522e37 | − | 6.79306e37i | −0.150638 | − | 0.560642i | ||||
\(241\) | 2.06335e38 | 1.59331 | 0.796655 | − | 0.604434i | \(-0.206601\pi\) | ||||
0.796655 | + | 0.604434i | \(0.206601\pi\) | |||||||
\(242\) | 4.64444e37 | + | 4.64444e37i | 0.335651 | + | 0.335651i | ||||
\(243\) | 8.71242e37 | − | 8.71242e37i | 0.589438 | − | 0.589438i | ||||
\(244\) | − | 2.41767e37i | − | 0.153165i | ||||||
\(245\) | −6.02403e36 | − | 3.47243e36i | −0.0357462 | − | 0.0206052i | ||||
\(246\) | −5.07485e37 | −0.282138 | ||||||||
\(247\) | −1.18252e38 | − | 1.18252e38i | −0.616107 | − | 0.616107i | ||||
\(248\) | −2.57535e36 | + | 2.57535e36i | −0.0125779 | + | 0.0125779i | ||||
\(249\) | − | 2.09437e37i | − | 0.0959100i | ||||||
\(250\) | −1.49626e38 | − | 1.49008e38i | −0.642641 | − | 0.639985i | ||||
\(251\) | −3.09148e38 | −1.24563 | −0.622813 | − | 0.782371i | \(-0.714010\pi\) | ||||
−0.622813 | + | 0.782371i | \(0.714010\pi\) | |||||||
\(252\) | −1.56266e37 | − | 1.56266e37i | −0.0590820 | − | 0.0590820i | ||||
\(253\) | 1.97456e38 | − | 1.97456e38i | 0.700714 | − | 0.700714i | ||||
\(254\) | − | 8.95528e37i | − | 0.298359i | ||||||
\(255\) | 1.39593e38 | − | 2.42169e38i | 0.436739 | − | 0.757661i | ||||
\(256\) | −1.75092e38 | −0.514549 | ||||||||
\(257\) | −1.74296e37 | − | 1.74296e37i | −0.0481235 | − | 0.0481235i | 0.682636 | − | 0.730759i | \(-0.260834\pi\) |
−0.730759 | + | 0.682636i | \(0.760834\pi\) | |||||||
\(258\) | 1.79250e38 | − | 1.79250e38i | 0.465098 | − | 0.465098i | ||||
\(259\) | 7.35855e38i | 1.79472i | ||||||||
\(260\) | −8.45768e37 | + | 2.27249e37i | −0.193945 | + | 0.0521108i | ||||
\(261\) | 2.78354e38 | 0.600274 | ||||||||
\(262\) | −1.36591e38 | − | 1.36591e38i | −0.277078 | − | 0.277078i | ||||
\(263\) | 6.54950e38 | − | 6.54950e38i | 1.25002 | − | 1.25002i | 0.294306 | − | 0.955711i | \(-0.404912\pi\) |
0.955711 | − | 0.294306i | \(-0.0950885\pi\) | |||||||
\(264\) | 3.01210e38i | 0.541012i | ||||||||
\(265\) | −8.35574e37 | − | 3.10982e38i | −0.141270 | − | 0.525776i | ||||
\(266\) | −4.47570e38 | −0.712451 | ||||||||
\(267\) | 6.65057e38 | + | 6.65057e38i | 0.996962 | + | 0.996962i | ||||
\(268\) | −2.41180e36 | + | 2.41180e36i | −0.00340553 | + | 0.00340553i | ||||
\(269\) | 1.20052e39i | 1.59710i | 0.601929 | + | 0.798550i | \(0.294399\pi\) | ||||
−0.601929 | + | 0.798550i | \(0.705601\pi\) | |||||||
\(270\) | −6.72207e38 | − | 3.87480e38i | −0.842719 | − | 0.485769i | ||||
\(271\) | −4.89496e38 | −0.578416 | −0.289208 | − | 0.957266i | \(-0.593392\pi\) | ||||
−0.289208 | + | 0.957266i | \(0.593392\pi\) | |||||||
\(272\) | 5.98388e38 | + | 5.98388e38i | 0.666623 | + | 0.666623i | ||||
\(273\) | −5.70489e38 | + | 5.70489e38i | −0.599300 | + | 0.599300i | ||||
\(274\) | − | 2.29168e38i | − | 0.227062i | ||||||
\(275\) | 3.70183e38 | + | 6.39136e38i | 0.346014 | + | 0.597407i | ||||
\(276\) | −2.11908e38 | −0.186897 | ||||||||
\(277\) | −9.08699e38 | − | 9.08699e38i | −0.756386 | − | 0.756386i | 0.219276 | − | 0.975663i | \(-0.429630\pi\) |
−0.975663 | + | 0.219276i | \(0.929630\pi\) | |||||||
\(278\) | 8.66124e38 | − | 8.66124e38i | 0.680555 | − | 0.680555i | ||||
\(279\) | 1.03616e37i | 0.00768705i | ||||||||
\(280\) | −7.76748e38 | + | 1.34751e39i | −0.544191 | + | 0.944072i | ||||
\(281\) | −1.02037e39 | −0.675234 | −0.337617 | − | 0.941284i | \(-0.609621\pi\) | ||||
−0.337617 | + | 0.941284i | \(0.609621\pi\) | |||||||
\(282\) | 4.76608e38 | + | 4.76608e38i | 0.297972 | + | 0.297972i | ||||
\(283\) | 1.63961e39 | − | 1.63961e39i | 0.968627 | − | 0.968627i | −0.0308960 | − | 0.999523i | \(-0.509836\pi\) |
0.999523 | + | 0.0308960i | \(0.00983608\pi\) | |||||||
\(284\) | − | 3.57883e38i | − | 0.199824i | ||||||
\(285\) | 1.03364e39 | − | 2.77728e38i | 0.545572 | − | 0.146589i | ||||
\(286\) | −1.42007e39 | −0.708685 | ||||||||
\(287\) | 6.48115e38 | + | 6.48115e38i | 0.305873 | + | 0.305873i | ||||
\(288\) | −2.56145e38 | + | 2.56145e38i | −0.114342 | + | 0.114342i | ||||
\(289\) | 9.94958e38i | 0.420184i | ||||||||
\(290\) | −7.66054e38 | − | 2.85108e39i | −0.306120 | − | 1.13931i | ||||
\(291\) | 8.47226e38 | 0.320414 | ||||||||
\(292\) | 2.31803e38 | + | 2.31803e38i | 0.0829838 | + | 0.0829838i | ||||
\(293\) | 1.46044e39 | − | 1.46044e39i | 0.494997 | − | 0.494997i | −0.414879 | − | 0.909876i | \(-0.636176\pi\) |
0.909876 | + | 0.414879i | \(0.136176\pi\) | |||||||
\(294\) | 8.55595e37i | 0.0274606i | ||||||||
\(295\) | −3.28726e39 | − | 1.89488e39i | −0.999268 | − | 0.576008i | ||||
\(296\) | 6.52237e39 | 1.87818 | ||||||||
\(297\) | 1.91897e39 | + | 1.91897e39i | 0.523558 | + | 0.523558i | ||||
\(298\) | −3.62079e39 | + | 3.62079e39i | −0.936145 | + | 0.936145i | ||||
\(299\) | − | 6.62964e39i | − | 1.62462i | ||||||
\(300\) | 1.44319e38 | − | 5.41597e38i | 0.0335262 | − | 0.125816i | ||||
\(301\) | −4.57844e39 | −1.00845 | ||||||||
\(302\) | −2.99692e39 | − | 2.99692e39i | −0.625985 | − | 0.625985i | ||||
\(303\) | −5.42369e38 | + | 5.42369e38i | −0.107452 | + | 0.107452i | ||||
\(304\) | 3.24034e39i | 0.608994i | ||||||||
\(305\) | −2.41754e39 | + | 4.19399e39i | −0.431098 | + | 0.747876i | ||||
\(306\) | 2.94753e39 | 0.498787 | ||||||||
\(307\) | −1.70789e39 | − | 1.70789e39i | −0.274313 | − | 0.274313i | 0.556521 | − | 0.830834i | \(-0.312136\pi\) |
−0.830834 | + | 0.556521i | \(0.812136\pi\) | |||||||
\(308\) | 5.79690e38 | − | 5.79690e38i | 0.0883861 | − | 0.0883861i | ||||
\(309\) | − | 6.84839e39i | − | 0.991409i | ||||||
\(310\) | 1.06130e38 | − | 2.85160e37i | 0.0145899 | − | 0.00392014i | ||||
\(311\) | 9.81154e39 | 1.28106 | 0.640532 | − | 0.767931i | \(-0.278714\pi\) | ||||
0.640532 | + | 0.767931i | \(0.278714\pi\) | |||||||
\(312\) | 5.05662e39 | + | 5.05662e39i | 0.627172 | + | 0.627172i | ||||
\(313\) | −8.21686e39 | + | 8.21686e39i | −0.968270 | + | 0.968270i | −0.999512 | − | 0.0312420i | \(-0.990054\pi\) |
0.0312420 | + | 0.999512i | \(0.490054\pi\) | |||||||
\(314\) | 1.20502e39i | 0.134934i | ||||||||
\(315\) | 1.14820e39 | + | 4.27336e39i | 0.122194 | + | 0.454779i | ||||
\(316\) | −1.36599e39 | −0.138183 | ||||||||
\(317\) | 4.52584e39 | + | 4.52584e39i | 0.435262 | + | 0.435262i | 0.890414 | − | 0.455152i | \(-0.150415\pi\) |
−0.455152 | + | 0.890414i | \(0.650415\pi\) | |||||||
\(318\) | −2.80183e39 | + | 2.80183e39i | −0.256217 | + | 0.256217i | ||||
\(319\) | 1.03259e40i | 0.898005i | ||||||||
\(320\) | 1.16142e40 | + | 6.69477e39i | 0.960702 | + | 0.553778i | ||||
\(321\) | −1.39853e40 | −1.10050 | ||||||||
\(322\) | −1.25462e40 | − | 1.25462e40i | −0.939334 | − | 0.939334i | ||||
\(323\) | −9.10516e39 | + | 9.10516e39i | −0.648705 | + | 0.648705i | ||||
\(324\) | − | 8.51858e38i | − | 0.0577627i | ||||||
\(325\) | 1.69441e40 | + | 4.51510e39i | 1.09367 | + | 0.291430i | ||||
\(326\) | 2.28076e40 | 1.40152 | ||||||||
\(327\) | −9.83477e39 | − | 9.83477e39i | −0.575440 | − | 0.575440i | ||||
\(328\) | 5.74467e39 | − | 5.74467e39i | 0.320099 | − | 0.320099i | ||||
\(329\) | − | 1.21736e40i | − | 0.646078i | ||||||
\(330\) | 4.53884e39 | − | 7.87404e39i | 0.229468 | − | 0.398084i | ||||
\(331\) | −2.93203e40 | −1.41228 | −0.706139 | − | 0.708073i | \(-0.749565\pi\) | ||||
−0.706139 | + | 0.708073i | \(0.749565\pi\) | |||||||
\(332\) | 3.57266e38 | + | 3.57266e38i | 0.0163977 | + | 0.0163977i | ||||
\(333\) | 1.31210e40 | − | 1.31210e40i | 0.573930 | − | 0.573930i | ||||
\(334\) | − | 3.27102e40i | − | 1.36377i | ||||||
\(335\) | 6.59549e38 | − | 1.77214e38i | 0.0262138 | − | 0.00704337i | ||||
\(336\) | 1.56326e40 | 0.592382 | ||||||||
\(337\) | −2.95040e40 | − | 2.95040e40i | −1.06611 | − | 1.06611i | −0.997654 | − | 0.0684559i | \(-0.978193\pi\) |
−0.0684559 | − | 0.997654i | \(-0.521807\pi\) | |||||||
\(338\) | −5.23002e39 | + | 5.23002e39i | −0.180234 | + | 0.180234i | ||||
\(339\) | − | 1.62063e40i | − | 0.532707i | ||||||
\(340\) | 1.74977e39 | + | 6.51226e39i | 0.0548680 | + | 0.204206i | ||||
\(341\) | −3.84378e38 | −0.0114998 | ||||||||
\(342\) | 7.98060e39 | + | 7.98060e39i | 0.227834 | + | 0.227834i | ||||
\(343\) | −2.53905e40 | + | 2.53905e40i | −0.691776 | + | 0.691776i | ||||
\(344\) | 4.05818e40i | 1.05535i | ||||||||
\(345\) | 3.67602e40 | + | 2.11897e40i | 0.912583 | + | 0.526040i | ||||
\(346\) | −3.99920e40 | −0.947885 | ||||||||
\(347\) | 5.13663e39 | + | 5.13663e39i | 0.116254 | + | 0.116254i | 0.762840 | − | 0.646587i | \(-0.223804\pi\) |
−0.646587 | + | 0.762840i | \(0.723804\pi\) | |||||||
\(348\) | 5.54086e39 | − | 5.54086e39i | 0.119759 | − | 0.119759i | ||||
\(349\) | − | 2.70211e40i | − | 0.557823i | −0.960317 | − | 0.278911i | \(-0.910026\pi\) | ||
0.960317 | − | 0.278911i | \(-0.0899735\pi\) | |||||||
\(350\) | 4.06105e40 | − | 2.35213e40i | 0.800846 | − | 0.463844i | ||||
\(351\) | 6.44300e40 | 1.21388 | ||||||||
\(352\) | −9.50206e39 | − | 9.50206e39i | −0.171055 | − | 0.171055i | ||||
\(353\) | 1.34381e39 | − | 1.34381e39i | 0.0231176 | − | 0.0231176i | −0.695454 | − | 0.718571i | \(-0.744796\pi\) |
0.718571 | + | 0.695454i | \(0.244796\pi\) | |||||||
\(354\) | 4.66891e40i | 0.767650i | ||||||||
\(355\) | −3.57864e40 | + | 6.20828e40i | −0.562425 | + | 0.975703i | ||||
\(356\) | −2.26897e40 | −0.340901 | ||||||||
\(357\) | 4.39266e40 | + | 4.39266e40i | 0.631009 | + | 0.631009i | ||||
\(358\) | −8.40575e40 | + | 8.40575e40i | −1.15464 | + | 1.15464i | ||||
\(359\) | 2.49711e40i | 0.328040i | 0.986457 | + | 0.164020i | \(0.0524462\pi\) | ||||
−0.986457 | + | 0.164020i | \(0.947554\pi\) | |||||||
\(360\) | 3.78776e40 | − | 1.01773e40i | 0.475929 | − | 0.127877i | ||||
\(361\) | 3.38930e40 | 0.407376 | ||||||||
\(362\) | −9.85765e40 | − | 9.85765e40i | −1.13354 | − | 1.13354i | ||||
\(363\) | 2.46835e40 | − | 2.46835e40i | 0.271582 | − | 0.271582i | ||||
\(364\) | − | 1.94633e40i | − | 0.204924i | ||||||
\(365\) | −1.70323e40 | − | 6.33905e40i | −0.171628 | − | 0.638761i | ||||
\(366\) | 5.95673e40 | 0.574528 | ||||||||
\(367\) | 3.75538e40 | + | 3.75538e40i | 0.346734 | + | 0.346734i | 0.858892 | − | 0.512157i | \(-0.171154\pi\) |
−0.512157 | + | 0.858892i | \(0.671154\pi\) | |||||||
\(368\) | −9.08329e40 | + | 9.08329e40i | −0.802930 | + | 0.802930i | ||||
\(369\) | − | 2.31130e40i | − | 0.195629i | ||||||
\(370\) | −1.70503e41 | − | 9.82834e40i | −1.38199 | − | 0.796622i | ||||
\(371\) | 7.15648e40 | 0.555542 | ||||||||
\(372\) | 2.06256e38 | + | 2.06256e38i | 0.00153363 | + | 0.00153363i | ||||
\(373\) | 1.13974e41 | − | 1.13974e41i | 0.811831 | − | 0.811831i | −0.173077 | − | 0.984908i | \(-0.555371\pi\) |
0.984908 | + | 0.173077i | \(0.0553710\pi\) | |||||||
\(374\) | 1.09343e41i | 0.746181i | ||||||||
\(375\) | −7.91923e40 | + | 7.95210e40i | −0.517825 | + | 0.519974i | ||||
\(376\) | −1.07903e41 | −0.676126 | ||||||||
\(377\) | 1.73348e41 | + | 1.73348e41i | 1.04102 | + | 1.04102i | ||||
\(378\) | 1.21931e41 | − | 1.21931e41i | 0.701849 | − | 0.701849i | ||||
\(379\) | − | 3.20505e41i | − | 1.76851i | −0.467004 | − | 0.884255i | \(-0.654667\pi\) | ||
0.467004 | − | 0.884255i | \(-0.345333\pi\) | |||||||
\(380\) | −1.28947e40 | + | 2.23699e40i | −0.0682140 | + | 0.118339i | ||||
\(381\) | −4.75940e40 | −0.241409 | ||||||||
\(382\) | 3.99726e40 | + | 3.99726e40i | 0.194424 | + | 0.194424i | ||||
\(383\) | 1.96001e41 | − | 1.96001e41i | 0.914279 | − | 0.914279i | −0.0823267 | − | 0.996605i | \(-0.526235\pi\) |
0.996605 | + | 0.0823267i | \(0.0262351\pi\) | |||||||
\(384\) | − | 1.07484e41i | − | 0.480887i | ||||||
\(385\) | −1.58526e41 | + | 4.25942e40i | −0.680345 | + | 0.182801i | ||||
\(386\) | 1.89460e41 | 0.780047 | ||||||||
\(387\) | 8.16380e40 | + | 8.16380e40i | 0.322490 | + | 0.322490i | ||||
\(388\) | −1.44523e40 | + | 1.44523e40i | −0.0547811 | + | 0.0547811i | ||||
\(389\) | − | 6.41335e40i | − | 0.233287i | −0.993174 | − | 0.116644i | \(-0.962786\pi\) | ||
0.993174 | − | 0.116644i | \(-0.0372136\pi\) | |||||||
\(390\) | −5.59903e40 | − | 2.08383e41i | −0.195470 | − | 0.727494i | ||||
\(391\) | −5.10470e41 | −1.71057 | ||||||||
\(392\) | −9.68523e39 | − | 9.68523e39i | −0.0311554 | − | 0.0311554i | ||||
\(393\) | −7.25931e40 | + | 7.25931e40i | −0.224189 | + | 0.224189i | ||||
\(394\) | 6.01301e41i | 1.78300i | ||||||||
\(395\) | 2.36962e41 | + | 1.36592e41i | 0.674721 | + | 0.388930i | ||||
\(396\) | −2.06728e40 | −0.0565297 | ||||||||
\(397\) | −7.36589e40 | − | 7.36589e40i | −0.193454 | − | 0.193454i | 0.603733 | − | 0.797187i | \(-0.293679\pi\) |
−0.797187 | + | 0.603733i | \(0.793679\pi\) | |||||||
\(398\) | 8.73868e40 | − | 8.73868e40i | 0.220453 | − | 0.220453i | ||||
\(399\) | 2.37867e41i | 0.576459i | ||||||||
\(400\) | −1.70290e41 | − | 2.94013e41i | −0.396488 | − | 0.684553i | ||||
\(401\) | −4.94593e41 | −1.10647 | −0.553233 | − | 0.833027i | \(-0.686606\pi\) | ||||
−0.553233 | + | 0.833027i | \(0.686606\pi\) | |||||||
\(402\) | −5.94229e39 | − | 5.94229e39i | −0.0127743 | − | 0.0127743i | ||||
\(403\) | −6.45282e39 | + | 6.45282e39i | −0.0133312 | + | 0.0133312i | ||||
\(404\) | − | 1.85039e40i | − | 0.0367419i | ||||||
\(405\) | −8.51814e40 | + | 1.47774e41i | −0.162579 | + | 0.282044i | ||||
\(406\) | 6.56106e41 | 1.20381 | ||||||||
\(407\) | 4.86741e41 | + | 4.86741e41i | 0.858593 | + | 0.858593i | ||||
\(408\) | 3.89350e41 | − | 3.89350e41i | 0.660356 | − | 0.660356i | ||||
\(409\) | 1.09263e42i | 1.78197i | 0.454030 | + | 0.890986i | \(0.349986\pi\) | ||||
−0.454030 | + | 0.890986i | \(0.650014\pi\) | |||||||
\(410\) | −2.36738e41 | + | 6.36089e40i | −0.371301 | + | 0.0997645i | ||||
\(411\) | −1.21794e41 | −0.183721 | ||||||||
\(412\) | 1.16823e41 | + | 1.16823e41i | 0.169501 | + | 0.169501i | ||||
\(413\) | 5.96271e41 | − | 5.96271e41i | 0.832229 | − | 0.832229i | ||||
\(414\) | 4.47423e41i | 0.600776i | ||||||||
\(415\) | −2.62511e40 | − | 9.77007e40i | −0.0339139 | − | 0.126220i | ||||
\(416\) | −3.19035e41 | −0.396593 | ||||||||
\(417\) | −4.60313e41 | − | 4.60313e41i | −0.550651 | − | 0.550651i | ||||
\(418\) | −2.96052e41 | + | 2.96052e41i | −0.340837 | + | 0.340837i | ||||
\(419\) | − | 6.94897e41i | − | 0.770010i | −0.922915 | − | 0.385005i | \(-0.874200\pi\) | ||
0.922915 | − | 0.385005i | \(-0.125800\pi\) | |||||||
\(420\) | 1.07921e41 | + | 6.22087e40i | 0.115111 | + | 0.0663533i | ||||
\(421\) | −1.06991e42 | −1.09858 | −0.549292 | − | 0.835631i | \(-0.685103\pi\) | ||||
−0.549292 | + | 0.835631i | \(0.685103\pi\) | |||||||
\(422\) | 2.56256e41 | + | 2.56256e41i | 0.253323 | + | 0.253323i | ||||
\(423\) | −2.17067e41 | + | 2.17067e41i | −0.206608 | + | 0.206608i | ||||
\(424\) | − | 6.34327e41i | − | 0.581379i | ||||||
\(425\) | 3.47654e41 | − | 1.30467e42i | 0.306849 | − | 1.15153i | ||||
\(426\) | 8.81764e41 | 0.749547 | ||||||||
\(427\) | −7.60741e41 | − | 7.60741e41i | −0.622860 | − | 0.622860i | ||||
\(428\) | 2.38567e41 | − | 2.38567e41i | 0.188153 | − | 0.188153i | ||||
\(429\) | 7.54715e41i | 0.573411i | ||||||||
\(430\) | 6.11513e41 | − | 1.06086e42i | 0.447621 | − | 0.776540i | ||||
\(431\) | 8.14754e41 | 0.574632 | 0.287316 | − | 0.957836i | \(-0.407237\pi\) | ||||
0.287316 | + | 0.957836i | \(0.407237\pi\) | |||||||
\(432\) | −8.82758e41 | − | 8.82758e41i | −0.599931 | − | 0.599931i | ||||
\(433\) | 7.61446e41 | − | 7.61446e41i | 0.498692 | − | 0.498692i | −0.412338 | − | 0.911031i | \(-0.635288\pi\) |
0.911031 | + | 0.412338i | \(0.135288\pi\) | |||||||
\(434\) | 2.44233e40i | 0.0154159i | ||||||||
\(435\) | −1.51524e42 | + | 4.07130e41i | −0.921838 | + | 0.247688i | ||||
\(436\) | 3.35531e41 | 0.196766 | ||||||||
\(437\) | −1.38213e42 | − | 1.38213e42i | −0.781348 | − | 0.781348i | ||||
\(438\) | −5.71124e41 | + | 5.71124e41i | −0.311276 | + | 0.311276i | ||||
\(439\) | − | 4.16393e41i | − | 0.218812i | −0.993997 | − | 0.109406i | \(-0.965105\pi\) | ||
0.993997 | − | 0.109406i | \(-0.0348949\pi\) | |||||||
\(440\) | 3.77541e41 | + | 1.40512e42i | 0.191303 | + | 0.711986i | ||||
\(441\) | −3.89673e40 | −0.0190407 | ||||||||
\(442\) | 1.83561e42 | + | 1.83561e42i | 0.865016 | + | 0.865016i | ||||
\(443\) | −1.39387e42 | + | 1.39387e42i | −0.633525 | + | 0.633525i | −0.948950 | − | 0.315425i | \(-0.897853\pi\) |
0.315425 | + | 0.948950i | \(0.397853\pi\) | |||||||
\(444\) | − | 5.22367e41i | − | 0.229007i | ||||||
\(445\) | 3.93603e42 | + | 2.26885e42i | 1.66456 | + | 0.959500i | ||||
\(446\) | −1.57559e41 | −0.0642814 | ||||||||
\(447\) | 1.92432e42 | + | 1.92432e42i | 0.757455 | + | 0.757455i | ||||
\(448\) | −2.10668e42 | + | 2.10668e42i | −0.800110 | + | 0.800110i | ||||
\(449\) | − | 1.23901e42i | − | 0.454081i | −0.973885 | − | 0.227040i | \(-0.927095\pi\) | ||
0.973885 | − | 0.227040i | \(-0.0729049\pi\) | |||||||
\(450\) | −1.14353e42 | − | 3.04716e41i | −0.404433 | − | 0.107769i | ||||
\(451\) | 8.57409e41 | 0.292660 | ||||||||
\(452\) | 2.76454e41 | + | 2.76454e41i | 0.0910768 | + | 0.0910768i | ||||
\(453\) | −1.59275e42 | + | 1.59275e42i | −0.506498 | + | 0.506498i | ||||
\(454\) | − | 9.21008e41i | − | 0.282728i | ||||||
\(455\) | −1.94623e42 | + | 3.37634e42i | −0.576781 | + | 1.00061i | ||||
\(456\) | 2.10838e42 | 0.603268 | ||||||||
\(457\) | −5.74881e41 | − | 5.74881e41i | −0.158825 | − | 0.158825i | 0.623221 | − | 0.782046i | \(-0.285824\pi\) |
−0.782046 | + | 0.623221i | \(0.785824\pi\) | |||||||
\(458\) | −1.59953e42 | + | 1.59953e42i | −0.426720 | + | 0.426720i | ||||
\(459\) | − | 4.96099e42i | − | 1.27810i | ||||||
\(460\) | −9.88534e41 | + | 2.65608e41i | −0.245961 | + | 0.0660870i | ||||
\(461\) | −2.91709e42 | −0.701028 | −0.350514 | − | 0.936557i | \(-0.613993\pi\) | ||||
−0.350514 | + | 0.936557i | \(0.613993\pi\) | |||||||
\(462\) | 1.42826e42 | + | 1.42826e42i | 0.331540 | + | 0.331540i | ||||
\(463\) | 2.70805e42 | − | 2.70805e42i | 0.607240 | − | 0.607240i | −0.334984 | − | 0.942224i | \(-0.608731\pi\) |
0.942224 | + | 0.334984i | \(0.108731\pi\) | |||||||
\(464\) | − | 4.75011e42i | − | 1.02900i | ||||||
\(465\) | −1.51552e40 | − | 5.64043e40i | −0.00317187 | − | 0.0118050i | ||||
\(466\) | 2.13295e42 | 0.431326 | ||||||||
\(467\) | −1.11563e42 | − | 1.11563e42i | −0.217996 | − | 0.217996i | 0.589657 | − | 0.807653i | \(-0.299263\pi\) |
−0.807653 | + | 0.589657i | \(0.799263\pi\) | |||||||
\(468\) | −3.47049e41 | + | 3.47049e41i | −0.0655325 | + | 0.0655325i | ||||
\(469\) | 1.51779e41i | 0.0276979i | ||||||||
\(470\) | 2.82073e42 | + | 1.62595e42i | 0.497502 | + | 0.286775i | ||||
\(471\) | 6.40425e41 | 0.109178 | ||||||||
\(472\) | −5.28515e42 | − | 5.28515e42i | −0.870934 | − | 0.870934i | ||||
\(473\) | −3.02848e42 | + | 3.02848e42i | −0.482443 | + | 0.482443i | ||||
\(474\) | − | 3.36557e42i | − | 0.518329i | ||||||
\(475\) | 4.47375e42 | − | 2.59116e42i | 0.666153 | − | 0.385831i | ||||
\(476\) | −1.49864e42 | −0.215767 | ||||||||
\(477\) | −1.27607e42 | − | 1.27607e42i | −0.177656 | − | 0.177656i | ||||
\(478\) | 2.36399e42 | − | 2.36399e42i | 0.318273 | − | 0.318273i | ||||
\(479\) | 8.04216e42i | 1.04714i | 0.851983 | + | 0.523569i | \(0.175400\pi\) | ||||
−0.851983 | + | 0.523569i | \(0.824600\pi\) | |||||||
\(480\) | 1.01970e42 | − | 1.76899e42i | 0.128414 | − | 0.222775i | ||||
\(481\) | 1.63425e43 | 1.99066 | ||||||||
\(482\) | −8.67209e42 | − | 8.67209e42i | −1.02181 | − | 1.02181i | ||||
\(483\) | −6.66787e42 | + | 6.66787e42i | −0.760034 | + | 0.760034i | ||||
\(484\) | 8.42124e41i | 0.0928646i | ||||||||
\(485\) | 3.95224e42 | − | 1.06192e42i | 0.421673 | − | 0.113299i | ||||
\(486\) | −7.32351e42 | −0.756030 | ||||||||
\(487\) | 7.74349e42 | + | 7.74349e42i | 0.773523 | + | 0.773523i | 0.978721 | − | 0.205197i | \(-0.0657836\pi\) |
−0.205197 | + | 0.978721i | \(0.565784\pi\) | |||||||
\(488\) | −6.74295e42 | + | 6.74295e42i | −0.651828 | + | 0.651828i | ||||
\(489\) | − | 1.21214e43i | − | 1.13400i | ||||||
\(490\) | 1.07241e41 | + | 3.99128e41i | 0.00971013 | + | 0.0361389i | ||||
\(491\) | 2.72662e41 | 0.0238957 | 0.0119479 | − | 0.999929i | \(-0.496197\pi\) | ||||
0.0119479 | + | 0.999929i | \(0.496197\pi\) | |||||||
\(492\) | −4.60083e41 | − | 4.60083e41i | −0.0390296 | − | 0.0390296i | ||||
\(493\) | 1.33475e43 | − | 1.33475e43i | 1.09610 | − | 1.09610i | ||||
\(494\) | 9.94003e42i | 0.790236i | ||||||||
\(495\) | 3.58617e42 | + | 2.06717e42i | 0.276024 | + | 0.159109i | ||||
\(496\) | 1.76821e41 | 0.0131773 | ||||||||
\(497\) | −1.12611e43 | − | 1.12611e43i | −0.812603 | − | 0.812603i | ||||
\(498\) | −8.80246e41 | + | 8.80246e41i | −0.0615084 | + | 0.0615084i | ||||
\(499\) | 1.35812e43i | 0.919031i | 0.888170 | + | 0.459515i | \(0.151977\pi\) | ||||
−0.888170 | + | 0.459515i | \(0.848023\pi\) | |||||||
\(500\) | −5.60628e39 | − | 2.70740e42i | −0.000367413 | − | 0.177432i | ||||
\(501\) | −1.73843e43 | −1.10345 | ||||||||
\(502\) | 1.29932e43 | + | 1.29932e43i | 0.798837 | + | 0.798837i | ||||
\(503\) | −8.85029e42 | + | 8.85029e42i | −0.527072 | + | 0.527072i | −0.919698 | − | 0.392626i | \(-0.871567\pi\) |
0.392626 | + | 0.919698i | \(0.371567\pi\) | |||||||
\(504\) | 8.71660e42i | 0.502873i | ||||||||
\(505\) | −1.85029e42 | + | 3.20992e42i | −0.103414 | + | 0.179404i | ||||
\(506\) | −1.65978e43 | −0.898756 | ||||||||
\(507\) | 2.77956e42 | + | 2.77956e42i | 0.145831 | + | 0.145831i | ||||
\(508\) | 8.11879e41 | − | 8.11879e41i | 0.0412736 | − | 0.0412736i | ||||
\(509\) | 1.49840e43i | 0.738146i | 0.929400 | + | 0.369073i | \(0.120325\pi\) | ||||
−0.929400 | + | 0.369073i | \(0.879675\pi\) | |||||||
\(510\) | −1.60451e43 | + | 4.31115e42i | −0.765985 | + | 0.205812i | ||||
\(511\) | 1.45878e43 | 0.674924 | ||||||||
\(512\) | 1.76925e43 | + | 1.76925e43i | 0.793359 | + | 0.793359i | ||||
\(513\) | 1.34322e43 | − | 1.34322e43i | 0.583805 | − | 0.583805i | ||||
\(514\) | 1.46510e42i | 0.0617246i | ||||||||
\(515\) | −8.58386e42 | − | 3.19472e43i | −0.350564 | − | 1.30472i | ||||
\(516\) | 3.25014e42 | 0.128679 | ||||||||
\(517\) | −8.05241e42 | − | 8.05241e42i | −0.309084 | − | 0.309084i | ||||
\(518\) | 3.09274e43 | − | 3.09274e43i | 1.15098 | − | 1.15098i | ||||
\(519\) | 2.12543e43i | 0.766953i | ||||||||
\(520\) | 2.99268e43 | + | 1.72507e43i | 1.04714 | + | 0.603606i | ||||
\(521\) | 2.06750e43 | 0.701523 | 0.350761 | − | 0.936465i | \(-0.385923\pi\) | ||||
0.350761 | + | 0.936465i | \(0.385923\pi\) | |||||||
\(522\) | −1.16990e43 | − | 1.16990e43i | −0.384964 | − | 0.384964i | ||||
\(523\) | −3.34965e42 | + | 3.34965e42i | −0.106899 | + | 0.106899i | −0.758533 | − | 0.651634i | \(-0.774084\pi\) |
0.651634 | + | 0.758533i | \(0.274084\pi\) | |||||||
\(524\) | − | 2.47665e42i | − | 0.0766591i | ||||||
\(525\) | −1.25007e43 | − | 2.15830e43i | −0.375306 | − | 0.647981i | ||||
\(526\) | −5.50540e43 | −1.60331 | ||||||||
\(527\) | 4.96855e41 | + | 4.96855e41i | 0.0140365 | + | 0.0140365i | ||||
\(528\) | 1.03404e43 | − | 1.03404e43i | 0.283396 | − | 0.283396i | ||||
\(529\) | − | 3.98783e43i | − | 1.06034i | ||||||
\(530\) | −9.55845e42 | + | 1.65821e43i | −0.246589 | + | 0.427786i | ||||
\(531\) | −2.12641e43 | −0.532274 | ||||||||
\(532\) | −4.05764e42 | − | 4.05764e42i | −0.0985570 | − | 0.0985570i | ||||
\(533\) | 1.43939e43 | − | 1.43939e43i | 0.339268 | − | 0.339268i | ||||
\(534\) | − | 5.59036e43i | − | 1.27873i | ||||||
\(535\) | −6.52403e43 | + | 1.75293e43i | −1.44829 | + | 0.389139i | ||||
\(536\) | 1.34532e42 | 0.0289860 | ||||||||
\(537\) | 4.46735e43 | + | 4.46735e43i | 0.934247 | + | 0.934247i | ||||
\(538\) | 5.04567e43 | − | 5.04567e43i | 1.02424 | − | 1.02424i | ||||
\(539\) | − | 1.44555e42i | − | 0.0284847i | ||||||
\(540\) | −2.58131e42 | − | 9.60705e42i | −0.0493787 | − | 0.183776i | ||||
\(541\) | −1.12660e43 | −0.209224 | −0.104612 | − | 0.994513i | \(-0.533360\pi\) | ||||
−0.104612 | + | 0.994513i | \(0.533360\pi\) | |||||||
\(542\) | 2.05731e43 | + | 2.05731e43i | 0.370946 | + | 0.370946i | ||||
\(543\) | −5.23898e43 | + | 5.23898e43i | −0.917169 | + | 0.917169i | ||||
\(544\) | 2.45651e43i | 0.417576i | ||||||||
\(545\) | −5.82055e43 | − | 3.35514e43i | −0.960771 | − | 0.553817i | ||||
\(546\) | 4.79543e43 | 0.768680 | ||||||||
\(547\) | 1.80975e43 | + | 1.80975e43i | 0.281723 | + | 0.281723i | 0.833796 | − | 0.552073i | \(-0.186163\pi\) |
−0.552073 | + | 0.833796i | \(0.686163\pi\) | |||||||
\(548\) | 2.07762e42 | − | 2.07762e42i | 0.0314107 | − | 0.0314107i | ||||
\(549\) | 2.71294e43i | 0.398367i | ||||||||
\(550\) | 1.13039e43 | − | 4.24208e43i | 0.161222 | − | 0.605029i | ||||
\(551\) | 7.22783e43 | 1.00134 | ||||||||
\(552\) | 5.91018e43 | + | 5.91018e43i | 0.795382 | + | 0.795382i | ||||
\(553\) | −4.29821e43 | + | 4.29821e43i | −0.561934 | + | 0.561934i | ||||
\(554\) | 7.63837e43i | 0.970162i | ||||||||
\(555\) | −5.22340e43 | + | 9.06164e43i | −0.644564 | + | 1.11820i | ||||
\(556\) | 1.57044e43 | 0.188289 | ||||||||
\(557\) | −7.51595e43 | − | 7.51595e43i | −0.875590 | − | 0.875590i | 0.117485 | − | 0.993075i | \(-0.462517\pi\) |
−0.993075 | + | 0.117485i | \(0.962517\pi\) | |||||||
\(558\) | 4.35490e41 | − | 4.35490e41i | 0.00492981 | − | 0.00492981i | ||||
\(559\) | 1.01682e44i | 1.11855i | ||||||||
\(560\) | 7.29247e43 | − | 1.95941e43i | 0.779590 | − | 0.209467i | ||||
\(561\) | 5.81117e43 | 0.603751 | ||||||||
\(562\) | 4.28851e43 | + | 4.28851e43i | 0.433037 | + | 0.433037i | ||||
\(563\) | 5.95350e43 | − | 5.95350e43i | 0.584303 | − | 0.584303i | −0.351780 | − | 0.936083i | \(-0.614423\pi\) |
0.936083 | + | 0.351780i | \(0.114423\pi\) | |||||||
\(564\) | 8.64179e42i | 0.0824400i | ||||||||
\(565\) | −2.03132e43 | − | 7.56011e43i | −0.188366 | − | 0.701056i | ||||
\(566\) | −1.37822e44 | −1.24239 | ||||||||
\(567\) | −2.68045e43 | − | 2.68045e43i | −0.234898 | − | 0.234898i | ||||
\(568\) | −9.98146e43 | + | 9.98146e43i | −0.850395 | + | 0.850395i | ||||
\(569\) | − | 7.38465e43i | − | 0.611693i | −0.952081 | − | 0.305847i | \(-0.901061\pi\) | ||
0.952081 | − | 0.305847i | \(-0.0989395\pi\) | |||||||
\(570\) | −5.51158e43 | − | 3.17704e43i | −0.443893 | − | 0.255873i | ||||
\(571\) | −1.06965e44 | −0.837654 | −0.418827 | − | 0.908066i | \(-0.637559\pi\) | ||||
−0.418827 | + | 0.908066i | \(0.637559\pi\) | |||||||
\(572\) | −1.28743e43 | − | 1.28743e43i | −0.0980360 | − | 0.0980360i | ||||
\(573\) | 2.12440e43 | − | 2.12440e43i | 0.157312 | − | 0.157312i | ||||
\(574\) | − | 5.44794e43i | − | 0.392322i | ||||||
\(575\) | 1.98043e44 | + | 5.27725e43i | 1.38699 | + | 0.369592i | ||||
\(576\) | 7.51281e43 | 0.511732 | ||||||||
\(577\) | −1.21439e44 | − | 1.21439e44i | −0.804535 | − | 0.804535i | 0.179266 | − | 0.983801i | \(-0.442628\pi\) |
−0.983801 | + | 0.179266i | \(0.942628\pi\) | |||||||
\(578\) | 4.18172e43 | − | 4.18172e43i | 0.269470 | − | 0.269470i | ||||
\(579\) | − | 1.00691e44i | − | 0.631152i | ||||||
\(580\) | 1.89027e43 | − | 3.27927e43i | 0.115259 | − | 0.199954i | ||||
\(581\) | 2.24834e43 | 0.133366 | ||||||||
\(582\) | −3.56082e43 | − | 3.56082e43i | −0.205486 | − | 0.205486i | ||||
\(583\) | 4.73375e43 | − | 4.73375e43i | 0.265772 | − | 0.265772i | ||||
\(584\) | − | 1.29301e44i | − | 0.706313i | ||||||
\(585\) | 9.49064e43 | − | 2.55003e43i | 0.504431 | − | 0.135535i | ||||
\(586\) | −1.22762e44 | −0.634897 | ||||||||
\(587\) | 3.83162e43 | + | 3.83162e43i | 0.192829 | + | 0.192829i | 0.796917 | − | 0.604088i | \(-0.206463\pi\) |
−0.604088 | + | 0.796917i | \(0.706463\pi\) | |||||||
\(588\) | −7.75676e41 | + | 7.75676e41i | −0.00379877 | + | 0.00379877i | ||||
\(589\) | 2.69053e42i | 0.0128231i | ||||||||
\(590\) | 5.85207e43 | + | 2.17801e44i | 0.271442 | + | 1.01025i | ||||
\(591\) | 3.19569e44 | 1.44266 | ||||||||
\(592\) | −2.23909e44 | − | 2.23909e44i | −0.983840 | − | 0.983840i | ||||
\(593\) | −4.71832e43 | + | 4.71832e43i | −0.201796 | + | 0.201796i | −0.800769 | − | 0.598973i | \(-0.795576\pi\) |
0.598973 | + | 0.800769i | \(0.295576\pi\) | |||||||
\(594\) | − | 1.61305e44i | − | 0.671530i | ||||||
\(595\) | 2.59972e44 | + | 1.49856e44i | 1.05355 | + | 0.607298i | ||||
\(596\) | −6.56517e43 | −0.259004 | ||||||||
\(597\) | −4.64429e43 | − | 4.64429e43i | −0.178373 | − | 0.178373i | ||||
\(598\) | −2.78638e44 | + | 2.78638e44i | −1.04189 | + | 1.04189i | ||||
\(599\) | 4.37547e44i | 1.59293i | 0.604686 | + | 0.796464i | \(0.293298\pi\) | ||||
−0.604686 | + | 0.796464i | \(0.706702\pi\) | |||||||
\(600\) | −1.91304e44 | + | 1.10802e44i | −0.678117 | + | 0.392760i | ||||
\(601\) | −1.15484e44 | −0.398594 | −0.199297 | − | 0.979939i | \(-0.563866\pi\) | ||||
−0.199297 | + | 0.979939i | \(0.563866\pi\) | |||||||
\(602\) | 1.92428e44 | + | 1.92428e44i | 0.646733 | + | 0.646733i | ||||
\(603\) | 2.70636e42 | − | 2.70636e42i | 0.00885746 | − | 0.00885746i | ||||
\(604\) | − | 5.43398e43i | − | 0.173192i | ||||||
\(605\) | 8.42080e43 | − | 1.46085e44i | 0.261377 | − | 0.453441i | ||||
\(606\) | 4.55906e43 | 0.137820 | ||||||||
\(607\) | −7.80195e43 | − | 7.80195e43i | −0.229712 | − | 0.229712i | 0.582860 | − | 0.812572i | \(-0.301934\pi\) |
−0.812572 | + | 0.582860i | \(0.801934\pi\) | |||||||
\(608\) | −6.65114e43 | + | 6.65114e43i | −0.190739 | + | 0.190739i | ||||
\(609\) | − | 3.48696e44i | − | 0.974027i | ||||||
\(610\) | 2.77877e44 | − | 7.46625e43i | 0.756093 | − | 0.203154i | ||||
\(611\) | −2.70362e44 | −0.716616 | ||||||||
\(612\) | 2.67221e43 | + | 2.67221e43i | 0.0689998 | + | 0.0689998i | ||||
\(613\) | 3.31005e44 | − | 3.31005e44i | 0.832659 | − | 0.832659i | −0.155221 | − | 0.987880i | \(-0.549609\pi\) |
0.987880 | + | 0.155221i | \(0.0496088\pi\) | |||||||
\(614\) | 1.43562e44i | 0.351841i | ||||||||
\(615\) | 3.38058e43 | + | 1.25818e44i | 0.0807215 | + | 0.300427i | ||||
\(616\) | −3.23355e44 | −0.752294 | ||||||||
\(617\) | 5.34985e43 | + | 5.34985e43i | 0.121277 | + | 0.121277i | 0.765141 | − | 0.643863i | \(-0.222669\pi\) |
−0.643863 | + | 0.765141i | \(0.722669\pi\) | |||||||
\(618\) | −2.87832e44 | + | 2.87832e44i | −0.635804 | + | 0.635804i | ||||
\(619\) | 5.67847e44i | 1.22231i | 0.791511 | + | 0.611155i | \(0.209295\pi\) | ||||
−0.791511 | + | 0.611155i | \(0.790705\pi\) | |||||||
\(620\) | 1.22069e42 | + | 7.03644e41i | 0.00256059 | + | 0.00147600i | ||||
\(621\) | 7.53058e44 | 1.53944 | ||||||||
\(622\) | −4.12371e44 | − | 4.12371e44i | −0.821564 | − | 0.821564i | ||||
\(623\) | −7.13950e44 | + | 7.13950e44i | −1.38631 | + | 1.38631i | ||||
\(624\) | − | 3.47182e44i | − | 0.657057i | ||||||
\(625\) | −2.69753e44 | + | 4.70220e44i | −0.497607 | + | 0.867403i | ||||
\(626\) | 6.90695e44 | 1.24193 | ||||||||
\(627\) | 1.57341e44 | + | 1.57341e44i | 0.275778 | + | 0.275778i | ||||
\(628\) | −1.09246e43 | + | 1.09246e43i | −0.0186661 | + | 0.0186661i | ||||
\(629\) | − | 1.25834e45i | − | 2.09599i | ||||||
\(630\) | 1.31347e44 | − | 2.27864e44i | 0.213291 | − | 0.370021i | ||||
\(631\) | −1.58265e44 | −0.250562 | −0.125281 | − | 0.992121i | \(-0.539983\pi\) | ||||
−0.125281 | + | 0.992121i | \(0.539983\pi\) | |||||||
\(632\) | 3.80979e44 | + | 3.80979e44i | 0.588068 | + | 0.588068i | ||||
\(633\) | 1.36190e44 | − | 1.36190e44i | 0.204969 | − | 0.204969i | ||||
\(634\) | − | 3.80435e44i | − | 0.558280i | ||||||
\(635\) | −2.22022e44 | + | 5.96550e43i | −0.317700 | + | 0.0853625i | ||||
\(636\) | −5.08023e43 | −0.0708875 | ||||||||
\(637\) | −2.42674e43 | − | 2.42674e43i | −0.0330211 | − | 0.0330211i | ||||
\(638\) | 4.33990e44 | − | 4.33990e44i | 0.575903 | − | 0.575903i | ||||
\(639\) | 4.01592e44i | 0.519722i | ||||||||
\(640\) | −1.34722e44 | − | 5.01403e44i | −0.170043 | − | 0.632860i | ||||
\(641\) | 2.56042e44 | 0.315198 | 0.157599 | − | 0.987503i | \(-0.449625\pi\) | ||||
0.157599 | + | 0.987503i | \(0.449625\pi\) | |||||||
\(642\) | 5.87790e44 | + | 5.87790e44i | 0.705767 | + | 0.705767i | ||||
\(643\) | −3.22789e44 | + | 3.22789e44i | −0.378045 | + | 0.378045i | −0.870396 | − | 0.492352i | \(-0.836137\pi\) |
0.492352 | + | 0.870396i | \(0.336137\pi\) | |||||||
\(644\) | − | 2.27487e44i | − | 0.259886i | ||||||
\(645\) | −5.63810e44 | − | 3.24997e44i | −0.628315 | − | 0.362180i | ||||
\(646\) | 7.65364e44 | 0.832047 | ||||||||
\(647\) | −1.31997e45 | − | 1.31997e45i | −1.39990 | − | 1.39990i | −0.800304 | − | 0.599595i | \(-0.795328\pi\) |
−0.599595 | − | 0.800304i | \(-0.704672\pi\) | |||||||
\(648\) | −2.37586e44 | + | 2.37586e44i | −0.245822 | + | 0.245822i | ||||
\(649\) | − | 7.88823e44i | − | 0.796278i | ||||||
\(650\) | −5.22381e44 | − | 9.01913e44i | −0.514486 | − | 0.888282i | ||||
\(651\) | 1.29801e43 | 0.0124733 | ||||||||
\(652\) | 2.06772e44 | + | 2.06772e44i | 0.193879 | + | 0.193879i | ||||
\(653\) | 1.19634e45 | − | 1.19634e45i | 1.09457 | − | 1.09457i | 0.0995407 | − | 0.995033i | \(-0.468263\pi\) |
0.995033 | − | 0.0995407i | \(-0.0317373\pi\) | |||||||
\(654\) | 8.26694e44i | 0.738076i | ||||||||
\(655\) | −2.47652e44 | + | 4.29630e44i | −0.215765 | + | 0.374312i | ||||
\(656\) | −3.94422e44 | −0.335351 | ||||||||
\(657\) | −2.60114e44 | − | 2.60114e44i | −0.215833 | − | 0.215833i | ||||
\(658\) | −5.11647e44 | + | 5.11647e44i | −0.414339 | + | 0.414339i | ||||
\(659\) | 2.44141e45i | 1.92963i | 0.262933 | + | 0.964814i | \(0.415310\pi\) | ||||
−0.262933 | + | 0.964814i | \(0.584690\pi\) | |||||||
\(660\) | 1.12534e44 | − | 3.02367e43i | 0.0868124 | − | 0.0233256i | ||||
\(661\) | −1.93434e45 | −1.45649 | −0.728247 | − | 0.685314i | \(-0.759665\pi\) | ||||
−0.728247 | + | 0.685314i | \(0.759665\pi\) | |||||||
\(662\) | 1.23231e45 | + | 1.23231e45i | 0.905714 | + | 0.905714i | ||||
\(663\) | 9.75560e44 | − | 9.75560e44i | 0.699902 | − | 0.699902i | ||||
\(664\) | − | 1.99286e44i | − | 0.139568i | ||||||
\(665\) | 2.98146e44 | + | 1.10963e45i | 0.203837 | + | 0.758635i | ||||
\(666\) | −1.10293e45 | −0.736138 | ||||||||
\(667\) | 2.02610e45 | + | 2.02610e45i | 1.32022 | + | 1.32022i | ||||
\(668\) | 2.96549e44 | − | 2.96549e44i | 0.188657 | − | 0.188657i | ||||
\(669\) | 8.37368e43i | 0.0520114i | ||||||||
\(670\) | −3.51684e43 | − | 2.02722e43i | −0.0213283 | − | 0.0122943i | ||||
\(671\) | −1.00640e45 | −0.595953 | ||||||||
\(672\) | 3.20875e44 | + | 3.20875e44i | 0.185536 | + | 0.185536i | ||||
\(673\) | 1.60472e45 | − | 1.60472e45i | 0.906065 | − | 0.906065i | −0.0898869 | − | 0.995952i | \(-0.528651\pi\) |
0.995952 | + | 0.0898869i | \(0.0286506\pi\) | |||||||
\(674\) | 2.48005e45i | 1.36742i | ||||||||
\(675\) | −5.12869e44 | + | 1.92468e45i | −0.276151 | + | 1.03633i | ||||
\(676\) | −9.48300e43 | −0.0498653 | ||||||||
\(677\) | −1.82987e45 | − | 1.82987e45i | −0.939727 | − | 0.939727i | 0.0585573 | − | 0.998284i | \(-0.481350\pi\) |
−0.998284 | + | 0.0585573i | \(0.981350\pi\) | |||||||
\(678\) | −6.81137e44 | + | 6.81137e44i | −0.341633 | + | 0.341633i | ||||
\(679\) | 9.09512e44i | 0.445545i | ||||||||
\(680\) | 1.32827e45 | − | 2.30431e45i | 0.635542 | − | 1.10255i | ||||
\(681\) | −4.89482e44 | −0.228761 | ||||||||
\(682\) | 1.61551e43 | + | 1.61551e43i | 0.00737496 | + | 0.00737496i | ||||
\(683\) | 6.03515e44 | − | 6.03515e44i | 0.269127 | − | 0.269127i | −0.559622 | − | 0.828748i | \(-0.689054\pi\) |
0.828748 | + | 0.559622i | \(0.189054\pi\) | |||||||
\(684\) | 1.44703e44i | 0.0630348i | ||||||||
\(685\) | −5.68162e44 | + | 1.52659e44i | −0.241781 | + | 0.0649640i | ||||
\(686\) | 2.13428e45 | 0.887291 | ||||||||
\(687\) | 8.50089e44 | + | 8.50089e44i | 0.345268 | + | 0.345268i | ||||
\(688\) | 1.39315e45 | − | 1.39315e45i | 0.552819 | − | 0.552819i | ||||
\(689\) | − | 1.58937e45i | − | 0.616195i | ||||||
\(690\) | −6.54415e44 | − | 2.43558e45i | −0.247895 | − | 0.922609i | ||||
\(691\) | 8.47415e43 | 0.0313652 | 0.0156826 | − | 0.999877i | \(-0.495008\pi\) | ||||
0.0156826 | + | 0.999877i | \(0.495008\pi\) | |||||||
\(692\) | −3.62565e44 | − | 3.62565e44i | −0.131126 | − | 0.131126i | ||||
\(693\) | −6.50489e44 | + | 6.50489e44i | −0.229884 | + | 0.229884i | ||||
\(694\) | − | 4.31777e44i | − | 0.149110i | ||||||
\(695\) | −2.72429e45 | − | 1.57036e45i | −0.919382 | − | 0.529960i | ||||
\(696\) | −3.09073e45 | −1.01933 | ||||||||
\(697\) | −1.10830e45 | − | 1.10830e45i | −0.357219 | − | 0.357219i | ||||
\(698\) | −1.13567e45 | + | 1.13567e45i | −0.357739 | + | 0.357739i | ||||
\(699\) | − | 1.13358e45i | − | 0.348994i | ||||||
\(700\) | 5.81414e44 | + | 1.54929e44i | 0.174951 | + | 0.0466193i | ||||
\(701\) | −4.47213e43 | −0.0131530 | −0.00657652 | − | 0.999978i | \(-0.502093\pi\) | ||||
−0.00657652 | + | 0.999978i | \(0.502093\pi\) | |||||||
\(702\) | −2.70794e45 | − | 2.70794e45i | −0.778476 | − | 0.778476i | ||||
\(703\) | 3.40703e45 | − | 3.40703e45i | 0.957395 | − | 0.957395i | ||||
\(704\) | 2.78698e45i | 0.765547i | ||||||||
\(705\) | 8.64134e44 | − | 1.49911e45i | 0.232036 | − | 0.402539i | ||||
\(706\) | −1.12958e44 | −0.0296513 | ||||||||
\(707\) | −5.82242e44 | − | 5.82242e44i | −0.149415 | − | 0.149415i | ||||
\(708\) | −4.23280e44 | + | 4.23280e44i | −0.106193 | + | 0.106193i | ||||
\(709\) | 3.36170e45i | 0.824555i | 0.911058 | + | 0.412278i | \(0.135267\pi\) | ||||
−0.911058 | + | 0.412278i | \(0.864733\pi\) | |||||||
\(710\) | 4.11336e45 | − | 1.10521e45i | 0.986423 | − | 0.265041i | ||||
\(711\) | 1.53282e45 | 0.359400 | ||||||||
\(712\) | 6.32822e45 | + | 6.32822e45i | 1.45078 | + | 1.45078i | ||||
\(713\) | −7.54206e43 | + | 7.54206e43i | −0.0169066 | + | 0.0169066i | ||||
\(714\) | − | 3.69239e45i | − | 0.809350i | ||||||
\(715\) | 9.45970e44 | + | 3.52069e45i | 0.202759 | + | 0.754624i | ||||
\(716\) | −1.52412e45 | −0.319456 | ||||||||
\(717\) | −1.25638e45 | − | 1.25638e45i | −0.257521 | − | 0.257521i | ||||
\(718\) | 1.04951e45 | − | 1.04951e45i | 0.210377 | − | 0.210377i | ||||
\(719\) | 9.15494e43i | 0.0179471i | 0.999960 | + | 0.00897353i | \(0.00285640\pi\) | ||||
−0.999960 | + | 0.00897353i | \(0.997144\pi\) | |||||||
\(720\) | −1.64970e45 | − | 9.50935e44i | −0.316289 | − | 0.182319i | ||||
\(721\) | 7.35186e45 | 1.37858 | ||||||||
\(722\) | −1.42449e45 | − | 1.42449e45i | −0.261256 | − | 0.261256i | ||||
\(723\) | −4.60890e45 | + | 4.60890e45i | −0.826770 | + | 0.826770i | ||||
\(724\) | − | 1.78738e45i | − | 0.313616i | ||||||
\(725\) | −6.55820e45 | + | 3.79846e45i | −1.12558 | + | 0.651927i | ||||
\(726\) | −2.07485e45 | −0.348339 | ||||||||
\(727\) | 1.12691e45 | + | 1.12691e45i | 0.185071 | + | 0.185071i | 0.793561 | − | 0.608490i | \(-0.208225\pi\) |
−0.608490 | + | 0.793561i | \(0.708225\pi\) | |||||||
\(728\) | −5.42837e45 | + | 5.42837e45i | −0.872102 | + | 0.872102i | ||||
\(729\) | 5.96353e45i | 0.937267i | ||||||||
\(730\) | −1.94840e45 | + | 3.38011e45i | −0.299579 | + | 0.519714i | ||||
\(731\) | 7.82933e45 | 1.17773 | ||||||||
\(732\) | 5.40033e44 | + | 5.40033e44i | 0.0794773 | + | 0.0794773i | ||||
\(733\) | −1.66007e45 | + | 1.66007e45i | −0.239036 | + | 0.239036i | −0.816451 | − | 0.577415i | \(-0.804062\pi\) |
0.577415 | + | 0.816451i | \(0.304062\pi\) | |||||||
\(734\) | − | 3.15671e45i | − | 0.444731i | ||||||
\(735\) | 2.12122e44 | − | 5.69949e43i | 0.0292407 | − | 0.00785667i | ||||
\(736\) | −3.72888e45 | −0.502960 | ||||||||
\(737\) | 1.00396e44 | + | 1.00396e44i | 0.0132507 | + | 0.0132507i | ||||
\(738\) | −9.71419e44 | + | 9.71419e44i | −0.125460 | + | 0.125460i | ||||
\(739\) | − | 1.30139e46i | − | 1.64474i | −0.568954 | − | 0.822370i | \(-0.692652\pi\) | ||
0.568954 | − | 0.822370i | \(-0.307348\pi\) | |||||||
\(740\) | −6.54742e44 | − | 2.43680e45i | −0.0809772 | − | 0.301379i | ||||
\(741\) | 5.28276e45 | 0.639396 | ||||||||
\(742\) | −3.00781e45 | − | 3.00781e45i | −0.356277 | − | 0.356277i | ||||
\(743\) | −6.13827e45 | + | 6.13827e45i | −0.711583 | + | 0.711583i | −0.966866 | − | 0.255284i | \(-0.917831\pi\) |
0.255284 | + | 0.966866i | \(0.417831\pi\) | |||||||
\(744\) | − | 1.15051e44i | − | 0.0130534i | ||||||
\(745\) | 1.13888e46 | + | 6.56483e45i | 1.26467 | + | 0.728992i | ||||
\(746\) | −9.58049e45 | −1.04128 | ||||||||
\(747\) | −4.00900e44 | − | 4.00900e44i | −0.0426488 | − | 0.0426488i | ||||
\(748\) | −9.91294e44 | + | 9.91294e44i | −0.103223 | + | 0.103223i | ||||
\(749\) | − | 1.50134e46i | − | 1.53028i | ||||||
\(750\) | 6.67059e45 | − | 1.38130e43i | 0.665555 | − | 0.00137818i | ||||
\(751\) | 1.18592e46 | 1.15829 | 0.579146 | − | 0.815224i | \(-0.303386\pi\) | ||||
0.579146 | + | 0.815224i | \(0.303386\pi\) | |||||||
\(752\) | 3.70424e45 | + | 3.70424e45i | 0.354172 | + | 0.354172i | ||||
\(753\) | 6.90544e45 | − | 6.90544e45i | 0.646355 | − | 0.646355i | ||||
\(754\) | − | 1.45714e46i | − | 1.33524i | ||||||
\(755\) | −5.43369e45 | + | 9.42645e45i | −0.487465 | + | 0.845662i | ||||
\(756\) | 2.21083e45 | 0.194181 | ||||||||
\(757\) | −5.54304e45 | − | 5.54304e45i | −0.476666 | − | 0.476666i | 0.427398 | − | 0.904064i | \(-0.359430\pi\) |
−0.904064 | + | 0.427398i | \(0.859430\pi\) | |||||||
\(758\) | −1.34706e46 | + | 1.34706e46i | −1.13417 | + | 1.13417i | ||||
\(759\) | 8.82111e45i | 0.727202i | ||||||||
\(760\) | 9.83541e45 | − | 2.64267e45i | 0.793917 | − | 0.213317i | ||||
\(761\) | −2.78615e45 | −0.220217 | −0.110108 | − | 0.993920i | \(-0.535120\pi\) | ||||
−0.110108 | + | 0.993920i | \(0.535120\pi\) | |||||||
\(762\) | 2.00034e45 | + | 2.00034e45i | 0.154819 | + | 0.154819i | ||||
\(763\) | 1.05578e46 | − | 1.05578e46i | 0.800167 | − | 0.800167i | ||||
\(764\) | 7.24778e44i | 0.0537912i | ||||||||
\(765\) | −1.96348e45 | − | 7.30762e45i | −0.142706 | − | 0.531120i | ||||
\(766\) | −1.64755e46 | −1.17268 | ||||||||
\(767\) | −1.32425e46 | − | 1.32425e46i | −0.923091 | − | 0.923091i | ||||
\(768\) | 3.91102e45 | − | 3.91102e45i | 0.266999 | − | 0.266999i | ||||
\(769\) | 1.81007e46i | 1.21025i | 0.796132 | + | 0.605123i | \(0.206876\pi\) | ||||
−0.796132 | + | 0.605123i | \(0.793124\pi\) | |||||||
\(770\) | 8.45292e45 | + | 4.87252e45i | 0.553548 | + | 0.319082i | ||||
\(771\) | 7.78649e44 | 0.0499426 | ||||||||
\(772\) | 1.71763e45 | + | 1.71763e45i | 0.107908 | + | 0.107908i | ||||
\(773\) | 1.12025e46 | − | 1.12025e46i | 0.689353 | − | 0.689353i | −0.272736 | − | 0.962089i | \(-0.587929\pi\) |
0.962089 | + | 0.272736i | \(0.0879286\pi\) | |||||||
\(774\) | − | 6.86235e45i | − | 0.413635i | ||||||
\(775\) | −1.41396e44 | − | 2.44126e44i | −0.00834852 | − | 0.0144141i | ||||
\(776\) | 8.06161e45 | 0.466266 | ||||||||
\(777\) | −1.64368e46 | − | 1.64368e46i | −0.931279 | − | 0.931279i | ||||
\(778\) | −2.69548e45 | + | 2.69548e45i | −0.149611 | + | 0.149611i | ||||
\(779\) | − | 6.00159e45i | − | 0.326337i | ||||||
\(780\) | 1.38158e45 | − | 2.39679e45i | 0.0735976 | − | 0.127678i | ||||
\(781\) | −1.48976e46 | −0.777500 | ||||||||
\(782\) | 2.14546e46 | + | 2.14546e46i | 1.09702 | + | 1.09702i | ||||
\(783\) | −1.96906e46 | + | 1.96906e46i | −0.986440 | + | 0.986440i | ||||
\(784\) | 6.64976e44i | 0.0326399i | ||||||||
\(785\) | 2.98753e45 | − | 8.02717e44i | 0.143681 | − | 0.0386054i | ||||
\(786\) | 6.10206e45 | 0.287551 | ||||||||
\(787\) | −1.27012e46 | − | 1.27012e46i | −0.586476 | − | 0.586476i | 0.350200 | − | 0.936675i | \(-0.386114\pi\) |
−0.936675 | + | 0.350200i | \(0.886114\pi\) | |||||||
\(788\) | −5.45135e45 | + | 5.45135e45i | −0.246652 | + | 0.246652i | ||||
\(789\) | 2.92592e46i | 1.29727i | ||||||||
\(790\) | −4.21846e45 | − | 1.57001e46i | −0.183282 | − | 0.682134i | ||||
\(791\) | 1.73977e46 | 0.740746 | ||||||||
\(792\) | 5.76572e45 | + | 5.76572e45i | 0.240575 | + | 0.240575i | ||||
\(793\) | −1.68952e46 | + | 1.68952e46i | −0.690863 | + | 0.690863i | ||||
\(794\) | 6.19164e45i | 0.248129i | ||||||||
\(795\) | 8.81280e45 | + | 5.07997e45i | 0.346131 | + | 0.199520i | ||||
\(796\) | 1.58449e45 | 0.0609929 | ||||||||
\(797\) | −1.87034e45 | − | 1.87034e45i | −0.0705648 | − | 0.0705648i | 0.670944 | − | 0.741508i | \(-0.265889\pi\) |
−0.741508 | + | 0.670944i | \(0.765889\pi\) | |||||||
\(798\) | 9.99736e45 | − | 9.99736e45i | 0.369691 | − | 0.369691i | ||||
\(799\) | 2.08174e46i | 0.754532i | ||||||||
\(800\) | 2.53955e45 | − | 9.53032e45i | 0.0902228 | − | 0.338585i | ||||
\(801\) | 2.54608e46 | 0.886650 | ||||||||
\(802\) | 2.07873e46 | + | 2.07873e46i | 0.709592 | + | 0.709592i | ||||
\(803\) | 9.64929e45 | − | 9.64929e45i | 0.322884 | − | 0.322884i | ||||
\(804\) | − | 1.07745e44i | − | 0.00353427i | ||||||
\(805\) | −2.27475e46 | + | 3.94627e46i | −0.731475 | + | 1.26897i | ||||
\(806\) | 5.42413e44 | 0.0170989 | ||||||||
\(807\) | −2.68159e46 | − | 2.68159e46i | −0.828736 | − | 0.828736i | ||||
\(808\) | −5.16080e45 | + | 5.16080e45i | −0.156363 | + | 0.156363i | ||||
\(809\) | 4.89689e46i | 1.45460i | 0.686320 | + | 0.727300i | \(0.259225\pi\) | ||||
−0.686320 | + | 0.727300i | \(0.740775\pi\) | |||||||
\(810\) | 9.79092e45 | − | 2.63071e45i | 0.285143 | − | 0.0766149i | ||||
\(811\) | −4.61301e46 | −1.31720 | −0.658599 | − | 0.752494i | \(-0.728850\pi\) | ||||
−0.658599 | + | 0.752494i | \(0.728850\pi\) | |||||||
\(812\) | 5.94821e45 | + | 5.94821e45i | 0.166529 | + | 0.166529i | ||||
\(813\) | 1.09338e46 | − | 1.09338e46i | 0.300140 | − | 0.300140i | ||||
\(814\) | − | 4.09146e46i | − | 1.10126i | ||||||
\(815\) | −1.51932e46 | − | 5.65455e46i | −0.400983 | − | 1.49237i | ||||
\(816\) | −2.67323e46 | −0.691822 | ||||||||
\(817\) | 2.11984e46 | + | 2.11984e46i | 0.537959 | + | 0.537959i | ||||
\(818\) | 4.59224e46 | − | 4.59224e46i | 1.14280 | − | 1.14280i | ||||
\(819\) | 2.18404e46i | 0.532988i | ||||||||
\(820\) | −2.72292e45 | − | 1.56958e45i | −0.0651649 | − | 0.0375630i | ||||
\(821\) | 8.84798e45 | 0.207660 | 0.103830 | − | 0.994595i | \(-0.466890\pi\) | ||||
0.103830 | + | 0.994595i | \(0.466890\pi\) | |||||||
\(822\) | 5.11892e45 | + | 5.11892e45i | 0.117823 | + | 0.117823i | ||||
\(823\) | 5.47403e46 | − | 5.47403e46i | 1.23569 | − | 1.23569i | 0.273945 | − | 0.961745i | \(-0.411671\pi\) |
0.961745 | − | 0.273945i | \(-0.0883285\pi\) | |||||||
\(824\) | − | 6.51645e46i | − | 1.44270i | ||||||
\(825\) | −2.25451e46 | − | 6.00760e45i | −0.489541 | − | 0.130448i | ||||
\(826\) | −5.01215e46 | −1.06744 | ||||||||
\(827\) | −2.97638e46 | − | 2.97638e46i | −0.621728 | − | 0.621728i | 0.324245 | − | 0.945973i | \(-0.394890\pi\) |
−0.945973 | + | 0.324245i | \(0.894890\pi\) | |||||||
\(828\) | −4.05630e45 | + | 4.05630e45i | −0.0831085 | + | 0.0831085i | ||||
\(829\) | − | 6.73611e46i | − | 1.35374i | −0.736100 | − | 0.676872i | \(-0.763335\pi\) | ||
0.736100 | − | 0.676872i | \(-0.236665\pi\) | |||||||
\(830\) | −3.00297e45 | + | 5.20959e45i | −0.0591972 | + | 0.102696i | ||||
\(831\) | 4.05951e46 | 0.784978 | ||||||||
\(832\) | 4.67869e46 | + | 4.67869e46i | 0.887465 | + | 0.887465i | ||||
\(833\) | −1.86854e45 | + | 1.86854e45i | −0.0347683 | + | 0.0347683i | ||||
\(834\) | 3.86932e46i | 0.706281i | ||||||||
\(835\) | −8.10964e46 | + | 2.17897e46i | −1.45217 | + | 0.390183i | ||||
\(836\) | −5.36797e45 | −0.0942995 | ||||||||
\(837\) | −7.32973e44 | − | 7.32973e44i | −0.0126323 | − | 0.0126323i | ||||
\(838\) | −2.92059e46 | + | 2.92059e46i | −0.493818 | + | 0.493818i | ||||
\(839\) | 1.61722e46i | 0.268274i | 0.990963 | + | 0.134137i | \(0.0428263\pi\) | ||||
−0.990963 | + | 0.134137i | \(0.957174\pi\) | |||||||
\(840\) | −1.27492e46 | − | 4.74496e46i | −0.207498 | − | 0.772260i | ||||
\(841\) | −4.33315e46 | −0.691939 | ||||||||
\(842\) | 4.49674e46 | + | 4.49674e46i | 0.704537 | + | 0.704537i | ||||
\(843\) | 2.27919e46 | − | 2.27919e46i | 0.350379 | − | 0.350379i | ||||
\(844\) | 4.64639e45i | 0.0700868i | ||||||||
\(845\) | 1.64504e46 | + | 9.48250e45i | 0.243483 | + | 0.140351i | ||||
\(846\) | 1.82463e46 | 0.265002 | ||||||||
\(847\) | 2.64982e46 | + | 2.64982e46i | 0.377643 | + | 0.377643i | ||||
\(848\) | −2.17761e46 | + | 2.17761e46i | −0.304541 | + | 0.304541i | ||||
\(849\) | 7.32476e46i | 1.00524i | ||||||||
\(850\) | −6.94456e46 | + | 4.02224e46i | −0.935281 | + | 0.541707i | ||||
\(851\) | 1.91011e47 | 2.52456 | ||||||||
\(852\) | 7.99401e45 | + | 7.99401e45i | 0.103689 | + | 0.103689i | ||||
\(853\) | −3.90613e45 | + | 3.90613e45i | −0.0497236 | + | 0.0497236i | −0.731531 | − | 0.681808i | \(-0.761194\pi\) |
0.681808 | + | 0.731531i | \(0.261194\pi\) | |||||||
\(854\) | 6.39466e46i | 0.798898i | ||||||||
\(855\) | 1.44696e46 | − | 2.51020e46i | 0.177418 | − | 0.307787i | ||||
\(856\) | −1.33074e47 | −1.60145 | ||||||||
\(857\) | 9.29511e46 | + | 9.29511e46i | 1.09790 | + | 1.09790i | 0.994656 | + | 0.103240i | \(0.0329209\pi\) |
0.103240 | + | 0.994656i | \(0.467079\pi\) | |||||||
\(858\) | 3.17200e46 | − | 3.17200e46i | 0.367737 | − | 0.367737i | ||||
\(859\) | − | 1.39216e47i | − | 1.58416i | −0.610419 | − | 0.792079i | \(-0.708999\pi\) | ||
0.610419 | − | 0.792079i | \(-0.291001\pi\) | |||||||
\(860\) | 1.51616e46 | − | 4.07377e45i | 0.169345 | − | 0.0455010i | ||||
\(861\) | −2.89538e46 | −0.317436 | ||||||||
\(862\) | −3.42434e46 | − | 3.42434e46i | −0.368520 | − | 0.368520i | ||||
\(863\) | −4.99342e46 | + | 4.99342e46i | −0.527504 | + | 0.527504i | −0.919827 | − | 0.392324i | \(-0.871671\pi\) |
0.392324 | + | 0.919827i | \(0.371671\pi\) | |||||||
\(864\) | − | 3.62391e46i | − | 0.375800i | ||||||
\(865\) | 2.66404e46 | + | 9.91496e46i | 0.271196 | + | 1.00933i | ||||
\(866\) | −6.40059e46 | −0.639637 | ||||||||
\(867\) | −2.22243e46 | − | 2.22243e46i | −0.218033 | − | 0.218033i | ||||
\(868\) | −2.21420e44 | + | 2.21420e44i | −0.00213256 | + | 0.00213256i | ||||
\(869\) | 5.68622e46i | 0.537659i | ||||||||
\(870\) | 8.07958e46 | + | 4.65731e46i | 0.750034 | + | 0.432342i | ||||
\(871\) | 3.37084e45 | 0.0307219 | ||||||||
\(872\) | −9.35808e46 | − | 9.35808e46i | −0.837381 | − | 0.837381i | ||||
\(873\) | 1.62174e46 | − | 1.62174e46i | 0.142480 | − | 0.142480i | ||||
\(874\) | 1.16179e47i | 1.00218i | ||||||||
\(875\) | −8.53672e46 | − | 8.50143e46i | −0.723039 | − | 0.720051i | ||||
\(876\) | −1.03555e46 | −0.0861207 | ||||||||
\(877\) | −1.03630e47 | − | 1.03630e47i | −0.846233 | − | 0.846233i | 0.143428 | − | 0.989661i | \(-0.454188\pi\) |
−0.989661 | + | 0.143428i | \(0.954188\pi\) | |||||||
\(878\) | −1.75007e46 | + | 1.75007e46i | −0.140327 | + | 0.140327i | ||||
\(879\) | 6.52437e46i | 0.513708i | ||||||||
\(880\) | 3.52763e46 | − | 6.11978e46i | 0.272747 | − | 0.473166i | ||||
\(881\) | 7.53777e46 | 0.572306 | 0.286153 | − | 0.958184i | \(-0.407623\pi\) | ||||
0.286153 | + | 0.958184i | \(0.407623\pi\) | |||||||
\(882\) | 1.63776e45 | + | 1.63776e45i | 0.0122111 | + | 0.0122111i | ||||
\(883\) | 1.25662e47 | − | 1.25662e47i | 0.920094 | − | 0.920094i | −0.0769415 | − | 0.997036i | \(-0.524515\pi\) |
0.997036 | + | 0.0769415i | \(0.0245155\pi\) | |||||||
\(884\) | 3.32830e46i | 0.239324i | ||||||||
\(885\) | 1.15753e47 | − | 3.11016e46i | 0.817411 | − | 0.219630i | ||||
\(886\) | 1.17167e47 | 0.812577 | ||||||||
\(887\) | −1.10198e47 | − | 1.10198e47i | −0.750578 | − | 0.750578i | 0.224009 | − | 0.974587i | \(-0.428085\pi\) |
−0.974587 | + | 0.224009i | \(0.928085\pi\) | |||||||
\(888\) | −1.45690e47 | + | 1.45690e47i | −0.974590 | + | 0.974590i | ||||
\(889\) | − | 5.10930e46i | − | 0.335686i | ||||||
\(890\) | −7.00703e46 | − | 2.60786e47i | −0.452162 | − | 1.68284i | ||||
\(891\) | −3.54604e46 | −0.224750 | ||||||||
\(892\) | −1.42842e45 | − | 1.42842e45i | −0.00889238 | − | 0.00889238i | ||||
\(893\) | −5.63643e46 | + | 5.63643e46i | −0.344652 | + | 0.344652i | ||||
\(894\) | − | 1.61755e47i | − | 0.971533i | ||||||
\(895\) | 2.64393e47 | + | 1.52404e47i | 1.55984 | + | 0.899141i | ||||
\(896\) | 1.15386e47 | 0.668689 | ||||||||
\(897\) | 1.48086e47 | + | 1.48086e47i | 0.843014 | + | 0.843014i | ||||
\(898\) | −5.20745e46 | + | 5.20745e46i | −0.291208 | + | 0.291208i | ||||
\(899\) | − | 3.94412e45i | − | 0.0216668i | ||||||
\(900\) | −7.60462e45 | − | 1.31297e46i | −0.0410391 | − | 0.0708556i | ||||
\(901\) | −1.22379e47 | −0.648798 | ||||||||
\(902\) | −3.60362e46 | − | 3.60362e46i | −0.187687 | − | 0.187687i | ||||
\(903\) | 1.02269e47 | − | 1.02269e47i | 0.523285 | − | 0.523285i | ||||
\(904\) | − | 1.54208e47i | − | 0.775196i | ||||||
\(905\) | −1.78728e47 | + | 3.10060e47i | −0.882705 | + | 1.53133i | ||||
\(906\) | 1.33884e47 | 0.649648 | ||||||||
\(907\) | −9.33158e46 | − | 9.33158e46i | −0.444876 | − | 0.444876i | 0.448771 | − | 0.893647i | \(-0.351862\pi\) |
−0.893647 | + | 0.448771i | \(0.851862\pi\) | |||||||
\(908\) | 8.34979e45 | − | 8.34979e45i | 0.0391113 | − | 0.0391113i | ||||
\(909\) | 2.07639e46i | 0.0955621i | ||||||||
\(910\) | 2.23703e47 | − | 6.01066e46i | 1.01160 | − | 0.271806i | ||||
\(911\) | −2.09272e47 | −0.929860 | −0.464930 | − | 0.885347i | \(-0.653921\pi\) | ||||
−0.464930 | + | 0.885347i | \(0.653921\pi\) | |||||||
\(912\) | −7.23793e46 | − | 7.23793e46i | −0.316007 | − | 0.316007i | ||||
\(913\) | 1.48720e46 | − | 1.48720e46i | 0.0638022 | − | 0.0638022i | ||||
\(914\) | 4.83235e46i | 0.203713i | ||||||||
\(915\) | −3.96804e46 | − | 1.47681e47i | −0.164376 | − | 0.611770i | ||||
\(916\) | −2.90024e46 | −0.118061 | ||||||||
\(917\) | −7.79300e46 | − | 7.79300e46i | −0.311742 | − | 0.311742i | ||||
\(918\) | −2.08506e47 | + | 2.08506e47i | −0.819665 | + | 0.819665i | ||||
\(919\) | − | 1.72180e46i | − | 0.0665175i | −0.999447 | − | 0.0332587i | \(-0.989411\pi\) | ||
0.999447 | − | 0.0332587i | \(-0.0105885\pi\) | |||||||
\(920\) | 3.49784e47 | + | 2.01626e47i | 1.32799 | + | 0.765494i | ||||
\(921\) | 7.62982e46 | 0.284682 | ||||||||
\(922\) | 1.22603e47 | + | 1.22603e47i | 0.449579 | + | 0.449579i | ||||
\(923\) | −2.50096e47 | + | 2.50096e47i | −0.901322 | + | 0.901322i | ||||
\(924\) | 2.58970e46i | 0.0917272i | ||||||||
\(925\) | −1.30088e47 | + | 4.88189e47i | −0.452865 | + | 1.69950i | ||||
\(926\) | −2.27634e47 | −0.778863 | ||||||||
\(927\) | −1.31091e47 | − | 1.31091e47i | −0.440855 | − | 0.440855i | ||||
\(928\) | 9.75009e46 | − | 9.75009e46i | 0.322286 | − | 0.322286i | ||||
\(929\) | − | 2.64416e47i | − | 0.859084i | −0.903047 | − | 0.429542i | \(-0.858675\pi\) | ||
0.903047 | − | 0.429542i | \(-0.141325\pi\) | |||||||
\(930\) | −1.73366e45 | + | 3.00759e45i | −0.00553653 | + | 0.00960486i | ||||
\(931\) | −1.01184e46 | −0.0317626 | ||||||||
\(932\) | 1.93371e46 | + | 1.93371e46i | 0.0596675 | + | 0.0596675i | ||||
\(933\) | −2.19160e47 | + | 2.19160e47i | −0.664745 | + | 0.664745i | ||||
\(934\) | 9.37776e46i | 0.279608i | ||||||||
\(935\) | 2.71086e47 | − | 7.28380e46i | 0.794551 | − | 0.213487i | ||||
\(936\) | 1.93586e47 | 0.557776 | ||||||||
\(937\) | 1.43168e47 | + | 1.43168e47i | 0.405522 | + | 0.405522i | 0.880174 | − | 0.474652i | \(-0.157426\pi\) |
−0.474652 | + | 0.880174i | \(0.657426\pi\) | |||||||
\(938\) | 6.37915e45 | − | 6.37915e45i | 0.0177630 | − | 0.0177630i | ||||
\(939\) | − | 3.67079e47i | − | 1.00487i | ||||||
\(940\) | 1.08317e46 | + | 4.03133e46i | 0.0291509 | + | 0.108493i | ||||
\(941\) | 3.89222e47 | 1.02983 | 0.514913 | − | 0.857242i | \(-0.327824\pi\) | ||||
0.514913 | + | 0.857242i | \(0.327824\pi\) | |||||||
\(942\) | −2.69165e46 | − | 2.69165e46i | −0.0700171 | − | 0.0700171i | ||||
\(943\) | 1.68236e47 | − | 1.68236e47i | 0.430261 | − | 0.430261i | ||||
\(944\) | 3.62872e47i | 0.912434i | ||||||||
\(945\) | −3.83518e47 | − | 2.21071e47i | −0.948149 | − | 0.546542i | ||||
\(946\) | 2.54569e47 | 0.618795 | ||||||||
\(947\) | 2.43935e47 | + | 2.43935e47i | 0.583009 | + | 0.583009i | 0.935729 | − | 0.352720i | \(-0.114743\pi\) |
−0.352720 | + | 0.935729i | \(0.614743\pi\) | |||||||
\(948\) | 3.05121e46 | − | 3.05121e46i | 0.0717031 | − | 0.0717031i | ||||
\(949\) | − | 3.23978e47i | − | 0.748611i | ||||||
\(950\) | −2.96932e47 | − | 7.91236e46i | −0.674652 | − | 0.179775i | ||||
\(951\) | −2.02187e47 | −0.451716 | ||||||||
\(952\) | 4.17974e47 | + | 4.17974e47i | 0.918245 | + | 0.918245i | ||||
\(953\) | −1.43165e47 | + | 1.43165e47i | −0.309280 | + | 0.309280i | −0.844630 | − | 0.535350i | \(-0.820180\pi\) |
0.535350 | + | 0.844630i | \(0.320180\pi\) | |||||||
\(954\) | 1.07264e47i | 0.227866i | ||||||||
\(955\) | 7.24740e46 | − | 1.25729e47i | 0.151401 | − | 0.262653i | ||||
\(956\) | 4.28636e46 | 0.0880567 | ||||||||
\(957\) | −2.30650e47 | − | 2.30650e47i | −0.465975 | − | 0.465975i | ||||
\(958\) | 3.38005e47 | − | 3.38005e47i | 0.671545 | − | 0.671545i | ||||
\(959\) | − | 1.30748e47i | − | 0.255469i | ||||||
\(960\) | −4.08966e47 | + | 1.09885e47i | −0.785865 | + | 0.211153i | ||||
\(961\) | −5.28998e47 | −0.999723 | ||||||||
\(962\) | −6.86862e47 | − | 6.86862e47i | −1.27664 | − | 1.27664i | ||||
\(963\) | −2.67704e47 | + | 2.67704e47i | −0.489366 | + | 0.489366i | ||||
\(964\) | − | 1.57241e47i | − | 0.282705i | ||||||
\(965\) | −1.26208e47 | − | 4.69716e47i | −0.223177 | − | 0.830612i | ||||
\(966\) | 5.60490e47 | 0.974841 | ||||||||
\(967\) | −3.42384e45 | − | 3.42384e45i | −0.00585721 | − | 0.00585721i | 0.704172 | − | 0.710029i | \(-0.251318\pi\) |
−0.710029 | + | 0.704172i | \(0.751318\pi\) | |||||||
\(968\) | 2.34871e47 | − | 2.34871e47i | 0.395206 | − | 0.395206i | ||||
\(969\) | − | 4.06763e47i | − | 0.673226i | ||||||
\(970\) | −2.10741e47 | − | 1.21478e47i | −0.343085 | − | 0.197765i | ||||
\(971\) | 4.09981e47 | 0.656532 | 0.328266 | − | 0.944585i | \(-0.393536\pi\) | ||||
0.328266 | + | 0.944585i | \(0.393536\pi\) | |||||||
\(972\) | −6.63945e46 | − | 6.63945e46i | −0.104586 | − | 0.104586i | ||||
\(973\) | 4.94154e47 | − | 4.94154e47i | 0.765697 | − | 0.765697i | ||||
\(974\) | − | 6.50905e47i | − | 0.992143i | ||||||
\(975\) | −4.79334e47 | + | 2.77626e47i | −0.718727 | + | 0.416281i | ||||
\(976\) | 4.62963e47 | 0.682888 | ||||||||
\(977\) | 6.06829e47 | + | 6.06829e47i | 0.880549 | + | 0.880549i | 0.993590 | − | 0.113042i | \(-0.0360593\pi\) |
−0.113042 | + | 0.993590i | \(0.536059\pi\) | |||||||
\(978\) | −5.09453e47 | + | 5.09453e47i | −0.727248 | + | 0.727248i | ||||
\(979\) | 9.44505e47i | 1.32642i | ||||||||
\(980\) | −2.64622e45 | + | 4.59071e45i | −0.00365603 | + | 0.00634253i | ||||
\(981\) | −3.76511e47 | −0.511768 | ||||||||
\(982\) | −1.14597e46 | − | 1.14597e46i | −0.0153247 | − | 0.0153247i | ||||
\(983\) | 1.63313e47 | − | 1.63313e47i | 0.214864 | − | 0.214864i | −0.591466 | − | 0.806330i | \(-0.701451\pi\) |
0.806330 | + | 0.591466i | \(0.201451\pi\) | |||||||
\(984\) | 2.56637e47i | 0.332199i | ||||||||
\(985\) | 1.49077e48 | − | 4.00553e47i | 1.89858 | − | 0.510129i | ||||
\(986\) | −1.12197e48 | −1.40589 | ||||||||
\(987\) | 2.71922e47 | + | 2.71922e47i | 0.335250 | + | 0.335250i | ||||
\(988\) | −9.01156e46 | + | 9.01156e46i | −0.109317 | + | 0.109317i | ||||
\(989\) | 1.18846e48i | 1.41855i | ||||||||
\(990\) | −6.38419e46 | − | 2.37605e47i | −0.0749795 | − | 0.279057i | ||||
\(991\) | −7.49308e47 | −0.865928 | −0.432964 | − | 0.901411i | \(-0.642532\pi\) | ||||
−0.432964 | + | 0.901411i | \(0.642532\pi\) | |||||||
\(992\) | 3.62943e45 | + | 3.62943e45i | 0.00412716 | + | 0.00412716i | ||||
\(993\) | 6.54926e47 | − | 6.54926e47i | 0.732832 | − | 0.732832i | ||||
\(994\) | 9.46589e47i | 1.04227i | ||||||||
\(995\) | −2.74865e47 | − | 1.58440e47i | −0.297817 | − | 0.171671i | ||||
\(996\) | −1.59605e46 | −0.0170175 | ||||||||
\(997\) | 1.54277e47 | + | 1.54277e47i | 0.161875 | + | 0.161875i | 0.783397 | − | 0.621522i | \(-0.213485\pi\) |
−0.621522 | + | 0.783397i | \(0.713485\pi\) | |||||||
\(998\) | 5.70807e47 | − | 5.70807e47i | 0.589387 | − | 0.589387i | ||||
\(999\) | 1.85634e48i | 1.88629i |
(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.2.4 | ✓ | 30 | |
5.2 | odd | 4 | 25.33.c.b.18.12 | 30 | |||
5.3 | odd | 4 | inner | 5.33.c.a.3.4 | yes | 30 | |
5.4 | even | 2 | 25.33.c.b.7.12 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.33.c.a.2.4 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5.33.c.a.3.4 | yes | 30 | 5.3 | odd | 4 | inner | |
25.33.c.b.7.12 | 30 | 5.4 | even | 2 | |||
25.33.c.b.18.12 | 30 | 5.2 | odd | 4 |