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 | 2.6 | ||
Character | \(\chi\) | \(=\) | 5.2 |
Dual form | 5.33.c.a.3.6 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −37971.9 | − | 37971.9i | −0.579405 | − | 0.579405i | 0.355334 | − | 0.934739i | \(-0.384367\pi\) |
−0.934739 | + | 0.355334i | \(0.884367\pi\) | |||||||
\(3\) | 3.04306e7 | − | 3.04306e7i | 0.706920 | − | 0.706920i | −0.258966 | − | 0.965886i | \(-0.583382\pi\) |
0.965886 | + | 0.258966i | \(0.0833818\pi\) | |||||||
\(4\) | − | 1.41124e9i | − | 0.328580i | ||||||
\(5\) | 7.42414e10 | − | 1.33309e11i | 0.486549 | − | 0.873654i | ||||
\(6\) | −2.31101e12 | −0.819186 | ||||||||
\(7\) | −9.26812e12 | − | 9.26812e12i | −0.278884 | − | 0.278884i | 0.553780 | − | 0.832663i | \(-0.313185\pi\) |
−0.832663 | + | 0.553780i | \(0.813185\pi\) | |||||||
\(8\) | −2.16675e14 | + | 2.16675e14i | −0.769786 | + | 0.769786i | ||||
\(9\) | 9.78102e11i | 0.000527842i | ||||||||
\(10\) | −7.88108e15 | + | 2.24291e15i | −0.788108 | + | 0.224291i | ||||
\(11\) | 1.98923e16 | 0.432914 | 0.216457 | − | 0.976292i | \(-0.430550\pi\) | ||||
0.216457 | + | 0.976292i | \(0.430550\pi\) | |||||||
\(12\) | −4.29449e16 | − | 4.29449e16i | −0.232280 | − | 0.232280i | ||||
\(13\) | −8.93581e17 | + | 8.93581e17i | −1.34289 | + | 1.34289i | −0.449719 | + | 0.893170i | \(0.648476\pi\) |
−0.893170 | + | 0.449719i | \(0.851524\pi\) | |||||||
\(14\) | 7.03856e17i | 0.323173i | ||||||||
\(15\) | −1.79746e18 | − | 6.31588e18i | −0.273652 | − | 0.961554i | ||||
\(16\) | 1.03939e19 | 0.563455 | ||||||||
\(17\) | −3.66719e19 | − | 3.66719e19i | −0.753617 | − | 0.753617i | 0.221536 | − | 0.975152i | \(-0.428893\pi\) |
−0.975152 | + | 0.221536i | \(0.928893\pi\) | |||||||
\(18\) | 3.71404e16 | − | 3.71404e16i | 0.000305834 | − | 0.000305834i | ||||
\(19\) | − | 2.80535e20i | − | 0.972589i | −0.873795 | − | 0.486295i | \(-0.838348\pi\) | ||
0.873795 | − | 0.486295i | \(-0.161652\pi\) | |||||||
\(20\) | −1.88131e20 | − | 1.04772e20i | −0.287065 | − | 0.159870i | ||||
\(21\) | −5.64069e20 | −0.394297 | ||||||||
\(22\) | −7.55348e20 | − | 7.55348e20i | −0.250833 | − | 0.250833i | ||||
\(23\) | −2.06972e21 | + | 2.06972e21i | −0.337495 | + | 0.337495i | −0.855424 | − | 0.517929i | \(-0.826703\pi\) |
0.517929 | + | 0.855424i | \(0.326703\pi\) | |||||||
\(24\) | 1.31871e22i | 1.08835i | ||||||||
\(25\) | −1.22595e22 | − | 1.97941e22i | −0.526541 | − | 0.850150i | ||||
\(26\) | 6.78619e22 | 1.55615 | ||||||||
\(27\) | 5.64183e22 | + | 5.64183e22i | 0.707293 | + | 0.707293i | ||||
\(28\) | −1.30795e22 | + | 1.30795e22i | −0.0916355 | + | 0.0916355i | ||||
\(29\) | 1.02359e23i | 0.409031i | 0.978863 | + | 0.204516i | \(0.0655620\pi\) | ||||
−0.978863 | + | 0.204516i | \(0.934438\pi\) | |||||||
\(30\) | −1.71573e23 | + | 3.08079e23i | −0.398574 | + | 0.715685i | ||||
\(31\) | −9.64778e23 | −1.32630 | −0.663148 | − | 0.748488i | \(-0.730780\pi\) | ||||
−0.663148 | + | 0.748488i | \(0.730780\pi\) | |||||||
\(32\) | 5.35937e23 | + | 5.35937e23i | 0.443317 | + | 0.443317i | ||||
\(33\) | 6.05335e23 | − | 6.05335e23i | 0.306036 | − | 0.306036i | ||||
\(34\) | 2.78500e24i | 0.873298i | ||||||||
\(35\) | −1.92360e24 | + | 5.47445e23i | −0.379338 | + | 0.107957i | ||||
\(36\) | 1.38034e21 | 0.000173438 | ||||||||
\(37\) | 7.27232e24 | + | 7.27232e24i | 0.589448 | + | 0.589448i | 0.937482 | − | 0.348034i | \(-0.113151\pi\) |
−0.348034 | + | 0.937482i | \(0.613151\pi\) | |||||||
\(38\) | −1.06524e25 | + | 1.06524e25i | −0.563523 | + | 0.563523i | ||||
\(39\) | 5.43844e25i | 1.89863i | ||||||||
\(40\) | 1.27985e25 | + | 4.49711e25i | 0.297988 | + | 1.04706i | ||||
\(41\) | 1.58648e25 | 0.248825 | 0.124412 | − | 0.992231i | \(-0.460295\pi\) | ||||
0.124412 | + | 0.992231i | \(0.460295\pi\) | |||||||
\(42\) | 2.14188e25 | + | 2.14188e25i | 0.228458 | + | 0.228458i | ||||
\(43\) | −9.21200e25 | + | 9.21200e25i | −0.674309 | + | 0.674309i | −0.958706 | − | 0.284398i | \(-0.908206\pi\) |
0.284398 | + | 0.958706i | \(0.408206\pi\) | |||||||
\(44\) | − | 2.80728e25i | − | 0.142247i | ||||||
\(45\) | 1.30390e23 | + | 7.26157e22i | 0.000461151 | + | 0.000256821i | ||||
\(46\) | 1.57183e26 | 0.391092 | ||||||||
\(47\) | −3.74128e26 | − | 3.74128e26i | −0.659863 | − | 0.659863i | 0.295484 | − | 0.955348i | \(-0.404519\pi\) |
−0.955348 | + | 0.295484i | \(0.904519\pi\) | |||||||
\(48\) | 3.16293e26 | − | 3.16293e26i | 0.398318 | − | 0.398318i | ||||
\(49\) | − | 9.32632e26i | − | 0.844448i | ||||||
\(50\) | −2.86103e26 | + | 1.21713e27i | −0.187501 | + | 0.797661i | ||||
\(51\) | −2.23189e27 | −1.06549 | ||||||||
\(52\) | 1.26106e27 | + | 1.26106e27i | 0.441246 | + | 0.441246i | ||||
\(53\) | 4.43458e27 | − | 4.43458e27i | 1.14403 | − | 1.14403i | 0.156328 | − | 0.987705i | \(-0.450034\pi\) |
0.987705 | − | 0.156328i | \(-0.0499658\pi\) | |||||||
\(54\) | − | 4.28462e27i | − | 0.819618i | ||||||
\(55\) | 1.47683e27 | − | 2.65182e27i | 0.210634 | − | 0.378217i | ||||
\(56\) | 4.01635e27 | 0.429361 | ||||||||
\(57\) | −8.53685e27 | − | 8.53685e27i | −0.687543 | − | 0.687543i | ||||
\(58\) | 3.88675e27 | − | 3.88675e27i | 0.236995 | − | 0.236995i | ||||
\(59\) | 4.27569e27i | 0.198323i | 0.995071 | + | 0.0991617i | \(0.0316161\pi\) | ||||
−0.995071 | + | 0.0991617i | \(0.968384\pi\) | |||||||
\(60\) | −8.91322e27 | + | 2.53665e27i | −0.315947 | + | 0.0899166i | ||||
\(61\) | −5.42671e28 | −1.47659 | −0.738295 | − | 0.674478i | \(-0.764369\pi\) | ||||
−0.738295 | + | 0.674478i | \(0.764369\pi\) | |||||||
\(62\) | 3.66344e28 | + | 3.66344e28i | 0.768462 | + | 0.768462i | ||||
\(63\) | 9.06517e24 | − | 9.06517e24i | 0.000147207 | − | 0.000147207i | ||||
\(64\) | − | 8.53426e28i | − | 1.07718i | ||||||
\(65\) | 5.27816e28 | + | 1.85463e29i | 0.519839 | + | 1.82660i | ||||
\(66\) | −4.59714e28 | −0.354637 | ||||||||
\(67\) | 1.45709e29 | + | 1.45709e29i | 0.883669 | + | 0.883669i | 0.993905 | − | 0.110236i | \(-0.0351607\pi\) |
−0.110236 | + | 0.993905i | \(0.535161\pi\) | |||||||
\(68\) | −5.17528e28 | + | 5.17528e28i | −0.247623 | + | 0.247623i | ||||
\(69\) | 1.25966e29i | 0.477163i | ||||||||
\(70\) | 9.38303e28 | + | 5.22553e28i | 0.282341 | + | 0.157239i | ||||
\(71\) | −1.17360e29 | −0.281441 | −0.140720 | − | 0.990049i | \(-0.544942\pi\) | ||||
−0.140720 | + | 0.990049i | \(0.544942\pi\) | |||||||
\(72\) | −2.11931e26 | − | 2.11931e26i | −0.000406325 | − | 0.000406325i | ||||
\(73\) | −8.02415e28 | + | 8.02415e28i | −0.123377 | + | 0.123377i | −0.766099 | − | 0.642722i | \(-0.777805\pi\) |
0.642722 | + | 0.766099i | \(0.277805\pi\) | |||||||
\(74\) | − | 5.52287e29i | − | 0.683058i | ||||||
\(75\) | −9.75409e29 | − | 2.29283e29i | −0.973210 | − | 0.228766i | ||||
\(76\) | −3.95902e29 | −0.319573 | ||||||||
\(77\) | −1.84364e29 | − | 1.84364e29i | −0.120733 | − | 0.120733i | ||||
\(78\) | 2.06508e30 | − | 2.06508e30i | 1.10008 | − | 1.10008i | ||||
\(79\) | − | 2.05013e30i | − | 0.890734i | −0.895348 | − | 0.445367i | \(-0.853073\pi\) | ||
0.895348 | − | 0.445367i | \(-0.146927\pi\) | |||||||
\(80\) | 7.71659e29 | − | 1.38560e30i | 0.274148 | − | 0.492265i | ||||
\(81\) | 3.43187e30 | 0.999472 | ||||||||
\(82\) | −6.02417e29 | − | 6.02417e29i | −0.144170 | − | 0.144170i | ||||
\(83\) | −4.06190e30 | + | 4.06190e30i | −0.800718 | + | 0.800718i | −0.983208 | − | 0.182490i | \(-0.941584\pi\) |
0.182490 | + | 0.983208i | \(0.441584\pi\) | |||||||
\(84\) | 7.96036e29i | 0.129558i | ||||||||
\(85\) | −7.61126e30 | + | 2.16612e30i | −1.02507 | + | 0.291729i | ||||
\(86\) | 6.99594e30 | 0.781396 | ||||||||
\(87\) | 3.11484e30 | + | 3.11484e30i | 0.289153 | + | 0.289153i | ||||
\(88\) | −4.31017e30 | + | 4.31017e30i | −0.333251 | + | 0.333251i | ||||
\(89\) | − | 1.23259e31i | − | 0.795386i | −0.917519 | − | 0.397693i | \(-0.869811\pi\) | ||
0.917519 | − | 0.397693i | \(-0.130189\pi\) | |||||||
\(90\) | −2.19379e27 | − | 7.70850e27i | −0.000118390 | − | 0.000415997i | ||||
\(91\) | 1.65636e31 | 0.749019 | ||||||||
\(92\) | 2.92087e30 | + | 2.92087e30i | 0.110894 | + | 0.110894i | ||||
\(93\) | −2.93588e31 | + | 2.93588e31i | −0.937585 | + | 0.937585i | ||||
\(94\) | 2.84127e31i | 0.764656i | ||||||||
\(95\) | −3.73978e31 | − | 2.08273e31i | −0.849706 | − | 0.473212i | ||||
\(96\) | 3.26178e31 | 0.626779 | ||||||||
\(97\) | 2.90974e31 | + | 2.90974e31i | 0.473704 | + | 0.473704i | 0.903111 | − | 0.429407i | \(-0.141277\pi\) |
−0.429407 | + | 0.903111i | \(0.641277\pi\) | |||||||
\(98\) | −3.54138e31 | + | 3.54138e31i | −0.489277 | + | 0.489277i | ||||
\(99\) | 1.94567e28i | 0.000228510i | ||||||||
\(100\) | −2.79342e31 | + | 1.73011e31i | −0.279342 | + | 0.173011i | ||||
\(101\) | 4.16959e31 | 0.355592 | 0.177796 | − | 0.984067i | \(-0.443103\pi\) | ||||
0.177796 | + | 0.984067i | \(0.443103\pi\) | |||||||
\(102\) | 8.47492e31 | + | 8.47492e31i | 0.617352 | + | 0.617352i | ||||
\(103\) | 1.50389e32 | − | 1.50389e32i | 0.937176 | − | 0.937176i | −0.0609644 | − | 0.998140i | \(-0.519418\pi\) |
0.998140 | + | 0.0609644i | \(0.0194176\pi\) | |||||||
\(104\) | − | 3.87234e32i | − | 2.06747i | ||||||
\(105\) | −4.18773e31 | + | 7.51954e31i | −0.191845 | + | 0.344479i | ||||
\(106\) | −3.36779e32 | −1.32572 | ||||||||
\(107\) | −4.62097e31 | − | 4.62097e31i | −0.156528 | − | 0.156528i | 0.624498 | − | 0.781026i | \(-0.285304\pi\) |
−0.781026 | + | 0.624498i | \(0.785304\pi\) | |||||||
\(108\) | 7.96197e31 | − | 7.96197e31i | 0.232402 | − | 0.232402i | ||||
\(109\) | − | 5.38999e32i | − | 1.35758i | −0.734334 | − | 0.678788i | \(-0.762505\pi\) | ||
0.734334 | − | 0.678788i | \(-0.237495\pi\) | |||||||
\(110\) | −1.56773e32 | + | 4.46165e31i | −0.341183 | + | 0.0970986i | ||||
\(111\) | 4.42602e32 | 0.833385 | ||||||||
\(112\) | −9.63321e31 | − | 9.63321e31i | −0.157138 | − | 0.157138i | ||||
\(113\) | −4.09133e32 | + | 4.09133e32i | −0.578908 | + | 0.578908i | −0.934602 | − | 0.355694i | \(-0.884244\pi\) |
0.355694 | + | 0.934602i | \(0.384244\pi\) | |||||||
\(114\) | 6.48320e32i | 0.796732i | ||||||||
\(115\) | 1.22253e32 | + | 4.29572e32i | 0.130646 | + | 0.459061i | ||||
\(116\) | 1.44453e32 | 0.134399 | ||||||||
\(117\) | −8.74013e29 | − | 8.74013e29i | −0.000708833 | − | 0.000708833i | ||||
\(118\) | 1.62356e32 | − | 1.62356e32i | 0.114910 | − | 0.114910i | ||||
\(119\) | 6.79759e32i | 0.420343i | ||||||||
\(120\) | 1.75796e33 | + | 9.79031e32i | 0.950844 | + | 0.529537i | ||||
\(121\) | −1.71567e33 | −0.812585 | ||||||||
\(122\) | 2.06063e33 | + | 2.06063e33i | 0.855543 | + | 0.855543i | ||||
\(123\) | 4.82776e32 | − | 4.82776e32i | 0.175899 | − | 0.175899i | ||||
\(124\) | 1.36153e33i | 0.435794i | ||||||||
\(125\) | −3.54889e33 | + | 1.64758e32i | −0.998924 | + | 0.0463752i | ||||
\(126\) | −6.88443e29 | −0.000170584 | ||||||||
\(127\) | −5.06270e33 | − | 5.06270e33i | −1.10541 | − | 1.10541i | −0.993746 | − | 0.111661i | \(-0.964383\pi\) |
−0.111661 | − | 0.993746i | \(-0.535617\pi\) | |||||||
\(128\) | −9.38787e32 | + | 9.38787e32i | −0.180804 | + | 0.180804i | ||||
\(129\) | 5.60654e33i | 0.953365i | ||||||||
\(130\) | 5.03816e33 | − | 9.04660e33i | 0.757144 | − | 1.35954i | ||||
\(131\) | 9.32687e32 | 0.123992 | 0.0619962 | − | 0.998076i | \(-0.480253\pi\) | ||||
0.0619962 | + | 0.998076i | \(0.480253\pi\) | |||||||
\(132\) | −8.54272e32 | − | 8.54272e32i | −0.100557 | − | 0.100557i | ||||
\(133\) | −2.60003e33 | + | 2.60003e33i | −0.271239 | + | 0.271239i | ||||
\(134\) | − | 1.10657e34i | − | 1.02400i | ||||||
\(135\) | 1.17096e34 | − | 3.33249e33i | 0.962062 | − | 0.273797i | ||||
\(136\) | 1.58918e34 | 1.16025 | ||||||||
\(137\) | −1.30606e34 | − | 1.30606e34i | −0.848072 | − | 0.848072i | 0.141820 | − | 0.989892i | \(-0.454704\pi\) |
−0.989892 | + | 0.141820i | \(0.954704\pi\) | |||||||
\(138\) | 4.78316e33 | − | 4.78316e33i | 0.276471 | − | 0.276471i | ||||
\(139\) | 1.49340e34i | 0.769025i | 0.923120 | + | 0.384513i | \(0.125631\pi\) | ||||
−0.923120 | + | 0.384513i | \(0.874369\pi\) | |||||||
\(140\) | 7.72576e32 | + | 2.71466e33i | 0.0354726 | + | 0.124643i | ||||
\(141\) | −2.27698e34 | −0.932941 | ||||||||
\(142\) | 4.45639e33 | + | 4.45639e33i | 0.163068 | + | 0.163068i | ||||
\(143\) | −1.77754e34 | + | 1.77754e34i | −0.581356 | + | 0.581356i | ||||
\(144\) | 1.01663e31i | 0.000297416i | ||||||||
\(145\) | 1.36453e34 | + | 7.59925e33i | 0.357352 | + | 0.199014i | ||||
\(146\) | 6.09384e33 | 0.142970 | ||||||||
\(147\) | −2.83805e34 | − | 2.83805e34i | −0.596957 | − | 0.596957i | ||||
\(148\) | 1.02630e34 | − | 1.02630e34i | 0.193681 | − | 0.193681i | ||||
\(149\) | − | 8.34768e33i | − | 0.141444i | −0.997496 | − | 0.0707222i | \(-0.977470\pi\) | ||
0.997496 | − | 0.0707222i | \(-0.0225304\pi\) | |||||||
\(150\) | 2.83318e34 | + | 4.57444e34i | 0.431335 | + | 0.696431i | ||||
\(151\) | −5.21301e34 | −0.713604 | −0.356802 | − | 0.934180i | \(-0.616133\pi\) | ||||
−0.356802 | + | 0.934180i | \(0.616133\pi\) | |||||||
\(152\) | 6.07851e34 | + | 6.07851e34i | 0.748685 | + | 0.748685i | ||||
\(153\) | 3.58688e31 | − | 3.58688e31i | 0.000397791 | − | 0.000397791i | ||||
\(154\) | 1.40013e34i | 0.139906i | ||||||||
\(155\) | −7.16265e34 | + | 1.28614e35i | −0.645307 | + | 1.15872i | ||||
\(156\) | 7.67494e34 | 0.623852 | ||||||||
\(157\) | 5.64726e34 | + | 5.64726e34i | 0.414422 | + | 0.414422i | 0.883276 | − | 0.468854i | \(-0.155333\pi\) |
−0.468854 | + | 0.883276i | \(0.655333\pi\) | |||||||
\(158\) | −7.78473e34 | + | 7.78473e34i | −0.516096 | + | 0.516096i | ||||
\(159\) | − | 2.69894e35i | − | 1.61748i | ||||||
\(160\) | 1.11234e35 | − | 3.16565e34i | 0.603001 | − | 0.171610i | ||||
\(161\) | 3.83649e34 | 0.188243 | ||||||||
\(162\) | −1.30315e35 | − | 1.30315e35i | −0.579099 | − | 0.579099i | ||||
\(163\) | −1.65579e35 | + | 1.65579e35i | −0.666814 | + | 0.666814i | −0.956977 | − | 0.290163i | \(-0.906290\pi\) |
0.290163 | + | 0.956977i | \(0.406290\pi\) | |||||||
\(164\) | − | 2.23891e34i | − | 0.0817587i | ||||||
\(165\) | −3.57556e34 | − | 1.25637e35i | −0.118468 | − | 0.416271i | ||||
\(166\) | 3.08476e35 | 0.927880 | ||||||||
\(167\) | −2.81705e35 | − | 2.81705e35i | −0.769718 | − | 0.769718i | 0.208339 | − | 0.978057i | \(-0.433194\pi\) |
−0.978057 | + | 0.208339i | \(0.933194\pi\) | |||||||
\(168\) | 1.22220e35 | − | 1.22220e35i | 0.303524 | − | 0.303524i | ||||
\(169\) | − | 1.15419e36i | − | 2.60670i | ||||||
\(170\) | 3.71265e35 | + | 2.06762e35i | 0.762960 | + | 0.424902i | ||||
\(171\) | 2.74392e32 | 0.000513374 | ||||||||
\(172\) | 1.30003e35 | + | 1.30003e35i | 0.221564 | + | 0.221564i | ||||
\(173\) | −8.17618e35 | + | 8.17618e35i | −1.27003 | + | 1.27003i | −0.323955 | + | 0.946073i | \(0.605012\pi\) |
−0.946073 | + | 0.323955i | \(0.894988\pi\) | |||||||
\(174\) | − | 2.36552e35i | − | 0.335073i | ||||||
\(175\) | −6.98316e34 | + | 2.97076e35i | −0.0902492 | + | 0.383936i | ||||
\(176\) | 2.06759e35 | 0.243928 | ||||||||
\(177\) | 1.30112e35 | + | 1.30112e35i | 0.140199 | + | 0.140199i | ||||
\(178\) | −4.68037e35 | + | 4.68037e35i | −0.460851 | + | 0.460851i | ||||
\(179\) | 1.95532e36i | 1.76023i | 0.474761 | + | 0.880115i | \(0.342535\pi\) | ||||
−0.474761 | + | 0.880115i | \(0.657465\pi\) | |||||||
\(180\) | 1.02478e32 | − | 1.84011e32i | 8.43862e−5 | − | 0.000151525i | ||||
\(181\) | 2.09841e36 | 1.58137 | 0.790683 | − | 0.612226i | \(-0.209726\pi\) | ||||
0.790683 | + | 0.612226i | \(0.209726\pi\) | |||||||
\(182\) | −6.28952e35 | − | 6.28952e35i | −0.433986 | − | 0.433986i | ||||
\(183\) | −1.65138e36 | + | 1.65138e36i | −1.04383 | + | 1.04383i | ||||
\(184\) | − | 8.96916e35i | − | 0.519597i | ||||||
\(185\) | 1.50937e36 | − | 4.29558e35i | 0.801768 | − | 0.228178i | ||||
\(186\) | 2.22962e36 | 1.08648 | ||||||||
\(187\) | −7.29488e35 | − | 7.29488e35i | −0.326251 | − | 0.326251i | ||||
\(188\) | −5.27984e35 | + | 5.27984e35i | −0.216818 | + | 0.216818i | ||||
\(189\) | − | 1.04578e36i | − | 0.394505i | ||||||
\(190\) | 6.29214e35 | + | 2.21092e36i | 0.218143 | + | 0.766505i | ||||
\(191\) | −5.67177e36 | −1.80794 | −0.903972 | − | 0.427591i | \(-0.859362\pi\) | ||||
−0.903972 | + | 0.427591i | \(0.859362\pi\) | |||||||
\(192\) | −2.59703e36 | − | 2.59703e36i | −0.761477 | − | 0.761477i | ||||
\(193\) | −7.44448e35 | + | 7.44448e35i | −0.200871 | + | 0.200871i | −0.800373 | − | 0.599502i | \(-0.795365\pi\) |
0.599502 | + | 0.800373i | \(0.295365\pi\) | |||||||
\(194\) | − | 2.20977e36i | − | 0.548933i | ||||||
\(195\) | 7.24992e36 | + | 4.03757e36i | 1.65875 | + | 0.923776i | ||||
\(196\) | −1.31617e36 | −0.277469 | ||||||||
\(197\) | −3.61428e36 | − | 3.61428e36i | −0.702365 | − | 0.702365i | 0.262553 | − | 0.964918i | \(-0.415436\pi\) |
−0.964918 | + | 0.262553i | \(0.915436\pi\) | |||||||
\(198\) | 7.38808e32 | − | 7.38808e32i | 0.000132400 | − | 0.000132400i | ||||
\(199\) | − | 9.57640e36i | − | 1.58326i | −0.610998 | − | 0.791632i | \(-0.709232\pi\) | ||
0.610998 | − | 0.791632i | \(-0.290768\pi\) | |||||||
\(200\) | 6.94522e36 | + | 1.63256e36i | 1.05976 | + | 0.249109i | ||||
\(201\) | 8.86803e36 | 1.24937 | ||||||||
\(202\) | −1.58327e36 | − | 1.58327e36i | −0.206032 | − | 0.206032i | ||||
\(203\) | 9.48672e35 | − | 9.48672e35i | 0.114072 | − | 0.114072i | ||||
\(204\) | 3.14974e36i | 0.350100i | ||||||||
\(205\) | 1.17783e36 | − | 2.11492e36i | 0.121065 | − | 0.217386i | ||||
\(206\) | −1.14211e37 | −1.08601 | ||||||||
\(207\) | −2.02440e33 | − | 2.02440e33i | −0.000178144 | − | 0.000178144i | ||||
\(208\) | −9.28780e36 | + | 9.28780e36i | −0.756658 | + | 0.756658i | ||||
\(209\) | − | 5.58049e36i | − | 0.421048i | ||||||
\(210\) | 4.44547e36 | − | 1.26515e36i | 0.310748 | − | 0.0884370i | ||||
\(211\) | 1.21317e37 | 0.785965 | 0.392982 | − | 0.919546i | \(-0.371443\pi\) | ||||
0.392982 | + | 0.919546i | \(0.371443\pi\) | |||||||
\(212\) | −6.25826e36 | − | 6.25826e36i | −0.375906 | − | 0.375906i | ||||
\(213\) | −3.57134e36 | + | 3.57134e36i | −0.198956 | + | 0.198956i | ||||
\(214\) | 3.50934e36i | 0.181386i | ||||||||
\(215\) | 5.44130e36 | + | 1.91196e37i | 0.261028 | + | 0.917196i | ||||
\(216\) | −2.44489e37 | −1.08893 | ||||||||
\(217\) | 8.94168e36 | + | 8.94168e36i | 0.369882 | + | 0.369882i | ||||
\(218\) | −2.04668e37 | + | 2.04668e37i | −0.786586 | + | 0.786586i | ||||
\(219\) | 4.88359e36i | 0.174435i | ||||||||
\(220\) | −3.74236e36 | − | 2.08416e36i | −0.124275 | − | 0.0692101i | ||||
\(221\) | 6.55386e37 | 2.02405 | ||||||||
\(222\) | −1.68064e37 | − | 1.68064e37i | −0.482867 | − | 0.482867i | ||||
\(223\) | −1.59220e37 | + | 1.59220e37i | −0.425716 | + | 0.425716i | −0.887166 | − | 0.461450i | \(-0.847329\pi\) |
0.461450 | + | 0.887166i | \(0.347329\pi\) | |||||||
\(224\) | − | 9.93426e36i | − | 0.247268i | ||||||
\(225\) | 1.93606e34 | − | 1.19910e34i | 0.000448745 | − | 0.000277931i | ||||
\(226\) | 3.10711e37 | 0.670844 | ||||||||
\(227\) | 2.21352e37 | + | 2.21352e37i | 0.445318 | + | 0.445318i | 0.893795 | − | 0.448477i | \(-0.148033\pi\) |
−0.448477 | + | 0.893795i | \(0.648033\pi\) | |||||||
\(228\) | −1.20475e37 | + | 1.20475e37i | −0.225913 | + | 0.225913i | ||||
\(229\) | − | 3.22541e37i | − | 0.563920i | −0.959426 | − | 0.281960i | \(-0.909016\pi\) | ||
0.959426 | − | 0.281960i | \(-0.0909845\pi\) | |||||||
\(230\) | 1.16695e37 | − | 2.09538e37i | 0.190285 | − | 0.341679i | ||||
\(231\) | −1.12206e37 | −0.170697 | ||||||||
\(232\) | −2.21786e37 | − | 2.21786e37i | −0.314867 | − | 0.314867i | ||||
\(233\) | 1.28133e37 | − | 1.28133e37i | 0.169812 | − | 0.169812i | −0.617085 | − | 0.786897i | \(-0.711686\pi\) |
0.786897 | + | 0.617085i | \(0.211686\pi\) | |||||||
\(234\) | 6.63759e34i | 0.000821403i | ||||||||
\(235\) | −7.76503e37 | + | 2.20988e37i | −0.897547 | + | 0.255436i | ||||
\(236\) | 6.03403e36 | 0.0651651 | ||||||||
\(237\) | −6.23867e37 | − | 6.23867e37i | −0.629678 | − | 0.629678i | ||||
\(238\) | 2.58117e37 | − | 2.58117e37i | 0.243549 | − | 0.243549i | ||||
\(239\) | − | 1.92792e38i | − | 1.70107i | −0.525915 | − | 0.850537i | \(-0.676277\pi\) | ||
0.525915 | − | 0.850537i | \(-0.323723\pi\) | |||||||
\(240\) | −1.86827e37 | − | 6.56468e37i | −0.154191 | − | 0.541793i | ||||
\(241\) | 4.16303e37 | 0.321467 | 0.160734 | − | 0.986998i | \(-0.448614\pi\) | ||||
0.160734 | + | 0.986998i | \(0.448614\pi\) | |||||||
\(242\) | 6.51474e37 | + | 6.51474e37i | 0.470816 | + | 0.470816i | ||||
\(243\) | −1.10337e35 | + | 1.10337e35i | −0.000746481 | + | 0.000746481i | ||||
\(244\) | 7.65840e37i | 0.485177i | ||||||||
\(245\) | −1.24328e38 | − | 6.92399e37i | −0.737755 | − | 0.410865i | ||||
\(246\) | −3.66638e37 | −0.203834 | ||||||||
\(247\) | 2.50681e38 | + | 2.50681e38i | 1.30608 | + | 1.30608i | ||||
\(248\) | 2.09044e38 | − | 2.09044e38i | 1.02096 | − | 1.02096i | ||||
\(249\) | 2.47212e38i | 1.13209i | ||||||||
\(250\) | 1.41014e38 | + | 1.28502e38i | 0.605652 | + | 0.551912i | ||||
\(251\) | −4.15942e38 | −1.67592 | −0.837961 | − | 0.545731i | \(-0.816252\pi\) | ||||
−0.837961 | + | 0.545731i | \(0.816252\pi\) | |||||||
\(252\) | −1.27931e34 | − | 1.27931e34i | −4.83691e−5 | − | 4.83691e-5i | ||||
\(253\) | −4.11715e37 | + | 4.11715e37i | −0.146106 | + | 0.146106i | ||||
\(254\) | 3.84480e38i | 1.28096i | ||||||||
\(255\) | −1.65699e38 | + | 2.97531e38i | −0.518414 | + | 0.930872i | ||||
\(256\) | −2.95249e38 | −0.867658 | ||||||||
\(257\) | 1.31184e38 | + | 1.31184e38i | 0.362201 | + | 0.362201i | 0.864623 | − | 0.502422i | \(-0.167557\pi\) |
−0.502422 | + | 0.864623i | \(0.667557\pi\) | |||||||
\(258\) | 2.12891e38 | − | 2.12891e38i | 0.552384 | − | 0.552384i | ||||
\(259\) | − | 1.34801e38i | − | 0.328775i | ||||||
\(260\) | 2.61733e38 | − | 7.44875e37i | 0.600184 | − | 0.170809i | ||||
\(261\) | −1.00117e35 | −0.000215904 | ||||||||
\(262\) | −3.54159e37 | − | 3.54159e37i | −0.0718419 | − | 0.0718419i | ||||
\(263\) | 1.43361e38 | − | 1.43361e38i | 0.273614 | − | 0.273614i | −0.556939 | − | 0.830553i | \(-0.688024\pi\) |
0.830553 | + | 0.556939i | \(0.188024\pi\) | |||||||
\(264\) | 2.62322e38i | 0.471164i | ||||||||
\(265\) | −2.61940e38 | − | 9.20399e38i | −0.442861 | − | 1.55612i | ||||
\(266\) | 1.97456e38 | 0.314315 | ||||||||
\(267\) | −3.75084e38 | − | 3.75084e38i | −0.562274 | − | 0.562274i | ||||
\(268\) | 2.05630e38 | − | 2.05630e38i | 0.290356 | − | 0.290356i | ||||
\(269\) | 5.49447e38i | 0.730952i | 0.930821 | + | 0.365476i | \(0.119094\pi\) | ||||
−0.930821 | + | 0.365476i | \(0.880906\pi\) | |||||||
\(270\) | −5.71178e38 | − | 3.18096e38i | −0.716063 | − | 0.398784i | ||||
\(271\) | 2.20854e38 | 0.260973 | 0.130487 | − | 0.991450i | \(-0.458346\pi\) | ||||
0.130487 | + | 0.991450i | \(0.458346\pi\) | |||||||
\(272\) | −3.81165e38 | − | 3.81165e38i | −0.424629 | − | 0.424629i | ||||
\(273\) | 5.04041e38 | − | 5.04041e38i | 0.529497 | − | 0.529497i | ||||
\(274\) | 9.91868e38i | 0.982754i | ||||||||
\(275\) | −2.43869e38 | − | 3.93750e38i | −0.227947 | − | 0.368042i | ||||
\(276\) | 1.77768e38 | 0.156786 | ||||||||
\(277\) | 6.85301e38 | + | 6.85301e38i | 0.570433 | + | 0.570433i | 0.932249 | − | 0.361816i | \(-0.117843\pi\) |
−0.361816 | + | 0.932249i | \(0.617843\pi\) | |||||||
\(278\) | 5.67074e38 | − | 5.67074e38i | 0.445577 | − | 0.445577i | ||||
\(279\) | − | 9.43652e35i | − | 0.000700075i | ||||||
\(280\) | 2.98179e38 | − | 5.35415e38i | 0.208905 | − | 0.375113i | ||||
\(281\) | −2.22254e39 | −1.47078 | −0.735392 | − | 0.677642i | \(-0.763002\pi\) | ||||
−0.735392 | + | 0.677642i | \(0.763002\pi\) | |||||||
\(282\) | 8.64614e38 | + | 8.64614e38i | 0.540551 | + | 0.540551i | ||||
\(283\) | 1.27238e39 | − | 1.27238e39i | 0.751683 | − | 0.751683i | −0.223111 | − | 0.974793i | \(-0.571621\pi\) |
0.974793 | + | 0.223111i | \(0.0716211\pi\) | |||||||
\(284\) | 1.65623e38i | 0.0924758i | ||||||||
\(285\) | −1.77183e39 | + | 5.04251e38i | −0.935197 | + | 0.266151i | ||||
\(286\) | 1.34993e39 | 0.673681 | ||||||||
\(287\) | −1.47037e38 | − | 1.47037e38i | −0.0693931 | − | 0.0693931i | ||||
\(288\) | −5.24201e35 | + | 5.24201e35i | −0.000234001 | + | 0.000234001i | ||||
\(289\) | 3.21742e38i | 0.135876i | ||||||||
\(290\) | −2.29581e38 | − | 8.06697e38i | −0.0917419 | − | 0.322361i | ||||
\(291\) | 1.77090e39 | 0.669742 | ||||||||
\(292\) | 1.13240e38 | + | 1.13240e38i | 0.0405391 | + | 0.0405391i | ||||
\(293\) | −4.00474e39 | + | 4.00474e39i | −1.35735 | + | 1.35735i | −0.480181 | + | 0.877169i | \(0.659429\pi\) |
−0.877169 | + | 0.480181i | \(0.840571\pi\) | |||||||
\(294\) | 2.15532e39i | 0.691760i | ||||||||
\(295\) | 5.69988e38 | + | 3.17433e38i | 0.173266 | + | 0.0964940i | ||||
\(296\) | −3.15147e39 | −0.907497 | ||||||||
\(297\) | 1.12229e39 | + | 1.12229e39i | 0.306197 | + | 0.306197i | ||||
\(298\) | −3.16977e38 | + | 3.16977e38i | −0.0819536 | + | 0.0819536i | ||||
\(299\) | − | 3.69893e39i | − | 0.906435i | ||||||
\(300\) | −3.23573e38 | + | 1.37654e39i | −0.0751678 | + | 0.319777i | ||||
\(301\) | 1.70756e39 | 0.376107 | ||||||||
\(302\) | 1.97948e39 | + | 1.97948e39i | 0.413466 | + | 0.413466i | ||||
\(303\) | 1.26883e39 | − | 1.26883e39i | 0.251375 | − | 0.251375i | ||||
\(304\) | − | 2.91586e39i | − | 0.548011i | ||||||
\(305\) | −4.02887e39 | + | 7.23430e39i | −0.718432 | + | 1.29003i | ||||
\(306\) | −2.72402e36 | −0.000460964 | ||||||||
\(307\) | 5.79148e39 | + | 5.79148e39i | 0.930199 | + | 0.930199i | 0.997718 | − | 0.0675191i | \(-0.0215084\pi\) |
−0.0675191 | + | 0.997718i | \(0.521508\pi\) | |||||||
\(308\) | −2.60182e38 | + | 2.60182e38i | −0.0396703 | + | 0.0396703i | ||||
\(309\) | − | 9.15286e39i | − | 1.32502i | ||||||
\(310\) | 7.60349e39 | − | 2.16391e39i | 1.04526 | − | 0.297476i | ||||
\(311\) | 2.40910e39 | 0.314549 | 0.157274 | − | 0.987555i | \(-0.449729\pi\) | ||||
0.157274 | + | 0.987555i | \(0.449729\pi\) | |||||||
\(312\) | −1.17838e40 | − | 1.17838e40i | −1.46154 | − | 1.46154i | ||||
\(313\) | 9.69168e39 | − | 9.69168e39i | 1.14206 | − | 1.14206i | 0.153989 | − | 0.988073i | \(-0.450788\pi\) |
0.988073 | − | 0.153989i | \(-0.0492121\pi\) | |||||||
\(314\) | − | 4.28874e39i | − | 0.480237i | ||||||
\(315\) | −5.35457e35 | − | 1.88148e36i | −5.69844e−5 | − | 0.000200231i | ||||
\(316\) | −2.89323e39 | −0.292677 | ||||||||
\(317\) | −1.29890e39 | − | 1.29890e39i | −0.124919 | − | 0.124919i | 0.641884 | − | 0.766802i | \(-0.278153\pi\) |
−0.766802 | + | 0.641884i | \(0.778153\pi\) | |||||||
\(318\) | −1.02484e40 | + | 1.02484e40i | −0.937176 | + | 0.937176i | ||||
\(319\) | 2.03615e39i | 0.177076i | ||||||||
\(320\) | −1.13769e40 | − | 6.33596e39i | −0.941078 | − | 0.524098i | ||||
\(321\) | −2.81238e39 | −0.221306 | ||||||||
\(322\) | −1.45679e39 | − | 1.45679e39i | −0.109069 | − | 0.109069i | ||||
\(323\) | −1.02877e40 | + | 1.02877e40i | −0.732959 | + | 0.732959i | ||||
\(324\) | − | 4.84319e39i | − | 0.328406i | ||||||
\(325\) | 2.86425e40 | + | 6.73278e39i | 1.84874 | + | 0.434571i | ||||
\(326\) | 1.25747e40 | 0.772711 | ||||||||
\(327\) | −1.64021e40 | − | 1.64021e40i | −0.959698 | − | 0.959698i | ||||
\(328\) | −3.43752e39 | + | 3.43752e39i | −0.191542 | + | 0.191542i | ||||
\(329\) | 6.93492e39i | 0.368050i | ||||||||
\(330\) | −3.41298e39 | + | 6.12840e39i | −0.172548 | + | 0.309830i | ||||
\(331\) | 2.60902e40 | 1.25670 | 0.628348 | − | 0.777932i | \(-0.283731\pi\) | ||||
0.628348 | + | 0.777932i | \(0.283731\pi\) | |||||||
\(332\) | 5.73231e39 | + | 5.73231e39i | 0.263100 | + | 0.263100i | ||||
\(333\) | −7.11307e36 | + | 7.11307e36i | −0.000311135 | + | 0.000311135i | ||||
\(334\) | 2.13938e40i | 0.891957i | ||||||||
\(335\) | 3.02420e40 | − | 8.60668e39i | 1.20197 | − | 0.342073i | ||||
\(336\) | −5.86288e39 | −0.222169 | ||||||||
\(337\) | −4.28358e39 | − | 4.28358e39i | −0.154785 | − | 0.154785i | 0.625466 | − | 0.780251i | \(-0.284909\pi\) |
−0.780251 | + | 0.625466i | \(0.784909\pi\) | |||||||
\(338\) | −4.38269e40 | + | 4.38269e40i | −1.51034 | + | 1.51034i | ||||
\(339\) | 2.49003e40i | 0.818483i | ||||||||
\(340\) | 3.05691e39 | + | 1.07413e40i | 0.0958562 | + | 0.336818i | ||||
\(341\) | −1.91917e40 | −0.574173 | ||||||||
\(342\) | −1.04192e37 | − | 1.04192e37i | −0.000297451 | − | 0.000297451i | ||||
\(343\) | −1.88797e40 | + | 1.88797e40i | −0.514386 | + | 0.514386i | ||||
\(344\) | − | 3.99203e40i | − | 1.03815i | ||||||
\(345\) | 1.67924e40 | + | 9.35188e39i | 0.416875 | + | 0.232163i | ||||
\(346\) | 6.20930e40 | 1.47172 | ||||||||
\(347\) | −3.86466e40 | − | 3.86466e40i | −0.874660 | − | 0.874660i | 0.118316 | − | 0.992976i | \(-0.462251\pi\) |
−0.992976 | + | 0.118316i | \(0.962251\pi\) | |||||||
\(348\) | 4.39578e39 | − | 4.39578e39i | 0.0950097 | − | 0.0950097i | ||||
\(349\) | − | 4.48483e40i | − | 0.925847i | −0.886398 | − | 0.462923i | \(-0.846800\pi\) | ||
0.886398 | − | 0.462923i | \(-0.153200\pi\) | |||||||
\(350\) | 1.39322e40 | − | 8.62891e39i | 0.274746 | − | 0.170164i | ||||
\(351\) | −1.00829e41 | −1.89963 | ||||||||
\(352\) | 1.06610e40 | + | 1.06610e40i | 0.191918 | + | 0.191918i | ||||
\(353\) | 5.56911e40 | − | 5.56911e40i | 0.958055 | − | 0.958055i | −0.0410999 | − | 0.999155i | \(-0.513086\pi\) |
0.999155 | + | 0.0410999i | \(0.0130862\pi\) | |||||||
\(354\) | − | 9.88118e39i | − | 0.162464i | ||||||
\(355\) | −8.71299e39 | + | 1.56452e40i | −0.136935 | + | 0.245882i | ||||
\(356\) | −1.73948e40 | −0.261348 | ||||||||
\(357\) | 2.06855e40 | + | 2.06855e40i | 0.297149 | + | 0.297149i | ||||
\(358\) | 7.42472e40 | − | 7.42472e40i | 1.01989 | − | 1.01989i | ||||
\(359\) | − | 1.15843e40i | − | 0.152180i | −0.997101 | − | 0.0760901i | \(-0.975756\pi\) | ||
0.997101 | − | 0.0760901i | \(-0.0242437\pi\) | |||||||
\(360\) | −4.39863e37 | + | 1.25182e37i | −0.000552685 | + | 0.000157291i | ||||
\(361\) | 4.49853e39 | 0.0540699 | ||||||||
\(362\) | −7.96805e40 | − | 7.96805e40i | −0.916251 | − | 0.916251i | ||||
\(363\) | −5.22090e40 | + | 5.22090e40i | −0.574433 | + | 0.574433i | ||||
\(364\) | − | 2.33752e40i | − | 0.246113i | ||||||
\(365\) | 4.73967e39 | + | 1.66542e40i | 0.0477597 | + | 0.167817i | ||||
\(366\) | 1.25412e41 | 1.20960 | ||||||||
\(367\) | 1.27160e41 | + | 1.27160e41i | 1.17407 | + | 1.17407i | 0.981230 | + | 0.192841i | \(0.0617703\pi\) |
0.192841 | + | 0.981230i | \(0.438230\pi\) | |||||||
\(368\) | −2.15125e40 | + | 2.15125e40i | −0.190163 | + | 0.190163i | ||||
\(369\) | 1.55174e37i | 0.000131340i | ||||||||
\(370\) | −7.36248e40 | − | 4.10026e40i | −0.596756 | − | 0.332341i | ||||
\(371\) | −8.22005e40 | −0.638104 | ||||||||
\(372\) | 4.14323e40 | + | 4.14323e40i | 0.308072 | + | 0.308072i | ||||
\(373\) | −5.10558e40 | + | 5.10558e40i | −0.363667 | + | 0.363667i | −0.865161 | − | 0.501494i | \(-0.832784\pi\) |
0.501494 | + | 0.865161i | \(0.332784\pi\) | |||||||
\(374\) | 5.54001e40i | 0.378063i | ||||||||
\(375\) | −1.02981e41 | + | 1.13009e41i | −0.673376 | + | 0.738943i | ||||
\(376\) | 1.62128e41 | 1.01591 | ||||||||
\(377\) | −9.14657e40 | − | 9.14657e40i | −0.549284 | − | 0.549284i | ||||
\(378\) | −3.97103e40 | + | 3.97103e40i | −0.228578 | + | 0.228578i | ||||
\(379\) | − | 1.53973e41i | − | 0.849605i | −0.905286 | − | 0.424802i | \(-0.860344\pi\) | ||
0.905286 | − | 0.424802i | \(-0.139656\pi\) | |||||||
\(380\) | −2.93923e40 | + | 5.27773e40i | −0.155488 | + | 0.279196i | ||||
\(381\) | −3.08122e41 | −1.56287 | ||||||||
\(382\) | 2.15368e41 | + | 2.15368e41i | 1.04753 | + | 1.04753i | ||||
\(383\) | 1.85557e41 | − | 1.85557e41i | 0.865558 | − | 0.865558i | −0.126419 | − | 0.991977i | \(-0.540348\pi\) |
0.991977 | + | 0.126419i | \(0.0403484\pi\) | |||||||
\(384\) | 5.71357e40i | 0.255628i | ||||||||
\(385\) | −3.82649e40 | + | 1.08899e40i | −0.164221 | + | 0.0467362i | ||||
\(386\) | 5.65362e40 | 0.232771 | ||||||||
\(387\) | −9.01028e37 | − | 9.01028e37i | −0.000355929 | − | 0.000355929i | ||||
\(388\) | 4.10635e40 | − | 4.10635e40i | 0.155650 | − | 0.155650i | ||||
\(389\) | 3.50497e41i | 1.27494i | 0.770474 | + | 0.637471i | \(0.220020\pi\) | ||||
−0.770474 | + | 0.637471i | \(0.779980\pi\) | |||||||
\(390\) | −1.21979e41 | − | 4.28608e41i | −0.425845 | − | 1.49633i | ||||
\(391\) | 1.51801e41 | 0.508683 | ||||||||
\(392\) | 2.02078e41 | + | 2.02078e41i | 0.650044 | + | 0.650044i | ||||
\(393\) | 2.83822e40 | − | 2.83822e40i | 0.0876528 | − | 0.0876528i | ||||
\(394\) | 2.74482e41i | 0.813907i | ||||||||
\(395\) | −2.73301e41 | − | 1.52205e41i | −0.778193 | − | 0.433385i | ||||
\(396\) | 2.74581e37 | 7.50839e−5 | ||||||||
\(397\) | −3.91560e40 | − | 3.91560e40i | −0.102837 | − | 0.102837i | 0.653816 | − | 0.756653i | \(-0.273167\pi\) |
−0.756653 | + | 0.653816i | \(0.773167\pi\) | |||||||
\(398\) | −3.63634e41 | + | 3.63634e41i | −0.917351 | + | 0.917351i | ||||
\(399\) | 1.58241e41i | 0.383489i | ||||||||
\(400\) | −1.27424e41 | − | 2.05738e41i | −0.296682 | − | 0.479022i | ||||
\(401\) | 1.53765e41 | 0.343992 | 0.171996 | − | 0.985098i | \(-0.444978\pi\) | ||||
0.171996 | + | 0.985098i | \(0.444978\pi\) | |||||||
\(402\) | −3.36736e41 | − | 3.36736e41i | −0.723890 | − | 0.723890i | ||||
\(403\) | 8.62107e41 | − | 8.62107e41i | 1.78107 | − | 1.78107i | ||||
\(404\) | − | 5.88430e40i | − | 0.116840i | ||||||
\(405\) | 2.54787e41 | − | 4.57499e41i | 0.486292 | − | 0.873192i | ||||
\(406\) | −7.20458e40 | −0.132188 | ||||||||
\(407\) | 1.44663e41 | + | 1.44663e41i | 0.255180 | + | 0.255180i | ||||
\(408\) | 4.83597e41 | − | 4.83597e41i | 0.820202 | − | 0.820202i | ||||
\(409\) | 7.74149e39i | 0.0126256i | 0.999980 | + | 0.00631279i | \(0.00200944\pi\) | ||||
−0.999980 | + | 0.00631279i | \(0.997991\pi\) | |||||||
\(410\) | −1.25032e41 | + | 3.55833e40i | −0.196101 | + | 0.0558090i | ||||
\(411\) | −7.94881e41 | −1.19904 | ||||||||
\(412\) | −2.12235e41 | − | 2.12235e41i | −0.307937 | − | 0.307937i | ||||
\(413\) | 3.96276e40 | − | 3.96276e40i | 0.0553092 | − | 0.0553092i | ||||
\(414\) | 1.53741e38i | 0.000206435i | ||||||||
\(415\) | 2.39926e41 | + | 8.43049e41i | 0.309962 | + | 1.08914i | ||||
\(416\) | −9.57806e41 | −1.19065 | ||||||||
\(417\) | 4.54452e41 | + | 4.54452e41i | 0.543640 | + | 0.543640i | ||||
\(418\) | −2.11902e41 | + | 2.11902e41i | −0.243957 | + | 0.243957i | ||||
\(419\) | − | 6.04668e41i | − | 0.670027i | −0.942213 | − | 0.335014i | \(-0.891259\pi\) | ||
0.942213 | − | 0.335014i | \(-0.108741\pi\) | |||||||
\(420\) | 1.06119e41 | + | 5.90989e40i | 0.113189 | + | 0.0630363i | ||||
\(421\) | 1.44307e41 | 0.148175 | 0.0740875 | − | 0.997252i | \(-0.476396\pi\) | ||||
0.0740875 | + | 0.997252i | \(0.476396\pi\) | |||||||
\(422\) | −4.60664e41 | − | 4.60664e41i | −0.455392 | − | 0.455392i | ||||
\(423\) | 3.65935e38 | − | 3.65935e38i | 0.000348304 | − | 0.000348304i | ||||
\(424\) | 1.92173e42i | 1.76132i | ||||||||
\(425\) | −2.76308e41 | + | 1.17546e42i | −0.243877 | + | 1.03750i | ||||
\(426\) | 2.71221e41 | 0.230553 | ||||||||
\(427\) | 5.02954e41 | + | 5.02954e41i | 0.411796 | + | 0.411796i | ||||
\(428\) | −6.52129e40 | + | 6.52129e40i | −0.0514320 | + | 0.0514320i | ||||
\(429\) | 1.08183e42i | 0.821945i | ||||||||
\(430\) | 5.19389e41 | − | 9.32622e41i | 0.380187 | − | 0.682669i | ||||
\(431\) | 5.52569e41 | 0.389717 | 0.194859 | − | 0.980831i | \(-0.437575\pi\) | ||||
0.194859 | + | 0.980831i | \(0.437575\pi\) | |||||||
\(432\) | 5.86407e41 | + | 5.86407e41i | 0.398528 | + | 0.398528i | ||||
\(433\) | −8.29703e40 | + | 8.29703e40i | −0.0543396 | + | 0.0543396i | −0.733754 | − | 0.679415i | \(-0.762234\pi\) |
0.679415 | + | 0.733754i | \(0.262234\pi\) | |||||||
\(434\) | − | 6.79065e41i | − | 0.428623i | ||||||
\(435\) | 6.46485e41 | − | 1.83986e41i | 0.393306 | − | 0.111932i | ||||
\(436\) | −7.60657e41 | −0.446072 | ||||||||
\(437\) | 5.80630e41 | + | 5.80630e41i | 0.328244 | + | 0.328244i | ||||
\(438\) | 1.85439e41 | − | 1.85439e41i | 0.101068 | − | 0.101068i | ||||
\(439\) | − | 1.61595e42i | − | 0.849169i | −0.905388 | − | 0.424585i | \(-0.860420\pi\) | ||
0.905388 | − | 0.424585i | \(-0.139580\pi\) | |||||||
\(440\) | 2.54591e41 | + | 8.94578e41i | 0.129003 | + | 0.453289i | ||||
\(441\) | 9.12209e38 | 0.000445735 | ||||||||
\(442\) | −2.48862e42 | − | 2.48862e42i | −1.17274 | − | 1.17274i | ||||
\(443\) | −6.83128e41 | + | 6.83128e41i | −0.310486 | + | 0.310486i | −0.845098 | − | 0.534611i | \(-0.820458\pi\) |
0.534611 | + | 0.845098i | \(0.320458\pi\) | |||||||
\(444\) | − | 6.24617e41i | − | 0.273834i | ||||||
\(445\) | −1.64315e42 | − | 9.15091e41i | −0.694892 | − | 0.386994i | ||||
\(446\) | 1.20918e42 | 0.493324 | ||||||||
\(447\) | −2.54025e41 | − | 2.54025e41i | −0.0999899 | − | 0.0999899i | ||||
\(448\) | −7.90966e41 | + | 7.90966e41i | −0.300407 | + | 0.300407i | ||||
\(449\) | − | 2.87136e42i | − | 1.05232i | −0.850386 | − | 0.526159i | \(-0.823632\pi\) | ||
0.850386 | − | 0.526159i | \(-0.176368\pi\) | |||||||
\(450\) | −1.19048e39 | − | 2.79838e38i | −0.000421039 | − | 9.89707e-5i | ||||
\(451\) | 3.15588e41 | 0.107720 | ||||||||
\(452\) | 5.77385e41 | + | 5.77385e41i | 0.190217 | + | 0.190217i | ||||
\(453\) | −1.58635e42 | + | 1.58635e42i | −0.504461 | + | 0.504461i | ||||
\(454\) | − | 1.68103e42i | − | 0.516039i | ||||||
\(455\) | 1.22971e42 | − | 2.20808e42i | 0.364434 | − | 0.654383i | ||||
\(456\) | 3.69945e42 | 1.05852 | ||||||||
\(457\) | −1.25651e42 | − | 1.25651e42i | −0.347142 | − | 0.347142i | 0.511902 | − | 0.859044i | \(-0.328941\pi\) |
−0.859044 | + | 0.511902i | \(0.828941\pi\) | |||||||
\(458\) | −1.22475e42 | + | 1.22475e42i | −0.326738 | + | 0.326738i | ||||
\(459\) | − | 4.13793e42i | − | 1.06606i | ||||||
\(460\) | 6.06229e41 | − | 1.72529e41i | 0.150838 | − | 0.0429276i | ||||
\(461\) | 4.94269e42 | 1.18781 | 0.593907 | − | 0.804534i | \(-0.297585\pi\) | ||||
0.593907 | + | 0.804534i | \(0.297585\pi\) | |||||||
\(462\) | 4.26068e41 | + | 4.26068e41i | 0.0989026 | + | 0.0989026i | ||||
\(463\) | −3.60441e42 | + | 3.60441e42i | −0.808236 | + | 0.808236i | −0.984367 | − | 0.176131i | \(-0.943642\pi\) |
0.176131 | + | 0.984367i | \(0.443642\pi\) | |||||||
\(464\) | 1.06391e42i | 0.230471i | ||||||||
\(465\) | 1.73415e42 | + | 6.09342e42i | 0.362944 | + | 1.27531i | ||||
\(466\) | −9.73093e41 | −0.196780 | ||||||||
\(467\) | −8.24322e41 | − | 8.24322e41i | −0.161074 | − | 0.161074i | 0.621968 | − | 0.783043i | \(-0.286333\pi\) |
−0.783043 | + | 0.621968i | \(0.786333\pi\) | |||||||
\(468\) | −1.23344e39 | + | 1.23344e39i | −0.000232908 | + | 0.000232908i | ||||
\(469\) | − | 2.70090e42i | − | 0.492882i | ||||||
\(470\) | 3.78766e42 | + | 2.10940e42i | 0.668044 | + | 0.372042i | ||||
\(471\) | 3.43699e42 | 0.585927 | ||||||||
\(472\) | −9.26437e41 | − | 9.26437e41i | −0.152667 | − | 0.152667i | ||||
\(473\) | −1.83248e42 | + | 1.83248e42i | −0.291918 | + | 0.291918i | ||||
\(474\) | 4.73788e42i | 0.729677i | ||||||||
\(475\) | −5.55294e42 | + | 3.43922e42i | −0.826847 | + | 0.512108i | ||||
\(476\) | 9.59302e41 | 0.138116 | ||||||||
\(477\) | 4.33747e39 | + | 4.33747e39i | 0.000603869 | + | 0.000603869i | ||||
\(478\) | −7.32069e42 | + | 7.32069e42i | −0.985611 | + | 0.985611i | ||||
\(479\) | − | 1.03862e41i | − | 0.0135235i | −0.999977 | − | 0.00676176i | \(-0.997848\pi\) | ||
0.999977 | − | 0.00676176i | \(-0.00215235\pi\) | |||||||
\(480\) | 2.42159e42 | − | 4.34824e42i | 0.304959 | − | 0.547588i | ||||
\(481\) | −1.29968e43 | −1.58313 | ||||||||
\(482\) | −1.58078e42 | − | 1.58078e42i | −0.186260 | − | 0.186260i | ||||
\(483\) | 1.16747e42 | − | 1.16747e42i | 0.133073 | − | 0.133073i | ||||
\(484\) | 2.42123e42i | 0.266999i | ||||||||
\(485\) | 6.03918e42 | − | 1.71871e42i | 0.644333 | − | 0.183373i | ||||
\(486\) | 8.37937e39 | 0.000865030 | ||||||||
\(487\) | −7.70886e40 | − | 7.70886e40i | −0.00770064 | − | 0.00770064i | 0.703246 | − | 0.710947i | \(-0.251733\pi\) |
−0.710947 | + | 0.703246i | \(0.751733\pi\) | |||||||
\(488\) | 1.17584e43 | − | 1.17584e43i | 1.13666 | − | 1.13666i | ||||
\(489\) | 1.00774e43i | 0.942768i | ||||||||
\(490\) | 2.09180e42 | + | 7.35014e42i | 0.189402 | + | 0.665516i | ||||
\(491\) | 6.83855e42 | 0.599322 | 0.299661 | − | 0.954046i | \(-0.403126\pi\) | ||||
0.299661 | + | 0.954046i | \(0.403126\pi\) | |||||||
\(492\) | −6.81312e41 | − | 6.81312e41i | −0.0577969 | − | 0.0577969i | ||||
\(493\) | 3.75369e42 | − | 3.75369e42i | 0.308253 | − | 0.308253i | ||||
\(494\) | − | 1.90376e43i | − | 1.51350i | ||||||
\(495\) | 2.59375e39 | + | 1.44449e39i | 0.000199639 | + | 0.000111181i | ||||
\(496\) | −1.00278e43 | −0.747309 | ||||||||
\(497\) | 1.08771e42 | + | 1.08771e42i | 0.0784893 | + | 0.0784893i | ||||
\(498\) | 9.38710e42 | − | 9.38710e42i | 0.655937 | − | 0.655937i | ||||
\(499\) | − | 8.46275e42i | − | 0.572668i | −0.958130 | − | 0.286334i | \(-0.907563\pi\) | ||
0.958130 | − | 0.286334i | \(-0.0924367\pi\) | |||||||
\(500\) | 2.32513e41 | + | 5.00834e42i | 0.0152379 | + | 0.328226i | ||||
\(501\) | −1.71449e43 | −1.08826 | ||||||||
\(502\) | 1.57941e43 | + | 1.57941e43i | 0.971037 | + | 0.971037i | ||||
\(503\) | −6.53699e42 | + | 6.53699e42i | −0.389305 | + | 0.389305i | −0.874440 | − | 0.485134i | \(-0.838771\pi\) |
0.485134 | + | 0.874440i | \(0.338771\pi\) | |||||||
\(504\) | 3.92840e39i | 0.000226635i | ||||||||
\(505\) | 3.09557e42 | − | 5.55844e42i | 0.173013 | − | 0.310664i | ||||
\(506\) | 3.12672e42 | 0.169309 | ||||||||
\(507\) | −3.51228e43 | − | 3.51228e43i | −1.84273 | − | 1.84273i | ||||
\(508\) | −7.14468e42 | + | 7.14468e42i | −0.363215 | + | 0.363215i | ||||
\(509\) | 2.49712e43i | 1.23014i | 0.788473 | + | 0.615069i | \(0.210872\pi\) | ||||
−0.788473 | + | 0.615069i | \(0.789128\pi\) | |||||||
\(510\) | 1.75897e43 | − | 5.00593e42i | 0.839724 | − | 0.238980i | ||||
\(511\) | 1.48738e42 | 0.0688155 | ||||||||
\(512\) | 1.52432e43 | + | 1.52432e43i | 0.683529 | + | 0.683529i | ||||
\(513\) | 1.58273e43 | − | 1.58273e43i | 0.687906 | − | 0.687906i | ||||
\(514\) | − | 9.96258e42i | − | 0.419722i | ||||||
\(515\) | −8.88312e42 | − | 3.12133e43i | −0.362785 | − | 1.27475i | ||||
\(516\) | 7.91217e42 | 0.313257 | ||||||||
\(517\) | −7.44226e42 | − | 7.44226e42i | −0.285664 | − | 0.285664i | ||||
\(518\) | −5.11866e42 | + | 5.11866e42i | −0.190494 | + | 0.190494i | ||||
\(519\) | 4.97612e43i | 1.79562i | ||||||||
\(520\) | −5.16217e43 | − | 2.87488e43i | −1.80626 | − | 1.00593i | ||||
\(521\) | 2.71941e43 | 0.922721 | 0.461361 | − | 0.887213i | \(-0.347361\pi\) | ||||
0.461361 | + | 0.887213i | \(0.347361\pi\) | |||||||
\(522\) | 3.80164e39 | + | 3.80164e39i | 0.000125096 | + | 0.000125096i | ||||
\(523\) | 4.64160e42 | − | 4.64160e42i | 0.148129 | − | 0.148129i | −0.629153 | − | 0.777282i | \(-0.716598\pi\) |
0.777282 | + | 0.629153i | \(0.216598\pi\) | |||||||
\(524\) | − | 1.31625e42i | − | 0.0407414i | ||||||
\(525\) | 6.91519e42 | + | 1.11652e43i | 0.207613 | + | 0.335211i | ||||
\(526\) | −1.08874e43 | −0.317067 | ||||||||
\(527\) | 3.53802e43 | + | 3.53802e43i | 0.999518 | + | 0.999518i | ||||
\(528\) | 6.29180e42 | − | 6.29180e42i | 0.172438 | − | 0.172438i | ||||
\(529\) | 2.90414e43i | 0.772195i | ||||||||
\(530\) | −2.50029e43 | + | 4.48956e43i | −0.645026 | + | 1.15822i | ||||
\(531\) | −4.18206e39 | −0.000104683 | ||||||||
\(532\) | 3.66927e42 | + | 3.66927e42i | 0.0891237 | + | 0.0891237i | ||||
\(533\) | −1.41765e43 | + | 1.41765e43i | −0.334144 | + | 0.334144i | ||||
\(534\) | 2.84853e43i | 0.651569i | ||||||||
\(535\) | −9.59084e42 | + | 2.72949e42i | −0.212910 | + | 0.0605928i | ||||
\(536\) | −6.31432e43 | −1.36047 | ||||||||
\(537\) | 5.95016e43 | + | 5.95016e43i | 1.24434 | + | 1.24434i | ||||
\(538\) | 2.08635e43 | − | 2.08635e43i | 0.423517 | − | 0.423517i | ||||
\(539\) | − | 1.85522e43i | − | 0.365574i | ||||||
\(540\) | −4.70294e42 | − | 1.65251e43i | −0.0899641 | − | 0.316114i | ||||
\(541\) | 6.85680e43 | 1.27340 | 0.636701 | − | 0.771111i | \(-0.280299\pi\) | ||||
0.636701 | + | 0.771111i | \(0.280299\pi\) | |||||||
\(542\) | −8.38623e42 | − | 8.38623e42i | −0.151209 | − | 0.151209i | ||||
\(543\) | 6.38558e43 | − | 6.38558e43i | 1.11790 | − | 1.11790i | ||||
\(544\) | − | 3.93076e43i | − | 0.668182i | ||||||
\(545\) | −7.18534e43 | − | 4.00161e43i | −1.18605 | − | 0.660527i | ||||
\(546\) | −3.82788e43 | −0.613586 | ||||||||
\(547\) | −1.12718e43 | − | 1.12718e43i | −0.175467 | − | 0.175467i | 0.613909 | − | 0.789377i | \(-0.289596\pi\) |
−0.789377 | + | 0.613909i | \(0.789596\pi\) | |||||||
\(548\) | −1.84316e43 | + | 1.84316e43i | −0.278659 | + | 0.278659i | ||||
\(549\) | − | 5.30788e40i | − | 0.000779406i | ||||||
\(550\) | −5.69125e42 | + | 2.42116e43i | −0.0811717 | + | 0.345319i | ||||
\(551\) | 2.87152e43 | 0.397820 | ||||||||
\(552\) | −2.72937e43 | − | 2.72937e43i | −0.367314 | − | 0.367314i | ||||
\(553\) | −1.90009e43 | + | 1.90009e43i | −0.248411 | + | 0.248411i | ||||
\(554\) | − | 5.20443e43i | − | 0.661024i | ||||||
\(555\) | 3.28594e43 | − | 5.90028e43i | 0.405482 | − | 0.728090i | ||||
\(556\) | 2.10755e43 | 0.252686 | ||||||||
\(557\) | −3.76653e43 | − | 3.76653e43i | −0.438792 | − | 0.438792i | 0.452814 | − | 0.891605i | \(-0.350420\pi\) |
−0.891605 | + | 0.452814i | \(0.850420\pi\) | |||||||
\(558\) | −3.58322e40 | + | 3.58322e40i | −0.000405627 | + | 0.000405627i | ||||
\(559\) | − | 1.64633e44i | − | 1.81104i | ||||||
\(560\) | −1.99938e43 | + | 5.69010e42i | −0.213740 | + | 0.0608291i | ||||
\(561\) | −4.43975e43 | −0.461267 | ||||||||
\(562\) | 8.43941e43 | + | 8.43941e43i | 0.852180 | + | 0.852180i | ||||
\(563\) | 8.27422e43 | − | 8.27422e43i | 0.812068 | − | 0.812068i | −0.172876 | − | 0.984944i | \(-0.555306\pi\) |
0.984944 | + | 0.172876i | \(0.0553058\pi\) | |||||||
\(564\) | 3.21337e43i | 0.306546i | ||||||||
\(565\) | 2.41665e43 | + | 8.49157e43i | 0.224098 | + | 0.787432i | ||||
\(566\) | −9.66295e43 | −0.871057 | ||||||||
\(567\) | −3.18070e43 | − | 3.18070e43i | −0.278736 | − | 0.278736i | ||||
\(568\) | 2.54291e43 | − | 2.54291e43i | 0.216649 | − | 0.216649i | ||||
\(569\) | 1.64760e44i | 1.36476i | 0.731000 | + | 0.682378i | \(0.239054\pi\) | ||||
−0.731000 | + | 0.682378i | \(0.760946\pi\) | |||||||
\(570\) | 8.64269e43 | + | 4.81322e43i | 0.696067 | + | 0.387649i | ||||
\(571\) | −6.10122e43 | −0.477792 | −0.238896 | − | 0.971045i | \(-0.576785\pi\) | ||||
−0.238896 | + | 0.971045i | \(0.576785\pi\) | |||||||
\(572\) | 2.50853e43 | + | 2.50853e43i | 0.191022 | + | 0.191022i | ||||
\(573\) | −1.72595e44 | + | 1.72595e44i | −1.27807 | + | 1.27807i | ||||
\(574\) | 1.11665e43i | 0.0804134i | ||||||||
\(575\) | 6.63420e43 | + | 1.55945e43i | 0.464626 | + | 0.109216i | ||||
\(576\) | 8.34738e40 | 0.000568579 | ||||||||
\(577\) | 4.83918e43 | + | 4.83918e43i | 0.320596 | + | 0.320596i | 0.848996 | − | 0.528399i | \(-0.177208\pi\) |
−0.528399 | + | 0.848996i | \(0.677208\pi\) | |||||||
\(578\) | 1.22171e43 | − | 1.22171e43i | 0.0787271 | − | 0.0787271i | ||||
\(579\) | 4.53080e43i | 0.283999i | ||||||||
\(580\) | 1.07244e43 | − | 1.92568e43i | 0.0653919 | − | 0.117419i | ||||
\(581\) | 7.52923e43 | 0.446614 | ||||||||
\(582\) | −6.72446e43 | − | 6.72446e43i | −0.388052 | − | 0.388052i | ||||
\(583\) | 8.82140e43 | − | 8.82140e43i | 0.495269 | − | 0.495269i | ||||
\(584\) | − | 3.47727e43i | − | 0.189947i | ||||||
\(585\) | −1.81402e41 | + | 5.16258e40i | −0.000964157 | + | 0.000274393i | ||||
\(586\) | 3.04135e44 | 1.57291 | ||||||||
\(587\) | −1.31935e44 | − | 1.31935e44i | −0.663972 | − | 0.663972i | 0.292342 | − | 0.956314i | \(-0.405566\pi\) |
−0.956314 | + | 0.292342i | \(0.905566\pi\) | |||||||
\(588\) | −4.00517e43 | + | 4.00517e43i | −0.196148 | + | 0.196148i | ||||
\(589\) | 2.70654e44i | 1.28994i | ||||||||
\(590\) | −9.58997e42 | − | 3.36971e43i | −0.0444821 | − | 0.156300i | ||||
\(591\) | −2.19970e44 | −0.993031 | ||||||||
\(592\) | 7.55879e43 | + | 7.55879e43i | 0.332128 | + | 0.332128i | ||||
\(593\) | −2.91544e44 | + | 2.91544e44i | −1.24689 | + | 1.24689i | −0.289809 | + | 0.957084i | \(0.593592\pi\) |
−0.957084 | + | 0.289809i | \(0.906408\pi\) | |||||||
\(594\) | − | 8.52309e43i | − | 0.354825i | ||||||
\(595\) | 9.06179e43 | + | 5.04663e43i | 0.367234 | + | 0.204517i | ||||
\(596\) | −1.17806e43 | −0.0464758 | ||||||||
\(597\) | −2.91416e44 | − | 2.91416e44i | −1.11924 | − | 1.11924i | ||||
\(598\) | −1.40455e44 | + | 1.40455e44i | −0.525193 | + | 0.525193i | ||||
\(599\) | − | 2.34634e44i | − | 0.854203i | −0.904204 | − | 0.427102i | \(-0.859535\pi\) | ||
0.904204 | − | 0.427102i | \(-0.140465\pi\) | |||||||
\(600\) | 2.61027e44 | − | 1.61667e44i | 0.925264 | − | 0.573063i | ||||
\(601\) | 2.26082e44 | 0.780324 | 0.390162 | − | 0.920746i | \(-0.372419\pi\) | ||||
0.390162 | + | 0.920746i | \(0.372419\pi\) | |||||||
\(602\) | −6.48392e43 | − | 6.48392e43i | −0.217918 | − | 0.217918i | ||||
\(603\) | −1.42518e41 | + | 1.42518e41i | −0.000466438 | + | 0.000466438i | ||||
\(604\) | 7.35681e43i | 0.234476i | ||||||||
\(605\) | −1.27374e44 | + | 2.28715e44i | −0.395362 | + | 0.709918i | ||||
\(606\) | −9.63599e43 | −0.291296 | ||||||||
\(607\) | −2.69846e44 | − | 2.69846e44i | −0.794505 | − | 0.794505i | 0.187718 | − | 0.982223i | \(-0.439891\pi\) |
−0.982223 | + | 0.187718i | \(0.939891\pi\) | |||||||
\(608\) | 1.50349e44 | − | 1.50349e44i | 0.431165 | − | 0.431165i | ||||
\(609\) | − | 5.77373e43i | − | 0.161280i | ||||||
\(610\) | 4.27684e44 | − | 1.21716e44i | 1.16371 | − | 0.331185i | ||||
\(611\) | 6.68626e44 | 1.77225 | ||||||||
\(612\) | −5.06195e40 | − | 5.06195e40i | −0.000130706 | − | 0.000130706i | ||||
\(613\) | 3.04960e43 | − | 3.04960e43i | 0.0767142 | − | 0.0767142i | −0.667709 | − | 0.744423i | \(-0.732725\pi\) |
0.744423 | + | 0.667709i | \(0.232725\pi\) | |||||||
\(614\) | − | 4.39827e44i | − | 1.07792i | ||||||
\(615\) | −2.85164e43 | − | 1.00200e44i | −0.0680914 | − | 0.239258i | ||||
\(616\) | 7.98944e43 | 0.185877 | ||||||||
\(617\) | 2.96717e44 | + | 2.96717e44i | 0.672636 | + | 0.672636i | 0.958323 | − | 0.285687i | \(-0.0922217\pi\) |
−0.285687 | + | 0.958323i | \(0.592222\pi\) | |||||||
\(618\) | −3.47551e44 | + | 3.47551e44i | −0.767721 | + | 0.767721i | ||||
\(619\) | − | 7.00694e44i | − | 1.50827i | −0.656722 | − | 0.754133i | \(-0.728058\pi\) | ||
0.656722 | − | 0.754133i | \(-0.271942\pi\) | |||||||
\(620\) | 1.81505e44 | + | 1.01082e44i | 0.380733 | + | 0.212035i | ||||
\(621\) | −2.33540e44 | −0.477415 | ||||||||
\(622\) | −9.14779e43 | − | 9.14779e43i | −0.182251 | − | 0.182251i | ||||
\(623\) | −1.14238e44 | + | 1.14238e44i | −0.221820 | + | 0.221820i | ||||
\(624\) | 5.65267e44i | 1.06979i | ||||||||
\(625\) | −2.41511e44 | + | 4.85331e44i | −0.445509 | + | 0.895277i | ||||
\(626\) | −7.36022e44 | −1.32343 | ||||||||
\(627\) | −1.69818e44 | − | 1.69818e44i | −0.297647 | − | 0.297647i | ||||
\(628\) | 7.96963e43 | − | 7.96963e43i | 0.136171 | − | 0.136171i | ||||
\(629\) | − | 5.33379e44i | − | 0.888435i | ||||||
\(630\) | −5.11110e40 | + | 9.17756e40i | −8.29976e−5 | + | 0.000149032i | ||||
\(631\) | −1.87514e44 | −0.296868 | −0.148434 | − | 0.988922i | \(-0.547423\pi\) | ||||
−0.148434 | + | 0.988922i | \(0.547423\pi\) | |||||||
\(632\) | 4.44213e44 | + | 4.44213e44i | 0.685674 | + | 0.685674i | ||||
\(633\) | 3.69175e44 | − | 3.69175e44i | 0.555614 | − | 0.555614i | ||||
\(634\) | 9.86432e43i | 0.144757i | ||||||||
\(635\) | −1.05076e45 | + | 2.99041e44i | −1.50358 | + | 0.427909i | ||||
\(636\) | −3.80885e44 | −0.531472 | ||||||||
\(637\) | 8.33382e44 | + | 8.33382e44i | 1.13400 | + | 1.13400i | ||||
\(638\) | 7.73164e43 | − | 7.73164e43i | 0.102598 | − | 0.102598i | ||||
\(639\) | − | 1.14790e41i | − | 0.000148556i | ||||||
\(640\) | 5.54518e43 | + | 1.94846e44i | 0.0699901 | + | 0.245930i | ||||
\(641\) | 4.10301e44 | 0.505096 | 0.252548 | − | 0.967584i | \(-0.418731\pi\) | ||||
0.252548 | + | 0.967584i | \(0.418731\pi\) | |||||||
\(642\) | 1.06791e44 | + | 1.06791e44i | 0.128226 | + | 0.128226i | ||||
\(643\) | −1.54009e44 | + | 1.54009e44i | −0.180373 | + | 0.180373i | −0.791518 | − | 0.611146i | \(-0.790709\pi\) |
0.611146 | + | 0.791518i | \(0.290709\pi\) | |||||||
\(644\) | − | 5.41420e43i | − | 0.0618530i | ||||||
\(645\) | 7.47401e44 | + | 4.16237e44i | 0.832911 | + | 0.463858i | ||||
\(646\) | 7.81290e44 | 0.849361 | ||||||||
\(647\) | −2.43956e44 | − | 2.43956e44i | −0.258727 | − | 0.258727i | 0.565809 | − | 0.824536i | \(-0.308564\pi\) |
−0.824536 | + | 0.565809i | \(0.808564\pi\) | |||||||
\(648\) | −7.43602e44 | + | 7.43602e44i | −0.769379 | + | 0.769379i | ||||
\(649\) | 8.50533e43i | 0.0858571i | ||||||||
\(650\) | −8.31952e44 | − | 1.34326e45i | −0.819378 | − | 1.32296i | ||||
\(651\) | 5.44201e44 | 0.522954 | ||||||||
\(652\) | 2.33672e44 | + | 2.33672e44i | 0.219102 | + | 0.219102i | ||||
\(653\) | 9.56793e43 | − | 9.56793e43i | 0.0875401 | − | 0.0875401i | −0.661981 | − | 0.749521i | \(-0.730284\pi\) |
0.749521 | + | 0.661981i | \(0.230284\pi\) | |||||||
\(654\) | 1.24563e45i | 1.11211i | ||||||||
\(655\) | 6.92440e43 | − | 1.24336e44i | 0.0603284 | − | 0.108326i | ||||
\(656\) | 1.64898e44 | 0.140202 | ||||||||
\(657\) | −7.84844e40 | − | 7.84844e40i | −6.51234e−5 | − | 6.51234e-5i | ||||
\(658\) | 2.63332e44 | − | 2.63332e44i | 0.213250 | − | 0.213250i | ||||
\(659\) | 9.18988e44i | 0.726346i | 0.931722 | + | 0.363173i | \(0.118307\pi\) | ||||
−0.931722 | + | 0.363173i | \(0.881693\pi\) | |||||||
\(660\) | −1.77304e44 | + | 5.04597e43i | −0.136778 | + | 0.0389262i | ||||
\(661\) | −1.01864e45 | −0.767005 | −0.383503 | − | 0.923540i | \(-0.625282\pi\) | ||||
−0.383503 | + | 0.923540i | \(0.625282\pi\) | |||||||
\(662\) | −9.90696e44 | − | 9.90696e44i | −0.728136 | − | 0.728136i | ||||
\(663\) | 1.99438e45 | − | 1.99438e45i | 1.43084 | − | 1.43084i | ||||
\(664\) | − | 1.76023e45i | − | 1.23276i | ||||||
\(665\) | 1.53577e44 | + | 5.39638e44i | 0.104998 | + | 0.368940i | ||||
\(666\) | 5.40193e41 | 0.000360547 | ||||||||
\(667\) | −2.11854e44 | − | 2.11854e44i | −0.138046 | − | 0.138046i | ||||
\(668\) | −3.97554e44 | + | 3.97554e44i | −0.252914 | + | 0.252914i | ||||
\(669\) | 9.69032e44i | 0.601894i | ||||||||
\(670\) | −1.47516e45 | − | 8.21533e44i | −0.894625 | − | 0.498228i | ||||
\(671\) | −1.07950e45 | −0.639237 | ||||||||
\(672\) | −3.02305e44 | − | 3.02305e44i | −0.174798 | − | 0.174798i | ||||
\(673\) | 8.87557e44 | − | 8.87557e44i | 0.501136 | − | 0.501136i | −0.410655 | − | 0.911791i | \(-0.634700\pi\) |
0.911791 | + | 0.410655i | \(0.134700\pi\) | |||||||
\(674\) | 3.25312e44i | 0.179366i | ||||||||
\(675\) | 4.25089e44 | − | 1.80841e45i | 0.228886 | − | 0.973724i | ||||
\(676\) | −1.62884e45 | −0.856510 | ||||||||
\(677\) | 8.12647e44 | + | 8.12647e44i | 0.417334 | + | 0.417334i | 0.884284 | − | 0.466950i | \(-0.154647\pi\) |
−0.466950 | + | 0.884284i | \(0.654647\pi\) | |||||||
\(678\) | 9.45512e44 | − | 9.45512e44i | 0.474233 | − | 0.474233i | ||||
\(679\) | − | 5.39357e44i | − | 0.264216i | ||||||
\(680\) | 1.17983e45 | − | 2.11852e45i | 0.564516 | − | 1.01365i | ||||
\(681\) | 1.34718e45 | 0.629608 | ||||||||
\(682\) | 7.28743e44 | + | 7.28743e44i | 0.332678 | + | 0.332678i | ||||
\(683\) | 8.59093e44 | − | 8.59093e44i | 0.383097 | − | 0.383097i | −0.489120 | − | 0.872217i | \(-0.662682\pi\) |
0.872217 | + | 0.489120i | \(0.162682\pi\) | |||||||
\(684\) | − | 3.87233e41i | − | 0.000168684i | ||||||
\(685\) | −2.71072e45 | + | 7.71455e44i | −1.15355 | + | 0.328293i | ||||
\(686\) | 1.43380e45 | 0.596076 | ||||||||
\(687\) | −9.81511e44 | − | 9.81511e44i | −0.398646 | − | 0.398646i | ||||
\(688\) | −9.57488e44 | + | 9.57488e44i | −0.379943 | + | 0.379943i | ||||
\(689\) | 7.92531e45i | 3.07262i | ||||||||
\(690\) | −2.82529e44 | − | 9.92746e44i | −0.107023 | − | 0.376056i | ||||
\(691\) | 1.46043e44 | 0.0540547 | 0.0270273 | − | 0.999635i | \(-0.491396\pi\) | ||||
0.0270273 | + | 0.999635i | \(0.491396\pi\) | |||||||
\(692\) | 1.15386e45 | + | 1.15386e45i | 0.417305 | + | 0.417305i | ||||
\(693\) | 1.80327e41 | − | 1.80327e41i | 6.37278e−5 | − | 6.37278e-5i | ||||
\(694\) | 2.93497e45i | 1.01357i | ||||||||
\(695\) | 1.99084e45 | + | 1.10872e45i | 0.671862 | + | 0.374168i | ||||
\(696\) | −1.34982e45 | −0.445171 | ||||||||
\(697\) | −5.81793e44 | − | 5.81793e44i | −0.187518 | − | 0.187518i | ||||
\(698\) | −1.70297e45 | + | 1.70297e45i | −0.536440 | + | 0.536440i | ||||
\(699\) | − | 7.79835e44i | − | 0.240087i | ||||||
\(700\) | 4.19246e44 | + | 9.85492e43i | 0.126154 | + | 0.0296541i | ||||
\(701\) | −2.54008e45 | −0.747066 | −0.373533 | − | 0.927617i | \(-0.621854\pi\) | ||||
−0.373533 | + | 0.927617i | \(0.621854\pi\) | |||||||
\(702\) | 3.82865e45 | + | 3.82865e45i | 1.10066 | + | 1.10066i | ||||
\(703\) | 2.04014e45 | − | 2.04014e45i | 0.573291 | − | 0.573291i | ||||
\(704\) | − | 1.69766e45i | − | 0.466325i | ||||||
\(705\) | −1.69047e45 | + | 3.03542e45i | −0.453921 | + | 0.815067i | ||||
\(706\) | −4.22939e45 | −1.11020 | ||||||||
\(707\) | −3.86443e44 | − | 3.86443e44i | −0.0991687 | − | 0.0991687i | ||||
\(708\) | 1.83619e44 | − | 1.83619e44i | 0.0460665 | − | 0.0460665i | ||||
\(709\) | − | 4.32665e45i | − | 1.06124i | −0.847611 | − | 0.530618i | \(-0.821960\pi\) | ||
0.847611 | − | 0.530618i | \(-0.178040\pi\) | |||||||
\(710\) | 9.24925e44 | − | 2.63228e44i | 0.221806 | − | 0.0631245i | ||||
\(711\) | 2.00524e42 | 0.000470167 | ||||||||
\(712\) | 2.67072e45 | + | 2.67072e45i | 0.612277 | + | 0.612277i | ||||
\(713\) | 1.99682e45 | − | 1.99682e45i | 0.447618 | − | 0.447618i | ||||
\(714\) | − | 1.57093e45i | − | 0.344339i | ||||||
\(715\) | 1.04995e45 | + | 3.68929e45i | 0.225046 | + | 0.790762i | ||||
\(716\) | 2.75943e45 | 0.578376 | ||||||||
\(717\) | −5.86679e45 | − | 5.86679e45i | −1.20252 | − | 1.20252i | ||||
\(718\) | −4.39877e44 | + | 4.39877e44i | −0.0881740 | + | 0.0881740i | ||||
\(719\) | − | 6.87903e45i | − | 1.34854i | −0.738483 | − | 0.674272i | \(-0.764458\pi\) | ||
0.738483 | − | 0.674272i | \(-0.235542\pi\) | |||||||
\(720\) | 1.35526e42 | + | 7.54762e41i | 0.000259838 | + | 0.000144707i | ||||
\(721\) | −2.78765e45 | −0.522726 | ||||||||
\(722\) | −1.70818e44 | − | 1.70818e44i | −0.0313283 | − | 0.0313283i | ||||
\(723\) | 1.26684e45 | − | 1.26684e45i | 0.227252 | − | 0.227252i | ||||
\(724\) | − | 2.96135e45i | − | 0.519605i | ||||||
\(725\) | 2.02610e45 | − | 1.25486e45i | 0.347738 | − | 0.215372i | ||||
\(726\) | 3.96495e45 | 0.665658 | ||||||||
\(727\) | −5.53466e45 | − | 5.53466e45i | −0.908951 | − | 0.908951i | 0.0872369 | − | 0.996188i | \(-0.472196\pi\) |
−0.996188 | + | 0.0872369i | \(0.972196\pi\) | |||||||
\(728\) | −3.58893e45 | + | 3.58893e45i | −0.576584 | + | 0.576584i | ||||
\(729\) | 6.36604e45i | 1.00053i | ||||||||
\(730\) | 4.52415e44 | − | 8.12364e44i | 0.0695619 | − | 0.124906i | ||||
\(731\) | 6.75643e45 | 1.01634 | ||||||||
\(732\) | 2.33050e45 | + | 2.33050e45i | 0.342982 | + | 0.342982i | ||||
\(733\) | −6.73077e45 | + | 6.73077e45i | −0.969173 | + | 0.969173i | −0.999539 | − | 0.0303658i | \(-0.990333\pi\) |
0.0303658 | + | 0.999539i | \(0.490333\pi\) | |||||||
\(734\) | − | 9.65703e45i | − | 1.36053i | ||||||
\(735\) | −5.89039e45 | + | 1.67637e45i | −0.811982 | + | 0.231085i | ||||
\(736\) | −2.21848e45 | −0.299234 | ||||||||
\(737\) | 2.89849e45 | + | 2.89849e45i | 0.382553 | + | 0.382553i | ||||
\(738\) | 5.89225e41 | − | 5.89225e41i | 7.60991e−5 | − | 7.60991e-5i | ||||
\(739\) | 4.32206e45i | 0.546236i | 0.961981 | + | 0.273118i | \(0.0880549\pi\) | ||||
−0.961981 | + | 0.273118i | \(0.911945\pi\) | |||||||
\(740\) | −6.06209e44 | − | 2.13009e45i | −0.0749747 | − | 0.263445i | ||||
\(741\) | 1.52567e46 | 1.84659 | ||||||||
\(742\) | 3.12131e45 | + | 3.12131e45i | 0.369721 | + | 0.369721i | ||||
\(743\) | 3.77652e45 | − | 3.77652e45i | 0.437796 | − | 0.437796i | −0.453474 | − | 0.891270i | \(-0.649815\pi\) |
0.891270 | + | 0.453474i | \(0.149815\pi\) | |||||||
\(744\) | − | 1.27226e46i | − | 1.44348i | ||||||
\(745\) | −1.11282e45 | − | 6.19744e44i | −0.123573 | − | 0.0688195i | ||||
\(746\) | 3.87737e45 | 0.421421 | ||||||||
\(747\) | −3.97295e42 | − | 3.97295e42i | −0.000422653 | − | 0.000422653i | ||||
\(748\) | −1.02948e45 | + | 1.02948e45i | −0.107200 | + | 0.107200i | ||||
\(749\) | 8.56554e44i | 0.0873063i | ||||||||
\(750\) | 8.20154e45 | − | 3.80757e44i | 0.818305 | − | 0.0379899i | ||||
\(751\) | −1.22236e46 | −1.19388 | −0.596939 | − | 0.802286i | \(-0.703617\pi\) | ||||
−0.596939 | + | 0.802286i | \(0.703617\pi\) | |||||||
\(752\) | −3.88865e45 | − | 3.88865e45i | −0.371804 | − | 0.371804i | ||||
\(753\) | −1.26574e46 | + | 1.26574e46i | −1.18474 | + | 1.18474i | ||||
\(754\) | 6.94625e45i | 0.636516i | ||||||||
\(755\) | −3.87021e45 | + | 6.94941e45i | −0.347203 | + | 0.623443i | ||||
\(756\) | −1.47585e45 | −0.129626 | ||||||||
\(757\) | −1.49130e46 | − | 1.49130e46i | −1.28242 | − | 1.28242i | −0.939287 | − | 0.343132i | \(-0.888512\pi\) |
−0.343132 | − | 0.939287i | \(-0.611488\pi\) | |||||||
\(758\) | −5.84664e45 | + | 5.84664e45i | −0.492265 | + | 0.492265i | ||||
\(759\) | 2.50575e45i | 0.206571i | ||||||||
\(760\) | 1.26160e46 | − | 3.59042e45i | 1.01836 | − | 0.289820i | ||||
\(761\) | 1.95741e46 | 1.54713 | 0.773564 | − | 0.633718i | \(-0.218472\pi\) | ||||
0.773564 | + | 0.633718i | \(0.218472\pi\) | |||||||
\(762\) | 1.17000e46 | + | 1.17000e46i | 0.905534 | + | 0.905534i | ||||
\(763\) | −4.99551e45 | + | 4.99551e45i | −0.378606 | + | 0.378606i | ||||
\(764\) | 8.00423e45i | 0.594054i | ||||||||
\(765\) | −2.11868e42 | − | 7.44459e42i | −0.000153987 | − | 0.000541076i | ||||
\(766\) | −1.40919e46 | −1.00302 | ||||||||
\(767\) | −3.82067e45 | − | 3.82067e45i | −0.266326 | − | 0.266326i | ||||
\(768\) | −8.98459e45 | + | 8.98459e45i | −0.613365 | + | 0.613365i | ||||
\(769\) | − | 4.03487e45i | − | 0.269779i | −0.990861 | − | 0.134889i | \(-0.956932\pi\) | ||
0.990861 | − | 0.134889i | \(-0.0430679\pi\) | |||||||
\(770\) | 1.86650e45 | + | 1.03948e45i | 0.122230 | + | 0.0680712i | ||||
\(771\) | 7.98399e45 | 0.512094 | ||||||||
\(772\) | 1.05059e45 | + | 1.05059e45i | 0.0660022 | + | 0.0660022i | ||||
\(773\) | 3.16149e45 | − | 3.16149e45i | 0.194545 | − | 0.194545i | −0.603112 | − | 0.797657i | \(-0.706073\pi\) |
0.797657 | + | 0.603112i | \(0.206073\pi\) | |||||||
\(774\) | 6.84275e42i | 0.000412454i | ||||||||
\(775\) | 1.18277e46 | + | 1.90969e46i | 0.698349 | + | 1.12755i | ||||
\(776\) | −1.26094e46 | −0.729301 | ||||||||
\(777\) | −4.10209e45 | − | 4.10209e45i | −0.232417 | − | 0.232417i | ||||
\(778\) | 1.33090e46 | − | 1.33090e46i | 0.738708 | − | 0.738708i | ||||
\(779\) | − | 4.45064e45i | − | 0.242004i | ||||||
\(780\) | 5.69798e45 | − | 1.02314e46i | 0.303534 | − | 0.545030i | ||||
\(781\) | −2.33456e45 | −0.121840 | ||||||||
\(782\) | −5.76418e45 | − | 5.76418e45i | −0.294733 | − | 0.294733i | ||||
\(783\) | −5.77490e45 | + | 5.77490e45i | −0.289305 | + | 0.289305i | ||||
\(784\) | − | 9.69370e45i | − | 0.475809i | ||||||
\(785\) | 1.17209e46 | − | 3.33569e45i | 0.563698 | − | 0.160425i | ||||
\(786\) | −2.15545e45 | −0.101573 | ||||||||
\(787\) | 5.12679e45 | + | 5.12679e45i | 0.236728 | + | 0.236728i | 0.815494 | − | 0.578766i | \(-0.196465\pi\) |
−0.578766 | + | 0.815494i | \(0.696465\pi\) | |||||||
\(788\) | −5.10062e45 | + | 5.10062e45i | −0.230783 | + | 0.230783i | ||||
\(789\) | − | 8.72510e45i | − | 0.386846i | ||||||
\(790\) | 4.59825e45 | + | 1.61572e46i | 0.199783 | + | 0.701994i | ||||
\(791\) | 7.58379e45 | 0.322896 | ||||||||
\(792\) | −4.21579e42 | − | 4.21579e42i | −0.000175904 | − | 0.000175904i | ||||
\(793\) | 4.84921e46 | − | 4.84921e46i | 1.98290 | − | 1.98290i | ||||
\(794\) | 2.97365e45i | 0.119169i | ||||||||
\(795\) | −3.59793e46 | − | 2.00373e46i | −1.41312 | − | 0.786983i | ||||
\(796\) | −1.35146e46 | −0.520229 | ||||||||
\(797\) | −1.66939e46 | − | 1.66939e46i | −0.629830 | − | 0.629830i | 0.318195 | − | 0.948025i | \(-0.396923\pi\) |
−0.948025 | + | 0.318195i | \(0.896923\pi\) | |||||||
\(798\) | 6.00871e45 | − | 6.00871e45i | 0.222195 | − | 0.222195i | ||||
\(799\) | 2.74399e46i | 0.994568i | ||||||||
\(800\) | 4.03808e45 | − | 1.71787e46i | 0.143461 | − | 0.610310i | ||||
\(801\) | 1.20560e43 | 0.000419838 | ||||||||
\(802\) | −5.83876e45 | − | 5.83876e45i | −0.199311 | − | 0.199311i | ||||
\(803\) | −1.59619e45 | + | 1.59619e45i | −0.0534116 | + | 0.0534116i | ||||
\(804\) | − | 1.25149e46i | − | 0.410517i | ||||||
\(805\) | 2.84826e45 | − | 5.11438e45i | 0.0915896 | − | 0.164459i | ||||
\(806\) | −6.54717e46 | −2.06392 | ||||||||
\(807\) | 1.67200e46 | + | 1.67200e46i | 0.516725 | + | 0.516725i | ||||
\(808\) | −9.03449e45 | + | 9.03449e45i | −0.273730 | + | 0.273730i | ||||
\(809\) | 2.47482e46i | 0.735135i | 0.929997 | + | 0.367568i | \(0.119809\pi\) | ||||
−0.929997 | + | 0.367568i | \(0.880191\pi\) | |||||||
\(810\) | −2.70468e46 | + | 7.69736e45i | −0.787692 | + | 0.224172i | ||||
\(811\) | 4.20312e46 | 1.20016 | 0.600078 | − | 0.799941i | \(-0.295136\pi\) | ||||
0.600078 | + | 0.799941i | \(0.295136\pi\) | |||||||
\(812\) | −1.33880e45 | − | 1.33880e45i | −0.0374818 | − | 0.0374818i | ||||
\(813\) | 6.72071e45 | − | 6.72071e45i | 0.184487 | − | 0.184487i | ||||
\(814\) | − | 1.09863e46i | − | 0.295706i | ||||||
\(815\) | 9.78037e45 | + | 3.43661e46i | 0.258127 | + | 0.907002i | ||||
\(816\) | −2.31981e46 | −0.600358 | ||||||||
\(817\) | 2.58429e46 | + | 2.58429e46i | 0.655826 | + | 0.655826i | ||||
\(818\) | 2.93959e44 | − | 2.93959e44i | 0.00731533 | − | 0.00731533i | ||||
\(819\) | 1.62009e43i | 0.000395364i | ||||||||
\(820\) | −2.98466e45 | − | 1.66220e45i | −0.0714288 | − | 0.0397796i | ||||
\(821\) | 1.83774e46 | 0.431313 | 0.215657 | − | 0.976469i | \(-0.430811\pi\) | ||||
0.215657 | + | 0.976469i | \(0.430811\pi\) | |||||||
\(822\) | 3.01831e46 | + | 3.01831e46i | 0.694729 | + | 0.694729i | ||||
\(823\) | 2.81942e46 | − | 2.81942e46i | 0.636448 | − | 0.636448i | −0.313229 | − | 0.949677i | \(-0.601411\pi\) |
0.949677 | + | 0.313229i | \(0.101411\pi\) | |||||||
\(824\) | 6.51713e46i | 1.44285i | ||||||||
\(825\) | −1.94031e46 | − | 4.56096e45i | −0.421317 | − | 0.0990359i | ||||
\(826\) | −3.00947e45 | −0.0640928 | ||||||||
\(827\) | −1.05051e46 | − | 1.05051e46i | −0.219438 | − | 0.219438i | 0.588824 | − | 0.808261i | \(-0.299591\pi\) |
−0.808261 | + | 0.588824i | \(0.799591\pi\) | |||||||
\(828\) | −2.85691e42 | + | 2.85691e42i | −5.85345e−5 | + | 5.85345e-5i | ||||
\(829\) | − | 6.99636e45i | − | 0.140605i | −0.997526 | − | 0.0703023i | \(-0.977604\pi\) | ||
0.997526 | − | 0.0703023i | \(-0.0223964\pi\) | |||||||
\(830\) | 2.29017e46 | − | 4.11226e46i | 0.451459 | − | 0.810646i | ||||
\(831\) | 4.17082e46 | 0.806502 | ||||||||
\(832\) | 7.62605e46 | + | 7.62605e46i | 1.44653 | + | 1.44653i | ||||
\(833\) | −3.42014e46 | + | 3.42014e46i | −0.636390 | + | 0.636390i | ||||
\(834\) | − | 3.45128e46i | − | 0.629975i | ||||||
\(835\) | −5.84681e46 | + | 1.66396e46i | −1.04697 | + | 0.297962i | ||||
\(836\) | −7.87541e45 | −0.138348 | ||||||||
\(837\) | −5.44311e46 | − | 5.44311e46i | −0.938080 | − | 0.938080i | ||||
\(838\) | −2.29604e46 | + | 2.29604e46i | −0.388217 | + | 0.388217i | ||||
\(839\) | 1.09639e47i | 1.81876i | 0.415966 | + | 0.909380i | \(0.363443\pi\) | ||||
−0.415966 | + | 0.909380i | \(0.636557\pi\) | |||||||
\(840\) | −7.21922e45 | − | 2.53668e46i | −0.117496 | − | 0.412854i | ||||
\(841\) | 5.21460e46 | 0.832693 | ||||||||
\(842\) | −5.47962e45 | − | 5.47962e45i | −0.0858534 | − | 0.0858534i | ||||
\(843\) | −6.76333e46 | + | 6.76333e46i | −1.03973 | + | 1.03973i | ||||
\(844\) | − | 1.71208e46i | − | 0.258252i | ||||||
\(845\) | −1.53864e47 | − | 8.56890e46i | −2.27735 | − | 1.26829i | ||||
\(846\) | −2.77905e43 | −0.000403618 | ||||||||
\(847\) | 1.59011e46 | + | 1.59011e46i | 0.226617 | + | 0.226617i | ||||
\(848\) | 4.60927e46 | − | 4.60927e46i | 0.644612 | − | 0.644612i | ||||
\(849\) | − | 7.74387e46i | − | 1.06276i | ||||||
\(850\) | 5.51266e46 | − | 3.41427e46i | 0.742434 | − | 0.459827i | ||||
\(851\) | −3.01034e46 | −0.397871 | ||||||||
\(852\) | 5.04002e45 | + | 5.04002e45i | 0.0653730 | + | 0.0653730i | ||||
\(853\) | 1.07796e47 | − | 1.07796e47i | 1.37220 | − | 1.37220i | 0.515016 | − | 0.857181i | \(-0.327786\pi\) |
0.857181 | − | 0.515016i | \(-0.172214\pi\) | |||||||
\(854\) | − | 3.81963e46i | − | 0.477194i | ||||||
\(855\) | 2.03712e43 | − | 3.65789e43i | 0.000249781 | − | 0.000448511i | ||||
\(856\) | 2.00250e46 | 0.240986 | ||||||||
\(857\) | −2.27708e46 | − | 2.27708e46i | −0.268958 | − | 0.268958i | 0.559722 | − | 0.828680i | \(-0.310908\pi\) |
−0.828680 | + | 0.559722i | \(0.810908\pi\) | |||||||
\(858\) | 4.10791e46 | − | 4.10791e46i | 0.476239 | − | 0.476239i | ||||
\(859\) | − | 6.87779e46i | − | 0.782633i | −0.920256 | − | 0.391316i | \(-0.872020\pi\) | ||
0.920256 | − | 0.391316i | \(-0.127980\pi\) | |||||||
\(860\) | 2.69823e46 | − | 7.67898e45i | 0.301372 | − | 0.0857686i | ||||
\(861\) | −8.94885e45 | −0.0981108 | ||||||||
\(862\) | −2.09821e46 | − | 2.09821e46i | −0.225804 | − | 0.225804i | ||||
\(863\) | 2.87435e46 | − | 2.87435e46i | 0.303646 | − | 0.303646i | −0.538793 | − | 0.842438i | \(-0.681119\pi\) |
0.842438 | + | 0.538793i | \(0.181119\pi\) | |||||||
\(864\) | 6.04733e46i | 0.627110i | ||||||||
\(865\) | 4.82947e46 | + | 1.69697e47i | 0.491634 | + | 1.72749i | ||||
\(866\) | 6.30108e45 | 0.0629692 | ||||||||
\(867\) | 9.79079e45 | + | 9.79079e45i | 0.0960533 | + | 0.0960533i | ||||
\(868\) | 1.26189e46 | − | 1.26189e46i | 0.121536 | − | 0.121536i | ||||
\(869\) | − | 4.07818e46i | − | 0.385612i | ||||||
\(870\) | −3.15345e46 | − | 1.75620e46i | −0.292738 | − | 0.163029i | ||||
\(871\) | −2.60406e47 | −2.37334 | ||||||||
\(872\) | 1.16788e47 | + | 1.16788e47i | 1.04504 | + | 1.04504i | ||||
\(873\) | −2.84603e43 | + | 2.84603e43i | −0.000250041 | + | 0.000250041i | ||||
\(874\) | − | 4.40952e46i | − | 0.380372i | ||||||
\(875\) | 3.44185e46 | + | 3.13646e46i | 0.291517 | + | 0.265650i | ||||
\(876\) | 6.89192e45 | 0.0573158 | ||||||||
\(877\) | −4.81552e46 | − | 4.81552e46i | −0.393233 | − | 0.393233i | 0.482605 | − | 0.875838i | \(-0.339691\pi\) |
−0.875838 | + | 0.482605i | \(0.839691\pi\) | |||||||
\(878\) | −6.13605e46 | + | 6.13605e46i | −0.492013 | + | 0.492013i | ||||
\(879\) | 2.43733e47i | 1.91908i | ||||||||
\(880\) | 1.53501e46 | − | 2.75628e46i | 0.118683 | − | 0.213109i | ||||
\(881\) | 1.32699e47 | 1.00752 | 0.503761 | − | 0.863843i | \(-0.331949\pi\) | ||||
0.503761 | + | 0.863843i | \(0.331949\pi\) | |||||||
\(882\) | −3.46383e43 | − | 3.46383e43i | −0.000258261 | − | 0.000258261i | ||||
\(883\) | 3.88616e46 | − | 3.88616e46i | 0.284544 | − | 0.284544i | −0.550374 | − | 0.834918i | \(-0.685515\pi\) |
0.834918 | + | 0.550374i | \(0.185515\pi\) | |||||||
\(884\) | − | 9.24906e46i | − | 0.665061i | ||||||
\(885\) | 2.70048e46 | − | 7.68538e45i | 0.190699 | − | 0.0542717i | ||||
\(886\) | 5.18793e46 | 0.359795 | ||||||||
\(887\) | −1.61402e47 | − | 1.61402e47i | −1.09934 | − | 1.09934i | −0.994488 | − | 0.104852i | \(-0.966563\pi\) |
−0.104852 | − | 0.994488i | \(-0.533437\pi\) | |||||||
\(888\) | −9.59010e46 | + | 9.59010e46i | −0.641528 | + | 0.641528i | ||||
\(889\) | 9.38434e46i | 0.616560i | ||||||||
\(890\) | 2.76458e46 | + | 9.71413e46i | 0.178398 | + | 0.626850i | ||||
\(891\) | 6.82678e46 | 0.432686 | ||||||||
\(892\) | 2.24698e46 | + | 2.24698e46i | 0.139882 | + | 0.139882i | ||||
\(893\) | −1.04956e47 | + | 1.04956e47i | −0.641776 | + | 0.641776i | ||||
\(894\) | 1.92916e46i | 0.115869i | ||||||||
\(895\) | 2.60662e47 | + | 1.45166e47i | 1.53783 | + | 0.856437i | ||||
\(896\) | 1.74016e46 | 0.100846 | ||||||||
\(897\) | −1.12561e47 | − | 1.12561e47i | −0.640777 | − | 0.640777i | ||||
\(898\) | −1.09031e47 | + | 1.09031e47i | −0.609718 | + | 0.609718i | ||||
\(899\) | − | 9.87534e46i | − | 0.542497i | ||||||
\(900\) | −1.69222e43 | − | 2.73225e43i | −9.13224e−5 | − | 0.000147449i | ||||
\(901\) | −3.25249e47 | −1.72433 | ||||||||
\(902\) | −1.19835e46 | − | 1.19835e46i | −0.0624134 | − | 0.0624134i | ||||
\(903\) | 5.19620e46 | − | 5.19620e46i | 0.265878 | − | 0.265878i | ||||
\(904\) | − | 1.77298e47i | − | 0.891270i | ||||||
\(905\) | 1.55789e47 | − | 2.79736e47i | 0.769412 | − | 1.38157i | ||||
\(906\) | 1.20473e47 | 0.584575 | ||||||||
\(907\) | 1.65407e47 | + | 1.65407e47i | 0.788567 | + | 0.788567i | 0.981259 | − | 0.192692i | \(-0.0617220\pi\) |
−0.192692 | + | 0.981259i | \(0.561722\pi\) | |||||||
\(908\) | 3.12381e46 | − | 3.12381e46i | 0.146322 | − | 0.146322i | ||||
\(909\) | 4.07829e43i | 0.000187696i | ||||||||
\(910\) | −1.30539e47 | + | 3.71506e46i | −0.590308 | + | 0.167998i | ||||
\(911\) | 7.63769e46 | 0.339366 | 0.169683 | − | 0.985499i | \(-0.445726\pi\) | ||||
0.169683 | + | 0.985499i | \(0.445726\pi\) | |||||||
\(912\) | −8.87313e46 | − | 8.87313e46i | −0.387400 | − | 0.387400i | ||||
\(913\) | −8.08005e46 | + | 8.08005e46i | −0.346642 | + | 0.346642i | ||||
\(914\) | 9.54241e46i | 0.402271i | ||||||||
\(915\) | 9.75430e46 | + | 3.42745e47i | 0.404072 | + | 1.41982i | ||||
\(916\) | −4.55183e46 | −0.185293 | ||||||||
\(917\) | −8.64426e45 | − | 8.64426e45i | −0.0345795 | − | 0.0345795i | ||||
\(918\) | −1.57125e47 | + | 1.57125e47i | −0.617678 | + | 0.617678i | ||||
\(919\) | − | 1.49043e47i | − | 0.575789i | −0.957662 | − | 0.287895i | \(-0.907045\pi\) | ||
0.957662 | − | 0.287895i | \(-0.0929553\pi\) | |||||||
\(920\) | −1.19567e47 | − | 6.65883e46i | −0.453948 | − | 0.252809i | ||||
\(921\) | 3.52477e47 | 1.31515 | ||||||||
\(922\) | −1.87683e47 | − | 1.87683e47i | −0.688225 | − | 0.688225i | ||||
\(923\) | 1.04871e47 | − | 1.04871e47i | 0.377944 | − | 0.377944i | ||||
\(924\) | 1.58350e46i | 0.0560875i | ||||||||
\(925\) | 5.47941e46 | − | 2.33104e47i | 0.190751 | − | 0.811487i | ||||
\(926\) | 2.73732e47 | 0.936591 | ||||||||
\(927\) | 1.47096e44 | + | 1.47096e44i | 0.000494681 | + | 0.000494681i | ||||
\(928\) | −5.48578e46 | + | 5.48578e46i | −0.181331 | + | 0.181331i | ||||
\(929\) | − | 1.79815e46i | − | 0.0584217i | −0.999573 | − | 0.0292108i | \(-0.990701\pi\) | ||
0.999573 | − | 0.0292108i | \(-0.00929942\pi\) | |||||||
\(930\) | 1.65530e47 | − | 2.97228e47i | 0.528627 | − | 0.949210i | ||||
\(931\) | −2.61636e47 | −0.821301 | ||||||||
\(932\) | −1.80827e46 | − | 1.80827e46i | −0.0557967 | − | 0.0557967i | ||||
\(933\) | 7.33102e46 | − | 7.33102e46i | 0.222361 | − | 0.222361i | ||||
\(934\) | 6.26021e46i | 0.186655i | ||||||||
\(935\) | −1.51406e47 | + | 4.30891e46i | −0.443768 | + | 0.126294i | ||||
\(936\) | 3.78754e44 | 0.00109130 | ||||||||
\(937\) | −1.10459e47 | − | 1.10459e47i | −0.312873 | − | 0.312873i | 0.533149 | − | 0.846022i | \(-0.321009\pi\) |
−0.846022 | + | 0.533149i | \(0.821009\pi\) | |||||||
\(938\) | −1.02558e47 | + | 1.02558e47i | −0.285578 | + | 0.285578i | ||||
\(939\) | − | 5.89847e47i | − | 1.61469i | ||||||
\(940\) | 3.11867e46 | + | 1.09583e47i | 0.0839312 | + | 0.294916i | ||||
\(941\) | 2.98277e47 | 0.789197 | 0.394599 | − | 0.918854i | \(-0.370884\pi\) | ||||
0.394599 | + | 0.918854i | \(0.370884\pi\) | |||||||
\(942\) | −1.30509e47 | − | 1.30509e47i | −0.339489 | − | 0.339489i | ||||
\(943\) | −3.28358e46 | + | 3.28358e46i | −0.0839769 | + | 0.0839769i | ||||
\(944\) | 4.44412e46i | 0.111746i | ||||||||
\(945\) | −1.39412e47 | − | 7.76404e46i | −0.344661 | − | 0.191946i | ||||
\(946\) | 1.39165e47 | 0.338278 | ||||||||
\(947\) | 2.75001e47 | + | 2.75001e47i | 0.657257 | + | 0.657257i | 0.954730 | − | 0.297473i | \(-0.0961439\pi\) |
−0.297473 | + | 0.954730i | \(0.596144\pi\) | |||||||
\(948\) | −8.80426e46 | + | 8.80426e46i | −0.206899 | + | 0.206899i | ||||
\(949\) | − | 1.43405e47i | − | 0.331363i | ||||||
\(950\) | 3.41449e47 | + | 8.02620e46i | 0.775797 | + | 0.182361i | ||||
\(951\) | −7.90525e46 | −0.176615 | ||||||||
\(952\) | −1.47287e47 | − | 1.47287e47i | −0.323574 | − | 0.323574i | ||||
\(953\) | −3.95004e47 | + | 3.95004e47i | −0.853326 | + | 0.853326i | −0.990541 | − | 0.137215i | \(-0.956185\pi\) |
0.137215 | + | 0.990541i | \(0.456185\pi\) | |||||||
\(954\) | − | 3.29404e44i | − | 0.000699770i | ||||||
\(955\) | −4.21081e47 | + | 7.56098e47i | −0.879653 | + | 1.57952i | ||||
\(956\) | −2.72076e47 | −0.558939 | ||||||||
\(957\) | 6.19612e46 | + | 6.19612e46i | 0.125178 | + | 0.125178i | ||||
\(958\) | −3.94384e45 | + | 3.94384e45i | −0.00783559 | + | 0.00783559i | ||||
\(959\) | 2.42094e47i | 0.473027i | ||||||||
\(960\) | −5.39014e47 | + | 1.53400e47i | −1.03576 | + | 0.294771i | ||||
\(961\) | 4.01653e47 | 0.759060 | ||||||||
\(962\) | 4.93513e47 | + | 4.93513e47i | 0.917271 | + | 0.917271i | ||||
\(963\) | 4.51978e43 | − | 4.51978e43i | 8.26222e−5 | − | 8.26222e-5i | ||||
\(964\) | − | 5.87504e46i | − | 0.105628i | ||||||
\(965\) | 4.39727e46 | + | 1.54510e47i | 0.0777581 | + | 0.273225i | ||||
\(966\) | −8.86617e46 | −0.154206 | ||||||||
\(967\) | 4.04439e47 | + | 4.04439e47i | 0.691878 | + | 0.691878i | 0.962645 | − | 0.270767i | \(-0.0872774\pi\) |
−0.270767 | + | 0.962645i | \(0.587277\pi\) | |||||||
\(968\) | 3.71744e47 | − | 3.71744e47i | 0.625516 | − | 0.625516i | ||||
\(969\) | 6.26125e47i | 1.03629i | ||||||||
\(970\) | −2.94582e47 | − | 1.64056e47i | −0.479577 | − | 0.267082i | ||||
\(971\) | −2.93551e47 | −0.470084 | −0.235042 | − | 0.971985i | \(-0.575523\pi\) | ||||
−0.235042 | + | 0.971985i | \(0.575523\pi\) | |||||||
\(972\) | 1.55711e44 | + | 1.55711e44i | 0.000245279 | + | 0.000245279i | ||||
\(973\) | 1.38411e47 | − | 1.38411e47i | 0.214469 | − | 0.214469i | ||||
\(974\) | 5.85440e45i | 0.00892358i | ||||||||
\(975\) | 1.07649e48 | − | 6.66725e47i | 1.61412 | − | 0.999707i | ||||
\(976\) | −5.64048e47 | −0.831992 | ||||||||
\(977\) | 3.14946e47 | + | 3.14946e47i | 0.457007 | + | 0.457007i | 0.897672 | − | 0.440664i | \(-0.145257\pi\) |
−0.440664 | + | 0.897672i | \(0.645257\pi\) | |||||||
\(978\) | 3.82656e47 | − | 3.82656e47i | 0.546245 | − | 0.546245i | ||||
\(979\) | − | 2.45190e47i | − | 0.344334i | ||||||
\(980\) | −9.77141e46 | + | 1.75457e47i | −0.135002 | + | 0.242411i | ||||
\(981\) | 5.27196e44 | 0.000716586 | ||||||||
\(982\) | −2.59673e47 | − | 2.59673e47i | −0.347250 | − | 0.347250i | ||||
\(983\) | 5.30346e47 | − | 5.30346e47i | 0.697756 | − | 0.697756i | −0.266170 | − | 0.963926i | \(-0.585758\pi\) |
0.963926 | + | 0.266170i | \(0.0857584\pi\) | |||||||
\(984\) | 2.09211e47i | 0.270809i | ||||||||
\(985\) | −7.50146e47 | + | 2.13487e47i | −0.955358 | + | 0.271889i | ||||
\(986\) | −2.85069e47 | −0.357206 | ||||||||
\(987\) | 2.11034e47 | + | 2.11034e47i | 0.260182 | + | 0.260182i | ||||
\(988\) | 3.53771e47 | − | 3.53771e47i | 0.429151 | − | 0.429151i | ||||
\(989\) | − | 3.81326e47i | − | 0.455151i | ||||||
\(990\) | −4.36395e43 | − | 1.53340e44i | −5.12527e−5 | − | 0.000180091i | ||||
\(991\) | −1.72114e48 | −1.98902 | −0.994509 | − | 0.104654i | \(-0.966626\pi\) | ||||
−0.994509 | + | 0.104654i | \(0.966626\pi\) | |||||||
\(992\) | −5.17060e47 | − | 5.17060e47i | −0.587969 | − | 0.587969i | ||||
\(993\) | 7.93942e47 | − | 7.93942e47i | 0.888384 | − | 0.888384i | ||||
\(994\) | − | 8.26047e46i | − | 0.0909541i | ||||||
\(995\) | −1.27662e48 | − | 7.10966e47i | −1.38322 | − | 0.770335i | ||||
\(996\) | 3.48875e47 | 0.371981 | ||||||||
\(997\) | −1.10465e47 | − | 1.10465e47i | −0.115905 | − | 0.115905i | 0.646775 | − | 0.762681i | \(-0.276117\pi\) |
−0.762681 | + | 0.646775i | \(0.776117\pi\) | |||||||
\(998\) | −3.21347e47 | + | 3.21347e47i | −0.331807 | + | 0.331807i | ||||
\(999\) | 8.20583e47i | 0.833825i |
(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.2.6 | ✓ | 30 | |
5.2 | odd | 4 | 25.33.c.b.18.10 | 30 | |||
5.3 | odd | 4 | inner | 5.33.c.a.3.6 | yes | 30 | |
5.4 | even | 2 | 25.33.c.b.7.10 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.33.c.a.2.6 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5.33.c.a.3.6 | yes | 30 | 5.3 | odd | 4 | inner | |
25.33.c.b.7.10 | 30 | 5.4 | even | 2 | |||
25.33.c.b.18.10 | 30 | 5.2 | odd | 4 |