Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,33,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
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("4.3");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.9466620569\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 72511313626452 x^{12} + \cdots + 62\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{182}\cdot 3^{20}\cdot 5^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.6 | ||
Root | \(1.78456e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.33.b.b.3.5 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −18058.8 | + | 62998.8i | −0.275555 | + | 0.961285i | ||||
\(3\) | 2.85529e7i | 0.663301i | 0.943402 | + | 0.331651i | \(0.107606\pi\) | ||||
−0.943402 | + | 0.331651i | \(0.892394\pi\) | |||||||
\(4\) | −3.64273e9 | − | 2.27536e9i | −0.848139 | − | 0.529774i | ||||
\(5\) | 1.21258e11 | 0.794679 | 0.397339 | − | 0.917672i | \(-0.369934\pi\) | ||||
0.397339 | + | 0.917672i | \(0.369934\pi\) | |||||||
\(6\) | −1.79880e12 | − | 5.15631e11i | −0.637622 | − | 0.182776i | ||||
\(7\) | − | 3.17263e10i | − | 0.000954666i | −1.00000 | 0.000477333i | \(-0.999848\pi\) | |||
1.00000 | 0.000477333i | \(-0.000151940\pi\) | ||||||||
\(8\) | 2.09128e14 | − | 1.88397e14i | 0.742973 | − | 0.669322i | ||||
\(9\) | 1.03775e15 | 0.560031 | ||||||||
\(10\) | −2.18978e15 | + | 7.63913e15i | −0.218978 | + | 0.763913i | ||||
\(11\) | 6.68515e16i | 1.45488i | 0.686169 | + | 0.727442i | \(0.259291\pi\) | ||||
−0.686169 | + | 0.727442i | \(0.740709\pi\) | |||||||
\(12\) | 6.49683e16 | − | 1.04011e17i | 0.351400 | − | 0.562572i | ||||
\(13\) | 5.92013e17 | 0.889688 | 0.444844 | − | 0.895608i | \(-0.353259\pi\) | ||||
0.444844 | + | 0.895608i | \(0.353259\pi\) | |||||||
\(14\) | 1.99872e15 | + | 5.72939e14i | 0.000917706 | + | 0.000263063i | ||||
\(15\) | 3.46228e18i | 0.527112i | ||||||||
\(16\) | 8.09220e18 | + | 1.65771e19i | 0.438679 | + | 0.898644i | ||||
\(17\) | 4.82732e19 | 0.992027 | 0.496014 | − | 0.868315i | \(-0.334797\pi\) | ||||
0.496014 | + | 0.868315i | \(0.334797\pi\) | |||||||
\(18\) | −1.87405e19 | + | 6.53770e19i | −0.154319 | + | 0.538350i | ||||
\(19\) | − | 9.57586e19i | − | 0.331986i | −0.986127 | − | 0.165993i | \(-0.946917\pi\) | ||
0.986127 | − | 0.165993i | \(-0.0530830\pi\) | |||||||
\(20\) | −4.41711e20 | − | 2.75907e20i | −0.673998 | − | 0.421000i | ||||
\(21\) | 9.05881e17 | 0.000633231 | ||||||||
\(22\) | −4.21156e21 | − | 1.20726e21i | −1.39856 | − | 0.400900i | ||||
\(23\) | − | 5.33527e20i | − | 0.0869984i | −0.999053 | − | 0.0434992i | \(-0.986149\pi\) | ||
0.999053 | − | 0.0434992i | \(-0.0138506\pi\) | |||||||
\(24\) | 5.37930e21 | + | 5.97123e21i | 0.443962 | + | 0.492815i | ||||
\(25\) | −8.57947e21 | −0.368485 | ||||||||
\(26\) | −1.06910e22 | + | 3.72961e22i | −0.245158 | + | 0.855244i | ||||
\(27\) | 8.25400e22i | 1.03477i | ||||||||
\(28\) | −7.21889e19 | + | 1.15570e20i | −0.000505757 | + | 0.000809689i | ||||
\(29\) | −4.06224e23 | −1.62330 | −0.811648 | − | 0.584147i | \(-0.801429\pi\) | ||||
−0.811648 | + | 0.584147i | \(0.801429\pi\) | |||||||
\(30\) | −2.18120e23 | − | 6.25246e22i | −0.506705 | − | 0.145248i | ||||
\(31\) | 4.12012e23i | 0.566399i | 0.959061 | + | 0.283200i | \(0.0913959\pi\) | ||||
−0.959061 | + | 0.283200i | \(0.908604\pi\) | |||||||
\(32\) | −1.19047e24 | + | 2.10438e23i | −0.984733 | + | 0.174070i | ||||
\(33\) | −1.90881e24 | −0.965026 | ||||||||
\(34\) | −8.71755e23 | + | 3.04116e24i | −0.273358 | + | 0.953621i | ||||
\(35\) | − | 3.84709e21i | − | 0.000758653i | ||||||
\(36\) | −3.78024e24 | − | 2.36126e24i | −0.474984 | − | 0.296690i | ||||
\(37\) | 1.13492e25 | 0.919897 | 0.459949 | − | 0.887946i | \(-0.347868\pi\) | ||||
0.459949 | + | 0.887946i | \(0.347868\pi\) | |||||||
\(38\) | 6.03268e24 | + | 1.72928e24i | 0.319134 | + | 0.0914805i | ||||
\(39\) | 1.69037e25i | 0.590131i | ||||||||
\(40\) | 2.53586e25 | − | 2.28447e25i | 0.590425 | − | 0.531896i | ||||
\(41\) | −2.76466e23 | −0.00433610 | −0.00216805 | − | 0.999998i | \(-0.500690\pi\) | ||||
−0.00216805 | + | 0.999998i | \(0.500690\pi\) | |||||||
\(42\) | −1.63591e22 | + | 5.70694e22i | −0.000174490 | + | 0.000608716i | ||||
\(43\) | − | 1.68374e26i | − | 1.23248i | −0.787559 | − | 0.616239i | \(-0.788655\pi\) | ||
0.787559 | − | 0.616239i | \(-0.211345\pi\) | |||||||
\(44\) | 1.52111e26 | − | 2.43522e26i | 0.770759 | − | 1.23394i | ||||
\(45\) | 1.25836e26 | 0.445045 | ||||||||
\(46\) | 3.36116e25 | + | 9.63485e24i | 0.0836303 | + | 0.0239728i | ||||
\(47\) | 7.88873e26i | 1.39137i | 0.718349 | + | 0.695683i | \(0.244898\pi\) | ||||
−0.718349 | + | 0.695683i | \(0.755102\pi\) | |||||||
\(48\) | −4.73324e26 | + | 2.31056e26i | −0.596072 | + | 0.290976i | ||||
\(49\) | 1.10443e27 | 0.999999 | ||||||||
\(50\) | 1.54935e26 | − | 5.40496e26i | 0.101538 | − | 0.354220i | ||||
\(51\) | 1.37834e27i | 0.658013i | ||||||||
\(52\) | −2.15654e27 | − | 1.34704e27i | −0.754579 | − | 0.471334i | ||||
\(53\) | −5.53595e27 | −1.42816 | −0.714082 | − | 0.700062i | \(-0.753156\pi\) | ||||
−0.714082 | + | 0.700062i | \(0.753156\pi\) | |||||||
\(54\) | −5.19992e27 | − | 1.49057e27i | −0.994710 | − | 0.285136i | ||||
\(55\) | 8.10630e27i | 1.15617i | ||||||||
\(56\) | −5.97716e24 | − | 6.63488e24i | −0.000638979 | − | 0.000709291i | ||||
\(57\) | 2.73419e27 | 0.220207 | ||||||||
\(58\) | 7.33590e27 | − | 2.55916e28i | 0.447307 | − | 1.56045i | ||||
\(59\) | 4.25442e28i | 1.97337i | 0.162647 | + | 0.986684i | \(0.447997\pi\) | ||||
−0.162647 | + | 0.986684i | \(0.552003\pi\) | |||||||
\(60\) | 7.87795e27 | − | 1.26122e28i | 0.279250 | − | 0.447064i | ||||
\(61\) | 5.00768e28 | 1.36257 | 0.681286 | − | 0.732018i | \(-0.261421\pi\) | ||||
0.681286 | + | 0.732018i | \(0.261421\pi\) | |||||||
\(62\) | −2.59563e28 | − | 7.44043e27i | −0.544472 | − | 0.156074i | ||||
\(63\) | − | 3.29240e25i | − | 0.000534643i | ||||||
\(64\) | 8.24109e27 | − | 7.87984e28i | 0.104017 | − | 0.994576i | ||||
\(65\) | 7.17866e28 | 0.707017 | ||||||||
\(66\) | 3.44707e28 | − | 1.20253e29i | 0.265918 | − | 0.927665i | ||||
\(67\) | 1.33261e29i | 0.808175i | 0.914720 | + | 0.404087i | \(0.132411\pi\) | ||||
−0.914720 | + | 0.404087i | \(0.867589\pi\) | |||||||
\(68\) | −1.75846e29 | − | 1.09839e29i | −0.841377 | − | 0.525550i | ||||
\(69\) | 1.52338e28 | 0.0577062 | ||||||||
\(70\) | 2.42362e26 | + | 6.94736e25i | 0.000729282 | + | 0.000209051i | ||||
\(71\) | 5.68414e29i | 1.36311i | 0.731767 | + | 0.681555i | \(0.238696\pi\) | ||||
−0.731767 | + | 0.681555i | \(0.761304\pi\) | |||||||
\(72\) | 2.17023e29 | − | 1.95509e29i | 0.416088 | − | 0.374841i | ||||
\(73\) | −6.17148e29 | −0.948906 | −0.474453 | − | 0.880281i | \(-0.657354\pi\) | ||||
−0.474453 | + | 0.880281i | \(0.657354\pi\) | |||||||
\(74\) | −2.04953e29 | + | 7.14989e29i | −0.253482 | + | 0.884284i | ||||
\(75\) | − | 2.44969e29i | − | 0.244417i | ||||||
\(76\) | −2.17885e29 | + | 3.48823e29i | −0.175878 | + | 0.281571i | ||||
\(77\) | 2.12095e27 | 0.00138893 | ||||||||
\(78\) | −1.06491e30 | − | 3.05261e29i | −0.567285 | − | 0.162614i | ||||
\(79\) | − | 1.44347e30i | − | 0.627152i | −0.949563 | − | 0.313576i | \(-0.898473\pi\) | ||
0.949563 | − | 0.313576i | \(-0.101527\pi\) | |||||||
\(80\) | 9.81247e29 | + | 2.01011e30i | 0.348609 | + | 0.714133i | ||||
\(81\) | −4.33789e29 | −0.126333 | ||||||||
\(82\) | 4.99263e27 | − | 1.74170e28i | 0.00119484 | − | 0.00416823i | ||||
\(83\) | − | 6.98874e30i | − | 1.37768i | −0.724912 | − | 0.688841i | \(-0.758120\pi\) | ||
0.724912 | − | 0.688841i | \(-0.241880\pi\) | |||||||
\(84\) | −3.29988e27 | − | 2.06121e27i | −0.000537068 | − | 0.000335469i | ||||
\(85\) | 5.85353e30 | 0.788343 | ||||||||
\(86\) | 1.06074e31 | + | 3.04063e30i | 1.18476 | + | 0.339616i | ||||
\(87\) | − | 1.15989e31i | − | 1.07673i | ||||||
\(88\) | 1.25946e31 | + | 1.39805e31i | 0.973785 | + | 1.08094i | ||||
\(89\) | −1.07508e31 | −0.693744 | −0.346872 | − | 0.937912i | \(-0.612756\pi\) | ||||
−0.346872 | + | 0.937912i | \(0.612756\pi\) | |||||||
\(90\) | −2.27244e30 | + | 7.92750e30i | −0.122634 | + | 0.427815i | ||||
\(91\) | − | 1.87824e28i | − | 0.000849355i | ||||||
\(92\) | −1.21397e30 | + | 1.94350e30i | −0.0460895 | + | 0.0737867i | ||||
\(93\) | −1.17642e31 | −0.375694 | ||||||||
\(94\) | −4.96981e31 | − | 1.42461e31i | −1.33750 | − | 0.383398i | ||||
\(95\) | − | 1.16115e31i | − | 0.263823i | ||||||
\(96\) | −6.00862e30 | − | 3.39914e31i | −0.115461 | − | 0.653175i | ||||
\(97\) | −3.35405e31 | −0.546036 | −0.273018 | − | 0.962009i | \(-0.588022\pi\) | ||||
−0.273018 | + | 0.962009i | \(0.588022\pi\) | |||||||
\(98\) | −1.99446e31 | + | 6.95775e31i | −0.275555 | + | 0.961284i | ||||
\(99\) | 6.93751e31i | 0.814780i | ||||||||
\(100\) | 3.12527e31 | + | 1.95214e31i | 0.312527 | + | 0.195214i | ||||
\(101\) | 1.12793e32 | 0.961922 | 0.480961 | − | 0.876742i | \(-0.340288\pi\) | ||||
0.480961 | + | 0.876742i | \(0.340288\pi\) | |||||||
\(102\) | −8.68340e31 | − | 2.48912e31i | −0.632538 | − | 0.181319i | ||||
\(103\) | 1.88551e32i | 1.17499i | 0.809228 | + | 0.587495i | \(0.199886\pi\) | ||||
−0.809228 | + | 0.587495i | \(0.800114\pi\) | |||||||
\(104\) | 1.23807e32 | − | 1.11534e32i | 0.661014 | − | 0.595488i | ||||
\(105\) | 1.09846e29 | 0.000503215 | ||||||||
\(106\) | 9.99725e31 | − | 3.48758e32i | 0.393538 | − | 1.37287i | ||||
\(107\) | − | 2.35968e31i | − | 0.0799306i | −0.999201 | − | 0.0399653i | \(-0.987275\pi\) | ||
0.999201 | − | 0.0399653i | \(-0.0127247\pi\) | |||||||
\(108\) | 1.87808e32 | − | 3.00671e32i | 0.548195 | − | 0.877629i | ||||
\(109\) | 1.86142e32 | 0.468835 | 0.234417 | − | 0.972136i | \(-0.424682\pi\) | ||||
0.234417 | + | 0.972136i | \(0.424682\pi\) | |||||||
\(110\) | −5.10687e32 | − | 1.46390e32i | −1.11140 | − | 0.318587i | ||||
\(111\) | 3.24054e32i | 0.610169i | ||||||||
\(112\) | 5.25929e29 | − | 2.56736e29i | 0.000857905 | − | 0.000418792i | ||||
\(113\) | 6.55553e31 | 0.0927583 | 0.0463791 | − | 0.998924i | \(-0.485232\pi\) | ||||
0.0463791 | + | 0.998924i | \(0.485232\pi\) | |||||||
\(114\) | −4.93761e31 | + | 1.72251e32i | −0.0606791 | + | 0.211682i | ||||
\(115\) | − | 6.46947e31i | − | 0.0691358i | ||||||
\(116\) | 1.47976e33 | + | 9.24306e32i | 1.37678 | + | 0.859979i | ||||
\(117\) | 6.14362e32 | 0.498253 | ||||||||
\(118\) | −2.68023e33 | − | 7.68296e32i | −1.89697 | − | 0.543772i | ||||
\(119\) | − | 1.53153e30i | − | 0.000947055i | ||||||
\(120\) | 6.52285e32 | + | 7.24061e32i | 0.352807 | + | 0.391630i | ||||
\(121\) | −2.35775e33 | −1.11669 | ||||||||
\(122\) | −9.04326e32 | + | 3.15478e33i | −0.375463 | + | 1.30982i | ||||
\(123\) | − | 7.89391e30i | − | 0.00287614i | ||||||
\(124\) | 9.37476e32 | − | 1.50085e33i | 0.300064 | − | 0.480385i | ||||
\(125\) | −3.86360e33 | −1.08751 | ||||||||
\(126\) | 2.07417e30 | + | 5.94567e29i | 0.000513944 | + | 0.000147324i | ||||
\(127\) | − | 7.32371e33i | − | 1.59908i | −0.600610 | − | 0.799542i | \(-0.705075\pi\) | ||
0.600610 | − | 0.799542i | \(-0.294925\pi\) | |||||||
\(128\) | 4.81538e33 | + | 1.94218e33i | 0.927408 | + | 0.374050i | ||||
\(129\) | 4.80757e33 | 0.817505 | ||||||||
\(130\) | −1.29638e33 | + | 4.52247e33i | −0.194822 | + | 0.679645i | ||||
\(131\) | − | 7.71918e33i | − | 1.02620i | −0.858330 | − | 0.513098i | \(-0.828498\pi\) | ||
0.858330 | − | 0.513098i | \(-0.171502\pi\) | |||||||
\(132\) | 6.95327e33 | + | 4.34323e33i | 0.818476 | + | 0.511246i | ||||
\(133\) | −3.03807e30 | −0.000316936 | ||||||||
\(134\) | −8.39526e33 | − | 2.40652e33i | −0.776887 | − | 0.222697i | ||||
\(135\) | 1.00087e34i | 0.822311i | ||||||||
\(136\) | 1.00953e34 | − | 9.09455e33i | 0.737049 | − | 0.663985i | ||||
\(137\) | 2.27924e34 | 1.47999 | 0.739997 | − | 0.672610i | \(-0.234827\pi\) | ||||
0.739997 | + | 0.672610i | \(0.234827\pi\) | |||||||
\(138\) | −2.75103e32 | + | 9.59710e32i | −0.0159012 | + | 0.0554721i | ||||
\(139\) | − | 1.27157e34i | − | 0.654791i | −0.944887 | − | 0.327396i | \(-0.893829\pi\) | ||
0.944887 | − | 0.327396i | \(-0.106171\pi\) | |||||||
\(140\) | −8.75351e30 | + | 1.40139e31i | −0.000401915 | + | 0.000643443i | ||||
\(141\) | −2.25247e34 | −0.922895 | ||||||||
\(142\) | −3.58094e34 | − | 1.02649e34i | −1.31034 | − | 0.375612i | ||||
\(143\) | 3.95770e34i | 1.29439i | ||||||||
\(144\) | 8.39768e33 | + | 1.72028e34i | 0.245674 | + | 0.503269i | ||||
\(145\) | −4.92580e34 | −1.29000 | ||||||||
\(146\) | 1.11449e34 | − | 3.88796e34i | 0.261476 | − | 0.912170i | ||||
\(147\) | 3.15346e34i | 0.663301i | ||||||||
\(148\) | −4.13422e34 | − | 2.58236e34i | −0.780201 | − | 0.487338i | ||||
\(149\) | 3.99267e34 | 0.676524 | 0.338262 | − | 0.941052i | \(-0.390161\pi\) | ||||
0.338262 | + | 0.941052i | \(0.390161\pi\) | |||||||
\(150\) | 1.54328e34 | + | 4.42384e33i | 0.234954 | + | 0.0673503i | ||||
\(151\) | 7.15918e34i | 0.980014i | 0.871719 | + | 0.490007i | \(0.163006\pi\) | ||||
−0.871719 | + | 0.490007i | \(0.836994\pi\) | |||||||
\(152\) | −1.80407e34 | − | 2.00258e34i | −0.222206 | − | 0.246657i | ||||
\(153\) | 5.00955e34 | 0.555567 | ||||||||
\(154\) | −3.83018e31 | + | 1.33618e32i | −0.000382726 | + | 0.00133516i | ||||
\(155\) | 4.99599e34i | 0.450106i | ||||||||
\(156\) | 3.84621e34 | − | 6.15757e34i | 0.312636 | − | 0.500513i | ||||
\(157\) | 9.50355e34 | 0.697415 | 0.348707 | − | 0.937232i | \(-0.386621\pi\) | ||||
0.348707 | + | 0.937232i | \(0.386621\pi\) | |||||||
\(158\) | 9.09366e34 | + | 2.60672e34i | 0.602872 | + | 0.172815i | ||||
\(159\) | − | 1.58068e35i | − | 0.947304i | ||||||
\(160\) | −1.44354e35 | + | 2.55174e34i | −0.782547 | + | 0.138330i | ||||
\(161\) | −1.69269e31 | −8.30544e−5 | ||||||||
\(162\) | 7.83370e33 | − | 2.73282e34i | 0.0348118 | − | 0.121442i | ||||
\(163\) | − | 4.30635e35i | − | 1.73423i | −0.498106 | − | 0.867116i | \(-0.665971\pi\) | ||
0.498106 | − | 0.867116i | \(-0.334029\pi\) | |||||||
\(164\) | 1.00709e33 | + | 6.29060e32i | 0.00367762 | + | 0.00229716i | ||||
\(165\) | −2.31459e35 | −0.766886 | ||||||||
\(166\) | 4.40282e35 | + | 1.26208e35i | 1.32435 | + | 0.379627i | ||||
\(167\) | 2.79090e35i | 0.762572i | 0.924457 | + | 0.381286i | \(0.124519\pi\) | ||||
−0.924457 | + | 0.381286i | \(0.875481\pi\) | |||||||
\(168\) | 1.89445e32 | − | 1.70665e32i | 0.000470474 | − | 0.000423835i | ||||
\(169\) | −9.22994e34 | −0.208455 | ||||||||
\(170\) | −1.05708e35 | + | 3.68766e35i | −0.217232 | + | 0.757823i | ||||
\(171\) | − | 9.93735e34i | − | 0.185923i | ||||||
\(172\) | −3.83111e35 | + | 6.13340e35i | −0.652935 | + | 1.04531i | ||||
\(173\) | 5.12088e34 | 0.0795439 | 0.0397719 | − | 0.999209i | \(-0.487337\pi\) | ||||
0.0397719 | + | 0.999209i | \(0.487337\pi\) | |||||||
\(174\) | 7.30716e35 | + | 2.09462e35i | 1.03505 | + | 0.296699i | ||||
\(175\) | 2.72195e32i | 0.000351781i | ||||||||
\(176\) | −1.10820e36 | + | 5.40976e35i | −1.30742 | + | 0.638227i | ||||
\(177\) | −1.21476e36 | −1.30894 | ||||||||
\(178\) | 1.94146e35 | − | 6.77285e35i | 0.191165 | − | 0.666886i | ||||
\(179\) | − | 1.91323e36i | − | 1.72234i | −0.508315 | − | 0.861172i | \(-0.669731\pi\) | ||
0.508315 | − | 0.861172i | \(-0.330269\pi\) | |||||||
\(180\) | −4.58386e35 | − | 2.86322e35i | −0.377460 | − | 0.235773i | ||||
\(181\) | 1.04359e36 | 0.786450 | 0.393225 | − | 0.919442i | \(-0.371359\pi\) | ||||
0.393225 | + | 0.919442i | \(0.371359\pi\) | |||||||
\(182\) | 1.18327e33 | + | 3.39187e32i | 0.000816473 | + | 0.000234044i | ||||
\(183\) | 1.42984e36i | 0.903795i | ||||||||
\(184\) | −1.00515e35 | − | 1.11576e35i | −0.0582299 | − | 0.0646374i | ||||
\(185\) | 1.37619e36 | 0.731023 | ||||||||
\(186\) | 2.12446e35 | − | 7.41128e35i | 0.103524 | − | 0.361149i | ||||
\(187\) | 3.22714e36i | 1.44328i | ||||||||
\(188\) | 1.79497e36 | − | 2.87365e36i | 0.737110 | − | 1.18007i | ||||
\(189\) | 2.61869e33 | 0.000987860 | ||||||||
\(190\) | 7.31513e35 | + | 2.09690e35i | 0.253609 | + | 0.0726976i | ||||
\(191\) | − | 1.14601e36i | − | 0.365304i | −0.983178 | − | 0.182652i | \(-0.941532\pi\) | ||
0.983178 | − | 0.182652i | \(-0.0584681\pi\) | |||||||
\(192\) | 2.24993e36 | + | 2.35307e35i | 0.659703 | + | 0.0689947i | ||||
\(193\) | 3.03069e36 | 0.817757 | 0.408878 | − | 0.912589i | \(-0.365920\pi\) | ||||
0.408878 | + | 0.912589i | \(0.365920\pi\) | |||||||
\(194\) | 6.05700e35 | − | 2.11301e36i | 0.150463 | − | 0.524897i | ||||
\(195\) | 2.04972e36i | 0.468965i | ||||||||
\(196\) | −4.02313e36 | − | 2.51297e36i | −0.848138 | − | 0.529773i | ||||
\(197\) | −2.82588e36 | −0.549154 | −0.274577 | − | 0.961565i | \(-0.588538\pi\) | ||||
−0.274577 | + | 0.961565i | \(0.588538\pi\) | |||||||
\(198\) | −4.37055e36 | − | 1.25283e36i | −0.783236 | − | 0.224517i | ||||
\(199\) | 4.12362e36i | 0.681757i | 0.940107 | + | 0.340879i | \(0.110725\pi\) | ||||
−0.940107 | + | 0.340879i | \(0.889275\pi\) | |||||||
\(200\) | −1.79421e36 | + | 1.61635e36i | −0.273775 | + | 0.246635i | ||||
\(201\) | −3.80499e36 | −0.536063 | ||||||||
\(202\) | −2.03690e36 | + | 7.10582e36i | −0.265062 | + | 0.924681i | ||||
\(203\) | 1.28880e34i | 0.00154970i | ||||||||
\(204\) | 3.13623e36 | − | 5.02093e36i | 0.348598 | − | 0.558087i | ||||
\(205\) | −3.35238e34 | −0.00344581 | ||||||||
\(206\) | −1.18785e37 | − | 3.40501e36i | −1.12950 | − | 0.323774i | ||||
\(207\) | − | 5.53668e35i | − | 0.0487218i | ||||||
\(208\) | 4.79069e36 | + | 9.81384e36i | 0.390288 | + | 0.799513i | ||||
\(209\) | 6.40161e36 | 0.483001 | ||||||||
\(210\) | −1.98368e33 | + | 6.92014e33i | −0.000138664 | + | 0.000483734i | ||||
\(211\) | − | 8.72796e36i | − | 0.565449i | −0.959201 | − | 0.282725i | \(-0.908762\pi\) | ||
0.959201 | − | 0.282725i | \(-0.0912382\pi\) | |||||||
\(212\) | 2.01660e37 | + | 1.25963e37i | 1.21128 | + | 0.756605i | ||||
\(213\) | −1.62299e37 | −0.904153 | ||||||||
\(214\) | 1.48657e36 | + | 4.26130e35i | 0.0768361 | + | 0.0220253i | ||||
\(215\) | − | 2.04167e37i | − | 0.979425i | ||||||
\(216\) | 1.55503e37 | + | 1.72614e37i | 0.692594 | + | 0.768807i | ||||
\(217\) | 1.30716e34 | 0.000540722 | ||||||||
\(218\) | −3.36149e36 | + | 1.17267e37i | −0.129190 | + | 0.450684i | ||||
\(219\) | − | 1.76214e37i | − | 0.629411i | ||||||
\(220\) | 1.84448e37 | − | 2.95291e37i | 0.612506 | − | 0.980589i | ||||
\(221\) | 2.85784e37 | 0.882595 | ||||||||
\(222\) | −2.04150e37 | − | 5.85202e36i | −0.586547 | − | 0.168135i | ||||
\(223\) | − | 3.46341e37i | − | 0.926033i | −0.886350 | − | 0.463016i | \(-0.846767\pi\) | ||
0.886350 | − | 0.463016i | \(-0.153233\pi\) | |||||||
\(224\) | 6.67642e33 | + | 3.77692e34i | 0.000166179 | + | 0.000940091i | ||||
\(225\) | −8.90334e36 | −0.206363 | ||||||||
\(226\) | −1.18385e36 | + | 4.12990e36i | −0.0255600 | + | 0.0891671i | ||||
\(227\) | 4.61174e37i | 0.927794i | 0.885889 | + | 0.463897i | \(0.153549\pi\) | ||||
−0.885889 | + | 0.463897i | \(0.846451\pi\) | |||||||
\(228\) | −9.95992e36 | − | 6.22127e36i | −0.186766 | − | 0.116660i | ||||
\(229\) | −2.33950e37 | −0.409030 | −0.204515 | − | 0.978863i | \(-0.565562\pi\) | ||||
−0.204515 | + | 0.978863i | \(0.565562\pi\) | |||||||
\(230\) | 4.07569e36 | + | 1.16831e36i | 0.0664592 | + | 0.0190507i | ||||
\(231\) | 6.05595e34i | 0.000921278i | ||||||||
\(232\) | −8.49529e37 | + | 7.65315e37i | −1.20606 | + | 1.08651i | ||||
\(233\) | 2.24295e37 | 0.297252 | 0.148626 | − | 0.988893i | \(-0.452515\pi\) | ||||
0.148626 | + | 0.988893i | \(0.452515\pi\) | |||||||
\(234\) | −1.10946e37 | + | 3.87040e37i | −0.137296 | + | 0.478964i | ||||
\(235\) | 9.56575e37i | 1.10569i | ||||||||
\(236\) | 9.68035e37 | − | 1.54977e38i | 1.04544 | − | 1.67369i | ||||
\(237\) | 4.12152e37 | 0.415991 | ||||||||
\(238\) | 9.64848e34 | + | 2.76576e34i | 0.000910390 | + | 0.000260966i | ||||
\(239\) | 7.63924e37i | 0.674037i | 0.941498 | + | 0.337018i | \(0.109418\pi\) | ||||
−0.941498 | + | 0.337018i | \(0.890582\pi\) | |||||||
\(240\) | −5.73945e37 | + | 2.80175e37i | −0.473685 | + | 0.231233i | ||||
\(241\) | −2.15781e38 | −1.66625 | −0.833124 | − | 0.553086i | \(-0.813450\pi\) | ||||
−0.833124 | + | 0.553086i | \(0.813450\pi\) | |||||||
\(242\) | 4.25780e37 | − | 1.48535e38i | 0.307708 | − | 1.07345i | ||||
\(243\) | 1.40562e38i | 0.950974i | ||||||||
\(244\) | −1.82416e38 | − | 1.13943e38i | −1.15565 | − | 0.721855i | ||||
\(245\) | 1.33921e38 | 0.794678 | ||||||||
\(246\) | 4.97307e35 | + | 1.42554e35i | 0.00276479 | + | 0.000792536i | ||||
\(247\) | − | 5.66904e37i | − | 0.295364i | ||||||
\(248\) | 7.76220e37 | + | 8.61634e37i | 0.379103 | + | 0.420819i | ||||
\(249\) | 1.99549e38 | 0.913819 | ||||||||
\(250\) | 6.97719e37 | − | 2.43402e38i | 0.299668 | − | 1.04540i | ||||
\(251\) | − | 3.23115e38i | − | 1.30190i | −0.759121 | − | 0.650949i | \(-0.774371\pi\) | ||
0.759121 | − | 0.650949i | \(-0.225629\pi\) | |||||||
\(252\) | −7.49140e34 | + | 1.19933e35i | −0.000283240 | + | 0.000453451i | ||||
\(253\) | 3.56671e37 | 0.126573 | ||||||||
\(254\) | 4.61385e38 | + | 1.32257e38i | 1.53718 | + | 0.440636i | ||||
\(255\) | 1.67136e38i | 0.522909i | ||||||||
\(256\) | −2.09315e38 | + | 2.68290e38i | −0.615121 | + | 0.788433i | ||||
\(257\) | 3.79367e38 | 1.04744 | 0.523721 | − | 0.851890i | \(-0.324543\pi\) | ||||
0.523721 | + | 0.851890i | \(0.324543\pi\) | |||||||
\(258\) | −8.68188e37 | + | 3.02871e38i | −0.225268 | + | 0.785855i | ||||
\(259\) | − | 3.60070e35i | − | 0.000878195i | ||||||
\(260\) | −2.61499e38 | − | 1.63340e38i | −0.599648 | − | 0.374559i | ||||
\(261\) | −4.21559e38 | −0.909096 | ||||||||
\(262\) | 4.86299e38 | + | 1.39399e38i | 0.986467 | + | 0.282774i | ||||
\(263\) | − | 5.28506e38i | − | 1.00869i | −0.863502 | − | 0.504345i | \(-0.831734\pi\) | ||
0.863502 | − | 0.504345i | \(-0.168266\pi\) | |||||||
\(264\) | −3.99186e38 | + | 3.59614e38i | −0.716988 | + | 0.645913i | ||||
\(265\) | −6.71281e38 | −1.13493 | ||||||||
\(266\) | 5.48638e34 | − | 1.91395e35i | 8.73333e−5 | − | 0.000304666i | ||||
\(267\) | − | 3.06966e38i | − | 0.460161i | ||||||
\(268\) | 3.03216e38 | − | 4.85433e38i | 0.428150 | − | 0.685444i | ||||
\(269\) | −7.48552e38 | −0.995831 | −0.497916 | − | 0.867226i | \(-0.665901\pi\) | ||||
−0.497916 | + | 0.867226i | \(0.665901\pi\) | |||||||
\(270\) | −6.30534e38 | − | 1.80744e38i | −0.790475 | − | 0.226592i | ||||
\(271\) | 1.81220e38i | 0.214140i | 0.994251 | + | 0.107070i | \(0.0341469\pi\) | ||||
−0.994251 | + | 0.107070i | \(0.965853\pi\) | |||||||
\(272\) | 3.90637e38 | + | 8.00228e38i | 0.435182 | + | 0.891479i | ||||
\(273\) | 5.36293e35 | 0.000563378 | ||||||||
\(274\) | −4.11602e38 | + | 1.43589e39i | −0.407820 | + | 1.42270i | ||||
\(275\) | − | 5.73551e38i | − | 0.536103i | ||||||
\(276\) | −5.54925e37 | − | 3.46624e37i | −0.0489428 | − | 0.0305712i | ||||
\(277\) | 5.50087e38 | 0.457884 | 0.228942 | − | 0.973440i | \(-0.426473\pi\) | ||||
0.228942 | + | 0.973440i | \(0.426473\pi\) | |||||||
\(278\) | 8.01073e38 | + | 2.29630e38i | 0.629441 | + | 0.180431i | ||||
\(279\) | 4.27565e38i | 0.317201i | ||||||||
\(280\) | −7.24780e35 | − | 8.04534e35i | −0.000507783 | − | 0.000563658i | ||||
\(281\) | 2.00956e39 | 1.32984 | 0.664921 | − | 0.746914i | \(-0.268465\pi\) | ||||
0.664921 | + | 0.746914i | \(0.268465\pi\) | |||||||
\(282\) | 4.06768e38 | − | 1.41903e39i | 0.254308 | − | 0.887166i | ||||
\(283\) | 1.10638e39i | 0.653613i | 0.945091 | + | 0.326806i | \(0.105973\pi\) | ||||
−0.945091 | + | 0.326806i | \(0.894027\pi\) | |||||||
\(284\) | 1.29335e39 | − | 2.07058e39i | 0.722140 | − | 1.15611i | ||||
\(285\) | 3.31544e38 | 0.174994 | ||||||||
\(286\) | −2.49330e39 | − | 7.14712e38i | −1.24428 | − | 0.356676i | ||||
\(287\) | 8.77125e33i | 4.13953e-6i | ||||||||
\(288\) | −1.23541e39 | + | 2.18382e38i | −0.551482 | + | 0.0974847i | ||||
\(289\) | −3.76060e37 | −0.0158815 | ||||||||
\(290\) | 8.89540e38 | − | 3.10320e39i | 0.355465 | − | 1.24006i | ||||
\(291\) | − | 9.57680e38i | − | 0.362187i | ||||||
\(292\) | 2.24810e39 | + | 1.40423e39i | 0.804804 | + | 0.502706i | ||||
\(293\) | 1.58688e39 | 0.537851 | 0.268926 | − | 0.963161i | \(-0.413331\pi\) | ||||
0.268926 | + | 0.963161i | \(0.413331\pi\) | |||||||
\(294\) | −1.98664e39 | − | 5.69477e38i | −0.637621 | − | 0.182776i | ||||
\(295\) | 5.15884e39i | 1.56819i | ||||||||
\(296\) | 2.37345e39 | − | 2.13817e39i | 0.683459 | − | 0.615707i | ||||
\(297\) | −5.51792e39 | −1.50547 | ||||||||
\(298\) | −7.21028e38 | + | 2.51534e39i | −0.186420 | + | 0.650333i | ||||
\(299\) | − | 3.15855e38i | − | 0.0774015i | ||||||
\(300\) | −5.57393e38 | + | 8.92356e38i | −0.129486 | + | 0.207299i | ||||
\(301\) | −5.34189e36 | −0.00117661 | ||||||||
\(302\) | −4.51020e39 | − | 1.29286e39i | −0.942073 | − | 0.270048i | ||||
\(303\) | 3.22057e39i | 0.638044i | ||||||||
\(304\) | 1.58740e39 | − | 7.74898e38i | 0.298337 | − | 0.145636i | ||||
\(305\) | 6.07223e39 | 1.08281 | ||||||||
\(306\) | −9.04664e38 | + | 3.15596e39i | −0.153089 | + | 0.534058i | ||||
\(307\) | − | 5.18035e38i | − | 0.0832042i | −0.999134 | − | 0.0416021i | \(-0.986754\pi\) | ||
0.999134 | − | 0.0416021i | \(-0.0132462\pi\) | |||||||
\(308\) | −7.72606e36 | − | 4.82594e36i | −0.00117800 | − | 0.000735818i | ||||
\(309\) | −5.38370e39 | −0.779373 | ||||||||
\(310\) | −3.14741e39 | − | 9.02215e38i | −0.432680 | − | 0.124029i | ||||
\(311\) | − | 4.91084e39i | − | 0.641194i | −0.947216 | − | 0.320597i | \(-0.896117\pi\) | ||
0.947216 | − | 0.320597i | \(-0.103883\pi\) | |||||||
\(312\) | 3.18462e39 | + | 3.53505e39i | 0.394988 | + | 0.438452i | ||||
\(313\) | −3.57734e39 | −0.421552 | −0.210776 | − | 0.977534i | \(-0.567599\pi\) | ||||
−0.210776 | + | 0.977534i | \(0.567599\pi\) | |||||||
\(314\) | −1.71622e39 | + | 5.98712e39i | −0.192176 | + | 0.670415i | ||||
\(315\) | − | 3.99231e36i | − | 0.000424869i | ||||||
\(316\) | −3.28441e39 | + | 5.25816e39i | −0.332249 | + | 0.531912i | ||||
\(317\) | 5.68505e39 | 0.546746 | 0.273373 | − | 0.961908i | \(-0.411861\pi\) | ||||
0.273373 | + | 0.961908i | \(0.411861\pi\) | |||||||
\(318\) | 9.95808e39 | + | 2.85451e39i | 0.910629 | + | 0.261034i | ||||
\(319\) | − | 2.71567e40i | − | 2.36171i | ||||||
\(320\) | 9.99301e38 | − | 9.55496e39i | 0.0826602 | − | 0.790368i | ||||
\(321\) | 6.73759e38 | 0.0530181 | ||||||||
\(322\) | 3.05679e35 | − | 1.06637e36i | 2.28861e−5 | − | 7.98390e-5i | ||||
\(323\) | − | 4.62258e39i | − | 0.329340i | ||||||
\(324\) | 1.58018e39 | + | 9.87027e38i | 0.107148 | + | 0.0669282i | ||||
\(325\) | −5.07916e39 | −0.327837 | ||||||||
\(326\) | 2.71295e40 | + | 7.77673e39i | 1.66709 | + | 0.477876i | ||||
\(327\) | 5.31490e39i | 0.310979i | ||||||||
\(328\) | −5.78168e37 | + | 5.20854e37i | −0.00322161 | + | 0.00290225i | ||||
\(329\) | 2.50281e37 | 0.00132829 | ||||||||
\(330\) | 4.17986e39 | − | 1.45816e40i | 0.211319 | − | 0.737196i | ||||
\(331\) | 1.18264e40i | 0.569643i | 0.958581 | + | 0.284822i | \(0.0919344\pi\) | ||||
−0.958581 | + | 0.284822i | \(0.908066\pi\) | |||||||
\(332\) | −1.59019e40 | + | 2.54581e40i | −0.729860 | + | 1.16847i | ||||
\(333\) | 1.17777e40 | 0.515171 | ||||||||
\(334\) | −1.75823e40 | − | 5.04002e39i | −0.733049 | − | 0.210130i | ||||
\(335\) | 1.61590e40i | 0.642239i | ||||||||
\(336\) | 7.33057e36 | + | 1.50168e37i | 0.000277785 | + | 0.000569049i | ||||
\(337\) | 2.80251e39 | 0.101267 | 0.0506336 | − | 0.998717i | \(-0.483876\pi\) | ||||
0.0506336 | + | 0.998717i | \(0.483876\pi\) | |||||||
\(338\) | 1.66681e39 | − | 5.81475e39i | 0.0574407 | − | 0.200384i | ||||
\(339\) | 1.87180e39i | 0.0615267i | ||||||||
\(340\) | −2.13228e40 | − | 1.33189e40i | −0.668625 | − | 0.417644i | ||||
\(341\) | −2.75436e40 | −0.824045 | ||||||||
\(342\) | 6.26041e39 | + | 1.79456e39i | 0.178725 | + | 0.0512320i | ||||
\(343\) | − | 7.00789e37i | − | 0.00190933i | ||||||
\(344\) | −3.17212e40 | − | 3.52117e40i | −0.824925 | − | 0.915698i | ||||
\(345\) | 1.84722e39 | 0.0458579 | ||||||||
\(346\) | −9.24768e38 | + | 3.22609e39i | −0.0219187 | + | 0.0764644i | ||||
\(347\) | 2.15434e40i | 0.487577i | 0.969828 | + | 0.243789i | \(0.0783903\pi\) | ||||
−0.969828 | + | 0.243789i | \(0.921610\pi\) | |||||||
\(348\) | −2.63917e40 | + | 4.22516e40i | −0.570425 | + | 0.913220i | ||||
\(349\) | −2.12404e40 | −0.438486 | −0.219243 | − | 0.975670i | \(-0.570359\pi\) | ||||
−0.219243 | + | 0.975670i | \(0.570359\pi\) | |||||||
\(350\) | −1.71480e37 | − | 4.91551e36i | −0.000338161 | − | 9.69349e-5i | ||||
\(351\) | 4.88648e40i | 0.920623i | ||||||||
\(352\) | −1.40681e40 | − | 7.95847e40i | −0.253252 | − | 1.43267i | ||||
\(353\) | 6.57081e40 | 1.13038 | 0.565189 | − | 0.824961i | \(-0.308803\pi\) | ||||
0.565189 | + | 0.824961i | \(0.308803\pi\) | |||||||
\(354\) | 2.19371e40 | − | 7.65286e40i | 0.360684 | − | 1.25826i | ||||
\(355\) | 6.89249e40i | 1.08324i | ||||||||
\(356\) | 3.91621e40 | + | 2.44619e40i | 0.588391 | + | 0.367528i | ||||
\(357\) | 4.37298e37 | 0.000628183 | ||||||||
\(358\) | 1.20531e41 | + | 3.45507e40i | 1.65566 | + | 0.474600i | ||||
\(359\) | − | 5.03977e40i | − | 0.662064i | −0.943620 | − | 0.331032i | \(-0.892603\pi\) | ||
0.943620 | − | 0.331032i | \(-0.107397\pi\) | |||||||
\(360\) | 2.63158e40 | − | 2.37071e40i | 0.330656 | − | 0.297878i | ||||
\(361\) | 7.40287e40 | 0.889785 | ||||||||
\(362\) | −1.88459e40 | + | 6.57447e40i | −0.216710 | + | 0.756003i | ||||
\(363\) | − | 6.73206e40i | − | 0.740699i | ||||||
\(364\) | −4.27368e37 | + | 6.84193e37i | −0.000449966 | + | 0.000720371i | ||||
\(365\) | −7.48343e40 | −0.754076 | ||||||||
\(366\) | −9.00782e40 | − | 2.58212e40i | −0.868805 | − | 0.249045i | ||||
\(367\) | − | 1.14455e41i | − | 1.05676i | −0.849008 | − | 0.528380i | \(-0.822800\pi\) | ||
0.849008 | − | 0.528380i | \(-0.177200\pi\) | |||||||
\(368\) | 8.84431e39 | − | 4.31741e39i | 0.0781806 | − | 0.0381644i | ||||
\(369\) | −2.86902e38 | −0.00242835 | ||||||||
\(370\) | −2.48523e40 | + | 8.66984e40i | −0.201437 | + | 0.702722i | ||||
\(371\) | 1.75636e38i | 0.00136342i | ||||||||
\(372\) | 4.28536e40 | + | 2.67677e40i | 0.318640 | + | 0.199033i | ||||
\(373\) | 1.14383e40 | 0.0814742 | 0.0407371 | − | 0.999170i | \(-0.487029\pi\) | ||||
0.0407371 | + | 0.999170i | \(0.487029\pi\) | |||||||
\(374\) | −2.03306e41 | − | 5.82782e40i | −1.38741 | − | 0.397704i | ||||
\(375\) | − | 1.10317e41i | − | 0.721344i | ||||||
\(376\) | 1.48622e41 | + | 1.64976e41i | 0.931272 | + | 1.03375i | ||||
\(377\) | −2.40490e41 | −1.44423 | ||||||||
\(378\) | −4.72904e37 | + | 1.64974e38i | −0.000272210 | + | 0.000949616i | ||||
\(379\) | − | 1.18219e41i | − | 0.652321i | −0.945314 | − | 0.326161i | \(-0.894245\pi\) | ||
0.945314 | − | 0.326161i | \(-0.105755\pi\) | |||||||
\(380\) | −2.64204e40 | + | 4.22977e40i | −0.139766 | + | 0.223758i | ||||
\(381\) | 2.09113e41 | 1.06067 | ||||||||
\(382\) | 7.21972e40 | + | 2.06955e40i | 0.351161 | + | 0.100661i | ||||
\(383\) | 3.95929e41i | 1.84687i | 0.383751 | + | 0.923437i | \(0.374632\pi\) | ||||
−0.383751 | + | 0.923437i | \(0.625368\pi\) | |||||||
\(384\) | −5.54550e40 | + | 1.37493e41i | −0.248108 | + | 0.615151i | ||||
\(385\) | 2.57183e38 | 0.00110375 | ||||||||
\(386\) | −5.47305e40 | + | 1.90930e41i | −0.225337 | + | 0.786098i | ||||
\(387\) | − | 1.74730e41i | − | 0.690227i | ||||||
\(388\) | 1.22179e41 | + | 7.63167e40i | 0.463115 | + | 0.289276i | ||||
\(389\) | −5.23472e41 | −1.90414 | −0.952072 | − | 0.305874i | \(-0.901052\pi\) | ||||
−0.952072 | + | 0.305874i | \(0.901052\pi\) | |||||||
\(390\) | −1.29130e41 | − | 3.70154e40i | −0.450809 | − | 0.129226i | ||||
\(391\) | − | 2.57551e40i | − | 0.0863048i | ||||||
\(392\) | 2.30967e41 | − | 2.08071e41i | 0.742972 | − | 0.669321i | ||||
\(393\) | 2.20405e41 | 0.680677 | ||||||||
\(394\) | 5.10319e40 | − | 1.78027e41i | 0.151322 | − | 0.527893i | ||||
\(395\) | − | 1.75032e41i | − | 0.498385i | ||||||
\(396\) | 1.57853e41 | − | 2.52715e41i | 0.431649 | − | 0.691047i | ||||
\(397\) | 2.03759e41 | 0.535143 | 0.267571 | − | 0.963538i | \(-0.413779\pi\) | ||||
0.267571 | + | 0.963538i | \(0.413779\pi\) | |||||||
\(398\) | −2.59783e41 | − | 7.44676e40i | −0.655363 | − | 0.187862i | ||||
\(399\) | − | 8.67459e37i | − | 0.000210224i | ||||||
\(400\) | −6.94268e40 | − | 1.42222e41i | −0.161647 | − | 0.331137i | ||||
\(401\) | 5.34108e41 | 1.19487 | 0.597433 | − | 0.801919i | \(-0.296187\pi\) | ||||
0.597433 | + | 0.801919i | \(0.296187\pi\) | |||||||
\(402\) | 6.87134e40 | − | 2.39710e41i | 0.147715 | − | 0.515310i | ||||
\(403\) | 2.43917e41i | 0.503919i | ||||||||
\(404\) | −4.10874e41 | − | 2.56645e41i | −0.815843 | − | 0.509601i | ||||
\(405\) | −5.26006e40 | −0.100395 | ||||||||
\(406\) | −8.11928e38 | − | 2.32741e38i | −0.00148971 | − | 0.000427029i | ||||
\(407\) | 7.58714e41i | 1.33834i | ||||||||
\(408\) | 2.59676e41 | + | 2.88250e41i | 0.440422 | + | 0.488886i | ||||
\(409\) | 3.50235e41 | 0.571199 | 0.285599 | − | 0.958349i | \(-0.407807\pi\) | ||||
0.285599 | + | 0.958349i | \(0.407807\pi\) | |||||||
\(410\) | 6.05399e38 | − | 2.11196e39i | 0.000949510 | − | 0.00331241i | ||||
\(411\) | 6.50789e41i | 0.981683i | ||||||||
\(412\) | 4.29023e41 | − | 6.86842e41i | 0.622479 | − | 0.996555i | ||||
\(413\) | 1.34977e39 | 0.00188391 | ||||||||
\(414\) | 3.48804e40 | + | 9.99856e39i | 0.0468356 | + | 0.0134255i | ||||
\(415\) | − | 8.47443e41i | − | 1.09482i | ||||||
\(416\) | −7.04774e41 | + | 1.24582e41i | −0.876106 | + | 0.154868i | ||||
\(417\) | 3.63070e41 | 0.434324 | ||||||||
\(418\) | −1.15605e41 | + | 4.03294e41i | −0.133093 | + | 0.464302i | ||||
\(419\) | − | 9.79209e40i | − | 0.108505i | −0.998527 | − | 0.0542526i | \(-0.982722\pi\) | ||
0.998527 | − | 0.0542526i | \(-0.0172776\pi\) | |||||||
\(420\) | −4.00138e38 | − | 2.49939e38i | −0.000426797 | − | 0.000266590i | ||||
\(421\) | −1.90222e42 | −1.95321 | −0.976603 | − | 0.215052i | \(-0.931008\pi\) | ||||
−0.976603 | + | 0.215052i | \(0.931008\pi\) | |||||||
\(422\) | 5.49851e41 | + | 1.57616e41i | 0.543558 | + | 0.155812i | ||||
\(423\) | 8.18653e41i | 0.779209i | ||||||||
\(424\) | −1.15772e42 | + | 1.04296e42i | −1.06109 | + | 0.955902i | ||||
\(425\) | −4.14159e41 | −0.365548 | ||||||||
\(426\) | 2.93092e41 | − | 1.02246e42i | 0.249144 | − | 0.869149i | ||||
\(427\) | − | 1.58875e39i | − | 0.00130080i | ||||||
\(428\) | −5.36913e40 | + | 8.59568e40i | −0.0423452 | + | 0.0677923i | ||||
\(429\) | −1.13004e42 | −0.858572 | ||||||||
\(430\) | 1.28623e42 | + | 3.68701e41i | 0.941507 | + | 0.269885i | ||||
\(431\) | − | 5.57257e41i | − | 0.393024i | −0.980501 | − | 0.196512i | \(-0.937039\pi\) | ||
0.980501 | − | 0.196512i | \(-0.0629615\pi\) | |||||||
\(432\) | −1.36827e42 | + | 6.67930e41i | −0.929890 | + | 0.453932i | ||||
\(433\) | 2.19637e42 | 1.43846 | 0.719231 | − | 0.694771i | \(-0.244494\pi\) | ||||
0.719231 | + | 0.694771i | \(0.244494\pi\) | |||||||
\(434\) | −2.36058e38 | + | 8.23497e38i | −0.000148999 | + | 0.000519788i | ||||
\(435\) | − | 1.40646e42i | − | 0.855658i | ||||||
\(436\) | −6.78064e41 | − | 4.23540e41i | −0.397637 | − | 0.248376i | ||||
\(437\) | −5.10898e40 | −0.0288823 | ||||||||
\(438\) | 1.11013e42 | + | 3.18221e41i | 0.605043 | + | 0.173437i | ||||
\(439\) | − | 2.85773e42i | − | 1.50172i | −0.660462 | − | 0.750859i | \(-0.729640\pi\) | ||
0.660462 | − | 0.750859i | \(-0.270360\pi\) | |||||||
\(440\) | 1.52721e42 | + | 1.69526e42i | 0.773846 | + | 0.858999i | ||||
\(441\) | 1.14612e42 | 0.560031 | ||||||||
\(442\) | −5.16091e41 | + | 1.80040e42i | −0.243204 | + | 0.848426i | ||||
\(443\) | − | 9.08746e41i | − | 0.413031i | −0.978443 | − | 0.206516i | \(-0.933788\pi\) | ||
0.978443 | − | 0.206516i | \(-0.0662124\pi\) | |||||||
\(444\) | 7.37341e41 | − | 1.18044e42i | 0.323252 | − | 0.517508i | ||||
\(445\) | −1.30362e42 | −0.551304 | ||||||||
\(446\) | 2.18191e42 | + | 6.25450e41i | 0.890182 | + | 0.255173i | ||||
\(447\) | 1.14003e42i | 0.448740i | ||||||||
\(448\) | −2.49999e39 | − | 2.61460e38i | −0.000949487 | − | 9.93016e-5i | ||||
\(449\) | 4.17788e42 | 1.53114 | 0.765570 | − | 0.643353i | \(-0.222457\pi\) | ||||
0.765570 | + | 0.643353i | \(0.222457\pi\) | |||||||
\(450\) | 1.60783e41 | − | 5.60900e41i | 0.0568645 | − | 0.198374i | ||||
\(451\) | − | 1.84822e40i | − | 0.00630853i | ||||||
\(452\) | −2.38800e41 | − | 1.49162e41i | −0.0786719 | − | 0.0491409i | ||||
\(453\) | −2.04416e42 | −0.650044 | ||||||||
\(454\) | −2.90534e42 | − | 8.32824e41i | −0.891874 | − | 0.255658i | ||||
\(455\) | − | 2.27753e39i | − | 0.000674965i | ||||||
\(456\) | 5.71796e41 | − | 5.15114e41i | 0.163608 | − | 0.147389i | ||||
\(457\) | −3.75807e42 | −1.03826 | −0.519130 | − | 0.854695i | \(-0.673744\pi\) | ||||
−0.519130 | + | 0.854695i | \(0.673744\pi\) | |||||||
\(458\) | 4.22484e41 | − | 1.47386e42i | 0.112710 | − | 0.393194i | ||||
\(459\) | 3.98447e42i | 1.02652i | ||||||||
\(460\) | −1.47204e41 | + | 2.35665e41i | −0.0366263 | + | 0.0586368i | ||||
\(461\) | −1.39943e42 | −0.336307 | −0.168153 | − | 0.985761i | \(-0.553780\pi\) | ||||
−0.168153 | + | 0.985761i | \(0.553780\pi\) | |||||||
\(462\) | −3.81517e39 | − | 1.09363e39i | −0.000885611 | − | 0.000253863i | ||||
\(463\) | − | 1.36252e42i | − | 0.305525i | −0.988263 | − | 0.152762i | \(-0.951183\pi\) | ||
0.988263 | − | 0.152762i | \(-0.0488169\pi\) | |||||||
\(464\) | −3.28725e42 | − | 6.73399e42i | −0.712106 | − | 1.45876i | ||||
\(465\) | −1.42650e42 | −0.298556 | ||||||||
\(466\) | −4.05050e41 | + | 1.41303e42i | −0.0819094 | + | 0.285744i | ||||
\(467\) | 7.19617e42i | 1.40615i | 0.711116 | + | 0.703074i | \(0.248190\pi\) | ||||
−0.711116 | + | 0.703074i | \(0.751810\pi\) | |||||||
\(468\) | −2.23795e42 | − | 1.39789e42i | −0.422588 | − | 0.263962i | ||||
\(469\) | 4.22788e39 | 0.000771537 | ||||||||
\(470\) | −6.02631e42 | − | 1.72746e42i | −1.06288 | − | 0.304678i | ||||
\(471\) | 2.71354e42i | 0.462596i | ||||||||
\(472\) | 8.01521e42 | + | 8.89719e42i | 1.32082 | + | 1.46616i | ||||
\(473\) | 1.12560e43 | 1.79311 | ||||||||
\(474\) | −7.44296e41 | + | 2.59651e42i | −0.114628 | + | 0.399886i | ||||
\(475\) | 8.21558e41i | 0.122332i | ||||||||
\(476\) | −3.48479e39 | + | 5.57896e39i | −0.000501725 | + | 0.000803234i | ||||
\(477\) | −5.74493e42 | −0.799817 | ||||||||
\(478\) | −4.81263e42 | − | 1.37955e42i | −0.647941 | − | 0.185734i | ||||
\(479\) | 3.01680e42i | 0.392806i | 0.980523 | + | 0.196403i | \(0.0629261\pi\) | ||||
−0.980523 | + | 0.196403i | \(0.937074\pi\) | |||||||
\(480\) | −7.28596e41 | − | 4.12174e42i | −0.0917544 | − | 0.519064i | ||||
\(481\) | 6.71890e42 | 0.818422 | ||||||||
\(482\) | 3.89673e42 | − | 1.35939e43i | 0.459143 | − | 1.60174i | ||||
\(483\) | − | 4.83312e38i | − | 5.50901e-5i | ||||||
\(484\) | 8.58863e42 | + | 5.36472e42i | 0.947105 | + | 0.591591i | ||||
\(485\) | −4.06706e42 | −0.433924 | ||||||||
\(486\) | −8.85526e42 | − | 2.53838e42i | −0.914157 | − | 0.262046i | ||||
\(487\) | − | 7.87682e42i | − | 0.786842i | −0.919358 | − | 0.393421i | \(-0.871292\pi\) | ||
0.919358 | − | 0.393421i | \(-0.128708\pi\) | |||||||
\(488\) | 1.04725e43 | − | 9.43434e42i | 1.01235 | − | 0.911999i | ||||
\(489\) | 1.22959e43 | 1.15032 | ||||||||
\(490\) | −2.41845e42 | + | 8.43686e42i | −0.218978 | + | 0.763912i | ||||
\(491\) | − | 1.58573e43i | − | 1.38971i | −0.719150 | − | 0.694855i | \(-0.755469\pi\) | ||
0.719150 | − | 0.694855i | \(-0.244531\pi\) | |||||||
\(492\) | −1.79615e40 | + | 2.87554e40i | −0.00152371 | + | 0.00243937i | ||||
\(493\) | −1.96097e43 | −1.61035 | ||||||||
\(494\) | 3.57143e42 | + | 1.02376e42i | 0.283929 | + | 0.0813891i | ||||
\(495\) | 8.41231e42i | 0.647489i | ||||||||
\(496\) | −6.82995e42 | + | 3.33409e42i | −0.508991 | + | 0.248468i | ||||
\(497\) | 1.80337e40 | 0.00130132 | ||||||||
\(498\) | −3.60361e42 | + | 1.25713e43i | −0.251807 | + | 0.878440i | ||||
\(499\) | − | 1.31326e43i | − | 0.888670i | −0.895861 | − | 0.444335i | \(-0.853440\pi\) | ||
0.895861 | − | 0.444335i | \(-0.146560\pi\) | |||||||
\(500\) | 1.40740e43 | + | 8.79109e42i | 0.922357 | + | 0.576133i | ||||
\(501\) | −7.96884e42 | −0.505815 | ||||||||
\(502\) | 2.03558e43 | + | 5.83506e42i | 1.25150 | + | 0.358745i | ||||
\(503\) | − | 4.56337e42i | − | 0.271767i | −0.990725 | − | 0.135884i | \(-0.956613\pi\) | ||
0.990725 | − | 0.135884i | \(-0.0433874\pi\) | |||||||
\(504\) | −6.20279e39 | − | 6.88534e39i | −0.000357848 | − | 0.000397225i | ||||
\(505\) | 1.36771e43 | 0.764419 | ||||||||
\(506\) | −6.44104e41 | + | 2.24698e42i | −0.0348777 | + | 0.121672i | ||||
\(507\) | − | 2.63542e42i | − | 0.138268i | ||||||
\(508\) | −1.66641e43 | + | 2.66783e43i | −0.847153 | + | 1.35625i | ||||
\(509\) | −1.03750e42 | −0.0511097 | −0.0255549 | − | 0.999673i | \(-0.508135\pi\) | ||||
−0.0255549 | + | 0.999673i | \(0.508135\pi\) | |||||||
\(510\) | −1.05293e43 | − | 3.01826e42i | −0.502665 | − | 0.144090i | ||||
\(511\) | 1.95798e40i | 0.000905889i | ||||||||
\(512\) | −1.31220e43 | − | 1.80316e43i | −0.588409 | − | 0.808563i | ||||
\(513\) | 7.90392e42 | 0.343530 | ||||||||
\(514\) | −6.85091e42 | + | 2.38997e43i | −0.288628 | + | 1.00689i | ||||
\(515\) | 2.28634e43i | 0.933740i | ||||||||
\(516\) | −1.75127e43 | − | 1.09390e43i | −0.693358 | − | 0.433093i | ||||
\(517\) | −5.27374e43 | −2.02428 | ||||||||
\(518\) | 2.26840e40 | + | 6.50242e39i | 0.000844196 | + | 0.000241991i | ||||
\(519\) | 1.46216e42i | 0.0527616i | ||||||||
\(520\) | 1.50126e43 | − | 1.35244e43i | 0.525294 | − | 0.473221i | ||||
\(521\) | 1.65964e43 | 0.563132 | 0.281566 | − | 0.959542i | \(-0.409146\pi\) | ||||
0.281566 | + | 0.959542i | \(0.409146\pi\) | |||||||
\(522\) | 7.61283e42 | − | 2.65577e43i | 0.250506 | − | 0.873901i | ||||
\(523\) | − | 4.85049e43i | − | 1.54795i | −0.633213 | − | 0.773977i | \(-0.718264\pi\) | ||
0.633213 | − | 0.773977i | \(-0.281736\pi\) | |||||||
\(524\) | −1.75639e43 | + | 2.81189e43i | −0.543652 | + | 0.870357i | ||||
\(525\) | −7.77198e39 | −0.000233336 | ||||||||
\(526\) | 3.32952e43 | + | 9.54416e42i | 0.969639 | + | 0.277950i | ||||
\(527\) | 1.98892e43i | 0.561884i | ||||||||
\(528\) | −1.54465e43 | − | 3.16424e43i | −0.423337 | − | 0.867215i | ||||
\(529\) | 3.73243e43 | 0.992431 | ||||||||
\(530\) | 1.21225e43 | − | 4.22899e43i | 0.312736 | − | 1.09099i | ||||
\(531\) | 4.41502e43i | 1.10515i | ||||||||
\(532\) | 1.10669e40 | + | 6.91271e39i | 0.000268806 | + | 0.000167904i | ||||
\(533\) | −1.63671e41 | −0.00385778 | ||||||||
\(534\) | 1.93385e43 | + | 5.54343e42i | 0.442346 | + | 0.126800i | ||||
\(535\) | − | 2.86131e42i | − | 0.0635192i | ||||||
\(536\) | 2.51060e43 | + | 2.78686e43i | 0.540929 | + | 0.600452i | ||||
\(537\) | 5.46285e43 | 1.14243 | ||||||||
\(538\) | 1.35179e43 | − | 4.71579e43i | 0.274406 | − | 0.957278i | ||||
\(539\) | 7.38326e43i | 1.45488i | ||||||||
\(540\) | 2.27733e43 | − | 3.64589e43i | 0.435639 | − | 0.697434i | ||||
\(541\) | −4.36755e43 | −0.811114 | −0.405557 | − | 0.914070i | \(-0.632922\pi\) | ||||
−0.405557 | + | 0.914070i | \(0.632922\pi\) | |||||||
\(542\) | −1.14166e43 | − | 3.27261e42i | −0.205849 | − | 0.0590073i | ||||
\(543\) | 2.97975e43i | 0.521653i | ||||||||
\(544\) | −5.74678e43 | + | 1.01585e43i | −0.976882 | + | 0.172682i | ||||
\(545\) | 2.25712e43 | 0.372573 | ||||||||
\(546\) | −9.68480e39 | + | 3.37858e40i | −0.000155242 | + | 0.000541567i | ||||
\(547\) | − | 1.01722e44i | − | 1.58351i | −0.610842 | − | 0.791753i | \(-0.709169\pi\) | ||
0.610842 | − | 0.791753i | \(-0.290831\pi\) | |||||||
\(548\) | −8.30264e43 | − | 5.18609e43i | −1.25524 | − | 0.784063i | ||||
\(549\) | 5.19672e43 | 0.763083 | ||||||||
\(550\) | 3.61330e43 | + | 1.03576e43i | 0.515348 | + | 0.147726i | ||||
\(551\) | 3.88994e43i | 0.538912i | ||||||||
\(552\) | 3.18581e42 | − | 2.87000e42i | 0.0428741 | − | 0.0386240i | ||||
\(553\) | −4.57959e40 | −0.000598721 | ||||||||
\(554\) | −9.93390e42 | + | 3.46548e43i | −0.126172 | + | 0.440157i | ||||
\(555\) | 3.92943e43i | 0.484888i | ||||||||
\(556\) | −2.89328e43 | + | 4.63198e43i | −0.346891 | + | 0.555354i | ||||
\(557\) | −1.35627e44 | −1.58002 | −0.790009 | − | 0.613096i | \(-0.789924\pi\) | ||||
−0.790009 | + | 0.613096i | \(0.789924\pi\) | |||||||
\(558\) | −2.69361e43 | − | 7.72130e42i | −0.304921 | − | 0.0874065i | ||||
\(559\) | − | 9.96796e43i | − | 1.09652i | ||||||
\(560\) | 6.37733e40 | − | 3.11314e40i | 0.000681759 | − | 0.000332805i | ||||
\(561\) | −9.21443e43 | −0.957332 | ||||||||
\(562\) | −3.62902e43 | + | 1.26600e44i | −0.366445 | + | 1.27836i | ||||
\(563\) | 2.89870e43i | 0.284492i | 0.989831 | + | 0.142246i | \(0.0454323\pi\) | ||||
−0.989831 | + | 0.142246i | \(0.954568\pi\) | |||||||
\(564\) | 8.20512e43 | + | 5.12517e43i | 0.782743 | + | 0.488926i | ||||
\(565\) | 7.94913e42 | 0.0737130 | ||||||||
\(566\) | −6.97005e43 | − | 1.99798e43i | −0.628309 | − | 0.180106i | ||||
\(567\) | 1.37625e40i | 0.000120606i | ||||||||
\(568\) | 1.07088e44 | + | 1.18871e44i | 0.912359 | + | 1.01275i | ||||
\(569\) | 5.38772e43 | 0.446281 | 0.223141 | − | 0.974786i | \(-0.428369\pi\) | ||||
0.223141 | + | 0.974786i | \(0.428369\pi\) | |||||||
\(570\) | −5.98727e42 | + | 2.08868e43i | −0.0482204 | + | 0.168219i | ||||
\(571\) | − | 1.44273e44i | − | 1.12982i | −0.825153 | − | 0.564909i | \(-0.808911\pi\) | ||
0.825153 | − | 0.564909i | \(-0.191089\pi\) | |||||||
\(572\) | 9.00520e43 | − | 1.44168e44i | 0.685736 | − | 1.09782i | ||||
\(573\) | 3.27219e43 | 0.242306 | ||||||||
\(574\) | −5.52578e38 | − | 1.58398e38i | −3.97927e−6 | − | 1.14067e-6i | ||||
\(575\) | 4.57738e42i | 0.0320576i | ||||||||
\(576\) | 8.55218e42 | − | 8.17730e43i | 0.0582529 | − | 0.556994i | ||||
\(577\) | −9.92412e42 | −0.0657474 | −0.0328737 | − | 0.999460i | \(-0.510466\pi\) | ||||
−0.0328737 | + | 0.999460i | \(0.510466\pi\) | |||||||
\(578\) | 6.79118e41 | − | 2.36913e42i | 0.00437623 | − | 0.0152666i | ||||
\(579\) | 8.65351e43i | 0.542419i | ||||||||
\(580\) | 1.79434e44 | + | 1.12080e44i | 1.09410 | + | 0.683407i | ||||
\(581\) | −2.21727e41 | −0.00131523 | ||||||||
\(582\) | 6.03327e43 | + | 1.72945e43i | 0.348165 | + | 0.0998023i | ||||
\(583\) | − | 3.70087e44i | − | 2.07781i | ||||||
\(584\) | −1.29063e44 | + | 1.16269e44i | −0.705012 | + | 0.635123i | ||||
\(585\) | 7.44965e43 | 0.395951 | ||||||||
\(586\) | −2.86571e43 | + | 9.99715e43i | −0.148208 | + | 0.517028i | ||||
\(587\) | 1.21624e44i | 0.612083i | 0.952018 | + | 0.306042i | \(0.0990046\pi\) | ||||
−0.952018 | + | 0.306042i | \(0.900995\pi\) | |||||||
\(588\) | 7.17527e43 | − | 1.14872e44i | 0.351399 | − | 0.562571i | ||||
\(589\) | 3.94537e43 | 0.188037 | ||||||||
\(590\) | −3.25001e44 | − | 9.31623e43i | −1.50748 | − | 0.432124i | ||||
\(591\) | − | 8.06871e43i | − | 0.364254i | ||||||
\(592\) | 9.18404e43 | + | 1.88137e44i | 0.403540 | + | 0.826660i | ||||
\(593\) | 1.18094e44 | 0.505071 | 0.252536 | − | 0.967588i | \(-0.418736\pi\) | ||||
0.252536 | + | 0.967588i | \(0.418736\pi\) | |||||||
\(594\) | 9.96469e43 | − | 3.47622e44i | 0.414840 | − | 1.44719i | ||||
\(595\) | − | 1.85711e41i | − | 0.000752604i | ||||||
\(596\) | −1.45442e44 | − | 9.08478e43i | −0.573787 | − | 0.358405i | ||||
\(597\) | −1.17742e44 | −0.452211 | ||||||||
\(598\) | 1.98985e43 | + | 5.70396e42i | 0.0744049 | + | 0.0213284i | ||||
\(599\) | 2.39488e44i | 0.871877i | 0.899977 | + | 0.435938i | \(0.143583\pi\) | ||||
−0.899977 | + | 0.435938i | \(0.856417\pi\) | |||||||
\(600\) | −4.61515e43 | − | 5.12300e43i | −0.163594 | − | 0.181595i | ||||
\(601\) | 1.10890e44 | 0.382737 | 0.191368 | − | 0.981518i | \(-0.438708\pi\) | ||||
0.191368 | + | 0.981518i | \(0.438708\pi\) | |||||||
\(602\) | 9.64679e40 | − | 3.36533e41i | 0.000324220 | − | 0.00113105i | ||||
\(603\) | 1.38291e44i | 0.452603i | ||||||||
\(604\) | 1.62897e44 | − | 2.60790e44i | 0.519186 | − | 0.831188i | ||||
\(605\) | −2.85896e44 | −0.887407 | ||||||||
\(606\) | −2.02892e44 | − | 5.81595e43i | −0.613342 | − | 0.175816i | ||||
\(607\) | 6.73326e44i | 1.98247i | 0.132121 | + | 0.991234i | \(0.457821\pi\) | ||||
−0.132121 | + | 0.991234i | \(0.542179\pi\) | |||||||
\(608\) | 2.01512e43 | + | 1.13998e44i | 0.0577889 | + | 0.326918i | ||||
\(609\) | −3.67990e41 | −0.00102792 | ||||||||
\(610\) | −1.09657e44 | + | 3.82543e44i | −0.298373 | + | 1.04089i | ||||
\(611\) | 4.67024e44i | 1.23788i | ||||||||
\(612\) | −1.82484e44 | − | 1.13985e44i | −0.471198 | − | 0.294325i | ||||
\(613\) | 1.55932e44 | 0.392254 | 0.196127 | − | 0.980579i | \(-0.437164\pi\) | ||||
0.196127 | + | 0.980579i | \(0.437164\pi\) | |||||||
\(614\) | 3.26356e43 | + | 9.35508e42i | 0.0799830 | + | 0.0229273i | ||||
\(615\) | − | 9.57203e41i | − | 0.00228561i | ||||||
\(616\) | 4.43551e41 | − | 3.99582e41i | 0.00103194 | − | 0.000929639i | ||||
\(617\) | −2.42947e44 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(618\) | 9.72230e43 | − | 3.39167e44i | 0.214760 | − | 0.749199i | ||||
\(619\) | − | 8.44075e44i | − | 1.81690i | −0.417996 | − | 0.908449i | \(-0.637267\pi\) | ||
0.417996 | − | 0.908449i | \(-0.362733\pi\) | |||||||
\(620\) | 1.13677e44 | − | 1.81990e44i | 0.238454 | − | 0.381752i | ||||
\(621\) | 4.40373e43 | 0.0900234 | ||||||||
\(622\) | 3.09377e44 | + | 8.86837e43i | 0.616370 | + | 0.176684i | ||||
\(623\) | 3.41083e41i | 0.000662294i | ||||||||
\(624\) | −2.80214e44 | + | 1.36788e44i | −0.530318 | + | 0.258878i | ||||
\(625\) | −2.68737e44 | −0.495733 | ||||||||
\(626\) | 6.46024e43 | − | 2.25368e44i | 0.116161 | − | 0.405231i | ||||
\(627\) | 1.82785e44i | 0.320376i | ||||||||
\(628\) | −3.46188e44 | − | 2.16240e44i | −0.591505 | − | 0.369472i | ||||
\(629\) | 5.47865e44 | 0.912563 | ||||||||
\(630\) | 2.51511e41 | + | 7.20962e40i | 0.000408421 | + | 0.000117075i | ||||
\(631\) | − | 5.16712e44i | − | 0.818048i | −0.912524 | − | 0.409024i | \(-0.865869\pi\) | ||
0.912524 | − | 0.409024i | \(-0.134131\pi\) | |||||||
\(632\) | −2.71945e44 | − | 3.01870e44i | −0.419767 | − | 0.465957i | ||||
\(633\) | 2.49209e44 | 0.375063 | ||||||||
\(634\) | −1.02665e44 | + | 3.58151e44i | −0.150659 | + | 0.525579i | ||||
\(635\) | − | 8.88061e44i | − | 1.27076i | ||||||
\(636\) | −3.59661e44 | + | 5.75798e44i | −0.501857 | + | 0.803445i | ||||
\(637\) | 6.53835e44 | 0.889687 | ||||||||
\(638\) | 1.71084e45 | + | 4.90416e44i | 2.27027 | + | 0.650780i | ||||
\(639\) | 5.89871e44i | 0.763385i | ||||||||
\(640\) | 5.83905e44 | + | 2.35506e44i | 0.736992 | + | 0.297250i | ||||
\(641\) | −1.90781e44 | −0.234859 | −0.117429 | − | 0.993081i | \(-0.537465\pi\) | ||||
−0.117429 | + | 0.993081i | \(0.537465\pi\) | |||||||
\(642\) | −1.21673e43 | + | 4.24460e43i | −0.0146094 | + | 0.0509655i | ||||
\(643\) | 2.24114e44i | 0.262478i | 0.991351 | + | 0.131239i | \(0.0418956\pi\) | ||||
−0.991351 | + | 0.131239i | \(0.958104\pi\) | |||||||
\(644\) | 6.16600e40 | + | 3.85148e40i | 7.04417e−5 | + | 4.40001e-5i | ||||
\(645\) | 5.82958e44 | 0.649654 | ||||||||
\(646\) | 2.91217e44 | + | 8.34781e43i | 0.316589 | + | 0.0907512i | ||||
\(647\) | − | 1.04450e45i | − | 1.10775i | −0.832601 | − | 0.553873i | \(-0.813149\pi\) | ||
0.832601 | − | 0.553873i | \(-0.186851\pi\) | |||||||
\(648\) | −9.07176e43 | + | 8.17247e43i | −0.0938623 | + | 0.0845577i | ||||
\(649\) | −2.84414e45 | −2.87102 | ||||||||
\(650\) | 9.17234e43 | − | 3.19981e44i | 0.0903372 | − | 0.315145i | ||||
\(651\) | 3.73234e41i | 0.000358662i | ||||||||
\(652\) | −9.79850e44 | + | 1.56869e45i | −0.918751 | + | 1.47087i | ||||
\(653\) | 1.37316e45 | 1.25635 | 0.628174 | − | 0.778073i | \(-0.283803\pi\) | ||||
0.628174 | + | 0.778073i | \(0.283803\pi\) | |||||||
\(654\) | −3.34832e44 | − | 9.59805e43i | −0.298939 | − | 0.0856917i | ||||
\(655\) | − | 9.36015e44i | − | 0.815497i | ||||||
\(656\) | −2.23722e42 | − | 4.58299e42i | −0.00190216 | − | 0.00389661i | ||||
\(657\) | −6.40445e44 | −0.531417 | ||||||||
\(658\) | −4.51976e41 | + | 1.57674e42i | −0.000366017 | + | 0.00127687i | ||||
\(659\) | − | 4.41987e43i | − | 0.0349336i | −0.999847 | − | 0.0174668i | \(-0.994440\pi\) | ||
0.999847 | − | 0.0174668i | \(-0.00556014\pi\) | |||||||
\(660\) | 8.43142e44 | + | 5.26653e44i | 0.650426 | + | 0.406276i | ||||
\(661\) | −2.19392e45 | −1.65195 | −0.825974 | − | 0.563708i | \(-0.809374\pi\) | ||||
−0.825974 | + | 0.563708i | \(0.809374\pi\) | |||||||
\(662\) | −7.45046e44 | − | 2.13569e44i | −0.547590 | − | 0.156968i | ||||
\(663\) | 8.15998e44i | 0.585427i | ||||||||
\(664\) | −1.31666e45 | − | 1.46154e45i | −0.922113 | − | 1.02358i | ||||
\(665\) | −3.68392e41 | −0.000251862 | ||||||||
\(666\) | −2.12690e44 | + | 7.41979e44i | −0.141958 | + | 0.495227i | ||||
\(667\) | 2.16732e44i | 0.141224i | ||||||||
\(668\) | 6.35031e44 | − | 1.01665e45i | 0.403991 | − | 0.646767i | ||||
\(669\) | 9.88906e44 | 0.614239 | ||||||||
\(670\) | −1.01800e45 | − | 2.91811e44i | −0.617375 | − | 0.176972i | ||||
\(671\) | 3.34771e45i | 1.98238i | ||||||||
\(672\) | −1.07842e42 | + | 1.90632e41i | −0.000623564 | + | 0.000110227i | ||||
\(673\) | 2.14147e45 | 1.20912 | 0.604562 | − | 0.796558i | \(-0.293348\pi\) | ||||
0.604562 | + | 0.796558i | \(0.293348\pi\) | |||||||
\(674\) | −5.06099e43 | + | 1.76555e44i | −0.0279047 | + | 0.0973467i | ||||
\(675\) | − | 7.08149e44i | − | 0.381298i | ||||||
\(676\) | 3.36222e44 | + | 2.10015e44i | 0.176799 | + | 0.110434i | ||||
\(677\) | 2.65983e45 | 1.36595 | 0.682975 | − | 0.730441i | \(-0.260686\pi\) | ||||
0.682975 | + | 0.730441i | \(0.260686\pi\) | |||||||
\(678\) | −1.17921e44 | − | 3.38023e43i | −0.0591447 | − | 0.0169540i | ||||
\(679\) | 1.06412e42i | 0.000521282i | ||||||||
\(680\) | 1.22414e45 | − | 1.10279e45i | 0.585718 | − | 0.527655i | ||||
\(681\) | −1.31679e45 | −0.615407 | ||||||||
\(682\) | 4.97404e44 | − | 1.73522e45i | 0.227070 | − | 0.792143i | ||||
\(683\) | − | 4.16209e44i | − | 0.185601i | −0.995685 | − | 0.0928005i | \(-0.970418\pi\) | ||
0.995685 | − | 0.0928005i | \(-0.0295819\pi\) | |||||||
\(684\) | −2.26111e44 | + | 3.61991e44i | −0.0984970 | + | 0.157688i | ||||
\(685\) | 2.76376e45 | 1.17612 | ||||||||
\(686\) | 4.41488e42 | + | 1.26554e42i | 0.00183541 | + | 0.000526126i | ||||
\(687\) | − | 6.67995e44i | − | 0.271310i | ||||||
\(688\) | 2.79114e45 | − | 1.36252e45i | 1.10756 | − | 0.540663i | ||||
\(689\) | −3.27736e45 | −1.27062 | ||||||||
\(690\) | −3.33586e43 | + | 1.16373e44i | −0.0126364 | + | 0.0440825i | ||||
\(691\) | 3.56018e45i | 1.31772i | 0.752265 | + | 0.658860i | \(0.228961\pi\) | ||||
−0.752265 | + | 0.658860i | \(0.771039\pi\) | |||||||
\(692\) | −1.86540e44 | − | 1.16518e44i | −0.0674643 | − | 0.0421403i | ||||
\(693\) | 2.20102e42 | 0.000777843 | ||||||||
\(694\) | −1.35721e45 | − | 3.89048e44i | −0.468701 | − | 0.134354i | ||||
\(695\) | − | 1.54188e45i | − | 0.520349i | ||||||
\(696\) | −2.18520e45 | − | 2.42566e45i | −0.720681 | − | 0.799984i | ||||
\(697\) | −1.33459e43 | −0.00430154 | ||||||||
\(698\) | 3.83575e44 | − | 1.33812e45i | 0.120827 | − | 0.421510i | ||||
\(699\) | 6.40429e44i | 0.197168i | ||||||||
\(700\) | 6.19343e41 | − | 9.91534e41i | 0.000186364 | − | 0.000298359i | ||||
\(701\) | 1.22041e45 | 0.358936 | 0.179468 | − | 0.983764i | \(-0.442562\pi\) | ||||
0.179468 | + | 0.983764i | \(0.442562\pi\) | |||||||
\(702\) | −3.07842e45 | − | 8.82438e44i | −0.884982 | − | 0.253682i | ||||
\(703\) | − | 1.08679e45i | − | 0.305393i | ||||||
\(704\) | 5.26779e45 | + | 5.50929e44i | 1.44699 | + | 0.151333i | ||||
\(705\) | −2.73130e45 | −0.733405 | ||||||||
\(706\) | −1.18661e45 | + | 4.13953e45i | −0.311481 | + | 1.08662i | ||||
\(707\) | − | 3.57851e42i | − | 0.000918314i | ||||||
\(708\) | 4.42505e45 | + | 2.76402e45i | 1.11016 | + | 0.693441i | ||||
\(709\) | −1.04935e45 | −0.257383 | −0.128691 | − | 0.991685i | \(-0.541078\pi\) | ||||
−0.128691 | + | 0.991685i | \(0.541078\pi\) | |||||||
\(710\) | −4.34219e45 | − | 1.24470e45i | −1.04130 | − | 0.298491i | ||||
\(711\) | − | 1.49796e45i | − | 0.351225i | ||||||
\(712\) | −2.24829e45 | + | 2.02542e45i | −0.515433 | + | 0.464338i | ||||
\(713\) | 2.19820e44 | 0.0492759 | ||||||||
\(714\) | −7.89706e41 | + | 2.75492e42i | −0.000173099 | + | 0.000603863i | ||||
\(715\) | 4.79904e45i | 1.02863i | ||||||||
\(716\) | −4.35330e45 | + | 6.96939e45i | −0.912452 | + | 1.46079i | ||||
\(717\) | −2.18123e45 | −0.447089 | ||||||||
\(718\) | 3.17500e45 | + | 9.10121e44i | 0.636432 | + | 0.182435i | ||||
\(719\) | − | 6.79956e45i | − | 1.33296i | −0.745521 | − | 0.666482i | \(-0.767799\pi\) | ||
0.745521 | − | 0.666482i | \(-0.232201\pi\) | |||||||
\(720\) | 1.01829e45 | + | 2.08599e45i | 0.195232 | + | 0.399937i | ||||
\(721\) | 5.98205e42 | 0.00112172 | ||||||||
\(722\) | −1.33687e45 | + | 4.66372e45i | −0.245185 | + | 0.855337i | ||||
\(723\) | − | 6.16117e45i | − | 1.10522i | ||||||
\(724\) | −3.80150e45 | − | 2.37454e45i | −0.667019 | − | 0.416641i | ||||
\(725\) | 3.48519e45 | 0.598161 | ||||||||
\(726\) | 4.24112e45 | + | 1.21573e45i | 0.712023 | + | 0.204103i | ||||
\(727\) | 1.35491e45i | 0.222515i | 0.993792 | + | 0.111257i | \(0.0354878\pi\) | ||||
−0.993792 | + | 0.111257i | \(0.964512\pi\) | |||||||
\(728\) | −3.53856e42 | − | 3.92793e42i | −0.000568492 | − | 0.000631048i | ||||
\(729\) | −4.81729e45 | −0.757116 | ||||||||
\(730\) | 1.35142e45 | − | 4.71447e45i | 0.207789 | − | 0.724882i | ||||
\(731\) | − | 8.12795e45i | − | 1.22265i | ||||||
\(732\) | 3.25340e45 | − | 5.20852e45i | 0.478807 | − | 0.766544i | ||||
\(733\) | 6.94890e45 | 1.00058 | 0.500291 | − | 0.865857i | \(-0.333226\pi\) | ||||
0.500291 | + | 0.865857i | \(0.333226\pi\) | |||||||
\(734\) | 7.21051e45 | + | 2.06691e45i | 1.01585 | + | 0.291196i | ||||
\(735\) | 3.82384e45i | 0.527111i | ||||||||
\(736\) | 1.12274e44 | + | 6.35148e44i | 0.0151438 | + | 0.0856702i | ||||
\(737\) | −8.90868e45 | −1.17580 | ||||||||
\(738\) | 5.18110e42 | − | 1.80745e43i | 0.000669145 | − | 0.00233434i | ||||
\(739\) | 7.67315e45i | 0.969757i | 0.874582 | + | 0.484879i | \(0.161136\pi\) | ||||
−0.874582 | + | 0.484879i | \(0.838864\pi\) | |||||||
\(740\) | −5.01309e45 | − | 3.13133e45i | −0.620009 | − | 0.387277i | ||||
\(741\) | 1.61868e45 | 0.195916 | ||||||||
\(742\) | −1.10648e43 | − | 3.17176e42i | −0.00131064 | − | 0.000375697i | ||||
\(743\) | − | 5.23761e45i | − | 0.607173i | −0.952804 | − | 0.303587i | \(-0.901816\pi\) | ||
0.952804 | − | 0.303587i | \(-0.0981842\pi\) | |||||||
\(744\) | −2.46022e45 | + | 2.21634e45i | −0.279130 | + | 0.251460i | ||||
\(745\) | 4.84145e45 | 0.537620 | ||||||||
\(746\) | −2.06562e44 | + | 7.20599e44i | −0.0224506 | + | 0.0783200i | ||||
\(747\) | − | 7.25256e45i | − | 0.771545i | ||||||
\(748\) | 7.34291e45 | − | 1.17556e46i | 0.764614 | − | 1.22411i | ||||
\(749\) | −7.48641e41 | −7.63070e−5 | ||||||||
\(750\) | 6.94985e45 | + | 1.99219e45i | 0.693418 | + | 0.198770i | ||||
\(751\) | 1.05662e46i | 1.03200i | 0.856587 | + | 0.516002i | \(0.172580\pi\) | ||||
−0.856587 | + | 0.516002i | \(0.827420\pi\) | |||||||
\(752\) | −1.30772e46 | + | 6.38372e45i | −1.25034 | + | 0.610364i | ||||
\(753\) | 9.22588e45 | 0.863551 | ||||||||
\(754\) | 4.34295e45 | − | 1.51506e46i | 0.397964 | − | 1.38831i | ||||
\(755\) | 8.68111e45i | 0.778796i | ||||||||
\(756\) | −9.53919e42 | − | 5.95847e42i | −0.000837843 | − | 0.000523343i | ||||
\(757\) | 9.35152e45 | 0.804171 | 0.402085 | − | 0.915602i | \(-0.368286\pi\) | ||||
0.402085 | + | 0.915602i | \(0.368286\pi\) | |||||||
\(758\) | 7.44768e45 | + | 2.13490e45i | 0.627067 | + | 0.179750i | ||||
\(759\) | 1.01840e45i | 0.0839557i | ||||||||
\(760\) | −2.18758e45 | − | 2.42830e45i | −0.176582 | − | 0.196013i | ||||
\(761\) | −1.90393e46 | −1.50486 | −0.752429 | − | 0.658673i | \(-0.771118\pi\) | ||||
−0.752429 | + | 0.658673i | \(0.771118\pi\) | |||||||
\(762\) | −3.77633e45 | + | 1.31739e46i | −0.292274 | + | 1.01961i | ||||
\(763\) | − | 5.90560e42i | − | 0.000447581i | ||||||
\(764\) | −2.60758e45 | + | 4.17460e45i | −0.193528 | + | 0.309828i | ||||
\(765\) | 6.07450e45 | 0.441497 | ||||||||
\(766\) | −2.49431e46 | − | 7.14999e45i | −1.77537 | − | 0.508915i | ||||
\(767\) | 2.51867e46i | 1.75568i | ||||||||
\(768\) | −7.66046e45 | − | 5.97656e45i | −0.522968 | − | 0.408011i | ||||
\(769\) | 6.00273e45 | 0.401354 | 0.200677 | − | 0.979657i | \(-0.435686\pi\) | ||||
0.200677 | + | 0.979657i | \(0.435686\pi\) | |||||||
\(770\) | −4.64442e42 | + | 1.62022e43i | −0.000304144 | + | 0.00106102i | ||||
\(771\) | 1.08321e46i | 0.694770i | ||||||||
\(772\) | −1.10400e46 | − | 6.89591e45i | −0.693571 | − | 0.433226i | ||||
\(773\) | −8.64477e45 | −0.531963 | −0.265981 | − | 0.963978i | \(-0.585696\pi\) | ||||
−0.265981 | + | 0.963978i | \(0.585696\pi\) | |||||||
\(774\) | 1.10078e46 | + | 3.15541e45i | 0.663505 | + | 0.190195i | ||||
\(775\) | − | 3.53485e45i | − | 0.208710i | ||||||
\(776\) | −7.01426e45 | + | 6.31894e45i | −0.405690 | + | 0.365474i | ||||
\(777\) | 1.02811e43 | 0.000582508 | ||||||||
\(778\) | 9.45326e45 | − | 3.29781e46i | 0.524696 | − | 1.83043i | ||||
\(779\) | 2.64740e43i | 0.00143953i | ||||||||
\(780\) | 4.66385e45 | − | 7.46657e45i | 0.248445 | − | 0.397747i | ||||
\(781\) | −3.79993e46 | −1.98317 | ||||||||
\(782\) | 1.62254e45 | + | 4.65105e44i | 0.0829635 | + | 0.0237817i | ||||
\(783\) | − | 3.35297e46i | − | 1.67974i | ||||||
\(784\) | 8.93724e45 | + | 1.83081e46i | 0.438679 | + | 0.898643i | ||||
\(785\) | 1.15238e46 | 0.554221 | ||||||||
\(786\) | −3.98025e45 | + | 1.38853e46i | −0.187564 | + | 0.654325i | ||||
\(787\) | − | 7.42361e45i | − | 0.342783i | −0.985203 | − | 0.171392i | \(-0.945174\pi\) | ||
0.985203 | − | 0.171392i | \(-0.0548263\pi\) | |||||||
\(788\) | 1.02939e46 | + | 6.42989e45i | 0.465758 | + | 0.290927i | ||||
\(789\) | 1.50904e46 | 0.669065 | ||||||||
\(790\) | 1.10268e46 | + | 3.16087e45i | 0.479090 | + | 0.137332i | ||||
\(791\) | − | 2.07983e42i | − | 8.85531e-5i | ||||||
\(792\) | 1.30701e46 | + | 1.45083e46i | 0.545350 | + | 0.605360i | ||||
\(793\) | 2.96461e46 | 1.21226 | ||||||||
\(794\) | −3.67964e45 | + | 1.28366e46i | −0.147461 | + | 0.514425i | ||||
\(795\) | − | 1.91670e46i | − | 0.752802i | ||||||
\(796\) | 9.38274e45 | − | 1.50212e46i | 0.361177 | − | 0.578225i | ||||
\(797\) | −2.06105e45 | −0.0777597 | −0.0388798 | − | 0.999244i | \(-0.512379\pi\) | ||||
−0.0388798 | + | 0.999244i | \(0.512379\pi\) | |||||||
\(798\) | 5.46489e42 | + | 1.56652e42i | 0.000202085 | + | 5.79283e-5i | ||||
\(799\) | 3.80815e46i | 1.38027i | ||||||||
\(800\) | 1.02136e46 | − | 1.80545e45i | 0.362860 | − | 0.0641423i | ||||
\(801\) | −1.11566e46 | −0.388519 | ||||||||
\(802\) | −9.64534e45 | + | 3.36482e46i | −0.329251 | + | 1.14861i | ||||
\(803\) | − | 4.12572e46i | − | 1.38055i | ||||||
\(804\) | 1.38605e46 | + | 8.65772e45i | 0.454656 | + | 0.283992i | ||||
\(805\) | −2.05253e42 | −6.60016e−5 | ||||||||
\(806\) | −1.53665e46 | − | 4.40484e45i | −0.484410 | − | 0.138857i | ||||
\(807\) | − | 2.13734e46i | − | 0.660536i | ||||||
\(808\) | 2.35882e46 | − | 2.12499e46i | 0.714682 | − | 0.643835i | ||||
\(809\) | 2.54117e46 | 0.754843 | 0.377422 | − | 0.926042i | \(-0.376811\pi\) | ||||
0.377422 | + | 0.926042i | \(0.376811\pi\) | |||||||
\(810\) | 9.49902e44 | − | 3.31377e45i | 0.0276642 | − | 0.0965078i | ||||
\(811\) | − | 4.73692e45i | − | 0.135258i | −0.997711 | − | 0.0676288i | \(-0.978457\pi\) | ||
0.997711 | − | 0.0676288i | \(-0.0215434\pi\) | |||||||
\(812\) | 2.93249e43 | − | 4.69475e43i | 0.000820993 | − | 0.00131436i | ||||
\(813\) | −5.17436e45 | −0.142039 | ||||||||
\(814\) | −4.77981e46 | − | 1.37014e46i | −1.28653 | − | 0.368787i | ||||
\(815\) | − | 5.22181e46i | − | 1.37816i | ||||||
\(816\) | −2.28489e46 | + | 1.11538e46i | −0.591319 | + | 0.288657i | ||||
\(817\) | −1.61233e46 | −0.409166 | ||||||||
\(818\) | −6.32482e45 | + | 2.20644e46i | −0.157397 | + | 0.549085i | ||||
\(819\) | − | 1.94914e43i | − | 0.000475666i | ||||||
\(820\) | 1.22118e44 | + | 7.62788e43i | 0.00292253 | + | 0.00182550i | ||||
\(821\) | −7.74502e46 | −1.81774 | −0.908870 | − | 0.417079i | \(-0.863054\pi\) | ||||
−0.908870 | + | 0.417079i | \(0.863054\pi\) | |||||||
\(822\) | −4.09989e46 | − | 1.17525e46i | −0.943677 | − | 0.270508i | ||||
\(823\) | 5.33360e46i | 1.20399i | 0.798500 | + | 0.601995i | \(0.205627\pi\) | ||||
−0.798500 | + | 0.601995i | \(0.794373\pi\) | |||||||
\(824\) | 3.55226e46 | + | 3.94314e46i | 0.786446 | + | 0.872986i | ||||
\(825\) | 1.63766e46 | 0.355598 | ||||||||
\(826\) | −2.43752e43 | + | 8.50340e43i | −0.000519120 | + | 0.00181097i | ||||
\(827\) | 5.53001e46i | 1.15515i | 0.816338 | + | 0.577574i | \(0.196001\pi\) | ||||
−0.816338 | + | 0.577574i | \(0.803999\pi\) | |||||||
\(828\) | −1.25979e45 | + | 2.01686e45i | −0.0258116 | + | 0.0413229i | ||||
\(829\) | −3.21975e46 | −0.647067 | −0.323534 | − | 0.946217i | \(-0.604871\pi\) | ||||
−0.323534 | + | 0.946217i | \(0.604871\pi\) | |||||||
\(830\) | 5.33879e46 | + | 1.53038e46i | 1.05243 | + | 0.301682i | ||||
\(831\) | 1.57066e46i | 0.303715i | ||||||||
\(832\) | 4.87883e45 | − | 4.66497e46i | 0.0925428 | − | 0.884862i | ||||
\(833\) | 5.33143e46 | 0.992027 | ||||||||
\(834\) | −6.55660e45 | + | 2.28730e46i | −0.119680 | + | 0.417509i | ||||
\(835\) | 3.38420e46i | 0.606000i | ||||||||
\(836\) | −2.33193e46 | − | 1.45660e46i | −0.409652 | − | 0.255882i | ||||
\(837\) | −3.40075e46 | −0.586094 | ||||||||
\(838\) | 6.16890e45 | + | 1.76833e45i | 0.104305 | + | 0.0298992i | ||||
\(839\) | − | 4.42433e45i | − | 0.0733932i | −0.999326 | − | 0.0366966i | \(-0.988316\pi\) | ||
0.999326 | − | 0.0366966i | \(-0.0116835\pi\) | |||||||
\(840\) | 2.29718e43 | − | 2.06946e43i | 0.000373875 | − | 0.000336813i | ||||
\(841\) | 1.02395e47 | 1.63509 | ||||||||
\(842\) | 3.43518e46 | − | 1.19838e47i | 0.538215 | − | 1.87759i | ||||
\(843\) | 5.73789e46i | 0.882086i | ||||||||
\(844\) | −1.98593e46 | + | 3.17936e46i | −0.299560 | + | 0.479579i | ||||
\(845\) | −1.11921e46 | −0.165655 | ||||||||
\(846\) | −5.15741e46 | − | 1.47839e46i | −0.749042 | − | 0.214715i | ||||
\(847\) | 7.48027e43i | 0.00106606i | ||||||||
\(848\) | −4.47980e46 | − | 9.17698e46i | −0.626506 | − | 1.28341i | ||||
\(849\) | −3.15904e46 | −0.433542 | ||||||||
\(850\) | 7.47920e45 | − | 2.60915e46i | 0.100728 | − | 0.351396i | ||||
\(851\) | − | 6.05513e45i | − | 0.0800296i | ||||||
\(852\) | 5.91211e46 | + | 3.69289e46i | 0.766847 | + | 0.478997i | ||||
\(853\) | 6.02455e46 | 0.766902 | 0.383451 | − | 0.923561i | \(-0.374735\pi\) | ||||
0.383451 | + | 0.923561i | \(0.374735\pi\) | |||||||
\(854\) | 1.00090e44 | + | 2.86910e43i | 0.00125044 | + | 0.000358442i | ||||
\(855\) | − | 1.20499e46i | − | 0.147749i | ||||||
\(856\) | −4.44558e45 | − | 4.93476e45i | −0.0534993 | − | 0.0593863i | ||||
\(857\) | 2.46922e46 | 0.291653 | 0.145826 | − | 0.989310i | \(-0.453416\pi\) | ||||
0.145826 | + | 0.989310i | \(0.453416\pi\) | |||||||
\(858\) | 2.04071e46 | − | 7.11911e46i | 0.236584 | − | 0.825333i | ||||
\(859\) | 2.00215e46i | 0.227828i | 0.993491 | + | 0.113914i | \(0.0363388\pi\) | ||||
−0.993491 | + | 0.113914i | \(0.963661\pi\) | |||||||
\(860\) | −4.64555e46 | + | 7.43727e46i | −0.518874 | + | 0.830688i | ||||
\(861\) | −2.50445e41 | −2.74576e−6 | ||||||||
\(862\) | 3.51065e46 | + | 1.00634e46i | 0.377808 | + | 0.108300i | ||||
\(863\) | − | 1.52936e47i | − | 1.61561i | −0.589450 | − | 0.807805i | \(-0.700655\pi\) | ||
0.589450 | − | 0.807805i | \(-0.299345\pi\) | |||||||
\(864\) | −1.73695e46 | − | 9.82613e46i | −0.180123 | − | 1.01897i | ||||
\(865\) | 6.20949e45 | 0.0632118 | ||||||||
\(866\) | −3.96637e46 | + | 1.38368e47i | −0.396375 | + | 1.38277i | ||||
\(867\) | − | 1.07376e45i | − | 0.0105342i | ||||||
\(868\) | −4.76164e43 | − | 2.97427e43i | −0.000458608 | − | 0.000286461i | ||||
\(869\) | 9.64979e46 | 0.912434 | ||||||||
\(870\) | 8.86054e46 | + | 2.53990e46i | 0.822531 | + | 0.235781i | ||||
\(871\) | 7.88921e46i | 0.719024i | ||||||||
\(872\) | 3.89275e46 | − | 3.50686e46i | 0.348331 | − | 0.313801i | ||||
\(873\) | −3.48066e46 | −0.305797 | ||||||||
\(874\) | 9.22620e44 | − | 3.21860e45i | 0.00795866 | − | 0.0277641i | ||||
\(875\) | 1.22578e44i | 0.00103821i | ||||||||
\(876\) | −4.00950e46 | + | 6.41899e46i | −0.333445 | + | 0.533828i | ||||
\(877\) | −2.36139e47 | −1.92830 | −0.964148 | − | 0.265367i | \(-0.914507\pi\) | ||||
−0.964148 | + | 0.265367i | \(0.914507\pi\) | |||||||
\(878\) | 1.80033e47 | + | 5.16071e46i | 1.44358 | + | 0.413806i | ||||
\(879\) | 4.53101e46i | 0.356757i | ||||||||
\(880\) | −1.34379e47 | + | 6.55979e46i | −1.03898 | + | 0.507186i | ||||
\(881\) | 3.98305e46 | 0.302413 | 0.151207 | − | 0.988502i | \(-0.451684\pi\) | ||||
0.151207 | + | 0.988502i | \(0.451684\pi\) | |||||||
\(882\) | −2.06975e46 | + | 7.22041e46i | −0.154319 | + | 0.538349i | ||||
\(883\) | − | 1.08523e47i | − | 0.794606i | −0.917688 | − | 0.397303i | \(-0.869946\pi\) | ||
0.917688 | − | 0.397303i | \(-0.130054\pi\) | |||||||
\(884\) | −1.04103e47 | − | 6.50262e46i | −0.748563 | − | 0.467576i | ||||
\(885\) | −1.47300e47 | −1.04019 | ||||||||
\(886\) | 5.72499e46 | + | 1.64108e46i | 0.397041 | + | 0.113813i | ||||
\(887\) | 7.95605e46i | 0.541900i | 0.962593 | + | 0.270950i | \(0.0873379\pi\) | ||||
−0.962593 | + | 0.270950i | \(0.912662\pi\) | |||||||
\(888\) | 6.10510e46 | + | 6.77689e46i | 0.408399 | + | 0.453339i | ||||
\(889\) | −2.32354e44 | −0.00152659 | ||||||||
\(890\) | 2.35418e46 | − | 8.21265e46i | 0.151915 | − | 0.529960i | ||||
\(891\) | − | 2.89995e46i | − | 0.183800i | ||||||
\(892\) | −7.88052e46 | + | 1.26163e47i | −0.490588 | + | 0.785404i | ||||
\(893\) | 7.55414e46 | 0.461915 | ||||||||
\(894\) | −7.18203e46 | − | 2.05875e46i | −0.431367 | − | 0.123652i | ||||
\(895\) | − | 2.31996e47i | − | 1.36871i | ||||||
\(896\) | 6.16183e43 | − | 1.52774e44i | 0.000357093 | − | 0.000885365i | ||||
\(897\) | 9.01860e45 | 0.0513405 | ||||||||
\(898\) | −7.54474e46 | + | 2.63201e47i | −0.421913 | + | 1.47186i | ||||
\(899\) | − | 1.67369e47i | − | 0.919434i | ||||||
\(900\) | 3.24325e46 | + | 2.02583e46i | 0.175025 | + | 0.109326i | ||||
\(901\) | −2.67238e47 | −1.41678 | ||||||||
\(902\) | 1.16435e45 | + | 3.33765e44i | 0.00606429 | + | 0.00173835i | ||||
\(903\) | − | 1.52527e44i | − | 0.000780444i | ||||||
\(904\) | 1.37095e46 | − | 1.23504e46i | 0.0689169 | − | 0.0620851i | ||||
\(905\) | 1.26544e47 | 0.624975 | ||||||||
\(906\) | 3.69150e46 | − | 1.28779e47i | 0.179123 | − | 0.624878i | ||||
\(907\) | − | 8.27618e46i | − | 0.394560i | −0.980347 | − | 0.197280i | \(-0.936789\pi\) | ||
0.980347 | − | 0.197280i | \(-0.0632108\pi\) | |||||||
\(908\) | 1.04934e47 | − | 1.67993e47i | 0.491521 | − | 0.786898i | ||||
\(909\) | 1.17051e47 | 0.538706 | ||||||||
\(910\) | 1.43481e44 | + | 4.11293e43i | 0.000648834 | + | 0.000185990i | ||||
\(911\) | 2.58323e47i | 1.14781i | 0.818922 | + | 0.573904i | \(0.194572\pi\) | ||||
−0.818922 | + | 0.573904i | \(0.805428\pi\) | |||||||
\(912\) | 2.21256e46 | + | 4.53248e46i | 0.0966002 | + | 0.197888i | ||||
\(913\) | 4.67208e47 | 2.00437 | ||||||||
\(914\) | 6.78662e46 | − | 2.36754e47i | 0.286098 | − | 0.998064i | ||||
\(915\) | 1.73380e47i | 0.718227i | ||||||||
\(916\) | 8.52215e46 | + | 5.32320e46i | 0.346914 | + | 0.216693i | ||||
\(917\) | −2.44901e44 | −0.000979675 | ||||||||
\(918\) | −2.51017e47 | − | 7.19547e46i | −0.986780 | − | 0.282863i | ||||
\(919\) | − | 2.31481e47i | − | 0.894267i | −0.894467 | − | 0.447134i | \(-0.852445\pi\) | ||
0.894467 | − | 0.447134i | \(-0.147555\pi\) | |||||||
\(920\) | −1.21883e46 | − | 1.35295e46i | −0.0462741 | − | 0.0513660i | ||||
\(921\) | 1.47914e46 | 0.0551894 | ||||||||
\(922\) | 2.52719e46 | − | 8.81622e46i | 0.0926709 | − | 0.323287i | ||||
\(923\) | 3.36509e47i | 1.21274i | ||||||||
\(924\) | 1.37795e44 | − | 2.20602e44i | 0.000488069 | − | 0.000781371i | ||||
\(925\) | −9.73705e46 | −0.338969 | ||||||||
\(926\) | 8.58370e46 | + | 2.46054e46i | 0.293697 | + | 0.0841889i | ||||
\(927\) | 1.95669e47i | 0.658031i | ||||||||
\(928\) | 4.83597e47 | − | 8.54849e46i | 1.59851 | − | 0.282567i | ||||
\(929\) | −1.59295e47 | −0.517547 | −0.258773 | − | 0.965938i | \(-0.583318\pi\) | ||||
−0.258773 | + | 0.965938i | \(0.583318\pi\) | |||||||
\(930\) | 2.57609e46 | − | 8.98680e46i | 0.0822685 | − | 0.286997i | ||||
\(931\) | − | 1.05758e47i | − | 0.331986i | ||||||
\(932\) | −8.17047e46 | − | 5.10353e46i | −0.252111 | − | 0.157477i | ||||
\(933\) | 1.40219e47 | 0.425305 | ||||||||
\(934\) | −4.53350e47 | − | 1.29954e47i | −1.35171 | − | 0.387471i | ||||
\(935\) | 3.91318e47i | 1.14695i | ||||||||
\(936\) | 1.28480e47 | − | 1.15744e47i | 0.370189 | − | 0.333492i | ||||
\(937\) | −2.80245e47 | −0.793788 | −0.396894 | − | 0.917864i | \(-0.629912\pi\) | ||||
−0.396894 | + | 0.917864i | \(0.629912\pi\) | |||||||
\(938\) | −7.63502e43 | + | 2.66351e44i | −0.000212601 | + | 0.000741667i | ||||
\(939\) | − | 1.02144e47i | − | 0.279616i | ||||||
\(940\) | 2.17655e47 | − | 3.48454e47i | 0.585766 | − | 0.937778i | ||||
\(941\) | 1.45598e47 | 0.385232 | 0.192616 | − | 0.981274i | \(-0.438303\pi\) | ||||
0.192616 | + | 0.981274i | \(0.438303\pi\) | |||||||
\(942\) | −1.70950e47 | − | 4.90032e46i | −0.444687 | − | 0.127471i | ||||
\(943\) | 1.47502e44i | 0.000377234i | ||||||||
\(944\) | −7.05257e47 | + | 3.44276e47i | −1.77336 | + | 0.865676i | ||||
\(945\) | 3.17538e44 | 0.000785032 | ||||||||
\(946\) | −2.03270e47 | + | 7.09117e47i | −0.494101 | + | 1.72369i | ||||
\(947\) | 8.61762e46i | 0.205962i | 0.994683 | + | 0.102981i | \(0.0328381\pi\) | ||||
−0.994683 | + | 0.102981i | \(0.967162\pi\) | |||||||
\(948\) | −1.50136e47 | − | 9.37795e46i | −0.352818 | − | 0.220381i | ||||
\(949\) | −3.65360e47 | −0.844231 | ||||||||
\(950\) | −5.17572e46 | − | 1.48363e46i | −0.117596 | − | 0.0337092i | ||||
\(951\) | 1.62325e47i | 0.362657i | ||||||||
\(952\) | −2.88537e44 | − | 3.20287e44i | −0.000633884 | − | 0.000703636i | ||||
\(953\) | −7.16117e47 | −1.54703 | −0.773513 | − | 0.633780i | \(-0.781502\pi\) | ||||
−0.773513 | + | 0.633780i | \(0.781502\pi\) | |||||||
\(954\) | 1.03746e47 | − | 3.61924e47i | 0.220394 | − | 0.768853i | ||||
\(955\) | − | 1.38963e47i | − | 0.290299i | ||||||
\(956\) | 1.73820e47 | − | 2.78277e47i | 0.357087 | − | 0.571677i | ||||
\(957\) | 7.75403e47 | 1.56652 | ||||||||
\(958\) | −1.90055e47 | − | 5.44797e46i | −0.377598 | − | 0.108240i | ||||
\(959\) | − | 7.23118e44i | − | 0.00141290i | ||||||
\(960\) | 2.72822e47 | + | 2.85330e46i | 0.524252 | + | 0.0548286i | ||||
\(961\) | 3.59390e47 | 0.679192 | ||||||||
\(962\) | −1.21335e47 | + | 4.23283e47i | −0.225520 | + | 0.786737i | ||||
\(963\) | − | 2.44876e46i | − | 0.0447636i | ||||||
\(964\) | 7.86030e47 | + | 4.90979e47i | 1.41321 | + | 0.882735i | ||||
\(965\) | 3.67496e47 | 0.649854 | ||||||||
\(966\) | 3.04481e43 | + | 8.72802e42i | 5.29573e−5 | + | 1.51804e-5i | ||||
\(967\) | − | 4.01544e47i | − | 0.686925i | −0.939166 | − | 0.343463i | \(-0.888400\pi\) | ||
0.939166 | − | 0.343463i | \(-0.111600\pi\) | |||||||
\(968\) | −4.93071e47 | + | 4.44193e47i | −0.829667 | + | 0.747422i | ||||
\(969\) | 1.31988e47 | 0.218451 | ||||||||
\(970\) | 7.34462e46 | − | 2.56220e47i | 0.119570 | − | 0.417124i | ||||
\(971\) | − | 3.71191e47i | − | 0.594415i | −0.954813 | − | 0.297208i | \(-0.903945\pi\) | ||
0.954813 | − | 0.297208i | \(-0.0960553\pi\) | |||||||
\(972\) | 3.19830e47 | − | 5.12030e47i | 0.503801 | − | 0.806558i | ||||
\(973\) | −4.03422e44 | −0.000625107 | ||||||||
\(974\) | 4.96230e47 | + | 1.42246e47i | 0.756380 | + | 0.216818i | ||||
\(975\) | − | 1.45025e47i | − | 0.217455i | ||||||
\(976\) | 4.05232e47 | + | 8.30126e47i | 0.597732 | + | 1.22447i | ||||
\(977\) | −1.04108e48 | −1.51068 | −0.755341 | − | 0.655332i | \(-0.772529\pi\) | ||||
−0.755341 | + | 0.655332i | \(0.772529\pi\) | |||||||
\(978\) | −2.22049e47 | + | 7.74626e47i | −0.316976 | + | 1.10578i | ||||
\(979\) | − | 7.18705e47i | − | 1.00932i | ||||||
\(980\) | −4.87838e47 | − | 3.04719e47i | −0.673997 | − | 0.421000i | ||||
\(981\) | 1.93169e47 | 0.262562 | ||||||||
\(982\) | 9.98988e47 | + | 2.86363e47i | 1.33591 | + | 0.382941i | ||||
\(983\) | − | 2.41310e47i | − | 0.317481i | −0.987320 | − | 0.158741i | \(-0.949257\pi\) | ||
0.987320 | − | 0.158741i | \(-0.0507434\pi\) | |||||||
\(984\) | −1.48719e45 | − | 1.65084e45i | −0.00192507 | − | 0.00213690i | ||||
\(985\) | −3.42661e47 | −0.436401 | ||||||||
\(986\) | 3.54128e47 | − | 1.23539e48i | 0.443741 | − | 1.54801i | ||||
\(987\) | 7.14625e44i | 0.000881057i | ||||||||
\(988\) | −1.28991e47 | + | 2.06508e47i | −0.156476 | + | 0.250510i | ||||
\(989\) | −8.98321e46 | −0.107224 | ||||||||
\(990\) | −5.29966e47 | − | 1.51916e47i | −0.622421 | − | 0.178419i | ||||
\(991\) | − | 1.70900e48i | − | 1.97498i | −0.157683 | − | 0.987490i | \(-0.550402\pi\) | ||
0.157683 | − | 0.987490i | \(-0.449598\pi\) | |||||||
\(992\) | −8.67029e46 | − | 4.90488e47i | −0.0985932 | − | 0.557752i | ||||
\(993\) | −3.37677e47 | −0.377845 | ||||||||
\(994\) | −3.25666e44 | + | 1.13610e45i | −0.000358584 | + | 0.00125094i | ||||
\(995\) | 5.00024e47i | 0.541778i | ||||||||
\(996\) | −7.26903e47 | − | 4.54046e47i | −0.775045 | − | 0.484117i | ||||
\(997\) | 1.51218e48 | 1.58665 | 0.793326 | − | 0.608797i | \(-0.208347\pi\) | ||||
0.793326 | + | 0.608797i | \(0.208347\pi\) | |||||||
\(998\) | 8.27335e47 | + | 2.37158e47i | 0.854265 | + | 0.244877i | ||||
\(999\) | 9.36766e47i | 0.951883i |
(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 | 4.33.b.b.3.6 | yes | 14 | |
3.2 | odd | 2 | 36.33.d.b.19.9 | 14 | |||
4.3 | odd | 2 | inner | 4.33.b.b.3.5 | ✓ | 14 | |
12.11 | even | 2 | 36.33.d.b.19.10 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.33.b.b.3.5 | ✓ | 14 | 4.3 | odd | 2 | inner | |
4.33.b.b.3.6 | yes | 14 | 1.1 | even | 1 | trivial | |
36.33.d.b.19.9 | 14 | 3.2 | odd | 2 | |||
36.33.d.b.19.10 | 14 | 12.11 | even | 2 |