Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,20,Mod(4,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.4");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(11.4408348278\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 726881x^{6} + 160513523376x^{4} + 10607307647230976x^{2} + 32429098232548950016 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{8}\cdot 5^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.1 | ||
Root | \(-607.943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.4 |
Dual form | 5.20.b.a.4.8 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1215.89i | − | 1.67922i | −0.543188 | − | 0.839611i | \(-0.682783\pi\) | ||
0.543188 | − | 0.839611i | \(-0.317217\pi\) | |||||||
\(3\) | 18754.1i | 0.550104i | 0.961429 | + | 0.275052i | \(0.0886951\pi\) | ||||
−0.961429 | + | 0.275052i | \(0.911305\pi\) | |||||||
\(4\) | −954092. | −1.81979 | ||||||||
\(5\) | 4.05746e6 | + | 1.61570e6i | 0.929051 | + | 0.369952i | ||||
\(6\) | 2.28029e7 | 0.923748 | ||||||||
\(7\) | 1.79878e8i | 1.68479i | 0.538861 | + | 0.842395i | \(0.318855\pi\) | ||||
−0.538861 | + | 0.842395i | \(0.681145\pi\) | |||||||
\(8\) | 5.22593e8i | 1.37660i | ||||||||
\(9\) | 8.10544e8 | 0.697385 | ||||||||
\(10\) | 1.96451e9 | − | 4.93341e9i | 0.621232 | − | 1.56008i | ||||
\(11\) | −3.61960e9 | −0.462840 | −0.231420 | − | 0.972854i | \(-0.574337\pi\) | ||||
−0.231420 | + | 0.972854i | \(0.574337\pi\) | |||||||
\(12\) | − | 1.78932e10i | − | 1.00107i | ||||||
\(13\) | − | 7.48125e9i | − | 0.195665i | −0.995203 | − | 0.0978323i | \(-0.968809\pi\) | ||
0.995203 | − | 0.0978323i | \(-0.0311909\pi\) | |||||||
\(14\) | 2.18711e11 | 2.82914 | ||||||||
\(15\) | −3.03011e10 | + | 7.60942e10i | −0.203512 | + | 0.511075i | ||||
\(16\) | 1.35195e11 | 0.491837 | ||||||||
\(17\) | 2.32175e11i | 0.474844i | 0.971407 | + | 0.237422i | \(0.0763024\pi\) | ||||
−0.971407 | + | 0.237422i | \(0.923698\pi\) | |||||||
\(18\) | − | 9.85529e11i | − | 1.17106i | ||||||
\(19\) | 2.12840e12 | 1.51319 | 0.756597 | − | 0.653881i | \(-0.226860\pi\) | ||||
0.756597 | + | 0.653881i | \(0.226860\pi\) | |||||||
\(20\) | −3.87119e12 | − | 1.54153e12i | −1.69067 | − | 0.673234i | ||||
\(21\) | −3.37345e12 | −0.926810 | ||||||||
\(22\) | 4.40103e12i | 0.777210i | ||||||||
\(23\) | 6.69298e12i | 0.774828i | 0.921906 | + | 0.387414i | \(0.126632\pi\) | ||||
−0.921906 | + | 0.387414i | \(0.873368\pi\) | |||||||
\(24\) | −9.80079e12 | −0.757276 | ||||||||
\(25\) | 1.38525e13 | + | 1.31113e13i | 0.726271 | + | 0.687409i | ||||
\(26\) | −9.09635e12 | −0.328564 | ||||||||
\(27\) | 3.69983e13i | 0.933739i | ||||||||
\(28\) | − | 1.71620e14i | − | 3.06596i | ||||||
\(29\) | −7.26252e13 | −0.929622 | −0.464811 | − | 0.885410i | \(-0.653878\pi\) | ||||
−0.464811 | + | 0.885410i | \(0.653878\pi\) | |||||||
\(30\) | 9.25219e13 | + | 3.68426e13i | 0.858208 | + | 0.341742i | ||||
\(31\) | 2.51555e14 | 1.70882 | 0.854410 | − | 0.519600i | \(-0.173919\pi\) | ||||
0.854410 | + | 0.519600i | \(0.173919\pi\) | |||||||
\(32\) | 1.09607e14i | 0.550700i | ||||||||
\(33\) | − | 6.78825e13i | − | 0.254610i | ||||||
\(34\) | 2.82299e14 | 0.797369 | ||||||||
\(35\) | −2.90628e14 | + | 7.29846e14i | −0.623291 | + | 1.56525i | ||||
\(36\) | −7.73334e14 | −1.26909 | ||||||||
\(37\) | − | 2.00511e14i | − | 0.253643i | −0.991926 | − | 0.126821i | \(-0.959522\pi\) | ||
0.991926 | − | 0.126821i | \(-0.0404775\pi\) | |||||||
\(38\) | − | 2.58790e15i | − | 2.54099i | ||||||
\(39\) | 1.40304e14 | 0.107636 | ||||||||
\(40\) | −8.44354e14 | + | 2.12040e15i | −0.509278 | + | 1.27894i | ||||
\(41\) | −2.32187e15 | −1.10762 | −0.553811 | − | 0.832642i | \(-0.686827\pi\) | ||||
−0.553811 | + | 0.832642i | \(0.686827\pi\) | |||||||
\(42\) | 4.10173e15i | 1.55632i | ||||||||
\(43\) | − | 1.85667e15i | − | 0.563359i | −0.959508 | − | 0.281680i | \(-0.909108\pi\) | ||
0.959508 | − | 0.281680i | \(-0.0908916\pi\) | |||||||
\(44\) | 3.45344e15 | 0.842269 | ||||||||
\(45\) | 3.28875e15 | + | 1.30960e15i | 0.647906 | + | 0.257999i | ||||
\(46\) | 8.13791e15 | 1.30111 | ||||||||
\(47\) | − | 9.40833e15i | − | 1.22626i | −0.789982 | − | 0.613130i | \(-0.789910\pi\) | ||
0.789982 | − | 0.613130i | \(-0.210090\pi\) | |||||||
\(48\) | 2.53547e15i | 0.270562i | ||||||||
\(49\) | −2.09570e16 | −1.83851 | ||||||||
\(50\) | 1.59418e16 | − | 1.68431e16i | 1.15431 | − | 1.21957i | ||||
\(51\) | −4.35425e15 | −0.261214 | ||||||||
\(52\) | 7.13780e15i | 0.356068i | ||||||||
\(53\) | 1.66277e16i | 0.692167i | 0.938204 | + | 0.346084i | \(0.112489\pi\) | ||||
−0.938204 | + | 0.346084i | \(0.887511\pi\) | |||||||
\(54\) | 4.49857e16 | 1.56796 | ||||||||
\(55\) | −1.46864e16 | − | 5.84819e15i | −0.430001 | − | 0.171229i | ||||
\(56\) | −9.40028e16 | −2.31929 | ||||||||
\(57\) | 3.99164e16i | 0.832415i | ||||||||
\(58\) | 8.83040e16i | 1.56104i | ||||||||
\(59\) | −1.59149e15 | −0.0239171 | −0.0119586 | − | 0.999928i | \(-0.503807\pi\) | ||||
−0.0119586 | + | 0.999928i | \(0.503807\pi\) | |||||||
\(60\) | 2.89100e16 | − | 7.26009e16i | 0.370349 | − | 0.930047i | ||||
\(61\) | −4.33362e16 | −0.474479 | −0.237240 | − | 0.971451i | \(-0.576243\pi\) | ||||
−0.237240 | + | 0.971451i | \(0.576243\pi\) | |||||||
\(62\) | − | 3.05862e17i | − | 2.86949i | ||||||
\(63\) | 1.45799e17i | 1.17495i | ||||||||
\(64\) | 2.04151e17 | 1.41659 | ||||||||
\(65\) | 1.20875e16 | − | 3.03549e16i | 0.0723865 | − | 0.181782i | ||||
\(66\) | −8.25375e16 | −0.427547 | ||||||||
\(67\) | 2.54117e17i | 1.14110i | 0.821263 | + | 0.570550i | \(0.193270\pi\) | ||||
−0.821263 | + | 0.570550i | \(0.806730\pi\) | |||||||
\(68\) | − | 2.21517e17i | − | 0.864115i | ||||||
\(69\) | −1.25521e17 | −0.426236 | ||||||||
\(70\) | 8.87410e17 | + | 3.53371e17i | 2.62841 | + | 1.04664i | ||||
\(71\) | −2.27564e17 | −0.589047 | −0.294524 | − | 0.955644i | \(-0.595161\pi\) | ||||
−0.294524 | + | 0.955644i | \(0.595161\pi\) | |||||||
\(72\) | 4.23585e17i | 0.960023i | ||||||||
\(73\) | − | 8.76951e17i | − | 1.74344i | −0.490000 | − | 0.871722i | \(-0.663003\pi\) | ||
0.490000 | − | 0.871722i | \(-0.336997\pi\) | |||||||
\(74\) | −2.43799e17 | −0.425923 | ||||||||
\(75\) | −2.45891e17 | + | 2.59792e17i | −0.378147 | + | 0.399525i | ||||
\(76\) | −2.03069e18 | −2.75369 | ||||||||
\(77\) | − | 6.51085e17i | − | 0.779787i | ||||||
\(78\) | − | 1.70594e17i | − | 0.180745i | ||||||
\(79\) | 5.76500e17 | 0.541181 | 0.270590 | − | 0.962695i | \(-0.412781\pi\) | ||||
0.270590 | + | 0.962695i | \(0.412781\pi\) | |||||||
\(80\) | 5.48549e17 | + | 2.18435e17i | 0.456942 | + | 0.181956i | ||||
\(81\) | 2.48193e17 | 0.183731 | ||||||||
\(82\) | 2.82313e18i | 1.85994i | ||||||||
\(83\) | − | 5.61483e17i | − | 0.329682i | −0.986320 | − | 0.164841i | \(-0.947289\pi\) | ||
0.986320 | − | 0.164841i | \(-0.0527110\pi\) | |||||||
\(84\) | 3.21858e18 | 1.68660 | ||||||||
\(85\) | −3.75125e17 | + | 9.42042e17i | −0.175670 | + | 0.441154i | ||||
\(86\) | −2.25751e18 | −0.946006 | ||||||||
\(87\) | − | 1.36202e18i | − | 0.511389i | ||||||
\(88\) | − | 1.89158e18i | − | 0.637147i | ||||||
\(89\) | 2.36138e18 | 0.714431 | 0.357215 | − | 0.934022i | \(-0.383726\pi\) | ||||
0.357215 | + | 0.934022i | \(0.383726\pi\) | |||||||
\(90\) | 1.59232e18 | − | 3.99875e18i | 0.433238 | − | 1.08798i | ||||
\(91\) | 1.34571e18 | 0.329654 | ||||||||
\(92\) | − | 6.38573e18i | − | 1.41002i | ||||||
\(93\) | 4.71769e18i | 0.940029i | ||||||||
\(94\) | −1.14395e19 | −2.05916 | ||||||||
\(95\) | 8.63592e18 | + | 3.43886e18i | 1.40583 | + | 0.559810i | ||||
\(96\) | −2.05559e18 | −0.302943 | ||||||||
\(97\) | − | 1.90922e18i | − | 0.254991i | −0.991839 | − | 0.127496i | \(-0.959306\pi\) | ||
0.991839 | − | 0.127496i | \(-0.0406939\pi\) | |||||||
\(98\) | 2.54814e19i | 3.08727i | ||||||||
\(99\) | −2.93385e18 | −0.322777 | ||||||||
\(100\) | −1.32166e19 | − | 1.25094e19i | −1.32166 | − | 1.25094i | ||||
\(101\) | 5.27814e18 | 0.480206 | 0.240103 | − | 0.970747i | \(-0.422819\pi\) | ||||
0.240103 | + | 0.970747i | \(0.422819\pi\) | |||||||
\(102\) | 5.29427e18i | 0.438636i | ||||||||
\(103\) | − | 5.05461e18i | − | 0.381710i | −0.981618 | − | 0.190855i | \(-0.938874\pi\) | ||
0.981618 | − | 0.190855i | \(-0.0611261\pi\) | |||||||
\(104\) | 3.90965e18 | 0.269353 | ||||||||
\(105\) | −1.36876e19 | − | 5.45048e18i | −0.861054 | − | 0.342875i | ||||
\(106\) | 2.02174e19 | 1.16230 | ||||||||
\(107\) | − | 5.80087e18i | − | 0.305033i | −0.988301 | − | 0.152517i | \(-0.951262\pi\) | ||
0.988301 | − | 0.152517i | \(-0.0487378\pi\) | |||||||
\(108\) | − | 3.52998e19i | − | 1.69921i | ||||||
\(109\) | −4.20726e17 | −0.0185544 | −0.00927722 | − | 0.999957i | \(-0.502953\pi\) | ||||
−0.00927722 | + | 0.999957i | \(0.502953\pi\) | |||||||
\(110\) | −7.11074e18 | + | 1.78570e19i | −0.287531 | + | 0.722068i | ||||
\(111\) | 3.76042e18 | 0.139530 | ||||||||
\(112\) | 2.43186e19i | 0.828642i | ||||||||
\(113\) | − | 1.52582e19i | − | 0.477813i | −0.971043 | − | 0.238907i | \(-0.923211\pi\) | ||
0.971043 | − | 0.238907i | \(-0.0767890\pi\) | |||||||
\(114\) | 4.85338e19 | 1.39781 | ||||||||
\(115\) | −1.08139e19 | + | 2.71565e19i | −0.286649 | + | 0.719855i | ||||
\(116\) | 6.92911e19 | 1.69171 | ||||||||
\(117\) | − | 6.06388e18i | − | 0.136454i | ||||||
\(118\) | 1.93507e18i | 0.0401622i | ||||||||
\(119\) | −4.17631e19 | −0.800012 | ||||||||
\(120\) | −3.97663e19 | − | 1.58351e19i | −0.703548 | − | 0.280156i | ||||
\(121\) | −4.80576e19 | −0.785780 | ||||||||
\(122\) | 5.26919e19i | 0.796756i | ||||||||
\(123\) | − | 4.35447e19i | − | 0.609308i | ||||||
\(124\) | −2.40006e20 | −3.10969 | ||||||||
\(125\) | 3.50222e19 | + | 7.55800e19i | 0.420434 | + | 0.907323i | ||||
\(126\) | 1.77275e20 | 1.97300 | ||||||||
\(127\) | − | 5.60376e19i | − | 0.578554i | −0.957245 | − | 0.289277i | \(-0.906585\pi\) | ||
0.957245 | − | 0.289277i | \(-0.0934149\pi\) | |||||||
\(128\) | − | 1.90759e20i | − | 1.82806i | ||||||
\(129\) | 3.48203e19 | 0.309907 | ||||||||
\(130\) | −3.69081e19 | − | 1.46970e19i | −0.305253 | − | 0.121553i | ||||
\(131\) | −8.10990e19 | −0.623646 | −0.311823 | − | 0.950140i | \(-0.600940\pi\) | ||||
−0.311823 | + | 0.950140i | \(0.600940\pi\) | |||||||
\(132\) | 6.47662e19i | 0.463336i | ||||||||
\(133\) | 3.82852e20i | 2.54941i | ||||||||
\(134\) | 3.08978e20 | 1.91616 | ||||||||
\(135\) | −5.97781e19 | + | 1.50119e20i | −0.345439 | + | 0.867491i | ||||
\(136\) | −1.21333e20 | −0.653672 | ||||||||
\(137\) | − | 3.62932e20i | − | 1.82381i | −0.410401 | − | 0.911905i | \(-0.634611\pi\) | ||
0.410401 | − | 0.911905i | \(-0.365389\pi\) | |||||||
\(138\) | 1.52619e20i | 0.715746i | ||||||||
\(139\) | 1.66383e20 | 0.728564 | 0.364282 | − | 0.931289i | \(-0.381314\pi\) | ||||
0.364282 | + | 0.931289i | \(0.381314\pi\) | |||||||
\(140\) | 2.77286e20 | − | 6.96341e20i | 1.13426 | − | 2.84843i | ||||
\(141\) | 1.76445e20 | 0.674571 | ||||||||
\(142\) | 2.76692e20i | 0.989141i | ||||||||
\(143\) | 2.70792e19i | 0.0905613i | ||||||||
\(144\) | 1.09582e20 | 0.343000 | ||||||||
\(145\) | −2.94674e20 | − | 1.17340e20i | −0.863666 | − | 0.343916i | ||||
\(146\) | −1.06627e21 | −2.92763 | ||||||||
\(147\) | − | 3.93031e20i | − | 1.01137i | ||||||
\(148\) | 1.91306e20i | 0.461576i | ||||||||
\(149\) | −1.41978e20 | −0.321330 | −0.160665 | − | 0.987009i | \(-0.551364\pi\) | ||||
−0.160665 | + | 0.987009i | \(0.551364\pi\) | |||||||
\(150\) | 3.15878e20 | + | 2.98975e20i | 0.670891 | + | 0.634992i | ||||
\(151\) | 4.28309e20 | 0.854036 | 0.427018 | − | 0.904243i | \(-0.359564\pi\) | ||||
0.427018 | + | 0.904243i | \(0.359564\pi\) | |||||||
\(152\) | 1.11229e21i | 2.08307i | ||||||||
\(153\) | 1.88188e20i | 0.331149i | ||||||||
\(154\) | −7.91646e20 | −1.30944 | ||||||||
\(155\) | 1.02067e21 | + | 4.06437e20i | 1.58758 | + | 0.632182i | ||||
\(156\) | −1.33863e20 | −0.195875 | ||||||||
\(157\) | − | 7.80079e20i | − | 1.07422i | −0.843513 | − | 0.537108i | \(-0.819517\pi\) | ||
0.843513 | − | 0.537108i | \(-0.180483\pi\) | |||||||
\(158\) | − | 7.00959e20i | − | 0.908762i | ||||||
\(159\) | −3.11838e20 | −0.380764 | ||||||||
\(160\) | −1.77093e20 | + | 4.44728e20i | −0.203733 | + | 0.511628i | ||||
\(161\) | −1.20392e21 | −1.30542 | ||||||||
\(162\) | − | 3.01775e20i | − | 0.308525i | ||||||
\(163\) | − | 1.09860e21i | − | 1.05939i | −0.848188 | − | 0.529696i | \(-0.822306\pi\) | ||
0.848188 | − | 0.529696i | \(-0.177694\pi\) | |||||||
\(164\) | 2.21528e21 | 2.01564 | ||||||||
\(165\) | 1.09678e20 | − | 2.75431e20i | 0.0941936 | − | 0.236546i | ||||
\(166\) | −6.82699e20 | −0.553608 | ||||||||
\(167\) | 3.21947e19i | 0.0246591i | 0.999924 | + | 0.0123296i | \(0.00392472\pi\) | ||||
−0.999924 | + | 0.0123296i | \(0.996075\pi\) | |||||||
\(168\) | − | 1.76294e21i | − | 1.27585i | ||||||
\(169\) | 1.40595e21 | 0.961715 | ||||||||
\(170\) | 1.14542e21 | + | 4.56110e20i | 0.740796 | + | 0.294988i | ||||
\(171\) | 1.72516e21 | 1.05528 | ||||||||
\(172\) | 1.77144e21i | 1.02519i | ||||||||
\(173\) | 2.65247e21i | 1.45282i | 0.687261 | + | 0.726410i | \(0.258813\pi\) | ||||
−0.687261 | + | 0.726410i | \(0.741187\pi\) | |||||||
\(174\) | −1.65607e21 | −0.858736 | ||||||||
\(175\) | −2.35843e21 | + | 2.49176e21i | −1.15814 | + | 1.22361i | ||||
\(176\) | −4.89353e20 | −0.227642 | ||||||||
\(177\) | − | 2.98470e19i | − | 0.0131569i | ||||||
\(178\) | − | 2.87117e21i | − | 1.19969i | ||||||
\(179\) | 1.15403e21 | 0.457206 | 0.228603 | − | 0.973520i | \(-0.426584\pi\) | ||||
0.228603 | + | 0.973520i | \(0.426584\pi\) | |||||||
\(180\) | −3.13777e21 | − | 1.24948e21i | −1.17905 | − | 0.469503i | ||||
\(181\) | −7.70360e20 | −0.274629 | −0.137315 | − | 0.990527i | \(-0.543847\pi\) | ||||
−0.137315 | + | 0.990527i | \(0.543847\pi\) | |||||||
\(182\) | − | 1.63623e21i | − | 0.553562i | ||||||
\(183\) | − | 8.12733e20i | − | 0.261013i | ||||||
\(184\) | −3.49771e21 | −1.06663 | ||||||||
\(185\) | 3.23966e20 | − | 8.13568e20i | 0.0938358 | − | 0.235647i | ||||
\(186\) | 5.73618e21 | 1.57852 | ||||||||
\(187\) | − | 8.40382e20i | − | 0.219777i | ||||||
\(188\) | 8.97641e21i | 2.23153i | ||||||||
\(189\) | −6.65516e21 | −1.57315 | ||||||||
\(190\) | 4.18127e21 | − | 1.05003e22i | 0.940045 | − | 2.36071i | ||||
\(191\) | −3.70311e21 | −0.792044 | −0.396022 | − | 0.918241i | \(-0.629610\pi\) | ||||
−0.396022 | + | 0.918241i | \(0.629610\pi\) | |||||||
\(192\) | 3.82868e21i | 0.779270i | ||||||||
\(193\) | 5.44930e21i | 1.05571i | 0.849333 | + | 0.527857i | \(0.177004\pi\) | ||||
−0.849333 | + | 0.527857i | \(0.822996\pi\) | |||||||
\(194\) | −2.32140e21 | −0.428187 | ||||||||
\(195\) | 5.69280e20 | + | 2.26690e20i | 0.0999993 | + | 0.0398202i | ||||
\(196\) | 1.99949e22 | 3.34570 | ||||||||
\(197\) | − | 5.28276e21i | − | 0.842231i | −0.907007 | − | 0.421116i | \(-0.861639\pi\) | ||
0.907007 | − | 0.421116i | \(-0.138361\pi\) | |||||||
\(198\) | 3.56723e21i | 0.542015i | ||||||||
\(199\) | 1.12121e22 | 1.62398 | 0.811991 | − | 0.583670i | \(-0.198384\pi\) | ||||
0.811991 | + | 0.583670i | \(0.198384\pi\) | |||||||
\(200\) | −6.85187e21 | + | 7.23923e21i | −0.946290 | + | 0.999787i | ||||
\(201\) | −4.76575e21 | −0.627724 | ||||||||
\(202\) | − | 6.41762e21i | − | 0.806373i | ||||||
\(203\) | − | 1.30636e22i | − | 1.56622i | ||||||
\(204\) | 4.15435e21 | 0.475354 | ||||||||
\(205\) | −9.42091e21 | − | 3.75145e21i | −1.02904 | − | 0.409767i | ||||
\(206\) | −6.14583e21 | −0.640976 | ||||||||
\(207\) | 5.42496e21i | 0.540354i | ||||||||
\(208\) | − | 1.01143e21i | − | 0.0962351i | ||||||
\(209\) | −7.70398e21 | −0.700366 | ||||||||
\(210\) | −6.62716e21 | + | 1.66426e22i | −0.575764 | + | 1.44590i | ||||
\(211\) | 1.02283e22 | 0.849416 | 0.424708 | − | 0.905330i | \(-0.360377\pi\) | ||||
0.424708 | + | 0.905330i | \(0.360377\pi\) | |||||||
\(212\) | − | 1.58644e22i | − | 1.25960i | ||||||
\(213\) | − | 4.26777e21i | − | 0.324037i | ||||||
\(214\) | −7.05320e21 | −0.512219 | ||||||||
\(215\) | 2.99983e21 | − | 7.53339e21i | 0.208416 | − | 0.523390i | ||||
\(216\) | −1.93350e22 | −1.28539 | ||||||||
\(217\) | 4.52490e22i | 2.87900i | ||||||||
\(218\) | 5.11556e20i | 0.0311570i | ||||||||
\(219\) | 1.64465e22 | 0.959077 | ||||||||
\(220\) | 1.40122e22 | + | 5.57972e21i | 0.782511 | + | 0.311599i | ||||
\(221\) | 1.73696e21 | 0.0929102 | ||||||||
\(222\) | − | 4.57224e21i | − | 0.234302i | ||||||
\(223\) | − | 9.30478e21i | − | 0.456888i | −0.973557 | − | 0.228444i | \(-0.926636\pi\) | ||
0.973557 | − | 0.228444i | \(-0.0733638\pi\) | |||||||
\(224\) | −1.97159e22 | −0.927814 | ||||||||
\(225\) | 1.12281e22 | + | 1.06273e22i | 0.506490 | + | 0.479389i | ||||
\(226\) | −1.85523e22 | −0.802355 | ||||||||
\(227\) | − | 7.54698e20i | − | 0.0312988i | −0.999878 | − | 0.0156494i | \(-0.995018\pi\) | ||
0.999878 | − | 0.0156494i | \(-0.00498156\pi\) | |||||||
\(228\) | − | 3.80839e22i | − | 1.51482i | ||||||
\(229\) | 6.69932e21 | 0.255619 | 0.127810 | − | 0.991799i | \(-0.459205\pi\) | ||||
0.127810 | + | 0.991799i | \(0.459205\pi\) | |||||||
\(230\) | 3.30193e22 | + | 1.31484e22i | 1.20880 | + | 0.481348i | ||||
\(231\) | 1.22105e22 | 0.428964 | ||||||||
\(232\) | − | 3.79534e22i | − | 1.27972i | ||||||
\(233\) | − | 2.31221e22i | − | 0.748421i | −0.927344 | − | 0.374211i | \(-0.877914\pi\) | ||
0.927344 | − | 0.374211i | \(-0.122086\pi\) | |||||||
\(234\) | −7.37299e21 | −0.229136 | ||||||||
\(235\) | 1.52010e22 | − | 3.81739e22i | 0.453658 | − | 1.13926i | ||||
\(236\) | 1.51843e21 | 0.0435241 | ||||||||
\(237\) | 1.08118e22i | 0.297706i | ||||||||
\(238\) | 5.07792e22i | 1.34340i | ||||||||
\(239\) | 4.10044e22 | 1.04244 | 0.521220 | − | 0.853423i | \(-0.325477\pi\) | ||||
0.521220 | + | 0.853423i | \(0.325477\pi\) | |||||||
\(240\) | −4.09656e21 | + | 1.02876e22i | −0.100095 | + | 0.251366i | ||||
\(241\) | −5.88872e22 | −1.38312 | −0.691559 | − | 0.722320i | \(-0.743076\pi\) | ||||
−0.691559 | + | 0.722320i | \(0.743076\pi\) | |||||||
\(242\) | 5.84325e22i | 1.31950i | ||||||||
\(243\) | 4.76563e22i | 1.03481i | ||||||||
\(244\) | 4.13467e22 | 0.863451 | ||||||||
\(245\) | −8.50324e22 | − | 3.38603e22i | −1.70807 | − | 0.680162i | ||||
\(246\) | −5.29454e22 | −1.02316 | ||||||||
\(247\) | − | 1.59231e22i | − | 0.296079i | ||||||
\(248\) | 1.31461e23i | 2.35237i | ||||||||
\(249\) | 1.05301e22 | 0.181359 | ||||||||
\(250\) | 9.18968e22 | − | 4.25830e22i | 1.52360 | − | 0.706002i | ||||
\(251\) | 2.44560e22 | 0.390378 | 0.195189 | − | 0.980766i | \(-0.437468\pi\) | ||||
0.195189 | + | 0.980766i | \(0.437468\pi\) | |||||||
\(252\) | − | 1.39105e23i | − | 2.13815i | ||||||
\(253\) | − | 2.42260e22i | − | 0.358621i | ||||||
\(254\) | −6.81354e22 | −0.971521 | ||||||||
\(255\) | −1.76672e22 | − | 7.03515e21i | −0.242681 | − | 0.0966366i | ||||
\(256\) | −1.24907e23 | −1.65314 | ||||||||
\(257\) | − | 5.03201e22i | − | 0.641767i | −0.947119 | − | 0.320883i | \(-0.896020\pi\) | ||
0.947119 | − | 0.320883i | \(-0.103980\pi\) | |||||||
\(258\) | − | 4.23376e22i | − | 0.520402i | ||||||
\(259\) | 3.60675e22 | 0.427335 | ||||||||
\(260\) | −1.15325e22 | + | 2.89614e22i | −0.131728 | + | 0.330805i | ||||
\(261\) | −5.88659e22 | −0.648304 | ||||||||
\(262\) | 9.86072e22i | 1.04724i | ||||||||
\(263\) | 6.26756e22i | 0.641976i | 0.947083 | + | 0.320988i | \(0.104015\pi\) | ||||
−0.947083 | + | 0.320988i | \(0.895985\pi\) | |||||||
\(264\) | 3.54750e22 | 0.350497 | ||||||||
\(265\) | −2.68654e22 | + | 6.74662e22i | −0.256069 | + | 0.643059i | ||||
\(266\) | 4.65505e23 | 4.28103 | ||||||||
\(267\) | 4.42856e22i | 0.393011i | ||||||||
\(268\) | − | 2.42451e23i | − | 2.07656i | ||||||
\(269\) | −2.88988e22 | −0.238910 | −0.119455 | − | 0.992840i | \(-0.538115\pi\) | ||||
−0.119455 | + | 0.992840i | \(0.538115\pi\) | |||||||
\(270\) | 1.82528e23 | + | 7.26834e22i | 1.45671 | + | 0.580069i | ||||
\(271\) | 2.97029e22 | 0.228871 | 0.114435 | − | 0.993431i | \(-0.463494\pi\) | ||||
0.114435 | + | 0.993431i | \(0.463494\pi\) | |||||||
\(272\) | 3.13890e22i | 0.233546i | ||||||||
\(273\) | 2.52376e22i | 0.181344i | ||||||||
\(274\) | −4.41284e23 | −3.06258 | ||||||||
\(275\) | −5.01406e22 | − | 4.74576e22i | −0.336147 | − | 0.318160i | ||||
\(276\) | 1.19759e23 | 0.775659 | ||||||||
\(277\) | 3.03186e23i | 1.89737i | 0.316223 | + | 0.948685i | \(0.397585\pi\) | ||||
−0.316223 | + | 0.948685i | \(0.602415\pi\) | |||||||
\(278\) | − | 2.02302e23i | − | 1.22342i | ||||||
\(279\) | 2.03896e23 | 1.19171 | ||||||||
\(280\) | −3.81413e23 | − | 1.51880e23i | −2.15474 | − | 0.858026i | ||||
\(281\) | −2.50158e23 | −1.36617 | −0.683084 | − | 0.730340i | \(-0.739362\pi\) | ||||
−0.683084 | + | 0.730340i | \(0.739362\pi\) | |||||||
\(282\) | − | 2.14537e23i | − | 1.13276i | ||||||
\(283\) | − | 1.87699e22i | − | 0.0958276i | −0.998851 | − | 0.0479138i | \(-0.984743\pi\) | ||
0.998851 | − | 0.0479138i | \(-0.0152573\pi\) | |||||||
\(284\) | 2.17117e23 | 1.07194 | ||||||||
\(285\) | −6.44929e22 | + | 1.61959e23i | −0.307954 | + | 0.773356i | ||||
\(286\) | 3.29252e22 | 0.152073 | ||||||||
\(287\) | − | 4.17652e23i | − | 1.86611i | ||||||
\(288\) | 8.88416e22i | 0.384050i | ||||||||
\(289\) | 1.85167e23 | 0.774523 | ||||||||
\(290\) | −1.42673e23 | + | 3.58290e23i | −0.577511 | + | 1.45029i | ||||
\(291\) | 3.58058e22 | 0.140272 | ||||||||
\(292\) | 8.36692e23i | 3.17270i | ||||||||
\(293\) | − | 1.83821e23i | − | 0.674764i | −0.941368 | − | 0.337382i | \(-0.890459\pi\) | ||
0.941368 | − | 0.337382i | \(-0.109541\pi\) | |||||||
\(294\) | −4.77881e23 | −1.69832 | ||||||||
\(295\) | −6.45740e21 | − | 2.57136e21i | −0.0222202 | − | 0.00884819i | ||||
\(296\) | 1.04786e23 | 0.349166 | ||||||||
\(297\) | − | 1.33919e23i | − | 0.432171i | ||||||
\(298\) | 1.72629e23i | 0.539584i | ||||||||
\(299\) | 5.00719e22 | 0.151606 | ||||||||
\(300\) | 2.34603e23 | − | 2.47866e23i | 0.688146 | − | 0.727050i | ||||
\(301\) | 3.33974e23 | 0.949142 | ||||||||
\(302\) | − | 5.20775e23i | − | 1.43412i | ||||||
\(303\) | 9.89869e22i | 0.264164i | ||||||||
\(304\) | 2.87750e23 | 0.744245 | ||||||||
\(305\) | −1.75835e23 | − | 7.00183e22i | −0.440815 | − | 0.175535i | ||||
\(306\) | 2.28815e23 | 0.556073 | ||||||||
\(307\) | − | 3.57199e23i | − | 0.841580i | −0.907158 | − | 0.420790i | \(-0.861753\pi\) | ||
0.907158 | − | 0.420790i | \(-0.138247\pi\) | |||||||
\(308\) | 6.21196e23i | 1.41905i | ||||||||
\(309\) | 9.47948e22 | 0.209981 | ||||||||
\(310\) | 4.94181e23 | − | 1.24102e24i | 1.06157 | − | 2.66590i | ||||
\(311\) | −2.61658e22 | −0.0545143 | −0.0272571 | − | 0.999628i | \(-0.508677\pi\) | ||||
−0.0272571 | + | 0.999628i | \(0.508677\pi\) | |||||||
\(312\) | 7.33221e22i | 0.148172i | ||||||||
\(313\) | 2.90894e23i | 0.570247i | 0.958491 | + | 0.285124i | \(0.0920347\pi\) | ||||
−0.958491 | + | 0.285124i | \(0.907965\pi\) | |||||||
\(314\) | −9.48488e23 | −1.80385 | ||||||||
\(315\) | −2.35567e23 | + | 5.91572e23i | −0.434674 | + | 1.09159i | ||||
\(316\) | −5.50035e23 | −0.984833 | ||||||||
\(317\) | − | 1.00748e24i | − | 1.75055i | −0.483628 | − | 0.875273i | \(-0.660681\pi\) | ||
0.483628 | − | 0.875273i | \(-0.339319\pi\) | |||||||
\(318\) | 3.79160e23i | 0.639388i | ||||||||
\(319\) | 2.62874e23 | 0.430266 | ||||||||
\(320\) | 8.28337e23 | + | 3.29847e23i | 1.31608 | + | 0.524069i | ||||
\(321\) | 1.08790e23 | 0.167800 | ||||||||
\(322\) | 1.46383e24i | 2.19209i | ||||||||
\(323\) | 4.94162e23i | 0.718532i | ||||||||
\(324\) | −2.36799e23 | −0.334351 | ||||||||
\(325\) | 9.80888e22 | − | 1.03634e23i | 0.134502 | − | 0.142105i | ||||
\(326\) | −1.33577e24 | −1.77895 | ||||||||
\(327\) | − | 7.89036e21i | − | 0.0102069i | ||||||
\(328\) | − | 1.21339e24i | − | 1.52476i | ||||||
\(329\) | 1.69235e24 | 2.06599 | ||||||||
\(330\) | −3.34893e23 | − | 1.33356e23i | −0.397213 | − | 0.158172i | ||||
\(331\) | −1.24050e24 | −1.42965 | −0.714827 | − | 0.699302i | \(-0.753494\pi\) | ||||
−0.714827 | + | 0.699302i | \(0.753494\pi\) | |||||||
\(332\) | 5.35706e23i | 0.599950i | ||||||||
\(333\) | − | 1.62523e23i | − | 0.176887i | ||||||
\(334\) | 3.91451e22 | 0.0414082 | ||||||||
\(335\) | −4.10577e23 | + | 1.03107e24i | −0.422152 | + | 1.06014i | ||||
\(336\) | −4.56074e23 | −0.455840 | ||||||||
\(337\) | 1.24721e24i | 1.21187i | 0.795513 | + | 0.605937i | \(0.207201\pi\) | ||||
−0.795513 | + | 0.605937i | \(0.792799\pi\) | |||||||
\(338\) | − | 1.70948e24i | − | 1.61493i | ||||||
\(339\) | 2.86155e23 | 0.262847 | ||||||||
\(340\) | 3.57904e23 | − | 8.98795e23i | 0.319681 | − | 0.802807i | ||||
\(341\) | −9.10528e23 | −0.790909 | ||||||||
\(342\) | − | 2.09760e24i | − | 1.77205i | ||||||
\(343\) | − | 1.71929e24i | − | 1.41272i | ||||||
\(344\) | 9.70286e23 | 0.775523 | ||||||||
\(345\) | −5.09297e23 | − | 2.02805e23i | −0.395995 | − | 0.157687i | ||||
\(346\) | 3.22510e24 | 2.43961 | ||||||||
\(347\) | 8.82339e23i | 0.649390i | 0.945819 | + | 0.324695i | \(0.105262\pi\) | ||||
−0.945819 | + | 0.324695i | \(0.894738\pi\) | |||||||
\(348\) | 1.29950e24i | 0.930619i | ||||||||
\(349\) | −6.79957e23 | −0.473849 | −0.236925 | − | 0.971528i | \(-0.576139\pi\) | ||||
−0.236925 | + | 0.971528i | \(0.576139\pi\) | |||||||
\(350\) | 3.02969e24 | + | 2.86758e24i | 2.05472 | + | 1.94477i | ||||
\(351\) | 2.76793e23 | 0.182700 | ||||||||
\(352\) | − | 3.96735e23i | − | 0.254886i | ||||||
\(353\) | 1.70063e24i | 1.06353i | 0.846892 | + | 0.531765i | \(0.178471\pi\) | ||||
−0.846892 | + | 0.531765i | \(0.821529\pi\) | |||||||
\(354\) | −3.62905e22 | −0.0220934 | ||||||||
\(355\) | −9.23334e23 | − | 3.67676e23i | −0.547255 | − | 0.217919i | ||||
\(356\) | −2.25297e24 | −1.30011 | ||||||||
\(357\) | − | 7.83231e23i | − | 0.440090i | ||||||
\(358\) | − | 1.40317e24i | − | 0.767751i | ||||||
\(359\) | −1.87542e24 | −0.999311 | −0.499656 | − | 0.866224i | \(-0.666540\pi\) | ||||
−0.499656 | + | 0.866224i | \(0.666540\pi\) | |||||||
\(360\) | −6.84386e23 | + | 1.71868e24i | −0.355163 | + | 0.891910i | ||||
\(361\) | 2.55168e24 | 1.28976 | ||||||||
\(362\) | 9.36670e23i | 0.461164i | ||||||||
\(363\) | − | 9.01278e23i | − | 0.432261i | ||||||
\(364\) | −1.28393e24 | −0.599899 | ||||||||
\(365\) | 1.41689e24 | − | 3.55820e24i | 0.644991 | − | 1.61975i | ||||
\(366\) | −9.88191e23 | −0.438299 | ||||||||
\(367\) | 1.73965e24i | 0.751856i | 0.926649 | + | 0.375928i | \(0.122676\pi\) | ||||
−0.926649 | + | 0.375928i | \(0.877324\pi\) | |||||||
\(368\) | 9.04859e23i | 0.381089i | ||||||||
\(369\) | −1.88198e24 | −0.772439 | ||||||||
\(370\) | −9.89206e23 | − | 3.93906e23i | −0.395704 | − | 0.157571i | ||||
\(371\) | −2.99095e24 | −1.16616 | ||||||||
\(372\) | − | 4.50111e24i | − | 1.71065i | ||||||
\(373\) | − | 1.95284e24i | − | 0.723491i | −0.932277 | − | 0.361746i | \(-0.882181\pi\) | ||
0.932277 | − | 0.361746i | \(-0.117819\pi\) | |||||||
\(374\) | −1.02181e24 | −0.369054 | ||||||||
\(375\) | −1.41744e24 | + | 6.56810e23i | −0.499122 | + | 0.231283i | ||||
\(376\) | 4.91673e24 | 1.68808 | ||||||||
\(377\) | 5.43327e23i | 0.181894i | ||||||||
\(378\) | 8.09192e24i | 2.64167i | ||||||||
\(379\) | 3.86854e24 | 1.23161 | 0.615806 | − | 0.787897i | \(-0.288830\pi\) | ||||
0.615806 | + | 0.787897i | \(0.288830\pi\) | |||||||
\(380\) | −8.23946e24 | − | 3.28099e24i | −2.55832 | − | 1.01873i | ||||
\(381\) | 1.05094e24 | 0.318265 | ||||||||
\(382\) | 4.50256e24i | 1.33002i | ||||||||
\(383\) | 5.32239e24i | 1.53362i | 0.641874 | + | 0.766810i | \(0.278157\pi\) | ||||
−0.641874 | + | 0.766810i | \(0.721843\pi\) | |||||||
\(384\) | 3.57752e24 | 1.00562 | ||||||||
\(385\) | 1.05196e24 | − | 2.64175e24i | 0.288484 | − | 0.724462i | ||||
\(386\) | 6.62573e24 | 1.77278 | ||||||||
\(387\) | − | 1.50492e24i | − | 0.392878i | ||||||
\(388\) | 1.82157e24i | 0.464030i | ||||||||
\(389\) | 4.85730e24 | 1.20746 | 0.603731 | − | 0.797188i | \(-0.293680\pi\) | ||||
0.603731 | + | 0.797188i | \(0.293680\pi\) | |||||||
\(390\) | 2.75629e23 | − | 6.92180e23i | 0.0668669 | − | 0.167921i | ||||
\(391\) | −1.55395e24 | −0.367923 | ||||||||
\(392\) | − | 1.09520e25i | − | 2.53091i | ||||||
\(393\) | − | 1.52094e24i | − | 0.343071i | ||||||
\(394\) | −6.42323e24 | −1.41429 | ||||||||
\(395\) | 2.33913e24 | + | 9.31451e23i | 0.502784 | + | 0.200211i | ||||
\(396\) | 2.79916e24 | 0.587386 | ||||||||
\(397\) | 5.78732e24i | 1.18568i | 0.805320 | + | 0.592841i | \(0.201994\pi\) | ||||
−0.805320 | + | 0.592841i | \(0.798006\pi\) | |||||||
\(398\) | − | 1.36326e25i | − | 2.72703i | ||||||
\(399\) | −7.18006e24 | −1.40244 | ||||||||
\(400\) | 1.87279e24 | + | 1.77258e24i | 0.357207 | + | 0.338093i | ||||
\(401\) | 6.31326e24 | 1.17593 | 0.587966 | − | 0.808886i | \(-0.299929\pi\) | ||||
0.587966 | + | 0.808886i | \(0.299929\pi\) | |||||||
\(402\) | 5.79461e24i | 1.05409i | ||||||||
\(403\) | − | 1.88194e24i | − | 0.334355i | ||||||
\(404\) | −5.03583e24 | −0.873873 | ||||||||
\(405\) | 1.00704e24 | + | 4.01006e23i | 0.170695 | + | 0.0679717i | ||||
\(406\) | −1.58839e25 | −2.63003 | ||||||||
\(407\) | 7.25772e23i | 0.117396i | ||||||||
\(408\) | − | 2.27550e24i | − | 0.359588i | ||||||
\(409\) | 5.68097e24 | 0.877104 | 0.438552 | − | 0.898706i | \(-0.355491\pi\) | ||||
0.438552 | + | 0.898706i | \(0.355491\pi\) | |||||||
\(410\) | −4.56133e24 | + | 1.14548e25i | −0.688090 | + | 1.72798i | ||||
\(411\) | 6.80647e24 | 1.00329 | ||||||||
\(412\) | 4.82256e24i | 0.694631i | ||||||||
\(413\) | − | 2.86273e23i | − | 0.0402953i | ||||||
\(414\) | 6.59613e24 | 0.907374 | ||||||||
\(415\) | 9.07188e23 | − | 2.27820e24i | 0.121966 | − | 0.306291i | ||||
\(416\) | 8.20001e23 | 0.107753 | ||||||||
\(417\) | 3.12036e24i | 0.400786i | ||||||||
\(418\) | 9.36716e24i | 1.17607i | ||||||||
\(419\) | −1.23198e25 | −1.51207 | −0.756033 | − | 0.654533i | \(-0.772865\pi\) | ||||
−0.756033 | + | 0.654533i | \(0.772865\pi\) | |||||||
\(420\) | 1.30593e25 | + | 5.20026e24i | 1.56693 | + | 0.623960i | ||||
\(421\) | −8.35914e24 | −0.980577 | −0.490289 | − | 0.871560i | \(-0.663109\pi\) | ||||
−0.490289 | + | 0.871560i | \(0.663109\pi\) | |||||||
\(422\) | − | 1.24365e25i | − | 1.42636i | ||||||
\(423\) | − | 7.62586e24i | − | 0.855176i | ||||||
\(424\) | −8.68952e24 | −0.952841 | ||||||||
\(425\) | −3.04411e24 | + | 3.21621e24i | −0.326412 | + | 0.344865i | ||||
\(426\) | −5.18913e24 | −0.544131 | ||||||||
\(427\) | − | 7.79520e24i | − | 0.799397i | ||||||
\(428\) | 5.53457e24i | 0.555096i | ||||||||
\(429\) | −5.07846e23 | −0.0498182 | ||||||||
\(430\) | −9.15975e24 | − | 3.64745e24i | −0.878887 | − | 0.349977i | ||||
\(431\) | −3.01638e23 | −0.0283108 | −0.0141554 | − | 0.999900i | \(-0.504506\pi\) | ||||
−0.0141554 | + | 0.999900i | \(0.504506\pi\) | |||||||
\(432\) | 5.00199e24i | 0.459248i | ||||||||
\(433\) | − | 1.90272e25i | − | 1.70899i | −0.519461 | − | 0.854494i | \(-0.673867\pi\) | ||
0.519461 | − | 0.854494i | \(-0.326133\pi\) | |||||||
\(434\) | 5.50177e25 | 4.83448 | ||||||||
\(435\) | 2.20062e24 | − | 5.52636e24i | 0.189189 | − | 0.475106i | ||||
\(436\) | 4.01412e23 | 0.0337651 | ||||||||
\(437\) | 1.42454e25i | 1.17247i | ||||||||
\(438\) | − | 1.99970e25i | − | 1.61050i | ||||||
\(439\) | 5.53042e24 | 0.435858 | 0.217929 | − | 0.975965i | \(-0.430070\pi\) | ||||
0.217929 | + | 0.975965i | \(0.430070\pi\) | |||||||
\(440\) | 3.05623e24 | − | 7.67502e24i | 0.235714 | − | 0.591942i | ||||
\(441\) | −1.69866e25 | −1.28215 | ||||||||
\(442\) | − | 2.11195e24i | − | 0.156017i | ||||||
\(443\) | 2.30459e25i | 1.66632i | 0.553031 | + | 0.833161i | \(0.313471\pi\) | ||||
−0.553031 | + | 0.833161i | \(0.686529\pi\) | |||||||
\(444\) | −3.58779e24 | −0.253915 | ||||||||
\(445\) | 9.58119e24 | + | 3.81527e24i | 0.663742 | + | 0.264305i | ||||
\(446\) | −1.13136e25 | −0.767217 | ||||||||
\(447\) | − | 2.66267e24i | − | 0.176765i | ||||||
\(448\) | 3.67223e25i | 2.38665i | ||||||||
\(449\) | −2.60186e25 | −1.65556 | −0.827778 | − | 0.561056i | \(-0.810395\pi\) | ||||
−0.827778 | + | 0.561056i | \(0.810395\pi\) | |||||||
\(450\) | 1.29216e25 | − | 1.36521e25i | 0.805000 | − | 0.850510i | ||||
\(451\) | 8.40425e24 | 0.512651 | ||||||||
\(452\) | 1.45577e25i | 0.869519i | ||||||||
\(453\) | 8.03256e24i | 0.469809i | ||||||||
\(454\) | −9.17627e23 | −0.0525576 | ||||||||
\(455\) | 5.46016e24 | + | 2.17426e24i | 0.306265 | + | 0.121956i | ||||
\(456\) | −2.08600e25 | −1.14591 | ||||||||
\(457\) | − | 2.31329e25i | − | 1.24459i | −0.782783 | − | 0.622295i | \(-0.786200\pi\) | ||
0.782783 | − | 0.622295i | \(-0.213800\pi\) | |||||||
\(458\) | − | 8.14561e24i | − | 0.429241i | ||||||
\(459\) | −8.59008e24 | −0.443380 | ||||||||
\(460\) | 1.03174e25 | − | 2.59098e25i | 0.521641 | − | 1.30998i | ||||
\(461\) | 2.86383e25 | 1.41837 | 0.709184 | − | 0.705023i | \(-0.249063\pi\) | ||||
0.709184 | + | 0.705023i | \(0.249063\pi\) | |||||||
\(462\) | − | 1.48466e25i | − | 0.720326i | ||||||
\(463\) | 2.65604e25i | 1.26245i | 0.775598 | + | 0.631227i | \(0.217448\pi\) | ||||
−0.775598 | + | 0.631227i | \(0.782552\pi\) | |||||||
\(464\) | −9.81857e24 | −0.457223 | ||||||||
\(465\) | −7.62237e24 | + | 1.91418e25i | −0.347766 | + | 0.873335i | ||||
\(466\) | −2.81139e25 | −1.25677 | ||||||||
\(467\) | − | 1.59314e25i | − | 0.697819i | −0.937156 | − | 0.348909i | \(-0.886552\pi\) | ||
0.937156 | − | 0.348909i | \(-0.113448\pi\) | |||||||
\(468\) | 5.78550e24i | 0.248316i | ||||||||
\(469\) | −4.57100e25 | −1.92251 | ||||||||
\(470\) | −4.64152e25 | − | 1.84827e25i | −1.91307 | − | 0.761792i | ||||
\(471\) | 1.46297e25 | 0.590931 | ||||||||
\(472\) | − | 8.31701e23i | − | 0.0329244i | ||||||
\(473\) | 6.72043e24i | 0.260745i | ||||||||
\(474\) | 1.31459e25 | 0.499914 | ||||||||
\(475\) | 2.94837e25 | + | 2.79061e25i | 1.09899 | + | 1.04018i | ||||
\(476\) | 3.98459e25 | 1.45585 | ||||||||
\(477\) | 1.34775e25i | 0.482707i | ||||||||
\(478\) | − | 4.98567e25i | − | 1.75049i | ||||||
\(479\) | 3.55269e25 | 1.22284 | 0.611420 | − | 0.791306i | \(-0.290599\pi\) | ||||
0.611420 | + | 0.791306i | \(0.290599\pi\) | |||||||
\(480\) | −8.34049e24 | − | 3.32122e24i | −0.281449 | − | 0.112074i | ||||
\(481\) | −1.50008e24 | −0.0496289 | ||||||||
\(482\) | 7.16002e25i | 2.32256i | ||||||||
\(483\) | − | 2.25784e25i | − | 0.718118i | ||||||
\(484\) | 4.58514e25 | 1.42995 | ||||||||
\(485\) | 3.08473e24 | − | 7.74660e24i | 0.0943345 | − | 0.236900i | ||||
\(486\) | 5.79447e25 | 1.73768 | ||||||||
\(487\) | − | 5.62096e25i | − | 1.65305i | −0.562902 | − | 0.826524i | \(-0.690315\pi\) | ||
0.562902 | − | 0.826524i | \(-0.309685\pi\) | |||||||
\(488\) | − | 2.26472e25i | − | 0.653170i | ||||||
\(489\) | 2.06032e25 | 0.582776 | ||||||||
\(490\) | −4.11703e25 | + | 1.03390e26i | −1.14214 | + | 2.86823i | ||||
\(491\) | −5.81507e25 | −1.58227 | −0.791135 | − | 0.611642i | \(-0.790509\pi\) | ||||
−0.791135 | + | 0.611642i | \(0.790509\pi\) | |||||||
\(492\) | 4.15457e25i | 1.10881i | ||||||||
\(493\) | − | 1.68618e25i | − | 0.441425i | ||||||
\(494\) | −1.93607e25 | −0.497182 | ||||||||
\(495\) | −1.19040e25 | − | 4.74022e24i | −0.299877 | − | 0.119412i | ||||
\(496\) | 3.40090e25 | 0.840461 | ||||||||
\(497\) | − | 4.09337e25i | − | 0.992420i | ||||||
\(498\) | − | 1.28034e25i | − | 0.304542i | ||||||
\(499\) | 1.33885e25 | 0.312447 | 0.156224 | − | 0.987722i | \(-0.450068\pi\) | ||||
0.156224 | + | 0.987722i | \(0.450068\pi\) | |||||||
\(500\) | −3.34144e25 | − | 7.21103e25i | −0.765100 | − | 1.65113i | ||||
\(501\) | −6.03784e23 | −0.0135651 | ||||||||
\(502\) | − | 2.97358e25i | − | 0.655532i | ||||||
\(503\) | − | 5.92007e25i | − | 1.28065i | −0.768103 | − | 0.640326i | \(-0.778799\pi\) | ||
0.768103 | − | 0.640326i | \(-0.221201\pi\) | |||||||
\(504\) | −7.61934e25 | −1.61744 | ||||||||
\(505\) | 2.14158e25 | + | 8.52789e24i | 0.446136 | + | 0.177653i | ||||
\(506\) | −2.94560e25 | −0.602205 | ||||||||
\(507\) | 2.63674e25i | 0.529044i | ||||||||
\(508\) | 5.34650e25i | 1.05285i | ||||||||
\(509\) | −4.36448e25 | −0.843555 | −0.421777 | − | 0.906699i | \(-0.638594\pi\) | ||||
−0.421777 | + | 0.906699i | \(0.638594\pi\) | |||||||
\(510\) | −8.55395e24 | + | 2.14813e25i | −0.162274 | + | 0.407515i | ||||
\(511\) | 1.57744e26 | 2.93734 | ||||||||
\(512\) | 5.18605e25i | 0.947920i | ||||||||
\(513\) | 7.87472e25i | 1.41293i | ||||||||
\(514\) | −6.11836e25 | −1.07767 | ||||||||
\(515\) | 8.16673e24 | − | 2.05089e25i | 0.141215 | − | 0.354628i | ||||
\(516\) | −3.32218e25 | −0.563964 | ||||||||
\(517\) | 3.40544e25i | 0.567562i | ||||||||
\(518\) | − | 4.38540e25i | − | 0.717590i | ||||||
\(519\) | −4.97447e25 | −0.799203 | ||||||||
\(520\) | 1.58633e25 | + | 6.31682e24i | 0.250242 | + | 0.0996476i | ||||
\(521\) | −7.24724e25 | −1.12257 | −0.561286 | − | 0.827622i | \(-0.689693\pi\) | ||||
−0.561286 | + | 0.827622i | \(0.689693\pi\) | |||||||
\(522\) | 7.15743e25i | 1.08865i | ||||||||
\(523\) | 3.62351e25i | 0.541207i | 0.962691 | + | 0.270604i | \(0.0872232\pi\) | ||||
−0.962691 | + | 0.270604i | \(0.912777\pi\) | |||||||
\(524\) | 7.73760e25 | 1.13490 | ||||||||
\(525\) | −4.67307e25 | − | 4.42302e25i | −0.673115 | − | 0.637097i | ||||
\(526\) | 7.62064e25 | 1.07802 | ||||||||
\(527\) | 5.84047e25i | 0.811423i | ||||||||
\(528\) | − | 9.17739e24i | − | 0.125227i | ||||||
\(529\) | 2.98194e25 | 0.399641 | ||||||||
\(530\) | 8.20313e25 | + | 3.26652e25i | 1.07984 | + | 0.429997i | ||||
\(531\) | −1.28997e24 | −0.0166794 | ||||||||
\(532\) | − | 3.65276e26i | − | 4.63939i | ||||||
\(533\) | 1.73705e25i | 0.216722i | ||||||||
\(534\) | 5.38462e25 | 0.659953 | ||||||||
\(535\) | 9.37246e24 | − | 2.35368e25i | 0.112848 | − | 0.283391i | ||||
\(536\) | −1.32800e26 | −1.57084 | ||||||||
\(537\) | 2.16428e25i | 0.251511i | ||||||||
\(538\) | 3.51377e25i | 0.401182i | ||||||||
\(539\) | 7.58561e25 | 0.850937 | ||||||||
\(540\) | 5.70338e25 | − | 1.43227e26i | 0.628625 | − | 1.57865i | ||||
\(541\) | −4.47583e24 | −0.0484730 | −0.0242365 | − | 0.999706i | \(-0.507715\pi\) | ||||
−0.0242365 | + | 0.999706i | \(0.507715\pi\) | |||||||
\(542\) | − | 3.61154e25i | − | 0.384325i | ||||||
\(543\) | − | 1.44474e25i | − | 0.151075i | ||||||
\(544\) | −2.54481e25 | −0.261497 | ||||||||
\(545\) | −1.70708e24 | − | 6.79768e23i | −0.0172380 | − | 0.00686426i | ||||
\(546\) | 3.06861e25 | 0.304517 | ||||||||
\(547\) | 2.13519e25i | 0.208237i | 0.994565 | + | 0.104118i | \(0.0332021\pi\) | ||||
−0.994565 | + | 0.104118i | \(0.966798\pi\) | |||||||
\(548\) | 3.46271e26i | 3.31895i | ||||||||
\(549\) | −3.51259e25 | −0.330895 | ||||||||
\(550\) | −5.77031e25 | + | 6.09653e25i | −0.534261 | + | 0.564465i | ||||
\(551\) | −1.54576e26 | −1.40670 | ||||||||
\(552\) | − | 6.55965e25i | − | 0.586759i | ||||||
\(553\) | 1.03699e26i | 0.911775i | ||||||||
\(554\) | 3.68640e26 | 3.18611 | ||||||||
\(555\) | 1.52578e25 | + | 6.07571e24i | 0.129631 | + | 0.0516195i | ||||
\(556\) | −1.58744e26 | −1.32583 | ||||||||
\(557\) | 7.41228e25i | 0.608593i | 0.952577 | + | 0.304297i | \(0.0984214\pi\) | ||||
−0.952577 | + | 0.304297i | \(0.901579\pi\) | |||||||
\(558\) | − | 2.47914e26i | − | 2.00114i | ||||||
\(559\) | −1.38902e25 | −0.110229 | ||||||||
\(560\) | −3.92915e25 | + | 9.86717e25i | −0.306558 | + | 0.769850i | ||||
\(561\) | 1.57606e25 | 0.120900 | ||||||||
\(562\) | 3.04164e26i | 2.29410i | ||||||||
\(563\) | − | 2.39164e26i | − | 1.77364i | −0.462116 | − | 0.886820i | \(-0.652910\pi\) | ||
0.462116 | − | 0.886820i | \(-0.347090\pi\) | |||||||
\(564\) | −1.68345e26 | −1.22758 | ||||||||
\(565\) | 2.46527e25 | − | 6.19096e25i | 0.176768 | − | 0.443913i | ||||
\(566\) | −2.28221e25 | −0.160916 | ||||||||
\(567\) | 4.46444e25i | 0.309548i | ||||||||
\(568\) | − | 1.18924e26i | − | 0.810885i | ||||||
\(569\) | −1.08135e26 | −0.725102 | −0.362551 | − | 0.931964i | \(-0.618094\pi\) | ||||
−0.362551 | + | 0.931964i | \(0.618094\pi\) | |||||||
\(570\) | 1.96924e26 | + | 7.84160e25i | 1.29864 | + | 0.517123i | ||||
\(571\) | −9.51568e25 | −0.617158 | −0.308579 | − | 0.951199i | \(-0.599853\pi\) | ||||
−0.308579 | + | 0.951199i | \(0.599853\pi\) | |||||||
\(572\) | − | 2.58360e25i | − | 0.164802i | ||||||
\(573\) | − | 6.94485e25i | − | 0.435707i | ||||||
\(574\) | −5.07818e26 | −3.13361 | ||||||||
\(575\) | −8.77536e25 | + | 9.27147e25i | −0.532624 | + | 0.562735i | ||||
\(576\) | 1.65474e26 | 0.987905 | ||||||||
\(577\) | − | 2.21789e26i | − | 1.30248i | −0.758873 | − | 0.651238i | \(-0.774250\pi\) | ||
0.758873 | − | 0.651238i | \(-0.225750\pi\) | |||||||
\(578\) | − | 2.25142e26i | − | 1.30060i | ||||||
\(579\) | −1.02197e26 | −0.580753 | ||||||||
\(580\) | 2.81146e26 | + | 1.11954e26i | 1.57169 | + | 0.625853i | ||||
\(581\) | 1.00998e26 | 0.555444 | ||||||||
\(582\) | − | 4.35358e25i | − | 0.235547i | ||||||
\(583\) | − | 6.01856e25i | − | 0.320362i | ||||||
\(584\) | 4.58289e26 | 2.40003 | ||||||||
\(585\) | 9.79741e24 | − | 2.46040e25i | 0.0504813 | − | 0.126772i | ||||
\(586\) | −2.23505e26 | −1.13308 | ||||||||
\(587\) | 3.00717e26i | 1.50002i | 0.661429 | + | 0.750008i | \(0.269950\pi\) | ||||
−0.661429 | + | 0.750008i | \(0.730050\pi\) | |||||||
\(588\) | 3.74988e26i | 1.84049i | ||||||||
\(589\) | 5.35410e26 | 2.58578 | ||||||||
\(590\) | −3.12649e24 | + | 7.85146e24i | −0.0148581 | + | 0.0373127i | ||||
\(591\) | 9.90735e25 | 0.463315 | ||||||||
\(592\) | − | 2.71082e25i | − | 0.124751i | ||||||
\(593\) | − | 2.27900e26i | − | 1.03211i | −0.856557 | − | 0.516053i | \(-0.827401\pi\) | ||
0.856557 | − | 0.516053i | \(-0.172599\pi\) | |||||||
\(594\) | −1.62830e26 | −0.725712 | ||||||||
\(595\) | −1.69452e26 | − | 6.74766e25i | −0.743252 | − | 0.295966i | ||||
\(596\) | 1.35460e26 | 0.584751 | ||||||||
\(597\) | 2.10273e26i | 0.893360i | ||||||||
\(598\) | − | 6.08817e25i | − | 0.254581i | ||||||
\(599\) | 9.07164e25 | 0.373363 | 0.186681 | − | 0.982420i | \(-0.440227\pi\) | ||||
0.186681 | + | 0.982420i | \(0.440227\pi\) | |||||||
\(600\) | −1.35766e26 | − | 1.28501e26i | −0.549987 | − | 0.520558i | ||||
\(601\) | 9.37859e25 | 0.373964 | 0.186982 | − | 0.982363i | \(-0.440129\pi\) | ||||
0.186982 | + | 0.982363i | \(0.440129\pi\) | |||||||
\(602\) | − | 4.06075e26i | − | 1.59382i | ||||||
\(603\) | 2.05973e26i | 0.795786i | ||||||||
\(604\) | −4.08646e26 | −1.55416 | ||||||||
\(605\) | −1.94992e26 | − | 7.76466e25i | −0.730029 | − | 0.290701i | ||||
\(606\) | 1.20357e26 | 0.443589 | ||||||||
\(607\) | 2.25098e26i | 0.816732i | 0.912818 | + | 0.408366i | \(0.133901\pi\) | ||||
−0.912818 | + | 0.408366i | \(0.866099\pi\) | |||||||
\(608\) | 2.33289e26i | 0.833317i | ||||||||
\(609\) | 2.44997e26 | 0.861583 | ||||||||
\(610\) | −8.51343e25 | + | 2.13795e26i | −0.294762 | + | 0.740227i | ||||
\(611\) | −7.03860e25 | −0.239936 | ||||||||
\(612\) | − | 1.79549e26i | − | 0.602621i | ||||||
\(613\) | − | 8.30040e25i | − | 0.274299i | −0.990550 | − | 0.137150i | \(-0.956206\pi\) | ||
0.990550 | − | 0.137150i | \(-0.0437941\pi\) | |||||||
\(614\) | −4.34313e26 | −1.41320 | ||||||||
\(615\) | 7.03552e25 | − | 1.76681e26i | 0.225415 | − | 0.566078i | ||||
\(616\) | 3.40253e26 | 1.07346 | ||||||||
\(617\) | − | 4.41321e26i | − | 1.37103i | −0.728061 | − | 0.685513i | \(-0.759578\pi\) | ||
0.728061 | − | 0.685513i | \(-0.240422\pi\) | |||||||
\(618\) | − | 1.15260e26i | − | 0.352604i | ||||||
\(619\) | 2.41336e26 | 0.727044 | 0.363522 | − | 0.931586i | \(-0.381574\pi\) | ||||
0.363522 | + | 0.931586i | \(0.381574\pi\) | |||||||
\(620\) | −9.73817e26 | − | 3.87778e26i | −2.88906 | − | 1.15044i | ||||
\(621\) | −2.47629e26 | −0.723487 | ||||||||
\(622\) | 3.18146e25i | 0.0915416i | ||||||||
\(623\) | 4.24758e26i | 1.20366i | ||||||||
\(624\) | 1.89685e25 | 0.0529394 | ||||||||
\(625\) | 1.99865e25 | + | 3.63248e26i | 0.0549383 | + | 0.998490i | ||||
\(626\) | 3.53694e26 | 0.957572 | ||||||||
\(627\) | − | 1.44481e26i | − | 0.385275i | ||||||
\(628\) | 7.44267e26i | 1.95485i | ||||||||
\(629\) | 4.65538e25 | 0.120441 | ||||||||
\(630\) | 7.19285e26 | + | 2.86423e26i | 1.83301 | + | 0.729914i | ||||
\(631\) | −1.75895e26 | −0.441545 | −0.220773 | − | 0.975325i | \(-0.570858\pi\) | ||||
−0.220773 | + | 0.975325i | \(0.570858\pi\) | |||||||
\(632\) | 3.01275e26i | 0.744991i | ||||||||
\(633\) | 1.91823e26i | 0.467268i | ||||||||
\(634\) | −1.22498e27 | −2.93956 | ||||||||
\(635\) | 9.05399e25 | − | 2.27370e26i | 0.214037 | − | 0.537506i | ||||
\(636\) | 2.97522e26 | 0.692910 | ||||||||
\(637\) | 1.56785e26i | 0.359732i | ||||||||
\(638\) | − | 3.19625e26i | − | 0.722512i | ||||||
\(639\) | −1.84451e26 | −0.410793 | ||||||||
\(640\) | 3.08210e26 | − | 7.73998e26i | 0.676295 | − | 1.69836i | ||||
\(641\) | 6.26722e26 | 1.35495 | 0.677475 | − | 0.735546i | \(-0.263074\pi\) | ||||
0.677475 | + | 0.735546i | \(0.263074\pi\) | |||||||
\(642\) | − | 1.32277e26i | − | 0.281774i | ||||||
\(643\) | 4.06756e25i | 0.0853748i | 0.999088 | + | 0.0426874i | \(0.0135919\pi\) | ||||
−0.999088 | + | 0.0426874i | \(0.986408\pi\) | |||||||
\(644\) | 1.14865e27 | 2.37559 | ||||||||
\(645\) | 1.41282e26 | + | 5.62592e25i | 0.287919 | + | 0.114651i | ||||
\(646\) | 6.00846e26 | 1.20657 | ||||||||
\(647\) | − | 5.94304e26i | − | 1.17603i | −0.808851 | − | 0.588014i | \(-0.799910\pi\) | ||
0.808851 | − | 0.588014i | \(-0.200090\pi\) | |||||||
\(648\) | 1.29704e26i | 0.252925i | ||||||||
\(649\) | 5.76055e24 | 0.0110698 | ||||||||
\(650\) | −1.26007e26 | − | 1.19265e26i | −0.238627 | − | 0.225858i | ||||
\(651\) | −8.48606e26 | −1.58375 | ||||||||
\(652\) | 1.04816e27i | 1.92787i | ||||||||
\(653\) | − | 4.38542e26i | − | 0.794944i | −0.917614 | − | 0.397472i | \(-0.869888\pi\) | ||
0.917614 | − | 0.397472i | \(-0.130112\pi\) | |||||||
\(654\) | −9.59378e24 | −0.0171396 | ||||||||
\(655\) | −3.29056e26 | − | 1.31032e26i | −0.579399 | − | 0.230719i | ||||
\(656\) | −3.13906e26 | −0.544770 | ||||||||
\(657\) | − | 7.10807e26i | − | 1.21585i | ||||||
\(658\) | − | 2.05770e27i | − | 3.46926i | ||||||
\(659\) | −5.41264e26 | −0.899493 | −0.449747 | − | 0.893156i | \(-0.648486\pi\) | ||||
−0.449747 | + | 0.893156i | \(0.648486\pi\) | |||||||
\(660\) | −1.04643e26 | + | 2.62786e26i | −0.171412 | + | 0.430463i | ||||
\(661\) | 7.96736e24 | 0.0128647 | 0.00643236 | − | 0.999979i | \(-0.497953\pi\) | ||||
0.00643236 | + | 0.999979i | \(0.497953\pi\) | |||||||
\(662\) | 1.50831e27i | 2.40071i | ||||||||
\(663\) | 3.25752e25i | 0.0511103i | ||||||||
\(664\) | 2.93427e26 | 0.453841 | ||||||||
\(665\) | −6.18574e26 | + | 1.55341e27i | −0.943161 | + | 2.36853i | ||||
\(666\) | −1.97610e26 | −0.297032 | ||||||||
\(667\) | − | 4.86079e26i | − | 0.720297i | ||||||
\(668\) | − | 3.07167e25i | − | 0.0448744i | ||||||
\(669\) | 1.74503e26 | 0.251336 | ||||||||
\(670\) | 1.25367e27 | + | 4.99215e26i | 1.78021 | + | 0.708888i | ||||
\(671\) | 1.56860e26 | 0.219608 | ||||||||
\(672\) | − | 3.69755e26i | − | 0.510394i | ||||||
\(673\) | 3.41589e26i | 0.464902i | 0.972608 | + | 0.232451i | \(0.0746745\pi\) | ||||
−0.972608 | + | 0.232451i | \(0.925325\pi\) | |||||||
\(674\) | 1.51647e27 | 2.03500 | ||||||||
\(675\) | −4.85095e26 | + | 5.12519e26i | −0.641860 | + | 0.678147i | ||||
\(676\) | −1.34141e27 | −1.75012 | ||||||||
\(677\) | 3.34901e26i | 0.430849i | 0.976521 | + | 0.215424i | \(0.0691135\pi\) | ||||
−0.976521 | + | 0.215424i | \(0.930887\pi\) | |||||||
\(678\) | − | 3.47932e26i | − | 0.441379i | ||||||
\(679\) | 3.43426e26 | 0.429606 | ||||||||
\(680\) | −4.92305e26 | − | 1.96038e26i | −0.607295 | − | 0.241828i | ||||
\(681\) | 1.41537e25 | 0.0172176 | ||||||||
\(682\) | 1.10710e27i | 1.32811i | ||||||||
\(683\) | 1.09285e27i | 1.29290i | 0.762956 | + | 0.646450i | \(0.223747\pi\) | ||||
−0.762956 | + | 0.646450i | \(0.776253\pi\) | |||||||
\(684\) | −1.64597e27 | −1.92038 | ||||||||
\(685\) | 5.86389e26 | − | 1.47258e27i | 0.674723 | − | 1.69441i | ||||
\(686\) | −2.09047e27 | −2.37227 | ||||||||
\(687\) | 1.25640e26i | 0.140617i | ||||||||
\(688\) | − | 2.51013e26i | − | 0.277081i | ||||||
\(689\) | 1.24396e26 | 0.135433 | ||||||||
\(690\) | −2.46587e26 | + | 6.19248e26i | −0.264792 | + | 0.664964i | ||||
\(691\) | −2.01449e26 | −0.213365 | −0.106682 | − | 0.994293i | \(-0.534023\pi\) | ||||
−0.106682 | + | 0.994293i | \(0.534023\pi\) | |||||||
\(692\) | − | 2.53070e27i | − | 2.64382i | ||||||
\(693\) | − | 5.27733e26i | − | 0.543812i | ||||||
\(694\) | 1.07282e27 | 1.09047 | ||||||||
\(695\) | 6.75092e26 | + | 2.68824e26i | 0.676873 | + | 0.269534i | ||||
\(696\) | 7.11784e26 | 0.703980 | ||||||||
\(697\) | − | 5.39081e26i | − | 0.525948i | ||||||
\(698\) | 8.26751e26i | 0.795698i | ||||||||
\(699\) | 4.33635e26 | 0.411710 | ||||||||
\(700\) | 2.25016e27 | − | 2.37737e27i | 2.10757 | − | 2.22671i | ||||
\(701\) | −4.28823e26 | −0.396239 | −0.198120 | − | 0.980178i | \(-0.563483\pi\) | ||||
−0.198120 | + | 0.980178i | \(0.563483\pi\) | |||||||
\(702\) | − | 3.36549e26i | − | 0.306793i | ||||||
\(703\) | − | 4.26769e26i | − | 0.383811i | ||||||
\(704\) | −7.38947e26 | −0.655652 | ||||||||
\(705\) | 7.15919e26 | + | 2.85082e26i | 0.626711 | + | 0.249559i | ||||
\(706\) | 2.06777e27 | 1.78590 | ||||||||
\(707\) | 9.49418e26i | 0.809046i | ||||||||
\(708\) | 2.84768e25i | 0.0239428i | ||||||||
\(709\) | −1.91128e27 | −1.58557 | −0.792783 | − | 0.609504i | \(-0.791369\pi\) | ||||
−0.792783 | + | 0.609504i | \(0.791369\pi\) | |||||||
\(710\) | −4.47052e26 | + | 1.12267e27i | −0.365935 | + | 0.918962i | ||||
\(711\) | 4.67279e26 | 0.377411 | ||||||||
\(712\) | 1.23404e27i | 0.983488i | ||||||||
\(713\) | 1.68365e27i | 1.32404i | ||||||||
\(714\) | −9.52320e26 | −0.739009 | ||||||||
\(715\) | −4.37518e25 | + | 1.09873e26i | −0.0335034 | + | 0.0841361i | ||||
\(716\) | −1.10105e27 | −0.832018 | ||||||||
\(717\) | 7.69003e26i | 0.573451i | ||||||||
\(718\) | 2.28030e27i | 1.67807i | ||||||||
\(719\) | 2.62640e27 | 1.90737 | 0.953687 | − | 0.300799i | \(-0.0972535\pi\) | ||||
0.953687 | + | 0.300799i | \(0.0972535\pi\) | |||||||
\(720\) | 4.44623e26 | + | 1.77051e26i | 0.318664 | + | 0.126894i | ||||
\(721\) | 9.09210e26 | 0.643101 | ||||||||
\(722\) | − | 3.10256e27i | − | 2.16579i | ||||||
\(723\) | − | 1.10438e27i | − | 0.760859i | ||||||
\(724\) | 7.34994e26 | 0.499767 | ||||||||
\(725\) | −1.00604e27 | − | 9.52209e26i | −0.675157 | − | 0.639030i | ||||
\(726\) | −1.09585e27 | −0.725862 | ||||||||
\(727\) | − | 7.24253e25i | − | 0.0473493i | −0.999720 | − | 0.0236747i | \(-0.992463\pi\) | ||
0.999720 | − | 0.0236747i | \(-0.00753658\pi\) | |||||||
\(728\) | 7.03258e26i | 0.453802i | ||||||||
\(729\) | −6.05287e26 | −0.385523 | ||||||||
\(730\) | −4.32636e27 | − | 1.72278e27i | −2.71992 | − | 1.08308i | ||||
\(731\) | 4.31074e26 | 0.267508 | ||||||||
\(732\) | 7.75422e26i | 0.474988i | ||||||||
\(733\) | − | 1.12113e27i | − | 0.677901i | −0.940804 | − | 0.338951i | \(-0.889928\pi\) | ||
0.940804 | − | 0.338951i | \(-0.110072\pi\) | |||||||
\(734\) | 2.11522e27 | 1.26253 | ||||||||
\(735\) | 6.35020e26 | − | 1.59471e27i | 0.374160 | − | 0.939619i | ||||
\(736\) | −7.33601e26 | −0.426698 | ||||||||
\(737\) | − | 9.19804e26i | − | 0.528146i | ||||||
\(738\) | 2.28827e27i | 1.29710i | ||||||||
\(739\) | −2.25754e27 | −1.26332 | −0.631661 | − | 0.775245i | \(-0.717627\pi\) | ||||
−0.631661 | + | 0.775245i | \(0.717627\pi\) | |||||||
\(740\) | −3.09094e26 | + | 7.76219e26i | −0.170761 | + | 0.428828i | ||||
\(741\) | 2.98624e26 | 0.162874 | ||||||||
\(742\) | 3.63665e27i | 1.95824i | ||||||||
\(743\) | − | 2.84762e27i | − | 1.51387i | −0.653491 | − | 0.756934i | \(-0.726696\pi\) | ||
0.653491 | − | 0.756934i | \(-0.273304\pi\) | |||||||
\(744\) | −2.46543e27 | −1.29405 | ||||||||
\(745\) | −5.76069e26 | − | 2.29393e26i | −0.298532 | − | 0.118877i | ||||
\(746\) | −2.37443e27 | −1.21490 | ||||||||
\(747\) | − | 4.55106e26i | − | 0.229915i | ||||||
\(748\) | 8.01802e26i | 0.399947i | ||||||||
\(749\) | 1.04345e27 | 0.513917 | ||||||||
\(750\) | 7.98607e26 | + | 1.72344e27i | 0.388375 | + | 0.838138i | ||||
\(751\) | 1.75682e27 | 0.843623 | 0.421812 | − | 0.906684i | \(-0.361394\pi\) | ||||
0.421812 | + | 0.906684i | \(0.361394\pi\) | |||||||
\(752\) | − | 1.27196e27i | − | 0.603121i | ||||||
\(753\) | 4.58652e26i | 0.214749i | ||||||||
\(754\) | 6.60624e26 | 0.305440 | ||||||||
\(755\) | 1.73785e27 | + | 6.92018e26i | 0.793442 | + | 0.315952i | ||||
\(756\) | 6.34963e27 | 2.86280 | ||||||||
\(757\) | 3.07775e27i | 1.37032i | 0.728392 | + | 0.685160i | \(0.240268\pi\) | ||||
−0.728392 | + | 0.685160i | \(0.759732\pi\) | |||||||
\(758\) | − | 4.70370e27i | − | 2.06815i | ||||||
\(759\) | 4.54337e26 | 0.197279 | ||||||||
\(760\) | −1.79713e27 | + | 4.51307e27i | −0.770636 | + | 1.93528i | ||||
\(761\) | −3.44812e27 | −1.46025 | −0.730127 | − | 0.683312i | \(-0.760539\pi\) | ||||
−0.730127 | + | 0.683312i | \(0.760539\pi\) | |||||||
\(762\) | − | 1.27782e27i | − | 0.534438i | ||||||
\(763\) | − | 7.56792e25i | − | 0.0312603i | ||||||
\(764\) | 3.53310e27 | 1.44135 | ||||||||
\(765\) | −3.04056e26 | + | 7.63566e26i | −0.122509 | + | 0.307654i | ||||
\(766\) | 6.47142e27 | 2.57529 | ||||||||
\(767\) | 1.19063e25i | 0.00467973i | ||||||||
\(768\) | − | 2.34253e27i | − | 0.909397i | ||||||
\(769\) | −3.66284e27 | −1.40449 | −0.702243 | − | 0.711937i | \(-0.747818\pi\) | ||||
−0.702243 | + | 0.711937i | \(0.747818\pi\) | |||||||
\(770\) | −3.21207e27 | − | 1.27906e27i | −1.21653 | − | 0.484429i | ||||
\(771\) | 9.43711e26 | 0.353039 | ||||||||
\(772\) | − | 5.19914e27i | − | 1.92117i | ||||||
\(773\) | 1.93533e27i | 0.706399i | 0.935548 | + | 0.353199i | \(0.114906\pi\) | ||||
−0.935548 | + | 0.353199i | \(0.885094\pi\) | |||||||
\(774\) | −1.82981e27 | −0.659730 | ||||||||
\(775\) | 3.48466e27 | + | 3.29820e27i | 1.24107 | + | 1.17466i | ||||
\(776\) | 9.97747e26 | 0.351022 | ||||||||
\(777\) | 6.76415e26i | 0.235079i | ||||||||
\(778\) | − | 5.90593e27i | − | 2.02760i | ||||||
\(779\) | −4.94188e27 | −1.67605 | ||||||||
\(780\) | −5.43145e26 | − | 2.16283e26i | −0.181977 | − | 0.0724642i | ||||
\(781\) | 8.23693e26 | 0.272634 | ||||||||
\(782\) | 1.88942e27i | 0.617824i | ||||||||
\(783\) | − | 2.68701e27i | − | 0.868024i | ||||||
\(784\) | −2.83329e27 | −0.904250 | ||||||||
\(785\) | 1.26037e27 | − | 3.16514e27i | 0.397409 | − | 0.998002i | ||||
\(786\) | −1.84929e27 | −0.576092 | ||||||||
\(787\) | 4.47507e27i | 1.37733i | 0.725077 | + | 0.688667i | \(0.241804\pi\) | ||||
−0.725077 | + | 0.688667i | \(0.758196\pi\) | |||||||
\(788\) | 5.04024e27i | 1.53268i | ||||||||
\(789\) | −1.17543e27 | −0.353154 | ||||||||
\(790\) | 1.13254e27 | − | 2.84412e27i | 0.336199 | − | 0.844286i | ||||
\(791\) | 2.74461e27 | 0.805015 | ||||||||
\(792\) | − | 1.53321e27i | − | 0.444337i | ||||||
\(793\) | 3.24209e26i | 0.0928388i | ||||||||
\(794\) | 7.03673e27 | 1.99102 | ||||||||
\(795\) | −1.26527e27 | − | 5.03837e26i | −0.353749 | − | 0.140865i | ||||
\(796\) | −1.06973e28 | −2.95530 | ||||||||
\(797\) | 2.99623e27i | 0.817939i | 0.912548 | + | 0.408969i | \(0.134112\pi\) | ||||
−0.912548 | + | 0.408969i | \(0.865888\pi\) | |||||||
\(798\) | 8.73014e27i | 2.35501i | ||||||||
\(799\) | 2.18438e27 | 0.582283 | ||||||||
\(800\) | −1.43709e27 | + | 1.51834e27i | −0.378556 | + | 0.399957i | ||||
\(801\) | 1.91400e27 | 0.498233 | ||||||||
\(802\) | − | 7.67621e27i | − | 1.97465i | ||||||
\(803\) | 3.17421e27i | 0.806935i | ||||||||
\(804\) | 4.54697e27 | 1.14232 | ||||||||
\(805\) | −4.88485e27 | − | 1.94517e27i | −1.21280 | − | 0.482944i | ||||
\(806\) | −2.28823e27 | −0.561457 | ||||||||
\(807\) | − | 5.41973e26i | − | 0.131425i | ||||||
\(808\) | 2.75832e27i | 0.661054i | ||||||||
\(809\) | −8.97271e26 | −0.212526 | −0.106263 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106263 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(810\) | 4.87578e26 | − | 1.22444e27i | 0.114140 | − | 0.286636i | ||||
\(811\) | −7.80812e27 | −1.80654 | −0.903271 | − | 0.429070i | \(-0.858841\pi\) | ||||
−0.903271 | + | 0.429070i | \(0.858841\pi\) | |||||||
\(812\) | 1.24639e28i | 2.85018i | ||||||||
\(813\) | 5.57052e26i | 0.125903i | ||||||||
\(814\) | 8.82456e26 | 0.197134 | ||||||||
\(815\) | 1.77500e27 | − | 4.45752e27i | 0.391924 | − | 0.984228i | ||||
\(816\) | −5.88673e26 | −0.128475 | ||||||||
\(817\) | − | 3.95175e27i | − | 0.852472i | ||||||
\(818\) | − | 6.90742e27i | − | 1.47285i | ||||||
\(819\) | 1.09076e27 | 0.229895 | ||||||||
\(820\) | 8.98841e27 | + | 3.57923e27i | 1.87263 | + | 0.745689i | ||||
\(821\) | 5.65133e27 | 1.16383 | 0.581917 | − | 0.813248i | \(-0.302303\pi\) | ||||
0.581917 | + | 0.813248i | \(0.302303\pi\) | |||||||
\(822\) | − | 8.27590e27i | − | 1.68474i | ||||||
\(823\) | 4.23337e27i | 0.851898i | 0.904747 | + | 0.425949i | \(0.140060\pi\) | ||||
−0.904747 | + | 0.425949i | \(0.859940\pi\) | |||||||
\(824\) | 2.64150e27 | 0.525464 | ||||||||
\(825\) | 8.90027e26 | − | 9.40344e26i | 0.175021 | − | 0.184916i | ||||
\(826\) | −3.48075e26 | −0.0676648 | ||||||||
\(827\) | − | 8.60057e27i | − | 1.65282i | −0.563071 | − | 0.826408i | \(-0.690380\pi\) | ||
0.563071 | − | 0.826408i | \(-0.309620\pi\) | |||||||
\(828\) | − | 5.17591e27i | − | 0.983328i | ||||||
\(829\) | −2.40358e27 | −0.451431 | −0.225715 | − | 0.974193i | \(-0.572472\pi\) | ||||
−0.225715 | + | 0.974193i | \(0.572472\pi\) | |||||||
\(830\) | −2.77003e27 | − | 1.10304e27i | −0.514330 | − | 0.204809i | ||||
\(831\) | −5.68600e27 | −1.04375 | ||||||||
\(832\) | − | 1.52731e27i | − | 0.277176i | ||||||
\(833\) | − | 4.86570e27i | − | 0.873008i | ||||||
\(834\) | 3.79401e27 | 0.673009 | ||||||||
\(835\) | −5.20170e25 | + | 1.30629e26i | −0.00912271 | + | 0.0229096i | ||||
\(836\) | 7.35031e27 | 1.27452 | ||||||||
\(837\) | 9.30708e27i | 1.59559i | ||||||||
\(838\) | 1.49795e28i | 2.53910i | ||||||||
\(839\) | 2.28307e27 | 0.382632 | 0.191316 | − | 0.981529i | \(-0.438725\pi\) | ||||
0.191316 | + | 0.981529i | \(0.438725\pi\) | |||||||
\(840\) | 2.84838e27 | − | 7.15307e27i | 0.472004 | − | 1.18533i | ||||
\(841\) | −8.28845e26 | −0.135804 | ||||||||
\(842\) | 1.01638e28i | 1.64661i | ||||||||
\(843\) | − | 4.69150e27i | − | 0.751535i | ||||||
\(844\) | −9.75875e27 | −1.54576 | ||||||||
\(845\) | 5.70459e27 | + | 2.27160e27i | 0.893482 | + | 0.355789i | ||||
\(846\) | −9.27218e27 | −1.43603 | ||||||||
\(847\) | − | 8.64448e27i | − | 1.32387i | ||||||
\(848\) | 2.24798e27i | 0.340434i | ||||||||
\(849\) | 3.52013e26 | 0.0527152 | ||||||||
\(850\) | 3.91055e27 | + | 3.70130e27i | 0.579106 | + | 0.548118i | ||||
\(851\) | 1.34202e27 | 0.196530 | ||||||||
\(852\) | 4.07185e27i | 0.589679i | ||||||||
\(853\) | 3.07333e27i | 0.440142i | 0.975484 | + | 0.220071i | \(0.0706289\pi\) | ||||
−0.975484 | + | 0.220071i | \(0.929371\pi\) | |||||||
\(854\) | −9.47809e27 | −1.34237 | ||||||||
\(855\) | 6.99979e27 | + | 2.78735e27i | 0.980408 | + | 0.390403i | ||||
\(856\) | 3.03150e27 | 0.419910 | ||||||||
\(857\) | − | 4.56647e27i | − | 0.625551i | −0.949827 | − | 0.312775i | \(-0.898741\pi\) | ||
0.949827 | − | 0.312775i | \(-0.101259\pi\) | |||||||
\(858\) | 6.17483e26i | 0.0836558i | ||||||||
\(859\) | 5.09546e27 | 0.682728 | 0.341364 | − | 0.939931i | \(-0.389111\pi\) | ||||
0.341364 | + | 0.939931i | \(0.389111\pi\) | |||||||
\(860\) | −2.86211e27 | + | 7.18755e27i | −0.379273 | + | 0.952457i | ||||
\(861\) | 7.83271e27 | 1.02655 | ||||||||
\(862\) | 3.66758e26i | 0.0475402i | ||||||||
\(863\) | 4.49338e27i | 0.576064i | 0.957621 | + | 0.288032i | \(0.0930010\pi\) | ||||
−0.957621 | + | 0.288032i | \(0.906999\pi\) | |||||||
\(864\) | −4.05528e27 | −0.514210 | ||||||||
\(865\) | −4.28559e27 | + | 1.07623e28i | −0.537474 | + | 1.34974i | ||||
\(866\) | −2.31349e28 | −2.86977 | ||||||||
\(867\) | 3.47265e27i | 0.426069i | ||||||||
\(868\) | − | 4.31717e28i | − | 5.23917i | ||||||
\(869\) | −2.08670e27 | −0.250480 | ||||||||
\(870\) | −6.71942e27 | − | 2.67570e27i | −0.797809 | − | 0.317691i | ||||
\(871\) | 1.90111e27 | 0.223273 | ||||||||
\(872\) | − | 2.19869e26i | − | 0.0255421i | ||||||
\(873\) | − | 1.54751e27i | − | 0.177827i | ||||||
\(874\) | 1.73208e28 | 1.96883 | ||||||||
\(875\) | −1.35952e28 | + | 6.29970e27i | −1.52865 | + | 0.708343i | ||||
\(876\) | −1.56914e28 | −1.74532 | ||||||||
\(877\) | − | 1.20133e28i | − | 1.32180i | −0.750473 | − | 0.660901i | \(-0.770174\pi\) | ||
0.750473 | − | 0.660901i | \(-0.229826\pi\) | |||||||
\(878\) | − | 6.72437e27i | − | 0.731903i | ||||||
\(879\) | 3.44740e27 | 0.371191 | ||||||||
\(880\) | −1.98553e27 | − | 7.90647e26i | −0.211491 | − | 0.0842166i | ||||
\(881\) | 5.81954e27 | 0.613221 | 0.306611 | − | 0.951835i | \(-0.400805\pi\) | ||||
0.306611 | + | 0.951835i | \(0.400805\pi\) | |||||||
\(882\) | 2.06538e28i | 2.15302i | ||||||||
\(883\) | 1.68577e28i | 1.73849i | 0.494386 | + | 0.869243i | \(0.335393\pi\) | ||||
−0.494386 | + | 0.869243i | \(0.664607\pi\) | |||||||
\(884\) | −1.65722e27 | −0.169077 | ||||||||
\(885\) | 4.82237e25 | − | 1.21103e26i | 0.00486743 | − | 0.0122234i | ||||
\(886\) | 2.80212e28 | 2.79812 | ||||||||
\(887\) | 8.09385e26i | 0.0799614i | 0.999200 | + | 0.0399807i | \(0.0127296\pi\) | ||||
−0.999200 | + | 0.0399807i | \(0.987270\pi\) | |||||||
\(888\) | 1.96517e27i | 0.192078i | ||||||||
\(889\) | 1.00799e28 | 0.974742 | ||||||||
\(890\) | 4.63894e27 | − | 1.16496e28i | 0.443827 | − | 1.11457i | ||||
\(891\) | −8.98362e26 | −0.0850380 | ||||||||
\(892\) | 8.87762e27i | 0.831439i | ||||||||
\(893\) | − | 2.00247e28i | − | 1.85557i | ||||||
\(894\) | −3.23750e27 | −0.296827 | ||||||||
\(895\) | 4.68242e27 | + | 1.86456e27i | 0.424768 | + | 0.169144i | ||||
\(896\) | 3.43133e28 | 3.07990 | ||||||||
\(897\) | 9.39055e26i | 0.0833994i | ||||||||
\(898\) | 3.16357e28i | 2.78004i | ||||||||
\(899\) | −1.82692e28 | −1.58856 | ||||||||
\(900\) | −1.07126e28 | − | 1.01394e28i | −0.921705 | − | 0.872385i | ||||
\(901\) | −3.86054e27 | −0.328672 | ||||||||
\(902\) | − | 1.02186e28i | − | 0.860855i | ||||||
\(903\) | 6.26340e27i | 0.522127i | ||||||||
\(904\) | 7.97384e27 | 0.657760 | ||||||||
\(905\) | −3.12571e27 | − | 1.24467e27i | −0.255145 | − | 0.101600i | ||||
\(906\) | 9.76668e27 | 0.788913 | ||||||||
\(907\) | − | 2.84041e27i | − | 0.227045i | −0.993535 | − | 0.113522i | \(-0.963787\pi\) | ||
0.993535 | − | 0.113522i | \(-0.0362134\pi\) | |||||||
\(908\) | 7.20051e26i | 0.0569571i | ||||||||
\(909\) | 4.27816e27 | 0.334889 | ||||||||
\(910\) | 2.64365e27 | − | 6.63894e27i | 0.204791 | − | 0.514287i | ||||
\(911\) | −1.43331e28 | −1.09879 | −0.549397 | − | 0.835561i | \(-0.685143\pi\) | ||||
−0.549397 | + | 0.835561i | \(0.685143\pi\) | |||||||
\(912\) | 5.39650e27i | 0.409413i | ||||||||
\(913\) | 2.03235e27i | 0.152590i | ||||||||
\(914\) | −2.81270e28 | −2.08994 | ||||||||
\(915\) | 1.31313e27 | − | 3.29763e27i | 0.0965624 | − | 0.242494i | ||||
\(916\) | −6.39177e27 | −0.465173 | ||||||||
\(917\) | − | 1.45879e28i | − | 1.05071i | ||||||
\(918\) | 1.04446e28i | 0.744534i | ||||||||
\(919\) | −1.84550e27 | −0.130202 | −0.0651009 | − | 0.997879i | \(-0.520737\pi\) | ||||
−0.0651009 | + | 0.997879i | \(0.520737\pi\) | |||||||
\(920\) | −1.41918e28 | − | 5.65125e27i | −0.990955 | − | 0.394603i | ||||
\(921\) | 6.69896e27 | 0.462957 | ||||||||
\(922\) | − | 3.48210e28i | − | 2.38176i | ||||||
\(923\) | 1.70247e27i | 0.115256i | ||||||||
\(924\) | −1.16500e28 | −0.780624 | ||||||||
\(925\) | 2.62896e27 | − | 2.77759e27i | 0.174356 | − | 0.184213i | ||||
\(926\) | 3.22945e28 | 2.11994 | ||||||||
\(927\) | − | 4.09698e27i | − | 0.266199i | ||||||
\(928\) | − | 7.96026e27i | − | 0.511943i | ||||||
\(929\) | 1.47827e28 | 0.941033 | 0.470516 | − | 0.882391i | \(-0.344068\pi\) | ||||
0.470516 | + | 0.882391i | \(0.344068\pi\) | |||||||
\(930\) | 2.32743e28 | + | 9.26794e27i | 1.46652 | + | 0.583976i | ||||
\(931\) | −4.46050e28 | −2.78203 | ||||||||
\(932\) | 2.20606e28i | 1.36197i | ||||||||
\(933\) | − | 4.90717e26i | − | 0.0299886i | ||||||
\(934\) | −1.93707e28 | −1.17179 | ||||||||
\(935\) | 1.35781e27 | − | 3.40982e27i | 0.0813069 | − | 0.204184i | ||||
\(936\) | 3.16894e27 | 0.187843 | ||||||||
\(937\) | 2.62877e28i | 1.54250i | 0.636531 | + | 0.771251i | \(0.280369\pi\) | ||||
−0.636531 | + | 0.771251i | \(0.719631\pi\) | |||||||
\(938\) | 5.55782e28i | 3.22833i | ||||||||
\(939\) | −5.45546e27 | −0.313696 | ||||||||
\(940\) | −1.45032e28 | + | 3.64215e28i | −0.825561 | + | 2.07321i | ||||
\(941\) | 5.29025e27 | 0.298109 | 0.149054 | − | 0.988829i | \(-0.452377\pi\) | ||||
0.149054 | + | 0.988829i | \(0.452377\pi\) | |||||||
\(942\) | − | 1.77881e28i | − | 0.992305i | ||||||
\(943\) | − | 1.55403e28i | − | 0.858217i | ||||||
\(944\) | −2.15161e26 | −0.0117633 | ||||||||
\(945\) | −2.70030e28 | − | 1.07527e28i | −1.46154 | − | 0.581992i | ||||
\(946\) | 8.17128e27 | 0.437849 | ||||||||
\(947\) | 2.77520e28i | 1.47221i | 0.676868 | + | 0.736105i | \(0.263337\pi\) | ||||
−0.676868 | + | 0.736105i | \(0.736663\pi\) | |||||||
\(948\) | − | 1.03154e28i | − | 0.541761i | ||||||
\(949\) | −6.56069e27 | −0.341130 | ||||||||
\(950\) | 3.39307e28 | − | 3.58489e28i | 1.74670 | − | 1.84545i | ||||
\(951\) | 1.88944e28 | 0.962984 | ||||||||
\(952\) | − | 2.18251e28i | − | 1.10130i | ||||||
\(953\) | 4.86733e27i | 0.243169i | 0.992581 | + | 0.121585i | \(0.0387976\pi\) | ||||
−0.992581 | + | 0.121585i | \(0.961202\pi\) | |||||||
\(954\) | 1.63871e28 | 0.810573 | ||||||||
\(955\) | −1.50252e28 | − | 5.98311e27i | −0.735849 | − | 0.293018i | ||||
\(956\) | −3.91220e28 | −1.89702 | ||||||||
\(957\) | 4.92998e27i | 0.236691i | ||||||||
\(958\) | − | 4.31966e28i | − | 2.05342i | ||||||
\(959\) | 6.52833e28 | 3.07274 | ||||||||
\(960\) | −6.18600e27 | + | 1.55347e28i | −0.288293 | + | 0.723981i | ||||
\(961\) | 4.16091e28 | 1.92006 | ||||||||
\(962\) | 1.82392e27i | 0.0833380i | ||||||||
\(963\) | − | 4.70186e27i | − | 0.212726i | ||||||
\(964\) | 5.61838e28 | 2.51698 | ||||||||
\(965\) | −8.80443e27 | + | 2.21103e28i | −0.390564 | + | 0.980812i | ||||
\(966\) | −2.74528e28 | −1.20588 | ||||||||
\(967\) | − | 1.90521e28i | − | 0.828689i | −0.910120 | − | 0.414345i | \(-0.864011\pi\) | ||
0.910120 | − | 0.414345i | \(-0.135989\pi\) | |||||||
\(968\) | − | 2.51146e28i | − | 1.08171i | ||||||
\(969\) | −9.26759e27 | −0.395267 | ||||||||
\(970\) | −9.41899e27 | − | 3.75068e27i | −0.397807 | − | 0.158409i | ||||
\(971\) | −4.36106e28 | −1.82394 | −0.911968 | − | 0.410261i | \(-0.865438\pi\) | ||||
−0.911968 | + | 0.410261i | \(0.865438\pi\) | |||||||
\(972\) | − | 4.54685e28i | − | 1.88313i | ||||||
\(973\) | 2.99285e28i | 1.22748i | ||||||||
\(974\) | −6.83445e28 | −2.77583 | ||||||||
\(975\) | 1.94357e27 | + | 1.83957e27i | 0.0781728 | + | 0.0739899i | ||||
\(976\) | −5.85884e27 | −0.233367 | ||||||||
\(977\) | 1.33368e28i | 0.526081i | 0.964785 | + | 0.263041i | \(0.0847254\pi\) | ||||
−0.964785 | + | 0.263041i | \(0.915275\pi\) | |||||||
\(978\) | − | 2.50512e28i | − | 0.978610i | ||||||
\(979\) | −8.54724e27 | −0.330667 | ||||||||
\(980\) | 8.11287e28 | + | 3.23058e28i | 3.10833 | + | 1.23775i | ||||
\(981\) | −3.41017e26 | −0.0129396 | ||||||||
\(982\) | 7.07046e28i | 2.65698i | ||||||||
\(983\) | − | 3.76958e28i | − | 1.40293i | −0.712706 | − | 0.701463i | \(-0.752531\pi\) | ||
0.712706 | − | 0.701463i | \(-0.247469\pi\) | |||||||
\(984\) | 2.27562e28 | 0.838775 | ||||||||
\(985\) | 8.53535e27 | − | 2.14346e28i | 0.311585 | − | 0.782476i | ||||
\(986\) | −2.05020e28 | −0.741251 | ||||||||
\(987\) | 3.17385e28i | 1.13651i | ||||||||
\(988\) | 1.51921e28i | 0.538800i | ||||||||
\(989\) | 1.24267e28 | 0.436507 | ||||||||
\(990\) | −5.76357e27 | + | 1.44739e28i | −0.200520 | + | 0.503559i | ||||
\(991\) | 2.77322e28 | 0.955620 | 0.477810 | − | 0.878463i | \(-0.341431\pi\) | ||||
0.477810 | + | 0.878463i | \(0.341431\pi\) | |||||||
\(992\) | 2.75723e28i | 0.941047i | ||||||||
\(993\) | − | 2.32645e28i | − | 0.786459i | ||||||
\(994\) | −4.97708e28 | −1.66649 | ||||||||
\(995\) | 4.54925e28 | + | 1.81153e28i | 1.50876 | + | 0.600796i | ||||
\(996\) | −1.00467e28 | −0.330035 | ||||||||
\(997\) | − | 4.18648e28i | − | 1.36221i | −0.732184 | − | 0.681107i | \(-0.761499\pi\) | ||
0.732184 | − | 0.681107i | \(-0.238501\pi\) | |||||||
\(998\) | − | 1.62789e28i | − | 0.524668i | ||||||
\(999\) | 7.41857e27 | 0.236836 |
(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 | 5.20.b.a.4.1 | ✓ | 8 | |
3.2 | odd | 2 | 45.20.b.b.19.8 | 8 | |||
4.3 | odd | 2 | 80.20.c.a.49.4 | 8 | |||
5.2 | odd | 4 | 25.20.a.f.1.8 | 8 | |||
5.3 | odd | 4 | 25.20.a.f.1.1 | 8 | |||
5.4 | even | 2 | inner | 5.20.b.a.4.8 | yes | 8 | |
15.14 | odd | 2 | 45.20.b.b.19.1 | 8 | |||
20.19 | odd | 2 | 80.20.c.a.49.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.20.b.a.4.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
5.20.b.a.4.8 | yes | 8 | 5.4 | even | 2 | inner | |
25.20.a.f.1.1 | 8 | 5.3 | odd | 4 | |||
25.20.a.f.1.8 | 8 | 5.2 | odd | 4 | |||
45.20.b.b.19.1 | 8 | 15.14 | odd | 2 | |||
45.20.b.b.19.8 | 8 | 3.2 | odd | 2 | |||
80.20.c.a.49.4 | 8 | 4.3 | odd | 2 | |||
80.20.c.a.49.5 | 8 | 20.19 | odd | 2 |