Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,11,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(1.90607175802\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-5}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.2 | ||
Root | \(2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.11.b.a.2.1 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 26.8328i | 0.838525i | 0.907865 | + | 0.419263i | \(0.137711\pi\) | ||||
−0.907865 | + | 0.419263i | \(0.862289\pi\) | |||||||
\(3\) | −27.0000 | + | 241.495i | −0.111111 | + | 0.993808i | ||||
\(4\) | 304.000 | 0.296875 | ||||||||
\(5\) | − | 2844.28i | − | 0.910169i | −0.890448 | − | 0.455085i | \(-0.849609\pi\) | ||
0.890448 | − | 0.455085i | \(-0.150391\pi\) | |||||||
\(6\) | −6480.00 | − | 724.486i | −0.833333 | − | 0.0931695i | ||||
\(7\) | 17234.0 | 1.02541 | 0.512703 | − | 0.858566i | \(-0.328644\pi\) | ||||
0.512703 | + | 0.858566i | \(0.328644\pi\) | |||||||
\(8\) | 35634.0i | 1.08746i | ||||||||
\(9\) | −57591.0 | − | 13040.7i | −0.975309 | − | 0.220846i | ||||
\(10\) | 76320.0 | 0.763200 | ||||||||
\(11\) | − | 186810.i | − | 1.15994i | −0.814637 | − | 0.579972i | \(-0.803064\pi\) | ||
0.814637 | − | 0.579972i | \(-0.196936\pi\) | |||||||
\(12\) | −8208.00 | + | 73414.6i | −0.0329861 | + | 0.295037i | ||||
\(13\) | −169654. | −0.456928 | −0.228464 | − | 0.973552i | \(-0.573370\pi\) | ||||
−0.228464 | + | 0.973552i | \(0.573370\pi\) | |||||||
\(14\) | 462437.i | 0.859829i | ||||||||
\(15\) | 686880. | + | 76795.5i | 0.904533 | + | 0.101130i | ||||
\(16\) | −644864. | −0.614990 | ||||||||
\(17\) | − | 343245.i | − | 0.241746i | −0.992668 | − | 0.120873i | \(-0.961431\pi\) | ||
0.992668 | − | 0.120873i | \(-0.0385695\pi\) | |||||||
\(18\) | 349920. | − | 1.54533e6i | 0.185185 | − | 0.817821i | ||||
\(19\) | −949462. | −0.383451 | −0.191725 | − | 0.981449i | \(-0.561408\pi\) | ||||
−0.191725 | + | 0.981449i | \(0.561408\pi\) | |||||||
\(20\) | − | 864661.i | − | 0.270206i | ||||||
\(21\) | −465318. | + | 4.16193e6i | −0.113934 | + | 1.01906i | ||||
\(22\) | 5.01264e6 | 0.972642 | ||||||||
\(23\) | 2.65763e6i | 0.412910i | 0.978456 | + | 0.206455i | \(0.0661927\pi\) | ||||
−0.978456 | + | 0.206455i | \(0.933807\pi\) | |||||||
\(24\) | −8.60544e6 | − | 962117.i | −1.08073 | − | 0.120829i | ||||
\(25\) | 1.67570e6 | 0.171592 | ||||||||
\(26\) | − | 4.55229e6i | − | 0.383145i | ||||||
\(27\) | 4.70424e6 | − | 1.35559e7i | 0.327846 | − | 0.944731i | ||||
\(28\) | 5.23914e6 | 0.304417 | ||||||||
\(29\) | 3.18221e6i | 0.155145i | 0.996987 | + | 0.0775727i | \(0.0247170\pi\) | ||||
−0.996987 | + | 0.0775727i | \(0.975283\pi\) | |||||||
\(30\) | −2.06064e6 | + | 1.84309e7i | −0.0848000 | + | 0.758474i | ||||
\(31\) | −2.97931e7 | −1.04066 | −0.520328 | − | 0.853966i | \(-0.674190\pi\) | ||||
−0.520328 | + | 0.853966i | \(0.674190\pi\) | |||||||
\(32\) | 1.91857e7i | 0.571778i | ||||||||
\(33\) | 4.51138e7 | + | 5.04387e6i | 1.15276 | + | 0.128883i | ||||
\(34\) | 9.21024e6 | 0.202711 | ||||||||
\(35\) | − | 4.90183e7i | − | 0.933293i | ||||||
\(36\) | −1.75077e7 | − | 3.96439e6i | −0.289545 | − | 0.0655637i | ||||
\(37\) | −6.08118e7 | −0.876960 | −0.438480 | − | 0.898741i | \(-0.644483\pi\) | ||||
−0.438480 | + | 0.898741i | \(0.644483\pi\) | |||||||
\(38\) | − | 2.54767e7i | − | 0.321533i | ||||||
\(39\) | 4.58066e6 | − | 4.09707e7i | 0.0507697 | − | 0.454098i | ||||
\(40\) | 1.01353e8 | 0.989775 | ||||||||
\(41\) | 1.81668e8i | 1.56805i | 0.620730 | + | 0.784024i | \(0.286836\pi\) | ||||
−0.620730 | + | 0.784024i | \(0.713164\pi\) | |||||||
\(42\) | −1.11676e8 | − | 1.24858e7i | −0.854505 | − | 0.0955366i | ||||
\(43\) | 1.07420e8 | 0.730704 | 0.365352 | − | 0.930869i | \(-0.380949\pi\) | ||||
0.365352 | + | 0.930869i | \(0.380949\pi\) | |||||||
\(44\) | − | 5.67903e7i | − | 0.344358i | ||||||
\(45\) | −3.70915e7 | + | 1.63805e8i | −0.201007 | + | 0.887696i | ||||
\(46\) | −7.13117e7 | −0.346235 | ||||||||
\(47\) | − | 2.67996e8i | − | 1.16853i | −0.811564 | − | 0.584263i | \(-0.801384\pi\) | ||
0.811564 | − | 0.584263i | \(-0.198616\pi\) | |||||||
\(48\) | 1.74113e7 | − | 1.55732e8i | 0.0683322 | − | 0.611182i | ||||
\(49\) | 1.45355e7 | 0.0514576 | ||||||||
\(50\) | 4.49639e7i | 0.143884i | ||||||||
\(51\) | 8.28922e7 | + | 9.26763e6i | 0.240250 | + | 0.0268607i | ||||
\(52\) | −5.15748e7 | −0.135650 | ||||||||
\(53\) | 1.92091e8i | 0.459332i | 0.973269 | + | 0.229666i | \(0.0737634\pi\) | ||||
−0.973269 | + | 0.229666i | \(0.926237\pi\) | |||||||
\(54\) | 3.63742e8 | + | 1.26228e8i | 0.792181 | + | 0.274908i | ||||
\(55\) | −5.31340e8 | −1.05574 | ||||||||
\(56\) | 6.14116e8i | 1.11509i | ||||||||
\(57\) | 2.56355e7 | − | 2.29291e8i | 0.0426056 | − | 0.381076i | ||||
\(58\) | −8.53877e7 | −0.130093 | ||||||||
\(59\) | − | 6.49158e8i | − | 0.908009i | −0.890999 | − | 0.454005i | \(-0.849995\pi\) | ||
0.890999 | − | 0.454005i | \(-0.150005\pi\) | |||||||
\(60\) | 2.08812e8 | + | 2.33458e7i | 0.268533 | + | 0.0300229i | ||||
\(61\) | 1.03079e9 | 1.22046 | 0.610229 | − | 0.792225i | \(-0.291078\pi\) | ||||
0.610229 | + | 0.792225i | \(0.291078\pi\) | |||||||
\(62\) | − | 7.99433e8i | − | 0.872617i | ||||||
\(63\) | −9.92523e8 | − | 2.24744e8i | −1.00009 | − | 0.226457i | ||||
\(64\) | −1.17515e9 | −1.09444 | ||||||||
\(65\) | 4.82543e8i | 0.415881i | ||||||||
\(66\) | −1.35341e8 | + | 1.21053e9i | −0.108071 | + | 0.966620i | ||||
\(67\) | 1.87674e9 | 1.39005 | 0.695025 | − | 0.718985i | \(-0.255393\pi\) | ||||
0.695025 | + | 0.718985i | \(0.255393\pi\) | |||||||
\(68\) | − | 1.04347e8i | − | 0.0717685i | ||||||
\(69\) | −6.41805e8 | − | 7.17560e7i | −0.410353 | − | 0.0458789i | ||||
\(70\) | 1.31530e9 | 0.782590 | ||||||||
\(71\) | 2.68338e9i | 1.48727i | 0.668585 | + | 0.743636i | \(0.266900\pi\) | ||||
−0.668585 | + | 0.743636i | \(0.733100\pi\) | |||||||
\(72\) | 4.64694e8 | − | 2.05220e9i | 0.240162 | − | 1.06061i | ||||
\(73\) | −2.84653e9 | −1.37310 | −0.686549 | − | 0.727084i | \(-0.740875\pi\) | ||||
−0.686549 | + | 0.727084i | \(0.740875\pi\) | |||||||
\(74\) | − | 1.63175e9i | − | 0.735353i | ||||||
\(75\) | −4.52440e7 | + | 4.04675e8i | −0.0190658 | + | 0.170530i | ||||
\(76\) | −2.88636e8 | −0.113837 | ||||||||
\(77\) | − | 3.21948e9i | − | 1.18941i | ||||||
\(78\) | 1.09936e9 | + | 1.22912e8i | 0.380773 | + | 0.0425717i | ||||
\(79\) | 1.48865e9 | 0.483790 | 0.241895 | − | 0.970302i | \(-0.422231\pi\) | ||||
0.241895 | + | 0.970302i | \(0.422231\pi\) | |||||||
\(80\) | 1.83417e9i | 0.559745i | ||||||||
\(81\) | 3.14666e9 | + | 1.50206e9i | 0.902454 | + | 0.430786i | ||||
\(82\) | −4.87467e9 | −1.31485 | ||||||||
\(83\) | 1.26585e9i | 0.321361i | 0.987006 | + | 0.160680i | \(0.0513688\pi\) | ||||
−0.987006 | + | 0.160680i | \(0.948631\pi\) | |||||||
\(84\) | −1.41457e8 | + | 1.26523e9i | −0.0338242 | + | 0.302532i | ||||
\(85\) | −9.76285e8 | −0.220030 | ||||||||
\(86\) | 2.88237e9i | 0.612714i | ||||||||
\(87\) | −7.68489e8 | − | 8.59197e7i | −0.154185 | − | 0.0172384i | ||||
\(88\) | 6.65679e9 | 1.26140 | ||||||||
\(89\) | − | 6.02052e9i | − | 1.07816i | −0.842254 | − | 0.539081i | \(-0.818772\pi\) | ||
0.842254 | − | 0.539081i | \(-0.181228\pi\) | |||||||
\(90\) | −4.39535e9 | − | 9.95270e8i | −0.744356 | − | 0.168550i | ||||
\(91\) | −2.92382e9 | −0.468536 | ||||||||
\(92\) | 8.07919e8i | 0.122583i | ||||||||
\(93\) | 8.04414e8 | − | 7.19490e9i | 0.115629 | − | 1.03421i | ||||
\(94\) | 7.19108e9 | 0.979839 | ||||||||
\(95\) | 2.70053e9i | 0.349005i | ||||||||
\(96\) | −4.63325e9 | − | 5.18013e8i | −0.568237 | − | 0.0635309i | ||||
\(97\) | −1.59295e9 | −0.185500 | −0.0927498 | − | 0.995689i | \(-0.529566\pi\) | ||||
−0.0927498 | + | 0.995689i | \(0.529566\pi\) | |||||||
\(98\) | 3.90029e8i | 0.0431485i | ||||||||
\(99\) | −2.43614e9 | + | 1.07586e10i | −0.256169 | + | 1.13130i | ||||
\(100\) | 5.09414e8 | 0.0509414 | ||||||||
\(101\) | 4.23015e9i | 0.402484i | 0.979542 | + | 0.201242i | \(0.0644978\pi\) | ||||
−0.979542 | + | 0.201242i | \(0.935502\pi\) | |||||||
\(102\) | −2.48676e8 | + | 2.22423e9i | −0.0225234 | + | 0.201455i | ||||
\(103\) | 4.41761e9 | 0.381067 | 0.190533 | − | 0.981681i | \(-0.438978\pi\) | ||||
0.190533 | + | 0.981681i | \(0.438978\pi\) | |||||||
\(104\) | − | 6.04545e9i | − | 0.496892i | ||||||
\(105\) | 1.18377e10 | + | 1.32349e9i | 0.927514 | + | 0.103699i | ||||
\(106\) | −5.15433e9 | −0.385162 | ||||||||
\(107\) | − | 3.19343e9i | − | 0.227687i | −0.993499 | − | 0.113844i | \(-0.963684\pi\) | ||
0.993499 | − | 0.113844i | \(-0.0363163\pi\) | |||||||
\(108\) | 1.43009e9 | − | 4.12098e9i | 0.0973294 | − | 0.280467i | ||||
\(109\) | −1.54650e10 | −1.00512 | −0.502561 | − | 0.864542i | \(-0.667609\pi\) | ||||
−0.502561 | + | 0.864542i | \(0.667609\pi\) | |||||||
\(110\) | − | 1.42573e10i | − | 0.885269i | ||||||
\(111\) | 1.64192e9 | − | 1.46858e10i | 0.0974400 | − | 0.871529i | ||||
\(112\) | −1.11136e10 | −0.630615 | ||||||||
\(113\) | 2.53338e10i | 1.37501i | 0.726177 | + | 0.687507i | \(0.241295\pi\) | ||||
−0.726177 | + | 0.687507i | \(0.758705\pi\) | |||||||
\(114\) | 6.15251e9 | + | 6.87872e8i | 0.319542 | + | 0.0357259i | ||||
\(115\) | 7.55904e9 | 0.375818 | ||||||||
\(116\) | 9.67392e8i | 0.0460588i | ||||||||
\(117\) | 9.77054e9 | + | 2.21242e9i | 0.445645 | + | 0.100911i | ||||
\(118\) | 1.74187e10 | 0.761389 | ||||||||
\(119\) | − | 5.91549e9i | − | 0.247888i | ||||||
\(120\) | −2.73653e9 | + | 2.44763e10i | −0.109975 | + | 0.983646i | ||||
\(121\) | −8.96058e9 | −0.345469 | ||||||||
\(122\) | 2.76591e10i | 1.02338i | ||||||||
\(123\) | −4.38720e10 | − | 4.90504e9i | −1.55834 | − | 0.174228i | ||||
\(124\) | −9.05711e9 | −0.308945 | ||||||||
\(125\) | − | 3.25423e10i | − | 1.06635i | ||||||
\(126\) | 6.03052e9 | − | 2.66322e10i | 0.189890 | − | 0.838599i | ||||
\(127\) | 5.84098e10 | 1.76794 | 0.883970 | − | 0.467544i | \(-0.154861\pi\) | ||||
0.883970 | + | 0.467544i | \(0.154861\pi\) | |||||||
\(128\) | − | 1.18864e10i | − | 0.345938i | ||||||
\(129\) | −2.90033e9 | + | 2.59414e10i | −0.0811894 | + | 0.726180i | ||||
\(130\) | −1.29480e10 | −0.348727 | ||||||||
\(131\) | − | 5.67731e10i | − | 1.47159i | −0.677205 | − | 0.735794i | \(-0.736809\pi\) | ||
0.677205 | − | 0.735794i | \(-0.263191\pi\) | |||||||
\(132\) | 1.37146e10 | + | 1.53334e9i | 0.342226 | + | 0.0382620i | ||||
\(133\) | −1.63630e10 | −0.393193 | ||||||||
\(134\) | 5.03583e10i | 1.16559i | ||||||||
\(135\) | −3.85566e10 | − | 1.33802e10i | −0.859865 | − | 0.298396i | ||||
\(136\) | 1.22312e10 | 0.262890 | ||||||||
\(137\) | 7.89283e10i | 1.63542i | 0.575629 | + | 0.817711i | \(0.304757\pi\) | ||||
−0.575629 | + | 0.817711i | \(0.695243\pi\) | |||||||
\(138\) | 1.92542e9 | − | 1.72214e10i | 0.0384706 | − | 0.344092i | ||||
\(139\) | 8.89683e9 | 0.171459 | 0.0857297 | − | 0.996318i | \(-0.472678\pi\) | ||||
0.0857297 | + | 0.996318i | \(0.472678\pi\) | |||||||
\(140\) | − | 1.49016e10i | − | 0.277071i | ||||||
\(141\) | 6.47197e10 | + | 7.23588e9i | 1.16129 | + | 0.129836i | ||||
\(142\) | −7.20026e10 | −1.24711 | ||||||||
\(143\) | 3.16931e10i | 0.530010i | ||||||||
\(144\) | 3.71384e10 | + | 8.40951e9i | 0.599805 | + | 0.135818i | ||||
\(145\) | 9.05109e9 | 0.141209 | ||||||||
\(146\) | − | 7.63804e10i | − | 1.15138i | ||||||
\(147\) | −3.92459e8 | + | 3.51026e9i | −0.00571751 | + | 0.0511390i | ||||
\(148\) | −1.84868e10 | −0.260347 | ||||||||
\(149\) | − | 7.43262e10i | − | 1.01207i | −0.862513 | − | 0.506035i | \(-0.831111\pi\) | ||
0.862513 | − | 0.506035i | \(-0.168889\pi\) | |||||||
\(150\) | −1.08586e10 | − | 1.21402e9i | −0.142993 | − | 0.0159872i | ||||
\(151\) | −5.90950e10 | −0.752776 | −0.376388 | − | 0.926462i | \(-0.622834\pi\) | ||||
−0.376388 | + | 0.926462i | \(0.622834\pi\) | |||||||
\(152\) | − | 3.38331e10i | − | 0.416988i | ||||||
\(153\) | −4.47618e9 | + | 1.97678e10i | −0.0533888 | + | 0.235777i | ||||
\(154\) | 8.63878e10 | 0.997353 | ||||||||
\(155\) | 8.47399e10i | 0.947174i | ||||||||
\(156\) | 1.39252e9 | − | 1.24551e10i | 0.0150723 | − | 0.134810i | ||||
\(157\) | −3.81863e10 | −0.400322 | −0.200161 | − | 0.979763i | \(-0.564147\pi\) | ||||
−0.200161 | + | 0.979763i | \(0.564147\pi\) | |||||||
\(158\) | 3.99446e10i | 0.405670i | ||||||||
\(159\) | −4.63890e10 | − | 5.18645e9i | −0.456488 | − | 0.0510369i | ||||
\(160\) | 5.45694e10 | 0.520414 | ||||||||
\(161\) | 4.58016e10i | 0.423400i | ||||||||
\(162\) | −4.03045e10 | + | 8.44338e10i | −0.361225 | + | 0.756731i | ||||
\(163\) | 1.61034e11 | 1.39952 | 0.699760 | − | 0.714378i | \(-0.253290\pi\) | ||||
0.699760 | + | 0.714378i | \(0.253290\pi\) | |||||||
\(164\) | 5.52271e10i | 0.465514i | ||||||||
\(165\) | 1.43462e10 | − | 1.28316e11i | 0.117305 | − | 1.04921i | ||||
\(166\) | −3.39664e10 | −0.269469 | ||||||||
\(167\) | − | 5.95748e10i | − | 0.458649i | −0.973350 | − | 0.229325i | \(-0.926348\pi\) | ||
0.973350 | − | 0.229325i | \(-0.0736517\pi\) | |||||||
\(168\) | −1.48306e11 | − | 1.65811e10i | −1.10819 | − | 0.123899i | ||||
\(169\) | −1.09076e11 | −0.791217 | ||||||||
\(170\) | − | 2.61965e10i | − | 0.184501i | ||||||
\(171\) | 5.46805e10 | + | 1.23817e10i | 0.373983 | + | 0.0846836i | ||||
\(172\) | 3.26556e10 | 0.216928 | ||||||||
\(173\) | − | 2.06971e11i | − | 1.33561i | −0.744336 | − | 0.667805i | \(-0.767234\pi\) | ||
0.744336 | − | 0.667805i | \(-0.232766\pi\) | |||||||
\(174\) | 2.30547e9 | − | 2.06207e10i | 0.0144548 | − | 0.129288i | ||||
\(175\) | 2.88791e10 | 0.175952 | ||||||||
\(176\) | 1.20467e11i | 0.713354i | ||||||||
\(177\) | 1.56769e11 | + | 1.75273e10i | 0.902387 | + | 0.100890i | ||||
\(178\) | 1.61547e11 | 0.904066 | ||||||||
\(179\) | 5.22122e10i | 0.284123i | 0.989858 | + | 0.142062i | \(0.0453732\pi\) | ||||
−0.989858 | + | 0.142062i | \(0.954627\pi\) | |||||||
\(180\) | −1.12758e10 | + | 4.97967e10i | −0.0596741 | + | 0.263535i | ||||
\(181\) | −3.38840e11 | −1.74422 | −0.872112 | − | 0.489306i | \(-0.837250\pi\) | ||||
−0.872112 | + | 0.489306i | \(0.837250\pi\) | |||||||
\(182\) | − | 7.84542e10i | − | 0.392880i | ||||||
\(183\) | −2.78314e10 | + | 2.48932e11i | −0.135606 | + | 1.21290i | ||||
\(184\) | −9.47019e10 | −0.449024 | ||||||||
\(185\) | 1.72966e11i | 0.798182i | ||||||||
\(186\) | 1.93059e11 | + | 2.15847e10i | 0.867214 | + | 0.0969575i | ||||
\(187\) | −6.41217e10 | −0.280412 | ||||||||
\(188\) | − | 8.14707e10i | − | 0.346906i | ||||||
\(189\) | 8.10728e10 | − | 2.33622e11i | 0.336176 | − | 0.968733i | ||||
\(190\) | −7.24629e10 | −0.292650 | ||||||||
\(191\) | 1.55519e11i | 0.611812i | 0.952062 | + | 0.305906i | \(0.0989593\pi\) | ||||
−0.952062 | + | 0.305906i | \(0.901041\pi\) | |||||||
\(192\) | 3.17290e10 | − | 2.83792e11i | 0.121604 | − | 1.08766i | ||||
\(193\) | 3.50355e11 | 1.30834 | 0.654172 | − | 0.756346i | \(-0.273017\pi\) | ||||
0.654172 | + | 0.756346i | \(0.273017\pi\) | |||||||
\(194\) | − | 4.27433e10i | − | 0.155546i | ||||||
\(195\) | −1.16532e11 | − | 1.30287e10i | −0.413306 | − | 0.0462090i | ||||
\(196\) | 4.41879e9 | 0.0152765 | ||||||||
\(197\) | − | 3.11997e11i | − | 1.05152i | −0.850632 | − | 0.525762i | \(-0.823780\pi\) | ||
0.850632 | − | 0.525762i | \(-0.176220\pi\) | |||||||
\(198\) | −2.88683e11 | − | 6.53686e10i | −0.948626 | − | 0.214804i | ||||
\(199\) | −1.51943e11 | −0.486871 | −0.243436 | − | 0.969917i | \(-0.578274\pi\) | ||||
−0.243436 | + | 0.969917i | \(0.578274\pi\) | |||||||
\(200\) | 5.97120e10i | 0.186600i | ||||||||
\(201\) | −5.06720e10 | + | 4.53225e11i | −0.154450 | + | 1.38144i | ||||
\(202\) | −1.13507e11 | −0.337493 | ||||||||
\(203\) | 5.48422e10i | 0.159087i | ||||||||
\(204\) | 2.51992e10 | + | 2.81736e9i | 0.0713241 | + | 0.00797428i | ||||
\(205\) | 5.16715e11 | 1.42719 | ||||||||
\(206\) | 1.18537e11i | 0.319534i | ||||||||
\(207\) | 3.46575e10 | − | 1.53056e11i | 0.0911896 | − | 0.402715i | ||||
\(208\) | 1.09404e11 | 0.281006 | ||||||||
\(209\) | 1.77369e11i | 0.444781i | ||||||||
\(210\) | −3.55131e10 | + | 3.17639e11i | −0.0869544 | + | 0.777744i | ||||
\(211\) | 1.36229e11 | 0.325729 | 0.162864 | − | 0.986648i | \(-0.447927\pi\) | ||||
0.162864 | + | 0.986648i | \(0.447927\pi\) | |||||||
\(212\) | 5.83956e10i | 0.136364i | ||||||||
\(213\) | −6.48023e11 | − | 7.24512e10i | −1.47806 | − | 0.165252i | ||||
\(214\) | 8.56887e10 | 0.190922 | ||||||||
\(215\) | − | 3.05532e11i | − | 0.665065i | ||||||
\(216\) | 4.83049e11 | + | 1.67631e11i | 1.02736 | + | 0.356521i | ||||
\(217\) | −5.13455e11 | −1.06710 | ||||||||
\(218\) | − | 4.14970e11i | − | 0.842820i | ||||||
\(219\) | 7.68563e10 | − | 6.87423e11i | 0.152566 | − | 1.36459i | ||||
\(220\) | −1.61527e11 | −0.313424 | ||||||||
\(221\) | 5.82330e10i | 0.110461i | ||||||||
\(222\) | 3.94061e11 | + | 4.40573e10i | 0.730800 | + | 0.0817059i | ||||
\(223\) | 1.15573e11 | 0.209571 | 0.104786 | − | 0.994495i | \(-0.466584\pi\) | ||||
0.104786 | + | 0.994495i | \(0.466584\pi\) | |||||||
\(224\) | 3.30646e11i | 0.586304i | ||||||||
\(225\) | −9.65055e10 | − | 2.18524e10i | −0.167355 | − | 0.0378955i | ||||
\(226\) | −6.79776e11 | −1.15298 | ||||||||
\(227\) | − | 2.22416e10i | − | 0.0369009i | −0.999830 | − | 0.0184505i | \(-0.994127\pi\) | ||
0.999830 | − | 0.0184505i | \(-0.00587330\pi\) | |||||||
\(228\) | 7.79318e9 | − | 6.97044e10i | 0.0126485 | − | 0.113132i | ||||
\(229\) | 5.48204e11 | 0.870492 | 0.435246 | − | 0.900311i | \(-0.356661\pi\) | ||||
0.435246 | + | 0.900311i | \(0.356661\pi\) | |||||||
\(230\) | 2.02830e11i | 0.315133i | ||||||||
\(231\) | 7.77491e11 | + | 8.69261e10i | 1.18205 | + | 0.132157i | ||||
\(232\) | −1.13395e11 | −0.168715 | ||||||||
\(233\) | 8.58665e11i | 1.25039i | 0.780470 | + | 0.625193i | \(0.214980\pi\) | ||||
−0.780470 | + | 0.625193i | \(0.785020\pi\) | |||||||
\(234\) | −5.93653e10 | + | 2.62171e11i | −0.0846162 | + | 0.373685i | ||||
\(235\) | −7.62254e11 | −1.06356 | ||||||||
\(236\) | − | 1.97344e11i | − | 0.269565i | ||||||
\(237\) | −4.01935e10 | + | 3.59501e11i | −0.0537544 | + | 0.480794i | ||||
\(238\) | 1.58729e11 | 0.207861 | ||||||||
\(239\) | − | 9.11055e11i | − | 1.16830i | −0.811645 | − | 0.584151i | \(-0.801428\pi\) | ||
0.811645 | − | 0.584151i | \(-0.198572\pi\) | |||||||
\(240\) | −4.42944e11 | − | 4.95227e10i | −0.556279 | − | 0.0621939i | ||||
\(241\) | 3.71250e11 | 0.456648 | 0.228324 | − | 0.973585i | \(-0.426676\pi\) | ||||
0.228324 | + | 0.973585i | \(0.426676\pi\) | |||||||
\(242\) | − | 2.40437e11i | − | 0.289685i | ||||||
\(243\) | −4.47700e11 | + | 7.19349e11i | −0.528392 | + | 0.849001i | ||||
\(244\) | 3.13361e11 | 0.362323 | ||||||||
\(245\) | − | 4.13430e10i | − | 0.0468351i | ||||||
\(246\) | 1.31616e11 | − | 1.17721e12i | 0.146094 | − | 1.30671i | ||||
\(247\) | 1.61080e11 | 0.175209 | ||||||||
\(248\) | − | 1.06165e12i | − | 1.13168i | ||||||
\(249\) | −3.05698e11 | − | 3.41780e10i | −0.319371 | − | 0.0357068i | ||||
\(250\) | 8.73202e11 | 0.894159 | ||||||||
\(251\) | 1.75865e11i | 0.176527i | 0.996097 | + | 0.0882636i | \(0.0281318\pi\) | ||||
−0.996097 | + | 0.0882636i | \(0.971868\pi\) | |||||||
\(252\) | −3.01727e11 | − | 6.83223e10i | −0.296901 | − | 0.0672294i | ||||
\(253\) | 4.96472e11 | 0.478952 | ||||||||
\(254\) | 1.56730e12i | 1.48246i | ||||||||
\(255\) | 2.63597e10 | − | 2.35768e11i | 0.0244478 | − | 0.218668i | ||||
\(256\) | −8.84406e11 | −0.804362 | ||||||||
\(257\) | 7.60350e11i | 0.678185i | 0.940753 | + | 0.339093i | \(0.110120\pi\) | ||||
−0.940753 | + | 0.339093i | \(0.889880\pi\) | |||||||
\(258\) | −6.96080e11 | − | 7.78241e10i | −0.608920 | − | 0.0680794i | ||||
\(259\) | −1.04803e12 | −0.899240 | ||||||||
\(260\) | 1.46693e11i | 0.123465i | ||||||||
\(261\) | 4.14984e10 | − | 1.83267e11i | 0.0342633 | − | 0.151315i | ||||
\(262\) | 1.52338e12 | 1.23396 | ||||||||
\(263\) | 2.37857e11i | 0.189033i | 0.995523 | + | 0.0945163i | \(0.0301304\pi\) | ||||
−0.995523 | + | 0.0945163i | \(0.969870\pi\) | |||||||
\(264\) | −1.79733e11 | + | 1.60758e12i | −0.140155 | + | 1.25358i | ||||
\(265\) | 5.46359e11 | 0.418070 | ||||||||
\(266\) | − | 4.39066e11i | − | 0.329702i | ||||||
\(267\) | 1.45393e12 | + | 1.62554e11i | 1.07149 | + | 0.119796i | ||||
\(268\) | 5.70530e11 | 0.412671 | ||||||||
\(269\) | − | 1.57259e12i | − | 1.11649i | −0.829678 | − | 0.558243i | \(-0.811476\pi\) | ||
0.829678 | − | 0.558243i | \(-0.188524\pi\) | |||||||
\(270\) | 3.59027e11 | − | 1.03458e12i | 0.250212 | − | 0.721019i | ||||
\(271\) | −1.66619e12 | −1.13993 | −0.569965 | − | 0.821669i | \(-0.693043\pi\) | ||||
−0.569965 | + | 0.821669i | \(0.693043\pi\) | |||||||
\(272\) | 2.21347e11i | 0.148672i | ||||||||
\(273\) | 7.89431e10 | − | 7.06088e11i | 0.0520596 | − | 0.465635i | ||||
\(274\) | −2.11787e12 | −1.37134 | ||||||||
\(275\) | − | 3.13039e11i | − | 0.199037i | ||||||
\(276\) | −1.95109e11 | − | 2.18138e10i | −0.121824 | − | 0.0136203i | ||||
\(277\) | −2.06519e12 | −1.26637 | −0.633186 | − | 0.774000i | \(-0.718253\pi\) | ||||
−0.633186 | + | 0.774000i | \(0.718253\pi\) | |||||||
\(278\) | 2.38727e11i | 0.143773i | ||||||||
\(279\) | 1.71582e12 | + | 3.88525e11i | 1.01496 | + | 0.229825i | ||||
\(280\) | 1.74672e12 | 1.01492 | ||||||||
\(281\) | − | 2.68989e12i | − | 1.53533i | −0.640849 | − | 0.767667i | \(-0.721417\pi\) | ||
0.640849 | − | 0.767667i | \(-0.278583\pi\) | |||||||
\(282\) | −1.94159e11 | + | 1.73661e12i | −0.108871 | + | 0.973772i | ||||
\(283\) | 1.44533e12 | 0.796225 | 0.398113 | − | 0.917337i | \(-0.369665\pi\) | ||||
0.398113 | + | 0.917337i | \(0.369665\pi\) | |||||||
\(284\) | 8.15747e11i | 0.441534i | ||||||||
\(285\) | −6.52166e11 | − | 7.29144e10i | −0.346844 | − | 0.0387783i | ||||
\(286\) | −8.50414e11 | −0.444427 | ||||||||
\(287\) | 3.13087e12i | 1.60789i | ||||||||
\(288\) | 2.50196e11 | − | 1.10492e12i | 0.126275 | − | 0.557660i | ||||
\(289\) | 1.89818e12 | 0.941559 | ||||||||
\(290\) | 2.42866e11i | 0.118407i | ||||||||
\(291\) | 4.30096e10 | − | 3.84690e11i | 0.0206111 | − | 0.184351i | ||||
\(292\) | −8.65345e11 | −0.407638 | ||||||||
\(293\) | 3.39085e12i | 1.57026i | 0.619332 | + | 0.785129i | \(0.287403\pi\) | ||||
−0.619332 | + | 0.785129i | \(0.712597\pi\) | |||||||
\(294\) | −9.41901e10 | − | 1.05308e10i | −0.0428814 | − | 0.00479428i | ||||
\(295\) | −1.84639e12 | −0.826442 | ||||||||
\(296\) | − | 2.16697e12i | − | 0.953661i | ||||||
\(297\) | −2.53237e12 | − | 8.78799e11i | −1.09583 | − | 0.380283i | ||||
\(298\) | 1.99438e12 | 0.848646 | ||||||||
\(299\) | − | 4.50877e11i | − | 0.188670i | ||||||
\(300\) | −1.37542e10 | + | 1.23021e11i | −0.00566016 | + | 0.0506260i | ||||
\(301\) | 1.85127e12 | 0.749269 | ||||||||
\(302\) | − | 1.58568e12i | − | 0.631222i | ||||||
\(303\) | −1.02156e12 | − | 1.14214e11i | −0.399992 | − | 0.0447205i | ||||
\(304\) | 6.12274e11 | 0.235818 | ||||||||
\(305\) | − | 2.93186e12i | − | 1.11082i | ||||||
\(306\) | −5.30427e11 | − | 1.20108e11i | −0.197705 | − | 0.0447679i | ||||
\(307\) | 2.07104e12 | 0.759447 | 0.379723 | − | 0.925100i | \(-0.376019\pi\) | ||||
0.379723 | + | 0.925100i | \(0.376019\pi\) | |||||||
\(308\) | − | 9.78723e11i | − | 0.353107i | ||||||
\(309\) | −1.19275e11 | + | 1.06683e12i | −0.0423407 | + | 0.378707i | ||||
\(310\) | −2.27381e12 | −0.794229 | ||||||||
\(311\) | 2.14388e12i | 0.736882i | 0.929651 | + | 0.368441i | \(0.120108\pi\) | ||||
−0.929651 | + | 0.368441i | \(0.879892\pi\) | |||||||
\(312\) | 1.45995e12 | + | 1.63227e11i | 0.493815 | + | 0.0552102i | ||||
\(313\) | −8.14838e11 | −0.271237 | −0.135619 | − | 0.990761i | \(-0.543302\pi\) | ||||
−0.135619 | + | 0.990761i | \(0.543302\pi\) | |||||||
\(314\) | − | 1.02465e12i | − | 0.335680i | ||||||
\(315\) | −6.39235e11 | + | 2.82301e12i | −0.206114 | + | 0.910249i | ||||
\(316\) | 4.52549e11 | 0.143625 | ||||||||
\(317\) | 8.21225e11i | 0.256546i | 0.991739 | + | 0.128273i | \(0.0409434\pi\) | ||||
−0.991739 | + | 0.128273i | \(0.959057\pi\) | |||||||
\(318\) | 1.39167e11 | − | 1.24475e12i | 0.0427958 | − | 0.382777i | ||||
\(319\) | 5.94469e11 | 0.179960 | ||||||||
\(320\) | 3.34244e12i | 0.996126i | ||||||||
\(321\) | 7.71199e11 | + | 8.62226e10i | 0.226277 | + | 0.0252986i | ||||
\(322\) | −1.22899e12 | −0.355032 | ||||||||
\(323\) | 3.25898e11i | 0.0926979i | ||||||||
\(324\) | 9.56585e11 | + | 4.56626e11i | 0.267916 | + | 0.127890i | ||||
\(325\) | −2.84290e11 | −0.0784052 | ||||||||
\(326\) | 4.32099e12i | 1.17353i | ||||||||
\(327\) | 4.17556e11 | − | 3.73473e12i | 0.111680 | − | 0.998898i | ||||
\(328\) | −6.47356e12 | −1.70519 | ||||||||
\(329\) | − | 4.61864e12i | − | 1.19821i | ||||||
\(330\) | 3.44308e12 | + | 3.84948e11i | 0.879787 | + | 0.0983632i | ||||
\(331\) | 1.76733e12 | 0.444814 | 0.222407 | − | 0.974954i | \(-0.428609\pi\) | ||||
0.222407 | + | 0.974954i | \(0.428609\pi\) | |||||||
\(332\) | 3.84819e11i | 0.0954040i | ||||||||
\(333\) | 3.50222e12 | + | 7.93032e11i | 0.855306 | + | 0.193673i | ||||
\(334\) | 1.59856e12 | 0.384589 | ||||||||
\(335\) | − | 5.33798e12i | − | 1.26518i | ||||||
\(336\) | 3.00067e11 | − | 2.68388e12i | 0.0700683 | − | 0.626710i | ||||
\(337\) | −5.35777e11 | −0.123264 | −0.0616318 | − | 0.998099i | \(-0.519630\pi\) | ||||
−0.0616318 | + | 0.998099i | \(0.519630\pi\) | |||||||
\(338\) | − | 2.92682e12i | − | 0.663456i | ||||||
\(339\) | −6.11798e12 | − | 6.84011e11i | −1.36650 | − | 0.152779i | ||||
\(340\) | −2.96791e11 | −0.0653214 | ||||||||
\(341\) | 5.56565e12i | 1.20710i | ||||||||
\(342\) | −3.32236e11 | + | 1.46723e12i | −0.0710094 | + | 0.313594i | ||||
\(343\) | −4.61767e12 | −0.972641 | ||||||||
\(344\) | 3.82779e12i | 0.794614i | ||||||||
\(345\) | −2.04094e11 | + | 1.82547e12i | −0.0417575 | + | 0.373491i | ||||
\(346\) | 5.55362e12 | 1.11994 | ||||||||
\(347\) | − | 4.87335e12i | − | 0.968681i | −0.874880 | − | 0.484340i | \(-0.839060\pi\) | ||
0.874880 | − | 0.484340i | \(-0.160940\pi\) | |||||||
\(348\) | −2.33621e11 | − | 2.61196e10i | −0.0457736 | − | 0.00511764i | ||||
\(349\) | 7.83766e10 | 0.0151377 | 0.00756884 | − | 0.999971i | \(-0.497591\pi\) | ||||
0.00756884 | + | 0.999971i | \(0.497591\pi\) | |||||||
\(350\) | 7.74908e11i | 0.147540i | ||||||||
\(351\) | −7.98093e11 | + | 2.29981e12i | −0.149802 | + | 0.431674i | ||||
\(352\) | 3.58408e12 | 0.663230 | ||||||||
\(353\) | 4.90804e12i | 0.895437i | 0.894175 | + | 0.447718i | \(0.147763\pi\) | ||||
−0.894175 | + | 0.447718i | \(0.852237\pi\) | |||||||
\(354\) | −4.70306e11 | + | 4.20654e12i | −0.0845988 | + | 0.756674i | ||||
\(355\) | 7.63227e12 | 1.35367 | ||||||||
\(356\) | − | 1.83024e12i | − | 0.320079i | ||||||
\(357\) | 1.42856e12 | + | 1.59718e11i | 0.246353 | + | 0.0275431i | ||||
\(358\) | −1.40100e12 | −0.238245 | ||||||||
\(359\) | − | 8.23695e11i | − | 0.138132i | −0.997612 | − | 0.0690660i | \(-0.977998\pi\) | ||
0.997612 | − | 0.0690660i | \(-0.0220019\pi\) | |||||||
\(360\) | −5.83702e12 | − | 1.32172e12i | −0.965336 | − | 0.218588i | ||||
\(361\) | −5.22959e12 | −0.852966 | ||||||||
\(362\) | − | 9.09204e12i | − | 1.46258i | ||||||
\(363\) | 2.41936e11 | − | 2.16394e12i | 0.0383854 | − | 0.343330i | ||||
\(364\) | −8.88840e11 | −0.139097 | ||||||||
\(365\) | 8.09632e12i | 1.24975i | ||||||||
\(366\) | −6.67954e12 | − | 7.46796e11i | −1.01705 | − | 0.113709i | ||||
\(367\) | 5.55933e12 | 0.835011 | 0.417506 | − | 0.908674i | \(-0.362904\pi\) | ||||
0.417506 | + | 0.908674i | \(0.362904\pi\) | |||||||
\(368\) | − | 1.71381e12i | − | 0.253936i | ||||||
\(369\) | 2.36909e12 | − | 1.04625e13i | 0.346298 | − | 1.52933i | ||||
\(370\) | −4.64116e12 | −0.669296 | ||||||||
\(371\) | 3.31049e12i | 0.471002i | ||||||||
\(372\) | 2.44542e11 | − | 2.18725e12i | 0.0343272 | − | 0.307032i | ||||
\(373\) | −4.21921e10 | −0.00584369 | −0.00292185 | − | 0.999996i | \(-0.500930\pi\) | ||||
−0.00292185 | + | 0.999996i | \(0.500930\pi\) | |||||||
\(374\) | − | 1.72057e12i | − | 0.235133i | ||||||
\(375\) | 7.85882e12 | + | 8.78643e11i | 1.05974 | + | 0.118483i | ||||
\(376\) | 9.54975e12 | 1.27073 | ||||||||
\(377\) | − | 5.39875e11i | − | 0.0708902i | ||||||
\(378\) | 6.26873e12 | + | 2.17541e12i | 0.812307 | + | 0.281892i | ||||
\(379\) | −9.51422e12 | −1.21668 | −0.608341 | − | 0.793676i | \(-0.708165\pi\) | ||||
−0.608341 | + | 0.793676i | \(0.708165\pi\) | |||||||
\(380\) | 8.20962e11i | 0.103611i | ||||||||
\(381\) | −1.57707e12 | + | 1.41057e13i | −0.196438 | + | 1.75699i | ||||
\(382\) | −4.17302e12 | −0.513020 | ||||||||
\(383\) | − | 2.82742e12i | − | 0.343081i | −0.985177 | − | 0.171540i | \(-0.945126\pi\) | ||
0.985177 | − | 0.171540i | \(-0.0548744\pi\) | |||||||
\(384\) | 2.87050e12 | + | 3.20932e11i | 0.343796 | + | 0.0384376i | ||||
\(385\) | −9.15711e12 | −1.08257 | ||||||||
\(386\) | 9.40101e12i | 1.09708i | ||||||||
\(387\) | −6.18641e12 | − | 1.40083e12i | −0.712662 | − | 0.161373i | ||||
\(388\) | −4.84256e11 | −0.0550702 | ||||||||
\(389\) | − | 1.12113e12i | − | 0.125866i | −0.998018 | − | 0.0629330i | \(-0.979955\pi\) | ||
0.998018 | − | 0.0629330i | \(-0.0200455\pi\) | |||||||
\(390\) | 3.49596e11 | − | 3.12688e12i | 0.0387475 | − | 0.346568i | ||||
\(391\) | 9.12219e11 | 0.0998195 | ||||||||
\(392\) | 5.17958e11i | 0.0559583i | ||||||||
\(393\) | 1.37104e13 | + | 1.53287e12i | 1.46248 | + | 0.163510i | ||||
\(394\) | 8.37176e12 | 0.881730 | ||||||||
\(395\) | − | 4.23413e12i | − | 0.440330i | ||||||
\(396\) | −7.40587e11 | + | 3.27061e12i | −0.0760502 | + | 0.335856i | ||||
\(397\) | −7.46731e12 | −0.757202 | −0.378601 | − | 0.925560i | \(-0.623595\pi\) | ||||
−0.378601 | + | 0.925560i | \(0.623595\pi\) | |||||||
\(398\) | − | 4.07705e12i | − | 0.408254i | ||||||
\(399\) | 4.41802e11 | − | 3.95160e12i | 0.0436881 | − | 0.390758i | ||||
\(400\) | −1.08060e12 | −0.105528 | ||||||||
\(401\) | − | 1.62961e13i | − | 1.57167i | −0.618438 | − | 0.785834i | \(-0.712234\pi\) | ||
0.618438 | − | 0.785834i | \(-0.287766\pi\) | |||||||
\(402\) | −1.21613e13 | − | 1.35967e12i | −1.15838 | − | 0.129510i | ||||
\(403\) | 5.05452e12 | 0.475505 | ||||||||
\(404\) | 1.28597e12i | 0.119488i | ||||||||
\(405\) | 4.27228e12 | − | 8.94998e12i | 0.392089 | − | 0.821386i | ||||
\(406\) | −1.47157e12 | −0.133399 | ||||||||
\(407\) | 1.13603e13i | 1.01722i | ||||||||
\(408\) | −3.30242e11 | + | 2.95378e12i | −0.0292100 | + | 0.261262i | ||||
\(409\) | 1.05134e13 | 0.918602 | 0.459301 | − | 0.888281i | \(-0.348100\pi\) | ||||
0.459301 | + | 0.888281i | \(0.348100\pi\) | |||||||
\(410\) | 1.38649e13i | 1.19673i | ||||||||
\(411\) | −1.90608e13 | − | 2.13106e12i | −1.62529 | − | 0.181713i | ||||
\(412\) | 1.34295e12 | 0.113129 | ||||||||
\(413\) | − | 1.11876e13i | − | 0.931078i | ||||||
\(414\) | 4.10691e12 | + | 9.29958e11i | 0.337686 | + | 0.0764648i | ||||
\(415\) | 3.60044e12 | 0.292493 | ||||||||
\(416\) | − | 3.25493e12i | − | 0.261261i | ||||||
\(417\) | −2.40214e11 | + | 2.14854e12i | −0.0190510 | + | 0.170398i | ||||
\(418\) | −4.75931e12 | −0.372960 | ||||||||
\(419\) | 2.18708e13i | 1.69354i | 0.531960 | + | 0.846769i | \(0.321456\pi\) | ||||
−0.531960 | + | 0.846769i | \(0.678544\pi\) | |||||||
\(420\) | 3.59866e12 | + | 4.02342e11i | 0.275356 | + | 0.0307857i | ||||
\(421\) | 6.75679e12 | 0.510893 | 0.255447 | − | 0.966823i | \(-0.417778\pi\) | ||||
0.255447 | + | 0.966823i | \(0.417778\pi\) | |||||||
\(422\) | 3.65540e12i | 0.273132i | ||||||||
\(423\) | −3.49486e12 | + | 1.54341e13i | −0.258065 | + | 1.13967i | ||||
\(424\) | −6.84496e12 | −0.499507 | ||||||||
\(425\) | − | 5.75178e11i | − | 0.0414818i | ||||||
\(426\) | 1.94407e12 | − | 1.73883e13i | 0.138568 | − | 1.23939i | ||||
\(427\) | 1.77647e13 | 1.25146 | ||||||||
\(428\) | − | 9.70803e11i | − | 0.0675946i | ||||||
\(429\) | −7.65373e12 | − | 8.55713e11i | −0.526728 | − | 0.0588900i | ||||
\(430\) | 8.19827e12 | 0.557674 | ||||||||
\(431\) | − | 1.58220e13i | − | 1.06383i | −0.846797 | − | 0.531917i | \(-0.821472\pi\) | ||
0.846797 | − | 0.531917i | \(-0.178528\pi\) | |||||||
\(432\) | −3.03359e12 | + | 8.74168e12i | −0.201622 | + | 0.581000i | ||||
\(433\) | −1.46123e13 | −0.960020 | −0.480010 | − | 0.877263i | \(-0.659367\pi\) | ||||
−0.480010 | + | 0.877263i | \(0.659367\pi\) | |||||||
\(434\) | − | 1.37774e13i | − | 0.894787i | ||||||
\(435\) | −2.44380e11 | + | 2.18580e12i | −0.0156898 | + | 0.140334i | ||||
\(436\) | −4.70137e12 | −0.298395 | ||||||||
\(437\) | − | 2.52332e12i | − | 0.158331i | ||||||
\(438\) | 1.84455e13 | + | 2.06227e12i | 1.14425 | + | 0.127931i | ||||
\(439\) | −1.26826e13 | −0.777831 | −0.388915 | − | 0.921273i | \(-0.627150\pi\) | ||||
−0.388915 | + | 0.921273i | \(0.627150\pi\) | |||||||
\(440\) | − | 1.89338e13i | − | 1.14808i | ||||||
\(441\) | −8.37114e11 | − | 1.89554e11i | −0.0501871 | − | 0.0113642i | ||||
\(442\) | −1.56255e12 | −0.0926240 | ||||||||
\(443\) | 4.68652e12i | 0.274683i | 0.990524 | + | 0.137341i | \(0.0438558\pi\) | ||||
−0.990524 | + | 0.137341i | \(0.956144\pi\) | |||||||
\(444\) | 4.99144e11 | − | 4.46448e12i | 0.0289275 | − | 0.258735i | ||||
\(445\) | −1.71240e13 | −0.981309 | ||||||||
\(446\) | 3.10115e12i | 0.175731i | ||||||||
\(447\) | 1.79494e13 | + | 2.00681e12i | 1.00580 | + | 0.112452i | ||||
\(448\) | −2.02525e13 | −1.12225 | ||||||||
\(449\) | 2.82413e13i | 1.54758i | 0.633443 | + | 0.773789i | \(0.281641\pi\) | ||||
−0.633443 | + | 0.773789i | \(0.718359\pi\) | |||||||
\(450\) | 5.86363e11 | − | 2.58952e12i | 0.0317763 | − | 0.140332i | ||||
\(451\) | 3.39374e13 | 1.81885 | ||||||||
\(452\) | 7.70146e12i | 0.408207i | ||||||||
\(453\) | 1.59556e12 | − | 1.42712e13i | 0.0836418 | − | 0.748115i | ||||
\(454\) | 5.96805e11 | 0.0309424 | ||||||||
\(455\) | 8.31615e12i | 0.426447i | ||||||||
\(456\) | 8.17054e12 | + | 9.13494e11i | 0.414406 | + | 0.0463320i | ||||
\(457\) | 9.22854e12 | 0.462969 | 0.231484 | − | 0.972839i | \(-0.425642\pi\) | ||||
0.231484 | + | 0.972839i | \(0.425642\pi\) | |||||||
\(458\) | 1.47099e13i | 0.729930i | ||||||||
\(459\) | −4.65299e12 | − | 1.61471e12i | −0.228385 | − | 0.0792557i | ||||
\(460\) | 2.29795e12 | 0.111571 | ||||||||
\(461\) | − | 7.80976e12i | − | 0.375088i | −0.982256 | − | 0.187544i | \(-0.939947\pi\) | ||
0.982256 | − | 0.187544i | \(-0.0600527\pi\) | |||||||
\(462\) | −2.33247e12 | + | 2.08623e13i | −0.110817 | + | 0.991178i | ||||
\(463\) | −3.30432e13 | −1.55302 | −0.776510 | − | 0.630105i | \(-0.783012\pi\) | ||||
−0.776510 | + | 0.630105i | \(0.783012\pi\) | |||||||
\(464\) | − | 2.05209e12i | − | 0.0954129i | ||||||
\(465\) | −2.04643e13 | − | 2.28798e12i | −0.941309 | − | 0.105242i | ||||
\(466\) | −2.30404e13 | −1.04848 | ||||||||
\(467\) | − | 4.06927e12i | − | 0.183203i | −0.995796 | − | 0.0916014i | \(-0.970801\pi\) | ||
0.995796 | − | 0.0916014i | \(-0.0291986\pi\) | |||||||
\(468\) | 2.97025e12 | + | 6.72574e11i | 0.132301 | + | 0.0299579i | ||||
\(469\) | 3.23438e13 | 1.42537 | ||||||||
\(470\) | − | 2.04534e13i | − | 0.891819i | ||||||
\(471\) | 1.03103e12 | − | 9.22182e12i | 0.0444802 | − | 0.397843i | ||||
\(472\) | 2.31321e13 | 0.987426 | ||||||||
\(473\) | − | 2.00671e13i | − | 0.847576i | ||||||
\(474\) | −9.64644e12 | − | 1.07850e12i | −0.403158 | − | 0.0450744i | ||||
\(475\) | −1.59102e12 | −0.0657972 | ||||||||
\(476\) | − | 1.79831e12i | − | 0.0735918i | ||||||
\(477\) | 2.50501e12 | − | 1.10627e13i | 0.101442 | − | 0.447991i | ||||
\(478\) | 2.44462e13 | 0.979651 | ||||||||
\(479\) | − | 1.29218e13i | − | 0.512444i | −0.966618 | − | 0.256222i | \(-0.917522\pi\) | ||
0.966618 | − | 0.256222i | \(-0.0824777\pi\) | |||||||
\(480\) | −1.47337e12 | + | 1.31783e13i | −0.0578238 | + | 0.517192i | ||||
\(481\) | 1.03170e13 | 0.400707 | ||||||||
\(482\) | 9.96168e12i | 0.382911i | ||||||||
\(483\) | −1.10609e13 | − | 1.23664e12i | −0.420779 | − | 0.0470445i | ||||
\(484\) | −2.72401e12 | −0.102561 | ||||||||
\(485\) | 4.53079e12i | 0.168836i | ||||||||
\(486\) | −1.93021e13 | − | 1.20131e13i | −0.711909 | − | 0.443070i | ||||
\(487\) | −2.16371e13 | −0.789867 | −0.394933 | − | 0.918710i | \(-0.629232\pi\) | ||||
−0.394933 | + | 0.918710i | \(0.629232\pi\) | |||||||
\(488\) | 3.67313e13i | 1.32720i | ||||||||
\(489\) | −4.34791e12 | + | 3.88889e13i | −0.155502 | + | 1.39085i | ||||
\(490\) | 1.10935e12 | 0.0392725 | ||||||||
\(491\) | − | 3.39340e13i | − | 1.18913i | −0.804049 | − | 0.594563i | \(-0.797325\pi\) | ||
0.804049 | − | 0.594563i | \(-0.202675\pi\) | |||||||
\(492\) | −1.33371e13 | − | 1.49113e12i | −0.462632 | − | 0.0517238i | ||||
\(493\) | 1.09228e12 | 0.0375059 | ||||||||
\(494\) | 4.32223e12i | 0.146917i | ||||||||
\(495\) | 3.06004e13 | + | 6.92907e12i | 1.02968 | + | 0.233157i | ||||
\(496\) | 1.92125e13 | 0.639994 | ||||||||
\(497\) | 4.62453e13i | 1.52506i | ||||||||
\(498\) | 9.17093e11 | − | 8.20273e12i | 0.0299410 | − | 0.267801i | ||||
\(499\) | −1.83375e13 | −0.592702 | −0.296351 | − | 0.955079i | \(-0.595770\pi\) | ||||
−0.296351 | + | 0.955079i | \(0.595770\pi\) | |||||||
\(500\) | − | 9.89287e12i | − | 0.316572i | ||||||
\(501\) | 1.43870e13 | + | 1.60852e12i | 0.455809 | + | 0.0509610i | ||||
\(502\) | −4.71896e12 | −0.148022 | ||||||||
\(503\) | 9.29154e12i | 0.288568i | 0.989536 | + | 0.144284i | \(0.0460879\pi\) | ||||
−0.989536 | + | 0.144284i | \(0.953912\pi\) | |||||||
\(504\) | 8.00853e12 | − | 3.53676e13i | 0.246264 | − | 1.08756i | ||||
\(505\) | 1.20317e13 | 0.366329 | ||||||||
\(506\) | 1.33217e13i | 0.401614i | ||||||||
\(507\) | 2.94505e12 | − | 2.63413e13i | 0.0879130 | − | 0.786318i | ||||
\(508\) | 1.77566e13 | 0.524857 | ||||||||
\(509\) | − | 1.53418e13i | − | 0.449044i | −0.974469 | − | 0.224522i | \(-0.927918\pi\) | ||
0.974469 | − | 0.224522i | \(-0.0720820\pi\) | |||||||
\(510\) | 6.32633e12 | + | 7.07305e11i | 0.183358 | + | 0.0205001i | ||||
\(511\) | −4.90571e13 | −1.40798 | ||||||||
\(512\) | − | 3.59027e13i | − | 1.02042i | ||||||
\(513\) | −4.46649e12 | + | 1.28708e13i | −0.125713 | + | 0.362258i | ||||
\(514\) | −2.04023e13 | −0.568675 | ||||||||
\(515\) | − | 1.25649e13i | − | 0.346835i | ||||||
\(516\) | −8.81701e11 | + | 7.88617e12i | −0.0241031 | + | 0.215585i | ||||
\(517\) | −5.00643e13 | −1.35542 | ||||||||
\(518\) | − | 2.81216e13i | − | 0.754035i | ||||||
\(519\) | 4.99826e13 | + | 5.58822e12i | 1.32734 | + | 0.148401i | ||||
\(520\) | −1.71949e13 | −0.452255 | ||||||||
\(521\) | 3.59230e13i | 0.935803i | 0.883781 | + | 0.467901i | \(0.154990\pi\) | ||||
−0.883781 | + | 0.467901i | \(0.845010\pi\) | |||||||
\(522\) | 4.91756e12 | + | 1.11352e12i | 0.126881 | + | 0.0287306i | ||||
\(523\) | 5.78871e13 | 1.47936 | 0.739679 | − | 0.672960i | \(-0.234978\pi\) | ||||
0.739679 | + | 0.672960i | \(0.234978\pi\) | |||||||
\(524\) | − | 1.72590e13i | − | 0.436878i | ||||||
\(525\) | −7.79736e11 | + | 6.97417e12i | −0.0195502 | + | 0.174862i | ||||
\(526\) | −6.38236e12 | −0.158509 | ||||||||
\(527\) | 1.02264e13i | 0.251575i | ||||||||
\(528\) | −2.90922e13 | − | 3.25261e12i | −0.708937 | − | 0.0792615i | ||||
\(529\) | 3.43635e13 | 0.829505 | ||||||||
\(530\) | 1.46604e13i | 0.350562i | ||||||||
\(531\) | −8.46550e12 | + | 3.73856e13i | −0.200530 | + | 0.885589i | ||||
\(532\) | −4.97436e12 | −0.116729 | ||||||||
\(533\) | − | 3.08207e13i | − | 0.716485i | ||||||
\(534\) | −4.36178e12 | + | 3.90130e13i | −0.100452 | + | 0.898468i | ||||
\(535\) | −9.08301e12 | −0.207234 | ||||||||
\(536\) | 6.68758e13i | 1.51163i | ||||||||
\(537\) | −1.26090e13 | − | 1.40973e12i | −0.282364 | − | 0.0315693i | ||||
\(538\) | 4.21969e13 | 0.936201 | ||||||||
\(539\) | − | 2.71538e12i | − | 0.0596879i | ||||||
\(540\) | −1.17212e13 | − | 4.06757e12i | −0.255272 | − | 0.0885862i | ||||
\(541\) | −3.16844e12 | −0.0683690 | −0.0341845 | − | 0.999416i | \(-0.510883\pi\) | ||||
−0.0341845 | + | 0.999416i | \(0.510883\pi\) | |||||||
\(542\) | − | 4.47086e13i | − | 0.955860i | ||||||
\(543\) | 9.14869e12 | − | 8.18284e13i | 0.193803 | − | 1.73342i | ||||
\(544\) | 6.58540e12 | 0.138225 | ||||||||
\(545\) | 4.39869e13i | 0.914830i | ||||||||
\(546\) | 1.89463e13 | + | 2.11826e12i | 0.390447 | + | 0.0436533i | ||||
\(547\) | −2.29070e13 | −0.467770 | −0.233885 | − | 0.972264i | \(-0.575144\pi\) | ||||
−0.233885 | + | 0.972264i | \(0.575144\pi\) | |||||||
\(548\) | 2.39942e13i | 0.485516i | ||||||||
\(549\) | −5.93644e13 | − | 1.34423e13i | −1.19032 | − | 0.269533i | ||||
\(550\) | 8.39971e12 | 0.166898 | ||||||||
\(551\) | − | 3.02139e12i | − | 0.0594906i | ||||||
\(552\) | 2.55695e12 | − | 2.28701e13i | 0.0498916 | − | 0.446244i | ||||
\(553\) | 2.56554e13 | 0.496081 | ||||||||
\(554\) | − | 5.54149e13i | − | 1.06188i | ||||||
\(555\) | −4.17704e13 | − | 4.67008e12i | −0.793239 | − | 0.0886868i | ||||
\(556\) | 2.70464e12 | 0.0509020 | ||||||||
\(557\) | − | 9.11885e13i | − | 1.70084i | −0.526103 | − | 0.850421i | \(-0.676347\pi\) | ||
0.526103 | − | 0.850421i | \(-0.323653\pi\) | |||||||
\(558\) | −1.04252e13 | + | 4.60402e13i | −0.192714 | + | 0.851071i | ||||
\(559\) | −1.82242e13 | −0.333879 | ||||||||
\(560\) | 3.16101e13i | 0.573966i | ||||||||
\(561\) | 1.73129e12 | − | 1.54851e13i | 0.0311569 | − | 0.278676i | ||||
\(562\) | 7.21773e13 | 1.28742 | ||||||||
\(563\) | 4.74869e13i | 0.839522i | 0.907635 | + | 0.419761i | \(0.137886\pi\) | ||||
−0.907635 | + | 0.419761i | \(0.862114\pi\) | |||||||
\(564\) | 1.96748e13 | + | 2.19971e12i | 0.344758 | + | 0.0385451i | ||||
\(565\) | 7.20562e13 | 1.25150 | ||||||||
\(566\) | 3.87824e13i | 0.667655i | ||||||||
\(567\) | 5.42296e13 | + | 2.58865e13i | 0.925382 | + | 0.441731i | ||||
\(568\) | −9.56194e13 | −1.61735 | ||||||||
\(569\) | − | 1.13850e13i | − | 0.190885i | −0.995435 | − | 0.0954426i | \(-0.969573\pi\) | ||
0.995435 | − | 0.0954426i | \(-0.0304266\pi\) | |||||||
\(570\) | 1.95650e12 | − | 1.74995e13i | 0.0325166 | − | 0.290838i | ||||
\(571\) | −1.99708e13 | −0.329014 | −0.164507 | − | 0.986376i | \(-0.552603\pi\) | ||||
−0.164507 | + | 0.986376i | \(0.552603\pi\) | |||||||
\(572\) | 9.63469e12i | 0.157347i | ||||||||
\(573\) | −3.75572e13 | − | 4.19902e12i | −0.608023 | − | 0.0679791i | ||||
\(574\) | −8.40100e13 | −1.34825 | ||||||||
\(575\) | 4.45340e12i | 0.0708521i | ||||||||
\(576\) | 6.76779e13 | + | 1.53248e13i | 1.06742 | + | 0.241703i | ||||
\(577\) | −8.52618e12 | −0.133314 | −0.0666569 | − | 0.997776i | \(-0.521233\pi\) | ||||
−0.0666569 | + | 0.997776i | \(0.521233\pi\) | |||||||
\(578\) | 5.09334e13i | 0.789521i | ||||||||
\(579\) | −9.45958e12 | + | 8.46091e13i | −0.145371 | + | 1.30024i | ||||
\(580\) | 2.75153e12 | 0.0419213 | ||||||||
\(581\) | 2.18157e13i | 0.329525i | ||||||||
\(582\) | 1.03223e13 | + | 1.15407e12i | 0.154583 | + | 0.0172829i | ||||
\(583\) | 3.58845e13 | 0.532800 | ||||||||
\(584\) | − | 1.01433e14i | − | 1.49319i | ||||||
\(585\) | 6.29272e12 | − | 2.77901e13i | 0.0918458 | − | 0.405613i | ||||
\(586\) | −9.09862e13 | −1.31670 | ||||||||
\(587\) | − | 1.48895e13i | − | 0.213644i | −0.994278 | − | 0.106822i | \(-0.965933\pi\) | ||
0.994278 | − | 0.106822i | \(-0.0340674\pi\) | |||||||
\(588\) | −1.19307e11 | + | 1.06712e12i | −0.00169739 | + | 0.0151819i | ||||
\(589\) | 2.82874e13 | 0.399041 | ||||||||
\(590\) | − | 4.95437e13i | − | 0.692993i | ||||||
\(591\) | 7.53458e13 | + | 8.42392e12i | 1.04501 | + | 0.116836i | ||||
\(592\) | 3.92154e13 | 0.539322 | ||||||||
\(593\) | − | 3.80871e13i | − | 0.519404i | −0.965689 | − | 0.259702i | \(-0.916376\pi\) | ||
0.965689 | − | 0.259702i | \(-0.0836243\pi\) | |||||||
\(594\) | 2.35806e13 | − | 6.79506e13i | 0.318877 | − | 0.918885i | ||||
\(595\) | −1.68253e13 | −0.225620 | ||||||||
\(596\) | − | 2.25952e13i | − | 0.300458i | ||||||
\(597\) | 4.10245e12 | − | 3.66934e13i | 0.0540968 | − | 0.483857i | ||||
\(598\) | 1.20983e13 | 0.158205 | ||||||||
\(599\) | 8.56425e13i | 1.11059i | 0.831652 | + | 0.555297i | \(0.187395\pi\) | ||||
−0.831652 | + | 0.555297i | \(0.812605\pi\) | |||||||
\(600\) | −1.44202e13 | − | 1.61223e12i | −0.185445 | − | 0.0207333i | ||||
\(601\) | −2.89732e13 | −0.369508 | −0.184754 | − | 0.982785i | \(-0.559149\pi\) | ||||
−0.184754 | + | 0.982785i | \(0.559149\pi\) | |||||||
\(602\) | 4.96748e13i | 0.628281i | ||||||||
\(603\) | −1.08083e14 | − | 2.44741e13i | −1.35573 | − | 0.306987i | ||||
\(604\) | −1.79649e13 | −0.223480 | ||||||||
\(605\) | 2.54864e13i | 0.314435i | ||||||||
\(606\) | 3.06468e12 | − | 2.74114e13i | 0.0374993 | − | 0.335404i | ||||
\(607\) | −8.41409e13 | −1.02109 | −0.510544 | − | 0.859851i | \(-0.670556\pi\) | ||||
−0.510544 | + | 0.859851i | \(0.670556\pi\) | |||||||
\(608\) | − | 1.82161e13i | − | 0.219249i | ||||||
\(609\) | −1.32441e13 | − | 1.48074e12i | −0.158102 | − | 0.0176763i | ||||
\(610\) | 7.86702e13 | 0.931453 | ||||||||
\(611\) | 4.54665e13i | 0.533932i | ||||||||
\(612\) | −1.36076e12 | + | 6.00942e12i | −0.0158498 | + | 0.0699964i | ||||
\(613\) | 2.27205e13 | 0.262492 | 0.131246 | − | 0.991350i | \(-0.458102\pi\) | ||||
0.131246 | + | 0.991350i | \(0.458102\pi\) | |||||||
\(614\) | 5.55719e13i | 0.636815i | ||||||||
\(615\) | −1.39513e13 | + | 1.24784e14i | −0.158577 | + | 1.41835i | ||||
\(616\) | 1.14723e14 | 1.29344 | ||||||||
\(617\) | − | 2.60898e13i | − | 0.291773i | −0.989301 | − | 0.145887i | \(-0.953397\pi\) | ||
0.989301 | − | 0.145887i | \(-0.0466034\pi\) | |||||||
\(618\) | −2.86261e13 | − | 3.20049e12i | −0.317555 | − | 0.0355038i | ||||
\(619\) | 1.71879e14 | 1.89134 | 0.945670 | − | 0.325127i | \(-0.105407\pi\) | ||||
0.945670 | + | 0.325127i | \(0.105407\pi\) | |||||||
\(620\) | 2.57609e13i | 0.281192i | ||||||||
\(621\) | 3.60264e13 | + | 1.25021e13i | 0.390089 | + | 0.135371i | ||||
\(622\) | −5.75263e13 | −0.617895 | ||||||||
\(623\) | − | 1.03758e14i | − | 1.10555i | ||||||
\(624\) | −2.95390e12 | + | 2.64205e13i | −0.0312229 | + | 0.279266i | ||||
\(625\) | −7.61951e13 | −0.798964 | ||||||||
\(626\) | − | 2.18644e13i | − | 0.227439i | ||||||
\(627\) | −4.28338e13 | − | 4.78896e12i | −0.442027 | − | 0.0494201i | ||||
\(628\) | −1.16086e13 | −0.118846 | ||||||||
\(629\) | 2.08734e13i | 0.212002i | ||||||||
\(630\) | −7.57494e13 | − | 1.71525e13i | −0.763267 | − | 0.172832i | ||||
\(631\) | −1.35624e12 | −0.0135578 | −0.00677891 | − | 0.999977i | \(-0.502158\pi\) | ||||
−0.00677891 | + | 0.999977i | \(0.502158\pi\) | |||||||
\(632\) | 5.30464e13i | 0.526103i | ||||||||
\(633\) | −3.67817e12 | + | 3.28986e13i | −0.0361921 | + | 0.323712i | ||||
\(634\) | −2.20358e13 | −0.215121 | ||||||||
\(635\) | − | 1.66134e14i | − | 1.60912i | ||||||
\(636\) | −1.41023e13 | − | 1.57668e12i | −0.135520 | − | 0.0151516i | ||||
\(637\) | −2.46601e12 | −0.0235124 | ||||||||
\(638\) | 1.59513e13i | 0.150901i | ||||||||
\(639\) | 3.49933e13 | − | 1.54538e14i | 0.328458 | − | 1.45055i | ||||
\(640\) | −3.38081e13 | −0.314863 | ||||||||
\(641\) | − | 1.17561e14i | − | 1.08635i | −0.839618 | − | 0.543177i | \(-0.817221\pi\) | ||
0.839618 | − | 0.543177i | \(-0.182779\pi\) | |||||||
\(642\) | −2.31360e12 | + | 2.06934e13i | −0.0212135 | + | 0.189739i | ||||
\(643\) | 1.36130e14 | 1.23851 | 0.619253 | − | 0.785192i | \(-0.287436\pi\) | ||||
0.619253 | + | 0.785192i | \(0.287436\pi\) | |||||||
\(644\) | 1.39237e13i | 0.125697i | ||||||||
\(645\) | 7.37844e13 | + | 8.24935e12i | 0.660946 | + | 0.0738961i | ||||
\(646\) | −8.74477e12 | −0.0777295 | ||||||||
\(647\) | 1.40299e14i | 1.23747i | 0.785601 | + | 0.618734i | \(0.212354\pi\) | ||||
−0.785601 | + | 0.618734i | \(0.787646\pi\) | |||||||
\(648\) | −5.35244e13 | + | 1.12128e14i | −0.468464 | + | 0.981385i | ||||
\(649\) | −1.21269e14 | −1.05324 | ||||||||
\(650\) | − | 7.62830e12i | − | 0.0657448i | ||||||
\(651\) | 1.38633e13 | − | 1.23997e14i | 0.118566 | − | 1.06049i | ||||
\(652\) | 4.89543e13 | 0.415482 | ||||||||
\(653\) | 1.23574e14i | 1.04078i | 0.853927 | + | 0.520392i | \(0.174214\pi\) | ||||
−0.853927 | + | 0.520392i | \(0.825786\pi\) | |||||||
\(654\) | 1.00213e14 | + | 1.12042e13i | 0.837601 | + | 0.0936466i | ||||
\(655\) | −1.61479e14 | −1.33939 | ||||||||
\(656\) | − | 1.17151e14i | − | 0.964335i | ||||||
\(657\) | 1.63934e14 | + | 3.71209e13i | 1.33919 | + | 0.303243i | ||||
\(658\) | 1.23931e14 | 1.00473 | ||||||||
\(659\) | 1.94120e14i | 1.56187i | 0.624615 | + | 0.780933i | \(0.285256\pi\) | ||||
−0.624615 | + | 0.780933i | \(0.714744\pi\) | |||||||
\(660\) | 4.36124e12 | − | 3.90081e13i | 0.0348249 | − | 0.311483i | ||||
\(661\) | −2.24813e14 | −1.78162 | −0.890810 | − | 0.454376i | \(-0.849862\pi\) | ||||
−0.890810 | + | 0.454376i | \(0.849862\pi\) | |||||||
\(662\) | 4.74225e13i | 0.372988i | ||||||||
\(663\) | −1.40630e13 | − | 1.57229e12i | −0.109777 | − | 0.0122734i | ||||
\(664\) | −4.51074e13 | −0.349468 | ||||||||
\(665\) | 4.65410e13i | 0.357872i | ||||||||
\(666\) | −2.12793e13 | + | 9.39743e13i | −0.162400 | + | 0.717196i | ||||
\(667\) | −8.45714e12 | −0.0640611 | ||||||||
\(668\) | − | 1.81107e13i | − | 0.136161i | ||||||
\(669\) | −3.12047e12 | + | 2.79103e13i | −0.0232857 | + | 0.208274i | ||||
\(670\) | 1.43233e14 | 1.06089 | ||||||||
\(671\) | − | 1.92563e14i | − | 1.41566i | ||||||
\(672\) | −7.98495e13 | − | 8.92744e12i | −0.582674 | − | 0.0651449i | ||||
\(673\) | 6.39293e13 | 0.463047 | 0.231523 | − | 0.972829i | \(-0.425629\pi\) | ||||
0.231523 | + | 0.972829i | \(0.425629\pi\) | |||||||
\(674\) | − | 1.43764e13i | − | 0.103360i | ||||||
\(675\) | 7.88291e12 | − | 2.27156e13i | 0.0562559 | − | 0.162108i | ||||
\(676\) | −3.31591e13 | −0.234893 | ||||||||
\(677\) | 6.84090e13i | 0.481027i | 0.970646 | + | 0.240514i | \(0.0773159\pi\) | ||||
−0.970646 | + | 0.240514i | \(0.922684\pi\) | |||||||
\(678\) | 1.83539e13 | − | 1.64163e14i | 0.128109 | − | 1.14585i | ||||
\(679\) | −2.74529e13 | −0.190213 | ||||||||
\(680\) | − | 3.47889e13i | − | 0.239275i | ||||||
\(681\) | 5.37125e12 | + | 6.00524e11i | 0.0366724 | + | 0.00410010i | ||||
\(682\) | −1.49342e14 | −1.01219 | ||||||||
\(683\) | − | 1.17660e14i | − | 0.791639i | −0.918328 | − | 0.395819i | \(-0.870461\pi\) | ||
0.918328 | − | 0.395819i | \(-0.129539\pi\) | |||||||
\(684\) | 1.66229e13 | + | 3.76404e12i | 0.111026 | + | 0.0251405i | ||||
\(685\) | 2.24494e14 | 1.48851 | ||||||||
\(686\) | − | 1.23905e14i | − | 0.815584i | ||||||
\(687\) | −1.48015e13 | + | 1.32389e14i | −0.0967214 | + | 0.865102i | ||||
\(688\) | −6.92711e13 | −0.449376 | ||||||||
\(689\) | − | 3.25890e13i | − | 0.209882i | ||||||
\(690\) | −4.89826e13 | − | 5.47642e12i | −0.313181 | − | 0.0350148i | ||||
\(691\) | 5.40492e13 | 0.343083 | 0.171541 | − | 0.985177i | \(-0.445125\pi\) | ||||
0.171541 | + | 0.985177i | \(0.445125\pi\) | |||||||
\(692\) | − | 6.29193e13i | − | 0.396509i | ||||||
\(693\) | −4.19845e13 | + | 1.85413e14i | −0.262677 | + | 1.16004i | ||||
\(694\) | 1.30766e14 | 0.812263 | ||||||||
\(695\) | − | 2.53051e13i | − | 0.156057i | ||||||
\(696\) | 3.06166e12 | − | 2.73843e13i | 0.0187461 | − | 0.167670i | ||||
\(697\) | 6.23568e13 | 0.379070 | ||||||||
\(698\) | 2.10307e12i | 0.0126933i | ||||||||
\(699\) | −2.07364e14 | − | 2.31840e13i | −1.24264 | − | 0.138932i | ||||
\(700\) | 8.77925e12 | 0.0522357 | ||||||||
\(701\) | 2.61865e14i | 1.54699i | 0.633804 | + | 0.773493i | \(0.281492\pi\) | ||||
−0.633804 | + | 0.773493i | \(0.718508\pi\) | |||||||
\(702\) | −6.17103e13 | − | 2.14151e13i | −0.361969 | − | 0.125613i | ||||
\(703\) | 5.77385e13 | 0.336271 | ||||||||
\(704\) | 2.19529e14i | 1.26949i | ||||||||
\(705\) | 2.05809e13 | − | 1.84081e14i | 0.118173 | − | 1.05697i | ||||
\(706\) | −1.31697e14 | −0.750846 | ||||||||
\(707\) | 7.29024e13i | 0.412710i | ||||||||
\(708\) | 4.76576e13 | + | 5.32829e12i | 0.267896 | + | 0.0299517i | ||||
\(709\) | −1.21603e14 | −0.678757 | −0.339378 | − | 0.940650i | \(-0.610217\pi\) | ||||
−0.339378 | + | 0.940650i | \(0.610217\pi\) | |||||||
\(710\) | 2.04795e14i | 1.13509i | ||||||||
\(711\) | −8.57327e13 | − | 1.94131e13i | −0.471844 | − | 0.106843i | ||||
\(712\) | 2.14535e14 | 1.17246 | ||||||||
\(713\) | − | 7.91791e13i | − | 0.429697i | ||||||
\(714\) | −4.28569e12 | + | 3.83324e13i | −0.0230956 | + | 0.206574i | ||||
\(715\) | 9.01439e13 | 0.482399 | ||||||||
\(716\) | 1.58725e13i | 0.0843492i | ||||||||
\(717\) | 2.20016e14 | + | 2.45985e13i | 1.16107 | + | 0.129811i | ||||
\(718\) | 2.21021e13 | 0.115827 | ||||||||
\(719\) | − | 2.82360e14i | − | 1.46946i | −0.678359 | − | 0.734731i | \(-0.737308\pi\) | ||
0.678359 | − | 0.734731i | \(-0.262692\pi\) | |||||||
\(720\) | 2.39190e13 | − | 1.05632e14i | 0.123618 | − | 0.545924i | ||||
\(721\) | 7.61330e13 | 0.390748 | ||||||||
\(722\) | − | 1.40325e14i | − | 0.715233i | ||||||
\(723\) | −1.00237e13 | + | 8.96551e13i | −0.0507386 | + | 0.453820i | ||||
\(724\) | −1.03007e14 | −0.517817 | ||||||||
\(725\) | 5.33245e12i | 0.0266217i | ||||||||
\(726\) | 5.80645e13 | + | 6.49181e12i | 0.287891 | + | 0.0321872i | ||||
\(727\) | −6.98010e13 | −0.343708 | −0.171854 | − | 0.985122i | \(-0.554976\pi\) | ||||
−0.171854 | + | 0.985122i | \(0.554976\pi\) | |||||||
\(728\) | − | 1.04187e14i | − | 0.509516i | ||||||
\(729\) | −1.61631e14 | − | 1.27540e14i | −0.785034 | − | 0.619453i | ||||
\(730\) | −2.17247e14 | −1.04795 | ||||||||
\(731\) | − | 3.68713e13i | − | 0.176645i | ||||||
\(732\) | −8.46075e12 | + | 7.56753e13i | −0.0402581 | + | 0.360080i | ||||
\(733\) | −3.28397e14 | −1.55196 | −0.775978 | − | 0.630760i | \(-0.782743\pi\) | ||||
−0.775978 | + | 0.630760i | \(0.782743\pi\) | |||||||
\(734\) | 1.49173e14i | 0.700178i | ||||||||
\(735\) | 9.98415e12 | + | 1.11626e12i | 0.0465451 | + | 0.00520391i | ||||
\(736\) | −5.09884e13 | −0.236093 | ||||||||
\(737\) | − | 3.50594e14i | − | 1.61238i | ||||||
\(738\) | 2.80737e14 | + | 6.35693e13i | 1.28238 | + | 0.290379i | ||||
\(739\) | 3.04479e14 | 1.38145 | 0.690726 | − | 0.723117i | \(-0.257291\pi\) | ||||
0.690726 | + | 0.723117i | \(0.257291\pi\) | |||||||
\(740\) | 5.25816e13i | 0.236960i | ||||||||
\(741\) | −4.34916e12 | + | 3.89001e13i | −0.0194677 | + | 0.174124i | ||||
\(742\) | −8.88298e13 | −0.394947 | ||||||||
\(743\) | 2.81759e14i | 1.24432i | 0.782888 | + | 0.622162i | \(0.213746\pi\) | ||||
−0.782888 | + | 0.622162i | \(0.786254\pi\) | |||||||
\(744\) | 2.56383e14 | + | 2.86645e13i | 1.12467 | + | 0.125742i | ||||
\(745\) | −2.11404e14 | −0.921154 | ||||||||
\(746\) | − | 1.13213e12i | − | 0.00490008i | ||||||
\(747\) | 1.65077e13 | − | 7.29017e13i | 0.0709713 | − | 0.313426i | ||||
\(748\) | −1.94930e13 | −0.0832474 | ||||||||
\(749\) | − | 5.50356e13i | − | 0.233472i | ||||||
\(750\) | −2.35765e13 | + | 2.10874e14i | −0.0993510 | + | 0.888623i | ||||
\(751\) | 3.86635e14 | 1.61846 | 0.809230 | − | 0.587492i | \(-0.199885\pi\) | ||||
0.809230 | + | 0.587492i | \(0.199885\pi\) | |||||||
\(752\) | 1.72821e14i | 0.718632i | ||||||||
\(753\) | −4.24706e13 | − | 4.74836e12i | −0.175434 | − | 0.0196141i | ||||
\(754\) | 1.44864e13 | 0.0594433 | ||||||||
\(755\) | 1.68083e14i | 0.685153i | ||||||||
\(756\) | 2.46461e13 | − | 7.10210e13i | 0.0998021 | − | 0.287593i | ||||
\(757\) | −1.76968e13 | −0.0711893 | −0.0355947 | − | 0.999366i | \(-0.511333\pi\) | ||||
−0.0355947 | + | 0.999366i | \(0.511333\pi\) | |||||||
\(758\) | − | 2.55293e14i | − | 1.02022i | ||||||
\(759\) | −1.34047e13 | + | 1.19896e14i | −0.0532169 | + | 0.475986i | ||||
\(760\) | −9.62308e13 | −0.379530 | ||||||||
\(761\) | 1.74325e14i | 0.683025i | 0.939877 | + | 0.341512i | \(0.110939\pi\) | ||||
−0.939877 | + | 0.341512i | \(0.889061\pi\) | |||||||
\(762\) | −3.78496e14 | − | 4.23171e13i | −1.47328 | − | 0.164718i | ||||
\(763\) | −2.66524e14 | −1.03066 | ||||||||
\(764\) | 4.72779e13i | 0.181632i | ||||||||
\(765\) | 5.62253e13 | + | 1.27315e13i | 0.214597 | + | 0.0485928i | ||||
\(766\) | 7.58677e13 | 0.287682 | ||||||||
\(767\) | 1.10132e14i | 0.414894i | ||||||||
\(768\) | 2.38790e13 | − | 2.13580e14i | 0.0893736 | − | 0.799382i | ||||
\(769\) | 1.93974e14 | 0.721293 | 0.360646 | − | 0.932703i | \(-0.382556\pi\) | ||||
0.360646 | + | 0.932703i | \(0.382556\pi\) | |||||||
\(770\) | − | 2.45711e14i | − | 0.907760i | ||||||
\(771\) | −1.83621e14 | − | 2.05295e13i | −0.673986 | − | 0.0753539i | ||||
\(772\) | 1.06508e14 | 0.388414 | ||||||||
\(773\) | − | 5.25639e13i | − | 0.190454i | −0.995456 | − | 0.0952270i | \(-0.969642\pi\) | ||
0.995456 | − | 0.0952270i | \(-0.0303577\pi\) | |||||||
\(774\) | 3.75883e13 | − | 1.65999e14i | 0.135316 | − | 0.597585i | ||||
\(775\) | −4.99245e13 | −0.178569 | ||||||||
\(776\) | − | 5.67631e13i | − | 0.201724i | ||||||
\(777\) | 2.82968e13 | − | 2.53095e14i | 0.0999155 | − | 0.893672i | ||||
\(778\) | 3.00831e13 | 0.105542 | ||||||||
\(779\) | − | 1.72487e14i | − | 0.601269i | ||||||
\(780\) | −3.54257e13 | − | 3.96071e12i | −0.122700 | − | 0.0137183i | ||||
\(781\) | 5.01282e14 | 1.72515 | ||||||||
\(782\) | 2.44774e13i | 0.0837012i | ||||||||
\(783\) | 4.31376e13 | + | 1.49699e13i | 0.146571 | + | 0.0508639i | ||||
\(784\) | −9.37343e12 | −0.0316459 | ||||||||
\(785\) | 1.08613e14i | 0.364361i | ||||||||
\(786\) | −4.11313e13 | + | 3.67890e14i | −0.137107 | + | 1.22632i | ||||
\(787\) | −1.52665e14 | −0.505669 | −0.252834 | − | 0.967510i | \(-0.581363\pi\) | ||||
−0.252834 | + | 0.967510i | \(0.581363\pi\) | |||||||
\(788\) | − | 9.48471e13i | − | 0.312171i | ||||||
\(789\) | −5.74413e13 | − | 6.42213e12i | −0.187862 | − | 0.0210036i | ||||
\(790\) | 1.13614e14 | 0.369228 | ||||||||
\(791\) | 4.36602e14i | 1.40995i | ||||||||
\(792\) | −3.83371e14 | − | 8.68095e13i | −1.23025 | − | 0.278574i | ||||
\(793\) | −1.74878e14 | −0.557661 | ||||||||
\(794\) | − | 2.00369e14i | − | 0.634933i | ||||||
\(795\) | −1.47517e13 | + | 1.31943e14i | −0.0464522 | + | 0.415481i | ||||
\(796\) | −4.61906e13 | −0.144540 | ||||||||
\(797\) | − | 3.21927e14i | − | 1.00107i | −0.865716 | − | 0.500536i | \(-0.833136\pi\) | ||
0.865716 | − | 0.500536i | \(-0.166864\pi\) | |||||||
\(798\) | 1.06032e14 | + | 1.18548e13i | 0.327661 | + | 0.0366336i | ||||
\(799\) | −9.19883e13 | −0.282487 | ||||||||
\(800\) | 3.21495e13i | 0.0981126i | ||||||||
\(801\) | −7.85121e13 | + | 3.46728e14i | −0.238108 | + | 1.05154i | ||||
\(802\) | 4.37269e14 | 1.31788 | ||||||||
\(803\) | 5.31760e14i | 1.59272i | ||||||||
\(804\) | −1.54043e13 | + | 1.37780e14i | −0.0458524 | + | 0.410116i | ||||
\(805\) | 1.30272e14 | 0.385366 | ||||||||
\(806\) | 1.35627e14i | 0.398723i | ||||||||
\(807\) | 3.79772e14 | + | 4.24598e13i | 1.10957 | + | 0.124054i | ||||
\(808\) | −1.50737e14 | −0.437687 | ||||||||
\(809\) | − | 4.22482e14i | − | 1.21917i | −0.792719 | − | 0.609587i | \(-0.791335\pi\) | ||
0.792719 | − | 0.609587i | \(-0.208665\pi\) | |||||||
\(810\) | 2.40153e14 | + | 1.14637e14i | 0.688753 | + | 0.328776i | ||||
\(811\) | −5.21066e14 | −1.48521 | −0.742607 | − | 0.669728i | \(-0.766411\pi\) | ||||
−0.742607 | + | 0.669728i | \(0.766411\pi\) | |||||||
\(812\) | 1.66720e13i | 0.0472290i | ||||||||
\(813\) | 4.49871e13 | − | 4.02377e14i | 0.126659 | − | 1.13287i | ||||
\(814\) | −3.04828e14 | −0.852968 | ||||||||
\(815\) | − | 4.58025e14i | − | 1.27380i | ||||||
\(816\) | −5.34542e13 | − | 5.97636e12i | −0.147751 | − | 0.0165191i | ||||
\(817\) | −1.01991e14 | −0.280189 | ||||||||
\(818\) | 2.82105e14i | 0.770272i | ||||||||
\(819\) | 1.68386e14 | + | 3.81288e13i | 0.456967 | + | 0.103474i | ||||
\(820\) | 1.57081e14 | 0.423697 | ||||||||
\(821\) | 1.86792e14i | 0.500775i | 0.968146 | + | 0.250387i | \(0.0805580\pi\) | ||||
−0.968146 | + | 0.250387i | \(0.919442\pi\) | |||||||
\(822\) | 5.71824e13 | − | 5.11455e14i | 0.152371 | − | 1.36285i | ||||
\(823\) | 6.22782e13 | 0.164944 | 0.0824721 | − | 0.996593i | \(-0.473718\pi\) | ||||
0.0824721 | + | 0.996593i | \(0.473718\pi\) | |||||||
\(824\) | 1.57417e14i | 0.414396i | ||||||||
\(825\) | 7.55974e13 | + | 8.45204e12i | 0.197805 | + | 0.0221153i | ||||
\(826\) | 3.00194e14 | 0.780733 | ||||||||
\(827\) | − | 3.99626e14i | − | 1.03306i | −0.856269 | − | 0.516530i | \(-0.827223\pi\) | ||
0.856269 | − | 0.516530i | \(-0.172777\pi\) | |||||||
\(828\) | 1.05359e13 | − | 4.65289e13i | 0.0270719 | − | 0.119556i | ||||
\(829\) | −5.51493e14 | −1.40853 | −0.704267 | − | 0.709935i | \(-0.748724\pi\) | ||||
−0.704267 | + | 0.709935i | \(0.748724\pi\) | |||||||
\(830\) | 9.66099e13i | 0.245263i | ||||||||
\(831\) | 5.57601e13 | − | 4.98734e14i | 0.140708 | − | 1.25853i | ||||
\(832\) | 1.99368e14 | 0.500080 | ||||||||
\(833\) | − | 4.98925e12i | − | 0.0124397i | ||||||
\(834\) | −5.76515e13 | − | 6.44563e12i | −0.142883 | − | 0.0159748i | ||||
\(835\) | −1.69447e14 | −0.417448 | ||||||||
\(836\) | 5.39202e13i | 0.132044i | ||||||||
\(837\) | −1.40154e14 | + | 4.03871e14i | −0.341176 | + | 0.983141i | ||||
\(838\) | −5.86856e14 | −1.42008 | ||||||||
\(839\) | − | 1.98481e14i | − | 0.477428i | −0.971090 | − | 0.238714i | \(-0.923274\pi\) | ||
0.971090 | − | 0.238714i | \(-0.0767259\pi\) | |||||||
\(840\) | −4.71614e13 | + | 4.21824e14i | −0.112769 | + | 1.00864i | ||||
\(841\) | 4.10581e14 | 0.975930 | ||||||||
\(842\) | 1.81304e14i | 0.428397i | ||||||||
\(843\) | 6.49596e14 | + | 7.26271e13i | 1.52583 | + | 0.170593i | ||||
\(844\) | 4.14135e13 | 0.0967007 | ||||||||
\(845\) | 3.10243e14i | 0.720141i | ||||||||
\(846\) | −4.14141e14 | − | 9.37770e13i | −0.955645 | − | 0.216394i | ||||
\(847\) | −1.54427e14 | −0.354246 | ||||||||
\(848\) | − | 1.23872e14i | − | 0.282485i | ||||||
\(849\) | −3.90240e13 | + | 3.49041e14i | −0.0884695 | + | 0.791295i | ||||
\(850\) | 1.54336e13 | 0.0347835 | ||||||||
\(851\) | − | 1.61615e14i | − | 0.362105i | ||||||
\(852\) | −1.96999e14 | − | 2.20252e13i | −0.438800 | − | 0.0490593i | ||||
\(853\) | 7.19132e14 | 1.59244 | 0.796221 | − | 0.605006i | \(-0.206829\pi\) | ||||
0.796221 | + | 0.605006i | \(0.206829\pi\) | |||||||
\(854\) | 4.76677e14i | 1.04938i | ||||||||
\(855\) | 3.52170e13 | − | 1.55526e14i | 0.0770764 | − | 0.340388i | ||||
\(856\) | 1.13795e14 | 0.247601 | ||||||||
\(857\) | 2.57463e14i | 0.556943i | 0.960444 | + | 0.278472i | \(0.0898279\pi\) | ||||
−0.960444 | + | 0.278472i | \(0.910172\pi\) | |||||||
\(858\) | 2.29612e13 | − | 2.05371e14i | 0.0493808 | − | 0.441675i | ||||
\(859\) | 4.81365e14 | 1.02922 | 0.514610 | − | 0.857424i | \(-0.327937\pi\) | ||||
0.514610 | + | 0.857424i | \(0.327937\pi\) | |||||||
\(860\) | − | 9.28816e13i | − | 0.197441i | ||||||
\(861\) | −7.56090e14 | − | 8.45335e13i | −1.59793 | − | 0.178654i | ||||
\(862\) | 4.24547e14 | 0.892052 | ||||||||
\(863\) | 1.08169e13i | 0.0225969i | 0.999936 | + | 0.0112985i | \(0.00359649\pi\) | ||||
−0.999936 | + | 0.0112985i | \(0.996404\pi\) | |||||||
\(864\) | 2.60078e14 | + | 9.02540e13i | 0.540176 | + | 0.187455i | ||||
\(865\) | −5.88684e14 | −1.21563 | ||||||||
\(866\) | − | 3.92090e14i | − | 0.805001i | ||||||
\(867\) | −5.12508e13 | + | 4.58401e14i | −0.104618 | + | 0.935729i | ||||
\(868\) | −1.56090e14 | −0.316794 | ||||||||
\(869\) | − | 2.78094e14i | − | 0.561169i | ||||||
\(870\) | −5.86511e13 | − | 6.55739e12i | −0.117674 | − | 0.0131563i | ||||
\(871\) | −3.18397e14 | −0.635152 | ||||||||
\(872\) | − | 5.51081e14i | − | 1.09303i | ||||||
\(873\) | 9.17395e13 | + | 2.07732e13i | 0.180919 | + | 0.0409669i | ||||
\(874\) | 6.77077e13 | 0.132764 | ||||||||
\(875\) | − | 5.60834e14i | − | 1.09344i | ||||||
\(876\) | 2.33643e13 | − | 2.08977e14i | 0.0452931 | − | 0.405114i | ||||
\(877\) | −6.94441e13 | −0.133856 | −0.0669280 | − | 0.997758i | \(-0.521320\pi\) | ||||
−0.0669280 | + | 0.997758i | \(0.521320\pi\) | |||||||
\(878\) | − | 3.40309e14i | − | 0.652231i | ||||||
\(879\) | −8.18875e14 | − | 9.15531e13i | −1.56053 | − | 0.174473i | ||||
\(880\) | 3.42642e14 | 0.649273 | ||||||||
\(881\) | 9.22199e14i | 1.73758i | 0.495180 | + | 0.868791i | \(0.335102\pi\) | ||||
−0.495180 | + | 0.868791i | \(0.664898\pi\) | |||||||
\(882\) | 5.08626e12 | − | 2.24621e13i | 0.00952919 | − | 0.0420831i | ||||
\(883\) | −3.03213e13 | −0.0564864 | −0.0282432 | − | 0.999601i | \(-0.508991\pi\) | ||||
−0.0282432 | + | 0.999601i | \(0.508991\pi\) | |||||||
\(884\) | 1.77028e13i | 0.0327930i | ||||||||
\(885\) | 4.98524e13 | − | 4.45893e14i | 0.0918269 | − | 0.821325i | ||||
\(886\) | −1.25753e14 | −0.230329 | ||||||||
\(887\) | 9.37729e14i | 1.70789i | 0.520365 | + | 0.853944i | \(0.325796\pi\) | ||||
−0.520365 | + | 0.853944i | \(0.674204\pi\) | |||||||
\(888\) | 5.23313e14 | + | 5.85081e13i | 0.947756 | + | 0.105962i | ||||
\(889\) | 1.00664e15 | 1.81286 | ||||||||
\(890\) | − | 4.59486e14i | − | 0.822853i | ||||||
\(891\) | 2.80600e14 | − | 5.87828e14i | 0.499688 | − | 1.04680i | ||||
\(892\) | 3.51342e13 | 0.0622165 | ||||||||
\(893\) | 2.54452e14i | 0.448072i | ||||||||
\(894\) | −5.38483e13 | + | 4.81634e14i | −0.0942940 | + | 0.843391i | ||||
\(895\) | 1.48506e14 | 0.258600 | ||||||||
\(896\) | − | 2.04849e14i | − | 0.354727i | ||||||
\(897\) | 1.08885e14 | + | 1.21737e13i | 0.187502 | + | 0.0209633i | ||||
\(898\) | −7.57793e14 | −1.29768 | ||||||||
\(899\) | − | 9.48080e13i | − | 0.161453i | ||||||
\(900\) | −2.93377e13 | − | 6.64314e12i | −0.0496836 | − | 0.0112502i | ||||
\(901\) | 6.59342e13 | 0.111042 | ||||||||
\(902\) | 9.10637e14i | 1.52515i | ||||||||
\(903\) | −4.99843e13 | + | 4.47073e14i | −0.0832521 | + | 0.744629i | ||||
\(904\) | −9.02742e14 | −1.49528 | ||||||||
\(905\) | 9.63756e14i | 1.58754i | ||||||||
\(906\) | 3.82935e14 | + | 4.28135e13i | 0.627313 | + | 0.0701357i | ||||
\(907\) | −9.15531e14 | −1.49155 | −0.745773 | − | 0.666200i | \(-0.767920\pi\) | ||||
−0.745773 | + | 0.666200i | \(0.767920\pi\) | |||||||
\(908\) | − | 6.76145e12i | − | 0.0109550i | ||||||
\(909\) | 5.51643e13 | − | 2.43619e14i | 0.0888871 | − | 0.392546i | ||||
\(910\) | −2.23146e14 | −0.357587 | ||||||||
\(911\) | − | 1.11284e15i | − | 1.77354i | −0.462210 | − | 0.886770i | \(-0.652943\pi\) | ||
0.462210 | − | 0.886770i | \(-0.347057\pi\) | |||||||
\(912\) | −1.65314e13 | + | 1.47861e14i | −0.0262021 | + | 0.234358i | ||||
\(913\) | 2.36474e14 | 0.372760 | ||||||||
\(914\) | 2.47628e14i | 0.388211i | ||||||||
\(915\) | 7.08032e14 | + | 7.91603e13i | 1.10394 | + | 0.123425i | ||||
\(916\) | 1.66654e14 | 0.258427 | ||||||||
\(917\) | − | 9.78428e14i | − | 1.50898i | ||||||
\(918\) | 4.33272e13 | − | 1.24853e14i | 0.0664579 | − | 0.191507i | ||||
\(919\) | 4.68203e14 | 0.714260 | 0.357130 | − | 0.934055i | \(-0.383755\pi\) | ||||
0.357130 | + | 0.934055i | \(0.383755\pi\) | |||||||
\(920\) | 2.69359e14i | 0.408688i | ||||||||
\(921\) | −5.59182e13 | + | 5.00147e14i | −0.0843830 | + | 0.754744i | ||||
\(922\) | 2.09558e14 | 0.314521 | ||||||||
\(923\) | − | 4.55246e14i | − | 0.679575i | ||||||
\(924\) | 2.36357e14 | + | 2.64255e13i | 0.350921 | + | 0.0392341i | ||||
\(925\) | −1.01903e14 | −0.150479 | ||||||||
\(926\) | − | 8.86642e14i | − | 1.30225i | ||||||
\(927\) | −2.54414e14 | − | 5.76089e13i | −0.371657 | − | 0.0841571i | ||||
\(928\) | −6.10529e13 | −0.0887087 | ||||||||
\(929\) | − | 4.05571e14i | − | 0.586123i | −0.956094 | − | 0.293062i | \(-0.905326\pi\) | ||
0.956094 | − | 0.293062i | \(-0.0946741\pi\) | |||||||
\(930\) | 6.13929e13 | − | 5.49115e14i | 0.0882477 | − | 0.789311i | ||||
\(931\) | −1.38009e13 | −0.0197315 | ||||||||
\(932\) | 2.61034e14i | 0.371208i | ||||||||
\(933\) | −5.17737e14 | − | 5.78847e13i | −0.732319 | − | 0.0818758i | ||||
\(934\) | 1.09190e14 | 0.153620 | ||||||||
\(935\) | 1.82380e14i | 0.255223i | ||||||||
\(936\) | −7.88372e13 | + | 3.48163e14i | −0.109737 | + | 0.484623i | ||||
\(937\) | −1.63835e14 | −0.226834 | −0.113417 | − | 0.993547i | \(-0.536180\pi\) | ||||
−0.113417 | + | 0.993547i | \(0.536180\pi\) | |||||||
\(938\) | 8.67875e14i | 1.19521i | ||||||||
\(939\) | 2.20006e13 | − | 1.96780e14i | 0.0301375 | − | 0.269558i | ||||
\(940\) | −2.31725e14 | −0.315743 | ||||||||
\(941\) | − | 7.62592e14i | − | 1.03358i | −0.856112 | − | 0.516790i | \(-0.827127\pi\) | ||
0.856112 | − | 0.516790i | \(-0.172873\pi\) | |||||||
\(942\) | 2.47447e14 | + | 2.76655e13i | 0.333602 | + | 0.0372978i | ||||
\(943\) | −4.82807e14 | −0.647463 | ||||||||
\(944\) | 4.18618e14i | 0.558417i | ||||||||
\(945\) | −6.64485e14 | − | 2.30594e14i | −0.881711 | − | 0.305977i | ||||
\(946\) | 5.38456e14 | 0.710714 | ||||||||
\(947\) | 1.00864e15i | 1.32430i | 0.749371 | + | 0.662150i | \(0.230356\pi\) | ||||
−0.749371 | + | 0.662150i | \(0.769644\pi\) | |||||||
\(948\) | −1.22188e13 | + | 1.09288e14i | −0.0159583 | + | 0.142736i | ||||
\(949\) | 4.82925e14 | 0.627406 | ||||||||
\(950\) | − | 4.26915e13i | − | 0.0551726i | ||||||
\(951\) | −1.98322e14 | − | 2.21731e13i | −0.254958 | − | 0.0285051i | ||||
\(952\) | 2.10792e14 | 0.269569 | ||||||||
\(953\) | 2.25382e14i | 0.286718i | 0.989671 | + | 0.143359i | \(0.0457903\pi\) | ||||
−0.989671 | + | 0.143359i | \(0.954210\pi\) | |||||||
\(954\) | 2.96843e14 | + | 6.72164e13i | 0.375652 | + | 0.0850615i | ||||
\(955\) | 4.42340e14 | 0.556852 | ||||||||
\(956\) | − | 2.76961e14i | − | 0.346840i | ||||||
\(957\) | −1.60507e13 | + | 1.43562e14i | −0.0199955 | + | 0.178846i | ||||
\(958\) | 3.46729e14 | 0.429697 | ||||||||
\(959\) | 1.36025e15i | 1.67697i | ||||||||
\(960\) | −8.07185e14 | − | 9.02460e13i | −0.989958 | − | 0.110681i | ||||
\(961\) | 6.80016e13 | 0.0829664 | ||||||||
\(962\) | 2.76833e14i | 0.336003i | ||||||||
\(963\) | −4.16447e13 | + | 1.83913e14i | −0.0502839 | + | 0.222065i | ||||
\(964\) | 1.12860e14 | 0.135567 | ||||||||
\(965\) | − | 9.96507e14i | − | 1.19081i | ||||||
\(966\) | 3.31826e13 | − | 2.96794e14i | 0.0394480 | − | 0.352834i | ||||
\(967\) | 7.89275e14 | 0.933460 | 0.466730 | − | 0.884400i | \(-0.345432\pi\) | ||||
0.466730 | + | 0.884400i | \(0.345432\pi\) | |||||||
\(968\) | − | 3.19301e14i | − | 0.375685i | ||||||
\(969\) | −7.87030e13 | − | 8.79926e12i | −0.0921239 | − | 0.0102998i | ||||
\(970\) | −1.21574e14 | −0.141573 | ||||||||
\(971\) | 2.37876e14i | 0.275584i | 0.990461 | + | 0.137792i | \(0.0440006\pi\) | ||||
−0.990461 | + | 0.137792i | \(0.955999\pi\) | |||||||
\(972\) | −1.36101e14 | + | 2.18682e14i | −0.156866 | + | 0.252047i | ||||
\(973\) | 1.53328e14 | 0.175816 | ||||||||
\(974\) | − | 5.80584e14i | − | 0.662324i | ||||||
\(975\) | 7.67583e12 | − | 6.86547e13i | 0.00871169 | − | 0.0779197i | ||||
\(976\) | −6.64722e14 | −0.750569 | ||||||||
\(977\) | − | 4.62892e14i | − | 0.520004i | −0.965608 | − | 0.260002i | \(-0.916277\pi\) | ||
0.965608 | − | 0.260002i | \(-0.0837232\pi\) | |||||||
\(978\) | −1.04350e15 | − | 1.16667e14i | −1.16627 | − | 0.130393i | ||||
\(979\) | −1.12469e15 | −1.25061 | ||||||||
\(980\) | − | 1.25683e13i | − | 0.0139042i | ||||||
\(981\) | 8.90647e14 | + | 2.01676e14i | 0.980303 | + | 0.221977i | ||||
\(982\) | 9.10545e14 | 0.997112 | ||||||||
\(983\) | − | 7.04750e14i | − | 0.767834i | −0.923368 | − | 0.383917i | \(-0.874575\pi\) | ||
0.923368 | − | 0.383917i | \(-0.125425\pi\) | |||||||
\(984\) | 1.74786e14 | − | 1.56333e15i | 0.189466 | − | 1.69464i | ||||
\(985\) | −8.87406e14 | −0.957065 | ||||||||
\(986\) | 2.93089e13i | 0.0314496i | ||||||||
\(987\) | 1.11538e15 | + | 1.24703e14i | 1.19079 | + | 0.133135i | ||||
\(988\) | 4.89683e13 | 0.0520152 | ||||||||
\(989\) | 2.85482e14i | 0.301715i | ||||||||
\(990\) | −1.85926e14 | + | 8.21095e14i | −0.195508 | + | 0.863410i | ||||
\(991\) | 9.64032e14 | 1.00861 | 0.504305 | − | 0.863526i | \(-0.331749\pi\) | ||||
0.504305 | + | 0.863526i | \(0.331749\pi\) | |||||||
\(992\) | − | 5.71601e14i | − | 0.595024i | ||||||
\(993\) | −4.77180e13 | + | 4.26803e14i | −0.0494238 | + | 0.442060i | ||||
\(994\) | −1.24089e15 | −1.27880 | ||||||||
\(995\) | 4.32167e14i | 0.443135i | ||||||||
\(996\) | −9.29321e13 | − | 1.03901e13i | −0.0948132 | − | 0.0106004i | ||||
\(997\) | −8.69673e14 | −0.882836 | −0.441418 | − | 0.897302i | \(-0.645524\pi\) | ||||
−0.441418 | + | 0.897302i | \(0.645524\pi\) | |||||||
\(998\) | − | 4.92045e14i | − | 0.496996i | ||||||
\(999\) | −2.86073e14 | + | 8.24357e14i | −0.287508 | + | 0.828491i |
(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 | 3.11.b.a.2.2 | yes | 2 | |
3.2 | odd | 2 | inner | 3.11.b.a.2.1 | ✓ | 2 | |
4.3 | odd | 2 | 48.11.e.c.17.1 | 2 | |||
5.2 | odd | 4 | 75.11.d.b.74.2 | 4 | |||
5.3 | odd | 4 | 75.11.d.b.74.3 | 4 | |||
5.4 | even | 2 | 75.11.c.d.26.1 | 2 | |||
8.3 | odd | 2 | 192.11.e.d.65.2 | 2 | |||
8.5 | even | 2 | 192.11.e.e.65.1 | 2 | |||
9.2 | odd | 6 | 81.11.d.d.53.1 | 4 | |||
9.4 | even | 3 | 81.11.d.d.26.1 | 4 | |||
9.5 | odd | 6 | 81.11.d.d.26.2 | 4 | |||
9.7 | even | 3 | 81.11.d.d.53.2 | 4 | |||
12.11 | even | 2 | 48.11.e.c.17.2 | 2 | |||
15.2 | even | 4 | 75.11.d.b.74.4 | 4 | |||
15.8 | even | 4 | 75.11.d.b.74.1 | 4 | |||
15.14 | odd | 2 | 75.11.c.d.26.2 | 2 | |||
24.5 | odd | 2 | 192.11.e.e.65.2 | 2 | |||
24.11 | even | 2 | 192.11.e.d.65.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.11.b.a.2.1 | ✓ | 2 | 3.2 | odd | 2 | inner | |
3.11.b.a.2.2 | yes | 2 | 1.1 | even | 1 | trivial | |
48.11.e.c.17.1 | 2 | 4.3 | odd | 2 | |||
48.11.e.c.17.2 | 2 | 12.11 | even | 2 | |||
75.11.c.d.26.1 | 2 | 5.4 | even | 2 | |||
75.11.c.d.26.2 | 2 | 15.14 | odd | 2 | |||
75.11.d.b.74.1 | 4 | 15.8 | even | 4 | |||
75.11.d.b.74.2 | 4 | 5.2 | odd | 4 | |||
75.11.d.b.74.3 | 4 | 5.3 | odd | 4 | |||
75.11.d.b.74.4 | 4 | 15.2 | even | 4 | |||
81.11.d.d.26.1 | 4 | 9.4 | even | 3 | |||
81.11.d.d.26.2 | 4 | 9.5 | odd | 6 | |||
81.11.d.d.53.1 | 4 | 9.2 | odd | 6 | |||
81.11.d.d.53.2 | 4 | 9.7 | even | 3 | |||
192.11.e.d.65.1 | 2 | 24.11 | even | 2 | |||
192.11.e.d.65.2 | 2 | 8.3 | odd | 2 | |||
192.11.e.e.65.1 | 2 | 8.5 | even | 2 | |||
192.11.e.e.65.2 | 2 | 24.5 | odd | 2 |