Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,11,Mod(13,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, 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("14.13");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.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: | \(8.89500153743\) |
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: | \( x^{8} + 14130x^{6} + 61043589x^{4} + 87066375930x^{2} + 12363031798119 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{28}\cdot 3^{2}\cdot 7^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 13.6 | ||
Root | \(-58.7309i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 14.13 |
Dual form | 14.11.b.a.13.7 |
$q$-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 \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 22.6274 | 0.707107 | ||||||||
\(3\) | − | 96.1268i | − | 0.395584i | −0.980244 | − | 0.197792i | \(-0.936623\pi\) | ||
0.980244 | − | 0.197792i | \(-0.0633770\pi\) | |||||||
\(4\) | 512.000 | 0.500000 | ||||||||
\(5\) | 5042.67i | 1.61365i | 0.590789 | + | 0.806826i | \(0.298817\pi\) | ||||
−0.590789 | + | 0.806826i | \(0.701183\pi\) | |||||||
\(6\) | − | 2175.10i | − | 0.279720i | ||||||
\(7\) | 15326.2 | − | 6897.94i | 0.911896 | − | 0.410421i | ||||
\(8\) | 11585.2 | 0.353553 | ||||||||
\(9\) | 49808.6 | 0.843514 | ||||||||
\(10\) | 114102.i | 1.14102i | ||||||||
\(11\) | 39488.6 | 0.245193 | 0.122597 | − | 0.992457i | \(-0.460878\pi\) | ||||
0.122597 | + | 0.992457i | \(0.460878\pi\) | |||||||
\(12\) | − | 49216.9i | − | 0.197792i | ||||||
\(13\) | 97801.9i | 0.263409i | 0.991289 | + | 0.131704i | \(0.0420450\pi\) | ||||
−0.991289 | + | 0.131704i | \(0.957955\pi\) | |||||||
\(14\) | 346793. | − | 156083.i | 0.644808 | − | 0.290211i | ||||
\(15\) | 484735. | 0.638335 | ||||||||
\(16\) | 262144. | 0.250000 | ||||||||
\(17\) | 2.49682e6i | 1.75850i | 0.476359 | + | 0.879251i | \(0.341956\pi\) | ||||
−0.476359 | + | 0.879251i | \(0.658044\pi\) | |||||||
\(18\) | 1.12704e6 | 0.596454 | ||||||||
\(19\) | − | 4.33604e6i | − | 1.75116i | −0.483076 | − | 0.875579i | \(-0.660480\pi\) | ||
0.483076 | − | 0.875579i | \(-0.339520\pi\) | |||||||
\(20\) | 2.58184e6i | 0.806826i | ||||||||
\(21\) | −663077. | − | 1.47326e6i | −0.162356 | − | 0.360731i | ||||
\(22\) | 893525. | 0.173378 | ||||||||
\(23\) | −7.59420e6 | −1.17989 | −0.589947 | − | 0.807442i | \(-0.700851\pi\) | ||||
−0.589947 | + | 0.807442i | \(0.700851\pi\) | |||||||
\(24\) | − | 1.11365e6i | − | 0.139860i | ||||||
\(25\) | −1.56628e7 | −1.60388 | ||||||||
\(26\) | 2.21300e6i | 0.186258i | ||||||||
\(27\) | − | 1.04641e7i | − | 0.729264i | ||||||
\(28\) | 7.84704e6 | − | 3.53174e6i | 0.455948 | − | 0.205210i | ||||
\(29\) | −1.43209e7 | −0.698201 | −0.349100 | − | 0.937085i | \(-0.613513\pi\) | ||||
−0.349100 | + | 0.937085i | \(0.613513\pi\) | |||||||
\(30\) | 1.09683e7 | 0.451371 | ||||||||
\(31\) | − | 1.71800e7i | − | 0.600088i | −0.953925 | − | 0.300044i | \(-0.902999\pi\) | ||
0.953925 | − | 0.300044i | \(-0.0970013\pi\) | |||||||
\(32\) | 5.93164e6 | 0.176777 | ||||||||
\(33\) | − | 3.79591e6i | − | 0.0969944i | ||||||
\(34\) | 5.64966e7i | 1.24345i | ||||||||
\(35\) | 3.47840e7 | + | 7.72851e7i | 0.662276 | + | 1.47148i | ||||
\(36\) | 2.55020e7 | 0.421757 | ||||||||
\(37\) | 7.22320e7 | 1.04165 | 0.520824 | − | 0.853664i | \(-0.325625\pi\) | ||||
0.520824 | + | 0.853664i | \(0.325625\pi\) | |||||||
\(38\) | − | 9.81134e7i | − | 1.23826i | ||||||
\(39\) | 9.40139e6 | 0.104200 | ||||||||
\(40\) | 5.84205e7i | 0.570512i | ||||||||
\(41\) | − | 8.80529e7i | − | 0.760019i | −0.924983 | − | 0.380009i | \(-0.875921\pi\) | ||
0.924983 | − | 0.380009i | \(-0.124079\pi\) | |||||||
\(42\) | −1.50037e7 | − | 3.33361e7i | −0.114803 | − | 0.255076i | ||||
\(43\) | −8.51402e7 | −0.579151 | −0.289576 | − | 0.957155i | \(-0.593514\pi\) | ||||
−0.289576 | + | 0.957155i | \(0.593514\pi\) | |||||||
\(44\) | 2.02182e7 | 0.122597 | ||||||||
\(45\) | 2.51168e8i | 1.36114i | ||||||||
\(46\) | −1.71837e8 | −0.834311 | ||||||||
\(47\) | − | 1.00540e8i | − | 0.438379i | −0.975682 | − | 0.219189i | \(-0.929659\pi\) | ||
0.975682 | − | 0.219189i | \(-0.0703413\pi\) | |||||||
\(48\) | − | 2.51991e7i | − | 0.0988959i | ||||||
\(49\) | 1.87312e8 | − | 2.11439e8i | 0.663110 | − | 0.748522i | ||||
\(50\) | −3.54410e8 | −1.13411 | ||||||||
\(51\) | 2.40011e8 | 0.695634 | ||||||||
\(52\) | 5.00746e7i | 0.131704i | ||||||||
\(53\) | −2.82493e8 | −0.675505 | −0.337752 | − | 0.941235i | \(-0.609667\pi\) | ||||
−0.337752 | + | 0.941235i | \(0.609667\pi\) | |||||||
\(54\) | − | 2.36776e8i | − | 0.515667i | ||||||
\(55\) | 1.99128e8i | 0.395656i | ||||||||
\(56\) | 1.77558e8 | − | 7.99143e7i | 0.322404 | − | 0.145106i | ||||
\(57\) | −4.16810e8 | −0.692729 | ||||||||
\(58\) | −3.24045e8 | −0.493702 | ||||||||
\(59\) | 1.83928e8i | 0.257269i | 0.991692 | + | 0.128635i | \(0.0410594\pi\) | ||||
−0.991692 | + | 0.128635i | \(0.958941\pi\) | |||||||
\(60\) | 2.48185e8 | 0.319167 | ||||||||
\(61\) | 1.70972e8i | 0.202430i | 0.994865 | + | 0.101215i | \(0.0322731\pi\) | ||||
−0.994865 | + | 0.101215i | \(0.967727\pi\) | |||||||
\(62\) | − | 3.88739e8i | − | 0.424326i | ||||||
\(63\) | 7.63379e8 | − | 3.43577e8i | 0.769197 | − | 0.346195i | ||||
\(64\) | 1.34218e8 | 0.125000 | ||||||||
\(65\) | −4.93182e8 | −0.425051 | ||||||||
\(66\) | − | 8.58917e7i | − | 0.0685854i | ||||||
\(67\) | 1.83033e9 | 1.35567 | 0.677835 | − | 0.735214i | \(-0.262918\pi\) | ||||
0.677835 | + | 0.735214i | \(0.262918\pi\) | |||||||
\(68\) | 1.27837e9i | 0.879251i | ||||||||
\(69\) | 7.30007e8i | 0.466747i | ||||||||
\(70\) | 7.87072e8 | + | 1.74876e9i | 0.468300 | + | 1.04050i | ||||
\(71\) | −1.43321e9 | −0.794361 | −0.397180 | − | 0.917741i | \(-0.630011\pi\) | ||||
−0.397180 | + | 0.917741i | \(0.630011\pi\) | |||||||
\(72\) | 5.77045e8 | 0.298227 | ||||||||
\(73\) | − | 2.62693e9i | − | 1.26717i | −0.773674 | − | 0.633584i | \(-0.781583\pi\) | ||
0.773674 | − | 0.633584i | \(-0.218417\pi\) | |||||||
\(74\) | 1.63442e9 | 0.736556 | ||||||||
\(75\) | 1.50562e9i | 0.634467i | ||||||||
\(76\) | − | 2.22005e9i | − | 0.875579i | ||||||
\(77\) | 6.05212e8 | − | 2.72390e8i | 0.223591 | − | 0.100632i | ||||
\(78\) | 2.12729e8 | 0.0736807 | ||||||||
\(79\) | −3.22612e9 | −1.04844 | −0.524221 | − | 0.851582i | \(-0.675644\pi\) | ||||
−0.524221 | + | 0.851582i | \(0.675644\pi\) | |||||||
\(80\) | 1.32190e9i | 0.403413i | ||||||||
\(81\) | 1.93527e9 | 0.555029 | ||||||||
\(82\) | − | 1.99241e9i | − | 0.537415i | ||||||
\(83\) | 4.12390e8i | 0.104693i | 0.998629 | + | 0.0523465i | \(0.0166700\pi\) | ||||
−0.998629 | + | 0.0523465i | \(0.983330\pi\) | |||||||
\(84\) | −3.39495e8 | − | 7.54311e8i | −0.0811778 | − | 0.180366i | ||||
\(85\) | −1.25906e10 | −2.83761 | ||||||||
\(86\) | −1.92650e9 | −0.409522 | ||||||||
\(87\) | 1.37662e9i | 0.276197i | ||||||||
\(88\) | 4.57485e8 | 0.0866888 | ||||||||
\(89\) | − | 8.95824e9i | − | 1.60425i | −0.597154 | − | 0.802126i | \(-0.703702\pi\) | ||
0.597154 | − | 0.802126i | \(-0.296298\pi\) | |||||||
\(90\) | 5.68329e9i | 0.962470i | ||||||||
\(91\) | 6.74632e8 | + | 1.49894e9i | 0.108108 | + | 0.240202i | ||||
\(92\) | −3.88823e9 | −0.589947 | ||||||||
\(93\) | −1.65146e9 | −0.237385 | ||||||||
\(94\) | − | 2.27496e9i | − | 0.309981i | ||||||
\(95\) | 2.18652e10 | 2.82576 | ||||||||
\(96\) | − | 5.70190e8i | − | 0.0699300i | ||||||
\(97\) | − | 1.03188e9i | − | 0.120163i | −0.998193 | − | 0.0600815i | \(-0.980864\pi\) | ||
0.998193 | − | 0.0600815i | \(-0.0191361\pi\) | |||||||
\(98\) | 4.23839e9 | − | 4.78432e9i | 0.468890 | − | 0.529285i | ||||
\(99\) | 1.96687e9 | 0.206824 | ||||||||
\(100\) | −8.01938e9 | −0.801938 | ||||||||
\(101\) | 1.85809e10i | 1.76790i | 0.467577 | + | 0.883952i | \(0.345127\pi\) | ||||
−0.467577 | + | 0.883952i | \(0.654873\pi\) | |||||||
\(102\) | 5.43084e9 | 0.491888 | ||||||||
\(103\) | 1.09696e10i | 0.946244i | 0.880997 | + | 0.473122i | \(0.156873\pi\) | ||||
−0.880997 | + | 0.473122i | \(0.843127\pi\) | |||||||
\(104\) | 1.13306e9i | 0.0931291i | ||||||||
\(105\) | 7.42917e9 | − | 3.34368e9i | 0.582095 | − | 0.261986i | ||||
\(106\) | −6.39209e9 | −0.477654 | ||||||||
\(107\) | 1.70919e10 | 1.21863 | 0.609313 | − | 0.792930i | \(-0.291445\pi\) | ||||
0.609313 | + | 0.792930i | \(0.291445\pi\) | |||||||
\(108\) | − | 5.35764e9i | − | 0.364632i | ||||||
\(109\) | −2.59945e9 | −0.168946 | −0.0844731 | − | 0.996426i | \(-0.526921\pi\) | ||||
−0.0844731 | + | 0.996426i | \(0.526921\pi\) | |||||||
\(110\) | 4.50575e9i | 0.279771i | ||||||||
\(111\) | − | 6.94343e9i | − | 0.412059i | ||||||
\(112\) | 4.01768e9 | − | 1.80825e9i | 0.227974 | − | 0.102605i | ||||
\(113\) | −2.04111e10 | −1.10783 | −0.553916 | − | 0.832572i | \(-0.686867\pi\) | ||||
−0.553916 | + | 0.832572i | \(0.686867\pi\) | |||||||
\(114\) | −9.43133e9 | −0.489834 | ||||||||
\(115\) | − | 3.82950e10i | − | 1.90394i | ||||||
\(116\) | −7.33230e9 | −0.349100 | ||||||||
\(117\) | 4.87138e9i | 0.222189i | ||||||||
\(118\) | 4.16182e9i | 0.181917i | ||||||||
\(119\) | 1.72229e10 | + | 3.82669e10i | 0.721725 | + | 1.60357i | ||||
\(120\) | 5.61578e9 | 0.225685 | ||||||||
\(121\) | −2.43781e10 | −0.939880 | ||||||||
\(122\) | 3.86865e9i | 0.143140i | ||||||||
\(123\) | −8.46425e9 | −0.300651 | ||||||||
\(124\) | − | 8.79616e9i | − | 0.300044i | ||||||
\(125\) | − | 2.97377e10i | − | 0.974446i | ||||||
\(126\) | 1.72733e10 | − | 7.77426e9i | 0.543904 | − | 0.244797i | ||||
\(127\) | −4.47220e10 | −1.35364 | −0.676819 | − | 0.736150i | \(-0.736642\pi\) | ||||
−0.676819 | + | 0.736150i | \(0.736642\pi\) | |||||||
\(128\) | 3.03700e9 | 0.0883883 | ||||||||
\(129\) | 8.18425e9i | 0.229103i | ||||||||
\(130\) | −1.11594e10 | −0.300556 | ||||||||
\(131\) | 2.11188e10i | 0.547410i | 0.961814 | + | 0.273705i | \(0.0882491\pi\) | ||||
−0.961814 | + | 0.273705i | \(0.911751\pi\) | |||||||
\(132\) | − | 1.94351e9i | − | 0.0484972i | ||||||
\(133\) | −2.99097e10 | − | 6.64552e10i | −0.718711 | − | 1.59687i | ||||
\(134\) | 4.14155e10 | 0.958604 | ||||||||
\(135\) | 5.27672e10 | 1.17678 | ||||||||
\(136\) | 2.89263e10i | 0.621724i | ||||||||
\(137\) | −1.93382e10 | −0.400694 | −0.200347 | − | 0.979725i | \(-0.564207\pi\) | ||||
−0.200347 | + | 0.979725i | \(0.564207\pi\) | |||||||
\(138\) | 1.65182e10i | 0.330040i | ||||||||
\(139\) | 5.61255e10i | 1.08165i | 0.841135 | + | 0.540825i | \(0.181888\pi\) | ||||
−0.841135 | + | 0.540825i | \(0.818112\pi\) | |||||||
\(140\) | 1.78094e10 | + | 3.95700e10i | 0.331138 | + | 0.735742i | ||||
\(141\) | −9.66459e9 | −0.173415 | ||||||||
\(142\) | −3.24298e10 | −0.561698 | ||||||||
\(143\) | 3.86206e9i | 0.0645860i | ||||||||
\(144\) | 1.30570e10 | 0.210878 | ||||||||
\(145\) | − | 7.22155e10i | − | 1.12665i | ||||||
\(146\) | − | 5.94407e10i | − | 0.896024i | ||||||
\(147\) | −2.03250e10 | − | 1.80057e10i | −0.296103 | − | 0.262315i | ||||
\(148\) | 3.69828e10 | 0.520824 | ||||||||
\(149\) | 1.24417e11 | 1.69414 | 0.847071 | − | 0.531480i | \(-0.178364\pi\) | ||||
0.847071 | + | 0.531480i | \(0.178364\pi\) | |||||||
\(150\) | 3.40683e10i | 0.448636i | ||||||||
\(151\) | −4.03799e10 | −0.514375 | −0.257188 | − | 0.966361i | \(-0.582796\pi\) | ||||
−0.257188 | + | 0.966361i | \(0.582796\pi\) | |||||||
\(152\) | − | 5.02340e10i | − | 0.619128i | ||||||
\(153\) | 1.24363e11i | 1.48332i | ||||||||
\(154\) | 1.36944e10 | − | 6.16348e9i | 0.158102 | − | 0.0711578i | ||||
\(155\) | 8.66330e10 | 0.968333 | ||||||||
\(156\) | 4.81351e9 | 0.0521001 | ||||||||
\(157\) | 5.25863e10i | 0.551282i | 0.961261 | + | 0.275641i | \(0.0888901\pi\) | ||||
−0.961261 | + | 0.275641i | \(0.911110\pi\) | |||||||
\(158\) | −7.29987e10 | −0.741361 | ||||||||
\(159\) | 2.71552e10i | 0.267219i | ||||||||
\(160\) | 2.99113e10i | 0.285256i | ||||||||
\(161\) | −1.16391e11 | + | 5.23844e10i | −1.07594 | + | 0.484253i | ||||
\(162\) | 4.37901e10 | 0.392465 | ||||||||
\(163\) | 4.26249e10 | 0.370447 | 0.185223 | − | 0.982696i | \(-0.440699\pi\) | ||||
0.185223 | + | 0.982696i | \(0.440699\pi\) | |||||||
\(164\) | − | 4.50831e10i | − | 0.380009i | ||||||
\(165\) | 1.91415e10 | 0.156515 | ||||||||
\(166\) | 9.33133e9i | 0.0740292i | ||||||||
\(167\) | − | 1.80191e11i | − | 1.38724i | −0.720341 | − | 0.693620i | \(-0.756015\pi\) | ||
0.720341 | − | 0.693620i | \(-0.243985\pi\) | |||||||
\(168\) | −7.68190e9 | − | 1.70681e10i | −0.0574014 | − | 0.127538i | ||||
\(169\) | 1.28293e11 | 0.930616 | ||||||||
\(170\) | −2.84893e11 | −2.00649 | ||||||||
\(171\) | − | 2.15972e11i | − | 1.47712i | ||||||
\(172\) | −4.35918e10 | −0.289576 | ||||||||
\(173\) | 1.11027e10i | 0.0716469i | 0.999358 | + | 0.0358234i | \(0.0114054\pi\) | ||||
−0.999358 | + | 0.0358234i | \(0.988595\pi\) | |||||||
\(174\) | 3.11494e10i | 0.195301i | ||||||||
\(175\) | −2.40053e11 | + | 1.08041e11i | −1.46257 | + | 0.658264i | ||||
\(176\) | 1.03517e10 | 0.0612983 | ||||||||
\(177\) | 1.76804e10 | 0.101772 | ||||||||
\(178\) | − | 2.02702e11i | − | 1.13438i | ||||||
\(179\) | −6.78324e10 | −0.369124 | −0.184562 | − | 0.982821i | \(-0.559087\pi\) | ||||
−0.184562 | + | 0.982821i | \(0.559087\pi\) | |||||||
\(180\) | 1.28598e11i | 0.680569i | ||||||||
\(181\) | − | 6.80794e10i | − | 0.350448i | −0.984529 | − | 0.175224i | \(-0.943935\pi\) | ||
0.984529 | − | 0.175224i | \(-0.0560649\pi\) | |||||||
\(182\) | 1.52652e10 | + | 3.39170e10i | 0.0764442 | + | 0.169848i | ||||
\(183\) | 1.64350e10 | 0.0800781 | ||||||||
\(184\) | −8.79807e10 | −0.417156 | ||||||||
\(185\) | 3.64242e11i | 1.68086i | ||||||||
\(186\) | −3.73683e10 | −0.167856 | ||||||||
\(187\) | 9.85959e10i | 0.431172i | ||||||||
\(188\) | − | 5.14765e10i | − | 0.219189i | ||||||
\(189\) | −7.21810e10 | − | 1.60376e11i | −0.299305 | − | 0.665013i | ||||
\(190\) | 4.94753e11 | 1.99811 | ||||||||
\(191\) | 1.49074e11 | 0.586457 | 0.293229 | − | 0.956042i | \(-0.405270\pi\) | ||||
0.293229 | + | 0.956042i | \(0.405270\pi\) | |||||||
\(192\) | − | 1.29019e10i | − | 0.0494480i | ||||||
\(193\) | 2.66294e11 | 0.994432 | 0.497216 | − | 0.867627i | \(-0.334356\pi\) | ||||
0.497216 | + | 0.867627i | \(0.334356\pi\) | |||||||
\(194\) | − | 2.33488e10i | − | 0.0849681i | ||||||
\(195\) | 4.74081e10i | 0.168143i | ||||||||
\(196\) | 9.59038e10 | − | 1.08257e11i | 0.331555 | − | 0.374261i | ||||
\(197\) | 2.10936e11 | 0.710919 | 0.355460 | − | 0.934692i | \(-0.384324\pi\) | ||||
0.355460 | + | 0.934692i | \(0.384324\pi\) | |||||||
\(198\) | 4.45052e10 | 0.146246 | ||||||||
\(199\) | 4.03047e10i | 0.129149i | 0.997913 | + | 0.0645744i | \(0.0205690\pi\) | ||||
−0.997913 | + | 0.0645744i | \(0.979431\pi\) | |||||||
\(200\) | −1.81458e11 | −0.567056 | ||||||||
\(201\) | − | 1.75943e11i | − | 0.536281i | ||||||
\(202\) | 4.20437e11i | 1.25010i | ||||||||
\(203\) | −2.19486e11 | + | 9.87847e10i | −0.636687 | + | 0.286556i | ||||
\(204\) | 1.22886e11 | 0.347817 | ||||||||
\(205\) | 4.44021e11 | 1.22641 | ||||||||
\(206\) | 2.48213e11i | 0.669095i | ||||||||
\(207\) | −3.78257e11 | −0.995257 | ||||||||
\(208\) | 2.56382e10i | 0.0658522i | ||||||||
\(209\) | − | 1.71224e11i | − | 0.429372i | ||||||
\(210\) | 1.68103e11 | − | 7.56587e10i | 0.411603 | − | 0.185252i | ||||
\(211\) | −4.75297e11 | −1.13646 | −0.568228 | − | 0.822871i | \(-0.692371\pi\) | ||||
−0.568228 | + | 0.822871i | \(0.692371\pi\) | |||||||
\(212\) | −1.44636e11 | −0.337752 | ||||||||
\(213\) | 1.37770e11i | 0.314236i | ||||||||
\(214\) | 3.86745e11 | 0.861699 | ||||||||
\(215\) | − | 4.29333e11i | − | 0.934549i | ||||||
\(216\) | − | 1.21230e11i | − | 0.257834i | ||||||
\(217\) | −1.18507e11 | − | 2.63305e11i | −0.246288 | − | 0.547218i | ||||
\(218\) | −5.88187e10 | −0.119463 | ||||||||
\(219\) | −2.52519e11 | −0.501271 | ||||||||
\(220\) | 1.01953e11i | 0.197828i | ||||||||
\(221\) | −2.44194e11 | −0.463205 | ||||||||
\(222\) | − | 1.57112e11i | − | 0.291370i | ||||||
\(223\) | 1.06930e11i | 0.193899i | 0.995289 | + | 0.0969496i | \(0.0309086\pi\) | ||||
−0.995289 | + | 0.0969496i | \(0.969091\pi\) | |||||||
\(224\) | 9.09098e10 | − | 4.09161e10i | 0.161202 | − | 0.0725528i | ||||
\(225\) | −7.80145e11 | −1.35289 | ||||||||
\(226\) | −4.61850e11 | −0.783356 | ||||||||
\(227\) | − | 4.70031e11i | − | 0.779825i | −0.920852 | − | 0.389913i | \(-0.872505\pi\) | ||
0.920852 | − | 0.389913i | \(-0.127495\pi\) | |||||||
\(228\) | −2.13407e11 | −0.346365 | ||||||||
\(229\) | 1.16834e12i | 1.85520i | 0.373573 | + | 0.927601i | \(0.378133\pi\) | ||||
−0.373573 | + | 0.927601i | \(0.621867\pi\) | |||||||
\(230\) | − | 8.66518e11i | − | 1.34629i | ||||||
\(231\) | −2.61840e10 | − | 5.81771e10i | −0.0398085 | − | 0.0884488i | ||||
\(232\) | −1.65911e11 | −0.246851 | ||||||||
\(233\) | 8.97263e11 | 1.30659 | 0.653296 | − | 0.757102i | \(-0.273386\pi\) | ||||
0.653296 | + | 0.757102i | \(0.273386\pi\) | |||||||
\(234\) | 1.10227e11i | 0.157111i | ||||||||
\(235\) | 5.06989e11 | 0.707391 | ||||||||
\(236\) | 9.41712e10i | 0.128635i | ||||||||
\(237\) | 3.10116e11i | 0.414747i | ||||||||
\(238\) | 3.89710e11 | + | 8.65880e11i | 0.510337 | + | 1.13390i | ||||
\(239\) | −2.07777e11 | −0.266445 | −0.133222 | − | 0.991086i | \(-0.542532\pi\) | ||||
−0.133222 | + | 0.991086i | \(0.542532\pi\) | |||||||
\(240\) | 1.27070e11 | 0.159584 | ||||||||
\(241\) | − | 1.42283e12i | − | 1.75012i | −0.484015 | − | 0.875060i | \(-0.660822\pi\) | ||
0.484015 | − | 0.875060i | \(-0.339178\pi\) | |||||||
\(242\) | −5.51613e11 | −0.664596 | ||||||||
\(243\) | − | 8.03928e11i | − | 0.948824i | ||||||
\(244\) | 8.75376e10i | 0.101215i | ||||||||
\(245\) | 1.06622e12 | + | 9.44552e11i | 1.20785 | + | 1.07003i | ||||
\(246\) | −1.91524e11 | −0.212592 | ||||||||
\(247\) | 4.24073e11 | 0.461271 | ||||||||
\(248\) | − | 1.99034e11i | − | 0.212163i | ||||||
\(249\) | 3.96418e10 | 0.0414149 | ||||||||
\(250\) | − | 6.72888e11i | − | 0.689037i | ||||||
\(251\) | 1.34718e12i | 1.35225i | 0.736788 | + | 0.676124i | \(0.236342\pi\) | ||||
−0.736788 | + | 0.676124i | \(0.763658\pi\) | |||||||
\(252\) | 3.90850e11 | − | 1.75911e11i | 0.384598 | − | 0.173098i | ||||
\(253\) | −2.99884e11 | −0.289302 | ||||||||
\(254\) | −1.01194e12 | −0.957166 | ||||||||
\(255\) | 1.21030e12i | 1.12251i | ||||||||
\(256\) | 6.87195e10 | 0.0625000 | ||||||||
\(257\) | 8.61095e11i | 0.768043i | 0.923324 | + | 0.384022i | \(0.125461\pi\) | ||||
−0.923324 | + | 0.384022i | \(0.874539\pi\) | |||||||
\(258\) | 1.85189e11i | 0.162000i | ||||||||
\(259\) | 1.10704e12 | − | 4.98252e11i | 0.949875 | − | 0.427514i | ||||
\(260\) | −2.52509e11 | −0.212525 | ||||||||
\(261\) | −7.13304e11 | −0.588942 | ||||||||
\(262\) | 4.77863e11i | 0.387077i | ||||||||
\(263\) | 1.81540e12 | 1.44276 | 0.721380 | − | 0.692540i | \(-0.243508\pi\) | ||||
0.721380 | + | 0.692540i | \(0.243508\pi\) | |||||||
\(264\) | − | 4.39765e10i | − | 0.0342927i | ||||||
\(265\) | − | 1.42452e12i | − | 1.09003i | ||||||
\(266\) | −6.76780e11 | − | 1.50371e12i | −0.508205 | − | 1.12916i | ||||
\(267\) | −8.61128e11 | −0.634616 | ||||||||
\(268\) | 9.37126e11 | 0.677835 | ||||||||
\(269\) | − | 5.43819e11i | − | 0.386094i | −0.981189 | − | 0.193047i | \(-0.938163\pi\) | ||
0.981189 | − | 0.193047i | \(-0.0618370\pi\) | |||||||
\(270\) | 1.19398e12 | 0.832108 | ||||||||
\(271\) | − | 5.87004e10i | − | 0.0401601i | −0.999798 | − | 0.0200800i | \(-0.993608\pi\) | ||
0.999798 | − | 0.0200800i | \(-0.00639210\pi\) | |||||||
\(272\) | 6.54526e11i | 0.439625i | ||||||||
\(273\) | 1.44088e11 | − | 6.48502e10i | 0.0950199 | − | 0.0427659i | ||||
\(274\) | −4.37573e11 | −0.283333 | ||||||||
\(275\) | −6.18504e11 | −0.393259 | ||||||||
\(276\) | 3.73763e11i | 0.233373i | ||||||||
\(277\) | 9.73590e11 | 0.597004 | 0.298502 | − | 0.954409i | \(-0.403513\pi\) | ||||
0.298502 | + | 0.954409i | \(0.403513\pi\) | |||||||
\(278\) | 1.26998e12i | 0.764842i | ||||||||
\(279\) | − | 8.55712e11i | − | 0.506182i | ||||||
\(280\) | 4.02981e11 | + | 8.95366e11i | 0.234150 | + | 0.520248i | ||||
\(281\) | −1.99761e12 | −1.14020 | −0.570098 | − | 0.821576i | \(-0.693095\pi\) | ||||
−0.570098 | + | 0.821576i | \(0.693095\pi\) | |||||||
\(282\) | −2.18685e11 | −0.122623 | ||||||||
\(283\) | 3.24795e12i | 1.78928i | 0.446790 | + | 0.894639i | \(0.352567\pi\) | ||||
−0.446790 | + | 0.894639i | \(0.647433\pi\) | |||||||
\(284\) | −7.33803e11 | −0.397180 | ||||||||
\(285\) | − | 2.10183e12i | − | 1.11782i | ||||||
\(286\) | 8.73884e10i | 0.0456692i | ||||||||
\(287\) | −6.07384e11 | − | 1.34952e12i | −0.311927 | − | 0.693059i | ||||
\(288\) | 2.95447e11 | 0.149114 | ||||||||
\(289\) | −4.21812e12 | −2.09233 | ||||||||
\(290\) | − | 1.63405e12i | − | 0.796664i | ||||||
\(291\) | −9.91915e10 | −0.0475346 | ||||||||
\(292\) | − | 1.34499e12i | − | 0.633584i | ||||||
\(293\) | 2.56632e11i | 0.118843i | 0.998233 | + | 0.0594214i | \(0.0189256\pi\) | ||||
−0.998233 | + | 0.0594214i | \(0.981074\pi\) | |||||||
\(294\) | −4.59901e11 | − | 4.07423e11i | −0.209377 | − | 0.185485i | ||||
\(295\) | −9.27488e11 | −0.415143 | ||||||||
\(296\) | 8.36825e11 | 0.368278 | ||||||||
\(297\) | − | 4.13214e11i | − | 0.178810i | ||||||
\(298\) | 2.81524e12 | 1.19794 | ||||||||
\(299\) | − | 7.42728e11i | − | 0.310795i | ||||||
\(300\) | 7.70878e11i | 0.317234i | ||||||||
\(301\) | −1.30488e12 | + | 5.87292e11i | −0.528126 | + | 0.237696i | ||||
\(302\) | −9.13692e11 | −0.363718 | ||||||||
\(303\) | 1.78612e12 | 0.699354 | ||||||||
\(304\) | − | 1.13667e12i | − | 0.437789i | ||||||
\(305\) | −8.62154e11 | −0.326652 | ||||||||
\(306\) | 2.81402e12i | 1.04887i | ||||||||
\(307\) | − | 2.54361e12i | − | 0.932735i | −0.884591 | − | 0.466368i | \(-0.845562\pi\) | ||
0.884591 | − | 0.466368i | \(-0.154438\pi\) | |||||||
\(308\) | 3.09868e11 | − | 1.39464e11i | 0.111795 | − | 0.0503161i | ||||
\(309\) | 1.05447e12 | 0.374319 | ||||||||
\(310\) | 1.96028e12 | 0.684715 | ||||||||
\(311\) | − | 2.25597e12i | − | 0.775410i | −0.921784 | − | 0.387705i | \(-0.873268\pi\) | ||
0.921784 | − | 0.387705i | \(-0.126732\pi\) | |||||||
\(312\) | 1.08917e11 | 0.0368404 | ||||||||
\(313\) | 4.18452e12i | 1.39291i | 0.717599 | + | 0.696457i | \(0.245241\pi\) | ||||
−0.717599 | + | 0.696457i | \(0.754759\pi\) | |||||||
\(314\) | 1.18989e12i | 0.389815i | ||||||||
\(315\) | 1.73254e12 | + | 3.84947e12i | 0.558639 | + | 1.24122i | ||||
\(316\) | −1.65177e12 | −0.524221 | ||||||||
\(317\) | 1.98589e11 | 0.0620382 | 0.0310191 | − | 0.999519i | \(-0.490125\pi\) | ||||
0.0310191 | + | 0.999519i | \(0.490125\pi\) | |||||||
\(318\) | 6.14451e11i | 0.188952i | ||||||||
\(319\) | −5.65512e11 | −0.171194 | ||||||||
\(320\) | 6.76815e11i | 0.201707i | ||||||||
\(321\) | − | 1.64299e12i | − | 0.482069i | ||||||
\(322\) | −2.63362e12 | + | 1.18532e12i | −0.760805 | + | 0.342418i | ||||
\(323\) | 1.08263e13 | 3.07941 | ||||||||
\(324\) | 9.90856e11 | 0.277514 | ||||||||
\(325\) | − | 1.53186e12i | − | 0.422475i | ||||||
\(326\) | 9.64492e11 | 0.261945 | ||||||||
\(327\) | 2.49876e11i | 0.0668323i | ||||||||
\(328\) | − | 1.02011e12i | − | 0.268707i | ||||||
\(329\) | −6.93519e11 | − | 1.54090e12i | −0.179920 | − | 0.399756i | ||||
\(330\) | 4.33123e11 | 0.110673 | ||||||||
\(331\) | −2.33599e12 | −0.587937 | −0.293969 | − | 0.955815i | \(-0.594976\pi\) | ||||
−0.293969 | + | 0.955815i | \(0.594976\pi\) | |||||||
\(332\) | 2.11144e11i | 0.0523465i | ||||||||
\(333\) | 3.59778e12 | 0.878644 | ||||||||
\(334\) | − | 4.07727e12i | − | 0.980927i | ||||||
\(335\) | 9.22972e12i | 2.18758i | ||||||||
\(336\) | −1.73822e11 | − | 3.86207e11i | −0.0405889 | − | 0.0901828i | ||||
\(337\) | −1.03795e12 | −0.238796 | −0.119398 | − | 0.992846i | \(-0.538096\pi\) | ||||
−0.119398 | + | 0.992846i | \(0.538096\pi\) | |||||||
\(338\) | 2.90295e12 | 0.658045 | ||||||||
\(339\) | 1.96205e12i | 0.438240i | ||||||||
\(340\) | −6.44640e12 | −1.41881 | ||||||||
\(341\) | − | 6.78414e11i | − | 0.147137i | ||||||
\(342\) | − | 4.88689e12i | − | 1.04448i | ||||||
\(343\) | 1.41230e12 | − | 4.53263e12i | 0.297479 | − | 0.954728i | ||||
\(344\) | −9.86369e11 | −0.204761 | ||||||||
\(345\) | −3.68118e12 | −0.753168 | ||||||||
\(346\) | 2.51225e11i | 0.0506620i | ||||||||
\(347\) | −8.68534e12 | −1.72639 | −0.863196 | − | 0.504870i | \(-0.831541\pi\) | ||||
−0.863196 | + | 0.504870i | \(0.831541\pi\) | |||||||
\(348\) | 7.04831e11i | 0.138098i | ||||||||
\(349\) | 8.13667e11i | 0.157152i | 0.996908 | + | 0.0785759i | \(0.0250373\pi\) | ||||
−0.996908 | + | 0.0785759i | \(0.974963\pi\) | |||||||
\(350\) | −5.43177e12 | + | 2.44470e12i | −1.03419 | + | 0.465463i | ||||
\(351\) | 1.02341e12 | 0.192095 | ||||||||
\(352\) | 2.34232e11 | 0.0433444 | ||||||||
\(353\) | 2.87814e11i | 0.0525095i | 0.999655 | + | 0.0262548i | \(0.00835811\pi\) | ||||
−0.999655 | + | 0.0262548i | \(0.991642\pi\) | |||||||
\(354\) | 4.00062e11 | 0.0719633 | ||||||||
\(355\) | − | 7.22720e12i | − | 1.28182i | ||||||
\(356\) | − | 4.58662e12i | − | 0.802126i | ||||||
\(357\) | 3.67847e12 | − | 1.65558e12i | 0.634347 | − | 0.285503i | ||||
\(358\) | −1.53487e12 | −0.261010 | ||||||||
\(359\) | −9.62233e10 | −0.0161365 | −0.00806823 | − | 0.999967i | \(-0.502568\pi\) | ||||
−0.00806823 | + | 0.999967i | \(0.502568\pi\) | |||||||
\(360\) | 2.90984e12i | 0.481235i | ||||||||
\(361\) | −1.26702e13 | −2.06655 | ||||||||
\(362\) | − | 1.54046e12i | − | 0.247804i | ||||||
\(363\) | 2.34339e12i | 0.371801i | ||||||||
\(364\) | 3.45411e11 | + | 7.67455e11i | 0.0540542 | + | 0.120101i | ||||
\(365\) | 1.32467e13 | 2.04477 | ||||||||
\(366\) | 3.71881e11 | 0.0566238 | ||||||||
\(367\) | 8.07225e11i | 0.121245i | 0.998161 | + | 0.0606226i | \(0.0193086\pi\) | ||||
−0.998161 | + | 0.0606226i | \(0.980691\pi\) | |||||||
\(368\) | −1.99078e12 | −0.294974 | ||||||||
\(369\) | − | 4.38580e12i | − | 0.641086i | ||||||
\(370\) | 8.24185e12i | 1.18855i | ||||||||
\(371\) | −4.32956e12 | + | 1.94862e12i | −0.615990 | + | 0.277241i | ||||
\(372\) | −8.45547e11 | −0.118692 | ||||||||
\(373\) | 9.10414e12 | 1.26094 | 0.630471 | − | 0.776213i | \(-0.282862\pi\) | ||||
0.630471 | + | 0.776213i | \(0.282862\pi\) | |||||||
\(374\) | 2.23097e12i | 0.304885i | ||||||||
\(375\) | −2.85859e12 | −0.385475 | ||||||||
\(376\) | − | 1.16478e12i | − | 0.154990i | ||||||
\(377\) | − | 1.40061e12i | − | 0.183912i | ||||||
\(378\) | −1.63327e12 | − | 3.62889e12i | −0.211641 | − | 0.470235i | ||||
\(379\) | 1.64205e12 | 0.209986 | 0.104993 | − | 0.994473i | \(-0.466518\pi\) | ||||
0.104993 | + | 0.994473i | \(0.466518\pi\) | |||||||
\(380\) | 1.11950e13 | 1.41288 | ||||||||
\(381\) | 4.29898e12i | 0.535477i | ||||||||
\(382\) | 3.37317e12 | 0.414688 | ||||||||
\(383\) | 1.35119e13i | 1.63954i | 0.572690 | + | 0.819772i | \(0.305900\pi\) | ||||
−0.572690 | + | 0.819772i | \(0.694100\pi\) | |||||||
\(384\) | − | 2.91937e11i | − | 0.0349650i | ||||||
\(385\) | 1.37357e12 | + | 3.05188e12i | 0.162386 | + | 0.360798i | ||||
\(386\) | 6.02555e12 | 0.703169 | ||||||||
\(387\) | −4.24071e12 | −0.488522 | ||||||||
\(388\) | − | 5.28323e11i | − | 0.0600815i | ||||||
\(389\) | 1.27779e12 | 0.143454 | 0.0717268 | − | 0.997424i | \(-0.477149\pi\) | ||||
0.0717268 | + | 0.997424i | \(0.477149\pi\) | |||||||
\(390\) | 1.07272e12i | 0.118895i | ||||||||
\(391\) | − | 1.89614e13i | − | 2.07485i | ||||||
\(392\) | 2.17006e12 | − | 2.44957e12i | 0.234445 | − | 0.264642i | ||||
\(393\) | 2.03008e12 | 0.216546 | ||||||||
\(394\) | 4.77294e12 | 0.502696 | ||||||||
\(395\) | − | 1.62682e13i | − | 1.69182i | ||||||
\(396\) | 1.00704e12 | 0.103412 | ||||||||
\(397\) | 1.15319e13i | 1.16936i | 0.811264 | + | 0.584680i | \(0.198780\pi\) | ||||
−0.811264 | + | 0.584680i | \(0.801220\pi\) | |||||||
\(398\) | 9.11991e11i | 0.0913219i | ||||||||
\(399\) | −6.38813e12 | + | 2.87513e12i | −0.631697 | + | 0.284310i | ||||
\(400\) | −4.10592e12 | −0.400969 | ||||||||
\(401\) | −9.31976e12 | −0.898841 | −0.449420 | − | 0.893320i | \(-0.648369\pi\) | ||||
−0.449420 | + | 0.893320i | \(0.648369\pi\) | |||||||
\(402\) | − | 3.98114e12i | − | 0.379208i | ||||||
\(403\) | 1.68024e12 | 0.158068 | ||||||||
\(404\) | 9.51340e12i | 0.883952i | ||||||||
\(405\) | 9.75889e12i | 0.895624i | ||||||||
\(406\) | −4.96639e12 | + | 2.23524e12i | −0.450205 | + | 0.202626i | ||||
\(407\) | 2.85234e12 | 0.255405 | ||||||||
\(408\) | 2.78059e12 | 0.245944 | ||||||||
\(409\) | 3.12572e12i | 0.273107i | 0.990633 | + | 0.136554i | \(0.0436026\pi\) | ||||
−0.990633 | + | 0.136554i | \(0.956397\pi\) | |||||||
\(410\) | 1.00471e13 | 0.867201 | ||||||||
\(411\) | 1.85892e12i | 0.158508i | ||||||||
\(412\) | 5.61641e12i | 0.473122i | ||||||||
\(413\) | 1.26872e12 | + | 2.81893e12i | 0.105589 | + | 0.234603i | ||||
\(414\) | −8.55898e12 | −0.703753 | ||||||||
\(415\) | −2.07955e12 | −0.168938 | ||||||||
\(416\) | 5.80126e11i | 0.0465646i | ||||||||
\(417\) | 5.39517e12 | 0.427883 | ||||||||
\(418\) | − | 3.87436e12i | − | 0.303612i | ||||||
\(419\) | − | 8.88404e12i | − | 0.687924i | −0.938984 | − | 0.343962i | \(-0.888231\pi\) | ||
0.938984 | − | 0.343962i | \(-0.111769\pi\) | |||||||
\(420\) | 3.80374e12 | − | 1.71196e12i | 0.291048 | − | 0.130993i | ||||
\(421\) | −7.26228e12 | −0.549114 | −0.274557 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274557 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(422\) | −1.07547e13 | −0.803595 | ||||||||
\(423\) | − | 5.00776e12i | − | 0.369778i | ||||||
\(424\) | −3.27275e12 | −0.238827 | ||||||||
\(425\) | − | 3.91073e13i | − | 2.82042i | ||||||
\(426\) | 3.11738e12i | 0.222199i | ||||||||
\(427\) | 1.17935e12 | + | 2.62036e12i | 0.0830816 | + | 0.184595i | ||||
\(428\) | 8.75104e12 | 0.609313 | ||||||||
\(429\) | 3.71247e11 | 0.0255492 | ||||||||
\(430\) | − | 9.71470e12i | − | 0.660826i | ||||||
\(431\) | −1.27855e13 | −0.859668 | −0.429834 | − | 0.902908i | \(-0.641428\pi\) | ||||
−0.429834 | + | 0.902908i | \(0.641428\pi\) | |||||||
\(432\) | − | 2.74311e12i | − | 0.182316i | ||||||
\(433\) | 7.88938e12i | 0.518327i | 0.965834 | + | 0.259163i | \(0.0834468\pi\) | ||||
−0.965834 | + | 0.259163i | \(0.916553\pi\) | |||||||
\(434\) | −2.68150e12 | − | 5.95791e12i | −0.174152 | − | 0.386941i | ||||
\(435\) | −6.94185e12 | −0.445686 | ||||||||
\(436\) | −1.33092e12 | −0.0844731 | ||||||||
\(437\) | 3.29288e13i | 2.06618i | ||||||||
\(438\) | −5.71384e12 | −0.354452 | ||||||||
\(439\) | 2.34378e13i | 1.43745i | 0.695293 | + | 0.718726i | \(0.255275\pi\) | ||||
−0.695293 | + | 0.718726i | \(0.744725\pi\) | |||||||
\(440\) | 2.30694e12i | 0.139886i | ||||||||
\(441\) | 9.32976e12 | − | 1.05315e13i | 0.559342 | − | 0.631388i | ||||
\(442\) | −5.52548e12 | −0.327535 | ||||||||
\(443\) | −1.82456e13 | −1.06940 | −0.534700 | − | 0.845042i | \(-0.679575\pi\) | ||||
−0.534700 | + | 0.845042i | \(0.679575\pi\) | |||||||
\(444\) | − | 3.55504e12i | − | 0.206029i | ||||||
\(445\) | 4.51734e13 | 2.58871 | ||||||||
\(446\) | 2.41955e12i | 0.137107i | ||||||||
\(447\) | − | 1.19598e13i | − | 0.670175i | ||||||
\(448\) | 2.05705e12 | − | 9.25826e11i | 0.113987 | − | 0.0513026i | ||||
\(449\) | −2.08618e13 | −1.14320 | −0.571598 | − | 0.820534i | \(-0.693676\pi\) | ||||
−0.571598 | + | 0.820534i | \(0.693676\pi\) | |||||||
\(450\) | −1.76527e13 | −0.956638 | ||||||||
\(451\) | − | 3.47708e12i | − | 0.186351i | ||||||
\(452\) | −1.04505e13 | −0.553916 | ||||||||
\(453\) | 3.88159e12i | 0.203478i | ||||||||
\(454\) | − | 1.06356e13i | − | 0.551420i | ||||||
\(455\) | −7.55863e12 | + | 3.40194e12i | −0.387602 | + | 0.174450i | ||||
\(456\) | −4.82884e12 | −0.244917 | ||||||||
\(457\) | 1.33766e13 | 0.671065 | 0.335533 | − | 0.942029i | \(-0.391084\pi\) | ||||
0.335533 | + | 0.942029i | \(0.391084\pi\) | |||||||
\(458\) | 2.64365e13i | 1.31183i | ||||||||
\(459\) | 2.61271e13 | 1.28241 | ||||||||
\(460\) | − | 1.96071e13i | − | 0.951970i | ||||||
\(461\) | 1.08265e12i | 0.0519977i | 0.999662 | + | 0.0259989i | \(0.00827663\pi\) | ||||
−0.999662 | + | 0.0259989i | \(0.991723\pi\) | |||||||
\(462\) | −5.92476e11 | − | 1.31640e12i | −0.0281488 | − | 0.0625427i | ||||
\(463\) | 3.18938e12 | 0.149900 | 0.0749499 | − | 0.997187i | \(-0.476120\pi\) | ||||
0.0749499 | + | 0.997187i | \(0.476120\pi\) | |||||||
\(464\) | −3.75414e12 | −0.174550 | ||||||||
\(465\) | − | 8.32776e12i | − | 0.383057i | ||||||
\(466\) | 2.03027e13 | 0.923901 | ||||||||
\(467\) | − | 1.95436e13i | − | 0.879873i | −0.898029 | − | 0.439937i | \(-0.855001\pi\) | ||
0.898029 | − | 0.439937i | \(-0.144999\pi\) | |||||||
\(468\) | 2.49415e12i | 0.111095i | ||||||||
\(469\) | 2.80520e13 | − | 1.26255e13i | 1.23623 | − | 0.556395i | ||||
\(470\) | 1.14719e13 | 0.500201 | ||||||||
\(471\) | 5.05495e12 | 0.218078 | ||||||||
\(472\) | 2.13085e12i | 0.0909584i | ||||||||
\(473\) | −3.36206e12 | −0.142004 | ||||||||
\(474\) | 7.01713e12i | 0.293270i | ||||||||
\(475\) | 6.79147e13i | 2.80864i | ||||||||
\(476\) | 8.81813e12 | + | 1.95926e13i | 0.360863 | + | 0.801785i | ||||
\(477\) | −1.40706e13 | −0.569798 | ||||||||
\(478\) | −4.70145e12 | −0.188405 | ||||||||
\(479\) | 1.01633e12i | 0.0403049i | 0.999797 | + | 0.0201525i | \(0.00641516\pi\) | ||||
−0.999797 | + | 0.0201525i | \(0.993585\pi\) | |||||||
\(480\) | 2.87528e12 | 0.112843 | ||||||||
\(481\) | 7.06443e12i | 0.274379i | ||||||||
\(482\) | − | 3.21950e13i | − | 1.23752i | ||||||
\(483\) | 5.03554e12 | + | 1.11883e13i | 0.191563 | + | 0.425625i | ||||
\(484\) | −1.24816e13 | −0.469940 | ||||||||
\(485\) | 5.20343e12 | 0.193901 | ||||||||
\(486\) | − | 1.81908e13i | − | 0.670920i | ||||||
\(487\) | 1.20527e13 | 0.439988 | 0.219994 | − | 0.975501i | \(-0.429396\pi\) | ||||
0.219994 | + | 0.975501i | \(0.429396\pi\) | |||||||
\(488\) | 1.98075e12i | 0.0715699i | ||||||||
\(489\) | − | 4.09740e12i | − | 0.146543i | ||||||
\(490\) | 2.41257e13 | + | 2.13728e13i | 0.854082 | + | 0.756625i | ||||
\(491\) | −1.64611e13 | −0.576836 | −0.288418 | − | 0.957505i | \(-0.593129\pi\) | ||||
−0.288418 | + | 0.957505i | \(0.593129\pi\) | |||||||
\(492\) | −4.33370e12 | −0.150326 | ||||||||
\(493\) | − | 3.57567e13i | − | 1.22779i | ||||||
\(494\) | 9.59567e12 | 0.326168 | ||||||||
\(495\) | 9.91828e12i | 0.333742i | ||||||||
\(496\) | − | 4.50363e12i | − | 0.150022i | ||||||
\(497\) | −2.19657e13 | + | 9.88619e12i | −0.724375 | + | 0.326022i | ||||
\(498\) | 8.96991e11 | 0.0292847 | ||||||||
\(499\) | 5.70754e13 | 1.84479 | 0.922394 | − | 0.386250i | \(-0.126230\pi\) | ||||
0.922394 | + | 0.386250i | \(0.126230\pi\) | |||||||
\(500\) | − | 1.52257e13i | − | 0.487223i | ||||||
\(501\) | −1.73212e13 | −0.548770 | ||||||||
\(502\) | 3.04832e13i | 0.956184i | ||||||||
\(503\) | − | 5.90671e13i | − | 1.83445i | −0.398371 | − | 0.917224i | \(-0.630424\pi\) | ||
0.398371 | − | 0.917224i | \(-0.369576\pi\) | |||||||
\(504\) | 8.84393e12 | − | 3.98042e12i | 0.271952 | − | 0.122399i | ||||
\(505\) | −9.36970e13 | −2.85278 | ||||||||
\(506\) | −6.78561e12 | −0.204567 | ||||||||
\(507\) | − | 1.23324e13i | − | 0.368136i | ||||||
\(508\) | −2.28977e13 | −0.676819 | ||||||||
\(509\) | 2.35370e13i | 0.688909i | 0.938803 | + | 0.344455i | \(0.111936\pi\) | ||||
−0.938803 | + | 0.344455i | \(0.888064\pi\) | |||||||
\(510\) | 2.73859e13i | 0.793736i | ||||||||
\(511\) | −1.81204e13 | − | 4.02610e13i | −0.520072 | − | 1.15553i | ||||
\(512\) | 1.55494e12 | 0.0441942 | ||||||||
\(513\) | −4.53729e13 | −1.27706 | ||||||||
\(514\) | 1.94844e13i | 0.543089i | ||||||||
\(515\) | −5.53158e13 | −1.52691 | ||||||||
\(516\) | 4.19034e12i | 0.114551i | ||||||||
\(517\) | − | 3.97018e12i | − | 0.107487i | ||||||
\(518\) | 2.50496e13 | − | 1.12741e13i | 0.671663 | − | 0.302298i | ||||
\(519\) | 1.06727e12 | 0.0283423 | ||||||||
\(520\) | −5.71363e12 | −0.150278 | ||||||||
\(521\) | − | 1.10415e13i | − | 0.287633i | −0.989604 | − | 0.143816i | \(-0.954063\pi\) | ||
0.989604 | − | 0.143816i | \(-0.0459374\pi\) | |||||||
\(522\) | −1.61402e13 | −0.416445 | ||||||||
\(523\) | − | 4.24447e13i | − | 1.08471i | −0.840148 | − | 0.542357i | \(-0.817532\pi\) | ||
0.840148 | − | 0.542357i | \(-0.182468\pi\) | |||||||
\(524\) | 1.08128e13i | 0.273705i | ||||||||
\(525\) | 1.03857e13 | + | 2.30755e13i | 0.260398 | + | 0.578568i | ||||
\(526\) | 4.10779e13 | 1.02019 | ||||||||
\(527\) | 4.28954e13 | 1.05525 | ||||||||
\(528\) | − | 9.95076e11i | − | 0.0242486i | ||||||
\(529\) | 1.62454e13 | 0.392150 | ||||||||
\(530\) | − | 3.22332e13i | − | 0.770768i | ||||||
\(531\) | 9.16120e12i | 0.217010i | ||||||||
\(532\) | −1.53138e13 | − | 3.40251e13i | −0.359355 | − | 0.798437i | ||||
\(533\) | 8.61174e12 | 0.200196 | ||||||||
\(534\) | −1.94851e13 | −0.448741 | ||||||||
\(535\) | 8.61886e13i | 1.96644i | ||||||||
\(536\) | 2.12048e13 | 0.479302 | ||||||||
\(537\) | 6.52052e12i | 0.146019i | ||||||||
\(538\) | − | 1.23052e13i | − | 0.273010i | ||||||
\(539\) | 7.39669e12 | − | 8.34942e12i | 0.162590 | − | 0.183532i | ||||
\(540\) | 2.70168e13 | 0.588389 | ||||||||
\(541\) | 3.26395e13 | 0.704298 | 0.352149 | − | 0.935944i | \(-0.385451\pi\) | ||||
0.352149 | + | 0.935944i | \(0.385451\pi\) | |||||||
\(542\) | − | 1.32824e12i | − | 0.0283975i | ||||||
\(543\) | −6.54426e12 | −0.138631 | ||||||||
\(544\) | 1.48102e13i | 0.310862i | ||||||||
\(545\) | − | 1.31081e13i | − | 0.272620i | ||||||
\(546\) | 3.26034e12 | − | 1.46739e12i | 0.0671892 | − | 0.0302401i | ||||
\(547\) | 5.34548e13 | 1.09157 | 0.545783 | − | 0.837927i | \(-0.316232\pi\) | ||||
0.545783 | + | 0.837927i | \(0.316232\pi\) | |||||||
\(548\) | −9.90115e12 | −0.200347 | ||||||||
\(549\) | 8.51588e12i | 0.170753i | ||||||||
\(550\) | −1.39951e13 | −0.278076 | ||||||||
\(551\) | 6.20960e13i | 1.22266i | ||||||||
\(552\) | 8.45730e12i | 0.165020i | ||||||||
\(553\) | −4.94443e13 | + | 2.22536e13i | −0.956071 | + | 0.430302i | ||||
\(554\) | 2.20298e13 | 0.422145 | ||||||||
\(555\) | 3.50134e13 | 0.664920 | ||||||||
\(556\) | 2.87363e13i | 0.540825i | ||||||||
\(557\) | 4.96209e13 | 0.925525 | 0.462763 | − | 0.886482i | \(-0.346858\pi\) | ||||
0.462763 | + | 0.886482i | \(0.346858\pi\) | |||||||
\(558\) | − | 1.93626e13i | − | 0.357925i | ||||||
\(559\) | − | 8.32687e12i | − | 0.152554i | ||||||
\(560\) | 9.11842e12 | + | 2.02598e13i | 0.165569 | + | 0.367871i | ||||
\(561\) | 9.47771e12 | 0.170565 | ||||||||
\(562\) | −4.52008e13 | −0.806241 | ||||||||
\(563\) | 4.43474e13i | 0.784019i | 0.919961 | + | 0.392009i | \(0.128220\pi\) | ||||
−0.919961 | + | 0.392009i | \(0.871780\pi\) | |||||||
\(564\) | −4.94827e12 | −0.0867077 | ||||||||
\(565\) | − | 1.02926e14i | − | 1.78766i | ||||||
\(566\) | 7.34928e13i | 1.26521i | ||||||||
\(567\) | 2.96603e13 | − | 1.33493e13i | 0.506129 | − | 0.227795i | ||||
\(568\) | −1.66041e13 | −0.280849 | ||||||||
\(569\) | 4.38072e12 | 0.0734486 | 0.0367243 | − | 0.999325i | \(-0.488308\pi\) | ||||
0.0367243 | + | 0.999325i | \(0.488308\pi\) | |||||||
\(570\) | − | 4.75590e13i | − | 0.790421i | ||||||
\(571\) | −1.53631e13 | −0.253104 | −0.126552 | − | 0.991960i | \(-0.540391\pi\) | ||||
−0.126552 | + | 0.991960i | \(0.540391\pi\) | |||||||
\(572\) | 1.97737e12i | 0.0322930i | ||||||||
\(573\) | − | 1.43300e13i | − | 0.231993i | ||||||
\(574\) | −1.37435e13 | − | 3.05362e13i | −0.220566 | − | 0.490066i | ||||
\(575\) | 1.18947e14 | 1.89240 | ||||||||
\(576\) | 6.68520e12 | 0.105439 | ||||||||
\(577\) | − | 3.53277e13i | − | 0.552378i | −0.961103 | − | 0.276189i | \(-0.910928\pi\) | ||
0.961103 | − | 0.276189i | \(-0.0890715\pi\) | |||||||
\(578\) | −9.54451e13 | −1.47950 | ||||||||
\(579\) | − | 2.55980e13i | − | 0.393381i | ||||||
\(580\) | − | 3.69743e13i | − | 0.563327i | ||||||
\(581\) | 2.84464e12 | + | 6.32039e12i | 0.0429682 | + | 0.0954692i | ||||
\(582\) | −2.24445e12 | −0.0336120 | ||||||||
\(583\) | −1.11553e13 | −0.165629 | ||||||||
\(584\) | − | 3.04336e13i | − | 0.448012i | ||||||
\(585\) | −2.45647e13 | −0.358536 | ||||||||
\(586\) | 5.80692e12i | 0.0840346i | ||||||||
\(587\) | 6.02124e13i | 0.863964i | 0.901882 | + | 0.431982i | \(0.142186\pi\) | ||||
−0.901882 | + | 0.431982i | \(0.857814\pi\) | |||||||
\(588\) | −1.04064e13 | − | 9.21893e12i | −0.148052 | − | 0.131158i | ||||
\(589\) | −7.44931e13 | −1.05085 | ||||||||
\(590\) | −2.09867e13 | −0.293551 | ||||||||
\(591\) | − | 2.02766e13i | − | 0.281228i | ||||||
\(592\) | 1.89352e13 | 0.260412 | ||||||||
\(593\) | 1.02677e14i | 1.40023i | 0.714028 | + | 0.700117i | \(0.246869\pi\) | ||||
−0.714028 | + | 0.700117i | \(0.753131\pi\) | |||||||
\(594\) | − | 9.34997e12i | − | 0.126438i | ||||||
\(595\) | −1.92967e14 | + | 8.68494e13i | −2.58761 | + | 1.16461i | ||||
\(596\) | 6.37017e13 | 0.847071 | ||||||||
\(597\) | 3.87436e12 | 0.0510891 | ||||||||
\(598\) | − | 1.68060e13i | − | 0.219765i | ||||||
\(599\) | −3.82993e13 | −0.496657 | −0.248329 | − | 0.968676i | \(-0.579881\pi\) | ||||
−0.248329 | + | 0.968676i | \(0.579881\pi\) | |||||||
\(600\) | 1.74430e13i | 0.224318i | ||||||||
\(601\) | − | 6.01419e13i | − | 0.767017i | −0.923537 | − | 0.383508i | \(-0.874716\pi\) | ||
0.923537 | − | 0.383508i | \(-0.125284\pi\) | |||||||
\(602\) | −2.95260e13 | + | 1.32889e13i | −0.373442 | + | 0.168076i | ||||
\(603\) | 9.11660e13 | 1.14353 | ||||||||
\(604\) | −2.06745e13 | −0.257188 | ||||||||
\(605\) | − | 1.22930e14i | − | 1.51664i | ||||||
\(606\) | 4.04152e13 | 0.494518 | ||||||||
\(607\) | 4.05317e13i | 0.491872i | 0.969286 | + | 0.245936i | \(0.0790953\pi\) | ||||
−0.969286 | + | 0.245936i | \(0.920905\pi\) | |||||||
\(608\) | − | 2.57198e13i | − | 0.309564i | ||||||
\(609\) | 9.49586e12 | + | 2.10985e13i | 0.113357 | + | 0.251863i | ||||
\(610\) | −1.95083e13 | −0.230978 | ||||||||
\(611\) | 9.83300e12 | 0.115473 | ||||||||
\(612\) | 6.36740e13i | 0.741660i | ||||||||
\(613\) | −2.41704e13 | −0.279242 | −0.139621 | − | 0.990205i | \(-0.544588\pi\) | ||||
−0.139621 | + | 0.990205i | \(0.544588\pi\) | |||||||
\(614\) | − | 5.75553e13i | − | 0.659544i | ||||||
\(615\) | − | 4.26824e13i | − | 0.485147i | ||||||
\(616\) | 7.01152e12 | − | 3.15570e12i | 0.0790512 | − | 0.0355789i | ||||
\(617\) | 6.61702e13 | 0.740008 | 0.370004 | − | 0.929030i | \(-0.379356\pi\) | ||||
0.370004 | + | 0.929030i | \(0.379356\pi\) | |||||||
\(618\) | 2.38599e13 | 0.264683 | ||||||||
\(619\) | − | 1.00883e14i | − | 1.11010i | −0.831816 | − | 0.555051i | \(-0.812699\pi\) | ||
0.831816 | − | 0.555051i | \(-0.187301\pi\) | |||||||
\(620\) | 4.43561e13 | 0.484167 | ||||||||
\(621\) | 7.94668e13i | 0.860454i | ||||||||
\(622\) | − | 5.10468e13i | − | 0.548298i | ||||||
\(623\) | −6.17934e13 | − | 1.37296e14i | −0.658418 | − | 1.46291i | ||||
\(624\) | 2.46452e12 | 0.0260501 | ||||||||
\(625\) | −3.00010e12 | −0.0314583 | ||||||||
\(626\) | 9.46849e13i | 0.984939i | ||||||||
\(627\) | −1.64592e13 | −0.169852 | ||||||||
\(628\) | 2.69242e13i | 0.275641i | ||||||||
\(629\) | 1.80350e14i | 1.83174i | ||||||||
\(630\) | 3.92030e13 | + | 8.71035e13i | 0.395017 | + | 0.877673i | ||||
\(631\) | 1.85415e13 | 0.185353 | 0.0926763 | − | 0.995696i | \(-0.470458\pi\) | ||||
0.0926763 | + | 0.995696i | \(0.470458\pi\) | |||||||
\(632\) | −3.73753e13 | −0.370680 | ||||||||
\(633\) | 4.56888e13i | 0.449563i | ||||||||
\(634\) | 4.49356e12 | 0.0438676 | ||||||||
\(635\) | − | 2.25518e14i | − | 2.18430i | ||||||
\(636\) | 1.39034e13i | 0.133609i | ||||||||
\(637\) | 2.06791e13 | + | 1.83195e13i | 0.197167 | + | 0.174669i | ||||
\(638\) | −1.27961e13 | −0.121052 | ||||||||
\(639\) | −7.13862e13 | −0.670054 | ||||||||
\(640\) | 1.53146e13i | 0.142628i | ||||||||
\(641\) | 9.19492e13 | 0.849685 | 0.424842 | − | 0.905267i | \(-0.360330\pi\) | ||||
0.424842 | + | 0.905267i | \(0.360330\pi\) | |||||||
\(642\) | − | 3.71766e13i | − | 0.340874i | ||||||
\(643\) | 7.63688e13i | 0.694802i | 0.937717 | + | 0.347401i | \(0.112936\pi\) | ||||
−0.937717 | + | 0.347401i | \(0.887064\pi\) | |||||||
\(644\) | −5.95920e13 | + | 2.68208e13i | −0.537971 | + | 0.242126i | ||||
\(645\) | −4.12705e13 | −0.369693 | ||||||||
\(646\) | 2.44971e14 | 2.17747 | ||||||||
\(647\) | 1.03621e14i | 0.913957i | 0.889478 | + | 0.456978i | \(0.151068\pi\) | ||||
−0.889478 | + | 0.456978i | \(0.848932\pi\) | |||||||
\(648\) | 2.24205e13 | 0.196232 | ||||||||
\(649\) | 7.26306e12i | 0.0630806i | ||||||||
\(650\) | − | 3.46620e13i | − | 0.298735i | ||||||
\(651\) | −2.53107e13 | + | 1.13917e13i | −0.216470 | + | 0.0974276i | ||||
\(652\) | 2.18240e13 | 0.185223 | ||||||||
\(653\) | −5.38975e13 | −0.453944 | −0.226972 | − | 0.973901i | \(-0.572883\pi\) | ||||
−0.226972 | + | 0.973901i | \(0.572883\pi\) | |||||||
\(654\) | 5.65406e12i | 0.0472576i | ||||||||
\(655\) | −1.06495e14 | −0.883329 | ||||||||
\(656\) | − | 2.30825e13i | − | 0.190005i | ||||||
\(657\) | − | 1.30844e14i | − | 1.06887i | ||||||
\(658\) | −1.56925e13 | − | 3.48666e13i | −0.127222 | − | 0.282670i | ||||
\(659\) | 2.43899e13 | 0.196238 | 0.0981189 | − | 0.995175i | \(-0.468717\pi\) | ||||
0.0981189 | + | 0.995175i | \(0.468717\pi\) | |||||||
\(660\) | 9.80046e12 | 0.0782576 | ||||||||
\(661\) | 1.05621e14i | 0.837032i | 0.908209 | + | 0.418516i | \(0.137450\pi\) | ||||
−0.908209 | + | 0.418516i | \(0.862550\pi\) | |||||||
\(662\) | −5.28574e13 | −0.415734 | ||||||||
\(663\) | 2.34736e13i | 0.183236i | ||||||||
\(664\) | 4.77764e12i | 0.0370146i | ||||||||
\(665\) | 3.35111e14 | − | 1.50825e14i | 2.57680 | − | 1.15975i | ||||
\(666\) | 8.14084e13 | 0.621295 | ||||||||
\(667\) | 1.08756e14 | 0.823803 | ||||||||
\(668\) | − | 9.22580e13i | − | 0.693620i | ||||||
\(669\) | 1.02789e13 | 0.0767033 | ||||||||
\(670\) | 2.08845e14i | 1.54685i | ||||||||
\(671\) | 6.75144e12i | 0.0496345i | ||||||||
\(672\) | −3.93314e12 | − | 8.73887e12i | −0.0287007 | − | 0.0637689i | ||||
\(673\) | −1.32177e14 | −0.957370 | −0.478685 | − | 0.877987i | \(-0.658886\pi\) | ||||
−0.478685 | + | 0.877987i | \(0.658886\pi\) | |||||||
\(674\) | −2.34862e13 | −0.168854 | ||||||||
\(675\) | 1.63898e14i | 1.16965i | ||||||||
\(676\) | 6.56862e13 | 0.465308 | ||||||||
\(677\) | 1.37178e14i | 0.964590i | 0.876009 | + | 0.482295i | \(0.160197\pi\) | ||||
−0.876009 | + | 0.482295i | \(0.839803\pi\) | |||||||
\(678\) | 4.43962e13i | 0.309883i | ||||||||
\(679\) | −7.11785e12 | − | 1.58149e13i | −0.0493174 | − | 0.109576i | ||||
\(680\) | −1.45865e14 | −1.00325 | ||||||||
\(681\) | −4.51826e13 | −0.308486 | ||||||||
\(682\) | − | 1.53508e13i | − | 0.104042i | ||||||
\(683\) | −1.60627e14 | −1.08073 | −0.540363 | − | 0.841432i | \(-0.681713\pi\) | ||||
−0.540363 | + | 0.841432i | \(0.681713\pi\) | |||||||
\(684\) | − | 1.10578e14i | − | 0.738562i | ||||||
\(685\) | − | 9.75160e13i | − | 0.646581i | ||||||
\(686\) | 3.19567e13 | − | 1.02562e14i | 0.210349 | − | 0.675095i | ||||
\(687\) | 1.12309e14 | 0.733888 | ||||||||
\(688\) | −2.23190e13 | −0.144788 | ||||||||
\(689\) | − | 2.76284e13i | − | 0.177934i | ||||||
\(690\) | −8.32956e13 | −0.532570 | ||||||||
\(691\) | − | 1.30063e14i | − | 0.825591i | −0.910824 | − | 0.412796i | \(-0.864552\pi\) | ||
0.910824 | − | 0.412796i | \(-0.135448\pi\) | |||||||
\(692\) | 5.68457e12i | 0.0358234i | ||||||||
\(693\) | 3.01448e13 | − | 1.35674e13i | 0.188602 | − | 0.0848847i | ||||
\(694\) | −1.96527e14 | −1.22074 | ||||||||
\(695\) | −2.83022e14 | −1.74541 | ||||||||
\(696\) | 1.59485e13i | 0.0976503i | ||||||||
\(697\) | 2.19852e14 | 1.33649 | ||||||||
\(698\) | 1.84112e13i | 0.111123i | ||||||||
\(699\) | − | 8.62511e13i | − | 0.516867i | ||||||
\(700\) | −1.22907e14 | + | 5.53172e13i | −0.731284 | + | 0.329132i | ||||
\(701\) | −1.86336e14 | −1.10079 | −0.550397 | − | 0.834903i | \(-0.685524\pi\) | ||||
−0.550397 | + | 0.834903i | \(0.685524\pi\) | |||||||
\(702\) | 2.31572e13 | 0.135831 | ||||||||
\(703\) | − | 3.13201e14i | − | 1.82409i | ||||||
\(704\) | 5.30007e12 | 0.0306491 | ||||||||
\(705\) | − | 4.87353e13i | − | 0.279832i | ||||||
\(706\) | 6.51248e12i | 0.0371298i | ||||||||
\(707\) | 1.28170e14 | + | 2.84775e14i | 0.725584 | + | 1.61215i | ||||
\(708\) | 9.05238e12 | 0.0508858 | ||||||||
\(709\) | 3.30040e13 | 0.184219 | 0.0921096 | − | 0.995749i | \(-0.470639\pi\) | ||||
0.0921096 | + | 0.995749i | \(0.470639\pi\) | |||||||
\(710\) | − | 1.63533e14i | − | 0.906386i | ||||||
\(711\) | −1.60688e14 | −0.884376 | ||||||||
\(712\) | − | 1.03783e14i | − | 0.567189i | ||||||
\(713\) | 1.30468e14i | 0.708040i | ||||||||
\(714\) | 8.32344e13 | − | 3.74616e13i | 0.448551 | − | 0.201881i | ||||
\(715\) | −1.94751e13 | −0.104219 | ||||||||
\(716\) | −3.47302e13 | −0.184562 | ||||||||
\(717\) | 1.99729e13i | 0.105401i | ||||||||
\(718\) | −2.17728e12 | −0.0114102 | ||||||||
\(719\) | 3.05955e14i | 1.59226i | 0.605127 | + | 0.796129i | \(0.293123\pi\) | ||||
−0.605127 | + | 0.796129i | \(0.706877\pi\) | |||||||
\(720\) | 6.58423e13i | 0.340285i | ||||||||
\(721\) | 7.56673e13 | + | 1.68122e14i | 0.388358 | + | 0.862876i | ||||
\(722\) | −2.86693e14 | −1.46127 | ||||||||
\(723\) | −1.36772e14 | −0.692319 | ||||||||
\(724\) | − | 3.48567e13i | − | 0.175224i | ||||||
\(725\) | 2.24306e14 | 1.11983 | ||||||||
\(726\) | 5.30248e13i | 0.262903i | ||||||||
\(727\) | − | 2.35104e13i | − | 0.115768i | −0.998323 | − | 0.0578839i | \(-0.981565\pi\) | ||
0.998323 | − | 0.0578839i | \(-0.0184353\pi\) | |||||||
\(728\) | 7.81577e12 | + | 1.73655e13i | 0.0382221 | + | 0.0849241i | ||||
\(729\) | 3.69964e13 | 0.179689 | ||||||||
\(730\) | 2.99739e14 | 1.44587 | ||||||||
\(731\) | − | 2.12580e14i | − | 1.01844i | ||||||
\(732\) | 8.41471e12 | 0.0400391 | ||||||||
\(733\) | − | 2.17768e14i | − | 1.02914i | −0.857449 | − | 0.514569i | \(-0.827952\pi\) | ||
0.857449 | − | 0.514569i | \(-0.172048\pi\) | |||||||
\(734\) | 1.82654e13i | 0.0857332i | ||||||||
\(735\) | 9.07968e13 | − | 1.02492e14i | 0.423286 | − | 0.477808i | ||||
\(736\) | −4.50461e13 | −0.208578 | ||||||||
\(737\) | 7.22769e13 | 0.332401 | ||||||||
\(738\) | − | 9.92392e13i | − | 0.453316i | ||||||
\(739\) | 1.43784e14 | 0.652360 | 0.326180 | − | 0.945308i | \(-0.394238\pi\) | ||||
0.326180 | + | 0.945308i | \(0.394238\pi\) | |||||||
\(740\) | 1.86492e14i | 0.840429i | ||||||||
\(741\) | − | 4.07648e13i | − | 0.182471i | ||||||
\(742\) | −9.79667e13 | + | 4.40922e13i | −0.435571 | + | 0.196039i | ||||
\(743\) | 1.11241e14 | 0.491272 | 0.245636 | − | 0.969362i | \(-0.421003\pi\) | ||||
0.245636 | + | 0.969362i | \(0.421003\pi\) | |||||||
\(744\) | −1.91325e13 | −0.0839282 | ||||||||
\(745\) | 6.27395e14i | 2.73376i | ||||||||
\(746\) | 2.06003e14 | 0.891620 | ||||||||
\(747\) | 2.05406e13i | 0.0883100i | ||||||||
\(748\) | 5.04811e13i | 0.215586i | ||||||||
\(749\) | 2.61954e14 | − | 1.17899e14i | 1.11126 | − | 0.500149i | ||||
\(750\) | −6.46826e13 | −0.272572 | ||||||||
\(751\) | 4.09610e14 | 1.71463 | 0.857316 | − | 0.514791i | \(-0.172131\pi\) | ||||
0.857316 | + | 0.514791i | \(0.172131\pi\) | |||||||
\(752\) | − | 2.63560e13i | − | 0.109595i | ||||||
\(753\) | 1.29500e14 | 0.534927 | ||||||||
\(754\) | − | 3.16922e13i | − | 0.130046i | ||||||
\(755\) | − | 2.03622e14i | − | 0.830023i | ||||||
\(756\) | −3.69567e13 | − | 8.21125e13i | −0.149652 | − | 0.332507i | ||||
\(757\) | −3.46638e14 | −1.39443 | −0.697215 | − | 0.716862i | \(-0.745578\pi\) | ||||
−0.697215 | + | 0.716862i | \(0.745578\pi\) | |||||||
\(758\) | 3.71553e13 | 0.148482 | ||||||||
\(759\) | 2.88269e13i | 0.114443i | ||||||||
\(760\) | 2.53313e14 | 0.999057 | ||||||||
\(761\) | − | 3.02067e14i | − | 1.18353i | −0.806109 | − | 0.591767i | \(-0.798431\pi\) | ||
0.806109 | − | 0.591767i | \(-0.201569\pi\) | |||||||
\(762\) | 9.72749e13i | 0.378639i | ||||||||
\(763\) | −3.98397e13 | + | 1.79308e13i | −0.154061 | + | 0.0693390i | ||||
\(764\) | 7.63261e13 | 0.293229 | ||||||||
\(765\) | −6.27122e14 | −2.39356 | ||||||||
\(766\) | 3.05740e14i | 1.15933i | ||||||||
\(767\) | −1.79885e13 | −0.0677670 | ||||||||
\(768\) | − | 6.60579e12i | − | 0.0247240i | ||||||
\(769\) | 2.65421e14i | 0.986968i | 0.869755 | + | 0.493484i | \(0.164277\pi\) | ||||
−0.869755 | + | 0.493484i | \(0.835723\pi\) | |||||||
\(770\) | 3.10804e13 | + | 6.90561e13i | 0.114824 | + | 0.255122i | ||||
\(771\) | 8.27744e13 | 0.303825 | ||||||||
\(772\) | 1.36343e14 | 0.497216 | ||||||||
\(773\) | 2.73467e13i | 0.0990848i | 0.998772 | + | 0.0495424i | \(0.0157763\pi\) | ||||
−0.998772 | + | 0.0495424i | \(0.984224\pi\) | |||||||
\(774\) | −9.59564e13 | −0.345437 | ||||||||
\(775\) | 2.69088e14i | 0.962466i | ||||||||
\(776\) | − | 1.19546e13i | − | 0.0424841i | ||||||
\(777\) | −4.78954e13 | − | 1.06417e14i | −0.169117 | − | 0.375755i | ||||
\(778\) | 2.89131e13 | 0.101437 | ||||||||
\(779\) | −3.81801e14 | −1.33091 | ||||||||
\(780\) | 2.42729e13i | 0.0840716i | ||||||||
\(781\) | −5.65954e13 | −0.194772 | ||||||||
\(782\) | − | 4.29047e14i | − | 1.46714i | ||||||
\(783\) | 1.49856e14i | 0.509173i | ||||||||
\(784\) | 4.91028e13 | − | 5.54275e13i | 0.165777 | − | 0.187131i | ||||
\(785\) | −2.65175e14 | −0.889578 | ||||||||
\(786\) | 4.59355e13 | 0.153121 | ||||||||
\(787\) | − | 3.56222e14i | − | 1.17991i | −0.807437 | − | 0.589953i | \(-0.799146\pi\) | ||
0.807437 | − | 0.589953i | \(-0.200854\pi\) | |||||||
\(788\) | 1.07999e14 | 0.355460 | ||||||||
\(789\) | − | 1.74509e14i | − | 0.570732i | ||||||
\(790\) | − | 3.68108e14i | − | 1.19630i | ||||||
\(791\) | −3.12825e14 | + | 1.40794e14i | −1.01023 | + | 0.454677i | ||||
\(792\) | 2.27867e13 | 0.0731232 | ||||||||
\(793\) | −1.67214e13 | −0.0533220 | ||||||||
\(794\) | 2.60937e14i | 0.826863i | ||||||||
\(795\) | −1.36934e14 | −0.431198 | ||||||||
\(796\) | 2.06360e13i | 0.0645744i | ||||||||
\(797\) | − | 2.34948e14i | − | 0.730600i | −0.930890 | − | 0.365300i | \(-0.880966\pi\) | ||
0.930890 | − | 0.365300i | \(-0.119034\pi\) | |||||||
\(798\) | −1.44547e14 | + | 6.50567e13i | −0.446677 | + | 0.201038i | ||||
\(799\) | 2.51030e14 | 0.770890 | ||||||||
\(800\) | −9.29064e13 | −0.283528 | ||||||||
\(801\) | − | 4.46198e14i | − | 1.35321i | ||||||
\(802\) | −2.10882e14 | −0.635576 | ||||||||
\(803\) | − | 1.03734e14i | − | 0.310701i | ||||||
\(804\) | − | 9.00830e13i | − | 0.268141i | ||||||
\(805\) | −2.64157e14 | − | 5.86919e14i | −0.781416 | − | 1.73620i | ||||
\(806\) | 3.80194e13 | 0.111771 | ||||||||
\(807\) | −5.22756e13 | −0.152733 | ||||||||
\(808\) | 2.15264e14i | 0.625049i | ||||||||
\(809\) | 3.70512e14 | 1.06920 | 0.534601 | − | 0.845104i | \(-0.320462\pi\) | ||||
0.534601 | + | 0.845104i | \(0.320462\pi\) | |||||||
\(810\) | 2.20819e14i | 0.633302i | ||||||||
\(811\) | 5.40725e14i | 1.54125i | 0.637291 | + | 0.770623i | \(0.280055\pi\) | ||||
−0.637291 | + | 0.770623i | \(0.719945\pi\) | |||||||
\(812\) | −1.12377e14 | + | 5.05778e13i | −0.318343 | + | 0.143278i | ||||
\(813\) | −5.64268e12 | −0.0158867 | ||||||||
\(814\) | 6.45410e13 | 0.180598 | ||||||||
\(815\) | 2.14943e14i | 0.597772i | ||||||||
\(816\) | 6.29176e13 | 0.173909 | ||||||||
\(817\) | 3.69171e14i | 1.01419i | ||||||||
\(818\) | 7.07269e13i | 0.193116i | ||||||||
\(819\) | 3.36025e13 | + | 7.46599e13i | 0.0911910 | + | 0.202613i | ||||
\(820\) | 2.27339e14 | 0.613203 | ||||||||
\(821\) | −5.34259e14 | −1.43231 | −0.716154 | − | 0.697942i | \(-0.754099\pi\) | ||||
−0.716154 | + | 0.697942i | \(0.754099\pi\) | |||||||
\(822\) | 4.20625e13i | 0.112082i | ||||||||
\(823\) | −7.86815e13 | −0.208388 | −0.104194 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104194 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(824\) | 1.27085e14i | 0.334548i | ||||||||
\(825\) | 5.94548e13i | 0.155567i | ||||||||
\(826\) | 2.87080e13 | + | 6.37850e13i | 0.0746624 | + | 0.165889i | ||||
\(827\) | 5.43521e14 | 1.40504 | 0.702520 | − | 0.711664i | \(-0.252058\pi\) | ||||
0.702520 | + | 0.711664i | \(0.252058\pi\) | |||||||
\(828\) | −1.93668e14 | −0.497628 | ||||||||
\(829\) | − | 4.54306e14i | − | 1.16031i | −0.814504 | − | 0.580157i | \(-0.802991\pi\) | ||
0.814504 | − | 0.580157i | \(-0.197009\pi\) | |||||||
\(830\) | −4.70547e13 | −0.119457 | ||||||||
\(831\) | − | 9.35881e13i | − | 0.236165i | ||||||
\(832\) | 1.31268e13i | 0.0329261i | ||||||||
\(833\) | 5.27925e14 | + | 4.67685e14i | 1.31628 | + | 1.16608i | ||||
\(834\) | 1.22079e14 | 0.302559 | ||||||||
\(835\) | 9.08645e14 | 2.23852 | ||||||||
\(836\) | − | 8.76667e13i | − | 0.214686i | ||||||
\(837\) | −1.79774e14 | −0.437622 | ||||||||
\(838\) | − | 2.01023e14i | − | 0.486436i | ||||||
\(839\) | − | 5.33758e14i | − | 1.28391i | −0.766742 | − | 0.641955i | \(-0.778123\pi\) | ||
0.766742 | − | 0.641955i | \(-0.221877\pi\) | |||||||
\(840\) | 8.60687e13 | − | 3.87373e13i | 0.205802 | − | 0.0926259i | ||||
\(841\) | −2.15619e14 | −0.512516 | ||||||||
\(842\) | −1.64327e14 | −0.388282 | ||||||||
\(843\) | 1.92024e14i | 0.451043i | ||||||||
\(844\) | −2.43352e14 | −0.568228 | ||||||||
\(845\) | 6.46940e14i | 1.50169i | ||||||||
\(846\) | − | 1.13313e14i | − | 0.261473i | ||||||
\(847\) | −3.73624e14 | + | 1.68158e14i | −0.857073 | + | 0.385746i | ||||
\(848\) | −7.40539e13 | −0.168876 | ||||||||
\(849\) | 3.12216e14 | 0.707809 | ||||||||
\(850\) | − | 8.84898e14i | − | 1.99434i | ||||||
\(851\) | −5.48544e14 | −1.22903 | ||||||||
\(852\) | 7.05382e13i | 0.157118i | ||||||||
\(853\) | − | 3.28172e14i | − | 0.726703i | −0.931652 | − | 0.363351i | \(-0.881632\pi\) | ||
0.931652 | − | 0.363351i | \(-0.118368\pi\) | |||||||
\(854\) | 2.66857e13 | + | 5.92919e13i | 0.0587475 | + | 0.130529i | ||||
\(855\) | 1.08908e15 | 2.38357 | ||||||||
\(856\) | 1.98013e14 | 0.430850 | ||||||||
\(857\) | 3.25327e14i | 0.703747i | 0.936048 | + | 0.351873i | \(0.114455\pi\) | ||||
−0.936048 | + | 0.351873i | \(0.885545\pi\) | |||||||
\(858\) | 8.40037e12 | 0.0180660 | ||||||||
\(859\) | 3.47684e14i | 0.743394i | 0.928354 | + | 0.371697i | \(0.121224\pi\) | ||||
−0.928354 | + | 0.371697i | \(0.878776\pi\) | |||||||
\(860\) | − | 2.19819e14i | − | 0.467275i | ||||||
\(861\) | −1.29725e14 | + | 5.83859e13i | −0.274163 | + | 0.123393i | ||||
\(862\) | −2.89302e14 | −0.607877 | ||||||||
\(863\) | 2.68408e14 | 0.560713 | 0.280357 | − | 0.959896i | \(-0.409547\pi\) | ||||
0.280357 | + | 0.959896i | \(0.409547\pi\) | |||||||
\(864\) | − | 6.20695e13i | − | 0.128917i | ||||||
\(865\) | −5.59871e13 | −0.115613 | ||||||||
\(866\) | 1.78516e14i | 0.366512i | ||||||||
\(867\) | 4.05474e14i | 0.827690i | ||||||||
\(868\) | −6.06754e13 | − | 1.34812e14i | −0.123144 | − | 0.273609i | ||||
\(869\) | −1.27395e14 | −0.257071 | ||||||||
\(870\) | −1.57076e14 | −0.315147 | ||||||||
\(871\) | 1.79009e14i | 0.357096i | ||||||||
\(872\) | −3.01152e13 | −0.0597315 | ||||||||
\(873\) | − | 5.13966e13i | − | 0.101359i | ||||||
\(874\) | 7.45093e14i | 1.46101i | ||||||||
\(875\) | −2.05129e14 | − | 4.55768e14i | −0.399933 | − | 0.888594i | ||||
\(876\) | −1.29290e14 | −0.250636 | ||||||||
\(877\) | 6.53459e14 | 1.25957 | 0.629783 | − | 0.776771i | \(-0.283144\pi\) | ||||
0.629783 | + | 0.776771i | \(0.283144\pi\) | |||||||
\(878\) | 5.30336e14i | 1.01643i | ||||||||
\(879\) | 2.46692e13 | 0.0470123 | ||||||||
\(880\) | 5.22001e13i | 0.0989141i | ||||||||
\(881\) | − | 2.35821e14i | − | 0.444327i | −0.975009 | − | 0.222164i | \(-0.928688\pi\) | ||
0.975009 | − | 0.222164i | \(-0.0713119\pi\) | |||||||
\(882\) | 2.11108e14 | − | 2.38300e14i | 0.395515 | − | 0.446459i | ||||
\(883\) | 5.53102e14 | 1.03039 | 0.515195 | − | 0.857073i | \(-0.327719\pi\) | ||||
0.515195 | + | 0.857073i | \(0.327719\pi\) | |||||||
\(884\) | −1.25027e14 | −0.231603 | ||||||||
\(885\) | 8.91565e13i | 0.164224i | ||||||||
\(886\) | −4.12851e14 | −0.756180 | ||||||||
\(887\) | − | 1.05990e15i | − | 1.93039i | −0.261529 | − | 0.965196i | \(-0.584227\pi\) | ||
0.261529 | − | 0.965196i | \(-0.415773\pi\) | |||||||
\(888\) | − | 8.04413e13i | − | 0.145685i | ||||||
\(889\) | −6.85420e14 | + | 3.08489e14i | −1.23438 | + | 0.555561i | ||||
\(890\) | 1.02216e15 | 1.83049 | ||||||||
\(891\) | 7.64209e13 | 0.136089 | ||||||||
\(892\) | 5.47482e13i | 0.0969496i | ||||||||
\(893\) | −4.35945e14 | −0.767670 | ||||||||
\(894\) | − | 2.70620e14i | − | 0.473885i | ||||||
\(895\) | − | 3.42056e14i | − | 0.595638i | ||||||
\(896\) | 4.65458e13 | − | 2.09490e13i | 0.0806010 | − | 0.0362764i | ||||
\(897\) | −7.13961e13 | −0.122945 | ||||||||
\(898\) | −4.72049e14 | −0.808361 | ||||||||
\(899\) | 2.46033e14i | 0.418982i | ||||||||
\(900\) | −3.99434e14 | −0.676445 | ||||||||
\(901\) | − | 7.05335e14i | − | 1.18788i | ||||||
\(902\) | − | 7.86774e13i | − | 0.131770i | ||||||
\(903\) | 5.64545e13 | + | 1.25434e14i | 0.0940285 | + | 0.208918i | ||||
\(904\) | −2.36467e14 | −0.391678 | ||||||||
\(905\) | 3.43302e14 | 0.565501 | ||||||||
\(906\) | 8.78303e13i | 0.143881i | ||||||||
\(907\) | −3.85480e14 | −0.628009 | −0.314005 | − | 0.949421i | \(-0.601671\pi\) | ||||
−0.314005 | + | 0.949421i | \(0.601671\pi\) | |||||||
\(908\) | − | 2.40656e14i | − | 0.389913i | ||||||
\(909\) | 9.25487e14i | 1.49125i | ||||||||
\(910\) | −1.71032e14 | + | 7.69771e13i | −0.274076 | + | 0.123354i | ||||
\(911\) | −1.10046e15 | −1.75381 | −0.876905 | − | 0.480663i | \(-0.840396\pi\) | ||||
−0.876905 | + | 0.480663i | \(0.840396\pi\) | |||||||
\(912\) | −1.09264e14 | −0.173182 | ||||||||
\(913\) | 1.62847e13i | 0.0256700i | ||||||||
\(914\) | 3.02678e14 | 0.474515 | ||||||||
\(915\) | 8.28761e13i | 0.129218i | ||||||||
\(916\) | 5.98189e14i | 0.927601i | ||||||||
\(917\) | 1.45676e14 | + | 3.23672e14i | 0.224668 | + | 0.499181i | ||||
\(918\) | 5.91188e14 | 0.906802 | ||||||||
\(919\) | 5.88693e14 | 0.898072 | 0.449036 | − | 0.893514i | \(-0.351767\pi\) | ||||
0.449036 | + | 0.893514i | \(0.351767\pi\) | |||||||
\(920\) | − | 4.43657e14i | − | 0.673144i | ||||||
\(921\) | −2.44509e14 | −0.368975 | ||||||||
\(922\) | 2.44976e13i | 0.0367680i | ||||||||
\(923\) | − | 1.40171e14i | − | 0.209242i | ||||||
\(924\) | −1.34062e13 | − | 2.97867e13i | −0.0199042 | − | 0.0442244i | ||||
\(925\) | −1.13136e15 | −1.67067 | ||||||||
\(926\) | 7.21674e13 | 0.105995 | ||||||||
\(927\) | 5.46379e14i | 0.798169i | ||||||||
\(928\) | −8.49464e13 | −0.123426 | ||||||||
\(929\) | − | 5.13603e14i | − | 0.742248i | −0.928583 | − | 0.371124i | \(-0.878972\pi\) | ||
0.928583 | − | 0.371124i | \(-0.121028\pi\) | |||||||
\(930\) | − | 1.88436e14i | − | 0.270862i | ||||||
\(931\) | −9.16807e14 | − | 8.12193e14i | −1.31078 | − | 1.16121i | ||||
\(932\) | 4.59399e14 | 0.653296 | ||||||||
\(933\) | −2.16859e14 | −0.306739 | ||||||||
\(934\) | − | 4.42221e14i | − | 0.622164i | ||||||
\(935\) | −4.97186e14 | −0.695762 | ||||||||
\(936\) | 5.64361e13i | 0.0785557i | ||||||||
\(937\) | − | 1.14018e15i | − | 1.57861i | −0.614001 | − | 0.789305i | \(-0.710441\pi\) | ||
0.614001 | − | 0.789305i | \(-0.289559\pi\) | |||||||
\(938\) | 6.34744e14 | − | 2.85682e14i | 0.874147 | − | 0.393431i | ||||
\(939\) | 4.02245e14 | 0.551014 | ||||||||
\(940\) | 2.59579e14 | 0.353696 | ||||||||
\(941\) | − | 4.03021e14i | − | 0.546235i | −0.961981 | − | 0.273118i | \(-0.911945\pi\) | ||
0.961981 | − | 0.273118i | \(-0.0880548\pi\) | |||||||
\(942\) | 1.14380e14 | 0.154205 | ||||||||
\(943\) | 6.68692e14i | 0.896742i | ||||||||
\(944\) | 4.82156e13i | 0.0643173i | ||||||||
\(945\) | 8.08722e14 | − | 3.63985e14i | 1.07310 | − | 0.482974i | ||||
\(946\) | −7.60748e13 | −0.100412 | ||||||||
\(947\) | −7.06243e14 | −0.927266 | −0.463633 | − | 0.886027i | \(-0.653454\pi\) | ||||
−0.463633 | + | 0.886027i | \(0.653454\pi\) | |||||||
\(948\) | 1.58780e14i | 0.207373i | ||||||||
\(949\) | 2.56919e14 | 0.333784 | ||||||||
\(950\) | 1.53673e15i | 1.98601i | ||||||||
\(951\) | − | 1.90897e13i | − | 0.0245413i | ||||||
\(952\) | 1.99532e14 | + | 4.43331e14i | 0.255168 | + | 0.566948i | ||||
\(953\) | 1.01961e15 | 1.29709 | 0.648545 | − | 0.761176i | \(-0.275378\pi\) | ||||
0.648545 | + | 0.761176i | \(0.275378\pi\) | |||||||
\(954\) | −3.18381e14 | −0.402908 | ||||||||
\(955\) | 7.51732e14i | 0.946338i | ||||||||
\(956\) | −1.06382e14 | −0.133222 | ||||||||
\(957\) | 5.43609e13i | 0.0677215i | ||||||||
\(958\) | 2.29970e13i | 0.0284999i | ||||||||
\(959\) | −2.96382e14 | + | 1.33394e14i | −0.365391 | + | 0.164453i | ||||
\(960\) | 6.50601e13 | 0.0797918 | ||||||||
\(961\) | 5.24476e14 | 0.639895 | ||||||||
\(962\) | 1.59850e14i | 0.194016i | ||||||||
\(963\) | 8.51322e14 | 1.02793 | ||||||||
\(964\) | − | 7.28489e14i | − | 0.875060i | ||||||
\(965\) | 1.34283e15i | 1.60467i | ||||||||
\(966\) | 1.13941e14 | + | 2.53161e14i | 0.135455 | + | 0.300962i | ||||
\(967\) | −9.35888e14 | −1.10686 | −0.553428 | − | 0.832897i | \(-0.686681\pi\) | ||||
−0.553428 | + | 0.832897i | \(0.686681\pi\) | |||||||
\(968\) | −2.82426e14 | −0.332298 | ||||||||
\(969\) | − | 1.04070e15i | − | 1.21817i | ||||||
\(970\) | 1.17740e14 | 0.137109 | ||||||||
\(971\) | 6.50229e14i | 0.753304i | 0.926355 | + | 0.376652i | \(0.122925\pi\) | ||||
−0.926355 | + | 0.376652i | \(0.877075\pi\) | |||||||
\(972\) | − | 4.11611e14i | − | 0.474412i | ||||||
\(973\) | 3.87151e14 | + | 8.60194e14i | 0.443931 | + | 0.986352i | ||||
\(974\) | 2.72722e14 | 0.311118 | ||||||||
\(975\) | −1.47253e14 | −0.167124 | ||||||||
\(976\) | 4.48193e13i | 0.0506076i | ||||||||
\(977\) | 1.27020e15 | 1.42692 | 0.713459 | − | 0.700697i | \(-0.247127\pi\) | ||||
0.713459 | + | 0.700697i | \(0.247127\pi\) | |||||||
\(978\) | − | 9.27136e13i | − | 0.103621i | ||||||
\(979\) | − | 3.53748e14i | − | 0.393352i | ||||||
\(980\) | 5.45903e14 | + | 4.83611e14i | 0.603927 | + | 0.535015i | ||||
\(981\) | −1.29475e14 | −0.142508 | ||||||||
\(982\) | −3.72473e14 | −0.407885 | ||||||||
\(983\) | − | 1.35838e15i | − | 1.47997i | −0.672621 | − | 0.739987i | \(-0.734832\pi\) | ||
0.672621 | − | 0.739987i | \(-0.265168\pi\) | |||||||
\(984\) | −9.80603e13 | −0.106296 | ||||||||
\(985\) | 1.06368e15i | 1.14718i | ||||||||
\(986\) | − | 8.09082e14i | − | 0.868176i | ||||||
\(987\) | −1.48122e14 | + | 6.66657e13i | −0.158137 | + | 0.0711733i | ||||
\(988\) | 2.17125e14 | 0.230635 | ||||||||
\(989\) | 6.46572e14 | 0.683337 | ||||||||
\(990\) | 2.24425e14i | 0.235991i | ||||||||
\(991\) | 1.11533e15 | 1.16690 | 0.583452 | − | 0.812147i | \(-0.301702\pi\) | ||||
0.583452 | + | 0.812147i | \(0.301702\pi\) | |||||||
\(992\) | − | 1.01906e14i | − | 0.106082i | ||||||
\(993\) | 2.24551e14i | 0.232578i | ||||||||
\(994\) | −4.97027e14 | + | 2.23699e14i | −0.512210 | + | 0.230532i | ||||
\(995\) | −2.03243e14 | −0.208401 | ||||||||
\(996\) | 2.02966e13 | 0.0207074 | ||||||||
\(997\) | − | 7.69493e14i | − | 0.781140i | −0.920573 | − | 0.390570i | \(-0.872278\pi\) | ||
0.920573 | − | 0.390570i | \(-0.127722\pi\) | |||||||
\(998\) | 1.29147e15 | 1.30446 | ||||||||
\(999\) | − | 7.55846e14i | − | 0.759636i |
(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 | 14.11.b.a.13.6 | ✓ | 8 | |
3.2 | odd | 2 | 126.11.c.a.55.1 | 8 | |||
4.3 | odd | 2 | 112.11.c.d.97.5 | 8 | |||
7.2 | even | 3 | 98.11.d.c.31.3 | 16 | |||
7.3 | odd | 6 | 98.11.d.c.19.3 | 16 | |||
7.4 | even | 3 | 98.11.d.c.19.2 | 16 | |||
7.5 | odd | 6 | 98.11.d.c.31.2 | 16 | |||
7.6 | odd | 2 | inner | 14.11.b.a.13.7 | yes | 8 | |
21.20 | even | 2 | 126.11.c.a.55.4 | 8 | |||
28.27 | even | 2 | 112.11.c.d.97.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.11.b.a.13.6 | ✓ | 8 | 1.1 | even | 1 | trivial | |
14.11.b.a.13.7 | yes | 8 | 7.6 | odd | 2 | inner | |
98.11.d.c.19.2 | 16 | 7.4 | even | 3 | |||
98.11.d.c.19.3 | 16 | 7.3 | odd | 6 | |||
98.11.d.c.31.2 | 16 | 7.5 | odd | 6 | |||
98.11.d.c.31.3 | 16 | 7.2 | even | 3 | |||
112.11.c.d.97.4 | 8 | 28.27 | even | 2 | |||
112.11.c.d.97.5 | 8 | 4.3 | odd | 2 | |||
126.11.c.a.55.1 | 8 | 3.2 | odd | 2 | |||
126.11.c.a.55.4 | 8 | 21.20 | even | 2 |