Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,9,Mod(61,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.61");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.m (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(34.2198032451\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + \cdots + 45\!\cdots\!96 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{10}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.1 | ||
Root | \(44.6586 - 77.3509i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.73 |
Dual form | 84.9.m.b.61.1 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 40.5000 | + | 23.3827i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −939.615 | + | 542.487i | −1.50338 | + | 0.867979i | −0.503392 | + | 0.864058i | \(0.667915\pi\) |
−0.999992 | + | 0.00392070i | \(0.998752\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1451.57 | − | 1912.52i | 0.604570 | − | 0.796552i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1093.50 | + | 1894.00i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8435.48 | + | 14610.7i | −0.576155 | + | 0.997929i | 0.419760 | + | 0.907635i | \(0.362114\pi\) |
−0.995915 | + | 0.0902942i | \(0.971219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9958.41i | 0.348672i | 0.984686 | + | 0.174336i | \(0.0557778\pi\) | ||||
−0.984686 | + | 0.174336i | \(0.944222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −50739.2 | −1.00226 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −91736.7 | − | 52964.2i | −1.09837 | − | 0.634142i | −0.162575 | − | 0.986696i | \(-0.551980\pi\) |
−0.935792 | + | 0.352554i | \(0.885313\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 147650. | − | 85245.9i | 1.13297 | − | 0.654122i | 0.188292 | − | 0.982113i | \(-0.439705\pi\) |
0.944681 | + | 0.327991i | \(0.106372\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 103509. | − | 43515.5i | 0.532230 | − | 0.223752i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −105694. | − | 183067.i | −0.377692 | − | 0.654183i | 0.613034 | − | 0.790057i | \(-0.289949\pi\) |
−0.990726 | + | 0.135874i | \(0.956616\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 393272. | − | 681166.i | 1.00678 | − | 1.74379i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 102276.i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −567529. | −0.802409 | −0.401205 | − | 0.915989i | \(-0.631408\pi\) | ||||
−0.401205 | + | 0.915989i | \(0.631408\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 549248. | + | 317108.i | 0.594732 | + | 0.343369i | 0.766967 | − | 0.641687i | \(-0.221765\pi\) |
−0.172234 | + | 0.985056i | \(0.555099\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −683274. | + | 394488.i | −0.576155 | + | 0.332643i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −326400. | + | 2.58449e6i | −0.217510 | + | 1.72228i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.07740e6 | − | 1.86611e6i | −0.574870 | − | 0.995703i | −0.996056 | − | 0.0887291i | \(-0.971719\pi\) |
0.421186 | − | 0.906974i | \(-0.361614\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −232854. | + | 403316.i | −0.100653 | + | 0.174336i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.45428e6i | − | 1.93020i | −0.261884 | − | 0.965099i | \(-0.584344\pi\) | ||
0.261884 | − | 0.965099i | \(-0.415656\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.56726e6 | 1.62842 | 0.814212 | − | 0.580568i | \(-0.197169\pi\) | ||||
0.814212 | + | 0.580568i | \(0.197169\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.05494e6 | − | 1.18642e6i | −0.501128 | − | 0.289326i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.76739e6 | − | 1.59775e6i | 0.567125 | − | 0.327430i | −0.188876 | − | 0.982001i | \(-0.560484\pi\) |
0.756000 | + | 0.654572i | \(0.227151\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.55068e6 | − | 5.55233e6i | −0.268991 | − | 0.963143i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.47689e6 | − | 4.29010e6i | −0.366122 | − | 0.634142i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.38272e6 | − | 7.59109e6i | 0.555443 | − | 0.962056i | −0.442425 | − | 0.896805i | \(-0.645882\pi\) |
0.997869 | − | 0.0652510i | \(-0.0207848\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.83046e7i | − | 2.00036i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.97311e6 | 0.755315 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.08566e6 | − | 4.66826e6i | −0.667279 | − | 0.385254i | 0.127766 | − | 0.991804i | \(-0.459219\pi\) |
−0.795045 | + | 0.606551i | \(0.792553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.13748e7 | + | 1.23407e7i | −1.54377 | + | 0.891296i | −0.545174 | + | 0.838323i | \(0.683536\pi\) |
−0.998596 | + | 0.0529726i | \(0.983130\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.20961e6 | + | 657931.i | 0.330706 | + | 0.0417655i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.40231e6 | − | 9.35707e6i | −0.302640 | − | 0.524187i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.91779e6 | + | 1.19820e7i | −0.343295 | + | 0.594605i | −0.985043 | − | 0.172311i | \(-0.944877\pi\) |
0.641747 | + | 0.766916i | \(0.278210\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 9.88562e6i | − | 0.436122i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.19189e7 | 0.469031 | 0.234515 | − | 0.972112i | \(-0.424650\pi\) | ||||
0.234515 | + | 0.972112i | \(0.424650\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.83300e7 | − | 1.05828e7i | −0.645463 | − | 0.372658i | 0.141253 | − | 0.989974i | \(-0.454887\pi\) |
−0.786716 | + | 0.617315i | \(0.788220\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.18550e7 | − | 1.83915e7i | 1.00678 | − | 0.581262i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.56985e7 | + | 3.73415e7i | 0.446577 | + | 1.06226i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.61190e6 | − | 1.49162e7i | −0.221101 | − | 0.382958i | 0.734042 | − | 0.679104i | \(-0.237632\pi\) |
−0.955143 | + | 0.296147i | \(0.904298\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.39148e6 | + | 4.14217e6i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.82663e7i | − | 1.43845i | −0.694779 | − | 0.719223i | \(-0.744498\pi\) | ||
0.694779 | − | 0.719223i | \(-0.255502\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.14930e8 | 2.20169 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.29849e7 | − | 1.32703e7i | −0.401205 | − | 0.231636i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.87155e7 | + | 4.54464e7i | −1.25459 | + | 0.724335i | −0.972017 | − | 0.234912i | \(-0.924520\pi\) |
−0.282569 | + | 0.959247i | \(0.591186\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.90457e7 | + | 1.44553e7i | 0.277735 | + | 0.210796i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.48297e7 | + | 2.56858e7i | 0.198244 | + | 0.343369i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.24895e7 | + | 1.60197e8i | −1.13553 | + | 1.96679i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.95376e7i | − | 0.446605i | −0.974749 | − | 0.223302i | \(-0.928316\pi\) | ||
0.974749 | − | 0.223302i | \(-0.0716837\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.68968e7 | −0.384103 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.01453e8 | + | 5.85738e7i | 0.974941 | + | 0.562882i | 0.900739 | − | 0.434361i | \(-0.143026\pi\) |
0.0742019 | + | 0.997243i | \(0.476359\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.22305e7 | + | 2.43818e7i | −0.375212 | + | 0.216629i | −0.675733 | − | 0.737146i | \(-0.736173\pi\) |
0.300521 | + | 0.953775i | \(0.402839\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.36516e7 | + | 9.70398e7i | −0.605934 | + | 0.798349i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.90508e7 | + | 1.02279e8i | 0.450496 | + | 0.780282i | 0.998417 | − | 0.0562482i | \(-0.0179138\pi\) |
−0.547921 | + | 0.836530i | \(0.684580\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.54688e6 | + | 1.30716e7i | −0.0534640 | + | 0.0926024i | −0.891519 | − | 0.452984i | \(-0.850360\pi\) |
0.838055 | + | 0.545586i | \(0.183693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.00770e8i | − | 0.663802i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.94293e7 | −0.425823 | −0.212911 | − | 0.977072i | \(-0.568295\pi\) | ||||
−0.212911 | + | 0.977072i | \(0.568295\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.98623e8 | + | 1.14675e8i | 1.13563 | + | 0.655658i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.88612e7 | + | 1.08895e7i | −0.100653 | + | 0.0581119i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.34458e8 | + | 9.85671e7i | −1.16917 | + | 0.491523i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.51352e7 | − | 6.08560e7i | −0.163908 | − | 0.283898i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.27536e8 | − | 2.20898e8i | 0.557200 | − | 0.965099i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.29561e8i | 1.75948i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00139e8 | −0.384934 | −0.192467 | − | 0.981303i | \(-0.561649\pi\) | ||||
−0.192467 | + | 0.981303i | \(0.561649\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.25474e8 | + | 1.30177e8i | 0.814212 | + | 0.470085i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.73342e6 | + | 3.88754e6i | −0.0228639 | + | 0.0132005i | −0.511388 | − | 0.859350i | \(-0.670869\pi\) |
0.488524 | + | 0.872550i | \(0.337535\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.12902e7 | − | 4.06125e8i | 0.163919 | − | 1.29793i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.54833e7 | − | 9.60999e7i | −0.167043 | − | 0.289326i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.53803e7 | + | 9.59215e7i | −0.157207 | + | 0.272291i | −0.933861 | − | 0.357637i | \(-0.883582\pi\) |
0.776653 | + | 0.629928i | \(0.216916\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.31664e8i | 0.888464i | 0.895912 | + | 0.444232i | \(0.146523\pi\) | ||||
−0.895912 | + | 0.444232i | \(0.853477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.49439e8 | 0.378083 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.45499e8 | − | 8.40040e7i | −0.347949 | − | 0.200889i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.33258e8 | − | 3.07877e8i | 1.20633 | − | 0.696474i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.70258e7 | − | 2.61128e8i | 0.143540 | − | 0.559222i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.47265e8 | + | 6.01481e8i | 0.704557 | + | 1.22033i | 0.966851 | + | 0.255341i | \(0.0821877\pi\) |
−0.262294 | + | 0.964988i | \(0.584479\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.10896e8 | + | 7.11694e8i | −0.790359 | + | 1.36894i | 0.135385 | + | 0.990793i | \(0.456773\pi\) |
−0.925745 | + | 0.378150i | \(0.876561\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.31665e8i | − | 0.422762i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.88109e8 | −1.19215 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.16332e8 | − | 2.40369e8i | −0.685238 | − | 0.395622i | 0.116588 | − | 0.993180i | \(-0.462804\pi\) |
−0.801825 | + | 0.597558i | \(0.796138\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.55000e8 | − | 2.04959e8i | 0.555443 | − | 0.320685i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.03542e8 | − | 6.35933e7i | −0.749432 | − | 0.0946472i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.04664e8 | − | 5.27694e8i | −0.431590 | − | 0.747536i | 0.565420 | − | 0.824803i | \(-0.308714\pi\) |
−0.997010 | + | 0.0772671i | \(0.975381\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.28010e8 | − | 7.41334e8i | 0.577454 | − | 1.00018i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.84576e8i | − | 0.237307i | −0.992936 | − | 0.118653i | \(-0.962142\pi\) | ||
0.992936 | − | 0.118653i | \(-0.0378577\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.16561e8 | 0.878428 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.22911e8 | + | 1.86433e8i | 0.377658 | + | 0.218041i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.92420e8 | + | 1.68829e8i | −0.326454 | + | 0.188478i | −0.654266 | − | 0.756265i | \(-0.727022\pi\) |
0.327812 | + | 0.944743i | \(0.393689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.31884e8 | − | 1.74090e9i | −0.780351 | − | 1.85619i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.18313e8 | − | 3.78129e8i | −0.222426 | − | 0.385254i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.92703e8 | − | 5.06977e8i | 0.285112 | − | 0.493828i | −0.687524 | − | 0.726161i | \(-0.741303\pi\) |
0.972636 | + | 0.232333i | \(0.0746359\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.29407e9i | − | 1.20571i | −0.797850 | − | 0.602856i | \(-0.794029\pi\) | ||
0.797850 | − | 0.602856i | \(-0.205971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.15424e9 | −1.02918 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.02468e9 | + | 1.16895e9i | 1.72850 | + | 0.997950i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.54769e9 | − | 8.93557e8i | 1.26566 | − | 0.730728i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.95605e8 | + | 1.48461e8i | 0.153297 | + | 0.116349i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.80043e8 | − | 1.35107e9i | −0.586118 | − | 1.01519i | −0.994735 | − | 0.102480i | \(-0.967322\pi\) |
0.408617 | − | 0.912706i | \(-0.366011\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.76806e8 | − | 1.51867e9i | 0.631937 | − | 1.09455i | −0.355218 | − | 0.934784i | \(-0.615593\pi\) |
0.987155 | − | 0.159764i | \(-0.0510734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 5.05282e8i | − | 0.349458i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.78624e9 | −1.18598 | −0.592988 | − | 0.805212i | \(-0.702052\pi\) | ||||
−0.592988 | + | 0.805212i | \(0.702052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.60521e9 | − | 1.50412e9i | −1.66123 | − | 0.959114i | −0.972127 | − | 0.234454i | \(-0.924670\pi\) |
−0.689107 | − | 0.724660i | \(-0.741997\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.60341e8 | + | 3.23513e8i | −0.343295 | + | 0.198202i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.23809e8 | + | 1.08541e9i | −0.485112 | + | 0.639161i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.95888e9 | + | 5.12492e9i | 1.67537 | + | 2.90183i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.31152e8 | − | 4.00368e8i | 0.125897 | − | 0.218061i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.87636e9i | 1.50750i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.33988e9 | 1.68501 | 0.842503 | − | 0.538692i | \(-0.181081\pi\) | ||||
0.842503 | + | 0.538692i | \(0.181081\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.82714e8 | + | 2.78695e8i | 0.234515 | + | 0.135398i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.23108e9 | + | 3.02016e9i | −2.44815 | + | 1.41344i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.40375e9 | − | 5.90143e8i | 0.633069 | − | 0.266145i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.94911e8 | − | 8.57210e8i | −0.215154 | − | 0.372658i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.27439e8 | − | 9.13552e8i | 0.221107 | − | 0.382969i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.94513e9i | − | 0.786556i | −0.919420 | − | 0.393278i | \(-0.871341\pi\) | ||
0.919420 | − | 0.393278i | \(-0.128659\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.72017e9 | 0.671184 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.17894e9 | + | 6.80660e8i | 0.444004 | + | 0.256346i | 0.705295 | − | 0.708914i | \(-0.250815\pi\) |
−0.261290 | + | 0.965260i | \(0.584148\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.23205e9 | + | 1.86603e9i | −1.17527 | + | 0.678541i | −0.954915 | − | 0.296880i | \(-0.904054\pi\) |
−0.220352 | + | 0.975420i | \(0.570721\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.37354e8 | + | 1.87940e9i | −0.0833581 | + | 0.660043i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.72263e8 | − | 2.98368e8i | −0.0584477 | − | 0.101234i | 0.835321 | − | 0.549762i | \(-0.185282\pi\) |
−0.893769 | + | 0.448528i | \(0.851948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.73352e9 | + | 3.00254e9i | −0.568404 | + | 0.984505i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 8.05477e8i | − | 0.255305i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.17982e9 | 0.974565 | 0.487283 | − | 0.873244i | \(-0.337988\pi\) | ||||
0.487283 | + | 0.873244i | \(0.337988\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.09977e9 | − | 2.36701e9i | −1.21532 | − | 0.701667i | −0.251409 | − | 0.967881i | \(-0.580894\pi\) |
−0.963914 | + | 0.266214i | \(0.914227\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.93710e8 | + | 1.11839e8i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.46911e9 | + | 4.37583e9i | 1.24038 | + | 1.21449i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.48913e8 | + | 1.47036e9i | 0.228074 | + | 0.395035i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.59625e9 | − | 2.76478e9i | 0.415244 | − | 0.719223i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 7.03152e9i | − | 1.77155i | −0.464112 | − | 0.885776i | \(-0.653627\pi\) | ||
0.464112 | − | 0.885776i | \(-0.346373\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.56631e9 | 0.870437 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.65465e9 | + | 2.68736e9i | 1.10084 | + | 0.635573i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.10931e9 | + | 6.40462e8i | −0.254286 | + | 0.146812i | −0.621725 | − | 0.783236i | \(-0.713568\pi\) |
0.367439 | + | 0.930047i | \(0.380235\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.13289e9 | − | 6.48243e8i | −1.14068 | − | 0.144058i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.20593e8 | − | 1.07490e9i | −0.133735 | − | 0.231636i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.37972e8 | − | 4.12179e8i | 0.0497396 | − | 0.0861516i | −0.840084 | − | 0.542457i | \(-0.817494\pi\) |
0.889823 | + | 0.456305i | \(0.150828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.51027e9i | 1.92845i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.25064e9 | −0.836390 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.95417e9 | − | 2.86029e9i | −0.946154 | − | 0.546262i | −0.0542696 | − | 0.998526i | \(-0.517283\pi\) |
−0.891884 | + | 0.452264i | \(0.850616\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.53293e9 | + | 3.19444e9i | −1.02584 | + | 0.592267i | −0.915789 | − | 0.401659i | \(-0.868434\pi\) |
−0.110048 | + | 0.993926i | \(0.535100\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.33345e8 | + | 1.03078e9i | 0.0780159 | + | 0.185573i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.63487e9 | + | 1.14919e10i | 1.16012 | + | 2.00938i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.63656e9 | + | 4.56666e9i | −0.447836 | + | 0.775675i | −0.998245 | − | 0.0592204i | \(-0.981139\pi\) |
0.550409 | + | 0.834895i | \(0.314472\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.38703e9i | 0.228913i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.48748e9 | 1.20091 | 0.600455 | − | 0.799658i | \(-0.294986\pi\) | ||||
0.600455 | + | 0.799658i | \(0.294986\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.62475e9 | − | 2.09275e9i | −0.565109 | − | 0.326266i | 0.190085 | − | 0.981768i | \(-0.439124\pi\) |
−0.755193 | + | 0.655502i | \(0.772457\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.49165e9 | + | 4.32531e9i | −1.13553 | + | 0.655598i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.04314e10 | − | 7.91728e9i | −1.53750 | − | 1.16694i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.12254e9 | + | 3.67634e9i | 0.304273 | + | 0.527017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.24495e8 | − | 1.60127e9i | 0.128924 | − | 0.223302i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.12022e9i | − | 0.151997i | −0.997108 | − | 0.0759983i | \(-0.975786\pi\) | ||
0.997108 | − | 0.0759983i | \(-0.0242143\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.01299e10 | 1.33757 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.49432e9 | − | 8.62746e8i | −0.192052 | − | 0.110881i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.82306e9 | − | 1.05254e9i | 0.228095 | − | 0.131691i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.08127e9 | − | 1.06475e10i | 0.984496 | − | 1.29712i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.73922e9 | + | 4.74447e9i | 0.324980 | + | 0.562882i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.33894e10 | − | 2.31911e10i | 1.54725 | − | 2.67992i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.02340e10i | − | 1.15210i | −0.817413 | − | 0.576051i | \(-0.804593\pi\) | ||
0.817413 | − | 0.576051i | \(-0.195407\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.28044e9 | −0.250141 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.99552e9 | + | 3.46151e9i | 0.640892 | + | 0.370019i | 0.784958 | − | 0.619549i | \(-0.212684\pi\) |
−0.144066 | + | 0.989568i | \(0.546018\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.79188e8 | − | 2.76659e8i | 0.0499262 | − | 0.0288249i | −0.474829 | − | 0.880078i | \(-0.657490\pi\) |
0.524755 | + | 0.851253i | \(0.324157\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.25194e9 | + | 2.20794e9i | −0.533430 | + | 0.224257i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.72093e8 | − | 1.16410e9i | −0.0665568 | − | 0.115280i | 0.830827 | − | 0.556531i | \(-0.187868\pi\) |
−0.897384 | + | 0.441251i | \(0.854535\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.78738e9 | − | 8.29198e9i | 0.462312 | − | 0.800747i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.52307e9i | 0.520188i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.80599e10 | −1.65923 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.78333e9 | + | 3.91636e9i | 0.608009 | + | 0.351034i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.11298e8 | + | 3.52933e8i | −0.0534640 | + | 0.0308675i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.61326e8 | − | 7.61194e9i | 0.0820516 | − | 0.649698i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.38567e8 | + | 5.86414e8i | 0.0282054 | + | 0.0488532i | 0.879784 | − | 0.475374i | \(-0.157687\pi\) |
−0.851578 | + | 0.524228i | \(0.824354\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.35627e9 | − | 4.08118e9i | 0.191623 | − | 0.331901i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.50112e10i | − | 1.19189i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.73692e10 | −1.34667 | −0.673333 | − | 0.739340i | \(-0.735138\pi\) | ||||
−0.673333 | + | 0.739340i | \(0.735138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.81189e9 | − | 1.62344e9i | −0.212911 | − | 0.122924i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.26634e9 | + | 5.34992e9i | −0.685316 | + | 0.395667i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.28699e10 | − | 5.09389e9i | −0.929817 | − | 0.368022i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.36282e9 | + | 9.28868e9i | 0.378545 | + | 0.655658i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.82405e9 | − | 1.52837e10i | 0.608626 | − | 1.05417i | −0.382842 | − | 0.923814i | \(-0.625054\pi\) |
0.991467 | − | 0.130356i | \(-0.0416122\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.49559e9i | 0.640059i | 0.947408 | + | 0.320030i | \(0.103693\pi\) | ||||
−0.947408 | + | 0.320030i | \(0.896307\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.01850e9 | −0.0671019 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.12231e9 | + | 3.53472e9i | 0.394290 | + | 0.227644i | 0.684017 | − | 0.729466i | \(-0.260231\pi\) |
−0.289727 | + | 0.957109i | \(0.593565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.11991e10 | + | 6.46583e9i | −0.705134 | + | 0.407109i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.18003e10 | − | 1.49028e9i | −0.726474 | − | 0.0917478i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.55145e9 | − | 1.13474e10i | −0.394421 | − | 0.683157i | 0.598606 | − | 0.801043i | \(-0.295721\pi\) |
−0.993027 | + | 0.117887i | \(0.962388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.04193e9 | − | 1.04649e10i | 0.355752 | − | 0.616180i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.28622e9i | − | 0.189265i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.29642e10 | 1.29384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.12630e10 | + | 1.22762e10i | 1.17209 | + | 0.676707i | 0.954172 | − | 0.299260i | \(-0.0967399\pi\) |
0.217919 | + | 0.975967i | \(0.430073\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.03304e10 | − | 5.96426e9i | 0.557200 | − | 0.321700i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.15629e9 | − | 1.94011e10i | −0.430524 | − | 1.02407i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.64618e9 | + | 9.77947e9i | 0.291689 | + | 0.505219i | 0.974209 | − | 0.225647i | \(-0.0724496\pi\) |
−0.682521 | + | 0.730866i | \(0.739116\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00443e10 | + | 1.73972e10i | −0.507919 | + | 0.879741i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.65168e9i | − | 0.279777i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.52545e9 | −0.170867 | −0.0854335 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854335 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.05561e9 | − | 2.34151e9i | −0.192467 | − | 0.111121i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.74394e10 | − | 1.58422e10i | 1.27521 | − | 0.736240i | 0.299243 | − | 0.954177i | \(-0.403266\pi\) |
0.975963 | + | 0.217937i | \(0.0699326\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.50079e10 | − | 2.65704e10i | −1.59339 | − | 1.20936i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.08779e9 | + | 1.05444e10i | 0.271404 | + | 0.470085i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.01146e9 | − | 3.48396e9i | 0.0878443 | − | 0.152151i | −0.818755 | − | 0.574143i | \(-0.805336\pi\) |
0.906600 | + | 0.421992i | \(0.138669\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.23920e10i | 0.958043i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.63605e8 | −0.0152426 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.61837e10 | + | 9.34368e9i | 0.664799 | + | 0.383822i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.37145e10 | + | 1.94651e10i | −1.35724 | + | 0.783600i | −0.989250 | − | 0.146232i | \(-0.953286\pi\) |
−0.367985 | + | 0.929832i | \(0.619952\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.15735e10 | − | 1.52487e10i | 0.456641 | − | 0.601648i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.03692e10 | + | 3.52804e10i | 0.787764 | + | 1.36445i | 0.927334 | + | 0.374234i | \(0.122094\pi\) |
−0.139571 | + | 0.990212i | \(0.544572\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.15790e9 | + | 5.46963e9i | −0.119723 | + | 0.207366i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 5.18940e9i | − | 0.192884i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.63535e10 | 1.32486 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.08712e10 | − | 6.27648e9i | −0.388493 | − | 0.224297i | 0.293014 | − | 0.956108i | \(-0.405342\pi\) |
−0.681507 | + | 0.731812i | \(0.738675\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.48580e9 | + | 2.58988e9i | −0.157207 | + | 0.0907637i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.06651e10 | + | 8.68769e9i | −0.710291 | + | 0.298610i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.70336e10 | + | 6.41440e10i | 1.24854 | + | 2.16254i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.75521e9 | + | 1.34324e10i | −0.256477 | + | 0.444232i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.94158e9i | − | 0.0629941i | −0.999504 | − | 0.0314970i | \(-0.989973\pi\) | ||
0.999504 | − | 0.0314970i | \(-0.0100275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.38803e9 | 0.0441846 | 0.0220923 | − | 0.999756i | \(-0.492967\pi\) | ||||
0.0220923 | + | 0.999756i | \(0.492967\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.05228e9 | + | 3.49428e9i | 0.189042 | + | 0.109143i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.21549e10 | + | 4.16586e10i | −2.21162 | + | 1.27688i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.42511e9 | + | 5.87932e10i | −0.223353 | + | 1.76854i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.92848e9 | − | 6.80432e9i | −0.115983 | − | 0.200889i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.62135e10 | + | 2.80826e10i | −0.469860 | + | 0.813821i | −0.999406 | − | 0.0344602i | \(-0.989029\pi\) |
0.529546 | + | 0.848281i | \(0.322362\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.65333e10i | − | 1.32377i | −0.749606 | − | 0.661884i | \(-0.769757\pi\) | ||
0.749606 | − | 0.661884i | \(-0.230243\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.87960e10 | 0.804219 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.12114e10 | − | 1.80199e10i | −0.855831 | − | 0.494114i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.44106e10 | + | 2.56404e10i | −1.19572 | + | 0.690347i | −0.959597 | − | 0.281377i | \(-0.909209\pi\) |
−0.236119 | + | 0.971724i | \(0.575876\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.82042e9 | − | 9.00845e9i | 0.233204 | − | 0.238175i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.09215e10 | + | 3.62371e10i | 0.543223 | + | 0.940891i | 0.998716 | + | 0.0506512i | \(0.0161297\pi\) |
−0.455493 | + | 0.890239i | \(0.650537\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.93082e10 | − | 8.54042e10i | 1.25742 | − | 2.17791i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.24800e10i | 0.813553i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.89337e10 | 0.711900 | 0.355950 | − | 0.934505i | \(-0.384157\pi\) | ||||
0.355950 | + | 0.934505i | \(0.384157\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.96907e10 | + | 4.60095e10i | 1.92620 | + | 1.11209i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.32826e10 | + | 1.92157e10i | −0.790359 | + | 0.456314i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.57374e10 | − | 3.25043e9i | −0.600509 | − | 0.0758394i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.38299e10 | − | 5.85951e10i | −0.775597 | − | 1.34337i | −0.934458 | − | 0.356072i | \(-0.884116\pi\) |
0.158862 | − | 0.987301i | \(-0.449218\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.41696e9 | − | 9.38245e9i | 0.122041 | − | 0.211381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.13195e10i | − | 0.472035i | −0.971749 | − | 0.236017i | \(-0.924158\pi\) | ||
0.971749 | − | 0.236017i | \(-0.0758422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.73662e10 | 1.24834 | 0.624168 | − | 0.781290i | \(-0.285438\pi\) | ||||
0.624168 | + | 0.781290i | \(0.285438\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.78684e10 | − | 1.60898e10i | −0.596074 | − | 0.344144i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.40331e10 | + | 8.10202e9i | −0.295044 | + | 0.170343i | −0.640214 | − | 0.768196i | \(-0.721154\pi\) |
0.345171 | + | 0.938540i | \(0.387821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.28741e10 | + | 3.06231e10i | 0.266088 | + | 0.632933i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.12410e10 | − | 1.94699e10i | −0.228413 | − | 0.395622i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.69625e10 | + | 8.13414e10i | −0.938224 | + | 1.62505i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.34099e11i | − | 2.63422i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.91700e10 | 0.370296 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.47162e10 | − | 4.89109e10i | −1.60925 | − | 0.929103i | −0.989537 | − | 0.144276i | \(-0.953915\pi\) |
−0.619716 | − | 0.784826i | \(-0.712752\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.85835e10 | − | 1.07292e10i | 0.347173 | − | 0.200441i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.89065e10 | − | 1.43497e10i | −0.347394 | − | 0.263666i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.14486e10 | + | 3.71501e10i | 0.387644 | + | 0.671418i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.47120e10 | − | 4.28025e10i | 0.439332 | − | 0.760945i | −0.558306 | − | 0.829635i | \(-0.688548\pi\) |
0.997638 | + | 0.0686896i | \(0.0218818\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2.84955e10i | − | 0.498357i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.36304e10 | 0.750695 | 0.375348 | − | 0.926884i | \(-0.377523\pi\) | ||||
0.375348 | + | 0.926884i | \(0.377523\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.20632e10 | + | 3.00587e10i | 0.881340 | + | 0.508842i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.46688e10 | − | 2.00160e10i | 0.577454 | − | 0.333393i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.73011e10 | − | 2.27951e10i | 0.283562 | − | 0.373608i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.70928e10 | + | 2.96057e10i | 0.275684 | + | 0.477499i | 0.970308 | − | 0.241874i | \(-0.0777622\pi\) |
−0.694623 | + | 0.719374i | \(0.744429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.31589e9 | − | 7.47534e9i | 0.0685045 | − | 0.118653i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.10624e10i | 0.172813i | 0.996260 | + | 0.0864063i | \(0.0275383\pi\) | ||||
−0.996260 | + | 0.0864063i | \(0.972462\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.27102e11 | −1.95428 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.90207e10 | + | 1.67551e10i | 0.439214 | + | 0.253580i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.58080e10 | + | 5.53148e10i | −1.42735 | + | 0.824081i | −0.996911 | − | 0.0785379i | \(-0.974975\pi\) |
−0.430440 | + | 0.902619i | \(0.641642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.68473e10 | + | 1.96948e10i | −0.687069 | + | 0.288847i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.71859e9 | + | 1.51010e10i | 0.125886 | + | 0.218041i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.64536e10 | − | 4.58189e10i | 0.376059 | − | 0.651353i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.39112e10i | 0.754600i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.57907e10 | −0.217636 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.11862e11 | + | 6.45834e10i | 1.51820 | + | 0.876536i | 0.999771 | + | 0.0214183i | \(0.00681818\pi\) |
0.518434 | + | 0.855118i | \(0.326515\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.41818e10 | − | 2.55084e10i | 0.590523 | − | 0.340939i | −0.174781 | − | 0.984607i | \(-0.555922\pi\) |
0.765304 | + | 0.643669i | \(0.222588\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.10657e10 | − | 8.76200e10i | 0.145660 | − | 1.15336i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.35908e10 | − | 5.81810e10i | −0.435490 | − | 0.754290i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.68131e10 | − | 2.91212e10i | 0.214697 | − | 0.371866i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.04190e10i | − | 0.256836i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.43159e10 | 0.673005 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.10970e11 | − | 6.40686e10i | −1.35454 | − | 0.782042i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.37090e10 | − | 1.36884e10i | 0.285112 | − | 0.164609i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.42040e10 | + | 2.41801e10i | 1.11613 | + | 0.286485i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.42593e10 | − | 9.39799e10i | −0.633410 | − | 1.09710i | −0.986850 | − | 0.161641i | \(-0.948321\pi\) |
0.353439 | − | 0.935457i | \(-0.385012\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.02588e10 | − | 5.24098e10i | 0.348059 | − | 0.602856i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.63763e10i | − | 0.185623i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.18018e10 | −0.690322 | −0.345161 | − | 0.938544i | \(-0.612176\pi\) | ||||
−0.345161 | + | 0.938544i | \(0.612176\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.67467e10 | − | 2.69892e10i | −0.514590 | − | 0.297099i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.37957e10 | + | 4.83795e10i | −0.909108 | + | 0.524874i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.10284e10 | − | 5.18156e9i | −0.438717 | − | 0.0554064i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.46663e10 | + | 9.46849e10i | 0.576166 | + | 0.997950i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.68485e10 | − | 4.65029e10i | 0.278932 | − | 0.483125i | −0.692188 | − | 0.721718i | \(-0.743353\pi\) |
0.971120 | + | 0.238593i | \(0.0766862\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.54410e10i | 0.567785i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.35751e10 | 0.843772 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.24343e11 | − | 7.17894e10i | −1.23762 | − | 0.714540i | −0.269013 | − | 0.963137i | \(-0.586697\pi\) |
−0.968607 | + | 0.248596i | \(0.920031\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.52368e10 | − | 3.76645e10i | 0.640175 | − | 0.369605i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.45058e9 | + | 1.05864e10i | 0.0430611 | + | 0.102428i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.80492e10 | + | 8.32237e10i | 0.458392 | + | 0.793958i | 0.998876 | − | 0.0473959i | \(-0.0150922\pi\) |
−0.540484 | + | 0.841354i | \(0.681759\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.02075e11 | − | 1.76799e11i | 0.960231 | − | 1.66317i | 0.238316 | − | 0.971188i | \(-0.423405\pi\) |
0.721915 | − | 0.691981i | \(-0.243262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 7.29580e10i | − | 0.676790i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.66266e11 | −1.52101 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.23039e10 | − | 7.10368e9i | −0.111005 | − | 0.0640885i | 0.443470 | − | 0.896289i | \(-0.353747\pi\) |
−0.554474 | + | 0.832201i | \(0.687081\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.10213e10 | − | 4.10041e10i | 0.631937 | − | 0.364849i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.30561e11 | − | 9.90934e10i | −1.14580 | − | 0.869641i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.39406e10 | + | 1.28069e11i | 0.640043 | + | 1.10859i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.18148e10 | − | 2.04639e10i | 0.100880 | − | 0.174729i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.63318e10i | 0.558688i | 0.960191 | + | 0.279344i | \(0.0901170\pi\) | ||||
−0.960191 | + | 0.279344i | \(0.909883\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.08129e11 | 0.898421 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.23428e10 | − | 4.17672e10i | −0.592988 | − | 0.342362i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.13541e10 | − | 5.27433e10i | 0.738770 | − | 0.426529i | −0.0828520 | − | 0.996562i | \(-0.526403\pi\) |
0.821622 | + | 0.570033i | \(0.193070\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.66829e11 | − | 2.19805e11i | 1.33107 | − | 1.75376i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.03407e10 | − | 1.21834e11i | −0.553745 | − | 0.959114i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.35115e10 | + | 1.27326e11i | −0.571016 | + | 0.989028i | 0.425446 | + | 0.904984i | \(0.360117\pi\) |
−0.996462 | + | 0.0840447i | \(0.973216\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.86033e11i | 1.42591i | 0.701210 | + | 0.712954i | \(0.252643\pi\) | ||||
−0.701210 | + | 0.712954i | \(0.747357\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.02584e10 | −0.228864 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.60272e10 | + | 3.81208e10i | 0.492834 | + | 0.284538i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.85799e10 | + | 3.38211e10i | −0.431513 | + | 0.249134i | −0.699991 | − | 0.714152i | \(-0.746813\pi\) |
0.268478 | + | 0.963286i | \(0.413479\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.87441e10 | + | 2.46963e10i | −0.427066 | + | 0.179541i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.59111e10 | + | 2.75588e10i | 0.114165 | + | 0.197740i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.19635e11 | + | 2.07214e11i | −0.847261 | + | 1.46750i | 0.0363824 | + | 0.999338i | \(0.488417\pi\) |
−0.883643 | + | 0.468161i | \(0.844917\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.76746e11i | 1.93455i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.40881e10 | −0.235214 | −0.117607 | − | 0.993060i | \(-0.537522\pi\) | ||||
−0.117607 | + | 0.993060i | \(0.537522\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.42286e10 | + | 4.86294e10i | 0.573716 | + | 0.331235i | 0.758632 | − | 0.651519i | \(-0.225868\pi\) |
−0.184916 | + | 0.982754i | \(0.559201\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.87233e10 | − | 1.08099e10i | 0.125897 | − | 0.0726870i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.73439e10 | + | 2.16514e11i | −0.181513 | + | 1.43725i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.94095e10 | − | 1.37541e11i | −0.520418 | − | 0.901391i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.72570e10 | + | 1.16493e11i | −0.435178 | + | 0.753751i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.28254e11i | 1.45820i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.63168e11 | −1.02924 | −0.514621 | − | 0.857418i | \(-0.672067\pi\) | ||||
−0.514621 | + | 0.857418i | \(0.672067\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.35265e11 | + | 7.80954e10i | 0.842503 | + | 0.486419i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.40916e10 | − | 5.43238e10i | 0.578704 | − | 0.334115i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.52923e10 | − | 1.54423e10i | 0.335820 | − | 0.0937895i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.30333e10 | + | 2.25743e10i | 0.0781718 | + | 0.135398i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.04255e10 | + | 3.53779e10i | −0.120987 | + | 0.209556i | −0.920157 | − | 0.391549i | \(-0.871939\pi\) |
0.799170 | + | 0.601105i | \(0.205273\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.66499e11i | 0.974022i | 0.873396 | + | 0.487011i | \(0.161913\pi\) | ||||
−0.873396 | + | 0.487011i | \(0.838087\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.82478e11 | −1.63210 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.33764e10 | − | 2.50434e10i | −0.247535 | − | 0.142914i | 0.371100 | − | 0.928593i | \(-0.378981\pi\) |
−0.618635 | + | 0.785678i | \(0.712314\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.36413e11 | − | 7.87580e10i | 0.768912 | − | 0.443931i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.06510e10 | + | 8.92265e9i | 0.393364 | + | 0.0496786i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.99393e10 | − | 5.18564e10i | −0.164660 | − | 0.285200i | 0.771874 | − | 0.635775i | \(-0.219319\pi\) |
−0.936535 | + | 0.350575i | \(0.885986\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.21788e9 | − | 7.30558e9i | 0.0229155 | − | 0.0396908i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4.62893e10i | − | 0.248439i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.62292e10 | −0.298140 | −0.149070 | − | 0.988827i | \(-0.547628\pi\) | ||||
−0.149070 | + | 0.988827i | \(0.547628\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.99084e11 | + | 1.14941e11i | 1.04287 | + | 0.602102i | 0.920645 | − | 0.390400i | \(-0.127663\pi\) |
0.122226 | + | 0.992502i | \(0.460997\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.27226e10 | − | 2.46659e10i | 0.221107 | − | 0.127656i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.72124e11 | + | 4.09425e11i | 0.880147 | + | 2.09357i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.99843e10 | + | 1.03896e11i | 0.303064 | + | 0.524922i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.54824e10 | − | 7.87779e10i | 0.227059 | − | 0.393278i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.16400e11i | − | 2.05410i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.84906e10 | 0.480103 | 0.240052 | − | 0.970760i | \(-0.422836\pi\) | ||||
0.240052 | + | 0.970760i | \(0.422836\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.96669e10 | + | 4.02222e10i | 0.335592 | + | 0.193754i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.28763e11 | − | 7.43413e10i | 0.612965 | − | 0.353896i | −0.161160 | − | 0.986928i | \(-0.551523\pi\) |
0.774125 | + | 0.633033i | \(0.218190\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.56165e10 | − | 5.73917e10i | −0.355744 | − | 0.270004i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.18313e10 | + | 5.51334e10i | 0.148001 | + | 0.256346i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.76448e11 | − | 3.05616e11i | 0.810836 | − | 1.40441i | −0.101444 | − | 0.994841i | \(-0.532346\pi\) |
0.912280 | − | 0.409568i | \(-0.134320\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.20172e11i | − | 0.545811i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.74531e11 | −0.783511 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.55951e10 | + | 4.36449e10i | 0.335442 | + | 0.193667i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.91147e11 | + | 1.68094e11i | −1.27703 | + | 0.737291i | −0.976300 | − | 0.216420i | \(-0.930562\pi\) |
−0.300725 | + | 0.953711i | \(0.597229\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.35583e10 | + | 7.05659e10i | −0.232217 | + | 0.305958i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.79924e11 | − | 3.11637e11i | −0.771168 | − | 1.33570i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.88882e11 | + | 5.00358e11i | −1.22402 | + | 2.12007i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1.61119e10i | − | 0.0674896i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.11369e11 | 1.70357 | 0.851784 | − | 0.523893i | \(-0.175521\pi\) | ||||
0.851784 | + | 0.523893i | \(0.175521\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.18156e11 | − | 1.83687e11i | −1.30262 | − | 0.752070i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.40415e11 | + | 8.10687e10i | −0.568404 | + | 0.328168i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.59290e11 | − | 1.09007e11i | 1.03778 | − | 0.436290i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.95122e10 | − | 1.20399e11i | −0.275091 | − | 0.476472i | 0.695067 | − | 0.718945i | \(-0.255375\pi\) |
−0.970158 | + | 0.242473i | \(0.922041\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.88342e10 | − | 3.26218e10i | 0.0737003 | − | 0.127653i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.34066e11i | − | 0.518751i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.82284e11 | 0.697469 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.28783e11 | + | 7.43527e10i | 0.487283 | + | 0.281333i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.01094e11 | + | 5.83667e10i | −0.378277 | + | 0.218398i | −0.677068 | − | 0.735920i | \(-0.736750\pi\) |
0.298791 | + | 0.954318i | \(0.403417\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.46699e10 | + | 1.16159e11i | −0.0542857 | + | 0.429843i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.10694e11 | − | 1.91727e11i | −0.405108 | − | 0.701667i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.23193e11 | + | 3.86581e11i | −0.807846 | + | 1.39923i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.43338e11i | 0.871109i | 0.900162 | + | 0.435555i | \(0.143448\pi\) | ||||
−0.900162 | + | 0.435555i | \(0.856552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.04604e10 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.10722e11 | − | 2.94865e11i | −1.78861 | − | 1.03265i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.20029e11 | − | 2.42504e11i | 1.45500 | − | 0.840046i | 0.456243 | − | 0.889855i | \(-0.349195\pi\) |
0.998759 | + | 0.0498097i | \(0.0158615\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.86802e10 | + | 2.81721e11i | 0.269598 | + | 0.965315i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.16710e11 | − | 2.02147e11i | −0.395582 | − | 0.685169i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.98657e11 | + | 3.44083e11i | −0.666078 | + | 1.15368i | 0.312913 | + | 0.949782i | \(0.398695\pi\) |
−0.978992 | + | 0.203900i | \(0.934638\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.93995e10i | 0.263357i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.20639e11 | 0.723980 | 0.361990 | − | 0.932182i | \(-0.382097\pi\) | ||||
0.361990 | + | 0.932182i | \(0.382097\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.52591e11 | − | 3.76774e11i | −2.11844 | − | 1.22308i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.29296e11 | − | 7.46492e10i | 0.415244 | − | 0.239741i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.81327e11 | + | 3.55294e10i | 0.893892 | + | 0.112891i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.44854e8 | + | 4.24099e8i | 0.000769745 | + | 0.00133324i | 0.866410 | − | 0.499333i | \(-0.166422\pi\) |
−0.865640 | + | 0.500666i | \(0.833088\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.64416e11 | − | 2.84776e11i | 0.511403 | − | 0.885776i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 8.91624e11i | − | 2.74406i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.35724e10 | −0.193591 | −0.0967955 | − | 0.995304i | \(-0.530859\pi\) | ||||
−0.0967955 | + | 0.995304i | \(0.530859\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.44436e11 | + | 8.33900e10i | 0.435219 | + | 0.251274i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.15892e10 | − | 2.97850e10i | 0.153823 | − | 0.0888095i | −0.421113 | − | 0.907008i | \(-0.638360\pi\) |
0.574936 | + | 0.818199i | \(0.305027\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.40449e10 | + | 3.34079e10i | 0.0414399 | + | 0.0985715i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.25675e11 | + | 2.17676e11i | 0.366948 | + | 0.635573i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.64884e10 | − | 8.05203e10i | 0.134327 | − | 0.232661i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.28466e11i | − | 0.939259i | −0.882864 | − | 0.469629i | \(-0.844388\pi\) | ||
0.882864 | − | 0.469629i | \(-0.155612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.99029e10 | −0.169524 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.19975e11 | + | 2.42473e11i | 1.17627 | + | 0.679117i | 0.955148 | − | 0.296130i | \(-0.0956962\pi\) |
0.221118 | + | 0.975247i | \(0.429030\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.32007e11 | − | 2.49420e11i | 1.19752 | − | 0.691391i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.92725e11 | − | 1.46275e11i | −0.528753 | − | 0.401315i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.64955e11 | − | 8.05325e11i | −1.26259 | − | 2.18686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.00541e11 | + | 1.74143e11i | −0.270234 | + | 0.468060i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 5.80445e10i | − | 0.154424i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.21589e11 | 1.37357 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.48776e11 | + | 1.43631e11i | 0.648500 | + | 0.374412i | 0.787881 | − | 0.615827i | \(-0.211178\pi\) |
−0.139381 | + | 0.990239i | \(0.544511\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.92757e10 | − | 1.11288e10i | 0.0497396 | − | 0.0287172i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.00782e11 | + | 1.32785e11i | −0.257440 | + | 0.339190i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.22894e11 | − | 2.12859e11i | −0.310769 | − | 0.538269i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.22376e11 | + | 3.85166e11i | −0.556697 | + | 0.964227i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.39071e11i | − | 0.592506i | −0.955109 | − | 0.296253i | \(-0.904263\pi\) | ||
0.955109 | − | 0.296253i | \(-0.0957372\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.38495e11 | −0.830548 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.72151e11 | − | 9.93913e10i | −0.418195 | − | 0.241445i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.09245e11 | − | 1.78543e11i | 0.743773 | − | 0.429418i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.07634e11 | − | 2.13412e11i | 1.20884 | − | 0.508200i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.33763e11 | − | 2.31684e11i | −0.315385 | − | 0.546262i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.36214e10 | − | 9.28750e10i | 0.125183 | − | 0.216823i | −0.796622 | − | 0.604478i | \(-0.793382\pi\) |
0.921804 | + | 0.387656i | \(0.126715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.36934e11i | 0.316540i | 0.987396 | + | 0.158270i | \(0.0505916\pi\) | ||||
−0.987396 | + | 0.158270i | \(0.949408\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.98778e11 | −0.683891 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.72535e11 | + | 3.30553e11i | 1.29769 | + | 0.749222i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.22006e11 | − | 4.74586e11i | 1.84496 | − | 1.06519i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.55194e9 | + | 5.18794e10i | −0.0145625 | + | 0.115308i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.88762e11 | − | 3.26945e11i | −0.415472 | − | 0.719619i | 0.580006 | − | 0.814612i | \(-0.303050\pi\) |
−0.995478 | + | 0.0949936i | \(0.969717\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.58340e11 | + | 6.20662e11i | −0.781080 | + | 1.35287i | 0.150233 | + | 0.988651i | \(0.451998\pi\) |
−0.931313 | + | 0.364220i | \(0.881336\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.20564e11i | 1.33959i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.45077e11 | −0.951510 | −0.475755 | − | 0.879578i | \(-0.657825\pi\) | ||||
−0.475755 | + | 0.879578i | \(0.657825\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.52361e11 | − | 2.03436e11i | −0.746053 | − | 0.430734i | 0.0782131 | − | 0.996937i | \(-0.475079\pi\) |
−0.824266 | + | 0.566203i | \(0.808412\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.13562e11 | + | 1.23300e11i | −0.447836 | + | 0.258558i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.51820e11 | + | 5.91483e11i | −0.315319 | + | 1.22846i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.00130e11 | + | 1.73431e11i | 0.205977 | + | 0.356763i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.24325e10 | + | 5.61748e10i | −0.0660814 | + | 0.114456i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.89090e11i | 0.583424i | 0.956506 | + | 0.291712i | \(0.0942249\pi\) | ||||
−0.956506 | + | 0.291712i | \(0.905775\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.78158e11 | −0.356140 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.03243e11 | + | 1.75077e11i | 0.600455 | + | 0.346673i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.73291e11 | + | 3.88725e11i | −1.32061 | + | 0.762457i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.67390e11 | − | 2.11400e10i | −0.325233 | − | 0.0410743i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.78682e10 | − | 1.69513e11i | −0.188370 | − | 0.326266i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.27749e11 | + | 3.94472e11i | −0.434248 | + | 0.752139i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.33755e11i | 1.57486i | 0.616404 | + | 0.787430i | \(0.288589\pi\) | ||||
−0.616404 | + | 0.787430i | \(0.711411\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.04549e11 | −0.757019 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.63733e11 | − | 3.25471e11i | −1.04508 | − | 0.603378i | −0.123813 | − | 0.992306i | \(-0.539512\pi\) |
−0.921268 | + | 0.388927i | \(0.872846\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.76570e11 | − | 4.48353e11i | 1.42629 | − | 0.823469i | 0.429464 | − | 0.903084i | \(-0.358702\pi\) |
0.996826 | + | 0.0796151i | \(0.0253691\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.37346e11 | − | 5.64565e11i | −0.431886 | − | 1.02731i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.04187e9 | + | 7.00073e9i | 0.00728684 | + | 0.0126212i | 0.869646 | − | 0.493676i | \(-0.164347\pi\) |
−0.862359 | + | 0.506297i | \(0.831014\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.83175e11 | − | 3.17268e11i | 0.327191 | − | 0.566711i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.98522e11i | 0.351345i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.90582e11 | 0.509553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.19321e11 | − | 6.88901e10i | −0.207322 | − | 0.119697i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.48841e10 | − | 4.32344e10i | 0.128924 | − | 0.0744341i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.21545e11 | + | 6.23539e11i | 1.40152 | + | 1.06373i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.91022e11 | − | 5.04065e11i | −0.491957 | − | 0.852095i | 0.508000 | − | 0.861357i | \(-0.330385\pi\) |
−0.999957 | + | 0.00926195i | \(0.997052\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.61938e10 | − | 4.53690e10i | 0.0438776 | − | 0.0759983i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.79168e11i | − | 0.629403i | −0.949191 | − | 0.314701i | \(-0.898096\pi\) | ||
0.949191 | − | 0.314701i | \(-0.101904\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.21424e11 | 0.364235 | 0.182118 | − | 0.983277i | \(-0.441705\pi\) | ||||
0.182118 | + | 0.983277i | \(0.441705\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.10260e11 | + | 2.36864e11i | 0.668784 | + | 0.386123i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.45661e11 | − | 1.41832e11i | 0.396863 | − | 0.229129i | −0.288266 | − | 0.957550i | \(-0.593079\pi\) |
0.685130 | + | 0.728421i | \(0.259745\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.45358e11 | + | 1.91517e11i | −0.232719 | + | 0.306620i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.03466e10 | − | 6.98824e10i | −0.0640172 | − | 0.110881i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.72403e11 | − | 4.71817e11i | 0.428358 | − | 0.741938i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.35151e11i | 0.989885i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.84451e10 | 0.152063 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.11714e11 | − | 1.79968e11i | −0.477219 | − | 0.275522i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.04112e11 | + | 4.64254e11i | −1.22016 | + | 0.704461i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.76259e11 | − | 2.42262e11i | 0.866695 | − | 0.364363i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.02016e11 | + | 1.21593e12i | 1.04653 | + | 1.81265i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.30665e11 | − | 5.72728e11i | 0.488606 | − | 0.846290i | −0.511308 | − | 0.859397i | \(-0.670839\pi\) |
0.999914 | + | 0.0131074i | \(0.00417235\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.56202e11i | 0.375255i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.94922e11 | −1.44449 | −0.722247 | − | 0.691635i | \(-0.756890\pi\) | ||||
−0.722247 | + | 0.691635i | \(0.756890\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.97417e11 | + | 5.75859e11i | 1.43547 | + | 0.828768i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.08454e12 | − | 6.26159e11i | 1.54725 | − | 0.893306i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.33903e9 | + | 1.85209e10i | −0.00330795 | + | 0.0261929i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.13835e11 | + | 5.43578e11i | 0.439986 | + | 0.762079i | 0.997688 | − | 0.0679630i | \(-0.0216500\pi\) |
−0.557702 | + | 0.830042i | \(0.688317\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.39298e11 | − | 4.14476e11i | 0.332583 | − | 0.576051i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.18693e11i | 0.163538i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.69484e12 | −2.31506 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.23580e10 | − | 5.33229e10i | −0.125071 | − | 0.0722096i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.80765e11 | − | 1.62100e11i | 0.376947 | − | 0.217631i | −0.299542 | − | 0.954083i | \(-0.596834\pi\) |
0.676489 | + | 0.736453i | \(0.263501\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.02271e11 | − | 6.87613e11i | −0.934772 | − | 0.915262i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.61879e11 | + | 2.80383e11i | 0.213631 | + | 0.370019i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.69486e11 | + | 1.67920e12i | −1.26851 | + | 2.19713i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.21189e12i | 1.57219i | 0.618108 | + | 0.786093i | \(0.287899\pi\) | ||||
−0.618108 | + | 0.786093i | \(0.712101\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.58762e10 | 0.0332841 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.35199e11 | − | 7.80573e10i | −0.172431 | − | 0.0995531i | 0.411301 | − | 0.911500i | \(-0.365075\pi\) |
−0.583732 | + | 0.811947i | \(0.698408\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.98499e11 | + | 5.76484e11i | −1.26270 | + | 0.729022i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.64331e11 | − | 3.33829e10i | −0.331452 | − | 0.0418598i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.78356e10 | + | 3.08921e10i | 0.0221762 | + | 0.0384103i | 0.876901 | − | 0.480672i | \(-0.159607\pi\) |
−0.854724 | + | 0.519082i | \(0.826274\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.05388e11 | − | 1.82538e11i | 0.129935 | − | 0.225055i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 6.28614e10i | − | 0.0768532i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.75336e11 | −0.212569 | −0.106284 | − | 0.994336i | \(-0.533895\pi\) | ||||
−0.106284 | + | 0.994336i | \(0.533895\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.46588e12 | + | 8.46326e11i | 1.76232 | + | 1.01748i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.87778e11 | − | 2.23883e11i | 0.462312 | − | 0.266916i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.03063e11 | + | 2.45153e11i | 0.121851 | + | 0.289843i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.25330e11 | − | 3.90283e11i | −0.264196 | − | 0.457600i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.29144e11 | + | 2.23684e11i | −0.150165 | + | 0.260094i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.90262e12i | 2.19403i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.32296e11 | −0.723127 | −0.361563 | − | 0.932348i | \(-0.617757\pi\) | ||||
−0.361563 | + | 0.932348i | \(0.617757\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.31427e11 | − | 4.22289e11i | −0.829613 | − | 0.478977i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.20551e11 | + | 2.42805e11i | −0.473088 | + | 0.273137i | −0.717531 | − | 0.696526i | \(-0.754728\pi\) |
0.244444 | + | 0.969664i | \(0.421395\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.34316e11 | + | 4.81435e11i | 0.707708 | + | 0.537138i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.83150e11 | + | 3.17225e11i | 0.202670 | + | 0.351034i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.84268e11 | + | 6.65572e11i | −0.421751 | + | 0.730495i | −0.996111 | − | 0.0881084i | \(-0.971918\pi\) |
0.574360 | + | 0.818603i | \(0.305251\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.53345e12i | − | 1.66932i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.30101e10 | −0.0356427 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.58883e10 | − | 5.53611e10i | −0.102695 | − | 0.0592913i | 0.447773 | − | 0.894147i | \(-0.352217\pi\) |
−0.550468 | + | 0.834856i | \(0.685551\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.67838e12 | − | 9.69014e11i | 1.78298 | − | 1.02940i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.16921e11 | − | 2.85805e11i | 0.228578 | − | 0.301163i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.88425e11 | − | 1.01918e12i | −0.615043 | − | 1.06529i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.66493e11 | − | 9.81195e11i | 0.587354 | − | 1.01733i | −0.407223 | − | 0.913329i | \(-0.633503\pi\) |
0.994577 | − | 0.103999i | \(-0.0331638\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.16664e10i | 0.0325688i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.26386e12 | 3.32996 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.13793e12 | − | 6.56982e11i | −1.15168 | − | 0.664925i | −0.202387 | − | 0.979306i | \(-0.564870\pi\) |
−0.949297 | + | 0.314380i | \(0.898203\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.90858e11 | − | 1.10192e11i | 0.191623 | − | 0.110634i |
(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 | 84.9.m.b.73.1 | yes | 12 | |
3.2 | odd | 2 | 252.9.z.d.73.6 | 12 | |||
7.5 | odd | 6 | inner | 84.9.m.b.61.1 | ✓ | 12 | |
21.5 | even | 6 | 252.9.z.d.145.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.m.b.61.1 | ✓ | 12 | 7.5 | odd | 6 | inner | |
84.9.m.b.73.1 | yes | 12 | 1.1 | even | 1 | trivial | |
252.9.z.d.73.6 | 12 | 3.2 | odd | 2 | |||
252.9.z.d.145.6 | 12 | 21.5 | even | 6 |