Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,14,Mod(9,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.9");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(10.7230928952\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 160950x^{3} + 43599609x^{2} + 975553632x + 10914144768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{21}\cdot 5^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 9.4 | ||
Root | \(-50.1479 + 50.1479i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.9 |
Dual form | 10.14.b.a.9.3 |
$q$-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 \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 64.0000i | 0.707107i | ||||||||
\(3\) | − | 948.958i | − | 0.751551i | −0.926711 | − | 0.375776i | \(-0.877376\pi\) | ||
0.926711 | − | 0.375776i | \(-0.122624\pi\) | |||||||
\(4\) | −4096.00 | −0.500000 | ||||||||
\(5\) | −272.592 | + | 34937.5i | −0.00780204 | + | 0.999970i | ||||
\(6\) | 60733.3 | 0.531427 | ||||||||
\(7\) | − | 454502.i | − | 1.46015i | −0.683365 | − | 0.730076i | \(-0.739484\pi\) | ||
0.683365 | − | 0.730076i | \(-0.260516\pi\) | |||||||
\(8\) | − | 262144.i | − | 0.353553i | ||||||
\(9\) | 693802. | 0.435170 | ||||||||
\(10\) | −2.23600e6 | − | 17445.9i | −0.707085 | − | 0.00551687i | ||||
\(11\) | 1.09205e7 | 1.85861 | 0.929307 | − | 0.369309i | \(-0.120406\pi\) | ||||
0.929307 | + | 0.369309i | \(0.120406\pi\) | |||||||
\(12\) | 3.88693e6i | 0.375776i | ||||||||
\(13\) | 1.27566e7i | 0.732998i | 0.930418 | + | 0.366499i | \(0.119444\pi\) | ||||
−0.930418 | + | 0.366499i | \(0.880556\pi\) | |||||||
\(14\) | 2.90881e7 | 1.03248 | ||||||||
\(15\) | 3.31542e7 | + | 258678.i | 0.751529 | + | 0.00586363i | ||||
\(16\) | 1.67772e7 | 0.250000 | ||||||||
\(17\) | − | 1.16344e8i | − | 1.16903i | −0.811384 | − | 0.584514i | \(-0.801285\pi\) | ||
0.811384 | − | 0.584514i | \(-0.198715\pi\) | |||||||
\(18\) | 4.44033e7i | 0.307712i | ||||||||
\(19\) | 2.73026e8 | 1.33139 | 0.665696 | − | 0.746223i | \(-0.268135\pi\) | ||||
0.665696 | + | 0.746223i | \(0.268135\pi\) | |||||||
\(20\) | 1.11654e6 | − | 1.43104e8i | 0.00390102 | − | 0.499985i | ||||
\(21\) | −4.31303e8 | −1.09738 | ||||||||
\(22\) | 6.98910e8i | 1.31424i | ||||||||
\(23\) | − | 1.52448e8i | − | 0.214729i | −0.994220 | − | 0.107365i | \(-0.965759\pi\) | ||
0.994220 | − | 0.107365i | \(-0.0342412\pi\) | |||||||
\(24\) | −2.48764e8 | −0.265714 | ||||||||
\(25\) | −1.22055e9 | − | 1.90474e7i | −0.999878 | − | 0.0156036i | ||||
\(26\) | −8.16422e8 | −0.518308 | ||||||||
\(27\) | − | 2.17133e9i | − | 1.07860i | ||||||
\(28\) | 1.86164e9i | 0.730076i | ||||||||
\(29\) | 8.89364e8 | 0.277647 | 0.138823 | − | 0.990317i | \(-0.455668\pi\) | ||||
0.138823 | + | 0.990317i | \(0.455668\pi\) | |||||||
\(30\) | −1.65554e7 | + | 2.12187e9i | −0.00414621 | + | 0.531411i | ||||
\(31\) | −4.78852e9 | −0.969060 | −0.484530 | − | 0.874775i | \(-0.661009\pi\) | ||||
−0.484530 | + | 0.874775i | \(0.661009\pi\) | |||||||
\(32\) | 1.07374e9i | 0.176777i | ||||||||
\(33\) | − | 1.03631e10i | − | 1.39684i | ||||||
\(34\) | 7.44600e9 | 0.826628 | ||||||||
\(35\) | 1.58792e10 | + | 1.23894e8i | 1.46011 | + | 0.0113922i | ||||
\(36\) | −2.84181e9 | −0.217585 | ||||||||
\(37\) | 5.25171e9i | 0.336504i | 0.985744 | + | 0.168252i | \(0.0538122\pi\) | ||||
−0.985744 | + | 0.168252i | \(0.946188\pi\) | |||||||
\(38\) | 1.74737e10i | 0.941437i | ||||||||
\(39\) | 1.21055e10 | 0.550886 | ||||||||
\(40\) | 9.15866e9 | + | 7.14583e7i | 0.353543 | + | 0.00275844i | ||||
\(41\) | −2.70484e9 | −0.0889295 | −0.0444648 | − | 0.999011i | \(-0.514158\pi\) | ||||
−0.0444648 | + | 0.999011i | \(0.514158\pi\) | |||||||
\(42\) | − | 2.76034e10i | − | 0.775965i | ||||||
\(43\) | 8.03912e9i | 0.193938i | 0.995287 | + | 0.0969692i | \(0.0309148\pi\) | ||||
−0.995287 | + | 0.0969692i | \(0.969085\pi\) | |||||||
\(44\) | −4.47303e10 | −0.929307 | ||||||||
\(45\) | −1.89125e8 | + | 2.42397e10i | −0.00339522 | + | 0.435157i | ||||
\(46\) | 9.75667e9 | 0.151836 | ||||||||
\(47\) | − | 3.35808e10i | − | 0.454418i | −0.973846 | − | 0.227209i | \(-0.927040\pi\) | ||
0.973846 | − | 0.227209i | \(-0.0729600\pi\) | |||||||
\(48\) | − | 1.59209e10i | − | 0.187888i | ||||||
\(49\) | −1.09683e11 | −1.13205 | ||||||||
\(50\) | 1.21903e9 | − | 7.81155e10i | 0.0110334 | − | 0.707021i | ||||
\(51\) | −1.10405e11 | −0.878585 | ||||||||
\(52\) | − | 5.22510e10i | − | 0.366499i | ||||||
\(53\) | 1.38540e11i | 0.858580i | 0.903167 | + | 0.429290i | \(0.141236\pi\) | ||||
−0.903167 | + | 0.429290i | \(0.858764\pi\) | |||||||
\(54\) | 1.38965e11 | 0.762688 | ||||||||
\(55\) | −2.97683e9 | + | 3.81534e11i | −0.0145010 | + | 1.85856i | ||||
\(56\) | −1.19145e11 | −0.516242 | ||||||||
\(57\) | − | 2.59090e11i | − | 1.00061i | ||||||
\(58\) | 5.69193e10i | 0.196326i | ||||||||
\(59\) | 3.13003e11 | 0.966074 | 0.483037 | − | 0.875600i | \(-0.339534\pi\) | ||||
0.483037 | + | 0.875600i | \(0.339534\pi\) | |||||||
\(60\) | −1.35800e11 | − | 1.05955e9i | −0.375764 | − | 0.00293182i | ||||
\(61\) | 7.15377e11 | 1.77783 | 0.888917 | − | 0.458069i | \(-0.151459\pi\) | ||||
0.888917 | + | 0.458069i | \(0.151459\pi\) | |||||||
\(62\) | − | 3.06465e11i | − | 0.685229i | ||||||
\(63\) | − | 3.15334e11i | − | 0.635415i | ||||||
\(64\) | −6.87195e10 | −0.125000 | ||||||||
\(65\) | −4.45683e11 | − | 3.47734e9i | −0.732976 | − | 0.00571888i | ||||
\(66\) | 6.63236e11 | 0.987718 | ||||||||
\(67\) | − | 4.70553e11i | − | 0.635510i | −0.948173 | − | 0.317755i | \(-0.897071\pi\) | ||
0.948173 | − | 0.317755i | \(-0.102929\pi\) | |||||||
\(68\) | 4.76544e11i | 0.584514i | ||||||||
\(69\) | −1.44667e11 | −0.161380 | ||||||||
\(70\) | −7.92919e9 | + | 1.01627e12i | −0.00805548 | + | 1.03245i | ||||
\(71\) | −4.88492e11 | −0.452562 | −0.226281 | − | 0.974062i | \(-0.572657\pi\) | ||||
−0.226281 | + | 0.974062i | \(0.572657\pi\) | |||||||
\(72\) | − | 1.81876e11i | − | 0.153856i | ||||||
\(73\) | 1.10937e12i | 0.857978i | 0.903310 | + | 0.428989i | \(0.141130\pi\) | ||||
−0.903310 | + | 0.428989i | \(0.858870\pi\) | |||||||
\(74\) | −3.36110e11 | −0.237944 | ||||||||
\(75\) | −1.80751e10 | + | 1.15825e12i | −0.0117269 | + | 0.751460i | ||||
\(76\) | −1.11832e12 | −0.665696 | ||||||||
\(77\) | − | 4.96338e12i | − | 2.71386i | ||||||
\(78\) | 7.74750e11i | 0.389535i | ||||||||
\(79\) | −2.70663e12 | −1.25272 | −0.626358 | − | 0.779536i | \(-0.715455\pi\) | ||||
−0.626358 | + | 0.779536i | \(0.715455\pi\) | |||||||
\(80\) | −4.57333e9 | + | 5.86154e11i | −0.00195051 | + | 0.249992i | ||||
\(81\) | −9.54360e11 | −0.375456 | ||||||||
\(82\) | − | 1.73110e11i | − | 0.0628827i | ||||||
\(83\) | 1.70813e12i | 0.573474i | 0.958009 | + | 0.286737i | \(0.0925706\pi\) | ||||
−0.958009 | + | 0.286737i | \(0.907429\pi\) | |||||||
\(84\) | 1.76662e12 | 0.548690 | ||||||||
\(85\) | 4.06476e12 | + | 3.17144e10i | 1.16899 | + | 0.00912080i | ||||
\(86\) | −5.14504e11 | −0.137135 | ||||||||
\(87\) | − | 8.43969e11i | − | 0.208666i | ||||||
\(88\) | − | 2.86274e12i | − | 0.657119i | ||||||
\(89\) | 7.89059e11 | 0.168296 | 0.0841481 | − | 0.996453i | \(-0.473183\pi\) | ||||
0.0841481 | + | 0.996453i | \(0.473183\pi\) | |||||||
\(90\) | −1.55134e12 | − | 1.21040e10i | −0.307703 | − | 0.00240078i | ||||
\(91\) | 5.79789e12 | 1.07029 | ||||||||
\(92\) | 6.24427e11i | 0.107365i | ||||||||
\(93\) | 4.54411e12i | 0.728298i | ||||||||
\(94\) | 2.14917e12 | 0.321322 | ||||||||
\(95\) | −7.44248e10 | + | 9.53886e12i | −0.0103876 | + | 1.33135i | ||||
\(96\) | 1.01894e12 | 0.132857 | ||||||||
\(97\) | − | 4.98929e12i | − | 0.608167i | −0.952645 | − | 0.304083i | \(-0.901650\pi\) | ||
0.952645 | − | 0.304083i | \(-0.0983501\pi\) | |||||||
\(98\) | − | 7.01970e12i | − | 0.800478i | ||||||
\(99\) | 7.57665e12 | 0.808814 | ||||||||
\(100\) | 4.99939e12 | + | 7.80180e10i | 0.499939 | + | 0.00780180i | ||||
\(101\) | −1.82670e13 | −1.71229 | −0.856146 | − | 0.516734i | \(-0.827147\pi\) | ||||
−0.856146 | + | 0.516734i | \(0.827147\pi\) | |||||||
\(102\) | − | 7.06594e12i | − | 0.621253i | ||||||
\(103\) | 4.35513e12i | 0.359385i | 0.983723 | + | 0.179692i | \(0.0575102\pi\) | ||||
−0.983723 | + | 0.179692i | \(0.942490\pi\) | |||||||
\(104\) | 3.34406e12 | 0.259154 | ||||||||
\(105\) | 1.17570e11 | − | 1.50686e13i | 0.00856180 | − | 1.09735i | ||||
\(106\) | −8.86653e12 | −0.607108 | ||||||||
\(107\) | 2.32112e13i | 1.49521i | 0.664142 | + | 0.747607i | \(0.268797\pi\) | ||||
−0.664142 | + | 0.747607i | \(0.731203\pi\) | |||||||
\(108\) | 8.89378e12i | 0.539302i | ||||||||
\(109\) | −1.51925e13 | −0.867676 | −0.433838 | − | 0.900991i | \(-0.642841\pi\) | ||||
−0.433838 | + | 0.900991i | \(0.642841\pi\) | |||||||
\(110\) | −2.44182e13 | − | 1.90517e11i | −1.31420 | − | 0.0102537i | ||||
\(111\) | 4.98365e12 | 0.252900 | ||||||||
\(112\) | − | 7.62527e12i | − | 0.365038i | ||||||
\(113\) | − | 2.90883e13i | − | 1.31434i | −0.753741 | − | 0.657172i | \(-0.771753\pi\) | ||
0.753741 | − | 0.657172i | \(-0.228247\pi\) | |||||||
\(114\) | 1.65818e13 | 0.707538 | ||||||||
\(115\) | 5.32615e12 | + | 4.15561e10i | 0.214722 | + | 0.00167532i | ||||
\(116\) | −3.64283e12 | −0.138823 | ||||||||
\(117\) | 8.85055e12i | 0.318979i | ||||||||
\(118\) | 2.00322e13i | 0.683118i | ||||||||
\(119\) | −5.28784e13 | −1.70696 | ||||||||
\(120\) | 6.78110e10 | − | 8.69118e12i | 0.00207311 | − | 0.265705i | ||||
\(121\) | 8.47341e13 | 2.45444 | ||||||||
\(122\) | 4.57841e13i | 1.25712i | ||||||||
\(123\) | 2.56678e12i | 0.0668351i | ||||||||
\(124\) | 1.96138e13 | 0.484530 | ||||||||
\(125\) | 9.98181e11 | − | 4.26379e13i | 0.0234042 | − | 0.999726i | ||||
\(126\) | 2.01814e13 | 0.449307 | ||||||||
\(127\) | 2.92844e13i | 0.619315i | 0.950848 | + | 0.309658i | \(0.100214\pi\) | ||||
−0.950848 | + | 0.309658i | \(0.899786\pi\) | |||||||
\(128\) | − | 4.39805e12i | − | 0.0883883i | ||||||
\(129\) | 7.62879e12 | 0.145755 | ||||||||
\(130\) | 2.22550e11 | − | 2.85237e13i | 0.00404386 | − | 0.518292i | ||||
\(131\) | −2.29979e13 | −0.397581 | −0.198790 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198790 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(132\) | 4.24471e13i | 0.698422i | ||||||||
\(133\) | − | 1.24091e14i | − | 1.94404i | ||||||
\(134\) | 3.01154e13 | 0.449374 | ||||||||
\(135\) | 7.58610e13 | + | 5.91888e11i | 1.07857 | + | 0.00841531i | ||||
\(136\) | −3.04988e13 | −0.413314 | ||||||||
\(137\) | 3.65959e13i | 0.472877i | 0.971646 | + | 0.236439i | \(0.0759802\pi\) | ||||
−0.971646 | + | 0.236439i | \(0.924020\pi\) | |||||||
\(138\) | − | 9.25867e12i | − | 0.114113i | ||||||
\(139\) | −3.84338e13 | −0.451978 | −0.225989 | − | 0.974130i | \(-0.572561\pi\) | ||||
−0.225989 | + | 0.974130i | \(0.572561\pi\) | |||||||
\(140\) | −6.50410e13 | − | 5.07468e11i | −0.730054 | − | 0.00569608i | ||||
\(141\) | −3.18668e13 | −0.341518 | ||||||||
\(142\) | − | 3.12635e13i | − | 0.320010i | ||||||
\(143\) | 1.39308e14i | 1.36236i | ||||||||
\(144\) | 1.16401e13 | 0.108793 | ||||||||
\(145\) | −2.42433e11 | + | 3.10721e13i | −0.00216621 | + | 0.277638i | ||||
\(146\) | −7.09994e13 | −0.606682 | ||||||||
\(147\) | 1.04084e14i | 0.850791i | ||||||||
\(148\) | − | 2.15110e13i | − | 0.168252i | ||||||
\(149\) | −2.20268e14 | −1.64907 | −0.824537 | − | 0.565808i | \(-0.808564\pi\) | ||||
−0.824537 | + | 0.565808i | \(0.808564\pi\) | |||||||
\(150\) | −7.41283e13 | − | 1.15681e12i | −0.531362 | − | 0.00829218i | ||||
\(151\) | 3.34504e12 | 0.0229642 | 0.0114821 | − | 0.999934i | \(-0.496345\pi\) | ||||
0.0114821 | + | 0.999934i | \(0.496345\pi\) | |||||||
\(152\) | − | 7.15722e13i | − | 0.470718i | ||||||
\(153\) | − | 8.07195e13i | − | 0.508726i | ||||||
\(154\) | 3.17656e14 | 1.91899 | ||||||||
\(155\) | 1.30531e12 | − | 1.67299e14i | 0.00756064 | − | 0.969030i | ||||
\(156\) | −4.95840e13 | −0.275443 | ||||||||
\(157\) | 1.34910e14i | 0.718946i | 0.933155 | + | 0.359473i | \(0.117044\pi\) | ||||
−0.933155 | + | 0.359473i | \(0.882956\pi\) | |||||||
\(158\) | − | 1.73224e14i | − | 0.885804i | ||||||
\(159\) | 1.31468e14 | 0.645267 | ||||||||
\(160\) | −3.75139e13 | − | 2.92693e11i | −0.176771 | − | 0.00137922i | ||||
\(161\) | −6.92879e13 | −0.313537 | ||||||||
\(162\) | − | 6.10790e13i | − | 0.265488i | ||||||
\(163\) | 3.24051e14i | 1.35330i | 0.736304 | + | 0.676651i | \(0.236569\pi\) | ||||
−0.736304 | + | 0.676651i | \(0.763431\pi\) | |||||||
\(164\) | 1.10790e13 | 0.0444648 | ||||||||
\(165\) | 3.62060e14 | + | 2.82489e12i | 1.39680 | + | 0.0108982i | ||||
\(166\) | −1.09320e14 | −0.405507 | ||||||||
\(167\) | − | 4.57413e14i | − | 1.63174i | −0.578234 | − | 0.815871i | \(-0.696258\pi\) | ||
0.578234 | − | 0.815871i | \(-0.303742\pi\) | |||||||
\(168\) | 1.13063e14i | 0.387982i | ||||||||
\(169\) | 1.40144e14 | 0.462714 | ||||||||
\(170\) | −2.02972e12 | + | 2.60145e14i | −0.00644938 | + | 0.826602i | ||||
\(171\) | 1.89426e14 | 0.579383 | ||||||||
\(172\) | − | 3.29283e13i | − | 0.0969692i | ||||||
\(173\) | 1.61397e14i | 0.457717i | 0.973460 | + | 0.228858i | \(0.0734993\pi\) | ||||
−0.973460 | + | 0.228858i | \(0.926501\pi\) | |||||||
\(174\) | 5.40140e13 | 0.147549 | ||||||||
\(175\) | −8.65706e12 | + | 5.54744e14i | −0.0227836 | + | 1.45998i | ||||
\(176\) | 1.83215e14 | 0.464653 | ||||||||
\(177\) | − | 2.97027e14i | − | 0.726055i | ||||||
\(178\) | 5.04998e13i | 0.119003i | ||||||||
\(179\) | −6.37281e14 | −1.44806 | −0.724030 | − | 0.689768i | \(-0.757712\pi\) | ||||
−0.724030 | + | 0.689768i | \(0.757712\pi\) | |||||||
\(180\) | 7.74656e11 | − | 9.92859e13i | 0.00169761 | − | 0.217579i | ||||
\(181\) | 1.68242e14 | 0.355651 | 0.177826 | − | 0.984062i | \(-0.443094\pi\) | ||||
0.177826 | + | 0.984062i | \(0.443094\pi\) | |||||||
\(182\) | 3.71065e14i | 0.756809i | ||||||||
\(183\) | − | 6.78863e14i | − | 1.33613i | ||||||
\(184\) | −3.99633e13 | −0.0759182 | ||||||||
\(185\) | −1.83482e14 | − | 1.43157e12i | −0.336493 | − | 0.00262541i | ||||
\(186\) | −2.90823e14 | −0.514985 | ||||||||
\(187\) | − | 1.27053e15i | − | 2.17277i | ||||||
\(188\) | 1.37547e14i | 0.227209i | ||||||||
\(189\) | −9.86875e14 | −1.57493 | ||||||||
\(190\) | −6.10487e14 | − | 4.76319e12i | −0.941408 | − | 0.00734512i | ||||
\(191\) | 5.12678e14 | 0.764060 | 0.382030 | − | 0.924150i | \(-0.375225\pi\) | ||||
0.382030 | + | 0.924150i | \(0.375225\pi\) | |||||||
\(192\) | 6.52119e13i | 0.0939439i | ||||||||
\(193\) | 7.31821e14i | 1.01925i | 0.860395 | + | 0.509627i | \(0.170217\pi\) | ||||
−0.860395 | + | 0.509627i | \(0.829783\pi\) | |||||||
\(194\) | 3.19315e14 | 0.430039 | ||||||||
\(195\) | −3.29985e12 | + | 4.22935e14i | −0.00429803 | + | 0.550869i | ||||
\(196\) | 4.49261e14 | 0.566023 | ||||||||
\(197\) | 6.00125e14i | 0.731495i | 0.930714 | + | 0.365748i | \(0.119187\pi\) | ||||
−0.930714 | + | 0.365748i | \(0.880813\pi\) | |||||||
\(198\) | 4.84906e14i | 0.571918i | ||||||||
\(199\) | −1.66629e14 | −0.190197 | −0.0950987 | − | 0.995468i | \(-0.530317\pi\) | ||||
−0.0950987 | + | 0.995468i | \(0.530317\pi\) | |||||||
\(200\) | −4.99315e12 | + | 3.19961e14i | −0.00551671 | + | 0.353510i | ||||
\(201\) | −4.46535e14 | −0.477619 | ||||||||
\(202\) | − | 1.16909e15i | − | 1.21077i | ||||||
\(203\) | − | 4.04217e14i | − | 0.405407i | ||||||
\(204\) | 4.52220e14 | 0.439292 | ||||||||
\(205\) | 7.37317e11 | − | 9.45002e13i | 0.000693831 | − | 0.0889268i | ||||
\(206\) | −2.78728e14 | −0.254123 | ||||||||
\(207\) | − | 1.05769e14i | − | 0.0934437i | ||||||
\(208\) | 2.14020e14i | 0.183250i | ||||||||
\(209\) | 2.98158e15 | 2.47454 | ||||||||
\(210\) | 9.64393e14 | + | 7.52446e12i | 0.775941 | + | 0.00605411i | ||||
\(211\) | −1.50601e14 | −0.117488 | −0.0587438 | − | 0.998273i | \(-0.518709\pi\) | ||||
−0.0587438 | + | 0.998273i | \(0.518709\pi\) | |||||||
\(212\) | − | 5.67458e14i | − | 0.429290i | ||||||
\(213\) | 4.63559e14i | 0.340124i | ||||||||
\(214\) | −1.48552e15 | −1.05728 | ||||||||
\(215\) | −2.80867e14 | − | 2.19140e12i | −0.193932 | − | 0.00151311i | ||||
\(216\) | −5.69202e14 | −0.381344 | ||||||||
\(217\) | 2.17639e15i | 1.41498i | ||||||||
\(218\) | − | 9.72322e14i | − | 0.613540i | ||||||
\(219\) | 1.05274e15 | 0.644815 | ||||||||
\(220\) | 1.21931e13 | − | 1.56276e15i | 0.00725049 | − | 0.929278i | ||||
\(221\) | 1.48415e15 | 0.856895 | ||||||||
\(222\) | 3.18954e14i | 0.178827i | ||||||||
\(223\) | − | 7.62572e14i | − | 0.415240i | −0.978210 | − | 0.207620i | \(-0.933428\pi\) | ||
0.978210 | − | 0.207620i | \(-0.0665718\pi\) | |||||||
\(224\) | 4.88018e14 | 0.258121 | ||||||||
\(225\) | −8.46823e14 | − | 1.32151e13i | −0.435117 | − | 0.00679022i | ||||
\(226\) | 1.86165e15 | 0.929381 | ||||||||
\(227\) | − | 8.39292e14i | − | 0.407141i | −0.979060 | − | 0.203570i | \(-0.934745\pi\) | ||
0.979060 | − | 0.203570i | \(-0.0652546\pi\) | |||||||
\(228\) | 1.06123e15i | 0.500305i | ||||||||
\(229\) | −3.20496e15 | −1.46856 | −0.734280 | − | 0.678847i | \(-0.762480\pi\) | ||||
−0.734280 | + | 0.678847i | \(0.762480\pi\) | |||||||
\(230\) | −2.65959e12 | + | 3.40874e14i | −0.00118463 | + | 0.151832i | ||||
\(231\) | −4.71003e15 | −2.03961 | ||||||||
\(232\) | − | 2.33141e14i | − | 0.0981629i | ||||||
\(233\) | 6.66372e14i | 0.272837i | 0.990651 | + | 0.136419i | \(0.0435592\pi\) | ||||
−0.990651 | + | 0.136419i | \(0.956441\pi\) | |||||||
\(234\) | −5.66435e14 | −0.225552 | ||||||||
\(235\) | 1.17323e15 | + | 9.15386e12i | 0.454404 | + | 0.00354538i | ||||
\(236\) | −1.28206e15 | −0.483037 | ||||||||
\(237\) | 2.56848e15i | 0.941480i | ||||||||
\(238\) | − | 3.38422e15i | − | 1.20700i | ||||||
\(239\) | 1.81256e15 | 0.629081 | 0.314540 | − | 0.949244i | \(-0.398150\pi\) | ||||
0.314540 | + | 0.949244i | \(0.398150\pi\) | |||||||
\(240\) | 5.56235e14 | + | 4.33990e12i | 0.187882 | + | 0.00146591i | ||||
\(241\) | −2.25908e15 | −0.742713 | −0.371357 | − | 0.928490i | \(-0.621107\pi\) | ||||
−0.371357 | + | 0.928490i | \(0.621107\pi\) | |||||||
\(242\) | 5.42298e15i | 1.73555i | ||||||||
\(243\) | − | 2.55616e15i | − | 0.796430i | ||||||
\(244\) | −2.93018e15 | −0.888917 | ||||||||
\(245\) | 2.98987e13 | − | 3.83205e15i | 0.00883227 | − | 1.13201i | ||||
\(246\) | −1.64274e14 | −0.0472596 | ||||||||
\(247\) | 3.48289e15i | 0.975908i | ||||||||
\(248\) | 1.25528e15i | 0.342614i | ||||||||
\(249\) | 1.62094e15 | 0.430995 | ||||||||
\(250\) | 2.72883e15 | + | 6.38836e13i | 0.706913 | + | 0.0165493i | ||||
\(251\) | 4.09678e15 | 1.03410 | 0.517051 | − | 0.855955i | \(-0.327030\pi\) | ||||
0.517051 | + | 0.855955i | \(0.327030\pi\) | |||||||
\(252\) | 1.29161e15i | 0.317708i | ||||||||
\(253\) | − | 1.66480e15i | − | 0.399098i | ||||||
\(254\) | −1.87420e15 | −0.437922 | ||||||||
\(255\) | 3.00956e13 | − | 3.85728e15i | 0.00685475 | − | 0.878558i | ||||
\(256\) | 2.81475e14 | 0.0625000 | ||||||||
\(257\) | − | 3.97811e15i | − | 0.861214i | −0.902540 | − | 0.430607i | \(-0.858299\pi\) | ||
0.902540 | − | 0.430607i | \(-0.141701\pi\) | |||||||
\(258\) | 4.88242e14i | 0.103064i | ||||||||
\(259\) | 2.38691e15 | 0.491347 | ||||||||
\(260\) | 1.82552e15 | + | 1.42432e13i | 0.366488 | + | 0.00285944i | ||||
\(261\) | 6.17042e14 | 0.120824 | ||||||||
\(262\) | − | 1.47187e15i | − | 0.281132i | ||||||
\(263\) | 4.00498e15i | 0.746257i | 0.927780 | + | 0.373128i | \(0.121715\pi\) | ||||
−0.927780 | + | 0.373128i | \(0.878285\pi\) | |||||||
\(264\) | −2.71662e15 | −0.493859 | ||||||||
\(265\) | −4.84023e15 | − | 3.77648e13i | −0.858554 | − | 0.00669867i | ||||
\(266\) | 7.94182e15 | 1.37464 | ||||||||
\(267\) | − | 7.48783e14i | − | 0.126483i | ||||||
\(268\) | 1.92739e15i | 0.317755i | ||||||||
\(269\) | 9.43541e15 | 1.51835 | 0.759174 | − | 0.650888i | \(-0.225603\pi\) | ||||
0.759174 | + | 0.650888i | \(0.225603\pi\) | |||||||
\(270\) | −3.78808e13 | + | 4.85510e15i | −0.00595052 | + | 0.762665i | ||||
\(271\) | 7.02518e15 | 1.07735 | 0.538675 | − | 0.842513i | \(-0.318925\pi\) | ||||
0.538675 | + | 0.842513i | \(0.318925\pi\) | |||||||
\(272\) | − | 1.95192e15i | − | 0.292257i | ||||||
\(273\) | − | 5.50196e15i | − | 0.804378i | ||||||
\(274\) | −2.34214e15 | −0.334375 | ||||||||
\(275\) | −1.33290e16 | − | 2.08006e14i | −1.85839 | − | 0.0290011i | ||||
\(276\) | 5.92555e14 | 0.0806900 | ||||||||
\(277\) | 1.03209e16i | 1.37278i | 0.727234 | + | 0.686389i | \(0.240805\pi\) | ||||
−0.727234 | + | 0.686389i | \(0.759195\pi\) | |||||||
\(278\) | − | 2.45977e15i | − | 0.319597i | ||||||
\(279\) | −3.32229e15 | −0.421706 | ||||||||
\(280\) | 3.24779e13 | − | 4.16263e15i | 0.00402774 | − | 0.516226i | ||||
\(281\) | −1.07766e16 | −1.30584 | −0.652922 | − | 0.757426i | \(-0.726457\pi\) | ||||
−0.652922 | + | 0.757426i | \(0.726457\pi\) | |||||||
\(282\) | − | 2.03947e15i | − | 0.241490i | ||||||
\(283\) | 1.28451e16i | 1.48637i | 0.669086 | + | 0.743185i | \(0.266686\pi\) | ||||
−0.669086 | + | 0.743185i | \(0.733314\pi\) | |||||||
\(284\) | 2.00086e15 | 0.226281 | ||||||||
\(285\) | 9.05197e15 | + | 7.06260e13i | 1.00058 | + | 0.00780680i | ||||
\(286\) | −8.91571e15 | −0.963334 | ||||||||
\(287\) | 1.22935e15i | 0.129851i | ||||||||
\(288\) | 7.44964e14i | 0.0769280i | ||||||||
\(289\) | −3.63128e15 | −0.366626 | ||||||||
\(290\) | −1.98862e15 | − | 1.55157e13i | −0.196320 | − | 0.00153174i | ||||
\(291\) | −4.73463e15 | −0.457069 | ||||||||
\(292\) | − | 4.54396e15i | − | 0.428989i | ||||||
\(293\) | − | 1.60607e16i | − | 1.48294i | −0.670983 | − | 0.741472i | \(-0.734128\pi\) | ||
0.670983 | − | 0.741472i | \(-0.265872\pi\) | |||||||
\(294\) | −6.66140e15 | −0.601600 | ||||||||
\(295\) | −8.53221e13 | + | 1.09355e16i | −0.00753735 | + | 0.966045i | ||||
\(296\) | 1.37671e15 | 0.118972 | ||||||||
\(297\) | − | 2.37120e16i | − | 2.00471i | ||||||
\(298\) | − | 1.40971e16i | − | 1.16607i | ||||||
\(299\) | 1.94472e15 | 0.157396 | ||||||||
\(300\) | 7.40358e13 | − | 4.74421e15i | 0.00586345 | − | 0.375730i | ||||
\(301\) | 3.65380e15 | 0.283180 | ||||||||
\(302\) | 2.14082e14i | 0.0162381i | ||||||||
\(303\) | 1.73346e16i | 1.28688i | ||||||||
\(304\) | 4.58062e15 | 0.332848 | ||||||||
\(305\) | −1.95006e14 | + | 2.49935e16i | −0.0138707 | + | 1.77778i | ||||
\(306\) | 5.16605e15 | 0.359724 | ||||||||
\(307\) | − | 3.69095e15i | − | 0.251616i | −0.992055 | − | 0.125808i | \(-0.959848\pi\) | ||
0.992055 | − | 0.125808i | \(-0.0401524\pi\) | |||||||
\(308\) | 2.03300e16i | 1.35693i | ||||||||
\(309\) | 4.13284e15 | 0.270096 | ||||||||
\(310\) | 1.07071e16 | + | 8.35400e13i | 0.685208 | + | 0.00534618i | ||||
\(311\) | −7.43457e15 | −0.465922 | −0.232961 | − | 0.972486i | \(-0.574841\pi\) | ||||
−0.232961 | + | 0.972486i | \(0.574841\pi\) | |||||||
\(312\) | − | 3.17338e15i | − | 0.194768i | ||||||
\(313\) | 1.39759e16i | 0.840122i | 0.907496 | + | 0.420061i | \(0.137991\pi\) | ||||
−0.907496 | + | 0.420061i | \(0.862009\pi\) | |||||||
\(314\) | −8.63424e15 | −0.508372 | ||||||||
\(315\) | 1.10170e16 | + | 8.59576e13i | 0.635396 | + | 0.00495753i | ||||
\(316\) | 1.10863e16 | 0.626358 | ||||||||
\(317\) | − | 1.71546e16i | − | 0.949502i | −0.880120 | − | 0.474751i | \(-0.842538\pi\) | ||
0.880120 | − | 0.474751i | \(-0.157462\pi\) | |||||||
\(318\) | 8.41396e15i | 0.456273i | ||||||||
\(319\) | 9.71227e15 | 0.516038 | ||||||||
\(320\) | 1.87324e13 | − | 2.40089e15i | 0.000975255 | − | 0.124996i | ||||
\(321\) | 2.20265e16 | 1.12373 | ||||||||
\(322\) | − | 4.43442e15i | − | 0.221704i | ||||||
\(323\) | − | 3.17649e16i | − | 1.55644i | ||||||
\(324\) | 3.90906e15 | 0.187728 | ||||||||
\(325\) | 2.42979e14 | − | 1.55701e16i | 0.0114374 | − | 0.732909i | ||||
\(326\) | −2.07393e16 | −0.956928 | ||||||||
\(327\) | 1.44171e16i | 0.652103i | ||||||||
\(328\) | 7.09057e14i | 0.0314413i | ||||||||
\(329\) | −1.52625e16 | −0.663519 | ||||||||
\(330\) | −1.80793e14 | + | 2.31718e16i | −0.00770621 | + | 0.987688i | ||||
\(331\) | −1.30144e15 | −0.0543928 | −0.0271964 | − | 0.999630i | \(-0.508658\pi\) | ||||
−0.0271964 | + | 0.999630i | \(0.508658\pi\) | |||||||
\(332\) | − | 6.99651e15i | − | 0.286737i | ||||||
\(333\) | 3.64365e15i | 0.146436i | ||||||||
\(334\) | 2.92744e16 | 1.15382 | ||||||||
\(335\) | 1.64400e16 | + | 1.28269e14i | 0.635491 | + | 0.00495827i | ||||
\(336\) | −7.23606e15 | −0.274345 | ||||||||
\(337\) | − | 4.26730e16i | − | 1.58694i | −0.608612 | − | 0.793468i | \(-0.708274\pi\) | ||
0.608612 | − | 0.793468i | \(-0.291726\pi\) | |||||||
\(338\) | 8.96925e15i | 0.327188i | ||||||||
\(339\) | −2.76036e16 | −0.987797 | ||||||||
\(340\) | −1.66492e16 | − | 1.29902e14i | −0.584496 | − | 0.00456040i | ||||
\(341\) | −5.22929e16 | −1.80111 | ||||||||
\(342\) | 1.21233e16i | 0.409685i | ||||||||
\(343\) | 5.81483e15i | 0.192808i | ||||||||
\(344\) | 2.10741e15 | 0.0685676 | ||||||||
\(345\) | 3.94350e13 | − | 5.05429e15i | 0.00125909 | − | 0.161375i | ||||
\(346\) | −1.03294e16 | −0.323655 | ||||||||
\(347\) | 1.84259e16i | 0.566613i | 0.959029 | + | 0.283306i | \(0.0914313\pi\) | ||||
−0.959029 | + | 0.283306i | \(0.908569\pi\) | |||||||
\(348\) | 3.45690e15i | 0.104333i | ||||||||
\(349\) | −6.19591e15 | −0.183544 | −0.0917720 | − | 0.995780i | \(-0.529253\pi\) | ||||
−0.0917720 | + | 0.995780i | \(0.529253\pi\) | |||||||
\(350\) | −3.55036e16 | − | 5.54052e14i | −1.03236 | − | 0.0161105i | ||||
\(351\) | 2.76988e16 | 0.790615 | ||||||||
\(352\) | 1.17258e16i | 0.328560i | ||||||||
\(353\) | 3.53266e16i | 0.971775i | 0.874021 | + | 0.485888i | \(0.161504\pi\) | ||||
−0.874021 | + | 0.485888i | \(0.838496\pi\) | |||||||
\(354\) | 1.90097e16 | 0.513398 | ||||||||
\(355\) | 1.33159e14 | − | 1.70667e16i | 0.00353091 | − | 0.452549i | ||||
\(356\) | −3.23198e15 | −0.0841481 | ||||||||
\(357\) | 5.01794e16i | 1.28287i | ||||||||
\(358\) | − | 4.07860e16i | − | 1.02393i | ||||||
\(359\) | −3.59772e15 | −0.0886979 | −0.0443490 | − | 0.999016i | \(-0.514121\pi\) | ||||
−0.0443490 | + | 0.999016i | \(0.514121\pi\) | |||||||
\(360\) | 6.35430e15 | + | 4.95780e13i | 0.153851 | + | 0.00120039i | ||||
\(361\) | 3.24904e16 | 0.772606 | ||||||||
\(362\) | 1.07675e16i | 0.251483i | ||||||||
\(363\) | − | 8.04090e16i | − | 1.84464i | ||||||
\(364\) | −2.37482e16 | −0.535145 | ||||||||
\(365\) | −3.87585e16 | − | 3.02404e14i | −0.857952 | − | 0.00669398i | ||||
\(366\) | 4.34472e16 | 0.944789 | ||||||||
\(367\) | 1.64558e16i | 0.351551i | 0.984430 | + | 0.175776i | \(0.0562434\pi\) | ||||
−0.984430 | + | 0.175776i | \(0.943757\pi\) | |||||||
\(368\) | − | 2.55765e15i | − | 0.0536823i | ||||||
\(369\) | −1.87662e15 | −0.0386995 | ||||||||
\(370\) | 9.16208e13 | − | 1.17428e16i | 0.00185645 | − | 0.237937i | ||||
\(371\) | 6.29665e16 | 1.25366 | ||||||||
\(372\) | − | 1.86127e16i | − | 0.364149i | ||||||
\(373\) | 4.96880e16i | 0.955310i | 0.878548 | + | 0.477655i | \(0.158513\pi\) | ||||
−0.878548 | + | 0.477655i | \(0.841487\pi\) | |||||||
\(374\) | 8.13138e16 | 1.53638 | ||||||||
\(375\) | −4.04616e16 | − | 9.47231e14i | −0.751346 | − | 0.0175895i | ||||
\(376\) | −8.80301e15 | −0.160661 | ||||||||
\(377\) | 1.13452e16i | 0.203514i | ||||||||
\(378\) | − | 6.31600e16i | − | 1.11364i | ||||||
\(379\) | −4.43290e16 | −0.768304 | −0.384152 | − | 0.923270i | \(-0.625506\pi\) | ||||
−0.384152 | + | 0.923270i | \(0.625506\pi\) | |||||||
\(380\) | 3.04844e14 | − | 3.90712e16i | 0.00519379 | − | 0.665676i | ||||
\(381\) | 2.77896e16 | 0.465447 | ||||||||
\(382\) | 3.28114e16i | 0.540272i | ||||||||
\(383\) | 3.51514e16i | 0.569050i | 0.958669 | + | 0.284525i | \(0.0918358\pi\) | ||||
−0.958669 | + | 0.284525i | \(0.908164\pi\) | |||||||
\(384\) | −4.17356e15 | −0.0664284 | ||||||||
\(385\) | 1.73408e17 | + | 1.35298e15i | 2.71378 | + | 0.0211736i | ||||
\(386\) | −4.68366e16 | −0.720722 | ||||||||
\(387\) | 5.57756e15i | 0.0843962i | ||||||||
\(388\) | 2.04361e16i | 0.304083i | ||||||||
\(389\) | 3.47937e16 | 0.509129 | 0.254565 | − | 0.967056i | \(-0.418068\pi\) | ||||
0.254565 | + | 0.967056i | \(0.418068\pi\) | |||||||
\(390\) | −2.70678e16 | − | 2.11191e14i | −0.389523 | − | 0.00303917i | ||||
\(391\) | −1.77364e16 | −0.251024 | ||||||||
\(392\) | 2.87527e16i | 0.400239i | ||||||||
\(393\) | 2.18241e16i | 0.298802i | ||||||||
\(394\) | −3.84080e16 | −0.517245 | ||||||||
\(395\) | 7.37805e14 | − | 9.45628e16i | 0.00977373 | − | 1.25268i | ||||
\(396\) | −3.10340e16 | −0.404407 | ||||||||
\(397\) | 1.15640e17i | 1.48241i | 0.671279 | + | 0.741205i | \(0.265745\pi\) | ||||
−0.671279 | + | 0.741205i | \(0.734255\pi\) | |||||||
\(398\) | − | 1.06642e16i | − | 0.134490i | ||||||
\(399\) | −1.17757e17 | −1.46104 | ||||||||
\(400\) | −2.04775e16 | − | 3.19562e14i | −0.249970 | − | 0.00390090i | ||||
\(401\) | −8.77040e16 | −1.05337 | −0.526685 | − | 0.850060i | \(-0.676565\pi\) | ||||
−0.526685 | + | 0.850060i | \(0.676565\pi\) | |||||||
\(402\) | − | 2.85782e16i | − | 0.337727i | ||||||
\(403\) | − | 6.10852e16i | − | 0.710319i | ||||||
\(404\) | 7.48215e16 | 0.856146 | ||||||||
\(405\) | 2.60151e14 | − | 3.33429e16i | 0.00292932 | − | 0.375445i | ||||
\(406\) | 2.58699e16 | 0.286666 | ||||||||
\(407\) | 5.73512e16i | 0.625430i | ||||||||
\(408\) | 2.89421e16i | 0.310627i | ||||||||
\(409\) | −1.35424e17 | −1.43053 | −0.715263 | − | 0.698856i | \(-0.753693\pi\) | ||||
−0.715263 | + | 0.698856i | \(0.753693\pi\) | |||||||
\(410\) | 6.04801e15 | + | 4.71883e13i | 0.0628807 | + | 0.000490613i | ||||
\(411\) | 3.47279e16 | 0.355392 | ||||||||
\(412\) | − | 1.78386e16i | − | 0.179692i | ||||||
\(413\) | − | 1.42260e17i | − | 1.41062i | ||||||
\(414\) | 6.76920e15 | 0.0660747 | ||||||||
\(415\) | −5.96778e16 | − | 4.65623e14i | −0.573457 | − | 0.00447427i | ||||
\(416\) | −1.36973e16 | −0.129577 | ||||||||
\(417\) | 3.64721e16i | 0.339685i | ||||||||
\(418\) | 1.90821e17i | 1.74977i | ||||||||
\(419\) | 1.31145e17 | 1.18402 | 0.592012 | − | 0.805929i | \(-0.298334\pi\) | ||||
0.592012 | + | 0.805929i | \(0.298334\pi\) | |||||||
\(420\) | −4.81566e14 | + | 6.17212e16i | −0.00428090 | + | 0.548673i | ||||
\(421\) | −1.44592e17 | −1.26565 | −0.632823 | − | 0.774297i | \(-0.718104\pi\) | ||||
−0.632823 | + | 0.774297i | \(0.718104\pi\) | |||||||
\(422\) | − | 9.63846e15i | − | 0.0830762i | ||||||
\(423\) | − | 2.32984e16i | − | 0.197749i | ||||||
\(424\) | 3.63173e16 | 0.303554 | ||||||||
\(425\) | −2.21604e15 | + | 1.42004e17i | −0.0182410 | + | 1.16889i | ||||
\(426\) | −2.96677e16 | −0.240504 | ||||||||
\(427\) | − | 3.25140e17i | − | 2.59591i | ||||||
\(428\) | − | 9.50731e16i | − | 0.747607i | ||||||
\(429\) | 1.32197e17 | 1.02388 | ||||||||
\(430\) | 1.40250e14 | − | 1.79755e16i | 0.00106993 | − | 0.137131i | ||||
\(431\) | 1.23829e17 | 0.930509 | 0.465255 | − | 0.885177i | \(-0.345963\pi\) | ||||
0.465255 | + | 0.885177i | \(0.345963\pi\) | |||||||
\(432\) | − | 3.64289e16i | − | 0.269651i | ||||||
\(433\) | 4.74018e15i | 0.0345639i | 0.999851 | + | 0.0172820i | \(0.00550129\pi\) | ||||
−0.999851 | + | 0.0172820i | \(0.994499\pi\) | |||||||
\(434\) | −1.39289e17 | −1.00054 | ||||||||
\(435\) | 2.94862e16 | + | 2.30059e14i | 0.208659 | + | 0.00162802i | ||||
\(436\) | 6.22286e16 | 0.433838 | ||||||||
\(437\) | − | 4.16223e16i | − | 0.285889i | ||||||
\(438\) | 6.73754e16i | 0.455953i | ||||||||
\(439\) | 1.55602e17 | 1.03752 | 0.518761 | − | 0.854920i | \(-0.326394\pi\) | ||||
0.518761 | + | 0.854920i | \(0.326394\pi\) | |||||||
\(440\) | 1.00017e17 | + | 7.80359e14i | 0.657099 | + | 0.00512687i | ||||
\(441\) | −7.60982e16 | −0.492633 | ||||||||
\(442\) | 9.49856e16i | 0.605917i | ||||||||
\(443\) | 7.61390e16i | 0.478611i | 0.970944 | + | 0.239306i | \(0.0769198\pi\) | ||||
−0.970944 | + | 0.239306i | \(0.923080\pi\) | |||||||
\(444\) | −2.04130e16 | −0.126450 | ||||||||
\(445\) | −2.15091e14 | + | 2.75677e16i | −0.00131305 | + | 0.168291i | ||||
\(446\) | 4.88046e16 | 0.293619 | ||||||||
\(447\) | 2.09025e17i | 1.23936i | ||||||||
\(448\) | 3.12331e16i | 0.182519i | ||||||||
\(449\) | 2.17774e17 | 1.25431 | 0.627156 | − | 0.778894i | \(-0.284219\pi\) | ||||
0.627156 | + | 0.778894i | \(0.284219\pi\) | |||||||
\(450\) | 8.45767e14 | − | 5.41967e16i | 0.00480141 | − | 0.307674i | ||||
\(451\) | −2.95381e16 | −0.165286 | ||||||||
\(452\) | 1.19146e17i | 0.657172i | ||||||||
\(453\) | − | 3.17430e15i | − | 0.0172588i | ||||||
\(454\) | 5.37147e16 | 0.287892 | ||||||||
\(455\) | −1.58046e15 | + | 2.02564e17i | −0.00835044 | + | 1.07026i | ||||
\(456\) | −6.79190e16 | −0.353769 | ||||||||
\(457\) | − | 3.26108e17i | − | 1.67458i | −0.546757 | − | 0.837291i | \(-0.684138\pi\) | ||
0.546757 | − | 0.837291i | \(-0.315862\pi\) | |||||||
\(458\) | − | 2.05117e17i | − | 1.03843i | ||||||
\(459\) | −2.52621e17 | −1.26092 | ||||||||
\(460\) | −2.18159e16 | − | 1.70214e14i | −0.107361 | − | 0.000837662i | ||||
\(461\) | 1.33954e17 | 0.649980 | 0.324990 | − | 0.945717i | \(-0.394639\pi\) | ||||
0.324990 | + | 0.945717i | \(0.394639\pi\) | |||||||
\(462\) | − | 3.01442e17i | − | 1.44222i | ||||||
\(463\) | 3.27858e17i | 1.54671i | 0.633974 | + | 0.773355i | \(0.281423\pi\) | ||||
−0.633974 | + | 0.773355i | \(0.718577\pi\) | |||||||
\(464\) | 1.49210e16 | 0.0694117 | ||||||||
\(465\) | −1.58760e17 | − | 1.23869e15i | −0.728276 | − | 0.00568221i | ||||
\(466\) | −4.26478e16 | −0.192925 | ||||||||
\(467\) | − | 3.01296e17i | − | 1.34411i | −0.740503 | − | 0.672053i | \(-0.765413\pi\) | ||
0.740503 | − | 0.672053i | \(-0.234587\pi\) | |||||||
\(468\) | − | 3.62519e16i | − | 0.159490i | ||||||
\(469\) | −2.13867e17 | −0.927942 | ||||||||
\(470\) | −5.85847e14 | + | 7.50867e16i | −0.00250696 | + | 0.321312i | ||||
\(471\) | 1.28024e17 | 0.540325 | ||||||||
\(472\) | − | 8.20519e16i | − | 0.341559i | ||||||
\(473\) | 8.77910e16i | 0.360456i | ||||||||
\(474\) | −1.64382e17 | −0.665727 | ||||||||
\(475\) | −3.33243e17 | − | 5.20043e15i | −1.33123 | − | 0.0207745i | ||||
\(476\) | 2.16590e17 | 0.853480 | ||||||||
\(477\) | 9.61190e16i | 0.373628i | ||||||||
\(478\) | 1.16004e17i | 0.444827i | ||||||||
\(479\) | −2.30889e17 | −0.873420 | −0.436710 | − | 0.899602i | \(-0.643856\pi\) | ||||
−0.436710 | + | 0.899602i | \(0.643856\pi\) | |||||||
\(480\) | −2.77754e14 | + | 3.55991e16i | −0.00103655 | + | 0.132853i | ||||
\(481\) | −6.69940e16 | −0.246657 | ||||||||
\(482\) | − | 1.44581e17i | − | 0.525178i | ||||||
\(483\) | 6.57513e16i | 0.235639i | ||||||||
\(484\) | −3.47071e17 | −1.22722 | ||||||||
\(485\) | 1.74313e17 | + | 1.36004e15i | 0.608148 | + | 0.00474494i | ||||
\(486\) | 1.63594e17 | 0.563161 | ||||||||
\(487\) | 1.33518e17i | 0.453526i | 0.973950 | + | 0.226763i | \(0.0728142\pi\) | ||||
−0.973950 | + | 0.226763i | \(0.927186\pi\) | |||||||
\(488\) | − | 1.87532e17i | − | 0.628559i | ||||||
\(489\) | 3.07511e17 | 1.01708 | ||||||||
\(490\) | 2.45251e17 | + | 1.91351e15i | 0.800453 | + | 0.00624536i | ||||
\(491\) | −4.64217e16 | −0.149517 | −0.0747586 | − | 0.997202i | \(-0.523819\pi\) | ||||
−0.0747586 | + | 0.997202i | \(0.523819\pi\) | |||||||
\(492\) | − | 1.05135e16i | − | 0.0334176i | ||||||
\(493\) | − | 1.03472e17i | − | 0.324577i | ||||||
\(494\) | −2.22905e17 | −0.690071 | ||||||||
\(495\) | −2.06533e15 | + | 2.64709e17i | −0.00631039 | + | 0.808789i | ||||
\(496\) | −8.03381e16 | −0.242265 | ||||||||
\(497\) | 2.22021e17i | 0.660810i | ||||||||
\(498\) | 1.03740e17i | 0.304760i | ||||||||
\(499\) | 6.34243e17 | 1.83909 | 0.919543 | − | 0.392988i | \(-0.128559\pi\) | ||||
0.919543 | + | 0.392988i | \(0.128559\pi\) | |||||||
\(500\) | −4.08855e15 | + | 1.74645e17i | −0.0117021 | + | 0.499863i | ||||
\(501\) | −4.34066e17 | −1.22634 | ||||||||
\(502\) | 2.62194e17i | 0.731220i | ||||||||
\(503\) | 3.40192e17i | 0.936552i | 0.883582 | + | 0.468276i | \(0.155125\pi\) | ||||
−0.883582 | + | 0.468276i | \(0.844875\pi\) | |||||||
\(504\) | −8.26630e16 | −0.224653 | ||||||||
\(505\) | 4.97943e15 | − | 6.38202e17i | 0.0133594 | − | 1.71224i | ||||
\(506\) | 1.06547e17 | 0.282205 | ||||||||
\(507\) | − | 1.32991e17i | − | 0.347753i | ||||||
\(508\) | − | 1.19949e17i | − | 0.309658i | ||||||
\(509\) | 1.87368e17 | 0.477562 | 0.238781 | − | 0.971073i | \(-0.423252\pi\) | ||||
0.238781 | + | 0.971073i | \(0.423252\pi\) | |||||||
\(510\) | 2.46866e17 | + | 1.92612e15i | 0.621234 | + | 0.00484704i | ||||
\(511\) | 5.04209e17 | 1.25278 | ||||||||
\(512\) | 1.80144e16i | 0.0441942i | ||||||||
\(513\) | − | 5.92831e17i | − | 1.43605i | ||||||
\(514\) | 2.54599e17 | 0.608970 | ||||||||
\(515\) | −1.52157e17 | − | 1.18717e15i | −0.359374 | − | 0.00280393i | ||||
\(516\) | −3.12475e16 | −0.0728773 | ||||||||
\(517\) | − | 3.66718e17i | − | 0.844587i | ||||||
\(518\) | 1.52762e17i | 0.347435i | ||||||||
\(519\) | 1.53159e17 | 0.343998 | ||||||||
\(520\) | −9.11565e14 | + | 1.16833e17i | −0.00202193 | + | 0.259146i | ||||
\(521\) | −5.24891e17 | −1.14980 | −0.574902 | − | 0.818222i | \(-0.694960\pi\) | ||||
−0.574902 | + | 0.818222i | \(0.694960\pi\) | |||||||
\(522\) | 3.94907e16i | 0.0854352i | ||||||||
\(523\) | − | 5.12722e17i | − | 1.09552i | −0.836635 | − | 0.547761i | \(-0.815480\pi\) | ||
0.836635 | − | 0.547761i | \(-0.184520\pi\) | |||||||
\(524\) | 9.41995e16 | 0.198790 | ||||||||
\(525\) | 5.26429e17 | + | 8.21518e15i | 1.09725 | + | 0.0171231i | ||||
\(526\) | −2.56319e17 | −0.527683 | ||||||||
\(527\) | 5.57115e17i | 1.13286i | ||||||||
\(528\) | − | 1.73863e17i | − | 0.349211i | ||||||
\(529\) | 4.80796e17 | 0.953891 | ||||||||
\(530\) | 2.41695e15 | − | 3.09774e17i | 0.00473668 | − | 0.607089i | ||||
\(531\) | 2.17162e17 | 0.420407 | ||||||||
\(532\) | 5.08277e17i | 0.972018i | ||||||||
\(533\) | − | 3.45045e16i | − | 0.0651852i | ||||||
\(534\) | 4.79221e16 | 0.0894372 | ||||||||
\(535\) | −8.10942e17 | − | 6.32719e15i | −1.49517 | − | 0.0116657i | ||||
\(536\) | −1.23353e17 | −0.224687 | ||||||||
\(537\) | 6.04753e17i | 1.08829i | ||||||||
\(538\) | 6.03866e17i | 1.07363i | ||||||||
\(539\) | −1.19779e18 | −2.10404 | ||||||||
\(540\) | −3.10727e17 | − | 2.42437e15i | −0.539286 | − | 0.00420766i | ||||
\(541\) | −6.25073e17 | −1.07189 | −0.535943 | − | 0.844254i | \(-0.680044\pi\) | ||||
−0.535943 | + | 0.844254i | \(0.680044\pi\) | |||||||
\(542\) | 4.49611e17i | 0.761802i | ||||||||
\(543\) | − | 1.59655e17i | − | 0.267290i | ||||||
\(544\) | 1.24923e17 | 0.206657 | ||||||||
\(545\) | 4.14136e15 | − | 5.30789e17i | 0.00676964 | − | 0.867650i | ||||
\(546\) | 3.52125e17 | 0.568781 | ||||||||
\(547\) | 7.14088e16i | 0.113981i | 0.998375 | + | 0.0569907i | \(0.0181505\pi\) | ||||
−0.998375 | + | 0.0569907i | \(0.981849\pi\) | |||||||
\(548\) | − | 1.49897e17i | − | 0.236439i | ||||||
\(549\) | 4.96330e17 | 0.773660 | ||||||||
\(550\) | 1.33124e16 | − | 8.53058e17i | 0.0205068 | − | 1.31408i | ||||
\(551\) | 2.42820e17 | 0.369657 | ||||||||
\(552\) | 3.79235e16i | 0.0570564i | ||||||||
\(553\) | 1.23017e18i | 1.82916i | ||||||||
\(554\) | −6.60540e17 | −0.970701 | ||||||||
\(555\) | −1.35850e15 | + | 1.74116e17i | −0.00197313 | + | 0.252892i | ||||
\(556\) | 1.57425e17 | 0.225989 | ||||||||
\(557\) | − | 3.05107e17i | − | 0.432905i | −0.976293 | − | 0.216453i | \(-0.930551\pi\) | ||
0.976293 | − | 0.216453i | \(-0.0694487\pi\) | |||||||
\(558\) | − | 2.12626e17i | − | 0.298191i | ||||||
\(559\) | −1.02552e17 | −0.142156 | ||||||||
\(560\) | 2.66408e17 | + | 2.07859e15i | 0.365027 | + | 0.00284804i | ||||
\(561\) | −1.20568e18 | −1.63295 | ||||||||
\(562\) | − | 6.89703e17i | − | 0.923370i | ||||||
\(563\) | − | 1.44683e18i | − | 1.91476i | −0.288831 | − | 0.957380i | \(-0.593267\pi\) | ||
0.288831 | − | 0.957380i | \(-0.406733\pi\) | |||||||
\(564\) | 1.30526e17 | 0.170759 | ||||||||
\(565\) | 1.01627e18 | + | 7.92925e15i | 1.31430 | + | 0.0102546i | ||||
\(566\) | −8.22089e17 | −1.05102 | ||||||||
\(567\) | 4.33758e17i | 0.548224i | ||||||||
\(568\) | 1.28055e17i | 0.160005i | ||||||||
\(569\) | −4.28308e17 | −0.529087 | −0.264543 | − | 0.964374i | \(-0.585221\pi\) | ||||
−0.264543 | + | 0.964374i | \(0.585221\pi\) | |||||||
\(570\) | −4.52006e15 | + | 5.79326e17i | −0.00552024 | + | 0.707517i | ||||
\(571\) | 1.54978e18 | 1.87126 | 0.935632 | − | 0.352978i | \(-0.114831\pi\) | ||||
0.935632 | + | 0.352978i | \(0.114831\pi\) | |||||||
\(572\) | − | 5.70606e17i | − | 0.681180i | ||||||
\(573\) | − | 4.86510e17i | − | 0.574231i | ||||||
\(574\) | −7.86786e16 | −0.0918183 | ||||||||
\(575\) | −2.90373e15 | + | 1.86071e17i | −0.00335055 | + | 0.214703i | ||||
\(576\) | −4.76777e16 | −0.0543963 | ||||||||
\(577\) | 1.38103e18i | 1.55797i | 0.627041 | + | 0.778986i | \(0.284266\pi\) | ||||
−0.627041 | + | 0.778986i | \(0.715734\pi\) | |||||||
\(578\) | − | 2.32402e17i | − | 0.259244i | ||||||
\(579\) | 6.94468e17 | 0.766022 | ||||||||
\(580\) | 9.93007e14 | − | 1.27271e17i | 0.00108310 | − | 0.138819i | ||||
\(581\) | 7.76349e17 | 0.837360 | ||||||||
\(582\) | − | 3.03016e17i | − | 0.323196i | ||||||
\(583\) | 1.51292e18i | 1.59577i | ||||||||
\(584\) | 2.90814e17 | 0.303341 | ||||||||
\(585\) | −3.09216e17 | − | 2.41259e15i | −0.318969 | − | 0.00248869i | ||||
\(586\) | 1.02788e18 | 1.04860 | ||||||||
\(587\) | 6.66857e17i | 0.672798i | 0.941720 | + | 0.336399i | \(0.109209\pi\) | ||||
−0.941720 | + | 0.336399i | \(0.890791\pi\) | |||||||
\(588\) | − | 4.26330e17i | − | 0.425396i | ||||||
\(589\) | −1.30739e18 | −1.29020 | ||||||||
\(590\) | −6.99875e17 | − | 5.46062e15i | −0.683097 | − | 0.00532971i | ||||
\(591\) | 5.69494e17 | 0.549756 | ||||||||
\(592\) | 8.81091e16i | 0.0841259i | ||||||||
\(593\) | − | 7.49253e17i | − | 0.707576i | −0.935326 | − | 0.353788i | \(-0.884893\pi\) | ||
0.935326 | − | 0.353788i | \(-0.115107\pi\) | |||||||
\(594\) | 1.51757e18 | 1.41754 | ||||||||
\(595\) | 1.44142e16 | − | 1.84744e18i | 0.0133178 | − | 1.70691i | ||||
\(596\) | 9.02217e17 | 0.824537 | ||||||||
\(597\) | 1.58124e17i | 0.142943i | ||||||||
\(598\) | 1.24462e17i | 0.111296i | ||||||||
\(599\) | −7.63979e17 | −0.675782 | −0.337891 | − | 0.941185i | \(-0.609714\pi\) | ||||
−0.337891 | + | 0.941185i | \(0.609714\pi\) | |||||||
\(600\) | 3.03630e17 | + | 4.73829e15i | 0.265681 | + | 0.00414609i | ||||
\(601\) | 7.28383e17 | 0.630486 | 0.315243 | − | 0.949011i | \(-0.397914\pi\) | ||||
0.315243 | + | 0.949011i | \(0.397914\pi\) | |||||||
\(602\) | 2.33843e17i | 0.200238i | ||||||||
\(603\) | − | 3.26471e17i | − | 0.276555i | ||||||
\(604\) | −1.37013e16 | −0.0114821 | ||||||||
\(605\) | −2.30978e16 | + | 2.96040e18i | −0.0191497 | + | 2.45437i | ||||
\(606\) | −1.10941e18 | −0.909958 | ||||||||
\(607\) | − | 1.97367e18i | − | 1.60158i | −0.598947 | − | 0.800789i | \(-0.704414\pi\) | ||
0.598947 | − | 0.800789i | \(-0.295586\pi\) | |||||||
\(608\) | 2.93160e17i | 0.235359i | ||||||||
\(609\) | −3.83585e17 | −0.304684 | ||||||||
\(610\) | −1.59958e18 | − | 1.24804e16i | −1.25708 | − | 0.00980808i | ||||
\(611\) | 4.28377e17 | 0.333087 | ||||||||
\(612\) | 3.30627e17i | 0.254363i | ||||||||
\(613\) | 1.55462e18i | 1.18340i | 0.806158 | + | 0.591701i | \(0.201543\pi\) | ||||
−0.806158 | + | 0.591701i | \(0.798457\pi\) | |||||||
\(614\) | 2.36221e17 | 0.177920 | ||||||||
\(615\) | −8.96767e16 | − | 6.99682e14i | −0.0668331 | − | 0.000521450i | ||||
\(616\) | −1.30112e18 | −0.959494 | ||||||||
\(617\) | − | 1.76969e18i | − | 1.29135i | −0.763612 | − | 0.645675i | \(-0.776576\pi\) | ||
0.763612 | − | 0.645675i | \(-0.223424\pi\) | |||||||
\(618\) | 2.64502e17i | 0.190987i | ||||||||
\(619\) | −1.17872e18 | −0.842213 | −0.421106 | − | 0.907011i | \(-0.638358\pi\) | ||||
−0.421106 | + | 0.907011i | \(0.638358\pi\) | |||||||
\(620\) | −5.34656e15 | + | 6.85257e17i | −0.00378032 | + | 0.484515i | ||||
\(621\) | −3.31015e17 | −0.231608 | ||||||||
\(622\) | − | 4.75813e17i | − | 0.329457i | ||||||
\(623\) | − | 3.58629e17i | − | 0.245738i | ||||||
\(624\) | 2.03096e17 | 0.137721 | ||||||||
\(625\) | 1.48939e18 | + | 4.64967e16i | 0.999513 | + | 0.0312034i | ||||
\(626\) | −8.94459e17 | −0.594056 | ||||||||
\(627\) | − | 2.82939e18i | − | 1.85975i | ||||||
\(628\) | − | 5.52591e17i | − | 0.359473i | ||||||
\(629\) | 6.11004e17 | 0.393382 | ||||||||
\(630\) | −5.50129e15 | + | 7.05088e17i | −0.00350551 | + | 0.449293i | ||||
\(631\) | −2.38732e18 | −1.50564 | −0.752818 | − | 0.658228i | \(-0.771306\pi\) | ||||
−0.752818 | + | 0.658228i | \(0.771306\pi\) | |||||||
\(632\) | 7.09526e17i | 0.442902i | ||||||||
\(633\) | 1.42914e17i | 0.0882979i | ||||||||
\(634\) | 1.09790e18 | 0.671399 | ||||||||
\(635\) | −1.02312e18 | − | 7.98269e15i | −0.619296 | − | 0.00483192i | ||||
\(636\) | −5.38494e17 | −0.322633 | ||||||||
\(637\) | − | 1.39918e18i | − | 0.829788i | ||||||
\(638\) | 6.21586e17i | 0.364894i | ||||||||
\(639\) | −3.38917e17 | −0.196942 | ||||||||
\(640\) | 1.53657e17 | + | 1.19887e15i | 0.0883857 | + | 0.000689609i | ||||
\(641\) | −1.87490e18 | −1.06758 | −0.533790 | − | 0.845617i | \(-0.679233\pi\) | ||||
−0.533790 | + | 0.845617i | \(0.679233\pi\) | |||||||
\(642\) | 1.40969e18i | 0.794597i | ||||||||
\(643\) | 2.53520e18i | 1.41462i | 0.706902 | + | 0.707312i | \(0.250092\pi\) | ||||
−0.706902 | + | 0.707312i | \(0.749908\pi\) | |||||||
\(644\) | 2.83803e17 | 0.156769 | ||||||||
\(645\) | −2.07955e15 | + | 2.66531e17i | −0.00113718 | + | 0.145750i | ||||
\(646\) | 2.03295e18 | 1.10057 | ||||||||
\(647\) | 3.57429e17i | 0.191563i | 0.995402 | + | 0.0957815i | \(0.0305350\pi\) | ||||
−0.995402 | + | 0.0957815i | \(0.969465\pi\) | |||||||
\(648\) | 2.50180e17i | 0.132744i | ||||||||
\(649\) | 3.41814e18 | 1.79556 | ||||||||
\(650\) | 9.96487e17 | + | 1.55507e16i | 0.518245 | + | 0.00808747i | ||||
\(651\) | 2.06530e18 | 1.06343 | ||||||||
\(652\) | − | 1.32731e18i | − | 0.676651i | ||||||
\(653\) | − | 9.68553e17i | − | 0.488864i | −0.969666 | − | 0.244432i | \(-0.921399\pi\) | ||
0.969666 | − | 0.244432i | \(-0.0786015\pi\) | |||||||
\(654\) | −9.22692e17 | −0.461107 | ||||||||
\(655\) | 6.26905e15 | − | 8.03490e17i | 0.00310194 | − | 0.397569i | ||||
\(656\) | −4.53796e16 | −0.0222324 | ||||||||
\(657\) | 7.69681e17i | 0.373367i | ||||||||
\(658\) | − | 9.76803e17i | − | 0.469179i | ||||||
\(659\) | −1.95073e18 | −0.927774 | −0.463887 | − | 0.885894i | \(-0.653546\pi\) | ||||
−0.463887 | + | 0.885894i | \(0.653546\pi\) | |||||||
\(660\) | −1.48300e18 | − | 1.15707e16i | −0.698401 | − | 0.00544911i | ||||
\(661\) | −3.27319e18 | −1.52638 | −0.763188 | − | 0.646177i | \(-0.776367\pi\) | ||||
−0.763188 | + | 0.646177i | \(0.776367\pi\) | |||||||
\(662\) | − | 8.32920e16i | − | 0.0384615i | ||||||
\(663\) | − | 1.40839e18i | − | 0.644001i | ||||||
\(664\) | 4.47776e17 | 0.202754 | ||||||||
\(665\) | 4.33543e18 | + | 3.38262e16i | 1.94398 | + | 0.0151674i | ||||
\(666\) | −2.33194e17 | −0.103546 | ||||||||
\(667\) | − | 1.35582e17i | − | 0.0596188i | ||||||
\(668\) | 1.87356e18i | 0.815871i | ||||||||
\(669\) | −7.23649e17 | −0.312074 | ||||||||
\(670\) | −8.20922e15 | + | 1.05216e18i | −0.00350603 | + | 0.449360i | ||||
\(671\) | 7.81226e18 | 3.30430 | ||||||||
\(672\) | − | 4.63108e17i | − | 0.193991i | ||||||
\(673\) | 3.71614e18i | 1.54168i | 0.637028 | + | 0.770840i | \(0.280163\pi\) | ||||
−0.637028 | + | 0.770840i | \(0.719837\pi\) | |||||||
\(674\) | 2.73107e18 | 1.12213 | ||||||||
\(675\) | −4.13582e16 | + | 2.65023e18i | −0.0168301 | + | 1.07847i | ||||
\(676\) | −5.74032e17 | −0.231357 | ||||||||
\(677\) | − | 2.14190e17i | − | 0.0855015i | −0.999086 | − | 0.0427507i | \(-0.986388\pi\) | ||
0.999086 | − | 0.0427507i | \(-0.0136121\pi\) | |||||||
\(678\) | − | 1.76663e18i | − | 0.698478i | ||||||
\(679\) | −2.26764e18 | −0.888017 | ||||||||
\(680\) | 8.31373e15 | − | 1.06555e18i | 0.00322469 | − | 0.413301i | ||||
\(681\) | −7.96452e17 | −0.305987 | ||||||||
\(682\) | − | 3.34675e18i | − | 1.27358i | ||||||
\(683\) | − | 3.43179e18i | − | 1.29356i | −0.762677 | − | 0.646779i | \(-0.776116\pi\) | ||
0.762677 | − | 0.646779i | \(-0.223884\pi\) | |||||||
\(684\) | −7.75890e17 | −0.289691 | ||||||||
\(685\) | −1.27857e18 | − | 9.97574e15i | −0.472863 | − | 0.00368941i | ||||
\(686\) | −3.72149e17 | −0.136336 | ||||||||
\(687\) | 3.04137e18i | 1.10370i | ||||||||
\(688\) | 1.34874e17i | 0.0484846i | ||||||||
\(689\) | −1.76729e18 | −0.629337 | ||||||||
\(690\) | 3.23475e17 | + | 2.52384e15i | 0.114109 | + | 0.000890313i | ||||
\(691\) | −2.29484e16 | −0.00801945 | −0.00400972 | − | 0.999992i | \(-0.501276\pi\) | ||||
−0.00400972 | + | 0.999992i | \(0.501276\pi\) | |||||||
\(692\) | − | 6.61084e17i | − | 0.228858i | ||||||
\(693\) | − | 3.44360e18i | − | 1.18099i | ||||||
\(694\) | −1.17926e18 | −0.400656 | ||||||||
\(695\) | 1.04768e16 | − | 1.34278e18i | 0.00352635 | − | 0.451964i | ||||
\(696\) | −2.21241e17 | −0.0737745 | ||||||||
\(697\) | 3.14691e17i | 0.103961i | ||||||||
\(698\) | − | 3.96538e17i | − | 0.129785i | ||||||
\(699\) | 6.32359e17 | 0.205051 | ||||||||
\(700\) | 3.54593e16 | − | 2.27223e18i | 0.0113918 | − | 0.729988i | ||||
\(701\) | −4.54324e18 | −1.44610 | −0.723050 | − | 0.690796i | \(-0.757260\pi\) | ||||
−0.723050 | + | 0.690796i | \(0.757260\pi\) | |||||||
\(702\) | 1.77272e18i | 0.559049i | ||||||||
\(703\) | 1.43386e18i | 0.448018i | ||||||||
\(704\) | −7.50449e17 | −0.232327 | ||||||||
\(705\) | 8.68663e15 | − | 1.11335e18i | 0.00266454 | − | 0.341508i | ||||
\(706\) | −2.26090e18 | −0.687149 | ||||||||
\(707\) | 8.30237e18i | 2.50021i | ||||||||
\(708\) | 1.21662e18i | 0.363027i | ||||||||
\(709\) | 1.83457e18 | 0.542417 | 0.271209 | − | 0.962521i | \(-0.412577\pi\) | ||||
0.271209 | + | 0.962521i | \(0.412577\pi\) | |||||||
\(710\) | 1.09227e18 | + | 8.52218e15i | 0.320000 | + | 0.00249673i | ||||
\(711\) | −1.87786e18 | −0.545145 | ||||||||
\(712\) | − | 2.06847e17i | − | 0.0595017i | ||||||
\(713\) | 7.30001e17i | 0.208085i | ||||||||
\(714\) | −3.21148e18 | −0.907125 | ||||||||
\(715\) | −4.86707e18 | − | 3.79743e16i | −1.36232 | − | 0.0106292i | ||||
\(716\) | 2.61030e18 | 0.724030 | ||||||||
\(717\) | − | 1.72004e18i | − | 0.472787i | ||||||
\(718\) | − | 2.30254e17i | − | 0.0627189i | ||||||
\(719\) | 4.11935e18 | 1.11196 | 0.555982 | − | 0.831195i | \(-0.312343\pi\) | ||||
0.555982 | + | 0.831195i | \(0.312343\pi\) | |||||||
\(720\) | −3.17299e15 | + | 4.06675e17i | −0.000848804 | + | 0.108789i | ||||
\(721\) | 1.97942e18 | 0.524756 | ||||||||
\(722\) | 2.07938e18i | 0.546315i | ||||||||
\(723\) | 2.14377e18i | 0.558187i | ||||||||
\(724\) | −6.89120e17 | −0.177826 | ||||||||
\(725\) | −1.08552e18 | − | 1.69400e16i | −0.277613 | − | 0.00433229i | ||||
\(726\) | 5.14618e18 | 1.30436 | ||||||||
\(727\) | − | 9.41236e17i | − | 0.236442i | −0.992987 | − | 0.118221i | \(-0.962281\pi\) | ||
0.992987 | − | 0.118221i | \(-0.0377192\pi\) | |||||||
\(728\) | − | 1.51988e18i | − | 0.378404i | ||||||
\(729\) | −3.94725e18 | −0.974014 | ||||||||
\(730\) | 1.93539e16 | − | 2.48054e18i | 0.00473336 | − | 0.606664i | ||||
\(731\) | 9.35301e17 | 0.226719 | ||||||||
\(732\) | 2.78062e18i | 0.668067i | ||||||||
\(733\) | − | 3.76919e17i | − | 0.0897577i | −0.998992 | − | 0.0448789i | \(-0.985710\pi\) | ||
0.998992 | − | 0.0448789i | \(-0.0142902\pi\) | |||||||
\(734\) | −1.05317e18 | −0.248584 | ||||||||
\(735\) | −3.63645e18 | − | 2.83726e16i | −0.850765 | − | 0.00663791i | ||||
\(736\) | 1.63690e17 | 0.0379591 | ||||||||
\(737\) | − | 5.13866e18i | − | 1.18117i | ||||||
\(738\) | − | 1.20104e17i | − | 0.0273647i | ||||||
\(739\) | 3.30244e18 | 0.745841 | 0.372921 | − | 0.927863i | \(-0.378356\pi\) | ||||
0.372921 | + | 0.927863i | \(0.378356\pi\) | |||||||
\(740\) | 7.51541e17 | + | 5.86373e15i | 0.168247 | + | 0.00131271i | ||||
\(741\) | 3.30511e18 | 0.733445 | ||||||||
\(742\) | 4.02985e18i | 0.886470i | ||||||||
\(743\) | − | 7.15981e18i | − | 1.56126i | −0.624995 | − | 0.780629i | \(-0.714899\pi\) | ||
0.624995 | − | 0.780629i | \(-0.285101\pi\) | |||||||
\(744\) | 1.19121e18 | 0.257492 | ||||||||
\(745\) | 6.00432e16 | − | 7.69560e18i | 0.0128661 | − | 1.64902i | ||||
\(746\) | −3.18003e18 | −0.675506 | ||||||||
\(747\) | 1.18511e18i | 0.249559i | ||||||||
\(748\) | 5.20408e18i | 1.08639i | ||||||||
\(749\) | 1.05495e19 | 2.18324 | ||||||||
\(750\) | 6.06228e16 | − | 2.58954e18i | 0.0124376 | − | 0.531282i | ||||
\(751\) | 2.67611e18 | 0.544307 | 0.272154 | − | 0.962254i | \(-0.412264\pi\) | ||||
0.272154 | + | 0.962254i | \(0.412264\pi\) | |||||||
\(752\) | − | 5.63393e17i | − | 0.113604i | ||||||
\(753\) | − | 3.88767e18i | − | 0.777181i | ||||||
\(754\) | −7.26096e17 | −0.143906 | ||||||||
\(755\) | −9.11831e14 | + | 1.16867e17i | −0.000179167 | + | 0.0229635i | ||||
\(756\) | 4.04224e18 | 0.787464 | ||||||||
\(757\) | 8.35791e18i | 1.61426i | 0.590371 | + | 0.807132i | \(0.298981\pi\) | ||||
−0.590371 | + | 0.807132i | \(0.701019\pi\) | |||||||
\(758\) | − | 2.83705e18i | − | 0.543273i | ||||||
\(759\) | −1.57983e18 | −0.299943 | ||||||||
\(760\) | 2.50055e18 | + | 1.95100e16i | 0.470704 | + | 0.00367256i | ||||
\(761\) | −1.33084e18 | −0.248385 | −0.124192 | − | 0.992258i | \(-0.539634\pi\) | ||||
−0.124192 | + | 0.992258i | \(0.539634\pi\) | |||||||
\(762\) | 1.77854e18i | 0.329121i | ||||||||
\(763\) | 6.90503e18i | 1.26694i | ||||||||
\(764\) | −2.09993e18 | −0.382030 | ||||||||
\(765\) | 2.82014e18 | + | 2.20035e16i | 0.508711 | + | 0.00396910i | ||||
\(766\) | −2.24969e18 | −0.402379 | ||||||||
\(767\) | 3.99285e18i | 0.708131i | ||||||||
\(768\) | − | 2.67108e17i | − | 0.0469720i | ||||||
\(769\) | −1.81901e18 | −0.317186 | −0.158593 | − | 0.987344i | \(-0.550696\pi\) | ||||
−0.158593 | + | 0.987344i | \(0.550696\pi\) | |||||||
\(770\) | −8.65905e16 | + | 1.10981e19i | −0.0149720 | + | 1.91893i | ||||
\(771\) | −3.77506e18 | −0.647247 | ||||||||
\(772\) | − | 2.99754e18i | − | 0.509627i | ||||||
\(773\) | − | 5.26289e18i | − | 0.887274i | −0.896207 | − | 0.443637i | \(-0.853688\pi\) | ||
0.896207 | − | 0.443637i | \(-0.146312\pi\) | |||||||
\(774\) | −3.56964e17 | −0.0596772 | ||||||||
\(775\) | 5.84465e18 | + | 9.12087e16i | 0.968942 | + | 0.0151208i | ||||
\(776\) | −1.30791e18 | −0.215019 | ||||||||
\(777\) | − | 2.26508e18i | − | 0.369272i | ||||||
\(778\) | 2.22680e18i | 0.360009i | ||||||||
\(779\) | −7.38491e17 | −0.118400 | ||||||||
\(780\) | 1.35162e16 | − | 1.73234e18i | 0.00214902 | − | 0.275435i | ||||
\(781\) | −5.33457e18 | −0.841139 | ||||||||
\(782\) | − | 1.13513e18i | − | 0.177501i | ||||||
\(783\) | − | 1.93111e18i | − | 0.299471i | ||||||
\(784\) | −1.84017e18 | −0.283012 | ||||||||
\(785\) | −4.71342e18 | − | 3.67754e16i | −0.718924 | − | 0.00560924i | ||||
\(786\) | −1.39674e18 | −0.211285 | ||||||||
\(787\) | − | 6.76678e18i | − | 1.01519i | −0.861596 | − | 0.507594i | \(-0.830535\pi\) | ||
0.861596 | − | 0.507594i | \(-0.169465\pi\) | |||||||
\(788\) | − | 2.45811e18i | − | 0.365748i | ||||||
\(789\) | 3.80056e18 | 0.560850 | ||||||||
\(790\) | 6.05202e18 | + | 4.72195e16i | 0.885777 | + | 0.00691107i | ||||
\(791\) | −1.32207e19 | −1.91914 | ||||||||
\(792\) | − | 1.98617e18i | − | 0.285959i | ||||||
\(793\) | 9.12577e18i | 1.30315i | ||||||||
\(794\) | −7.40094e18 | −1.04822 | ||||||||
\(795\) | −3.58372e16 | + | 4.59317e18i | −0.00503440 | + | 0.645247i | ||||
\(796\) | 6.82511e17 | 0.0950987 | ||||||||
\(797\) | − | 7.80908e17i | − | 0.107925i | −0.998543 | − | 0.0539623i | \(-0.982815\pi\) | ||
0.998543 | − | 0.0539623i | \(-0.0171851\pi\) | |||||||
\(798\) | − | 7.53645e18i | − | 1.03311i | ||||||
\(799\) | −3.90692e18 | −0.531227 | ||||||||
\(800\) | 2.04520e16 | − | 1.31056e18i | 0.00275835 | − | 0.176755i | ||||
\(801\) | 5.47451e17 | 0.0732375 | ||||||||
\(802\) | − | 5.61306e18i | − | 0.744845i | ||||||
\(803\) | 1.21148e19i | 1.59465i | ||||||||
\(804\) | 1.82901e18 | 0.238809 | ||||||||
\(805\) | 1.88873e16 | − | 2.42075e18i | 0.00244623 | − | 0.313528i | ||||
\(806\) | 3.90946e18 | 0.502271 | ||||||||
\(807\) | − | 8.95381e18i | − | 1.14112i | ||||||
\(808\) | 4.78858e18i | 0.605386i | ||||||||
\(809\) | −3.20569e18 | −0.402028 | −0.201014 | − | 0.979588i | \(-0.564424\pi\) | ||||
−0.201014 | + | 0.979588i | \(0.564424\pi\) | |||||||
\(810\) | 2.13395e18 | + | 1.66496e16i | 0.265480 | + | 0.00207134i | ||||
\(811\) | 7.89507e18 | 0.974362 | 0.487181 | − | 0.873301i | \(-0.338025\pi\) | ||||
0.487181 | + | 0.873301i | \(0.338025\pi\) | |||||||
\(812\) | 1.65567e18i | 0.202703i | ||||||||
\(813\) | − | 6.66660e18i | − | 0.809684i | ||||||
\(814\) | −3.67048e18 | −0.442246 | ||||||||
\(815\) | −1.13215e19 | − | 8.83338e16i | −1.35326 | − | 0.0105585i | ||||
\(816\) | −1.85229e18 | −0.219646 | ||||||||
\(817\) | 2.19489e18i | 0.258208i | ||||||||
\(818\) | − | 8.66717e18i | − | 1.01153i | ||||||
\(819\) | 4.02259e18 | 0.465758 | ||||||||
\(820\) | −3.02005e15 | + | 3.87073e17i | −0.000346916 | + | 0.0444634i | ||||
\(821\) | 3.93857e18 | 0.448857 | 0.224429 | − | 0.974491i | \(-0.427948\pi\) | ||||
0.224429 | + | 0.974491i | \(0.427948\pi\) | |||||||
\(822\) | 2.22259e18i | 0.251300i | ||||||||
\(823\) | − | 4.32313e18i | − | 0.484953i | −0.970157 | − | 0.242476i | \(-0.922040\pi\) | ||
0.970157 | − | 0.242476i | \(-0.0779597\pi\) | |||||||
\(824\) | 1.14167e18 | 0.127062 | ||||||||
\(825\) | −1.97389e17 | + | 1.26487e19i | −0.0217958 | + | 1.39667i | ||||
\(826\) | 9.10467e18 | 0.997456 | ||||||||
\(827\) | 4.71227e18i | 0.512206i | 0.966650 | + | 0.256103i | \(0.0824386\pi\) | ||||
−0.966650 | + | 0.256103i | \(0.917561\pi\) | |||||||
\(828\) | 4.33229e17i | 0.0467219i | ||||||||
\(829\) | −2.15058e17 | −0.0230118 | −0.0115059 | − | 0.999934i | \(-0.503663\pi\) | ||||
−0.0115059 | + | 0.999934i | \(0.503663\pi\) | |||||||
\(830\) | 2.97999e16 | − | 3.81938e18i | 0.00316378 | − | 0.405495i | ||||
\(831\) | 9.79413e18 | 1.03171 | ||||||||
\(832\) | − | 8.76626e17i | − | 0.0916248i | ||||||
\(833\) | 1.27609e19i | 1.32339i | ||||||||
\(834\) | −2.33421e18 | −0.240193 | ||||||||
\(835\) | 1.59809e19 | + | 1.24687e17i | 1.63169 | + | 0.0127309i | ||||
\(836\) | −1.22125e19 | −1.23727 | ||||||||
\(837\) | 1.03975e19i | 1.04523i | ||||||||
\(838\) | 8.39328e18i | 0.837231i | ||||||||
\(839\) | 1.32950e19 | 1.31594 | 0.657971 | − | 0.753043i | \(-0.271415\pi\) | ||||
0.657971 | + | 0.753043i | \(0.271415\pi\) | |||||||
\(840\) | −3.95016e18 | − | 3.08202e16i | −0.387971 | − | 0.00302705i | ||||
\(841\) | −9.46966e18 | −0.922912 | ||||||||
\(842\) | − | 9.25392e18i | − | 0.894946i | ||||||
\(843\) | 1.02265e19i | 0.981408i | ||||||||
\(844\) | 6.16861e17 | 0.0587438 | ||||||||
\(845\) | −3.82023e16 | + | 4.89630e18i | −0.00361011 | + | 0.462700i | ||||
\(846\) | 1.49110e18 | 0.139830 | ||||||||
\(847\) | − | 3.85118e19i | − | 3.58386i | ||||||
\(848\) | 2.32431e18i | 0.214645i | ||||||||
\(849\) | 1.21895e19 | 1.11708 | ||||||||
\(850\) | −9.08825e18 | − | 1.41827e17i | −0.826527 | − | 0.0128984i | ||||
\(851\) | 8.00613e17 | 0.0722571 | ||||||||
\(852\) | − | 1.89874e18i | − | 0.170062i | ||||||
\(853\) | − | 8.46944e18i | − | 0.752811i | −0.926455 | − | 0.376406i | \(-0.877160\pi\) | ||
0.926455 | − | 0.376406i | \(-0.122840\pi\) | |||||||
\(854\) | 2.08090e19 | 1.83558 | ||||||||
\(855\) | −5.16361e16 | + | 6.61808e18i | −0.00452036 | + | 0.579365i | ||||
\(856\) | 6.08468e18 | 0.528638 | ||||||||
\(857\) | − | 1.71134e19i | − | 1.47557i | −0.675033 | − | 0.737787i | \(-0.735871\pi\) | ||
0.675033 | − | 0.737787i | \(-0.264129\pi\) | |||||||
\(858\) | 8.46064e18i | 0.723995i | ||||||||
\(859\) | −7.13031e18 | −0.605554 | −0.302777 | − | 0.953061i | \(-0.597914\pi\) | ||||
−0.302777 | + | 0.953061i | \(0.597914\pi\) | |||||||
\(860\) | 1.15043e18 | + | 8.97598e15i | 0.0969662 | + | 0.000756557i | ||||
\(861\) | 1.16660e18 | 0.0975895 | ||||||||
\(862\) | 7.92507e18i | 0.657969i | ||||||||
\(863\) | − | 2.60805e18i | − | 0.214905i | −0.994210 | − | 0.107452i | \(-0.965731\pi\) | ||
0.994210 | − | 0.107452i | \(-0.0342693\pi\) | |||||||
\(864\) | 2.33145e18 | 0.190672 | ||||||||
\(865\) | −5.63882e18 | − | 4.39956e16i | −0.457703 | − | 0.00357112i | ||||
\(866\) | −3.03371e17 | −0.0244404 | ||||||||
\(867\) | 3.44593e18i | 0.275539i | ||||||||
\(868\) | − | 8.91450e18i | − | 0.707488i | ||||||
\(869\) | −2.95577e19 | −2.32831 | ||||||||
\(870\) | −1.47238e16 | + | 1.88711e18i | −0.00115118 | + | 0.147544i | ||||
\(871\) | 6.00266e18 | 0.465828 | ||||||||
\(872\) | 3.98263e18i | 0.306770i | ||||||||
\(873\) | − | 3.46158e18i | − | 0.264656i | ||||||
\(874\) | 2.66383e18 | 0.202154 | ||||||||
\(875\) | −1.93790e19 | − | 4.53675e17i | −1.45975 | − | 0.0341737i | ||||
\(876\) | −4.31203e18 | −0.322407 | ||||||||
\(877\) | 2.51744e19i | 1.86836i | 0.356796 | + | 0.934182i | \(0.383869\pi\) | ||||
−0.356796 | + | 0.934182i | \(0.616131\pi\) | |||||||
\(878\) | 9.95855e18i | 0.733638i | ||||||||
\(879\) | −1.52409e19 | −1.11451 | ||||||||
\(880\) | −4.99430e16 | + | 6.40108e18i | −0.00362524 | + | 0.464639i | ||||
\(881\) | 9.05516e18 | 0.652458 | 0.326229 | − | 0.945291i | \(-0.394222\pi\) | ||||
0.326229 | + | 0.945291i | \(0.394222\pi\) | |||||||
\(882\) | − | 4.87029e18i | − | 0.348344i | ||||||
\(883\) | − | 2.14294e19i | − | 1.52148i | −0.649057 | − | 0.760739i | \(-0.724836\pi\) | ||
0.649057 | − | 0.760739i | \(-0.275164\pi\) | |||||||
\(884\) | −6.07908e18 | −0.428448 | ||||||||
\(885\) | 1.03774e19 | + | 8.09671e16i | 0.726032 | + | 0.00566470i | ||||
\(886\) | −4.87290e18 | −0.338429 | ||||||||
\(887\) | 3.82856e18i | 0.263956i | 0.991253 | + | 0.131978i | \(0.0421328\pi\) | ||||
−0.991253 | + | 0.131978i | \(0.957867\pi\) | |||||||
\(888\) | − | 1.30644e18i | − | 0.0894136i | ||||||
\(889\) | 1.33098e19 | 0.904295 | ||||||||
\(890\) | −1.76434e18 | − | 1.37658e16i | −0.119000 | − | 0.000928469i | ||||
\(891\) | −1.04221e19 | −0.697828 | ||||||||
\(892\) | 3.12350e18i | 0.207620i | ||||||||
\(893\) | − | 9.16845e18i | − | 0.605008i | ||||||
\(894\) | −1.33776e19 | −0.876363 | ||||||||
\(895\) | 1.73718e17 | − | 2.22650e19i | 0.0112978 | − | 1.44802i | ||||
\(896\) | −1.99892e18 | −0.129061 | ||||||||
\(897\) | − | 1.84545e18i | − | 0.118291i | ||||||
\(898\) | 1.39375e19i | 0.886932i | ||||||||
\(899\) | −4.25874e18 | −0.269056 | ||||||||
\(900\) | 3.46859e18 | + | 5.41291e16i | 0.217559 | + | 0.00339511i | ||||
\(901\) | 1.61182e19 | 1.00370 | ||||||||
\(902\) | − | 1.89044e18i | − | 0.116875i | ||||||
\(903\) | − | 3.46730e18i | − | 0.212824i | ||||||
\(904\) | −7.62533e18 | −0.464691 | ||||||||
\(905\) | −4.58615e16 | + | 5.87796e18i | −0.00277480 | + | 0.355640i | ||||
\(906\) | 2.03155e17 | 0.0122038 | ||||||||
\(907\) | 1.30005e19i | 0.775374i | 0.921791 | + | 0.387687i | \(0.126726\pi\) | ||||
−0.921791 | + | 0.387687i | \(0.873274\pi\) | |||||||
\(908\) | 3.43774e18i | 0.203570i | ||||||||
\(909\) | −1.26737e19 | −0.745139 | ||||||||
\(910\) | −1.29641e19 | − | 1.01149e17i | −0.756786 | − | 0.00590465i | ||||
\(911\) | −1.73341e18 | −0.100469 | −0.0502345 | − | 0.998737i | \(-0.515997\pi\) | ||||
−0.0502345 | + | 0.998737i | \(0.515997\pi\) | |||||||
\(912\) | − | 4.34682e18i | − | 0.250152i | ||||||
\(913\) | 1.86536e19i | 1.06587i | ||||||||
\(914\) | 2.08709e19 | 1.18411 | ||||||||
\(915\) | 2.37178e19 | + | 1.85052e17i | 1.33609 | + | 0.0104246i | ||||
\(916\) | 1.31275e19 | 0.734280 | ||||||||
\(917\) | 1.04526e19i | 0.580529i | ||||||||
\(918\) | − | 1.61677e19i | − | 0.891604i | ||||||
\(919\) | −8.77898e18 | −0.480721 | −0.240361 | − | 0.970684i | \(-0.577266\pi\) | ||||
−0.240361 | + | 0.970684i | \(0.577266\pi\) | |||||||
\(920\) | 1.08937e16 | − | 1.39622e18i | 0.000592316 | − | 0.0759159i | ||||
\(921\) | −3.50256e18 | −0.189103 | ||||||||
\(922\) | 8.57306e18i | 0.459605i | ||||||||
\(923\) | − | 6.23150e18i | − | 0.331727i | ||||||
\(924\) | 1.92923e19 | 1.01980 | ||||||||
\(925\) | 1.00031e17 | − | 6.41000e18i | 0.00525067 | − | 0.336463i | ||||
\(926\) | −2.09829e19 | −1.09369 | ||||||||
\(927\) | 3.02160e18i | 0.156394i | ||||||||
\(928\) | 9.54947e17i | 0.0490815i | ||||||||
\(929\) | 1.99358e18 | 0.101749 | 0.0508746 | − | 0.998705i | \(-0.483799\pi\) | ||||
0.0508746 | + | 0.998705i | \(0.483799\pi\) | |||||||
\(930\) | 7.92760e16 | − | 1.01606e19i | 0.00401793 | − | 0.514969i | ||||
\(931\) | −2.99463e19 | −1.50720 | ||||||||
\(932\) | − | 2.72946e18i | − | 0.136419i | ||||||
\(933\) | 7.05510e18i | 0.350165i | ||||||||
\(934\) | 1.92829e19 | 0.950426 | ||||||||
\(935\) | 4.43891e19 | + | 3.46336e17i | 2.17271 | + | 0.0169520i | ||||
\(936\) | 2.32012e18 | 0.112776 | ||||||||
\(937\) | 1.14570e18i | 0.0553051i | 0.999618 | + | 0.0276525i | \(0.00880320\pi\) | ||||
−0.999618 | + | 0.0276525i | \(0.991197\pi\) | |||||||
\(938\) | − | 1.36875e19i | − | 0.656154i | ||||||
\(939\) | 1.32626e19 | 0.631395 | ||||||||
\(940\) | −4.80555e18 | − | 3.74942e16i | −0.227202 | − | 0.00177269i | ||||
\(941\) | 3.92402e19 | 1.84246 | 0.921232 | − | 0.389014i | \(-0.127184\pi\) | ||||
0.921232 | + | 0.389014i | \(0.127184\pi\) | |||||||
\(942\) | 8.19353e18i | 0.382067i | ||||||||
\(943\) | 4.12347e17i | 0.0190957i | ||||||||
\(944\) | 5.25132e18 | 0.241519 | ||||||||
\(945\) | 2.69014e17 | − | 3.44790e19i | 0.0122876 | − | 1.57488i | ||||
\(946\) | −5.61863e18 | −0.254881 | ||||||||
\(947\) | 2.02669e19i | 0.913087i | 0.889701 | + | 0.456543i | \(0.150913\pi\) | ||||
−0.889701 | + | 0.456543i | \(0.849087\pi\) | |||||||
\(948\) | − | 1.05205e19i | − | 0.470740i | ||||||
\(949\) | −1.41517e19 | −0.628896 | ||||||||
\(950\) | 3.32828e17 | − | 2.13276e19i | 0.0146898 | − | 0.941322i | ||||
\(951\) | −1.62790e19 | −0.713599 | ||||||||
\(952\) | 1.38618e19i | 0.603501i | ||||||||
\(953\) | 7.79187e18i | 0.336929i | 0.985708 | + | 0.168464i | \(0.0538808\pi\) | ||||
−0.985708 | + | 0.168464i | \(0.946119\pi\) | |||||||
\(954\) | −6.15162e18 | −0.264195 | ||||||||
\(955\) | −1.39752e17 | + | 1.79117e19i | −0.00596123 | + | 0.764037i | ||||
\(956\) | −7.42425e18 | −0.314540 | ||||||||
\(957\) | − | 9.21654e18i | − | 0.387829i | ||||||
\(958\) | − | 1.47769e19i | − | 0.617601i | ||||||
\(959\) | 1.66329e19 | 0.690473 | ||||||||
\(960\) | −2.27834e18 | − | 1.77762e16i | −0.0939411 | − | 0.000732954i | ||||
\(961\) | −1.48759e18 | −0.0609231 | ||||||||
\(962\) | − | 4.28761e18i | − | 0.174413i | ||||||
\(963\) | 1.61040e19i | 0.650673i | ||||||||
\(964\) | 9.25320e18 | 0.371357 | ||||||||
\(965\) | −2.55680e19 | − | 1.99489e17i | −1.01922 | − | 0.00795226i | ||||
\(966\) | −4.20808e18 | −0.166622 | ||||||||
\(967\) | 1.54167e19i | 0.606345i | 0.952936 | + | 0.303173i | \(0.0980458\pi\) | ||||
−0.952936 | + | 0.303173i | \(0.901954\pi\) | |||||||
\(968\) | − | 2.22125e19i | − | 0.867777i | ||||||
\(969\) | −3.01435e19 | −1.16974 | ||||||||
\(970\) | −8.70426e16 | + | 1.11561e19i | −0.00335518 | + | 0.430026i | ||||
\(971\) | 3.87568e17 | 0.0148396 | 0.00741982 | − | 0.999972i | \(-0.497638\pi\) | ||||
0.00741982 | + | 0.999972i | \(0.497638\pi\) | |||||||
\(972\) | 1.04700e19i | 0.398215i | ||||||||
\(973\) | 1.74682e19i | 0.659957i | ||||||||
\(974\) | −8.54516e18 | −0.320691 | ||||||||
\(975\) | −1.47754e19 | − | 2.30577e17i | −0.550819 | − | 0.00859580i | ||||
\(976\) | 1.20020e19 | 0.444458 | ||||||||
\(977\) | 5.59657e18i | 0.205877i | 0.994688 | + | 0.102938i | \(0.0328245\pi\) | ||||
−0.994688 | + | 0.102938i | \(0.967176\pi\) | |||||||
\(978\) | 1.96807e19i | 0.719181i | ||||||||
\(979\) | 8.61690e18 | 0.312798 | ||||||||
\(980\) | −1.22465e17 | + | 1.56961e19i | −0.00441613 | + | 0.566006i | ||||
\(981\) | −1.05406e19 | −0.377587 | ||||||||
\(982\) | − | 2.97099e18i | − | 0.105725i | ||||||
\(983\) | − | 2.41541e19i | − | 0.853873i | −0.904282 | − | 0.426937i | \(-0.859593\pi\) | ||
0.904282 | − | 0.426937i | \(-0.140407\pi\) | |||||||
\(984\) | 6.72865e17 | 0.0236298 | ||||||||
\(985\) | −2.09669e19 | − | 1.63589e17i | −0.731473 | − | 0.00570715i | ||||
\(986\) | 6.62220e18 | 0.229510 | ||||||||
\(987\) | 1.44835e19i | 0.498669i | ||||||||
\(988\) | − | 1.42659e19i | − | 0.487954i | ||||||
\(989\) | 1.22555e18 | 0.0416442 | ||||||||
\(990\) | −1.69414e19 | − | 1.32181e17i | −0.571900 | − | 0.00446212i | ||||
\(991\) | −2.43063e19 | −0.815154 | −0.407577 | − | 0.913171i | \(-0.633626\pi\) | ||||
−0.407577 | + | 0.913171i | \(0.633626\pi\) | |||||||
\(992\) | − | 5.14164e18i | − | 0.171307i | ||||||
\(993\) | 1.23501e18i | 0.0408790i | ||||||||
\(994\) | −1.42093e19 | −0.467263 | ||||||||
\(995\) | 4.54216e16 | − | 5.82159e18i | 0.00148393 | − | 0.190192i | ||||
\(996\) | −6.63939e18 | −0.215498 | ||||||||
\(997\) | − | 2.66249e19i | − | 0.858558i | −0.903172 | − | 0.429279i | \(-0.858768\pi\) | ||
0.903172 | − | 0.429279i | \(-0.141232\pi\) | |||||||
\(998\) | 4.05916e19i | 1.30043i | ||||||||
\(999\) | 1.14032e19 | 0.362954 |
(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 | 10.14.b.a.9.4 | yes | 6 | |
3.2 | odd | 2 | 90.14.c.b.19.2 | 6 | |||
4.3 | odd | 2 | 80.14.c.b.49.5 | 6 | |||
5.2 | odd | 4 | 50.14.a.i.1.1 | 3 | |||
5.3 | odd | 4 | 50.14.a.j.1.3 | 3 | |||
5.4 | even | 2 | inner | 10.14.b.a.9.3 | ✓ | 6 | |
15.14 | odd | 2 | 90.14.c.b.19.5 | 6 | |||
20.19 | odd | 2 | 80.14.c.b.49.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.14.b.a.9.3 | ✓ | 6 | 5.4 | even | 2 | inner | |
10.14.b.a.9.4 | yes | 6 | 1.1 | even | 1 | trivial | |
50.14.a.i.1.1 | 3 | 5.2 | odd | 4 | |||
50.14.a.j.1.3 | 3 | 5.3 | odd | 4 | |||
80.14.c.b.49.2 | 6 | 20.19 | odd | 2 | |||
80.14.c.b.49.5 | 6 | 4.3 | odd | 2 | |||
90.14.c.b.19.2 | 6 | 3.2 | odd | 2 | |||
90.14.c.b.19.5 | 6 | 15.14 | odd | 2 |