Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,14,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.57847431615\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 5 x^{9} + 752 x^{8} + 708 x^{7} - 743866 x^{6} + 96647426 x^{5} + 2540283092 x^{4} - 180067834748 x^{3} + 15101451375489 x^{2} + \cdots + 31\!\cdots\!68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{48}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.5 | ||
Root | \(1.33949 - 44.8086i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.14.b.b.5.6 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 12.6790 | − | 89.6172i | 0.140084 | − | 0.990140i | ||||
\(3\) | 86.8898i | 0.0688146i | 0.999408 | + | 0.0344073i | \(0.0109544\pi\) | ||||
−0.999408 | + | 0.0344073i | \(0.989046\pi\) | |||||||
\(4\) | −7870.49 | − | 2272.51i | −0.960753 | − | 0.277406i | ||||
\(5\) | 45531.7i | 1.30319i | 0.758566 | + | 0.651596i | \(0.225900\pi\) | ||||
−0.758566 | + | 0.651596i | \(0.774100\pi\) | |||||||
\(6\) | 7786.82 | + | 1101.67i | 0.0681361 | + | 0.00963984i | ||||
\(7\) | −249036. | −0.800063 | −0.400032 | − | 0.916501i | \(-0.631001\pi\) | ||||
−0.400032 | + | 0.916501i | \(0.631001\pi\) | |||||||
\(8\) | −303446. | + | 676518.i | −0.409257 | + | 0.912419i | ||||
\(9\) | 1.58677e6 | 0.995265 | ||||||||
\(10\) | 4.08042e6 | + | 577295.i | 1.29034 | + | 0.182557i | ||||
\(11\) | 5.28836e6i | 0.900054i | 0.893015 | + | 0.450027i | \(0.148586\pi\) | ||||
−0.893015 | + | 0.450027i | \(0.851414\pi\) | |||||||
\(12\) | 197458. | − | 683865.i | 0.0190896 | − | 0.0661139i | ||||
\(13\) | 1.17535e7i | 0.675358i | 0.941261 | + | 0.337679i | \(0.109642\pi\) | ||||
−0.941261 | + | 0.337679i | \(0.890358\pi\) | |||||||
\(14\) | −3.15752e6 | + | 2.23179e7i | −0.112076 | + | 0.792174i | ||||
\(15\) | −3.95624e6 | −0.0896787 | ||||||||
\(16\) | 5.67803e7 | + | 3.57715e7i | 0.846092 | + | 0.533037i | ||||
\(17\) | −1.22707e8 | −1.23297 | −0.616483 | − | 0.787368i | \(-0.711443\pi\) | ||||
−0.616483 | + | 0.787368i | \(0.711443\pi\) | |||||||
\(18\) | 2.01187e7 | − | 1.42202e8i | 0.139421 | − | 0.985451i | ||||
\(19\) | − | 5.19560e7i | − | 0.253359i | −0.991944 | − | 0.126680i | \(-0.959568\pi\) | ||
0.991944 | − | 0.126680i | \(-0.0404320\pi\) | |||||||
\(20\) | 1.03471e8 | − | 3.58356e8i | 0.361513 | − | 1.25205i | ||||
\(21\) | − | 2.16387e7i | − | 0.0550560i | ||||||
\(22\) | 4.73928e8 | + | 6.70510e7i | 0.891179 | + | 0.126083i | ||||
\(23\) | −1.22082e9 | −1.71957 | −0.859784 | − | 0.510659i | \(-0.829402\pi\) | ||||
−0.859784 | + | 0.510659i | \(0.829402\pi\) | |||||||
\(24\) | −5.87825e7 | − | 2.63663e7i | −0.0627878 | − | 0.0281629i | ||||
\(25\) | −8.52431e8 | −0.698311 | ||||||||
\(26\) | 1.05331e9 | + | 1.49022e8i | 0.668699 | + | 0.0946070i | ||||
\(27\) | 2.76405e8i | 0.137303i | ||||||||
\(28\) | 1.96003e9 | + | 5.65936e8i | 0.768663 | + | 0.221942i | ||||
\(29\) | 4.04054e9i | 1.26140i | 0.776027 | + | 0.630699i | \(0.217232\pi\) | ||||
−0.776027 | + | 0.630699i | \(0.782768\pi\) | |||||||
\(30\) | −5.01611e7 | + | 3.54547e8i | −0.0125626 | + | 0.0887945i | ||||
\(31\) | 1.61058e9 | 0.325935 | 0.162967 | − | 0.986631i | \(-0.447893\pi\) | ||||
0.162967 | + | 0.986631i | \(0.447893\pi\) | |||||||
\(32\) | 3.92566e9 | − | 4.63494e9i | 0.646305 | − | 0.763079i | ||||
\(33\) | −4.59505e8 | −0.0619369 | ||||||||
\(34\) | −1.55580e9 | + | 1.09967e10i | −0.172719 | + | 1.22081i | ||||
\(35\) | − | 1.13390e10i | − | 1.04264i | ||||||
\(36\) | −1.24887e10 | − | 3.60596e9i | −0.956203 | − | 0.276092i | ||||
\(37\) | 4.09023e9i | 0.262081i | 0.991377 | + | 0.131041i | \(0.0418318\pi\) | ||||
−0.991377 | + | 0.131041i | \(0.958168\pi\) | |||||||
\(38\) | −4.65615e9 | − | 6.58749e8i | −0.250861 | − | 0.0354917i | ||||
\(39\) | −1.02126e9 | −0.0464745 | ||||||||
\(40\) | −3.08030e10 | − | 1.38164e10i | −1.18906 | − | 0.533341i | ||||
\(41\) | 4.23280e10 | 1.39166 | 0.695830 | − | 0.718207i | \(-0.255037\pi\) | ||||
0.695830 | + | 0.718207i | \(0.255037\pi\) | |||||||
\(42\) | −1.93920e9 | − | 2.74356e8i | −0.0545132 | − | 0.00771248i | ||||
\(43\) | − | 7.66300e10i | − | 1.84865i | −0.381611 | − | 0.924323i | \(-0.624631\pi\) | ||
0.381611 | − | 0.924323i | \(-0.375369\pi\) | |||||||
\(44\) | 1.20178e10 | − | 4.16220e10i | 0.249680 | − | 0.864729i | ||||
\(45\) | 7.22484e10i | 1.29702i | ||||||||
\(46\) | −1.54787e10 | + | 1.09406e11i | −0.240884 | + | 1.70261i | ||||
\(47\) | 6.09947e10 | 0.825384 | 0.412692 | − | 0.910871i | \(-0.364589\pi\) | ||||
0.412692 | + | 0.910871i | \(0.364589\pi\) | |||||||
\(48\) | −3.10818e9 | + | 4.93363e9i | −0.0366807 | + | 0.0582235i | ||||
\(49\) | −3.48703e10 | −0.359899 | ||||||||
\(50\) | −1.08079e10 | + | 7.63924e10i | −0.0978224 | + | 0.691426i | ||||
\(51\) | − | 1.06620e10i | − | 0.0848461i | ||||||
\(52\) | 2.67098e10 | − | 9.25055e10i | 0.187348 | − | 0.648852i | ||||
\(53\) | 2.24645e11i | 1.39220i | 0.717943 | + | 0.696102i | \(0.245084\pi\) | ||||
−0.717943 | + | 0.696102i | \(0.754916\pi\) | |||||||
\(54\) | 2.47706e10 | + | 3.50453e9i | 0.135950 | + | 0.0192340i | ||||
\(55\) | −2.40788e11 | −1.17294 | ||||||||
\(56\) | 7.55688e10 | − | 1.68477e11i | 0.327431 | − | 0.729993i | ||||
\(57\) | 4.51445e9 | 0.0174348 | ||||||||
\(58\) | 3.62102e11 | + | 5.12299e10i | 1.24896 | + | 0.176702i | ||||
\(59\) | − | 4.64215e11i | − | 1.43279i | −0.697697 | − | 0.716393i | \(-0.745792\pi\) | ||
0.697697 | − | 0.716393i | \(-0.254208\pi\) | |||||||
\(60\) | 3.11375e10 | + | 8.99059e9i | 0.0861591 | + | 0.0248774i | ||||
\(61\) | − | 4.58331e10i | − | 0.113903i | −0.998377 | − | 0.0569515i | \(-0.981862\pi\) | ||
0.998377 | − | 0.0569515i | \(-0.0181381\pi\) | |||||||
\(62\) | 2.04205e10 | − | 1.44336e11i | 0.0456583 | − | 0.322721i | ||||
\(63\) | −3.95163e11 | −0.796274 | ||||||||
\(64\) | −3.65597e11 | − | 4.10573e11i | −0.665018 | − | 0.746828i | ||||
\(65\) | −5.35155e11 | −0.880121 | ||||||||
\(66\) | −5.82605e9 | + | 4.11795e10i | −0.00867638 | + | 0.0613262i | ||||
\(67\) | 8.92905e11i | 1.20592i | 0.797771 | + | 0.602961i | \(0.206012\pi\) | ||||
−0.797771 | + | 0.602961i | \(0.793988\pi\) | |||||||
\(68\) | 9.65764e11 | + | 2.78853e11i | 1.18458 | + | 0.342032i | ||||
\(69\) | − | 1.06076e11i | − | 0.118331i | ||||||
\(70\) | −1.01617e12 | − | 1.43767e11i | −1.03236 | − | 0.146057i | ||||
\(71\) | 1.53438e12 | 1.42152 | 0.710762 | − | 0.703432i | \(-0.248350\pi\) | ||||
0.710762 | + | 0.703432i | \(0.248350\pi\) | |||||||
\(72\) | −4.81499e11 | + | 1.07348e12i | −0.407319 | + | 0.908098i | ||||
\(73\) | 8.01210e11 | 0.619652 | 0.309826 | − | 0.950793i | \(-0.399729\pi\) | ||||
0.309826 | + | 0.950793i | \(0.399729\pi\) | |||||||
\(74\) | 3.66555e11 | + | 5.18599e10i | 0.259497 | + | 0.0367135i | ||||
\(75\) | − | 7.40675e10i | − | 0.0480540i | ||||||
\(76\) | −1.18070e11 | + | 4.08919e11i | −0.0702834 | + | 0.243416i | ||||
\(77\) | − | 1.31699e12i | − | 0.720100i | ||||||
\(78\) | −1.29485e10 | + | 9.15221e10i | −0.00651034 | + | 0.0460162i | ||||
\(79\) | 5.92669e10 | 0.0274306 | 0.0137153 | − | 0.999906i | \(-0.495634\pi\) | ||||
0.0137153 | + | 0.999906i | \(0.495634\pi\) | |||||||
\(80\) | −1.62874e12 | + | 2.58530e12i | −0.694650 | + | 1.10262i | ||||
\(81\) | 2.50581e12 | 0.985816 | ||||||||
\(82\) | 5.36676e11 | − | 3.79332e12i | 0.194950 | − | 1.37794i | ||||
\(83\) | 4.57014e12i | 1.53434i | 0.641444 | + | 0.767170i | \(0.278336\pi\) | ||||
−0.641444 | + | 0.767170i | \(0.721664\pi\) | |||||||
\(84\) | −4.91741e10 | + | 1.70307e11i | −0.0152729 | + | 0.0528953i | ||||
\(85\) | − | 5.58705e12i | − | 1.60679i | ||||||
\(86\) | −6.86736e12 | − | 9.71590e11i | −1.83042 | − | 0.258966i | ||||
\(87\) | −3.51082e11 | −0.0868026 | ||||||||
\(88\) | −3.57767e12 | − | 1.60473e12i | −0.821227 | − | 0.368353i | ||||
\(89\) | −5.17348e12 | −1.10344 | −0.551719 | − | 0.834030i | \(-0.686028\pi\) | ||||
−0.551719 | + | 0.834030i | \(0.686028\pi\) | |||||||
\(90\) | 6.47470e12 | + | 9.16036e11i | 1.28423 | + | 0.181692i | ||||
\(91\) | − | 2.92703e12i | − | 0.540329i | ||||||
\(92\) | 9.60841e12 | + | 2.77431e12i | 1.65208 | + | 0.477018i | ||||
\(93\) | 1.39943e11i | 0.0224291i | ||||||||
\(94\) | 7.73351e11 | − | 5.46618e12i | 0.115623 | − | 0.817246i | ||||
\(95\) | 2.36564e12 | 0.330176 | ||||||||
\(96\) | 4.02729e11 | + | 3.41100e11i | 0.0525110 | + | 0.0444752i | ||||
\(97\) | −3.32642e12 | −0.405472 | −0.202736 | − | 0.979233i | \(-0.564983\pi\) | ||||
−0.202736 | + | 0.979233i | \(0.564983\pi\) | |||||||
\(98\) | −4.42119e11 | + | 3.12498e12i | −0.0504162 | + | 0.356350i | ||||
\(99\) | 8.39143e12i | 0.895792i | ||||||||
\(100\) | 6.70904e12 | + | 1.93716e12i | 0.670904 | + | 0.193716i | ||||
\(101\) | 1.04951e13i | 0.983783i | 0.870657 | + | 0.491891i | \(0.163694\pi\) | ||||
−0.870657 | + | 0.491891i | \(0.836306\pi\) | |||||||
\(102\) | −9.55498e11 | − | 1.35183e11i | −0.0840095 | − | 0.0118856i | ||||
\(103\) | −1.41996e13 | −1.17175 | −0.585873 | − | 0.810403i | \(-0.699248\pi\) | ||||
−0.585873 | + | 0.810403i | \(0.699248\pi\) | |||||||
\(104\) | −7.95143e12 | − | 3.56654e12i | −0.616210 | − | 0.276395i | ||||
\(105\) | 9.85245e11 | 0.0717486 | ||||||||
\(106\) | 2.01320e13 | + | 2.84826e12i | 1.37848 | + | 0.195026i | ||||
\(107\) | − | 1.68471e12i | − | 0.108525i | −0.998527 | − | 0.0542625i | \(-0.982719\pi\) | ||
0.998527 | − | 0.0542625i | \(-0.0172808\pi\) | |||||||
\(108\) | 6.28133e11 | − | 2.17544e12i | 0.0380888 | − | 0.131915i | ||||
\(109\) | 1.19613e12i | 0.0683133i | 0.999416 | + | 0.0341566i | \(0.0108745\pi\) | ||||
−0.999416 | + | 0.0341566i | \(0.989125\pi\) | |||||||
\(110\) | −3.05294e12 | + | 2.15787e13i | −0.164311 | + | 1.16138i | ||||
\(111\) | −3.55399e11 | −0.0180350 | ||||||||
\(112\) | −1.41403e13 | − | 8.90838e12i | −0.676927 | − | 0.426463i | ||||
\(113\) | 1.04130e13 | 0.470506 | 0.235253 | − | 0.971934i | \(-0.424408\pi\) | ||||
0.235253 | + | 0.971934i | \(0.424408\pi\) | |||||||
\(114\) | 5.72386e10 | − | 4.04572e11i | 0.00244235 | − | 0.0172629i | ||||
\(115\) | − | 5.55858e13i | − | 2.24093i | ||||||
\(116\) | 9.18216e12 | − | 3.18010e13i | 0.349919 | − | 1.21189i | ||||
\(117\) | 1.86501e13i | 0.672160i | ||||||||
\(118\) | −4.16017e13 | − | 5.88578e12i | −1.41866 | − | 0.200711i | ||||
\(119\) | 3.05584e13 | 0.986451 | ||||||||
\(120\) | 1.20050e12 | − | 2.67647e12i | 0.0367016 | − | 0.0818246i | ||||
\(121\) | 6.55596e12 | 0.189903 | ||||||||
\(122\) | −4.10744e12 | − | 5.81117e11i | −0.112780 | − | 0.0159560i | ||||
\(123\) | 3.67788e12i | 0.0957666i | ||||||||
\(124\) | −1.26760e13 | − | 3.66005e12i | −0.313143 | − | 0.0904162i | ||||
\(125\) | 1.67681e13i | 0.393159i | ||||||||
\(126\) | −5.01026e12 | + | 3.54134e13i | −0.111545 | + | 0.788423i | ||||
\(127\) | 2.30936e12 | 0.0488391 | 0.0244195 | − | 0.999702i | \(-0.492226\pi\) | ||||
0.0244195 | + | 0.999702i | \(0.492226\pi\) | |||||||
\(128\) | −4.14298e13 | + | 2.75582e13i | −0.832622 | + | 0.553842i | ||||
\(129\) | 6.65837e12 | 0.127214 | ||||||||
\(130\) | −6.78522e12 | + | 4.79591e13i | −0.123291 | + | 0.871443i | ||||
\(131\) | − | 2.94834e13i | − | 0.509699i | −0.966981 | − | 0.254850i | \(-0.917974\pi\) | ||
0.966981 | − | 0.254850i | \(-0.0820259\pi\) | |||||||
\(132\) | 3.61653e12 | + | 1.04423e12i | 0.0595060 | + | 0.0171817i | ||||
\(133\) | 1.29389e13i | 0.202704i | ||||||||
\(134\) | 8.00196e13 | + | 1.13211e13i | 1.19403 | + | 0.168931i | ||||
\(135\) | −1.25852e13 | −0.178933 | ||||||||
\(136\) | 3.72349e13 | − | 8.30135e13i | 0.504600 | − | 1.12498i | ||||
\(137\) | 7.84391e13 | 1.01356 | 0.506779 | − | 0.862076i | \(-0.330836\pi\) | ||||
0.506779 | + | 0.862076i | \(0.330836\pi\) | |||||||
\(138\) | −9.50628e12 | − | 1.34494e12i | −0.117165 | − | 0.0165764i | ||||
\(139\) | 9.83230e13i | 1.15627i | 0.815941 | + | 0.578135i | \(0.196219\pi\) | ||||
−0.815941 | + | 0.578135i | \(0.803781\pi\) | |||||||
\(140\) | −2.57680e13 | + | 8.92435e13i | −0.289233 | + | 1.00172i | ||||
\(141\) | 5.29982e12i | 0.0567985i | ||||||||
\(142\) | 1.94544e13 | − | 1.37507e14i | 0.199133 | − | 1.40751i | ||||
\(143\) | −6.21565e13 | −0.607859 | ||||||||
\(144\) | 9.00974e13 | + | 5.67613e13i | 0.842085 | + | 0.530513i | ||||
\(145\) | −1.83972e14 | −1.64384 | ||||||||
\(146\) | 1.01585e13 | − | 7.18022e13i | 0.0868034 | − | 0.613542i | ||||
\(147\) | − | 3.02987e12i | − | 0.0247663i | ||||||
\(148\) | 9.29507e12 | − | 3.21921e13i | 0.0727029 | − | 0.251795i | ||||
\(149\) | − | 1.46382e14i | − | 1.09591i | −0.836507 | − | 0.547957i | \(-0.815406\pi\) | ||
0.836507 | − | 0.547957i | \(-0.184594\pi\) | |||||||
\(150\) | −6.63773e12 | − | 9.39101e11i | −0.0475802 | − | 0.00673161i | ||||
\(151\) | 5.37629e12 | 0.0369090 | 0.0184545 | − | 0.999830i | \(-0.494125\pi\) | ||||
0.0184545 | + | 0.999830i | \(0.494125\pi\) | |||||||
\(152\) | 3.51492e13 | + | 1.57658e13i | 0.231170 | + | 0.103689i | ||||
\(153\) | −1.94708e14 | −1.22713 | ||||||||
\(154\) | −1.18025e14 | − | 1.66981e13i | −0.713000 | − | 0.100875i | ||||
\(155\) | 7.33323e13i | 0.424756i | ||||||||
\(156\) | 8.03778e12 | + | 2.32081e12i | 0.0446505 | + | 0.0128923i | ||||
\(157\) | − | 1.49568e14i | − | 0.797060i | −0.917155 | − | 0.398530i | \(-0.869521\pi\) | ||
0.917155 | − | 0.398530i | \(-0.130479\pi\) | |||||||
\(158\) | 7.51444e11 | − | 5.31133e12i | 0.00384260 | − | 0.0271602i | ||||
\(159\) | −1.95193e13 | −0.0958040 | ||||||||
\(160\) | 2.11037e14 | + | 1.78742e14i | 0.994439 | + | 0.842260i | ||||
\(161\) | 3.04027e14 | 1.37576 | ||||||||
\(162\) | 3.17711e13 | − | 2.24564e14i | 0.138097 | − | 0.976096i | ||||
\(163\) | 3.22488e14i | 1.34677i | 0.739291 | + | 0.673386i | \(0.235161\pi\) | ||||
−0.739291 | + | 0.673386i | \(0.764839\pi\) | |||||||
\(164\) | −3.33142e14 | − | 9.61909e13i | −1.33704 | − | 0.386055i | ||||
\(165\) | − | 2.09220e13i | − | 0.0807157i | ||||||
\(166\) | 4.09563e14 | + | 5.79447e13i | 1.51921 | + | 0.214937i | ||||
\(167\) | 1.29327e14 | 0.461351 | 0.230675 | − | 0.973031i | \(-0.425906\pi\) | ||||
0.230675 | + | 0.973031i | \(0.425906\pi\) | |||||||
\(168\) | 1.46389e13 | + | 6.56616e12i | 0.0502342 | + | 0.0225321i | ||||
\(169\) | 1.64731e14 | 0.543892 | ||||||||
\(170\) | −5.00696e14 | − | 7.08381e13i | −1.59095 | − | 0.225086i | ||||
\(171\) | − | 8.24424e13i | − | 0.252160i | ||||||
\(172\) | −1.74142e14 | + | 6.03115e14i | −0.512825 | + | 1.77609i | ||||
\(173\) | − | 4.84488e13i | − | 0.137399i | −0.997637 | − | 0.0686995i | \(-0.978115\pi\) | ||
0.997637 | − | 0.0686995i | \(-0.0218850\pi\) | |||||||
\(174\) | −4.45136e12 | + | 3.14630e13i | −0.0121597 | + | 0.0859467i | ||||
\(175\) | 2.12286e14 | 0.558693 | ||||||||
\(176\) | −1.89173e14 | + | 3.00275e14i | −0.479762 | + | 0.761528i | ||||
\(177\) | 4.03356e13 | 0.0985967 | ||||||||
\(178\) | −6.55945e13 | + | 4.63633e14i | −0.154574 | + | 1.09256i | ||||
\(179\) | − | 1.35115e14i | − | 0.307014i | −0.988148 | − | 0.153507i | \(-0.950943\pi\) | ||
0.988148 | − | 0.153507i | \(-0.0490567\pi\) | |||||||
\(180\) | 1.64185e14 | − | 5.68630e14i | 0.359801 | − | 1.24612i | ||||
\(181\) | 2.37822e14i | 0.502738i | 0.967891 | + | 0.251369i | \(0.0808808\pi\) | ||||
−0.967891 | + | 0.251369i | \(0.919119\pi\) | |||||||
\(182\) | −2.62312e14 | − | 3.71118e13i | −0.535001 | − | 0.0756916i | ||||
\(183\) | 3.98243e12 | 0.00783820 | ||||||||
\(184\) | 3.70451e14 | − | 8.25904e14i | 0.703745 | − | 1.56897i | ||||
\(185\) | −1.86235e14 | −0.341542 | ||||||||
\(186\) | 1.25413e13 | + | 1.77433e12i | 0.0222079 | + | 0.00314196i | ||||
\(187\) | − | 6.48919e14i | − | 1.10974i | ||||||
\(188\) | −4.80058e14 | − | 1.38611e14i | −0.792990 | − | 0.228966i | ||||
\(189\) | − | 6.88347e13i | − | 0.109851i | ||||||
\(190\) | 2.99939e13 | − | 2.12002e14i | 0.0462525 | − | 0.326921i | ||||
\(191\) | 2.46109e14 | 0.366784 | 0.183392 | − | 0.983040i | \(-0.441292\pi\) | ||||
0.183392 | + | 0.983040i | \(0.441292\pi\) | |||||||
\(192\) | 3.56746e13 | − | 3.17667e13i | 0.0513927 | − | 0.0457629i | ||||
\(193\) | −1.27091e14 | −0.177008 | −0.0885039 | − | 0.996076i | \(-0.528209\pi\) | ||||
−0.0885039 | + | 0.996076i | \(0.528209\pi\) | |||||||
\(194\) | −4.21756e13 | + | 2.98104e14i | −0.0568002 | + | 0.401473i | ||||
\(195\) | − | 4.64995e13i | − | 0.0605652i | ||||||
\(196\) | 2.74446e14 | + | 7.92430e13i | 0.345774 | + | 0.0998381i | ||||
\(197\) | 4.31897e14i | 0.526442i | 0.964736 | + | 0.263221i | \(0.0847848\pi\) | ||||
−0.964736 | + | 0.263221i | \(0.915215\pi\) | |||||||
\(198\) | 7.52016e14 | + | 1.06395e14i | 0.886959 | + | 0.125486i | ||||
\(199\) | −1.16464e15 | −1.32937 | −0.664687 | − | 0.747122i | \(-0.731435\pi\) | ||||
−0.664687 | + | 0.747122i | \(0.731435\pi\) | |||||||
\(200\) | 2.58666e14 | − | 5.76685e14i | 0.285789 | − | 0.637153i | ||||
\(201\) | −7.75843e13 | −0.0829850 | ||||||||
\(202\) | 9.40545e14 | + | 1.33068e14i | 0.974082 | + | 0.137812i | ||||
\(203\) | − | 1.00624e15i | − | 1.00920i | ||||||
\(204\) | −2.42295e13 | + | 8.39150e13i | −0.0235368 | + | 0.0815162i | ||||
\(205\) | 1.92727e15i | 1.81360i | ||||||||
\(206\) | −1.80036e14 | + | 1.27253e15i | −0.164143 | + | 1.16019i | ||||
\(207\) | −1.93716e15 | −1.71142 | ||||||||
\(208\) | −4.20439e14 | + | 6.67365e14i | −0.359991 | + | 0.571415i | ||||
\(209\) | 2.74762e14 | 0.228037 | ||||||||
\(210\) | 1.24919e13 | − | 8.82949e13i | 0.0100509 | − | 0.0710412i | ||||
\(211\) | 1.10642e15i | 0.863146i | 0.902078 | + | 0.431573i | \(0.142041\pi\) | ||||
−0.902078 | + | 0.431573i | \(0.857959\pi\) | |||||||
\(212\) | 5.10507e14 | − | 1.76806e15i | 0.386205 | − | 1.33756i | ||||
\(213\) | 1.33322e14i | 0.0978217i | ||||||||
\(214\) | −1.50979e14 | − | 2.13604e13i | −0.107455 | − | 0.0152026i | ||||
\(215\) | 3.48909e15 | 2.40914 | ||||||||
\(216\) | −1.86993e14 | − | 8.38739e13i | −0.125278 | − | 0.0561924i | ||||
\(217\) | −4.01091e14 | −0.260768 | ||||||||
\(218\) | 1.07194e14 | + | 1.51657e13i | 0.0676397 | + | 0.00956962i | ||||
\(219\) | 6.96170e13i | 0.0426411i | ||||||||
\(220\) | 1.89512e15 | + | 5.47193e14i | 1.12691 | + | 0.325381i | ||||
\(221\) | − | 1.44223e15i | − | 0.832694i | ||||||
\(222\) | −4.50610e12 | + | 3.18499e13i | −0.00252642 | + | 0.0178572i | ||||
\(223\) | −6.47353e14 | −0.352500 | −0.176250 | − | 0.984345i | \(-0.556397\pi\) | ||||
−0.176250 | + | 0.984345i | \(0.556397\pi\) | |||||||
\(224\) | −9.77629e14 | + | 1.15427e15i | −0.517085 | + | 0.610511i | ||||
\(225\) | −1.35261e15 | −0.695004 | ||||||||
\(226\) | 1.32026e14 | − | 9.33183e14i | 0.0659105 | − | 0.465867i | ||||
\(227\) | − | 2.07784e15i | − | 1.00796i | −0.863715 | − | 0.503981i | \(-0.831868\pi\) | ||
0.863715 | − | 0.503981i | \(-0.168132\pi\) | |||||||
\(228\) | −3.55309e13 | − | 1.02591e13i | −0.0167506 | − | 0.00483653i | ||||
\(229\) | − | 2.11802e15i | − | 0.970509i | −0.874373 | − | 0.485254i | \(-0.838727\pi\) | ||
0.874373 | − | 0.485254i | \(-0.161273\pi\) | |||||||
\(230\) | −4.98144e15 | − | 7.04771e14i | −2.21883 | − | 0.313919i | ||||
\(231\) | 1.14433e14 | 0.0495534 | ||||||||
\(232\) | −2.73350e15 | − | 1.22608e15i | −1.15092 | − | 0.516236i | ||||
\(233\) | 3.45947e15 | 1.41643 | 0.708217 | − | 0.705995i | \(-0.249500\pi\) | ||||
0.708217 | + | 0.705995i | \(0.249500\pi\) | |||||||
\(234\) | 1.67137e15 | + | 2.36464e14i | 0.665532 | + | 0.0941590i | ||||
\(235\) | 2.77719e15i | 1.07563i | ||||||||
\(236\) | −1.05493e15 | + | 3.65360e15i | −0.397463 | + | 1.37655i | ||||
\(237\) | 5.14969e12i | 0.00188763i | ||||||||
\(238\) | 3.87449e14 | − | 2.73856e15i | 0.138186 | − | 0.976724i | ||||
\(239\) | 7.67582e14 | 0.266402 | 0.133201 | − | 0.991089i | \(-0.457474\pi\) | ||||
0.133201 | + | 0.991089i | \(0.457474\pi\) | |||||||
\(240\) | −2.24636e14 | − | 1.41521e14i | −0.0758764 | − | 0.0478021i | ||||
\(241\) | 3.34399e14 | 0.109940 | 0.0549698 | − | 0.998488i | \(-0.482494\pi\) | ||||
0.0549698 | + | 0.998488i | \(0.482494\pi\) | |||||||
\(242\) | 8.31229e13 | − | 5.87527e14i | 0.0266024 | − | 0.188030i | ||||
\(243\) | 6.58408e14i | 0.205142i | ||||||||
\(244\) | −1.04156e14 | + | 3.60729e14i | −0.0315974 | + | 0.109433i | ||||
\(245\) | − | 1.58770e15i | − | 0.469018i | ||||||
\(246\) | 3.29601e14 | + | 4.66317e13i | 0.0948223 | + | 0.0134154i | ||||
\(247\) | 6.10663e14 | 0.171108 | ||||||||
\(248\) | −4.88723e14 | + | 1.08959e15i | −0.133391 | + | 0.297389i | ||||
\(249\) | −3.97098e14 | −0.105585 | ||||||||
\(250\) | 1.50271e15 | + | 2.12602e14i | 0.389282 | + | 0.0550753i | ||||
\(251\) | 6.50564e15i | 1.64214i | 0.570825 | + | 0.821071i | \(0.306623\pi\) | ||||
−0.570825 | + | 0.821071i | \(0.693377\pi\) | |||||||
\(252\) | 3.11013e15 | + | 8.98012e14i | 0.765023 | + | 0.220891i | ||||
\(253\) | − | 6.45611e15i | − | 1.54770i | ||||||
\(254\) | 2.92803e13 | − | 2.06958e14i | 0.00684158 | − | 0.0483575i | ||||
\(255\) | 4.85458e14 | 0.110571 | ||||||||
\(256\) | 1.94440e15 | + | 4.06223e15i | 0.431743 | + | 0.901997i | ||||
\(257\) | 1.04460e14 | 0.0226143 | 0.0113072 | − | 0.999936i | \(-0.496401\pi\) | ||||
0.0113072 | + | 0.999936i | \(0.496401\pi\) | |||||||
\(258\) | 8.44213e13 | − | 5.96704e14i | 0.0178207 | − | 0.125960i | ||||
\(259\) | − | 1.01861e15i | − | 0.209682i | ||||||
\(260\) | 4.21193e15 | + | 1.21614e15i | 0.845579 | + | 0.244151i | ||||
\(261\) | 6.41142e15i | 1.25542i | ||||||||
\(262\) | −2.64222e15 | − | 3.73819e14i | −0.504673 | − | 0.0714008i | ||||
\(263\) | −4.31849e14 | −0.0804673 | −0.0402337 | − | 0.999190i | \(-0.512810\pi\) | ||||
−0.0402337 | + | 0.999190i | \(0.512810\pi\) | |||||||
\(264\) | 1.39435e14 | − | 3.10863e14i | 0.0253481 | − | 0.0565124i | ||||
\(265\) | −1.02284e16 | −1.81431 | ||||||||
\(266\) | 1.15955e15 | + | 1.64052e14i | 0.200705 | + | 0.0283956i | ||||
\(267\) | − | 4.49523e14i | − | 0.0759327i | ||||||
\(268\) | 2.02913e15 | − | 7.02760e15i | 0.334530 | − | 1.15859i | ||||
\(269\) | 6.51041e15i | 1.04765i | 0.851824 | + | 0.523827i | \(0.175496\pi\) | ||||
−0.851824 | + | 0.523827i | \(0.824504\pi\) | |||||||
\(270\) | −1.59567e14 | + | 1.12785e15i | −0.0250657 | + | 0.177168i | ||||
\(271\) | −7.50666e15 | −1.15119 | −0.575594 | − | 0.817735i | \(-0.695229\pi\) | ||||
−0.575594 | + | 0.817735i | \(0.695229\pi\) | |||||||
\(272\) | −6.96734e15 | − | 4.38941e15i | −1.04320 | − | 0.657217i | ||||
\(273\) | 2.54329e14 | 0.0371825 | ||||||||
\(274\) | 9.94527e14 | − | 7.02949e15i | 0.141984 | − | 1.00356i | ||||
\(275\) | − | 4.50796e15i | − | 0.628518i | ||||||
\(276\) | −2.41060e14 | + | 8.34873e14i | −0.0328258 | + | 0.113687i | ||||
\(277\) | − | 9.31932e15i | − | 1.23955i | −0.784778 | − | 0.619777i | \(-0.787223\pi\) | ||
0.784778 | − | 0.619777i | \(-0.212777\pi\) | |||||||
\(278\) | 8.81143e15 | + | 1.24663e15i | 1.14487 | + | 0.161975i | ||||
\(279\) | 2.55562e15 | 0.324391 | ||||||||
\(280\) | 7.67104e15 | + | 3.44077e15i | 0.951321 | + | 0.426706i | ||||
\(281\) | 7.70003e15 | 0.933042 | 0.466521 | − | 0.884510i | \(-0.345507\pi\) | ||||
0.466521 | + | 0.884510i | \(0.345507\pi\) | |||||||
\(282\) | 4.74955e14 | + | 6.71963e13i | 0.0562385 | + | 0.00795658i | ||||
\(283\) | − | 5.78501e15i | − | 0.669410i | −0.942323 | − | 0.334705i | \(-0.891363\pi\) | ||
0.942323 | − | 0.334705i | \(-0.108637\pi\) | |||||||
\(284\) | −1.20763e16 | − | 3.48690e15i | −1.36573 | − | 0.394339i | ||||
\(285\) | 2.05550e14i | 0.0227210i | ||||||||
\(286\) | −7.88081e14 | + | 5.57029e15i | −0.0851514 | + | 0.601865i | ||||
\(287\) | −1.05412e16 | −1.11342 | ||||||||
\(288\) | 6.22913e15 | − | 7.35460e15i | 0.643245 | − | 0.759466i | ||||
\(289\) | 5.15243e15 | 0.520206 | ||||||||
\(290\) | −2.33258e15 | + | 1.64871e16i | −0.230277 | + | 1.62764i | ||||
\(291\) | − | 2.89032e14i | − | 0.0279024i | ||||||
\(292\) | −6.30591e15 | − | 1.82076e15i | −0.595332 | − | 0.171895i | ||||
\(293\) | 1.41861e16i | 1.30985i | 0.755693 | + | 0.654926i | \(0.227300\pi\) | ||||
−0.755693 | + | 0.654926i | \(0.772700\pi\) | |||||||
\(294\) | −2.71529e14 | − | 3.84157e13i | −0.0245221 | − | 0.00346937i | ||||
\(295\) | 2.11365e16 | 1.86720 | ||||||||
\(296\) | −2.76711e15 | − | 1.24116e15i | −0.239128 | − | 0.107259i | ||||
\(297\) | −1.46173e15 | −0.123580 | ||||||||
\(298\) | −1.31183e16 | − | 1.85597e15i | −1.08511 | − | 0.153520i | ||||
\(299\) | − | 1.43488e16i | − | 1.16132i | ||||||
\(300\) | −1.68319e14 | + | 5.82948e14i | −0.0133305 | + | 0.0461680i | ||||
\(301\) | 1.90836e16i | 1.47903i | ||||||||
\(302\) | 6.81658e13 | − | 4.81808e14i | 0.00517037 | − | 0.0365451i | ||||
\(303\) | −9.11921e14 | −0.0676987 | ||||||||
\(304\) | 1.85854e15 | − | 2.95007e15i | 0.135050 | − | 0.214365i | ||||
\(305\) | 2.08686e15 | 0.148438 | ||||||||
\(306\) | −2.46870e15 | + | 1.74492e16i | −0.171901 | + | 1.21503i | ||||
\(307\) | 9.07714e15i | 0.618799i | 0.950932 | + | 0.309400i | \(0.100128\pi\) | ||||
−0.950932 | + | 0.309400i | \(0.899872\pi\) | |||||||
\(308\) | −2.99287e15 | + | 1.03654e16i | −0.199760 | + | 0.691838i | ||||
\(309\) | − | 1.23380e15i | − | 0.0806333i | ||||||
\(310\) | 6.57184e15 | + | 9.29779e14i | 0.420568 | + | 0.0595016i | ||||
\(311\) | 1.48689e16 | 0.931827 | 0.465914 | − | 0.884830i | \(-0.345726\pi\) | ||||
0.465914 | + | 0.884830i | \(0.345726\pi\) | |||||||
\(312\) | 3.09896e14 | − | 6.90898e14i | 0.0190200 | − | 0.0424042i | ||||
\(313\) | 9.98994e15 | 0.600516 | 0.300258 | − | 0.953858i | \(-0.402927\pi\) | ||||
0.300258 | + | 0.953858i | \(0.402927\pi\) | |||||||
\(314\) | −1.34039e16 | − | 1.89637e15i | −0.789200 | − | 0.111656i | ||||
\(315\) | − | 1.79924e16i | − | 1.03770i | ||||||
\(316\) | −4.66459e14 | − | 1.34685e14i | −0.0263541 | − | 0.00760942i | ||||
\(317\) | − | 2.22336e16i | − | 1.23062i | −0.788284 | − | 0.615311i | \(-0.789030\pi\) | ||
0.788284 | − | 0.615311i | \(-0.210970\pi\) | |||||||
\(318\) | −2.47485e14 | + | 1.74927e15i | −0.0134206 | + | 0.0948593i | ||||
\(319\) | −2.13678e16 | −1.13533 | ||||||||
\(320\) | 1.86941e16 | − | 1.66463e16i | 0.973260 | − | 0.866646i | ||||
\(321\) | 1.46384e14 | 0.00746811 | ||||||||
\(322\) | 3.85475e15 | − | 2.72460e16i | 0.192723 | − | 1.36220i | ||||
\(323\) | 6.37536e15i | 0.312384i | ||||||||
\(324\) | −1.97220e16 | − | 5.69448e15i | −0.947126 | − | 0.273471i | ||||
\(325\) | − | 1.00190e16i | − | 0.471610i | ||||||
\(326\) | 2.89005e16 | + | 4.08881e15i | 1.33349 | + | 0.188661i | ||||
\(327\) | −1.03931e14 | −0.00470095 | ||||||||
\(328\) | −1.28443e16 | + | 2.86357e16i | −0.569546 | + | 1.26978i | ||||
\(329\) | −1.51899e16 | −0.660360 | ||||||||
\(330\) | −1.87497e15 | − | 2.65270e14i | −0.0799198 | − | 0.0113070i | ||||
\(331\) | 2.73268e16i | 1.14211i | 0.820913 | + | 0.571053i | \(0.193465\pi\) | ||||
−0.820913 | + | 0.571053i | \(0.806535\pi\) | |||||||
\(332\) | 1.03857e16 | − | 3.59692e16i | 0.425635 | − | 1.47412i | ||||
\(333\) | 6.49026e15i | 0.260840i | ||||||||
\(334\) | 1.63973e15 | − | 1.15899e16i | 0.0646280 | − | 0.456802i | ||||
\(335\) | −4.06555e16 | −1.57155 | ||||||||
\(336\) | 7.74048e14 | − | 1.22865e15i | 0.0293469 | − | 0.0465825i | ||||
\(337\) | −1.93018e16 | −0.717801 | −0.358900 | − | 0.933376i | \(-0.616848\pi\) | ||||
−0.358900 | + | 0.933376i | \(0.616848\pi\) | |||||||
\(338\) | 2.08862e15 | − | 1.47628e16i | 0.0761906 | − | 0.538529i | ||||
\(339\) | 9.04782e14i | 0.0323777i | ||||||||
\(340\) | −1.26966e16 | + | 4.39728e16i | −0.445734 | + | 1.54373i | ||||
\(341\) | 8.51732e15i | 0.293359i | ||||||||
\(342\) | −7.38825e15 | − | 1.04528e15i | −0.249673 | − | 0.0353236i | ||||
\(343\) | 3.28128e16 | 1.08801 | ||||||||
\(344\) | 5.18416e16 | + | 2.32530e16i | 1.68674 | + | 0.756571i | ||||
\(345\) | 4.82984e15 | 0.154209 | ||||||||
\(346\) | −4.34185e15 | − | 6.14281e14i | −0.136044 | − | 0.0192474i | ||||
\(347\) | 7.29553e15i | 0.224344i | 0.993689 | + | 0.112172i | \(0.0357808\pi\) | ||||
−0.993689 | + | 0.112172i | \(0.964219\pi\) | |||||||
\(348\) | 2.76318e15 | + | 7.97836e14i | 0.0833959 | + | 0.0240796i | ||||
\(349\) | − | 5.37690e16i | − | 1.59282i | −0.604758 | − | 0.796409i | \(-0.706730\pi\) | ||
0.604758 | − | 0.796409i | \(-0.293270\pi\) | |||||||
\(350\) | 2.69156e15 | − | 1.90244e16i | 0.0782641 | − | 0.553184i | ||||
\(351\) | −3.24871e15 | −0.0927289 | ||||||||
\(352\) | 2.45112e16 | + | 2.07603e16i | 0.686812 | + | 0.581710i | ||||
\(353\) | −4.64817e16 | −1.27863 | −0.639317 | − | 0.768943i | \(-0.720783\pi\) | ||||
−0.639317 | + | 0.768943i | \(0.720783\pi\) | |||||||
\(354\) | 5.11414e14 | − | 3.61476e15i | 0.0138118 | − | 0.0976245i | ||||
\(355\) | 6.98630e16i | 1.85252i | ||||||||
\(356\) | 4.07178e16 | + | 1.17568e16i | 1.06013 | + | 0.306100i | ||||
\(357\) | 2.65522e15i | 0.0678823i | ||||||||
\(358\) | −1.21086e16 | − | 1.71311e15i | −0.303986 | − | 0.0430077i | ||||
\(359\) | 4.50239e16 | 1.11002 | 0.555008 | − | 0.831845i | \(-0.312715\pi\) | ||||
0.555008 | + | 0.831845i | \(0.312715\pi\) | |||||||
\(360\) | −4.88774e16 | − | 2.19235e16i | −1.18343 | − | 0.530815i | ||||
\(361\) | 3.93536e16 | 0.935809 | ||||||||
\(362\) | 2.13130e16 | + | 3.01534e15i | 0.497781 | + | 0.0704257i | ||||
\(363\) | 5.69646e14i | 0.0130681i | ||||||||
\(364\) | −6.65170e15 | + | 2.30372e16i | −0.149890 | + | 0.519123i | ||||
\(365\) | 3.64804e16i | 0.807526i | ||||||||
\(366\) | 5.04932e13 | − | 3.56894e14i | 0.00109801 | − | 0.00776091i | ||||
\(367\) | −1.88578e16 | −0.402868 | −0.201434 | − | 0.979502i | \(-0.564560\pi\) | ||||
−0.201434 | + | 0.979502i | \(0.564560\pi\) | |||||||
\(368\) | −6.93182e16 | − | 4.36704e16i | −1.45491 | − | 0.916593i | ||||
\(369\) | 6.71650e16 | 1.38507 | ||||||||
\(370\) | −2.36127e15 | + | 1.66898e16i | −0.0478447 | + | 0.338175i | ||||
\(371\) | − | 5.59445e16i | − | 1.11385i | ||||||
\(372\) | 3.18021e14 | − | 1.10142e15i | 0.00622196 | − | 0.0215488i | ||||
\(373\) | − | 7.72158e16i | − | 1.48456i | −0.670088 | − | 0.742282i | \(-0.733744\pi\) | ||
0.670088 | − | 0.742282i | \(-0.266256\pi\) | |||||||
\(374\) | −5.81543e16 | − | 8.22763e15i | −1.09879 | − | 0.155457i | ||||
\(375\) | −1.45697e15 | −0.0270551 | ||||||||
\(376\) | −1.85086e16 | + | 4.12640e16i | −0.337794 | + | 0.753097i | ||||
\(377\) | −4.74903e16 | −0.851895 | ||||||||
\(378\) | −6.16877e15 | − | 8.72753e14i | −0.108768 | − | 0.0153884i | ||||
\(379\) | 2.71019e16i | 0.469726i | 0.972028 | + | 0.234863i | \(0.0754642\pi\) | ||||
−0.972028 | + | 0.234863i | \(0.924536\pi\) | |||||||
\(380\) | −1.86188e16 | − | 5.37594e15i | −0.317218 | − | 0.0915928i | ||||
\(381\) | 2.00660e14i | 0.00336084i | ||||||||
\(382\) | 3.12041e15 | − | 2.20556e16i | 0.0513806 | − | 0.363167i | ||||
\(383\) | −7.57350e16 | −1.22604 | −0.613020 | − | 0.790067i | \(-0.710045\pi\) | ||||
−0.613020 | + | 0.790067i | \(0.710045\pi\) | |||||||
\(384\) | −2.39452e15 | − | 3.59983e15i | −0.0381124 | − | 0.0572966i | ||||
\(385\) | 5.99648e16 | 0.938429 | ||||||||
\(386\) | −1.61138e15 | + | 1.13895e16i | −0.0247960 | + | 0.175262i | ||||
\(387\) | − | 1.21594e17i | − | 1.83989i | ||||||
\(388\) | 2.61805e16 | + | 7.55931e15i | 0.389558 | + | 0.112480i | ||||
\(389\) | 4.92786e16i | 0.721085i | 0.932743 | + | 0.360542i | \(0.117408\pi\) | ||||
−0.932743 | + | 0.360542i | \(0.882592\pi\) | |||||||
\(390\) | −4.16716e15 | − | 5.89566e14i | −0.0599680 | − | 0.00848423i | ||||
\(391\) | 1.49803e17 | 2.12017 | ||||||||
\(392\) | 1.05812e16 | − | 2.35904e16i | 0.147291 | − | 0.328379i | ||||
\(393\) | 2.56181e15 | 0.0350748 | ||||||||
\(394\) | 3.87054e16 | + | 5.47602e15i | 0.521251 | + | 0.0737462i | ||||
\(395\) | 2.69852e15i | 0.0357474i | ||||||||
\(396\) | 1.90696e16 | − | 6.60446e16i | 0.248498 | − | 0.860635i | ||||
\(397\) | 3.19333e16i | 0.409361i | 0.978829 | + | 0.204680i | \(0.0656155\pi\) | ||||
−0.978829 | + | 0.204680i | \(0.934385\pi\) | |||||||
\(398\) | −1.47665e16 | + | 1.04372e17i | −0.186224 | + | 1.31627i | ||||
\(399\) | −1.12426e15 | −0.0139490 | ||||||||
\(400\) | −4.84012e16 | − | 3.04927e16i | −0.590835 | − | 0.372226i | ||||
\(401\) | −4.73693e16 | −0.568930 | −0.284465 | − | 0.958686i | \(-0.591816\pi\) | ||||
−0.284465 | + | 0.958686i | \(0.591816\pi\) | |||||||
\(402\) | −9.83690e14 | + | 6.95289e15i | −0.0116249 | + | 0.0821668i | ||||
\(403\) | 1.89299e16i | 0.220123i | ||||||||
\(404\) | 2.38503e16 | − | 8.26019e16i | 0.272907 | − | 0.945172i | ||||
\(405\) | 1.14094e17i | 1.28471i | ||||||||
\(406\) | −9.01762e16 | − | 1.27581e16i | −0.999247 | − | 0.141373i | ||||
\(407\) | −2.16306e16 | −0.235887 | ||||||||
\(408\) | 7.21303e15 | + | 3.23533e15i | 0.0774152 | + | 0.0347239i | ||||
\(409\) | −6.85823e16 | −0.724453 | −0.362227 | − | 0.932090i | \(-0.617983\pi\) | ||||
−0.362227 | + | 0.932090i | \(0.617983\pi\) | |||||||
\(410\) | 1.72716e17 | + | 2.44358e16i | 1.79572 | + | 0.254057i | ||||
\(411\) | 6.81556e15i | 0.0697477i | ||||||||
\(412\) | 1.11758e17 | + | 3.22687e16i | 1.12576 | + | 0.325049i | ||||
\(413\) | 1.15606e17i | 1.14632i | ||||||||
\(414\) | −2.45612e16 | + | 1.73603e17i | −0.239744 | + | 1.69455i | ||||
\(415\) | −2.08086e17 | −1.99954 | ||||||||
\(416\) | 5.44766e16 | + | 4.61401e16i | 0.515351 | + | 0.436487i | ||||
\(417\) | −8.54327e15 | −0.0795682 | ||||||||
\(418\) | 3.48370e15 | − | 2.46234e16i | 0.0319444 | − | 0.225789i | ||||
\(419\) | − | 8.53203e16i | − | 0.770302i | −0.922853 | − | 0.385151i | \(-0.874149\pi\) | ||
0.922853 | − | 0.385151i | \(-0.125851\pi\) | |||||||
\(420\) | −7.75436e15 | − | 2.23898e15i | −0.0689327 | − | 0.0199035i | ||||
\(421\) | − | 8.55909e16i | − | 0.749193i | −0.927188 | − | 0.374597i | \(-0.877781\pi\) | ||
0.927188 | − | 0.374597i | \(-0.122219\pi\) | |||||||
\(422\) | 9.91543e16 | + | 1.40283e16i | 0.854635 | + | 0.120913i | ||||
\(423\) | 9.67848e16 | 0.821476 | ||||||||
\(424\) | −1.51976e17 | − | 6.81674e16i | −1.27027 | − | 0.569769i | ||||
\(425\) | 1.04599e17 | 0.860994 | ||||||||
\(426\) | 1.19480e16 | + | 1.69039e15i | 0.0968571 | + | 0.0137033i | ||||
\(427\) | 1.14141e16i | 0.0911297i | ||||||||
\(428\) | −3.82851e15 | + | 1.32595e16i | −0.0301055 | + | 0.104266i | ||||
\(429\) | − | 5.40077e15i | − | 0.0418296i | ||||||
\(430\) | 4.42381e16 | − | 3.12683e17i | 0.337483 | − | 2.38539i | ||||
\(431\) | −2.15111e17 | −1.61644 | −0.808220 | − | 0.588880i | \(-0.799569\pi\) | ||||
−0.808220 | + | 0.588880i | \(0.799569\pi\) | |||||||
\(432\) | −9.88742e15 | + | 1.56943e16i | −0.0731878 | + | 0.116171i | ||||
\(433\) | −6.08494e16 | −0.443696 | −0.221848 | − | 0.975081i | \(-0.571209\pi\) | ||||
−0.221848 | + | 0.975081i | \(0.571209\pi\) | |||||||
\(434\) | −5.08543e15 | + | 3.59447e16i | −0.0365295 | + | 0.258197i | ||||
\(435\) | − | 1.59853e16i | − | 0.113121i | ||||||
\(436\) | 2.71821e15 | − | 9.41411e15i | 0.0189505 | − | 0.0656322i | ||||
\(437\) | 6.34287e16i | 0.435669i | ||||||||
\(438\) | 6.23888e15 | + | 8.82672e14i | 0.0422206 | + | 0.00597335i | ||||
\(439\) | 2.01095e17 | 1.34086 | 0.670428 | − | 0.741975i | \(-0.266111\pi\) | ||||
0.670428 | + | 0.741975i | \(0.266111\pi\) | |||||||
\(440\) | 7.30660e16 | − | 1.62897e17i | 0.480035 | − | 1.07022i | ||||
\(441\) | −5.53312e16 | −0.358195 | ||||||||
\(442\) | −1.29249e17 | − | 1.82860e16i | −0.824483 | − | 0.116647i | ||||
\(443\) | − | 7.60262e16i | − | 0.477902i | −0.971032 | − | 0.238951i | \(-0.923196\pi\) | ||
0.971032 | − | 0.238951i | \(-0.0768036\pi\) | |||||||
\(444\) | 2.79716e15 | + | 8.07647e14i | 0.0173272 | + | 0.00500302i | ||||
\(445\) | − | 2.35557e17i | − | 1.43799i | ||||||
\(446\) | −8.20777e15 | + | 5.80139e16i | −0.0493797 | + | 0.349024i | ||||
\(447\) | 1.27191e16 | 0.0754149 | ||||||||
\(448\) | 9.10468e16 | + | 1.02247e17i | 0.532056 | + | 0.597509i | ||||
\(449\) | 8.77575e16 | 0.505455 | 0.252728 | − | 0.967537i | \(-0.418672\pi\) | ||||
0.252728 | + | 0.967537i | \(0.418672\pi\) | |||||||
\(450\) | −1.71498e16 | + | 1.21217e17i | −0.0973591 | + | 0.688151i | ||||
\(451\) | 2.23846e17i | 1.25257i | ||||||||
\(452\) | −8.19553e16 | − | 2.36636e16i | −0.452040 | − | 0.130521i | ||||
\(453\) | 4.67145e14i | 0.00253988i | ||||||||
\(454\) | −1.86210e17 | − | 2.63449e16i | −0.998023 | − | 0.141200i | ||||
\(455\) | 1.33273e17 | 0.704153 | ||||||||
\(456\) | −1.36989e15 | + | 3.05410e15i | −0.00713533 | + | 0.0159079i | ||||
\(457\) | −8.19691e16 | −0.420916 | −0.210458 | − | 0.977603i | \(-0.567495\pi\) | ||||
−0.210458 | + | 0.977603i | \(0.567495\pi\) | |||||||
\(458\) | −1.89811e17 | − | 2.68543e16i | −0.960939 | − | 0.135953i | ||||
\(459\) | − | 3.39168e16i | − | 0.169290i | ||||||
\(460\) | −1.26319e17 | + | 4.37487e17i | −0.621646 | + | 2.15298i | ||||
\(461\) | − | 1.34599e17i | − | 0.653110i | −0.945178 | − | 0.326555i | \(-0.894112\pi\) | ||
0.945178 | − | 0.326555i | \(-0.105888\pi\) | |||||||
\(462\) | 1.45089e15 | − | 1.02552e16i | 0.00694165 | − | 0.0490648i | ||||
\(463\) | 1.44197e17 | 0.680269 | 0.340135 | − | 0.940377i | \(-0.389527\pi\) | ||||
0.340135 | + | 0.940377i | \(0.389527\pi\) | |||||||
\(464\) | −1.44536e17 | + | 2.29423e17i | −0.672372 | + | 1.06726i | ||||
\(465\) | −6.37183e15 | −0.0292294 | ||||||||
\(466\) | 4.38626e16 | − | 3.10028e17i | 0.198420 | − | 1.40247i | ||||
\(467\) | 3.32854e17i | 1.48489i | 0.669908 | + | 0.742444i | \(0.266333\pi\) | ||||
−0.669908 | + | 0.742444i | \(0.733667\pi\) | |||||||
\(468\) | 4.23825e16 | − | 1.46785e17i | 0.186461 | − | 0.645779i | ||||
\(469\) | − | 2.22365e17i | − | 0.964813i | ||||||
\(470\) | 2.48884e17 | + | 3.52120e16i | 1.06503 | + | 0.150679i | ||||
\(471\) | 1.29959e16 | 0.0548494 | ||||||||
\(472\) | 3.14050e17 | + | 1.40864e17i | 1.30730 | + | 0.586378i | ||||
\(473\) | 4.05247e17 | 1.66388 | ||||||||
\(474\) | 4.61501e14 | + | 6.52928e13i | 0.00186902 | + | 0.000264427i | ||||
\(475\) | 4.42889e16i | 0.176924i | ||||||||
\(476\) | −2.40510e17 | − | 6.94443e16i | −0.947736 | − | 0.273647i | ||||
\(477\) | 3.56460e17i | 1.38561i | ||||||||
\(478\) | 9.73215e15 | − | 6.87885e16i | 0.0373188 | − | 0.263776i | ||||
\(479\) | 1.65749e17 | 0.627004 | 0.313502 | − | 0.949588i | \(-0.398498\pi\) | ||||
0.313502 | + | 0.949588i | \(0.398498\pi\) | |||||||
\(480\) | −1.55308e16 | + | 1.83369e16i | −0.0579598 | + | 0.0684320i | ||||
\(481\) | −4.80743e16 | −0.176999 | ||||||||
\(482\) | 4.23984e15 | − | 2.99679e16i | 0.0154008 | − | 0.108856i | ||||
\(483\) | 2.64168e16i | 0.0946726i | ||||||||
\(484\) | −5.15986e16 | − | 1.48985e16i | −0.182450 | − | 0.0526802i | ||||
\(485\) | − | 1.51457e17i | − | 0.528408i | ||||||
\(486\) | 5.90047e16 | + | 8.34794e15i | 0.203119 | + | 0.0287372i | ||||
\(487\) | −4.13371e17 | −1.40411 | −0.702056 | − | 0.712122i | \(-0.747734\pi\) | ||||
−0.702056 | + | 0.712122i | \(0.747734\pi\) | |||||||
\(488\) | 3.10069e16 | + | 1.39079e16i | 0.103927 | + | 0.0466156i | ||||
\(489\) | −2.80209e16 | −0.0926776 | ||||||||
\(490\) | −1.42285e17 | − | 2.01304e16i | −0.464393 | − | 0.0657020i | ||||
\(491\) | − | 2.41125e17i | − | 0.776626i | −0.921527 | − | 0.388313i | \(-0.873058\pi\) | ||
0.921527 | − | 0.388313i | \(-0.126942\pi\) | |||||||
\(492\) | 8.35801e15 | − | 2.89467e16i | 0.0265662 | − | 0.0920080i | ||||
\(493\) | − | 4.95802e17i | − | 1.55526i | ||||||
\(494\) | 7.74258e15 | − | 5.47259e16i | 0.0239696 | − | 0.169421i | ||||
\(495\) | −3.82076e17 | −1.16739 | ||||||||
\(496\) | 9.14491e16 | + | 5.76128e16i | 0.275771 | + | 0.173735i | ||||
\(497\) | −3.82116e17 | −1.13731 | ||||||||
\(498\) | −5.03480e15 | + | 3.55869e16i | −0.0147908 | + | 0.104544i | ||||
\(499\) | 2.61865e17i | 0.759319i | 0.925126 | + | 0.379660i | \(0.123959\pi\) | ||||
−0.925126 | + | 0.379660i | \(0.876041\pi\) | |||||||
\(500\) | 3.81056e16 | − | 1.31973e17i | 0.109065 | − | 0.377728i | ||||
\(501\) | 1.12372e16i | 0.0317477i | ||||||||
\(502\) | 5.83017e17 | + | 8.24849e16i | 1.62595 | + | 0.230038i | ||||
\(503\) | 4.41721e17 | 1.21606 | 0.608031 | − | 0.793913i | \(-0.291960\pi\) | ||||
0.608031 | + | 0.793913i | \(0.291960\pi\) | |||||||
\(504\) | 1.19911e17 | − | 2.67335e17i | 0.325881 | − | 0.726536i | ||||
\(505\) | −4.77861e17 | −1.28206 | ||||||||
\(506\) | −5.78579e17 | − | 8.18569e16i | −1.53244 | − | 0.216809i | ||||
\(507\) | 1.43135e16i | 0.0374277i | ||||||||
\(508\) | −1.81758e16 | − | 5.24804e15i | −0.0469223 | − | 0.0135482i | ||||
\(509\) | 6.01276e17i | 1.53253i | 0.642527 | + | 0.766263i | \(0.277886\pi\) | ||||
−0.642527 | + | 0.766263i | \(0.722114\pi\) | |||||||
\(510\) | 6.15511e15 | − | 4.35054e16i | 0.0154892 | − | 0.109481i | ||||
\(511\) | −1.99530e17 | −0.495761 | ||||||||
\(512\) | 3.88699e17 | − | 1.22747e17i | 0.953583 | − | 0.301131i | ||||
\(513\) | 1.43609e16 | 0.0347871 | ||||||||
\(514\) | 1.32444e15 | − | 9.36139e15i | 0.00316791 | − | 0.0223913i | ||||
\(515\) | − | 6.46531e17i | − | 1.52701i | ||||||
\(516\) | −5.24046e16 | − | 1.51312e16i | −0.122221 | − | 0.0352899i | ||||
\(517\) | 3.22562e17i | 0.742890i | ||||||||
\(518\) | −9.12852e16 | − | 1.29150e16i | −0.207614 | − | 0.0293731i | ||||
\(519\) | 4.20971e15 | 0.00945506 | ||||||||
\(520\) | 1.62390e17 | − | 3.62042e17i | 0.360196 | − | 0.803040i | ||||
\(521\) | −1.78457e16 | −0.0390921 | −0.0195460 | − | 0.999809i | \(-0.506222\pi\) | ||||
−0.0195460 | + | 0.999809i | \(0.506222\pi\) | |||||||
\(522\) | 5.74573e17 | + | 8.12902e16i | 1.24305 | + | 0.175865i | ||||
\(523\) | 3.35491e17i | 0.716836i | 0.933561 | + | 0.358418i | \(0.116684\pi\) | ||||
−0.933561 | + | 0.358418i | \(0.883316\pi\) | |||||||
\(524\) | −6.70012e16 | + | 2.32049e17i | −0.141394 | + | 0.489695i | ||||
\(525\) | 1.84455e16i | 0.0384463i | ||||||||
\(526\) | −5.47540e15 | + | 3.87011e16i | −0.0112722 | + | 0.0796739i | ||||
\(527\) | −1.97629e17 | −0.401867 | ||||||||
\(528\) | −2.60908e16 | − | 1.64372e16i | −0.0524043 | − | 0.0330146i | ||||
\(529\) | 9.86354e17 | 1.95691 | ||||||||
\(530\) | −1.29686e17 | + | 9.16644e17i | −0.254156 | + | 1.79642i | ||||
\(531\) | − | 7.36605e17i | − | 1.42600i | ||||||
\(532\) | 2.94037e16 | − | 1.01835e17i | 0.0562312 | − | 0.194748i | ||||
\(533\) | 4.97501e17i | 0.939869i | ||||||||
\(534\) | −4.02850e16 | − | 5.69949e15i | −0.0751840 | − | 0.0106370i | ||||
\(535\) | 7.67075e16 | 0.141429 | ||||||||
\(536\) | −6.04066e17 | − | 2.70948e17i | −1.10031 | − | 0.493531i | ||||
\(537\) | 1.17401e16 | 0.0211270 | ||||||||
\(538\) | 5.83444e17 | + | 8.25453e16i | 1.03732 | + | 0.146760i | ||||
\(539\) | − | 1.84406e17i | − | 0.323929i | ||||||
\(540\) | 9.90515e16 | + | 2.85999e16i | 0.171910 | + | 0.0496370i | ||||
\(541\) | 2.18609e17i | 0.374874i | 0.982277 | + | 0.187437i | \(0.0600181\pi\) | ||||
−0.982277 | + | 0.187437i | \(0.939982\pi\) | |||||||
\(542\) | −9.51768e16 | + | 6.72726e17i | −0.161263 | + | 1.13984i | ||||
\(543\) | −2.06643e16 | −0.0345958 | ||||||||
\(544\) | −4.81706e17 | + | 5.68740e17i | −0.796873 | + | 0.940851i | ||||
\(545\) | −5.44617e16 | −0.0890254 | ||||||||
\(546\) | 3.22463e15 | − | 2.27923e16i | 0.00520869 | − | 0.0368159i | ||||
\(547\) | 5.87423e17i | 0.937633i | 0.883296 | + | 0.468817i | \(0.155319\pi\) | ||||
−0.883296 | + | 0.468817i | \(0.844681\pi\) | |||||||
\(548\) | −6.17354e17 | − | 1.78254e17i | −0.973779 | − | 0.281167i | ||||
\(549\) | − | 7.27268e16i | − | 0.113364i | ||||||
\(550\) | −4.03991e17 | − | 5.71563e16i | −0.622320 | − | 0.0880454i | ||||
\(551\) | 2.09930e17 | 0.319587 | ||||||||
\(552\) | 7.17626e16 | + | 3.21884e16i | 0.107968 | + | 0.0484279i | ||||
\(553\) | −1.47596e16 | −0.0219462 | ||||||||
\(554\) | −8.35171e17 | − | 1.18159e17i | −1.22733 | − | 0.173642i | ||||
\(555\) | − | 1.61819e16i | − | 0.0235031i | ||||||
\(556\) | 2.23440e17 | − | 7.73850e17i | 0.320756 | − | 1.11089i | ||||
\(557\) | − | 6.63373e17i | − | 0.941237i | −0.882337 | − | 0.470619i | \(-0.844031\pi\) | ||
0.882337 | − | 0.470619i | \(-0.155969\pi\) | |||||||
\(558\) | 3.24027e16 | − | 2.29028e17i | 0.0454421 | − | 0.321193i | ||||
\(559\) | 9.00667e17 | 1.24850 | ||||||||
\(560\) | 4.05613e17 | − | 6.43832e17i | 0.555764 | − | 0.882166i | ||||
\(561\) | 5.63844e16 | 0.0763661 | ||||||||
\(562\) | 9.76285e16 | − | 6.90055e17i | 0.130705 | − | 0.923842i | ||||
\(563\) | − | 1.15064e18i | − | 1.52277i | −0.648298 | − | 0.761387i | \(-0.724519\pi\) | ||
0.648298 | − | 0.761387i | \(-0.275481\pi\) | |||||||
\(564\) | 1.20439e16 | − | 4.17122e16i | 0.0157562 | − | 0.0545693i | ||||
\(565\) | 4.74121e17i | 0.613160i | ||||||||
\(566\) | −5.18436e17 | − | 7.33480e16i | −0.662809 | − | 0.0937737i | ||||
\(567\) | −6.24037e17 | −0.788715 | ||||||||
\(568\) | −4.65602e17 | + | 1.03804e18i | −0.581769 | + | 1.29703i | ||||
\(569\) | 8.26006e17 | 1.02036 | 0.510180 | − | 0.860068i | \(-0.329579\pi\) | ||||
0.510180 | + | 0.860068i | \(0.329579\pi\) | |||||||
\(570\) | 1.84208e16 | + | 2.60617e15i | 0.0224969 | + | 0.00318285i | ||||
\(571\) | − | 3.74515e17i | − | 0.452204i | −0.974104 | − | 0.226102i | \(-0.927402\pi\) | ||
0.974104 | − | 0.226102i | \(-0.0725983\pi\) | |||||||
\(572\) | 4.89202e17 | + | 1.41251e17i | 0.584002 | + | 0.168624i | ||||
\(573\) | 2.13843e16i | 0.0252401i | ||||||||
\(574\) | −1.33652e17 | + | 9.44672e17i | −0.155972 | + | 1.10244i | ||||
\(575\) | 1.04066e18 | 1.20079 | ||||||||
\(576\) | −5.80120e17 | − | 6.51486e17i | −0.661868 | − | 0.743291i | ||||
\(577\) | −1.13319e18 | −1.27838 | −0.639189 | − | 0.769050i | \(-0.720730\pi\) | ||||
−0.639189 | + | 0.769050i | \(0.720730\pi\) | |||||||
\(578\) | 6.53275e16 | − | 4.61746e17i | 0.0728727 | − | 0.515077i | ||||
\(579\) | − | 1.10429e16i | − | 0.0121807i | ||||||
\(580\) | 1.44795e18 | + | 4.18079e17i | 1.57933 | + | 0.456012i | ||||
\(581\) | − | 1.13813e18i | − | 1.22757i | ||||||
\(582\) | −2.59022e16 | − | 3.66463e15i | −0.0276272 | − | 0.00390868i | ||||
\(583\) | −1.18800e18 | −1.25306 | ||||||||
\(584\) | −2.43124e17 | + | 5.42033e17i | −0.253597 | + | 0.565382i | ||||
\(585\) | −8.49169e17 | −0.875954 | ||||||||
\(586\) | 1.27132e18 | + | 1.79865e17i | 1.29694 | + | 0.183490i | ||||
\(587\) | 1.80779e18i | 1.82390i | 0.410301 | + | 0.911950i | \(0.365424\pi\) | ||||
−0.410301 | + | 0.911950i | \(0.634576\pi\) | |||||||
\(588\) | −6.88541e15 | + | 2.38466e16i | −0.00687032 | + | 0.0237943i | ||||
\(589\) | − | 8.36792e16i | − | 0.0825787i | ||||||
\(590\) | 2.67989e17 | − | 1.89419e18i | 0.261565 | − | 1.84879i | ||||
\(591\) | −3.75275e16 | −0.0362269 | ||||||||
\(592\) | −1.46314e17 | + | 2.32244e17i | −0.139699 | + | 0.221745i | ||||
\(593\) | 4.84457e17 | 0.457509 | 0.228755 | − | 0.973484i | \(-0.426535\pi\) | ||||
0.228755 | + | 0.973484i | \(0.426535\pi\) | |||||||
\(594\) | −1.85332e16 | + | 1.30996e17i | −0.0173117 | + | 0.122362i | ||||
\(595\) | 1.39138e18i | 1.28554i | ||||||||
\(596\) | −3.32654e17 | + | 1.15210e18i | −0.304013 | + | 1.05290i | ||||
\(597\) | − | 1.01195e17i | − | 0.0914803i | ||||||
\(598\) | −1.28590e18 | − | 1.81928e17i | −1.14987 | − | 0.162683i | ||||
\(599\) | −1.07468e18 | −0.950620 | −0.475310 | − | 0.879818i | \(-0.657664\pi\) | ||||
−0.475310 | + | 0.879818i | \(0.657664\pi\) | |||||||
\(600\) | 5.01080e16 | + | 2.24755e16i | 0.0438454 | + | 0.0196664i | ||||
\(601\) | 3.25263e17 | 0.281547 | 0.140774 | − | 0.990042i | \(-0.455041\pi\) | ||||
0.140774 | + | 0.990042i | \(0.455041\pi\) | |||||||
\(602\) | 1.71022e18 | + | 2.41960e17i | 1.46445 | + | 0.207189i | ||||
\(603\) | 1.41684e18i | 1.20021i | ||||||||
\(604\) | −4.23140e16 | − | 1.22177e16i | −0.0354604 | − | 0.0102388i | ||||
\(605\) | 2.98504e17i | 0.247480i | ||||||||
\(606\) | −1.15622e16 | + | 8.17238e16i | −0.00948351 | + | 0.0670311i | ||||
\(607\) | −4.02710e16 | −0.0326788 | −0.0163394 | − | 0.999867i | \(-0.505201\pi\) | ||||
−0.0163394 | + | 0.999867i | \(0.505201\pi\) | |||||||
\(608\) | −2.40813e17 | − | 2.03961e17i | −0.193333 | − | 0.163748i | ||||
\(609\) | 8.74318e16 | 0.0694476 | ||||||||
\(610\) | 2.64592e16 | − | 1.87018e17i | 0.0207938 | − | 0.146974i | ||||
\(611\) | 7.16899e17i | 0.557430i | ||||||||
\(612\) | 1.53245e18 | + | 4.42476e17i | 1.17897 | + | 0.340412i | ||||
\(613\) | − | 8.13502e17i | − | 0.619250i | −0.950859 | − | 0.309625i | \(-0.899797\pi\) | ||
0.950859 | − | 0.309625i | \(-0.100203\pi\) | |||||||
\(614\) | 8.13468e17 | + | 1.15089e17i | 0.612698 | + | 0.0866840i | ||||
\(615\) | −1.67460e17 | −0.124802 | ||||||||
\(616\) | 8.90968e17 | + | 3.99635e17i | 0.657033 | + | 0.294706i | ||||
\(617\) | −4.37374e17 | −0.319153 | −0.159577 | − | 0.987186i | \(-0.551013\pi\) | ||||
−0.159577 | + | 0.987186i | \(0.551013\pi\) | |||||||
\(618\) | −1.10570e17 | − | 1.56433e16i | −0.0798382 | − | 0.0112955i | ||||
\(619\) | − | 2.59586e18i | − | 1.85478i | −0.374099 | − | 0.927389i | \(-0.622048\pi\) | ||
0.374099 | − | 0.927389i | \(-0.377952\pi\) | |||||||
\(620\) | 1.66648e17 | − | 5.77161e17i | 0.117830 | − | 0.408085i | ||||
\(621\) | − | 3.37439e17i | − | 0.236102i | ||||||
\(622\) | 1.88522e17 | − | 1.33251e18i | 0.130534 | − | 0.922639i | ||||
\(623\) | 1.28838e18 | 0.882820 | ||||||||
\(624\) | −5.79872e16 | − | 3.65319e16i | −0.0393217 | − | 0.0247726i | ||||
\(625\) | −1.80404e18 | −1.21067 | ||||||||
\(626\) | 1.26662e17 | − | 8.95270e17i | 0.0841228 | − | 0.594595i | ||||
\(627\) | 2.38740e16i | 0.0156923i | ||||||||
\(628\) | −3.39895e17 | + | 1.17717e18i | −0.221109 | + | 0.765777i | ||||
\(629\) | − | 5.01899e17i | − | 0.323137i | ||||||
\(630\) | −1.61243e18 | − | 2.28126e17i | −1.02747 | − | 0.145365i | ||||
\(631\) | 2.52029e16 | 0.0158950 | 0.00794748 | − | 0.999968i | \(-0.497470\pi\) | ||||
0.00794748 | + | 0.999968i | \(0.497470\pi\) | |||||||
\(632\) | −1.79843e16 | + | 4.00951e16i | −0.0112262 | + | 0.0250283i | ||||
\(633\) | −9.61366e16 | −0.0593970 | ||||||||
\(634\) | −1.99251e18 | − | 2.81899e17i | −1.21849 | − | 0.172391i | ||||
\(635\) | 1.05149e17i | 0.0636467i | ||||||||
\(636\) | 1.53627e17 | + | 4.43578e16i | 0.0920439 | + | 0.0265766i | ||||
\(637\) | − | 4.09846e17i | − | 0.243061i | ||||||
\(638\) | −2.70922e17 | + | 1.91492e18i | −0.159041 | + | 1.12413i | ||||
\(639\) | 2.43472e18 | 1.41479 | ||||||||
\(640\) | −1.25477e18 | − | 1.88637e18i | −0.721762 | − | 1.08507i | ||||
\(641\) | 5.97617e17 | 0.340287 | 0.170144 | − | 0.985419i | \(-0.445577\pi\) | ||||
0.170144 | + | 0.985419i | \(0.445577\pi\) | |||||||
\(642\) | 1.85600e15 | − | 1.31185e16i | 0.00104616 | − | 0.00739447i | ||||
\(643\) | 2.19754e17i | 0.122621i | 0.998119 | + | 0.0613106i | \(0.0195280\pi\) | ||||
−0.998119 | + | 0.0613106i | \(0.980472\pi\) | |||||||
\(644\) | −2.39284e18 | − | 6.90903e17i | −1.32177 | − | 0.381645i | ||||
\(645\) | 3.03167e17i | 0.165784i | ||||||||
\(646\) | 5.71342e17 | + | 8.08331e16i | 0.309304 | + | 0.0437600i | ||||
\(647\) | −3.20518e18 | −1.71781 | −0.858905 | − | 0.512135i | \(-0.828855\pi\) | ||||
−0.858905 | + | 0.512135i | \(0.828855\pi\) | |||||||
\(648\) | −7.60378e17 | + | 1.69523e18i | −0.403452 | + | 0.899478i | ||||
\(649\) | 2.45494e18 | 1.28959 | ||||||||
\(650\) | −8.97876e17 | − | 1.27031e17i | −0.466960 | − | 0.0660651i | ||||
\(651\) | − | 3.48508e16i | − | 0.0179447i | ||||||
\(652\) | 7.32856e17 | − | 2.53814e18i | 0.373602 | − | 1.29391i | ||||
\(653\) | 2.61177e17i | 0.131826i | 0.997825 | + | 0.0659128i | \(0.0209959\pi\) | ||||
−0.997825 | + | 0.0659128i | \(0.979004\pi\) | |||||||
\(654\) | −1.31774e15 | + | 9.31403e15i | −0.000658530 | + | 0.00465460i | ||||
\(655\) | 1.34243e18 | 0.664236 | ||||||||
\(656\) | 2.40340e18 | + | 1.51414e18i | 1.17747 | + | 0.741806i | ||||
\(657\) | 1.27134e18 | 0.616717 | ||||||||
\(658\) | −1.92592e17 | + | 1.36127e18i | −0.0925060 | + | 0.653848i | ||||
\(659\) | 2.06165e17i | 0.0980529i | 0.998797 | + | 0.0490265i | \(0.0156119\pi\) | ||||
−0.998797 | + | 0.0490265i | \(0.984388\pi\) | |||||||
\(660\) | −4.75455e16 | + | 1.64666e17i | −0.0223910 | + | 0.0775478i | ||||
\(661\) | 1.46618e18i | 0.683718i | 0.939751 | + | 0.341859i | \(0.111057\pi\) | ||||
−0.939751 | + | 0.341859i | \(0.888943\pi\) | |||||||
\(662\) | 2.44895e18 | + | 3.46475e17i | 1.13084 | + | 0.159991i | ||||
\(663\) | 1.25315e17 | 0.0573015 | ||||||||
\(664\) | −3.09178e18 | − | 1.38679e18i | −1.39996 | − | 0.627939i | ||||
\(665\) | −5.89129e17 | −0.264162 | ||||||||
\(666\) | 5.81639e17 | + | 8.22899e16i | 0.258268 | + | 0.0365396i | ||||
\(667\) | − | 4.93275e18i | − | 2.16906i | ||||||
\(668\) | −1.01786e18 | − | 2.93896e17i | −0.443244 | − | 0.127981i | ||||
\(669\) | − | 5.62484e16i | − | 0.0242572i | ||||||
\(670\) | −5.15470e17 | + | 3.64343e18i | −0.220149 | + | 1.55605i | ||||
\(671\) | 2.42382e17 | 0.102519 | ||||||||
\(672\) | −1.00294e17 | − | 8.49460e16i | −0.0420121 | − | 0.0355830i | ||||
\(673\) | 2.71250e18 | 1.12531 | 0.562655 | − | 0.826692i | \(-0.309780\pi\) | ||||
0.562655 | + | 0.826692i | \(0.309780\pi\) | |||||||
\(674\) | −2.44727e17 | + | 1.72977e18i | −0.100553 | + | 0.710723i | ||||
\(675\) | − | 2.35616e17i | − | 0.0958805i | ||||||
\(676\) | −1.29652e18 | − | 3.74353e17i | −0.522546 | − | 0.150879i | ||||
\(677\) | 3.72209e18i | 1.48580i | 0.669402 | + | 0.742901i | \(0.266550\pi\) | ||||
−0.669402 | + | 0.742901i | \(0.733450\pi\) | |||||||
\(678\) | 8.10841e16 | + | 1.14717e16i | 0.0320585 | + | 0.00453561i | ||||
\(679\) | 8.28396e17 | 0.324403 | ||||||||
\(680\) | 3.77974e18 | + | 1.69537e18i | 1.46607 | + | 0.657591i | ||||
\(681\) | 1.80543e17 | 0.0693626 | ||||||||
\(682\) | 7.63298e17 | + | 1.07991e17i | 0.290466 | + | 0.0410950i | ||||
\(683\) | 8.34945e17i | 0.314719i | 0.987541 | + | 0.157360i | \(0.0502982\pi\) | ||||
−0.987541 | + | 0.157360i | \(0.949702\pi\) | |||||||
\(684\) | −1.87351e17 | + | 6.48861e17i | −0.0699506 | + | 0.242263i | ||||
\(685\) | 3.57146e18i | 1.32086i | ||||||||
\(686\) | 4.16032e17 | − | 2.94059e18i | 0.152412 | − | 1.07728i | ||||
\(687\) | 1.84034e17 | 0.0667852 | ||||||||
\(688\) | 2.74117e18 | − | 4.35107e18i | 0.985397 | − | 1.56412i | ||||
\(689\) | −2.64035e18 | −0.940235 | ||||||||
\(690\) | 6.12374e16 | − | 4.32837e17i | 0.0216022 | − | 0.152688i | ||||
\(691\) | 9.77059e17i | 0.341439i | 0.985320 | + | 0.170720i | \(0.0546092\pi\) | ||||
−0.985320 | + | 0.170720i | \(0.945391\pi\) | |||||||
\(692\) | −1.10100e17 | + | 3.81316e17i | −0.0381153 | + | 0.132006i | ||||
\(693\) | − | 2.08976e18i | − | 0.716690i | ||||||
\(694\) | 6.53805e17 | + | 9.24999e16i | 0.222132 | + | 0.0314271i | ||||
\(695\) | −4.47681e18 | −1.50684 | ||||||||
\(696\) | 1.06534e17 | − | 2.37513e17i | 0.0355246 | − | 0.0792004i | ||||
\(697\) | −5.19395e18 | −1.71587 | ||||||||
\(698\) | −4.81862e18 | − | 6.81735e17i | −1.57711 | − | 0.223129i | ||||
\(699\) | 3.00593e17i | 0.0974714i | ||||||||
\(700\) | −1.67079e18 | − | 4.82421e17i | −0.536766 | − | 0.154985i | ||||
\(701\) | − | 1.70397e18i | − | 0.542370i | −0.962527 | − | 0.271185i | \(-0.912584\pi\) | ||
0.962527 | − | 0.271185i | \(-0.0874156\pi\) | |||||||
\(702\) | −4.11904e16 | + | 2.91141e17i | −0.0129899 | + | 0.0918146i | ||||
\(703\) | 2.12512e17 | 0.0664008 | ||||||||
\(704\) | 2.17126e18 | − | 1.93341e18i | 0.672185 | − | 0.598552i | ||||
\(705\) | −2.41310e17 | −0.0740194 | ||||||||
\(706\) | −5.89340e17 | + | 4.16556e18i | −0.179116 | + | 1.26603i | ||||
\(707\) | − | 2.61366e18i | − | 0.787088i | ||||||
\(708\) | −3.17461e17 | − | 9.16630e16i | −0.0947270 | − | 0.0273513i | ||||
\(709\) | 5.77024e17i | 0.170605i | 0.996355 | + | 0.0853027i | \(0.0271857\pi\) | ||||
−0.996355 | + | 0.0853027i | \(0.972814\pi\) | |||||||
\(710\) | 6.26093e18 | + | 8.85792e17i | 1.83425 | + | 0.259509i | ||||
\(711\) | 9.40431e16 | 0.0273008 | ||||||||
\(712\) | 1.56987e18 | − | 3.49995e18i | 0.451590 | − | 1.00680i | ||||
\(713\) | −1.96622e18 | −0.560467 | ||||||||
\(714\) | 2.37953e17 | + | 3.36654e16i | 0.0672129 | + | 0.00950923i | ||||
\(715\) | − | 2.83009e18i | − | 0.792157i | ||||||
\(716\) | −3.07049e17 | + | 1.06342e18i | −0.0851673 | + | 0.294964i | ||||
\(717\) | 6.66950e16i | 0.0183324i | ||||||||
\(718\) | 5.70857e17 | − | 4.03491e18i | 0.155496 | − | 1.09907i | ||||
\(719\) | 2.65402e18 | 0.716417 | 0.358209 | − | 0.933642i | \(-0.383388\pi\) | ||||
0.358209 | + | 0.933642i | \(0.383388\pi\) | |||||||
\(720\) | −2.58444e18 | + | 4.10229e18i | −0.691360 | + | 1.09740i | ||||
\(721\) | 3.53620e18 | 0.937471 | ||||||||
\(722\) | 4.98963e17 | − | 3.52676e18i | 0.131092 | − | 0.926582i | ||||
\(723\) | 2.90559e16i | 0.00756546i | ||||||||
\(724\) | 5.40454e17 | − | 1.87178e18i | 0.139463 | − | 0.483007i | ||||
\(725\) | − | 3.44428e18i | − | 0.880848i | ||||||
\(726\) | 5.10501e16 | + | 7.22253e15i | 0.0129392 | + | 0.00183063i | ||||
\(727\) | −6.78102e18 | −1.70342 | −0.851710 | − | 0.524014i | \(-0.824434\pi\) | ||||
−0.851710 | + | 0.524014i | \(0.824434\pi\) | |||||||
\(728\) | 1.98019e18 | + | 8.88195e17i | 0.493007 | + | 0.221133i | ||||
\(729\) | 3.93786e18 | 0.971699 | ||||||||
\(730\) | 3.26927e18 | + | 4.62534e17i | 0.799563 | + | 0.113122i | ||||
\(731\) | 9.40303e18i | 2.27932i | ||||||||
\(732\) | −3.13437e16 | − | 9.05011e15i | −0.00753057 | − | 0.00217436i | ||||
\(733\) | − | 3.94118e17i | − | 0.0938535i | −0.998898 | − | 0.0469267i | \(-0.985057\pi\) | ||
0.998898 | − | 0.0469267i | \(-0.0149427\pi\) | |||||||
\(734\) | −2.39098e17 | + | 1.68999e18i | −0.0564354 | + | 0.398895i | ||||
\(735\) | 1.37955e17 | 0.0322753 | ||||||||
\(736\) | −4.79250e18 | + | 5.65841e18i | −1.11137 | + | 1.31217i | ||||
\(737\) | −4.72200e18 | −1.08539 | ||||||||
\(738\) | 8.51584e17 | − | 6.01914e18i | 0.194026 | − | 1.37141i | ||||
\(739\) | − | 2.42319e18i | − | 0.547266i | −0.961834 | − | 0.273633i | \(-0.911775\pi\) | ||
0.961834 | − | 0.273633i | \(-0.0882253\pi\) | |||||||
\(740\) | 1.46576e18 | + | 4.23220e17i | 0.328138 | + | 0.0947459i | ||||
\(741\) | 5.30604e16i | 0.0117748i | ||||||||
\(742\) | −5.01359e18 | − | 7.09319e17i | −1.10287 | − | 0.156033i | ||||
\(743\) | 2.76079e18 | 0.602013 | 0.301006 | − | 0.953622i | \(-0.402677\pi\) | ||||
0.301006 | + | 0.953622i | \(0.402677\pi\) | |||||||
\(744\) | −9.46739e16 | − | 4.24651e16i | −0.0204647 | − | 0.00917926i | ||||
\(745\) | 6.66501e18 | 1.42819 | ||||||||
\(746\) | −6.91986e18 | − | 9.79017e17i | −1.46992 | − | 0.207964i | ||||
\(747\) | 7.25177e18i | 1.52707i | ||||||||
\(748\) | −1.47467e18 | + | 5.10731e18i | −0.307847 | + | 1.06618i | ||||
\(749\) | 4.19552e17i | 0.0868269i | ||||||||
\(750\) | −1.84729e16 | + | 1.30570e17i | −0.00378999 | + | 0.0267883i | ||||
\(751\) | 7.34720e18 | 1.49438 | 0.747192 | − | 0.664608i | \(-0.231402\pi\) | ||||
0.747192 | + | 0.664608i | \(0.231402\pi\) | |||||||
\(752\) | 3.46330e18 | + | 2.18187e18i | 0.698351 | + | 0.439960i | ||||
\(753\) | −5.65274e17 | −0.113003 | ||||||||
\(754\) | −6.02128e17 | + | 4.25595e18i | −0.119337 | + | 0.843495i | ||||
\(755\) | 2.44791e17i | 0.0480995i | ||||||||
\(756\) | −1.56427e17 | + | 5.41762e17i | −0.0304734 | + | 0.105540i | ||||
\(757\) | − | 1.26012e18i | − | 0.243382i | −0.992568 | − | 0.121691i | \(-0.961168\pi\) | ||
0.992568 | − | 0.121691i | \(-0.0388317\pi\) | |||||||
\(758\) | 2.42880e18 | + | 3.43624e17i | 0.465095 | + | 0.0658012i | ||||
\(759\) | 5.60970e17 | 0.106505 | ||||||||
\(760\) | −7.17844e17 | + | 1.60040e18i | −0.135127 | + | 0.301259i | ||||
\(761\) | −3.58935e18 | −0.669908 | −0.334954 | − | 0.942235i | \(-0.608721\pi\) | ||||
−0.334954 | + | 0.942235i | \(0.608721\pi\) | |||||||
\(762\) | 1.79826e16 | + | 2.54416e15i | 0.00332770 | + | 0.000470801i | ||||
\(763\) | − | 2.97878e17i | − | 0.0546550i | ||||||
\(764\) | −1.93700e18 | − | 5.59284e17i | −0.352389 | − | 0.101748i | ||||
\(765\) | − | 8.86539e18i | − | 1.59918i | ||||||
\(766\) | −9.60242e17 | + | 6.78716e18i | −0.171749 | + | 1.21395i | ||||
\(767\) | 5.45614e18 | 0.967644 | ||||||||
\(768\) | −3.52967e17 | + | 1.68948e17i | −0.0620706 | + | 0.0297103i | ||||
\(769\) | −4.46415e17 | −0.0778426 | −0.0389213 | − | 0.999242i | \(-0.512392\pi\) | ||||
−0.0389213 | + | 0.999242i | \(0.512392\pi\) | |||||||
\(770\) | 7.60292e17 | − | 5.37388e18i | 0.131459 | − | 0.929176i | ||||
\(771\) | 9.07648e15i | 0.00155620i | ||||||||
\(772\) | 1.00027e18 | + | 2.88815e17i | 0.170061 | + | 0.0491030i | ||||
\(773\) | − | 6.26507e18i | − | 1.05623i | −0.849172 | − | 0.528116i | \(-0.822899\pi\) | ||
0.849172 | − | 0.528116i | \(-0.177101\pi\) | |||||||
\(774\) | −1.08969e19 | − | 1.54169e18i | −1.82175 | − | 0.257740i | ||||
\(775\) | −1.37291e18 | −0.227604 | ||||||||
\(776\) | 1.00939e18 | − | 2.25038e18i | 0.165942 | − | 0.369960i | ||||
\(777\) | 8.85070e16 | 0.0144292 | ||||||||
\(778\) | 4.41621e18 | + | 6.24803e17i | 0.713975 | + | 0.101013i | ||||
\(779\) | − | 2.19920e18i | − | 0.352590i | ||||||
\(780\) | −1.05671e17 | + | 3.65974e17i | −0.0168012 | + | 0.0581882i | ||||
\(781\) | 8.11437e18i | 1.27945i | ||||||||
\(782\) | 1.89934e18 | − | 1.34249e19i | 0.297002 | − | 2.09926i | ||||
\(783\) | −1.11682e18 | −0.173194 | ||||||||
\(784\) | −1.97994e18 | − | 1.24736e18i | −0.304508 | − | 0.191839i | ||||
\(785\) | 6.81008e18 | 1.03872 | ||||||||
\(786\) | 3.24811e16 | − | 2.29582e17i | 0.00491342 | − | 0.0347289i | ||||
\(787\) | − | 1.07781e16i | − | 0.00161698i | −1.00000 | 0.000808492i | \(-0.999743\pi\) | |||
1.00000 | 0.000808492i | \(-0.000257351\pi\) | ||||||||
\(788\) | 9.81491e17 | − | 3.39924e18i | 0.146038 | − | 0.505780i | ||||
\(789\) | − | 3.75233e16i | − | 0.00553733i | ||||||
\(790\) | 2.41834e17 | + | 3.42145e16i | 0.0353949 | + | 0.00500765i | ||||
\(791\) | −2.59320e18 | −0.376435 | ||||||||
\(792\) | −5.67695e18 | − | 2.54634e18i | −0.817338 | − | 0.366609i | ||||
\(793\) | 5.38698e17 | 0.0769254 | ||||||||
\(794\) | 2.86178e18 | + | 4.04882e17i | 0.405324 | + | 0.0573449i | ||||
\(795\) | − | 8.88748e17i | − | 0.124851i | ||||||
\(796\) | 9.16629e18 | + | 2.64666e18i | 1.27720 | + | 0.368776i | ||||
\(797\) | − | 8.45030e18i | − | 1.16787i | −0.811802 | − | 0.583933i | \(-0.801513\pi\) | ||
0.811802 | − | 0.583933i | \(-0.198487\pi\) | |||||||
\(798\) | −1.42544e16 | + | 1.00753e17i | −0.00195403 | + | 0.0138114i | ||||
\(799\) | −7.48448e18 | −1.01767 | ||||||||
\(800\) | −3.34635e18 | + | 3.95097e18i | −0.451322 | + | 0.532867i | ||||
\(801\) | −8.20914e18 | −1.09821 | ||||||||
\(802\) | −6.00594e17 | + | 4.24511e18i | −0.0796981 | + | 0.563320i | ||||
\(803\) | 4.23709e18i | 0.557720i | ||||||||
\(804\) | 6.10627e17 | + | 1.76311e17i | 0.0797281 | + | 0.0230205i | ||||
\(805\) | 1.38428e19i | 1.79288i | ||||||||
\(806\) | 1.69644e18 | + | 2.40011e17i | 0.217952 | + | 0.0308357i | ||||
\(807\) | −5.65688e17 | −0.0720940 | ||||||||
\(808\) | −7.10015e18 | − | 3.18470e18i | −0.897622 | − | 0.402620i | ||||
\(809\) | −1.02697e18 | −0.128794 | −0.0643968 | − | 0.997924i | \(-0.520512\pi\) | ||||
−0.0643968 | + | 0.997924i | \(0.520512\pi\) | |||||||
\(810\) | 1.02248e19 | + | 1.44659e18i | 1.27204 | + | 0.179967i | ||||
\(811\) | − | 6.09641e18i | − | 0.752382i | −0.926542 | − | 0.376191i | \(-0.877234\pi\) | ||
0.926542 | − | 0.376191i | \(-0.122766\pi\) | |||||||
\(812\) | −2.28668e18 | + | 7.91958e18i | −0.279957 | + | 0.969590i | ||||
\(813\) | − | 6.52253e17i | − | 0.0792186i | ||||||
\(814\) | −2.74254e17 | + | 1.93847e18i | −0.0330441 | + | 0.233561i | ||||
\(815\) | −1.46834e19 | −1.75510 | ||||||||
\(816\) | 3.81395e17 | − | 6.05391e17i | 0.0452261 | − | 0.0717876i | ||||
\(817\) | −3.98139e18 | −0.468372 | ||||||||
\(818\) | −8.69553e17 | + | 6.14615e18i | −0.101484 | + | 0.717310i | ||||
\(819\) | − | 4.64453e18i | − | 0.537770i | ||||||
\(820\) | 4.37973e18 | − | 1.51685e19i | 0.503104 | − | 1.74242i | ||||
\(821\) | 4.75938e18i | 0.542400i | 0.962523 | + | 0.271200i | \(0.0874205\pi\) | ||||
−0.962523 | + | 0.271200i | \(0.912579\pi\) | |||||||
\(822\) | 6.10791e17 | + | 8.64143e16i | 0.0690599 | + | 0.00977055i | ||||
\(823\) | 1.35115e19 | 1.51567 | 0.757835 | − | 0.652446i | \(-0.226257\pi\) | ||||
0.757835 | + | 0.652446i | \(0.226257\pi\) | |||||||
\(824\) | 4.30880e18 | − | 9.60627e18i | 0.479545 | − | 1.06912i | ||||
\(825\) | 3.91696e17 | 0.0432512 | ||||||||
\(826\) | 1.03603e19 | + | 1.46577e18i | 1.13502 | + | 0.160581i | ||||
\(827\) | − | 3.80345e18i | − | 0.413420i | −0.978402 | − | 0.206710i | \(-0.933724\pi\) | ||
0.978402 | − | 0.206710i | \(-0.0662757\pi\) | |||||||
\(828\) | 1.52464e19 | + | 4.40221e18i | 1.64426 | + | 0.474759i | ||||
\(829\) | 1.29267e19i | 1.38319i | 0.722284 | + | 0.691597i | \(0.243093\pi\) | ||||
−0.722284 | + | 0.691597i | \(0.756907\pi\) | |||||||
\(830\) | −2.63832e18 | + | 1.86481e19i | −0.280104 | + | 1.97982i | ||||
\(831\) | 8.09754e17 | 0.0852995 | ||||||||
\(832\) | 4.82565e18 | − | 4.29703e18i | 0.504376 | − | 0.449125i | ||||
\(833\) | 4.27882e18 | 0.443743 | ||||||||
\(834\) | −1.08320e17 | + | 7.65624e17i | −0.0111463 | + | 0.0787837i | ||||
\(835\) | 5.88846e18i | 0.601229i | ||||||||
\(836\) | −2.16251e18 | − | 6.24399e17i | −0.219087 | − | 0.0632589i | ||||
\(837\) | 4.45172e17i | 0.0447520i | ||||||||
\(838\) | −7.64617e18 | − | 1.08177e18i | −0.762707 | − | 0.107907i | ||||
\(839\) | 4.18489e18 | 0.414220 | 0.207110 | − | 0.978318i | \(-0.433594\pi\) | ||||
0.207110 | + | 0.978318i | \(0.433594\pi\) | |||||||
\(840\) | −2.98968e17 | + | 6.66536e17i | −0.0293636 | + | 0.0654648i | ||||
\(841\) | −6.06532e18 | −0.591125 | ||||||||
\(842\) | −7.67041e18 | − | 1.08520e18i | −0.741806 | − | 0.104950i | ||||
\(843\) | 6.69054e17i | 0.0642070i | ||||||||
\(844\) | 2.51435e18 | − | 8.70806e18i | 0.239442 | − | 0.829270i | ||||
\(845\) | 7.50049e18i | 0.708796i | ||||||||
\(846\) | 1.22713e18 | − | 8.67358e18i | 0.115076 | − | 0.813376i | ||||
\(847\) | −1.63267e18 | −0.151934 | ||||||||
\(848\) | −8.03587e18 | + | 1.27554e19i | −0.742096 | + | 1.17793i | ||||
\(849\) | 5.02658e17 | 0.0460652 | ||||||||
\(850\) | 1.32621e18 | − | 9.37389e18i | 0.120612 | − | 0.852505i | ||||
\(851\) | − | 4.99341e18i | − | 0.450666i | ||||||
\(852\) | 3.02976e17 | − | 1.04931e18i | 0.0271363 | − | 0.0939825i | ||||
\(853\) | − | 5.09953e18i | − | 0.453275i | −0.973979 | − | 0.226637i | \(-0.927227\pi\) | ||
0.973979 | − | 0.226637i | \(-0.0727732\pi\) | |||||||
\(854\) | 1.02290e18 | + | 1.44719e17i | 0.0902311 | + | 0.0127658i | ||||
\(855\) | 3.75374e18 | 0.328613 | ||||||||
\(856\) | 1.13973e18 | + | 5.11217e17i | 0.0990203 | + | 0.0444146i | ||||
\(857\) | 8.40331e18 | 0.724562 | 0.362281 | − | 0.932069i | \(-0.381998\pi\) | ||||
0.362281 | + | 0.932069i | \(0.381998\pi\) | |||||||
\(858\) | −4.84002e17 | − | 6.84762e16i | −0.0414171 | − | 0.00585966i | ||||
\(859\) | − | 2.21269e19i | − | 1.87917i | −0.342317 | − | 0.939584i | \(-0.611212\pi\) | ||
0.342317 | − | 0.939584i | \(-0.388788\pi\) | |||||||
\(860\) | −2.74608e19 | − | 7.92899e18i | −2.31459 | − | 0.668310i | ||||
\(861\) | − | 9.15922e17i | − | 0.0766193i | ||||||
\(862\) | −2.72738e18 | + | 1.92776e19i | −0.226438 | + | 1.60050i | ||||
\(863\) | −6.01097e18 | −0.495307 | −0.247653 | − | 0.968849i | \(-0.579659\pi\) | ||||
−0.247653 | + | 0.968849i | \(0.579659\pi\) | |||||||
\(864\) | 1.28112e18 | + | 1.08507e18i | 0.104773 | + | 0.0887399i | ||||
\(865\) | 2.20596e18 | 0.179057 | ||||||||
\(866\) | −7.71508e17 | + | 5.45316e18i | −0.0621548 | + | 0.439321i | ||||
\(867\) | 4.47693e17i | 0.0357978i | ||||||||
\(868\) | 3.15678e18 | + | 9.11484e17i | 0.250534 | + | 0.0723387i | ||||
\(869\) | 3.13425e17i | 0.0246891i | ||||||||
\(870\) | −1.43256e18 | − | 2.02678e17i | −0.112005 | − | 0.0158464i | ||||
\(871\) | −1.04947e19 | −0.814428 | ||||||||
\(872\) | −8.09202e17 | − | 3.62960e17i | −0.0623304 | − | 0.0279577i | ||||
\(873\) | −5.27827e18 | −0.403551 | ||||||||
\(874\) | 5.68430e18 | + | 8.04211e17i | 0.431373 | + | 0.0610303i | ||||
\(875\) | − | 4.17585e18i | − | 0.314552i | ||||||
\(876\) | 1.58205e17 | − | 5.47920e17i | 0.0118289 | − | 0.0409676i | ||||
\(877\) | − | 1.14586e19i | − | 0.850421i | −0.905094 | − | 0.425211i | \(-0.860200\pi\) | ||
0.905094 | − | 0.425211i | \(-0.139800\pi\) | |||||||
\(878\) | 2.54968e18 | − | 1.80216e19i | 0.187833 | − | 1.32763i | ||||
\(879\) | −1.23262e18 | −0.0901370 | ||||||||
\(880\) | −1.36720e19 | − | 8.61335e18i | −0.992418 | − | 0.625222i | ||||
\(881\) | 2.52139e19 | 1.81676 | 0.908378 | − | 0.418149i | \(-0.137321\pi\) | ||||
0.908378 | + | 0.418149i | \(0.137321\pi\) | |||||||
\(882\) | −7.01543e17 | + | 4.95863e18i | −0.0501774 | + | 0.354663i | ||||
\(883\) | 8.81682e18i | 0.625990i | 0.949755 | + | 0.312995i | \(0.101332\pi\) | ||||
−0.949755 | + | 0.312995i | \(0.898668\pi\) | |||||||
\(884\) | −3.27748e18 | + | 1.13511e19i | −0.230994 | + | 0.800013i | ||||
\(885\) | 1.83655e18i | 0.128490i | ||||||||
\(886\) | −6.81326e18 | − | 9.63935e17i | −0.473190 | − | 0.0669466i | ||||
\(887\) | 2.63061e19 | 1.81365 | 0.906823 | − | 0.421512i | \(-0.138501\pi\) | ||||
0.906823 | + | 0.421512i | \(0.138501\pi\) | |||||||
\(888\) | 1.07844e17 | − | 2.40434e17i | 0.00738096 | − | 0.0164555i | ||||
\(889\) | −5.75113e17 | −0.0390743 | ||||||||
\(890\) | −2.11100e19 | − | 2.98663e18i | −1.42381 | − | 0.201440i | ||||
\(891\) | 1.32516e19i | 0.887288i | ||||||||
\(892\) | 5.09498e18 | + | 1.47111e18i | 0.338666 | + | 0.0977856i | ||||
\(893\) | − | 3.16904e18i | − | 0.209119i | ||||||
\(894\) | 1.61265e17 | − | 1.13985e18i | 0.0105644 | − | 0.0746712i | ||||
\(895\) | 6.15199e18 | 0.400098 | ||||||||
\(896\) | 1.03175e19 | − | 6.86297e18i | 0.666150 | − | 0.443108i | ||||
\(897\) | 1.24677e18 | 0.0799160 | ||||||||
\(898\) | 1.11267e18 | − | 7.86458e18i | 0.0708063 | − | 0.500471i | ||||
\(899\) | 6.50760e18i | 0.411134i | ||||||||
\(900\) | 1.06457e19 | + | 3.07383e18i | 0.667727 | + | 0.192798i | ||||
\(901\) | − | 2.75655e19i | − | 1.71654i | ||||||
\(902\) | 2.00604e19 | + | 2.83814e18i | 1.24022 | + | 0.175465i | ||||
\(903\) | −1.65817e18 | −0.101779 | ||||||||
\(904\) | −3.15977e18 | + | 7.04457e18i | −0.192558 | + | 0.429299i | ||||
\(905\) | −1.08285e19 | −0.655165 | ||||||||
\(906\) | 4.18642e16 | + | 5.92292e15i | 0.00251483 | + | 0.000355797i | ||||
\(907\) | 1.16508e19i | 0.694877i | 0.937703 | + | 0.347439i | \(0.112948\pi\) | ||||
−0.937703 | + | 0.347439i | \(0.887052\pi\) | |||||||
\(908\) | −4.72191e18 | + | 1.63536e19i | −0.279615 | + | 0.968403i | ||||
\(909\) | 1.66534e19i | 0.979124i | ||||||||
\(910\) | 1.68976e18 | − | 1.19435e19i | 0.0986407 | − | 0.697209i | ||||
\(911\) | 6.57470e18 | 0.381071 | 0.190536 | − | 0.981680i | \(-0.438977\pi\) | ||||
0.190536 | + | 0.981680i | \(0.438977\pi\) | |||||||
\(912\) | 2.56331e17 | + | 1.61489e17i | 0.0147515 | + | 0.00929341i | ||||
\(913\) | −2.41685e19 | −1.38099 | ||||||||
\(914\) | −1.03928e18 | + | 7.34584e18i | −0.0589636 | + | 0.416765i | ||||
\(915\) | 1.81327e17i | 0.0102147i | ||||||||
\(916\) | −4.81322e18 | + | 1.66698e19i | −0.269225 | + | 0.932419i | ||||
\(917\) | 7.34241e18i | 0.407791i | ||||||||
\(918\) | −3.03953e18 | − | 4.30030e17i | −0.167621 | − | 0.0237149i | ||||
\(919\) | −7.15001e18 | −0.391522 | −0.195761 | − | 0.980652i | \(-0.562718\pi\) | ||||
−0.195761 | + | 0.980652i | \(0.562718\pi\) | |||||||
\(920\) | 3.76048e19 | + | 1.68673e19i | 2.04467 | + | 0.917115i | ||||
\(921\) | −7.88711e17 | −0.0425824 | ||||||||
\(922\) | −1.20624e19 | − | 1.70658e18i | −0.646670 | − | 0.0914904i | ||||
\(923\) | 1.80343e19i | 0.960038i | ||||||||
\(924\) | −9.00644e17 | − | 2.60050e17i | −0.0476086 | − | 0.0137464i | ||||
\(925\) | − | 3.48663e18i | − | 0.183014i | ||||||
\(926\) | 1.82828e18 | − | 1.29226e19i | 0.0952950 | − | 0.673562i | ||||
\(927\) | −2.25315e19 | −1.16620 | ||||||||
\(928\) | 1.87277e19 | + | 1.58618e19i | 0.962547 | + | 0.815248i | ||||
\(929\) | −1.97713e19 | −1.00910 | −0.504550 | − | 0.863383i | \(-0.668342\pi\) | ||||
−0.504550 | + | 0.863383i | \(0.668342\pi\) | |||||||
\(930\) | −8.07883e16 | + | 5.71026e17i | −0.00409458 | + | 0.0289412i | ||||
\(931\) | 1.81172e18i | 0.0911838i | ||||||||
\(932\) | −2.72277e19 | − | 7.86168e18i | −1.36084 | − | 0.392927i | ||||
\(933\) | 1.29195e18i | 0.0641233i | ||||||||
\(934\) | 2.98294e19 | + | 4.22024e18i | 1.47025 | + | 0.208009i | ||||
\(935\) | 2.95464e19 | 1.44620 | ||||||||
\(936\) | −1.26171e19 | − | 5.65928e18i | −0.613291 | − | 0.275086i | ||||
\(937\) | 2.48380e19 | 1.19897 | 0.599487 | − | 0.800384i | \(-0.295371\pi\) | ||||
0.599487 | + | 0.800384i | \(0.295371\pi\) | |||||||
\(938\) | −1.99277e19 | − | 2.81936e18i | −0.955300 | − | 0.135155i | ||||
\(939\) | 8.68024e17i | 0.0413243i | ||||||||
\(940\) | 6.31119e18 | − | 2.18579e19i | 0.298387 | − | 1.03342i | ||||
\(941\) | − | 3.79177e19i | − | 1.78036i | −0.455605 | − | 0.890182i | \(-0.650577\pi\) | ||
0.455605 | − | 0.890182i | \(-0.349423\pi\) | |||||||
\(942\) | 1.64775e17 | − | 1.16466e18i | 0.00768353 | − | 0.0543085i | ||||
\(943\) | −5.16747e19 | −2.39305 | ||||||||
\(944\) | 1.66057e19 | − | 2.63583e19i | 0.763728 | − | 1.21227i | ||||
\(945\) | 3.13416e18 | 0.143158 | ||||||||
\(946\) | 5.13812e18 | − | 3.63171e19i | 0.233083 | − | 1.64747i | ||||
\(947\) | 3.17492e18i | 0.143040i | 0.997439 | + | 0.0715200i | \(0.0227850\pi\) | ||||
−0.997439 | + | 0.0715200i | \(0.977215\pi\) | |||||||
\(948\) | 1.17027e16 | − | 4.05306e16i | 0.000523640 | − | 0.00181355i | ||||
\(949\) | 9.41699e18i | 0.418487i | ||||||||
\(950\) | 3.96904e18 | + | 5.61538e17i | 0.175179 | + | 0.0247842i | ||||
\(951\) | 1.93187e18 | 0.0846848 | ||||||||
\(952\) | −9.27282e18 | + | 2.06733e19i | −0.403712 | + | 0.900057i | ||||
\(953\) | −8.65721e17 | −0.0374347 | −0.0187173 | − | 0.999825i | \(-0.505958\pi\) | ||||
−0.0187173 | + | 0.999825i | \(0.505958\pi\) | |||||||
\(954\) | 3.19449e19 | + | 4.51955e18i | 1.37195 | + | 0.194102i | ||||
\(955\) | 1.12057e19i | 0.477990i | ||||||||
\(956\) | −6.04124e18 | − | 1.74434e18i | −0.255947 | − | 0.0739016i | ||||
\(957\) | − | 1.85665e18i | − | 0.0781271i | ||||||
\(958\) | 2.10153e18 | − | 1.48540e19i | 0.0878334 | − | 0.620821i | ||||
\(959\) | −1.95341e19 | −0.810911 | ||||||||
\(960\) | 1.44639e18 | + | 1.62432e18i | 0.0596379 | + | 0.0669745i | ||||
\(961\) | −2.18236e19 | −0.893766 | ||||||||
\(962\) | −6.09533e17 | + | 4.30828e18i | −0.0247947 | + | 0.175253i | ||||
\(963\) | − | 2.67325e18i | − | 0.108011i | ||||||
\(964\) | −2.63188e18 | − | 7.59925e17i | −0.105625 | − | 0.0304979i | ||||
\(965\) | − | 5.78667e18i | − | 0.230675i | ||||||
\(966\) | 2.36740e18 | + | 3.34938e17i | 0.0937391 | + | 0.0132621i | ||||
\(967\) | 3.62918e19 | 1.42737 | 0.713685 | − | 0.700467i | \(-0.247025\pi\) | ||||
0.713685 | + | 0.700467i | \(0.247025\pi\) | |||||||
\(968\) | −1.98938e18 | + | 4.43523e18i | −0.0777190 | + | 0.173271i | ||||
\(969\) | −5.53954e17 | −0.0214966 | ||||||||
\(970\) | −1.35732e19 | − | 1.92032e18i | −0.523197 | − | 0.0740216i | ||||
\(971\) | − | 1.43624e19i | − | 0.549923i | −0.961455 | − | 0.274962i | \(-0.911335\pi\) | ||
0.961455 | − | 0.274962i | \(-0.0886652\pi\) | |||||||
\(972\) | 1.49624e18 | − | 5.18199e18i | 0.0569076 | − | 0.197091i | ||||
\(973\) | − | 2.44859e19i | − | 0.925088i | ||||||
\(974\) | −5.24112e18 | + | 3.70451e19i | −0.196694 | + | 1.39027i | ||||
\(975\) | 8.70550e17 | 0.0324537 | ||||||||
\(976\) | 1.63952e18 | − | 2.60242e18i | 0.0607146 | − | 0.0963725i | ||||
\(977\) | 3.27934e19 | 1.20635 | 0.603173 | − | 0.797610i | \(-0.293903\pi\) | ||||
0.603173 | + | 0.797610i | \(0.293903\pi\) | |||||||
\(978\) | −3.55276e17 | + | 2.51116e18i | −0.0129827 | + | 0.0917637i | ||||
\(979\) | − | 2.73592e19i | − | 0.993154i | ||||||
\(980\) | −3.60807e18 | + | 1.24960e19i | −0.130108 | + | 0.450610i | ||||
\(981\) | 1.89798e18i | 0.0679898i | ||||||||
\(982\) | −2.16089e19 | − | 3.05722e18i | −0.768969 | − | 0.108793i | ||||
\(983\) | 2.04182e19 | 0.721806 | 0.360903 | − | 0.932603i | \(-0.382469\pi\) | ||||
0.360903 | + | 0.932603i | \(0.382469\pi\) | |||||||
\(984\) | −2.48815e18 | − | 1.11604e18i | −0.0873793 | − | 0.0391931i | ||||
\(985\) | −1.96650e19 | −0.686055 | ||||||||
\(986\) | −4.44324e19 | − | 6.28626e18i | −1.53993 | − | 0.217868i | ||||
\(987\) | − | 1.31984e18i | − | 0.0454424i | ||||||
\(988\) | −4.80621e18 | − | 1.38774e18i | −0.164393 | − | 0.0474665i | ||||
\(989\) | 9.35511e19i | 3.17887i | ||||||||
\(990\) | −4.84433e18 | + | 3.42406e19i | −0.163533 | + | 1.15588i | ||||
\(991\) | 3.13618e18 | 0.105177 | 0.0525887 | − | 0.998616i | \(-0.483253\pi\) | ||||
0.0525887 | + | 0.998616i | \(0.483253\pi\) | |||||||
\(992\) | 6.32258e18 | − | 7.46494e18i | 0.210653 | − | 0.248714i | ||||
\(993\) | −2.37442e18 | −0.0785936 | ||||||||
\(994\) | −4.84484e18 | + | 3.42442e19i | −0.159319 | + | 1.12610i | ||||
\(995\) | − | 5.30280e19i | − | 1.73243i | ||||||
\(996\) | 3.12536e18 | + | 9.02410e17i | 0.101441 | + | 0.0292899i | ||||
\(997\) | 3.08455e19i | 0.994658i | 0.867562 | + | 0.497329i | \(0.165686\pi\) | ||||
−0.867562 | + | 0.497329i | \(0.834314\pi\) | |||||||
\(998\) | 2.34676e19 | + | 3.32018e18i | 0.751832 | + | 0.106369i | ||||
\(999\) | −1.13056e18 | −0.0359847 |
(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 | 8.14.b.b.5.5 | ✓ | 10 | |
3.2 | odd | 2 | 72.14.d.c.37.6 | 10 | |||
4.3 | odd | 2 | 32.14.b.b.17.5 | 10 | |||
8.3 | odd | 2 | 32.14.b.b.17.6 | 10 | |||
8.5 | even | 2 | inner | 8.14.b.b.5.6 | yes | 10 | |
24.5 | odd | 2 | 72.14.d.c.37.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.14.b.b.5.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
8.14.b.b.5.6 | yes | 10 | 8.5 | even | 2 | inner | |
32.14.b.b.17.5 | 10 | 4.3 | odd | 2 | |||
32.14.b.b.17.6 | 10 | 8.3 | odd | 2 | |||
72.14.d.c.37.5 | 10 | 24.5 | odd | 2 | |||
72.14.d.c.37.6 | 10 | 3.2 | odd | 2 |