Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,27,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 27, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 27);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 27 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.4146460365\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.3 | ||
Character | \(\chi\) | \(=\) | 5.3 |
Dual form | 5.27.c.a.2.3 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8964.00 | + | 8964.00i | −1.09424 | + | 1.09424i | −0.0991676 | + | 0.995071i | \(0.531618\pi\) |
−0.995071 | + | 0.0991676i | \(0.968382\pi\) | |||||||
\(3\) | −84346.8 | − | 84346.8i | −0.0529045 | − | 0.0529045i | 0.680160 | − | 0.733064i | \(-0.261910\pi\) |
−0.733064 | + | 0.680160i | \(0.761910\pi\) | |||||||
\(4\) | − | 9.35978e7i | − | 1.39472i | ||||||
\(5\) | −6.90551e8 | + | 1.00661e9i | −0.565700 | + | 0.824611i | ||||
\(6\) | 1.51217e9 | 0.115780 | ||||||||
\(7\) | −8.97185e10 | + | 8.97185e10i | −0.925993 | + | 0.925993i | −0.997444 | − | 0.0714511i | \(-0.977237\pi\) |
0.0714511 | + | 0.997444i | \(0.477237\pi\) | |||||||
\(8\) | 2.37446e11 | + | 2.37446e11i | 0.431912 | + | 0.431912i | ||||
\(9\) | − | 2.52764e12i | − | 0.994402i | ||||||
\(10\) | −2.83311e12 | − | 1.52133e13i | −0.283311 | − | 1.52133i | ||||
\(11\) | −9.83010e12 | −0.284743 | −0.142371 | − | 0.989813i | \(-0.545473\pi\) | ||||
−0.142371 | + | 0.989813i | \(0.545473\pi\) | |||||||
\(12\) | −7.89467e12 | + | 7.89467e12i | −0.0737867 | + | 0.0737867i | ||||
\(13\) | −2.69524e14 | − | 2.69524e14i | −0.889886 | − | 0.889886i | 0.104626 | − | 0.994512i | \(-0.466635\pi\) |
−0.994512 | + | 0.104626i | \(0.966635\pi\) | |||||||
\(14\) | − | 1.60847e15i | − | 2.02651i | ||||||
\(15\) | 1.43150e14 | − | 2.66582e13i | 0.0735537 | − | 0.0136976i | ||||
\(16\) | 2.02430e15 | 0.449485 | ||||||||
\(17\) | −8.05943e15 | + | 8.05943e15i | −0.813708 | + | 0.813708i | −0.985188 | − | 0.171480i | \(-0.945145\pi\) |
0.171480 | + | 0.985188i | \(0.445145\pi\) | |||||||
\(18\) | 2.26577e16 | + | 2.26577e16i | 1.08811 | + | 1.08811i | ||||
\(19\) | 1.22289e15i | 0.0290796i | 0.999894 | + | 0.0145398i | \(0.00462833\pi\) | ||||
−0.999894 | + | 0.0145398i | \(0.995372\pi\) | |||||||
\(20\) | 9.42160e16 | + | 6.46340e16i | 1.15010 | + | 0.788990i | ||||
\(21\) | 1.51349e16 | 0.0979783 | ||||||||
\(22\) | 8.81170e16 | − | 8.81170e16i | 0.311577 | − | 0.311577i | ||||
\(23\) | 2.54183e17 | + | 2.54183e17i | 0.504296 | + | 0.504296i | 0.912770 | − | 0.408474i | \(-0.133939\pi\) |
−0.408474 | + | 0.912770i | \(0.633939\pi\) | |||||||
\(24\) | − | 4.00557e16i | − | 0.0457002i | ||||||
\(25\) | −5.36394e17 | − | 1.39023e18i | −0.359968 | − | 0.932965i | ||||
\(26\) | 4.83203e18 | 1.94749 | ||||||||
\(27\) | −4.27596e17 | + | 4.27596e17i | −0.105513 | + | 0.105513i | ||||
\(28\) | 8.39745e18 | + | 8.39745e18i | 1.29150 | + | 1.29150i | ||||
\(29\) | 9.37717e18i | 0.913898i | 0.889493 | + | 0.456949i | \(0.151058\pi\) | ||||
−0.889493 | + | 0.456949i | \(0.848942\pi\) | |||||||
\(30\) | −1.04423e18 | + | 1.52216e18i | −0.0654968 | + | 0.0954737i | ||||
\(31\) | 3.37841e19 | 1.38360 | 0.691800 | − | 0.722090i | \(-0.256818\pi\) | ||||
0.691800 | + | 0.722090i | \(0.256818\pi\) | |||||||
\(32\) | −3.40806e19 | + | 3.40806e19i | −0.923756 | + | 0.923756i | ||||
\(33\) | 8.29138e17 | + | 8.29138e17i | 0.0150642 | + | 0.0150642i | ||||
\(34\) | − | 1.44489e20i | − | 1.78078i | ||||||
\(35\) | −2.83559e19 | − | 1.52266e20i | −0.239750 | − | 1.28742i | ||||
\(36\) | −2.36581e20 | −1.38691 | ||||||||
\(37\) | −1.40139e20 | + | 1.40139e20i | −0.575358 | + | 0.575358i | −0.933621 | − | 0.358263i | \(-0.883369\pi\) |
0.358263 | + | 0.933621i | \(0.383369\pi\) | |||||||
\(38\) | −1.09619e19 | − | 1.09619e19i | −0.0318201 | − | 0.0318201i | ||||
\(39\) | 4.54670e19i | 0.0941579i | ||||||||
\(40\) | −4.02984e20 | + | 7.50460e19i | −0.600493 | + | 0.111827i | ||||
\(41\) | 5.50191e20 | 0.594735 | 0.297368 | − | 0.954763i | \(-0.403891\pi\) | ||||
0.297368 | + | 0.954763i | \(0.403891\pi\) | |||||||
\(42\) | −1.35670e20 | + | 1.35670e20i | −0.107212 | + | 0.107212i | ||||
\(43\) | −2.83578e20 | − | 2.83578e20i | −0.165037 | − | 0.165037i | 0.619757 | − | 0.784794i | \(-0.287231\pi\) |
−0.784794 | + | 0.619757i | \(0.787231\pi\) | |||||||
\(44\) | 9.20075e20i | 0.397135i | ||||||||
\(45\) | 2.54433e21 | + | 1.74546e21i | 0.819995 | + | 0.562533i | ||||
\(46\) | −4.55700e21 | −1.10364 | ||||||||
\(47\) | 6.66549e21 | − | 6.66549e21i | 1.22056 | − | 1.22056i | 0.253129 | − | 0.967432i | \(-0.418540\pi\) |
0.967432 | − | 0.253129i | \(-0.0814598\pi\) | |||||||
\(48\) | −1.70743e20 | − | 1.70743e20i | −0.0237798 | − | 0.0237798i | ||||
\(49\) | − | 6.71135e21i | − | 0.714926i | ||||||
\(50\) | 1.72702e22 | + | 7.65375e21i | 1.41478 | + | 0.626995i | ||||
\(51\) | 1.35957e21 | 0.0860975 | ||||||||
\(52\) | −2.52269e22 | + | 2.52269e22i | −1.24114 | + | 1.24114i | ||||
\(53\) | 3.12389e22 | + | 3.12389e22i | 1.19980 | + | 1.19980i | 0.974226 | + | 0.225576i | \(0.0724265\pi\) |
0.225576 | + | 0.974226i | \(0.427574\pi\) | |||||||
\(54\) | − | 7.66595e21i | − | 0.230912i | ||||||
\(55\) | 6.78819e21 | − | 9.89503e21i | 0.161079 | − | 0.234802i | ||||
\(56\) | −4.26067e22 | −0.799896 | ||||||||
\(57\) | 1.03147e20 | − | 1.03147e20i | 0.00153844 | − | 0.00153844i | ||||
\(58\) | −8.40570e22 | − | 8.40570e22i | −1.00002 | − | 1.00002i | ||||
\(59\) | − | 2.03375e23i | − | 1.93741i | −0.248214 | − | 0.968705i | \(-0.579844\pi\) | ||
0.248214 | − | 0.968705i | \(-0.420156\pi\) | |||||||
\(60\) | −2.49515e21 | − | 1.33985e22i | −0.0191042 | − | 0.102586i | ||||
\(61\) | −1.20939e23 | −0.746927 | −0.373464 | − | 0.927645i | \(-0.621830\pi\) | ||||
−0.373464 | + | 0.927645i | \(0.621830\pi\) | |||||||
\(62\) | −3.02841e23 | + | 3.02841e23i | −1.51399 | + | 1.51399i | ||||
\(63\) | 2.26776e23 | + | 2.26776e23i | 0.920810 | + | 0.920810i | ||||
\(64\) | − | 4.75148e23i | − | 1.57213i | ||||||
\(65\) | 4.57425e23 | − | 8.51843e22i | 1.23722 | − | 0.230402i | ||||
\(66\) | −1.48648e22 | −0.0329676 | ||||||||
\(67\) | −3.15073e23 | + | 3.15073e23i | −0.574698 | + | 0.574698i | −0.933438 | − | 0.358740i | \(-0.883206\pi\) |
0.358740 | + | 0.933438i | \(0.383206\pi\) | |||||||
\(68\) | 7.54345e23 | + | 7.54345e23i | 1.13489 | + | 1.13489i | ||||
\(69\) | − | 4.28791e22i | − | 0.0533590i | ||||||
\(70\) | 1.61910e24 | + | 1.11073e24i | 1.67109 | + | 1.14640i | ||||
\(71\) | −1.27673e24 | −1.09583 | −0.547914 | − | 0.836535i | \(-0.684578\pi\) | ||||
−0.547914 | + | 0.836535i | \(0.684578\pi\) | |||||||
\(72\) | 6.00178e23 | − | 6.00178e23i | 0.429495 | − | 0.429495i | ||||
\(73\) | −9.38292e23 | − | 9.38292e23i | −0.561230 | − | 0.561230i | 0.368427 | − | 0.929657i | \(-0.379897\pi\) |
−0.929657 | + | 0.368427i | \(0.879897\pi\) | |||||||
\(74\) | − | 2.51242e24i | − | 1.25916i | ||||||
\(75\) | −7.20180e22 | + | 1.62504e23i | −0.0303141 | + | 0.0684019i | ||||
\(76\) | 1.14459e23 | 0.0405578 | ||||||||
\(77\) | 8.81942e23 | − | 8.81942e23i | 0.263670 | − | 0.263670i | ||||
\(78\) | −4.07566e23 | − | 4.07566e23i | −0.103031 | − | 0.103031i | ||||
\(79\) | 2.70121e24i | 0.578637i | 0.957233 | + | 0.289319i | \(0.0934287\pi\) | ||||
−0.957233 | + | 0.289319i | \(0.906571\pi\) | |||||||
\(80\) | −1.39788e24 | + | 2.03767e24i | −0.254273 | + | 0.370650i | ||||
\(81\) | −6.35278e24 | −0.983238 | ||||||||
\(82\) | −4.93192e24 | + | 4.93192e24i | −0.650782 | + | 0.650782i | ||||
\(83\) | 3.59611e24 | + | 3.59611e24i | 0.405338 | + | 0.405338i | 0.880109 | − | 0.474771i | \(-0.157469\pi\) |
−0.474771 | + | 0.880109i | \(0.657469\pi\) | |||||||
\(84\) | − | 1.41660e24i | − | 0.136652i | ||||||
\(85\) | −2.54722e24 | − | 1.36781e25i | −0.210678 | − | 1.13131i | ||||
\(86\) | 5.08398e24 | 0.361180 | ||||||||
\(87\) | 7.90935e23 | − | 7.90935e23i | 0.0483493 | − | 0.0483493i | ||||
\(88\) | −2.33412e24 | − | 2.33412e24i | −0.122984 | − | 0.122984i | ||||
\(89\) | − | 1.92808e25i | − | 0.877114i | −0.898703 | − | 0.438557i | \(-0.855490\pi\) | ||
0.898703 | − | 0.438557i | \(-0.144510\pi\) | |||||||
\(90\) | −3.84537e25 | + | 7.16108e24i | −1.51282 | + | 0.281725i | ||||
\(91\) | 4.83626e25 | 1.64806 | ||||||||
\(92\) | 2.37910e25 | − | 2.37910e25i | 0.703349 | − | 0.703349i | ||||
\(93\) | −2.84958e24 | − | 2.84958e24i | −0.0731986 | − | 0.0731986i | ||||
\(94\) | 1.19499e26i | 2.67117i | ||||||||
\(95\) | −1.23096e24 | − | 8.44465e23i | −0.0239794 | − | 0.0164503i | ||||
\(96\) | 5.74918e24 | 0.0977416 | ||||||||
\(97\) | 7.59970e25 | − | 7.59970e25i | 1.12918 | − | 1.12918i | 0.138872 | − | 0.990310i | \(-0.455652\pi\) |
0.990310 | − | 0.138872i | \(-0.0443476\pi\) | |||||||
\(98\) | 6.01606e25 | + | 6.01606e25i | 0.782300 | + | 0.782300i | ||||
\(99\) | 2.48469e25i | 0.283149i | ||||||||
\(100\) | −1.30122e26 | + | 5.02053e25i | −1.30122 | + | 0.502053i | ||||
\(101\) | 7.94753e25 | 0.698319 | 0.349160 | − | 0.937063i | \(-0.386467\pi\) | ||||
0.349160 | + | 0.937063i | \(0.386467\pi\) | |||||||
\(102\) | −1.21872e25 | + | 1.21872e25i | −0.0942112 | + | 0.0942112i | ||||
\(103\) | −1.31492e26 | − | 1.31492e26i | −0.895396 | − | 0.895396i | 0.0996284 | − | 0.995025i | \(-0.468235\pi\) |
−0.995025 | + | 0.0996284i | \(0.968235\pi\) | |||||||
\(104\) | − | 1.27995e26i | − | 0.768706i | ||||||
\(105\) | −1.04515e25 | + | 1.52349e25i | −0.0554263 | + | 0.0807941i | ||||
\(106\) | −5.60051e26 | −2.62574 | ||||||||
\(107\) | 2.17748e26 | − | 2.17748e26i | 0.903577 | − | 0.903577i | −0.0921667 | − | 0.995744i | \(-0.529379\pi\) |
0.995744 | + | 0.0921667i | \(0.0293793\pi\) | |||||||
\(108\) | 4.00221e25 | + | 4.00221e25i | 0.147160 | + | 0.147160i | ||||
\(109\) | − | 3.29008e26i | − | 1.07315i | −0.843852 | − | 0.536577i | \(-0.819717\pi\) | ||
0.843852 | − | 0.536577i | \(-0.180283\pi\) | |||||||
\(110\) | 2.78498e25 | + | 1.49548e26i | 0.0806709 | + | 0.433188i | ||||
\(111\) | 2.36406e25 | 0.0608780 | ||||||||
\(112\) | −1.81617e26 | + | 1.81617e26i | −0.416220 | + | 0.416220i | ||||
\(113\) | 3.52291e26 | + | 3.52291e26i | 0.719253 | + | 0.719253i | 0.968452 | − | 0.249199i | \(-0.0801675\pi\) |
−0.249199 | + | 0.968452i | \(0.580167\pi\) | |||||||
\(114\) | 1.84921e24i | 0.00336685i | ||||||||
\(115\) | −4.31389e26 | + | 8.03358e25i | −0.701128 | + | 0.130568i | ||||
\(116\) | 8.77682e26 | 1.27463 | ||||||||
\(117\) | −6.81259e26 | + | 6.81259e26i | −0.884904 | + | 0.884904i | ||||
\(118\) | 1.82305e27 | + | 1.82305e27i | 2.11999 | + | 2.11999i | ||||
\(119\) | − | 1.44616e27i | − | 1.50698i | ||||||
\(120\) | 4.03203e25 | + | 2.76605e25i | 0.0376849 | + | 0.0258526i | ||||
\(121\) | −1.09519e27 | −0.918921 | ||||||||
\(122\) | 1.08410e27 | − | 1.08410e27i | 0.817316 | − | 0.817316i | ||||
\(123\) | −4.64069e25 | − | 4.64069e25i | −0.0314642 | − | 0.0314642i | ||||
\(124\) | − | 3.16212e27i | − | 1.92973i | ||||||
\(125\) | 1.76982e27 | + | 4.20085e26i | 0.972967 | + | 0.230944i | ||||
\(126\) | −4.06564e27 | −2.01517 | ||||||||
\(127\) | 6.25503e25 | − | 6.25503e25i | 0.0279757 | − | 0.0279757i | −0.692981 | − | 0.720956i | \(-0.743703\pi\) |
0.720956 | + | 0.692981i | \(0.243703\pi\) | |||||||
\(128\) | 1.97212e27 | + | 1.97212e27i | 0.796533 | + | 0.796533i | ||||
\(129\) | 4.78377e25i | 0.0174624i | ||||||||
\(130\) | −3.33677e27 | + | 4.86395e27i | −1.10170 | + | 1.60593i | ||||
\(131\) | 3.29287e26 | 0.0984119 | 0.0492059 | − | 0.998789i | \(-0.484331\pi\) | ||||
0.0492059 | + | 0.998789i | \(0.484331\pi\) | |||||||
\(132\) | 7.76054e25 | − | 7.76054e25i | 0.0210102 | − | 0.0210102i | ||||
\(133\) | −1.09716e26 | − | 1.09716e26i | −0.0269275 | − | 0.0269275i | ||||
\(134\) | − | 5.64864e27i | − | 1.25771i | ||||||
\(135\) | −1.35144e26 | − | 7.25698e26i | −0.0273185 | − | 0.146696i | ||||
\(136\) | −3.82737e27 | −0.702901 | ||||||||
\(137\) | 4.19917e27 | − | 4.19917e27i | 0.701126 | − | 0.701126i | −0.263526 | − | 0.964652i | \(-0.584886\pi\) |
0.964652 | + | 0.263526i | \(0.0848856\pi\) | |||||||
\(138\) | 3.84368e26 | + | 3.84368e26i | 0.0583875 | + | 0.0583875i | ||||
\(139\) | 9.48817e27i | 1.31217i | 0.754687 | + | 0.656085i | \(0.227789\pi\) | ||||
−0.754687 | + | 0.656085i | \(0.772211\pi\) | |||||||
\(140\) | −1.42518e28 | + | 2.65405e27i | −1.79558 | + | 0.334384i | ||||
\(141\) | −1.12443e27 | −0.129146 | ||||||||
\(142\) | 1.14447e28 | − | 1.14447e28i | 1.19910 | − | 1.19910i | ||||
\(143\) | 2.64945e27 | + | 2.64945e27i | 0.253389 | + | 0.253389i | ||||
\(144\) | − | 5.11669e27i | − | 0.446969i | ||||||
\(145\) | −9.43912e27 | − | 6.47542e27i | −0.753611 | − | 0.516992i | ||||
\(146\) | 1.68217e28 | 1.22824 | ||||||||
\(147\) | −5.66081e26 | + | 5.66081e26i | −0.0378228 | + | 0.0378228i | ||||
\(148\) | 1.31167e28 | + | 1.31167e28i | 0.802460 | + | 0.802460i | ||||
\(149\) | 2.65633e27i | 0.148888i | 0.997225 | + | 0.0744441i | \(0.0237182\pi\) | ||||
−0.997225 | + | 0.0744441i | \(0.976282\pi\) | |||||||
\(150\) | −8.11119e26 | − | 2.10226e27i | −0.0416772 | − | 0.108019i | ||||
\(151\) | 1.36487e28 | 0.643269 | 0.321634 | − | 0.946864i | \(-0.395768\pi\) | ||||
0.321634 | + | 0.946864i | \(0.395768\pi\) | |||||||
\(152\) | −2.90370e26 | + | 2.90370e26i | −0.0125599 | + | 0.0125599i | ||||
\(153\) | 2.03713e28 | + | 2.03713e28i | 0.809153 | + | 0.809153i | ||||
\(154\) | 1.58115e28i | 0.577036i | ||||||||
\(155\) | −2.33297e28 | + | 3.40073e28i | −0.782702 | + | 1.14093i | ||||
\(156\) | 4.25561e27 | 0.131323 | ||||||||
\(157\) | −8.68963e27 | + | 8.68963e27i | −0.246778 | + | 0.246778i | −0.819647 | − | 0.572869i | \(-0.805830\pi\) |
0.572869 | + | 0.819647i | \(0.305830\pi\) | |||||||
\(158\) | −2.42137e28 | − | 2.42137e28i | −0.633167 | − | 0.633167i | ||||
\(159\) | − | 5.26980e27i | − | 0.126950i | ||||||
\(160\) | −1.07713e28 | − | 5.78401e28i | −0.239171 | − | 1.28431i | ||||
\(161\) | −4.56099e28 | −0.933949 | ||||||||
\(162\) | 5.69463e28 | − | 5.69463e28i | 1.07590 | − | 1.07590i | ||||
\(163\) | −4.92408e28 | − | 4.92408e28i | −0.858788 | − | 0.858788i | 0.132407 | − | 0.991195i | \(-0.457729\pi\) |
−0.991195 | + | 0.132407i | \(0.957729\pi\) | |||||||
\(164\) | − | 5.14967e28i | − | 0.829486i | ||||||
\(165\) | −1.40718e27 | + | 2.62053e26i | −0.0209439 | + | 0.00390029i | ||||
\(166\) | −6.44710e28 | −0.887073 | ||||||||
\(167\) | −6.09628e28 | + | 6.09628e28i | −0.775802 | + | 0.775802i | −0.979114 | − | 0.203312i | \(-0.934830\pi\) |
0.203312 | + | 0.979114i | \(0.434830\pi\) | |||||||
\(168\) | 3.59374e27 | + | 3.59374e27i | 0.0423181 | + | 0.0423181i | ||||
\(169\) | 5.35533e28i | 0.583793i | ||||||||
\(170\) | 1.45444e29 | + | 9.97774e28i | 1.46845 | + | 1.00739i | ||||
\(171\) | 3.09101e27 | 0.0289169 | ||||||||
\(172\) | −2.65422e28 | + | 2.65422e28i | −0.230180 | + | 0.230180i | ||||
\(173\) | −2.12399e28 | − | 2.12399e28i | −0.170826 | − | 0.170826i | 0.616516 | − | 0.787342i | \(-0.288543\pi\) |
−0.787342 | + | 0.616516i | \(0.788543\pi\) | |||||||
\(174\) | 1.41799e28i | 0.105811i | ||||||||
\(175\) | 1.72854e29 | + | 7.66046e28i | 1.19725 | + | 0.530591i | ||||
\(176\) | −1.98991e28 | −0.127988 | ||||||||
\(177\) | −1.71540e28 | + | 1.71540e28i | −0.102498 | + | 0.102498i | ||||
\(178\) | 1.72833e29 | + | 1.72833e29i | 0.959772 | + | 0.959772i | ||||
\(179\) | − | 2.77609e29i | − | 1.43332i | −0.697421 | − | 0.716662i | \(-0.745669\pi\) | ||
0.697421 | − | 0.716662i | \(-0.254331\pi\) | |||||||
\(180\) | 1.63371e29 | − | 2.38144e29i | 0.784573 | − | 1.14366i | ||||
\(181\) | 2.40334e29 | 1.07397 | 0.536986 | − | 0.843591i | \(-0.319563\pi\) | ||||
0.536986 | + | 0.843591i | \(0.319563\pi\) | |||||||
\(182\) | −4.33523e29 | + | 4.33523e29i | −1.80337 | + | 1.80337i | ||||
\(183\) | 1.02008e28 | + | 1.02008e28i | 0.0395158 | + | 0.0395158i | ||||
\(184\) | 1.20710e29i | 0.435623i | ||||||||
\(185\) | −4.42917e28 | − | 2.37839e29i | −0.148967 | − | 0.799926i | ||||
\(186\) | 5.10873e28 | 0.160193 | ||||||||
\(187\) | 7.92250e28 | − | 7.92250e28i | 0.231697 | − | 0.231697i | ||||
\(188\) | −6.23875e29 | − | 6.23875e29i | −1.70234 | − | 1.70234i | ||||
\(189\) | − | 7.67267e28i | − | 0.195408i | ||||||
\(190\) | 1.86041e28 | − | 3.46457e27i | 0.0442398 | − | 0.00823859i | ||||
\(191\) | 3.18701e29 | 0.707865 | 0.353932 | − | 0.935271i | \(-0.384844\pi\) | ||||
0.353932 | + | 0.935271i | \(0.384844\pi\) | |||||||
\(192\) | −4.00772e28 | + | 4.00772e28i | −0.0831729 | + | 0.0831729i | ||||
\(193\) | −4.50231e28 | − | 4.50231e28i | −0.0873355 | − | 0.0873355i | 0.662089 | − | 0.749425i | \(-0.269670\pi\) |
−0.749425 | + | 0.662089i | \(0.769670\pi\) | |||||||
\(194\) | 1.36247e30i | 2.47119i | ||||||||
\(195\) | −4.57674e28 | − | 3.13973e28i | −0.0776437 | − | 0.0532651i | ||||
\(196\) | −6.28168e29 | −0.997118 | ||||||||
\(197\) | 4.50941e29 | − | 4.50941e29i | 0.669976 | − | 0.669976i | −0.287734 | − | 0.957710i | \(-0.592902\pi\) |
0.957710 | + | 0.287734i | \(0.0929020\pi\) | |||||||
\(198\) | −2.22728e29 | − | 2.22728e29i | −0.309832 | − | 0.309832i | ||||
\(199\) | 3.91154e29i | 0.509633i | 0.966989 | + | 0.254816i | \(0.0820150\pi\) | ||||
−0.966989 | + | 0.254816i | \(0.917985\pi\) | |||||||
\(200\) | 2.02739e29 | − | 4.57469e29i | 0.247484 | − | 0.558434i | ||||
\(201\) | 5.31509e28 | 0.0608081 | ||||||||
\(202\) | −7.12416e29 | + | 7.12416e29i | −0.764128 | + | 0.764128i | ||||
\(203\) | −8.41306e29 | − | 8.41306e29i | −0.846264 | − | 0.846264i | ||||
\(204\) | − | 1.27253e29i | − | 0.120082i | ||||||
\(205\) | −3.79935e29 | + | 5.53826e29i | −0.336441 | + | 0.490425i | ||||
\(206\) | 2.35739e30 | 1.95955 | ||||||||
\(207\) | 6.42483e29 | − | 6.42483e29i | 0.501473 | − | 0.501473i | ||||
\(208\) | −5.45598e29 | − | 5.45598e29i | −0.399990 | − | 0.399990i | ||||
\(209\) | − | 1.20211e28i | − | 0.00828022i | ||||||
\(210\) | −4.28790e28 | − | 2.30253e29i | −0.0277584 | − | 0.149058i | ||||
\(211\) | −9.64793e29 | −0.587168 | −0.293584 | − | 0.955933i | \(-0.594848\pi\) | ||||
−0.293584 | + | 0.955933i | \(0.594848\pi\) | |||||||
\(212\) | 2.92389e30 | − | 2.92389e30i | 1.67338 | − | 1.67338i | ||||
\(213\) | 1.07689e29 | + | 1.07689e29i | 0.0579742 | + | 0.0579742i | ||||
\(214\) | 3.90379e30i | 1.97746i | ||||||||
\(215\) | 4.81276e29 | − | 8.96260e28i | 0.229453 | − | 0.0427301i | ||||
\(216\) | −2.03062e29 | −0.0911446 | ||||||||
\(217\) | −3.03106e30 | + | 3.03106e30i | −1.28120 | + | 1.28120i | ||||
\(218\) | 2.94923e30 | + | 2.94923e30i | 1.17429 | + | 1.17429i | ||||
\(219\) | 1.58284e29i | 0.0593832i | ||||||||
\(220\) | −9.26153e29 | − | 6.35359e29i | −0.327482 | − | 0.224659i | ||||
\(221\) | 4.34442e30 | 1.44821 | ||||||||
\(222\) | −2.11915e29 | + | 2.11915e29i | −0.0666150 | + | 0.0666150i | ||||
\(223\) | 1.53799e29 | + | 1.53799e29i | 0.0456026 | + | 0.0456026i | 0.729540 | − | 0.683938i | \(-0.239734\pi\) |
−0.683938 | + | 0.729540i | \(0.739734\pi\) | |||||||
\(224\) | − | 6.11532e30i | − | 1.71078i | ||||||
\(225\) | −3.51399e30 | + | 1.35581e30i | −0.927742 | + | 0.357953i | ||||
\(226\) | −6.31587e30 | −1.57407 | ||||||||
\(227\) | −1.71810e30 | + | 1.71810e30i | −0.404309 | + | 0.404309i | −0.879748 | − | 0.475440i | \(-0.842289\pi\) |
0.475440 | + | 0.879748i | \(0.342289\pi\) | |||||||
\(228\) | −9.65428e27 | − | 9.65428e27i | −0.00214569 | − | 0.00214569i | ||||
\(229\) | − | 6.62235e30i | − | 1.39043i | −0.718800 | − | 0.695217i | \(-0.755308\pi\) | ||
0.718800 | − | 0.695217i | \(-0.244692\pi\) | |||||||
\(230\) | 3.14684e30 | − | 4.58710e30i | 0.624328 | − | 0.910074i | ||||
\(231\) | −1.48778e29 | −0.0278986 | ||||||||
\(232\) | −2.22658e30 | + | 2.22658e30i | −0.394724 | + | 0.394724i | ||||
\(233\) | −2.40704e30 | − | 2.40704e30i | −0.403511 | − | 0.403511i | 0.475957 | − | 0.879468i | \(-0.342102\pi\) |
−0.879468 | + | 0.475957i | \(0.842102\pi\) | |||||||
\(234\) | − | 1.22136e31i | − | 1.93659i | ||||||
\(235\) | 2.10666e30 | + | 1.13124e31i | 0.316018 | + | 1.69696i | ||||
\(236\) | −1.90355e31 | −2.70214 | ||||||||
\(237\) | 2.27839e29 | − | 2.27839e29i | 0.0306125 | − | 0.0306125i | ||||
\(238\) | 1.29634e31 | + | 1.29634e31i | 1.64899 | + | 1.64899i | ||||
\(239\) | − | 2.78542e29i | − | 0.0335520i | −0.999859 | − | 0.0167760i | \(-0.994660\pi\) | ||
0.999859 | − | 0.0167760i | \(-0.00534022\pi\) | |||||||
\(240\) | 2.89778e29 | − | 5.39641e28i | 0.0330613 | − | 0.00615686i | ||||
\(241\) | 8.49659e30 | 0.918381 | 0.459190 | − | 0.888338i | \(-0.348140\pi\) | ||||
0.459190 | + | 0.888338i | \(0.348140\pi\) | |||||||
\(242\) | 9.81726e30 | − | 9.81726e30i | 1.00552 | − | 1.00552i | ||||
\(243\) | 1.62273e30 | + | 1.62273e30i | 0.157530 | + | 0.157530i | ||||
\(244\) | 1.13196e31i | 1.04175i | ||||||||
\(245\) | 6.75569e30 | + | 4.63453e30i | 0.589536 | + | 0.404433i | ||||
\(246\) | 8.31983e29 | 0.0688586 | ||||||||
\(247\) | 3.29597e29 | − | 3.29597e29i | 0.0258776 | − | 0.0258776i | ||||
\(248\) | 8.02191e30 | + | 8.02191e30i | 0.597594 | + | 0.597594i | ||||
\(249\) | − | 6.06640e29i | − | 0.0428884i | ||||||
\(250\) | −1.96303e31 | + | 1.20990e31i | −1.31737 | + | 0.811950i | ||||
\(251\) | −1.21653e30 | −0.0775111 | −0.0387555 | − | 0.999249i | \(-0.512339\pi\) | ||||
−0.0387555 | + | 0.999249i | \(0.512339\pi\) | |||||||
\(252\) | 2.12257e31 | − | 2.12257e31i | 1.28427 | − | 1.28427i | ||||
\(253\) | −2.49865e30 | − | 2.49865e30i | −0.143595 | − | 0.143595i | ||||
\(254\) | 1.12140e30i | 0.0612242i | ||||||||
\(255\) | −9.38856e29 | + | 1.36856e30i | −0.0487053 | + | 0.0709970i | ||||
\(256\) | −3.46951e30 | −0.171060 | ||||||||
\(257\) | −1.59515e31 | + | 1.59515e31i | −0.747603 | + | 0.747603i | −0.974028 | − | 0.226425i | \(-0.927296\pi\) |
0.226425 | + | 0.974028i | \(0.427296\pi\) | |||||||
\(258\) | −4.28818e29 | − | 4.28818e29i | −0.0191081 | − | 0.0191081i | ||||
\(259\) | − | 2.51462e31i | − | 1.06555i | ||||||
\(260\) | −7.97306e30 | − | 4.28139e31i | −0.321345 | − | 1.72557i | ||||
\(261\) | 2.37021e31 | 0.908783 | ||||||||
\(262\) | −2.95173e30 | + | 2.95173e30i | −0.107686 | + | 0.107686i | ||||
\(263\) | −2.07498e31 | − | 2.07498e31i | −0.720427 | − | 0.720427i | 0.248265 | − | 0.968692i | \(-0.420140\pi\) |
−0.968692 | + | 0.248265i | \(0.920140\pi\) | |||||||
\(264\) | 3.93751e29i | 0.0130128i | ||||||||
\(265\) | −5.30173e31 | + | 9.87319e30i | −1.66810 | + | 0.310643i | ||||
\(266\) | 1.96698e30 | 0.0589303 | ||||||||
\(267\) | −1.62628e30 | + | 1.62628e30i | −0.0464032 | + | 0.0464032i | ||||
\(268\) | 2.94902e31 | + | 2.94902e31i | 0.801539 | + | 0.801539i | ||||
\(269\) | 4.94553e31i | 1.28066i | 0.768101 | + | 0.640329i | \(0.221202\pi\) | ||||
−0.768101 | + | 0.640329i | \(0.778798\pi\) | |||||||
\(270\) | 7.71659e30 | + | 5.29373e30i | 0.190413 | + | 0.130627i | ||||
\(271\) | −6.61593e30 | −0.155593 | −0.0777965 | − | 0.996969i | \(-0.524788\pi\) | ||||
−0.0777965 | + | 0.996969i | \(0.524788\pi\) | |||||||
\(272\) | −1.63147e31 | + | 1.63147e31i | −0.365749 | + | 0.365749i | ||||
\(273\) | −4.07924e30 | − | 4.07924e30i | −0.0871895 | − | 0.0871895i | ||||
\(274\) | 7.52827e31i | 1.53440i | ||||||||
\(275\) | 5.27280e30 | + | 1.36661e31i | 0.102498 | + | 0.265655i | ||||
\(276\) | −4.01339e30 | −0.0744206 | ||||||||
\(277\) | 6.26247e31 | − | 6.26247e31i | 1.10792 | − | 1.10792i | 0.114497 | − | 0.993424i | \(-0.463474\pi\) |
0.993424 | − | 0.114497i | \(-0.0365257\pi\) | |||||||
\(278\) | −8.50519e31 | − | 8.50519e31i | −1.43583 | − | 1.43583i | ||||
\(279\) | − | 8.53939e31i | − | 1.37585i | ||||||
\(280\) | 2.94221e31 | − | 4.28881e31i | 0.452501 | − | 0.659603i | ||||
\(281\) | 1.04830e32 | 1.53923 | 0.769616 | − | 0.638507i | \(-0.220448\pi\) | ||||
0.769616 | + | 0.638507i | \(0.220448\pi\) | |||||||
\(282\) | 1.00793e31 | − | 1.00793e31i | 0.141317 | − | 0.141317i | ||||
\(283\) | −1.67783e31 | − | 1.67783e31i | −0.224659 | − | 0.224659i | 0.585798 | − | 0.810457i | \(-0.300781\pi\) |
−0.810457 | + | 0.585798i | \(0.800781\pi\) | |||||||
\(284\) | 1.19500e32i | 1.52837i | ||||||||
\(285\) | 3.25999e28 | + | 1.75056e29i | 0.000398321 | + | 0.00213891i | ||||
\(286\) | −4.74993e31 | −0.554535 | ||||||||
\(287\) | −4.93624e31 | + | 4.93624e31i | −0.550721 | + | 0.550721i | ||||
\(288\) | 8.61433e31 | + | 8.61433e31i | 0.918585 | + | 0.918585i | ||||
\(289\) | − | 3.18082e31i | − | 0.324240i | ||||||
\(290\) | 1.42658e32 | − | 2.65666e31i | 1.39034 | − | 0.258918i | ||||
\(291\) | −1.28202e31 | −0.119478 | ||||||||
\(292\) | −8.78220e31 | + | 8.78220e31i | −0.782756 | + | 0.782756i | ||||
\(293\) | −8.11379e31 | − | 8.11379e31i | −0.691743 | − | 0.691743i | 0.270872 | − | 0.962615i | \(-0.412688\pi\) |
−0.962615 | + | 0.270872i | \(0.912688\pi\) | |||||||
\(294\) | − | 1.01487e31i | − | 0.0827743i | ||||||
\(295\) | 2.04719e32 | + | 1.40441e32i | 1.59761 | + | 1.09599i | ||||
\(296\) | −6.65512e31 | −0.497008 | ||||||||
\(297\) | 4.20332e30 | − | 4.20332e30i | 0.0300440 | − | 0.0300440i | ||||
\(298\) | −2.38113e31 | − | 2.38113e31i | −0.162919 | − | 0.162919i | ||||
\(299\) | − | 1.37017e32i | − | 0.897531i | ||||||
\(300\) | 1.52100e31 | + | 6.74072e30i | 0.0954012 | + | 0.0422795i | ||||
\(301\) | 5.08843e31 | 0.305647 | ||||||||
\(302\) | −1.22347e32 | + | 1.22347e32i | −0.703889 | + | 0.703889i | ||||
\(303\) | −6.70348e30 | − | 6.70348e30i | −0.0369442 | − | 0.0369442i | ||||
\(304\) | 2.47549e30i | 0.0130709i | ||||||||
\(305\) | 8.35145e31 | − | 1.21738e32i | 0.422536 | − | 0.615925i | ||||
\(306\) | −3.65217e32 | −1.77081 | ||||||||
\(307\) | −1.90717e32 | + | 1.90717e32i | −0.886318 | + | 0.886318i | −0.994167 | − | 0.107849i | \(-0.965604\pi\) |
0.107849 | + | 0.994167i | \(0.465604\pi\) | |||||||
\(308\) | −8.25478e31 | − | 8.25478e31i | −0.367744 | − | 0.367744i | ||||
\(309\) | 2.21819e31i | 0.0947409i | ||||||||
\(310\) | −9.57141e31 | − | 5.13968e32i | −0.391989 | − | 2.10491i | ||||
\(311\) | 2.95453e32 | 1.16039 | 0.580195 | − | 0.814478i | \(-0.302977\pi\) | ||||
0.580195 | + | 0.814478i | \(0.302977\pi\) | |||||||
\(312\) | −1.07960e31 | + | 1.07960e31i | −0.0406680 | + | 0.0406680i | ||||
\(313\) | −4.09862e31 | − | 4.09862e31i | −0.148102 | − | 0.148102i | 0.629168 | − | 0.777270i | \(-0.283396\pi\) |
−0.777270 | + | 0.629168i | \(0.783396\pi\) | |||||||
\(314\) | − | 1.55788e32i | − | 0.540067i | ||||||
\(315\) | −3.84874e32 | + | 7.16735e31i | −1.28021 | + | 0.238408i | ||||
\(316\) | 2.52827e32 | 0.807034 | ||||||||
\(317\) | −5.56585e31 | + | 5.56585e31i | −0.170514 | + | 0.170514i | −0.787205 | − | 0.616691i | \(-0.788473\pi\) |
0.616691 | + | 0.787205i | \(0.288473\pi\) | |||||||
\(318\) | 4.72385e31 | + | 4.72385e31i | 0.138913 | + | 0.138913i | ||||
\(319\) | − | 9.21785e31i | − | 0.260226i | ||||||
\(320\) | 4.78287e32 | + | 3.28114e32i | 1.29640 | + | 0.889355i | ||||
\(321\) | −3.67327e31 | −0.0956065 | ||||||||
\(322\) | 4.08847e32 | − | 4.08847e32i | 1.02196 | − | 1.02196i | ||||
\(323\) | −9.85576e30 | − | 9.85576e30i | −0.0236623 | − | 0.0236623i | ||||
\(324\) | 5.94606e32i | 1.37134i | ||||||||
\(325\) | −2.30128e32 | + | 5.19271e32i | −0.509902 | + | 1.15056i | ||||
\(326\) | 8.82788e32 | 1.87944 | ||||||||
\(327\) | −2.77508e31 | + | 2.77508e31i | −0.0567746 | + | 0.0567746i | ||||
\(328\) | 1.30641e32 | + | 1.30641e32i | 0.256874 | + | 0.256874i | ||||
\(329\) | 1.19604e33i | 2.26046i | ||||||||
\(330\) | 1.02649e31 | − | 1.49630e31i | 0.0186498 | − | 0.0271855i | ||||
\(331\) | −1.08201e33 | −1.89002 | −0.945011 | − | 0.327039i | \(-0.893949\pi\) | ||||
−0.945011 | + | 0.327039i | \(0.893949\pi\) | |||||||
\(332\) | 3.36588e32 | − | 3.36588e32i | 0.565331 | − | 0.565331i | ||||
\(333\) | 3.54222e32 | + | 3.54222e32i | 0.572137 | + | 0.572137i | ||||
\(334\) | − | 1.09294e33i | − | 1.69783i | ||||||
\(335\) | −9.95803e31 | − | 5.34729e32i | −0.148796 | − | 0.799008i | ||||
\(336\) | 3.06377e31 | 0.0440398 | ||||||||
\(337\) | 9.36294e32 | − | 9.36294e32i | 1.29486 | − | 1.29486i | 0.363120 | − | 0.931742i | \(-0.381711\pi\) |
0.931742 | − | 0.363120i | \(-0.118289\pi\) | |||||||
\(338\) | −4.80052e32 | − | 4.80052e32i | −0.638809 | − | 0.638809i | ||||
\(339\) | − | 5.94292e31i | − | 0.0761034i | ||||||
\(340\) | −1.28024e33 | + | 2.38414e32i | −1.57785 | + | 0.293836i | ||||
\(341\) | −3.32101e32 | −0.393970 | ||||||||
\(342\) | −2.77078e31 | + | 2.77078e31i | −0.0316419 | + | 0.0316419i | ||||
\(343\) | −2.40098e32 | − | 2.40098e32i | −0.263976 | − | 0.263976i | ||||
\(344\) | − | 1.34669e32i | − | 0.142563i | ||||||
\(345\) | 4.31624e31 | + | 2.96102e31i | 0.0440004 | + | 0.0301852i | ||||
\(346\) | 3.80790e32 | 0.373849 | ||||||||
\(347\) | −4.22093e32 | + | 4.22093e32i | −0.399140 | + | 0.399140i | −0.877930 | − | 0.478790i | \(-0.841076\pi\) |
0.478790 | + | 0.877930i | \(0.341076\pi\) | |||||||
\(348\) | −7.40297e31 | − | 7.40297e31i | −0.0674335 | − | 0.0674335i | ||||
\(349\) | − | 2.85347e31i | − | 0.0250405i | −0.999922 | − | 0.0125203i | \(-0.996015\pi\) | ||
0.999922 | − | 0.0125203i | \(-0.00398543\pi\) | |||||||
\(350\) | −2.23614e33 | + | 8.62776e32i | −1.89067 | + | 0.729480i | ||||
\(351\) | 2.30495e32 | 0.187789 | ||||||||
\(352\) | 3.35015e32 | − | 3.35015e32i | 0.263033 | − | 0.263033i | ||||
\(353\) | 8.87104e32 | + | 8.87104e32i | 0.671279 | + | 0.671279i | 0.958011 | − | 0.286732i | \(-0.0925688\pi\) |
−0.286732 | + | 0.958011i | \(0.592569\pi\) | |||||||
\(354\) | − | 3.07538e32i | − | 0.224314i | ||||||
\(355\) | 8.81651e32 | − | 1.28517e33i | 0.619909 | − | 0.903632i | ||||
\(356\) | −1.80464e33 | −1.22332 | ||||||||
\(357\) | −1.21979e32 | + | 1.21979e32i | −0.0797257 | + | 0.0797257i | ||||
\(358\) | 2.48849e33 | + | 2.48849e33i | 1.56840 | + | 1.56840i | ||||
\(359\) | − | 3.07101e32i | − | 0.186661i | −0.995635 | − | 0.0933305i | \(-0.970249\pi\) | ||
0.995635 | − | 0.0933305i | \(-0.0297513\pi\) | |||||||
\(360\) | 1.89689e32 | + | 1.01860e33i | 0.111201 | + | 0.597131i | ||||
\(361\) | 1.76696e33 | 0.999154 | ||||||||
\(362\) | −2.15435e33 | + | 2.15435e33i | −1.17518 | + | 1.17518i | ||||
\(363\) | 9.23755e31 | + | 9.23755e31i | 0.0486151 | + | 0.0486151i | ||||
\(364\) | − | 4.52663e33i | − | 2.29857i | ||||||
\(365\) | 1.59243e33 | − | 2.96551e32i | 0.780284 | − | 0.145309i | ||||
\(366\) | −1.82880e32 | −0.0864794 | ||||||||
\(367\) | 1.14835e33 | − | 1.14835e33i | 0.524101 | − | 0.524101i | −0.394707 | − | 0.918807i | \(-0.629154\pi\) |
0.918807 | + | 0.394707i | \(0.129154\pi\) | |||||||
\(368\) | 5.14543e32 | + | 5.14543e32i | 0.226673 | + | 0.226673i | ||||
\(369\) | − | 1.39068e33i | − | 0.591406i | ||||||
\(370\) | 2.52902e33 | + | 1.73495e33i | 1.03831 | + | 0.712304i | ||||
\(371\) | −5.60542e33 | −2.22202 | ||||||||
\(372\) | −2.66714e32 | + | 2.66714e32i | −0.102091 | + | 0.102091i | ||||
\(373\) | −6.01167e32 | − | 6.01167e32i | −0.222218 | − | 0.222218i | 0.587214 | − | 0.809432i | \(-0.300225\pi\) |
−0.809432 | + | 0.587214i | \(0.800225\pi\) | |||||||
\(374\) | 1.42035e33i | 0.507065i | ||||||||
\(375\) | −1.13846e32 | − | 1.84711e32i | −0.0392563 | − | 0.0636923i | ||||
\(376\) | 3.16539e33 | 1.05435 | ||||||||
\(377\) | 2.52738e33 | − | 2.52738e33i | 0.813265 | − | 0.813265i | ||||
\(378\) | 6.87778e32 | + | 6.87778e32i | 0.213823 | + | 0.213823i | ||||
\(379\) | 3.08824e32i | 0.0927687i | 0.998924 | + | 0.0463844i | \(0.0147699\pi\) | ||||
−0.998924 | + | 0.0463844i | \(0.985230\pi\) | |||||||
\(380\) | −7.90401e31 | + | 1.15215e32i | −0.0229435 | + | 0.0334444i | ||||
\(381\) | −1.05518e31 | −0.00296008 | ||||||||
\(382\) | −2.85684e33 | + | 2.85684e33i | −0.774573 | + | 0.774573i | ||||
\(383\) | 1.84392e33 | + | 1.84392e33i | 0.483234 | + | 0.483234i | 0.906163 | − | 0.422929i | \(-0.138998\pi\) |
−0.422929 | + | 0.906163i | \(0.638998\pi\) | |||||||
\(384\) | − | 3.32684e32i | − | 0.0842803i | ||||||
\(385\) | 2.78742e32 | + | 1.49679e33i | 0.0682672 | + | 0.366583i | ||||
\(386\) | 8.07175e32 | 0.191132 | ||||||||
\(387\) | −7.16781e32 | + | 7.16781e32i | −0.164113 | + | 0.164113i | ||||
\(388\) | −7.11315e33 | − | 7.11315e33i | −1.57489 | − | 1.57489i | ||||
\(389\) | 2.44569e33i | 0.523669i | 0.965113 | + | 0.261834i | \(0.0843274\pi\) | ||||
−0.965113 | + | 0.261834i | \(0.915673\pi\) | |||||||
\(390\) | 6.91704e32 | − | 1.28813e32i | 0.143245 | − | 0.0266760i | ||||
\(391\) | −4.09715e33 | −0.820699 | ||||||||
\(392\) | 1.59359e33 | − | 1.59359e33i | 0.308786 | − | 0.308786i | ||||
\(393\) | −2.77743e31 | − | 2.77743e31i | −0.00520643 | − | 0.00520643i | ||||
\(394\) | 8.08448e33i | 1.46623i | ||||||||
\(395\) | −2.71905e33 | − | 1.86532e33i | −0.477151 | − | 0.327335i | ||||
\(396\) | 2.32562e33 | 0.394912 | ||||||||
\(397\) | −4.48928e31 | + | 4.48928e31i | −0.00737735 | + | 0.00737735i | −0.710786 | − | 0.703408i | \(-0.751660\pi\) |
0.703408 | + | 0.710786i | \(0.251660\pi\) | |||||||
\(398\) | −3.50630e33 | − | 3.50630e33i | −0.557660 | − | 0.557660i | ||||
\(399\) | 1.85083e31i | 0.00284918i | ||||||||
\(400\) | −1.08582e33 | − | 2.81423e33i | −0.161800 | − | 0.419353i | ||||
\(401\) | −2.32372e31 | −0.00335202 | −0.00167601 | − | 0.999999i | \(-0.500533\pi\) | ||||
−0.00167601 | + | 0.999999i | \(0.500533\pi\) | |||||||
\(402\) | −4.76445e32 | + | 4.76445e32i | −0.0665386 | + | 0.0665386i | ||||
\(403\) | −9.10563e33 | − | 9.10563e33i | −1.23125 | − | 1.23125i | ||||
\(404\) | − | 7.43870e33i | − | 0.973957i | ||||||
\(405\) | 4.38692e33 | − | 6.39475e33i | 0.556217 | − | 0.810789i | ||||
\(406\) | 1.50829e34 | 1.85203 | ||||||||
\(407\) | 1.37758e33 | − | 1.37758e33i | 0.163829 | − | 0.163829i | ||||
\(408\) | 3.22826e32 | + | 3.22826e32i | 0.0371866 | + | 0.0371866i | ||||
\(409\) | 1.02905e34i | 1.14825i | 0.818769 | + | 0.574123i | \(0.194657\pi\) | ||||
−0.818769 | + | 0.574123i | \(0.805343\pi\) | |||||||
\(410\) | −1.55875e33 | − | 8.37024e33i | −0.168495 | − | 0.904789i | ||||
\(411\) | −7.08373e32 | −0.0741854 | ||||||||
\(412\) | −1.23074e34 | + | 1.23074e34i | −1.24882 | + | 1.24882i | ||||
\(413\) | 1.82465e34 | + | 1.82465e34i | 1.79403 | + | 1.79403i | ||||
\(414\) | 1.15184e34i | 1.09746i | ||||||||
\(415\) | −6.10316e33 | + | 1.13657e33i | −0.563546 | + | 0.104947i | ||||
\(416\) | 1.83711e34 | 1.64407 | ||||||||
\(417\) | 8.00297e32 | − | 8.00297e32i | 0.0694196 | − | 0.0694196i | ||||
\(418\) | 1.07757e32 | + | 1.07757e32i | 0.00906054 | + | 0.00906054i | ||||
\(419\) | 1.34539e34i | 1.09665i | 0.836267 | + | 0.548323i | \(0.184733\pi\) | ||||
−0.836267 | + | 0.548323i | \(0.815267\pi\) | |||||||
\(420\) | 1.42595e33 | + | 9.78233e32i | 0.112685 | + | 0.0773039i | ||||
\(421\) | 3.02346e33 | 0.231652 | 0.115826 | − | 0.993269i | \(-0.463048\pi\) | ||||
0.115826 | + | 0.993269i | \(0.463048\pi\) | |||||||
\(422\) | 8.64840e33 | − | 8.64840e33i | 0.642501 | − | 0.642501i | ||||
\(423\) | −1.68479e34 | − | 1.68479e34i | −1.21373 | − | 1.21373i | ||||
\(424\) | 1.48351e34i | 1.03642i | ||||||||
\(425\) | 1.55275e34 | + | 6.88140e33i | 1.05207 | + | 0.466252i | ||||
\(426\) | −1.93064e33 | −0.126875 | ||||||||
\(427\) | 1.08505e34 | − | 1.08505e34i | 0.691649 | − | 0.691649i | ||||
\(428\) | −2.03807e34 | − | 2.03807e34i | −1.26023 | − | 1.26023i | ||||
\(429\) | − | 4.46945e32i | − | 0.0268108i | ||||||
\(430\) | −3.51075e33 | + | 5.11756e33i | −0.204320 | + | 0.297833i | ||||
\(431\) | −1.60367e34 | −0.905548 | −0.452774 | − | 0.891625i | \(-0.649565\pi\) | ||||
−0.452774 | + | 0.891625i | \(0.649565\pi\) | |||||||
\(432\) | −8.65583e32 | + | 8.65583e32i | −0.0474264 | + | 0.0474264i | ||||
\(433\) | 5.55564e33 | + | 5.55564e33i | 0.295387 | + | 0.295387i | 0.839204 | − | 0.543817i | \(-0.183021\pi\) |
−0.543817 | + | 0.839204i | \(0.683021\pi\) | |||||||
\(434\) | − | 5.43408e34i | − | 2.80388i | ||||||
\(435\) | 2.49978e32 | + | 1.34234e33i | 0.0125182 | + | 0.0672206i | ||||
\(436\) | −3.07944e34 | −1.49674 | ||||||||
\(437\) | −3.10837e32 | + | 3.10837e32i | −0.0146647 | + | 0.0146647i | ||||
\(438\) | −1.41886e33 | − | 1.41886e33i | −0.0649793 | − | 0.0649793i | ||||
\(439\) | − | 4.57273e33i | − | 0.203300i | −0.994820 | − | 0.101650i | \(-0.967588\pi\) | ||
0.994820 | − | 0.101650i | \(-0.0324121\pi\) | |||||||
\(440\) | 3.96137e33 | − | 7.37709e32i | 0.170986 | − | 0.0318420i | ||||
\(441\) | −1.69639e34 | −0.710924 | ||||||||
\(442\) | −3.89434e34 | + | 3.89434e34i | −1.58469 | + | 1.58469i | ||||
\(443\) | 1.70975e33 | + | 1.70975e33i | 0.0675593 | + | 0.0675593i | 0.740079 | − | 0.672520i | \(-0.234788\pi\) |
−0.672520 | + | 0.740079i | \(0.734788\pi\) | |||||||
\(444\) | − | 2.21271e33i | − | 0.0849074i | ||||||
\(445\) | 1.94082e34 | + | 1.33144e34i | 0.723278 | + | 0.496183i | ||||
\(446\) | −2.75730e33 | −0.0998002 | ||||||||
\(447\) | 2.24053e32 | − | 2.24053e32i | 0.00787685 | − | 0.00787685i | ||||
\(448\) | 4.26296e34 | + | 4.26296e34i | 1.45578 | + | 1.45578i | ||||
\(449\) | − | 1.11957e34i | − | 0.371405i | −0.982606 | − | 0.185703i | \(-0.940544\pi\) | ||
0.982606 | − | 0.185703i | \(-0.0594561\pi\) | |||||||
\(450\) | 1.93459e34 | − | 4.36528e34i | 0.623485 | − | 1.40686i | ||||
\(451\) | −5.40844e33 | −0.169347 | ||||||||
\(452\) | 3.29736e34 | − | 3.29736e34i | 1.00315 | − | 1.00315i | ||||
\(453\) | −1.15123e33 | − | 1.15123e33i | −0.0340318 | − | 0.0340318i | ||||
\(454\) | − | 3.08022e34i | − | 0.884820i | ||||||
\(455\) | −3.33969e34 | + | 4.86821e34i | −0.932305 | + | 1.35901i | ||||
\(456\) | 4.89835e31 | 0.00132895 | ||||||||
\(457\) | −3.37862e34 | + | 3.37862e34i | −0.890900 | + | 0.890900i | −0.994608 | − | 0.103707i | \(-0.966929\pi\) |
0.103707 | + | 0.994608i | \(0.466929\pi\) | |||||||
\(458\) | 5.93627e34 | + | 5.93627e34i | 1.52147 | + | 1.52147i | ||||
\(459\) | − | 6.89237e33i | − | 0.171713i | ||||||
\(460\) | 7.51925e33 | + | 4.03771e34i | 0.182105 | + | 0.977874i | ||||
\(461\) | 4.11229e34 | 0.968214 | 0.484107 | − | 0.875009i | \(-0.339145\pi\) | ||||
0.484107 | + | 0.875009i | \(0.339145\pi\) | |||||||
\(462\) | 1.33365e33 | − | 1.33365e33i | 0.0305278 | − | 0.0305278i | ||||
\(463\) | −6.06259e34 | − | 6.06259e34i | −1.34929 | − | 1.34929i | −0.886432 | − | 0.462859i | \(-0.846824\pi\) |
−0.462859 | − | 0.886432i | \(-0.653176\pi\) | |||||||
\(464\) | 1.89822e34i | 0.410783i | ||||||||
\(465\) | 4.83619e33 | − | 9.00623e32i | 0.101769 | − | 0.0189520i | ||||
\(466\) | 4.31533e34 | 0.883075 | ||||||||
\(467\) | 1.18106e34 | − | 1.18106e34i | 0.235045 | − | 0.235045i | −0.579750 | − | 0.814795i | \(-0.696850\pi\) |
0.814795 | + | 0.579750i | \(0.196850\pi\) | |||||||
\(468\) | 6.37644e34 | + | 6.37644e34i | 1.23419 | + | 1.23419i | ||||
\(469\) | − | 5.65359e34i | − | 1.06433i | ||||||
\(470\) | −1.20288e35 | − | 8.25201e34i | −2.20268 | − | 1.51108i | ||||
\(471\) | 1.46589e33 | 0.0261113 | ||||||||
\(472\) | 4.82907e34 | − | 4.82907e34i | 0.836792 | − | 0.836792i | ||||
\(473\) | 2.78760e33 | + | 2.78760e33i | 0.0469932 | + | 0.0469932i | ||||
\(474\) | 4.08469e33i | 0.0669947i | ||||||||
\(475\) | 1.70009e33 | − | 6.55948e32i | 0.0271303 | − | 0.0104677i | ||||
\(476\) | −1.35357e35 | −2.10180 | ||||||||
\(477\) | 7.89606e34 | − | 7.89606e34i | 1.19309 | − | 1.19309i | ||||
\(478\) | 2.49685e33 | + | 2.49685e33i | 0.0367139 | + | 0.0367139i | ||||
\(479\) | 2.39443e34i | 0.342642i | 0.985215 | + | 0.171321i | \(0.0548035\pi\) | ||||
−0.985215 | + | 0.171321i | \(0.945197\pi\) | |||||||
\(480\) | −3.97010e33 | + | 5.78715e33i | −0.0552924 | + | 0.0805989i | ||||
\(481\) | 7.55419e34 | 1.02401 | ||||||||
\(482\) | −7.61634e34 | + | 7.61634e34i | −1.00493 | + | 1.00493i | ||||
\(483\) | 3.84705e33 | + | 3.84705e33i | 0.0494101 | + | 0.0494101i | ||||
\(484\) | 1.02507e35i | 1.28163i | ||||||||
\(485\) | 2.40192e34 | + | 1.28979e35i | 0.292359 | + | 1.56991i | ||||
\(486\) | −2.90923e34 | −0.344752 | ||||||||
\(487\) | 3.55738e34 | − | 3.55738e34i | 0.410444 | − | 0.410444i | −0.471449 | − | 0.881893i | \(-0.656269\pi\) |
0.881893 | + | 0.471449i | \(0.156269\pi\) | |||||||
\(488\) | −2.87165e34 | − | 2.87165e34i | −0.322607 | − | 0.322607i | ||||
\(489\) | 8.30660e33i | 0.0908674i | ||||||||
\(490\) | −1.02102e35 | + | 1.90140e34i | −1.08764 | + | 0.202547i | ||||
\(491\) | −7.77826e34 | −0.806906 | −0.403453 | − | 0.915000i | \(-0.632190\pi\) | ||||
−0.403453 | + | 0.915000i | \(0.632190\pi\) | |||||||
\(492\) | −4.34358e33 | + | 4.34358e33i | −0.0438835 | + | 0.0438835i | ||||
\(493\) | −7.55747e34 | − | 7.55747e34i | −0.743646 | − | 0.743646i | ||||
\(494\) | 5.90902e33i | 0.0566324i | ||||||||
\(495\) | −2.50111e34 | − | 1.71581e34i | −0.233488 | − | 0.160177i | ||||
\(496\) | 6.83891e34 | 0.621907 | ||||||||
\(497\) | 1.14547e35 | − | 1.14547e35i | 1.01473 | − | 1.01473i | ||||
\(498\) | 5.43792e33 | + | 5.43792e33i | 0.0469301 | + | 0.0469301i | ||||
\(499\) | − | 9.60514e34i | − | 0.807600i | −0.914847 | − | 0.403800i | \(-0.867689\pi\) | ||
0.914847 | − | 0.403800i | \(-0.132311\pi\) | |||||||
\(500\) | 3.93190e34 | − | 1.65651e35i | 0.322101 | − | 1.35701i | ||||
\(501\) | 1.02840e34 | 0.0820868 | ||||||||
\(502\) | 1.09050e34 | − | 1.09050e34i | 0.0848156 | − | 0.0848156i | ||||
\(503\) | −5.67041e34 | − | 5.67041e34i | −0.429765 | − | 0.429765i | 0.458784 | − | 0.888548i | \(-0.348285\pi\) |
−0.888548 | + | 0.458784i | \(0.848285\pi\) | |||||||
\(504\) | 1.07694e35i | 0.795418i | ||||||||
\(505\) | −5.48817e34 | + | 8.00002e34i | −0.395039 | + | 0.575842i | ||||
\(506\) | 4.47958e34 | 0.314254 | ||||||||
\(507\) | 4.51705e33 | − | 4.51705e33i | 0.0308853 | − | 0.0308853i | ||||
\(508\) | −5.85457e33 | − | 5.85457e33i | −0.0390181 | − | 0.0390181i | ||||
\(509\) | 2.56612e35i | 1.66704i | 0.552492 | + | 0.833518i | \(0.313677\pi\) | ||||
−0.552492 | + | 0.833518i | \(0.686323\pi\) | |||||||
\(510\) | −3.85183e33 | − | 2.06836e34i | −0.0243924 | − | 0.130983i | ||||
\(511\) | 1.68364e35 | 1.03939 | ||||||||
\(512\) | −1.01246e35 | + | 1.01246e35i | −0.609352 | + | 0.609352i | ||||
\(513\) | −5.22902e32 | − | 5.22902e32i | −0.00306827 | − | 0.00306827i | ||||
\(514\) | − | 2.85979e35i | − | 1.63611i | ||||||
\(515\) | 2.23163e35 | − | 4.15586e34i | 1.24488 | − | 0.231829i | ||||
\(516\) | 4.47751e33 | 0.0243551 | ||||||||
\(517\) | −6.55224e34 | + | 6.55224e34i | −0.347546 | + | 0.347546i | ||||
\(518\) | 2.25411e35 | + | 2.25411e35i | 1.16597 | + | 1.16597i | ||||
\(519\) | 3.58304e33i | 0.0180749i | ||||||||
\(520\) | 1.28841e35 | + | 8.83872e34i | 0.633883 | + | 0.434856i | ||||
\(521\) | −3.63605e34 | −0.174478 | −0.0872388 | − | 0.996187i | \(-0.527804\pi\) | ||||
−0.0872388 | + | 0.996187i | \(0.527804\pi\) | |||||||
\(522\) | −2.12466e35 | + | 2.12466e35i | −0.994425 | + | 0.994425i | ||||
\(523\) | 3.70335e34 | + | 3.70335e34i | 0.169072 | + | 0.169072i | 0.786571 | − | 0.617499i | \(-0.211854\pi\) |
−0.617499 | + | 0.786571i | \(0.711854\pi\) | |||||||
\(524\) | − | 3.08205e34i | − | 0.137257i | ||||||
\(525\) | −8.11829e33 | − | 2.10410e34i | −0.0352691 | − | 0.0914103i | ||||
\(526\) | 3.72003e35 | 1.57664 | ||||||||
\(527\) | −2.72281e35 | + | 2.72281e35i | −1.12585 | + | 1.12585i | ||||
\(528\) | 1.67842e33 | + | 1.67842e33i | 0.00677112 | + | 0.00677112i | ||||
\(529\) | − | 1.24834e35i | − | 0.491372i | ||||||
\(530\) | 3.86744e35 | − | 5.63751e35i | 1.48538 | − | 2.16521i | ||||
\(531\) | −5.14058e35 | −1.92657 | ||||||||
\(532\) | −1.02691e34 | + | 1.02691e34i | −0.0375563 | + | 0.0375563i | ||||
\(533\) | −1.48290e35 | − | 1.48290e35i | −0.529246 | − | 0.529246i | ||||
\(534\) | − | 2.91559e34i | − | 0.101552i | ||||||
\(535\) | 6.88202e34 | + | 3.69553e35i | 0.233947 | + | 1.25625i | ||||
\(536\) | −1.49626e35 | −0.496438 | ||||||||
\(537\) | −2.34154e34 | + | 2.34154e34i | −0.0758292 | + | 0.0758292i | ||||
\(538\) | −4.43317e35 | − | 4.43317e35i | −1.40134 | − | 1.40134i | ||||
\(539\) | 6.59733e34i | 0.203570i | ||||||||
\(540\) | −6.79237e34 | + | 1.26491e34i | −0.204599 | + | 0.0381015i | ||||
\(541\) | −4.27082e35 | −1.25588 | −0.627939 | − | 0.778263i | \(-0.716101\pi\) | ||||
−0.627939 | + | 0.778263i | \(0.716101\pi\) | |||||||
\(542\) | 5.93052e34 | − | 5.93052e34i | 0.170256 | − | 0.170256i | ||||
\(543\) | −2.02714e34 | − | 2.02714e34i | −0.0568179 | − | 0.0568179i | ||||
\(544\) | − | 5.49340e35i | − | 1.50333i | ||||||
\(545\) | 3.31181e35 | + | 2.27197e35i | 0.884934 | + | 0.607082i | ||||
\(546\) | 7.31325e34 | 0.190812 | ||||||||
\(547\) | 2.55888e35 | − | 2.55888e35i | 0.651951 | − | 0.651951i | −0.301511 | − | 0.953463i | \(-0.597491\pi\) |
0.953463 | + | 0.301511i | \(0.0974911\pi\) | |||||||
\(548\) | −3.93033e35 | − | 3.93033e35i | −0.977871 | − | 0.977871i | ||||
\(549\) | 3.05690e35i | 0.742746i | ||||||||
\(550\) | −1.69768e35 | − | 7.52371e34i | −0.402848 | − | 0.178532i | ||||
\(551\) | −1.14672e34 | −0.0265758 | ||||||||
\(552\) | 1.01815e34 | − | 1.01815e34i | 0.0230464 | − | 0.0230464i | ||||
\(553\) | −2.42349e35 | − | 2.42349e35i | −0.535814 | − | 0.535814i | ||||
\(554\) | 1.12274e36i | 2.42466i | ||||||||
\(555\) | −1.63251e34 | + | 2.37968e34i | −0.0344387 | + | 0.0502007i | ||||
\(556\) | 8.88071e35 | 1.83010 | ||||||||
\(557\) | 3.97433e35 | − | 3.97433e35i | 0.800104 | − | 0.800104i | −0.183008 | − | 0.983111i | \(-0.558583\pi\) |
0.983111 | + | 0.183008i | \(0.0585834\pi\) | |||||||
\(558\) | 7.65471e35 | + | 7.65471e35i | 1.50551 | + | 1.50551i | ||||
\(559\) | 1.52862e35i | 0.293729i | ||||||||
\(560\) | −5.74009e34 | − | 3.08233e35i | −0.107764 | − | 0.578675i | ||||
\(561\) | −1.33648e34 | −0.0245157 | ||||||||
\(562\) | −9.39698e35 | + | 9.39698e35i | −1.68429 | + | 1.68429i | ||||
\(563\) | 4.73022e35 | + | 4.73022e35i | 0.828462 | + | 0.828462i | 0.987304 | − | 0.158842i | \(-0.0507761\pi\) |
−0.158842 | + | 0.987304i | \(0.550776\pi\) | |||||||
\(564\) | 1.05244e35i | 0.180122i | ||||||||
\(565\) | −5.97893e35 | + | 1.11343e35i | −0.999985 | + | 0.186223i | ||||
\(566\) | 3.00801e35 | 0.491660 | ||||||||
\(567\) | 5.69962e35 | − | 5.69962e35i | 0.910472 | − | 0.910472i | ||||
\(568\) | −3.03156e35 | − | 3.03156e35i | −0.473302 | − | 0.473302i | ||||
\(569\) | 2.84905e35i | 0.434751i | 0.976088 | + | 0.217375i | \(0.0697496\pi\) | ||||
−0.976088 | + | 0.217375i | \(0.930250\pi\) | |||||||
\(570\) | −1.86143e33 | − | 1.27697e33i | −0.00277634 | − | 0.00190462i | ||||
\(571\) | 9.43778e35 | 1.37594 | 0.687972 | − | 0.725737i | \(-0.258501\pi\) | ||||
0.687972 | + | 0.725737i | \(0.258501\pi\) | |||||||
\(572\) | 2.47983e35 | − | 2.47983e35i | 0.353405 | − | 0.353405i | ||||
\(573\) | −2.68815e34 | − | 2.68815e34i | −0.0374492 | − | 0.0374492i | ||||
\(574\) | − | 8.84969e35i | − | 1.20524i | ||||||
\(575\) | 2.17030e35 | − | 4.89715e35i | 0.288960 | − | 0.652020i | ||||
\(576\) | −1.20100e36 | −1.56333 | ||||||||
\(577\) | 5.34296e35 | − | 5.34296e35i | 0.679981 | − | 0.679981i | −0.280015 | − | 0.959996i | \(-0.590339\pi\) |
0.959996 | + | 0.280015i | \(0.0903395\pi\) | |||||||
\(578\) | 2.85128e35 | + | 2.85128e35i | 0.354796 | + | 0.354796i | ||||
\(579\) | 7.59512e33i | 0.00924088i | ||||||||
\(580\) | −6.06085e35 | + | 8.83480e35i | −0.721057 | + | 1.05107i | ||||
\(581\) | −6.45275e35 | −0.750680 | ||||||||
\(582\) | 1.14920e35 | − | 1.14920e35i | 0.130737 | − | 0.130737i | ||||
\(583\) | −3.07082e35 | − | 3.07082e35i | −0.341635 | − | 0.341635i | ||||
\(584\) | − | 4.45588e35i | − | 0.484805i | ||||||
\(585\) | −2.15315e35 | − | 1.15620e36i | −0.229112 | − | 1.23029i | ||||
\(586\) | 1.45464e36 | 1.51386 | ||||||||
\(587\) | −2.83557e35 | + | 2.83557e35i | −0.288633 | + | 0.288633i | −0.836539 | − | 0.547907i | \(-0.815425\pi\) |
0.547907 | + | 0.836539i | \(0.315425\pi\) | |||||||
\(588\) | 5.29839e34 | + | 5.29839e34i | 0.0527520 | + | 0.0527520i | ||||
\(589\) | 4.13141e34i | 0.0402346i | ||||||||
\(590\) | −3.09401e36 | + | 5.76184e35i | −2.94744 | + | 0.548890i | ||||
\(591\) | −7.60709e34 | −0.0708894 | ||||||||
\(592\) | −2.83684e35 | + | 2.83684e35i | −0.258614 | + | 0.258614i | ||||
\(593\) | −4.24891e35 | − | 4.24891e35i | −0.378936 | − | 0.378936i | 0.491782 | − | 0.870718i | \(-0.336346\pi\) |
−0.870718 | + | 0.491782i | \(0.836346\pi\) | |||||||
\(594\) | 7.53570e34i | 0.0657506i | ||||||||
\(595\) | 1.45571e36 | + | 9.98648e35i | 1.24267 | + | 0.852495i | ||||
\(596\) | 2.48626e35 | 0.207657 | ||||||||
\(597\) | 3.29926e34 | − | 3.29926e34i | 0.0269619 | − | 0.0269619i | ||||
\(598\) | 1.22822e36 | + | 1.22822e36i | 0.982113 | + | 0.982113i | ||||
\(599\) | 6.56146e35i | 0.513395i | 0.966492 | + | 0.256698i | \(0.0826345\pi\) | ||||
−0.966492 | + | 0.256698i | \(0.917366\pi\) | |||||||
\(600\) | −5.56865e34 | + | 2.14856e34i | −0.0426367 | + | 0.0164506i | ||||
\(601\) | −2.21403e36 | −1.65888 | −0.829441 | − | 0.558594i | \(-0.811341\pi\) | ||||
−0.829441 | + | 0.558594i | \(0.811341\pi\) | |||||||
\(602\) | −4.56127e35 | + | 4.56127e35i | −0.334450 | + | 0.334450i | ||||
\(603\) | 7.96391e35 | + | 7.96391e35i | 0.571480 | + | 0.571480i | ||||
\(604\) | − | 1.27749e36i | − | 0.897177i | ||||||
\(605\) | 7.56283e35 | − | 1.10242e36i | 0.519834 | − | 0.757753i | ||||
\(606\) | 1.20180e35 | 0.0808516 | ||||||||
\(607\) | 1.40817e36 | − | 1.40817e36i | 0.927262 | − | 0.927262i | −0.0702659 | − | 0.997528i | \(-0.522385\pi\) |
0.997528 | + | 0.0702659i | \(0.0223848\pi\) | |||||||
\(608\) | −4.16767e34 | − | 4.16767e34i | −0.0268625 | − | 0.0268625i | ||||
\(609\) | 1.41923e35i | 0.0895423i | ||||||||
\(610\) | 3.42634e35 | + | 1.83988e36i | 0.211613 | + | 1.13632i | ||||
\(611\) | −3.59302e36 | −2.17232 | ||||||||
\(612\) | 1.90671e36 | − | 1.90671e36i | 1.12854 | − | 1.12854i | ||||
\(613\) | −5.66636e34 | − | 5.66636e34i | −0.0328335 | − | 0.0328335i | 0.690499 | − | 0.723333i | \(-0.257391\pi\) |
−0.723333 | + | 0.690499i | \(0.757391\pi\) | |||||||
\(614\) | − | 3.41917e36i | − | 1.93969i | ||||||
\(615\) | 7.87598e34 | − | 1.46671e34i | 0.0437450 | − | 0.00814644i | ||||
\(616\) | 4.18828e35 | 0.227765 | ||||||||
\(617\) | −3.02814e35 | + | 3.02814e35i | −0.161239 | + | 0.161239i | −0.783115 | − | 0.621877i | \(-0.786371\pi\) |
0.621877 | + | 0.783115i | \(0.286371\pi\) | |||||||
\(618\) | −1.98838e35 | − | 1.98838e35i | −0.103669 | − | 0.103669i | ||||
\(619\) | − | 3.50224e35i | − | 0.178800i | −0.995996 | − | 0.0894001i | \(-0.971505\pi\) | ||
0.995996 | − | 0.0894001i | \(-0.0284950\pi\) | |||||||
\(620\) | 3.18300e36 | + | 2.18360e36i | 1.59127 | + | 1.09165i | ||||
\(621\) | −2.17376e35 | −0.106419 | ||||||||
\(622\) | −2.64844e36 | + | 2.64844e36i | −1.26974 | + | 1.26974i | ||||
\(623\) | 1.72985e36 | + | 1.72985e36i | 0.812201 | + | 0.812201i | ||||
\(624\) | 9.20389e34i | 0.0423225i | ||||||||
\(625\) | −1.64501e36 | + | 1.49142e36i | −0.740846 | + | 0.671675i | ||||
\(626\) | 7.34800e35 | 0.324118 | ||||||||
\(627\) | −1.01394e33 | + | 1.01394e33i | −0.000438061 | + | 0.000438061i | ||||
\(628\) | 8.13330e35 | + | 8.13330e35i | 0.344185 | + | 0.344185i | ||||
\(629\) | − | 2.25889e36i | − | 0.936346i | ||||||
\(630\) | 2.80753e36 | − | 4.09250e36i | 1.13998 | − | 1.66173i | ||||
\(631\) | 3.41731e36 | 1.35926 | 0.679630 | − | 0.733555i | \(-0.262140\pi\) | ||||
0.679630 | + | 0.733555i | \(0.262140\pi\) | |||||||
\(632\) | −6.41393e35 | + | 6.41393e35i | −0.249921 | + | 0.249921i | ||||
\(633\) | 8.13772e34 | + | 8.13772e34i | 0.0310638 | + | 0.0310638i | ||||
\(634\) | − | 9.97845e35i | − | 0.373167i | ||||||
\(635\) | 1.97693e34 | + | 1.06158e35i | 0.00724324 | + | 0.0388949i | ||||
\(636\) | −4.93242e35 | −0.177059 | ||||||||
\(637\) | −1.80887e36 | + | 1.80887e36i | −0.636203 | + | 0.636203i | ||||
\(638\) | 8.26288e35 | + | 8.26288e35i | 0.284749 | + | 0.284749i | ||||
\(639\) | 3.22712e36i | 1.08969i | ||||||||
\(640\) | −3.34700e36 | + | 6.23297e35i | −1.10743 | + | 0.206232i | ||||
\(641\) | −6.27166e35 | −0.203343 | −0.101671 | − | 0.994818i | \(-0.532419\pi\) | ||||
−0.101671 | + | 0.994818i | \(0.532419\pi\) | |||||||
\(642\) | 3.29272e35 | − | 3.29272e35i | 0.104616 | − | 0.104616i | ||||
\(643\) | −1.40071e36 | − | 1.40071e36i | −0.436119 | − | 0.436119i | 0.454584 | − | 0.890704i | \(-0.349788\pi\) |
−0.890704 | + | 0.454584i | \(0.849788\pi\) | |||||||
\(644\) | 4.26899e36i | 1.30259i | ||||||||
\(645\) | −4.81537e34 | − | 3.30344e34i | −0.0143997 | − | 0.00987849i | ||||
\(646\) | 1.76694e35 | 0.0517844 | ||||||||
\(647\) | 2.66811e36 | − | 2.66811e36i | 0.766387 | − | 0.766387i | −0.211081 | − | 0.977468i | \(-0.567699\pi\) |
0.977468 | + | 0.211081i | \(0.0676985\pi\) | |||||||
\(648\) | −1.50845e36 | − | 1.50845e36i | −0.424673 | − | 0.424673i | ||||
\(649\) | 1.99920e36i | 0.551664i | ||||||||
\(650\) | −2.59187e36 | − | 6.71761e36i | −0.701035 | − | 1.81694i | ||||
\(651\) | 5.11321e35 | 0.135563 | ||||||||
\(652\) | −4.60882e36 | + | 4.60882e36i | −1.19776 | + | 1.19776i | ||||
\(653\) | −6.58518e35 | − | 6.58518e35i | −0.167763 | − | 0.167763i | 0.618232 | − | 0.785995i | \(-0.287849\pi\) |
−0.785995 | + | 0.618232i | \(0.787849\pi\) | |||||||
\(654\) | − | 4.97516e35i | − | 0.124250i | ||||||
\(655\) | −2.27389e35 | + | 3.31462e35i | −0.0556715 | + | 0.0811515i | ||||
\(656\) | 1.11375e36 | 0.267324 | ||||||||
\(657\) | −2.37166e36 | + | 2.37166e36i | −0.558088 | + | 0.558088i | ||||
\(658\) | −1.07213e37 | − | 1.07213e37i | −2.47349 | − | 2.47349i | ||||
\(659\) | − | 3.01706e36i | − | 0.682453i | −0.939981 | − | 0.341227i | \(-0.889158\pi\) | ||
0.939981 | − | 0.341227i | \(-0.110842\pi\) | |||||||
\(660\) | 2.45275e34 | + | 1.31709e35i | 0.00543980 | + | 0.0292108i | ||||
\(661\) | 6.13427e36 | 1.33396 | 0.666981 | − | 0.745074i | \(-0.267586\pi\) | ||||
0.666981 | + | 0.745074i | \(0.267586\pi\) | |||||||
\(662\) | 9.69913e36 | − | 9.69913e36i | 2.06813 | − | 2.06813i | ||||
\(663\) | −3.66438e35 | − | 3.66438e35i | −0.0766170 | − | 0.0766170i | ||||
\(664\) | 1.70777e36i | 0.350141i | ||||||||
\(665\) | 1.86204e35 | − | 3.46761e34i | 0.0374377 | − | 0.00697186i | ||||
\(666\) | −6.35048e36 | −1.25211 | ||||||||
\(667\) | −2.38352e36 | + | 2.38352e36i | −0.460875 | + | 0.460875i | ||||
\(668\) | 5.70598e36 | + | 5.70598e36i | 1.08202 | + | 1.08202i | ||||
\(669\) | − | 2.59449e34i | − | 0.00482516i | ||||||
\(670\) | 5.68595e36 | + | 3.90067e36i | 1.03712 | + | 0.711487i | ||||
\(671\) | 1.18884e36 | 0.212682 | ||||||||
\(672\) | −5.15808e35 | + | 5.15808e35i | −0.0905081 | + | 0.0905081i | ||||
\(673\) | −3.25937e36 | − | 3.25937e36i | −0.560967 | − | 0.560967i | 0.368615 | − | 0.929582i | \(-0.379832\pi\) |
−0.929582 | + | 0.368615i | \(0.879832\pi\) | |||||||
\(674\) | 1.67859e37i | 2.83378i | ||||||||
\(675\) | 8.23816e35 | + | 3.65095e35i | 0.136421 | + | 0.0604585i | ||||
\(676\) | 5.01247e36 | 0.814225 | ||||||||
\(677\) | 6.85098e35 | − | 6.85098e35i | 0.109169 | − | 0.109169i | −0.650412 | − | 0.759581i | \(-0.725404\pi\) |
0.759581 | + | 0.650412i | \(0.225404\pi\) | |||||||
\(678\) | 5.32724e35 | + | 5.32724e35i | 0.0832752 | + | 0.0832752i | ||||
\(679\) | 1.36367e37i | 2.09123i | ||||||||
\(680\) | 2.64299e36 | − | 3.85265e36i | 0.397631 | − | 0.579620i | ||||
\(681\) | 2.89833e35 | 0.0427795 | ||||||||
\(682\) | 2.97695e36 | − | 2.97695e36i | 0.431097 | − | 0.431097i | ||||
\(683\) | −1.14607e35 | − | 1.14607e35i | −0.0162832 | − | 0.0162832i | 0.698918 | − | 0.715202i | \(-0.253665\pi\) |
−0.715202 | + | 0.698918i | \(0.753665\pi\) | |||||||
\(684\) | − | 2.89312e35i | − | 0.0403308i | ||||||
\(685\) | 1.32717e36 | + | 7.12665e36i | 0.181530 | + | 0.974783i | ||||
\(686\) | 4.30448e36 | 0.577706 | ||||||||
\(687\) | −5.58574e35 | + | 5.58574e35i | −0.0735602 | + | 0.0735602i | ||||
\(688\) | −5.74046e35 | − | 5.74046e35i | −0.0741817 | − | 0.0741817i | ||||
\(689\) | − | 1.68393e37i | − | 2.13537i | ||||||
\(690\) | −6.52334e35 | + | 1.21481e35i | −0.0811767 | + | 0.0151172i | ||||
\(691\) | 9.17260e36 | 1.12015 | 0.560077 | − | 0.828441i | \(-0.310772\pi\) | ||||
0.560077 | + | 0.828441i | \(0.310772\pi\) | |||||||
\(692\) | −1.98801e36 | + | 1.98801e36i | −0.238254 | + | 0.238254i | ||||
\(693\) | −2.22923e36 | − | 2.22923e36i | −0.262194 | − | 0.262194i | ||||
\(694\) | − | 7.56728e36i | − | 0.873508i | ||||||
\(695\) | −9.55084e36 | − | 6.55207e36i | −1.08203 | − | 0.742294i | ||||
\(696\) | 3.75609e35 | 0.0417653 | ||||||||
\(697\) | −4.43423e36 | + | 4.43423e36i | −0.483941 | + | 0.483941i | ||||
\(698\) | 2.55785e35 | + | 2.55785e35i | 0.0274003 | + | 0.0274003i | ||||
\(699\) | 4.06052e35i | 0.0426951i | ||||||||
\(700\) | 7.17001e36 | − | 1.61787e37i | 0.740023 | − | 1.66982i | ||||
\(701\) | −1.56278e37 | −1.58330 | −0.791652 | − | 0.610972i | \(-0.790779\pi\) | ||||
−0.791652 | + | 0.610972i | \(0.790779\pi\) | |||||||
\(702\) | −2.06616e36 | + | 2.06616e36i | −0.205486 | + | 0.205486i | ||||
\(703\) | −1.71374e35 | − | 1.71374e35i | −0.0167312 | − | 0.0167312i | ||||
\(704\) | 4.67075e36i | 0.447654i | ||||||||
\(705\) | 7.76473e35 | − | 1.13185e36i | 0.0730580 | − | 0.106496i | ||||
\(706\) | −1.59040e37 | −1.46908 | ||||||||
\(707\) | −7.13040e36 | + | 7.13040e36i | −0.646639 | + | 0.646639i | ||||
\(708\) | 1.60558e36 | + | 1.60558e36i | 0.142955 | + | 0.142955i | ||||
\(709\) | − | 1.30662e37i | − | 1.14222i | −0.820875 | − | 0.571108i | \(-0.806514\pi\) | ||
0.820875 | − | 0.571108i | \(-0.193486\pi\) | |||||||
\(710\) | 3.61713e36 | + | 1.94234e37i | 0.310460 | + | 1.66712i | ||||
\(711\) | 6.82768e36 | 0.575398 | ||||||||
\(712\) | 4.57817e36 | − | 4.57817e36i | 0.378836 | − | 0.378836i | ||||
\(713\) | 8.58736e36 | + | 8.58736e36i | 0.697743 | + | 0.697743i | ||||
\(714\) | − | 2.18684e36i | − | 0.174478i | ||||||
\(715\) | −4.49653e36 | + | 8.37370e35i | −0.352289 | + | 0.0656053i | ||||
\(716\) | −2.59836e37 | −1.99908 | ||||||||
\(717\) | −2.34942e34 | + | 2.34942e34i | −0.00177505 | + | 0.00177505i | ||||
\(718\) | 2.75286e36 | + | 2.75286e36i | 0.204252 | + | 0.204252i | ||||
\(719\) | − | 2.21512e37i | − | 1.61407i | −0.590506 | − | 0.807033i | \(-0.701072\pi\) | ||
0.590506 | − | 0.807033i | \(-0.298928\pi\) | |||||||
\(720\) | 5.15049e36 | + | 3.53334e36i | 0.368575 | + | 0.252850i | ||||
\(721\) | 2.35945e37 | 1.65826 | ||||||||
\(722\) | −1.58390e37 | + | 1.58390e37i | −1.09331 | + | 1.09331i | ||||
\(723\) | −7.16660e35 | − | 7.16660e35i | −0.0485865 | − | 0.0485865i | ||||
\(724\) | − | 2.24947e37i | − | 1.49789i | ||||||
\(725\) | 1.30364e37 | − | 5.02986e36i | 0.852635 | − | 0.328974i | ||||
\(726\) | −1.65611e36 | −0.106393 | ||||||||
\(727\) | −9.58321e34 | + | 9.58321e34i | −0.00604733 | + | 0.00604733i | −0.710124 | − | 0.704077i | \(-0.751361\pi\) |
0.704077 | + | 0.710124i | \(0.251361\pi\) | |||||||
\(728\) | 1.14835e37 | + | 1.14835e37i | 0.711816 | + | 0.711816i | ||||
\(729\) | 1.58742e37i | 0.966570i | ||||||||
\(730\) | −1.16162e37 | + | 1.69328e37i | −0.694814 | + | 1.01282i | ||||
\(731\) | 4.57095e36 | 0.268584 | ||||||||
\(732\) | 9.54773e35 | − | 9.54773e35i | 0.0551133 | − | 0.0551133i | ||||
\(733\) | 1.42443e37 | + | 1.42443e37i | 0.807771 | + | 0.807771i | 0.984296 | − | 0.176525i | \(-0.0564858\pi\) |
−0.176525 | + | 0.984296i | \(0.556486\pi\) | |||||||
\(734\) | 2.05876e37i | 1.14698i | ||||||||
\(735\) | −1.78913e35 | − | 9.60729e35i | −0.00979276 | − | 0.0525854i | ||||
\(736\) | −1.73254e37 | −0.931692 | ||||||||
\(737\) | 3.09720e36 | − | 3.09720e36i | 0.163641 | − | 0.163641i | ||||
\(738\) | 1.24661e37 | + | 1.24661e37i | 0.647139 | + | 0.647139i | ||||
\(739\) | − | 3.72231e37i | − | 1.89861i | −0.314362 | − | 0.949303i | \(-0.601790\pi\) | ||
0.314362 | − | 0.949303i | \(-0.398210\pi\) | |||||||
\(740\) | −2.22612e37 | + | 4.14560e36i | −1.11567 | + | 0.207766i | ||||
\(741\) | −5.56010e34 | −0.00273808 | ||||||||
\(742\) | 5.02470e37 | − | 5.02470e37i | 2.43142 | − | 2.43142i | ||||
\(743\) | −2.34225e37 | − | 2.34225e37i | −1.11372 | − | 1.11372i | −0.992642 | − | 0.121082i | \(-0.961363\pi\) |
−0.121082 | − | 0.992642i | \(-0.538637\pi\) | |||||||
\(744\) | − | 1.35325e36i | − | 0.0632308i | ||||||
\(745\) | −2.67387e36 | − | 1.83433e36i | −0.122775 | − | 0.0842260i | ||||
\(746\) | 1.07777e37 | 0.486320 | ||||||||
\(747\) | 9.08965e36 | − | 9.08965e36i | 0.403069 | − | 0.403069i | ||||
\(748\) | −7.41528e36 | − | 7.41528e36i | −0.323152 | − | 0.323152i | ||||
\(749\) | 3.90721e37i | 1.67341i | ||||||||
\(750\) | 2.67626e36 | + | 6.35240e35i | 0.112650 | + | 0.0267388i | ||||
\(751\) | −1.24516e37 | −0.515115 | −0.257558 | − | 0.966263i | \(-0.582918\pi\) | ||||
−0.257558 | + | 0.966263i | \(0.582918\pi\) | |||||||
\(752\) | 1.34929e37 | − | 1.34929e37i | 0.548624 | − | 0.548624i | ||||
\(753\) | 1.02610e35 | + | 1.02610e35i | 0.00410068 | + | 0.00410068i | ||||
\(754\) | 4.53108e37i | 1.77981i | ||||||||
\(755\) | −9.42516e36 | + | 1.37389e37i | −0.363897 | + | 0.530447i | ||||
\(756\) | −7.18144e36 | −0.272539 | ||||||||
\(757\) | 3.91841e36 | − | 3.91841e36i | 0.146172 | − | 0.146172i | −0.630234 | − | 0.776406i | \(-0.717041\pi\) |
0.776406 | + | 0.630234i | \(0.217041\pi\) | |||||||
\(758\) | −2.76830e36 | − | 2.76830e36i | −0.101511 | − | 0.101511i | ||||
\(759\) | 4.21506e35i | 0.0151936i | ||||||||
\(760\) | −9.17726e34 | − | 4.92803e35i | −0.00325190 | − | 0.0174621i | ||||
\(761\) | 4.63473e37 | 1.61445 | 0.807223 | − | 0.590247i | \(-0.200970\pi\) | ||||
0.807223 | + | 0.590247i | \(0.200970\pi\) | |||||||
\(762\) | 9.45867e34 | − | 9.45867e34i | 0.00323903 | − | 0.00323903i | ||||
\(763\) | 2.95181e37 | + | 2.95181e37i | 0.993732 | + | 0.993732i | ||||
\(764\) | − | 2.98297e37i | − | 0.987270i | ||||||
\(765\) | −3.45733e37 | + | 6.43844e36i | −1.12497 | + | 0.209499i | ||||
\(766\) | −3.30577e37 | −1.05755 | ||||||||
\(767\) | −5.48145e37 | + | 5.48145e37i | −1.72407 | + | 1.72407i | ||||
\(768\) | 2.92642e35 | + | 2.92642e35i | 0.00904985 | + | 0.00904985i | ||||
\(769\) | − | 3.88888e36i | − | 0.118245i | −0.998251 | − | 0.0591224i | \(-0.981170\pi\) | ||
0.998251 | − | 0.0591224i | \(-0.0188302\pi\) | |||||||
\(770\) | −1.59159e37 | − | 1.09186e37i | −0.475830 | − | 0.326429i | ||||
\(771\) | 2.69092e36 | 0.0791031 | ||||||||
\(772\) | −4.21407e36 | + | 4.21407e36i | −0.121808 | + | 0.121808i | ||||
\(773\) | −7.78554e36 | − | 7.78554e36i | −0.221287 | − | 0.221287i | 0.587753 | − | 0.809040i | \(-0.300012\pi\) |
−0.809040 | + | 0.587753i | \(0.800012\pi\) | |||||||
\(774\) | − | 1.28505e37i | − | 0.359158i | ||||||
\(775\) | −1.81216e37 | − | 4.69675e37i | −0.498051 | − | 1.29085i | ||||
\(776\) | 3.60904e37 | 0.975416 | ||||||||
\(777\) | −2.12100e36 | + | 2.12100e36i | −0.0563726 | + | 0.0563726i | ||||
\(778\) | −2.19232e37 | − | 2.19232e37i | −0.573018 | − | 0.573018i | ||||
\(779\) | 6.72821e35i | 0.0172947i | ||||||||
\(780\) | −2.93872e36 | + | 4.28372e36i | −0.0742896 | + | 0.108291i | ||||
\(781\) | 1.25504e37 | 0.312029 | ||||||||
\(782\) | 3.67268e37 | − | 3.67268e37i | 0.898040 | − | 0.898040i | ||||
\(783\) | −4.00965e36 | − | 4.00965e36i | −0.0964280 | − | 0.0964280i | ||||
\(784\) | − | 1.35858e37i | − | 0.321348i | ||||||
\(785\) | −2.74640e36 | − | 1.47477e37i | −0.0638936 | − | 0.343098i | ||||
\(786\) | 4.97938e35 | 0.0113941 | ||||||||
\(787\) | −1.85666e37 | + | 1.85666e37i | −0.417888 | + | 0.417888i | −0.884475 | − | 0.466587i | \(-0.845483\pi\) |
0.466587 | + | 0.884475i | \(0.345483\pi\) | |||||||
\(788\) | −4.22071e37 | − | 4.22071e37i | −0.934425 | − | 0.934425i | ||||
\(789\) | 3.50037e36i | 0.0762276i | ||||||||
\(790\) | 4.10944e37 | − | 7.65283e36i | 0.880299 | − | 0.163934i | ||||
\(791\) | −6.32140e37 | −1.33205 | ||||||||
\(792\) | −5.89981e36 | + | 5.89981e36i | −0.122296 | + | 0.122296i | ||||
\(793\) | 3.25960e37 | + | 3.25960e37i | 0.664680 | + | 0.664680i | ||||
\(794\) | − | 8.04839e35i | − | 0.0161452i | ||||||
\(795\) | 5.30462e36 | + | 3.63907e36i | 0.104684 | + | 0.0718154i | ||||
\(796\) | 3.66111e37 | 0.710793 | ||||||||
\(797\) | 4.55035e36 | − | 4.55035e36i | 0.0869133 | − | 0.0869133i | −0.662313 | − | 0.749227i | \(-0.730425\pi\) |
0.749227 | + | 0.662313i | \(0.230425\pi\) | |||||||
\(798\) | −1.65909e35 | − | 1.65909e35i | −0.00311768 | − | 0.00311768i | ||||
\(799\) | 1.07440e38i | 1.98636i | ||||||||
\(800\) | 6.56603e37 | + | 2.90991e37i | 1.19435 | + | 0.529309i | ||||
\(801\) | −4.87350e37 | −0.872204 | ||||||||
\(802\) | 2.08298e35 | − | 2.08298e35i | 0.00366791 | − | 0.00366791i | ||||
\(803\) | 9.22350e36 | + | 9.22350e36i | 0.159806 | + | 0.159806i | ||||
\(804\) | − | 4.97480e36i | − | 0.0848100i | ||||||
\(805\) | 3.14960e37 | − | 4.59112e37i | 0.528334 | − | 0.770145i | ||||
\(806\) | 1.63246e38 | 2.69455 | ||||||||
\(807\) | 4.17139e36 | − | 4.17139e36i | 0.0677525 | − | 0.0677525i | ||||
\(808\) | 1.88711e37 | + | 1.88711e37i | 0.301613 | + | 0.301613i | ||||
\(809\) | 3.55257e36i | 0.0558743i | 0.999610 | + | 0.0279372i | \(0.00889383\pi\) | ||||
−0.999610 | + | 0.0279372i | \(0.991106\pi\) | |||||||
\(810\) | 1.79981e37 | + | 9.66469e37i | 0.278562 | + | 1.49583i | ||||
\(811\) | −8.50898e37 | −1.29600 | −0.648002 | − | 0.761639i | \(-0.724395\pi\) | ||||
−0.648002 | + | 0.761639i | \(0.724395\pi\) | |||||||
\(812\) | −7.87444e37 | + | 7.87444e37i | −1.18030 | + | 1.18030i | ||||
\(813\) | 5.58032e35 | + | 5.58032e35i | 0.00823156 | + | 0.00823156i | ||||
\(814\) | 2.46973e37i | 0.358536i | ||||||||
\(815\) | 8.35693e37 | − | 1.55628e37i | 1.19398 | − | 0.222350i | ||||
\(816\) | 2.75219e36 | 0.0386995 | ||||||||
\(817\) | 3.46783e35 | − | 3.46783e35i | 0.00479923 | − | 0.00479923i | ||||
\(818\) | −9.22443e37 | − | 9.22443e37i | −1.25645 | − | 1.25645i | ||||
\(819\) | − | 1.22243e38i | − | 1.63883i | ||||||
\(820\) | 5.18368e37 | + | 3.55611e37i | 0.684004 | + | 0.469240i | ||||
\(821\) | 1.21680e38 | 1.58037 | 0.790185 | − | 0.612868i | \(-0.209984\pi\) | ||||
0.790185 | + | 0.612868i | \(0.209984\pi\) | |||||||
\(822\) | 6.34986e36 | − | 6.34986e36i | 0.0811765 | − | 0.0811765i | ||||
\(823\) | 2.49097e37 | + | 2.49097e37i | 0.313452 | + | 0.313452i | 0.846245 | − | 0.532794i | \(-0.178858\pi\) |
−0.532794 | + | 0.846245i | \(0.678858\pi\) | |||||||
\(824\) | − | 6.24446e37i | − | 0.773466i | ||||||
\(825\) | 7.07944e35 | − | 1.59743e36i | 0.00863172 | − | 0.0194770i | ||||
\(826\) | −3.27124e38 | −3.92619 | ||||||||
\(827\) | 3.02704e37 | − | 3.02704e37i | 0.357640 | − | 0.357640i | −0.505302 | − | 0.862942i | \(-0.668619\pi\) |
0.862942 | + | 0.505302i | \(0.168619\pi\) | |||||||
\(828\) | −6.01350e37 | − | 6.01350e37i | −0.699412 | − | 0.699412i | ||||
\(829\) | 2.53344e37i | 0.290069i | 0.989427 | + | 0.145035i | \(0.0463294\pi\) | ||||
−0.989427 | + | 0.145035i | \(0.953671\pi\) | |||||||
\(830\) | 4.45205e37 | − | 6.48969e37i | 0.501817 | − | 0.731490i | ||||
\(831\) | −1.05644e37 | −0.117228 | ||||||||
\(832\) | −1.28064e38 | + | 1.28064e38i | −1.39902 | + | 1.39902i | ||||
\(833\) | 5.40897e37 | + | 5.40897e37i | 0.581741 | + | 0.581741i | ||||
\(834\) | 1.43477e37i | 0.151923i | ||||||||
\(835\) | −1.92676e37 | − | 1.03464e38i | −0.200864 | − | 1.07861i | ||||
\(836\) | −1.12515e36 | −0.0115486 | ||||||||
\(837\) | −1.44460e37 | + | 1.44460e37i | −0.145987 | + | 0.145987i | ||||
\(838\) | −1.20601e38 | − | 1.20601e38i | −1.19999 | − | 1.19999i | ||||
\(839\) | − | 1.15547e38i | − | 1.13202i | −0.824399 | − | 0.566009i | \(-0.808487\pi\) | ||
0.824399 | − | 0.566009i | \(-0.191513\pi\) | |||||||
\(840\) | −6.09914e36 | + | 1.13582e36i | −0.0588353 | + | 0.0109566i | ||||
\(841\) | 1.73491e37 | 0.164790 | ||||||||
\(842\) | −2.71023e37 | + | 2.71023e37i | −0.253483 | + | 0.253483i | ||||
\(843\) | −8.84209e36 | − | 8.84209e36i | −0.0814323 | − | 0.0814323i | ||||
\(844\) | 9.03024e37i | 0.818932i | ||||||||
\(845\) | −5.39070e37 | − | 3.69813e37i | −0.481403 | − | 0.330252i | ||||
\(846\) | 3.02050e38 | 2.65622 | ||||||||
\(847\) | 9.82586e37 | − | 9.82586e37i | 0.850915 | − | 0.850915i | ||||
\(848\) | 6.32369e37 | + | 6.32369e37i | 0.539293 | + | 0.539293i | ||||
\(849\) | 2.83038e36i | 0.0237709i | ||||||||
\(850\) | −2.00873e38 | + | 7.75033e37i | −1.66140 | + | 0.641024i | ||||
\(851\) | −7.12422e37 | −0.580301 | ||||||||
\(852\) | 1.00794e37 | − | 1.00794e37i | 0.0808575 | − | 0.0808575i | ||||
\(853\) | 8.06083e37 | + | 8.06083e37i | 0.636858 | + | 0.636858i | 0.949779 | − | 0.312921i | \(-0.101308\pi\) |
−0.312921 | + | 0.949779i | \(0.601308\pi\) | |||||||
\(854\) | 1.94527e38i | 1.51366i | ||||||||
\(855\) | −2.13450e36 | + | 3.11143e36i | −0.0163583 | + | 0.0238452i | ||||
\(856\) | 1.03407e38 | 0.780532 | ||||||||
\(857\) | −6.92117e37 | + | 6.92117e37i | −0.514552 | + | 0.514552i | −0.915918 | − | 0.401366i | \(-0.868536\pi\) |
0.401366 | + | 0.915918i | \(0.368536\pi\) | |||||||
\(858\) | 4.00642e36 | + | 4.00642e36i | 0.0293374 | + | 0.0293374i | ||||
\(859\) | 1.81048e38i | 1.30582i | 0.757436 | + | 0.652909i | \(0.226452\pi\) | ||||
−0.757436 | + | 0.652909i | \(0.773548\pi\) | |||||||
\(860\) | −8.38879e36 | − | 4.50463e37i | −0.0595963 | − | 0.320022i | ||||
\(861\) | 8.32712e36 | 0.0582712 | ||||||||
\(862\) | 1.43753e38 | − | 1.43753e38i | 0.990885 | − | 0.990885i | ||||
\(863\) | −8.05209e37 | − | 8.05209e37i | −0.546724 | − | 0.546724i | 0.378768 | − | 0.925492i | \(-0.376348\pi\) |
−0.925492 | + | 0.378768i | \(0.876348\pi\) | |||||||
\(864\) | − | 2.91455e37i | − | 0.194936i | ||||||
\(865\) | 3.60475e37 | − | 6.71298e36i | 0.237501 | − | 0.0442289i | ||||
\(866\) | −9.96016e37 | −0.646448 | ||||||||
\(867\) | −2.68292e36 | + | 2.68292e36i | −0.0171537 | + | 0.0171537i | ||||
\(868\) | 2.83700e38 | + | 2.83700e38i | 1.78691 | + | 1.78691i | ||||
\(869\) | − | 2.65532e37i | − | 0.164763i | ||||||
\(870\) | −1.42735e37 | − | 9.79193e36i | −0.0872532 | − | 0.0598574i | ||||
\(871\) | 1.69840e38 | 1.02283 | ||||||||
\(872\) | 7.81217e37 | − | 7.81217e37i | 0.463508 | − | 0.463508i | ||||
\(873\) | −1.92093e38 | − | 1.92093e38i | −1.12286 | − | 1.12286i | ||||
\(874\) | − | 5.57269e36i | − | 0.0320934i | ||||||
\(875\) | −1.96475e38 | + | 1.21096e38i | −1.11481 | + | 0.687108i | ||||
\(876\) | 1.48150e37 | 0.0828226 | ||||||||
\(877\) | 1.19542e38 | − | 1.19542e38i | 0.658455 | − | 0.658455i | −0.296559 | − | 0.955014i | \(-0.595839\pi\) |
0.955014 | + | 0.296559i | \(0.0958392\pi\) | |||||||
\(878\) | 4.09900e37 | + | 4.09900e37i | 0.222458 | + | 0.222458i | ||||
\(879\) | 1.36875e37i | 0.0731926i | ||||||||
\(880\) | 1.37413e37 | − | 2.00305e37i | 0.0724025 | − | 0.105540i | ||||
\(881\) | −6.33187e37 | −0.328735 | −0.164367 | − | 0.986399i | \(-0.552558\pi\) | ||||
−0.164367 | + | 0.986399i | \(0.552558\pi\) | |||||||
\(882\) | 1.52064e38 | − | 1.52064e38i | 0.777920 | − | 0.777920i | ||||
\(883\) | −3.05685e37 | − | 3.05685e37i | −0.154094 | − | 0.154094i | 0.625850 | − | 0.779944i | \(-0.284752\pi\) |
−0.779944 | + | 0.625850i | \(0.784752\pi\) | |||||||
\(884\) | − | 4.06628e38i | − | 2.01985i | ||||||
\(885\) | −5.42161e36 | − | 2.91131e37i | −0.0265379 | − | 0.142504i | ||||
\(886\) | −3.06525e37 | −0.147852 | ||||||||
\(887\) | −1.07750e38 | + | 1.07750e38i | −0.512167 | + | 0.512167i | −0.915190 | − | 0.403023i | \(-0.867959\pi\) |
0.403023 | + | 0.915190i | \(0.367959\pi\) | |||||||
\(888\) | 5.61338e36 | + | 5.61338e36i | 0.0262940 | + | 0.0262940i | ||||
\(889\) | 1.12238e37i | 0.0518106i | ||||||||
\(890\) | −2.93326e38 | + | 5.46248e37i | −1.33438 | + | 0.248496i | ||||
\(891\) | 6.24485e37 | 0.279970 | ||||||||
\(892\) | 1.43952e37 | − | 1.43952e37i | 0.0636027 | − | 0.0636027i | ||||
\(893\) | 8.15113e36 | + | 8.15113e36i | 0.0354935 | + | 0.0354935i | ||||
\(894\) | 4.01682e36i | 0.0172383i | ||||||||
\(895\) | 2.79443e38 | + | 1.91703e38i | 1.18194 | + | 0.810831i | ||||
\(896\) | −3.53872e38 | −1.47517 | ||||||||
\(897\) | −1.15570e37 | + | 1.15570e37i | −0.0474834 | + | 0.0474834i | ||||
\(898\) | 1.00358e38 | + | 1.00358e38i | 0.406406 | + | 0.406406i | ||||
\(899\) | 3.16799e38i | 1.26447i | ||||||||
\(900\) | 1.26901e38 | + | 3.28901e38i | 0.499242 | + | 1.29394i | ||||
\(901\) | −5.03536e38 | −1.95258 | ||||||||
\(902\) | 4.84812e37 | − | 4.84812e37i | 0.185306 | − | 0.185306i | ||||
\(903\) | −4.29193e36 | − | 4.29193e36i | −0.0161701 | − | 0.0161701i | ||||
\(904\) | 1.67300e38i | 0.621309i | ||||||||
\(905\) | −1.65963e38 | + | 2.41921e38i | −0.607546 | + | 0.885610i | ||||
\(906\) | 2.06392e37 | 0.0744778 | ||||||||
\(907\) | 1.17592e38 | − | 1.17592e38i | 0.418294 | − | 0.418294i | −0.466321 | − | 0.884615i | \(-0.654421\pi\) |
0.884615 | + | 0.466321i | \(0.154421\pi\) | |||||||
\(908\) | 1.60811e38 | + | 1.60811e38i | 0.563896 | + | 0.563896i | ||||
\(909\) | − | 2.00885e38i | − | 0.694410i | ||||||
\(910\) | −1.37017e38 | − | 7.35756e38i | −0.466913 | − | 2.50724i | ||||
\(911\) | 4.02801e38 | 1.35317 | 0.676585 | − | 0.736365i | \(-0.263459\pi\) | ||||
0.676585 | + | 0.736365i | \(0.263459\pi\) | |||||||
\(912\) | 2.08799e35 | − | 2.08799e35i | 0.000691507 | − | 0.000691507i | ||||
\(913\) | −3.53501e37 | − | 3.53501e37i | −0.115417 | − | 0.115417i | ||||
\(914\) | − | 6.05720e38i | − | 1.94971i | ||||||
\(915\) | −1.73124e37 | + | 3.22401e36i | −0.0549392 | + | 0.0102311i | ||||
\(916\) | −6.19837e38 | −1.93926 | ||||||||
\(917\) | −2.95431e37 | + | 2.95431e37i | −0.0911287 | + | 0.0911287i | ||||
\(918\) | 6.17832e37 | + | 6.17832e37i | 0.187895 | + | 0.187895i | ||||
\(919\) | − | 4.81218e38i | − | 1.44291i | −0.692460 | − | 0.721456i | \(-0.743473\pi\) | ||
0.692460 | − | 0.721456i | \(-0.256527\pi\) | |||||||
\(920\) | −1.21507e38 | − | 8.33564e37i | −0.359220 | − | 0.246432i | ||||
\(921\) | 3.21727e37 | 0.0937804 | ||||||||
\(922\) | −3.68625e38 | + | 3.68625e38i | −1.05946 | + | 1.05946i | ||||
\(923\) | 3.44111e38 | + | 3.44111e38i | 0.975161 | + | 0.975161i | ||||
\(924\) | 1.39253e37i | 0.0389107i | ||||||||
\(925\) | 2.69995e38 | + | 1.19655e38i | 0.743899 | + | 0.329678i | ||||
\(926\) | 1.08690e39 | 2.95289 | ||||||||
\(927\) | −3.32364e38 | + | 3.32364e38i | −0.890384 | + | 0.890384i | ||||
\(928\) | −3.19579e38 | − | 3.19579e38i | −0.844219 | − | 0.844219i | ||||
\(929\) | − | 3.71177e38i | − | 0.966889i | −0.875375 | − | 0.483444i | \(-0.839386\pi\) | ||
0.875375 | − | 0.483444i | \(-0.160614\pi\) | |||||||
\(930\) | −3.52784e37 | + | 5.14248e37i | −0.0906214 | + | 0.132097i | ||||
\(931\) | 8.20722e36 | 0.0207898 | ||||||||
\(932\) | −2.25293e38 | + | 2.25293e38i | −0.562783 | + | 0.562783i | ||||
\(933\) | −2.49205e37 | − | 2.49205e37i | −0.0613898 | − | 0.0613898i | ||||
\(934\) | 2.11740e38i | 0.514391i | ||||||||
\(935\) | 2.50394e37 | + | 1.34457e38i | 0.0599892 | + | 0.322132i | ||||
\(936\) | −3.23525e38 | −0.764402 | ||||||||
\(937\) | −1.66704e37 | + | 1.66704e37i | −0.0388446 | + | 0.0388446i | −0.726262 | − | 0.687418i | \(-0.758744\pi\) |
0.687418 | + | 0.726262i | \(0.258744\pi\) | |||||||
\(938\) | 5.06787e38 | + | 5.06787e38i | 1.16463 | + | 1.16463i | ||||
\(939\) | 6.91410e36i | 0.0156705i | ||||||||
\(940\) | 1.05881e39 | − | 1.97178e38i | 2.36678 | − | 0.440755i | ||||
\(941\) | −3.76950e38 | −0.831034 | −0.415517 | − | 0.909585i | \(-0.636399\pi\) | ||||
−0.415517 | + | 0.909585i | \(0.636399\pi\) | |||||||
\(942\) | −1.31402e37 | + | 1.31402e37i | −0.0285720 | + | 0.0285720i | ||||
\(943\) | 1.39850e38 | + | 1.39850e38i | 0.299922 | + | 0.299922i | ||||
\(944\) | − | 4.11692e38i | − | 0.870836i | ||||||
\(945\) | 7.72335e37 | + | 5.29837e37i | 0.161136 | + | 0.110542i | ||||
\(946\) | −4.99760e37 | −0.102844 | ||||||||
\(947\) | 5.14523e38 | − | 5.14523e38i | 1.04437 | − | 1.04437i | 0.0454024 | − | 0.998969i | \(-0.485543\pi\) |
0.998969 | − | 0.0454024i | \(-0.0144570\pi\) | |||||||
\(948\) | −2.13252e37 | − | 2.13252e37i | −0.0426957 | − | 0.0426957i | ||||
\(949\) | 5.05785e38i | 0.998861i | ||||||||
\(950\) | −9.35966e36 | + | 2.11195e37i | −0.0182328 | + | 0.0411412i | ||||
\(951\) | 9.38923e36 | 0.0180419 | ||||||||
\(952\) | 3.43386e38 | − | 3.43386e38i | 0.650881 | − | 0.650881i | ||||
\(953\) | −3.88881e38 | − | 3.88881e38i | −0.727125 | − | 0.727125i | 0.242921 | − | 0.970046i | \(-0.421894\pi\) |
−0.970046 | + | 0.242921i | \(0.921894\pi\) | |||||||
\(954\) | 1.41561e39i | 2.61104i | ||||||||
\(955\) | −2.20080e38 | + | 3.20807e38i | −0.400439 | + | 0.583713i | ||||
\(956\) | −2.60709e37 | −0.0467955 | ||||||||
\(957\) | −7.77497e36 | + | 7.77497e36i | −0.0137671 | + | 0.0137671i | ||||
\(958\) | −2.14637e38 | − | 2.14637e38i | −0.374932 | − | 0.374932i | ||||
\(959\) | 7.53487e38i | 1.29848i | ||||||||
\(960\) | −1.26666e37 | − | 6.80174e37i | −0.0215344 | − | 0.115636i | ||||
\(961\) | 5.45149e38 | 0.914347 | ||||||||
\(962\) | −6.77158e38 | + | 6.77158e38i | −1.12051 | + | 1.12051i | ||||
\(963\) | −5.50388e38 | − | 5.50388e38i | −0.898519 | − | 0.898519i | ||||
\(964\) | − | 7.95261e38i | − | 1.28088i | ||||||
\(965\) | 7.64114e37 | − | 1.42298e37i | 0.121424 | − | 0.0226122i | ||||
\(966\) | −6.89700e37 | −0.108133 | ||||||||
\(967\) | 3.28550e38 | − | 3.28550e38i | 0.508227 | − | 0.508227i | −0.405755 | − | 0.913982i | \(-0.632991\pi\) |
0.913982 | + | 0.405755i | \(0.132991\pi\) | |||||||
\(968\) | −2.60048e38 | − | 2.60048e38i | −0.396894 | − | 0.396894i | ||||
\(969\) | 1.66260e36i | 0.00250369i | ||||||||
\(970\) | −1.37147e39 | − | 9.40859e38i | −2.03777 | − | 1.39795i | ||||
\(971\) | 4.07409e38 | 0.597284 | 0.298642 | − | 0.954365i | \(-0.403466\pi\) | ||||
0.298642 | + | 0.954365i | \(0.403466\pi\) | |||||||
\(972\) | 1.51884e38 | − | 1.51884e38i | 0.219710 | − | 0.219710i | ||||
\(973\) | −8.51265e38 | − | 8.51265e38i | −1.21506 | − | 1.21506i | ||||
\(974\) | 6.37767e38i | 0.898247i | ||||||||
\(975\) | 6.32094e37 | − | 2.43882e37i | 0.0878460 | − | 0.0338938i | ||||
\(976\) | −2.44817e38 | −0.335732 | ||||||||
\(977\) | −3.81179e37 | + | 3.81179e37i | −0.0515822 | + | 0.0515822i | −0.732427 | − | 0.680845i | \(-0.761613\pi\) |
0.680845 | + | 0.732427i | \(0.261613\pi\) | |||||||
\(978\) | −7.44604e37 | − | 7.44604e37i | −0.0994306 | − | 0.0994306i | ||||
\(979\) | 1.89533e38i | 0.249752i | ||||||||
\(980\) | 4.33782e38 | − | 6.32317e38i | 0.564069 | − | 0.822235i | ||||
\(981\) | −8.31612e38 | −1.06715 | ||||||||
\(982\) | 6.97243e38 | − | 6.97243e38i | 0.882948 | − | 0.882948i | ||||
\(983\) | −9.88158e38 | − | 9.88158e38i | −1.23490 | − | 1.23490i | −0.962060 | − | 0.272837i | \(-0.912038\pi\) |
−0.272837 | − | 0.962060i | \(-0.587962\pi\) | |||||||
\(984\) | − | 2.20383e37i | − | 0.0271795i | ||||||
\(985\) | 1.42522e38 | + | 7.65318e38i | 0.173465 | + | 0.931475i | ||||
\(986\) | 1.35490e39 | 1.62745 | ||||||||
\(987\) | 1.00882e38 | − | 1.00882e38i | 0.119589 | − | 0.119589i | ||||
\(988\) | −3.08496e37 | − | 3.08496e37i | −0.0360918 | − | 0.0360918i | ||||
\(989\) | − | 1.44161e38i | − | 0.166455i | ||||||
\(990\) | 3.78004e38 | − | 7.03941e37i | 0.430764 | − | 0.0802193i | ||||
\(991\) | 1.01547e39 | 1.14211 | 0.571056 | − | 0.820911i | \(-0.306534\pi\) | ||||
0.571056 | + | 0.820911i | \(0.306534\pi\) | |||||||
\(992\) | −1.15138e39 | + | 1.15138e39i | −1.27811 | + | 1.27811i | ||||
\(993\) | 9.12640e37 | + | 9.12640e37i | 0.0999906 | + | 0.0999906i | ||||
\(994\) | 2.05360e39i | 2.22071i | ||||||||
\(995\) | −3.93738e38 | − | 2.70112e38i | −0.420249 | − | 0.288299i | ||||
\(996\) | −5.67802e37 | −0.0598171 | ||||||||
\(997\) | −2.28478e38 | + | 2.28478e38i | −0.237579 | + | 0.237579i | −0.815847 | − | 0.578268i | \(-0.803729\pi\) |
0.578268 | + | 0.815847i | \(0.303729\pi\) | |||||||
\(998\) | 8.61005e38 | + | 8.61005e38i | 0.883707 | + | 0.883707i | ||||
\(999\) | − | 1.19846e38i | − | 0.121415i |
(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 | 5.27.c.a.3.3 | yes | 24 | |
5.2 | odd | 4 | inner | 5.27.c.a.2.3 | ✓ | 24 | |
5.3 | odd | 4 | 25.27.c.b.7.10 | 24 | |||
5.4 | even | 2 | 25.27.c.b.18.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.27.c.a.2.3 | ✓ | 24 | 5.2 | odd | 4 | inner | |
5.27.c.a.3.3 | yes | 24 | 1.1 | even | 1 | trivial | |
25.27.c.b.7.10 | 24 | 5.3 | odd | 4 | |||
25.27.c.b.18.10 | 24 | 5.4 | even | 2 |