Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,33,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, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
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: | \(32.4333275711\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2.5 | ||
Character | \(\chi\) | \(=\) | 5.2 |
Dual form | 5.33.c.a.3.5 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −39535.2 | − | 39535.2i | −0.603260 | − | 0.603260i | 0.337916 | − | 0.941176i | \(-0.390278\pi\) |
−0.941176 | + | 0.337916i | \(0.890278\pi\) | |||||||
\(3\) | 4.69567e7 | − | 4.69567e7i | 1.09083 | − | 1.09083i | 0.0953909 | − | 0.995440i | \(-0.469590\pi\) |
0.995440 | − | 0.0953909i | \(-0.0304101\pi\) | |||||||
\(4\) | − | 1.16890e9i | − | 0.272156i | ||||||
\(5\) | −7.61848e10 | + | 1.32208e11i | −0.499284 | + | 0.866438i | ||||
\(6\) | −3.71289e12 | −1.31611 | ||||||||
\(7\) | 2.85172e13 | + | 2.85172e13i | 0.858100 | + | 0.858100i | 0.991114 | − | 0.133014i | \(-0.0424655\pi\) |
−0.133014 | + | 0.991114i | \(0.542466\pi\) | |||||||
\(8\) | −2.16015e14 | + | 2.16015e14i | −0.767440 | + | 0.767440i | ||||
\(9\) | − | 2.55684e15i | − | 1.37982i | ||||||
\(10\) | 8.23885e15 | − | 2.21489e15i | 0.823885 | − | 0.221489i | ||||
\(11\) | 6.29088e16 | 1.36908 | 0.684540 | − | 0.728975i | \(-0.260003\pi\) | ||||
0.684540 | + | 0.728975i | \(0.260003\pi\) | |||||||
\(12\) | −5.48877e16 | − | 5.48877e16i | −0.296876 | − | 0.296876i | ||||
\(13\) | 6.68945e17 | − | 6.68945e17i | 1.00530 | − | 1.00530i | 0.00531621 | − | 0.999986i | \(-0.498308\pi\) |
0.999986 | − | 0.00531621i | \(-0.00169221\pi\) | |||||||
\(14\) | − | 2.25487e18i | − | 1.03531i | ||||||
\(15\) | 2.63066e18 | + | 9.78543e18i | 0.400503 | + | 1.48977i | ||||
\(16\) | 1.20600e19 | 0.653776 | ||||||||
\(17\) | 9.86415e17 | + | 9.86415e17i | 0.0202711 | + | 0.0202711i | 0.717170 | − | 0.696899i | \(-0.245437\pi\) |
−0.696899 | + | 0.717170i | \(0.745437\pi\) | |||||||
\(18\) | −1.01085e20 | + | 1.01085e20i | −0.832392 | + | 0.832392i | ||||
\(19\) | 3.77787e20i | 1.30975i | 0.755736 | + | 0.654876i | \(0.227279\pi\) | ||||
−0.755736 | + | 0.654876i | \(0.772721\pi\) | |||||||
\(20\) | 1.54538e20 | + | 8.90523e19i | 0.235806 | + | 0.135883i | ||||
\(21\) | 2.67814e21 | 1.87208 | ||||||||
\(22\) | −2.48712e21 | − | 2.48712e21i | −0.825911 | − | 0.825911i | ||||
\(23\) | 5.92343e21 | − | 5.92343e21i | 0.965890 | − | 0.965890i | −0.0335474 | − | 0.999437i | \(-0.510680\pi\) |
0.999437 | + | 0.0335474i | \(0.0106805\pi\) | |||||||
\(24\) | 2.02867e22i | 1.67429i | ||||||||
\(25\) | −1.16748e22 | − | 2.01445e22i | −0.501430 | − | 0.865198i | ||||
\(26\) | −5.28938e22 | −1.21292 | ||||||||
\(27\) | −3.30491e22 | − | 3.30491e22i | −0.414323 | − | 0.414323i | ||||
\(28\) | 3.33337e22 | − | 3.33337e22i | 0.233537 | − | 0.233537i | ||||
\(29\) | − | 2.77779e19i | − | 0.000111002i | −1.00000 | 5.55011e-5i | \(-0.999982\pi\) | |||
1.00000 | 5.55011e-5i | \(-1.76665e-5\pi\) | ||||||||
\(30\) | 2.82865e23 | − | 4.90873e23i | 0.657112 | − | 1.14033i | ||||
\(31\) | −3.93433e23 | −0.540858 | −0.270429 | − | 0.962740i | \(-0.587166\pi\) | ||||
−0.270429 | + | 0.962740i | \(0.587166\pi\) | |||||||
\(32\) | 4.50982e23 | + | 4.50982e23i | 0.373044 | + | 0.373044i | ||||
\(33\) | 2.95399e24 | − | 2.95399e24i | 1.49343 | − | 1.49343i | ||||
\(34\) | − | 7.79962e22i | − | 0.0244574i | ||||||
\(35\) | −5.94277e24 | + | 1.59762e24i | −1.17193 | + | 0.315055i | ||||
\(36\) | −2.98869e24 | −0.375527 | ||||||||
\(37\) | −4.19934e24 | − | 4.19934e24i | −0.340371 | − | 0.340371i | 0.516136 | − | 0.856507i | \(-0.327370\pi\) |
−0.856507 | + | 0.516136i | \(0.827370\pi\) | |||||||
\(38\) | 1.49359e25 | − | 1.49359e25i | 0.790121 | − | 0.790121i | ||||
\(39\) | − | 6.28229e25i | − | 2.19323i | ||||||
\(40\) | −1.21019e25 | − | 4.50160e25i | −0.281768 | − | 1.04811i | ||||
\(41\) | 8.53049e25 | 1.33793 | 0.668964 | − | 0.743295i | \(-0.266738\pi\) | ||||
0.668964 | + | 0.743295i | \(0.266738\pi\) | |||||||
\(42\) | −1.05881e26 | − | 1.05881e26i | −1.12935 | − | 1.12935i | ||||
\(43\) | −8.89872e25 | + | 8.89872e25i | −0.651377 | + | 0.651377i | −0.953324 | − | 0.301948i | \(-0.902363\pi\) |
0.301948 | + | 0.953324i | \(0.402363\pi\) | |||||||
\(44\) | − | 7.35341e25i | − | 0.372603i | ||||||
\(45\) | 3.38035e26 | + | 1.94792e26i | 1.19553 | + | 0.688925i | ||||
\(46\) | −4.68368e26 | −1.16536 | ||||||||
\(47\) | 3.07295e26 | + | 3.07295e26i | 0.541988 | + | 0.541988i | 0.924111 | − | 0.382124i | \(-0.124807\pi\) |
−0.382124 | + | 0.924111i | \(0.624807\pi\) | |||||||
\(48\) | 5.66299e26 | − | 5.66299e26i | 0.713159 | − | 0.713159i | ||||
\(49\) | 5.22031e26i | 0.472671i | ||||||||
\(50\) | −3.34849e26 | + | 1.25798e27i | −0.219447 | + | 0.824432i | ||||
\(51\) | 9.26375e25 | 0.0442246 | ||||||||
\(52\) | −7.81929e26 | − | 7.81929e26i | −0.273599 | − | 0.273599i | ||||
\(53\) | 4.54942e26 | − | 4.54942e26i | 0.117366 | − | 0.117366i | −0.645984 | − | 0.763351i | \(-0.723553\pi\) |
0.763351 | + | 0.645984i | \(0.223553\pi\) | |||||||
\(54\) | 2.61321e27i | 0.499889i | ||||||||
\(55\) | −4.79270e27 | + | 8.31705e27i | −0.683560 | + | 1.18622i | ||||
\(56\) | −1.23203e28 | −1.31708 | ||||||||
\(57\) | 1.77396e28 | + | 1.77396e28i | 1.42872 | + | 1.42872i | ||||
\(58\) | −1.09821e24 | + | 1.09821e24i | −6.69631e−5 | + | 6.69631e-5i | ||||
\(59\) | − | 1.68462e28i | − | 0.781393i | −0.920520 | − | 0.390696i | \(-0.872234\pi\) | ||
0.920520 | − | 0.390696i | \(-0.127766\pi\) | |||||||
\(60\) | 1.14382e28 | − | 3.07498e27i | 0.405450 | − | 0.108999i | ||||
\(61\) | −1.17239e28 | −0.319004 | −0.159502 | − | 0.987198i | \(-0.550989\pi\) | ||||
−0.159502 | + | 0.987198i | \(0.550989\pi\) | |||||||
\(62\) | 1.55544e28 | + | 1.55544e28i | 0.326278 | + | 0.326278i | ||||
\(63\) | 7.29139e28 | − | 7.29139e28i | 1.18403 | − | 1.18403i | ||||
\(64\) | − | 8.74568e28i | − | 1.10386i | ||||||
\(65\) | 3.74764e28 | + | 1.39403e29i | 0.369100 | + | 1.37296i | ||||
\(66\) | −2.33573e29 | −1.80186 | ||||||||
\(67\) | −1.91395e29 | − | 1.91395e29i | −1.16074 | − | 1.16074i | −0.984315 | − | 0.176422i | \(-0.943548\pi\) |
−0.176422 | − | 0.984315i | \(-0.556452\pi\) | |||||||
\(68\) | 1.15302e27 | − | 1.15302e27i | 0.00551689 | − | 0.00551689i | ||||
\(69\) | − | 5.56289e29i | − | 2.10724i | ||||||
\(70\) | 2.98111e29 | + | 1.71786e29i | 0.897036 | + | 0.516916i | ||||
\(71\) | −1.41479e29 | −0.339279 | −0.169640 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169640 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(72\) | 5.52317e29 | + | 5.52317e29i | 1.05893 | + | 1.05893i | ||||
\(73\) | 5.53990e29 | − | 5.53990e29i | 0.851797 | − | 0.851797i | −0.138558 | − | 0.990354i | \(-0.544247\pi\) |
0.990354 | + | 0.138558i | \(0.0442467\pi\) | |||||||
\(74\) | 3.32043e29i | 0.410665i | ||||||||
\(75\) | −1.49413e30 | − | 3.97706e29i | −1.49076 | − | 0.396809i | ||||
\(76\) | 4.41595e29 | 0.356456 | ||||||||
\(77\) | 1.79398e30 | + | 1.79398e30i | 1.17481 | + | 1.17481i | ||||
\(78\) | −2.48372e30 | + | 2.48372e30i | −1.32309 | + | 1.32309i | ||||
\(79\) | 1.90483e30i | 0.827604i | 0.910367 | + | 0.413802i | \(0.135799\pi\) | ||||
−0.910367 | + | 0.413802i | \(0.864201\pi\) | |||||||
\(80\) | −9.18791e29 | + | 1.59443e30i | −0.326420 | + | 0.566456i | ||||
\(81\) | 1.63413e30 | 0.475910 | ||||||||
\(82\) | −3.37255e30 | − | 3.37255e30i | −0.807117 | − | 0.807117i | ||||
\(83\) | 2.78325e30 | − | 2.78325e30i | 0.548659 | − | 0.548659i | −0.377394 | − | 0.926053i | \(-0.623180\pi\) |
0.926053 | + | 0.377394i | \(0.123180\pi\) | |||||||
\(84\) | − | 3.13048e30i | − | 0.509498i | ||||||
\(85\) | −2.05562e29 | + | 5.52621e28i | −0.0276847 | + | 0.00744260i | ||||
\(86\) | 7.03626e30 | 0.785898 | ||||||||
\(87\) | −1.30436e27 | − | 1.30436e27i | −0.000121085 | − | 0.000121085i | ||||
\(88\) | −1.35893e31 | + | 1.35893e31i | −1.05069 | + | 1.05069i | ||||
\(89\) | − | 2.46808e30i | − | 0.159265i | −0.996824 | − | 0.0796323i | \(-0.974625\pi\) | ||
0.996824 | − | 0.0796323i | \(-0.0253746\pi\) | |||||||
\(90\) | −5.66312e30 | − | 2.10654e31i | −0.305616 | − | 1.13682i | ||||
\(91\) | 3.81528e31 | 1.72530 | ||||||||
\(92\) | −6.92389e30 | − | 6.92389e30i | −0.262872 | − | 0.262872i | ||||
\(93\) | −1.84743e31 | + | 1.84743e31i | −0.589985 | + | 0.589985i | ||||
\(94\) | − | 2.42979e31i | − | 0.653919i | ||||||
\(95\) | −4.99464e31 | − | 2.87816e31i | −1.13482 | − | 0.653939i | ||||
\(96\) | 4.23533e31 | 0.813855 | ||||||||
\(97\) | 4.72097e31 | + | 4.72097e31i | 0.768569 | + | 0.768569i | 0.977855 | − | 0.209285i | \(-0.0671137\pi\) |
−0.209285 | + | 0.977855i | \(0.567114\pi\) | |||||||
\(98\) | 2.06386e31 | − | 2.06386e31i | 0.285144 | − | 0.285144i | ||||
\(99\) | − | 1.60848e32i | − | 1.88909i | ||||||
\(100\) | −2.35469e31 | + | 1.36467e31i | −0.235469 | + | 0.136467i | ||||
\(101\) | −7.50238e31 | −0.639819 | −0.319909 | − | 0.947448i | \(-0.603652\pi\) | ||||
−0.319909 | + | 0.947448i | \(0.603652\pi\) | |||||||
\(102\) | −3.66245e30 | − | 3.66245e30i | −0.0266789 | − | 0.0266789i | ||||
\(103\) | −7.84408e30 | + | 7.84408e30i | −0.0488817 | + | 0.0488817i | −0.731125 | − | 0.682243i | \(-0.761004\pi\) |
0.682243 | + | 0.731125i | \(0.261004\pi\) | |||||||
\(104\) | 2.89004e32i | 1.54302i | ||||||||
\(105\) | −2.04034e32 | + | 3.54072e32i | −0.934702 | + | 1.62204i | ||||
\(106\) | −3.59725e31 | −0.141604 | ||||||||
\(107\) | 2.98505e32 | + | 2.98505e32i | 1.01114 | + | 1.01114i | 0.999937 | + | 0.0112018i | \(0.00356572\pi\) |
0.0112018 | + | 0.999937i | \(0.496434\pi\) | |||||||
\(108\) | −3.86311e31 | + | 3.86311e31i | −0.112760 | + | 0.112760i | ||||
\(109\) | − | 2.49847e32i | − | 0.629289i | −0.949210 | − | 0.314644i | \(-0.898115\pi\) | ||
0.949210 | − | 0.314644i | \(-0.101885\pi\) | |||||||
\(110\) | 5.18297e32 | − | 1.39336e32i | 1.12796 | − | 0.303236i | ||||
\(111\) | −3.94374e32 | −0.742575 | ||||||||
\(112\) | 3.43918e32 | + | 3.43918e32i | 0.561005 | + | 0.561005i | ||||
\(113\) | 1.36893e32 | − | 1.36893e32i | 0.193699 | − | 0.193699i | −0.603593 | − | 0.797292i | \(-0.706265\pi\) |
0.797292 | + | 0.603593i | \(0.206265\pi\) | |||||||
\(114\) | − | 1.40268e33i | − | 1.72378i | ||||||
\(115\) | 3.31849e32 | + | 1.23440e33i | 0.354630 | + | 1.31914i | ||||
\(116\) | −3.24696e28 | −3.02099e−5 | ||||||||
\(117\) | −1.71039e33 | − | 1.71039e33i | −1.38714 | − | 1.38714i | ||||
\(118\) | −6.66018e32 | + | 6.66018e32i | −0.471383 | + | 0.471383i | ||||
\(119\) | 5.62595e31i | 0.0347892i | ||||||||
\(120\) | −2.68207e33 | − | 1.54554e33i | −1.45067 | − | 0.835949i | ||||
\(121\) | 1.84615e33 | 0.874379 | ||||||||
\(122\) | 4.63508e32 | + | 4.63508e32i | 0.192442 | + | 0.192442i | ||||
\(123\) | 4.00564e33 | − | 4.00564e33i | 1.45945 | − | 1.45945i | ||||
\(124\) | 4.59883e32i | 0.147198i | ||||||||
\(125\) | 3.55270e33 | − | 8.80412e30i | 0.999997 | − | 0.00247814i | ||||
\(126\) | −5.76533e33 | −1.42855 | ||||||||
\(127\) | 9.12962e32 | + | 9.12962e32i | 0.199339 | + | 0.199339i | 0.799717 | − | 0.600377i | \(-0.204983\pi\) |
−0.600377 | + | 0.799717i | \(0.704983\pi\) | |||||||
\(128\) | −1.52067e33 | + | 1.52067e33i | −0.292871 | + | 0.292871i | ||||
\(129\) | 8.35709e33i | 1.42108i | ||||||||
\(130\) | 4.02970e33 | − | 6.99298e33i | 0.605590 | − | 1.05092i | ||||
\(131\) | 8.11479e33 | 1.07879 | 0.539394 | − | 0.842053i | \(-0.318653\pi\) | ||||
0.539394 | + | 0.842053i | \(0.318653\pi\) | |||||||
\(132\) | −3.45292e33 | − | 3.45292e33i | −0.406447 | − | 0.406447i | ||||
\(133\) | −1.07734e34 | + | 1.07734e34i | −1.12390 | + | 1.12390i | ||||
\(134\) | 1.51337e34i | 1.40045i | ||||||||
\(135\) | 6.88719e33 | − | 1.85152e33i | 0.565851 | − | 0.152120i | ||||
\(136\) | −4.26161e32 | −0.0311137 | ||||||||
\(137\) | −1.69300e34 | − | 1.69300e34i | −1.09933 | − | 1.09933i | −0.994489 | − | 0.104842i | \(-0.966566\pi\) |
−0.104842 | − | 0.994489i | \(-0.533434\pi\) | |||||||
\(138\) | −2.19930e34 | + | 2.19930e34i | −1.27122 | + | 1.27122i | ||||
\(139\) | 2.64534e32i | 0.0136221i | 0.999977 | + | 0.00681107i | \(0.00216805\pi\) | ||||
−0.999977 | + | 0.00681107i | \(0.997832\pi\) | |||||||
\(140\) | 1.86746e33 | + | 6.94650e33i | 0.0857439 | + | 0.318946i | ||||
\(141\) | 2.88591e34 | 1.18243 | ||||||||
\(142\) | 5.59339e33 | + | 5.59339e33i | 0.204673 | + | 0.204673i | ||||
\(143\) | 4.20825e34 | − | 4.20825e34i | 1.37634 | − | 1.37634i | ||||
\(144\) | − | 3.08356e34i | − | 0.902095i | ||||||
\(145\) | 3.67246e30 | + | 2.11625e30i | 9.61765e−5 | + | 5.54217e-5i | ||||
\(146\) | −4.38042e34 | −1.02771 | ||||||||
\(147\) | 2.45129e34 | + | 2.45129e34i | 0.515605 | + | 0.515605i | ||||
\(148\) | −4.90860e33 | + | 4.90860e33i | −0.0926340 | + | 0.0926340i | ||||
\(149\) | − | 7.97866e33i | − | 0.135192i | −0.997713 | − | 0.0675958i | \(-0.978467\pi\) | ||
0.997713 | − | 0.0675958i | \(-0.0215328\pi\) | |||||||
\(150\) | 4.33473e34 | + | 7.47941e34i | 0.659936 | + | 1.13869i | ||||
\(151\) | −5.06801e34 | −0.693756 | −0.346878 | − | 0.937910i | \(-0.612758\pi\) | ||||
−0.346878 | + | 0.937910i | \(0.612758\pi\) | |||||||
\(152\) | −8.16077e34 | − | 8.16077e34i | −1.00516 | − | 1.00516i | ||||
\(153\) | 2.52211e33 | − | 2.52211e33i | 0.0279705 | − | 0.0279705i | ||||
\(154\) | − | 1.41851e35i | − | 1.41743i | ||||||
\(155\) | 2.99736e34 | − | 5.20149e34i | 0.270042 | − | 0.468620i | ||||
\(156\) | −7.34336e34 | −0.596900 | ||||||||
\(157\) | 7.62382e34 | + | 7.62382e34i | 0.559472 | + | 0.559472i | 0.929157 | − | 0.369685i | \(-0.120535\pi\) |
−0.369685 | + | 0.929157i | \(0.620535\pi\) | |||||||
\(158\) | 7.53079e34 | − | 7.53079e34i | 0.499260 | − | 0.499260i | ||||
\(159\) | − | 4.27252e34i | − | 0.256053i | ||||||
\(160\) | −9.39814e34 | + | 2.52655e34i | −0.509474 | + | 0.136964i | ||||
\(161\) | 3.37839e35 | 1.65766 | ||||||||
\(162\) | −6.46055e34 | − | 6.46055e34i | −0.287097 | − | 0.287097i | ||||
\(163\) | −2.81526e35 | + | 2.81526e35i | −1.13375 | + | 1.13375i | −0.144200 | + | 0.989549i | \(0.546061\pi\) |
−0.989549 | + | 0.144200i | \(0.953939\pi\) | |||||||
\(164\) | − | 9.97129e34i | − | 0.364124i | ||||||
\(165\) | 1.65492e35 | + | 6.15590e35i | 0.548320 | + | 2.03962i | ||||
\(166\) | −2.20073e35 | −0.661968 | ||||||||
\(167\) | 1.74820e35 | + | 1.74820e35i | 0.477670 | + | 0.477670i | 0.904386 | − | 0.426716i | \(-0.140330\pi\) |
−0.426716 | + | 0.904386i | \(0.640330\pi\) | |||||||
\(168\) | −5.78520e35 | + | 5.78520e35i | −1.43671 | + | 1.43671i | ||||
\(169\) | − | 4.52195e35i | − | 1.02126i | ||||||
\(170\) | 1.03117e34 | + | 5.94213e33i | 0.0211909 | + | 0.0122112i | ||||
\(171\) | 9.65941e35 | 1.80723 | ||||||||
\(172\) | 1.04017e35 | + | 1.04017e35i | 0.177276 | + | 0.177276i | ||||
\(173\) | −4.55117e35 | + | 4.55117e35i | −0.706944 | + | 0.706944i | −0.965891 | − | 0.258947i | \(-0.916624\pi\) |
0.258947 | + | 0.965891i | \(0.416624\pi\) | |||||||
\(174\) | 1.03136e32i | 0.000146091i | ||||||||
\(175\) | 2.41530e35 | − | 9.07397e35i | 0.312149 | − | 1.17270i | ||||
\(176\) | 7.58683e35 | 0.895071 | ||||||||
\(177\) | −7.91041e35 | − | 7.91041e35i | −0.852367 | − | 0.852367i | ||||
\(178\) | −9.75761e34 | + | 9.75761e34i | −0.0960778 | + | 0.0960778i | ||||
\(179\) | − | 1.66069e36i | − | 1.49500i | −0.664262 | − | 0.747500i | \(-0.731254\pi\) | ||
0.664262 | − | 0.747500i | \(-0.268746\pi\) | |||||||
\(180\) | 2.27693e35 | − | 3.95129e35i | 0.187495 | − | 0.325371i | ||||
\(181\) | −5.92307e35 | −0.446365 | −0.223182 | − | 0.974777i | \(-0.571645\pi\) | ||||
−0.223182 | + | 0.974777i | \(0.571645\pi\) | |||||||
\(182\) | −1.50838e36 | − | 1.50838e36i | −1.04080 | − | 1.04080i | ||||
\(183\) | −5.50517e35 | + | 5.50517e35i | −0.347979 | + | 0.347979i | ||||
\(184\) | 2.55910e36i | 1.48253i | ||||||||
\(185\) | 8.75111e35 | − | 2.35260e35i | 0.464853 | − | 0.124969i | ||||
\(186\) | 1.46077e36 | 0.711828 | ||||||||
\(187\) | 6.20542e34 | + | 6.20542e34i | 0.0277527 | + | 0.0277527i | ||||
\(188\) | 3.59197e35 | − | 3.59197e35i | 0.147505 | − | 0.147505i | ||||
\(189\) | − | 1.88493e36i | − | 0.711062i | ||||||
\(190\) | 8.36756e35 | + | 3.11253e36i | 0.290096 | + | 1.07909i | ||||
\(191\) | 2.28483e36 | 0.728317 | 0.364158 | − | 0.931337i | \(-0.381357\pi\) | ||||
0.364158 | + | 0.931337i | \(0.381357\pi\) | |||||||
\(192\) | −4.10668e36 | − | 4.10668e36i | −1.20412 | − | 1.20412i | ||||
\(193\) | −2.78936e36 | + | 2.78936e36i | −0.752640 | + | 0.752640i | −0.974971 | − | 0.222331i | \(-0.928633\pi\) |
0.222331 | + | 0.974971i | \(0.428633\pi\) | |||||||
\(194\) | − | 3.73289e36i | − | 0.927294i | ||||||
\(195\) | 8.30568e36 | + | 4.78614e36i | 1.90030 | + | 1.09505i | ||||
\(196\) | 6.10202e35 | 0.128640 | ||||||||
\(197\) | 3.43604e36 | + | 3.43604e36i | 0.667726 | + | 0.667726i | 0.957189 | − | 0.289463i | \(-0.0934768\pi\) |
−0.289463 | + | 0.957189i | \(0.593477\pi\) | |||||||
\(198\) | −6.35916e36 | + | 6.35916e36i | −1.13961 | + | 1.13961i | ||||
\(199\) | − | 6.51209e36i | − | 1.07664i | −0.842740 | − | 0.538321i | \(-0.819059\pi\) | ||
0.842740 | − | 0.538321i | \(-0.180941\pi\) | |||||||
\(200\) | 6.87345e36 | + | 1.82957e36i | 1.04881 | + | 0.279170i | ||||
\(201\) | −1.79745e37 | −2.53233 | ||||||||
\(202\) | 2.96608e36 | + | 2.96608e36i | 0.385977 | + | 0.385977i | ||||
\(203\) | 7.92147e32 | − | 7.92147e32i | 9.52510e−5 | − | 9.52510e-5i | ||||
\(204\) | − | 1.08284e35i | − | 0.0120360i | ||||||
\(205\) | −6.49894e36 | + | 1.12780e37i | −0.668006 | + | 1.15923i | ||||
\(206\) | 6.20235e35 | 0.0589767 | ||||||||
\(207\) | −1.51453e37 | − | 1.51453e37i | −1.33276 | − | 1.33276i | ||||
\(208\) | 8.06749e36 | − | 8.06749e36i | 0.657242 | − | 0.657242i | ||||
\(209\) | 2.37661e37i | 1.79316i | ||||||||
\(210\) | 2.20648e37 | − | 5.93180e36i | 1.54238 | − | 0.414646i | ||||
\(211\) | 2.09448e37 | 1.35693 | 0.678464 | − | 0.734633i | \(-0.262646\pi\) | ||||
0.678464 | + | 0.734633i | \(0.262646\pi\) | |||||||
\(212\) | −5.31782e35 | − | 5.31782e35i | −0.0319418 | − | 0.0319418i | ||||
\(213\) | −6.64337e36 | + | 6.64337e36i | −0.370096 | + | 0.370096i | ||||
\(214\) | − | 2.36029e37i | − | 1.21996i | ||||||
\(215\) | −4.98535e36 | − | 1.85443e37i | −0.239155 | − | 0.889600i | ||||
\(216\) | 1.42782e37 | 0.635937 | ||||||||
\(217\) | −1.12196e37 | − | 1.12196e37i | −0.464110 | − | 0.464110i | ||||
\(218\) | −9.87775e36 | + | 9.87775e36i | −0.379625 | + | 0.379625i | ||||
\(219\) | − | 5.20270e37i | − | 1.85833i | ||||||
\(220\) | 9.72180e36 | + | 5.60218e36i | 0.322837 | + | 0.186035i | ||||
\(221\) | 1.31971e36 | 0.0407571 | ||||||||
\(222\) | 1.55917e37 | + | 1.55917e37i | 0.447966 | + | 0.447966i | ||||
\(223\) | −4.23335e37 | + | 4.23335e37i | −1.13190 | + | 1.13190i | −0.142035 | + | 0.989862i | \(0.545365\pi\) |
−0.989862 | + | 0.142035i | \(0.954635\pi\) | |||||||
\(224\) | 2.57215e37i | 0.640218i | ||||||||
\(225\) | −5.15062e37 | + | 2.98507e37i | −1.19382 | + | 0.691885i | ||||
\(226\) | −1.08242e37 | −0.233701 | ||||||||
\(227\) | −2.72163e37 | − | 2.72163e37i | −0.547540 | − | 0.547540i | 0.378189 | − | 0.925729i | \(-0.376547\pi\) |
−0.925729 | + | 0.378189i | \(0.876547\pi\) | |||||||
\(228\) | 2.07358e37 | − | 2.07358e37i | 0.388834 | − | 0.388834i | ||||
\(229\) | − | 8.21268e37i | − | 1.43588i | −0.696107 | − | 0.717938i | \(-0.745086\pi\) | ||
0.696107 | − | 0.717938i | \(-0.254914\pi\) | |||||||
\(230\) | 3.56825e37 | − | 6.19220e37i | 0.581848 | − | 1.00972i | ||||
\(231\) | 1.68479e38 | 2.56303 | ||||||||
\(232\) | 6.00045e33 | + | 6.00045e33i | 8.51875e−5 | + | 8.51875e-5i | ||||
\(233\) | −8.56463e37 | + | 8.56463e37i | −1.13505 | + | 1.13505i | −0.145721 | + | 0.989326i | \(0.546550\pi\) |
−0.989326 | + | 0.145721i | \(0.953450\pi\) | |||||||
\(234\) | 1.35241e38i | 1.67361i | ||||||||
\(235\) | −6.40380e37 | + | 1.72156e37i | −0.740205 | + | 0.198993i | ||||
\(236\) | −1.96915e37 | −0.212660 | ||||||||
\(237\) | 8.94445e37 | + | 8.94445e37i | 0.902776 | + | 0.902776i | ||||
\(238\) | 2.22423e36 | − | 2.22423e36i | 0.0209869 | − | 0.0209869i | ||||
\(239\) | 6.49375e37i | 0.572966i | 0.958085 | + | 0.286483i | \(0.0924862\pi\) | ||||
−0.958085 | + | 0.286483i | \(0.907514\pi\) | |||||||
\(240\) | 3.17259e37 | + | 1.18013e38i | 0.261839 | + | 0.973977i | ||||
\(241\) | −4.79578e37 | −0.370328 | −0.185164 | − | 0.982708i | \(-0.559282\pi\) | ||||
−0.185164 | + | 0.982708i | \(0.559282\pi\) | |||||||
\(242\) | −7.29878e37 | − | 7.29878e37i | −0.527478 | − | 0.527478i | ||||
\(243\) | 1.37974e38 | − | 1.37974e38i | 0.933461 | − | 0.933461i | ||||
\(244\) | 1.37041e37i | 0.0868187i | ||||||||
\(245\) | −6.90167e37 | − | 3.97708e37i | −0.409541 | − | 0.235998i | ||||
\(246\) | −3.16728e38 | −1.76086 | ||||||||
\(247\) | 2.52718e38 | + | 2.52718e38i | 1.31670 | + | 1.31670i | ||||
\(248\) | 8.49874e37 | − | 8.49874e37i | 0.415076 | − | 0.415076i | ||||
\(249\) | − | 2.61384e38i | − | 1.19699i | ||||||
\(250\) | −1.40805e38 | − | 1.40109e38i | −0.604753 | − | 0.601763i | ||||
\(251\) | −1.70220e38 | −0.685851 | −0.342926 | − | 0.939363i | \(-0.611418\pi\) | ||||
−0.342926 | + | 0.939363i | \(0.611418\pi\) | |||||||
\(252\) | −8.52290e37 | − | 8.52290e37i | −0.322240 | − | 0.322240i | ||||
\(253\) | 3.72636e38 | − | 3.72636e38i | 1.32238 | − | 1.32238i | ||||
\(254\) | − | 7.21883e37i | − | 0.240507i | ||||||
\(255\) | −7.05757e36 | + | 1.22474e37i | −0.0220807 | + | 0.0383179i | ||||
\(256\) | −2.55384e38 | −0.750506 | ||||||||
\(257\) | 2.03465e38 | + | 2.03465e38i | 0.561772 | + | 0.561772i | 0.929810 | − | 0.368039i | \(-0.119971\pi\) |
−0.368039 | + | 0.929810i | \(0.619971\pi\) | |||||||
\(258\) | 3.30399e38 | − | 3.30399e38i | 0.857282 | − | 0.857282i | ||||
\(259\) | − | 2.39506e38i | − | 0.584145i | ||||||
\(260\) | 1.62948e38 | − | 4.38062e37i | 0.373660 | − | 0.100453i | ||||
\(261\) | −7.10237e34 | −0.000153163 | ||||||||
\(262\) | −3.20820e38 | − | 3.20820e38i | −0.650790 | − | 0.650790i | ||||
\(263\) | −5.13008e38 | + | 5.13008e38i | −0.979111 | + | 0.979111i | −0.999786 | − | 0.0206750i | \(-0.993418\pi\) |
0.0206750 | + | 0.999786i | \(0.493418\pi\) | |||||||
\(264\) | 1.27621e39i | 2.29224i | ||||||||
\(265\) | 2.54873e37 | + | 9.48067e37i | 0.0430914 | + | 0.160289i | ||||
\(266\) | 8.51859e38 | 1.35601 | ||||||||
\(267\) | −1.15893e38 | − | 1.15893e38i | −0.173731 | − | 0.173731i | ||||
\(268\) | −2.23721e38 | + | 2.23721e38i | −0.315901 | + | 0.315901i | ||||
\(269\) | 9.62084e38i | 1.27990i | 0.768416 | + | 0.639951i | \(0.221045\pi\) | ||||
−0.768416 | + | 0.639951i | \(0.778955\pi\) | |||||||
\(270\) | −3.45487e38 | − | 1.99087e38i | −0.433123 | − | 0.249587i | ||||
\(271\) | −9.79970e38 | −1.15799 | −0.578994 | − | 0.815332i | \(-0.696555\pi\) | ||||
−0.578994 | + | 0.815332i | \(0.696555\pi\) | |||||||
\(272\) | 1.18962e37 | + | 1.18962e37i | 0.0132527 | + | 0.0132527i | ||||
\(273\) | 1.79153e39 | − | 1.79153e39i | 1.88201 | − | 1.88201i | ||||
\(274\) | 1.33866e39i | 1.32636i | ||||||||
\(275\) | −7.34450e38 | − | 1.26727e39i | −0.686498 | − | 1.18453i | ||||
\(276\) | −6.50246e38 | −0.573498 | ||||||||
\(277\) | 1.18648e39 | + | 1.18648e39i | 0.987607 | + | 0.987607i | 0.999924 | − | 0.0123171i | \(-0.00392076\pi\) |
−0.0123171 | + | 0.999924i | \(0.503921\pi\) | |||||||
\(278\) | 1.04584e37 | − | 1.04584e37i | 0.00821769 | − | 0.00821769i | ||||
\(279\) | 1.00594e39i | 0.746289i | ||||||||
\(280\) | 9.38618e38 | − | 1.62884e39i | 0.657598 | − | 1.14117i | ||||
\(281\) | 1.83305e39 | 1.21303 | 0.606516 | − | 0.795071i | \(-0.292567\pi\) | ||||
0.606516 | + | 0.795071i | \(0.292567\pi\) | |||||||
\(282\) | −1.14095e39 | − | 1.14095e39i | −0.713315 | − | 0.713315i | ||||
\(283\) | −1.81229e39 | + | 1.81229e39i | −1.07064 | + | 1.07064i | −0.0733339 | + | 0.997307i | \(0.523364\pi\) |
−0.997307 | + | 0.0733339i | \(0.976636\pi\) | |||||||
\(284\) | 1.65374e38i | 0.0923368i | ||||||||
\(285\) | −3.69681e39 | + | 9.93830e38i | −1.95123 | + | 0.524559i | ||||
\(286\) | −3.32749e39 | −1.66058 | ||||||||
\(287\) | 2.43266e39 | + | 2.43266e39i | 1.14808 | + | 1.14808i | ||||
\(288\) | 1.15309e39 | − | 1.15309e39i | 0.514735 | − | 0.514735i | ||||
\(289\) | − | 2.36597e39i | − | 0.999178i | ||||||
\(290\) | −6.15250e34 | − | 2.28858e35i | −2.45858e−5 | − | 9.14531e-5i | ||||
\(291\) | 4.43362e39 | 1.67676 | ||||||||
\(292\) | −6.47558e38 | − | 6.47558e38i | −0.231821 | − | 0.231821i | ||||
\(293\) | 2.36618e39 | − | 2.36618e39i | 0.801985 | − | 0.801985i | −0.181421 | − | 0.983406i | \(-0.558070\pi\) |
0.983406 | + | 0.181421i | \(0.0580696\pi\) | |||||||
\(294\) | − | 1.93824e39i | − | 0.622087i | ||||||
\(295\) | 2.22720e39 | + | 1.28342e39i | 0.677029 | + | 0.390137i | ||||
\(296\) | 1.81424e39 | 0.522429 | ||||||||
\(297\) | −2.07908e39 | − | 2.07908e39i | −0.567242 | − | 0.567242i | ||||
\(298\) | −3.15438e38 | + | 3.15438e38i | −0.0815557 | + | 0.0815557i | ||||
\(299\) | − | 7.92489e39i | − | 1.94202i | ||||||
\(300\) | −4.64878e38 | + | 1.74649e39i | −0.107994 | + | 0.405719i | ||||
\(301\) | −5.07533e39 | −1.11789 | ||||||||
\(302\) | 2.00365e39 | + | 2.00365e39i | 0.418515 | + | 0.418515i | ||||
\(303\) | −3.52287e39 | + | 3.52287e39i | −0.697934 | + | 0.697934i | ||||
\(304\) | 4.55612e39i | 0.856284i | ||||||||
\(305\) | 8.93185e38 | − | 1.55000e39i | 0.159274 | − | 0.276397i | ||||
\(306\) | −1.99424e38 | −0.0337470 | ||||||||
\(307\) | −2.91493e39 | − | 2.91493e39i | −0.468182 | − | 0.468182i | 0.433143 | − | 0.901325i | \(-0.357404\pi\) |
−0.901325 | + | 0.433143i | \(0.857404\pi\) | |||||||
\(308\) | 2.09699e39 | − | 2.09699e39i | 0.319730 | − | 0.319730i | ||||
\(309\) | 7.36664e38i | 0.106643i | ||||||||
\(310\) | −3.24143e39 | + | 8.71410e38i | −0.445605 | + | 0.119794i | ||||
\(311\) | −1.21125e40 | −1.58150 | −0.790749 | − | 0.612140i | \(-0.790309\pi\) | ||||
−0.790749 | + | 0.612140i | \(0.790309\pi\) | |||||||
\(312\) | 1.35707e40 | + | 1.35707e40i | 1.68317 | + | 1.68317i | ||||
\(313\) | −2.91575e39 | + | 2.91575e39i | −0.343590 | + | 0.343590i | −0.857715 | − | 0.514125i | \(-0.828117\pi\) |
0.514125 | + | 0.857715i | \(0.328117\pi\) | |||||||
\(314\) | − | 6.02819e39i | − | 0.675013i | ||||||
\(315\) | 4.08487e39 | + | 1.51947e40i | 0.434720 | + | 1.61705i | ||||
\(316\) | 2.22655e39 | 0.225237 | ||||||||
\(317\) | −1.73245e39 | − | 1.73245e39i | −0.166614 | − | 0.166614i | 0.618875 | − | 0.785489i | \(-0.287589\pi\) |
−0.785489 | + | 0.618875i | \(0.787589\pi\) | |||||||
\(318\) | −1.68915e39 | + | 1.68915e39i | −0.154466 | + | 0.154466i | ||||
\(319\) | − | 1.74748e36i | − | 0.000151971i | ||||||
\(320\) | 1.15625e40 | + | 6.66288e39i | 0.956426 | + | 0.551140i | ||||
\(321\) | 2.80336e40 | 2.20596 | ||||||||
\(322\) | −1.33565e40 | − | 1.33565e40i | −0.999999 | − | 0.999999i | ||||
\(323\) | −3.72654e38 | + | 3.72654e38i | −0.0265501 | + | 0.0265501i | ||||
\(324\) | − | 1.91013e39i | − | 0.129522i | ||||||
\(325\) | −2.12853e40 | − | 5.66572e39i | −1.37387 | − | 0.365697i | ||||
\(326\) | 2.22604e40 | 1.36789 | ||||||||
\(327\) | −1.17320e40 | − | 1.17320e40i | −0.686448 | − | 0.686448i | ||||
\(328\) | −1.84272e40 | + | 1.84272e40i | −1.02678 | + | 1.02678i | ||||
\(329\) | 1.75264e40i | 0.930159i | ||||||||
\(330\) | 1.77947e40 | − | 3.08803e40i | 0.899639 | − | 1.56120i | ||||
\(331\) | −3.29585e40 | −1.58752 | −0.793761 | − | 0.608230i | \(-0.791880\pi\) | ||||
−0.793761 | + | 0.608230i | \(0.791880\pi\) | |||||||
\(332\) | −3.25334e39 | − | 3.25334e39i | −0.149321 | − | 0.149321i | ||||
\(333\) | −1.07370e40 | + | 1.07370e40i | −0.469652 | + | 0.469652i | ||||
\(334\) | − | 1.38231e40i | − | 0.576318i | ||||||
\(335\) | 3.98853e40 | − | 1.07226e40i | 1.58524 | − | 0.426169i | ||||
\(336\) | 3.22985e40 | 1.22392 | ||||||||
\(337\) | −2.99278e40 | − | 2.99278e40i | −1.08143 | − | 1.08143i | −0.996377 | − | 0.0850487i | \(-0.972895\pi\) |
−0.0850487 | − | 0.996377i | \(-0.527105\pi\) | |||||||
\(338\) | −1.78776e40 | + | 1.78776e40i | −0.616088 | + | 0.616088i | ||||
\(339\) | − | 1.28561e40i | − | 0.422585i | ||||||
\(340\) | 6.45959e37 | + | 2.40281e38i | 0.00202555 | + | 0.00753454i | ||||
\(341\) | −2.47504e40 | −0.740478 | ||||||||
\(342\) | −3.81887e40 | − | 3.81887e40i | −1.09023 | − | 1.09023i | ||||
\(343\) | 1.66083e40 | − | 1.66083e40i | 0.452501 | − | 0.452501i | ||||
\(344\) | − | 3.84452e40i | − | 0.999785i | ||||||
\(345\) | 7.35458e40 | + | 4.23807e40i | 1.82580 | + | 1.05211i | ||||
\(346\) | 3.59863e40 | 0.852942 | ||||||||
\(347\) | 4.29749e40 | + | 4.29749e40i | 0.972619 | + | 0.972619i | 0.999635 | − | 0.0270159i | \(-0.00860047\pi\) |
−0.0270159 | + | 0.999635i | \(0.508600\pi\) | |||||||
\(348\) | −1.52466e36 | + | 1.52466e36i | −3.29539e−5 | + | 3.29539e-5i | ||||
\(349\) | 2.89824e40i | 0.598311i | 0.954204 | + | 0.299156i | \(0.0967049\pi\) | ||||
−0.954204 | + | 0.299156i | \(0.903295\pi\) | |||||||
\(350\) | −4.54231e40 | + | 2.63252e40i | −0.895752 | + | 0.519138i | ||||
\(351\) | −4.42160e40 | −0.833040 | ||||||||
\(352\) | 2.83708e40 | + | 2.83708e40i | 0.510727 | + | 0.510727i | ||||
\(353\) | 3.40782e39 | − | 3.40782e39i | 0.0586248 | − | 0.0586248i | −0.677187 | − | 0.735811i | \(-0.736801\pi\) |
0.735811 | + | 0.677187i | \(0.236801\pi\) | |||||||
\(354\) | 6.25480e40i | 1.02840i | ||||||||
\(355\) | 1.07785e40 | − | 1.87046e40i | 0.169397 | − | 0.293965i | ||||
\(356\) | −2.88494e39 | −0.0433447 | ||||||||
\(357\) | 2.64176e39 | + | 2.64176e39i | 0.0379492 | + | 0.0379492i | ||||
\(358\) | −6.56559e40 | + | 6.56559e40i | −0.901873 | + | 0.901873i | ||||
\(359\) | 5.42658e39i | 0.0712877i | 0.999365 | + | 0.0356439i | \(0.0113482\pi\) | ||||
−0.999365 | + | 0.0356439i | \(0.988652\pi\) | |||||||
\(360\) | −1.15099e41 | + | 3.09425e40i | −1.44621 | + | 0.388791i | ||||
\(361\) | −5.95244e40 | −0.715451 | ||||||||
\(362\) | 2.34170e40 | + | 2.34170e40i | 0.269274 | + | 0.269274i | ||||
\(363\) | 8.66889e40 | − | 8.66889e40i | 0.953800 | − | 0.953800i | ||||
\(364\) | − | 4.45968e40i | − | 0.469550i | ||||||
\(365\) | 3.10363e40 | + | 1.15447e41i | 0.312740 | + | 1.16332i | ||||
\(366\) | 4.35296e40 | 0.419844 | ||||||||
\(367\) | 1.06545e40 | + | 1.06545e40i | 0.0983731 | + | 0.0983731i | 0.754581 | − | 0.656207i | \(-0.227840\pi\) |
−0.656207 | + | 0.754581i | \(0.727840\pi\) | |||||||
\(368\) | 7.14367e40 | − | 7.14367e40i | 0.631475 | − | 0.631475i | ||||
\(369\) | − | 2.18111e41i | − | 1.84610i | ||||||
\(370\) | −4.38988e40 | − | 2.52966e40i | −0.355815 | − | 0.205038i | ||||
\(371\) | 2.59473e40 | 0.201424 | ||||||||
\(372\) | 2.15946e40 | + | 2.15946e40i | 0.160568 | + | 0.160568i | ||||
\(373\) | −7.61669e40 | + | 7.61669e40i | −0.542531 | + | 0.542531i | −0.924270 | − | 0.381739i | \(-0.875325\pi\) |
0.381739 | + | 0.924270i | \(0.375325\pi\) | |||||||
\(374\) | − | 4.90665e39i | − | 0.0334842i | ||||||
\(375\) | 1.66410e41 | − | 1.67237e41i | 1.08812 | − | 1.09353i | ||||
\(376\) | −1.32761e41 | −0.831886 | ||||||||
\(377\) | −1.85819e37 | − | 1.85819e37i | −0.000111591 | − | 0.000111591i | ||||
\(378\) | −7.45213e40 | + | 7.45213e40i | −0.428955 | + | 0.428955i | ||||
\(379\) | 1.33071e40i | 0.0734272i | 0.999326 | + | 0.0367136i | \(0.0116889\pi\) | ||||
−0.999326 | + | 0.0367136i | \(0.988311\pi\) | |||||||
\(380\) | −3.36428e40 | + | 5.83824e40i | −0.177973 | + | 0.308847i | ||||
\(381\) | 8.57394e40 | 0.434891 | ||||||||
\(382\) | −9.03313e40 | − | 9.03313e40i | −0.439364 | − | 0.439364i | ||||
\(383\) | 1.44371e41 | − | 1.44371e41i | 0.673443 | − | 0.673443i | −0.285065 | − | 0.958508i | \(-0.592015\pi\) |
0.958508 | + | 0.285065i | \(0.0920153\pi\) | |||||||
\(384\) | 1.42811e41i | 0.638944i | ||||||||
\(385\) | −3.73853e41 | + | 1.00505e41i | −1.60446 | + | 0.431335i | ||||
\(386\) | 2.20556e41 | 0.908075 | ||||||||
\(387\) | 2.27526e41 | + | 2.27526e41i | 0.898785 | + | 0.898785i | ||||
\(388\) | 5.51834e40 | − | 5.51834e40i | 0.209171 | − | 0.209171i | ||||
\(389\) | 2.16396e41i | 0.787146i | 0.919293 | + | 0.393573i | \(0.128761\pi\) | ||||
−0.919293 | + | 0.393573i | \(0.871239\pi\) | |||||||
\(390\) | −1.39146e41 | − | 5.17588e41i | −0.485776 | − | 1.80697i | ||||
\(391\) | 1.16859e40 | 0.0391592 | ||||||||
\(392\) | −1.12767e41 | − | 1.12767e41i | −0.362747 | − | 0.362747i | ||||
\(393\) | 3.81043e41 | − | 3.81043e41i | 1.17678 | − | 1.17678i | ||||
\(394\) | − | 2.71689e41i | − | 0.805624i | ||||||
\(395\) | −2.51834e41 | − | 1.45119e41i | −0.717068 | − | 0.413210i | ||||
\(396\) | −1.88015e41 | −0.514126 | ||||||||
\(397\) | −2.96206e40 | − | 2.96206e40i | −0.0777938 | − | 0.0777938i | 0.667139 | − | 0.744933i | \(-0.267519\pi\) |
−0.744933 | + | 0.667139i | \(0.767519\pi\) | |||||||
\(398\) | −2.57457e41 | + | 2.57457e41i | −0.649494 | + | 0.649494i | ||||
\(399\) | 1.01177e42i | 2.45197i | ||||||||
\(400\) | −1.40799e41 | − | 2.42943e41i | −0.327823 | − | 0.565646i | ||||
\(401\) | 2.99873e41 | 0.670853 | 0.335427 | − | 0.942066i | \(-0.391120\pi\) | ||||
0.335427 | + | 0.942066i | \(0.391120\pi\) | |||||||
\(402\) | 7.10628e41 | + | 7.10628e41i | 1.52765 | + | 1.52765i | ||||
\(403\) | −2.63185e41 | + | 2.63185e41i | −0.543726 | + | 0.543726i | ||||
\(404\) | 8.76953e40i | 0.174130i | ||||||||
\(405\) | −1.24495e41 | + | 2.16044e41i | −0.237615 | + | 0.412347i | ||||
\(406\) | −6.26355e37 | −0.000114922 | ||||||||
\(407\) | −2.64175e41 | − | 2.64175e41i | −0.465996 | − | 0.465996i | ||||
\(408\) | −2.00111e40 | + | 2.00111e40i | −0.0339398 | + | 0.0339398i | ||||
\(409\) | 3.93446e40i | 0.0641670i | 0.999485 | + | 0.0320835i | \(0.0102143\pi\) | ||||
−0.999485 | + | 0.0320835i | \(0.989786\pi\) | |||||||
\(410\) | 7.02815e41 | − | 1.88941e41i | 1.10230 | − | 0.296336i | ||||
\(411\) | −1.58995e42 | −2.39837 | ||||||||
\(412\) | 9.16894e39 | + | 9.16894e39i | 0.0133034 | + | 0.0133034i | ||||
\(413\) | 4.80406e41 | − | 4.80406e41i | 0.670513 | − | 0.670513i | ||||
\(414\) | 1.19754e42i | 1.60800i | ||||||||
\(415\) | 1.55927e41 | + | 5.80009e41i | 0.201442 | + | 0.749316i | ||||
\(416\) | 6.03364e41 | 0.750043 | ||||||||
\(417\) | 1.24217e40 | + | 1.24217e40i | 0.0148595 | + | 0.0148595i | ||||
\(418\) | 9.39599e41 | − | 9.39599e41i | 1.08174 | − | 1.08174i | ||||
\(419\) | − | 7.00287e41i | − | 0.775982i | −0.921663 | − | 0.387991i | \(-0.873169\pi\) | ||
0.921663 | − | 0.387991i | \(-0.126831\pi\) | |||||||
\(420\) | 4.13875e41 | + | 2.38495e41i | 0.441449 | + | 0.254385i | ||||
\(421\) | −9.56131e41 | −0.981756 | −0.490878 | − | 0.871228i | \(-0.663324\pi\) | ||||
−0.490878 | + | 0.871228i | \(0.663324\pi\) | |||||||
\(422\) | −8.28058e41 | − | 8.28058e41i | −0.818580 | − | 0.818580i | ||||
\(423\) | 7.85704e41 | − | 7.85704e41i | 0.747848 | − | 0.747848i | ||||
\(424\) | 1.96549e41i | 0.180143i | ||||||||
\(425\) | 8.35457e39 | − | 3.13870e40i | 0.00737397 | − | 0.0277030i | ||||
\(426\) | 5.25294e41 | 0.446528 | ||||||||
\(427\) | −3.34333e41 | − | 3.34333e41i | −0.273737 | − | 0.273737i | ||||
\(428\) | 3.48922e41 | − | 3.48922e41i | 0.275187 | − | 0.275187i | ||||
\(429\) | − | 3.95211e42i | − | 3.00271i | ||||||
\(430\) | −5.36055e41 | + | 9.30249e41i | −0.392387 | + | 0.680932i | ||||
\(431\) | −1.48305e42 | −1.04597 | −0.522987 | − | 0.852341i | \(-0.675182\pi\) | ||||
−0.522987 | + | 0.852341i | \(0.675182\pi\) | |||||||
\(432\) | −3.98573e41 | − | 3.98573e41i | −0.270875 | − | 0.270875i | ||||
\(433\) | −1.27440e41 | + | 1.27440e41i | −0.0834641 | + | 0.0834641i | −0.747606 | − | 0.664142i | \(-0.768797\pi\) |
0.664142 | + | 0.747606i | \(0.268797\pi\) | |||||||
\(434\) | 8.87138e41i | 0.559958i | ||||||||
\(435\) | 2.71819e38 | − | 7.30743e37i | 0.000165368 | − | 4.44567e-5i | ||||
\(436\) | −2.92046e41 | −0.171265 | ||||||||
\(437\) | 2.23779e42 | + | 2.23779e42i | 1.26508 | + | 1.26508i | ||||
\(438\) | −2.05690e42 | + | 2.05690e42i | −1.12106 | + | 1.12106i | ||||
\(439\) | 2.12587e42i | 1.11713i | 0.829460 | + | 0.558566i | \(0.188648\pi\) | ||||
−0.829460 | + | 0.558566i | \(0.811352\pi\) | |||||||
\(440\) | −7.61314e41 | − | 2.83190e42i | −0.385764 | − | 1.43495i | ||||
\(441\) | 1.33475e42 | 0.652203 | ||||||||
\(442\) | −5.21752e40 | − | 5.21752e40i | −0.0245871 | − | 0.0245871i | ||||
\(443\) | −2.43354e42 | + | 2.43354e42i | −1.10606 | + | 1.10606i | −0.112396 | + | 0.993663i | \(0.535853\pi\) |
−0.993663 | + | 0.112396i | \(0.964147\pi\) | |||||||
\(444\) | 4.60983e41i | 0.202096i | ||||||||
\(445\) | 3.26300e41 | + | 1.88030e41i | 0.137993 | + | 0.0795183i | ||||
\(446\) | 3.34733e42 | 1.36566 | ||||||||
\(447\) | −3.74652e41 | − | 3.74652e41i | −0.147471 | − | 0.147471i | ||||
\(448\) | 2.49402e42 | − | 2.49402e42i | 0.947222 | − | 0.947222i | ||||
\(449\) | − | 3.20066e42i | − | 1.17300i | −0.809950 | − | 0.586499i | \(-0.800506\pi\) | ||
0.809950 | − | 0.586499i | \(-0.199494\pi\) | |||||||
\(450\) | 3.21646e42 | + | 8.56156e41i | 1.13757 | + | 0.302798i | ||||
\(451\) | 5.36644e42 | 1.83173 | ||||||||
\(452\) | −1.60014e41 | − | 1.60014e41i | −0.0527162 | − | 0.0527162i | ||||
\(453\) | −2.37977e42 | + | 2.37977e42i | −0.756770 | + | 0.756770i | ||||
\(454\) | 2.15201e42i | 0.660617i | ||||||||
\(455\) | −2.90666e42 | + | 5.04411e42i | −0.861415 | + | 1.49487i | ||||
\(456\) | −7.66405e42 | −2.19291 | ||||||||
\(457\) | 1.65118e42 | + | 1.65118e42i | 0.456180 | + | 0.456180i | 0.897399 | − | 0.441219i | \(-0.145454\pi\) |
−0.441219 | + | 0.897399i | \(0.645454\pi\) | |||||||
\(458\) | −3.24690e42 | + | 3.24690e42i | −0.866206 | + | 0.866206i | ||||
\(459\) | − | 6.52002e40i | − | 0.0167976i | ||||||
\(460\) | 1.44289e42 | − | 3.87898e41i | 0.359011 | − | 0.0965145i | ||||
\(461\) | 2.76608e42 | 0.664738 | 0.332369 | − | 0.943150i | \(-0.392152\pi\) | ||||
0.332369 | + | 0.943150i | \(0.392152\pi\) | |||||||
\(462\) | −6.66085e42 | − | 6.66085e42i | −1.54617 | − | 1.54617i | ||||
\(463\) | −2.83244e42 | + | 2.83244e42i | −0.635134 | + | 0.635134i | −0.949351 | − | 0.314217i | \(-0.898258\pi\) |
0.314217 | + | 0.949351i | \(0.398258\pi\) | |||||||
\(464\) | − | 3.35002e38i | − | 7.25705e-5i | ||||||
\(465\) | −1.03499e42 | − | 3.84991e42i | −0.216615 | − | 0.805755i | ||||
\(466\) | 6.77209e42 | 1.36946 | ||||||||
\(467\) | −3.50143e42 | − | 3.50143e42i | −0.684187 | − | 0.684187i | 0.276754 | − | 0.960941i | \(-0.410741\pi\) |
−0.960941 | + | 0.276754i | \(0.910741\pi\) | |||||||
\(468\) | −1.99927e42 | + | 1.99927e42i | −0.377518 | + | 0.377518i | ||||
\(469\) | − | 1.09161e43i | − | 1.99206i | ||||||
\(470\) | 3.21238e42 | + | 1.85113e42i | 0.566580 | + | 0.326491i | ||||
\(471\) | 7.15978e42 | 1.22058 | ||||||||
\(472\) | 3.63903e42 | + | 3.63903e42i | 0.599672 | + | 0.599672i | ||||
\(473\) | −5.59808e42 | + | 5.59808e42i | −0.891786 | + | 0.891786i | ||||
\(474\) | − | 7.07242e42i | − | 1.08922i | ||||||
\(475\) | 7.61031e42 | − | 4.41060e42i | 1.13320 | − | 0.656749i | ||||
\(476\) | 6.57617e40 | 0.00946808 | ||||||||
\(477\) | −1.16322e42 | − | 1.16322e42i | −0.161944 | − | 0.161944i | ||||
\(478\) | 2.56732e42 | − | 2.56732e42i | 0.345647 | − | 0.345647i | ||||
\(479\) | − | 2.15369e41i | − | 0.0280424i | −0.999902 | − | 0.0140212i | \(-0.995537\pi\) | ||
0.999902 | − | 0.0140212i | \(-0.00446323\pi\) | |||||||
\(480\) | −3.22667e42 | + | 5.59944e42i | −0.406345 | + | 0.705155i | ||||
\(481\) | −5.61825e42 | −0.684352 | ||||||||
\(482\) | 1.89602e42 | + | 1.89602e42i | 0.223404 | + | 0.223404i | ||||
\(483\) | 1.58638e43 | − | 1.58638e43i | 1.80823 | − | 1.80823i | ||||
\(484\) | − | 2.15796e42i | − | 0.237967i | ||||||
\(485\) | −9.83815e42 | + | 2.64484e42i | −1.04965 | + | 0.282183i | ||||
\(486\) | −1.09096e43 | −1.12624 | ||||||||
\(487\) | 5.13317e42 | + | 5.13317e42i | 0.512770 | + | 0.512770i | 0.915374 | − | 0.402604i | \(-0.131895\pi\) |
−0.402604 | + | 0.915374i | \(0.631895\pi\) | |||||||
\(488\) | 2.53255e42 | − | 2.53255e42i | 0.244816 | − | 0.244816i | ||||
\(489\) | 2.64390e43i | 2.47345i | ||||||||
\(490\) | 1.15624e42 | + | 4.30094e42i | 0.104692 | + | 0.389427i | ||||
\(491\) | −1.66880e43 | −1.46251 | −0.731256 | − | 0.682103i | \(-0.761066\pi\) | ||||
−0.731256 | + | 0.682103i | \(0.761066\pi\) | |||||||
\(492\) | −4.68219e42 | − | 4.68219e42i | −0.397198 | − | 0.397198i | ||||
\(493\) | 2.74005e37 | − | 2.74005e37i | 2.25013e−6 | − | 2.25013e-6i | ||||
\(494\) | − | 1.99826e43i | − | 1.58862i | ||||||
\(495\) | 2.12654e43 | + | 1.22542e43i | 1.63678 | + | 0.943193i | ||||
\(496\) | −4.74481e42 | −0.353600 | ||||||||
\(497\) | −4.03457e42 | − | 4.03457e42i | −0.291136 | − | 0.291136i | ||||
\(498\) | −1.03339e43 | + | 1.03339e43i | −0.722095 | + | 0.722095i | ||||
\(499\) | − | 9.79318e41i | − | 0.0662697i | −0.999451 | − | 0.0331348i | \(-0.989451\pi\) | ||
0.999451 | − | 0.0331348i | \(-0.0105491\pi\) | |||||||
\(500\) | −1.02911e40 | − | 4.15275e42i | −0.000674439 | − | 0.272155i | ||||
\(501\) | 1.64179e43 | 1.04211 | ||||||||
\(502\) | 6.72967e42 | + | 6.72967e42i | 0.413747 | + | 0.413747i | ||||
\(503\) | 9.12414e41 | − | 9.12414e41i | 0.0543381 | − | 0.0543381i | −0.679416 | − | 0.733754i | \(-0.737767\pi\) |
0.733754 | + | 0.679416i | \(0.237767\pi\) | |||||||
\(504\) | 3.15010e43i | 1.81734i | ||||||||
\(505\) | 5.71567e42 | − | 9.91874e42i | 0.319452 | − | 0.554363i | ||||
\(506\) | −2.94645e43 | −1.59548 | ||||||||
\(507\) | −2.12336e43 | − | 2.12336e43i | −1.11403 | − | 1.11403i | ||||
\(508\) | 1.06716e42 | − | 1.06716e42i | 0.0542514 | − | 0.0542514i | ||||
\(509\) | 7.86389e42i | 0.387394i | 0.981061 | + | 0.193697i | \(0.0620479\pi\) | ||||
−0.981061 | + | 0.193697i | \(0.937952\pi\) | |||||||
\(510\) | 7.63227e41 | − | 2.05182e41i | 0.0364360 | − | 0.00979527i | ||||
\(511\) | 3.15964e43 | 1.46185 | ||||||||
\(512\) | 1.66279e43 | + | 1.66279e43i | 0.745621 | + | 0.745621i | ||||
\(513\) | 1.24855e43 | − | 1.24855e43i | 0.542661 | − | 0.542661i | ||||
\(514\) | − | 1.60881e43i | − | 0.677788i | ||||||
\(515\) | −4.39450e41 | − | 1.63465e42i | −0.0179471 | − | 0.0667589i | ||||
\(516\) | 9.76859e42 | 0.386756 | ||||||||
\(517\) | 1.93316e43 | + | 1.93316e43i | 0.742024 | + | 0.742024i | ||||
\(518\) | −9.46894e42 | + | 9.46894e42i | −0.352391 | + | 0.352391i | ||||
\(519\) | 4.27415e43i | 1.54231i | ||||||||
\(520\) | −3.82087e43 | − | 2.20177e43i | −1.33693 | − | 0.770405i | ||||
\(521\) | −2.00091e43 | −0.678930 | −0.339465 | − | 0.940619i | \(-0.610246\pi\) | ||||
−0.339465 | + | 0.940619i | \(0.610246\pi\) | |||||||
\(522\) | 2.80794e39 | + | 2.80794e39i | 9.23973e−5 | + | 9.23973e-5i | ||||
\(523\) | −2.61260e43 | + | 2.61260e43i | −0.833771 | + | 0.833771i | −0.988030 | − | 0.154260i | \(-0.950701\pi\) |
0.154260 | + | 0.988030i | \(0.450701\pi\) | |||||||
\(524\) | − | 9.48537e42i | − | 0.293598i | ||||||
\(525\) | −3.12669e43 | − | 5.39498e43i | −0.938719 | − | 1.61972i | ||||
\(526\) | 4.05638e43 | 1.18132 | ||||||||
\(527\) | −3.88088e41 | − | 3.88088e41i | −0.0109638 | − | 0.0109638i | ||||
\(528\) | 3.56252e43 | − | 3.56252e43i | 0.976371 | − | 0.976371i | ||||
\(529\) | − | 3.25650e43i | − | 0.865886i | ||||||
\(530\) | 2.74056e42 | − | 4.75585e42i | 0.0707009 | − | 0.122691i | ||||
\(531\) | −4.30730e43 | −1.07818 | ||||||||
\(532\) | 1.25930e43 | + | 1.25930e43i | 0.305875 | + | 0.305875i | ||||
\(533\) | 5.70643e43 | − | 5.70643e43i | 1.34502 | − | 1.34502i | ||||
\(534\) | 9.16370e42i | 0.209609i | ||||||||
\(535\) | −6.22062e43 | + | 1.67232e43i | −1.38094 | + | 0.371243i | ||||
\(536\) | 8.26884e43 | 1.78159 | ||||||||
\(537\) | −7.79807e43 | − | 7.79807e43i | −1.63079 | − | 1.63079i | ||||
\(538\) | 3.80362e43 | − | 3.80362e43i | 0.772113 | − | 0.772113i | ||||
\(539\) | 3.28404e43i | 0.647125i | ||||||||
\(540\) | −2.16424e42 | − | 8.05044e42i | −0.0414004 | − | 0.153999i | ||||
\(541\) | −8.85705e42 | −0.164488 | −0.0822438 | − | 0.996612i | \(-0.526209\pi\) | ||||
−0.0822438 | + | 0.996612i | \(0.526209\pi\) | |||||||
\(542\) | 3.87433e43 | + | 3.87433e43i | 0.698568 | + | 0.698568i | ||||
\(543\) | −2.78128e43 | + | 2.78128e43i | −0.486908 | + | 0.486908i | ||||
\(544\) | 8.89711e41i | 0.0151240i | ||||||||
\(545\) | 3.30318e43 | + | 1.90345e43i | 0.545240 | + | 0.314194i | ||||
\(546\) | −1.41657e44 | −2.27068 | ||||||||
\(547\) | 5.56967e43 | + | 5.56967e43i | 0.867026 | + | 0.867026i | 0.992142 | − | 0.125116i | \(-0.0399302\pi\) |
−0.125116 | + | 0.992142i | \(0.539930\pi\) | |||||||
\(548\) | −1.97895e43 | + | 1.97895e43i | −0.299189 | + | 0.299189i | ||||
\(549\) | 2.99762e43i | 0.440169i | ||||||||
\(550\) | −2.10650e43 | + | 7.91383e43i | −0.300440 | + | 1.12871i | ||||
\(551\) | 1.04941e40 | 0.000145385 | ||||||||
\(552\) | 1.20167e44 | + | 1.20167e44i | 1.61718 | + | 1.61718i | ||||
\(553\) | −5.43204e43 | + | 5.43204e43i | −0.710167 | + | 0.710167i | ||||
\(554\) | − | 9.38155e43i | − | 1.19157i | ||||||
\(555\) | 3.00453e43 | − | 5.21394e43i | 0.370756 | − | 0.643395i | ||||
\(556\) | 3.09214e41 | 0.00370734 | ||||||||
\(557\) | 9.98545e42 | + | 9.98545e42i | 0.116328 | + | 0.116328i | 0.762875 | − | 0.646547i | \(-0.223787\pi\) |
−0.646547 | + | 0.762875i | \(0.723787\pi\) | |||||||
\(558\) | 3.97702e43 | − | 3.97702e43i | 0.450206 | − | 0.450206i | ||||
\(559\) | 1.19055e44i | 1.30966i | ||||||||
\(560\) | −7.16700e43 | + | 1.92674e43i | −0.766177 | + | 0.205975i | ||||
\(561\) | 5.82772e42 | 0.0605470 | ||||||||
\(562\) | −7.24699e43 | − | 7.24699e43i | −0.731773 | − | 0.731773i | ||||
\(563\) | −3.53624e43 | + | 3.53624e43i | −0.347062 | + | 0.347062i | −0.859014 | − | 0.511952i | \(-0.828923\pi\) |
0.511952 | + | 0.859014i | \(0.328923\pi\) | |||||||
\(564\) | − | 3.37334e43i | − | 0.321806i | ||||||
\(565\) | 7.66920e42 | + | 2.85276e43i | 0.0711172 | + | 0.264539i | ||||
\(566\) | 1.43298e44 | 1.29175 | ||||||||
\(567\) | 4.66006e43 | + | 4.66006e43i | 0.408379 | + | 0.408379i | ||||
\(568\) | 3.05615e43 | − | 3.05615e43i | 0.260377 | − | 0.260377i | ||||
\(569\) | − | 2.03561e44i | − | 1.68616i | −0.537787 | − | 0.843080i | \(-0.680740\pi\) | ||
0.537787 | − | 0.843080i | \(-0.319260\pi\) | |||||||
\(570\) | 1.85445e44 | + | 1.06863e44i | 1.49355 | + | 0.860655i | ||||
\(571\) | −9.39789e43 | −0.735957 | −0.367979 | − | 0.929834i | \(-0.619950\pi\) | ||||
−0.367979 | + | 0.929834i | \(0.619950\pi\) | |||||||
\(572\) | −4.91903e43 | − | 4.91903e43i | −0.374578 | − | 0.374578i | ||||
\(573\) | 1.07288e44 | − | 1.07288e44i | 0.794470 | − | 0.794470i | ||||
\(574\) | − | 1.92351e44i | − | 1.38518i | ||||||
\(575\) | −1.88479e44 | − | 5.01693e43i | −1.32001 | − | 0.351360i | ||||
\(576\) | −2.23613e44 | −1.52313 | ||||||||
\(577\) | −1.19785e44 | − | 1.19785e44i | −0.793578 | − | 0.793578i | 0.188496 | − | 0.982074i | \(-0.439639\pi\) |
−0.982074 | + | 0.188496i | \(0.939639\pi\) | |||||||
\(578\) | −9.35390e43 | + | 9.35390e43i | −0.602764 | + | 0.602764i | ||||
\(579\) | 2.61958e44i | 1.64201i | ||||||||
\(580\) | 2.47369e39 | − | 4.29274e39i | 1.50833e−5 | − | 2.61750e-5i | ||||
\(581\) | 1.58741e44 | 0.941609 | ||||||||
\(582\) | −1.75284e44 | − | 1.75284e44i | −1.01152 | − | 1.01152i | ||||
\(583\) | 2.86199e43 | − | 2.86199e43i | 0.160683 | − | 0.160683i | ||||
\(584\) | 2.39340e44i | 1.30741i | ||||||||
\(585\) | 3.56432e44 | − | 9.58213e43i | 1.89445 | − | 0.509293i | ||||
\(586\) | −1.87095e44 | −0.967610 | ||||||||
\(587\) | 1.61244e44 | + | 1.61244e44i | 0.811471 | + | 0.811471i | 0.984854 | − | 0.173384i | \(-0.0554700\pi\) |
−0.173384 | + | 0.984854i | \(0.555470\pi\) | |||||||
\(588\) | 2.86531e43 | − | 2.86531e43i | 0.140325 | − | 0.140325i | ||||
\(589\) | − | 1.48634e44i | − | 0.708390i | ||||||
\(590\) | −3.73124e43 | − | 1.38793e44i | −0.173070 | − | 0.643778i | ||||
\(591\) | 3.22690e44 | 1.45675 | ||||||||
\(592\) | −5.06441e43 | − | 5.06441e43i | −0.222527 | − | 0.222527i | ||||
\(593\) | 9.91752e43 | − | 9.91752e43i | 0.424158 | − | 0.424158i | −0.462474 | − | 0.886633i | \(-0.653038\pi\) |
0.886633 | + | 0.462474i | \(0.153038\pi\) | |||||||
\(594\) | 1.64394e44i | 0.684388i | ||||||||
\(595\) | −7.43796e42 | − | 4.28612e42i | −0.0301427 | − | 0.0173697i | ||||
\(596\) | −9.32626e42 | −0.0367932 | ||||||||
\(597\) | −3.05786e44 | − | 3.05786e44i | −1.17443 | − | 1.17443i | ||||
\(598\) | −3.13312e44 | + | 3.13312e44i | −1.17154 | + | 1.17154i | ||||
\(599\) | − | 1.31082e44i | − | 0.477216i | −0.971116 | − | 0.238608i | \(-0.923309\pi\) | ||
0.971116 | − | 0.238608i | \(-0.0766911\pi\) | |||||||
\(600\) | 4.08665e44 | − | 2.36844e44i | 1.44860 | − | 0.839542i | ||||
\(601\) | 3.67921e44 | 1.26988 | 0.634940 | − | 0.772561i | \(-0.281025\pi\) | ||||
0.634940 | + | 0.772561i | \(0.281025\pi\) | |||||||
\(602\) | 2.00654e44 | + | 2.00654e44i | 0.674379 | + | 0.674379i | ||||
\(603\) | −4.89366e44 | + | 4.89366e44i | −1.60161 | + | 1.60161i | ||||
\(604\) | 5.92400e43i | 0.188809i | ||||||||
\(605\) | −1.40648e44 | + | 2.44075e44i | −0.436564 | + | 0.757596i | ||||
\(606\) | 2.78555e44 | 0.842071 | ||||||||
\(607\) | −3.15598e44 | − | 3.15598e44i | −0.929213 | − | 0.929213i | 0.0684420 | − | 0.997655i | \(-0.478197\pi\) |
−0.997655 | + | 0.0684420i | \(0.978197\pi\) | |||||||
\(608\) | −1.70375e44 | + | 1.70375e44i | −0.488595 | + | 0.488595i | ||||
\(609\) | − | 7.43932e40i | − | 0.000207805i | ||||||
\(610\) | −9.65917e43 | + | 2.59672e43i | −0.262823 | + | 0.0706558i | ||||
\(611\) | 4.11126e44 | 1.08972 | ||||||||
\(612\) | −2.94809e42 | − | 2.94809e42i | −0.00761233 | − | 0.00761233i | ||||
\(613\) | −7.90423e43 | + | 7.90423e43i | −0.198835 | + | 0.198835i | −0.799500 | − | 0.600666i | \(-0.794902\pi\) |
0.600666 | + | 0.799500i | \(0.294902\pi\) | |||||||
\(614\) | 2.30485e44i | 0.564870i | ||||||||
\(615\) | 2.24409e44 | + | 8.34746e44i | 0.535843 | + | 1.99321i | ||||
\(616\) | −7.75055e44 | −1.80319 | ||||||||
\(617\) | −3.84469e44 | − | 3.84469e44i | −0.871563 | − | 0.871563i | 0.121080 | − | 0.992643i | \(-0.461364\pi\) |
−0.992643 | + | 0.121080i | \(0.961364\pi\) | |||||||
\(618\) | 2.91242e43 | − | 2.91242e43i | 0.0643336 | − | 0.0643336i | ||||
\(619\) | − | 7.77858e44i | − | 1.67436i | −0.546924 | − | 0.837182i | \(-0.684201\pi\) | ||
0.546924 | − | 0.837182i | \(-0.315799\pi\) | |||||||
\(620\) | −6.08002e43 | − | 3.50361e43i | −0.127538 | − | 0.0734934i | ||||
\(621\) | −3.91528e44 | −0.800381 | ||||||||
\(622\) | 4.78872e44 | + | 4.78872e44i | 0.954054 | + | 0.954054i | ||||
\(623\) | 7.03827e43 | − | 7.03827e43i | 0.136665 | − | 0.136665i | ||||
\(624\) | − | 7.57646e44i | − | 1.43388i | ||||||
\(625\) | −2.69498e44 | + | 4.70366e44i | −0.497136 | + | 0.867673i | ||||
\(626\) | 2.30550e44 | 0.414548 | ||||||||
\(627\) | 1.11598e45 | + | 1.11598e45i | 1.95603 | + | 1.95603i | ||||
\(628\) | 8.91148e43 | − | 8.91148e43i | 0.152263 | − | 0.152263i | ||||
\(629\) | − | 8.28457e42i | − | 0.0137994i | ||||||
\(630\) | 4.39231e44 | − | 7.62223e44i | 0.713253 | − | 1.23775i | ||||
\(631\) | −1.02238e44 | −0.161861 | −0.0809306 | − | 0.996720i | \(-0.525789\pi\) | ||||
−0.0809306 | + | 0.996720i | \(0.525789\pi\) | |||||||
\(632\) | −4.11472e44 | − | 4.11472e44i | −0.635137 | − | 0.635137i | ||||
\(633\) | 9.83499e44 | − | 9.83499e44i | 1.48018 | − | 1.48018i | ||||
\(634\) | 1.36986e44i | 0.201024i | ||||||||
\(635\) | −1.90255e44 | + | 5.11471e43i | −0.272242 | + | 0.0731882i | ||||
\(636\) | −4.99414e43 | −0.0696863 | ||||||||
\(637\) | 3.49210e44 | + | 3.49210e44i | 0.475178 | + | 0.475178i | ||||
\(638\) | −6.90868e40 | + | 6.90868e40i | −9.16779e−5 | + | 9.16779e-5i | ||||
\(639\) | 3.61738e44i | 0.468146i | ||||||||
\(640\) | −8.51928e43 | − | 3.16897e44i | −0.107528 | − | 0.399980i | ||||
\(641\) | −3.10298e44 | −0.381989 | −0.190995 | − | 0.981591i | \(-0.561171\pi\) | ||||
−0.190995 | + | 0.981591i | \(0.561171\pi\) | |||||||
\(642\) | −1.10831e45 | − | 1.10831e45i | −1.33077 | − | 1.33077i | ||||
\(643\) | −8.25926e43 | + | 8.25926e43i | −0.0967310 | + | 0.0967310i | −0.753816 | − | 0.657085i | \(-0.771789\pi\) |
0.657085 | + | 0.753816i | \(0.271789\pi\) | |||||||
\(644\) | − | 3.94900e44i | − | 0.451142i | ||||||
\(645\) | −1.10487e45 | − | 6.36683e44i | −1.23128 | − | 0.709525i | ||||
\(646\) | 2.94660e43 | 0.0320332 | ||||||||
\(647\) | 5.97296e44 | + | 5.97296e44i | 0.633463 | + | 0.633463i | 0.948935 | − | 0.315472i | \(-0.102163\pi\) |
−0.315472 | + | 0.948935i | \(0.602163\pi\) | |||||||
\(648\) | −3.52996e44 | + | 3.52996e44i | −0.365233 | + | 0.365233i | ||||
\(649\) | − | 1.05977e45i | − | 1.06979i | ||||||
\(650\) | 6.17526e44 | + | 1.06552e45i | 0.608193 | + | 1.04941i | ||||
\(651\) | −1.05367e45 | −1.01253 | ||||||||
\(652\) | 3.29075e44 | + | 3.29075e44i | 0.308556 | + | 0.308556i | ||||
\(653\) | −3.68464e44 | + | 3.68464e44i | −0.337120 | + | 0.337120i | −0.855282 | − | 0.518163i | \(-0.826616\pi\) |
0.518163 | + | 0.855282i | \(0.326616\pi\) | |||||||
\(654\) | 9.27653e44i | 0.828212i | ||||||||
\(655\) | −6.18223e44 | + | 1.07284e45i | −0.538622 | + | 0.934703i | ||||
\(656\) | 1.02878e45 | 0.874704 | ||||||||
\(657\) | −1.41646e45 | − | 1.41646e45i | −1.17533 | − | 1.17533i | ||||
\(658\) | 6.92909e44 | − | 6.92909e44i | 0.561128 | − | 0.561128i | ||||
\(659\) | − | 1.44815e45i | − | 1.14458i | −0.820050 | − | 0.572291i | \(-0.806055\pi\) | ||
0.820050 | − | 0.572291i | \(-0.193945\pi\) | |||||||
\(660\) | 7.19563e44 | − | 1.93444e44i | 0.555093 | − | 0.149228i | ||||
\(661\) | 1.61686e45 | 1.21744 | 0.608722 | − | 0.793384i | \(-0.291683\pi\) | ||||
0.608722 | + | 0.793384i | \(0.291683\pi\) | |||||||
\(662\) | 1.30302e45 | + | 1.30302e45i | 0.957688 | + | 0.957688i | ||||
\(663\) | 6.19694e43 | − | 6.19694e43i | 0.0444591 | − | 0.0444591i | ||||
\(664\) | 1.20245e45i | 0.842126i | ||||||||
\(665\) | −6.03561e44 | − | 2.24510e45i | −0.412643 | − | 1.53493i | ||||
\(666\) | 8.48982e44 | 0.566645 | ||||||||
\(667\) | −1.64540e41 | − | 1.64540e41i | −0.000107216 | − | 0.000107216i | ||||
\(668\) | 2.04347e44 | − | 2.04347e44i | 0.130000 | − | 0.130000i | ||||
\(669\) | 3.97569e45i | 2.46942i | ||||||||
\(670\) | −2.00079e45 | − | 1.15296e45i | −1.21340 | − | 0.699223i | ||||
\(671\) | −7.37539e44 | −0.436742 | ||||||||
\(672\) | 1.20780e45 | + | 1.20780e45i | 0.698369 | + | 0.698369i | ||||
\(673\) | −2.46534e44 | + | 2.46534e44i | −0.139199 | + | 0.139199i | −0.773273 | − | 0.634074i | \(-0.781382\pi\) |
0.634074 | + | 0.773273i | \(0.281382\pi\) | |||||||
\(674\) | 2.36641e45i | 1.30476i | ||||||||
\(675\) | −2.79914e44 | + | 1.05160e45i | −0.150718 | + | 0.566226i | ||||
\(676\) | −5.28570e44 | −0.277943 | ||||||||
\(677\) | 2.18968e44 | + | 2.18968e44i | 0.112451 | + | 0.112451i | 0.761093 | − | 0.648643i | \(-0.224663\pi\) |
−0.648643 | + | 0.761093i | \(0.724663\pi\) | |||||||
\(678\) | −5.08269e44 | + | 5.08269e44i | −0.254929 | + | 0.254929i | ||||
\(679\) | 2.69257e45i | 1.31902i | ||||||||
\(680\) | 3.24670e43 | − | 5.63419e43i | 0.0155346 | − | 0.0269581i | ||||
\(681\) | −2.55598e45 | −1.19455 | ||||||||
\(682\) | 9.78512e44 | + | 9.78512e44i | 0.446700 | + | 0.446700i | ||||
\(683\) | 1.73095e45 | − | 1.73095e45i | 0.771886 | − | 0.771886i | −0.206550 | − | 0.978436i | \(-0.566223\pi\) |
0.978436 | + | 0.206550i | \(0.0662235\pi\) | |||||||
\(684\) | − | 1.12909e45i | − | 0.491847i | ||||||
\(685\) | 3.52809e45 | − | 9.48474e44i | 1.50138 | − | 0.403623i | ||||
\(686\) | −1.31323e45 | −0.545951 | ||||||||
\(687\) | −3.85640e45 | − | 3.85640e45i | −1.56630 | − | 1.56630i | ||||
\(688\) | −1.07319e45 | + | 1.07319e45i | −0.425854 | + | 0.425854i | ||||
\(689\) | − | 6.08662e44i | − | 0.235977i | ||||||
\(690\) | −1.23212e45 | − | 4.58318e45i | −0.466731 | − | 1.73613i | ||||
\(691\) | 1.12336e45 | 0.415785 | 0.207892 | − | 0.978152i | \(-0.433340\pi\) | ||||
0.207892 | + | 0.978152i | \(0.433340\pi\) | |||||||
\(692\) | 5.31986e44 | + | 5.31986e44i | 0.192399 | + | 0.192399i | ||||
\(693\) | 4.58693e45 | − | 4.58693e45i | 1.62103 | − | 1.62103i | ||||
\(694\) | − | 3.39804e45i | − | 1.17348i | ||||||
\(695\) | −3.49736e43 | − | 2.01535e43i | −0.0118027 | − | 0.00680132i | ||||
\(696\) | 5.63522e41 | 0.000185850 | ||||||||
\(697\) | 8.41460e43 | + | 8.41460e43i | 0.0271212 | + | 0.0271212i | ||||
\(698\) | 1.14582e45 | − | 1.14582e45i | 0.360937 | − | 0.360937i | ||||
\(699\) | 8.04333e45i | 2.47629i | ||||||||
\(700\) | −1.06066e45 | − | 2.82324e44i | −0.319158 | − | 0.0849532i | ||||
\(701\) | −3.92745e45 | −1.15511 | −0.577554 | − | 0.816352i | \(-0.695993\pi\) | ||||
−0.577554 | + | 0.816352i | \(0.695993\pi\) | |||||||
\(702\) | 1.74809e45 | + | 1.74809e45i | 0.502540 | + | 0.502540i | ||||
\(703\) | 1.58645e45 | − | 1.58645e45i | 0.445802 | − | 0.445802i | ||||
\(704\) | − | 5.50181e45i | − | 1.51127i | ||||||
\(705\) | −2.19862e45 | + | 3.81540e45i | −0.590371 | + | 1.02451i | ||||
\(706\) | −2.69458e44 | −0.0707319 | ||||||||
\(707\) | −2.13947e45 | − | 2.13947e45i | −0.549028 | − | 0.549028i | ||||
\(708\) | −9.24648e44 | + | 9.24648e44i | −0.231977 | + | 0.231977i | ||||
\(709\) | − | 7.48151e45i | − | 1.83506i | −0.397671 | − | 0.917528i | \(-0.630181\pi\) | ||
0.397671 | − | 0.917528i | \(-0.369819\pi\) | |||||||
\(710\) | −1.16562e45 | + | 3.13360e44i | −0.279527 | + | 0.0751466i | ||||
\(711\) | 4.87035e45 | 1.14195 | ||||||||
\(712\) | 5.33143e44 | + | 5.33143e44i | 0.122226 | + | 0.122226i | ||||
\(713\) | −2.33047e45 | + | 2.33047e45i | −0.522409 | + | 0.522409i | ||||
\(714\) | − | 2.08885e44i | − | 0.0457864i | ||||||
\(715\) | 2.35760e45 | + | 8.76970e45i | 0.505328 | + | 1.87970i | ||||
\(716\) | −1.94119e45 | −0.406873 | ||||||||
\(717\) | 3.04925e45 | + | 3.04925e45i | 0.625009 | + | 0.625009i | ||||
\(718\) | 2.14541e44 | − | 2.14541e44i | 0.0430050 | − | 0.0430050i | ||||
\(719\) | 1.61834e45i | 0.317254i | 0.987339 | + | 0.158627i | \(0.0507067\pi\) | ||||
−0.987339 | + | 0.158627i | \(0.949293\pi\) | |||||||
\(720\) | 4.07671e45 | + | 2.34920e45i | 0.781610 | + | 0.450402i | ||||
\(721\) | −4.47382e44 | −0.0838908 | ||||||||
\(722\) | 2.35331e45 | + | 2.35331e45i | 0.431603 | + | 0.431603i | ||||
\(723\) | −2.25194e45 | + | 2.25194e45i | −0.403965 | + | 0.403965i | ||||
\(724\) | 6.92348e44i | 0.121481i | ||||||||
\(725\) | −5.59571e41 | + | 3.24302e41i | −9.60389e−5 | + | 5.56598e-5i | ||||
\(726\) | −6.85453e45 | −1.15078 | ||||||||
\(727\) | 3.84402e45 | + | 3.84402e45i | 0.631299 | + | 0.631299i | 0.948394 | − | 0.317095i | \(-0.102707\pi\) |
−0.317095 | + | 0.948394i | \(0.602707\pi\) | |||||||
\(728\) | −8.24159e45 | + | 8.24159e45i | −1.32406 | + | 1.32406i | ||||
\(729\) | − | 9.92952e45i | − | 1.56059i | ||||||
\(730\) | 3.33721e45 | − | 5.79127e45i | 0.513119 | − | 0.890446i | ||||
\(731\) | −1.75556e44 | −0.0264082 | ||||||||
\(732\) | 6.43499e44 | + | 6.43499e44i | 0.0947045 | + | 0.0947045i | ||||
\(733\) | 8.30891e45 | − | 8.30891e45i | 1.19641 | − | 1.19641i | 0.221178 | − | 0.975233i | \(-0.429010\pi\) |
0.975233 | − | 0.221178i | \(-0.0709903\pi\) | |||||||
\(734\) | − | 8.42456e44i | − | 0.118689i | ||||||
\(735\) | −5.10830e45 | + | 1.37329e45i | −0.704173 | + | 0.189306i | ||||
\(736\) | 5.34272e45 | 0.720638 | ||||||||
\(737\) | −1.20404e46 | − | 1.20404e46i | −1.58914 | − | 1.58914i | ||||
\(738\) | −8.62307e45 | + | 8.62307e45i | −1.11368 | + | 1.11368i | ||||
\(739\) | 1.31493e46i | 1.66185i | 0.556384 | + | 0.830925i | \(0.312188\pi\) | ||||
−0.556384 | + | 0.830925i | \(0.687812\pi\) | |||||||
\(740\) | −2.74996e44 | − | 1.02292e45i | −0.0340109 | − | 0.126512i | ||||
\(741\) | 2.37336e46 | 2.87259 | ||||||||
\(742\) | −1.02583e45 | − | 1.02583e45i | −0.121511 | − | 0.121511i | ||||
\(743\) | −2.01767e45 | + | 2.01767e45i | −0.233899 | + | 0.233899i | −0.814318 | − | 0.580419i | \(-0.802889\pi\) |
0.580419 | + | 0.814318i | \(0.302889\pi\) | |||||||
\(744\) | − | 7.98146e45i | − | 0.905556i | ||||||
\(745\) | 1.05484e45 | + | 6.07853e44i | 0.117135 | + | 0.0674991i | ||||
\(746\) | 6.02255e45 | 0.654574 | ||||||||
\(747\) | −7.11633e45 | − | 7.11633e45i | −0.757053 | − | 0.757053i | ||||
\(748\) | 7.25351e43 | − | 7.25351e43i | 0.00755306 | − | 0.00755306i | ||||
\(749\) | 1.70250e46i | 1.73532i | ||||||||
\(750\) | −1.31908e46 | + | 3.26887e43i | −1.31610 | + | 0.00326150i | ||||
\(751\) | −1.37535e46 | −1.34330 | −0.671651 | − | 0.740867i | \(-0.734415\pi\) | ||||
−0.671651 | + | 0.740867i | \(0.734415\pi\) | |||||||
\(752\) | 3.70599e45 | + | 3.70599e45i | 0.354338 | + | 0.354338i | ||||
\(753\) | −7.99295e45 | + | 7.99295e45i | −0.748148 | + | 0.748148i | ||||
\(754\) | 1.46928e42i | 0.000134636i | ||||||||
\(755\) | 3.86105e45 | − | 6.70032e45i | 0.346381 | − | 0.601096i | ||||
\(756\) | −2.20330e45 | −0.193520 | ||||||||
\(757\) | 8.00852e45 | + | 8.00852e45i | 0.688681 | + | 0.688681i | 0.961940 | − | 0.273259i | \(-0.0881016\pi\) |
−0.273259 | + | 0.961940i | \(0.588102\pi\) | |||||||
\(758\) | 5.26100e44 | − | 5.26100e44i | 0.0442957 | − | 0.0442957i | ||||
\(759\) | − | 3.49955e46i | − | 2.88499i | ||||||
\(760\) | 1.70064e46 | − | 4.57192e45i | 1.37276 | − | 0.369047i | ||||
\(761\) | 2.20783e46 | 1.74506 | 0.872530 | − | 0.488560i | \(-0.162478\pi\) | ||||
0.872530 | + | 0.488560i | \(0.162478\pi\) | |||||||
\(762\) | −3.38973e45 | − | 3.38973e45i | −0.262352 | − | 0.262352i | ||||
\(763\) | 7.12493e45 | − | 7.12493e45i | 0.539993 | − | 0.539993i | ||||
\(764\) | − | 2.67074e45i | − | 0.198215i | ||||||
\(765\) | 1.41296e44 | + | 5.25588e44i | 0.0102695 | + | 0.0382000i | ||||
\(766\) | −1.14155e46 | −0.812522 | ||||||||
\(767\) | −1.12692e46 | − | 1.12692e46i | −0.785536 | − | 0.785536i | ||||
\(768\) | −1.19920e46 | + | 1.19920e46i | −0.818675 | + | 0.818675i | ||||
\(769\) | − | 1.38404e46i | − | 0.925394i | −0.886517 | − | 0.462697i | \(-0.846882\pi\) | ||
0.886517 | − | 0.462697i | \(-0.153118\pi\) | |||||||
\(770\) | 1.87538e46 | + | 1.08069e46i | 1.22811 | + | 0.707700i | ||||
\(771\) | 1.91081e46 | 1.22560 | ||||||||
\(772\) | 3.26048e45 | + | 3.26048e45i | 0.204835 | + | 0.204835i | ||||
\(773\) | −1.26312e46 | + | 1.26312e46i | −0.777272 | + | 0.777272i | −0.979366 | − | 0.202094i | \(-0.935225\pi\) |
0.202094 | + | 0.979366i | \(0.435225\pi\) | |||||||
\(774\) | − | 1.79906e46i | − | 1.08440i | ||||||
\(775\) | 4.59326e45 | + | 7.92549e45i | 0.271202 | + | 0.467949i | ||||
\(776\) | −2.03960e46 | −1.17966 | ||||||||
\(777\) | −1.12464e46 | − | 1.12464e46i | −0.637204 | − | 0.637204i | ||||
\(778\) | 8.55526e45 | − | 8.55526e45i | 0.474853 | − | 0.474853i | ||||
\(779\) | 3.22271e46i | 1.75235i | ||||||||
\(780\) | 5.59452e45 | − | 9.70851e45i | 0.298023 | − | 0.517177i | ||||
\(781\) | −8.90026e45 | −0.464500 | ||||||||
\(782\) | −4.62005e44 | − | 4.62005e44i | −0.0236232 | − | 0.0236232i | ||||
\(783\) | −9.18035e41 | + | 9.18035e41i | −4.59908e−5 | + | 4.59908e-5i | ||||
\(784\) | 6.29572e45i | 0.309021i | ||||||||
\(785\) | −1.58875e46 | + | 4.27111e45i | −0.764083 | + | 0.205412i | ||||
\(786\) | −3.01293e46 | −1.41980 | ||||||||
\(787\) | −1.68108e46 | − | 1.68108e46i | −0.776234 | − | 0.776234i | 0.202954 | − | 0.979188i | \(-0.434946\pi\) |
−0.979188 | + | 0.202954i | \(0.934946\pi\) | |||||||
\(788\) | 4.01638e45 | − | 4.01638e45i | 0.181725 | − | 0.181725i | ||||
\(789\) | 4.81783e46i | 2.13609i | ||||||||
\(790\) | 4.21899e45 | + | 1.56936e46i | 0.183305 | + | 0.681851i | ||||
\(791\) | 7.80762e45 | 0.332426 | ||||||||
\(792\) | 3.47456e46 | + | 3.47456e46i | 1.44976 | + | 1.44976i | ||||
\(793\) | −7.84266e45 | + | 7.84266e45i | −0.320695 | + | 0.320695i | ||||
\(794\) | 2.34211e45i | 0.0938598i | ||||||||
\(795\) | 5.64861e45 | + | 3.25501e45i | 0.221854 | + | 0.127843i | ||||
\(796\) | −7.61198e45 | −0.293014 | ||||||||
\(797\) | −1.80369e45 | − | 1.80369e45i | −0.0680502 | − | 0.0680502i | 0.672263 | − | 0.740313i | \(-0.265323\pi\) |
−0.740313 | + | 0.672263i | \(0.765323\pi\) | |||||||
\(798\) | 4.00005e46 | − | 4.00005e46i | 1.47917 | − | 1.47917i | ||||
\(799\) | 6.06240e44i | 0.0219733i | ||||||||
\(800\) | 3.81965e45 | − | 1.43499e46i | 0.135701 | − | 0.509812i | ||||
\(801\) | −6.31049e45 | −0.219757 | ||||||||
\(802\) | −1.18556e46 | − | 1.18556e46i | −0.404699 | − | 0.404699i | ||||
\(803\) | 3.48508e46 | − | 3.48508e46i | 1.16618 | − | 1.16618i | ||||
\(804\) | 2.10104e46i | 0.689189i | ||||||||
\(805\) | −2.57382e46 | + | 4.46650e46i | −0.827644 | + | 1.43626i | ||||
\(806\) | 2.08101e46 | 0.656015 | ||||||||
\(807\) | 4.51763e46 | + | 4.51763e46i | 1.39616 | + | 1.39616i | ||||
\(808\) | 1.62063e46 | − | 1.62063e46i | 0.491023 | − | 0.491023i | ||||
\(809\) | − | 2.60290e46i | − | 0.773181i | −0.922251 | − | 0.386590i | \(-0.873653\pi\) | ||
0.922251 | − | 0.386590i | \(-0.126347\pi\) | |||||||
\(810\) | 1.34633e46 | − | 3.61941e45i | 0.392095 | − | 0.105409i | ||||
\(811\) | −6.35697e46 | −1.81517 | −0.907584 | − | 0.419871i | \(-0.862075\pi\) | ||||
−0.907584 | + | 0.419871i | \(0.862075\pi\) | |||||||
\(812\) | −9.25941e41 | − | 9.25941e41i | −2.59231e−5 | − | 2.59231e-5i | ||||
\(813\) | −4.60162e46 | + | 4.60162e46i | −1.26317 | + | 1.26317i | ||||
\(814\) | 2.08885e46i | 0.562233i | ||||||||
\(815\) | −1.57720e46 | − | 5.86679e46i | −0.416260 | − | 1.54839i | ||||
\(816\) | 1.11721e45 | 0.0289130 | ||||||||
\(817\) | −3.36182e46 | − | 3.36182e46i | −0.853142 | − | 0.853142i | ||||
\(818\) | 1.55550e45 | − | 1.55550e45i | 0.0387094 | − | 0.0387094i | ||||
\(819\) | − | 9.75507e46i | − | 2.38061i | ||||||
\(820\) | 1.31828e46 | + | 7.59660e45i | 0.315491 | + | 0.181802i | ||||
\(821\) | 3.29602e46 | 0.773569 | 0.386785 | − | 0.922170i | \(-0.373586\pi\) | ||||
0.386785 | + | 0.922170i | \(0.373586\pi\) | |||||||
\(822\) | 6.28592e46 | + | 6.28592e46i | 1.44684 | + | 1.44684i | ||||
\(823\) | 1.46966e46 | − | 1.46966e46i | 0.331756 | − | 0.331756i | −0.521497 | − | 0.853253i | \(-0.674626\pi\) |
0.853253 | + | 0.521497i | \(0.174626\pi\) | |||||||
\(824\) | − | 3.38888e45i | − | 0.0750276i | ||||||
\(825\) | −9.39939e46 | − | 2.50192e46i | −2.04097 | − | 0.543264i | ||||
\(826\) | −3.79859e46 | −0.808987 | ||||||||
\(827\) | −3.35463e46 | − | 3.35463e46i | −0.700739 | − | 0.700739i | 0.263830 | − | 0.964569i | \(-0.415014\pi\) |
−0.964569 | + | 0.263830i | \(0.915014\pi\) | |||||||
\(828\) | −1.77033e46 | + | 1.77033e46i | −0.362717 | + | 0.362717i | ||||
\(829\) | 3.75145e46i | 0.753923i | 0.926229 | + | 0.376961i | \(0.123031\pi\) | ||||
−0.926229 | + | 0.376961i | \(0.876969\pi\) | |||||||
\(830\) | 1.67662e46 | − | 2.90954e46i | 0.330510 | − | 0.573554i | ||||
\(831\) | 1.11426e47 | 2.15462 | ||||||||
\(832\) | −5.85038e46 | − | 5.85038e46i | −1.10971 | − | 1.10971i | ||||
\(833\) | −5.14939e44 | + | 5.14939e44i | −0.00958156 | + | 0.00958156i | ||||
\(834\) | − | 9.82186e44i | − | 0.0179282i | ||||||
\(835\) | −3.64312e46 | + | 9.79398e45i | −0.652364 | + | 0.175378i | ||||
\(836\) | 2.77802e46 | 0.488017 | ||||||||
\(837\) | 1.30026e46 | + | 1.30026e46i | 0.224090 | + | 0.224090i | ||||
\(838\) | −2.76860e46 | + | 2.76860e46i | −0.468119 | + | 0.468119i | ||||
\(839\) | 4.26224e46i | 0.707044i | 0.935426 | + | 0.353522i | \(0.115016\pi\) | ||||
−0.935426 | + | 0.353522i | \(0.884984\pi\) | |||||||
\(840\) | −3.24105e46 | − | 1.20559e47i | −0.527494 | − | 1.96215i | ||||
\(841\) | 6.26233e46 | 1.00000 | ||||||||
\(842\) | 3.78008e46 | + | 3.78008e46i | 0.592254 | + | 0.592254i | ||||
\(843\) | 8.60738e46 | − | 8.60738e46i | 1.32321 | − | 1.32321i | ||||
\(844\) | − | 2.44824e46i | − | 0.369296i | ||||||
\(845\) | 5.97837e46 | + | 3.44503e46i | 0.884863 | + | 0.509901i | ||||
\(846\) | −6.21260e46 | −0.902292 | ||||||||
\(847\) | 5.26469e46 | + | 5.26469e46i | 0.750305 | + | 0.750305i | ||||
\(848\) | 5.48662e45 | − | 5.48662e45i | 0.0767311 | − | 0.0767311i | ||||
\(849\) | 1.70198e47i | 2.33578i | ||||||||
\(850\) | −1.57119e45 | + | 9.10593e44i | −0.0211605 | + | 0.0122637i | ||||
\(851\) | −4.97489e46 | −0.657522 | ||||||||
\(852\) | 7.76543e45 | + | 7.76543e45i | 0.100724 | + | 0.100724i | ||||
\(853\) | 3.51606e46 | − | 3.51606e46i | 0.447581 | − | 0.447581i | −0.446969 | − | 0.894550i | \(-0.647496\pi\) |
0.894550 | + | 0.446969i | \(0.147496\pi\) | |||||||
\(854\) | 2.64359e46i | 0.330269i | ||||||||
\(855\) | −7.35900e46 | + | 1.27705e47i | −0.902320 | + | 1.56585i | ||||
\(856\) | −1.28963e47 | −1.55198 | ||||||||
\(857\) | 2.08023e46 | + | 2.08023e46i | 0.245707 | + | 0.245707i | 0.819206 | − | 0.573499i | \(-0.194414\pi\) |
−0.573499 | + | 0.819206i | \(0.694414\pi\) | |||||||
\(858\) | −1.56248e47 | + | 1.56248e47i | −1.81141 | + | 1.81141i | ||||
\(859\) | − | 5.96305e46i | − | 0.678544i | −0.940688 | − | 0.339272i | \(-0.889819\pi\) | ||
0.940688 | − | 0.339272i | \(-0.110181\pi\) | |||||||
\(860\) | −2.16764e46 | + | 5.82737e45i | −0.242110 | + | 0.0650875i | ||||
\(861\) | 2.28459e47 | 2.50471 | ||||||||
\(862\) | 5.86329e46 | + | 5.86329e46i | 0.630993 | + | 0.630993i | ||||
\(863\) | 1.98909e46 | − | 1.98909e46i | 0.210127 | − | 0.210127i | −0.594194 | − | 0.804322i | \(-0.702529\pi\) |
0.804322 | + | 0.594194i | \(0.202529\pi\) | |||||||
\(864\) | − | 2.98091e46i | − | 0.309121i | ||||||
\(865\) | −2.54971e46 | − | 9.48430e46i | −0.259557 | − | 0.965490i | ||||
\(866\) | 1.00767e46 | 0.100701 | ||||||||
\(867\) | −1.11098e47 | − | 1.11098e47i | −1.08993 | − | 1.08993i | ||||
\(868\) | −1.31146e46 | + | 1.31146e46i | −0.126310 | + | 0.126310i | ||||
\(869\) | 1.19831e47i | 1.13306i | ||||||||
\(870\) | −1.36354e43 | − | 7.85741e42i | −0.000126579 | − | 7.29409e-5i | ||||
\(871\) | −2.56065e47 | −2.33378 | ||||||||
\(872\) | 5.39707e46 | + | 5.39707e46i | 0.482942 | + | 0.482942i | ||||
\(873\) | 1.20708e47 | − | 1.20708e47i | 1.06049 | − | 1.06049i | ||||
\(874\) | − | 1.76943e47i | − | 1.52634i | ||||||
\(875\) | 1.01564e47 | + | 1.01062e47i | 0.860224 | + | 0.855971i | ||||
\(876\) | −6.08144e46 | −0.505756 | ||||||||
\(877\) | 8.41422e46 | + | 8.41422e46i | 0.687101 | + | 0.687101i | 0.961590 | − | 0.274490i | \(-0.0885089\pi\) |
−0.274490 | + | 0.961590i | \(0.588509\pi\) | |||||||
\(878\) | 8.40468e46 | − | 8.40468e46i | 0.673921 | − | 0.673921i | ||||
\(879\) | − | 2.22216e47i | − | 1.74966i | ||||||
\(880\) | −5.78001e46 | + | 1.00304e47i | −0.446895 | + | 0.775524i | ||||
\(881\) | −1.37730e47 | −1.04572 | −0.522859 | − | 0.852419i | \(-0.675134\pi\) | ||||
−0.522859 | + | 0.852419i | \(0.675134\pi\) | |||||||
\(882\) | −5.27697e46 | − | 5.27697e46i | −0.393448 | − | 0.393448i | ||||
\(883\) | 1.33961e46 | − | 1.33961e46i | 0.0980858 | − | 0.0980858i | −0.656361 | − | 0.754447i | \(-0.727905\pi\) |
0.754447 | + | 0.656361i | \(0.227905\pi\) | |||||||
\(884\) | − | 1.54261e45i | − | 0.0110923i | ||||||
\(885\) | 1.64847e47 | − | 4.43167e46i | 1.16410 | − | 0.312950i | ||||
\(886\) | 1.92421e47 | 1.33448 | ||||||||
\(887\) | −8.50711e46 | − | 8.50711e46i | −0.579434 | − | 0.579434i | 0.355313 | − | 0.934747i | \(-0.384374\pi\) |
−0.934747 | + | 0.355313i | \(0.884374\pi\) | |||||||
\(888\) | 8.51907e46 | − | 8.51907e46i | 0.569882 | − | 0.569882i | ||||
\(889\) | 5.20702e46i | 0.342106i | ||||||||
\(890\) | −5.46652e45 | − | 2.03341e46i | −0.0352753 | − | 0.131216i | ||||
\(891\) | 1.02801e47 | 0.651559 | ||||||||
\(892\) | 4.94837e46 | + | 4.94837e46i | 0.308052 | + | 0.308052i | ||||
\(893\) | −1.16092e47 | + | 1.16092e47i | −0.709870 | + | 0.709870i | ||||
\(894\) | 2.96239e46i | 0.177927i | ||||||||
\(895\) | 2.19557e47 | + | 1.26520e47i | 1.29533 | + | 0.746430i | ||||
\(896\) | −8.67305e46 | −0.502624 | ||||||||
\(897\) | −3.72127e47 | − | 3.72127e47i | −2.11842 | − | 2.11842i | ||||
\(898\) | −1.26539e47 | + | 1.26539e47i | −0.707623 | + | 0.707623i | ||||
\(899\) | 1.09287e43i | 6.00364e-5i | ||||||||
\(900\) | 3.48925e46 | + | 6.02056e46i | 0.188300 | + | 0.324905i | ||||
\(901\) | 8.97523e44 | 0.00475827 | ||||||||
\(902\) | −2.12163e47 | − | 2.12163e47i | −1.10501 | − | 1.10501i | ||||
\(903\) | −2.38321e47 | + | 2.38321e47i | −1.21943 | + | 1.21943i | ||||
\(904\) | 5.91420e46i | 0.297304i | ||||||||
\(905\) | 4.51248e46 | − | 7.83078e46i | 0.222863 | − | 0.386747i | ||||
\(906\) | 1.88170e47 | 0.913058 | ||||||||
\(907\) | 5.21733e46 | + | 5.21733e46i | 0.248732 | + | 0.248732i | 0.820450 | − | 0.571718i | \(-0.193723\pi\) |
−0.571718 | + | 0.820450i | \(0.693723\pi\) | |||||||
\(908\) | −3.18132e46 | + | 3.18132e46i | −0.149016 | + | 0.149016i | ||||
\(909\) | 1.91824e47i | 0.882837i | ||||||||
\(910\) | 3.14336e47 | − | 8.45043e46i | 1.42145 | − | 0.382135i | ||||
\(911\) | 9.62130e46 | 0.427504 | 0.213752 | − | 0.976888i | \(-0.431432\pi\) | ||||
0.213752 | + | 0.976888i | \(0.431432\pi\) | |||||||
\(912\) | 2.13940e47 | + | 2.13940e47i | 0.934061 | + | 0.934061i | ||||
\(913\) | 1.75091e47 | − | 1.75091e47i | 0.751158 | − | 0.751158i | ||||
\(914\) | − | 1.30560e47i | − | 0.550390i | ||||||
\(915\) | −3.08417e46 | − | 1.14724e47i | −0.127762 | − | 0.475243i | ||||
\(916\) | −9.59980e46 | −0.390782 | ||||||||
\(917\) | 2.31411e47 | + | 2.31411e47i | 0.925708 | + | 0.925708i | ||||
\(918\) | −2.57771e45 | + | 2.57771e45i | −0.0101333 | + | 0.0101333i | ||||
\(919\) | − | 2.47961e47i | − | 0.957934i | −0.877833 | − | 0.478967i | \(-0.841011\pi\) | ||
0.877833 | − | 0.478967i | \(-0.158989\pi\) | |||||||
\(920\) | −3.38333e47 | − | 1.94964e47i | −1.28452 | − | 0.740202i | ||||
\(921\) | −2.73751e47 | −1.02141 | ||||||||
\(922\) | −1.09358e47 | − | 1.09358e47i | −0.401009 | − | 0.401009i | ||||
\(923\) | −9.46414e46 | + | 9.46414e46i | −0.341078 | + | 0.341078i | ||||
\(924\) | − | 1.96935e47i | − | 0.697544i | ||||||
\(925\) | −3.55668e46 | + | 1.33620e47i | −0.123816 | + | 0.465161i | ||||
\(926\) | 2.23963e47 | 0.766302 | ||||||||
\(927\) | 2.00561e46 | + | 2.00561e46i | 0.0674481 | + | 0.0674481i | ||||
\(928\) | 1.25273e43 | − | 1.25273e43i | 4.14087e−5 | − | 4.14087e-5i | ||||
\(929\) | 2.99823e47i | 0.974123i | 0.873368 | + | 0.487062i | \(0.161931\pi\) | ||||
−0.873368 | + | 0.487062i | \(0.838069\pi\) | |||||||
\(930\) | −1.11288e47 | + | 1.93125e47i | −0.355404 | + | 0.616755i | ||||
\(931\) | −1.97217e47 | −0.619083 | ||||||||
\(932\) | 1.00112e47 | + | 1.00112e47i | 0.308909 | + | 0.308909i | ||||
\(933\) | −5.68765e47 | + | 5.68765e47i | −1.72515 | + | 1.72515i | ||||
\(934\) | 2.76859e47i | 0.825485i | ||||||||
\(935\) | −1.29316e46 | + | 3.47648e45i | −0.0379025 | + | 0.0101895i | ||||
\(936\) | 7.38938e47 | 2.12909 | ||||||||
\(937\) | −3.46305e46 | − | 3.46305e46i | −0.0980900 | − | 0.0980900i | 0.656359 | − | 0.754449i | \(-0.272096\pi\) |
−0.754449 | + | 0.656359i | \(0.772096\pi\) | |||||||
\(938\) | −4.31570e47 | + | 4.31570e47i | −1.20173 | + | 1.20173i | ||||
\(939\) | 2.73828e47i | 0.749598i | ||||||||
\(940\) | 2.01234e46 | + | 7.48540e46i | 0.0541570 | + | 0.201451i | ||||
\(941\) | 3.57451e47 | 0.945763 | 0.472881 | − | 0.881126i | \(-0.343214\pi\) | ||||
0.472881 | + | 0.881126i | \(0.343214\pi\) | |||||||
\(942\) | −2.83064e47 | − | 2.83064e47i | −0.736325 | − | 0.736325i | ||||
\(943\) | 5.05297e47 | − | 5.05297e47i | 1.29229 | − | 1.29229i | ||||
\(944\) | − | 2.03166e47i | − | 0.510856i | ||||||
\(945\) | 2.49203e47 | + | 1.43603e47i | 0.616091 | + | 0.355022i | ||||
\(946\) | 4.42643e47 | 1.07596 | ||||||||
\(947\) | −1.27440e47 | − | 1.27440e47i | −0.304583 | − | 0.304583i | 0.538221 | − | 0.842804i | \(-0.319097\pi\) |
−0.842804 | + | 0.538221i | \(0.819097\pi\) | |||||||
\(948\) | 1.04552e47 | − | 1.04552e47i | 0.245696 | − | 0.245696i | ||||
\(949\) | − | 7.41177e47i | − | 1.71263i | ||||||
\(950\) | −4.75249e47 | − | 1.26502e47i | −1.07980 | − | 0.287421i | ||||
\(951\) | −1.62700e47 | −0.363496 | ||||||||
\(952\) | −1.21529e46 | − | 1.21529e46i | −0.0266986 | − | 0.0266986i | ||||
\(953\) | −9.30380e46 | + | 9.30380e46i | −0.200990 | + | 0.200990i | −0.800424 | − | 0.599434i | \(-0.795392\pi\) |
0.599434 | + | 0.800424i | \(0.295392\pi\) | |||||||
\(954\) | 9.19759e46i | 0.195389i | ||||||||
\(955\) | −1.74069e47 | + | 3.02073e47i | −0.363637 | + | 0.631041i | ||||
\(956\) | 7.59054e46 | 0.155936 | ||||||||
\(957\) | −8.20557e43 | − | 8.20557e43i | −0.000165774 | − | 0.000165774i | ||||
\(958\) | −8.51466e45 | + | 8.51466e45i | −0.0169168 | + | 0.0169168i | ||||
\(959\) | − | 9.65593e47i | − | 1.88667i | ||||||
\(960\) | 8.55803e47 | − | 2.30069e47i | 1.64450 | − | 0.442099i | ||||
\(961\) | −3.74355e47 | −0.707473 | ||||||||
\(962\) | 2.22119e47 | + | 2.22119e47i | 0.412842 | + | 0.412842i | ||||
\(963\) | 7.63229e47 | − | 7.63229e47i | 1.39519 | − | 1.39519i | ||||
\(964\) | 5.60578e46i | 0.100787i | ||||||||
\(965\) | −1.56269e47 | − | 5.81282e47i | −0.276335 | − | 1.02790i | ||||
\(966\) | −1.25436e48 | −2.18166 | ||||||||
\(967\) | 3.22631e47 | + | 3.22631e47i | 0.551928 | + | 0.551928i | 0.926997 | − | 0.375069i | \(-0.122381\pi\) |
−0.375069 | + | 0.926997i | \(0.622381\pi\) | |||||||
\(968\) | −3.98795e47 | + | 3.98795e47i | −0.671034 | + | 0.671034i | ||||
\(969\) | 3.49972e46i | 0.0579233i | ||||||||
\(970\) | 4.93518e47 | + | 2.84389e47i | 0.803443 | + | 0.462983i | ||||
\(971\) | −4.89239e47 | −0.783454 | −0.391727 | − | 0.920081i | \(-0.628122\pi\) | ||||
−0.391727 | + | 0.920081i | \(0.628122\pi\) | |||||||
\(972\) | −1.61277e47 | − | 1.61277e47i | −0.254047 | − | 0.254047i | ||||
\(973\) | −7.54378e45 | + | 7.54378e45i | −0.0116892 | + | 0.0116892i | ||||
\(974\) | − | 4.05882e47i | − | 0.618666i | ||||||
\(975\) | −1.26553e48 | + | 7.33446e47i | −1.89758 | + | 1.09975i | ||||
\(976\) | −1.41391e47 | −0.208557 | ||||||||
\(977\) | −8.39845e46 | − | 8.39845e46i | −0.121867 | − | 0.121867i | 0.643543 | − | 0.765410i | \(-0.277464\pi\) |
−0.765410 | + | 0.643543i | \(0.777464\pi\) | |||||||
\(978\) | 1.04527e48 | − | 1.04527e48i | 1.49214 | − | 1.49214i | ||||
\(979\) | − | 1.55264e47i | − | 0.218046i | ||||||
\(980\) | −4.64881e46 | + | 8.06736e46i | −0.0642281 | + | 0.111459i | ||||
\(981\) | −6.38819e47 | −0.868308 | ||||||||
\(982\) | 6.59763e47 | + | 6.59763e47i | 0.882275 | + | 0.882275i | ||||
\(983\) | 8.80136e47 | − | 8.80136e47i | 1.15796 | − | 1.15796i | 0.173046 | − | 0.984914i | \(-0.444639\pi\) |
0.984914 | − | 0.173046i | \(-0.0553609\pi\) | |||||||
\(984\) | 1.73056e48i | 2.24008i | ||||||||
\(985\) | −7.16045e47 | + | 1.92498e47i | −0.911928 | + | 0.245158i | ||||
\(986\) | −2.16657e42 | −2.71483e−6 | ||||||||
\(987\) | 8.22980e47 | + | 8.22980e47i | 1.01465 | + | 1.01465i | ||||
\(988\) | 2.95403e47 | − | 2.95403e47i | 0.358346 | − | 0.358346i | ||||
\(989\) | 1.05422e48i | 1.25832i | ||||||||
\(990\) | −3.56260e47 | − | 1.32520e48i | −0.418412 | − | 1.55639i | ||||
\(991\) | 7.10636e47 | 0.821237 | 0.410619 | − | 0.911807i | \(-0.365313\pi\) | ||||
0.410619 | + | 0.911807i | \(0.365313\pi\) | |||||||
\(992\) | −1.77431e47 | − | 1.77431e47i | −0.201764 | − | 0.201764i | ||||
\(993\) | −1.54762e48 | + | 1.54762e48i | −1.73172 | + | 1.73172i | ||||
\(994\) | 3.19015e47i | 0.351261i | ||||||||
\(995\) | 8.60950e47 | + | 4.96122e47i | 0.932843 | + | 0.537550i | ||||
\(996\) | −3.05532e47 | −0.325767 | ||||||||
\(997\) | 3.03618e47 | + | 3.03618e47i | 0.318570 | + | 0.318570i | 0.848218 | − | 0.529648i | \(-0.177676\pi\) |
−0.529648 | + | 0.848218i | \(0.677676\pi\) | |||||||
\(998\) | −3.87176e46 | + | 3.87176e46i | −0.0399778 | + | 0.0399778i | ||||
\(999\) | 2.77569e47i | 0.282048i |
(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 | 5.33.c.a.2.5 | ✓ | 30 | |
5.2 | odd | 4 | 25.33.c.b.18.11 | 30 | |||
5.3 | odd | 4 | inner | 5.33.c.a.3.5 | yes | 30 | |
5.4 | even | 2 | 25.33.c.b.7.11 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.33.c.a.2.5 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5.33.c.a.3.5 | yes | 30 | 5.3 | odd | 4 | inner | |
25.33.c.b.7.11 | 30 | 5.4 | even | 2 | |||
25.33.c.b.18.11 | 30 | 5.2 | odd | 4 |