Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [87,2,Mod(17,87)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(87, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("87.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 87 = 3 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 87.f (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: | \(0.694698497585\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 41.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 87.41 |
Dual form | 87.2.f.a.17.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/87\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(59\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | + | 1.36603i | −0.965926 | + | 0.965926i | −0.999438 | − | 0.0335125i | \(-0.989331\pi\) |
0.0335125 | + | 0.999438i | \(0.489331\pi\) | |||||||
\(3\) | 0.866025 | + | 1.50000i | 0.500000 | + | 0.866025i | ||||
\(4\) | − | 1.73205i | − | 0.866025i | ||||||
\(5\) | 3.73205 | 1.66902 | 0.834512 | − | 0.550990i | \(-0.185750\pi\) | ||||
0.834512 | + | 0.550990i | \(0.185750\pi\) | |||||||
\(6\) | −3.23205 | − | 0.866025i | −1.31948 | − | 0.353553i | ||||
\(7\) | −2.73205 | −1.03262 | −0.516309 | − | 0.856402i | \(-0.672694\pi\) | ||||
−0.516309 | + | 0.856402i | \(0.672694\pi\) | |||||||
\(8\) | −0.366025 | − | 0.366025i | −0.129410 | − | 0.129410i | ||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | −5.09808 | + | 5.09808i | −1.61215 | + | 1.61215i | ||||
\(11\) | −0.366025 | + | 0.366025i | −0.110361 | + | 0.110361i | −0.760131 | − | 0.649770i | \(-0.774865\pi\) |
0.649770 | + | 0.760131i | \(0.274865\pi\) | |||||||
\(12\) | 2.59808 | − | 1.50000i | 0.750000 | − | 0.433013i | ||||
\(13\) | − | 5.73205i | − | 1.58978i | −0.606750 | − | 0.794892i | \(-0.707527\pi\) | ||
0.606750 | − | 0.794892i | \(-0.292473\pi\) | |||||||
\(14\) | 3.73205 | − | 3.73205i | 0.997433 | − | 0.997433i | ||||
\(15\) | 3.23205 | + | 5.59808i | 0.834512 | + | 1.44542i | ||||
\(16\) | 4.46410 | 1.11603 | ||||||||
\(17\) | −0.732051 | + | 0.732051i | −0.177548 | + | 0.177548i | −0.790286 | − | 0.612738i | \(-0.790068\pi\) |
0.612738 | + | 0.790286i | \(0.290068\pi\) | |||||||
\(18\) | −1.50000 | − | 5.59808i | −0.353553 | − | 1.31948i | ||||
\(19\) | 1.73205 | + | 1.73205i | 0.397360 | + | 0.397360i | 0.877301 | − | 0.479941i | \(-0.159342\pi\) |
−0.479941 | + | 0.877301i | \(0.659342\pi\) | |||||||
\(20\) | − | 6.46410i | − | 1.44542i | ||||||
\(21\) | −2.36603 | − | 4.09808i | −0.516309 | − | 0.894274i | ||||
\(22\) | − | 1.00000i | − | 0.213201i | ||||||
\(23\) | − | 1.46410i | − | 0.305286i | −0.988281 | − | 0.152643i | \(-0.951221\pi\) | ||
0.988281 | − | 0.152643i | \(-0.0487785\pi\) | |||||||
\(24\) | 0.232051 | − | 0.866025i | 0.0473672 | − | 0.176777i | ||||
\(25\) | 8.92820 | 1.78564 | ||||||||
\(26\) | 7.83013 | + | 7.83013i | 1.53561 | + | 1.53561i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 4.73205i | 0.894274i | ||||||||
\(29\) | 2.00000 | − | 5.00000i | 0.371391 | − | 0.928477i | ||||
\(30\) | −12.0622 | − | 3.23205i | −2.20224 | − | 0.590089i | ||||
\(31\) | 0.633975 | + | 0.633975i | 0.113865 | + | 0.113865i | 0.761744 | − | 0.647878i | \(-0.224344\pi\) |
−0.647878 | + | 0.761744i | \(0.724344\pi\) | |||||||
\(32\) | −5.36603 | + | 5.36603i | −0.948588 | + | 0.948588i | ||||
\(33\) | −0.866025 | − | 0.232051i | −0.150756 | − | 0.0403949i | ||||
\(34\) | − | 2.00000i | − | 0.342997i | ||||||
\(35\) | −10.1962 | −1.72346 | ||||||||
\(36\) | 4.50000 | + | 2.59808i | 0.750000 | + | 0.433013i | ||||
\(37\) | −3.46410 | + | 3.46410i | −0.569495 | + | 0.569495i | −0.931987 | − | 0.362492i | \(-0.881926\pi\) |
0.362492 | + | 0.931987i | \(0.381926\pi\) | |||||||
\(38\) | −4.73205 | −0.767640 | ||||||||
\(39\) | 8.59808 | − | 4.96410i | 1.37679 | − | 0.794892i | ||||
\(40\) | −1.36603 | − | 1.36603i | −0.215988 | − | 0.215988i | ||||
\(41\) | 5.19615 | + | 5.19615i | 0.811503 | + | 0.811503i | 0.984859 | − | 0.173356i | \(-0.0554613\pi\) |
−0.173356 | + | 0.984859i | \(0.555461\pi\) | |||||||
\(42\) | 8.83013 | + | 2.36603i | 1.36252 | + | 0.365086i | ||||
\(43\) | −3.56218 | − | 3.56218i | −0.543227 | − | 0.543227i | 0.381246 | − | 0.924473i | \(-0.375495\pi\) |
−0.924473 | + | 0.381246i | \(0.875495\pi\) | |||||||
\(44\) | 0.633975 | + | 0.633975i | 0.0955753 | + | 0.0955753i | ||||
\(45\) | −5.59808 | + | 9.69615i | −0.834512 | + | 1.44542i | ||||
\(46\) | 2.00000 | + | 2.00000i | 0.294884 | + | 0.294884i | ||||
\(47\) | 0.830127 | + | 0.830127i | 0.121086 | + | 0.121086i | 0.765053 | − | 0.643967i | \(-0.222713\pi\) |
−0.643967 | + | 0.765053i | \(0.722713\pi\) | |||||||
\(48\) | 3.86603 | + | 6.69615i | 0.558013 | + | 0.966506i | ||||
\(49\) | 0.464102 | 0.0663002 | ||||||||
\(50\) | −12.1962 | + | 12.1962i | −1.72480 | + | 1.72480i | ||||
\(51\) | −1.73205 | − | 0.464102i | −0.242536 | − | 0.0649872i | ||||
\(52\) | −9.92820 | −1.37679 | ||||||||
\(53\) | − | 3.92820i | − | 0.539580i | −0.962919 | − | 0.269790i | \(-0.913046\pi\) | ||
0.962919 | − | 0.269790i | \(-0.0869543\pi\) | |||||||
\(54\) | 7.09808 | − | 7.09808i | 0.965926 | − | 0.965926i | ||||
\(55\) | −1.36603 | + | 1.36603i | −0.184195 | + | 0.184195i | ||||
\(56\) | 1.00000 | + | 1.00000i | 0.133631 | + | 0.133631i | ||||
\(57\) | −1.09808 | + | 4.09808i | −0.145444 | + | 0.542803i | ||||
\(58\) | 4.09808 | + | 9.56218i | 0.538104 | + | 1.25558i | ||||
\(59\) | 0.535898i | 0.0697680i | 0.999391 | + | 0.0348840i | \(0.0111062\pi\) | ||||
−0.999391 | + | 0.0348840i | \(0.988894\pi\) | |||||||
\(60\) | 9.69615 | − | 5.59808i | 1.25177 | − | 0.722709i | ||||
\(61\) | −2.00000 | − | 2.00000i | −0.256074 | − | 0.256074i | 0.567381 | − | 0.823455i | \(-0.307957\pi\) |
−0.823455 | + | 0.567381i | \(0.807957\pi\) | |||||||
\(62\) | −1.73205 | −0.219971 | ||||||||
\(63\) | 4.09808 | − | 7.09808i | 0.516309 | − | 0.894274i | ||||
\(64\) | − | 5.73205i | − | 0.716506i | ||||||
\(65\) | − | 21.3923i | − | 2.65339i | ||||||
\(66\) | 1.50000 | − | 0.866025i | 0.184637 | − | 0.106600i | ||||
\(67\) | − | 8.92820i | − | 1.09075i | −0.838191 | − | 0.545377i | \(-0.816387\pi\) | ||
0.838191 | − | 0.545377i | \(-0.183613\pi\) | |||||||
\(68\) | 1.26795 | + | 1.26795i | 0.153761 | + | 0.153761i | ||||
\(69\) | 2.19615 | − | 1.26795i | 0.264386 | − | 0.152643i | ||||
\(70\) | 13.9282 | − | 13.9282i | 1.66474 | − | 1.66474i | ||||
\(71\) | −16.7321 | −1.98573 | −0.992865 | − | 0.119248i | \(-0.961952\pi\) | ||||
−0.992865 | + | 0.119248i | \(0.961952\pi\) | |||||||
\(72\) | 1.50000 | − | 0.401924i | 0.176777 | − | 0.0473672i | ||||
\(73\) | −4.00000 | + | 4.00000i | −0.468165 | + | 0.468165i | −0.901319 | − | 0.433155i | \(-0.857400\pi\) |
0.433155 | + | 0.901319i | \(0.357400\pi\) | |||||||
\(74\) | − | 9.46410i | − | 1.10018i | ||||||
\(75\) | 7.73205 | + | 13.3923i | 0.892820 | + | 1.54641i | ||||
\(76\) | 3.00000 | − | 3.00000i | 0.344124 | − | 0.344124i | ||||
\(77\) | 1.00000 | − | 1.00000i | 0.113961 | − | 0.113961i | ||||
\(78\) | −4.96410 | + | 18.5263i | −0.562074 | + | 2.09769i | ||||
\(79\) | 1.83013 | + | 1.83013i | 0.205905 | + | 0.205905i | 0.802525 | − | 0.596619i | \(-0.203490\pi\) |
−0.596619 | + | 0.802525i | \(0.703490\pi\) | |||||||
\(80\) | 16.6603 | 1.86267 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −14.1962 | −1.56770 | ||||||||
\(83\) | 13.8564i | 1.52094i | 0.649374 | + | 0.760469i | \(0.275031\pi\) | ||||
−0.649374 | + | 0.760469i | \(0.724969\pi\) | |||||||
\(84\) | −7.09808 | + | 4.09808i | −0.774464 | + | 0.447137i | ||||
\(85\) | −2.73205 | + | 2.73205i | −0.296333 | + | 0.296333i | ||||
\(86\) | 9.73205 | 1.04943 | ||||||||
\(87\) | 9.23205 | − | 1.33013i | 0.989780 | − | 0.142605i | ||||
\(88\) | 0.267949 | 0.0285635 | ||||||||
\(89\) | 5.00000 | − | 5.00000i | 0.529999 | − | 0.529999i | −0.390573 | − | 0.920572i | \(-0.627723\pi\) |
0.920572 | + | 0.390573i | \(0.127723\pi\) | |||||||
\(90\) | −5.59808 | − | 20.8923i | −0.590089 | − | 2.20224i | ||||
\(91\) | 15.6603i | 1.64164i | ||||||||
\(92\) | −2.53590 | −0.264386 | ||||||||
\(93\) | −0.401924 | + | 1.50000i | −0.0416776 | + | 0.155543i | ||||
\(94\) | −2.26795 | −0.233921 | ||||||||
\(95\) | 6.46410 | + | 6.46410i | 0.663203 | + | 0.663203i | ||||
\(96\) | −12.6962 | − | 3.40192i | −1.29580 | − | 0.347207i | ||||
\(97\) | −7.73205 | + | 7.73205i | −0.785071 | + | 0.785071i | −0.980682 | − | 0.195611i | \(-0.937331\pi\) |
0.195611 | + | 0.980682i | \(0.437331\pi\) | |||||||
\(98\) | −0.633975 | + | 0.633975i | −0.0640411 | + | 0.0640411i | ||||
\(99\) | −0.401924 | − | 1.50000i | −0.0403949 | − | 0.150756i | ||||
\(100\) | − | 15.4641i | − | 1.54641i | ||||||
\(101\) | −4.19615 | + | 4.19615i | −0.417533 | + | 0.417533i | −0.884352 | − | 0.466820i | \(-0.845400\pi\) |
0.466820 | + | 0.884352i | \(0.345400\pi\) | |||||||
\(102\) | 3.00000 | − | 1.73205i | 0.297044 | − | 0.171499i | ||||
\(103\) | 10.7321 | 1.05746 | 0.528730 | − | 0.848790i | \(-0.322668\pi\) | ||||
0.528730 | + | 0.848790i | \(0.322668\pi\) | |||||||
\(104\) | −2.09808 | + | 2.09808i | −0.205733 | + | 0.205733i | ||||
\(105\) | −8.83013 | − | 15.2942i | −0.861732 | − | 1.49256i | ||||
\(106\) | 5.36603 | + | 5.36603i | 0.521194 | + | 0.521194i | ||||
\(107\) | 5.26795i | 0.509272i | 0.967037 | + | 0.254636i | \(0.0819556\pi\) | ||||
−0.967037 | + | 0.254636i | \(0.918044\pi\) | |||||||
\(108\) | 9.00000i | 0.866025i | ||||||||
\(109\) | − | 7.00000i | − | 0.670478i | −0.942133 | − | 0.335239i | \(-0.891183\pi\) | ||
0.942133 | − | 0.335239i | \(-0.108817\pi\) | |||||||
\(110\) | − | 3.73205i | − | 0.355837i | ||||||
\(111\) | −8.19615 | − | 2.19615i | −0.777944 | − | 0.208450i | ||||
\(112\) | −12.1962 | −1.15243 | ||||||||
\(113\) | −5.92820 | − | 5.92820i | −0.557678 | − | 0.557678i | 0.370967 | − | 0.928646i | \(-0.379026\pi\) |
−0.928646 | + | 0.370967i | \(0.879026\pi\) | |||||||
\(114\) | −4.09808 | − | 7.09808i | −0.383820 | − | 0.664796i | ||||
\(115\) | − | 5.46410i | − | 0.509530i | ||||||
\(116\) | −8.66025 | − | 3.46410i | −0.804084 | − | 0.321634i | ||||
\(117\) | 14.8923 | + | 8.59808i | 1.37679 | + | 0.794892i | ||||
\(118\) | −0.732051 | − | 0.732051i | −0.0673907 | − | 0.0673907i | ||||
\(119\) | 2.00000 | − | 2.00000i | 0.183340 | − | 0.183340i | ||||
\(120\) | 0.866025 | − | 3.23205i | 0.0790569 | − | 0.295045i | ||||
\(121\) | 10.7321i | 0.975641i | ||||||||
\(122\) | 5.46410 | 0.494697 | ||||||||
\(123\) | −3.29423 | + | 12.2942i | −0.297031 | + | 1.10853i | ||||
\(124\) | 1.09808 | − | 1.09808i | 0.0986102 | − | 0.0986102i | ||||
\(125\) | 14.6603 | 1.31125 | ||||||||
\(126\) | 4.09808 | + | 15.2942i | 0.365086 | + | 1.36252i | ||||
\(127\) | 9.00000 | + | 9.00000i | 0.798621 | + | 0.798621i | 0.982878 | − | 0.184257i | \(-0.0589879\pi\) |
−0.184257 | + | 0.982878i | \(0.558988\pi\) | |||||||
\(128\) | −2.90192 | − | 2.90192i | −0.256496 | − | 0.256496i | ||||
\(129\) | 2.25833 | − | 8.42820i | 0.198835 | − | 0.742062i | ||||
\(130\) | 29.2224 | + | 29.2224i | 2.56298 | + | 2.56298i | ||||
\(131\) | −11.3923 | − | 11.3923i | −0.995350 | − | 0.995350i | 0.00463894 | − | 0.999989i | \(-0.498523\pi\) |
−0.999989 | + | 0.00463894i | \(0.998523\pi\) | |||||||
\(132\) | −0.401924 | + | 1.50000i | −0.0349830 | + | 0.130558i | ||||
\(133\) | −4.73205 | − | 4.73205i | −0.410321 | − | 0.410321i | ||||
\(134\) | 12.1962 | + | 12.1962i | 1.05359 | + | 1.05359i | ||||
\(135\) | −19.3923 | −1.66902 | ||||||||
\(136\) | 0.535898 | 0.0459529 | ||||||||
\(137\) | −4.73205 | + | 4.73205i | −0.404286 | + | 0.404286i | −0.879741 | − | 0.475454i | \(-0.842284\pi\) |
0.475454 | + | 0.879741i | \(0.342284\pi\) | |||||||
\(138\) | −1.26795 | + | 4.73205i | −0.107935 | + | 0.402819i | ||||
\(139\) | −11.4641 | −0.972372 | −0.486186 | − | 0.873855i | \(-0.661612\pi\) | ||||
−0.486186 | + | 0.873855i | \(0.661612\pi\) | |||||||
\(140\) | 17.6603i | 1.49256i | ||||||||
\(141\) | −0.526279 | + | 1.96410i | −0.0443207 | + | 0.165407i | ||||
\(142\) | 22.8564 | − | 22.8564i | 1.91807 | − | 1.91807i | ||||
\(143\) | 2.09808 | + | 2.09808i | 0.175450 | + | 0.175450i | ||||
\(144\) | −6.69615 | + | 11.5981i | −0.558013 | + | 0.966506i | ||||
\(145\) | 7.46410 | − | 18.6603i | 0.619860 | − | 1.54965i | ||||
\(146\) | − | 10.9282i | − | 0.904425i | ||||||
\(147\) | 0.401924 | + | 0.696152i | 0.0331501 | + | 0.0574177i | ||||
\(148\) | 6.00000 | + | 6.00000i | 0.493197 | + | 0.493197i | ||||
\(149\) | 11.5359 | 0.945058 | 0.472529 | − | 0.881315i | \(-0.343341\pi\) | ||||
0.472529 | + | 0.881315i | \(0.343341\pi\) | |||||||
\(150\) | −28.8564 | − | 7.73205i | −2.35612 | − | 0.631319i | ||||
\(151\) | 5.66025i | 0.460625i | 0.973117 | + | 0.230312i | \(0.0739748\pi\) | ||||
−0.973117 | + | 0.230312i | \(0.926025\pi\) | |||||||
\(152\) | − | 1.26795i | − | 0.102844i | ||||||
\(153\) | −0.803848 | − | 3.00000i | −0.0649872 | − | 0.242536i | ||||
\(154\) | 2.73205i | 0.220155i | ||||||||
\(155\) | 2.36603 | + | 2.36603i | 0.190044 | + | 0.190044i | ||||
\(156\) | −8.59808 | − | 14.8923i | −0.688397 | − | 1.19234i | ||||
\(157\) | 5.53590 | − | 5.53590i | 0.441813 | − | 0.441813i | −0.450808 | − | 0.892621i | \(-0.648864\pi\) |
0.892621 | + | 0.450808i | \(0.148864\pi\) | |||||||
\(158\) | −5.00000 | −0.397779 | ||||||||
\(159\) | 5.89230 | − | 3.40192i | 0.467290 | − | 0.269790i | ||||
\(160\) | −20.0263 | + | 20.0263i | −1.58322 | + | 1.58322i | ||||
\(161\) | 4.00000i | 0.315244i | ||||||||
\(162\) | 16.7942 | + | 4.50000i | 1.31948 | + | 0.353553i | ||||
\(163\) | 9.09808 | − | 9.09808i | 0.712616 | − | 0.712616i | −0.254466 | − | 0.967082i | \(-0.581900\pi\) |
0.967082 | + | 0.254466i | \(0.0818995\pi\) | |||||||
\(164\) | 9.00000 | − | 9.00000i | 0.702782 | − | 0.702782i | ||||
\(165\) | −3.23205 | − | 0.866025i | −0.251615 | − | 0.0674200i | ||||
\(166\) | −18.9282 | − | 18.9282i | −1.46911 | − | 1.46911i | ||||
\(167\) | −3.26795 | −0.252882 | −0.126441 | − | 0.991974i | \(-0.540355\pi\) | ||||
−0.126441 | + | 0.991974i | \(0.540355\pi\) | |||||||
\(168\) | −0.633975 | + | 2.36603i | −0.0489122 | + | 0.182543i | ||||
\(169\) | −19.8564 | −1.52742 | ||||||||
\(170\) | − | 7.46410i | − | 0.572470i | ||||||
\(171\) | −7.09808 | + | 1.90192i | −0.542803 | + | 0.145444i | ||||
\(172\) | −6.16987 | + | 6.16987i | −0.470448 | + | 0.470448i | ||||
\(173\) | 13.4641 | 1.02366 | 0.511828 | − | 0.859088i | \(-0.328968\pi\) | ||||
0.511828 | + | 0.859088i | \(0.328968\pi\) | |||||||
\(174\) | −10.7942 | + | 14.4282i | −0.818308 | + | 1.09380i | ||||
\(175\) | −24.3923 | −1.84388 | ||||||||
\(176\) | −1.63397 | + | 1.63397i | −0.123165 | + | 0.123165i | ||||
\(177\) | −0.803848 | + | 0.464102i | −0.0604209 | + | 0.0348840i | ||||
\(178\) | 13.6603i | 1.02388i | ||||||||
\(179\) | 16.5885 | 1.23988 | 0.619940 | − | 0.784649i | \(-0.287157\pi\) | ||||
0.619940 | + | 0.784649i | \(0.287157\pi\) | |||||||
\(180\) | 16.7942 | + | 9.69615i | 1.25177 | + | 0.722709i | ||||
\(181\) | 16.3205 | 1.21309 | 0.606547 | − | 0.795048i | \(-0.292554\pi\) | ||||
0.606547 | + | 0.795048i | \(0.292554\pi\) | |||||||
\(182\) | −21.3923 | − | 21.3923i | −1.58570 | − | 1.58570i | ||||
\(183\) | 1.26795 | − | 4.73205i | 0.0937295 | − | 0.349803i | ||||
\(184\) | −0.535898 | + | 0.535898i | −0.0395070 | + | 0.0395070i | ||||
\(185\) | −12.9282 | + | 12.9282i | −0.950500 | + | 0.950500i | ||||
\(186\) | −1.50000 | − | 2.59808i | −0.109985 | − | 0.190500i | ||||
\(187\) | − | 0.535898i | − | 0.0391888i | ||||||
\(188\) | 1.43782 | − | 1.43782i | 0.104864 | − | 0.104864i | ||||
\(189\) | 14.1962 | 1.03262 | ||||||||
\(190\) | −17.6603 | −1.28121 | ||||||||
\(191\) | 15.9282 | − | 15.9282i | 1.15252 | − | 1.15252i | 0.166479 | − | 0.986045i | \(-0.446760\pi\) |
0.986045 | − | 0.166479i | \(-0.0532399\pi\) | |||||||
\(192\) | 8.59808 | − | 4.96410i | 0.620513 | − | 0.358253i | ||||
\(193\) | −9.92820 | − | 9.92820i | −0.714648 | − | 0.714648i | 0.252856 | − | 0.967504i | \(-0.418630\pi\) |
−0.967504 | + | 0.252856i | \(0.918630\pi\) | |||||||
\(194\) | − | 21.1244i | − | 1.51664i | ||||||
\(195\) | 32.0885 | − | 18.5263i | 2.29790 | − | 1.32669i | ||||
\(196\) | − | 0.803848i | − | 0.0574177i | ||||||
\(197\) | 24.9282i | 1.77606i | 0.459785 | + | 0.888030i | \(0.347927\pi\) | ||||
−0.459785 | + | 0.888030i | \(0.652073\pi\) | |||||||
\(198\) | 2.59808 | + | 1.50000i | 0.184637 | + | 0.106600i | ||||
\(199\) | 2.73205 | 0.193670 | 0.0968350 | − | 0.995300i | \(-0.469128\pi\) | ||||
0.0968350 | + | 0.995300i | \(0.469128\pi\) | |||||||
\(200\) | −3.26795 | − | 3.26795i | −0.231079 | − | 0.231079i | ||||
\(201\) | 13.3923 | − | 7.73205i | 0.944620 | − | 0.545377i | ||||
\(202\) | − | 11.4641i | − | 0.806611i | ||||||
\(203\) | −5.46410 | + | 13.6603i | −0.383505 | + | 0.958762i | ||||
\(204\) | −0.803848 | + | 3.00000i | −0.0562806 | + | 0.210042i | ||||
\(205\) | 19.3923 | + | 19.3923i | 1.35442 | + | 1.35442i | ||||
\(206\) | −14.6603 | + | 14.6603i | −1.02143 | + | 1.02143i | ||||
\(207\) | 3.80385 | + | 2.19615i | 0.264386 | + | 0.152643i | ||||
\(208\) | − | 25.5885i | − | 1.77424i | ||||||
\(209\) | −1.26795 | −0.0877059 | ||||||||
\(210\) | 32.9545 | + | 8.83013i | 2.27408 | + | 0.609337i | ||||
\(211\) | 14.0263 | − | 14.0263i | 0.965609 | − | 0.965609i | −0.0338191 | − | 0.999428i | \(-0.510767\pi\) |
0.999428 | + | 0.0338191i | \(0.0107670\pi\) | |||||||
\(212\) | −6.80385 | −0.467290 | ||||||||
\(213\) | −14.4904 | − | 25.0981i | −0.992865 | − | 1.71969i | ||||
\(214\) | −7.19615 | − | 7.19615i | −0.491919 | − | 0.491919i | ||||
\(215\) | −13.2942 | − | 13.2942i | −0.906659 | − | 0.906659i | ||||
\(216\) | 1.90192 | + | 1.90192i | 0.129410 | + | 0.129410i | ||||
\(217\) | −1.73205 | − | 1.73205i | −0.117579 | − | 0.117579i | ||||
\(218\) | 9.56218 | + | 9.56218i | 0.647632 | + | 0.647632i | ||||
\(219\) | −9.46410 | − | 2.53590i | −0.639525 | − | 0.171360i | ||||
\(220\) | 2.36603 | + | 2.36603i | 0.159517 | + | 0.159517i | ||||
\(221\) | 4.19615 | + | 4.19615i | 0.282264 | + | 0.282264i | ||||
\(222\) | 14.1962 | − | 8.19615i | 0.952783 | − | 0.550090i | ||||
\(223\) | 0.732051 | 0.0490217 | 0.0245109 | − | 0.999700i | \(-0.492197\pi\) | ||||
0.0245109 | + | 0.999700i | \(0.492197\pi\) | |||||||
\(224\) | 14.6603 | − | 14.6603i | 0.979529 | − | 0.979529i | ||||
\(225\) | −13.3923 | + | 23.1962i | −0.892820 | + | 1.54641i | ||||
\(226\) | 16.1962 | 1.07735 | ||||||||
\(227\) | − | 9.12436i | − | 0.605605i | −0.953053 | − | 0.302802i | \(-0.902078\pi\) | ||
0.953053 | − | 0.302802i | \(-0.0979222\pi\) | |||||||
\(228\) | 7.09808 | + | 1.90192i | 0.470082 | + | 0.125958i | ||||
\(229\) | −20.3205 | + | 20.3205i | −1.34282 | + | 1.34282i | −0.449574 | + | 0.893243i | \(0.648424\pi\) |
−0.893243 | + | 0.449574i | \(0.851576\pi\) | |||||||
\(230\) | 7.46410 | + | 7.46410i | 0.492168 | + | 0.492168i | ||||
\(231\) | 2.36603 | + | 0.633975i | 0.155673 | + | 0.0417125i | ||||
\(232\) | −2.56218 | + | 1.09808i | −0.168215 | + | 0.0720922i | ||||
\(233\) | 20.1244i | 1.31839i | 0.751972 | + | 0.659195i | \(0.229103\pi\) | ||||
−0.751972 | + | 0.659195i | \(0.770897\pi\) | |||||||
\(234\) | −32.0885 | + | 8.59808i | −2.09769 | + | 0.562074i | ||||
\(235\) | 3.09808 | + | 3.09808i | 0.202096 | + | 0.202096i | ||||
\(236\) | 0.928203 | 0.0604209 | ||||||||
\(237\) | −1.16025 | + | 4.33013i | −0.0753666 | + | 0.281272i | ||||
\(238\) | 5.46410i | 0.354185i | ||||||||
\(239\) | 6.00000i | 0.388108i | 0.980991 | + | 0.194054i | \(0.0621637\pi\) | ||||
−0.980991 | + | 0.194054i | \(0.937836\pi\) | |||||||
\(240\) | 14.4282 | + | 24.9904i | 0.931337 | + | 1.61312i | ||||
\(241\) | 13.5359i | 0.871924i | 0.899965 | + | 0.435962i | \(0.143592\pi\) | ||||
−0.899965 | + | 0.435962i | \(0.856408\pi\) | |||||||
\(242\) | −14.6603 | − | 14.6603i | −0.942397 | − | 0.942397i | ||||
\(243\) | 7.79423 | − | 13.5000i | 0.500000 | − | 0.866025i | ||||
\(244\) | −3.46410 | + | 3.46410i | −0.221766 | + | 0.221766i | ||||
\(245\) | 1.73205 | 0.110657 | ||||||||
\(246\) | −12.2942 | − | 21.2942i | −0.783851 | − | 1.35767i | ||||
\(247\) | 9.92820 | − | 9.92820i | 0.631716 | − | 0.631716i | ||||
\(248\) | − | 0.464102i | − | 0.0294705i | ||||||
\(249\) | −20.7846 | + | 12.0000i | −1.31717 | + | 0.760469i | ||||
\(250\) | −20.0263 | + | 20.0263i | −1.26657 | + | 1.26657i | ||||
\(251\) | −10.6340 | + | 10.6340i | −0.671211 | + | 0.671211i | −0.957995 | − | 0.286785i | \(-0.907414\pi\) |
0.286785 | + | 0.957995i | \(0.407414\pi\) | |||||||
\(252\) | −12.2942 | − | 7.09808i | −0.774464 | − | 0.447137i | ||||
\(253\) | 0.535898 | + | 0.535898i | 0.0336916 | + | 0.0336916i | ||||
\(254\) | −24.5885 | −1.54282 | ||||||||
\(255\) | −6.46410 | − | 1.73205i | −0.404798 | − | 0.108465i | ||||
\(256\) | 19.3923 | 1.21202 | ||||||||
\(257\) | − | 9.92820i | − | 0.619304i | −0.950850 | − | 0.309652i | \(-0.899787\pi\) | ||
0.950850 | − | 0.309652i | \(-0.100213\pi\) | |||||||
\(258\) | 8.42820 | + | 14.5981i | 0.524717 | + | 0.908837i | ||||
\(259\) | 9.46410 | − | 9.46410i | 0.588071 | − | 0.588071i | ||||
\(260\) | −37.0526 | −2.29790 | ||||||||
\(261\) | 9.99038 | + | 12.6962i | 0.618389 | + | 0.785872i | ||||
\(262\) | 31.1244 | 1.92287 | ||||||||
\(263\) | −15.2942 | + | 15.2942i | −0.943083 | + | 0.943083i | −0.998465 | − | 0.0553827i | \(-0.982362\pi\) |
0.0553827 | + | 0.998465i | \(0.482362\pi\) | |||||||
\(264\) | 0.232051 | + | 0.401924i | 0.0142817 | + | 0.0247367i | ||||
\(265\) | − | 14.6603i | − | 0.900572i | ||||||
\(266\) | 12.9282 | 0.792679 | ||||||||
\(267\) | 11.8301 | + | 3.16987i | 0.723992 | + | 0.193993i | ||||
\(268\) | −15.4641 | −0.944620 | ||||||||
\(269\) | −2.00000 | − | 2.00000i | −0.121942 | − | 0.121942i | 0.643502 | − | 0.765444i | \(-0.277481\pi\) |
−0.765444 | + | 0.643502i | \(0.777481\pi\) | |||||||
\(270\) | 26.4904 | − | 26.4904i | 1.61215 | − | 1.61215i | ||||
\(271\) | −7.16987 | + | 7.16987i | −0.435539 | + | 0.435539i | −0.890507 | − | 0.454969i | \(-0.849650\pi\) |
0.454969 | + | 0.890507i | \(0.349650\pi\) | |||||||
\(272\) | −3.26795 | + | 3.26795i | −0.198149 | + | 0.198149i | ||||
\(273\) | −23.4904 | + | 13.5622i | −1.42170 | + | 0.820820i | ||||
\(274\) | − | 12.9282i | − | 0.781021i | ||||||
\(275\) | −3.26795 | + | 3.26795i | −0.197065 | + | 0.197065i | ||||
\(276\) | −2.19615 | − | 3.80385i | −0.132193 | − | 0.228965i | ||||
\(277\) | 5.60770 | 0.336934 | 0.168467 | − | 0.985707i | \(-0.446118\pi\) | ||||
0.168467 | + | 0.985707i | \(0.446118\pi\) | |||||||
\(278\) | 15.6603 | − | 15.6603i | 0.939240 | − | 0.939240i | ||||
\(279\) | −2.59808 | + | 0.696152i | −0.155543 | + | 0.0416776i | ||||
\(280\) | 3.73205 | + | 3.73205i | 0.223033 | + | 0.223033i | ||||
\(281\) | 1.73205i | 0.103325i | 0.998665 | + | 0.0516627i | \(0.0164521\pi\) | ||||
−0.998665 | + | 0.0516627i | \(0.983548\pi\) | |||||||
\(282\) | −1.96410 | − | 3.40192i | −0.116961 | − | 0.202582i | ||||
\(283\) | − | 6.00000i | − | 0.356663i | −0.983970 | − | 0.178331i | \(-0.942930\pi\) | ||
0.983970 | − | 0.178331i | \(-0.0570699\pi\) | |||||||
\(284\) | 28.9808i | 1.71969i | ||||||||
\(285\) | −4.09808 | + | 15.2942i | −0.242749 | + | 0.905952i | ||||
\(286\) | −5.73205 | −0.338943 | ||||||||
\(287\) | −14.1962 | − | 14.1962i | −0.837972 | − | 0.837972i | ||||
\(288\) | −5.89230 | − | 21.9904i | −0.347207 | − | 1.29580i | ||||
\(289\) | 15.9282i | 0.936953i | ||||||||
\(290\) | 15.2942 | + | 35.6865i | 0.898108 | + | 2.09559i | ||||
\(291\) | −18.2942 | − | 4.90192i | −1.07243 | − | 0.287356i | ||||
\(292\) | 6.92820 | + | 6.92820i | 0.405442 | + | 0.405442i | ||||
\(293\) | 16.1244 | − | 16.1244i | 0.941995 | − | 0.941995i | −0.0564126 | − | 0.998408i | \(-0.517966\pi\) |
0.998408 | + | 0.0564126i | \(0.0179662\pi\) | |||||||
\(294\) | −1.50000 | − | 0.401924i | −0.0874818 | − | 0.0234407i | ||||
\(295\) | 2.00000i | 0.116445i | ||||||||
\(296\) | 2.53590 | 0.147396 | ||||||||
\(297\) | 1.90192 | − | 1.90192i | 0.110361 | − | 0.110361i | ||||
\(298\) | −15.7583 | + | 15.7583i | −0.912856 | + | 0.912856i | ||||
\(299\) | −8.39230 | −0.485340 | ||||||||
\(300\) | 23.1962 | − | 13.3923i | 1.33923 | − | 0.773205i | ||||
\(301\) | 9.73205 | + | 9.73205i | 0.560946 | + | 0.560946i | ||||
\(302\) | −7.73205 | − | 7.73205i | −0.444930 | − | 0.444930i | ||||
\(303\) | −9.92820 | − | 2.66025i | −0.570360 | − | 0.152828i | ||||
\(304\) | 7.73205 | + | 7.73205i | 0.443464 | + | 0.443464i | ||||
\(305\) | −7.46410 | − | 7.46410i | −0.427393 | − | 0.427393i | ||||
\(306\) | 5.19615 | + | 3.00000i | 0.297044 | + | 0.171499i | ||||
\(307\) | 2.49038 | + | 2.49038i | 0.142134 | + | 0.142134i | 0.774593 | − | 0.632460i | \(-0.217955\pi\) |
−0.632460 | + | 0.774593i | \(0.717955\pi\) | |||||||
\(308\) | −1.73205 | − | 1.73205i | −0.0986928 | − | 0.0986928i | ||||
\(309\) | 9.29423 | + | 16.0981i | 0.528730 | + | 0.915788i | ||||
\(310\) | −6.46410 | −0.367136 | ||||||||
\(311\) | 16.4641 | − | 16.4641i | 0.933594 | − | 0.933594i | −0.0643348 | − | 0.997928i | \(-0.520493\pi\) |
0.997928 | + | 0.0643348i | \(0.0204926\pi\) | |||||||
\(312\) | −4.96410 | − | 1.33013i | −0.281037 | − | 0.0753036i | ||||
\(313\) | 7.58846 | 0.428925 | 0.214462 | − | 0.976732i | \(-0.431200\pi\) | ||||
0.214462 | + | 0.976732i | \(0.431200\pi\) | |||||||
\(314\) | 15.1244i | 0.853517i | ||||||||
\(315\) | 15.2942 | − | 26.4904i | 0.861732 | − | 1.49256i | ||||
\(316\) | 3.16987 | − | 3.16987i | 0.178319 | − | 0.178319i | ||||
\(317\) | 18.3923 | + | 18.3923i | 1.03301 | + | 1.03301i | 0.999436 | + | 0.0335787i | \(0.0106904\pi\) |
0.0335787 | + | 0.999436i | \(0.489310\pi\) | |||||||
\(318\) | −3.40192 | + | 12.6962i | −0.190770 | + | 0.711965i | ||||
\(319\) | 1.09808 | + | 2.56218i | 0.0614805 | + | 0.143454i | ||||
\(320\) | − | 21.3923i | − | 1.19587i | ||||||
\(321\) | −7.90192 | + | 4.56218i | −0.441042 | + | 0.254636i | ||||
\(322\) | −5.46410 | − | 5.46410i | −0.304502 | − | 0.304502i | ||||
\(323\) | −2.53590 | −0.141101 | ||||||||
\(324\) | −13.5000 | + | 7.79423i | −0.750000 | + | 0.433013i | ||||
\(325\) | − | 51.1769i | − | 2.83878i | ||||||
\(326\) | 24.8564i | 1.37667i | ||||||||
\(327\) | 10.5000 | − | 6.06218i | 0.580651 | − | 0.335239i | ||||
\(328\) | − | 3.80385i | − | 0.210032i | ||||||
\(329\) | −2.26795 | − | 2.26795i | −0.125036 | − | 0.125036i | ||||
\(330\) | 5.59808 | − | 3.23205i | 0.308164 | − | 0.177919i | ||||
\(331\) | −2.36603 | + | 2.36603i | −0.130049 | + | 0.130049i | −0.769135 | − | 0.639086i | \(-0.779313\pi\) |
0.639086 | + | 0.769135i | \(0.279313\pi\) | |||||||
\(332\) | 24.0000 | 1.31717 | ||||||||
\(333\) | −3.80385 | − | 14.1962i | −0.208450 | − | 0.777944i | ||||
\(334\) | 4.46410 | − | 4.46410i | 0.244265 | − | 0.244265i | ||||
\(335\) | − | 33.3205i | − | 1.82049i | ||||||
\(336\) | −10.5622 | − | 18.2942i | −0.576214 | − | 0.998032i | ||||
\(337\) | −1.07180 | + | 1.07180i | −0.0583845 | + | 0.0583845i | −0.735696 | − | 0.677312i | \(-0.763145\pi\) |
0.677312 | + | 0.735696i | \(0.263145\pi\) | |||||||
\(338\) | 27.1244 | − | 27.1244i | 1.47537 | − | 1.47537i | ||||
\(339\) | 3.75833 | − | 14.0263i | 0.204124 | − | 0.761803i | ||||
\(340\) | 4.73205 | + | 4.73205i | 0.256631 | + | 0.256631i | ||||
\(341\) | −0.464102 | −0.0251325 | ||||||||
\(342\) | 7.09808 | − | 12.2942i | 0.383820 | − | 0.664796i | ||||
\(343\) | 17.8564 | 0.964155 | ||||||||
\(344\) | 2.60770i | 0.140598i | ||||||||
\(345\) | 8.19615 | − | 4.73205i | 0.441266 | − | 0.254765i | ||||
\(346\) | −18.3923 | + | 18.3923i | −0.988776 | + | 0.988776i | ||||
\(347\) | 19.5167 | 1.04771 | 0.523855 | − | 0.851808i | \(-0.324494\pi\) | ||||
0.523855 | + | 0.851808i | \(0.324494\pi\) | |||||||
\(348\) | −2.30385 | − | 15.9904i | −0.123499 | − | 0.857174i | ||||
\(349\) | 26.6603 | 1.42709 | 0.713545 | − | 0.700609i | \(-0.247088\pi\) | ||||
0.713545 | + | 0.700609i | \(0.247088\pi\) | |||||||
\(350\) | 33.3205 | − | 33.3205i | 1.78106 | − | 1.78106i | ||||
\(351\) | 29.7846i | 1.58978i | ||||||||
\(352\) | − | 3.92820i | − | 0.209374i | ||||||
\(353\) | −8.78461 | −0.467558 | −0.233779 | − | 0.972290i | \(-0.575109\pi\) | ||||
−0.233779 | + | 0.972290i | \(0.575109\pi\) | |||||||
\(354\) | 0.464102 | − | 1.73205i | 0.0246667 | − | 0.0920575i | ||||
\(355\) | −62.4449 | −3.31423 | ||||||||
\(356\) | −8.66025 | − | 8.66025i | −0.458993 | − | 0.458993i | ||||
\(357\) | 4.73205 | + | 1.26795i | 0.250447 | + | 0.0671070i | ||||
\(358\) | −22.6603 | + | 22.6603i | −1.19763 | + | 1.19763i | ||||
\(359\) | −6.49038 | + | 6.49038i | −0.342549 | + | 0.342549i | −0.857325 | − | 0.514776i | \(-0.827875\pi\) |
0.514776 | + | 0.857325i | \(0.327875\pi\) | |||||||
\(360\) | 5.59808 | − | 1.50000i | 0.295045 | − | 0.0790569i | ||||
\(361\) | − | 13.0000i | − | 0.684211i | ||||||
\(362\) | −22.2942 | + | 22.2942i | −1.17176 | + | 1.17176i | ||||
\(363\) | −16.0981 | + | 9.29423i | −0.844930 | + | 0.487820i | ||||
\(364\) | 27.1244 | 1.42170 | ||||||||
\(365\) | −14.9282 | + | 14.9282i | −0.781378 | + | 0.781378i | ||||
\(366\) | 4.73205 | + | 8.19615i | 0.247348 | + | 0.428420i | ||||
\(367\) | −7.53590 | − | 7.53590i | −0.393371 | − | 0.393371i | 0.482516 | − | 0.875887i | \(-0.339723\pi\) |
−0.875887 | + | 0.482516i | \(0.839723\pi\) | |||||||
\(368\) | − | 6.53590i | − | 0.340707i | ||||||
\(369\) | −21.2942 | + | 5.70577i | −1.10853 | + | 0.297031i | ||||
\(370\) | − | 35.3205i | − | 1.83623i | ||||||
\(371\) | 10.7321i | 0.557180i | ||||||||
\(372\) | 2.59808 | + | 0.696152i | 0.134704 | + | 0.0360938i | ||||
\(373\) | −24.4641 | −1.26670 | −0.633352 | − | 0.773864i | \(-0.718321\pi\) | ||||
−0.633352 | + | 0.773864i | \(0.718321\pi\) | |||||||
\(374\) | 0.732051 | + | 0.732051i | 0.0378534 | + | 0.0378534i | ||||
\(375\) | 12.6962 | + | 21.9904i | 0.655626 | + | 1.13558i | ||||
\(376\) | − | 0.607695i | − | 0.0313395i | ||||||
\(377\) | −28.6603 | − | 11.4641i | −1.47608 | − | 0.590431i | ||||
\(378\) | −19.3923 | + | 19.3923i | −0.997433 | + | 0.997433i | ||||
\(379\) | −8.85641 | − | 8.85641i | −0.454923 | − | 0.454923i | 0.442062 | − | 0.896985i | \(-0.354247\pi\) |
−0.896985 | + | 0.442062i | \(0.854247\pi\) | |||||||
\(380\) | 11.1962 | − | 11.1962i | 0.574351 | − | 0.574351i | ||||
\(381\) | −5.70577 | + | 21.2942i | −0.292316 | + | 1.09094i | ||||
\(382\) | 43.5167i | 2.22651i | ||||||||
\(383\) | 9.26795 | 0.473570 | 0.236785 | − | 0.971562i | \(-0.423906\pi\) | ||||
0.236785 | + | 0.971562i | \(0.423906\pi\) | |||||||
\(384\) | 1.83975 | − | 6.86603i | 0.0938841 | − | 0.350380i | ||||
\(385\) | 3.73205 | − | 3.73205i | 0.190203 | − | 0.190203i | ||||
\(386\) | 27.1244 | 1.38059 | ||||||||
\(387\) | 14.5981 | − | 3.91154i | 0.742062 | − | 0.198835i | ||||
\(388\) | 13.3923 | + | 13.3923i | 0.679891 | + | 0.679891i | ||||
\(389\) | 11.8038 | + | 11.8038i | 0.598479 | + | 0.598479i | 0.939908 | − | 0.341429i | \(-0.110911\pi\) |
−0.341429 | + | 0.939908i | \(0.610911\pi\) | |||||||
\(390\) | −18.5263 | + | 69.1410i | −0.938115 | + | 3.50109i | ||||
\(391\) | 1.07180 | + | 1.07180i | 0.0542031 | + | 0.0542031i | ||||
\(392\) | −0.169873 | − | 0.169873i | −0.00857988 | − | 0.00857988i | ||||
\(393\) | 7.22243 | − | 26.9545i | 0.364323 | − | 1.35967i | ||||
\(394\) | −34.0526 | − | 34.0526i | −1.71554 | − | 1.71554i | ||||
\(395\) | 6.83013 | + | 6.83013i | 0.343661 | + | 0.343661i | ||||
\(396\) | −2.59808 | + | 0.696152i | −0.130558 | + | 0.0349830i | ||||
\(397\) | −8.32051 | −0.417594 | −0.208797 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208797 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(398\) | −3.73205 | + | 3.73205i | −0.187071 | + | 0.187071i | ||||
\(399\) | 3.00000 | − | 11.1962i | 0.150188 | − | 0.560509i | ||||
\(400\) | 39.8564 | 1.99282 | ||||||||
\(401\) | − | 26.2679i | − | 1.31176i | −0.754866 | − | 0.655879i | \(-0.772298\pi\) | ||
0.754866 | − | 0.655879i | \(-0.227702\pi\) | |||||||
\(402\) | −7.73205 | + | 28.8564i | −0.385640 | + | 1.43923i | ||||
\(403\) | 3.63397 | − | 3.63397i | 0.181021 | − | 0.181021i | ||||
\(404\) | 7.26795 | + | 7.26795i | 0.361594 | + | 0.361594i | ||||
\(405\) | −16.7942 | − | 29.0885i | −0.834512 | − | 1.44542i | ||||
\(406\) | −11.1962 | − | 26.1244i | −0.555656 | − | 1.29653i | ||||
\(407\) | − | 2.53590i | − | 0.125700i | ||||||
\(408\) | 0.464102 | + | 0.803848i | 0.0229765 | + | 0.0397964i | ||||
\(409\) | 4.60770 | + | 4.60770i | 0.227836 | + | 0.227836i | 0.811788 | − | 0.583952i | \(-0.198494\pi\) |
−0.583952 | + | 0.811788i | \(0.698494\pi\) | |||||||
\(410\) | −52.9808 | −2.61653 | ||||||||
\(411\) | −11.1962 | − | 3.00000i | −0.552265 | − | 0.147979i | ||||
\(412\) | − | 18.5885i | − | 0.915788i | ||||||
\(413\) | − | 1.46410i | − | 0.0720437i | ||||||
\(414\) | −8.19615 | + | 2.19615i | −0.402819 | + | 0.107935i | ||||
\(415\) | 51.7128i | 2.53848i | ||||||||
\(416\) | 30.7583 | + | 30.7583i | 1.50805 | + | 1.50805i | ||||
\(417\) | −9.92820 | − | 17.1962i | −0.486186 | − | 0.842099i | ||||
\(418\) | 1.73205 | − | 1.73205i | 0.0847174 | − | 0.0847174i | ||||
\(419\) | 2.33975 | 0.114304 | 0.0571520 | − | 0.998365i | \(-0.481798\pi\) | ||||
0.0571520 | + | 0.998365i | \(0.481798\pi\) | |||||||
\(420\) | −26.4904 | + | 15.2942i | −1.29260 | + | 0.746282i | ||||
\(421\) | −6.19615 | + | 6.19615i | −0.301982 | + | 0.301982i | −0.841789 | − | 0.539807i | \(-0.818497\pi\) |
0.539807 | + | 0.841789i | \(0.318497\pi\) | |||||||
\(422\) | 38.3205i | 1.86541i | ||||||||
\(423\) | −3.40192 | + | 0.911543i | −0.165407 | + | 0.0443207i | ||||
\(424\) | −1.43782 | + | 1.43782i | −0.0698268 | + | 0.0698268i | ||||
\(425\) | −6.53590 | + | 6.53590i | −0.317038 | + | 0.317038i | ||||
\(426\) | 54.0788 | + | 14.4904i | 2.62013 | + | 0.702061i | ||||
\(427\) | 5.46410 | + | 5.46410i | 0.264426 | + | 0.264426i | ||||
\(428\) | 9.12436 | 0.441042 | ||||||||
\(429\) | −1.33013 | + | 4.96410i | −0.0642191 | + | 0.239669i | ||||
\(430\) | 36.3205 | 1.75153 | ||||||||
\(431\) | − | 30.3923i | − | 1.46395i | −0.681334 | − | 0.731973i | \(-0.738600\pi\) | ||
0.681334 | − | 0.731973i | \(-0.261400\pi\) | |||||||
\(432\) | −23.1962 | −1.11603 | ||||||||
\(433\) | 5.46410 | − | 5.46410i | 0.262588 | − | 0.262588i | −0.563517 | − | 0.826105i | \(-0.690552\pi\) |
0.826105 | + | 0.563517i | \(0.190552\pi\) | |||||||
\(434\) | 4.73205 | 0.227146 | ||||||||
\(435\) | 34.4545 | − | 4.96410i | 1.65197 | − | 0.238010i | ||||
\(436\) | −12.1244 | −0.580651 | ||||||||
\(437\) | 2.53590 | − | 2.53590i | 0.121308 | − | 0.121308i | ||||
\(438\) | 16.3923 | − | 9.46410i | 0.783255 | − | 0.452212i | ||||
\(439\) | − | 26.2487i | − | 1.25278i | −0.779509 | − | 0.626391i | \(-0.784531\pi\) | ||
0.779509 | − | 0.626391i | \(-0.215469\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | −0.696152 | + | 1.20577i | −0.0331501 | + | 0.0574177i | ||||
\(442\) | −11.4641 | −0.545292 | ||||||||
\(443\) | 17.9282 | + | 17.9282i | 0.851795 | + | 0.851795i | 0.990354 | − | 0.138559i | \(-0.0442472\pi\) |
−0.138559 | + | 0.990354i | \(0.544247\pi\) | |||||||
\(444\) | −3.80385 | + | 14.1962i | −0.180523 | + | 0.673720i | ||||
\(445\) | 18.6603 | − | 18.6603i | 0.884581 | − | 0.884581i | ||||
\(446\) | −1.00000 | + | 1.00000i | −0.0473514 | + | 0.0473514i | ||||
\(447\) | 9.99038 | + | 17.3038i | 0.472529 | + | 0.818444i | ||||
\(448\) | 15.6603i | 0.739877i | ||||||||
\(449\) | 0.856406 | − | 0.856406i | 0.0404163 | − | 0.0404163i | −0.686610 | − | 0.727026i | \(-0.740902\pi\) |
0.727026 | + | 0.686610i | \(0.240902\pi\) | |||||||
\(450\) | −13.3923 | − | 49.9808i | −0.631319 | − | 2.35612i | ||||
\(451\) | −3.80385 | −0.179116 | ||||||||
\(452\) | −10.2679 | + | 10.2679i | −0.482964 | + | 0.482964i | ||||
\(453\) | −8.49038 | + | 4.90192i | −0.398913 | + | 0.230312i | ||||
\(454\) | 12.4641 | + | 12.4641i | 0.584969 | + | 0.584969i | ||||
\(455\) | 58.4449i | 2.73994i | ||||||||
\(456\) | 1.90192 | − | 1.09808i | 0.0890657 | − | 0.0514221i | ||||
\(457\) | 28.2487i | 1.32142i | 0.750642 | + | 0.660709i | \(0.229744\pi\) | ||||
−0.750642 | + | 0.660709i | \(0.770256\pi\) | |||||||
\(458\) | − | 55.5167i | − | 2.59412i | ||||||
\(459\) | 3.80385 | − | 3.80385i | 0.177548 | − | 0.177548i | ||||
\(460\) | −9.46410 | −0.441266 | ||||||||
\(461\) | −16.8564 | − | 16.8564i | −0.785081 | − | 0.785081i | 0.195602 | − | 0.980683i | \(-0.437334\pi\) |
−0.980683 | + | 0.195602i | \(0.937334\pi\) | |||||||
\(462\) | −4.09808 | + | 2.36603i | −0.190660 | + | 0.110077i | ||||
\(463\) | − | 22.0000i | − | 1.02243i | −0.859454 | − | 0.511213i | \(-0.829196\pi\) | ||
0.859454 | − | 0.511213i | \(-0.170804\pi\) | |||||||
\(464\) | 8.92820 | − | 22.3205i | 0.414481 | − | 1.03620i | ||||
\(465\) | −1.50000 | + | 5.59808i | −0.0695608 | + | 0.259605i | ||||
\(466\) | −27.4904 | − | 27.4904i | −1.27347 | − | 1.27347i | ||||
\(467\) | 4.90192 | − | 4.90192i | 0.226834 | − | 0.226834i | −0.584535 | − | 0.811369i | \(-0.698723\pi\) |
0.811369 | + | 0.584535i | \(0.198723\pi\) | |||||||
\(468\) | 14.8923 | − | 25.7942i | 0.688397 | − | 1.19234i | ||||
\(469\) | 24.3923i | 1.12633i | ||||||||
\(470\) | −8.46410 | −0.390420 | ||||||||
\(471\) | 13.0981 | + | 3.50962i | 0.603527 | + | 0.161715i | ||||
\(472\) | 0.196152 | − | 0.196152i | 0.00902865 | − | 0.00902865i | ||||
\(473\) | 2.60770 | 0.119902 | ||||||||
\(474\) | −4.33013 | − | 7.50000i | −0.198889 | − | 0.344486i | ||||
\(475\) | 15.4641 | + | 15.4641i | 0.709542 | + | 0.709542i | ||||
\(476\) | −3.46410 | − | 3.46410i | −0.158777 | − | 0.158777i | ||||
\(477\) | 10.2058 | + | 5.89230i | 0.467290 | + | 0.269790i | ||||
\(478\) | −8.19615 | − | 8.19615i | −0.374883 | − | 0.374883i | ||||
\(479\) | −2.90192 | − | 2.90192i | −0.132592 | − | 0.132592i | 0.637696 | − | 0.770288i | \(-0.279888\pi\) |
−0.770288 | + | 0.637696i | \(0.779888\pi\) | |||||||
\(480\) | −47.3827 | − | 12.6962i | −2.16271 | − | 0.579497i | ||||
\(481\) | 19.8564 | + | 19.8564i | 0.905374 | + | 0.905374i | ||||
\(482\) | −18.4904 | − | 18.4904i | −0.842214 | − | 0.842214i | ||||
\(483\) | −6.00000 | + | 3.46410i | −0.273009 | + | 0.157622i | ||||
\(484\) | 18.5885 | 0.844930 | ||||||||
\(485\) | −28.8564 | + | 28.8564i | −1.31030 | + | 1.31030i | ||||
\(486\) | 7.79423 | + | 29.0885i | 0.353553 | + | 1.31948i | ||||
\(487\) | −32.4449 | −1.47022 | −0.735109 | − | 0.677949i | \(-0.762869\pi\) | ||||
−0.735109 | + | 0.677949i | \(0.762869\pi\) | |||||||
\(488\) | 1.46410i | 0.0662768i | ||||||||
\(489\) | 21.5263 | + | 5.76795i | 0.973452 | + | 0.260836i | ||||
\(490\) | −2.36603 | + | 2.36603i | −0.106886 | + | 0.106886i | ||||
\(491\) | −28.5622 | − | 28.5622i | −1.28899 | − | 1.28899i | −0.935399 | − | 0.353594i | \(-0.884959\pi\) |
−0.353594 | − | 0.935399i | \(-0.615041\pi\) | |||||||
\(492\) | 21.2942 | + | 5.70577i | 0.960018 | + | 0.257236i | ||||
\(493\) | 2.19615 | + | 5.12436i | 0.0989097 | + | 0.230789i | ||||
\(494\) | 27.1244i | 1.22038i | ||||||||
\(495\) | −1.50000 | − | 5.59808i | −0.0674200 | − | 0.251615i | ||||
\(496\) | 2.83013 | + | 2.83013i | 0.127076 | + | 0.127076i | ||||
\(497\) | 45.7128 | 2.05050 | ||||||||
\(498\) | 12.0000 | − | 44.7846i | 0.537733 | − | 2.00685i | ||||
\(499\) | 38.6410i | 1.72981i | 0.501936 | + | 0.864905i | \(0.332621\pi\) | ||||
−0.501936 | + | 0.864905i | \(0.667379\pi\) | |||||||
\(500\) | − | 25.3923i | − | 1.13558i | ||||||
\(501\) | −2.83013 | − | 4.90192i | −0.126441 | − | 0.219002i | ||||
\(502\) | − | 29.0526i | − | 1.29668i | ||||||
\(503\) | −14.1699 | − | 14.1699i | −0.631803 | − | 0.631803i | 0.316717 | − | 0.948520i | \(-0.397420\pi\) |
−0.948520 | + | 0.316717i | \(0.897420\pi\) | |||||||
\(504\) | −4.09808 | + | 1.09808i | −0.182543 | + | 0.0489122i | ||||
\(505\) | −15.6603 | + | 15.6603i | −0.696872 | + | 0.696872i | ||||
\(506\) | −1.46410 | −0.0650873 | ||||||||
\(507\) | −17.1962 | − | 29.7846i | −0.763708 | − | 1.32278i | ||||
\(508\) | 15.5885 | − | 15.5885i | 0.691626 | − | 0.691626i | ||||
\(509\) | 27.6410i | 1.22517i | 0.790406 | + | 0.612583i | \(0.209870\pi\) | ||||
−0.790406 | + | 0.612583i | \(0.790130\pi\) | |||||||
\(510\) | 11.1962 | − | 6.46410i | 0.495774 | − | 0.286235i | ||||
\(511\) | 10.9282 | − | 10.9282i | 0.483435 | − | 0.483435i | ||||
\(512\) | −20.6865 | + | 20.6865i | −0.914224 | + | 0.914224i | ||||
\(513\) | −9.00000 | − | 9.00000i | −0.397360 | − | 0.397360i | ||||
\(514\) | 13.5622 | + | 13.5622i | 0.598202 | + | 0.598202i | ||||
\(515\) | 40.0526 | 1.76493 | ||||||||
\(516\) | −14.5981 | − | 3.91154i | −0.642644 | − | 0.172196i | ||||
\(517\) | −0.607695 | −0.0267264 | ||||||||
\(518\) | 25.8564i | 1.13607i | ||||||||
\(519\) | 11.6603 | + | 20.1962i | 0.511828 | + | 0.886513i | ||||
\(520\) | −7.83013 | + | 7.83013i | −0.343374 | + | 0.343374i | ||||
\(521\) | 18.3205 | 0.802636 | 0.401318 | − | 0.915939i | \(-0.368552\pi\) | ||||
0.401318 | + | 0.915939i | \(0.368552\pi\) | |||||||
\(522\) | −30.9904 | − | 3.69615i | −1.35641 | − | 0.161776i | ||||
\(523\) | 20.9282 | 0.915126 | 0.457563 | − | 0.889177i | \(-0.348722\pi\) | ||||
0.457563 | + | 0.889177i | \(0.348722\pi\) | |||||||
\(524\) | −19.7321 | + | 19.7321i | −0.861999 | + | 0.861999i | ||||
\(525\) | −21.1244 | − | 36.5885i | −0.921942 | − | 1.59685i | ||||
\(526\) | − | 41.7846i | − | 1.82190i | ||||||
\(527\) | −0.928203 | −0.0404332 | ||||||||
\(528\) | −3.86603 | − | 1.03590i | −0.168247 | − | 0.0450817i | ||||
\(529\) | 20.8564 | 0.906800 | ||||||||
\(530\) | 20.0263 | + | 20.0263i | 0.869886 | + | 0.869886i | ||||
\(531\) | −1.39230 | − | 0.803848i | −0.0604209 | − | 0.0348840i | ||||
\(532\) | −8.19615 | + | 8.19615i | −0.355348 | + | 0.355348i | ||||
\(533\) | 29.7846 | − | 29.7846i | 1.29011 | − | 1.29011i | ||||
\(534\) | −20.4904 | + | 11.8301i | −0.886706 | + | 0.511940i | ||||
\(535\) | 19.6603i | 0.849987i | ||||||||
\(536\) | −3.26795 | + | 3.26795i | −0.141154 | + | 0.141154i | ||||
\(537\) | 14.3660 | + | 24.8827i | 0.619940 | + | 1.07377i | ||||
\(538\) | 5.46410 | 0.235574 | ||||||||
\(539\) | −0.169873 | + | 0.169873i | −0.00731695 | + | 0.00731695i | ||||
\(540\) | 33.5885i | 1.44542i | ||||||||
\(541\) | −15.2679 | − | 15.2679i | −0.656420 | − | 0.656420i | 0.298111 | − | 0.954531i | \(-0.403643\pi\) |
−0.954531 | + | 0.298111i | \(0.903643\pi\) | |||||||
\(542\) | − | 19.5885i | − | 0.841396i | ||||||
\(543\) | 14.1340 | + | 24.4808i | 0.606547 | + | 1.05057i | ||||
\(544\) | − | 7.85641i | − | 0.336841i | ||||||
\(545\) | − | 26.1244i | − | 1.11904i | ||||||
\(546\) | 13.5622 | − | 50.6147i | 0.580408 | − | 2.16611i | ||||
\(547\) | 3.66025 | 0.156501 | 0.0782506 | − | 0.996934i | \(-0.475067\pi\) | ||||
0.0782506 | + | 0.996934i | \(0.475067\pi\) | |||||||
\(548\) | 8.19615 | + | 8.19615i | 0.350122 | + | 0.350122i | ||||
\(549\) | 8.19615 | − | 2.19615i | 0.349803 | − | 0.0937295i | ||||
\(550\) | − | 8.92820i | − | 0.380700i | ||||||
\(551\) | 12.1244 | − | 5.19615i | 0.516515 | − | 0.221364i | ||||
\(552\) | −1.26795 | − | 0.339746i | −0.0539675 | − | 0.0144605i | ||||
\(553\) | −5.00000 | − | 5.00000i | −0.212622 | − | 0.212622i | ||||
\(554\) | −7.66025 | + | 7.66025i | −0.325453 | + | 0.325453i | ||||
\(555\) | −30.5885 | − | 8.19615i | −1.29841 | − | 0.347907i | ||||
\(556\) | 19.8564i | 0.842099i | ||||||||
\(557\) | −23.0718 | −0.977583 | −0.488792 | − | 0.872401i | \(-0.662562\pi\) | ||||
−0.488792 | + | 0.872401i | \(0.662562\pi\) | |||||||
\(558\) | 2.59808 | − | 4.50000i | 0.109985 | − | 0.190500i | ||||
\(559\) | −20.4186 | + | 20.4186i | −0.863614 | + | 0.863614i | ||||
\(560\) | −45.5167 | −1.92343 | ||||||||
\(561\) | 0.803848 | − | 0.464102i | 0.0339385 | − | 0.0195944i | ||||
\(562\) | −2.36603 | − | 2.36603i | −0.0998048 | − | 0.0998048i | ||||
\(563\) | −15.9545 | − | 15.9545i | −0.672401 | − | 0.672401i | 0.285868 | − | 0.958269i | \(-0.407718\pi\) |
−0.958269 | + | 0.285868i | \(0.907718\pi\) | |||||||
\(564\) | 3.40192 | + | 0.911543i | 0.143247 | + | 0.0383829i | ||||
\(565\) | −22.1244 | − | 22.1244i | −0.930779 | − | 0.930779i | ||||
\(566\) | 8.19615 | + | 8.19615i | 0.344510 | + | 0.344510i | ||||
\(567\) | 12.2942 | + | 21.2942i | 0.516309 | + | 0.894274i | ||||
\(568\) | 6.12436 | + | 6.12436i | 0.256972 | + | 0.256972i | ||||
\(569\) | −15.7846 | − | 15.7846i | −0.661725 | − | 0.661725i | 0.294061 | − | 0.955787i | \(-0.404993\pi\) |
−0.955787 | + | 0.294061i | \(0.904993\pi\) | |||||||
\(570\) | −15.2942 | − | 26.4904i | −0.640605 | − | 1.10956i | ||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 3.63397 | − | 3.63397i | 0.151944 | − | 0.151944i | ||||
\(573\) | 37.6865 | + | 10.0981i | 1.57438 | + | 0.421853i | ||||
\(574\) | 38.7846 | 1.61884 | ||||||||
\(575\) | − | 13.0718i | − | 0.545132i | ||||||
\(576\) | 14.8923 | + | 8.59808i | 0.620513 | + | 0.358253i | ||||
\(577\) | 12.3923 | − | 12.3923i | 0.515898 | − | 0.515898i | −0.400429 | − | 0.916328i | \(-0.631139\pi\) |
0.916328 | + | 0.400429i | \(0.131139\pi\) | |||||||
\(578\) | −21.7583 | − | 21.7583i | −0.905027 | − | 0.905027i | ||||
\(579\) | 6.29423 | − | 23.4904i | 0.261579 | − | 0.976227i | ||||
\(580\) | −32.3205 | − | 12.9282i | −1.34204 | − | 0.536814i | ||||
\(581\) | − | 37.8564i | − | 1.57055i | ||||||
\(582\) | 31.6865 | − | 18.2942i | 1.31345 | − | 0.758320i | ||||
\(583\) | 1.43782 | + | 1.43782i | 0.0595485 | + | 0.0595485i | ||||
\(584\) | 2.92820 | 0.121170 | ||||||||
\(585\) | 55.5788 | + | 32.0885i | 2.29790 | + | 1.32669i | ||||
\(586\) | 44.0526i | 1.81979i | ||||||||
\(587\) | 21.6077i | 0.891845i | 0.895072 | + | 0.445923i | \(0.147124\pi\) | ||||
−0.895072 | + | 0.445923i | \(0.852876\pi\) | |||||||
\(588\) | 1.20577 | − | 0.696152i | 0.0497252 | − | 0.0287088i | ||||
\(589\) | 2.19615i | 0.0904909i | ||||||||
\(590\) | −2.73205 | − | 2.73205i | −0.112477 | − | 0.112477i | ||||
\(591\) | −37.3923 | + | 21.5885i | −1.53811 | + | 0.888030i | ||||
\(592\) | −15.4641 | + | 15.4641i | −0.635571 | + | 0.635571i | ||||
\(593\) | 21.3923 | 0.878477 | 0.439238 | − | 0.898371i | \(-0.355248\pi\) | ||||
0.439238 | + | 0.898371i | \(0.355248\pi\) | |||||||
\(594\) | 5.19615i | 0.213201i | ||||||||
\(595\) | 7.46410 | − | 7.46410i | 0.305998 | − | 0.305998i | ||||
\(596\) | − | 19.9808i | − | 0.818444i | ||||||
\(597\) | 2.36603 | + | 4.09808i | 0.0968350 | + | 0.167723i | ||||
\(598\) | 11.4641 | − | 11.4641i | 0.468802 | − | 0.468802i | ||||
\(599\) | −0.437822 | + | 0.437822i | −0.0178889 | + | 0.0178889i | −0.715995 | − | 0.698106i | \(-0.754027\pi\) |
0.698106 | + | 0.715995i | \(0.254027\pi\) | |||||||
\(600\) | 2.07180 | − | 7.73205i | 0.0845807 | − | 0.315660i | ||||
\(601\) | −21.5885 | − | 21.5885i | −0.880612 | − | 0.880612i | 0.112985 | − | 0.993597i | \(-0.463959\pi\) |
−0.993597 | + | 0.112985i | \(0.963959\pi\) | |||||||
\(602\) | −26.5885 | −1.08366 | ||||||||
\(603\) | 23.1962 | + | 13.3923i | 0.944620 | + | 0.545377i | ||||
\(604\) | 9.80385 | 0.398913 | ||||||||
\(605\) | 40.0526i | 1.62837i | ||||||||
\(606\) | 17.1962 | − | 9.92820i | 0.698546 | − | 0.403306i | ||||
\(607\) | 17.3660 | − | 17.3660i | 0.704865 | − | 0.704865i | −0.260586 | − | 0.965451i | \(-0.583916\pi\) |
0.965451 | + | 0.260586i | \(0.0839156\pi\) | |||||||
\(608\) | −18.5885 | −0.753861 | ||||||||
\(609\) | −25.2224 | + | 3.63397i | −1.02206 | + | 0.147256i | ||||
\(610\) | 20.3923 | 0.825660 | ||||||||
\(611\) | 4.75833 | − | 4.75833i | 0.192501 | − | 0.192501i | ||||
\(612\) | −5.19615 | + | 1.39230i | −0.210042 | + | 0.0562806i | ||||
\(613\) | 19.7846i | 0.799093i | 0.916713 | + | 0.399546i | \(0.130832\pi\) | ||||
−0.916713 | + | 0.399546i | \(0.869168\pi\) | |||||||
\(614\) | −6.80385 | −0.274581 | ||||||||
\(615\) | −12.2942 | + | 45.8827i | −0.495751 | + | 1.85017i | ||||
\(616\) | −0.732051 | −0.0294952 | ||||||||
\(617\) | −15.8038 | − | 15.8038i | −0.636239 | − | 0.636239i | 0.313387 | − | 0.949626i | \(-0.398536\pi\) |
−0.949626 | + | 0.313387i | \(0.898536\pi\) | |||||||
\(618\) | −34.6865 | − | 9.29423i | −1.39530 | − | 0.373869i | ||||
\(619\) | 17.6865 | − | 17.6865i | 0.710882 | − | 0.710882i | −0.255838 | − | 0.966720i | \(-0.582351\pi\) |
0.966720 | + | 0.255838i | \(0.0823513\pi\) | |||||||
\(620\) | 4.09808 | − | 4.09808i | 0.164583 | − | 0.164583i | ||||
\(621\) | 7.60770i | 0.305286i | ||||||||
\(622\) | 44.9808i | 1.80356i | ||||||||
\(623\) | −13.6603 | + | 13.6603i | −0.547287 | + | 0.547287i | ||||
\(624\) | 38.3827 | − | 22.1603i | 1.53654 | − | 0.887120i | ||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | −10.3660 | + | 10.3660i | −0.414310 | + | 0.414310i | ||||
\(627\) | −1.09808 | − | 1.90192i | −0.0438529 | − | 0.0759555i | ||||
\(628\) | −9.58846 | − | 9.58846i | −0.382621 | − | 0.382621i | ||||
\(629\) | − | 5.07180i | − | 0.202226i | ||||||
\(630\) | 15.2942 | + | 57.0788i | 0.609337 | + | 2.27408i | ||||
\(631\) | − | 22.5885i | − | 0.899232i | −0.893222 | − | 0.449616i | \(-0.851561\pi\) | ||
0.893222 | − | 0.449616i | \(-0.148439\pi\) | |||||||
\(632\) | − | 1.33975i | − | 0.0532922i | ||||||
\(633\) | 33.1865 | + | 8.89230i | 1.31905 | + | 0.353437i | ||||
\(634\) | −50.2487 | −1.99563 | ||||||||
\(635\) | 33.5885 | + | 33.5885i | 1.33292 | + | 1.33292i | ||||
\(636\) | −5.89230 | − | 10.2058i | −0.233645 | − | 0.404685i | ||||
\(637\) | − | 2.66025i | − | 0.105403i | ||||||
\(638\) | −5.00000 | − | 2.00000i | −0.197952 | − | 0.0791808i | ||||
\(639\) | 25.0981 | − | 43.4711i | 0.992865 | − | 1.71969i | ||||
\(640\) | −10.8301 | − | 10.8301i | −0.428098 | − | 0.428098i | ||||
\(641\) | −30.0526 | + | 30.0526i | −1.18700 | + | 1.18700i | −0.209113 | + | 0.977891i | \(0.567058\pi\) |
−0.977891 | + | 0.209113i | \(0.932942\pi\) | |||||||
\(642\) | 4.56218 | − | 17.0263i | 0.180055 | − | 0.671974i | ||||
\(643\) | − | 12.4449i | − | 0.490778i | −0.969425 | − | 0.245389i | \(-0.921084\pi\) | ||
0.969425 | − | 0.245389i | \(-0.0789156\pi\) | |||||||
\(644\) | 6.92820 | 0.273009 | ||||||||
\(645\) | 8.42820 | − | 31.4545i | 0.331860 | − | 1.23852i | ||||
\(646\) | 3.46410 | − | 3.46410i | 0.136293 | − | 0.136293i | ||||
\(647\) | −9.85641 | −0.387495 | −0.193748 | − | 0.981051i | \(-0.562064\pi\) | ||||
−0.193748 | + | 0.981051i | \(0.562064\pi\) | |||||||
\(648\) | −1.20577 | + | 4.50000i | −0.0473672 | + | 0.176777i | ||||
\(649\) | −0.196152 | − | 0.196152i | −0.00769966 | − | 0.00769966i | ||||
\(650\) | 69.9090 | + | 69.9090i | 2.74206 | + | 2.74206i | ||||
\(651\) | 1.09808 | − | 4.09808i | 0.0430370 | − | 0.160616i | ||||
\(652\) | −15.7583 | − | 15.7583i | −0.617144 | − | 0.617144i | ||||
\(653\) | 9.39230 | + | 9.39230i | 0.367549 | + | 0.367549i | 0.866583 | − | 0.499033i | \(-0.166312\pi\) |
−0.499033 | + | 0.866583i | \(0.666312\pi\) | |||||||
\(654\) | −6.06218 | + | 22.6244i | −0.237050 | + | 0.884682i | ||||
\(655\) | −42.5167 | − | 42.5167i | −1.66126 | − | 1.66126i | ||||
\(656\) | 23.1962 | + | 23.1962i | 0.905658 | + | 0.905658i | ||||
\(657\) | −4.39230 | − | 16.3923i | −0.171360 | − | 0.639525i | ||||
\(658\) | 6.19615 | 0.241551 | ||||||||
\(659\) | −5.75833 | + | 5.75833i | −0.224313 | + | 0.224313i | −0.810312 | − | 0.585999i | \(-0.800702\pi\) |
0.585999 | + | 0.810312i | \(0.300702\pi\) | |||||||
\(660\) | −1.50000 | + | 5.59808i | −0.0583874 | + | 0.217905i | ||||
\(661\) | −26.3923 | −1.02654 | −0.513271 | − | 0.858227i | \(-0.671566\pi\) | ||||
−0.513271 | + | 0.858227i | \(0.671566\pi\) | |||||||
\(662\) | − | 6.46410i | − | 0.251234i | ||||||
\(663\) | −2.66025 | + | 9.92820i | −0.103316 | + | 0.385579i | ||||
\(664\) | 5.07180 | − | 5.07180i | 0.196824 | − | 0.196824i | ||||
\(665\) | −17.6603 | − | 17.6603i | −0.684835 | − | 0.684835i | ||||
\(666\) | 24.5885 | + | 14.1962i | 0.952783 | + | 0.550090i | ||||
\(667\) | −7.32051 | − | 2.92820i | −0.283451 | − | 0.113380i | ||||
\(668\) | 5.66025i | 0.219002i | ||||||||
\(669\) | 0.633975 | + | 1.09808i | 0.0245109 | + | 0.0424541i | ||||
\(670\) | 45.5167 | + | 45.5167i | 1.75846 | + | 1.75846i | ||||
\(671\) | 1.46410 | 0.0565210 | ||||||||
\(672\) | 34.6865 | + | 9.29423i | 1.33806 | + | 0.358533i | ||||
\(673\) | 10.3205i | 0.397826i | 0.980017 | + | 0.198913i | \(0.0637412\pi\) | ||||
−0.980017 | + | 0.198913i | \(0.936259\pi\) | |||||||
\(674\) | − | 2.92820i | − | 0.112790i | ||||||
\(675\) | −46.3923 | −1.78564 | ||||||||
\(676\) | 34.3923i | 1.32278i | ||||||||
\(677\) | 15.0526 | + | 15.0526i | 0.578517 | + | 0.578517i | 0.934494 | − | 0.355978i | \(-0.115852\pi\) |
−0.355978 | + | 0.934494i | \(0.615852\pi\) | |||||||
\(678\) | 14.0263 | + | 24.2942i | 0.538676 | + | 0.933014i | ||||
\(679\) | 21.1244 | − | 21.1244i | 0.810678 | − | 0.810678i | ||||
\(680\) | 2.00000 | 0.0766965 | ||||||||
\(681\) | 13.6865 | − | 7.90192i | 0.524469 | − | 0.302802i | ||||
\(682\) | 0.633975 | − | 0.633975i | 0.0242761 | − | 0.0242761i | ||||
\(683\) | 12.9282i | 0.494684i | 0.968928 | + | 0.247342i | \(0.0795571\pi\) | ||||
−0.968928 | + | 0.247342i | \(0.920443\pi\) | |||||||
\(684\) | 3.29423 | + | 12.2942i | 0.125958 | + | 0.470082i | ||||
\(685\) | −17.6603 | + | 17.6603i | −0.674764 | + | 0.674764i | ||||
\(686\) | −24.3923 | + | 24.3923i | −0.931303 | + | 0.931303i | ||||
\(687\) | −48.0788 | − | 12.8827i | −1.83432 | − | 0.491505i | ||||
\(688\) | −15.9019 | − | 15.9019i | −0.606255 | − | 0.606255i | ||||
\(689\) | −22.5167 | −0.857816 | ||||||||
\(690\) | −4.73205 | + | 17.6603i | −0.180146 | + | 0.672314i | ||||
\(691\) | −25.7128 | −0.978162 | −0.489081 | − | 0.872239i | \(-0.662668\pi\) | ||||
−0.489081 | + | 0.872239i | \(0.662668\pi\) | |||||||
\(692\) | − | 23.3205i | − | 0.886513i | ||||||
\(693\) | 1.09808 | + | 4.09808i | 0.0417125 | + | 0.155673i | ||||
\(694\) | −26.6603 | + | 26.6603i | −1.01201 | + | 1.01201i | ||||
\(695\) | −42.7846 | −1.62291 | ||||||||
\(696\) | −3.86603 | − | 2.89230i | −0.146541 | − | 0.109633i | ||||
\(697\) | −7.60770 | −0.288162 | ||||||||
\(698\) | −36.4186 | + | 36.4186i | −1.37846 | + | 1.37846i | ||||
\(699\) | −30.1865 | + | 17.4282i | −1.14176 | + | 0.659195i | ||||
\(700\) | 42.2487i | 1.59685i | ||||||||
\(701\) | −41.1051 | −1.55252 | −0.776259 | − | 0.630414i | \(-0.782885\pi\) | ||||
−0.776259 | + | 0.630414i | \(0.782885\pi\) | |||||||
\(702\) | −40.6865 | − | 40.6865i | −1.53561 | − | 1.53561i | ||||
\(703\) | −12.0000 | −0.452589 | ||||||||
\(704\) | 2.09808 | + | 2.09808i | 0.0790742 | + | 0.0790742i | ||||
\(705\) | −1.96410 | + | 7.33013i | −0.0739723 | + | 0.276069i | ||||
\(706\) | 12.0000 | − | 12.0000i | 0.451626 | − | 0.451626i | ||||
\(707\) | 11.4641 | − | 11.4641i | 0.431152 | − | 0.431152i | ||||
\(708\) | 0.803848 | + | 1.39230i | 0.0302104 | + | 0.0523260i | ||||
\(709\) | − | 9.58846i | − | 0.360102i | −0.983657 | − | 0.180051i | \(-0.942374\pi\) | ||
0.983657 | − | 0.180051i | \(-0.0576263\pi\) | |||||||
\(710\) | 85.3013 | − | 85.3013i | 3.20130 | − | 3.20130i | ||||
\(711\) | −7.50000 | + | 2.00962i | −0.281272 | + | 0.0753666i | ||||
\(712\) | −3.66025 | −0.137174 | ||||||||
\(713\) | 0.928203 | − | 0.928203i | 0.0347615 | − | 0.0347615i | ||||
\(714\) | −8.19615 | + | 4.73205i | −0.306733 | + | 0.177093i | ||||
\(715\) | 7.83013 | + | 7.83013i | 0.292830 | + | 0.292830i | ||||
\(716\) | − | 28.7321i | − | 1.07377i | ||||||
\(717\) | −9.00000 | + | 5.19615i | −0.336111 | + | 0.194054i | ||||
\(718\) | − | 17.7321i | − | 0.661754i | ||||||
\(719\) | − | 42.0526i | − | 1.56830i | −0.620574 | − | 0.784148i | \(-0.713100\pi\) | ||
0.620574 | − | 0.784148i | \(-0.286900\pi\) | |||||||
\(720\) | −24.9904 | + | 43.2846i | −0.931337 | + | 1.61312i | ||||
\(721\) | −29.3205 | −1.09195 | ||||||||
\(722\) | 17.7583 | + | 17.7583i | 0.660897 | + | 0.660897i | ||||
\(723\) | −20.3038 | + | 11.7224i | −0.755108 | + | 0.435962i | ||||
\(724\) | − | 28.2679i | − | 1.05057i | ||||||
\(725\) | 17.8564 | − | 44.6410i | 0.663170 | − | 1.65793i | ||||
\(726\) | 9.29423 | − | 34.6865i | 0.344941 | − | 1.28734i | ||||
\(727\) | 34.3205 | + | 34.3205i | 1.27288 | + | 1.27288i | 0.944572 | + | 0.328306i | \(0.106478\pi\) |
0.328306 | + | 0.944572i | \(0.393522\pi\) | |||||||
\(728\) | 5.73205 | − | 5.73205i | 0.212444 | − | 0.212444i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | − | 40.7846i | − | 1.50951i | ||||||
\(731\) | 5.21539 | 0.192898 | ||||||||
\(732\) | −8.19615 | − | 2.19615i | −0.302939 | − | 0.0811721i | ||||
\(733\) | 30.9808 | − | 30.9808i | 1.14430 | − | 1.14430i | 0.156646 | − | 0.987655i | \(-0.449932\pi\) |
0.987655 | − | 0.156646i | \(-0.0500681\pi\) | |||||||
\(734\) | 20.5885 | 0.759934 | ||||||||
\(735\) | 1.50000 | + | 2.59808i | 0.0553283 | + | 0.0958315i | ||||
\(736\) | 7.85641 | + | 7.85641i | 0.289591 | + | 0.289591i | ||||
\(737\) | 3.26795 | + | 3.26795i | 0.120376 | + | 0.120376i | ||||
\(738\) | 21.2942 | − | 36.8827i | 0.783851 | − | 1.35767i | ||||
\(739\) | 32.6147 | + | 32.6147i | 1.19975 | + | 1.19975i | 0.974240 | + | 0.225512i | \(0.0724055\pi\) |
0.225512 | + | 0.974240i | \(0.427594\pi\) | |||||||
\(740\) | 22.3923 | + | 22.3923i | 0.823157 | + | 0.823157i | ||||
\(741\) | 23.4904 | + | 6.29423i | 0.862941 | + | 0.231224i | ||||
\(742\) | −14.6603 | − | 14.6603i | −0.538195 | − | 0.538195i | ||||
\(743\) | −7.19615 | − | 7.19615i | −0.264001 | − | 0.264001i | 0.562676 | − | 0.826677i | \(-0.309772\pi\) |
−0.826677 | + | 0.562676i | \(0.809772\pi\) | |||||||
\(744\) | 0.696152 | − | 0.401924i | 0.0255222 | − | 0.0147352i | ||||
\(745\) | 43.0526 | 1.57732 | ||||||||
\(746\) | 33.4186 | − | 33.4186i | 1.22354 | − | 1.22354i | ||||
\(747\) | −36.0000 | − | 20.7846i | −1.31717 | − | 0.760469i | ||||
\(748\) | −0.928203 | −0.0339385 | ||||||||
\(749\) | − | 14.3923i | − | 0.525883i | ||||||
\(750\) | −47.3827 | − | 12.6962i | −1.73017 | − | 0.463598i | ||||
\(751\) | 30.7128 | − | 30.7128i | 1.12073 | − | 1.12073i | 0.129094 | − | 0.991632i | \(-0.458793\pi\) |
0.991632 | − | 0.129094i | \(-0.0412069\pi\) | |||||||
\(752\) | 3.70577 | + | 3.70577i | 0.135136 | + | 0.135136i | ||||
\(753\) | −25.1603 | − | 6.74167i | −0.916891 | − | 0.245680i | ||||
\(754\) | 54.8109 | − | 23.4904i | 1.99609 | − | 0.855469i | ||||
\(755\) | 21.1244i | 0.768794i | ||||||||
\(756\) | − | 24.5885i | − | 0.894274i | ||||||
\(757\) | 2.58846 | + | 2.58846i | 0.0940791 | + | 0.0940791i | 0.752580 | − | 0.658501i | \(-0.228809\pi\) |
−0.658501 | + | 0.752580i | \(0.728809\pi\) | |||||||
\(758\) | 24.1962 | 0.878844 | ||||||||
\(759\) | −0.339746 | + | 1.26795i | −0.0123320 | + | 0.0460236i | ||||
\(760\) | − | 4.73205i | − | 0.171650i | ||||||
\(761\) | 11.7128i | 0.424589i | 0.977206 | + | 0.212295i | \(0.0680936\pi\) | ||||
−0.977206 | + | 0.212295i | \(0.931906\pi\) | |||||||
\(762\) | −21.2942 | − | 36.8827i | −0.771409 | − | 1.33612i | ||||
\(763\) | 19.1244i | 0.692348i | ||||||||
\(764\) | −27.5885 | − | 27.5885i | −0.998115 | − | 0.998115i | ||||
\(765\) | −3.00000 | − | 11.1962i | −0.108465 | − | 0.404798i | ||||
\(766\) | −12.6603 | + | 12.6603i | −0.457434 | + | 0.457434i | ||||
\(767\) | 3.07180 | 0.110916 | ||||||||
\(768\) | 16.7942 | + | 29.0885i | 0.606010 | + | 1.04964i | ||||
\(769\) | −2.19615 | + | 2.19615i | −0.0791953 | + | 0.0791953i | −0.745595 | − | 0.666400i | \(-0.767835\pi\) |
0.666400 | + | 0.745595i | \(0.267835\pi\) | |||||||
\(770\) | 10.1962i | 0.367444i | ||||||||
\(771\) | 14.8923 | − | 8.59808i | 0.536333 | − | 0.309652i | ||||
\(772\) | −17.1962 | + | 17.1962i | −0.618903 | + | 0.618903i | ||||
\(773\) | 3.00000 | − | 3.00000i | 0.107903 | − | 0.107903i | −0.651094 | − | 0.758997i | \(-0.725690\pi\) |
0.758997 | + | 0.651094i | \(0.225690\pi\) | |||||||
\(774\) | −14.5981 | + | 25.2846i | −0.524717 | + | 0.908837i | ||||
\(775\) | 5.66025 | + | 5.66025i | 0.203322 | + | 0.203322i | ||||
\(776\) | 5.66025 | 0.203191 | ||||||||
\(777\) | 22.3923 | + | 6.00000i | 0.803319 | + | 0.215249i | ||||
\(778\) | −32.2487 | −1.15617 | ||||||||
\(779\) | 18.0000i | 0.644917i | ||||||||
\(780\) | −32.0885 | − | 55.5788i | −1.14895 | − | 1.99004i | ||||
\(781\) | 6.12436 | − | 6.12436i | 0.219147 | − | 0.219147i | ||||
\(782\) | −2.92820 | −0.104712 | ||||||||
\(783\) | −10.3923 | + | 25.9808i | −0.371391 | + | 0.928477i | ||||
\(784\) | 2.07180 | 0.0739927 | ||||||||
\(785\) | 20.6603 | − | 20.6603i | 0.737396 | − | 0.737396i | ||||
\(786\) | 26.9545 | + | 46.6865i | 0.961435 | + | 1.66525i | ||||
\(787\) | 31.5167i | 1.12345i | 0.827325 | + | 0.561724i | \(0.189862\pi\) | ||||
−0.827325 | + | 0.561724i | \(0.810138\pi\) | |||||||
\(788\) | 43.1769 | 1.53811 | ||||||||
\(789\) | −36.1865 | − | 9.69615i | −1.28827 | − | 0.345192i | ||||
\(790\) | −18.6603 | −0.663902 | ||||||||
\(791\) | 16.1962 | + | 16.1962i | 0.575869 | + | 0.575869i | ||||
\(792\) | −0.401924 | + | 0.696152i | −0.0142817 | + | 0.0247367i | ||||
\(793\) | −11.4641 | + | 11.4641i | −0.407102 | + | 0.407102i | ||||
\(794\) | 11.3660 | − | 11.3660i | 0.403365 | − | 0.403365i | ||||
\(795\) | 21.9904 | − | 12.6962i | 0.779918 | − | 0.450286i | ||||
\(796\) | − | 4.73205i | − | 0.167723i | ||||||
\(797\) | 22.3923 | − | 22.3923i | 0.793176 | − | 0.793176i | −0.188833 | − | 0.982009i | \(-0.560471\pi\) |
0.982009 | + | 0.188833i | \(0.0604705\pi\) | |||||||
\(798\) | 11.1962 | + | 19.3923i | 0.396339 | + | 0.686480i | ||||
\(799\) | −1.21539 | −0.0429974 | ||||||||
\(800\) | −47.9090 | + | 47.9090i | −1.69384 | + | 1.69384i | ||||
\(801\) | 5.49038 | + | 20.4904i | 0.193993 | + | 0.723992i | ||||
\(802\) | 35.8827 | + | 35.8827i | 1.26706 | + | 1.26706i | ||||
\(803\) | − | 2.92820i | − | 0.103334i | ||||||
\(804\) | −13.3923 | − | 23.1962i | −0.472310 | − | 0.818065i | ||||
\(805\) | 14.9282i | 0.526150i | ||||||||
\(806\) | 9.92820i | 0.349706i | ||||||||
\(807\) | 1.26795 | − | 4.73205i | 0.0446339 | − | 0.166576i | ||||
\(808\) | 3.07180 | 0.108065 | ||||||||
\(809\) | 34.7846 | + | 34.7846i | 1.22296 | + | 1.22296i | 0.966574 | + | 0.256388i | \(0.0825324\pi\) |
0.256388 | + | 0.966574i | \(0.417468\pi\) | |||||||
\(810\) | 62.6769 | + | 16.7942i | 2.20224 | + | 0.590089i | ||||
\(811\) | − | 3.51666i | − | 0.123487i | −0.998092 | − | 0.0617433i | \(-0.980334\pi\) | ||
0.998092 | − | 0.0617433i | \(-0.0196660\pi\) | |||||||
\(812\) | 23.6603 | + | 9.46410i | 0.830312 | + | 0.332125i | ||||
\(813\) | −16.9641 | − | 4.54552i | −0.594957 | − | 0.159418i | ||||
\(814\) | 3.46410 | + | 3.46410i | 0.121417 | + | 0.121417i | ||||
\(815\) | 33.9545 | − | 33.9545i | 1.18937 | − | 1.18937i | ||||
\(816\) | −7.73205 | − | 2.07180i | −0.270676 | − | 0.0725274i | ||||
\(817\) | − | 12.3397i | − | 0.431713i | ||||||
\(818\) | −12.5885 | −0.440145 | ||||||||
\(819\) | −40.6865 | − | 23.4904i | −1.42170 | − | 0.820820i | ||||
\(820\) | 33.5885 | − | 33.5885i | 1.17296 | − | 1.17296i | ||||
\(821\) | 3.00000 | 0.104701 | 0.0523504 | − | 0.998629i | \(-0.483329\pi\) | ||||
0.0523504 | + | 0.998629i | \(0.483329\pi\) | |||||||
\(822\) | 19.3923 | − | 11.1962i | 0.676384 | − | 0.390511i | ||||
\(823\) | 25.5359 | + | 25.5359i | 0.890125 | + | 0.890125i | 0.994534 | − | 0.104409i | \(-0.0332951\pi\) |
−0.104409 | + | 0.994534i | \(0.533295\pi\) | |||||||
\(824\) | −3.92820 | − | 3.92820i | −0.136845 | − | 0.136845i | ||||
\(825\) | −7.73205 | − | 2.07180i | −0.269195 | − | 0.0721307i | ||||
\(826\) | 2.00000 | + | 2.00000i | 0.0695889 | + | 0.0695889i | ||||
\(827\) | 5.36603 | + | 5.36603i | 0.186595 | + | 0.186595i | 0.794222 | − | 0.607627i | \(-0.207879\pi\) |
−0.607627 | + | 0.794222i | \(0.707879\pi\) | |||||||
\(828\) | 3.80385 | − | 6.58846i | 0.132193 | − | 0.228965i | ||||
\(829\) | −10.1962 | − | 10.1962i | −0.354127 | − | 0.354127i | 0.507516 | − | 0.861643i | \(-0.330564\pi\) |
−0.861643 | + | 0.507516i | \(0.830564\pi\) | |||||||
\(830\) | −70.6410 | − | 70.6410i | −2.45199 | − | 2.45199i | ||||
\(831\) | 4.85641 | + | 8.41154i | 0.168467 | + | 0.291793i | ||||
\(832\) | −32.8564 | −1.13909 | ||||||||
\(833\) | −0.339746 | + | 0.339746i | −0.0117715 | + | 0.0117715i | ||||
\(834\) | 37.0526 | + | 9.92820i | 1.28303 | + | 0.343786i | ||||
\(835\) | −12.1962 | −0.422065 | ||||||||
\(836\) | 2.19615i | 0.0759555i | ||||||||
\(837\) | −3.29423 | − | 3.29423i | −0.113865 | − | 0.113865i | ||||
\(838\) | −3.19615 | + | 3.19615i | −0.110409 | + | 0.110409i | ||||
\(839\) | −14.0981 | − | 14.0981i | −0.486720 | − | 0.486720i | 0.420550 | − | 0.907269i | \(-0.361837\pi\) |
−0.907269 | + | 0.420550i | \(0.861837\pi\) | |||||||
\(840\) | −2.36603 | + | 8.83013i | −0.0816356 | + | 0.304668i | ||||
\(841\) | −21.0000 | − | 20.0000i | −0.724138 | − | 0.689655i | ||||
\(842\) | − | 16.9282i | − | 0.583384i | ||||||
\(843\) | −2.59808 | + | 1.50000i | −0.0894825 | + | 0.0516627i | ||||
\(844\) | −24.2942 | − | 24.2942i | −0.836242 | − | 0.836242i | ||||
\(845\) | −74.1051 | −2.54929 | ||||||||
\(846\) | 3.40192 | − | 5.89230i | 0.116961 | − | 0.202582i | ||||
\(847\) | − | 29.3205i | − | 1.00746i | ||||||
\(848\) | − | 17.5359i | − | 0.602185i | ||||||
\(849\) | 9.00000 | − | 5.19615i | 0.308879 | − | 0.178331i | ||||
\(850\) | − | 17.8564i | − | 0.612470i | ||||||
\(851\) | 5.07180 | + | 5.07180i | 0.173859 | + | 0.173859i | ||||
\(852\) | −43.4711 | + | 25.0981i | −1.48930 | + | 0.859846i | ||||
\(853\) | −24.8564 | + | 24.8564i | −0.851067 | + | 0.851067i | −0.990265 | − | 0.139197i | \(-0.955548\pi\) |
0.139197 | + | 0.990265i | \(0.455548\pi\) | |||||||
\(854\) | −14.9282 | −0.510833 | ||||||||
\(855\) | −26.4904 | + | 7.09808i | −0.905952 | + | 0.242749i | ||||
\(856\) | 1.92820 | − | 1.92820i | 0.0659046 | − | 0.0659046i | ||||
\(857\) | − | 32.3205i | − | 1.10405i | −0.833828 | − | 0.552024i | \(-0.813856\pi\) | ||
0.833828 | − | 0.552024i | \(-0.186144\pi\) | |||||||
\(858\) | −4.96410 | − | 8.59808i | −0.169472 | − | 0.293533i | ||||
\(859\) | −28.5429 | + | 28.5429i | −0.973873 | + | 0.973873i | −0.999667 | − | 0.0257947i | \(-0.991788\pi\) |
0.0257947 | + | 0.999667i | \(0.491788\pi\) | |||||||
\(860\) | −23.0263 | + | 23.0263i | −0.785190 | + | 0.785190i | ||||
\(861\) | 9.00000 | − | 33.5885i | 0.306719 | − | 1.14469i | ||||
\(862\) | 41.5167 | + | 41.5167i | 1.41406 | + | 1.41406i | ||||
\(863\) | 24.5885 | 0.837001 | 0.418500 | − | 0.908217i | \(-0.362556\pi\) | ||||
0.418500 | + | 0.908217i | \(0.362556\pi\) | |||||||
\(864\) | 27.8827 | − | 27.8827i | 0.948588 | − | 0.948588i | ||||
\(865\) | 50.2487 | 1.70851 | ||||||||
\(866\) | 14.9282i | 0.507281i | ||||||||
\(867\) | −23.8923 | + | 13.7942i | −0.811425 | + | 0.468477i | ||||
\(868\) | −3.00000 | + | 3.00000i | −0.101827 | + | 0.101827i | ||||
\(869\) | −1.33975 | −0.0454478 | ||||||||
\(870\) | −40.2846 | + | 53.8468i | −1.36578 | + | 1.82558i | ||||
\(871\) | −51.1769 | −1.73406 | ||||||||
\(872\) | −2.56218 | + | 2.56218i | −0.0867663 | + | 0.0867663i | ||||
\(873\) | −8.49038 | − | 31.6865i | −0.287356 | − | 1.07243i | ||||
\(874\) | 6.92820i | 0.234350i | ||||||||
\(875\) | −40.0526 | −1.35402 | ||||||||
\(876\) | −4.39230 | + | 16.3923i | −0.148402 | + | 0.553845i | ||||
\(877\) | 22.2679 | 0.751935 | 0.375968 | − | 0.926633i | \(-0.377310\pi\) | ||||
0.375968 | + | 0.926633i | \(0.377310\pi\) | |||||||
\(878\) | 35.8564 | + | 35.8564i | 1.21010 | + | 1.21010i | ||||
\(879\) | 38.1506 | + | 10.2224i | 1.28679 | + | 0.344794i | ||||
\(880\) | −6.09808 | + | 6.09808i | −0.205566 | + | 0.205566i | ||||
\(881\) | −21.7321 | + | 21.7321i | −0.732171 | + | 0.732171i | −0.971050 | − | 0.238878i | \(-0.923220\pi\) |
0.238878 | + | 0.971050i | \(0.423220\pi\) | |||||||
\(882\) | −0.696152 | − | 2.59808i | −0.0234407 | − | 0.0874818i | ||||
\(883\) | 33.1244i | 1.11472i | 0.830270 | + | 0.557362i | \(0.188186\pi\) | ||||
−0.830270 | + | 0.557362i | \(0.811814\pi\) | |||||||
\(884\) | 7.26795 | − | 7.26795i | 0.244448 | − | 0.244448i | ||||
\(885\) | −3.00000 | + | 1.73205i | −0.100844 | + | 0.0582223i | ||||
\(886\) | −48.9808 | −1.64554 | ||||||||
\(887\) | −21.4904 | + | 21.4904i | −0.721576 | + | 0.721576i | −0.968926 | − | 0.247350i | \(-0.920440\pi\) |
0.247350 | + | 0.968926i | \(0.420440\pi\) | |||||||
\(888\) | 2.19615 | + | 3.80385i | 0.0736980 | + | 0.127649i | ||||
\(889\) | −24.5885 | − | 24.5885i | −0.824670 | − | 0.824670i | ||||
\(890\) | 50.9808i | 1.70888i | ||||||||
\(891\) | 4.50000 | + | 1.20577i | 0.150756 | + | 0.0403949i | ||||
\(892\) | − | 1.26795i | − | 0.0424541i | ||||||
\(893\) | 2.87564i | 0.0962298i | ||||||||
\(894\) | −37.2846 | − | 9.99038i | −1.24698 | − | 0.334128i | ||||
\(895\) | 61.9090 | 2.06939 | ||||||||
\(896\) | 7.92820 | + | 7.92820i | 0.264863 | + | 0.264863i | ||||
\(897\) | −7.26795 | − | 12.5885i | −0.242670 | − | 0.420316i | ||||
\(898\) | 2.33975i | 0.0780783i | ||||||||
\(899\) | 4.43782 | − | 1.90192i | 0.148010 | − | 0.0634327i | ||||
\(900\) | 40.1769 | + | 23.1962i | 1.33923 | + | 0.773205i | ||||
\(901\) | 2.87564 | + | 2.87564i | 0.0958016 | + | 0.0958016i | ||||
\(902\) | 5.19615 | − | 5.19615i | 0.173013 | − | 0.173013i | ||||
\(903\) | −6.16987 | + | 23.0263i | −0.205321 | + | 0.766267i | ||||
\(904\) | 4.33975i | 0.144338i | ||||||||
\(905\) | 60.9090 | 2.02468 | ||||||||
\(906\) | 4.90192 | − | 18.2942i | 0.162856 | − | 0.607785i | ||||
\(907\) | 5.92820 | − | 5.92820i | 0.196843 | − | 0.196843i | −0.601802 | − | 0.798645i | \(-0.705550\pi\) |
0.798645 | + | 0.601802i | \(0.205550\pi\) | |||||||
\(908\) | −15.8038 | −0.524469 | ||||||||
\(909\) | −4.60770 | − | 17.1962i | −0.152828 | − | 0.570360i | ||||
\(910\) | −79.8372 | − | 79.8372i | −2.64658 | − | 2.64658i | ||||
\(911\) | 22.0788 | + | 22.0788i | 0.731505 | + | 0.731505i | 0.970918 | − | 0.239413i | \(-0.0769551\pi\) |
−0.239413 | + | 0.970918i | \(0.576955\pi\) | |||||||
\(912\) | −4.90192 | + | 18.2942i | −0.162319 | + | 0.605782i | ||||
\(913\) | −5.07180 | − | 5.07180i | −0.167852 | − | 0.167852i | ||||
\(914\) | −38.5885 | − | 38.5885i | −1.27639 | − | 1.27639i | ||||
\(915\) | 4.73205 | − | 17.6603i | 0.156437 | − | 0.583830i | ||||
\(916\) | 35.1962 | + | 35.1962i | 1.16291 | + | 1.16291i | ||||
\(917\) | 31.1244 | + | 31.1244i | 1.02782 | + | 1.02782i | ||||
\(918\) | 10.3923i | 0.342997i | ||||||||
\(919\) | −42.4449 | −1.40013 | −0.700063 | − | 0.714081i | \(-0.746845\pi\) | ||||
−0.700063 | + | 0.714081i | \(0.746845\pi\) | |||||||
\(920\) | −2.00000 | + | 2.00000i | −0.0659380 | + | 0.0659380i | ||||
\(921\) | −1.57884 | + | 5.89230i | −0.0520245 | + | 0.194158i | ||||
\(922\) | 46.0526 | 1.51666 | ||||||||
\(923\) | 95.9090i | 3.15688i | ||||||||
\(924\) | 1.09808 | − | 4.09808i | 0.0361241 | − | 0.134817i | ||||
\(925\) | −30.9282 | + | 30.9282i | −1.01691 | + | 1.01691i | ||||
\(926\) | 30.0526 | + | 30.0526i | 0.987588 | + | 0.987588i | ||||
\(927\) | −16.0981 | + | 27.8827i | −0.528730 | + | 0.915788i | ||||
\(928\) | 16.0981 | + | 37.5622i | 0.528445 | + | 1.23304i | ||||
\(929\) | 34.2487i | 1.12366i | 0.827251 | + | 0.561832i | \(0.189903\pi\) | ||||
−0.827251 | + | 0.561832i | \(0.810097\pi\) | |||||||
\(930\) | −5.59808 | − | 9.69615i | −0.183568 | − | 0.317949i | ||||
\(931\) | 0.803848 | + | 0.803848i | 0.0263450 | + | 0.0263450i | ||||
\(932\) | 34.8564 | 1.14176 | ||||||||
\(933\) | 38.9545 | + | 10.4378i | 1.27531 | + | 0.341719i | ||||
\(934\) | 13.3923i | 0.438210i | ||||||||
\(935\) | − | 2.00000i | − | 0.0654070i | ||||||
\(936\) | −2.30385 | − | 8.59808i | −0.0753036 | − | 0.281037i | ||||
\(937\) | − | 54.1051i | − | 1.76754i | −0.467924 | − | 0.883769i | \(-0.654998\pi\) | ||
0.467924 | − | 0.883769i | \(-0.345002\pi\) | |||||||
\(938\) | −33.3205 | − | 33.3205i | −1.08795 | − | 1.08795i | ||||
\(939\) | 6.57180 | + | 11.3827i | 0.214462 | + | 0.371460i | ||||
\(940\) | 5.36603 | − | 5.36603i | 0.175020 | − | 0.175020i | ||||
\(941\) | −26.8038 | −0.873780 | −0.436890 | − | 0.899515i | \(-0.643920\pi\) | ||||
−0.436890 | + | 0.899515i | \(0.643920\pi\) | |||||||
\(942\) | −22.6865 | + | 13.0981i | −0.739167 | + | 0.426758i | ||||
\(943\) | 7.60770 | − | 7.60770i | 0.247741 | − | 0.247741i | ||||
\(944\) | 2.39230i | 0.0778629i | ||||||||
\(945\) | 52.9808 | 1.72346 | ||||||||
\(946\) | −3.56218 | + | 3.56218i | −0.115816 | + | 0.115816i | ||||
\(947\) | 21.0981 | − | 21.0981i | 0.685595 | − | 0.685595i | −0.275660 | − | 0.961255i | \(-0.588896\pi\) |
0.961255 | + | 0.275660i | \(0.0888963\pi\) | |||||||
\(948\) | 7.50000 | + | 2.00962i | 0.243589 | + | 0.0652694i | ||||
\(949\) | 22.9282 | + | 22.9282i | 0.744281 | + | 0.744281i | ||||
\(950\) | −42.2487 | −1.37073 | ||||||||
\(951\) | −11.6603 | + | 43.5167i | −0.378110 | + | 1.41112i | ||||
\(952\) | −1.46410 | −0.0474518 | ||||||||
\(953\) | − | 7.58846i | − | 0.245814i | −0.992418 | − | 0.122907i | \(-0.960778\pi\) | ||
0.992418 | − | 0.122907i | \(-0.0392217\pi\) | |||||||
\(954\) | −21.9904 | + | 5.89230i | −0.711965 | + | 0.190770i | ||||
\(955\) | 59.4449 | − | 59.4449i | 1.92359 | − | 1.92359i | ||||
\(956\) | 10.3923 | 0.336111 | ||||||||
\(957\) | −2.89230 | + | 3.86603i | −0.0934949 | + | 0.124971i | ||||
\(958\) | 7.92820 | 0.256149 | ||||||||
\(959\) | 12.9282 | − | 12.9282i | 0.417473 | − | 0.417473i | ||||
\(960\) | 32.0885 | − | 18.5263i | 1.03565 | − | 0.597933i | ||||
\(961\) | − | 30.1962i | − | 0.974069i | ||||||
\(962\) | −54.2487 | −1.74905 | ||||||||
\(963\) | −13.6865 | − | 7.90192i | −0.441042 | − | 0.254636i | ||||
\(964\) | 23.4449 | 0.755108 | ||||||||
\(965\) | −37.0526 | − | 37.0526i | −1.19276 | − | 1.19276i | ||||
\(966\) | 3.46410 | − | 12.9282i | 0.111456 | − | 0.415958i | ||||
\(967\) | 12.1699 | − | 12.1699i | 0.391357 | − | 0.391357i | −0.483814 | − | 0.875171i | \(-0.660749\pi\) |
0.875171 | + | 0.483814i | \(0.160749\pi\) | |||||||
\(968\) | 3.92820 | − | 3.92820i | 0.126257 | − | 0.126257i | ||||
\(969\) | −2.19615 | − | 3.80385i | −0.0705506 | − | 0.122197i | ||||
\(970\) | − | 78.8372i | − | 2.53131i | ||||||
\(971\) | −25.7846 | + | 25.7846i | −0.827468 | + | 0.827468i | −0.987166 | − | 0.159698i | \(-0.948948\pi\) |
0.159698 | + | 0.987166i | \(0.448948\pi\) | |||||||
\(972\) | −23.3827 | − | 13.5000i | −0.750000 | − | 0.433013i | ||||
\(973\) | 31.3205 | 1.00409 | ||||||||
\(974\) | 44.3205 | − | 44.3205i | 1.42012 | − | 1.42012i | ||||
\(975\) | 76.7654 | − | 44.3205i | 2.45846 | − | 1.41939i | ||||
\(976\) | −8.92820 | − | 8.92820i | −0.285785 | − | 0.285785i | ||||
\(977\) | 21.0000i | 0.671850i | 0.941889 | + | 0.335925i | \(0.109049\pi\) | ||||
−0.941889 | + | 0.335925i | \(0.890951\pi\) | |||||||
\(978\) | −37.2846 | + | 21.5263i | −1.19223 | + | 0.688335i | ||||
\(979\) | 3.66025i | 0.116982i | ||||||||
\(980\) | − | 3.00000i | − | 0.0958315i | ||||||
\(981\) | 18.1865 | + | 10.5000i | 0.580651 | + | 0.335239i | ||||
\(982\) | 78.0333 | 2.49014 | ||||||||
\(983\) | −34.6865 | − | 34.6865i | −1.10633 | − | 1.10633i | −0.993629 | − | 0.112699i | \(-0.964050\pi\) |
−0.112699 | − | 0.993629i | \(-0.535950\pi\) | |||||||
\(984\) | 5.70577 | − | 3.29423i | 0.181893 | − | 0.105016i | ||||
\(985\) | 93.0333i | 2.96429i | ||||||||
\(986\) | −10.0000 | − | 4.00000i | −0.318465 | − | 0.127386i | ||||
\(987\) | 1.43782 | − | 5.36603i | 0.0457664 | − | 0.170802i | ||||
\(988\) | −17.1962 | − | 17.1962i | −0.547082 | − | 0.547082i | ||||
\(989\) | −5.21539 | + | 5.21539i | −0.165840 | + | 0.165840i | ||||
\(990\) | 9.69615 | + | 5.59808i | 0.308164 | + | 0.177919i | ||||
\(991\) | − | 29.8038i | − | 0.946750i | −0.880861 | − | 0.473375i | \(-0.843035\pi\) | ||
0.880861 | − | 0.473375i | \(-0.156965\pi\) | |||||||
\(992\) | −6.80385 | −0.216022 | ||||||||
\(993\) | −5.59808 | − | 1.50000i | −0.177650 | − | 0.0476011i | ||||
\(994\) | −62.4449 | + | 62.4449i | −1.98063 | + | 1.98063i | ||||
\(995\) | 10.1962 | 0.323240 | ||||||||
\(996\) | 20.7846 | + | 36.0000i | 0.658586 | + | 1.14070i | ||||
\(997\) | −18.9282 | − | 18.9282i | −0.599462 | − | 0.599462i | 0.340707 | − | 0.940169i | \(-0.389334\pi\) |
−0.940169 | + | 0.340707i | \(0.889334\pi\) | |||||||
\(998\) | −52.7846 | − | 52.7846i | −1.67087 | − | 1.67087i | ||||
\(999\) | 18.0000 | − | 18.0000i | 0.569495 | − | 0.569495i |
(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 | 87.2.f.a.41.1 | yes | 4 | |
3.2 | odd | 2 | 87.2.f.b.41.2 | yes | 4 | ||
29.17 | odd | 4 | 87.2.f.b.17.2 | yes | 4 | ||
87.17 | even | 4 | inner | 87.2.f.a.17.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
87.2.f.a.17.1 | ✓ | 4 | 87.17 | even | 4 | inner | |
87.2.f.a.41.1 | yes | 4 | 1.1 | even | 1 | trivial | |
87.2.f.b.17.2 | yes | 4 | 29.17 | odd | 4 | ||
87.2.f.b.41.2 | yes | 4 | 3.2 | odd | 2 |