Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(573,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.573");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.l (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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 573.10 | ||
Character | \(\chi\) | \(=\) | 770.573 |
Dual form | 770.2.l.c.727.10 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 2.03841 | − | 2.03841i | 1.17688 | − | 1.17688i | 0.196342 | − | 0.980535i | \(-0.437094\pi\) |
0.980535 | − | 0.196342i | \(-0.0629064\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.07139 | − | 0.842227i | 0.926354 | − | 0.376655i | ||||
\(6\) | 2.88275i | 1.17688i | ||||||||
\(7\) | 0.703324 | + | 2.55056i | 0.265832 | + | 0.964019i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | − | 5.31025i | − | 1.77008i | ||||||
\(10\) | −0.869149 | + | 2.06024i | −0.274849 | + | 0.651504i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −2.03841 | − | 2.03841i | −0.588439 | − | 0.588439i | ||||
\(13\) | 3.99211 | − | 3.99211i | 1.10721 | − | 1.10721i | 0.113697 | − | 0.993515i | \(-0.463731\pi\) |
0.993515 | − | 0.113697i | \(-0.0362694\pi\) | |||||||
\(14\) | −2.30084 | − | 1.30619i | −0.614926 | − | 0.349094i | ||||
\(15\) | 2.50554 | − | 5.93915i | 0.646928 | − | 1.53348i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.39509 | + | 3.39509i | 0.823431 | + | 0.823431i | 0.986598 | − | 0.163167i | \(-0.0521710\pi\) |
−0.163167 | + | 0.986598i | \(0.552171\pi\) | |||||||
\(18\) | 3.75491 | + | 3.75491i | 0.885041 | + | 0.885041i | ||||
\(19\) | −4.95398 | −1.13652 | −0.568260 | − | 0.822849i | \(-0.692383\pi\) | ||||
−0.568260 | + | 0.822849i | \(0.692383\pi\) | |||||||
\(20\) | −0.842227 | − | 2.07139i | −0.188328 | − | 0.463177i | ||||
\(21\) | 6.63275 | + | 3.76542i | 1.44738 | + | 0.821682i | ||||
\(22\) | 0.707107 | − | 0.707107i | 0.150756 | − | 0.150756i | ||||
\(23\) | −2.50907 | − | 2.50907i | −0.523177 | − | 0.523177i | 0.395353 | − | 0.918529i | \(-0.370622\pi\) |
−0.918529 | + | 0.395353i | \(0.870622\pi\) | |||||||
\(24\) | 2.88275 | 0.588439 | ||||||||
\(25\) | 3.58131 | − | 3.48916i | 0.716262 | − | 0.697832i | ||||
\(26\) | 5.64570i | 1.10721i | ||||||||
\(27\) | −4.70924 | − | 4.70924i | −0.906293 | − | 0.906293i | ||||
\(28\) | 2.55056 | − | 0.703324i | 0.482010 | − | 0.132916i | ||||
\(29\) | 7.25017i | 1.34632i | 0.739495 | + | 0.673162i | \(0.235064\pi\) | ||||
−0.739495 | + | 0.673162i | \(0.764936\pi\) | |||||||
\(30\) | 2.42793 | + | 5.97130i | 0.443277 | + | 1.09020i | ||||
\(31\) | 3.87087i | 0.695229i | 0.937637 | + | 0.347615i | \(0.113008\pi\) | ||||
−0.937637 | + | 0.347615i | \(0.886992\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −2.03841 | + | 2.03841i | −0.354842 | + | 0.354842i | ||||
\(34\) | −4.80139 | −0.823431 | ||||||||
\(35\) | 3.60500 | + | 4.69084i | 0.609357 | + | 0.792896i | ||||
\(36\) | −5.31025 | −0.885041 | ||||||||
\(37\) | −2.92514 | + | 2.92514i | −0.480889 | + | 0.480889i | −0.905416 | − | 0.424526i | \(-0.860441\pi\) |
0.424526 | + | 0.905416i | \(0.360441\pi\) | |||||||
\(38\) | 3.50299 | − | 3.50299i | 0.568260 | − | 0.568260i | ||||
\(39\) | − | 16.2751i | − | 2.60611i | ||||||
\(40\) | 2.06024 | + | 0.869149i | 0.325752 | + | 0.137425i | ||||
\(41\) | − | 4.22571i | − | 0.659945i | −0.943990 | − | 0.329973i | \(-0.892960\pi\) | ||
0.943990 | − | 0.329973i | \(-0.107040\pi\) | |||||||
\(42\) | −7.35261 | + | 2.02751i | −1.13453 | + | 0.312851i | ||||
\(43\) | 1.04912 | + | 1.04912i | 0.159989 | + | 0.159989i | 0.782562 | − | 0.622573i | \(-0.213912\pi\) |
−0.622573 | + | 0.782562i | \(0.713912\pi\) | |||||||
\(44\) | 1.00000i | 0.150756i | ||||||||
\(45\) | −4.47243 | − | 10.9996i | −0.666711 | − | 1.63972i | ||||
\(46\) | 3.54836 | 0.523177 | ||||||||
\(47\) | −6.21956 | − | 6.21956i | −0.907216 | − | 0.907216i | 0.0888309 | − | 0.996047i | \(-0.471687\pi\) |
−0.996047 | + | 0.0888309i | \(0.971687\pi\) | |||||||
\(48\) | −2.03841 | + | 2.03841i | −0.294219 | + | 0.294219i | ||||
\(49\) | −6.01067 | + | 3.58774i | −0.858667 | + | 0.512534i | ||||
\(50\) | −0.0651599 | + | 4.99958i | −0.00921500 | + | 0.707047i | ||||
\(51\) | 13.8412 | 1.93816 | ||||||||
\(52\) | −3.99211 | − | 3.99211i | −0.553606 | − | 0.553606i | ||||
\(53\) | −0.793267 | − | 0.793267i | −0.108964 | − | 0.108964i | 0.650523 | − | 0.759487i | \(-0.274550\pi\) |
−0.759487 | + | 0.650523i | \(0.774550\pi\) | |||||||
\(54\) | 6.65986 | 0.906293 | ||||||||
\(55\) | −2.07139 | + | 0.842227i | −0.279306 | + | 0.113566i | ||||
\(56\) | −1.30619 | + | 2.30084i | −0.174547 | + | 0.307463i | ||||
\(57\) | −10.0982 | + | 10.0982i | −1.33755 | + | 1.33755i | ||||
\(58\) | −5.12665 | − | 5.12665i | −0.673162 | − | 0.673162i | ||||
\(59\) | 8.39914 | 1.09348 | 0.546738 | − | 0.837304i | \(-0.315870\pi\) | ||||
0.546738 | + | 0.837304i | \(0.315870\pi\) | |||||||
\(60\) | −5.93915 | − | 2.50554i | −0.766741 | − | 0.323464i | ||||
\(61\) | − | 12.9348i | − | 1.65613i | −0.560634 | − | 0.828063i | \(-0.689443\pi\) | ||
0.560634 | − | 0.828063i | \(-0.310557\pi\) | |||||||
\(62\) | −2.73712 | − | 2.73712i | −0.347615 | − | 0.347615i | ||||
\(63\) | 13.5441 | − | 3.73483i | 1.70639 | − | 0.470544i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 4.90696 | − | 11.6315i | 0.608633 | − | 1.44271i | ||||
\(66\) | − | 2.88275i | − | 0.354842i | ||||||
\(67\) | 3.04387 | − | 3.04387i | 0.371868 | − | 0.371868i | −0.496289 | − | 0.868157i | \(-0.665304\pi\) |
0.868157 | + | 0.496289i | \(0.165304\pi\) | |||||||
\(68\) | 3.39509 | − | 3.39509i | 0.411716 | − | 0.411716i | ||||
\(69\) | −10.2290 | −1.23143 | ||||||||
\(70\) | −5.86605 | − | 0.767799i | −0.701126 | − | 0.0917695i | ||||
\(71\) | −9.47305 | −1.12424 | −0.562122 | − | 0.827054i | \(-0.690015\pi\) | ||||
−0.562122 | + | 0.827054i | \(0.690015\pi\) | |||||||
\(72\) | 3.75491 | − | 3.75491i | 0.442521 | − | 0.442521i | ||||
\(73\) | −8.93324 | + | 8.93324i | −1.04556 | + | 1.04556i | −0.0466449 | + | 0.998912i | \(0.514853\pi\) |
−0.998912 | + | 0.0466449i | \(0.985147\pi\) | |||||||
\(74\) | − | 4.13677i | − | 0.480889i | ||||||
\(75\) | 0.187840 | − | 14.4125i | 0.0216899 | − | 1.66422i | ||||
\(76\) | 4.95398i | 0.568260i | ||||||||
\(77\) | −0.703324 | − | 2.55056i | −0.0801512 | − | 0.290663i | ||||
\(78\) | 11.5083 | + | 11.5083i | 1.30305 | + | 1.30305i | ||||
\(79\) | − | 4.65746i | − | 0.524005i | −0.965067 | − | 0.262002i | \(-0.915617\pi\) | ||
0.965067 | − | 0.262002i | \(-0.0843829\pi\) | |||||||
\(80\) | −2.07139 | + | 0.842227i | −0.231588 | + | 0.0941638i | ||||
\(81\) | −3.26798 | −0.363109 | ||||||||
\(82\) | 2.98803 | + | 2.98803i | 0.329973 | + | 0.329973i | ||||
\(83\) | −10.6779 | + | 10.6779i | −1.17205 | + | 1.17205i | −0.190326 | + | 0.981721i | \(0.560954\pi\) |
−0.981721 | + | 0.190326i | \(0.939046\pi\) | |||||||
\(84\) | 3.76542 | − | 6.63275i | 0.410841 | − | 0.723692i | ||||
\(85\) | 9.89200 | + | 4.17312i | 1.07294 | + | 0.452639i | ||||
\(86\) | −1.48368 | −0.159989 | ||||||||
\(87\) | 14.7788 | + | 14.7788i | 1.58446 | + | 1.58446i | ||||
\(88\) | −0.707107 | − | 0.707107i | −0.0753778 | − | 0.0753778i | ||||
\(89\) | 16.0121 | 1.69727 | 0.848637 | − | 0.528975i | \(-0.177424\pi\) | ||||
0.848637 | + | 0.528975i | \(0.177424\pi\) | |||||||
\(90\) | 10.9404 | + | 4.61540i | 1.15322 | + | 0.486506i | ||||
\(91\) | 12.9899 | + | 7.37436i | 1.36171 | + | 0.773043i | ||||
\(92\) | −2.50907 | + | 2.50907i | −0.261588 | + | 0.261588i | ||||
\(93\) | 7.89044 | + | 7.89044i | 0.818200 | + | 0.818200i | ||||
\(94\) | 8.79578 | 0.907216 | ||||||||
\(95\) | −10.2616 | + | 4.17237i | −1.05282 | + | 0.428076i | ||||
\(96\) | − | 2.88275i | − | 0.294219i | ||||||
\(97\) | −5.64356 | − | 5.64356i | −0.573017 | − | 0.573017i | 0.359954 | − | 0.932970i | \(-0.382792\pi\) |
−0.932970 | + | 0.359954i | \(0.882792\pi\) | |||||||
\(98\) | 1.71327 | − | 6.78710i | 0.173067 | − | 0.685600i | ||||
\(99\) | 5.31025i | 0.533700i | ||||||||
\(100\) | −3.48916 | − | 3.58131i | −0.348916 | − | 0.358131i | ||||
\(101\) | 11.6120i | 1.15544i | 0.816236 | + | 0.577718i | \(0.196057\pi\) | ||||
−0.816236 | + | 0.577718i | \(0.803943\pi\) | |||||||
\(102\) | −9.78720 | + | 9.78720i | −0.969078 | + | 0.969078i | ||||
\(103\) | −9.90062 | + | 9.90062i | −0.975537 | + | 0.975537i | −0.999708 | − | 0.0241711i | \(-0.992305\pi\) |
0.0241711 | + | 0.999708i | \(0.492305\pi\) | |||||||
\(104\) | 5.64570 | 0.553606 | ||||||||
\(105\) | 16.9103 | + | 2.21337i | 1.65028 | + | 0.216003i | ||||
\(106\) | 1.12185 | 0.108964 | ||||||||
\(107\) | −2.83307 | + | 2.83307i | −0.273884 | + | 0.273884i | −0.830661 | − | 0.556778i | \(-0.812037\pi\) |
0.556778 | + | 0.830661i | \(0.312037\pi\) | |||||||
\(108\) | −4.70924 | + | 4.70924i | −0.453146 | + | 0.453146i | ||||
\(109\) | − | 9.33658i | − | 0.894282i | −0.894463 | − | 0.447141i | \(-0.852442\pi\) | ||
0.894463 | − | 0.447141i | \(-0.147558\pi\) | |||||||
\(110\) | 0.869149 | − | 2.06024i | 0.0828701 | − | 0.196436i | ||||
\(111\) | 11.9253i | 1.13190i | ||||||||
\(112\) | −0.703324 | − | 2.55056i | −0.0664579 | − | 0.241005i | ||||
\(113\) | 9.75494 | + | 9.75494i | 0.917667 | + | 0.917667i | 0.996859 | − | 0.0791920i | \(-0.0252340\pi\) |
−0.0791920 | + | 0.996859i | \(0.525234\pi\) | |||||||
\(114\) | − | 14.2811i | − | 1.33755i | ||||||
\(115\) | −7.31046 | − | 3.08405i | −0.681704 | − | 0.287589i | ||||
\(116\) | 7.25017 | 0.673162 | ||||||||
\(117\) | −21.1991 | − | 21.1991i | −1.95986 | − | 1.95986i | ||||
\(118\) | −5.93909 | + | 5.93909i | −0.546738 | + | 0.546738i | ||||
\(119\) | −6.27152 | + | 11.0472i | −0.574910 | + | 1.01270i | ||||
\(120\) | 5.97130 | − | 2.42793i | 0.545102 | − | 0.221639i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 9.14626 | + | 9.14626i | 0.828063 | + | 0.828063i | ||||
\(123\) | −8.61374 | − | 8.61374i | −0.776675 | − | 0.776675i | ||||
\(124\) | 3.87087 | 0.347615 | ||||||||
\(125\) | 4.47962 | − | 10.2437i | 0.400670 | − | 0.916223i | ||||
\(126\) | −6.93619 | + | 12.2180i | −0.617925 | + | 1.08847i | ||||
\(127\) | 11.3283 | − | 11.3283i | 1.00523 | − | 1.00523i | 0.00524084 | − | 0.999986i | \(-0.498332\pi\) |
0.999986 | − | 0.00524084i | \(-0.00166822\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 4.27708 | 0.376576 | ||||||||
\(130\) | 4.75496 | + | 11.6944i | 0.417037 | + | 1.02567i | ||||
\(131\) | 20.7934i | 1.81673i | 0.418178 | + | 0.908365i | \(0.362669\pi\) | ||||
−0.418178 | + | 0.908365i | \(0.637331\pi\) | |||||||
\(132\) | 2.03841 | + | 2.03841i | 0.177421 | + | 0.177421i | ||||
\(133\) | −3.48425 | − | 12.6354i | −0.302123 | − | 1.09563i | ||||
\(134\) | 4.30469i | 0.371868i | ||||||||
\(135\) | −13.7209 | − | 5.78842i | −1.18091 | − | 0.498188i | ||||
\(136\) | 4.80139i | 0.411716i | ||||||||
\(137\) | −1.11354 | + | 1.11354i | −0.0951365 | + | 0.0951365i | −0.753073 | − | 0.657937i | \(-0.771429\pi\) |
0.657937 | + | 0.753073i | \(0.271429\pi\) | |||||||
\(138\) | 7.23301 | − | 7.23301i | 0.615715 | − | 0.615715i | ||||
\(139\) | −3.80609 | −0.322828 | −0.161414 | − | 0.986887i | \(-0.551605\pi\) | ||||
−0.161414 | + | 0.986887i | \(0.551605\pi\) | |||||||
\(140\) | 4.69084 | − | 3.60500i | 0.396448 | − | 0.304678i | ||||
\(141\) | −25.3560 | −2.13536 | ||||||||
\(142\) | 6.69846 | − | 6.69846i | 0.562122 | − | 0.562122i | ||||
\(143\) | −3.99211 | + | 3.99211i | −0.333837 | + | 0.333837i | ||||
\(144\) | 5.31025i | 0.442521i | ||||||||
\(145\) | 6.10629 | + | 15.0179i | 0.507100 | + | 1.24717i | ||||
\(146\) | − | 12.6335i | − | 1.04556i | ||||||
\(147\) | −4.93894 | + | 19.5655i | −0.407357 | + | 1.61374i | ||||
\(148\) | 2.92514 | + | 2.92514i | 0.240445 | + | 0.240445i | ||||
\(149\) | 3.56176i | 0.291791i | 0.989300 | + | 0.145895i | \(0.0466063\pi\) | ||||
−0.989300 | + | 0.145895i | \(0.953394\pi\) | |||||||
\(150\) | 10.0584 | + | 10.3240i | 0.821263 | + | 0.842952i | ||||
\(151\) | 8.31210 | 0.676429 | 0.338215 | − | 0.941069i | \(-0.390177\pi\) | ||||
0.338215 | + | 0.941069i | \(0.390177\pi\) | |||||||
\(152\) | −3.50299 | − | 3.50299i | −0.284130 | − | 0.284130i | ||||
\(153\) | 18.0288 | − | 18.0288i | 1.45754 | − | 1.45754i | ||||
\(154\) | 2.30084 | + | 1.30619i | 0.185407 | + | 0.105256i | ||||
\(155\) | 3.26015 | + | 8.01809i | 0.261862 | + | 0.644028i | ||||
\(156\) | −16.2751 | −1.30305 | ||||||||
\(157\) | 2.81649 | + | 2.81649i | 0.224781 | + | 0.224781i | 0.810508 | − | 0.585727i | \(-0.199191\pi\) |
−0.585727 | + | 0.810508i | \(0.699191\pi\) | |||||||
\(158\) | 3.29332 | + | 3.29332i | 0.262002 | + | 0.262002i | ||||
\(159\) | −3.23401 | −0.256474 | ||||||||
\(160\) | 0.869149 | − | 2.06024i | 0.0687123 | − | 0.162876i | ||||
\(161\) | 4.63483 | − | 8.16420i | 0.365276 | − | 0.643429i | ||||
\(162\) | 2.31081 | − | 2.31081i | 0.181555 | − | 0.181555i | ||||
\(163\) | −15.1063 | − | 15.1063i | −1.18322 | − | 1.18322i | −0.978905 | − | 0.204314i | \(-0.934504\pi\) |
−0.204314 | − | 0.978905i | \(-0.565496\pi\) | |||||||
\(164\) | −4.22571 | −0.329973 | ||||||||
\(165\) | −2.50554 | + | 5.93915i | −0.195056 | + | 0.462362i | ||||
\(166\) | − | 15.1008i | − | 1.17205i | ||||||
\(167\) | 2.40075 | + | 2.40075i | 0.185776 | + | 0.185776i | 0.793867 | − | 0.608091i | \(-0.208065\pi\) |
−0.608091 | + | 0.793867i | \(0.708065\pi\) | |||||||
\(168\) | 2.02751 | + | 7.35261i | 0.156426 | + | 0.567267i | ||||
\(169\) | − | 18.8739i | − | 1.45184i | ||||||
\(170\) | −9.94554 | + | 4.04386i | −0.762788 | + | 0.310150i | ||||
\(171\) | 26.3068i | 2.01173i | ||||||||
\(172\) | 1.04912 | − | 1.04912i | 0.0799947 | − | 0.0799947i | ||||
\(173\) | −4.15568 | + | 4.15568i | −0.315950 | + | 0.315950i | −0.847209 | − | 0.531259i | \(-0.821719\pi\) |
0.531259 | + | 0.847209i | \(0.321719\pi\) | |||||||
\(174\) | −20.9004 | −1.58446 | ||||||||
\(175\) | 11.4181 | + | 6.68032i | 0.863128 | + | 0.504985i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 17.1209 | − | 17.1209i | 1.28689 | − | 1.28689i | ||||
\(178\) | −11.3222 | + | 11.3222i | −0.848637 | + | 0.848637i | ||||
\(179\) | 6.60014i | 0.493318i | 0.969102 | + | 0.246659i | \(0.0793327\pi\) | ||||
−0.969102 | + | 0.246659i | \(0.920667\pi\) | |||||||
\(180\) | −10.9996 | + | 4.47243i | −0.819861 | + | 0.333355i | ||||
\(181\) | 14.4577i | 1.07463i | 0.843381 | + | 0.537315i | \(0.180562\pi\) | ||||
−0.843381 | + | 0.537315i | \(0.819438\pi\) | |||||||
\(182\) | −14.3997 | + | 3.97076i | −1.06737 | + | 0.294332i | ||||
\(183\) | −26.3664 | − | 26.3664i | −1.94906 | − | 1.94906i | ||||
\(184\) | − | 3.54836i | − | 0.261588i | ||||||
\(185\) | −3.59547 | + | 8.52272i | −0.264344 | + | 0.626603i | ||||
\(186\) | −11.1588 | −0.818200 | ||||||||
\(187\) | −3.39509 | − | 3.39509i | −0.248274 | − | 0.248274i | ||||
\(188\) | −6.21956 | + | 6.21956i | −0.453608 | + | 0.453608i | ||||
\(189\) | 8.69905 | − | 15.3233i | 0.632763 | − | 1.11461i | ||||
\(190\) | 4.30575 | − | 10.2064i | 0.312372 | − | 0.740448i | ||||
\(191\) | −10.1657 | −0.735567 | −0.367783 | − | 0.929912i | \(-0.619883\pi\) | ||||
−0.367783 | + | 0.929912i | \(0.619883\pi\) | |||||||
\(192\) | 2.03841 | + | 2.03841i | 0.147110 | + | 0.147110i | ||||
\(193\) | −7.16762 | − | 7.16762i | −0.515937 | − | 0.515937i | 0.400403 | − | 0.916339i | \(-0.368870\pi\) |
−0.916339 | + | 0.400403i | \(0.868870\pi\) | |||||||
\(194\) | 7.98120 | 0.573017 | ||||||||
\(195\) | −13.7074 | − | 33.7122i | −0.981604 | − | 2.41418i | ||||
\(196\) | 3.58774 | + | 6.01067i | 0.256267 | + | 0.429334i | ||||
\(197\) | −12.8091 | + | 12.8091i | −0.912608 | + | 0.912608i | −0.996477 | − | 0.0838687i | \(-0.973272\pi\) |
0.0838687 | + | 0.996477i | \(0.473272\pi\) | |||||||
\(198\) | −3.75491 | − | 3.75491i | −0.266850 | − | 0.266850i | ||||
\(199\) | 10.6361 | 0.753972 | 0.376986 | − | 0.926219i | \(-0.376961\pi\) | ||||
0.376986 | + | 0.926219i | \(0.376961\pi\) | |||||||
\(200\) | 4.99958 | + | 0.0651599i | 0.353523 | + | 0.00460750i | ||||
\(201\) | − | 12.4093i | − | 0.875287i | ||||||
\(202\) | −8.21092 | − | 8.21092i | −0.577718 | − | 0.577718i | ||||
\(203\) | −18.4920 | + | 5.09922i | −1.29788 | + | 0.357895i | ||||
\(204\) | − | 13.8412i | − | 0.969078i | ||||||
\(205\) | −3.55901 | − | 8.75310i | −0.248572 | − | 0.611343i | ||||
\(206\) | − | 14.0016i | − | 0.975537i | ||||||
\(207\) | −13.3238 | + | 13.3238i | −0.926066 | + | 0.926066i | ||||
\(208\) | −3.99211 | + | 3.99211i | −0.276803 | + | 0.276803i | ||||
\(209\) | 4.95398 | 0.342674 | ||||||||
\(210\) | −13.5225 | + | 10.3923i | −0.933142 | + | 0.717139i | ||||
\(211\) | 17.8348 | 1.22780 | 0.613899 | − | 0.789385i | \(-0.289600\pi\) | ||||
0.613899 | + | 0.789385i | \(0.289600\pi\) | |||||||
\(212\) | −0.793267 | + | 0.793267i | −0.0544818 | + | 0.0544818i | ||||
\(213\) | −19.3100 | + | 19.3100i | −1.32310 | + | 1.32310i | ||||
\(214\) | − | 4.00657i | − | 0.273884i | ||||||
\(215\) | 3.05674 | + | 1.28954i | 0.208468 | + | 0.0879460i | ||||
\(216\) | − | 6.65986i | − | 0.453146i | ||||||
\(217\) | −9.87288 | + | 2.72248i | −0.670215 | + | 0.184814i | ||||
\(218\) | 6.60196 | + | 6.60196i | 0.447141 | + | 0.447141i | ||||
\(219\) | 36.4192i | 2.46098i | ||||||||
\(220\) | 0.842227 | + | 2.07139i | 0.0567829 | + | 0.139653i | ||||
\(221\) | 27.1072 | 1.82343 | ||||||||
\(222\) | −8.43243 | − | 8.43243i | −0.565948 | − | 0.565948i | ||||
\(223\) | −1.13707 | + | 1.13707i | −0.0761441 | + | 0.0761441i | −0.744153 | − | 0.668009i | \(-0.767147\pi\) |
0.668009 | + | 0.744153i | \(0.267147\pi\) | |||||||
\(224\) | 2.30084 | + | 1.30619i | 0.153731 | + | 0.0872735i | ||||
\(225\) | −18.5283 | − | 19.0176i | −1.23522 | − | 1.26784i | ||||
\(226\) | −13.7956 | −0.917667 | ||||||||
\(227\) | −0.774054 | − | 0.774054i | −0.0513758 | − | 0.0513758i | 0.680952 | − | 0.732328i | \(-0.261566\pi\) |
−0.732328 | + | 0.680952i | \(0.761566\pi\) | |||||||
\(228\) | 10.0982 | + | 10.0982i | 0.668773 | + | 0.668773i | ||||
\(229\) | −3.16280 | −0.209004 | −0.104502 | − | 0.994525i | \(-0.533325\pi\) | ||||
−0.104502 | + | 0.994525i | \(0.533325\pi\) | |||||||
\(230\) | 7.35003 | − | 2.98852i | 0.484647 | − | 0.197057i | ||||
\(231\) | −6.63275 | − | 3.76542i | −0.436403 | − | 0.247746i | ||||
\(232\) | −5.12665 | + | 5.12665i | −0.336581 | + | 0.336581i | ||||
\(233\) | 1.78200 | + | 1.78200i | 0.116743 | + | 0.116743i | 0.763065 | − | 0.646322i | \(-0.223694\pi\) |
−0.646322 | + | 0.763065i | \(0.723694\pi\) | |||||||
\(234\) | 29.9801 | 1.95986 | ||||||||
\(235\) | −18.1214 | − | 7.64485i | −1.18211 | − | 0.498695i | ||||
\(236\) | − | 8.39914i | − | 0.546738i | ||||||
\(237\) | −9.49382 | − | 9.49382i | −0.616690 | − | 0.616690i | ||||
\(238\) | −3.37693 | − | 12.2462i | −0.218894 | − | 0.793804i | ||||
\(239\) | 10.5851i | 0.684692i | 0.939574 | + | 0.342346i | \(0.111221\pi\) | ||||
−0.939574 | + | 0.342346i | \(0.888779\pi\) | |||||||
\(240\) | −2.50554 | + | 5.93915i | −0.161732 | + | 0.383370i | ||||
\(241\) | − | 16.7551i | − | 1.07929i | −0.841892 | − | 0.539646i | \(-0.818558\pi\) | ||
0.841892 | − | 0.539646i | \(-0.181442\pi\) | |||||||
\(242\) | −0.707107 | + | 0.707107i | −0.0454545 | + | 0.0454545i | ||||
\(243\) | 7.46621 | − | 7.46621i | 0.478958 | − | 0.478958i | ||||
\(244\) | −12.9348 | −0.828063 | ||||||||
\(245\) | −9.42875 | + | 12.4939i | −0.602381 | + | 0.798209i | ||||
\(246\) | 12.1817 | 0.776675 | ||||||||
\(247\) | −19.7768 | + | 19.7768i | −1.25837 | + | 1.25837i | ||||
\(248\) | −2.73712 | + | 2.73712i | −0.173807 | + | 0.173807i | ||||
\(249\) | 43.5317i | 2.75871i | ||||||||
\(250\) | 4.07580 | + | 10.4109i | 0.257776 | + | 0.658446i | ||||
\(251\) | 12.0951i | 0.763438i | 0.924278 | + | 0.381719i | \(0.124668\pi\) | ||||
−0.924278 | + | 0.381719i | \(0.875332\pi\) | |||||||
\(252\) | −3.73483 | − | 13.5441i | −0.235272 | − | 0.853197i | ||||
\(253\) | 2.50907 | + | 2.50907i | 0.157744 | + | 0.157744i | ||||
\(254\) | 16.0207i | 1.00523i | ||||||||
\(255\) | 28.6705 | − | 11.6574i | 1.79542 | − | 0.730016i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.75224 | + | 5.75224i | 0.358815 | + | 0.358815i | 0.863376 | − | 0.504561i | \(-0.168346\pi\) |
−0.504561 | + | 0.863376i | \(0.668346\pi\) | |||||||
\(258\) | −3.02435 | + | 3.02435i | −0.188288 | + | 0.188288i | ||||
\(259\) | −9.51804 | − | 5.40340i | −0.591422 | − | 0.335751i | ||||
\(260\) | −11.6315 | − | 4.90696i | −0.721354 | − | 0.304317i | ||||
\(261\) | 38.5002 | 2.38310 | ||||||||
\(262\) | −14.7032 | − | 14.7032i | −0.908365 | − | 0.908365i | ||||
\(263\) | 10.6818 | + | 10.6818i | 0.658665 | + | 0.658665i | 0.955064 | − | 0.296399i | \(-0.0957858\pi\) |
−0.296399 | + | 0.955064i | \(0.595786\pi\) | |||||||
\(264\) | −2.88275 | −0.177421 | ||||||||
\(265\) | −2.31127 | − | 0.975054i | −0.141980 | − | 0.0598971i | ||||
\(266\) | 11.3983 | + | 6.47083i | 0.698875 | + | 0.396752i | ||||
\(267\) | 32.6392 | − | 32.6392i | 1.99748 | − | 1.99748i | ||||
\(268\) | −3.04387 | − | 3.04387i | −0.185934 | − | 0.185934i | ||||
\(269\) | 6.24110 | 0.380527 | 0.190263 | − | 0.981733i | \(-0.439066\pi\) | ||||
0.190263 | + | 0.981733i | \(0.439066\pi\) | |||||||
\(270\) | 13.7952 | − | 5.60912i | 0.839548 | − | 0.341360i | ||||
\(271\) | 19.1386i | 1.16259i | 0.813693 | + | 0.581294i | \(0.197453\pi\) | ||||
−0.813693 | + | 0.581294i | \(0.802547\pi\) | |||||||
\(272\) | −3.39509 | − | 3.39509i | −0.205858 | − | 0.205858i | ||||
\(273\) | 41.5107 | − | 11.4467i | 2.51234 | − | 0.692786i | ||||
\(274\) | − | 1.57479i | − | 0.0951365i | ||||||
\(275\) | −3.58131 | + | 3.48916i | −0.215961 | + | 0.210404i | ||||
\(276\) | 10.2290i | 0.615715i | ||||||||
\(277\) | −16.1046 | + | 16.1046i | −0.967629 | + | 0.967629i | −0.999492 | − | 0.0318632i | \(-0.989856\pi\) |
0.0318632 | + | 0.999492i | \(0.489856\pi\) | |||||||
\(278\) | 2.69131 | − | 2.69131i | 0.161414 | − | 0.161414i | ||||
\(279\) | 20.5553 | 1.23061 | ||||||||
\(280\) | −0.767799 | + | 5.86605i | −0.0458848 | + | 0.350563i | ||||
\(281\) | 1.15556 | 0.0689351 | 0.0344676 | − | 0.999406i | \(-0.489026\pi\) | ||||
0.0344676 | + | 0.999406i | \(0.489026\pi\) | |||||||
\(282\) | 17.9294 | − | 17.9294i | 1.06768 | − | 1.06768i | ||||
\(283\) | −0.394143 | + | 0.394143i | −0.0234294 | + | 0.0234294i | −0.718724 | − | 0.695295i | \(-0.755274\pi\) |
0.695295 | + | 0.718724i | \(0.255274\pi\) | |||||||
\(284\) | 9.47305i | 0.562122i | ||||||||
\(285\) | −12.4124 | + | 29.4224i | −0.735246 | + | 1.74283i | ||||
\(286\) | − | 5.64570i | − | 0.333837i | ||||||
\(287\) | 10.7779 | − | 2.97205i | 0.636200 | − | 0.175434i | ||||
\(288\) | −3.75491 | − | 3.75491i | −0.221260 | − | 0.221260i | ||||
\(289\) | 6.05332i | 0.356077i | ||||||||
\(290\) | −14.9371 | − | 6.30148i | −0.877136 | − | 0.370036i | ||||
\(291\) | −23.0078 | −1.34874 | ||||||||
\(292\) | 8.93324 | + | 8.93324i | 0.522778 | + | 0.522778i | ||||
\(293\) | −21.2666 | + | 21.2666i | −1.24241 | + | 1.24241i | −0.283413 | + | 0.958998i | \(0.591467\pi\) |
−0.958998 | + | 0.283413i | \(0.908533\pi\) | |||||||
\(294\) | −10.3425 | − | 17.3273i | −0.603189 | − | 1.01055i | ||||
\(295\) | 17.3979 | − | 7.07398i | 1.01294 | − | 0.411863i | ||||
\(296\) | −4.13677 | −0.240445 | ||||||||
\(297\) | 4.70924 | + | 4.70924i | 0.273258 | + | 0.273258i | ||||
\(298\) | −2.51854 | − | 2.51854i | −0.145895 | − | 0.145895i | ||||
\(299\) | −20.0330 | −1.15854 | ||||||||
\(300\) | −14.4125 | − | 0.187840i | −0.832108 | − | 0.0108449i | ||||
\(301\) | −1.93797 | + | 3.41371i | −0.111703 | + | 0.196763i | ||||
\(302\) | −5.87754 | + | 5.87754i | −0.338215 | + | 0.338215i | ||||
\(303\) | 23.6700 | + | 23.6700i | 1.35981 | + | 1.35981i | ||||
\(304\) | 4.95398 | 0.284130 | ||||||||
\(305\) | −10.8940 | − | 26.7929i | −0.623789 | − | 1.53416i | ||||
\(306\) | 25.4966i | 1.45754i | ||||||||
\(307\) | −20.7732 | − | 20.7732i | −1.18559 | − | 1.18559i | −0.978274 | − | 0.207315i | \(-0.933528\pi\) |
−0.207315 | − | 0.978274i | \(-0.566472\pi\) | |||||||
\(308\) | −2.55056 | + | 0.703324i | −0.145331 | + | 0.0400756i | ||||
\(309\) | 40.3631i | 2.29617i | ||||||||
\(310\) | −7.97492 | − | 3.36437i | −0.452945 | − | 0.191083i | ||||
\(311\) | − | 19.8702i | − | 1.12673i | −0.826207 | − | 0.563367i | \(-0.809506\pi\) | ||
0.826207 | − | 0.563367i | \(-0.190494\pi\) | |||||||
\(312\) | 11.5083 | − | 11.5083i | 0.651527 | − | 0.651527i | ||||
\(313\) | 8.66468 | − | 8.66468i | 0.489757 | − | 0.489757i | −0.418473 | − | 0.908229i | \(-0.637434\pi\) |
0.908229 | + | 0.418473i | \(0.137434\pi\) | |||||||
\(314\) | −3.98313 | −0.224781 | ||||||||
\(315\) | 24.9095 | − | 19.1435i | 1.40349 | − | 1.07861i | ||||
\(316\) | −4.65746 | −0.262002 | ||||||||
\(317\) | 7.80201 | − | 7.80201i | 0.438205 | − | 0.438205i | −0.453203 | − | 0.891407i | \(-0.649719\pi\) |
0.891407 | + | 0.453203i | \(0.149719\pi\) | |||||||
\(318\) | 2.28679 | − | 2.28679i | 0.128237 | − | 0.128237i | ||||
\(319\) | − | 7.25017i | − | 0.405932i | ||||||
\(320\) | 0.842227 | + | 2.07139i | 0.0470819 | + | 0.115794i | ||||
\(321\) | 11.5499i | 0.644655i | ||||||||
\(322\) | 2.49565 | + | 9.05028i | 0.139077 | + | 0.504353i | ||||
\(323\) | −16.8192 | − | 16.8192i | −0.935846 | − | 0.935846i | ||||
\(324\) | 3.26798i | 0.181555i | ||||||||
\(325\) | 0.367873 | − | 28.2261i | 0.0204059 | − | 1.56570i | ||||
\(326\) | 21.3636 | 1.18322 | ||||||||
\(327\) | −19.0318 | − | 19.0318i | −1.05246 | − | 1.05246i | ||||
\(328\) | 2.98803 | − | 2.98803i | 0.164986 | − | 0.164986i | ||||
\(329\) | 11.4890 | − | 20.2377i | 0.633407 | − | 1.11574i | ||||
\(330\) | −2.42793 | − | 5.97130i | −0.133653 | − | 0.328709i | ||||
\(331\) | 3.80505 | 0.209145 | 0.104572 | − | 0.994517i | \(-0.466653\pi\) | ||||
0.104572 | + | 0.994517i | \(0.466653\pi\) | |||||||
\(332\) | 10.6779 | + | 10.6779i | 0.586023 | + | 0.586023i | ||||
\(333\) | 15.5332 | + | 15.5332i | 0.851214 | + | 0.851214i | ||||
\(334\) | −3.39518 | −0.185776 | ||||||||
\(335\) | 3.74142 | − | 8.86868i | 0.204415 | − | 0.484548i | ||||
\(336\) | −6.63275 | − | 3.76542i | −0.361846 | − | 0.205420i | ||||
\(337\) | 22.5106 | − | 22.5106i | 1.22623 | − | 1.22623i | 0.260853 | − | 0.965379i | \(-0.415996\pi\) |
0.965379 | − | 0.260853i | \(-0.0840037\pi\) | |||||||
\(338\) | 13.3459 | + | 13.3459i | 0.725920 | + | 0.725920i | ||||
\(339\) | 39.7692 | 2.15996 | ||||||||
\(340\) | 4.17312 | − | 9.89200i | 0.226319 | − | 0.536469i | ||||
\(341\) | − | 3.87087i | − | 0.209620i | ||||||
\(342\) | −18.6017 | − | 18.6017i | −1.00587 | − | 1.00587i | ||||
\(343\) | −13.3782 | − | 12.8072i | −0.722353 | − | 0.691524i | ||||
\(344\) | 1.48368i | 0.0799947i | ||||||||
\(345\) | −21.1883 | + | 8.61516i | −1.14074 | + | 0.463825i | ||||
\(346\) | − | 5.87702i | − | 0.315950i | ||||||
\(347\) | 13.9134 | − | 13.9134i | 0.746912 | − | 0.746912i | −0.226986 | − | 0.973898i | \(-0.572887\pi\) |
0.973898 | + | 0.226986i | \(0.0728871\pi\) | |||||||
\(348\) | 14.7788 | − | 14.7788i | 0.792229 | − | 0.792229i | ||||
\(349\) | 1.48453 | 0.0794652 | 0.0397326 | − | 0.999210i | \(-0.487349\pi\) | ||||
0.0397326 | + | 0.999210i | \(0.487349\pi\) | |||||||
\(350\) | −12.7975 | + | 3.35013i | −0.684056 | + | 0.179072i | ||||
\(351\) | −37.5996 | −2.00692 | ||||||||
\(352\) | −0.707107 | + | 0.707107i | −0.0376889 | + | 0.0376889i | ||||
\(353\) | 3.45605 | − | 3.45605i | 0.183947 | − | 0.183947i | −0.609126 | − | 0.793073i | \(-0.708480\pi\) |
0.793073 | + | 0.609126i | \(0.208480\pi\) | |||||||
\(354\) | 24.2126i | 1.28689i | ||||||||
\(355\) | −19.6224 | + | 7.97846i | −1.04145 | + | 0.423452i | ||||
\(356\) | − | 16.0121i | − | 0.848637i | ||||||
\(357\) | 9.73485 | + | 35.3027i | 0.515223 | + | 1.86842i | ||||
\(358\) | −4.66701 | − | 4.66701i | −0.246659 | − | 0.246659i | ||||
\(359\) | 16.7966i | 0.886489i | 0.896401 | + | 0.443244i | \(0.146173\pi\) | ||||
−0.896401 | + | 0.443244i | \(0.853827\pi\) | |||||||
\(360\) | 4.61540 | − | 10.9404i | 0.243253 | − | 0.576608i | ||||
\(361\) | 5.54188 | 0.291678 | ||||||||
\(362\) | −10.2231 | − | 10.2231i | −0.537315 | − | 0.537315i | ||||
\(363\) | 2.03841 | − | 2.03841i | 0.106989 | − | 0.106989i | ||||
\(364\) | 7.37436 | − | 12.9899i | 0.386521 | − | 0.680853i | ||||
\(365\) | −10.9804 | + | 26.0280i | −0.574741 | + | 1.36237i | ||||
\(366\) | 37.2877 | 1.94906 | ||||||||
\(367\) | 6.67097 | + | 6.67097i | 0.348222 | + | 0.348222i | 0.859447 | − | 0.511225i | \(-0.170808\pi\) |
−0.511225 | + | 0.859447i | \(0.670808\pi\) | |||||||
\(368\) | 2.50907 | + | 2.50907i | 0.130794 | + | 0.130794i | ||||
\(369\) | −22.4396 | −1.16816 | ||||||||
\(370\) | −3.48409 | − | 8.56885i | −0.181129 | − | 0.445474i | ||||
\(371\) | 1.46535 | − | 2.58119i | 0.0760770 | − | 0.134009i | ||||
\(372\) | 7.89044 | − | 7.89044i | 0.409100 | − | 0.409100i | ||||
\(373\) | −1.53906 | − | 1.53906i | −0.0796893 | − | 0.0796893i | 0.666139 | − | 0.745828i | \(-0.267946\pi\) |
−0.745828 | + | 0.666139i | \(0.767946\pi\) | |||||||
\(374\) | 4.80139 | 0.248274 | ||||||||
\(375\) | −11.7495 | − | 30.0122i | −0.606743 | − | 1.54982i | ||||
\(376\) | − | 8.79578i | − | 0.453608i | ||||||
\(377\) | 28.9435 | + | 28.9435i | 1.49067 | + | 1.49067i | ||||
\(378\) | 4.68404 | + | 16.9864i | 0.240921 | + | 0.873684i | ||||
\(379\) | − | 15.4053i | − | 0.791315i | −0.918398 | − | 0.395657i | \(-0.870517\pi\) | ||
0.918398 | − | 0.395657i | \(-0.129483\pi\) | |||||||
\(380\) | 4.17237 | + | 10.2616i | 0.214038 | + | 0.526410i | ||||
\(381\) | − | 46.1836i | − | 2.36606i | ||||||
\(382\) | 7.18826 | − | 7.18826i | 0.367783 | − | 0.367783i | ||||
\(383\) | −2.84084 | + | 2.84084i | −0.145160 | + | 0.145160i | −0.775952 | − | 0.630792i | \(-0.782730\pi\) |
0.630792 | + | 0.775952i | \(0.282730\pi\) | |||||||
\(384\) | −2.88275 | −0.147110 | ||||||||
\(385\) | −3.60500 | − | 4.69084i | −0.183728 | − | 0.239067i | ||||
\(386\) | 10.1365 | 0.515937 | ||||||||
\(387\) | 5.57109 | − | 5.57109i | 0.283195 | − | 0.283195i | ||||
\(388\) | −5.64356 | + | 5.64356i | −0.286508 | + | 0.286508i | ||||
\(389\) | 14.6913i | 0.744878i | 0.928057 | + | 0.372439i | \(0.121478\pi\) | ||||
−0.928057 | + | 0.372439i | \(0.878522\pi\) | |||||||
\(390\) | 33.5307 | + | 14.1455i | 1.69789 | + | 0.716287i | ||||
\(391\) | − | 17.0370i | − | 0.861600i | ||||||
\(392\) | −6.78710 | − | 1.71327i | −0.342800 | − | 0.0865334i | ||||
\(393\) | 42.3856 | + | 42.3856i | 2.13807 | + | 2.13807i | ||||
\(394\) | − | 18.1148i | − | 0.912608i | ||||||
\(395\) | −3.92263 | − | 9.64741i | −0.197369 | − | 0.485414i | ||||
\(396\) | 5.31025 | 0.266850 | ||||||||
\(397\) | −6.91985 | − | 6.91985i | −0.347297 | − | 0.347297i | 0.511805 | − | 0.859102i | \(-0.328977\pi\) |
−0.859102 | + | 0.511805i | \(0.828977\pi\) | |||||||
\(398\) | −7.52085 | + | 7.52085i | −0.376986 | + | 0.376986i | ||||
\(399\) | −32.8585 | − | 18.6538i | −1.64498 | − | 0.933858i | ||||
\(400\) | −3.58131 | + | 3.48916i | −0.179065 | + | 0.174458i | ||||
\(401\) | 30.3644 | 1.51633 | 0.758163 | − | 0.652065i | \(-0.226097\pi\) | ||||
0.758163 | + | 0.652065i | \(0.226097\pi\) | |||||||
\(402\) | 8.77473 | + | 8.77473i | 0.437644 | + | 0.437644i | ||||
\(403\) | 15.4530 | + | 15.4530i | 0.769767 | + | 0.769767i | ||||
\(404\) | 11.6120 | 0.577718 | ||||||||
\(405\) | −6.76927 | + | 2.75238i | −0.336368 | + | 0.136767i | ||||
\(406\) | 9.47010 | − | 16.6815i | 0.469993 | − | 0.827889i | ||||
\(407\) | 2.92514 | − | 2.92514i | 0.144994 | − | 0.144994i | ||||
\(408\) | 9.78720 | + | 9.78720i | 0.484539 | + | 0.484539i | ||||
\(409\) | 5.57334 | 0.275584 | 0.137792 | − | 0.990461i | \(-0.455999\pi\) | ||||
0.137792 | + | 0.990461i | \(0.455999\pi\) | |||||||
\(410\) | 8.70597 | + | 3.67277i | 0.429957 | + | 0.181385i | ||||
\(411\) | 4.53972i | 0.223928i | ||||||||
\(412\) | 9.90062 | + | 9.90062i | 0.487768 | + | 0.487768i | ||||
\(413\) | 5.90732 | + | 21.4225i | 0.290680 | + | 1.05413i | ||||
\(414\) | − | 18.8427i | − | 0.926066i | ||||||
\(415\) | −13.1248 | + | 31.1112i | −0.644272 | + | 1.52719i | ||||
\(416\) | − | 5.64570i | − | 0.276803i | ||||||
\(417\) | −7.75838 | + | 7.75838i | −0.379929 | + | 0.379929i | ||||
\(418\) | −3.50299 | + | 3.50299i | −0.171337 | + | 0.171337i | ||||
\(419\) | 35.9081 | 1.75422 | 0.877112 | − | 0.480286i | \(-0.159467\pi\) | ||||
0.877112 | + | 0.480286i | \(0.159467\pi\) | |||||||
\(420\) | 2.21337 | − | 16.9103i | 0.108001 | − | 0.825140i | ||||
\(421\) | −7.31996 | −0.356753 | −0.178377 | − | 0.983962i | \(-0.557085\pi\) | ||||
−0.178377 | + | 0.983962i | \(0.557085\pi\) | |||||||
\(422\) | −12.6111 | + | 12.6111i | −0.613899 | + | 0.613899i | ||||
\(423\) | −33.0274 | + | 33.0274i | −1.60585 | + | 1.60585i | ||||
\(424\) | − | 1.12185i | − | 0.0544818i | ||||||
\(425\) | 24.0049 | + | 0.312858i | 1.16441 | + | 0.0151758i | ||||
\(426\) | − | 27.3084i | − | 1.32310i | ||||||
\(427\) | 32.9908 | − | 9.09733i | 1.59654 | − | 0.440251i | ||||
\(428\) | 2.83307 | + | 2.83307i | 0.136942 | + | 0.136942i | ||||
\(429\) | 16.2751i | 0.785771i | ||||||||
\(430\) | −3.07328 | + | 1.24960i | −0.148207 | + | 0.0602609i | ||||
\(431\) | −15.5322 | −0.748162 | −0.374081 | − | 0.927396i | \(-0.622042\pi\) | ||||
−0.374081 | + | 0.927396i | \(0.622042\pi\) | |||||||
\(432\) | 4.70924 | + | 4.70924i | 0.226573 | + | 0.226573i | ||||
\(433\) | 22.3747 | − | 22.3747i | 1.07526 | − | 1.07526i | 0.0783304 | − | 0.996927i | \(-0.475041\pi\) |
0.996927 | − | 0.0783304i | \(-0.0249589\pi\) | |||||||
\(434\) | 5.05610 | − | 8.90626i | 0.242700 | − | 0.427514i | ||||
\(435\) | 43.0599 | + | 18.1656i | 2.06456 | + | 0.870974i | ||||
\(436\) | −9.33658 | −0.447141 | ||||||||
\(437\) | 12.4299 | + | 12.4299i | 0.594601 | + | 0.594601i | ||||
\(438\) | −25.7523 | − | 25.7523i | −1.23049 | − | 1.23049i | ||||
\(439\) | −37.7109 | −1.79984 | −0.899922 | − | 0.436052i | \(-0.856376\pi\) | ||||
−0.899922 | + | 0.436052i | \(0.856376\pi\) | |||||||
\(440\) | −2.06024 | − | 0.869149i | −0.0982180 | − | 0.0414351i | ||||
\(441\) | 19.0518 | + | 31.9181i | 0.907227 | + | 1.51991i | ||||
\(442\) | −19.1677 | + | 19.1677i | −0.911713 | + | 0.911713i | ||||
\(443\) | −27.1381 | − | 27.1381i | −1.28937 | − | 1.28937i | −0.935170 | − | 0.354198i | \(-0.884754\pi\) |
−0.354198 | − | 0.935170i | \(-0.615246\pi\) | |||||||
\(444\) | 11.9253 | 0.565948 | ||||||||
\(445\) | 33.1672 | − | 13.4858i | 1.57228 | − | 0.639287i | ||||
\(446\) | − | 1.60807i | − | 0.0761441i | ||||||
\(447\) | 7.26033 | + | 7.26033i | 0.343402 | + | 0.343402i | ||||
\(448\) | −2.55056 | + | 0.703324i | −0.120502 | + | 0.0332290i | ||||
\(449\) | − | 33.2293i | − | 1.56819i | −0.620643 | − | 0.784093i | \(-0.713128\pi\) | ||
0.620643 | − | 0.784093i | \(-0.286872\pi\) | |||||||
\(450\) | 26.5490 | + | 0.346015i | 1.25153 | + | 0.0163113i | ||||
\(451\) | 4.22571i | 0.198981i | ||||||||
\(452\) | 9.75494 | − | 9.75494i | 0.458834 | − | 0.458834i | ||||
\(453\) | 16.9435 | − | 16.9435i | 0.796075 | − | 0.796075i | ||||
\(454\) | 1.09468 | 0.0513758 | ||||||||
\(455\) | 33.1179 | + | 4.33476i | 1.55259 | + | 0.203217i | ||||
\(456\) | −14.2811 | −0.668773 | ||||||||
\(457\) | −6.27630 | + | 6.27630i | −0.293593 | + | 0.293593i | −0.838498 | − | 0.544905i | \(-0.816566\pi\) |
0.544905 | + | 0.838498i | \(0.316566\pi\) | |||||||
\(458\) | 2.23644 | − | 2.23644i | 0.104502 | − | 0.104502i | ||||
\(459\) | − | 31.9766i | − | 1.49254i | ||||||
\(460\) | −3.08405 | + | 7.31046i | −0.143795 | + | 0.340852i | ||||
\(461\) | − | 19.2476i | − | 0.896449i | −0.893921 | − | 0.448225i | \(-0.852057\pi\) | ||
0.893921 | − | 0.448225i | \(-0.147943\pi\) | |||||||
\(462\) | 7.35261 | − | 2.02751i | 0.342075 | − | 0.0943282i | ||||
\(463\) | −7.44058 | − | 7.44058i | −0.345793 | − | 0.345793i | 0.512747 | − | 0.858540i | \(-0.328628\pi\) |
−0.858540 | + | 0.512747i | \(0.828628\pi\) | |||||||
\(464\) | − | 7.25017i | − | 0.336581i | ||||||
\(465\) | 22.9897 | + | 9.69863i | 1.06612 | + | 0.449763i | ||||
\(466\) | −2.52013 | −0.116743 | ||||||||
\(467\) | −1.72747 | − | 1.72747i | −0.0799379 | − | 0.0799379i | 0.666007 | − | 0.745945i | \(-0.268002\pi\) |
−0.745945 | + | 0.666007i | \(0.768002\pi\) | |||||||
\(468\) | −21.1991 | + | 21.1991i | −0.979929 | + | 0.979929i | ||||
\(469\) | 9.90440 | + | 5.62274i | 0.457343 | + | 0.259634i | ||||
\(470\) | 18.2195 | − | 7.40804i | 0.840403 | − | 0.341708i | ||||
\(471\) | 11.4824 | 0.529079 | ||||||||
\(472\) | 5.93909 | + | 5.93909i | 0.273369 | + | 0.273369i | ||||
\(473\) | −1.04912 | − | 1.04912i | −0.0482386 | − | 0.0482386i | ||||
\(474\) | 13.4263 | 0.616690 | ||||||||
\(475\) | −17.7417 | + | 17.2852i | −0.814046 | + | 0.793100i | ||||
\(476\) | 11.0472 | + | 6.27152i | 0.506349 | + | 0.287455i | ||||
\(477\) | −4.21244 | + | 4.21244i | −0.192874 | + | 0.192874i | ||||
\(478\) | −7.48478 | − | 7.48478i | −0.342346 | − | 0.342346i | ||||
\(479\) | −3.14575 | −0.143733 | −0.0718664 | − | 0.997414i | \(-0.522896\pi\) | ||||
−0.0718664 | + | 0.997414i | \(0.522896\pi\) | |||||||
\(480\) | −2.42793 | − | 5.97130i | −0.110819 | − | 0.272551i | ||||
\(481\) | 23.3549i | 1.06489i | ||||||||
\(482\) | 11.8477 | + | 11.8477i | 0.539646 | + | 0.539646i | ||||
\(483\) | −7.19432 | − | 26.0897i | −0.327353 | − | 1.18712i | ||||
\(484\) | − | 1.00000i | − | 0.0454545i | ||||||
\(485\) | −16.4432 | − | 6.93685i | −0.746646 | − | 0.314986i | ||||
\(486\) | 10.5588i | 0.478958i | ||||||||
\(487\) | 10.6347 | − | 10.6347i | 0.481903 | − | 0.481903i | −0.423836 | − | 0.905739i | \(-0.639317\pi\) |
0.905739 | + | 0.423836i | \(0.139317\pi\) | |||||||
\(488\) | 9.14626 | − | 9.14626i | 0.414032 | − | 0.414032i | ||||
\(489\) | −61.5859 | −2.78501 | ||||||||
\(490\) | −2.16742 | − | 15.5017i | −0.0979140 | − | 0.700295i | ||||
\(491\) | 10.7113 | 0.483395 | 0.241698 | − | 0.970352i | \(-0.422296\pi\) | ||||
0.241698 | + | 0.970352i | \(0.422296\pi\) | |||||||
\(492\) | −8.61374 | + | 8.61374i | −0.388337 | + | 0.388337i | ||||
\(493\) | −24.6150 | + | 24.6150i | −1.10860 | + | 1.10860i | ||||
\(494\) | − | 27.9687i | − | 1.25837i | ||||||
\(495\) | 4.47243 | + | 10.9996i | 0.201021 | + | 0.494395i | ||||
\(496\) | − | 3.87087i | − | 0.173807i | ||||||
\(497\) | −6.66263 | − | 24.1615i | −0.298860 | − | 1.08379i | ||||
\(498\) | −30.7816 | − | 30.7816i | −1.37936 | − | 1.37936i | ||||
\(499\) | 17.5095i | 0.783835i | 0.920000 | + | 0.391917i | \(0.128188\pi\) | ||||
−0.920000 | + | 0.391917i | \(0.871812\pi\) | |||||||
\(500\) | −10.2437 | − | 4.47962i | −0.458111 | − | 0.200335i | ||||
\(501\) | 9.78745 | 0.437271 | ||||||||
\(502\) | −8.55255 | − | 8.55255i | −0.381719 | − | 0.381719i | ||||
\(503\) | 24.1937 | − | 24.1937i | 1.07874 | − | 1.07874i | 0.0821196 | − | 0.996622i | \(-0.473831\pi\) |
0.996622 | − | 0.0821196i | \(-0.0261689\pi\) | |||||||
\(504\) | 12.2180 | + | 6.93619i | 0.544234 | + | 0.308963i | ||||
\(505\) | 9.77993 | + | 24.0530i | 0.435201 | + | 1.07034i | ||||
\(506\) | −3.54836 | −0.157744 | ||||||||
\(507\) | −38.4728 | − | 38.4728i | −1.70864 | − | 1.70864i | ||||
\(508\) | −11.3283 | − | 11.3283i | −0.502614 | − | 0.502614i | ||||
\(509\) | −36.3493 | −1.61116 | −0.805578 | − | 0.592490i | \(-0.798145\pi\) | ||||
−0.805578 | + | 0.592490i | \(0.798145\pi\) | |||||||
\(510\) | −12.0301 | + | 28.5162i | −0.532700 | + | 1.26272i | ||||
\(511\) | −29.0677 | − | 16.5018i | −1.28588 | − | 0.729995i | ||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 23.3294 | + | 23.3294i | 1.03002 | + | 1.03002i | ||||
\(514\) | −8.13490 | −0.358815 | ||||||||
\(515\) | −12.1695 | + | 28.8466i | −0.536251 | + | 1.27113i | ||||
\(516\) | − | 4.27708i | − | 0.188288i | ||||||
\(517\) | 6.21956 | + | 6.21956i | 0.273536 | + | 0.273536i | ||||
\(518\) | 10.5511 | − | 2.90949i | 0.463587 | − | 0.127836i | ||||
\(519\) | 16.9420i | 0.743670i | ||||||||
\(520\) | 11.6944 | − | 4.75496i | 0.512835 | − | 0.208519i | ||||
\(521\) | − | 5.91957i | − | 0.259341i | −0.991557 | − | 0.129671i | \(-0.958608\pi\) | ||
0.991557 | − | 0.129671i | \(-0.0413920\pi\) | |||||||
\(522\) | −27.2238 | + | 27.2238i | −1.19155 | + | 1.19155i | ||||
\(523\) | 3.66023 | − | 3.66023i | 0.160051 | − | 0.160051i | −0.622539 | − | 0.782589i | \(-0.713899\pi\) |
0.782589 | + | 0.622539i | \(0.213899\pi\) | |||||||
\(524\) | 20.7934 | 0.908365 | ||||||||
\(525\) | 36.8921 | − | 9.65758i | 1.61010 | − | 0.421492i | ||||
\(526\) | −15.1063 | −0.658665 | ||||||||
\(527\) | −13.1420 | + | 13.1420i | −0.572474 | + | 0.572474i | ||||
\(528\) | 2.03841 | − | 2.03841i | 0.0887105 | − | 0.0887105i | ||||
\(529\) | − | 10.4092i | − | 0.452572i | ||||||
\(530\) | 2.32378 | − | 0.944850i | 0.100939 | − | 0.0410417i | ||||
\(531\) | − | 44.6015i | − | 1.93554i | ||||||
\(532\) | −12.6354 | + | 3.48425i | −0.547814 | + | 0.151061i | ||||
\(533\) | −16.8695 | − | 16.8695i | −0.730700 | − | 0.730700i | ||||
\(534\) | 46.1587i | 1.99748i | ||||||||
\(535\) | −3.48231 | + | 8.25449i | −0.150553 | + | 0.356873i | ||||
\(536\) | 4.30469 | 0.185934 | ||||||||
\(537\) | 13.4538 | + | 13.4538i | 0.580575 | + | 0.580575i | ||||
\(538\) | −4.41312 | + | 4.41312i | −0.190263 | + | 0.190263i | ||||
\(539\) | 6.01067 | − | 3.58774i | 0.258898 | − | 0.154535i | ||||
\(540\) | −5.78842 | + | 13.7209i | −0.249094 | + | 0.590454i | ||||
\(541\) | 0.483794 | 0.0207999 | 0.0104000 | − | 0.999946i | \(-0.496690\pi\) | ||||
0.0104000 | + | 0.999946i | \(0.496690\pi\) | |||||||
\(542\) | −13.5331 | − | 13.5331i | −0.581294 | − | 0.581294i | ||||
\(543\) | 29.4707 | + | 29.4707i | 1.26471 | + | 1.26471i | ||||
\(544\) | 4.80139 | 0.205858 | ||||||||
\(545\) | −7.86352 | − | 19.3397i | −0.336836 | − | 0.828421i | ||||
\(546\) | −21.2584 | + | 37.4465i | −0.909777 | + | 1.60256i | ||||
\(547\) | −25.3812 | + | 25.3812i | −1.08522 | + | 1.08522i | −0.0892091 | + | 0.996013i | \(0.528434\pi\) |
−0.996013 | + | 0.0892091i | \(0.971566\pi\) | |||||||
\(548\) | 1.11354 | + | 1.11354i | 0.0475682 | + | 0.0475682i | ||||
\(549\) | −68.6868 | −2.93148 | ||||||||
\(550\) | 0.0651599 | − | 4.99958i | 0.00277843 | − | 0.213183i | ||||
\(551\) | − | 35.9172i | − | 1.53012i | ||||||
\(552\) | −7.23301 | − | 7.23301i | −0.307858 | − | 0.307858i | ||||
\(553\) | 11.8791 | − | 3.27570i | 0.505151 | − | 0.139297i | ||||
\(554\) | − | 22.7753i | − | 0.967629i | ||||||
\(555\) | 10.0438 | + | 24.7019i | 0.426334 | + | 1.04854i | ||||
\(556\) | 3.80609i | 0.161414i | ||||||||
\(557\) | 4.55744 | − | 4.55744i | 0.193105 | − | 0.193105i | −0.603931 | − | 0.797036i | \(-0.706400\pi\) |
0.797036 | + | 0.603931i | \(0.206400\pi\) | |||||||
\(558\) | −14.5348 | + | 14.5348i | −0.615307 | + | 0.615307i | ||||
\(559\) | 8.37642 | 0.354285 | ||||||||
\(560\) | −3.60500 | − | 4.69084i | −0.152339 | − | 0.198224i | ||||
\(561\) | −13.8412 | −0.584376 | ||||||||
\(562\) | −0.817106 | + | 0.817106i | −0.0344676 | + | 0.0344676i | ||||
\(563\) | −11.4679 | + | 11.4679i | −0.483316 | + | 0.483316i | −0.906189 | − | 0.422873i | \(-0.861022\pi\) |
0.422873 | + | 0.906189i | \(0.361022\pi\) | |||||||
\(564\) | 25.3560i | 1.06768i | ||||||||
\(565\) | 28.4221 | + | 11.9904i | 1.19573 | + | 0.504440i | ||||
\(566\) | − | 0.557403i | − | 0.0234294i | ||||||
\(567\) | −2.29845 | − | 8.33517i | −0.0965259 | − | 0.350044i | ||||
\(568\) | −6.69846 | − | 6.69846i | −0.281061 | − | 0.281061i | ||||
\(569\) | − | 47.4536i | − | 1.98936i | −0.103021 | − | 0.994679i | \(-0.532851\pi\) | ||
0.103021 | − | 0.994679i | \(-0.467149\pi\) | |||||||
\(570\) | −12.0279 | − | 29.5817i | −0.503793 | − | 1.23904i | ||||
\(571\) | −14.9321 | −0.624890 | −0.312445 | − | 0.949936i | \(-0.601148\pi\) | ||||
−0.312445 | + | 0.949936i | \(0.601148\pi\) | |||||||
\(572\) | 3.99211 | + | 3.99211i | 0.166919 | + | 0.166919i | ||||
\(573\) | −20.7220 | + | 20.7220i | −0.865672 | + | 0.865672i | ||||
\(574\) | −5.51958 | + | 9.72269i | −0.230383 | + | 0.405817i | ||||
\(575\) | −17.7403 | − | 0.231211i | −0.739821 | − | 0.00964215i | ||||
\(576\) | 5.31025 | 0.221260 | ||||||||
\(577\) | 24.7173 | + | 24.7173i | 1.02900 | + | 1.02900i | 0.999567 | + | 0.0294289i | \(0.00936885\pi\) |
0.0294289 | + | 0.999567i | \(0.490631\pi\) | |||||||
\(578\) | −4.28034 | − | 4.28034i | −0.178039 | − | 0.178039i | ||||
\(579\) | −29.2211 | −1.21439 | ||||||||
\(580\) | 15.0179 | − | 6.10629i | 0.623586 | − | 0.253550i | ||||
\(581\) | −34.7445 | − | 19.7245i | −1.44144 | − | 0.818309i | ||||
\(582\) | 16.2690 | − | 16.2690i | 0.674370 | − | 0.674370i | ||||
\(583\) | 0.793267 | + | 0.793267i | 0.0328537 | + | 0.0328537i | ||||
\(584\) | −12.6335 | −0.522778 | ||||||||
\(585\) | −61.7660 | − | 26.0572i | −2.55371 | − | 1.07733i | ||||
\(586\) | − | 30.0756i | − | 1.24241i | ||||||
\(587\) | −17.4764 | − | 17.4764i | −0.721328 | − | 0.721328i | 0.247548 | − | 0.968876i | \(-0.420375\pi\) |
−0.968876 | + | 0.247548i | \(0.920375\pi\) | |||||||
\(588\) | 19.5655 | + | 4.93894i | 0.806868 | + | 0.203678i | ||||
\(589\) | − | 19.1762i | − | 0.790142i | ||||||
\(590\) | −7.30011 | + | 17.3042i | −0.300541 | + | 0.712404i | ||||
\(591\) | 52.2203i | 2.14806i | ||||||||
\(592\) | 2.92514 | − | 2.92514i | 0.120222 | − | 0.120222i | ||||
\(593\) | −5.44521 | + | 5.44521i | −0.223608 | + | 0.223608i | −0.810016 | − | 0.586408i | \(-0.800542\pi\) |
0.586408 | + | 0.810016i | \(0.300542\pi\) | |||||||
\(594\) | −6.65986 | −0.273258 | ||||||||
\(595\) | −3.68650 | + | 28.1652i | −0.151132 | + | 1.15466i | ||||
\(596\) | 3.56176 | 0.145895 | ||||||||
\(597\) | 21.6807 | − | 21.6807i | 0.887333 | − | 0.887333i | ||||
\(598\) | 14.1654 | − | 14.1654i | 0.579268 | − | 0.579268i | ||||
\(599\) | 1.24075i | 0.0506958i | 0.999679 | + | 0.0253479i | \(0.00806936\pi\) | ||||
−0.999679 | + | 0.0253479i | \(0.991931\pi\) | |||||||
\(600\) | 10.3240 | − | 10.0584i | 0.421476 | − | 0.410631i | ||||
\(601\) | − | 2.86931i | − | 0.117042i | −0.998286 | − | 0.0585208i | \(-0.981362\pi\) | ||
0.998286 | − | 0.0585208i | \(-0.0186384\pi\) | |||||||
\(602\) | −1.04351 | − | 3.78421i | −0.0425303 | − | 0.154233i | ||||
\(603\) | −16.1637 | − | 16.1637i | −0.658238 | − | 0.658238i | ||||
\(604\) | − | 8.31210i | − | 0.338215i | ||||||
\(605\) | 2.07139 | − | 0.842227i | 0.0842140 | − | 0.0342414i | ||||
\(606\) | −33.4745 | −1.35981 | ||||||||
\(607\) | −7.78887 | − | 7.78887i | −0.316141 | − | 0.316141i | 0.531142 | − | 0.847283i | \(-0.321763\pi\) |
−0.847283 | + | 0.531142i | \(0.821763\pi\) | |||||||
\(608\) | −3.50299 | + | 3.50299i | −0.142065 | + | 0.142065i | ||||
\(609\) | −27.2999 | + | 48.0886i | −1.10625 | + | 1.94865i | ||||
\(610\) | 26.6487 | + | 11.2422i | 1.07897 | + | 0.455185i | ||||
\(611\) | −49.6584 | −2.00896 | ||||||||
\(612\) | −18.0288 | − | 18.0288i | −0.728770 | − | 0.728770i | ||||
\(613\) | 0.261621 | + | 0.261621i | 0.0105668 | + | 0.0105668i | 0.712370 | − | 0.701804i | \(-0.247622\pi\) |
−0.701804 | + | 0.712370i | \(0.747622\pi\) | |||||||
\(614\) | 29.3777 | 1.18559 | ||||||||
\(615\) | −25.0971 | − | 10.5877i | −1.01201 | − | 0.426937i | ||||
\(616\) | 1.30619 | − | 2.30084i | 0.0526279 | − | 0.0927035i | ||||
\(617\) | −2.56934 | + | 2.56934i | −0.103438 | + | 0.103438i | −0.756932 | − | 0.653494i | \(-0.773303\pi\) |
0.653494 | + | 0.756932i | \(0.273303\pi\) | |||||||
\(618\) | −28.5410 | − | 28.5410i | −1.14809 | − | 1.14809i | ||||
\(619\) | −10.5621 | −0.424528 | −0.212264 | − | 0.977212i | \(-0.568084\pi\) | ||||
−0.212264 | + | 0.977212i | \(0.568084\pi\) | |||||||
\(620\) | 8.01809 | − | 3.26015i | 0.322014 | − | 0.130931i | ||||
\(621\) | 23.6316i | 0.948303i | ||||||||
\(622\) | 14.0503 | + | 14.0503i | 0.563367 | + | 0.563367i | ||||
\(623\) | 11.2617 | + | 40.8396i | 0.451189 | + | 1.63621i | ||||
\(624\) | 16.2751i | 0.651527i | ||||||||
\(625\) | 0.651544 | − | 24.9915i | 0.0260618 | − | 0.999660i | ||||
\(626\) | 12.2537i | 0.489757i | ||||||||
\(627\) | 10.0982 | − | 10.0982i | 0.403285 | − | 0.403285i | ||||
\(628\) | 2.81649 | − | 2.81649i | 0.112390 | − | 0.112390i | ||||
\(629\) | −19.8622 | −0.791958 | ||||||||
\(630\) | −4.07720 | + | 31.1501i | −0.162440 | + | 1.24105i | ||||
\(631\) | −17.1559 | −0.682967 | −0.341483 | − | 0.939888i | \(-0.610929\pi\) | ||||
−0.341483 | + | 0.939888i | \(0.610929\pi\) | |||||||
\(632\) | 3.29332 | − | 3.29332i | 0.131001 | − | 0.131001i | ||||
\(633\) | 36.3547 | − | 36.3547i | 1.44497 | − | 1.44497i | ||||
\(634\) | 11.0337i | 0.438205i | ||||||||
\(635\) | 13.9244 | − | 33.0064i | 0.552572 | − | 1.30982i | ||||
\(636\) | 3.23401i | 0.128237i | ||||||||
\(637\) | −9.67262 | + | 38.3179i | −0.383243 | + | 1.51821i | ||||
\(638\) | 5.12665 | + | 5.12665i | 0.202966 | + | 0.202966i | ||||
\(639\) | 50.3042i | 1.99001i | ||||||||
\(640\) | −2.06024 | − | 0.869149i | −0.0814380 | − | 0.0343561i | ||||
\(641\) | 11.8476 | 0.467954 | 0.233977 | − | 0.972242i | \(-0.424826\pi\) | ||||
0.233977 | + | 0.972242i | \(0.424826\pi\) | |||||||
\(642\) | −8.16704 | − | 8.16704i | −0.322328 | − | 0.322328i | ||||
\(643\) | 16.2690 | − | 16.2690i | 0.641586 | − | 0.641586i | −0.309359 | − | 0.950945i | \(-0.600115\pi\) |
0.950945 | + | 0.309359i | \(0.100115\pi\) | |||||||
\(644\) | −8.16420 | − | 4.63483i | −0.321715 | − | 0.182638i | ||||
\(645\) | 8.85950 | − | 3.60227i | 0.348843 | − | 0.141839i | ||||
\(646\) | 23.7860 | 0.935846 | ||||||||
\(647\) | 17.9057 | + | 17.9057i | 0.703945 | + | 0.703945i | 0.965255 | − | 0.261310i | \(-0.0841544\pi\) |
−0.261310 | + | 0.965255i | \(0.584154\pi\) | |||||||
\(648\) | −2.31081 | − | 2.31081i | −0.0907773 | − | 0.0907773i | ||||
\(649\) | −8.39914 | −0.329695 | ||||||||
\(650\) | 19.6987 | + | 20.2190i | 0.772648 | + | 0.793054i | ||||
\(651\) | −14.5755 | + | 25.6745i | −0.571257 | + | 1.00626i | ||||
\(652\) | −15.1063 | + | 15.1063i | −0.591610 | + | 0.591610i | ||||
\(653\) | −18.2688 | − | 18.2688i | −0.714915 | − | 0.714915i | 0.252644 | − | 0.967559i | \(-0.418700\pi\) |
−0.967559 | + | 0.252644i | \(0.918700\pi\) | |||||||
\(654\) | 26.9150 | 1.05246 | ||||||||
\(655\) | 17.5128 | + | 43.0713i | 0.684281 | + | 1.68293i | ||||
\(656\) | 4.22571i | 0.164986i | ||||||||
\(657\) | 47.4377 | + | 47.4377i | 1.85072 | + | 1.85072i | ||||
\(658\) | 6.18629 | + | 22.4341i | 0.241167 | + | 0.874574i | ||||
\(659\) | − | 29.9625i | − | 1.16718i | −0.812050 | − | 0.583588i | \(-0.801648\pi\) | ||
0.812050 | − | 0.583588i | \(-0.198352\pi\) | |||||||
\(660\) | 5.93915 | + | 2.50554i | 0.231181 | + | 0.0975280i | ||||
\(661\) | − | 36.3565i | − | 1.41410i | −0.707162 | − | 0.707051i | \(-0.750025\pi\) | ||
0.707162 | − | 0.707051i | \(-0.249975\pi\) | |||||||
\(662\) | −2.69058 | + | 2.69058i | −0.104572 | + | 0.104572i | ||||
\(663\) | 55.2556 | − | 55.2556i | 2.14595 | − | 2.14595i | ||||
\(664\) | −15.1008 | −0.586023 | ||||||||
\(665\) | −17.8591 | − | 23.2383i | −0.692546 | − | 0.901142i | ||||
\(666\) | −21.9673 | −0.851214 | ||||||||
\(667\) | 18.1912 | − | 18.1912i | 0.704365 | − | 0.704365i | ||||
\(668\) | 2.40075 | − | 2.40075i | 0.0928879 | − | 0.0928879i | ||||
\(669\) | 4.63565i | 0.179225i | ||||||||
\(670\) | 3.62552 | + | 8.91669i | 0.140066 | + | 0.344482i | ||||
\(671\) | 12.9348i | 0.499341i | ||||||||
\(672\) | 7.35261 | − | 2.02751i | 0.283633 | − | 0.0782128i | ||||
\(673\) | 10.7229 | + | 10.7229i | 0.413336 | + | 0.413336i | 0.882899 | − | 0.469563i | \(-0.155589\pi\) |
−0.469563 | + | 0.882899i | \(0.655589\pi\) | |||||||
\(674\) | 31.8348i | 1.22623i | ||||||||
\(675\) | −33.2965 | − | 0.433956i | −1.28158 | − | 0.0167030i | ||||
\(676\) | −18.8739 | −0.725920 | ||||||||
\(677\) | 0.526391 | + | 0.526391i | 0.0202308 | + | 0.0202308i | 0.717150 | − | 0.696919i | \(-0.245446\pi\) |
−0.696919 | + | 0.717150i | \(0.745446\pi\) | |||||||
\(678\) | −28.1210 | + | 28.1210i | −1.07998 | + | 1.07998i | ||||
\(679\) | 10.4250 | − | 18.3635i | 0.400073 | − | 0.704725i | ||||
\(680\) | 4.04386 | + | 9.94554i | 0.155075 | + | 0.381394i | ||||
\(681\) | −3.15568 | −0.120926 | ||||||||
\(682\) | 2.73712 | + | 2.73712i | 0.104810 | + | 0.104810i | ||||
\(683\) | −26.5539 | − | 26.5539i | −1.01606 | − | 1.01606i | −0.999869 | − | 0.0161871i | \(-0.994847\pi\) |
−0.0161871 | − | 0.999869i | \(-0.505153\pi\) | |||||||
\(684\) | 26.3068 | 1.00587 | ||||||||
\(685\) | −1.36873 | + | 3.24444i | −0.0522964 | + | 0.123964i | ||||
\(686\) | 18.5159 | − | 0.403733i | 0.706939 | − | 0.0154146i | ||||
\(687\) | −6.44709 | + | 6.44709i | −0.245972 | + | 0.245972i | ||||
\(688\) | −1.04912 | − | 1.04912i | −0.0399974 | − | 0.0399974i | ||||
\(689\) | −6.33362 | −0.241292 | ||||||||
\(690\) | 8.89055 | − | 21.0742i | 0.338458 | − | 0.802282i | ||||
\(691\) | 44.7424i | 1.70208i | 0.525099 | + | 0.851041i | \(0.324028\pi\) | ||||
−0.525099 | + | 0.851041i | \(0.675972\pi\) | |||||||
\(692\) | 4.15568 | + | 4.15568i | 0.157975 | + | 0.157975i | ||||
\(693\) | −13.5441 | + | 3.73483i | −0.514497 | + | 0.141874i | ||||
\(694\) | 19.6766i | 0.746912i | ||||||||
\(695\) | −7.88389 | + | 3.20559i | −0.299053 | + | 0.121595i | ||||
\(696\) | 20.9004i | 0.792229i | ||||||||
\(697\) | 14.3467 | − | 14.3467i | 0.543419 | − | 0.543419i | ||||
\(698\) | −1.04972 | + | 1.04972i | −0.0397326 | + | 0.0397326i | ||||
\(699\) | 7.26492 | 0.274784 | ||||||||
\(700\) | 6.68032 | − | 11.4181i | 0.252492 | − | 0.431564i | ||||
\(701\) | 25.7985 | 0.974394 | 0.487197 | − | 0.873292i | \(-0.338019\pi\) | ||||
0.487197 | + | 0.873292i | \(0.338019\pi\) | |||||||
\(702\) | 26.5869 | − | 26.5869i | 1.00346 | − | 1.00346i | ||||
\(703\) | 14.4911 | − | 14.4911i | 0.546540 | − | 0.546540i | ||||
\(704\) | − | 1.00000i | − | 0.0376889i | ||||||
\(705\) | −52.5222 | + | 21.3555i | −1.97810 | + | 0.804296i | ||||
\(706\) | 4.88759i | 0.183947i | ||||||||
\(707\) | −29.6170 | + | 8.16700i | −1.11386 | + | 0.307152i | ||||
\(708\) | −17.1209 | − | 17.1209i | −0.643443 | − | 0.643443i | ||||
\(709\) | 1.81465i | 0.0681505i | 0.999419 | + | 0.0340752i | \(0.0108486\pi\) | ||||
−0.999419 | + | 0.0340752i | \(0.989151\pi\) | |||||||
\(710\) | 8.23350 | − | 19.5167i | 0.308998 | − | 0.732450i | ||||
\(711\) | −24.7322 | −0.927532 | ||||||||
\(712\) | 11.3222 | + | 11.3222i | 0.424319 | + | 0.424319i | ||||
\(713\) | 9.71228 | − | 9.71228i | 0.363728 | − | 0.363728i | ||||
\(714\) | −31.8464 | − | 18.0792i | −1.19182 | − | 0.676598i | ||||
\(715\) | −4.90696 | + | 11.6315i | −0.183510 | + | 0.434993i | ||||
\(716\) | 6.60014 | 0.246659 | ||||||||
\(717\) | 21.5767 | + | 21.5767i | 0.805798 | + | 0.805798i | ||||
\(718\) | −11.8770 | − | 11.8770i | −0.443244 | − | 0.443244i | ||||
\(719\) | −8.10544 | −0.302282 | −0.151141 | − | 0.988512i | \(-0.548295\pi\) | ||||
−0.151141 | + | 0.988512i | \(0.548295\pi\) | |||||||
\(720\) | 4.47243 | + | 10.9996i | 0.166678 | + | 0.409931i | ||||
\(721\) | −32.2154 | − | 18.2887i | −1.19976 | − | 0.681108i | ||||
\(722\) | −3.91870 | + | 3.91870i | −0.145839 | + | 0.145839i | ||||
\(723\) | −34.1538 | − | 34.1538i | −1.27019 | − | 1.27019i | ||||
\(724\) | 14.4577 | 0.537315 | ||||||||
\(725\) | 25.2970 | + | 25.9651i | 0.939507 | + | 0.964320i | ||||
\(726\) | 2.88275i | 0.106989i | ||||||||
\(727\) | −26.0738 | − | 26.0738i | −0.967025 | − | 0.967025i | 0.0324487 | − | 0.999473i | \(-0.489669\pi\) |
−0.999473 | + | 0.0324487i | \(0.989669\pi\) | |||||||
\(728\) | 3.97076 | + | 14.3997i | 0.147166 | + | 0.533687i | ||||
\(729\) | − | 40.2424i | − | 1.49046i | ||||||
\(730\) | −10.6403 | − | 26.1689i | −0.393814 | − | 0.968555i | ||||
\(731\) | 7.12373i | 0.263481i | ||||||||
\(732\) | −26.3664 | + | 26.3664i | −0.974529 | + | 0.974529i | ||||
\(733\) | 7.51195 | − | 7.51195i | 0.277460 | − | 0.277460i | −0.554634 | − | 0.832094i | \(-0.687142\pi\) |
0.832094 | + | 0.554634i | \(0.187142\pi\) | |||||||
\(734\) | −9.43418 | −0.348222 | ||||||||
\(735\) | 6.24813 | + | 44.6875i | 0.230466 | + | 1.64832i | ||||
\(736\) | −3.54836 | −0.130794 | ||||||||
\(737\) | −3.04387 | + | 3.04387i | −0.112123 | + | 0.112123i | ||||
\(738\) | 15.8672 | − | 15.8672i | 0.584079 | − | 0.584079i | ||||
\(739\) | − | 24.9390i | − | 0.917396i | −0.888592 | − | 0.458698i | \(-0.848316\pi\) | ||
0.888592 | − | 0.458698i | \(-0.151684\pi\) | |||||||
\(740\) | 8.52272 | + | 3.59547i | 0.313301 | + | 0.132172i | ||||
\(741\) | 80.6267i | 2.96189i | ||||||||
\(742\) | 0.789023 | + | 2.86134i | 0.0289660 | + | 0.105043i | ||||
\(743\) | −19.2817 | − | 19.2817i | −0.707377 | − | 0.707377i | 0.258606 | − | 0.965983i | \(-0.416737\pi\) |
−0.965983 | + | 0.258606i | \(0.916737\pi\) | |||||||
\(744\) | 11.1588i | 0.409100i | ||||||||
\(745\) | 2.99981 | + | 7.37779i | 0.109904 | + | 0.270301i | ||||
\(746\) | 2.17655 | 0.0796893 | ||||||||
\(747\) | 56.7020 | + | 56.7020i | 2.07462 | + | 2.07462i | ||||
\(748\) | −3.39509 | + | 3.39509i | −0.124137 | + | 0.124137i | ||||
\(749\) | −9.21848 | − | 5.23334i | −0.336836 | − | 0.191222i | ||||
\(750\) | 29.5300 | + | 12.9136i | 1.07828 | + | 0.471539i | ||||
\(751\) | 29.2201 | 1.06626 | 0.533129 | − | 0.846034i | \(-0.321016\pi\) | ||||
0.533129 | + | 0.846034i | \(0.321016\pi\) | |||||||
\(752\) | 6.21956 | + | 6.21956i | 0.226804 | + | 0.226804i | ||||
\(753\) | 24.6549 | + | 24.6549i | 0.898473 | + | 0.898473i | ||||
\(754\) | −40.9323 | −1.49067 | ||||||||
\(755\) | 17.2176 | − | 7.00067i | 0.626613 | − | 0.254781i | ||||
\(756\) | −15.3233 | − | 8.69905i | −0.557303 | − | 0.316381i | ||||
\(757\) | 23.4814 | − | 23.4814i | 0.853445 | − | 0.853445i | −0.137111 | − | 0.990556i | \(-0.543782\pi\) |
0.990556 | + | 0.137111i | \(0.0437818\pi\) | |||||||
\(758\) | 10.8932 | + | 10.8932i | 0.395657 | + | 0.395657i | ||||
\(759\) | 10.2290 | 0.371290 | ||||||||
\(760\) | −10.2064 | − | 4.30575i | −0.370224 | − | 0.156186i | ||||
\(761\) | 12.4697i | 0.452027i | 0.974124 | + | 0.226013i | \(0.0725693\pi\) | ||||
−0.974124 | + | 0.226013i | \(0.927431\pi\) | |||||||
\(762\) | 32.6568 | + | 32.6568i | 1.18303 | + | 1.18303i | ||||
\(763\) | 23.8135 | − | 6.56664i | 0.862105 | − | 0.237728i | ||||
\(764\) | 10.1657i | 0.367783i | ||||||||
\(765\) | 22.1603 | − | 52.5290i | 0.801208 | − | 1.89919i | ||||
\(766\) | − | 4.01756i | − | 0.145160i | ||||||
\(767\) | 33.5303 | − | 33.5303i | 1.21071 | − | 1.21071i | ||||
\(768\) | 2.03841 | − | 2.03841i | 0.0735549 | − | 0.0735549i | ||||
\(769\) | 42.2430 | 1.52332 | 0.761661 | − | 0.647976i | \(-0.224384\pi\) | ||||
0.761661 | + | 0.647976i | \(0.224384\pi\) | |||||||
\(770\) | 5.86605 | + | 0.767799i | 0.211398 | + | 0.0276695i | ||||
\(771\) | 23.4509 | 0.844563 | ||||||||
\(772\) | −7.16762 | + | 7.16762i | −0.257968 | + | 0.257968i | ||||
\(773\) | −12.7135 | + | 12.7135i | −0.457272 | + | 0.457272i | −0.897759 | − | 0.440487i | \(-0.854806\pi\) |
0.440487 | + | 0.897759i | \(0.354806\pi\) | |||||||
\(774\) | 7.87872i | 0.283195i | ||||||||
\(775\) | 13.5061 | + | 13.8628i | 0.485153 | + | 0.497966i | ||||
\(776\) | − | 7.98120i | − | 0.286508i | ||||||
\(777\) | −30.4160 | + | 8.38733i | −1.09117 | + | 0.300894i | ||||
\(778\) | −10.3883 | − | 10.3883i | −0.372439 | − | 0.372439i | ||||
\(779\) | 20.9341i | 0.750041i | ||||||||
\(780\) | −33.7122 | + | 13.7074i | −1.20709 | + | 0.490802i | ||||
\(781\) | 9.47305 | 0.338972 | ||||||||
\(782\) | 12.0470 | + | 12.0470i | 0.430800 | + | 0.430800i | ||||
\(783\) | 34.1428 | − | 34.1428i | 1.22016 | − | 1.22016i | ||||
\(784\) | 6.01067 | − | 3.58774i | 0.214667 | − | 0.128133i | ||||
\(785\) | 8.20619 | + | 3.46193i | 0.292891 | + | 0.123562i | ||||
\(786\) | −59.9422 | −2.13807 | ||||||||
\(787\) | −36.0382 | − | 36.0382i | −1.28462 | − | 1.28462i | −0.938008 | − | 0.346614i | \(-0.887331\pi\) |
−0.346614 | − | 0.938008i | \(-0.612669\pi\) | |||||||
\(788\) | 12.8091 | + | 12.8091i | 0.456304 | + | 0.456304i | ||||
\(789\) | 43.5476 | 1.55034 | ||||||||
\(790\) | 9.59547 | + | 4.04803i | 0.341391 | + | 0.144022i | ||||
\(791\) | −18.0196 | + | 31.7414i | −0.640704 | + | 1.12859i | ||||
\(792\) | −3.75491 | + | 3.75491i | −0.133425 | + | 0.133425i | ||||
\(793\) | −51.6370 | − | 51.6370i | −1.83368 | − | 1.83368i | ||||
\(794\) | 9.78614 | 0.347297 | ||||||||
\(795\) | −6.69889 | + | 2.72377i | −0.237585 | + | 0.0966021i | ||||
\(796\) | − | 10.6361i | − | 0.376986i | ||||||
\(797\) | 13.3328 | + | 13.3328i | 0.472274 | + | 0.472274i | 0.902650 | − | 0.430376i | \(-0.141619\pi\) |
−0.430376 | + | 0.902650i | \(0.641619\pi\) | |||||||
\(798\) | 36.4247 | − | 10.0442i | 1.28942 | − | 0.355562i | ||||
\(799\) | − | 42.2320i | − | 1.49406i | ||||||
\(800\) | 0.0651599 | − | 4.99958i | 0.00230375 | − | 0.176762i | ||||
\(801\) | − | 85.0280i | − | 3.00432i | ||||||
\(802\) | −21.4709 | + | 21.4709i | −0.758163 | + | 0.758163i | ||||
\(803\) | 8.93324 | − | 8.93324i | 0.315247 | − | 0.315247i | ||||
\(804\) | −12.4093 | −0.437644 | ||||||||
\(805\) | 2.72442 | − | 20.8148i | 0.0960233 | − | 0.733626i | ||||
\(806\) | −21.8538 | −0.769767 | ||||||||
\(807\) | 12.7219 | − | 12.7219i | 0.447833 | − | 0.447833i | ||||
\(808\) | −8.21092 | + | 8.21092i | −0.288859 | + | 0.288859i | ||||
\(809\) | − | 53.6514i | − | 1.88628i | −0.332394 | − | 0.943141i | \(-0.607856\pi\) | ||
0.332394 | − | 0.943141i | \(-0.392144\pi\) | |||||||
\(810\) | 2.84037 | − | 6.73282i | 0.0998003 | − | 0.236567i | ||||
\(811\) | 6.67559i | 0.234412i | 0.993108 | + | 0.117206i | \(0.0373937\pi\) | ||||
−0.993108 | + | 0.117206i | \(0.962606\pi\) | |||||||
\(812\) | 5.09922 | + | 18.4920i | 0.178948 | + | 0.648941i | ||||
\(813\) | 39.0124 | + | 39.0124i | 1.36822 | + | 1.36822i | ||||
\(814\) | 4.13677i | 0.144994i | ||||||||
\(815\) | −44.0141 | − | 18.5681i | −1.54174 | − | 0.650414i | ||||
\(816\) | −13.8412 | −0.484539 | ||||||||
\(817\) | −5.19732 | − | 5.19732i | −0.181831 | − | 0.181831i | ||||
\(818\) | −3.94095 | + | 3.94095i | −0.137792 | + | 0.137792i | ||||
\(819\) | 39.1597 | − | 68.9793i | 1.36835 | − | 2.41033i | ||||
\(820\) | −8.75310 | + | 3.55901i | −0.305671 | + | 0.124286i | ||||
\(821\) | 4.69542 | 0.163871 | 0.0819357 | − | 0.996638i | \(-0.473890\pi\) | ||||
0.0819357 | + | 0.996638i | \(0.473890\pi\) | |||||||
\(822\) | −3.21007 | − | 3.21007i | −0.111964 | − | 0.111964i | ||||
\(823\) | 21.8412 | + | 21.8412i | 0.761336 | + | 0.761336i | 0.976564 | − | 0.215228i | \(-0.0690495\pi\) |
−0.215228 | + | 0.976564i | \(0.569050\pi\) | |||||||
\(824\) | −14.0016 | −0.487768 | ||||||||
\(825\) | −0.187840 | + | 14.4125i | −0.00653974 | + | 0.501780i | ||||
\(826\) | −19.3251 | − | 10.9709i | −0.672406 | − | 0.381726i | ||||
\(827\) | −4.03102 | + | 4.03102i | −0.140172 | + | 0.140172i | −0.773711 | − | 0.633539i | \(-0.781602\pi\) |
0.633539 | + | 0.773711i | \(0.281602\pi\) | |||||||
\(828\) | 13.3238 | + | 13.3238i | 0.463033 | + | 0.463033i | ||||
\(829\) | 33.3279 | 1.15753 | 0.578764 | − | 0.815495i | \(-0.303535\pi\) | ||||
0.578764 | + | 0.815495i | \(0.303535\pi\) | |||||||
\(830\) | −12.7183 | − | 31.2796i | −0.441458 | − | 1.08573i | ||||
\(831\) | 65.6554i | 2.27756i | ||||||||
\(832\) | 3.99211 | + | 3.99211i | 0.138402 | + | 0.138402i | ||||
\(833\) | −32.5875 | − | 8.22609i | −1.12909 | − | 0.285017i | ||||
\(834\) | − | 10.9720i | − | 0.379929i | ||||||
\(835\) | 6.99487 | + | 2.95092i | 0.242068 | + | 0.102121i | ||||
\(836\) | − | 4.95398i | − | 0.171337i | ||||||
\(837\) | 18.2289 | − | 18.2289i | 0.630081 | − | 0.630081i | ||||
\(838\) | −25.3908 | + | 25.3908i | −0.877112 | + | 0.877112i | ||||
\(839\) | 30.5646 | 1.05521 | 0.527604 | − | 0.849491i | \(-0.323091\pi\) | ||||
0.527604 | + | 0.849491i | \(0.323091\pi\) | |||||||
\(840\) | 10.3923 | + | 13.5225i | 0.358569 | + | 0.466571i | ||||
\(841\) | −23.5650 | −0.812587 | ||||||||
\(842\) | 5.17599 | − | 5.17599i | 0.178377 | − | 0.178377i | ||||
\(843\) | 2.35551 | − | 2.35551i | 0.0811282 | − | 0.0811282i | ||||
\(844\) | − | 17.8348i | − | 0.613899i | ||||||
\(845\) | −15.8961 | − | 39.0952i | −0.546843 | − | 1.34492i | ||||
\(846\) | − | 46.7078i | − | 1.60585i | ||||||
\(847\) | 0.703324 | + | 2.55056i | 0.0241665 | + | 0.0876381i | ||||
\(848\) | 0.793267 | + | 0.793267i | 0.0272409 | + | 0.0272409i | ||||
\(849\) | 1.60685i | 0.0551471i | ||||||||
\(850\) | −17.1952 | + | 16.7528i | −0.589792 | + | 0.574616i | ||||
\(851\) | 14.6787 | 0.503180 | ||||||||
\(852\) | 19.3100 | + | 19.3100i | 0.661549 | + | 0.661549i | ||||
\(853\) | 15.3416 | − | 15.3416i | 0.525288 | − | 0.525288i | −0.393876 | − | 0.919164i | \(-0.628866\pi\) |
0.919164 | + | 0.393876i | \(0.128866\pi\) | |||||||
\(854\) | −16.8953 | + | 29.7608i | −0.578144 | + | 1.01839i | ||||
\(855\) | 22.1563 | + | 54.4917i | 0.757730 | + | 1.86358i | ||||
\(856\) | −4.00657 | −0.136942 | ||||||||
\(857\) | 31.7855 | + | 31.7855i | 1.08577 | + | 1.08577i | 0.995959 | + | 0.0898137i | \(0.0286272\pi\) |
0.0898137 | + | 0.995959i | \(0.471373\pi\) | |||||||
\(858\) | −11.5083 | − | 11.5083i | −0.392886 | − | 0.392886i | ||||
\(859\) | 7.02928 | 0.239836 | 0.119918 | − | 0.992784i | \(-0.461737\pi\) | ||||
0.119918 | + | 0.992784i | \(0.461737\pi\) | |||||||
\(860\) | 1.28954 | − | 3.05674i | 0.0439730 | − | 0.104234i | ||||
\(861\) | 15.9116 | − | 28.0281i | 0.542265 | − | 0.955195i | ||||
\(862\) | 10.9830 | − | 10.9830i | 0.374081 | − | 0.374081i | ||||
\(863\) | −3.04516 | − | 3.04516i | −0.103659 | − | 0.103659i | 0.653375 | − | 0.757034i | \(-0.273352\pi\) |
−0.757034 | + | 0.653375i | \(0.773352\pi\) | |||||||
\(864\) | −6.65986 | −0.226573 | ||||||||
\(865\) | −5.10801 | + | 12.1081i | −0.173677 | + | 0.411686i | ||||
\(866\) | 31.6426i | 1.07526i | ||||||||
\(867\) | 12.3392 | + | 12.3392i | 0.419060 | + | 0.419060i | ||||
\(868\) | 2.72248 | + | 9.87288i | 0.0924070 | + | 0.335107i | ||||
\(869\) | 4.65746i | 0.157993i | ||||||||
\(870\) | −43.2929 | + | 17.6029i | −1.46777 | + | 0.596794i | ||||
\(871\) | − | 24.3030i | − | 0.823475i | ||||||
\(872\) | 6.60196 | − | 6.60196i | 0.223571 | − | 0.223571i | ||||
\(873\) | −29.9687 | + | 29.9687i | −1.01429 | + | 1.01429i | ||||
\(874\) | −17.5785 | −0.594601 | ||||||||
\(875\) | 29.2777 | + | 4.22090i | 0.989767 | + | 0.142692i | ||||
\(876\) | 36.4192 | 1.23049 | ||||||||
\(877\) | −3.88099 | + | 3.88099i | −0.131052 | + | 0.131052i | −0.769590 | − | 0.638538i | \(-0.779539\pi\) |
0.638538 | + | 0.769590i | \(0.279539\pi\) | |||||||
\(878\) | 26.6656 | − | 26.6656i | 0.899922 | − | 0.899922i | ||||
\(879\) | 86.7004i | 2.92433i | ||||||||
\(880\) | 2.07139 | − | 0.842227i | 0.0698265 | − | 0.0283915i | ||||
\(881\) | 14.1935i | 0.478192i | 0.970996 | + | 0.239096i | \(0.0768510\pi\) | ||||
−0.970996 | + | 0.239096i | \(0.923149\pi\) | |||||||
\(882\) | −36.0412 | − | 9.09790i | −1.21357 | − | 0.306342i | ||||
\(883\) | 30.1032 | + | 30.1032i | 1.01305 | + | 1.01305i | 0.999914 | + | 0.0131401i | \(0.00418273\pi\) |
0.0131401 | + | 0.999914i | \(0.495817\pi\) | |||||||
\(884\) | − | 27.1072i | − | 0.911713i | ||||||
\(885\) | 21.0444 | − | 49.8838i | 0.707400 | − | 1.67682i | ||||
\(886\) | 38.3790 | 1.28937 | ||||||||
\(887\) | −0.346940 | − | 0.346940i | −0.0116491 | − | 0.0116491i | 0.701258 | − | 0.712907i | \(-0.252622\pi\) |
−0.712907 | + | 0.701258i | \(0.752622\pi\) | |||||||
\(888\) | −8.43243 | + | 8.43243i | −0.282974 | + | 0.282974i | ||||
\(889\) | 36.8610 | + | 20.9261i | 1.23628 | + | 0.701837i | ||||
\(890\) | −13.9169 | + | 32.9886i | −0.466494 | + | 1.10578i | ||||
\(891\) | 3.26798 | 0.109482 | ||||||||
\(892\) | 1.13707 | + | 1.13707i | 0.0380721 | + | 0.0380721i | ||||
\(893\) | 30.8115 | + | 30.8115i | 1.03107 | + | 1.03107i | ||||
\(894\) | −10.2677 | −0.343402 | ||||||||
\(895\) | 5.55882 | + | 13.6715i | 0.185811 | + | 0.456987i | ||||
\(896\) | 1.30619 | − | 2.30084i | 0.0436367 | − | 0.0768657i | ||||
\(897\) | −40.8354 | + | 40.8354i | −1.36346 | + | 1.36346i | ||||
\(898\) | 23.4966 | + | 23.4966i | 0.784093 | + | 0.784093i | ||||
\(899\) | −28.0645 | −0.936004 | ||||||||
\(900\) | −19.0176 | + | 18.5283i | −0.633921 | + | 0.617610i | ||||
\(901\) | − | 5.38643i | − | 0.179448i | ||||||
\(902\) | −2.98803 | − | 2.98803i | −0.0994905 | − | 0.0994905i | ||||
\(903\) | 3.00818 | + | 10.9089i | 0.100106 | + | 0.363027i | ||||
\(904\) | 13.7956i | 0.458834i | ||||||||
\(905\) | 12.1766 | + | 29.9475i | 0.404765 | + | 0.995488i | ||||
\(906\) | 23.9617i | 0.796075i | ||||||||
\(907\) | −0.417174 | + | 0.417174i | −0.0138520 | + | 0.0138520i | −0.713999 | − | 0.700147i | \(-0.753118\pi\) |
0.700147 | + | 0.713999i | \(0.253118\pi\) | |||||||
\(908\) | −0.774054 | + | 0.774054i | −0.0256879 | + | 0.0256879i | ||||
\(909\) | 61.6626 | 2.04522 | ||||||||
\(910\) | −26.4830 | + | 20.3528i | −0.877905 | + | 0.674688i | ||||
\(911\) | 46.8741 | 1.55301 | 0.776504 | − | 0.630112i | \(-0.216991\pi\) | ||||
0.776504 | + | 0.630112i | \(0.216991\pi\) | |||||||
\(912\) | 10.0982 | − | 10.0982i | 0.334386 | − | 0.334386i | ||||
\(913\) | 10.6779 | − | 10.6779i | 0.353385 | − | 0.353385i | ||||
\(914\) | − | 8.87603i | − | 0.293593i | ||||||
\(915\) | −76.8215 | − | 32.4086i | −2.53964 | − | 1.07139i | ||||
\(916\) | 3.16280i | 0.104502i | ||||||||
\(917\) | −53.0348 | + | 14.6245i | −1.75136 | + | 0.482944i | ||||
\(918\) | 22.6109 | + | 22.6109i | 0.746270 | + | 0.746270i | ||||
\(919\) | − | 41.8925i | − | 1.38190i | −0.722900 | − | 0.690952i | \(-0.757191\pi\) | ||
0.722900 | − | 0.690952i | \(-0.242809\pi\) | |||||||
\(920\) | −2.98852 | − | 7.35003i | −0.0985286 | − | 0.242323i | ||||
\(921\) | −84.6887 | −2.79059 | ||||||||
\(922\) | 13.6101 | + | 13.6101i | 0.448225 | + | 0.448225i | ||||
\(923\) | −37.8175 | + | 37.8175i | −1.24478 | + | 1.24478i | ||||
\(924\) | −3.76542 | + | 6.63275i | −0.123873 | + | 0.218201i | ||||
\(925\) | −0.269551 | + | 20.6821i | −0.00886279 | + | 0.680022i | ||||
\(926\) | 10.5226 | 0.345793 | ||||||||
\(927\) | 52.5747 | + | 52.5747i | 1.72678 | + | 1.72678i | ||||
\(928\) | 5.12665 | + | 5.12665i | 0.168290 | + | 0.168290i | ||||
\(929\) | −27.7966 | −0.911977 | −0.455988 | − | 0.889986i | \(-0.650714\pi\) | ||||
−0.455988 | + | 0.889986i | \(0.650714\pi\) | |||||||
\(930\) | −23.1141 | + | 9.39821i | −0.757943 | + | 0.308179i | ||||
\(931\) | 29.7767 | − | 17.7736i | 0.975892 | − | 0.582505i | ||||
\(932\) | 1.78200 | − | 1.78200i | 0.0583715 | − | 0.0583715i | ||||
\(933\) | −40.5036 | − | 40.5036i | −1.32603 | − | 1.32603i | ||||
\(934\) | 2.44301 | 0.0799379 | ||||||||
\(935\) | −9.89200 | − | 4.17312i | −0.323503 | − | 0.136476i | ||||
\(936\) | − | 29.9801i | − | 0.979929i | ||||||
\(937\) | −35.1304 | − | 35.1304i | −1.14766 | − | 1.14766i | −0.987011 | − | 0.160650i | \(-0.948641\pi\) |
−0.160650 | − | 0.987011i | \(-0.551359\pi\) | |||||||
\(938\) | −10.9793 | + | 3.02759i | −0.358488 | + | 0.0988544i | ||||
\(939\) | − | 35.3244i | − | 1.15277i | ||||||
\(940\) | −7.64485 | + | 18.1214i | −0.249348 | + | 0.591055i | ||||
\(941\) | − | 29.0178i | − | 0.945952i | −0.881075 | − | 0.472976i | \(-0.843180\pi\) | ||
0.881075 | − | 0.472976i | \(-0.156820\pi\) | |||||||
\(942\) | −8.11925 | + | 8.11925i | −0.264539 | + | 0.264539i | ||||
\(943\) | −10.6026 | + | 10.6026i | −0.345268 | + | 0.345268i | ||||
\(944\) | −8.39914 | −0.273369 | ||||||||
\(945\) | 5.11344 | − | 39.0671i | 0.166340 | − | 1.27085i | ||||
\(946\) | 1.48368 | 0.0482386 | ||||||||
\(947\) | −8.51386 | + | 8.51386i | −0.276663 | + | 0.276663i | −0.831775 | − | 0.555112i | \(-0.812675\pi\) |
0.555112 | + | 0.831775i | \(0.312675\pi\) | |||||||
\(948\) | −9.49382 | + | 9.49382i | −0.308345 | + | 0.308345i | ||||
\(949\) | 71.3250i | 2.31531i | ||||||||
\(950\) | 0.322801 | − | 24.7678i | 0.0104730 | − | 0.803573i | ||||
\(951\) | − | 31.8074i | − | 1.03143i | ||||||
\(952\) | −12.2462 | + | 3.37693i | −0.396902 | + | 0.109447i | ||||
\(953\) | 0.0324873 | + | 0.0324873i | 0.00105237 | + | 0.00105237i | 0.707633 | − | 0.706580i | \(-0.249763\pi\) |
−0.706580 | + | 0.707633i | \(0.749763\pi\) | |||||||
\(954\) | − | 5.95729i | − | 0.192874i | ||||||
\(955\) | −21.0572 | + | 8.56185i | −0.681395 | + | 0.277055i | ||||
\(956\) | 10.5851 | 0.342346 | ||||||||
\(957\) | −14.7788 | − | 14.7788i | −0.477732 | − | 0.477732i | ||||
\(958\) | 2.22438 | − | 2.22438i | 0.0718664 | − | 0.0718664i | ||||
\(959\) | −3.62334 | − | 2.05697i | −0.117004 | − | 0.0664231i | ||||
\(960\) | 5.93915 | + | 2.50554i | 0.191685 | + | 0.0808660i | ||||
\(961\) | 16.0163 | 0.516656 | ||||||||
\(962\) | −16.5144 | − | 16.5144i | −0.532447 | − | 0.532447i | ||||
\(963\) | 15.0443 | + | 15.0443i | 0.484797 | + | 0.484797i | ||||
\(964\) | −16.7551 | −0.539646 | ||||||||
\(965\) | −20.8837 | − | 8.81017i | −0.672270 | − | 0.283610i | ||||
\(966\) | 23.5354 | + | 13.3611i | 0.757238 | + | 0.429885i | ||||
\(967\) | 13.0637 | − | 13.0637i | 0.420099 | − | 0.420099i | −0.465139 | − | 0.885238i | \(-0.653995\pi\) |
0.885238 | + | 0.465139i | \(0.153995\pi\) | |||||||
\(968\) | 0.707107 | + | 0.707107i | 0.0227273 | + | 0.0227273i | ||||
\(969\) | −68.5690 | −2.20275 | ||||||||
\(970\) | 16.5322 | − | 6.72198i | 0.530816 | − | 0.215830i | ||||
\(971\) | − | 26.9200i | − | 0.863905i | −0.901896 | − | 0.431952i | \(-0.857825\pi\) | ||
0.901896 | − | 0.431952i | \(-0.142175\pi\) | |||||||
\(972\) | −7.46621 | − | 7.46621i | −0.239479 | − | 0.239479i | ||||
\(973\) | −2.67692 | − | 9.70764i | −0.0858180 | − | 0.311213i | ||||
\(974\) | 15.0397i | 0.481903i | ||||||||
\(975\) | −56.7865 | − | 58.2863i | −1.81862 | − | 1.86666i | ||||
\(976\) | 12.9348i | 0.414032i | ||||||||
\(977\) | −36.5953 | + | 36.5953i | −1.17079 | + | 1.17079i | −0.188765 | + | 0.982022i | \(0.560448\pi\) |
−0.982022 | + | 0.188765i | \(0.939552\pi\) | |||||||
\(978\) | 43.5478 | − | 43.5478i | 1.39250 | − | 1.39250i | ||||
\(979\) | −16.0121 | −0.511747 | ||||||||
\(980\) | 12.4939 | + | 9.42875i | 0.399104 | + | 0.301190i | ||||
\(981\) | −49.5795 | −1.58295 | ||||||||
\(982\) | −7.57405 | + | 7.57405i | −0.241698 | + | 0.241698i | ||||
\(983\) | 7.49060 | − | 7.49060i | 0.238913 | − | 0.238913i | −0.577487 | − | 0.816400i | \(-0.695967\pi\) |
0.816400 | + | 0.577487i | \(0.195967\pi\) | |||||||
\(984\) | − | 12.1817i | − | 0.388337i | ||||||
\(985\) | −15.7444 | + | 37.3207i | −0.501659 | + | 1.18914i | ||||
\(986\) | − | 34.8109i | − | 1.10860i | ||||||
\(987\) | −17.8335 | − | 64.6720i | −0.567647 | − | 2.05853i | ||||
\(988\) | 19.7768 | + | 19.7768i | 0.629185 | + | 0.629185i | ||||
\(989\) | − | 5.26463i | − | 0.167406i | ||||||
\(990\) | −10.9404 | − | 4.61540i | −0.347708 | − | 0.146687i | ||||
\(991\) | 44.1927 | 1.40383 | 0.701914 | − | 0.712262i | \(-0.252329\pi\) | ||||
0.701914 | + | 0.712262i | \(0.252329\pi\) | |||||||
\(992\) | 2.73712 | + | 2.73712i | 0.0869037 | + | 0.0869037i | ||||
\(993\) | 7.75627 | − | 7.75627i | 0.246138 | − | 0.246138i | ||||
\(994\) | 21.7960 | + | 12.3736i | 0.691327 | + | 0.392467i | ||||
\(995\) | 22.0315 | − | 8.95799i | 0.698444 | − | 0.283987i | ||||
\(996\) | 43.5317 | 1.37936 | ||||||||
\(997\) | −13.0234 | − | 13.0234i | −0.412454 | − | 0.412454i | 0.470138 | − | 0.882593i | \(-0.344204\pi\) |
−0.882593 | + | 0.470138i | \(0.844204\pi\) | |||||||
\(998\) | −12.3811 | − | 12.3811i | −0.391917 | − | 0.391917i | ||||
\(999\) | 27.5503 | 0.871653 |
(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 | 770.2.l.c.573.10 | yes | 40 | |
5.2 | odd | 4 | inner | 770.2.l.c.727.1 | yes | 40 | |
7.6 | odd | 2 | inner | 770.2.l.c.573.1 | ✓ | 40 | |
35.27 | even | 4 | inner | 770.2.l.c.727.10 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.l.c.573.1 | ✓ | 40 | 7.6 | odd | 2 | inner | |
770.2.l.c.573.10 | yes | 40 | 1.1 | even | 1 | trivial | |
770.2.l.c.727.1 | yes | 40 | 5.2 | odd | 4 | inner | |
770.2.l.c.727.10 | yes | 40 | 35.27 | even | 4 | inner |