Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,3,Mod(43,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.r (of order \(18\), degree \(6\), 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: | \(5.88557371018\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{18})\) |
Coefficient field: | 12.0.101559956668416.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 8x^{6} + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 43.2 | ||
Root | \(0.483690 - 1.32893i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.43 |
Dual form | 216.3.r.a.211.2 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.53209 | − | 1.28558i | −0.766044 | − | 0.642788i | ||||
\(3\) | 1.90707 | + | 2.31583i | 0.635691 | + | 0.771944i | ||||
\(4\) | 0.694593 | + | 3.93923i | 0.173648 | + | 0.984808i | ||||
\(5\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(6\) | 0.0553729 | − | 5.99974i | 0.00922881 | − | 0.999957i | ||||
\(7\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(8\) | 4.00000 | − | 6.92820i | 0.500000 | − | 0.866025i | ||||
\(9\) | −1.72616 | + | 8.83292i | −0.191795 | + | 0.981435i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.4204 | − | 4.88462i | 1.22003 | − | 0.444056i | 0.349861 | − | 0.936802i | \(-0.386229\pi\) |
0.870173 | + | 0.492746i | \(0.164007\pi\) | |||||||
\(12\) | −7.79796 | + | 9.12096i | −0.649830 | + | 0.760080i | ||||
\(13\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15.0351 | + | 5.47232i | −0.939693 | + | 0.342020i | ||||
\(17\) | 10.1424 | + | 17.5672i | 0.596613 | + | 1.03336i | 0.993317 | + | 0.115418i | \(0.0368206\pi\) |
−0.396704 | + | 0.917947i | \(0.629846\pi\) | |||||||
\(18\) | 14.0000 | − | 11.3137i | 0.777778 | − | 0.628539i | ||||
\(19\) | −18.8769 | + | 32.6958i | −0.993522 | + | 1.72083i | −0.398343 | + | 0.917236i | \(0.630415\pi\) |
−0.595178 | + | 0.803594i | \(0.702919\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −26.8408 | − | 9.76924i | −1.22003 | − | 0.444056i | ||||
\(23\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(24\) | 23.6728 | − | 3.94925i | 0.986368 | − | 0.164552i | ||||
\(25\) | 19.1511 | + | 16.0697i | 0.766044 | + | 0.642788i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −23.7474 | + | 12.8475i | −0.879535 | + | 0.475834i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(32\) | 30.0702 | + | 10.9446i | 0.939693 | + | 0.342020i | ||||
\(33\) | 36.9056 | + | 21.7640i | 1.11835 | + | 0.659516i | ||||
\(34\) | 7.04485 | − | 39.9533i | 0.207202 | − | 1.17510i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −35.9939 | − | 0.664446i | −0.999830 | − | 0.0184568i | ||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | 70.9540 | − | 25.8251i | 1.86721 | − | 0.679609i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 50.8983 | − | 42.7087i | 1.24142 | − | 1.04168i | 0.244009 | − | 0.969773i | \(-0.421537\pi\) |
0.997412 | − | 0.0719030i | \(-0.0229072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 41.1752 | − | 14.9865i | 0.957562 | − | 0.348524i | 0.184485 | − | 0.982835i | \(-0.440938\pi\) |
0.773078 | + | 0.634311i | \(0.218716\pi\) | |||||||
\(44\) | 28.5633 | + | 49.4731i | 0.649167 | + | 1.12439i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(48\) | −41.3460 | − | 24.3826i | −0.861374 | − | 0.507971i | ||||
\(49\) | −46.0449 | − | 16.7590i | −0.939693 | − | 0.342020i | ||||
\(50\) | −8.68241 | − | 49.2404i | −0.173648 | − | 0.984808i | ||||
\(51\) | −21.3403 | + | 56.9900i | −0.418438 | + | 1.11745i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 52.8997 | + | 10.8456i | 0.979623 | + | 0.200844i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −111.718 | + | 18.6374i | −1.95996 | + | 0.326972i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −45.1367 | − | 16.4284i | −0.765028 | − | 0.278447i | −0.0701128 | − | 0.997539i | \(-0.522336\pi\) |
−0.694915 | + | 0.719092i | \(0.744558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32.0000 | − | 55.4256i | −0.500000 | − | 0.866025i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −28.5633 | − | 80.7893i | −0.432778 | − | 1.22408i | ||||
\(67\) | −81.3715 | + | 68.2788i | −1.21450 | + | 1.01909i | −0.215407 | + | 0.976524i | \(0.569108\pi\) |
−0.999094 | + | 0.0425626i | \(0.986448\pi\) | |||||||
\(68\) | −62.1564 | + | 52.1554i | −0.914064 | + | 0.766991i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(72\) | 54.2916 | + | 47.2908i | 0.754050 | + | 0.656817i | ||||
\(73\) | 65.2976 | − | 113.099i | 0.894488 | − | 1.54930i | 0.0600510 | − | 0.998195i | \(-0.480874\pi\) |
0.834437 | − | 0.551103i | \(-0.185793\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.692161 | + | 74.9968i | −0.00922881 | + | 0.999957i | ||||
\(76\) | −141.908 | − | 51.6503i | −1.86721 | − | 0.679609i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −75.0408 | − | 30.4940i | −0.926429 | − | 0.376469i | ||||
\(82\) | −132.886 | −1.62056 | ||||||||
\(83\) | −26.7420 | − | 22.4392i | −0.322193 | − | 0.270352i | 0.467317 | − | 0.884090i | \(-0.345221\pi\) |
−0.789510 | + | 0.613738i | \(0.789665\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −82.3504 | − | 29.9731i | −0.957562 | − | 0.348524i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 19.8399 | − | 112.518i | 0.225453 | − | 1.27861i | ||||
\(89\) | 80.5908 | − | 139.587i | 0.905515 | − | 1.56840i | 0.0852901 | − | 0.996356i | \(-0.472818\pi\) |
0.820225 | − | 0.572041i | \(-0.193848\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 32.0000 | + | 90.5097i | 0.333333 | + | 0.942809i | ||||
\(97\) | 172.387 | − | 62.7437i | 1.77718 | − | 0.646842i | 0.777343 | − | 0.629077i | \(-0.216567\pi\) |
0.999842 | − | 0.0177651i | \(-0.00565510\pi\) | |||||||
\(98\) | 49.0000 | + | 84.8705i | 0.500000 | + | 0.866025i | ||||
\(99\) | 19.9798 | + | 126.973i | 0.201816 | + | 1.28255i | ||||
\(100\) | −50.0000 | + | 86.6025i | −0.500000 | + | 0.866025i | ||||
\(101\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(102\) | 105.960 | − | 59.8792i | 1.03883 | − | 0.587051i | ||||
\(103\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −59.9966 | −0.560716 | −0.280358 | − | 0.959895i | \(-0.590453\pi\) | ||||
−0.280358 | + | 0.959895i | \(0.590453\pi\) | |||||||
\(108\) | −67.1041 | − | 84.6229i | −0.621335 | − | 0.783545i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −119.682 | − | 43.5608i | −1.05914 | − | 0.385494i | −0.247032 | − | 0.969007i | \(-0.579455\pi\) |
−0.812103 | + | 0.583513i | \(0.801678\pi\) | |||||||
\(114\) | 195.121 | + | 115.067i | 1.71159 | + | 1.00936i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 48.0334 | + | 83.1963i | 0.407063 | + | 0.705054i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 63.5557 | − | 53.3295i | 0.525253 | − | 0.440740i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 195.973 | + | 36.4232i | 1.59327 | + | 0.296124i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(128\) | −22.2270 | + | 126.055i | −0.173648 | + | 0.984808i | ||||
\(129\) | 113.230 | + | 66.7744i | 0.877755 | + | 0.517631i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −43.6645 | − | 247.634i | −0.333317 | − | 1.89034i | −0.443253 | − | 0.896397i | \(-0.646176\pi\) |
0.109936 | − | 0.993939i | \(-0.464935\pi\) | |||||||
\(132\) | −60.0992 | + | 160.497i | −0.455297 | + | 1.21588i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 212.446 | 1.58542 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 162.279 | 1.19323 | ||||||||
\(137\) | 70.7623 | + | 59.3766i | 0.516513 | + | 0.433406i | 0.863414 | − | 0.504496i | \(-0.168322\pi\) |
−0.346901 | + | 0.937902i | \(0.612766\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 38.1352 | + | 216.275i | 0.274354 | + | 1.55594i | 0.741007 | + | 0.671497i | \(0.234348\pi\) |
−0.466653 | + | 0.884440i | \(0.654540\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −22.3837 | − | 142.250i | −0.155442 | − | 0.987845i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −245.439 | + | 89.3324i | −1.68109 | + | 0.611866i | ||||
\(147\) | −49.0000 | − | 138.593i | −0.333333 | − | 0.942809i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(150\) | 97.4745 | − | 114.012i | 0.649830 | − | 0.760080i | ||||
\(151\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(152\) | 151.015 | + | 261.566i | 0.993522 | + | 1.72083i | ||||
\(153\) | −172.677 | + | 59.2635i | −1.12861 | + | 0.387343i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 75.7669 | + | 143.190i | 0.467697 | + | 0.883889i | ||||
\(163\) | 205.091 | 1.25823 | 0.629113 | − | 0.777314i | \(-0.283418\pi\) | ||||
0.629113 | + | 0.777314i | \(0.283418\pi\) | |||||||
\(164\) | 203.593 | + | 170.835i | 1.24142 | + | 1.04168i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.1238 | + | 68.7577i | 0.0730351 | + | 0.414203i | ||||
\(167\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.3465 | − | 166.433i | 0.173648 | − | 0.984808i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −256.214 | − | 223.176i | −1.49833 | − | 1.30512i | ||||
\(172\) | 87.6354 | + | 151.789i | 0.509508 | + | 0.882494i | ||||
\(173\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −175.046 | + | 146.881i | −0.994581 | + | 0.834553i | ||||
\(177\) | −48.0334 | − | 135.859i | −0.271375 | − | 0.767565i | ||||
\(178\) | −302.922 | + | 110.255i | −1.70181 | + | 0.619409i | ||||
\(179\) | −162.818 | − | 282.009i | −0.909597 | − | 1.57547i | −0.814625 | − | 0.579988i | \(-0.803057\pi\) |
−0.0949721 | − | 0.995480i | \(-0.530276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 221.924 | + | 186.216i | 1.18676 | + | 0.995810i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(192\) | 67.3301 | − | 179.807i | 0.350678 | − | 0.936496i | ||||
\(193\) | 6.18260 | + | 35.0633i | 0.0320342 | + | 0.181675i | 0.996627 | − | 0.0820705i | \(-0.0261533\pi\) |
−0.964592 | + | 0.263745i | \(0.915042\pi\) | |||||||
\(194\) | −344.774 | − | 125.487i | −1.77718 | − | 0.646842i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 34.0350 | − | 193.022i | 0.173648 | − | 0.984808i | ||||
\(197\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(198\) | 132.622 | − | 220.219i | 0.669809 | − | 1.11222i | ||||
\(199\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(200\) | 187.939 | − | 68.4040i | 0.939693 | − | 0.342020i | ||||
\(201\) | −313.304 | − | 58.2302i | −1.55872 | − | 0.289702i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −239.320 | − | 44.4796i | −1.17314 | − | 0.218037i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −93.6289 | + | 530.996i | −0.447985 | + | 2.54065i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −396.208 | − | 144.208i | −1.87776 | − | 0.683450i | −0.953090 | − | 0.302688i | \(-0.902116\pi\) |
−0.924673 | − | 0.380762i | \(-0.875662\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 91.9202 | + | 77.1302i | 0.429534 | + | 0.360421i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.97959 | + | 215.917i | −0.0276833 | + | 0.999617i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 386.445 | − | 64.4692i | 1.76459 | − | 0.294380i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −175.000 | + | 141.421i | −0.777778 | + | 0.628539i | ||||
\(226\) | 127.363 | + | 220.600i | 0.563554 | + | 0.976105i | ||||
\(227\) | −269.798 | + | 98.1986i | −1.18854 | + | 0.432593i | −0.859210 | − | 0.511622i | \(-0.829045\pi\) |
−0.329329 | + | 0.944215i | \(0.606822\pi\) | |||||||
\(228\) | −151.015 | − | 427.136i | −0.662348 | − | 1.87340i | ||||
\(229\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 174.892 | + | 302.922i | 0.750609 | + | 1.30009i | 0.947528 | + | 0.319673i | \(0.103573\pi\) |
−0.196919 | + | 0.980420i | \(0.563093\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 33.3637 | − | 189.215i | 0.141371 | − | 0.801757i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 358.677 | + | 300.965i | 1.48828 | + | 1.24882i | 0.896748 | + | 0.442541i | \(0.145923\pi\) |
0.591536 | + | 0.806279i | \(0.298522\pi\) | |||||||
\(242\) | −165.932 | −0.685670 | ||||||||
\(243\) | −72.4892 | − | 231.936i | −0.298310 | − | 0.954469i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −253.423 | − | 307.741i | −1.03017 | − | 1.25098i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.966511 | − | 104.723i | 0.00388157 | − | 0.420575i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 238.485 | − | 413.068i | 0.950139 | − | 1.64569i | 0.205020 | − | 0.978758i | \(-0.434274\pi\) |
0.745119 | − | 0.666932i | \(-0.232393\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 196.107 | − | 164.554i | 0.766044 | − | 0.642788i | ||||
\(257\) | 307.401 | − | 257.940i | 1.19611 | − | 1.00366i | 0.196379 | − | 0.980528i | \(-0.437082\pi\) |
0.999732 | − | 0.0231286i | \(-0.00736271\pi\) | |||||||
\(258\) | −87.6354 | − | 247.870i | −0.339672 | − | 0.960738i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −251.454 | + | 435.531i | −0.959748 | + | 1.66233i | ||||
\(263\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(264\) | 298.408 | − | 168.633i | 1.13033 | − | 0.638762i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 476.953 | − | 79.5684i | 1.78634 | − | 0.298009i | ||||
\(268\) | −325.486 | − | 273.115i | −1.21450 | − | 1.01909i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −248.625 | − | 208.622i | −0.914064 | − | 0.766991i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −32.0810 | − | 181.941i | −0.117084 | − | 0.664017i | ||||
\(275\) | 335.509 | + | 122.115i | 1.22003 | + | 0.444056i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(278\) | 219.612 | − | 380.379i | 0.789970 | − | 1.36827i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −526.142 | + | 191.500i | −1.87239 | + | 0.681494i | −0.906713 | + | 0.421749i | \(0.861416\pi\) |
−0.965677 | + | 0.259746i | \(0.916361\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −340.123 | + | 285.397i | −1.20185 | + | 1.00847i | −0.202273 | + | 0.979329i | \(0.564833\pi\) |
−0.999575 | + | 0.0291408i | \(0.990723\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −148.579 | + | 246.715i | −0.515899 | + | 0.856649i | ||||
\(289\) | −61.2375 | + | 106.066i | −0.211894 | + | 0.367012i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 474.058 | + | 279.562i | 1.62907 | + | 0.960696i | ||||
\(292\) | 490.878 | + | 178.665i | 1.68109 | + | 0.611866i | ||||
\(293\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(294\) | −103.099 | + | 275.330i | −0.350678 | + | 0.936496i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −255.945 | + | 288.416i | −0.861766 | + | 0.971097i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −295.911 | + | 49.3657i | −0.986368 | + | 0.164552i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 104.894 | − | 594.884i | 0.345046 | − | 1.95686i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 340.744 | + | 131.192i | 1.11354 | + | 0.428733i | ||||
\(307\) | 303.993 | + | 526.531i | 0.990205 | + | 1.71509i | 0.616016 | + | 0.787734i | \(0.288746\pi\) |
0.374189 | + | 0.927352i | \(0.377921\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −355.385 | + | 129.350i | −1.13542 | + | 0.413257i | −0.840256 | − | 0.542191i | \(-0.817595\pi\) |
−0.295160 | + | 0.955448i | \(0.595373\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −114.418 | − | 138.942i | −0.356442 | − | 0.432842i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −765.830 | −2.37099 | ||||||||
\(324\) | 68.0000 | − | 316.784i | 0.209877 | − | 0.977728i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −314.217 | − | 263.660i | −0.963857 | − | 0.808772i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −92.3016 | − | 523.468i | −0.281407 | − | 1.59594i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 98.3162 | − | 557.579i | 0.297028 | − | 1.68453i | −0.361816 | − | 0.932249i | \(-0.617843\pi\) |
0.658844 | − | 0.752279i | \(-0.271046\pi\) | |||||||
\(332\) | 69.8184 | − | 120.929i | 0.210296 | − | 0.364244i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −46.5235 | + | 39.0379i | −0.138052 | + | 0.115839i | −0.709199 | − | 0.705009i | \(-0.750943\pi\) |
0.571147 | + | 0.820848i | \(0.306499\pi\) | |||||||
\(338\) | −258.923 | + | 217.262i | −0.766044 | + | 0.642788i | ||||
\(339\) | −127.363 | − | 360.238i | −0.375703 | − | 1.06265i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 105.634 | + | 671.309i | 0.308870 | + | 1.96289i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 60.8709 | − | 345.216i | 0.176950 | − | 1.00354i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 120.472 | + | 683.233i | 0.347183 | + | 1.96897i | 0.198761 | + | 0.980048i | \(0.436308\pi\) |
0.148422 | + | 0.988924i | \(0.452580\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 457.013 | 1.29833 | ||||||||
\(353\) | 448.099 | + | 375.999i | 1.26940 | + | 1.06515i | 0.994614 | + | 0.103649i | \(0.0330520\pi\) |
0.274788 | + | 0.961505i | \(0.411392\pi\) | |||||||
\(354\) | −101.066 | + | 269.899i | −0.285496 | + | 0.762426i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 605.845 | + | 220.509i | 1.70181 | + | 0.619409i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −113.092 | + | 641.377i | −0.315900 | + | 1.79156i | ||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −532.176 | − | 921.755i | −1.47417 | − | 2.55334i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 244.707 | + | 45.4810i | 0.674125 | + | 0.125292i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 289.384 | + | 523.302i | 0.784239 | + | 1.41816i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(374\) | −100.612 | − | 570.600i | −0.269017 | − | 1.52567i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −534.348 | −1.40989 | −0.704944 | − | 0.709262i | \(-0.749028\pi\) | ||||
−0.704944 | + | 0.709262i | \(0.749028\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(384\) | −334.312 | + | 188.923i | −0.870603 | + | 0.491986i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 35.6042 | − | 61.6682i | 0.0922388 | − | 0.159762i | ||||
\(387\) | 61.3001 | + | 389.566i | 0.158398 | + | 1.00663i | ||||
\(388\) | 366.901 | + | 635.491i | 0.945620 | + | 1.63786i | ||||
\(389\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −300.289 | + | 251.973i | −0.766044 | + | 0.642788i | ||||
\(393\) | 490.207 | − | 573.375i | 1.24735 | − | 1.45897i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −486.297 | + | 166.899i | −1.22802 | + | 0.421463i | ||||
\(397\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −375.877 | − | 136.808i | −0.939693 | − | 0.342020i | ||||
\(401\) | 110.882 | + | 628.844i | 0.276514 | + | 1.56819i | 0.734111 | + | 0.679029i | \(0.237599\pi\) |
−0.457597 | + | 0.889160i | \(0.651290\pi\) | |||||||
\(402\) | 405.150 | + | 491.989i | 1.00784 | + | 1.22385i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 309.477 | + | 375.810i | 0.758523 | + | 0.921104i | ||||
\(409\) | −127.776 | − | 724.652i | −0.312410 | − | 1.77177i | −0.586388 | − | 0.810030i | \(-0.699451\pi\) |
0.273978 | − | 0.961736i | \(-0.411661\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.55750 | + | 277.109i | −0.00622262 | + | 0.674232i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −428.131 | + | 500.767i | −1.02669 | + | 1.20088i | ||||
\(418\) | 826.083 | − | 693.166i | 1.97628 | − | 1.65829i | ||||
\(419\) | 635.955 | − | 533.630i | 1.51779 | − | 1.27358i | 0.671291 | − | 0.741194i | \(-0.265740\pi\) |
0.846502 | − | 0.532385i | \(-0.178704\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(422\) | 421.636 | + | 730.294i | 0.999137 | + | 1.73056i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −88.0607 | + | 499.417i | −0.207202 | + | 1.17510i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −41.6732 | − | 236.341i | −0.0973674 | − | 0.552198i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 286.739 | − | 323.117i | 0.663748 | − | 0.747956i | ||||
\(433\) | 28.2519 | 0.0652469 | 0.0326235 | − | 0.999468i | \(-0.489614\pi\) | ||||
0.0326235 | + | 0.999468i | \(0.489614\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −674.948 | − | 398.032i | −1.54098 | − | 0.908748i | ||||
\(439\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 227.511 | − | 377.782i | 0.515899 | − | 0.856649i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 737.114 | − | 268.288i | 1.66391 | − | 0.605615i | 0.672943 | − | 0.739694i | \(-0.265030\pi\) |
0.990971 | + | 0.134079i | \(0.0428076\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −192.179 | − | 332.864i | −0.428015 | − | 0.741344i | 0.568681 | − | 0.822558i | \(-0.307454\pi\) |
−0.996697 | + | 0.0812137i | \(0.974120\pi\) | |||||||
\(450\) | 449.923 | + | 8.30558i | 0.999830 | + | 0.0184568i | ||||
\(451\) | 474.458 | − | 821.786i | 1.05201 | − | 1.82214i | ||||
\(452\) | 88.4656 | − | 501.713i | 0.195720 | − | 1.10999i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 539.597 | + | 196.397i | 1.18854 | + | 0.432593i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −317.746 | + | 848.551i | −0.696812 | + | 1.86086i | ||||
\(457\) | 402.533 | + | 337.765i | 0.880816 | + | 0.739092i | 0.966347 | − | 0.257244i | \(-0.0828143\pi\) |
−0.0855311 | + | 0.996336i | \(0.527259\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −466.551 | − | 286.871i | −1.01645 | − | 0.624991i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 121.479 | − | 688.940i | 0.260684 | − | 1.47841i | ||||
\(467\) | −175.592 | + | 304.135i | −0.376001 | + | 0.651252i | −0.990476 | − | 0.137684i | \(-0.956034\pi\) |
0.614476 | + | 0.788936i | \(0.289368\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −294.366 | + | 247.002i | −0.623657 | + | 0.523310i | ||||
\(473\) | 479.383 | − | 402.250i | 1.01349 | − | 0.850423i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −886.925 | + | 322.814i | −1.86721 | + | 0.679609i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −162.611 | − | 922.211i | −0.337367 | − | 1.91330i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 254.223 | + | 213.318i | 0.525253 | + | 0.440740i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −187.111 | + | 448.537i | −0.385003 | + | 0.922916i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 391.123 | + | 474.956i | 0.799842 | + | 0.971280i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −204.149 | − | 74.3040i | −0.415781 | − | 0.151332i | 0.125655 | − | 0.992074i | \(-0.459897\pi\) |
−0.541436 | + | 0.840742i | \(0.682119\pi\) | |||||||
\(492\) | −7.35827 | + | 797.282i | −0.0149558 | + | 1.62049i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −136.110 | + | 159.203i | −0.273314 | + | 0.319684i | ||||
\(499\) | −763.106 | + | 640.322i | −1.52927 | + | 1.28321i | −0.725663 | + | 0.688050i | \(0.758467\pi\) |
−0.803607 | + | 0.595160i | \(0.797089\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −896.410 | + | 326.267i | −1.78568 | + | 0.649933i | ||||
\(503\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 441.396 | − | 249.437i | 0.870603 | − | 0.491986i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −1.00000 | ||||||||
\(513\) | 28.2190 | − | 1018.96i | 0.0550079 | − | 1.98628i | ||||
\(514\) | −802.566 | −1.56141 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −184.391 | + | 492.421i | −0.357347 | + | 0.954305i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 298.053 | − | 516.242i | 0.572078 | − | 0.990868i | −0.424274 | − | 0.905534i | \(-0.639471\pi\) |
0.996352 | − | 0.0853344i | \(-0.0271959\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −319.363 | − | 553.153i | −0.610636 | − | 1.05765i | −0.991133 | − | 0.132871i | \(-0.957580\pi\) |
0.380497 | − | 0.924782i | \(-0.375753\pi\) | |||||||
\(524\) | 945.158 | − | 344.009i | 1.80374 | − | 0.656507i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −673.978 | − | 125.265i | −1.27647 | − | 0.237244i | ||||
\(529\) | −497.097 | + | 180.929i | −0.939693 | + | 0.342020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 223.024 | − | 370.330i | 0.420007 | − | 0.697420i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −833.026 | − | 491.254i | −1.55997 | − | 0.919951i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 147.563 | + | 836.874i | 0.275305 | + | 1.56133i | ||||
\(537\) | 342.580 | − | 914.870i | 0.637951 | − | 1.70367i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −699.802 | −1.29833 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 112.718 | + | 639.254i | 0.207202 | + | 1.17510i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 92.3813 | − | 523.920i | 0.168887 | − | 0.957807i | −0.776078 | − | 0.630637i | \(-0.782794\pi\) |
0.944965 | − | 0.327170i | \(-0.106095\pi\) | |||||||
\(548\) | −184.747 | + | 319.992i | −0.337130 | + | 0.583927i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −357.042 | − | 618.414i | −0.649167 | − | 1.12439i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −825.470 | + | 300.446i | −1.48466 | + | 0.540371i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.02080 | + | 869.067i | −0.0142973 | + | 1.54914i | ||||
\(562\) | 1052.28 | + | 383.000i | 1.87239 | + | 0.681494i | ||||
\(563\) | 181.824 | + | 1031.18i | 0.322956 | + | 1.83157i | 0.523666 | + | 0.851923i | \(0.324564\pi\) |
−0.200710 | + | 0.979651i | \(0.564325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 887.998 | 1.56890 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −699.618 | − | 587.050i | −1.22956 | − | 1.03172i | −0.998268 | − | 0.0588367i | \(-0.981261\pi\) |
−0.231290 | − | 0.972885i | \(-0.574295\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.6543 | + | 94.4514i | 0.0291670 | + | 0.165414i | 0.995912 | − | 0.0903277i | \(-0.0287914\pi\) |
−0.966745 | + | 0.255742i | \(0.917680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 544.807 | − | 186.980i | 0.945845 | − | 0.324618i | ||||
\(577\) | −568.407 | − | 984.510i | −0.985107 | − | 1.70626i | −0.641459 | − | 0.767157i | \(-0.721671\pi\) |
−0.343648 | − | 0.939098i | \(-0.611663\pi\) | |||||||
\(578\) | 230.178 | − | 83.7778i | 0.398231 | − | 0.144944i | ||||
\(579\) | −69.4099 | + | 81.1860i | −0.119879 | + | 0.140218i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −366.901 | − | 1037.75i | −0.630414 | − | 1.78308i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −522.381 | − | 904.790i | −0.894488 | − | 1.54930i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.0214 | − | 85.1908i | 0.0255902 | − | 0.145129i | −0.969336 | − | 0.245741i | \(-0.920969\pi\) |
0.994926 | + | 0.100612i | \(0.0320799\pi\) | |||||||
\(588\) | 511.915 | − | 289.288i | 0.870603 | − | 0.491986i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1136.45 | 1.91645 | 0.958223 | − | 0.286021i | \(-0.0923326\pi\) | ||||
0.958223 | + | 0.286021i | \(0.0923326\pi\) | |||||||
\(594\) | 762.910 | − | 112.843i | 1.28436 | − | 0.189971i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(600\) | 516.824 | + | 304.783i | 0.861374 | + | 0.507971i | ||||
\(601\) | −105.938 | + | 600.803i | −0.176269 | + | 0.999673i | 0.760399 | + | 0.649456i | \(0.225003\pi\) |
−0.936669 | + | 0.350217i | \(0.886108\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −462.641 | − | 836.608i | −0.767233 | − | 1.38741i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(608\) | −925.475 | + | 776.566i | −1.52216 | + | 1.27725i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −353.393 | − | 639.050i | −0.577439 | − | 1.04420i | ||||
\(613\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(614\) | 211.151 | − | 1197.50i | 0.343895 | − | 1.95032i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −213.221 | − | 1209.24i | −0.345577 | − | 1.95986i | −0.270665 | − | 0.962674i | \(-0.587243\pi\) |
−0.0749124 | − | 0.997190i | \(-0.523868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 115.542 | + | 96.9513i | 0.186659 | + | 0.156626i | 0.731329 | − | 0.682025i | \(-0.238901\pi\) |
−0.544670 | + | 0.838651i | \(0.683345\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 108.530 | + | 615.505i | 0.173648 | + | 0.984808i | ||||
\(626\) | 710.770 | + | 258.699i | 1.13542 | + | 0.413257i | ||||
\(627\) | −1408.25 | + | 795.819i | −2.24602 | + | 1.26925i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −421.636 | − | 1192.57i | −0.666091 | − | 1.88399i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.09767 | + | 45.9242i | −0.0126329 | + | 0.0716446i | −0.990472 | − | 0.137711i | \(-0.956025\pi\) |
0.977840 | + | 0.209356i | \(0.0671366\pi\) | |||||||
\(642\) | −3.32219 | + | 359.965i | −0.00517474 | + | 0.560692i | ||||
\(643\) | 194.525 | + | 70.8015i | 0.302528 | + | 0.110111i | 0.488824 | − | 0.872383i | \(-0.337426\pi\) |
−0.186296 | + | 0.982494i | \(0.559648\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1173.32 | + | 984.533i | 1.81629 | + | 1.52404i | ||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | −511.431 | + | 397.922i | −0.789246 | + | 0.614077i | ||||
\(649\) | −685.997 | −1.05701 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 142.455 | + | 807.900i | 0.218489 | + | 1.23911i | ||||
\(653\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −531.544 | + | 920.661i | −0.810280 | + | 1.40345i | ||||
\(657\) | 886.278 | + | 771.994i | 1.34898 | + | 1.17503i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 237.314 | − | 86.3751i | 0.360112 | − | 0.131070i | −0.155627 | − | 0.987816i | \(-0.549740\pi\) |
0.515739 | + | 0.856746i | \(0.327518\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(662\) | −867.439 | + | 727.868i | −1.31033 | + | 1.09950i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −262.431 | + | 95.5172i | −0.395228 | + | 0.143851i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 815.001 | + | 683.867i | 1.21100 | + | 1.01615i | 0.999246 | + | 0.0388234i | \(0.0123610\pi\) |
0.211751 | + | 0.977324i | \(0.432083\pi\) | |||||||
\(674\) | 121.464 | 0.180214 | ||||||||
\(675\) | −661.246 | − | 135.570i | −0.979623 | − | 0.200844i | ||||
\(676\) | 676.000 | 1.00000 | ||||||||
\(677\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(678\) | −267.981 | + | 715.651i | −0.395252 | + | 1.05553i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −741.936 | − | 437.536i | −1.08948 | − | 0.642491i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −677.997 | + | 1174.32i | −0.992674 | + | 1.71936i | −0.391703 | + | 0.920092i | \(0.628114\pi\) |
−0.600971 | + | 0.799271i | \(0.705219\pi\) | |||||||
\(684\) | 701.178 | − | 1164.30i | 1.02511 | − | 1.70220i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −537.061 | + | 450.648i | −0.780612 | + | 0.655011i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1297.80 | − | 472.360i | 1.87815 | − | 0.683589i | 0.926655 | − | 0.375913i | \(-0.122671\pi\) |
0.951491 | − | 0.307676i | \(-0.0995512\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 693.773 | − | 1201.65i | 0.999673 | − | 1.73149i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1266.50 | + | 460.970i | 1.81708 | + | 0.661363i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −367.984 | + | 982.714i | −0.526444 | + | 1.40589i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −700.185 | − | 587.525i | −0.994581 | − | 0.834553i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −203.151 | − | 1152.13i | −0.287750 | − | 1.63191i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 501.816 | − | 283.581i | 0.708780 | − | 0.400539i | ||||
\(709\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −644.727 | − | 1116.70i | −0.905515 | − | 1.56840i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 997.806 | − | 837.258i | 1.39358 | − | 1.16936i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −369.645 | + | 2096.36i | −0.511974 | + | 2.90355i | ||||
\(723\) | −12.9633 | + | 1404.60i | −0.0179299 | + | 1.94273i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −316.444 | − | 384.271i | −0.435874 | − | 0.529299i | ||||
\(727\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 398.883 | − | 610.191i | 0.547164 | − | 0.837025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 680.888 | + | 571.333i | 0.931447 | + | 0.781577i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −758.521 | + | 1313.80i | −1.02920 | + | 1.78263i | ||||
\(738\) | 229.382 | − | 1173.77i | 0.310815 | − | 1.59047i | ||||
\(739\) | 738.249 | + | 1278.68i | 0.998984 | + | 1.73029i | 0.538528 | + | 0.842608i | \(0.318981\pi\) |
0.460456 | + | 0.887683i | \(0.347686\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 244.364 | − | 197.476i | 0.327128 | − | 0.264359i | ||||
\(748\) | −579.403 | + | 1003.56i | −0.774603 | + | 1.34165i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1411.40 | − | 235.459i | 1.87437 | − | 0.312695i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 818.669 | + | 686.944i | 1.08004 | + | 0.906259i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1309.93 | − | 476.776i | −1.72133 | − | 0.626513i | −0.723376 | − | 0.690455i | \(-0.757410\pi\) |
−0.997954 | + | 0.0639422i | \(0.979633\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 755.069 | + | 140.336i | 0.983163 | + | 0.182729i | ||||
\(769\) | 1146.77 | − | 962.252i | 1.49124 | − | 1.25130i | 0.598190 | − | 0.801355i | \(-0.295887\pi\) |
0.893055 | − | 0.449948i | \(-0.148558\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1183.58 | + | 219.979i | 1.53512 | + | 0.285316i | ||||
\(772\) | −133.828 | + | 48.7094i | −0.173352 | + | 0.0630950i | ||||
\(773\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(774\) | 406.899 | − | 675.656i | 0.525710 | − | 0.872940i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 254.847 | − | 1445.31i | 0.328410 | − | 1.86251i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 435.592 | + | 2470.37i | 0.559168 | + | 3.17120i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 1.00000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1488.16 | + | 248.264i | −1.89333 | + | 0.315857i | ||||
\(787\) | 111.008 | + | 629.558i | 0.141052 | + | 0.799947i | 0.970452 | + | 0.241292i | \(0.0775713\pi\) |
−0.829400 | + | 0.558655i | \(0.811318\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 959.611 | + | 369.467i | 1.21163 | + | 0.466499i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 400.000 | + | 692.820i | 0.500000 | + | 0.866025i | ||||
\(801\) | 1093.85 | + | 952.801i | 1.36561 | + | 1.18951i | ||||
\(802\) | 638.545 | − | 1105.99i | 0.796190 | − | 1.37904i | ||||
\(803\) | 323.874 | − | 1836.78i | 0.403330 | − | 2.28740i | ||||
\(804\) | 11.7637 | − | 1274.62i | 0.0146315 | − | 1.58535i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1430.05 | −1.76768 | −0.883839 | − | 0.467791i | \(-0.845050\pi\) | ||||
−0.883839 | + | 0.467791i | \(0.845050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1556.80 | 1.91961 | 0.959803 | − | 0.280673i | \(-0.0905577\pi\) | ||||
0.959803 | + | 0.280673i | \(0.0905577\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.98584 | − | 973.631i | 0.0110121 | − | 1.19318i | ||||
\(817\) | −287.264 | + | 1629.15i | −0.351608 | + | 1.99407i | ||||
\(818\) | −735.831 | + | 1274.50i | −0.899549 | + | 1.55807i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(822\) | 360.163 | − | 421.268i | 0.438155 | − | 0.512492i | ||||
\(823\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 357.042 | + | 1009.87i | 0.432778 | + | 1.22408i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −631.000 | − | 1092.92i | −0.762999 | − | 1.32155i | −0.941298 | − | 0.337576i | \(-0.890393\pi\) |
0.178299 | − | 0.983976i | \(-0.442940\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −172.599 | − | 978.857i | −0.207202 | − | 1.17510i | ||||
\(834\) | 1299.71 | − | 216.825i | 1.55840 | − | 0.259983i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2156.75 | −2.57984 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1660.36 | −1.98134 | ||||||||
\(839\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 146.038 | + | 828.223i | 0.173648 | + | 0.984808i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1446.87 | − | 853.251i | −1.71634 | − | 1.01216i | ||||
\(844\) | 292.865 | − | 1660.92i | 0.346997 | − | 1.96792i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1309.57 | − | 243.395i | −1.54249 | − | 0.286684i | ||||
\(850\) | 776.955 | − | 651.942i | 0.914064 | − | 0.766991i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −239.987 | + | 415.669i | −0.280358 | + | 0.485595i | ||||
\(857\) | 208.725 | − | 1183.74i | 0.243553 | − | 1.38126i | −0.580276 | − | 0.814420i | \(-0.697055\pi\) |
0.823829 | − | 0.566839i | \(-0.191834\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −724.028 | − | 263.525i | −0.842873 | − | 0.306781i | −0.115742 | − | 0.993279i | \(-0.536925\pi\) |
−0.727131 | + | 0.686499i | \(0.759147\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | −854.701 | + | 126.420i | −0.989237 | + | 0.146319i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −43.2845 | − | 36.3200i | −0.0499821 | − | 0.0419399i | ||||
\(867\) | −362.416 | + | 60.4606i | −0.418012 | + | 0.0697354i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 256.643 | + | 1630.98i | 0.293979 | + | 1.86825i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 522.381 | + | 1477.52i | 0.596325 | + | 1.68666i | ||||
\(877\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 81.4082 | + | 141.003i | 0.0924043 | + | 0.160049i | 0.908522 | − | 0.417836i | \(-0.137211\pi\) |
−0.816118 | + | 0.577885i | \(0.803878\pi\) | |||||||
\(882\) | −834.235 | + | 286.313i | −0.945845 | + | 0.324618i | ||||
\(883\) | 636.706 | − | 1102.81i | 0.721071 | − | 1.24893i | −0.239500 | − | 0.970896i | \(-0.576984\pi\) |
0.960571 | − | 0.278035i | \(-0.0896831\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1474.23 | − | 536.575i | −1.66391 | − | 0.605615i | ||||
\(887\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1156.03 | − | 42.6950i | −1.29745 | − | 0.0479181i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −133.486 | + | 757.037i | −0.148648 | + | 0.843025i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −678.645 | − | 591.135i | −0.754050 | − | 0.656817i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −1783.38 | + | 649.097i | −1.97714 | + | 0.719620i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −780.527 | + | 654.940i | −0.863415 | + | 0.724491i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −269.986 | + | 98.2668i | −0.297669 | + | 0.108343i | −0.486537 | − | 0.873660i | \(-0.661740\pi\) |
0.188868 | + | 0.982002i | \(0.439518\pi\) | |||||||
\(908\) | −574.227 | − | 994.590i | −0.632409 | − | 1.09536i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(912\) | 1577.69 | − | 891.570i | 1.72993 | − | 0.977598i | ||||
\(913\) | −468.494 | − | 170.518i | −0.513137 | − | 0.186767i | ||||
\(914\) | −182.494 | − | 1034.97i | −0.199665 | − | 1.13235i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 346.004 | + | 1039.30i | 0.376911 | + | 1.13213i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −639.622 | + | 1708.13i | −0.694486 | + | 1.85465i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −994.195 | + | 361.857i | −1.07018 | + | 0.389513i | −0.816243 | − | 0.577709i | \(-0.803947\pi\) |
−0.253934 | + | 0.967221i | \(0.581725\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1417.13 | − | 1189.12i | 1.52216 | − | 1.27725i | ||||
\(932\) | −1071.80 | + | 899.347i | −1.15000 | + | 0.964964i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 660.011 | − | 240.224i | 0.706650 | − | 0.257200i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −929.044 | + | 1609.15i | −0.991509 | + | 1.71734i | −0.383138 | + | 0.923691i | \(0.625157\pi\) |
−0.608371 | + | 0.793653i | \(0.708177\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −977.297 | − | 576.333i | −1.04078 | − | 0.613773i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 768.535 | 0.814126 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1251.58 | −1.32302 | ||||||||
\(947\) | −1377.16 | − | 1155.57i | −1.45423 | − | 1.22025i | −0.929418 | − | 0.369030i | \(-0.879690\pi\) |
−0.524815 | − | 0.851216i | \(-0.675866\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1773.85 | + | 645.628i | 1.86721 | + | 0.679609i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 948.243 | − | 1642.40i | 0.995008 | − | 1.72340i | 0.411078 | − | 0.911600i | \(-0.365152\pi\) |
0.583930 | − | 0.811804i | \(-0.301514\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −903.045 | + | 328.681i | −0.939693 | + | 0.342020i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 103.564 | − | 529.945i | 0.107543 | − | 0.550307i | ||||
\(964\) | −936.438 | + | 1621.96i | −0.971409 | + | 1.68253i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(968\) | −115.255 | − | 653.645i | −0.119065 | − | 0.675253i | ||||
\(969\) | −1460.49 | − | 1773.53i | −1.50722 | − | 1.83027i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 974.000 | 1.00309 | 0.501545 | − | 0.865132i | \(-0.332765\pi\) | ||||
0.501545 | + | 0.865132i | \(0.332765\pi\) | |||||||
\(972\) | 863.299 | − | 446.653i | 0.888168 | − | 0.459519i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1813.63 | − | 660.107i | −1.85633 | − | 0.675647i | −0.981576 | − | 0.191071i | \(-0.938804\pi\) |
−0.874749 | − | 0.484576i | \(-0.838974\pi\) | |||||||
\(978\) | 11.3565 | − | 1230.49i | 0.0116119 | − | 1.25817i | ||||
\(979\) | 399.728 | − | 2266.97i | 0.408302 | − | 2.31560i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 217.250 | + | 376.289i | 0.221233 | + | 0.383186i | ||||
\(983\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(984\) | 1036.24 | − | 1212.05i | 1.05309 | − | 1.23175i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1478.76 | − | 835.659i | 1.48918 | − | 0.841550i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 413.200 | − | 68.9326i | 0.414859 | − | 0.0692094i | ||||
\(997\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(998\) | 1992.33 | 1.99632 | ||||||||
\(999\) | 0 | 0 |
(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 | 216.3.r.a.43.2 | ✓ | 12 | |
8.3 | odd | 2 | CM | 216.3.r.a.43.2 | ✓ | 12 | |
27.22 | even | 9 | inner | 216.3.r.a.211.2 | yes | 12 | |
216.211 | odd | 18 | inner | 216.3.r.a.211.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.3.r.a.43.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
216.3.r.a.43.2 | ✓ | 12 | 8.3 | odd | 2 | CM | |
216.3.r.a.211.2 | yes | 12 | 27.22 | even | 9 | inner | |
216.3.r.a.211.2 | yes | 12 | 216.211 | odd | 18 | inner |