Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,3,Mod(17,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([33, 64]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.o (of order \(66\), degree \(20\), 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: | \(5.47685331364\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{66}]$ |
Embedding invariants
Embedding label | 83.1 | ||
Root | \(0.0475819 - 0.998867i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.83 |
Dual form | 201.3.o.a.155.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{33}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(3\) | −1.24625 | − | 2.72890i | −0.415415 | − | 0.909632i | ||||
\(4\) | 3.71347 | + | 1.48665i | 0.928368 | + | 0.371662i | ||||
\(5\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.57895 | + | 13.2300i | 0.654136 | + | 1.89000i | 0.327586 | + | 0.944821i | \(0.393765\pi\) |
0.326550 | + | 0.945180i | \(0.394114\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.89375 | + | 6.80175i | −0.654861 | + | 0.755750i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(12\) | −0.570983 | − | 11.9864i | −0.0475819 | − | 0.998867i | ||||
\(13\) | 5.24308 | + | 2.70300i | 0.403314 | + | 0.207923i | 0.647934 | − | 0.761696i | \(-0.275633\pi\) |
−0.244621 | + | 0.969619i | \(0.578663\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.5797 | + | 11.0413i | 0.723734 | + | 0.690079i | ||||
\(17\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.71229 | − | 13.6153i | 0.248015 | − | 0.716593i | −0.750435 | − | 0.660944i | \(-0.770156\pi\) |
0.998450 | − | 0.0556487i | \(-0.0177227\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 30.3968 | − | 28.9833i | 1.44747 | − | 1.38016i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 21.0313 | − | 13.5160i | 0.841254 | − | 0.540641i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 25.9063 | + | 7.60678i | 0.959493 | + | 0.281733i | ||||
\(28\) | −2.66459 | + | 55.9366i | −0.0951638 | + | 1.99773i | ||||
\(29\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −26.2673 | + | 13.5418i | −0.847334 | + | 0.436831i | −0.826490 | − | 0.562952i | \(-0.809666\pi\) |
−0.0208440 | + | 0.999783i | \(0.506635\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −31.9981 | + | 16.4962i | −0.888835 | + | 0.458227i | ||||
\(37\) | 7.79205 | + | 13.4962i | 0.210596 | + | 0.364763i | 0.951901 | − | 0.306405i | \(-0.0991262\pi\) |
−0.741305 | + | 0.671168i | \(0.765793\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.842032 | − | 17.6764i | 0.0215906 | − | 0.453241i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.9674 | − | 83.2351i | 0.278312 | − | 1.93570i | −0.0682370 | − | 0.997669i | \(-0.521737\pi\) |
0.346549 | − | 0.938032i | \(-0.387354\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(48\) | 15.6993 | − | 45.3600i | 0.327068 | − | 0.945001i | ||||
\(49\) | −115.550 | + | 90.8693i | −2.35816 | + | 1.85448i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 15.4516 | + | 17.8321i | 0.297147 | + | 0.342925i | ||||
\(53\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −43.0273 | + | 4.10861i | −0.754865 | + | 0.0720809i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −19.5408 | − | 80.5485i | −0.320342 | − | 1.32047i | −0.873269 | − | 0.487238i | \(-0.838005\pi\) |
0.552928 | − | 0.833229i | \(-0.313511\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −116.974 | − | 46.8295i | −1.85674 | − | 0.743325i | ||||
\(64\) | 26.5866 | + | 58.2164i | 0.415415 | + | 0.909632i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24.7789 | + | 62.2495i | −0.369835 | + | 0.929098i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −30.3921 | − | 125.278i | −0.416331 | − | 1.71614i | −0.664384 | − | 0.747392i | \(-0.731306\pi\) |
0.248053 | − | 0.968746i | \(-0.420209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −63.0940 | − | 40.5481i | −0.841254 | − | 0.540641i | ||||
\(76\) | 37.7401 | − | 43.5544i | 0.496580 | − | 0.573084i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.51611 | + | 157.783i | 0.0951406 | + | 1.99725i | 0.0696203 | + | 0.997574i | \(0.477821\pi\) |
0.0255204 | + | 0.999674i | \(0.491876\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.5275 | − | 80.1755i | −0.142315 | − | 0.989821i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(84\) | 155.966 | − | 62.4393i | 1.85674 | − | 0.743325i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.7529 | + | 81.7429i | −0.129152 | + | 0.898274i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 69.6896 | + | 54.8045i | 0.749350 | + | 0.589296i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −79.5897 | − | 137.853i | −0.820513 | − | 1.42117i | −0.905301 | − | 0.424771i | \(-0.860355\pi\) |
0.0847884 | − | 0.996399i | \(-0.472979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 98.1929 | − | 18.9251i | 0.981929 | − | 0.189251i | ||||
\(101\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 159.460 | − | 82.2071i | 1.54815 | − | 0.798128i | 0.548866 | − | 0.835911i | \(-0.315060\pi\) |
0.999286 | + | 0.0377830i | \(0.0120296\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(108\) | 84.8937 | + | 66.7612i | 0.786053 | + | 0.618159i | ||||
\(109\) | −106.160 | + | 68.2251i | −0.973948 | + | 0.625918i | −0.927824 | − | 0.373017i | \(-0.878323\pi\) |
−0.0461237 | + | 0.998936i | \(0.514687\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 27.1190 | − | 38.0833i | 0.244315 | − | 0.343093i | ||||
\(112\) | −93.0529 | + | 203.758i | −0.830830 | + | 1.81926i | ||||
\(113\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −49.2865 | + | 19.7313i | −0.421252 | + | 0.168644i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −107.549 | − | 55.4454i | −0.888835 | − | 0.458227i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −117.675 | + | 11.2366i | −0.948991 | + | 0.0906177i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 65.6307 | + | 189.627i | 0.516777 | + | 1.49313i | 0.837757 | + | 0.546043i | \(0.183867\pi\) |
−0.320980 | + | 0.947086i | \(0.604012\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −242.054 | + | 71.0736i | −1.87639 | + | 0.550958i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 201.707 | 1.51660 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 228.842 | − | 67.1941i | 1.64635 | − | 0.483411i | 0.678426 | − | 0.734669i | \(-0.262662\pi\) |
0.967920 | + | 0.251258i | \(0.0808442\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −143.348 | + | 13.6881i | −0.995472 | + | 0.0950560i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 391.976 | + | 202.078i | 2.66651 | + | 1.37468i | ||||
\(148\) | 8.87140 | + | 61.7019i | 0.0599419 | + | 0.416905i | ||||
\(149\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.9115 | − | 9.97306i | 0.164977 | − | 0.0660468i | −0.287704 | − | 0.957719i | \(-0.592892\pi\) |
0.452681 | + | 0.891673i | \(0.350468\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 29.4055 | − | 64.3891i | 0.188497 | − | 0.412750i | ||||
\(157\) | 172.384 | − | 242.080i | 1.09799 | − | 1.54191i | 0.286006 | − | 0.958228i | \(-0.407672\pi\) |
0.811983 | − | 0.583681i | \(-0.198388\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 157.666 | − | 273.085i | 0.967273 | − | 1.67537i | 0.263894 | − | 0.964552i | \(-0.414993\pi\) |
0.703379 | − | 0.710815i | \(-0.251674\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −77.8459 | − | 109.319i | −0.460627 | − | 0.646860i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 64.8345 | + | 112.297i | 0.379149 | + | 0.656706i | ||||
\(172\) | 168.182 | − | 291.300i | 0.977803 | − | 1.69360i | ||||
\(173\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 275.119 | + | 216.356i | 1.57211 | + | 1.23632i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −35.2453 | − | 3.36552i | −0.194725 | − | 0.0185940i | −0.00276243 | − | 0.999996i | \(-0.500879\pi\) |
−0.191963 | + | 0.981402i | \(0.561485\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −195.456 | + | 153.708i | −1.06806 | + | 0.839935i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 17.9860 | + | 377.572i | 0.0951638 | + | 1.99773i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(192\) | 125.733 | − | 145.104i | 0.654861 | − | 0.755750i | ||||
\(193\) | −306.727 | − | 197.122i | −1.58926 | − | 1.02136i | −0.972114 | − | 0.234507i | \(-0.924652\pi\) |
−0.617146 | − | 0.786849i | \(-0.711711\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −564.182 | + | 165.659i | −2.87848 | + | 0.845197i | ||||
\(197\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −239.059 | − | 46.0748i | −1.20130 | − | 0.231532i | −0.450936 | − | 0.892556i | \(-0.648910\pi\) |
−0.750364 | + | 0.661025i | \(0.770122\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 200.753 | − | 9.95906i | 0.998772 | − | 0.0495476i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 30.8690 | + | 89.1902i | 0.148409 | + | 0.428799i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −146.928 | + | 14.0299i | −0.696342 | + | 0.0664926i | −0.437224 | − | 0.899353i | \(-0.644038\pi\) |
−0.259119 | + | 0.965845i | \(0.583432\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −299.434 | − | 285.510i | −1.37988 | − | 1.31572i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −303.995 | + | 239.064i | −1.38810 | + | 1.09162i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 179.911 | − | 393.951i | 0.806777 | − | 1.76660i | 0.186099 | − | 0.982531i | \(-0.440416\pi\) |
0.620679 | − | 0.784065i | \(-0.286857\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −32.0208 | + | 222.710i | −0.142315 | + | 0.989821i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(228\) | −165.889 | − | 48.7093i | −0.727582 | − | 0.213637i | ||||
\(229\) | −11.0694 | + | 232.376i | −0.0483380 | + | 1.01474i | 0.836245 | + | 0.548357i | \(0.184746\pi\) |
−0.884583 | + | 0.466384i | \(0.845557\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 421.205 | − | 217.146i | 1.77724 | − | 0.916230i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −414.491 | − | 121.705i | −1.71988 | − | 0.505002i | −0.734973 | − | 0.678096i | \(-0.762805\pi\) |
−0.984905 | + | 0.173094i | \(0.944624\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −204.425 | + | 131.376i | −0.841254 | + | 0.540641i | ||||
\(244\) | 47.1830 | − | 328.165i | 0.193373 | − | 1.34494i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 61.5089 | − | 58.6486i | 0.249024 | − | 0.237444i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(252\) | −364.762 | − | 347.800i | −1.44747 | − | 1.38016i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.1810 | + | 255.710i | 0.0475819 | + | 0.998867i | ||||
\(257\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −142.876 | + | 164.887i | −0.551644 | + | 0.636631i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −184.559 | + | 194.324i | −0.688653 | + | 0.725091i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 136.841 | + | 299.641i | 0.504950 | + | 1.10569i | 0.974829 | + | 0.222955i | \(0.0715702\pi\) |
−0.469879 | + | 0.882731i | \(0.655703\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 237.715 | − | 69.7994i | 0.870750 | − | 0.255675i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 57.3563 | − | 66.1927i | 0.207062 | − | 0.238963i | −0.642714 | − | 0.766106i | \(-0.722192\pi\) |
0.849776 | + | 0.527144i | \(0.176737\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 62.7055 | − | 258.475i | 0.224751 | − | 0.926435i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 349.132 | + | 402.920i | 1.23368 | + | 1.42374i | 0.870604 | + | 0.491985i | \(0.163729\pi\) |
0.363078 | + | 0.931759i | \(0.381726\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 209.159 | − | 199.433i | 0.723734 | − | 0.690079i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −276.999 | + | 388.991i | −0.951888 | + | 1.33674i | ||||
\(292\) | 73.3843 | − | 510.399i | 0.251316 | − | 1.74794i | ||||
\(293\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −174.017 | − | 244.373i | −0.580057 | − | 0.814576i | ||||
\(301\) | 1156.00 | − | 222.801i | 3.84053 | − | 0.740202i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 204.897 | − | 105.632i | 0.674003 | − | 0.347472i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.28232 | + | 26.9191i | −0.00417692 | + | 0.0876844i | −0.999993 | − | 0.00369387i | \(-0.998824\pi\) |
0.995816 | + | 0.0913783i | \(0.0291272\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −423.060 | − | 332.698i | −1.36913 | − | 1.07669i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −152.780 | + | 334.541i | −0.488115 | + | 1.06882i | 0.492037 | + | 0.870574i | \(0.336252\pi\) |
−0.980152 | + | 0.198248i | \(0.936475\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −206.657 | + | 597.095i | −0.653977 | + | 1.88954i | ||||
\(317\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 76.3859 | − | 314.867i | 0.235759 | − | 0.971812i | ||||
\(325\) | 146.803 | − | 14.0180i | 0.451701 | − | 0.0431322i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 318.481 | + | 204.675i | 0.973948 | + | 0.625918i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −285.636 | − | 114.351i | −0.862949 | − | 0.345473i | −0.102392 | − | 0.994744i | \(-0.532650\pi\) |
−0.760557 | + | 0.649272i | \(0.775074\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −137.722 | − | 26.5438i | −0.413580 | − | 0.0797111i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 672.000 | 2.00000 | ||||||||
\(337\) | 484.600 | + | 93.3990i | 1.43798 | + | 0.277148i | 0.847884 | − | 0.530182i | \(-0.177877\pi\) |
0.590099 | + | 0.807331i | \(0.299089\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1154.20 | − | 741.759i | −3.36501 | − | 2.16256i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 41.8566 | + | 291.119i | 0.119933 | + | 0.834153i | 0.957627 | + | 0.288012i | \(0.0929944\pi\) |
−0.837694 | + | 0.546140i | \(0.816097\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 115.268 | + | 109.908i | 0.328398 | + | 0.313127i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 120.595 | + | 94.8373i | 0.334060 | + | 0.262707i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.2722 | + | 362.589i | −0.0475819 | + | 0.998867i | ||||
\(364\) | −165.167 | + | 286.078i | −0.453755 | + | 0.785927i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 424.519 | + | 596.154i | 1.15673 | + | 1.62440i | 0.640553 | + | 0.767914i | \(0.278705\pi\) |
0.516175 | + | 0.856483i | \(0.327356\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 177.315 | + | 307.119i | 0.476654 | + | 0.825589i | ||||
\(373\) | −367.605 | + | 636.711i | −0.985537 | + | 1.70700i | −0.346012 | + | 0.938230i | \(0.612465\pi\) |
−0.639525 | + | 0.768771i | \(0.720869\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −361.820 | + | 508.106i | −0.954671 | + | 1.34065i | −0.0145184 | + | 0.999895i | \(0.504622\pi\) |
−0.940153 | + | 0.340753i | \(0.889318\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 435.681 | − | 415.421i | 1.14352 | − | 1.09035i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 495.611 | + | 571.966i | 1.28065 | + | 1.47795i | ||||
\(388\) | −90.6144 | − | 630.237i | −0.233542 | − | 1.62432i | ||||
\(389\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −146.119 | + | 42.9043i | −0.368057 | + | 0.108071i | −0.460531 | − | 0.887644i | \(-0.652341\pi\) |
0.0924735 | + | 0.995715i | \(0.470523\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −251.377 | − | 550.438i | −0.630017 | − | 1.37954i | ||||
\(400\) | 392.771 | + | 75.7005i | 0.981929 | + | 0.189251i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −174.325 | −0.432568 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 147.932 | + | 427.422i | 0.361693 | + | 1.04504i | 0.968246 | + | 0.249999i | \(0.0804304\pi\) |
−0.606554 | + | 0.795043i | \(0.707448\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 714.362 | − | 68.2133i | 1.73389 | − | 0.165566i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −468.559 | − | 540.746i | −1.12364 | − | 1.29675i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 254.548 | − | 735.469i | 0.604628 | − | 1.74696i | −0.0583265 | − | 0.998298i | \(-0.518576\pi\) |
0.662954 | − | 0.748660i | \(-0.269302\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 976.180 | − | 627.353i | 2.28614 | − | 1.46921i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | 216.000 | + | 374.123i | 0.500000 | + | 0.866025i | ||||
\(433\) | 604.597 | − | 311.691i | 1.39630 | − | 0.719842i | 0.414550 | − | 0.910027i | \(-0.363939\pi\) |
0.981748 | + | 0.190185i | \(0.0609088\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −495.650 | + | 95.5288i | −1.13681 | + | 0.219103i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −118.589 | − | 205.402i | −0.270134 | − | 0.467886i | 0.698762 | − | 0.715354i | \(-0.253735\pi\) |
−0.968896 | + | 0.247469i | \(0.920401\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 62.9508 | − | 1321.50i | 0.142746 | − | 2.99660i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(444\) | 157.322 | − | 101.105i | 0.354329 | − | 0.227714i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −648.466 | + | 618.311i | −1.44747 | + | 1.38016i | ||||
\(449\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −58.2613 | − | 55.5520i | −0.128612 | − | 0.122631i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.3595 | + | 658.316i | 0.0686203 | + | 1.44052i | 0.726382 | + | 0.687291i | \(0.241200\pi\) |
−0.657762 | + | 0.753226i | \(0.728497\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 216.996 | + | 894.470i | 0.468674 | + | 1.93190i | 0.340907 | + | 0.940097i | \(0.389266\pi\) |
0.127767 | + | 0.991804i | \(0.459219\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(468\) | −212.358 | −0.453755 | ||||||||
\(469\) | −937.023 | − | 42.7879i | −1.99792 | − | 0.0912321i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −875.443 | − | 168.728i | −1.85869 | − | 0.358233i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −84.9184 | − | 350.039i | −0.178776 | − | 0.736923i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.37410 | + | 91.8237i | 0.00909377 | + | 0.190902i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −316.953 | − | 365.783i | −0.654861 | − | 0.755750i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −746.545 | + | 587.090i | −1.53295 | + | 1.20552i | −0.629363 | + | 0.777111i | \(0.716684\pi\) |
−0.903584 | + | 0.428412i | \(0.859073\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −941.710 | − | 89.9224i | −1.92579 | − | 0.183890i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −453.687 | − | 133.215i | −0.914692 | − | 0.268578i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 258.752 | + | 448.171i | 0.518541 | + | 0.898139i | 0.999768 | + | 0.0215432i | \(0.00685793\pi\) |
−0.481227 | + | 0.876596i | \(0.659809\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −201.306 | + | 348.672i | −0.397053 | + | 0.687716i | ||||
\(508\) | −38.1919 | + | 801.746i | −0.0751808 | + | 1.57824i | ||||
\(509\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1518.27 | − | 975.730i | 2.97117 | − | 1.90945i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 225.646 | − | 316.876i | 0.439856 | − | 0.617692i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1004.52 | − | 95.9204i | −1.94675 | − | 0.185892i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −813.591 | − | 419.435i | −1.55562 | − | 0.801979i | −0.556048 | − | 0.831150i | \(-0.687683\pi\) |
−0.999574 | + | 0.0291707i | \(0.990713\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 247.547 | − | 1020.40i | 0.471518 | − | 1.94362i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −173.019 | − | 499.905i | −0.327068 | − | 0.945001i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 749.035 | + | 299.868i | 1.40796 | + | 0.563662i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −807.399 | + | 237.074i | −1.49242 | + | 0.438214i | −0.923312 | − | 0.384050i | \(-0.874529\pi\) |
−0.569107 | + | 0.822264i | \(0.692711\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34.7401 | + | 100.375i | 0.0639782 | + | 0.184853i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 195.738 | − | 806.844i | 0.357840 | − | 1.47504i | −0.453919 | − | 0.891043i | \(-0.649975\pi\) |
0.811759 | − | 0.583992i | \(-0.198510\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 663.039 | + | 341.820i | 1.20772 | + | 0.622624i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2053.05 | + | 821.917i | −3.71257 | + | 1.48629i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 949.693 | + | 90.6847i | 1.70808 | + | 0.163102i | ||||
\(557\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 287.730 | − | 404.061i | 0.514723 | − | 0.722828i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1007.94 | − | 519.629i | 1.77767 | − | 0.916453i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 471.875 | + | 662.655i | 0.826400 | + | 1.16052i | 0.984894 | + | 0.173157i | \(0.0553968\pi\) |
−0.158494 | + | 0.987360i | \(0.550664\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −552.668 | − | 162.278i | −0.959493 | − | 0.281733i | ||||
\(577\) | −893.023 | − | 702.281i | −1.54770 | − | 1.21712i | −0.882350 | − | 0.470593i | \(-0.844040\pi\) |
−0.665350 | − | 0.746532i | \(-0.731718\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −155.667 | + | 1082.69i | −0.268855 | + | 1.86993i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(588\) | 1155.17 | + | 1333.14i | 1.96458 | + | 2.26725i | ||||
\(589\) | 60.5953 | + | 421.449i | 0.102878 | + | 0.715534i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −58.7855 | + | 242.317i | −0.0992998 | + | 0.409319i | ||||
\(593\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 172.192 | + | 709.787i | 0.288429 | + | 1.18892i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 909.585 | + | 175.308i | 1.51345 | + | 0.291694i | 0.877327 | − | 0.479892i | \(-0.159324\pi\) |
0.636125 | + | 0.771586i | \(0.280536\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −277.365 | − | 535.423i | −0.459975 | − | 0.887932i | ||||
\(604\) | 107.335 | 0.177706 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −583.793 | − | 233.715i | −0.961767 | − | 0.385034i | −0.162968 | − | 0.986631i | \(-0.552107\pi\) |
−0.798799 | + | 0.601598i | \(0.794531\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −582.654 | + | 55.6367i | −0.950496 | + | 0.0907614i | −0.558772 | − | 0.829321i | \(-0.688727\pi\) |
−0.391724 | + | 0.920083i | \(0.628121\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −894.133 | − | 852.554i | −1.44448 | − | 1.37731i | −0.766559 | − | 0.642174i | \(-0.778033\pi\) |
−0.677921 | − | 0.735135i | \(-0.737119\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 204.920 | − | 195.391i | 0.328398 | − | 0.313127i | ||||
\(625\) | 259.634 | − | 568.520i | 0.415415 | − | 0.909632i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1000.03 | − | 642.681i | 1.59241 | − | 1.02338i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 59.5019 | − | 1249.10i | 0.0942978 | − | 1.97955i | −0.0873006 | − | 0.996182i | \(-0.527824\pi\) |
0.181598 | − | 0.983373i | \(-0.441873\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 221.395 | + | 383.467i | 0.349755 | + | 0.605793i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −851.456 | + | 164.105i | −1.33667 | + | 0.257621i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1227.26 | + | 360.356i | 1.90864 | + | 0.560429i | 0.983531 | + | 0.180739i | \(0.0578488\pi\) |
0.925114 | + | 0.379690i | \(0.123969\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −405.959 | + | 1172.94i | −0.623593 | + | 1.80175i | ||||
\(652\) | 991.468 | − | 779.699i | 1.52066 | − | 1.19586i | ||||
\(653\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1031.23 | + | 531.638i | 1.56961 | + | 0.809190i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −394.555 | + | 455.341i | −0.596906 | + | 0.688866i | −0.971151 | − | 0.238463i | \(-0.923356\pi\) |
0.374245 | + | 0.927330i | \(0.377902\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1299.26 | −1.94210 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 392.715 | + | 859.927i | 0.583529 | + | 1.27775i | 0.939274 | + | 0.343168i | \(0.111500\pi\) |
−0.355745 | + | 0.934583i | \(0.615773\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 647.658 | − | 190.169i | 0.959493 | − | 0.281733i | ||||
\(676\) | −126.559 | − | 521.684i | −0.187218 | − | 0.771721i | ||||
\(677\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1459.36 | − | 1684.20i | 2.14929 | − | 2.48041i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(684\) | 73.8153 | + | 513.397i | 0.107917 | + | 0.750580i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 647.924 | − | 259.390i | 0.943121 | − | 0.377569i | ||||
\(688\) | 1057.60 | − | 831.706i | 1.53721 | − | 1.20888i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −965.108 | + | 920.229i | −1.39668 | + | 1.33173i | −0.517153 | + | 0.855893i | \(0.673008\pi\) |
−0.879531 | + | 0.475842i | \(0.842144\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 700.000 | + | 1212.44i | 1.00000 | + | 1.73205i | ||||
\(701\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 220.473 | − | 42.4927i | 0.313617 | − | 0.0604448i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.7178 | − | 581.868i | 0.0390942 | − | 0.820689i | −0.891141 | − | 0.453726i | \(-0.850095\pi\) |
0.930236 | − | 0.366963i | \(-0.119602\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1117.50 | − | 878.808i | −1.57172 | − | 1.23602i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1817.76 | + | 1733.23i | 2.52116 | + | 2.40392i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 184.435 | + | 1282.78i | 0.255098 | + | 1.77424i | ||||
\(724\) | −125.879 | − | 64.8952i | −0.173866 | − | 0.0896342i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −466.979 | + | 44.5911i | −0.642337 | + | 0.0613358i | −0.411141 | − | 0.911572i | \(-0.634870\pi\) |
−0.231196 | + | 0.972907i | \(0.574264\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 613.274 | + | 394.127i | 0.841254 | + | 0.540641i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −954.329 | + | 280.216i | −1.30373 | + | 0.382809i | ||||
\(733\) | −1357.76 | − | 543.565i | −1.85233 | − | 0.741562i | −0.951745 | − | 0.306889i | \(-0.900712\pi\) |
−0.900588 | − | 0.434674i | \(-0.856864\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 438.558 | + | 84.5251i | 0.593448 | + | 0.114378i | 0.477128 | − | 0.878834i | \(-0.341678\pi\) |
0.116320 | + | 0.993212i | \(0.462890\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −236.701 | − | 94.7608i | −0.319435 | − | 0.127882i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 151.218 | + | 1051.75i | 0.201356 | + | 1.40046i | 0.800266 | + | 0.599645i | \(0.204691\pi\) |
−0.598910 | + | 0.800816i | \(0.704399\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −494.527 | + | 1428.84i | −0.654136 | + | 1.89000i | ||||
\(757\) | 1416.51 | + | 135.260i | 1.87122 | + | 0.178680i | 0.968075 | − | 0.250660i | \(-0.0806478\pi\) |
0.903143 | + | 0.429340i | \(0.141254\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1388.72 | − | 1092.10i | −1.82008 | − | 1.43133i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 682.626 | − | 351.918i | 0.888835 | − | 0.458227i | ||||
\(769\) | 21.8885 | + | 30.7381i | 0.0284635 | + | 0.0399715i | 0.828563 | − | 0.559897i | \(-0.189159\pi\) |
−0.800099 | + | 0.599868i | \(0.795220\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −845.972 | − | 1188.00i | −1.09582 | − | 1.53886i | ||||
\(773\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −369.407 | + | 639.831i | −0.476654 | + | 0.825589i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 628.019 | + | 184.403i | 0.808261 | + | 0.237327i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2341.35 | − | 223.572i | −2.98641 | − | 0.285168i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1317.28 | − | 527.358i | 1.67380 | − | 0.670087i | 0.676028 | − | 0.736876i | \(-0.263700\pi\) |
0.997767 | + | 0.0667893i | \(0.0212755\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 115.268 | − | 475.141i | 0.145357 | − | 0.599169i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −819.240 | − | 526.494i | −1.02920 | − | 0.661424i | ||||
\(797\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 760.297 | + | 261.467i | 0.945643 | + | 0.325208i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 352.914 | + | 1019.68i | 0.435159 | + | 1.25731i | 0.923143 | + | 0.384457i | \(0.125611\pi\) |
−0.487984 | + | 0.872853i | \(0.662268\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 647.151 | − | 746.852i | 0.796003 | − | 0.918637i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1076.87 | − | 555.167i | −1.31808 | − | 0.679519i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −486.726 | − | 561.712i | −0.594293 | − | 0.685851i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −417.834 | + | 1207.25i | −0.507696 | + | 1.46689i | 0.342041 | + | 0.939685i | \(0.388882\pi\) |
−0.849737 | + | 0.527206i | \(0.823239\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 855.918 | − | 550.065i | 1.03247 | − | 0.663528i | 0.0893571 | − | 0.996000i | \(-0.471519\pi\) |
0.943113 | + | 0.332471i | \(0.107882\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −252.113 | − | 74.0270i | −0.303385 | − | 0.0890818i | ||||
\(832\) | −17.9633 | + | 377.097i | −0.0215906 | + | 0.453241i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −783.499 | + | 151.007i | −0.936080 | + | 0.180415i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −420.500 | − | 728.327i | −0.500000 | − | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −566.472 | − | 166.331i | −0.671175 | − | 0.197075i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 241.081 | − | 1676.76i | 0.284630 | − | 1.97964i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 664.422 | − | 1454.88i | 0.782593 | − | 1.71364i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 253.494 | − | 199.350i | 0.297180 | − | 0.233705i | −0.458424 | − | 0.888733i | \(-0.651586\pi\) |
0.755604 | + | 0.655029i | \(0.227344\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.3101 | + | 1035.15i | 0.0574041 | + | 1.20506i | 0.825378 | + | 0.564580i | \(0.190962\pi\) |
−0.767974 | + | 0.640481i | \(0.778735\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −804.895 | − | 322.231i | −0.928368 | − | 0.371662i | ||||
\(868\) | −687.488 | − | 1505.39i | −0.792037 | − | 1.73432i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −298.178 | + | 259.402i | −0.342340 | + | 0.297821i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1406.73 | + | 271.124i | 1.61137 | + | 0.310566i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1484.28 | + | 435.824i | −1.69438 | + | 0.497516i | ||||
\(877\) | 413.476 | + | 1704.37i | 0.471467 | + | 1.94341i | 0.250030 | + | 0.968238i | \(0.419559\pi\) |
0.221437 | + | 0.975175i | \(0.428925\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.0331 | − | 1134.29i | −0.0611926 | − | 1.28459i | −0.795575 | − | 0.605855i | \(-0.792831\pi\) |
0.734382 | − | 0.678736i | \(-0.237472\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2208.25 | + | 1736.59i | −2.48397 | + | 1.95342i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1253.76 | − | 1195.46i | 1.40556 | − | 1.34020i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −450.000 | + | 779.423i | −0.500000 | + | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2048.66 | − | 2876.94i | −2.26873 | − | 3.18598i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −633.585 | + | 326.636i | −0.698550 | + | 0.360127i | −0.770640 | − | 0.637271i | \(-0.780063\pi\) |
0.0720903 | + | 0.997398i | \(0.477033\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(912\) | −543.609 | − | 427.499i | −0.596063 | − | 0.468749i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −386.567 | + | 846.464i | −0.422016 | + | 0.924087i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 122.381 | − | 353.597i | 0.133168 | − | 0.384763i | −0.858628 | − | 0.512600i | \(-0.828682\pi\) |
0.991795 | + | 0.127837i | \(0.0408036\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 75.0575 | − | 30.0485i | 0.0814957 | − | 0.0326259i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 346.293 | + | 178.526i | 0.374370 | + | 0.193001i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −380.662 | + | 1569.11i | −0.410639 | + | 1.69268i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 692.706 | + | 2001.44i | 0.744045 | + | 2.14978i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.8835 | 0.0543047 | 0.0271524 | − | 0.999631i | \(-0.491356\pi\) | ||||
0.0271524 | + | 0.999631i | \(0.491356\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1103.33 | 1.17501 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(948\) | 1886.95 | − | 180.182i | 1.99046 | − | 0.190066i | ||||
\(949\) | 179.278 | − | 738.993i | 0.188912 | − | 0.778707i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −50.8406 | + | 71.3956i | −0.0529038 | + | 0.0742930i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1358.27 | − | 1068.15i | −1.40899 | − | 1.10804i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 924.605 | − | 1601.46i | 0.956158 | − | 1.65611i | 0.224464 | − | 0.974482i | \(-0.427937\pi\) |
0.731695 | − | 0.681633i | \(-0.238730\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(972\) | −954.435 | + | 183.952i | −0.981929 | + | 0.189251i | ||||
\(973\) | 1936.84 | + | 2719.90i | 1.99058 | + | 2.79538i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −221.206 | − | 383.140i | −0.226878 | − | 0.392964i | ||||
\(976\) | 663.079 | − | 1148.49i | 0.679384 | − | 1.17673i | ||||
\(977\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 161.632 | − | 1124.18i | 0.164763 | − | 1.14595i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 315.602 | − | 126.348i | 0.319435 | − | 0.127882i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 73.1650 | + | 508.874i | 0.0738295 | + | 0.513495i | 0.992858 | + | 0.119304i | \(0.0380663\pi\) |
−0.919028 | + | 0.394192i | \(0.871025\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.9194 | + | 921.981i | 0.0442290 | + | 0.928480i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1139.05 | − | 732.020i | −1.14247 | − | 0.734223i | −0.174347 | − | 0.984684i | \(-0.555781\pi\) |
−0.968127 | + | 0.250461i | \(0.919418\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 99.2005 | + | 408.910i | 0.0992998 | + | 0.409319i |
(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 | 201.3.o.a.83.1 | ✓ | 20 | |
3.2 | odd | 2 | CM | 201.3.o.a.83.1 | ✓ | 20 | |
67.21 | even | 33 | inner | 201.3.o.a.155.1 | yes | 20 | |
201.155 | odd | 66 | inner | 201.3.o.a.155.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.3.o.a.83.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
201.3.o.a.83.1 | ✓ | 20 | 3.2 | odd | 2 | CM | |
201.3.o.a.155.1 | yes | 20 | 67.21 | even | 33 | inner | |
201.3.o.a.155.1 | yes | 20 | 201.155 | odd | 66 | inner |