Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,4,Mod(361,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.k (of order \(3\), degree \(2\), not 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: | \(104.079369250\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1549.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1549 |
Dual form | 1764.4.k.l.361.1 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | − | 5.19615i | 0.268328 | − | 0.464758i | −0.700102 | − | 0.714043i | \(-0.746862\pi\) |
0.968430 | + | 0.249285i | \(0.0801955\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.0000 | + | 31.1769i | 0.493382 | + | 0.854563i | 0.999971 | − | 0.00762479i | \(-0.00242707\pi\) |
−0.506589 | + | 0.862188i | \(0.669094\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 62.0000 | 1.32275 | 0.661373 | − | 0.750057i | \(-0.269974\pi\) | ||||
0.661373 | + | 0.750057i | \(0.269974\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 57.0000 | + | 98.7269i | 0.813208 | + | 1.40852i | 0.910608 | + | 0.413272i | \(0.135614\pi\) |
−0.0974001 | + | 0.995245i | \(0.531053\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38.0000 | − | 65.8179i | 0.458831 | − | 0.794719i | −0.540068 | − | 0.841621i | \(-0.681602\pi\) |
0.998899 | + | 0.0469020i | \(0.0149348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −12.0000 | + | 20.7846i | −0.108790 | + | 0.188430i | −0.915280 | − | 0.402817i | \(-0.868031\pi\) |
0.806490 | + | 0.591247i | \(0.201364\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.5000 | + | 77.0763i | 0.356000 | + | 0.616610i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −54.0000 | −0.345778 | −0.172889 | − | 0.984941i | \(-0.555310\pi\) | ||||
−0.172889 | + | 0.984941i | \(0.555310\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 56.0000 | + | 96.9948i | 0.324448 | + | 0.561961i | 0.981401 | − | 0.191971i | \(-0.0614880\pi\) |
−0.656952 | + | 0.753932i | \(0.728155\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 89.0000 | − | 154.153i | 0.395446 | − | 0.684933i | −0.597712 | − | 0.801711i | \(-0.703923\pi\) |
0.993158 | + | 0.116778i | \(0.0372566\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −378.000 | −1.43985 | −0.719923 | − | 0.694054i | \(-0.755823\pi\) | ||||
−0.719923 | + | 0.694054i | \(0.755823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −172.000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −96.0000 | + | 166.277i | −0.297937 | + | 0.516042i | −0.975664 | − | 0.219272i | \(-0.929632\pi\) |
0.677727 | + | 0.735314i | \(0.262965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −201.000 | − | 348.142i | −0.520933 | − | 0.902283i | −0.999704 | − | 0.0243430i | \(-0.992251\pi\) |
0.478770 | − | 0.877940i | \(-0.341083\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 216.000 | 0.529553 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 198.000 | + | 342.946i | 0.436905 | + | 0.756742i | 0.997449 | − | 0.0713828i | \(-0.0227412\pi\) |
−0.560544 | + | 0.828125i | \(0.689408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −127.000 | + | 219.970i | −0.266569 | + | 0.461710i | −0.967973 | − | 0.251053i | \(-0.919223\pi\) |
0.701405 | + | 0.712763i | \(0.252557\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 186.000 | − | 322.161i | 0.354930 | − | 0.614757i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 506.000 | + | 876.418i | 0.922653 | + | 1.59808i | 0.795293 | + | 0.606225i | \(0.207317\pi\) |
0.127360 | + | 0.991857i | \(0.459350\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −840.000 | −1.40408 | −0.702040 | − | 0.712138i | \(-0.747727\pi\) | ||||
−0.702040 | + | 0.712138i | \(0.747727\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −445.000 | − | 770.763i | −0.713470 | − | 1.23577i | −0.963547 | − | 0.267540i | \(-0.913789\pi\) |
0.250077 | − | 0.968226i | \(-0.419544\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −40.0000 | + | 69.2820i | −0.0569665 | + | 0.0986688i | −0.893102 | − | 0.449854i | \(-0.851476\pi\) |
0.836136 | + | 0.548522i | \(0.184809\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 108.000 | 0.142826 | 0.0714129 | − | 0.997447i | \(-0.477249\pi\) | ||||
0.0714129 | + | 0.997447i | \(0.477249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 684.000 | 0.872826 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −819.000 | + | 1418.55i | −0.975436 | + | 1.68951i | −0.296948 | + | 0.954894i | \(0.595969\pi\) |
−0.678488 | + | 0.734612i | \(0.737364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −228.000 | − | 394.908i | −0.246235 | − | 0.426491i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1010.00 | 1.05722 | 0.528608 | − | 0.848866i | \(-0.322714\pi\) | ||||
0.528608 | + | 0.848866i | \(0.322714\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | + | 5.19615i | 0.00295556 | + | 0.00511917i | 0.867499 | − | 0.497438i | \(-0.165726\pi\) |
−0.864544 | + | 0.502557i | \(0.832393\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 236.000 | − | 408.764i | 0.225765 | − | 0.391036i | −0.730784 | − | 0.682609i | \(-0.760845\pi\) |
0.956549 | + | 0.291573i | \(0.0941786\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −486.000 | + | 841.777i | −0.439097 | + | 0.760539i | −0.997620 | − | 0.0689505i | \(-0.978035\pi\) |
0.558523 | + | 0.829489i | \(0.311368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 893.000 | + | 1546.72i | 0.784715 | + | 1.35917i | 0.929169 | + | 0.369654i | \(0.120524\pi\) |
−0.144455 | + | 0.989511i | \(0.546143\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2286.00 | 1.90309 | 0.951543 | − | 0.307515i | \(-0.0994973\pi\) | ||||
0.951543 | + | 0.307515i | \(0.0994973\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 72.0000 | + | 124.708i | 0.0583829 | + | 0.101122i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.5000 | − | 30.3109i | 0.0131480 | − | 0.0227730i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1328.00 | 0.927881 | 0.463941 | − | 0.885866i | \(-0.346435\pi\) | ||||
0.463941 | + | 0.885866i | \(0.346435\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −606.000 | + | 1049.62i | −0.404171 | + | 0.700046i | −0.994225 | − | 0.107319i | \(-0.965773\pi\) |
0.590053 | + | 0.807364i | \(0.299107\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −627.000 | − | 1086.00i | −0.391009 | − | 0.677247i | 0.601574 | − | 0.798817i | \(-0.294541\pi\) |
−0.992583 | + | 0.121570i | \(0.961207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −340.000 | −0.207471 | −0.103735 | − | 0.994605i | \(-0.533079\pi\) | ||||
−0.103735 | + | 0.994605i | \(0.533079\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1116.00 | + | 1932.97i | 0.652620 | + | 1.13037i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −162.000 | + | 280.592i | −0.0927818 | + | 0.160703i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 519.000 | − | 898.934i | 0.285357 | − | 0.494252i | −0.687339 | − | 0.726337i | \(-0.741221\pi\) |
0.972696 | + | 0.232085i | \(0.0745546\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1468.00 | − | 2542.65i | −0.791153 | − | 1.37032i | −0.925253 | − | 0.379350i | \(-0.876148\pi\) |
0.134100 | − | 0.990968i | \(-0.457186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 672.000 | 0.348234 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 665.000 | + | 1151.81i | 0.338043 | + | 0.585508i | 0.984065 | − | 0.177811i | \(-0.0569017\pi\) |
−0.646021 | + | 0.763319i | \(0.723568\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1682.00 | − | 2913.31i | 0.808248 | − | 1.39993i | −0.105828 | − | 0.994384i | \(-0.533749\pi\) |
0.914076 | − | 0.405542i | \(-0.132917\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3048.00 | −1.41234 | −0.706172 | − | 0.708041i | \(-0.749579\pi\) | ||||
−0.706172 | + | 0.708041i | \(0.749579\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1647.00 | 0.749659 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1353.00 | + | 2343.46i | −0.594605 | + | 1.02989i | 0.398997 | + | 0.916952i | \(0.369358\pi\) |
−0.993602 | + | 0.112934i | \(0.963975\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2358.00 | + | 4084.18i | 0.984610 | + | 1.70539i | 0.643657 | + | 0.765314i | \(0.277416\pi\) |
0.340953 | + | 0.940080i | \(0.389250\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1910.00 | 0.784360 | 0.392180 | − | 0.919888i | \(-0.371721\pi\) | ||||
0.392180 | + | 0.919888i | \(0.371721\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −534.000 | − | 924.915i | −0.212219 | − | 0.367574i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2052.00 | + | 3554.17i | −0.802444 | + | 1.38987i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2040.00 | − | 3533.38i | 0.772823 | − | 1.33857i | −0.163187 | − | 0.986595i | \(-0.552177\pi\) |
0.936010 | − | 0.351974i | \(-0.114489\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1343.00 | + | 2326.14i | 0.500887 | + | 0.867562i | 0.999999 | + | 0.00102491i | \(0.000326238\pi\) |
−0.499112 | + | 0.866537i | \(0.666340\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −510.000 | −0.184447 | −0.0922233 | − | 0.995738i | \(-0.529397\pi\) | ||||
−0.0922233 | + | 0.995738i | \(0.529397\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −676.000 | − | 1170.87i | −0.240806 | − | 0.417088i | 0.720138 | − | 0.693831i | \(-0.244078\pi\) |
−0.960944 | + | 0.276743i | \(0.910745\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1134.00 | + | 1964.15i | −0.386351 | + | 0.669180i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2736.00 | 0.905517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3364.00 | −1.09757 | −0.548785 | − | 0.835963i | \(-0.684909\pi\) | ||||
−0.548785 | + | 0.835963i | \(0.684909\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −516.000 | + | 893.738i | −0.163679 | + | 0.283500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3534.00 | + | 6121.07i | 1.07567 | + | 1.86311i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4768.00 | −1.43179 | −0.715894 | − | 0.698209i | \(-0.753981\pi\) | ||||
−0.715894 | + | 0.698209i | \(0.753981\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 210.000 | + | 363.731i | 0.0614017 | + | 0.106351i | 0.895092 | − | 0.445881i | \(-0.147110\pi\) |
−0.833690 | + | 0.552232i | \(0.813776\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 941.000 | − | 1629.86i | 0.271542 | − | 0.470324i | −0.697715 | − | 0.716375i | \(-0.745800\pi\) |
0.969257 | + | 0.246051i | \(0.0791332\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2541.00 | − | 4401.14i | 0.714448 | − | 1.23746i | −0.248724 | − | 0.968574i | \(-0.580011\pi\) |
0.963172 | − | 0.268886i | \(-0.0866556\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 576.000 | + | 997.661i | 0.159890 | + | 0.276937i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5424.00 | 1.46799 | 0.733995 | − | 0.679155i | \(-0.237654\pi\) | ||||
0.733995 | + | 0.679155i | \(0.237654\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1295.00 | + | 2243.01i | 0.346134 | + | 0.599522i | 0.985559 | − | 0.169332i | \(-0.0541609\pi\) |
−0.639425 | + | 0.768853i | \(0.720828\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2356.00 | − | 4080.71i | 0.606918 | − | 1.05121i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4932.00 | 1.24026 | 0.620130 | − | 0.784499i | \(-0.287080\pi\) | ||||
0.620130 | + | 0.784499i | \(0.287080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −864.000 | −0.214700 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1719.00 | + | 2977.40i | −0.417231 | + | 0.722665i | −0.995660 | − | 0.0930680i | \(-0.970333\pi\) |
0.578429 | + | 0.815733i | \(0.303666\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3060.00 | + | 5300.08i | 0.717444 | + | 1.24265i | 0.962009 | + | 0.273016i | \(0.0880213\pi\) |
−0.244566 | + | 0.969633i | \(0.578645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2412.00 | −0.559124 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.00000 | − | 15.5885i | −0.00203992 | − | 0.00353325i | 0.865004 | − | 0.501766i | \(-0.167316\pi\) |
−0.867044 | + | 0.498232i | \(0.833983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3448.00 | + | 5972.11i | −0.772882 | + | 1.33867i | 0.163095 | + | 0.986610i | \(0.447852\pi\) |
−0.935977 | + | 0.352061i | \(0.885481\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1602.00 | + | 2774.75i | −0.351288 | + | 0.608449i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3127.00 | − | 5416.12i | −0.678279 | − | 1.17481i | −0.975499 | − | 0.220004i | \(-0.929393\pi\) |
0.297220 | − | 0.954809i | \(-0.403940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1194.00 | −0.253481 | −0.126740 | − | 0.991936i | \(-0.540451\pi\) | ||||
−0.126740 | + | 0.991936i | \(0.540451\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3578.00 | + | 6197.28i | 0.751555 | + | 1.30173i | 0.947069 | + | 0.321030i | \(0.104029\pi\) |
−0.195514 | + | 0.980701i | \(0.562638\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4041.50 | + | 7000.08i | −0.822613 | + | 1.42481i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3738.00 | 0.745312 | 0.372656 | − | 0.927970i | \(-0.378447\pi\) | ||||
0.372656 | + | 0.927970i | \(0.378447\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2376.00 | 0.468936 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −744.000 | + | 1288.65i | −0.143902 | + | 0.249245i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 762.000 | + | 1319.82i | 0.143056 | + | 0.247780i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −844.000 | −0.156904 | −0.0784522 | − | 0.996918i | \(-0.524998\pi\) | ||||
−0.0784522 | + | 0.996918i | \(0.524998\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3156.00 | + | 5466.35i | 0.575435 | + | 0.996683i | 0.995994 | + | 0.0894178i | \(0.0285006\pi\) |
−0.420559 | + | 0.907265i | \(0.638166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4141.00 | + | 7172.42i | −0.747806 | + | 1.29524i | 0.201067 | + | 0.979578i | \(0.435559\pi\) |
−0.948872 | + | 0.315660i | \(0.897774\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4659.00 | − | 8069.62i | 0.825475 | − | 1.42976i | −0.0760811 | − | 0.997102i | \(-0.524241\pi\) |
0.901556 | − | 0.432663i | \(-0.142426\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −972.000 | − | 1683.55i | −0.170600 | − | 0.295489i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8664.00 | 1.49250 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2759.00 | + | 4778.73i | 0.470898 | + | 0.815619i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −826.000 | + | 1430.67i | −0.137163 | + | 0.237574i | −0.926422 | − | 0.376487i | \(-0.877132\pi\) |
0.789258 | + | 0.614061i | \(0.210465\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6072.00 | 0.990295 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1294.00 | −0.209165 | −0.104583 | − | 0.994516i | \(-0.533351\pi\) | ||||
−0.104583 | + | 0.994516i | \(0.533351\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2016.00 | + | 3491.81i | −0.320154 | + | 0.554523i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1818.00 | + | 3148.87i | 0.281255 | + | 0.487147i | 0.971694 | − | 0.236243i | \(-0.0759161\pi\) |
−0.690439 | + | 0.723390i | \(0.742583\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10478.0 | 1.60709 | 0.803545 | − | 0.595244i | \(-0.202945\pi\) | ||||
0.803545 | + | 0.595244i | \(0.202945\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3783.00 | − | 6552.35i | −0.570393 | − | 0.987950i | −0.996525 | − | 0.0832890i | \(-0.973458\pi\) |
0.426132 | − | 0.904661i | \(-0.359876\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2520.00 | + | 4364.77i | −0.376754 | + | 0.652557i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4020.00 | + | 6962.84i | −0.590996 | + | 1.02363i | 0.403103 | + | 0.915155i | \(0.367932\pi\) |
−0.994099 | + | 0.108480i | \(0.965402\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 541.500 | + | 937.906i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5340.00 | −0.765776 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3784.00 | − | 6554.08i | −0.538210 | − | 0.932208i | −0.999001 | − | 0.0446985i | \(-0.985767\pi\) |
0.460790 | − | 0.887509i | \(-0.347566\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6761.00 | − | 11710.4i | 0.938529 | − | 1.62558i | 0.170312 | − | 0.985390i | \(-0.445522\pi\) |
0.768217 | − | 0.640190i | \(-0.221144\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3348.00 | −0.457376 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2468.00 | 0.334492 | 0.167246 | − | 0.985915i | \(-0.446513\pi\) | ||||
0.167246 | + | 0.985915i | \(0.446513\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6168.00 | + | 10683.3i | −0.822898 | + | 1.42530i | 0.0806166 | + | 0.996745i | \(0.474311\pi\) |
−0.903515 | + | 0.428557i | \(0.859022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1881.00 | − | 3257.99i | −0.245168 | − | 0.424644i | 0.717011 | − | 0.697062i | \(-0.245510\pi\) |
−0.962179 | + | 0.272418i | \(0.912177\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2736.00 | −0.353876 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 240.000 | + | 415.692i | 0.0305714 | + | 0.0529513i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4385.00 | − | 7595.04i | 0.554350 | − | 0.960162i | −0.443604 | − | 0.896223i | \(-0.646300\pi\) |
0.997954 | − | 0.0639390i | \(-0.0203663\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3321.00 | − | 5752.14i | 0.413573 | − | 0.716330i | −0.581704 | − | 0.813400i | \(-0.697614\pi\) |
0.995277 | + | 0.0970706i | \(0.0309473\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3472.00 | + | 6013.68i | 0.429163 | + | 0.743332i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6408.00 | 0.780424 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 755.000 | + | 1307.70i | 0.0912771 | + | 0.158097i | 0.908049 | − | 0.418864i | \(-0.137572\pi\) |
−0.816772 | + | 0.576961i | \(0.804238\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 324.000 | − | 561.184i | 0.0383242 | − | 0.0663794i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1260.00 | 0.146909 | 0.0734547 | − | 0.997299i | \(-0.476598\pi\) | ||||
0.0734547 | + | 0.997299i | \(0.476598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3998.00 | 0.462828 | 0.231414 | − | 0.972855i | \(-0.425665\pi\) | ||||
0.231414 | + | 0.972855i | \(0.425665\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5073.00 | + | 8786.69i | −0.579004 | + | 1.00286i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1368.00 | − | 2369.45i | −0.152887 | − | 0.264808i | 0.779401 | − | 0.626526i | \(-0.215524\pi\) |
−0.932288 | + | 0.361718i | \(0.882190\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2690.00 | 0.298552 | 0.149276 | − | 0.988796i | \(-0.452306\pi\) | ||||
0.149276 | + | 0.988796i | \(0.452306\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 912.000 | + | 1579.63i | 0.0998327 | + | 0.172915i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 620.000 | − | 1073.87i | 0.0674054 | − | 0.116750i | −0.830353 | − | 0.557238i | \(-0.811861\pi\) |
0.897758 | + | 0.440488i | \(0.145195\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1950.00 | + | 3377.50i | −0.209136 | + | 0.362234i | −0.951443 | − | 0.307826i | \(-0.900399\pi\) |
0.742307 | + | 0.670060i | \(0.233732\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4914.00 | + | 8511.30i | 0.523474 | + | 0.906684i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10878.0 | 1.14335 | 0.571675 | − | 0.820480i | \(-0.306294\pi\) | ||||
0.571675 | + | 0.820480i | \(0.306294\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6804.00 | − | 11784.9i | −0.710394 | − | 1.23044i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1165.00 | + | 2017.84i | −0.119248 | + | 0.206544i | −0.919470 | − | 0.393160i | \(-0.871382\pi\) |
0.800222 | + | 0.599704i | \(0.204715\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15150.0 | −1.53060 | −0.765299 | − | 0.643675i | \(-0.777409\pi\) | ||||
−0.765299 | + | 0.643675i | \(0.777409\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2992.00 | −0.300324 | −0.150162 | − | 0.988661i | \(-0.547980\pi\) | ||||
−0.150162 | + | 0.988661i | \(0.547980\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4362.00 | − | 7555.21i | 0.432225 | − | 0.748636i | −0.564839 | − | 0.825201i | \(-0.691062\pi\) |
0.997065 | + | 0.0765646i | \(0.0243951\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3096.00 | − | 5362.43i | −0.300960 | − | 0.521279i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6764.00 | 0.653376 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4872.00 | + | 8438.55i | 0.464734 | + | 0.804942i | 0.999189 | − | 0.0402542i | \(-0.0128168\pi\) |
−0.534456 | + | 0.845196i | \(0.679483\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5518.00 | − | 9557.46i | 0.523075 | − | 0.905993i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3030.00 | − | 5248.11i | 0.283681 | − | 0.491350i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2068.00 | − | 3581.88i | −0.192423 | − | 0.333286i | 0.753630 | − | 0.657299i | \(-0.228301\pi\) |
−0.946053 | + | 0.324013i | \(0.894968\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16212.0 | −1.49010 | −0.745048 | − | 0.667011i | \(-0.767574\pi\) | ||||
−0.745048 | + | 0.667011i | \(0.767574\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3078.00 | − | 5331.25i | −0.281189 | − | 0.487034i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1198.00 | + | 2075.00i | −0.107475 | + | 0.186152i | −0.914747 | − | 0.404028i | \(-0.867610\pi\) |
0.807272 | + | 0.590180i | \(0.200943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13128.0 | −1.16371 | −0.581857 | − | 0.813291i | \(-0.697674\pi\) | ||||
−0.581857 | + | 0.813291i | \(0.697674\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 0.00317224 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6399.00 | − | 11083.4i | 0.557231 | − | 0.965153i | −0.440495 | − | 0.897755i | \(-0.645197\pi\) |
0.997726 | − | 0.0673977i | \(-0.0214696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1416.00 | − | 2452.58i | −0.121158 | − | 0.209852i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6912.00 | −0.587987 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3693.00 | + | 6396.46i | 0.310544 | + | 0.537877i | 0.978480 | − | 0.206341i | \(-0.0661556\pi\) |
−0.667936 | + | 0.744218i | \(0.732822\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2590.00 | + | 4486.01i | −0.216545 | + | 0.375066i | −0.953749 | − | 0.300603i | \(-0.902812\pi\) |
0.737205 | + | 0.675669i | \(0.236145\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6384.00 | + | 11057.4i | −0.527688 | + | 0.913982i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5795.50 | + | 10038.1i | 0.476329 | + | 0.825027i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23436.0 | −1.90455 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2916.00 | + | 5050.66i | 0.235644 | + | 0.408148i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2035.00 | + | 3524.72i | −0.161722 | + | 0.280110i | −0.935486 | − | 0.353363i | \(-0.885038\pi\) |
0.773764 | + | 0.633473i | \(0.218371\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10716.0 | 0.842244 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14780.0 | 1.15530 | 0.577648 | − | 0.816286i | \(-0.303971\pi\) | ||||
0.577648 | + | 0.816286i | \(0.303971\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2052.00 | + | 3554.17i | −0.158654 | + | 0.274796i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3429.00 | − | 5939.20i | −0.260846 | − | 0.451799i | 0.705621 | − | 0.708590i | \(-0.250668\pi\) |
−0.966467 | + | 0.256791i | \(0.917335\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10664.0 | −0.806868 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3330.00 | + | 5767.73i | 0.249277 | + | 0.431760i | 0.963325 | − | 0.268336i | \(-0.0864738\pi\) |
−0.714049 | + | 0.700096i | \(0.753140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6858.00 | − | 11878.4i | 0.510652 | − | 0.884475i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −75.0000 | + | 129.904i | −0.00552577 | + | 0.00957092i | −0.868775 | − | 0.495207i | \(-0.835092\pi\) |
0.863249 | + | 0.504778i | \(0.168426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4094.00 | + | 7091.02i | 0.300050 | + | 0.519702i | 0.976147 | − | 0.217111i | \(-0.0696633\pi\) |
−0.676097 | + | 0.736813i | \(0.736330\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2136.00 | −0.154917 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2927.00 | + | 5069.71i | 0.211183 | + | 0.365780i | 0.952085 | − | 0.305833i | \(-0.0989351\pi\) |
−0.740902 | + | 0.671613i | \(0.765602\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7236.00 | − | 12533.1i | 0.514039 | − | 0.890341i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17580.0 | −1.23612 | −0.618062 | − | 0.786130i | \(-0.712082\pi\) | ||||
−0.618062 | + | 0.786130i | \(0.712082\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8512.00 | 0.595468 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8577.00 | − | 14855.8i | 0.593955 | − | 1.02876i | −0.399739 | − | 0.916629i | \(-0.630899\pi\) |
0.993693 | − | 0.112131i | \(-0.0357675\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9060.00 | − | 15692.4i | −0.617999 | − | 1.07041i | −0.989850 | − | 0.142114i | \(-0.954610\pi\) |
0.371851 | − | 0.928292i | \(-0.378723\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17546.0 | 1.19088 | 0.595438 | − | 0.803401i | \(-0.296979\pi\) | ||||
0.595438 | + | 0.803401i | \(0.296979\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −105.000 | − | 181.865i | −0.00705596 | − | 0.0122213i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7280.00 | − | 12609.3i | 0.486798 | − | 0.843158i | −0.513087 | − | 0.858336i | \(-0.671498\pi\) |
0.999885 | + | 0.0151784i | \(0.00483163\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5952.00 | + | 10309.2i | −0.394095 | + | 0.682593i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2249.00 | + | 3895.38i | 0.148183 | + | 0.256661i | 0.930556 | − | 0.366150i | \(-0.119324\pi\) |
−0.782373 | + | 0.622810i | \(0.785991\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5478.00 | 0.357433 | 0.178716 | − | 0.983901i | \(-0.442806\pi\) | ||||
0.178716 | + | 0.983901i | \(0.442806\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3022.00 | − | 5234.26i | −0.196227 | − | 0.339875i | 0.751075 | − | 0.660217i | \(-0.229536\pi\) |
−0.947302 | + | 0.320342i | \(0.896202\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1710.50 | + | 2962.67i | −0.109472 | + | 0.189611i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20292.0 | 1.28632 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15352.0 | −0.968547 | −0.484274 | − | 0.874917i | \(-0.660916\pi\) | ||||
−0.484274 | + | 0.874917i | \(0.660916\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3984.00 | − | 6900.49i | 0.248977 | − | 0.431240i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11199.0 | − | 19397.2i | −0.690068 | − | 1.19523i | −0.971815 | − | 0.235745i | \(-0.924247\pi\) |
0.281746 | − | 0.959489i | \(-0.409086\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3764.00 | 0.230852 | 0.115426 | − | 0.993316i | \(-0.463177\pi\) | ||||
0.115426 | + | 0.993316i | \(0.463177\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8844.00 | − | 15318.3i | −0.537393 | − | 0.930793i | −0.999043 | − | 0.0437305i | \(-0.986076\pi\) |
0.461650 | − | 0.887062i | \(-0.347258\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7128.00 | + | 12346.1i | −0.431122 | + | 0.746726i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9939.00 | − | 17214.9i | 0.595625 | − | 1.03165i | −0.397833 | − | 0.917458i | \(-0.630238\pi\) |
0.993458 | − | 0.114195i | \(-0.0364289\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3636.00 | + | 6297.74i | 0.216901 | + | 0.375684i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20004.0 | 1.18247 | 0.591233 | − | 0.806501i | \(-0.298641\pi\) | ||||
0.591233 | + | 0.806501i | \(0.298641\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 653.000 | + | 1131.03i | 0.0384247 | + | 0.0665536i | 0.884598 | − | 0.466354i | \(-0.154433\pi\) |
−0.846173 | + | 0.532908i | \(0.821099\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 648.000 | − | 1122.37i | 0.0376172 | − | 0.0651549i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9144.00 | −0.526081 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13054.0 | −0.747689 | −0.373845 | − | 0.927491i | \(-0.621961\pi\) | ||||
−0.373845 | + | 0.927491i | \(0.621961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2523.00 | − | 4369.96i | 0.143230 | − | 0.248082i | −0.785481 | − | 0.618886i | \(-0.787584\pi\) |
0.928711 | + | 0.370804i | \(0.120918\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6234.00 | + | 10797.6i | 0.349249 | + | 0.604918i | 0.986116 | − | 0.166056i | \(-0.0531032\pi\) |
−0.636867 | + | 0.770974i | \(0.719770\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7524.00 | −0.419675 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12462.0 | − | 21584.8i | −0.689063 | − | 1.19349i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11606.0 | − | 20102.2i | 0.638948 | − | 1.10669i | −0.346716 | − | 0.937970i | \(-0.612703\pi\) |
0.985664 | − | 0.168720i | \(-0.0539634\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1020.00 | + | 1766.69i | −0.0556702 | + | 0.0964237i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21546.0 | − | 37318.8i | −1.17089 | − | 2.02805i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35958.0 | −1.93740 | −0.968698 | − | 0.248241i | \(-0.920147\pi\) | ||||
−0.968698 | + | 0.248241i | \(0.920147\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6764.00 | − | 11715.6i | −0.362886 | − | 0.628538i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3223.00 | + | 5582.40i | −0.170723 | + | 0.295700i | −0.938673 | − | 0.344809i | \(-0.887944\pi\) |
0.767950 | + | 0.640510i | \(0.221277\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2688.00 | −0.141187 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13392.0 | 0.700465 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2352.00 | + | 4073.78i | −0.121996 | + | 0.211302i | −0.920555 | − | 0.390614i | \(-0.872263\pi\) |
0.798559 | + | 0.601917i | \(0.205596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2403.00 | − | 4162.12i | −0.123097 | − | 0.213210i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10600.0 | −0.540760 | −0.270380 | − | 0.962754i | \(-0.587149\pi\) | ||||
−0.270380 | + | 0.962754i | \(0.587149\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9804.00 | − | 16981.0i | −0.496052 | − | 0.859187i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6271.00 | + | 10861.7i | −0.315995 | + | 0.547320i | −0.979649 | − | 0.200720i | \(-0.935672\pi\) |
0.663653 | + | 0.748040i | \(0.269005\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18216.0 | + | 31551.0i | −0.910441 | + | 1.57693i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11662.0 | − | 20199.2i | −0.580506 | − | 1.00547i | −0.995419 | − | 0.0956044i | \(-0.969522\pi\) |
0.414914 | − | 0.909861i | \(-0.363812\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6312.00 | 0.311662 | 0.155831 | − | 0.987784i | \(-0.450194\pi\) | ||||
0.155831 | + | 0.987784i | \(0.450194\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3114.00 | − | 5393.61i | −0.153138 | − | 0.265244i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17920.0 | + | 31038.4i | −0.870719 | + | 1.50813i | −0.00946509 | + | 0.999955i | \(0.503013\pi\) |
−0.861254 | + | 0.508175i | \(0.830320\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17616.0 | −0.849155 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34594.0 | −1.66095 | −0.830476 | − | 0.557055i | \(-0.811931\pi\) | ||||
−0.830476 | + | 0.557055i | \(0.811931\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11973.0 | − | 20737.8i | 0.570330 | − | 0.987840i | −0.426202 | − | 0.904628i | \(-0.640149\pi\) |
0.996532 | − | 0.0832121i | \(-0.0265179\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12276.0 | + | 21262.7i | 0.577915 | + | 1.00098i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18770.0 | 0.880187 | 0.440093 | − | 0.897952i | \(-0.354945\pi\) | ||||
0.440093 | + | 0.897952i | \(0.354945\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15171.0 | + | 26276.9i | 0.705903 | + | 1.22266i | 0.966365 | + | 0.257176i | \(0.0827919\pi\) |
−0.260462 | + | 0.965484i | \(0.583875\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4984.00 | + | 8632.54i | −0.231007 | + | 0.400116i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14364.0 | + | 24879.2i | −0.660647 | + | 1.14427i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15120.0 | − | 26188.6i | −0.692748 | − | 1.19987i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7980.00 | 0.362826 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13094.0 | + | 22679.5i | 0.593076 | + | 1.02724i | 0.993815 | + | 0.111045i | \(0.0354199\pi\) |
−0.400739 | + | 0.916192i | \(0.631247\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7874.00 | + | 13638.2i | −0.352603 | + | 0.610726i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34818.0 |