Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,4,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (of order \(6\), 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: | \(59.4739252858\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.8 | ||
Character | \(\chi\) | \(=\) | 1008.17 |
Dual form | 1008.4.bt.d.593.8 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.34783 | − | 5.79860i | −0.299439 | − | 0.518643i | 0.676569 | − | 0.736379i | \(-0.263466\pi\) |
−0.976008 | + | 0.217736i | \(0.930133\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.7404 | − | 13.4418i | 0.687915 | − | 0.725792i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −28.2958 | − | 16.3366i | −0.775593 | − | 0.447789i | 0.0592734 | − | 0.998242i | \(-0.481122\pi\) |
−0.834866 | + | 0.550453i | \(0.814455\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 67.9019i | − | 1.44866i | −0.689452 | − | 0.724331i | \(-0.742149\pi\) | ||
0.689452 | − | 0.724331i | \(-0.257851\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −15.3179 | + | 26.5313i | −0.218537 | + | 0.378517i | −0.954361 | − | 0.298656i | \(-0.903462\pi\) |
0.735824 | + | 0.677173i | \(0.236795\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.8820 | − | 12.6336i | 0.264215 | − | 0.152544i | −0.362041 | − | 0.932162i | \(-0.617920\pi\) |
0.626256 | + | 0.779618i | \(0.284587\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 68.6216 | − | 39.6187i | 0.622113 | − | 0.359177i | −0.155578 | − | 0.987824i | \(-0.549724\pi\) |
0.777691 | + | 0.628647i | \(0.216391\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 40.0841 | − | 69.4277i | 0.320673 | − | 0.555422i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 109.668i | 0.702236i | 0.936331 | + | 0.351118i | \(0.114198\pi\) | ||||
−0.936331 | + | 0.351118i | \(0.885802\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −238.527 | − | 137.714i | −1.38196 | − | 0.797875i | −0.389568 | − | 0.920998i | \(-0.627376\pi\) |
−0.992391 | + | 0.123123i | \(0.960709\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −120.596 | − | 28.8753i | −0.582415 | − | 0.139452i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 160.221 | + | 277.511i | 0.711898 | + | 1.23304i | 0.964144 | + | 0.265380i | \(0.0854975\pi\) |
−0.252246 | + | 0.967663i | \(0.581169\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −184.846 | −0.704100 | −0.352050 | − | 0.935981i | \(-0.614515\pi\) | ||||
−0.352050 | + | 0.935981i | \(0.614515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −364.766 | −1.29363 | −0.646817 | − | 0.762645i | \(-0.723900\pi\) | ||||
−0.646817 | + | 0.762645i | \(0.723900\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −25.7730 | − | 44.6402i | −0.0799868 | − | 0.138541i | 0.823257 | − | 0.567669i | \(-0.192154\pi\) |
−0.903244 | + | 0.429127i | \(0.858821\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −18.3666 | − | 342.508i | −0.0535471 | − | 0.998565i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 532.671 | + | 307.538i | 1.38053 | + | 0.797048i | 0.992222 | − | 0.124483i | \(-0.0397271\pi\) |
0.388306 | + | 0.921531i | \(0.373060\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 218.769i | 0.536341i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −207.843 | + | 359.995i | −0.458625 | + | 0.794362i | −0.998889 | − | 0.0471340i | \(-0.984991\pi\) |
0.540263 | + | 0.841496i | \(0.318325\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 411.761 | − | 237.730i | 0.864271 | − | 0.498987i | −0.00116918 | − | 0.999999i | \(-0.500372\pi\) |
0.865440 | + | 0.501012i | \(0.167039\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −393.736 | + | 227.324i | −0.751338 | + | 0.433785i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −142.188 | + | 246.277i | −0.259269 | + | 0.449068i | −0.966046 | − | 0.258369i | \(-0.916815\pi\) |
0.706777 | + | 0.707436i | \(0.250148\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 965.404i | − | 1.61370i | −0.590759 | − | 0.806848i | \(-0.701172\pi\) | ||
0.590759 | − | 0.806848i | \(-0.298828\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 225.387 | + | 130.127i | 0.361364 | + | 0.208633i | 0.669679 | − | 0.742651i | \(-0.266432\pi\) |
−0.308315 | + | 0.951284i | \(0.599765\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −580.093 | + | 172.214i | −0.858543 | + | 0.254878i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −219.163 | − | 379.602i | −0.312124 | − | 0.540615i | 0.666698 | − | 0.745328i | \(-0.267707\pi\) |
−0.978822 | + | 0.204713i | \(0.934374\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −76.4726 | −0.101132 | −0.0505660 | − | 0.998721i | \(-0.516103\pi\) | ||||
−0.0505660 | + | 0.998721i | \(0.516103\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 205.126 | 0.261753 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 356.559 | + | 617.579i | 0.424665 | + | 0.735542i | 0.996389 | − | 0.0849045i | \(-0.0270585\pi\) |
−0.571724 | + | 0.820446i | \(0.693725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −912.728 | − | 865.095i | −1.05143 | − | 0.996556i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −146.514 | − | 84.5900i | −0.158232 | − | 0.0913553i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 410.607i | − | 0.429803i | −0.976636 | − | 0.214901i | \(-0.931057\pi\) | ||
0.976636 | − | 0.214901i | \(-0.0689430\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −953.656 | + | 1651.78i | −0.939527 | + | 1.62731i | −0.173173 | + | 0.984891i | \(0.555402\pi\) |
−0.766355 | + | 0.642418i | \(0.777931\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1177.37 | + | 679.756i | −1.12631 | + | 0.650276i | −0.943004 | − | 0.332780i | \(-0.892013\pi\) |
−0.183306 | + | 0.983056i | \(0.558680\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1555.77 | + | 898.226i | −1.40563 | + | 0.811540i | −0.994963 | − | 0.100246i | \(-0.968037\pi\) |
−0.410666 | + | 0.911786i | \(0.634704\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 42.0727 | − | 72.8720i | 0.0369709 | − | 0.0640355i | −0.846948 | − | 0.531676i | \(-0.821562\pi\) |
0.883919 | + | 0.467640i | \(0.154896\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 117.441i | 0.0977688i | 0.998804 | + | 0.0488844i | \(0.0155666\pi\) | ||||
−0.998804 | + | 0.0488844i | \(0.984433\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −459.466 | − | 265.273i | −0.372569 | − | 0.215103i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 161.475 | + | 543.918i | 0.124390 | + | 0.418999i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −131.730 | − | 228.163i | −0.0989707 | − | 0.171422i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1373.74 | −0.982965 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 510.925 | 0.356986 | 0.178493 | − | 0.983941i | \(-0.442878\pi\) | ||||
0.178493 | + | 0.983941i | \(0.442878\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −991.274 | − | 1716.94i | −0.661130 | − | 1.14511i | −0.980319 | − | 0.197419i | \(-0.936744\pi\) |
0.319189 | − | 0.947691i | \(-0.396589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 108.966 | − | 455.091i | 0.0710416 | − | 0.296702i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −857.943 | − | 495.334i | −0.535029 | − | 0.308899i | 0.208033 | − | 0.978122i | \(-0.433294\pi\) |
−0.743062 | + | 0.669223i | \(0.766627\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 369.921i | − | 0.225729i | −0.993610 | − | 0.112864i | \(-0.963997\pi\) | ||
0.993610 | − | 0.112864i | \(-0.0360026\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1109.29 | + | 1921.34i | −0.648694 | + | 1.12357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 635.922 | − | 367.149i | 0.364210 | − | 0.210277i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1054.73 | + | 608.947i | −0.579910 | + | 0.334811i | −0.761098 | − | 0.648637i | \(-0.775339\pi\) |
0.181188 | + | 0.983449i | \(0.442006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 764.206 | − | 1323.64i | 0.411856 | − | 0.713355i | −0.583237 | − | 0.812302i | \(-0.698214\pi\) |
0.995093 | + | 0.0989470i | \(0.0315474\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1844.17i | 0.955658i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2610.74 | − | 1507.31i | −1.32713 | − | 0.766220i | −0.342277 | − | 0.939599i | \(-0.611198\pi\) |
−0.984855 | + | 0.173379i | \(0.944531\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 341.715 | − | 1427.16i | 0.167273 | − | 0.698607i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −822.212 | − | 1424.11i | −0.395096 | − | 0.684326i | 0.598018 | − | 0.801483i | \(-0.295955\pi\) |
−0.993113 | + | 0.117157i | \(0.962622\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2783.64 | −1.28985 | −0.644923 | − | 0.764248i | \(-0.723111\pi\) | ||||
−0.644923 | + | 0.764248i | \(0.723111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2413.67 | −1.09862 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −64.1081 | − | 111.038i | −0.0281737 | − | 0.0487983i | 0.851595 | − | 0.524201i | \(-0.175636\pi\) |
−0.879768 | + | 0.475402i | \(0.842302\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −422.551 | − | 1423.34i | −0.182525 | − | 0.614825i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1676.79 | + | 968.093i | 0.700161 | + | 0.404238i | 0.807408 | − | 0.589994i | \(-0.200870\pi\) |
−0.107246 | + | 0.994233i | \(0.534203\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1596.97i | − | 0.655810i | −0.944711 | − | 0.327905i | \(-0.893657\pi\) | ||
0.944711 | − | 0.327905i | \(-0.106343\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1072.79 | − | 1858.12i | 0.426340 | − | 0.738442i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 866.863 | − | 500.484i | 0.338991 | − | 0.195717i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 715.285 | − | 412.970i | 0.270975 | − | 0.156448i | −0.358356 | − | 0.933585i | \(-0.616662\pi\) |
0.629331 | + | 0.777138i | \(0.283329\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 927.072 | − | 1605.74i | 0.345762 | − | 0.598878i | −0.639730 | − | 0.768600i | \(-0.720954\pi\) |
0.985492 | + | 0.169722i | \(0.0542870\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2938.42i | 1.06271i | 0.847150 | + | 0.531355i | \(0.178317\pi\) | ||||
−0.847150 | + | 0.531355i | \(0.821683\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2850.16 | + | 1645.54i | 1.01529 | + | 0.586178i | 0.912736 | − | 0.408550i | \(-0.133965\pi\) |
0.102554 | + | 0.994727i | \(0.467299\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1474.14 | + | 1397.21i | 0.509677 | + | 0.483078i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 618.833 | + | 1071.85i | 0.210835 | + | 0.365177i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −825.560 | −0.273230 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1133.21 | 0.369733 | 0.184867 | − | 0.982764i | \(-0.440815\pi\) | ||||
0.184867 | + | 0.982764i | \(0.440815\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1221.17 | + | 2115.13i | 0.387364 | + | 0.670934i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4890.05 | + | 1451.72i | −1.52976 | + | 0.454145i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1801.53 | + | 1040.11i | 0.548343 | + | 0.316586i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1631.23i | − | 0.489845i | −0.969543 | − | 0.244922i | \(-0.921238\pi\) | ||
0.969543 | − | 0.244922i | \(-0.0787624\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 584.886 | − | 1013.05i | 0.171014 | − | 0.296205i | −0.767760 | − | 0.640737i | \(-0.778629\pi\) |
0.938775 | + | 0.344532i | \(0.111962\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4457.87 | + | 2573.75i | −1.28640 | + | 0.742701i | −0.978009 | − | 0.208561i | \(-0.933122\pi\) |
−0.308386 | + | 0.951261i | \(0.599789\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3811.38 | + | 2200.50i | −1.07164 | + | 0.618710i | −0.928629 | − | 0.371011i | \(-0.879011\pi\) |
−0.143009 | + | 0.989721i | \(0.545678\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −172.567 | + | 298.895i | −0.0479023 | + | 0.0829692i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5998.62i | 1.62351i | 0.583998 | + | 0.811755i | \(0.301487\pi\) | ||||
−0.583998 | + | 0.811755i | \(0.698513\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 796.548 | + | 459.887i | 0.212905 | + | 0.122921i | 0.602661 | − | 0.797997i | \(-0.294107\pi\) |
−0.389756 | + | 0.920918i | \(0.627441\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1924.58 | + | 1253.16i | −0.501865 | + | 0.326781i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −857.845 | − | 1485.83i | −0.220985 | − | 0.382758i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −701.991 | −0.176531 | −0.0882655 | − | 0.996097i | \(-0.528132\pi\) | ||||
−0.0882655 | + | 0.996097i | \(0.528132\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2588.94 | −0.643341 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2170.80 | − | 3759.94i | −0.526891 | − | 0.912602i | −0.999509 | − | 0.0313343i | \(-0.990024\pi\) |
0.472618 | − | 0.881267i | \(-0.343309\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5771.54 | + | 1381.92i | 1.38466 | + | 0.331539i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3606.74 | − | 2082.35i | −0.845632 | − | 0.488226i | 0.0135429 | − | 0.999908i | \(-0.495689\pi\) |
−0.859175 | + | 0.511683i | \(0.829022\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4118.33i | − | 0.954668i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4219.12 | − | 7307.74i | 0.956299 | − | 1.65636i | 0.224933 | − | 0.974374i | \(-0.427784\pi\) |
0.731366 | − | 0.681985i | \(-0.238883\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4544.68 | + | 2623.87i | −1.01871 | + | 0.588150i | −0.913729 | − | 0.406324i | \(-0.866810\pi\) |
−0.104977 | + | 0.994475i | \(0.533477\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2268.43 | + | 1309.68i | −0.497423 | + | 0.287187i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 198.173 | − | 343.245i | 0.0429857 | − | 0.0744534i | −0.843732 | − | 0.536765i | \(-0.819646\pi\) |
0.886718 | + | 0.462311i | \(0.152980\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5244.36i | − | 1.11335i | −0.830729 | − | 0.556677i | \(-0.812076\pi\) | ||
0.830729 | − | 0.556677i | \(-0.187924\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4113.33 | + | 2374.83i | 0.864000 | + | 0.498830i | 0.865350 | − | 0.501169i | \(-0.167096\pi\) |
−0.00134996 | + | 0.999999i | \(0.500430\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2355.01 | + | 2484.67i | −0.484361 | + | 0.511030i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1987.23 | + | 3441.98i | 0.404483 | + | 0.700586i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3597.22 | 0.717242 | 0.358621 | − | 0.933483i | \(-0.383247\pi\) | ||||
0.358621 | + | 0.933483i | \(0.383247\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2783.29 | 0.549320 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2690.19 | − | 4659.54i | −0.520326 | − | 0.901231i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4647.25 | + | 4903.13i | −0.889910 | + | 0.938909i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2757.00 | − | 1591.76i | −0.517592 | − | 0.298832i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 27.5911i | − | 0.00512933i | −0.999997 | − | 0.00256467i | \(-0.999184\pi\) | ||
0.999997 | − | 0.00256467i | \(-0.000816359\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 621.896 | − | 1077.15i | 0.113391 | − | 0.196398i | −0.803745 | − | 0.594974i | \(-0.797162\pi\) |
0.917135 | + | 0.398576i | \(0.130496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7541.55 | − | 4354.12i | 1.36190 | − | 0.786292i | 0.372021 | − | 0.928224i | \(-0.378665\pi\) |
0.989876 | + | 0.141933i | \(0.0453317\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7799.09 | + | 4502.81i | −1.38183 | + | 0.797801i | −0.992376 | − | 0.123245i | \(-0.960670\pi\) |
−0.389455 | + | 0.921046i | \(0.627337\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1791.60 | − | 3103.15i | 0.314453 | − | 0.544649i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 774.077i | 0.133346i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4714.28 | − | 2721.79i | −0.804619 | − | 0.464547i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −928.404 | − | 222.295i | −0.155576 | − | 0.0372508i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1194.18 | − | 2068.38i | −0.198302 | − | 0.343470i | 0.749676 | − | 0.661805i | \(-0.230209\pi\) |
−0.947978 | + | 0.318336i | \(0.896876\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1904.08 | 0.310541 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11637.2 | 1.88106 | 0.940531 | − | 0.339707i | \(-0.110328\pi\) | ||||
0.940531 | + | 0.339707i | \(0.110328\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4499.55 | + | 7793.45i | 0.714558 | + | 1.23765i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4837.94 | − | 4116.79i | −0.761586 | − | 0.648064i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2539.63 | + | 1466.26i | 0.392895 | + | 0.226838i | 0.683414 | − | 0.730031i | \(-0.260494\pi\) |
−0.290519 | + | 0.956869i | \(0.593828\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 63.0106i | 0.00966442i | 0.999988 | + | 0.00483221i | \(0.00153815\pi\) | ||||
−0.999988 | + | 0.00483221i | \(0.998462\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 386.737 | − | 669.848i | 0.0583114 | − | 0.100998i | −0.835396 | − | 0.549648i | \(-0.814762\pi\) |
0.893708 | + | 0.448650i | \(0.148095\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5598.00 | + | 3232.00i | −0.836932 | + | 0.483203i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10567.3 | − | 6101.03i | 1.55354 | − | 0.896936i | 0.555689 | − | 0.831390i | \(-0.312454\pi\) |
0.997850 | − | 0.0655458i | \(-0.0208788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3110.29 | + | 5387.17i | −0.453460 | + | 0.785417i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1742.57i | − | 0.249892i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4835.15 | + | 2791.58i | 0.687719 | + | 0.397055i | 0.802757 | − | 0.596306i | \(-0.203366\pi\) |
−0.115038 | + | 0.993361i | \(0.536699\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10920.3 | − | 3241.94i | 1.52818 | − | 0.453674i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1656.22 | + | 2868.66i | 0.229909 | + | 0.398213i | 0.957781 | − | 0.287499i | \(-0.0928240\pi\) |
−0.727872 | + | 0.685713i | \(0.759491\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7446.67 | 1.01730 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1118.64 | 0.151611 | 0.0758057 | − | 0.997123i | \(-0.475847\pi\) | ||||
0.0758057 | + | 0.997123i | \(0.475847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4388.43 | − | 7600.98i | −0.585479 | − | 1.01408i | −0.994816 | − | 0.101695i | \(-0.967573\pi\) |
0.409337 | − | 0.912383i | \(-0.365760\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2940.65 | + | 2787.19i | 0.389272 | + | 0.368957i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8285.22 | + | 4783.47i | 1.07989 | + | 0.623475i | 0.930867 | − | 0.365359i | \(-0.119054\pi\) |
0.149023 | + | 0.988834i | \(0.452387\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2427.49i | 0.313973i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1467.44 | + | 2541.68i | −0.186924 | + | 0.323762i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8470.20 | − | 4890.27i | 1.07080 | − | 0.618226i | 0.142399 | − | 0.989809i | \(-0.454518\pi\) |
0.928399 | + | 0.371584i | \(0.121185\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10450.1 | − | 6033.35i | 1.30137 | − | 0.751349i | 0.320735 | − | 0.947169i | \(-0.396070\pi\) |
0.980640 | + | 0.195820i | \(0.0627369\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9351.03 | + | 16196.5i | −1.15585 | + | 2.00199i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 10469.9i | − | 1.27512i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6194.67 | + | 3576.49i | 0.748916 | + | 0.432387i | 0.825302 | − | 0.564691i | \(-0.191005\pi\) |
−0.0763859 | + | 0.997078i | \(0.524338\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2191.00 | + | 7380.26i | 0.261046 | + | 0.879319i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 256.017 | + | 443.434i | 0.0302828 | + | 0.0524514i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5703.45 | −0.664992 | −0.332496 | − | 0.943105i | \(-0.607891\pi\) | ||||
−0.332496 | + | 0.943105i | \(0.607891\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10027.7 | −1.16086 | −0.580428 | − | 0.814312i | \(-0.697115\pi\) | ||||
−0.580428 | + | 0.814312i | \(0.697115\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1228.01 | + | 2126.97i | 0.140158 | + | 0.242760i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2050.44 | − | 8563.59i | 0.232384 | − | 0.970541i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12128.8 | + | 7002.59i | 1.35551 | + | 0.782605i | 0.989015 | − | 0.147814i | \(-0.0472238\pi\) |
0.366497 | + | 0.930419i | \(0.380557\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3410.83i | − | 0.378554i | −0.981924 | − | 0.189277i | \(-0.939386\pi\) | ||
0.981924 | − | 0.189277i | \(-0.0606145\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1001.05 | − | 1733.87i | 0.109581 | − | 0.189800i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11009.7 | + | 6356.44i | −1.19695 | + | 0.691062i | −0.959875 | − | 0.280428i | \(-0.909524\pi\) |
−0.237080 | + | 0.971490i | \(0.576190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10853.8 | − | 6266.44i | 1.16406 | − | 0.672071i | 0.211787 | − | 0.977316i | \(-0.432072\pi\) |
0.952274 | + | 0.305245i | \(0.0987382\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2387.40 | − | 4135.09i | 0.254322 | − | 0.440499i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 10884.1i | − | 1.14399i | −0.820258 | − | 0.571993i | \(-0.806170\pi\) | ||
0.820258 | − | 0.571993i | \(-0.193830\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5230.38 | + | 3019.76i | 0.546095 | + | 0.315288i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1960.69 | + | 8188.73i | −0.202019 | + | 0.843722i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9222.57 | + | 15974.0i | 0.944012 | + | 1.63508i | 0.757717 | + | 0.652583i | \(0.226315\pi\) |
0.186295 | + | 0.982494i | \(0.440352\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4657.01 | −0.470496 | −0.235248 | − | 0.971935i | \(-0.575590\pi\) | ||||
−0.235248 | + | 0.971935i | \(0.575590\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5088.08 | 0.510720 | 0.255360 | − | 0.966846i | \(-0.417806\pi\) | ||||
0.255360 | + | 0.966846i | \(0.417806\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7950.04 | − | 13769.9i | −0.787760 | − | 1.36444i | −0.927336 | − | 0.374229i | \(-0.877908\pi\) |
0.139577 | − | 0.990211i | \(-0.455426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1498.89 | + | 5048.93i | 0.147574 | + | 0.497096i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10321.4 | + | 5959.04i | 1.00333 | + | 0.579275i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2025.62i | − | 0.195667i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9702.00 | − | 16804.4i | 0.925461 | − | 1.60295i | 0.134643 | − | 0.990894i | \(-0.457011\pi\) |
0.790818 | − | 0.612051i | \(-0.209655\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18843.6 | − | 10879.3i | 1.78626 | − | 1.03130i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2380.95 | + | 1374.64i | −0.222914 | + | 0.128700i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6123.60 | + | 10606.4i | −0.569788 | + | 0.986903i | 0.426798 | + | 0.904347i | \(0.359642\pi\) |
−0.996586 | + | 0.0825556i | \(0.973692\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7773.35i | − | 0.714473i | −0.934014 | − | 0.357237i | \(-0.883719\pi\) | ||
0.934014 | − | 0.357237i | \(-0.116281\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2909.64 | − | 1679.88i | −0.265808 | − | 0.153464i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12976.8 | − | 12299.6i | −1.17121 | − | 1.11008i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9518.91 | − | 16487.2i | −0.853958 | − | 1.47910i | −0.877609 | − | 0.479378i | \(-0.840862\pi\) |
0.0236507 | − | 0.999720i | \(-0.492471\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14323.9 | −1.26973 | −0.634863 | − | 0.772624i | \(-0.718944\pi\) | ||||
−0.634863 | + | 0.772624i | \(0.718944\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12770.7 | 1.12532 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4294.66 | + | 7438.57i | 0.373983 | + | 0.647758i | 0.990174 | − | 0.139839i | \(-0.0446585\pi\) |
−0.616191 | + | 0.787597i | \(0.711325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4620.66 | − | 1371.75i | 0.400012 | − | 0.118753i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7883.28 | + | 4551.41i | 0.674522 | + | 0.389435i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1684.17i | 0.143269i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11308.3 | − | 19586.6i | 0.950917 | − | 1.64704i | 0.207471 | − | 0.978241i | \(-0.433477\pi\) |
0.743447 | − | 0.668795i | \(-0.233190\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −122.551 | + | 70.7547i | −0.0102462 | + | 0.00591566i | −0.505114 | − | 0.863052i | \(-0.668550\pi\) |
0.494868 | + | 0.868968i | \(0.335216\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7307.45 | − | 4218.96i | 0.604018 | − | 0.348730i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2944.22 | + | 5099.53i | −0.241984 | + | 0.419128i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12551.4i | 1.02000i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10416.9 | + | 6014.21i | 0.841799 | + | 0.486013i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5075.72 | + | 9991.60i | −0.405615 | + | 0.798458i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4655.90 | + | 8064.25i | 0.370005 | + | 0.640867i | 0.989566 | − | 0.144081i | \(-0.0460227\pi\) |
−0.619561 | + | 0.784949i | \(0.712689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −563.408 | −0.0442821 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11888.7 | −0.929294 | −0.464647 | − | 0.885496i | \(-0.653819\pi\) | ||||
−0.464647 | + | 0.885496i | \(0.653819\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1385.50 | + | 2399.76i | 0.107122 | + | 0.185541i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7894.77 | − | 1890.30i | −0.607088 | − | 0.145360i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18409.4 | + | 10628.7i | 1.40042 | + | 0.808530i | 0.994435 | − | 0.105352i | \(-0.0335969\pi\) |
0.405980 | + | 0.913882i | \(0.366930\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24768.3i | 1.87404i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4661.33 | + | 8073.66i | −0.348937 | + | 0.604377i | −0.986061 | − | 0.166385i | \(-0.946791\pi\) |
0.637124 | + | 0.770762i | \(0.280124\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 680.991 | − | 393.170i | 0.0507071 | − | 0.0292758i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14734.2 | + | 8506.79i | −1.08557 | + | 0.626754i | −0.932394 | − | 0.361445i | \(-0.882284\pi\) |
−0.153176 | + | 0.988199i | \(0.548950\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1134.69 | − | 1965.34i | 0.0831617 | − | 0.144040i | −0.821445 | − | 0.570288i | \(-0.806832\pi\) |
0.904606 | + | 0.426248i | \(0.140165\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6352.32i | − | 0.460713i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2687.93 | + | 1551.88i | 0.193934 | + | 0.111968i | 0.593823 | − | 0.804596i | \(-0.297618\pi\) |
−0.399889 | + | 0.916564i | \(0.630951\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −974.288 | + | 1027.93i | −0.0695702 | + | 0.0734008i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10048.2 | − | 17404.1i | −0.713818 | − | 1.23637i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12544.8 | 0.882075 | 0.441038 | − | 0.897489i | \(-0.354611\pi\) | ||||
0.441038 | + | 0.897489i | \(0.354611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6959.27 | −0.486845 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2644.32 | − | 4580.09i | −0.183118 | − | 0.317170i | 0.759823 | − | 0.650131i | \(-0.225286\pi\) |
−0.942941 | + | 0.332960i | \(0.891952\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2613.38 | − | 2757.27i | 0.180064 | − | 0.189978i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5058.01 | − | 2920.24i | −0.345016 | − | 0.199195i | 0.317472 | − | 0.948268i | \(-0.397166\pi\) |
−0.662488 | + | 0.749073i | \(0.730499\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10801.2i | − | 0.733098i | −0.930399 | − | 0.366549i | \(-0.880539\pi\) | ||
0.930399 | − | 0.366549i | \(-0.119461\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −882.018 | + | 1527.70i | −0.0592713 | + | 0.102661i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21239.7 | − | 12262.8i | 1.42025 | − | 0.819984i | 0.423934 | − | 0.905693i | \(-0.360649\pi\) |
0.996320 | + | 0.0857094i | \(0.0273157\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3031.15 | + | 1750.04i | −0.200699 | + | 0.115874i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8223.34 | + | 14243.2i | −0.541823 | + | 0.938465i | 0.456976 | + | 0.889479i | \(0.348932\pi\) |
−0.998799 | + | 0.0489865i | \(0.984401\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 23852.4i | − | 1.55634i | −0.628055 | − | 0.778169i | \(-0.716149\pi\) | ||
0.628055 | − | 0.778169i | \(-0.283851\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14617.4 | + | 8439.34i | 0.949147 | + | 0.547990i | 0.892816 | − | 0.450422i | \(-0.148726\pi\) |
0.0563309 | + | 0.998412i | \(0.482060\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12844.1 | + | 3075.36i | 0.825983 | + | 0.197771i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −411.490 | − | 712.722i | −0.0263354 | − | 0.0456142i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9816.99 | −0.622304 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19613.0 | 1.23737 | 0.618686 | − | 0.785638i | \(-0.287665\pi\) | ||||
0.618686 | + | 0.785638i | \(0.287665\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1710.49 | − | 2962.65i | −0.106895 | − | 0.185148i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23257.0 | + | 1247.13i | −1.44658 | + | 0.0775716i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7437.62 | − | 4294.11i | −0.458297 | − | 0.264598i | 0.253031 | − | 0.967458i | \(-0.418573\pi\) |
−0.711328 | + | 0.702860i | \(0.751906\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11966.4i | 0.733920i | 0.930237 | + | 0.366960i | \(0.119601\pi\) | ||||
−0.930237 | + | 0.366960i | \(0.880399\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3663.93 | + | 6346.11i | −0.222634 | + | 0.385613i | −0.955607 | − | 0.294645i | \(-0.904799\pi\) |
0.732973 | + | 0.680257i | \(0.238132\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11762.2 | − | 6790.91i | 0.711412 | − | 0.410734i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3124.09 | + | 1803.69i | −0.187221 | + | 0.108092i | −0.590681 | − | 0.806905i | \(-0.701141\pi\) |
0.403460 | + | 0.914997i | \(0.367807\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6637.22 | + | 11496.0i | −0.395936 | + | 0.685780i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3244.57i | 0.191792i | 0.995391 | + | 0.0958958i | \(0.0305716\pi\) | ||||
−0.995391 | + | 0.0958958i | \(0.969428\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12548.2 | − | 7244.69i | −0.738377 | − | 0.426302i | 0.0831019 | − | 0.996541i | \(-0.473517\pi\) |
−0.821479 | + | 0.570239i | \(0.806851\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3003.69 | + | 891.715i | −0.175155 | + | 0.0519989i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4344.90 | + | 7525.60i | 0.252227 | + | 0.436870i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15534.8 | −0.893763 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27609.5 | −1.58138 | −0.790688 | − | 0.612219i | \(-0.790277\pi\) | ||||
−0.790688 | + | 0.612219i | \(0.790277\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7610.03 | + | 13181.0i | 0.432019 | + | 0.748279i | 0.997047 | − | 0.0767925i | \(-0.0244679\pi\) |
−0.565028 | + | 0.825072i | \(0.691135\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5519.32 | − | 5231.28i | −0.311947 | − | 0.295668i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14491.6 | − | 8366.71i | −0.811866 | − | 0.468731i | 0.0357376 | − | 0.999361i | \(-0.488622\pi\) |
−0.847603 | + | 0.530630i | \(0.821955\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6633.16i | 0.369986i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20882.4 | − | 36169.4i | 1.15465 | − | 1.99992i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3981.41 | + | 2298.67i | −0.219190 | + | 0.126549i | −0.605575 | − | 0.795788i | \(-0.707057\pi\) |
0.386385 | + | 0.922337i | \(0.373724\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2145.03 | + | 1238.43i | −0.117073 | + | 0.0675920i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2831.45 | − | 4904.21i | 0.153872 | − | 0.266514i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 7621.26i | − | 0.410629i | −0.978696 | − | 0.205315i | \(-0.934178\pi\) | ||
0.978696 | − | 0.205315i | \(-0.0658217\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7011.93 | + | 4048.34i | 0.376188 | + | 0.217192i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10053.1 | + | 33863.2i | 0.534773 | + | 1.80135i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3850.25 | + | 6668.83i | 0.203948 | + | 0.353249i | 0.949797 | − | 0.312867i | \(-0.101289\pi\) |
−0.745849 | + | 0.666115i | \(0.767956\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21824.2 | −1.14631 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14854.8 | 0.776977 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5049.89 | + | 8746.67i | 0.261932 | + | 0.453680i | 0.966755 | − | 0.255703i | \(-0.0823070\pi\) |
−0.704823 | + | 0.709383i | \(0.748974\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5862.96 | + | 24486.4i | −0.302841 | + | 1.26480i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7614.00 | + | 4395.95i | 0.390037 | + | 0.225188i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23945.7i | − | 1.22159i | −0.791789 | − | 0.610795i | \(-0.790850\pi\) | ||
0.791789 | − | 0.610795i | \(-0.209150\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5587.43 | − | 9677.71i | 0.282707 | − | 0.489662i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18035.8 | − | 10413.0i | 0.908822 | − | 0.524708i | 0.0287698 | − | 0.999586i | \(-0.490841\pi\) |
0.880052 | + | 0.474878i | \(0.157508\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8046.67 | − | 4645.75i | 0.402175 | − | 0.232196i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7648.41 | − | 13247.4i | 0.380719 | − | 0.659424i | −0.610446 | − | 0.792058i | \(-0.709010\pi\) |
0.991165 | + | 0.132633i | \(0.0423433\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27249.8i | 1.34549i | 0.739875 | + | 0.672744i | \(0.234885\pi\) | ||||
−0.739875 | + | 0.672744i | \(0.765115\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7062.08 | + | 4077.29i | 0.347295 | + | 0.200511i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7747.28 | + | 32356.2i | −0.377943 | + | 1.57846i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19864.5 | − | 34406.4i | −0.965203 | − | 1.67178i | −0.709069 | − | 0.705139i | \(-0.750884\pi\) |
−0.256134 | − | 0.966641i | \(-0.582449\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10233.7 | −0.493302 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24557.2 | −1.17906 | −0.589530 | − | 0.807747i | \(-0.700687\pi\) | ||||
−0.589530 | + | 0.807747i | \(0.700687\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9686.45 | − | 16777.4i | −0.461411 | − | 0.799187i | 0.537621 | − | 0.843187i | \(-0.319323\pi\) |
−0.999032 | + | 0.0440000i | \(0.985990\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −443.514 | − | 1493.95i | −0.0210436 | − | 0.0708842i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24444.4 | + | 14113.0i | 1.15076 | + | 0.664393i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 39937.6i | − | 1.87280i | −0.350930 | − | 0.936402i | \(-0.614134\pi\) | ||
0.350930 | − | 0.936402i | \(-0.385866\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8058.12 | − | 13957.1i | 0.374942 | − | 0.649419i | −0.615376 | − | 0.788234i | \(-0.710996\pi\) |
0.990318 | + | 0.138815i | \(0.0443292\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19122.3 | + | 11040.3i | −0.886314 | + | 0.511714i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4044.80 | + | 2335.27i | −0.186034 | + | 0.107407i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15771.4 | + | 27316.9i | −0.722594 | + | 1.25157i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20184.9i | 0.917744i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19040.0 | + | 10992.8i | 0.862394 | + | 0.497903i | 0.864813 | − | 0.502094i | \(-0.167437\pi\) |
−0.00241936 | + | 0.999997i | \(0.500770\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1578.62 | + | 1496.23i | 0.0709598 | + | 0.0672566i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16142.3 | − | 27959.3i | −0.722864 | − | 1.25204i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2291.42 | −0.101840 | −0.0509198 | − | 0.998703i | \(-0.516215\pi\) | ||||
−0.0509198 | + | 0.998703i | \(0.516215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1579.15 | 0.0699202 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4251.67 | − | 7364.12i | −0.186847 | − | 0.323629i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9419.52 | + | 2796.40i | −0.412416 | + | 0.122435i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12856.7 | − | 7422.83i | −0.558737 | − | 0.322587i | 0.193901 | − | 0.981021i | \(-0.437886\pi\) |
−0.752638 | + | 0.658434i | \(0.771219\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 41094.7i | − | 1.77932i | −0.456621 | − | 0.889661i | \(-0.650941\pi\) | ||
0.456621 | − | 0.889661i | \(-0.349059\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5505.25 | + | 9535.37i | −0.236614 | + | 0.409827i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7981.81 | + | 4608.30i | −0.341797 | + | 0.197337i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30664.0 | + | 17703.9i | −1.30351 | + | 0.752582i | −0.981004 | − | 0.193986i | \(-0.937858\pi\) |
−0.322505 | + | 0.946568i | \(0.604525\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2744.14 | − | 4752.98i | 0.116227 | − | 0.201311i | −0.802043 | − | 0.597267i | \(-0.796253\pi\) |
0.918269 | + | 0.395956i | \(0.129587\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 96.9958i | − | 0.00407844i | −0.999998 | − | 0.00203922i | \(-0.999351\pi\) | ||
0.999998 | − | 0.00203922i | \(-0.000649105\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9914.41 | − | 5724.09i | −0.415370 | − | 0.239814i | 0.277724 | − | 0.960661i | \(-0.410420\pi\) |
−0.693094 | + | 0.720847i | \(0.743753\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9368.52 | + | 4759.19i | 0.389676 | + | 0.197955i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9319.13 | + | 16141.2i | 0.386230 | + | 0.668969i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25083.7 | −1.03216 | −0.516082 | − | 0.856539i | \(-0.672610\pi\) | ||||
−0.516082 | + | 0.856539i | \(0.672610\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12361.9 | 0.506865 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8080.56 | + | 13995.9i | 0.328970 | + | 0.569793i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4745.22 | − | 1136.18i | −0.192500 | − | 0.0460918i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21989.3 | + | 12695.5i | 0.885762 | + | 0.511395i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 48196.0i | − | 1.93458i | −0.253668 | − | 0.967291i | \(-0.581637\pi\) | ||
0.253668 | − | 0.967291i | \(-0.418363\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9301.67 | − | 16111.0i | 0.370757 | − | 0.642171i | −0.618925 | − | 0.785450i | \(-0.712431\pi\) |
0.989682 | + | 0.143280i | \(0.0457648\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7453.04 | − | 4303.02i | 0.296036 | − | 0.170916i | −0.344625 | − | 0.938740i | \(-0.611994\pi\) |
0.640661 | + | 0.767824i | \(0.278661\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37188.6 | + | 21470.8i | −1.46687 | + | 0.846901i | −0.999313 | − | 0.0370598i | \(-0.988201\pi\) |
−0.467562 | + | 0.883960i | \(0.654867\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −429.245 | + | 743.475i | −0.0168726 | + | 0.0292242i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14321.5i | 0.559062i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16722.7 | + | 9654.85i | 0.650547 | + | 0.375594i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17501.9 | + | 18465.5i | −0.676196 | + | 0.713428i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19724.6 | − | 34163.9i | −0.759465 | − | 1.31543i | −0.943124 | − | 0.332442i | \(-0.892127\pi\) |
0.183659 | − | 0.982990i | \(-0.441206\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31686.9 | −1.21176 | −0.605879 | − | 0.795556i | \(-0.707179\pi\) | ||||
−0.605879 | + | 0.795556i | \(0.707179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21170.2 | −0.806832 | −0.403416 | − | 0.915017i | \(-0.632177\pi\) | ||||
−0.403416 | + | 0.915017i | \(0.632177\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23404.6 | − | 40538.0i | −0.885964 | − | 1.53454i | −0.844604 | − | 0.535391i | \(-0.820164\pi\) |
−0.0413598 | − | 0.999144i | \(-0.513169\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6509.36 | − | 6867.77i | 0.245576 | − | 0.259097i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1127.93 | − | 651.211i | −0.0422673 | − | 0.0244031i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 12964.0i | − | 0.484178i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15102.8 | − | 26158.8i | 0.560296 | − | 0.970462i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16318.7 | + | 9421.63i | −0.603392 | + | 0.348369i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9260.18 | + | 5346.37i | −0.340131 | + | 0.196375i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13950.8 | + | 24163.5i | −0.510726 | + | 0.884604i | 0.489196 | + | 0.872174i | \(0.337290\pi\) |
−0.999923 | + | 0.0124304i | \(0.996043\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22732.2i | 0.826732i | 0.910565 | + | 0.413366i | \(0.135647\pi\) | ||||
−0.910565 | + | 0.413366i | \(0.864353\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2163.86 | + | 1249.30i | 0.0784373 | + | 0.0452858i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35708.0 | − | 8549.83i | −1.28591 | − | 0.307896i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16454.0 | − | 28499.1i | −0.590605 | − | 1.02296i | −0.994151 | − | 0.107998i | \(-0.965556\pi\) |
0.403546 | − | 0.914959i | \(-0.367777\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −65552.8 | −2.33770 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25689.3 | 0.913146 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.8811 | + | 51.7556i | 0.00105529 | + | 0.00182782i | 0.866553 | − | 0.499086i | \(-0.166331\pi\) |
−0.865497 | + | 0.500914i | \(0.832997\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4729.00 | − | 7262.72i | −0.166473 | − | 0.255667i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5804.21 | − | 3351.06i | −0.203014 | − | 0.117210i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43382.1i | 1.51252i | 0.654270 | + | 0.756261i | \(0.272976\pi\) | ||||
−0.654270 | + | 0.756261i | \(0.727024\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22210.7 | + | 38470.0i | −0.769444 | + | 1.33272i | 0.168421 | + | 0.985715i | \(0.446133\pi\) |
−0.937865 | + | 0.347001i | \(0.887200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12684.4 | + | 7323.36i | −0.438030 | + | 0.252897i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27136.7 | − | 15667.4i | 0.931175 | − | 0.537614i | 0.0439922 | − | 0.999032i | \(-0.485992\pi\) |
0.887183 | + | 0.461418i | \(0.152659\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8835.89 | − | 15304.2i | 0.302239 | − | 0.523494i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 20504.7i | − | 0.696971i | −0.937314 | − | 0.348486i | \(-0.886696\pi\) | ||
0.937314 | − | 0.348486i | \(-0.113304\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4789.30 | − | 2765.10i | −0.162281 | − | 0.0936929i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17588.7 | + | 5221.61i | −0.592251 | + | 0.175823i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23034.6 | + | 39897.2i | 0.773208 | + | 1.33924i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12414.7 | −0.414138 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2538.92 | 0.0844325 | 0.0422162 | − | 0.999108i | \(-0.486558\pi\) | ||||
0.0422162 | + | 0.999108i | \(0.486558\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8357.65 | + | 14475.9i | 0.276220 | + | 0.478427i | 0.970442 | − | 0.241333i | \(-0.0775848\pi\) |
−0.694222 | + | 0.719761i | \(0.744251\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4972.43 | − | 4712.93i | −0.163832 | − | 0.155282i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25809.0 | + | 14900.8i | 0.845140 | + | 0.487942i | 0.859008 | − | 0.511962i | \(-0.171081\pi\) |
−0.0138678 | + | 0.999904i | \(0.504414\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 23299.9i | − | 0.760641i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19946.2 | − | 34547.8i | 0.647186 | − | 1.12096i | −0.336605 | − | 0.941646i | \(-0.609279\pi\) |
0.983792 | − | 0.179314i | \(-0.0573878\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17038.7 | − | 9837.31i | 0.551167 | − | 0.318216i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25030.8 | + | 14451.5i | −0.804786 | + | 0.464644i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23250.0 | + | 40270.2i | −0.745268 | + | 1.29084i | 0.204801 | + | 0.978804i | \(0.434345\pi\) |
−0.950069 | + | 0.312039i | \(0.898988\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 22036.0i | − | 0.702097i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31402.7 | + | 18130.4i | 0.997527 | + | 0.575923i | 0.907516 | − | 0.420018i | \(-0.137976\pi\) |
0.0900114 | + | 0.995941i | \(0.471310\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.4.bt.d.17.8 | 48 | ||
3.2 | odd | 2 | inner | 1008.4.bt.d.17.17 | 48 | ||
4.3 | odd | 2 | 504.4.bl.a.17.8 | ✓ | 48 | ||
7.5 | odd | 6 | inner | 1008.4.bt.d.593.17 | 48 | ||
12.11 | even | 2 | 504.4.bl.a.17.17 | yes | 48 | ||
21.5 | even | 6 | inner | 1008.4.bt.d.593.8 | 48 | ||
28.19 | even | 6 | 504.4.bl.a.89.17 | yes | 48 | ||
84.47 | odd | 6 | 504.4.bl.a.89.8 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.4.bl.a.17.8 | ✓ | 48 | 4.3 | odd | 2 | ||
504.4.bl.a.17.17 | yes | 48 | 12.11 | even | 2 | ||
504.4.bl.a.89.8 | yes | 48 | 84.47 | odd | 6 | ||
504.4.bl.a.89.17 | yes | 48 | 28.19 | even | 6 | ||
1008.4.bt.d.17.8 | 48 | 1.1 | even | 1 | trivial | ||
1008.4.bt.d.17.17 | 48 | 3.2 | odd | 2 | inner | ||
1008.4.bt.d.593.8 | 48 | 21.5 | even | 6 | inner | ||
1008.4.bt.d.593.17 | 48 | 7.5 | odd | 6 | inner |