Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(445,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.445");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 445.10 | ||
Character | \(\chi\) | \(=\) | 684.445 |
Dual form | 684.3.s.a.601.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −2.21812 | − | 2.01989i | −0.739374 | − | 0.673295i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.05295 | − | 3.55582i | −0.410591 | − | 0.711164i | 0.584364 | − | 0.811492i | \(-0.301344\pi\) |
−0.994954 | + | 0.100328i | \(0.968011\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.48935 | − | 11.2399i | −0.927049 | − | 1.60570i | −0.788231 | − | 0.615379i | \(-0.789003\pi\) |
−0.138818 | − | 0.990318i | \(-0.544330\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.840121 | + | 8.96070i | 0.0933468 | + | 0.995634i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.93892 | − | 13.7506i | −0.721720 | − | 1.25006i | −0.960310 | − | 0.278936i | \(-0.910018\pi\) |
0.238590 | − | 0.971120i | \(-0.423315\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.390460i | 0.0300354i | 0.999887 | + | 0.0150177i | \(0.00478046\pi\) | ||||
−0.999887 | + | 0.0150177i | \(0.995220\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.62865 | + | 12.0340i | −0.175243 | + | 0.802265i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.48023 | − | 12.9561i | 0.440014 | − | 0.762126i | −0.557676 | − | 0.830059i | \(-0.688307\pi\) |
0.997690 | + | 0.0679325i | \(0.0216402\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.33801 | − | 16.5469i | −0.491474 | − | 0.870892i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.30912 | + | 38.0391i | −0.395672 | + | 1.81139i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −18.6837 | −0.812335 | −0.406167 | − | 0.913799i | \(-0.633135\pi\) | ||||
−0.406167 | + | 0.913799i | \(0.633135\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.07076 | − | 7.05077i | 0.162831 | − | 0.282031i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.2361 | − | 21.5729i | 0.601337 | − | 0.798995i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.2027 | + | 7.62259i | 0.455266 | + | 0.262848i | 0.710052 | − | 0.704150i | \(-0.248672\pi\) |
−0.254785 | + | 0.966998i | \(0.582005\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.7235 | + | 7.34592i | 0.410436 | + | 0.236965i | 0.690977 | − | 0.722877i | \(-0.257181\pi\) |
−0.280541 | + | 0.959842i | \(0.590514\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.1652 | + | 46.5363i | −0.308036 | + | 1.41019i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −26.6447 | + | 46.1499i | −0.761276 | + | 1.31857i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 35.7838i | 0.967131i | 0.875308 | + | 0.483565i | \(0.160658\pi\) | ||||
−0.875308 | + | 0.483565i | \(0.839342\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.788684 | − | 0.866087i | 0.0202227 | − | 0.0222074i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 19.8233 | − | 11.4450i | 0.483496 | − | 0.279146i | −0.238377 | − | 0.971173i | \(-0.576615\pi\) |
0.721872 | + | 0.692027i | \(0.243282\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16.0986 | 0.374387 | 0.187193 | − | 0.982323i | \(-0.440061\pi\) | ||||
0.187193 | + | 0.982323i | \(0.440061\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 30.1379 | − | 21.3832i | 0.669731 | − | 0.475183i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 21.4855 | − | 37.2140i | 0.457139 | − | 0.791787i | −0.541670 | − | 0.840591i | \(-0.682208\pi\) |
0.998808 | + | 0.0488042i | \(0.0155410\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −59.7232 | + | 103.444i | −1.21884 | + | 2.11110i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −42.7620 | + | 13.6291i | −0.838471 | + | 0.267237i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 17.6872 | − | 10.2117i | 0.333720 | − | 0.192674i | −0.323771 | − | 0.946135i | \(-0.604951\pi\) |
0.657492 | + | 0.753462i | \(0.271617\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −32.5965 | + | 56.4588i | −0.592663 | + | 1.02652i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.7101 | + | 55.5649i | −0.222984 | + | 0.974822i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −60.1406 | + | 34.7222i | −1.01933 | + | 0.588511i | −0.913910 | − | 0.405916i | \(-0.866952\pi\) |
−0.105421 | + | 0.994428i | \(0.533619\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38.0444 | − | 65.8948i | 0.623679 | − | 1.08024i | −0.365116 | − | 0.930962i | \(-0.618971\pi\) |
0.988795 | − | 0.149281i | \(-0.0476959\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 95.2654 | − | 67.5920i | 1.51215 | − | 1.07289i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.38840 | − | 0.801596i | 0.0213601 | − | 0.0123322i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 44.8495i | 0.669396i | 0.942325 | + | 0.334698i | \(0.108634\pi\) | ||||
−0.942325 | + | 0.334698i | \(0.891366\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 41.4427 | + | 37.7389i | 0.600619 | + | 0.546941i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 20.3029 | + | 11.7219i | 0.285957 | + | 0.165097i | 0.636117 | − | 0.771593i | \(-0.280540\pi\) |
−0.350160 | + | 0.936690i | \(0.613873\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33.0816 | − | 57.2991i | 0.453173 | − | 0.784919i | −0.545408 | − | 0.838171i | \(-0.683625\pi\) |
0.998581 | + | 0.0532517i | \(0.0169586\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −23.2712 | + | 7.41698i | −0.310283 | + | 0.0988931i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −103.037 | + | 178.465i | −1.33814 | + | 2.31773i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 120.865i | 1.52994i | 0.644068 | + | 0.764968i | \(0.277245\pi\) | ||||
−0.644068 | + | 0.764968i | \(0.722755\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −79.5884 | + | 15.0562i | −0.982573 | + | 0.185878i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −65.1021 | − | 112.760i | −0.784363 | − | 1.35856i | −0.929379 | − | 0.369127i | \(-0.879657\pi\) |
0.145016 | − | 0.989429i | \(-0.453677\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −61.4263 | −0.722662 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.8885 | − | 43.5758i | −0.159637 | − | 0.500872i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −113.522 | + | 65.5419i | −1.27553 | + | 0.736426i | −0.976023 | − | 0.217669i | \(-0.930155\pi\) |
−0.299505 | + | 0.954095i | \(0.596821\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.38872 | − | 2.53383i | 0.0482277 | − | 0.0278443i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.3844 | − | 41.9942i | −0.143918 | − | 0.451550i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −39.6675 | + | 67.1744i | −0.417552 | + | 0.707099i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 144.324i | 1.48788i | 0.668249 | + | 0.743938i | \(0.267044\pi\) | ||||
−0.668249 | + | 0.743938i | \(0.732956\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 116.546 | − | 82.6905i | 1.17723 | − | 0.835258i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 90.9289 | − | 157.493i | 0.900286 | − | 1.55934i | 0.0731633 | − | 0.997320i | \(-0.476691\pi\) |
0.827123 | − | 0.562021i | \(-0.189976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 123.209 | + | 71.1348i | 1.19621 | + | 0.690629i | 0.959707 | − | 0.281002i | \(-0.0906669\pi\) |
0.236498 | + | 0.971632i | \(0.424000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 152.319 | − | 48.5469i | 1.45065 | − | 0.462351i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.60032i | 0.0710310i | 0.999369 | + | 0.0355155i | \(0.0113073\pi\) | ||||
−0.999369 | + | 0.0355155i | \(0.988693\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −48.7475 | − | 28.1444i | −0.447225 | − | 0.258205i | 0.259433 | − | 0.965761i | \(-0.416464\pi\) |
−0.706657 | + | 0.707556i | \(0.749798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 72.2793 | − | 79.3729i | 0.651165 | − | 0.715071i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 42.3909 | + | 24.4744i | 0.375141 | + | 0.216588i | 0.675702 | − | 0.737175i | \(-0.263841\pi\) |
−0.300561 | + | 0.953763i | \(0.597174\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 38.3568 | + | 66.4359i | 0.333537 | + | 0.577703i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.49879 | + | 0.328034i | −0.0299042 | + | 0.00280371i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −194.167 | −1.63166 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −65.5530 | + | 113.541i | −0.541760 | + | 0.938356i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −67.0881 | − | 14.6545i | −0.545432 | − | 0.119142i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −136.076 | −1.08861 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 198.477 | − | 114.591i | 1.56281 | − | 0.902288i | 0.565838 | − | 0.824516i | \(-0.308553\pi\) |
0.996971 | − | 0.0777721i | \(-0.0247807\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −35.7087 | − | 32.5174i | −0.276812 | − | 0.252073i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 32.2676 | + | 55.8891i | 0.246317 | + | 0.426634i | 0.962501 | − | 0.271278i | \(-0.0874461\pi\) |
−0.716184 | + | 0.697912i | \(0.754113\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −125.388 | + | 212.337i | −0.942767 | + | 1.59652i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −110.041 | − | 13.4446i | −0.815120 | − | 0.0995894i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 49.4849 | − | 85.7103i | 0.361204 | − | 0.625623i | −0.626956 | − | 0.779055i | \(-0.715699\pi\) |
0.988159 | + | 0.153432i | \(0.0490326\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 123.733 | 0.890166 | 0.445083 | − | 0.895489i | \(-0.353174\pi\) | ||||
0.445083 | + | 0.895489i | \(0.353174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −122.825 | + | 39.1469i | −0.871103 | + | 0.277637i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.36906 | − | 3.09983i | 0.0375459 | − | 0.0216771i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 62.5953i | − | 0.431692i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 341.418 | − | 108.816i | 2.32257 | − | 0.740248i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −76.3395 | − | 132.224i | −0.512345 | − | 0.887408i | −0.999898 | − | 0.0143143i | \(-0.995443\pi\) |
0.487552 | − | 0.873094i | \(-0.337890\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −77.0133 | + | 44.4637i | −0.510022 | + | 0.294461i | −0.732843 | − | 0.680398i | \(-0.761807\pi\) |
0.222821 | + | 0.974859i | \(0.428474\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 122.380 | + | 56.1434i | 0.799872 | + | 0.366950i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 60.3234i | − | 0.389183i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −95.5975 | − | 165.580i | −0.608901 | − | 1.05465i | −0.991422 | − | 0.130701i | \(-0.958277\pi\) |
0.382521 | − | 0.923947i | \(-0.375056\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −59.8588 | − | 13.0753i | −0.376470 | − | 0.0822346i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 121.245 | + | 210.002i | 0.753074 | + | 1.30436i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.9541 | 0.0856080 | 0.0428040 | − | 0.999083i | \(-0.486371\pi\) | ||||
0.0428040 | + | 0.999083i | \(0.486371\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 186.343 | − | 59.3912i | 1.12935 | − | 0.359947i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 238.675i | − | 1.42919i | −0.699538 | − | 0.714596i | \(-0.746611\pi\) | ||
0.699538 | − | 0.714596i | \(-0.253389\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 168.848 | 0.999098 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 140.427 | − | 97.5766i | 0.821212 | − | 0.570623i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 141.566i | − | 0.818300i | −0.912467 | − | 0.409150i | \(-0.865825\pi\) | ||
0.912467 | − | 0.409150i | \(-0.134175\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −105.666 | −0.603808 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 203.534 | + | 44.4591i | 1.14991 | + | 0.251181i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 253.540i | − | 1.41643i | −0.705998 | − | 0.708214i | \(-0.749501\pi\) | ||
0.705998 | − | 0.708214i | \(-0.250499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −200.068 | + | 115.509i | −1.10535 | + | 0.638173i | −0.937620 | − | 0.347661i | \(-0.886976\pi\) |
−0.167727 | + | 0.985833i | \(0.553643\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −217.487 | + | 69.3173i | −1.18845 | + | 0.378783i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 127.241 | − | 73.4626i | 0.687789 | − | 0.397095i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −237.540 | −1.27027 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −347.838 | − | 42.4980i | −1.84041 | − | 0.224857i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −135.073 | − | 233.954i | −0.707190 | − | 1.22489i | −0.965895 | − | 0.258933i | \(-0.916629\pi\) |
0.258705 | − | 0.965956i | \(-0.416704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.6562 | − | 12.5032i | 0.112208 | − | 0.0647835i | −0.442845 | − | 0.896598i | \(-0.646031\pi\) |
0.555054 | + | 0.831814i | \(0.312698\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.69878 | − | 1.02638i | −0.0240963 | − | 0.00526350i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 243.933 | 1.23824 | 0.619119 | − | 0.785297i | \(-0.287490\pi\) | ||||
0.619119 | + | 0.785297i | \(0.287490\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −86.3189 | − | 149.509i | −0.433763 | − | 0.751300i | 0.563431 | − | 0.826163i | \(-0.309481\pi\) |
−0.997194 | + | 0.0748635i | \(0.976148\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 90.5910 | − | 99.4817i | 0.450701 | − | 0.494934i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 197.863i | − | 0.974693i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −81.3927 | − | 46.9921i | −0.397038 | − | 0.229230i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.6966 | − | 167.419i | −0.0758289 | − | 0.808788i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −153.397 | + | 259.768i | −0.733957 | + | 1.24291i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −69.6073 | + | 40.1878i | −0.329892 | + | 0.190463i | −0.655793 | − | 0.754941i | \(-0.727666\pi\) |
0.325901 | + | 0.945404i | \(0.394332\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.3574 | − | 67.0101i | −0.100270 | − | 0.314602i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −33.0497 | − | 57.2438i | −0.153720 | − | 0.266250i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 190.681i | − | 0.878714i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −189.117 | + | 60.2752i | −0.863547 | + | 0.275229i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.05885 | + | 2.92073i | 0.0228907 | + | 0.0132160i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 130.404i | − | 0.584772i | −0.956300 | − | 0.292386i | \(-0.905551\pi\) | ||
0.956300 | − | 0.292386i | \(-0.0944493\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 66.5998 | + | 30.5534i | 0.295999 | + | 0.135793i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −32.0290 | + | 18.4920i | −0.141097 | + | 0.0814624i | −0.568887 | − | 0.822416i | \(-0.692626\pi\) |
0.427790 | + | 0.903878i | \(0.359292\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −79.1349 | + | 137.066i | −0.345567 | + | 0.598540i | −0.985457 | − | 0.169927i | \(-0.945647\pi\) |
0.639889 | + | 0.768467i | \(0.278980\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 589.027 | − | 187.734i | 2.54990 | − | 0.812703i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −125.476 | + | 217.331i | −0.538525 | + | 0.932753i | 0.460459 | + | 0.887681i | \(0.347685\pi\) |
−0.998984 | + | 0.0450717i | \(0.985648\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −176.435 | −0.750787 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 244.133 | − | 268.093i | 1.03010 | − | 1.13119i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −87.5050 | + | 151.563i | −0.366130 | + | 0.634155i | −0.988957 | − | 0.148204i | \(-0.952651\pi\) |
0.622827 | + | 0.782360i | \(0.285984\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 296.093 | + | 170.949i | 1.22860 | + | 0.709333i | 0.966737 | − | 0.255772i | \(-0.0823298\pi\) |
0.261863 | + | 0.965105i | \(0.415663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 206.948 | + | 127.363i | 0.851640 | + | 0.524128i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 490.436 | 2.00178 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.46092 | − | 3.64612i | 0.0261576 | − | 0.0147616i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −83.3583 | + | 381.615i | −0.334772 | + | 1.53259i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −138.459 | − | 239.818i | −0.551630 | − | 0.955451i | −0.998157 | − | 0.0606811i | \(-0.980673\pi\) |
0.446527 | − | 0.894770i | \(-0.352661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 148.328 | + | 256.912i | 0.586278 | + | 1.01546i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 136.251 | + | 124.074i | 0.534317 | + | 0.486565i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 94.7767i | − | 0.368781i | −0.982853 | − | 0.184390i | \(-0.940969\pi\) | ||
0.982853 | − | 0.184390i | \(-0.0590311\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 402.206 | − | 232.214i | 1.55292 | − | 0.896578i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −57.2119 | + | 124.710i | −0.219203 | + | 0.477814i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 104.855 | 0.398688 | 0.199344 | − | 0.979930i | \(-0.436119\pi\) | ||||
0.199344 | + | 0.979930i | \(0.436119\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −72.6219 | − | 41.9283i | −0.274045 | − | 0.158220i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 384.193 | + | 83.9215i | 1.43892 | + | 0.314313i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 122.868 | + | 70.9381i | 0.456760 | + | 0.263711i | 0.710681 | − | 0.703514i | \(-0.248387\pi\) |
−0.253921 | + | 0.967225i | \(0.581720\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −48.7803 | + | 84.4900i | −0.180001 | + | 0.311771i | −0.941881 | − | 0.335948i | \(-0.890943\pi\) |
0.761879 | + | 0.647719i | \(0.224277\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.8528 | − | 3.24437i | −0.0544057 | − | 0.0118842i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −129.270 | −0.470072 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 85.1441 | + | 147.474i | 0.307379 | + | 0.532397i | 0.977788 | − | 0.209595i | \(-0.0672146\pi\) |
−0.670409 | + | 0.741992i | \(0.733881\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −55.1353 | + | 120.183i | −0.197618 | + | 0.430764i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −424.449 | − | 245.056i | −1.51050 | − | 0.872085i | −0.999925 | − | 0.0122499i | \(-0.996101\pi\) |
−0.510571 | − | 0.859835i | \(-0.670566\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 218.630 | + | 378.679i | 0.772545 | + | 1.33809i | 0.936164 | + | 0.351564i | \(0.114350\pi\) |
−0.163619 | + | 0.986524i | \(0.552317\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 223.672 | − | 68.8772i | 0.784814 | − | 0.241674i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −257.281 | − | 148.541i | −0.896449 | − | 0.517565i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.5922 | + | 56.4514i | 0.112776 | + | 0.195333i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 291.518 | − | 320.128i | 1.00178 | − | 1.10010i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 232.886 | + | 134.457i | 0.794831 | + | 0.458896i | 0.841661 | − | 0.540007i | \(-0.181578\pi\) |
−0.0468294 | + | 0.998903i | \(0.514912\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 246.932 | + | 142.566i | 0.837056 | + | 0.483275i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −425.538 | − | 51.9911i | −1.43279 | − | 0.175054i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 7.29523i | − | 0.0243988i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −104.470 | − | 180.947i | −0.347075 | − | 0.601152i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −519.810 | + | 165.674i | −1.71554 | + | 0.546777i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −312.413 | −1.02431 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 222.433 | + | 128.422i | 0.724536 | + | 0.418311i | 0.816420 | − | 0.577459i | \(-0.195956\pi\) |
−0.0918838 | + | 0.995770i | \(0.529289\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −129.609 | − | 406.654i | −0.419445 | − | 1.31603i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 77.6546 | − | 134.502i | 0.249693 | − | 0.432482i | −0.713747 | − | 0.700403i | \(-0.753004\pi\) |
0.963441 | + | 0.267922i | \(0.0863369\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −82.9289 | + | 143.637i | −0.264949 | + | 0.458905i | −0.967550 | − | 0.252679i | \(-0.918688\pi\) |
0.702602 | + | 0.711584i | \(0.252022\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −435.920 | − | 199.983i | −1.38387 | − | 0.634868i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −240.589 | − | 138.904i | −0.758957 | − | 0.438184i | 0.0699642 | − | 0.997550i | \(-0.477711\pi\) |
−0.828921 | + | 0.559366i | \(0.811045\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 242.061i | − | 0.758811i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.3518 | − | 16.8584i | 0.0478248 | − | 0.0525185i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −284.235 | − | 2.79038i | −0.879985 | − | 0.00863893i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.75304 | + | 1.58947i | 0.00847090 | + | 0.00489067i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 51.2794 | + | 160.892i | 0.156818 | + | 0.492025i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −557.708 | −1.69516 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −231.109 | + | 133.431i | −0.698213 | + | 0.403113i | −0.806682 | − | 0.590986i | \(-0.798739\pi\) |
0.108468 | + | 0.994100i | \(0.465405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −320.648 | + | 30.0628i | −0.962908 | + | 0.0902786i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 159.477 | − | 92.0740i | 0.476050 | − | 0.274848i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 339.761 | − | 196.161i | 1.00819 | − | 0.582080i | 0.0975308 | − | 0.995233i | \(-0.468906\pi\) |
0.910662 | + | 0.413152i | \(0.135572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −44.5927 | − | 139.912i | −0.131542 | − | 0.412720i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 233.275i | − | 0.684090i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 914.303 | 2.66561 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 49.1129 | − | 224.839i | 0.142356 | − | 0.651707i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 234.248 | + | 405.730i | 0.675067 | + | 1.16925i | 0.976449 | + | 0.215747i | \(0.0692186\pi\) |
−0.301382 | + | 0.953503i | \(0.597448\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −292.595 | − | 506.789i | −0.838380 | − | 1.45212i | −0.891248 | − | 0.453515i | \(-0.850170\pi\) |
0.0528684 | − | 0.998601i | \(-0.483164\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.42334 | + | 6.33955i | 0.0239981 | + | 0.0180614i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.23602 | − | 7.33701i | −0.0120001 | − | 0.0207847i | 0.859963 | − | 0.510356i | \(-0.170486\pi\) |
−0.871963 | + | 0.489572i | \(0.837153\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 96.2580i | − | 0.271149i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 430.687 | + | 392.196i | 1.20640 | + | 1.09859i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −134.445 | + | 232.865i | −0.374498 | + | 0.648650i | −0.990252 | − | 0.139289i | \(-0.955518\pi\) |
0.615754 | + | 0.787939i | \(0.288852\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −186.603 | + | 309.031i | −0.516906 | + | 0.856042i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 374.745 | − | 119.438i | 1.03235 | − | 0.329031i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −271.660 | −0.744275 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −300.091 | + | 519.773i | −0.817686 | + | 1.41627i | 0.0896967 | + | 0.995969i | \(0.471410\pi\) |
−0.907383 | + | 0.420305i | \(0.861923\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 119.209 | + | 168.016i | 0.323060 | + | 0.455327i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −229.557 | − | 132.535i | −0.618751 | − | 0.357236i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −468.871 | − | 270.703i | −1.25703 | − | 0.725745i | −0.284531 | − | 0.958667i | \(-0.591838\pi\) |
−0.972495 | + | 0.232922i | \(0.925171\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 301.833 | + | 274.858i | 0.804888 | + | 0.732955i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.97632 | + | 5.15513i | −0.00789474 | + | 0.0136741i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 387.805i | − | 1.02323i | −0.859214 | − | 0.511617i | \(-0.829047\pi\) | ||
0.859214 | − | 0.511617i | \(-0.170953\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −671.706 | − | 146.725i | −1.76301 | − | 0.385104i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 83.5548 | − | 48.2404i | 0.218159 | − | 0.125954i | −0.386939 | − | 0.922105i | \(-0.626467\pi\) |
0.605097 | + | 0.796151i | \(0.293134\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 846.119 | 2.19771 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.5248 | + | 144.255i | 0.0349478 | + | 0.372752i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −173.311 | + | 300.183i | −0.445530 | + | 0.771680i | −0.998089 | − | 0.0617937i | \(-0.980318\pi\) |
0.552559 | + | 0.833474i | \(0.313651\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −139.758 | + | 242.069i | −0.357438 | + | 0.619102i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 41.3162 | − | 189.146i | 0.105130 | − | 0.481286i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 429.774 | − | 248.130i | 1.08804 | − | 0.628177i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 42.6512 | − | 73.8740i | 0.107434 | − | 0.186081i | −0.807296 | − | 0.590146i | \(-0.799070\pi\) |
0.914730 | + | 0.404066i | \(0.132403\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 707.022 | − | 217.720i | 1.77199 | − | 0.545663i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −418.030 | + | 241.350i | −1.04247 | + | 0.601870i | −0.920532 | − | 0.390668i | \(-0.872244\pi\) |
−0.121937 | + | 0.992538i | \(0.538911\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.86829 | + | 4.96802i | −0.00711734 | + | 0.0123276i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 216.928 | + | 252.092i | 0.535625 | + | 0.622450i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 492.050 | − | 284.085i | 1.20897 | − | 0.697998i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 539.601i | 1.31932i | 0.751566 | + | 0.659658i | \(0.229299\pi\) | ||||
−0.751566 | + | 0.659658i | \(0.770701\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −282.889 | + | 90.1621i | −0.688293 | + | 0.219372i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 780.546 | + | 450.648i | 1.88994 | + | 1.09116i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −267.303 | + | 462.983i | −0.644104 | + | 1.11562i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −274.455 | − | 249.927i | −0.658165 | − | 0.599345i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −345.181 | + | 597.871i | −0.823820 | + | 1.42690i | 0.0789970 | + | 0.996875i | \(0.474828\pi\) |
−0.902817 | + | 0.430024i | \(0.858505\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 426.877i | − | 1.01396i | −0.861958 | − | 0.506980i | \(-0.830762\pi\) | ||
0.861958 | − | 0.506980i | \(-0.169238\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 351.514 | + | 161.261i | 0.831002 | + | 0.381232i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −60.9005 | − | 105.483i | −0.143295 | − | 0.248195i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −987.533 | −2.31272 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.1705 | − | 3.96910i | −0.0423556 | − | 0.00925197i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −132.173 | + | 76.3101i | −0.306666 | + | 0.177054i | −0.645434 | − | 0.763816i | \(-0.723323\pi\) |
0.338768 | + | 0.940870i | \(0.389990\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −272.158 | + | 157.131i | −0.628541 | + | 0.362889i | −0.780187 | − | 0.625546i | \(-0.784876\pi\) |
0.151646 | + | 0.988435i | \(0.451543\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −126.435 | + | 138.844i | −0.290656 | + | 0.319182i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 174.469 | + | 309.158i | 0.399242 | + | 0.707456i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 679.923i | − | 1.54880i | −0.632697 | − | 0.774399i | \(-0.718052\pi\) | ||
0.632697 | − | 0.774399i | \(-0.281948\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −977.103 | − | 448.257i | −2.21565 | − | 1.01646i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −51.4605 | + | 89.1323i | −0.116164 | + | 0.201201i | −0.918244 | − | 0.396014i | \(-0.870393\pi\) |
0.802081 | + | 0.597216i | \(0.203726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 466.111 | + | 269.109i | 1.04744 | + | 0.604739i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −97.7469 | + | 447.485i | −0.218673 | + | 1.00109i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 723.036i | 1.61033i | 0.593053 | + | 0.805163i | \(0.297922\pi\) | ||||
−0.593053 | + | 0.805163i | \(0.702078\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −314.752 | − | 181.722i | −0.697897 | − | 0.402931i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 260.636 | + | 56.9324i | 0.575356 | + | 0.125679i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.0197 | − | 10.4037i | −0.0396037 | − | 0.0228652i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 68.0568 | + | 117.878i | 0.148921 | + | 0.257938i | 0.930829 | − | 0.365455i | \(-0.119087\pi\) |
−0.781908 | + | 0.623394i | \(0.785753\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −158.051 | − | 371.727i | −0.344339 | − | 0.809864i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 793.339 | 1.72091 | 0.860455 | − | 0.509527i | \(-0.170180\pi\) | ||||
0.860455 | + | 0.509527i | \(0.170180\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.1918 | + | 22.8488i | −0.0284919 | + | 0.0493495i | −0.879920 | − | 0.475122i | \(-0.842404\pi\) |
0.851428 | + | 0.524472i | \(0.175737\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −121.846 | + | 133.804i | −0.262035 | + | 0.287752i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 220.125 | 0.471361 | 0.235680 | − | 0.971831i | \(-0.424268\pi\) | ||||
0.235680 | + | 0.971831i | \(0.424268\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 504.103 | − | 291.044i | 1.07485 | − | 0.620563i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −122.405 | + | 560.372i | −0.259884 | + | 1.18975i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −127.806 | − | 221.366i | −0.270202 | − | 0.468004i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −154.682 | − | 1.51853i | −0.325645 | − | 0.00319691i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 106.363 | + | 149.911i | 0.222984 | + | 0.314278i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −117.813 | + | 204.057i | −0.245955 | + | 0.426007i | −0.962400 | − | 0.271637i | \(-0.912435\pi\) |
0.716445 | + | 0.697644i | \(0.245768\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.9721 | −0.0290481 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 155.245 | − | 710.712i | 0.321418 | − | 1.47145i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 513.190 | − | 296.290i | 1.05812 | − | 0.610908i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 511.738i | 1.05080i | 0.850856 | + | 0.525398i | \(0.176084\pi\) | ||||
−0.850856 | + | 0.525398i | \(0.823916\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −30.9519 | − | 28.1857i | −0.0632963 | − | 0.0576395i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.5262 | − | 51.1408i | −0.0601348 | − | 0.104156i | 0.834391 | − | 0.551173i | \(-0.185820\pi\) |
−0.894526 | + | 0.447017i | \(0.852486\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 197.519 | − | 114.038i | 0.400647 | − | 0.231314i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −533.295 | − | 244.655i | −1.07736 | − | 0.494253i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 304.270i | − | 0.612213i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 137.211 | + | 237.656i | 0.274971 | + | 0.476264i | 0.970128 | − | 0.242594i | \(-0.0779983\pi\) |
−0.695157 | + | 0.718858i | \(0.744665\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −482.096 | + | 529.410i | −0.962268 | + | 1.05671i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 301.952 | + | 522.996i | 0.600302 | + | 1.03975i | 0.992775 | + | 0.119990i | \(0.0382863\pi\) |
−0.392473 | + | 0.919763i | \(0.628380\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −746.691 | −1.47860 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −374.524 | − | 341.053i | −0.738707 | − | 0.672688i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 684.790i | − | 1.34536i | −0.739932 | − | 0.672682i | \(-0.765142\pi\) | ||
0.739932 | − | 0.672682i | \(-0.234858\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −858.713 | −1.68046 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −508.578 | − | 67.2102i | −0.991381 | − | 0.131014i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 584.146i | − | 1.13426i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −682.287 | −1.31970 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −285.947 | + | 314.010i | −0.550957 | + | 0.605029i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 868.338i | 1.66668i | 0.552763 | + | 0.833338i | \(0.313573\pi\) | ||||
−0.552763 | + | 0.833338i | \(0.686427\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −746.158 | + | 430.795i | −1.42669 | + | 0.823699i | −0.996858 | − | 0.0792098i | \(-0.974760\pi\) |
−0.429831 | + | 0.902909i | \(0.641427\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 234.381 | + | 213.434i | 0.446440 | + | 0.406541i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 190.350 | − | 109.898i | 0.361195 | − | 0.208536i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −179.919 | −0.340112 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −361.660 | − | 509.731i | −0.681093 | − | 0.959945i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.46881 | + | 7.74021i | 0.00838426 | + | 0.0145220i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.0254 | − | 15.6031i | 0.0505147 | − | 0.0291647i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −512.123 | + | 562.383i | −0.953674 | + | 1.04727i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1896.55 | 3.51865 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −395.214 | − | 684.531i | −0.730526 | − | 1.26531i | −0.956659 | − | 0.291211i | \(-0.905942\pi\) |
0.226133 | − | 0.974096i | \(-0.427392\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 677.090 | + | 147.901i | 1.24694 | + | 0.272377i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 231.116i | 0.424067i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −391.263 | − | 225.896i | −0.715288 | − | 0.412972i | 0.0977278 | − | 0.995213i | \(-0.468843\pi\) |
−0.813016 | + | 0.582241i | \(0.802176\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 622.426 | + | 285.545i | 1.13374 | + | 0.520118i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.84348 | − | 289.645i | 0.00516058 | − | 0.525671i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1358.51 | − | 784.334i | 2.45661 | − | 1.41833i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −430.622 | − | 94.0632i | −0.775895 | − | 0.169483i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −510.833 | − | 884.789i | −0.917115 | − | 1.58849i | −0.803775 | − | 0.594934i | \(-0.797178\pi\) |
−0.113341 | − | 0.993556i | \(-0.536155\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.28587i | 0.0112448i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 526.892 | + | 479.804i | 0.939202 | + | 0.855265i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 264.370 | + | 152.634i | 0.469574 | + | 0.271109i | 0.716061 | − | 0.698037i | \(-0.245943\pi\) |
−0.246487 | + | 0.969146i | \(0.579276\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 200.979i | − | 0.355716i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 685.706 | + | 796.859i | 1.20936 | + | 1.40540i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −576.757 | + | 332.991i | −1.01363 | + | 0.585221i | −0.912253 | − | 0.409626i | \(-0.865659\pi\) |
−0.101380 | + | 0.994848i | \(0.532326\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 111.463 | − | 193.060i | 0.195207 | − | 0.338108i | −0.751761 | − | 0.659435i | \(-0.770795\pi\) |
0.946968 | + | 0.321327i | \(0.104129\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −172.951 | + | 791.770i | −0.301834 | + | 1.38180i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −76.0569 | + | 131.734i | −0.132273 | + | 0.229103i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −422.219 | −0.731749 | −0.365875 | − | 0.930664i | \(-0.619230\pi\) | ||||
−0.365875 | + | 0.930664i | \(0.619230\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −73.2912 | − | 16.0094i | −0.126582 | − | 0.0276501i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −844.940 | + | 1463.48i | −1.45429 | + | 2.51890i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −280.834 | − | 162.140i | −0.481706 | − | 0.278113i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.34929 | + | 11.7676i | 0.0142723 | + | 0.0201156i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −48.5657 | −0.0827354 | −0.0413677 | − | 0.999144i | \(-0.513172\pi\) | ||||
−0.0413677 | + | 0.999144i | \(0.513172\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.74027 | − | 279.132i | 0.00465242 | − | 0.473908i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −541.073 | − | 492.717i | −0.915521 | − | 0.833700i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 545.462 | + | 944.768i | 0.919835 | + | 1.59320i | 0.799664 | + | 0.600448i | \(0.205011\pi\) |
0.120171 | + | 0.992753i | \(0.461656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 398.616 | + | 690.424i | 0.669944 | + | 1.16038i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −110.525 | + | 505.983i | −0.185134 | + | 0.847542i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 588.855i | 0.983063i | 0.870860 | + | 0.491532i | \(0.163563\pi\) | ||||
−0.870860 | + | 0.491532i | \(0.836437\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 838.716 | − | 484.233i | 1.39553 | − | 0.805712i | 0.401613 | − | 0.915809i | \(-0.368450\pi\) |
0.993921 | + | 0.110097i | \(0.0351163\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −401.883 | + | 37.6791i | −0.666473 | + | 0.0624860i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 538.309 | 0.889767 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 129.306 | + | 74.6547i | 0.213024 | + | 0.122990i | 0.602716 | − | 0.797956i | \(-0.294085\pi\) |
−0.389692 | + | 0.920945i | \(0.627418\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −399.660 | + | 438.883i | −0.656256 | + | 0.720662i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.5306 | + | 8.38923i | 0.0237816 | + | 0.0137303i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 480.397 | − | 832.071i | 0.783681 | − | 1.35738i | −0.146102 | − | 0.989269i | \(-0.546673\pi\) |
0.929784 | − | 0.368106i | \(-0.119994\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 85.6202 | + | 268.638i | 0.139220 | + | 0.436810i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 546.118 | 0.885119 | 0.442559 | − | 0.896739i | \(-0.354071\pi\) | ||||
0.442559 | + | 0.896739i | \(0.354071\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 292.910 | + | 507.336i | 0.473199 | + | 0.819605i | 0.999529 | − | 0.0306750i | \(-0.00976569\pi\) |
−0.526330 | + | 0.850280i | \(0.676432\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −303.351 | + | 403.061i | −0.488487 | + | 0.649052i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1473.37 | + | 850.649i | 2.36495 | + | 1.36541i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 177.589 | + | 307.593i | 0.284142 | + | 0.492148i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 864.956 | − | 266.353i | 1.37951 | − | 0.424806i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 463.621 | + | 267.671i | 0.737076 | + | 0.425551i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 174.403 | + | 302.075i | 0.276392 | + | 0.478725i | 0.970485 | − | 0.241160i | \(-0.0775279\pi\) |
−0.694093 | + | 0.719885i | \(0.744195\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 235.572 | + | 51.4574i | 0.372152 | + | 0.0812913i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −814.927 | − | 470.498i | −1.28335 | − | 0.740942i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −40.3906 | − | 23.3195i | −0.0634075 | − | 0.0366083i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −87.9795 | + | 191.776i | −0.137683 | + | 0.300119i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 817.703i | − | 1.27567i | −0.770174 | − | 0.637834i | \(-0.779831\pi\) | ||
0.770174 | − | 0.637834i | \(-0.220169\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −160.386 | − | 277.797i | −0.249434 | − | 0.432033i | 0.713935 | − | 0.700212i | \(-0.246911\pi\) |
−0.963369 | + | 0.268179i | \(0.913578\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −42.3177 | + | 193.730i | −0.0656088 | + | 0.300357i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −499.685 | −0.772310 | −0.386155 | − | 0.922434i | \(-0.626197\pi\) | ||||
−0.386155 | + | 0.922434i | \(0.626197\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 954.903 | + | 551.313i | 1.47134 | + | 0.849481i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −385.154 | + | 422.953i | −0.591634 | + | 0.649698i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 510.680 | − | 884.524i | 0.782052 | − | 1.35455i | −0.148692 | − | 0.988884i | \(-0.547506\pi\) |
0.930744 | − | 0.365671i | \(-0.119160\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 132.488 | − | 229.475i | 0.202271 | − | 0.350344i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 541.233 | + | 248.297i | 0.823794 | + | 0.377925i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −359.383 | − | 207.490i | −0.545346 | − | 0.314856i | 0.201897 | − | 0.979407i | \(-0.435289\pi\) |
−0.747243 | + | 0.664551i | \(0.768623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 277.158i | − | 0.419301i | −0.977776 | − | 0.209650i | \(-0.932767\pi\) | ||
0.977776 | − | 0.209650i | \(-0.0672325\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.32161 | − | 16.6968i | −0.00802655 | − | 0.0251838i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1012.45 | + | 9.93934i | 1.52248 | + | 0.0149464i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −246.676 | − | 142.418i | −0.369829 | − | 0.213521i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −263.402 | + | 289.252i | −0.393725 | + | 0.432365i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1208.13 | −1.80049 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −780.615 | + | 450.688i | −1.15990 | + | 0.669670i | −0.951281 | − | 0.308326i | \(-0.900231\pi\) |
−0.208622 | + | 0.977996i | \(0.566898\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −86.0120 | − | 202.295i | −0.127425 | − | 0.299696i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 341.330 | − | 197.067i | 0.504181 | − | 0.291089i | −0.226258 | − | 0.974067i | \(-0.572649\pi\) |
0.730438 | + | 0.682979i | \(0.239316\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1622.18 | − | 936.568i | 2.38908 | − | 1.37933i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 108.396 | + | 23.6776i | 0.159172 | + | 0.0347688i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 591.311i | − | 0.865755i | −0.901453 | − | 0.432878i | \(-0.857498\pi\) | ||
0.901453 | − | 0.432878i | \(-0.142502\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −406.361 | −0.593227 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 452.388 | − | 144.185i | 0.658498 | − | 0.209876i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.98726 | + | 6.90613i | 0.00578702 | + | 0.0100234i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.4269 | − | 76.9497i | −0.0642937 | − | 0.111360i | 0.832087 | − | 0.554645i | \(-0.187146\pi\) |
−0.896380 | + | 0.443286i | \(0.853813\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1685.74 | − | 773.350i | −2.43252 | − | 1.11595i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −254.018 | − | 439.973i | −0.365494 | − | 0.633054i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 342.445i | − | 0.491313i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 717.306 | − | 228.619i | 1.02619 | − | 0.327066i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −545.551 | + | 944.922i | −0.778247 | + | 1.34796i | 0.154704 | + | 0.987961i | \(0.450558\pi\) |
−0.932951 | + | 0.360003i | \(0.882776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 592.113 | − | 334.150i | 0.842266 | − | 0.475320i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 391.354 | + | 356.379i | 0.555112 | + | 0.505502i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2360.28 | −3.33844 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 509.445 | − | 882.385i | 0.718541 | − | 1.24455i | −0.243037 | − | 0.970017i | \(-0.578144\pi\) |
0.961578 | − | 0.274532i | \(-0.0885229\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1083.03 | + | 101.541i | −1.52326 | + | 0.142815i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −237.722 | − | 137.249i | −0.333411 | − | 0.192495i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.0449 | − | 12.7276i | −0.0308320 | − | 0.0178009i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 500.237 | − | 159.435i | 0.697681 | − | 0.222364i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −162.296 | + | 281.105i | −0.225725 | + | 0.390967i | −0.956537 | − | 0.291612i | \(-0.905808\pi\) |
0.730812 | + | 0.682579i | \(0.239142\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1846.47i | − | 2.56099i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −311.471 | − | 977.259i | −0.430804 | − | 1.35167i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 107.490 | − | 62.0596i | 0.148263 | − | 0.0855994i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 208.135 | 0.286293 | 0.143146 | − | 0.989702i | \(-0.454278\pi\) | ||||
0.143146 | + | 0.989702i | \(0.454278\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −201.778 | − | 700.519i | −0.276787 | − | 0.960931i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 120.421 | − | 208.576i | 0.164735 | − | 0.285330i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 178.182 | − | 308.619i | 0.243085 | − | 0.421036i | −0.718506 | − | 0.695521i | \(-0.755174\pi\) |
0.961592 | + | 0.274484i | \(0.0885072\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1087.85 | − | 990.625i | −1.48006 | − | 1.34779i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 616.709 | − | 356.057i | 0.836783 | − | 0.483117i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.3234 | − | 21.3448i | 0.0166758 | − | 0.0288833i | −0.857567 | − | 0.514372i | \(-0.828025\pi\) |
0.874243 | + | 0.485489i | \(0.161358\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.6958 | − | 4.96278i | −0.0292791 | − | 0.00669741i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −956.068 | + | 551.986i | −1.28677 | + | 0.742915i | −0.978076 | − | 0.208247i | \(-0.933224\pi\) |
−0.308691 | + | 0.951162i | \(0.599891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −313.443 | + | 542.899i | −0.420728 | + | 0.728723i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 955.717 | − | 678.093i | 1.27941 | − | 0.907755i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 85.4266 | − | 49.3211i | 0.114054 | − | 0.0658493i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 114.360i | − | 0.152277i | −0.997097 | − | 0.0761384i | \(-0.975741\pi\) | ||
0.997097 | − | 0.0761384i | \(-0.0242591\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −177.286 | + | 811.618i | −0.235440 | + | 1.07785i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 316.210 | + | 182.564i | 0.418821 | + | 0.241806i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −463.471 | + | 802.756i | −0.612248 | + | 1.06044i | 0.378613 | + | 0.925555i | \(0.376401\pi\) |
−0.990861 | + | 0.134889i | \(0.956932\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 189.923 | − | 869.469i | 0.250228 | − | 1.14555i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 291.762 | − | 505.347i | 0.383393 | − | 0.664056i | −0.608152 | − | 0.793821i | \(-0.708089\pi\) |
0.991545 | + | 0.129765i | \(0.0414222\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 730.555i | 0.957477i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −51.6055 | − | 550.423i | −0.0674582 | − | 0.719507i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.5576 | − | 23.4825i | −0.0176762 | − | 0.0306160i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 890.370 | 1.15783 | 0.578914 | − | 0.815388i | \(-0.303477\pi\) | ||||
0.578914 | + | 0.815388i | \(0.303477\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −191.438 | + | 210.226i | −0.248298 | + | 0.272667i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1247.51 | − | 720.250i | 1.61385 | − | 0.931759i | 0.625388 | − | 0.780314i | \(-0.284941\pi\) |
0.988466 | − | 0.151445i | \(-0.0483928\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 103.589 | − | 59.8070i | 0.133663 | − | 0.0771704i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1361.19 | − | 297.332i | −1.75185 | − | 0.382667i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −374.490 | − | 221.142i | −0.480732 | − | 0.283879i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 372.237i | − | 0.476616i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 378.802 | − | 161.059i | 0.483783 | − | 0.205695i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −392.514 | + | 679.855i | −0.500018 | + | 0.866057i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −885.613 | − | 511.309i | −1.12530 | − | 0.649693i | −0.182553 | − | 0.983196i | \(-0.558436\pi\) |
−0.942749 | + | 0.333503i | \(0.891769\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −232.581 | − | 211.795i | −0.294780 | − | 0.268435i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 635.292i | − | 0.803150i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.7293 | + | 14.8548i | 0.0324455 | + | 0.0187324i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 76.3939 | + | 239.690i | 0.0960929 | + | 0.301497i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 424.917 | + | 245.326i | 0.533146 | + | 0.307812i | 0.742297 | − | 0.670071i | \(-0.233737\pi\) |
−0.209151 | + | 0.977883i | \(0.567070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −321.433 | − | 556.739i | −0.402294 | − | 0.696794i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −682.674 | − | 962.173i | −0.852277 | − | 1.20122i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1050.53 | −1.30826 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 497.821 | − | 862.251i | 0.618411 | − | 1.07112i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −129.250 | − | 405.530i | −0.160161 | − | 0.502515i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 654.603 | 0.809151 | 0.404575 | − | 0.914505i | \(-0.367419\pi\) | ||||
0.404575 | + | 0.914505i | \(0.367419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −231.770 | + | 133.812i | −0.285783 | + | 0.164997i | −0.636038 | − | 0.771657i | \(-0.719428\pi\) |
0.350256 | + | 0.936654i | \(0.386095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 278.861 | − | 88.8783i | 0.343002 | − | 0.109321i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.6471 | − | 49.6183i | −0.0351499 | − | 0.0608813i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −150.329 | − | 266.383i | −0.184001 | − | 0.326050i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 26.3919 | + | 37.1973i | 0.0322246 | + | 0.0454179i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 390.814 | − | 676.909i | 0.476022 | − | 0.824494i | −0.523601 | − | 0.851964i | \(-0.675412\pi\) |
0.999623 | + | 0.0274699i | \(0.00874504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.6833 | 0.0287767 | 0.0143884 | − | 0.999896i | \(-0.495420\pi\) | ||||
0.0143884 | + | 0.999896i | \(0.495420\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 286.736 | + | 261.110i | 0.347559 | + | 0.316498i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 215.842 | − | 124.616i | 0.260994 | − | 0.150685i | −0.363794 | − | 0.931479i | \(-0.618519\pi\) |
0.624788 | + | 0.780794i | \(0.285185\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1194.32i | − | 1.44068i | −0.693622 | − | 0.720339i | \(-0.743986\pi\) | ||
0.693622 | − | 0.720339i | \(-0.256014\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 109.021 | − | 499.096i | 0.131192 | − | 0.600597i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 893.487 | + | 1547.57i | 1.07261 | + | 1.85782i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −848.685 | + | 489.989i | −1.01639 | + | 0.586813i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 365.053 | − | 155.214i | 0.436144 | − | 0.185440i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 545.157i | 0.649770i | 0.945754 | + | 0.324885i | \(0.105326\pi\) | ||||
−0.945754 | + | 0.324885i | \(0.894674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −304.292 | − | 527.049i | −0.361822 | − | 0.626694i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 446.495 | + | 1400.90i | 0.529650 | + | 1.66181i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −346.636 | − | 600.391i | −0.410220 | − | 0.710522i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1701.58 | 2.00895 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 279.940 | − | 1281.56i | 0.329729 | − | 1.50950i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 668.574i | − | 0.785634i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 888.831 | 1.04201 | 0.521003 | − | 0.853555i | \(-0.325558\pi\) | ||||
0.521003 | + | 0.853555i | \(0.325558\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −635.255 | − | 299.014i | −0.742989 | − | 0.349724i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 181.233i | 0.211474i | 0.994394 | + | 0.105737i | \(0.0337202\pi\) | ||||
−0.994394 | + | 0.105737i | \(0.966280\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1255.94 | 1.46210 | 0.731048 | − | 0.682326i | \(-0.239032\pi\) | ||||
0.731048 | + | 0.682326i | \(0.239032\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 270.644 | + | 849.160i | 0.314336 | + | 0.986248i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 267.394i | 0.309843i | 0.987927 | + | 0.154921i | \(0.0495124\pi\) | ||||
−0.987927 | + | 0.154921i | \(0.950488\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −503.383 | + | 290.628i | −0.581945 | + | 0.335986i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 41.7319 | − | 191.049i | 0.0481336 | − | 0.220356i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1661.97 | − | 959.537i | 1.91251 | − | 1.10419i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.5119 | −0.0201056 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1293.24 | + | 121.250i | −1.48138 | + | 0.138888i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 883.045 | + | 1529.48i | 1.00919 | + | 1.74797i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1082.85 | + | 625.186i | −1.23472 | + | 0.712869i | −0.968011 | − | 0.250907i | \(-0.919271\pi\) |
−0.266714 | + | 0.963776i | \(0.585938\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −244.981 | − | 768.643i | −0.278705 | − | 0.874452i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 596.782 | 0.677392 | 0.338696 | − | 0.940896i | \(-0.390014\pi\) | ||||
0.338696 | + | 0.940896i | \(0.390014\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 438.181 | + | 758.951i | 0.496241 | + | 0.859514i | 0.999991 | − | 0.00433543i | \(-0.00138001\pi\) |
−0.503750 | + | 0.863850i | \(0.668047\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −259.757 | − | 815.002i | −0.293511 | − | 0.920907i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1133.01i | − | 1.27735i | −0.769478 | − | 0.638673i | \(-0.779484\pi\) | ||
0.769478 | − | 0.638673i | \(-0.220516\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2575.97 | − | 1487.24i | −2.89760 | − | 1.67293i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 838.878 | + | 974.860i | 0.941501 | + | 1.09412i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −816.410 | − | 8.01481i | −0.914233 | − | 0.00897515i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −901.544 | + | 520.507i | −1.00731 | + | 0.581572i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.7355 | + | 16.1817i | −0.0164276 | + | 0.0180398i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 111.990 | + | 193.972i | 0.124572 | + | 0.215765i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 305.544i | − | 0.339116i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −133.765 | + | 612.378i | −0.148134 | + | 0.678160i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 821.460 | + | 474.270i | 0.907691 | + | 0.524056i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 410.807i | − | 0.452930i | −0.974019 | − | 0.226465i | \(-0.927283\pi\) | ||
0.974019 | − | 0.226465i | \(-0.0727168\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1487.64 | + | 682.473i | 1.63657 | + | 0.750796i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 822.448 | − | 474.840i | 0.902797 | − | 0.521230i | 0.0246902 | − | 0.999695i | \(-0.492140\pi\) |
0.878107 | + | 0.478465i | \(0.158807\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1033.68 | + | 1790.39i | −1.13218 | + | 1.96100i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 692.971 | + | 631.040i | 0.757345 | + | 0.689661i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 418.791 | − | 725.367i | 0.456697 | − | 0.791022i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 943.523 | 1.02668 | 0.513342 | − | 0.858184i | \(-0.328407\pi\) | ||||
0.513342 | + | 0.858184i | \(0.328407\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −233.986 | − | 734.143i | −0.254056 | − | 0.797115i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.57693 | + | 7.92747i | −0.00495875 | + | 0.00858881i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 252.304 | + | 145.668i | 0.272761 | + | 0.157478i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −533.907 | + | 1163.80i | −0.575952 | + | 1.25545i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −162.170 | −0.174564 | −0.0872819 | − | 0.996184i | \(-0.527818\pi\) | ||||
−0.0872819 | + | 0.996184i | \(0.527818\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2269.37 | + | 22.2787i | 2.43757 | + | 0.0239299i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −443.926 | + | 141.488i | −0.475804 | + | 0.151648i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 487.659 | + | 844.649i | 0.521560 | + | 0.903368i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −118.230 | − | 204.780i | −0.126179 | − | 0.218548i | 0.796014 | − | 0.605278i | \(-0.206938\pi\) |
−0.922193 | + | 0.386730i | \(0.873605\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 474.077 | − | 151.098i | 0.504874 | − | 0.160913i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 193.356i | − | 0.205479i | −0.994708 | − | 0.102740i | \(-0.967239\pi\) | ||
0.994708 | − | 0.102740i | \(-0.0327608\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −370.373 | + | 213.835i | −0.392760 | + | 0.226760i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 562.980 | + | 1324.10i | 0.595746 | + | 1.40116i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 409.213 | 0.432115 | 0.216058 | − | 0.976381i | \(-0.430680\pi\) | ||||
0.216058 | + | 0.976381i | \(0.430680\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.3730 | + | 12.9170i | 0.0235753 | + | 0.0136112i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 253.085 | + | 794.070i | 0.266126 | + | 0.834984i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1046.85 | − | 604.399i | −1.09848 | − | 0.634207i | −0.162658 | − | 0.986683i | \(-0.552007\pi\) |
−0.935821 | + | 0.352476i | \(0.885340\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −554.598 | + | 960.593i | −0.580731 | + | 1.00586i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −488.935 | + | 536.920i | −0.510904 | + | 0.561045i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1284.50 | −1.33941 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −372.575 | − | 645.319i | −0.387695 | − | 0.671507i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −68.1042 | + | 6.38519i | −0.0707209 | + | 0.00663052i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −88.9184 | − | 51.3371i | −0.0921434 | − | 0.0531990i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −589.929 | − | 1021.79i | −0.610061 | − | 1.05666i | −0.991230 | − | 0.132151i | \(-0.957812\pi\) |
0.381169 | − | 0.924505i | \(-0.375522\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 624.832 | + | 580.312i | 0.644821 | + | 0.598877i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 927.828 | + | 535.682i | 0.955538 | + | 0.551680i | 0.894797 | − | 0.446473i | \(-0.147320\pi\) |
0.0607413 | + | 0.998154i | \(0.480654\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −802.947 | − | 1390.74i | −0.825228 | − | 1.42934i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.89603 | − | 9.08646i | −0.00297029 | − | 0.00931945i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 489.309 | + | 282.503i | 0.500828 | + | 0.289153i | 0.729055 | − | 0.684455i | \(-0.239960\pi\) |
−0.228228 | + | 0.973608i | \(0.573293\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1802.48 | + | 1040.66i | 1.84115 | + | 1.06299i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 211.240 | − | 460.457i | 0.215331 | − | 0.469375i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 425.809i | 0.433173i | 0.976263 | + | 0.216586i | \(0.0694923\pi\) | ||||
−0.976263 | + | 0.216586i | \(0.930508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −500.783 | − | 867.382i | −0.508409 | − | 0.880591i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1237.06 | + | 1126.51i | 1.25336 | + | 1.14134i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −300.782 | −0.304127 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −618.826 | − | 357.279i | −0.624446 | − | 0.360524i | 0.154152 | − | 0.988047i | \(-0.450735\pi\) |
−0.778598 | + | 0.627523i | \(0.784069\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 782.141 | + | 170.848i | 0.787655 | + | 0.172052i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −354.417 | + | 613.869i | −0.356198 | + | 0.616954i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 204.374 | − | 353.986i | 0.204989 | − | 0.355051i | −0.745140 | − | 0.666908i | \(-0.767618\pi\) |
0.950129 | + | 0.311857i | \(0.100951\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 771.960 | + | 580.990i | 0.772733 | + | 0.581572i |
(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 | 684.3.s.a.445.10 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.s.a.901.29 | 80 | |||
9.2 | odd | 6 | 2052.3.bl.a.1585.12 | 80 | |||
9.7 | even | 3 | 684.3.bl.a.673.4 | yes | 80 | ||
19.12 | odd | 6 | 684.3.bl.a.373.4 | yes | 80 | ||
57.50 | even | 6 | 2052.3.bl.a.145.12 | 80 | |||
171.88 | odd | 6 | inner | 684.3.s.a.601.10 | yes | 80 | |
171.164 | even | 6 | 2052.3.s.a.829.29 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.s.a.445.10 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.s.a.601.10 | yes | 80 | 171.88 | odd | 6 | inner | |
684.3.bl.a.373.4 | yes | 80 | 19.12 | odd | 6 | ||
684.3.bl.a.673.4 | yes | 80 | 9.7 | even | 3 | ||
2052.3.s.a.829.29 | 80 | 171.164 | even | 6 | |||
2052.3.s.a.901.29 | 80 | 3.2 | odd | 2 | |||
2052.3.bl.a.145.12 | 80 | 57.50 | even | 6 | |||
2052.3.bl.a.1585.12 | 80 | 9.2 | odd | 6 |