Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [57,3,Mod(10,57)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(57, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 17]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("57.10");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 57 = 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 57.k (of order \(18\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.55313750685\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 40.1 | ||
Character | \(\chi\) | \(=\) | 57.40 |
Dual form | 57.3.k.b.10.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/57\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(40\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.75842 | − | 0.662712i | −1.87921 | − | 0.331356i | −0.887601 | − | 0.460613i | \(-0.847630\pi\) |
−0.991611 | + | 0.129257i | \(0.958741\pi\) | |||||||
\(3\) | −1.11334 | + | 1.32683i | −0.371114 | + | 0.442276i | ||||
\(4\) | 9.92780 | + | 3.61342i | 2.48195 | + | 0.903356i | ||||
\(5\) | −0.758325 | + | 0.276008i | −0.151665 | + | 0.0552015i | −0.416737 | − | 0.909027i | \(-0.636826\pi\) |
0.265072 | + | 0.964229i | \(0.414604\pi\) | |||||||
\(6\) | 5.06371 | − | 4.24896i | 0.843952 | − | 0.708160i | ||||
\(7\) | −5.10471 | − | 8.84162i | −0.729245 | − | 1.26309i | −0.957203 | − | 0.289418i | \(-0.906538\pi\) |
0.227958 | − | 0.973671i | \(-0.426795\pi\) | |||||||
\(8\) | −21.6978 | − | 12.5272i | −2.71222 | − | 1.56590i | ||||
\(9\) | −0.520945 | − | 2.95442i | −0.0578827 | − | 0.328269i | ||||
\(10\) | 3.03302 | − | 0.534803i | 0.303302 | − | 0.0534803i | ||||
\(11\) | 7.18408 | − | 12.4432i | 0.653098 | − | 1.13120i | −0.329269 | − | 0.944236i | \(-0.606802\pi\) |
0.982367 | − | 0.186963i | \(-0.0598643\pi\) | |||||||
\(12\) | −15.8474 | + | 9.14951i | −1.32062 | + | 0.762459i | ||||
\(13\) | −2.56999 | − | 3.06280i | −0.197692 | − | 0.235600i | 0.658087 | − | 0.752942i | \(-0.271366\pi\) |
−0.855779 | + | 0.517342i | \(0.826921\pi\) | |||||||
\(14\) | 13.3262 | + | 36.6135i | 0.951874 | + | 2.61525i | ||||
\(15\) | 0.478059 | − | 1.31346i | 0.0318706 | − | 0.0875638i | ||||
\(16\) | 40.8747 | + | 34.2980i | 2.55467 | + | 2.14362i | ||||
\(17\) | 2.00780 | − | 11.3868i | 0.118106 | − | 0.669812i | −0.867059 | − | 0.498205i | \(-0.833993\pi\) |
0.985165 | − | 0.171607i | \(-0.0548960\pi\) | |||||||
\(18\) | 11.4492i | 0.636067i | ||||||||
\(19\) | −13.0262 | − | 13.8318i | −0.685590 | − | 0.727988i | ||||
\(20\) | −8.52583 | −0.426291 | ||||||||
\(21\) | 17.4146 | + | 3.07066i | 0.829267 | + | 0.146222i | ||||
\(22\) | −35.2470 | + | 42.0058i | −1.60214 | + | 1.90935i | ||||
\(23\) | 15.8782 | + | 5.77919i | 0.690357 | + | 0.251269i | 0.663288 | − | 0.748364i | \(-0.269160\pi\) |
0.0270687 | + | 0.999634i | \(0.491383\pi\) | |||||||
\(24\) | 40.7785 | − | 14.8422i | 1.69911 | − | 0.618424i | ||||
\(25\) | −18.6522 | + | 15.6511i | −0.746089 | + | 0.626043i | ||||
\(26\) | 7.62937 | + | 13.2145i | 0.293437 | + | 0.508248i | ||||
\(27\) | 4.50000 | + | 2.59808i | 0.166667 | + | 0.0962250i | ||||
\(28\) | −18.7300 | − | 106.223i | −0.668930 | − | 3.79369i | ||||
\(29\) | −34.6065 | + | 6.10206i | −1.19333 | + | 0.210416i | −0.734812 | − | 0.678271i | \(-0.762730\pi\) |
−0.458515 | + | 0.888687i | \(0.651619\pi\) | |||||||
\(30\) | −2.66719 | + | 4.61971i | −0.0889064 | + | 0.153990i | ||||
\(31\) | 32.6597 | − | 18.8561i | 1.05354 | − | 0.608261i | 0.129901 | − | 0.991527i | \(-0.458534\pi\) |
0.923638 | + | 0.383266i | \(0.125201\pi\) | |||||||
\(32\) | −66.4762 | − | 79.2232i | −2.07738 | − | 2.47573i | ||||
\(33\) | 8.51164 | + | 23.3855i | 0.257928 | + | 0.708653i | ||||
\(34\) | −15.0923 | + | 41.4658i | −0.443892 | + | 1.21958i | ||||
\(35\) | 6.31139 | + | 5.29588i | 0.180325 | + | 0.151311i | ||||
\(36\) | 5.50375 | − | 31.2133i | 0.152882 | − | 0.867036i | ||||
\(37\) | − | 11.2648i | − | 0.304453i | −0.988346 | − | 0.152227i | \(-0.951356\pi\) | ||
0.988346 | − | 0.152227i | \(-0.0486443\pi\) | |||||||
\(38\) | 39.7915 | + | 60.6183i | 1.04715 | + | 1.59522i | ||||
\(39\) | 6.92508 | 0.177566 | ||||||||
\(40\) | 19.9116 | + | 3.51095i | 0.497790 | + | 0.0877738i | ||||
\(41\) | −24.1933 | + | 28.8324i | −0.590080 | + | 0.703230i | −0.975621 | − | 0.219460i | \(-0.929570\pi\) |
0.385541 | + | 0.922691i | \(0.374015\pi\) | |||||||
\(42\) | −63.4165 | − | 23.0817i | −1.50992 | − | 0.549565i | ||||
\(43\) | −3.41774 | + | 1.24396i | −0.0794824 | + | 0.0289292i | −0.381455 | − | 0.924387i | \(-0.624577\pi\) |
0.301973 | + | 0.953316i | \(0.402355\pi\) | |||||||
\(44\) | 116.285 | − | 97.5743i | 2.64283 | − | 2.21760i | ||||
\(45\) | 1.21049 | + | 2.09663i | 0.0268997 | + | 0.0465917i | ||||
\(46\) | −55.8471 | − | 32.2433i | −1.21407 | − | 0.700942i | ||||
\(47\) | 1.47054 | + | 8.33987i | 0.0312882 | + | 0.177444i | 0.996447 | − | 0.0842200i | \(-0.0268399\pi\) |
−0.965159 | + | 0.261664i | \(0.915729\pi\) | |||||||
\(48\) | −91.0150 | + | 16.0484i | −1.89615 | + | 0.334342i | ||||
\(49\) | −27.6162 | + | 47.8327i | −0.563596 | + | 0.976177i | ||||
\(50\) | 80.4752 | − | 46.4624i | 1.60950 | − | 0.929247i | ||||
\(51\) | 12.8730 | + | 15.3414i | 0.252411 | + | 0.300812i | ||||
\(52\) | −14.4472 | − | 39.6933i | −0.277830 | − | 0.763333i | ||||
\(53\) | 13.6946 | − | 37.6257i | 0.258389 | − | 0.709918i | −0.740878 | − | 0.671640i | \(-0.765590\pi\) |
0.999267 | − | 0.0382786i | \(-0.0121874\pi\) | |||||||
\(54\) | −15.1911 | − | 12.7469i | −0.281317 | − | 0.236053i | ||||
\(55\) | −2.01345 | + | 11.4188i | −0.0366082 | + | 0.207615i | ||||
\(56\) | 255.792i | 4.56771i | ||||||||
\(57\) | 32.8550 | − | 1.88406i | 0.576403 | − | 0.0330537i | ||||
\(58\) | 134.110 | 2.31224 | ||||||||
\(59\) | 28.3041 | + | 4.99078i | 0.479731 | + | 0.0845895i | 0.408284 | − | 0.912855i | \(-0.366127\pi\) |
0.0714468 | + | 0.997444i | \(0.477238\pi\) | |||||||
\(60\) | 9.49215 | − | 11.3123i | 0.158202 | − | 0.188538i | ||||
\(61\) | 7.10306 | + | 2.58530i | 0.116444 | + | 0.0423820i | 0.399585 | − | 0.916696i | \(-0.369154\pi\) |
−0.283141 | + | 0.959078i | \(0.591377\pi\) | |||||||
\(62\) | −135.245 | + | 49.2253i | −2.18138 | + | 0.793956i | ||||
\(63\) | −23.4626 | + | 19.6875i | −0.372423 | + | 0.312500i | ||||
\(64\) | 90.6271 | + | 156.971i | 1.41605 | + | 2.45267i | ||||
\(65\) | 2.79424 | + | 1.61326i | 0.0429884 | + | 0.0248193i | ||||
\(66\) | −16.4925 | − | 93.5335i | −0.249886 | − | 1.41717i | ||||
\(67\) | −63.7908 | + | 11.2480i | −0.952102 | + | 0.167881i | −0.628063 | − | 0.778163i | \(-0.716152\pi\) |
−0.324039 | + | 0.946044i | \(0.605041\pi\) | |||||||
\(68\) | 61.0784 | − | 105.791i | 0.898211 | − | 1.55575i | ||||
\(69\) | −25.3458 | + | 14.6334i | −0.367331 | + | 0.212079i | ||||
\(70\) | −20.2112 | − | 24.0868i | −0.288732 | − | 0.344097i | ||||
\(71\) | −39.3311 | − | 108.061i | −0.553959 | − | 1.52199i | −0.828259 | − | 0.560346i | \(-0.810668\pi\) |
0.274299 | − | 0.961644i | \(-0.411554\pi\) | |||||||
\(72\) | −25.7074 | + | 70.6305i | −0.357047 | + | 0.980979i | ||||
\(73\) | 80.3264 | + | 67.4019i | 1.10036 | + | 0.923313i | 0.997449 | − | 0.0713770i | \(-0.0227394\pi\) |
0.102913 | + | 0.994690i | \(0.467184\pi\) | |||||||
\(74\) | −7.46529 | + | 42.3378i | −0.100882 | + | 0.572132i | ||||
\(75\) | − | 42.1733i | − | 0.562311i | ||||||
\(76\) | −79.3415 | − | 184.388i | −1.04397 | − | 2.42616i | ||||
\(77\) | −146.691 | −1.90507 | ||||||||
\(78\) | −26.0274 | − | 4.58933i | −0.333685 | − | 0.0588376i | ||||
\(79\) | 83.3614 | − | 99.3463i | 1.05521 | − | 1.25755i | 0.0900337 | − | 0.995939i | \(-0.471303\pi\) |
0.965174 | − | 0.261609i | \(-0.0842530\pi\) | |||||||
\(80\) | −40.4628 | − | 14.7273i | −0.505785 | − | 0.184091i | ||||
\(81\) | −8.45723 | + | 3.07818i | −0.104410 | + | 0.0380022i | ||||
\(82\) | 110.036 | − | 92.3314i | 1.34191 | − | 1.12599i | ||||
\(83\) | −11.0696 | − | 19.1731i | −0.133368 | − | 0.231001i | 0.791605 | − | 0.611034i | \(-0.209246\pi\) |
−0.924973 | + | 0.380033i | \(0.875913\pi\) | |||||||
\(84\) | 161.793 | + | 93.4112i | 1.92611 | + | 1.11204i | ||||
\(85\) | 1.62028 | + | 9.18906i | 0.0190621 | + | 0.108107i | ||||
\(86\) | 13.6697 | − | 2.41034i | 0.158950 | − | 0.0280272i | ||||
\(87\) | 30.4324 | − | 52.7105i | 0.349798 | − | 0.605868i | ||||
\(88\) | −311.757 | + | 179.993i | −3.54270 | + | 2.04538i | ||||
\(89\) | 46.0553 | + | 54.8865i | 0.517475 | + | 0.616702i | 0.959982 | − | 0.280063i | \(-0.0903553\pi\) |
−0.442507 | + | 0.896765i | \(0.645911\pi\) | |||||||
\(90\) | −3.16007 | − | 8.68222i | −0.0351119 | − | 0.0964691i | ||||
\(91\) | −13.9610 | + | 38.3576i | −0.153418 | + | 0.421512i | ||||
\(92\) | 136.753 | + | 114.749i | 1.48644 | + | 1.24727i | ||||
\(93\) | −11.3426 | + | 64.3271i | −0.121963 | + | 0.691689i | ||||
\(94\) | − | 32.3193i | − | 0.343822i | ||||||
\(95\) | 13.6958 | + | 6.89364i | 0.144166 | + | 0.0725646i | ||||
\(96\) | 179.126 | 1.86590 | ||||||||
\(97\) | 77.6822 | + | 13.6975i | 0.800847 | + | 0.141211i | 0.559070 | − | 0.829121i | \(-0.311158\pi\) |
0.241778 | + | 0.970332i | \(0.422270\pi\) | |||||||
\(98\) | 135.493 | − | 161.474i | 1.38258 | − | 1.64769i | ||||
\(99\) | −40.5049 | − | 14.7426i | −0.409141 | − | 0.148915i | ||||
\(100\) | −241.730 | + | 87.9824i | −2.41730 | + | 0.879824i | ||||
\(101\) | 7.27595 | − | 6.10525i | 0.0720391 | − | 0.0604480i | −0.606057 | − | 0.795421i | \(-0.707250\pi\) |
0.678096 | + | 0.734973i | \(0.262805\pi\) | |||||||
\(102\) | −38.2151 | − | 66.1905i | −0.374658 | − | 0.648927i | ||||
\(103\) | 9.77043 | + | 5.64096i | 0.0948586 | + | 0.0547666i | 0.546679 | − | 0.837342i | \(-0.315892\pi\) |
−0.451820 | + | 0.892109i | \(0.649225\pi\) | |||||||
\(104\) | 17.3948 | + | 98.6508i | 0.167258 | + | 0.948566i | ||||
\(105\) | −14.0534 | + | 2.47800i | −0.133842 | + | 0.0236000i | ||||
\(106\) | −76.4052 | + | 132.338i | −0.720803 | + | 1.24847i | ||||
\(107\) | 59.0157 | − | 34.0727i | 0.551548 | − | 0.318437i | −0.198198 | − | 0.980162i | \(-0.563509\pi\) |
0.749746 | + | 0.661726i | \(0.230176\pi\) | |||||||
\(108\) | 35.2871 | + | 42.0536i | 0.326733 | + | 0.389385i | ||||
\(109\) | 25.6718 | + | 70.5327i | 0.235521 | + | 0.647089i | 0.999997 | + | 0.00243677i | \(0.000775650\pi\) |
−0.764476 | + | 0.644652i | \(0.777002\pi\) | |||||||
\(110\) | 15.1348 | − | 41.5825i | 0.137589 | − | 0.378023i | ||||
\(111\) | 14.9464 | + | 12.5415i | 0.134652 | + | 0.112987i | ||||
\(112\) | 94.5960 | − | 536.480i | 0.844607 | − | 4.79000i | ||||
\(113\) | − | 52.4802i | − | 0.464427i | −0.972665 | − | 0.232213i | \(-0.925403\pi\) | ||
0.972665 | − | 0.232213i | \(-0.0745968\pi\) | |||||||
\(114\) | −124.732 | − | 14.6923i | −1.09414 | − | 0.128880i | ||||
\(115\) | −13.6359 | −0.118573 | ||||||||
\(116\) | −365.615 | − | 64.4679i | −3.15186 | − | 0.555757i | ||||
\(117\) | −7.70998 | + | 9.18839i | −0.0658972 | + | 0.0785333i | ||||
\(118\) | −103.071 | − | 37.5149i | −0.873487 | − | 0.317923i | ||||
\(119\) | −110.927 | + | 40.3742i | −0.932160 | + | 0.339279i | ||||
\(120\) | −26.8268 | + | 22.5104i | −0.223557 | + | 0.187586i | ||||
\(121\) | −42.7219 | − | 73.9965i | −0.353074 | − | 0.611541i | ||||
\(122\) | −24.9830 | − | 14.4239i | −0.204779 | − | 0.118229i | ||||
\(123\) | −11.3203 | − | 64.2007i | −0.0920350 | − | 0.521957i | ||||
\(124\) | 392.374 | − | 69.1861i | 3.16431 | − | 0.557953i | ||||
\(125\) | 19.9120 | − | 34.4887i | 0.159296 | − | 0.275909i | ||||
\(126\) | 101.230 | − | 58.4450i | 0.803410 | − | 0.463849i | ||||
\(127\) | 85.8326 | + | 102.291i | 0.675847 | + | 0.805443i | 0.989567 | − | 0.144072i | \(-0.0460198\pi\) |
−0.313720 | + | 0.949516i | \(0.601575\pi\) | |||||||
\(128\) | −95.1039 | − | 261.296i | −0.742999 | − | 2.04137i | ||||
\(129\) | 2.15460 | − | 5.91970i | 0.0167023 | − | 0.0458892i | ||||
\(130\) | −9.43283 | − | 7.91508i | −0.0725602 | − | 0.0608853i | ||||
\(131\) | −37.0892 | + | 210.344i | −0.283124 | + | 1.60568i | 0.428787 | + | 0.903406i | \(0.358941\pi\) |
−0.711911 | + | 0.702270i | \(0.752170\pi\) | |||||||
\(132\) | 262.923i | 1.99184i | ||||||||
\(133\) | −55.8002 | + | 185.780i | −0.419551 | + | 1.39684i | ||||
\(134\) | 247.207 | 1.84483 | ||||||||
\(135\) | −4.12955 | − | 0.728151i | −0.0305893 | − | 0.00539371i | ||||
\(136\) | −186.210 | + | 221.916i | −1.36919 | + | 1.63174i | ||||
\(137\) | 48.0864 | + | 17.5020i | 0.350995 | + | 0.127752i | 0.511500 | − | 0.859283i | \(-0.329090\pi\) |
−0.160505 | + | 0.987035i | \(0.551312\pi\) | |||||||
\(138\) | 104.958 | − | 38.2017i | 0.760567 | − | 0.276824i | ||||
\(139\) | 54.4335 | − | 45.6751i | 0.391608 | − | 0.328598i | −0.425631 | − | 0.904897i | \(-0.639948\pi\) |
0.817239 | + | 0.576299i | \(0.195503\pi\) | |||||||
\(140\) | 43.5219 | + | 75.3821i | 0.310871 | + | 0.538444i | ||||
\(141\) | −12.7028 | − | 7.33396i | −0.0900907 | − | 0.0520139i | ||||
\(142\) | 76.2095 | + | 432.205i | 0.536687 | + | 3.04370i | ||||
\(143\) | −56.5740 | + | 9.97552i | −0.395622 | + | 0.0697589i | ||||
\(144\) | 80.0373 | − | 138.629i | 0.555814 | − | 0.962699i | ||||
\(145\) | 24.5587 | − | 14.1790i | 0.169371 | − | 0.0977862i | ||||
\(146\) | −257.233 | − | 306.558i | −1.76187 | − | 2.09971i | ||||
\(147\) | −32.7195 | − | 89.8960i | −0.222581 | − | 0.611538i | ||||
\(148\) | 40.7044 | − | 111.834i | 0.275029 | − | 0.755637i | ||||
\(149\) | −51.7136 | − | 43.3928i | −0.347071 | − | 0.291227i | 0.452542 | − | 0.891743i | \(-0.350517\pi\) |
−0.799613 | + | 0.600516i | \(0.794962\pi\) | |||||||
\(150\) | −27.9487 | + | 158.505i | −0.186325 | + | 1.05670i | ||||
\(151\) | − | 252.846i | − | 1.67448i | −0.546839 | − | 0.837238i | \(-0.684169\pi\) | ||
0.546839 | − | 0.837238i | \(-0.315831\pi\) | |||||||
\(152\) | 109.366 | + | 463.301i | 0.719515 | + | 3.04803i | ||||
\(153\) | −34.6874 | −0.226715 | ||||||||
\(154\) | 551.326 | + | 97.2136i | 3.58004 | + | 0.631257i | ||||
\(155\) | −19.5623 | + | 23.3134i | −0.126208 | + | 0.150409i | ||||
\(156\) | 68.7508 | + | 25.0232i | 0.440710 | + | 0.160405i | ||||
\(157\) | −14.2543 | + | 5.18816i | −0.0907920 | + | 0.0330456i | −0.387017 | − | 0.922073i | \(-0.626494\pi\) |
0.296225 | + | 0.955118i | \(0.404272\pi\) | |||||||
\(158\) | −379.145 | + | 318.141i | −2.39965 | + | 2.01355i | ||||
\(159\) | 34.6760 | + | 60.0606i | 0.218088 | + | 0.377740i | ||||
\(160\) | 72.2767 | + | 41.7290i | 0.451730 | + | 0.260806i | ||||
\(161\) | −29.9562 | − | 169.890i | −0.186064 | − | 1.05522i | ||||
\(162\) | 33.8258 | − | 5.96440i | 0.208801 | − | 0.0368173i | ||||
\(163\) | −62.6267 | + | 108.473i | −0.384213 | + | 0.665476i | −0.991660 | − | 0.128884i | \(-0.958860\pi\) |
0.607447 | + | 0.794360i | \(0.292194\pi\) | |||||||
\(164\) | −344.370 | + | 198.822i | −2.09982 | + | 1.21233i | ||||
\(165\) | −12.9092 | − | 15.3846i | −0.0782374 | − | 0.0932397i | ||||
\(166\) | 28.8980 | + | 79.3965i | 0.174084 | + | 0.478292i | ||||
\(167\) | 58.9012 | − | 161.830i | 0.352702 | − | 0.969040i | −0.628797 | − | 0.777570i | \(-0.716452\pi\) |
0.981498 | − | 0.191470i | \(-0.0613255\pi\) | |||||||
\(168\) | −339.392 | − | 284.783i | −2.02019 | − | 1.69514i | ||||
\(169\) | 26.5707 | − | 150.690i | 0.157223 | − | 0.891656i | ||||
\(170\) | − | 35.6102i | − | 0.209472i | ||||||
\(171\) | −34.0790 | + | 45.6905i | −0.199292 | + | 0.267196i | ||||
\(172\) | −38.4256 | −0.223405 | ||||||||
\(173\) | 266.529 | + | 46.9963i | 1.54063 | + | 0.271655i | 0.878503 | − | 0.477737i | \(-0.158543\pi\) |
0.662127 | + | 0.749392i | \(0.269654\pi\) | |||||||
\(174\) | −149.310 | + | 177.941i | −0.858103 | + | 1.02265i | ||||
\(175\) | 233.595 | + | 85.0217i | 1.33483 | + | 0.485839i | ||||
\(176\) | 720.423 | − | 262.213i | 4.09331 | − | 1.48984i | ||||
\(177\) | −38.1340 | + | 31.9983i | −0.215447 | + | 0.180781i | ||||
\(178\) | −136.721 | − | 236.808i | −0.768097 | − | 1.33038i | ||||
\(179\) | 75.1193 | + | 43.3701i | 0.419661 | + | 0.242291i | 0.694932 | − | 0.719075i | \(-0.255434\pi\) |
−0.275271 | + | 0.961367i | \(0.588768\pi\) | |||||||
\(180\) | 4.44148 | + | 25.1889i | 0.0246749 | + | 0.139938i | ||||
\(181\) | −150.643 | + | 26.5624i | −0.832281 | + | 0.146754i | −0.573524 | − | 0.819189i | \(-0.694424\pi\) |
−0.258757 | + | 0.965942i | \(0.583313\pi\) | |||||||
\(182\) | 77.8915 | − | 134.912i | 0.427975 | − | 0.741275i | ||||
\(183\) | −11.3384 | + | 6.54621i | −0.0619583 | + | 0.0357717i | ||||
\(184\) | −272.125 | − | 324.306i | −1.47894 | − | 1.76253i | ||||
\(185\) | 3.10916 | + | 8.54235i | 0.0168063 | + | 0.0461749i | ||||
\(186\) | 85.2606 | − | 234.252i | 0.458391 | − | 1.25942i | ||||
\(187\) | −127.264 | − | 106.787i | −0.680556 | − | 0.571054i | ||||
\(188\) | −15.5362 | + | 88.1102i | −0.0826394 | + | 0.468671i | ||||
\(189\) | − | 53.0497i | − | 0.280686i | ||||||
\(190\) | −46.9060 | − | 34.9856i | −0.246874 | − | 0.184135i | ||||
\(191\) | 190.773 | 0.998814 | 0.499407 | − | 0.866368i | \(-0.333551\pi\) | ||||
0.499407 | + | 0.866368i | \(0.333551\pi\) | |||||||
\(192\) | −309.172 | − | 54.5154i | −1.61027 | − | 0.283934i | ||||
\(193\) | −27.7430 | + | 33.0628i | −0.143746 | + | 0.171310i | −0.833114 | − | 0.553102i | \(-0.813444\pi\) |
0.689368 | + | 0.724412i | \(0.257888\pi\) | |||||||
\(194\) | −282.885 | − | 102.962i | −1.45817 | − | 0.530731i | ||||
\(195\) | −5.25146 | + | 1.91138i | −0.0269306 | + | 0.00980193i | ||||
\(196\) | −447.008 | + | 375.084i | −2.28065 | + | 1.91369i | ||||
\(197\) | −128.366 | − | 222.336i | −0.651602 | − | 1.12861i | −0.982734 | − | 0.185023i | \(-0.940764\pi\) |
0.331132 | − | 0.943584i | \(-0.392569\pi\) | |||||||
\(198\) | 142.465 | + | 82.2520i | 0.719519 | + | 0.415414i | ||||
\(199\) | −52.5660 | − | 298.117i | −0.264151 | − | 1.49807i | −0.771442 | − | 0.636299i | \(-0.780464\pi\) |
0.507291 | − | 0.861775i | \(-0.330647\pi\) | |||||||
\(200\) | 600.777 | − | 105.933i | 3.00389 | − | 0.529666i | ||||
\(201\) | 56.0967 | − | 97.1623i | 0.279088 | − | 0.483395i | ||||
\(202\) | −31.3921 | + | 18.1243i | −0.155407 | + | 0.0897240i | ||||
\(203\) | 230.608 | + | 274.828i | 1.13600 | + | 1.35383i | ||||
\(204\) | 72.3652 | + | 198.822i | 0.354731 | + | 0.974616i | ||||
\(205\) | 10.3884 | − | 28.5419i | 0.0506751 | − | 0.139229i | ||||
\(206\) | −32.9831 | − | 27.6761i | −0.160112 | − | 0.134350i | ||||
\(207\) | 8.80252 | − | 49.9216i | 0.0425243 | − | 0.241167i | ||||
\(208\) | − | 213.337i | − | 1.02566i | ||||||
\(209\) | −265.693 | + | 62.7190i | −1.27126 | + | 0.300091i | ||||
\(210\) | 54.4610 | 0.259338 | ||||||||
\(211\) | −275.737 | − | 48.6199i | −1.30681 | − | 0.230426i | −0.523484 | − | 0.852035i | \(-0.675368\pi\) |
−0.783328 | + | 0.621609i | \(0.786479\pi\) | |||||||
\(212\) | 271.915 | − | 324.055i | 1.28262 | − | 1.52856i | ||||
\(213\) | 187.168 | + | 68.1235i | 0.878722 | + | 0.319829i | ||||
\(214\) | −244.386 | + | 88.9493i | −1.14199 | + | 0.415651i | ||||
\(215\) | 2.24842 | − | 1.88665i | 0.0104578 | − | 0.00877510i | ||||
\(216\) | −65.0934 | − | 112.745i | −0.301358 | − | 0.521968i | ||||
\(217\) | −333.437 | − | 192.510i | −1.53658 | − | 0.887143i | ||||
\(218\) | −49.7427 | − | 282.105i | −0.228178 | − | 1.29406i | ||||
\(219\) | −178.861 | + | 31.5381i | −0.816719 | + | 0.144010i | ||||
\(220\) | −61.2502 | + | 106.088i | −0.278410 | + | 0.482220i | ||||
\(221\) | −40.0355 | + | 23.1145i | −0.181156 | + | 0.104591i | ||||
\(222\) | −47.8635 | − | 57.0415i | −0.215601 | − | 0.256944i | ||||
\(223\) | −40.2404 | − | 110.560i | −0.180450 | − | 0.495783i | 0.816181 | − | 0.577796i | \(-0.196087\pi\) |
−0.996631 | + | 0.0820132i | \(0.973865\pi\) | |||||||
\(224\) | −361.120 | + | 992.169i | −1.61214 | + | 4.42933i | ||||
\(225\) | 55.9567 | + | 46.9533i | 0.248696 | + | 0.208681i | ||||
\(226\) | −34.7793 | + | 197.243i | −0.153891 | + | 0.872757i | ||||
\(227\) | 156.884i | 0.691120i | 0.938397 | + | 0.345560i | \(0.112311\pi\) | ||||
−0.938397 | + | 0.345560i | \(0.887689\pi\) | |||||||
\(228\) | 332.986 | + | 100.014i | 1.46046 | + | 0.438659i | ||||
\(229\) | 42.7264 | 0.186578 | 0.0932890 | − | 0.995639i | \(-0.470262\pi\) | ||||
0.0932890 | + | 0.995639i | \(0.470262\pi\) | |||||||
\(230\) | 51.2496 | + | 9.03669i | 0.222824 | + | 0.0392900i | ||||
\(231\) | 163.317 | − | 194.633i | 0.706998 | − | 0.842568i | ||||
\(232\) | 827.327 | + | 301.122i | 3.56606 | + | 1.29794i | ||||
\(233\) | 307.843 | − | 112.046i | 1.32122 | − | 0.480883i | 0.417368 | − | 0.908737i | \(-0.362953\pi\) |
0.903848 | + | 0.427854i | \(0.140730\pi\) | |||||||
\(234\) | 35.0666 | − | 29.4244i | 0.149857 | − | 0.125745i | ||||
\(235\) | −3.41702 | − | 5.91845i | −0.0145405 | − | 0.0251849i | ||||
\(236\) | 262.964 | + | 151.822i | 1.11425 | + | 0.643314i | ||||
\(237\) | 39.0057 | + | 221.212i | 0.164581 | + | 0.933386i | ||||
\(238\) | 443.667 | − | 78.2305i | 1.86415 | − | 0.328700i | ||||
\(239\) | −103.866 | + | 179.901i | −0.434585 | + | 0.752724i | −0.997262 | − | 0.0739536i | \(-0.976438\pi\) |
0.562677 | + | 0.826677i | \(0.309772\pi\) | |||||||
\(240\) | 64.5895 | − | 37.2908i | 0.269123 | − | 0.155378i | ||||
\(241\) | 259.894 | + | 309.729i | 1.07840 | + | 1.28518i | 0.956212 | + | 0.292677i | \(0.0945459\pi\) |
0.122186 | + | 0.992507i | \(0.461010\pi\) | |||||||
\(242\) | 111.529 | + | 306.423i | 0.460862 | + | 1.26621i | ||||
\(243\) | 5.33157 | − | 14.6484i | 0.0219406 | − | 0.0602813i | ||||
\(244\) | 61.1759 | + | 51.3327i | 0.250721 | + | 0.210380i | ||||
\(245\) | 7.73987 | − | 43.8950i | 0.0315913 | − | 0.179163i | ||||
\(246\) | 248.795i | 1.01136i | ||||||||
\(247\) | −8.88666 | + | 75.4442i | −0.0359784 | + | 0.305442i | ||||
\(248\) | −944.859 | −3.80992 | ||||||||
\(249\) | 37.7636 | + | 6.65874i | 0.151661 | + | 0.0267419i | ||||
\(250\) | −97.6939 | + | 116.427i | −0.390776 | + | 0.465708i | ||||
\(251\) | 77.1487 | + | 28.0798i | 0.307365 | + | 0.111872i | 0.491098 | − | 0.871104i | \(-0.336596\pi\) |
−0.183732 | + | 0.982976i | \(0.558818\pi\) | |||||||
\(252\) | −304.071 | + | 110.673i | −1.20663 | + | 0.439178i | ||||
\(253\) | 185.982 | − | 156.057i | 0.735106 | − | 0.616827i | ||||
\(254\) | −254.806 | − | 441.336i | −1.00317 | − | 1.73754i | ||||
\(255\) | −13.9962 | − | 8.08073i | −0.0548872 | − | 0.0316891i | ||||
\(256\) | 58.3791 | + | 331.084i | 0.228043 | + | 1.29330i | ||||
\(257\) | −356.286 | + | 62.8228i | −1.38633 | + | 0.244447i | −0.816513 | − | 0.577327i | \(-0.804096\pi\) |
−0.569814 | + | 0.821774i | \(0.692985\pi\) | |||||||
\(258\) | −12.0209 | + | 20.8209i | −0.0465928 | + | 0.0807011i | ||||
\(259\) | −99.5988 | + | 57.5034i | −0.384551 | + | 0.222021i | ||||
\(260\) | 21.9113 | + | 26.1129i | 0.0842743 | + | 0.100434i | ||||
\(261\) | 36.0561 | + | 99.0634i | 0.138146 | + | 0.379553i | ||||
\(262\) | 278.794 | − | 765.981i | 1.06410 | − | 2.92359i | ||||
\(263\) | 98.1615 | + | 82.3673i | 0.373238 | + | 0.313184i | 0.810041 | − | 0.586374i | \(-0.199445\pi\) |
−0.436803 | + | 0.899557i | \(0.643889\pi\) | |||||||
\(264\) | 108.272 | − | 614.042i | 0.410122 | − | 2.32592i | ||||
\(265\) | 32.3123i | 0.121933i | ||||||||
\(266\) | 332.840 | − | 661.261i | 1.25128 | − | 2.48594i | ||||
\(267\) | −124.100 | −0.464795 | ||||||||
\(268\) | −673.946 | − | 118.835i | −2.51472 | − | 0.443414i | ||||
\(269\) | −52.5563 | + | 62.6341i | −0.195377 | + | 0.232841i | −0.854834 | − | 0.518901i | \(-0.826341\pi\) |
0.659458 | + | 0.751741i | \(0.270786\pi\) | |||||||
\(270\) | 15.0380 | + | 5.47340i | 0.0556965 | + | 0.0202719i | ||||
\(271\) | −485.007 | + | 176.528i | −1.78969 | + | 0.651395i | −0.790448 | + | 0.612530i | \(0.790152\pi\) |
−0.999244 | + | 0.0388650i | \(0.987626\pi\) | |||||||
\(272\) | 472.613 | − | 396.569i | 1.73755 | − | 1.45797i | ||||
\(273\) | −35.3506 | − | 61.2290i | −0.129489 | − | 0.224282i | ||||
\(274\) | −169.130 | − | 97.6474i | −0.617264 | − | 0.356377i | ||||
\(275\) | 60.7502 | + | 344.532i | 0.220910 | + | 1.25284i | ||||
\(276\) | −304.505 | + | 53.6925i | −1.10328 | + | 0.194538i | ||||
\(277\) | 111.488 | − | 193.104i | 0.402485 | − | 0.697125i | −0.591540 | − | 0.806276i | \(-0.701480\pi\) |
0.994025 | + | 0.109151i | \(0.0348131\pi\) | |||||||
\(278\) | −234.854 | + | 135.593i | −0.844797 | + | 0.487744i | ||||
\(279\) | −72.7228 | − | 86.6677i | −0.260655 | − | 0.310637i | ||||
\(280\) | −70.6005 | − | 193.973i | −0.252145 | − | 0.692761i | ||||
\(281\) | −4.76197 | + | 13.0834i | −0.0169465 | + | 0.0465601i | −0.947877 | − | 0.318635i | \(-0.896776\pi\) |
0.930931 | + | 0.365195i | \(0.118998\pi\) | |||||||
\(282\) | 42.8822 | + | 35.9824i | 0.152064 | + | 0.127597i | ||||
\(283\) | −65.7446 | + | 372.856i | −0.232313 | + | 1.31751i | 0.615885 | + | 0.787836i | \(0.288798\pi\) |
−0.848199 | + | 0.529678i | \(0.822313\pi\) | |||||||
\(284\) | − | 1214.93i | − | 4.27792i | ||||||
\(285\) | −24.3947 | + | 10.4970i | −0.0855956 | + | 0.0368314i | ||||
\(286\) | 219.240 | 0.766573 | ||||||||
\(287\) | 378.425 | + | 66.7266i | 1.31856 | + | 0.232497i | ||||
\(288\) | −199.428 | + | 237.670i | −0.692460 | + | 0.825242i | ||||
\(289\) | 145.943 | + | 53.1190i | 0.504994 | + | 0.183803i | ||||
\(290\) | −101.699 | + | 37.0153i | −0.350685 | + | 0.127639i | ||||
\(291\) | −104.661 | + | 87.8209i | −0.359660 | + | 0.301790i | ||||
\(292\) | 553.913 | + | 959.405i | 1.89696 | + | 3.28563i | ||||
\(293\) | 280.800 | + | 162.120i | 0.958363 | + | 0.553311i | 0.895669 | − | 0.444722i | \(-0.146697\pi\) |
0.0626942 | + | 0.998033i | \(0.480031\pi\) | |||||||
\(294\) | 63.3985 | + | 359.551i | 0.215641 | + | 1.22296i | ||||
\(295\) | −22.8412 | + | 4.02752i | −0.0774278 | + | 0.0136526i | ||||
\(296\) | −141.116 | + | 244.421i | −0.476744 | + | 0.825745i | ||||
\(297\) | 64.6567 | − | 37.3296i | 0.217699 | − | 0.125689i | ||||
\(298\) | 165.605 | + | 197.360i | 0.555720 | + | 0.662282i | ||||
\(299\) | −23.1064 | − | 63.4842i | −0.0772788 | − | 0.212322i | ||||
\(300\) | 152.390 | − | 418.688i | 0.507966 | − | 1.39563i | ||||
\(301\) | 28.4452 | + | 23.8683i | 0.0945023 | + | 0.0792968i | ||||
\(302\) | −167.564 | + | 950.302i | −0.554847 | + | 3.14670i | ||||
\(303\) | 16.4512i | 0.0542942i | ||||||||
\(304\) | −58.0411 | − | 1012.14i | −0.190925 | − | 3.32942i | ||||
\(305\) | −6.09999 | −0.0200000 | ||||||||
\(306\) | 130.370 | + | 22.9877i | 0.426046 | + | 0.0751233i | ||||
\(307\) | 75.2631 | − | 89.6951i | 0.245157 | − | 0.292166i | −0.629408 | − | 0.777075i | \(-0.716703\pi\) |
0.874565 | + | 0.484908i | \(0.161147\pi\) | |||||||
\(308\) | −1456.31 | − | 530.055i | −4.72829 | − | 1.72096i | ||||
\(309\) | −18.3624 | + | 6.68337i | −0.0594253 | + | 0.0216290i | ||||
\(310\) | 88.9733 | − | 74.6575i | 0.287011 | − | 0.240831i | ||||
\(311\) | 272.485 | + | 471.957i | 0.876156 | + | 1.51755i | 0.855526 | + | 0.517759i | \(0.173234\pi\) |
0.0206297 | + | 0.999787i | \(0.493433\pi\) | |||||||
\(312\) | −150.259 | − | 86.7521i | −0.481599 | − | 0.278052i | ||||
\(313\) | −17.0790 | − | 96.8599i | −0.0545656 | − | 0.309457i | 0.945294 | − | 0.326220i | \(-0.105775\pi\) |
−0.999859 | + | 0.0167632i | \(0.994664\pi\) | |||||||
\(314\) | 57.0121 | − | 10.0528i | 0.181567 | − | 0.0320152i | ||||
\(315\) | 12.3584 | − | 21.4054i | 0.0392330 | − | 0.0679536i | ||||
\(316\) | 1186.57 | − | 685.069i | 3.75498 | − | 2.16794i | ||||
\(317\) | −267.936 | − | 319.314i | −0.845225 | − | 1.00730i | −0.999813 | − | 0.0193206i | \(-0.993850\pi\) |
0.154589 | − | 0.987979i | \(-0.450595\pi\) | |||||||
\(318\) | −90.5243 | − | 248.713i | −0.284668 | − | 0.782118i | ||||
\(319\) | −172.687 | + | 474.453i | −0.541337 | + | 1.48731i | ||||
\(320\) | −112.050 | − | 94.0210i | −0.350156 | − | 0.293816i | ||||
\(321\) | −20.4959 | + | 116.238i | −0.0638502 | + | 0.362113i | ||||
\(322\) | 658.372i | 2.04463i | ||||||||
\(323\) | −183.654 | + | 120.555i | −0.568587 | + | 0.373237i | ||||
\(324\) | −95.0845 | −0.293471 | ||||||||
\(325\) | 95.8722 | + | 16.9049i | 0.294991 | + | 0.0520149i | ||||
\(326\) | 307.264 | − | 366.183i | 0.942526 | − | 1.12326i | ||||
\(327\) | −122.166 | − | 44.4649i | −0.373597 | − | 0.135978i | ||||
\(328\) | 886.132 | − | 322.526i | 2.70162 | − | 0.983310i | ||||
\(329\) | 66.2313 | − | 55.5746i | 0.201311 | − | 0.168920i | ||||
\(330\) | 38.3226 | + | 66.3767i | 0.116129 | + | 0.201142i | ||||
\(331\) | 20.8715 | + | 12.0502i | 0.0630559 | + | 0.0364053i | 0.531197 | − | 0.847249i | \(-0.321743\pi\) |
−0.468141 | + | 0.883654i | \(0.655076\pi\) | |||||||
\(332\) | −40.6161 | − | 230.345i | −0.122338 | − | 0.693812i | ||||
\(333\) | −33.2809 | + | 5.86832i | −0.0999426 | + | 0.0176226i | ||||
\(334\) | −328.622 | + | 569.190i | −0.983898 | + | 1.70416i | ||||
\(335\) | 45.2696 | − | 26.1364i | 0.135133 | − | 0.0780192i | ||||
\(336\) | 606.500 | + | 722.798i | 1.80506 | + | 2.15119i | ||||
\(337\) | −155.682 | − | 427.733i | −0.461965 | − | 1.26924i | −0.924005 | − | 0.382379i | \(-0.875105\pi\) |
0.462041 | − | 0.886859i | \(-0.347117\pi\) | |||||||
\(338\) | −199.728 | + | 548.747i | −0.590910 | + | 1.62351i | ||||
\(339\) | 69.6322 | + | 58.4284i | 0.205405 | + | 0.172355i | ||||
\(340\) | −17.1182 | + | 97.0819i | −0.0503475 | + | 0.285535i | ||||
\(341\) | − | 541.855i | − | 1.58902i | ||||||
\(342\) | 158.363 | − | 149.140i | 0.463049 | − | 0.436081i | ||||
\(343\) | 63.6294 | 0.185509 | ||||||||
\(344\) | 89.7408 | + | 15.8237i | 0.260874 | + | 0.0459992i | ||||
\(345\) | 15.1814 | − | 18.0925i | 0.0440042 | − | 0.0524421i | ||||
\(346\) | −970.584 | − | 353.264i | −2.80516 | − | 1.02099i | ||||
\(347\) | −288.764 | + | 105.102i | −0.832174 | + | 0.302887i | −0.722751 | − | 0.691109i | \(-0.757123\pi\) |
−0.109423 | + | 0.993995i | \(0.534900\pi\) | |||||||
\(348\) | 492.592 | − | 413.334i | 1.41550 | − | 1.18774i | ||||
\(349\) | −23.7847 | − | 41.1963i | −0.0681510 | − | 0.118041i | 0.829936 | − | 0.557858i | \(-0.188377\pi\) |
−0.898087 | + | 0.439817i | \(0.855043\pi\) | |||||||
\(350\) | −821.605 | − | 474.354i | −2.34744 | − | 1.35530i | ||||
\(351\) | −3.60758 | − | 20.4596i | −0.0102780 | − | 0.0582895i | ||||
\(352\) | −1463.36 | + | 258.030i | −4.15727 | + | 0.733039i | ||||
\(353\) | 129.154 | − | 223.702i | 0.365877 | − | 0.633717i | −0.623040 | − | 0.782190i | \(-0.714103\pi\) |
0.988916 | + | 0.148473i | \(0.0474359\pi\) | |||||||
\(354\) | 164.530 | − | 94.9912i | 0.464773 | − | 0.268337i | ||||
\(355\) | 59.6515 | + | 71.0899i | 0.168032 | + | 0.200253i | ||||
\(356\) | 258.899 | + | 711.319i | 0.727244 | + | 1.99809i | ||||
\(357\) | 69.9301 | − | 192.131i | 0.195883 | − | 0.538183i | ||||
\(358\) | −253.588 | − | 212.786i | −0.708347 | − | 0.594374i | ||||
\(359\) | 79.5725 | − | 451.278i | 0.221650 | − | 1.25704i | −0.647336 | − | 0.762205i | \(-0.724117\pi\) |
0.868986 | − | 0.494837i | \(-0.164772\pi\) | |||||||
\(360\) | − | 60.6563i | − | 0.168490i | ||||||
\(361\) | −21.6358 | + | 360.351i | −0.0599328 | + | 0.998202i | ||||
\(362\) | 583.783 | 1.61266 | ||||||||
\(363\) | 145.745 | + | 25.6987i | 0.401500 | + | 0.0707954i | ||||
\(364\) | −277.204 | + | 330.359i | −0.761551 | + | 0.907581i | ||||
\(365\) | −79.5170 | − | 28.9418i | −0.217855 | − | 0.0792926i | ||||
\(366\) | 46.9527 | − | 17.0894i | 0.128286 | − | 0.0466923i | ||||
\(367\) | 552.155 | − | 463.313i | 1.50451 | − | 1.26243i | 0.630840 | − | 0.775913i | \(-0.282711\pi\) |
0.873670 | − | 0.486520i | \(-0.161734\pi\) | |||||||
\(368\) | 450.803 | + | 780.813i | 1.22501 | + | 2.12178i | ||||
\(369\) | 97.7866 | + | 56.4571i | 0.265004 | + | 0.153000i | ||||
\(370\) | −6.02443 | − | 34.1663i | −0.0162823 | − | 0.0923412i | ||||
\(371\) | −402.579 | + | 70.9856i | −1.08512 | + | 0.191336i | ||||
\(372\) | −345.048 | + | 597.641i | −0.927548 | + | 1.60656i | ||||
\(373\) | 143.915 | − | 83.0893i | 0.385831 | − | 0.222760i | −0.294521 | − | 0.955645i | \(-0.595160\pi\) |
0.680352 | + | 0.732885i | \(0.261827\pi\) | |||||||
\(374\) | 407.543 | + | 485.690i | 1.08969 | + | 1.29864i | ||||
\(375\) | 23.5916 | + | 64.8175i | 0.0629110 | + | 0.172847i | ||||
\(376\) | 72.5679 | − | 199.379i | 0.193000 | − | 0.530262i | ||||
\(377\) | 107.628 | + | 90.3104i | 0.285485 | + | 0.239550i | ||||
\(378\) | −35.1567 | + | 199.383i | −0.0930071 | + | 0.527469i | ||||
\(379\) | − | 200.874i | − | 0.530009i | −0.964247 | − | 0.265005i | \(-0.914626\pi\) | ||
0.964247 | − | 0.265005i | \(-0.0853735\pi\) | |||||||
\(380\) | 111.059 | + | 117.927i | 0.292261 | + | 0.310335i | ||||
\(381\) | −231.284 | −0.607044 | ||||||||
\(382\) | −717.008 | − | 126.428i | −1.87698 | − | 0.330963i | ||||
\(383\) | 197.571 | − | 235.455i | 0.515850 | − | 0.614766i | −0.443744 | − | 0.896153i | \(-0.646350\pi\) |
0.959594 | + | 0.281387i | \(0.0907946\pi\) | |||||||
\(384\) | 452.578 | + | 164.725i | 1.17859 | + | 0.428971i | ||||
\(385\) | 111.239 | − | 40.4877i | 0.288933 | − | 0.105163i | ||||
\(386\) | 126.181 | − | 105.878i | 0.326894 | − | 0.274296i | ||||
\(387\) | 5.45563 | + | 9.44942i | 0.0140972 | + | 0.0244171i | ||||
\(388\) | 721.718 | + | 416.684i | 1.86010 | + | 1.07393i | ||||
\(389\) | −73.4022 | − | 416.285i | −0.188695 | − | 1.07014i | −0.921116 | − | 0.389289i | \(-0.872721\pi\) |
0.732421 | − | 0.680852i | \(-0.238390\pi\) | |||||||
\(390\) | 21.0039 | − | 3.70356i | 0.0538562 | − | 0.00949630i | ||||
\(391\) | 97.6868 | − | 169.199i | 0.249838 | − | 0.432733i | ||||
\(392\) | 1198.42 | − | 691.909i | 3.05720 | − | 1.76507i | ||||
\(393\) | −237.797 | − | 283.395i | −0.605081 | − | 0.721107i | ||||
\(394\) | 335.108 | + | 920.701i | 0.850527 | + | 2.33681i | ||||
\(395\) | −35.7947 | + | 98.3451i | −0.0906195 | + | 0.248975i | ||||
\(396\) | −348.854 | − | 292.723i | −0.880943 | − | 0.739199i | ||||
\(397\) | −12.4364 | + | 70.5302i | −0.0313259 | + | 0.177658i | −0.996456 | − | 0.0841113i | \(-0.973195\pi\) |
0.965130 | + | 0.261769i | \(0.0843060\pi\) | |||||||
\(398\) | 1155.29i | 2.90273i | ||||||||
\(399\) | −184.373 | − | 280.874i | −0.462089 | − | 0.703944i | ||||
\(400\) | −1299.21 | −3.24801 | ||||||||
\(401\) | −85.4138 | − | 15.0608i | −0.213002 | − | 0.0375580i | 0.0661287 | − | 0.997811i | \(-0.478935\pi\) |
−0.279131 | + | 0.960253i | \(0.590046\pi\) | |||||||
\(402\) | −275.226 | + | 328.001i | −0.684641 | + | 0.815924i | ||||
\(403\) | −141.688 | − | 51.5701i | −0.351582 | − | 0.127965i | ||||
\(404\) | 94.2950 | − | 34.3206i | 0.233403 | − | 0.0849519i | ||||
\(405\) | 5.56373 | − | 4.66852i | 0.0137376 | − | 0.0115272i | ||||
\(406\) | −684.592 | − | 1185.75i | −1.68619 | − | 2.92056i | ||||
\(407\) | −140.170 | − | 80.9269i | −0.344397 | − | 0.198838i | ||||
\(408\) | −87.1297 | − | 494.137i | −0.213553 | − | 1.21112i | ||||
\(409\) | 560.747 | − | 98.8748i | 1.37102 | − | 0.241748i | 0.560838 | − | 0.827926i | \(-0.310479\pi\) |
0.810182 | + | 0.586178i | \(0.199368\pi\) | |||||||
\(410\) | −57.9590 | + | 100.388i | −0.141364 | + | 0.244849i | ||||
\(411\) | −76.7587 | + | 44.3166i | −0.186761 | + | 0.107826i | ||||
\(412\) | 76.6157 | + | 91.3070i | 0.185960 | + | 0.221619i | ||||
\(413\) | −100.358 | − | 275.731i | −0.242997 | − | 0.667629i | ||||
\(414\) | −66.1672 | + | 181.793i | −0.159824 | + | 0.439113i | ||||
\(415\) | 13.6863 | + | 11.4841i | 0.0329789 | + | 0.0276726i | ||||
\(416\) | −71.8014 | + | 407.206i | −0.172600 | + | 0.978861i | ||||
\(417\) | 123.076i | 0.295146i | ||||||||
\(418\) | 1040.15 | − | 59.6472i | 2.48840 | − | 0.142697i | ||||
\(419\) | −780.746 | −1.86336 | −0.931678 | − | 0.363286i | \(-0.881655\pi\) | ||||
−0.931678 | + | 0.363286i | \(0.881655\pi\) | |||||||
\(420\) | −148.474 | − | 26.1799i | −0.353509 | − | 0.0623332i | ||||
\(421\) | −155.537 | + | 185.362i | −0.369448 | + | 0.440290i | −0.918454 | − | 0.395528i | \(-0.870562\pi\) |
0.549007 | + | 0.835818i | \(0.315006\pi\) | |||||||
\(422\) | 1004.12 | + | 365.469i | 2.37942 | + | 0.866039i | ||||
\(423\) | 23.8734 | − | 8.68922i | 0.0564384 | − | 0.0205419i | ||||
\(424\) | −768.489 | + | 644.838i | −1.81247 | + | 1.52085i | ||||
\(425\) | 140.766 | + | 243.814i | 0.331214 | + | 0.573679i | ||||
\(426\) | −658.309 | − | 380.075i | −1.54533 | − | 0.892195i | ||||
\(427\) | −13.4008 | − | 75.9998i | −0.0313836 | − | 0.177985i | ||||
\(428\) | 709.014 | − | 125.018i | 1.65658 | − | 0.292099i | ||||
\(429\) | 49.7503 | − | 86.1701i | 0.115968 | − | 0.200863i | ||||
\(430\) | −9.70081 | + | 5.60076i | −0.0225600 | + | 0.0130250i | ||||
\(431\) | −360.584 | − | 429.727i | −0.836622 | − | 0.997047i | −0.999945 | − | 0.0104742i | \(-0.996666\pi\) |
0.163324 | − | 0.986573i | \(-0.447779\pi\) | |||||||
\(432\) | 94.8276 | + | 260.537i | 0.219508 | + | 0.603094i | ||||
\(433\) | −134.748 | + | 370.218i | −0.311197 | + | 0.855006i | 0.681219 | + | 0.732080i | \(0.261450\pi\) |
−0.992416 | + | 0.122926i | \(0.960772\pi\) | |||||||
\(434\) | 1125.62 | + | 944.507i | 2.59359 | + | 2.17628i | ||||
\(435\) | −8.52916 | + | 48.3713i | −0.0196073 | + | 0.111198i | ||||
\(436\) | 792.997i | 1.81880i | ||||||||
\(437\) | −126.896 | − | 294.905i | −0.290381 | − | 0.674839i | ||||
\(438\) | 693.138 | 1.58251 | ||||||||
\(439\) | 200.865 | + | 35.4179i | 0.457552 | + | 0.0806787i | 0.397673 | − | 0.917527i | \(-0.369818\pi\) |
0.0598781 | + | 0.998206i | \(0.480929\pi\) | |||||||
\(440\) | 186.734 | − | 222.541i | 0.424395 | − | 0.505774i | ||||
\(441\) | 155.704 | + | 56.6718i | 0.353071 | + | 0.128507i | ||||
\(442\) | 165.789 | − | 60.3421i | 0.375087 | − | 0.136521i | ||||
\(443\) | −498.811 | + | 418.552i | −1.12598 | + | 0.944813i | −0.998891 | − | 0.0470774i | \(-0.985009\pi\) |
−0.127093 | + | 0.991891i | \(0.540565\pi\) | |||||||
\(444\) | 103.067 | + | 178.517i | 0.232133 | + | 0.402066i | ||||
\(445\) | −50.0739 | − | 28.9102i | −0.112526 | − | 0.0649667i | ||||
\(446\) | 77.9714 | + | 442.198i | 0.174824 | + | 0.991475i | ||||
\(447\) | 115.150 | − | 20.3040i | 0.257606 | − | 0.0454228i | ||||
\(448\) | 925.251 | − | 1602.58i | 2.06529 | − | 3.57719i | ||||
\(449\) | 55.4448 | − | 32.0111i | 0.123485 | − | 0.0712942i | −0.436985 | − | 0.899469i | \(-0.643954\pi\) |
0.560470 | + | 0.828175i | \(0.310620\pi\) | |||||||
\(450\) | −179.193 | − | 213.553i | −0.398206 | − | 0.474563i | ||||
\(451\) | 184.961 | + | 508.176i | 0.410113 | + | 1.12678i | ||||
\(452\) | 189.633 | − | 521.013i | 0.419543 | − | 1.15268i | ||||
\(453\) | 335.483 | + | 281.504i | 0.740581 | + | 0.621421i | ||||
\(454\) | 103.969 | − | 589.637i | 0.229007 | − | 1.29876i | ||||
\(455\) | − | 32.9409i | − | 0.0723975i | ||||||
\(456\) | −736.483 | − | 370.702i | −1.61509 | − | 0.812943i | ||||
\(457\) | −144.971 | −0.317222 | −0.158611 | − | 0.987341i | \(-0.550702\pi\) | ||||
−0.158611 | + | 0.987341i | \(0.550702\pi\) | |||||||
\(458\) | −160.584 | − | 28.3152i | −0.350620 | − | 0.0618237i | ||||
\(459\) | 38.6189 | − | 46.0242i | 0.0841370 | − | 0.100271i | ||||
\(460\) | −135.375 | − | 49.2724i | −0.294293 | − | 0.107114i | ||||
\(461\) | 250.938 | − | 91.3340i | 0.544335 | − | 0.198122i | −0.0551930 | − | 0.998476i | \(-0.517577\pi\) |
0.599528 | + | 0.800354i | \(0.295355\pi\) | |||||||
\(462\) | −742.799 | + | 623.282i | −1.60779 | + | 1.34910i | ||||
\(463\) | −55.8383 | − | 96.7148i | −0.120601 | − | 0.208887i | 0.799404 | − | 0.600794i | \(-0.205149\pi\) |
−0.920005 | + | 0.391907i | \(0.871816\pi\) | |||||||
\(464\) | −1623.82 | − | 937.513i | −3.49961 | − | 2.02050i | ||||
\(465\) | −9.15340 | − | 51.9115i | −0.0196847 | − | 0.111638i | ||||
\(466\) | −1231.26 | + | 217.104i | −2.64219 | + | 0.465889i | ||||
\(467\) | 306.297 | − | 530.523i | 0.655883 | − | 1.13602i | −0.325789 | − | 0.945443i | \(-0.605630\pi\) |
0.981672 | − | 0.190580i | \(-0.0610369\pi\) | |||||||
\(468\) | −109.745 | + | 63.3611i | −0.234497 | + | 0.135387i | ||||
\(469\) | 425.085 | + | 506.596i | 0.906364 | + | 1.08016i | ||||
\(470\) | 8.92038 | + | 24.5085i | 0.0189795 | + | 0.0521458i | ||||
\(471\) | 8.98615 | − | 24.6892i | 0.0190789 | − | 0.0524188i | ||||
\(472\) | −551.617 | − | 462.861i | −1.16868 | − | 0.980638i | ||||
\(473\) | −9.07454 | + | 51.4643i | −0.0191851 | + | 0.108804i | ||||
\(474\) | − | 857.260i | − | 1.80857i | ||||||
\(475\) | 459.450 | + | 54.1191i | 0.967263 | + | 0.113935i | ||||
\(476\) | −1247.15 | −2.62006 | ||||||||
\(477\) | −118.296 | − | 20.8588i | −0.248001 | − | 0.0437292i | ||||
\(478\) | 509.594 | − | 607.311i | 1.06610 | − | 1.27053i | ||||
\(479\) | 726.353 | + | 264.371i | 1.51639 | + | 0.551922i | 0.960245 | − | 0.279160i | \(-0.0900561\pi\) |
0.556149 | + | 0.831082i | \(0.312278\pi\) | |||||||
\(480\) | −135.836 | + | 49.4402i | −0.282991 | + | 0.103000i | ||||
\(481\) | −34.5017 | + | 28.9504i | −0.0717291 | + | 0.0601879i | ||||
\(482\) | −771.530 | − | 1336.33i | −1.60068 | − | 2.77247i | ||||
\(483\) | 258.767 | + | 149.399i | 0.535749 | + | 0.309315i | ||||
\(484\) | −156.754 | − | 888.994i | −0.323871 | − | 1.83677i | ||||
\(485\) | −62.6889 | + | 11.0537i | −0.129256 | + | 0.0227912i | ||||
\(486\) | −29.7459 | + | 51.5215i | −0.0612056 | + | 0.106011i | ||||
\(487\) | −333.969 | + | 192.817i | −0.685769 | + | 0.395929i | −0.802025 | − | 0.597290i | \(-0.796244\pi\) |
0.116256 | + | 0.993219i | \(0.462911\pi\) | |||||||
\(488\) | −121.734 | − | 145.077i | −0.249455 | − | 0.297289i | ||||
\(489\) | −74.1996 | − | 203.862i | −0.151737 | − | 0.416895i | ||||
\(490\) | −58.1794 | + | 159.847i | −0.118734 | + | 0.326218i | ||||
\(491\) | −562.897 | − | 472.327i | −1.14643 | − | 0.961969i | −0.146800 | − | 0.989166i | \(-0.546897\pi\) |
−0.999630 | + | 0.0271973i | \(0.991342\pi\) | |||||||
\(492\) | 119.598 | − | 678.276i | 0.243086 | − | 1.37861i | ||||
\(493\) | 406.309i | 0.824156i | ||||||||
\(494\) | 83.3976 | − | 277.662i | 0.168821 | − | 0.562069i | ||||
\(495\) | 34.7850 | 0.0702727 | ||||||||
\(496\) | 1981.68 | + | 349.424i | 3.99533 | + | 0.704485i | ||||
\(497\) | −754.664 | + | 899.373i | −1.51844 | + | 1.80960i | ||||
\(498\) | −137.519 | − | 50.0527i | −0.276142 | − | 0.100507i | ||||
\(499\) | 667.960 | − | 243.118i | 1.33860 | − | 0.487209i | 0.429227 | − | 0.903197i | \(-0.358786\pi\) |
0.909370 | + | 0.415987i | \(0.136564\pi\) | |||||||
\(500\) | 322.305 | − | 270.446i | 0.644609 | − | 0.540892i | ||||
\(501\) | 149.143 | + | 258.323i | 0.297691 | + | 0.515615i | ||||
\(502\) | −271.349 | − | 156.663i | −0.540535 | − | 0.312078i | ||||
\(503\) | 48.3936 | + | 274.454i | 0.0962099 | + | 0.545634i | 0.994370 | + | 0.105965i | \(0.0337931\pi\) |
−0.898160 | + | 0.439669i | \(0.855096\pi\) | |||||||
\(504\) | 755.717 | − | 133.253i | 1.49944 | − | 0.264391i | ||||
\(505\) | −3.83244 | + | 6.63798i | −0.00758899 | + | 0.0131445i | ||||
\(506\) | −802.419 | + | 463.277i | −1.58581 | + | 0.915567i | ||||
\(507\) | 170.357 | + | 203.024i | 0.336010 | + | 0.400441i | ||||
\(508\) | 482.507 | + | 1325.68i | 0.949816 | + | 2.60960i | ||||
\(509\) | 14.6160 | − | 40.1572i | 0.0287152 | − | 0.0788943i | −0.924507 | − | 0.381166i | \(-0.875523\pi\) |
0.953222 | + | 0.302271i | \(0.0977449\pi\) | |||||||
\(510\) | 47.2486 | + | 39.6463i | 0.0926443 | + | 0.0777378i | ||||
\(511\) | 185.899 | − | 1054.28i | 0.363794 | − | 2.06318i | ||||
\(512\) | − | 170.784i | − | 0.333562i | ||||||
\(513\) | −22.6819 | − | 96.0861i | −0.0442143 | − | 0.187302i | ||||
\(514\) | 1380.71 | 2.68620 | ||||||||
\(515\) | −8.96611 | − | 1.58097i | −0.0174099 | − | 0.00306984i | ||||
\(516\) | 42.7808 | − | 50.9841i | 0.0829084 | − | 0.0988064i | ||||
\(517\) | 114.339 | + | 41.6160i | 0.221159 | + | 0.0804952i | ||||
\(518\) | 412.443 | − | 150.117i | 0.796222 | − | 0.289801i | ||||
\(519\) | −359.094 | + | 301.315i | −0.691895 | + | 0.580569i | ||||
\(520\) | −40.4193 | − | 70.0083i | −0.0777294 | − | 0.134631i | ||||
\(521\) | 530.648 | + | 306.370i | 1.01852 | + | 0.588041i | 0.913674 | − | 0.406447i | \(-0.133233\pi\) |
0.104843 | + | 0.994489i | \(0.466566\pi\) | |||||||
\(522\) | −69.8638 | − | 396.217i | −0.133839 | − | 0.759036i | ||||
\(523\) | −614.198 | + | 108.300i | −1.17438 | + | 0.207074i | −0.726593 | − | 0.687068i | \(-0.758897\pi\) |
−0.447783 | + | 0.894142i | \(0.647786\pi\) | |||||||
\(524\) | −1128.27 | + | 1954.23i | −2.15320 | + | 3.72944i | ||||
\(525\) | −372.880 | + | 215.283i | −0.710248 | + | 0.410062i | ||||
\(526\) | −314.347 | − | 374.624i | −0.597618 | − | 0.712213i | ||||
\(527\) | −149.137 | − | 409.749i | −0.282991 | − | 0.777513i | ||||
\(528\) | −454.166 | + | 1247.81i | −0.860162 | + | 2.36328i | ||||
\(529\) | −186.519 | − | 156.508i | −0.352588 | − | 0.295857i | ||||
\(530\) | 21.4137 | − | 121.443i | 0.0404033 | − | 0.229138i | ||||
\(531\) | − | 86.2223i | − | 0.162377i | ||||||
\(532\) | −1225.28 | + | 1642.76i | −2.30315 | + | 3.08789i | ||||
\(533\) | 150.484 | 0.282335 | ||||||||
\(534\) | 466.421 | + | 82.2426i | 0.873448 | + | 0.154012i | ||||
\(535\) | −35.3487 | + | 42.1270i | −0.0660724 | + | 0.0787420i | ||||
\(536\) | 1525.03 | + | 555.064i | 2.84520 | + | 1.03557i | ||||
\(537\) | −141.178 | + | 51.3846i | −0.262901 | + | 0.0956883i | ||||
\(538\) | 239.037 | − | 200.576i | 0.444307 | − | 0.372818i | ||||
\(539\) | 396.794 | + | 687.267i | 0.736167 | + | 1.27508i | ||||
\(540\) | −38.3662 | − | 22.1507i | −0.0710485 | − | 0.0410199i | ||||
\(541\) | 84.6062 | + | 479.826i | 0.156389 | + | 0.886924i | 0.957505 | + | 0.288415i | \(0.0931284\pi\) |
−0.801117 | + | 0.598508i | \(0.795760\pi\) | |||||||
\(542\) | 1939.85 | − | 342.047i | 3.57905 | − | 0.631084i | ||||
\(543\) | 132.473 | − | 229.450i | 0.243965 | − | 0.422560i | ||||
\(544\) | −1035.57 | + | 597.887i | −1.90362 | + | 1.09906i | ||||
\(545\) | −38.9351 | − | 46.4011i | −0.0714406 | − | 0.0851396i | ||||
\(546\) | 92.2853 | + | 253.552i | 0.169021 | + | 0.464380i | ||||
\(547\) | −311.420 | + | 855.619i | −0.569323 | + | 1.56420i | 0.236241 | + | 0.971695i | \(0.424085\pi\) |
−0.805564 | + | 0.592508i | \(0.798138\pi\) | |||||||
\(548\) | 414.150 | + | 347.513i | 0.755747 | + | 0.634147i | ||||
\(549\) | 3.93778 | − | 22.3322i | 0.00717263 | − | 0.0406780i | ||||
\(550\) | − | 1335.16i | − | 2.42756i | ||||||
\(551\) | 535.194 | + | 399.182i | 0.971313 | + | 0.724469i | ||||
\(552\) | 733.265 | 1.32838 | ||||||||
\(553\) | −1303.92 | − | 229.916i | −2.35790 | − | 0.415761i | ||||
\(554\) | −546.993 | + | 651.881i | −0.987352 | + | 1.17668i | ||||
\(555\) | −14.7958 | − | 5.38523i | −0.0266591 | − | 0.00970311i | ||||
\(556\) | 705.448 | − | 256.762i | 1.26879 | − | 0.461802i | ||||
\(557\) | −51.7400 | + | 43.4151i | −0.0928906 | + | 0.0779444i | −0.688050 | − | 0.725663i | \(-0.741533\pi\) |
0.595160 | + | 0.803607i | \(0.297089\pi\) | |||||||
\(558\) | 215.888 | + | 373.928i | 0.386895 | + | 0.670122i | ||||
\(559\) | 12.5936 | + | 7.27089i | 0.0225287 | + | 0.0130070i | ||||
\(560\) | 76.3382 | + | 432.936i | 0.136318 | + | 0.773099i | ||||
\(561\) | 283.376 | − | 49.9669i | 0.505127 | − | 0.0890675i | ||||
\(562\) | 26.5680 | − | 46.0171i | 0.0472740 | − | 0.0818810i | ||||
\(563\) | 750.115 | − | 433.079i | 1.33235 | − | 0.769235i | 0.346693 | − | 0.937978i | \(-0.387304\pi\) |
0.985660 | + | 0.168744i | \(0.0539711\pi\) | |||||||
\(564\) | −99.6100 | − | 118.711i | −0.176613 | − | 0.210480i | ||||
\(565\) | 14.4849 | + | 39.7971i | 0.0256371 | + | 0.0704373i | ||||
\(566\) | 494.193 | − | 1357.78i | 0.873132 | − | 2.39891i | ||||
\(567\) | 70.3879 | + | 59.0624i | 0.124141 | + | 0.104167i | ||||
\(568\) | −500.311 | + | 2837.40i | −0.880829 | + | 4.99543i | ||||
\(569\) | − | 84.8290i | − | 0.149084i | −0.997218 | − | 0.0745422i | \(-0.976250\pi\) | ||
0.997218 | − | 0.0745422i | \(-0.0237495\pi\) | |||||||
\(570\) | 98.6422 | − | 23.2854i | 0.173057 | − | 0.0408515i | ||||
\(571\) | 729.038 | 1.27677 | 0.638387 | − | 0.769715i | \(-0.279602\pi\) | ||||
0.638387 | + | 0.769715i | \(0.279602\pi\) | |||||||
\(572\) | −597.701 | − | 105.391i | −1.04493 | − | 0.184250i | ||||
\(573\) | −212.396 | + | 253.124i | −0.370673 | + | 0.441751i | ||||
\(574\) | −1378.06 | − | 501.574i | −2.40081 | − | 0.873822i | ||||
\(575\) | −386.615 | + | 140.716i | −0.672373 | + | 0.244724i | ||||
\(576\) | 416.546 | − | 349.524i | 0.723171 | − | 0.606812i | ||||
\(577\) | −344.596 | − | 596.857i | −0.597220 | − | 1.03441i | −0.993230 | − | 0.116168i | \(-0.962939\pi\) |
0.396010 | − | 0.918246i | \(-0.370395\pi\) | |||||||
\(578\) | −513.314 | − | 296.362i | −0.888086 | − | 0.512737i | ||||
\(579\) | −12.9812 | − | 73.6203i | −0.0224201 | − | 0.127151i | ||||
\(580\) | 295.049 | − | 52.0251i | 0.508705 | − | 0.0896984i | ||||
\(581\) | −113.014 | + | 195.746i | −0.194516 | + | 0.336912i | ||||
\(582\) | 451.560 | − | 260.708i | 0.775876 | − | 0.447952i | ||||
\(583\) | −369.800 | − | 440.710i | −0.634305 | − | 0.755935i | ||||
\(584\) | −898.548 | − | 2468.74i | −1.53861 | − | 4.22729i | ||||
\(585\) | 3.31060 | − | 9.09580i | 0.00565914 | − | 0.0155484i | ||||
\(586\) | −947.928 | − | 795.406i | −1.61762 | − | 1.35735i | ||||
\(587\) | 97.3221 | − | 551.941i | 0.165796 | − | 0.940275i | −0.782444 | − | 0.622721i | \(-0.786027\pi\) |
0.948240 | − | 0.317554i | \(-0.102862\pi\) | |||||||
\(588\) | − | 1010.70i | − | 1.71888i | ||||||
\(589\) | −686.246 | − | 206.118i | −1.16510 | − | 0.349946i | ||||
\(590\) | 88.5161 | 0.150027 | ||||||||
\(591\) | 437.916 | + | 77.2164i | 0.740974 | + | 0.130654i | ||||
\(592\) | 386.359 | − | 460.444i | 0.652633 | − | 0.777778i | ||||
\(593\) | −815.522 | − | 296.826i | −1.37525 | − | 0.500550i | −0.454514 | − | 0.890739i | \(-0.650187\pi\) |
−0.920734 | + | 0.390190i | \(0.872409\pi\) | |||||||
\(594\) | −267.746 | + | 97.4516i | −0.450751 | + | 0.164060i | ||||
\(595\) | 72.9752 | − | 61.2334i | 0.122647 | − | 0.102913i | ||||
\(596\) | −356.605 | − | 617.658i | −0.598331 | − | 1.03634i | ||||
\(597\) | 454.073 | + | 262.159i | 0.760592 | + | 0.439128i | ||||
\(598\) | 44.7718 | + | 253.913i | 0.0748692 | + | 0.424604i | ||||
\(599\) | 273.974 | − | 48.3090i | 0.457386 | − | 0.0806494i | 0.0597917 | − | 0.998211i | \(-0.480956\pi\) |
0.397594 | + | 0.917561i | \(0.369845\pi\) | |||||||
\(600\) | −528.315 | + | 915.068i | −0.880524 | + | 1.52511i | ||||
\(601\) | 351.932 | − | 203.188i | 0.585577 | − | 0.338083i | −0.177770 | − | 0.984072i | \(-0.556888\pi\) |
0.763347 | + | 0.645989i | \(0.223555\pi\) | |||||||
\(602\) | −91.0912 | − | 108.558i | −0.151314 | − | 0.180329i | ||||
\(603\) | 66.4630 | + | 182.605i | 0.110220 | + | 0.302828i | ||||
\(604\) | 913.639 | − | 2510.20i | 1.51265 | − | 4.15596i | ||||
\(605\) | 52.8207 | + | 44.3218i | 0.0873069 | + | 0.0732592i | ||||
\(606\) | 10.9024 | − | 61.8304i | 0.0179907 | − | 0.102030i | ||||
\(607\) | 533.407i | 0.878759i | 0.898302 | + | 0.439380i | \(0.144802\pi\) | ||||
−0.898302 | + | 0.439380i | \(0.855198\pi\) | |||||||
\(608\) | −229.865 | + | 1951.46i | −0.378067 | + | 3.20964i | ||||
\(609\) | −621.395 | −1.02035 | ||||||||
\(610\) | 22.9263 | + | 4.04253i | 0.0375842 | + | 0.00662710i | ||||
\(611\) | 21.7640 | − | 25.9374i | 0.0356204 | − | 0.0424507i | ||||
\(612\) | −344.369 | − | 125.340i | −0.562695 | − | 0.204804i | ||||
\(613\) | −59.4482 | + | 21.6374i | −0.0969790 | + | 0.0352975i | −0.390054 | − | 0.920792i | \(-0.627544\pi\) |
0.293075 | + | 0.956089i | \(0.405321\pi\) | |||||||
\(614\) | −342.313 | + | 287.234i | −0.557513 | + | 0.467809i | ||||
\(615\) | 26.3043 | + | 45.5605i | 0.0427713 | + | 0.0740820i | ||||
\(616\) | 3182.86 | + | 1837.63i | 5.16699 | + | 2.98316i | ||||
\(617\) | 151.412 | + | 858.698i | 0.245400 | + | 1.39173i | 0.819563 | + | 0.572989i | \(0.194216\pi\) |
−0.574163 | + | 0.818741i | \(0.694672\pi\) | |||||||
\(618\) | 73.4429 | − | 12.9500i | 0.118840 | − | 0.0209546i | ||||
\(619\) | −298.431 | + | 516.897i | −0.482117 | + | 0.835052i | −0.999789 | − | 0.0205274i | \(-0.993465\pi\) |
0.517672 | + | 0.855579i | \(0.326799\pi\) | |||||||
\(620\) | −278.451 | + | 160.764i | −0.449115 | + | 0.259297i | ||||
\(621\) | 56.4371 | + | 67.2591i | 0.0908810 | + | 0.108308i | ||||
\(622\) | −711.341 | − | 1954.39i | −1.14364 | − | 3.14211i | ||||
\(623\) | 250.187 | − | 687.383i | 0.401584 | − | 1.10334i | ||||
\(624\) | 283.061 | + | 237.516i | 0.453623 | + | 0.380635i | ||||
\(625\) | 100.122 | − | 567.822i | 0.160196 | − | 0.908515i | ||||
\(626\) | 375.359i | 0.599615i | ||||||||
\(627\) | 212.589 | − | 422.356i | 0.339057 | − | 0.673614i | ||||
\(628\) | −160.261 | −0.255193 | ||||||||
\(629\) | −128.270 | − | 22.6174i | −0.203926 | − | 0.0359577i | ||||
\(630\) | −60.6337 | + | 72.2604i | −0.0962439 | + | 0.114699i | ||||
\(631\) | 531.199 | + | 193.341i | 0.841837 | + | 0.306404i | 0.726708 | − | 0.686947i | \(-0.241050\pi\) |
0.115129 | + | 0.993351i | \(0.463272\pi\) | |||||||
\(632\) | −3053.29 | + | 1111.31i | −4.83116 | + | 1.75840i | ||||
\(633\) | 371.500 | − | 311.725i | 0.586888 | − | 0.492457i | ||||
\(634\) | 795.405 | + | 1377.68i | 1.25458 | + | 2.17300i | ||||
\(635\) | −93.3222 | − | 53.8796i | −0.146964 | − | 0.0848497i | ||||
\(636\) | 127.232 | + | 721.568i | 0.200050 | + | 1.13454i | ||||
\(637\) | 217.475 | − | 38.3468i | 0.341405 | − | 0.0601990i | ||||
\(638\) | 963.455 | − | 1668.75i | 1.51012 | − | 2.61560i | ||||
\(639\) | −298.770 | + | 172.495i | −0.467558 | + | 0.269945i | ||||
\(640\) | 144.239 | + | 171.898i | 0.225374 | + | 0.268590i | ||||
\(641\) | 235.695 | + | 647.566i | 0.367699 | + | 1.01024i | 0.976234 | + | 0.216717i | \(0.0695350\pi\) |
−0.608536 | + | 0.793526i | \(0.708243\pi\) | |||||||
\(642\) | 154.065 | − | 423.289i | 0.239976 | − | 0.659329i | ||||
\(643\) | −938.258 | − | 787.292i | −1.45919 | − | 1.22440i | −0.925513 | − | 0.378715i | \(-0.876366\pi\) |
−0.533676 | − | 0.845689i | \(-0.679190\pi\) | |||||||
\(644\) | 316.486 | − | 1794.88i | 0.491438 | − | 2.78708i | ||||
\(645\) | 5.08374i | 0.00788177i | ||||||||
\(646\) | 770.142 | − | 331.389i | 1.19217 | − | 0.512986i | ||||
\(647\) | −104.343 | −0.161271 | −0.0806357 | − | 0.996744i | \(-0.525695\pi\) | ||||
−0.0806357 | + | 0.996744i | \(0.525695\pi\) | |||||||
\(648\) | 222.064 | + | 39.1560i | 0.342692 | + | 0.0604259i | ||||
\(649\) | 265.440 | − | 316.339i | 0.408999 | − | 0.487426i | ||||
\(650\) | −349.125 | − | 127.071i | −0.537116 | − | 0.195494i | ||||
\(651\) | 626.657 | − | 228.084i | 0.962606 | − | 0.350360i | ||||
\(652\) | −1013.70 | + | 850.597i | −1.55476 | + | 1.30460i | ||||
\(653\) | 517.233 | + | 895.874i | 0.792087 | + | 1.37194i | 0.924672 | + | 0.380764i | \(0.124339\pi\) |
−0.132585 | + | 0.991172i | \(0.542328\pi\) | |||||||
\(654\) | 429.685 | + | 248.079i | 0.657011 | + | 0.379325i | ||||
\(655\) | −29.9307 | − | 169.746i | −0.0456958 | − | 0.259154i | ||||
\(656\) | −1977.79 | + | 348.738i | −3.01492 | + | 0.531612i | ||||
\(657\) | 157.288 | − | 272.431i | 0.239403 | − | 0.414659i | ||||
\(658\) | −285.755 | + | 164.981i | −0.434278 | + | 0.250731i | ||||
\(659\) | −486.845 | − | 580.199i | −0.738763 | − | 0.880424i | 0.257545 | − | 0.966266i | \(-0.417086\pi\) |
−0.996309 | + | 0.0858423i | \(0.972642\pi\) | |||||||
\(660\) | −72.5688 | − | 199.381i | −0.109953 | − | 0.302092i | ||||
\(661\) | −311.703 | + | 856.397i | −0.471563 | + | 1.29561i | 0.444932 | + | 0.895564i | \(0.353228\pi\) |
−0.916496 | + | 0.400045i | \(0.868995\pi\) | |||||||
\(662\) | −70.4582 | − | 59.1214i | −0.106432 | − | 0.0893073i | ||||
\(663\) | 13.9042 | − | 78.8545i | 0.0209716 | − | 0.118936i | ||||
\(664\) | 554.685i | 0.835369i | ||||||||
\(665\) | −8.96202 | − | 156.283i | −0.0134767 | − | 0.235012i | ||||
\(666\) | 128.973 | 0.193653 | ||||||||
\(667\) | −584.754 | − | 103.108i | −0.876692 | − | 0.154585i | ||||
\(668\) | 1169.52 | − | 1393.78i | 1.75077 | − | 2.08649i | ||||
\(669\) | 191.495 | + | 69.6985i | 0.286241 | + | 0.104183i | ||||
\(670\) | −187.463 | + | 68.2311i | −0.279796 | + | 0.101837i | ||||
\(671\) | 83.1983 | − | 69.8116i | 0.123991 | − | 0.104041i | ||||
\(672\) | −914.388 | − | 1583.77i | −1.36070 | − | 2.35680i | ||||
\(673\) | 39.6796 | + | 22.9090i | 0.0589593 | + | 0.0340402i | 0.529190 | − | 0.848503i | \(-0.322496\pi\) |
−0.470231 | + | 0.882544i | \(0.655829\pi\) | |||||||
\(674\) | 301.656 | + | 1710.78i | 0.447561 | + | 2.53824i | ||||
\(675\) | −124.598 | + | 21.9699i | −0.184589 | + | 0.0325481i | ||||
\(676\) | 808.294 | − | 1400.01i | 1.19570 | − | 2.07102i | ||||
\(677\) | −228.036 | + | 131.657i | −0.336834 | + | 0.194471i | −0.658871 | − | 0.752256i | \(-0.728966\pi\) |
0.322037 | + | 0.946727i | \(0.395632\pi\) | |||||||
\(678\) | −222.986 | − | 265.745i | −0.328888 | − | 0.391954i | ||||
\(679\) | −275.437 | − | 756.758i | −0.405652 | − | 1.11452i | ||||
\(680\) | 79.9570 | − | 219.680i | 0.117584 | − | 0.323059i | ||||
\(681\) | −208.158 | − | 174.666i | −0.305666 | − | 0.256484i | ||||
\(682\) | −359.093 | + | 2036.52i | −0.526530 | + | 2.98610i | ||||
\(683\) | − | 417.979i | − | 0.611975i | −0.952035 | − | 0.305988i | \(-0.901013\pi\) | ||
0.952035 | − | 0.305988i | \(-0.0989867\pi\) | |||||||
\(684\) | −503.428 | + | 330.464i | −0.736006 | + | 0.483135i | ||||
\(685\) | −41.2958 | −0.0602858 | ||||||||
\(686\) | −239.146 | − | 42.1680i | −0.348610 | − | 0.0614693i | ||||
\(687\) | −47.5690 | + | 56.6905i | −0.0692416 | + | 0.0825189i | ||||
\(688\) | −182.364 | − | 66.3752i | −0.265065 | − | 0.0964756i | ||||
\(689\) | −150.435 | + | 54.7538i | −0.218338 | + | 0.0794685i | ||||
\(690\) | −69.0484 | + | 57.9385i | −0.100070 | + | 0.0839689i | ||||
\(691\) | −192.965 | − | 334.225i | −0.279255 | − | 0.483684i | 0.691945 | − | 0.721950i | \(-0.256754\pi\) |
−0.971200 | + | 0.238267i | \(0.923421\pi\) | |||||||
\(692\) | 2476.23 | + | 1429.65i | 3.57836 | + | 2.06597i | ||||
\(693\) | 76.4177 | + | 433.386i | 0.110271 | + | 0.625377i | ||||
\(694\) | 1154.95 | − | 203.649i | 1.66419 | − | 0.293442i | ||||
\(695\) | −28.6716 | + | 49.6607i | −0.0412541 | + | 0.0714542i | ||||
\(696\) | −1320.63 | + | 762.468i | −1.89746 | + | 1.09550i | ||||
\(697\) | 279.734 | + | 333.374i | 0.401340 | + | 0.478298i | ||||
\(698\) | 62.0917 | + | 170.596i | 0.0889566 | + | 0.244406i | ||||
\(699\) | −194.069 | + | 533.200i | −0.277638 | + | 0.762804i | ||||
\(700\) | 2011.87 | + | 1688.16i | 2.87410 | + | 2.41165i | ||||
\(701\) | −91.6632 | + | 519.848i | −0.130761 | + | 0.741580i | 0.846958 | + | 0.531660i | \(0.178432\pi\) |
−0.977719 | + | 0.209920i | \(0.932680\pi\) | |||||||
\(702\) | 79.2867i | 0.112944i | ||||||||
\(703\) | −155.812 | + | 146.737i | −0.221638 | + | 0.208730i | ||||
\(704\) | 2604.29 | 3.69927 | ||||||||
\(705\) | 11.6571 | + | 2.05546i | 0.0165348 | + | 0.00291554i | ||||
\(706\) | −633.667 | + | 755.175i | −0.897546 | + | 1.06965i | ||||
\(707\) | −91.1219 | − | 33.1657i | −0.128885 | − | 0.0469104i | ||||
\(708\) | −494.210 | + | 179.878i | −0.698037 | + | 0.254065i | ||||
\(709\) | 988.966 | − | 829.841i | 1.39487 | − | 1.17044i | 0.431553 | − | 0.902088i | \(-0.357966\pi\) |
0.963321 | − | 0.268351i | \(-0.0864785\pi\) | |||||||
\(710\) | −177.084 | − | 306.718i | −0.249413 | − | 0.431997i | ||||
\(711\) | −336.938 | − | 194.531i | −0.473892 | − | 0.273602i | ||||
\(712\) | −311.722 | − | 1767.86i | −0.437811 | − | 2.48295i | ||||
\(713\) | 627.551 | − | 110.654i | 0.880155 | − | 0.155195i | ||||
\(714\) | −390.155 | + | 675.768i | −0.546435 | + | 0.946453i | ||||
\(715\) | 40.1481 | − | 23.1795i | 0.0561512 | − | 0.0324189i | ||||
\(716\) | 589.054 | + | 702.007i | 0.822701 | + | 0.980457i | ||||
\(717\) | −123.059 | − | 338.103i | −0.171631 | − | 0.471553i | ||||
\(718\) | −598.134 | + | 1643.36i | −0.833056 | + | 2.28880i | ||||
\(719\) | −60.7779 | − | 50.9987i | −0.0845311 | − | 0.0709300i | 0.599543 | − | 0.800343i | \(-0.295349\pi\) |
−0.684074 | + | 0.729413i | \(0.739794\pi\) | |||||||
\(720\) | −22.4317 | + | 127.216i | −0.0311551 | + | 0.176689i | ||||
\(721\) | − | 115.182i | − | 0.159753i | ||||||
\(722\) | 320.125 | − | 1340.01i | 0.443387 | − | 1.85597i | ||||
\(723\) | −700.308 | −0.968614 | ||||||||
\(724\) | −1591.53 | − | 280.630i | −2.19825 | − | 0.387611i | ||||
\(725\) | 549.985 | − | 655.446i | 0.758599 | − | 0.904064i | ||||
\(726\) | −530.739 | − | 193.173i | −0.731046 | − | 0.266079i | ||||
\(727\) | 700.401 | − | 254.925i | 0.963413 | − | 0.350654i | 0.188043 | − | 0.982161i | \(-0.439786\pi\) |
0.775370 | + | 0.631507i | \(0.217563\pi\) | |||||||
\(728\) | 783.438 | − | 657.383i | 1.07615 | − | 0.902998i | ||||
\(729\) | 13.5000 | + | 23.3827i | 0.0185185 | + | 0.0320750i | ||||
\(730\) | 279.678 | + | 161.472i | 0.383121 | + | 0.221195i | ||||
\(731\) | 7.30254 | + | 41.4148i | 0.00998980 | + | 0.0566549i | ||||
\(732\) | −136.219 | + | 24.0191i | −0.186092 | + | 0.0328130i | ||||
\(733\) | −203.715 | + | 352.844i | −0.277919 | + | 0.481370i | −0.970867 | − | 0.239617i | \(-0.922978\pi\) |
0.692948 | + | 0.720987i | \(0.256311\pi\) | |||||||
\(734\) | −2382.28 | + | 1375.41i | −3.24561 | + | 1.87385i | ||||
\(735\) | 49.6240 | + | 59.1396i | 0.0675156 | + | 0.0804620i | ||||
\(736\) | −597.676 | − | 1642.10i | −0.812059 | − | 2.23112i | ||||
\(737\) | −318.317 | + | 874.568i | −0.431909 | + | 1.18666i | ||||
\(738\) | −330.109 | − | 276.994i | −0.447302 | − | 0.375331i | ||||
\(739\) | −63.7674 | + | 361.643i | −0.0862888 | + | 0.489368i | 0.910782 | + | 0.412887i | \(0.135480\pi\) |
−0.997071 | + | 0.0764811i | \(0.975632\pi\) | |||||||
\(740\) | 96.0414i | 0.129786i | ||||||||
\(741\) | −90.2076 | − | 95.7861i | −0.121738 | − | 0.129266i | ||||
\(742\) | 1560.11 | 2.10257 | ||||||||
\(743\) | −346.891 | − | 61.1662i | −0.466878 | − | 0.0823232i | −0.0647399 | − | 0.997902i | \(-0.520622\pi\) |
−0.402138 | + | 0.915579i | \(0.631733\pi\) | |||||||
\(744\) | 1051.95 | − | 1253.67i | 1.41391 | − | 1.68503i | ||||
\(745\) | 51.1924 | + | 18.6325i | 0.0687147 | + | 0.0250101i | ||||
\(746\) | −595.958 | + | 216.911i | −0.798871 | + | 0.290765i | ||||
\(747\) | −50.8787 | + | 42.6923i | −0.0681108 | + | 0.0571517i | ||||
\(748\) | −877.583 | − | 1520.02i | −1.17324 | − | 2.03211i | ||||
\(749\) | −602.516 | − | 347.863i | −0.804427 | − | 0.464436i | ||||
\(750\) | −45.7121 | − | 259.246i | −0.0609494 | − | 0.345661i | ||||
\(751\) | 970.745 | − | 171.169i | 1.29260 | − | 0.227921i | 0.515280 | − | 0.857022i | \(-0.327688\pi\) |
0.777323 | + | 0.629101i | \(0.216577\pi\) | |||||||
\(752\) | −225.933 | + | 391.327i | −0.300442 | + | 0.520381i | ||||
\(753\) | −123.150 | + | 71.1006i | −0.163546 | + | 0.0944232i | ||||
\(754\) | −344.661 | − | 410.751i | −0.457110 | − | 0.544763i | ||||
\(755\) | 69.7874 | + | 191.739i | 0.0924336 | + | 0.253959i | ||||
\(756\) | 191.691 | − | 526.667i | 0.253560 | − | 0.696649i | ||||
\(757\) | 92.5004 | + | 77.6171i | 0.122193 | + | 0.102532i | 0.701837 | − | 0.712338i | \(-0.252364\pi\) |
−0.579643 | + | 0.814870i | \(0.696808\pi\) | |||||||
\(758\) | −133.121 | + | 754.968i | −0.175622 | + | 0.996000i | ||||
\(759\) | 420.511i | 0.554033i | ||||||||
\(760\) | −210.810 | − | 321.147i | −0.277381 | − | 0.422562i | ||||
\(761\) | 1054.02 | 1.38504 | 0.692522 | − | 0.721396i | \(-0.256499\pi\) | ||||
0.692522 | + | 0.721396i | \(0.256499\pi\) | |||||||
\(762\) | 869.263 | + | 153.274i | 1.14076 | + | 0.201148i | ||||
\(763\) | 492.577 | − | 587.030i | 0.645579 | − | 0.769371i | ||||
\(764\) | 1893.96 | + | 689.345i | 2.47900 | + | 0.902284i | ||||
\(765\) | 26.3043 | − | 9.57399i | 0.0343847 | − | 0.0125150i | ||||
\(766\) | −898.593 | + | 754.009i | −1.17310 | + | 0.984346i | ||||
\(767\) | −57.4556 | − | 99.5161i | −0.0749096 | − | 0.129747i | ||||
\(768\) | −504.288 | − | 291.151i | −0.656625 | − | 0.379103i | ||||
\(769\) | 161.080 | + | 913.530i | 0.209467 | + | 1.18795i | 0.890254 | + | 0.455464i | \(0.150527\pi\) |
−0.680787 | + | 0.732481i | \(0.738362\pi\) | |||||||
\(770\) | −444.916 | + | 78.4506i | −0.577812 | + | 0.101884i | ||||
\(771\) | 313.313 | − | 542.674i | 0.406372 | − | 0.703857i | ||||
\(772\) | −394.896 | + | 227.994i | −0.511524 | + | 0.295328i | ||||
\(773\) | 103.239 | + | 123.036i | 0.133557 | + | 0.159166i | 0.828678 | − | 0.559726i | \(-0.189094\pi\) |
−0.695121 | + | 0.718893i | \(0.744649\pi\) | |||||||
\(774\) | −14.2423 | − | 39.1304i | −0.0184009 | − | 0.0505561i | ||||
\(775\) | −314.058 | + | 862.869i | −0.405237 | + | 1.11338i | ||||
\(776\) | −1513.94 | − | 1270.35i | −1.95095 | − | 1.63705i | ||||
\(777\) | 34.5903 | − | 196.171i | 0.0445178 | − | 0.252473i | ||||
\(778\) | 1613.22i | 2.07355i | ||||||||
\(779\) | 713.950 | − | 40.9414i | 0.916496 | − | 0.0525563i | ||||
\(780\) | −59.0420 | −0.0756949 | ||||||||
\(781\) | −1627.18 | − | 286.917i | −2.08346 | − | 0.367371i | ||||
\(782\) | −479.278 | + | 571.182i | −0.612888 | + | 0.730411i | ||||
\(783\) | −171.583 | − | 62.4510i | −0.219135 | − | 0.0797587i | ||||
\(784\) | −2769.37 | + | 1007.97i | −3.53236 | + | 1.28567i | ||||
\(785\) | 9.37745 | − | 7.86862i | 0.0119458 | − | 0.0100237i | ||||
\(786\) | 705.932 | + | 1222.71i | 0.898132 | + | 1.55561i | ||||
\(787\) | −261.220 | − | 150.815i | −0.331918 | − | 0.191633i | 0.324774 | − | 0.945792i | \(-0.394712\pi\) |
−0.656692 | + | 0.754159i | \(0.728045\pi\) | |||||||
\(788\) | −470.994 | − | 2671.14i | −0.597709 | − | 3.38977i | ||||
\(789\) | −218.574 | + | 38.5406i | −0.277027 | + | 0.0488474i | ||||
\(790\) | 199.706 | − | 345.901i | 0.252793 | − | 0.437849i | ||||
\(791\) | −464.010 | + | 267.897i | −0.586612 | + | 0.338681i | ||||
\(792\) | 694.184 | + | 827.297i | 0.876495 | + | 1.04457i | ||||
\(793\) | −10.3365 | − | 28.3994i | −0.0130347 | − | 0.0358126i | ||||
\(794\) | 93.4824 | − | 256.841i | 0.117736 | − | 0.323477i | ||||
\(795\) | −42.8729 | − | 35.9746i | −0.0539281 | − | 0.0452511i | ||||
\(796\) | 555.357 | − | 3149.59i | 0.697684 | − | 3.95677i | ||||
\(797\) | 147.084i | 0.184547i | 0.995734 | + | 0.0922733i | \(0.0294133\pi\) | ||||
−0.995734 | + | 0.0922733i | \(0.970587\pi\) | |||||||
\(798\) | 506.815 | + | 1177.83i | 0.635107 | + | 1.47598i | ||||
\(799\) | 97.9170 | 0.122549 | ||||||||
\(800\) | 2479.86 | + | 437.266i | 3.09982 | + | 0.546582i | ||||
\(801\) | 138.166 | − | 164.660i | 0.172492 | − | 0.205567i | ||||
\(802\) | 311.040 | + | 113.209i | 0.387831 | + | 0.141159i | ||||
\(803\) | 1415.77 | − | 515.296i | 1.76309 | − | 0.641714i | ||||
\(804\) | 908.005 | − | 761.907i | 1.12936 | − | 0.947645i | ||||
\(805\) | 69.6076 | + | 120.564i | 0.0864690 | + | 0.149769i | ||||
\(806\) | 498.346 | + | 287.720i | 0.618296 | + | 0.356973i | ||||
\(807\) | −24.5917 | − | 139.466i | −0.0304729 | − | 0.172821i | ||||
\(808\) | −234.354 | + | 41.3229i | −0.290042 | + | 0.0511422i | ||||
\(809\) | −278.307 | + | 482.042i | −0.344013 | + | 0.595849i | −0.985174 | − | 0.171558i | \(-0.945120\pi\) |
0.641161 | + | 0.767407i | \(0.278453\pi\) | |||||||
\(810\) | −24.0047 | + | 13.8591i | −0.0296355 | + | 0.0171101i | ||||
\(811\) | 302.655 | + | 360.690i | 0.373187 | + | 0.444747i | 0.919652 | − | 0.392735i | \(-0.128471\pi\) |
−0.546464 | + | 0.837482i | \(0.684027\pi\) | |||||||
\(812\) | 1296.36 | + | 3561.72i | 1.59650 | + | 4.38636i | ||||
\(813\) | 305.755 | − | 840.056i | 0.376083 | − | 1.03328i | ||||
\(814\) | 473.185 | + | 397.050i | 0.581309 | + | 0.487776i | ||||
\(815\) | 17.5521 | − | 99.5429i | 0.0215363 | − | 0.122139i | ||||
\(816\) | 1068.59i | 1.30955i | ||||||||
\(817\) | 61.7263 | + | 31.0694i | 0.0755524 | + | 0.0380286i | ||||
\(818\) | −2173.05 | −2.65654 | ||||||||
\(819\) | 120.598 | + | 21.2646i | 0.147250 | + | 0.0259641i | ||||
\(820\) | 206.268 | − | 245.820i | 0.251546 | − | 0.299781i | ||||
\(821\) | −1255.36 | − | 456.914i | −1.52906 | − | 0.556534i | −0.565673 | − | 0.824630i | \(-0.691383\pi\) |
−0.963392 | + | 0.268096i | \(0.913606\pi\) | |||||||
\(822\) | 317.861 | − | 115.692i | 0.386692 | − | 0.140744i | ||||
\(823\) | −379.854 | + | 318.735i | −0.461548 | + | 0.387285i | −0.843700 | − | 0.536815i | \(-0.819627\pi\) |
0.382152 | + | 0.924099i | \(0.375183\pi\) | |||||||
\(824\) | −141.331 | − | 244.793i | −0.171519 | − | 0.297079i | ||||
\(825\) | −524.770 | − | 302.976i | −0.636085 | − | 0.367244i | ||||
\(826\) | 194.457 | + | 1102.82i | 0.235420 | + | 1.33514i | ||||
\(827\) | 364.014 | − | 64.1856i | 0.440163 | − | 0.0776125i | 0.0508248 | − | 0.998708i | \(-0.483815\pi\) |
0.389338 | + | 0.921095i | \(0.372704\pi\) | |||||||
\(828\) | 267.777 | − | 463.804i | 0.323403 | − | 0.560150i | ||||
\(829\) | 242.593 | − | 140.061i | 0.292633 | − | 0.168952i | −0.346496 | − | 0.938052i | \(-0.612628\pi\) |
0.639129 | + | 0.769100i | \(0.279295\pi\) | |||||||
\(830\) | −43.8281 | − | 52.2323i | −0.0528049 | − | 0.0629304i | ||||
\(831\) | 132.091 | + | 362.916i | 0.158954 | + | 0.436722i | ||||
\(832\) | 247.859 | − | 680.986i | 0.297907 | − | 0.818493i | ||||
\(833\) | 489.213 | + | 410.499i | 0.587291 | + | 0.492796i | ||||
\(834\) | 81.5638 | − | 462.571i | 0.0977983 | − | 0.554642i | ||||
\(835\) | 138.977i | 0.166439i | ||||||||
\(836\) | −2864.37 | − | 337.398i | −3.42628 | − | 0.403586i | ||||
\(837\) | 195.958 | 0.234120 | ||||||||
\(838\) | 2934.37 | + | 517.409i | 3.50164 | + | 0.617434i | ||||
\(839\) | −339.285 | + | 404.344i | −0.404392 | + | 0.481935i | −0.929354 | − | 0.369190i | \(-0.879635\pi\) |
0.524962 | + | 0.851126i | \(0.324080\pi\) | |||||||
\(840\) | 335.971 | + | 122.284i | 0.399966 | + | 0.145576i | ||||
\(841\) | 370.092 | − | 134.703i | 0.440062 | − | 0.160170i | ||||
\(842\) | 707.417 | − | 593.594i | 0.840163 | − | 0.704981i | ||||
\(843\) | −12.0577 | − | 20.8846i | −0.0143033 | − | 0.0247741i | ||||
\(844\) | −2561.78 | − | 1479.04i | −3.03528 | − | 1.75242i | ||||
\(845\) | 21.4423 | + | 121.606i | 0.0253755 | + | 0.143912i | ||||
\(846\) | −95.4849 | + | 16.8366i | −0.112866 | + | 0.0199014i | ||||
\(847\) | −436.166 | + | 755.462i | −0.514954 | + | 0.891927i | ||||
\(848\) | 1850.25 | − | 1068.24i | 2.18190 | − | 1.25972i | ||||
\(849\) | −421.520 | − | 502.348i | −0.496490 | − | 0.591694i | ||||
\(850\) | −367.480 | − | 1009.64i | −0.432329 | − | 1.18781i | ||||
\(851\) | 65.1013 | − | 178.864i | 0.0764997 | − | 0.210181i | ||||
\(852\) | 1612.00 | + | 1352.63i | 1.89202 | + | 1.58760i | ||||
\(853\) | 38.7576 | − | 219.806i | 0.0454369 | − | 0.257685i | −0.953625 | − | 0.300998i | \(-0.902680\pi\) |
0.999062 | + | 0.0433130i | \(0.0137913\pi\) | |||||||
\(854\) | 294.520i | 0.344872i | ||||||||
\(855\) | 13.2320 | − | 44.0543i | 0.0154760 | − | 0.0515255i | ||||
\(856\) | −1707.35 | −1.99456 | ||||||||
\(857\) | 795.215 | + | 140.218i | 0.927906 | + | 0.163615i | 0.617124 | − | 0.786866i | \(-0.288298\pi\) |
0.310782 | + | 0.950481i | \(0.399409\pi\) | |||||||
\(858\) | −244.089 | + | 290.894i | −0.284486 | + | 0.339037i | ||||
\(859\) | 742.496 | + | 270.246i | 0.864372 | + | 0.314606i | 0.735886 | − | 0.677106i | \(-0.236766\pi\) |
0.128486 | + | 0.991711i | \(0.458988\pi\) | |||||||
\(860\) | 29.1391 | − | 10.6058i | 0.0338826 | − | 0.0123323i | ||||
\(861\) | −509.851 | + | 427.816i | −0.592162 | + | 0.496883i | ||||
\(862\) | 1070.44 | + | 1854.06i | 1.24181 | + | 2.15088i | ||||
\(863\) | −396.502 | − | 228.921i | −0.459446 | − | 0.265261i | 0.252365 | − | 0.967632i | \(-0.418792\pi\) |
−0.711811 | + | 0.702371i | \(0.752125\pi\) | |||||||
\(864\) | −93.3148 | − | 529.215i | −0.108003 | − | 0.612517i | ||||
\(865\) | −215.087 | + | 37.9256i | −0.248655 | + | 0.0438446i | ||||
\(866\) | 751.788 | − | 1302.14i | 0.868116 | − | 1.50362i | ||||
\(867\) | −232.964 | + | 134.502i | −0.268701 | + | 0.155135i | ||||
\(868\) | −2614.68 | − | 3116.05i | −3.01230 | − | 3.58992i | ||||
\(869\) | −637.309 | − | 1750.99i | −0.733382 | − | 2.01495i | ||||
\(870\) | 64.1124 | − | 176.147i | 0.0736924 | − | 0.202468i | ||||
\(871\) | 198.392 | + | 166.471i | 0.227775 | + | 0.191126i | ||||
\(872\) | 326.558 | − | 1852.00i | 0.374493 | − | 2.12385i | ||||
\(873\) | − | 236.642i | − | 0.271067i | ||||||
\(874\) | 281.493 | + | 1192.47i | 0.322075 | + | 1.36438i | ||||
\(875\) | −406.581 | −0.464664 | ||||||||
\(876\) | −1889.66 | − | 333.198i | −2.15715 | − | 0.380363i | ||||
\(877\) | −298.305 | + | 355.506i | −0.340142 | + | 0.405366i | −0.908816 | − | 0.417197i | \(-0.863012\pi\) |
0.568674 | + | 0.822563i | \(0.307457\pi\) | |||||||
\(878\) | −731.465 | − | 266.231i | −0.833103 | − | 0.303225i | ||||
\(879\) | −527.732 | + | 192.079i | −0.600378 | + | 0.218520i | ||||
\(880\) | −473.942 | + | 397.685i | −0.538571 | + | 0.451914i | ||||
\(881\) | 717.960 | + | 1243.54i | 0.814938 | + | 1.41151i | 0.909373 | + | 0.415983i | \(0.136562\pi\) |
−0.0944349 | + | 0.995531i | \(0.530104\pi\) | |||||||
\(882\) | −547.646 | − | 316.184i | −0.620914 | − | 0.358485i | ||||
\(883\) | −287.842 | − | 1632.43i | −0.325982 | − | 1.84874i | −0.502682 | − | 0.864471i | \(-0.667653\pi\) |
0.176700 | − | 0.984265i | \(-0.443458\pi\) | |||||||
\(884\) | −480.987 | + | 84.8109i | −0.544103 | + | 0.0959400i | ||||
\(885\) | 20.0862 | − | 34.7904i | 0.0226963 | − | 0.0393111i | ||||
\(886\) | 2152.12 | − | 1242.53i | 2.42903 | − | 1.40240i | ||||
\(887\) | −866.790 | − | 1033.00i | −0.977215 | − | 1.16460i | −0.986353 | − | 0.164642i | \(-0.947353\pi\) |
0.00913822 | − | 0.999958i | \(-0.497091\pi\) | |||||||
\(888\) | −167.194 | − | 459.361i | −0.188281 | − | 0.517298i | ||||
\(889\) | 466.270 | − | 1281.07i | 0.524489 | − | 1.44102i | ||||
\(890\) | 169.040 | + | 141.841i | 0.189933 | + | 0.159372i | ||||
\(891\) | −22.4550 | + | 127.349i | −0.0252021 | + | 0.142928i | ||||
\(892\) | − | 1243.02i | − | 1.39352i | ||||||
\(893\) | 96.1995 | − | 128.977i | 0.107726 | − | 0.144431i | ||||
\(894\) | −446.237 | −0.499147 | ||||||||
\(895\) | −68.9353 | − | 12.1552i | −0.0770227 | − | 0.0135812i | ||||
\(896\) | −1824.80 | + | 2174.71i | −2.03661 | + | 2.42713i | ||||
\(897\) | 109.958 | + | 40.0214i | 0.122584 | + | 0.0446169i | ||||
\(898\) | −229.599 | + | 83.5673i | −0.255678 | + | 0.0930593i | ||||
\(899\) | −1015.18 | + | 851.835i | −1.12923 | + | 0.947536i | ||||
\(900\) | 385.865 | + | 668.337i | 0.428739 | + | 0.742597i | ||||
\(901\) | −400.940 | − | 231.483i | −0.444994 | − | 0.256918i | ||||
\(902\) | −358.388 | − | 2032.52i | −0.397325 | − | 2.25334i | ||||
\(903\) | −63.3384 | + | 11.1683i | −0.0701422 | + | 0.0123680i | ||||
\(904\) | −657.432 | + | 1138.71i | −0.727248 | + | 1.25963i | ||||
\(905\) | 106.905 | − | 61.7215i | 0.118127 | − | 0.0682006i | ||||
\(906\) | −1074.33 | − | 1280.34i | −1.18580 | − | 1.41318i | ||||
\(907\) | 419.032 | + | 1151.28i | 0.461998 | + | 1.26933i | 0.923981 | + | 0.382439i | \(0.124916\pi\) |
−0.461983 | + | 0.886889i | \(0.652862\pi\) | |||||||
\(908\) | −566.889 | + | 1557.51i | −0.624327 | + | 1.71532i | ||||
\(909\) | −21.8279 | − | 18.3157i | −0.0240130 | − | 0.0201493i | ||||
\(910\) | −21.8303 | + | 123.806i | −0.0239893 | + | 0.136050i | ||||
\(911\) | 675.569i | 0.741569i | 0.928719 | + | 0.370784i | \(0.120911\pi\) | ||||
−0.928719 | + | 0.370784i | \(0.879089\pi\) | |||||||
\(912\) | 1407.56 | + | 1049.85i | 1.54338 | + | 1.15115i | ||||
\(913\) | −318.099 | −0.348411 | ||||||||
\(914\) | 544.861 | + | 96.0737i | 0.596128 | + | 0.105113i | ||||
\(915\) | 6.79136 | − | 8.09363i | 0.00742226 | − | 0.00884550i | ||||
\(916\) | 424.178 | + | 154.388i | 0.463077 | + | 0.168546i | ||||
\(917\) | 2049.11 | − | 745.814i | 2.23458 | − | 0.813320i | ||||
\(918\) | −175.647 | + | 147.385i | −0.191337 | + | 0.160550i | ||||
\(919\) | 449.172 | + | 777.988i | 0.488762 | + | 0.846560i | 0.999916 | − | 0.0129288i | \(-0.00411548\pi\) |
−0.511155 | + | 0.859489i | \(0.670782\pi\) | |||||||
\(920\) | 295.870 | + | 170.821i | 0.321598 | + | 0.185674i | ||||
\(921\) | 35.2165 | + | 199.722i | 0.0382372 | + | 0.216854i | ||||
\(922\) | −1003.66 | + | 176.972i | −1.08857 | + | 0.191944i | ||||
\(923\) | −229.889 | + | 398.180i | −0.249067 | + | 0.431398i | ||||
\(924\) | 2324.67 | − | 1342.15i | 2.51587 | − | 1.45254i | ||||
\(925\) | 176.306 | + | 210.113i | 0.190601 | + | 0.227149i | ||||
\(926\) | 145.770 | + | 400.500i | 0.157419 | + | 0.432505i | ||||
\(927\) | 11.5759 | − | 31.8046i | 0.0124875 | − | 0.0343092i | ||||
\(928\) | 2783.93 | + | 2336.00i | 2.99993 | + | 2.51724i | ||||
\(929\) | 8.21121 | − | 46.5681i | 0.00883876 | − | 0.0501271i | −0.980069 | − | 0.198655i | \(-0.936343\pi\) |
0.988908 | + | 0.148528i | \(0.0474536\pi\) | |||||||
\(930\) | 201.171i | 0.216313i | ||||||||
\(931\) | 1021.35 | − | 241.097i | 1.09704 | − | 0.258966i | ||||
\(932\) | 3461.07 | 3.71360 | ||||||||
\(933\) | −929.574 | − | 163.909i | −0.996328 | − | 0.175679i | ||||
\(934\) | −1502.78 | + | 1790.94i | −1.60897 | + | 1.91750i | ||||
\(935\) | 125.981 | + | 45.8535i | 0.134740 | + | 0.0490412i | ||||
\(936\) | 282.395 | − | 102.783i | 0.301704 | − | 0.109811i | ||||
\(937\) | 1271.36 | − | 1066.80i | 1.35684 | − | 1.13853i | 0.379901 | − | 0.925027i | \(-0.375958\pi\) |
0.976943 | − | 0.213500i | \(-0.0684865\pi\) | |||||||
\(938\) | −1261.92 | − | 2185.71i | −1.34533 | − | 2.33018i | ||||
\(939\) | 147.531 | + | 85.1772i | 0.157115 | + | 0.0907105i | ||||
\(940\) | −12.5376 | − | 71.1043i | −0.0133379 | − | 0.0756428i | ||||
\(941\) | −851.242 | + | 150.097i | −0.904614 | + | 0.159508i | −0.606557 | − | 0.795040i | \(-0.707450\pi\) |
−0.298057 | + | 0.954548i | \(0.596339\pi\) | |||||||
\(942\) | −50.1356 | + | 86.8374i | −0.0532225 | + | 0.0921841i | ||||
\(943\) | −550.774 | + | 317.990i | −0.584066 | + | 0.337211i | ||||
\(944\) | 985.750 | + | 1174.77i | 1.04423 | + | 1.24446i | ||||
\(945\) | 14.6421 | + | 40.2289i | 0.0154943 | + | 0.0425703i | ||||
\(946\) | 68.2119 | − | 187.411i | 0.0721056 | − | 0.198109i | ||||
\(947\) | −1146.68 | − | 962.182i | −1.21086 | − | 1.01603i | −0.999252 | − | 0.0386773i | \(-0.987686\pi\) |
−0.211608 | − | 0.977355i | \(-0.567870\pi\) | |||||||
\(948\) | −412.093 | + | 2337.10i | −0.434697 | + | 2.46529i | ||||
\(949\) | − | 419.246i | − | 0.441776i | ||||||
\(950\) | −1690.94 | − | 507.886i | −1.77994 | − | 0.534616i | ||||
\(951\) | 721.979 | 0.759179 | ||||||||
\(952\) | 2912.65 | + | 513.579i | 3.05951 | + | 0.539473i | ||||
\(953\) | −1164.48 | + | 1387.78i | −1.22191 | + | 1.45622i | −0.372882 | + | 0.927879i | \(0.621630\pi\) |
−0.849032 | + | 0.528342i | \(0.822814\pi\) | |||||||
\(954\) | 430.784 | + | 156.793i | 0.451556 | + | 0.164353i | ||||
\(955\) | −144.668 | + | 52.6549i | −0.151485 | + | 0.0551361i | ||||
\(956\) | −1681.22 | + | 1410.71i | −1.75860 | + | 1.47564i | ||||
\(957\) | −437.258 | − | 757.353i | −0.456905 | − | 0.791382i | ||||
\(958\) | −2554.74 | − | 1474.98i | −2.66674 | − | 1.53964i | ||||
\(959\) | −90.7210 | − | 514.504i | −0.0945996 | − | 0.536501i | ||||
\(960\) | 249.499 | − | 43.9935i | 0.259895 | − | 0.0458266i | ||||
\(961\) | 230.605 | − | 399.420i | 0.239964 | − | 0.415629i | ||||
\(962\) | 148.858 | − | 85.9431i | 0.154738 | − | 0.0893379i | ||||
\(963\) | −131.409 | − | 156.607i | −0.136458 | − | 0.162624i | ||||
\(964\) | 1460.99 | + | 4014.03i | 1.51555 | + | 4.16394i | ||||
\(965\) | 11.9126 | − | 32.7296i | 0.0123447 | − | 0.0339167i | ||||
\(966\) | −873.546 | − | 732.992i | −0.904292 | − | 0.758791i | ||||
\(967\) | 121.153 | − | 687.093i | 0.125287 | − | 0.710540i | −0.855849 | − | 0.517225i | \(-0.826965\pi\) |
0.981137 | − | 0.193315i | \(-0.0619240\pi\) | |||||||
\(968\) | 2140.75i | 2.21152i | ||||||||
\(969\) | 44.5128 | − | 377.896i | 0.0459369 | − | 0.389986i | ||||
\(970\) | 242.937 | 0.250451 | ||||||||
\(971\) | 462.024 | + | 81.4674i | 0.475823 | + | 0.0839005i | 0.406416 | − | 0.913688i | \(-0.366778\pi\) |
0.0694069 | + | 0.997588i | \(0.477889\pi\) | |||||||
\(972\) | 105.861 | − | 126.161i | 0.108911 | − | 0.129795i | ||||
\(973\) | −681.710 | − | 248.122i | −0.700627 | − | 0.255007i | ||||
\(974\) | 1382.98 | − | 503.364i | 1.41990 | − | 0.516801i | ||||
\(975\) | −129.168 | + | 108.385i | −0.132480 | + | 0.111164i | ||||
\(976\) | 201.665 | + | 349.294i | 0.206624 | + | 0.357883i | ||||
\(977\) | 1314.55 | + | 758.955i | 1.34550 | + | 0.776822i | 0.987608 | − | 0.156943i | \(-0.0501638\pi\) |
0.357888 | + | 0.933765i | \(0.383497\pi\) | |||||||
\(978\) | 143.772 | + | 815.372i | 0.147006 | + | 0.833714i | ||||
\(979\) | 1013.83 | − | 178.765i | 1.03557 | − | 0.182600i | ||||
\(980\) | 235.451 | − | 407.813i | 0.240256 | − | 0.416136i | ||||
\(981\) | 195.010 | − | 112.589i | 0.198787 | − | 0.114770i | ||||
\(982\) | 1802.59 | + | 2148.24i | 1.83563 | + | 2.18762i | ||||
\(983\) | −34.9170 | − | 95.9336i | −0.0355208 | − | 0.0975927i | 0.920664 | − | 0.390355i | \(-0.127648\pi\) |
−0.956185 | + | 0.292762i | \(0.905426\pi\) | |||||||
\(984\) | −558.631 | + | 1534.83i | −0.567714 | + | 1.55978i | ||||
\(985\) | 158.709 | + | 133.173i | 0.161126 | + | 0.135201i | ||||
\(986\) | 269.266 | − | 1527.08i | 0.273089 | − | 1.54876i | ||||
\(987\) | 149.751i | 0.151723i | ||||||||
\(988\) | −360.837 | + | 716.883i | −0.365219 | + | 0.725590i | ||||
\(989\) | −61.4567 | −0.0621402 | ||||||||
\(990\) | −130.737 | − | 23.0524i | −0.132057 | − | 0.0232853i | ||||
\(991\) | −679.205 | + | 809.445i | −0.685373 | + | 0.816796i | −0.990788 | − | 0.135424i | \(-0.956760\pi\) |
0.305415 | + | 0.952219i | \(0.401205\pi\) | |||||||
\(992\) | −3664.93 | − | 1333.93i | −3.69449 | − | 1.34468i | ||||
\(993\) | −39.2256 | + | 14.2769i | −0.0395021 | + | 0.0143776i | ||||
\(994\) | 3432.37 | − | 2880.10i | 3.45309 | − | 2.89749i | ||||
\(995\) | 122.145 | + | 211.561i | 0.122758 | + | 0.212624i | ||||
\(996\) | 350.848 | + | 202.562i | 0.352257 | + | 0.203376i | ||||
\(997\) | 66.2899 | + | 375.949i | 0.0664893 | + | 0.377080i | 0.999836 | + | 0.0181037i | \(0.00576291\pi\) |
−0.933347 | + | 0.358976i | \(0.883126\pi\) | |||||||
\(998\) | −2671.59 | + | 471.074i | −2.67695 | + | 0.472018i | ||||
\(999\) | 29.2667 | − | 50.6914i | 0.0292960 | − | 0.0507422i |
(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 | 57.3.k.b.40.1 | yes | 24 | |
3.2 | odd | 2 | 171.3.ba.d.154.4 | 24 | |||
19.10 | odd | 18 | inner | 57.3.k.b.10.1 | ✓ | 24 | |
57.29 | even | 18 | 171.3.ba.d.10.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.3.k.b.10.1 | ✓ | 24 | 19.10 | odd | 18 | inner | |
57.3.k.b.40.1 | yes | 24 | 1.1 | even | 1 | trivial | |
171.3.ba.d.10.4 | 24 | 57.29 | even | 18 | |||
171.3.ba.d.154.4 | 24 | 3.2 | odd | 2 |