Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1000,2,Mod(101,1000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1000, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1000.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1000 = 2^{3} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1000.t (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.98504020213\) |
Analytic rank: | \(0\) |
Dimension: | \(224\) |
Relative dimension: | \(56\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 101.7 | ||
Character | \(\chi\) | \(=\) | 1000.101 |
Dual form | 1000.2.t.b.901.7 |
$q$-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 \(\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times\).
\(n\) | \(377\) | \(501\) | \(751\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.31025 | + | 0.532208i | −0.926486 | + | 0.376328i | ||||
\(3\) | −0.171463 | + | 0.235999i | −0.0989945 | + | 0.136254i | −0.855641 | − | 0.517570i | \(-0.826837\pi\) |
0.756646 | + | 0.653825i | \(0.226837\pi\) | |||||||
\(4\) | 1.43351 | − | 1.39465i | 0.716754 | − | 0.697326i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0990593 | − | 0.400472i | 0.0404408 | − | 0.163492i | ||||
\(7\) | 0.234809 | 0.0887494 | 0.0443747 | − | 0.999015i | \(-0.485870\pi\) | ||||
0.0443747 | + | 0.999015i | \(0.485870\pi\) | |||||||
\(8\) | −1.13601 | + | 2.59027i | −0.401640 | + | 0.915798i | ||||
\(9\) | 0.900755 | + | 2.77224i | 0.300252 | + | 0.924080i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.50105 | + | 1.78740i | 1.65863 | + | 0.538921i | 0.980584 | − | 0.196099i | \(-0.0628276\pi\) |
0.678045 | + | 0.735021i | \(0.262828\pi\) | |||||||
\(12\) | 0.0833422 | + | 0.577439i | 0.0240588 | + | 0.166692i | ||||
\(13\) | 1.78589 | − | 0.580270i | 0.495316 | − | 0.160938i | −0.0506981 | − | 0.998714i | \(-0.516145\pi\) |
0.546014 | + | 0.837776i | \(0.316145\pi\) | |||||||
\(14\) | −0.307658 | + | 0.124967i | −0.0822252 | + | 0.0333989i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.109896 | − | 3.99849i | 0.0274739 | − | 0.999623i | ||||
\(17\) | −3.34149 | + | 2.42773i | −0.810429 | + | 0.588811i | −0.913955 | − | 0.405815i | \(-0.866988\pi\) |
0.103526 | + | 0.994627i | \(0.466988\pi\) | |||||||
\(18\) | −2.65562 | − | 3.15294i | −0.625936 | − | 0.743154i | ||||
\(19\) | −1.59154 | − | 2.19056i | −0.365124 | − | 0.502550i | 0.586443 | − | 0.809990i | \(-0.300528\pi\) |
−0.951567 | + | 0.307440i | \(0.900528\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0402612 | + | 0.0554147i | −0.00878571 | + | 0.0120925i | ||||
\(22\) | −8.15902 | + | 0.585764i | −1.73951 | + | 0.124885i | ||||
\(23\) | 0.754772 | − | 2.32295i | 0.157381 | − | 0.484369i | −0.841013 | − | 0.541014i | \(-0.818041\pi\) |
0.998394 | + | 0.0566456i | \(0.0180405\pi\) | |||||||
\(24\) | −0.416517 | − | 0.712234i | −0.0850211 | − | 0.145384i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.03113 | + | 1.71076i | −0.398338 | + | 0.335508i | ||||
\(27\) | −1.64099 | − | 0.533191i | −0.315809 | − | 0.102613i | ||||
\(28\) | 0.336601 | − | 0.327477i | 0.0636116 | − | 0.0618873i | ||||
\(29\) | 3.89100 | − | 5.35551i | 0.722541 | − | 0.994493i | −0.276894 | − | 0.960900i | \(-0.589305\pi\) |
0.999436 | − | 0.0335922i | \(-0.0106948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.28302 | + | 3.11180i | −0.769253 | + | 0.558895i | −0.901734 | − | 0.432291i | \(-0.857705\pi\) |
0.132482 | + | 0.991185i | \(0.457705\pi\) | |||||||
\(32\) | 1.98404 | + | 5.29751i | 0.350732 | + | 0.936476i | ||||
\(33\) | −1.36505 | + | 0.991770i | −0.237625 | + | 0.172645i | ||||
\(34\) | 3.08612 | − | 4.95930i | 0.529266 | − | 0.850513i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.15755 | + | 2.71779i | 0.859591 | + | 0.452965i | ||||
\(37\) | −1.92303 | + | 0.624829i | −0.316144 | + | 0.102721i | −0.462791 | − | 0.886468i | \(-0.653152\pi\) |
0.146647 | + | 0.989189i | \(0.453152\pi\) | |||||||
\(38\) | 3.25115 | + | 2.02316i | 0.527406 | + | 0.328199i | ||||
\(39\) | −0.169271 | + | 0.520963i | −0.0271051 | + | 0.0834208i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.13805 | + | 6.58023i | 0.333907 | + | 1.02766i | 0.967258 | + | 0.253795i | \(0.0816787\pi\) |
−0.633352 | + | 0.773864i | \(0.718321\pi\) | |||||||
\(42\) | 0.0232600 | − | 0.0940345i | 0.00358910 | − | 0.0145098i | ||||
\(43\) | 8.04419i | 1.22673i | 0.789801 | + | 0.613364i | \(0.210184\pi\) | ||||
−0.789801 | + | 0.613364i | \(0.789816\pi\) | |||||||
\(44\) | 10.3786 | − | 5.10979i | 1.56463 | − | 0.770330i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.247353 | + | 3.44534i | 0.0364702 | + | 0.507988i | ||||
\(47\) | 8.51367 | + | 6.18554i | 1.24185 | + | 0.902254i | 0.997720 | − | 0.0674892i | \(-0.0214988\pi\) |
0.244126 | + | 0.969743i | \(0.421499\pi\) | |||||||
\(48\) | 0.924798 | + | 0.711530i | 0.133483 | + | 0.102701i | ||||
\(49\) | −6.94486 | −0.992124 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 1.20486i | − | 0.168714i | ||||||
\(52\) | 1.75081 | − | 3.32251i | 0.242794 | − | 0.460749i | ||||
\(53\) | 2.22765 | − | 3.06610i | 0.305991 | − | 0.421161i | −0.628135 | − | 0.778105i | \(-0.716181\pi\) |
0.934126 | + | 0.356944i | \(0.116181\pi\) | |||||||
\(54\) | 2.43388 | − | 0.174737i | 0.331209 | − | 0.0237787i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.266745 | + | 0.608218i | −0.0356453 | + | 0.0812765i | ||||
\(57\) | 0.789862 | 0.104620 | ||||||||
\(58\) | −2.24794 | + | 9.08787i | −0.295169 | + | 1.19330i | ||||
\(59\) | 6.66931 | − | 2.16699i | 0.868270 | − | 0.282118i | 0.159192 | − | 0.987248i | \(-0.449111\pi\) |
0.709078 | + | 0.705130i | \(0.249111\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.54958 | − | 0.503489i | −0.198403 | − | 0.0644651i | 0.208130 | − | 0.978101i | \(-0.433262\pi\) |
−0.406533 | + | 0.913636i | \(0.633262\pi\) | |||||||
\(62\) | 3.95570 | − | 6.35669i | 0.502375 | − | 0.807300i | ||||
\(63\) | 0.211505 | + | 0.650947i | 0.0266472 | + | 0.0820116i | ||||
\(64\) | −5.41896 | − | 5.88514i | −0.677370 | − | 0.735642i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.26073 | − | 2.02596i | 0.155186 | − | 0.249378i | ||||
\(67\) | 6.54617 | + | 9.01003i | 0.799742 | + | 1.10075i | 0.992826 | + | 0.119569i | \(0.0381511\pi\) |
−0.193084 | + | 0.981182i | \(0.561849\pi\) | |||||||
\(68\) | −1.40421 | + | 8.14038i | −0.170286 | + | 0.987166i | ||||
\(69\) | 0.418799 | + | 0.576427i | 0.0504174 | + | 0.0693936i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.21139 | + | 1.60667i | 0.262443 | + | 0.190676i | 0.711223 | − | 0.702966i | \(-0.248141\pi\) |
−0.448780 | + | 0.893642i | \(0.648141\pi\) | |||||||
\(72\) | −8.20411 | − | 0.816095i | −0.966863 | − | 0.0961777i | ||||
\(73\) | 4.67339 | − | 14.3832i | 0.546979 | − | 1.68343i | −0.169258 | − | 0.985572i | \(-0.554137\pi\) |
0.716237 | − | 0.697857i | \(-0.245863\pi\) | |||||||
\(74\) | 2.18711 | − | 1.84213i | 0.254246 | − | 0.214144i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.33656 | − | 0.920553i | −0.612145 | − | 0.105595i | ||||
\(77\) | 1.29170 | + | 0.419697i | 0.147202 | + | 0.0478290i | ||||
\(78\) | −0.0554733 | − | 0.772679i | −0.00628111 | − | 0.0874886i | ||||
\(79\) | 10.3770 | + | 7.53932i | 1.16750 | + | 0.848240i | 0.990708 | − | 0.136008i | \(-0.0434272\pi\) |
0.176795 | + | 0.984248i | \(0.443427\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.66742 | + | 4.84416i | −0.740824 | + | 0.538240i | ||||
\(82\) | −6.30342 | − | 7.48385i | −0.696097 | − | 0.826454i | ||||
\(83\) | −1.85452 | − | 2.55253i | −0.203560 | − | 0.280176i | 0.695016 | − | 0.718994i | \(-0.255397\pi\) |
−0.898576 | + | 0.438818i | \(0.855397\pi\) | |||||||
\(84\) | 0.0195695 | + | 0.135588i | 0.00213521 | + | 0.0147938i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.28118 | − | 10.5399i | −0.461652 | − | 1.13655i | ||||
\(87\) | 0.596730 | + | 1.83655i | 0.0639762 | + | 0.196899i | ||||
\(88\) | −10.8791 | + | 12.2187i | −1.15971 | + | 1.30252i | ||||
\(89\) | −3.51258 | + | 10.8106i | −0.372333 | + | 1.14592i | 0.572927 | + | 0.819606i | \(0.305808\pi\) |
−0.945260 | + | 0.326317i | \(0.894192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.419342 | − | 0.136252i | 0.0439590 | − | 0.0142831i | ||||
\(92\) | −2.15773 | − | 4.38261i | −0.224959 | − | 0.456919i | ||||
\(93\) | − | 1.54435i | − | 0.160141i | ||||||
\(94\) | −14.4470 | − | 3.57356i | −1.49010 | − | 0.368585i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.59040 | − | 0.440098i | −0.162319 | − | 0.0449173i | ||||
\(97\) | −5.66961 | − | 4.11921i | −0.575661 | − | 0.418243i | 0.261496 | − | 0.965205i | \(-0.415784\pi\) |
−0.837157 | + | 0.546962i | \(0.815784\pi\) | |||||||
\(98\) | 9.09951 | − | 3.69611i | 0.919189 | − | 0.373364i | ||||
\(99\) | 16.8602i | 1.69452i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.9484i | 1.08941i | 0.838628 | + | 0.544704i | \(0.183358\pi\) | ||||
−0.838628 | + | 0.544704i | \(0.816642\pi\) | |||||||
\(102\) | 0.641234 | + | 1.57866i | 0.0634916 | + | 0.156311i | ||||
\(103\) | 9.47147 | + | 6.88143i | 0.933252 | + | 0.678047i | 0.946787 | − | 0.321861i | \(-0.104308\pi\) |
−0.0135350 | + | 0.999908i | \(0.504308\pi\) | |||||||
\(104\) | −0.525731 | + | 5.28511i | −0.0515522 | + | 0.518248i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.28698 | + | 5.20293i | −0.125002 | + | 0.505353i | ||||
\(107\) | − | 0.352640i | − | 0.0340910i | −0.999855 | − | 0.0170455i | \(-0.994574\pi\) | ||
0.999855 | − | 0.0170455i | \(-0.00542602\pi\) | |||||||
\(108\) | −3.09600 | + | 1.52428i | −0.297912 | + | 0.146674i | ||||
\(109\) | −9.24706 | + | 3.00455i | −0.885708 | + | 0.287784i | −0.716325 | − | 0.697767i | \(-0.754177\pi\) |
−0.169382 | + | 0.985550i | \(0.554177\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.182270 | − | 0.560968i | 0.0173003 | − | 0.0532448i | ||||
\(112\) | 0.0258045 | − | 0.938881i | 0.00243829 | − | 0.0887159i | ||||
\(113\) | −0.101189 | − | 0.311428i | −0.00951907 | − | 0.0292967i | 0.946184 | − | 0.323629i | \(-0.104903\pi\) |
−0.955703 | + | 0.294332i | \(0.904903\pi\) | |||||||
\(114\) | −1.03492 | + | 0.420371i | −0.0969288 | + | 0.0393714i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.89128 | − | 13.1038i | −0.175601 | − | 1.21665i | ||||
\(117\) | 3.21729 | + | 4.42822i | 0.297439 | + | 0.409389i | ||||
\(118\) | −7.58517 | + | 6.38876i | −0.698272 | + | 0.588133i | ||||
\(119\) | −0.784611 | + | 0.570053i | −0.0719252 | + | 0.0522567i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.1676 | + | 13.1995i | 1.65160 | + | 1.19995i | ||||
\(122\) | 2.29830 | − | 0.165003i | 0.208078 | − | 0.0149386i | ||||
\(123\) | −1.91953 | − | 0.623691i | −0.173078 | − | 0.0562364i | ||||
\(124\) | −1.79988 | + | 10.4341i | −0.161634 | + | 0.937010i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.623564 | − | 0.740338i | −0.0555515 | − | 0.0659545i | ||||
\(127\) | −2.85478 | + | 8.78610i | −0.253320 | + | 0.779640i | 0.740835 | + | 0.671687i | \(0.234430\pi\) |
−0.994156 | + | 0.107954i | \(0.965570\pi\) | |||||||
\(128\) | 10.2323 | + | 4.82698i | 0.904417 | + | 0.426649i | ||||
\(129\) | −1.89842 | − | 1.37928i | −0.167147 | − | 0.121439i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.46019 | − | 6.13893i | −0.389689 | − | 0.536361i | 0.568430 | − | 0.822732i | \(-0.307551\pi\) |
−0.958119 | + | 0.286371i | \(0.907551\pi\) | |||||||
\(132\) | −0.573644 | + | 3.32548i | −0.0499293 | + | 0.289446i | ||||
\(133\) | −0.373707 | − | 0.514364i | −0.0324045 | − | 0.0446010i | ||||
\(134\) | −13.3723 | − | 8.32147i | −1.15519 | − | 0.718865i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.49251 | − | 11.4133i | −0.213731 | − | 0.978680i | ||||
\(137\) | 4.08531 | + | 12.5733i | 0.349032 | + | 1.07421i | 0.959390 | + | 0.282083i | \(0.0910255\pi\) |
−0.610358 | + | 0.792125i | \(0.708975\pi\) | |||||||
\(138\) | −0.855510 | − | 0.532375i | −0.0728258 | − | 0.0453188i | ||||
\(139\) | 2.15160 | + | 0.699096i | 0.182496 | + | 0.0592965i | 0.398839 | − | 0.917021i | \(-0.369413\pi\) |
−0.216343 | + | 0.976317i | \(0.569413\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.91957 | + | 0.948625i | −0.245872 | + | 0.0798886i | ||||
\(142\) | −3.75255 | − | 0.928216i | −0.314907 | − | 0.0778941i | ||||
\(143\) | 10.8614 | 0.908278 | ||||||||
\(144\) | 11.1838 | − | 3.29700i | 0.931980 | − | 0.274750i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.53156 | + | 21.3328i | 0.126753 | + | 1.76552i | ||||
\(147\) | 1.19079 | − | 1.63898i | 0.0982148 | − | 0.135181i | ||||
\(148\) | −1.88526 | + | 3.57765i | −0.154967 | + | 0.294081i | ||||
\(149\) | − | 15.3980i | − | 1.26145i | −0.776004 | − | 0.630727i | \(-0.782757\pi\) | ||
0.776004 | − | 0.630727i | \(-0.217243\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.300063 | 0.0244187 | 0.0122094 | − | 0.999925i | \(-0.496114\pi\) | ||||
0.0122094 | + | 0.999925i | \(0.496114\pi\) | |||||||
\(152\) | 7.48215 | − | 1.63401i | 0.606882 | − | 0.132535i | ||||
\(153\) | −9.74011 | − | 7.07661i | −0.787441 | − | 0.572110i | ||||
\(154\) | −1.91581 | + | 0.137543i | −0.154380 | + | 0.0110835i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.483910 | + | 0.982879i | 0.0387438 | + | 0.0786933i | ||||
\(157\) | − | 20.8929i | − | 1.66744i | −0.552189 | − | 0.833719i | \(-0.686207\pi\) | ||
0.552189 | − | 0.833719i | \(-0.313793\pi\) | |||||||
\(158\) | −17.6089 | − | 4.35568i | −1.40089 | − | 0.346519i | ||||
\(159\) | 0.341636 | + | 1.05145i | 0.0270935 | + | 0.0833852i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.177227 | − | 0.545449i | 0.0139675 | − | 0.0429874i | ||||
\(162\) | 6.15788 | − | 9.89552i | 0.483809 | − | 0.777465i | ||||
\(163\) | −11.8991 | + | 3.86624i | −0.932006 | + | 0.302827i | −0.735383 | − | 0.677652i | \(-0.762998\pi\) |
−0.196624 | + | 0.980479i | \(0.562998\pi\) | |||||||
\(164\) | 12.2420 | + | 6.45099i | 0.955942 | + | 0.503737i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.78836 | + | 2.35746i | 0.294034 | + | 0.182974i | ||||
\(167\) | 17.4355 | − | 12.6676i | 1.34920 | − | 0.980251i | 0.350149 | − | 0.936694i | \(-0.386131\pi\) |
0.999051 | − | 0.0435571i | \(-0.0138691\pi\) | |||||||
\(168\) | −0.0978019 | − | 0.167239i | −0.00754558 | − | 0.0129028i | ||||
\(169\) | −7.66454 | + | 5.56862i | −0.589580 | + | 0.428355i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.63918 | − | 6.38529i | 0.354767 | − | 0.488295i | ||||
\(172\) | 11.2188 | + | 11.5314i | 0.855428 | + | 0.879262i | ||||
\(173\) | −1.51552 | − | 0.492423i | −0.115223 | − | 0.0374382i | 0.250838 | − | 0.968029i | \(-0.419294\pi\) |
−0.366061 | + | 0.930591i | \(0.619294\pi\) | |||||||
\(174\) | −1.75929 | − | 2.08875i | −0.133372 | − | 0.158348i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.75144 | − | 21.7995i | 0.584287 | − | 1.64320i | ||||
\(177\) | −0.632135 | + | 1.94551i | −0.0475142 | + | 0.146234i | ||||
\(178\) | −1.15114 | − | 16.0340i | −0.0862815 | − | 1.20180i | ||||
\(179\) | −6.51305 | + | 8.96444i | −0.486808 | + | 0.670034i | −0.979795 | − | 0.200003i | \(-0.935905\pi\) |
0.492987 | + | 0.870037i | \(0.335905\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.7991 | − | 16.2401i | −0.877020 | − | 1.20711i | −0.977237 | − | 0.212149i | \(-0.931954\pi\) |
0.100217 | − | 0.994966i | \(-0.468046\pi\) | |||||||
\(182\) | −0.476928 | + | 0.401702i | −0.0353523 | + | 0.0297761i | ||||
\(183\) | 0.384519 | − | 0.279369i | 0.0284245 | − | 0.0206516i | ||||
\(184\) | 5.15963 | + | 4.59396i | 0.380373 | + | 0.338671i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.821915 | + | 2.02348i | 0.0602657 | + | 0.148369i | ||||
\(187\) | −22.7210 | + | 7.38250i | −1.66152 | + | 0.539862i | ||||
\(188\) | 20.8311 | − | 3.00657i | 1.51926 | − | 0.219277i | ||||
\(189\) | −0.385320 | − | 0.125198i | −0.0280279 | − | 0.00910682i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.85762 | − | 18.0279i | −0.423842 | − | 1.30445i | −0.904099 | − | 0.427324i | \(-0.859456\pi\) |
0.480256 | − | 0.877128i | \(-0.340544\pi\) | |||||||
\(192\) | 2.31804 | − | 0.269785i | 0.167290 | − | 0.0194701i | ||||
\(193\) | −2.63353 | −0.189566 | −0.0947828 | − | 0.995498i | \(-0.530216\pi\) | ||||
−0.0947828 | + | 0.995498i | \(0.530216\pi\) | |||||||
\(194\) | 9.62088 | + | 2.37978i | 0.690739 | + | 0.170859i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.95553 | + | 9.68566i | −0.711109 | + | 0.691833i | ||||
\(197\) | 14.8363 | − | 20.4204i | 1.05704 | − | 1.45489i | 0.174498 | − | 0.984658i | \(-0.444170\pi\) |
0.882542 | − | 0.470233i | \(-0.155830\pi\) | |||||||
\(198\) | −8.97315 | − | 22.0911i | −0.637694 | − | 1.56995i | ||||
\(199\) | −3.97231 | −0.281589 | −0.140795 | − | 0.990039i | \(-0.544966\pi\) | ||||
−0.140795 | + | 0.990039i | \(0.544966\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.24879 | −0.229152 | ||||||||
\(202\) | −5.82683 | − | 14.3452i | −0.409975 | − | 1.00932i | ||||
\(203\) | 0.913642 | − | 1.25752i | 0.0641251 | − | 0.0882607i | ||||
\(204\) | −1.68035 | − | 1.72717i | −0.117648 | − | 0.120926i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.0723 | − | 3.97559i | −1.11981 | − | 0.276993i | ||||
\(207\) | 7.11964 | 0.494849 | ||||||||
\(208\) | −2.12394 | − | 7.20462i | −0.147269 | − | 0.499550i | ||||
\(209\) | −4.83972 | − | 14.8951i | −0.334770 | − | 1.03032i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.9414 | + | 4.52984i | 0.959766 | + | 0.311847i | 0.746678 | − | 0.665186i | \(-0.231648\pi\) |
0.213088 | + | 0.977033i | \(0.431648\pi\) | |||||||
\(212\) | −1.08278 | − | 7.50207i | −0.0743656 | − | 0.515244i | ||||
\(213\) | −0.758344 | + | 0.246401i | −0.0519609 | + | 0.0168831i | ||||
\(214\) | 0.187678 | + | 0.462047i | 0.0128294 | + | 0.0315849i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.24529 | − | 3.64490i | 0.220814 | − | 0.248004i | ||||
\(217\) | −1.00569 | + | 0.730677i | −0.0682708 | + | 0.0496016i | ||||
\(218\) | 10.5169 | − | 8.85807i | 0.712295 | − | 0.599944i | ||||
\(219\) | 2.59311 | + | 3.56911i | 0.175226 | + | 0.241178i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.55877 | + | 6.27461i | −0.306656 | + | 0.422076i | ||||
\(222\) | 0.0597331 | + | 0.832014i | 0.00400903 | + | 0.0558411i | ||||
\(223\) | 5.26920 | − | 16.2169i | 0.352852 | − | 1.08597i | −0.604393 | − | 0.796686i | \(-0.706584\pi\) |
0.957245 | − | 0.289280i | \(-0.0934157\pi\) | |||||||
\(224\) | 0.465870 | + | 1.24390i | 0.0311272 | + | 0.0831117i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.298328 | + | 0.354195i | 0.0198445 | + | 0.0235607i | ||||
\(227\) | 13.9216 | + | 4.52341i | 0.924011 | + | 0.300229i | 0.732111 | − | 0.681185i | \(-0.238535\pi\) |
0.191900 | + | 0.981414i | \(0.438535\pi\) | |||||||
\(228\) | 1.13227 | − | 1.10158i | 0.0749867 | − | 0.0729541i | ||||
\(229\) | −3.58252 | + | 4.93092i | −0.236740 | + | 0.325844i | −0.910812 | − | 0.412821i | \(-0.864544\pi\) |
0.674072 | + | 0.738665i | \(0.264544\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.320527 | + | 0.232876i | −0.0210891 | + | 0.0153221i | ||||
\(232\) | 9.45197 | + | 16.1626i | 0.620552 | + | 1.06113i | ||||
\(233\) | −5.77365 | + | 4.19480i | −0.378244 | + | 0.274811i | −0.760621 | − | 0.649196i | \(-0.775106\pi\) |
0.382377 | + | 0.924006i | \(0.375106\pi\) | |||||||
\(234\) | −6.57219 | − | 4.08981i | −0.429638 | − | 0.267359i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.53832 | − | 12.4078i | 0.425608 | − | 0.807676i | ||||
\(237\) | −3.55855 | + | 1.15624i | −0.231153 | + | 0.0751060i | ||||
\(238\) | 0.724649 | − | 1.16449i | 0.0469720 | − | 0.0754826i | ||||
\(239\) | 1.65706 | − | 5.09989i | 0.107186 | − | 0.329885i | −0.883051 | − | 0.469276i | \(-0.844515\pi\) |
0.990237 | + | 0.139392i | \(0.0445148\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.583541 | − | 1.79595i | −0.0375892 | − | 0.115688i | 0.930501 | − | 0.366289i | \(-0.119372\pi\) |
−0.968090 | + | 0.250601i | \(0.919372\pi\) | |||||||
\(242\) | −30.8289 | − | 7.62572i | −1.98176 | − | 0.490200i | ||||
\(243\) | − | 7.58043i | − | 0.486285i | ||||||
\(244\) | −2.92353 | + | 1.43937i | −0.187160 | + | 0.0921460i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.84699 | − | 0.204395i | 0.181518 | − | 0.0130318i | ||||
\(247\) | −4.11342 | − | 2.98858i | −0.261731 | − | 0.190159i | ||||
\(248\) | −3.19483 | − | 14.6292i | −0.202872 | − | 0.928954i | ||||
\(249\) | 0.920377 | 0.0583265 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4.55040i | − | 0.287219i | −0.989634 | − | 0.143609i | \(-0.954129\pi\) | ||
0.989634 | − | 0.143609i | \(-0.0458709\pi\) | |||||||
\(252\) | 1.21104 | + | 0.638161i | 0.0762882 | + | 0.0402004i | ||||
\(253\) | 8.30408 | − | 11.4296i | 0.522073 | − | 0.718572i | ||||
\(254\) | −0.935563 | − | 13.0313i | −0.0587025 | − | 0.817658i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.9758 | − | 0.878833i | −0.998490 | − | 0.0549271i | ||||
\(257\) | −6.99079 | −0.436074 | −0.218037 | − | 0.975941i | \(-0.569965\pi\) | ||||
−0.218037 | + | 0.975941i | \(0.569965\pi\) | |||||||
\(258\) | 3.22147 | + | 0.796851i | 0.200560 | + | 0.0496098i | ||||
\(259\) | −0.451544 | + | 0.146716i | −0.0280576 | + | 0.00911646i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.3516 | + | 5.96279i | 1.13593 | + | 0.369088i | ||||
\(262\) | 9.11115 | + | 5.66978i | 0.562889 | + | 0.350280i | ||||
\(263\) | 6.99005 | + | 21.5131i | 0.431025 | + | 1.32656i | 0.897106 | + | 0.441816i | \(0.145665\pi\) |
−0.466081 | + | 0.884742i | \(0.654335\pi\) | |||||||
\(264\) | −1.01823 | − | 4.66251i | −0.0626679 | − | 0.286958i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.763399 | + | 0.475055i | 0.0468070 | + | 0.0291275i | ||||
\(267\) | −1.94902 | − | 2.68259i | −0.119278 | − | 0.164172i | ||||
\(268\) | 21.9499 | + | 3.78634i | 1.34080 | + | 0.231287i | ||||
\(269\) | 3.68963 | + | 5.07835i | 0.224961 | + | 0.309632i | 0.906546 | − | 0.422106i | \(-0.138709\pi\) |
−0.681585 | + | 0.731739i | \(0.738709\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.75055 | − | 1.99839i | −0.167084 | − | 0.121393i | 0.501101 | − | 0.865389i | \(-0.332928\pi\) |
−0.668185 | + | 0.743995i | \(0.732928\pi\) | |||||||
\(272\) | 9.34005 | + | 13.6277i | 0.566323 | + | 0.826300i | ||||
\(273\) | −0.0397464 | + | 0.122327i | −0.00240556 | + | 0.00740355i | ||||
\(274\) | −12.0444 | − | 14.2999i | −0.727628 | − | 0.863890i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.40427 | + | 0.242235i | 0.0845269 | + | 0.0145808i | ||||
\(277\) | −24.4846 | − | 7.95552i | −1.47114 | − | 0.478001i | −0.539684 | − | 0.841868i | \(-0.681456\pi\) |
−0.931451 | + | 0.363867i | \(0.881456\pi\) | |||||||
\(278\) | −3.19119 | + | 0.229107i | −0.191395 | + | 0.0137409i | ||||
\(279\) | −12.4846 | − | 9.07059i | −0.747433 | − | 0.543042i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.16034 | + | 2.29612i | −0.188530 | + | 0.136975i | −0.678047 | − | 0.735019i | \(-0.737173\pi\) |
0.489517 | + | 0.871994i | \(0.337173\pi\) | |||||||
\(282\) | 3.32050 | − | 2.79675i | 0.197733 | − | 0.166544i | ||||
\(283\) | −0.754960 | − | 1.03911i | −0.0448777 | − | 0.0617689i | 0.785988 | − | 0.618241i | \(-0.212155\pi\) |
−0.830866 | + | 0.556472i | \(0.812155\pi\) | |||||||
\(284\) | 5.41078 | − | 0.780942i | 0.321071 | − | 0.0463404i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.2312 | + | 5.78054i | −0.841507 | + | 0.341810i | ||||
\(287\) | 0.502032 | + | 1.54510i | 0.0296340 | + | 0.0912041i | ||||
\(288\) | −12.8988 | + | 10.2720i | −0.760071 | + | 0.605283i | ||||
\(289\) | 0.0183581 | − | 0.0565005i | 0.00107989 | − | 0.00332356i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.94426 | − | 0.631729i | 0.113975 | − | 0.0370326i | ||||
\(292\) | −13.3602 | − | 27.1362i | −0.781848 | − | 1.58803i | ||||
\(293\) | − | 8.55020i | − | 0.499508i | −0.968309 | − | 0.249754i | \(-0.919650\pi\) | ||
0.968309 | − | 0.249754i | \(-0.0803498\pi\) | |||||||
\(294\) | −0.687953 | + | 2.78123i | −0.0401222 | + | 0.162204i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.566103 | − | 5.69096i | 0.0329041 | − | 0.330781i | ||||
\(297\) | −8.07416 | − | 5.86622i | −0.468510 | − | 0.340393i | ||||
\(298\) | 8.19495 | + | 20.1753i | 0.474721 | + | 1.16872i | ||||
\(299\) | − | 4.58650i | − | 0.265244i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.88885i | 0.108871i | ||||||||
\(302\) | −0.393157 | + | 0.159696i | −0.0226236 | + | 0.00918946i | ||||
\(303\) | −2.58382 | − | 1.87725i | −0.148436 | − | 0.107845i | ||||
\(304\) | −8.93385 | + | 6.12302i | −0.512392 | + | 0.351179i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 16.5282 | + | 4.08835i | 0.944855 | + | 0.233716i | ||||
\(307\) | 11.0920i | 0.633052i | 0.948584 | + | 0.316526i | \(0.102517\pi\) | ||||
−0.948584 | + | 0.316526i | \(0.897483\pi\) | |||||||
\(308\) | 2.43699 | − | 1.19983i | 0.138860 | − | 0.0683664i | ||||
\(309\) | −3.24802 | + | 1.05535i | −0.184774 | + | 0.0600366i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.28886 | − | 28.5882i | 0.526723 | − | 1.62109i | −0.234160 | − | 0.972198i | \(-0.575234\pi\) |
0.760883 | − | 0.648889i | \(-0.224766\pi\) | |||||||
\(312\) | −1.15714 | − | 1.03028i | −0.0655101 | − | 0.0583279i | ||||
\(313\) | 0.0113715 | + | 0.0349980i | 0.000642758 | + | 0.00197820i | 0.951377 | − | 0.308028i | \(-0.0996690\pi\) |
−0.950735 | + | 0.310006i | \(0.899669\pi\) | |||||||
\(314\) | 11.1194 | + | 27.3750i | 0.627504 | + | 1.54486i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.3902 | − | 3.66459i | 1.42831 | − | 0.206149i | ||||
\(317\) | 9.56085 | + | 13.1594i | 0.536991 | + | 0.739104i | 0.988176 | − | 0.153326i | \(-0.0489985\pi\) |
−0.451185 | + | 0.892431i | \(0.648998\pi\) | |||||||
\(318\) | −1.00722 | − | 1.19584i | −0.0564819 | − | 0.0670592i | ||||
\(319\) | 30.9770 | − | 22.5061i | 1.73438 | − | 1.26010i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0832228 | + | 0.0604649i | 0.00464505 | + | 0.00337482i | ||||
\(322\) | 0.0580807 | + | 0.808997i | 0.00323671 | + | 0.0450836i | ||||
\(323\) | 10.6362 | + | 3.45591i | 0.591814 | + | 0.192292i | ||||
\(324\) | −2.80189 | + | 16.2429i | −0.155660 | + | 0.902382i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.5331 | − | 11.3985i | 0.749529 | − | 0.631305i | ||||
\(327\) | 0.876461 | − | 2.69747i | 0.0484684 | − | 0.149170i | ||||
\(328\) | −19.4734 | − | 1.93710i | −1.07524 | − | 0.106958i | ||||
\(329\) | 1.99909 | + | 1.45242i | 0.110213 | + | 0.0800746i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.3539 | − | 18.3800i | −0.733995 | − | 1.01026i | −0.998942 | − | 0.0459939i | \(-0.985355\pi\) |
0.264947 | − | 0.964263i | \(-0.414645\pi\) | |||||||
\(332\) | −6.21836 | − | 1.07266i | −0.341277 | − | 0.0588700i | ||||
\(333\) | −3.46435 | − | 4.76827i | −0.189845 | − | 0.261300i | ||||
\(334\) | −16.1030 | + | 25.8771i | −0.881120 | + | 1.41593i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.217151 | + | 0.167074i | 0.0118465 | + | 0.00911462i | ||||
\(337\) | −5.81367 | − | 17.8926i | −0.316691 | − | 0.974674i | −0.975053 | − | 0.221972i | \(-0.928751\pi\) |
0.658362 | − | 0.752701i | \(-0.271249\pi\) | |||||||
\(338\) | 7.07880 | − | 11.3754i | 0.385036 | − | 0.618741i | ||||
\(339\) | 0.0908470 | + | 0.0295180i | 0.00493413 | + | 0.00160320i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.1231 | + | 9.46267i | −1.57711 | + | 0.512433i | ||||
\(342\) | −2.68019 | + | 10.8353i | −0.144928 | + | 0.585908i | ||||
\(343\) | −3.27438 | −0.176800 | ||||||||
\(344\) | −20.8366 | − | 9.13828i | −1.12343 | − | 0.492703i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.24778 | − | 0.161376i | 0.120842 | − | 0.00867564i | ||||
\(347\) | 17.3624 | − | 23.8972i | 0.932060 | − | 1.28287i | −0.0269903 | − | 0.999636i | \(-0.508592\pi\) |
0.959051 | − | 0.283235i | \(-0.0914077\pi\) | |||||||
\(348\) | 3.41676 | + | 1.80048i | 0.183158 | + | 0.0965157i | ||||
\(349\) | − | 15.7634i | − | 0.843797i | −0.906643 | − | 0.421898i | \(-0.861364\pi\) | ||
0.906643 | − | 0.421898i | \(-0.138636\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.24002 | −0.172940 | ||||||||
\(352\) | 1.44553 | + | 32.6881i | 0.0770471 | + | 1.74228i | ||||
\(353\) | −6.60477 | − | 4.79864i | −0.351536 | − | 0.255406i | 0.397977 | − | 0.917395i | \(-0.369712\pi\) |
−0.749513 | + | 0.661989i | \(0.769712\pi\) | |||||||
\(354\) | −0.207162 | − | 2.88553i | −0.0110106 | − | 0.153364i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.0417 | + | 20.3960i | 0.532210 | + | 1.08098i | ||||
\(357\) | − | 0.282911i | − | 0.0149732i | ||||||
\(358\) | 3.76277 | − | 15.2120i | 0.198869 | − | 0.803977i | ||||
\(359\) | 9.42480 | + | 29.0065i | 0.497422 | + | 1.53091i | 0.813148 | + | 0.582056i | \(0.197752\pi\) |
−0.315727 | + | 0.948850i | \(0.602248\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.60574 | − | 11.0973i | 0.189776 | − | 0.584071i | ||||
\(362\) | 24.1029 | + | 14.9990i | 1.26682 | + | 0.788328i | ||||
\(363\) | −6.23015 | + | 2.02430i | −0.326998 | + | 0.106248i | ||||
\(364\) | 0.411106 | − | 0.780155i | 0.0215478 | − | 0.0408912i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.355133 | + | 0.570688i | −0.0185631 | + | 0.0298303i | ||||
\(367\) | −6.06821 | + | 4.40881i | −0.316758 | + | 0.230138i | −0.734791 | − | 0.678294i | \(-0.762720\pi\) |
0.418033 | + | 0.908432i | \(0.362720\pi\) | |||||||
\(368\) | −9.20535 | − | 3.27323i | −0.479862 | − | 0.170629i | ||||
\(369\) | −16.3161 | + | 11.8543i | −0.849383 | + | 0.617113i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.523072 | − | 0.719947i | 0.0271565 | − | 0.0373778i | ||||
\(372\) | −2.15383 | − | 2.21384i | −0.111671 | − | 0.114782i | ||||
\(373\) | 12.1334 | + | 3.94238i | 0.628243 | + | 0.204129i | 0.605797 | − | 0.795619i | \(-0.292854\pi\) |
0.0224465 | + | 0.999748i | \(0.492854\pi\) | |||||||
\(374\) | 25.8412 | − | 21.7652i | 1.33621 | − | 1.12545i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −25.6938 | + | 15.0258i | −1.32506 | + | 0.774898i | ||||
\(377\) | 3.84125 | − | 11.8222i | 0.197834 | − | 0.608872i | ||||
\(378\) | 0.571497 | − | 0.0410297i | 0.0293946 | − | 0.00211034i | ||||
\(379\) | 7.20040 | − | 9.91051i | 0.369860 | − | 0.509069i | −0.583003 | − | 0.812470i | \(-0.698122\pi\) |
0.952863 | + | 0.303402i | \(0.0981224\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.58402 | − | 2.18022i | −0.0811519 | − | 0.111696i | ||||
\(382\) | 17.2695 | + | 20.5036i | 0.883586 | + | 1.04905i | ||||
\(383\) | −21.7829 | + | 15.8262i | −1.11305 | + | 0.808681i | −0.983142 | − | 0.182844i | \(-0.941470\pi\) |
−0.129912 | + | 0.991525i | \(0.541470\pi\) | |||||||
\(384\) | −2.89363 | + | 1.58717i | −0.147665 | + | 0.0809948i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.45058 | − | 1.40159i | 0.175630 | − | 0.0713388i | ||||
\(387\) | −22.3004 | + | 7.24584i | −1.13359 | + | 0.368327i | ||||
\(388\) | −13.8723 | + | 2.00220i | −0.704259 | + | 0.101646i | ||||
\(389\) | 9.06656 | + | 2.94590i | 0.459693 | + | 0.149363i | 0.529703 | − | 0.848183i | \(-0.322303\pi\) |
−0.0700104 | + | 0.997546i | \(0.522303\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.11744 | + | 9.59449i | 0.157656 | + | 0.485214i | ||||
\(392\) | 7.88944 | − | 17.9891i | 0.398477 | − | 0.908584i | ||||
\(393\) | 2.21354 | 0.111658 | ||||||||
\(394\) | −8.57133 | + | 34.6518i | −0.431817 | + | 1.74573i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 23.5141 | + | 24.1693i | 1.18163 | + | 1.21455i | ||||
\(397\) | −13.6774 | + | 18.8253i | −0.686449 | + | 0.944816i | −0.999989 | − | 0.00475885i | \(-0.998485\pi\) |
0.313539 | + | 0.949575i | \(0.398485\pi\) | |||||||
\(398\) | 5.20471 | − | 2.11409i | 0.260889 | − | 0.105970i | ||||
\(399\) | 0.185467 | 0.00928495 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.2917 | 0.613820 | 0.306910 | − | 0.951739i | \(-0.400705\pi\) | ||||
0.306910 | + | 0.951739i | \(0.400705\pi\) | |||||||
\(402\) | 4.25673 | − | 1.72903i | 0.212306 | − | 0.0862363i | ||||
\(403\) | −5.84330 | + | 8.04262i | −0.291076 | + | 0.400631i | ||||
\(404\) | 15.2692 | + | 15.6946i | 0.759672 | + | 0.780838i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.527837 | + | 2.13391i | −0.0261961 | + | 0.105904i | ||||
\(407\) | −11.6955 | −0.579724 | ||||||||
\(408\) | 3.12090 | + | 1.36873i | 0.154507 | + | 0.0677621i | ||||
\(409\) | −9.76563 | − | 30.0555i | −0.482879 | − | 1.48615i | −0.835029 | − | 0.550206i | \(-0.814549\pi\) |
0.352150 | − | 0.935944i | \(-0.385451\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.66777 | − | 1.19173i | −0.180918 | − | 0.0587837i | ||||
\(412\) | 23.1746 | − | 3.34481i | 1.14173 | − | 0.164787i | ||||
\(413\) | 1.56601 | − | 0.508829i | 0.0770585 | − | 0.0250378i | ||||
\(414\) | −9.32850 | + | 3.78913i | −0.458471 | + | 0.186226i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.61725 | + | 8.30947i | 0.324437 | + | 0.407405i | ||||
\(417\) | −0.533906 | + | 0.387905i | −0.0261455 | + | 0.0189958i | ||||
\(418\) | 14.2685 | + | 16.9406i | 0.697897 | + | 0.828591i | ||||
\(419\) | −5.07417 | − | 6.98399i | −0.247889 | − | 0.341190i | 0.666881 | − | 0.745164i | \(-0.267629\pi\) |
−0.914771 | + | 0.403973i | \(0.867629\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.53026 | − | 10.3645i | 0.367002 | − | 0.505135i | −0.585081 | − | 0.810975i | \(-0.698937\pi\) |
0.952083 | + | 0.305840i | \(0.0989371\pi\) | |||||||
\(422\) | −20.6775 | + | 1.48451i | −1.00657 | + | 0.0722649i | ||||
\(423\) | −9.47907 | + | 29.1736i | −0.460888 | + | 1.41847i | ||||
\(424\) | 5.41138 | + | 9.25332i | 0.262800 | + | 0.449381i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.862483 | − | 0.726443i | 0.0417874 | − | 0.0351963i | ||||
\(427\) | −0.363855 | − | 0.118224i | −0.0176082 | − | 0.00572124i | ||||
\(428\) | −0.491810 | − | 0.505513i | −0.0237725 | − | 0.0244349i | ||||
\(429\) | −1.86234 | + | 2.56329i | −0.0899145 | + | 0.123757i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.3298 | + | 17.6766i | −1.17193 | + | 0.851454i | −0.991238 | − | 0.132087i | \(-0.957832\pi\) |
−0.180688 | + | 0.983541i | \(0.557832\pi\) | |||||||
\(432\) | −2.31230 | + | 6.50290i | −0.111251 | + | 0.312871i | ||||
\(433\) | 1.30079 | − | 0.945079i | 0.0625120 | − | 0.0454176i | −0.556090 | − | 0.831122i | \(-0.687699\pi\) |
0.618602 | + | 0.785704i | \(0.287699\pi\) | |||||||
\(434\) | 0.928834 | − | 1.49261i | 0.0445855 | − | 0.0716474i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.06544 | + | 17.2035i | −0.434156 | + | 0.823897i | ||||
\(437\) | −6.28982 | + | 2.04369i | −0.300883 | + | 0.0977628i | ||||
\(438\) | −5.29714 | − | 3.29636i | −0.253107 | − | 0.157506i | ||||
\(439\) | 11.7350 | − | 36.1165i | 0.560079 | − | 1.72374i | −0.122061 | − | 0.992523i | \(-0.538950\pi\) |
0.682139 | − | 0.731222i | \(-0.261050\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.25562 | − | 19.2528i | −0.297887 | − | 0.916801i | ||||
\(442\) | 2.63373 | − | 10.6475i | 0.125274 | − | 0.506451i | ||||
\(443\) | 19.5670i | 0.929654i | 0.885402 | + | 0.464827i | \(0.153883\pi\) | ||||
−0.885402 | + | 0.464827i | \(0.846117\pi\) | |||||||
\(444\) | −0.521070 | − | 1.05836i | −0.0247289 | − | 0.0502273i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.72681 | + | 24.0525i | 0.0817670 | + | 1.13892i | ||||
\(447\) | 3.63392 | + | 2.64020i | 0.171879 | + | 0.124877i | ||||
\(448\) | −1.27242 | − | 1.38188i | −0.0601162 | − | 0.0652878i | ||||
\(449\) | 33.2573 | 1.56951 | 0.784755 | − | 0.619806i | \(-0.212789\pi\) | ||||
0.784755 | + | 0.619806i | \(0.212789\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.0197i | 1.88445i | ||||||||
\(452\) | −0.579389 | − | 0.305311i | −0.0272522 | − | 0.0143606i | ||||
\(453\) | −0.0514498 | + | 0.0708145i | −0.00241732 | + | 0.00332716i | ||||
\(454\) | −20.6482 | + | 1.48241i | −0.969069 | + | 0.0695728i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.897291 | + | 2.04595i | −0.0420195 | + | 0.0958106i | ||||
\(457\) | −15.5897 | −0.729254 | −0.364627 | − | 0.931154i | \(-0.618803\pi\) | ||||
−0.364627 | + | 0.931154i | \(0.618803\pi\) | |||||||
\(458\) | 2.06972 | − | 8.36739i | 0.0967119 | − | 0.390982i | ||||
\(459\) | 6.77780 | − | 2.20224i | 0.316361 | − | 0.102792i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.51241 | − | 1.79109i | −0.256739 | − | 0.0834194i | 0.177820 | − | 0.984063i | \(-0.443096\pi\) |
−0.434558 | + | 0.900644i | \(0.643096\pi\) | |||||||
\(462\) | 0.296032 | − | 0.475713i | 0.0137726 | − | 0.0221322i | ||||
\(463\) | −3.67309 | − | 11.3046i | −0.170703 | − | 0.525370i | 0.828708 | − | 0.559681i | \(-0.189076\pi\) |
−0.999411 | + | 0.0343111i | \(0.989076\pi\) | |||||||
\(464\) | −20.9863 | − | 16.1467i | −0.974266 | − | 0.749591i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.33242 | − | 8.56902i | 0.247019 | − | 0.396952i | ||||
\(467\) | 14.6630 | + | 20.1818i | 0.678521 | + | 0.933903i | 0.999915 | − | 0.0130420i | \(-0.00415151\pi\) |
−0.321394 | + | 0.946945i | \(0.604152\pi\) | |||||||
\(468\) | 10.7878 | + | 1.86090i | 0.498668 | + | 0.0860199i | ||||
\(469\) | 1.53710 | + | 2.11564i | 0.0709767 | + | 0.0976910i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.93072 | + | 3.58238i | 0.227196 | + | 0.165067i | ||||
\(472\) | −1.96332 | + | 19.7370i | −0.0903691 | + | 0.908470i | ||||
\(473\) | −14.3782 | + | 44.2515i | −0.661109 | + | 2.03468i | ||||
\(474\) | 4.04723 | − | 3.40886i | 0.185895 | − | 0.156574i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.329721 | + | 1.91143i | −0.0151127 | + | 0.0876105i | ||||
\(477\) | 10.5065 | + | 3.41377i | 0.481060 | + | 0.156306i | ||||
\(478\) | 0.543048 | + | 7.56403i | 0.0248384 | + | 0.345971i | ||||
\(479\) | −12.4287 | − | 9.02994i | −0.567880 | − | 0.412589i | 0.266455 | − | 0.963847i | \(-0.414148\pi\) |
−0.834334 | + | 0.551259i | \(0.814148\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.07174 | + | 2.23175i | −0.140059 | + | 0.101759i | ||||
\(482\) | 1.72041 | + | 2.04258i | 0.0783624 | + | 0.0930372i | ||||
\(483\) | 0.0983377 | + | 0.135350i | 0.00447452 | + | 0.00615865i | ||||
\(484\) | 44.4521 | − | 6.41580i | 2.02055 | − | 0.291627i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.03437 | + | 9.93226i | 0.183003 | + | 0.450536i | ||||
\(487\) | −6.97042 | − | 21.4527i | −0.315860 | − | 0.972117i | −0.975399 | − | 0.220447i | \(-0.929249\pi\) |
0.659539 | − | 0.751670i | \(-0.270751\pi\) | |||||||
\(488\) | 3.06451 | − | 3.44185i | 0.138724 | − | 0.155805i | ||||
\(489\) | 1.12782 | − | 3.47109i | 0.0510020 | − | 0.156968i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.25634 | + | 2.35773i | −0.327474 | + | 0.106403i | −0.468140 | − | 0.883654i | \(-0.655076\pi\) |
0.140666 | + | 0.990057i | \(0.455076\pi\) | |||||||
\(492\) | −3.62149 | + | 1.78300i | −0.163269 | + | 0.0803839i | ||||
\(493\) | 27.3417i | 1.23141i | ||||||||
\(494\) | 6.98016 | + | 1.72658i | 0.314052 | + | 0.0776827i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.9718 | + | 17.4676i | 0.537550 | + | 0.784317i | ||||
\(497\) | 0.519253 | + | 0.377259i | 0.0232917 | + | 0.0169224i | ||||
\(498\) | −1.20592 | + | 0.489832i | −0.0540387 | + | 0.0219499i | ||||
\(499\) | 26.9689i | 1.20729i | 0.797252 | + | 0.603647i | \(0.206286\pi\) | ||||
−0.797252 | + | 0.603647i | \(0.793714\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.28680i | 0.280874i | ||||||||
\(502\) | 2.42176 | + | 5.96216i | 0.108088 | + | 0.266104i | ||||
\(503\) | −24.9059 | − | 18.0952i | −1.11050 | − | 0.806825i | −0.127757 | − | 0.991805i | \(-0.540778\pi\) |
−0.982742 | + | 0.184980i | \(0.940778\pi\) | |||||||
\(504\) | −1.92640 | − | 0.191626i | −0.0858086 | − | 0.00853572i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.79750 | + | 19.3951i | −0.213275 | + | 0.862218i | ||||
\(507\) | − | 2.76364i | − | 0.122738i | ||||||
\(508\) | 8.16120 | + | 16.5764i | 0.362095 | + | 0.735458i | ||||
\(509\) | −3.29675 | + | 1.07118i | −0.146126 | + | 0.0474792i | −0.381167 | − | 0.924506i | \(-0.624478\pi\) |
0.235041 | + | 0.971986i | \(0.424478\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.09735 | − | 3.37731i | 0.0485441 | − | 0.149403i | ||||
\(512\) | 21.4001 | − | 7.35098i | 0.945758 | − | 0.324871i | ||||
\(513\) | 1.44371 | + | 4.44330i | 0.0637416 | + | 0.196176i | ||||
\(514\) | 9.15968 | − | 3.72056i | 0.404016 | − | 0.164107i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.64503 | + | 0.670420i | −0.204486 | + | 0.0295136i | ||||
\(517\) | 35.7781 | + | 49.2443i | 1.57352 | + | 2.16576i | ||||
\(518\) | 0.513552 | − | 0.432549i | 0.0225642 | − | 0.0190051i | ||||
\(519\) | 0.376068 | − | 0.273229i | 0.0165076 | − | 0.0119934i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.2980 | − | 23.4659i | −1.41500 | − | 1.02806i | −0.992571 | − | 0.121663i | \(-0.961177\pi\) |
−0.422430 | − | 0.906395i | \(-0.638823\pi\) | |||||||
\(522\) | −27.2186 | + | 1.95412i | −1.19133 | + | 0.0855294i | ||||
\(523\) | −5.94816 | − | 1.93267i | −0.260095 | − | 0.0845099i | 0.176067 | − | 0.984378i | \(-0.443662\pi\) |
−0.436162 | + | 0.899868i | \(0.643662\pi\) | |||||||
\(524\) | −14.9554 | − | 2.57980i | −0.653329 | − | 0.112699i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.6082 | − | 24.4674i | −0.898559 | − | 1.06683i | ||||
\(527\) | 6.75704 | − | 20.7960i | 0.294341 | − | 0.905890i | ||||
\(528\) | 3.81557 | + | 5.56715i | 0.166051 | + | 0.242279i | ||||
\(529\) | 13.7810 | + | 10.0125i | 0.599173 | + | 0.435325i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0148 | + | 16.5370i | 0.521399 | + | 0.717644i | ||||
\(532\) | −1.25307 | − | 0.216154i | −0.0543275 | − | 0.00937147i | ||||
\(533\) | 7.63661 | + | 10.5109i | 0.330778 | + | 0.455277i | ||||
\(534\) | 3.98140 | + | 2.47758i | 0.172292 | + | 0.107216i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −30.7749 | + | 6.72085i | −1.32927 | + | 0.290296i | ||||
\(537\) | −0.998852 | − | 3.07415i | −0.0431036 | − | 0.132659i | ||||
\(538\) | −7.53708 | − | 4.69025i | −0.324947 | − | 0.202211i | ||||
\(539\) | −38.2040 | − | 12.4132i | −1.64556 | − | 0.534676i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.5034 | − | 6.33705i | 0.838518 | − | 0.272451i | 0.141889 | − | 0.989883i | \(-0.454682\pi\) |
0.696629 | + | 0.717432i | \(0.254682\pi\) | |||||||
\(542\) | 4.66746 | + | 1.15453i | 0.200485 | + | 0.0495911i | ||||
\(543\) | 5.85576 | 0.251295 | ||||||||
\(544\) | −19.4906 | − | 12.8848i | −0.835651 | − | 0.552433i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.0130256 | − | 0.181432i | −0.000557445 | − | 0.00776457i | ||||
\(547\) | 13.0358 | − | 17.9423i | 0.557372 | − | 0.767157i | −0.433617 | − | 0.901097i | \(-0.642763\pi\) |
0.990989 | + | 0.133940i | \(0.0427629\pi\) | |||||||
\(548\) | 23.3917 | + | 12.3263i | 0.999243 | + | 0.526555i | ||||
\(549\) | − | 4.74932i | − | 0.202696i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.9243 | −0.763599 | ||||||||
\(552\) | −1.96886 | + | 0.429973i | −0.0838002 | + | 0.0183009i | ||||
\(553\) | 2.43661 | + | 1.77030i | 0.103615 | + | 0.0752808i | ||||
\(554\) | 36.3149 | − | 2.60717i | 1.54287 | − | 0.110768i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.05933 | − | 1.99857i | 0.172154 | − | 0.0847580i | ||||
\(557\) | − | 36.8641i | − | 1.56198i | −0.624543 | − | 0.780991i | \(-0.714715\pi\) | ||
0.624543 | − | 0.780991i | \(-0.285285\pi\) | |||||||
\(558\) | 21.1854 | + | 5.24033i | 0.896848 | + | 0.221841i | ||||
\(559\) | 4.66780 | + | 14.3660i | 0.197427 | + | 0.607617i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.15356 | − | 6.62797i | 0.0909233 | − | 0.279833i | ||||
\(562\) | 2.91882 | − | 4.69045i | 0.123123 | − | 0.197855i | ||||
\(563\) | 39.1294 | − | 12.7139i | 1.64911 | − | 0.535828i | 0.670561 | − | 0.741854i | \(-0.266053\pi\) |
0.978546 | + | 0.206027i | \(0.0660534\pi\) | |||||||
\(564\) | −2.86222 | + | 5.43164i | −0.120521 | + | 0.228713i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.54221 | + | 0.959702i | 0.0648240 | + | 0.0403393i | ||||
\(567\) | −1.56557 | + | 1.13745i | −0.0657477 | + | 0.0477685i | ||||
\(568\) | −6.67385 | + | 3.90289i | −0.280028 | + | 0.163762i | ||||
\(569\) | 2.43983 | − | 1.77264i | 0.102283 | − | 0.0743130i | −0.535468 | − | 0.844555i | \(-0.679865\pi\) |
0.637751 | + | 0.770242i | \(0.279865\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.11104 | − | 11.1639i | 0.339436 | − | 0.467194i | −0.604840 | − | 0.796347i | \(-0.706763\pi\) |
0.944277 | + | 0.329153i | \(0.106763\pi\) | |||||||
\(572\) | 15.5699 | − | 15.1479i | 0.651012 | − | 0.633365i | ||||
\(573\) | 5.25893 | + | 1.70873i | 0.219695 | + | 0.0713833i | ||||
\(574\) | −1.48010 | − | 1.75728i | −0.0617782 | − | 0.0733473i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 11.4338 | − | 20.3237i | 0.476410 | − | 0.846822i | ||||
\(577\) | 4.07686 | − | 12.5473i | 0.169722 | − | 0.522351i | −0.829631 | − | 0.558312i | \(-0.811449\pi\) |
0.999353 | + | 0.0359612i | \(0.0114493\pi\) | |||||||
\(578\) | 0.00601630 | + | 0.0838002i | 0.000250245 | + | 0.00348563i | ||||
\(579\) | 0.451554 | − | 0.621511i | 0.0187659 | − | 0.0258291i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.435458 | − | 0.599356i | −0.0180658 | − | 0.0248655i | ||||
\(582\) | −2.21126 | + | 1.86247i | −0.0916595 | + | 0.0772020i | ||||
\(583\) | 17.7347 | − | 12.8850i | 0.734498 | − | 0.533644i | ||||
\(584\) | 31.9474 | + | 28.4448i | 1.32199 | + | 1.17705i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.55049 | + | 11.2029i | 0.187979 | + | 0.462788i | ||||
\(587\) | −25.8189 | + | 8.38908i | −1.06566 | + | 0.346254i | −0.788796 | − | 0.614655i | \(-0.789295\pi\) |
−0.276865 | + | 0.960909i | \(0.589295\pi\) | |||||||
\(588\) | −0.578800 | − | 4.01023i | −0.0238693 | − | 0.165379i | ||||
\(589\) | 13.6332 | + | 4.42969i | 0.561745 | + | 0.182522i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.27531 | + | 7.00269i | 0.0935939 | + | 0.288052i | ||||
\(592\) | 2.28704 | + | 7.75787i | 0.0939968 | + | 0.318846i | ||||
\(593\) | 10.5301 | 0.432420 | 0.216210 | − | 0.976347i | \(-0.430630\pi\) | ||||
0.216210 | + | 0.976347i | \(0.430630\pi\) | |||||||
\(594\) | 13.7012 | + | 3.38908i | 0.562168 | + | 0.139056i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.4749 | − | 22.0732i | −0.879645 | − | 0.904153i | ||||
\(597\) | 0.681105 | − | 0.937461i | 0.0278758 | − | 0.0383677i | ||||
\(598\) | 2.44097 | + | 6.00945i | 0.0998187 | + | 0.245745i | ||||
\(599\) | −20.1787 | −0.824481 | −0.412241 | − | 0.911075i | \(-0.635254\pi\) | ||||
−0.412241 | + | 0.911075i | \(0.635254\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.7592 | 0.479669 | 0.239834 | − | 0.970814i | \(-0.422907\pi\) | ||||
0.239834 | + | 0.970814i | \(0.422907\pi\) | |||||||
\(602\) | −1.00526 | − | 2.47486i | −0.0409713 | − | 0.100868i | ||||
\(603\) | −19.0815 | + | 26.2634i | −0.777058 | + | 1.06953i | ||||
\(604\) | 0.430142 | − | 0.418483i | 0.0175022 | − | 0.0170278i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.38453 | + | 1.08454i | 0.178110 | + | 0.0440565i | ||||
\(607\) | −35.8362 | −1.45455 | −0.727274 | − | 0.686347i | \(-0.759213\pi\) | ||||
−0.727274 | + | 0.686347i | \(0.759213\pi\) | |||||||
\(608\) | 8.44686 | − | 12.7774i | 0.342565 | − | 0.518190i | ||||
\(609\) | 0.140118 | + | 0.431238i | 0.00567785 | + | 0.0174746i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.7937 | + | 6.10645i | 0.760313 | + | 0.247041i | ||||
\(612\) | −23.8319 | + | 3.43968i | −0.963349 | + | 0.139041i | ||||
\(613\) | −12.1564 | + | 3.94986i | −0.490994 | + | 0.159533i | −0.544041 | − | 0.839059i | \(-0.683106\pi\) |
0.0530477 | + | 0.998592i | \(0.483106\pi\) | |||||||
\(614\) | −5.90324 | − | 14.5333i | −0.238235 | − | 0.586515i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.55451 | + | 2.86906i | −0.102924 | + | 0.115598i | ||||
\(617\) | −12.6424 | + | 9.18527i | −0.508965 | + | 0.369785i | −0.812431 | − | 0.583057i | \(-0.801856\pi\) |
0.303466 | + | 0.952842i | \(0.401856\pi\) | |||||||
\(618\) | 3.69406 | − | 3.11139i | 0.148597 | − | 0.125159i | ||||
\(619\) | −20.9771 | − | 28.8724i | −0.843139 | − | 1.16048i | −0.985333 | − | 0.170643i | \(-0.945416\pi\) |
0.142194 | − | 0.989839i | \(-0.454584\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.47715 | + | 3.40951i | −0.0994048 | + | 0.136819i | ||||
\(622\) | 3.04413 | + | 42.4013i | 0.122059 | + | 1.70014i | ||||
\(623\) | −0.824786 | + | 2.53843i | −0.0330444 | + | 0.101700i | ||||
\(624\) | 2.06446 | + | 0.734080i | 0.0826446 | + | 0.0293867i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.0335258 | − | 0.0398041i | −0.00133996 | − | 0.00159089i | ||||
\(627\) | 4.34507 | + | 1.41180i | 0.173525 | + | 0.0563818i | ||||
\(628\) | −29.1384 | − | 29.9502i | −1.16275 | − | 1.19514i | ||||
\(629\) | 4.90885 | − | 6.75645i | 0.195729 | − | 0.269397i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.4157 | − | 26.4575i | 1.44969 | − | 1.05326i | 0.463781 | − | 0.885950i | \(-0.346492\pi\) |
0.985905 | − | 0.167308i | \(-0.0535075\pi\) | |||||||
\(632\) | −31.3172 | + | 18.3144i | −1.24573 | + | 0.728509i | ||||
\(633\) | −3.45948 | + | 2.51346i | −0.137502 | + | 0.0999010i | ||||
\(634\) | −19.5306 | − | 12.1537i | −0.775660 | − | 0.482686i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.95614 | + | 1.03080i | 0.0775660 | + | 0.0408737i | ||||
\(637\) | −12.4027 | + | 4.02989i | −0.491414 | + | 0.159670i | ||||
\(638\) | −28.6097 | + | 45.9749i | −1.13267 | + | 1.82016i | ||||
\(639\) | −2.46214 | + | 7.57770i | −0.0974009 | + | 0.299769i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.02897 | + | 12.3999i | 0.159135 | + | 0.489766i | 0.998556 | − | 0.0537145i | \(-0.0171061\pi\) |
−0.839422 | + | 0.543481i | \(0.817106\pi\) | |||||||
\(642\) | −0.141223 | − | 0.0349323i | −0.00557361 | − | 0.00137867i | ||||
\(643\) | − | 34.5558i | − | 1.36275i | −0.731935 | − | 0.681375i | \(-0.761382\pi\) | ||
0.731935 | − | 0.681375i | \(-0.238618\pi\) | |||||||
\(644\) | −0.506655 | − | 1.02908i | −0.0199650 | − | 0.0405513i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.7753 | + | 1.13257i | −0.620673 | + | 0.0445602i | ||||
\(647\) | −7.76508 | − | 5.64166i | −0.305277 | − | 0.221797i | 0.424590 | − | 0.905386i | \(-0.360418\pi\) |
−0.729867 | + | 0.683589i | \(0.760418\pi\) | |||||||
\(648\) | −4.97342 | − | 22.7734i | −0.195374 | − | 0.894624i | ||||
\(649\) | 40.5615 | 1.59218 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 0.362627i | − | 0.0142125i | ||||||
\(652\) | −11.6654 | + | 22.1373i | −0.456851 | + | 0.866965i | ||||
\(653\) | −14.3680 | + | 19.7759i | −0.562263 | + | 0.773889i | −0.991612 | − | 0.129250i | \(-0.958743\pi\) |
0.429349 | + | 0.903139i | \(0.358743\pi\) | |||||||
\(654\) | 0.287233 | + | 4.00082i | 0.0112317 | + | 0.156444i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 26.5459 | − | 7.82581i | 1.03644 | − | 0.305547i | ||||
\(657\) | 44.0833 | 1.71985 | ||||||||
\(658\) | −3.39229 | − | 0.839104i | −0.132245 | − | 0.0327117i | ||||
\(659\) | 41.1516 | − | 13.3710i | 1.60304 | − | 0.520859i | 0.635184 | − | 0.772361i | \(-0.280924\pi\) |
0.967857 | + | 0.251502i | \(0.0809245\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.1551 | + | 10.7728i | 1.28958 | + | 0.419012i | 0.871946 | − | 0.489602i | \(-0.162858\pi\) |
0.417639 | + | 0.908613i | \(0.362858\pi\) | |||||||
\(662\) | 27.2789 | + | 16.9754i | 1.06022 | + | 0.659767i | ||||
\(663\) | −0.699141 | − | 2.15173i | −0.0271524 | − | 0.0835664i | ||||
\(664\) | 8.71848 | − | 1.90400i | 0.338343 | − | 0.0738897i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.07688 | + | 4.40387i | 0.274224 | + | 0.170647i | ||||
\(667\) | −9.50375 | − | 13.0808i | −0.367987 | − | 0.506490i | ||||
\(668\) | 7.32702 | − | 42.4756i | 0.283491 | − | 1.64343i | ||||
\(669\) | 2.92371 | + | 4.02414i | 0.113037 | + | 0.155582i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.62437 | − | 5.53943i | −0.294336 | − | 0.213847i | ||||
\(672\) | −0.373440 | − | 0.103339i | −0.0144057 | − | 0.00398638i | ||||
\(673\) | 3.33688 | − | 10.2698i | 0.128627 | − | 0.395874i | −0.865917 | − | 0.500187i | \(-0.833265\pi\) |
0.994544 | + | 0.104314i | \(0.0332646\pi\) | |||||||
\(674\) | 17.1400 | + | 20.3497i | 0.660207 | + | 0.783842i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.22091 | + | 18.6720i | −0.123881 | + | 0.718155i | ||||
\(677\) | −39.7626 | − | 12.9196i | −1.52820 | − | 0.496542i | −0.580109 | − | 0.814539i | \(-0.696990\pi\) |
−0.948092 | + | 0.317997i | \(0.896990\pi\) | |||||||
\(678\) | −0.134742 | + | 0.00967359i | −0.00517474 | + | 0.000371512i | ||||
\(679\) | −1.33127 | − | 0.967228i | −0.0510896 | − | 0.0371188i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.45457 | + | 2.50989i | −0.132380 | + | 0.0961794i | ||||
\(682\) | 33.1224 | − | 27.8980i | 1.26832 | − | 1.06827i | ||||
\(683\) | 11.6635 | + | 16.0534i | 0.446291 | + | 0.614267i | 0.971596 | − | 0.236647i | \(-0.0760486\pi\) |
−0.525305 | + | 0.850914i | \(0.676049\pi\) | |||||||
\(684\) | −2.25494 | − | 15.6234i | −0.0862197 | − | 0.597376i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.29025 | − | 1.74265i | 0.163803 | − | 0.0665347i | ||||
\(687\) | −0.549422 | − | 1.69095i | −0.0209617 | − | 0.0645136i | ||||
\(688\) | 32.1646 | + | 0.884021i | 1.22626 | + | 0.0337030i | ||||
\(689\) | 2.19917 | − | 6.76834i | 0.0837815 | − | 0.257853i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.2658 | + | 4.96017i | −0.580740 | + | 0.188694i | −0.584632 | − | 0.811299i | \(-0.698761\pi\) |
0.00389213 | + | 0.999992i | \(0.498761\pi\) | |||||||
\(692\) | −2.85927 | + | 1.40773i | −0.108693 | + | 0.0535139i | ||||
\(693\) | 3.95893i | 0.150387i | ||||||||
\(694\) | −10.0307 | + | 40.5517i | −0.380761 | + | 1.53932i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.43504 | − | 0.540645i | −0.206015 | − | 0.0204931i | ||||
\(697\) | −23.1193 | − | 16.7971i | −0.875705 | − | 0.636237i | ||||
\(698\) | 8.38942 | + | 20.6540i | 0.317544 | + | 0.781766i | ||||
\(699\) | − | 2.08183i | − | 0.0787422i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.2259i | − | 0.575073i | −0.957770 | − | 0.287537i | \(-0.907164\pi\) | ||
0.957770 | − | 0.287537i | \(-0.0928363\pi\) | |||||||
\(702\) | 4.24524 | − | 1.72437i | 0.160226 | − | 0.0650820i | ||||
\(703\) | 4.42930 | + | 3.21807i | 0.167054 | + | 0.121372i | ||||
\(704\) | −19.2909 | − | 42.0603i | −0.727053 | − | 1.58521i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.2078 | + | 2.77231i | 0.421810 | + | 0.104337i | ||||
\(707\) | 2.57079i | 0.0966843i | ||||||||
\(708\) | 1.80714 | + | 3.67052i | 0.0679164 | + | 0.137946i | ||||
\(709\) | −35.0361 | + | 11.3839i | −1.31581 | + | 0.427532i | −0.881053 | − | 0.473018i | \(-0.843165\pi\) |
−0.434754 | + | 0.900549i | \(0.643165\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.5537 | + | 35.5586i | −0.433297 | + | 1.33355i | ||||
\(712\) | −24.0121 | − | 21.3795i | −0.899890 | − | 0.801231i | ||||
\(713\) | 3.99584 | + | 12.2979i | 0.149645 | + | 0.460561i | ||||
\(714\) | 0.150567 | + | 0.370684i | 0.00563485 | + | 0.0138725i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.16576 | + | 21.9340i | 0.118310 | + | 0.819714i | ||||
\(717\) | 0.919446 | + | 1.26551i | 0.0343373 | + | 0.0472613i | ||||
\(718\) | −27.7864 | − | 32.9899i | −1.03698 | − | 1.23117i | ||||
\(719\) | −17.8070 | + | 12.9375i | −0.664088 | + | 0.482488i | −0.868041 | − | 0.496492i | \(-0.834621\pi\) |
0.203953 | + | 0.978981i | \(0.434621\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.22399 | + | 1.61582i | 0.0828256 | + | 0.0601763i | ||||
\(722\) | 1.18167 | + | 16.4593i | 0.0439772 | + | 0.612551i | ||||
\(723\) | 0.523900 | + | 0.170225i | 0.0194840 | + | 0.00633075i | ||||
\(724\) | −39.5633 | − | 6.82465i | −1.47036 | − | 0.253636i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.08570 | − | 5.96807i | 0.262975 | − | 0.221496i | ||||
\(727\) | −12.1809 | + | 37.4888i | −0.451763 | + | 1.39038i | 0.423131 | + | 0.906069i | \(0.360931\pi\) |
−0.874894 | + | 0.484315i | \(0.839069\pi\) | |||||||
\(728\) | −0.123446 | + | 1.24099i | −0.00457523 | + | 0.0459942i | ||||
\(729\) | −18.2133 | − | 13.2327i | −0.674566 | − | 0.490101i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.5291 | − | 26.8795i | −0.722311 | − | 0.994176i | ||||
\(732\) | 0.161589 | − | 0.936748i | 0.00597248 | − | 0.0346232i | ||||
\(733\) | −14.9803 | − | 20.6186i | −0.553309 | − | 0.761565i | 0.437147 | − | 0.899390i | \(-0.355989\pi\) |
−0.990457 | + | 0.137825i | \(0.955989\pi\) | |||||||
\(734\) | 5.60446 | − | 9.00619i | 0.206864 | − | 0.332425i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.8033 | − | 0.610410i | 0.508798 | − | 0.0225000i | ||||
\(737\) | 19.9063 | + | 61.2653i | 0.733258 | + | 2.25674i | ||||
\(738\) | 15.0692 | − | 24.2157i | 0.554705 | − | 0.891393i | ||||
\(739\) | 8.47753 | + | 2.75452i | 0.311851 | + | 0.101327i | 0.460761 | − | 0.887524i | \(-0.347576\pi\) |
−0.148910 | + | 0.988851i | \(0.547576\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.41060 | − | 0.458333i | 0.0518198 | − | 0.0168373i | ||||
\(742\) | −0.302193 | + | 1.22169i | −0.0110939 | + | 0.0448498i | ||||
\(743\) | −21.5410 | −0.790261 | −0.395130 | − | 0.918625i | \(-0.629301\pi\) | ||||
−0.395130 | + | 0.918625i | \(0.629301\pi\) | |||||||
\(744\) | 4.00027 | + | 1.75439i | 0.146657 | + | 0.0643192i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.9959 | + | 1.29199i | −0.658878 | + | 0.0473031i | ||||
\(747\) | 5.40575 | − | 7.44038i | 0.197786 | − | 0.272229i | ||||
\(748\) | −22.2747 | + | 42.2708i | −0.814445 | + | 1.54557i | ||||
\(749\) | − | 0.0828031i | − | 0.00302556i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.4361 | 1.14712 | 0.573561 | − | 0.819163i | \(-0.305562\pi\) | ||||
0.573561 | + | 0.819163i | \(0.305562\pi\) | |||||||
\(752\) | 25.6684 | − | 33.3621i | 0.936032 | − | 1.21659i | ||||
\(753\) | 1.07389 | + | 0.780227i | 0.0391347 | + | 0.0284331i | ||||
\(754\) | 1.25885 | + | 17.5343i | 0.0458446 | + | 0.638562i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.726967 | + | 0.357915i | −0.0264396 | + | 0.0130172i | ||||
\(757\) | 3.46461i | 0.125924i | 0.998016 | + | 0.0629618i | \(0.0200546\pi\) | ||||
−0.998016 | + | 0.0629618i | \(0.979945\pi\) | |||||||
\(758\) | −4.15988 | + | 16.8174i | −0.151093 | + | 0.610834i | ||||
\(759\) | 1.27353 | + | 3.91951i | 0.0462261 | + | 0.142269i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.25196 | + | 19.2415i | −0.226633 | + | 0.697505i | 0.771488 | + | 0.636243i | \(0.219513\pi\) |
−0.998122 | + | 0.0612621i | \(0.980487\pi\) | |||||||
\(762\) | 3.23580 | + | 2.01360i | 0.117221 | + | 0.0729452i | ||||
\(763\) | −2.17129 | + | 0.705496i | −0.0786061 | + | 0.0255407i | ||||
\(764\) | −33.5396 | − | 17.6738i | −1.21342 | − | 0.639416i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.1182 | − | 32.3293i | 0.726900 | − | 1.16811i | ||||
\(767\) | 10.6532 | − | 7.73999i | 0.384664 | − | 0.279475i | ||||
\(768\) | 2.94668 | − | 3.61960i | 0.106329 | − | 0.130611i | ||||
\(769\) | 6.10205 | − | 4.43340i | 0.220046 | − | 0.159872i | −0.472302 | − | 0.881437i | \(-0.656577\pi\) |
0.692347 | + | 0.721565i | \(0.256577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.19867 | − | 1.64982i | 0.0431689 | − | 0.0594169i | ||||
\(772\) | −3.77519 | + | 3.67285i | −0.135872 | + | 0.132189i | ||||
\(773\) | −23.4983 | − | 7.63507i | −0.845176 | − | 0.274614i | −0.145752 | − | 0.989321i | \(-0.546560\pi\) |
−0.699424 | + | 0.714707i | \(0.746560\pi\) | |||||||
\(774\) | 25.3628 | − | 21.3623i | 0.911647 | − | 0.767853i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.1106 | − | 10.0063i | 0.614234 | − | 0.359206i | ||||
\(777\) | 0.0427985 | − | 0.131720i | 0.00153539 | − | 0.00472544i | ||||
\(778\) | −13.4473 | + | 0.965428i | −0.482109 | + | 0.0346123i | ||||
\(779\) | 11.0116 | − | 15.1562i | 0.394533 | − | 0.543027i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.29319 | + | 12.7910i | 0.332536 | + | 0.457697i | ||||
\(782\) | −9.19089 | − | 10.9121i | −0.328666 | − | 0.390214i | ||||
\(783\) | −9.24062 | + | 6.71371i | −0.330233 | + | 0.239928i | ||||
\(784\) | −0.763210 | + | 27.7690i | −0.0272575 | + | 0.991749i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.90029 | + | 1.17807i | −0.103450 | + | 0.0420202i | ||||
\(787\) | 9.13248 | − | 2.96732i | 0.325538 | − | 0.105774i | −0.141689 | − | 0.989911i | \(-0.545253\pi\) |
0.467227 | + | 0.884138i | \(0.345253\pi\) | |||||||
\(788\) | −7.21137 | − | 49.9642i | −0.256895 | − | 1.77990i | ||||
\(789\) | −6.27562 | − | 2.03907i | −0.223418 | − | 0.0725930i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.0237601 | − | 0.0731261i | −0.000844812 | − | 0.00260007i | ||||
\(792\) | −43.6725 | − | 19.1534i | −1.55183 | − | 0.680586i | ||||
\(793\) | −3.05953 | −0.108647 | ||||||||
\(794\) | 7.90182 | − | 31.9451i | 0.280425 | − | 1.13369i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.69434 | + | 5.53998i | −0.201830 | + | 0.196359i | ||||
\(797\) | −18.7330 | + | 25.7837i | −0.663556 | + | 0.913306i | −0.999593 | − | 0.0285428i | \(-0.990913\pi\) |
0.336037 | + | 0.941849i | \(0.390913\pi\) | |||||||
\(798\) | −0.243008 | + | 0.0987069i | −0.00860238 | + | 0.00349419i | ||||
\(799\) | −43.4651 | −1.53769 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.1336 | −1.17072 | ||||||||
\(802\) | −16.1052 | + | 6.54176i | −0.568696 | + | 0.230998i | ||||
\(803\) | 51.4171 | − | 70.7696i | 1.81447 | − | 2.49740i | ||||
\(804\) | −4.65717 | + | 4.53093i | −0.164246 | + | 0.159794i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.37584 | − | 13.6477i | 0.118909 | − | 0.480719i | ||||
\(807\) | −1.83112 | −0.0644586 | ||||||||
\(808\) | −28.3593 | − | 12.4375i | −0.997677 | − | 0.437550i | ||||
\(809\) | 1.35706 | + | 4.17661i | 0.0477118 | + | 0.146842i | 0.972074 | − | 0.234674i | \(-0.0754022\pi\) |
−0.924362 | + | 0.381516i | \(0.875402\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.8697 | − | 11.9797i | −1.29467 | − | 0.420664i | −0.420947 | − | 0.907085i | \(-0.638302\pi\) |
−0.873725 | + | 0.486421i | \(0.838302\pi\) | |||||||
\(812\) | −0.444089 | − | 3.07688i | −0.0155845 | − | 0.107977i | ||||
\(813\) | 0.943236 | − | 0.306476i | 0.0330807 | − | 0.0107486i | ||||
\(814\) | 15.3240 | − | 6.22443i | 0.537106 | − | 0.218166i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.81760 | − | 0.132408i | −0.168650 | − | 0.00463522i | ||||
\(817\) | 17.6213 | − | 12.8026i | 0.616492 | − | 0.447907i | ||||
\(818\) | 28.7912 | + | 34.1829i | 1.00666 | + | 1.19518i | ||||
\(819\) | 0.755449 | + | 1.03979i | 0.0263975 | + | 0.0363331i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.5877 | − | 35.2185i | 0.893017 | − | 1.22913i | −0.0796254 | − | 0.996825i | \(-0.525372\pi\) |
0.972642 | − | 0.232308i | \(-0.0746276\pi\) | |||||||
\(822\) | 5.43994 | − | 0.390552i | 0.189740 | − | 0.0136221i | ||||
\(823\) | 1.45020 | − | 4.46326i | 0.0505509 | − | 0.155580i | −0.922594 | − | 0.385771i | \(-0.873935\pi\) |
0.973145 | + | 0.230192i | \(0.0739354\pi\) | |||||||
\(824\) | −28.5844 | + | 16.7163i | −0.995785 | + | 0.582339i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.78107 | + | 1.50014i | −0.0619712 | + | 0.0521965i | ||||
\(827\) | −11.1274 | − | 3.61552i | −0.386938 | − | 0.125724i | 0.109087 | − | 0.994032i | \(-0.465207\pi\) |
−0.496025 | + | 0.868308i | \(0.665207\pi\) | |||||||
\(828\) | 10.2061 | − | 9.92941i | 0.354685 | − | 0.345071i | ||||
\(829\) | 0.462729 | − | 0.636892i | 0.0160712 | − | 0.0221202i | −0.800906 | − | 0.598790i | \(-0.795648\pi\) |
0.816977 | + | 0.576670i | \(0.195648\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.07571 | − | 4.41426i | 0.210764 | − | 0.153129i | ||||
\(832\) | −13.0926 | − | 7.36573i | −0.453905 | − | 0.255361i | ||||
\(833\) | 23.2062 | − | 16.8603i | 0.804046 | − | 0.584174i | ||||
\(834\) | 0.493104 | − | 0.792402i | 0.0170748 | − | 0.0274386i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −27.7113 | − | 14.6026i | −0.958414 | − | 0.505040i | ||||
\(837\) | 8.68759 | − | 2.82277i | 0.300287 | − | 0.0975692i | ||||
\(838\) | 10.3654 | + | 6.45026i | 0.358066 | + | 0.222821i | ||||
\(839\) | −10.8077 | + | 33.2628i | −0.373124 | + | 1.14836i | 0.571611 | + | 0.820524i | \(0.306318\pi\) |
−0.944736 | + | 0.327833i | \(0.893682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.58005 | − | 14.0959i | −0.157933 | − | 0.486067i | ||||
\(842\) | −4.35044 | + | 17.5878i | −0.149926 | + | 0.606114i | ||||
\(843\) | − | 1.13954i | − | 0.0392478i | ||||||
\(844\) | 26.3027 | − | 12.9498i | 0.905375 | − | 0.445752i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.10647 | − | 43.2695i | −0.106803 | − | 1.48764i | ||||
\(847\) | 4.26591 | + | 3.09936i | 0.146578 | + | 0.106495i | ||||
\(848\) | −12.0149 | − | 9.24418i | −0.412595 | − | 0.317447i | ||||
\(849\) | 0.374678 | 0.0128589 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.93870i | 0.169296i | ||||||||
\(852\) | −0.743449 | + | 1.41084i | −0.0254702 | + | 0.0483347i | ||||
\(853\) | −6.54252 | + | 9.00501i | −0.224012 | + | 0.308326i | −0.906199 | − | 0.422852i | \(-0.861029\pi\) |
0.682187 | + | 0.731178i | \(0.261029\pi\) | |||||||
\(854\) | 0.539660 | − | 0.0387441i | 0.0184668 | − | 0.00132579i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.913432 | + | 0.400603i | 0.0312205 | + | 0.0136923i | ||||
\(857\) | 53.1600 | 1.81591 | 0.907955 | − | 0.419068i | \(-0.137643\pi\) | ||||
0.907955 | + | 0.419068i | \(0.137643\pi\) | |||||||
\(858\) | 1.07592 | − | 4.34970i | 0.0367314 | − | 0.148496i | ||||
\(859\) | 32.6009 | − | 10.5927i | 1.11233 | − | 0.361417i | 0.305493 | − | 0.952194i | \(-0.401179\pi\) |
0.806835 | + | 0.590777i | \(0.201179\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.450722 | − | 0.146448i | −0.0153606 | − | 0.00499095i | ||||
\(862\) | 22.4705 | − | 36.1093i | 0.765347 | − | 1.22989i | ||||
\(863\) | −12.2926 | − | 37.8328i | −0.418446 | − | 1.28784i | −0.909132 | − | 0.416508i | \(-0.863254\pi\) |
0.490686 | − | 0.871336i | \(-0.336746\pi\) | |||||||
\(864\) | −0.431210 | − | 9.75105i | −0.0146701 | − | 0.331738i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.20138 | + | 1.93058i | −0.0408246 | + | 0.0656038i | ||||
\(867\) | 0.0101863 | + | 0.0140203i | 0.000345946 | + | 0.000476154i | ||||
\(868\) | −0.422627 | + | 2.45002i | −0.0143449 | + | 0.0831591i | ||||
\(869\) | 43.6085 | + | 60.0220i | 1.47932 | + | 2.03611i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9190 | + | 12.2923i | 0.573277 | + | 0.416510i | ||||
\(872\) | 2.72216 | − | 27.3655i | 0.0921840 | − | 0.926714i | ||||
\(873\) | 6.31251 | − | 19.4279i | 0.213646 | − | 0.657535i | ||||
\(874\) | 7.15357 | − | 6.02523i | 0.241973 | − | 0.203807i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.69492 | + | 1.49987i | 0.293774 | + | 0.0506759i | ||||
\(877\) | 38.4191 | + | 12.4831i | 1.29732 | + | 0.421525i | 0.874649 | − | 0.484758i | \(-0.161092\pi\) |
0.422672 | + | 0.906283i | \(0.361092\pi\) | |||||||
\(878\) | 3.84576 | + | 53.5670i | 0.129788 | + | 1.80780i | ||||
\(879\) | 2.01784 | + | 1.46605i | 0.0680601 | + | 0.0494486i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.2858 | − | 19.0977i | 0.885591 | − | 0.643419i | −0.0491339 | − | 0.998792i | \(-0.515646\pi\) |
0.934725 | + | 0.355373i | \(0.115646\pi\) | |||||||
\(882\) | 18.4429 | + | 21.8967i | 0.621006 | + | 0.737301i | ||||
\(883\) | −22.5652 | − | 31.0584i | −0.759380 | − | 1.04520i | −0.997265 | − | 0.0739039i | \(-0.976454\pi\) |
0.237885 | − | 0.971293i | \(-0.423546\pi\) | |||||||
\(884\) | 2.21586 | + | 15.3526i | 0.0745273 | + | 0.516364i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.4137 | − | 25.6376i | −0.349855 | − | 0.861312i | ||||
\(887\) | 4.72737 | + | 14.5493i | 0.158729 | + | 0.488519i | 0.998520 | − | 0.0543921i | \(-0.0173221\pi\) |
−0.839790 | + | 0.542911i | \(0.817322\pi\) | |||||||
\(888\) | 1.24600 | + | 1.10939i | 0.0418129 | + | 0.0372288i | ||||
\(889\) | −0.670327 | + | 2.06305i | −0.0224821 | + | 0.0691926i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −45.3363 | + | 14.7306i | −1.51882 | + | 0.493495i | ||||
\(892\) | −15.0635 | − | 30.5958i | −0.504364 | − | 1.02442i | ||||
\(893\) | − | 28.4943i | − | 0.953524i | ||||||
\(894\) | −6.16648 | − | 1.52532i | −0.206238 | − | 0.0510142i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.40264 | + | 1.13342i | 0.0802665 | + | 0.0378649i | ||||
\(897\) | 1.08241 | + | 0.786416i | 0.0361406 | + | 0.0262577i | ||||
\(898\) | −43.5754 | + | 17.6998i | −1.45413 | + | 0.590651i | ||||
\(899\) | 35.0457i | 1.16884i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.6535i | 0.521492i | ||||||||
\(902\) | −21.2988 | − | 52.4358i | −0.709173 | − | 1.74592i | ||||
\(903\) | −0.445767 | − | 0.323868i | −0.0148342 | − | 0.0107777i | ||||
\(904\) | 0.921634 | + | 0.0916786i | 0.0306531 | + | 0.00304918i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.0297240 | − | 0.120167i | 0.000987513 | − | 0.00399227i | ||||
\(907\) | − | 31.6503i | − | 1.05093i | −0.850815 | − | 0.525465i | \(-0.823891\pi\) | ||
0.850815 | − | 0.525465i | \(-0.176109\pi\) | |||||||
\(908\) | 26.2654 | − | 12.9315i | 0.871647 | − | 0.429146i | ||||
\(909\) | −30.3516 | + | 9.86184i | −1.00670 | + | 0.327096i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.64977 | + | 5.07747i | −0.0546593 | + | 0.168224i | −0.974659 | − | 0.223694i | \(-0.928188\pi\) |
0.920000 | + | 0.391918i | \(0.128188\pi\) | |||||||
\(912\) | 0.0868024 | − | 3.15826i | 0.00287431 | − | 0.104580i | ||||
\(913\) | −5.63942 | − | 17.3564i | −0.186638 | − | 0.574411i | ||||
\(914\) | 20.4264 | − | 8.29695i | 0.675644 | − | 0.274439i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.74134 | + | 12.0649i | 0.0575353 | + | 0.398635i | ||||
\(917\) | −1.04729 | − | 1.44148i | −0.0345847 | − | 0.0476017i | ||||
\(918\) | −7.70856 | + | 6.49269i | −0.254421 | + | 0.214291i | ||||
\(919\) | −11.6067 | + | 8.43275i | −0.382869 | + | 0.278171i | −0.762527 | − | 0.646956i | \(-0.776042\pi\) |
0.379658 | + | 0.925127i | \(0.376042\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.61770 | − | 1.90187i | −0.0862561 | − | 0.0626687i | ||||
\(922\) | 8.17587 | − | 0.586974i | 0.269258 | − | 0.0193309i | ||||
\(923\) | 4.88158 | + | 1.58612i | 0.160679 | + | 0.0522078i | ||||
\(924\) | −0.134697 | + | 0.780854i | −0.00443120 | + | 0.0256882i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 10.8291 | + | 12.8570i | 0.355865 | + | 0.422508i | ||||
\(927\) | −10.5455 | + | 32.4557i | −0.346359 | + | 1.06598i | ||||
\(928\) | 36.0907 | + | 9.98709i | 1.18474 | + | 0.327842i | ||||
\(929\) | −5.50414 | − | 3.99899i | −0.180585 | − | 0.131203i | 0.493820 | − | 0.869564i | \(-0.335600\pi\) |
−0.674405 | + | 0.738361i | \(0.735600\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.0530 | + | 15.2132i | 0.362248 | + | 0.498592i | ||||
\(932\) | −2.42629 | + | 14.0655i | −0.0794759 | + | 0.460731i | ||||
\(933\) | 5.15409 | + | 7.09400i | 0.168737 | + | 0.232247i | ||||
\(934\) | −29.9531 | − | 18.6395i | −0.980094 | − | 0.609903i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15.1252 | + | 3.30314i | −0.494381 | + | 0.107966i | ||||
\(937\) | 5.15839 | + | 15.8759i | 0.168517 | + | 0.518643i | 0.999278 | − | 0.0379863i | \(-0.0120943\pi\) |
−0.830761 | + | 0.556629i | \(0.812094\pi\) | |||||||
\(938\) | −3.13994 | − | 1.95396i | −0.102523 | − | 0.0637989i | ||||
\(939\) | −0.0102093 | − | 0.00331721i | −0.000333168 | − | 0.000108253i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5188 | + | 3.41775i | −0.342902 | + | 0.111416i | −0.475405 | − | 0.879767i | \(-0.657699\pi\) |
0.132503 | + | 0.991183i | \(0.457699\pi\) | |||||||
\(942\) | −8.36704 | − | 2.06964i | −0.272613 | − | 0.0674325i | ||||
\(943\) | 16.8993 | 0.550316 | ||||||||
\(944\) | −7.93176 | − | 26.9053i | −0.258157 | − | 0.875693i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.71199 | − | 65.6327i | −0.153200 | − | 2.13390i | ||||
\(947\) | 11.6464 | − | 16.0299i | 0.378457 | − | 0.520901i | −0.576718 | − | 0.816943i | \(-0.695667\pi\) |
0.955175 | + | 0.296042i | \(0.0956669\pi\) | |||||||
\(948\) | −3.48866 | + | 6.62042i | −0.113306 | + | 0.215021i | ||||
\(949\) | − | 28.3986i | − | 0.921858i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.74494 | −0.153865 | ||||||||
\(952\) | −0.585264 | − | 2.67994i | −0.0189685 | − | 0.0868573i | ||||
\(953\) | 39.2091 | + | 28.4871i | 1.27011 | + | 0.922787i | 0.999207 | − | 0.0398210i | \(-0.0126788\pi\) |
0.270900 | + | 0.962608i | \(0.412679\pi\) | |||||||
\(954\) | −15.5830 | + | 1.11876i | −0.504518 | + | 0.0362211i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.73717 | − | 9.62175i | −0.153211 | − | 0.311190i | ||||
\(957\) | 11.1695i | 0.361060i | ||||||||
\(958\) | 21.0905 | + | 5.21685i | 0.681402 | + | 0.168549i | ||||
\(959\) | 0.959267 | + | 2.95232i | 0.0309764 | + | 0.0953354i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.918548 | + | 2.82700i | −0.0296306 | + | 0.0911936i | ||||
\(962\) | 2.83699 | − | 4.55895i | 0.0914682 | − | 0.146986i | ||||
\(963\) | 0.977603 | − | 0.317642i | 0.0315028 | − | 0.0102359i | ||||
\(964\) | −3.34124 | − | 1.76068i | −0.107614 | − | 0.0567077i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.200881 | − | 0.125006i | −0.00646325 | − | 0.00402202i | ||||
\(967\) | 15.9495 | − | 11.5880i | 0.512901 | − | 0.372645i | −0.301022 | − | 0.953617i | \(-0.597328\pi\) |
0.813923 | + | 0.580973i | \(0.197328\pi\) | |||||||
\(968\) | −54.8288 | + | 32.0641i | −1.76226 | + | 1.03058i | ||||
\(969\) | −2.63931 | + | 1.91757i | −0.0847870 | + | 0.0616013i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.31463 | + | 1.80943i | −0.0421885 | + | 0.0580675i | −0.829590 | − | 0.558373i | \(-0.811426\pi\) |
0.787402 | + | 0.616440i | \(0.211426\pi\) | |||||||
\(972\) | −10.5721 | − | 10.8666i | −0.339099 | − | 0.348547i | ||||
\(973\) | 0.505214 | + | 0.164154i | 0.0161964 | + | 0.00526253i | ||||
\(974\) | 20.5503 | + | 24.3987i | 0.658475 | + | 0.781786i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.18349 | + | 6.14064i | −0.0698917 | + | 0.196557i | ||||
\(977\) | 3.71838 | − | 11.4440i | 0.118962 | − | 0.366126i | −0.873791 | − | 0.486301i | \(-0.838346\pi\) |
0.992753 | + | 0.120175i | \(0.0383457\pi\) | |||||||
\(978\) | 0.369609 | + | 5.14823i | 0.0118188 | + | 0.164622i | ||||
\(979\) | −38.6458 | + | 53.1914i | −1.23512 | + | 1.70000i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.6587 | − | 22.9287i | −0.531870 | − | 0.732057i | ||||
\(982\) | 8.25281 | − | 6.95109i | 0.263358 | − | 0.221818i | ||||
\(983\) | 37.4796 | − | 27.2305i | 1.19541 | − | 0.868518i | 0.201587 | − | 0.979471i | \(-0.435390\pi\) |
0.993826 | + | 0.110952i | \(0.0353901\pi\) | |||||||
\(984\) | 3.79613 | − | 4.26356i | 0.121016 | − | 0.135917i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −14.5515 | − | 35.8244i | −0.463413 | − | 1.14088i | ||||
\(987\) | −0.685540 | + | 0.222746i | −0.0218210 | + | 0.00709007i | ||||
\(988\) | −10.0647 | + | 1.45264i | −0.320199 | + | 0.0462146i | ||||
\(989\) | 18.6862 | + | 6.07153i | 0.594188 | + | 0.193063i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.8475 | + | 58.0065i | 0.598710 | + | 1.84264i | 0.535319 | + | 0.844650i | \(0.320191\pi\) |
0.0633902 | + | 0.997989i | \(0.479809\pi\) | |||||||
\(992\) | −24.9824 | − | 16.5154i | −0.793193 | − | 0.524365i | ||||
\(993\) | 6.62737 | 0.210313 | ||||||||
\(994\) | −0.881132 | − | 0.217953i | −0.0279478 | − | 0.00691306i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.31937 | − | 1.28361i | 0.0418058 | − | 0.0406726i | ||||
\(997\) | 19.0954 | − | 26.2826i | 0.604758 | − | 0.832378i | −0.391375 | − | 0.920231i | \(-0.628001\pi\) |
0.996133 | + | 0.0878532i | \(0.0280006\pi\) | |||||||
\(998\) | −14.3531 | − | 35.3360i | −0.454339 | − | 1.11854i | ||||
\(999\) | 3.48883 | 0.110382 |
(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 | 1000.2.t.b.101.7 | 224 | ||
5.2 | odd | 4 | 200.2.o.a.29.12 | yes | 112 | ||
5.3 | odd | 4 | 1000.2.o.a.149.17 | 112 | |||
5.4 | even | 2 | inner | 1000.2.t.b.101.50 | 224 | ||
8.5 | even | 2 | inner | 1000.2.t.b.101.39 | 224 | ||
20.7 | even | 4 | 800.2.be.a.529.13 | 112 | |||
25.6 | even | 5 | inner | 1000.2.t.b.901.39 | 224 | ||
25.8 | odd | 20 | 200.2.o.a.69.6 | yes | 112 | ||
25.17 | odd | 20 | 1000.2.o.a.349.23 | 112 | |||
25.19 | even | 10 | inner | 1000.2.t.b.901.18 | 224 | ||
40.13 | odd | 4 | 1000.2.o.a.149.23 | 112 | |||
40.27 | even | 4 | 800.2.be.a.529.16 | 112 | |||
40.29 | even | 2 | inner | 1000.2.t.b.101.18 | 224 | ||
40.37 | odd | 4 | 200.2.o.a.29.6 | ✓ | 112 | ||
100.83 | even | 20 | 800.2.be.a.369.16 | 112 | |||
200.69 | even | 10 | inner | 1000.2.t.b.901.50 | 224 | ||
200.83 | even | 20 | 800.2.be.a.369.13 | 112 | |||
200.117 | odd | 20 | 1000.2.o.a.349.17 | 112 | |||
200.133 | odd | 20 | 200.2.o.a.69.12 | yes | 112 | ||
200.181 | even | 10 | inner | 1000.2.t.b.901.7 | 224 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.2.o.a.29.6 | ✓ | 112 | 40.37 | odd | 4 | ||
200.2.o.a.29.12 | yes | 112 | 5.2 | odd | 4 | ||
200.2.o.a.69.6 | yes | 112 | 25.8 | odd | 20 | ||
200.2.o.a.69.12 | yes | 112 | 200.133 | odd | 20 | ||
800.2.be.a.369.13 | 112 | 200.83 | even | 20 | |||
800.2.be.a.369.16 | 112 | 100.83 | even | 20 | |||
800.2.be.a.529.13 | 112 | 20.7 | even | 4 | |||
800.2.be.a.529.16 | 112 | 40.27 | even | 4 | |||
1000.2.o.a.149.17 | 112 | 5.3 | odd | 4 | |||
1000.2.o.a.149.23 | 112 | 40.13 | odd | 4 | |||
1000.2.o.a.349.17 | 112 | 200.117 | odd | 20 | |||
1000.2.o.a.349.23 | 112 | 25.17 | odd | 20 | |||
1000.2.t.b.101.7 | 224 | 1.1 | even | 1 | trivial | ||
1000.2.t.b.101.18 | 224 | 40.29 | even | 2 | inner | ||
1000.2.t.b.101.39 | 224 | 8.5 | even | 2 | inner | ||
1000.2.t.b.101.50 | 224 | 5.4 | even | 2 | inner | ||
1000.2.t.b.901.7 | 224 | 200.181 | even | 10 | inner | ||
1000.2.t.b.901.18 | 224 | 25.19 | even | 10 | inner | ||
1000.2.t.b.901.39 | 224 | 25.6 | even | 5 | inner | ||
1000.2.t.b.901.50 | 224 | 200.69 | even | 10 | inner |