Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(25,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bk (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 26 x^{18} + 431 x^{16} - 4370 x^{14} + 32381 x^{12} - 160412 x^{10} + 573820 x^{8} + \cdots + 810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 25.2 | ||
Root | \(-2.18313 - 1.26043i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.25 |
Dual form | 546.2.bk.c.415.2 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −2.18313 | + | 1.26043i | −0.976324 | + | 0.563681i | −0.901158 | − | 0.433490i | \(-0.857282\pi\) |
−0.0751659 | + | 0.997171i | \(0.523949\pi\) | |||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 1.47350 | + | 2.19745i | 0.556931 | + | 0.830559i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.26043 | − | 2.18313i | 0.398583 | − | 0.690366i | ||||
\(11\) | −4.88772 | − | 2.82193i | −1.47370 | − | 0.850843i | −0.474141 | − | 0.880449i | \(-0.657241\pi\) |
−0.999562 | + | 0.0296062i | \(0.990575\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | −3.13524 | − | 1.78052i | −0.869561 | − | 0.493826i | ||||
\(14\) | −2.37482 | − | 1.16630i | −0.634696 | − | 0.311706i | ||||
\(15\) | 2.52086i | 0.650883i | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.123703 | − | 0.214260i | 0.0300024 | − | 0.0519656i | −0.850634 | − | 0.525758i | \(-0.823782\pi\) |
0.880637 | + | 0.473792i | \(0.157115\pi\) | |||||||
\(18\) | 0.866025 | + | 0.500000i | 0.204124 | + | 0.117851i | ||||
\(19\) | 2.70459 | − | 1.56150i | 0.620476 | − | 0.358232i | −0.156578 | − | 0.987666i | \(-0.550046\pi\) |
0.777054 | + | 0.629434i | \(0.216713\pi\) | |||||||
\(20\) | 2.52086i | 0.563681i | ||||||||
\(21\) | 2.63980 | − | 0.177364i | 0.576051 | − | 0.0387041i | ||||
\(22\) | 5.64385 | 1.20327 | ||||||||
\(23\) | −1.80107 | − | 3.11954i | −0.375548 | − | 0.650469i | 0.614860 | − | 0.788636i | \(-0.289212\pi\) |
−0.990409 | + | 0.138167i | \(0.955879\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | 0.677364 | − | 1.17323i | 0.135473 | − | 0.234646i | ||||
\(26\) | 3.60546 | − | 0.0256500i | 0.707089 | − | 0.00503038i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.63980 | − | 0.177364i | 0.498875 | − | 0.0335187i | ||||
\(29\) | −4.24895 | −0.789010 | −0.394505 | − | 0.918894i | \(-0.629084\pi\) | ||||
−0.394505 | + | 0.918894i | \(0.629084\pi\) | |||||||
\(30\) | −1.26043 | − | 2.18313i | −0.230122 | − | 0.398583i | ||||
\(31\) | −5.30267 | − | 3.06150i | −0.952387 | − | 0.549861i | −0.0585655 | − | 0.998284i | \(-0.518653\pi\) |
−0.893822 | + | 0.448423i | \(0.851986\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −4.88772 | + | 2.82193i | −0.850843 | + | 0.491234i | ||||
\(34\) | 0.247406i | 0.0424298i | ||||||||
\(35\) | −5.98657 | − | 2.94007i | −1.01192 | − | 0.496963i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −7.01858 | + | 4.05218i | −1.15385 | + | 0.666174i | −0.949822 | − | 0.312791i | \(-0.898736\pi\) |
−0.204026 | + | 0.978966i | \(0.565403\pi\) | |||||||
\(38\) | −1.56150 | + | 2.70459i | −0.253308 | + | 0.438743i | ||||
\(39\) | −3.10959 | + | 1.82494i | −0.497934 | + | 0.292225i | ||||
\(40\) | −1.26043 | − | 2.18313i | −0.199291 | − | 0.345183i | ||||
\(41\) | − | 8.59917i | − | 1.34296i | −0.741020 | − | 0.671482i | \(-0.765658\pi\) | ||
0.741020 | − | 0.671482i | \(-0.234342\pi\) | |||||||
\(42\) | −2.19745 | + | 1.47350i | −0.339074 | + | 0.227366i | ||||
\(43\) | 5.56103 | 0.848050 | 0.424025 | − | 0.905651i | \(-0.360617\pi\) | ||||
0.424025 | + | 0.905651i | \(0.360617\pi\) | |||||||
\(44\) | −4.88772 | + | 2.82193i | −0.736851 | + | 0.425421i | ||||
\(45\) | 2.18313 | + | 1.26043i | 0.325441 | + | 0.187894i | ||||
\(46\) | 3.11954 | + | 1.80107i | 0.459951 | + | 0.265553i | ||||
\(47\) | −5.78854 | + | 3.34201i | −0.844345 | + | 0.487483i | −0.858739 | − | 0.512414i | \(-0.828751\pi\) |
0.0143939 | + | 0.999896i | \(0.495418\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −2.65759 | + | 6.47590i | −0.379655 | + | 0.925128i | ||||
\(50\) | 1.35473i | 0.191588i | ||||||||
\(51\) | −0.123703 | − | 0.214260i | −0.0173219 | − | 0.0300024i | ||||
\(52\) | −3.10959 | + | 1.82494i | −0.431223 | + | 0.253074i | ||||
\(53\) | −3.28052 | + | 5.68202i | −0.450614 | + | 0.780486i | −0.998424 | − | 0.0561167i | \(-0.982128\pi\) |
0.547811 | + | 0.836602i | \(0.315461\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 14.2274 | 1.91842 | ||||||||
\(56\) | −2.19745 | + | 1.47350i | −0.293647 | + | 0.196905i | ||||
\(57\) | − | 3.12299i | − | 0.413651i | ||||||
\(58\) | 3.67970 | − | 2.12447i | 0.483168 | − | 0.278957i | ||||
\(59\) | 6.89004 | + | 3.97797i | 0.897007 | + | 0.517887i | 0.876228 | − | 0.481897i | \(-0.160052\pi\) |
0.0207791 | + | 0.999784i | \(0.493385\pi\) | |||||||
\(60\) | 2.18313 | + | 1.26043i | 0.281841 | + | 0.162721i | ||||
\(61\) | −6.39419 | − | 11.0751i | −0.818693 | − | 1.41802i | −0.906646 | − | 0.421892i | \(-0.861366\pi\) |
0.0879534 | − | 0.996125i | \(-0.471967\pi\) | |||||||
\(62\) | 6.12299 | 0.777621 | ||||||||
\(63\) | 1.16630 | − | 2.37482i | 0.146940 | − | 0.299199i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 9.08886 | − | 0.0646601i | 1.12733 | − | 0.00802010i | ||||
\(66\) | 2.82193 | − | 4.88772i | 0.347355 | − | 0.601637i | ||||
\(67\) | −10.5562 | − | 6.09461i | −1.28964 | − | 0.744575i | −0.311051 | − | 0.950393i | \(-0.600681\pi\) |
−0.978590 | + | 0.205818i | \(0.934014\pi\) | |||||||
\(68\) | −0.123703 | − | 0.214260i | −0.0150012 | − | 0.0259828i | ||||
\(69\) | −3.60213 | −0.433646 | ||||||||
\(70\) | 6.65456 | − | 0.447110i | 0.795372 | − | 0.0534399i | ||||
\(71\) | 4.06419i | 0.482330i | 0.970484 | + | 0.241165i | \(0.0775295\pi\) | ||||
−0.970484 | + | 0.241165i | \(0.922470\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | 6.81789 | + | 3.93631i | 0.797974 | + | 0.460710i | 0.842762 | − | 0.538286i | \(-0.180928\pi\) |
−0.0447882 | + | 0.998997i | \(0.514261\pi\) | |||||||
\(74\) | 4.05218 | − | 7.01858i | 0.471056 | − | 0.815894i | ||||
\(75\) | −0.677364 | − | 1.17323i | −0.0782153 | − | 0.135473i | ||||
\(76\) | − | 3.12299i | − | 0.358232i | ||||||
\(77\) | −1.00102 | − | 14.8986i | −0.114077 | − | 1.69786i | ||||
\(78\) | 1.78052 | − | 3.13524i | 0.201604 | − | 0.354997i | ||||
\(79\) | 3.22763 | + | 5.59041i | 0.363136 | + | 0.628971i | 0.988475 | − | 0.151383i | \(-0.0483726\pi\) |
−0.625339 | + | 0.780353i | \(0.715039\pi\) | |||||||
\(80\) | 2.18313 | + | 1.26043i | 0.244081 | + | 0.140920i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 4.29959 | + | 7.44710i | 0.474810 | + | 0.822395i | ||||
\(83\) | 0.662485i | 0.0727172i | 0.999339 | + | 0.0363586i | \(0.0115759\pi\) | ||||
−0.999339 | + | 0.0363586i | \(0.988424\pi\) | |||||||
\(84\) | 1.16630 | − | 2.37482i | 0.127254 | − | 0.259114i | ||||
\(85\) | 0.623675i | 0.0676471i | ||||||||
\(86\) | −4.81600 | + | 2.78052i | −0.519322 | + | 0.299831i | ||||
\(87\) | −2.12447 | + | 3.67970i | −0.227768 | + | 0.394505i | ||||
\(88\) | 2.82193 | − | 4.88772i | 0.300818 | − | 0.521033i | ||||
\(89\) | 4.86906 | − | 2.81116i | 0.516120 | − | 0.297982i | −0.219226 | − | 0.975674i | \(-0.570353\pi\) |
0.735346 | + | 0.677692i | \(0.237020\pi\) | |||||||
\(90\) | −2.52086 | −0.265722 | ||||||||
\(91\) | −0.707191 | − | 9.51314i | −0.0741337 | − | 0.997248i | ||||
\(92\) | −3.60213 | −0.375548 | ||||||||
\(93\) | −5.30267 | + | 3.06150i | −0.549861 | + | 0.317462i | ||||
\(94\) | 3.34201 | − | 5.78854i | 0.344702 | − | 0.597042i | ||||
\(95\) | −3.93631 | + | 6.81789i | −0.403857 | + | 0.699501i | ||||
\(96\) | 0.866025 | − | 0.500000i | 0.0883883 | − | 0.0510310i | ||||
\(97\) | − | 16.8748i | − | 1.71337i | −0.515836 | − | 0.856687i | \(-0.672519\pi\) | ||
0.515836 | − | 0.856687i | \(-0.327481\pi\) | |||||||
\(98\) | −0.936412 | − | 6.93708i | −0.0945919 | − | 0.700751i | ||||
\(99\) | 5.64385i | 0.567228i | ||||||||
\(100\) | −0.677364 | − | 1.17323i | −0.0677364 | − | 0.117323i | ||||
\(101\) | −5.75972 | + | 9.97613i | −0.573114 | + | 0.992662i | 0.423130 | + | 0.906069i | \(0.360931\pi\) |
−0.996244 | + | 0.0865929i | \(0.972402\pi\) | |||||||
\(102\) | 0.214260 | + | 0.123703i | 0.0212149 | + | 0.0122484i | ||||
\(103\) | 2.89422 | + | 5.01294i | 0.285176 | + | 0.493939i | 0.972652 | − | 0.232268i | \(-0.0746146\pi\) |
−0.687476 | + | 0.726207i | \(0.741281\pi\) | |||||||
\(104\) | 1.78052 | − | 3.13524i | 0.174594 | − | 0.307436i | ||||
\(105\) | −5.53946 | + | 3.71449i | −0.540596 | + | 0.362497i | ||||
\(106\) | − | 6.56103i | − | 0.637264i | ||||||
\(107\) | 7.96501 | + | 13.7958i | 0.770006 | + | 1.33369i | 0.937559 | + | 0.347827i | \(0.113080\pi\) |
−0.167553 | + | 0.985863i | \(0.553586\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 1.28231 | + | 0.740342i | 0.122823 | + | 0.0709119i | 0.560153 | − | 0.828389i | \(-0.310742\pi\) |
−0.437330 | + | 0.899301i | \(0.644076\pi\) | |||||||
\(110\) | −12.3212 | + | 7.11368i | −1.17479 | + | 0.678262i | ||||
\(111\) | 8.10436i | 0.769232i | ||||||||
\(112\) | 1.16630 | − | 2.37482i | 0.110205 | − | 0.224399i | ||||
\(113\) | 10.0373 | 0.944233 | 0.472117 | − | 0.881536i | \(-0.343490\pi\) | ||||
0.472117 | + | 0.881536i | \(0.343490\pi\) | |||||||
\(114\) | 1.56150 | + | 2.70459i | 0.146248 | + | 0.253308i | ||||
\(115\) | 7.86392 | + | 4.54024i | 0.733314 | + | 0.423379i | ||||
\(116\) | −2.12447 | + | 3.67970i | −0.197253 | + | 0.341651i | ||||
\(117\) | 0.0256500 | + | 3.60546i | 0.00237135 | + | 0.333325i | ||||
\(118\) | −7.95594 | −0.732403 | ||||||||
\(119\) | 0.653102 | − | 0.0438810i | 0.0598698 | − | 0.00402256i | ||||
\(120\) | −2.52086 | −0.230122 | ||||||||
\(121\) | 10.4265 | + | 18.0593i | 0.947867 | + | 1.64175i | ||||
\(122\) | 11.0751 | + | 6.39419i | 1.00269 | + | 0.578903i | ||||
\(123\) | −7.44710 | − | 4.29959i | −0.671482 | − | 0.387681i | ||||
\(124\) | −5.30267 | + | 3.06150i | −0.476194 | + | 0.274931i | ||||
\(125\) | − | 9.18921i | − | 0.821908i | ||||||
\(126\) | 0.177364 | + | 2.63980i | 0.0158009 | + | 0.235172i | ||||
\(127\) | 10.3136 | 0.915186 | 0.457593 | − | 0.889162i | \(-0.348712\pi\) | ||||
0.457593 | + | 0.889162i | \(0.348712\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 2.78052 | − | 4.81600i | 0.244811 | − | 0.424025i | ||||
\(130\) | −7.83885 | + | 4.60042i | −0.687513 | + | 0.403484i | ||||
\(131\) | −9.24892 | − | 16.0196i | −0.808082 | − | 1.39964i | −0.914191 | − | 0.405285i | \(-0.867172\pi\) |
0.106109 | − | 0.994355i | \(-0.466161\pi\) | |||||||
\(132\) | 5.64385i | 0.491234i | ||||||||
\(133\) | 7.41653 | + | 3.64234i | 0.643095 | + | 0.315831i | ||||
\(134\) | 12.1892 | 1.05299 | ||||||||
\(135\) | 2.18313 | − | 1.26043i | 0.187894 | − | 0.108480i | ||||
\(136\) | 0.214260 | + | 0.123703i | 0.0183726 | + | 0.0106074i | ||||
\(137\) | 11.8669 | + | 6.85133i | 1.01385 | + | 0.585349i | 0.912318 | − | 0.409483i | \(-0.134291\pi\) |
0.101536 | + | 0.994832i | \(0.467624\pi\) | |||||||
\(138\) | 3.11954 | − | 1.80107i | 0.265553 | − | 0.153317i | ||||
\(139\) | −8.01474 | −0.679802 | −0.339901 | − | 0.940461i | \(-0.610394\pi\) | ||||
−0.339901 | + | 0.940461i | \(0.610394\pi\) | |||||||
\(140\) | −5.53946 | + | 3.71449i | −0.468170 | + | 0.313932i | ||||
\(141\) | 6.68403i | 0.562897i | ||||||||
\(142\) | −2.03209 | − | 3.51969i | −0.170529 | − | 0.295366i | ||||
\(143\) | 10.2997 | + | 17.5501i | 0.861305 | + | 1.46761i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 9.27600 | − | 5.35550i | 0.770330 | − | 0.444750i | ||||
\(146\) | −7.87262 | −0.651543 | ||||||||
\(147\) | 4.27950 | + | 5.53948i | 0.352967 | + | 0.456889i | ||||
\(148\) | 8.10436i | 0.666174i | ||||||||
\(149\) | 1.62420 | − | 0.937732i | 0.133060 | − | 0.0768220i | −0.431993 | − | 0.901877i | \(-0.642189\pi\) |
0.565052 | + | 0.825055i | \(0.308856\pi\) | |||||||
\(150\) | 1.17323 | + | 0.677364i | 0.0957938 | + | 0.0553066i | ||||
\(151\) | 2.34699 | + | 1.35504i | 0.190995 | + | 0.110271i | 0.592449 | − | 0.805608i | \(-0.298161\pi\) |
−0.401453 | + | 0.915880i | \(0.631495\pi\) | |||||||
\(152\) | 1.56150 | + | 2.70459i | 0.126654 | + | 0.219371i | ||||
\(153\) | −0.247406 | −0.0200016 | ||||||||
\(154\) | 8.31623 | + | 12.4021i | 0.670141 | + | 0.999389i | ||||
\(155\) | 15.4352 | 1.23979 | ||||||||
\(156\) | 0.0256500 | + | 3.60546i | 0.00205365 | + | 0.288668i | ||||
\(157\) | 8.55178 | − | 14.8121i | 0.682506 | − | 1.18214i | −0.291707 | − | 0.956508i | \(-0.594223\pi\) |
0.974214 | − | 0.225628i | \(-0.0724433\pi\) | |||||||
\(158\) | −5.59041 | − | 3.22763i | −0.444749 | − | 0.256776i | ||||
\(159\) | 3.28052 | + | 5.68202i | 0.260162 | + | 0.450614i | ||||
\(160\) | −2.52086 | −0.199291 | ||||||||
\(161\) | 4.20116 | − | 8.55441i | 0.331098 | − | 0.674182i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −16.1125 | + | 9.30258i | −1.26203 | + | 0.728635i | −0.973467 | − | 0.228826i | \(-0.926511\pi\) |
−0.288565 | + | 0.957460i | \(0.593178\pi\) | |||||||
\(164\) | −7.44710 | − | 4.29959i | −0.581521 | − | 0.335741i | ||||
\(165\) | 7.11368 | − | 12.3212i | 0.553799 | − | 0.959208i | ||||
\(166\) | −0.331243 | − | 0.573729i | −0.0257094 | − | 0.0445300i | ||||
\(167\) | 14.5835i | 1.12851i | 0.825602 | + | 0.564253i | \(0.190836\pi\) | ||||
−0.825602 | + | 0.564253i | \(0.809164\pi\) | |||||||
\(168\) | 0.177364 | + | 2.63980i | 0.0136840 | + | 0.203665i | ||||
\(169\) | 6.65952 | + | 11.1647i | 0.512271 | + | 0.858824i | ||||
\(170\) | −0.311838 | − | 0.540119i | −0.0239169 | − | 0.0414252i | ||||
\(171\) | −2.70459 | − | 1.56150i | −0.206825 | − | 0.119411i | ||||
\(172\) | 2.78052 | − | 4.81600i | 0.212012 | − | 0.367216i | ||||
\(173\) | −1.96945 | − | 3.41119i | −0.149735 | − | 0.259348i | 0.781395 | − | 0.624037i | \(-0.214509\pi\) |
−0.931129 | + | 0.364689i | \(0.881175\pi\) | |||||||
\(174\) | − | 4.24895i | − | 0.322112i | ||||||
\(175\) | 3.57621 | − | 0.240280i | 0.270336 | − | 0.0181635i | ||||
\(176\) | 5.64385i | 0.425421i | ||||||||
\(177\) | 6.89004 | − | 3.97797i | 0.517887 | − | 0.299002i | ||||
\(178\) | −2.81116 | + | 4.86906i | −0.210705 | + | 0.364952i | ||||
\(179\) | −2.35319 | + | 4.07584i | −0.175885 | + | 0.304642i | −0.940467 | − | 0.339884i | \(-0.889612\pi\) |
0.764582 | + | 0.644526i | \(0.222945\pi\) | |||||||
\(180\) | 2.18313 | − | 1.26043i | 0.162721 | − | 0.0939469i | ||||
\(181\) | −15.6400 | −1.16251 | −0.581255 | − | 0.813722i | \(-0.697438\pi\) | ||||
−0.581255 | + | 0.813722i | \(0.697438\pi\) | |||||||
\(182\) | 5.36902 | + | 7.88503i | 0.397978 | + | 0.584477i | ||||
\(183\) | −12.7884 | −0.945345 | ||||||||
\(184\) | 3.11954 | − | 1.80107i | 0.229976 | − | 0.132776i | ||||
\(185\) | 10.2150 | − | 17.6929i | 0.751020 | − | 1.30080i | ||||
\(186\) | 3.06150 | − | 5.30267i | 0.224480 | − | 0.388810i | ||||
\(187\) | −1.20925 | + | 0.698161i | −0.0884292 | + | 0.0510546i | ||||
\(188\) | 6.68403i | 0.487483i | ||||||||
\(189\) | −1.47350 | − | 2.19745i | −0.107181 | − | 0.159841i | ||||
\(190\) | − | 7.87262i | − | 0.571140i | ||||||
\(191\) | −4.48843 | − | 7.77419i | −0.324771 | − | 0.562521i | 0.656695 | − | 0.754157i | \(-0.271954\pi\) |
−0.981466 | + | 0.191636i | \(0.938621\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 6.09697 | + | 3.52009i | 0.438869 | + | 0.253381i | 0.703118 | − | 0.711073i | \(-0.251791\pi\) |
−0.264248 | + | 0.964455i | \(0.585124\pi\) | |||||||
\(194\) | 8.43739 | + | 14.6140i | 0.605769 | + | 1.04922i | ||||
\(195\) | 4.48843 | − | 7.90351i | 0.321423 | − | 0.565982i | ||||
\(196\) | 4.27950 | + | 5.53948i | 0.305678 | + | 0.395677i | ||||
\(197\) | − | 11.7101i | − | 0.834308i | −0.908836 | − | 0.417154i | \(-0.863028\pi\) | ||
0.908836 | − | 0.417154i | \(-0.136972\pi\) | |||||||
\(198\) | −2.82193 | − | 4.88772i | −0.200546 | − | 0.347355i | ||||
\(199\) | −9.05076 | + | 15.6764i | −0.641591 | + | 1.11127i | 0.343486 | + | 0.939158i | \(0.388392\pi\) |
−0.985078 | + | 0.172111i | \(0.944941\pi\) | |||||||
\(200\) | 1.17323 | + | 0.677364i | 0.0829598 | + | 0.0478969i | ||||
\(201\) | −10.5562 | + | 6.09461i | −0.744575 | + | 0.429880i | ||||
\(202\) | − | 11.5194i | − | 0.810505i | ||||||
\(203\) | −6.26083 | − | 9.33686i | −0.439424 | − | 0.655319i | ||||
\(204\) | −0.247406 | −0.0173219 | ||||||||
\(205\) | 10.8386 | + | 18.7731i | 0.757004 | + | 1.31117i | ||||
\(206\) | −5.01294 | − | 2.89422i | −0.349268 | − | 0.201650i | ||||
\(207\) | −1.80107 | + | 3.11954i | −0.125183 | + | 0.216823i | ||||
\(208\) | 0.0256500 | + | 3.60546i | 0.00177851 | + | 0.249994i | ||||
\(209\) | −17.6257 | −1.21920 | ||||||||
\(210\) | 2.94007 | − | 5.98657i | 0.202884 | − | 0.413113i | ||||
\(211\) | −23.2252 | −1.59889 | −0.799444 | − | 0.600741i | \(-0.794872\pi\) | ||||
−0.799444 | + | 0.600741i | \(0.794872\pi\) | |||||||
\(212\) | 3.28052 | + | 5.68202i | 0.225307 | + | 0.390243i | ||||
\(213\) | 3.51969 | + | 2.03209i | 0.241165 | + | 0.139237i | ||||
\(214\) | −13.7958 | − | 7.96501i | −0.943061 | − | 0.544477i | ||||
\(215\) | −12.1404 | + | 7.00929i | −0.827971 | + | 0.478030i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −1.08600 | − | 16.1635i | −0.0737225 | − | 1.09725i | ||||
\(218\) | −1.48068 | −0.100285 | ||||||||
\(219\) | 6.81789 | − | 3.93631i | 0.460710 | − | 0.265991i | ||||
\(220\) | 7.11368 | − | 12.3212i | 0.479604 | − | 0.830698i | ||||
\(221\) | −0.769332 | + | 0.451502i | −0.0517509 | + | 0.0303713i | ||||
\(222\) | −4.05218 | − | 7.01858i | −0.271965 | − | 0.471056i | ||||
\(223\) | − | 7.16762i | − | 0.479979i | −0.970775 | − | 0.239990i | \(-0.922856\pi\) | ||
0.970775 | − | 0.239990i | \(-0.0771440\pi\) | |||||||
\(224\) | 0.177364 | + | 2.63980i | 0.0118506 | + | 0.176379i | ||||
\(225\) | −1.35473 | −0.0903152 | ||||||||
\(226\) | −8.69259 | + | 5.01867i | −0.578222 | + | 0.333837i | ||||
\(227\) | 18.6007 | + | 10.7391i | 1.23457 | + | 0.712782i | 0.967980 | − | 0.251027i | \(-0.0807683\pi\) |
0.266594 | + | 0.963809i | \(0.414102\pi\) | |||||||
\(228\) | −2.70459 | − | 1.56150i | −0.179116 | − | 0.103413i | ||||
\(229\) | 7.15978 | − | 4.13370i | 0.473132 | − | 0.273163i | −0.244418 | − | 0.969670i | \(-0.578597\pi\) |
0.717550 | + | 0.696507i | \(0.245264\pi\) | |||||||
\(230\) | −9.08047 | −0.598749 | ||||||||
\(231\) | −13.4031 | − | 6.58241i | −0.881860 | − | 0.433091i | ||||
\(232\) | − | 4.24895i | − | 0.278957i | ||||||
\(233\) | −13.4460 | − | 23.2892i | −0.880877 | − | 1.52572i | −0.850368 | − | 0.526189i | \(-0.823621\pi\) |
−0.0305088 | − | 0.999534i | \(-0.509713\pi\) | |||||||
\(234\) | −1.82494 | − | 3.10959i | −0.119300 | − | 0.203281i | ||||
\(235\) | 8.42474 | − | 14.5921i | 0.549570 | − | 0.951882i | ||||
\(236\) | 6.89004 | − | 3.97797i | 0.448504 | − | 0.258944i | ||||
\(237\) | 6.45525 | 0.419314 | ||||||||
\(238\) | −0.543662 | + | 0.364553i | −0.0352404 | + | 0.0236305i | ||||
\(239\) | 4.37478i | 0.282981i | 0.989940 | + | 0.141491i | \(0.0451895\pi\) | ||||
−0.989940 | + | 0.141491i | \(0.954811\pi\) | |||||||
\(240\) | 2.18313 | − | 1.26043i | 0.140920 | − | 0.0813604i | ||||
\(241\) | 1.33779 | + | 0.772373i | 0.0861746 | + | 0.0497529i | 0.542468 | − | 0.840076i | \(-0.317490\pi\) |
−0.456293 | + | 0.889829i | \(0.650823\pi\) | |||||||
\(242\) | −18.0593 | − | 10.4265i | −1.16089 | − | 0.670243i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −12.7884 | −0.818693 | ||||||||
\(245\) | −2.36056 | − | 17.4874i | −0.150811 | − | 1.11723i | ||||
\(246\) | 8.59917 | 0.548263 | ||||||||
\(247\) | −11.2598 | + | 0.0801049i | −0.716446 | + | 0.00509695i | ||||
\(248\) | 3.06150 | − | 5.30267i | 0.194405 | − | 0.336720i | ||||
\(249\) | 0.573729 | + | 0.331243i | 0.0363586 | + | 0.0209916i | ||||
\(250\) | 4.59461 | + | 7.95809i | 0.290588 | + | 0.503314i | ||||
\(251\) | 13.4321 | 0.847828 | 0.423914 | − | 0.905703i | \(-0.360656\pi\) | ||||
0.423914 | + | 0.905703i | \(0.360656\pi\) | |||||||
\(252\) | −1.47350 | − | 2.19745i | −0.0928219 | − | 0.138426i | ||||
\(253\) | 20.3299i | 1.27813i | ||||||||
\(254\) | −8.93186 | + | 5.15681i | −0.560435 | + | 0.323567i | ||||
\(255\) | 0.540119 | + | 0.311838i | 0.0338235 | + | 0.0195280i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −10.9173 | − | 18.9093i | −0.681003 | − | 1.17953i | −0.974675 | − | 0.223625i | \(-0.928211\pi\) |
0.293672 | − | 0.955906i | \(-0.405123\pi\) | |||||||
\(258\) | 5.56103i | 0.346215i | ||||||||
\(259\) | −19.2464 | − | 9.45210i | −1.19591 | − | 0.587325i | ||||
\(260\) | 4.48843 | − | 7.90351i | 0.278361 | − | 0.490155i | ||||
\(261\) | 2.12447 | + | 3.67970i | 0.131502 | + | 0.227768i | ||||
\(262\) | 16.0196 | + | 9.24892i | 0.989694 | + | 0.571400i | ||||
\(263\) | −4.24994 | + | 7.36111i | −0.262062 | + | 0.453906i | −0.966790 | − | 0.255573i | \(-0.917736\pi\) |
0.704727 | + | 0.709478i | \(0.251069\pi\) | |||||||
\(264\) | −2.82193 | − | 4.88772i | −0.173678 | − | 0.300818i | ||||
\(265\) | − | 16.5394i | − | 1.01601i | ||||||
\(266\) | −8.24408 | + | 0.553907i | −0.505477 | + | 0.0339622i | ||||
\(267\) | − | 5.62231i | − | 0.344080i | ||||||
\(268\) | −10.5562 | + | 6.09461i | −0.644821 | + | 0.372287i | ||||
\(269\) | 10.3107 | − | 17.8587i | 0.628656 | − | 1.08886i | −0.359166 | − | 0.933274i | \(-0.616939\pi\) |
0.987822 | − | 0.155590i | \(-0.0497280\pi\) | |||||||
\(270\) | −1.26043 | + | 2.18313i | −0.0767073 | + | 0.132861i | ||||
\(271\) | −20.7402 | + | 11.9744i | −1.25988 | + | 0.727392i | −0.973051 | − | 0.230590i | \(-0.925934\pi\) |
−0.286829 | + | 0.957982i | \(0.592601\pi\) | |||||||
\(272\) | −0.247406 | −0.0150012 | ||||||||
\(273\) | −8.59222 | − | 4.14413i | −0.520025 | − | 0.250814i | ||||
\(274\) | −13.7027 | −0.827808 | ||||||||
\(275\) | −6.62153 | + | 3.82294i | −0.399293 | + | 0.230532i | ||||
\(276\) | −1.80107 | + | 3.11954i | −0.108412 | + | 0.187774i | ||||
\(277\) | 2.06106 | − | 3.56986i | 0.123837 | − | 0.214492i | −0.797441 | − | 0.603397i | \(-0.793813\pi\) |
0.921278 | + | 0.388905i | \(0.127147\pi\) | |||||||
\(278\) | 6.94097 | − | 4.00737i | 0.416292 | − | 0.240346i | ||||
\(279\) | 6.12299i | 0.366574i | ||||||||
\(280\) | 2.94007 | − | 5.98657i | 0.175703 | − | 0.357766i | ||||
\(281\) | − | 10.3018i | − | 0.614556i | −0.951620 | − | 0.307278i | \(-0.900582\pi\) | ||
0.951620 | − | 0.307278i | \(-0.0994181\pi\) | |||||||
\(282\) | −3.34201 | − | 5.78854i | −0.199014 | − | 0.344702i | ||||
\(283\) | 5.43112 | − | 9.40698i | 0.322847 | − | 0.559187i | −0.658227 | − | 0.752819i | \(-0.728693\pi\) |
0.981074 | + | 0.193632i | \(0.0620268\pi\) | |||||||
\(284\) | 3.51969 | + | 2.03209i | 0.208855 | + | 0.120583i | ||||
\(285\) | 3.93631 | + | 6.81789i | 0.233167 | + | 0.403857i | ||||
\(286\) | −17.6949 | − | 10.0490i | −1.04632 | − | 0.594208i | ||||
\(287\) | 18.8963 | − | 12.6709i | 1.11541 | − | 0.747939i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 8.46940 | + | 14.6694i | 0.498200 | + | 0.862907i | ||||
\(290\) | −5.35550 | + | 9.27600i | −0.314486 | + | 0.544705i | ||||
\(291\) | −14.6140 | − | 8.43739i | −0.856687 | − | 0.494609i | ||||
\(292\) | 6.81789 | − | 3.93631i | 0.398987 | − | 0.230355i | ||||
\(293\) | − | 3.72513i | − | 0.217624i | −0.994062 | − | 0.108812i | \(-0.965295\pi\) | ||
0.994062 | − | 0.108812i | \(-0.0347047\pi\) | |||||||
\(294\) | −6.47590 | − | 2.65759i | −0.377682 | − | 0.154994i | ||||
\(295\) | −20.0558 | −1.16769 | ||||||||
\(296\) | −4.05218 | − | 7.01858i | −0.235528 | − | 0.407947i | ||||
\(297\) | 4.88772 | + | 2.82193i | 0.283614 | + | 0.163745i | ||||
\(298\) | −0.937732 | + | 1.62420i | −0.0543213 | + | 0.0940873i | ||||
\(299\) | 0.0923948 | + | 12.9874i | 0.00534333 | + | 0.751078i | ||||
\(300\) | −1.35473 | −0.0782153 | ||||||||
\(301\) | 8.19419 | + | 12.2201i | 0.472305 | + | 0.704355i | ||||
\(302\) | −2.71007 | −0.155947 | ||||||||
\(303\) | 5.75972 | + | 9.97613i | 0.330887 | + | 0.573114i | ||||
\(304\) | −2.70459 | − | 1.56150i | −0.155119 | − | 0.0895580i | ||||
\(305\) | 27.9187 | + | 16.1189i | 1.59862 | + | 0.922963i | ||||
\(306\) | 0.214260 | − | 0.123703i | 0.0122484 | − | 0.00707163i | ||||
\(307\) | − | 21.0104i | − | 1.19912i | −0.800328 | − | 0.599562i | \(-0.795341\pi\) | ||
0.800328 | − | 0.599562i | \(-0.204659\pi\) | |||||||
\(308\) | −13.4031 | − | 6.58241i | −0.763713 | − | 0.375068i | ||||
\(309\) | 5.78844 | 0.329293 | ||||||||
\(310\) | −13.3673 | + | 7.71760i | −0.759210 | + | 0.438330i | ||||
\(311\) | 3.19739 | − | 5.53804i | 0.181307 | − | 0.314034i | −0.761019 | − | 0.648730i | \(-0.775300\pi\) |
0.942326 | + | 0.334696i | \(0.108634\pi\) | |||||||
\(312\) | −1.82494 | − | 3.10959i | −0.103317 | − | 0.176046i | ||||
\(313\) | −7.73685 | − | 13.4006i | −0.437313 | − | 0.757448i | 0.560168 | − | 0.828379i | \(-0.310736\pi\) |
−0.997481 | + | 0.0709307i | \(0.977403\pi\) | |||||||
\(314\) | 17.1036i | 0.965210i | ||||||||
\(315\) | 0.447110 | + | 6.65456i | 0.0251918 | + | 0.374942i | ||||
\(316\) | 6.45525 | 0.363136 | ||||||||
\(317\) | 16.3604 | − | 9.44569i | 0.918893 | − | 0.530523i | 0.0356109 | − | 0.999366i | \(-0.488662\pi\) |
0.883282 | + | 0.468843i | \(0.155329\pi\) | |||||||
\(318\) | −5.68202 | − | 3.28052i | −0.318632 | − | 0.183962i | ||||
\(319\) | 20.7677 | + | 11.9902i | 1.16277 | + | 0.671323i | ||||
\(320\) | 2.18313 | − | 1.26043i | 0.122041 | − | 0.0704601i | ||||
\(321\) | 15.9300 | 0.889127 | ||||||||
\(322\) | 0.638890 | + | 9.50891i | 0.0356039 | + | 0.529911i | ||||
\(323\) | − | 0.772647i | − | 0.0429912i | ||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | −4.21266 | + | 2.47230i | −0.233676 | + | 0.137139i | ||||
\(326\) | 9.30258 | − | 16.1125i | 0.515222 | − | 0.892391i | ||||
\(327\) | 1.28231 | − | 0.740342i | 0.0709119 | − | 0.0409410i | ||||
\(328\) | 8.59917 | 0.474810 | ||||||||
\(329\) | −15.8733 | − | 7.79557i | −0.875125 | − | 0.429783i | ||||
\(330\) | 14.2274i | 0.783190i | ||||||||
\(331\) | −22.1676 | + | 12.7985i | −1.21844 | + | 0.703468i | −0.964585 | − | 0.263774i | \(-0.915033\pi\) |
−0.253857 | + | 0.967242i | \(0.581699\pi\) | |||||||
\(332\) | 0.573729 | + | 0.331243i | 0.0314875 | + | 0.0181793i | ||||
\(333\) | 7.01858 | + | 4.05218i | 0.384616 | + | 0.222058i | ||||
\(334\) | −7.29175 | − | 12.6297i | −0.398987 | − | 0.691065i | ||||
\(335\) | 30.7273 | 1.67881 | ||||||||
\(336\) | −1.47350 | − | 2.19745i | −0.0803861 | − | 0.119881i | ||||
\(337\) | −35.2040 | −1.91769 | −0.958843 | − | 0.283938i | \(-0.908359\pi\) | ||||
−0.958843 | + | 0.283938i | \(0.908359\pi\) | |||||||
\(338\) | −11.3497 | − | 6.33916i | −0.617341 | − | 0.344805i | ||||
\(339\) | 5.01867 | − | 8.69259i | 0.272577 | − | 0.472117i | ||||
\(340\) | 0.540119 | + | 0.311838i | 0.0292920 | + | 0.0169118i | ||||
\(341\) | 17.2786 | + | 29.9275i | 0.935690 | + | 1.62066i | ||||
\(342\) | 3.12299 | 0.168872 | ||||||||
\(343\) | −18.1464 | + | 3.70233i | −0.979815 | + | 0.199907i | ||||
\(344\) | 5.56103i | 0.299831i | ||||||||
\(345\) | 7.86392 | − | 4.54024i | 0.423379 | − | 0.244438i | ||||
\(346\) | 3.41119 | + | 1.96945i | 0.183387 | + | 0.105878i | ||||
\(347\) | −6.34130 | + | 10.9835i | −0.340419 | + | 0.589623i | −0.984511 | − | 0.175325i | \(-0.943902\pi\) |
0.644092 | + | 0.764948i | \(0.277236\pi\) | |||||||
\(348\) | 2.12447 | + | 3.67970i | 0.113884 | + | 0.197253i | ||||
\(349\) | 16.7258i | 0.895311i | 0.894206 | + | 0.447656i | \(0.147741\pi\) | ||||
−0.894206 | + | 0.447656i | \(0.852259\pi\) | |||||||
\(350\) | −2.97695 | + | 1.99619i | −0.159125 | + | 0.106701i | ||||
\(351\) | 3.13524 | + | 1.78052i | 0.167347 | + | 0.0950369i | ||||
\(352\) | −2.82193 | − | 4.88772i | −0.150409 | − | 0.260516i | ||||
\(353\) | 8.35129 | + | 4.82162i | 0.444494 | + | 0.256629i | 0.705502 | − | 0.708708i | \(-0.250722\pi\) |
−0.261008 | + | 0.965337i | \(0.584055\pi\) | |||||||
\(354\) | −3.97797 | + | 6.89004i | −0.211427 | + | 0.366202i | ||||
\(355\) | −5.12262 | − | 8.87264i | −0.271880 | − | 0.470911i | ||||
\(356\) | − | 5.62231i | − | 0.297982i | ||||||
\(357\) | 0.288549 | − | 0.587543i | 0.0152716 | − | 0.0310961i | ||||
\(358\) | − | 4.70637i | − | 0.248739i | ||||||
\(359\) | 0.491107 | − | 0.283541i | 0.0259197 | − | 0.0149647i | −0.486984 | − | 0.873411i | \(-0.661903\pi\) |
0.512904 | + | 0.858446i | \(0.328570\pi\) | |||||||
\(360\) | −1.26043 | + | 2.18313i | −0.0664305 | + | 0.115061i | ||||
\(361\) | −4.62346 | + | 8.00806i | −0.243340 | + | 0.421477i | ||||
\(362\) | 13.5446 | − | 7.81998i | 0.711889 | − | 0.411009i | ||||
\(363\) | 20.8531 | 1.09450 | ||||||||
\(364\) | −8.59222 | − | 4.14413i | −0.450355 | − | 0.217211i | ||||
\(365\) | −19.8458 | −1.03878 | ||||||||
\(366\) | 11.0751 | − | 6.39419i | 0.578903 | − | 0.334230i | ||||
\(367\) | 6.62549 | − | 11.4757i | 0.345848 | − | 0.599026i | −0.639660 | − | 0.768658i | \(-0.720925\pi\) |
0.985507 | + | 0.169632i | \(0.0542580\pi\) | |||||||
\(368\) | −1.80107 | + | 3.11954i | −0.0938871 | + | 0.162617i | ||||
\(369\) | −7.44710 | + | 4.29959i | −0.387681 | + | 0.223827i | ||||
\(370\) | 20.4299i | 1.06210i | ||||||||
\(371\) | −17.3198 | + | 1.16369i | −0.899200 | + | 0.0604159i | ||||
\(372\) | 6.12299i | 0.317462i | ||||||||
\(373\) | −11.9476 | − | 20.6939i | −0.618624 | − | 1.07149i | −0.989737 | − | 0.142900i | \(-0.954357\pi\) |
0.371113 | − | 0.928588i | \(-0.378976\pi\) | |||||||
\(374\) | 0.698161 | − | 1.20925i | 0.0361011 | − | 0.0625289i | ||||
\(375\) | −7.95809 | − | 4.59461i | −0.410954 | − | 0.237264i | ||||
\(376\) | −3.34201 | − | 5.78854i | −0.172351 | − | 0.298521i | ||||
\(377\) | 13.3215 | + | 7.56532i | 0.686092 | + | 0.389634i | ||||
\(378\) | 2.37482 | + | 1.16630i | 0.122147 | + | 0.0599879i | ||||
\(379\) | 1.46025i | 0.0750081i | 0.999296 | + | 0.0375040i | \(0.0119407\pi\) | ||||
−0.999296 | + | 0.0375040i | \(0.988059\pi\) | |||||||
\(380\) | 3.93631 | + | 6.81789i | 0.201929 | + | 0.349751i | ||||
\(381\) | 5.15681 | − | 8.93186i | 0.264192 | − | 0.457593i | ||||
\(382\) | 7.77419 | + | 4.48843i | 0.397762 | + | 0.229648i | ||||
\(383\) | 5.64718 | − | 3.26040i | 0.288557 | − | 0.166599i | −0.348734 | − | 0.937222i | \(-0.613388\pi\) |
0.637291 | + | 0.770623i | \(0.280055\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 20.9640 | + | 31.2639i | 1.06843 | + | 1.59336i | ||||
\(386\) | −7.04017 | −0.358335 | ||||||||
\(387\) | −2.78052 | − | 4.81600i | −0.141342 | − | 0.244811i | ||||
\(388\) | −14.6140 | − | 8.43739i | −0.741913 | − | 0.428344i | ||||
\(389\) | −12.8010 | + | 22.1719i | −0.649035 | + | 1.12416i | 0.334319 | + | 0.942460i | \(0.391494\pi\) |
−0.983354 | + | 0.181702i | \(0.941839\pi\) | |||||||
\(390\) | 0.0646601 | + | 9.08886i | 0.00327419 | + | 0.460232i | ||||
\(391\) | −0.891189 | −0.0450694 | ||||||||
\(392\) | −6.47590 | − | 2.65759i | −0.327082 | − | 0.134228i | ||||
\(393\) | −18.4978 | −0.933093 | ||||||||
\(394\) | 5.85504 | + | 10.1412i | 0.294972 | + | 0.510907i | ||||
\(395\) | −14.0926 | − | 8.13639i | −0.709078 | − | 0.409386i | ||||
\(396\) | 4.88772 | + | 2.82193i | 0.245617 | + | 0.141807i | ||||
\(397\) | 13.4505 | − | 7.76567i | 0.675063 | − | 0.389748i | −0.122929 | − | 0.992415i | \(-0.539229\pi\) |
0.797992 | + | 0.602668i | \(0.205895\pi\) | |||||||
\(398\) | − | 18.1015i | − | 0.907347i | ||||||
\(399\) | 6.86263 | − | 4.60174i | 0.343561 | − | 0.230375i | ||||
\(400\) | −1.35473 | −0.0677364 | ||||||||
\(401\) | −30.2703 | + | 17.4765i | −1.51163 | + | 0.872737i | −0.511717 | + | 0.859154i | \(0.670991\pi\) |
−0.999908 | + | 0.0135833i | \(0.995676\pi\) | |||||||
\(402\) | 6.09461 | − | 10.5562i | 0.303971 | − | 0.526494i | ||||
\(403\) | 11.1741 | + | 19.0400i | 0.556622 | + | 0.948451i | ||||
\(404\) | 5.75972 | + | 9.97613i | 0.286557 | + | 0.496331i | ||||
\(405\) | − | 2.52086i | − | 0.125262i | ||||||
\(406\) | 10.0905 | + | 4.95554i | 0.500782 | + | 0.245939i | ||||
\(407\) | 45.7398 | 2.26724 | ||||||||
\(408\) | 0.214260 | − | 0.123703i | 0.0106074 | − | 0.00612421i | ||||
\(409\) | −11.0002 | − | 6.35099i | −0.543927 | − | 0.314036i | 0.202742 | − | 0.979232i | \(-0.435015\pi\) |
−0.746669 | + | 0.665196i | \(0.768348\pi\) | |||||||
\(410\) | −18.7731 | − | 10.8386i | −0.927137 | − | 0.535283i | ||||
\(411\) | 11.8669 | − | 6.85133i | 0.585349 | − | 0.337951i | ||||
\(412\) | 5.78844 | 0.285176 | ||||||||
\(413\) | 1.41110 | + | 21.0021i | 0.0694356 | + | 1.03344i | ||||
\(414\) | − | 3.60213i | − | 0.177035i | ||||||
\(415\) | −0.835016 | − | 1.44629i | −0.0409893 | − | 0.0709956i | ||||
\(416\) | −1.82494 | − | 3.10959i | −0.0894752 | − | 0.152460i | ||||
\(417\) | −4.00737 | + | 6.94097i | −0.196242 | + | 0.339901i | ||||
\(418\) | 15.2643 | − | 8.81286i | 0.746602 | − | 0.431051i | ||||
\(419\) | −23.7483 | −1.16018 | −0.580091 | − | 0.814552i | \(-0.696983\pi\) | ||||
−0.580091 | + | 0.814552i | \(0.696983\pi\) | |||||||
\(420\) | 0.447110 | + | 6.65456i | 0.0218167 | + | 0.324709i | ||||
\(421\) | 4.91285i | 0.239438i | 0.992808 | + | 0.119719i | \(0.0381993\pi\) | ||||
−0.992808 | + | 0.119719i | \(0.961801\pi\) | |||||||
\(422\) | 20.1136 | − | 11.6126i | 0.979115 | − | 0.565292i | ||||
\(423\) | 5.78854 | + | 3.34201i | 0.281448 | + | 0.162494i | ||||
\(424\) | −5.68202 | − | 3.28052i | −0.275943 | − | 0.159316i | ||||
\(425\) | −0.167584 | − | 0.290264i | −0.00812901 | − | 0.0140799i | ||||
\(426\) | −4.06419 | −0.196910 | ||||||||
\(427\) | 14.9151 | − | 30.3701i | 0.721791 | − | 1.46971i | ||||
\(428\) | 15.9300 | 0.770006 | ||||||||
\(429\) | 20.3487 | − | 0.144765i | 0.982444 | − | 0.00698932i | ||||
\(430\) | 7.00929 | − | 12.1404i | 0.338018 | − | 0.585464i | ||||
\(431\) | −21.7888 | − | 12.5798i | −1.04953 | − | 0.605947i | −0.127013 | − | 0.991901i | \(-0.540539\pi\) |
−0.922518 | + | 0.385954i | \(0.873872\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 6.16471 | 0.296257 | 0.148129 | − | 0.988968i | \(-0.452675\pi\) | ||||
0.148129 | + | 0.988968i | \(0.452675\pi\) | |||||||
\(434\) | 9.02224 | + | 13.4550i | 0.433081 | + | 0.645860i | ||||
\(435\) | − | 10.7110i | − | 0.513553i | ||||||
\(436\) | 1.28231 | − | 0.740342i | 0.0614115 | − | 0.0354560i | ||||
\(437\) | −9.74230 | − | 5.62472i | −0.466038 | − | 0.269067i | ||||
\(438\) | −3.93631 | + | 6.81789i | −0.188084 | + | 0.325772i | ||||
\(439\) | −4.44890 | − | 7.70572i | −0.212334 | − | 0.367774i | 0.740110 | − | 0.672486i | \(-0.234773\pi\) |
−0.952445 | + | 0.304712i | \(0.901440\pi\) | |||||||
\(440\) | 14.2274i | 0.678262i | ||||||||
\(441\) | 6.93708 | − | 0.936412i | 0.330337 | − | 0.0445911i | ||||
\(442\) | 0.440510 | − | 0.775678i | 0.0209529 | − | 0.0368952i | ||||
\(443\) | −17.0804 | − | 29.5842i | −0.811516 | − | 1.40559i | −0.911803 | − | 0.410629i | \(-0.865309\pi\) |
0.100286 | − | 0.994959i | \(-0.468024\pi\) | |||||||
\(444\) | 7.01858 | + | 4.05218i | 0.333087 | + | 0.192308i | ||||
\(445\) | −7.08653 | + | 12.2742i | −0.335934 | + | 0.581854i | ||||
\(446\) | 3.58381 | + | 6.20734i | 0.169698 | + | 0.293926i | ||||
\(447\) | − | 1.87546i | − | 0.0887064i | ||||||
\(448\) | −1.47350 | − | 2.19745i | −0.0696164 | − | 0.103820i | ||||
\(449\) | − | 29.0848i | − | 1.37260i | −0.727320 | − | 0.686298i | \(-0.759234\pi\) | ||
0.727320 | − | 0.686298i | \(-0.240766\pi\) | |||||||
\(450\) | 1.17323 | − | 0.677364i | 0.0553066 | − | 0.0319313i | ||||
\(451\) | −24.2662 | + | 42.0303i | −1.14265 | + | 1.97913i | ||||
\(452\) | 5.01867 | − | 8.69259i | 0.236058 | − | 0.408865i | ||||
\(453\) | 2.34699 | − | 1.35504i | 0.110271 | − | 0.0636652i | ||||
\(454\) | −21.4783 | −1.00803 | ||||||||
\(455\) | 13.5345 | + | 19.8770i | 0.634509 | + | 0.931850i | ||||
\(456\) | 3.12299 | 0.146248 | ||||||||
\(457\) | −30.7370 | + | 17.7460i | −1.43782 | + | 0.830124i | −0.997698 | − | 0.0678157i | \(-0.978397\pi\) |
−0.440119 | + | 0.897940i | \(0.645064\pi\) | |||||||
\(458\) | −4.13370 | + | 7.15978i | −0.193155 | + | 0.334555i | ||||
\(459\) | −0.123703 | + | 0.214260i | −0.00577396 | + | 0.0100008i | ||||
\(460\) | 7.86392 | − | 4.54024i | 0.366657 | − | 0.211690i | ||||
\(461\) | − | 7.57380i | − | 0.352747i | −0.984323 | − | 0.176373i | \(-0.943563\pi\) | ||
0.984323 | − | 0.176373i | \(-0.0564366\pi\) | |||||||
\(462\) | 14.8986 | − | 1.00102i | 0.693147 | − | 0.0465716i | ||||
\(463\) | 25.0299i | 1.16324i | 0.813462 | + | 0.581618i | \(0.197580\pi\) | ||||
−0.813462 | + | 0.581618i | \(0.802420\pi\) | |||||||
\(464\) | 2.12447 | + | 3.67970i | 0.0986263 | + | 0.170826i | ||||
\(465\) | 7.71760 | − | 13.3673i | 0.357895 | − | 0.619893i | ||||
\(466\) | 23.2892 | + | 13.4460i | 1.07885 | + | 0.622874i | ||||
\(467\) | 15.6334 | + | 27.0778i | 0.723427 | + | 1.25301i | 0.959618 | + | 0.281306i | \(0.0907675\pi\) |
−0.236191 | + | 0.971707i | \(0.575899\pi\) | |||||||
\(468\) | 3.13524 | + | 1.78052i | 0.144927 | + | 0.0823044i | ||||
\(469\) | −2.16193 | − | 32.1771i | −0.0998287 | − | 1.48580i | ||||
\(470\) | 16.8495i | 0.777209i | ||||||||
\(471\) | −8.55178 | − | 14.8121i | −0.394045 | − | 0.682506i | ||||
\(472\) | −3.97797 | + | 6.89004i | −0.183101 | + | 0.317140i | ||||
\(473\) | −27.1808 | − | 15.6928i | −1.24977 | − | 0.721557i | ||||
\(474\) | −5.59041 | + | 3.22763i | −0.256776 | + | 0.148250i | ||||
\(475\) | − | 4.23081i | − | 0.194123i | ||||||
\(476\) | 0.288549 | − | 0.587543i | 0.0132256 | − | 0.0269300i | ||||
\(477\) | 6.56103 | 0.300409 | ||||||||
\(478\) | −2.18739 | − | 3.78867i | −0.100049 | − | 0.173290i | ||||
\(479\) | 13.4394 | + | 7.75926i | 0.614063 | + | 0.354529i | 0.774554 | − | 0.632508i | \(-0.217974\pi\) |
−0.160491 | + | 0.987037i | \(0.551308\pi\) | |||||||
\(480\) | −1.26043 | + | 2.18313i | −0.0575305 | + | 0.0996457i | ||||
\(481\) | 29.2199 | − | 0.207877i | 1.33231 | − | 0.00947838i | ||||
\(482\) | −1.54475 | −0.0703613 | ||||||||
\(483\) | −5.30775 | − | 7.91552i | −0.241511 | − | 0.360168i | ||||
\(484\) | 20.8531 | 0.947867 | ||||||||
\(485\) | 21.2695 | + | 36.8398i | 0.965797 | + | 1.67281i | ||||
\(486\) | −0.866025 | − | 0.500000i | −0.0392837 | − | 0.0226805i | ||||
\(487\) | 28.0472 | + | 16.1931i | 1.27094 | + | 0.733778i | 0.975165 | − | 0.221479i | \(-0.0710886\pi\) |
0.295776 | + | 0.955257i | \(0.404422\pi\) | |||||||
\(488\) | 11.0751 | − | 6.39419i | 0.501345 | − | 0.289452i | ||||
\(489\) | 18.6052i | 0.841355i | ||||||||
\(490\) | 10.7880 | + | 13.9643i | 0.487353 | + | 0.630841i | ||||
\(491\) | −9.22056 | −0.416118 | −0.208059 | − | 0.978116i | \(-0.566715\pi\) | ||||
−0.208059 | + | 0.978116i | \(0.566715\pi\) | |||||||
\(492\) | −7.44710 | + | 4.29959i | −0.335741 | + | 0.193840i | ||||
\(493\) | −0.525608 | + | 0.910379i | −0.0236722 | + | 0.0410014i | ||||
\(494\) | 9.71124 | − | 5.69929i | 0.436930 | − | 0.256423i | ||||
\(495\) | −7.11368 | − | 12.3212i | −0.319736 | − | 0.553799i | ||||
\(496\) | 6.12299i | 0.274931i | ||||||||
\(497\) | −8.93085 | + | 5.98858i | −0.400603 | + | 0.268625i | ||||
\(498\) | −0.662485 | −0.0296867 | ||||||||
\(499\) | 6.56445 | − | 3.78999i | 0.293865 | − | 0.169663i | −0.345818 | − | 0.938301i | \(-0.612399\pi\) |
0.639684 | + | 0.768638i | \(0.279065\pi\) | |||||||
\(500\) | −7.95809 | − | 4.59461i | −0.355897 | − | 0.205477i | ||||
\(501\) | 12.6297 | + | 7.29175i | 0.564253 | + | 0.325771i | ||||
\(502\) | −11.6326 | + | 6.71606i | −0.519186 | + | 0.299752i | ||||
\(503\) | 1.86195 | 0.0830203 | 0.0415102 | − | 0.999138i | \(-0.486783\pi\) | ||||
0.0415102 | + | 0.999138i | \(0.486783\pi\) | |||||||
\(504\) | 2.37482 | + | 1.16630i | 0.105783 | + | 0.0519510i | ||||
\(505\) | − | 29.0389i | − | 1.29221i | ||||||
\(506\) | −10.1650 | − | 17.6062i | −0.451887 | − | 0.782692i | ||||
\(507\) | 12.9987 | − | 0.184960i | 0.577292 | − | 0.00821437i | ||||
\(508\) | 5.15681 | − | 8.93186i | 0.228797 | − | 0.396287i | ||||
\(509\) | −6.91271 | + | 3.99105i | −0.306400 | + | 0.176900i | −0.645315 | − | 0.763917i | \(-0.723274\pi\) |
0.338914 | + | 0.940817i | \(0.389940\pi\) | |||||||
\(510\) | −0.623675 | −0.0276168 | ||||||||
\(511\) | 1.39632 | + | 20.7822i | 0.0617697 | + | 0.919348i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −2.70459 | + | 1.56150i | −0.119411 | + | 0.0689418i | ||||
\(514\) | 18.9093 | + | 10.9173i | 0.834055 | + | 0.481542i | ||||
\(515\) | −12.6369 | − | 7.29592i | −0.556849 | − | 0.321497i | ||||
\(516\) | −2.78052 | − | 4.81600i | −0.122405 | − | 0.212012i | ||||
\(517\) | 37.7237 | 1.65908 | ||||||||
\(518\) | 21.3939 | − | 1.43742i | 0.939993 | − | 0.0631568i | ||||
\(519\) | −3.93890 | −0.172899 | ||||||||
\(520\) | 0.0646601 | + | 9.08886i | 0.00283553 | + | 0.398573i | ||||
\(521\) | −8.61209 | + | 14.9166i | −0.377303 | + | 0.653507i | −0.990669 | − | 0.136291i | \(-0.956482\pi\) |
0.613366 | + | 0.789799i | \(0.289815\pi\) | |||||||
\(522\) | −3.67970 | − | 2.12447i | −0.161056 | − | 0.0929857i | ||||
\(523\) | 12.7325 | + | 22.0534i | 0.556755 | + | 0.964328i | 0.997765 | + | 0.0668258i | \(0.0212872\pi\) |
−0.441010 | + | 0.897502i | \(0.645379\pi\) | |||||||
\(524\) | −18.4978 | −0.808082 | ||||||||
\(525\) | 1.58002 | − | 3.21723i | 0.0689576 | − | 0.140411i | ||||
\(526\) | − | 8.49988i | − | 0.370612i | ||||||
\(527\) | −1.31191 | + | 0.757432i | −0.0571478 | + | 0.0329943i | ||||
\(528\) | 4.88772 | + | 2.82193i | 0.212711 | + | 0.122809i | ||||
\(529\) | 5.01231 | − | 8.68158i | 0.217927 | − | 0.377460i | ||||
\(530\) | 8.26972 | + | 14.3236i | 0.359214 | + | 0.622176i | ||||
\(531\) | − | 7.95594i | − | 0.345258i | ||||||
\(532\) | 6.86263 | − | 4.60174i | 0.297533 | − | 0.199511i | ||||
\(533\) | −15.3110 | + | 26.9605i | −0.663192 | + | 1.16779i | ||||
\(534\) | 2.81116 | + | 4.86906i | 0.121651 | + | 0.210705i | ||||
\(535\) | −34.7773 | − | 20.0787i | −1.50355 | − | 0.868076i | ||||
\(536\) | 6.09461 | − | 10.5562i | 0.263247 | − | 0.455957i | ||||
\(537\) | 2.35319 | + | 4.07584i | 0.101547 | + | 0.175885i | ||||
\(538\) | 20.6215i | 0.889054i | ||||||||
\(539\) | 31.2640 | − | 24.1529i | 1.34664 | − | 1.04034i | ||||
\(540\) | − | 2.52086i | − | 0.108480i | ||||||
\(541\) | 16.1619 | − | 9.33109i | 0.694855 | − | 0.401175i | −0.110573 | − | 0.993868i | \(-0.535269\pi\) |
0.805428 | + | 0.592693i | \(0.201935\pi\) | |||||||
\(542\) | 11.9744 | − | 20.7402i | 0.514344 | − | 0.890870i | ||||
\(543\) | −7.81998 | + | 13.5446i | −0.335587 | + | 0.581255i | ||||
\(544\) | 0.214260 | − | 0.123703i | 0.00918631 | − | 0.00530372i | ||||
\(545\) | −3.73260 | −0.159887 | ||||||||
\(546\) | 9.51314 | − | 0.707191i | 0.407125 | − | 0.0302650i | ||||
\(547\) | 32.1949 | 1.37655 | 0.688277 | − | 0.725448i | \(-0.258367\pi\) | ||||
0.688277 | + | 0.725448i | \(0.258367\pi\) | |||||||
\(548\) | 11.8669 | − | 6.85133i | 0.506927 | − | 0.292674i | ||||
\(549\) | −6.39419 | + | 11.0751i | −0.272898 | + | 0.472672i | ||||
\(550\) | 3.82294 | − | 6.62153i | 0.163011 | − | 0.282343i | ||||
\(551\) | −11.4917 | + | 6.63472i | −0.489562 | + | 0.282649i | ||||
\(552\) | − | 3.60213i | − | 0.153317i | ||||||
\(553\) | −7.52875 | + | 15.3300i | −0.320155 | + | 0.651899i | ||||
\(554\) | 4.12212i | 0.175132i | ||||||||
\(555\) | −10.2150 | − | 17.6929i | −0.433601 | − | 0.751020i | ||||
\(556\) | −4.00737 | + | 6.94097i | −0.169950 | + | 0.294363i | ||||
\(557\) | −7.52338 | − | 4.34362i | −0.318776 | − | 0.184045i | 0.332071 | − | 0.943254i | \(-0.392253\pi\) |
−0.650847 | + | 0.759209i | \(0.725586\pi\) | |||||||
\(558\) | −3.06150 | − | 5.30267i | −0.129603 | − | 0.224480i | ||||
\(559\) | −17.4352 | − | 9.90151i | −0.737430 | − | 0.418789i | ||||
\(560\) | 0.447110 | + | 6.65456i | 0.0188939 | + | 0.281207i | ||||
\(561\) | 1.39632i | 0.0589528i | ||||||||
\(562\) | 5.15092 | + | 8.92165i | 0.217278 | + | 0.376337i | ||||
\(563\) | −7.67650 | + | 13.2961i | −0.323526 | + | 0.560363i | −0.981213 | − | 0.192928i | \(-0.938202\pi\) |
0.657687 | + | 0.753291i | \(0.271535\pi\) | |||||||
\(564\) | 5.78854 | + | 3.34201i | 0.243741 | + | 0.140724i | ||||
\(565\) | −21.9128 | + | 12.6514i | −0.921878 | + | 0.532246i | ||||
\(566\) | 10.8622i | 0.456574i | ||||||||
\(567\) | −2.63980 | + | 0.177364i | −0.110861 | + | 0.00744860i | ||||
\(568\) | −4.06419 | −0.170529 | ||||||||
\(569\) | −18.4292 | − | 31.9204i | −0.772594 | − | 1.33817i | −0.936137 | − | 0.351636i | \(-0.885626\pi\) |
0.163543 | − | 0.986536i | \(-0.447708\pi\) | |||||||
\(570\) | −6.81789 | − | 3.93631i | −0.285570 | − | 0.164874i | ||||
\(571\) | −5.61735 | + | 9.72953i | −0.235079 | + | 0.407168i | −0.959296 | − | 0.282404i | \(-0.908868\pi\) |
0.724217 | + | 0.689572i | \(0.242201\pi\) | |||||||
\(572\) | 20.3487 | − | 0.144765i | 0.850821 | − | 0.00605293i | ||||
\(573\) | −8.97686 | −0.375014 | ||||||||
\(574\) | −10.0292 | + | 20.4214i | −0.418611 | + | 0.852375i | ||||
\(575\) | −4.87991 | −0.203506 | ||||||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −24.5422 | − | 14.1694i | −1.02170 | − | 0.589881i | −0.107107 | − | 0.994247i | \(-0.534159\pi\) |
−0.914597 | + | 0.404366i | \(0.867492\pi\) | |||||||
\(578\) | −14.6694 | − | 8.46940i | −0.610168 | − | 0.352280i | ||||
\(579\) | 6.09697 | − | 3.52009i | 0.253381 | − | 0.146290i | ||||
\(580\) | − | 10.7110i | − | 0.444750i | ||||||
\(581\) | −1.45578 | + | 0.976173i | −0.0603959 | + | 0.0404985i | ||||
\(582\) | 16.8748 | 0.699482 | ||||||||
\(583\) | 32.0685 | − | 18.5147i | 1.32814 | − | 0.766803i | ||||
\(584\) | −3.93631 | + | 6.81789i | −0.162886 | + | 0.282126i | ||||
\(585\) | −4.60042 | − | 7.83885i | −0.190204 | − | 0.324097i | ||||
\(586\) | 1.86256 | + | 3.22606i | 0.0769418 | + | 0.133267i | ||||
\(587\) | 0.0179623i | 0.000741383i | 1.00000 | 0.000370692i | \(0.000117995\pi\) | |||||
−1.00000 | 0.000370692i | \(0.999882\pi\) | ||||||||
\(588\) | 6.93708 | − | 0.936412i | 0.286081 | − | 0.0386170i | ||||
\(589\) | −19.1221 | −0.787911 | ||||||||
\(590\) | 17.3688 | − | 10.0279i | 0.715063 | − | 0.412842i | ||||
\(591\) | −10.1412 | − | 5.85504i | −0.417154 | − | 0.240844i | ||||
\(592\) | 7.01858 | + | 4.05218i | 0.288462 | + | 0.166544i | ||||
\(593\) | 41.5164 | − | 23.9695i | 1.70487 | − | 0.984309i | 0.764209 | − | 0.644969i | \(-0.223130\pi\) |
0.940664 | − | 0.339340i | \(-0.110204\pi\) | |||||||
\(594\) | −5.64385 | −0.231570 | ||||||||
\(595\) | −1.37050 | + | 0.918987i | −0.0561849 | + | 0.0376748i | ||||
\(596\) | − | 1.87546i | − | 0.0768220i | ||||||
\(597\) | 9.05076 | + | 15.6764i | 0.370423 | + | 0.641591i | ||||
\(598\) | −6.57369 | − | 11.2012i | −0.268818 | − | 0.458050i | ||||
\(599\) | 7.47580 | − | 12.9485i | 0.305453 | − | 0.529060i | −0.671909 | − | 0.740634i | \(-0.734525\pi\) |
0.977362 | + | 0.211573i | \(0.0678588\pi\) | |||||||
\(600\) | 1.17323 | − | 0.677364i | 0.0478969 | − | 0.0276533i | ||||
\(601\) | 19.7525 | 0.805723 | 0.402861 | − | 0.915261i | \(-0.368016\pi\) | ||||
0.402861 | + | 0.915261i | \(0.368016\pi\) | |||||||
\(602\) | −13.2064 | − | 6.48582i | −0.538254 | − | 0.264342i | ||||
\(603\) | 12.1892i | 0.496383i | ||||||||
\(604\) | 2.34699 | − | 1.35504i | 0.0954977 | − | 0.0551357i | ||||
\(605\) | −45.5249 | − | 26.2838i | −1.85085 | − | 1.06859i | ||||
\(606\) | −9.97613 | − | 5.75972i | −0.405252 | − | 0.233973i | ||||
\(607\) | 5.09059 | + | 8.81716i | 0.206621 | + | 0.357878i | 0.950648 | − | 0.310272i | \(-0.100420\pi\) |
−0.744027 | + | 0.668149i | \(0.767087\pi\) | |||||||
\(608\) | 3.12299 | 0.126654 | ||||||||
\(609\) | −11.2164 | + | 0.753612i | −0.454510 | + | 0.0305379i | ||||
\(610\) | −32.2377 | −1.30527 | ||||||||
\(611\) | 24.0990 | − | 0.171445i | 0.974941 | − | 0.00693594i | ||||
\(612\) | −0.123703 | + | 0.214260i | −0.00500040 | + | 0.00866094i | ||||
\(613\) | −26.1938 | − | 15.1230i | −1.05796 | − | 0.610812i | −0.133091 | − | 0.991104i | \(-0.542490\pi\) |
−0.924867 | + | 0.380292i | \(0.875824\pi\) | |||||||
\(614\) | 10.5052 | + | 18.1955i | 0.423955 | + | 0.734311i | ||||
\(615\) | 21.6773 | 0.874113 | ||||||||
\(616\) | 14.8986 | − | 1.00102i | 0.600283 | − | 0.0403322i | ||||
\(617\) | − | 18.4715i | − | 0.743636i | −0.928306 | − | 0.371818i | \(-0.878735\pi\) | ||
0.928306 | − | 0.371818i | \(-0.121265\pi\) | |||||||
\(618\) | −5.01294 | + | 2.89422i | −0.201650 | + | 0.116423i | ||||
\(619\) | 3.42519 | + | 1.97754i | 0.137670 | + | 0.0794839i | 0.567253 | − | 0.823543i | \(-0.308006\pi\) |
−0.429583 | + | 0.903027i | \(0.641339\pi\) | |||||||
\(620\) | 7.71760 | − | 13.3673i | 0.309946 | − | 0.536843i | ||||
\(621\) | 1.80107 | + | 3.11954i | 0.0722743 | + | 0.125183i | ||||
\(622\) | 6.39478i | 0.256407i | ||||||||
\(623\) | 13.3520 | + | 6.55729i | 0.534935 | + | 0.262712i | ||||
\(624\) | 3.13524 | + | 1.78052i | 0.125510 | + | 0.0712777i | ||||
\(625\) | 14.9692 | + | 25.9274i | 0.598767 | + | 1.03709i | ||||
\(626\) | 13.4006 | + | 7.73685i | 0.535597 | + | 0.309227i | ||||
\(627\) | −8.81286 | + | 15.2643i | −0.351952 | + | 0.609598i | ||||
\(628\) | −8.55178 | − | 14.8121i | −0.341253 | − | 0.591068i | ||||
\(629\) | 2.00507i | 0.0799472i | ||||||||
\(630\) | −3.71449 | − | 5.53946i | −0.147989 | − | 0.220698i | ||||
\(631\) | − | 24.3547i | − | 0.969546i | −0.874640 | − | 0.484773i | \(-0.838902\pi\) | ||
0.874640 | − | 0.484773i | \(-0.161098\pi\) | |||||||
\(632\) | −5.59041 | + | 3.22763i | −0.222375 | + | 0.128388i | ||||
\(633\) | −11.6126 | + | 20.1136i | −0.461559 | + | 0.799444i | ||||
\(634\) | −9.44569 | + | 16.3604i | −0.375136 | + | 0.649755i | ||||
\(635\) | −22.5160 | + | 12.9996i | −0.893519 | + | 0.515873i | ||||
\(636\) | 6.56103 | 0.260162 | ||||||||
\(637\) | 19.8626 | − | 15.5716i | 0.786986 | − | 0.616971i | ||||
\(638\) | −23.9804 | −0.949395 | ||||||||
\(639\) | 3.51969 | − | 2.03209i | 0.139237 | − | 0.0803883i | ||||
\(640\) | −1.26043 | + | 2.18313i | −0.0498228 | + | 0.0862957i | ||||
\(641\) | −0.398610 | + | 0.690412i | −0.0157441 | + | 0.0272696i | −0.873790 | − | 0.486303i | \(-0.838345\pi\) |
0.858046 | + | 0.513573i | \(0.171678\pi\) | |||||||
\(642\) | −13.7958 | + | 7.96501i | −0.544477 | + | 0.314354i | ||||
\(643\) | − | 36.3986i | − | 1.43542i | −0.696342 | − | 0.717710i | \(-0.745190\pi\) | ||
0.696342 | − | 0.717710i | \(-0.254810\pi\) | |||||||
\(644\) | −5.30775 | − | 7.91552i | −0.209155 | − | 0.311915i | ||||
\(645\) | 14.0186i | 0.551981i | ||||||||
\(646\) | 0.386323 | + | 0.669132i | 0.0151997 | + | 0.0263266i | ||||
\(647\) | −18.3127 | + | 31.7185i | −0.719945 | + | 1.24698i | 0.241076 | + | 0.970506i | \(0.422500\pi\) |
−0.961021 | + | 0.276475i | \(0.910834\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | −22.4511 | − | 38.8864i | −0.881281 | − | 1.52642i | ||||
\(650\) | 2.41212 | − | 4.24741i | 0.0946110 | − | 0.166597i | ||||
\(651\) | −14.5410 | − | 7.14123i | −0.569906 | − | 0.279887i | ||||
\(652\) | 18.6052i | 0.728635i | ||||||||
\(653\) | −18.1837 | − | 31.4951i | −0.711583 | − | 1.23250i | −0.964263 | − | 0.264948i | \(-0.914645\pi\) |
0.252680 | − | 0.967550i | \(-0.418688\pi\) | |||||||
\(654\) | −0.740342 | + | 1.28231i | −0.0289497 | + | 0.0501423i | ||||
\(655\) | 40.3832 | + | 23.3152i | 1.57790 | + | 0.911001i | ||||
\(656\) | −7.44710 | + | 4.29959i | −0.290760 | + | 0.167871i | ||||
\(657\) | − | 7.87262i | − | 0.307140i | ||||||
\(658\) | 17.6445 | − | 1.18551i | 0.687854 | − | 0.0462159i | ||||
\(659\) | −18.7720 | −0.731252 | −0.365626 | − | 0.930762i | \(-0.619145\pi\) | ||||
−0.365626 | + | 0.930762i | \(0.619145\pi\) | |||||||
\(660\) | −7.11368 | − | 12.3212i | −0.276899 | − | 0.479604i | ||||
\(661\) | −36.4244 | − | 21.0297i | −1.41675 | − | 0.817959i | −0.420735 | − | 0.907184i | \(-0.638228\pi\) |
−0.996012 | + | 0.0892249i | \(0.971561\pi\) | |||||||
\(662\) | 12.7985 | − | 22.1676i | 0.497427 | − | 0.861569i | ||||
\(663\) | 0.00634597 | + | 0.892012i | 0.000246457 | + | 0.0346429i | ||||
\(664\) | −0.662485 | −0.0257094 | ||||||||
\(665\) | −20.7822 | + | 1.39632i | −0.805897 | + | 0.0541471i | ||||
\(666\) | −8.10436 | −0.314038 | ||||||||
\(667\) | 7.65264 | + | 13.2548i | 0.296312 | + | 0.513227i | ||||
\(668\) | 12.6297 | + | 7.29175i | 0.488657 | + | 0.282126i | ||||
\(669\) | −6.20734 | − | 3.58381i | −0.239990 | − | 0.138558i | ||||
\(670\) | −26.6106 | + | 15.3636i | −1.02806 | + | 0.593549i | ||||
\(671\) | 72.1758i | 2.78631i | ||||||||
\(672\) | 2.37482 | + | 1.16630i | 0.0916105 | + | 0.0449909i | ||||
\(673\) | 29.6123 | 1.14147 | 0.570736 | − | 0.821134i | \(-0.306658\pi\) | ||||
0.570736 | + | 0.821134i | \(0.306658\pi\) | |||||||
\(674\) | 30.4876 | − | 17.6020i | 1.17434 | − | 0.678004i | ||||
\(675\) | −0.677364 | + | 1.17323i | −0.0260718 | + | 0.0451576i | ||||
\(676\) | 12.9987 | − | 0.184960i | 0.499949 | − | 0.00711386i | ||||
\(677\) | −6.35028 | − | 10.9990i | −0.244061 | − | 0.422726i | 0.717806 | − | 0.696243i | \(-0.245146\pi\) |
−0.961867 | + | 0.273517i | \(0.911813\pi\) | |||||||
\(678\) | 10.0373i | 0.385482i | ||||||||
\(679\) | 37.0815 | − | 24.8650i | 1.42306 | − | 0.954232i | ||||
\(680\) | −0.623675 | −0.0239169 | ||||||||
\(681\) | 18.6007 | − | 10.7391i | 0.712782 | − | 0.411525i | ||||
\(682\) | −29.9275 | − | 17.2786i | −1.14598 | − | 0.661633i | ||||
\(683\) | 36.7165 | + | 21.1983i | 1.40492 | + | 0.811130i | 0.994892 | − | 0.100944i | \(-0.0321863\pi\) |
0.410026 | + | 0.912074i | \(0.365520\pi\) | |||||||
\(684\) | −2.70459 | + | 1.56150i | −0.103413 | + | 0.0597053i | ||||
\(685\) | −34.5425 | −1.31980 | ||||||||
\(686\) | 13.8641 | − | 12.2795i | 0.529334 | − | 0.468834i | ||||
\(687\) | − | 8.26740i | − | 0.315421i | ||||||
\(688\) | −2.78052 | − | 4.81600i | −0.106006 | − | 0.183608i | ||||
\(689\) | 20.4022 | − | 11.9735i | 0.777260 | − | 0.456155i | ||||
\(690\) | −4.54024 | + | 7.86392i | −0.172844 | + | 0.299374i | ||||
\(691\) | 27.7470 | − | 16.0197i | 1.05554 | − | 0.609419i | 0.131348 | − | 0.991336i | \(-0.458070\pi\) |
0.924196 | + | 0.381918i | \(0.124736\pi\) | |||||||
\(692\) | −3.93890 | −0.149735 | ||||||||
\(693\) | −12.4021 | + | 8.31623i | −0.471116 | + | 0.315907i | ||||
\(694\) | − | 12.6826i | − | 0.481425i | ||||||
\(695\) | 17.4972 | − | 10.1020i | 0.663707 | − | 0.383191i | ||||
\(696\) | −3.67970 | − | 2.12447i | −0.139479 | − | 0.0805280i | ||||
\(697\) | −1.84246 | − | 1.06374i | −0.0697880 | − | 0.0402921i | ||||
\(698\) | −8.36290 | − | 14.4850i | −0.316540 | − | 0.548264i | ||||
\(699\) | −26.8920 | −1.01715 | ||||||||
\(700\) | 1.58002 | − | 3.21723i | 0.0597190 | − | 0.121600i | ||||
\(701\) | 50.5029 | 1.90747 | 0.953734 | − | 0.300651i | \(-0.0972039\pi\) | ||||
0.953734 | + | 0.300651i | \(0.0972039\pi\) | |||||||
\(702\) | −3.60546 | + | 0.0256500i | −0.136079 | + | 0.000968098i | ||||
\(703\) | −12.6549 | + | 21.9190i | −0.477290 | + | 0.826690i | ||||
\(704\) | 4.88772 | + | 2.82193i | 0.184213 | + | 0.106355i | ||||
\(705\) | −8.42474 | − | 14.5921i | −0.317294 | − | 0.549570i | ||||
\(706\) | −9.64324 | −0.362928 | ||||||||
\(707\) | −30.4090 | + | 2.04314i | −1.14365 | + | 0.0768401i | ||||
\(708\) | − | 7.95594i | − | 0.299002i | ||||||
\(709\) | 12.8665 | − | 7.42845i | 0.483210 | − | 0.278981i | −0.238543 | − | 0.971132i | \(-0.576670\pi\) |
0.721753 | + | 0.692151i | \(0.243337\pi\) | |||||||
\(710\) | 8.87264 | + | 5.12262i | 0.332984 | + | 0.192248i | ||||
\(711\) | 3.22763 | − | 5.59041i | 0.121045 | − | 0.209657i | ||||
\(712\) | 2.81116 | + | 4.86906i | 0.105353 | + | 0.182476i | ||||
\(713\) | 22.0558i | 0.825998i | ||||||||
\(714\) | 0.0438810 | + | 0.653102i | 0.00164220 | + | 0.0244417i | ||||
\(715\) | −44.6062 | − | 25.3320i | −1.66818 | − | 0.947364i | ||||
\(716\) | 2.35319 | + | 4.07584i | 0.0879427 | + | 0.152321i | ||||
\(717\) | 3.78867 | + | 2.18739i | 0.141491 | + | 0.0816896i | ||||
\(718\) | −0.283541 | + | 0.491107i | −0.0105817 | + | 0.0183280i | ||||
\(719\) | −8.46051 | − | 14.6540i | −0.315524 | − | 0.546503i | 0.664025 | − | 0.747710i | \(-0.268847\pi\) |
−0.979549 | + | 0.201207i | \(0.935514\pi\) | |||||||
\(720\) | − | 2.52086i | − | 0.0939469i | ||||||
\(721\) | −6.75105 | + | 13.7465i | −0.251422 | + | 0.511946i | ||||
\(722\) | − | 9.24691i | − | 0.344134i | ||||||
\(723\) | 1.33779 | − | 0.772373i | 0.0497529 | − | 0.0287249i | ||||
\(724\) | −7.81998 | + | 13.5446i | −0.290627 | + | 0.503381i | ||||
\(725\) | −2.87809 | + | 4.98499i | −0.106889 | + | 0.185138i | ||||
\(726\) | −18.0593 | + | 10.4265i | −0.670243 | + | 0.386965i | ||||
\(727\) | 31.4510 | 1.16645 | 0.583227 | − | 0.812309i | \(-0.301790\pi\) | ||||
0.583227 | + | 0.812309i | \(0.301790\pi\) | |||||||
\(728\) | 9.51314 | − | 0.707191i | 0.352581 | − | 0.0262102i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 17.1869 | − | 9.92289i | 0.636117 | − | 0.367263i | ||||
\(731\) | 0.687916 | − | 1.19151i | 0.0254435 | − | 0.0440694i | ||||
\(732\) | −6.39419 | + | 11.0751i | −0.236336 | + | 0.409346i | ||||
\(733\) | −13.3249 | + | 7.69312i | −0.492166 | + | 0.284152i | −0.725472 | − | 0.688251i | \(-0.758379\pi\) |
0.233307 | + | 0.972403i | \(0.425045\pi\) | |||||||
\(734\) | 13.2510i | 0.489103i | ||||||||
\(735\) | −16.3248 | − | 6.69940i | −0.602150 | − | 0.247111i | ||||
\(736\) | − | 3.60213i | − | 0.132776i | ||||||
\(737\) | 34.3971 | + | 59.5775i | 1.26703 | + | 2.19456i | ||||
\(738\) | 4.29959 | − | 7.44710i | 0.158270 | − | 0.274132i | ||||
\(739\) | −9.93208 | − | 5.73429i | −0.365357 | − | 0.210939i | 0.306071 | − | 0.952009i | \(-0.400986\pi\) |
−0.671428 | + | 0.741070i | \(0.734319\pi\) | |||||||
\(740\) | −10.2150 | − | 17.6929i | −0.375510 | − | 0.650402i | ||||
\(741\) | −5.56054 | + | 9.79135i | −0.204272 | + | 0.359694i | ||||
\(742\) | 14.4176 | − | 9.66769i | 0.529285 | − | 0.354912i | ||||
\(743\) | 16.4784i | 0.604534i | 0.953223 | + | 0.302267i | \(0.0977434\pi\) | ||||
−0.953223 | + | 0.302267i | \(0.902257\pi\) | |||||||
\(744\) | −3.06150 | − | 5.30267i | −0.112240 | − | 0.194405i | ||||
\(745\) | −2.36389 | + | 4.09438i | −0.0866062 | + | 0.150006i | ||||
\(746\) | 20.6939 | + | 11.9476i | 0.757656 | + | 0.437433i | ||||
\(747\) | 0.573729 | − | 0.331243i | 0.0209916 | − | 0.0121195i | ||||
\(748\) | 1.39632i | 0.0510546i | ||||||||
\(749\) | −18.5791 | + | 37.8308i | −0.678867 | + | 1.38231i | ||||
\(750\) | 9.18921 | 0.335543 | ||||||||
\(751\) | −15.2492 | − | 26.4123i | −0.556450 | − | 0.963800i | −0.997789 | − | 0.0664593i | \(-0.978830\pi\) |
0.441339 | − | 0.897340i | \(-0.354504\pi\) | |||||||
\(752\) | 5.78854 | + | 3.34201i | 0.211086 | + | 0.121871i | ||||
\(753\) | 6.71606 | − | 11.6326i | 0.244747 | − | 0.423914i | ||||
\(754\) | −15.3194 | + | 0.108986i | −0.557900 | + | 0.00396902i | ||||
\(755\) | −6.83171 | −0.248631 | ||||||||
\(756\) | −2.63980 | + | 0.177364i | −0.0960086 | + | 0.00645068i | ||||
\(757\) | 32.1769 | 1.16949 | 0.584744 | − | 0.811218i | \(-0.301195\pi\) | ||||
0.584744 | + | 0.811218i | \(0.301195\pi\) | |||||||
\(758\) | −0.730126 | − | 1.26462i | −0.0265194 | − | 0.0459329i | ||||
\(759\) | 17.6062 | + | 10.1650i | 0.639065 | + | 0.368965i | ||||
\(760\) | −6.81789 | − | 3.93631i | −0.247311 | − | 0.142785i | ||||
\(761\) | −23.8111 | + | 13.7473i | −0.863151 | + | 0.498341i | −0.865066 | − | 0.501657i | \(-0.832724\pi\) |
0.00191497 | + | 0.999998i | \(0.499390\pi\) | |||||||
\(762\) | 10.3136i | 0.373623i | ||||||||
\(763\) | 0.262621 | + | 3.90871i | 0.00950750 | + | 0.141505i | ||||
\(764\) | −8.97686 | −0.324771 | ||||||||
\(765\) | 0.540119 | − | 0.311838i | 0.0195280 | − | 0.0112745i | ||||
\(766\) | −3.26040 | + | 5.64718i | −0.117803 | + | 0.204041i | ||||
\(767\) | −14.5191 | − | 24.7397i | −0.524256 | − | 0.893300i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 5.03709i | 0.181642i | 0.995867 | + | 0.0908210i | \(0.0289491\pi\) | ||||
−0.995867 | + | 0.0908210i | \(0.971051\pi\) | |||||||
\(770\) | −33.7873 | − | 16.5933i | −1.21761 | − | 0.597982i | ||||
\(771\) | −21.8346 | −0.786354 | ||||||||
\(772\) | 6.09697 | − | 3.52009i | 0.219435 | − | 0.126691i | ||||
\(773\) | −11.3640 | − | 6.56103i | −0.408736 | − | 0.235984i | 0.281510 | − | 0.959558i | \(-0.409165\pi\) |
−0.690247 | + | 0.723574i | \(0.742498\pi\) | |||||||
\(774\) | 4.81600 | + | 2.78052i | 0.173107 | + | 0.0999436i | ||||
\(775\) | −7.18368 | + | 4.14750i | −0.258045 | + | 0.148982i | ||||
\(776\) | 16.8748 | 0.605769 | ||||||||
\(777\) | −17.8089 | + | 11.9418i | −0.638892 | + | 0.428409i | ||||
\(778\) | − | 25.6019i | − | 0.917874i | ||||||
\(779\) | −13.4276 | − | 23.2572i | −0.481093 | − | 0.833277i | ||||
\(780\) | −4.60042 | − | 7.83885i | −0.164722 | − | 0.280676i | ||||
\(781\) | 11.4688 | − | 19.8646i | 0.410387 | − | 0.710811i | ||||
\(782\) | 0.771793 | − | 0.445595i | 0.0275992 | − | 0.0159344i | ||||
\(783\) | 4.24895 | 0.151845 | ||||||||
\(784\) | 6.93708 | − | 0.936412i | 0.247753 | − | 0.0334433i | ||||
\(785\) | 43.1156i | 1.53886i | ||||||||
\(786\) | 16.0196 | − | 9.24892i | 0.571400 | − | 0.329898i | ||||
\(787\) | −8.11053 | − | 4.68261i | −0.289109 | − | 0.166917i | 0.348431 | − | 0.937334i | \(-0.386715\pi\) |
−0.637540 | + | 0.770417i | \(0.720048\pi\) | |||||||
\(788\) | −10.1412 | − | 5.85504i | −0.361266 | − | 0.208577i | ||||
\(789\) | 4.24994 | + | 7.36111i | 0.151302 | + | 0.262062i | ||||
\(790\) | 16.2728 | 0.578960 | ||||||||
\(791\) | 14.7900 | + | 22.0566i | 0.525873 | + | 0.784241i | ||||
\(792\) | −5.64385 | −0.200546 | ||||||||
\(793\) | 0.328022 | + | 46.1080i | 0.0116484 | + | 1.63734i | ||||
\(794\) | −7.76567 | + | 13.4505i | −0.275593 | + | 0.477342i | ||||
\(795\) | −14.3236 | − | 8.26972i | −0.508005 | − | 0.293297i | ||||
\(796\) | 9.05076 | + | 15.6764i | 0.320796 | + | 0.555634i | ||||
\(797\) | −23.1485 | −0.819963 | −0.409982 | − | 0.912094i | \(-0.634465\pi\) | ||||
−0.409982 | + | 0.912094i | \(0.634465\pi\) | |||||||
\(798\) | −3.64234 | + | 7.41653i | −0.128937 | + | 0.262542i | ||||
\(799\) | 1.65367i | 0.0585026i | ||||||||
\(800\) | 1.17323 | − | 0.677364i | 0.0414799 | − | 0.0239484i | ||||
\(801\) | −4.86906 | − | 2.81116i | −0.172040 | − | 0.0993273i | ||||
\(802\) | 17.4765 | − | 30.2703i | 0.617118 | − | 1.06888i | ||||
\(803\) | −22.2160 | − | 38.4792i | −0.783984 | − | 1.35790i | ||||
\(804\) | 12.1892i | 0.429880i | ||||||||
\(805\) | 1.61055 | + | 23.9706i | 0.0567645 | + | 0.844854i | ||||
\(806\) | −19.1971 | − | 10.9021i | −0.676188 | − | 0.384010i | ||||
\(807\) | −10.3107 | − | 17.8587i | −0.362955 | − | 0.628656i | ||||
\(808\) | −9.97613 | − | 5.75972i | −0.350959 | − | 0.202626i | ||||
\(809\) | −27.8984 | + | 48.3215i | −0.980856 | + | 1.69889i | −0.321784 | + | 0.946813i | \(0.604282\pi\) |
−0.659073 | + | 0.752079i | \(0.729051\pi\) | |||||||
\(810\) | 1.26043 | + | 2.18313i | 0.0442870 | + | 0.0767073i | ||||
\(811\) | − | 49.1611i | − | 1.72628i | −0.504966 | − | 0.863139i | \(-0.668495\pi\) | ||
0.504966 | − | 0.863139i | \(-0.331505\pi\) | |||||||
\(812\) | −11.2164 | + | 0.753612i | −0.393618 | + | 0.0264466i | ||||
\(813\) | 23.9488i | 0.839920i | ||||||||
\(814\) | −39.6118 | + | 22.8699i | −1.38839 | + | 0.801590i | ||||
\(815\) | 23.4505 | − | 40.6175i | 0.821435 | − | 1.42277i | ||||
\(816\) | −0.123703 | + | 0.214260i | −0.00433047 | + | 0.00750059i | ||||
\(817\) | 15.0403 | − | 8.68353i | 0.526194 | − | 0.303798i | ||||
\(818\) | 12.7020 | 0.444115 | ||||||||
\(819\) | −7.88503 | + | 5.36902i | −0.275525 | + | 0.187609i | ||||
\(820\) | 21.6773 | 0.757004 | ||||||||
\(821\) | 28.9550 | − | 16.7172i | 1.01054 | − | 0.583433i | 0.0991875 | − | 0.995069i | \(-0.468376\pi\) |
0.911349 | + | 0.411635i | \(0.135042\pi\) | |||||||
\(822\) | −6.85133 | + | 11.8669i | −0.238968 | + | 0.413904i | ||||
\(823\) | 18.3644 | − | 31.8081i | 0.640142 | − | 1.10876i | −0.345258 | − | 0.938508i | \(-0.612209\pi\) |
0.985401 | − | 0.170251i | \(-0.0544580\pi\) | |||||||
\(824\) | −5.01294 | + | 2.89422i | −0.174634 | + | 0.100825i | ||||
\(825\) | 7.64589i | 0.266196i | ||||||||
\(826\) | −11.7231 | − | 17.4828i | −0.407898 | − | 0.608304i | ||||
\(827\) | 45.4204i | 1.57942i | 0.613478 | + | 0.789712i | \(0.289770\pi\) | ||||
−0.613478 | + | 0.789712i | \(0.710230\pi\) | |||||||
\(828\) | 1.80107 | + | 3.11954i | 0.0625914 | + | 0.108412i | ||||
\(829\) | 11.4353 | − | 19.8065i | 0.397164 | − | 0.687909i | −0.596211 | − | 0.802828i | \(-0.703328\pi\) |
0.993375 | + | 0.114920i | \(0.0366610\pi\) | |||||||
\(830\) | 1.44629 | + | 0.835016i | 0.0502014 | + | 0.0289838i | ||||
\(831\) | −2.06106 | − | 3.56986i | −0.0714974 | − | 0.123837i | ||||
\(832\) | 3.13524 | + | 1.78052i | 0.108695 | + | 0.0617283i | ||||
\(833\) | 1.05877 | + | 1.37050i | 0.0366843 | + | 0.0474851i | ||||
\(834\) | − | 8.01474i | − | 0.277528i | ||||||
\(835\) | −18.3815 | − | 31.8376i | −0.636117 | − | 1.10179i | ||||
\(836\) | −8.81286 | + | 15.2643i | −0.304799 | + | 0.527927i | ||||
\(837\) | 5.30267 | + | 3.06150i | 0.183287 | + | 0.105821i | ||||
\(838\) | 20.5667 | − | 11.8742i | 0.710464 | − | 0.410186i | ||||
\(839\) | 7.31572i | 0.252567i | 0.991994 | + | 0.126283i | \(0.0403048\pi\) | ||||
−0.991994 | + | 0.126283i | \(0.959695\pi\) | |||||||
\(840\) | −3.71449 | − | 5.53946i | −0.128162 | − | 0.191130i | ||||
\(841\) | −10.9464 | −0.377463 | ||||||||
\(842\) | −2.45643 | − | 4.25466i | −0.0846541 | − | 0.146625i | ||||
\(843\) | −8.92165 | − | 5.15092i | −0.307278 | − | 0.177407i | ||||
\(844\) | −11.6126 | + | 20.1136i | −0.399722 | + | 0.692339i | ||||
\(845\) | −28.6109 | − | 15.9801i | −0.984245 | − | 0.549733i | ||||
\(846\) | −6.68403 | −0.229802 | ||||||||
\(847\) | −24.3209 | + | 49.5222i | −0.835675 | + | 1.70160i | ||||
\(848\) | 6.56103 | 0.225307 | ||||||||
\(849\) | −5.43112 | − | 9.40698i | −0.186396 | − | 0.322847i | ||||
\(850\) | 0.290264 | + | 0.167584i | 0.00995597 | + | 0.00574808i | ||||
\(851\) | 25.2819 | + | 14.5965i | 0.866651 | + | 0.500361i | ||||
\(852\) | 3.51969 | − | 2.03209i | 0.120583 | − | 0.0696184i | ||||
\(853\) | 34.5603i | 1.18332i | 0.806187 | + | 0.591661i | \(0.201528\pi\) | ||||
−0.806187 | + | 0.591661i | \(0.798472\pi\) | |||||||
\(854\) | 2.26820 | + | 33.7588i | 0.0776163 | + | 1.15520i | ||||
\(855\) | 7.87262 | 0.269238 | ||||||||
\(856\) | −13.7958 | + | 7.96501i | −0.471531 | + | 0.272238i | ||||
\(857\) | 11.9237 | − | 20.6525i | 0.407307 | − | 0.705476i | −0.587280 | − | 0.809384i | \(-0.699801\pi\) |
0.994587 | + | 0.103908i | \(0.0331347\pi\) | |||||||
\(858\) | −17.5501 | + | 10.2997i | −0.599150 | + | 0.351626i | ||||
\(859\) | 11.2768 | + | 19.5320i | 0.384760 | + | 0.666424i | 0.991736 | − | 0.128296i | \(-0.0409509\pi\) |
−0.606976 | + | 0.794720i | \(0.707618\pi\) | |||||||
\(860\) | 14.0186i | 0.478030i | ||||||||
\(861\) | −1.52519 | − | 22.7001i | −0.0519782 | − | 0.773617i | ||||
\(862\) | 25.1596 | 0.856939 | ||||||||
\(863\) | −31.6139 | + | 18.2523i | −1.07615 | + | 0.621316i | −0.929855 | − | 0.367925i | \(-0.880068\pi\) |
−0.146295 | + | 0.989241i | \(0.546735\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 8.59912 | + | 4.96471i | 0.292379 | + | 0.168805i | ||||
\(866\) | −5.33880 | + | 3.08236i | −0.181420 | + | 0.104743i | ||||
\(867\) | 16.9388 | 0.575271 | ||||||||
\(868\) | −14.5410 | − | 7.14123i | −0.493553 | − | 0.242389i | ||||
\(869\) | − | 36.4325i | − | 1.23589i | ||||||
\(870\) | 5.35550 | + | 9.27600i | 0.181568 | + | 0.314486i | ||||
\(871\) | 22.2446 | + | 37.9035i | 0.753730 | + | 1.28431i | ||||
\(872\) | −0.740342 | + | 1.28231i | −0.0250712 | + | 0.0434245i | ||||
\(873\) | −14.6140 | + | 8.43739i | −0.494609 | + | 0.285562i | ||||
\(874\) | 11.2494 | 0.380518 | ||||||||
\(875\) | 20.1929 | − | 13.5403i | 0.682643 | − | 0.457746i | ||||
\(876\) | − | 7.87262i | − | 0.265991i | ||||||
\(877\) | −5.89748 | + | 3.40491i | −0.199144 | + | 0.114976i | −0.596256 | − | 0.802794i | \(-0.703346\pi\) |
0.397112 | + | 0.917770i | \(0.370012\pi\) | |||||||
\(878\) | 7.70572 | + | 4.44890i | 0.260055 | + | 0.150143i | ||||
\(879\) | −3.22606 | − | 1.86256i | −0.108812 | − | 0.0628227i | ||||
\(880\) | −7.11368 | − | 12.3212i | −0.239802 | − | 0.415349i | ||||
\(881\) | 10.4558 | 0.352265 | 0.176132 | − | 0.984366i | \(-0.443641\pi\) | ||||
0.176132 | + | 0.984366i | \(0.443641\pi\) | |||||||
\(882\) | −5.53948 | + | 4.27950i | −0.186524 | + | 0.144098i | ||||
\(883\) | −22.2786 | −0.749736 | −0.374868 | − | 0.927078i | \(-0.622312\pi\) | ||||
−0.374868 | + | 0.927078i | \(0.622312\pi\) | |||||||
\(884\) | 0.00634597 | + | 0.892012i | 0.000213438 | + | 0.0300016i | ||||
\(885\) | −10.0279 | + | 17.3688i | −0.337084 | + | 0.583847i | ||||
\(886\) | 29.5842 | + | 17.0804i | 0.993901 | + | 0.573829i | ||||
\(887\) | −20.8726 | − | 36.1524i | −0.700832 | − | 1.21388i | −0.968175 | − | 0.250276i | \(-0.919479\pi\) |
0.267342 | − | 0.963602i | \(-0.413855\pi\) | |||||||
\(888\) | −8.10436 | −0.271965 | ||||||||
\(889\) | 15.1971 | + | 22.6637i | 0.509696 | + | 0.760116i | ||||
\(890\) | − | 14.1731i | − | 0.475082i | ||||||
\(891\) | 4.88772 | − | 2.82193i | 0.163745 | − | 0.0945381i | ||||
\(892\) | −6.20734 | − | 3.58381i | −0.207837 | − | 0.119995i | ||||
\(893\) | −10.4371 | + | 18.0776i | −0.349264 | + | 0.604942i | ||||
\(894\) | 0.937732 | + | 1.62420i | 0.0313624 | + | 0.0543213i | ||||
\(895\) | − | 11.8641i | − | 0.396573i | ||||||
\(896\) | 2.37482 | + | 1.16630i | 0.0793370 | + | 0.0389633i | ||||
\(897\) | 11.2936 | + | 6.41366i | 0.377081 | + | 0.214146i | ||||
\(898\) | 14.5424 | + | 25.1882i | 0.485286 | + | 0.840540i | ||||
\(899\) | 22.5308 | + | 13.0081i | 0.751443 | + | 0.433846i | ||||
\(900\) | −0.677364 | + | 1.17323i | −0.0225788 | + | 0.0391076i | ||||
\(901\) | 0.811619 | + | 1.40577i | 0.0270390 | + | 0.0468328i | ||||
\(902\) | − | 48.5325i | − | 1.61595i | ||||||
\(903\) | 14.6800 | − | 0.986329i | 0.488520 | − | 0.0328230i | ||||
\(904\) | 10.0373i | 0.333837i | ||||||||
\(905\) | 34.1440 | − | 19.7131i | 1.13499 | − | 0.655285i | ||||
\(906\) | −1.35504 | + | 2.34699i | −0.0450181 | + | 0.0779736i | ||||
\(907\) | 24.6748 | − | 42.7379i | 0.819312 | − | 1.41909i | −0.0868777 | − | 0.996219i | \(-0.527689\pi\) |
0.906190 | − | 0.422871i | \(-0.138978\pi\) | |||||||
\(908\) | 18.6007 | − | 10.7391i | 0.617287 | − | 0.356391i | ||||
\(909\) | 11.5194 | 0.382076 | ||||||||
\(910\) | −21.6598 | − | 10.4468i | −0.718014 | − | 0.346307i | ||||
\(911\) | 15.7093 | 0.520473 | 0.260237 | − | 0.965545i | \(-0.416199\pi\) | ||||
0.260237 | + | 0.965545i | \(0.416199\pi\) | |||||||
\(912\) | −2.70459 | + | 1.56150i | −0.0895580 | + | 0.0517063i | ||||
\(913\) | 1.86948 | − | 3.23804i | 0.0618709 | − | 0.107164i | ||||
\(914\) | 17.7460 | − | 30.7370i | 0.586986 | − | 1.01669i | ||||
\(915\) | 27.9187 | − | 16.1189i | 0.922963 | − | 0.532873i | ||||
\(916\) | − | 8.26740i | − | 0.273163i | ||||||
\(917\) | 21.5740 | − | 43.9290i | 0.712436 | − | 1.45066i | ||||
\(918\) | − | 0.247406i | − | 0.00816561i | ||||||
\(919\) | −16.4337 | − | 28.4639i | −0.542096 | − | 0.938938i | −0.998783 | − | 0.0493110i | \(-0.984297\pi\) |
0.456687 | − | 0.889627i | \(-0.349036\pi\) | |||||||
\(920\) | −4.54024 | + | 7.86392i | −0.149687 | + | 0.259266i | ||||
\(921\) | −18.1955 | − | 10.5052i | −0.599562 | − | 0.346157i | ||||
\(922\) | 3.78690 | + | 6.55910i | 0.124715 | + | 0.216012i | ||||
\(923\) | 7.23635 | − | 12.7422i | 0.238187 | − | 0.419415i | ||||
\(924\) | −12.4021 | + | 8.31623i | −0.407999 | + | 0.273584i | ||||
\(925\) | 10.9792i | 0.360994i | ||||||||
\(926\) | −12.5149 | − | 21.6765i | −0.411266 | − | 0.712334i | ||||
\(927\) | 2.89422 | − | 5.01294i | 0.0950587 | − | 0.164646i | ||||
\(928\) | −3.67970 | − | 2.12447i | −0.120792 | − | 0.0697393i | ||||
\(929\) | −13.5536 | + | 7.82520i | −0.444680 | + | 0.256736i | −0.705581 | − | 0.708629i | \(-0.749314\pi\) |
0.260901 | + | 0.965366i | \(0.415981\pi\) | |||||||
\(930\) | 15.4352i | 0.506140i | ||||||||
\(931\) | 2.92441 | + | 21.6645i | 0.0958436 | + | 0.710024i | ||||
\(932\) | −26.8920 | −0.880877 | ||||||||
\(933\) | −3.19739 | − | 5.53804i | −0.104678 | − | 0.181307i | ||||
\(934\) | −27.0778 | − | 15.6334i | −0.886013 | − | 0.511540i | ||||
\(935\) | 1.75997 | − | 3.04835i | 0.0575570 | − | 0.0996917i | ||||
\(936\) | −3.60546 | + | 0.0256500i | −0.117848 | + | 0.000838397i | ||||
\(937\) | 3.71754 | 0.121447 | 0.0607233 | − | 0.998155i | \(-0.480659\pi\) | ||||
0.0607233 | + | 0.998155i | \(0.480659\pi\) | |||||||
\(938\) | 17.9608 | + | 26.7852i | 0.586442 | + | 0.874568i | ||||
\(939\) | −15.4737 | −0.504965 | ||||||||
\(940\) | −8.42474 | − | 14.5921i | −0.274785 | − | 0.475941i | ||||
\(941\) | −34.6486 | − | 20.0044i | −1.12951 | − | 0.652124i | −0.185700 | − | 0.982607i | \(-0.559455\pi\) |
−0.943812 | + | 0.330482i | \(0.892789\pi\) | |||||||
\(942\) | 14.8121 | + | 8.55178i | 0.482605 | + | 0.278632i | ||||
\(943\) | −26.8255 | + | 15.4877i | −0.873557 | + | 0.504348i | ||||
\(944\) | − | 7.95594i | − | 0.258944i | ||||||
\(945\) | 5.98657 | + | 2.94007i | 0.194743 | + | 0.0956406i | ||||
\(946\) | 31.3856 | 1.02044 | ||||||||
\(947\) | 20.0418 | − | 11.5712i | 0.651272 | − | 0.376012i | −0.137671 | − | 0.990478i | \(-0.543962\pi\) |
0.788943 | + | 0.614466i | \(0.210628\pi\) | |||||||
\(948\) | 3.22763 | − | 5.59041i | 0.104828 | − | 0.181568i | ||||
\(949\) | −14.3671 | − | 24.4807i | −0.466376 | − | 0.794676i | ||||
\(950\) | 2.11540 | + | 3.66399i | 0.0686328 | + | 0.118875i | ||||
\(951\) | − | 18.8914i | − | 0.612595i | ||||||
\(952\) | 0.0438810 | + | 0.653102i | 0.00142219 | + | 0.0211672i | ||||
\(953\) | −9.61707 | −0.311527 | −0.155764 | − | 0.987794i | \(-0.549784\pi\) | ||||
−0.155764 | + | 0.987794i | \(0.549784\pi\) | |||||||
\(954\) | −5.68202 | + | 3.28052i | −0.183962 | + | 0.106211i | ||||
\(955\) | 19.5976 | + | 11.3147i | 0.634165 | + | 0.366135i | ||||
\(956\) | 3.78867 | + | 2.18739i | 0.122534 | + | 0.0707453i | ||||
\(957\) | 20.7677 | − | 11.9902i | 0.671323 | − | 0.387589i | ||||
\(958\) | −15.5185 | −0.501380 | ||||||||
\(959\) | 2.43036 | + | 36.1723i | 0.0784805 | + | 1.16806i | ||||
\(960\) | − | 2.52086i | − | 0.0813604i | ||||||
\(961\) | 3.24552 | + | 5.62141i | 0.104694 | + | 0.181336i | ||||
\(962\) | −25.2013 | + | 14.7900i | −0.812522 | + | 0.476849i | ||||
\(963\) | 7.96501 | − | 13.7958i | 0.256669 | − | 0.444563i | ||||
\(964\) | 1.33779 | − | 0.772373i | 0.0430873 | − | 0.0248765i | ||||
\(965\) | −17.7473 | −0.571305 | ||||||||
\(966\) | 8.55441 | + | 4.20116i | 0.275233 | + | 0.135170i | ||||
\(967\) | − | 19.4428i | − | 0.625238i | −0.949879 | − | 0.312619i | \(-0.898794\pi\) | ||
0.949879 | − | 0.312619i | \(-0.101206\pi\) | |||||||
\(968\) | −18.0593 | + | 10.4265i | −0.580447 | + | 0.335121i | ||||
\(969\) | −0.669132 | − | 0.386323i | −0.0214956 | − | 0.0124105i | ||||
\(970\) | −36.8398 | − | 21.2695i | −1.18285 | − | 0.682922i | ||||
\(971\) | −18.4152 | − | 31.8960i | −0.590971 | − | 1.02359i | −0.994102 | − | 0.108450i | \(-0.965411\pi\) |
0.403131 | − | 0.915142i | \(-0.367922\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −11.8097 | − | 17.6120i | −0.378603 | − | 0.564615i | ||||
\(974\) | −32.3861 | −1.03772 | ||||||||
\(975\) | 0.0347488 | + | 4.88442i | 0.00111285 | + | 0.156427i | ||||
\(976\) | −6.39419 | + | 11.0751i | −0.204673 | + | 0.354504i | ||||
\(977\) | 23.3376 | + | 13.4740i | 0.746635 | + | 0.431070i | 0.824477 | − | 0.565896i | \(-0.191470\pi\) |
−0.0778417 | + | 0.996966i | \(0.524803\pi\) | |||||||
\(978\) | −9.30258 | − | 16.1125i | −0.297464 | − | 0.515222i | ||||
\(979\) | −31.7315 | −1.01414 | ||||||||
\(980\) | −16.3248 | − | 6.69940i | −0.521477 | − | 0.214004i | ||||
\(981\) | − | 1.48068i | − | 0.0472746i | ||||||
\(982\) | 7.98524 | − | 4.61028i | 0.254819 | − | 0.147120i | ||||
\(983\) | −45.1202 | − | 26.0502i | −1.43911 | − | 0.830872i | −0.441324 | − | 0.897348i | \(-0.645491\pi\) |
−0.997788 | + | 0.0664765i | \(0.978824\pi\) | |||||||
\(984\) | 4.29959 | − | 7.44710i | 0.137066 | − | 0.237405i | ||||
\(985\) | 14.7597 | + | 25.5646i | 0.470284 | + | 0.814555i | ||||
\(986\) | − | 1.05122i | − | 0.0334775i | ||||||
\(987\) | −14.6878 | + | 9.84892i | −0.467519 | + | 0.313495i | ||||
\(988\) | −5.56054 | + | 9.79135i | −0.176904 | + | 0.311504i | ||||
\(989\) | −10.0158 | − | 17.3479i | −0.318484 | − | 0.551630i | ||||
\(990\) | 12.3212 | + | 7.11368i | 0.391595 | + | 0.226087i | ||||
\(991\) | 18.7490 | − | 32.4743i | 0.595583 | − | 1.03158i | −0.397881 | − | 0.917437i | \(-0.630254\pi\) |
0.993464 | − | 0.114143i | \(-0.0364123\pi\) | |||||||
\(992\) | −3.06150 | − | 5.30267i | −0.0972026 | − | 0.168360i | ||||
\(993\) | 25.5969i | 0.812295i | ||||||||
\(994\) | 4.74005 | − | 9.65169i | 0.150345 | − | 0.306133i | ||||
\(995\) | − | 45.6314i | − | 1.44661i | ||||||
\(996\) | 0.573729 | − | 0.331243i | 0.0181793 | − | 0.0104958i | ||||
\(997\) | −3.03388 | + | 5.25484i | −0.0960840 | + | 0.166422i | −0.910061 | − | 0.414475i | \(-0.863965\pi\) |
0.813976 | + | 0.580898i | \(0.197298\pi\) | |||||||
\(998\) | −3.78999 | + | 6.56445i | −0.119970 | + | 0.207794i | ||||
\(999\) | 7.01858 | − | 4.05218i | 0.222058 | − | 0.128205i |
(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 | 546.2.bk.c.25.2 | ✓ | 20 | |
3.2 | odd | 2 | 1638.2.dm.e.1117.9 | 20 | |||
7.2 | even | 3 | inner | 546.2.bk.c.415.9 | yes | 20 | |
7.3 | odd | 6 | 3822.2.c.n.883.4 | 10 | |||
7.4 | even | 3 | 3822.2.c.m.883.2 | 10 | |||
13.12 | even | 2 | inner | 546.2.bk.c.25.9 | yes | 20 | |
21.2 | odd | 6 | 1638.2.dm.e.415.2 | 20 | |||
39.38 | odd | 2 | 1638.2.dm.e.1117.2 | 20 | |||
91.25 | even | 6 | 3822.2.c.m.883.9 | 10 | |||
91.38 | odd | 6 | 3822.2.c.n.883.7 | 10 | |||
91.51 | even | 6 | inner | 546.2.bk.c.415.2 | yes | 20 | |
273.233 | odd | 6 | 1638.2.dm.e.415.9 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bk.c.25.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
546.2.bk.c.25.9 | yes | 20 | 13.12 | even | 2 | inner | |
546.2.bk.c.415.2 | yes | 20 | 91.51 | even | 6 | inner | |
546.2.bk.c.415.9 | yes | 20 | 7.2 | even | 3 | inner | |
1638.2.dm.e.415.2 | 20 | 21.2 | odd | 6 | |||
1638.2.dm.e.415.9 | 20 | 273.233 | odd | 6 | |||
1638.2.dm.e.1117.2 | 20 | 39.38 | odd | 2 | |||
1638.2.dm.e.1117.9 | 20 | 3.2 | odd | 2 | |||
3822.2.c.m.883.2 | 10 | 7.4 | even | 3 | |||
3822.2.c.m.883.9 | 10 | 91.25 | even | 6 | |||
3822.2.c.n.883.4 | 10 | 7.3 | odd | 6 | |||
3822.2.c.n.883.7 | 10 | 91.38 | odd | 6 |