Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(24,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.u (of order \(18\), degree \(6\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 74.6 | ||
Character | \(\chi\) | \(=\) | 475.74 |
Dual form | 475.2.u.c.199.6 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.58240 | + | 0.455347i | 1.82603 | + | 0.321979i | 0.978101 | − | 0.208129i | \(-0.0667373\pi\) |
0.847930 | + | 0.530108i | \(0.177848\pi\) | |||||||
\(3\) | −0.597006 | + | 0.711484i | −0.344681 | + | 0.410775i | −0.910338 | − | 0.413866i | \(-0.864178\pi\) |
0.565657 | + | 0.824641i | \(0.308623\pi\) | |||||||
\(4\) | 4.58206 | + | 1.66773i | 2.29103 | + | 0.833867i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.86568 | + | 1.56549i | −0.761660 | + | 0.639109i | ||||
\(7\) | −3.31824 | + | 1.91579i | −1.25418 | + | 0.724100i | −0.971936 | − | 0.235244i | \(-0.924411\pi\) |
−0.282241 | + | 0.959344i | \(0.591078\pi\) | |||||||
\(8\) | 6.53146 | + | 3.77094i | 2.30922 | + | 1.33323i | ||||
\(9\) | 0.371151 | + | 2.10490i | 0.123717 | + | 0.701634i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.63362 | − | 2.82951i | 0.492554 | − | 0.853128i | −0.507409 | − | 0.861705i | \(-0.669397\pi\) |
0.999963 | + | 0.00857679i | \(0.00273011\pi\) | |||||||
\(12\) | −3.92208 | + | 2.26441i | −1.13221 | + | 0.653680i | ||||
\(13\) | 0.234066 | + | 0.278949i | 0.0649182 | + | 0.0773665i | 0.797526 | − | 0.603284i | \(-0.206142\pi\) |
−0.732608 | + | 0.680651i | \(0.761697\pi\) | |||||||
\(14\) | −9.44137 | + | 3.43638i | −2.52331 | + | 0.918411i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.67910 | + | 6.44353i | 1.91977 | + | 1.61088i | ||||
\(17\) | −0.673822 | − | 0.118813i | −0.163426 | − | 0.0288164i | 0.0913364 | − | 0.995820i | \(-0.470886\pi\) |
−0.254762 | + | 0.967004i | \(0.581997\pi\) | |||||||
\(18\) | 5.60470i | 1.32104i | ||||||||
\(19\) | 3.86613 | − | 2.01323i | 0.886950 | − | 0.461866i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.617958 | − | 3.50461i | 0.134849 | − | 0.764769i | ||||
\(22\) | 5.50706 | − | 6.56305i | 1.17411 | − | 1.39925i | ||||
\(23\) | 3.20407 | − | 8.80310i | 0.668094 | − | 1.83557i | 0.132331 | − | 0.991206i | \(-0.457754\pi\) |
0.535763 | − | 0.844368i | \(-0.320024\pi\) | |||||||
\(24\) | −6.58228 | + | 2.39576i | −1.34360 | + | 0.489031i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.477433 | + | 0.826939i | 0.0936324 | + | 0.162176i | ||||
\(27\) | −4.13222 | − | 2.38574i | −0.795245 | − | 0.459135i | ||||
\(28\) | −18.3994 | + | 3.24431i | −3.47716 | + | 0.613117i | ||||
\(29\) | −0.267393 | − | 1.51646i | −0.0496536 | − | 0.281600i | 0.949864 | − | 0.312664i | \(-0.101221\pi\) |
−0.999517 | + | 0.0310645i | \(0.990110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.22444 | + | 2.12080i | 0.219916 | + | 0.380906i | 0.954782 | − | 0.297306i | \(-0.0960882\pi\) |
−0.734866 | + | 0.678213i | \(0.762755\pi\) | |||||||
\(32\) | 7.20079 | + | 8.58157i | 1.27293 | + | 1.51702i | ||||
\(33\) | 1.03787 | + | 2.85152i | 0.180670 | + | 0.496387i | ||||
\(34\) | −1.68598 | − | 0.613646i | −0.289143 | − | 0.105239i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.80978 | + | 10.2638i | −0.301630 | + | 1.71063i | ||||
\(37\) | 0.163399i | 0.0268627i | 0.999910 | + | 0.0134313i | \(0.00427545\pi\) | ||||
−0.999910 | + | 0.0134313i | \(0.995725\pi\) | |||||||
\(38\) | 10.9006 | − | 3.43852i | 1.76831 | − | 0.557802i | ||||
\(39\) | −0.338206 | −0.0541564 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.64858 | − | 4.73972i | −0.882160 | − | 0.740220i | 0.0844622 | − | 0.996427i | \(-0.473083\pi\) |
−0.966622 | + | 0.256207i | \(0.917527\pi\) | |||||||
\(42\) | 3.19163 | − | 8.76892i | 0.492479 | − | 1.35307i | ||||
\(43\) | 0.885107 | + | 2.43181i | 0.134978 | + | 0.370848i | 0.988705 | − | 0.149872i | \(-0.0478860\pi\) |
−0.853728 | + | 0.520719i | \(0.825664\pi\) | |||||||
\(44\) | 12.2042 | − | 10.2405i | 1.83985 | − | 1.54382i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.2826 | − | 21.2742i | 1.81098 | − | 3.13670i | ||||
\(47\) | −8.66316 | + | 1.52755i | −1.26365 | + | 0.222816i | −0.765025 | − | 0.644001i | \(-0.777273\pi\) |
−0.498627 | + | 0.866817i | \(0.666162\pi\) | |||||||
\(48\) | −9.16893 | + | 1.61673i | −1.32342 | + | 0.233355i | ||||
\(49\) | 3.84048 | − | 6.65191i | 0.548640 | − | 0.950273i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.486809 | − | 0.408482i | 0.0681670 | − | 0.0571989i | ||||
\(52\) | 0.607292 | + | 1.66852i | 0.0842162 | + | 0.231382i | ||||
\(53\) | −3.80291 | + | 10.4484i | −0.522370 | + | 1.43520i | 0.345505 | + | 0.938417i | \(0.387708\pi\) |
−0.867875 | + | 0.496783i | \(0.834515\pi\) | |||||||
\(54\) | −9.58469 | − | 8.04251i | −1.30431 | − | 1.09445i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −28.8973 | −3.86156 | ||||||||
\(57\) | −0.875722 | + | 3.95259i | −0.115992 | + | 0.523534i | ||||
\(58\) | − | 4.03786i | − | 0.530197i | ||||||
\(59\) | 1.35268 | − | 7.67146i | 0.176105 | − | 0.998739i | −0.760757 | − | 0.649037i | \(-0.775172\pi\) |
0.936861 | − | 0.349701i | \(-0.113717\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.27305 | − | 0.827322i | −0.291034 | − | 0.105928i | 0.192377 | − | 0.981321i | \(-0.438380\pi\) |
−0.483411 | + | 0.875393i | \(0.660602\pi\) | |||||||
\(62\) | 2.19630 | + | 6.03429i | 0.278931 | + | 0.766356i | ||||
\(63\) | −5.26412 | − | 6.27353i | −0.663216 | − | 0.790391i | ||||
\(64\) | 4.66339 | + | 8.07723i | 0.582924 | + | 1.00965i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.38176 | + | 7.83636i | 0.170083 | + | 0.964590i | ||||
\(67\) | 9.41216 | − | 1.65962i | 1.14988 | − | 0.202755i | 0.433956 | − | 0.900934i | \(-0.357117\pi\) |
0.715923 | + | 0.698180i | \(0.246006\pi\) | |||||||
\(68\) | −2.88935 | − | 1.66816i | −0.350385 | − | 0.202295i | ||||
\(69\) | 4.35042 | + | 7.53515i | 0.523729 | + | 0.907125i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.81203 | − | 1.75144i | 0.571083 | − | 0.207857i | −0.0403062 | − | 0.999187i | \(-0.512833\pi\) |
0.611389 | + | 0.791330i | \(0.290611\pi\) | |||||||
\(72\) | −5.51331 | + | 15.1477i | −0.649749 | + | 1.78517i | ||||
\(73\) | −5.06782 | + | 6.03960i | −0.593144 | + | 0.706881i | −0.976207 | − | 0.216841i | \(-0.930425\pi\) |
0.383063 | + | 0.923722i | \(0.374869\pi\) | |||||||
\(74\) | −0.0744033 | + | 0.421962i | −0.00864920 | + | 0.0490521i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 21.0723 | − | 2.77705i | 2.41716 | − | 0.318550i | ||||
\(77\) | 12.5186i | 1.42663i | ||||||||
\(78\) | −0.873384 | − | 0.154001i | −0.0988913 | − | 0.0174372i | ||||
\(79\) | 7.14004 | + | 5.99121i | 0.803317 | + | 0.674063i | 0.949003 | − | 0.315268i | \(-0.102094\pi\) |
−0.145685 | + | 0.989331i | \(0.546539\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.86106 | + | 0.677369i | −0.206784 | + | 0.0752633i | ||||
\(82\) | −12.4287 | − | 14.8119i | −1.37252 | − | 1.63570i | ||||
\(83\) | −0.631436 | + | 0.364559i | −0.0693091 | + | 0.0400156i | −0.534254 | − | 0.845324i | \(-0.679407\pi\) |
0.464945 | + | 0.885340i | \(0.346074\pi\) | |||||||
\(84\) | 8.67627 | − | 15.0277i | 0.946659 | − | 1.63966i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.17838 | + | 6.68294i | 0.127068 | + | 0.720640i | ||||
\(87\) | 1.23857 | + | 0.715090i | 0.132789 | + | 0.0766657i | ||||
\(88\) | 21.3398 | − | 12.3205i | 2.27483 | − | 1.31337i | ||||
\(89\) | −9.68319 | + | 8.12516i | −1.02642 | + | 0.861265i | −0.990420 | − | 0.138087i | \(-0.955905\pi\) |
−0.0359958 | + | 0.999352i | \(0.511460\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.31109 | − | 0.477199i | −0.137440 | − | 0.0500241i | ||||
\(92\) | 29.3625 | − | 34.9928i | 3.06125 | − | 3.64825i | ||||
\(93\) | −2.23991 | − | 0.394957i | −0.232268 | − | 0.0409551i | ||||
\(94\) | −23.0673 | −2.37921 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −10.4046 | −1.06191 | ||||||||
\(97\) | −7.43249 | − | 1.31055i | −0.754655 | − | 0.133066i | −0.216931 | − | 0.976187i | \(-0.569605\pi\) |
−0.537724 | + | 0.843121i | \(0.680716\pi\) | |||||||
\(98\) | 12.9466 | − | 15.4291i | 1.30780 | − | 1.55858i | ||||
\(99\) | 6.56216 | + | 2.38843i | 0.659522 | + | 0.240046i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.10910 | − | 2.60884i | 0.309367 | − | 0.259589i | −0.474864 | − | 0.880059i | \(-0.657503\pi\) |
0.784230 | + | 0.620470i | \(0.213058\pi\) | |||||||
\(102\) | 1.44314 | − | 0.833196i | 0.142892 | − | 0.0824987i | ||||
\(103\) | 11.9321 | + | 6.88900i | 1.17571 | + | 0.678794i | 0.955017 | − | 0.296551i | \(-0.0958363\pi\) |
0.220688 | + | 0.975344i | \(0.429170\pi\) | |||||||
\(104\) | 0.476893 | + | 2.70459i | 0.0467632 | + | 0.265207i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.5783 | + | 25.2503i | −1.41597 | + | 2.45253i | ||||
\(107\) | 5.65047 | − | 3.26230i | 0.546252 | − | 0.315379i | −0.201357 | − | 0.979518i | \(-0.564535\pi\) |
0.747609 | + | 0.664139i | \(0.231202\pi\) | |||||||
\(108\) | −14.9553 | − | 17.8230i | −1.43907 | − | 1.71502i | ||||
\(109\) | −8.46545 | + | 3.08117i | −0.810843 | + | 0.295123i | −0.713972 | − | 0.700174i | \(-0.753106\pi\) |
−0.0968707 | + | 0.995297i | \(0.530883\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.116256 | − | 0.0975503i | −0.0110345 | − | 0.00925906i | ||||
\(112\) | −37.8255 | − | 6.66966i | −3.57418 | − | 0.630224i | ||||
\(113\) | − | 13.1464i | − | 1.23670i | −0.785901 | − | 0.618352i | \(-0.787800\pi\) | ||
0.785901 | − | 0.618352i | \(-0.212200\pi\) | |||||||
\(114\) | −4.06126 | + | 9.80841i | −0.380372 | + | 0.918642i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.30384 | − | 7.39445i | 0.121059 | − | 0.686557i | ||||
\(117\) | −0.500287 | + | 0.596218i | −0.0462515 | + | 0.0551204i | ||||
\(118\) | 6.98634 | − | 19.1948i | 0.643145 | − | 1.76703i | ||||
\(119\) | 2.46353 | − | 0.896650i | 0.225831 | − | 0.0821958i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.162595 | + | 0.281622i | 0.0147813 | + | 0.0256020i | ||||
\(122\) | −5.49320 | − | 3.17150i | −0.497331 | − | 0.287134i | ||||
\(123\) | 6.74447 | − | 1.18923i | 0.608128 | − | 0.107229i | ||||
\(124\) | 2.07355 | + | 11.7597i | 0.186210 | + | 1.05605i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −10.7374 | − | 18.5978i | −0.956565 | − | 1.65682i | ||||
\(127\) | −5.63783 | − | 6.71890i | −0.500276 | − | 0.596206i | 0.455524 | − | 0.890224i | \(-0.349452\pi\) |
−0.955800 | + | 0.294018i | \(0.905008\pi\) | |||||||
\(128\) | 0.701866 | + | 1.92836i | 0.0620368 | + | 0.170445i | ||||
\(129\) | −2.25861 | − | 0.822066i | −0.198859 | − | 0.0723789i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.80469 | − | 10.2349i | 0.157676 | − | 0.894226i | −0.798622 | − | 0.601833i | \(-0.794437\pi\) |
0.956298 | − | 0.292393i | \(-0.0944515\pi\) | |||||||
\(132\) | 14.7967i | 1.28789i | ||||||||
\(133\) | −8.97182 | + | 14.0870i | −0.777956 | + | 1.22150i | ||||
\(134\) | 25.0616 | 2.16500 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.95301 | − | 3.31697i | −0.338968 | − | 0.284428i | ||||
\(137\) | 1.21940 | − | 3.35026i | 0.104180 | − | 0.286232i | −0.876640 | − | 0.481146i | \(-0.840221\pi\) |
0.980820 | + | 0.194914i | \(0.0624428\pi\) | |||||||
\(138\) | 7.80341 | + | 21.4397i | 0.664271 | + | 1.82507i | ||||
\(139\) | −6.64270 | + | 5.57389i | −0.563427 | + | 0.472771i | −0.879457 | − | 0.475978i | \(-0.842094\pi\) |
0.316030 | + | 0.948749i | \(0.397650\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.08513 | − | 7.07565i | 0.344030 | − | 0.595877i | ||||
\(142\) | 13.2241 | − | 2.33176i | 1.10974 | − | 0.195677i | ||||
\(143\) | 1.17166 | − | 0.206596i | 0.0979793 | − | 0.0172764i | ||||
\(144\) | −10.7129 | + | 18.5553i | −0.892741 | + | 1.54627i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −15.8373 | + | 13.2890i | −1.31070 | + | 1.09981i | ||||
\(147\) | 2.43994 | + | 6.70367i | 0.201243 | + | 0.552910i | ||||
\(148\) | −0.272506 | + | 0.748705i | −0.0223999 | + | 0.0615431i | ||||
\(149\) | 12.9946 | + | 10.9038i | 1.06456 | + | 0.893274i | 0.994549 | − | 0.104272i | \(-0.0332513\pi\) |
0.0700136 | + | 0.997546i | \(0.477696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.0821 | −0.901849 | −0.450925 | − | 0.892562i | \(-0.648906\pi\) | ||||
−0.450925 | + | 0.892562i | \(0.648906\pi\) | |||||||
\(152\) | 32.8432 | + | 1.42963i | 2.66394 | + | 0.115958i | ||||
\(153\) | − | 1.46243i | − | 0.118230i | ||||||
\(154\) | −5.70032 | + | 32.3281i | −0.459345 | + | 2.60508i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.54968 | − | 0.564038i | −0.124074 | − | 0.0451592i | ||||
\(157\) | 0.318919 | + | 0.876222i | 0.0254525 | + | 0.0699302i | 0.951768 | − | 0.306818i | \(-0.0992644\pi\) |
−0.926316 | + | 0.376748i | \(0.877042\pi\) | |||||||
\(158\) | 15.7104 | + | 18.7229i | 1.24985 | + | 1.48951i | ||||
\(159\) | −5.16352 | − | 8.94347i | −0.409493 | − | 0.709264i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.23301 | + | 35.3491i | 0.491230 | + | 2.78590i | ||||
\(162\) | −5.11443 | + | 0.901812i | −0.401828 | + | 0.0708530i | ||||
\(163\) | 6.99149 | + | 4.03654i | 0.547616 | + | 0.316166i | 0.748160 | − | 0.663519i | \(-0.230938\pi\) |
−0.200544 | + | 0.979685i | \(0.564271\pi\) | |||||||
\(164\) | −17.9775 | − | 31.1380i | −1.40381 | − | 2.43147i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.79662 | + | 0.653916i | −0.139445 | + | 0.0507537i | ||||
\(167\) | −4.66839 | + | 12.8263i | −0.361251 | + | 0.992529i | 0.617337 | + | 0.786699i | \(0.288212\pi\) |
−0.978588 | + | 0.205830i | \(0.934011\pi\) | |||||||
\(168\) | 17.2518 | − | 20.5599i | 1.33101 | − | 1.58623i | ||||
\(169\) | 2.23440 | − | 12.6719i | 0.171877 | − | 0.974763i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.67256 | + | 7.39061i | 0.433792 | + | 0.565174i | ||||
\(172\) | 12.6188i | 0.962176i | ||||||||
\(173\) | −8.24695 | − | 1.45416i | −0.627004 | − | 0.110558i | −0.148888 | − | 0.988854i | \(-0.547569\pi\) |
−0.478117 | + | 0.878296i | \(0.658680\pi\) | |||||||
\(174\) | 2.87287 | + | 2.41063i | 0.217792 | + | 0.182749i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 30.7767 | − | 11.2018i | 2.31988 | − | 0.844368i | ||||
\(177\) | 4.65056 | + | 5.54232i | 0.349557 | + | 0.416586i | ||||
\(178\) | −28.7056 | + | 16.5732i | −2.15158 | + | 1.24221i | ||||
\(179\) | −2.85227 | + | 4.94028i | −0.213189 | + | 0.369254i | −0.952711 | − | 0.303879i | \(-0.901718\pi\) |
0.739522 | + | 0.673132i | \(0.235052\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.57719 | + | 14.6160i | 0.191561 | + | 1.08640i | 0.917231 | + | 0.398355i | \(0.130419\pi\) |
−0.725670 | + | 0.688043i | \(0.758470\pi\) | |||||||
\(182\) | −3.16848 | − | 1.82932i | −0.234863 | − | 0.135598i | ||||
\(183\) | 1.94565 | − | 1.12332i | 0.143827 | − | 0.0830383i | ||||
\(184\) | 54.1232 | − | 45.4148i | 3.99002 | − | 3.34802i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.60451 | − | 2.03987i | −0.410942 | − | 0.149571i | ||||
\(187\) | −1.43695 | + | 1.71249i | −0.105080 | + | 0.125230i | ||||
\(188\) | −42.2426 | − | 7.44852i | −3.08086 | − | 0.543239i | ||||
\(189\) | 18.2822 | 1.32984 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.7204 | −1.42692 | −0.713460 | − | 0.700695i | \(-0.752873\pi\) | ||||
−0.713460 | + | 0.700695i | \(0.752873\pi\) | |||||||
\(192\) | −8.53088 | − | 1.50423i | −0.615664 | − | 0.108558i | ||||
\(193\) | −2.65500 | + | 3.16411i | −0.191111 | + | 0.227758i | −0.853088 | − | 0.521767i | \(-0.825273\pi\) |
0.661977 | + | 0.749524i | \(0.269718\pi\) | |||||||
\(194\) | −18.5969 | − | 6.76871i | −1.33518 | − | 0.485965i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 28.6909 | − | 24.0746i | 2.04935 | − | 1.71961i | ||||
\(197\) | 0.144293 | − | 0.0833078i | 0.0102805 | − | 0.00593544i | −0.494851 | − | 0.868978i | \(-0.664777\pi\) |
0.505131 | + | 0.863042i | \(0.331444\pi\) | |||||||
\(198\) | 15.8585 | + | 9.15593i | 1.12702 | + | 0.650684i | ||||
\(199\) | 0.900606 | + | 5.10759i | 0.0638423 | + | 0.362068i | 0.999946 | + | 0.0103448i | \(0.00329292\pi\) |
−0.936104 | + | 0.351723i | \(0.885596\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.43832 | + | 7.68740i | −0.313055 | + | 0.542227i | ||||
\(202\) | 9.21685 | − | 5.32135i | 0.648495 | − | 0.374409i | ||||
\(203\) | 3.79249 | + | 4.51971i | 0.266181 | + | 0.317222i | ||||
\(204\) | 2.91183 | − | 1.05982i | 0.203869 | − | 0.0742022i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 27.6766 | + | 23.2234i | 1.92832 | + | 1.61805i | ||||
\(207\) | 19.7189 | + | 3.47697i | 1.37056 | + | 0.241666i | ||||
\(208\) | 3.65029i | 0.253102i | ||||||||
\(209\) | 0.619331 | − | 14.2281i | 0.0428400 | − | 0.984176i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.853752 | + | 4.84187i | −0.0587747 | + | 0.333328i | −0.999990 | − | 0.00447940i | \(-0.998574\pi\) |
0.941215 | + | 0.337807i | \(0.109685\pi\) | |||||||
\(212\) | −34.8503 | + | 41.5330i | −2.39353 | + | 2.85250i | ||||
\(213\) | −1.62669 | + | 4.46930i | −0.111459 | + | 0.306231i | ||||
\(214\) | 16.0772 | − | 5.85164i | 1.09902 | − | 0.400010i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −17.9929 | − | 31.1647i | −1.22426 | − | 2.12049i | ||||
\(217\) | −8.12599 | − | 4.69155i | −0.551628 | − | 0.318483i | ||||
\(218\) | −23.2642 | + | 4.10210i | −1.57565 | + | 0.277829i | ||||
\(219\) | −1.27156 | − | 7.21135i | −0.0859237 | − | 0.487298i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.124576 | − | 0.215772i | −0.00837990 | − | 0.0145144i | ||||
\(222\) | −0.255800 | − | 0.304850i | −0.0171682 | − | 0.0204602i | ||||
\(223\) | −2.99672 | − | 8.23341i | −0.200675 | − | 0.551350i | 0.798008 | − | 0.602646i | \(-0.205887\pi\) |
−0.998683 | + | 0.0512961i | \(0.983665\pi\) | |||||||
\(224\) | −40.3344 | − | 14.6805i | −2.69496 | − | 0.980885i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.98615 | − | 33.9491i | 0.398193 | − | 2.25826i | ||||
\(227\) | − | 5.53943i | − | 0.367665i | −0.982958 | − | 0.183833i | \(-0.941150\pi\) | ||
0.982958 | − | 0.183833i | \(-0.0588504\pi\) | |||||||
\(228\) | −10.6045 | + | 16.6505i | −0.702299 | + | 1.10271i | ||||
\(229\) | −26.8762 | −1.77603 | −0.888014 | − | 0.459816i | \(-0.847915\pi\) | ||||
−0.888014 | + | 0.459816i | \(0.847915\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.90682 | − | 7.47371i | −0.586025 | − | 0.491734i | ||||
\(232\) | 3.97201 | − | 10.9130i | 0.260776 | − | 0.716475i | ||||
\(233\) | 0.873055 | + | 2.39870i | 0.0571958 | + | 0.157144i | 0.965000 | − | 0.262250i | \(-0.0844646\pi\) |
−0.907804 | + | 0.419394i | \(0.862242\pi\) | |||||||
\(234\) | −1.56343 | + | 1.31187i | −0.102204 | + | 0.0857596i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 18.9920 | − | 32.8952i | 1.23628 | − | 2.14129i | ||||
\(237\) | −8.52529 | + | 1.50324i | −0.553777 | + | 0.0976459i | ||||
\(238\) | 6.77009 | − | 1.19375i | 0.438840 | − | 0.0773793i | ||||
\(239\) | −12.7663 | + | 22.1119i | −0.825784 | + | 1.43030i | 0.0755339 | + | 0.997143i | \(0.475934\pi\) |
−0.901318 | + | 0.433157i | \(0.857399\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.759825 | + | 0.637569i | −0.0489446 | + | 0.0410694i | −0.666932 | − | 0.745119i | \(-0.732393\pi\) |
0.617987 | + | 0.786188i | \(0.287948\pi\) | |||||||
\(242\) | 0.291648 | + | 0.801298i | 0.0187479 | + | 0.0515094i | ||||
\(243\) | 5.52494 | − | 15.1797i | 0.354425 | − | 0.973775i | ||||
\(244\) | −9.03549 | − | 7.58168i | −0.578438 | − | 0.485367i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 17.9584 | 1.14499 | ||||||||
\(247\) | 1.46652 | + | 0.607224i | 0.0933121 | + | 0.0386367i | ||||
\(248\) | 18.4692i | 1.17280i | ||||||||
\(249\) | 0.117593 | − | 0.666900i | 0.00745212 | − | 0.0422631i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.6599 | + | 4.97181i | 0.862207 | + | 0.313818i | 0.735007 | − | 0.678059i | \(-0.237179\pi\) |
0.127200 | + | 0.991877i | \(0.459401\pi\) | |||||||
\(252\) | −13.6579 | − | 37.5248i | −0.860368 | − | 2.36384i | ||||
\(253\) | −19.6742 | − | 23.4468i | −1.23691 | − | 1.47409i | ||||
\(254\) | −11.4997 | − | 19.9180i | −0.721555 | − | 1.24977i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.30473 | − | 13.0708i | −0.144046 | − | 0.816923i | ||||
\(257\) | 16.9069 | − | 2.98115i | 1.05463 | − | 0.185959i | 0.380655 | − | 0.924717i | \(-0.375698\pi\) |
0.673971 | + | 0.738758i | \(0.264587\pi\) | |||||||
\(258\) | −5.45830 | − | 3.15135i | −0.339819 | − | 0.196195i | ||||
\(259\) | −0.313038 | − | 0.542198i | −0.0194512 | − | 0.0336905i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.09276 | − | 1.12567i | 0.191437 | − | 0.0696773i | ||||
\(262\) | 9.32083 | − | 25.6088i | 0.575843 | − | 1.58212i | ||||
\(263\) | 0.806105 | − | 0.960678i | 0.0497066 | − | 0.0592380i | −0.740618 | − | 0.671926i | \(-0.765467\pi\) |
0.790325 | + | 0.612688i | \(0.209912\pi\) | |||||||
\(264\) | −3.97412 | + | 22.5384i | −0.244590 | + | 1.38714i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −29.5833 | + | 32.2931i | −1.81387 | + | 1.98002i | ||||
\(267\) | − | 11.7402i | − | 0.718489i | ||||||
\(268\) | 45.8949 | + | 8.09250i | 2.80347 | + | 0.494328i | ||||
\(269\) | 10.4753 | + | 8.78981i | 0.638689 | + | 0.535924i | 0.903615 | − | 0.428345i | \(-0.140903\pi\) |
−0.264926 | + | 0.964269i | \(0.585348\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.6289 | + | 4.59653i | −0.767150 | + | 0.279220i | −0.695804 | − | 0.718232i | \(-0.744952\pi\) |
−0.0713459 | + | 0.997452i | \(0.522729\pi\) | |||||||
\(272\) | −4.40877 | − | 5.25417i | −0.267321 | − | 0.318581i | ||||
\(273\) | 1.12225 | − | 0.647932i | 0.0679217 | − | 0.0392146i | ||||
\(274\) | 4.67450 | − | 8.09647i | 0.282397 | − | 0.489126i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.36726 | + | 41.7818i | 0.443457 | + | 2.51497i | ||||
\(277\) | 10.4219 | + | 6.01711i | 0.626194 | + | 0.361533i | 0.779277 | − | 0.626680i | \(-0.215587\pi\) |
−0.153083 | + | 0.988213i | \(0.548920\pi\) | |||||||
\(278\) | −19.6922 | + | 11.3693i | −1.18106 | + | 0.681884i | ||||
\(279\) | −4.00962 | + | 3.36447i | −0.240050 | + | 0.201426i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.4574 | + | 4.89810i | 0.802802 | + | 0.292196i | 0.710647 | − | 0.703549i | \(-0.248402\pi\) |
0.0921549 | + | 0.995745i | \(0.470625\pi\) | |||||||
\(282\) | 13.7713 | − | 16.4120i | 0.820069 | − | 0.977321i | ||||
\(283\) | −5.22943 | − | 0.922089i | −0.310857 | − | 0.0548125i | 0.0160432 | − | 0.999871i | \(-0.494893\pi\) |
−0.326900 | + | 0.945059i | \(0.606004\pi\) | |||||||
\(284\) | 24.9699 | 1.48169 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.11977 | 0.184476 | ||||||||
\(287\) | 27.8236 | + | 4.90606i | 1.64238 | + | 0.289596i | ||||
\(288\) | −15.3908 | + | 18.3420i | −0.906911 | + | 1.08081i | ||||
\(289\) | −15.5349 | − | 5.65422i | −0.913815 | − | 0.332601i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.36967 | − | 4.50569i | 0.314776 | − | 0.264128i | ||||
\(292\) | −33.2935 | + | 19.2220i | −1.94835 | + | 1.12488i | ||||
\(293\) | −0.766360 | − | 0.442458i | −0.0447712 | − | 0.0258487i | 0.477447 | − | 0.878660i | \(-0.341562\pi\) |
−0.522219 | + | 0.852812i | \(0.674895\pi\) | |||||||
\(294\) | 3.24840 | + | 18.4226i | 0.189450 | + | 1.07443i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.616169 | + | 1.06724i | −0.0358141 | + | 0.0620318i | ||||
\(297\) | −13.5009 | + | 7.79475i | −0.783402 | + | 0.452297i | ||||
\(298\) | 28.5923 | + | 34.0750i | 1.65631 | + | 1.97391i | ||||
\(299\) | 3.20558 | − | 1.16674i | 0.185383 | − | 0.0674741i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.59583 | − | 6.37366i | −0.437816 | − | 0.367372i | ||||
\(302\) | −28.6184 | − | 5.04620i | −1.64681 | − | 0.290376i | ||||
\(303\) | 3.76956i | 0.216556i | ||||||||
\(304\) | 42.6606 | + | 9.45173i | 2.44675 | + | 0.542094i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.665912 | − | 3.77657i | 0.0380677 | − | 0.215892i | ||||
\(307\) | 15.9728 | − | 19.0356i | 0.911614 | − | 1.08642i | −0.0843293 | − | 0.996438i | \(-0.526875\pi\) |
0.995943 | − | 0.0899815i | \(-0.0286808\pi\) | |||||||
\(308\) | −20.8778 | + | 57.3612i | −1.18962 | + | 3.26846i | ||||
\(309\) | −12.0250 | + | 4.37672i | −0.684076 | + | 0.248983i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.25003 | − | 16.0215i | −0.524521 | − | 0.908497i | −0.999592 | − | 0.0285497i | \(-0.990911\pi\) |
0.475071 | − | 0.879947i | \(-0.342422\pi\) | |||||||
\(312\) | −2.20898 | − | 1.27536i | −0.125059 | − | 0.0722028i | ||||
\(313\) | 32.7069 | − | 5.76710i | 1.84870 | − | 0.325976i | 0.864445 | − | 0.502727i | \(-0.167670\pi\) |
0.984256 | + | 0.176751i | \(0.0565588\pi\) | |||||||
\(314\) | 0.424591 | + | 2.40797i | 0.0239611 | + | 0.135890i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22.7244 | + | 39.3597i | 1.27835 | + | 2.21416i | ||||
\(317\) | 4.24865 | + | 5.06335i | 0.238628 | + | 0.284386i | 0.872046 | − | 0.489424i | \(-0.162793\pi\) |
−0.633418 | + | 0.773810i | \(0.718349\pi\) | |||||||
\(318\) | −9.26188 | − | 25.4468i | −0.519380 | − | 1.42699i | ||||
\(319\) | −4.72765 | − | 1.72072i | −0.264698 | − | 0.0963420i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.05229 | + | 5.96783i | −0.0587331 | + | 0.333092i | ||||
\(322\) | 94.1237i | 5.24531i | ||||||||
\(323\) | −2.84428 | + | 0.897210i | −0.158260 | + | 0.0499221i | ||||
\(324\) | −9.65715 | −0.536508 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.2168 | + | 13.6075i | 0.898165 | + | 0.753650i | ||||
\(327\) | 2.86172 | − | 7.86250i | 0.158253 | − | 0.434797i | ||||
\(328\) | −19.0203 | − | 52.2578i | −1.05022 | − | 2.88545i | ||||
\(329\) | 25.8200 | − | 21.6655i | 1.42350 | − | 1.19446i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.25075 | + | 14.2907i | −0.453502 | + | 0.785489i | −0.998601 | − | 0.0528830i | \(-0.983159\pi\) |
0.545098 | + | 0.838372i | \(0.316492\pi\) | |||||||
\(332\) | −3.50126 | + | 0.617367i | −0.192157 | + | 0.0338824i | ||||
\(333\) | −0.343939 | + | 0.0606458i | −0.0188478 | + | 0.00332337i | ||||
\(334\) | −17.8961 | + | 30.9969i | −0.979229 | + | 1.69608i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 27.3274 | − | 22.9304i | 1.49083 | − | 1.25096i | ||||
\(337\) | 2.03595 | + | 5.59372i | 0.110905 | + | 0.304709i | 0.982712 | − | 0.185140i | \(-0.0592740\pi\) |
−0.871807 | + | 0.489849i | \(0.837052\pi\) | |||||||
\(338\) | 11.5402 | − | 31.7065i | 0.627706 | − | 1.72461i | ||||
\(339\) | 9.35342 | + | 7.84845i | 0.508008 | + | 0.426269i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00108 | 0.433283 | ||||||||
\(342\) | 11.2835 | + | 21.6685i | 0.610143 | + | 1.17170i | ||||
\(343\) | 2.60918i | 0.140882i | ||||||||
\(344\) | −3.38917 | + | 19.2210i | −0.182732 | + | 1.03632i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.6348 | − | 7.51044i | −1.10933 | − | 0.403764i | ||||
\(347\) | −7.39194 | − | 20.3092i | −0.396820 | − | 1.09025i | −0.963824 | − | 0.266539i | \(-0.914120\pi\) |
0.567004 | − | 0.823715i | \(-0.308102\pi\) | |||||||
\(348\) | 4.48263 | + | 5.34219i | 0.240294 | + | 0.286371i | ||||
\(349\) | −1.21095 | − | 2.09743i | −0.0648208 | − | 0.112273i | 0.831794 | − | 0.555085i | \(-0.187314\pi\) |
−0.896614 | + | 0.442812i | \(0.853981\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.301713 | − | 1.71110i | −0.0161042 | − | 0.0913316i | ||||
\(352\) | 36.0450 | − | 6.35570i | 1.92120 | − | 0.338760i | ||||
\(353\) | 6.62643 | + | 3.82577i | 0.352690 | + | 0.203625i | 0.665869 | − | 0.746069i | \(-0.268061\pi\) |
−0.313180 | + | 0.949694i | \(0.601394\pi\) | |||||||
\(354\) | 9.48592 | + | 16.4301i | 0.504171 | + | 0.873250i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −57.9195 | + | 21.0810i | −3.06973 | + | 1.11729i | ||||
\(357\) | −0.832787 | + | 2.28806i | −0.0440758 | + | 0.121097i | ||||
\(358\) | −9.61525 | + | 11.4590i | −0.508182 | + | 0.605627i | ||||
\(359\) | −1.18268 | + | 6.70733i | −0.0624197 | + | 0.353999i | 0.937561 | + | 0.347820i | \(0.113078\pi\) |
−0.999981 | + | 0.00617924i | \(0.998033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.8938 | − | 15.5668i | 0.573360 | − | 0.819303i | ||||
\(362\) | 38.9178i | 2.04548i | ||||||||
\(363\) | −0.297440 | − | 0.0524466i | −0.0156115 | − | 0.00275273i | ||||
\(364\) | −5.21167 | − | 4.37311i | −0.273166 | − | 0.229213i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.53595 | − | 2.01492i | 0.289369 | − | 0.105322i | ||||
\(367\) | −8.84542 | − | 10.5416i | −0.461727 | − | 0.550265i | 0.484067 | − | 0.875031i | \(-0.339159\pi\) |
−0.945795 | + | 0.324766i | \(0.894715\pi\) | |||||||
\(368\) | 81.3274 | − | 46.9544i | 4.23948 | − | 2.44767i | ||||
\(369\) | 7.88018 | − | 13.6489i | 0.410226 | − | 0.710532i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.39796 | − | 41.9559i | −0.384083 | − | 2.17824i | ||||
\(372\) | −9.60473 | − | 5.54529i | −0.497982 | − | 0.287510i | ||||
\(373\) | −26.2495 | + | 15.1552i | −1.35915 | + | 0.784705i | −0.989509 | − | 0.144470i | \(-0.953852\pi\) |
−0.369640 | + | 0.929175i | \(0.620519\pi\) | |||||||
\(374\) | −4.49055 | + | 3.76802i | −0.232201 | + | 0.194840i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −62.3434 | − | 22.6911i | −3.21511 | − | 1.17021i | ||||
\(377\) | 0.360427 | − | 0.429541i | 0.0185630 | − | 0.0221225i | ||||
\(378\) | 47.2121 | + | 8.32476i | 2.42833 | + | 0.428179i | ||||
\(379\) | 3.43860 | 0.176629 | 0.0883144 | − | 0.996093i | \(-0.471852\pi\) | ||||
0.0883144 | + | 0.996093i | \(0.471852\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.14620 | 0.417343 | ||||||||
\(382\) | −50.9260 | − | 8.97964i | −2.60560 | − | 0.459438i | ||||
\(383\) | 11.7836 | − | 14.0432i | 0.602114 | − | 0.717572i | −0.375771 | − | 0.926712i | \(-0.622622\pi\) |
0.977886 | + | 0.209141i | \(0.0670666\pi\) | |||||||
\(384\) | −1.79102 | − | 0.651876i | −0.0913974 | − | 0.0332659i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.29704 | + | 6.96205i | −0.422308 | + | 0.354359i | ||||
\(387\) | −4.79022 | + | 2.76563i | −0.243500 | + | 0.140585i | ||||
\(388\) | −31.8704 | − | 18.4004i | −1.61798 | − | 0.934139i | ||||
\(389\) | −0.723319 | − | 4.10215i | −0.0366737 | − | 0.207987i | 0.960965 | − | 0.276671i | \(-0.0892312\pi\) |
−0.997638 | + | 0.0686838i | \(0.978120\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.20490 | + | 5.55104i | −0.162079 | + | 0.280728i | ||||
\(392\) | 50.1679 | − | 28.9645i | 2.53386 | − | 1.46293i | ||||
\(393\) | 6.20454 | + | 7.39429i | 0.312978 | + | 0.372992i | ||||
\(394\) | 0.410557 | − | 0.149431i | 0.0206836 | − | 0.00752820i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 26.0849 | + | 21.8879i | 1.31082 | + | 1.09991i | ||||
\(397\) | −19.5995 | − | 3.45592i | −0.983669 | − | 0.173447i | −0.341393 | − | 0.939921i | \(-0.610899\pi\) |
−0.642276 | + | 0.766473i | \(0.722010\pi\) | |||||||
\(398\) | 13.5999i | 0.681703i | ||||||||
\(399\) | −4.66647 | − | 14.7934i | −0.233616 | − | 0.740594i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.64601 | + | 9.33496i | −0.0821976 | + | 0.466166i | 0.915729 | + | 0.401797i | \(0.131614\pi\) |
−0.997926 | + | 0.0643684i | \(0.979497\pi\) | |||||||
\(402\) | −14.9619 | + | 17.8310i | −0.746234 | + | 0.889327i | ||||
\(403\) | −0.304994 | + | 0.837964i | −0.0151928 | + | 0.0417419i | ||||
\(404\) | 18.5969 | − | 6.76872i | 0.925231 | − | 0.336756i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.73568 | + | 13.3986i | 0.383915 | + | 0.664961i | ||||
\(407\) | 0.462339 | + | 0.266932i | 0.0229173 | + | 0.0132313i | ||||
\(408\) | 4.71994 | − | 0.832252i | 0.233672 | − | 0.0412026i | ||||
\(409\) | 4.04137 | + | 22.9197i | 0.199833 | + | 1.13331i | 0.905366 | + | 0.424632i | \(0.139596\pi\) |
−0.705533 | + | 0.708677i | \(0.749292\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.65567 | + | 2.86771i | 0.0816682 | + | 0.141454i | ||||
\(412\) | 43.1846 | + | 51.4654i | 2.12755 | + | 2.53552i | ||||
\(413\) | 10.2083 | + | 28.0472i | 0.502320 | + | 1.38011i | ||||
\(414\) | 49.3388 | + | 17.9578i | 2.42487 | + | 0.882580i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.708360 | + | 4.01731i | −0.0347302 | + | 0.196965i | ||||
\(417\) | − | 8.05382i | − | 0.394397i | ||||||
\(418\) | 8.07806 | − | 36.4605i | 0.395111 | − | 1.78334i | ||||
\(419\) | −3.05296 | −0.149147 | −0.0745735 | − | 0.997216i | \(-0.523760\pi\) | ||||
−0.0745735 | + | 0.997216i | \(0.523760\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.4803 | + | 18.0241i | 1.04689 | + | 0.878441i | 0.992763 | − | 0.120093i | \(-0.0383194\pi\) |
0.0541226 | + | 0.998534i | \(0.482764\pi\) | |||||||
\(422\) | −4.40946 | + | 12.1149i | −0.214649 | + | 0.589743i | ||||
\(423\) | −6.43068 | − | 17.6682i | −0.312670 | − | 0.859055i | ||||
\(424\) | −64.2389 | + | 53.9028i | −3.11972 | + | 2.61775i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.23585 | + | 10.8008i | −0.302128 | + | 0.523301i | ||||
\(427\) | 9.12750 | − | 1.60942i | 0.441711 | − | 0.0778855i | ||||
\(428\) | 31.3314 | − | 5.52458i | 1.51446 | − | 0.267041i | ||||
\(429\) | −0.552500 | + | 0.956957i | −0.0266749 | + | 0.0462023i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.1461 | − | 19.4219i | 1.11491 | − | 0.935521i | 0.116574 | − | 0.993182i | \(-0.462809\pi\) |
0.998336 | + | 0.0576610i | \(0.0183642\pi\) | |||||||
\(432\) | −16.3591 | − | 44.9463i | −0.787079 | − | 2.16248i | ||||
\(433\) | −5.14314 | + | 14.1306i | −0.247163 | + | 0.679076i | 0.752624 | + | 0.658451i | \(0.228788\pi\) |
−0.999787 | + | 0.0206251i | \(0.993434\pi\) | |||||||
\(434\) | −18.8483 | − | 15.8156i | −0.904746 | − | 0.759172i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −43.9277 | −2.10376 | ||||||||
\(437\) | −5.33530 | − | 40.4844i | −0.255222 | − | 1.93663i | ||||
\(438\) | − | 19.2016i | − | 0.917487i | ||||||
\(439\) | 6.70915 | − | 38.0495i | 0.320210 | − | 1.81600i | −0.221181 | − | 0.975233i | \(-0.570991\pi\) |
0.541391 | − | 0.840771i | \(-0.317898\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.4270 | + | 5.61498i | 0.734621 | + | 0.267380i | ||||
\(442\) | −0.223454 | − | 0.613935i | −0.0106286 | − | 0.0292019i | ||||
\(443\) | −2.82052 | − | 3.36137i | −0.134007 | − | 0.159703i | 0.694868 | − | 0.719138i | \(-0.255463\pi\) |
−0.828875 | + | 0.559434i | \(0.811018\pi\) | |||||||
\(444\) | −0.370003 | − | 0.640865i | −0.0175596 | − | 0.0304141i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.98966 | − | 22.6265i | −0.188916 | − | 1.07140i | ||||
\(447\) | −15.5158 | + | 2.73585i | −0.733870 | + | 0.129401i | ||||
\(448\) | −30.9485 | − | 17.8681i | −1.46218 | − | 0.844189i | ||||
\(449\) | −12.3966 | − | 21.4716i | −0.585032 | − | 1.01331i | −0.994871 | − | 0.101148i | \(-0.967749\pi\) |
0.409839 | − | 0.912158i | \(-0.365585\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.6387 | + | 8.23981i | −1.06601 | + | 0.387997i | ||||
\(452\) | 21.9246 | − | 60.2374i | 1.03125 | − | 2.83333i | ||||
\(453\) | 6.61608 | − | 7.88474i | 0.310851 | − | 0.370457i | ||||
\(454\) | 2.52236 | − | 14.3050i | 0.118380 | − | 0.671368i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20.6247 | + | 22.5139i | −0.965842 | + | 1.05431i | ||||
\(457\) | − | 21.1249i | − | 0.988182i | −0.869410 | − | 0.494091i | \(-0.835501\pi\) | ||
0.869410 | − | 0.494091i | \(-0.164499\pi\) | |||||||
\(458\) | −69.4051 | − | 12.2380i | −3.24309 | − | 0.571843i | ||||
\(459\) | 2.50092 | + | 2.09852i | 0.116733 | + | 0.0979507i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.4865 | − | 3.81677i | 0.488405 | − | 0.177765i | −0.0860668 | − | 0.996289i | \(-0.527430\pi\) |
0.574471 | + | 0.818525i | \(0.305208\pi\) | |||||||
\(462\) | −19.5978 | − | 23.3558i | −0.911773 | − | 1.08661i | ||||
\(463\) | 3.50260 | − | 2.02223i | 0.162779 | − | 0.0939808i | −0.416397 | − | 0.909183i | \(-0.636707\pi\) |
0.579177 | + | 0.815202i | \(0.303374\pi\) | |||||||
\(464\) | 7.71801 | − | 13.3680i | 0.358300 | − | 0.620593i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.16234 | + | 6.59194i | 0.0538442 | + | 0.305366i | ||||
\(467\) | −18.2919 | − | 10.5608i | −0.846448 | − | 0.488697i | 0.0130026 | − | 0.999915i | \(-0.495861\pi\) |
−0.859451 | + | 0.511218i | \(0.829194\pi\) | |||||||
\(468\) | −3.28668 | + | 1.89756i | −0.151927 | + | 0.0877149i | ||||
\(469\) | −28.0523 | + | 23.5387i | −1.29534 | + | 1.08692i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.813815 | − | 0.296204i | −0.0374986 | − | 0.0136484i | ||||
\(472\) | 37.7636 | − | 45.0049i | 1.73821 | − | 2.07152i | ||||
\(473\) | 8.32675 | + | 1.46823i | 0.382864 | + | 0.0675093i | ||||
\(474\) | −22.7002 | −1.04265 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.7834 | 0.585926 | ||||||||
\(477\) | −23.4044 | − | 4.12682i | −1.07161 | − | 0.188954i | ||||
\(478\) | −43.0363 | + | 51.2887i | −1.96844 | + | 2.34589i | ||||
\(479\) | 32.1446 | + | 11.6997i | 1.46872 | + | 0.534572i | 0.947754 | − | 0.319003i | \(-0.103348\pi\) |
0.520971 | + | 0.853575i | \(0.325570\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0455800 | + | 0.0382462i | −0.00207827 | + | 0.00174388i | ||||
\(482\) | −2.25249 | + | 1.30047i | −0.102598 | + | 0.0592349i | ||||
\(483\) | −28.8715 | − | 16.6690i | −1.31370 | − | 0.758464i | ||||
\(484\) | 0.275348 | + | 1.56157i | 0.0125158 | + | 0.0709806i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 21.1796 | − | 36.6842i | 0.960727 | − | 1.66403i | ||||
\(487\) | 1.53876 | − | 0.888403i | 0.0697278 | − | 0.0402574i | −0.464731 | − | 0.885452i | \(-0.653849\pi\) |
0.534459 | + | 0.845195i | \(0.320516\pi\) | |||||||
\(488\) | −11.7265 | − | 13.9752i | −0.530836 | − | 0.632626i | ||||
\(489\) | −7.04589 | + | 2.56449i | −0.318626 | + | 0.115970i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.8336 | − | 13.2860i | −0.714562 | − | 0.599589i | 0.211313 | − | 0.977418i | \(-0.432226\pi\) |
−0.925875 | + | 0.377830i | \(0.876670\pi\) | |||||||
\(492\) | 32.8869 | + | 5.79884i | 1.48265 | + | 0.261432i | ||||
\(493\) | 1.05359i | 0.0474515i | ||||||||
\(494\) | 3.51063 | + | 2.23587i | 0.157951 | + | 0.100596i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.26280 | + | 24.1755i | −0.191405 | + | 1.08551i | ||||
\(497\) | −12.6121 | + | 15.0305i | −0.565730 | + | 0.674211i | ||||
\(498\) | 0.607342 | − | 1.66866i | 0.0272156 | − | 0.0747743i | ||||
\(499\) | −40.0666 | + | 14.5830i | −1.79363 | + | 0.652826i | −0.794675 | + | 0.607036i | \(0.792359\pi\) |
−0.998951 | + | 0.0457908i | \(0.985419\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.33865 | − | 10.9789i | −0.283190 | − | 0.490500i | ||||
\(502\) | 33.0115 | + | 19.0592i | 1.47338 | + | 0.850654i | ||||
\(503\) | 24.0995 | − | 4.24940i | 1.07455 | − | 0.189471i | 0.391743 | − | 0.920075i | \(-0.371872\pi\) |
0.682802 | + | 0.730603i | \(0.260761\pi\) | |||||||
\(504\) | −10.7253 | − | 60.8260i | −0.477741 | − | 2.70940i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −40.1303 | − | 69.5076i | −1.78401 | − | 3.08999i | ||||
\(507\) | 7.68191 | + | 9.15495i | 0.341166 | + | 0.406585i | ||||
\(508\) | −14.6275 | − | 40.1888i | −0.648991 | − | 1.78309i | ||||
\(509\) | 31.7212 | + | 11.5456i | 1.40602 | + | 0.511749i | 0.929959 | − | 0.367664i | \(-0.119842\pi\) |
0.476060 | + | 0.879413i | \(0.342064\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.24568 | − | 29.7497i | 0.232055 | − | 1.31605i | ||||
\(512\) | − | 38.9076i | − | 1.71949i | ||||||
\(513\) | −20.7787 | − | 0.904472i | −0.917401 | − | 0.0399334i | ||||
\(514\) | 45.0179 | 1.98566 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.97809 | − | 7.53351i | −0.395238 | − | 0.331644i | ||||
\(517\) | −9.83007 | + | 27.0079i | −0.432326 | + | 1.18781i | ||||
\(518\) | −0.561501 | − | 1.54271i | −0.0246710 | − | 0.0677829i | ||||
\(519\) | 5.95809 | − | 4.99943i | 0.261531 | − | 0.219451i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.743494 | − | 1.28777i | 0.0325731 | − | 0.0564182i | −0.849279 | − | 0.527944i | \(-0.822963\pi\) |
0.881852 | + | 0.471526i | \(0.156297\pi\) | |||||||
\(522\) | 8.49931 | − | 1.49866i | 0.372005 | − | 0.0655944i | ||||
\(523\) | 6.21793 | − | 1.09639i | 0.271891 | − | 0.0479417i | −0.0360402 | − | 0.999350i | \(-0.511474\pi\) |
0.307931 | + | 0.951409i | \(0.400363\pi\) | |||||||
\(524\) | 25.3382 | − | 43.8871i | 1.10691 | − | 1.91722i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.51913 | − | 2.11380i | 0.109839 | − | 0.0921660i | ||||
\(527\) | −0.573079 | − | 1.57452i | −0.0249637 | − | 0.0685872i | ||||
\(528\) | −10.4040 | + | 28.5847i | −0.452775 | + | 1.24399i | ||||
\(529\) | −49.6096 | − | 41.6274i | −2.15694 | − | 1.80989i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.6497 | 0.722537 | ||||||||
\(532\) | −64.6029 | + | 49.5850i | −2.80089 | + | 2.14978i | ||||
\(533\) | − | 2.68507i | − | 0.116303i | ||||||
\(534\) | 5.34586 | − | 30.3179i | 0.231338 | − | 1.31198i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 67.7335 | + | 24.6530i | 2.92564 | + | 1.06485i | ||||
\(537\) | −1.81211 | − | 4.97872i | −0.0781982 | − | 0.214848i | ||||
\(538\) | 23.0490 | + | 27.4687i | 0.993711 | + | 1.18426i | ||||
\(539\) | −12.5478 | − | 21.7333i | −0.540470 | − | 0.936122i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.19461 | − | 29.4601i | −0.223334 | − | 1.26659i | −0.865845 | − | 0.500312i | \(-0.833218\pi\) |
0.642511 | − | 0.766276i | \(-0.277893\pi\) | |||||||
\(542\) | −34.7058 | + | 6.11957i | −1.49074 | + | 0.262858i | ||||
\(543\) | −11.9376 | − | 6.89220i | −0.512293 | − | 0.295773i | ||||
\(544\) | −3.83245 | − | 6.63800i | −0.164315 | − | 0.284602i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.19313 | − | 1.16220i | 0.136653 | − | 0.0497378i | ||||
\(547\) | −10.2591 | + | 28.1867i | −0.438648 | + | 1.20518i | 0.501724 | + | 0.865028i | \(0.332699\pi\) |
−0.940372 | + | 0.340147i | \(0.889523\pi\) | |||||||
\(548\) | 11.1747 | − | 13.3175i | 0.477359 | − | 0.568894i | ||||
\(549\) | 0.897788 | − | 5.09161i | 0.0383167 | − | 0.217305i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.08675 | − | 5.32450i | −0.174101 | − | 0.226831i | ||||
\(552\) | 65.6207i | 2.79300i | ||||||||
\(553\) | −35.1703 | − | 6.20147i | −1.49559 | − | 0.263713i | ||||
\(554\) | 24.1737 | + | 20.2842i | 1.02704 | + | 0.861792i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −39.7330 | + | 14.4616i | −1.68506 | + | 0.613310i | ||||
\(557\) | 17.4418 | + | 20.7864i | 0.739034 | + | 0.880746i | 0.996331 | − | 0.0855864i | \(-0.0272764\pi\) |
−0.257297 | + | 0.966332i | \(0.582832\pi\) | |||||||
\(558\) | −11.8864 | + | 6.86264i | −0.503193 | + | 0.290519i | ||||
\(559\) | −0.471178 | + | 0.816104i | −0.0199287 | + | 0.0345175i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.360542 | − | 2.04473i | −0.0152221 | − | 0.0863287i | ||||
\(562\) | 32.5221 | + | 18.7766i | 1.37186 | + | 0.792044i | ||||
\(563\) | 34.4334 | − | 19.8801i | 1.45119 | − | 0.837847i | 0.452643 | − | 0.891692i | \(-0.350481\pi\) |
0.998549 | + | 0.0538451i | \(0.0171477\pi\) | |||||||
\(564\) | 30.5186 | − | 25.6081i | 1.28506 | − | 1.07830i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.0846 | − | 4.76241i | −0.549987 | − | 0.200179i | ||||
\(567\) | 4.87774 | − | 5.81307i | 0.204846 | − | 0.244126i | ||||
\(568\) | 38.0341 | + | 6.70644i | 1.59588 | + | 0.281396i | ||||
\(569\) | 6.66486 | 0.279405 | 0.139703 | − | 0.990194i | \(-0.455385\pi\) | ||||
0.139703 | + | 0.990194i | \(0.455385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.6502 | −1.15713 | −0.578563 | − | 0.815638i | \(-0.696386\pi\) | ||||
−0.578563 | + | 0.815638i | \(0.696386\pi\) | |||||||
\(572\) | 5.71317 | + | 1.00739i | 0.238880 | + | 0.0421209i | ||||
\(573\) | 11.7732 | − | 14.0308i | 0.491833 | − | 0.586144i | ||||
\(574\) | 69.6178 | + | 25.3388i | 2.90579 | + | 1.05762i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −15.2710 | + | 12.8139i | −0.636290 | + | 0.533911i | ||||
\(577\) | 26.0039 | − | 15.0134i | 1.08256 | − | 0.625015i | 0.150972 | − | 0.988538i | \(-0.451760\pi\) |
0.931585 | + | 0.363523i | \(0.118426\pi\) | |||||||
\(578\) | −37.5426 | − | 21.6752i | −1.56156 | − | 0.901570i | ||||
\(579\) | −0.666160 | − | 3.77798i | −0.0276847 | − | 0.157008i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.39684 | − | 2.41939i | 0.0579506 | − | 0.100373i | ||||
\(582\) | 15.9183 | − | 9.19042i | 0.659834 | − | 0.380955i | ||||
\(583\) | 23.3514 | + | 27.8291i | 0.967114 | + | 1.15256i | ||||
\(584\) | −55.8752 | + | 20.3369i | −2.31213 | + | 0.841548i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.77757 | − | 1.49156i | −0.0734309 | − | 0.0616159i | ||||
\(587\) | −13.0717 | − | 2.30489i | −0.539527 | − | 0.0951332i | −0.102757 | − | 0.994706i | \(-0.532766\pi\) |
−0.436770 | + | 0.899573i | \(0.643878\pi\) | |||||||
\(588\) | 34.7858i | 1.43454i | ||||||||
\(589\) | 9.00349 | + | 5.73419i | 0.370982 | + | 0.236273i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0268718 | + | 0.152398i | −0.00110536 | + | 0.00626880i | ||||
\(592\) | −1.05287 | + | 1.25476i | −0.0432726 | + | 0.0515702i | ||||
\(593\) | −4.26638 | + | 11.7218i | −0.175199 | + | 0.481356i | −0.995948 | − | 0.0899335i | \(-0.971335\pi\) |
0.820748 | + | 0.571290i | \(0.193557\pi\) | |||||||
\(594\) | −38.4141 | + | 13.9816i | −1.57615 | + | 0.573671i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 41.3576 | + | 71.6334i | 1.69407 | + | 2.93422i | ||||
\(597\) | −4.17164 | − | 2.40850i | −0.170734 | − | 0.0985732i | ||||
\(598\) | 8.80935 | − | 1.55333i | 0.360241 | − | 0.0635203i | ||||
\(599\) | 5.75729 | + | 32.6512i | 0.235237 | + | 1.33409i | 0.842115 | + | 0.539298i | \(0.181310\pi\) |
−0.606878 | + | 0.794795i | \(0.707578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.4753 | + | 21.6079i | 0.508879 | + | 0.881404i | 0.999947 | + | 0.0102826i | \(0.00327313\pi\) |
−0.491069 | + | 0.871121i | \(0.663394\pi\) | |||||||
\(602\) | −16.7132 | − | 19.9181i | −0.681181 | − | 0.811800i | ||||
\(603\) | 6.98667 | + | 19.1957i | 0.284519 | + | 0.781710i | ||||
\(604\) | −50.7789 | − | 18.4820i | −2.06616 | − | 0.752022i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.71646 | + | 9.73452i | −0.0697264 | + | 0.395438i | ||||
\(607\) | − | 3.04625i | − | 0.123644i | −0.998087 | − | 0.0618218i | \(-0.980309\pi\) | ||
0.998087 | − | 0.0618218i | \(-0.0196911\pi\) | |||||||
\(608\) | 45.1158 | + | 18.6806i | 1.82969 | + | 0.757599i | ||||
\(609\) | −5.47984 | −0.222054 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.45386 | − | 2.05903i | −0.0992725 | − | 0.0832995i | ||||
\(612\) | 2.43894 | − | 6.70093i | 0.0985883 | − | 0.270869i | ||||
\(613\) | 7.55293 | + | 20.7515i | 0.305060 | + | 0.838145i | 0.993601 | + | 0.112948i | \(0.0360292\pi\) |
−0.688541 | + | 0.725197i | \(0.741749\pi\) | |||||||
\(614\) | 49.9159 | − | 41.8844i | 2.01444 | − | 1.69032i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −47.2071 | + | 81.7651i | −1.90203 | + | 3.29441i | ||||
\(617\) | 44.1410 | − | 7.78325i | 1.77705 | − | 0.313342i | 0.813638 | − | 0.581371i | \(-0.197484\pi\) |
0.963411 | + | 0.268030i | \(0.0863725\pi\) | |||||||
\(618\) | −33.0462 | + | 5.82693i | −1.32931 | + | 0.234393i | ||||
\(619\) | 3.64323 | − | 6.31025i | 0.146434 | − | 0.253630i | −0.783473 | − | 0.621425i | \(-0.786554\pi\) |
0.929907 | + | 0.367795i | \(0.119887\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −34.2418 | + | 28.7323i | −1.37408 | + | 1.15299i | ||||
\(622\) | −16.5919 | − | 45.5859i | −0.665275 | − | 1.82783i | ||||
\(623\) | 16.5651 | − | 45.5122i | 0.663666 | − | 1.82341i | ||||
\(624\) | −2.59712 | − | 2.17924i | −0.103968 | − | 0.0872395i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 87.0882 | 3.48074 | ||||||||
\(627\) | 9.75329 | + | 8.93488i | 0.389509 | + | 0.356825i | ||||
\(628\) | 4.54677i | 0.181436i | ||||||||
\(629\) | 0.0194140 | − | 0.110102i | 0.000774085 | − | 0.00439006i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.7879 | + | 13.7537i | 1.50431 | + | 0.547525i | 0.957173 | − | 0.289517i | \(-0.0934945\pi\) |
0.547139 | + | 0.837042i | \(0.315717\pi\) | |||||||
\(632\) | 24.0424 | + | 66.0560i | 0.956356 | + | 2.62757i | ||||
\(633\) | −2.93522 | − | 3.49806i | −0.116664 | − | 0.139035i | ||||
\(634\) | 8.66614 | + | 15.0102i | 0.344176 | + | 0.596131i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.74421 | − | 49.5909i | −0.346731 | − | 1.96641i | ||||
\(637\) | 2.75447 | − | 0.485687i | 0.109136 | − | 0.0192436i | ||||
\(638\) | −11.4252 | − | 6.59632i | −0.452326 | − | 0.261151i | ||||
\(639\) | 5.47259 | + | 9.47881i | 0.216492 | + | 0.374976i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.9377 | − | 8.71261i | 0.945482 | − | 0.344127i | 0.177154 | − | 0.984183i | \(-0.443311\pi\) |
0.768328 | + | 0.640056i | \(0.221089\pi\) | |||||||
\(642\) | −5.43486 | + | 14.9322i | −0.214497 | + | 0.589326i | ||||
\(643\) | −27.1888 | + | 32.4023i | −1.07222 | + | 1.27782i | −0.113480 | + | 0.993540i | \(0.536200\pi\) |
−0.958741 | + | 0.284283i | \(0.908245\pi\) | |||||||
\(644\) | −30.3929 | + | 172.367i | −1.19765 | + | 6.79220i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.75361 | + | 1.02182i | −0.305062 | + | 0.0402030i | ||||
\(647\) | 1.66919i | 0.0656226i | 0.999462 | + | 0.0328113i | \(0.0104460\pi\) | ||||
−0.999462 | + | 0.0328113i | \(0.989554\pi\) | |||||||
\(648\) | −14.7097 | − | 2.59372i | −0.577853 | − | 0.101891i | ||||
\(649\) | −19.4967 | − | 16.3597i | −0.765311 | − | 0.642172i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.18922 | − | 2.98063i | 0.320961 | − | 0.116820i | ||||
\(652\) | 25.3035 | + | 30.1556i | 0.990963 | + | 1.18098i | ||||
\(653\) | −5.01760 | + | 2.89691i | −0.196354 | + | 0.113365i | −0.594954 | − | 0.803760i | \(-0.702830\pi\) |
0.398600 | + | 0.917125i | \(0.369496\pi\) | |||||||
\(654\) | 10.9703 | − | 19.0010i | 0.428971 | − | 0.743000i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12.8355 | − | 72.7935i | −0.501141 | − | 2.84211i | ||||
\(657\) | −14.5937 | − | 8.42567i | −0.569354 | − | 0.328717i | ||||
\(658\) | 76.5428 | − | 44.1920i | 2.98395 | − | 1.72278i | ||||
\(659\) | −17.0351 | + | 14.2942i | −0.663595 | + | 0.556822i | −0.911162 | − | 0.412049i | \(-0.864813\pi\) |
0.247567 | + | 0.968871i | \(0.420369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.72292 | + | 3.17488i | 0.339282 | + | 0.123489i | 0.506042 | − | 0.862509i | \(-0.331108\pi\) |
−0.166759 | + | 0.985998i | \(0.553330\pi\) | |||||||
\(662\) | −27.8140 | + | 33.1474i | −1.08102 | + | 1.28831i | ||||
\(663\) | 0.227891 | + | 0.0401833i | 0.00885056 | + | 0.00156059i | ||||
\(664\) | −5.49893 | −0.213400 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.915804 | −0.0354867 | ||||||||
\(667\) | −14.2063 | − | 2.50495i | −0.550070 | − | 0.0969922i | ||||
\(668\) | −42.7817 | + | 50.9853i | −1.65527 | + | 1.97268i | ||||
\(669\) | 7.64700 | + | 2.78328i | 0.295650 | + | 0.107608i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.05420 | + | 5.08008i | −0.233720 | + | 0.196114i | ||||
\(672\) | 34.5249 | − | 19.9329i | 1.33183 | − | 0.768930i | ||||
\(673\) | 26.7229 | + | 15.4285i | 1.03009 | + | 0.594723i | 0.917011 | − | 0.398862i | \(-0.130595\pi\) |
0.113080 | + | 0.993586i | \(0.463928\pi\) | |||||||
\(674\) | 2.71055 | + | 15.3723i | 0.104406 | + | 0.592118i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 31.3715 | − | 54.3371i | 1.20660 | − | 2.08989i | ||||
\(677\) | −35.2722 | + | 20.3644i | −1.35562 | + | 0.782669i | −0.989030 | − | 0.147713i | \(-0.952809\pi\) |
−0.366592 | + | 0.930382i | \(0.619475\pi\) | |||||||
\(678\) | 20.5805 | + | 24.5269i | 0.790389 | + | 0.941949i | ||||
\(679\) | 27.1735 | − | 9.89035i | 1.04282 | − | 0.379557i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.94122 | + | 3.30707i | 0.151028 | + | 0.126727i | ||||
\(682\) | 20.6620 | + | 3.64327i | 0.791188 | + | 0.139508i | ||||
\(683\) | − | 16.1788i | − | 0.619066i | −0.950889 | − | 0.309533i | \(-0.899827\pi\) | ||
0.950889 | − | 0.309533i | \(-0.100173\pi\) | |||||||
\(684\) | 13.6665 | + | 43.3245i | 0.522550 | + | 1.65655i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.18808 | + | 6.73793i | −0.0453611 | + | 0.257255i | ||||
\(687\) | 16.0452 | − | 19.1220i | 0.612164 | − | 0.729549i | ||||
\(688\) | −8.87262 | + | 24.3773i | −0.338265 | + | 0.929376i | ||||
\(689\) | −3.80471 | + | 1.38480i | −0.144948 | + | 0.0527567i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.33032 | − | 12.6965i | −0.278859 | − | 0.482997i | 0.692243 | − | 0.721665i | \(-0.256623\pi\) |
−0.971101 | + | 0.238667i | \(0.923289\pi\) | |||||||
\(692\) | −35.3629 | − | 20.4168i | −1.34429 | − | 0.776129i | ||||
\(693\) | −26.3505 | + | 4.64631i | −1.00097 | + | 0.176499i | ||||
\(694\) | −9.84122 | − | 55.8123i | −0.373568 | − | 2.11861i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.39312 | + | 9.34116i | 0.204426 | + | 0.354076i | ||||
\(697\) | 3.24300 | + | 3.86485i | 0.122837 | + | 0.146392i | ||||
\(698\) | −2.17210 | − | 5.96781i | −0.0822153 | − | 0.225885i | ||||
\(699\) | −2.22786 | − | 0.810873i | −0.0842652 | − | 0.0306700i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.53070 | + | 14.3523i | −0.0955833 | + | 0.542080i | 0.898984 | + | 0.437982i | \(0.144307\pi\) |
−0.994567 | + | 0.104098i | \(0.966804\pi\) | |||||||
\(702\) | − | 4.55612i | − | 0.171960i | ||||||
\(703\) | 0.328959 | + | 0.631722i | 0.0124069 | + | 0.0238258i | ||||
\(704\) | 30.4728 | 1.14848 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.3700 | + | 12.8970i | 0.578459 | + | 0.485385i | ||||
\(707\) | −5.31874 | + | 14.6131i | −0.200032 | + | 0.549583i | ||||
\(708\) | 12.0660 | + | 33.1511i | 0.453469 | + | 1.24590i | ||||
\(709\) | 9.07912 | − | 7.61829i | 0.340974 | − | 0.286111i | −0.456180 | − | 0.889888i | \(-0.650783\pi\) |
0.797153 | + | 0.603777i | \(0.206338\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.96088 | + | 17.2527i | −0.373562 | + | 0.647028i | ||||
\(712\) | −93.8849 | + | 16.5544i | −3.51848 | + | 0.620404i | ||||
\(713\) | 22.5928 | − | 3.98372i | 0.846107 | − | 0.149191i | ||||
\(714\) | −3.19245 | + | 5.52949i | −0.119474 | + | 0.206936i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.3083 | + | 17.8798i | −0.796330 | + | 0.668201i | ||||
\(717\) | −8.11070 | − | 22.2840i | −0.302900 | − | 0.832210i | ||||
\(718\) | −6.10832 | + | 16.7825i | −0.227961 | + | 0.626316i | ||||
\(719\) | −13.0707 | − | 10.9676i | −0.487455 | − | 0.409023i | 0.365658 | − | 0.930749i | \(-0.380844\pi\) |
−0.853113 | + | 0.521726i | \(0.825288\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.7915 | −1.96606 | ||||||||
\(722\) | 35.2205 | − | 35.2391i | 1.31077 | − | 1.31146i | ||||
\(723\) | − | 0.921235i | − | 0.0342611i | ||||||
\(724\) | −12.5667 | + | 71.2694i | −0.467039 | + | 2.64871i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.744226 | − | 0.270876i | −0.0276208 | − | 0.0100532i | ||||
\(727\) | 4.52829 | + | 12.4414i | 0.167945 | + | 0.461425i | 0.994903 | − | 0.100839i | \(-0.0321527\pi\) |
−0.826958 | + | 0.562264i | \(0.809930\pi\) | |||||||
\(728\) | −6.76387 | − | 8.06087i | −0.250686 | − | 0.298756i | ||||
\(729\) | 4.53091 | + | 7.84777i | 0.167812 | + | 0.290658i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.307474 | − | 1.74377i | −0.0113723 | − | 0.0644957i | ||||
\(732\) | 10.7885 | − | 1.90230i | 0.398754 | − | 0.0703111i | ||||
\(733\) | −46.3491 | − | 26.7597i | −1.71194 | − | 0.988391i | −0.931938 | − | 0.362618i | \(-0.881883\pi\) |
−0.780005 | − | 0.625773i | \(-0.784784\pi\) | |||||||
\(734\) | −18.0423 | − | 31.2503i | −0.665955 | − | 1.15347i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 98.6163 | − | 35.8934i | 3.63505 | − | 1.32305i | ||||
\(737\) | 10.6800 | − | 29.3429i | 0.393401 | − | 1.08086i | ||||
\(738\) | 26.5647 | − | 31.6586i | 0.977861 | − | 1.16537i | ||||
\(739\) | 7.32823 | − | 41.5604i | 0.269573 | − | 1.52883i | −0.486116 | − | 0.873894i | \(-0.661587\pi\) |
0.755689 | − | 0.654931i | \(-0.227302\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.30755 | + | 0.680886i | −0.0480340 | + | 0.0250130i | ||||
\(742\) | − | 111.716i | − | 4.10121i | ||||||
\(743\) | 17.8079 | + | 3.14002i | 0.653310 | + | 0.115196i | 0.490472 | − | 0.871457i | \(-0.336824\pi\) |
0.162838 | + | 0.986653i | \(0.447935\pi\) | |||||||
\(744\) | −13.1405 | − | 11.0262i | −0.481756 | − | 0.404241i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −74.6876 | + | 27.1841i | −2.73451 | + | 0.995280i | ||||
\(747\) | −1.00172 | − | 1.19380i | −0.0366510 | − | 0.0436790i | ||||
\(748\) | −9.44016 | + | 5.45028i | −0.345167 | + | 0.199282i | ||||
\(749\) | −12.4998 | + | 21.6502i | −0.456731 | + | 0.791081i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.514525 | + | 2.91802i | 0.0187753 | + | 0.106480i | 0.992755 | − | 0.120154i | \(-0.0383389\pi\) |
−0.973980 | + | 0.226634i | \(0.927228\pi\) | |||||||
\(752\) | −76.3680 | − | 44.0911i | −2.78485 | − | 1.60784i | ||||
\(753\) | −11.6924 | + | 6.75062i | −0.426096 | + | 0.246006i | ||||
\(754\) | 1.12636 | − | 0.945126i | 0.0410195 | − | 0.0344194i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 83.7703 | + | 30.4899i | 3.04670 | + | 1.10891i | ||||
\(757\) | −3.06821 | + | 3.65655i | −0.111516 | + | 0.132900i | −0.818915 | − | 0.573915i | \(-0.805424\pi\) |
0.707399 | + | 0.706814i | \(0.249868\pi\) | |||||||
\(758\) | 8.87983 | + | 1.56575i | 0.322530 | + | 0.0568707i | ||||
\(759\) | 28.4277 | 1.03186 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.1552 | 1.12938 | 0.564688 | − | 0.825305i | \(-0.308997\pi\) | ||||
0.564688 | + | 0.825305i | \(0.308997\pi\) | |||||||
\(762\) | 21.0367 | + | 3.70935i | 0.762081 | + | 0.134375i | ||||
\(763\) | 22.1875 | − | 26.4421i | 0.803242 | − | 0.957267i | ||||
\(764\) | −90.3602 | − | 32.8884i | −3.26912 | − | 1.18986i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36.8245 | − | 30.8994i | 1.33052 | − | 1.11644i | ||||
\(767\) | 2.45656 | − | 1.41830i | 0.0887013 | − | 0.0512117i | ||||
\(768\) | 10.6756 | + | 6.16355i | 0.385222 | + | 0.222408i | ||||
\(769\) | 8.40236 | + | 47.6522i | 0.302997 | + | 1.71838i | 0.632786 | + | 0.774327i | \(0.281911\pi\) |
−0.329789 | + | 0.944055i | \(0.606978\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.97250 | + | 13.8088i | −0.287123 | + | 0.497311i | ||||
\(772\) | −17.4423 | + | 10.0703i | −0.627761 | + | 0.362438i | ||||
\(773\) | 30.1312 | + | 35.9089i | 1.08374 | + | 1.29155i | 0.953934 | + | 0.300015i | \(0.0969917\pi\) |
0.129808 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(774\) | −13.6296 | + | 4.96076i | −0.489905 | + | 0.178311i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −43.6030 | − | 36.5873i | −1.56526 | − | 1.31341i | ||||
\(777\) | 0.572651 | + | 0.100974i | 0.0205437 | + | 0.00362241i | ||||
\(778\) | − | 10.9227i | − | 0.391599i | ||||||
\(779\) | −31.3802 | − | 6.95249i | −1.12431 | − | 0.249099i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.90531 | − | 16.4768i | 0.103960 | − | 0.589588i | ||||
\(782\) | −10.8040 | + | 12.8757i | −0.386349 | + | 0.460433i | ||||
\(783\) | −2.51295 | + | 6.90427i | −0.0898054 | + | 0.246738i | ||||
\(784\) | 72.3532 | − | 26.3344i | 2.58404 | − | 0.940515i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.6556 | + | 21.9202i | 0.451412 | + | 0.781868i | ||||
\(787\) | 43.9042 | + | 25.3481i | 1.56502 | + | 0.903563i | 0.996736 | + | 0.0807272i | \(0.0257243\pi\) |
0.568280 | + | 0.822835i | \(0.307609\pi\) | |||||||
\(788\) | 0.800096 | − | 0.141079i | 0.0285022 | − | 0.00502571i | ||||
\(789\) | 0.202258 | + | 1.14706i | 0.00720057 | + | 0.0408365i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.1856 | + | 43.6228i | 0.895497 | + | 1.55105i | ||||
\(792\) | 33.8538 | + | 40.3454i | 1.20294 | + | 1.43361i | ||||
\(793\) | −0.301263 | − | 0.827713i | −0.0106982 | − | 0.0293929i | ||||
\(794\) | −49.0400 | − | 17.8491i | −1.74036 | − | 0.633441i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.39147 | + | 24.9053i | −0.155652 | + | 0.882744i | ||||
\(797\) | − | 11.3007i | − | 0.400291i | −0.979766 | − | 0.200146i | \(-0.935858\pi\) | ||
0.979766 | − | 0.200146i | \(-0.0641415\pi\) | |||||||
\(798\) | −5.31459 | − | 40.3272i | −0.188134 | − | 1.42757i | ||||
\(799\) | 6.01892 | 0.212934 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.6966 | − | 17.3665i | −0.731279 | − | 0.613616i | ||||
\(802\) | −8.50129 | + | 23.3571i | −0.300191 | + | 0.824768i | ||||
\(803\) | 8.81020 | + | 24.2058i | 0.310905 | + | 0.854205i | ||||
\(804\) | −33.1572 | + | 27.8222i | −1.16936 | + | 0.981213i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.16918 | + | 2.02508i | −0.0411826 | + | 0.0713303i | ||||
\(807\) | −12.5076 | + | 2.20543i | −0.440289 | + | 0.0776348i | ||||
\(808\) | 30.1447 | − | 5.31533i | 1.06049 | − | 0.186993i | ||||
\(809\) | −2.98372 | + | 5.16796i | −0.104902 | + | 0.181696i | −0.913698 | − | 0.406393i | \(-0.866786\pi\) |
0.808796 | + | 0.588089i | \(0.200120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.0275 | + | 15.1268i | −0.633030 | + | 0.531175i | −0.901869 | − | 0.432010i | \(-0.857804\pi\) |
0.268839 | + | 0.963185i | \(0.413360\pi\) | |||||||
\(812\) | 9.83973 | + | 27.0344i | 0.345307 | + | 0.948723i | ||||
\(813\) | 4.26915 | − | 11.7294i | 0.149726 | − | 0.411368i | ||||
\(814\) | 1.07240 | + | 0.899848i | 0.0375875 | + | 0.0315397i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.37032 | 0.223006 | ||||||||
\(817\) | 8.31772 | + | 7.61977i | 0.291000 | + | 0.266582i | ||||
\(818\) | 61.0282i | 2.13380i | ||||||||
\(819\) | 0.517844 | − | 2.93684i | 0.0180949 | − | 0.102621i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.1921 | − | 10.2611i | −0.983911 | − | 0.358114i | −0.200551 | − | 0.979683i | \(-0.564273\pi\) |
−0.783359 | + | 0.621569i | \(0.786496\pi\) | |||||||
\(822\) | 2.96980 | + | 8.15947i | 0.103584 | + | 0.284594i | ||||
\(823\) | −5.40876 | − | 6.44591i | −0.188538 | − | 0.224690i | 0.663493 | − | 0.748183i | \(-0.269073\pi\) |
−0.852030 | + | 0.523492i | \(0.824629\pi\) | |||||||
\(824\) | 51.9561 | + | 89.9905i | 1.80997 | + | 3.13497i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.5908 | + | 77.0774i | 0.472885 | + | 2.68187i | ||||
\(827\) | −27.2794 | + | 4.81009i | −0.948597 | + | 0.167263i | −0.626481 | − | 0.779437i | \(-0.715505\pi\) |
−0.322116 | + | 0.946700i | \(0.604394\pi\) | |||||||
\(828\) | 84.5544 | + | 48.8175i | 2.93847 | + | 1.69653i | ||||
\(829\) | 24.1279 | + | 41.7908i | 0.837998 | + | 1.45145i | 0.891566 | + | 0.452890i | \(0.149607\pi\) |
−0.0535685 | + | 0.998564i | \(0.517060\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.5030 | + | 3.82279i | −0.364346 | + | 0.132611i | ||||
\(832\) | −1.16159 | + | 3.19145i | −0.0402710 | + | 0.110644i | ||||
\(833\) | −3.37814 | + | 4.02591i | −0.117046 | + | 0.139489i | ||||
\(834\) | 3.66728 | − | 20.7982i | 0.126988 | − | 0.720182i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 26.5664 | − | 64.1610i | 0.918819 | − | 2.21905i | ||||
\(837\) | − | 11.6848i | − | 0.403885i | ||||||
\(838\) | −7.88397 | − | 1.39016i | −0.272347 | − | 0.0480222i | ||||
\(839\) | 14.9006 | + | 12.5031i | 0.514425 | + | 0.431653i | 0.862683 | − | 0.505745i | \(-0.168782\pi\) |
−0.348258 | + | 0.937399i | \(0.613227\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0229 | − | 9.10760i | 0.862860 | − | 0.314055i | ||||
\(842\) | 47.2635 | + | 56.3264i | 1.62881 | + | 1.94114i | ||||
\(843\) | −11.5191 | + | 6.65054i | −0.396738 | + | 0.229057i | ||||
\(844\) | −11.9869 | + | 20.7619i | −0.412606 | + | 0.714654i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.56145 | − | 48.5544i | −0.294349 | − | 1.66934i | ||||
\(847\) | −1.07906 | − | 0.622993i | −0.0370768 | − | 0.0214063i | ||||
\(848\) | −96.5275 | + | 55.7302i | −3.31477 | + | 1.91378i | ||||
\(849\) | 3.77805 | − | 3.17016i | 0.129662 | − | 0.108800i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.43842 | + | 0.523542i | 0.0493084 | + | 0.0179468i | ||||
\(852\) | −14.9072 | + | 17.7657i | −0.510712 | + | 0.608643i | ||||
\(853\) | −35.5818 | − | 6.27404i | −1.21830 | − | 0.214819i | −0.472706 | − | 0.881220i | \(-0.656723\pi\) |
−0.745593 | + | 0.666401i | \(0.767834\pi\) | |||||||
\(854\) | 24.3037 | 0.831655 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 49.2078 | 1.68189 | ||||||||
\(857\) | 46.1479 | + | 8.13712i | 1.57638 | + | 0.277959i | 0.892299 | − | 0.451446i | \(-0.149092\pi\) |
0.684083 | + | 0.729404i | \(0.260203\pi\) | |||||||
\(858\) | −1.86252 | + | 2.21967i | −0.0635854 | + | 0.0757782i | ||||
\(859\) | 13.1861 | + | 4.79933i | 0.449903 | + | 0.163751i | 0.557027 | − | 0.830494i | \(-0.311942\pi\) |
−0.107124 | + | 0.994246i | \(0.534164\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.1015 | + | 16.8671i | −0.685056 | + | 0.574830i | ||||
\(862\) | 68.6163 | − | 39.6156i | 2.33708 | − | 1.34931i | ||||
\(863\) | −35.1649 | − | 20.3025i | −1.19703 | − | 0.691105i | −0.237137 | − | 0.971476i | \(-0.576209\pi\) |
−0.959892 | + | 0.280371i | \(0.909542\pi\) | |||||||
\(864\) | −9.28187 | − | 52.6401i | −0.315776 | − | 1.79085i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.7160 | + | 34.1491i | −0.669976 | + | 1.16043i | ||||
\(867\) | 13.2973 | − | 7.67719i | 0.451600 | − | 0.260731i | ||||
\(868\) | −29.4095 | − | 35.0489i | −0.998225 | − | 1.18964i | ||||
\(869\) | 28.6162 | − | 10.4155i | 0.970740 | − | 0.353320i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.66601 | + | 2.23705i | 0.0903344 | + | 0.0757996i | ||||
\(872\) | −66.9106 | − | 11.7981i | −2.26588 | − | 0.399536i | ||||
\(873\) | − | 16.1311i | − | 0.545954i | ||||||
\(874\) | 4.65655 | − | 106.976i | 0.157510 | − | 3.61853i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.20026 | − | 35.1634i | 0.209487 | − | 1.18806i | ||||
\(877\) | −17.2321 | + | 20.5365i | −0.581888 | + | 0.693467i | −0.974025 | − | 0.226439i | \(-0.927291\pi\) |
0.392137 | + | 0.919907i | \(0.371736\pi\) | |||||||
\(878\) | 34.6514 | − | 95.2040i | 1.16943 | − | 3.21298i | ||||
\(879\) | 0.772323 | − | 0.281103i | 0.0260498 | − | 0.00948135i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.1410 | − | 43.5454i | −0.847021 | − | 1.46708i | −0.883855 | − | 0.467761i | \(-0.845061\pi\) |
0.0368343 | − | 0.999321i | \(-0.488273\pi\) | |||||||
\(882\) | 37.2820 | + | 21.5248i | 1.25535 | + | 0.724777i | ||||
\(883\) | 10.9144 | − | 1.92450i | 0.367298 | − | 0.0647645i | 0.0130467 | − | 0.999915i | \(-0.495847\pi\) |
0.354251 | + | 0.935150i | \(0.384736\pi\) | |||||||
\(884\) | −0.210965 | − | 1.19644i | −0.00709551 | − | 0.0402406i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.75313 | − | 9.96471i | −0.193280 | − | 0.334771i | ||||
\(887\) | 6.37238 | + | 7.59431i | 0.213964 | + | 0.254992i | 0.862342 | − | 0.506326i | \(-0.168997\pi\) |
−0.648378 | + | 0.761318i | \(0.724552\pi\) | |||||||
\(888\) | −0.391464 | − | 1.07554i | −0.0131367 | − | 0.0360927i | ||||
\(889\) | 31.5797 | + | 11.4941i | 1.05915 | + | 0.385498i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.12363 | + | 6.37244i | −0.0376431 | + | 0.213485i | ||||
\(892\) | − | 42.7237i | − | 1.43050i | ||||||
\(893\) | −30.4175 | + | 23.3466i | −1.01788 | + | 0.781263i | ||||
\(894\) | −41.3136 | −1.38173 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.02329 | − | 5.05414i | −0.201224 | − | 0.168847i | ||||
\(897\) | −1.08364 | + | 2.97727i | −0.0361816 | + | 0.0994080i | ||||
\(898\) | −22.2360 | − | 61.0929i | −0.742025 | − | 2.03870i | ||||
\(899\) | 2.88870 | − | 2.42390i | 0.0963434 | − | 0.0808417i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.80390 | − | 6.58854i | 0.126726 | − | 0.219496i | ||||
\(902\) | −62.2141 | + | 10.9700i | −2.07150 | + | 0.365262i | ||||
\(903\) | 9.06951 | − | 1.59920i | 0.301814 | − | 0.0532180i | ||||
\(904\) | 49.5741 | − | 85.8649i | 1.64881 | − | 2.85582i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 20.6757 | − | 17.3489i | 0.686903 | − | 0.576380i | ||||
\(907\) | −6.23529 | − | 17.1313i | −0.207039 | − | 0.568836i | 0.792097 | − | 0.610396i | \(-0.208990\pi\) |
−0.999136 | + | 0.0415596i | \(0.986767\pi\) | |||||||
\(908\) | 9.23830 | − | 25.3820i | 0.306584 | − | 0.842332i | ||||
\(909\) | 6.64530 | + | 5.57607i | 0.220411 | + | 0.184947i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.7792 | 0.721576 | 0.360788 | − | 0.932648i | \(-0.382508\pi\) | ||||
0.360788 | + | 0.932648i | \(0.382508\pi\) | |||||||
\(912\) | −32.1934 | + | 24.7096i | −1.06603 | + | 0.818217i | ||||
\(913\) | 2.38220i | 0.0788394i | ||||||||
\(914\) | 9.61916 | − | 54.5530i | 0.318174 | − | 1.80445i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −123.148 | − | 44.8223i | −4.06893 | − | 1.48097i | ||||
\(917\) | 13.6195 | + | 37.4192i | 0.449755 | + | 1.23569i | ||||
\(918\) | 5.50283 | + | 6.55801i | 0.181620 | + | 0.216447i | ||||
\(919\) | −13.1150 | − | 22.7158i | −0.432623 | − | 0.749325i | 0.564475 | − | 0.825450i | \(-0.309079\pi\) |
−0.997098 | + | 0.0761249i | \(0.975745\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.00769 | + | 22.7287i | 0.132058 | + | 0.748937i | ||||
\(922\) | 28.8183 | − | 5.08144i | 0.949079 | − | 0.167348i | ||||
\(923\) | 1.61489 | + | 0.932359i | 0.0531549 | + | 0.0306890i | ||||
\(924\) | −28.3474 | − | 49.0991i | −0.932561 | − | 1.61524i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.96592 | − | 3.62730i | 0.327500 | − | 0.119200i | ||||
\(927\) | −10.0721 | + | 27.6728i | −0.330810 | + | 0.908894i | ||||
\(928\) | 11.0882 | − | 13.2144i | 0.363987 | − | 0.433783i | ||||
\(929\) | 1.81278 | − | 10.2808i | 0.0594754 | − | 0.337302i | −0.940522 | − | 0.339734i | \(-0.889663\pi\) |
0.999997 | + | 0.00243204i | \(0.000774142\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.45599 | − | 33.4489i | 0.0477182 | − | 1.09624i | ||||
\(932\) | 12.4470i | 0.407715i | ||||||||
\(933\) | 16.9214 | + | 2.98369i | 0.553981 | + | 0.0976818i | ||||
\(934\) | −42.4282 | − | 35.6014i | −1.38829 | − | 1.16491i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.51591 | + | 2.00763i | −0.180293 | + | 0.0656213i | ||||
\(937\) | 13.6398 | + | 16.2552i | 0.445591 | + | 0.531035i | 0.941353 | − | 0.337424i | \(-0.109555\pi\) |
−0.495762 | + | 0.868459i | \(0.665111\pi\) | |||||||
\(938\) | −83.1606 | + | 48.0128i | −2.71529 | + | 1.56767i | ||||
\(939\) | −15.4230 | + | 26.7134i | −0.503310 | + | 0.871759i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.76643 | + | 49.7169i | 0.285778 | + | 1.62072i | 0.702495 | + | 0.711689i | \(0.252069\pi\) |
−0.416717 | + | 0.909036i | \(0.636820\pi\) | |||||||
\(942\) | −1.96672 | − | 1.13549i | −0.0640791 | − | 0.0369961i | ||||
\(943\) | −59.8227 | + | 34.5386i | −1.94809 | + | 1.12473i | ||||
\(944\) | 59.8186 | − | 50.1938i | 1.94693 | − | 1.63367i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.8344 | + | 7.58312i | 0.677386 | + | 0.246548i | ||||
\(947\) | −7.70259 | + | 9.17959i | −0.250301 | + | 0.298297i | −0.876535 | − | 0.481338i | \(-0.840151\pi\) |
0.626234 | + | 0.779635i | \(0.284595\pi\) | |||||||
\(948\) | −41.5704 | − | 7.32998i | −1.35014 | − | 0.238067i | ||||
\(949\) | −2.87094 | −0.0931948 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.13896 | −0.199069 | ||||||||
\(952\) | 19.4716 | + | 3.43338i | 0.631079 | + | 0.111276i | ||||
\(953\) | 21.9823 | − | 26.1975i | 0.712077 | − | 0.848620i | −0.281759 | − | 0.959485i | \(-0.590918\pi\) |
0.993835 | + | 0.110865i | \(0.0353622\pi\) | |||||||
\(954\) | −58.5602 | − | 21.3142i | −1.89596 | − | 0.690072i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −95.3728 | + | 80.0273i | −3.08458 | + | 2.58827i | ||||
\(957\) | 4.04670 | − | 2.33636i | 0.130811 | − | 0.0755239i | ||||
\(958\) | 77.6828 | + | 44.8502i | 2.50982 | + | 1.44904i | ||||
\(959\) | 2.37214 | + | 13.4531i | 0.0766005 | + | 0.434423i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.5015 | − | 21.6532i | 0.403274 | − | 0.698490i | ||||
\(962\) | −0.135121 | + | 0.0780122i | −0.00435648 | + | 0.00251521i | ||||
\(963\) | 8.96401 | + | 10.6829i | 0.288861 | + | 0.344251i | ||||
\(964\) | −4.54486 | + | 1.65419i | −0.146380 | + | 0.0532780i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −66.9675 | − | 56.1924i | −2.15464 | − | 1.80796i | ||||
\(967\) | −12.0223 | − | 2.11985i | −0.386610 | − | 0.0681698i | −0.0230349 | − | 0.999735i | \(-0.507333\pi\) |
−0.363575 | + | 0.931565i | \(0.618444\pi\) | |||||||
\(968\) | 2.45254i | 0.0788276i | ||||||||
\(969\) | 1.05970 | − | 2.55930i | 0.0340425 | − | 0.0822165i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.56830 | + | 14.5656i | −0.0824207 | + | 0.467431i | 0.915463 | + | 0.402403i | \(0.131825\pi\) |
−0.997883 | + | 0.0650281i | \(0.979286\pi\) | |||||||
\(972\) | 50.6312 | − | 60.3399i | 1.62400 | − | 1.93540i | ||||
\(973\) | 11.3637 | − | 31.2215i | 0.364304 | − | 1.00092i | ||||
\(974\) | 4.37822 | − | 1.59354i | 0.140287 | − | 0.0510604i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.1241 | − | 20.9995i | −0.388083 | − | 0.672179i | ||||
\(977\) | −11.6876 | − | 6.74782i | −0.373919 | − | 0.215882i | 0.301250 | − | 0.953545i | \(-0.402596\pi\) |
−0.675169 | + | 0.737663i | \(0.735929\pi\) | |||||||
\(978\) | −19.3630 | + | 3.41423i | −0.619162 | + | 0.109175i | ||||
\(979\) | 7.17158 | + | 40.6720i | 0.229205 | + | 1.29988i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.62753 | − | 16.6754i | −0.307383 | − | 0.532403i | ||||
\(982\) | −34.8390 | − | 41.5195i | −1.11176 | − | 1.32494i | ||||
\(983\) | 16.4163 | + | 45.1035i | 0.523600 | + | 1.43858i | 0.866486 | + | 0.499202i | \(0.166373\pi\) |
−0.342886 | + | 0.939377i | \(0.611404\pi\) | |||||||
\(984\) | 48.5358 | + | 17.6656i | 1.54726 | + | 0.563158i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.479751 | + | 2.72080i | −0.0152784 | + | 0.0866480i | ||||
\(987\) | 31.3050i | 0.996448i | ||||||||
\(988\) | 5.70697 | + | 5.22809i | 0.181563 | + | 0.166328i | ||||
\(989\) | 24.2434 | 0.770896 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.3075 | + | 34.6611i | 1.31217 | + | 1.10105i | 0.987902 | + | 0.155081i | \(0.0495640\pi\) |
0.324273 | + | 0.945964i | \(0.394880\pi\) | |||||||
\(992\) | −9.38282 | + | 25.7791i | −0.297905 | + | 0.818486i | ||||
\(993\) | −5.24187 | − | 14.4019i | −0.166346 | − | 0.457031i | ||||
\(994\) | −39.4136 | + | 33.0719i | −1.25012 | + | 1.04898i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.65103 | − | 2.85966i | 0.0523148 | − | 0.0906119i | ||||
\(997\) | −33.0855 | + | 5.83386i | −1.04783 | + | 0.184760i | −0.670950 | − | 0.741503i | \(-0.734113\pi\) |
−0.376878 | + | 0.926263i | \(0.623002\pi\) | |||||||
\(998\) | −110.108 | + | 19.4150i | −3.48541 | + | 0.614572i | ||||
\(999\) | 0.389827 | − | 0.675201i | 0.0123336 | − | 0.0213624i |
(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 | 475.2.u.c.74.6 | 36 | ||
5.2 | odd | 4 | 475.2.l.b.226.1 | 18 | |||
5.3 | odd | 4 | 95.2.k.b.36.3 | ✓ | 18 | ||
5.4 | even | 2 | inner | 475.2.u.c.74.1 | 36 | ||
15.8 | even | 4 | 855.2.bs.b.226.1 | 18 | |||
19.9 | even | 9 | inner | 475.2.u.c.199.1 | 36 | ||
95.3 | even | 36 | 1805.2.a.u.1.1 | 9 | |||
95.9 | even | 18 | inner | 475.2.u.c.199.6 | 36 | ||
95.22 | even | 36 | 9025.2.a.cd.1.9 | 9 | |||
95.28 | odd | 36 | 95.2.k.b.66.3 | yes | 18 | ||
95.47 | odd | 36 | 475.2.l.b.351.1 | 18 | |||
95.73 | odd | 36 | 1805.2.a.t.1.9 | 9 | |||
95.92 | odd | 36 | 9025.2.a.ce.1.1 | 9 | |||
285.218 | even | 36 | 855.2.bs.b.541.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.b.36.3 | ✓ | 18 | 5.3 | odd | 4 | ||
95.2.k.b.66.3 | yes | 18 | 95.28 | odd | 36 | ||
475.2.l.b.226.1 | 18 | 5.2 | odd | 4 | |||
475.2.l.b.351.1 | 18 | 95.47 | odd | 36 | |||
475.2.u.c.74.1 | 36 | 5.4 | even | 2 | inner | ||
475.2.u.c.74.6 | 36 | 1.1 | even | 1 | trivial | ||
475.2.u.c.199.1 | 36 | 19.9 | even | 9 | inner | ||
475.2.u.c.199.6 | 36 | 95.9 | even | 18 | inner | ||
855.2.bs.b.226.1 | 18 | 15.8 | even | 4 | |||
855.2.bs.b.541.1 | 18 | 285.218 | even | 36 | |||
1805.2.a.t.1.9 | 9 | 95.73 | odd | 36 | |||
1805.2.a.u.1.1 | 9 | 95.3 | even | 36 | |||
9025.2.a.cd.1.9 | 9 | 95.22 | even | 36 | |||
9025.2.a.ce.1.1 | 9 | 95.92 | odd | 36 |