Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.324000000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 511.1 | ||
Root | \(1.40126 + 1.01807i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.511 |
Dual form | 605.2.g.h.251.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.535233 | − | 1.64728i | −0.378467 | − | 1.16480i | −0.941110 | − | 0.338101i | \(-0.890215\pi\) |
0.562643 | − | 0.826700i | \(-0.309785\pi\) | |||||||
\(3\) | −1.61803 | − | 1.17557i | −0.934172 | − | 0.678716i | 0.0128385 | − | 0.999918i | \(-0.495913\pi\) |
−0.947011 | + | 0.321202i | \(0.895913\pi\) | |||||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | 0.309017 | − | 0.951057i | 0.138197 | − | 0.425325i | ||||
\(6\) | −1.07047 | + | 3.29456i | −0.437016 | + | 1.34500i | ||||
\(7\) | 2.80252 | − | 2.03615i | 1.05925 | − | 0.769592i | 0.0853021 | − | 0.996355i | \(-0.472814\pi\) |
0.973950 | + | 0.226764i | \(0.0728145\pi\) | |||||||
\(8\) | −1.40126 | − | 1.01807i | −0.495420 | − | 0.359943i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | −1.73205 | −0.547723 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(14\) | −4.85410 | − | 3.52671i | −1.29731 | − | 0.942553i | ||||
\(15\) | −1.61803 | + | 1.17557i | −0.417775 | + | 0.303531i | ||||
\(16\) | −1.54508 | + | 4.75528i | −0.386271 | + | 1.18882i | ||||
\(17\) | 2.14093 | − | 6.58911i | 0.519252 | − | 1.59809i | −0.256157 | − | 0.966635i | \(-0.582456\pi\) |
0.775409 | − | 0.631459i | \(-0.217544\pi\) | |||||||
\(18\) | 1.40126 | − | 1.01807i | 0.330280 | − | 0.239962i | ||||
\(19\) | −5.60503 | − | 4.07230i | −1.28588 | − | 0.934249i | −0.286169 | − | 0.958179i | \(-0.592382\pi\) |
−0.999714 | + | 0.0239303i | \(0.992382\pi\) | |||||||
\(20\) | 0.309017 | + | 0.951057i | 0.0690983 | + | 0.212663i | ||||
\(21\) | −6.92820 | −1.51186 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | 1.07047 | + | 3.29456i | 0.218508 | + | 0.672499i | ||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.23607 | + | 3.80423i | −0.237881 | + | 0.732124i | ||||
\(28\) | −1.07047 | + | 3.29456i | −0.202299 | + | 0.622613i | ||||
\(29\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(30\) | 2.80252 | + | 2.03615i | 0.511667 | + | 0.371748i | ||||
\(31\) | 1.23607 | + | 3.80423i | 0.222004 | + | 0.683259i | 0.998582 | + | 0.0532375i | \(0.0169540\pi\) |
−0.776578 | + | 0.630022i | \(0.783046\pi\) | |||||||
\(32\) | 5.19615 | 0.918559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.0000 | −2.05798 | ||||||||
\(35\) | −1.07047 | − | 3.29456i | −0.180942 | − | 0.556882i | ||||
\(36\) | −0.809017 | − | 0.587785i | −0.134836 | − | 0.0979642i | ||||
\(37\) | −8.09017 | + | 5.87785i | −1.33002 | + | 0.966313i | −0.330267 | + | 0.943887i | \(0.607139\pi\) |
−0.999749 | + | 0.0224255i | \(0.992861\pi\) | |||||||
\(38\) | −3.70820 | + | 11.4127i | −0.601550 | + | 1.85138i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.40126 | + | 1.01807i | −0.221558 | + | 0.160972i | ||||
\(41\) | 5.60503 | + | 4.07230i | 0.875359 | + | 0.635986i | 0.932020 | − | 0.362408i | \(-0.118045\pi\) |
−0.0566604 | + | 0.998394i | \(0.518045\pi\) | |||||||
\(42\) | 3.70820 | + | 11.4127i | 0.572188 | + | 1.76101i | ||||
\(43\) | 3.46410 | 0.528271 | 0.264135 | − | 0.964486i | \(-0.414913\pi\) | ||||
0.264135 | + | 0.964486i | \(0.414913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −3.21140 | − | 9.88367i | −0.473495 | − | 1.45727i | ||||
\(47\) | 4.85410 | + | 3.52671i | 0.708044 | + | 0.514424i | 0.882542 | − | 0.470234i | \(-0.155830\pi\) |
−0.174498 | + | 0.984657i | \(0.555830\pi\) | |||||||
\(48\) | 8.09017 | − | 5.87785i | 1.16772 | − | 0.848395i | ||||
\(49\) | 1.54508 | − | 4.75528i | 0.220726 | − | 0.679326i | ||||
\(50\) | −0.535233 | + | 1.64728i | −0.0756934 | + | 0.232960i | ||||
\(51\) | −11.2101 | + | 8.14459i | −1.56972 | + | 1.14047i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.85410 | − | 5.70634i | −0.254680 | − | 0.783826i | −0.993892 | − | 0.110353i | \(-0.964802\pi\) |
0.739212 | − | 0.673473i | \(-0.235198\pi\) | |||||||
\(54\) | 6.92820 | 0.942809 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.00000 | −0.801784 | ||||||||
\(57\) | 4.28187 | + | 13.1782i | 0.567147 | + | 1.74550i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(60\) | 0.618034 | − | 1.90211i | 0.0797878 | − | 0.245562i | ||||
\(61\) | −2.14093 | + | 6.58911i | −0.274118 | + | 0.843649i | 0.715333 | + | 0.698784i | \(0.246275\pi\) |
−0.989451 | + | 0.144866i | \(0.953725\pi\) | |||||||
\(62\) | 5.60503 | − | 4.07230i | 0.711840 | − | 0.517182i | ||||
\(63\) | 2.80252 | + | 2.03615i | 0.353084 | + | 0.256531i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0000 | 1.22169 | 0.610847 | − | 0.791748i | \(-0.290829\pi\) | ||||
0.610847 | + | 0.791748i | \(0.290829\pi\) | |||||||
\(68\) | 2.14093 | + | 6.58911i | 0.259626 | + | 0.799047i | ||||
\(69\) | −9.70820 | − | 7.05342i | −1.16873 | − | 0.849132i | ||||
\(70\) | −4.85410 | + | 3.52671i | −0.580176 | + | 0.421523i | ||||
\(71\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(72\) | 0.535233 | − | 1.64728i | 0.0630778 | − | 0.194134i | ||||
\(73\) | −5.60503 | + | 4.07230i | −0.656020 | + | 0.476626i | −0.865316 | − | 0.501226i | \(-0.832883\pi\) |
0.209297 | + | 0.977852i | \(0.432883\pi\) | |||||||
\(74\) | 14.0126 | + | 10.1807i | 1.62893 | + | 1.18349i | ||||
\(75\) | 0.618034 | + | 1.90211i | 0.0713644 | + | 0.219637i | ||||
\(76\) | 6.92820 | 0.794719 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.14093 | + | 6.58911i | 0.240874 | + | 0.741333i | 0.996288 | + | 0.0860853i | \(0.0274358\pi\) |
−0.755414 | + | 0.655248i | \(0.772564\pi\) | |||||||
\(80\) | 4.04508 | + | 2.93893i | 0.452254 | + | 0.328582i | ||||
\(81\) | 8.89919 | − | 6.46564i | 0.988799 | − | 0.718404i | ||||
\(82\) | 3.70820 | − | 11.4127i | 0.409503 | − | 1.26032i | ||||
\(83\) | 5.35233 | − | 16.4728i | 0.587495 | − | 1.80812i | −0.00151786 | − | 0.999999i | \(-0.500483\pi\) |
0.589013 | − | 0.808124i | \(-0.299517\pi\) | |||||||
\(84\) | 5.60503 | − | 4.07230i | 0.611559 | − | 0.444324i | ||||
\(85\) | −5.60503 | − | 4.07230i | −0.607951 | − | 0.441702i | ||||
\(86\) | −1.85410 | − | 5.70634i | −0.199933 | − | 0.615330i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | −0.535233 | − | 1.64728i | −0.0564185 | − | 0.173638i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.85410 | + | 3.52671i | −0.506075 | + | 0.367685i | ||||
\(93\) | 2.47214 | − | 7.60845i | 0.256349 | − | 0.788960i | ||||
\(94\) | 3.21140 | − | 9.88367i | 0.331230 | − | 1.01942i | ||||
\(95\) | −5.60503 | + | 4.07230i | −0.575064 | + | 0.417809i | ||||
\(96\) | −8.40755 | − | 6.10844i | −0.858092 | − | 0.623440i | ||||
\(97\) | −3.09017 | − | 9.51057i | −0.313759 | − | 0.965652i | −0.976262 | − | 0.216592i | \(-0.930506\pi\) |
0.662503 | − | 0.749059i | \(-0.269494\pi\) | |||||||
\(98\) | −8.66025 | −0.874818 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −4.28187 | − | 13.1782i | −0.426061 | − | 1.31128i | −0.901974 | − | 0.431790i | \(-0.857882\pi\) |
0.475913 | − | 0.879493i | \(-0.342118\pi\) | |||||||
\(102\) | 19.4164 | + | 14.1068i | 1.92251 | + | 1.39679i | ||||
\(103\) | −1.61803 | + | 1.17557i | −0.159430 | + | 0.115832i | −0.664640 | − | 0.747164i | \(-0.731415\pi\) |
0.505210 | + | 0.862996i | \(0.331415\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.14093 | + | 6.58911i | −0.208934 | + | 0.643032i | ||||
\(106\) | −8.40755 | + | 6.10844i | −0.816614 | + | 0.593304i | ||||
\(107\) | −2.80252 | − | 2.03615i | −0.270930 | − | 0.196842i | 0.444022 | − | 0.896016i | \(-0.353551\pi\) |
−0.714951 | + | 0.699174i | \(0.753551\pi\) | |||||||
\(108\) | −1.23607 | − | 3.80423i | −0.118941 | − | 0.366062i | ||||
\(109\) | −6.92820 | −0.663602 | −0.331801 | − | 0.943349i | \(-0.607656\pi\) | ||||
−0.331801 | + | 0.943349i | \(0.607656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 20.0000 | 1.89832 | ||||||||
\(112\) | 5.35233 | + | 16.4728i | 0.505748 | + | 1.55653i | ||||
\(113\) | −4.85410 | − | 3.52671i | −0.456636 | − | 0.331765i | 0.335575 | − | 0.942014i | \(-0.391070\pi\) |
−0.792210 | + | 0.610249i | \(0.791070\pi\) | |||||||
\(114\) | 19.4164 | − | 14.1068i | 1.81851 | − | 1.32123i | ||||
\(115\) | 1.85410 | − | 5.70634i | 0.172896 | − | 0.532119i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.41641 | − | 22.8254i | −0.679861 | − | 2.09240i | ||||
\(120\) | 3.46410 | 0.316228 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 12.0000 | 1.08643 | ||||||||
\(123\) | −4.28187 | − | 13.1782i | −0.386083 | − | 1.18824i | ||||
\(124\) | −3.23607 | − | 2.35114i | −0.290607 | − | 0.211139i | ||||
\(125\) | −0.809017 | + | 0.587785i | −0.0723607 | + | 0.0525731i | ||||
\(126\) | 1.85410 | − | 5.70634i | 0.165177 | − | 0.508361i | ||||
\(127\) | −3.21140 | + | 9.88367i | −0.284966 | + | 0.877034i | 0.701443 | + | 0.712725i | \(0.252539\pi\) |
−0.986409 | + | 0.164309i | \(0.947461\pi\) | |||||||
\(128\) | 9.80881 | − | 7.12652i | 0.866984 | − | 0.629901i | ||||
\(129\) | −5.60503 | − | 4.07230i | −0.493496 | − | 0.358546i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.92820 | −0.605320 | −0.302660 | − | 0.953099i | \(-0.597875\pi\) | ||||
−0.302660 | + | 0.953099i | \(0.597875\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.0000 | −2.08106 | ||||||||
\(134\) | −5.35233 | − | 16.4728i | −0.462371 | − | 1.42303i | ||||
\(135\) | 3.23607 | + | 2.35114i | 0.278516 | + | 0.202354i | ||||
\(136\) | −9.70820 | + | 7.05342i | −0.832472 | + | 0.604826i | ||||
\(137\) | 1.85410 | − | 5.70634i | 0.158407 | − | 0.487525i | −0.840083 | − | 0.542457i | \(-0.817494\pi\) |
0.998490 | + | 0.0549317i | \(0.0174941\pi\) | |||||||
\(138\) | −6.42280 | + | 19.7673i | −0.546745 | + | 1.68271i | ||||
\(139\) | 11.2101 | − | 8.14459i | 0.950826 | − | 0.690815i | −0.000176405 | − | 1.00000i | \(-0.500056\pi\) |
0.951002 | + | 0.309185i | \(0.100056\pi\) | |||||||
\(140\) | 2.80252 | + | 2.03615i | 0.236856 | + | 0.172086i | ||||
\(141\) | −3.70820 | − | 11.4127i | −0.312287 | − | 0.961121i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.00000 | −0.416667 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.70820 | + | 7.05342i | 0.803457 | + | 0.583745i | ||||
\(147\) | −8.09017 | + | 5.87785i | −0.667266 | + | 0.484797i | ||||
\(148\) | 3.09017 | − | 9.51057i | 0.254010 | − | 0.781764i | ||||
\(149\) | −2.14093 | + | 6.58911i | −0.175392 | + | 0.539801i | −0.999651 | − | 0.0264116i | \(-0.991592\pi\) |
0.824259 | + | 0.566213i | \(0.191592\pi\) | |||||||
\(150\) | 2.80252 | − | 2.03615i | 0.228825 | − | 0.166251i | ||||
\(151\) | 5.60503 | + | 4.07230i | 0.456131 | + | 0.331399i | 0.792012 | − | 0.610506i | \(-0.209034\pi\) |
−0.335881 | + | 0.941905i | \(0.609034\pi\) | |||||||
\(152\) | 3.70820 | + | 11.4127i | 0.300775 | + | 0.925690i | ||||
\(153\) | 6.92820 | 0.560112 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.61803 | + | 1.17557i | 0.129133 | + | 0.0938207i | 0.650477 | − | 0.759526i | \(-0.274569\pi\) |
−0.521344 | + | 0.853347i | \(0.674569\pi\) | |||||||
\(158\) | 9.70820 | − | 7.05342i | 0.772343 | − | 0.561140i | ||||
\(159\) | −3.70820 | + | 11.4127i | −0.294080 | + | 0.905084i | ||||
\(160\) | 1.60570 | − | 4.94183i | 0.126942 | − | 0.390686i | ||||
\(161\) | 16.8151 | − | 12.2169i | 1.32522 | − | 0.962826i | ||||
\(162\) | −15.4138 | − | 11.1988i | −1.21103 | − | 0.879862i | ||||
\(163\) | 0.618034 | + | 1.90211i | 0.0484082 | + | 0.148985i | 0.972339 | − | 0.233575i | \(-0.0750425\pi\) |
−0.923931 | + | 0.382560i | \(0.875042\pi\) | |||||||
\(164\) | −6.92820 | −0.541002 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −30.0000 | −2.32845 | ||||||||
\(167\) | −3.21140 | − | 9.88367i | −0.248506 | − | 0.764821i | −0.995040 | − | 0.0994747i | \(-0.968284\pi\) |
0.746535 | − | 0.665347i | \(-0.231716\pi\) | |||||||
\(168\) | 9.70820 | + | 7.05342i | 0.749004 | + | 0.544183i | ||||
\(169\) | 10.5172 | − | 7.64121i | 0.809017 | − | 0.587785i | ||||
\(170\) | −3.70820 | + | 11.4127i | −0.284406 | + | 0.875312i | ||||
\(171\) | 2.14093 | − | 6.58911i | 0.163721 | − | 0.503882i | ||||
\(172\) | −2.80252 | + | 2.03615i | −0.213690 | + | 0.155255i | ||||
\(173\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.46410 | −0.261861 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.21140 | + | 9.88367i | 0.240705 | + | 0.740812i | ||||
\(179\) | 9.70820 | + | 7.05342i | 0.725625 | + | 0.527198i | 0.888176 | − | 0.459503i | \(-0.151972\pi\) |
−0.162551 | + | 0.986700i | \(0.551972\pi\) | |||||||
\(180\) | −0.809017 | + | 0.587785i | −0.0603006 | + | 0.0438109i | ||||
\(181\) | 4.32624 | − | 13.3148i | 0.321567 | − | 0.989681i | −0.651400 | − | 0.758735i | \(-0.725818\pi\) |
0.972967 | − | 0.230946i | \(-0.0741821\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2101 | − | 8.14459i | 0.828672 | − | 0.602066i | ||||
\(184\) | −8.40755 | − | 6.10844i | −0.619813 | − | 0.450320i | ||||
\(185\) | 3.09017 | + | 9.51057i | 0.227194 | + | 0.699231i | ||||
\(186\) | −13.8564 | −1.01600 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 4.28187 | + | 13.1782i | 0.311460 | + | 0.958575i | ||||
\(190\) | 9.70820 | + | 7.05342i | 0.704307 | + | 0.511709i | ||||
\(191\) | 9.70820 | − | 7.05342i | 0.702461 | − | 0.510368i | −0.178272 | − | 0.983981i | \(-0.557051\pi\) |
0.880733 | + | 0.473614i | \(0.157051\pi\) | |||||||
\(192\) | 0.618034 | − | 1.90211i | 0.0446028 | − | 0.137273i | ||||
\(193\) | 2.14093 | − | 6.58911i | 0.154108 | − | 0.474295i | −0.843962 | − | 0.536403i | \(-0.819783\pi\) |
0.998069 | + | 0.0621087i | \(0.0197826\pi\) | |||||||
\(194\) | −14.0126 | + | 10.1807i | −1.00605 | + | 0.730934i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.54508 | + | 4.75528i | 0.110363 | + | 0.339663i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | 0.535233 | + | 1.64728i | 0.0378467 | + | 0.116480i | ||||
\(201\) | −16.1803 | − | 11.7557i | −1.14127 | − | 0.829184i | ||||
\(202\) | −19.4164 | + | 14.1068i | −1.36613 | + | 0.992554i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.28187 | − | 13.1782i | 0.299791 | − | 0.922660i | ||||
\(205\) | 5.60503 | − | 4.07230i | 0.391473 | − | 0.284421i | ||||
\(206\) | 2.80252 | + | 2.03615i | 0.195261 | + | 0.141865i | ||||
\(207\) | 1.85410 | + | 5.70634i | 0.128869 | + | 0.396618i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 12.0000 | 0.828079 | ||||||||
\(211\) | 6.42280 | + | 19.7673i | 0.442164 | + | 1.36084i | 0.885565 | + | 0.464516i | \(0.153772\pi\) |
−0.443401 | + | 0.896323i | \(0.646228\pi\) | |||||||
\(212\) | 4.85410 | + | 3.52671i | 0.333381 | + | 0.242216i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.85410 | + | 5.70634i | −0.126744 | + | 0.390077i | ||||
\(215\) | 1.07047 | − | 3.29456i | 0.0730052 | − | 0.224687i | ||||
\(216\) | 5.60503 | − | 4.07230i | 0.381374 | − | 0.277085i | ||||
\(217\) | 11.2101 | + | 8.14459i | 0.760989 | + | 0.552891i | ||||
\(218\) | 3.70820 | + | 11.4127i | 0.251151 | + | 0.772964i | ||||
\(219\) | 13.8564 | 0.936329 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.7047 | − | 32.9456i | −0.718450 | − | 2.21116i | ||||
\(223\) | −11.3262 | − | 8.22899i | −0.758461 | − | 0.551054i | 0.139977 | − | 0.990155i | \(-0.455297\pi\) |
−0.898438 | + | 0.439101i | \(0.855297\pi\) | |||||||
\(224\) | 14.5623 | − | 10.5801i | 0.972985 | − | 0.706915i | ||||
\(225\) | 0.309017 | − | 0.951057i | 0.0206011 | − | 0.0634038i | ||||
\(226\) | −3.21140 | + | 9.88367i | −0.213619 | + | 0.657452i | ||||
\(227\) | 2.80252 | − | 2.03615i | 0.186010 | − | 0.135144i | −0.490883 | − | 0.871225i | \(-0.663326\pi\) |
0.676893 | + | 0.736081i | \(0.263326\pi\) | |||||||
\(228\) | −11.2101 | − | 8.14459i | −0.742405 | − | 0.539389i | ||||
\(229\) | −0.618034 | − | 1.90211i | −0.0408408 | − | 0.125695i | 0.928557 | − | 0.371189i | \(-0.121050\pi\) |
−0.969398 | + | 0.245494i | \(0.921050\pi\) | |||||||
\(230\) | −10.3923 | −0.685248 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.14093 | − | 6.58911i | −0.140257 | − | 0.431667i | 0.856113 | − | 0.516788i | \(-0.172872\pi\) |
−0.996371 | + | 0.0851207i | \(0.972872\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.85410 | − | 3.52671i | 0.316647 | − | 0.230057i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.28187 | − | 13.1782i | 0.278137 | − | 0.856018i | ||||
\(238\) | −33.6302 | + | 24.4338i | −2.17992 | + | 1.58381i | ||||
\(239\) | −5.60503 | − | 4.07230i | −0.362560 | − | 0.263415i | 0.391559 | − | 0.920153i | \(-0.371936\pi\) |
−0.754119 | + | 0.656738i | \(0.771936\pi\) | |||||||
\(240\) | −3.09017 | − | 9.51057i | −0.199470 | − | 0.613904i | ||||
\(241\) | 20.7846 | 1.33885 | 0.669427 | − | 0.742878i | \(-0.266540\pi\) | ||||
0.669427 | + | 0.742878i | \(0.266540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.0000 | −0.641500 | ||||||||
\(244\) | −2.14093 | − | 6.58911i | −0.137059 | − | 0.421825i | ||||
\(245\) | −4.04508 | − | 2.93893i | −0.258431 | − | 0.187761i | ||||
\(246\) | −19.4164 | + | 14.1068i | −1.23794 | + | 0.899420i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.14093 | − | 6.58911i | 0.135949 | − | 0.418409i | ||||
\(249\) | −28.0252 | + | 20.3615i | −1.77602 | + | 1.29036i | ||||
\(250\) | 1.40126 | + | 1.01807i | 0.0886234 | + | 0.0643886i | ||||
\(251\) | 3.70820 | + | 11.4127i | 0.234060 | + | 0.720362i | 0.997245 | + | 0.0741818i | \(0.0236345\pi\) |
−0.763185 | + | 0.646180i | \(0.776365\pi\) | |||||||
\(252\) | −3.46410 | −0.218218 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 18.0000 | 1.12942 | ||||||||
\(255\) | 4.28187 | + | 13.1782i | 0.268141 | + | 0.825253i | ||||
\(256\) | −15.3713 | − | 11.1679i | −0.960708 | − | 0.697995i | ||||
\(257\) | 4.85410 | − | 3.52671i | 0.302791 | − | 0.219990i | −0.426006 | − | 0.904720i | \(-0.640080\pi\) |
0.728797 | + | 0.684730i | \(0.240080\pi\) | |||||||
\(258\) | −3.70820 | + | 11.4127i | −0.230863 | + | 0.710522i | ||||
\(259\) | −10.7047 | + | 32.9456i | −0.665155 | + | 2.04714i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.70820 | + | 11.4127i | 0.229094 | + | 0.705078i | ||||
\(263\) | −3.46410 | −0.213606 | −0.106803 | − | 0.994280i | \(-0.534061\pi\) | ||||
−0.106803 | + | 0.994280i | \(0.534061\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 12.8456 | + | 39.5347i | 0.787614 | + | 2.42403i | ||||
\(267\) | 9.70820 | + | 7.05342i | 0.594132 | + | 0.431662i | ||||
\(268\) | −8.09017 | + | 5.87785i | −0.494186 | + | 0.359047i | ||||
\(269\) | −9.27051 | + | 28.5317i | −0.565233 | + | 1.73961i | 0.102025 | + | 0.994782i | \(0.467468\pi\) |
−0.667258 | + | 0.744826i | \(0.732532\pi\) | |||||||
\(270\) | 2.14093 | − | 6.58911i | 0.130293 | − | 0.401001i | ||||
\(271\) | 5.60503 | − | 4.07230i | 0.340482 | − | 0.247374i | −0.404383 | − | 0.914590i | \(-0.632514\pi\) |
0.744865 | + | 0.667215i | \(0.232514\pi\) | |||||||
\(272\) | 28.0252 | + | 20.3615i | 1.69928 | + | 1.23460i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.3923 | −0.627822 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.0000 | 0.722315 | ||||||||
\(277\) | −8.56373 | − | 26.3565i | −0.514545 | − | 1.58361i | −0.784109 | − | 0.620623i | \(-0.786880\pi\) |
0.269564 | − | 0.962982i | \(-0.413120\pi\) | |||||||
\(278\) | −19.4164 | − | 14.1068i | −1.16452 | − | 0.846072i | ||||
\(279\) | −3.23607 | + | 2.35114i | −0.193738 | + | 0.140759i | ||||
\(280\) | −1.85410 | + | 5.70634i | −0.110804 | + | 0.341019i | ||||
\(281\) | 2.14093 | − | 6.58911i | 0.127717 | − | 0.393074i | −0.866669 | − | 0.498884i | \(-0.833744\pi\) |
0.994386 | + | 0.105810i | \(0.0337435\pi\) | |||||||
\(282\) | −16.8151 | + | 12.2169i | −1.00132 | + | 0.727505i | ||||
\(283\) | 19.6176 | + | 14.2530i | 1.16615 | + | 0.847255i | 0.990543 | − | 0.137206i | \(-0.0438122\pi\) |
0.175604 | + | 0.984461i | \(0.443812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.8564 | 0.820783 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.0000 | 1.41668 | ||||||||
\(288\) | 1.60570 | + | 4.94183i | 0.0946167 | + | 0.291200i | ||||
\(289\) | −25.0795 | − | 18.2213i | −1.47527 | − | 1.07184i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.18034 | + | 19.0211i | −0.362298 | + | 1.11504i | ||||
\(292\) | 2.14093 | − | 6.58911i | 0.125289 | − | 0.385599i | ||||
\(293\) | 11.2101 | − | 8.14459i | 0.654899 | − | 0.475812i | −0.210037 | − | 0.977693i | \(-0.567359\pi\) |
0.864937 | + | 0.501881i | \(0.167359\pi\) | |||||||
\(294\) | 14.0126 | + | 10.1807i | 0.817231 | + | 0.593753i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.3205 | 1.00673 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.0000 | 0.695141 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.61803 | − | 1.17557i | −0.0934172 | − | 0.0678716i | ||||
\(301\) | 9.70820 | − | 7.05342i | 0.559572 | − | 0.406553i | ||||
\(302\) | 3.70820 | − | 11.4127i | 0.213383 | − | 0.656726i | ||||
\(303\) | −8.56373 | + | 26.3565i | −0.491973 | + | 1.51414i | ||||
\(304\) | 28.0252 | − | 20.3615i | 1.60735 | − | 1.16781i | ||||
\(305\) | 5.60503 | + | 4.07230i | 0.320943 | + | 0.233179i | ||||
\(306\) | −3.70820 | − | 11.4127i | −0.211984 | − | 0.652419i | ||||
\(307\) | 3.46410 | 0.197707 | 0.0988534 | − | 0.995102i | \(-0.468483\pi\) | ||||
0.0988534 | + | 0.995102i | \(0.468483\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | −2.14093 | − | 6.58911i | −0.121597 | − | 0.374236i | ||||
\(311\) | 19.4164 | + | 14.1068i | 1.10100 | + | 0.799926i | 0.981223 | − | 0.192875i | \(-0.0617811\pi\) |
0.119780 | + | 0.992800i | \(0.461781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5066 | − | 32.3359i | 0.593867 | − | 1.82773i | 0.0335795 | − | 0.999436i | \(-0.489309\pi\) |
0.560287 | − | 0.828298i | \(-0.310691\pi\) | |||||||
\(314\) | 1.07047 | − | 3.29456i | 0.0604099 | − | 0.185923i | ||||
\(315\) | 2.80252 | − | 2.03615i | 0.157904 | − | 0.114724i | ||||
\(316\) | −5.60503 | − | 4.07230i | −0.315308 | − | 0.229085i | ||||
\(317\) | −5.56231 | − | 17.1190i | −0.312410 | − | 0.961500i | −0.976807 | − | 0.214120i | \(-0.931312\pi\) |
0.664397 | − | 0.747380i | \(-0.268688\pi\) | |||||||
\(318\) | 20.7846 | 1.16554 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 2.14093 | + | 6.58911i | 0.119495 | + | 0.367768i | ||||
\(322\) | −29.1246 | − | 21.1603i | −1.62305 | − | 1.17922i | ||||
\(323\) | −38.8328 | + | 28.2137i | −2.16072 | + | 1.56985i | ||||
\(324\) | −3.39919 | + | 10.4616i | −0.188844 | + | 0.581201i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.80252 | − | 2.03615i | 0.155217 | − | 0.112772i | ||||
\(327\) | 11.2101 | + | 8.14459i | 0.619918 | + | 0.450397i | ||||
\(328\) | −3.70820 | − | 11.4127i | −0.204751 | − | 0.630160i | ||||
\(329\) | 20.7846 | 1.14589 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 5.35233 | + | 16.4728i | 0.293747 | + | 0.904061i | ||||
\(333\) | −8.09017 | − | 5.87785i | −0.443339 | − | 0.322104i | ||||
\(334\) | −14.5623 | + | 10.5801i | −0.796814 | + | 0.578919i | ||||
\(335\) | 3.09017 | − | 9.51057i | 0.168834 | − | 0.519618i | ||||
\(336\) | 10.7047 | − | 32.9456i | 0.583987 | − | 1.79733i | ||||
\(337\) | −16.8151 | + | 12.2169i | −0.915977 | + | 0.665496i | −0.942519 | − | 0.334151i | \(-0.891550\pi\) |
0.0265424 | + | 0.999648i | \(0.491550\pi\) | |||||||
\(338\) | −18.2164 | − | 13.2350i | −0.990839 | − | 0.719887i | ||||
\(339\) | 3.70820 | + | 11.4127i | 0.201402 | + | 0.619852i | ||||
\(340\) | 6.92820 | 0.375735 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −12.0000 | −0.648886 | ||||||||
\(343\) | 2.14093 | + | 6.58911i | 0.115599 | + | 0.355779i | ||||
\(344\) | −4.85410 | − | 3.52671i | −0.261716 | − | 0.190148i | ||||
\(345\) | −9.70820 | + | 7.05342i | −0.522672 | + | 0.379744i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.49326 | + | 23.0619i | −0.402259 | + | 1.23803i | 0.520902 | + | 0.853616i | \(0.325596\pi\) |
−0.923162 | + | 0.384411i | \(0.874404\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.2101 | − | 8.14459i | −0.600061 | − | 0.435970i | 0.245839 | − | 0.969311i | \(-0.420936\pi\) |
−0.845901 | + | 0.533341i | \(0.820936\pi\) | |||||||
\(350\) | 1.85410 | + | 5.70634i | 0.0991059 | + | 0.305017i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.85410 | − | 3.52671i | 0.257267 | − | 0.186915i | ||||
\(357\) | −14.8328 | + | 45.6507i | −0.785036 | + | 2.41609i | ||||
\(358\) | 6.42280 | − | 19.7673i | 0.339455 | − | 1.04474i | ||||
\(359\) | −28.0252 | + | 20.3615i | −1.47911 | + | 1.07464i | −0.501271 | + | 0.865291i | \(0.667134\pi\) |
−0.977841 | + | 0.209347i | \(0.932866\pi\) | |||||||
\(360\) | −1.40126 | − | 1.01807i | −0.0738528 | − | 0.0536572i | ||||
\(361\) | 8.96149 | + | 27.5806i | 0.471658 | + | 1.45161i | ||||
\(362\) | −24.2487 | −1.27448 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.14093 | + | 6.58911i | 0.112062 | + | 0.344890i | ||||
\(366\) | −19.4164 | − | 14.1068i | −1.01491 | − | 0.737377i | ||||
\(367\) | −1.61803 | + | 1.17557i | −0.0844607 | + | 0.0613643i | −0.629214 | − | 0.777232i | \(-0.716623\pi\) |
0.544754 | + | 0.838596i | \(0.316623\pi\) | |||||||
\(368\) | −9.27051 | + | 28.5317i | −0.483259 | + | 1.48732i | ||||
\(369\) | −2.14093 | + | 6.58911i | −0.111452 | + | 0.343016i | ||||
\(370\) | 14.0126 | − | 10.1807i | 0.728480 | − | 0.529271i | ||||
\(371\) | −16.8151 | − | 12.2169i | −0.872997 | − | 0.634269i | ||||
\(372\) | 2.47214 | + | 7.60845i | 0.128174 | + | 0.394480i | ||||
\(373\) | −27.7128 | −1.43492 | −0.717458 | − | 0.696602i | \(-0.754694\pi\) | ||||
−0.717458 | + | 0.696602i | \(0.754694\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.00000 | 0.103280 | ||||||||
\(376\) | −3.21140 | − | 9.88367i | −0.165615 | − | 0.509711i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 19.4164 | − | 14.1068i | 0.998672 | − | 0.725578i | ||||
\(379\) | 9.88854 | − | 30.4338i | 0.507940 | − | 1.56328i | −0.287830 | − | 0.957681i | \(-0.592934\pi\) |
0.795771 | − | 0.605598i | \(-0.207066\pi\) | |||||||
\(380\) | 2.14093 | − | 6.58911i | 0.109828 | − | 0.338014i | ||||
\(381\) | 16.8151 | − | 12.2169i | 0.861464 | − | 0.625890i | ||||
\(382\) | −16.8151 | − | 12.2169i | −0.860335 | − | 0.625070i | ||||
\(383\) | 5.56231 | + | 17.1190i | 0.284221 | + | 0.874741i | 0.986631 | + | 0.162969i | \(0.0521070\pi\) |
−0.702411 | + | 0.711772i | \(0.747893\pi\) | |||||||
\(384\) | −24.2487 | −1.23744 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.0000 | −0.610784 | ||||||||
\(387\) | 1.07047 | + | 3.29456i | 0.0544149 | + | 0.167472i | ||||
\(388\) | 8.09017 | + | 5.87785i | 0.410716 | + | 0.298403i | ||||
\(389\) | −4.85410 | + | 3.52671i | −0.246113 | + | 0.178811i | −0.704002 | − | 0.710198i | \(-0.748606\pi\) |
0.457890 | + | 0.889009i | \(0.348606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.8456 | − | 39.5347i | 0.649630 | − | 1.99935i | ||||
\(392\) | −7.00629 | + | 5.09037i | −0.353871 | + | 0.257102i | ||||
\(393\) | 11.2101 | + | 8.14459i | 0.565473 | + | 0.410840i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.92820 | 0.348596 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.0000 | −1.70641 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | −2.14093 | − | 6.58911i | −0.107315 | − | 0.330282i | ||||
\(399\) | 38.8328 | + | 28.2137i | 1.94407 | + | 1.41245i | ||||
\(400\) | 4.04508 | − | 2.93893i | 0.202254 | − | 0.146946i | ||||
\(401\) | −5.56231 | + | 17.1190i | −0.277768 | + | 0.854883i | 0.710705 | + | 0.703490i | \(0.248376\pi\) |
−0.988474 | + | 0.151393i | \(0.951624\pi\) | |||||||
\(402\) | −10.7047 | + | 32.9456i | −0.533900 | + | 1.64318i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 11.2101 | + | 8.14459i | 0.557722 | + | 0.405209i | ||||
\(405\) | −3.39919 | − | 10.4616i | −0.168907 | − | 0.519842i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 24.0000 | 1.18818 | ||||||||
\(409\) | −6.42280 | − | 19.7673i | −0.317587 | − | 0.977432i | −0.974677 | − | 0.223620i | \(-0.928213\pi\) |
0.657090 | − | 0.753812i | \(-0.271787\pi\) | |||||||
\(410\) | −9.70820 | − | 7.05342i | −0.479454 | − | 0.348344i | ||||
\(411\) | −9.70820 | + | 7.05342i | −0.478870 | + | 0.347920i | ||||
\(412\) | 0.618034 | − | 1.90211i | 0.0304483 | − | 0.0937104i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.40755 | − | 6.10844i | 0.413209 | − | 0.300214i | ||||
\(415\) | −14.0126 | − | 10.1807i | −0.687851 | − | 0.499753i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27.7128 | −1.35710 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | −2.14093 | − | 6.58911i | −0.104467 | − | 0.321516i | ||||
\(421\) | 21.0344 | + | 15.2824i | 1.02516 | + | 0.744819i | 0.967333 | − | 0.253507i | \(-0.0815842\pi\) |
0.0578225 | + | 0.998327i | \(0.481584\pi\) | |||||||
\(422\) | 29.1246 | − | 21.1603i | 1.41776 | − | 1.03007i | ||||
\(423\) | −1.85410 | + | 5.70634i | −0.0901495 | + | 0.277452i | ||||
\(424\) | −3.21140 | + | 9.88367i | −0.155959 | + | 0.479993i | ||||
\(425\) | −5.60503 | + | 4.07230i | −0.271884 | + | 0.197535i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.41641 | + | 22.8254i | 0.358905 | + | 1.10460i | ||||
\(428\) | 3.46410 | 0.167444 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.00000 | −0.289346 | ||||||||
\(431\) | −8.56373 | − | 26.3565i | −0.412500 | − | 1.26955i | −0.914468 | − | 0.404659i | \(-0.867390\pi\) |
0.501967 | − | 0.864887i | \(-0.332610\pi\) | |||||||
\(432\) | −16.1803 | − | 11.7557i | −0.778477 | − | 0.565597i | ||||
\(433\) | 27.5066 | − | 19.9847i | 1.32188 | − | 0.960403i | 0.321975 | − | 0.946748i | \(-0.395653\pi\) |
0.999907 | − | 0.0136552i | \(-0.00434671\pi\) | |||||||
\(434\) | 7.41641 | − | 22.8254i | 0.355999 | − | 1.09565i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.60503 | − | 4.07230i | 0.268432 | − | 0.195028i | ||||
\(437\) | −33.6302 | − | 24.4338i | −1.60875 | − | 1.16883i | ||||
\(438\) | −7.41641 | − | 22.8254i | −0.354370 | − | 1.09064i | ||||
\(439\) | −13.8564 | −0.661330 | −0.330665 | − | 0.943748i | \(-0.607273\pi\) | ||||
−0.330665 | + | 0.943748i | \(0.607273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000 | 0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.85410 | + | 3.52671i | 0.230625 | + | 0.167559i | 0.697097 | − | 0.716977i | \(-0.254475\pi\) |
−0.466471 | + | 0.884536i | \(0.654475\pi\) | |||||||
\(444\) | −16.1803 | + | 11.7557i | −0.767885 | + | 0.557901i | ||||
\(445\) | −1.85410 | + | 5.70634i | −0.0878929 | + | 0.270506i | ||||
\(446\) | −7.49326 | + | 23.0619i | −0.354816 | + | 1.09201i | ||||
\(447\) | 11.2101 | − | 8.14459i | 0.530218 | − | 0.385226i | ||||
\(448\) | 2.80252 | + | 2.03615i | 0.132406 | + | 0.0961989i | ||||
\(449\) | 9.27051 | + | 28.5317i | 0.437502 | + | 1.34649i | 0.890500 | + | 0.454982i | \(0.150354\pi\) |
−0.452998 | + | 0.891512i | \(0.649646\pi\) | |||||||
\(450\) | −1.73205 | −0.0816497 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | −4.28187 | − | 13.1782i | −0.201180 | − | 0.619167i | ||||
\(454\) | −4.85410 | − | 3.52671i | −0.227814 | − | 0.165517i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.41641 | − | 22.8254i | 0.347305 | − | 1.06890i | ||||
\(457\) | −6.42280 | + | 19.7673i | −0.300446 | + | 0.924677i | 0.680892 | + | 0.732384i | \(0.261592\pi\) |
−0.981338 | + | 0.192293i | \(0.938408\pi\) | |||||||
\(458\) | −2.80252 | + | 2.03615i | −0.130953 | + | 0.0951429i | ||||
\(459\) | 22.4201 | + | 16.2892i | 1.04648 | + | 0.760314i | ||||
\(460\) | 1.85410 | + | 5.70634i | 0.0864479 | + | 0.266059i | ||||
\(461\) | 27.7128 | 1.29071 | 0.645357 | − | 0.763881i | \(-0.276709\pi\) | ||||
0.645357 | + | 0.763881i | \(0.276709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.47214 | − | 4.70228i | −0.300138 | − | 0.218063i | ||||
\(466\) | −9.70820 | + | 7.05342i | −0.449724 | + | 0.326744i | ||||
\(467\) | 5.56231 | − | 17.1190i | 0.257393 | − | 0.792174i | −0.735956 | − | 0.677029i | \(-0.763267\pi\) |
0.993349 | − | 0.115144i | \(-0.0367330\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.0252 | − | 20.3615i | 1.29408 | − | 0.940206i | ||||
\(470\) | −8.40755 | − | 6.10844i | −0.387811 | − | 0.281761i | ||||
\(471\) | −1.23607 | − | 3.80423i | −0.0569550 | − | 0.175289i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −24.0000 | −1.10236 | ||||||||
\(475\) | 2.14093 | + | 6.58911i | 0.0982327 | + | 0.302329i | ||||
\(476\) | 19.4164 | + | 14.1068i | 0.889950 | + | 0.646586i | ||||
\(477\) | 4.85410 | − | 3.52671i | 0.222254 | − | 0.161477i | ||||
\(478\) | −3.70820 | + | 11.4127i | −0.169609 | + | 0.522004i | ||||
\(479\) | 6.42280 | − | 19.7673i | 0.293465 | − | 0.903193i | −0.690268 | − | 0.723554i | \(-0.742507\pi\) |
0.983733 | − | 0.179639i | \(-0.0574928\pi\) | |||||||
\(480\) | −8.40755 | + | 6.10844i | −0.383750 | + | 0.278811i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −11.1246 | − | 34.2380i | −0.506712 | − | 1.55950i | ||||
\(483\) | −41.5692 | −1.89146 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.0000 | −0.454077 | ||||||||
\(486\) | 5.35233 | + | 16.4728i | 0.242787 | + | 0.747221i | ||||
\(487\) | 11.3262 | + | 8.22899i | 0.513241 | + | 0.372891i | 0.814052 | − | 0.580793i | \(-0.197257\pi\) |
−0.300811 | + | 0.953684i | \(0.597257\pi\) | |||||||
\(488\) | 9.70820 | − | 7.05342i | 0.439470 | − | 0.319293i | ||||
\(489\) | 1.23607 | − | 3.80423i | 0.0558969 | − | 0.172033i | ||||
\(490\) | −2.67617 | + | 8.23639i | −0.120897 | + | 0.372082i | ||||
\(491\) | 11.2101 | − | 8.14459i | 0.505903 | − | 0.367560i | −0.305364 | − | 0.952236i | \(-0.598778\pi\) |
0.811267 | + | 0.584675i | \(0.198778\pi\) | |||||||
\(492\) | 11.2101 | + | 8.14459i | 0.505389 | + | 0.367187i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.0000 | −0.898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 48.5410 | + | 35.2671i | 2.17518 | + | 1.58036i | ||||
\(499\) | −12.9443 | + | 9.40456i | −0.579465 | + | 0.421006i | −0.838531 | − | 0.544853i | \(-0.816585\pi\) |
0.259066 | + | 0.965860i | \(0.416585\pi\) | |||||||
\(500\) | 0.309017 | − | 0.951057i | 0.0138197 | − | 0.0425325i | ||||
\(501\) | −6.42280 | + | 19.7673i | −0.286949 | + | 0.883140i | ||||
\(502\) | 16.8151 | − | 12.2169i | 0.750495 | − | 0.545266i | ||||
\(503\) | −14.0126 | − | 10.1807i | −0.624790 | − | 0.453937i | 0.229801 | − | 0.973238i | \(-0.426192\pi\) |
−0.854591 | + | 0.519301i | \(0.826192\pi\) | |||||||
\(504\) | −1.85410 | − | 5.70634i | −0.0825883 | − | 0.254181i | ||||
\(505\) | −13.8564 | −0.616602 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.0000 | −1.15470 | ||||||||
\(508\) | −3.21140 | − | 9.88367i | −0.142483 | − | 0.438517i | ||||
\(509\) | −4.85410 | − | 3.52671i | −0.215154 | − | 0.156319i | 0.474988 | − | 0.879992i | \(-0.342452\pi\) |
−0.690143 | + | 0.723673i | \(0.742452\pi\) | |||||||
\(510\) | 19.4164 | − | 14.1068i | 0.859773 | − | 0.624662i | ||||
\(511\) | −7.41641 | + | 22.8254i | −0.328083 | + | 1.00973i | ||||
\(512\) | −2.67617 | + | 8.23639i | −0.118271 | + | 0.364000i | ||||
\(513\) | 22.4201 | − | 16.2892i | 0.989873 | − | 0.719185i | ||||
\(514\) | −8.40755 | − | 6.10844i | −0.370841 | − | 0.269432i | ||||
\(515\) | 0.618034 | + | 1.90211i | 0.0272338 | + | 0.0838171i | ||||
\(516\) | 6.92820 | 0.304997 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 60.0000 | 2.63625 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.9787 | − | 24.6870i | 1.48863 | − | 1.08156i | 0.513990 | − | 0.857796i | \(-0.328167\pi\) |
0.974644 | − | 0.223760i | \(-0.0718333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.49326 | − | 23.0619i | 0.327658 | − | 1.00843i | −0.642569 | − | 0.766228i | \(-0.722131\pi\) |
0.970227 | − | 0.242199i | \(-0.0778685\pi\) | |||||||
\(524\) | 5.60503 | − | 4.07230i | 0.244857 | − | 0.177899i | ||||
\(525\) | 5.60503 | + | 4.07230i | 0.244624 | + | 0.177730i | ||||
\(526\) | 1.85410 | + | 5.70634i | 0.0808427 | + | 0.248808i | ||||
\(527\) | 27.7128 | 1.20719 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 3.21140 | + | 9.88367i | 0.139494 | + | 0.429319i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 19.4164 | − | 14.1068i | 0.841808 | − | 0.611609i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.42280 | − | 19.7673i | 0.277942 | − | 0.855416i | ||||
\(535\) | −2.80252 | + | 2.03615i | −0.121163 | + | 0.0880303i | ||||
\(536\) | −14.0126 | − | 10.1807i | −0.605252 | − | 0.439741i | ||||
\(537\) | −7.41641 | − | 22.8254i | −0.320042 | − | 0.984987i | ||||
\(538\) | 51.9615 | 2.24022 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.00000 | −0.172133 | ||||||||
\(541\) | 4.28187 | + | 13.1782i | 0.184092 | + | 0.566576i | 0.999932 | − | 0.0117018i | \(-0.00372490\pi\) |
−0.815840 | + | 0.578278i | \(0.803725\pi\) | |||||||
\(542\) | −9.70820 | − | 7.05342i | −0.417003 | − | 0.302970i | ||||
\(543\) | −22.6525 | + | 16.4580i | −0.972111 | + | 0.706280i | ||||
\(544\) | 11.1246 | − | 34.2380i | 0.476964 | − | 1.46794i | ||||
\(545\) | −2.14093 | + | 6.58911i | −0.0917075 | + | 0.282247i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0126 | + | 10.1807i | 0.599135 | + | 0.435297i | 0.845572 | − | 0.533862i | \(-0.179260\pi\) |
−0.246437 | + | 0.969159i | \(0.579260\pi\) | |||||||
\(548\) | 1.85410 | + | 5.70634i | 0.0792033 | + | 0.243763i | ||||
\(549\) | −6.92820 | −0.295689 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 6.42280 | + | 19.7673i | 0.273372 | + | 0.841354i | ||||
\(553\) | 19.4164 | + | 14.1068i | 0.825670 | + | 0.599884i | ||||
\(554\) | −38.8328 | + | 28.2137i | −1.64985 | + | 1.19868i | ||||
\(555\) | 6.18034 | − | 19.0211i | 0.262341 | − | 0.807402i | ||||
\(556\) | −4.28187 | + | 13.1782i | −0.181592 | + | 0.558881i | ||||
\(557\) | −22.4201 | + | 16.2892i | −0.949972 | + | 0.690195i | −0.950800 | − | 0.309805i | \(-0.899736\pi\) |
0.000828494 | 1.00000i | \(0.499736\pi\) | ||||||||
\(558\) | 5.60503 | + | 4.07230i | 0.237280 | + | 0.172394i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 17.3205 | 0.731925 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.0000 | −0.506189 | ||||||||
\(563\) | 3.21140 | + | 9.88367i | 0.135344 | + | 0.416547i | 0.995643 | − | 0.0932426i | \(-0.0297232\pi\) |
−0.860299 | + | 0.509790i | \(0.829723\pi\) | |||||||
\(564\) | 9.70820 | + | 7.05342i | 0.408789 | + | 0.297003i | ||||
\(565\) | −4.85410 | + | 3.52671i | −0.204214 | + | 0.148370i | ||||
\(566\) | 12.9787 | − | 39.9444i | 0.545536 | − | 1.67899i | ||||
\(567\) | 11.7751 | − | 36.2401i | 0.494509 | − | 1.52194i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.60503 | − | 4.07230i | −0.234975 | − | 0.170720i | 0.464067 | − | 0.885800i | \(-0.346390\pi\) |
−0.699042 | + | 0.715081i | \(0.746390\pi\) | |||||||
\(570\) | −7.41641 | − | 22.8254i | −0.310639 | − | 0.956049i | ||||
\(571\) | −27.7128 | −1.15975 | −0.579873 | − | 0.814707i | \(-0.696898\pi\) | ||||
−0.579873 | + | 0.814707i | \(0.696898\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.0000 | −1.00261 | ||||||||
\(574\) | −12.8456 | − | 39.5347i | −0.536165 | − | 1.65015i | ||||
\(575\) | −4.85410 | − | 3.52671i | −0.202430 | − | 0.147074i | ||||
\(576\) | −0.809017 | + | 0.587785i | −0.0337090 | + | 0.0244911i | ||||
\(577\) | −0.618034 | + | 1.90211i | −0.0257291 | + | 0.0791860i | −0.963097 | − | 0.269156i | \(-0.913255\pi\) |
0.937367 | + | 0.348342i | \(0.113255\pi\) | |||||||
\(578\) | −16.5922 | + | 51.0656i | −0.690146 | + | 2.12405i | ||||
\(579\) | −11.2101 | + | 8.14459i | −0.465875 | + | 0.338478i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.5410 | − | 57.0634i | −0.769211 | − | 2.36739i | ||||
\(582\) | 34.6410 | 1.43592 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.0000 | 0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.4164 | − | 14.1068i | −0.802084 | − | 0.582748i | ||||
\(587\) | 24.2705 | − | 17.6336i | 1.00175 | − | 0.727815i | 0.0392882 | − | 0.999228i | \(-0.487491\pi\) |
0.962463 | + | 0.271413i | \(0.0874910\pi\) | |||||||
\(588\) | 3.09017 | − | 9.51057i | 0.127436 | − | 0.392209i | ||||
\(589\) | 8.56373 | − | 26.3565i | 0.352862 | − | 1.08600i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15.4508 | − | 47.5528i | −0.635026 | − | 1.95441i | ||||
\(593\) | 6.92820 | 0.284507 | 0.142254 | − | 0.989830i | \(-0.454565\pi\) | ||||
0.142254 | + | 0.989830i | \(0.454565\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.0000 | −0.983904 | ||||||||
\(596\) | −2.14093 | − | 6.58911i | −0.0876960 | − | 0.269901i | ||||
\(597\) | −6.47214 | − | 4.70228i | −0.264887 | − | 0.192452i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.41641 | − | 22.8254i | 0.303026 | − | 0.932619i | −0.677380 | − | 0.735633i | \(-0.736885\pi\) |
0.980406 | − | 0.196986i | \(-0.0631152\pi\) | |||||||
\(600\) | 1.07047 | − | 3.29456i | 0.0437016 | − | 0.134500i | ||||
\(601\) | −39.2352 | + | 28.5061i | −1.60044 | + | 1.16279i | −0.713772 | + | 0.700378i | \(0.753015\pi\) |
−0.886667 | + | 0.462408i | \(0.846985\pi\) | |||||||
\(602\) | −16.8151 | − | 12.2169i | −0.685332 | − | 0.497923i | ||||
\(603\) | 3.09017 | + | 9.51057i | 0.125841 | + | 0.387300i | ||||
\(604\) | −6.92820 | −0.281905 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 48.0000 | 1.94987 | ||||||||
\(607\) | 1.07047 | + | 3.29456i | 0.0434489 | + | 0.133722i | 0.970428 | − | 0.241391i | \(-0.0776038\pi\) |
−0.926979 | + | 0.375113i | \(0.877604\pi\) | |||||||
\(608\) | −29.1246 | − | 21.1603i | −1.18116 | − | 0.858162i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.70820 | − | 11.4127i | 0.150141 | − | 0.462086i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.60503 | + | 4.07230i | −0.226570 | + | 0.164613i | ||||
\(613\) | 22.4201 | + | 16.2892i | 0.905541 | + | 0.657914i | 0.939883 | − | 0.341496i | \(-0.110934\pi\) |
−0.0343424 | + | 0.999410i | \(0.510934\pi\) | |||||||
\(614\) | −1.85410 | − | 5.70634i | −0.0748255 | − | 0.230289i | ||||
\(615\) | −13.8564 | −0.558744 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | −2.14093 | − | 6.58911i | −0.0861209 | − | 0.265053i | ||||
\(619\) | 22.6525 | + | 16.4580i | 0.910480 | + | 0.661502i | 0.941136 | − | 0.338028i | \(-0.109760\pi\) |
−0.0306563 | + | 0.999530i | \(0.509760\pi\) | |||||||
\(620\) | −3.23607 | + | 2.35114i | −0.129964 | + | 0.0944241i | ||||
\(621\) | −7.41641 | + | 22.8254i | −0.297610 | + | 0.915950i | ||||
\(622\) | 12.8456 | − | 39.5347i | 0.515061 | − | 1.58520i | ||||
\(623\) | −16.8151 | + | 12.2169i | −0.673683 | + | 0.489459i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | −58.8897 | −2.35371 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.00000 | −0.0798087 | ||||||||
\(629\) | 21.4093 | + | 65.8911i | 0.853646 | + | 2.62725i | ||||
\(630\) | −4.85410 | − | 3.52671i | −0.193392 | − | 0.140508i | ||||
\(631\) | −12.9443 | + | 9.40456i | −0.515303 | + | 0.374390i | −0.814832 | − | 0.579698i | \(-0.803171\pi\) |
0.299528 | + | 0.954087i | \(0.403171\pi\) | |||||||
\(632\) | 3.70820 | − | 11.4127i | 0.147504 | − | 0.453972i | ||||
\(633\) | 12.8456 | − | 39.5347i | 0.510567 | − | 1.57136i | ||||
\(634\) | −25.2227 | + | 18.3253i | −1.00172 | + | 0.727792i | ||||
\(635\) | 8.40755 | + | 6.10844i | 0.333643 | + | 0.242406i | ||||
\(636\) | −3.70820 | − | 11.4127i | −0.147040 | − | 0.452542i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.74663 | − | 11.5309i | −0.148099 | − | 0.455801i | ||||
\(641\) | 33.9787 | + | 24.6870i | 1.34208 | + | 0.975077i | 0.999365 | + | 0.0356372i | \(0.0113461\pi\) |
0.342714 | + | 0.939440i | \(0.388654\pi\) | |||||||
\(642\) | 9.70820 | − | 7.05342i | 0.383152 | − | 0.278376i | ||||
\(643\) | 8.03444 | − | 24.7275i | 0.316847 | − | 0.975156i | −0.658140 | − | 0.752896i | \(-0.728656\pi\) |
0.974987 | − | 0.222261i | \(-0.0713435\pi\) | |||||||
\(644\) | −6.42280 | + | 19.7673i | −0.253094 | + | 0.778942i | ||||
\(645\) | −5.60503 | + | 4.07230i | −0.220698 | + | 0.160346i | ||||
\(646\) | 67.2604 | + | 48.8675i | 2.64633 | + | 1.92267i | ||||
\(647\) | 1.85410 | + | 5.70634i | 0.0728923 | + | 0.224339i | 0.980865 | − | 0.194691i | \(-0.0623703\pi\) |
−0.907972 | + | 0.419030i | \(0.862370\pi\) | |||||||
\(648\) | −19.0526 | −0.748455 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.56373 | − | 26.3565i | −0.335639 | − | 1.03299i | ||||
\(652\) | −1.61803 | − | 1.17557i | −0.0633671 | − | 0.0460389i | ||||
\(653\) | 4.85410 | − | 3.52671i | 0.189956 | − | 0.138011i | −0.488743 | − | 0.872428i | \(-0.662544\pi\) |
0.678698 | + | 0.734417i | \(0.262544\pi\) | |||||||
\(654\) | 7.41641 | − | 22.8254i | 0.290004 | − | 0.892542i | ||||
\(655\) | −2.14093 | + | 6.58911i | −0.0836532 | + | 0.257458i | ||||
\(656\) | −28.0252 | + | 20.3615i | −1.09420 | + | 0.794982i | ||||
\(657\) | −5.60503 | − | 4.07230i | −0.218673 | − | 0.158875i | ||||
\(658\) | −11.1246 | − | 34.2380i | −0.433683 | − | 1.33474i | ||||
\(659\) | 27.7128 | 1.07954 | 0.539769 | − | 0.841813i | \(-0.318512\pi\) | ||||
0.539769 | + | 0.841813i | \(0.318512\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | −4.28187 | − | 13.1782i | −0.166419 | − | 0.512186i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.2705 | + | 17.6336i | −0.941878 | + | 0.684315i | ||||
\(665\) | −7.41641 | + | 22.8254i | −0.287596 | + | 0.885129i | ||||
\(666\) | −5.35233 | + | 16.4728i | −0.207399 | + | 0.638307i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 8.40755 | + | 6.10844i | 0.325298 | + | 0.236343i | ||||
\(669\) | 8.65248 | + | 26.6296i | 0.334524 | + | 1.02956i | ||||
\(670\) | −17.3205 | −0.669150 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −36.0000 | −1.38873 | ||||||||
\(673\) | 10.7047 | + | 32.9456i | 0.412634 | + | 1.26996i | 0.914350 | + | 0.404925i | \(0.132703\pi\) |
−0.501715 | + | 0.865033i | \(0.667297\pi\) | |||||||
\(674\) | 29.1246 | + | 21.1603i | 1.12184 | + | 0.815063i | ||||
\(675\) | 3.23607 | − | 2.35114i | 0.124556 | − | 0.0904955i | ||||
\(676\) | −4.01722 | + | 12.3637i | −0.154508 | + | 0.475528i | ||||
\(677\) | 4.28187 | − | 13.1782i | 0.164565 | − | 0.506480i | −0.834439 | − | 0.551101i | \(-0.814208\pi\) |
0.999004 | + | 0.0446206i | \(0.0142079\pi\) | |||||||
\(678\) | 16.8151 | − | 12.2169i | 0.645780 | − | 0.469187i | ||||
\(679\) | −28.0252 | − | 20.3615i | −1.07551 | − | 0.781402i | ||||
\(680\) | 3.70820 | + | 11.4127i | 0.142203 | + | 0.437656i | ||||
\(681\) | −6.92820 | −0.265489 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.0000 | −1.60709 | −0.803543 | − | 0.595247i | \(-0.797054\pi\) | ||||
−0.803543 | + | 0.595247i | \(0.797054\pi\) | |||||||
\(684\) | 2.14093 | + | 6.58911i | 0.0818606 | + | 0.251941i | ||||
\(685\) | −4.85410 | − | 3.52671i | −0.185466 | − | 0.134749i | ||||
\(686\) | 9.70820 | − | 7.05342i | 0.370661 | − | 0.269301i | ||||
\(687\) | −1.23607 | + | 3.80423i | −0.0471589 | + | 0.145140i | ||||
\(688\) | −5.35233 | + | 16.4728i | −0.204056 | + | 0.628019i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 16.8151 | + | 12.2169i | 0.640140 | + | 0.465089i | ||||
\(691\) | 6.18034 | + | 19.0211i | 0.235111 | + | 0.723598i | 0.997107 | + | 0.0760155i | \(0.0242198\pi\) |
−0.761995 | + | 0.647582i | \(0.775780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 42.0000 | 1.59430 | ||||||||
\(695\) | −4.28187 | − | 13.1782i | −0.162420 | − | 0.499879i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.8328 | − | 28.2137i | 1.47090 | − | 1.06867i | ||||
\(698\) | −7.41641 | + | 22.8254i | −0.280715 | + | 0.863952i | ||||
\(699\) | −4.28187 | + | 13.1782i | −0.161955 | + | 0.498446i | ||||
\(700\) | 2.80252 | − | 2.03615i | 0.105925 | − | 0.0769592i | ||||
\(701\) | 16.8151 | + | 12.2169i | 0.635098 | + | 0.461425i | 0.858162 | − | 0.513378i | \(-0.171606\pi\) |
−0.223065 | + | 0.974804i | \(0.571606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 69.2820 | 2.61302 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.0000 | −0.451946 | ||||||||
\(706\) | 3.21140 | + | 9.88367i | 0.120863 | + | 0.371977i | ||||
\(707\) | −38.8328 | − | 28.2137i | −1.46046 | − | 1.06109i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.03444 | + | 24.7275i | −0.301740 | + | 0.928660i | 0.679134 | + | 0.734014i | \(0.262356\pi\) |
−0.980874 | + | 0.194645i | \(0.937644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.60503 | + | 4.07230i | −0.210205 | + | 0.152723i | ||||
\(712\) | 8.40755 | + | 6.10844i | 0.315086 | + | 0.228924i | ||||
\(713\) | 7.41641 | + | 22.8254i | 0.277747 | + | 0.854816i | ||||
\(714\) | 83.1384 | 3.11138 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 4.28187 | + | 13.1782i | 0.159909 | + | 0.492150i | ||||
\(718\) | 48.5410 | + | 35.2671i | 1.81153 | + | 1.31616i | ||||
\(719\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(720\) | −1.54508 | + | 4.75528i | −0.0575819 | + | 0.177219i | ||||
\(721\) | −2.14093 | + | 6.58911i | −0.0797325 | + | 0.245391i | ||||
\(722\) | 40.6365 | − | 29.5241i | 1.51233 | − | 1.09877i | ||||
\(723\) | −33.6302 | − | 24.4338i | −1.25072 | − | 0.908702i | ||||
\(724\) | 4.32624 | + | 13.3148i | 0.160783 | + | 0.494840i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.0000 | 1.70605 | 0.853023 | − | 0.521874i | \(-0.174767\pi\) | ||||
0.853023 | + | 0.521874i | \(0.174767\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.5172 | − | 7.64121i | −0.389527 | − | 0.283008i | ||||
\(730\) | 9.70820 | − | 7.05342i | 0.359317 | − | 0.261059i | ||||
\(731\) | 7.41641 | − | 22.8254i | 0.274306 | − | 0.844226i | ||||
\(732\) | −4.28187 | + | 13.1782i | −0.158262 | + | 0.487081i | ||||
\(733\) | −33.6302 | + | 24.4338i | −1.24216 | + | 0.902482i | −0.997740 | − | 0.0671875i | \(-0.978597\pi\) |
−0.244420 | + | 0.969670i | \(0.578597\pi\) | |||||||
\(734\) | 2.80252 | + | 2.03615i | 0.103443 | + | 0.0751556i | ||||
\(735\) | 3.09017 | + | 9.51057i | 0.113983 | + | 0.350802i | ||||
\(736\) | 31.1769 | 1.14920 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 12.0000 | 0.441726 | ||||||||
\(739\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(740\) | −8.09017 | − | 5.87785i | −0.297401 | − | 0.216074i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.1246 | + | 34.2380i | −0.408397 | + | 1.25692i | ||||
\(743\) | −9.63420 | + | 29.6510i | −0.353444 | + | 1.08779i | 0.603462 | + | 0.797392i | \(0.293788\pi\) |
−0.956906 | + | 0.290398i | \(0.906212\pi\) | |||||||
\(744\) | −11.2101 | + | 8.14459i | −0.410981 | + | 0.298595i | ||||
\(745\) | 5.60503 | + | 4.07230i | 0.205353 | + | 0.149197i | ||||
\(746\) | 14.8328 | + | 45.6507i | 0.543068 | + | 1.67139i | ||||
\(747\) | 17.3205 | 0.633724 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | −1.07047 | − | 3.29456i | −0.0390879 | − | 0.120300i | ||||
\(751\) | −12.9443 | − | 9.40456i | −0.472343 | − | 0.343177i | 0.326011 | − | 0.945366i | \(-0.394295\pi\) |
−0.798354 | + | 0.602189i | \(0.794295\pi\) | |||||||
\(752\) | −24.2705 | + | 17.6336i | −0.885054 | + | 0.643030i | ||||
\(753\) | 7.41641 | − | 22.8254i | 0.270269 | − | 0.831802i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.60503 | − | 4.07230i | 0.203988 | − | 0.148206i | ||||
\(756\) | −11.2101 | − | 8.14459i | −0.407706 | − | 0.296216i | ||||
\(757\) | −0.618034 | − | 1.90211i | −0.0224628 | − | 0.0691335i | 0.939197 | − | 0.343380i | \(-0.111572\pi\) |
−0.961660 | + | 0.274246i | \(0.911572\pi\) | |||||||
\(758\) | −55.4256 | −2.01315 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | 0.435286 | ||||||||
\(761\) | −4.28187 | − | 13.1782i | −0.155217 | − | 0.477710i | 0.842965 | − | 0.537968i | \(-0.180808\pi\) |
−0.998183 | + | 0.0602575i | \(0.980808\pi\) | |||||||
\(762\) | −29.1246 | − | 21.1603i | −1.05507 | − | 0.766556i | ||||
\(763\) | −19.4164 | + | 14.1068i | −0.702921 | + | 0.510702i | ||||
\(764\) | −3.70820 | + | 11.4127i | −0.134158 | + | 0.412896i | ||||
\(765\) | 2.14093 | − | 6.58911i | 0.0774056 | − | 0.238230i | ||||
\(766\) | 25.2227 | − | 18.3253i | 0.911332 | − | 0.662121i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 11.7426 | + | 36.1401i | 0.423726 | + | 1.30410i | ||||
\(769\) | −41.5692 | −1.49902 | −0.749512 | − | 0.661991i | \(-0.769712\pi\) | ||||
−0.749512 | + | 0.661991i | \(0.769712\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 2.14093 | + | 6.58911i | 0.0770538 | + | 0.237147i | ||||
\(773\) | 4.85410 | + | 3.52671i | 0.174590 | + | 0.126847i | 0.671648 | − | 0.740870i | \(-0.265587\pi\) |
−0.497059 | + | 0.867717i | \(0.665587\pi\) | |||||||
\(774\) | 4.85410 | − | 3.52671i | 0.174477 | − | 0.126765i | ||||
\(775\) | 1.23607 | − | 3.80423i | 0.0444009 | − | 0.136652i | ||||
\(776\) | −5.35233 | + | 16.4728i | −0.192137 | + | 0.591338i | ||||
\(777\) | 56.0503 | − | 40.7230i | 2.01079 | − | 1.46093i | ||||
\(778\) | 8.40755 | + | 6.10844i | 0.301425 | + | 0.218998i | ||||
\(779\) | −14.8328 | − | 45.6507i | −0.531441 | − | 1.63561i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −72.0000 | −2.57471 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.2254 | + | 14.6946i | 0.722337 | + | 0.524808i | ||||
\(785\) | 1.61803 | − | 1.17557i | 0.0577501 | − | 0.0419579i | ||||
\(786\) | 7.41641 | − | 22.8254i | 0.264535 | − | 0.814154i | ||||
\(787\) | 13.9161 | − | 42.8292i | 0.496054 | − | 1.52670i | −0.319254 | − | 0.947669i | \(-0.603432\pi\) |
0.815308 | − | 0.579028i | \(-0.196568\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.60503 | + | 4.07230i | 0.199544 | + | 0.144978i | ||||
\(790\) | −3.70820 | − | 11.4127i | −0.131932 | − | 0.406045i | ||||
\(791\) | −20.7846 | −0.739016 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 18.1979 | + | 56.0075i | 0.645820 | + | 1.98763i | ||||
\(795\) | 9.70820 | + | 7.05342i | 0.344315 | + | 0.250159i | ||||
\(796\) | −3.23607 | + | 2.35114i | −0.114699 | + | 0.0833340i | ||||
\(797\) | −5.56231 | + | 17.1190i | −0.197027 | + | 0.606387i | 0.802920 | + | 0.596087i | \(0.203279\pi\) |
−0.999947 | + | 0.0102999i | \(0.996721\pi\) | |||||||
\(798\) | 25.6912 | − | 79.0694i | 0.909458 | − | 2.79902i | ||||
\(799\) | 33.6302 | − | 24.4338i | 1.18975 | − | 0.864405i | ||||
\(800\) | −4.20378 | − | 3.05422i | −0.148626 | − | 0.107983i | ||||
\(801\) | −1.85410 | − | 5.70634i | −0.0655115 | − | 0.201624i | ||||
\(802\) | 31.1769 | 1.10090 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 20.0000 | 0.705346 | ||||||||
\(805\) | −6.42280 | − | 19.7673i | −0.226374 | − | 0.696707i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48.5410 | − | 35.2671i | 1.70872 | − | 1.24146i | ||||
\(808\) | −7.41641 | + | 22.8254i | −0.260908 | + | 0.802993i | ||||
\(809\) | −4.28187 | + | 13.1782i | −0.150542 | + | 0.463322i | −0.997682 | − | 0.0680486i | \(-0.978323\pi\) |
0.847140 | + | 0.531370i | \(0.178323\pi\) | |||||||
\(810\) | −15.4138 | + | 11.1988i | −0.541587 | + | 0.393486i | ||||
\(811\) | −11.2101 | − | 8.14459i | −0.393639 | − | 0.285995i | 0.373306 | − | 0.927708i | \(-0.378224\pi\) |
−0.766945 | + | 0.641713i | \(0.778224\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.8564 | −0.485965 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.00000 | 0.0700569 | ||||||||
\(816\) | −21.4093 | − | 65.8911i | −0.749476 | − | 2.30665i | ||||
\(817\) | −19.4164 | − | 14.1068i | −0.679294 | − | 0.493536i | ||||
\(818\) | −29.1246 | + | 21.1603i | −1.01832 | + | 0.739851i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.14093 | + | 6.58911i | −0.0747646 | + | 0.230102i | ||||
\(821\) | −39.2352 | + | 28.5061i | −1.36932 | + | 0.994869i | −0.371529 | + | 0.928421i | \(0.621166\pi\) |
−0.997790 | + | 0.0664475i | \(0.978834\pi\) | |||||||
\(822\) | 16.8151 | + | 12.2169i | 0.586494 | + | 0.426113i | ||||
\(823\) | 8.03444 | + | 24.7275i | 0.280063 | + | 0.861945i | 0.987835 | + | 0.155505i | \(0.0497003\pi\) |
−0.707772 | + | 0.706441i | \(0.750300\pi\) | |||||||
\(824\) | 3.46410 | 0.120678 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.35233 | + | 16.4728i | 0.186119 | + | 0.572815i | 0.999966 | − | 0.00826439i | \(-0.00263067\pi\) |
−0.813847 | + | 0.581079i | \(0.802631\pi\) | |||||||
\(828\) | −4.85410 | − | 3.52671i | −0.168692 | − | 0.122562i | ||||
\(829\) | 27.5066 | − | 19.9847i | 0.955343 | − | 0.694097i | 0.00327844 | − | 0.999995i | \(-0.498956\pi\) |
0.952064 | + | 0.305897i | \(0.0989564\pi\) | |||||||
\(830\) | −9.27051 | + | 28.5317i | −0.321784 | + | 0.990350i | ||||
\(831\) | −17.1275 | + | 52.7129i | −0.594145 | + | 1.82859i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.0252 | − | 20.3615i | −0.971015 | − | 0.705483i | ||||
\(834\) | 14.8328 | + | 45.6507i | 0.513618 | + | 1.58075i | ||||
\(835\) | −10.3923 | −0.359641 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.0000 | −0.553041 | ||||||||
\(838\) | 6.42280 | + | 19.7673i | 0.221872 | + | 0.682851i | ||||
\(839\) | 9.70820 | + | 7.05342i | 0.335164 | + | 0.243511i | 0.742619 | − | 0.669714i | \(-0.233583\pi\) |
−0.407454 | + | 0.913226i | \(0.633583\pi\) | |||||||
\(840\) | 9.70820 | − | 7.05342i | 0.334965 | − | 0.243366i | ||||
\(841\) | −8.96149 | + | 27.5806i | −0.309017 | + | 0.951057i | ||||
\(842\) | 13.9161 | − | 42.8292i | 0.479579 | − | 1.47599i | ||||
\(843\) | −11.2101 | + | 8.14459i | −0.386095 | + | 0.280515i | ||||
\(844\) | −16.8151 | − | 12.2169i | −0.578800 | − | 0.420523i | ||||
\(845\) | −4.01722 | − | 12.3637i | −0.138197 | − | 0.425325i | ||||
\(846\) | 10.3923 | 0.357295 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 30.0000 | 1.03020 | ||||||||
\(849\) | −14.9865 | − | 46.1238i | −0.514336 | − | 1.58296i | ||||
\(850\) | 9.70820 | + | 7.05342i | 0.332989 | + | 0.241930i | ||||
\(851\) | −48.5410 | + | 35.2671i | −1.66396 | + | 1.20894i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.8456 | + | 39.5347i | −0.439825 | + | 1.35364i | 0.448236 | + | 0.893915i | \(0.352052\pi\) |
−0.888061 | + | 0.459726i | \(0.847948\pi\) | |||||||
\(854\) | 33.6302 | − | 24.4338i | 1.15080 | − | 0.836107i | ||||
\(855\) | −5.60503 | − | 4.07230i | −0.191688 | − | 0.139270i | ||||
\(856\) | 1.85410 | + | 5.70634i | 0.0633719 | + | 0.195039i | ||||
\(857\) | −20.7846 | −0.709989 | −0.354994 | − | 0.934868i | \(-0.615517\pi\) | ||||
−0.354994 | + | 0.934868i | \(0.615517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | −0.136478 | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | 1.07047 | + | 3.29456i | 0.0365026 | + | 0.112343i | ||||
\(861\) | −38.8328 | − | 28.2137i | −1.32342 | − | 0.961520i | ||||
\(862\) | −38.8328 | + | 28.2137i | −1.32265 | + | 0.960962i | ||||
\(863\) | −16.6869 | + | 51.3571i | −0.568029 | + | 1.74821i | 0.0907454 | + | 0.995874i | \(0.471075\pi\) |
−0.658775 | + | 0.752340i | \(0.728925\pi\) | |||||||
\(864\) | −6.42280 | + | 19.7673i | −0.218508 | + | 0.672499i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −47.6428 | − | 34.6145i | −1.61897 | − | 1.17625i | ||||
\(867\) | 19.1591 | + | 58.9655i | 0.650676 | + | 2.00257i | ||||
\(868\) | −13.8564 | −0.470317 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 9.70820 | + | 7.05342i | 0.328761 | + | 0.238859i | ||||
\(873\) | 8.09017 | − | 5.87785i | 0.273811 | − | 0.198935i | ||||
\(874\) | −22.2492 | + | 68.4761i | −0.752591 | + | 2.31624i | ||||
\(875\) | −1.07047 | + | 3.29456i | −0.0361884 | + | 0.111376i | ||||
\(876\) | −11.2101 | + | 8.14459i | −0.378753 | + | 0.275180i | ||||
\(877\) | 22.4201 | + | 16.2892i | 0.757074 | + | 0.550047i | 0.898012 | − | 0.439972i | \(-0.145012\pi\) |
−0.140937 | + | 0.990019i | \(0.545012\pi\) | |||||||
\(878\) | 7.41641 | + | 22.8254i | 0.250292 | + | 0.770318i | ||||
\(879\) | −27.7128 | −0.934730 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | −2.67617 | − | 8.23639i | −0.0901112 | − | 0.277334i | ||||
\(883\) | −27.5066 | − | 19.9847i | −0.925670 | − | 0.672539i | 0.0192588 | − | 0.999815i | \(-0.493869\pi\) |
−0.944929 | + | 0.327276i | \(0.893869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.21140 | − | 9.88367i | 0.107889 | − | 0.332048i | ||||
\(887\) | −14.0126 | + | 10.1807i | −0.470497 | + | 0.341836i | −0.797635 | − | 0.603141i | \(-0.793916\pi\) |
0.327138 | + | 0.944977i | \(0.393916\pi\) | |||||||
\(888\) | −28.0252 | − | 20.3615i | −0.940463 | − | 0.683286i | ||||
\(889\) | 11.1246 | + | 34.2380i | 0.373108 | + | 1.14831i | ||||
\(890\) | 10.3923 | 0.348351 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.0000 | 0.468755 | ||||||||
\(893\) | −12.8456 | − | 39.5347i | −0.429861 | − | 1.32298i | ||||
\(894\) | −19.4164 | − | 14.1068i | −0.649382 | − | 0.471804i | ||||
\(895\) | 9.70820 | − | 7.05342i | 0.324509 | − | 0.235770i | ||||
\(896\) | 12.9787 | − | 39.9444i | 0.433588 | − | 1.33445i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 42.0378 | − | 30.5422i | 1.40282 | − | 1.01921i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.309017 | + | 0.951057i | 0.0103006 | + | 0.0317019i | ||||
\(901\) | −41.5692 | −1.38487 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.0000 | −0.798670 | ||||||||
\(904\) | 3.21140 | + | 9.88367i | 0.106810 | + | 0.328726i | ||||
\(905\) | −11.3262 | − | 8.22899i | −0.376497 | − | 0.273541i | ||||
\(906\) | −19.4164 | + | 14.1068i | −0.645067 | + | 0.468669i | ||||
\(907\) | 8.03444 | − | 24.7275i | 0.266779 | − | 0.821062i | −0.724499 | − | 0.689276i | \(-0.757929\pi\) |
0.991278 | − | 0.131786i | \(-0.0420712\pi\) | |||||||
\(908\) | −1.07047 | + | 3.29456i | −0.0355247 | + | 0.109334i | ||||
\(909\) | 11.2101 | − | 8.14459i | 0.371814 | − | 0.270139i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.1246 | − | 34.2380i | −0.368575 | − | 1.13436i | −0.947712 | − | 0.319127i | \(-0.896610\pi\) |
0.579137 | − | 0.815230i | \(-0.303390\pi\) | |||||||
\(912\) | −69.2820 | −2.29416 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 36.0000 | 1.19077 | ||||||||
\(915\) | −4.28187 | − | 13.1782i | −0.141554 | − | 0.435659i | ||||
\(916\) | 1.61803 | + | 1.17557i | 0.0534613 | + | 0.0388419i | ||||
\(917\) | −19.4164 | + | 14.1068i | −0.641186 | + | 0.465849i | ||||
\(918\) | 14.8328 | − | 45.6507i | 0.489556 | − | 1.50670i | ||||
\(919\) | 4.28187 | − | 13.1782i | 0.141246 | − | 0.434710i | −0.855263 | − | 0.518193i | \(-0.826605\pi\) |
0.996509 | + | 0.0834839i | \(0.0266047\pi\) | |||||||
\(920\) | −8.40755 | + | 6.10844i | −0.277189 | + | 0.201389i | ||||
\(921\) | −5.60503 | − | 4.07230i | −0.184692 | − | 0.134187i | ||||
\(922\) | −14.8328 | − | 45.6507i | −0.488493 | − | 1.50343i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0000 | 0.328798 | ||||||||
\(926\) | −7.49326 | − | 23.0619i | −0.246244 | − | 0.757861i | ||||
\(927\) | −1.61803 | − | 1.17557i | −0.0531432 | − | 0.0386108i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.85410 | + | 5.70634i | −0.0608311 | + | 0.187219i | −0.976854 | − | 0.213907i | \(-0.931381\pi\) |
0.916023 | + | 0.401126i | \(0.131381\pi\) | |||||||
\(930\) | −4.28187 | + | 13.1782i | −0.140408 | + | 0.432131i | ||||
\(931\) | −28.0252 | + | 20.3615i | −0.918488 | + | 0.667321i | ||||
\(932\) | 5.60503 | + | 4.07230i | 0.183599 | + | 0.133392i | ||||
\(933\) | −14.8328 | − | 45.6507i | −0.485605 | − | 1.49454i | ||||
\(934\) | −31.1769 | −1.02014 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.7047 | + | 32.9456i | 0.349706 | + | 1.07628i | 0.959016 | + | 0.283352i | \(0.0914466\pi\) |
−0.609310 | + | 0.792932i | \(0.708553\pi\) | |||||||
\(938\) | −48.5410 | − | 35.2671i | −1.58492 | − | 1.15151i | ||||
\(939\) | −55.0132 | + | 39.9694i | −1.79529 | + | 1.30435i | ||||
\(940\) | −1.85410 | + | 5.70634i | −0.0604741 | + | 0.186120i | ||||
\(941\) | 4.28187 | − | 13.1782i | 0.139585 | − | 0.429598i | −0.856690 | − | 0.515831i | \(-0.827483\pi\) |
0.996275 | + | 0.0862335i | \(0.0274831\pi\) | |||||||
\(942\) | −5.60503 | + | 4.07230i | −0.182622 | + | 0.132683i | ||||
\(943\) | 33.6302 | + | 24.4338i | 1.09515 | + | 0.795673i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.8564 | 0.450749 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.00000 | −0.194974 | −0.0974869 | − | 0.995237i | \(-0.531080\pi\) | ||||
−0.0974869 | + | 0.995237i | \(0.531080\pi\) | |||||||
\(948\) | 4.28187 | + | 13.1782i | 0.139069 | + | 0.428009i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 9.70820 | − | 7.05342i | 0.314976 | − | 0.228843i | ||||
\(951\) | −11.1246 | + | 34.2380i | −0.360740 | + | 1.11024i | ||||
\(952\) | −12.8456 | + | 39.5347i | −0.416328 | + | 1.28133i | ||||
\(953\) | 28.0252 | − | 20.3615i | 0.907824 | − | 0.659573i | −0.0326393 | − | 0.999467i | \(-0.510391\pi\) |
0.940464 | + | 0.339894i | \(0.110391\pi\) | |||||||
\(954\) | −8.40755 | − | 6.10844i | −0.272205 | − | 0.197768i | ||||
\(955\) | −3.70820 | − | 11.4127i | −0.119995 | − | 0.369306i | ||||
\(956\) | 6.92820 | 0.224074 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36.0000 | −1.16311 | ||||||||
\(959\) | −6.42280 | − | 19.7673i | −0.207403 | − | 0.638321i | ||||
\(960\) | −1.61803 | − | 1.17557i | −0.0522218 | − | 0.0379414i | ||||
\(961\) | 12.1353 | − | 8.81678i | 0.391460 | − | 0.284412i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.07047 | − | 3.29456i | 0.0344953 | − | 0.106166i | ||||
\(964\) | −16.8151 | + | 12.2169i | −0.541578 | + | 0.393479i | ||||
\(965\) | −5.60503 | − | 4.07230i | −0.180432 | − | 0.131092i | ||||
\(966\) | 22.2492 | + | 68.4761i | 0.715857 | + | 2.20318i | ||||
\(967\) | −24.2487 | −0.779786 | −0.389893 | − | 0.920860i | \(-0.627488\pi\) | ||||
−0.389893 | + | 0.920860i | \(0.627488\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 96.0000 | 3.08396 | ||||||||
\(970\) | 5.35233 | + | 16.4728i | 0.171853 | + | 0.528909i | ||||
\(971\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(972\) | 8.09017 | − | 5.87785i | 0.259492 | − | 0.188532i | ||||
\(973\) | 14.8328 | − | 45.6507i | 0.475518 | − | 1.46349i | ||||
\(974\) | 7.49326 | − | 23.0619i | 0.240100 | − | 0.738951i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28.0252 | − | 20.3615i | −0.897064 | − | 0.651755i | ||||
\(977\) | −12.9787 | − | 39.9444i | −0.415226 | − | 1.27793i | −0.912049 | − | 0.410082i | \(-0.865500\pi\) |
0.496823 | − | 0.867852i | \(-0.334500\pi\) | |||||||
\(978\) | −6.92820 | −0.221540 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 5.00000 | 0.159719 | ||||||||
\(981\) | −2.14093 | − | 6.58911i | −0.0683547 | − | 0.210374i | ||||
\(982\) | −19.4164 | − | 14.1068i | −0.619602 | − | 0.450168i | ||||
\(983\) | −33.9787 | + | 24.6870i | −1.08375 | + | 0.787392i | −0.978333 | − | 0.207035i | \(-0.933618\pi\) |
−0.105419 | + | 0.994428i | \(0.533618\pi\) | |||||||
\(984\) | −7.41641 | + | 22.8254i | −0.236426 | + | 0.727646i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −33.6302 | − | 24.4338i | −1.07046 | − | 0.777736i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.7846 | 0.660912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.0000 | 0.889449 | 0.444725 | − | 0.895667i | \(-0.353302\pi\) | ||||
0.444725 | + | 0.895667i | \(0.353302\pi\) | |||||||
\(992\) | 6.42280 | + | 19.7673i | 0.203924 | + | 0.627614i | ||||
\(993\) | −12.9443 | − | 9.40456i | −0.410774 | − | 0.298445i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.23607 | − | 3.80423i | 0.0391860 | − | 0.120602i | ||||
\(996\) | 10.7047 | − | 32.9456i | 0.339190 | − | 1.04392i | ||||
\(997\) | 33.6302 | − | 24.4338i | 1.06508 | − | 0.773825i | 0.0900579 | − | 0.995937i | \(-0.471295\pi\) |
0.975021 | + | 0.222111i | \(0.0712948\pi\) | |||||||
\(998\) | 22.4201 | + | 16.2892i | 0.709697 | + | 0.515625i | ||||
\(999\) | −12.3607 | − | 38.0423i | −0.391075 | − | 1.20360i |
(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 | 605.2.g.h.511.1 | 8 | ||
11.2 | odd | 10 | inner | 605.2.g.h.251.2 | 8 | ||
11.3 | even | 5 | 605.2.a.f.1.1 | ✓ | 2 | ||
11.4 | even | 5 | inner | 605.2.g.h.366.2 | 8 | ||
11.5 | even | 5 | inner | 605.2.g.h.81.2 | 8 | ||
11.6 | odd | 10 | inner | 605.2.g.h.81.1 | 8 | ||
11.7 | odd | 10 | inner | 605.2.g.h.366.1 | 8 | ||
11.8 | odd | 10 | 605.2.a.f.1.2 | yes | 2 | ||
11.9 | even | 5 | inner | 605.2.g.h.251.1 | 8 | ||
11.10 | odd | 2 | inner | 605.2.g.h.511.2 | 8 | ||
33.8 | even | 10 | 5445.2.a.r.1.1 | 2 | |||
33.14 | odd | 10 | 5445.2.a.r.1.2 | 2 | |||
44.3 | odd | 10 | 9680.2.a.bg.1.2 | 2 | |||
44.19 | even | 10 | 9680.2.a.bg.1.1 | 2 | |||
55.14 | even | 10 | 3025.2.a.j.1.2 | 2 | |||
55.19 | odd | 10 | 3025.2.a.j.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.f.1.1 | ✓ | 2 | 11.3 | even | 5 | ||
605.2.a.f.1.2 | yes | 2 | 11.8 | odd | 10 | ||
605.2.g.h.81.1 | 8 | 11.6 | odd | 10 | inner | ||
605.2.g.h.81.2 | 8 | 11.5 | even | 5 | inner | ||
605.2.g.h.251.1 | 8 | 11.9 | even | 5 | inner | ||
605.2.g.h.251.2 | 8 | 11.2 | odd | 10 | inner | ||
605.2.g.h.366.1 | 8 | 11.7 | odd | 10 | inner | ||
605.2.g.h.366.2 | 8 | 11.4 | even | 5 | inner | ||
605.2.g.h.511.1 | 8 | 1.1 | even | 1 | trivial | ||
605.2.g.h.511.2 | 8 | 11.10 | odd | 2 | inner | ||
3025.2.a.j.1.1 | 2 | 55.19 | odd | 10 | |||
3025.2.a.j.1.2 | 2 | 55.14 | even | 10 | |||
5445.2.a.r.1.1 | 2 | 33.8 | even | 10 | |||
5445.2.a.r.1.2 | 2 | 33.14 | odd | 10 | |||
9680.2.a.bg.1.1 | 2 | 44.19 | even | 10 | |||
9680.2.a.bg.1.2 | 2 | 44.3 | odd | 10 |