Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(46,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.h (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 136.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.136 |
Dual form | 225.2.h.b.91.1 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.363271i | 0.353553 | − | 0.256872i | −0.396805 | − | 0.917903i | \(-0.629881\pi\) |
0.750358 | + | 0.661031i | \(0.229881\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 1.53884i | −0.250000 | + | 0.769421i | ||||
\(5\) | 1.80902 | + | 1.31433i | 0.809017 | + | 0.587785i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.61803 | −0.611559 | −0.305780 | − | 0.952102i | \(-0.598917\pi\) | ||||
−0.305780 | + | 0.952102i | \(0.598917\pi\) | |||||||
\(8\) | 0.690983 | + | 2.12663i | 0.244299 | + | 0.751876i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.38197 | 0.437016 | ||||||||
\(11\) | −0.618034 | + | 0.449028i | −0.186344 | + | 0.135387i | −0.677046 | − | 0.735940i | \(-0.736740\pi\) |
0.490702 | + | 0.871327i | \(0.336740\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.92705 | + | 2.85317i | 1.08917 | + | 0.791327i | 0.979259 | − | 0.202615i | \(-0.0649439\pi\) |
0.109909 | + | 0.993942i | \(0.464944\pi\) | |||||||
\(14\) | −0.809017 | + | 0.587785i | −0.216219 | + | 0.157092i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | − | 1.08981i | −0.375000 | − | 0.272453i | ||||
\(17\) | 0.236068 | + | 0.726543i | 0.0572549 | + | 0.176212i | 0.975594 | − | 0.219582i | \(-0.0704693\pi\) |
−0.918339 | + | 0.395794i | \(0.870469\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.80902 | − | 5.56758i | −0.415017 | − | 1.27729i | −0.912236 | − | 0.409666i | \(-0.865645\pi\) |
0.497219 | − | 0.867625i | \(-0.334355\pi\) | |||||||
\(20\) | −2.92705 | + | 2.12663i | −0.654508 | + | 0.475528i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.145898 | + | 0.449028i | −0.0311056 | + | 0.0957331i | ||||
\(23\) | 6.66312 | − | 4.84104i | 1.38936 | − | 1.00943i | 0.393421 | − | 0.919359i | \(-0.371292\pi\) |
0.995936 | − | 0.0900679i | \(-0.0287084\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.54508 | + | 4.75528i | 0.309017 | + | 0.951057i | ||||
\(26\) | 3.00000 | 0.588348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.809017 | − | 2.48990i | 0.152890 | − | 0.470547i | ||||
\(29\) | 0.427051 | − | 1.31433i | 0.0793014 | − | 0.244065i | −0.903544 | − | 0.428495i | \(-0.859044\pi\) |
0.982846 | + | 0.184430i | \(0.0590440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.927051 | − | 2.85317i | −0.166503 | − | 0.512444i | 0.832641 | − | 0.553814i | \(-0.186828\pi\) |
−0.999144 | + | 0.0413693i | \(0.986828\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.381966 | + | 0.277515i | 0.0655066 | + | 0.0475934i | ||||
\(35\) | −2.92705 | − | 2.12663i | −0.494762 | − | 0.359466i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.42705 | − | 2.48990i | −0.563404 | − | 0.409337i | 0.269299 | − | 0.963057i | \(-0.413208\pi\) |
−0.832703 | + | 0.553720i | \(0.813208\pi\) | |||||||
\(38\) | −2.92705 | − | 2.12663i | −0.474830 | − | 0.344984i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.54508 | + | 4.75528i | −0.244299 | + | 0.751876i | ||||
\(41\) | −4.23607 | − | 3.07768i | −0.661563 | − | 0.480653i | 0.205628 | − | 0.978630i | \(-0.434076\pi\) |
−0.867190 | + | 0.497977i | \(0.834076\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.85410 | 0.282748 | 0.141374 | − | 0.989956i | \(-0.454848\pi\) | ||||
0.141374 | + | 0.989956i | \(0.454848\pi\) | |||||||
\(44\) | −0.381966 | − | 1.17557i | −0.0575835 | − | 0.177224i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.57295 | − | 4.84104i | 0.231919 | − | 0.713772i | ||||
\(47\) | 0.500000 | − | 1.53884i | 0.0729325 | − | 0.224463i | −0.907945 | − | 0.419089i | \(-0.862349\pi\) |
0.980877 | + | 0.194626i | \(0.0623494\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.38197 | −0.625995 | ||||||||
\(50\) | 2.50000 | + | 1.81636i | 0.353553 | + | 0.256872i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.35410 | + | 4.61653i | −0.881155 | + | 0.640197i | ||||
\(53\) | −1.69098 | + | 5.20431i | −0.232274 | + | 0.714867i | 0.765197 | + | 0.643796i | \(0.222642\pi\) |
−0.997471 | + | 0.0710707i | \(0.977358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.70820 | −0.230334 | ||||||||
\(56\) | −1.11803 | − | 3.44095i | −0.149404 | − | 0.459817i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.263932 | − | 0.812299i | −0.0346560 | − | 0.106660i | ||||
\(59\) | −3.35410 | − | 2.43690i | −0.436667 | − | 0.317257i | 0.347642 | − | 0.937627i | \(-0.386982\pi\) |
−0.784309 | + | 0.620370i | \(0.786982\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.80902 | − | 2.76741i | 0.487695 | − | 0.354331i | −0.316602 | − | 0.948558i | \(-0.602542\pi\) |
0.804297 | + | 0.594227i | \(0.202542\pi\) | |||||||
\(62\) | −1.50000 | − | 1.08981i | −0.190500 | − | 0.138406i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.190983 | − | 0.138757i | 0.0238729 | − | 0.0173447i | ||||
\(65\) | 3.35410 | + | 10.3229i | 0.416025 | + | 1.28039i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.85410 | + | 8.78402i | 0.348684 | + | 1.07314i | 0.959582 | + | 0.281430i | \(0.0908086\pi\) |
−0.610898 | + | 0.791709i | \(0.709191\pi\) | |||||||
\(68\) | −1.23607 | −0.149895 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.23607 | −0.267261 | ||||||||
\(71\) | 1.35410 | − | 4.16750i | 0.160702 | − | 0.494591i | −0.837992 | − | 0.545683i | \(-0.816270\pi\) |
0.998694 | + | 0.0510922i | \(0.0162702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.28115 | − | 5.29007i | 0.852194 | − | 0.619156i | −0.0735557 | − | 0.997291i | \(-0.523435\pi\) |
0.925750 | + | 0.378136i | \(0.123435\pi\) | |||||||
\(74\) | −2.61803 | −0.304340 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.47214 | 1.08653 | ||||||||
\(77\) | 1.00000 | − | 0.726543i | 0.113961 | − | 0.0827972i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.954915 | − | 2.93893i | 0.107436 | − | 0.330655i | −0.882858 | − | 0.469640i | \(-0.844384\pi\) |
0.990295 | + | 0.138985i | \(0.0443839\pi\) | |||||||
\(80\) | −1.28115 | − | 3.94298i | −0.143237 | − | 0.440839i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.23607 | −0.357364 | ||||||||
\(83\) | 0.545085 | + | 1.67760i | 0.0598308 | + | 0.184140i | 0.976505 | − | 0.215495i | \(-0.0691366\pi\) |
−0.916674 | + | 0.399636i | \(0.869137\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.527864 | + | 1.62460i | −0.0572549 | + | 0.176212i | ||||
\(86\) | 0.927051 | − | 0.673542i | 0.0999665 | − | 0.0726299i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.38197 | − | 1.00406i | −0.147318 | − | 0.107033i | ||||
\(89\) | 7.23607 | − | 5.25731i | 0.767022 | − | 0.557274i | −0.134034 | − | 0.990977i | \(-0.542793\pi\) |
0.901056 | + | 0.433703i | \(0.142793\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.35410 | − | 4.61653i | −0.666091 | − | 0.483943i | ||||
\(92\) | 4.11803 | + | 12.6740i | 0.429335 | + | 1.32136i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.309017 | − | 0.951057i | −0.0318727 | − | 0.0980940i | ||||
\(95\) | 4.04508 | − | 12.4495i | 0.415017 | − | 1.27729i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.881966 | − | 2.71441i | 0.0895501 | − | 0.275607i | −0.896245 | − | 0.443559i | \(-0.853716\pi\) |
0.985795 | + | 0.167953i | \(0.0537155\pi\) | |||||||
\(98\) | −2.19098 | + | 1.59184i | −0.221323 | + | 0.160800i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.09017 | −0.809017 | ||||||||
\(101\) | 7.47214 | 0.743505 | 0.371753 | − | 0.928332i | \(-0.378757\pi\) | ||||
0.371753 | + | 0.928332i | \(0.378757\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.57295 | + | 10.9964i | −0.352053 | + | 1.08351i | 0.605645 | + | 0.795735i | \(0.292915\pi\) |
−0.957699 | + | 0.287773i | \(0.907085\pi\) | |||||||
\(104\) | −3.35410 | + | 10.3229i | −0.328897 | + | 1.01224i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.04508 | + | 3.21644i | 0.101508 | + | 0.312408i | ||||
\(107\) | −10.4164 | −1.00699 | −0.503496 | − | 0.863998i | \(-0.667953\pi\) | ||||
−0.503496 | + | 0.863998i | \(0.667953\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.09017 | − | 5.87785i | −0.774898 | − | 0.562996i | 0.128546 | − | 0.991704i | \(-0.458969\pi\) |
−0.903443 | + | 0.428707i | \(0.858969\pi\) | |||||||
\(110\) | −0.854102 | + | 0.620541i | −0.0814354 | + | 0.0591663i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.42705 | + | 1.76336i | 0.229335 | + | 0.166621i | ||||
\(113\) | 8.20820 | + | 5.96361i | 0.772163 | + | 0.561009i | 0.902617 | − | 0.430445i | \(-0.141643\pi\) |
−0.130454 | + | 0.991454i | \(0.541643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.4164 | 1.71734 | ||||||||
\(116\) | 1.80902 | + | 1.31433i | 0.167963 | + | 0.122032i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.56231 | −0.235879 | ||||||||
\(119\) | −0.381966 | − | 1.17557i | −0.0350148 | − | 0.107764i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.21885 | + | 9.90659i | −0.292622 | + | 0.900599i | ||||
\(122\) | 0.899187 | − | 2.76741i | 0.0814086 | − | 0.250550i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.85410 | 0.435911 | ||||||||
\(125\) | −3.45492 | + | 10.6331i | −0.309017 | + | 0.951057i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.8541 | − | 9.33905i | 1.14062 | − | 0.828707i | 0.153412 | − | 0.988162i | \(-0.450974\pi\) |
0.987205 | + | 0.159455i | \(0.0509738\pi\) | |||||||
\(128\) | 3.51722 | − | 10.8249i | 0.310881 | − | 0.956794i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.42705 | + | 3.94298i | 0.475984 | + | 0.345823i | ||||
\(131\) | 5.50000 | + | 16.9273i | 0.480537 | + | 1.47894i | 0.838342 | + | 0.545145i | \(0.183525\pi\) |
−0.357805 | + | 0.933797i | \(0.616475\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.92705 | + | 9.00854i | 0.253808 | + | 0.781139i | ||||
\(134\) | 4.61803 | + | 3.35520i | 0.398937 | + | 0.289845i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.38197 | + | 1.00406i | −0.118503 | + | 0.0860972i | ||||
\(137\) | 4.80902 | + | 3.49396i | 0.410862 | + | 0.298509i | 0.773951 | − | 0.633246i | \(-0.218278\pi\) |
−0.363089 | + | 0.931755i | \(0.618278\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.04508 | + | 2.93893i | −0.343100 | + | 0.249276i | −0.745968 | − | 0.665981i | \(-0.768013\pi\) |
0.402869 | + | 0.915258i | \(0.368013\pi\) | |||||||
\(140\) | 4.73607 | − | 3.44095i | 0.400271 | − | 0.290814i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.836881 | − | 2.57565i | −0.0702295 | − | 0.216144i | ||||
\(143\) | −3.70820 | −0.310096 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.50000 | − | 1.81636i | 0.207614 | − | 0.150840i | ||||
\(146\) | 1.71885 | − | 5.29007i | 0.142253 | − | 0.437809i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.54508 | − | 4.02874i | 0.455803 | − | 0.331160i | ||||
\(149\) | −13.9443 | −1.14236 | −0.571180 | − | 0.820825i | \(-0.693514\pi\) | ||||
−0.571180 | + | 0.820825i | \(0.693514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.56231 | −0.452654 | −0.226327 | − | 0.974051i | \(-0.572672\pi\) | ||||
−0.226327 | + | 0.974051i | \(0.572672\pi\) | |||||||
\(152\) | 10.5902 | − | 7.69421i | 0.858976 | − | 0.624083i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.236068 | − | 0.726543i | 0.0190229 | − | 0.0585465i | ||||
\(155\) | 2.07295 | − | 6.37988i | 0.166503 | − | 0.512444i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.18034 | −0.732671 | −0.366335 | − | 0.930483i | \(-0.619388\pi\) | ||||
−0.366335 | + | 0.930483i | \(0.619388\pi\) | |||||||
\(158\) | −0.590170 | − | 1.81636i | −0.0469514 | − | 0.144502i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.1631 | − | 7.38394i | −0.803465 | − | 0.583752i | ||||
\(161\) | −10.7812 | + | 7.83297i | −0.849674 | + | 0.617324i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.89919 | − | 6.46564i | −0.697038 | − | 0.506428i | 0.181928 | − | 0.983312i | \(-0.441766\pi\) |
−0.878966 | + | 0.476884i | \(0.841766\pi\) | |||||||
\(164\) | 6.85410 | − | 4.97980i | 0.535215 | − | 0.388857i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.881966 | + | 0.640786i | 0.0684538 | + | 0.0497346i | ||||
\(167\) | 1.71885 | + | 5.29007i | 0.133008 | + | 0.409358i | 0.995275 | − | 0.0970971i | \(-0.0309557\pi\) |
−0.862267 | + | 0.506455i | \(0.830956\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.26393 | + | 10.0453i | 0.251072 | + | 0.772719i | ||||
\(170\) | 0.326238 | + | 1.00406i | 0.0250213 | + | 0.0770077i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.927051 | + | 2.85317i | −0.0706870 | + | 0.217552i | ||||
\(173\) | −13.6631 | + | 9.92684i | −1.03879 | + | 0.754723i | −0.970049 | − | 0.242911i | \(-0.921898\pi\) |
−0.0687392 | + | 0.997635i | \(0.521898\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50000 | − | 7.69421i | −0.188982 | − | 0.581628i | ||||
\(176\) | 1.41641 | 0.106766 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.70820 | − | 5.25731i | 0.128035 | − | 0.394052i | ||||
\(179\) | 2.92705 | − | 9.00854i | 0.218778 | − | 0.673330i | −0.780086 | − | 0.625673i | \(-0.784825\pi\) |
0.998864 | − | 0.0476570i | \(-0.0151754\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.23607 | + | 13.0373i | 0.314864 | + | 0.969053i | 0.975810 | + | 0.218619i | \(0.0701553\pi\) |
−0.660946 | + | 0.750434i | \(0.729845\pi\) | |||||||
\(182\) | −4.85410 | −0.359810 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 14.8992 | + | 10.8249i | 1.09838 | + | 0.798022i | ||||
\(185\) | −2.92705 | − | 9.00854i | −0.215201 | − | 0.662321i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.472136 | − | 0.343027i | −0.0345260 | − | 0.0250846i | ||||
\(188\) | 2.11803 | + | 1.53884i | 0.154474 | + | 0.112232i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.50000 | − | 7.69421i | −0.181369 | − | 0.558197i | ||||
\(191\) | −19.5623 | − | 14.2128i | −1.41548 | − | 1.02841i | −0.992497 | − | 0.122267i | \(-0.960984\pi\) |
−0.422982 | − | 0.906138i | \(-0.639016\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.70820 | −0.410886 | −0.205443 | − | 0.978669i | \(-0.565863\pi\) | ||||
−0.205443 | + | 0.978669i | \(0.565863\pi\) | |||||||
\(194\) | −0.545085 | − | 1.67760i | −0.0391348 | − | 0.120445i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.19098 | − | 6.74315i | 0.156499 | − | 0.481654i | ||||
\(197\) | 3.00000 | − | 9.23305i | 0.213741 | − | 0.657828i | −0.785499 | − | 0.618862i | \(-0.787594\pi\) |
0.999241 | − | 0.0389652i | \(-0.0124062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.56231 | 0.181637 | 0.0908185 | − | 0.995867i | \(-0.471052\pi\) | ||||
0.0908185 | + | 0.995867i | \(0.471052\pi\) | |||||||
\(200\) | −9.04508 | + | 6.57164i | −0.639584 | + | 0.464685i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.73607 | − | 2.71441i | 0.262869 | − | 0.190985i | ||||
\(203\) | −0.690983 | + | 2.12663i | −0.0484975 | + | 0.149260i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.61803 | − | 11.1352i | −0.252694 | − | 0.777714i | ||||
\(206\) | 2.20820 | + | 6.79615i | 0.153853 | + | 0.473510i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.78115 | − | 8.55951i | −0.192838 | − | 0.593495i | ||||
\(209\) | 3.61803 | + | 2.62866i | 0.250265 | + | 0.181828i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6631 | + | 7.74721i | −0.734079 | + | 0.533340i | −0.890851 | − | 0.454295i | \(-0.849891\pi\) |
0.156772 | + | 0.987635i | \(0.449891\pi\) | |||||||
\(212\) | −7.16312 | − | 5.20431i | −0.491965 | − | 0.357434i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.20820 | + | 3.78398i | −0.356025 | + | 0.258668i | ||||
\(215\) | 3.35410 | + | 2.43690i | 0.228748 | + | 0.166195i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.50000 | + | 4.61653i | 0.101827 | + | 0.313390i | ||||
\(218\) | −6.18034 | −0.418585 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.854102 | − | 2.62866i | 0.0575835 | − | 0.177224i | ||||
\(221\) | −1.14590 | + | 3.52671i | −0.0770814 | + | 0.237232i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.9443 | + | 13.0373i | −1.20164 | + | 0.873041i | −0.994445 | − | 0.105260i | \(-0.966433\pi\) |
−0.207193 | + | 0.978300i | \(0.566433\pi\) | |||||||
\(224\) | 9.09017 | 0.607363 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.27051 | 0.417108 | ||||||||
\(227\) | 15.5623 | − | 11.3067i | 1.03291 | − | 0.750451i | 0.0640182 | − | 0.997949i | \(-0.479608\pi\) |
0.968888 | + | 0.247498i | \(0.0796084\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.56231 | − | 7.88597i | 0.169322 | − | 0.521119i | −0.830007 | − | 0.557753i | \(-0.811664\pi\) |
0.999329 | + | 0.0366339i | \(0.0116635\pi\) | |||||||
\(230\) | 9.20820 | − | 6.69015i | 0.607171 | − | 0.441136i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.09017 | 0.202880 | ||||||||
\(233\) | −4.61803 | − | 14.2128i | −0.302537 | − | 0.931115i | −0.980585 | − | 0.196096i | \(-0.937174\pi\) |
0.678047 | − | 0.735018i | \(-0.262826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.92705 | − | 2.12663i | 0.190940 | − | 0.138726i | ||||
\(236\) | 5.42705 | − | 3.94298i | 0.353271 | − | 0.256666i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.618034 | − | 0.449028i | −0.0400612 | − | 0.0291062i | ||||
\(239\) | −23.8435 | + | 17.3233i | −1.54231 | + | 1.12055i | −0.593436 | + | 0.804881i | \(0.702229\pi\) |
−0.948869 | + | 0.315669i | \(0.897771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.28115 | − | 6.74315i | −0.597852 | − | 0.434365i | 0.247264 | − | 0.968948i | \(-0.420468\pi\) |
−0.845116 | + | 0.534584i | \(0.820468\pi\) | |||||||
\(242\) | 1.98936 | + | 6.12261i | 0.127881 | + | 0.393576i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.35410 | + | 7.24518i | 0.150706 | + | 0.463825i | ||||
\(245\) | −7.92705 | − | 5.75934i | −0.506441 | − | 0.367951i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.78115 | − | 27.0256i | 0.558731 | − | 1.71960i | ||||
\(248\) | 5.42705 | − | 3.94298i | 0.344618 | − | 0.250380i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.13525 | + | 6.57164i | 0.135045 | + | 0.415627i | ||||
\(251\) | 6.81966 | 0.430453 | 0.215227 | − | 0.976564i | \(-0.430951\pi\) | ||||
0.215227 | + | 0.976564i | \(0.430951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.94427 | + | 5.98385i | −0.122235 | + | 0.376202i | ||||
\(254\) | 3.03444 | − | 9.33905i | 0.190398 | − | 0.585984i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.02786 | − | 6.24112i | −0.126742 | − | 0.390070i | ||||
\(257\) | −16.1459 | −1.00715 | −0.503577 | − | 0.863951i | \(-0.667983\pi\) | ||||
−0.503577 | + | 0.863951i | \(0.667983\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.54508 | + | 4.02874i | 0.344555 | + | 0.250334i | ||||
\(260\) | −17.5623 | −1.08917 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.89919 | + | 6.46564i | 0.549794 | + | 0.399448i | ||||
\(263\) | −17.8713 | − | 12.9843i | −1.10199 | − | 0.800645i | −0.120609 | − | 0.992700i | \(-0.538485\pi\) |
−0.981384 | + | 0.192055i | \(0.938485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.89919 | + | 7.19218i | −0.608102 | + | 0.441812i | ||||
\(266\) | 4.73607 | + | 3.44095i | 0.290387 | + | 0.210978i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.9443 | −0.912867 | ||||||||
\(269\) | 5.32624 | + | 16.3925i | 0.324746 | + | 0.999467i | 0.971555 | + | 0.236814i | \(0.0761033\pi\) |
−0.646808 | + | 0.762652i | \(0.723897\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.47214 | + | 7.60845i | −0.150172 | + | 0.462181i | −0.997640 | − | 0.0686657i | \(-0.978126\pi\) |
0.847468 | + | 0.530846i | \(0.178126\pi\) | |||||||
\(272\) | 0.437694 | − | 1.34708i | 0.0265391 | − | 0.0816790i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.67376 | 0.221940 | ||||||||
\(275\) | −3.09017 | − | 2.24514i | −0.186344 | − | 0.135387i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.13525 | − | 6.63715i | 0.548884 | − | 0.398788i | −0.278490 | − | 0.960439i | \(-0.589834\pi\) |
0.827374 | + | 0.561651i | \(0.189834\pi\) | |||||||
\(278\) | −0.954915 | + | 2.93893i | −0.0572720 | + | 0.176265i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.50000 | − | 7.69421i | 0.149404 | − | 0.459817i | ||||
\(281\) | 0.336881 | + | 1.03681i | 0.0200966 | + | 0.0618511i | 0.960602 | − | 0.277928i | \(-0.0896477\pi\) |
−0.940505 | + | 0.339779i | \(0.889648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.15248 | − | 22.0131i | −0.425171 | − | 1.30854i | −0.902831 | − | 0.429996i | \(-0.858515\pi\) |
0.477660 | − | 0.878545i | \(-0.341485\pi\) | |||||||
\(284\) | 5.73607 | + | 4.16750i | 0.340373 | + | 0.247295i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.85410 | + | 1.34708i | −0.109635 | + | 0.0796547i | ||||
\(287\) | 6.85410 | + | 4.97980i | 0.404585 | + | 0.293948i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.2812 | − | 9.64932i | 0.781244 | − | 0.567607i | ||||
\(290\) | 0.590170 | − | 1.81636i | 0.0346560 | − | 0.106660i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.50000 | + | 13.8496i | 0.263343 | + | 0.810485i | ||||
\(293\) | 28.4721 | 1.66336 | 0.831680 | − | 0.555255i | \(-0.187379\pi\) | ||||
0.831680 | + | 0.555255i | \(0.187379\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.86475 | − | 8.81678i | −0.166792 | − | 0.513333i | ||||
\(296\) | 2.92705 | − | 9.00854i | 0.170131 | − | 0.523611i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.97214 | + | 5.06555i | −0.403885 | + | 0.293440i | ||||
\(299\) | 39.9787 | 2.31203 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | −0.172917 | ||||||||
\(302\) | −2.78115 | + | 2.02063i | −0.160037 | + | 0.116274i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.35410 | + | 10.3229i | −0.192371 | + | 0.592057i | ||||
\(305\) | 10.5279 | 0.602824 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.76393 | 0.271892 | 0.135946 | − | 0.990716i | \(-0.456593\pi\) | ||||
0.135946 | + | 0.990716i | \(0.456593\pi\) | |||||||
\(308\) | 0.618034 | + | 1.90211i | 0.0352158 | + | 0.108383i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.28115 | − | 3.94298i | −0.0727646 | − | 0.223946i | ||||
\(311\) | −23.8713 | + | 17.3435i | −1.35362 | + | 0.983461i | −0.354796 | + | 0.934944i | \(0.615450\pi\) |
−0.998822 | + | 0.0485178i | \(0.984550\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.1803 | + | 12.4822i | 0.971090 | + | 0.705538i | 0.955700 | − | 0.294343i | \(-0.0951009\pi\) |
0.0153904 | + | 0.999882i | \(0.495101\pi\) | |||||||
\(314\) | −4.59017 | + | 3.33495i | −0.259038 | + | 0.188202i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.04508 | + | 2.93893i | 0.227554 | + | 0.165328i | ||||
\(317\) | 7.30902 | + | 22.4948i | 0.410515 | + | 1.26344i | 0.916201 | + | 0.400719i | \(0.131239\pi\) |
−0.505686 | + | 0.862718i | \(0.668761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.326238 | + | 1.00406i | 0.0182658 | + | 0.0562164i | ||||
\(320\) | 0.527864 | 0.0295085 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.54508 | + | 7.83297i | −0.141832 | + | 0.436514i | ||||
\(323\) | 3.61803 | − | 2.62866i | 0.201313 | − | 0.146262i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.50000 | + | 23.0826i | −0.416025 | + | 1.28039i | ||||
\(326\) | −6.79837 | −0.376527 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.61803 | − | 11.1352i | 0.199773 | − | 0.614837i | ||||
\(329\) | −0.809017 | + | 2.48990i | −0.0446026 | + | 0.137273i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.29180 | + | 16.2865i | 0.290863 | + | 0.895186i | 0.984580 | + | 0.174937i | \(0.0559722\pi\) |
−0.693716 | + | 0.720248i | \(0.744028\pi\) | |||||||
\(332\) | −2.85410 | −0.156639 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.78115 | + | 2.02063i | 0.152178 | + | 0.110564i | ||||
\(335\) | −6.38197 | + | 19.6417i | −0.348684 | + | 1.07314i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.927051 | − | 0.673542i | −0.0504997 | − | 0.0366902i | 0.562249 | − | 0.826968i | \(-0.309936\pi\) |
−0.612749 | + | 0.790278i | \(0.709936\pi\) | |||||||
\(338\) | 5.28115 | + | 3.83698i | 0.287257 | + | 0.208704i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.23607 | − | 1.62460i | −0.121268 | − | 0.0881062i | ||||
\(341\) | 1.85410 | + | 1.34708i | 0.100405 | + | 0.0729487i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4164 | 0.994393 | ||||||||
\(344\) | 1.28115 | + | 3.94298i | 0.0690751 | + | 0.212591i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.22542 | + | 9.92684i | −0.173400 | + | 0.533670i | ||||
\(347\) | 9.60739 | − | 29.5685i | 0.515752 | − | 1.58732i | −0.266158 | − | 0.963929i | \(-0.585754\pi\) |
0.781910 | − | 0.623391i | \(-0.214246\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.29180 | 0.443850 | 0.221925 | − | 0.975064i | \(-0.428766\pi\) | ||||
0.221925 | + | 0.975064i | \(0.428766\pi\) | |||||||
\(350\) | −4.04508 | − | 2.93893i | −0.216219 | − | 0.157092i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.47214 | − | 2.52265i | 0.185065 | − | 0.134458i | ||||
\(353\) | −7.44427 | + | 22.9111i | −0.396219 | + | 1.21944i | 0.531790 | + | 0.846876i | \(0.321520\pi\) |
−0.928008 | + | 0.372559i | \(0.878480\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.92705 | − | 5.75934i | 0.420724 | − | 0.305674i | ||||
\(356\) | 4.47214 | + | 13.7638i | 0.237023 | + | 0.729481i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.80902 | − | 5.56758i | −0.0956095 | − | 0.294256i | ||||
\(359\) | −23.2533 | − | 16.8945i | −1.22726 | − | 0.891658i | −0.230580 | − | 0.973053i | \(-0.574062\pi\) |
−0.996682 | + | 0.0813956i | \(0.974062\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3541 | + | 8.97578i | −0.650216 | + | 0.472409i | ||||
\(362\) | 6.85410 | + | 4.97980i | 0.360244 | + | 0.261732i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.2812 | − | 7.46969i | 0.538879 | − | 0.391518i | ||||
\(365\) | 20.1246 | 1.05337 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.68034 | − | 5.17155i | −0.0877130 | − | 0.269953i | 0.897573 | − | 0.440866i | \(-0.145328\pi\) |
−0.985286 | + | 0.170913i | \(0.945328\pi\) | |||||||
\(368\) | −15.2705 | −0.796030 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.73607 | − | 3.44095i | −0.246216 | − | 0.178887i | ||||
\(371\) | 2.73607 | − | 8.42075i | 0.142050 | − | 0.437184i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.26393 | + | 3.09793i | −0.220778 | + | 0.160405i | −0.692677 | − | 0.721248i | \(-0.743569\pi\) |
0.471899 | + | 0.881653i | \(0.343569\pi\) | |||||||
\(374\) | −0.360680 | −0.0186503 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.61803 | 0.186586 | ||||||||
\(377\) | 5.42705 | − | 3.94298i | 0.279507 | − | 0.203074i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.6910 | + | 32.9035i | −0.549159 | + | 1.69014i | 0.161732 | + | 0.986835i | \(0.448292\pi\) |
−0.710891 | + | 0.703303i | \(0.751708\pi\) | |||||||
\(380\) | 17.1353 | + | 12.4495i | 0.879020 | + | 0.638645i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.9443 | −0.764615 | ||||||||
\(383\) | 3.51064 | + | 10.8046i | 0.179385 | + | 0.552092i | 0.999807 | − | 0.0196680i | \(-0.00626093\pi\) |
−0.820421 | + | 0.571760i | \(0.806261\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.76393 | 0.140863 | ||||||||
\(386\) | −2.85410 | + | 2.07363i | −0.145270 | + | 0.105545i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.73607 | + | 2.71441i | 0.189670 | + | 0.137803i | ||||
\(389\) | 12.1353 | − | 8.81678i | 0.615282 | − | 0.447028i | −0.235988 | − | 0.971756i | \(-0.575833\pi\) |
0.851270 | + | 0.524727i | \(0.175833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.09017 | + | 3.69822i | 0.257421 | + | 0.187027i | ||||
\(392\) | −3.02786 | − | 9.31881i | −0.152930 | − | 0.470671i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.85410 | − | 5.70634i | −0.0934083 | − | 0.287481i | ||||
\(395\) | 5.59017 | − | 4.06150i | 0.281272 | − | 0.204356i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.0106431 | + | 0.0327561i | −0.000534163 | + | 0.00164398i | −0.951323 | − | 0.308195i | \(-0.900275\pi\) |
0.950789 | + | 0.309839i | \(0.100275\pi\) | |||||||
\(398\) | 1.28115 | − | 0.930812i | 0.0642184 | − | 0.0466574i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.86475 | − | 8.81678i | 0.143237 | − | 0.440839i | ||||
\(401\) | 22.5967 | 1.12843 | 0.564214 | − | 0.825629i | \(-0.309179\pi\) | ||||
0.564214 | + | 0.825629i | \(0.309179\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.50000 | − | 13.8496i | 0.224161 | − | 0.689897i | ||||
\(404\) | −3.73607 | + | 11.4984i | −0.185876 | + | 0.572069i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.427051 | + | 1.31433i | 0.0211942 | + | 0.0652290i | ||||
\(407\) | 3.23607 | 0.160406 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.9894 | − | 16.7027i | −1.13675 | − | 0.825898i | −0.150087 | − | 0.988673i | \(-0.547955\pi\) |
−0.986663 | + | 0.162775i | \(0.947955\pi\) | |||||||
\(410\) | −5.85410 | − | 4.25325i | −0.289113 | − | 0.210053i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.1353 | − | 10.9964i | −0.745660 | − | 0.541754i | ||||
\(413\) | 5.42705 | + | 3.94298i | 0.267048 | + | 0.194022i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.21885 | + | 3.75123i | −0.0598308 | + | 0.184140i | ||||
\(416\) | −22.0623 | − | 16.0292i | −1.08169 | − | 0.785896i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.76393 | 0.135188 | ||||||||
\(419\) | 0.163119 | + | 0.502029i | 0.00796888 | + | 0.0245257i | 0.954962 | − | 0.296728i | \(-0.0958956\pi\) |
−0.946993 | + | 0.321254i | \(0.895896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.88854 | − | 30.4338i | 0.481938 | − | 1.48325i | −0.354429 | − | 0.935083i | \(-0.615325\pi\) |
0.836367 | − | 0.548170i | \(-0.184675\pi\) | |||||||
\(422\) | −2.51722 | + | 7.74721i | −0.122536 | + | 0.377128i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.2361 | −0.594236 | ||||||||
\(425\) | −3.09017 | + | 2.24514i | −0.149895 | + | 0.108905i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.16312 | + | 4.47777i | −0.298254 | + | 0.216694i | ||||
\(428\) | 5.20820 | − | 16.0292i | 0.251748 | − | 0.774801i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.56231 | 0.123565 | ||||||||
\(431\) | −7.36475 | − | 22.6664i | −0.354747 | − | 1.09180i | −0.956156 | − | 0.292858i | \(-0.905394\pi\) |
0.601409 | − | 0.798942i | \(-0.294606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.22542 | + | 19.1599i | 0.299175 | + | 0.920765i | 0.981787 | + | 0.189985i | \(0.0608438\pi\) |
−0.682612 | + | 0.730781i | \(0.739156\pi\) | |||||||
\(434\) | 2.42705 | + | 1.76336i | 0.116502 | + | 0.0846438i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.0902 | − | 9.51057i | 0.626905 | − | 0.455473i | ||||
\(437\) | −39.0066 | − | 28.3399i | −1.86594 | − | 1.35568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.83688 | + | 3.51420i | −0.230852 | + | 0.167724i | −0.697198 | − | 0.716879i | \(-0.745570\pi\) |
0.466346 | + | 0.884602i | \(0.345570\pi\) | |||||||
\(440\) | −1.18034 | − | 3.63271i | −0.0562705 | − | 0.173183i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.708204 | + | 2.17963i | 0.0336858 | + | 0.103674i | ||||
\(443\) | −12.0557 | −0.572785 | −0.286392 | − | 0.958112i | \(-0.592456\pi\) | ||||
−0.286392 | + | 0.958112i | \(0.592456\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.0000 | 0.948091 | ||||||||
\(446\) | −4.23607 | + | 13.0373i | −0.200584 | + | 0.617333i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.309017 | + | 0.224514i | −0.0145997 | + | 0.0106073i | ||||
\(449\) | −20.3262 | −0.959254 | −0.479627 | − | 0.877472i | \(-0.659228\pi\) | ||||
−0.479627 | + | 0.877472i | \(0.659228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | −13.2812 | + | 9.64932i | −0.624693 | + | 0.453866i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.67376 | − | 11.3067i | 0.172418 | − | 0.530649i | ||||
\(455\) | −5.42705 | − | 16.7027i | −0.254424 | − | 0.783037i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.41641 | 0.253369 | 0.126684 | − | 0.991943i | \(-0.459566\pi\) | ||||
0.126684 | + | 0.991943i | \(0.459566\pi\) | |||||||
\(458\) | −1.58359 | − | 4.87380i | −0.0739964 | − | 0.227738i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.20820 | + | 28.3399i | −0.429335 | + | 1.32136i | ||||
\(461\) | 18.7533 | − | 13.6251i | 0.873428 | − | 0.634582i | −0.0580768 | − | 0.998312i | \(-0.518497\pi\) |
0.931505 | + | 0.363730i | \(0.118497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.0451 | − | 9.47781i | −0.606257 | − | 0.440471i | 0.241838 | − | 0.970317i | \(-0.422250\pi\) |
−0.848094 | + | 0.529846i | \(0.822250\pi\) | |||||||
\(464\) | −2.07295 | + | 1.50609i | −0.0962342 | + | 0.0699183i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.47214 | − | 5.42882i | −0.346140 | − | 0.251485i | ||||
\(467\) | 8.79180 | + | 27.0584i | 0.406836 | + | 1.25211i | 0.919353 | + | 0.393435i | \(0.128713\pi\) |
−0.512517 | + | 0.858677i | \(0.671287\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.61803 | − | 14.2128i | −0.213241 | − | 0.656288i | ||||
\(470\) | 0.690983 | − | 2.12663i | 0.0318727 | − | 0.0980940i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.86475 | − | 8.81678i | 0.131861 | − | 0.405825i | ||||
\(473\) | −1.14590 | + | 0.832544i | −0.0526884 | + | 0.0382804i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.6803 | − | 17.2048i | 1.08653 | − | 0.789409i | ||||
\(476\) | 2.00000 | 0.0916698 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.62868 | + | 17.3233i | −0.257450 | + | 0.792349i | ||||
\(479\) | 1.28115 | − | 3.94298i | 0.0585374 | − | 0.180160i | −0.917512 | − | 0.397708i | \(-0.869806\pi\) |
0.976050 | + | 0.217548i | \(0.0698059\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.35410 | − | 19.5559i | −0.289722 | − | 0.891673i | ||||
\(482\) | −7.09017 | −0.322948 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.6353 | − | 9.90659i | −0.619784 | − | 0.450300i | ||||
\(485\) | 5.16312 | − | 3.75123i | 0.234445 | − | 0.170334i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.75329 | + | 5.63309i | 0.351335 | + | 0.255260i | 0.749429 | − | 0.662085i | \(-0.230328\pi\) |
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(488\) | 8.51722 | + | 6.18812i | 0.385556 | + | 0.280123i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.05573 | −0.273570 | ||||||||
\(491\) | 30.1353 | + | 21.8945i | 1.35999 | + | 0.988087i | 0.998446 | + | 0.0557300i | \(0.0177486\pi\) |
0.361539 | + | 0.932357i | \(0.382251\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.05573 | 0.0475476 | ||||||||
\(494\) | −5.42705 | − | 16.7027i | −0.244175 | − | 0.751492i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.71885 | + | 5.29007i | −0.0771785 | + | 0.237531i | ||||
\(497\) | −2.19098 | + | 6.74315i | −0.0982790 | + | 0.302472i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.5623 | −0.562366 | −0.281183 | − | 0.959654i | \(-0.590727\pi\) | ||||
−0.281183 | + | 0.959654i | \(0.590727\pi\) | |||||||
\(500\) | −14.6353 | − | 10.6331i | −0.654508 | − | 0.475528i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.40983 | − | 2.47739i | 0.152188 | − | 0.110571i | ||||
\(503\) | 3.27051 | − | 10.0656i | 0.145825 | − | 0.448803i | −0.851291 | − | 0.524693i | \(-0.824180\pi\) |
0.997116 | + | 0.0758907i | \(0.0241800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5172 | + | 9.82084i | 0.601508 | + | 0.437021i | ||||
\(506\) | 1.20163 | + | 3.69822i | 0.0534188 | + | 0.164406i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.94427 | + | 24.4500i | 0.352470 | + | 1.08479i | ||||
\(509\) | −3.78115 | − | 2.74717i | −0.167597 | − | 0.121766i | 0.500825 | − | 0.865548i | \(-0.333030\pi\) |
−0.668422 | + | 0.743782i | \(0.733030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.7812 | + | 8.55951i | −0.521168 | + | 0.378650i | ||||
\(512\) | 15.1353 | + | 10.9964i | 0.668890 | + | 0.485977i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.07295 | + | 5.86534i | −0.356083 | + | 0.258709i | ||||
\(515\) | −20.9164 | + | 15.1967i | −0.921687 | + | 0.669645i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.381966 | + | 1.17557i | 0.0167988 | + | 0.0517015i | ||||
\(518\) | 4.23607 | 0.186122 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −19.6353 | + | 14.2658i | −0.861063 | + | 0.625599i | ||||
\(521\) | 4.74671 | − | 14.6089i | 0.207957 | − | 0.640026i | −0.791622 | − | 0.611011i | \(-0.790763\pi\) |
0.999579 | − | 0.0290150i | \(-0.00923706\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0623 | − | 11.6699i | 0.702356 | − | 0.510291i | −0.178343 | − | 0.983968i | \(-0.557074\pi\) |
0.880699 | + | 0.473677i | \(0.157074\pi\) | |||||||
\(524\) | −28.7984 | −1.25806 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.6525 | −0.595276 | ||||||||
\(527\) | 1.85410 | − | 1.34708i | 0.0807660 | − | 0.0586799i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.8541 | − | 42.6385i | 0.602352 | − | 1.85385i | ||||
\(530\) | −2.33688 | + | 7.19218i | −0.101508 | + | 0.312408i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −15.3262 | −0.664477 | ||||||||
\(533\) | −7.85410 | − | 24.1724i | −0.340199 | − | 1.04702i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.8435 | − | 13.6906i | −0.814674 | − | 0.591895i | ||||
\(536\) | −16.7082 | + | 12.1392i | −0.721684 | + | 0.524334i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.61803 | + | 6.26137i | 0.371550 | + | 0.269947i | ||||
\(539\) | 2.70820 | − | 1.96763i | 0.116651 | − | 0.0847516i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.6180 | + | 7.71445i | 0.456505 | + | 0.331670i | 0.792159 | − | 0.610315i | \(-0.208957\pi\) |
−0.335654 | + | 0.941985i | \(0.608957\pi\) | |||||||
\(542\) | 1.52786 | + | 4.70228i | 0.0656274 | + | 0.201980i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.32624 | − | 4.08174i | −0.0568620 | − | 0.175003i | ||||
\(545\) | −6.90983 | − | 21.2663i | −0.295985 | − | 0.910947i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.7254 | + | 33.0095i | −0.458586 | + | 1.41138i | 0.408287 | + | 0.912854i | \(0.366126\pi\) |
−0.866873 | + | 0.498529i | \(0.833874\pi\) | |||||||
\(548\) | −7.78115 | + | 5.65334i | −0.332394 | + | 0.241499i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.36068 | −0.100660 | ||||||||
\(551\) | −8.09017 | −0.344653 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.54508 | + | 4.75528i | −0.0657037 | + | 0.202215i | ||||
\(554\) | 2.15654 | − | 6.63715i | 0.0916227 | − | 0.281986i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.50000 | − | 7.69421i | −0.106024 | − | 0.326307i | ||||
\(557\) | −9.23607 | −0.391345 | −0.195672 | − | 0.980669i | \(-0.562689\pi\) | ||||
−0.195672 | + | 0.980669i | \(0.562689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.28115 | + | 5.29007i | 0.307960 | + | 0.223746i | ||||
\(560\) | 2.07295 | + | 6.37988i | 0.0875981 | + | 0.269599i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.545085 | + | 0.396027i | 0.0229930 | + | 0.0167054i | ||||
\(563\) | 7.78115 | + | 5.65334i | 0.327936 | + | 0.238260i | 0.739555 | − | 0.673097i | \(-0.235036\pi\) |
−0.411618 | + | 0.911356i | \(0.635036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.01064 | + | 21.5765i | 0.294940 | + | 0.907732i | ||||
\(566\) | −11.5729 | − | 8.40824i | −0.486447 | − | 0.353425i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.79837 | 0.411131 | ||||||||
\(569\) | −9.10739 | − | 28.0297i | −0.381802 | − | 1.17506i | −0.938774 | − | 0.344534i | \(-0.888037\pi\) |
0.556972 | − | 0.830531i | \(-0.311963\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.92705 | − | 30.5523i | 0.415434 | − | 1.27857i | −0.496428 | − | 0.868078i | \(-0.665355\pi\) |
0.911862 | − | 0.410497i | \(-0.134645\pi\) | |||||||
\(572\) | 1.85410 | − | 5.70634i | 0.0775239 | − | 0.238594i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.23607 | 0.218549 | ||||||||
\(575\) | 33.3156 | + | 24.2052i | 1.38936 | + | 1.00943i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.5623 | + | 22.2048i | −1.27233 | + | 0.924399i | −0.999293 | − | 0.0376062i | \(-0.988027\pi\) |
−0.273033 | + | 0.962005i | \(0.588027\pi\) | |||||||
\(578\) | 3.13525 | − | 9.64932i | 0.130409 | − | 0.401359i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.54508 | + | 4.75528i | 0.0641562 | + | 0.197452i | ||||
\(581\) | −0.881966 | − | 2.71441i | −0.0365901 | − | 0.112613i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.29180 | − | 3.97574i | −0.0535007 | − | 0.164658i | ||||
\(584\) | 16.2812 | + | 11.8290i | 0.673719 | + | 0.489485i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.2361 | − | 10.3431i | 0.588087 | − | 0.427270i | ||||
\(587\) | 15.1353 | + | 10.9964i | 0.624699 | + | 0.453870i | 0.854560 | − | 0.519353i | \(-0.173827\pi\) |
−0.229861 | + | 0.973224i | \(0.573827\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.2082 | + | 10.3229i | −0.585439 | + | 0.425346i | ||||
\(590\) | −4.63525 | − | 3.36771i | −0.190830 | − | 0.138646i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.42705 | + | 7.46969i | 0.0997512 | + | 0.307003i | ||||
\(593\) | 22.0902 | 0.907135 | 0.453567 | − | 0.891222i | \(-0.350151\pi\) | ||||
0.453567 | + | 0.891222i | \(0.350151\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.854102 | − | 2.62866i | 0.0350148 | − | 0.107764i | ||||
\(596\) | 6.97214 | − | 21.4580i | 0.285590 | − | 0.878955i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 19.9894 | − | 14.5231i | 0.817426 | − | 0.593894i | ||||
\(599\) | 0.527864 | 0.0215679 | 0.0107840 | − | 0.999942i | \(-0.496567\pi\) | ||||
0.0107840 | + | 0.999942i | \(0.496567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2705 | 1.47950 | 0.739752 | − | 0.672879i | \(-0.234943\pi\) | ||||
0.739752 | + | 0.672879i | \(0.234943\pi\) | |||||||
\(602\) | −1.50000 | + | 1.08981i | −0.0611354 | + | 0.0444175i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.78115 | − | 8.55951i | 0.113164 | − | 0.348281i | ||||
\(605\) | −18.8435 | + | 13.6906i | −0.766096 | + | 0.556601i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.4377 | −0.626597 | −0.313298 | − | 0.949655i | \(-0.601434\pi\) | ||||
−0.313298 | + | 0.949655i | \(0.601434\pi\) | |||||||
\(608\) | 10.1631 | + | 31.2789i | 0.412169 | + | 1.26853i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.26393 | − | 3.82447i | 0.213130 | − | 0.154848i | ||||
\(611\) | 6.35410 | − | 4.61653i | 0.257059 | − | 0.186765i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.8713 | − | 18.7966i | −1.04493 | − | 0.759188i | −0.0736905 | − | 0.997281i | \(-0.523478\pi\) |
−0.971242 | + | 0.238093i | \(0.923478\pi\) | |||||||
\(614\) | 2.38197 | − | 1.73060i | 0.0961283 | − | 0.0698413i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.23607 | + | 1.62460i | 0.0900937 | + | 0.0654569i | ||||
\(617\) | −3.01722 | − | 9.28605i | −0.121469 | − | 0.373842i | 0.871772 | − | 0.489911i | \(-0.162971\pi\) |
−0.993241 | + | 0.116069i | \(0.962971\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.1976 | + | 37.5402i | 0.490261 | + | 1.50887i | 0.824213 | + | 0.566279i | \(0.191618\pi\) |
−0.333952 | + | 0.942590i | \(0.608382\pi\) | |||||||
\(620\) | 8.78115 | + | 6.37988i | 0.352660 | + | 0.256222i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.63525 | + | 17.3435i | −0.225953 | + | 0.695412i | ||||
\(623\) | −11.7082 | + | 8.50651i | −0.469079 | + | 0.340806i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.2254 | + | 14.6946i | −0.809017 | + | 0.587785i | ||||
\(626\) | 13.1246 | 0.524565 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.59017 | − | 14.1271i | 0.183168 | − | 0.563732i | ||||
\(629\) | 1.00000 | − | 3.07768i | 0.0398726 | − | 0.122715i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.78115 | − | 5.48183i | −0.0709066 | − | 0.218228i | 0.909323 | − | 0.416090i | \(-0.136600\pi\) |
−0.980230 | + | 0.197862i | \(0.936600\pi\) | |||||||
\(632\) | 6.90983 | 0.274858 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.8262 | + | 8.59226i | 0.469680 | + | 0.341242i | ||||
\(635\) | 35.5279 | 1.40988 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.2082 | − | 12.5025i | −0.681814 | − | 0.495367i | ||||
\(638\) | 0.527864 | + | 0.383516i | 0.0208983 | + | 0.0151835i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.5902 | − | 14.9596i | 0.813898 | − | 0.591331i | ||||
\(641\) | 8.16312 | + | 5.93085i | 0.322424 | + | 0.234255i | 0.737209 | − | 0.675665i | \(-0.236143\pi\) |
−0.414785 | + | 0.909919i | \(0.636143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.8328 | 0.900438 | 0.450219 | − | 0.892918i | \(-0.351346\pi\) | ||||
0.450219 | + | 0.892918i | \(0.351346\pi\) | |||||||
\(644\) | −6.66312 | − | 20.5070i | −0.262564 | − | 0.808088i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.854102 | − | 2.62866i | 0.0336042 | − | 0.103423i | ||||
\(647\) | −9.43769 | + | 29.0462i | −0.371034 | + | 1.14193i | 0.575082 | + | 0.818096i | \(0.304970\pi\) |
−0.946116 | + | 0.323829i | \(0.895030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.16718 | 0.124323 | ||||||||
\(650\) | 4.63525 | + | 14.2658i | 0.181810 | + | 0.559553i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.3992 | − | 10.4616i | 0.563916 | − | 0.409709i | ||||
\(653\) | −2.44427 | + | 7.52270i | −0.0956518 | + | 0.294386i | −0.987423 | − | 0.158101i | \(-0.949463\pi\) |
0.891771 | + | 0.452487i | \(0.149463\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.2984 | + | 37.8505i | −0.480537 | + | 1.47894i | ||||
\(656\) | 3.00000 | + | 9.23305i | 0.117130 | + | 0.360490i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.500000 | + | 1.53884i | 0.0194920 | + | 0.0599903i | ||||
\(659\) | 19.7984 | + | 14.3844i | 0.771235 | + | 0.560335i | 0.902336 | − | 0.431034i | \(-0.141851\pi\) |
−0.131101 | + | 0.991369i | \(0.541851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.9164 | − | 23.9152i | 1.28030 | − | 0.930192i | 0.280738 | − | 0.959784i | \(-0.409421\pi\) |
0.999562 | + | 0.0295922i | \(0.00942086\pi\) | |||||||
\(662\) | 8.56231 | + | 6.22088i | 0.332783 | + | 0.241781i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.19098 | + | 2.31838i | −0.123834 | + | 0.0899708i | ||||
\(665\) | −6.54508 | + | 20.1437i | −0.253808 | + | 0.781139i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.51722 | − | 10.8249i | −0.136187 | − | 0.419142i | ||||
\(668\) | −9.00000 | −0.348220 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.94427 | + | 12.1392i | 0.152381 | + | 0.468979i | ||||
\(671\) | −1.11146 | + | 3.42071i | −0.0429073 | + | 0.132055i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.23607 | − | 5.98385i | 0.317477 | − | 0.230661i | −0.417621 | − | 0.908621i | \(-0.637136\pi\) |
0.735098 | + | 0.677961i | \(0.237136\pi\) | |||||||
\(674\) | −0.708204 | −0.0272790 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.0902 | −0.657314 | ||||||||
\(677\) | 6.78115 | − | 4.92680i | 0.260621 | − | 0.189352i | −0.449800 | − | 0.893129i | \(-0.648505\pi\) |
0.710421 | + | 0.703777i | \(0.248505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.42705 | + | 4.39201i | −0.0547652 | + | 0.168550i | ||||
\(680\) | −3.81966 | −0.146477 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.41641 | 0.0542371 | ||||||||
\(683\) | 1.39919 | + | 4.30625i | 0.0535384 | + | 0.164774i | 0.974251 | − | 0.225468i | \(-0.0723912\pi\) |
−0.920712 | + | 0.390242i | \(0.872391\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.10739 | + | 12.6412i | 0.156935 | + | 0.482997i | ||||
\(686\) | 9.20820 | − | 6.69015i | 0.351571 | − | 0.255431i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.78115 | − | 2.02063i | −0.106030 | − | 0.0770356i | ||||
\(689\) | −21.4894 | + | 15.6129i | −0.818679 | + | 0.594805i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.20820 | − | 1.60435i | −0.0840040 | − | 0.0610325i | 0.544991 | − | 0.838442i | \(-0.316533\pi\) |
−0.628995 | + | 0.777410i | \(0.716533\pi\) | |||||||
\(692\) | −8.44427 | − | 25.9888i | −0.321003 | − | 0.987946i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.93769 | − | 18.2743i | −0.225392 | − | 0.693685i | ||||
\(695\) | −11.1803 | −0.424094 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.23607 | − | 3.80423i | 0.0468194 | − | 0.144095i | ||||
\(698\) | 4.14590 | − | 3.01217i | 0.156925 | − | 0.114012i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 13.0902 | 0.494762 | ||||||||
\(701\) | −35.0132 | −1.32243 | −0.661214 | − | 0.750197i | \(-0.729959\pi\) | ||||
−0.661214 | + | 0.750197i | \(0.729959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.66312 | + | 23.5847i | −0.289020 | + | 0.889512i | ||||
\(704\) | −0.0557281 | + | 0.171513i | −0.00210033 | + | 0.00646416i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.60081 | + | 14.1598i | 0.173154 | + | 0.532913i | ||||
\(707\) | −12.0902 | −0.454698 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.1353 | − | 19.7149i | −1.01909 | − | 0.740409i | −0.0529906 | − | 0.998595i | \(-0.516875\pi\) |
−0.966095 | + | 0.258186i | \(0.916875\pi\) | |||||||
\(710\) | 1.87132 | − | 5.75934i | 0.0702295 | − | 0.216144i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.1803 | + | 11.7557i | 0.606384 | + | 0.440564i | ||||
\(713\) | −19.9894 | − | 14.5231i | −0.748607 | − | 0.543895i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.70820 | − | 4.87380i | −0.250873 | − | 0.182270i | ||||
\(716\) | 12.3992 | + | 9.00854i | 0.463379 | + | 0.336665i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17.7639 | −0.662944 | ||||||||
\(719\) | 11.3435 | + | 34.9116i | 0.423040 | + | 1.30198i | 0.904859 | + | 0.425712i | \(0.139976\pi\) |
−0.481819 | + | 0.876271i | \(0.660024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.78115 | − | 17.7926i | 0.215301 | − | 0.662630i | ||||
\(722\) | −2.91641 | + | 8.97578i | −0.108537 | + | 0.334044i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.1803 | −0.824326 | ||||||||
\(725\) | 6.90983 | 0.256625 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.59017 | + | 2.60841i | −0.133152 | + | 0.0967406i | −0.652368 | − | 0.757903i | \(-0.726224\pi\) |
0.519216 | + | 0.854643i | \(0.326224\pi\) | |||||||
\(728\) | 5.42705 | − | 16.7027i | 0.201140 | − | 0.619045i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.0623 | − | 7.31069i | 0.372423 | − | 0.270581i | ||||
\(731\) | 0.437694 | + | 1.34708i | 0.0161887 | + | 0.0498237i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.33688 | + | 25.6583i | 0.307930 | + | 0.947710i | 0.978568 | + | 0.205925i | \(0.0660204\pi\) |
−0.670638 | + | 0.741785i | \(0.733980\pi\) | |||||||
\(734\) | −2.71885 | − | 1.97536i | −0.100354 | − | 0.0729118i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −37.4336 | + | 27.1971i | −1.37982 | + | 1.00250i | ||||
\(737\) | −5.70820 | − | 4.14725i | −0.210264 | − | 0.152766i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.0623 | − | 18.2088i | 0.921932 | − | 0.669823i | −0.0220723 | − | 0.999756i | \(-0.507026\pi\) |
0.944004 | + | 0.329934i | \(0.107026\pi\) | |||||||
\(740\) | 15.3262 | 0.563404 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.69098 | − | 5.20431i | −0.0620779 | − | 0.191056i | ||||
\(743\) | 16.3607 | 0.600215 | 0.300108 | − | 0.953905i | \(-0.402977\pi\) | ||||
0.300108 | + | 0.953905i | \(0.402977\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.2254 | − | 18.3273i | −0.924188 | − | 0.671462i | ||||
\(746\) | −1.00658 | + | 3.09793i | −0.0368534 | + | 0.113423i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.763932 | − | 0.555029i | 0.0279321 | − | 0.0202939i | ||||
\(749\) | 16.8541 | 0.615835 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.8885 | −1.49204 | −0.746022 | − | 0.665921i | \(-0.768039\pi\) | ||||
−0.746022 | + | 0.665921i | \(0.768039\pi\) | |||||||
\(752\) | −2.42705 | + | 1.76336i | −0.0885054 | + | 0.0643030i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.28115 | − | 3.94298i | 0.0466568 | − | 0.143595i | ||||
\(755\) | −10.0623 | − | 7.31069i | −0.366205 | − | 0.266063i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.58359 | 0.130248 | 0.0651239 | − | 0.997877i | \(-0.479256\pi\) | ||||
0.0651239 | + | 0.997877i | \(0.479256\pi\) | |||||||
\(758\) | 6.60739 | + | 20.3355i | 0.239991 | + | 0.738617i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 29.2705 | 1.06175 | ||||||||
\(761\) | 30.2984 | − | 22.0131i | 1.09832 | − | 0.797973i | 0.117531 | − | 0.993069i | \(-0.462502\pi\) |
0.980784 | + | 0.195096i | \(0.0625020\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.0902 | + | 9.51057i | 0.473896 | + | 0.344306i | ||||
\(764\) | 31.6525 | − | 22.9969i | 1.14515 | − | 0.831998i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.68034 | + | 4.12701i | 0.205239 | + | 0.149115i | ||||
\(767\) | −6.21885 | − | 19.1396i | −0.224550 | − | 0.691092i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.14590 | − | 12.7598i | −0.149505 | − | 0.460129i | 0.848058 | − | 0.529904i | \(-0.177772\pi\) |
−0.997563 | + | 0.0697749i | \(0.977772\pi\) | |||||||
\(770\) | 1.38197 | − | 1.00406i | 0.0498026 | − | 0.0361837i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.85410 | − | 8.78402i | 0.102721 | − | 0.316144i | ||||
\(773\) | 26.8262 | − | 19.4904i | 0.964873 | − | 0.701021i | 0.0105954 | − | 0.999944i | \(-0.496627\pi\) |
0.954277 | + | 0.298923i | \(0.0966273\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.1353 | − | 8.81678i | 0.435911 | − | 0.316708i | ||||
\(776\) | 6.38197 | 0.229099 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.86475 | − | 8.81678i | 0.102706 | − | 0.316097i | ||||
\(779\) | −9.47214 | + | 29.1522i | −0.339374 | + | 1.04449i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.03444 | + | 3.18368i | 0.0370152 | + | 0.113921i | ||||
\(782\) | 3.88854 | 0.139054 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.57295 | + | 4.77553i | 0.234748 | + | 0.170555i | ||||
\(785\) | −16.6074 | − | 12.0660i | −0.592743 | − | 0.430653i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.6525 | + | 20.0907i | 0.985704 | + | 0.716156i | 0.958976 | − | 0.283487i | \(-0.0914912\pi\) |
0.0267281 | + | 0.999643i | \(0.491491\pi\) | |||||||
\(788\) | 12.7082 | + | 9.23305i | 0.452711 | + | 0.328914i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.31966 | − | 4.06150i | 0.0469514 | − | 0.144502i | ||||
\(791\) | −13.2812 | − | 9.64932i | −0.472223 | − | 0.343090i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.8541 | 0.811573 | ||||||||
\(794\) | 0.00657781 | + | 0.0202444i | 0.000233438 | + | 0.000718447i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.28115 | + | 3.94298i | −0.0454093 | + | 0.139755i | ||||
\(797\) | −4.39919 | + | 13.5393i | −0.155827 | + | 0.479587i | −0.998244 | − | 0.0592400i | \(-0.981132\pi\) |
0.842417 | + | 0.538827i | \(0.181132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.23607 | 0.0437289 | ||||||||
\(800\) | −8.68034 | − | 26.7153i | −0.306896 | − | 0.944530i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.2984 | − | 8.20875i | 0.398959 | − | 0.289861i | ||||
\(803\) | −2.12461 | + | 6.53888i | −0.0749759 | + | 0.230752i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.7984 | −1.05025 | ||||||||
\(806\) | −2.78115 | − | 8.55951i | −0.0979619 | − | 0.301496i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.16312 | + | 15.8904i | 0.181638 | + | 0.559024i | ||||
\(809\) | −12.9271 | − | 9.39205i | −0.454491 | − | 0.330207i | 0.336875 | − | 0.941549i | \(-0.390630\pi\) |
−0.791366 | + | 0.611342i | \(0.790630\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.04508 | − | 0.759299i | 0.0366979 | − | 0.0266626i | −0.569285 | − | 0.822140i | \(-0.692780\pi\) |
0.605983 | + | 0.795478i | \(0.292780\pi\) | |||||||
\(812\) | −2.92705 | − | 2.12663i | −0.102719 | − | 0.0746300i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.61803 | − | 1.17557i | 0.0567121 | − | 0.0412037i | ||||
\(815\) | −7.60081 | − | 23.3929i | −0.266245 | − | 0.819417i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.35410 | − | 10.3229i | −0.117345 | − | 0.361151i | ||||
\(818\) | −17.5623 | −0.614052 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.9443 | 0.661563 | ||||||||
\(821\) | −6.08359 | + | 18.7234i | −0.212319 | + | 0.653450i | 0.787014 | + | 0.616935i | \(0.211626\pi\) |
−0.999333 | + | 0.0365154i | \(0.988374\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.7426 | + | 20.1562i | −0.967048 | + | 0.702601i | −0.954777 | − | 0.297323i | \(-0.903906\pi\) |
−0.0122710 | + | 0.999925i | \(0.503906\pi\) | |||||||
\(824\) | −25.8541 | −0.900670 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.14590 | 0.144254 | ||||||||
\(827\) | −24.2984 | + | 17.6538i | −0.844937 | + | 0.613883i | −0.923745 | − | 0.383007i | \(-0.874889\pi\) |
0.0788082 | + | 0.996890i | \(0.474889\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.00658 | + | 27.7194i | −0.312811 | + | 0.962734i | 0.663835 | + | 0.747879i | \(0.268928\pi\) |
−0.976646 | + | 0.214855i | \(0.931072\pi\) | |||||||
\(830\) | 0.753289 | + | 2.31838i | 0.0261470 | + | 0.0804723i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.14590 | 0.0397269 | ||||||||
\(833\) | −1.03444 | − | 3.18368i | −0.0358413 | − | 0.110308i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.84346 | + | 11.8290i | −0.133008 | + | 0.409358i | ||||
\(836\) | −5.85410 | + | 4.25325i | −0.202468 | + | 0.147102i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.263932 | + | 0.191758i | 0.00911738 | + | 0.00662416i | ||||
\(839\) | 3.35410 | − | 2.43690i | 0.115796 | − | 0.0841311i | −0.528380 | − | 0.849008i | \(-0.677200\pi\) |
0.644176 | + | 0.764877i | \(0.277200\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.9164 | + | 15.9232i | 0.755738 | + | 0.549076i | ||||
\(842\) | −6.11146 | − | 18.8091i | −0.210615 | − | 0.648205i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.59017 | − | 20.2825i | −0.226843 | − | 0.698151i | ||||
\(845\) | −7.29837 | + | 22.4621i | −0.251072 | + | 0.772719i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.20820 | − | 16.0292i | 0.178956 | − | 0.550770i | ||||
\(848\) | 8.20820 | − | 5.96361i | 0.281871 | − | 0.204791i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.729490 | + | 2.24514i | −0.0250213 | + | 0.0770077i | ||||
\(851\) | −34.8885 | −1.19596 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.6180 | − | 44.9897i | 0.500512 | − | 1.54042i | −0.307675 | − | 0.951491i | \(-0.599551\pi\) |
0.808187 | − | 0.588926i | \(-0.200449\pi\) | |||||||
\(854\) | −1.45492 | + | 4.47777i | −0.0497862 | + | 0.153226i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.19756 | − | 22.1518i | −0.246008 | − | 0.757133i | ||||
\(857\) | 40.6869 | 1.38984 | 0.694919 | − | 0.719088i | \(-0.255440\pi\) | ||||
0.694919 | + | 0.719088i | \(0.255440\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.9894 | + | 16.7027i | 0.784387 | + | 0.569890i | 0.906292 | − | 0.422651i | \(-0.138901\pi\) |
−0.121906 | + | 0.992542i | \(0.538901\pi\) | |||||||
\(860\) | −5.42705 | + | 3.94298i | −0.185061 | + | 0.134455i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.9164 | − | 8.65778i | −0.405874 | − | 0.294885i | ||||
\(863\) | −33.6246 | − | 24.4297i | −1.14460 | − | 0.831597i | −0.156842 | − | 0.987624i | \(-0.550131\pi\) |
−0.987753 | + | 0.156027i | \(0.950131\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.7639 | −1.28401 | ||||||||
\(866\) | 10.0729 | + | 7.31843i | 0.342293 | + | 0.248690i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.85410 | −0.266586 | ||||||||
\(869\) | 0.729490 | + | 2.24514i | 0.0247463 | + | 0.0761612i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.8541 | + | 42.6385i | −0.469428 | + | 1.44475i | ||||
\(872\) | 6.90983 | − | 21.2663i | 0.233996 | − | 0.720167i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −29.7984 | −1.00795 | ||||||||
\(875\) | 5.59017 | − | 17.2048i | 0.188982 | − | 0.581628i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.7082 | + | 17.9516i | −0.834337 | + | 0.606181i | −0.920783 | − | 0.390075i | \(-0.872449\pi\) |
0.0864462 | + | 0.996257i | \(0.472449\pi\) | |||||||
\(878\) | −1.14183 | + | 3.51420i | −0.0385350 | + | 0.118598i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.56231 | + | 1.86162i | 0.0863753 | + | 0.0627553i | ||||
\(881\) | −1.34752 | − | 4.14725i | −0.0453992 | − | 0.139725i | 0.925787 | − | 0.378044i | \(-0.123403\pi\) |
−0.971187 | + | 0.238320i | \(0.923403\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.6525 | − | 45.0957i | −0.493095 | − | 1.51759i | −0.819904 | − | 0.572500i | \(-0.805974\pi\) |
0.326809 | − | 0.945090i | \(-0.394026\pi\) | |||||||
\(884\) | −4.85410 | − | 3.52671i | −0.163261 | − | 0.118616i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.02786 | + | 4.37950i | −0.202510 | + | 0.147132i | ||||
\(887\) | −4.76393 | − | 3.46120i | −0.159957 | − | 0.116216i | 0.504927 | − | 0.863162i | \(-0.331519\pi\) |
−0.664885 | + | 0.746946i | \(0.731519\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.7984 | + | 15.1109i | −0.697555 | + | 0.506803i | ||||
\(890\) | 10.0000 | − | 7.26543i | 0.335201 | − | 0.243538i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.0902 | − | 34.1320i | −0.371326 | − | 1.14283i | ||||
\(893\) | −9.47214 | −0.316973 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.1353 | − | 12.4495i | 0.572768 | − | 0.416141i | ||||
\(896\) | −5.69098 | + | 17.5150i | −0.190122 | + | 0.585137i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.1631 | + | 7.38394i | −0.339148 | + | 0.246405i | ||||
\(899\) | −4.14590 | −0.138273 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.18034 | −0.139267 | ||||||||
\(902\) | 2.00000 | − | 1.45309i | 0.0665927 | − | 0.0483824i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.01064 | + | 21.5765i | −0.233171 | + | 0.717625i | ||||
\(905\) | −9.47214 | + | 29.1522i | −0.314864 | + | 0.969053i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.2492 | 1.56888 | 0.784442 | − | 0.620202i | \(-0.212949\pi\) | ||||
0.784442 | + | 0.620202i | \(0.212949\pi\) | |||||||
\(908\) | 9.61803 | + | 29.6013i | 0.319186 | + | 0.982352i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.78115 | − | 6.37988i | −0.291092 | − | 0.211491i | ||||
\(911\) | −28.9336 | + | 21.0215i | −0.958614 | + | 0.696474i | −0.952828 | − | 0.303510i | \(-0.901842\pi\) |
−0.00578548 | + | 0.999983i | \(0.501842\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.09017 | − | 0.792055i | −0.0360794 | − | 0.0262132i | ||||
\(914\) | 2.70820 | − | 1.96763i | 0.0895794 | − | 0.0650833i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.8541 | + | 7.88597i | 0.358630 | + | 0.260560i | ||||
\(917\) | −8.89919 | − | 27.3889i | −0.293877 | − | 0.904461i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.551663 | − | 1.69784i | −0.0181977 | − | 0.0560067i | 0.941545 | − | 0.336886i | \(-0.109374\pi\) |
−0.959743 | + | 0.280880i | \(0.909374\pi\) | |||||||
\(920\) | 12.7254 | + | 39.1648i | 0.419545 | + | 1.29123i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.42705 | − | 13.6251i | 0.145797 | − | 0.448718i | ||||
\(923\) | 17.2082 | − | 12.5025i | 0.566415 | − | 0.411525i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.54508 | − | 20.1437i | 0.215201 | − | 0.662321i | ||||
\(926\) | −9.96556 | −0.327489 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.39919 | + | 7.38394i | −0.0787572 | + | 0.242390i | ||||
\(929\) | 11.3197 | − | 34.8383i | 0.371386 | − | 1.14301i | −0.574499 | − | 0.818506i | \(-0.694803\pi\) |
0.945885 | − | 0.324503i | \(-0.105197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.92705 | + | 24.3970i | 0.259799 | + | 0.799578i | ||||
\(932\) | 24.1803 | 0.792053 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 14.2254 | + | 10.3354i | 0.465470 | + | 0.338184i | ||||
\(935\) | −0.403252 | − | 1.24108i | −0.0131878 | − | 0.0405877i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.4787 | − | 30.1360i | −1.35505 | − | 0.984502i | −0.998743 | − | 0.0501333i | \(-0.984035\pi\) |
−0.356308 | − | 0.934369i | \(-0.615965\pi\) | |||||||
\(938\) | −7.47214 | − | 5.42882i | −0.243974 | − | 0.177257i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.80902 | + | 5.56758i | 0.0590036 | + | 0.181594i | ||||
\(941\) | −15.8435 | − | 11.5109i | −0.516482 | − | 0.375246i | 0.298795 | − | 0.954317i | \(-0.403415\pi\) |
−0.815277 | + | 0.579071i | \(0.803415\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43.1246 | −1.40433 | ||||||||
\(944\) | 2.37539 | + | 7.31069i | 0.0773123 | + | 0.237943i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.270510 | + | 0.832544i | −0.00879503 | + | 0.0270683i | ||||
\(947\) | 8.85410 | − | 27.2501i | 0.287720 | − | 0.885510i | −0.697851 | − | 0.716243i | \(-0.745860\pi\) |
0.985570 | − | 0.169267i | \(-0.0541399\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.6869 | 1.41814 | ||||||||
\(950\) | 5.59017 | − | 17.2048i | 0.181369 | − | 0.558197i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.23607 | − | 1.62460i | 0.0724714 | − | 0.0526535i | ||||
\(953\) | −10.7361 | + | 33.0422i | −0.347775 | + | 1.07034i | 0.612306 | + | 0.790621i | \(0.290242\pi\) |
−0.960081 | + | 0.279721i | \(0.909758\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.7082 | − | 51.4226i | −0.540665 | − | 1.66400i | ||||
\(956\) | −14.7361 | − | 45.3530i | −0.476598 | − | 1.46682i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.791796 | − | 2.43690i | −0.0255818 | − | 0.0787326i | ||||
\(959\) | −7.78115 | − | 5.65334i | −0.251267 | − | 0.182556i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.7984 | − | 12.9313i | 0.574141 | − | 0.417138i | ||||
\(962\) | −10.2812 | − | 7.46969i | −0.331478 | − | 0.240833i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.0172 | − | 10.9106i | 0.483672 | − | 0.351408i | ||||
\(965\) | −10.3262 | − | 7.50245i | −0.332413 | − | 0.241512i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.3262 | + | 37.9363i | 0.396385 | + | 1.21995i | 0.927878 | + | 0.372885i | \(0.121631\pi\) |
−0.531493 | + | 0.847063i | \(0.678369\pi\) | |||||||
\(968\) | −23.2918 | −0.748627 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.21885 | − | 3.75123i | 0.0391348 | − | 0.120445i | ||||
\(971\) | −1.04508 | + | 3.21644i | −0.0335384 | + | 0.103220i | −0.966424 | − | 0.256951i | \(-0.917282\pi\) |
0.932886 | + | 0.360172i | \(0.117282\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.54508 | − | 4.75528i | 0.209826 | − | 0.152447i | ||||
\(974\) | 5.92299 | 0.189785 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.72949 | −0.279424 | ||||||||
\(977\) | −27.2254 | + | 19.7804i | −0.871019 | + | 0.632832i | −0.930860 | − | 0.365376i | \(-0.880940\pi\) |
0.0598416 | + | 0.998208i | \(0.480940\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.11146 | + | 6.49839i | −0.0674824 | + | 0.207690i | ||||
\(980\) | 12.8262 | − | 9.31881i | 0.409719 | − | 0.297678i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23.0213 | 0.734639 | ||||||||
\(983\) | −2.28115 | − | 7.02067i | −0.0727575 | − | 0.223924i | 0.908064 | − | 0.418830i | \(-0.137560\pi\) |
−0.980822 | + | 0.194906i | \(0.937560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.5623 | − | 12.7598i | 0.559582 | − | 0.406560i | ||||
\(986\) | 0.527864 | − | 0.383516i | 0.0168106 | − | 0.0122136i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 37.1976 | + | 27.0256i | 1.18341 | + | 0.859799i | ||||
\(989\) | 12.3541 | − | 8.97578i | 0.392838 | − | 0.285413i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.7533 | − | 17.2578i | −0.754548 | − | 0.548211i | 0.142685 | − | 0.989768i | \(-0.454426\pi\) |
−0.897233 | + | 0.441557i | \(0.854426\pi\) | |||||||
\(992\) | 5.20820 | + | 16.0292i | 0.165361 | + | 0.508928i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.35410 | + | 4.16750i | 0.0429495 | + | 0.132185i | ||||
\(995\) | 4.63525 | + | 3.36771i | 0.146947 | + | 0.106764i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.36475 | + | 10.3556i | −0.106563 | + | 0.327966i | −0.990094 | − | 0.140406i | \(-0.955159\pi\) |
0.883531 | + | 0.468372i | \(0.155159\pi\) | |||||||
\(998\) | −6.28115 | + | 4.56352i | −0.198826 | + | 0.144456i | ||||
\(999\) | 0 | 0 |
(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 | 225.2.h.b.136.1 | 4 | ||
3.2 | odd | 2 | 25.2.d.a.11.1 | ✓ | 4 | ||
12.11 | even | 2 | 400.2.u.b.161.1 | 4 | |||
15.2 | even | 4 | 125.2.e.a.74.1 | 8 | |||
15.8 | even | 4 | 125.2.e.a.74.2 | 8 | |||
15.14 | odd | 2 | 125.2.d.a.51.1 | 4 | |||
25.4 | even | 10 | 5625.2.a.d.1.2 | 2 | |||
25.16 | even | 5 | inner | 225.2.h.b.91.1 | 4 | ||
25.21 | even | 5 | 5625.2.a.f.1.1 | 2 | |||
75.2 | even | 20 | 625.2.e.c.499.1 | 8 | |||
75.8 | even | 20 | 625.2.e.c.124.1 | 8 | |||
75.11 | odd | 10 | 625.2.d.h.126.1 | 4 | |||
75.14 | odd | 10 | 625.2.d.b.126.1 | 4 | |||
75.17 | even | 20 | 625.2.e.c.124.2 | 8 | |||
75.23 | even | 20 | 625.2.e.c.499.2 | 8 | |||
75.29 | odd | 10 | 625.2.a.c.1.1 | 2 | |||
75.38 | even | 20 | 125.2.e.a.49.1 | 8 | |||
75.41 | odd | 10 | 25.2.d.a.16.1 | yes | 4 | ||
75.44 | odd | 10 | 625.2.d.b.501.1 | 4 | |||
75.47 | even | 20 | 625.2.b.a.624.3 | 4 | |||
75.53 | even | 20 | 625.2.b.a.624.2 | 4 | |||
75.56 | odd | 10 | 625.2.d.h.501.1 | 4 | |||
75.59 | odd | 10 | 125.2.d.a.76.1 | 4 | |||
75.62 | even | 20 | 125.2.e.a.49.2 | 8 | |||
75.71 | odd | 10 | 625.2.a.b.1.2 | 2 | |||
300.71 | even | 10 | 10000.2.a.c.1.2 | 2 | |||
300.179 | even | 10 | 10000.2.a.l.1.1 | 2 | |||
300.191 | even | 10 | 400.2.u.b.241.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.d.a.11.1 | ✓ | 4 | 3.2 | odd | 2 | ||
25.2.d.a.16.1 | yes | 4 | 75.41 | odd | 10 | ||
125.2.d.a.51.1 | 4 | 15.14 | odd | 2 | |||
125.2.d.a.76.1 | 4 | 75.59 | odd | 10 | |||
125.2.e.a.49.1 | 8 | 75.38 | even | 20 | |||
125.2.e.a.49.2 | 8 | 75.62 | even | 20 | |||
125.2.e.a.74.1 | 8 | 15.2 | even | 4 | |||
125.2.e.a.74.2 | 8 | 15.8 | even | 4 | |||
225.2.h.b.91.1 | 4 | 25.16 | even | 5 | inner | ||
225.2.h.b.136.1 | 4 | 1.1 | even | 1 | trivial | ||
400.2.u.b.161.1 | 4 | 12.11 | even | 2 | |||
400.2.u.b.241.1 | 4 | 300.191 | even | 10 | |||
625.2.a.b.1.2 | 2 | 75.71 | odd | 10 | |||
625.2.a.c.1.1 | 2 | 75.29 | odd | 10 | |||
625.2.b.a.624.2 | 4 | 75.53 | even | 20 | |||
625.2.b.a.624.3 | 4 | 75.47 | even | 20 | |||
625.2.d.b.126.1 | 4 | 75.14 | odd | 10 | |||
625.2.d.b.501.1 | 4 | 75.44 | odd | 10 | |||
625.2.d.h.126.1 | 4 | 75.11 | odd | 10 | |||
625.2.d.h.501.1 | 4 | 75.56 | odd | 10 | |||
625.2.e.c.124.1 | 8 | 75.8 | even | 20 | |||
625.2.e.c.124.2 | 8 | 75.17 | even | 20 | |||
625.2.e.c.499.1 | 8 | 75.2 | even | 20 | |||
625.2.e.c.499.2 | 8 | 75.23 | even | 20 | |||
5625.2.a.d.1.2 | 2 | 25.4 | even | 10 | |||
5625.2.a.f.1.1 | 2 | 25.21 | even | 5 | |||
10000.2.a.c.1.2 | 2 | 300.71 | even | 10 | |||
10000.2.a.l.1.1 | 2 | 300.179 | even | 10 |