Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(45,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.45");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.g (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 18x^{14} + 226x^{12} + 1434x^{10} + 6585x^{8} + 14406x^{6} + 22423x^{4} + 8085x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 229.8 | ||
Root | \(-1.21724 + 2.10833i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.229 |
Dual form | 322.2.g.a.45.8 |
$q$-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 \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 2.81338 | − | 1.62431i | 1.62431 | − | 0.937794i | 0.638557 | − | 0.769575i | \(-0.279532\pi\) |
0.985750 | − | 0.168219i | \(-0.0538017\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.55135 | − | 2.68702i | 0.693785 | − | 1.20167i | −0.276803 | − | 0.960927i | \(-0.589275\pi\) |
0.970588 | − | 0.240745i | \(-0.0773917\pi\) | |||||||
\(6\) | 3.24861i | 1.32624i | ||||||||
\(7\) | −0.334108 | + | 2.62457i | −0.126281 | + | 0.991995i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.77674 | − | 6.54151i | 1.25891 | − | 2.18050i | ||||
\(10\) | 1.55135 | + | 2.68702i | 0.490580 | + | 0.849710i | ||||
\(11\) | −4.07503 | + | 2.35272i | −1.22867 | + | 0.709372i | −0.966751 | − | 0.255718i | \(-0.917688\pi\) |
−0.261917 | + | 0.965090i | \(0.584355\pi\) | |||||||
\(12\) | −2.81338 | − | 1.62431i | −0.812153 | − | 0.468897i | ||||
\(13\) | 3.22606i | 0.894747i | 0.894347 | + | 0.447374i | \(0.147641\pi\) | ||||
−0.894347 | + | 0.447374i | \(0.852359\pi\) | |||||||
\(14\) | −2.10589 | − | 1.60163i | −0.562823 | − | 0.428054i | ||||
\(15\) | − | 10.0795i | − | 2.60251i | ||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.465345 | + | 0.806002i | 0.112863 | + | 0.195484i | 0.916923 | − | 0.399063i | \(-0.130665\pi\) |
−0.804061 | + | 0.594547i | \(0.797331\pi\) | |||||||
\(18\) | 3.77674 | + | 6.54151i | 0.890187 | + | 1.54185i | ||||
\(19\) | 1.55135 | − | 2.68702i | 0.355904 | − | 0.616444i | −0.631368 | − | 0.775483i | \(-0.717506\pi\) |
0.987272 | + | 0.159039i | \(0.0508395\pi\) | |||||||
\(20\) | −3.10270 | −0.693785 | ||||||||
\(21\) | 3.32313 | + | 7.92661i | 0.725167 | + | 1.72973i | ||||
\(22\) | − | 4.70544i | − | 1.00320i | ||||||
\(23\) | −3.61167 | − | 3.15529i | −0.753085 | − | 0.657923i | ||||
\(24\) | 2.81338 | − | 1.62431i | 0.574279 | − | 0.331560i | ||||
\(25\) | −2.31338 | − | 4.00689i | −0.462676 | − | 0.801379i | ||||
\(26\) | −2.79385 | − | 1.61303i | −0.547919 | − | 0.316341i | ||||
\(27\) | − | 14.7925i | − | 2.84682i | ||||||
\(28\) | 2.44000 | − | 1.02294i | 0.461116 | − | 0.193317i | ||||
\(29\) | 1.03907 | 0.192950 | 0.0964751 | − | 0.995335i | \(-0.469243\pi\) | ||||
0.0964751 | + | 0.995335i | \(0.469243\pi\) | |||||||
\(30\) | 8.72909 | + | 5.03974i | 1.59371 | + | 0.920126i | ||||
\(31\) | −8.51685 | + | 4.91721i | −1.52967 | + | 0.883156i | −0.530296 | + | 0.847813i | \(0.677919\pi\) |
−0.999375 | + | 0.0353436i | \(0.988747\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −7.64308 | + | 13.2382i | −1.33049 | + | 2.30448i | ||||
\(34\) | −0.930691 | −0.159612 | ||||||||
\(35\) | 6.53395 | + | 4.96939i | 1.10444 | + | 0.839980i | ||||
\(36\) | −7.55349 | −1.25891 | ||||||||
\(37\) | 9.60671 | + | 5.54644i | 1.57933 | + | 0.911828i | 0.994952 | + | 0.100349i | \(0.0319959\pi\) |
0.584381 | + | 0.811480i | \(0.301337\pi\) | |||||||
\(38\) | 1.55135 | + | 2.68702i | 0.251662 | + | 0.435892i | ||||
\(39\) | 5.24011 | + | 9.07613i | 0.839088 | + | 1.45334i | ||||
\(40\) | 1.55135 | − | 2.68702i | 0.245290 | − | 0.424855i | ||||
\(41\) | 3.22606i | 0.503825i | 0.967750 | + | 0.251913i | \(0.0810596\pi\) | ||||
−0.967750 | + | 0.251913i | \(0.918940\pi\) | |||||||
\(42\) | −8.52622 | − | 1.08539i | −1.31562 | − | 0.167479i | ||||
\(43\) | − | 0.943407i | − | 0.143868i | −0.997409 | − | 0.0719341i | \(-0.977083\pi\) | ||
0.997409 | − | 0.0719341i | \(-0.0229171\pi\) | |||||||
\(44\) | 4.07503 | + | 2.35272i | 0.614334 | + | 0.354686i | ||||
\(45\) | −11.7181 | − | 20.2964i | −1.74683 | − | 3.02560i | ||||
\(46\) | 4.53839 | − | 1.55015i | 0.669150 | − | 0.228558i | ||||
\(47\) | 4.29385 | + | 2.47905i | 0.626322 | + | 0.361607i | 0.779326 | − | 0.626618i | \(-0.215561\pi\) |
−0.153004 | + | 0.988226i | \(0.548895\pi\) | |||||||
\(48\) | 3.24861i | 0.468897i | ||||||||
\(49\) | −6.77674 | − | 1.75378i | −0.968106 | − | 0.250540i | ||||
\(50\) | 4.62676 | 0.654323 | ||||||||
\(51\) | 2.61839 | + | 1.51173i | 0.366648 | + | 0.211684i | ||||
\(52\) | 2.79385 | − | 1.61303i | 0.387437 | − | 0.223687i | ||||
\(53\) | 6.11070 | − | 3.52801i | 0.839369 | − | 0.484610i | −0.0176807 | − | 0.999844i | \(-0.505628\pi\) |
0.857050 | + | 0.515234i | \(0.172295\pi\) | |||||||
\(54\) | 12.8107 | + | 7.39626i | 1.74332 | + | 1.00650i | ||||
\(55\) | 14.5996i | 1.96861i | ||||||||
\(56\) | −0.334108 | + | 2.62457i | −0.0446471 | + | 0.350723i | ||||
\(57\) | − | 10.0795i | − | 1.33506i | ||||||
\(58\) | −0.519534 | + | 0.899859i | −0.0682182 | + | 0.118157i | ||||
\(59\) | 0.109914 | − | 0.0634586i | 0.0143095 | − | 0.00826161i | −0.492828 | − | 0.870127i | \(-0.664037\pi\) |
0.507138 | + | 0.861865i | \(0.330704\pi\) | |||||||
\(60\) | −8.72909 | + | 5.03974i | −1.12692 | + | 0.650628i | ||||
\(61\) | −2.63736 | + | 4.56804i | −0.337679 | + | 0.584877i | −0.983996 | − | 0.178192i | \(-0.942975\pi\) |
0.646317 | + | 0.763069i | \(0.276308\pi\) | |||||||
\(62\) | − | 9.83441i | − | 1.24897i | ||||||
\(63\) | 15.9068 | + | 12.0979i | 2.00407 | + | 1.52419i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.66848 | + | 5.00475i | 1.07519 | + | 0.620763i | ||||
\(66\) | −7.64308 | − | 13.2382i | −0.940798 | − | 1.62951i | ||||
\(67\) | −0.0606084 | + | 0.0349923i | −0.00740450 | + | 0.00427499i | −0.503698 | − | 0.863880i | \(-0.668027\pi\) |
0.496293 | + | 0.868155i | \(0.334694\pi\) | |||||||
\(68\) | 0.465345 | − | 0.806002i | 0.0564314 | − | 0.0977421i | ||||
\(69\) | −15.2862 | − | 3.01057i | −1.84024 | − | 0.362430i | ||||
\(70\) | −7.57059 | + | 3.17388i | −0.904859 | + | 0.379351i | ||||
\(71\) | −5.66583 | −0.672410 | −0.336205 | − | 0.941789i | \(-0.609144\pi\) | ||||
−0.336205 | + | 0.941789i | \(0.609144\pi\) | |||||||
\(72\) | 3.77674 | − | 6.54151i | 0.445094 | − | 0.770925i | ||||
\(73\) | −8.51685 | + | 4.91721i | −0.996822 | + | 0.575515i | −0.907306 | − | 0.420470i | \(-0.861865\pi\) |
−0.0895154 | + | 0.995985i | \(0.528532\pi\) | |||||||
\(74\) | −9.60671 | + | 5.54644i | −1.11676 | + | 0.644760i | ||||
\(75\) | −13.0168 | − | 7.51528i | −1.50306 | − | 0.867790i | ||||
\(76\) | −3.10270 | −0.355904 | ||||||||
\(77\) | −4.81338 | − | 11.4813i | −0.548536 | − | 1.30841i | ||||
\(78\) | −10.4802 | −1.18665 | ||||||||
\(79\) | −1.39604 | − | 0.806002i | −0.157066 | − | 0.0906823i | 0.419407 | − | 0.907798i | \(-0.362238\pi\) |
−0.576473 | + | 0.817116i | \(0.695571\pi\) | |||||||
\(80\) | 1.55135 | + | 2.68702i | 0.173446 | + | 0.300418i | ||||
\(81\) | −12.6974 | − | 21.9925i | −1.41082 | − | 2.44361i | ||||
\(82\) | −2.79385 | − | 1.61303i | −0.308529 | − | 0.178129i | ||||
\(83\) | −1.34746 | −0.147903 | −0.0739513 | − | 0.997262i | \(-0.523561\pi\) | ||||
−0.0739513 | + | 0.997262i | \(0.523561\pi\) | |||||||
\(84\) | 5.20308 | − | 6.84123i | 0.567703 | − | 0.746439i | ||||
\(85\) | 2.88766 | 0.313210 | ||||||||
\(86\) | 0.817014 | + | 0.471703i | 0.0881009 | + | 0.0508651i | ||||
\(87\) | 2.92330 | − | 1.68777i | 0.313410 | − | 0.180947i | ||||
\(88\) | −4.07503 | + | 2.35272i | −0.434400 | + | 0.250801i | ||||
\(89\) | 6.59871 | − | 11.4293i | 0.699462 | − | 1.21150i | −0.269191 | − | 0.963087i | \(-0.586756\pi\) |
0.968653 | − | 0.248417i | \(-0.0799104\pi\) | |||||||
\(90\) | 23.4362 | 2.47039 | ||||||||
\(91\) | −8.46702 | − | 1.07785i | −0.887584 | − | 0.112990i | ||||
\(92\) | −0.926724 | + | 4.70544i | −0.0966177 | + | 0.490576i | ||||
\(93\) | −15.9741 | + | 27.6679i | −1.65644 | + | 2.86903i | ||||
\(94\) | −4.29385 | + | 2.47905i | −0.442877 | + | 0.255695i | ||||
\(95\) | −4.81338 | − | 8.33702i | −0.493843 | − | 0.855360i | ||||
\(96\) | −2.81338 | − | 1.62431i | −0.287140 | − | 0.165780i | ||||
\(97\) | −7.02996 | −0.713784 | −0.356892 | − | 0.934146i | \(-0.616164\pi\) | ||||
−0.356892 | + | 0.934146i | \(0.616164\pi\) | |||||||
\(98\) | 4.90719 | − | 4.99194i | 0.495701 | − | 0.504262i | ||||
\(99\) | 35.5425i | 3.57216i | ||||||||
\(100\) | −2.31338 | + | 4.00689i | −0.231338 | + | 0.400689i | ||||
\(101\) | 11.4401 | − | 6.60497i | 1.13834 | − | 0.657219i | 0.192319 | − | 0.981333i | \(-0.438399\pi\) |
0.946018 | + | 0.324113i | \(0.105066\pi\) | |||||||
\(102\) | −2.61839 | + | 1.51173i | −0.259259 | + | 0.149683i | ||||
\(103\) | −0.113676 | + | 0.196893i | −0.0112009 | + | 0.0194005i | −0.871572 | − | 0.490268i | \(-0.836899\pi\) |
0.860371 | + | 0.509669i | \(0.170232\pi\) | |||||||
\(104\) | 3.22606i | 0.316341i | ||||||||
\(105\) | 26.4543 | + | 3.36764i | 2.58168 | + | 0.328648i | ||||
\(106\) | 7.05603i | 0.685342i | ||||||||
\(107\) | −3.77643 | − | 2.18032i | −0.365081 | − | 0.210780i | 0.306226 | − | 0.951959i | \(-0.400934\pi\) |
−0.671307 | + | 0.741179i | \(0.734267\pi\) | |||||||
\(108\) | −12.8107 | + | 7.39626i | −1.23271 | + | 0.711705i | ||||
\(109\) | −4.89205 | + | 2.82442i | −0.468573 | + | 0.270531i | −0.715642 | − | 0.698467i | \(-0.753866\pi\) |
0.247069 | + | 0.968998i | \(0.420533\pi\) | |||||||
\(110\) | −12.6436 | − | 7.29979i | −1.20552 | − | 0.696008i | ||||
\(111\) | 36.0364 | 3.42043 | ||||||||
\(112\) | −2.10589 | − | 1.60163i | −0.198988 | − | 0.151340i | ||||
\(113\) | − | 10.4033i | − | 0.978658i | −0.872099 | − | 0.489329i | \(-0.837242\pi\) | ||
0.872099 | − | 0.489329i | \(-0.162758\pi\) | |||||||
\(114\) | 8.72909 | + | 5.03974i | 0.817554 | + | 0.472015i | ||||
\(115\) | −14.0813 | + | 4.80967i | −1.31309 | + | 0.448504i | ||||
\(116\) | −0.519534 | − | 0.899859i | −0.0482375 | − | 0.0835498i | ||||
\(117\) | 21.1033 | + | 12.1840i | 1.95100 | + | 1.12641i | ||||
\(118\) | 0.126917i | 0.0116837i | ||||||||
\(119\) | −2.27088 | + | 0.952040i | −0.208172 | + | 0.0872734i | ||||
\(120\) | − | 10.0795i | − | 0.920126i | ||||||
\(121\) | 5.57059 | − | 9.64855i | 0.506417 | − | 0.877141i | ||||
\(122\) | −2.63736 | − | 4.56804i | −0.238775 | − | 0.413571i | ||||
\(123\) | 5.24011 | + | 9.07613i | 0.472484 | + | 0.818367i | ||||
\(124\) | 8.51685 | + | 4.91721i | 0.764836 | + | 0.441578i | ||||
\(125\) | 1.15804 | 0.103579 | ||||||||
\(126\) | −18.4305 | + | 7.72676i | −1.64192 | + | 0.688354i | ||||
\(127\) | −5.96093 | −0.528947 | −0.264474 | − | 0.964393i | \(-0.585198\pi\) | ||||
−0.264474 | + | 0.964393i | \(0.585198\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.53238 | − | 2.65416i | −0.134919 | − | 0.233686i | ||||
\(130\) | −8.66848 | + | 5.00475i | −0.760276 | + | 0.438945i | ||||
\(131\) | −8.59355 | − | 4.96149i | −0.750822 | − | 0.433487i | 0.0751686 | − | 0.997171i | \(-0.476050\pi\) |
−0.825991 | + | 0.563683i | \(0.809384\pi\) | |||||||
\(132\) | 15.2862 | 1.33049 | ||||||||
\(133\) | 6.53395 | + | 4.96939i | 0.566566 | + | 0.430900i | ||||
\(134\) | − | 0.0699846i | − | 0.00604575i | ||||||
\(135\) | −39.7478 | − | 22.9484i | −3.42094 | − | 1.97508i | ||||
\(136\) | 0.465345 | + | 0.806002i | 0.0399030 | + | 0.0691141i | ||||
\(137\) | −0.877623 | + | 0.506696i | −0.0749804 | + | 0.0432899i | −0.537021 | − | 0.843569i | \(-0.680451\pi\) |
0.462041 | + | 0.886859i | \(0.347117\pi\) | |||||||
\(138\) | 10.2503 | − | 11.7329i | 0.872564 | − | 0.998772i | ||||
\(139\) | − | 7.73063i | − | 0.655704i | −0.944729 | − | 0.327852i | \(-0.893675\pi\) | ||
0.944729 | − | 0.327852i | \(-0.106325\pi\) | |||||||
\(140\) | 1.03664 | − | 8.14326i | 0.0876119 | − | 0.688231i | ||||
\(141\) | 16.1070 | 1.35645 | ||||||||
\(142\) | 2.83292 | − | 4.90675i | 0.237733 | − | 0.411766i | ||||
\(143\) | −7.59001 | − | 13.1463i | −0.634709 | − | 1.09935i | ||||
\(144\) | 3.77674 | + | 6.54151i | 0.314729 | + | 0.545126i | ||||
\(145\) | 1.61196 | − | 2.79200i | 0.133866 | − | 0.231863i | ||||
\(146\) | − | 9.83441i | − | 0.813902i | ||||||
\(147\) | −21.9142 | + | 6.07346i | −1.80746 | + | 0.500930i | ||||
\(148\) | − | 11.0929i | − | 0.911828i | ||||||
\(149\) | −8.15006 | − | 4.70544i | −0.667679 | − | 0.385485i | 0.127517 | − | 0.991836i | \(-0.459299\pi\) |
−0.795197 | + | 0.606352i | \(0.792632\pi\) | |||||||
\(150\) | 13.0168 | − | 7.51528i | 1.06282 | − | 0.613620i | ||||
\(151\) | 5.05349 | + | 8.75290i | 0.411247 | + | 0.712301i | 0.995026 | − | 0.0996117i | \(-0.0317600\pi\) |
−0.583779 | + | 0.811912i | \(0.698427\pi\) | |||||||
\(152\) | 1.55135 | − | 2.68702i | 0.125831 | − | 0.217946i | ||||
\(153\) | 7.02996 | 0.568339 | ||||||||
\(154\) | 12.3498 | + | 1.57213i | 0.995172 | + | 0.126686i | ||||
\(155\) | 30.5133i | 2.45088i | ||||||||
\(156\) | 5.24011 | − | 9.07613i | 0.419544 | − | 0.726672i | ||||
\(157\) | 11.1922 | + | 19.3854i | 0.893231 | + | 1.54712i | 0.835978 | + | 0.548763i | \(0.184901\pi\) |
0.0572532 | + | 0.998360i | \(0.481766\pi\) | |||||||
\(158\) | 1.39604 | − | 0.806002i | 0.111063 | − | 0.0641221i | ||||
\(159\) | 11.4612 | − | 19.8513i | 0.908928 | − | 1.57431i | ||||
\(160\) | −3.10270 | −0.245290 | ||||||||
\(161\) | 9.48796 | − | 8.42488i | 0.747756 | − | 0.663973i | ||||
\(162\) | 25.3947 | 1.99520 | ||||||||
\(163\) | 5.77674 | − | 10.0056i | 0.452469 | − | 0.783700i | −0.546069 | − | 0.837740i | \(-0.683876\pi\) |
0.998539 | + | 0.0540399i | \(0.0172098\pi\) | |||||||
\(164\) | 2.79385 | − | 1.61303i | 0.218163 | − | 0.125956i | ||||
\(165\) | 23.7142 | + | 41.0742i | 1.84615 | + | 3.19762i | ||||
\(166\) | 0.673729 | − | 1.16693i | 0.0522915 | − | 0.0905715i | ||||
\(167\) | − | 3.07824i | − | 0.238201i | −0.992882 | − | 0.119101i | \(-0.961999\pi\) | ||
0.992882 | − | 0.119101i | \(-0.0380011\pi\) | |||||||
\(168\) | 3.32313 | + | 7.92661i | 0.256385 | + | 0.611551i | ||||
\(169\) | 2.59256 | 0.199427 | ||||||||
\(170\) | −1.44383 | + | 2.50078i | −0.110737 | + | 0.191801i | ||||
\(171\) | −11.7181 | − | 20.2964i | −0.896106 | − | 1.55210i | ||||
\(172\) | −0.817014 | + | 0.471703i | −0.0622968 | + | 0.0359670i | ||||
\(173\) | 15.6768 | + | 9.05102i | 1.19189 | + | 0.688136i | 0.958734 | − | 0.284304i | \(-0.0917625\pi\) |
0.233152 | + | 0.972440i | \(0.425096\pi\) | |||||||
\(174\) | 3.37553i | 0.255898i | ||||||||
\(175\) | 11.2893 | − | 4.73290i | 0.853391 | − | 0.357773i | ||||
\(176\) | − | 4.70544i | − | 0.354686i | ||||||
\(177\) | 0.206153 | − | 0.357067i | 0.0154954 | − | 0.0268388i | ||||
\(178\) | 6.59871 | + | 11.4293i | 0.494594 | + | 0.856663i | ||||
\(179\) | 1.27674 | + | 2.21138i | 0.0954283 | + | 0.165287i | 0.909787 | − | 0.415075i | \(-0.136245\pi\) |
−0.814359 | + | 0.580361i | \(0.802911\pi\) | |||||||
\(180\) | −11.7181 | + | 20.2964i | −0.873417 | + | 1.51280i | ||||
\(181\) | −16.4063 | −1.21947 | −0.609734 | − | 0.792606i | \(-0.708724\pi\) | ||||
−0.609734 | + | 0.792606i | \(0.708724\pi\) | |||||||
\(182\) | 5.16695 | − | 6.79372i | 0.383000 | − | 0.503584i | ||||
\(183\) | 17.1355i | 1.26669i | ||||||||
\(184\) | −3.61167 | − | 3.15529i | −0.266256 | − | 0.232611i | ||||
\(185\) | 29.8068 | − | 17.2089i | 2.19144 | − | 1.26523i | ||||
\(186\) | −15.9741 | − | 27.6679i | −1.17128 | − | 2.02871i | ||||
\(187\) | −3.79259 | − | 2.18966i | −0.277342 | − | 0.160123i | ||||
\(188\) | − | 4.95811i | − | 0.361607i | ||||||
\(189\) | 38.8240 | + | 4.94230i | 2.82403 | + | 0.359499i | ||||
\(190\) | 9.62676 | 0.698399 | ||||||||
\(191\) | 5.23308 | + | 3.02132i | 0.378652 | + | 0.218615i | 0.677232 | − | 0.735770i | \(-0.263179\pi\) |
−0.298580 | + | 0.954385i | \(0.596513\pi\) | |||||||
\(192\) | 2.81338 | − | 1.62431i | 0.203038 | − | 0.117224i | ||||
\(193\) | −0.409620 | − | 0.709483i | −0.0294851 | − | 0.0510697i | 0.850906 | − | 0.525317i | \(-0.176053\pi\) |
−0.880391 | + | 0.474248i | \(0.842720\pi\) | |||||||
\(194\) | 3.51498 | − | 6.08812i | 0.252361 | − | 0.437102i | ||||
\(195\) | 32.5170 | 2.32859 | ||||||||
\(196\) | 1.86955 | + | 6.74572i | 0.133540 | + | 0.481837i | ||||
\(197\) | −10.9536 | −0.780409 | −0.390205 | − | 0.920728i | \(-0.627596\pi\) | ||||
−0.390205 | + | 0.920728i | \(0.627596\pi\) | |||||||
\(198\) | −30.7807 | − | 17.7712i | −2.18749 | − | 1.26295i | ||||
\(199\) | 3.12167 | + | 5.40689i | 0.221289 | + | 0.383285i | 0.955200 | − | 0.295962i | \(-0.0956401\pi\) |
−0.733910 | + | 0.679246i | \(0.762307\pi\) | |||||||
\(200\) | −2.31338 | − | 4.00689i | −0.163581 | − | 0.283330i | ||||
\(201\) | −0.113676 | + | 0.196893i | −0.00801811 | + | 0.0138878i | ||||
\(202\) | 13.2099i | 0.929448i | ||||||||
\(203\) | −0.347161 | + | 2.72711i | −0.0243659 | + | 0.191405i | ||||
\(204\) | − | 3.02345i | − | 0.211684i | ||||||
\(205\) | 8.66848 | + | 5.00475i | 0.605433 | + | 0.349547i | ||||
\(206\) | −0.113676 | − | 0.196893i | −0.00792021 | − | 0.0137182i | ||||
\(207\) | −34.2807 | + | 11.7091i | −2.38267 | + | 0.813837i | ||||
\(208\) | −2.79385 | − | 1.61303i | −0.193718 | − | 0.111843i | ||||
\(209\) | 14.5996i | 1.00987i | ||||||||
\(210\) | −16.1436 | + | 21.2263i | −1.11402 | + | 1.46475i | ||||
\(211\) | −7.26575 | −0.500195 | −0.250098 | − | 0.968221i | \(-0.580463\pi\) | ||||
−0.250098 | + | 0.968221i | \(0.580463\pi\) | |||||||
\(212\) | −6.11070 | − | 3.52801i | −0.419684 | − | 0.242305i | ||||
\(213\) | −15.9401 | + | 9.20305i | −1.09220 | + | 0.630582i | ||||
\(214\) | 3.77643 | − | 2.18032i | 0.258152 | − | 0.149044i | ||||
\(215\) | −2.53495 | − | 1.46356i | −0.172882 | − | 0.0998136i | ||||
\(216\) | − | 14.7925i | − | 1.00650i | ||||||
\(217\) | −10.0600 | − | 23.9960i | −0.682918 | − | 1.62895i | ||||
\(218\) | − | 5.64885i | − | 0.382588i | ||||||
\(219\) | −15.9741 | + | 27.6679i | −1.07943 | + | 1.86963i | ||||
\(220\) | 12.6436 | − | 7.29979i | 0.852432 | − | 0.492152i | ||||
\(221\) | −2.60021 | + | 1.50123i | −0.174909 | + | 0.100984i | ||||
\(222\) | −18.0182 | + | 31.2085i | −1.20930 | + | 2.09458i | ||||
\(223\) | − | 16.5020i | − | 1.10506i | −0.833494 | − | 0.552528i | \(-0.813663\pi\) | ||
0.833494 | − | 0.552528i | \(-0.186337\pi\) | |||||||
\(224\) | 2.44000 | − | 1.02294i | 0.163029 | − | 0.0683480i | ||||
\(225\) | −34.9482 | −2.32988 | ||||||||
\(226\) | 9.00951 | + | 5.20164i | 0.599303 | + | 0.346008i | ||||
\(227\) | −1.02540 | − | 1.77604i | −0.0680580 | − | 0.117880i | 0.829988 | − | 0.557781i | \(-0.188347\pi\) |
−0.898046 | + | 0.439901i | \(0.855014\pi\) | |||||||
\(228\) | −8.72909 | + | 5.03974i | −0.578098 | + | 0.333765i | ||||
\(229\) | 7.23080 | − | 12.5241i | 0.477825 | − | 0.827617i | −0.521852 | − | 0.853036i | \(-0.674759\pi\) |
0.999677 | + | 0.0254191i | \(0.00809201\pi\) | |||||||
\(230\) | 2.87535 | − | 14.5996i | 0.189595 | − | 0.962668i | ||||
\(231\) | −32.1910 | − | 24.4828i | −2.11801 | − | 1.61085i | ||||
\(232\) | 1.03907 | 0.0682182 | ||||||||
\(233\) | 6.58670 | − | 11.4085i | 0.431509 | − | 0.747395i | −0.565495 | − | 0.824752i | \(-0.691315\pi\) |
0.997003 | + | 0.0773568i | \(0.0246481\pi\) | |||||||
\(234\) | −21.1033 | + | 12.1840i | −1.37957 | + | 0.796492i | ||||
\(235\) | 13.3225 | − | 7.69177i | 0.869066 | − | 0.501756i | ||||
\(236\) | −0.109914 | − | 0.0634586i | −0.00715477 | − | 0.00413081i | ||||
\(237\) | −5.23678 | −0.340165 | ||||||||
\(238\) | 0.310951 | − | 2.44266i | 0.0201560 | − | 0.158334i | ||||
\(239\) | 25.1016 | 1.62369 | 0.811844 | − | 0.583874i | \(-0.198464\pi\) | ||||
0.811844 | + | 0.583874i | \(0.198464\pi\) | |||||||
\(240\) | 8.72909 | + | 5.03974i | 0.563460 | + | 0.325314i | ||||
\(241\) | −10.3525 | − | 17.9310i | −0.666862 | − | 1.15504i | −0.978777 | − | 0.204928i | \(-0.934304\pi\) |
0.311916 | − | 0.950110i | \(-0.399029\pi\) | |||||||
\(242\) | 5.57059 | + | 9.64855i | 0.358091 | + | 0.620232i | ||||
\(243\) | −33.0129 | − | 19.0600i | −2.11778 | − | 1.22270i | ||||
\(244\) | 5.27471 | 0.337679 | ||||||||
\(245\) | −15.2256 | + | 15.4885i | −0.972725 | + | 0.989525i | ||||
\(246\) | −10.4802 | −0.668194 | ||||||||
\(247\) | 8.66848 | + | 5.00475i | 0.551562 | + | 0.318444i | ||||
\(248\) | −8.51685 | + | 4.91721i | −0.540820 | + | 0.312243i | ||||
\(249\) | −3.79091 | + | 2.18868i | −0.240239 | + | 0.138702i | ||||
\(250\) | −0.579022 | + | 1.00290i | −0.0366205 | + | 0.0634286i | ||||
\(251\) | −17.3900 | −1.09765 | −0.548823 | − | 0.835939i | \(-0.684924\pi\) | ||||
−0.548823 | + | 0.835939i | \(0.684924\pi\) | |||||||
\(252\) | 2.52368 | − | 19.8247i | 0.158977 | − | 1.24884i | ||||
\(253\) | 22.1412 | + | 4.36065i | 1.39200 | + | 0.274152i | ||||
\(254\) | 2.98047 | − | 5.16232i | 0.187011 | − | 0.323913i | ||||
\(255\) | 8.12408 | − | 4.69044i | 0.508750 | − | 0.293727i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −16.2301 | − | 9.37043i | −1.01240 | − | 0.584511i | −0.100509 | − | 0.994936i | \(-0.532047\pi\) |
−0.911894 | + | 0.410425i | \(0.865380\pi\) | |||||||
\(258\) | 3.06476 | 0.190804 | ||||||||
\(259\) | −17.7667 | + | 23.3604i | −1.10397 | + | 1.45154i | ||||
\(260\) | − | 10.0095i | − | 0.620763i | ||||||
\(261\) | 3.92429 | − | 6.79708i | 0.242908 | − | 0.420728i | ||||
\(262\) | 8.59355 | − | 4.96149i | 0.530912 | − | 0.306522i | ||||
\(263\) | −14.2608 | + | 8.23345i | −0.879356 | + | 0.507697i | −0.870446 | − | 0.492264i | \(-0.836170\pi\) |
−0.00891017 | + | 0.999960i | \(0.502836\pi\) | |||||||
\(264\) | −7.64308 | + | 13.2382i | −0.470399 | + | 0.814755i | ||||
\(265\) | − | 21.8928i | − | 1.34486i | ||||||
\(266\) | −7.57059 | + | 3.17388i | −0.464183 | + | 0.194603i | ||||
\(267\) | − | 42.8733i | − | 2.62381i | ||||||
\(268\) | 0.0606084 | + | 0.0349923i | 0.00370225 | + | 0.00213749i | ||||
\(269\) | −19.0168 | + | 10.9794i | −1.15948 | + | 0.669425i | −0.951179 | − | 0.308640i | \(-0.900126\pi\) |
−0.208299 | + | 0.978065i | \(0.566793\pi\) | |||||||
\(270\) | 39.7478 | − | 22.9484i | 2.41897 | − | 1.39659i | ||||
\(271\) | 20.0532 | + | 11.5777i | 1.21815 | + | 0.703298i | 0.964521 | − | 0.264005i | \(-0.0850435\pi\) |
0.253626 | + | 0.967302i | \(0.418377\pi\) | |||||||
\(272\) | −0.930691 | −0.0564314 | ||||||||
\(273\) | −25.5717 | + | 10.7206i | −1.54767 | + | 0.648841i | ||||
\(274\) | − | 1.01339i | − | 0.0612212i | ||||||
\(275\) | 18.8542 | + | 10.8855i | 1.13695 | + | 0.656419i | ||||
\(276\) | 5.03585 | + | 14.7435i | 0.303123 | + | 0.887454i | ||||
\(277\) | −15.3874 | − | 26.6518i | −0.924539 | − | 1.60135i | −0.792300 | − | 0.610131i | \(-0.791117\pi\) |
−0.132239 | − | 0.991218i | \(-0.542217\pi\) | |||||||
\(278\) | 6.69492 | + | 3.86532i | 0.401535 | + | 0.231826i | ||||
\(279\) | 74.2841i | 4.44727i | ||||||||
\(280\) | 6.53395 | + | 4.96939i | 0.390478 | + | 0.296978i | ||||
\(281\) | 17.0698i | 1.01830i | 0.860678 | + | 0.509149i | \(0.170040\pi\) | ||||
−0.860678 | + | 0.509149i | \(0.829960\pi\) | |||||||
\(282\) | −8.05349 | + | 13.9490i | −0.479578 | + | 0.830654i | ||||
\(283\) | −0.484315 | − | 0.838858i | −0.0287895 | − | 0.0498649i | 0.851272 | − | 0.524725i | \(-0.175832\pi\) |
−0.880061 | + | 0.474860i | \(0.842499\pi\) | |||||||
\(284\) | 2.83292 | + | 4.90675i | 0.168103 | + | 0.291162i | ||||
\(285\) | −27.0838 | − | 15.6368i | −1.60430 | − | 0.926245i | ||||
\(286\) | 15.1800 | 0.897614 | ||||||||
\(287\) | −8.46702 | − | 1.07785i | −0.499792 | − | 0.0636236i | ||||
\(288\) | −7.55349 | −0.445094 | ||||||||
\(289\) | 8.06691 | − | 13.9723i | 0.474524 | − | 0.821900i | ||||
\(290\) | 1.61196 | + | 2.79200i | 0.0946575 | + | 0.163952i | ||||
\(291\) | −19.7780 | + | 11.4188i | −1.15940 | + | 0.669382i | ||||
\(292\) | 8.51685 | + | 4.91721i | 0.498411 | + | 0.287758i | ||||
\(293\) | −17.0414 | −0.995570 | −0.497785 | − | 0.867301i | \(-0.665853\pi\) | ||||
−0.497785 | + | 0.867301i | \(0.665853\pi\) | |||||||
\(294\) | 5.69735 | − | 22.0150i | 0.332276 | − | 1.28394i | ||||
\(295\) | − | 0.393787i | − | 0.0229271i | ||||||
\(296\) | 9.60671 | + | 5.54644i | 0.558379 | + | 0.322380i | ||||
\(297\) | 34.8027 | + | 60.2800i | 2.01946 | + | 3.49780i | ||||
\(298\) | 8.15006 | − | 4.70544i | 0.472121 | − | 0.272579i | ||||
\(299\) | 10.1791 | − | 11.6515i | 0.588675 | − | 0.673821i | ||||
\(300\) | 15.0306i | 0.867790i | ||||||||
\(301\) | 2.47604 | + | 0.315200i | 0.142716 | + | 0.0181678i | ||||
\(302\) | −10.1070 | −0.581591 | ||||||||
\(303\) | 21.4570 | − | 37.1646i | 1.23267 | − | 2.13505i | ||||
\(304\) | 1.55135 | + | 2.68702i | 0.0889761 | + | 0.154111i | ||||
\(305\) | 8.18293 | + | 14.1733i | 0.468553 | + | 0.811558i | ||||
\(306\) | −3.51498 | + | 6.08812i | −0.200938 | + | 0.348035i | ||||
\(307\) | − | 1.94919i | − | 0.111246i | −0.998452 | − | 0.0556231i | \(-0.982285\pi\) | ||
0.998452 | − | 0.0556231i | \(-0.0177145\pi\) | |||||||
\(308\) | −7.53638 | + | 9.90915i | −0.429425 | + | 0.564626i | ||||
\(309\) | 0.738581i | 0.0420164i | ||||||||
\(310\) | −26.4253 | − | 15.2566i | −1.50085 | − | 0.866518i | ||||
\(311\) | 3.54032 | − | 2.04401i | 0.200753 | − | 0.115905i | −0.396254 | − | 0.918141i | \(-0.629690\pi\) |
0.597007 | + | 0.802236i | \(0.296357\pi\) | |||||||
\(312\) | 5.24011 | + | 9.07613i | 0.296663 | + | 0.513835i | ||||
\(313\) | 3.35966 | − | 5.81911i | 0.189899 | − | 0.328916i | −0.755317 | − | 0.655360i | \(-0.772517\pi\) |
0.945217 | + | 0.326444i | \(0.105850\pi\) | |||||||
\(314\) | −22.3843 | −1.26322 | ||||||||
\(315\) | 57.1844 | − | 23.9738i | 3.22197 | − | 1.35077i | ||||
\(316\) | 1.61200i | 0.0906823i | ||||||||
\(317\) | 9.99120 | − | 17.3053i | 0.561162 | − | 0.971961i | −0.436234 | − | 0.899833i | \(-0.643688\pi\) |
0.997395 | − | 0.0721273i | \(-0.0229788\pi\) | |||||||
\(318\) | 11.4612 | + | 19.8513i | 0.642709 | + | 1.11321i | ||||
\(319\) | −4.23424 | + | 2.44464i | −0.237072 | + | 0.136873i | ||||
\(320\) | 1.55135 | − | 2.68702i | 0.0867232 | − | 0.150209i | ||||
\(321\) | −14.1661 | −0.790672 | ||||||||
\(322\) | 2.55218 | + | 12.4293i | 0.142227 | + | 0.692655i | ||||
\(323\) | 2.88766 | 0.160673 | ||||||||
\(324\) | −12.6974 | + | 21.9925i | −0.705409 | + | 1.22180i | ||||
\(325\) | 12.9265 | − | 7.46310i | 0.717032 | − | 0.413978i | ||||
\(326\) | 5.77674 | + | 10.0056i | 0.319944 | + | 0.554160i | ||||
\(327\) | −9.17546 | + | 15.8924i | −0.507404 | + | 0.878850i | ||||
\(328\) | 3.22606i | 0.178129i | ||||||||
\(329\) | −7.94106 | + | 10.4412i | −0.437805 | + | 0.575644i | ||||
\(330\) | −47.4284 | −2.61085 | ||||||||
\(331\) | −10.1864 | + | 17.6433i | −0.559893 | + | 0.969763i | 0.437612 | + | 0.899164i | \(0.355825\pi\) |
−0.997505 | + | 0.0705994i | \(0.977509\pi\) | |||||||
\(332\) | 0.673729 | + | 1.16693i | 0.0369757 | + | 0.0640437i | ||||
\(333\) | 72.5642 | − | 41.8949i | 3.97649 | − | 2.29583i | ||||
\(334\) | 2.66583 | + | 1.53912i | 0.145868 | + | 0.0842168i | ||||
\(335\) | 0.217141i | 0.0118637i | ||||||||
\(336\) | −8.52622 | − | 1.08539i | −0.465143 | − | 0.0592128i | ||||
\(337\) | − | 20.0890i | − | 1.09432i | −0.837029 | − | 0.547158i | \(-0.815710\pi\) | ||
0.837029 | − | 0.547158i | \(-0.184290\pi\) | |||||||
\(338\) | −1.29628 | + | 2.24522i | −0.0705082 | + | 0.122124i | ||||
\(339\) | −16.8981 | − | 29.2684i | −0.917780 | − | 1.58964i | ||||
\(340\) | −1.44383 | − | 2.50078i | −0.0783026 | − | 0.135624i | ||||
\(341\) | 23.1376 | − | 40.0755i | 1.25297 | − | 2.17021i | ||||
\(342\) | 23.4362 | 1.26729 | ||||||||
\(343\) | 6.86709 | − | 17.2001i | 0.370788 | − | 0.928718i | ||||
\(344\) | − | 0.943407i | − | 0.0508651i | ||||||
\(345\) | −31.8037 | + | 36.4038i | −1.71225 | + | 1.95991i | ||||
\(346\) | −15.6768 | + | 9.05102i | −0.842791 | + | 0.486586i | ||||
\(347\) | −6.94257 | − | 12.0249i | −0.372697 | − | 0.645530i | 0.617283 | − | 0.786742i | \(-0.288234\pi\) |
−0.989979 | + | 0.141212i | \(0.954900\pi\) | |||||||
\(348\) | −2.92330 | − | 1.68777i | −0.156705 | − | 0.0904737i | ||||
\(349\) | − | 20.1833i | − | 1.08038i | −0.841542 | − | 0.540192i | \(-0.818351\pi\) | ||
0.841542 | − | 0.540192i | \(-0.181649\pi\) | |||||||
\(350\) | −1.54584 | + | 12.1433i | −0.0826286 | + | 0.649085i | ||||
\(351\) | 47.7215 | 2.54719 | ||||||||
\(352\) | 4.07503 | + | 2.35272i | 0.217200 | + | 0.125400i | ||||
\(353\) | −4.57228 | + | 2.63981i | −0.243358 | + | 0.140503i | −0.616719 | − | 0.787183i | \(-0.711539\pi\) |
0.373361 | + | 0.927686i | \(0.378205\pi\) | |||||||
\(354\) | 0.206153 | + | 0.357067i | 0.0109569 | + | 0.0189779i | ||||
\(355\) | −8.78969 | + | 15.2242i | −0.466509 | + | 0.808016i | ||||
\(356\) | −13.1974 | −0.699462 | ||||||||
\(357\) | −4.84246 | + | 6.36706i | −0.256290 | + | 0.336981i | ||||
\(358\) | −2.55349 | −0.134956 | ||||||||
\(359\) | −2.79577 | − | 1.61414i | −0.147555 | − | 0.0851910i | 0.424405 | − | 0.905473i | \(-0.360483\pi\) |
−0.571960 | + | 0.820282i | \(0.693817\pi\) | |||||||
\(360\) | −11.7181 | − | 20.2964i | −0.617599 | − | 1.06971i | ||||
\(361\) | 4.68662 | + | 8.11746i | 0.246664 | + | 0.427235i | ||||
\(362\) | 8.20313 | − | 14.2082i | 0.431147 | − | 0.746769i | ||||
\(363\) | − | 36.1934i | − | 1.89966i | ||||||
\(364\) | 3.30006 | + | 7.87158i | 0.172970 | + | 0.412583i | ||||
\(365\) | 30.5133i | 1.59714i | ||||||||
\(366\) | −14.8398 | − | 8.56775i | −0.775688 | − | 0.447844i | ||||
\(367\) | 11.5097 | + | 19.9354i | 0.600803 | + | 1.04062i | 0.992700 | + | 0.120612i | \(0.0384857\pi\) |
−0.391897 | + | 0.920009i | \(0.628181\pi\) | |||||||
\(368\) | 4.53839 | − | 1.55015i | 0.236580 | − | 0.0808074i | ||||
\(369\) | 21.1033 | + | 12.1840i | 1.09859 | + | 0.634273i | ||||
\(370\) | 34.4179i | 1.78930i | ||||||||
\(371\) | 7.21789 | + | 17.2167i | 0.374734 | + | 0.893846i | ||||
\(372\) | 31.9482 | 1.65644 | ||||||||
\(373\) | 21.6500 | + | 12.4996i | 1.12099 | + | 0.647206i | 0.941654 | − | 0.336581i | \(-0.109271\pi\) |
0.179339 | + | 0.983787i | \(0.442604\pi\) | |||||||
\(374\) | 3.79259 | − | 2.18966i | 0.196110 | − | 0.113224i | ||||
\(375\) | 3.25802 | − | 1.88102i | 0.168243 | − | 0.0971353i | ||||
\(376\) | 4.29385 | + | 2.47905i | 0.221438 | + | 0.127847i | ||||
\(377\) | 3.35209i | 0.172642i | ||||||||
\(378\) | −23.6922 | + | 31.1514i | −1.21859 | + | 1.60226i | ||||
\(379\) | 28.1584i | 1.44640i | 0.690639 | + | 0.723200i | \(0.257329\pi\) | ||||
−0.690639 | + | 0.723200i | \(0.742671\pi\) | |||||||
\(380\) | −4.81338 | + | 8.33702i | −0.246921 | + | 0.427680i | ||||
\(381\) | −16.7704 | + | 9.68238i | −0.859172 | + | 0.496043i | ||||
\(382\) | −5.23308 | + | 3.02132i | −0.267747 | + | 0.154584i | ||||
\(383\) | 10.7874 | − | 18.6844i | 0.551211 | − | 0.954726i | −0.446976 | − | 0.894546i | \(-0.647499\pi\) |
0.998188 | − | 0.0601804i | \(-0.0191676\pi\) | |||||||
\(384\) | 3.24861i | 0.165780i | ||||||||
\(385\) | −38.3176 | − | 4.87784i | −1.95285 | − | 0.248598i | ||||
\(386\) | 0.819241 | 0.0416983 | ||||||||
\(387\) | −6.17131 | − | 3.56301i | −0.313705 | − | 0.181118i | ||||
\(388\) | 3.51498 | + | 6.08812i | 0.178446 | + | 0.309078i | ||||
\(389\) | 17.4619 | − | 10.0816i | 0.885352 | − | 0.511158i | 0.0129327 | − | 0.999916i | \(-0.495883\pi\) |
0.872419 | + | 0.488758i | \(0.162550\pi\) | |||||||
\(390\) | −16.2585 | + | 28.1605i | −0.823281 | + | 1.42596i | ||||
\(391\) | 0.862494 | − | 4.37931i | 0.0436182 | − | 0.221471i | ||||
\(392\) | −6.77674 | − | 1.75378i | −0.342277 | − | 0.0885793i | ||||
\(393\) | −32.2359 | −1.62609 | ||||||||
\(394\) | 5.47678 | − | 9.48607i | 0.275916 | − | 0.477901i | ||||
\(395\) | −4.33148 | + | 2.50078i | −0.217941 | + | 0.125828i | ||||
\(396\) | 30.7807 | − | 17.7712i | 1.54679 | − | 0.893039i | ||||
\(397\) | −11.7504 | − | 6.78407i | −0.589733 | − | 0.340483i | 0.175259 | − | 0.984522i | \(-0.443924\pi\) |
−0.764992 | + | 0.644040i | \(0.777257\pi\) | |||||||
\(398\) | −6.24334 | −0.312951 | ||||||||
\(399\) | 26.4543 | + | 3.36764i | 1.32437 | + | 0.168593i | ||||
\(400\) | 4.62676 | 0.231338 | ||||||||
\(401\) | 23.8069 | + | 13.7449i | 1.18886 | + | 0.686387i | 0.958047 | − | 0.286611i | \(-0.0925288\pi\) |
0.230811 | + | 0.972999i | \(0.425862\pi\) | |||||||
\(402\) | −0.113676 | − | 0.196893i | −0.00566966 | − | 0.00982014i | ||||
\(403\) | −15.8632 | − | 27.4758i | −0.790202 | − | 1.36867i | ||||
\(404\) | −11.4401 | − | 6.60497i | −0.569168 | − | 0.328610i | ||||
\(405\) | −78.7922 | −3.91522 | ||||||||
\(406\) | −2.18816 | − | 1.66420i | −0.108597 | − | 0.0825931i | ||||
\(407\) | −52.1969 | −2.58730 | ||||||||
\(408\) | 2.61839 | + | 1.51173i | 0.129630 | + | 0.0748416i | ||||
\(409\) | 16.4277 | − | 9.48455i | 0.812299 | − | 0.468981i | −0.0354549 | − | 0.999371i | \(-0.511288\pi\) |
0.847753 | + | 0.530390i | \(0.177955\pi\) | |||||||
\(410\) | −8.66848 | + | 5.00475i | −0.428106 | + | 0.247167i | ||||
\(411\) | −1.64606 | + | 2.85106i | −0.0811941 | + | 0.140632i | ||||
\(412\) | 0.227353 | 0.0112009 | ||||||||
\(413\) | 0.129829 | + | 0.309678i | 0.00638845 | + | 0.0152383i | ||||
\(414\) | 7.00000 | − | 35.5425i | 0.344031 | − | 1.74682i | ||||
\(415\) | −2.09038 | + | 3.62064i | −0.102613 | + | 0.177730i | ||||
\(416\) | 2.79385 | − | 1.61303i | 0.136980 | − | 0.0790852i | ||||
\(417\) | −12.5569 | − | 21.7492i | −0.614915 | − | 1.06506i | ||||
\(418\) | −12.6436 | − | 7.29979i | −0.618419 | − | 0.357045i | ||||
\(419\) | 18.6542 | 0.911315 | 0.455658 | − | 0.890155i | \(-0.349404\pi\) | ||||
0.455658 | + | 0.890155i | \(0.349404\pi\) | |||||||
\(420\) | −10.3107 | − | 24.5939i | −0.503110 | − | 1.20006i | ||||
\(421\) | 9.45988i | 0.461046i | 0.973067 | + | 0.230523i | \(0.0740437\pi\) | ||||
−0.973067 | + | 0.230523i | \(0.925956\pi\) | |||||||
\(422\) | 3.63288 | − | 6.29233i | 0.176846 | − | 0.306306i | ||||
\(423\) | 32.4335 | − | 18.7255i | 1.57697 | − | 0.910465i | ||||
\(424\) | 6.11070 | − | 3.52801i | 0.296762 | − | 0.171335i | ||||
\(425\) | 2.15304 | − | 3.72918i | 0.104438 | − | 0.180892i | ||||
\(426\) | − | 18.4061i | − | 0.891778i | ||||||
\(427\) | −11.1080 | − | 8.44815i | −0.537553 | − | 0.408835i | ||||
\(428\) | 4.36065i | 0.210780i | ||||||||
\(429\) | −42.7072 | − | 24.6570i | −2.06192 | − | 1.19045i | ||||
\(430\) | 2.53495 | − | 1.46356i | 0.122246 | − | 0.0705789i | ||||
\(431\) | 21.5150 | − | 12.4217i | 1.03634 | − | 0.598332i | 0.117547 | − | 0.993067i | \(-0.462497\pi\) |
0.918795 | + | 0.394735i | \(0.129164\pi\) | |||||||
\(432\) | 12.8107 | + | 7.39626i | 0.616355 | + | 0.355853i | ||||
\(433\) | −10.4433 | −0.501873 | −0.250936 | − | 0.968004i | \(-0.580738\pi\) | ||||
−0.250936 | + | 0.968004i | \(0.580738\pi\) | |||||||
\(434\) | 25.8111 | + | 3.28576i | 1.23897 | + | 0.157721i | ||||
\(435\) | − | 10.4733i | − | 0.502155i | ||||||
\(436\) | 4.89205 | + | 2.82442i | 0.234287 | + | 0.135265i | ||||
\(437\) | −14.0813 | + | 4.80967i | −0.673599 | + | 0.230078i | ||||
\(438\) | −15.9741 | − | 27.6679i | −0.763272 | − | 1.32203i | ||||
\(439\) | −5.77431 | − | 3.33380i | −0.275593 | − | 0.159114i | 0.355834 | − | 0.934549i | \(-0.384197\pi\) |
−0.631427 | + | 0.775436i | \(0.717530\pi\) | |||||||
\(440\) | 14.5996i | 0.696008i | ||||||||
\(441\) | −37.0664 | + | 37.7066i | −1.76507 | + | 1.79555i | ||||
\(442\) | − | 3.00246i | − | 0.142813i | ||||||
\(443\) | 4.21957 | − | 7.30851i | 0.200478 | − | 0.347238i | −0.748205 | − | 0.663468i | \(-0.769084\pi\) |
0.948683 | + | 0.316230i | \(0.102417\pi\) | |||||||
\(444\) | −18.0182 | − | 31.2085i | −0.855107 | − | 1.48109i | ||||
\(445\) | −20.4738 | − | 35.4617i | −0.970553 | − | 1.68105i | ||||
\(446\) | 14.2912 | + | 8.25101i | 0.676706 | + | 0.390696i | ||||
\(447\) | −30.5723 | −1.44602 | ||||||||
\(448\) | −0.334108 | + | 2.62457i | −0.0157851 | + | 0.123999i | ||||
\(449\) | −1.33217 | −0.0628690 | −0.0314345 | − | 0.999506i | \(-0.510008\pi\) | ||||
−0.0314345 | + | 0.999506i | \(0.510008\pi\) | |||||||
\(450\) | 17.4741 | − | 30.2660i | 0.823737 | − | 1.42675i | ||||
\(451\) | −7.59001 | − | 13.1463i | −0.357400 | − | 0.619034i | ||||
\(452\) | −9.00951 | + | 5.20164i | −0.423772 | + | 0.244665i | ||||
\(453\) | 28.4348 | + | 16.4168i | 1.33598 | + | 0.771330i | ||||
\(454\) | 2.05080 | 0.0962486 | ||||||||
\(455\) | −16.0315 | + | 21.0789i | −0.751569 | + | 0.988194i | ||||
\(456\) | − | 10.0795i | − | 0.472015i | ||||||
\(457\) | 26.4216 | + | 15.2545i | 1.23595 | + | 0.713575i | 0.968263 | − | 0.249932i | \(-0.0804082\pi\) |
0.267685 | + | 0.963507i | \(0.413742\pi\) | |||||||
\(458\) | 7.23080 | + | 12.5241i | 0.337873 | + | 0.585214i | ||||
\(459\) | 11.9228 | − | 6.88363i | 0.556508 | − | 0.321300i | ||||
\(460\) | 11.2059 | + | 9.78992i | 0.522480 | + | 0.456457i | ||||
\(461\) | 33.1586i | 1.54435i | 0.635410 | + | 0.772175i | \(0.280831\pi\) | ||||
−0.635410 | + | 0.772175i | \(0.719169\pi\) | |||||||
\(462\) | 37.2982 | − | 15.6368i | 1.73527 | − | 0.727490i | ||||
\(463\) | −13.9556 | −0.648570 | −0.324285 | − | 0.945959i | \(-0.605124\pi\) | ||||
−0.324285 | + | 0.945959i | \(0.605124\pi\) | |||||||
\(464\) | −0.519534 | + | 0.899859i | −0.0241188 | + | 0.0417749i | ||||
\(465\) | 49.5629 | + | 85.8454i | 2.29842 | + | 3.98099i | ||||
\(466\) | 6.58670 | + | 11.4085i | 0.305123 | + | 0.528488i | ||||
\(467\) | 0.703338 | − | 1.21822i | 0.0325466 | − | 0.0563724i | −0.849293 | − | 0.527921i | \(-0.822972\pi\) |
0.881840 | + | 0.471549i | \(0.156305\pi\) | |||||||
\(468\) | − | 24.3680i | − | 1.12641i | ||||||
\(469\) | −0.0715900 | − | 0.170762i | −0.00330572 | − | 0.00788507i | ||||
\(470\) | 15.3835i | 0.709590i | ||||||||
\(471\) | 62.9756 | + | 36.3590i | 2.90176 | + | 1.67533i | ||||
\(472\) | 0.109914 | − | 0.0634586i | 0.00505918 | − | 0.00292092i | ||||
\(473\) | 2.21957 | + | 3.84441i | 0.102056 | + | 0.176766i | ||||
\(474\) | 2.61839 | − | 4.53518i | 0.120267 | − | 0.208308i | ||||
\(475\) | −14.3555 | −0.658674 | ||||||||
\(476\) | 1.95993 | + | 1.49062i | 0.0898334 | + | 0.0683226i | ||||
\(477\) | − | 53.2976i | − | 2.44033i | ||||||
\(478\) | −12.5508 | + | 21.7386i | −0.574060 | + | 0.994302i | ||||
\(479\) | 6.46237 | + | 11.1931i | 0.295273 | + | 0.511428i | 0.975048 | − | 0.221992i | \(-0.0712560\pi\) |
−0.679775 | + | 0.733420i | \(0.737923\pi\) | |||||||
\(480\) | −8.72909 | + | 5.03974i | −0.398426 | + | 0.230032i | ||||
\(481\) | −17.8931 | + | 30.9918i | −0.815856 | + | 1.41310i | ||||
\(482\) | 20.7049 | 0.943085 | ||||||||
\(483\) | 13.0087 | − | 39.1138i | 0.591915 | − | 1.77974i | ||||
\(484\) | −11.1412 | −0.506417 | ||||||||
\(485\) | −10.9059 | + | 18.8896i | −0.495213 | + | 0.857734i | ||||
\(486\) | 33.0129 | − | 19.0600i | 1.49750 | − | 0.864580i | ||||
\(487\) | 16.7694 | + | 29.0454i | 0.759893 | + | 1.31617i | 0.942905 | + | 0.333063i | \(0.108082\pi\) |
−0.183012 | + | 0.983111i | \(0.558585\pi\) | |||||||
\(488\) | −2.63736 | + | 4.56804i | −0.119388 | + | 0.206785i | ||||
\(489\) | − | 37.5328i | − | 1.69729i | ||||||
\(490\) | −5.80067 | − | 20.9300i | −0.262047 | − | 0.945520i | ||||
\(491\) | 29.8359 | 1.34647 | 0.673237 | − | 0.739427i | \(-0.264904\pi\) | ||||
0.673237 | + | 0.739427i | \(0.264904\pi\) | |||||||
\(492\) | 5.24011 | − | 9.07613i | 0.236242 | − | 0.409184i | ||||
\(493\) | 0.483525 | + | 0.837491i | 0.0217769 | + | 0.0377187i | ||||
\(494\) | −8.66848 | + | 5.00475i | −0.390013 | + | 0.225174i | ||||
\(495\) | 95.5034 | + | 55.1389i | 4.29256 | + | 2.47831i | ||||
\(496\) | − | 9.83441i | − | 0.441578i | ||||||
\(497\) | 1.89300 | − | 14.8704i | 0.0849126 | − | 0.667027i | ||||
\(498\) | − | 4.37737i | − | 0.196155i | ||||||
\(499\) | −6.64018 | + | 11.5011i | −0.297255 | + | 0.514861i | −0.975507 | − | 0.219968i | \(-0.929405\pi\) |
0.678252 | + | 0.734830i | \(0.262738\pi\) | |||||||
\(500\) | −0.579022 | − | 1.00290i | −0.0258946 | − | 0.0448508i | ||||
\(501\) | −5.00000 | − | 8.66025i | −0.223384 | − | 0.386912i | ||||
\(502\) | 8.69499 | − | 15.0602i | 0.388076 | − | 0.672168i | ||||
\(503\) | −29.8310 | −1.33010 | −0.665050 | − | 0.746799i | \(-0.731590\pi\) | ||||
−0.665050 | + | 0.746799i | \(0.731590\pi\) | |||||||
\(504\) | 15.9068 | + | 12.0979i | 0.708546 | + | 0.538883i | ||||
\(505\) | − | 40.9865i | − | 1.82388i | ||||||
\(506\) | −14.8470 | + | 16.9945i | −0.660031 | + | 0.755498i | ||||
\(507\) | 7.29385 | − | 4.21110i | 0.323931 | − | 0.187022i | ||||
\(508\) | 2.98047 | + | 5.16232i | 0.132237 | + | 0.229041i | ||||
\(509\) | −14.9680 | − | 8.64177i | −0.663444 | − | 0.383040i | 0.130144 | − | 0.991495i | \(-0.458456\pi\) |
−0.793588 | + | 0.608455i | \(0.791789\pi\) | |||||||
\(510\) | 9.38088i | 0.415392i | ||||||||
\(511\) | −10.0600 | − | 23.9960i | −0.445028 | − | 1.06152i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −39.7478 | − | 22.9484i | −1.75491 | − | 1.01320i | ||||
\(514\) | 16.2301 | − | 9.37043i | 0.715877 | − | 0.413312i | ||||
\(515\) | 0.352704 | + | 0.610901i | 0.0155420 | + | 0.0269195i | ||||
\(516\) | −1.53238 | + | 2.65416i | −0.0674593 | + | 0.116843i | ||||
\(517\) | −23.3301 | −1.02606 | ||||||||
\(518\) | −11.3473 | − | 27.0666i | −0.498573 | − | 1.18924i | ||||
\(519\) | 58.8065 | 2.58132 | ||||||||
\(520\) | 8.66848 | + | 5.00475i | 0.380138 | + | 0.219473i | ||||
\(521\) | −10.3631 | − | 17.9494i | −0.454016 | − | 0.786379i | 0.544615 | − | 0.838686i | \(-0.316676\pi\) |
−0.998631 | + | 0.0523071i | \(0.983343\pi\) | |||||||
\(522\) | 3.92429 | + | 6.79708i | 0.171762 | + | 0.297500i | ||||
\(523\) | −22.7019 | + | 39.3208i | −0.992684 | + | 1.71938i | −0.391779 | + | 0.920060i | \(0.628140\pi\) |
−0.600906 | + | 0.799320i | \(0.705193\pi\) | |||||||
\(524\) | 9.92298i | 0.433487i | ||||||||
\(525\) | 24.0734 | − | 31.6527i | 1.05065 | − | 1.38144i | ||||
\(526\) | − | 16.4669i | − | 0.717991i | ||||||
\(527\) | −7.92655 | − | 4.57640i | −0.345286 | − | 0.199351i | ||||
\(528\) | −7.64308 | − | 13.2382i | −0.332622 | − | 0.576119i | ||||
\(529\) | 3.08832 | + | 22.7917i | 0.134275 | + | 0.990944i | ||||
\(530\) | 18.9597 | + | 10.9464i | 0.823556 | + | 0.475480i | ||||
\(531\) | − | 0.958668i | − | 0.0416027i | ||||||
\(532\) | 1.03664 | − | 8.14326i | 0.0449440 | − | 0.353055i | ||||
\(533\) | −10.4074 | −0.450796 | ||||||||
\(534\) | 37.1294 | + | 21.4367i | 1.60675 | + | 0.927655i | ||||
\(535\) | −11.7171 | + | 6.76490i | −0.506576 | + | 0.292472i | ||||
\(536\) | −0.0606084 | + | 0.0349923i | −0.00261788 | + | 0.00151144i | ||||
\(537\) | 7.18393 | + | 4.14765i | 0.310010 | + | 0.178984i | ||||
\(538\) | − | 21.9588i | − | 0.946710i | ||||||
\(539\) | 31.7416 | − | 8.79707i | 1.36721 | − | 0.378917i | ||||
\(540\) | 45.8968i | 1.97508i | ||||||||
\(541\) | −9.86344 | + | 17.0840i | −0.424062 | + | 0.734498i | −0.996332 | − | 0.0855677i | \(-0.972730\pi\) |
0.572270 | + | 0.820065i | \(0.306063\pi\) | |||||||
\(542\) | −20.0532 | + | 11.5777i | −0.861360 | + | 0.497306i | ||||
\(543\) | −46.1571 | + | 26.6488i | −1.98079 | + | 1.14361i | ||||
\(544\) | 0.465345 | − | 0.806002i | 0.0199515 | − | 0.0345570i | ||||
\(545\) | 17.5267i | 0.750761i | ||||||||
\(546\) | 3.50152 | − | 27.5061i | 0.149851 | − | 1.17715i | ||||
\(547\) | 19.4631 | 0.832183 | 0.416092 | − | 0.909323i | \(-0.363400\pi\) | ||||
0.416092 | + | 0.909323i | \(0.363400\pi\) | |||||||
\(548\) | 0.877623 | + | 0.506696i | 0.0374902 | + | 0.0216450i | ||||
\(549\) | 19.9212 | + | 34.5046i | 0.850218 | + | 1.47262i | ||||
\(550\) | −18.8542 | + | 10.8855i | −0.803946 | + | 0.464159i | ||||
\(551\) | 1.61196 | − | 2.79200i | 0.0686718 | − | 0.118943i | ||||
\(552\) | −15.2862 | − | 3.01057i | −0.650622 | − | 0.128138i | ||||
\(553\) | 2.58184 | − | 3.39470i | 0.109791 | − | 0.144357i | ||||
\(554\) | 30.7748 | 1.30750 | ||||||||
\(555\) | 55.9052 | − | 96.8306i | 2.37304 | − | 4.11023i | ||||
\(556\) | −6.69492 | + | 3.86532i | −0.283928 | + | 0.163926i | ||||
\(557\) | −34.7308 | + | 20.0518i | −1.47159 | + | 0.849624i | −0.999490 | − | 0.0319201i | \(-0.989838\pi\) |
−0.472102 | + | 0.881544i | \(0.656504\pi\) | |||||||
\(558\) | −64.3319 | − | 37.1420i | −2.72339 | − | 1.57235i | ||||
\(559\) | 3.04348 | 0.128726 | ||||||||
\(560\) | −7.57059 | + | 3.17388i | −0.319916 | + | 0.134121i | ||||
\(561\) | −14.2267 | −0.600651 | ||||||||
\(562\) | −14.7829 | − | 8.53490i | −0.623578 | − | 0.360023i | ||||
\(563\) | −11.9265 | − | 20.6573i | −0.502642 | − | 0.870601i | −0.999995 | − | 0.00305324i | \(-0.999028\pi\) |
0.497353 | − | 0.867548i | \(-0.334305\pi\) | |||||||
\(564\) | −8.05349 | − | 13.9490i | −0.339113 | − | 0.587361i | ||||
\(565\) | −27.9538 | − | 16.1391i | −1.17603 | − | 0.678979i | ||||
\(566\) | 0.968630 | 0.0407145 | ||||||||
\(567\) | 61.9631 | − | 25.9772i | 2.60220 | − | 1.09094i | ||||
\(568\) | −5.66583 | −0.237733 | ||||||||
\(569\) | −30.9726 | − | 17.8820i | −1.29844 | − | 0.749653i | −0.318303 | − | 0.947989i | \(-0.603113\pi\) |
−0.980134 | + | 0.198336i | \(0.936446\pi\) | |||||||
\(570\) | 27.0838 | − | 15.6368i | 1.13441 | − | 0.654954i | ||||
\(571\) | 35.9107 | − | 20.7331i | 1.50282 | − | 0.867652i | 0.502823 | − | 0.864389i | \(-0.332295\pi\) |
0.999995 | − | 0.00326291i | \(-0.00103862\pi\) | |||||||
\(572\) | −7.59001 | + | 13.1463i | −0.317354 | + | 0.549674i | ||||
\(573\) | 19.6302 | 0.820063 | ||||||||
\(574\) | 5.16695 | − | 6.79372i | 0.215665 | − | 0.283565i | ||||
\(575\) | −4.28773 | + | 21.7710i | −0.178811 | + | 0.907912i | ||||
\(576\) | 3.77674 | − | 6.54151i | 0.157364 | − | 0.272563i | ||||
\(577\) | 17.3612 | − | 10.0235i | 0.722758 | − | 0.417285i | −0.0930089 | − | 0.995665i | \(-0.529649\pi\) |
0.815767 | + | 0.578381i | \(0.196315\pi\) | |||||||
\(578\) | 8.06691 | + | 13.9723i | 0.335539 | + | 0.581171i | ||||
\(579\) | −2.30484 | − | 1.33070i | −0.0957858 | − | 0.0553019i | ||||
\(580\) | −3.22392 | −0.133866 | ||||||||
\(581\) | 0.450196 | − | 3.53650i | 0.0186773 | − | 0.146719i | ||||
\(582\) | − | 22.8376i | − | 0.946650i | ||||||
\(583\) | −16.6009 | + | 28.7535i | −0.687537 | + | 1.19085i | ||||
\(584\) | −8.51685 | + | 4.91721i | −0.352430 | + | 0.203475i | ||||
\(585\) | 65.4772 | − | 37.8033i | 2.70715 | − | 1.56297i | ||||
\(586\) | 8.52070 | − | 14.7583i | 0.351987 | − | 0.609659i | ||||
\(587\) | 8.10913i | 0.334699i | 0.985898 | + | 0.167350i | \(0.0535209\pi\) | ||||
−0.985898 | + | 0.167350i | \(0.946479\pi\) | |||||||
\(588\) | 16.2169 | + | 15.9416i | 0.668773 | + | 0.657419i | ||||
\(589\) | 30.5133i | 1.25728i | ||||||||
\(590\) | 0.341029 | + | 0.196893i | 0.0140399 | + | 0.00810597i | ||||
\(591\) | −30.8166 | + | 17.7919i | −1.26762 | + | 0.731863i | ||||
\(592\) | −9.60671 | + | 5.54644i | −0.394833 | + | 0.227957i | ||||
\(593\) | −26.6773 | − | 15.4022i | −1.09551 | − | 0.632491i | −0.160469 | − | 0.987041i | \(-0.551301\pi\) |
−0.935037 | + | 0.354550i | \(0.884634\pi\) | |||||||
\(594\) | −69.6053 | −2.85594 | ||||||||
\(595\) | −0.964789 | + | 7.57886i | −0.0395525 | + | 0.310703i | ||||
\(596\) | 9.41088i | 0.385485i | ||||||||
\(597\) | 17.5649 | + | 10.1411i | 0.718884 | + | 0.415048i | ||||
\(598\) | 5.00089 | + | 14.6411i | 0.204501 | + | 0.598720i | ||||
\(599\) | 18.4909 | + | 32.0273i | 0.755520 | + | 1.30860i | 0.945116 | + | 0.326736i | \(0.105949\pi\) |
−0.189596 | + | 0.981862i | \(0.560718\pi\) | |||||||
\(600\) | −13.0168 | − | 7.51528i | −0.531411 | − | 0.306810i | ||||
\(601\) | 26.9636i | 1.09987i | 0.835208 | + | 0.549935i | \(0.185347\pi\) | ||||
−0.835208 | + | 0.549935i | \(0.814653\pi\) | |||||||
\(602\) | −1.51099 | + | 1.98671i | −0.0615834 | + | 0.0809723i | ||||
\(603\) | 0.528628i | 0.0215274i | ||||||||
\(604\) | 5.05349 | − | 8.75290i | 0.205623 | − | 0.356150i | ||||
\(605\) | −17.2839 | − | 29.9366i | −0.702690 | − | 1.21709i | ||||
\(606\) | 21.4570 | + | 37.1646i | 0.871631 | + | 1.50971i | ||||
\(607\) | −30.8119 | − | 17.7893i | −1.25062 | − | 0.722043i | −0.279384 | − | 0.960179i | \(-0.590130\pi\) |
−0.971232 | + | 0.238136i | \(0.923464\pi\) | |||||||
\(608\) | −3.10270 | −0.125831 | ||||||||
\(609\) | 3.45296 | + | 8.23629i | 0.139921 | + | 0.333751i | ||||
\(610\) | −16.3659 | −0.662635 | ||||||||
\(611\) | −7.99757 | + | 13.8522i | −0.323547 | + | 0.560400i | ||||
\(612\) | −3.51498 | − | 6.08812i | −0.142085 | − | 0.246098i | ||||
\(613\) | −8.48739 | + | 4.90020i | −0.342803 | + | 0.197917i | −0.661511 | − | 0.749936i | \(-0.730084\pi\) |
0.318708 | + | 0.947853i | \(0.396751\pi\) | |||||||
\(614\) | 1.68805 | + | 0.974596i | 0.0681241 | + | 0.0393315i | ||||
\(615\) | 32.5170 | 1.31121 | ||||||||
\(616\) | −4.81338 | − | 11.4813i | −0.193937 | − | 0.462594i | ||||
\(617\) | 29.4350i | 1.18501i | 0.805567 | + | 0.592504i | \(0.201861\pi\) | ||||
−0.805567 | + | 0.592504i | \(0.798139\pi\) | |||||||
\(618\) | −0.639630 | − | 0.369291i | −0.0257297 | − | 0.0148550i | ||||
\(619\) | −16.5761 | − | 28.7106i | −0.666248 | − | 1.15398i | −0.978945 | − | 0.204123i | \(-0.934566\pi\) |
0.312697 | − | 0.949853i | \(-0.398767\pi\) | |||||||
\(620\) | 26.4253 | − | 15.2566i | 1.06126 | − | 0.612721i | ||||
\(621\) | −46.6747 | + | 53.4257i | −1.87299 | + | 2.14390i | ||||
\(622\) | 4.08801i | 0.163914i | ||||||||
\(623\) | 27.7923 | + | 21.1374i | 1.11348 | + | 0.846853i | ||||
\(624\) | −10.4802 | −0.419544 | ||||||||
\(625\) | 13.3634 | − | 23.1462i | 0.534538 | − | 0.925846i | ||||
\(626\) | 3.35966 | + | 5.81911i | 0.134279 | + | 0.232578i | ||||
\(627\) | 23.7142 | + | 41.0742i | 0.947054 | + | 1.64035i | ||||
\(628\) | 11.1922 | − | 19.3854i | 0.446616 | − | 0.773561i | ||||
\(629\) | 10.3240i | 0.411646i | ||||||||
\(630\) | −7.83023 | + | 61.5100i | −0.311964 | + | 2.45062i | ||||
\(631\) | 10.1452i | 0.403874i | 0.979399 | + | 0.201937i | \(0.0647236\pi\) | ||||
−0.979399 | + | 0.201937i | \(0.935276\pi\) | |||||||
\(632\) | −1.39604 | − | 0.806002i | −0.0555313 | − | 0.0320610i | ||||
\(633\) | −20.4413 | + | 11.8018i | −0.812470 | + | 0.469080i | ||||
\(634\) | 9.99120 | + | 17.3053i | 0.396801 | + | 0.687280i | ||||
\(635\) | −9.24750 | + | 16.0171i | −0.366976 | + | 0.635621i | ||||
\(636\) | −22.9223 | −0.908928 | ||||||||
\(637\) | 5.65780 | − | 21.8622i | 0.224170 | − | 0.866210i | ||||
\(638\) | − | 4.88927i | − | 0.193568i | ||||||
\(639\) | −21.3984 | + | 37.0631i | −0.846507 | + | 1.46619i | ||||
\(640\) | 1.55135 | + | 2.68702i | 0.0613225 | + | 0.106214i | ||||
\(641\) | 30.2623 | − | 17.4719i | 1.19529 | − | 0.690100i | 0.235787 | − | 0.971805i | \(-0.424233\pi\) |
0.959501 | + | 0.281704i | \(0.0908998\pi\) | |||||||
\(642\) | 7.08303 | − | 12.2682i | 0.279545 | − | 0.484186i | ||||
\(643\) | 42.1949 | 1.66401 | 0.832003 | − | 0.554771i | \(-0.187194\pi\) | ||||
0.832003 | + | 0.554771i | \(0.187194\pi\) | |||||||
\(644\) | −12.0401 | − | 4.00438i | −0.474448 | − | 0.157795i | ||||
\(645\) | −9.50905 | −0.374418 | ||||||||
\(646\) | −1.44383 | + | 2.50078i | −0.0568067 | + | 0.0983920i | ||||
\(647\) | −33.1663 | + | 19.1486i | −1.30390 | + | 0.752809i | −0.981071 | − | 0.193648i | \(-0.937968\pi\) |
−0.322832 | + | 0.946456i | \(0.604635\pi\) | |||||||
\(648\) | −12.6974 | − | 21.9925i | −0.498799 | − | 0.863946i | ||||
\(649\) | −0.298601 | + | 0.517192i | −0.0117211 | + | 0.0203016i | ||||
\(650\) | 14.9262i | 0.585454i | ||||||||
\(651\) | −67.2794 | − | 51.1692i | −2.63689 | − | 2.00548i | ||||
\(652\) | −11.5535 | −0.452469 | ||||||||
\(653\) | 5.35245 | − | 9.27071i | 0.209458 | − | 0.362791i | −0.742086 | − | 0.670304i | \(-0.766164\pi\) |
0.951544 | + | 0.307513i | \(0.0994969\pi\) | |||||||
\(654\) | −9.17546 | − | 15.8924i | −0.358789 | − | 0.621441i | ||||
\(655\) | −26.6632 | + | 15.3940i | −1.04182 | + | 0.601495i | ||||
\(656\) | −2.79385 | − | 1.61303i | −0.109081 | − | 0.0629782i | ||||
\(657\) | 74.2841i | 2.89810i | ||||||||
\(658\) | −5.07184 | − | 12.0978i | −0.197721 | − | 0.471621i | ||||
\(659\) | 0.414779i | 0.0161575i | 0.999967 | + | 0.00807875i | \(0.00257157\pi\) | ||||
−0.999967 | + | 0.00807875i | \(0.997428\pi\) | |||||||
\(660\) | 23.7142 | − | 41.0742i | 0.923074 | − | 1.59881i | ||||
\(661\) | 10.5494 | + | 18.2721i | 0.410325 | + | 0.710704i | 0.994925 | − | 0.100618i | \(-0.0320819\pi\) |
−0.584600 | + | 0.811322i | \(0.698749\pi\) | |||||||
\(662\) | −10.1864 | − | 17.6433i | −0.395904 | − | 0.685726i | ||||
\(663\) | −4.87692 | + | 8.44707i | −0.189404 | + | 0.328057i | ||||
\(664\) | −1.34746 | −0.0522915 | ||||||||
\(665\) | 23.4893 | − | 9.84759i | 0.910876 | − | 0.381873i | ||||
\(666\) | 83.7899i | 3.24679i | ||||||||
\(667\) | −3.75277 | − | 3.27856i | −0.145308 | − | 0.126946i | ||||
\(668\) | −2.66583 | + | 1.53912i | −0.103144 | + | 0.0595503i | ||||
\(669\) | −26.8043 | − | 46.4265i | −1.03632 | − | 1.79495i | ||||
\(670\) | −0.188050 | − | 0.108571i | −0.00726500 | − | 0.00419445i | ||||
\(671\) | − | 24.8199i | − | 0.958160i | ||||||
\(672\) | 5.20308 | − | 6.84123i | 0.200713 | − | 0.263906i | ||||
\(673\) | 45.4558 | 1.75219 | 0.876095 | − | 0.482138i | \(-0.160140\pi\) | ||||
0.876095 | + | 0.482138i | \(0.160140\pi\) | |||||||
\(674\) | 17.3976 | + | 10.0445i | 0.670129 | + | 0.386899i | ||||
\(675\) | −59.2721 | + | 34.2207i | −2.28138 | + | 1.31716i | ||||
\(676\) | −1.29628 | − | 2.24522i | −0.0498568 | − | 0.0863546i | ||||
\(677\) | −1.96363 | + | 3.40110i | −0.0754684 | + | 0.130715i | −0.901290 | − | 0.433217i | \(-0.857379\pi\) |
0.825821 | + | 0.563932i | \(0.190712\pi\) | |||||||
\(678\) | 33.7962 | 1.29794 | ||||||||
\(679\) | 2.34877 | − | 18.4506i | 0.0901374 | − | 0.708070i | ||||
\(680\) | 2.88766 | 0.110737 | ||||||||
\(681\) | −5.76967 | − | 3.33112i | −0.221094 | − | 0.127649i | ||||
\(682\) | 23.1376 | + | 40.0755i | 0.885985 | + | 1.53457i | ||||
\(683\) | −15.8947 | − | 27.5304i | −0.608194 | − | 1.05342i | −0.991538 | − | 0.129817i | \(-0.958561\pi\) |
0.383344 | − | 0.923606i | \(-0.374772\pi\) | |||||||
\(684\) | −11.7181 | + | 20.2964i | −0.448053 | + | 0.776051i | ||||
\(685\) | 3.14425i | 0.120136i | ||||||||
\(686\) | 11.4622 | + | 14.5471i | 0.437628 | + | 0.555411i | ||||
\(687\) | − | 46.9802i | − | 1.79240i | ||||||
\(688\) | 0.817014 | + | 0.471703i | 0.0311484 | + | 0.0179835i | ||||
\(689\) | 11.3816 | + | 19.7135i | 0.433603 | + | 0.751023i | ||||
\(690\) | −15.6247 | − | 45.7447i | −0.594824 | − | 1.74147i | ||||
\(691\) | −0.651666 | − | 0.376240i | −0.0247906 | − | 0.0143128i | 0.487554 | − | 0.873093i | \(-0.337889\pi\) |
−0.512344 | + | 0.858780i | \(0.671223\pi\) | |||||||
\(692\) | − | 18.1020i | − | 0.688136i | ||||||
\(693\) | −93.2838 | − | 11.8750i | −3.54356 | − | 0.451095i | ||||
\(694\) | 13.8851 | 0.527073 | ||||||||
\(695\) | −20.7724 | − | 11.9929i | −0.787940 | − | 0.454918i | ||||
\(696\) | 2.92330 | − | 1.68777i | 0.110807 | − | 0.0639746i | ||||
\(697\) | −2.60021 | + | 1.50123i | −0.0984899 | + | 0.0568632i | ||||
\(698\) | 17.4792 | + | 10.0916i | 0.661598 | + | 0.381974i | ||||
\(699\) | − | 42.7953i | − | 1.61867i | ||||||
\(700\) | −9.74346 | − | 7.41037i | −0.368268 | − | 0.280086i | ||||
\(701\) | 50.4674i | 1.90613i | 0.302771 | + | 0.953063i | \(0.402088\pi\) | ||||
−0.302771 | + | 0.953063i | \(0.597912\pi\) | |||||||
\(702\) | −23.8608 | + | 41.3280i | −0.900566 | + | 1.55983i | ||||
\(703\) | 29.8068 | − | 17.2089i | 1.12418 | − | 0.649047i | ||||
\(704\) | −4.07503 | + | 2.35272i | −0.153584 | + | 0.0886715i | ||||
\(705\) | 24.9876 | − | 43.2798i | 0.941087 | − | 1.63001i | ||||
\(706\) | − | 5.27961i | − | 0.198701i | ||||||
\(707\) | 13.5130 | + | 32.2322i | 0.508207 | + | 1.21222i | ||||
\(708\) | −0.412305 | −0.0154954 | ||||||||
\(709\) | −2.83450 | − | 1.63650i | −0.106452 | − | 0.0614600i | 0.445829 | − | 0.895118i | \(-0.352909\pi\) |
−0.552281 | + | 0.833658i | \(0.686242\pi\) | |||||||
\(710\) | −8.78969 | − | 15.2242i | −0.329871 | − | 0.571354i | ||||
\(711\) | −10.5449 | + | 6.08812i | −0.395466 | + | 0.228322i | ||||
\(712\) | 6.59871 | − | 11.4293i | 0.247297 | − | 0.428331i | ||||
\(713\) | 46.2752 | + | 9.11379i | 1.73302 | + | 0.341314i | ||||
\(714\) | −3.09281 | − | 7.37722i | −0.115745 | − | 0.276086i | ||||
\(715\) | −47.0991 | −1.76141 | ||||||||
\(716\) | 1.27674 | − | 2.21138i | 0.0477141 | − | 0.0826433i | ||||
\(717\) | 70.6204 | − | 40.7727i | 2.63737 | − | 1.52268i | ||||
\(718\) | 2.79577 | − | 1.61414i | 0.104337 | − | 0.0602392i | ||||
\(719\) | −13.9709 | − | 8.06611i | −0.521027 | − | 0.300815i | 0.216328 | − | 0.976321i | \(-0.430592\pi\) |
−0.737355 | + | 0.675506i | \(0.763925\pi\) | |||||||
\(720\) | 23.4362 | 0.873417 | ||||||||
\(721\) | −0.478780 | − | 0.364135i | −0.0178307 | − | 0.0135611i | ||||
\(722\) | −9.37324 | −0.348836 | ||||||||
\(723\) | −58.2509 | − | 33.6312i | −2.16638 | − | 1.25076i | ||||
\(724\) | 8.20313 | + | 14.2082i | 0.304867 | + | 0.528045i | ||||
\(725\) | −2.40376 | − | 4.16344i | −0.0892734 | − | 0.154626i | ||||
\(726\) | 31.3444 | + | 18.0967i | 1.16330 | + | 0.671631i | ||||
\(727\) | 46.2373 | 1.71485 | 0.857423 | − | 0.514612i | \(-0.172064\pi\) | ||||
0.857423 | + | 0.514612i | \(0.172064\pi\) | |||||||
\(728\) | −8.46702 | − | 1.07785i | −0.313808 | − | 0.0399478i | ||||
\(729\) | −47.6531 | −1.76493 | ||||||||
\(730\) | −26.4253 | − | 15.2566i | −0.978042 | − | 0.564673i | ||||
\(731\) | 0.760387 | − | 0.439010i | 0.0281239 | − | 0.0162374i | ||||
\(732\) | 14.8398 | − | 8.56775i | 0.548494 | − | 0.316673i | ||||
\(733\) | −19.9439 | + | 34.5439i | −0.736645 | + | 1.27591i | 0.217352 | + | 0.976093i | \(0.430258\pi\) |
−0.953998 | + | 0.299814i | \(0.903075\pi\) | |||||||
\(734\) | −23.0195 | −0.849664 | ||||||||
\(735\) | −17.6772 | + | 68.3061i | −0.652033 | + | 2.51951i | ||||
\(736\) | −0.926724 | + | 4.70544i | −0.0341595 | + | 0.173445i | ||||
\(737\) | 0.164654 | − | 0.285189i | 0.00606511 | − | 0.0105051i | ||||
\(738\) | −21.1033 | + | 12.1840i | −0.776823 | + | 0.448499i | ||||
\(739\) | 20.0129 | + | 34.6634i | 0.736187 | + | 1.27511i | 0.954201 | + | 0.299167i | \(0.0967089\pi\) |
−0.218014 | + | 0.975946i | \(0.569958\pi\) | |||||||
\(740\) | −29.8068 | − | 17.2089i | −1.09572 | − | 0.632613i | ||||
\(741\) | 32.5170 | 1.19454 | ||||||||
\(742\) | −18.5190 | − | 2.35748i | −0.679855 | − | 0.0865456i | ||||
\(743\) | − | 48.3916i | − | 1.77532i | −0.460503 | − | 0.887658i | \(-0.652331\pi\) | ||
0.460503 | − | 0.887658i | \(-0.347669\pi\) | |||||||
\(744\) | −15.9741 | + | 27.6679i | −0.585639 | + | 1.01436i | ||||
\(745\) | −25.2872 | + | 14.5996i | −0.926452 | + | 0.534887i | ||||
\(746\) | −21.6500 | + | 12.4996i | −0.792662 | + | 0.457644i | ||||
\(747\) | −5.08900 | + | 8.81441i | −0.186197 | + | 0.322502i | ||||
\(748\) | 4.37931i | 0.160123i | ||||||||
\(749\) | 6.98415 | − | 9.18305i | 0.255195 | − | 0.335541i | ||||
\(750\) | 3.76203i | 0.137370i | ||||||||
\(751\) | −24.0230 | − | 13.8697i | −0.876611 | − | 0.506111i | −0.00707137 | − | 0.999975i | \(-0.502251\pi\) |
−0.869539 | + | 0.493864i | \(0.835584\pi\) | |||||||
\(752\) | −4.29385 | + | 2.47905i | −0.156581 | + | 0.0904018i | ||||
\(753\) | −48.9246 | + | 28.2467i | −1.78291 | + | 1.02937i | ||||
\(754\) | −2.90300 | − | 1.67605i | −0.105721 | − | 0.0610380i | ||||
\(755\) | 31.3589 | 1.14127 | ||||||||
\(756\) | −15.1318 | − | 36.0937i | −0.550340 | − | 1.31272i | ||||
\(757\) | − | 19.0317i | − | 0.691720i | −0.938286 | − | 0.345860i | \(-0.887587\pi\) | ||
0.938286 | − | 0.345860i | \(-0.112413\pi\) | |||||||
\(758\) | −24.3859 | − | 14.0792i | −0.885735 | − | 0.511379i | ||||
\(759\) | 69.3746 | − | 23.6959i | 2.51814 | − | 0.860107i | ||||
\(760\) | −4.81338 | − | 8.33702i | −0.174600 | − | 0.302416i | ||||
\(761\) | 24.2384 | + | 13.9940i | 0.878640 | + | 0.507283i | 0.870210 | − | 0.492682i | \(-0.163983\pi\) |
0.00843014 | + | 0.999964i | \(0.497317\pi\) | |||||||
\(762\) | − | 19.3648i | − | 0.701511i | ||||||
\(763\) | −5.77843 | − | 13.7832i | −0.209193 | − | 0.498985i | ||||
\(764\) | − | 6.04264i | − | 0.218615i | ||||||
\(765\) | 10.9059 | − | 18.8896i | 0.394305 | − | 0.682956i | ||||
\(766\) | 10.7874 | + | 18.6844i | 0.389765 | + | 0.675093i | ||||
\(767\) | 0.204721 | + | 0.354588i | 0.00739205 | + | 0.0128034i | ||||
\(768\) | −2.81338 | − | 1.62431i | −0.101519 | − | 0.0586121i | ||||
\(769\) | 30.0343 | 1.08307 | 0.541533 | − | 0.840680i | \(-0.317844\pi\) | ||||
0.541533 | + | 0.840680i | \(0.317844\pi\) | |||||||
\(770\) | 23.3832 | − | 30.7451i | 0.842670 | − | 1.10798i | ||||
\(771\) | −60.8818 | −2.19260 | ||||||||
\(772\) | −0.409620 | + | 0.709483i | −0.0147426 | + | 0.0255349i | ||||
\(773\) | 1.35500 | + | 2.34692i | 0.0487359 | + | 0.0844130i | 0.889364 | − | 0.457199i | \(-0.151147\pi\) |
−0.840628 | + | 0.541612i | \(0.817814\pi\) | |||||||
\(774\) | 6.17131 | − | 3.56301i | 0.221823 | − | 0.128070i | ||||
\(775\) | 39.4054 | + | 22.7507i | 1.41549 | + | 0.817231i | ||||
\(776\) | −7.02996 | −0.252361 | ||||||||
\(777\) | −12.0401 | + | 94.5802i | −0.431935 | + | 3.39305i | ||||
\(778\) | 20.1632i | 0.722887i | ||||||||
\(779\) | 8.66848 | + | 5.00475i | 0.310580 | + | 0.179314i | ||||
\(780\) | −16.2585 | − | 28.1605i | −0.582147 | − | 1.00831i | ||||
\(781\) | 23.0884 | − | 13.3301i | 0.826169 | − | 0.476989i | ||||
\(782\) | 3.36135 | + | 2.93660i | 0.120202 | + | 0.105012i | ||||
\(783\) | − | 15.3704i | − | 0.549295i | ||||||
\(784\) | 4.90719 | − | 4.99194i | 0.175257 | − | 0.178284i | ||||
\(785\) | 69.4519 | 2.47884 | ||||||||
\(786\) | 16.1180 | − | 27.9171i | 0.574909 | − | 0.995771i | ||||
\(787\) | −11.7106 | − | 20.2833i | −0.417437 | − | 0.723022i | 0.578244 | − | 0.815864i | \(-0.303738\pi\) |
−0.995681 | + | 0.0928421i | \(0.970405\pi\) | |||||||
\(788\) | 5.47678 | + | 9.48607i | 0.195102 | + | 0.337927i | ||||
\(789\) | −26.7473 | + | 46.3277i | −0.952229 | + | 1.64931i | ||||
\(790\) | − | 5.00157i | − | 0.177948i | ||||||
\(791\) | 27.3042 | + | 3.47582i | 0.970824 | + | 0.123586i | ||||
\(792\) | 35.5425i | 1.26295i | ||||||||
\(793\) | −14.7367 | − | 8.50827i | −0.523317 | − | 0.302137i | ||||
\(794\) | 11.7504 | − | 6.78407i | 0.417004 | − | 0.240758i | ||||
\(795\) | −35.5605 | − | 61.5927i | −1.26120 | − | 2.18447i | ||||
\(796\) | 3.12167 | − | 5.40689i | 0.110645 | − | 0.191642i | ||||
\(797\) | −28.7489 | −1.01834 | −0.509169 | − | 0.860667i | \(-0.670047\pi\) | ||||
−0.509169 | + | 0.860667i | \(0.670047\pi\) | |||||||
\(798\) | −16.1436 | + | 21.2263i | −0.571478 | + | 0.751402i | ||||
\(799\) | 4.61446i | 0.163248i | ||||||||
\(800\) | −2.31338 | + | 4.00689i | −0.0817904 | + | 0.141665i | ||||
\(801\) | −49.8433 | − | 86.3311i | −1.76113 | − | 3.05036i | ||||
\(802\) | −23.8069 | + | 13.7449i | −0.840650 | + | 0.485349i | ||||
\(803\) | 23.1376 | − | 40.0755i | 0.816509 | − | 1.41424i | ||||
\(804\) | 0.227353 | 0.00801811 | ||||||||
\(805\) | −7.91864 | − | 38.5643i | −0.279095 | − | 1.35921i | ||||
\(806\) | 31.7264 | 1.11751 | ||||||||
\(807\) | −35.6678 | + | 61.7784i | −1.25556 | + | 2.17470i | ||||
\(808\) | 11.4401 | − | 6.60497i | 0.402463 | − | 0.232362i | ||||
\(809\) | 16.6368 | + | 28.8157i | 0.584917 | + | 1.01311i | 0.994886 | + | 0.101007i | \(0.0322063\pi\) |
−0.409969 | + | 0.912100i | \(0.634460\pi\) | |||||||
\(810\) | 39.3961 | − | 68.2361i | 1.38424 | − | 2.39757i | ||||
\(811\) | 26.7933i | 0.940839i | 0.882443 | + | 0.470419i | \(0.155897\pi\) | ||||
−0.882443 | + | 0.470419i | \(0.844103\pi\) | |||||||
\(812\) | 2.53533 | − | 1.06290i | 0.0889725 | − | 0.0373006i | ||||
\(813\) | 75.2232 | 2.63819 | ||||||||
\(814\) | 26.0984 | − | 45.2038i | 0.914750 | − | 1.58439i | ||||
\(815\) | −17.9235 | − | 31.0444i | −0.627833 | − | 1.08744i | ||||
\(816\) | −2.61839 | + | 1.51173i | −0.0916619 | + | 0.0529210i | ||||
\(817\) | −2.53495 | − | 1.46356i | −0.0886867 | − | 0.0512033i | ||||
\(818\) | 18.9691i | 0.663239i | ||||||||
\(819\) | −39.0285 | + | 51.3163i | −1.36377 | + | 1.79314i | ||||
\(820\) | − | 10.0095i | − | 0.349547i | ||||||
\(821\) | 0.649981 | − | 1.12580i | 0.0226845 | − | 0.0392907i | −0.854460 | − | 0.519517i | \(-0.826112\pi\) |
0.877145 | + | 0.480226i | \(0.159445\pi\) | |||||||
\(822\) | −1.64606 | − | 2.85106i | −0.0574129 | − | 0.0994420i | ||||
\(823\) | −4.01854 | − | 6.96031i | −0.140077 | − | 0.242621i | 0.787448 | − | 0.616381i | \(-0.211402\pi\) |
−0.927526 | + | 0.373760i | \(0.878068\pi\) | |||||||
\(824\) | −0.113676 | + | 0.196893i | −0.00396010 | + | 0.00685910i | ||||
\(825\) | 70.7254 | 2.46234 | ||||||||
\(826\) | −0.333103 | − | 0.0424041i | −0.0115901 | − | 0.00147543i | ||||
\(827\) | 56.3043i | 1.95789i | 0.204115 | + | 0.978947i | \(0.434568\pi\) | ||||
−0.204115 | + | 0.978947i | \(0.565432\pi\) | |||||||
\(828\) | 27.2807 | + | 23.8334i | 0.948070 | + | 0.828269i | ||||
\(829\) | −0.720317 | + | 0.415875i | −0.0250177 | + | 0.0144439i | −0.512457 | − | 0.858713i | \(-0.671264\pi\) |
0.487439 | + | 0.873157i | \(0.337931\pi\) | |||||||
\(830\) | −2.09038 | − | 3.62064i | −0.0725581 | − | 0.125674i | ||||
\(831\) | −86.5813 | − | 49.9877i | −3.00347 | − | 1.73405i | ||||
\(832\) | 3.22606i | 0.111843i | ||||||||
\(833\) | −1.73998 | − | 6.27818i | −0.0602866 | − | 0.217526i | ||||
\(834\) | 25.1138 | 0.869621 | ||||||||
\(835\) | −8.27128 | − | 4.77543i | −0.286239 | − | 0.165260i | ||||
\(836\) | 12.6436 | − | 7.29979i | 0.437288 | − | 0.252469i | ||||
\(837\) | 72.7379 | + | 125.986i | 2.51419 | + | 4.35470i | ||||
\(838\) | −9.32708 | + | 16.1550i | −0.322199 | + | 0.558064i | ||||
\(839\) | −44.8066 | −1.54689 | −0.773447 | − | 0.633861i | \(-0.781469\pi\) | ||||
−0.773447 | + | 0.633861i | \(0.781469\pi\) | |||||||
\(840\) | 26.4543 | + | 3.36764i | 0.912760 | + | 0.116194i | ||||
\(841\) | −27.9203 | −0.962770 | ||||||||
\(842\) | −8.19249 | − | 4.72994i | −0.282332 | − | 0.163004i | ||||
\(843\) | 27.7266 | + | 48.0238i | 0.954954 | + | 1.65403i | ||||
\(844\) | 3.63288 | + | 6.29233i | 0.125049 | + | 0.216591i | ||||
\(845\) | 4.02196 | − | 6.96625i | 0.138360 | − | 0.239646i | ||||
\(846\) | 37.4510i | 1.28759i | ||||||||
\(847\) | 23.4621 | + | 17.8441i | 0.806168 | + | 0.613129i | ||||
\(848\) | 7.05603i | 0.242305i | ||||||||
\(849\) | −2.72512 | − | 1.57335i | −0.0935260 | − | 0.0539973i | ||||
\(850\) | 2.15304 | + | 3.72918i | 0.0738487 | + | 0.127910i | ||||
\(851\) | −17.1957 | − | 50.3438i | −0.589460 | − | 1.72576i | ||||
\(852\) | 15.9401 | + | 9.20305i | 0.546100 | + | 0.315291i | ||||
\(853\) | − | 46.7117i | − | 1.59938i | −0.600414 | − | 0.799690i | \(-0.704997\pi\) | ||
0.600414 | − | 0.799690i | \(-0.295003\pi\) | |||||||
\(854\) | 12.8703 | − | 5.39571i | 0.440413 | − | 0.184637i | ||||
\(855\) | −72.7156 | −2.48682 | ||||||||
\(856\) | −3.77643 | − | 2.18032i | −0.129076 | − | 0.0745219i | ||||
\(857\) | −26.9819 | + | 15.5780i | −0.921684 | + | 0.532135i | −0.884172 | − | 0.467162i | \(-0.845277\pi\) |
−0.0375121 | + | 0.999296i | \(0.511943\pi\) | |||||||
\(858\) | 42.7072 | − | 24.6570i | 1.45800 | − | 0.841777i | ||||
\(859\) | 43.3969 | + | 25.0552i | 1.48068 | + | 0.854873i | 0.999760 | − | 0.0218902i | \(-0.00696842\pi\) |
0.480923 | + | 0.876763i | \(0.340302\pi\) | |||||||
\(860\) | 2.92711i | 0.0998136i | ||||||||
\(861\) | −25.5717 | + | 10.7206i | −0.871481 | + | 0.365358i | ||||
\(862\) | 24.8434i | 0.846170i | ||||||||
\(863\) | 7.05717 | − | 12.2234i | 0.240229 | − | 0.416089i | −0.720551 | − | 0.693402i | \(-0.756111\pi\) |
0.960779 | + | 0.277314i | \(0.0894442\pi\) | |||||||
\(864\) | −12.8107 | + | 7.39626i | −0.435829 | + | 0.251626i | ||||
\(865\) | 48.6405 | − | 28.0826i | 1.65383 | − | 0.954837i | ||||
\(866\) | 5.22165 | − | 9.04416i | 0.177439 | − | 0.307333i | ||||
\(867\) | − | 52.4125i | − | 1.78002i | ||||||
\(868\) | −15.7511 | + | 20.7102i | −0.534627 | + | 0.702950i | ||||
\(869\) | 7.58519 | 0.257310 | ||||||||
\(870\) | 9.07012 | + | 5.23663i | 0.307506 | + | 0.177538i | ||||
\(871\) | −0.112887 | − | 0.195526i | −0.00382503 | − | 0.00662515i | ||||
\(872\) | −4.89205 | + | 2.82442i | −0.165666 | + | 0.0956471i | ||||
\(873\) | −26.5504 | + | 45.9866i | −0.898593 | + | 1.55641i | ||||
\(874\) | 2.87535 | − | 14.5996i | 0.0972602 | − | 0.493838i | ||||
\(875\) | −0.386912 | + | 3.03937i | −0.0130800 | + | 0.102749i | ||||
\(876\) | 31.9482 | 1.07943 | ||||||||
\(877\) | −10.1192 | + | 17.5270i | −0.341702 | + | 0.591845i | −0.984749 | − | 0.173982i | \(-0.944337\pi\) |
0.643047 | + | 0.765827i | \(0.277670\pi\) | |||||||
\(878\) | 5.77431 | − | 3.33380i | 0.194874 | − | 0.112510i | ||||
\(879\) | −47.9440 | + | 27.6805i | −1.61711 | + | 0.933639i | ||||
\(880\) | −12.6436 | − | 7.29979i | −0.426216 | − | 0.246076i | ||||
\(881\) | −15.7711 | −0.531343 | −0.265671 | − | 0.964064i | \(-0.585594\pi\) | ||||
−0.265671 | + | 0.964064i | \(0.585594\pi\) | |||||||
\(882\) | −14.1216 | − | 50.9537i | −0.475501 | − | 1.71570i | ||||
\(883\) | −54.7968 | −1.84406 | −0.922029 | − | 0.387120i | \(-0.873470\pi\) | ||||
−0.922029 | + | 0.387120i | \(0.873470\pi\) | |||||||
\(884\) | 2.60021 | + | 1.50123i | 0.0874544 | + | 0.0504918i | ||||
\(885\) | −0.639630 | − | 1.10787i | −0.0215009 | − | 0.0372407i | ||||
\(886\) | 4.21957 | + | 7.30851i | 0.141759 | + | 0.245534i | ||||
\(887\) | 4.24959 | + | 2.45350i | 0.142687 | + | 0.0823805i | 0.569644 | − | 0.821891i | \(-0.307081\pi\) |
−0.426957 | + | 0.904272i | \(0.640414\pi\) | |||||||
\(888\) | 36.0364 | 1.20930 | ||||||||
\(889\) | 1.99160 | − | 15.6449i | 0.0667960 | − | 0.524713i | ||||
\(890\) | 40.9477 | 1.37257 | ||||||||
\(891\) | 103.484 | + | 59.7467i | 3.46685 | + | 2.00159i | ||||
\(892\) | −14.2912 | + | 8.25101i | −0.478504 | + | 0.276264i | ||||
\(893\) | 13.3225 | − | 7.69177i | 0.445822 | − | 0.257395i | ||||
\(894\) | 15.2862 | − | 26.4764i | 0.511246 | − | 0.885503i | ||||
\(895\) | 7.92271 | 0.264827 | ||||||||
\(896\) | −2.10589 | − | 1.60163i | −0.0703529 | − | 0.0535068i | ||||
\(897\) | 9.71227 | − | 49.3140i | 0.324283 | − | 1.64655i | ||||
\(898\) | 0.666086 | − | 1.15369i | 0.0222276 | − | 0.0384993i | ||||
\(899\) | −8.84959 | + | 5.10931i | −0.295150 | + | 0.170405i | ||||
\(900\) | 17.4741 | + | 30.2660i | 0.582470 | + | 1.00887i | ||||
\(901\) | 5.68717 | + | 3.28349i | 0.189467 | + | 0.109389i | ||||
\(902\) | 15.1800 | 0.505440 | ||||||||
\(903\) | 7.47802 | − | 3.13507i | 0.248853 | − | 0.104329i | ||||
\(904\) | − | 10.4033i | − | 0.346008i | ||||||
\(905\) | −25.4519 | + | 44.0839i | −0.846049 | + | 1.46540i | ||||
\(906\) | −28.4348 | + | 16.4168i | −0.944682 | + | 0.545412i | ||||
\(907\) | 27.2884 | − | 15.7550i | 0.906096 | − | 0.523135i | 0.0269232 | − | 0.999638i | \(-0.491429\pi\) |
0.879173 | + | 0.476503i | \(0.158096\pi\) | |||||||
\(908\) | −1.02540 | + | 1.77604i | −0.0340290 | + | 0.0589400i | ||||
\(909\) | − | 99.7811i | − | 3.30953i | ||||||
\(910\) | −10.2391 | − | 24.4232i | −0.339423 | − | 0.809620i | ||||
\(911\) | − | 20.6927i | − | 0.685580i | −0.939412 | − | 0.342790i | \(-0.888628\pi\) | ||
0.939412 | − | 0.342790i | \(-0.111372\pi\) | |||||||
\(912\) | 8.72909 | + | 5.03974i | 0.289049 | + | 0.166882i | ||||
\(913\) | 5.49093 | − | 3.17019i | 0.181723 | − | 0.104918i | ||||
\(914\) | −26.4216 | + | 15.2545i | −0.873947 | + | 0.504574i | ||||
\(915\) | 46.0434 | + | 26.5832i | 1.52215 | + | 0.878813i | ||||
\(916\) | −14.4616 | −0.477825 | ||||||||
\(917\) | 15.8930 | − | 20.8967i | 0.524832 | − | 0.690070i | ||||
\(918\) | 13.7673i | 0.454387i | ||||||||
\(919\) | 6.28438 | + | 3.62829i | 0.207303 | + | 0.119686i | 0.600057 | − | 0.799957i | \(-0.295144\pi\) |
−0.392755 | + | 0.919643i | \(0.628478\pi\) | |||||||
\(920\) | −14.0813 | + | 4.80967i | −0.464246 | + | 0.158570i | ||||
\(921\) | −3.16609 | − | 5.48382i | −0.104326 | − | 0.180698i | ||||
\(922\) | −28.7162 | − | 16.5793i | −0.945718 | − | 0.546010i | ||||
\(923\) | − | 18.2783i | − | 0.601637i | ||||||
\(924\) | −5.10723 | + | 40.1196i | −0.168015 | + | 1.31984i | ||||
\(925\) | − | 51.3241i | − | 1.68753i | ||||||
\(926\) | 6.97778 | − | 12.0859i | 0.229304 | − | 0.397166i | ||||
\(927\) | 0.858653 | + | 1.48723i | 0.0282019 | + | 0.0488471i | ||||
\(928\) | −0.519534 | − | 0.899859i | −0.0170545 | − | 0.0295393i | ||||
\(929\) | 2.05400 | + | 1.18588i | 0.0673894 | + | 0.0389073i | 0.533316 | − | 0.845916i | \(-0.320946\pi\) |
−0.465927 | + | 0.884823i | \(0.654279\pi\) | |||||||
\(930\) | −99.1257 | −3.25046 | ||||||||
\(931\) | −15.2256 | + | 15.4885i | −0.498997 | + | 0.507615i | ||||
\(932\) | −13.1734 | −0.431509 | ||||||||
\(933\) | 6.64018 | − | 11.5011i | 0.217390 | − | 0.376530i | ||||
\(934\) | 0.703338 | + | 1.21822i | 0.0230139 | + | 0.0398613i | ||||
\(935\) | −11.7673 | + | 6.79385i | −0.384832 | + | 0.222183i | ||||
\(936\) | 21.1033 | + | 12.1840i | 0.689783 | + | 0.398246i | ||||
\(937\) | 19.4559 | 0.635595 | 0.317797 | − | 0.948159i | \(-0.397057\pi\) | ||||
0.317797 | + | 0.948159i | \(0.397057\pi\) | |||||||
\(938\) | 0.183679 | + | 0.0233824i | 0.00599735 | + | 0.000763463i | ||||
\(939\) | − | 21.8285i | − | 0.712346i | ||||||
\(940\) | −13.3225 | − | 7.69177i | −0.434533 | − | 0.250878i | ||||
\(941\) | 0.566992 | + | 0.982059i | 0.0184834 | + | 0.0320142i | 0.875119 | − | 0.483907i | \(-0.160783\pi\) |
−0.856636 | + | 0.515922i | \(0.827450\pi\) | |||||||
\(942\) | −62.9756 | + | 36.3590i | −2.05186 | + | 1.18464i | ||||
\(943\) | 10.1791 | − | 11.6515i | 0.331478 | − | 0.379424i | ||||
\(944\) | 0.126917i | 0.00413081i | ||||||||
\(945\) | 73.5097 | − | 96.6536i | 2.39127 | − | 3.14414i | ||||
\(946\) | −4.43915 | −0.144329 | ||||||||
\(947\) | −13.1070 | + | 22.7019i | −0.425919 | + | 0.737714i | −0.996506 | − | 0.0835235i | \(-0.973383\pi\) |
0.570586 | + | 0.821238i | \(0.306716\pi\) | |||||||
\(948\) | 2.61839 | + | 4.53518i | 0.0850413 | + | 0.147296i | ||||
\(949\) | −15.8632 | − | 27.4758i | −0.514941 | − | 0.891904i | ||||
\(950\) | 7.17773 | − | 12.4322i | 0.232876 | − | 0.403354i | ||||
\(951\) | − | 64.9151i | − | 2.10502i | ||||||
\(952\) | −2.27088 | + | 0.952040i | −0.0735998 | + | 0.0308558i | ||||
\(953\) | 37.8441i | 1.22589i | 0.790125 | + | 0.612945i | \(0.210015\pi\) | ||||
−0.790125 | + | 0.612945i | \(0.789985\pi\) | |||||||
\(954\) | 46.1571 | + | 26.6488i | 1.49439 | + | 0.862787i | ||||
\(955\) | 16.2367 | − | 9.37425i | 0.525407 | − | 0.303344i | ||||
\(956\) | −12.5508 | − | 21.7386i | −0.405922 | − | 0.703077i | ||||
\(957\) | −7.94168 | + | 13.7554i | −0.256718 | + | 0.444649i | ||||
\(958\) | −12.9247 | −0.417579 | ||||||||
\(959\) | −1.03664 | − | 2.47267i | −0.0334748 | − | 0.0798468i | ||||
\(960\) | − | 10.0795i | − | 0.325314i | ||||||
\(961\) | 32.8578 | − | 56.9114i | 1.05993 | − | 1.83585i | ||||
\(962\) | −17.8931 | − | 30.9918i | −0.576897 | − | 0.999215i | ||||
\(963\) | −28.5252 | + | 16.4690i | −0.919213 | + | 0.530708i | ||||
\(964\) | −10.3525 | + | 17.9310i | −0.333431 | + | 0.577519i | ||||
\(965\) | −2.54186 | −0.0818254 | ||||||||
\(966\) | 27.3692 | + | 30.8227i | 0.880588 | + | 0.991705i | ||||
\(967\) | 31.3048 | 1.00670 | 0.503348 | − | 0.864084i | \(-0.332102\pi\) | ||||
0.503348 | + | 0.864084i | \(0.332102\pi\) | |||||||
\(968\) | 5.57059 | − | 9.64855i | 0.179046 | − | 0.310116i | ||||
\(969\) | 8.12408 | − | 4.69044i | 0.260983 | − | 0.150679i | ||||
\(970\) | −10.9059 | − | 18.8896i | −0.350169 | − | 0.606510i | ||||
\(971\) | −24.9884 | + | 43.2811i | −0.801915 | + | 1.38896i | 0.116439 | + | 0.993198i | \(0.462852\pi\) |
−0.918354 | + | 0.395759i | \(0.870481\pi\) | |||||||
\(972\) | 38.1200i | 1.22270i | ||||||||
\(973\) | 20.2896 | + | 2.58287i | 0.650454 | + | 0.0828029i | ||||
\(974\) | −33.5388 | −1.07465 | ||||||||
\(975\) | 24.2447 | − | 41.9931i | 0.776453 | − | 1.34486i | ||||
\(976\) | −2.63736 | − | 4.56804i | −0.0844197 | − | 0.146219i | ||||
\(977\) | −25.2635 | + | 14.5859i | −0.808251 | + | 0.466644i | −0.846348 | − | 0.532630i | \(-0.821204\pi\) |
0.0380970 | + | 0.999274i | \(0.487870\pi\) | |||||||
\(978\) | 32.5044 | + | 18.7664i | 1.03938 | + | 0.600083i | ||||
\(979\) | 62.0997i | 1.98472i | ||||||||
\(980\) | 21.0262 | + | 5.44146i | 0.671658 | + | 0.173821i | ||||
\(981\) | 42.6685i | 1.36230i | ||||||||
\(982\) | −14.9179 | + | 25.8386i | −0.476050 | + | 0.824543i | ||||
\(983\) | 16.1562 | + | 27.9834i | 0.515304 | + | 0.892533i | 0.999842 | + | 0.0177627i | \(0.00565435\pi\) |
−0.484538 | + | 0.874770i | \(0.661012\pi\) | |||||||
\(984\) | 5.24011 | + | 9.07613i | 0.167048 | + | 0.289336i | ||||
\(985\) | −16.9928 | + | 29.4324i | −0.541436 | + | 0.937795i | ||||
\(986\) | −0.967051 | −0.0307972 | ||||||||
\(987\) | −5.38147 | + | 42.2739i | −0.171294 | + | 1.34559i | ||||
\(988\) | − | 10.0095i | − | 0.318444i | ||||||
\(989\) | −2.97672 | + | 3.40727i | −0.0946542 | + | 0.108345i | ||||
\(990\) | −95.5034 | + | 55.1389i | −3.03530 | + | 1.75243i | ||||
\(991\) | 21.1885 | + | 36.6996i | 0.673076 | + | 1.16580i | 0.977027 | + | 0.213114i | \(0.0683607\pi\) |
−0.303951 | + | 0.952688i | \(0.598306\pi\) | |||||||
\(992\) | 8.51685 | + | 4.91721i | 0.270410 | + | 0.156121i | ||||
\(993\) | 66.1831i | 2.10026i | ||||||||
\(994\) | 11.9316 | + | 9.07457i | 0.378448 | + | 0.287828i | ||||
\(995\) | 19.3712 | 0.614110 | ||||||||
\(996\) | 3.79091 | + | 2.18868i | 0.120120 | + | 0.0693511i | ||||
\(997\) | −17.4915 | + | 10.0987i | −0.553960 | + | 0.319829i | −0.750718 | − | 0.660623i | \(-0.770292\pi\) |
0.196758 | + | 0.980452i | \(0.436959\pi\) | |||||||
\(998\) | −6.64018 | − | 11.5011i | −0.210191 | − | 0.364062i | ||||
\(999\) | 82.0458 | − | 142.107i | 2.59581 | − | 4.49608i |
(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 | 322.2.g.a.229.8 | yes | 16 | |
7.2 | even | 3 | 2254.2.c.c.2253.15 | 16 | |||
7.3 | odd | 6 | inner | 322.2.g.a.45.7 | ✓ | 16 | |
7.5 | odd | 6 | 2254.2.c.c.2253.2 | 16 | |||
23.22 | odd | 2 | inner | 322.2.g.a.229.7 | yes | 16 | |
161.45 | even | 6 | inner | 322.2.g.a.45.8 | yes | 16 | |
161.68 | even | 6 | 2254.2.c.c.2253.1 | 16 | |||
161.114 | odd | 6 | 2254.2.c.c.2253.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.g.a.45.7 | ✓ | 16 | 7.3 | odd | 6 | inner | |
322.2.g.a.45.8 | yes | 16 | 161.45 | even | 6 | inner | |
322.2.g.a.229.7 | yes | 16 | 23.22 | odd | 2 | inner | |
322.2.g.a.229.8 | yes | 16 | 1.1 | even | 1 | trivial | |
2254.2.c.c.2253.1 | 16 | 161.68 | even | 6 | |||
2254.2.c.c.2253.2 | 16 | 7.5 | odd | 6 | |||
2254.2.c.c.2253.15 | 16 | 7.2 | even | 3 | |||
2254.2.c.c.2253.16 | 16 | 161.114 | odd | 6 |