Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(239,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.l (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.386672896.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.3 | ||
Root | \(0.621372 - 1.27039i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 420.239 |
Dual form | 420.2.l.f.239.4 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.621372 | − | 1.27039i | −0.439377 | − | 0.898303i | ||||
\(3\) | 1.72779 | + | 0.121372i | 0.997542 | + | 0.0700743i | ||||
\(4\) | −1.22779 | + | 1.57877i | −0.613897 | + | 0.789387i | ||||
\(5\) | 1.00000 | − | 2.00000i | 0.447214 | − | 0.894427i | ||||
\(6\) | −0.919412 | − | 2.27039i | −0.375348 | − | 0.926884i | ||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.76858 | + | 0.578773i | 0.978840 | + | 0.204627i | ||||
\(9\) | 2.97054 | + | 0.419412i | 0.990179 | + | 0.139804i | ||||
\(10\) | −3.16216 | − | 0.0276478i | −0.999962 | − | 0.00874299i | ||||
\(11\) | 3.45559 | 1.04190 | 0.520949 | − | 0.853588i | \(-0.325578\pi\) | ||||
0.520949 | + | 0.853588i | \(0.325578\pi\) | |||||||
\(12\) | −2.31299 | + | 2.57877i | −0.667703 | + | 0.744428i | ||||
\(13\) | 4.83882i | 1.34205i | 0.741435 | + | 0.671024i | \(0.234145\pi\) | ||||
−0.741435 | + | 0.671024i | \(0.765855\pi\) | |||||||
\(14\) | −0.621372 | − | 1.27039i | −0.166069 | − | 0.339527i | ||||
\(15\) | 1.97054 | − | 3.33421i | 0.508791 | − | 0.860890i | ||||
\(16\) | −0.985049 | − | 3.87681i | −0.246262 | − | 0.969203i | ||||
\(17\) | −5.94108 | −1.44092 | −0.720461 | − | 0.693495i | \(-0.756070\pi\) | ||||
−0.720461 | + | 0.693495i | \(0.756070\pi\) | |||||||
\(18\) | −1.31299 | − | 4.03436i | −0.309475 | − | 0.950908i | ||||
\(19\) | − | 1.08157i | − | 0.248129i | −0.992274 | − | 0.124064i | \(-0.960407\pi\) | ||
0.992274 | − | 0.124064i | \(-0.0395930\pi\) | |||||||
\(20\) | 1.92975 | + | 4.03436i | 0.431506 | + | 0.902110i | ||||
\(21\) | 1.72779 | + | 0.121372i | 0.377035 | + | 0.0264856i | ||||
\(22\) | −2.14721 | − | 4.38995i | −0.457786 | − | 0.935940i | ||||
\(23\) | 0.596080i | 0.124291i | 0.998067 | + | 0.0621456i | \(0.0197943\pi\) | ||||
−0.998067 | + | 0.0621456i | \(0.980206\pi\) | |||||||
\(24\) | 4.71328 | + | 1.33603i | 0.962095 | + | 0.272716i | ||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 6.14721 | − | 3.00671i | 1.20557 | − | 0.589665i | ||||
\(27\) | 5.08157 | + | 1.08520i | 0.977948 | + | 0.208847i | ||||
\(28\) | −1.22779 | + | 1.57877i | −0.232031 | + | 0.298360i | ||||
\(29\) | − | 4.83882i | − | 0.898547i | −0.893394 | − | 0.449274i | \(-0.851683\pi\) | ||
0.893394 | − | 0.449274i | \(-0.148317\pi\) | |||||||
\(30\) | −5.46020 | − | 0.431568i | −0.996891 | − | 0.0787931i | ||||
\(31\) | − | 9.56706i | − | 1.71829i | −0.511729 | − | 0.859147i | \(-0.670995\pi\) | ||
0.511729 | − | 0.859147i | \(-0.329005\pi\) | |||||||
\(32\) | −4.31299 | + | 3.66034i | −0.762436 | + | 0.647063i | ||||
\(33\) | 5.97054 | + | 0.419412i | 1.03934 | + | 0.0730103i | ||||
\(34\) | 3.69162 | + | 7.54750i | 0.633107 | + | 1.29438i | ||||
\(35\) | 1.00000 | − | 2.00000i | 0.169031 | − | 0.338062i | ||||
\(36\) | −4.30936 | + | 4.17485i | −0.718227 | + | 0.695809i | ||||
\(37\) | 2.91117i | 0.478594i | 0.970946 | + | 0.239297i | \(0.0769169\pi\) | ||||
−0.970946 | + | 0.239297i | \(0.923083\pi\) | |||||||
\(38\) | −1.37402 | + | 0.672057i | −0.222895 | + | 0.109022i | ||||
\(39\) | −0.587299 | + | 8.36049i | −0.0940431 | + | 1.33875i | ||||
\(40\) | 3.92612 | − | 4.95838i | 0.620775 | − | 0.783989i | ||||
\(41\) | 6.91117i | 1.07934i | 0.841875 | + | 0.539672i | \(0.181452\pi\) | ||||
−0.841875 | + | 0.539672i | \(0.818548\pi\) | |||||||
\(42\) | −0.919412 | − | 2.27039i | −0.141868 | − | 0.350329i | ||||
\(43\) | 7.39666 | 1.12798 | 0.563990 | − | 0.825782i | \(-0.309266\pi\) | ||||
0.563990 | + | 0.825782i | \(0.309266\pi\) | |||||||
\(44\) | −4.24274 | + | 5.45559i | −0.639618 | + | 0.822461i | ||||
\(45\) | 3.80936 | − | 5.52166i | 0.567866 | − | 0.823121i | ||||
\(46\) | 0.757255 | − | 0.370388i | 0.111651 | − | 0.0546107i | ||||
\(47\) | − | 0.242745i | − | 0.0354079i | −0.999843 | − | 0.0177040i | \(-0.994364\pi\) | ||
0.999843 | − | 0.0177040i | \(-0.00563564\pi\) | |||||||
\(48\) | −1.23142 | − | 6.81789i | −0.177741 | − | 0.984077i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.21745 | + | 6.29667i | −0.455016 | + | 0.890483i | ||||
\(51\) | −10.2649 | − | 0.721082i | −1.43738 | − | 0.100972i | ||||
\(52\) | −7.63941 | − | 5.94108i | −1.05939 | − | 0.823879i | ||||
\(53\) | −11.8223 | −1.62392 | −0.811962 | − | 0.583710i | \(-0.801600\pi\) | ||||
−0.811962 | + | 0.583710i | \(0.801600\pi\) | |||||||
\(54\) | −1.77892 | − | 7.12990i | −0.242080 | − | 0.970256i | ||||
\(55\) | 3.45559 | − | 6.91117i | 0.465951 | − | 0.931902i | ||||
\(56\) | 2.76858 | + | 0.578773i | 0.369967 | + | 0.0773418i | ||||
\(57\) | 0.131272 | − | 1.86873i | 0.0173875 | − | 0.247519i | ||||
\(58\) | −6.14721 | + | 3.00671i | −0.807168 | + | 0.394801i | ||||
\(59\) | 3.25197 | 0.423370 | 0.211685 | − | 0.977338i | \(-0.432105\pi\) | ||||
0.211685 | + | 0.977338i | \(0.432105\pi\) | |||||||
\(60\) | 2.84455 | + | 7.20476i | 0.367230 | + | 0.930130i | ||||
\(61\) | −12.6486 | −1.61949 | −0.809745 | − | 0.586781i | \(-0.800395\pi\) | ||||
−0.809745 | + | 0.586781i | \(0.800395\pi\) | |||||||
\(62\) | −12.1539 | + | 5.94470i | −1.54355 | + | 0.754978i | ||||
\(63\) | 2.97054 | + | 0.419412i | 0.374253 | + | 0.0528410i | ||||
\(64\) | 7.33004 | + | 3.20476i | 0.916255 | + | 0.400595i | ||||
\(65\) | 9.67765 | + | 4.83882i | 1.20036 | + | 0.600182i | ||||
\(66\) | −3.17711 | − | 7.84554i | −0.391075 | − | 0.965719i | ||||
\(67\) | −5.71901 | −0.698689 | −0.349344 | − | 0.936994i | \(-0.613596\pi\) | ||||
−0.349344 | + | 0.936994i | \(0.613596\pi\) | |||||||
\(68\) | 7.29441 | − | 9.37961i | 0.884577 | − | 1.13744i | ||||
\(69\) | −0.0723476 | + | 1.02990i | −0.00870963 | + | 0.123986i | ||||
\(70\) | −3.16216 | − | 0.0276478i | −0.377950 | − | 0.00330454i | ||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 7.98142 | + | 2.88044i | 0.940619 | + | 0.339463i | ||||
\(73\) | 8.00000i | 0.936329i | 0.883641 | + | 0.468165i | \(0.155085\pi\) | ||||
−0.883641 | + | 0.468165i | \(0.844915\pi\) | |||||||
\(74\) | 3.69833 | − | 1.80892i | 0.429922 | − | 0.210283i | ||||
\(75\) | −4.69789 | − | 7.27529i | −0.542466 | − | 0.840078i | ||||
\(76\) | 1.70755 | + | 1.32794i | 0.195870 | + | 0.152326i | ||||
\(77\) | 3.45559 | 0.393801 | ||||||||
\(78\) | 10.9860 | − | 4.44887i | 1.24392 | − | 0.503736i | ||||
\(79\) | 0.949416i | 0.106818i | 0.998573 | + | 0.0534088i | \(0.0170086\pi\) | ||||
−0.998573 | + | 0.0534088i | \(0.982991\pi\) | |||||||
\(80\) | −8.73867 | − | 1.90672i | −0.977014 | − | 0.213177i | ||||
\(81\) | 8.64819 | + | 2.49176i | 0.960910 | + | 0.276862i | ||||
\(82\) | 8.77990 | − | 4.29441i | 0.969578 | − | 0.474238i | ||||
\(83\) | 16.9637i | 1.86201i | 0.365006 | + | 0.931005i | \(0.381067\pi\) | ||||
−0.365006 | + | 0.931005i | \(0.618933\pi\) | |||||||
\(84\) | −2.31299 | + | 2.57877i | −0.252368 | + | 0.281367i | ||||
\(85\) | −5.94108 | + | 11.8822i | −0.644400 | + | 1.28880i | ||||
\(86\) | −4.59608 | − | 9.39666i | −0.495608 | − | 1.01327i | ||||
\(87\) | 0.587299 | − | 8.36049i | 0.0629651 | − | 0.896338i | ||||
\(88\) | 9.56706 | + | 2.00000i | 1.01985 | + | 0.213201i | ||||
\(89\) | 5.23352i | 0.554752i | 0.960761 | + | 0.277376i | \(0.0894648\pi\) | ||||
−0.960761 | + | 0.277376i | \(0.910535\pi\) | |||||||
\(90\) | −9.38171 | − | 1.40838i | −0.988919 | − | 0.148456i | ||||
\(91\) | 4.83882i | 0.507247i | ||||||||
\(92\) | −0.941075 | − | 0.731863i | −0.0981139 | − | 0.0763020i | ||||
\(93\) | 1.16118 | − | 16.5299i | 0.120408 | − | 1.71407i | ||||
\(94\) | −0.308381 | + | 0.150835i | −0.0318070 | + | 0.0155574i | ||||
\(95\) | −2.16314 | − | 1.08157i | −0.221933 | − | 0.110967i | ||||
\(96\) | −7.89622 | + | 5.80084i | −0.805905 | + | 0.592045i | ||||
\(97\) | − | 3.30587i | − | 0.335660i | −0.985816 | − | 0.167830i | \(-0.946324\pi\) | ||
0.985816 | − | 0.167830i | \(-0.0536760\pi\) | |||||||
\(98\) | −0.621372 | − | 1.27039i | −0.0627681 | − | 0.128329i | ||||
\(99\) | 10.2649 | + | 1.44932i | 1.03167 | + | 0.145662i | ||||
\(100\) | 9.99847 | + | 0.174853i | 0.999847 | + | 0.0174853i | ||||
\(101\) | 7.73746i | 0.769906i | 0.922936 | + | 0.384953i | \(0.125782\pi\) | ||||
−0.922936 | + | 0.384953i | \(0.874218\pi\) | |||||||
\(102\) | 5.46230 | + | 13.4886i | 0.540848 | + | 1.33557i | ||||
\(103\) | −5.61872 | −0.553629 | −0.276815 | − | 0.960923i | \(-0.589279\pi\) | ||||
−0.276815 | + | 0.960923i | \(0.589279\pi\) | |||||||
\(104\) | −2.80058 | + | 13.3967i | −0.274620 | + | 1.31365i | ||||
\(105\) | 1.97054 | − | 3.33421i | 0.192305 | − | 0.325386i | ||||
\(106\) | 7.34608 | + | 15.0190i | 0.713514 | + | 1.45878i | ||||
\(107\) | − | 1.68491i | − | 0.162886i | −0.996678 | − | 0.0814431i | \(-0.974047\pi\) | ||
0.996678 | − | 0.0814431i | \(-0.0259529\pi\) | |||||||
\(108\) | −7.95240 | + | 6.69025i | −0.765220 | + | 0.643769i | ||||
\(109\) | 9.94108 | 0.952182 | 0.476091 | − | 0.879396i | \(-0.342053\pi\) | ||||
0.476091 | + | 0.879396i | \(0.342053\pi\) | |||||||
\(110\) | −10.9271 | − | 0.0955392i | −1.04186 | − | 0.00910931i | ||||
\(111\) | −0.353336 | + | 5.02990i | −0.0335371 | + | 0.477417i | ||||
\(112\) | −0.985049 | − | 3.87681i | −0.0930783 | − | 0.366324i | ||||
\(113\) | 3.23352 | 0.304184 | 0.152092 | − | 0.988366i | \(-0.451399\pi\) | ||||
0.152092 | + | 0.988366i | \(0.451399\pi\) | |||||||
\(114\) | −2.45559 | + | 0.994408i | −0.229987 | + | 0.0931348i | ||||
\(115\) | 1.19216 | + | 0.596080i | 0.111170 | + | 0.0555848i | ||||
\(116\) | 7.63941 | + | 5.94108i | 0.709301 | + | 0.551615i | ||||
\(117\) | −2.02946 | + | 14.3739i | −0.187624 | + | 1.32887i | ||||
\(118\) | −2.02068 | − | 4.13127i | −0.186019 | − | 0.380314i | ||||
\(119\) | −5.94108 | −0.544617 | ||||||||
\(120\) | 7.38534 | − | 8.09054i | 0.674186 | − | 0.738561i | ||||
\(121\) | 0.941075 | 0.0855523 | ||||||||
\(122\) | 7.85951 | + | 16.0687i | 0.711566 | + | 1.45479i | ||||
\(123\) | −0.838825 | + | 11.9411i | −0.0756343 | + | 1.07669i | ||||
\(124\) | 15.1042 | + | 11.7464i | 1.35640 | + | 1.05485i | ||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | −1.31299 | − | 4.03436i | −0.116971 | − | 0.359409i | ||||
\(127\) | 1.08883 | 0.0966178 | 0.0483089 | − | 0.998832i | \(-0.484617\pi\) | ||||
0.0483089 | + | 0.998832i | \(0.484617\pi\) | |||||||
\(128\) | −0.483388 | − | 11.3034i | −0.0427259 | − | 0.999087i | ||||
\(129\) | 12.7799 | + | 0.897749i | 1.12521 | + | 0.0790424i | ||||
\(130\) | 0.133783 | − | 15.3011i | 0.0117335 | − | 1.34200i | ||||
\(131\) | 6.30783 | 0.551118 | 0.275559 | − | 0.961284i | \(-0.411137\pi\) | ||||
0.275559 | + | 0.961284i | \(0.411137\pi\) | |||||||
\(132\) | −7.99274 | + | 8.91117i | −0.695679 | + | 0.775618i | ||||
\(133\) | − | 1.08157i | − | 0.0937839i | ||||||
\(134\) | 3.55364 | + | 7.26539i | 0.306987 | + | 0.627634i | ||||
\(135\) | 7.25197 | − | 9.07794i | 0.624150 | − | 0.781305i | ||||
\(136\) | −16.4483 | − | 3.43853i | −1.41043 | − | 0.294852i | ||||
\(137\) | 8.64863 | 0.738902 | 0.369451 | − | 0.929250i | \(-0.379546\pi\) | ||||
0.369451 | + | 0.929250i | \(0.379546\pi\) | |||||||
\(138\) | 1.35334 | − | 0.548043i | 0.115204 | − | 0.0466525i | ||||
\(139\) | 5.82960i | 0.494460i | 0.968957 | + | 0.247230i | \(0.0795204\pi\) | ||||
−0.968957 | + | 0.247230i | \(0.920480\pi\) | |||||||
\(140\) | 1.92975 | + | 4.03436i | 0.163094 | + | 0.340966i | ||||
\(141\) | 0.0294624 | − | 0.419412i | 0.00248119 | − | 0.0353209i | ||||
\(142\) | 4.97098 | + | 10.1631i | 0.417155 | + | 0.852872i | ||||
\(143\) | 16.7210i | 1.39828i | ||||||||
\(144\) | −1.30014 | − | 11.9294i | −0.108345 | − | 0.994113i | ||||
\(145\) | −9.67765 | − | 4.83882i | −0.803685 | − | 0.401843i | ||||
\(146\) | 10.1631 | − | 4.97098i | 0.841107 | − | 0.411401i | ||||
\(147\) | 1.72779 | + | 0.121372i | 0.142506 | + | 0.0100106i | ||||
\(148\) | −4.59608 | − | 3.57432i | −0.377795 | − | 0.293807i | ||||
\(149\) | − | 17.8223i | − | 1.46006i | −0.683413 | − | 0.730032i | \(-0.739505\pi\) | ||
0.683413 | − | 0.730032i | \(-0.260495\pi\) | |||||||
\(150\) | −6.32333 | + | 10.4888i | −0.516298 | + | 0.856409i | ||||
\(151\) | 15.7427i | 1.28113i | 0.767906 | + | 0.640563i | \(0.221299\pi\) | ||||
−0.767906 | + | 0.640563i | \(0.778701\pi\) | |||||||
\(152\) | 0.625983 | − | 2.99441i | 0.0507739 | − | 0.242879i | ||||
\(153\) | −17.6482 | − | 2.49176i | −1.42677 | − | 0.201447i | ||||
\(154\) | −2.14721 | − | 4.38995i | −0.173027 | − | 0.353752i | ||||
\(155\) | −19.1341 | − | 9.56706i | −1.53689 | − | 0.768445i | ||||
\(156\) | −12.4782 | − | 11.1922i | −0.999058 | − | 0.896090i | ||||
\(157\) | − | 17.8223i | − | 1.42238i | −0.703001 | − | 0.711189i | \(-0.748157\pi\) | ||
0.703001 | − | 0.711189i | \(-0.251843\pi\) | |||||||
\(158\) | 1.20613 | − | 0.589941i | 0.0959546 | − | 0.0469331i | ||||
\(159\) | −20.4266 | − | 1.43490i | −1.61993 | − | 0.113795i | ||||
\(160\) | 3.00769 | + | 12.2863i | 0.237779 | + | 0.971319i | ||||
\(161\) | 0.596080i | 0.0469777i | ||||||||
\(162\) | −2.20823 | − | 12.5349i | −0.173495 | − | 0.984835i | ||||
\(163\) | −11.2520 | −0.881322 | −0.440661 | − | 0.897674i | \(-0.645256\pi\) | ||||
−0.440661 | + | 0.897674i | \(0.645256\pi\) | |||||||
\(164\) | −10.9112 | − | 8.48549i | −0.852019 | − | 0.662605i | ||||
\(165\) | 6.80936 | − | 11.5217i | 0.530108 | − | 0.896960i | ||||
\(166\) | 21.5506 | − | 10.5408i | 1.67265 | − | 0.818124i | ||||
\(167\) | − | 16.7137i | − | 1.29335i | −0.762767 | − | 0.646673i | \(-0.776160\pi\) | ||
0.762767 | − | 0.646673i | \(-0.223840\pi\) | |||||||
\(168\) | 4.71328 | + | 1.33603i | 0.363638 | + | 0.103077i | ||||
\(169\) | −10.4142 | −0.801094 | ||||||||
\(170\) | 18.7866 | + | 0.164257i | 1.44087 | + | 0.0125980i | ||||
\(171\) | 0.453623 | − | 3.21284i | 0.0346894 | − | 0.245692i | ||||
\(172\) | −9.08157 | + | 11.6776i | −0.692463 | + | 0.890412i | ||||
\(173\) | −1.94108 | −0.147577 | −0.0737886 | − | 0.997274i | \(-0.523509\pi\) | ||||
−0.0737886 | + | 0.997274i | \(0.523509\pi\) | |||||||
\(174\) | −10.9860 | + | 4.44887i | −0.832849 | + | 0.337268i | ||||
\(175\) | −3.00000 | − | 4.00000i | −0.226779 | − | 0.302372i | ||||
\(176\) | −3.40392 | − | 13.3967i | −0.256580 | − | 1.00981i | ||||
\(177\) | 5.61872 | + | 0.394698i | 0.422329 | + | 0.0296674i | ||||
\(178\) | 6.64863 | − | 3.25197i | 0.498336 | − | 0.243745i | ||||
\(179\) | 6.80784 | 0.508842 | 0.254421 | − | 0.967094i | \(-0.418115\pi\) | ||||
0.254421 | + | 0.967094i | \(0.418115\pi\) | |||||||
\(180\) | 4.04034 | + | 12.7936i | 0.301149 | + | 0.953577i | ||||
\(181\) | −2.97098 | −0.220831 | −0.110416 | − | 0.993886i | \(-0.535218\pi\) | ||||
−0.110416 | + | 0.993886i | \(0.535218\pi\) | |||||||
\(182\) | 6.14721 | − | 3.00671i | 0.455661 | − | 0.222872i | ||||
\(183\) | −21.8542 | − | 1.53519i | −1.61551 | − | 0.113485i | ||||
\(184\) | −0.344995 | + | 1.65029i | −0.0254334 | + | 0.121661i | ||||
\(185\) | 5.82234 | + | 2.91117i | 0.428067 | + | 0.214034i | ||||
\(186\) | −21.7210 | + | 8.79607i | −1.59266 | + | 0.644959i | ||||
\(187\) | −20.5299 | −1.50129 | ||||||||
\(188\) | 0.383238 | + | 0.298040i | 0.0279505 | + | 0.0217368i | ||||
\(189\) | 5.08157 | + | 1.08520i | 0.369630 | + | 0.0789366i | ||||
\(190\) | −0.0299030 | + | 3.42009i | −0.00216939 | + | 0.248119i | ||||
\(191\) | 20.6477 | 1.49402 | 0.747009 | − | 0.664814i | \(-0.231489\pi\) | ||||
0.747009 | + | 0.664814i | \(0.231489\pi\) | |||||||
\(192\) | 12.2758 | + | 6.42682i | 0.885932 | + | 0.463816i | ||||
\(193\) | − | 9.55980i | − | 0.688129i | −0.938946 | − | 0.344065i | \(-0.888196\pi\) | ||
0.938946 | − | 0.344065i | \(-0.111804\pi\) | |||||||
\(194\) | −4.19975 | + | 2.05418i | −0.301525 | + | 0.147481i | ||||
\(195\) | 16.1337 | + | 9.53509i | 1.15536 | + | 0.682822i | ||||
\(196\) | −1.22779 | + | 1.57877i | −0.0876995 | + | 0.112770i | ||||
\(197\) | 11.5598 | 0.823602 | 0.411801 | − | 0.911274i | \(-0.364900\pi\) | ||||
0.411801 | + | 0.911274i | \(0.364900\pi\) | |||||||
\(198\) | −4.53716 | − | 13.9411i | −0.322442 | − | 0.990749i | ||||
\(199\) | 16.9637i | 1.20253i | 0.799051 | + | 0.601263i | \(0.205336\pi\) | ||||
−0.799051 | + | 0.601263i | \(0.794664\pi\) | |||||||
\(200\) | −5.99064 | − | 12.8106i | −0.423602 | − | 0.905848i | ||||
\(201\) | −9.88127 | − | 0.694129i | −0.696971 | − | 0.0489601i | ||||
\(202\) | 9.82960 | − | 4.80784i | 0.691608 | − | 0.338278i | ||||
\(203\) | − | 4.83882i | − | 0.339619i | ||||||
\(204\) | 13.7417 | − | 15.3207i | 0.962108 | − | 1.07266i | ||||
\(205\) | 13.8223 | + | 6.91117i | 0.965394 | + | 0.482697i | ||||
\(206\) | 3.49132 | + | 7.13798i | 0.243252 | + | 0.497327i | ||||
\(207\) | −0.250003 | + | 1.77068i | −0.0173764 | + | 0.123071i | ||||
\(208\) | 18.7592 | − | 4.76648i | 1.30072 | − | 0.330496i | ||||
\(209\) | − | 3.73746i | − | 0.258525i | ||||||
\(210\) | −5.46020 | − | 0.431568i | −0.376789 | − | 0.0297810i | ||||
\(211\) | − | 16.7137i | − | 1.15062i | −0.817936 | − | 0.575310i | \(-0.804881\pi\) | ||
0.817936 | − | 0.575310i | \(-0.195119\pi\) | |||||||
\(212\) | 14.5154 | − | 18.6648i | 0.996921 | − | 1.28190i | ||||
\(213\) | −13.8223 | − | 0.970978i | −0.947091 | − | 0.0665303i | ||||
\(214\) | −2.14049 | + | 1.04696i | −0.146321 | + | 0.0715684i | ||||
\(215\) | 7.39666 | − | 14.7933i | 0.504448 | − | 1.00890i | ||||
\(216\) | 13.4406 | + | 5.94553i | 0.914519 | + | 0.404542i | ||||
\(217\) | − | 9.56706i | − | 0.649454i | ||||||
\(218\) | −6.17711 | − | 12.6291i | −0.418367 | − | 0.855348i | ||||
\(219\) | −0.970978 | + | 13.8223i | −0.0656126 | + | 0.934027i | ||||
\(220\) | 6.66843 | + | 13.9411i | 0.449585 | + | 0.939907i | ||||
\(221\) | − | 28.7478i | − | 1.93379i | ||||||
\(222\) | 6.60950 | − | 2.67657i | 0.443601 | − | 0.179639i | ||||
\(223\) | −8.76736 | −0.587106 | −0.293553 | − | 0.955943i | \(-0.594838\pi\) | ||||
−0.293553 | + | 0.955943i | \(0.594838\pi\) | |||||||
\(224\) | −4.31299 | + | 3.66034i | −0.288174 | + | 0.244567i | ||||
\(225\) | −7.23396 | − | 13.1404i | −0.482264 | − | 0.876026i | ||||
\(226\) | −2.00922 | − | 4.10784i | −0.133651 | − | 0.273250i | ||||
\(227\) | 0.242745i | 0.0161115i | 0.999968 | + | 0.00805576i | \(0.00256426\pi\) | ||||
−0.999968 | + | 0.00805576i | \(0.997436\pi\) | |||||||
\(228\) | 2.78912 | + | 2.50166i | 0.184714 | + | 0.165676i | ||||
\(229\) | −26.3531 | −1.74146 | −0.870732 | − | 0.491758i | \(-0.836354\pi\) | ||||
−0.870732 | + | 0.491758i | \(0.836354\pi\) | |||||||
\(230\) | 0.0164803 | − | 1.88490i | 0.00108668 | − | 0.124287i | ||||
\(231\) | 5.97054 | + | 0.419412i | 0.392833 | + | 0.0275953i | ||||
\(232\) | 2.80058 | − | 13.3967i | 0.183867 | − | 0.879534i | ||||
\(233\) | −6.44413 | −0.422169 | −0.211084 | − | 0.977468i | \(-0.567699\pi\) | ||||
−0.211084 | + | 0.977468i | \(0.567699\pi\) | |||||||
\(234\) | 19.5216 | − | 6.35334i | 1.27616 | − | 0.415331i | ||||
\(235\) | −0.485489 | − | 0.242745i | −0.0316698 | − | 0.0158349i | ||||
\(236\) | −3.99274 | + | 5.13412i | −0.259905 | + | 0.334202i | ||||
\(237\) | −0.115233 | + | 1.64039i | −0.00748517 | + | 0.106555i | ||||
\(238\) | 3.69162 | + | 7.54750i | 0.239292 | + | 0.489231i | ||||
\(239\) | 16.6495 | 1.07697 | 0.538484 | − | 0.842636i | \(-0.318997\pi\) | ||||
0.538484 | + | 0.842636i | \(0.318997\pi\) | |||||||
\(240\) | −14.8672 | − | 4.35504i | −0.959674 | − | 0.281117i | ||||
\(241\) | −5.61784 | −0.361877 | −0.180939 | − | 0.983494i | \(-0.557914\pi\) | ||||
−0.180939 | + | 0.983494i | \(0.557914\pi\) | |||||||
\(242\) | −0.584758 | − | 1.19553i | −0.0375897 | − | 0.0768519i | ||||
\(243\) | 14.6398 | + | 5.35490i | 0.939147 | + | 0.343517i | ||||
\(244\) | 15.5299 | − | 19.9693i | 0.994200 | − | 1.27840i | ||||
\(245\) | 1.00000 | − | 2.00000i | 0.0638877 | − | 0.127775i | ||||
\(246\) | 15.6911 | − | 6.35422i | 1.00043 | − | 0.405130i | ||||
\(247\) | 5.23352 | 0.333001 | ||||||||
\(248\) | 5.53716 | − | 26.4871i | 0.351610 | − | 1.68194i | ||||
\(249\) | −2.05892 | + | 29.3098i | −0.130479 | + | 1.85743i | ||||
\(250\) | 9.37588 | + | 12.7316i | 0.592983 | + | 0.805215i | ||||
\(251\) | 3.25197 | 0.205262 | 0.102631 | − | 0.994719i | \(-0.467274\pi\) | ||||
0.102631 | + | 0.994719i | \(0.467274\pi\) | |||||||
\(252\) | −4.30936 | + | 4.17485i | −0.271464 | + | 0.262991i | ||||
\(253\) | 2.05981i | 0.129499i | ||||||||
\(254\) | −0.676567 | − | 1.38324i | −0.0424516 | − | 0.0867921i | ||||
\(255\) | −11.7071 | + | 19.8088i | −0.733128 | + | 1.24048i | ||||
\(256\) | −14.0594 | + | 7.63770i | −0.878710 | + | 0.477356i | ||||
\(257\) | 0.467046 | 0.0291335 | 0.0145668 | − | 0.999894i | \(-0.495363\pi\) | ||||
0.0145668 | + | 0.999894i | \(0.495363\pi\) | |||||||
\(258\) | −6.80058 | − | 16.7933i | −0.423386 | − | 1.04551i | ||||
\(259\) | 2.91117i | 0.180891i | ||||||||
\(260\) | −19.5216 | + | 9.33774i | −1.21068 | + | 0.579102i | ||||
\(261\) | 2.02946 | − | 14.3739i | 0.125621 | − | 0.889723i | ||||
\(262\) | −3.91951 | − | 8.01342i | −0.242148 | − | 0.495071i | ||||
\(263\) | 8.47823i | 0.522790i | 0.965232 | + | 0.261395i | \(0.0841825\pi\) | ||||
−0.965232 | + | 0.261395i | \(0.915817\pi\) | |||||||
\(264\) | 16.2872 | + | 4.61676i | 1.00240 | + | 0.284142i | ||||
\(265\) | −11.8223 | + | 23.6447i | −0.726241 | + | 1.45248i | ||||
\(266\) | −1.37402 | + | 0.672057i | −0.0842464 | + | 0.0412065i | ||||
\(267\) | −0.635205 | + | 9.04244i | −0.0388739 | + | 0.553389i | ||||
\(268\) | 7.02176 | − | 9.02902i | 0.428922 | − | 0.551535i | ||||
\(269\) | 0.144695i | 0.00882222i | 0.999990 | + | 0.00441111i | \(0.00140410\pi\) | ||||
−0.999990 | + | 0.00441111i | \(0.998596\pi\) | |||||||
\(270\) | −16.0387 | − | 3.57206i | −0.976085 | − | 0.217389i | ||||
\(271\) | − | 23.1251i | − | 1.40475i | −0.711807 | − | 0.702375i | \(-0.752123\pi\) | ||
0.711807 | − | 0.702375i | \(-0.247877\pi\) | |||||||
\(272\) | 5.85225 | + | 23.0324i | 0.354845 | + | 1.39655i | ||||
\(273\) | −0.587299 | + | 8.36049i | −0.0355450 | + | 0.506000i | ||||
\(274\) | −5.37402 | − | 10.9871i | −0.324656 | − | 0.663758i | ||||
\(275\) | −10.3668 | − | 13.8223i | −0.625139 | − | 0.833519i | ||||
\(276\) | −1.53716 | − | 1.37873i | −0.0925259 | − | 0.0829897i | ||||
\(277\) | 0.826283i | 0.0496465i | 0.999692 | + | 0.0248233i | \(0.00790230\pi\) | ||||
−0.999692 | + | 0.0248233i | \(0.992098\pi\) | |||||||
\(278\) | 7.40588 | − | 3.62235i | 0.444175 | − | 0.217254i | ||||
\(279\) | 4.01254 | − | 28.4193i | 0.240225 | − | 1.70142i | ||||
\(280\) | 3.92612 | − | 4.95838i | 0.234631 | − | 0.296320i | ||||
\(281\) | 14.6612i | 0.874612i | 0.899313 | + | 0.437306i | \(0.144067\pi\) | ||||
−0.899313 | + | 0.437306i | \(0.855933\pi\) | |||||||
\(282\) | −0.551125 | + | 0.223182i | −0.0328190 | + | 0.0132903i | ||||
\(283\) | 20.4266 | 1.21423 | 0.607117 | − | 0.794613i | \(-0.292326\pi\) | ||||
0.607117 | + | 0.794613i | \(0.292326\pi\) | |||||||
\(284\) | 9.82234 | − | 12.6302i | 0.582849 | − | 0.749464i | ||||
\(285\) | −3.60618 | − | 2.13127i | −0.213612 | − | 0.126246i | ||||
\(286\) | 21.2422 | − | 10.3899i | 1.25608 | − | 0.614371i | ||||
\(287\) | 6.91117i | 0.407954i | ||||||||
\(288\) | −14.3471 | + | 9.06426i | −0.845411 | + | 0.534117i | ||||
\(289\) | 18.2964 | 1.07626 | ||||||||
\(290\) | −0.133783 | + | 15.3011i | −0.00785599 | + | 0.898513i | ||||
\(291\) | 0.401241 | − | 5.71186i | 0.0235212 | − | 0.334835i | ||||
\(292\) | −12.6302 | − | 9.82234i | −0.739126 | − | 0.574809i | ||||
\(293\) | −5.41422 | −0.316302 | −0.158151 | − | 0.987415i | \(-0.550553\pi\) | ||||
−0.158151 | + | 0.987415i | \(0.550553\pi\) | |||||||
\(294\) | −0.919412 | − | 2.27039i | −0.0536212 | − | 0.132412i | ||||
\(295\) | 3.25197 | − | 6.50393i | 0.189337 | − | 0.378674i | ||||
\(296\) | −1.68491 | + | 8.05981i | −0.0979333 | + | 0.468467i | ||||
\(297\) | 17.5598 | + | 3.75000i | 1.01892 | + | 0.217597i | ||||
\(298\) | −22.6414 | + | 11.0743i | −1.31158 | + | 0.641518i | ||||
\(299\) | −2.88433 | −0.166805 | ||||||||
\(300\) | 17.2541 | + | 1.51565i | 0.996164 | + | 0.0875059i | ||||
\(301\) | 7.39666 | 0.426336 | ||||||||
\(302\) | 19.9995 | − | 9.78210i | 1.15084 | − | 0.562897i | ||||
\(303\) | −0.939112 | + | 13.3687i | −0.0539506 | + | 0.768013i | ||||
\(304\) | −4.19304 | + | 1.06540i | −0.240487 | + | 0.0611048i | ||||
\(305\) | −12.6486 | + | 25.2973i | −0.724258 | + | 1.44852i | ||||
\(306\) | 7.80058 | + | 23.9684i | 0.445930 | + | 1.37018i | ||||
\(307\) | −16.3070 | −0.930687 | −0.465343 | − | 0.885130i | \(-0.654069\pi\) | ||||
−0.465343 | + | 0.885130i | \(0.654069\pi\) | |||||||
\(308\) | −4.24274 | + | 5.45559i | −0.241753 | + | 0.310861i | ||||
\(309\) | −9.70799 | − | 0.681957i | −0.552268 | − | 0.0387952i | ||||
\(310\) | −0.264508 | + | 30.2525i | −0.0150230 | + | 1.71823i | ||||
\(311\) | −24.3531 | −1.38094 | −0.690469 | − | 0.723362i | \(-0.742596\pi\) | ||||
−0.690469 | + | 0.723362i | \(0.742596\pi\) | |||||||
\(312\) | −6.46481 | + | 22.8067i | −0.365998 | + | 1.29118i | ||||
\(313\) | 30.6612i | 1.73307i | 0.499115 | + | 0.866536i | \(0.333659\pi\) | ||||
−0.499115 | + | 0.866536i | \(0.666341\pi\) | |||||||
\(314\) | −22.6414 | + | 11.0743i | −1.27773 | + | 0.624959i | ||||
\(315\) | 3.80936 | − | 5.52166i | 0.214633 | − | 0.311110i | ||||
\(316\) | −1.49891 | − | 1.16569i | −0.0843204 | − | 0.0655750i | ||||
\(317\) | −13.8822 | −0.779699 | −0.389850 | − | 0.920879i | \(-0.627473\pi\) | ||||
−0.389850 | + | 0.920879i | \(0.627473\pi\) | |||||||
\(318\) | 10.8696 | + | 26.8414i | 0.609537 | + | 1.50519i | ||||
\(319\) | − | 16.7210i | − | 0.936195i | ||||||
\(320\) | 13.7396 | − | 11.4553i | 0.768065 | − | 0.640372i | ||||
\(321\) | 0.204501 | − | 2.91117i | 0.0114141 | − | 0.162486i | ||||
\(322\) | 0.757255 | − | 0.370388i | 0.0422002 | − | 0.0206409i | ||||
\(323\) | 6.42568i | 0.357535i | ||||||||
\(324\) | −14.5521 | + | 10.5942i | −0.808450 | + | 0.588564i | ||||
\(325\) | 19.3553 | − | 14.5165i | 1.07364 | − | 0.805229i | ||||
\(326\) | 6.99166 | + | 14.2944i | 0.387232 | + | 0.791694i | ||||
\(327\) | 17.1761 | + | 1.20657i | 0.949842 | + | 0.0667235i | ||||
\(328\) | −4.00000 | + | 19.1341i | −0.220863 | + | 1.05650i | ||||
\(329\) | − | 0.242745i | − | 0.0133829i | ||||||
\(330\) | −18.8682 | − | 1.49132i | −1.03866 | − | 0.0820944i | ||||
\(331\) | 18.1559i | 0.997937i | 0.866620 | + | 0.498969i | \(0.166288\pi\) | ||||
−0.866620 | + | 0.498969i | \(0.833712\pi\) | |||||||
\(332\) | −26.7819 | − | 20.8279i | −1.46985 | − | 1.14308i | ||||
\(333\) | −1.22098 | + | 8.64775i | −0.0669094 | + | 0.473894i | ||||
\(334\) | −21.2330 | + | 10.3854i | −1.16182 | + | 0.568266i | ||||
\(335\) | −5.71901 | + | 11.4380i | −0.312463 | + | 0.624926i | ||||
\(336\) | −1.23142 | − | 6.81789i | −0.0671796 | − | 0.371946i | ||||
\(337\) | 17.4419i | 0.950124i | 0.879952 | + | 0.475062i | \(0.157574\pi\) | ||||
−0.879952 | + | 0.475062i | \(0.842426\pi\) | |||||||
\(338\) | 6.47111 | + | 13.2301i | 0.351982 | + | 0.719625i | ||||
\(339\) | 5.58686 | + | 0.392460i | 0.303437 | + | 0.0213155i | ||||
\(340\) | −11.4648 | − | 23.9684i | −0.621766 | − | 1.29987i | ||||
\(341\) | − | 33.0598i | − | 1.79029i | ||||||
\(342\) | −4.36344 | + | 1.42009i | −0.235948 | + | 0.0767897i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 20.4782 | + | 4.28099i | 1.10411 | + | 0.230815i | ||||
\(345\) | 1.98746 | + | 1.17460i | 0.107001 | + | 0.0632382i | ||||
\(346\) | 1.20613 | + | 2.46593i | 0.0648420 | + | 0.132569i | ||||
\(347\) | − | 33.8564i | − | 1.81751i | −0.417331 | − | 0.908755i | \(-0.637034\pi\) | ||
0.417331 | − | 0.908755i | \(-0.362966\pi\) | |||||||
\(348\) | 12.4782 | + | 11.1922i | 0.668903 | + | 0.599963i | ||||
\(349\) | −9.29333 | −0.497460 | −0.248730 | − | 0.968573i | \(-0.580013\pi\) | ||||
−0.248730 | + | 0.968573i | \(0.580013\pi\) | |||||||
\(350\) | −3.21745 | + | 6.29667i | −0.171980 | + | 0.336571i | ||||
\(351\) | −5.25108 | + | 24.5888i | −0.280282 | + | 1.31245i | ||||
\(352\) | −14.9039 | + | 12.6486i | −0.794381 | + | 0.674174i | ||||
\(353\) | 7.47403 | 0.397802 | 0.198901 | − | 0.980020i | \(-0.436263\pi\) | ||||
0.198901 | + | 0.980020i | \(0.436263\pi\) | |||||||
\(354\) | −2.98990 | − | 7.38324i | −0.158911 | − | 0.392415i | ||||
\(355\) | −8.00000 | + | 16.0000i | −0.424596 | + | 0.849192i | ||||
\(356\) | −8.26254 | − | 6.42568i | −0.437914 | − | 0.340561i | ||||
\(357\) | −10.2649 | − | 0.721082i | −0.543279 | − | 0.0381637i | ||||
\(358\) | −4.23020 | − | 8.64863i | −0.223573 | − | 0.457094i | ||||
\(359\) | −11.3553 | −0.599310 | −0.299655 | − | 0.954048i | \(-0.596872\pi\) | ||||
−0.299655 | + | 0.954048i | \(0.596872\pi\) | |||||||
\(360\) | 13.7423 | − | 13.0824i | 0.724283 | − | 0.689503i | ||||
\(361\) | 17.8302 | 0.938432 | ||||||||
\(362\) | 1.84608 | + | 3.77431i | 0.0970280 | + | 0.198373i | ||||
\(363\) | 1.62598 | + | 0.114220i | 0.0853420 | + | 0.00599502i | ||||
\(364\) | −7.63941 | − | 5.94108i | −0.400414 | − | 0.311397i | ||||
\(365\) | 16.0000 | + | 8.00000i | 0.837478 | + | 0.418739i | ||||
\(366\) | 11.6293 | + | 28.7173i | 0.607873 | + | 1.50108i | ||||
\(367\) | 4.24051 | 0.221353 | 0.110676 | − | 0.993857i | \(-0.464698\pi\) | ||||
0.110676 | + | 0.993857i | \(0.464698\pi\) | |||||||
\(368\) | 2.31089 | − | 0.587168i | 0.120464 | − | 0.0306082i | ||||
\(369\) | −2.89863 | + | 20.5299i | −0.150897 | + | 1.06874i | ||||
\(370\) | 0.0804874 | − | 9.20558i | 0.00418434 | − | 0.478575i | ||||
\(371\) | −11.8223 | −0.613786 | ||||||||
\(372\) | 24.6713 | + | 22.1285i | 1.27915 | + | 1.14731i | ||||
\(373\) | − | 23.0559i | − | 1.19379i | −0.802320 | − | 0.596894i | \(-0.796401\pi\) | ||
0.802320 | − | 0.596894i | \(-0.203599\pi\) | |||||||
\(374\) | 12.7567 | + | 26.0810i | 0.659634 | + | 1.34862i | ||||
\(375\) | −19.2485 | + | 2.12049i | −0.993987 | + | 0.109502i | ||||
\(376\) | 0.140494 | − | 0.672057i | 0.00724542 | − | 0.0346587i | ||||
\(377\) | 23.4142 | 1.20589 | ||||||||
\(378\) | −1.77892 | − | 7.12990i | −0.0914977 | − | 0.366722i | ||||
\(379\) | − | 28.8441i | − | 1.48162i | −0.671713 | − | 0.740811i | \(-0.734441\pi\) | ||
0.671713 | − | 0.740811i | \(-0.265559\pi\) | |||||||
\(380\) | 4.36344 | − | 2.08716i | 0.223840 | − | 0.107069i | ||||
\(381\) | 1.88127 | + | 0.132153i | 0.0963803 | + | 0.00677043i | ||||
\(382\) | −12.8299 | − | 26.2307i | −0.656437 | − | 1.34208i | ||||
\(383\) | 6.51119i | 0.332706i | 0.986066 | + | 0.166353i | \(0.0531992\pi\) | ||||
−0.986066 | + | 0.166353i | \(0.946801\pi\) | |||||||
\(384\) | 0.536721 | − | 19.5886i | 0.0273894 | − | 0.999625i | ||||
\(385\) | 3.45559 | − | 6.91117i | 0.176113 | − | 0.352226i | ||||
\(386\) | −12.1447 | + | 5.94019i | −0.618149 | + | 0.302348i | ||||
\(387\) | 21.9721 | + | 3.10225i | 1.11690 | + | 0.157696i | ||||
\(388\) | 5.21922 | + | 4.05892i | 0.264966 | + | 0.206061i | ||||
\(389\) | − | 22.8059i | − | 1.15630i | −0.815929 | − | 0.578152i | \(-0.803774\pi\) | ||
0.815929 | − | 0.578152i | \(-0.196226\pi\) | |||||||
\(390\) | 2.08828 | − | 26.4209i | 0.105744 | − | 1.33788i | ||||
\(391\) | − | 3.54136i | − | 0.179094i | ||||||
\(392\) | 2.76858 | + | 0.578773i | 0.139834 | + | 0.0292325i | ||||
\(393\) | 10.8986 | + | 0.765596i | 0.549763 | + | 0.0386192i | ||||
\(394\) | −7.18294 | − | 14.6855i | −0.361871 | − | 0.739844i | ||||
\(395\) | 1.89883 | + | 0.949416i | 0.0955406 | + | 0.0477703i | ||||
\(396\) | −14.8914 | + | 14.4266i | −0.748320 | + | 0.724962i | ||||
\(397\) | − | 13.1031i | − | 0.657627i | −0.944395 | − | 0.328814i | \(-0.893351\pi\) | ||
0.944395 | − | 0.328814i | \(-0.106649\pi\) | |||||||
\(398\) | 21.5506 | − | 10.5408i | 1.08023 | − | 0.528362i | ||||
\(399\) | 0.131272 | − | 1.86873i | 0.00657184 | − | 0.0935534i | ||||
\(400\) | −12.5521 | + | 15.5706i | −0.627605 | + | 0.778532i | ||||
\(401\) | 10.7808i | 0.538366i | 0.963089 | + | 0.269183i | \(0.0867537\pi\) | ||||
−0.963089 | + | 0.269183i | \(0.913246\pi\) | |||||||
\(402\) | 5.25813 | + | 12.9844i | 0.262252 | + | 0.647603i | ||||
\(403\) | 46.2933 | 2.30603 | ||||||||
\(404\) | −12.2157 | − | 9.49999i | −0.607753 | − | 0.472642i | ||||
\(405\) | 13.6317 | − | 14.8046i | 0.677365 | − | 0.735647i | ||||
\(406\) | −6.14721 | + | 3.00671i | −0.305081 | + | 0.149221i | ||||
\(407\) | 10.0598i | 0.498646i | ||||||||
\(408\) | −28.0020 | − | 7.93745i | −1.38630 | − | 0.392962i | ||||
\(409\) | 15.7045 | 0.776537 | 0.388269 | − | 0.921546i | \(-0.373073\pi\) | ||||
0.388269 | + | 0.921546i | \(0.373073\pi\) | |||||||
\(410\) | 0.191078 | − | 21.8542i | 0.00943669 | − | 1.07930i | ||||
\(411\) | 14.9430 | + | 1.04970i | 0.737086 | + | 0.0517781i | ||||
\(412\) | 6.89863 | − | 8.87069i | 0.339871 | − | 0.437028i | ||||
\(413\) | 3.25197 | 0.160019 | ||||||||
\(414\) | 2.40480 | − | 0.782648i | 0.118190 | − | 0.0384651i | ||||
\(415\) | 33.9274 | + | 16.9637i | 1.66543 | + | 0.832716i | ||||
\(416\) | −17.7118 | − | 20.8698i | −0.868390 | − | 1.02323i | ||||
\(417\) | −0.707552 | + | 10.0723i | −0.0346490 | + | 0.493245i | ||||
\(418\) | −4.74803 | + | 2.32235i | −0.232234 | + | 0.113590i | ||||
\(419\) | −33.0743 | −1.61579 | −0.807893 | − | 0.589329i | \(-0.799392\pi\) | ||||
−0.807893 | + | 0.589329i | \(0.799392\pi\) | |||||||
\(420\) | 2.84455 | + | 7.20476i | 0.138800 | + | 0.351556i | ||||
\(421\) | 7.88127 | 0.384110 | 0.192055 | − | 0.981384i | \(-0.438485\pi\) | ||||
0.192055 | + | 0.981384i | \(0.438485\pi\) | |||||||
\(422\) | −21.2330 | + | 10.3854i | −1.03361 | + | 0.505555i | ||||
\(423\) | 0.101810 | − | 0.721082i | 0.00495017 | − | 0.0350602i | ||||
\(424\) | −32.7311 | − | 6.84245i | −1.58956 | − | 0.332299i | ||||
\(425\) | 17.8232 | + | 23.7643i | 0.864553 | + | 1.15274i | ||||
\(426\) | 7.35530 | + | 18.1631i | 0.356365 | + | 0.880007i | ||||
\(427\) | −12.6486 | −0.612110 | ||||||||
\(428\) | 2.66009 | + | 2.06872i | 0.128580 | + | 0.0999953i | ||||
\(429\) | −2.02946 | + | 28.8904i | −0.0979834 | + | 1.39484i | ||||
\(430\) | −23.3894 | − | 0.204501i | −1.12794 | − | 0.00986192i | ||||
\(431\) | 26.3522 | 1.26934 | 0.634671 | − | 0.772782i | \(-0.281135\pi\) | ||||
0.634671 | + | 0.772782i | \(0.281135\pi\) | |||||||
\(432\) | −0.798481 | − | 20.7693i | −0.0384169 | − | 0.999262i | ||||
\(433\) | − | 37.2973i | − | 1.79239i | −0.443659 | − | 0.896196i | \(-0.646320\pi\) | ||
0.443659 | − | 0.896196i | \(-0.353680\pi\) | |||||||
\(434\) | −12.1539 | + | 5.94470i | −0.583407 | + | 0.285355i | ||||
\(435\) | −16.1337 | − | 9.53509i | −0.773551 | − | 0.457172i | ||||
\(436\) | −12.2056 | + | 15.6947i | −0.584541 | + | 0.751640i | ||||
\(437\) | 0.644702 | 0.0308403 | ||||||||
\(438\) | 18.1631 | − | 7.35530i | 0.867868 | − | 0.351450i | ||||
\(439\) | − | 12.6229i | − | 0.602459i | −0.953552 | − | 0.301230i | \(-0.902603\pi\) | ||
0.953552 | − | 0.301230i | \(-0.0973971\pi\) | |||||||
\(440\) | 13.5671 | − | 17.1341i | 0.646784 | − | 0.816837i | ||||
\(441\) | 2.97054 | + | 0.419412i | 0.141454 | + | 0.0199720i | ||||
\(442\) | −36.5210 | + | 17.8631i | −1.73713 | + | 0.849661i | ||||
\(443\) | − | 21.7118i | − | 1.03156i | −0.856722 | − | 0.515778i | \(-0.827503\pi\) | ||
0.856722 | − | 0.515778i | \(-0.172497\pi\) | |||||||
\(444\) | −7.50725 | − | 6.73352i | −0.356278 | − | 0.319559i | ||||
\(445\) | 10.4670 | + | 5.23352i | 0.496186 | + | 0.248093i | ||||
\(446\) | 5.44779 | + | 11.1380i | 0.257960 | + | 0.527399i | ||||
\(447\) | 2.16314 | − | 30.7933i | 0.102313 | − | 1.45647i | ||||
\(448\) | 7.33004 | + | 3.20476i | 0.346312 | + | 0.151410i | ||||
\(449\) | − | 14.6361i | − | 0.690720i | −0.938470 | − | 0.345360i | \(-0.887757\pi\) | ||
0.938470 | − | 0.345360i | \(-0.112243\pi\) | |||||||
\(450\) | −12.1985 | + | 17.3550i | −0.575041 | + | 0.818125i | ||||
\(451\) | 23.8822i | 1.12457i | ||||||||
\(452\) | −3.97010 | + | 5.10500i | −0.186738 | + | 0.240119i | ||||
\(453\) | −1.91073 | + | 27.2002i | −0.0897740 | + | 1.27798i | ||||
\(454\) | 0.308381 | − | 0.150835i | 0.0144730 | − | 0.00707902i | ||||
\(455\) | 9.67765 | + | 4.83882i | 0.453695 | + | 0.226848i | ||||
\(456\) | 1.44501 | − | 5.09774i | 0.0676687 | − | 0.238724i | ||||
\(457\) | − | 4.00176i | − | 0.187195i | −0.995610 | − | 0.0935973i | \(-0.970163\pi\) | ||
0.995610 | − | 0.0935973i | \(-0.0298366\pi\) | |||||||
\(458\) | 16.3751 | + | 33.4788i | 0.765158 | + | 1.56436i | ||||
\(459\) | −30.1900 | − | 6.44725i | −1.40915 | − | 0.300932i | ||||
\(460\) | −2.40480 | + | 1.15029i | −0.112124 | + | 0.0536324i | ||||
\(461\) | 36.9419i | 1.72056i | 0.509824 | + | 0.860279i | \(0.329711\pi\) | ||||
−0.509824 | + | 0.860279i | \(0.670289\pi\) | |||||||
\(462\) | −3.17711 | − | 7.84554i | −0.147812 | − | 0.365007i | ||||
\(463\) | 6.12178 | 0.284503 | 0.142252 | − | 0.989831i | \(-0.454566\pi\) | ||||
0.142252 | + | 0.989831i | \(0.454566\pi\) | |||||||
\(464\) | −18.7592 | + | 4.76648i | −0.870875 | + | 0.221278i | ||||
\(465\) | −31.8986 | − | 18.8522i | −1.47926 | − | 0.874252i | ||||
\(466\) | 4.00420 | + | 8.18657i | 0.185491 | + | 0.379235i | ||||
\(467\) | 14.0651i | 0.650855i | 0.945567 | + | 0.325427i | \(0.105508\pi\) | ||||
−0.945567 | + | 0.325427i | \(0.894492\pi\) | |||||||
\(468\) | −20.2014 | − | 20.8522i | −0.933809 | − | 0.963895i | ||||
\(469\) | −5.71901 | −0.264079 | ||||||||
\(470\) | −0.00671134 | + | 0.767596i | −0.000309571 | + | 0.0354066i | ||||
\(471\) | 2.16314 | − | 30.7933i | 0.0996721 | − | 1.41888i | ||||
\(472\) | 9.00332 | + | 1.88215i | 0.414411 | + | 0.0866330i | ||||
\(473\) | 25.5598 | 1.17524 | ||||||||
\(474\) | 2.15555 | − | 0.872904i | 0.0990075 | − | 0.0400938i | ||||
\(475\) | −4.32628 | + | 3.24471i | −0.198503 | + | 0.148877i | ||||
\(476\) | 7.29441 | − | 9.37961i | 0.334339 | − | 0.429914i | ||||
\(477\) | −35.1187 | − | 4.95844i | −1.60798 | − | 0.227031i | ||||
\(478\) | −10.3455 | − | 21.1514i | −0.473194 | − | 0.967443i | ||||
\(479\) | 33.4419 | 1.52800 | 0.764001 | − | 0.645215i | \(-0.223232\pi\) | ||||
0.764001 | + | 0.645215i | \(0.223232\pi\) | |||||||
\(480\) | 3.70545 | + | 21.5933i | 0.169130 | + | 0.985594i | ||||
\(481\) | −14.0867 | −0.642296 | ||||||||
\(482\) | 3.49077 | + | 7.13686i | 0.159000 | + | 0.325075i | ||||
\(483\) | −0.0723476 | + | 1.02990i | −0.00329193 | + | 0.0468622i | ||||
\(484\) | −1.15545 | + | 1.48574i | −0.0525202 | + | 0.0675338i | ||||
\(485\) | −6.61174 | − | 3.30587i | −0.300224 | − | 0.150112i | ||||
\(486\) | −2.29398 | − | 21.9257i | −0.104057 | − | 0.994571i | ||||
\(487\) | 17.8241 | 0.807687 | 0.403844 | − | 0.914828i | \(-0.367674\pi\) | ||||
0.403844 | + | 0.914828i | \(0.367674\pi\) | |||||||
\(488\) | −35.0187 | − | 7.32068i | −1.58522 | − | 0.331392i | ||||
\(489\) | −19.4411 | − | 1.36568i | −0.879156 | − | 0.0617580i | ||||
\(490\) | −3.16216 | − | 0.0276478i | −0.142852 | − | 0.00124900i | ||||
\(491\) | −12.3087 | −0.555485 | −0.277742 | − | 0.960656i | \(-0.589586\pi\) | ||||
−0.277742 | + | 0.960656i | \(0.589586\pi\) | |||||||
\(492\) | −17.8223 | − | 15.9855i | −0.803493 | − | 0.720681i | ||||
\(493\) | 28.7478i | 1.29474i | ||||||||
\(494\) | −3.25197 | − | 6.64863i | −0.146313 | − | 0.299136i | ||||
\(495\) | 13.1636 | − | 19.0806i | 0.591659 | − | 0.857608i | ||||
\(496\) | −37.0897 | + | 9.42402i | −1.66538 | + | 0.423151i | ||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | 38.5143 | − | 15.5967i | 1.72587 | − | 0.698903i | ||||
\(499\) | − | 13.0941i | − | 0.586173i | −0.956086 | − | 0.293086i | \(-0.905318\pi\) | ||
0.956086 | − | 0.293086i | \(-0.0946824\pi\) | |||||||
\(500\) | 10.3482 | − | 19.8221i | 0.462785 | − | 0.886471i | ||||
\(501\) | 2.02858 | − | 28.8778i | 0.0906303 | − | 1.29017i | ||||
\(502\) | −2.02068 | − | 4.13127i | −0.0901874 | − | 0.184388i | ||||
\(503\) | 15.9639i | 0.711796i | 0.934525 | + | 0.355898i | \(0.115825\pi\) | ||||
−0.934525 | + | 0.355898i | \(0.884175\pi\) | |||||||
\(504\) | 7.98142 | + | 2.88044i | 0.355521 | + | 0.128305i | ||||
\(505\) | 15.4749 | + | 7.73746i | 0.688624 | + | 0.344312i | ||||
\(506\) | 2.61676 | − | 1.27991i | 0.116329 | − | 0.0568988i | ||||
\(507\) | −17.9936 | − | 1.26400i | −0.799125 | − | 0.0561361i | ||||
\(508\) | −1.33686 | + | 1.71901i | −0.0593134 | + | 0.0762688i | ||||
\(509\) | − | 13.6776i | − | 0.606251i | −0.952951 | − | 0.303126i | \(-0.901970\pi\) | ||
0.952951 | − | 0.303126i | \(-0.0980302\pi\) | |||||||
\(510\) | 32.4394 | + | 2.56398i | 1.43644 | + | 0.113535i | ||||
\(511\) | 8.00000i | 0.353899i | ||||||||
\(512\) | 18.4390 | + | 13.1150i | 0.814895 | + | 0.579609i | ||||
\(513\) | 1.17372 | − | 5.49607i | 0.0518209 | − | 0.242657i | ||||
\(514\) | −0.290209 | − | 0.593332i | −0.0128006 | − | 0.0261707i | ||||
\(515\) | −5.61872 | + | 11.2374i | −0.247591 | + | 0.495181i | ||||
\(516\) | −17.1084 | + | 19.0743i | −0.753156 | + | 0.839700i | ||||
\(517\) | − | 0.838825i | − | 0.0368915i | ||||||
\(518\) | 3.69833 | − | 1.80892i | 0.162495 | − | 0.0794795i | ||||
\(519\) | −3.35378 | − | 0.235593i | −0.147214 | − | 0.0103414i | ||||
\(520\) | 23.9927 | + | 18.9978i | 1.05215 | + | 0.833110i | ||||
\(521\) | 22.4112i | 0.981851i | 0.871202 | + | 0.490925i | \(0.163341\pi\) | ||||
−0.871202 | + | 0.490925i | \(0.836659\pi\) | |||||||
\(522\) | −19.5216 | + | 6.35334i | −0.854435 | + | 0.278078i | ||||
\(523\) | 8.74980 | 0.382602 | 0.191301 | − | 0.981531i | \(-0.438729\pi\) | ||||
0.191301 | + | 0.981531i | \(0.438729\pi\) | |||||||
\(524\) | −7.74471 | + | 9.95864i | −0.338329 | + | 0.435045i | ||||
\(525\) | −4.69789 | − | 7.27529i | −0.205033 | − | 0.317520i | ||||
\(526\) | 10.7707 | − | 5.26814i | 0.469624 | − | 0.229702i | ||||
\(527\) | 56.8386i | 2.47593i | ||||||||
\(528\) | −4.25529 | − | 23.5598i | −0.185188 | − | 1.02531i | ||||
\(529\) | 22.6447 | 0.984552 | ||||||||
\(530\) | 37.3841 | + | 0.326861i | 1.62386 | + | 0.0141979i | ||||
\(531\) | 9.66009 | + | 1.36391i | 0.419212 | + | 0.0591888i | ||||
\(532\) | 1.70755 | + | 1.32794i | 0.0740318 | + | 0.0575736i | ||||
\(533\) | −33.4419 | −1.44853 | ||||||||
\(534\) | 11.8822 | − | 4.81177i | 0.514191 | − | 0.208225i | ||||
\(535\) | −3.36982 | − | 1.68491i | −0.145690 | − | 0.0728449i | ||||
\(536\) | −15.8335 | − | 3.31001i | −0.683904 | − | 0.142971i | ||||
\(537\) | 11.7625 | + | 0.826283i | 0.507591 | + | 0.0356567i | ||||
\(538\) | 0.183820 | − | 0.0899096i | 0.00792503 | − | 0.00387628i | ||||
\(539\) | 3.45559 | 0.148843 | ||||||||
\(540\) | 5.42809 | + | 22.5950i | 0.233588 | + | 0.972336i | ||||
\(541\) | 23.3562 | 1.00416 | 0.502080 | − | 0.864821i | \(-0.332568\pi\) | ||||
0.502080 | + | 0.864821i | \(0.332568\pi\) | |||||||
\(542\) | −29.3779 | + | 14.3693i | −1.26189 | + | 0.617214i | ||||
\(543\) | −5.13324 | − | 0.360594i | −0.220288 | − | 0.0154746i | ||||
\(544\) | 25.6238 | − | 21.7464i | 1.09861 | − | 0.932368i | ||||
\(545\) | 9.94108 | − | 19.8822i | 0.425829 | − | 0.851658i | ||||
\(546\) | 10.9860 | − | 4.44887i | 0.470159 | − | 0.190394i | ||||
\(547\) | 27.7229 | 1.18535 | 0.592674 | − | 0.805443i | \(-0.298072\pi\) | ||||
0.592674 | + | 0.805443i | \(0.298072\pi\) | |||||||
\(548\) | −10.6187 | + | 13.6542i | −0.453609 | + | 0.583279i | ||||
\(549\) | −37.5732 | − | 5.30499i | −1.60359 | − | 0.226411i | ||||
\(550\) | −11.1182 | + | 21.7587i | −0.474081 | + | 0.927793i | ||||
\(551\) | −5.23352 | −0.222956 | ||||||||
\(552\) | −0.796380 | + | 2.80949i | −0.0338962 | + | 0.119580i | ||||
\(553\) | 0.949416i | 0.0403733i | ||||||||
\(554\) | 1.04970 | − | 0.513429i | 0.0445976 | − | 0.0218135i | ||||
\(555\) | 9.70647 | + | 5.73657i | 0.412017 | + | 0.243504i | ||||
\(556\) | −9.20362 | − | 7.15755i | −0.390320 | − | 0.303548i | ||||
\(557\) | −15.8241 | −0.670489 | −0.335244 | − | 0.942131i | \(-0.608819\pi\) | ||||
−0.335244 | + | 0.942131i | \(0.608819\pi\) | |||||||
\(558\) | −38.5969 | + | 12.5615i | −1.63394 | + | 0.531769i | ||||
\(559\) | 35.7911i | 1.51380i | ||||||||
\(560\) | −8.73867 | − | 1.90672i | −0.369276 | − | 0.0805735i | ||||
\(561\) | −35.4714 | − | 2.49176i | −1.49760 | − | 0.105202i | ||||
\(562\) | 18.6254 | − | 9.11004i | 0.785667 | − | 0.384284i | ||||
\(563\) | − | 37.5112i | − | 1.58091i | −0.612522 | − | 0.790454i | \(-0.709845\pi\) | ||
0.612522 | − | 0.790454i | \(-0.290155\pi\) | |||||||
\(564\) | 0.625983 | + | 0.561466i | 0.0263586 | + | 0.0236420i | ||||
\(565\) | 3.23352 | − | 6.46705i | 0.136035 | − | 0.272071i | ||||
\(566\) | −12.6925 | − | 25.9497i | −0.533506 | − | 1.09075i | ||||
\(567\) | 8.64819 | + | 2.49176i | 0.363190 | + | 0.104644i | ||||
\(568\) | −22.1486 | − | 4.63018i | −0.929335 | − | 0.194278i | ||||
\(569\) | 19.8804i | 0.833429i | 0.909037 | + | 0.416715i | \(0.136819\pi\) | ||||
−0.909037 | + | 0.416715i | \(0.863181\pi\) | |||||||
\(570\) | −0.466770 | + | 5.90558i | −0.0195509 | + | 0.247358i | ||||
\(571\) | − | 3.37707i | − | 0.141326i | −0.997500 | − | 0.0706631i | \(-0.977488\pi\) | ||
0.997500 | − | 0.0706631i | \(-0.0225115\pi\) | |||||||
\(572\) | −26.3986 | − | 20.5299i | −1.10378 | − | 0.858398i | ||||
\(573\) | 35.6750 | + | 2.50606i | 1.49035 | + | 0.104692i | ||||
\(574\) | 8.77990 | − | 4.29441i | 0.366466 | − | 0.179245i | ||||
\(575\) | 2.38432 | − | 1.78824i | 0.0994330 | − | 0.0745748i | ||||
\(576\) | 20.4301 | + | 12.5942i | 0.851252 | + | 0.524757i | ||||
\(577\) | − | 6.66117i | − | 0.277308i | −0.990341 | − | 0.138654i | \(-0.955722\pi\) | ||
0.990341 | − | 0.138654i | \(-0.0442776\pi\) | |||||||
\(578\) | −11.3689 | − | 23.2436i | −0.472882 | − | 0.966805i | ||||
\(579\) | 1.16029 | − | 16.5174i | 0.0482202 | − | 0.686438i | ||||
\(580\) | 19.5216 | − | 9.33774i | 0.810588 | − | 0.387728i | ||||
\(581\) | 16.9637i | 0.703774i | ||||||||
\(582\) | −7.50562 | + | 3.03946i | −0.311118 | + | 0.125990i | ||||
\(583\) | −40.8531 | −1.69196 | ||||||||
\(584\) | −4.63018 | + | 22.1486i | −0.191598 | + | 0.916516i | ||||
\(585\) | 26.7184 | + | 18.4328i | 1.10467 | + | 0.762104i | ||||
\(586\) | 3.36425 | + | 6.87819i | 0.138976 | + | 0.284135i | ||||
\(587\) | − | 31.7716i | − | 1.31135i | −0.755042 | − | 0.655676i | \(-0.772384\pi\) | ||
0.755042 | − | 0.655676i | \(-0.227616\pi\) | |||||||
\(588\) | −2.31299 | + | 2.57877i | −0.0953862 | + | 0.106347i | ||||
\(589\) | −10.3474 | −0.426359 | ||||||||
\(590\) | −10.2832 | − | 0.0899096i | −0.423354 | − | 0.00370152i | ||||
\(591\) | 19.9729 | + | 1.40304i | 0.821577 | + | 0.0577133i | ||||
\(592\) | 11.2861 | − | 2.86765i | 0.463855 | − | 0.117860i | ||||
\(593\) | −24.2903 | −0.997482 | −0.498741 | − | 0.866751i | \(-0.666204\pi\) | ||||
−0.498741 | + | 0.866751i | \(0.666204\pi\) | |||||||
\(594\) | −6.14721 | − | 24.6380i | −0.252223 | − | 1.01091i | ||||
\(595\) | −5.94108 | + | 11.8822i | −0.243560 | + | 0.487121i | ||||
\(596\) | 28.1374 | + | 21.8822i | 1.15255 | + | 0.896328i | ||||
\(597\) | −2.05892 | + | 29.3098i | −0.0842662 | + | 1.19957i | ||||
\(598\) | 1.79224 | + | 3.66423i | 0.0732902 | + | 0.149841i | ||||
\(599\) | 34.0277 | 1.39034 | 0.695168 | − | 0.718848i | \(-0.255330\pi\) | ||||
0.695168 | + | 0.718848i | \(0.255330\pi\) | |||||||
\(600\) | −8.79573 | − | 22.8612i | −0.359084 | − | 0.933305i | ||||
\(601\) | 8.99390 | 0.366869 | 0.183434 | − | 0.983032i | \(-0.441279\pi\) | ||||
0.183434 | + | 0.983032i | \(0.441279\pi\) | |||||||
\(602\) | −4.59608 | − | 9.39666i | −0.187322 | − | 0.382979i | ||||
\(603\) | −16.9885 | − | 2.39862i | −0.691827 | − | 0.0976795i | ||||
\(604\) | −24.8542 | − | 19.3288i | −1.01130 | − | 0.786479i | ||||
\(605\) | 0.941075 | − | 1.88215i | 0.0382601 | − | 0.0765203i | ||||
\(606\) | 17.5671 | − | 7.11391i | 0.713613 | − | 0.288983i | ||||
\(607\) | −0.649508 | −0.0263627 | −0.0131814 | − | 0.999913i | \(-0.504196\pi\) | ||||
−0.0131814 | + | 0.999913i | \(0.504196\pi\) | |||||||
\(608\) | 3.95891 | + | 4.66480i | 0.160555 | + | 0.189183i | ||||
\(609\) | 0.587299 | − | 8.36049i | 0.0237986 | − | 0.338784i | ||||
\(610\) | 39.9969 | + | 0.349706i | 1.61943 | + | 0.0141592i | ||||
\(611\) | 1.17460 | 0.0475192 | ||||||||
\(612\) | 25.6022 | − | 24.8031i | 1.03491 | − | 1.00261i | ||||
\(613\) | 24.6157i | 0.994217i | 0.867688 | + | 0.497109i | \(0.165605\pi\) | ||||
−0.867688 | + | 0.497109i | \(0.834395\pi\) | |||||||
\(614\) | 10.1327 | + | 20.7162i | 0.408922 | + | 0.836039i | ||||
\(615\) | 23.0433 | + | 13.6187i | 0.929197 | + | 0.549160i | ||||
\(616\) | 9.56706 | + | 2.00000i | 0.385468 | + | 0.0805823i | ||||
\(617\) | −26.9710 | −1.08581 | −0.542905 | − | 0.839794i | \(-0.682676\pi\) | ||||
−0.542905 | + | 0.839794i | \(0.682676\pi\) | |||||||
\(618\) | 5.16592 | + | 12.7567i | 0.207804 | + | 0.513150i | ||||
\(619\) | − | 35.7302i | − | 1.43612i | −0.695982 | − | 0.718059i | \(-0.745031\pi\) | ||
0.695982 | − | 0.718059i | \(-0.254969\pi\) | |||||||
\(620\) | 38.5969 | − | 18.4621i | 1.55009 | − | 0.741454i | ||||
\(621\) | −0.646865 | + | 3.02902i | −0.0259578 | + | 0.121550i | ||||
\(622\) | 15.1324 | + | 30.9380i | 0.606752 | + | 1.24050i | ||||
\(623\) | 5.23352i | 0.209677i | ||||||||
\(624\) | 32.9906 | − | 5.95864i | 1.32068 | − | 0.238536i | ||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 38.9517 | − | 19.0520i | 1.55682 | − | 0.761471i | ||||
\(627\) | 0.453623 | − | 6.45755i | 0.0181160 | − | 0.257890i | ||||
\(628\) | 28.1374 | + | 21.8822i | 1.12281 | + | 0.873193i | ||||
\(629\) | − | 17.2955i | − | 0.689616i | ||||||
\(630\) | −9.38171 | − | 1.40838i | −0.373776 | − | 0.0561110i | ||||
\(631\) | 28.1517i | 1.12070i | 0.828255 | + | 0.560352i | \(0.189334\pi\) | ||||
−0.828255 | + | 0.560352i | \(0.810666\pi\) | |||||||
\(632\) | −0.549496 | + | 2.62853i | −0.0218578 | + | 0.104557i | ||||
\(633\) | 2.02858 | − | 28.8778i | 0.0806289 | − | 1.14779i | ||||
\(634\) | 8.62598 | + | 17.6358i | 0.342582 | + | 0.700406i | ||||
\(635\) | 1.08883 | − | 2.17766i | 0.0432088 | − | 0.0864176i | ||||
\(636\) | 27.3450 | − | 30.4871i | 1.08430 | − | 1.20889i | ||||
\(637\) | 4.83882i | 0.191721i | ||||||||
\(638\) | −21.2422 | + | 10.3899i | −0.840987 | + | 0.411342i | ||||
\(639\) | −23.7643 | − | 3.35530i | −0.940101 | − | 0.132734i | ||||
\(640\) | −23.0901 | − | 10.3366i | −0.912718 | − | 0.408590i | ||||
\(641\) | − | 36.5329i | − | 1.44296i | −0.692433 | − | 0.721482i | \(-0.743461\pi\) | ||
0.692433 | − | 0.721482i | \(-0.256539\pi\) | |||||||
\(642\) | −3.82540 | + | 1.54913i | −0.150977 | + | 0.0611391i | ||||
\(643\) | −29.7221 | −1.17212 | −0.586062 | − | 0.810266i | \(-0.699322\pi\) | ||||
−0.586062 | + | 0.810266i | \(0.699322\pi\) | |||||||
\(644\) | −0.941075 | − | 0.731863i | −0.0370836 | − | 0.0288394i | ||||
\(645\) | 14.5754 | − | 24.6620i | 0.573906 | − | 0.971067i | ||||
\(646\) | 8.16314 | − | 3.99274i | 0.321174 | − | 0.157092i | ||||
\(647\) | 6.11899i | 0.240562i | 0.992740 | + | 0.120281i | \(0.0383796\pi\) | ||||
−0.992740 | + | 0.120281i | \(0.961620\pi\) | |||||||
\(648\) | 22.5010 | + | 11.9040i | 0.883923 | + | 0.467632i | ||||
\(649\) | 11.2374 | 0.441108 | ||||||||
\(650\) | −30.4685 | − | 15.5687i | −1.19507 | − | 0.610654i | ||||
\(651\) | 1.16118 | − | 16.5299i | 0.0455101 | − | 0.647858i | ||||
\(652\) | 13.8151 | − | 17.7643i | 0.541041 | − | 0.695704i | ||||
\(653\) | 21.9090 | 0.857365 | 0.428683 | − | 0.903455i | \(-0.358978\pi\) | ||||
0.428683 | + | 0.903455i | \(0.358978\pi\) | |||||||
\(654\) | −9.13995 | − | 22.5701i | −0.357400 | − | 0.882562i | ||||
\(655\) | 6.30783 | − | 12.6157i | 0.246467 | − | 0.492935i | ||||
\(656\) | 26.7933 | − | 6.80784i | 1.04610 | − | 0.265801i | ||||
\(657\) | −3.35530 | + | 23.7643i | −0.130903 | + | 0.927134i | ||||
\(658\) | −0.308381 | + | 0.150835i | −0.0120219 | + | 0.00588015i | ||||
\(659\) | 45.4864 | 1.77190 | 0.885948 | − | 0.463784i | \(-0.153509\pi\) | ||||
0.885948 | + | 0.463784i | \(0.153509\pi\) | |||||||
\(660\) | 9.82960 | + | 24.8967i | 0.382617 | + | 0.969101i | ||||
\(661\) | 18.7335 | 0.728649 | 0.364325 | − | 0.931272i | \(-0.381300\pi\) | ||||
0.364325 | + | 0.931272i | \(0.381300\pi\) | |||||||
\(662\) | 23.0651 | − | 11.2816i | 0.896450 | − | 0.438470i | ||||
\(663\) | 3.48919 | − | 49.6703i | 0.135509 | − | 1.92903i | ||||
\(664\) | −9.81814 | + | 46.9654i | −0.381018 | + | 1.82261i | ||||
\(665\) | −2.16314 | − | 1.08157i | −0.0838829 | − | 0.0419414i | ||||
\(666\) | 11.7447 | − | 3.82234i | 0.455098 | − | 0.148113i | ||||
\(667\) | 2.88433 | 0.111682 | ||||||||
\(668\) | 26.3872 | + | 20.5210i | 1.02095 | + | 0.793981i | ||||
\(669\) | −15.1482 | − | 1.06411i | −0.585662 | − | 0.0411410i | ||||
\(670\) | 18.0844 | + | 0.158118i | 0.698662 | + | 0.00610863i | ||||
\(671\) | −43.7084 | −1.68734 | ||||||||
\(672\) | −7.89622 | + | 5.80084i | −0.304603 | + | 0.223772i | ||||
\(673\) | − | 5.67589i | − | 0.218789i | −0.993998 | − | 0.109395i | \(-0.965109\pi\) | ||
0.993998 | − | 0.109395i | \(-0.0348912\pi\) | |||||||
\(674\) | 22.1581 | − | 10.8379i | 0.853499 | − | 0.417462i | ||||
\(675\) | −10.9039 | − | 23.5819i | −0.419692 | − | 0.907667i | ||||
\(676\) | 12.7865 | − | 16.4417i | 0.491789 | − | 0.632373i | ||||
\(677\) | −29.7036 | −1.14160 | −0.570801 | − | 0.821088i | \(-0.693367\pi\) | ||||
−0.570801 | + | 0.821088i | \(0.693367\pi\) | |||||||
\(678\) | −2.97294 | − | 7.34137i | −0.114175 | − | 0.281943i | ||||
\(679\) | − | 3.30587i | − | 0.126868i | ||||||
\(680\) | −23.3254 | + | 29.4581i | −0.894488 | + | 1.12967i | ||||
\(681\) | −0.0294624 | + | 0.419412i | −0.00112900 | + | 0.0160719i | ||||
\(682\) | −41.9989 | + | 20.5424i | −1.60822 | + | 0.786611i | ||||
\(683\) | − | 44.4223i | − | 1.69977i | −0.526965 | − | 0.849887i | \(-0.676670\pi\) | ||
0.526965 | − | 0.849887i | \(-0.323330\pi\) | |||||||
\(684\) | 4.51539 | + | 4.66087i | 0.172650 | + | 0.178213i | ||||
\(685\) | 8.64863 | − | 17.2973i | 0.330447 | − | 0.660894i | ||||
\(686\) | −0.621372 | − | 1.27039i | −0.0237241 | − | 0.0485038i | ||||
\(687\) | −45.5327 | − | 3.19854i | −1.73718 | − | 0.122032i | ||||
\(688\) | −7.28607 | − | 28.6755i | −0.277779 | − | 1.09324i | ||||
\(689\) | − | 57.2062i | − | 2.17938i | ||||||
\(690\) | 0.257249 | − | 3.25471i | 0.00979330 | − | 0.123905i | ||||
\(691\) | 6.30057i | 0.239685i | 0.992793 | + | 0.119843i | \(0.0382390\pi\) | ||||
−0.992793 | + | 0.119843i | \(0.961761\pi\) | |||||||
\(692\) | 2.38324 | − | 3.06452i | 0.0905971 | − | 0.116495i | ||||
\(693\) | 10.2649 | + | 1.44932i | 0.389933 | + | 0.0550549i | ||||
\(694\) | −43.0110 | + | 21.0375i | −1.63267 | + | 0.798571i | ||||
\(695\) | 11.6592 | + | 5.82960i | 0.442259 | + | 0.221129i | ||||
\(696\) | 6.46481 | − | 22.8067i | 0.245048 | − | 0.864487i | ||||
\(697\) | − | 41.0598i | − | 1.55525i | ||||||
\(698\) | 5.77462 | + | 11.8062i | 0.218572 | + | 0.446870i | ||||
\(699\) | −11.1341 | − | 0.782138i | −0.421131 | − | 0.0295832i | ||||
\(700\) | 9.99847 | + | 0.174853i | 0.377907 | + | 0.00660882i | ||||
\(701\) | 40.7478i | 1.53902i | 0.638632 | + | 0.769512i | \(0.279500\pi\) | ||||
−0.638632 | + | 0.769512i | \(0.720500\pi\) | |||||||
\(702\) | 34.5003 | − | 8.60787i | 1.30213 | − | 0.324883i | ||||
\(703\) | 3.14863 | 0.118753 | ||||||||
\(704\) | 25.3296 | + | 11.0743i | 0.954645 | + | 0.417379i | ||||
\(705\) | −0.809362 | − | 0.478337i | −0.0304823 | − | 0.0180152i | ||||
\(706\) | −4.64415 | − | 9.49495i | −0.174785 | − | 0.357347i | ||||
\(707\) | 7.73746i | 0.290997i | ||||||||
\(708\) | −7.52177 | + | 8.38608i | −0.282685 | + | 0.315168i | ||||
\(709\) | −38.8830 | −1.46028 | −0.730141 | − | 0.683296i | \(-0.760546\pi\) | ||||
−0.730141 | + | 0.683296i | \(0.760546\pi\) | |||||||
\(710\) | 25.2973 | + | 0.221182i | 0.949389 | + | 0.00830081i | ||||
\(711\) | −0.398197 | + | 2.82027i | −0.0149335 | + | 0.105769i | ||||
\(712\) | −3.02902 | + | 14.4894i | −0.113517 | + | 0.543014i | ||||
\(713\) | 5.70273 | 0.213569 | ||||||||
\(714\) | 5.46230 | + | 13.4886i | 0.204421 | + | 0.504797i | ||||
\(715\) | 33.4419 | + | 16.7210i | 1.25066 | + | 0.625329i | ||||
\(716\) | −8.35862 | + | 10.7480i | −0.312376 | + | 0.401673i | ||||
\(717\) | 28.7669 | + | 2.02079i | 1.07432 | + | 0.0754677i | ||||
\(718\) | 7.05587 | + | 14.4257i | 0.263323 | + | 0.538362i | ||||
\(719\) | −5.03295 | −0.187697 | −0.0938486 | − | 0.995586i | \(-0.529917\pi\) | ||||
−0.0938486 | + | 0.995586i | \(0.529917\pi\) | |||||||
\(720\) | −25.1589 | − | 9.32908i | −0.937615 | − | 0.347674i | ||||
\(721\) | −5.61872 | −0.209252 | ||||||||
\(722\) | −11.0792 | − | 22.6514i | −0.412325 | − | 0.842996i | ||||
\(723\) | −9.70647 | − | 0.681850i | −0.360988 | − | 0.0253583i | ||||
\(724\) | 3.64775 | − | 4.69050i | 0.135567 | − | 0.174321i | ||||
\(725\) | −19.3553 | + | 14.5165i | −0.718838 | + | 0.539128i | ||||
\(726\) | −0.865236 | − | 2.13661i | −0.0321119 | − | 0.0792970i | ||||
\(727\) | −11.3553 | −0.421145 | −0.210572 | − | 0.977578i | \(-0.567533\pi\) | ||||
−0.210572 | + | 0.977578i | \(0.567533\pi\) | |||||||
\(728\) | −2.80058 | + | 13.3967i | −0.103796 | + | 0.496513i | ||||
\(729\) | 24.6447 | + | 11.0290i | 0.912766 | + | 0.408482i | ||||
\(730\) | 0.221182 | − | 25.2973i | 0.00818631 | − | 0.936293i | ||||
\(731\) | −43.9441 | −1.62533 | ||||||||
\(732\) | 29.2562 | − | 32.6179i | 1.08134 | − | 1.20559i | ||||
\(733\) | − | 14.7808i | − | 0.545941i | −0.962022 | − | 0.272970i | \(-0.911994\pi\) | ||
0.962022 | − | 0.272970i | \(-0.0880061\pi\) | |||||||
\(734\) | −2.63493 | − | 5.38711i | −0.0972571 | − | 0.198842i | ||||
\(735\) | 1.97054 | − | 3.33421i | 0.0726844 | − | 0.122984i | ||||
\(736\) | −2.18186 | − | 2.57089i | −0.0804243 | − | 0.0947642i | ||||
\(737\) | −19.7625 | −0.727962 | ||||||||
\(738\) | 27.8822 | − | 9.07431i | 1.02636 | − | 0.334030i | ||||
\(739\) | 36.3478i | 1.33708i | 0.743678 | + | 0.668538i | \(0.233080\pi\) | ||||
−0.743678 | + | 0.668538i | \(0.766920\pi\) | |||||||
\(740\) | −11.7447 | + | 5.61784i | −0.431744 | + | 0.206516i | ||||
\(741\) | 9.04244 | + | 0.635205i | 0.332183 | + | 0.0233348i | ||||
\(742\) | 7.34608 | + | 15.0190i | 0.269683 | + | 0.551365i | ||||
\(743\) | − | 1.48881i | − | 0.0546191i | −0.999627 | − | 0.0273096i | \(-0.991306\pi\) | ||
0.999627 | − | 0.0273096i | \(-0.00869398\pi\) | |||||||
\(744\) | 12.7819 | − | 45.0922i | 0.468606 | − | 1.65316i | ||||
\(745\) | −35.6447 | − | 17.8223i | −1.30592 | − | 0.652960i | ||||
\(746\) | −29.2900 | + | 14.3263i | −1.07238 | + | 0.524522i | ||||
\(747\) | −7.11479 | + | 50.3914i | −0.260317 | + | 1.84372i | ||||
\(748\) | 25.2065 | − | 32.4120i | 0.921640 | − | 1.18510i | ||||
\(749\) | − | 1.68491i | − | 0.0615652i | ||||||
\(750\) | 14.6543 | + | 23.1355i | 0.535100 | + | 0.844789i | ||||
\(751\) | 7.56116i | 0.275911i | 0.990438 | + | 0.137955i | \(0.0440530\pi\) | ||||
−0.990438 | + | 0.137955i | \(0.955947\pi\) | |||||||
\(752\) | −0.941075 | + | 0.239115i | −0.0343175 | + | 0.00871963i | ||||
\(753\) | 5.61872 | + | 0.394698i | 0.204758 | + | 0.0143836i | ||||
\(754\) | −14.5489 | − | 29.7452i | −0.529841 | − | 1.08326i | ||||
\(755\) | 31.4855 | + | 15.7427i | 1.14587 | + | 0.572937i | ||||
\(756\) | −7.95240 | + | 6.69025i | −0.289226 | + | 0.243322i | ||||
\(757\) | 9.61568i | 0.349488i | 0.984614 | + | 0.174744i | \(0.0559098\pi\) | ||||
−0.984614 | + | 0.174744i | \(0.944090\pi\) | |||||||
\(758\) | −36.6433 | + | 17.9229i | −1.33095 | + | 0.650990i | ||||
\(759\) | −0.250003 | + | 3.55892i | −0.00907454 | + | 0.129181i | ||||
\(760\) | −5.36283 | − | 4.24637i | −0.194530 | − | 0.154032i | ||||
\(761\) | 26.2665i | 0.952159i | 0.879402 | + | 0.476079i | \(0.157943\pi\) | ||||
−0.879402 | + | 0.476079i | \(0.842057\pi\) | |||||||
\(762\) | −1.00108 | − | 2.47207i | −0.0362654 | − | 0.0895535i | ||||
\(763\) | 9.94108 | 0.359891 | ||||||||
\(764\) | −25.3512 | + | 32.5981i | −0.917173 | + | 1.17936i | ||||
\(765\) | −22.6317 | + | 32.8046i | −0.818251 | + | 1.18605i | ||||
\(766\) | 8.27177 | − | 4.04587i | 0.298871 | − | 0.146183i | ||||
\(767\) | 15.7357i | 0.568183i | ||||||||
\(768\) | −25.2187 | + | 11.4899i | −0.910000 | + | 0.414608i | ||||
\(769\) | 35.5849 | 1.28322 | 0.641612 | − | 0.767029i | \(-0.278266\pi\) | ||||
0.641612 | + | 0.767029i | \(0.278266\pi\) | |||||||
\(770\) | −10.9271 | − | 0.0955392i | −0.393786 | − | 0.00344299i | ||||
\(771\) | 0.806959 | + | 0.0566864i | 0.0290619 | + | 0.00204151i | ||||
\(772\) | 15.0928 | + | 11.7375i | 0.543200 | + | 0.422440i | ||||
\(773\) | 28.5338 | 1.02629 | 0.513145 | − | 0.858302i | \(-0.328480\pi\) | ||||
0.513145 | + | 0.858302i | \(0.328480\pi\) | |||||||
\(774\) | −9.71175 | − | 29.8408i | −0.349082 | − | 1.07260i | ||||
\(775\) | −38.2682 | + | 28.7012i | −1.37464 | + | 1.03098i | ||||
\(776\) | 1.91335 | − | 9.15256i | 0.0686852 | − | 0.328558i | ||||
\(777\) | −0.353336 | + | 5.02990i | −0.0126758 | + | 0.180447i | ||||
\(778\) | −28.9724 | + | 14.1709i | −1.03871 | + | 0.508052i | ||||
\(779\) | 7.47491 | 0.267816 | ||||||||
\(780\) | −34.8626 | + | 13.7643i | −1.24828 | + | 0.492841i | ||||
\(781\) | −27.6447 | −0.989205 | ||||||||
\(782\) | −4.49891 | + | 2.20050i | −0.160881 | + | 0.0786897i | ||||
\(783\) | 5.25108 | − | 24.5888i | 0.187658 | − | 0.878733i | ||||
\(784\) | −0.985049 | − | 3.87681i | −0.0351803 | − | 0.138458i | ||||
\(785\) | −35.6447 | − | 17.8223i | −1.27221 | − | 0.636107i | ||||
\(786\) | −5.79950 | − | 14.3213i | −0.206861 | − | 0.510822i | ||||
\(787\) | −12.1372 | −0.432644 | −0.216322 | − | 0.976322i | \(-0.569406\pi\) | ||||
−0.216322 | + | 0.976322i | \(0.569406\pi\) | |||||||
\(788\) | −14.1930 | + | 18.2503i | −0.505606 | + | 0.650140i | ||||
\(789\) | −1.02902 | + | 14.6486i | −0.0366342 | + | 0.521505i | ||||
\(790\) | 0.0262492 | − | 3.00220i | 0.000933905 | − | 0.106814i | ||||
\(791\) | 3.23352 | 0.114971 | ||||||||
\(792\) | 27.5805 | + | 9.95362i | 0.980030 | + | 0.353686i | ||||
\(793\) | − | 61.2045i | − | 2.17344i | ||||||
\(794\) | −16.6461 | + | 8.14192i | −0.590749 | + | 0.288946i | ||||
\(795\) | −23.2964 | + | 39.4182i | −0.826237 | + | 1.39802i | ||||
\(796\) | −26.7819 | − | 20.8279i | −0.949258 | − | 0.738227i | ||||
\(797\) | 48.9428 | 1.73364 | 0.866822 | − | 0.498618i | \(-0.166159\pi\) | ||||
0.866822 | + | 0.498618i | \(0.166159\pi\) | |||||||
\(798\) | −2.45559 | + | 0.994408i | −0.0869268 | + | 0.0352017i | ||||
\(799\) | 1.44216i | 0.0510201i | ||||||||
\(800\) | 27.5803 | + | 6.27094i | 0.975112 | + | 0.221711i | ||||
\(801\) | −2.19500 | + | 15.5464i | −0.0775566 | + | 0.549304i | ||||
\(802\) | 13.6958 | − | 6.69888i | 0.483616 | − | 0.236546i | ||||
\(803\) | 27.6447i | 0.975560i | ||||||||
\(804\) | 13.2280 | − | 14.7480i | 0.466517 | − | 0.520123i | ||||
\(805\) | 1.19216 | + | 0.596080i | 0.0420181 | + | 0.0210091i | ||||
\(806\) | −28.7654 | − | 58.8107i | −1.01322 | − | 2.07152i | ||||
\(807\) | −0.0175620 | + | 0.250003i | −0.000618211 | + | 0.00880053i | ||||
\(808\) | −4.47823 | + | 21.4217i | −0.157544 | + | 0.753614i | ||||
\(809\) | 28.7478i | 1.01072i | 0.862909 | + | 0.505360i | \(0.168640\pi\) | ||||
−0.862909 | + | 0.505360i | \(0.831360\pi\) | |||||||
\(810\) | −27.2780 | − | 8.11844i | −0.958452 | − | 0.285253i | ||||
\(811\) | − | 16.2821i | − | 0.571743i | −0.958268 | − | 0.285871i | \(-0.907717\pi\) | ||
0.958268 | − | 0.285871i | \(-0.0922830\pi\) | |||||||
\(812\) | 7.63941 | + | 5.94108i | 0.268091 | + | 0.208491i | ||||
\(813\) | 2.80675 | − | 39.9554i | 0.0984368 | − | 1.40130i | ||||
\(814\) | 12.7799 | − | 6.25088i | 0.447935 | − | 0.219093i | ||||
\(815\) | −11.2520 | + | 22.5039i | −0.394139 | + | 0.788278i | ||||
\(816\) | 7.31597 | + | 40.5056i | 0.256110 | + | 1.41798i | ||||
\(817\) | − | 8.00000i | − | 0.279885i | ||||||
\(818\) | −9.75834 | − | 19.9509i | −0.341192 | − | 0.697566i | ||||
\(819\) | −2.02946 | + | 14.3739i | −0.0709152 | + | 0.502265i | ||||
\(820\) | −27.8822 | + | 13.3369i | −0.973687 | + | 0.465743i | ||||
\(821\) | − | 36.0780i | − | 1.25913i | −0.776947 | − | 0.629566i | \(-0.783233\pi\) | ||
0.776947 | − | 0.629566i | \(-0.216767\pi\) | |||||||
\(822\) | −7.95165 | − | 19.6358i | −0.277346 | − | 0.684876i | ||||
\(823\) | −45.6117 | −1.58992 | −0.794962 | − | 0.606659i | \(-0.792509\pi\) | ||||
−0.794962 | + | 0.606659i | \(0.792509\pi\) | |||||||
\(824\) | −15.5559 | − | 3.25197i | −0.541915 | − | 0.113288i | ||||
\(825\) | −16.2340 | − | 25.1404i | −0.565194 | − | 0.875276i | ||||
\(826\) | −2.02068 | − | 4.13127i | −0.0703085 | − | 0.143745i | ||||
\(827\) | 27.6374i | 0.961048i | 0.876982 | + | 0.480524i | \(0.159553\pi\) | ||||
−0.876982 | + | 0.480524i | \(0.840447\pi\) | |||||||
\(828\) | −2.48855 | − | 2.56872i | −0.0864830 | − | 0.0892694i | ||||
\(829\) | 4.88609 | 0.169701 | 0.0848504 | − | 0.996394i | \(-0.472959\pi\) | ||||
0.0848504 | + | 0.996394i | \(0.472959\pi\) | |||||||
\(830\) | 0.469009 | − | 53.6419i | 0.0162795 | − | 1.86194i | ||||
\(831\) | −0.100288 | + | 1.42765i | −0.00347895 | + | 0.0495245i | ||||
\(832\) | −15.5073 | + | 35.4688i | −0.537617 | + | 1.22966i | ||||
\(833\) | −5.94108 | −0.205846 | ||||||||
\(834\) | 13.2355 | − | 5.35981i | 0.458307 | − | 0.185595i | ||||
\(835\) | −33.4274 | − | 16.7137i | −1.15680 | − | 0.578402i | ||||
\(836\) | 5.90059 | + | 4.58882i | 0.204076 | + | 0.158708i | ||||
\(837\) | 10.3822 | − | 48.6157i | 0.358860 | − | 1.68040i | ||||
\(838\) | 20.5515 | + | 42.0173i | 0.709938 | + | 1.45147i | ||||
\(839\) | 41.3592 | 1.42788 | 0.713939 | − | 0.700207i | \(-0.246909\pi\) | ||||
0.713939 | + | 0.700207i | \(0.246909\pi\) | |||||||
\(840\) | 7.38534 | − | 8.09054i | 0.254818 | − | 0.279150i | ||||
\(841\) | 5.58578 | 0.192613 | ||||||||
\(842\) | −4.89720 | − | 10.0123i | −0.168769 | − | 0.345047i | ||||
\(843\) | −1.77946 | + | 25.3315i | −0.0612878 | + | 0.872462i | ||||
\(844\) | 26.3872 | + | 20.5210i | 0.908284 | + | 0.706361i | ||||
\(845\) | −10.4142 | + | 20.8284i | −0.358260 | + | 0.716520i | ||||
\(846\) | −0.979319 | + | 0.318721i | −0.0336697 | + | 0.0109579i | ||||
\(847\) | 0.941075 | 0.0323357 | ||||||||
\(848\) | 11.6456 | + | 45.8330i | 0.399911 | + | 1.57391i | ||||
\(849\) | 35.2929 | + | 2.47922i | 1.21125 | + | 0.0850865i | ||||
\(850\) | 19.1151 | − | 37.4090i | 0.655643 | − | 1.28312i | ||||
\(851\) | −1.73529 | −0.0594850 | ||||||||
\(852\) | 18.5039 | − | 20.6302i | 0.633934 | − | 0.706778i | ||||
\(853\) | − | 17.2973i | − | 0.592247i | −0.955150 | − | 0.296123i | \(-0.904306\pi\) | ||
0.955150 | − | 0.296123i | \(-0.0956939\pi\) | |||||||
\(854\) | 7.85951 | + | 16.0687i | 0.268947 | + | 0.549860i | ||||
\(855\) | −5.97206 | − | 4.12009i | −0.204240 | − | 0.140904i | ||||
\(856\) | 0.975179 | − | 4.66480i | 0.0333309 | − | 0.159440i | ||||
\(857\) | −40.4749 | −1.38260 | −0.691298 | − | 0.722570i | \(-0.742961\pi\) | ||||
−0.691298 | + | 0.722570i | \(0.742961\pi\) | |||||||
\(858\) | 37.9632 | − | 15.3735i | 1.29604 | − | 0.524842i | ||||
\(859\) | 40.6849i | 1.38815i | 0.719902 | + | 0.694075i | \(0.244187\pi\) | ||||
−0.719902 | + | 0.694075i | \(0.755813\pi\) | |||||||
\(860\) | 14.2737 | + | 29.8408i | 0.486730 | + | 1.01756i | ||||
\(861\) | −0.838825 | + | 11.9411i | −0.0285871 | + | 0.406951i | ||||
\(862\) | −16.3746 | − | 33.4777i | −0.557719 | − | 1.14025i | ||||
\(863\) | − | 7.84981i | − | 0.267211i | −0.991035 | − | 0.133605i | \(-0.957345\pi\) | ||
0.991035 | − | 0.133605i | \(-0.0426554\pi\) | |||||||
\(864\) | −25.8890 | + | 13.9198i | −0.880760 | + | 0.473562i | ||||
\(865\) | −1.94108 | + | 3.88215i | −0.0659985 | + | 0.131997i | ||||
\(866\) | −47.3821 | + | 23.1755i | −1.61011 | + | 0.787535i | ||||
\(867\) | 31.6123 | + | 2.22067i | 1.07361 | + | 0.0754180i | ||||
\(868\) | 15.1042 | + | 11.7464i | 0.512670 | + | 0.398698i | ||||
\(869\) | 3.28079i | 0.111293i | ||||||||
\(870\) | −2.08828 | + | 26.4209i | −0.0707993 | + | 0.895754i | ||||
\(871\) | − | 27.6733i | − | 0.937674i | ||||||
\(872\) | 27.5226 | + | 5.75363i | 0.932034 | + | 0.194842i | ||||
\(873\) | 1.38652 | − | 9.82021i | 0.0469267 | − | 0.332364i | ||||
\(874\) | −0.400600 | − | 0.819024i | −0.0135505 | − | 0.0277039i | ||||
\(875\) | −11.0000 | + | 2.00000i | −0.371868 | + | 0.0676123i | ||||
\(876\) | −20.6302 | − | 18.5039i | −0.697029 | − | 0.625190i | ||||
\(877\) | − | 4.58882i | − | 0.154953i | −0.996994 | − | 0.0774767i | \(-0.975314\pi\) | ||
0.996994 | − | 0.0774767i | \(-0.0246864\pi\) | |||||||
\(878\) | −16.0361 | + | 7.84354i | −0.541191 | + | 0.264707i | ||||
\(879\) | −9.35466 | − | 0.657136i | −0.315525 | − | 0.0221647i | ||||
\(880\) | −30.1972 | − | 6.58882i | −1.01795 | − | 0.222109i | ||||
\(881\) | 13.0906i | 0.441033i | 0.975383 | + | 0.220517i | \(0.0707743\pi\) | ||||
−0.975383 | + | 0.220517i | \(0.929226\pi\) | |||||||
\(882\) | −1.31299 | − | 4.03436i | −0.0442107 | − | 0.135844i | ||||
\(883\) | 19.4335 | 0.653991 | 0.326995 | − | 0.945026i | \(-0.393964\pi\) | ||||
0.326995 | + | 0.945026i | \(0.393964\pi\) | |||||||
\(884\) | 45.3863 | + | 35.2964i | 1.52651 | + | 1.18715i | ||||
\(885\) | 6.40812 | − | 10.8427i | 0.215407 | − | 0.364475i | ||||
\(886\) | −27.5824 | + | 13.4911i | −0.926650 | + | 0.453242i | ||||
\(887\) | − | 33.1704i | − | 1.11375i | −0.830595 | − | 0.556876i | \(-0.812000\pi\) | ||
0.830595 | − | 0.556876i | \(-0.188000\pi\) | |||||||
\(888\) | −3.88941 | + | 13.7212i | −0.130520 | + | 0.460452i | ||||
\(889\) | 1.08883 | 0.0365181 | ||||||||
\(890\) | 0.144695 | − | 16.5492i | 0.00485019 | − | 0.554731i | ||||
\(891\) | 29.8846 | + | 8.61049i | 1.00117 | + | 0.288462i | ||||
\(892\) | 10.7645 | − | 13.8417i | 0.360422 | − | 0.463453i | ||||
\(893\) | −0.262545 | −0.00878573 | ||||||||
\(894\) | −40.4637 | + | 16.3861i | −1.35331 | + | 0.548033i | ||||
\(895\) | 6.80784 | − | 13.6157i | 0.227561 | − | 0.455122i | ||||
\(896\) | −0.483388 | − | 11.3034i | −0.0161489 | − | 0.377619i | ||||
\(897\) | −4.98352 | − | 0.350077i | −0.166395 | − | 0.0116887i | ||||
\(898\) | −18.5936 | + | 9.09446i | −0.620475 | + | 0.303486i | ||||
\(899\) | −46.2933 | −1.54397 | ||||||||
\(900\) | 29.6275 | + | 4.71289i | 0.987583 | + | 0.157096i | ||||
\(901\) | 70.2374 | 2.33995 | ||||||||
\(902\) | 30.3397 | − | 14.8397i | 1.01020 | − | 0.494108i | ||||
\(903\) | 12.7799 | + | 0.897749i | 0.425288 | + | 0.0298752i | ||||
\(904\) | 8.95226 | + | 1.87148i | 0.297748 | + | 0.0622444i | ||||
\(905\) | −2.97098 | + | 5.94196i | −0.0987587 | + | 0.197517i | ||||
\(906\) | 35.7422 | − | 14.4741i | 1.18745 | − | 0.480869i | ||||
\(907\) | −35.6051 | −1.18225 | −0.591124 | − | 0.806581i | \(-0.701316\pi\) | ||||
−0.591124 | + | 0.806581i | \(0.701316\pi\) | |||||||
\(908\) | −0.383238 | − | 0.298040i | −0.0127182 | − | 0.00989081i | ||||
\(909\) | −3.24518 | + | 22.9844i | −0.107636 | + | 0.762344i | ||||
\(910\) | 0.133783 | − | 15.3011i | 0.00443485 | − | 0.507227i | ||||
\(911\) | 2.26038 | 0.0748898 | 0.0374449 | − | 0.999299i | \(-0.488078\pi\) | ||||
0.0374449 | + | 0.999299i | \(0.488078\pi\) | |||||||
\(912\) | −7.37402 | + | 1.33187i | −0.244178 | + | 0.0441026i | ||||
\(913\) | 58.6196i | 1.94003i | ||||||||
\(914\) | −5.08381 | + | 2.48658i | −0.168157 | + | 0.0822489i | ||||
\(915\) | −24.9246 | + | 42.1732i | −0.823982 | + | 1.39420i | ||||
\(916\) | 32.3562 | − | 41.6056i | 1.06908 | − | 1.37469i | ||||
\(917\) | 6.30783 | 0.208303 | ||||||||
\(918\) | 10.5687 | + | 42.3593i | 0.348819 | + | 1.39806i | ||||
\(919\) | 2.42040i | 0.0798416i | 0.999203 | + | 0.0399208i | \(0.0127106\pi\) | ||||
−0.999203 | + | 0.0399208i | \(0.987289\pi\) | |||||||
\(920\) | 2.95559 | + | 2.34028i | 0.0974430 | + | 0.0771569i | ||||
\(921\) | −28.1750 | − | 1.97921i | −0.928399 | − | 0.0652172i | ||||
\(922\) | 46.9308 | − | 22.9547i | 1.54558 | − | 0.755973i | ||||
\(923\) | − | 38.7106i | − | 1.27417i | ||||||
\(924\) | −7.99274 | + | 8.91117i | −0.262942 | + | 0.293156i | ||||
\(925\) | 11.6447 | − | 8.73352i | 0.382875 | − | 0.287156i | ||||
\(926\) | −3.80390 | − | 7.77706i | −0.125004 | − | 0.255570i | ||||
\(927\) | −16.6906 | − | 2.35656i | −0.548192 | − | 0.0773996i | ||||
\(928\) | 17.7118 | + | 20.8698i | 0.581417 | + | 0.685085i | ||||
\(929\) | − | 18.9380i | − | 0.621336i | −0.950518 | − | 0.310668i | \(-0.899447\pi\) | ||
0.950518 | − | 0.310668i | \(-0.100553\pi\) | |||||||
\(930\) | −4.12883 | + | 52.2380i | −0.135390 | + | 1.71295i | ||||
\(931\) | − | 1.08157i | − | 0.0354470i | ||||||
\(932\) | 7.91205 | − | 10.1738i | 0.259168 | − | 0.333254i | ||||
\(933\) | −42.0772 | − | 2.95579i | −1.37754 | − | 0.0967683i | ||||
\(934\) | 17.8682 | − | 8.73966i | 0.584665 | − | 0.285970i | ||||
\(935\) | −20.5299 | + | 41.0598i | −0.671399 | + | 1.34280i | ||||
\(936\) | −13.9380 | + | 38.6207i | −0.455576 | + | 1.26236i | ||||
\(937\) | 13.4835i | 0.440488i | 0.975445 | + | 0.220244i | \(0.0706853\pi\) | ||||
−0.975445 | + | 0.220244i | \(0.929315\pi\) | |||||||
\(938\) | 3.55364 | + | 7.26539i | 0.116030 | + | 0.237223i | ||||
\(939\) | −3.72142 | + | 52.9762i | −0.121444 | + | 1.72881i | ||||
\(940\) | 0.979319 | − | 0.468437i | 0.0319418 | − | 0.0152787i | ||||
\(941\) | 60.5598i | 1.97419i | 0.160128 | + | 0.987096i | \(0.448809\pi\) | ||||
−0.160128 | + | 0.987096i | \(0.551191\pi\) | |||||||
\(942\) | −40.4637 | + | 16.3861i | −1.31838 | + | 0.533887i | ||||
\(943\) | −4.11961 | −0.134153 | ||||||||
\(944\) | −3.20334 | − | 12.6073i | −0.104260 | − | 0.410332i | ||||
\(945\) | 7.25197 | − | 9.07794i | 0.235906 | − | 0.295305i | ||||
\(946\) | −15.8822 | − | 32.4710i | −0.516373 | − | 1.05572i | ||||
\(947\) | − | 27.9514i | − | 0.908298i | −0.890926 | − | 0.454149i | \(-0.849943\pi\) | ||
0.890926 | − | 0.454149i | \(-0.150057\pi\) | |||||||
\(948\) | −2.44833 | − | 2.19599i | −0.0795180 | − | 0.0713224i | ||||
\(949\) | −38.7106 | −1.25660 | ||||||||
\(950\) | 6.81028 | + | 3.47990i | 0.220955 | + | 0.112903i | ||||
\(951\) | −23.9855 | − | 1.68491i | −0.777783 | − | 0.0546369i | ||||
\(952\) | −16.4483 | − | 3.43853i | −0.533093 | − | 0.111444i | ||||
\(953\) | 28.4112 | 0.920328 | 0.460164 | − | 0.887834i | \(-0.347791\pi\) | ||||
0.460164 | + | 0.887834i | \(0.347791\pi\) | |||||||
\(954\) | 15.5226 | + | 47.6956i | 0.502564 | + | 1.54420i | ||||
\(955\) | 20.6477 | − | 41.2955i | 0.668145 | − | 1.33629i | ||||
\(956\) | −20.4422 | + | 26.2858i | −0.661146 | + | 0.850143i | ||||
\(957\) | 2.02946 | − | 28.8904i | 0.0656032 | − | 0.933893i | ||||
\(958\) | −20.7799 | − | 42.4844i | −0.671368 | − | 1.37261i | ||||
\(959\) | 8.64863 | 0.279279 | ||||||||
\(960\) | 25.1295 | − | 18.1248i | 0.811050 | − | 0.584977i | ||||
\(961\) | −60.5286 | −1.95254 | ||||||||
\(962\) | 8.75305 | + | 17.8956i | 0.282210 | + | 0.576976i | ||||
\(963\) | 0.706671 | − | 5.00508i | 0.0227722 | − | 0.161287i | ||||
\(964\) | 6.89755 | − | 8.86930i | 0.222155 | − | 0.285661i | ||||
\(965\) | −19.1196 | − | 9.55980i | −0.615482 | − | 0.307741i | ||||
\(966\) | 1.35334 | − | 0.548043i | 0.0435429 | − | 0.0176330i | ||||
\(967\) | 41.1776 | 1.32418 | 0.662092 | − | 0.749423i | \(-0.269669\pi\) | ||||
0.662092 | + | 0.749423i | \(0.269669\pi\) | |||||||
\(968\) | 2.60544 | + | 0.544669i | 0.0837420 | + | 0.0175063i | ||||
\(969\) | −0.779900 | + | 11.1023i | −0.0250540 | + | 0.356656i | ||||
\(970\) | −0.0913999 | + | 10.4537i | −0.00293467 | + | 0.335647i | ||||
\(971\) | 35.1592 | 1.12831 | 0.564156 | − | 0.825668i | \(-0.309202\pi\) | ||||
0.564156 | + | 0.825668i | \(0.309202\pi\) | |||||||
\(972\) | −26.4289 | + | 16.5383i | −0.847706 | + | 0.530466i | ||||
\(973\) | 5.82960i | 0.186888i | ||||||||
\(974\) | −11.0754 | − | 22.6436i | −0.354879 | − | 0.725548i | ||||
\(975\) | 35.2038 | − | 22.7323i | 1.12743 | − | 0.728015i | ||||
\(976\) | 12.4595 | + | 49.0364i | 0.398819 | + | 1.56962i | ||||
\(977\) | 48.4129 | 1.54887 | 0.774433 | − | 0.632655i | \(-0.218035\pi\) | ||||
0.774433 | + | 0.632655i | \(0.218035\pi\) | |||||||
\(978\) | 10.3452 | + | 25.5464i | 0.330803 | + | 0.816883i | ||||
\(979\) | 18.0849i | 0.577996i | ||||||||
\(980\) | 1.92975 | + | 4.03436i | 0.0616437 | + | 0.128873i | ||||
\(981\) | 29.5303 | + | 4.16941i | 0.942831 | + | 0.133119i | ||||
\(982\) | 7.64829 | + | 15.6369i | 0.244067 | + | 0.498993i | ||||
\(983\) | − | 18.6557i | − | 0.595024i | −0.954718 | − | 0.297512i | \(-0.903843\pi\) | ||
0.954718 | − | 0.297512i | \(-0.0961568\pi\) | |||||||
\(984\) | −9.23352 | + | 32.5743i | −0.294354 | + | 1.03843i | ||||
\(985\) | 11.5598 | − | 23.1196i | 0.368326 | − | 0.736652i | ||||
\(986\) | 36.5210 | − | 17.8631i | 1.16307 | − | 0.568877i | ||||
\(987\) | 0.0294624 | − | 0.419412i | 0.000937800 | − | 0.0133500i | ||||
\(988\) | −6.42568 | + | 8.26254i | −0.204428 | + | 0.262867i | ||||
\(989\) | 4.40900i | 0.140198i | ||||||||
\(990\) | −32.4193 | − | 4.86676i | −1.03035 | − | 0.154676i | ||||
\(991\) | − | 11.8876i | − | 0.377624i | −0.982013 | − | 0.188812i | \(-0.939536\pi\) | ||
0.982013 | − | 0.188812i | \(-0.0604636\pi\) | |||||||
\(992\) | 35.0187 | + | 41.2626i | 1.11185 | + | 1.31009i | ||||
\(993\) | −2.20362 | + | 31.3696i | −0.0699298 | + | 0.995484i | ||||
\(994\) | 4.97098 | + | 10.1631i | 0.157670 | + | 0.322355i | ||||
\(995\) | 33.9274 | + | 16.9637i | 1.07557 | + | 0.537786i | ||||
\(996\) | −43.7456 | − | 39.2369i | −1.38613 | − | 1.24327i | ||||
\(997\) | 46.0451i | 1.45826i | 0.684374 | + | 0.729131i | \(0.260076\pi\) | ||||
−0.684374 | + | 0.729131i | \(0.739924\pi\) | |||||||
\(998\) | −16.6347 | + | 8.13632i | −0.526561 | + | 0.257551i | ||||
\(999\) | −3.15920 | + | 14.7933i | −0.0999527 | + | 0.468040i |
(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 | 420.2.l.f.239.3 | yes | 8 | |
3.2 | odd | 2 | 420.2.l.e.239.6 | yes | 8 | ||
4.3 | odd | 2 | 420.2.l.d.239.4 | yes | 8 | ||
5.4 | even | 2 | 420.2.l.c.239.6 | yes | 8 | ||
12.11 | even | 2 | 420.2.l.c.239.5 | ✓ | 8 | ||
15.14 | odd | 2 | 420.2.l.d.239.3 | yes | 8 | ||
20.19 | odd | 2 | 420.2.l.e.239.5 | yes | 8 | ||
60.59 | even | 2 | inner | 420.2.l.f.239.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.l.c.239.5 | ✓ | 8 | 12.11 | even | 2 | ||
420.2.l.c.239.6 | yes | 8 | 5.4 | even | 2 | ||
420.2.l.d.239.3 | yes | 8 | 15.14 | odd | 2 | ||
420.2.l.d.239.4 | yes | 8 | 4.3 | odd | 2 | ||
420.2.l.e.239.5 | yes | 8 | 20.19 | odd | 2 | ||
420.2.l.e.239.6 | yes | 8 | 3.2 | odd | 2 | ||
420.2.l.f.239.3 | yes | 8 | 1.1 | even | 1 | trivial | |
420.2.l.f.239.4 | yes | 8 | 60.59 | even | 2 | inner |