Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(439,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.439");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.o (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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 549.13 | ||
Character | \(\chi\) | \(=\) | 770.549 |
Dual form | 770.2.o.a.439.13 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.0752187 | − | 0.130283i | 0.0434275 | − | 0.0752187i | −0.843495 | − | 0.537138i | \(-0.819506\pi\) |
0.886922 | + | 0.461919i | \(0.152839\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.87081 | − | 1.22477i | −0.836652 | − | 0.547734i | ||||
\(6\) | −0.150437 | −0.0614158 | ||||||||
\(7\) | −2.53943 | + | 0.742498i | −0.959814 | + | 0.280638i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.48868 | + | 2.57848i | 0.496228 | + | 0.859492i | ||||
\(10\) | −0.125277 | + | 2.23256i | −0.0396161 | + | 0.705996i | ||||
\(11\) | 2.31492 | − | 2.37511i | 0.697975 | − | 0.716122i | ||||
\(12\) | 0.0752187 | + | 0.130283i | 0.0217138 | + | 0.0376094i | ||||
\(13\) | 2.51463i | 0.697433i | 0.937228 | + | 0.348717i | \(0.113382\pi\) | ||||
−0.937228 | + | 0.348717i | \(0.886618\pi\) | |||||||
\(14\) | 1.91274 | + | 1.82796i | 0.511200 | + | 0.488543i | ||||
\(15\) | −0.300286 | + | 0.151609i | −0.0775336 | + | 0.0391452i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.99073 | − | 1.14935i | −0.482823 | − | 0.278758i | 0.238769 | − | 0.971076i | \(-0.423256\pi\) |
−0.721592 | + | 0.692318i | \(0.756589\pi\) | |||||||
\(18\) | 1.48868 | − | 2.57848i | 0.350886 | − | 0.607753i | ||||
\(19\) | 3.16071 | + | 5.47452i | 0.725118 | + | 1.25594i | 0.958926 | + | 0.283658i | \(0.0915480\pi\) |
−0.233808 | + | 0.972283i | \(0.575119\pi\) | |||||||
\(20\) | 1.99609 | − | 1.00778i | 0.446339 | − | 0.225348i | ||||
\(21\) | −0.0942780 | + | 0.386693i | −0.0205731 | + | 0.0843834i | ||||
\(22\) | −3.21436 | − | 0.817226i | −0.685305 | − | 0.174233i | ||||
\(23\) | 4.94308 | − | 2.85389i | 1.03070 | − | 0.595077i | 0.113517 | − | 0.993536i | \(-0.463788\pi\) |
0.917186 | + | 0.398459i | \(0.130455\pi\) | |||||||
\(24\) | 0.0752187 | − | 0.130283i | 0.0153540 | − | 0.0265938i | ||||
\(25\) | 1.99987 | + | 4.58263i | 0.399974 | + | 0.916526i | ||||
\(26\) | 2.17773 | − | 1.25732i | 0.427089 | − | 0.246580i | ||||
\(27\) | 0.899220 | 0.173055 | ||||||||
\(28\) | 0.626692 | − | 2.57046i | 0.118434 | − | 0.485771i | ||||
\(29\) | − | 6.85099i | − | 1.27220i | −0.771608 | − | 0.636099i | \(-0.780547\pi\) | ||
0.771608 | − | 0.636099i | \(-0.219453\pi\) | |||||||
\(30\) | 0.281440 | + | 0.184251i | 0.0513837 | + | 0.0336395i | ||||
\(31\) | 1.82057 | + | 1.05111i | 0.326985 | + | 0.188785i | 0.654502 | − | 0.756061i | \(-0.272879\pi\) |
−0.327517 | + | 0.944845i | \(0.606212\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −0.135310 | − | 0.480247i | −0.0235545 | − | 0.0836002i | ||||
\(34\) | 2.29870i | 0.394224i | ||||||||
\(35\) | 5.66018 | + | 1.72114i | 0.956745 | + | 0.290927i | ||||
\(36\) | −2.97737 | −0.496228 | ||||||||
\(37\) | 9.79562 | − | 5.65550i | 1.61039 | − | 0.929759i | 0.621110 | − | 0.783723i | \(-0.286682\pi\) |
0.989279 | − | 0.146036i | \(-0.0466514\pi\) | |||||||
\(38\) | 3.16071 | − | 5.47452i | 0.512736 | − | 0.888084i | ||||
\(39\) | 0.327613 | + | 0.189147i | 0.0524600 | + | 0.0302878i | ||||
\(40\) | −1.87081 | − | 1.22477i | −0.295801 | − | 0.193653i | ||||
\(41\) | −0.710102 | −0.110899 | −0.0554496 | − | 0.998461i | \(-0.517659\pi\) | ||||
−0.0554496 | + | 0.998461i | \(0.517659\pi\) | |||||||
\(42\) | 0.382025 | − | 0.111699i | 0.0589477 | − | 0.0172356i | ||||
\(43\) | −2.99747 | −0.457109 | −0.228555 | − | 0.973531i | \(-0.573400\pi\) | ||||
−0.228555 | + | 0.973531i | \(0.573400\pi\) | |||||||
\(44\) | 0.899444 | + | 3.19233i | 0.135596 | + | 0.481263i | ||||
\(45\) | 0.372996 | − | 6.64714i | 0.0556030 | − | 0.990897i | ||||
\(46\) | −4.94308 | − | 2.85389i | −0.728818 | − | 0.420783i | ||||
\(47\) | 3.34066 | + | 5.78618i | 0.487285 | + | 0.844002i | 0.999893 | − | 0.0146208i | \(-0.00465410\pi\) |
−0.512608 | + | 0.858622i | \(0.671321\pi\) | |||||||
\(48\) | −0.150437 | −0.0217138 | ||||||||
\(49\) | 5.89739 | − | 3.77104i | 0.842485 | − | 0.538720i | ||||
\(50\) | 2.96874 | − | 4.02326i | 0.419843 | − | 0.568974i | ||||
\(51\) | −0.299480 | + | 0.172905i | −0.0419357 | + | 0.0242116i | ||||
\(52\) | −2.17773 | − | 1.25732i | −0.301997 | − | 0.174358i | ||||
\(53\) | 3.78207 | + | 2.18358i | 0.519507 | + | 0.299938i | 0.736733 | − | 0.676184i | \(-0.236367\pi\) |
−0.217226 | + | 0.976121i | \(0.569701\pi\) | |||||||
\(54\) | −0.449610 | − | 0.778747i | −0.0611842 | − | 0.105974i | ||||
\(55\) | −7.23975 | + | 1.60813i | −0.976207 | + | 0.216841i | ||||
\(56\) | −2.53943 | + | 0.742498i | −0.339345 | + | 0.0992204i | ||||
\(57\) | 0.950979 | 0.125960 | ||||||||
\(58\) | −5.93313 | + | 3.42550i | −0.779059 | + | 0.449790i | ||||
\(59\) | 7.75012 | + | 4.47453i | 1.00898 | + | 0.582535i | 0.910893 | − | 0.412643i | \(-0.135394\pi\) |
0.0980868 | + | 0.995178i | \(0.468728\pi\) | |||||||
\(60\) | 0.0188464 | − | 0.335860i | 0.00243305 | − | 0.0433593i | ||||
\(61\) | 5.17631 | + | 8.96564i | 0.662759 | + | 1.14793i | 0.979888 | + | 0.199550i | \(0.0639479\pi\) |
−0.317129 | + | 0.948382i | \(0.602719\pi\) | |||||||
\(62\) | − | 2.10222i | − | 0.266982i | ||||||
\(63\) | −5.69492 | − | 5.44251i | −0.717493 | − | 0.685692i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.07985 | − | 4.70440i | 0.382008 | − | 0.583509i | ||||
\(66\) | −0.348251 | + | 0.357305i | −0.0428667 | + | 0.0439812i | ||||
\(67\) | −6.84041 | − | 3.94931i | −0.835689 | − | 0.482485i | 0.0201077 | − | 0.999798i | \(-0.493599\pi\) |
−0.855796 | + | 0.517313i | \(0.826932\pi\) | |||||||
\(68\) | 1.99073 | − | 1.14935i | 0.241412 | − | 0.139379i | ||||
\(69\) | − | 0.858663i | − | 0.103371i | ||||||
\(70\) | −1.33954 | − | 5.76243i | −0.160105 | − | 0.688743i | ||||
\(71\) | −11.7961 | −1.39994 | −0.699969 | − | 0.714173i | \(-0.746803\pi\) | ||||
−0.699969 | + | 0.714173i | \(0.746803\pi\) | |||||||
\(72\) | 1.48868 | + | 2.57848i | 0.175443 | + | 0.303876i | ||||
\(73\) | 11.5308 | + | 6.65729i | 1.34957 | + | 0.779177i | 0.988189 | − | 0.153240i | \(-0.0489706\pi\) |
0.361385 | + | 0.932417i | \(0.382304\pi\) | |||||||
\(74\) | −9.79562 | − | 5.65550i | −1.13872 | − | 0.657439i | ||||
\(75\) | 0.747465 | + | 0.0841511i | 0.0863098 | + | 0.00971693i | ||||
\(76\) | −6.32143 | −0.725118 | ||||||||
\(77\) | −4.11506 | + | 7.75024i | −0.468955 | + | 0.883222i | ||||
\(78\) | − | 0.378295i | − | 0.0428334i | ||||||
\(79\) | 7.29423 | − | 4.21133i | 0.820665 | − | 0.473811i | −0.0299808 | − | 0.999550i | \(-0.509545\pi\) |
0.850646 | + | 0.525739i | \(0.176211\pi\) | |||||||
\(80\) | −0.125277 | + | 2.23256i | −0.0140064 | + | 0.249607i | ||||
\(81\) | −4.39841 | + | 7.61828i | −0.488713 | + | 0.846475i | ||||
\(82\) | 0.355051 | + | 0.614966i | 0.0392088 | + | 0.0679116i | ||||
\(83\) | 8.40993i | 0.923110i | 0.887112 | + | 0.461555i | \(0.152708\pi\) | ||||
−0.887112 | + | 0.461555i | \(0.847292\pi\) | |||||||
\(84\) | −0.287747 | − | 0.274994i | −0.0313958 | − | 0.0300043i | ||||
\(85\) | 2.31659 | + | 4.58841i | 0.251270 | + | 0.497683i | ||||
\(86\) | 1.49873 | + | 2.59588i | 0.161613 | + | 0.279921i | ||||
\(87\) | −0.892565 | − | 0.515323i | −0.0956931 | − | 0.0552484i | ||||
\(88\) | 2.31492 | − | 2.37511i | 0.246771 | − | 0.253187i | ||||
\(89\) | 3.02422 | − | 1.74604i | 0.320567 | − | 0.185080i | −0.331078 | − | 0.943603i | \(-0.607412\pi\) |
0.651645 | + | 0.758524i | \(0.274079\pi\) | |||||||
\(90\) | −5.94309 | + | 3.00055i | −0.626457 | + | 0.316285i | ||||
\(91\) | −1.86711 | − | 6.38573i | −0.195726 | − | 0.669406i | ||||
\(92\) | 5.70778i | 0.595077i | ||||||||
\(93\) | 0.273882 | − | 0.158126i | 0.0284003 | − | 0.0163969i | ||||
\(94\) | 3.34066 | − | 5.78618i | 0.344562 | − | 0.596799i | ||||
\(95\) | 0.791930 | − | 14.1129i | 0.0812503 | − | 1.44796i | ||||
\(96\) | 0.0752187 | + | 0.130283i | 0.00767698 | + | 0.0132969i | ||||
\(97\) | −9.73846 | −0.988791 | −0.494395 | − | 0.869237i | \(-0.664610\pi\) | ||||
−0.494395 | + | 0.869237i | \(0.664610\pi\) | |||||||
\(98\) | −6.21451 | − | 3.22177i | −0.627761 | − | 0.325448i | ||||
\(99\) | 9.57035 | + | 2.43318i | 0.961856 | + | 0.244544i | ||||
\(100\) | −4.96861 | − | 0.559376i | −0.496861 | − | 0.0559376i | ||||
\(101\) | 9.39320 | − | 16.2695i | 0.934658 | − | 1.61888i | 0.159416 | − | 0.987212i | \(-0.449039\pi\) |
0.775243 | − | 0.631664i | \(-0.217628\pi\) | |||||||
\(102\) | 0.299480 | + | 0.172905i | 0.0296530 | + | 0.0171202i | ||||
\(103\) | −2.31245 | − | 4.00529i | −0.227853 | − | 0.394653i | 0.729319 | − | 0.684174i | \(-0.239837\pi\) |
−0.957172 | + | 0.289521i | \(0.906504\pi\) | |||||||
\(104\) | 2.51463i | 0.246580i | ||||||||
\(105\) | 0.649987 | − | 0.607961i | 0.0634322 | − | 0.0593309i | ||||
\(106\) | − | 4.36716i | − | 0.424176i | ||||||
\(107\) | 3.71349 | + | 6.43195i | 0.358996 | + | 0.621800i | 0.987793 | − | 0.155770i | \(-0.0497858\pi\) |
−0.628797 | + | 0.777569i | \(0.716452\pi\) | |||||||
\(108\) | −0.449610 | + | 0.778747i | −0.0432637 | + | 0.0749350i | ||||
\(109\) | 0.976031 | + | 0.563512i | 0.0934868 | + | 0.0539746i | 0.546015 | − | 0.837776i | \(-0.316144\pi\) |
−0.452528 | + | 0.891750i | \(0.649478\pi\) | |||||||
\(110\) | 5.01256 | + | 5.46574i | 0.477929 | + | 0.521138i | ||||
\(111\) | − | 1.70160i | − | 0.161509i | ||||||
\(112\) | 1.91274 | + | 1.82796i | 0.180737 | + | 0.172726i | ||||
\(113\) | 13.0798i | 1.23045i | 0.788353 | + | 0.615223i | \(0.210934\pi\) | ||||
−0.788353 | + | 0.615223i | \(0.789066\pi\) | |||||||
\(114\) | −0.475490 | − | 0.823572i | −0.0445337 | − | 0.0771346i | ||||
\(115\) | −12.7429 | − | 0.715054i | −1.18828 | − | 0.0666791i | ||||
\(116\) | 5.93313 | + | 3.42550i | 0.550878 | + | 0.318049i | ||||
\(117\) | −6.48392 | + | 3.74349i | −0.599438 | + | 0.346086i | ||||
\(118\) | − | 8.94907i | − | 0.823828i | ||||||
\(119\) | 5.90871 | + | 1.44058i | 0.541651 | + | 0.132057i | ||||
\(120\) | −0.300286 | + | 0.151609i | −0.0274123 | + | 0.0138399i | ||||
\(121\) | −0.282284 | − | 10.9964i | −0.0256622 | − | 0.999671i | ||||
\(122\) | 5.17631 | − | 8.96564i | 0.468641 | − | 0.811711i | ||||
\(123\) | −0.0534129 | + | 0.0925139i | −0.00481608 | + | 0.00834170i | ||||
\(124\) | −1.82057 | + | 1.05111i | −0.163492 | + | 0.0943923i | ||||
\(125\) | 1.87129 | − | 11.0226i | 0.167373 | − | 0.985894i | ||||
\(126\) | −1.86589 | + | 7.65320i | −0.166227 | + | 0.681801i | ||||
\(127\) | −5.56609 | −0.493911 | −0.246955 | − | 0.969027i | \(-0.579430\pi\) | ||||
−0.246955 | + | 0.969027i | \(0.579430\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −0.225466 | + | 0.390518i | −0.0198511 | + | 0.0343832i | ||||
\(130\) | −5.61405 | − | 0.315026i | −0.492385 | − | 0.0276296i | ||||
\(131\) | 4.48765 | + | 7.77284i | 0.392088 | + | 0.679117i | 0.992725 | − | 0.120406i | \(-0.0384195\pi\) |
−0.600637 | + | 0.799522i | \(0.705086\pi\) | |||||||
\(132\) | 0.483561 | + | 0.122941i | 0.0420886 | + | 0.0107007i | ||||
\(133\) | −12.0912 | − | 11.5553i | −1.04844 | − | 1.00197i | ||||
\(134\) | 7.89862i | 0.682337i | ||||||||
\(135\) | −1.68227 | − | 1.10134i | −0.144787 | − | 0.0947881i | ||||
\(136\) | −1.99073 | − | 1.14935i | −0.170704 | − | 0.0985559i | ||||
\(137\) | 5.60178 | + | 3.23419i | 0.478593 | + | 0.276316i | 0.719830 | − | 0.694151i | \(-0.244220\pi\) |
−0.241237 | + | 0.970466i | \(0.577553\pi\) | |||||||
\(138\) | −0.743624 | + | 0.429332i | −0.0633015 | + | 0.0365471i | ||||
\(139\) | −15.0603 | −1.27740 | −0.638698 | − | 0.769457i | \(-0.720527\pi\) | ||||
−0.638698 | + | 0.769457i | \(0.720527\pi\) | |||||||
\(140\) | −4.32065 | + | 4.04129i | −0.365161 | + | 0.341551i | ||||
\(141\) | 1.00512 | 0.0846463 | ||||||||
\(142\) | 5.89804 | + | 10.2157i | 0.494953 | + | 0.857283i | ||||
\(143\) | 5.97252 | + | 5.82117i | 0.499447 | + | 0.486791i | ||||
\(144\) | 1.48868 | − | 2.57848i | 0.124057 | − | 0.214873i | ||||
\(145\) | −8.39090 | + | 12.8169i | −0.696826 | + | 1.06439i | ||||
\(146\) | − | 13.3146i | − | 1.10192i | ||||||
\(147\) | −0.0477067 | − | 1.05198i | −0.00393478 | − | 0.0867659i | ||||
\(148\) | 11.3110i | 0.929759i | ||||||||
\(149\) | 10.8989 | − | 6.29248i | 0.892872 | − | 0.515500i | 0.0179911 | − | 0.999838i | \(-0.494273\pi\) |
0.874881 | + | 0.484338i | \(0.160940\pi\) | |||||||
\(150\) | −0.300856 | − | 0.689399i | −0.0245648 | − | 0.0562892i | ||||
\(151\) | −15.4680 | − | 8.93044i | −1.25877 | − | 0.726749i | −0.285932 | − | 0.958250i | \(-0.592303\pi\) |
−0.972835 | + | 0.231501i | \(0.925636\pi\) | |||||||
\(152\) | 3.16071 | + | 5.47452i | 0.256368 | + | 0.444042i | ||||
\(153\) | − | 6.84407i | − | 0.553311i | ||||||
\(154\) | 8.76944 | − | 0.311373i | 0.706661 | − | 0.0250911i | ||||
\(155\) | −2.11858 | − | 4.19621i | −0.170169 | − | 0.337048i | ||||
\(156\) | −0.327613 | + | 0.189147i | −0.0262300 | + | 0.0151439i | ||||
\(157\) | −10.7967 | + | 18.7004i | −0.861670 | + | 1.49246i | 0.00864568 | + | 0.999963i | \(0.497248\pi\) |
−0.870316 | + | 0.492494i | \(0.836085\pi\) | |||||||
\(158\) | −7.29423 | − | 4.21133i | −0.580298 | − | 0.335035i | ||||
\(159\) | 0.568965 | − | 0.328492i | 0.0451218 | − | 0.0260511i | ||||
\(160\) | 1.99609 | − | 1.00778i | 0.157805 | − | 0.0796724i | ||||
\(161\) | −10.4336 | + | 10.9175i | −0.822282 | + | 0.860417i | ||||
\(162\) | 8.79683 | 0.691144 | ||||||||
\(163\) | 1.09053 | − | 0.629619i | 0.0854170 | − | 0.0493155i | −0.456683 | − | 0.889629i | \(-0.650963\pi\) |
0.542100 | + | 0.840314i | \(0.317629\pi\) | |||||||
\(164\) | 0.355051 | − | 0.614966i | 0.0277248 | − | 0.0480208i | ||||
\(165\) | −0.335052 | + | 1.06417i | −0.0260838 | + | 0.0828459i | ||||
\(166\) | 7.28322 | − | 4.20497i | 0.565287 | − | 0.326369i | ||||
\(167\) | − | 5.74722i | − | 0.444733i | −0.974963 | − | 0.222366i | \(-0.928622\pi\) | ||
0.974963 | − | 0.222366i | \(-0.0713781\pi\) | |||||||
\(168\) | −0.0942780 | + | 0.386693i | −0.00727370 | + | 0.0298340i | ||||
\(169\) | 6.67663 | 0.513587 | ||||||||
\(170\) | 2.81538 | − | 4.30043i | 0.215930 | − | 0.329828i | ||||
\(171\) | −9.41061 | + | 16.2997i | −0.719648 | + | 1.24647i | ||||
\(172\) | 1.49873 | − | 2.59588i | 0.114277 | − | 0.197934i | ||||
\(173\) | −1.41797 | + | 0.818664i | −0.107806 | + | 0.0622418i | −0.552934 | − | 0.833225i | \(-0.686492\pi\) |
0.445128 | + | 0.895467i | \(0.353158\pi\) | |||||||
\(174\) | 1.03065i | 0.0781330i | ||||||||
\(175\) | −8.48113 | − | 10.1524i | −0.641113 | − | 0.767447i | ||||
\(176\) | −3.21436 | − | 0.817226i | −0.242292 | − | 0.0616007i | ||||
\(177\) | 1.16591 | − | 0.673137i | 0.0876350 | − | 0.0505961i | ||||
\(178\) | −3.02422 | − | 1.74604i | −0.226675 | − | 0.130871i | ||||
\(179\) | −9.81605 | + | 17.0019i | −0.733686 | + | 1.27078i | 0.221612 | + | 0.975135i | \(0.428868\pi\) |
−0.955297 | + | 0.295646i | \(0.904465\pi\) | |||||||
\(180\) | 5.57010 | + | 3.64659i | 0.415170 | + | 0.271801i | ||||
\(181\) | 3.38062i | 0.251279i | 0.992076 | + | 0.125640i | \(0.0400983\pi\) | ||||
−0.992076 | + | 0.125640i | \(0.959902\pi\) | |||||||
\(182\) | −4.59665 | + | 4.80983i | −0.340726 | + | 0.356528i | ||||
\(183\) | 1.55742 | 0.115128 | ||||||||
\(184\) | 4.94308 | − | 2.85389i | 0.364409 | − | 0.210391i | ||||
\(185\) | −25.2525 | − | 1.41701i | −1.85660 | − | 0.104181i | ||||
\(186\) | −0.273882 | − | 0.158126i | −0.0200820 | − | 0.0115944i | ||||
\(187\) | −7.33822 | + | 2.06755i | −0.536623 | + | 0.151194i | ||||
\(188\) | −6.68131 | −0.487285 | ||||||||
\(189\) | −2.28350 | + | 0.667669i | −0.166101 | + | 0.0485658i | ||||
\(190\) | −12.6181 | + | 6.37064i | −0.915416 | + | 0.462175i | ||||
\(191\) | −2.09173 | − | 3.62298i | −0.151352 | − | 0.262150i | 0.780373 | − | 0.625315i | \(-0.215029\pi\) |
−0.931725 | + | 0.363165i | \(0.881696\pi\) | |||||||
\(192\) | 0.0752187 | − | 0.130283i | 0.00542844 | − | 0.00940234i | ||||
\(193\) | −4.48341 | + | 7.76550i | −0.322723 | + | 0.558973i | −0.981049 | − | 0.193760i | \(-0.937932\pi\) |
0.658326 | + | 0.752733i | \(0.271265\pi\) | |||||||
\(194\) | 4.86923 | + | 8.43375i | 0.349590 | + | 0.605508i | ||||
\(195\) | −0.381240 | − | 0.755110i | −0.0273011 | − | 0.0540745i | ||||
\(196\) | 0.317120 | + | 6.99281i | 0.0226514 | + | 0.499487i | ||||
\(197\) | 19.3704 | 1.38009 | 0.690044 | − | 0.723768i | \(-0.257591\pi\) | ||||
0.690044 | + | 0.723768i | \(0.257591\pi\) | |||||||
\(198\) | −2.67798 | − | 9.50476i | −0.190316 | − | 0.675474i | ||||
\(199\) | 14.4670 | + | 8.35255i | 1.02554 | + | 0.592097i | 0.915704 | − | 0.401853i | \(-0.131634\pi\) |
0.109837 | + | 0.993950i | \(0.464967\pi\) | |||||||
\(200\) | 1.99987 | + | 4.58263i | 0.141412 | + | 0.324041i | ||||
\(201\) | −1.02905 | + | 0.594124i | −0.0725838 | + | 0.0419063i | ||||
\(202\) | −18.7864 | −1.32181 | ||||||||
\(203\) | 5.08685 | + | 17.3976i | 0.357027 | + | 1.22107i | ||||
\(204\) | − | 0.345810i | − | 0.0242116i | ||||||
\(205\) | 1.32847 | + | 0.869712i | 0.0927841 | + | 0.0607433i | ||||
\(206\) | −2.31245 | + | 4.00529i | −0.161116 | + | 0.279062i | ||||
\(207\) | 14.7174 | + | 8.49708i | 1.02293 | + | 0.590588i | ||||
\(208\) | 2.17773 | − | 1.25732i | 0.150999 | − | 0.0871792i | ||||
\(209\) | 20.3194 | + | 5.16603i | 1.40552 | + | 0.357342i | ||||
\(210\) | −0.851503 | − | 0.258925i | −0.0587593 | − | 0.0178675i | ||||
\(211\) | 18.4793i | 1.27217i | 0.771620 | + | 0.636083i | \(0.219447\pi\) | ||||
−0.771620 | + | 0.636083i | \(0.780553\pi\) | |||||||
\(212\) | −3.78207 | + | 2.18358i | −0.259754 | + | 0.149969i | ||||
\(213\) | −0.887286 | + | 1.53682i | −0.0607958 | + | 0.105301i | ||||
\(214\) | 3.71349 | − | 6.43195i | 0.253849 | − | 0.439679i | ||||
\(215\) | 5.60769 | + | 3.67121i | 0.382442 | + | 0.250374i | ||||
\(216\) | 0.899220 | 0.0611842 | ||||||||
\(217\) | −5.40366 | − | 1.31744i | −0.366824 | − | 0.0894339i | ||||
\(218\) | − | 1.12702i | − | 0.0763316i | ||||||
\(219\) | 1.73466 | − | 1.00151i | 0.117217 | − | 0.0676755i | ||||
\(220\) | 2.22719 | − | 7.07387i | 0.150157 | − | 0.476920i | ||||
\(221\) | 2.89019 | − | 5.00596i | 0.194415 | − | 0.336737i | ||||
\(222\) | −1.47363 | + | 0.850799i | −0.0989034 | + | 0.0571019i | ||||
\(223\) | −8.16431 | −0.546723 | −0.273361 | − | 0.961911i | \(-0.588135\pi\) | ||||
−0.273361 | + | 0.961911i | \(0.588135\pi\) | |||||||
\(224\) | 0.626692 | − | 2.57046i | 0.0418726 | − | 0.171746i | ||||
\(225\) | −8.83903 | + | 11.9787i | −0.589269 | + | 0.798581i | ||||
\(226\) | 11.3275 | − | 6.53991i | 0.753491 | − | 0.435028i | ||||
\(227\) | −25.3374 | − | 14.6286i | −1.68171 | − | 0.970933i | −0.960528 | − | 0.278182i | \(-0.910268\pi\) |
−0.721177 | − | 0.692751i | \(-0.756398\pi\) | |||||||
\(228\) | −0.475490 | + | 0.823572i | −0.0314901 | + | 0.0545424i | ||||
\(229\) | 6.32273 | − | 3.65043i | 0.417818 | − | 0.241227i | −0.276325 | − | 0.961064i | \(-0.589117\pi\) |
0.694143 | + | 0.719837i | \(0.255783\pi\) | |||||||
\(230\) | 5.75221 | + | 11.3932i | 0.379290 | + | 0.751247i | ||||
\(231\) | 0.700192 | + | 1.11908i | 0.0460693 | + | 0.0736303i | ||||
\(232\) | − | 6.85099i | − | 0.449790i | ||||||
\(233\) | 9.93050 | + | 17.2001i | 0.650569 | + | 1.12682i | 0.982985 | + | 0.183685i | \(0.0588027\pi\) |
−0.332416 | + | 0.943133i | \(0.607864\pi\) | |||||||
\(234\) | 6.48392 | + | 3.74349i | 0.423867 | + | 0.244720i | ||||
\(235\) | 0.837015 | − | 14.9164i | 0.0546008 | − | 0.973039i | ||||
\(236\) | −7.75012 | + | 4.47453i | −0.504490 | + | 0.291267i | ||||
\(237\) | − | 1.26708i | − | 0.0823058i | ||||||
\(238\) | −1.70678 | − | 5.83738i | −0.110634 | − | 0.378381i | ||||
\(239\) | − | 21.5398i | − | 1.39329i | −0.717414 | − | 0.696647i | \(-0.754674\pi\) | ||
0.717414 | − | 0.696647i | \(-0.245326\pi\) | |||||||
\(240\) | 0.281440 | + | 0.184251i | 0.0181669 | + | 0.0118934i | ||||
\(241\) | −0.352616 | + | 0.610749i | −0.0227140 | + | 0.0393418i | −0.877159 | − | 0.480200i | \(-0.840564\pi\) |
0.854445 | + | 0.519542i | \(0.173897\pi\) | |||||||
\(242\) | −9.38200 | + | 5.74265i | −0.603098 | + | 0.369152i | ||||
\(243\) | 2.01052 | + | 3.48232i | 0.128975 | + | 0.223391i | ||||
\(244\) | −10.3526 | −0.662759 | ||||||||
\(245\) | −15.6516 | − | 0.168052i | −0.999942 | − | 0.0107364i | ||||
\(246\) | 0.106826 | 0.00681097 | ||||||||
\(247\) | −13.7664 | + | 7.94803i | −0.875935 | + | 0.505721i | ||||
\(248\) | 1.82057 | + | 1.05111i | 0.115607 | + | 0.0667455i | ||||
\(249\) | 1.09567 | + | 0.632584i | 0.0694351 | + | 0.0400884i | ||||
\(250\) | −10.4815 | + | 3.89073i | −0.662909 | + | 0.246071i | ||||
\(251\) | 3.87831i | 0.244796i | 0.992481 | + | 0.122398i | \(0.0390585\pi\) | ||||
−0.992481 | + | 0.122398i | \(0.960941\pi\) | |||||||
\(252\) | 7.56081 | − | 2.21069i | 0.476287 | − | 0.139260i | ||||
\(253\) | 4.66454 | − | 18.3469i | 0.293257 | − | 1.15346i | ||||
\(254\) | 2.78304 | + | 4.82037i | 0.174624 | + | 0.302457i | ||||
\(255\) | 0.772041 | + | 0.0433221i | 0.0483471 | + | 0.00271293i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −9.94552 | − | 17.2261i | −0.620384 | − | 1.07454i | −0.989414 | − | 0.145120i | \(-0.953643\pi\) |
0.369030 | − | 0.929418i | \(-0.379690\pi\) | |||||||
\(258\) | 0.450931 | 0.0280737 | ||||||||
\(259\) | −20.6761 | + | 21.6350i | −1.28475 | + | 1.34433i | ||||
\(260\) | 2.53421 | + | 5.01943i | 0.157165 | + | 0.311292i | ||||
\(261\) | 17.6651 | − | 10.1990i | 1.09344 | − | 0.631300i | ||||
\(262\) | 4.48765 | − | 7.77284i | 0.277248 | − | 0.480208i | ||||
\(263\) | −8.95455 | + | 15.5097i | −0.552161 | + | 0.956371i | 0.445957 | + | 0.895054i | \(0.352863\pi\) |
−0.998118 | + | 0.0613168i | \(0.980470\pi\) | |||||||
\(264\) | −0.135310 | − | 0.480247i | −0.00832776 | − | 0.0295571i | ||||
\(265\) | −4.40116 | − | 8.71723i | −0.270361 | − | 0.535495i | ||||
\(266\) | −3.96159 | + | 16.2490i | −0.242901 | + | 0.996288i | ||||
\(267\) | − | 0.525339i | − | 0.0321502i | ||||||
\(268\) | 6.84041 | − | 3.94931i | 0.417844 | − | 0.241243i | ||||
\(269\) | 8.49686 | + | 4.90567i | 0.518063 | + | 0.299104i | 0.736142 | − | 0.676827i | \(-0.236646\pi\) |
−0.218079 | + | 0.975931i | \(0.569979\pi\) | |||||||
\(270\) | −0.112652 | + | 2.00756i | −0.00685576 | + | 0.122176i | ||||
\(271\) | −7.77154 | − | 13.4607i | −0.472087 | − | 0.817680i | 0.527402 | − | 0.849616i | \(-0.323166\pi\) |
−0.999490 | + | 0.0319361i | \(0.989833\pi\) | |||||||
\(272\) | 2.29870i | 0.139379i | ||||||||
\(273\) | −0.972391 | − | 0.237074i | −0.0588518 | − | 0.0143484i | ||||
\(274\) | − | 6.46838i | − | 0.390769i | ||||||
\(275\) | 15.5138 | + | 5.85852i | 0.935517 | + | 0.353282i | ||||
\(276\) | 0.743624 | + | 0.429332i | 0.0447609 | + | 0.0258427i | ||||
\(277\) | 14.3031 | − | 24.7737i | 0.859388 | − | 1.48850i | −0.0131248 | − | 0.999914i | \(-0.504178\pi\) |
0.872513 | − | 0.488591i | \(-0.162489\pi\) | |||||||
\(278\) | 7.53014 | + | 13.0426i | 0.451628 | + | 0.782242i | ||||
\(279\) | 6.25908i | 0.374721i | ||||||||
\(280\) | 5.66018 | + | 1.72114i | 0.338261 | + | 0.102858i | ||||
\(281\) | − | 28.9870i | − | 1.72922i | −0.502445 | − | 0.864609i | \(-0.667566\pi\) | ||
0.502445 | − | 0.864609i | \(-0.332434\pi\) | |||||||
\(282\) | −0.502559 | − | 0.870459i | −0.0299270 | − | 0.0518351i | ||||
\(283\) | 15.1298 | + | 8.73518i | 0.899372 | + | 0.519252i | 0.876996 | − | 0.480497i | \(-0.159544\pi\) |
0.0223753 | + | 0.999750i | \(0.492877\pi\) | |||||||
\(284\) | 5.89804 | − | 10.2157i | 0.349984 | − | 0.606191i | ||||
\(285\) | −1.77910 | − | 1.16473i | −0.105385 | − | 0.0689928i | ||||
\(286\) | 2.05502 | − | 8.08294i | 0.121516 | − | 0.477954i | ||||
\(287\) | 1.80325 | − | 0.527249i | 0.106443 | − | 0.0311225i | ||||
\(288\) | −2.97737 | −0.175443 | ||||||||
\(289\) | −5.85799 | − | 10.1463i | −0.344588 | − | 0.596844i | ||||
\(290\) | 15.2952 | + | 0.858272i | 0.898167 | + | 0.0503995i | ||||
\(291\) | −0.732514 | + | 1.26875i | −0.0429407 | + | 0.0743755i | ||||
\(292\) | −11.5308 | + | 6.65729i | −0.674787 | + | 0.389588i | ||||
\(293\) | 0.637578i | 0.0372477i | 0.999827 | + | 0.0186239i | \(0.00592850\pi\) | ||||
−0.999827 | + | 0.0186239i | \(0.994071\pi\) | |||||||
\(294\) | −0.887189 | + | 0.567306i | −0.0517419 | + | 0.0330859i | ||||
\(295\) | −9.01873 | − | 17.8631i | −0.525091 | − | 1.04003i | ||||
\(296\) | 9.79562 | − | 5.65550i | 0.569359 | − | 0.328719i | ||||
\(297\) | 2.08162 | − | 2.13574i | 0.120788 | − | 0.123928i | ||||
\(298\) | −10.8989 | − | 6.29248i | −0.631356 | − | 0.364513i | ||||
\(299\) | 7.17648 | + | 12.4300i | 0.415026 | + | 0.718847i | ||||
\(300\) | −0.446609 | + | 0.605248i | −0.0257850 | + | 0.0349440i | ||||
\(301\) | 7.61185 | − | 2.22561i | 0.438740 | − | 0.128282i | ||||
\(302\) | 17.8609i | 1.02778i | ||||||||
\(303\) | −1.41309 | − | 2.44754i | −0.0811798 | − | 0.140608i | ||||
\(304\) | 3.16071 | − | 5.47452i | 0.181279 | − | 0.313985i | ||||
\(305\) | 1.29695 | − | 23.1128i | 0.0742629 | − | 1.32344i | ||||
\(306\) | −5.92714 | + | 3.42204i | −0.338832 | + | 0.195625i | ||||
\(307\) | − | 17.8871i | − | 1.02087i | −0.859917 | − | 0.510434i | \(-0.829485\pi\) | ||
0.859917 | − | 0.510434i | \(-0.170515\pi\) | |||||||
\(308\) | −4.65438 | − | 7.43887i | −0.265208 | − | 0.423869i | ||||
\(309\) | −0.695759 | −0.0395804 | ||||||||
\(310\) | −2.57473 | + | 3.93285i | −0.146235 | + | 0.223371i | ||||
\(311\) | −19.0018 | − | 10.9707i | −1.07749 | − | 0.622091i | −0.147274 | − | 0.989096i | \(-0.547050\pi\) |
−0.930219 | + | 0.367005i | \(0.880383\pi\) | |||||||
\(312\) | 0.327613 | + | 0.189147i | 0.0185474 | + | 0.0107084i | ||||
\(313\) | −0.686648 | − | 1.18931i | −0.0388117 | − | 0.0672238i | 0.845967 | − | 0.533235i | \(-0.179024\pi\) |
−0.884779 | + | 0.466011i | \(0.845691\pi\) | |||||||
\(314\) | 21.5934 | 1.21859 | ||||||||
\(315\) | 3.98829 | + | 17.1569i | 0.224715 | + | 0.966681i | ||||
\(316\) | 8.42265i | 0.473811i | ||||||||
\(317\) | 3.93592 | − | 2.27240i | 0.221063 | − | 0.127631i | −0.385379 | − | 0.922758i | \(-0.625929\pi\) |
0.606442 | + | 0.795127i | \(0.292596\pi\) | |||||||
\(318\) | −0.568965 | − | 0.328492i | −0.0319060 | − | 0.0184209i | ||||
\(319\) | −16.2719 | − | 15.8595i | −0.911049 | − | 0.887962i | ||||
\(320\) | −1.87081 | − | 1.22477i | −0.104582 | − | 0.0684668i | ||||
\(321\) | 1.11729 | 0.0623613 | ||||||||
\(322\) | 14.6716 | + | 3.57702i | 0.817617 | + | 0.199340i | ||||
\(323\) | − | 14.5311i | − | 0.808530i | ||||||
\(324\) | −4.39841 | − | 7.61828i | −0.244356 | − | 0.423238i | ||||
\(325\) | −11.5236 | + | 5.02894i | −0.639216 | + | 0.278955i | ||||
\(326\) | −1.09053 | − | 0.629619i | −0.0603990 | − | 0.0348714i | ||||
\(327\) | 0.146832 | − | 0.0847732i | 0.00811980 | − | 0.00468797i | ||||
\(328\) | −0.710102 | −0.0392088 | ||||||||
\(329\) | −12.7796 | − | 12.2132i | −0.704561 | − | 0.673334i | ||||
\(330\) | 1.08913 | − | 0.241923i | 0.0599545 | − | 0.0133174i | ||||
\(331\) | 8.20177 | + | 14.2059i | 0.450810 | + | 0.780826i | 0.998437 | − | 0.0558972i | \(-0.0178019\pi\) |
−0.547627 | + | 0.836723i | \(0.684469\pi\) | |||||||
\(332\) | −7.28322 | − | 4.20497i | −0.399718 | − | 0.230778i | ||||
\(333\) | 29.1652 | + | 16.8385i | 1.59824 | + | 0.922745i | ||||
\(334\) | −4.97724 | + | 2.87361i | −0.272342 | + | 0.157237i | ||||
\(335\) | 7.96011 | + | 15.7664i | 0.434907 | + | 0.861408i | ||||
\(336\) | 0.382025 | − | 0.111699i | 0.0208412 | − | 0.00609370i | ||||
\(337\) | 10.0052 | 0.545019 | 0.272509 | − | 0.962153i | \(-0.412146\pi\) | ||||
0.272509 | + | 0.962153i | \(0.412146\pi\) | |||||||
\(338\) | −3.33831 | − | 5.78213i | −0.181580 | − | 0.314506i | ||||
\(339\) | 1.70407 | + | 0.983847i | 0.0925525 | + | 0.0534352i | ||||
\(340\) | −5.13197 | − | 0.287974i | −0.278320 | − | 0.0156176i | ||||
\(341\) | 6.71098 | − | 1.89083i | 0.363420 | − | 0.102394i | ||||
\(342\) | 18.8212 | 1.01774 | ||||||||
\(343\) | −12.1760 | + | 13.9551i | −0.657443 | + | 0.753504i | ||||
\(344\) | −2.99747 | −0.161613 | ||||||||
\(345\) | −1.05167 | + | 1.60640i | −0.0566198 | + | 0.0864855i | ||||
\(346\) | 1.41797 | + | 0.818664i | 0.0762304 | + | 0.0440116i | ||||
\(347\) | 11.3115 | − | 19.5921i | 0.607234 | − | 1.05176i | −0.384460 | − | 0.923142i | \(-0.625612\pi\) |
0.991694 | − | 0.128619i | \(-0.0410545\pi\) | |||||||
\(348\) | 0.892565 | − | 0.515323i | 0.0478465 | − | 0.0276242i | ||||
\(349\) | −5.52218 | −0.295596 | −0.147798 | − | 0.989018i | \(-0.547218\pi\) | ||||
−0.147798 | + | 0.989018i | \(0.547218\pi\) | |||||||
\(350\) | −4.55164 | + | 12.4211i | −0.243296 | + | 0.663933i | ||||
\(351\) | 2.26121i | 0.120694i | ||||||||
\(352\) | 0.899444 | + | 3.19233i | 0.0479405 | + | 0.170152i | ||||
\(353\) | 15.4786 | − | 26.8097i | 0.823843 | − | 1.42694i | −0.0789574 | − | 0.996878i | \(-0.525159\pi\) |
0.902800 | − | 0.430060i | \(-0.141508\pi\) | |||||||
\(354\) | −1.16591 | − | 0.673137i | −0.0619673 | − | 0.0357768i | ||||
\(355\) | 22.0683 | + | 14.4475i | 1.17126 | + | 0.766794i | ||||
\(356\) | 3.49207i | 0.185080i | ||||||||
\(357\) | 0.632128 | − | 0.661444i | 0.0334557 | − | 0.0350073i | ||||
\(358\) | 19.6321 | 1.03759 | ||||||||
\(359\) | −10.3087 | + | 5.95171i | −0.544070 | + | 0.314119i | −0.746727 | − | 0.665131i | \(-0.768376\pi\) |
0.202657 | + | 0.979250i | \(0.435042\pi\) | |||||||
\(360\) | 0.372996 | − | 6.64714i | 0.0196586 | − | 0.350335i | ||||
\(361\) | −10.4802 | + | 18.1523i | −0.551591 | + | 0.955384i | ||||
\(362\) | 2.92770 | − | 1.69031i | 0.153877 | − | 0.0888407i | ||||
\(363\) | −1.45387 | − | 0.790357i | −0.0763084 | − | 0.0414830i | ||||
\(364\) | 6.46376 | + | 1.57590i | 0.338793 | + | 0.0825996i | ||||
\(365\) | −13.4182 | − | 26.5771i | −0.702342 | − | 1.39111i | ||||
\(366\) | −0.778711 | − | 1.34877i | −0.0407039 | − | 0.0705012i | ||||
\(367\) | −1.17584 | + | 2.03662i | −0.0613785 | + | 0.106311i | −0.895082 | − | 0.445902i | \(-0.852883\pi\) |
0.833703 | + | 0.552213i | \(0.186216\pi\) | |||||||
\(368\) | −4.94308 | − | 2.85389i | −0.257676 | − | 0.148769i | ||||
\(369\) | −1.05712 | − | 1.83098i | −0.0550313 | − | 0.0953170i | ||||
\(370\) | 11.3991 | + | 22.5778i | 0.592609 | + | 1.17376i | ||||
\(371\) | −11.2256 | − | 2.73686i | −0.582804 | − | 0.142091i | ||||
\(372\) | 0.316252i | 0.0163969i | ||||||||
\(373\) | −1.20762 | − | 2.09166i | −0.0625284 | − | 0.108302i | 0.833067 | − | 0.553173i | \(-0.186583\pi\) |
−0.895595 | + | 0.444870i | \(0.853250\pi\) | |||||||
\(374\) | 5.45966 | + | 5.32131i | 0.282312 | + | 0.275158i | ||||
\(375\) | −1.29530 | − | 1.07290i | −0.0668890 | − | 0.0554045i | ||||
\(376\) | 3.34066 | + | 5.78618i | 0.172281 | + | 0.298400i | ||||
\(377\) | 17.2277 | 0.887273 | ||||||||
\(378\) | 1.71997 | + | 1.64374i | 0.0884657 | + | 0.0845448i | ||||
\(379\) | 21.8665 | 1.12321 | 0.561604 | − | 0.827406i | \(-0.310184\pi\) | ||||
0.561604 | + | 0.827406i | \(0.310184\pi\) | |||||||
\(380\) | 11.8262 | + | 7.74230i | 0.606671 | + | 0.397172i | ||||
\(381\) | −0.418674 | + | 0.725165i | −0.0214493 | + | 0.0371513i | ||||
\(382\) | −2.09173 | + | 3.62298i | −0.107022 | + | 0.185368i | ||||
\(383\) | 0.897916 | + | 1.55524i | 0.0458814 | + | 0.0794688i | 0.888054 | − | 0.459739i | \(-0.152057\pi\) |
−0.842173 | + | 0.539208i | \(0.818724\pi\) | |||||||
\(384\) | −0.150437 | −0.00767698 | ||||||||
\(385\) | 17.1908 | − | 9.45923i | 0.876123 | − | 0.482087i | ||||
\(386\) | 8.96683 | 0.456399 | ||||||||
\(387\) | −4.46228 | − | 7.72890i | −0.226830 | − | 0.392882i | ||||
\(388\) | 4.86923 | − | 8.43375i | 0.247198 | − | 0.428159i | ||||
\(389\) | −11.6237 | + | 20.1329i | −0.589346 | + | 1.02078i | 0.404972 | + | 0.914329i | \(0.367281\pi\) |
−0.994318 | + | 0.106448i | \(0.966052\pi\) | |||||||
\(390\) | −0.463324 | + | 0.707718i | −0.0234613 | + | 0.0358367i | ||||
\(391\) | −13.1205 | −0.663530 | ||||||||
\(392\) | 5.89739 | − | 3.77104i | 0.297863 | − | 0.190466i | ||||
\(393\) | 1.35022 | 0.0681097 | ||||||||
\(394\) | −9.68522 | − | 16.7753i | −0.487934 | − | 0.845127i | ||||
\(395\) | −18.8040 | − | 1.05516i | −0.946134 | − | 0.0530911i | ||||
\(396\) | −6.89237 | + | 7.07157i | −0.346355 | + | 0.355360i | ||||
\(397\) | −9.25277 | − | 16.0263i | −0.464383 | − | 0.804335i | 0.534790 | − | 0.844985i | \(-0.320391\pi\) |
−0.999173 | + | 0.0406495i | \(0.987057\pi\) | |||||||
\(398\) | − | 16.7051i | − | 0.837351i | ||||||
\(399\) | −2.41494 | + | 0.706100i | −0.120898 | + | 0.0353492i | ||||
\(400\) | 2.96874 | − | 4.02326i | 0.148437 | − | 0.201163i | ||||
\(401\) | −0.501146 | − | 0.868010i | −0.0250260 | − | 0.0433463i | 0.853241 | − | 0.521517i | \(-0.174634\pi\) |
−0.878267 | + | 0.478170i | \(0.841300\pi\) | |||||||
\(402\) | 1.02905 | + | 0.594124i | 0.0513245 | + | 0.0296322i | ||||
\(403\) | −2.64315 | + | 4.57807i | −0.131665 | + | 0.228050i | ||||
\(404\) | 9.39320 | + | 16.2695i | 0.467329 | + | 0.809438i | ||||
\(405\) | 17.5593 | − | 8.86531i | 0.872526 | − | 0.440521i | ||||
\(406\) | 12.5233 | − | 13.1041i | 0.621523 | − | 0.650348i | ||||
\(407\) | 9.24364 | − | 36.3577i | 0.458190 | − | 1.80218i | ||||
\(408\) | −0.299480 | + | 0.172905i | −0.0148265 | + | 0.00856008i | ||||
\(409\) | 19.4357 | − | 33.6637i | 0.961035 | − | 1.66456i | 0.241123 | − | 0.970494i | \(-0.422484\pi\) |
0.719911 | − | 0.694066i | \(-0.244182\pi\) | |||||||
\(410\) | 0.0889594 | − | 1.58534i | 0.00439339 | − | 0.0782944i | ||||
\(411\) | 0.842718 | − | 0.486543i | 0.0415682 | − | 0.0239994i | ||||
\(412\) | 4.62491 | 0.227853 | ||||||||
\(413\) | −23.0032 | − | 5.60831i | −1.13191 | − | 0.275967i | ||||
\(414\) | − | 16.9942i | − | 0.835217i | ||||||
\(415\) | 10.3002 | − | 15.7334i | 0.505619 | − | 0.772322i | ||||
\(416\) | −2.17773 | − | 1.25732i | −0.106772 | − | 0.0616450i | ||||
\(417\) | −1.13281 | + | 1.96209i | −0.0554742 | + | 0.0960841i | ||||
\(418\) | −5.68577 | − | 20.1801i | −0.278100 | − | 0.987042i | ||||
\(419\) | 3.06449i | 0.149710i | 0.997194 | + | 0.0748551i | \(0.0238494\pi\) | ||||
−0.997194 | + | 0.0748551i | \(0.976151\pi\) | |||||||
\(420\) | 0.201516 | + | 0.866886i | 0.00983299 | + | 0.0422997i | ||||
\(421\) | 1.36943 | 0.0667418 | 0.0333709 | − | 0.999443i | \(-0.489376\pi\) | ||||
0.0333709 | + | 0.999443i | \(0.489376\pi\) | |||||||
\(422\) | 16.0035 | − | 9.23964i | 0.779040 | − | 0.449779i | ||||
\(423\) | −9.94636 | + | 17.2276i | −0.483609 | + | 0.837635i | ||||
\(424\) | 3.78207 | + | 2.18358i | 0.183674 | + | 0.106044i | ||||
\(425\) | 1.28584 | − | 11.4213i | 0.0623723 | − | 0.554016i | ||||
\(426\) | 1.77457 | 0.0859783 | ||||||||
\(427\) | −19.8018 | − | 18.9242i | −0.958278 | − | 0.915806i | ||||
\(428\) | −7.42697 | −0.358996 | ||||||||
\(429\) | 1.20764 | − | 0.340255i | 0.0583056 | − | 0.0164277i | ||||
\(430\) | 0.375514 | − | 6.69201i | 0.0181089 | − | 0.322717i | ||||
\(431\) | 4.27542 | + | 2.46842i | 0.205940 | + | 0.118899i | 0.599423 | − | 0.800432i | \(-0.295397\pi\) |
−0.393483 | + | 0.919332i | \(0.628730\pi\) | |||||||
\(432\) | −0.449610 | − | 0.778747i | −0.0216319 | − | 0.0374675i | ||||
\(433\) | 21.0664 | 1.01239 | 0.506194 | − | 0.862420i | \(-0.331052\pi\) | ||||
0.506194 | + | 0.862420i | \(0.331052\pi\) | |||||||
\(434\) | 1.56089 | + | 5.33843i | 0.0749252 | + | 0.256253i | ||||
\(435\) | 1.03867 | + | 2.05726i | 0.0498004 | + | 0.0986381i | ||||
\(436\) | −0.976031 | + | 0.563512i | −0.0467434 | + | 0.0269873i | ||||
\(437\) | 31.2473 | + | 18.0407i | 1.49476 | + | 0.863002i | ||||
\(438\) | −1.73466 | − | 1.00151i | −0.0828852 | − | 0.0478538i | ||||
\(439\) | 0.332519 | + | 0.575940i | 0.0158703 | + | 0.0274881i | 0.873851 | − | 0.486193i | \(-0.161615\pi\) |
−0.857981 | + | 0.513681i | \(0.828281\pi\) | |||||||
\(440\) | −7.23975 | + | 1.60813i | −0.345141 | + | 0.0766647i | ||||
\(441\) | 18.5029 | + | 9.59241i | 0.881090 | + | 0.456781i | ||||
\(442\) | −5.78038 | −0.274945 | ||||||||
\(443\) | 11.1850 | − | 6.45766i | 0.531415 | − | 0.306813i | −0.210177 | − | 0.977663i | \(-0.567404\pi\) |
0.741592 | + | 0.670851i | \(0.234071\pi\) | |||||||
\(444\) | 1.47363 | + | 0.850799i | 0.0699353 | + | 0.0403771i | ||||
\(445\) | −7.79625 | − | 0.437477i | −0.369578 | − | 0.0207384i | ||||
\(446\) | 4.08216 | + | 7.07050i | 0.193296 | + | 0.334798i | ||||
\(447\) | − | 1.89325i | − | 0.0895476i | ||||||
\(448\) | −2.53943 | + | 0.742498i | −0.119977 | + | 0.0350797i | ||||
\(449\) | 5.67095 | 0.267629 | 0.133814 | − | 0.991006i | \(-0.457277\pi\) | ||||
0.133814 | + | 0.991006i | \(0.457277\pi\) | |||||||
\(450\) | 14.7934 | + | 1.66547i | 0.697367 | + | 0.0785109i | ||||
\(451\) | −1.64383 | + | 1.68657i | −0.0774049 | + | 0.0794174i | ||||
\(452\) | −11.3275 | − | 6.53991i | −0.532799 | − | 0.307611i | ||||
\(453\) | −2.32696 | + | 1.34347i | −0.109330 | + | 0.0631218i | ||||
\(454\) | 29.2572i | 1.37311i | ||||||||
\(455\) | −4.32804 | + | 14.2333i | −0.202902 | + | 0.667266i | ||||
\(456\) | 0.950979 | 0.0445337 | ||||||||
\(457\) | 7.46931 | + | 12.9372i | 0.349400 | + | 0.605178i | 0.986143 | − | 0.165898i | \(-0.0530523\pi\) |
−0.636743 | + | 0.771076i | \(0.719719\pi\) | |||||||
\(458\) | −6.32273 | − | 3.65043i | −0.295442 | − | 0.170573i | ||||
\(459\) | −1.79011 | − | 1.03352i | −0.0835550 | − | 0.0482405i | ||||
\(460\) | 6.99072 | − | 10.6782i | 0.325944 | − | 0.497873i | ||||
\(461\) | −25.3833 | −1.18222 | −0.591108 | − | 0.806592i | \(-0.701309\pi\) | ||||
−0.591108 | + | 0.806592i | \(0.701309\pi\) | |||||||
\(462\) | 0.619059 | − | 1.16593i | 0.0288012 | − | 0.0542438i | ||||
\(463\) | − | 1.50092i | − | 0.0697538i | −0.999392 | − | 0.0348769i | \(-0.988896\pi\) | ||
0.999392 | − | 0.0348769i | \(-0.0111039\pi\) | |||||||
\(464\) | −5.93313 | + | 3.42550i | −0.275439 | + | 0.159025i | ||||
\(465\) | −0.706050 | − | 0.0396191i | −0.0327423 | − | 0.00183729i | ||||
\(466\) | 9.93050 | − | 17.2001i | 0.460022 | − | 0.796781i | ||||
\(467\) | 19.9490 | + | 34.5527i | 0.923130 | + | 1.59891i | 0.794541 | + | 0.607210i | \(0.207711\pi\) |
0.128588 | + | 0.991698i | \(0.458955\pi\) | |||||||
\(468\) | − | 7.48698i | − | 0.346086i | ||||||
\(469\) | 20.3031 | + | 4.95001i | 0.937509 | + | 0.228570i | ||||
\(470\) | −13.3365 | + | 6.73332i | −0.615166 | + | 0.310585i | ||||
\(471\) | 1.62423 | + | 2.81324i | 0.0748404 | + | 0.129627i | ||||
\(472\) | 7.75012 | + | 4.47453i | 0.356728 | + | 0.205957i | ||||
\(473\) | −6.93890 | + | 7.11931i | −0.319051 | + | 0.327346i | ||||
\(474\) | −1.09732 | + | 0.633541i | −0.0504018 | + | 0.0290995i | ||||
\(475\) | −18.7667 | + | 25.4327i | −0.861074 | + | 1.16693i | ||||
\(476\) | −4.20193 | + | 4.39680i | −0.192595 | + | 0.201527i | ||||
\(477\) | 13.0026i | 0.595350i | ||||||||
\(478\) | −18.6540 | + | 10.7699i | −0.853215 | + | 0.492604i | ||||
\(479\) | 0.799999 | − | 1.38564i | 0.0365529 | − | 0.0633114i | −0.847170 | − | 0.531322i | \(-0.821696\pi\) |
0.883723 | + | 0.468010i | \(0.155029\pi\) | |||||||
\(480\) | 0.0188464 | − | 0.335860i | 0.000860215 | − | 0.0153298i | ||||
\(481\) | 14.2215 | + | 24.6324i | 0.648445 | + | 1.12314i | ||||
\(482\) | 0.705232 | 0.0321224 | ||||||||
\(483\) | 0.637556 | + | 2.18051i | 0.0290098 | + | 0.0992168i | ||||
\(484\) | 9.66428 | + | 5.25372i | 0.439286 | + | 0.238806i | ||||
\(485\) | 18.2188 | + | 11.9274i | 0.827274 | + | 0.541594i | ||||
\(486\) | 2.01052 | − | 3.48232i | 0.0911989 | − | 0.157961i | ||||
\(487\) | −1.38080 | − | 0.797207i | −0.0625702 | − | 0.0361249i | 0.468389 | − | 0.883523i | \(-0.344835\pi\) |
−0.530959 | + | 0.847398i | \(0.678168\pi\) | |||||||
\(488\) | 5.17631 | + | 8.96564i | 0.234321 | + | 0.405855i | ||||
\(489\) | − | 0.189436i | − | 0.00856661i | ||||||
\(490\) | 7.68025 | + | 13.6387i | 0.346958 | + | 0.616133i | ||||
\(491\) | − | 12.5303i | − | 0.565484i | −0.959196 | − | 0.282742i | \(-0.908756\pi\) | ||
0.959196 | − | 0.282742i | \(-0.0912441\pi\) | |||||||
\(492\) | −0.0534129 | − | 0.0925139i | −0.00240804 | − | 0.00417085i | ||||
\(493\) | −7.87418 | + | 13.6385i | −0.354635 | + | 0.614247i | ||||
\(494\) | 13.7664 | + | 7.94803i | 0.619379 | + | 0.357599i | ||||
\(495\) | −14.9242 | − | 16.2735i | −0.670794 | − | 0.731440i | ||||
\(496\) | − | 2.10222i | − | 0.0943923i | ||||||
\(497\) | 29.9553 | − | 8.75857i | 1.34368 | − | 0.392875i | ||||
\(498\) | − | 1.26517i | − | 0.0566936i | ||||||
\(499\) | −1.40578 | − | 2.43488i | −0.0629314 | − | 0.109000i | 0.832843 | − | 0.553509i | \(-0.186712\pi\) |
−0.895775 | + | 0.444509i | \(0.853378\pi\) | |||||||
\(500\) | 8.61023 | + | 7.13190i | 0.385061 | + | 0.318948i | ||||
\(501\) | −0.748762 | − | 0.432298i | −0.0334522 | − | 0.0193137i | ||||
\(502\) | 3.35871 | − | 1.93915i | 0.149907 | − | 0.0865486i | ||||
\(503\) | − | 33.6599i | − | 1.50082i | −0.660971 | − | 0.750411i | \(-0.729855\pi\) | ||
0.660971 | − | 0.750411i | \(-0.270145\pi\) | |||||||
\(504\) | −5.69492 | − | 5.44251i | −0.253672 | − | 0.242429i | ||||
\(505\) | −37.4993 | + | 18.9326i | −1.66870 | + | 0.842492i | ||||
\(506\) | −18.2211 | + | 5.13383i | −0.810028 | + | 0.228226i | ||||
\(507\) | 0.502207 | − | 0.869849i | 0.0223038 | − | 0.0386313i | ||||
\(508\) | 2.78304 | − | 4.82037i | 0.123478 | − | 0.213870i | ||||
\(509\) | −37.2991 | + | 21.5346i | −1.65325 | + | 0.954505i | −0.677528 | + | 0.735497i | \(0.736949\pi\) |
−0.975723 | + | 0.219008i | \(0.929718\pi\) | |||||||
\(510\) | −0.348502 | − | 0.690268i | −0.0154319 | − | 0.0305656i | ||||
\(511\) | −34.2246 | − | 8.34415i | −1.51401 | − | 0.369123i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.84218 | + | 4.92280i | 0.125485 | + | 0.217347i | ||||
\(514\) | −9.94552 | + | 17.2261i | −0.438678 | + | 0.759812i | ||||
\(515\) | −0.579395 | + | 10.3254i | −0.0255312 | + | 0.454990i | ||||
\(516\) | −0.225466 | − | 0.390518i | −0.00992557 | − | 0.0171916i | ||||
\(517\) | 21.4762 | + | 5.46014i | 0.944521 | + | 0.240137i | ||||
\(518\) | 29.0745 | + | 7.08852i | 1.27746 | + | 0.311452i | ||||
\(519\) | 0.246315i | 0.0108120i | ||||||||
\(520\) | 3.07985 | − | 4.70440i | 0.135060 | − | 0.206302i | ||||
\(521\) | −11.7930 | − | 6.80870i | −0.516661 | − | 0.298295i | 0.218906 | − | 0.975746i | \(-0.429751\pi\) |
−0.735568 | + | 0.677451i | \(0.763084\pi\) | |||||||
\(522\) | −17.6651 | − | 10.1990i | −0.773182 | − | 0.446397i | ||||
\(523\) | −8.25059 | + | 4.76348i | −0.360773 | + | 0.208293i | −0.669420 | − | 0.742884i | \(-0.733457\pi\) |
0.308647 | + | 0.951177i | \(0.400124\pi\) | |||||||
\(524\) | −8.97531 | −0.392088 | ||||||||
\(525\) | −1.96062 | + | 0.341295i | −0.0855683 | + | 0.0148954i | ||||
\(526\) | 17.9091 | 0.780874 | ||||||||
\(527\) | −2.41618 | − | 4.18495i | −0.105251 | − | 0.182299i | ||||
\(528\) | −0.348251 | + | 0.357305i | −0.0151557 | + | 0.0155497i | ||||
\(529\) | 4.78937 | − | 8.29543i | 0.208233 | − | 0.360671i | ||||
\(530\) | −5.34877 | + | 8.17013i | −0.232336 | + | 0.354888i | ||||
\(531\) | 26.6447i | 1.15628i | ||||||||
\(532\) | 16.0528 | − | 4.69365i | 0.695978 | − | 0.203495i | ||||
\(533\) | − | 1.78564i | − | 0.0773448i | ||||||
\(534\) | −0.454957 | + | 0.262669i | −0.0196879 | + | 0.0113668i | ||||
\(535\) | 0.930429 | − | 16.5811i | 0.0402260 | − | 0.716865i | ||||
\(536\) | −6.84041 | − | 3.94931i | −0.295461 | − | 0.170584i | ||||
\(537\) | 1.47670 | + | 2.55772i | 0.0637243 | + | 0.110374i | ||||
\(538\) | − | 9.81133i | − | 0.422997i | ||||||
\(539\) | 4.69537 | − | 22.7366i | 0.202244 | − | 0.979335i | ||||
\(540\) | 1.79492 | − | 0.906220i | 0.0772412 | − | 0.0389975i | ||||
\(541\) | 12.8688 | − | 7.42981i | 0.553273 | − | 0.319433i | −0.197168 | − | 0.980370i | \(-0.563174\pi\) |
0.750441 | + | 0.660937i | \(0.229841\pi\) | |||||||
\(542\) | −7.77154 | + | 13.4607i | −0.333816 | + | 0.578187i | ||||
\(543\) | 0.440436 | + | 0.254286i | 0.0189009 | + | 0.0109124i | ||||
\(544\) | 1.99073 | − | 1.14935i | 0.0853519 | − | 0.0492779i | ||||
\(545\) | −1.13580 | − | 2.24964i | −0.0486522 | − | 0.0963639i | ||||
\(546\) | 0.280883 | + | 0.960652i | 0.0120207 | + | 0.0411121i | ||||
\(547\) | −26.3597 | −1.12706 | −0.563530 | − | 0.826096i | \(-0.690557\pi\) | ||||
−0.563530 | + | 0.826096i | \(0.690557\pi\) | |||||||
\(548\) | −5.60178 | + | 3.23419i | −0.239296 | + | 0.138158i | ||||
\(549\) | −15.4118 | + | 26.6940i | −0.657759 | + | 1.13927i | ||||
\(550\) | −2.68327 | − | 16.3646i | −0.114415 | − | 0.697789i | ||||
\(551\) | 37.5059 | − | 21.6540i | 1.59780 | − | 0.922493i | ||||
\(552\) | − | 0.858663i | − | 0.0365471i | ||||||
\(553\) | −15.3963 | + | 16.1103i | −0.654716 | + | 0.685080i | ||||
\(554\) | −28.6061 | −1.21536 | ||||||||
\(555\) | −2.08407 | + | 3.18337i | −0.0884638 | + | 0.135127i | ||||
\(556\) | 7.53014 | − | 13.0426i | 0.319349 | − | 0.553129i | ||||
\(557\) | 0.427951 | − | 0.741233i | 0.0181329 | − | 0.0314070i | −0.856817 | − | 0.515621i | \(-0.827561\pi\) |
0.874949 | + | 0.484214i | \(0.160894\pi\) | |||||||
\(558\) | 5.42052 | − | 3.12954i | 0.229469 | − | 0.132484i | ||||
\(559\) | − | 7.53752i | − | 0.318803i | ||||||
\(560\) | −1.33954 | − | 5.76243i | −0.0566057 | − | 0.243507i | ||||
\(561\) | −0.282605 | + | 1.11156i | −0.0119316 | + | 0.0469301i | ||||
\(562\) | −25.1035 | + | 14.4935i | −1.05893 | + | 0.611371i | ||||
\(563\) | 13.2721 | + | 7.66263i | 0.559351 | + | 0.322941i | 0.752885 | − | 0.658152i | \(-0.228662\pi\) |
−0.193534 | + | 0.981094i | \(0.561995\pi\) | |||||||
\(564\) | −0.502559 | + | 0.870459i | −0.0211616 | + | 0.0366529i | ||||
\(565\) | 16.0198 | − | 24.4699i | 0.673957 | − | 1.02946i | ||||
\(566\) | − | 17.4704i | − | 0.734334i | ||||||
\(567\) | 5.51290 | − | 22.6119i | 0.231520 | − | 0.949610i | ||||
\(568\) | −11.7961 | −0.494953 | ||||||||
\(569\) | −5.29602 | + | 3.05766i | −0.222021 | + | 0.128184i | −0.606886 | − | 0.794789i | \(-0.707581\pi\) |
0.384865 | + | 0.922973i | \(0.374248\pi\) | |||||||
\(570\) | −0.119136 | + | 2.12311i | −0.00499005 | + | 0.0889275i | ||||
\(571\) | 0.258367 | + | 0.149168i | 0.0108123 | + | 0.00624250i | 0.505396 | − | 0.862887i | \(-0.331346\pi\) |
−0.494584 | + | 0.869130i | \(0.664680\pi\) | |||||||
\(572\) | −8.02754 | + | 2.26177i | −0.335648 | + | 0.0945694i | ||||
\(573\) | −0.629348 | −0.0262914 | ||||||||
\(574\) | −1.35824 | − | 1.29804i | −0.0566917 | − | 0.0541790i | ||||
\(575\) | 22.9639 | + | 16.9449i | 0.957659 | + | 0.706651i | ||||
\(576\) | 1.48868 | + | 2.57848i | 0.0620285 | + | 0.107437i | ||||
\(577\) | 6.51423 | − | 11.2830i | 0.271191 | − | 0.469716i | −0.697976 | − | 0.716121i | \(-0.745916\pi\) |
0.969167 | + | 0.246405i | \(0.0792492\pi\) | |||||||
\(578\) | −5.85799 | + | 10.1463i | −0.243660 | + | 0.422032i | ||||
\(579\) | 0.674473 | + | 1.16822i | 0.0280301 | + | 0.0485496i | ||||
\(580\) | −6.90433 | − | 13.6752i | −0.286687 | − | 0.567831i | ||||
\(581\) | −6.24436 | − | 21.3564i | −0.259060 | − | 0.886014i | ||||
\(582\) | 1.46503 | 0.0607274 | ||||||||
\(583\) | 13.9414 | − | 3.92802i | 0.577395 | − | 0.162682i | ||||
\(584\) | 11.5308 | + | 6.65729i | 0.477147 | + | 0.275481i | ||||
\(585\) | 16.7151 | + | 0.937947i | 0.691085 | + | 0.0387793i | ||||
\(586\) | 0.552159 | − | 0.318789i | 0.0228095 | − | 0.0131691i | ||||
\(587\) | −12.5469 | −0.517865 | −0.258933 | − | 0.965895i | \(-0.583371\pi\) | ||||
−0.258933 | + | 0.965895i | \(0.583371\pi\) | |||||||
\(588\) | 0.934895 | + | 0.484675i | 0.0385544 | + | 0.0199877i | ||||
\(589\) | 13.2890i | 0.547564i | ||||||||
\(590\) | −10.9606 | + | 16.7420i | −0.451239 | + | 0.689258i | ||||
\(591\) | 1.45702 | − | 2.52363i | 0.0599338 | − | 0.103808i | ||||
\(592\) | −9.79562 | − | 5.65550i | −0.402597 | − | 0.232440i | ||||
\(593\) | −3.60727 | + | 2.08266i | −0.148133 | + | 0.0855244i | −0.572234 | − | 0.820090i | \(-0.693923\pi\) |
0.424102 | + | 0.905615i | \(0.360590\pi\) | |||||||
\(594\) | −2.89042 | − | 0.734866i | −0.118595 | − | 0.0301519i | ||||
\(595\) | −9.28971 | − | 9.93186i | −0.380841 | − | 0.407167i | ||||
\(596\) | 12.5850i | 0.515500i | ||||||||
\(597\) | 2.17638 | − | 1.25654i | 0.0890735 | − | 0.0514266i | ||||
\(598\) | 7.17648 | − | 12.4300i | 0.293468 | − | 0.508302i | ||||
\(599\) | 1.73769 | − | 3.00977i | 0.0710001 | − | 0.122976i | −0.828340 | − | 0.560226i | \(-0.810714\pi\) |
0.899340 | + | 0.437250i | \(0.144048\pi\) | |||||||
\(600\) | 0.747465 | + | 0.0841511i | 0.0305151 | + | 0.00343545i | ||||
\(601\) | 16.4938 | 0.672798 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(602\) | −5.73336 | − | 5.47925i | −0.233674 | − | 0.223318i | ||||
\(603\) | − | 23.5171i | − | 0.957691i | ||||||
\(604\) | 15.4680 | − | 8.93044i | 0.629383 | − | 0.363374i | ||||
\(605\) | −12.9399 | + | 20.9179i | −0.526084 | + | 0.850433i | ||||
\(606\) | −1.41309 | + | 2.44754i | −0.0574028 | + | 0.0994245i | ||||
\(607\) | −2.49553 | + | 1.44079i | −0.101290 | + | 0.0584800i | −0.549789 | − | 0.835303i | \(-0.685292\pi\) |
0.448499 | + | 0.893783i | \(0.351959\pi\) | |||||||
\(608\) | −6.32143 | −0.256368 | ||||||||
\(609\) | 2.64923 | + | 0.645898i | 0.107352 | + | 0.0261731i | ||||
\(610\) | −20.6648 | + | 10.4332i | −0.836692 | + | 0.422429i | ||||
\(611\) | −14.5501 | + | 8.40052i | −0.588635 | + | 0.339848i | ||||
\(612\) | 5.92714 | + | 3.42204i | 0.239590 | + | 0.138328i | ||||
\(613\) | −18.5685 | + | 32.1616i | −0.749974 | + | 1.29899i | 0.197861 | + | 0.980230i | \(0.436601\pi\) |
−0.947835 | + | 0.318763i | \(0.896733\pi\) | |||||||
\(614\) | −15.4906 | + | 8.94353i | −0.625152 | + | 0.360931i | ||||
\(615\) | 0.213234 | − | 0.107657i | 0.00859842 | − | 0.00434117i | ||||
\(616\) | −4.11506 | + | 7.75024i | −0.165801 | + | 0.312266i | ||||
\(617\) | − | 26.7017i | − | 1.07497i | −0.843274 | − | 0.537484i | \(-0.819375\pi\) | ||
0.843274 | − | 0.537484i | \(-0.180625\pi\) | |||||||
\(618\) | 0.347880 | + | 0.602545i | 0.0139938 | + | 0.0242379i | ||||
\(619\) | −27.9452 | − | 16.1342i | −1.12321 | − | 0.648488i | −0.180994 | − | 0.983484i | \(-0.557932\pi\) |
−0.942219 | + | 0.334996i | \(0.891265\pi\) | |||||||
\(620\) | 4.69332 | + | 0.263360i | 0.188488 | + | 0.0105768i | ||||
\(621\) | 4.44492 | − | 2.56627i | 0.178368 | − | 0.102981i | ||||
\(622\) | 21.9414i | 0.879770i | ||||||||
\(623\) | −6.38337 | + | 6.67942i | −0.255744 | + | 0.267605i | ||||
\(624\) | − | 0.378295i | − | 0.0151439i | ||||||
\(625\) | −17.0010 | + | 18.3294i | −0.680041 | + | 0.733174i | ||||
\(626\) | −0.686648 | + | 1.18931i | −0.0274440 | + | 0.0475344i | ||||
\(627\) | 2.20144 | − | 2.25868i | 0.0879171 | − | 0.0902030i | ||||
\(628\) | −10.7967 | − | 18.7004i | −0.430835 | − | 0.746228i | ||||
\(629\) | −26.0006 | −1.03671 | ||||||||
\(630\) | 12.8642 | − | 12.0324i | 0.512520 | − | 0.479383i | ||||
\(631\) | −3.18917 | −0.126959 | −0.0634793 | − | 0.997983i | \(-0.520220\pi\) | ||||
−0.0634793 | + | 0.997983i | \(0.520220\pi\) | |||||||
\(632\) | 7.29423 | − | 4.21133i | 0.290149 | − | 0.167518i | ||||
\(633\) | 2.40753 | + | 1.38999i | 0.0956907 | + | 0.0552471i | ||||
\(634\) | −3.93592 | − | 2.27240i | −0.156315 | − | 0.0902487i | ||||
\(635\) | 10.4131 | + | 6.81718i | 0.413231 | + | 0.270532i | ||||
\(636\) | 0.656984i | 0.0260511i | ||||||||
\(637\) | 9.48278 | + | 14.8298i | 0.375721 | + | 0.587577i | ||||
\(638\) | −5.59881 | + | 22.0216i | −0.221659 | + | 0.871843i | ||||
\(639\) | −17.5606 | − | 30.4159i | −0.694688 | − | 1.20324i | ||||
\(640\) | −0.125277 | + | 2.23256i | −0.00495201 | + | 0.0882495i | ||||
\(641\) | 19.0098 | − | 32.9259i | 0.750842 | − | 1.30050i | −0.196573 | − | 0.980489i | \(-0.562981\pi\) |
0.947415 | − | 0.320007i | \(-0.103685\pi\) | |||||||
\(642\) | −0.558647 | − | 0.967605i | −0.0220480 | − | 0.0381883i | ||||
\(643\) | −12.9770 | −0.511762 | −0.255881 | − | 0.966708i | \(-0.582365\pi\) | ||||
−0.255881 | + | 0.966708i | \(0.582365\pi\) | |||||||
\(644\) | −4.23801 | − | 14.4945i | −0.167001 | − | 0.571163i | ||||
\(645\) | 0.900098 | − | 0.454441i | 0.0354413 | − | 0.0178936i | ||||
\(646\) | −12.5843 | + | 7.26553i | −0.495121 | + | 0.285858i | ||||
\(647\) | −13.7688 | + | 23.8482i | −0.541307 | + | 0.937571i | 0.457523 | + | 0.889198i | \(0.348737\pi\) |
−0.998829 | + | 0.0483728i | \(0.984596\pi\) | |||||||
\(648\) | −4.39841 | + | 7.61828i | −0.172786 | + | 0.299274i | ||||
\(649\) | 28.5684 | − | 8.04919i | 1.12141 | − | 0.315958i | ||||
\(650\) | 10.1170 | + | 7.46529i | 0.396822 | + | 0.292813i | ||||
\(651\) | −0.578096 | + | 0.604907i | −0.0226574 | + | 0.0237082i | ||||
\(652\) | 1.25924i | 0.0493155i | ||||||||
\(653\) | −29.3260 | + | 16.9314i | −1.14762 | + | 0.662577i | −0.948305 | − | 0.317359i | \(-0.897204\pi\) |
−0.199312 | + | 0.979936i | \(0.563871\pi\) | |||||||
\(654\) | −0.146832 | − | 0.0847732i | −0.00574157 | − | 0.00331490i | ||||
\(655\) | 1.12440 | − | 20.0379i | 0.0439339 | − | 0.782945i | ||||
\(656\) | 0.355051 | + | 0.614966i | 0.0138624 | + | 0.0240104i | ||||
\(657\) | 39.6424i | 1.54660i | ||||||||
\(658\) | −4.18713 | + | 17.1740i | −0.163231 | + | 0.669513i | ||||
\(659\) | 34.5640i | 1.34642i | 0.739450 | + | 0.673211i | \(0.235086\pi\) | ||||
−0.739450 | + | 0.673211i | \(0.764914\pi\) | |||||||
\(660\) | −0.754076 | − | 0.822251i | −0.0293524 | − | 0.0320061i | ||||
\(661\) | −1.63580 | − | 0.944428i | −0.0636252 | − | 0.0367340i | 0.467850 | − | 0.883808i | \(-0.345029\pi\) |
−0.531475 | + | 0.847074i | \(0.678362\pi\) | |||||||
\(662\) | 8.20177 | − | 14.2059i | 0.318771 | − | 0.552127i | ||||
\(663\) | −0.434793 | − | 0.753083i | −0.0168859 | − | 0.0292473i | ||||
\(664\) | 8.40993i | 0.326369i | ||||||||
\(665\) | 8.46778 | + | 36.4268i | 0.328366 | + | 1.41257i | ||||
\(666\) | − | 33.6770i | − | 1.30496i | ||||||
\(667\) | −19.5520 | − | 33.8650i | −0.757056 | − | 1.31126i | ||||
\(668\) | 4.97724 | + | 2.87361i | 0.192575 | + | 0.111183i | ||||
\(669\) | −0.614109 | + | 1.06367i | −0.0237428 | + | 0.0411238i | ||||
\(670\) | 9.67400 | − | 14.7768i | 0.373739 | − | 0.570879i | ||||
\(671\) | 33.2771 | + | 8.46043i | 1.28465 | + | 0.326611i | ||||
\(672\) | −0.287747 | − | 0.274994i | −0.0111001 | − | 0.0106081i | ||||
\(673\) | 5.08760 | 0.196113 | 0.0980563 | − | 0.995181i | \(-0.468737\pi\) | ||||
0.0980563 | + | 0.995181i | \(0.468737\pi\) | |||||||
\(674\) | −5.00261 | − | 8.66477i | −0.192693 | − | 0.333754i | ||||
\(675\) | 1.79832 | + | 4.12079i | 0.0692175 | + | 0.158609i | ||||
\(676\) | −3.33831 | + | 5.78213i | −0.128397 | + | 0.222390i | ||||
\(677\) | 3.07608 | − | 1.77597i | 0.118223 | − | 0.0682562i | −0.439722 | − | 0.898134i | \(-0.644923\pi\) |
0.557946 | + | 0.829878i | \(0.311590\pi\) | |||||||
\(678\) | − | 1.96769i | − | 0.0755688i | ||||||
\(679\) | 24.7301 | − | 7.23078i | 0.949055 | − | 0.277492i | ||||
\(680\) | 2.31659 | + | 4.58841i | 0.0888373 | + | 0.175957i | ||||
\(681\) | −3.81170 | + | 2.20069i | −0.146065 | + | 0.0843305i | ||||
\(682\) | −4.99299 | − | 4.86647i | −0.191192 | − | 0.186347i | ||||
\(683\) | −7.34303 | − | 4.23950i | −0.280973 | − | 0.162220i | 0.352891 | − | 0.935665i | \(-0.385199\pi\) |
−0.633864 | + | 0.773445i | \(0.718532\pi\) | |||||||
\(684\) | −9.41061 | − | 16.2997i | −0.359824 | − | 0.623233i | ||||
\(685\) | −6.51874 | − | 12.9115i | −0.249068 | − | 0.493322i | ||||
\(686\) | 18.1735 | + | 3.56720i | 0.693866 | + | 0.136196i | ||||
\(687\) | − | 1.09832i | − | 0.0419036i | ||||||
\(688\) | 1.49873 | + | 2.59588i | 0.0571387 | + | 0.0989671i | ||||
\(689\) | −5.49090 | + | 9.51051i | −0.209186 | + | 0.362322i | ||||
\(690\) | 1.91701 | + | 0.107571i | 0.0729795 | + | 0.00409515i | ||||
\(691\) | 12.5036 | − | 7.21898i | 0.475661 | − | 0.274623i | −0.242945 | − | 0.970040i | \(-0.578114\pi\) |
0.718607 | + | 0.695417i | \(0.244780\pi\) | |||||||
\(692\) | − | 1.63733i | − | 0.0622418i | ||||||
\(693\) | −26.1098 | + | 0.927071i | −0.991831 | + | 0.0352165i | ||||
\(694\) | −22.6230 | −0.858759 | ||||||||
\(695\) | 28.1749 | + | 18.4454i | 1.06874 | + | 0.699674i | ||||
\(696\) | −0.892565 | − | 0.515323i | −0.0338326 | − | 0.0195333i | ||||
\(697\) | 1.41362 | + | 0.816155i | 0.0535447 | + | 0.0309141i | ||||
\(698\) | 2.76109 | + | 4.78235i | 0.104509 | + | 0.181015i | ||||
\(699\) | 2.98784 | 0.113010 | ||||||||
\(700\) | 13.0328 | − | 2.26869i | 0.492592 | − | 0.0857483i | ||||
\(701\) | 17.2789i | 0.652617i | 0.945263 | + | 0.326308i | \(0.105805\pi\) | ||||
−0.945263 | + | 0.326308i | \(0.894195\pi\) | |||||||
\(702\) | 1.95826 | − | 1.13060i | 0.0739098 | − | 0.0426719i | ||||
\(703\) | 61.9223 | + | 35.7509i | 2.33544 | + | 1.34837i | ||||
\(704\) | 2.31492 | − | 2.37511i | 0.0872469 | − | 0.0895153i | ||||
\(705\) | −1.88039 | − | 1.23104i | −0.0708195 | − | 0.0463637i | ||||
\(706\) | −30.9572 | −1.16509 | ||||||||
\(707\) | −11.7733 | + | 48.2896i | −0.442780 | + | 1.81612i | ||||
\(708\) | 1.34627i | 0.0505961i | ||||||||
\(709\) | −21.2909 | − | 36.8769i | −0.799597 | − | 1.38494i | −0.919879 | − | 0.392202i | \(-0.871713\pi\) |
0.120282 | − | 0.992740i | \(-0.461620\pi\) | |||||||
\(710\) | 1.47778 | − | 26.3354i | 0.0554600 | − | 0.988351i | ||||
\(711\) | 21.7176 | + | 12.5387i | 0.814474 | + | 0.470237i | ||||
\(712\) | 3.02422 | − | 1.74604i | 0.113338 | − | 0.0654355i | ||||
\(713\) | 11.9990 | 0.449366 | ||||||||
\(714\) | −0.888891 | − | 0.216717i | −0.0332659 | − | 0.00811042i | ||||
\(715\) | −4.04386 | − | 18.2053i | −0.151232 | − | 0.680839i | ||||
\(716\) | −9.81605 | − | 17.0019i | −0.366843 | − | 0.635391i | ||||
\(717\) | −2.80626 | − | 1.62020i | −0.104802 | − | 0.0605073i | ||||
\(718\) | 10.3087 | + | 5.95171i | 0.384716 | + | 0.222116i | ||||
\(719\) | −42.3616 | + | 24.4575i | −1.57982 | + | 0.912109i | −0.584937 | + | 0.811079i | \(0.698881\pi\) |
−0.994883 | + | 0.101030i | \(0.967786\pi\) | |||||||
\(720\) | −5.94309 | + | 3.00055i | −0.221486 | + | 0.111824i | ||||
\(721\) | 8.84623 | + | 8.45415i | 0.329451 | + | 0.314849i | ||||
\(722\) | 20.9605 | 0.780068 | ||||||||
\(723\) | 0.0530466 | + | 0.0918795i | 0.00197283 | + | 0.00341703i | ||||
\(724\) | −2.92770 | − | 1.69031i | −0.108807 | − | 0.0628199i | ||||
\(725\) | 31.3956 | − | 13.7011i | 1.16600 | − | 0.508846i | ||||
\(726\) | 0.0424661 | + | 1.65427i | 0.00157606 | + | 0.0613956i | ||||
\(727\) | −15.2692 | −0.566303 | −0.283151 | − | 0.959075i | \(-0.591380\pi\) | ||||
−0.283151 | + | 0.959075i | \(0.591380\pi\) | |||||||
\(728\) | −1.86711 | − | 6.38573i | −0.0691996 | − | 0.236671i | ||||
\(729\) | −25.7856 | −0.955021 | ||||||||
\(730\) | −16.3073 | + | 24.9091i | −0.603561 | + | 0.921926i | ||||
\(731\) | 5.96715 | + | 3.44514i | 0.220703 | + | 0.127423i | ||||
\(732\) | −0.778711 | + | 1.34877i | −0.0287820 | + | 0.0498519i | ||||
\(733\) | 19.4734 | − | 11.2430i | 0.719266 | − | 0.415269i | −0.0952162 | − | 0.995457i | \(-0.530354\pi\) |
0.814483 | + | 0.580188i | \(0.197021\pi\) | |||||||
\(734\) | 2.35169 | 0.0868024 | ||||||||
\(735\) | −1.19919 | + | 2.02649i | −0.0442326 | + | 0.0747481i | ||||
\(736\) | 5.70778i | 0.210391i | ||||||||
\(737\) | −25.2150 | + | 7.10437i | −0.928808 | + | 0.261693i | ||||
\(738\) | −1.05712 | + | 1.83098i | −0.0389130 | + | 0.0673993i | ||||
\(739\) | 29.6892 | + | 17.1411i | 1.09213 | + | 0.630544i | 0.934144 | − | 0.356897i | \(-0.116165\pi\) |
0.157990 | + | 0.987441i | \(0.449499\pi\) | |||||||
\(740\) | 13.8534 | − | 21.1608i | 0.509261 | − | 0.777885i | ||||
\(741\) | 2.39136i | 0.0878489i | ||||||||
\(742\) | 3.24261 | + | 11.0901i | 0.119040 | + | 0.407130i | ||||
\(743\) | 15.1161 | 0.554555 | 0.277277 | − | 0.960790i | \(-0.410568\pi\) | ||||
0.277277 | + | 0.960790i | \(0.410568\pi\) | |||||||
\(744\) | 0.273882 | − | 0.158126i | 0.0100410 | − | 0.00579718i | ||||
\(745\) | −28.0966 | − | 1.57661i | −1.02938 | − | 0.0577624i | ||||
\(746\) | −1.20762 | + | 2.09166i | −0.0442142 | + | 0.0765813i | ||||
\(747\) | −21.6848 | + | 12.5197i | −0.793406 | + | 0.458073i | ||||
\(748\) | 1.87856 | − | 7.38886i | 0.0686868 | − | 0.270163i | ||||
\(749\) | −14.2058 | − | 13.5762i | −0.519070 | − | 0.496064i | ||||
\(750\) | −0.281512 | + | 1.65822i | −0.0102794 | + | 0.0605495i | ||||
\(751\) | 26.8014 | + | 46.4215i | 0.977998 | + | 1.69394i | 0.669663 | + | 0.742665i | \(0.266439\pi\) |
0.308336 | + | 0.951278i | \(0.400228\pi\) | |||||||
\(752\) | 3.34066 | − | 5.78618i | 0.121821 | − | 0.211000i | ||||
\(753\) | 0.505276 | + | 0.291721i | 0.0184133 | + | 0.0106309i | ||||
\(754\) | −8.61386 | − | 14.9196i | −0.313698 | − | 0.543341i | ||||
\(755\) | 17.9999 | + | 35.6519i | 0.655084 | + | 1.29751i | ||||
\(756\) | 0.563534 | − | 2.31141i | 0.0204955 | − | 0.0840651i | ||||
\(757\) | 24.8459i | 0.903038i | 0.892261 | + | 0.451519i | \(0.149118\pi\) | ||||
−0.892261 | + | 0.451519i | \(0.850882\pi\) | |||||||
\(758\) | −10.9333 | − | 18.9370i | −0.397114 | − | 0.687822i | ||||
\(759\) | −2.03942 | − | 1.98774i | −0.0740262 | − | 0.0721503i | ||||
\(760\) | 0.791930 | − | 14.1129i | 0.0287263 | − | 0.511930i | ||||
\(761\) | −18.1534 | − | 31.4425i | −0.658059 | − | 1.13979i | −0.981118 | − | 0.193413i | \(-0.938044\pi\) |
0.323059 | − | 0.946379i | \(-0.395289\pi\) | |||||||
\(762\) | 0.837348 | 0.0303339 | ||||||||
\(763\) | −2.89697 | − | 0.706297i | −0.104877 | − | 0.0255697i | ||||
\(764\) | 4.18346 | 0.151352 | ||||||||
\(765\) | −8.38242 | + | 12.8040i | −0.303067 | + | 0.462929i | ||||
\(766\) | 0.897916 | − | 1.55524i | 0.0324430 | − | 0.0561930i | ||||
\(767\) | −11.2518 | + | 19.4887i | −0.406279 | + | 0.703696i | ||||
\(768\) | 0.0752187 | + | 0.130283i | 0.00271422 | + | 0.00470117i | ||||
\(769\) | −4.82841 | −0.174117 | −0.0870584 | − | 0.996203i | \(-0.527747\pi\) | ||||
−0.0870584 | + | 0.996203i | \(0.527747\pi\) | |||||||
\(770\) | −16.7873 | − | 10.1580i | −0.604973 | − | 0.366070i | ||||
\(771\) | −2.99236 | −0.107767 | ||||||||
\(772\) | −4.48341 | − | 7.76550i | −0.161362 | − | 0.279486i | ||||
\(773\) | −19.2709 | + | 33.3781i | −0.693125 | + | 1.20053i | 0.277684 | + | 0.960672i | \(0.410433\pi\) |
−0.970809 | + | 0.239855i | \(0.922900\pi\) | |||||||
\(774\) | −4.46228 | + | 7.72890i | −0.160393 | + | 0.277809i | ||||
\(775\) | −1.17593 | + | 10.4451i | −0.0422407 | + | 0.375199i | ||||
\(776\) | −9.73846 | −0.349590 | ||||||||
\(777\) | 1.26343 | + | 4.32109i | 0.0453254 | + | 0.155018i | ||||
\(778\) | 23.2474 | 0.833461 | ||||||||
\(779\) | −2.24443 | − | 3.88746i | −0.0804150 | − | 0.139283i | ||||
\(780\) | 0.844564 | + | 0.0473916i | 0.0302402 | + | 0.00169689i | ||||
\(781\) | −27.3070 | + | 28.0170i | −0.977121 | + | 1.00253i | ||||
\(782\) | 6.56023 | + | 11.3627i | 0.234593 | + | 0.406328i | ||||
\(783\) | − | 6.16055i | − | 0.220160i | ||||||
\(784\) | −6.21451 | − | 3.22177i | −0.221947 | − | 0.115063i | ||||
\(785\) | 43.1023 | − | 21.7615i | 1.53839 | − | 0.776701i | ||||
\(786\) | −0.675111 | − | 1.16933i | −0.0240804 | − | 0.0417085i | ||||
\(787\) | −33.0637 | − | 19.0893i | −1.17859 | − | 0.680461i | −0.222905 | − | 0.974840i | \(-0.571554\pi\) |
−0.955689 | + | 0.294379i | \(0.904887\pi\) | |||||||
\(788\) | −9.68522 | + | 16.7753i | −0.345022 | + | 0.597595i | ||||
\(789\) | 1.34710 | + | 2.33324i | 0.0479580 | + | 0.0830657i | ||||
\(790\) | 8.48822 | + | 16.8124i | 0.301997 | + | 0.598157i | ||||
\(791\) | −9.71174 | − | 33.2153i | −0.345310 | − | 1.18100i | ||||
\(792\) | 9.57035 | + | 2.43318i | 0.340068 | + | 0.0864594i | ||||
\(793\) | −22.5453 | + | 13.0165i | −0.800606 | + | 0.462230i | ||||
\(794\) | −9.25277 | + | 16.0263i | −0.328369 | + | 0.568751i | ||||
\(795\) | −1.46675 | − | 0.0823050i | −0.0520204 | − | 0.00291906i | ||||
\(796\) | −14.4670 | + | 8.35255i | −0.512771 | + | 0.296048i | ||||
\(797\) | 4.95216 | 0.175415 | 0.0877073 | − | 0.996146i | \(-0.472046\pi\) | ||||
0.0877073 | + | 0.996146i | \(0.472046\pi\) | |||||||
\(798\) | 1.81897 | + | 1.73835i | 0.0643909 | + | 0.0615370i | ||||
\(799\) | − | 15.3583i | − | 0.543338i | ||||||
\(800\) | −4.96861 | − | 0.559376i | −0.175667 | − | 0.0197769i | ||||
\(801\) | 9.00423 | + | 5.19860i | 0.318149 | + | 0.183683i | ||||
\(802\) | −0.501146 | + | 0.868010i | −0.0176961 | + | 0.0306505i | ||||
\(803\) | 42.5046 | − | 11.9757i | 1.49995 | − | 0.422614i | ||||
\(804\) | − | 1.18825i | − | 0.0419063i | ||||||
\(805\) | 32.8907 | − | 7.64577i | 1.15924 | − | 0.269478i | ||||
\(806\) | 5.28630 | 0.186202 | ||||||||
\(807\) | 1.27825 | − | 0.737996i | 0.0449964 | − | 0.0259787i | ||||
\(808\) | 9.39320 | − | 16.2695i | 0.330452 | − | 0.572359i | ||||
\(809\) | −27.1876 | − | 15.6968i | −0.955865 | − | 0.551869i | −0.0609670 | − | 0.998140i | \(-0.519418\pi\) |
−0.894898 | + | 0.446271i | \(0.852752\pi\) | |||||||
\(810\) | −16.4572 | − | 10.7741i | −0.578247 | − | 0.378563i | ||||
\(811\) | 31.0236 | 1.08938 | 0.544692 | − | 0.838636i | \(-0.316647\pi\) | ||||
0.544692 | + | 0.838636i | \(0.316647\pi\) | |||||||
\(812\) | −17.6102 | − | 4.29346i | −0.617997 | − | 0.150671i | ||||
\(813\) | −2.33826 | −0.0820064 | ||||||||
\(814\) | −36.1085 | + | 10.1736i | −1.26560 | + | 0.356585i | ||||
\(815\) | −2.81132 | − | 0.157754i | −0.0984762 | − | 0.00552587i | ||||
\(816\) | 0.299480 | + | 0.172905i | 0.0104839 | + | 0.00605289i | ||||
\(817\) | −9.47414 | − | 16.4097i | −0.331458 | − | 0.574102i | ||||
\(818\) | −38.8714 | −1.35911 | ||||||||
\(819\) | 13.6859 | − | 14.3206i | 0.478224 | − | 0.500403i | ||||
\(820\) | −1.41743 | + | 0.715630i | −0.0494986 | + | 0.0249909i | ||||
\(821\) | −17.5276 | + | 10.1196i | −0.611719 | + | 0.353176i | −0.773638 | − | 0.633628i | \(-0.781565\pi\) |
0.161919 | + | 0.986804i | \(0.448232\pi\) | |||||||
\(822\) | −0.842718 | − | 0.486543i | −0.0293932 | − | 0.0169701i | ||||
\(823\) | 31.6000 | + | 18.2443i | 1.10151 | + | 0.635955i | 0.936616 | − | 0.350357i | \(-0.113940\pi\) |
0.164890 | + | 0.986312i | \(0.447273\pi\) | |||||||
\(824\) | −2.31245 | − | 4.00529i | −0.0805581 | − | 0.139531i | ||||
\(825\) | 1.93019 | − | 1.58051i | 0.0672006 | − | 0.0550262i | ||||
\(826\) | 6.64466 | + | 22.7255i | 0.231197 | + | 0.790722i | ||||
\(827\) | −32.3840 | −1.12610 | −0.563051 | − | 0.826422i | \(-0.690373\pi\) | ||||
−0.563051 | + | 0.826422i | \(0.690373\pi\) | |||||||
\(828\) | −14.7174 | + | 8.49708i | −0.511464 | + | 0.295294i | ||||
\(829\) | −36.0031 | − | 20.7864i | −1.25044 | − | 0.721941i | −0.279242 | − | 0.960221i | \(-0.590083\pi\) |
−0.971197 | + | 0.238280i | \(0.923417\pi\) | |||||||
\(830\) | −18.7756 | − | 1.05357i | −0.651712 | − | 0.0365700i | ||||
\(831\) | −2.15172 | − | 3.72688i | −0.0746423 | − | 0.129284i | ||||
\(832\) | 2.51463i | 0.0871792i | ||||||||
\(833\) | −16.0744 | + | 0.728963i | −0.556944 | + | 0.0252571i | ||||
\(834\) | 2.26563 | 0.0784523 | ||||||||
\(835\) | −7.03902 | + | 10.7520i | −0.243595 | + | 0.372087i | ||||
\(836\) | −14.6336 | + | 15.0141i | −0.506114 | + | 0.519273i | ||||
\(837\) | 1.63710 | + | 0.945178i | 0.0565863 | + | 0.0326701i | ||||
\(838\) | 2.65393 | − | 1.53224i | 0.0916784 | − | 0.0529305i | ||||
\(839\) | − | 34.7899i | − | 1.20108i | −0.799595 | − | 0.600540i | \(-0.794952\pi\) | ||
0.799595 | − | 0.600540i | \(-0.205048\pi\) | |||||||
\(840\) | 0.649987 | − | 0.607961i | 0.0224267 | − | 0.0209766i | ||||
\(841\) | −17.9361 | −0.618487 | ||||||||
\(842\) | −0.684714 | − | 1.18596i | −0.0235968 | − | 0.0408708i | ||||
\(843\) | −3.77650 | − | 2.18036i | −0.130070 | − | 0.0750957i | ||||
\(844\) | −16.0035 | − | 9.23964i | −0.550864 | − | 0.318042i | ||||
\(845\) | −12.4907 | − | 8.17734i | −0.429694 | − | 0.281309i | ||||
\(846\) | 19.8927 | 0.683926 | ||||||||
\(847\) | 8.88163 | + | 27.7149i | 0.305176 | + | 0.952296i | ||||
\(848\) | − | 4.36716i | − | 0.149969i | ||||||
\(849\) | 2.27608 | − | 1.31410i | 0.0781150 | − | 0.0450997i | ||||
\(850\) | −10.5341 | + | 4.59710i | −0.361316 | + | 0.157679i | ||||
\(851\) | 32.2804 | − | 55.9112i | 1.10656 | − | 1.91661i | ||||
\(852\) | −0.887286 | − | 1.53682i | −0.0303979 | − | 0.0526507i | ||||
\(853\) | − | 45.0615i | − | 1.54288i | −0.636305 | − | 0.771438i | \(-0.719538\pi\) | ||
0.636305 | − | 0.771438i | \(-0.280462\pi\) | |||||||
\(854\) | −6.48791 | + | 26.6110i | −0.222012 | + | 0.910609i | ||||
\(855\) | 37.5688 | − | 18.9677i | 1.28483 | − | 0.648683i | ||||
\(856\) | 3.71349 | + | 6.43195i | 0.126924 | + | 0.219839i | ||||
\(857\) | −17.5391 | − | 10.1262i | −0.599126 | − | 0.345905i | 0.169572 | − | 0.985518i | \(-0.445762\pi\) |
−0.768698 | + | 0.639612i | \(0.779095\pi\) | |||||||
\(858\) | −0.898491 | − | 0.875722i | −0.0306740 | − | 0.0298967i | ||||
\(859\) | −49.0561 | + | 28.3226i | −1.67377 | + | 0.966354i | −0.708279 | + | 0.705933i | \(0.750528\pi\) |
−0.965495 | + | 0.260421i | \(0.916139\pi\) | |||||||
\(860\) | −5.98321 | + | 3.02080i | −0.204026 | + | 0.103008i | ||||
\(861\) | 0.0669469 | − | 0.274591i | 0.00228155 | − | 0.00935805i | ||||
\(862\) | − | 4.93683i | − | 0.168149i | ||||||
\(863\) | 17.7679 | − | 10.2583i | 0.604828 | − | 0.349198i | −0.166111 | − | 0.986107i | \(-0.553121\pi\) |
0.770939 | + | 0.636910i | \(0.219788\pi\) | |||||||
\(864\) | −0.449610 | + | 0.778747i | −0.0152960 | + | 0.0264935i | ||||
\(865\) | 3.65542 | + | 0.205120i | 0.124288 | + | 0.00697427i | ||||
\(866\) | −10.5332 | − | 18.2441i | −0.357933 | − | 0.619959i | ||||
\(867\) | −1.76252 | −0.0598584 | ||||||||
\(868\) | 3.84277 | − | 4.02099i | 0.130432 | − | 0.136481i | ||||
\(869\) | 6.88321 | − | 27.0735i | 0.233497 | − | 0.918405i | ||||
\(870\) | 1.26231 | − | 1.92814i | 0.0427961 | − | 0.0653702i | ||||
\(871\) | 9.93106 | − | 17.2011i | 0.336501 | − | 0.582837i | ||||
\(872\) | 0.976031 | + | 0.563512i | 0.0330526 | + | 0.0190829i | ||||
\(873\) | −14.4975 | − | 25.1104i | −0.490666 | − | 0.849858i | ||||
\(874\) | − | 36.0813i | − | 1.22047i | ||||||
\(875\) | 3.43226 | + | 29.3806i | 0.116032 | + | 0.993246i | ||||
\(876\) | 2.00301i | 0.0676755i | ||||||||
\(877\) | 12.2237 | + | 21.1721i | 0.412765 | + | 0.714930i | 0.995191 | − | 0.0979537i | \(-0.0312297\pi\) |
−0.582426 | + | 0.812884i | \(0.697896\pi\) | |||||||
\(878\) | 0.332519 | − | 0.575940i | 0.0112220 | − | 0.0194370i | ||||
\(879\) | 0.0830654 | + | 0.0479578i | 0.00280173 | + | 0.00161758i | ||||
\(880\) | 5.01256 | + | 5.46574i | 0.168973 | + | 0.184250i | ||||
\(881\) | 14.8378i | 0.499900i | 0.968259 | + | 0.249950i | \(0.0804141\pi\) | ||||
−0.968259 | + | 0.249950i | \(0.919586\pi\) | |||||||
\(882\) | −0.944182 | − | 20.8202i | −0.0317923 | − | 0.701052i | ||||
\(883\) | − | 10.1754i | − | 0.342430i | −0.985234 | − | 0.171215i | \(-0.945231\pi\) | ||
0.985234 | − | 0.171215i | \(-0.0547693\pi\) | |||||||
\(884\) | 2.89019 | + | 5.00596i | 0.0972076 | + | 0.168369i | ||||
\(885\) | −3.00563 | − | 0.168657i | −0.101033 | − | 0.00566935i | ||||
\(886\) | −11.1850 | − | 6.45766i | −0.375767 | − | 0.216949i | ||||
\(887\) | −13.4692 | + | 7.77646i | −0.452252 | + | 0.261108i | −0.708781 | − | 0.705429i | \(-0.750755\pi\) |
0.256529 | + | 0.966537i | \(0.417421\pi\) | |||||||
\(888\) | − | 1.70160i | − | 0.0571019i | ||||||
\(889\) | 14.1347 | − | 4.13281i | 0.474062 | − | 0.138610i | ||||
\(890\) | 3.51926 | + | 6.97049i | 0.117966 | + | 0.233651i | ||||
\(891\) | 7.91226 | + | 28.0824i | 0.265071 | + | 0.940797i | ||||
\(892\) | 4.08216 | − | 7.07050i | 0.136681 | − | 0.236738i | ||||
\(893\) | −21.1177 | + | 36.5770i | −0.706677 | + | 1.22400i | ||||
\(894\) | −1.63960 | + | 0.946624i | −0.0548365 | + | 0.0316598i | ||||
\(895\) | 39.1874 | − | 19.7849i | 1.30989 | − | 0.661337i | ||||
\(896\) | 1.91274 | + | 1.82796i | 0.0639000 | + | 0.0610679i | ||||
\(897\) | 2.15922 | 0.0720943 | ||||||||
\(898\) | −2.83548 | − | 4.91119i | −0.0946211 | − | 0.163888i | ||||
\(899\) | 7.20114 | − | 12.4727i | 0.240171 | − | 0.415989i | ||||
\(900\) | −5.95436 | − | 13.6442i | −0.198479 | − | 0.454806i | ||||
\(901\) | −5.01939 | − | 8.69384i | −0.167220 | − | 0.289634i | ||||
\(902\) | 2.28253 | + | 0.580313i | 0.0759998 | + | 0.0193223i | ||||
\(903\) | 0.282595 | − | 1.15910i | 0.00940417 | − | 0.0385724i | ||||
\(904\) | 13.0798i | 0.435028i | ||||||||
\(905\) | 4.14049 | − | 6.32450i | 0.137634 | − | 0.210234i | ||||
\(906\) | 2.32696 | + | 1.34347i | 0.0773082 | + | 0.0446339i | ||||
\(907\) | −17.8776 | − | 10.3216i | −0.593616 | − | 0.342725i | 0.172910 | − | 0.984938i | \(-0.444683\pi\) |
−0.766526 | + | 0.642213i | \(0.778016\pi\) | |||||||
\(908\) | 25.3374 | − | 14.6286i | 0.840853 | − | 0.485466i | ||||
\(909\) | 55.9340 | 1.85521 | ||||||||
\(910\) | 14.4904 | − | 3.36844i | 0.480352 | − | 0.111663i | ||||
\(911\) | −2.08440 | −0.0690591 | −0.0345296 | − | 0.999404i | \(-0.510993\pi\) | ||||
−0.0345296 | + | 0.999404i | \(0.510993\pi\) | |||||||
\(912\) | −0.475490 | − | 0.823572i | −0.0157450 | − | 0.0272712i | ||||
\(913\) | 19.9745 | + | 19.4683i | 0.661060 | + | 0.644308i | ||||
\(914\) | 7.46931 | − | 12.9372i | 0.247063 | − | 0.427925i | ||||
\(915\) | −2.91364 | − | 1.90749i | −0.0963221 | − | 0.0630595i | ||||
\(916\) | 7.30086i | 0.241227i | ||||||||
\(917\) | −17.1674 | − | 16.4065i | −0.566917 | − | 0.541791i | ||||
\(918\) | 2.06704i | 0.0682223i | ||||||||
\(919\) | −36.7923 | + | 21.2420i | −1.21367 | + | 0.700710i | −0.963556 | − | 0.267507i | \(-0.913800\pi\) |
−0.250110 | + | 0.968217i | \(0.580467\pi\) | |||||||
\(920\) | −12.7429 | − | 0.715054i | −0.420122 | − | 0.0235746i | ||||
\(921\) | −2.33037 | − | 1.34544i | −0.0767884 | − | 0.0443338i | ||||
\(922\) | 12.6916 | + | 21.9826i | 0.417977 | + | 0.723957i | ||||
\(923\) | − | 29.6628i | − | 0.976363i | ||||||
\(924\) | −1.31925 | + | 0.0468421i | −0.0434002 | + | 0.00154099i | ||||
\(925\) | 45.5071 | + | 33.5794i | 1.49626 | + | 1.10408i | ||||
\(926\) | −1.29984 | + | 0.750461i | −0.0427153 | + | 0.0246617i | ||||
\(927\) | 6.88503 | − | 11.9252i | 0.226134 | − | 0.391676i | ||||
\(928\) | 5.93313 | + | 3.42550i | 0.194765 | + | 0.112447i | ||||
\(929\) | −1.28969 | + | 0.744603i | −0.0423134 | + | 0.0244296i | −0.521007 | − | 0.853552i | \(-0.674444\pi\) |
0.478694 | + | 0.877982i | \(0.341110\pi\) | |||||||
\(930\) | 0.318714 | + | 0.631267i | 0.0104510 | + | 0.0207001i | ||||
\(931\) | 39.2846 | + | 20.3662i | 1.28750 | + | 0.667476i | ||||
\(932\) | −19.8610 | −0.650569 | ||||||||
\(933\) | −2.85858 | + | 1.65040i | −0.0935858 | + | 0.0540318i | ||||
\(934\) | 19.9490 | − | 34.5527i | 0.652751 | − | 1.13060i | ||||
\(935\) | 16.2607 | + | 5.11963i | 0.531782 | + | 0.167430i | ||||
\(936\) | −6.48392 | + | 3.74349i | −0.211934 | + | 0.122360i | ||||
\(937\) | − | 6.06069i | − | 0.197994i | −0.995088 | − | 0.0989970i | \(-0.968437\pi\) | ||
0.995088 | − | 0.0989970i | \(-0.0315634\pi\) | |||||||
\(938\) | −5.86471 | − | 20.0580i | −0.191490 | − | 0.654916i | ||||
\(939\) | −0.206595 | −0.00674198 | ||||||||
\(940\) | 12.4995 | + | 8.18308i | 0.407688 | + | 0.266902i | ||||
\(941\) | −8.92371 | + | 15.4563i | −0.290905 | + | 0.503861i | −0.974024 | − | 0.226445i | \(-0.927290\pi\) |
0.683119 | + | 0.730307i | \(0.260623\pi\) | |||||||
\(942\) | 1.62423 | − | 2.81324i | 0.0529202 | − | 0.0916604i | ||||
\(943\) | −3.51009 | + | 2.02655i | −0.114304 | + | 0.0659936i | ||||
\(944\) | − | 8.94907i | − | 0.291267i | ||||||
\(945\) | 5.08975 | + | 1.54769i | 0.165570 | + | 0.0503463i | ||||
\(946\) | 9.63495 | + | 2.44961i | 0.313259 | + | 0.0796436i | ||||
\(947\) | 41.8092 | − | 24.1385i | 1.35862 | − | 0.784397i | 0.369179 | − | 0.929358i | \(-0.379639\pi\) |
0.989437 | + | 0.144961i | \(0.0463057\pi\) | |||||||
\(948\) | 1.09732 | + | 0.633541i | 0.0356395 | + | 0.0205764i | ||||
\(949\) | −16.7406 | + | 28.9956i | −0.543424 | + | 0.941238i | ||||
\(950\) | 31.4087 | + | 3.53606i | 1.01903 | + | 0.114725i | ||||
\(951\) | − | 0.683709i | − | 0.0221708i | ||||||
\(952\) | 5.90871 | + | 1.44058i | 0.191502 | + | 0.0466894i | ||||
\(953\) | 2.66449 | 0.0863114 | 0.0431557 | − | 0.999068i | \(-0.486259\pi\) | ||||
0.0431557 | + | 0.999068i | \(0.486259\pi\) | |||||||
\(954\) | 11.2606 | − | 6.50132i | 0.364576 | − | 0.210488i | ||||
\(955\) | −0.524091 | + | 9.33980i | −0.0169592 | + | 0.302229i | ||||
\(956\) | 18.6540 | + | 10.7699i | 0.603314 | + | 0.348323i | ||||
\(957\) | −3.29017 | + | 0.927008i | −0.106356 | + | 0.0299659i | ||||
\(958\) | −1.60000 | −0.0516936 | ||||||||
\(959\) | −16.6267 | − | 4.05369i | −0.536904 | − | 0.130900i | ||||
\(960\) | −0.300286 | + | 0.151609i | −0.00969170 | + | 0.00489314i | ||||
\(961\) | −13.2903 | − | 23.0195i | −0.428721 | − | 0.742566i | ||||
\(962\) | 14.2215 | − | 24.6324i | 0.458520 | − | 0.794179i | ||||
\(963\) | −11.0564 | + | 19.1503i | −0.356288 | + | 0.617109i | ||||
\(964\) | −0.352616 | − | 0.610749i | −0.0113570 | − | 0.0196709i | ||||
\(965\) | 17.8986 | − | 9.03663i | 0.576176 | − | 0.290899i | ||||
\(966\) | 1.56960 | − | 1.64240i | 0.0505011 | − | 0.0528432i | ||||
\(967\) | −34.3843 | −1.10572 | −0.552862 | − | 0.833273i | \(-0.686464\pi\) | ||||
−0.552862 | + | 0.833273i | \(0.686464\pi\) | |||||||
\(968\) | −0.282284 | − | 10.9964i | −0.00907295 | − | 0.353437i | ||||
\(969\) | −1.89314 | − | 1.09301i | −0.0608166 | − | 0.0351125i | ||||
\(970\) | 1.22001 | − | 21.7416i | 0.0391720 | − | 0.698082i | ||||
\(971\) | −4.41826 | + | 2.55088i | −0.141789 | + | 0.0818617i | −0.569216 | − | 0.822188i | \(-0.692753\pi\) |
0.427428 | + | 0.904050i | \(0.359420\pi\) | |||||||
\(972\) | −4.02103 | −0.128975 | ||||||||
\(973\) | 38.2445 | − | 11.1822i | 1.22606 | − | 0.358486i | ||||
\(974\) | 1.59441i | 0.0510883i | ||||||||
\(975\) | −0.211609 | + | 1.87960i | −0.00677691 | + | 0.0601953i | ||||
\(976\) | 5.17631 | − | 8.96564i | 0.165690 | − | 0.286983i | ||||
\(977\) | 29.4505 | + | 17.0032i | 0.942203 | + | 0.543981i | 0.890650 | − | 0.454689i | \(-0.150250\pi\) |
0.0515531 | + | 0.998670i | \(0.483583\pi\) | |||||||
\(978\) | −0.164057 | + | 0.0947182i | −0.00524596 | + | 0.00302875i | ||||
\(979\) | 2.85381 | − | 11.2248i | 0.0912082 | − | 0.358746i | ||||
\(980\) | 7.97132 | − | 13.4706i | 0.254635 | − | 0.430304i | ||||
\(981\) | 3.35556i | 0.107135i | ||||||||
\(982\) | −10.8516 | + | 6.26515i | −0.346287 | + | 0.199929i | ||||
\(983\) | 17.6465 | − | 30.5646i | 0.562835 | − | 0.974858i | −0.434413 | − | 0.900714i | \(-0.643044\pi\) |
0.997248 | − | 0.0741445i | \(-0.0236226\pi\) | |||||||
\(984\) | −0.0534129 | + | 0.0925139i | −0.00170274 | + | 0.00294924i | ||||
\(985\) | −36.2385 | − | 23.7244i | −1.15465 | − | 0.755921i | ||||
\(986\) | 15.7484 | 0.501530 | ||||||||
\(987\) | −2.55243 | + | 0.746299i | −0.0812447 | + | 0.0237549i | ||||
\(988\) | − | 15.8961i | − | 0.505721i | ||||||
\(989\) | −14.8167 | + | 8.55444i | −0.471144 | + | 0.272015i | ||||
\(990\) | −6.63116 | + | 21.0615i | −0.210752 | + | 0.669379i | ||||
\(991\) | −5.37871 | + | 9.31619i | −0.170860 | + | 0.295939i | −0.938721 | − | 0.344678i | \(-0.887988\pi\) |
0.767861 | + | 0.640617i | \(0.221321\pi\) | |||||||
\(992\) | −1.82057 | + | 1.05111i | −0.0578033 | + | 0.0333727i | ||||
\(993\) | 2.46771 | 0.0783103 | ||||||||
\(994\) | −22.5628 | − | 21.5628i | −0.715648 | − | 0.683930i | ||||
\(995\) | −16.8351 | − | 33.3449i | −0.533710 | − | 1.05710i | ||||
\(996\) | −1.09567 | + | 0.632584i | −0.0347176 | + | 0.0200442i | ||||
\(997\) | 17.5630 | + | 10.1400i | 0.556225 | + | 0.321137i | 0.751629 | − | 0.659586i | \(-0.229268\pi\) |
−0.195404 | + | 0.980723i | \(0.562602\pi\) | |||||||
\(998\) | −1.40578 | + | 2.43488i | −0.0444992 | + | 0.0770749i | ||||
\(999\) | 8.80841 | − | 5.08554i | 0.278686 | − | 0.160899i |
(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 | 770.2.o.a.549.13 | yes | 48 | |
5.4 | even | 2 | 770.2.o.b.549.12 | yes | 48 | ||
7.5 | odd | 6 | inner | 770.2.o.a.439.12 | ✓ | 48 | |
11.10 | odd | 2 | 770.2.o.b.549.13 | yes | 48 | ||
35.19 | odd | 6 | 770.2.o.b.439.13 | yes | 48 | ||
55.54 | odd | 2 | inner | 770.2.o.a.549.12 | yes | 48 | |
77.54 | even | 6 | 770.2.o.b.439.12 | yes | 48 | ||
385.54 | even | 6 | inner | 770.2.o.a.439.13 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.o.a.439.12 | ✓ | 48 | 7.5 | odd | 6 | inner | |
770.2.o.a.439.13 | yes | 48 | 385.54 | even | 6 | inner | |
770.2.o.a.549.12 | yes | 48 | 55.54 | odd | 2 | inner | |
770.2.o.a.549.13 | yes | 48 | 1.1 | even | 1 | trivial | |
770.2.o.b.439.12 | yes | 48 | 77.54 | even | 6 | ||
770.2.o.b.439.13 | yes | 48 | 35.19 | odd | 6 | ||
770.2.o.b.549.12 | yes | 48 | 5.4 | even | 2 | ||
770.2.o.b.549.13 | yes | 48 | 11.10 | odd | 2 |