Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(99,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.u (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 899.4 | ||
Character | \(\chi\) | \(=\) | 950.899 |
Dual form | 950.2.u.g.149.4 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.642788 | + | 0.766044i | 0.454519 | + | 0.541675i | ||||
\(3\) | −0.811037 | + | 2.22831i | −0.468252 | + | 1.28651i | 0.450887 | + | 0.892581i | \(0.351108\pi\) |
−0.919140 | + | 0.393932i | \(0.871115\pi\) | |||||||
\(4\) | −0.173648 | + | 0.984808i | −0.0868241 | + | 0.492404i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.22831 | + | 0.811037i | −0.909702 | + | 0.331104i | ||||
\(7\) | 2.73267 | + | 1.57771i | 1.03285 | + | 0.596318i | 0.917801 | − | 0.397041i | \(-0.129963\pi\) |
0.115053 | + | 0.993359i | \(0.463296\pi\) | |||||||
\(8\) | −0.866025 | + | 0.500000i | −0.306186 | + | 0.176777i | ||||
\(9\) | −2.00943 | − | 1.68611i | −0.669811 | − | 0.562038i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.688886 | − | 1.19319i | −0.207707 | − | 0.359759i | 0.743285 | − | 0.668975i | \(-0.233267\pi\) |
−0.950992 | + | 0.309216i | \(0.899933\pi\) | |||||||
\(12\) | −2.05362 | − | 1.18566i | −0.592828 | − | 0.342270i | ||||
\(13\) | 1.47931 | + | 4.06437i | 0.410286 | + | 1.12725i | 0.957039 | + | 0.289958i | \(0.0936415\pi\) |
−0.546753 | + | 0.837294i | \(0.684136\pi\) | |||||||
\(14\) | 0.547933 | + | 3.10748i | 0.146441 | + | 0.830509i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.939693 | − | 0.342020i | −0.234923 | − | 0.0855050i | ||||
\(17\) | 0.833438 | + | 0.993253i | 0.202138 | + | 0.240899i | 0.857585 | − | 0.514342i | \(-0.171964\pi\) |
−0.655446 | + | 0.755242i | \(0.727520\pi\) | |||||||
\(18\) | − | 2.62313i | − | 0.618277i | ||||||
\(19\) | −1.08907 | + | 4.22066i | −0.249849 | + | 0.968285i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.73192 | + | 4.80965i | −1.25081 | + | 1.04955i | ||||
\(22\) | 0.471226 | − | 1.29468i | 0.100466 | − | 0.276027i | ||||
\(23\) | −2.09271 | − | 0.369001i | −0.436360 | − | 0.0769420i | −0.0488468 | − | 0.998806i | \(-0.515555\pi\) |
−0.387513 | + | 0.921864i | \(0.626666\pi\) | |||||||
\(24\) | −0.411774 | − | 2.33529i | −0.0840531 | − | 0.476689i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.16260 | + | 3.74574i | −0.424122 | + | 0.734600i | ||||
\(27\) | −0.773953 | + | 0.446842i | −0.148947 | + | 0.0859948i | ||||
\(28\) | −2.02826 | + | 2.41719i | −0.383306 | + | 0.456806i | ||||
\(29\) | 0.0998515 | + | 0.0837854i | 0.0185420 | + | 0.0155586i | 0.652012 | − | 0.758209i | \(-0.273925\pi\) |
−0.633470 | + | 0.773768i | \(0.718370\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.173355 | + | 0.300259i | −0.0311355 | + | 0.0539282i | −0.881173 | − | 0.472793i | \(-0.843246\pi\) |
0.850038 | + | 0.526722i | \(0.176579\pi\) | |||||||
\(32\) | −0.342020 | − | 0.939693i | −0.0604612 | − | 0.166116i | ||||
\(33\) | 3.21749 | − | 0.567331i | 0.560094 | − | 0.0987596i | ||||
\(34\) | −0.225152 | + | 1.27690i | −0.0386133 | + | 0.218987i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.00943 | − | 1.68611i | 0.334905 | − | 0.281019i | ||||
\(37\) | − | 10.3150i | − | 1.69578i | −0.530174 | − | 0.847889i | \(-0.677873\pi\) | ||
0.530174 | − | 0.847889i | \(-0.322127\pi\) | |||||||
\(38\) | −3.93325 | + | 1.87871i | −0.638057 | + | 0.304768i | ||||
\(39\) | −10.2564 | −1.64234 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.3451 | − | 3.76531i | −1.61563 | − | 0.588042i | −0.633089 | − | 0.774079i | \(-0.718213\pi\) |
−0.982543 | + | 0.186037i | \(0.940436\pi\) | |||||||
\(42\) | −7.36881 | − | 1.29932i | −1.13703 | − | 0.200490i | ||||
\(43\) | 11.3501 | − | 2.00132i | 1.73087 | − | 0.305199i | 0.782567 | − | 0.622566i | \(-0.213910\pi\) |
0.948303 | + | 0.317367i | \(0.102799\pi\) | |||||||
\(44\) | 1.29468 | − | 0.471226i | 0.195181 | − | 0.0710400i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.06250 | − | 1.84030i | −0.156656 | − | 0.271337i | ||||
\(47\) | 0.0491361 | − | 0.0585581i | 0.00716723 | − | 0.00854158i | −0.762449 | − | 0.647048i | \(-0.776003\pi\) |
0.769616 | + | 0.638507i | \(0.220448\pi\) | |||||||
\(48\) | 1.52425 | − | 1.81653i | 0.220007 | − | 0.262194i | ||||
\(49\) | 1.47834 | + | 2.56055i | 0.211191 | + | 0.365793i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.88922 | + | 1.05159i | −0.404572 | + | 0.147252i | ||||
\(52\) | −4.25950 | + | 0.751065i | −0.590686 | + | 0.104154i | ||||
\(53\) | 6.12511 | + | 1.08002i | 0.841348 | + | 0.148352i | 0.577682 | − | 0.816262i | \(-0.303957\pi\) |
0.263666 | + | 0.964614i | \(0.415068\pi\) | |||||||
\(54\) | −0.839788 | − | 0.305658i | −0.114281 | − | 0.0415948i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.15542 | −0.421661 | ||||||||
\(57\) | −8.52164 | − | 5.84988i | −1.12872 | − | 0.774835i | ||||
\(58\) | 0.130347i | 0.0171154i | ||||||||
\(59\) | 6.27104 | − | 5.26202i | 0.816419 | − | 0.685057i | −0.135711 | − | 0.990748i | \(-0.543332\pi\) |
0.952131 | + | 0.305691i | \(0.0988875\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.36244 | − | 7.72680i | 0.174443 | − | 0.989315i | −0.764342 | − | 0.644811i | \(-0.776936\pi\) |
0.938785 | − | 0.344504i | \(-0.111953\pi\) | |||||||
\(62\) | −0.341442 | + | 0.0602055i | −0.0433632 | + | 0.00764611i | ||||
\(63\) | −2.83092 | − | 7.77790i | −0.356663 | − | 0.979923i | ||||
\(64\) | 0.500000 | − | 0.866025i | 0.0625000 | − | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.50277 | + | 2.10007i | 0.308069 | + | 0.258501i | ||||
\(67\) | −0.662508 | + | 0.789546i | −0.0809382 | + | 0.0964584i | −0.804994 | − | 0.593283i | \(-0.797831\pi\) |
0.724056 | + | 0.689742i | \(0.242276\pi\) | |||||||
\(68\) | −1.12289 | + | 0.648300i | −0.136170 | + | 0.0786179i | ||||
\(69\) | 2.51951 | − | 4.36392i | 0.303313 | − | 0.525354i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.02349 | + | 11.4758i | 0.240144 | + | 1.36192i | 0.831505 | + | 0.555517i | \(0.187480\pi\) |
−0.591361 | + | 0.806407i | \(0.701409\pi\) | |||||||
\(72\) | 2.58328 | + | 0.455501i | 0.304442 | + | 0.0536813i | ||||
\(73\) | −4.18756 | + | 11.5052i | −0.490117 | + | 1.34659i | 0.410456 | + | 0.911881i | \(0.365370\pi\) |
−0.900573 | + | 0.434705i | \(0.856853\pi\) | |||||||
\(74\) | 7.90176 | − | 6.63036i | 0.918561 | − | 0.770764i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.96742 | − | 1.80543i | −0.455094 | − | 0.207097i | ||||
\(77\) | − | 4.34745i | − | 0.495438i | ||||||
\(78\) | −6.59270 | − | 7.85688i | −0.746477 | − | 0.889616i | ||||
\(79\) | 13.1650 | + | 4.79168i | 1.48118 | + | 0.539106i | 0.951111 | − | 0.308848i | \(-0.0999436\pi\) |
0.530070 | + | 0.847954i | \(0.322166\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.73450 | − | 9.83684i | −0.192722 | − | 1.09298i | ||||
\(82\) | −3.76531 | − | 10.3451i | −0.415808 | − | 1.14242i | ||||
\(83\) | −9.85443 | − | 5.68946i | −1.08166 | − | 0.624499i | −0.150319 | − | 0.988637i | \(-0.548030\pi\) |
−0.931345 | + | 0.364138i | \(0.881364\pi\) | |||||||
\(84\) | −3.74124 | − | 6.48003i | −0.408203 | − | 0.707029i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.82879 | + | 7.40823i | 0.952033 | + | 0.798850i | ||||
\(87\) | −0.267683 | + | 0.154547i | −0.0286986 | + | 0.0165691i | ||||
\(88\) | 1.19319 | + | 0.688886i | 0.127194 | + | 0.0734355i | ||||
\(89\) | −17.1195 | + | 6.23099i | −1.81466 | + | 0.660484i | −0.818348 | + | 0.574723i | \(0.805110\pi\) |
−0.996316 | + | 0.0857608i | \(0.972668\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.36992 | + | 13.4405i | −0.248436 | + | 1.40895i | ||||
\(92\) | 0.726790 | − | 1.99684i | 0.0757731 | − | 0.208185i | ||||
\(93\) | −0.528473 | − | 0.629809i | −0.0548000 | − | 0.0653082i | ||||
\(94\) | 0.0764422 | 0.00788441 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.37131 | 0.242021 | ||||||||
\(97\) | 10.4271 | + | 12.4265i | 1.05871 | + | 1.26172i | 0.963910 | + | 0.266227i | \(0.0857771\pi\) |
0.0948014 | + | 0.995496i | \(0.469778\pi\) | |||||||
\(98\) | −1.01124 | + | 2.77836i | −0.102151 | + | 0.280657i | ||||
\(99\) | −0.627577 | + | 3.55916i | −0.0630738 | + | 0.357710i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.22381 | + | 2.26528i | −0.619293 | + | 0.225404i | −0.632564 | − | 0.774508i | \(-0.717998\pi\) |
0.0132716 | + | 0.999912i | \(0.495775\pi\) | |||||||
\(102\) | −2.66272 | − | 1.53732i | −0.263649 | − | 0.152218i | ||||
\(103\) | −10.7020 | + | 6.17880i | −1.05450 | + | 0.608815i | −0.923906 | − | 0.382621i | \(-0.875022\pi\) |
−0.130594 | + | 0.991436i | \(0.541688\pi\) | |||||||
\(104\) | −3.31330 | − | 2.78019i | −0.324896 | − | 0.272620i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.10980 | + | 5.38633i | 0.302050 | + | 0.523167i | ||||
\(107\) | 9.48714 | + | 5.47740i | 0.917156 | + | 0.529521i | 0.882727 | − | 0.469887i | \(-0.155705\pi\) |
0.0344297 | + | 0.999407i | \(0.489039\pi\) | |||||||
\(108\) | −0.305658 | − | 0.839788i | −0.0294120 | − | 0.0808087i | ||||
\(109\) | −1.29211 | − | 7.32792i | −0.123762 | − | 0.701887i | −0.982036 | − | 0.188695i | \(-0.939574\pi\) |
0.858274 | − | 0.513192i | \(-0.171537\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 22.9850 | + | 8.36586i | 2.18164 | + | 0.794052i | ||||
\(112\) | −2.02826 | − | 2.41719i | −0.191653 | − | 0.228403i | ||||
\(113\) | − | 11.6014i | − | 1.09137i | −0.837990 | − | 0.545686i | \(-0.816269\pi\) | ||
0.837990 | − | 0.545686i | \(-0.183731\pi\) | |||||||
\(114\) | −0.996338 | − | 10.2882i | −0.0933156 | − | 0.963577i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0998515 | + | 0.0837854i | −0.00927098 | + | 0.00777928i | ||||
\(117\) | 3.88041 | − | 10.6613i | 0.358744 | − | 0.985642i | ||||
\(118\) | 8.06189 | + | 1.42153i | 0.742157 | + | 0.130862i | ||||
\(119\) | 0.710449 | + | 4.02916i | 0.0651268 | + | 0.369352i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.55087 | − | 7.88234i | 0.413716 | − | 0.716577i | ||||
\(122\) | 6.79483 | − | 3.92300i | 0.615175 | − | 0.355172i | ||||
\(123\) | 16.7805 | − | 19.9982i | 1.51305 | − | 1.80318i | ||||
\(124\) | −0.265595 | − | 0.222861i | −0.0238511 | − | 0.0200135i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.13853 | − | 7.16815i | 0.368690 | − | 0.638589i | ||||
\(127\) | 5.60862 | + | 15.4096i | 0.497685 | + | 1.36738i | 0.893507 | + | 0.449050i | \(0.148237\pi\) |
−0.395822 | + | 0.918327i | \(0.629540\pi\) | |||||||
\(128\) | 0.984808 | − | 0.173648i | 0.0870455 | − | 0.0153485i | ||||
\(129\) | −4.74577 | + | 26.9146i | −0.417841 | + | 2.36970i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.53118 | − | 7.15851i | 0.745373 | − | 0.625442i | −0.188902 | − | 0.981996i | \(-0.560493\pi\) |
0.934275 | + | 0.356554i | \(0.116048\pi\) | |||||||
\(132\) | 3.26713i | 0.284367i | ||||||||
\(133\) | −9.63503 | + | 9.81545i | −0.835463 | + | 0.851107i | ||||
\(134\) | −1.03068 | −0.0890371 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.21840 | − | 0.443463i | −0.104477 | − | 0.0380266i | ||||
\(137\) | −7.23011 | − | 1.27486i | −0.617710 | − | 0.108919i | −0.143968 | − | 0.989582i | \(-0.545986\pi\) |
−0.473743 | + | 0.880663i | \(0.657097\pi\) | |||||||
\(138\) | 4.96247 | − | 0.875017i | 0.422433 | − | 0.0744864i | ||||
\(139\) | 11.0992 | − | 4.03978i | 0.941422 | − | 0.342650i | 0.174695 | − | 0.984623i | \(-0.444106\pi\) |
0.766727 | + | 0.641973i | \(0.221884\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0906342 | + | 0.156983i | 0.00763277 | + | 0.0132203i | ||||
\(142\) | −7.49028 | + | 8.92657i | −0.628570 | + | 0.749101i | ||||
\(143\) | 3.83047 | − | 4.56497i | 0.320320 | − | 0.381742i | ||||
\(144\) | 1.31156 | + | 2.27169i | 0.109297 | + | 0.189308i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.5052 | + | 4.18756i | −0.952180 | + | 0.346565i | ||||
\(147\) | −6.90468 | + | 1.21748i | −0.569488 | + | 0.100416i | ||||
\(148\) | 10.1583 | + | 1.79118i | 0.835007 | + | 0.147234i | ||||
\(149\) | 3.30256 | + | 1.20203i | 0.270556 | + | 0.0984745i | 0.473736 | − | 0.880667i | \(-0.342905\pi\) |
−0.203179 | + | 0.979142i | \(0.565127\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.212620 | −0.0173028 | −0.00865139 | − | 0.999963i | \(-0.502754\pi\) | ||||
−0.00865139 | + | 0.999963i | \(0.502754\pi\) | |||||||
\(152\) | −1.16717 | − | 4.19973i | −0.0946700 | − | 0.340643i | ||||
\(153\) | − | 3.40114i | − | 0.274966i | ||||||
\(154\) | 3.33034 | − | 2.79449i | 0.268366 | − | 0.225186i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.78101 | − | 10.1006i | 0.142595 | − | 0.808696i | ||||
\(157\) | 7.57072 | − | 1.33492i | 0.604210 | − | 0.106538i | 0.136829 | − | 0.990595i | \(-0.456309\pi\) |
0.467381 | + | 0.884056i | \(0.345198\pi\) | |||||||
\(158\) | 4.79168 | + | 13.1650i | 0.381205 | + | 1.04735i | ||||
\(159\) | −7.37431 | + | 12.7727i | −0.584821 | + | 1.01294i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.13651 | − | 4.31004i | −0.404814 | − | 0.339679i | ||||
\(162\) | 6.42054 | − | 7.65170i | 0.504445 | − | 0.601174i | ||||
\(163\) | −6.34537 | + | 3.66350i | −0.497008 | + | 0.286948i | −0.727477 | − | 0.686132i | \(-0.759307\pi\) |
0.230469 | + | 0.973080i | \(0.425974\pi\) | |||||||
\(164\) | 5.50451 | − | 9.53409i | 0.429830 | − | 0.744487i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.97593 | − | 11.2060i | −0.153362 | − | 0.869758i | ||||
\(167\) | 15.6032 | + | 2.75126i | 1.20741 | + | 0.212899i | 0.740899 | − | 0.671617i | \(-0.234400\pi\) |
0.466511 | + | 0.884515i | \(0.345511\pi\) | |||||||
\(168\) | 2.55916 | − | 7.03124i | 0.197444 | − | 0.542472i | ||||
\(169\) | −4.37215 | + | 3.66867i | −0.336319 | + | 0.282205i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.30491 | − | 6.64483i | 0.711564 | − | 0.508143i | ||||
\(172\) | 11.5252i | 0.878786i | ||||||||
\(173\) | 10.6961 | + | 12.7471i | 0.813211 | + | 0.969147i | 0.999912 | − | 0.0132697i | \(-0.00422402\pi\) |
−0.186701 | + | 0.982417i | \(0.559780\pi\) | |||||||
\(174\) | −0.290453 | − | 0.105716i | −0.0220192 | − | 0.00801432i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.239248 | + | 1.35684i | 0.0180340 | + | 0.102276i | ||||
\(177\) | 6.63936 | + | 18.2415i | 0.499045 | + | 1.37111i | ||||
\(178\) | −15.7774 | − | 9.10910i | −1.18257 | − | 0.682756i | ||||
\(179\) | −2.28553 | − | 3.95866i | −0.170829 | − | 0.295884i | 0.767881 | − | 0.640592i | \(-0.221311\pi\) |
−0.938710 | + | 0.344708i | \(0.887978\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.29338 | + | 1.08527i | 0.0961360 | + | 0.0806677i | 0.689589 | − | 0.724201i | \(-0.257791\pi\) |
−0.593453 | + | 0.804869i | \(0.702236\pi\) | |||||||
\(182\) | −11.8194 | + | 6.82392i | −0.876111 | + | 0.505823i | ||||
\(183\) | 16.1127 | + | 9.30266i | 1.19108 | + | 0.687673i | ||||
\(184\) | 1.99684 | − | 0.726790i | 0.147209 | − | 0.0535796i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.142766 | − | 0.809667i | 0.0104681 | − | 0.0593677i | ||||
\(187\) | 0.610991 | − | 1.67868i | 0.0446801 | − | 0.122758i | ||||
\(188\) | 0.0491361 | + | 0.0585581i | 0.00358362 | + | 0.00427079i | ||||
\(189\) | −2.81995 | −0.205121 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2207 | 0.811901 | 0.405951 | − | 0.913895i | \(-0.366941\pi\) | ||||
0.405951 | + | 0.913895i | \(0.366941\pi\) | |||||||
\(192\) | 1.52425 | + | 1.81653i | 0.110003 | + | 0.131097i | ||||
\(193\) | −7.34927 | + | 20.1920i | −0.529012 | + | 1.45345i | 0.331223 | + | 0.943552i | \(0.392539\pi\) |
−0.860236 | + | 0.509897i | \(0.829684\pi\) | |||||||
\(194\) | −2.81687 | + | 15.9752i | −0.202239 | + | 1.14696i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.77836 | + | 1.01124i | −0.198455 | + | 0.0722315i | ||||
\(197\) | 13.2315 | + | 7.63921i | 0.942705 | + | 0.544271i | 0.890807 | − | 0.454381i | \(-0.150140\pi\) |
0.0518981 | + | 0.998652i | \(0.483473\pi\) | |||||||
\(198\) | −3.12988 | + | 1.80704i | −0.222431 | + | 0.128420i | ||||
\(199\) | −0.542940 | − | 0.455581i | −0.0384880 | − | 0.0322953i | 0.623341 | − | 0.781950i | \(-0.285775\pi\) |
−0.661829 | + | 0.749655i | \(0.730219\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.22203 | − | 2.11662i | −0.0861955 | − | 0.149295i | ||||
\(202\) | −5.73590 | − | 3.31162i | −0.403576 | − | 0.233005i | ||||
\(203\) | 0.140673 | + | 0.386495i | 0.00987328 | + | 0.0271266i | ||||
\(204\) | −0.533906 | − | 3.02793i | −0.0373809 | − | 0.211998i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.6123 | − | 4.22655i | −0.809071 | − | 0.294478i | ||||
\(207\) | 3.58298 | + | 4.27002i | 0.249034 | + | 0.296787i | ||||
\(208\) | − | 4.32521i | − | 0.299899i | ||||||
\(209\) | 5.78627 | − | 1.60809i | 0.400244 | − | 0.111234i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.7852 | − | 9.04988i | 0.742486 | − | 0.623020i | −0.191018 | − | 0.981586i | \(-0.561179\pi\) |
0.933504 | + | 0.358567i | \(0.116735\pi\) | |||||||
\(212\) | −2.12723 | + | 5.84451i | −0.146099 | + | 0.401403i | ||||
\(213\) | −27.2126 | − | 4.79832i | −1.86458 | − | 0.328776i | ||||
\(214\) | 1.90228 | + | 10.7884i | 0.130037 | + | 0.737478i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.446842 | − | 0.773953i | 0.0304038 | − | 0.0526608i | ||||
\(217\) | −0.947444 | + | 0.547007i | −0.0643167 | + | 0.0371333i | ||||
\(218\) | 4.78296 | − | 5.70011i | 0.323943 | − | 0.386060i | ||||
\(219\) | −22.2409 | − | 18.6623i | −1.50290 | − | 1.26108i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.80403 | + | 4.85673i | −0.188620 | + | 0.326699i | ||||
\(222\) | 8.36586 | + | 22.9850i | 0.561479 | + | 1.54265i | ||||
\(223\) | −11.5389 | + | 2.03461i | −0.772699 | + | 0.136248i | −0.546077 | − | 0.837735i | \(-0.683879\pi\) |
−0.226622 | + | 0.973983i | \(0.572768\pi\) | |||||||
\(224\) | 0.547933 | − | 3.10748i | 0.0366103 | − | 0.207627i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.88722 | − | 7.45727i | 0.591169 | − | 0.496050i | ||||
\(227\) | 10.2265i | 0.678758i | 0.940650 | + | 0.339379i | \(0.110217\pi\) | ||||
−0.940650 | + | 0.339379i | \(0.889783\pi\) | |||||||
\(228\) | 7.24077 | − | 7.37636i | 0.479532 | − | 0.488511i | ||||
\(229\) | 5.05689 | 0.334169 | 0.167084 | − | 0.985943i | \(-0.446565\pi\) | ||||
0.167084 | + | 0.985943i | \(0.446565\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.68744 | + | 3.52594i | 0.637387 | + | 0.231990i | ||||
\(232\) | −0.128367 | − | 0.0226345i | −0.00842768 | − | 0.00148603i | ||||
\(233\) | 7.14818 | − | 1.26042i | 0.468293 | − | 0.0825727i | 0.0654778 | − | 0.997854i | \(-0.479143\pi\) |
0.402815 | + | 0.915281i | \(0.368032\pi\) | |||||||
\(234\) | 10.6613 | − | 3.88041i | 0.696954 | − | 0.253671i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.09313 | + | 7.08951i | 0.266440 | + | 0.461488i | ||||
\(237\) | −21.3546 | + | 25.4495i | −1.38713 | + | 1.65312i | ||||
\(238\) | −2.62985 | + | 3.13413i | −0.170468 | + | 0.203155i | ||||
\(239\) | 7.98657 | + | 13.8331i | 0.516608 | + | 0.894792i | 0.999814 | + | 0.0192850i | \(0.00613899\pi\) |
−0.483206 | + | 0.875507i | \(0.660528\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.8564 | + | 7.59111i | −1.34348 | + | 0.488986i | −0.910906 | − | 0.412613i | \(-0.864616\pi\) |
−0.432572 | + | 0.901599i | \(0.642394\pi\) | |||||||
\(242\) | 8.96347 | − | 1.58050i | 0.576194 | − | 0.101598i | ||||
\(243\) | 20.6859 | + | 3.64748i | 1.32700 | + | 0.233986i | ||||
\(244\) | 7.37283 | + | 2.68349i | 0.471997 | + | 0.171793i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 26.1058 | 1.66445 | ||||||||
\(247\) | −18.7654 | + | 1.81729i | −1.19401 | + | 0.115632i | ||||
\(248\) | − | 0.346710i | − | 0.0220161i | ||||||
\(249\) | 20.6702 | − | 17.3443i | 1.30992 | − | 1.09915i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.91622 | − | 22.2100i | 0.247190 | − | 1.40188i | −0.568162 | − | 0.822917i | \(-0.692345\pi\) |
0.815352 | − | 0.578966i | \(-0.196544\pi\) | |||||||
\(252\) | 8.15132 | − | 1.43730i | 0.513485 | − | 0.0905412i | ||||
\(253\) | 1.00135 | + | 2.75119i | 0.0629544 | + | 0.172966i | ||||
\(254\) | −8.19925 | + | 14.2015i | −0.514467 | + | 0.891083i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.766044 | + | 0.642788i | 0.0478778 | + | 0.0401742i | ||||
\(257\) | 6.88718 | − | 8.20783i | 0.429611 | − | 0.511990i | −0.507199 | − | 0.861829i | \(-0.669319\pi\) |
0.936810 | + | 0.349839i | \(0.113764\pi\) | |||||||
\(258\) | −23.6683 | + | 13.6649i | −1.47352 | + | 0.850739i | ||||
\(259\) | 16.2741 | − | 28.1876i | 1.01122 | − | 1.75149i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0593732 | − | 0.336722i | −0.00367511 | − | 0.0208426i | ||||
\(262\) | 10.9675 | + | 1.93386i | 0.677573 | + | 0.119474i | ||||
\(263\) | 9.12051 | − | 25.0584i | 0.562395 | − | 1.54517i | −0.253720 | − | 0.967278i | \(-0.581654\pi\) |
0.816115 | − | 0.577890i | \(-0.196124\pi\) | |||||||
\(264\) | −2.50277 | + | 2.10007i | −0.154035 | + | 0.129250i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −13.7123 | − | 1.07161i | −0.840758 | − | 0.0657049i | ||||
\(267\) | − | 43.2011i | − | 2.64386i | ||||||
\(268\) | −0.662508 | − | 0.789546i | −0.0404691 | − | 0.0482292i | ||||
\(269\) | 1.34180 | + | 0.488375i | 0.0818110 | + | 0.0297768i | 0.382601 | − | 0.923913i | \(-0.375028\pi\) |
−0.300790 | + | 0.953690i | \(0.597250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.27969 | + | 7.25749i | 0.0777357 | + | 0.440861i | 0.998689 | + | 0.0511882i | \(0.0163008\pi\) |
−0.920953 | + | 0.389673i | \(0.872588\pi\) | |||||||
\(272\) | −0.443463 | − | 1.21840i | −0.0268889 | − | 0.0738766i | ||||
\(273\) | −28.0275 | − | 16.1817i | −1.69630 | − | 0.979359i | ||||
\(274\) | −3.67083 | − | 6.35806i | −0.221763 | − | 0.384104i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.86011 | + | 3.23902i | 0.232351 | + | 0.194966i | ||||
\(277\) | 2.18698 | − | 1.26266i | 0.131403 | − | 0.0758656i | −0.432857 | − | 0.901462i | \(-0.642495\pi\) |
0.564261 | + | 0.825597i | \(0.309161\pi\) | |||||||
\(278\) | 10.2291 | + | 5.90576i | 0.613500 | + | 0.354204i | ||||
\(279\) | 0.854616 | − | 0.311055i | 0.0511645 | − | 0.0186224i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.99175 | − | 16.9671i | 0.178473 | − | 1.01217i | −0.755586 | − | 0.655050i | \(-0.772648\pi\) |
0.934058 | − | 0.357120i | \(-0.116241\pi\) | |||||||
\(282\) | −0.0619974 | + | 0.170336i | −0.00369189 | + | 0.0101434i | ||||
\(283\) | 18.1400 | + | 21.6184i | 1.07831 | + | 1.28508i | 0.956248 | + | 0.292556i | \(0.0945058\pi\) |
0.122061 | + | 0.992523i | \(0.461050\pi\) | |||||||
\(284\) | −11.6528 | −0.691467 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.95915 | 0.352372 | ||||||||
\(287\) | −22.3292 | − | 26.6109i | −1.31805 | − | 1.57079i | ||||
\(288\) | −0.897162 | + | 2.46493i | −0.0528658 | + | 0.145248i | ||||
\(289\) | 2.66009 | − | 15.0861i | 0.156476 | − | 0.887418i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −36.1469 | + | 13.1564i | −2.11897 | + | 0.771241i | ||||
\(292\) | −10.6033 | − | 6.12181i | −0.620510 | − | 0.358252i | ||||
\(293\) | −10.9276 | + | 6.30904i | −0.638396 | + | 0.368578i | −0.783996 | − | 0.620766i | \(-0.786822\pi\) |
0.145601 | + | 0.989343i | \(0.453489\pi\) | |||||||
\(294\) | −5.37089 | − | 4.50671i | −0.313237 | − | 0.262837i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.15751 | + | 8.93306i | 0.299774 | + | 0.519224i | ||||
\(297\) | 1.06633 | + | 0.615647i | 0.0618748 | + | 0.0357234i | ||||
\(298\) | 1.20203 | + | 3.30256i | 0.0696320 | + | 0.191312i | ||||
\(299\) | −1.59601 | − | 9.05140i | −0.0922994 | − | 0.523456i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.1735 | + | 12.4382i | 1.96973 | + | 0.716923i | ||||
\(302\) | −0.136670 | − | 0.162877i | −0.00786445 | − | 0.00937249i | ||||
\(303\) | − | 15.7058i | − | 0.902274i | ||||||
\(304\) | 2.46694 | − | 3.59364i | 0.141488 | − | 0.206109i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.60543 | − | 2.18621i | 0.148942 | − | 0.124978i | ||||
\(307\) | −3.10031 | + | 8.51802i | −0.176944 | + | 0.486149i | −0.996182 | − | 0.0873047i | \(-0.972175\pi\) |
0.819238 | + | 0.573454i | \(0.194397\pi\) | |||||||
\(308\) | 4.28140 | + | 0.754926i | 0.243955 | + | 0.0430159i | ||||
\(309\) | −5.08854 | − | 28.8586i | −0.289477 | − | 1.64171i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.8562 | − | 18.8035i | 0.615599 | − | 1.06625i | −0.374680 | − | 0.927154i | \(-0.622247\pi\) |
0.990279 | − | 0.139095i | \(-0.0444192\pi\) | |||||||
\(312\) | 8.88232 | − | 5.12821i | 0.502863 | − | 0.290328i | ||||
\(313\) | 6.45746 | − | 7.69570i | 0.364997 | − | 0.434987i | −0.552022 | − | 0.833829i | \(-0.686144\pi\) |
0.917019 | + | 0.398843i | \(0.130588\pi\) | |||||||
\(314\) | 5.88898 | + | 4.94144i | 0.332334 | + | 0.278862i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.00496 | + | 12.1330i | −0.394060 | + | 0.682532i | ||||
\(317\) | −0.721135 | − | 1.98130i | −0.0405030 | − | 0.111281i | 0.917792 | − | 0.397061i | \(-0.129970\pi\) |
−0.958295 | + | 0.285780i | \(0.907747\pi\) | |||||||
\(318\) | −14.5245 | + | 2.56107i | −0.814496 | + | 0.143618i | ||||
\(319\) | 0.0311852 | − | 0.176860i | 0.00174604 | − | 0.00990226i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.8997 | + | 16.6979i | −1.11070 | + | 0.931984i | ||||
\(322\) | − | 6.70524i | − | 0.373668i | ||||||
\(323\) | −5.09985 | + | 2.43594i | −0.283763 | + | 0.135539i | ||||
\(324\) | 9.98859 | 0.554921 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.88513 | − | 2.50598i | −0.381332 | − | 0.138794i | ||||
\(327\) | 17.3768 | + | 3.06400i | 0.960939 | + | 0.169439i | ||||
\(328\) | 10.8418 | − | 1.91170i | 0.598636 | − | 0.105556i | ||||
\(329\) | 0.226661 | − | 0.0824977i | 0.0124962 | − | 0.00454824i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.72204 | + | 2.98267i | 0.0946521 | + | 0.163942i | 0.909463 | − | 0.415784i | \(-0.136493\pi\) |
−0.814811 | + | 0.579726i | \(0.803159\pi\) | |||||||
\(332\) | 7.31423 | − | 8.71676i | 0.401420 | − | 0.478394i | ||||
\(333\) | −17.3923 | + | 20.7273i | −0.953091 | + | 1.13585i | ||||
\(334\) | 7.92194 | + | 13.7212i | 0.433469 | + | 0.750791i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.03124 | − | 2.55916i | 0.383586 | − | 0.139614i | ||||
\(337\) | −25.4658 | + | 4.49031i | −1.38721 | + | 0.244603i | −0.816877 | − | 0.576811i | \(-0.804297\pi\) |
−0.570332 | + | 0.821414i | \(0.693186\pi\) | |||||||
\(338\) | −5.62072 | − | 0.991085i | −0.305727 | − | 0.0539079i | ||||
\(339\) | 25.8516 | + | 9.40920i | 1.40406 | + | 0.511038i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.477687 | 0.0258682 | ||||||||
\(342\) | 11.0713 | + | 2.85676i | 0.598668 | + | 0.154476i | ||||
\(343\) | − | 12.7584i | − | 0.688889i | ||||||
\(344\) | −8.82879 | + | 7.40823i | −0.476016 | + | 0.399425i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.88954 | + | 16.3874i | −0.155343 | + | 0.880992i | ||||
\(347\) | 2.48488 | − | 0.438152i | 0.133395 | − | 0.0235212i | −0.106552 | − | 0.994307i | \(-0.533981\pi\) |
0.239947 | + | 0.970786i | \(0.422870\pi\) | |||||||
\(348\) | −0.105716 | − | 0.290453i | −0.00566698 | − | 0.0155699i | ||||
\(349\) | 1.83973 | − | 3.18650i | 0.0984782 | − | 0.170569i | −0.812577 | − | 0.582854i | \(-0.801936\pi\) |
0.911055 | + | 0.412285i | \(0.135269\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.96105 | − | 2.48461i | −0.158049 | − | 0.132619i | ||||
\(352\) | −0.885615 | + | 1.05543i | −0.0472034 | + | 0.0562548i | ||||
\(353\) | 2.42172 | − | 1.39818i | 0.128895 | − | 0.0744175i | −0.434166 | − | 0.900833i | \(-0.642957\pi\) |
0.563061 | + | 0.826415i | \(0.309624\pi\) | |||||||
\(354\) | −9.70609 | + | 16.8114i | −0.515873 | + | 0.893518i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.16356 | − | 17.9414i | −0.167668 | − | 0.950893i | ||||
\(357\) | −9.55440 | − | 1.68470i | −0.505672 | − | 0.0891637i | ||||
\(358\) | 1.56340 | − | 4.29540i | 0.0826281 | − | 0.227019i | ||||
\(359\) | −15.4284 | + | 12.9460i | −0.814280 | + | 0.683262i | −0.951625 | − | 0.307261i | \(-0.900587\pi\) |
0.137345 | + | 0.990523i | \(0.456143\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.6279 | − | 9.19314i | −0.875151 | − | 0.483849i | ||||
\(362\) | 1.68838i | 0.0887395i | ||||||||
\(363\) | 13.8733 | + | 16.5336i | 0.728162 | + | 0.867789i | ||||
\(364\) | −12.8248 | − | 4.66784i | −0.672201 | − | 0.244661i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.23078 | + | 18.3227i | 0.168876 | + | 0.957741i | ||||
\(367\) | −1.54639 | − | 4.24866i | −0.0807207 | − | 0.221778i | 0.892767 | − | 0.450520i | \(-0.148761\pi\) |
−0.973487 | + | 0.228741i | \(0.926539\pi\) | |||||||
\(368\) | 1.84030 | + | 1.06250i | 0.0959321 | + | 0.0553864i | ||||
\(369\) | 14.4390 | + | 25.0091i | 0.751666 | + | 1.30192i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.0340 | + | 12.6150i | 0.780524 | + | 0.654938i | ||||
\(372\) | 0.712009 | − | 0.411079i | 0.0369160 | − | 0.0213134i | ||||
\(373\) | −20.1528 | − | 11.6352i | −1.04347 | − | 0.602449i | −0.122657 | − | 0.992449i | \(-0.539142\pi\) |
−0.920815 | + | 0.390000i | \(0.872475\pi\) | |||||||
\(374\) | 1.67868 | − | 0.610991i | 0.0868027 | − | 0.0315936i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.0132740 | + | 0.0752808i | −0.000684556 | + | 0.00388231i | ||||
\(377\) | −0.192823 | + | 0.529778i | −0.00993091 | + | 0.0272849i | ||||
\(378\) | −1.81263 | − | 2.16021i | −0.0932315 | − | 0.111109i | ||||
\(379\) | −9.34667 | −0.480106 | −0.240053 | − | 0.970760i | \(-0.577165\pi\) | ||||
−0.240053 | + | 0.970760i | \(0.577165\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −38.8860 | −1.99219 | ||||||||
\(382\) | 7.21252 | + | 8.59555i | 0.369025 | + | 0.439787i | ||||
\(383\) | 11.2306 | − | 30.8559i | 0.573858 | − | 1.57666i | −0.224497 | − | 0.974475i | \(-0.572074\pi\) |
0.798355 | − | 0.602187i | \(-0.205704\pi\) | |||||||
\(384\) | −0.411774 | + | 2.33529i | −0.0210133 | + | 0.119172i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.1920 | + | 7.34927i | −1.02774 | + | 0.374068i | ||||
\(387\) | −26.1817 | − | 15.1160i | −1.33089 | − | 0.768389i | ||||
\(388\) | −14.0484 | + | 8.11084i | −0.713199 | + | 0.411766i | ||||
\(389\) | −8.17650 | − | 6.86090i | −0.414565 | − | 0.347862i | 0.411526 | − | 0.911398i | \(-0.364996\pi\) |
−0.826091 | + | 0.563537i | \(0.809440\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.37763 | − | 2.38613i | −0.0696698 | − | 0.120672i | ||||
\(392\) | −2.56055 | − | 1.47834i | −0.129327 | − | 0.0746673i | ||||
\(393\) | 9.03225 | + | 24.8159i | 0.455617 | + | 1.25180i | ||||
\(394\) | 2.65307 | + | 15.0463i | 0.133660 | + | 0.758022i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.39612 | − | 1.23608i | −0.170661 | − | 0.0621156i | ||||
\(397\) | −6.46404 | − | 7.70354i | −0.324421 | − | 0.386630i | 0.579041 | − | 0.815299i | \(-0.303427\pi\) |
−0.903462 | + | 0.428669i | \(0.858983\pi\) | |||||||
\(398\) | − | 0.708758i | − | 0.0355268i | ||||||
\(399\) | −14.0574 | − | 29.4305i | −0.703753 | − | 1.47337i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.25312 | − | 7.76429i | 0.462079 | − | 0.387730i | −0.381817 | − | 0.924238i | \(-0.624701\pi\) |
0.843895 | + | 0.536508i | \(0.180257\pi\) | |||||||
\(402\) | 0.835919 | − | 2.29667i | 0.0416918 | − | 0.114547i | ||||
\(403\) | −1.47681 | − | 0.260401i | −0.0735651 | − | 0.0129715i | ||||
\(404\) | −1.15011 | − | 6.52262i | −0.0572203 | − | 0.324513i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.205650 | + | 0.356196i | −0.0102062 | + | 0.0176777i | ||||
\(407\) | −12.3077 | + | 7.10587i | −0.610071 | + | 0.352225i | ||||
\(408\) | 1.97634 | − | 2.35531i | 0.0978435 | − | 0.116605i | ||||
\(409\) | 30.2942 | + | 25.4198i | 1.49795 | + | 1.25693i | 0.883911 | + | 0.467655i | \(0.154901\pi\) |
0.614040 | + | 0.789275i | \(0.289543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.70468 | − | 15.0769i | 0.429370 | − | 0.743691i | ||||
\(412\) | −4.22655 | − | 11.6123i | −0.208227 | − | 0.572099i | ||||
\(413\) | 25.4386 | − | 4.48552i | 1.25175 | − | 0.220718i | ||||
\(414\) | −0.967936 | + | 5.48944i | −0.0475715 | + | 0.269791i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.31330 | − | 2.78019i | 0.162448 | − | 0.136310i | ||||
\(417\) | 28.0088i | 1.37160i | ||||||||
\(418\) | 4.95121 | + | 3.39887i | 0.242172 | + | 0.166244i | ||||
\(419\) | −28.5326 | −1.39391 | −0.696954 | − | 0.717116i | \(-0.745462\pi\) | ||||
−0.696954 | + | 0.717116i | \(0.745462\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.91607 | − | 0.697393i | −0.0933836 | − | 0.0339888i | 0.294906 | − | 0.955526i | \(-0.404712\pi\) |
−0.388289 | + | 0.921537i | \(0.626934\pi\) | |||||||
\(422\) | 13.8652 | + | 2.44481i | 0.674949 | + | 0.119012i | ||||
\(423\) | −0.197471 | + | 0.0348195i | −0.00960138 | + | 0.00169298i | ||||
\(424\) | −5.84451 | + | 2.12723i | −0.283834 | + | 0.103307i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −13.8162 | − | 23.9304i | −0.669398 | − | 1.15943i | ||||
\(427\) | 15.9138 | − | 18.9653i | 0.770121 | − | 0.917794i | ||||
\(428\) | −7.04161 | + | 8.39187i | −0.340369 | + | 0.405636i | ||||
\(429\) | 7.06551 | + | 12.2378i | 0.341126 | + | 0.590847i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.7523 | + | 4.64147i | −0.614258 | + | 0.223572i | −0.630365 | − | 0.776299i | \(-0.717095\pi\) |
0.0161074 | + | 0.999870i | \(0.494873\pi\) | |||||||
\(432\) | 0.880107 | − | 0.155187i | 0.0423442 | − | 0.00746642i | ||||
\(433\) | 28.5238 | + | 5.02952i | 1.37077 | + | 0.241703i | 0.810078 | − | 0.586323i | \(-0.199425\pi\) |
0.560690 | + | 0.828026i | \(0.310536\pi\) | |||||||
\(434\) | −1.02804 | − | 0.374175i | −0.0493474 | − | 0.0179610i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.44096 | 0.356357 | ||||||||
\(437\) | 3.83652 | − | 8.43073i | 0.183526 | − | 0.403297i | ||||
\(438\) | − | 29.0334i | − | 1.38727i | ||||||
\(439\) | 8.59028 | − | 7.20810i | 0.409992 | − | 0.344024i | −0.414349 | − | 0.910118i | \(-0.635991\pi\) |
0.824341 | + | 0.566094i | \(0.191546\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.34677 | − | 7.63790i | 0.0641318 | − | 0.363710i | ||||
\(442\) | −5.52286 | + | 0.973830i | −0.262696 | + | 0.0463204i | ||||
\(443\) | −2.54804 | − | 7.00068i | −0.121061 | − | 0.332612i | 0.864329 | − | 0.502927i | \(-0.167744\pi\) |
−0.985390 | + | 0.170315i | \(0.945521\pi\) | |||||||
\(444\) | −12.2301 | + | 21.1831i | −0.580413 | + | 1.00530i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.97564 | − | 7.53146i | −0.425009 | − | 0.356625i | ||||
\(447\) | −5.35700 | + | 6.38422i | −0.253377 | + | 0.301963i | ||||
\(448\) | 2.73267 | − | 1.57771i | 0.129107 | − | 0.0745398i | ||||
\(449\) | 2.65192 | − | 4.59326i | 0.125152 | − | 0.216769i | −0.796640 | − | 0.604453i | \(-0.793392\pi\) |
0.921792 | + | 0.387684i | \(0.126725\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.63388 | + | 14.9375i | 0.124025 | + | 0.703378i | ||||
\(452\) | 11.4252 | + | 2.01457i | 0.537396 | + | 0.0947574i | ||||
\(453\) | 0.172443 | − | 0.473783i | 0.00810207 | − | 0.0222603i | ||||
\(454\) | −7.83397 | + | 6.57348i | −0.367667 | + | 0.308509i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.3049 | + | 0.805323i | 0.482571 | + | 0.0377127i | ||||
\(457\) | − | 14.9890i | − | 0.701154i | −0.936534 | − | 0.350577i | \(-0.885986\pi\) | ||
0.936534 | − | 0.350577i | \(-0.114014\pi\) | |||||||
\(458\) | 3.25051 | + | 3.87381i | 0.151886 | + | 0.181011i | ||||
\(459\) | −1.08887 | − | 0.396316i | −0.0508241 | − | 0.0184984i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.19157 | − | 6.75771i | −0.0554968 | − | 0.314738i | 0.944405 | − | 0.328786i | \(-0.106639\pi\) |
−0.999901 | + | 0.0140479i | \(0.995528\pi\) | |||||||
\(462\) | 3.52594 | + | 9.68744i | 0.164042 | + | 0.450701i | ||||
\(463\) | −17.8738 | − | 10.3194i | −0.830665 | − | 0.479585i | 0.0234152 | − | 0.999726i | \(-0.492546\pi\) |
−0.854080 | + | 0.520141i | \(0.825879\pi\) | |||||||
\(464\) | −0.0651735 | − | 0.112884i | −0.00302560 | − | 0.00524050i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.56030 | + | 4.66564i | 0.257576 | + | 0.216132i | ||||
\(467\) | 10.4226 | − | 6.01750i | 0.482301 | − | 0.278457i | −0.239074 | − | 0.971001i | \(-0.576844\pi\) |
0.721375 | + | 0.692545i | \(0.243510\pi\) | |||||||
\(468\) | 9.82555 | + | 5.67279i | 0.454186 | + | 0.262225i | ||||
\(469\) | −3.05609 | + | 1.11233i | −0.141117 | + | 0.0513625i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.16552 | + | 17.9526i | −0.145859 | + | 0.827210i | ||||
\(472\) | −2.79986 | + | 7.69256i | −0.128874 | + | 0.354079i | ||||
\(473\) | −10.2069 | − | 12.1641i | −0.469312 | − | 0.559304i | ||||
\(474\) | −33.2219 | −1.52593 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.09132 | −0.187525 | ||||||||
\(477\) | −10.4869 | − | 12.4979i | −0.480164 | − | 0.572238i | ||||
\(478\) | −5.46314 | + | 15.0098i | −0.249878 | + | 0.686534i | ||||
\(479\) | −3.95553 | + | 22.4329i | −0.180733 | + | 1.02499i | 0.750583 | + | 0.660776i | \(0.229773\pi\) |
−0.931316 | + | 0.364211i | \(0.881339\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 41.9240 | − | 15.2591i | 1.91157 | − | 0.695754i | ||||
\(482\) | −19.2214 | − | 11.0975i | −0.875509 | − | 0.505475i | ||||
\(483\) | 13.7700 | − | 7.95011i | 0.626556 | − | 0.361743i | ||||
\(484\) | 6.97234 | + | 5.85049i | 0.316925 | + | 0.265931i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10.5025 | + | 18.1909i | 0.476403 | + | 0.825155i | ||||
\(487\) | 5.58510 | + | 3.22456i | 0.253085 | + | 0.146119i | 0.621176 | − | 0.783671i | \(-0.286655\pi\) |
−0.368091 | + | 0.929790i | \(0.619989\pi\) | |||||||
\(488\) | 2.68349 | + | 7.37283i | 0.121476 | + | 0.333752i | ||||
\(489\) | −3.01707 | − | 17.1107i | −0.136437 | − | 0.773771i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.8944 | + | 8.33289i | 1.03321 | + | 0.376058i | 0.802303 | − | 0.596917i | \(-0.203608\pi\) |
0.230908 | + | 0.972975i | \(0.425830\pi\) | |||||||
\(492\) | 16.7805 | + | 19.9982i | 0.756524 | + | 0.901590i | ||||
\(493\) | 0.169008i | 0.00761173i | ||||||||
\(494\) | −13.4543 | − | 13.2070i | −0.605336 | − | 0.594209i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.265595 | − | 0.222861i | 0.0119256 | − | 0.0100067i | ||||
\(497\) | −12.5759 | + | 34.5520i | −0.564106 | + | 1.54987i | ||||
\(498\) | 26.5730 | + | 4.68554i | 1.19077 | + | 0.209964i | ||||
\(499\) | −0.282127 | − | 1.60002i | −0.0126298 | − | 0.0716269i | 0.977841 | − | 0.209347i | \(-0.0671337\pi\) |
−0.990471 | + | 0.137720i | \(0.956023\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.7854 | + | 32.5373i | −0.839270 | + | 1.45366i | ||||
\(502\) | 19.5311 | − | 11.2763i | 0.871717 | − | 0.503286i | ||||
\(503\) | −22.6234 | + | 26.9615i | −1.00873 | + | 1.20215i | −0.0294632 | + | 0.999566i | \(0.509380\pi\) |
−0.979264 | + | 0.202588i | \(0.935065\pi\) | |||||||
\(504\) | 6.34060 | + | 5.32040i | 0.282433 | + | 0.236989i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.46388 | + | 2.53551i | −0.0650772 | + | 0.112717i | ||||
\(507\) | −4.62894 | − | 12.7179i | −0.205578 | − | 0.564822i | ||||
\(508\) | −16.1494 | + | 2.84757i | −0.716513 | + | 0.126341i | ||||
\(509\) | 4.20711 | − | 23.8597i | 0.186477 | − | 1.05756i | −0.737567 | − | 0.675274i | \(-0.764025\pi\) |
0.924043 | − | 0.382288i | \(-0.124864\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.5952 | + | 24.8333i | −1.30921 | + | 1.09856i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −1.04308 | − | 3.75323i | −0.0460532 | − | 0.165709i | ||||
\(514\) | 10.7146 | 0.472599 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −25.6816 | − | 9.34733i | −1.13057 | − | 0.411493i | ||||
\(517\) | −0.103720 | − | 0.0182886i | −0.00456159 | − | 0.000804332i | ||||
\(518\) | 32.0537 | − | 5.65193i | 1.40836 | − | 0.248332i | ||||
\(519\) | −37.0795 | + | 13.4958i | −1.62761 | + | 0.592401i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.95859 | + | 6.85648i | 0.173429 | + | 0.300388i | 0.939616 | − | 0.342229i | \(-0.111182\pi\) |
−0.766187 | + | 0.642617i | \(0.777849\pi\) | |||||||
\(522\) | 0.219780 | − | 0.261923i | 0.00961950 | − | 0.0114641i | ||||
\(523\) | 1.57943 | − | 1.88229i | 0.0690637 | − | 0.0823069i | −0.730406 | − | 0.683013i | \(-0.760669\pi\) |
0.799470 | + | 0.600706i | \(0.205114\pi\) | |||||||
\(524\) | 5.56833 | + | 9.64464i | 0.243254 | + | 0.421328i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.0584 | − | 9.12051i | 1.09260 | − | 0.397673i | ||||
\(527\) | −0.442714 | + | 0.0780624i | −0.0192849 | + | 0.00340045i | ||||
\(528\) | −3.21749 | − | 0.567331i | −0.140023 | − | 0.0246899i | ||||
\(529\) | −17.3697 | − | 6.32204i | −0.755203 | − | 0.274871i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.4736 | −0.931874 | ||||||||
\(532\) | −7.99322 | − | 11.1931i | −0.346550 | − | 0.485282i | ||||
\(533\) | − | 47.6163i | − | 2.06249i | ||||||
\(534\) | 33.0939 | − | 27.7691i | 1.43211 | − | 1.20169i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.178976 | − | 1.01502i | 0.00773057 | − | 0.0438422i | ||||
\(537\) | 10.6748 | − | 1.88225i | 0.460650 | − | 0.0812250i | ||||
\(538\) | 0.488375 | + | 1.34180i | 0.0210554 | + | 0.0578491i | ||||
\(539\) | 2.03681 | − | 3.52786i | 0.0877316 | − | 0.151956i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.2132 | + | 14.4436i | 0.740054 | + | 0.620979i | 0.932852 | − | 0.360260i | \(-0.117312\pi\) |
−0.192798 | + | 0.981238i | \(0.561756\pi\) | |||||||
\(542\) | −4.73699 | + | 5.64532i | −0.203471 | + | 0.242487i | ||||
\(543\) | −3.46730 | + | 2.00184i | −0.148796 | + | 0.0859074i | ||||
\(544\) | 0.648300 | − | 1.12289i | 0.0277956 | − | 0.0481434i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.61983 | − | 31.8717i | −0.240507 | − | 1.36398i | ||||
\(547\) | 26.3908 | + | 4.65342i | 1.12839 | + | 0.198966i | 0.706522 | − | 0.707691i | \(-0.250263\pi\) |
0.421869 | + | 0.906657i | \(0.361374\pi\) | |||||||
\(548\) | 2.51099 | − | 6.89889i | 0.107264 | − | 0.294706i | ||||
\(549\) | −15.7660 | + | 13.2292i | −0.672876 | + | 0.564610i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.462374 | + | 0.330191i | −0.0196978 | + | 0.0140666i | ||||
\(552\) | 5.03902i | 0.214475i | ||||||||
\(553\) | 28.4158 | + | 33.8647i | 1.20836 | + | 1.44007i | ||||
\(554\) | 2.37302 | + | 0.863707i | 0.100820 | + | 0.0366954i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.05105 | + | 11.6321i | 0.0869839 | + | 0.493310i | ||||
\(557\) | −13.3749 | − | 36.7473i | −0.566714 | − | 1.55704i | −0.809601 | − | 0.586980i | \(-0.800317\pi\) |
0.242887 | − | 0.970055i | \(-0.421906\pi\) | |||||||
\(558\) | 0.787619 | + | 0.454732i | 0.0333426 | + | 0.0192503i | ||||
\(559\) | 24.9244 | + | 43.1703i | 1.05419 | + | 1.82591i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.24508 | + | 2.72295i | 0.137008 | + | 0.114963i | ||||
\(562\) | 14.9206 | − | 8.61440i | 0.629387 | − | 0.363377i | ||||
\(563\) | −7.46645 | − | 4.31076i | −0.314673 | − | 0.181677i | 0.334343 | − | 0.942452i | \(-0.391486\pi\) |
−0.649016 | + | 0.760775i | \(0.724819\pi\) | |||||||
\(564\) | −0.170336 | + | 0.0619974i | −0.00717246 | + | 0.00261056i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.90049 | + | 27.7920i | −0.205983 | + | 1.16819i | ||||
\(567\) | 10.7799 | − | 29.6174i | 0.452711 | − | 1.24381i | ||||
\(568\) | −7.49028 | − | 8.92657i | −0.314285 | − | 0.374550i | ||||
\(569\) | −23.0260 | −0.965300 | −0.482650 | − | 0.875813i | \(-0.660326\pi\) | ||||
−0.482650 | + | 0.875813i | \(0.660326\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.9673 | −1.25409 | −0.627047 | − | 0.778981i | \(-0.715737\pi\) | ||||
−0.627047 | + | 0.778981i | \(0.715737\pi\) | |||||||
\(572\) | 3.83047 | + | 4.56497i | 0.160160 | + | 0.190871i | ||||
\(573\) | −9.10040 | + | 25.0031i | −0.380175 | + | 1.04452i | ||||
\(574\) | 6.03220 | − | 34.2103i | 0.251779 | − | 1.42791i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.46493 | + | 0.897162i | −0.102706 | + | 0.0373818i | ||||
\(577\) | 3.93622 | + | 2.27258i | 0.163867 | + | 0.0946087i | 0.579691 | − | 0.814837i | \(-0.303173\pi\) |
−0.415824 | + | 0.909445i | \(0.636507\pi\) | |||||||
\(578\) | 13.2665 | − | 7.65941i | 0.551813 | − | 0.318590i | ||||
\(579\) | −39.0333 | − | 32.7529i | −1.62217 | − | 1.36116i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.9526 | − | 31.0949i | −0.744800 | − | 1.29003i | ||||
\(582\) | −33.3131 | − | 19.2334i | −1.38087 | − | 0.797248i | ||||
\(583\) | −2.93083 | − | 8.05240i | −0.121383 | − | 0.333496i | ||||
\(584\) | −2.12608 | − | 12.0576i | −0.0879779 | − | 0.498947i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.8571 | − | 4.31563i | −0.489813 | − | 0.178277i | ||||
\(587\) | −11.8709 | − | 14.1471i | −0.489963 | − | 0.583915i | 0.463245 | − | 0.886230i | \(-0.346685\pi\) |
−0.953208 | + | 0.302315i | \(0.902240\pi\) | |||||||
\(588\) | − | 7.01120i | − | 0.289137i | ||||||
\(589\) | −1.07850 | − | 1.05867i | −0.0444387 | − | 0.0436219i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.7537 | + | 23.2881i | −1.14164 | + | 0.957946i | ||||
\(592\) | −3.52794 | + | 9.69294i | −0.144998 | + | 0.398377i | ||||
\(593\) | −15.7488 | − | 2.77694i | −0.646726 | − | 0.114035i | −0.159343 | − | 0.987223i | \(-0.550938\pi\) |
−0.487384 | + | 0.873188i | \(0.662049\pi\) | |||||||
\(594\) | 0.213812 | + | 1.21259i | 0.00877280 | + | 0.0497530i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.75726 | + | 3.04366i | −0.0719800 | + | 0.124673i | ||||
\(597\) | 1.45552 | − | 0.840343i | 0.0595704 | − | 0.0343930i | ||||
\(598\) | 5.90788 | − | 7.04074i | 0.241591 | − | 0.287917i | ||||
\(599\) | −3.02967 | − | 2.54220i | −0.123789 | − | 0.103871i | 0.578792 | − | 0.815476i | \(-0.303524\pi\) |
−0.702581 | + | 0.711604i | \(0.747969\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.10855 | − | 1.92006i | 0.0452186 | − | 0.0783209i | −0.842530 | − | 0.538649i | \(-0.818935\pi\) |
0.887749 | + | 0.460328i | \(0.152268\pi\) | |||||||
\(602\) | 12.4382 | + | 34.1735i | 0.506941 | + | 1.39281i | ||||
\(603\) | 2.66253 | − | 0.469476i | 0.108427 | − | 0.0191185i | ||||
\(604\) | 0.0369211 | − | 0.209390i | 0.00150230 | − | 0.00851996i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.0313 | − | 10.0955i | 0.488739 | − | 0.410101i | ||||
\(607\) | − | 17.4964i | − | 0.710155i | −0.934837 | − | 0.355078i | \(-0.884454\pi\) | ||
0.934837 | − | 0.355078i | \(-0.115546\pi\) | |||||||
\(608\) | 4.33860 | − | 0.420163i | 0.175954 | − | 0.0170399i | ||||
\(609\) | −0.975319 | −0.0395219 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.310689 | + | 0.113082i | 0.0125691 | + | 0.00457479i | ||||
\(612\) | 3.34947 | + | 0.590603i | 0.135394 | + | 0.0238737i | ||||
\(613\) | −8.98922 | + | 1.58504i | −0.363071 | + | 0.0640193i | −0.352208 | − | 0.935922i | \(-0.614569\pi\) |
−0.0108633 | + | 0.999941i | \(0.503458\pi\) | |||||||
\(614\) | −8.51802 | + | 3.10031i | −0.343759 | + | 0.125118i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.17372 | + | 3.76500i | 0.0875818 | + | 0.151696i | ||||
\(617\) | 1.00026 | − | 1.19206i | 0.0402689 | − | 0.0479906i | −0.745534 | − | 0.666467i | \(-0.767806\pi\) |
0.785803 | + | 0.618477i | \(0.212250\pi\) | |||||||
\(618\) | 18.8361 | − | 22.4480i | 0.757699 | − | 0.902990i | ||||
\(619\) | 16.2140 | + | 28.0835i | 0.651695 | + | 1.12877i | 0.982711 | + | 0.185144i | \(0.0592753\pi\) |
−0.331016 | + | 0.943625i | \(0.607391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.78454 | − | 0.649520i | 0.0716112 | − | 0.0260644i | ||||
\(622\) | 21.3826 | − | 3.77032i | 0.857362 | − | 0.151176i | ||||
\(623\) | −56.6127 | − | 9.98235i | −2.26814 | − | 0.399934i | ||||
\(624\) | 9.63789 | + | 3.50790i | 0.385824 | + | 0.140429i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.0460 | 0.401520 | ||||||||
\(627\) | −1.10955 | + | 14.1978i | −0.0443112 | + | 0.567005i | ||||
\(628\) | 7.68751i | 0.306765i | ||||||||
\(629\) | 10.2454 | − | 8.59692i | 0.408511 | − | 0.342782i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.67744 | + | 9.51323i | −0.0667778 | + | 0.378716i | 0.933043 | + | 0.359766i | \(0.117143\pi\) |
−0.999820 | + | 0.0189499i | \(0.993968\pi\) | |||||||
\(632\) | −13.7971 | + | 2.43280i | −0.548819 | + | 0.0967715i | ||||
\(633\) | 11.4187 | + | 31.3726i | 0.453852 | + | 1.24695i | ||||
\(634\) | 1.05423 | − | 1.82598i | 0.0418688 | − | 0.0725189i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11.2981 | − | 9.48023i | −0.447999 | − | 0.375915i | ||||
\(637\) | −8.22011 | + | 9.79635i | −0.325693 | + | 0.388145i | ||||
\(638\) | 0.155528 | − | 0.0897942i | 0.00615741 | − | 0.00355498i | ||||
\(639\) | 15.2834 | − | 26.4716i | 0.604602 | − | 1.04720i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.05763 | + | 40.0258i | 0.278759 | + | 1.58092i | 0.726761 | + | 0.686891i | \(0.241025\pi\) |
−0.448001 | + | 0.894033i | \(0.647864\pi\) | |||||||
\(642\) | −25.5826 | − | 4.51091i | −1.00967 | − | 0.178031i | ||||
\(643\) | −14.3882 | + | 39.5312i | −0.567414 | + | 1.55896i | 0.241112 | + | 0.970497i | \(0.422488\pi\) |
−0.808526 | + | 0.588460i | \(0.799734\pi\) | |||||||
\(644\) | 5.13651 | − | 4.31004i | 0.202407 | − | 0.169840i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.14416 | − | 2.34092i | −0.202394 | − | 0.0921022i | ||||
\(647\) | − | 18.0072i | − | 0.707936i | −0.935258 | − | 0.353968i | \(-0.884832\pi\) | ||
0.935258 | − | 0.353968i | \(-0.115168\pi\) | |||||||
\(648\) | 6.42054 | + | 7.65170i | 0.252223 | + | 0.300587i | ||||
\(649\) | −10.5986 | − | 3.85757i | −0.416031 | − | 0.151423i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.450487 | − | 2.55484i | −0.0176560 | − | 0.100132i | ||||
\(652\) | −2.50598 | − | 6.88513i | −0.0981419 | − | 0.269643i | ||||
\(653\) | −34.1968 | − | 19.7435i | −1.33822 | − | 0.772624i | −0.351680 | − | 0.936120i | \(-0.614390\pi\) |
−0.986544 | + | 0.163496i | \(0.947723\pi\) | |||||||
\(654\) | 8.82243 | + | 15.2809i | 0.344984 | + | 0.597530i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.43340 | + | 7.07646i | 0.329269 | + | 0.276289i | ||||
\(657\) | 27.8138 | − | 16.0583i | 1.08512 | − | 0.626493i | ||||
\(658\) | 0.208891 | + | 0.120604i | 0.00814344 | + | 0.00470162i | ||||
\(659\) | 33.6395 | − | 12.2438i | 1.31041 | − | 0.476949i | 0.410035 | − | 0.912070i | \(-0.365516\pi\) |
0.900372 | + | 0.435120i | \(0.143294\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.36241 | − | 13.3979i | 0.0918871 | − | 0.521118i | −0.903770 | − | 0.428019i | \(-0.859212\pi\) |
0.995657 | − | 0.0930988i | \(-0.0296772\pi\) | |||||||
\(662\) | −1.17795 | + | 3.23639i | −0.0457822 | + | 0.125786i | ||||
\(663\) | −8.54809 | − | 10.1872i | −0.331980 | − | 0.395639i | ||||
\(664\) | 11.3789 | 0.441588 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −27.0576 | −1.04846 | ||||||||
\(667\) | −0.178043 | − | 0.212184i | −0.00689386 | − | 0.00821578i | ||||
\(668\) | −5.41893 | + | 14.8884i | −0.209665 | + | 0.576049i | ||||
\(669\) | 4.82470 | − | 27.3623i | 0.186534 | − | 1.05789i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.1581 | + | 3.69724i | −0.392148 | + | 0.142730i | ||||
\(672\) | 6.48003 | + | 3.74124i | 0.249972 | + | 0.144322i | ||||
\(673\) | −36.5649 | + | 21.1108i | −1.40947 | + | 0.813760i | −0.995337 | − | 0.0964549i | \(-0.969250\pi\) |
−0.414136 | + | 0.910215i | \(0.635916\pi\) | |||||||
\(674\) | −19.8089 | − | 16.6216i | −0.763009 | − | 0.640241i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.85372 | − | 4.94278i | −0.109758 | − | 0.190107i | ||||
\(677\) | −37.8202 | − | 21.8355i | −1.45355 | − | 0.839207i | −0.454869 | − | 0.890558i | \(-0.650314\pi\) |
−0.998681 | + | 0.0513514i | \(0.983647\pi\) | |||||||
\(678\) | 9.40920 | + | 25.8516i | 0.361358 | + | 0.992824i | ||||
\(679\) | 8.88840 | + | 50.4086i | 0.341105 | + | 1.93450i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.7878 | − | 8.29409i | −0.873231 | − | 0.317830i | ||||
\(682\) | 0.307051 | + | 0.365929i | 0.0117576 | + | 0.0140122i | ||||
\(683\) | 9.22100i | 0.352832i | 0.984316 | + | 0.176416i | \(0.0564504\pi\) | ||||
−0.984316 | + | 0.176416i | \(0.943550\pi\) | |||||||
\(684\) | 4.92810 | + | 10.3174i | 0.188431 | + | 0.394496i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.77350 | − | 8.20094i | 0.373154 | − | 0.313113i | ||||
\(687\) | −4.10133 | + | 11.2683i | −0.156475 | + | 0.429913i | ||||
\(688\) | −11.3501 | − | 2.00132i | −0.432717 | − | 0.0762998i | ||||
\(689\) | 4.67132 | + | 26.4924i | 0.177963 | + | 1.00928i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0044 | − | 34.6487i | 0.761004 | − | 1.31810i | −0.181330 | − | 0.983422i | \(-0.558040\pi\) |
0.942334 | − | 0.334675i | \(-0.108626\pi\) | |||||||
\(692\) | −14.4108 | + | 8.32010i | −0.547818 | + | 0.316283i | ||||
\(693\) | −7.33029 | + | 8.73590i | −0.278455 | + | 0.331849i | ||||
\(694\) | 1.93290 | + | 1.62189i | 0.0733717 | + | 0.0615662i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.154547 | − | 0.267683i | 0.00585808 | − | 0.0101465i | ||||
\(697\) | −4.88209 | − | 13.4134i | −0.184922 | − | 0.508070i | ||||
\(698\) | 3.62355 | − | 0.638930i | 0.137153 | − | 0.0241839i | ||||
\(699\) | −2.98884 | + | 16.9506i | −0.113048 | + | 0.641130i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.37655 | + | 1.15507i | −0.0519917 | + | 0.0436262i | −0.668413 | − | 0.743790i | \(-0.733026\pi\) |
0.616422 | + | 0.787416i | \(0.288582\pi\) | |||||||
\(702\) | − | 3.86537i | − | 0.145889i | ||||||
\(703\) | 43.5361 | + | 11.2337i | 1.64200 | + | 0.423688i | ||||
\(704\) | −1.37777 | −0.0519267 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.62772 | + | 0.956410i | 0.0988954 | + | 0.0359950i | ||||
\(707\) | −20.5816 | − | 3.62909i | −0.774051 | − | 0.136486i | ||||
\(708\) | −19.1173 | + | 3.37089i | −0.718471 | + | 0.126686i | ||||
\(709\) | 31.8904 | − | 11.6072i | 1.19767 | − | 0.435916i | 0.335259 | − | 0.942126i | \(-0.391176\pi\) |
0.862410 | + | 0.506210i | \(0.168954\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.3749 | − | 31.8263i | −0.689113 | − | 1.19358i | ||||
\(712\) | 11.7104 | − | 13.9559i | 0.438867 | − | 0.523021i | ||||
\(713\) | 0.473577 | − | 0.564387i | 0.0177356 | − | 0.0211365i | ||||
\(714\) | −4.85090 | − | 8.40200i | −0.181540 | − | 0.314437i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.29540 | − | 1.56340i | 0.160527 | − | 0.0584269i | ||||
\(717\) | −37.3019 | + | 6.57733i | −1.39306 | + | 0.245635i | ||||
\(718\) | −19.8344 | − | 3.49734i | −0.740212 | − | 0.130519i | ||||
\(719\) | −4.77790 | − | 1.73901i | −0.178186 | − | 0.0648542i | 0.251387 | − | 0.967887i | \(-0.419113\pi\) |
−0.429572 | + | 0.903033i | \(0.641336\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.9934 | −1.45219 | ||||||||
\(722\) | −3.64584 | − | 18.6469i | −0.135684 | − | 0.693967i | ||||
\(723\) | − | 52.6311i | − | 1.95737i | ||||||
\(724\) | −1.29338 | + | 1.08527i | −0.0480680 | + | 0.0403338i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.74786 | + | 21.2552i | −0.139096 | + | 0.788854i | ||||
\(727\) | −21.2529 | + | 3.74747i | −0.788228 | + | 0.138986i | −0.553250 | − | 0.833015i | \(-0.686613\pi\) |
−0.234977 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(728\) | −4.66784 | − | 12.8248i | −0.173002 | − | 0.475318i | ||||
\(729\) | −9.92186 | + | 17.1852i | −0.367476 | + | 0.636487i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.4474 | + | 9.60551i | 0.423397 | + | 0.355273i | ||||
\(732\) | −11.9593 | + | 14.2525i | −0.442027 | + | 0.526788i | ||||
\(733\) | 8.20601 | − | 4.73774i | 0.303096 | − | 0.174993i | −0.340737 | − | 0.940159i | \(-0.610677\pi\) |
0.643833 | + | 0.765166i | \(0.277343\pi\) | |||||||
\(734\) | 2.26066 | − | 3.91559i | 0.0834426 | − | 0.144527i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.369001 | + | 2.09271i | 0.0136015 | + | 0.0771382i | ||||
\(737\) | 1.39847 | + | 0.246588i | 0.0515132 | + | 0.00908317i | ||||
\(738\) | −9.87687 | + | 27.1365i | −0.363573 | + | 0.998908i | ||||
\(739\) | 6.02954 | − | 5.05938i | 0.221800 | − | 0.186112i | −0.525116 | − | 0.851031i | \(-0.675978\pi\) |
0.746916 | + | 0.664918i | \(0.231534\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.1699 | − | 43.2888i | 0.410337 | − | 1.59026i | ||||
\(742\) | 19.6254i | 0.720473i | ||||||||
\(743\) | 31.1013 | + | 37.0651i | 1.14100 | + | 1.35979i | 0.923442 | + | 0.383737i | \(0.125363\pi\) |
0.217553 | + | 0.976049i | \(0.430193\pi\) | |||||||
\(744\) | 0.772575 | + | 0.281194i | 0.0283240 | + | 0.0103091i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.04087 | − | 22.9169i | −0.147947 | − | 0.839048i | ||||
\(747\) | 10.2087 | + | 28.0483i | 0.373518 | + | 1.02623i | ||||
\(748\) | 1.54708 | + | 0.893209i | 0.0565670 | + | 0.0326590i | ||||
\(749\) | 17.2835 | + | 29.9359i | 0.631525 | + | 1.09383i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.30243 | − | 7.80567i | −0.339451 | − | 0.284833i | 0.457087 | − | 0.889422i | \(-0.348893\pi\) |
−0.796537 | + | 0.604589i | \(0.793337\pi\) | |||||||
\(752\) | −0.0662008 | + | 0.0382211i | −0.00241410 | + | 0.00139378i | ||||
\(753\) | 46.3145 | + | 26.7397i | 1.68779 | + | 0.974447i | ||||
\(754\) | −0.529778 | + | 0.192823i | −0.0192934 | + | 0.00702221i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.489679 | − | 2.77711i | 0.0178095 | − | 0.101002i | ||||
\(757\) | −11.9596 | + | 32.8586i | −0.434677 | + | 1.19427i | 0.508233 | + | 0.861220i | \(0.330299\pi\) |
−0.942910 | + | 0.333046i | \(0.891923\pi\) | |||||||
\(758\) | −6.00792 | − | 7.15997i | −0.218218 | − | 0.260062i | ||||
\(759\) | −6.94262 | −0.252001 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.9073 | 1.70039 | 0.850194 | − | 0.526470i | \(-0.176485\pi\) | ||||
0.850194 | + | 0.526470i | \(0.176485\pi\) | |||||||
\(762\) | −24.9954 | − | 29.7884i | −0.905489 | − | 1.07912i | ||||
\(763\) | 8.03041 | − | 22.0634i | 0.290720 | − | 0.798748i | ||||
\(764\) | −1.94845 | + | 11.0502i | −0.0704926 | + | 0.399783i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.8559 | − | 11.2306i | 1.11487 | − | 0.405779i | ||||
\(767\) | 30.6636 | + | 17.7036i | 1.10720 | + | 0.639241i | ||||
\(768\) | −2.05362 | + | 1.18566i | −0.0741035 | + | 0.0427837i | ||||
\(769\) | −1.06182 | − | 0.890969i | −0.0382900 | − | 0.0321292i | 0.623442 | − | 0.781870i | \(-0.285734\pi\) |
−0.661732 | + | 0.749741i | \(0.730178\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.7038 | + | 22.0036i | 0.457516 | + | 0.792440i | ||||
\(772\) | −18.6090 | − | 10.7439i | −0.669753 | − | 0.386682i | ||||
\(773\) | −2.20242 | − | 6.05111i | −0.0792157 | − | 0.217643i | 0.893762 | − | 0.448541i | \(-0.148056\pi\) |
−0.972978 | + | 0.230897i | \(0.925834\pi\) | |||||||
\(774\) | −5.24973 | − | 29.7727i | −0.188698 | − | 1.07016i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −15.2434 | − | 5.54814i | −0.547206 | − | 0.199167i | ||||
\(777\) | 49.6116 | + | 59.1248i | 1.77981 | + | 2.12109i | ||||
\(778\) | − | 10.6737i | − | 0.382670i | ||||||
\(779\) | 27.1585 | − | 39.5624i | 0.973056 | − | 1.41747i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.2988 | − | 10.3199i | 0.440085 | − | 0.369275i | ||||
\(782\) | 0.942355 | − | 2.58910i | 0.0336985 | − | 0.0925860i | ||||
\(783\) | −0.114719 | − | 0.0202281i | −0.00409973 | − | 0.000722893i | ||||
\(784\) | −0.513421 | − | 2.91175i | −0.0183365 | − | 0.103991i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −13.2043 | + | 22.8705i | −0.470981 | + | 0.815762i | ||||
\(787\) | −7.30651 | + | 4.21842i | −0.260449 | + | 0.150370i | −0.624539 | − | 0.780993i | \(-0.714713\pi\) |
0.364090 | + | 0.931364i | \(0.381380\pi\) | |||||||
\(788\) | −9.82078 | + | 11.7040i | −0.349851 | + | 0.416936i | ||||
\(789\) | 48.4407 | + | 40.6466i | 1.72453 | + | 1.44706i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.3037 | − | 31.7030i | 0.650805 | − | 1.12723i | ||||
\(792\) | −1.23608 | − | 3.39612i | −0.0439224 | − | 0.120676i | ||||
\(793\) | 33.4200 | − | 5.89285i | 1.18678 | − | 0.209261i | ||||
\(794\) | 1.74625 | − | 9.90348i | 0.0619721 | − | 0.351461i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.542940 | − | 0.455581i | 0.0192440 | − | 0.0161476i | ||||
\(797\) | 32.4342i | 1.14888i | 0.818548 | + | 0.574438i | \(0.194779\pi\) | ||||
−0.818548 | + | 0.574438i | \(0.805221\pi\) | |||||||
\(798\) | 13.5091 | − | 29.6862i | 0.478217 | − | 1.05088i | ||||
\(799\) | 0.0991149 | 0.00350643 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 44.9066 | + | 16.3447i | 1.58670 | + | 0.577511i | ||||
\(802\) | 11.8956 | + | 2.09751i | 0.420047 | + | 0.0740657i | ||||
\(803\) | 16.6126 | − | 2.92926i | 0.586247 | − | 0.103371i | ||||
\(804\) | 2.29667 | − | 0.835919i | 0.0809973 | − | 0.0294806i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.749796 | − | 1.29868i | −0.0264104 | − | 0.0457442i | ||||
\(807\) | −2.17650 | + | 2.59385i | −0.0766164 | + | 0.0913079i | ||||
\(808\) | 4.25734 | − | 5.07370i | 0.149773 | − | 0.178492i | ||||
\(809\) | −9.01013 | − | 15.6060i | −0.316779 | − | 0.548678i | 0.663035 | − | 0.748589i | \(-0.269268\pi\) |
−0.979814 | + | 0.199911i | \(0.935935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.5830 | − | 8.94748i | 0.863226 | − | 0.314189i | 0.127805 | − | 0.991799i | \(-0.459207\pi\) |
0.735421 | + | 0.677611i | \(0.236985\pi\) | |||||||
\(812\) | −0.405051 | + | 0.0714214i | −0.0142145 | + | 0.00250640i | ||||
\(813\) | −17.2098 | − | 3.03455i | −0.603573 | − | 0.106426i | ||||
\(814\) | −13.3547 | − | 4.86070i | −0.468081 | − | 0.170367i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.07464 | 0.107634 | ||||||||
\(817\) | −3.91407 | + | 50.0843i | −0.136936 | + | 1.75223i | ||||
\(818\) | 39.5462i | 1.38270i | ||||||||
\(819\) | 27.4244 | − | 23.0118i | 0.958287 | − | 0.804098i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.91249 | + | 27.8601i | −0.171447 | + | 0.972325i | 0.770718 | + | 0.637176i | \(0.219898\pi\) |
−0.942165 | + | 0.335149i | \(0.891213\pi\) | |||||||
\(822\) | 17.1449 | − | 3.02310i | 0.597996 | − | 0.105443i | ||||
\(823\) | −17.0857 | − | 46.9427i | −0.595571 | − | 1.63632i | −0.759995 | − | 0.649929i | \(-0.774799\pi\) |
0.164424 | − | 0.986390i | \(-0.447423\pi\) | |||||||
\(824\) | 6.17880 | − | 10.7020i | 0.215249 | − | 0.372822i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.7878 | + | 16.6039i | 0.688504 | + | 0.577723i | ||||
\(827\) | −3.41471 | + | 4.06949i | −0.118741 | + | 0.141510i | −0.822140 | − | 0.569285i | \(-0.807220\pi\) |
0.703399 | + | 0.710795i | \(0.251665\pi\) | |||||||
\(828\) | −4.82733 | + | 2.78706i | −0.167761 | + | 0.0968570i | ||||
\(829\) | 18.4308 | − | 31.9231i | 0.640129 | − | 1.10874i | −0.345275 | − | 0.938502i | \(-0.612214\pi\) |
0.985404 | − | 0.170234i | \(-0.0544524\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.03986 | + | 5.89733i | 0.0360723 | + | 0.204576i | ||||
\(832\) | 4.25950 | + | 0.751065i | 0.147672 | + | 0.0260385i | ||||
\(833\) | −1.31118 | + | 3.60242i | −0.0454295 | + | 0.124817i | ||||
\(834\) | −21.4560 | + | 18.0037i | −0.742961 | + | 0.623418i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.578889 | + | 5.97760i | 0.0200213 | + | 0.206740i | ||||
\(837\) | − | 0.309849i | − | 0.0107099i | ||||||
\(838\) | −18.3404 | − | 21.8572i | −0.633558 | − | 0.755045i | ||||
\(839\) | −42.0154 | − | 15.2924i | −1.45053 | − | 0.527951i | −0.507793 | − | 0.861479i | \(-0.669538\pi\) |
−0.942740 | + | 0.333528i | \(0.891761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.03285 | − | 28.5427i | −0.173546 | − | 0.984231i | ||||
\(842\) | −0.697393 | − | 1.91607i | −0.0240337 | − | 0.0660321i | ||||
\(843\) | 35.3814 | + | 20.4275i | 1.21860 | + | 0.703559i | ||||
\(844\) | 7.03956 | + | 12.1929i | 0.242312 | + | 0.419696i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.153605 | − | 0.128890i | −0.00528106 | − | 0.00443133i | ||||
\(847\) | 24.8721 | − | 14.3599i | 0.854615 | − | 0.493412i | ||||
\(848\) | −5.38633 | − | 3.10980i | −0.184967 | − | 0.106791i | ||||
\(849\) | −62.8845 | + | 22.8881i | −2.15819 | + | 0.785517i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.80625 | + | 21.5863i | −0.130476 | + | 0.739969i | ||||
\(852\) | 9.45085 | − | 25.9660i | 0.323781 | − | 0.889581i | ||||
\(853\) | −18.9389 | − | 22.5705i | −0.648457 | − | 0.772800i | 0.337224 | − | 0.941424i | \(-0.390512\pi\) |
−0.985680 | + | 0.168624i | \(0.946068\pi\) | |||||||
\(854\) | 24.7574 | 0.847181 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.9548 | −0.374428 | ||||||||
\(857\) | 30.5152 | + | 36.3667i | 1.04238 | + | 1.24226i | 0.969544 | + | 0.244917i | \(0.0787608\pi\) |
0.0728369 | + | 0.997344i | \(0.476795\pi\) | |||||||
\(858\) | −4.83309 | + | 13.2788i | −0.164999 | + | 0.453331i | ||||
\(859\) | −0.165772 | + | 0.940140i | −0.00565607 | + | 0.0320772i | −0.987505 | − | 0.157587i | \(-0.949629\pi\) |
0.981849 | + | 0.189664i | \(0.0607398\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 77.4070 | − | 28.1739i | 2.63802 | − | 0.960162i | ||||
\(862\) | −11.7526 | − | 6.78537i | −0.400295 | − | 0.231111i | ||||
\(863\) | 40.7257 | − | 23.5130i | 1.38632 | − | 0.800392i | 0.393421 | − | 0.919359i | \(-0.371292\pi\) |
0.992898 | + | 0.118967i | \(0.0379583\pi\) | |||||||
\(864\) | 0.684602 | + | 0.574449i | 0.0232906 | + | 0.0195432i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.4819 | + | 25.0834i | 0.492116 | + | 0.852370i | ||||
\(867\) | 31.4590 | + | 18.1629i | 1.06840 | + | 0.616843i | ||||
\(868\) | −0.374175 | − | 1.02804i | −0.0127003 | − | 0.0348939i | ||||
\(869\) | −3.35184 | − | 19.0092i | −0.113703 | − | 0.644844i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.18906 | − | 1.52469i | −0.141941 | − | 0.0516622i | ||||
\(872\) | 4.78296 | + | 5.70011i | 0.161971 | + | 0.193030i | ||||
\(873\) | − | 42.5515i | − | 1.44015i | ||||||
\(874\) | 8.92438 | − | 2.48023i | 0.301872 | − | 0.0838949i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 22.2409 | − | 18.6623i | 0.751451 | − | 0.630542i | ||||
\(877\) | 14.6358 | − | 40.2114i | 0.494215 | − | 1.35784i | −0.402575 | − | 0.915387i | \(-0.631885\pi\) |
0.896790 | − | 0.442457i | \(-0.145893\pi\) | |||||||
\(878\) | 11.0435 | + | 1.94726i | 0.372699 | + | 0.0657168i | ||||
\(879\) | −5.19580 | − | 29.4668i | −0.175250 | − | 0.993891i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.53664 | + | 7.85770i | −0.152843 | + | 0.264733i | −0.932272 | − | 0.361759i | \(-0.882176\pi\) |
0.779428 | + | 0.626491i | \(0.215510\pi\) | |||||||
\(882\) | 6.71666 | − | 3.87786i | 0.226162 | − | 0.130574i | ||||
\(883\) | 20.1333 | − | 23.9939i | 0.677539 | − | 0.807460i | −0.312250 | − | 0.950000i | \(-0.601083\pi\) |
0.989789 | + | 0.142540i | \(0.0455270\pi\) | |||||||
\(884\) | −4.29603 | − | 3.60479i | −0.144491 | − | 0.121242i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.72498 | − | 6.45186i | 0.125143 | − | 0.216755i | ||||
\(887\) | −1.16097 | − | 3.18973i | −0.0389814 | − | 0.107101i | 0.918675 | − | 0.395015i | \(-0.129260\pi\) |
−0.957656 | + | 0.287914i | \(0.907038\pi\) | |||||||
\(888\) | −24.0885 | + | 4.24746i | −0.808358 | + | 0.142535i | ||||
\(889\) | −8.98528 | + | 50.9581i | −0.301357 | + | 1.70908i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.5423 | + | 8.84604i | −0.353180 | + | 0.296353i | ||||
\(892\) | − | 11.7169i | − | 0.392310i | ||||||
\(893\) | 0.193641 | + | 0.271160i | 0.00647995 | + | 0.00907402i | ||||
\(894\) | −8.33401 | −0.278731 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.96512 | + | 1.07922i | 0.0990579 | + | 0.0360541i | ||||
\(897\) | 21.4637 | + | 3.78463i | 0.716652 | + | 0.126365i | ||||
\(898\) | 5.22326 | − | 0.921002i | 0.174303 | − | 0.0307342i | ||||
\(899\) | −0.0424671 | + | 0.0154568i | −0.00141636 | + | 0.000515512i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.03216 | + | 6.98391i | 0.134331 | + | 0.232668i | ||||
\(902\) | −9.74975 | + | 11.6193i | −0.324631 | + | 0.386880i | ||||
\(903\) | −55.4320 | + | 66.0613i | −1.84466 | + | 2.19838i | ||||
\(904\) | 5.80072 | + | 10.0471i | 0.192929 | + | 0.334163i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.473783 | − | 0.172443i | 0.0157404 | − | 0.00572903i | ||||
\(907\) | 39.0053 | − | 6.87769i | 1.29515 | − | 0.228370i | 0.516749 | − | 0.856137i | \(-0.327142\pi\) |
0.778401 | + | 0.627767i | \(0.216031\pi\) | |||||||
\(908\) | −10.0712 | − | 1.77582i | −0.334223 | − | 0.0589326i | ||||
\(909\) | 16.3259 | + | 5.94213i | 0.541494 | + | 0.197088i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0316 | −0.796204 | −0.398102 | − | 0.917341i | \(-0.630331\pi\) | ||||
−0.398102 | + | 0.917341i | \(0.630331\pi\) | |||||||
\(912\) | 6.00695 | + | 8.41166i | 0.198910 | + | 0.278538i | ||||
\(913\) | 15.6776i | 0.518851i | ||||||||
\(914\) | 11.4822 | − | 9.63471i | 0.379798 | − | 0.318688i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.878120 | + | 4.98007i | −0.0290139 | + | 0.164546i | ||||
\(917\) | 34.6070 | − | 6.10215i | 1.14282 | − | 0.201511i | ||||
\(918\) | −0.396316 | − | 1.08887i | −0.0130804 | − | 0.0359380i | ||||
\(919\) | 1.92860 | − | 3.34044i | 0.0636187 | − | 0.110191i | −0.832462 | − | 0.554083i | \(-0.813069\pi\) |
0.896080 | + | 0.443892i | \(0.146403\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.4663 | − | 13.8169i | −0.542583 | − | 0.455281i | ||||
\(922\) | 4.41078 | − | 5.25656i | 0.145261 | − | 0.173116i | ||||
\(923\) | −43.6484 | + | 25.2004i | −1.43670 | + | 0.829481i | ||||
\(924\) | −5.15458 | + | 8.92800i | −0.169573 | + | 0.293710i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.58390 | − | 20.3253i | −0.117774 | − | 0.667931i | ||||
\(927\) | 31.9231 | + | 5.62890i | 1.04849 | + | 0.184877i | ||||
\(928\) | 0.0445813 | − | 0.122486i | 0.00146345 | − | 0.00402080i | ||||
\(929\) | −15.5371 | + | 13.0371i | −0.509755 | + | 0.427735i | −0.861043 | − | 0.508532i | \(-0.830188\pi\) |
0.351288 | + | 0.936267i | \(0.385744\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.4172 | + | 3.45094i | −0.406958 | + | 0.113100i | ||||
\(932\) | 7.25845i | 0.237759i | ||||||||
\(933\) | 33.0952 | + | 39.4413i | 1.08349 | + | 1.29125i | ||||
\(934\) | 11.3092 | + | 4.11621i | 0.370048 | + | 0.134687i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.97014 | + | 11.1732i | 0.0643960 | + | 0.365208i | ||||
\(937\) | −9.43723 | − | 25.9286i | −0.308301 | − | 0.847050i | −0.992988 | − | 0.118213i | \(-0.962283\pi\) |
0.684687 | − | 0.728837i | \(-0.259939\pi\) | |||||||
\(938\) | −2.81651 | − | 1.62611i | −0.0919623 | − | 0.0530945i | ||||
\(939\) | 11.9111 | + | 20.6307i | 0.388705 | + | 0.673257i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.5704 | − | 14.7433i | −0.572780 | − | 0.480619i | 0.309787 | − | 0.950806i | \(-0.399742\pi\) |
−0.882567 | + | 0.470187i | \(0.844187\pi\) | |||||||
\(942\) | −15.7872 | + | 9.11475i | −0.514375 | + | 0.296975i | ||||
\(943\) | 20.2599 | + | 11.6970i | 0.659752 | + | 0.380908i | ||||
\(944\) | −7.69256 | + | 2.79986i | −0.250372 | + | 0.0911278i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.75737 | − | 15.6378i | 0.0896498 | − | 0.508429i | ||||
\(947\) | −9.60233 | + | 26.3822i | −0.312034 | + | 0.857306i | 0.680212 | + | 0.733016i | \(0.261888\pi\) |
−0.992246 | + | 0.124291i | \(0.960334\pi\) | |||||||
\(948\) | −21.3546 | − | 25.4495i | −0.693566 | − | 0.826560i | ||||
\(949\) | −52.9562 | −1.71903 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.99982 | 0.162130 | ||||||||
\(952\) | −2.62985 | − | 3.13413i | −0.0852338 | − | 0.101578i | ||||
\(953\) | 11.7324 | − | 32.2346i | 0.380050 | − | 1.04418i | −0.591284 | − | 0.806463i | \(-0.701379\pi\) |
0.971335 | − | 0.237717i | \(-0.0763989\pi\) | |||||||
\(954\) | 2.83303 | − | 16.0669i | 0.0917229 | − | 0.520186i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.0098 | + | 5.46314i | −0.485453 | + | 0.176690i | ||||
\(957\) | 0.368806 | + | 0.212930i | 0.0119218 | + | 0.00688305i | ||||
\(958\) | −19.7272 | + | 11.3895i | −0.637357 | + | 0.367978i | ||||
\(959\) | −17.7462 | − | 14.8908i | −0.573054 | − | 0.480849i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4399 | + | 26.7427i | 0.498061 | + | 0.862667i | ||||
\(962\) | 38.6374 | + | 22.3073i | 1.24572 | + | 0.719216i | ||||
\(963\) | −9.82824 | − | 27.0029i | −0.316711 | − | 0.870155i | ||||
\(964\) | −3.85411 | − | 21.8577i | −0.124132 | − | 0.703990i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 14.9413 | + | 5.43820i | 0.480729 | + | 0.174971i | ||||
\(967\) | −9.34181 | − | 11.1331i | −0.300412 | − | 0.358017i | 0.594629 | − | 0.804000i | \(-0.297299\pi\) |
−0.895042 | + | 0.445983i | \(0.852854\pi\) | |||||||
\(968\) | 9.10174i | 0.292541i | ||||||||
\(969\) | −1.29185 | − | 13.3397i | −0.0415002 | − | 0.428531i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.8612 | − | 31.7693i | 1.21502 | − | 1.01952i | 0.215952 | − | 0.976404i | \(-0.430714\pi\) |
0.999070 | − | 0.0431208i | \(-0.0137300\pi\) | |||||||
\(972\) | −7.18414 | + | 19.7383i | −0.230431 | + | 0.633105i | ||||
\(973\) | 36.7041 | + | 6.47192i | 1.17668 | + | 0.207480i | ||||
\(974\) | 1.11988 | + | 6.35114i | 0.0358832 | + | 0.203504i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.92300 | + | 6.79483i | −0.125572 | + | 0.217497i | ||||
\(977\) | 2.52147 | − | 1.45577i | 0.0806691 | − | 0.0465743i | −0.459123 | − | 0.888373i | \(-0.651836\pi\) |
0.539792 | + | 0.841798i | \(0.318503\pi\) | |||||||
\(978\) | 11.1682 | − | 13.3097i | 0.357120 | − | 0.425599i | ||||
\(979\) | 19.2281 | + | 16.1343i | 0.614533 | + | 0.515655i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.75929 | + | 16.9036i | −0.311590 | + | 0.539690i | ||||
\(982\) | 8.33289 | + | 22.8944i | 0.265913 | + | 0.730591i | ||||
\(983\) | −40.6242 | + | 7.16313i | −1.29571 | + | 0.228469i | −0.778638 | − | 0.627474i | \(-0.784089\pi\) |
−0.517072 | + | 0.855942i | \(0.672978\pi\) | |||||||
\(984\) | −4.53323 | + | 25.7092i | −0.144514 | + | 0.819580i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.129467 | + | 0.108636i | −0.00412308 | + | 0.00345968i | ||||
\(987\) | 0.571978i | 0.0182062i | ||||||||
\(988\) | 1.46889 | − | 18.7958i | 0.0467315 | − | 0.597975i | ||||
\(989\) | −24.4909 | −0.778764 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.2089 | + | 9.90324i | 0.864320 | + | 0.314587i | 0.735865 | − | 0.677129i | \(-0.236776\pi\) |
0.128455 | + | 0.991715i | \(0.458998\pi\) | |||||||
\(992\) | 0.341442 | + | 0.0602055i | 0.0108408 | + | 0.00191153i | ||||
\(993\) | −8.04294 | + | 1.41819i | −0.255235 | + | 0.0450048i | ||||
\(994\) | −34.5520 | + | 12.5759i | −1.09592 | + | 0.398883i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.4915 | + | 23.3679i | 0.427494 | + | 0.740442i | ||||
\(997\) | 0.422618 | − | 0.503657i | 0.0133844 | − | 0.0159510i | −0.759311 | − | 0.650728i | \(-0.774464\pi\) |
0.772695 | + | 0.634777i | \(0.218908\pi\) | |||||||
\(998\) | 1.04434 | − | 1.24460i | 0.0330580 | − | 0.0393970i | ||||
\(999\) | 4.60918 | + | 7.98334i | 0.145828 | + | 0.252582i |
(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 | 950.2.u.g.899.4 | 36 | ||
5.2 | odd | 4 | 190.2.k.d.101.3 | ✓ | 18 | ||
5.3 | odd | 4 | 950.2.l.i.101.1 | 18 | |||
5.4 | even | 2 | inner | 950.2.u.g.899.3 | 36 | ||
19.16 | even | 9 | inner | 950.2.u.g.149.3 | 36 | ||
95.42 | odd | 36 | 3610.2.a.bi.1.2 | 9 | |||
95.54 | even | 18 | inner | 950.2.u.g.149.4 | 36 | ||
95.72 | even | 36 | 3610.2.a.bj.1.8 | 9 | |||
95.73 | odd | 36 | 950.2.l.i.301.1 | 18 | |||
95.92 | odd | 36 | 190.2.k.d.111.3 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.k.d.101.3 | ✓ | 18 | 5.2 | odd | 4 | ||
190.2.k.d.111.3 | yes | 18 | 95.92 | odd | 36 | ||
950.2.l.i.101.1 | 18 | 5.3 | odd | 4 | |||
950.2.l.i.301.1 | 18 | 95.73 | odd | 36 | |||
950.2.u.g.149.3 | 36 | 19.16 | even | 9 | inner | ||
950.2.u.g.149.4 | 36 | 95.54 | even | 18 | inner | ||
950.2.u.g.899.3 | 36 | 5.4 | even | 2 | inner | ||
950.2.u.g.899.4 | 36 | 1.1 | even | 1 | trivial | ||
3610.2.a.bi.1.2 | 9 | 95.42 | odd | 36 | |||
3610.2.a.bj.1.8 | 9 | 95.72 | even | 36 |