Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (of order \(3\), degree \(2\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Root | \(0.500000 + 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.193 |
Dual form | 1008.2.t.h.961.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | −0.796790 | + | 1.53790i | −0.460027 | + | 0.887905i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.593579 | 0.265457 | 0.132728 | − | 0.991152i | \(-0.457626\pi\) | ||||
0.132728 | + | 0.991152i | \(0.457626\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0665372 | − | 2.64491i | 0.0251487 | − | 0.999684i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.73025 | − | 2.45076i | −0.576751 | − | 0.816920i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.593579 | 0.178971 | 0.0894855 | − | 0.995988i | \(-0.471478\pi\) | ||||
0.0894855 | + | 0.995988i | \(0.471478\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.25729 | + | 2.17770i | −0.348711 | + | 0.603985i | −0.986021 | − | 0.166623i | \(-0.946714\pi\) |
0.637310 | + | 0.770608i | \(0.280047\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.472958 | + | 0.912864i | −0.122117 | + | 0.235700i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.46050 | − | 2.52967i | 0.354224 | − | 0.613535i | −0.632760 | − | 0.774348i | \(-0.718078\pi\) |
0.986985 | + | 0.160813i | \(0.0514116\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.69076 | − | 4.66053i | −0.617302 | − | 1.06920i | −0.989976 | − | 0.141236i | \(-0.954892\pi\) |
0.372674 | − | 0.927962i | \(-0.378441\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.01459 | + | 2.20977i | 0.876055 | + | 0.482211i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.46050 | −0.930080 | −0.465040 | − | 0.885290i | \(-0.653960\pi\) | ||||
−0.465040 | + | 0.885290i | \(0.653960\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.64766 | −0.929533 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.14766 | − | 0.708209i | 0.990668 | − | 0.136295i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.09718 | − | 5.36447i | −0.575132 | − | 0.996157i | −0.996027 | − | 0.0890480i | \(-0.971618\pi\) |
0.420896 | − | 0.907109i | \(-0.361716\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.93346 | − | 6.81296i | −0.706471 | − | 1.22364i | −0.966158 | − | 0.257951i | \(-0.916953\pi\) |
0.259687 | − | 0.965693i | \(-0.416380\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.472958 | + | 0.912864i | −0.0823314 | + | 0.158909i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0394951 | − | 1.56997i | 0.00667590 | − | 0.265373i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | + | 0.866025i | 0.0821995 | + | 0.142374i | 0.904194 | − | 0.427121i | \(-0.140472\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.34728 | − | 3.66876i | −0.375865 | − | 0.587471i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.136673 | + | 0.236725i | −0.0213448 | + | 0.0369702i | −0.876500 | − | 0.481401i | \(-0.840128\pi\) |
0.855156 | + | 0.518371i | \(0.173461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.58113 | + | 9.66679i | 0.851114 | + | 1.47417i | 0.880204 | + | 0.474596i | \(0.157406\pi\) |
−0.0290902 | + | 0.999577i | \(0.509261\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.02704 | − | 1.45472i | −0.153102 | − | 0.216857i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.08113 | − | 10.5328i | 0.887023 | − | 1.53637i | 0.0436467 | − | 0.999047i | \(-0.486102\pi\) |
0.843377 | − | 0.537323i | \(-0.180564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99115 | − | 0.351971i | −0.998735 | − | 0.0502815i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.72665 | + | 4.26172i | 0.381808 | + | 0.596760i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.02704 | − | 6.97504i | 0.553157 | − | 0.958096i | −0.444888 | − | 0.895586i | \(-0.646756\pi\) |
0.998044 | − | 0.0625092i | \(-0.0199103\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.352336 | 0.0475090 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.31138 | − | 0.424646i | 1.23332 | − | 0.0562457i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.32383 | + | 7.48910i | 0.562915 | + | 0.974997i | 0.997240 | + | 0.0742412i | \(0.0236535\pi\) |
−0.434325 | + | 0.900756i | \(0.643013\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.32383 | − | 5.75705i | 0.425573 | − | 0.737114i | −0.570901 | − | 0.821019i | \(-0.693406\pi\) |
0.996474 | + | 0.0839050i | \(0.0267392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.59718 | + | 4.41330i | −0.831166 | + | 0.556024i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.746304 | + | 1.29264i | −0.0925676 | + | 0.160332i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.956906 | − | 1.65741i | −0.116905 | − | 0.202485i | 0.801635 | − | 0.597814i | \(-0.203964\pi\) |
−0.918540 | + | 0.395329i | \(0.870631\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.55408 | − | 6.85980i | 0.427861 | − | 0.825822i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.4107 | 1.71023 | 0.855117 | − | 0.518435i | \(-0.173485\pi\) | ||||
0.855117 | + | 0.518435i | \(0.173485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.95691 | − | 6.85356i | 0.463121 | − | 0.802149i | −0.535994 | − | 0.844222i | \(-0.680063\pi\) |
0.999115 | + | 0.0420732i | \(0.0133963\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.70321 | − | 7.14763i | 0.427610 | − | 0.825337i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0394951 | − | 1.56997i | 0.00450089 | − | 0.178914i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.62422 | + | 8.00938i | −0.520265 | + | 0.901126i | 0.479457 | + | 0.877565i | \(0.340834\pi\) |
−0.999722 | + | 0.0235607i | \(0.992500\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.01245 | + | 8.48087i | −0.334717 | + | 0.942319i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.85087 | − | 6.66991i | −0.422688 | − | 0.732118i | 0.573513 | − | 0.819196i | \(-0.305580\pi\) |
−0.996201 | + | 0.0870787i | \(0.972247\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.866926 | − | 1.50156i | 0.0940313 | − | 0.162867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.7178 | − | 0.488786i | 1.14907 | − | 0.0524033i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.21780 | − | 10.7695i | −0.659085 | − | 1.14157i | −0.980853 | − | 0.194751i | \(-0.937610\pi\) |
0.321767 | − | 0.946819i | \(-0.395723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.67617 | + | 3.47033i | 0.595024 | + | 0.363790i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.6118 | − | 0.620765i | 1.41147 | − | 0.0643704i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.59718 | − | 2.76639i | −0.163867 | − | 0.283826i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.86693 | + | 10.1618i | 0.595696 | + | 1.03178i | 0.993448 | + | 0.114283i | \(0.0364570\pi\) |
−0.397752 | + | 0.917493i | \(0.630210\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.02704 | − | 1.45472i | −0.103222 | − | 0.146205i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.62276 | −0.161470 | −0.0807352 | − | 0.996736i | \(-0.525727\pi\) | ||||
−0.0807352 | + | 0.996736i | \(0.525727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.38151 | −0.628789 | −0.314395 | − | 0.949292i | \(-0.601802\pi\) | ||||
−0.314395 | + | 0.949292i | \(0.601802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.38298 | + | 1.31167i | 0.232555 | + | 0.128006i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.35447 | − | 16.2024i | −0.904331 | − | 1.56635i | −0.821813 | − | 0.569758i | \(-0.807037\pi\) |
−0.0825182 | − | 0.996590i | \(-0.526296\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.43346 | + | 2.48283i | −0.137301 | + | 0.237812i | −0.926474 | − | 0.376359i | \(-0.877176\pi\) |
0.789173 | + | 0.614171i | \(0.210509\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.73025 | + | 0.0789082i | −0.164228 | + | 0.00748964i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.16012 | + | 10.6696i | −0.579495 | + | 1.00371i | 0.416042 | + | 0.909345i | \(0.363417\pi\) |
−0.995537 | + | 0.0943695i | \(0.969916\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.64766 | −0.246896 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.51245 | − | 0.686640i | 0.694527 | − | 0.0634799i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.59358 | − | 4.03123i | −0.604432 | − | 0.369542i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6477 | −0.967969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.255158 | − | 0.398809i | −0.0230069 | − | 0.0359594i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.72665 | −0.512207 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.3346 | −1.09452 | −0.547261 | − | 0.836962i | \(-0.684329\pi\) | ||||
−0.547261 | + | 0.836962i | \(0.684329\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −19.3135 | + | 0.880794i | −1.70046 | + | 0.0775496i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.18716 | 0.103723 | 0.0518613 | − | 0.998654i | \(-0.483485\pi\) | ||||
0.0518613 | + | 0.998654i | \(0.483485\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.5057 | + | 6.80672i | −1.08438 | + | 0.590218i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.05555 | − | 0.420378i | 0.262980 | − | 0.0361804i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.52179 | 0.215451 | 0.107725 | − | 0.994181i | \(-0.465643\pi\) | ||||
0.107725 | + | 0.994181i | \(0.465643\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.45691 | + | 4.25549i | −0.208392 | + | 0.360946i | −0.951208 | − | 0.308550i | \(-0.900156\pi\) |
0.742816 | + | 0.669496i | \(0.233490\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.3530 | + | 17.7446i | 0.956096 | + | 1.49436i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.746304 | + | 1.29264i | −0.0624091 | + | 0.108096i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.83842 | − | 3.18424i | −0.152673 | − | 0.264437i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.11177 | − | 10.4712i | 0.504090 | − | 0.863651i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.0512 | 1.47881 | 0.739404 | − | 0.673262i | \(-0.235107\pi\) | ||||
0.739404 | + | 0.673262i | \(0.235107\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.64766 | −0.134085 | −0.0670425 | − | 0.997750i | \(-0.521356\pi\) | ||||
−0.0670425 | + | 0.997750i | \(0.521356\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.72665 | + | 0.797618i | −0.705508 | + | 0.0644836i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.33482 | − | 4.04403i | −0.187537 | − | 0.324824i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.30039 | + | 5.71644i | 0.263400 | + | 0.456222i | 0.967143 | − | 0.254233i | \(-0.0818229\pi\) |
−0.703743 | + | 0.710454i | \(0.748490\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.51819 | + | 11.7508i | 0.596231 | + | 0.931900i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.296790 | + | 11.7977i | −0.0233903 | + | 0.929785i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.99115 | + | 5.18082i | 0.234285 | + | 0.405793i | 0.959065 | − | 0.283188i | \(-0.0913919\pi\) |
−0.724780 | + | 0.688980i | \(0.758059\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.280738 | + | 0.541857i | −0.0218554 | + | 0.0421835i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.73025 | + | 6.46099i | −0.288656 | + | 0.499966i | −0.973489 | − | 0.228733i | \(-0.926542\pi\) |
0.684833 | + | 0.728700i | \(0.259875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.33842 | + | 5.78231i | 0.256802 | + | 0.444793i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.76615 | + | 14.6583i | −0.517420 | + | 1.12095i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.8296 | − | 22.2215i | 0.975414 | − | 1.68947i | 0.296851 | − | 0.954924i | \(-0.404063\pi\) |
0.678562 | − | 0.734543i | \(-0.262603\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.309243 | + | 12.2927i | −0.0233766 | + | 0.929239i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.9626 | + | 0.682372i | −1.12466 | + | 0.0512902i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.51819 | + | 13.0219i | −0.561936 | + | 0.973301i | 0.435392 | + | 0.900241i | \(0.356610\pi\) |
−0.997328 | + | 0.0730602i | \(0.976723\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.0861875 | −0.00640627 | −0.00320313 | − | 0.999995i | \(-0.501020\pi\) | ||||
−0.00320313 | + | 0.999995i | \(0.501020\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.20535 | + | 9.69886i | 0.458712 | + | 0.716961i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.296790 | + | 0.514055i | 0.0218204 | + | 0.0377941i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.866926 | − | 1.50156i | 0.0633959 | − | 0.109805i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.53064 | − | 13.6623i | −0.111338 | − | 0.993783i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.99115 | − | 3.44877i | 0.144074 | − | 0.249544i | −0.784953 | − | 0.619555i | \(-0.787313\pi\) |
0.929027 | + | 0.370011i | \(0.120646\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.39037 | − | 5.87229i | −0.244044 | − | 0.422697i | 0.717818 | − | 0.696230i | \(-0.245141\pi\) |
−0.961862 | + | 0.273534i | \(0.911808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.39329 | − | 2.17770i | −0.0997759 | − | 0.155948i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.0584 | 0.787875 | 0.393938 | − | 0.919137i | \(-0.371113\pi\) | ||||
0.393938 | + | 0.919137i | \(0.371113\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.80924 | + | 4.86575i | −0.199142 | + | 0.344924i | −0.948250 | − | 0.317523i | \(-0.897149\pi\) |
0.749109 | + | 0.662447i | \(0.230482\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.31138 | − | 0.151016i | 0.233567 | − | 0.0106518i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.3946 | + | 7.83483i | −1.01031 | + | 0.549898i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0811263 | + | 0.140515i | −0.00566611 | + | 0.00981399i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.71780 | + | 10.9316i | 0.536424 | + | 0.759801i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.59718 | − | 2.76639i | −0.110479 | − | 0.191355i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.66225 | + | 16.7355i | −0.665177 | + | 1.15212i | 0.314060 | + | 0.949403i | \(0.398311\pi\) |
−0.979237 | + | 0.202717i | \(0.935023\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.4823 | + | 22.1622i | −0.786754 | + | 1.51853i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.31284 | + | 5.73801i | 0.225934 | + | 0.391329i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.2814 | + | 9.95036i | −1.24102 | + | 0.675474i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.38725 | + | 11.5462i | 0.499184 | + | 0.780217i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.67257 | + | 6.36108i | 0.247044 | + | 0.427892i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.6623 | − | 21.9317i | −0.847927 | − | 1.46865i | −0.883055 | − | 0.469270i | \(-0.844517\pi\) |
0.0351275 | − | 0.999383i | \(-0.488816\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.04163 | + | 11.3903i | 0.536109 | + | 0.759354i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.81711 | −0.319723 | −0.159862 | − | 0.987139i | \(-0.551105\pi\) | ||||
−0.159862 | + | 0.987139i | \(0.551105\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.29533 | −0.614253 | −0.307126 | − | 0.951669i | \(-0.599367\pi\) | ||||
−0.307126 | + | 0.951669i | \(0.599367\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.38298 | + | 1.31167i | 0.156788 | + | 0.0863017i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.0971780 | + | 0.168317i | 0.00636634 | + | 0.0110268i | 0.869191 | − | 0.494476i | \(-0.164640\pi\) |
−0.862825 | + | 0.505503i | \(0.831307\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.60963 | − | 6.25206i | 0.235466 | − | 0.407840i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.63307 | − | 13.4934i | −0.560778 | − | 0.876488i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.82743 | − | 11.8255i | 0.441630 | − | 0.764925i | −0.556181 | − | 0.831061i | \(-0.687734\pi\) |
0.997811 | + | 0.0661361i | \(0.0210672\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | −0.837404 | −0.418702 | − | 0.908124i | \(-0.637515\pi\) | ||||
−0.418702 | + | 0.908124i | \(0.637515\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.6424 | − | 11.3903i | −0.682711 | − | 0.730689i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.14980 | − | 0.208922i | −0.265121 | − | 0.0133476i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.5323 | 0.861039 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.3260 | − | 0.607731i | 0.844499 | − | 0.0385134i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.5438 | 1.23359 | 0.616796 | − | 0.787123i | \(-0.288430\pi\) | ||||
0.616796 | + | 0.787123i | \(0.288430\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.64766 | −0.166457 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.61849 | + | 2.52967i | 0.101353 | + | 0.158414i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.32743 | 0.519451 | 0.259725 | − | 0.965683i | \(-0.416368\pi\) | ||||
0.259725 | + | 0.965683i | \(0.416368\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.32383 | − | 1.26483i | 0.144396 | − | 0.0785930i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.78813 | + | 16.8723i | −0.482073 | + | 1.04437i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.0905 | 1.05384 | 0.526921 | − | 0.849914i | \(-0.323346\pi\) | ||||
0.526921 | + | 0.849914i | \(0.323346\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.39037 | − | 4.14024i | 0.146839 | − | 0.254333i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.5167 | − | 0.981271i | 1.31680 | − | 0.0600528i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.00720 | + | 8.67272i | −0.305294 | + | 0.528785i | −0.977327 | − | 0.211737i | \(-0.932088\pi\) |
0.672033 | + | 0.740522i | \(0.265421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.10457 | − | 8.84137i | −0.310081 | − | 0.537075i | 0.668299 | − | 0.743893i | \(-0.267023\pi\) |
−0.978380 | + | 0.206818i | \(0.933689\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.85973 | + | 5.96423i | −0.596738 | + | 0.360972i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.75876 | −0.166359 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.3422 | 1.16216 | 0.581081 | − | 0.813846i | \(-0.302630\pi\) | ||||
0.581081 | + | 0.813846i | \(0.302630\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.89104 | + | 21.4281i | −0.592161 | + | 1.28287i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.40136 | − | 11.0875i | −0.381873 | − | 0.661424i | 0.609457 | − | 0.792819i | \(-0.291388\pi\) |
−0.991330 | + | 0.131396i | \(0.958054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.17617 | − | 14.1615i | −0.486023 | − | 0.841816i | 0.513848 | − | 0.857881i | \(-0.328219\pi\) |
−0.999871 | + | 0.0160650i | \(0.994886\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.52704 | − | 0.252061i | 0.327394 | − | 0.0149308i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.617023 | + | 0.377240i | 0.0364217 | + | 0.0222678i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.23385 | + | 7.33325i | 0.249050 | + | 0.431367i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.3025 | + | 0.925898i | −1.19016 | + | 0.0542771i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.3889 | + | 17.9941i | −0.606926 | + | 1.05123i | 0.384817 | + | 0.922993i | \(0.374264\pi\) |
−0.991744 | + | 0.128235i | \(0.959069\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.56654 | + | 4.44537i | 0.149430 | + | 0.258820i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.05555 | − | 0.420378i | 0.177301 | − | 0.0243928i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.60817 | − | 9.71363i | 0.324329 | − | 0.561754i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.9392 | − | 14.1184i | 1.49511 | − | 0.813771i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.29300 | − | 2.49563i | 0.0742807 | − | 0.143370i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.97296 | − | 3.41726i | 0.112971 | − | 0.195672i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.6768 | 1.29424 | 0.647118 | − | 0.762390i | \(-0.275974\pi\) | ||||
0.647118 | + | 0.762390i | \(0.275974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.08472 | − | 9.81411i | 0.289260 | − | 0.558305i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.25729 | − | 5.64180i | −0.184704 | − | 0.319917i | 0.758773 | − | 0.651356i | \(-0.225799\pi\) |
−0.943477 | + | 0.331439i | \(0.892466\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.133074 | + | 0.230492i | −0.00752181 | + | 0.0130282i | −0.869762 | − | 0.493472i | \(-0.835728\pi\) |
0.862240 | + | 0.506500i | \(0.169061\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.91595 | + | 2.61965i | −0.220639 | + | 0.147600i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.86186 | + | 13.6171i | −0.441566 | + | 0.764815i | −0.997806 | − | 0.0662067i | \(-0.978910\pi\) |
0.556240 | + | 0.831022i | \(0.312244\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.83842 | − | 3.18424i | −0.102932 | − | 0.178283i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 32.3712 | − | 1.47629i | 1.80678 | − | 0.0823985i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.7195 | −0.874654 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.84348 | − | 10.1212i | 0.324138 | − | 0.561424i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.67617 | − | 4.18281i | −0.147992 | − | 0.231310i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.4538 | − | 16.7849i | −1.51358 | − | 0.925381i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.5811 | + | 21.7912i | −0.691521 | + | 1.19775i | 0.279818 | + | 0.960053i | \(0.409726\pi\) |
−0.971339 | + | 0.237697i | \(0.923608\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.25729 | − | 2.72382i | 0.0688993 | − | 0.149265i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.568000 | − | 0.983804i | −0.0310331 | − | 0.0537510i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.36693 | + | 16.2240i | −0.510249 | + | 0.883777i | 0.489681 | + | 0.871902i | \(0.337113\pi\) |
−0.999929 | + | 0.0118752i | \(0.996220\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.5005 | − | 17.9751i | −0.624620 | − | 0.976272i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.33482 | − | 4.04403i | −0.126438 | − | 0.218997i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.39610 | + | 18.4676i | −0.0753825 | + | 0.997155i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.10963 | − | 4.07183i | 0.113579 | − | 0.219220i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.2719 | + | 19.5235i | 0.605106 | + | 1.04808i | 0.992035 | + | 0.125965i | \(0.0402028\pi\) |
−0.386928 | + | 0.922110i | \(0.626464\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.89543 | + | 3.28298i | 0.101460 | + | 0.175734i | 0.912286 | − | 0.409553i | \(-0.134315\pi\) |
−0.810826 | + | 0.585287i | \(0.800982\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.92986 | + | 12.1005i | −0.263137 | + | 0.645876i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.83482 | 0.363781 | 0.181890 | − | 0.983319i | \(-0.441778\pi\) | ||||
0.181890 | + | 0.983319i | \(0.441778\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.55389 | 0.453993 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.4533 | − | 6.92820i | 0.606173 | − | 0.366679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.32237 | + | 10.9507i | 0.333682 | + | 0.577954i | 0.983231 | − | 0.182366i | \(-0.0583755\pi\) |
−0.649549 | + | 0.760320i | \(0.725042\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.98035 | + | 8.62622i | −0.262124 | + | 0.454012i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.48395 | − | 16.3750i | 0.445292 | − | 0.859465i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.34874 | − | 4.06813i | 0.122939 | − | 0.212936i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.54377 | −0.341582 | −0.170791 | − | 0.985307i | \(-0.554632\pi\) | ||||
−0.170791 | + | 0.985307i | \(0.554632\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.816635 | − | 0.0746406i | 0.0425123 | − | 0.00388563i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.1804 | − | 11.1153i | −0.943881 | − | 0.577077i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.42840 | 0.488184 | 0.244092 | − | 0.969752i | \(-0.421510\pi\) | ||||
0.244092 | + | 0.969752i | \(0.421510\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.56294 | − | 8.80700i | 0.235629 | − | 0.454792i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.5763 | 0.802218 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.27762 | 0.373826 | 0.186913 | − | 0.982376i | \(-0.440152\pi\) | ||||
0.186913 | + | 0.982376i | \(0.440152\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.82810 | − | 18.9694i | 0.503509 | − | 0.971831i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.0833 | 1.23060 | 0.615299 | − | 0.788294i | \(-0.289035\pi\) | ||||
0.615299 | + | 0.788294i | \(0.289035\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0234435 | − | 0.931900i | 0.00119479 | − | 0.0474940i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.0342 | − | 30.4040i | 0.713400 | − | 1.54552i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.2983 | −0.826354 | −0.413177 | − | 0.910651i | \(-0.635581\pi\) | ||||
−0.413177 | + | 0.910651i | \(0.635581\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.51459 | + | 11.2836i | −0.329457 | + | 0.570636i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.945916 | + | 1.82573i | −0.0477151 | + | 0.0920958i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.74484 | + | 4.75420i | −0.138108 | + | 0.239210i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.08619 | − | 10.5416i | −0.305457 | − | 0.529067i | 0.671906 | − | 0.740636i | \(-0.265476\pi\) |
−0.977363 | + | 0.211569i | \(0.932143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.503599 | − | 24.6561i | −0.0252115 | − | 1.23435i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.3609 | −1.66596 | −0.832981 | − | 0.553301i | \(-0.813368\pi\) | ||||
−0.832981 | + | 0.553301i | \(0.813368\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.7821 | 0.985416 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.78813 | + | 5.03407i | −0.0888529 | + | 0.250145i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.296790 | + | 0.514055i | 0.0147113 | + | 0.0254808i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.89037 | + | 5.00627i | 0.142920 | + | 0.247544i | 0.928595 | − | 0.371095i | \(-0.121018\pi\) |
−0.785675 | + | 0.618639i | \(0.787684\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.00933 | + | 3.87825i | −0.0991131 | + | 0.191300i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.0957 | − | 10.9379i | 0.988846 | − | 0.538217i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.28580 | − | 3.95912i | −0.112205 | − | 0.194346i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.58686 | − | 7.16920i | −0.224620 | − | 0.351077i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.4356 | + | 26.7352i | −0.754078 | + | 1.30610i | 0.191753 | + | 0.981443i | \(0.438583\pi\) |
−0.945831 | + | 0.324659i | \(0.894751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.86693 | − | 3.23361i | −0.0909884 | − | 0.157597i | 0.816939 | − | 0.576724i | \(-0.195669\pi\) |
−0.907927 | + | 0.419128i | \(0.862336\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −36.3353 | + | 3.32105i | −1.76668 | + | 0.161475i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.78794 | + | 11.7570i | −0.329263 | + | 0.570301i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.0057 | − | 9.17431i | −0.726178 | − | 0.443976i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.39329 | − | 2.17770i | −0.0672689 | − | 0.105140i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.0979 | − | 24.4182i | 0.679070 | − | 1.17618i | −0.296192 | − | 0.955128i | \(-0.595717\pi\) |
0.975261 | − | 0.221055i | \(-0.0709499\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5438 | 0.602815 | 0.301407 | − | 0.953495i | \(-0.402544\pi\) | ||||
0.301407 | + | 0.953495i | \(0.402544\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.36186 | − | 0.290133i | 0.305028 | − | 0.0139108i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.0021 | + | 20.7883i | 0.574140 | + | 0.994440i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.0203 | − | 22.5519i | 0.621426 | − | 1.07634i | −0.367794 | − | 0.929907i | \(-0.619887\pi\) |
0.989220 | − | 0.146434i | \(-0.0467797\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.2339 | + | 17.7426i | 0.534945 | + | 0.844887i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.7865 | + | 20.4148i | −0.559992 | + | 0.969935i | 0.437504 | + | 0.899216i | \(0.355863\pi\) |
−0.997496 | + | 0.0707186i | \(0.977471\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.69076 | − | 6.39258i | −0.174959 | − | 0.303037i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.3830 | + | 27.7608i | −0.680291 | + | 1.31304i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.6870 | 0.645928 | 0.322964 | − | 0.946411i | \(-0.395321\pi\) | ||||
0.322964 | + | 0.946411i | \(0.395321\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0811263 | + | 0.140515i | −0.00382009 | + | 0.00661659i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.31284 | − | 2.53394i | 0.0616827 | − | 0.119055i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.36926 | + | 2.05992i | 0.157953 | + | 0.0965705i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.1762 | − | 19.3577i | 0.522799 | − | 0.905515i | −0.476849 | − | 0.878985i | \(-0.658221\pi\) |
0.999648 | − | 0.0265293i | \(-0.00844554\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.72665 | − | 14.0562i | 0.267297 | − | 0.656088i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.98755 | − | 6.90663i | −0.185719 | − | 0.321674i | 0.758100 | − | 0.652138i | \(-0.226128\pi\) |
−0.943818 | + | 0.330464i | \(0.892795\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.3676 | − | 24.8854i | 0.667719 | − | 1.15652i | −0.310821 | − | 0.950468i | \(-0.600604\pi\) |
0.978540 | − | 0.206055i | \(-0.0660625\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.07966 | − | 0.368473i | 0.374685 | − | 0.0170875i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.7829 | − | 29.0688i | −0.776619 | − | 1.34514i | −0.933880 | − | 0.357586i | \(-0.883600\pi\) |
0.157261 | − | 0.987557i | \(-0.449733\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.44738 | + | 2.42066i | −0.205361 | + | 0.111775i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.4210 | + | 0.520856i | −0.526252 | + | 0.0239998i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.31284 | + | 5.73801i | 0.152325 | + | 0.263834i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.5057 | + | 21.6606i | 0.573802 | + | 0.993855i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.0620 | + | 2.19927i | −1.10172 | + | 0.100698i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.367120 | −0.0167741 | −0.00838707 | − | 0.999965i | \(-0.502670\pi\) | ||||
−0.00838707 | + | 0.999965i | \(0.502670\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.51459 | −0.114655 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −17.9071 | − | 9.85668i | −0.814801 | − | 0.448495i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.48249 | + | 6.03184i | 0.158132 | + | 0.273892i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.9538 | − | 25.9007i | 0.677621 | − | 1.17367i | −0.298075 | − | 0.954543i | \(-0.596344\pi\) |
0.975695 | − | 0.219131i | \(-0.0703222\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.3509 | + | 0.472052i | −0.468083 | + | 0.0213469i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.255158 | − | 0.441947i | 0.0115151 | − | 0.0199448i | −0.860210 | − | 0.509939i | \(-0.829668\pi\) |
0.871726 | + | 0.489994i | \(0.163001\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0938 | −0.814903 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.609631 | − | 0.863492i | −0.0274009 | − | 0.0388111i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.958848 | − | 38.1151i | 0.0430102 | − | 1.70969i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.0191 | 0.851410 | 0.425705 | − | 0.904862i | \(-0.360026\pi\) | ||||
0.425705 | + | 0.904862i | \(0.360026\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.96410 | − | 10.8848i | −0.311133 | − | 0.486297i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.7807 | 1.68456 | 0.842280 | − | 0.539040i | \(-0.181213\pi\) | ||||
0.842280 | + | 0.539040i | \(0.181213\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.963235 | −0.0428634 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.5526 | + | 0.526858i | −0.513070 | + | 0.0233986i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.2163 | −0.497155 | −0.248578 | − | 0.968612i | \(-0.579963\pi\) | ||||
−0.248578 | + | 0.968612i | \(0.579963\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.8638 | − | 10.9217i | −0.790248 | − | 0.483147i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.1517 | − | 22.0852i | −0.757268 | − | 0.975086i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.78794 | −0.166916 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.60963 | − | 6.25206i | 0.158751 | − | 0.274965i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.9518 | + | 37.4364i | 1.05137 | + | 1.64327i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.7360 | + | 23.7914i | −0.601785 | + | 1.04232i | 0.390766 | + | 0.920490i | \(0.372210\pi\) |
−0.992551 | + | 0.121831i | \(0.961123\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.0919 | − | 19.2118i | −0.485016 | − | 0.840072i | 0.514836 | − | 0.857289i | \(-0.327853\pi\) |
−0.999852 | + | 0.0172166i | \(0.994520\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.6585 | − | 10.2703i | −0.814322 | − | 0.448231i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.9794 | −1.00100 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.10390 | −0.134952 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.8727 | − | 23.5547i | 0.471833 | − | 1.02219i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.343677 | − | 0.595265i | −0.0148863 | − | 0.0257838i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.55262 | − | 9.61742i | −0.240061 | − | 0.415797i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.0359 | − | 21.9379i | −0.605694 | − | 0.946690i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.14980 | − | 0.208922i | −0.178745 | − | 0.00899893i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.9246 | + | 25.8502i | 0.641659 | + | 1.11139i | 0.985062 | + | 0.172198i | \(0.0550869\pi\) |
−0.343403 | + | 0.939188i | \(0.611580\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.0686733 | − | 0.132547i | 0.00294705 | − | 0.00568816i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.850874 | + | 1.47376i | −0.0364474 | + | 0.0631288i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.84348 | − | 15.3174i | −0.378120 | − | 0.654923i | 0.612669 | − | 0.790340i | \(-0.290096\pi\) |
−0.990789 | + | 0.135417i | \(0.956763\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.8602 | + | 1.81523i | −0.847613 | + | 0.0774720i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.6675 | + | 28.8690i | −0.710060 | + | 1.22986i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.8765 | + | 12.7636i | 0.887757 | + | 0.542763i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.02704 | + | 0.0468383i | −0.0435955 | + | 0.00198818i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.0651 | − | 26.0935i | 0.638328 | − | 1.10562i | −0.347472 | − | 0.937690i | \(-0.612960\pi\) |
0.985800 | − | 0.167926i | \(-0.0537069\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.0685 | −1.18717 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.61849 | + | 2.52967i | 0.0683325 | + | 0.106803i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.04883 | + | 3.54867i | 0.0863478 | + | 0.149559i | 0.905965 | − | 0.423353i | \(-0.139147\pi\) |
−0.819617 | + | 0.572912i | \(0.805814\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.65652 | + | 6.33327i | −0.153831 | + | 0.266443i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.2307 | + | 8.53197i | 0.933603 | + | 0.358309i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.11849 | + | 5.40138i | −0.130734 | + | 0.226437i | −0.923960 | − | 0.382490i | \(-0.875067\pi\) |
0.793226 | + | 0.608927i | \(0.208400\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.8011 | + | 30.8323i | 0.744951 | + | 1.29029i | 0.950218 | + | 0.311587i | \(0.100861\pi\) |
−0.205266 | + | 0.978706i | \(0.565806\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.71732 | + | 5.81012i | 0.155293 | + | 0.242721i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.7309 | 0.864539 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.1388 | − | 40.0776i | 0.963281 | − | 1.66845i | 0.249118 | − | 0.968473i | \(-0.419859\pi\) |
0.714164 | − | 0.699979i | \(-0.246807\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.7324 | − | 0.535056i | 0.487581 | − | 0.0222362i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.8976 | + | 9.74143i | −0.742516 | + | 0.404143i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.39037 | − | 4.14024i | 0.0989990 | − | 0.171471i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.45924 | − | 0.407575i | 0.184367 | − | 0.0168512i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.13161 | − | 1.96001i | −0.0467066 | − | 0.0808982i | 0.841727 | − | 0.539903i | \(-0.181539\pi\) |
−0.888434 | + | 0.459005i | \(0.848206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.1680 | + | 36.6640i | −0.872212 | + | 1.51072i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.81118 | + | 17.0066i | −0.362444 | + | 0.699558i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.0979 | + | 40.0067i | 0.948515 | + | 1.64288i | 0.748555 | + | 0.663072i | \(0.230748\pi\) |
0.199960 | + | 0.979804i | \(0.435919\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.91381 | − | 2.39285i | −0.160451 | − | 0.0980974i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.24465 | − | 8.19731i | −0.214649 | − | 0.335493i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.39037 | − | 14.5325i | −0.342821 | − | 0.593784i | 0.642134 | − | 0.766592i | \(-0.278049\pi\) |
−0.984955 | + | 0.172808i | \(0.944716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.69961 | − | 9.87202i | −0.232492 | − | 0.402688i | 0.726049 | − | 0.687643i | \(-0.241355\pi\) |
−0.958541 | + | 0.284955i | \(0.908021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.40623 | + | 5.21289i | −0.0979891 | + | 0.212285i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.32023 | −0.256954 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.4284 | 0.585631 | 0.292815 | − | 0.956169i | \(-0.405408\pi\) | ||||
0.292815 | + | 0.956169i | \(0.405408\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.579664 | − | 28.3802i | −0.0234892 | − | 1.15002i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.2915 | + | 26.4857i | 0.618629 | + | 1.07150i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.2053 | − | 21.1403i | 0.492969 | − | 0.853848i | −0.506998 | − | 0.861947i | \(-0.669245\pi\) |
0.999967 | + | 0.00809942i | \(0.00257815\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.151457 | − | 0.236725i | −0.00610733 | − | 0.00954566i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.4698 | − | 42.3830i | 0.985119 | − | 1.70628i | 0.343710 | − | 0.939076i | \(-0.388316\pi\) |
0.641408 | − | 0.767200i | \(-0.278350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.6591 | 1.79500 | 0.897501 | − | 0.441012i | \(-0.145380\pi\) | ||||
0.897501 | + | 0.441012i | \(0.145380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.9612 | + | 3.15897i | −0.921400 | + | 0.126765i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −28.8982 | + | 15.7290i | −1.15778 | + | 0.630168i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.8391 | 0.793564 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.52704 | − | 0.252061i | 0.220729 | − | 0.0100663i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.92101 | 0.116468 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.2852 | −1.32506 | −0.662532 | − | 0.749034i | \(-0.730518\pi\) | ||||
−0.662532 | + | 0.749034i | \(0.730518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.0387 | − | 28.1942i | −0.716974 | − | 1.12062i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.32158 | −0.290548 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.55641 | − | 14.7821i | 0.378639 | − | 0.585687i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.9341 | − | 35.3172i | −0.986379 | − | 1.39713i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.7879 | 1.21605 | 0.608025 | − | 0.793918i | \(-0.291962\pi\) | ||||
0.608025 | + | 0.793918i | \(0.291962\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.7345 | − | 23.7889i | 0.541637 | − | 0.938142i | −0.457174 | − | 0.889378i | \(-0.651138\pi\) |
0.998810 | − | 0.0487649i | \(-0.0155285\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.4641 | + | 0.522821i | −0.451399 | + | 0.0205861i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.63521 | − | 11.4925i | 0.260857 | − | 0.451818i | −0.705613 | − | 0.708598i | \(-0.749328\pi\) |
0.966470 | + | 0.256780i | \(0.0826615\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.56654 | + | 4.44537i | 0.100745 | + | 0.174496i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.736182 | − | 36.0433i | −0.0288532 | − | 1.41265i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.1416 | −0.670803 | −0.335402 | − | 0.942075i | \(-0.608872\pi\) | ||||
−0.335402 | + | 0.942075i | \(0.608872\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.704673 | 0.0275338 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −23.6429 | + | 2.16096i | −0.922397 | + | 0.0843072i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.26089 | − | 7.38008i | −0.165981 | − | 0.287487i | 0.771022 | − | 0.636808i | \(-0.219746\pi\) |
−0.937003 | + | 0.349321i | \(0.886412\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.1680 | − | 29.7358i | −0.667757 | − | 1.15659i | −0.978530 | − | 0.206105i | \(-0.933921\pi\) |
0.310773 | − | 0.950484i | \(-0.399412\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.7089 | + | 0.579592i | −0.493575 | + | 0.0225095i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.42315 | + | 4.04033i | −0.287857 | + | 0.156677i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.8150 | + | 23.9282i | 0.534918 | + | 0.926505i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 43.8178 | − | 1.99831i | 1.69409 | − | 0.0772592i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.97296 | − | 3.41726i | 0.0761652 | − | 0.131922i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.70155 | − | 13.3395i | −0.296873 | − | 0.514199i | 0.678546 | − | 0.734558i | \(-0.262610\pi\) |
−0.975419 | + | 0.220359i | \(0.929277\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.9246 | + | 3.29152i | −0.920859 | + | 0.126691i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.69076 | − | 6.39258i | 0.141847 | − | 0.245687i | −0.786345 | − | 0.617788i | \(-0.788029\pi\) |
0.928192 | + | 0.372101i | \(0.121362\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.2675 | − | 14.8414i | 1.04643 | − | 0.569560i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.83823 | − | 7.40822i | 0.147081 | − | 0.283884i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.79893 | + | 8.31198i | −0.183626 | + | 0.318049i | −0.943113 | − | 0.332474i | \(-0.892117\pi\) |
0.759487 | + | 0.650523i | \(0.225450\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.49688 | 0.0571929 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.40642 | − | 14.2953i | 0.282573 | − | 0.545398i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.1264 | + | 17.5394i | 0.385783 | + | 0.668197i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.07227 | + | 12.2495i | −0.269042 | + | 0.465994i | −0.968615 | − | 0.248567i | \(-0.920040\pi\) |
0.699573 | + | 0.714561i | \(0.253374\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.91595 | + | 2.61965i | −0.148755 | + | 0.0995121i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.45837 | + | 2.52597i | −0.0553191 | + | 0.0958155i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.399223 | + | 0.691475i | 0.0151217 | + | 0.0261915i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.336285 | + | 0.0153363i | −0.0127195 | + | 0.000580072i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.3753 | 1.41164 | 0.705822 | − | 0.708389i | \(-0.250578\pi\) | ||||
0.705822 | + | 0.708389i | \(0.250578\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.69076 | − | 4.66053i | 0.101484 | − | 0.175775i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.73891 | + | 10.5328i | 0.253802 | + | 0.396689i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.107974 | + | 4.29205i | −0.00406077 | + | 0.161419i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.24338 | − | 9.08180i | 0.196919 | − | 0.341074i | −0.750609 | − | 0.660747i | \(-0.770240\pi\) |
0.947528 | + | 0.319673i | \(0.103573\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.6301 | − | 2.52540i | 1.03621 | − | 0.0947099i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.5452 | + | 30.3892i | 0.657074 | + | 1.13809i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.442991 | + | 0.767282i | −0.0165669 | + | 0.0286947i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.7463 | + | 19.9223i | 0.476019 | + | 0.744011i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.11995 | − | 1.93981i | −0.0417670 | − | 0.0723426i | 0.844386 | − | 0.535735i | \(-0.179965\pi\) |
−0.886153 | + | 0.463392i | \(0.846632\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.424608 | + | 16.8786i | −0.0158132 | + | 0.628590i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.3583 | − | 19.9927i | 0.385228 | − | 0.743535i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.3946 | + | 24.9322i | 0.534604 | + | 0.925961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.185023 | − | 0.320469i | −0.00686211 | − | 0.0118855i | 0.862574 | − | 0.505931i | \(-0.168851\pi\) |
−0.869436 | + | 0.494045i | \(0.835518\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.9969 | − | 7.29124i | 0.962847 | − | 0.270046i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.6050 | 1.20594 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0191 | 0.517806 | 0.258903 | − | 0.965903i | \(-0.416639\pi\) | ||||
0.258903 | + | 0.965903i | \(0.416639\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.62782 | − | 6.21550i | 0.133814 | − | 0.229262i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.568000 | − | 0.983804i | −0.0209225 | − | 0.0362389i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.3872 | + | 23.1874i | −0.492458 | + | 0.852962i | −0.999962 | − | 0.00868705i | \(-0.997235\pi\) |
0.507504 | + | 0.861649i | \(0.330568\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.7824 | + | 20.8113i | −0.396101 | + | 0.764521i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.04669 | − | 8.74113i | 0.185145 | − | 0.320681i | −0.758480 | − | 0.651696i | \(-0.774058\pi\) |
0.943625 | + | 0.331015i | \(0.107391\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.7148 | 0.392560 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.68337 | + | 20.9782i | −0.354296 | + | 0.767552i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −43.4764 | + | 23.6637i | −1.58859 | + | 0.864653i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5146 | −0.420173 | −0.210087 | − | 0.977683i | \(-0.567375\pi\) | ||||
−0.210087 | + | 0.977683i | \(0.567375\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.5723 | + | 30.0563i | −0.567485 | + | 1.09531i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.978019 | −0.0355938 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.2484 | −0.554214 | −0.277107 | − | 0.960839i | \(-0.589376\pi\) | ||||
−0.277107 | + | 0.960839i | \(0.589376\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.10963 | − | 4.07183i | 0.0765748 | − | 0.147798i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.70175 | −0.0616883 | −0.0308442 | − | 0.999524i | \(-0.509820\pi\) | ||||
−0.0308442 | + | 0.999524i | \(0.509820\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.47150 | + | 3.95659i | 0.234284 | + | 0.143238i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.17996 | + | 0.473449i | −0.187282 | + | 0.0171176i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.7453 | −0.785178 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.1211 | − | 41.7790i | 0.869829 | − | 1.50659i | 0.00765823 | − | 0.999971i | \(-0.497562\pi\) |
0.862171 | − | 0.506618i | \(-0.169104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.63521 | + | 12.8067i | −0.238961 | + | 0.461223i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.10243 | − | 5.37357i | 0.111587 | − | 0.193274i | −0.804823 | − | 0.593514i | \(-0.797740\pi\) |
0.916410 | + | 0.400240i | \(0.131073\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.2814 | + | 31.6643i | 0.656688 | + | 1.13742i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0935793 | + | 4.58162i | 0.00335714 | + | 0.164365i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.47102 | 0.0527046 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.55389 | 0.306082 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.7424 | − | 25.4210i | −0.705536 | − | 0.908474i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.95904 | + | 3.39316i | 0.0699212 | + | 0.121107i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.04883 | + | 5.28073i | 0.108679 | + | 0.188238i | 0.915235 | − | 0.402920i | \(-0.132005\pi\) |
−0.806556 | + | 0.591157i | \(0.798671\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.6175 | + | 26.2834i | −0.484796 | + | 0.935712i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.8104 | + | 17.0029i | 0.988824 | + | 0.604554i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.35807 | + | 14.4766i | 0.296804 | + | 0.514079i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.46264 | + | 6.97504i | 0.158274 | + | 0.247379i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.22860 | + | 10.7882i | −0.220628 | + | 0.382139i | −0.954999 | − | 0.296609i | \(-0.904144\pi\) |
0.734371 | + | 0.678749i | \(0.237477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.7630 | − | 30.7665i | −0.628411 | − | 1.08844i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.6352 | + | 33.8724i | −0.552443 | + | 1.19682i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.34874 | − | 4.06813i | 0.0828852 | − | 0.143561i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.176168 | + | 7.00284i | −0.00620911 | + | 0.246818i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.34806 | − | 14.6109i | −0.329067 | − | 0.514328i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.81644 | + | 4.87822i | −0.0990208 | + | 0.171509i | −0.911280 | − | 0.411788i | \(-0.864904\pi\) |
0.812259 | + | 0.583297i | \(0.198238\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.6414 | 1.60269 | 0.801344 | − | 0.598204i | \(-0.204119\pi\) | ||||
0.801344 | + | 0.598204i | \(0.204119\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.6644 | − | 0.805585i | 0.619517 | − | 0.0282531i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.77548 | + | 3.07523i | 0.0621924 | + | 0.107720i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.0349 | − | 52.0220i | 1.05079 | − | 1.82002i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.31625 | − | 19.9155i | −0.0459933 | − | 0.695903i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.3473 | + | 28.3143i | −0.570524 | + | 0.988176i | 0.425988 | + | 0.904729i | \(0.359926\pi\) |
−0.996512 | + | 0.0834476i | \(0.973407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.21994 | − | 9.04119i | −0.181956 | − | 0.315156i | 0.760591 | − | 0.649231i | \(-0.224909\pi\) |
−0.942546 | + | 0.334075i | \(0.891576\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.19815 | − | 4.24268i | 0.0765297 | − | 0.147711i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.7060 | −0.580925 | −0.290463 | − | 0.956886i | \(-0.593809\pi\) | ||||
−0.290463 | + | 0.956886i | \(0.593809\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.1046 | + | 22.6978i | −0.455141 | + | 0.788327i | −0.998696 | − | 0.0510466i | \(-0.983744\pi\) |
0.543556 | + | 0.839373i | \(0.317078\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.4117 | + | 29.7463i | −0.534625 | + | 1.03189i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.1010 | + | 17.1712i | −0.384626 | + | 0.594948i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.21420 | + | 3.83511i | −0.0766256 | + | 0.132719i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.0731 | − | 32.2851i | −0.866655 | − | 1.11594i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.1886 | − | 19.3793i | −0.386274 | − | 0.669046i | 0.605671 | − | 0.795715i | \(-0.292905\pi\) |
−0.991945 | + | 0.126669i | \(0.959571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.68502 | + | 8.11470i | −0.161553 | + | 0.279817i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.1519 | − | 1.01024i | 0.762953 | − | 0.0347945i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.98162 | + | 3.43226i | 0.0681697 | + | 0.118073i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.708466 | + | 28.1622i | −0.0243432 | + | 0.967663i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.2937 | − | 1.29033i | 0.971036 | − | 0.0442842i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.23025 | − | 3.86291i | −0.0764521 | − | 0.132419i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.96264 | + | 8.59555i | 0.169918 | + | 0.294306i | 0.938391 | − | 0.345576i | \(-0.112317\pi\) |
−0.768473 | + | 0.639882i | \(0.778983\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.01625 | + | 8.70086i | −0.137353 | + | 0.297563i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.79552 | 0.266290 | 0.133145 | − | 0.991097i | \(-0.457492\pi\) | ||||
0.133145 | + | 0.991097i | \(0.457492\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.3422 | −0.557589 | −0.278795 | − | 0.960351i | \(-0.589935\pi\) | ||||
−0.278795 | + | 0.960351i | \(0.589935\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.07179 | + | 0.648337i | −0.0365266 | + | 0.0220953i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.730252 | − | 1.26483i | −0.0248581 | − | 0.0430555i | 0.853329 | − | 0.521373i | \(-0.174580\pi\) |
−0.878187 | + | 0.478318i | \(0.841247\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.61537 | − | 13.1902i | 0.258930 | − | 0.448480i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.6513 | + | 0.668172i | −0.497583 | + | 0.0226923i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.74484 | + | 4.75420i | −0.0931124 | + | 0.161275i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.81245 | 0.163064 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.7529 | − | 31.9609i | 0.499310 | − | 1.08171i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.381036 | + | 15.1465i | −0.0128814 | + | 0.512045i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.40935 | −0.0813578 | −0.0406789 | − | 0.999172i | \(-0.512952\pi\) | ||||
−0.0406789 | + | 0.999172i | \(0.512952\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.3953 | − | 30.3146i | −0.654188 | − | 1.02249i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.9607 | −0.638802 | −0.319401 | − | 0.947620i | \(-0.603482\pi\) | ||||
−0.319401 | + | 0.947620i | \(0.603482\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.64008 | −0.122498 | −0.0612492 | − | 0.998123i | \(-0.519508\pi\) | ||||
−0.0612492 | + | 0.998123i | \(0.519508\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.88151 | + | 0.405042i | −0.298549 | + | 0.0136153i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.4572 | 0.821192 | 0.410596 | − | 0.911817i | \(-0.365321\pi\) | ||||
0.410596 | + | 0.911817i | \(0.365321\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.820712 | + | 32.6240i | −0.0275258 | + | 1.09418i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.78813 | + | 5.03407i | −0.0599046 | + | 0.168648i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −65.4513 | −2.19025 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.46264 | + | 7.72952i | −0.149170 | + | 0.258369i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.4700 | + | 16.3645i | 0.349584 | + | 0.546395i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.3653 | + | 42.2019i | −0.812627 | + | 1.40751i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.7630 | − | 20.3742i | −0.391883 | − | 0.678762i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.04456 | + | 51.1412i | 0.0347607 | + | 1.70187i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.0511591 | −0.00170059 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0368 | −0.333265 | −0.166633 | − | 0.986019i | \(-0.553289\pi\) | ||||
−0.166633 | + | 0.986019i | \(0.553289\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.80778 | + | 3.97699i | 0.0931282 | + | 0.131908i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.4459 | − | 19.8249i | −0.379220 | − | 0.656828i | 0.611729 | − | 0.791067i | \(-0.290474\pi\) |
−0.990949 | + | 0.134239i | \(0.957141\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.28580 | − | 3.95912i | −0.0756489 | − | 0.131028i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.68337 | + | 5.75705i | 0.121768 | + | 0.190322i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.0789903 | − | 3.13993i | 0.00260849 | − | 0.103690i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.8910 | − | 18.8638i | −0.359262 | − | 0.622261i | 0.628575 | − | 0.777749i | \(-0.283638\pi\) |
−0.987838 | + | 0.155488i | \(0.950305\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.0687 | + | 34.8746i | −0.595383 | + | 1.14916i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.1185 | + | 31.3821i | −0.596377 | + | 1.03296i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.32383 | − | 4.02499i | −0.0764071 | − | 0.132341i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.0416 | + | 15.6396i | 0.362655 | + | 0.513671i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.4189 | − | 28.4383i | 0.538686 | − | 0.933031i | −0.460289 | − | 0.887769i | \(-0.652254\pi\) |
0.998975 | − | 0.0452622i | \(-0.0144123\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.1711 | + | 33.5295i | 0.562760 | + | 1.09888i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.2719 | − | 0.514055i | 0.369025 | − | 0.0168294i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.514589 | − | 0.891294i | 0.0168289 | − | 0.0291484i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.78074 | −0.286854 | −0.143427 | − | 0.989661i | \(-0.545812\pi\) | ||||
−0.143427 | + | 0.989661i | \(0.545812\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.248440 | − | 0.388308i | −0.00810754 | − | 0.0126720i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.13307 | − | 3.69459i | −0.0695362 | − | 0.120440i | 0.829161 | − | 0.559010i | \(-0.188819\pi\) |
−0.898697 | + | 0.438570i | \(0.855485\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.609631 | − | 1.05591i | 0.0198523 | − | 0.0343852i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.908557 | − | 8.10963i | −0.0295554 | − | 0.263806i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.5292 | + | 19.9691i | −0.374648 | + | 0.648909i | −0.990274 | − | 0.139129i | \(-0.955570\pi\) |
0.615626 | + | 0.788038i | \(0.288903\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.94999 | + | 17.2339i | 0.322990 | + | 0.559436i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.6775 | − | 22.9407i | −0.475951 | − | 0.743904i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.5552 | −1.18414 | −0.592070 | − | 0.805886i | \(-0.701689\pi\) | ||||
−0.592070 | + | 0.805886i | \(0.701689\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.18190 | − | 2.04712i | 0.0382455 | − | 0.0662431i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.36186 | − | 0.290133i | 0.205650 | − | 0.00937867i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.167793 | − | 6.66991i | 0.00541831 | − | 0.215383i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4443 | + | 26.7502i | −0.498202 | + | 0.862911i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.5227 | + | 50.9599i | −0.758007 | + | 1.64216i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.01245 | − | 3.48567i | −0.0647832 | − | 0.112208i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.7719 | + | 46.3703i | −0.860926 | + | 1.49117i | 0.0101108 | + | 0.999949i | \(0.496782\pi\) |
−0.871037 | + | 0.491218i | \(0.836552\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.5251 | − | 24.1749i | 0.402364 | − | 0.776610i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.9897 | + | 27.6949i | 0.513133 | + | 0.888773i | 0.999884 | + | 0.0152321i | \(0.00484870\pi\) |
−0.486751 | + | 0.873541i | \(0.661818\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.0919 | + | 6.78146i | 0.355591 | + | 0.217403i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.9093 | + | 17.0511i | 0.349379 | + | 0.546074i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.7104 | + | 23.7471i | 0.438635 | + | 0.759738i | 0.997584 | − | 0.0694638i | \(-0.0221288\pi\) |
−0.558950 | + | 0.829202i | \(0.688796\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.69076 | − | 6.39258i | −0.117957 | − | 0.204308i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.56507 | − | 0.782849i | 0.273462 | − | 0.0249945i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 59.1564 | 1.88680 | 0.943398 | − | 0.331662i | \(-0.107610\pi\) | ||||
0.943398 | + | 0.331662i | \(0.107610\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.56401 | 0.209147 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 47.6883 | − | 28.8471i | 1.51794 | − | 0.918212i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.8946 | − | 43.1188i | −0.791604 | − | 1.37110i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.41887 | + | 11.1178i | −0.203902 | + | 0.353169i | −0.949782 | − | 0.312911i | \(-0.898696\pi\) |
0.745880 | + | 0.666080i | \(0.232029\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.4880 | − | 36.7114i | −0.745370 | − | 1.16500i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.66751 | + | 2.88821i | −0.0528636 | + | 0.0915624i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.78074 | −0.183078 | −0.0915389 | − | 0.995802i | \(-0.529179\pi\) | ||||
−0.0915389 | + | 0.995802i | \(0.529179\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.18716 | + | 4.10390i | 0.100837 | + | 0.129842i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))