Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,2,Mod(149,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.ba (of order \(8\), degree \(4\), 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: | \(6.38803216170\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 749.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.749 |
Dual form | 800.2.ba.b.549.1 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 1.00000 | ||||||||
\(3\) | 1.70711 | + | 0.707107i | 0.985599 | + | 0.408248i | 0.816497 | − | 0.577350i | \(-0.195913\pi\) |
0.169102 | + | 0.985599i | \(0.445913\pi\) | |||||||
\(4\) | 2.00000 | 1.00000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.41421 | + | 1.00000i | 0.985599 | + | 0.408248i | ||||
\(7\) | −1.00000 | − | 1.00000i | −0.377964 | − | 0.377964i | 0.492403 | − | 0.870367i | \(-0.336119\pi\) |
−0.870367 | + | 0.492403i | \(0.836119\pi\) | |||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 0.292893 | + | 0.292893i | 0.0976311 | + | 0.0976311i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.121320 | + | 0.292893i | 0.0365795 | + | 0.0883106i | 0.941113 | − | 0.338091i | \(-0.109781\pi\) |
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 3.41421 | + | 1.41421i | 0.985599 | + | 0.408248i | ||||
\(13\) | −0.707107 | + | 1.70711i | −0.196116 | + | 0.473466i | −0.991093 | − | 0.133174i | \(-0.957483\pi\) |
0.794977 | + | 0.606640i | \(0.207483\pi\) | |||||||
\(14\) | −1.41421 | − | 1.41421i | −0.377964 | − | 0.377964i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 2.82843 | 0.685994 | 0.342997 | − | 0.939336i | \(-0.388558\pi\) | ||||
0.342997 | + | 0.939336i | \(0.388558\pi\) | |||||||
\(18\) | 0.414214 | + | 0.414214i | 0.0976311 | + | 0.0976311i | ||||
\(19\) | 5.53553 | + | 2.29289i | 1.26994 | + | 0.526026i | 0.912946 | − | 0.408081i | \(-0.133802\pi\) |
0.356993 | + | 0.934107i | \(0.383802\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | − | 2.41421i | −0.218218 | − | 0.526825i | ||||
\(22\) | 0.171573 | + | 0.414214i | 0.0365795 | + | 0.0883106i | ||||
\(23\) | −0.171573 | + | 0.171573i | −0.0357754 | + | 0.0357754i | −0.724768 | − | 0.688993i | \(-0.758053\pi\) |
0.688993 | + | 0.724768i | \(0.258053\pi\) | |||||||
\(24\) | 4.82843 | + | 2.00000i | 0.985599 | + | 0.408248i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.00000 | + | 2.41421i | −0.196116 | + | 0.473466i | ||||
\(27\) | −1.82843 | − | 4.41421i | −0.351881 | − | 0.849516i | ||||
\(28\) | −2.00000 | − | 2.00000i | −0.377964 | − | 0.377964i | ||||
\(29\) | −1.12132 | + | 2.70711i | −0.208224 | + | 0.502697i | −0.993144 | − | 0.116900i | \(-0.962704\pi\) |
0.784920 | + | 0.619598i | \(0.212704\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 5.65685 | 1.00000 | ||||||||
\(33\) | 0.585786i | 0.101972i | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.585786 | + | 0.585786i | 0.0976311 | + | 0.0976311i | ||||
\(37\) | −0.707107 | − | 1.70711i | −0.116248 | − | 0.280647i | 0.855037 | − | 0.518567i | \(-0.173534\pi\) |
−0.971285 | + | 0.237920i | \(0.923534\pi\) | |||||||
\(38\) | 7.82843 | + | 3.24264i | 1.26994 | + | 0.526026i | ||||
\(39\) | −2.41421 | + | 2.41421i | −0.386584 | + | 0.386584i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.82843 | − | 5.82843i | −0.910247 | − | 0.910247i | 0.0860440 | − | 0.996291i | \(-0.472577\pi\) |
−0.996291 | + | 0.0860440i | \(0.972577\pi\) | |||||||
\(42\) | −1.41421 | − | 3.41421i | −0.218218 | − | 0.526825i | ||||
\(43\) | −7.94975 | + | 3.29289i | −1.21233 | + | 0.502162i | −0.894962 | − | 0.446143i | \(-0.852797\pi\) |
−0.317363 | + | 0.948304i | \(0.602797\pi\) | |||||||
\(44\) | 0.242641 | + | 0.585786i | 0.0365795 | + | 0.0883106i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.242641 | + | 0.242641i | −0.0357754 | + | 0.0357754i | ||||
\(47\) | −11.6569 | −1.70033 | −0.850163 | − | 0.526519i | \(-0.823497\pi\) | ||||
−0.850163 | + | 0.526519i | \(0.823497\pi\) | |||||||
\(48\) | 6.82843 | + | 2.82843i | 0.985599 | + | 0.408248i | ||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.82843 | + | 2.00000i | 0.676115 | + | 0.280056i | ||||
\(52\) | −1.41421 | + | 3.41421i | −0.196116 | + | 0.473466i | ||||
\(53\) | −7.53553 | + | 3.12132i | −1.03509 | + | 0.428746i | −0.834545 | − | 0.550939i | \(-0.814270\pi\) |
−0.200540 | + | 0.979686i | \(0.564270\pi\) | |||||||
\(54\) | −2.58579 | − | 6.24264i | −0.351881 | − | 0.849516i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.82843 | − | 2.82843i | −0.377964 | − | 0.377964i | ||||
\(57\) | 7.82843 | + | 7.82843i | 1.03690 | + | 1.03690i | ||||
\(58\) | −1.58579 | + | 3.82843i | −0.208224 | + | 0.502697i | ||||
\(59\) | 6.12132 | − | 2.53553i | 0.796928 | − | 0.330098i | 0.0532027 | − | 0.998584i | \(-0.483057\pi\) |
0.743725 | + | 0.668485i | \(0.233057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.292893 | − | 0.707107i | 0.0375011 | − | 0.0905357i | −0.904019 | − | 0.427492i | \(-0.859397\pi\) |
0.941520 | + | 0.336956i | \(0.109397\pi\) | |||||||
\(62\) | −5.65685 | −0.718421 | ||||||||
\(63\) | − | 0.585786i | − | 0.0738022i | ||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.828427i | 0.101972i | ||||||||
\(67\) | −3.70711 | − | 1.53553i | −0.452895 | − | 0.187595i | 0.144563 | − | 0.989496i | \(-0.453822\pi\) |
−0.597458 | + | 0.801900i | \(0.703822\pi\) | |||||||
\(68\) | 5.65685 | 0.685994 | ||||||||
\(69\) | −0.414214 | + | 0.171573i | −0.0498655 | + | 0.0206549i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.171573 | + | 0.171573i | −0.0203620 | + | 0.0203620i | −0.717214 | − | 0.696853i | \(-0.754583\pi\) |
0.696853 | + | 0.717214i | \(0.254583\pi\) | |||||||
\(72\) | 0.828427 | + | 0.828427i | 0.0976311 | + | 0.0976311i | ||||
\(73\) | −7.00000 | + | 7.00000i | −0.819288 | + | 0.819288i | −0.986005 | − | 0.166717i | \(-0.946683\pi\) |
0.166717 | + | 0.986005i | \(0.446683\pi\) | |||||||
\(74\) | −1.00000 | − | 2.41421i | −0.116248 | − | 0.280647i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.0711 | + | 4.58579i | 1.26994 | + | 0.526026i | ||||
\(77\) | 0.171573 | − | 0.414214i | 0.0195525 | − | 0.0472040i | ||||
\(78\) | −3.41421 | + | 3.41421i | −0.386584 | + | 0.386584i | ||||
\(79\) | − | 6.00000i | − | 0.675053i | −0.941316 | − | 0.337526i | \(-0.890410\pi\) | ||
0.941316 | − | 0.337526i | \(-0.109590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 10.0711i | − | 1.11901i | ||||||
\(82\) | −8.24264 | − | 8.24264i | −0.910247 | − | 0.910247i | ||||
\(83\) | −2.53553 | + | 6.12132i | −0.278311 | + | 0.671902i | −0.999789 | − | 0.0205350i | \(-0.993463\pi\) |
0.721478 | + | 0.692437i | \(0.243463\pi\) | |||||||
\(84\) | −2.00000 | − | 4.82843i | −0.218218 | − | 0.526825i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.2426 | + | 4.65685i | −1.21233 | + | 0.502162i | ||||
\(87\) | −3.82843 | + | 3.82843i | −0.410450 | + | 0.410450i | ||||
\(88\) | 0.343146 | + | 0.828427i | 0.0365795 | + | 0.0883106i | ||||
\(89\) | 2.65685 | − | 2.65685i | 0.281626 | − | 0.281626i | −0.552131 | − | 0.833757i | \(-0.686185\pi\) |
0.833757 | + | 0.552131i | \(0.186185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.41421 | − | 1.00000i | 0.253078 | − | 0.104828i | ||||
\(92\) | −0.343146 | + | 0.343146i | −0.0357754 | + | 0.0357754i | ||||
\(93\) | −6.82843 | − | 2.82843i | −0.708075 | − | 0.293294i | ||||
\(94\) | −16.4853 | −1.70033 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.65685 | + | 4.00000i | 0.985599 | + | 0.408248i | ||||
\(97\) | 1.51472i | 0.153796i | 0.997039 | + | 0.0768982i | \(0.0245016\pi\) | ||||
−0.997039 | + | 0.0768982i | \(0.975498\pi\) | |||||||
\(98\) | − | 7.07107i | − | 0.714286i | ||||||
\(99\) | −0.0502525 | + | 0.121320i | −0.00505057 | + | 0.0121932i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.3640 | − | 4.70711i | 1.13076 | − | 0.468375i | 0.262718 | − | 0.964873i | \(-0.415381\pi\) |
0.868038 | + | 0.496498i | \(0.165381\pi\) | |||||||
\(102\) | 6.82843 | + | 2.82843i | 0.676115 | + | 0.280056i | ||||
\(103\) | −7.48528 | − | 7.48528i | −0.737547 | − | 0.737547i | 0.234556 | − | 0.972103i | \(-0.424636\pi\) |
−0.972103 | + | 0.234556i | \(0.924636\pi\) | |||||||
\(104\) | −2.00000 | + | 4.82843i | −0.196116 | + | 0.473466i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.6569 | + | 4.41421i | −1.03509 | + | 0.428746i | ||||
\(107\) | 0.292893 | − | 0.121320i | 0.0283151 | − | 0.0117285i | −0.368481 | − | 0.929635i | \(-0.620122\pi\) |
0.396796 | + | 0.917907i | \(0.370122\pi\) | |||||||
\(108\) | −3.65685 | − | 8.82843i | −0.351881 | − | 0.849516i | ||||
\(109\) | 4.29289 | + | 1.77817i | 0.411185 | + | 0.170318i | 0.578680 | − | 0.815555i | \(-0.303568\pi\) |
−0.167496 | + | 0.985873i | \(0.553568\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.41421i | − | 0.324063i | ||||||
\(112\) | −4.00000 | − | 4.00000i | −0.377964 | − | 0.377964i | ||||
\(113\) | 17.6569 | 1.66102 | 0.830509 | − | 0.557006i | \(-0.188050\pi\) | ||||
0.830509 | + | 0.557006i | \(0.188050\pi\) | |||||||
\(114\) | 11.0711 | + | 11.0711i | 1.03690 | + | 1.03690i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.24264 | + | 5.41421i | −0.208224 | + | 0.502697i | ||||
\(117\) | −0.707107 | + | 0.292893i | −0.0653720 | + | 0.0270780i | ||||
\(118\) | 8.65685 | − | 3.58579i | 0.796928 | − | 0.330098i | ||||
\(119\) | −2.82843 | − | 2.82843i | −0.259281 | − | 0.259281i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.70711 | − | 7.70711i | 0.700646 | − | 0.700646i | ||||
\(122\) | 0.414214 | − | 1.00000i | 0.0375011 | − | 0.0905357i | ||||
\(123\) | −5.82843 | − | 14.0711i | −0.525532 | − | 1.26875i | ||||
\(124\) | −8.00000 | −0.718421 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 0.828427i | − | 0.0738022i | ||||||
\(127\) | 20.9706i | 1.86084i | 0.366499 | + | 0.930418i | \(0.380556\pi\) | ||||
−0.366499 | + | 0.930418i | \(0.619444\pi\) | |||||||
\(128\) | 11.3137 | 1.00000 | ||||||||
\(129\) | −15.8995 | −1.39987 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.63604 | + | 8.77817i | −0.317682 | + | 0.766953i | 0.681694 | + | 0.731637i | \(0.261244\pi\) |
−0.999376 | + | 0.0353153i | \(0.988756\pi\) | |||||||
\(132\) | 1.17157i | 0.101972i | ||||||||
\(133\) | −3.24264 | − | 7.82843i | −0.281173 | − | 0.678811i | ||||
\(134\) | −5.24264 | − | 2.17157i | −0.452895 | − | 0.187595i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.00000 | 0.685994 | ||||||||
\(137\) | 2.65685 | − | 2.65685i | 0.226990 | − | 0.226990i | −0.584444 | − | 0.811434i | \(-0.698687\pi\) |
0.811434 | + | 0.584444i | \(0.198687\pi\) | |||||||
\(138\) | −0.585786 | + | 0.242641i | −0.0498655 | + | 0.0206549i | ||||
\(139\) | 5.19239 | + | 12.5355i | 0.440413 | + | 1.06325i | 0.975804 | + | 0.218646i | \(0.0701640\pi\) |
−0.535392 | + | 0.844604i | \(0.679836\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.8995 | − | 8.24264i | −1.67584 | − | 0.694156i | ||||
\(142\) | −0.242641 | + | 0.242641i | −0.0203620 | + | 0.0203620i | ||||
\(143\) | −0.585786 | −0.0489859 | ||||||||
\(144\) | 1.17157 | + | 1.17157i | 0.0976311 | + | 0.0976311i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.89949 | + | 9.89949i | −0.819288 | + | 0.819288i | ||||
\(147\) | 3.53553 | − | 8.53553i | 0.291606 | − | 0.703999i | ||||
\(148\) | −1.41421 | − | 3.41421i | −0.116248 | − | 0.280647i | ||||
\(149\) | −5.60660 | − | 13.5355i | −0.459311 | − | 1.10887i | −0.968677 | − | 0.248324i | \(-0.920120\pi\) |
0.509366 | − | 0.860550i | \(-0.329880\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.4853 | + | 15.4853i | 1.26017 | + | 1.26017i | 0.951008 | + | 0.309166i | \(0.100050\pi\) |
0.309166 | + | 0.951008i | \(0.399950\pi\) | |||||||
\(152\) | 15.6569 | + | 6.48528i | 1.26994 | + | 0.526026i | ||||
\(153\) | 0.828427 | + | 0.828427i | 0.0669744 | + | 0.0669744i | ||||
\(154\) | 0.242641 | − | 0.585786i | 0.0195525 | − | 0.0472040i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.82843 | + | 4.82843i | −0.386584 | + | 0.386584i | ||||
\(157\) | −0.707107 | − | 0.292893i | −0.0564333 | − | 0.0233754i | 0.354288 | − | 0.935136i | \(-0.384723\pi\) |
−0.410722 | + | 0.911761i | \(0.634723\pi\) | |||||||
\(158\) | − | 8.48528i | − | 0.675053i | ||||||
\(159\) | −15.0711 | −1.19521 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.343146 | 0.0270437 | ||||||||
\(162\) | − | 14.2426i | − | 1.11901i | ||||||
\(163\) | 18.1924 | + | 7.53553i | 1.42494 | + | 0.590229i | 0.956096 | − | 0.293054i | \(-0.0946714\pi\) |
0.468842 | + | 0.883282i | \(0.344671\pi\) | |||||||
\(164\) | −11.6569 | − | 11.6569i | −0.910247 | − | 0.910247i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.58579 | + | 8.65685i | −0.278311 | + | 0.671902i | ||||
\(167\) | −3.34315 | − | 3.34315i | −0.258700 | − | 0.258700i | 0.565825 | − | 0.824525i | \(-0.308558\pi\) |
−0.824525 | + | 0.565825i | \(0.808558\pi\) | |||||||
\(168\) | −2.82843 | − | 6.82843i | −0.218218 | − | 0.526825i | ||||
\(169\) | 6.77817 | + | 6.77817i | 0.521398 | + | 0.521398i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.949747 | + | 2.29289i | 0.0726290 | + | 0.175342i | ||||
\(172\) | −15.8995 | + | 6.58579i | −1.21233 | + | 0.502162i | ||||
\(173\) | 0.464466 | − | 1.12132i | 0.0353127 | − | 0.0852524i | −0.905239 | − | 0.424902i | \(-0.860309\pi\) |
0.940552 | + | 0.339650i | \(0.110309\pi\) | |||||||
\(174\) | −5.41421 | + | 5.41421i | −0.410450 | + | 0.410450i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.485281 | + | 1.17157i | 0.0365795 | + | 0.0883106i | ||||
\(177\) | 12.2426 | 0.920213 | ||||||||
\(178\) | 3.75736 | − | 3.75736i | 0.281626 | − | 0.281626i | ||||
\(179\) | 14.3640 | + | 5.94975i | 1.07361 | + | 0.444705i | 0.848264 | − | 0.529573i | \(-0.177648\pi\) |
0.225349 | + | 0.974278i | \(0.427648\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.19239 | − | 5.29289i | −0.162959 | − | 0.393418i | 0.821216 | − | 0.570618i | \(-0.193296\pi\) |
−0.984175 | + | 0.177200i | \(0.943296\pi\) | |||||||
\(182\) | 3.41421 | − | 1.41421i | 0.253078 | − | 0.104828i | ||||
\(183\) | 1.00000 | − | 1.00000i | 0.0739221 | − | 0.0739221i | ||||
\(184\) | −0.485281 | + | 0.485281i | −0.0357754 | + | 0.0357754i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.65685 | − | 4.00000i | −0.708075 | − | 0.293294i | ||||
\(187\) | 0.343146 | + | 0.828427i | 0.0250933 | + | 0.0605806i | ||||
\(188\) | −23.3137 | −1.70033 | ||||||||
\(189\) | −2.58579 | + | 6.24264i | −0.188088 | + | 0.454085i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 13.6569 | + | 5.65685i | 0.985599 | + | 0.408248i | ||||
\(193\) | − | 18.4853i | − | 1.33060i | −0.746576 | − | 0.665300i | \(-0.768304\pi\) | ||
0.746576 | − | 0.665300i | \(-0.231696\pi\) | |||||||
\(194\) | 2.14214i | 0.153796i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | − | 10.0000i | − | 0.714286i | ||||||
\(197\) | −7.19239 | − | 17.3640i | −0.512436 | − | 1.23713i | −0.942462 | − | 0.334314i | \(-0.891495\pi\) |
0.430025 | − | 0.902817i | \(-0.358505\pi\) | |||||||
\(198\) | −0.0710678 | + | 0.171573i | −0.00505057 | + | 0.0121932i | ||||
\(199\) | −17.9706 | + | 17.9706i | −1.27390 | + | 1.27390i | −0.329875 | + | 0.944025i | \(0.607006\pi\) |
−0.944025 | + | 0.329875i | \(0.892994\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.24264 | − | 5.24264i | −0.369787 | − | 0.369787i | ||||
\(202\) | 16.0711 | − | 6.65685i | 1.13076 | − | 0.468375i | ||||
\(203\) | 3.82843 | − | 1.58579i | 0.268703 | − | 0.111300i | ||||
\(204\) | 9.65685 | + | 4.00000i | 0.676115 | + | 0.280056i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.5858 | − | 10.5858i | −0.737547 | − | 0.737547i | ||||
\(207\) | −0.100505 | −0.00698558 | ||||||||
\(208\) | −2.82843 | + | 6.82843i | −0.196116 | + | 0.473466i | ||||
\(209\) | 1.89949i | 0.131391i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.464466 | + | 0.192388i | 0.0319752 | + | 0.0132445i | 0.398614 | − | 0.917119i | \(-0.369491\pi\) |
−0.366639 | + | 0.930363i | \(0.619491\pi\) | |||||||
\(212\) | −15.0711 | + | 6.24264i | −1.03509 | + | 0.428746i | ||||
\(213\) | −0.414214 | + | 0.171573i | −0.0283814 | + | 0.0117560i | ||||
\(214\) | 0.414214 | − | 0.171573i | 0.0283151 | − | 0.0117285i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.17157 | − | 12.4853i | −0.351881 | − | 0.849516i | ||||
\(217\) | 4.00000 | + | 4.00000i | 0.271538 | + | 0.271538i | ||||
\(218\) | 6.07107 | + | 2.51472i | 0.411185 | + | 0.170318i | ||||
\(219\) | −16.8995 | + | 7.00000i | −1.14196 | + | 0.473016i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | + | 4.82843i | −0.134535 | + | 0.324795i | ||||
\(222\) | − | 4.82843i | − | 0.324063i | ||||||
\(223\) | 12.9706i | 0.868573i | 0.900775 | + | 0.434287i | \(0.142999\pi\) | ||||
−0.900775 | + | 0.434287i | \(0.857001\pi\) | |||||||
\(224\) | −5.65685 | − | 5.65685i | −0.377964 | − | 0.377964i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.9706 | 1.66102 | ||||||||
\(227\) | 6.29289 | + | 2.60660i | 0.417674 | + | 0.173006i | 0.581616 | − | 0.813464i | \(-0.302421\pi\) |
−0.163942 | + | 0.986470i | \(0.552421\pi\) | |||||||
\(228\) | 15.6569 | + | 15.6569i | 1.03690 | + | 1.03690i | ||||
\(229\) | 24.7782 | − | 10.2635i | 1.63739 | − | 0.678228i | 0.641357 | − | 0.767242i | \(-0.278372\pi\) |
0.996030 | + | 0.0890139i | \(0.0283716\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.585786 | − | 0.585786i | 0.0385419 | − | 0.0385419i | ||||
\(232\) | −3.17157 | + | 7.65685i | −0.208224 | + | 0.502697i | ||||
\(233\) | −8.65685 | + | 8.65685i | −0.567129 | + | 0.567129i | −0.931323 | − | 0.364194i | \(-0.881345\pi\) |
0.364194 | + | 0.931323i | \(0.381345\pi\) | |||||||
\(234\) | −1.00000 | + | 0.414214i | −0.0653720 | + | 0.0270780i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.2426 | − | 5.07107i | 0.796928 | − | 0.330098i | ||||
\(237\) | 4.24264 | − | 10.2426i | 0.275589 | − | 0.665331i | ||||
\(238\) | −4.00000 | − | 4.00000i | −0.259281 | − | 0.259281i | ||||
\(239\) | − | 17.3137i | − | 1.11993i | −0.828516 | − | 0.559965i | \(-0.810814\pi\) | ||
0.828516 | − | 0.559965i | \(-0.189186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.48528i | 0.546585i | 0.961931 | + | 0.273293i | \(0.0881127\pi\) | ||||
−0.961931 | + | 0.273293i | \(0.911887\pi\) | |||||||
\(242\) | 10.8995 | − | 10.8995i | 0.700646 | − | 0.700646i | ||||
\(243\) | 1.63604 | − | 3.94975i | 0.104952 | − | 0.253376i | ||||
\(244\) | 0.585786 | − | 1.41421i | 0.0375011 | − | 0.0905357i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.24264 | − | 19.8995i | −0.525532 | − | 1.26875i | ||||
\(247\) | −7.82843 | + | 7.82843i | −0.498111 | + | 0.498111i | ||||
\(248\) | −11.3137 | −0.718421 | ||||||||
\(249\) | −8.65685 | + | 8.65685i | −0.548606 | + | 0.548606i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.6066 | + | 6.05025i | −0.921961 | + | 0.381889i | −0.792623 | − | 0.609712i | \(-0.791285\pi\) |
−0.129338 | + | 0.991601i | \(0.541285\pi\) | |||||||
\(252\) | − | 1.17157i | − | 0.0738022i | ||||||
\(253\) | −0.0710678 | − | 0.0294373i | −0.00446800 | − | 0.00185070i | ||||
\(254\) | 29.6569i | 1.86084i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | − | 6.00000i | − | 0.374270i | −0.982334 | − | 0.187135i | \(-0.940080\pi\) | ||
0.982334 | − | 0.187135i | \(-0.0599201\pi\) | |||||||
\(258\) | −22.4853 | −1.39987 | ||||||||
\(259\) | −1.00000 | + | 2.41421i | −0.0621370 | + | 0.150012i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.12132 | + | 0.464466i | −0.0694080 | + | 0.0287497i | ||||
\(262\) | −5.14214 | + | 12.4142i | −0.317682 | + | 0.766953i | ||||
\(263\) | −0.171573 | − | 0.171573i | −0.0105796 | − | 0.0105796i | 0.701797 | − | 0.712377i | \(-0.252381\pi\) |
−0.712377 | + | 0.701797i | \(0.752381\pi\) | |||||||
\(264\) | 1.65685i | 0.101972i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.58579 | − | 11.0711i | −0.281173 | − | 0.678811i | ||||
\(267\) | 6.41421 | − | 2.65685i | 0.392543 | − | 0.162597i | ||||
\(268\) | −7.41421 | − | 3.07107i | −0.452895 | − | 0.187595i | ||||
\(269\) | −4.87868 | − | 2.02082i | −0.297458 | − | 0.123211i | 0.228963 | − | 0.973435i | \(-0.426467\pi\) |
−0.526421 | + | 0.850224i | \(0.676467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0000i | 1.09342i | 0.837321 | + | 0.546711i | \(0.184120\pi\) | ||||
−0.837321 | + | 0.546711i | \(0.815880\pi\) | |||||||
\(272\) | 11.3137 | 0.685994 | ||||||||
\(273\) | 4.82843 | 0.292230 | ||||||||
\(274\) | 3.75736 | − | 3.75736i | 0.226990 | − | 0.226990i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.828427 | + | 0.343146i | −0.0498655 | + | 0.0206549i | ||||
\(277\) | 0.707107 | − | 0.292893i | 0.0424859 | − | 0.0175982i | −0.361339 | − | 0.932434i | \(-0.617680\pi\) |
0.403825 | + | 0.914836i | \(0.367680\pi\) | |||||||
\(278\) | 7.34315 | + | 17.7279i | 0.440413 | + | 1.06325i | ||||
\(279\) | −1.17157 | − | 1.17157i | −0.0701402 | − | 0.0701402i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.17157 | + | 6.17157i | −0.368165 | + | 0.368165i | −0.866808 | − | 0.498643i | \(-0.833832\pi\) |
0.498643 | + | 0.866808i | \(0.333832\pi\) | |||||||
\(282\) | −28.1421 | − | 11.6569i | −1.67584 | − | 0.694156i | ||||
\(283\) | −4.05025 | − | 9.77817i | −0.240763 | − | 0.581252i | 0.756596 | − | 0.653882i | \(-0.226861\pi\) |
−0.997359 | + | 0.0726300i | \(0.976861\pi\) | |||||||
\(284\) | −0.343146 | + | 0.343146i | −0.0203620 | + | 0.0203620i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.828427 | −0.0489859 | ||||||||
\(287\) | 11.6569i | 0.688082i | ||||||||
\(288\) | 1.65685 | + | 1.65685i | 0.0976311 | + | 0.0976311i | ||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.07107 | + | 2.58579i | −0.0627871 | + | 0.151581i | ||||
\(292\) | −14.0000 | + | 14.0000i | −0.819288 | + | 0.819288i | ||||
\(293\) | −4.80761 | − | 11.6066i | −0.280864 | − | 0.678065i | 0.718993 | − | 0.695018i | \(-0.244603\pi\) |
−0.999856 | + | 0.0169528i | \(0.994603\pi\) | |||||||
\(294\) | 5.00000 | − | 12.0711i | 0.291606 | − | 0.703999i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | − | 4.82843i | −0.116248 | − | 0.280647i | ||||
\(297\) | 1.07107 | − | 1.07107i | 0.0621497 | − | 0.0621497i | ||||
\(298\) | −7.92893 | − | 19.1421i | −0.459311 | − | 1.10887i | ||||
\(299\) | −0.171573 | − | 0.414214i | −0.00992232 | − | 0.0239546i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.2426 | + | 4.65685i | 0.648015 | + | 0.268417i | ||||
\(302\) | 21.8995 | + | 21.8995i | 1.26017 | + | 1.26017i | ||||
\(303\) | 22.7279 | 1.30569 | ||||||||
\(304\) | 22.1421 | + | 9.17157i | 1.26994 | + | 0.526026i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.17157 | + | 1.17157i | 0.0669744 | + | 0.0669744i | ||||
\(307\) | 1.22183 | − | 2.94975i | 0.0697333 | − | 0.168351i | −0.885170 | − | 0.465267i | \(-0.845958\pi\) |
0.954904 | + | 0.296916i | \(0.0959582\pi\) | |||||||
\(308\) | 0.343146 | − | 0.828427i | 0.0195525 | − | 0.0472040i | ||||
\(309\) | −7.48528 | − | 18.0711i | −0.425823 | − | 1.02803i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.65685 | + | 8.65685i | 0.490885 | + | 0.490885i | 0.908585 | − | 0.417700i | \(-0.137164\pi\) |
−0.417700 | + | 0.908585i | \(0.637164\pi\) | |||||||
\(312\) | −6.82843 | + | 6.82843i | −0.386584 | + | 0.386584i | ||||
\(313\) | 9.48528 | + | 9.48528i | 0.536140 | + | 0.536140i | 0.922393 | − | 0.386253i | \(-0.126231\pi\) |
−0.386253 | + | 0.922393i | \(0.626231\pi\) | |||||||
\(314\) | −1.00000 | − | 0.414214i | −0.0564333 | − | 0.0233754i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 12.0000i | − | 0.675053i | ||||||
\(317\) | −11.1924 | − | 4.63604i | −0.628627 | − | 0.260386i | 0.0455425 | − | 0.998962i | \(-0.485498\pi\) |
−0.674170 | + | 0.738577i | \(0.735498\pi\) | |||||||
\(318\) | −21.3137 | −1.19521 | ||||||||
\(319\) | −0.928932 | −0.0520102 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.585786 | 0.0326954 | ||||||||
\(322\) | 0.485281 | 0.0270437 | ||||||||
\(323\) | 15.6569 | + | 6.48528i | 0.871171 | + | 0.360851i | ||||
\(324\) | − | 20.1421i | − | 1.11901i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 25.7279 | + | 10.6569i | 1.42494 | + | 0.590229i | ||||
\(327\) | 6.07107 | + | 6.07107i | 0.335731 | + | 0.335731i | ||||
\(328\) | −16.4853 | − | 16.4853i | −0.910247 | − | 0.910247i | ||||
\(329\) | 11.6569 | + | 11.6569i | 0.642663 | + | 0.642663i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.70711 | − | 6.53553i | −0.148796 | − | 0.359225i | 0.831854 | − | 0.554995i | \(-0.187280\pi\) |
−0.980650 | + | 0.195769i | \(0.937280\pi\) | |||||||
\(332\) | −5.07107 | + | 12.2426i | −0.278311 | + | 0.671902i | ||||
\(333\) | 0.292893 | − | 0.707107i | 0.0160504 | − | 0.0387492i | ||||
\(334\) | −4.72792 | − | 4.72792i | −0.258700 | − | 0.258700i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.00000 | − | 9.65685i | −0.218218 | − | 0.526825i | ||||
\(337\) | 16.9706 | 0.924445 | 0.462223 | − | 0.886764i | \(-0.347052\pi\) | ||||
0.462223 | + | 0.886764i | \(0.347052\pi\) | |||||||
\(338\) | 9.58579 | + | 9.58579i | 0.521398 | + | 0.521398i | ||||
\(339\) | 30.1421 | + | 12.4853i | 1.63710 | + | 0.678107i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.485281 | − | 1.17157i | −0.0262795 | − | 0.0634442i | ||||
\(342\) | 1.34315 | + | 3.24264i | 0.0726290 | + | 0.175342i | ||||
\(343\) | −12.0000 | + | 12.0000i | −0.647939 | + | 0.647939i | ||||
\(344\) | −22.4853 | + | 9.31371i | −1.21233 | + | 0.502162i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.656854 | − | 1.58579i | 0.0353127 | − | 0.0852524i | ||||
\(347\) | −5.94975 | − | 14.3640i | −0.319399 | − | 0.771098i | −0.999286 | − | 0.0377808i | \(-0.987971\pi\) |
0.679887 | − | 0.733317i | \(-0.262029\pi\) | |||||||
\(348\) | −7.65685 | + | 7.65685i | −0.410450 | + | 0.410450i | ||||
\(349\) | 10.6777 | − | 25.7782i | 0.571563 | − | 1.37987i | −0.328662 | − | 0.944448i | \(-0.606598\pi\) |
0.900224 | − | 0.435426i | \(-0.143402\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.82843 | 0.471227 | ||||||||
\(352\) | 0.686292 | + | 1.65685i | 0.0365795 | + | 0.0883106i | ||||
\(353\) | 6.00000i | 0.319348i | 0.987170 | + | 0.159674i | \(0.0510443\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(354\) | 17.3137 | 0.920213 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.31371 | − | 5.31371i | 0.281626 | − | 0.281626i | ||||
\(357\) | −2.82843 | − | 6.82843i | −0.149696 | − | 0.361399i | ||||
\(358\) | 20.3137 | + | 8.41421i | 1.07361 | + | 0.444705i | ||||
\(359\) | 12.1716 | − | 12.1716i | 0.642391 | − | 0.642391i | −0.308752 | − | 0.951143i | \(-0.599911\pi\) |
0.951143 | + | 0.308752i | \(0.0999112\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.9497 | + | 11.9497i | 0.628934 | + | 0.628934i | ||||
\(362\) | −3.10051 | − | 7.48528i | −0.162959 | − | 0.393418i | ||||
\(363\) | 18.6066 | − | 7.70711i | 0.976593 | − | 0.404518i | ||||
\(364\) | 4.82843 | − | 2.00000i | 0.253078 | − | 0.104828i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.41421 | − | 1.41421i | 0.0739221 | − | 0.0739221i | ||||
\(367\) | −6.00000 | −0.313197 | −0.156599 | − | 0.987662i | \(-0.550053\pi\) | ||||
−0.156599 | + | 0.987662i | \(0.550053\pi\) | |||||||
\(368\) | −0.686292 | + | 0.686292i | −0.0357754 | + | 0.0357754i | ||||
\(369\) | − | 3.41421i | − | 0.177737i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.6569 | + | 4.41421i | 0.553276 | + | 0.229175i | ||||
\(372\) | −13.6569 | − | 5.65685i | −0.708075 | − | 0.293294i | ||||
\(373\) | 28.2635 | − | 11.7071i | 1.46343 | − | 0.606171i | 0.498077 | − | 0.867133i | \(-0.334040\pi\) |
0.965349 | + | 0.260962i | \(0.0840396\pi\) | |||||||
\(374\) | 0.485281 | + | 1.17157i | 0.0250933 | + | 0.0605806i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −32.9706 | −1.70033 | ||||||||
\(377\) | −3.82843 | − | 3.82843i | −0.197174 | − | 0.197174i | ||||
\(378\) | −3.65685 | + | 8.82843i | −0.188088 | + | 0.454085i | ||||
\(379\) | −21.6777 | + | 8.97918i | −1.11351 | + | 0.461230i | −0.862144 | − | 0.506663i | \(-0.830879\pi\) |
−0.251363 | + | 0.967893i | \(0.580879\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.8284 | + | 35.7990i | −0.759683 | + | 1.83404i | ||||
\(382\) | −16.9706 | −0.868290 | ||||||||
\(383\) | 16.9706i | 0.867155i | 0.901116 | + | 0.433578i | \(0.142749\pi\) | ||||
−0.901116 | + | 0.433578i | \(0.857251\pi\) | |||||||
\(384\) | 19.3137 | + | 8.00000i | 0.985599 | + | 0.408248i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 26.1421i | − | 1.33060i | ||||||
\(387\) | −3.29289 | − | 1.36396i | −0.167387 | − | 0.0693340i | ||||
\(388\) | 3.02944i | 0.153796i | ||||||||
\(389\) | 29.6066 | − | 12.2635i | 1.50111 | − | 0.621782i | 0.527413 | − | 0.849609i | \(-0.323162\pi\) |
0.973702 | + | 0.227827i | \(0.0731622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.485281 | + | 0.485281i | −0.0245417 | + | 0.0245417i | ||||
\(392\) | − | 14.1421i | − | 0.714286i | ||||||
\(393\) | −12.4142 | + | 12.4142i | −0.626214 | + | 0.626214i | ||||
\(394\) | −10.1716 | − | 24.5563i | −0.512436 | − | 1.23713i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.100505 | + | 0.242641i | −0.00505057 | + | 0.0121932i | ||||
\(397\) | −10.2635 | + | 24.7782i | −0.515108 | + | 1.24358i | 0.425769 | + | 0.904832i | \(0.360004\pi\) |
−0.940877 | + | 0.338749i | \(0.889996\pi\) | |||||||
\(398\) | −25.4142 | + | 25.4142i | −1.27390 | + | 1.27390i | ||||
\(399\) | − | 15.6569i | − | 0.783823i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.82843i | 0.141245i | 0.997503 | + | 0.0706225i | \(0.0224986\pi\) | ||||
−0.997503 | + | 0.0706225i | \(0.977501\pi\) | |||||||
\(402\) | −7.41421 | − | 7.41421i | −0.369787 | − | 0.369787i | ||||
\(403\) | 2.82843 | − | 6.82843i | 0.140894 | − | 0.340148i | ||||
\(404\) | 22.7279 | − | 9.41421i | 1.13076 | − | 0.468375i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.41421 | − | 2.24264i | 0.268703 | − | 0.111300i | ||||
\(407\) | 0.414214 | − | 0.414214i | 0.0205318 | − | 0.0205318i | ||||
\(408\) | 13.6569 | + | 5.65685i | 0.676115 | + | 0.280056i | ||||
\(409\) | −4.51472 | + | 4.51472i | −0.223238 | + | 0.223238i | −0.809861 | − | 0.586622i | \(-0.800457\pi\) |
0.586622 | + | 0.809861i | \(0.300457\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.41421 | − | 2.65685i | 0.316390 | − | 0.131053i | ||||
\(412\) | −14.9706 | − | 14.9706i | −0.737547 | − | 0.737547i | ||||
\(413\) | −8.65685 | − | 3.58579i | −0.425976 | − | 0.176445i | ||||
\(414\) | −0.142136 | −0.00698558 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.00000 | + | 9.65685i | −0.196116 | + | 0.473466i | ||||
\(417\) | 25.0711i | 1.22774i | ||||||||
\(418\) | 2.68629i | 0.131391i | ||||||||
\(419\) | 8.60660 | − | 20.7782i | 0.420460 | − | 1.01508i | −0.561752 | − | 0.827306i | \(-0.689873\pi\) |
0.982212 | − | 0.187775i | \(-0.0601275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.70711 | − | 3.19239i | 0.375621 | − | 0.155587i | −0.186882 | − | 0.982382i | \(-0.559838\pi\) |
0.562504 | + | 0.826795i | \(0.309838\pi\) | |||||||
\(422\) | 0.656854 | + | 0.272078i | 0.0319752 | + | 0.0132445i | ||||
\(423\) | −3.41421 | − | 3.41421i | −0.166005 | − | 0.166005i | ||||
\(424\) | −21.3137 | + | 8.82843i | −1.03509 | + | 0.428746i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.585786 | + | 0.242641i | −0.0283814 | + | 0.0117560i | ||||
\(427\) | −1.00000 | + | 0.414214i | −0.0483934 | + | 0.0200452i | ||||
\(428\) | 0.585786 | − | 0.242641i | 0.0283151 | − | 0.0117285i | ||||
\(429\) | −1.00000 | − | 0.414214i | −0.0482805 | − | 0.0199984i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 23.6569i | − | 1.13951i | −0.821814 | − | 0.569755i | \(-0.807038\pi\) | ||
0.821814 | − | 0.569755i | \(-0.192962\pi\) | |||||||
\(432\) | −7.31371 | − | 17.6569i | −0.351881 | − | 0.849516i | ||||
\(433\) | 32.4853 | 1.56114 | 0.780571 | − | 0.625067i | \(-0.214928\pi\) | ||||
0.780571 | + | 0.625067i | \(0.214928\pi\) | |||||||
\(434\) | 5.65685 | + | 5.65685i | 0.271538 | + | 0.271538i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.58579 | + | 3.55635i | 0.411185 | + | 0.170318i | ||||
\(437\) | −1.34315 | + | 0.556349i | −0.0642514 | + | 0.0266138i | ||||
\(438\) | −23.8995 | + | 9.89949i | −1.14196 | + | 0.473016i | ||||
\(439\) | 17.0000 | + | 17.0000i | 0.811366 | + | 0.811366i | 0.984839 | − | 0.173473i | \(-0.0554989\pi\) |
−0.173473 | + | 0.984839i | \(0.555499\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.46447 | − | 1.46447i | 0.0697365 | − | 0.0697365i | ||||
\(442\) | −2.82843 | + | 6.82843i | −0.134535 | + | 0.324795i | ||||
\(443\) | −8.53553 | − | 20.6066i | −0.405535 | − | 0.979049i | −0.986298 | − | 0.164976i | \(-0.947245\pi\) |
0.580762 | − | 0.814073i | \(-0.302755\pi\) | |||||||
\(444\) | − | 6.82843i | − | 0.324063i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 18.3431i | 0.868573i | ||||||||
\(447\) | − | 27.0711i | − | 1.28042i | ||||||
\(448\) | −8.00000 | − | 8.00000i | −0.377964 | − | 0.377964i | ||||
\(449\) | −31.4558 | −1.48449 | −0.742247 | − | 0.670127i | \(-0.766240\pi\) | ||||
−0.742247 | + | 0.670127i | \(0.766240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.00000 | − | 2.41421i | 0.0470882 | − | 0.113681i | ||||
\(452\) | 35.3137 | 1.66102 | ||||||||
\(453\) | 15.4853 | + | 37.3848i | 0.727562 | + | 1.75649i | ||||
\(454\) | 8.89949 | + | 3.68629i | 0.417674 | + | 0.173006i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 22.1421 | + | 22.1421i | 1.03690 | + | 1.03690i | ||||
\(457\) | 9.48528 | − | 9.48528i | 0.443703 | − | 0.443703i | −0.449552 | − | 0.893254i | \(-0.648416\pi\) |
0.893254 | + | 0.449552i | \(0.148416\pi\) | |||||||
\(458\) | 35.0416 | − | 14.5147i | 1.63739 | − | 0.678228i | ||||
\(459\) | −5.17157 | − | 12.4853i | −0.241388 | − | 0.582763i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.3640 | + | 5.53553i | 0.622422 | + | 0.257816i | 0.671529 | − | 0.740978i | \(-0.265638\pi\) |
−0.0491076 | + | 0.998793i | \(0.515638\pi\) | |||||||
\(462\) | 0.828427 | − | 0.828427i | 0.0385419 | − | 0.0385419i | ||||
\(463\) | 10.9706 | 0.509845 | 0.254923 | − | 0.966961i | \(-0.417950\pi\) | ||||
0.254923 | + | 0.966961i | \(0.417950\pi\) | |||||||
\(464\) | −4.48528 | + | 10.8284i | −0.208224 | + | 0.502697i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.2426 | + | 12.2426i | −0.567129 | + | 0.567129i | ||||
\(467\) | 12.0503 | − | 29.0919i | 0.557619 | − | 1.34621i | −0.354027 | − | 0.935235i | \(-0.615188\pi\) |
0.911646 | − | 0.410977i | \(-0.134812\pi\) | |||||||
\(468\) | −1.41421 | + | 0.585786i | −0.0653720 | + | 0.0270780i | ||||
\(469\) | 2.17157 | + | 5.24264i | 0.100274 | + | 0.242083i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.00000 | − | 1.00000i | −0.0460776 | − | 0.0460776i | ||||
\(472\) | 17.3137 | − | 7.17157i | 0.796928 | − | 0.330098i | ||||
\(473\) | −1.92893 | − | 1.92893i | −0.0886924 | − | 0.0886924i | ||||
\(474\) | 6.00000 | − | 14.4853i | 0.275589 | − | 0.665331i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.65685 | − | 5.65685i | −0.259281 | − | 0.259281i | ||||
\(477\) | −3.12132 | − | 1.29289i | −0.142915 | − | 0.0591975i | ||||
\(478\) | − | 24.4853i | − | 1.11993i | ||||||
\(479\) | 4.97056 | 0.227111 | 0.113555 | − | 0.993532i | \(-0.463776\pi\) | ||||
0.113555 | + | 0.993532i | \(0.463776\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.41421 | 0.155675 | ||||||||
\(482\) | 12.0000i | 0.546585i | ||||||||
\(483\) | 0.585786 | + | 0.242641i | 0.0266542 | + | 0.0110405i | ||||
\(484\) | 15.4142 | − | 15.4142i | 0.700646 | − | 0.700646i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.31371 | − | 5.58579i | 0.104952 | − | 0.253376i | ||||
\(487\) | 11.0000 | + | 11.0000i | 0.498458 | + | 0.498458i | 0.910958 | − | 0.412500i | \(-0.135344\pi\) |
−0.412500 | + | 0.910958i | \(0.635344\pi\) | |||||||
\(488\) | 0.828427 | − | 2.00000i | 0.0375011 | − | 0.0905357i | ||||
\(489\) | 25.7279 | + | 25.7279i | 1.16346 | + | 1.16346i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.33452 | − | 17.7071i | −0.331002 | − | 0.799111i | −0.998513 | − | 0.0545104i | \(-0.982640\pi\) |
0.667511 | − | 0.744600i | \(-0.267360\pi\) | |||||||
\(492\) | −11.6569 | − | 28.1421i | −0.525532 | − | 1.26875i | ||||
\(493\) | −3.17157 | + | 7.65685i | −0.142840 | + | 0.344847i | ||||
\(494\) | −11.0711 | + | 11.0711i | −0.498111 | + | 0.498111i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.0000 | −0.718421 | ||||||||
\(497\) | 0.343146 | 0.0153922 | ||||||||
\(498\) | −12.2426 | + | 12.2426i | −0.548606 | + | 0.548606i | ||||
\(499\) | −8.94975 | − | 3.70711i | −0.400646 | − | 0.165953i | 0.173256 | − | 0.984877i | \(-0.444571\pi\) |
−0.573902 | + | 0.818924i | \(0.694571\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.34315 | − | 8.07107i | −0.149361 | − | 0.360589i | ||||
\(502\) | −20.6569 | + | 8.55635i | −0.921961 | + | 0.381889i | ||||
\(503\) | −17.1421 | + | 17.1421i | −0.764330 | + | 0.764330i | −0.977102 | − | 0.212772i | \(-0.931751\pi\) |
0.212772 | + | 0.977102i | \(0.431751\pi\) | |||||||
\(504\) | − | 1.65685i | − | 0.0738022i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.100505 | − | 0.0416306i | −0.00446800 | − | 0.00185070i | ||||
\(507\) | 6.77817 | + | 16.3640i | 0.301029 | + | 0.726749i | ||||
\(508\) | 41.9411i | 1.86084i | ||||||||
\(509\) | −12.0919 | + | 29.1924i | −0.535963 | + | 1.29393i | 0.391556 | + | 0.920154i | \(0.371937\pi\) |
−0.927519 | + | 0.373776i | \(0.878063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0000 | 0.619324 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | − | 28.6274i | − | 1.26393i | ||||||
\(514\) | − | 8.48528i | − | 0.374270i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −31.7990 | −1.39987 | ||||||||
\(517\) | −1.41421 | − | 3.41421i | −0.0621970 | − | 0.150157i | ||||
\(518\) | −1.41421 | + | 3.41421i | −0.0621370 | + | 0.150012i | ||||
\(519\) | 1.58579 | − | 1.58579i | 0.0696083 | − | 0.0696083i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.6569 | + | 14.6569i | 0.642128 | + | 0.642128i | 0.951078 | − | 0.308950i | \(-0.0999775\pi\) |
−0.308950 | + | 0.951078i | \(0.599978\pi\) | |||||||
\(522\) | −1.58579 | + | 0.656854i | −0.0694080 | + | 0.0287497i | ||||
\(523\) | −1.94975 | + | 0.807612i | −0.0852565 | + | 0.0353144i | −0.424904 | − | 0.905238i | \(-0.639692\pi\) |
0.339648 | + | 0.940553i | \(0.389692\pi\) | |||||||
\(524\) | −7.27208 | + | 17.5563i | −0.317682 | + | 0.766953i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.242641 | − | 0.242641i | −0.0105796 | − | 0.0105796i | ||||
\(527\) | −11.3137 | −0.492833 | ||||||||
\(528\) | 2.34315i | 0.101972i | ||||||||
\(529\) | 22.9411i | 0.997440i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.53553 | + | 1.05025i | 0.110033 | + | 0.0455771i | ||||
\(532\) | −6.48528 | − | 15.6569i | −0.281173 | − | 0.678811i | ||||
\(533\) | 14.0711 | − | 5.82843i | 0.609486 | − | 0.252457i | ||||
\(534\) | 9.07107 | − | 3.75736i | 0.392543 | − | 0.162597i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.4853 | − | 4.34315i | −0.452895 | − | 0.187595i | ||||
\(537\) | 20.3137 | + | 20.3137i | 0.876601 | + | 0.876601i | ||||
\(538\) | −6.89949 | − | 2.85786i | −0.297458 | − | 0.123211i | ||||
\(539\) | 1.46447 | − | 0.606602i | 0.0630790 | − | 0.0261282i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.26346 | − | 12.7071i | 0.226294 | − | 0.546321i | −0.769427 | − | 0.638735i | \(-0.779458\pi\) |
0.995721 | + | 0.0924135i | \(0.0294582\pi\) | |||||||
\(542\) | 25.4558i | 1.09342i | ||||||||
\(543\) | − | 10.5858i | − | 0.454280i | ||||||
\(544\) | 16.0000 | 0.685994 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.82843 | 0.292230 | ||||||||
\(547\) | 25.2635 | + | 10.4645i | 1.08019 | + | 0.447428i | 0.850575 | − | 0.525854i | \(-0.176254\pi\) |
0.229612 | + | 0.973282i | \(0.426254\pi\) | |||||||
\(548\) | 5.31371 | − | 5.31371i | 0.226990 | − | 0.226990i | ||||
\(549\) | 0.292893 | − | 0.121320i | 0.0125004 | − | 0.00517783i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.4142 | + | 12.4142i | −0.528863 | + | 0.528863i | ||||
\(552\) | −1.17157 | + | 0.485281i | −0.0498655 | + | 0.0206549i | ||||
\(553\) | −6.00000 | + | 6.00000i | −0.255146 | + | 0.255146i | ||||
\(554\) | 1.00000 | − | 0.414214i | 0.0424859 | − | 0.0175982i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.3848 | + | 25.0711i | 0.440413 | + | 1.06325i | ||||
\(557\) | 4.50610 | − | 10.8787i | 0.190929 | − | 0.460944i | −0.799206 | − | 0.601057i | \(-0.794746\pi\) |
0.990136 | + | 0.140113i | \(0.0447464\pi\) | |||||||
\(558\) | −1.65685 | − | 1.65685i | −0.0701402 | − | 0.0701402i | ||||
\(559\) | − | 15.8995i | − | 0.672477i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.65685i | 0.0699524i | ||||||||
\(562\) | −8.72792 | + | 8.72792i | −0.368165 | + | 0.368165i | ||||
\(563\) | −5.02082 | + | 12.1213i | −0.211602 | + | 0.510853i | −0.993670 | − | 0.112341i | \(-0.964165\pi\) |
0.782068 | + | 0.623194i | \(0.214165\pi\) | |||||||
\(564\) | −39.7990 | − | 16.4853i | −1.67584 | − | 0.694156i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.72792 | − | 13.8284i | −0.240763 | − | 0.581252i | ||||
\(567\) | −10.0711 | + | 10.0711i | −0.422945 | + | 0.422945i | ||||
\(568\) | −0.485281 | + | 0.485281i | −0.0203620 | + | 0.0203620i | ||||
\(569\) | −3.34315 | + | 3.34315i | −0.140152 | + | 0.140152i | −0.773702 | − | 0.633550i | \(-0.781597\pi\) |
0.633550 | + | 0.773702i | \(0.281597\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.29289 | + | 0.535534i | −0.0541059 | + | 0.0224114i | −0.409572 | − | 0.912278i | \(-0.634322\pi\) |
0.355466 | + | 0.934689i | \(0.384322\pi\) | |||||||
\(572\) | −1.17157 | −0.0489859 | ||||||||
\(573\) | −20.4853 | − | 8.48528i | −0.855785 | − | 0.354478i | ||||
\(574\) | 16.4853i | 0.688082i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.34315 | + | 2.34315i | 0.0976311 | + | 0.0976311i | ||||
\(577\) | 14.9706i | 0.623233i | 0.950208 | + | 0.311616i | \(0.100870\pi\) | ||||
−0.950208 | + | 0.311616i | \(0.899130\pi\) | |||||||
\(578\) | −12.7279 | −0.529412 | ||||||||
\(579\) | 13.0711 | − | 31.5563i | 0.543215 | − | 1.31144i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.65685 | − | 3.58579i | 0.359147 | − | 0.148763i | ||||
\(582\) | −1.51472 | + | 3.65685i | −0.0627871 | + | 0.151581i | ||||
\(583\) | −1.82843 | − | 1.82843i | −0.0757257 | − | 0.0757257i | ||||
\(584\) | −19.7990 | + | 19.7990i | −0.819288 | + | 0.819288i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.79899 | − | 16.4142i | −0.280864 | − | 0.678065i | ||||
\(587\) | 20.7782 | − | 8.60660i | 0.857607 | − | 0.355232i | 0.0898359 | − | 0.995957i | \(-0.471366\pi\) |
0.767771 | + | 0.640724i | \(0.221366\pi\) | |||||||
\(588\) | 7.07107 | − | 17.0711i | 0.291606 | − | 0.703999i | ||||
\(589\) | −22.1421 | − | 9.17157i | −0.912351 | − | 0.377908i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 34.7279i | − | 1.42852i | ||||||
\(592\) | −2.82843 | − | 6.82843i | −0.116248 | − | 0.280647i | ||||
\(593\) | −28.2843 | −1.16150 | −0.580748 | − | 0.814083i | \(-0.697240\pi\) | ||||
−0.580748 | + | 0.814083i | \(0.697240\pi\) | |||||||
\(594\) | 1.51472 | − | 1.51472i | 0.0621497 | − | 0.0621497i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.2132 | − | 27.0711i | −0.459311 | − | 1.10887i | ||||
\(597\) | −43.3848 | + | 17.9706i | −1.77562 | + | 0.735486i | ||||
\(598\) | −0.242641 | − | 0.585786i | −0.00992232 | − | 0.0239546i | ||||
\(599\) | 15.3431 | + | 15.3431i | 0.626904 | + | 0.626904i | 0.947288 | − | 0.320384i | \(-0.103812\pi\) |
−0.320384 | + | 0.947288i | \(0.603812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.9706 | − | 11.9706i | 0.488289 | − | 0.488289i | −0.419477 | − | 0.907766i | \(-0.637786\pi\) |
0.907766 | + | 0.419477i | \(0.137786\pi\) | |||||||
\(602\) | 15.8995 | + | 6.58579i | 0.648015 | + | 0.268417i | ||||
\(603\) | −0.636039 | − | 1.53553i | −0.0259015 | − | 0.0625318i | ||||
\(604\) | 30.9706 | + | 30.9706i | 1.26017 | + | 1.26017i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 32.1421 | 1.30569 | ||||||||
\(607\) | − | 0.970563i | − | 0.0393939i | −0.999806 | − | 0.0196970i | \(-0.993730\pi\) | ||
0.999806 | − | 0.0196970i | \(-0.00627014\pi\) | |||||||
\(608\) | 31.3137 | + | 12.9706i | 1.26994 | + | 0.526026i | ||||
\(609\) | 7.65685 | 0.310271 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.24264 | − | 19.8995i | 0.333462 | − | 0.805047i | ||||
\(612\) | 1.65685 | + | 1.65685i | 0.0669744 | + | 0.0669744i | ||||
\(613\) | 15.1924 | + | 36.6777i | 0.613615 | + | 1.48140i | 0.859002 | + | 0.511972i | \(0.171085\pi\) |
−0.245387 | + | 0.969425i | \(0.578915\pi\) | |||||||
\(614\) | 1.72792 | − | 4.17157i | 0.0697333 | − | 0.168351i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.485281 | − | 1.17157i | 0.0195525 | − | 0.0472040i | ||||
\(617\) | −16.7990 | + | 16.7990i | −0.676302 | + | 0.676302i | −0.959161 | − | 0.282859i | \(-0.908717\pi\) |
0.282859 | + | 0.959161i | \(0.408717\pi\) | |||||||
\(618\) | −10.5858 | − | 25.5563i | −0.425823 | − | 1.02803i | ||||
\(619\) | 6.22183 | + | 15.0208i | 0.250076 | + | 0.603738i | 0.998210 | − | 0.0598107i | \(-0.0190497\pi\) |
−0.748133 | + | 0.663548i | \(0.769050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.07107 | + | 0.443651i | 0.0429805 | + | 0.0178031i | ||||
\(622\) | 12.2426 | + | 12.2426i | 0.490885 | + | 0.490885i | ||||
\(623\) | −5.31371 | −0.212889 | ||||||||
\(624\) | −9.65685 | + | 9.65685i | −0.386584 | + | 0.386584i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.4142 | + | 13.4142i | 0.536140 | + | 0.536140i | ||||
\(627\) | −1.34315 | + | 3.24264i | −0.0536401 | + | 0.129499i | ||||
\(628\) | −1.41421 | − | 0.585786i | −0.0564333 | − | 0.0233754i | ||||
\(629\) | −2.00000 | − | 4.82843i | −0.0797452 | − | 0.192522i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4558 | − | 18.4558i | −0.734716 | − | 0.734716i | 0.236834 | − | 0.971550i | \(-0.423890\pi\) |
−0.971550 | + | 0.236834i | \(0.923890\pi\) | |||||||
\(632\) | − | 16.9706i | − | 0.675053i | ||||||
\(633\) | 0.656854 | + | 0.656854i | 0.0261076 | + | 0.0261076i | ||||
\(634\) | −15.8284 | − | 6.55635i | −0.628627 | − | 0.260386i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −30.1421 | −1.19521 | ||||||||
\(637\) | 8.53553 | + | 3.53553i | 0.338190 | + | 0.140083i | ||||
\(638\) | −1.31371 | −0.0520102 | ||||||||
\(639\) | −0.100505 | −0.00397592 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.4558 | −1.71640 | −0.858201 | − | 0.513313i | \(-0.828418\pi\) | ||||
−0.858201 | + | 0.513313i | \(0.828418\pi\) | |||||||
\(642\) | 0.828427 | 0.0326954 | ||||||||
\(643\) | −37.2635 | − | 15.4350i | −1.46953 | − | 0.608698i | −0.502776 | − | 0.864417i | \(-0.667688\pi\) |
−0.966751 | + | 0.255719i | \(0.917688\pi\) | |||||||
\(644\) | 0.686292 | 0.0270437 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22.1421 | + | 9.17157i | 0.871171 | + | 0.360851i | ||||
\(647\) | −11.8284 | − | 11.8284i | −0.465023 | − | 0.465023i | 0.435274 | − | 0.900298i | \(-0.356651\pi\) |
−0.900298 | + | 0.435274i | \(0.856651\pi\) | |||||||
\(648\) | − | 28.4853i | − | 1.11901i | ||||||
\(649\) | 1.48528 | + | 1.48528i | 0.0583024 | + | 0.0583024i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | + | 9.65685i | 0.156772 | + | 0.378482i | ||||
\(652\) | 36.3848 | + | 15.0711i | 1.42494 | + | 0.590229i | ||||
\(653\) | 14.9497 | − | 36.0919i | 0.585029 | − | 1.41238i | −0.303175 | − | 0.952935i | \(-0.598047\pi\) |
0.888204 | − | 0.459450i | \(-0.151953\pi\) | |||||||
\(654\) | 8.58579 | + | 8.58579i | 0.335731 | + | 0.335731i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −23.3137 | − | 23.3137i | −0.910247 | − | 0.910247i | ||||
\(657\) | −4.10051 | −0.159976 | ||||||||
\(658\) | 16.4853 | + | 16.4853i | 0.642663 | + | 0.642663i | ||||
\(659\) | 5.87868 | + | 2.43503i | 0.229001 | + | 0.0948553i | 0.494234 | − | 0.869329i | \(-0.335449\pi\) |
−0.265233 | + | 0.964184i | \(0.585449\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.74874 | + | 18.7071i | 0.301391 | + | 0.727622i | 0.999927 | + | 0.0120477i | \(0.00383499\pi\) |
−0.698536 | + | 0.715574i | \(0.746165\pi\) | |||||||
\(662\) | −3.82843 | − | 9.24264i | −0.148796 | − | 0.359225i | ||||
\(663\) | −6.82843 | + | 6.82843i | −0.265194 | + | 0.265194i | ||||
\(664\) | −7.17157 | + | 17.3137i | −0.278311 | + | 0.671902i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.414214 | − | 1.00000i | 0.0160504 | − | 0.0387492i | ||||
\(667\) | −0.272078 | − | 0.656854i | −0.0105349 | − | 0.0254335i | ||||
\(668\) | −6.68629 | − | 6.68629i | −0.258700 | − | 0.258700i | ||||
\(669\) | −9.17157 | + | 22.1421i | −0.354593 | + | 0.856064i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.242641 | 0.00936704 | ||||||||
\(672\) | −5.65685 | − | 13.6569i | −0.218218 | − | 0.526825i | ||||
\(673\) | 5.51472i | 0.212577i | 0.994335 | + | 0.106288i | \(0.0338967\pi\) | ||||
−0.994335 | + | 0.106288i | \(0.966103\pi\) | |||||||
\(674\) | 24.0000 | 0.924445 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.5563 | + | 13.5563i | 0.521398 | + | 0.521398i | ||||
\(677\) | 2.32233 | + | 5.60660i | 0.0892544 | + | 0.215479i | 0.962203 | − | 0.272333i | \(-0.0877952\pi\) |
−0.872949 | + | 0.487812i | \(0.837795\pi\) | |||||||
\(678\) | 42.6274 | + | 17.6569i | 1.63710 | + | 0.678107i | ||||
\(679\) | 1.51472 | − | 1.51472i | 0.0581296 | − | 0.0581296i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.89949 | + | 8.89949i | 0.341029 | + | 0.341029i | ||||
\(682\) | −0.686292 | − | 1.65685i | −0.0262795 | − | 0.0634442i | ||||
\(683\) | 14.1924 | − | 5.87868i | 0.543057 | − | 0.224941i | −0.0942543 | − | 0.995548i | \(-0.530047\pi\) |
0.637311 | + | 0.770607i | \(0.280047\pi\) | |||||||
\(684\) | 1.89949 | + | 4.58579i | 0.0726290 | + | 0.175342i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.9706 | + | 16.9706i | −0.647939 | + | 0.647939i | ||||
\(687\) | 49.5563 | 1.89069 | ||||||||
\(688\) | −31.7990 | + | 13.1716i | −1.21233 | + | 0.502162i | ||||
\(689\) | − | 15.0711i | − | 0.574162i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5061 | − | 11.8076i | −1.08442 | − | 0.449183i | −0.232364 | − | 0.972629i | \(-0.574646\pi\) |
−0.852059 | + | 0.523446i | \(0.824646\pi\) | |||||||
\(692\) | 0.928932 | − | 2.24264i | 0.0353127 | − | 0.0852524i | ||||
\(693\) | 0.171573 | − | 0.0710678i | 0.00651751 | − | 0.00269964i | ||||
\(694\) | −8.41421 | − | 20.3137i | −0.319399 | − | 0.771098i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.8284 | + | 10.8284i | −0.410450 | + | 0.410450i | ||||
\(697\) | −16.4853 | − | 16.4853i | −0.624425 | − | 0.624425i | ||||
\(698\) | 15.1005 | − | 36.4558i | 0.571563 | − | 1.37987i | ||||
\(699\) | −20.8995 | + | 8.65685i | −0.790491 | + | 0.327432i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.12132 | − | 17.1924i | 0.268969 | − | 0.649348i | −0.730467 | − | 0.682948i | \(-0.760697\pi\) |
0.999435 | + | 0.0336007i | \(0.0106974\pi\) | |||||||
\(702\) | 12.4853 | 0.471227 | ||||||||
\(703\) | − | 11.0711i | − | 0.417553i | ||||||
\(704\) | 0.970563 | + | 2.34315i | 0.0365795 | + | 0.0883106i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.48528i | 0.319348i | ||||||||
\(707\) | −16.0711 | − | 6.65685i | −0.604415 | − | 0.250357i | ||||
\(708\) | 24.4853 | 0.920213 | ||||||||
\(709\) | 6.77817 | − | 2.80761i | 0.254560 | − | 0.105442i | −0.251755 | − | 0.967791i | \(-0.581008\pi\) |
0.506314 | + | 0.862349i | \(0.331008\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.75736 | − | 1.75736i | 0.0659061 | − | 0.0659061i | ||||
\(712\) | 7.51472 | − | 7.51472i | 0.281626 | − | 0.281626i | ||||
\(713\) | 0.686292 | − | 0.686292i | 0.0257018 | − | 0.0257018i | ||||
\(714\) | −4.00000 | − | 9.65685i | −0.149696 | − | 0.361399i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 28.7279 | + | 11.8995i | 1.07361 | + | 0.444705i | ||||
\(717\) | 12.2426 | − | 29.5563i | 0.457210 | − | 1.10380i | ||||
\(718\) | 17.2132 | − | 17.2132i | 0.642391 | − | 0.642391i | ||||
\(719\) | − | 24.3431i | − | 0.907846i | −0.891041 | − | 0.453923i | \(-0.850024\pi\) | ||
0.891041 | − | 0.453923i | \(-0.149976\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.9706i | 0.557533i | ||||||||
\(722\) | 16.8995 | + | 16.8995i | 0.628934 | + | 0.628934i | ||||
\(723\) | −6.00000 | + | 14.4853i | −0.223142 | + | 0.538713i | ||||
\(724\) | −4.38478 | − | 10.5858i | −0.162959 | − | 0.393418i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 26.3137 | − | 10.8995i | 0.976593 | − | 0.404518i | ||||
\(727\) | 23.9706 | − | 23.9706i | 0.889019 | − | 0.889019i | −0.105410 | − | 0.994429i | \(-0.533615\pi\) |
0.994429 | + | 0.105410i | \(0.0336155\pi\) | |||||||
\(728\) | 6.82843 | − | 2.82843i | 0.253078 | − | 0.104828i | ||||
\(729\) | −15.7782 | + | 15.7782i | −0.584377 | + | 0.584377i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.4853 | + | 9.31371i | −0.831648 | + | 0.344480i | ||||
\(732\) | 2.00000 | − | 2.00000i | 0.0739221 | − | 0.0739221i | ||||
\(733\) | −1.77817 | − | 0.736544i | −0.0656784 | − | 0.0272049i | 0.349602 | − | 0.936898i | \(-0.386317\pi\) |
−0.415281 | + | 0.909693i | \(0.636317\pi\) | |||||||
\(734\) | −8.48528 | −0.313197 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.970563 | + | 0.970563i | −0.0357754 | + | 0.0357754i | ||||
\(737\) | − | 1.27208i | − | 0.0468576i | ||||||
\(738\) | − | 4.82843i | − | 0.177737i | ||||||
\(739\) | −7.53553 | + | 18.1924i | −0.277199 | + | 0.669218i | −0.999756 | − | 0.0220937i | \(-0.992967\pi\) |
0.722557 | + | 0.691312i | \(0.242967\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.8995 | + | 7.82843i | −0.694290 | + | 0.287584i | ||||
\(742\) | 15.0711 | + | 6.24264i | 0.553276 | + | 0.229175i | ||||
\(743\) | −13.6274 | − | 13.6274i | −0.499941 | − | 0.499941i | 0.411478 | − | 0.911420i | \(-0.365013\pi\) |
−0.911420 | + | 0.411478i | \(0.865013\pi\) | |||||||
\(744\) | −19.3137 | − | 8.00000i | −0.708075 | − | 0.293294i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 39.9706 | − | 16.5563i | 1.46343 | − | 0.606171i | ||||
\(747\) | −2.53553 | + | 1.05025i | −0.0927703 | + | 0.0384267i | ||||
\(748\) | 0.686292 | + | 1.65685i | 0.0250933 | + | 0.0605806i | ||||
\(749\) | −0.414214 | − | 0.171573i | −0.0151350 | − | 0.00626914i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.9706i | 0.838208i | 0.907938 | + | 0.419104i | \(0.137656\pi\) | ||||
−0.907938 | + | 0.419104i | \(0.862344\pi\) | |||||||
\(752\) | −46.6274 | −1.70033 | ||||||||
\(753\) | −29.2132 | −1.06459 | ||||||||
\(754\) | −5.41421 | − | 5.41421i | −0.197174 | − | 0.197174i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.17157 | + | 12.4853i | −0.188088 | + | 0.454085i | ||||
\(757\) | −1.77817 | + | 0.736544i | −0.0646289 | + | 0.0267701i | −0.414764 | − | 0.909929i | \(-0.636136\pi\) |
0.350135 | + | 0.936699i | \(0.386136\pi\) | |||||||
\(758\) | −30.6569 | + | 12.6985i | −1.11351 | + | 0.461230i | ||||
\(759\) | −0.100505 | − | 0.100505i | −0.00364810 | − | 0.00364810i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.1716 | + | 24.1716i | −0.876219 | + | 0.876219i | −0.993141 | − | 0.116922i | \(-0.962697\pi\) |
0.116922 | + | 0.993141i | \(0.462697\pi\) | |||||||
\(762\) | −20.9706 | + | 50.6274i | −0.759683 | + | 1.83404i | ||||
\(763\) | −2.51472 | − | 6.07107i | −0.0910389 | − | 0.219787i | ||||
\(764\) | −24.0000 | −0.868290 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000i | 0.867155i | ||||||||
\(767\) | 12.2426i | 0.442056i | ||||||||
\(768\) | 27.3137 | + | 11.3137i | 0.985599 | + | 0.408248i | ||||
\(769\) | −22.4853 | −0.810840 | −0.405420 | − | 0.914131i | \(-0.632875\pi\) | ||||
−0.405420 | + | 0.914131i | \(0.632875\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.24264 | − | 10.2426i | 0.152795 | − | 0.368880i | ||||
\(772\) | − | 36.9706i | − | 1.33060i | ||||||
\(773\) | −10.8076 | − | 26.0919i | −0.388723 | − | 0.938460i | −0.990211 | − | 0.139578i | \(-0.955425\pi\) |
0.601488 | − | 0.798882i | \(-0.294575\pi\) | |||||||
\(774\) | −4.65685 | − | 1.92893i | −0.167387 | − | 0.0693340i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.28427i | 0.153796i | ||||||||
\(777\) | −3.41421 | + | 3.41421i | −0.122484 | + | 0.122484i | ||||
\(778\) | 41.8701 | − | 17.3431i | 1.50111 | − | 0.621782i | ||||
\(779\) | −18.8995 | − | 45.6274i | −0.677145 | − | 1.63477i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0710678 | − | 0.0294373i | −0.00254301 | − | 0.00105335i | ||||
\(782\) | −0.686292 | + | 0.686292i | −0.0245417 | + | 0.0245417i | ||||
\(783\) | 14.0000 | 0.500319 | ||||||||
\(784\) | − | 20.0000i | − | 0.714286i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −17.5563 | + | 17.5563i | −0.626214 | + | 0.626214i | ||||
\(787\) | 3.70711 | − | 8.94975i | 0.132144 | − | 0.319024i | −0.843933 | − | 0.536448i | \(-0.819766\pi\) |
0.976077 | + | 0.217424i | \(0.0697656\pi\) | |||||||
\(788\) | −14.3848 | − | 34.7279i | −0.512436 | − | 1.23713i | ||||
\(789\) | −0.171573 | − | 0.414214i | −0.00610816 | − | 0.0147464i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.6569 | − | 17.6569i | −0.627805 | − | 0.627805i | ||||
\(792\) | −0.142136 | + | 0.343146i | −0.00505057 | + | 0.0121932i | ||||
\(793\) | 1.00000 | + | 1.00000i | 0.0355110 | + | 0.0355110i | ||||
\(794\) | −14.5147 | + | 35.0416i | −0.515108 | + | 1.24358i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −35.9411 | + | 35.9411i | −1.27390 | + | 1.27390i | ||||
\(797\) | −29.1924 | − | 12.0919i | −1.03405 | − | 0.428316i | −0.199876 | − | 0.979821i | \(-0.564054\pi\) |
−0.834172 | + | 0.551505i | \(0.814054\pi\) | |||||||
\(798\) | − | 22.1421i | − | 0.783823i | ||||||
\(799\) | −32.9706 | −1.16641 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.55635 | 0.0549909 | ||||||||
\(802\) | 4.00000i | 0.141245i | ||||||||
\(803\) | −2.89949 | − | 1.20101i | −0.102321 | − | 0.0423827i | ||||
\(804\) | −10.4853 | − | 10.4853i | −0.369787 | − | 0.369787i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.00000 | − | 9.65685i | 0.140894 | − | 0.340148i | ||||
\(807\) | −6.89949 | − | 6.89949i | −0.242874 | − | 0.242874i | ||||
\(808\) | 32.1421 | − | 13.3137i | 1.13076 | − | 0.468375i | ||||
\(809\) | 0.857864 | + | 0.857864i | 0.0301609 | + | 0.0301609i | 0.722026 | − | 0.691865i | \(-0.243211\pi\) |
−0.691865 | + | 0.722026i | \(0.743211\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.73654 | − | 23.5061i | −0.341896 | − | 0.825411i | −0.997524 | − | 0.0703264i | \(-0.977596\pi\) |
0.655628 | − | 0.755084i | \(-0.272404\pi\) | |||||||
\(812\) | 7.65685 | − | 3.17157i | 0.268703 | − | 0.111300i | ||||
\(813\) | −12.7279 | + | 30.7279i | −0.446388 | + | 1.07768i | ||||
\(814\) | 0.585786 | − | 0.585786i | 0.0205318 | − | 0.0205318i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 19.3137 | + | 8.00000i | 0.676115 | + | 0.280056i | ||||
\(817\) | −51.5563 | −1.80373 | ||||||||
\(818\) | −6.38478 | + | 6.38478i | −0.223238 | + | 0.223238i | ||||
\(819\) | 1.00000 | + | 0.414214i | 0.0349428 | + | 0.0144738i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.393398 | − | 0.949747i | −0.0137297 | − | 0.0331464i | 0.916866 | − | 0.399195i | \(-0.130710\pi\) |
−0.930596 | + | 0.366049i | \(0.880710\pi\) | |||||||
\(822\) | 9.07107 | − | 3.75736i | 0.316390 | − | 0.131053i | ||||
\(823\) | −2.02944 | + | 2.02944i | −0.0707417 | + | 0.0707417i | −0.741592 | − | 0.670851i | \(-0.765929\pi\) |
0.670851 | + | 0.741592i | \(0.265929\pi\) | |||||||
\(824\) | −21.1716 | − | 21.1716i | −0.737547 | − | 0.737547i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.2426 | − | 5.07107i | −0.425976 | − | 0.176445i | ||||
\(827\) | −4.92031 | − | 11.8787i | −0.171096 | − | 0.413062i | 0.814951 | − | 0.579530i | \(-0.196764\pi\) |
−0.986047 | + | 0.166468i | \(0.946764\pi\) | |||||||
\(828\) | −0.201010 | −0.00698558 | ||||||||
\(829\) | −15.8076 | + | 38.1630i | −0.549021 | + | 1.32545i | 0.369187 | + | 0.929355i | \(0.379636\pi\) |
−0.918208 | + | 0.396099i | \(0.870364\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.41421 | 0.0490585 | ||||||||
\(832\) | −5.65685 | + | 13.6569i | −0.196116 | + | 0.473466i | ||||
\(833\) | − | 14.1421i | − | 0.489996i | ||||||
\(834\) | 35.4558i | 1.22774i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.79899i | 0.131391i | ||||||||
\(837\) | 7.31371 | + | 17.6569i | 0.252799 | + | 0.610310i | ||||
\(838\) | 12.1716 | − | 29.3848i | 0.420460 | − | 1.01508i | ||||
\(839\) | −32.3137 | + | 32.3137i | −1.11559 | + | 1.11559i | −0.123213 | + | 0.992380i | \(0.539320\pi\) |
−0.992380 | + | 0.123213i | \(0.960680\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4350 | + | 14.4350i | 0.497760 | + | 0.497760i | ||||
\(842\) | 10.8995 | − | 4.51472i | 0.375621 | − | 0.155587i | ||||
\(843\) | −14.8995 | + | 6.17157i | −0.513166 | + | 0.212560i | ||||
\(844\) | 0.928932 | + | 0.384776i | 0.0319752 | + | 0.0132445i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.82843 | − | 4.82843i | −0.166005 | − | 0.166005i | ||||
\(847\) | −15.4142 | −0.529639 | ||||||||
\(848\) | −30.1421 | + | 12.4853i | −1.03509 | + | 0.428746i | ||||
\(849\) | − | 19.5563i | − | 0.671172i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.414214 | + | 0.171573i | 0.0141991 | + | 0.00588144i | ||||
\(852\) | −0.828427 | + | 0.343146i | −0.0283814 | + | 0.0117560i | ||||
\(853\) | 2.80761 | − | 1.16295i | 0.0961308 | − | 0.0398187i | −0.334100 | − | 0.942538i | \(-0.608432\pi\) |
0.430231 | + | 0.902719i | \(0.358432\pi\) | |||||||
\(854\) | −1.41421 | + | 0.585786i | −0.0483934 | + | 0.0200452i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.828427 | − | 0.343146i | 0.0283151 | − | 0.0117285i | ||||
\(857\) | −32.3137 | − | 32.3137i | −1.10382 | − | 1.10382i | −0.993946 | − | 0.109869i | \(-0.964957\pi\) |
−0.109869 | − | 0.993946i | \(-0.535043\pi\) | |||||||
\(858\) | −1.41421 | − | 0.585786i | −0.0482805 | − | 0.0199984i | ||||
\(859\) | −33.6777 | + | 13.9497i | −1.14907 | + | 0.475959i | −0.874221 | − | 0.485529i | \(-0.838627\pi\) |
−0.274847 | + | 0.961488i | \(0.588627\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.24264 | + | 19.8995i | −0.280908 | + | 0.678173i | ||||
\(862\) | − | 33.4558i | − | 1.13951i | ||||||
\(863\) | − | 45.9411i | − | 1.56385i | −0.623370 | − | 0.781927i | \(-0.714237\pi\) | ||
0.623370 | − | 0.781927i | \(-0.285763\pi\) | |||||||
\(864\) | −10.3431 | − | 24.9706i | −0.351881 | − | 0.849516i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 45.9411 | 1.56114 | ||||||||
\(867\) | −15.3640 | − | 6.36396i | −0.521787 | − | 0.216131i | ||||
\(868\) | 8.00000 | + | 8.00000i | 0.271538 | + | 0.271538i | ||||
\(869\) | 1.75736 | − | 0.727922i | 0.0596143 | − | 0.0246931i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.24264 | − | 5.24264i | 0.177640 | − | 0.177640i | ||||
\(872\) | 12.1421 | + | 5.02944i | 0.411185 | + | 0.170318i | ||||
\(873\) | −0.443651 | + | 0.443651i | −0.0150153 | + | 0.0150153i | ||||
\(874\) | −1.89949 | + | 0.786797i | −0.0642514 | + | 0.0266138i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −33.7990 | + | 14.0000i | −1.14196 | + | 0.473016i | ||||
\(877\) | −13.7782 | + | 33.2635i | −0.465256 | + | 1.12323i | 0.500955 | + | 0.865473i | \(0.332982\pi\) |
−0.966211 | + | 0.257754i | \(0.917018\pi\) | |||||||
\(878\) | 24.0416 | + | 24.0416i | 0.811366 | + | 0.811366i | ||||
\(879\) | − | 23.2132i | − | 0.782962i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 22.6274i | − | 0.762337i | −0.924506 | − | 0.381169i | \(-0.875522\pi\) | ||
0.924506 | − | 0.381169i | \(-0.124478\pi\) | |||||||
\(882\) | 2.07107 | − | 2.07107i | 0.0697365 | − | 0.0697365i | ||||
\(883\) | −19.6482 | + | 47.4350i | −0.661216 | + | 1.59632i | 0.134685 | + | 0.990888i | \(0.456998\pi\) |
−0.795901 | + | 0.605427i | \(0.793002\pi\) | |||||||
\(884\) | −4.00000 | + | 9.65685i | −0.134535 | + | 0.324795i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0711 | − | 29.1421i | −0.405535 | − | 0.979049i | ||||
\(887\) | −20.3137 | + | 20.3137i | −0.682068 | + | 0.682068i | −0.960466 | − | 0.278398i | \(-0.910197\pi\) |
0.278398 | + | 0.960466i | \(0.410197\pi\) | |||||||
\(888\) | − | 9.65685i | − | 0.324063i | ||||||
\(889\) | 20.9706 | − | 20.9706i | 0.703330 | − | 0.703330i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.94975 | − | 1.22183i | 0.0988203 | − | 0.0409327i | ||||
\(892\) | 25.9411i | 0.868573i | ||||||||
\(893\) | −64.5269 | − | 26.7279i | −2.15931 | − | 0.894416i | ||||
\(894\) | − | 38.2843i | − | 1.28042i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11.3137 | − | 11.3137i | −0.377964 | − | 0.377964i | ||||
\(897\) | − | 0.828427i | − | 0.0276604i | ||||||
\(898\) | −44.4853 | −1.48449 | ||||||||
\(899\) | 4.48528 | − | 10.8284i | 0.149593 | − | 0.361148i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.3137 | + | 8.82843i | −0.710063 | + | 0.294118i | ||||
\(902\) | 1.41421 | − | 3.41421i | 0.0470882 | − | 0.113681i | ||||
\(903\) | 15.8995 | + | 15.8995i | 0.529102 | + | 0.529102i | ||||
\(904\) | 49.9411 | 1.66102 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 21.8995 | + | 52.8701i | 0.727562 | + | 1.75649i | ||||
\(907\) | −0.535534 | + | 0.221825i | −0.0177821 | + | 0.00736559i | −0.391557 | − | 0.920154i | \(-0.628063\pi\) |
0.373775 | + | 0.927520i | \(0.378063\pi\) | |||||||
\(908\) | 12.5858 | + | 5.21320i | 0.417674 | + | 0.173006i | ||||
\(909\) | 4.70711 | + | 1.94975i | 0.156125 | + | 0.0646690i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45.5980i | − | 1.51073i | −0.655305 | − | 0.755364i | \(-0.727460\pi\) | ||
0.655305 | − | 0.755364i | \(-0.272540\pi\) | |||||||
\(912\) | 31.3137 | + | 31.3137i | 1.03690 | + | 1.03690i | ||||
\(913\) | −2.10051 | −0.0695166 | ||||||||
\(914\) | 13.4142 | − | 13.4142i | 0.443703 | − | 0.443703i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 49.5563 | − | 20.5269i | 1.63739 | − | 0.678228i | ||||
\(917\) | 12.4142 | − | 5.14214i | 0.409953 | − | 0.169808i | ||||
\(918\) | −7.31371 | − | 17.6569i | −0.241388 | − | 0.582763i | ||||
\(919\) | 25.4853 | + | 25.4853i | 0.840682 | + | 0.840682i | 0.988948 | − | 0.148266i | \(-0.0473691\pi\) |
−0.148266 | + | 0.988948i | \(0.547369\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.17157 | − | 4.17157i | 0.137458 | − | 0.137458i | ||||
\(922\) | 18.8995 | + | 7.82843i | 0.622422 | + | 0.257816i | ||||
\(923\) | −0.171573 | − | 0.414214i | −0.00564739 | − | 0.0136340i | ||||
\(924\) | 1.17157 | − | 1.17157i | 0.0385419 | − | 0.0385419i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.5147 | 0.509845 | ||||||||
\(927\) | − | 4.38478i | − | 0.144015i | ||||||
\(928\) | −6.34315 | + | 15.3137i | −0.208224 | + | 0.502697i | ||||
\(929\) | 26.4853 | 0.868954 | 0.434477 | − | 0.900683i | \(-0.356933\pi\) | ||||
0.434477 | + | 0.900683i | \(0.356933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.4645 | − | 27.6777i | 0.375733 | − | 0.907099i | ||||
\(932\) | −17.3137 | + | 17.3137i | −0.567129 | + | 0.567129i | ||||
\(933\) | 8.65685 | + | 20.8995i | 0.283413 | + | 0.684219i | ||||
\(934\) | 17.0416 | − | 41.1421i | 0.557619 | − | 1.34621i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.00000 | + | 0.828427i | −0.0653720 | + | 0.0270780i | ||||
\(937\) | 19.0000 | − | 19.0000i | 0.620703 | − | 0.620703i | −0.325008 | − | 0.945711i | \(-0.605367\pi\) |
0.945711 | + | 0.325008i | \(0.105367\pi\) | |||||||
\(938\) | 3.07107 | + | 7.41421i | 0.100274 | + | 0.242083i | ||||
\(939\) | 9.48528 | + | 22.8995i | 0.309540 | + | 0.747297i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.3640 | + | 5.53553i | 0.435653 | + | 0.180453i | 0.589721 | − | 0.807607i | \(-0.299238\pi\) |
−0.154068 | + | 0.988060i | \(0.549238\pi\) | |||||||
\(942\) | −1.41421 | − | 1.41421i | −0.0460776 | − | 0.0460776i | ||||
\(943\) | 2.00000 | 0.0651290 | ||||||||
\(944\) | 24.4853 | − | 10.1421i | 0.796928 | − | 0.330098i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.72792 | − | 2.72792i | −0.0886924 | − | 0.0886924i | ||||
\(947\) | −15.4645 | + | 37.3345i | −0.502528 | + | 1.21321i | 0.445575 | + | 0.895245i | \(0.352999\pi\) |
−0.948103 | + | 0.317964i | \(0.897001\pi\) | |||||||
\(948\) | 8.48528 | − | 20.4853i | 0.275589 | − | 0.665331i | ||||
\(949\) | −7.00000 | − | 16.8995i | −0.227230 | − | 0.548581i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.8284 | − | 15.8284i | −0.513272 | − | 0.513272i | ||||
\(952\) | −8.00000 | − | 8.00000i | −0.259281 | − | 0.259281i | ||||
\(953\) | 3.34315 | + | 3.34315i | 0.108295 | + | 0.108295i | 0.759178 | − | 0.650883i | \(-0.225601\pi\) |
−0.650883 | + | 0.759178i | \(0.725601\pi\) | |||||||
\(954\) | −4.41421 | − | 1.82843i | −0.142915 | − | 0.0591975i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 34.6274i | − | 1.11993i | ||||||
\(957\) | −1.58579 | − | 0.656854i | −0.0512612 | − | 0.0212331i | ||||
\(958\) | 7.02944 | 0.227111 | ||||||||
\(959\) | −5.31371 | −0.171589 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 4.82843 | 0.155675 | ||||||||
\(963\) | 0.121320 | + | 0.0502525i | 0.00390949 | + | 0.00161937i | ||||
\(964\) | 16.9706i | 0.546585i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.828427 | + | 0.343146i | 0.0266542 | + | 0.0110405i | ||||
\(967\) | 39.9706 | + | 39.9706i | 1.28537 | + | 1.28537i | 0.937570 | + | 0.347797i | \(0.113070\pi\) |
0.347797 | + | 0.937570i | \(0.386930\pi\) | |||||||
\(968\) | 21.7990 | − | 21.7990i | 0.700646 | − | 0.700646i | ||||
\(969\) | 22.1421 | + | 22.1421i | 0.711308 | + | 0.711308i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.63604 | + | 23.2635i | 0.309235 | + | 0.746560i | 0.999730 | + | 0.0232228i | \(0.00739270\pi\) |
−0.690495 | + | 0.723337i | \(0.742607\pi\) | |||||||
\(972\) | 3.27208 | − | 7.89949i | 0.104952 | − | 0.253376i | ||||
\(973\) | 7.34315 | − | 17.7279i | 0.235410 | − | 0.568331i | ||||
\(974\) | 15.5563 | + | 15.5563i | 0.498458 | + | 0.498458i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.17157 | − | 2.82843i | 0.0375011 | − | 0.0905357i | ||||
\(977\) | −14.1421 | −0.452447 | −0.226224 | − | 0.974075i | \(-0.572638\pi\) | ||||
−0.226224 | + | 0.974075i | \(0.572638\pi\) | |||||||
\(978\) | 36.3848 | + | 36.3848i | 1.16346 | + | 1.16346i | ||||
\(979\) | 1.10051 | + | 0.455844i | 0.0351723 | + | 0.0145688i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.736544 | + | 1.77817i | 0.0235160 | + | 0.0567727i | ||||
\(982\) | −10.3726 | − | 25.0416i | −0.331002 | − | 0.799111i | ||||
\(983\) | −25.6274 | + | 25.6274i | −0.817388 | + | 0.817388i | −0.985729 | − | 0.168341i | \(-0.946159\pi\) |
0.168341 | + | 0.985729i | \(0.446159\pi\) | |||||||
\(984\) | −16.4853 | − | 39.7990i | −0.525532 | − | 1.26875i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.48528 | + | 10.8284i | −0.142840 | + | 0.344847i | ||||
\(987\) | 11.6569 | + | 28.1421i | 0.371042 | + | 0.895774i | ||||
\(988\) | −15.6569 | + | 15.6569i | −0.498111 | + | 0.498111i | ||||
\(989\) | 0.798990 | − | 1.92893i | 0.0254064 | − | 0.0613365i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | −22.6274 | −0.718421 | ||||||||
\(993\) | − | 13.0711i | − | 0.414798i | ||||||
\(994\) | 0.485281 | 0.0153922 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −17.3137 | + | 17.3137i | −0.548606 | + | 0.548606i | ||||
\(997\) | 0.748737 | + | 1.80761i | 0.0237127 | + | 0.0572476i | 0.935292 | − | 0.353876i | \(-0.115136\pi\) |
−0.911580 | + | 0.411124i | \(0.865136\pi\) | |||||||
\(998\) | −12.6569 | − | 5.24264i | −0.400646 | − | 0.165953i | ||||
\(999\) | −6.24264 | + | 6.24264i | −0.197508 | + | 0.197508i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))