Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(17,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.df (of order \(6\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.4 | ||
Root | \(1.68124 - 0.416458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1601 |
Dual form | 3024.2.df.d.17.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.699656 | −0.312896 | −0.156448 | − | 0.987686i | \(-0.550004\pi\) | ||||
−0.156448 | + | 0.987686i | \(0.550004\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.461278 | + | 2.60523i | 0.174347 | + | 0.984684i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.265217i | 0.0799659i | 0.999200 | + | 0.0399829i | \(0.0127304\pi\) | ||||
−0.999200 | + | 0.0399829i | \(0.987270\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.13823 | + | 0.657156i | −0.315688 | + | 0.182262i | −0.649469 | − | 0.760388i | \(-0.725009\pi\) |
0.333781 | + | 0.942651i | \(0.391675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.86392 | − | 3.22840i | −0.452067 | − | 0.783003i | 0.546447 | − | 0.837493i | \(-0.315980\pi\) |
−0.998514 | + | 0.0544906i | \(0.982646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.382449 | + | 0.220807i | 0.0877398 | + | 0.0506566i | 0.543228 | − | 0.839585i | \(-0.317202\pi\) |
−0.455488 | + | 0.890242i | \(0.650535\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.96463i | 1.03520i | 0.855624 | + | 0.517598i | \(0.173174\pi\) | ||||
−0.855624 | + | 0.517598i | \(0.826826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.51048 | −0.902096 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.273287 | + | 0.157782i | 0.0507480 | + | 0.0292994i | 0.525159 | − | 0.851004i | \(-0.324006\pi\) |
−0.474411 | + | 0.880303i | \(0.657339\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.85521 | + | 2.80316i | 0.872022 | + | 0.503462i | 0.868020 | − | 0.496530i | \(-0.165393\pi\) |
0.00400255 | + | 0.999992i | \(0.498726\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.322736 | − | 1.82276i | −0.0545523 | − | 0.308103i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.351124 | + | 0.608164i | −0.0577244 | + | 0.0999816i | −0.893444 | − | 0.449175i | \(-0.851718\pi\) |
0.835719 | + | 0.549157i | \(0.185051\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.39354 | − | 9.34189i | −0.842330 | − | 1.45896i | −0.887920 | − | 0.459998i | \(-0.847850\pi\) |
0.0455900 | − | 0.998960i | \(-0.485483\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.73131 | + | 6.46283i | −0.569020 | + | 0.985572i | 0.427643 | + | 0.903948i | \(0.359344\pi\) |
−0.996663 | + | 0.0816240i | \(0.973989\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.50285 | − | 6.06712i | −0.510943 | − | 0.884980i | −0.999920 | − | 0.0126827i | \(-0.995963\pi\) |
0.488976 | − | 0.872297i | \(-0.337370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.57445 | + | 2.40347i | −0.939207 | + | 0.343353i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.51919 | − | 4.91856i | 1.17020 | − | 0.675616i | 0.216474 | − | 0.976288i | \(-0.430544\pi\) |
0.953727 | + | 0.300672i | \(0.0972111\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.185561i | − | 0.0250210i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.73182 | + | 11.6598i | −0.876408 | + | 1.51798i | −0.0211522 | + | 0.999776i | \(0.506733\pi\) |
−0.855256 | + | 0.518206i | \(0.826600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.89484 | + | 2.82604i | −0.626720 | + | 0.361837i | −0.779481 | − | 0.626426i | \(-0.784517\pi\) |
0.152761 | + | 0.988263i | \(0.451184\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.796368 | − | 0.459783i | 0.0987773 | − | 0.0570291i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.97060 | + | 5.14523i | −0.362916 | + | 0.628590i | −0.988439 | − | 0.151616i | \(-0.951552\pi\) |
0.625523 | + | 0.780206i | \(0.284886\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.4323i | − | 1.59412i | −0.603900 | − | 0.797060i | \(-0.706387\pi\) | ||
0.603900 | − | 0.797060i | \(-0.293613\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.66182 | + | 3.84620i | −0.779707 | + | 0.450164i | −0.836326 | − | 0.548232i | \(-0.815301\pi\) |
0.0566194 | + | 0.998396i | \(0.481968\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.690951 | + | 0.122339i | −0.0787412 | + | 0.0139418i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.698360 | + | 1.20959i | 0.0785716 | + | 0.136090i | 0.902634 | − | 0.430409i | \(-0.141631\pi\) |
−0.824062 | + | 0.566499i | \(0.808297\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.72399 | − | 6.45014i | 0.408761 | − | 0.707995i | −0.585990 | − | 0.810318i | \(-0.699294\pi\) |
0.994751 | + | 0.102323i | \(0.0326276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.30410 | + | 2.25877i | 0.141450 | + | 0.244998i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.59261 | − | 9.68668i | 0.592815 | − | 1.02679i | −0.401036 | − | 0.916062i | \(-0.631350\pi\) |
0.993851 | − | 0.110724i | \(-0.0353168\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.23708 | − | 2.66221i | −0.234510 | − | 0.279076i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.267582 | − | 0.154489i | −0.0274534 | − | 0.0158502i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.18225 | + | 5.30138i | 0.932316 | + | 0.538273i | 0.887543 | − | 0.460724i | \(-0.152410\pi\) |
0.0447729 | + | 0.998997i | \(0.485744\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.5071 | −1.74203 | −0.871013 | − | 0.491260i | \(-0.836537\pi\) | ||||
−0.871013 | + | 0.491260i | \(0.836537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.54219i | − | 0.841687i | −0.907133 | − | 0.420844i | \(-0.861734\pi\) | ||
0.907133 | − | 0.420844i | \(-0.138266\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.09489 | − | 5.25093i | −0.879236 | − | 0.507627i | −0.00882940 | − | 0.999961i | \(-0.502811\pi\) |
−0.870406 | + | 0.492334i | \(0.836144\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.12110 | − | 12.3341i | −0.682078 | − | 1.18139i | −0.974346 | − | 0.225057i | \(-0.927743\pi\) |
0.292268 | − | 0.956337i | \(-0.405590\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.3783 | + | 7.72396i | −1.25852 | + | 0.726609i | −0.972788 | − | 0.231699i | \(-0.925572\pi\) |
−0.285737 | + | 0.958308i | \(0.592238\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 3.47353i | − | 0.323908i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.55095 | − | 6.34513i | 0.692194 | − | 0.581657i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9297 | 0.993605 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.65406 | 0.595157 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.8304 | −1.93713 | −0.968566 | − | 0.248758i | \(-0.919978\pi\) | ||||
−0.968566 | + | 0.248758i | \(0.919978\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.20922 | 0.455132 | 0.227566 | − | 0.973763i | \(-0.426923\pi\) | ||||
0.227566 | + | 0.973763i | \(0.426923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.398838 | + | 1.09822i | −0.0345836 | + | 0.0952278i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.69725i | 0.230442i | 0.993340 | + | 0.115221i | \(0.0367576\pi\) | ||||
−0.993340 | + | 0.115221i | \(0.963242\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.1448 | + | 5.85710i | −0.860470 | + | 0.496793i | −0.864170 | − | 0.503200i | \(-0.832156\pi\) |
0.00369951 | + | 0.999993i | \(0.498822\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.174289 | − | 0.301877i | −0.0145748 | − | 0.0252442i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.191206 | − | 0.110393i | −0.0158788 | − | 0.00916765i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.8280i | 1.54245i | 0.636564 | + | 0.771224i | \(0.280355\pi\) | ||||
−0.636564 | + | 0.771224i | \(0.719645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0029 | −0.814021 | −0.407010 | − | 0.913424i | \(-0.633429\pi\) | ||||
−0.407010 | + | 0.913424i | \(0.633429\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.39698 | − | 1.96125i | −0.272852 | − | 0.157531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.218293 | − | 0.126032i | −0.0174217 | − | 0.0100584i | 0.491264 | − | 0.871011i | \(-0.336535\pi\) |
−0.508686 | + | 0.860952i | \(0.669868\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.9340 | + | 2.29007i | −1.01934 | + | 0.180483i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.29780 | + | 7.44400i | −0.336629 | + | 0.583059i | −0.983796 | − | 0.179289i | \(-0.942620\pi\) |
0.647167 | + | 0.762348i | \(0.275954\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.24437 | − | 3.88736i | −0.173674 | − | 0.300813i | 0.766027 | − | 0.642808i | \(-0.222231\pi\) |
−0.939702 | + | 0.341995i | \(0.888897\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.63629 | + | 9.76234i | −0.433561 | + | 0.750949i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.56072 | + | 6.16736i | 0.270717 | + | 0.468895i | 0.969046 | − | 0.246882i | \(-0.0794060\pi\) |
−0.698329 | + | 0.715777i | \(0.746073\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.08059 | − | 11.7508i | −0.157277 | − | 0.888280i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.1270 | + | 12.7750i | −1.65385 | + | 0.954848i | −0.678376 | + | 0.734715i | \(0.737316\pi\) |
−0.975470 | + | 0.220134i | \(0.929351\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.943175i | 0.0701057i | 0.999385 | + | 0.0350528i | \(0.0111599\pi\) | ||||
−0.999385 | + | 0.0350528i | \(0.988840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.245666 | − | 0.425506i | 0.0180617 | − | 0.0312838i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.856227 | − | 0.494343i | 0.0626135 | − | 0.0361499i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.57413 | + | 1.48617i | −0.186258 | + | 0.107536i | −0.590229 | − | 0.807236i | \(-0.700963\pi\) |
0.403972 | + | 0.914771i | \(0.367629\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.25721 | − | 16.0340i | 0.666348 | − | 1.15415i | −0.312570 | − | 0.949895i | \(-0.601190\pi\) |
0.978918 | − | 0.204254i | \(-0.0654769\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1774i | 1.01010i | 0.863091 | + | 0.505048i | \(0.168525\pi\) | ||||
−0.863091 | + | 0.505048i | \(0.831475\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.5293 | − | 11.8526i | 1.45529 | − | 0.840209i | 0.456512 | − | 0.889717i | \(-0.349099\pi\) |
0.998774 | + | 0.0495081i | \(0.0157654\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.284998 | + | 0.784756i | −0.0200029 | + | 0.0550790i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.77362 | + | 6.53611i | 0.263561 | + | 0.456502i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0585617 | + | 0.101432i | −0.00405080 | + | 0.00701619i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.04004 | − | 5.26550i | −0.209285 | − | 0.362492i | 0.742205 | − | 0.670173i | \(-0.233780\pi\) |
−0.951489 | + | 0.307681i | \(0.900447\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.61063 | − | 4.52175i | 0.178044 | − | 0.308381i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.06327 | + | 13.9420i | −0.343717 | + | 0.946444i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.24313 | + | 2.44977i | 0.285424 | + | 0.164790i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.796137 | + | 0.459650i | 0.0533133 | + | 0.0307804i | 0.526420 | − | 0.850225i | \(-0.323534\pi\) |
−0.473106 | + | 0.881005i | \(0.656867\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.0059 | 0.664118 | 0.332059 | − | 0.943259i | \(-0.392257\pi\) | ||||
0.332059 | + | 0.943259i | \(0.392257\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.75025i | − | 0.181742i | −0.995863 | − | 0.0908710i | \(-0.971035\pi\) | ||
0.995863 | − | 0.0908710i | \(-0.0289651\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.55513 | − | 3.20725i | −0.363928 | − | 0.210114i | 0.306874 | − | 0.951750i | \(-0.400717\pi\) |
−0.670803 | + | 0.741636i | \(0.734050\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.45079 | + | 4.24489i | 0.159872 | + | 0.276906i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.4288 | + | 6.59844i | −0.739270 | + | 0.426818i | −0.821804 | − | 0.569770i | \(-0.807032\pi\) |
0.0825337 | + | 0.996588i | \(0.473699\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.54868i | 0.164175i | 0.996625 | + | 0.0820874i | \(0.0261587\pi\) | ||||
−0.996625 | + | 0.0820874i | \(0.973841\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.59985 | − | 1.68160i | 0.293874 | − | 0.107434i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.580418 | −0.0369311 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.7893 | −1.18597 | −0.592986 | − | 0.805213i | \(-0.702051\pi\) | ||||
−0.592986 | + | 0.805213i | \(0.702051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.31670 | −0.0827804 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.3945 | −0.897907 | −0.448953 | − | 0.893555i | \(-0.648203\pi\) | ||||
−0.448953 | + | 0.893555i | \(0.648203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.74637 | − | 0.634226i | −0.108514 | − | 0.0394089i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.84976i | 0.484037i | 0.970272 | + | 0.242019i | \(0.0778095\pi\) | ||||
−0.970272 | + | 0.242019i | \(0.922190\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.96050 | + | 3.44130i | −0.366151 | + | 0.211397i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.72267 | − | 13.3760i | −0.470859 | − | 0.815552i | 0.528585 | − | 0.848880i | \(-0.322723\pi\) |
−0.999444 | + | 0.0333281i | \(0.989389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.9476 | − | 6.32057i | −0.665016 | − | 0.383947i | 0.129169 | − | 0.991623i | \(-0.458769\pi\) |
−0.794186 | + | 0.607675i | \(0.792102\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.19626i | − | 0.0721369i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8906 | −0.714439 | −0.357219 | − | 0.934021i | \(-0.616275\pi\) | ||||
−0.357219 | + | 0.934021i | \(0.616275\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.75411 | + | 1.59009i | 0.164297 | + | 0.0948568i | 0.579894 | − | 0.814692i | \(-0.303094\pi\) |
−0.415597 | + | 0.909549i | \(0.636427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0195 | + | 9.24889i | 0.952263 | + | 0.549789i | 0.893783 | − | 0.448499i | \(-0.148041\pi\) |
0.0584799 | + | 0.998289i | \(0.481375\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.8499 | − | 18.3606i | 1.28976 | − | 1.08379i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.55161 | − | 2.68746i | 0.0912711 | − | 0.158086i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.42975 | − | 2.47639i | −0.0835266 | − | 0.144672i | 0.821236 | − | 0.570589i | \(-0.193285\pi\) |
−0.904762 | + | 0.425917i | \(0.859952\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.70995 | − | 8.15788i | 0.274224 | − | 0.474970i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.26254 | − | 5.65088i | −0.188677 | − | 0.326799i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.5583 | − | 6.73977i | −1.06968 | − | 0.388474i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.42470 | − | 1.97725i | 0.196098 | − | 0.113217i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6746i | 1.23704i | 0.785771 | + | 0.618518i | \(0.212266\pi\) | ||||
−0.785771 | + | 0.618518i | \(0.787734\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.8462 | + | 20.5183i | −0.671738 | + | 1.16348i | 0.305673 | + | 0.952136i | \(0.401119\pi\) |
−0.977411 | + | 0.211348i | \(0.932215\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.6283 | − | 13.6418i | 1.33555 | − | 0.771081i | 0.349407 | − | 0.936971i | \(-0.386383\pi\) |
0.986144 | + | 0.165890i | \(0.0530496\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.2647 | − | 12.2772i | 1.19435 | − | 0.689556i | 0.235057 | − | 0.971982i | \(-0.424472\pi\) |
0.959289 | + | 0.282426i | \(0.0911391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0418465 | + | 0.0724802i | −0.00234295 | + | 0.00405811i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.64626i | − | 0.0916006i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.13396 | − | 2.96409i | 0.284781 | − | 0.164418i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.1904 | − | 11.9244i | 0.782344 | − | 0.657411i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.15579 | + | 14.1262i | 0.448283 | + | 0.776449i | 0.998274 | − | 0.0587215i | \(-0.0187024\pi\) |
−0.549991 | + | 0.835170i | \(0.685369\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.07840 | − | 3.59989i | 0.113555 | − | 0.196683i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6580 | + | 23.6563i | 0.743998 | + | 1.28864i | 0.950661 | + | 0.310230i | \(0.100406\pi\) |
−0.206663 | + | 0.978412i | \(0.566261\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.743445 | + | 1.28768i | −0.0402598 | + | 0.0697320i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.29424 | − | 16.0193i | −0.501842 | − | 0.864960i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.37986 | − | 3.10606i | −0.288806 | − | 0.166742i | 0.348597 | − | 0.937273i | \(-0.386658\pi\) |
−0.637403 | + | 0.770530i | \(0.719991\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.6529 | − | 14.2334i | −1.31964 | − | 0.761896i | −0.335971 | − | 0.941872i | \(-0.609064\pi\) |
−0.983671 | + | 0.179977i | \(0.942398\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.98691 | −0.158977 | −0.0794887 | − | 0.996836i | \(-0.525329\pi\) | ||||
−0.0794887 | + | 0.996836i | \(0.525329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.39798i | 0.498793i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.5977 | + | 15.3562i | 1.40377 | + | 0.810468i | 0.994777 | − | 0.102070i | \(-0.0325465\pi\) |
0.408994 | + | 0.912537i | \(0.365880\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.40249 | − | 16.2856i | −0.494868 | − | 0.857136i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.66098 | − | 2.69102i | 0.243967 | − | 0.140854i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.0384i | 0.993794i | 0.867809 | + | 0.496897i | \(0.165527\pi\) | ||||
−0.867809 | + | 0.496897i | \(0.834473\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.7437 | + | 19.9256i | 0.869289 | + | 1.03449i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.11738 | 0.213190 | 0.106595 | − | 0.994303i | \(-0.466005\pi\) | ||||
0.106595 | + | 0.994303i | \(0.466005\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.414750 | −0.0213607 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.2436 | 0.577546 | 0.288773 | − | 0.957398i | \(-0.406753\pi\) | ||||
0.288773 | + | 0.957398i | \(0.406753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.6093 | 1.61516 | 0.807580 | − | 0.589758i | \(-0.200777\pi\) | ||||
0.807580 | + | 0.589758i | \(0.200777\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.483428 | − | 0.0855949i | 0.0246378 | − | 0.00436232i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 21.2485i | − | 1.07734i | −0.842516 | − | 0.538672i | \(-0.818926\pi\) | ||
0.842516 | − | 0.538672i | \(-0.181074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0278 | − | 9.25367i | 0.810562 | − | 0.467978i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.488611 | − | 0.846300i | −0.0245847 | − | 0.0425820i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.6927 | + | 11.9469i | 1.03854 | + | 0.599599i | 0.919419 | − | 0.393281i | \(-0.128660\pi\) |
0.119118 | + | 0.992880i | \(0.461993\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.4174i | 1.26928i | 0.772806 | + | 0.634642i | \(0.218853\pi\) | ||||
−0.772806 | + | 0.634642i | \(0.781147\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.36845 | −0.367049 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.161295 | − | 0.0931240i | −0.00799512 | − | 0.00461598i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.3831 | − | 11.1908i | −0.958433 | − | 0.553351i | −0.0627424 | − | 0.998030i | \(-0.519985\pi\) |
−0.895690 | + | 0.444678i | \(0.853318\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.4818 | − | 12.1595i | −1.64753 | − | 0.598330i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.60551 | + | 4.51288i | −0.127900 | + | 0.221528i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.04181 | − | 12.1968i | −0.344015 | − | 0.595851i | 0.641159 | − | 0.767408i | \(-0.278454\pi\) |
−0.985174 | + | 0.171556i | \(0.945120\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.07639 | − | 13.9887i | 0.393619 | − | 0.681768i | −0.599305 | − | 0.800521i | \(-0.704556\pi\) |
0.992924 | + | 0.118753i | \(0.0378896\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.40717 | + | 14.5617i | 0.407808 | + | 0.706344i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.62036 | − | 11.4486i | −0.465562 | − | 0.554036i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.16179 | − | 4.13486i | 0.344971 | − | 0.199169i | −0.317497 | − | 0.948259i | \(-0.602842\pi\) |
0.662468 | + | 0.749090i | \(0.269509\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.35102i | 0.209097i | 0.994520 | + | 0.104548i | \(0.0333397\pi\) | ||||
−0.994520 | + | 0.104548i | \(0.966660\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.09622 | + | 1.89872i | −0.0524395 | + | 0.0908279i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.0200 | − | 10.4039i | 0.860048 | − | 0.496549i | −0.00398054 | − | 0.999992i | \(-0.501267\pi\) |
0.864028 | + | 0.503443i | \(0.167934\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.7927 | + | 15.4688i | −1.27296 | + | 0.734945i | −0.975544 | − | 0.219803i | \(-0.929459\pi\) |
−0.297417 | + | 0.954748i | \(0.596125\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.91290 | + | 6.77734i | −0.185489 | + | 0.321277i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.9215i | − | 0.987346i | −0.869648 | − | 0.493673i | \(-0.835654\pi\) | ||
0.869648 | − | 0.493673i | \(-0.164346\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.47763 | − | 1.43046i | 0.116667 | − | 0.0673577i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.56519 | + | 1.86263i | 0.0733771 | + | 0.0873216i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.15058 | − | 1.99286i | −0.0538217 | − | 0.0932218i | 0.837859 | − | 0.545886i | \(-0.183807\pi\) |
−0.891681 | + | 0.452664i | \(0.850474\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.92497 | − | 15.4585i | 0.415677 | − | 0.719974i | −0.579822 | − | 0.814743i | \(-0.696878\pi\) |
0.995499 | + | 0.0947688i | \(0.0302112\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.24034 | + | 10.8086i | 0.290013 | + | 0.502318i | 0.973813 | − | 0.227353i | \(-0.0730070\pi\) |
−0.683799 | + | 0.729670i | \(0.739674\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.42799 | − | 4.20541i | 0.112354 | − | 0.194603i | −0.804365 | − | 0.594136i | \(-0.797494\pi\) |
0.916719 | + | 0.399533i | \(0.130828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.7748 | − | 5.36571i | −0.682236 | − | 0.247766i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.71405 | − | 0.989607i | −0.0788121 | − | 0.0455022i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.72503 | − | 0.995945i | −0.0791497 | − | 0.0456971i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.81084 | 0.402577 | 0.201289 | − | 0.979532i | \(-0.435487\pi\) | ||||
0.201289 | + | 0.979532i | \(0.435487\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 0.922973i | − | 0.0420839i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.42441 | − | 3.70914i | −0.291718 | − | 0.168423i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.66185 | − | 8.07456i | −0.211249 | − | 0.365893i | 0.740857 | − | 0.671663i | \(-0.234420\pi\) |
−0.952106 | + | 0.305770i | \(0.901086\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.9192 | + | 15.5418i | −1.21485 | + | 0.701391i | −0.963811 | − | 0.266587i | \(-0.914104\pi\) |
−0.251034 | + | 0.967978i | \(0.580771\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.17637i | − | 0.0529811i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.9942 | − | 6.19602i | 1.56971 | − | 0.277930i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.3388 | 1.00002 | 0.500010 | − | 0.866020i | \(-0.333330\pi\) | ||||
0.500010 | + | 0.866020i | \(0.333330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.2396 | 0.545738 | 0.272869 | − | 0.962051i | \(-0.412027\pi\) | ||||
0.272869 | + | 0.962051i | \(0.412027\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.2490 | 0.545072 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.1099 | 0.625411 | 0.312706 | − | 0.949850i | \(-0.398765\pi\) | ||||
0.312706 | + | 0.949850i | \(0.398765\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0932 | − | 15.5814i | −0.579209 | − | 0.689281i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.97659i | 0.263360i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.60910 | − | 0.929015i | 0.0707682 | − | 0.0408580i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.81632 | + | 4.87800i | 0.123385 | + | 0.213709i | 0.921101 | − | 0.389325i | \(-0.127292\pi\) |
−0.797715 | + | 0.603034i | \(0.793958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.2293 | + | 19.1849i | 1.45302 | + | 0.838899i | 0.998651 | − | 0.0519176i | \(-0.0165333\pi\) |
0.454364 | + | 0.890816i | \(0.349867\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 20.8995i | − | 0.910395i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.64754 | −0.0716321 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.2782 | + | 7.08880i | 0.531826 | + | 0.307050i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.36329 | + | 3.67385i | 0.275109 | + | 0.158834i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.637441 | − | 1.74365i | −0.0274565 | − | 0.0751045i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.21673 | + | 5.57154i | −0.138298 | + | 0.239539i | −0.926852 | − | 0.375426i | \(-0.877496\pi\) |
0.788555 | + | 0.614965i | \(0.210830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.98232 | + | 8.62963i | 0.213419 | + | 0.369653i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.52889 | − | 11.3084i | 0.279155 | − | 0.483511i | −0.692020 | − | 0.721878i | \(-0.743279\pi\) |
0.971175 | + | 0.238368i | \(0.0766124\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0696787 | + | 0.120687i | 0.00296841 | + | 0.00514144i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.82913 | + | 2.37735i | −0.120307 | + | 0.101095i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.5409 | + | 14.7460i | −1.08220 | + | 0.624809i | −0.931489 | − | 0.363769i | \(-0.881490\pi\) |
−0.150712 | + | 0.988578i | \(0.548157\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.80822i | − | 0.414844i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.25934 | + | 9.10944i | −0.221655 | + | 0.383917i | −0.955311 | − | 0.295604i | \(-0.904479\pi\) |
0.733656 | + | 0.679521i | \(0.237812\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.36020 | − | 5.40411i | 0.393787 | − | 0.227353i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.8054 | − | 13.1667i | 0.956053 | − | 0.551977i | 0.0610967 | − | 0.998132i | \(-0.480540\pi\) |
0.894956 | + | 0.446155i | \(0.147207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0295 | + | 38.1562i | −0.921906 | + | 1.59679i | −0.125444 | + | 0.992101i | \(0.540035\pi\) |
−0.796463 | + | 0.604688i | \(0.793298\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 22.3929i | − | 0.933847i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.1535 | − | 7.01684i | 0.505957 | − | 0.292115i | −0.225213 | − | 0.974310i | \(-0.572308\pi\) |
0.731170 | + | 0.682195i | \(0.238974\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.5219 | + | 6.72654i | 0.768418 | + | 0.279064i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.30448 | + | 2.25943i | 0.0540262 | + | 0.0935762i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.52469 | + | 2.64085i | −0.0629308 | + | 0.108999i | −0.895774 | − | 0.444509i | \(-0.853378\pi\) |
0.832843 | + | 0.553509i | \(0.186711\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.23791 | + | 2.14413i | 0.0510073 | + | 0.0883473i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.3041 | − | 23.0434i | 0.546334 | − | 0.946278i | −0.452188 | − | 0.891923i | \(-0.649356\pi\) |
0.998522 | − | 0.0543552i | \(-0.0173103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.28306 | + | 4.43941i | −0.216585 | + | 0.181998i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.86333 | − | 2.23050i | −0.157852 | − | 0.0911356i | 0.418993 | − | 0.907989i | \(-0.362383\pi\) |
−0.576845 | + | 0.816854i | \(0.695716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.25019 | − | 3.03120i | −0.214160 | − | 0.123645i | 0.389083 | − | 0.921203i | \(-0.372792\pi\) |
−0.603243 | + | 0.797557i | \(0.706125\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.64700 | −0.310895 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 45.3313i | − | 1.83994i | −0.391986 | − | 0.919971i | \(-0.628212\pi\) | ||
0.391986 | − | 0.919971i | \(-0.371788\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.97409 | + | 4.60384i | 0.322597 | + | 0.186251i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6294 | + | 28.8029i | 0.671654 | + | 1.16334i | 0.977435 | + | 0.211237i | \(0.0677492\pi\) |
−0.305781 | + | 0.952102i | \(0.598917\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.3001 | + | 18.0711i | −1.26010 | + | 0.727516i | −0.973093 | − | 0.230414i | \(-0.925992\pi\) |
−0.287002 | + | 0.957930i | \(0.592659\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 26.4462i | − | 1.06296i | −0.847069 | − | 0.531482i | \(-0.821635\pi\) | ||
0.847069 | − | 0.531482i | \(-0.178365\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.8158 | + | 10.1018i | 1.11442 | + | 0.404719i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8969 | 0.715874 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.61787 | 0.104381 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0484 | 1.27583 | 0.637914 | − | 0.770107i | \(-0.279797\pi\) | ||||
0.637914 | + | 0.770107i | \(0.279797\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.2737 | 0.606120 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.90376 | − | 7.05613i | 0.233916 | − | 0.279574i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.4154i | 0.964351i | 0.876075 | + | 0.482176i | \(0.160153\pi\) | ||||
−0.876075 | + | 0.482176i | \(0.839847\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.9014 | + | 18.4183i | −1.25807 | + | 0.726346i | −0.972699 | − | 0.232071i | \(-0.925450\pi\) |
−0.285370 | + | 0.958418i | \(0.592116\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.2847 | − | 23.0098i | −0.522276 | − | 0.904608i | −0.999664 | − | 0.0259155i | \(-0.991750\pi\) |
0.477389 | − | 0.878692i | \(-0.341583\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.09239 | − | 1.78539i | −0.121387 | − | 0.0700827i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.3418i | 1.18737i | 0.804699 | + | 0.593683i | \(0.202327\pi\) | ||||
−0.804699 | + | 0.593683i | \(0.797673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.64466 | −0.142409 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.9873 | + | 23.6640i | 1.59664 | + | 0.921820i | 0.992129 | + | 0.125223i | \(0.0399647\pi\) |
0.604511 | + | 0.796597i | \(0.293369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.4187 | + | 17.5623i | 1.18315 | + | 0.683092i | 0.956741 | − | 0.290940i | \(-0.0939679\pi\) |
0.226409 | + | 0.974032i | \(0.427301\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.279049 | − | 0.768376i | 0.0108211 | − | 0.0297963i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.783329 | + | 1.35677i | −0.0303306 | + | 0.0525342i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.749513 | − | 1.29819i | −0.0289346 | − | 0.0501162i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.54758 | + | 4.41254i | −0.0982020 | + | 0.170091i | −0.910940 | − | 0.412538i | \(-0.864642\pi\) |
0.812738 | + | 0.582629i | \(0.197976\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.42072 | + | 14.5851i | 0.323635 | + | 0.560551i | 0.981235 | − | 0.192815i | \(-0.0617618\pi\) |
−0.657601 | + | 0.753367i | \(0.728429\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.57573 | + | 26.3673i | −0.367483 | + | 1.01188i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.7555 | + | 9.09645i | −0.602868 | + | 0.348066i | −0.770169 | − | 0.637840i | \(-0.779828\pi\) |
0.167301 | + | 0.985906i | \(0.446495\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.88715i | − | 0.0721042i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.46452 | + | 11.1969i | −0.246279 | + | 0.426567i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.05405 | − | 1.76326i | 0.116182 | − | 0.0670775i | −0.440783 | − | 0.897614i | \(-0.645299\pi\) |
0.556965 | + | 0.830536i | \(0.311966\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.09786 | − | 4.09795i | 0.269237 | − | 0.155444i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.1063 | + | 34.8251i | −0.761579 | + | 1.31909i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3502i | 0.504229i | 0.967697 | + | 0.252114i | \(0.0811259\pi\) | ||||
−0.967697 | + | 0.252114i | \(0.918874\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.268574 | + | 0.155061i | −0.0101295 | + | 0.00584824i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.07566 | − | 45.6101i | −0.303716 | − | 1.71535i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.1447 | + | 36.6237i | 0.794107 | + | 1.37543i | 0.923405 | + | 0.383827i | \(0.125394\pi\) |
−0.129298 | + | 0.991606i | \(0.541273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.9166 | + | 24.1043i | −0.521182 | + | 0.902715i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.121942 | + | 0.211210i | 0.00456038 | + | 0.00789881i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.2035 | + | 26.3332i | −0.566994 | + | 0.982062i | 0.429868 | + | 0.902892i | \(0.358560\pi\) |
−0.996861 | + | 0.0791697i | \(0.974773\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.2544 | − | 3.94032i | 0.828796 | − | 0.146745i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.23265 | − | 0.711673i | −0.0457796 | − | 0.0264309i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.3671 | − | 6.56280i | −0.421583 | − | 0.243401i | 0.274171 | − | 0.961681i | \(-0.411596\pi\) |
−0.695754 | + | 0.718280i | \(0.744930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.8195 | 1.02894 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 37.7588i | − | 1.39465i | −0.716753 | − | 0.697327i | \(-0.754372\pi\) | ||
0.716753 | − | 0.697327i | \(-0.245628\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.36460 | − | 0.787853i | −0.0502657 | − | 0.0290209i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.1215 | + | 22.7271i | 0.482683 | + | 0.836031i | 0.999802 | − | 0.0198820i | \(-0.00632906\pi\) |
−0.517119 | + | 0.855913i | \(0.672996\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.78379 | + | 5.07132i | −0.322246 | + | 0.186049i | −0.652393 | − | 0.757881i | \(-0.726235\pi\) |
0.330147 | + | 0.943929i | \(0.392902\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 13.1731i | − | 0.482625i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.48462 | − | 26.1164i | 0.346561 | − | 0.954273i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.90737 | −0.288544 | −0.144272 | − | 0.989538i | \(-0.546084\pi\) | ||||
−0.144272 | + | 0.989538i | \(0.546084\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.99855 | 0.254703 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.8903 | 1.08638 | 0.543191 | − | 0.839609i | \(-0.317216\pi\) | ||||
0.543191 | + | 0.839609i | \(0.317216\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.11374 | 0.221623 | 0.110811 | − | 0.993841i | \(-0.464655\pi\) | ||||
0.110811 | + | 0.993841i | \(0.464655\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.8484 | − | 24.2416i | 1.04438 | − | 0.877604i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 17.6954i | − | 0.638944i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.79863 | − | 5.65724i | 0.353348 | − | 0.204005i | −0.312811 | − | 0.949815i | \(-0.601271\pi\) |
0.666159 | + | 0.745810i | \(0.267937\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.2106 | + | 33.2737i | 0.690956 | + | 1.19677i | 0.971525 | + | 0.236937i | \(0.0761437\pi\) |
−0.280569 | + | 0.959834i | \(0.590523\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.8994 | − | 12.6436i | −0.786648 | − | 0.454172i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 4.76373i | − | 0.170678i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.56247 | 0.127475 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.152730 | + | 0.0881788i | 0.00545117 | + | 0.00314723i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.2747 | − | 23.8300i | −1.47129 | − | 0.849447i | −0.471806 | − | 0.881703i | \(-0.656398\pi\) |
−0.999480 | + | 0.0322557i | \(0.989731\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.2938 | − | 31.2906i | −0.934900 | − | 1.11257i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.71430 | − | 6.43335i | 0.131898 | − | 0.228455i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.1359 | − | 26.2161i | −0.536139 | − | 0.928621i | −0.999107 | − | 0.0422457i | \(-0.986549\pi\) |
0.462968 | − | 0.886375i | \(-0.346785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.0581 | + | 22.6172i | −0.461961 | + | 0.800140i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.02008 | − | 1.76683i | −0.0359978 | − | 0.0623500i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.04935 | − | 1.60226i | 0.318948 | − | 0.0564723i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.219373 | − | 0.126655i | 0.00771273 | − | 0.00445295i | −0.496139 | − | 0.868243i | \(-0.665249\pi\) |
0.503851 | + | 0.863790i | \(0.331916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.0629i | − | 0.774735i | −0.921925 | − | 0.387367i | \(-0.873385\pi\) | ||
0.921925 | − | 0.387367i | \(-0.126615\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.00698 | − | 5.20824i | 0.105330 | − | 0.182437i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.85407 | + | 1.64780i | −0.0998514 | + | 0.0576492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.2467 | + | 13.9988i | −0.846214 | + | 0.488562i | −0.859372 | − | 0.511352i | \(-0.829145\pi\) |
0.0131576 | + | 0.999913i | \(0.495812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.4771 | − | 42.3955i | 0.853217 | − | 1.47782i | −0.0250719 | − | 0.999686i | \(-0.507981\pi\) |
0.878289 | − | 0.478130i | \(-0.158685\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.641658i | 0.0223126i | 0.999938 | + | 0.0111563i | \(0.00355124\pi\) | ||||
−0.999938 | + | 0.0111563i | \(0.996449\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.57180 | − | 5.52628i | 0.332442 | − | 0.191936i | −0.324483 | − | 0.945892i | \(-0.605190\pi\) |
0.656925 | + | 0.753956i | \(0.271857\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.0136 | + | 16.7451i | 0.693430 | + | 0.580183i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.57029 | + | 2.71981i | 0.0543420 | + | 0.0941230i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.62330 | − | 8.00780i | 0.159614 | − | 0.276460i | −0.775115 | − | 0.631820i | \(-0.782308\pi\) |
0.934730 | + | 0.355360i | \(0.115642\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4502 | − | 25.0285i | −0.498283 | − | 0.863052i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.94346 | − | 6.83028i | 0.135659 | − | 0.234969i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.04161 | + | 28.4743i | 0.173232 | + | 0.978388i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.01931 | − | 1.74320i | −0.103501 | − | 0.0597561i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.3256 | + | 19.8179i | 1.17529 | + | 0.678551i | 0.954919 | − | 0.296866i | \(-0.0959414\pi\) |
0.220366 | + | 0.975417i | \(0.429275\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.8520 | 0.814770 | 0.407385 | − | 0.913256i | \(-0.366441\pi\) | ||||
0.407385 | + | 0.913256i | \(0.366441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.1138i | 0.379197i | 0.981862 | + | 0.189598i | \(0.0607186\pi\) | ||||
−0.981862 | + | 0.189598i | \(0.939281\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.7780 | + | 22.3885i | 1.32002 | + | 0.762113i | 0.983731 | − | 0.179646i | \(-0.0574954\pi\) |
0.336287 | + | 0.941759i | \(0.390829\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.49128 | − | 4.31503i | −0.0847061 | − | 0.146715i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.320805 | + | 0.185217i | −0.0108826 | + | 0.00628305i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 7.80859i | − | 0.264584i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.06937 | + | 17.3354i | 0.103764 | + | 0.586042i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.68191 | 0.124329 | 0.0621647 | − | 0.998066i | \(-0.480200\pi\) | ||||
0.0621647 | + | 0.998066i | \(0.480200\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.3992 | 0.586194 | 0.293097 | − | 0.956083i | \(-0.405314\pi\) | ||||
0.293097 | + | 0.956083i | \(0.405314\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.02834 | 0.0682592 | 0.0341296 | − | 0.999417i | \(-0.489134\pi\) | ||||
0.0341296 | + | 0.999417i | \(0.489134\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.3780 | 1.55722 | 0.778610 | − | 0.627508i | \(-0.215925\pi\) | ||||
0.778610 | + | 0.627508i | \(0.215925\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0699 | − | 56.8731i | −0.337732 | − | 1.90746i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 3.09381i | − | 0.103531i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4812 | − | 8.93810i | 0.517481 | − | 0.298768i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.884576 | + | 1.53213i | 0.0295023 | + | 0.0510994i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.7582 | − | 18.3356i | −1.05802 | − | 0.610847i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 0.659898i | − | 0.0219357i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0391 | −0.532571 | −0.266285 | − | 0.963894i | \(-0.585796\pi\) | ||||
−0.266285 | + | 0.963894i | \(0.585796\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7833 | + | 10.2672i | 0.589187 | + | 0.340167i | 0.764776 | − | 0.644296i | \(-0.222850\pi\) |
−0.175589 | + | 0.984464i | \(0.556183\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.71069 | + | 0.987665i | 0.0566154 | + | 0.0326869i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.40290 | + | 13.5712i | 0.0793507 | + | 0.448161i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.7069 | − | 30.6693i | 0.584097 | − | 1.01169i | −0.410890 | − | 0.911685i | \(-0.634782\pi\) |
0.994987 | − | 0.100001i | \(-0.0318846\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.82712 | + | 15.2890i | 0.290548 | + | 0.503244i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.58374 | − | 2.74311i | 0.0520730 | − | 0.0901930i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.8626 | + | 34.4030i | 0.651670 | + | 1.12873i | 0.982718 | + | 0.185111i | \(0.0592646\pi\) |
−0.331048 | + | 0.943614i | \(0.607402\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.04509 | − | 0.532479i | −0.0997988 | − | 0.0174513i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.599064 | + | 0.345870i | −0.0195915 | + | 0.0113112i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.2142i | 0.758376i | 0.925320 | + | 0.379188i | \(0.123797\pi\) | ||||
−0.925320 | + | 0.379188i | \(0.876203\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.9616 | − | 31.1104i | 0.585531 | − | 1.01417i | −0.409278 | − | 0.912410i | \(-0.634219\pi\) |
0.994809 | − | 0.101760i | \(-0.0324474\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.3790 | − | 26.7769i | 1.51031 | − | 0.871977i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.7365 | + | 15.4363i | −0.868818 | + | 0.501612i | −0.866955 | − | 0.498386i | \(-0.833926\pi\) |
−0.00186277 | + | 0.999998i | \(0.500593\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.05511 | − | 8.75571i | 0.164096 | − | 0.284222i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 30.4640i | − | 0.986826i | −0.869795 | − | 0.493413i | \(-0.835749\pi\) | ||
0.869795 | − | 0.493413i | \(-0.164251\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.80100 | − | 1.03981i | 0.0582791 | − | 0.0336475i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.02696 | + | 1.24418i | −0.226912 | + | 0.0401768i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.215406 | + | 0.373095i | 0.00694859 | + | 0.0120353i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.47686 | + | 11.2182i | −0.208497 | + | 0.361128i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.75865 | + | 11.7063i | 0.217343 | + | 0.376450i | 0.953995 | − | 0.299823i | \(-0.0969275\pi\) |
−0.736652 | + | 0.676272i | \(0.763594\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.6428 | + | 28.8261i | −0.534092 | + | 0.925074i | 0.465115 | + | 0.885250i | \(0.346013\pi\) |
−0.999207 | + | 0.0398238i | \(0.987320\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.9387 | − | 23.7278i | −0.639204 | − | 0.760677i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.9127 | − | 22.4662i | −1.24493 | − | 0.718758i | −0.274833 | − | 0.961492i | \(-0.588623\pi\) |
−0.970093 | + | 0.242734i | \(0.921956\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.56907 | + | 1.48325i | 0.0821079 | + | 0.0474050i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.8949 | −0.857813 | −0.428907 | − | 0.903349i | \(-0.641101\pi\) | ||||
−0.428907 | + | 0.903349i | \(0.641101\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9.91929i | − | 0.316055i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32.0855 | − | 18.5246i | −1.02026 | − | 0.589048i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.7201 | − | 30.6920i | −0.562896 | − | 0.974965i | −0.997242 | − | 0.0742186i | \(-0.976354\pi\) |
0.434346 | − | 0.900746i | \(-0.356980\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.3635 | + | 8.29275i | −0.455352 | + | 0.262898i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.4953i | 1.02914i | 0.857449 | + | 0.514568i | \(0.172048\pi\) | ||||
−0.857449 | + | 0.514568i | \(0.827952\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))