Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,2,Mod(5,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.k (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.670743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.17 |
Dual form | 84.2.k.b.5.1 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.50000 | − | 2.59808i | −0.670820 | − | 1.16190i | −0.977672 | − | 0.210138i | \(-0.932609\pi\) |
0.306851 | − | 0.951757i | \(-0.400725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.50000 | + | 2.59808i | 1.35680 | + | 0.783349i | 0.989191 | − | 0.146631i | \(-0.0468429\pi\) |
0.367610 | + | 0.929980i | \(0.380176\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.50000 | + | 2.59808i | −1.16190 | + | 0.670820i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50000 | − | 0.866025i | 0.344124 | − | 0.198680i | −0.317970 | − | 0.948101i | \(-0.603001\pi\) |
0.662094 | + | 0.749421i | \(0.269668\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | − | 3.46410i | 0.654654 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.50000 | + | 2.59808i | −0.938315 | + | 0.541736i | −0.889432 | − | 0.457068i | \(-0.848900\pi\) |
−0.0488832 | + | 0.998805i | \(0.515566\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.50000 | − | 7.79423i | 0.783349 | − | 1.35680i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.50000 | − | 7.79423i | 0.253546 | − | 1.31747i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.50000 | − | 6.06218i | −0.575396 | − | 0.996616i | −0.995998 | − | 0.0893706i | \(-0.971514\pi\) |
0.420602 | − | 0.907245i | \(-0.361819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.50000 | + | 7.79423i | 0.670820 | + | 1.16190i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.50000 | − | 2.59808i | −0.218797 | − | 0.378968i | 0.735643 | − | 0.677369i | \(-0.236880\pi\) |
−0.954441 | + | 0.298401i | \(0.903547\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.50000 | + | 2.59808i | 0.630126 | + | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.50000 | − | 2.59808i | −0.618123 | − | 0.356873i | 0.158015 | − | 0.987437i | \(-0.449491\pi\) |
−0.776138 | + | 0.630563i | \(0.782824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 15.5885i | − | 2.10195i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.50000 | − | 2.59808i | −0.198680 | − | 0.344124i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50000 | − | 2.59808i | 0.195283 | − | 0.338241i | −0.751710 | − | 0.659494i | \(-0.770771\pi\) |
0.946993 | + | 0.321253i | \(0.104104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.5000 | + | 6.06218i | −1.34439 | + | 0.776182i | −0.987448 | − | 0.157945i | \(-0.949513\pi\) |
−0.356939 | + | 0.934128i | \(0.616180\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.00000 | − | 5.19615i | −0.755929 | − | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.50000 | + | 4.33013i | −0.305424 | + | 0.529009i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
0.671932 | + | 0.740613i | \(0.265465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.50000 | + | 7.79423i | 0.541736 | + | 0.938315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3923i | 1.23334i | 0.787222 | + | 0.616670i | \(0.211519\pi\) | ||||
−0.787222 | + | 0.616670i | \(0.788481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.5000 | − | 6.06218i | −1.22893 | − | 0.709524i | −0.262126 | − | 0.965034i | \(-0.584423\pi\) |
−0.966807 | + | 0.255510i | \(0.917757\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.00000 | + | 3.46410i | 0.692820 | + | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.50000 | + | 12.9904i | 0.512823 | + | 1.48039i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | 0.976187 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.50000 | + | 7.79423i | 0.476999 | + | 0.826187i | 0.999653 | − | 0.0263586i | \(-0.00839118\pi\) |
−0.522654 | + | 0.852545i | \(0.675058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | + | 2.59808i | −0.155543 | + | 0.269408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.50000 | − | 2.59808i | −0.461690 | − | 0.266557i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.92820i | 0.703452i | 0.936103 | + | 0.351726i | \(0.114405\pi\) | ||||
−0.936103 | + | 0.351726i | \(0.885595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.5000 | − | 7.79423i | −1.35680 | − | 0.783349i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.50000 | − | 7.79423i | 0.447767 | − | 0.775555i | −0.550474 | − | 0.834853i | \(-0.685553\pi\) |
0.998240 | + | 0.0592978i | \(0.0188862\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.50000 | + | 2.59808i | −0.443398 | + | 0.255996i | −0.705038 | − | 0.709170i | \(-0.749070\pi\) |
0.261640 | + | 0.965166i | \(0.415737\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.5000 | − | 2.59808i | −1.31747 | − | 0.253546i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.5000 | − | 7.79423i | 1.30509 | − | 0.753497i | 0.323821 | − | 0.946118i | \(-0.395032\pi\) |
0.981273 | + | 0.192622i | \(0.0616990\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.50000 | − | 14.7224i | 0.814152 | − | 1.41015i | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) |
0.909935 | − | 0.414751i | \(-0.136131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.5000 | + | 6.06218i | −0.996616 | + | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 20.7846i | − | 1.95525i | −0.210352 | − | 0.977626i | \(-0.567461\pi\) | ||
0.210352 | − | 0.977626i | \(-0.432539\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.5000 | + | 7.79423i | 1.25888 | + | 0.726816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.50000 | + | 2.59808i | −0.687524 | + | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.00000 | + | 13.8564i | 0.727273 | + | 1.25967i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 10.3923i | − | 0.937043i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 6.92820i | − | 0.609994i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.50000 | + | 7.79423i | 0.393167 | + | 0.680985i | 0.992865 | − | 0.119241i | \(-0.0380462\pi\) |
−0.599699 | + | 0.800226i | \(0.704713\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.50000 | + | 0.866025i | 0.390199 | + | 0.0750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.5000 | − | 7.79423i | 1.16190 | − | 0.670820i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.50000 | − | 2.59808i | −0.384461 | − | 0.221969i | 0.295296 | − | 0.955406i | \(-0.404582\pi\) |
−0.679757 | + | 0.733437i | \(0.737915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.3923i | − | 0.881464i | −0.897639 | − | 0.440732i | \(-0.854719\pi\) | ||
0.897639 | − | 0.440732i | \(-0.145281\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.50000 | + | 2.59808i | −0.378968 | + | 0.218797i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.0000 | − | 1.73205i | 0.989743 | − | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.50000 | + | 2.59808i | −0.368654 | + | 0.212843i | −0.672870 | − | 0.739760i | \(-0.734939\pi\) |
0.304216 | + | 0.952603i | \(0.401606\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.50000 | + | 11.2583i | −0.528962 | + | 0.916190i | 0.470467 | + | 0.882418i | \(0.344085\pi\) |
−0.999430 | + | 0.0337724i | \(0.989248\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.50000 | − | 7.79423i | 0.363803 | − | 0.630126i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.19615i | 0.417365i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.50000 | − | 2.59808i | −0.359139 | − | 0.207349i | 0.309564 | − | 0.950879i | \(-0.399817\pi\) |
−0.668703 | + | 0.743530i | \(0.733150\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.50000 | + | 7.79423i | −0.356873 | + | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.5000 | − | 2.59808i | −1.06395 | − | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.500000 | + | 0.866025i | 0.0391630 | + | 0.0678323i | 0.884943 | − | 0.465700i | \(-0.154198\pi\) |
−0.845780 | + | 0.533533i | \(0.820864\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −27.0000 | −2.10195 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.50000 | + | 2.59808i | −0.344124 | + | 0.198680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.50000 | + | 7.79423i | 0.342129 | + | 0.592584i | 0.984828 | − | 0.173534i | \(-0.0555188\pi\) |
−0.642699 | + | 0.766119i | \(0.722185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0000 | + | 3.46410i | −0.755929 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.50000 | − | 2.59808i | −0.338241 | − | 0.195283i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.50000 | + | 2.59808i | 0.336346 | + | 0.194189i | 0.658655 | − | 0.752445i | \(-0.271126\pi\) |
−0.322309 | + | 0.946634i | \(0.604459\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.92820i | − | 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.5000 | + | 18.1865i | 0.776182 | + | 1.34439i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.5000 | + | 18.1865i | −0.771975 | + | 1.33710i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.5000 | + | 7.79423i | −0.987218 | + | 0.569970i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.00000 | + | 10.3923i | −0.654654 | + | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.5000 | − | 7.79423i | 0.976826 | − | 0.563971i | 0.0755154 | − | 0.997145i | \(-0.475940\pi\) |
0.901310 | + | 0.433174i | \(0.142606\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.50000 | − | 4.33013i | 0.179954 | − | 0.311689i | −0.761911 | − | 0.647682i | \(-0.775738\pi\) |
0.941865 | + | 0.335993i | \(0.109072\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.50000 | − | 0.866025i | −0.106332 | − | 0.0613909i | 0.445891 | − | 0.895087i | \(-0.352887\pi\) |
−0.552223 | + | 0.833696i | \(0.686220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.50000 | + | 4.33013i | 0.529009 | + | 0.305424i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | − | 15.5885i | −0.628587 | − | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.5000 | − | 7.79423i | 0.938315 | − | 0.541736i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.00000 | 0.622543 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.0000 | 1.23334 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.00000 | − | 10.3923i | −0.409197 | − | 0.708749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.50000 | − | 4.33013i | −0.101827 | − | 0.293948i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.5000 | + | 18.1865i | −0.709524 | + | 1.22893i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3923i | 0.695920i | 0.937509 | + | 0.347960i | \(0.113126\pi\) | ||||
−0.937509 | + | 0.347960i | \(0.886874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.00000 | − | 10.3923i | 0.400000 | − | 0.692820i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.50000 | + | 7.79423i | −0.298675 | + | 0.517321i | −0.975833 | − | 0.218517i | \(-0.929878\pi\) |
0.677158 | + | 0.735838i | \(0.263211\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.5000 | − | 11.2583i | 1.28860 | − | 0.743971i | 0.310192 | − | 0.950674i | \(-0.399607\pi\) |
0.978404 | + | 0.206702i | \(0.0662732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22.5000 | − | 7.79423i | 1.48039 | − | 0.512823i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.50000 | + | 2.59808i | −0.294805 | + | 0.170206i | −0.640107 | − | 0.768286i | \(-0.721110\pi\) |
0.345302 | + | 0.938492i | \(0.387777\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.50000 | + | 7.79423i | −0.293548 | + | 0.508439i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.50000 | − | 0.866025i | 0.0974355 | − | 0.0562544i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.50000 | + | 0.866025i | 0.0966235 | + | 0.0557856i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.5000 | − | 12.9904i | 1.05415 | − | 0.829925i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.7846i | 1.31717i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.0000 | −1.69748 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 15.5885i | − | 0.976187i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.5000 | − | 23.3827i | −0.842107 | − | 1.45857i | −0.888110 | − | 0.459631i | \(-0.847982\pi\) |
0.0460033 | − | 0.998941i | \(-0.485352\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.50000 | − | 18.1865i | 0.217479 | − | 1.13006i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.50000 | + | 2.59808i | 0.277482 | + | 0.160204i | 0.632283 | − | 0.774738i | \(-0.282118\pi\) |
−0.354801 | + | 0.934942i | \(0.615451\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.5885i | 0.957591i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.5000 | − | 7.79423i | 0.826187 | − | 0.476999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.5000 | − | 18.1865i | 0.640196 | − | 1.10885i | −0.345192 | − | 0.938532i | \(-0.612186\pi\) |
0.985389 | − | 0.170321i | \(-0.0544803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.5000 | − | 11.2583i | 1.18454 | − | 0.683895i | 0.227480 | − | 0.973783i | \(-0.426951\pi\) |
0.957061 | + | 0.289888i | \(0.0936180\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.0000 | + | 10.3923i | −1.08544 | + | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.50000 | − | 11.2583i | 0.390547 | − | 0.676448i | −0.601975 | − | 0.798515i | \(-0.705619\pi\) |
0.992522 | + | 0.122068i | \(0.0389525\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.50000 | + | 2.59808i | 0.269408 | + | 0.155543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.7846i | 1.23991i | 0.784639 | + | 0.619953i | \(0.212848\pi\) | ||||
−0.784639 | + | 0.619953i | \(0.787152\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.50000 | − | 4.33013i | −0.445829 | − | 0.257399i | 0.260238 | − | 0.965544i | \(-0.416199\pi\) |
−0.706067 | + | 0.708145i | \(0.749532\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.50000 | + | 7.79423i | −0.266557 | + | 0.461690i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000 | + | 10.3923i | 0.708338 | + | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000 | 0.703452 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.00000 | −0.524000 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.5000 | + | 23.3827i | −0.783349 | + | 1.35680i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | + | 6.92820i | 0.461112 | + | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.5000 | − | 7.79423i | −0.775555 | − | 0.447767i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 31.5000 | + | 18.1865i | 1.80368 | + | 1.04136i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3205i | 0.988534i | 0.869310 | + | 0.494267i | \(0.164563\pi\) | ||||
−0.869310 | + | 0.494267i | \(0.835437\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.50000 | + | 7.79423i | 0.255996 | + | 0.443398i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.50000 | − | 12.9904i | 0.425286 | − | 0.736617i | −0.571161 | − | 0.820838i | \(-0.693507\pi\) |
0.996447 | + | 0.0842210i | \(0.0268402\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.5000 | + | 6.06218i | −0.593495 | + | 0.342655i | −0.766478 | − | 0.642270i | \(-0.777993\pi\) |
0.172983 | + | 0.984925i | \(0.444659\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.50000 | + | 23.3827i | −0.253546 | + | 1.31747i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.5000 | + | 12.9904i | −1.26373 | + | 0.729612i | −0.973793 | − | 0.227435i | \(-0.926966\pi\) |
−0.289933 | + | 0.957047i | \(0.593633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.5000 | − | 23.3827i | −0.753497 | − | 1.30509i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.19615i | 0.289122i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −25.5000 | − | 14.7224i | −1.41015 | − | 0.814152i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.50000 | − | 7.79423i | 0.0826977 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.5000 | − | 26.8468i | −0.851957 | − | 1.47563i | −0.879440 | − | 0.476011i | \(-0.842082\pi\) |
0.0274825 | − | 0.999622i | \(-0.491251\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.5000 | + | 18.1865i | 0.575396 | + | 0.996616i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.0000 | 0.819538 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −36.0000 | −1.95525 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.50000 | − | 7.79423i | −0.243689 | − | 0.422081i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.5000 | − | 23.3827i | 0.726816 | − | 1.25888i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.5000 | − | 7.79423i | −0.724718 | − | 0.418416i | 0.0917687 | − | 0.995780i | \(-0.470748\pi\) |
−0.816487 | + | 0.577364i | \(0.804081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.8564i | 0.741716i | 0.928689 | + | 0.370858i | \(0.120936\pi\) | ||||
−0.928689 | + | 0.370858i | \(0.879064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.50000 | + | 2.59808i | −0.0798369 | + | 0.138282i | −0.903179 | − | 0.429263i | \(-0.858773\pi\) |
0.823343 | + | 0.567545i | \(0.192107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.0000 | − | 15.5885i | 1.43301 | − | 0.827349i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.50000 | + | 12.9904i | 0.238165 | + | 0.687524i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.5000 | + | 12.9904i | −1.18750 | + | 0.685606i | −0.957739 | − | 0.287640i | \(-0.907129\pi\) |
−0.229766 | + | 0.973246i | \(0.573796\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.0000 | − | 13.8564i | 1.25967 | − | 0.727273i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.3731i | 1.90385i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.5000 | + | 16.4545i | 1.48769 | + | 0.858917i | 0.999901 | − | 0.0140459i | \(-0.00447111\pi\) |
0.487787 | + | 0.872963i | \(0.337804\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.0000 | −0.937043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.50000 | − | 12.9904i | −0.233628 | − | 0.674427i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5000 | + | 21.6506i | 0.647225 | + | 1.12103i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) |
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.19615i | 0.268328i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 13.8564i | − | 0.709885i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.5000 | + | 18.1865i | 0.536525 | + | 0.929288i | 0.999088 | + | 0.0427020i | \(0.0135966\pi\) |
−0.462563 | + | 0.886586i | \(0.653070\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.0000 | − | 31.1769i | 1.37605 | − | 1.58892i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.0000 | −0.609994 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.5000 | − | 12.9904i | −1.14080 | − | 0.658638i | −0.194168 | − | 0.980968i | \(-0.562201\pi\) |
−0.946627 | + | 0.322330i | \(0.895534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15.5885i | − | 0.788342i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.5000 | − | 7.79423i | 0.680985 | − | 0.393167i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.50000 | − | 2.59808i | 0.0754732 | − | 0.130723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.50000 | − | 4.33013i | 0.376414 | − | 0.217323i | −0.299843 | − | 0.953989i | \(-0.596934\pi\) |
0.676257 | + | 0.736666i | \(0.263601\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.50000 | − | 7.79423i | 0.0750939 | − | 0.390199i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.5000 | − | 18.1865i | 1.57303 | − | 0.908192i | 0.577241 | − | 0.816574i | \(-0.304129\pi\) |
0.995794 | − | 0.0916181i | \(-0.0292039\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.5000 | − | 23.3827i | −0.670820 | − | 1.16190i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 36.3731i | − | 1.80295i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.50000 | − | 2.59808i | −0.222511 | − | 0.128467i | 0.384602 | − | 0.923083i | \(-0.374339\pi\) |
−0.607112 | + | 0.794616i | \(0.707672\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.50000 | + | 7.79423i | −0.221969 | + | 0.384461i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.50000 | − | 2.59808i | 0.369051 | − | 0.127843i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.0000 | + | 31.1769i | 0.883585 | + | 1.53041i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.0000 | −0.881464 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.50000 | + | 7.79423i | 0.218797 | + | 0.378968i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | − | 10.3923i | −0.291043 | − | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.5000 | − | 6.06218i | −1.52439 | − | 0.293369i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.5000 | − | 7.79423i | −0.650272 | − | 0.375435i | 0.138288 | − | 0.990392i | \(-0.455840\pi\) |
−0.788560 | + | 0.614957i | \(0.789173\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.6410i | 1.66474i | 0.554220 | + | 0.832370i | \(0.313017\pi\) | ||||
−0.554220 | + | 0.832370i | \(0.686983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.50000 | + | 7.79423i | −0.215264 | + | 0.372849i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.5000 | − | 7.79423i | 0.644320 | − | 0.371998i | −0.141957 | − | 0.989873i | \(-0.545339\pi\) |
0.786277 | + | 0.617875i | \(0.212006\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | − | 20.7846i | −0.142857 | − | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.5000 | − | 7.79423i | 0.641404 | − | 0.370315i | −0.143751 | − | 0.989614i | \(-0.545916\pi\) |
0.785155 | + | 0.619299i | \(0.212583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5000 | − | 23.3827i | 0.639961 | − | 1.10845i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.50000 | + | 7.79423i | 0.212843 | + | 0.368654i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.7846i | − | 0.980886i | −0.871473 | − | 0.490443i | \(-0.836835\pi\) | ||
0.871473 | − | 0.490443i | \(-0.163165\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.0000 | + | 15.5885i | 1.27138 | + | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.5000 | + | 11.2583i | 0.916190 | + | 0.528962i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.5000 | − | 26.8468i | −0.725059 | − | 1.25584i | −0.958950 | − | 0.283577i | \(-0.908479\pi\) |
0.233890 | − | 0.972263i | \(-0.424854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.5000 | − | 7.79423i | −0.630126 | − | 0.363803i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.00000 | 0.417365 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.50000 | + | 7.79423i | 0.208235 | + | 0.360674i | 0.951159 | − | 0.308702i | \(-0.0998947\pi\) |
−0.742923 | + | 0.669376i | \(0.766561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.5000 | + | 4.33013i | −0.577196 | + | 0.199947i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.50000 | + | 7.79423i | −0.207349 | + | 0.359139i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.0000 | + | 10.3923i | 0.827641 | + | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.92820i | 0.317888i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.5000 | + | 7.79423i | 0.618123 | + | 0.356873i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.5000 | + | 28.5788i | −0.753904 | + | 1.30580i | 0.192013 | + | 0.981392i | \(0.438498\pi\) |
−0.945917 | + | 0.324408i | \(0.894835\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.50000 | + | 23.3827i | −0.204757 | + | 1.06395i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.0000 | − | 10.3923i | 0.817338 | − | 0.471890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.500000 | + | 0.866025i | −0.0226572 | + | 0.0392434i | −0.877132 | − | 0.480250i | \(-0.840546\pi\) |
0.854475 | + | 0.519493i | \(0.173879\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.50000 | − | 0.866025i | 0.0678323 | − | 0.0391630i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.3923i | 0.468998i | 0.972116 | + | 0.234499i | \(0.0753450\pi\) | ||||
−0.972116 | + | 0.234499i | \(0.924655\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 46.7654i | 2.10195i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.0000 | + | 20.7846i | −0.807410 | + | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.50000 | − | 6.06218i | −0.156682 | − | 0.271380i | 0.776989 | − | 0.629515i | \(-0.216746\pi\) |
−0.933670 | + | 0.358134i | \(0.883413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 20.7846i | − | 0.928588i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.0000 | −1.20148 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 22.5167i | − | 1.00000i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.5000 | + | 18.1865i | 0.465404 | + | 0.806104i | 0.999220 | − | 0.0394971i | \(-0.0125756\pi\) |
−0.533815 | + | 0.845601i | \(0.679242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5000 | − | 30.3109i | −0.464493 | − | 1.34087i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.50000 | + | 7.79423i | 0.198680 | + | 0.344124i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.5000 | + | 7.79423i | 0.594881 | + | 0.343455i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 15.5885i | − | 0.685580i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.5000 | − | 7.79423i | 0.592584 | − | 0.342129i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.50000 | + | 12.9904i | −0.328581 | + | 0.569119i | −0.982231 | − | 0.187678i | \(-0.939904\pi\) |
0.653650 | + | 0.756797i | \(0.273237\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.5000 | + | 12.9904i | −0.983856 | + | 0.568030i | −0.903432 | − | 0.428731i | \(-0.858961\pi\) |
−0.0804241 | + | 0.996761i | \(0.525627\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.00000 | + | 17.3205i | 0.261861 | + | 0.755929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.50000 | − | 2.59808i | 0.196023 | − | 0.113174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.00000 | − | 3.46410i | 0.0869565 | − | 0.150613i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.50000 | + | 7.79423i | −0.195283 | + | 0.338241i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.5000 | − | 23.3827i | −1.75097 | − | 1.01092i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.50000 | − | 7.79423i | 0.194189 | − | 0.336346i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.5000 | + | 33.7750i | −0.581486 | + | 1.45479i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5000 | + | 32.0429i | 0.795377 | + | 1.37763i | 0.922599 | + | 0.385759i | \(0.126061\pi\) |
−0.127222 | + | 0.991874i | \(0.540606\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.0000 | −0.514969 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −51.0000 | −2.18460 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0000 | 1.36822 | 0.684111 | − | 0.729378i | \(-0.260191\pi\) | ||||
0.684111 | + | 0.729378i | \(0.260191\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31.5000 | − | 18.1865i | 1.34439 | − | 0.776182i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.500000 | + | 2.59808i | −0.0212622 | + | 0.110481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 31.5000 | + | 18.1865i | 1.33710 | + | 0.771975i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.5000 | − | 12.9904i | −0.953356 | − | 0.550420i | −0.0592339 | − | 0.998244i | \(-0.518866\pi\) |
−0.894122 | + | 0.447824i | \(0.852199\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.5000 | + | 23.3827i | 0.569970 | + | 0.987218i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.5000 | − | 23.3827i | 0.568957 | − | 0.985463i | −0.427712 | − | 0.903915i | \(-0.640680\pi\) |
0.996669 | − | 0.0815478i | \(-0.0259863\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −54.0000 | + | 31.1769i | −2.27180 | + | 1.31162i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.0000 | + | 15.5885i | 0.755929 | + | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.5000 | − | 7.79423i | 0.565949 | − | 0.326751i | −0.189580 | − | 0.981865i | \(-0.560713\pi\) |
0.755530 | + | 0.655114i | \(0.227379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.50000 | − | 6.06218i | 0.146470 | − | 0.253694i | −0.783450 | − | 0.621455i | \(-0.786542\pi\) |
0.929921 | + | 0.367760i | \(0.119875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.5000 | − | 23.3827i | −0.563971 | − | 0.976826i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 20.7846i | − | 0.866778i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.5000 | − | 12.9904i | −0.936687 | − | 0.540797i | −0.0477669 | − | 0.998859i | \(-0.515210\pi\) |
−0.888920 | + | 0.458062i | \(0.848544\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.50000 | − | 4.33013i | −0.311689 | − | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | − | 20.7846i | −0.995688 | − | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.5000 | − | 23.3827i | −0.559113 | − | 0.968412i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.0000 | 1.48588 | 0.742940 | − | 0.669359i | \(-0.233431\pi\) | ||||
0.742940 | + | 0.669359i | \(0.233431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.00000 | −0.123613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5000 | + | 18.1865i | 0.431183 | + | 0.746831i | 0.996976 | − | 0.0777165i | \(-0.0247629\pi\) |
−0.565792 | + | 0.824548i | \(0.691430\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.0000 | + | 15.5885i | 0.737928 | + | 0.639064i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.50000 | + | 2.59808i | −0.0613909 | + | 0.106332i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.50000 | + | 2.59808i | 0.183865 | + | 0.106155i | 0.589107 | − | 0.808055i | \(-0.299480\pi\) |
−0.405242 | + | 0.914209i | \(0.632813\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 34.6410i | − | 1.41304i | −0.707695 | − | 0.706518i | \(-0.750265\pi\) | ||
0.707695 | − | 0.706518i | \(-0.249735\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.50000 | − | 12.9904i | 0.305424 | − | 0.529009i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.0000 | − | 41.5692i | 0.975739 | − | 1.69003i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.5000 | − | 14.7224i | 1.03501 | − | 0.597565i | 0.116596 | − | 0.993179i | \(-0.462802\pi\) |
0.918417 | + | 0.395614i | \(0.129468\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.500000 | − | 0.866025i | 0.0201948 | − | 0.0349784i | −0.855751 | − | 0.517387i | \(-0.826905\pi\) |
0.875946 | + | 0.482409i | \(0.160238\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.0000 | + | 15.5885i | −1.08875 | + | 0.628587i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 20.7846i | − | 0.836757i | −0.908273 | − | 0.418378i | \(-0.862599\pi\) | ||
0.908273 | − | 0.418378i | \(-0.137401\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.5000 | + | 12.9904i | 0.904351 | + | 0.522127i | 0.878609 | − | 0.477541i | \(-0.158472\pi\) |
0.0257420 | + | 0.999669i | \(0.491805\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.5000 | − | 23.3827i | −0.541736 | − | 0.938315i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.50000 | + | 23.3827i | −0.180289 | + | 0.936808i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 15.5885i | − | 0.622543i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.0000 | 0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.6410i | 1.37686i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.0000 | − | 20.7846i | −0.476205 | − | 0.824812i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 31.1769i | − | 1.23334i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.5000 | + | 7.79423i | 0.533218 | + | 0.307854i | 0.742326 | − | 0.670039i | \(-0.233723\pi\) |
−0.209108 | + | 0.977893i | \(0.567056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.46410i | 0.136611i | 0.997664 | + | 0.0683054i | \(0.0217592\pi\) | ||||
−0.997664 | + | 0.0683054i | \(0.978241\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.0000 | + | 10.3923i | −0.708749 | + | 0.409197i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.50000 | + | 7.79423i | −0.176913 | + | 0.306423i | −0.940822 | − | 0.338902i | \(-0.889945\pi\) |
0.763908 | + | 0.645325i | \(0.223278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5000 | − | 7.79423i | 0.529921 | − | 0.305950i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.50000 | + | 2.59808i | −0.293948 | + | 0.101827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.5000 | − | 7.79423i | 0.528296 | − | 0.305012i | −0.212026 | − | 0.977264i | \(-0.568006\pi\) |
0.740322 | + | 0.672252i | \(0.234673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.5000 | − | 23.3827i | 0.527489 | − | 0.913637i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.5000 | + | 18.1865i | 1.22893 | + | 0.709524i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 10.3923i | − | 0.404827i | −0.979300 | − | 0.202413i | \(-0.935122\pi\) | ||
0.979300 | − | 0.202413i | \(-0.0648785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.5000 | + | 11.2583i | 0.758462 | + | 0.437898i | 0.828743 | − | 0.559629i | \(-0.189056\pi\) |
−0.0702812 | + | 0.997527i | \(0.522390\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.50000 | − | 12.9904i | −0.174503 | − | 0.503745i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.0000 | 0.695920 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −63.0000 | −2.43209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0000 | 0.848038 | 0.424019 | − | 0.905653i | \(-0.360619\pi\) | ||||
0.424019 | + | 0.905653i | \(0.360619\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.0000 | − | 10.3923i | −0.692820 | − | 0.400000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.5000 | + | 38.9711i | 0.864745 | + | 1.49778i | 0.867300 | + | 0.497786i | \(0.165853\pi\) |
−0.00255466 | + | 0.999997i | \(0.500813\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0000 | + | 13.8564i | −0.460518 | + | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.5000 | + | 7.79423i | 0.517321 | + | 0.298675i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.5000 | − | 18.1865i | −1.20531 | − | 0.695888i | −0.243582 | − | 0.969880i | \(-0.578323\pi\) |
−0.961732 | + | 0.273992i | \(0.911656\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.5885i | 0.595604i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.5000 | − | 33.7750i | −0.743971 | − | 1.28860i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5000 | + | 16.4545i | −1.08419 | + | 0.625958i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.5000 | − | 38.9711i | −0.512823 | − | 1.48039i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.0000 | + | 15.5885i | −1.02417 | + | 0.591304i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | + | 15.5885i | −0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.50000 | + | 7.79423i | 0.170206 | + | 0.294805i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7846i | 0.785024i | 0.919747 | + | 0.392512i | \(0.128394\pi\) | ||||
−0.919747 | + | 0.392512i | \(0.871606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.5000 | − | 6.06218i | −0.396015 | − | 0.228639i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.5000 | + | 7.79423i | 0.508439 | + | 0.293548i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.5000 | − | 7.79423i | 0.846200 | − | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.5000 | − | 26.8468i | −0.582115 | − | 1.00825i | −0.995228 | − | 0.0975728i | \(-0.968892\pi\) |
0.413114 | − | 0.910679i | \(-0.364441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.50000 | − | 2.59808i | −0.0562544 | − | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.00000 | 0.337053 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.0000 | −0.672222 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.50000 | − | 12.9904i | −0.279703 | − | 0.484459i | 0.691608 | − | 0.722273i | \(-0.256903\pi\) |
−0.971311 | + | 0.237814i | \(0.923569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5000 | − | 2.59808i | −0.502766 | − | 0.0967574i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.50000 | − | 2.59808i | 0.0557856 | − | 0.0966235i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.2487i | 0.899335i | 0.893196 | + | 0.449667i | \(0.148458\pi\) | ||||
−0.893196 | + | 0.449667i | \(0.851542\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.00000 | + | 10.3923i | −0.221918 | + | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.5000 | − | 14.7224i | 0.941864 | − | 0.543785i | 0.0513199 | − | 0.998682i | \(-0.483657\pi\) |
0.890544 | + | 0.454897i | \(0.150324\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −22.5000 | − | 28.5788i | −0.829925 | − | 1.05415i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.5000 | + | 12.9904i | −0.828798 | + | 0.478507i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.50000 | + | 14.7224i | −0.312678 | + | 0.541573i | −0.978941 | − | 0.204143i | \(-0.934559\pi\) |
0.666264 | + | 0.745716i | \(0.267893\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 51.9615i | 1.90628i | 0.302524 | + | 0.953142i | \(0.402171\pi\) | ||||
−0.302524 | + | 0.953142i | \(0.597829\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5000 | + | 7.79423i | 0.494602 | + | 0.285558i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36.0000 | 1.31717 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 40.5000 | + | 7.79423i | 1.47984 | + | 0.284795i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.5000 | + | 25.1147i | 0.529113 | + | 0.916450i | 0.999424 | + | 0.0339490i | \(0.0108084\pi\) |
−0.470311 | + | 0.882501i | \(0.655858\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 41.5692i | 1.51487i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.0000 | 1.41936 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 46.7654i | 1.69748i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5000 | + | 18.1865i | 0.380625 | + | 0.659261i | 0.991152 | − | 0.132734i | \(-0.0423756\pi\) |
−0.610527 | + | 0.791995i | \(0.709042\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.5000 | − | 14.7224i | 1.53860 | − | 0.532988i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −27.0000 | −0.976187 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 34.6410i | − | 1.24919i | −0.780950 | − | 0.624593i | \(-0.785265\pi\) | ||
0.780950 | − | 0.624593i | \(-0.214735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.5000 | + | 23.3827i | −1.45857 | + | 0.842107i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.5000 | + | 33.7750i | −0.701366 | + | 1.21480i | 0.266621 | + | 0.963802i | \(0.414093\pi\) |
−0.967987 | + | 0.251000i | \(0.919240\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | − | 3.46410i | 0.215526 | − | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −31.5000 | − | 6.06218i | −1.13006 | − | 0.217479i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.00000 | − | 5.19615i | 0.322458 | − | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0000 | + | 46.7654i | −0.966136 | + | 1.67340i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.5885i | 0.556376i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.50000 | − | 0.866025i | −0.0534692 | − | 0.0308705i | 0.473027 | − | 0.881048i | \(-0.343161\pi\) |
−0.526496 | + | 0.850177i | \(0.676495\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.50000 | − | 7.79423i | 0.160204 | − | 0.277482i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.0000 | − | 41.5692i | 1.28001 | − | 1.47803i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27.0000 | 0.957591 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.0000 | 0.637593 | 0.318796 | − | 0.947823i | \(-0.396721\pi\) | ||||
0.318796 | + | 0.947823i | \(0.396721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.00000 | 0.318397 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.5000 | − | 23.3827i | −0.476999 | − | 0.826187i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −31.5000 | − | 54.5596i | −1.11161 | − | 1.92537i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.5000 | + | 38.9711i | 0.475812 | + | 1.37355i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.5000 | − | 18.1865i | −1.10885 | − | 0.640196i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.5000 | − | 12.9904i | −0.791058 | − | 0.456717i | 0.0492770 | − | 0.998785i | \(-0.484308\pi\) |
−0.840335 | + | 0.542068i | \(0.817642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 51.9615i | − | 1.82462i | −0.409505 | − | 0.912308i | \(-0.634299\pi\) | ||
0.409505 | − | 0.912308i | \(-0.365701\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.5000 | − | 33.7750i | −0.683895 | − | 1.18454i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.50000 | − | 2.59808i | 0.0525427 | − | 0.0910066i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.00000 | − | 3.46410i | 0.209913 | − | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.50000 | + | 2.59808i | −0.157051 | + | 0.0906735i | −0.576466 | − | 0.817121i | \(-0.695569\pi\) |
0.419415 | + | 0.907795i | \(0.362235\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.50000 | − | 6.06218i | 0.122002 | − | 0.211314i | −0.798555 | − | 0.601922i | \(-0.794402\pi\) |
0.920557 | + | 0.390608i | \(0.127735\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.0000 | + | 31.1769i | 0.626680 | + | 1.08544i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 10.3923i | − | 0.361376i | −0.983540 | − | 0.180688i | \(-0.942168\pi\) | ||
0.983540 | − | 0.180688i | \(-0.0578324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.50000 | + | 0.866025i | 0.0520972 | + | 0.0300783i | 0.525822 | − | 0.850594i | \(-0.323758\pi\) |
−0.473725 | + | 0.880673i | \(0.657091\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.5000 | − | 11.2583i | −0.676448 | − | 0.390547i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.5000 | − | 7.79423i | −0.675635 | − | 0.270054i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.0000 | − | 31.1769i | −0.622916 | − | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.50000 | − | 7.79423i | 0.155543 | − | 0.269408i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 36.0000 | 1.23991 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.5000 | − | 33.7750i | −0.670820 | − | 1.16190i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.00000 | + | 41.5692i | −0.274883 | + | 1.42834i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.50000 | + | 12.9904i | −0.257399 | + | 0.445829i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.5000 | + | 18.1865i | 1.07981 | + | 0.623426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.8564i | 0.474434i | 0.971457 | + | 0.237217i | \(0.0762353\pi\) | ||||
−0.971457 | + | 0.237217i | \(0.923765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.5000 | + | 7.79423i | 0.461690 | + | 0.266557i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.5000 | − | 28.5788i | 0.563629 | − | 0.976235i | −0.433546 | − | 0.901131i | \(-0.642738\pi\) |
0.997176 | − | 0.0751033i | \(-0.0239287\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.5000 | + | 19.9186i | −1.17712 | + | 0.679613i | −0.955348 | − | 0.295484i | \(-0.904519\pi\) |
−0.221777 | + | 0.975097i | \(0.571186\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.0000 | − | 20.7846i | 0.613438 | − | 0.708338i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.50000 | + | 2.59808i | −0.153182 | + | 0.0884395i | −0.574632 | − | 0.818412i | \(-0.694855\pi\) |
0.421450 | + | 0.906852i | \(0.361521\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.5000 | − | 23.3827i | 0.459014 | − | 0.795035i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.0000 | − | 6.92820i | 0.407541 | − | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.19615i | 0.176267i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 20.7846i | − | 0.703452i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.00000 | − | 5.19615i | −0.202837 | − | 0.175662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.50000 | − | 9.52628i | −0.185722 | − | 0.321680i | 0.758098 | − | 0.652141i | \(-0.226129\pi\) |
−0.943820 | + | 0.330461i | \(0.892796\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 10.3923i | − | 0.350524i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.5885i | 0.524000i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.50000 | − | 2.59808i | −0.0503651 | − | 0.0872349i | 0.839744 | − | 0.542983i | \(-0.182705\pi\) |
−0.890109 | + | 0.455748i | \(0.849372\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | + | 13.8564i | 0.536623 | + | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 40.5000 | + | 23.3827i | 1.35680 | + | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.50000 | − | 2.59808i | −0.150587 | − | 0.0869413i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 15.5885i | − | 0.521065i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.5000 | − | 7.79423i | 0.449750 | − | 0.259663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.0000 | − | 13.8564i | 0.399335 | − | 0.461112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.0000 | + | 10.3923i | −0.598340 | + | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.5000 | + | 32.0429i | −0.614282 | + | 1.06397i | 0.376228 | + | 0.926527i | \(0.377221\pi\) |
−0.990510 | + | 0.137441i | \(0.956112\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.5000 | + | 23.3827i | −0.447767 | + | 0.775555i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3923i | 0.344312i | 0.985070 | + | 0.172156i | \(0.0550734\pi\) | ||||
−0.985070 | + | 0.172156i | \(0.944927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.0000 | − | 31.1769i | −1.78714 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.5000 | − | 54.5596i | 1.04136 | − | 1.80368i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.50000 | + | 23.3827i | −0.148603 | + | 0.772164i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.50000 | − | 16.4545i | −0.313376 | − | 0.542783i | 0.665715 | − | 0.746206i | \(-0.268127\pi\) |
−0.979091 | + | 0.203423i | \(0.934793\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.0000 | 0.988534 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.0000 | 0.920634 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.5000 | − | 7.79423i | 0.443398 | − | 0.255996i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.5000 | − | 33.7750i | −0.639774 | − | 1.10812i | −0.985482 | − | 0.169779i | \(-0.945695\pi\) |
0.345708 | − | 0.938342i | \(-0.387639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.50000 | + | 9.52628i | 0.245803 | + | 0.312211i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.5000 | − | 12.9904i | −0.736617 | − | 0.425286i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 40.5000 | + | 23.3827i | 1.32449 | + | 0.764696i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 41.5692i | − | 1.35801i | −0.734135 | − | 0.679004i | \(-0.762412\pi\) | ||
0.734135 | − | 0.679004i | \(-0.237588\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.5000 | + | 18.1865i | 0.342655 | + | 0.593495i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.5000 | − | 18.1865i | 0.342290 | − | 0.592864i | −0.642567 | − | 0.766229i | \(-0.722131\pi\) |
0.984858 | + | 0.173365i | \(0.0554641\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.0000 | + | 15.5885i | −0.879241 | + | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 40.5000 | + | 7.79423i | 1.31747 | + | 0.253546i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.5000 | + | 23.3827i | −1.31607 | + | 0.759835i | −0.983094 | − | 0.183099i | \(-0.941387\pi\) |
−0.332979 | + | 0.942934i | \(0.608054\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.5000 | + | 38.9711i | 0.729612 | + | 1.26373i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 20.7846i | − | 0.673280i | −0.941634 | − | 0.336640i | \(-0.890710\pi\) | ||
0.941634 | − | 0.336640i | \(-0.109290\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.5000 | − | 23.3827i | −1.31055 | − | 0.756646i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.50000 | − | 12.9904i | −0.145313 | − | 0.419481i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −40.5000 | + | 23.3827i | −1.30509 | + | 0.753497i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.0000 | −0.482867 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.0000 | −1.28631 | −0.643157 | − | 0.765735i | \(-0.722376\pi\) | ||||
−0.643157 | + | 0.765735i | \(0.722376\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.00000 | 0.289122 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.5000 | + | 49.3634i | 0.914609 | + | 1.58415i | 0.807473 | + | 0.589904i | \(0.200834\pi\) |
0.107135 | + | 0.994244i | \(0.465832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.0000 | − | 20.7846i | 0.577054 | − | 0.666324i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.5000 | + | 18.1865i | 1.00777 | + | 0.581839i | 0.910539 | − | 0.413423i | \(-0.135667\pi\) |
0.0972351 | + | 0.995261i | \(0.469000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.7654i | 1.49463i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.5000 | + | 44.1673i | −0.814152 | + | 1.41015i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.50000 | − | 2.59808i | 0.0478426 | − | 0.0828658i | −0.841112 | − | 0.540860i | \(-0.818099\pi\) |
0.888955 | + | 0.457995i | \(0.151432\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.5000 | − | 2.59808i | −0.429710 | − | 0.0826977i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.0000 | + | 10.3923i | −0.572367 | + | 0.330456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.5000 | + | 21.6506i | −0.397076 | + | 0.687755i | −0.993364 | − | 0.115015i | \(-0.963308\pi\) |
0.596288 | + | 0.802771i | \(0.296642\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −46.5000 | + | 26.8468i | −1.47563 | + | 0.851957i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.19615i | 0.164729i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.5000 | + | 11.2583i | 0.617571 | + | 0.356555i | 0.775923 | − | 0.630828i | \(-0.217285\pi\) |
−0.158352 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 31.5000 | − | 18.1865i | 0.996616 | − | 0.575396i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))