Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(249,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.bh (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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 849.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.849 |
Dual form | 1400.2.bh.a.249.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | −0.228714 | − | 0.973494i | \(-0.573452\pi\) |
0.728714 | + | 0.684819i | \(0.240119\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.73205 | − | 2.00000i | −0.654654 | − | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 1.73205i | −0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000i | 1.66410i | 0.554700 | + | 0.832050i | \(0.312833\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.33013 | + | 2.50000i | −1.05021 | + | 0.606339i | −0.922708 | − | 0.385499i | \(-0.874029\pi\) |
−0.127502 | + | 0.991838i | \(0.540696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.50000 | − | 0.866025i | −0.545545 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.06218 | − | 3.50000i | −1.26405 | − | 0.729800i | −0.290196 | − | 0.956967i | \(-0.593720\pi\) |
−0.973856 | + | 0.227167i | \(0.927054\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50000 | + | 4.33013i | 0.449013 | + | 0.777714i | 0.998322 | − | 0.0579057i | \(-0.0184423\pi\) |
−0.549309 | + | 0.835619i | \(0.685109\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.59808 | − | 1.50000i | −0.452267 | − | 0.261116i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.59808 | − | 1.50000i | −0.427121 | − | 0.246598i | 0.270998 | − | 0.962580i | \(-0.412646\pi\) |
−0.698119 | + | 0.715981i | \(0.745980\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.00000 | + | 5.19615i | 0.480384 | + | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.33013 | − | 2.50000i | −0.631614 | − | 0.364662i | 0.149763 | − | 0.988722i | \(-0.452149\pi\) |
−0.781377 | + | 0.624059i | \(0.785482\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.50000 | + | 4.33013i | −0.350070 | + | 0.606339i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.866025 | − | 0.500000i | 0.118958 | − | 0.0686803i | −0.439340 | − | 0.898321i | \(-0.644788\pi\) |
0.558298 | + | 0.829640i | \(0.311454\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.00000i | − | 0.132453i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.50000 | + | 12.9904i | 0.976417 | + | 1.69120i | 0.675178 | + | 0.737655i | \(0.264067\pi\) |
0.301239 | + | 0.953549i | \(0.402600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.50000 | − | 4.33013i | 0.320092 | − | 0.554416i | −0.660415 | − | 0.750901i | \(-0.729619\pi\) |
0.980507 | + | 0.196485i | \(0.0629528\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.19615 | − | 1.00000i | 0.654654 | − | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.79423 | + | 4.50000i | −0.952217 | + | 0.549762i | −0.893769 | − | 0.448528i | \(-0.851948\pi\) |
−0.0584478 | + | 0.998290i | \(0.518615\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.00000 | −0.842701 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.06218 | + | 3.50000i | −0.709524 | + | 0.409644i | −0.810885 | − | 0.585206i | \(-0.801014\pi\) |
0.101361 | + | 0.994850i | \(0.467680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.59808 | + | 7.50000i | −0.296078 | + | 0.854704i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | − | 0.866025i | 0.0562544 | − | 0.0974355i | −0.836527 | − | 0.547926i | \(-0.815418\pi\) |
0.892781 | + | 0.450490i | \(0.148751\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.0000i | − | 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.73205 | + | 1.00000i | −0.185695 | + | 0.107211i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.50000 | − | 6.06218i | 0.370999 | − | 0.642590i | −0.618720 | − | 0.785611i | \(-0.712349\pi\) |
0.989720 | + | 0.143022i | \(0.0456819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | − | 10.3923i | 1.25794 | − | 1.08941i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.33013 | + | 2.50000i | 0.449013 | + | 0.259238i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.00000i | − | 0.203069i | −0.994832 | − | 0.101535i | \(-0.967625\pi\) | ||
0.994832 | − | 0.101535i | \(-0.0323753\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.50000 | − | 2.59808i | −0.149256 | − | 0.258518i | 0.781697 | − | 0.623658i | \(-0.214354\pi\) |
−0.930953 | + | 0.365140i | \(0.881021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.9904 | − | 7.50000i | −1.27998 | − | 0.738997i | −0.303136 | − | 0.952947i | \(-0.598034\pi\) |
−0.976845 | + | 0.213950i | \(0.931367\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.79423 | − | 4.50000i | −0.753497 | − | 0.435031i | 0.0734594 | − | 0.997298i | \(-0.476596\pi\) |
−0.826956 | + | 0.562267i | \(0.809929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.50000 | − | 4.33013i | −0.239457 | − | 0.414751i | 0.721102 | − | 0.692829i | \(-0.243636\pi\) |
−0.960558 | + | 0.278078i | \(0.910303\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | −0.284747 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000i | 1.69330i | 0.532152 | + | 0.846649i | \(0.321383\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.3923 | − | 6.00000i | −0.960769 | − | 0.554700i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.5000 | + | 4.33013i | 1.14587 | + | 0.396942i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.73205 | + | 1.00000i | −0.156174 | + | 0.0901670i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000i | 0.709885i | 0.934888 | + | 0.354943i | \(0.115500\pi\) | ||||
−0.934888 | + | 0.354943i | \(0.884500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.00000 | + | 3.46410i | 0.176090 | + | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.50000 | + | 4.33013i | −0.218426 | + | 0.378325i | −0.954327 | − | 0.298764i | \(-0.903426\pi\) |
0.735901 | + | 0.677089i | \(0.236759\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.59808 | + | 0.500000i | −0.225282 | + | 0.0433555i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.52628 | − | 5.50000i | 0.813885 | − | 0.469897i | −0.0344182 | − | 0.999408i | \(-0.510958\pi\) |
0.848303 | + | 0.529511i | \(0.177624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.00000 | −0.421076 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.5885 | − | 9.00000i | 1.30357 | − | 0.752618i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.59808 | + | 6.50000i | 0.214286 | + | 0.536111i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.50000 | + | 14.7224i | −0.696347 | + | 1.20611i | 0.273377 | + | 0.961907i | \(0.411859\pi\) |
−0.969724 | + | 0.244202i | \(0.921474\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.50000 | + | 4.33013i | 0.203447 | + | 0.352381i | 0.949637 | − | 0.313353i | \(-0.101452\pi\) |
−0.746190 | + | 0.665733i | \(0.768119\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 10.0000i | − | 0.808452i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.79423 | + | 4.50000i | −0.622047 | + | 0.359139i | −0.777666 | − | 0.628678i | \(-0.783596\pi\) |
0.155618 | + | 0.987817i | \(0.450263\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.500000 | − | 0.866025i | 0.0396526 | − | 0.0686803i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.50000 | + | 18.1865i | 0.275839 | + | 1.43330i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2583 | + | 6.50000i | 0.881820 | + | 0.509119i | 0.871258 | − | 0.490825i | \(-0.163305\pi\) |
0.0105623 | + | 0.999944i | \(0.496638\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.0000i | − | 0.928588i | −0.885681 | − | 0.464294i | \(-0.846308\pi\) | ||
0.885681 | − | 0.464294i | \(-0.153692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | + | 1.73205i | 0.0764719 | + | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.2583 | − | 6.50000i | −0.855955 | − | 0.494186i | 0.00670064 | − | 0.999978i | \(-0.497867\pi\) |
−0.862656 | + | 0.505792i | \(0.831200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.9904 | + | 7.50000i | 0.976417 | + | 0.563735i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.50000 | − | 11.2583i | −0.485833 | − | 0.841487i | 0.514035 | − | 0.857769i | \(-0.328150\pi\) |
−0.999867 | + | 0.0162823i | \(0.994817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 5.00000i | − | 0.369611i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9904 | + | 7.50000i | 0.949951 | + | 0.548454i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.0000 | − | 8.66025i | 0.727393 | − | 0.629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.50000 | − | 9.52628i | 0.397966 | − | 0.689297i | −0.595509 | − | 0.803349i | \(-0.703050\pi\) |
0.993475 | + | 0.114051i | \(0.0363829\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.59808 | + | 1.50000i | −0.187014 | + | 0.107972i | −0.590584 | − | 0.806976i | \(-0.701102\pi\) |
0.403570 | + | 0.914949i | \(0.367769\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.00000i | − | 0.427482i | −0.976890 | − | 0.213741i | \(-0.931435\pi\) | ||
0.976890 | − | 0.213741i | \(-0.0685649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.50000 | − | 11.2583i | −0.460773 | − | 0.798082i | 0.538227 | − | 0.842800i | \(-0.319094\pi\) |
−0.999000 | + | 0.0447181i | \(0.985761\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.50000 | + | 7.79423i | −0.317406 | + | 0.549762i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.46410 | + | 4.00000i | 0.243132 | + | 0.280745i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.1244 | − | 7.00000i | 0.842701 | − | 0.486534i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.33013 | − | 12.5000i | 0.293948 | − | 0.848555i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.50000 | + | 6.06218i | −0.236508 | + | 0.409644i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0000 | − | 25.9808i | −1.00901 | − | 1.74766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000i | 1.60716i | 0.595198 | + | 0.803579i | \(0.297074\pi\) | ||||
−0.595198 | + | 0.803579i | \(0.702926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.52628 | − | 5.50000i | 0.632281 | − | 0.365048i | −0.149354 | − | 0.988784i | \(-0.547719\pi\) |
0.781635 | + | 0.623736i | \(0.214386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.5000 | − | 19.9186i | 0.759941 | − | 1.31626i | −0.182939 | − | 0.983124i | \(-0.558561\pi\) |
0.942880 | − | 0.333133i | \(-0.108106\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.50000 | + | 7.79423i | 0.0986928 | + | 0.512823i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.52628 | + | 5.50000i | 0.624087 | + | 0.360317i | 0.778459 | − | 0.627696i | \(-0.216002\pi\) |
−0.154371 | + | 0.988013i | \(0.549335\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.00000i | − | 0.0649570i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.50000 | + | 14.7224i | 0.547533 | + | 0.948355i | 0.998443 | + | 0.0557856i | \(0.0177663\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.8564 | − | 8.00000i | −0.888889 | − | 0.513200i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.19615 | + | 3.00000i | 0.330623 | + | 0.190885i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0000 | 1.00991 | 0.504956 | − | 0.863145i | \(-0.331509\pi\) | ||||
0.504956 | + | 0.863145i | \(0.331509\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.0000i | 1.32026i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.1865 | + | 10.5000i | 1.13444 | + | 0.654972i | 0.945049 | − | 0.326929i | \(-0.106014\pi\) |
0.189396 | + | 0.981901i | \(0.439347\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.50000 | + | 7.79423i | 0.0932055 | + | 0.484310i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | − | 3.46410i | 0.123797 | − | 0.214423i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.79423 | − | 4.50000i | 0.480613 | − | 0.277482i | −0.240059 | − | 0.970758i | \(-0.577167\pi\) |
0.720672 | + | 0.693276i | \(0.243833\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 7.00000i | − | 0.428393i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.50000 | − | 7.79423i | −0.274370 | − | 0.475223i | 0.695606 | − | 0.718423i | \(-0.255136\pi\) |
−0.969976 | + | 0.243201i | \(0.921803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.50000 | − | 6.06218i | 0.212610 | − | 0.368251i | −0.739921 | − | 0.672694i | \(-0.765137\pi\) |
0.952531 | + | 0.304443i | \(0.0984703\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.19615 | − | 15.0000i | 0.314485 | − | 0.907841i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.7224 | + | 8.50000i | −0.884585 | + | 0.510716i | −0.872167 | − | 0.489207i | \(-0.837286\pi\) |
−0.0124177 | + | 0.999923i | \(0.503953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.0000 | −0.598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.2583 | − | 6.50000i | 0.669238 | − | 0.386385i | −0.126550 | − | 0.991960i | \(-0.540390\pi\) |
0.795788 | + | 0.605575i | \(0.207057\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.46410 | + | 4.00000i | 0.204479 | + | 0.236113i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.00000 | − | 1.73205i | −0.0586210 | − | 0.101535i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.00000i | − | 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.9904 | − | 7.50000i | 0.753778 | − | 0.435194i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.0000 | − | 36.3731i | 1.21446 | − | 2.10351i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | − | 6.92820i | 0.461112 | − | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.59808 | − | 1.50000i | −0.149256 | − | 0.0861727i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000i | 0.228292i | 0.993464 | + | 0.114146i | \(0.0364132\pi\) | ||||
−0.993464 | + | 0.114146i | \(0.963587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0000 | −0.853320 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.50000 | − | 12.9904i | −0.425286 | − | 0.736617i | 0.571161 | − | 0.820838i | \(-0.306493\pi\) |
−0.996447 | + | 0.0842210i | \(0.973160\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.866025 | − | 0.500000i | −0.0489506 | − | 0.0282617i | 0.475325 | − | 0.879810i | \(-0.342331\pi\) |
−0.524276 | + | 0.851549i | \(0.675664\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.59808 | − | 1.50000i | −0.145922 | − | 0.0842484i | 0.425261 | − | 0.905071i | \(-0.360182\pi\) |
−0.571184 | + | 0.820822i | \(0.693516\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000 | + | 5.19615i | 0.167968 | + | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.00000 | −0.502331 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.00000i | 0.278207i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.33013 | − | 2.50000i | −0.239457 | − | 0.138250i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.50000 | + | 12.9904i | 0.137829 | + | 0.716183i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5000 | + | 25.1147i | −0.796992 | + | 1.38043i | 0.124574 | + | 0.992210i | \(0.460243\pi\) |
−0.921567 | + | 0.388221i | \(0.873090\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.19615 | − | 3.00000i | 0.284747 | − | 0.164399i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.0000i | − | 0.544735i | −0.962193 | − | 0.272367i | \(-0.912193\pi\) | ||
0.962193 | − | 0.272367i | \(-0.0878066\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.00000 | + | 15.5885i | 0.488813 | + | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.50000 | − | 12.9904i | 0.406148 | − | 0.703469i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.9904 | − | 7.50000i | 0.697360 | − | 0.402621i | −0.109003 | − | 0.994041i | \(-0.534766\pi\) |
0.806363 | + | 0.591420i | \(0.201433\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −30.0000 | −1.60128 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.59808 | + | 1.50000i | −0.138282 | + | 0.0798369i | −0.567545 | − | 0.823343i | \(-0.692107\pi\) |
0.429263 | + | 0.903179i | \(0.358773\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.9904 | − | 2.50000i | 0.687524 | − | 0.132314i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.5000 | − | 18.1865i | 0.554169 | − | 0.959849i | −0.443799 | − | 0.896126i | \(-0.646370\pi\) |
0.997968 | − | 0.0637221i | \(-0.0202971\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.00000i | − | 0.104973i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.9186 | − | 11.5000i | 1.03974 | − | 0.600295i | 0.119982 | − | 0.992776i | \(-0.461716\pi\) |
0.919760 | + | 0.392481i | \(0.128383\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.00000 | − | 3.46410i | 0.104116 | − | 0.180334i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.50000 | − | 0.866025i | −0.129794 | − | 0.0449618i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.52628 | + | 5.50000i | 0.493252 | + | 0.284779i | 0.725923 | − | 0.687776i | \(-0.241413\pi\) |
−0.232671 | + | 0.972556i | \(0.574746\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0000 | −1.23280 | −0.616399 | − | 0.787434i | \(-0.711409\pi\) | ||||
−0.616399 | + | 0.787434i | \(0.711409\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.00000 | + | 6.92820i | 0.204926 | + | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.59808 | − | 1.50000i | −0.132755 | − | 0.0766464i | 0.432151 | − | 0.901801i | \(-0.357755\pi\) |
−0.564907 | + | 0.825155i | \(0.691088\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.92820 | − | 4.00000i | −0.352180 | − | 0.203331i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.5000 | − | 25.1147i | −0.735179 | − | 1.27337i | −0.954645 | − | 0.297747i | \(-0.903765\pi\) |
0.219465 | − | 0.975620i | \(-0.429569\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35.0000 | 1.77003 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.00000i | 0.252217i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.7224 | + | 8.50000i | 0.738898 | + | 0.426603i | 0.821668 | − | 0.569966i | \(-0.193044\pi\) |
−0.0827707 | + | 0.996569i | \(0.526377\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.00000 | + | 1.73205i | −0.100125 | + | 0.0867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5000 | + | 23.3827i | −0.674158 | + | 1.16768i | 0.302556 | + | 0.953131i | \(0.402160\pi\) |
−0.976714 | + | 0.214544i | \(0.931173\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.9808 | + | 15.0000i | −1.29419 | + | 0.747203i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.00000i | 0.446113i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.5000 | + | 23.3827i | 0.667532 | + | 1.15620i | 0.978592 | + | 0.205809i | \(0.0659826\pi\) |
−0.311060 | + | 0.950390i | \(0.600684\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.50000 | − | 9.52628i | 0.271295 | − | 0.469897i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.9904 | − | 37.5000i | 0.639215 | − | 1.84525i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.3923 | − | 6.00000i | 0.508913 | − | 0.293821i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.0000 | −0.977064 | −0.488532 | − | 0.872546i | \(-0.662467\pi\) | ||||
−0.488532 | + | 0.872546i | \(0.662467\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0000 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.66025 | − | 5.00000i | 0.421076 | − | 0.243108i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.9904 | + | 2.50000i | −0.628649 | + | 0.120983i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.00000 | − | 15.5885i | 0.434524 | − | 0.752618i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.50000 | − | 2.59808i | −0.0722525 | − | 0.125145i | 0.827636 | − | 0.561266i | \(-0.189685\pi\) |
−0.899888 | + | 0.436121i | \(0.856352\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000i | 0.0961139i | 0.998845 | + | 0.0480569i | \(0.0153029\pi\) | ||||
−0.998845 | + | 0.0480569i | \(0.984697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.06218 | + | 3.50000i | −0.289993 | + | 0.167428i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5000 | − | 18.1865i | 0.501138 | − | 0.867996i | −0.498861 | − | 0.866682i | \(-0.666248\pi\) |
0.999999 | − | 0.00131415i | \(-0.000418308\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.0000 | − | 8.66025i | −0.523810 | − | 0.412393i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.8468 | − | 15.5000i | −1.27553 | − | 0.736427i | −0.299506 | − | 0.954094i | \(-0.596822\pi\) |
−0.976023 | + | 0.217667i | \(0.930155\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.0000i | 0.804072i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.0000 | 1.22702 | 0.613508 | − | 0.789689i | \(-0.289758\pi\) | ||||
0.613508 | + | 0.789689i | \(0.289758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.00000 | + | 5.19615i | 0.141264 | + | 0.244677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.33013 | + | 2.50000i | 0.203447 | + | 0.117460i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.7224 | + | 8.50000i | 0.688686 | + | 0.397613i | 0.803120 | − | 0.595818i | \(-0.203172\pi\) |
−0.114433 | + | 0.993431i | \(0.536505\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.5000 | − | 21.6506i | −0.583450 | − | 1.01057i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000i | 0.743583i | 0.928316 | + | 0.371792i | \(0.121256\pi\) | ||||
−0.928316 | + | 0.371792i | \(0.878744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.59808 | + | 1.50000i | 0.120225 | + | 0.0694117i | 0.558906 | − | 0.829231i | \(-0.311221\pi\) |
−0.438682 | + | 0.898642i | \(0.644554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.5000 | + | 7.79423i | 1.03895 | + | 0.359904i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.50000 | + | 7.79423i | −0.207349 | + | 0.359139i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.3923 | − | 6.00000i | 0.477839 | − | 0.275880i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000i | 0.0915737i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.5000 | + | 26.8468i | 0.708213 | + | 1.22666i | 0.965519 | + | 0.260331i | \(0.0838317\pi\) |
−0.257306 | + | 0.966330i | \(0.582835\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.00000 | − | 15.5885i | 0.410365 | − | 0.710772i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.1244 | + | 14.0000i | 0.551677 | + | 0.637022i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.06218 | − | 3.50000i | 0.274703 | − | 0.158600i | −0.356320 | − | 0.934364i | \(-0.615969\pi\) |
0.631023 | + | 0.775764i | \(0.282635\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.0000 | 0.587880 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.0000 | −1.08310 | −0.541552 | − | 0.840667i | \(-0.682163\pi\) | ||||
−0.541552 | + | 0.840667i | \(0.682163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.66025 | − | 5.00000i | 0.390038 | − | 0.225189i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.5000 | + | 30.3109i | −0.783408 | + | 1.35690i | 0.146538 | + | 0.989205i | \(0.453187\pi\) |
−0.929946 | + | 0.367697i | \(0.880146\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | − | 10.3923i | −0.268060 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.0000i | 1.42681i | 0.700752 | + | 0.713405i | \(0.252848\pi\) | ||||
−0.700752 | + | 0.713405i | \(0.747152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.9186 | + | 11.5000i | −0.884615 | + | 0.510733i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.50000 | + | 7.79423i | −0.199459 | + | 0.345473i | −0.948353 | − | 0.317217i | \(-0.897252\pi\) |
0.748894 | + | 0.662690i | \(0.230585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.5000 | + | 6.06218i | 0.774154 | + | 0.268175i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.33013 | + | 2.50000i | 0.191180 | + | 0.110378i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.0000i | 0.659699i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.0000 | −0.570637 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.5000 | + | 28.5788i | 0.722878 | + | 1.25206i | 0.959841 | + | 0.280543i | \(0.0905145\pi\) |
−0.236963 | + | 0.971519i | \(0.576152\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.06218 | − | 3.50000i | −0.265081 | − | 0.153044i | 0.361569 | − | 0.932345i | \(-0.382241\pi\) |
−0.626650 | + | 0.779301i | \(0.715574\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.6506 | − | 12.5000i | −0.943116 | − | 0.544509i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | + | 22.5167i | 0.565217 | + | 0.978985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30.0000 | −1.30189 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 12.0000i | − | 0.519778i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.2583 | − | 6.50000i | −0.485833 | − | 0.280496i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.5000 | − | 7.79423i | 0.839924 | − | 0.335721i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5000 | − | 35.5070i | 0.881364 | − | 1.52657i | 0.0315385 | − | 0.999503i | \(-0.489959\pi\) |
0.849825 | − | 0.527064i | \(-0.176707\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.66025 | + | 5.00000i | −0.371647 | + | 0.214571i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.00000i | − | 0.342055i | −0.985266 | − | 0.171028i | \(-0.945291\pi\) | ||
0.985266 | − | 0.171028i | \(-0.0547087\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.00000 | + | 8.66025i | 0.213395 | + | 0.369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.00000 | + | 1.73205i | −0.0426014 | + | 0.0737878i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.59808 | + | 0.500000i | −0.110481 | + | 0.0212622i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.33013 | + | 2.50000i | −0.183473 | + | 0.105928i | −0.588924 | − | 0.808189i | \(-0.700448\pi\) |
0.405450 | + | 0.914117i | \(0.367115\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.0000 | −1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.0000 | 0.633300 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.5070 | − | 20.5000i | 1.49644 | − | 0.863972i | 0.496452 | − | 0.868064i | \(-0.334636\pi\) |
0.999992 | + | 0.00409232i | \(0.00130263\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.866025 | + | 2.50000i | −0.0363696 | + | 0.104990i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.5000 | + | 28.5788i | −0.691716 | + | 1.19809i | 0.279559 | + | 0.960128i | \(0.409812\pi\) |
−0.971275 | + | 0.237959i | \(0.923522\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.50000 | + | 11.2583i | 0.272017 | + | 0.471146i | 0.969378 | − | 0.245573i | \(-0.0789761\pi\) |
−0.697362 | + | 0.716720i | \(0.745643\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 11.0000i | − | 0.459532i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.5788 | + | 16.5000i | −1.18975 | + | 0.686904i | −0.958250 | − | 0.285930i | \(-0.907697\pi\) |
−0.231502 | + | 0.972834i | \(0.574364\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.50000 | + | 2.59808i | −0.0623379 | + | 0.107972i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | + | 20.7846i | −0.995688 | + | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.59808 | − | 1.50000i | −0.107601 | − | 0.0621237i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 20.0000i | − | 0.825488i | −0.910847 | − | 0.412744i | \(-0.864570\pi\) | ||
0.910847 | − | 0.412744i | \(-0.135430\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.00000 | 0.206021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00000 | − | 5.19615i | −0.123404 | − | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.9711 | − | 22.5000i | −1.60035 | − | 0.923964i | −0.991416 | − | 0.130746i | \(-0.958263\pi\) |
−0.608937 | − | 0.793219i | \(-0.708404\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.2583 | − | 6.50000i | −0.460773 | − | 0.266027i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.50000 | − | 14.7224i | −0.347301 | − | 0.601542i | 0.638468 | − | 0.769648i | \(-0.279568\pi\) |
−0.985769 | + | 0.168106i | \(0.946235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 18.0000i | − | 0.733017i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2583 | − | 6.50000i | −0.456962 | − | 0.263827i | 0.253804 | − | 0.967256i | \(-0.418318\pi\) |
−0.710766 | + | 0.703429i | \(0.751651\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.00000 | + | 1.73205i | 0.202610 | + | 0.0701862i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0000 | − | 25.9808i | 0.606835 | − | 1.05107i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.2391 | + | 21.5000i | −1.50407 | + | 0.868377i | −0.504084 | + | 0.863655i | \(0.668170\pi\) |
−0.999989 | + | 0.00472215i | \(0.998497\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.0000i | 1.20775i | 0.797077 | + | 0.603877i | \(0.206378\pi\) | ||||
−0.797077 | + | 0.603877i | \(0.793622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.50000 | − | 7.79423i | −0.180870 | − | 0.313276i | 0.761307 | − | 0.648392i | \(-0.224558\pi\) |
−0.942177 | + | 0.335115i | \(0.891225\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.5000 | − | 30.3109i | 0.702251 | − | 1.21633i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.1865 | + | 3.50000i | −0.728628 | + | 0.140225i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.59808 | + | 1.50000i | −0.103757 | + | 0.0599042i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.0000 | 0.598089 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.46410 | + | 2.00000i | −0.137686 | + | 0.0794929i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −41.5692 | − | 6.00000i | −1.64703 | − | 0.237729i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.50000 | + | 14.7224i | 0.335730 | + | 0.581501i | 0.983625 | − | 0.180229i | \(-0.0576838\pi\) |
−0.647895 | + | 0.761730i | \(0.724350\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.0000i | 1.73519i | 0.497271 | + | 0.867595i | \(0.334335\pi\) | ||||
−0.497271 | + | 0.867595i | \(0.665665\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.9904 | − | 7.50000i | 0.510705 | − | 0.294855i | −0.222419 | − | 0.974951i | \(-0.571395\pi\) |
0.733123 | + | 0.680096i | \(0.238062\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.5000 | − | 38.9711i | 0.883202 | − | 1.52975i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.50000 | − | 12.9904i | −0.0979827 | − | 0.509133i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.3109 | + | 17.5000i | 1.18616 | + | 0.684828i | 0.957431 | − | 0.288663i | \(-0.0932107\pi\) |
0.228726 | + | 0.973491i | \(0.426544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 14.0000i | − | 0.546192i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −44.0000 | −1.71400 | −0.856998 | − | 0.515319i | \(-0.827673\pi\) | ||||
−0.856998 | + | 0.515319i | \(0.827673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.5000 | − | 19.9186i | −0.447298 | − | 0.774743i | 0.550911 | − | 0.834564i | \(-0.314280\pi\) |
−0.998209 | + | 0.0598209i | \(0.980947\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −25.9808 | − | 15.0000i | −1.00901 | − | 0.582552i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.1244 | + | 7.00000i | 0.469457 | + | 0.271041i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.0000 | + | 20.7846i | 0.463947 | + | 0.803579i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0000 | −0.579069 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.0000i | 1.00223i | 0.865382 | + | 0.501113i | \(0.167076\pi\) | ||||
−0.865382 | + | 0.501113i | \(0.832924\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.7750 | − | 19.5000i | −1.29808 | − | 0.749446i | −0.318006 | − | 0.948089i | \(-0.603013\pi\) |
−0.980072 | + | 0.198643i | \(0.936347\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.00000 | + | 3.46410i | −0.153506 | + | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.50000 | − | 9.52628i | 0.210760 | − | 0.365048i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.3827 | + | 13.5000i | −0.894714 | + | 0.516563i | −0.875481 | − | 0.483252i | \(-0.839456\pi\) |
−0.0192323 | + | 0.999815i | \(0.506122\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 23.0000i | − | 0.877505i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.00000 | + | 5.19615i | 0.114291 | + | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.50000 | + | 4.33013i | −0.0951045 | + | 0.164726i | −0.909652 | − | 0.415371i | \(-0.863652\pi\) |
0.814548 | + | 0.580097i | \(0.196985\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.3923 | − | 12.0000i | −0.394771 | − | 0.455842i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.66025 | − | 5.00000i | 0.328031 | − | 0.189389i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.0000 | 0.416058 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −50.0000 | −1.88847 | −0.944237 | − | 0.329267i | \(-0.893198\pi\) | ||||
−0.944237 | + | 0.329267i | \(0.893198\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.59808 | + | 1.50000i | −0.0979883 | + | 0.0565736i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.59808 | + | 7.50000i | −0.0977107 | + | 0.282067i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.5000 | + | 25.1147i | −0.544559 | + | 0.943204i | 0.454076 | + | 0.890963i | \(0.349970\pi\) |
−0.998635 | + | 0.0522406i | \(0.983364\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.00000 | + | 1.73205i | 0.0375029 | + | 0.0649570i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 35.0000i | − | 1.31076i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.3205 | + | 10.0000i | −0.646846 | + | 0.373457i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.5000 | + | 33.7750i | −0.727227 | + | 1.25959i | 0.230823 | + | 0.972996i | \(0.425858\pi\) |
−0.958051 | + | 0.286599i | \(0.907475\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.50000 | + | 38.9711i | 0.279315 | + | 1.45136i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.7224 | + | 8.50000i | 0.547533 | + | 0.316118i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000i | 1.18681i | 0.804902 | + | 0.593407i | \(0.202218\pi\) | ||||
−0.804902 | + | 0.593407i | \(0.797782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.0000 | − | 17.3205i | −0.369863 | − | 0.640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.4545 | + | 9.50000i | 0.607760 | + | 0.350891i | 0.772088 | − | 0.635515i | \(-0.219212\pi\) |
−0.164328 | + | 0.986406i | \(0.552546\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.3827 | + | 13.5000i | 0.861312 | + | 0.497279i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.50000 | − | 4.33013i | −0.0919640 | − | 0.159286i | 0.816373 | − | 0.577524i | \(-0.195981\pi\) |
−0.908337 | + | 0.418238i | \(0.862648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.00000 | 0.220416 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.0000i | 0.586983i | 0.955962 | + | 0.293492i | \(0.0948173\pi\) | ||||
−0.955962 | + | 0.293492i | \(0.905183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.7846 | + | 12.0000i | 0.760469 | + | 0.439057i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.50000 | + | 23.3827i | 0.164426 | + | 0.854385i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.5000 | + | 45.8993i | −0.966999 | + | 1.67489i | −0.262852 | + | 0.964836i | \(0.584663\pi\) |
−0.704146 | + | 0.710055i | \(0.748670\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.8564 | − | 8.00000i | 0.504956 | − | 0.291536i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000i | 0.363456i | 0.983349 | + | 0.181728i | \(0.0581691\pi\) | ||||
−0.983349 | + | 0.181728i | \(0.941831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.5000 | + | 18.1865i | 0.381126 | + | 0.660129i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.50000 | + | 2.59808i | −0.0543750 | + | 0.0941802i | −0.891932 | − | 0.452170i | \(-0.850650\pi\) |
0.837557 | + | 0.546350i | \(0.183983\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.33013 | + | 12.5000i | −0.156761 | + | 0.452530i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −77.9423 | + | 45.0000i | −2.81433 | + | 1.62486i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.0000 | 0.756297 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.4545 | + | 9.50000i | −0.591827 | + | 0.341691i | −0.765819 | − | 0.643056i | \(-0.777666\pi\) |
0.173993 | + | 0.984747i | \(0.444333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.19615 | + | 6.00000i | 0.186411 | + | 0.215249i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.00000 | + | 1.73205i | −0.0358287 | + | 0.0620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 10.0000i | − | 0.357371i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.7224 | + | 8.50000i | −0.524798 | + | 0.302992i | −0.738896 | − | 0.673820i | \(-0.764652\pi\) |
0.214097 | + | 0.976812i | \(0.431319\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.50000 | − | 7.79423i | 0.160204 | − | 0.277482i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.0000 | − | 31.1769i | 1.28001 | − | 1.10852i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.9808 | + | 15.0000i | 0.922604 | + | 0.532666i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.0000i | 0.637593i | 0.947823 | + | 0.318796i | \(0.103279\pi\) | ||||
−0.947823 | + | 0.318796i | \(0.896721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.0000 | 0.884436 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.00000 | + | 12.1244i | 0.247333 | + | 0.428393i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.1865 | + | 10.5000i | 0.641789 | + | 0.370537i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.79423 | − | 4.50000i | −0.274370 | − | 0.158408i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5000 | + | 33.7750i | 0.685583 | + | 1.18747i | 0.973253 | + | 0.229736i | \(0.0737862\pi\) |
−0.287670 | + | 0.957730i | \(0.592880\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.0000 | 0.421377 | 0.210688 | − | 0.977553i | \(-0.432429\pi\) | ||||
0.210688 | + | 0.977553i | \(0.432429\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 7.00000i | − | 0.245501i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.46410 | + | 2.00000i | 0.121194 | + | 0.0699711i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.00000 | + | 31.1769i | 0.209657 | + | 1.08941i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.50000 | − | 7.79423i | 0.157051 | − | 0.272020i | −0.776753 | − | 0.629805i | \(-0.783135\pi\) |
0.933804 | + | 0.357785i | \(0.116468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.7032 | + | 23.5000i | −1.41882 | + | 0.819159i | −0.996196 | − | 0.0871445i | \(-0.972226\pi\) |
−0.422628 | + | 0.906303i | \(0.638892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36.0000i | − | 1.25184i | −0.779886 | − | 0.625921i | \(-0.784723\pi\) | ||
0.779886 | − | 0.625921i | \(-0.215277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.50000 | + | 9.52628i | 0.191023 | + | 0.330861i | 0.945589 | − | 0.325362i | \(-0.105486\pi\) |
−0.754567 | + | 0.656223i | \(0.772153\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.50000 | + | 14.7224i | −0.294862 | + | 0.510716i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.9904 | − | 32.5000i | −0.450090 | − | 1.12606i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.6506 | + | 12.5000i | −0.748355 | + | 0.432063i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.19615 | − | 3.00000i | 0.178965 | − | 0.103325i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.19615 | + | 1.00000i | −0.178542 | + | 0.0343604i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.50000 | − | 11.2583i | 0.223079 | − | 0.386385i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.5000 | + | 18.1865i | 0.359935 | + | 0.623426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 34.0000i | − | 1.16414i | −0.813139 | − | 0.582069i | \(-0.802243\pi\) | ||
0.813139 | − | 0.582069i | \(-0.197757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.7750 | − | 19.5000i | 1.15373 | − | 0.666107i | 0.203938 | − | 0.978984i | \(-0.434626\pi\) |
0.949794 | + | 0.312877i | \(0.101293\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.500000 | − | 0.866025i | 0.0170598 | − | 0.0295484i | −0.857369 | − | 0.514701i | \(-0.827903\pi\) |
0.874429 | + | 0.485153i | \(0.161236\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.00000 | + | 1.73205i | 0.170400 | + | 0.0590281i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.7224 | + | 8.50000i | 0.501157 | + | 0.289343i | 0.729191 | − | 0.684310i | \(-0.239896\pi\) |
−0.228034 | + | 0.973653i | \(0.573230\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 8.00000i | − | 0.271694i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.00000 | −0.101768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.0000 | − | 46.7654i | −0.914860 | − | 1.58458i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.46410 | + | 2.00000i | 0.117242 | + | 0.0676897i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.9186 | − | 11.5000i | −0.672603 | − | 0.388327i | 0.124459 | − | 0.992225i | \(-0.460280\pi\) |
−0.797062 | + | 0.603897i | \(0.793614\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.00000 | − | 5.19615i | −0.101187 | − | 0.175262i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.0000 | −0.471672 | −0.235836 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235836 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000i | 0.673054i | 0.941674 | + | 0.336527i | \(0.109252\pi\) | ||||
−0.941674 | + | 0.336527i | \(0.890748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.59808 | + | 1.50000i | 0.0872349 | + | 0.0503651i | 0.542983 | − | 0.839744i | \(-0.317295\pi\) |
−0.455748 | + | 0.890109i | \(0.650628\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | − | 13.8564i | 0.536623 | − | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | + | 2.59808i | −0.0502519 | + | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.33013 | + | 2.50000i | −0.144902 | + | 0.0836593i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 42.0000i | − | 1.40234i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.00000 | − | 8.66025i | −0.166759 | − | 0.288836i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.50000 | + | 4.33013i | −0.0832871 | + | 0.144257i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.46410 | − | 10.0000i | 0.115278 | − | 0.332779i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.866025 | + | 0.500000i | −0.0287559 | + | 0.0166022i | −0.514309 | − | 0.857605i | \(-0.671952\pi\) |
0.485553 | + | 0.874207i | \(0.338618\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0000 | 0.530104 | 0.265052 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265052 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.1769 | + | 18.0000i | −1.03181 | + | 0.595713i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.9904 | − | 2.50000i | 0.428980 | − | 0.0825573i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.50000 | + | 9.52628i | −0.181428 | + | 0.314243i | −0.942367 | − | 0.334581i | \(-0.891405\pi\) |
0.760939 | + | 0.648824i | \(0.224739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.00000 | + | 3.46410i | 0.0659022 | + | 0.114146i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.9808 | − | 15.0000i | 0.853320 | − | 0.492665i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.50000 | − | 6.06218i | 0.114831 | − | 0.198894i | −0.802881 | − | 0.596139i | \(-0.796701\pi\) |
0.917712 | + | 0.397246i | \(0.130034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.50000 | + | 4.33013i | 0.180255 | + | 0.141914i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.9904 | − | 7.50000i | −0.425286 | − | 0.245539i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 6.00000i | − | 0.196011i | −0.995186 | − | 0.0980057i | \(-0.968754\pi\) | ||
0.995186 | − | 0.0980057i | \(-0.0312463\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.00000 | −0.0326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.5000 | + | 28.5788i | 0.537885 | + | 0.931644i | 0.999018 | + | 0.0443125i | \(0.0141097\pi\) |
−0.461133 | + | 0.887331i | \(0.652557\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.1244 | + | 7.00000i | 0.394823 | + | 0.227951i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.0429 | − | 18.5000i | −1.04126 | − | 0.601169i | −0.121067 | − | 0.992644i | \(-0.538632\pi\) |
−0.920189 | + | 0.391475i | \(0.871965\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.0000 | − | 36.3731i | −0.681689 | − | 1.18072i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.00000 | −0.0972817 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 22.0000i | − | 0.712650i | −0.934362 | − | 0.356325i | \(-0.884030\pi\) | ||
0.934362 | − | 0.356325i | \(-0.115970\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.19615 | + | 3.00000i | 0.167968 | + | 0.0969762i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.5000 | − | 9.52628i | −0.888021 | − | 0.307620i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.5885 | − | 9.00000i | 0.502331 | − | 0.290021i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.0000i | 1.54358i | 0.635880 | + | 0.771788i | \(0.280637\pi\) | ||||
−0.635880 | + | 0.771788i | \(0.719363\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.50000 | + | 4.33013i | 0.0803116 | + | 0.139104i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.5000 | − | 30.3109i | 0.561602 | − | 0.972723i | −0.435755 | − | 0.900065i | \(-0.643519\pi\) |
0.997357 | − | 0.0726575i | \(-0.0231480\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.7846 | − | 24.0000i | −0.666324 | − | 0.769405i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.59808 | − | 1.50000i | 0.0831198 | − | 0.0479893i | −0.457864 | − | 0.889022i | \(-0.651385\pi\) |
0.540984 | + | 0.841033i | \(0.318052\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.0000 | −0.671163 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.1865 | − | 10.5000i | 0.580060 | − | 0.334898i | −0.181097 | − | 0.983465i | \(-0.557965\pi\) |
0.761157 | + | 0.648567i | \(0.224631\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.66025 | + | 10.0000i | 0.275659 | + | 0.318304i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.0000 | − | 24.2487i | 0.445174 | − | 0.771064i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.50000 | − | 12.9904i | −0.238245 | − | 0.412653i | 0.721966 | − | 0.691929i | \(-0.243239\pi\) |
−0.960211 | + | 0.279276i | \(0.909906\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.0000i | 0.920287i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.5070 | + | 20.5000i | −1.12452 | + | 0.649242i | −0.942551 | − | 0.334063i | \(-0.891580\pi\) |
−0.181968 | + | 0.983304i | \(0.558247\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.50000 | − | 12.9904i | 0.237289 | − | 0.410997i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))