Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [56,2,Mod(9,56)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(56, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("56.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 56 = 2^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 56.i (of order \(3\), 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: | \(0.447162251319\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 56.9 |
Dual form | 56.2.i.b.25.1 |
$q$-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 \(\left(\mathbb{Z}/56\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | 0.973494 | − | 0.228714i | \(-0.0734519\pi\) |
−0.684819 | + | 0.728714i | \(0.740119\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | 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 | ||||||||
\(13\) | −6.00000 | −1.66410 | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.50000 | + | 4.33013i | 0.606339 | + | 1.05021i | 0.991838 | + | 0.127502i | \(0.0406959\pi\) |
−0.385499 | + | 0.922708i | \(0.625971\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.50000 | − | 0.866025i | −0.545545 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.50000 | − | 6.06218i | 0.729800 | − | 1.26405i | −0.227167 | − | 0.973856i | \(-0.572946\pi\) |
0.956967 | − | 0.290196i | \(-0.0937204\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 1.50000 | − | 2.59808i | 0.261116 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.500000 | + | 2.59808i | 0.0845154 | + | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50000 | + | 2.59808i | −0.246598 | + | 0.427121i | −0.962580 | − | 0.270998i | \(-0.912646\pi\) |
0.715981 | + | 0.698119i | \(0.245980\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.50000 | + | 4.33013i | −0.364662 | + | 0.631614i | −0.988722 | − | 0.149763i | \(-0.952149\pi\) |
0.624059 | + | 0.781377i | \(0.285482\pi\) | |||||||
\(48\) | 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 | ||||||||
\(53\) | 0.500000 | + | 0.866025i | 0.0686803 | + | 0.118958i | 0.898321 | − | 0.439340i | \(-0.144788\pi\) |
−0.829640 | + | 0.558298i | \(0.811454\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.50000 | − | 12.9904i | −0.976417 | − | 1.69120i | −0.675178 | − | 0.737655i | \(-0.735933\pi\) |
−0.301239 | − | 0.953549i | \(-0.597400\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 1.00000 | + | 5.19615i | 0.125988 | + | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | + | 5.19615i | −0.372104 | + | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.50000 | + | 7.79423i | 0.549762 | + | 0.952217i | 0.998290 | + | 0.0584478i | \(0.0186151\pi\) |
−0.448528 | + | 0.893769i | \(0.648052\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −3.50000 | − | 6.06218i | −0.409644 | − | 0.709524i | 0.585206 | − | 0.810885i | \(-0.301014\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.00000 | + | 3.46410i | −0.230940 | + | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.50000 | + | 2.59808i | 0.854704 | + | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.500000 | + | 0.866025i | −0.0562544 | + | 0.0974355i | −0.892781 | − | 0.450490i | \(-0.851249\pi\) |
0.836527 | + | 0.547926i | \(0.184582\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00000 | 0.542326 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | + | 1.73205i | 0.107211 | + | 0.185695i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.50000 | + | 6.06218i | −0.370999 | + | 0.642590i | −0.989720 | − | 0.143022i | \(-0.954318\pi\) |
0.618720 | + | 0.785611i | \(0.287651\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | − | 10.3923i | 1.25794 | − | 1.08941i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.50000 | + | 4.33013i | −0.259238 | + | 0.449013i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.500000 | + | 0.866025i | 0.0512989 | + | 0.0888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | 7.50000 | − | 12.9904i | 0.738997 | − | 1.27998i | −0.213950 | − | 0.976845i | \(-0.568633\pi\) |
0.952947 | − | 0.303136i | \(-0.0980336\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | + | 1.73205i | −0.195180 | + | 0.169031i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.50000 | + | 7.79423i | −0.435031 | + | 0.753497i | −0.997298 | − | 0.0734594i | \(-0.976596\pi\) |
0.562267 | + | 0.826956i | \(0.309929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.50000 | + | 4.33013i | 0.239457 | + | 0.414751i | 0.960558 | − | 0.278078i | \(-0.0896974\pi\) |
−0.721102 | + | 0.692829i | \(0.756364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | −0.284747 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.50000 | − | 6.06218i | −0.326377 | − | 0.565301i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.00000 | + | 10.3923i | −0.554700 | + | 0.960769i | ||||
\(118\) | 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 | ||||||||
\(123\) | −1.00000 | − | 1.73205i | −0.0901670 | − | 0.156174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −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 | ||||||||
\(133\) | −0.500000 | − | 2.59808i | −0.0433555 | − | 0.225282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.50000 | − | 4.33013i | 0.215166 | − | 0.372678i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.50000 | − | 9.52628i | −0.469897 | − | 0.813885i | 0.529511 | − | 0.848303i | \(-0.322376\pi\) |
−0.999408 | + | 0.0344182i | \(0.989042\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.00000 | −0.421076 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.00000 | + | 15.5885i | 0.752618 | + | 1.30357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | − | 1.73205i | 0.0830455 | − | 0.143839i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.50000 | − | 2.59808i | 0.536111 | − | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.50000 | − | 14.7224i | 0.696347 | − | 1.20611i | −0.273377 | − | 0.961907i | \(-0.588141\pi\) |
0.969724 | − | 0.244202i | \(-0.0785259\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 10.0000 | 0.808452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.00000 | 0.401610 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.50000 | + | 7.79423i | 0.359139 | + | 0.622047i | 0.987817 | − | 0.155618i | \(-0.0497370\pi\) |
−0.628678 | + | 0.777666i | \(0.716404\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | −6.50000 | + | 11.2583i | −0.509119 | + | 0.881820i | 0.490825 | + | 0.871258i | \(0.336695\pi\) |
−0.999944 | + | 0.0105623i | \(0.996638\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.50000 | − | 2.59808i | −0.116775 | − | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | + | 1.73205i | 0.0764719 | + | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.50000 | − | 11.2583i | 0.494186 | − | 0.855955i | −0.505792 | − | 0.862656i | \(-0.668800\pi\) |
0.999978 | + | 0.00670064i | \(0.00213290\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0000 | − | 3.46410i | −0.755929 | − | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.50000 | − | 12.9904i | 0.563735 | − | 0.976417i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.50000 | + | 11.2583i | 0.485833 | + | 0.841487i | 0.999867 | − | 0.0162823i | \(-0.00518305\pi\) |
−0.514035 | + | 0.857769i | \(0.671850\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.00000 | 0.369611 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.50000 | + | 2.59808i | 0.110282 | + | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.50000 | − | 12.9904i | 0.548454 | − | 0.949951i | ||||
\(188\) | 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 | ||||||||
\(193\) | −1.50000 | − | 2.59808i | −0.107972 | − | 0.187014i | 0.806976 | − | 0.590584i | \(-0.201102\pi\) |
−0.914949 | + | 0.403570i | \(0.867769\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.00000 | −0.429669 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.50000 | + | 11.2583i | 0.460773 | + | 0.798082i | 0.999000 | − | 0.0447181i | \(-0.0142390\pi\) |
−0.538227 | + | 0.842800i | \(0.680906\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.50000 | + | 7.79423i | −0.317406 | + | 0.549762i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.00000 | + | 3.46410i | −0.280745 | + | 0.243132i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.00000 | + | 1.73205i | −0.0698430 | + | 0.120972i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.00000 | − | 12.1244i | −0.486534 | − | 0.842701i | ||||
\(208\) | 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 | ||||||||
\(215\) | −2.00000 | + | 3.46410i | −0.136399 | + | 0.236250i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5000 | − | 4.33013i | −0.848555 | − | 0.293948i | ||||
\(218\) | 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 | ||||||||
\(223\) | −24.0000 | −1.60716 | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||||
−0.803579 | + | 0.595198i | \(0.797074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.00000 | 0.533333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.50000 | − | 9.52628i | −0.365048 | − | 0.632281i | 0.623736 | − | 0.781635i | \(-0.285614\pi\) |
−0.988784 | + | 0.149354i | \(0.952281\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.5000 | + | 19.9186i | −0.759941 | + | 1.31626i | 0.182939 | + | 0.983124i | \(0.441439\pi\) |
−0.942880 | + | 0.333133i | \(0.891894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.50000 | + | 7.79423i | 0.0986928 | + | 0.512823i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.50000 | + | 9.52628i | −0.360317 | + | 0.624087i | −0.988013 | − | 0.154371i | \(-0.950665\pi\) |
0.627696 | + | 0.778459i | \(0.283998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.50000 | + | 4.33013i | 0.163082 | + | 0.282466i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 8.00000 | − | 13.8564i | 0.513200 | − | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.50000 | − | 4.33013i | −0.351382 | − | 0.276642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00000 | − | 5.19615i | 0.190885 | − | 0.330623i | ||||
\(248\) | 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 | ||||||||
\(253\) | −21.0000 | −1.32026 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.50000 | + | 4.33013i | 0.156556 | + | 0.271163i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.5000 | − | 18.1865i | 0.654972 | − | 1.13444i | −0.326929 | − | 0.945049i | \(-0.606014\pi\) |
0.981901 | − | 0.189396i | \(-0.0606529\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | 4.50000 | + | 7.79423i | 0.277482 | + | 0.480613i | 0.970758 | − | 0.240059i | \(-0.0771668\pi\) |
−0.693276 | + | 0.720672i | \(0.743833\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.00000 | 0.0614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.00000 | −0.428393 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.50000 | + | 7.79423i | 0.274370 | + | 0.475223i | 0.969976 | − | 0.243201i | \(-0.0781974\pi\) |
−0.695606 | + | 0.718423i | \(0.744864\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 15.0000 | + | 5.19615i | 0.907841 | + | 0.314485i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.00000 | − | 10.3923i | 0.361814 | − | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.50000 | + | 14.7224i | 0.510716 | + | 0.884585i | 0.999923 | + | 0.0124177i | \(0.00395278\pi\) |
−0.489207 | + | 0.872167i | \(0.662714\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 6.50000 | + | 11.2583i | 0.386385 | + | 0.669238i | 0.991960 | − | 0.126550i | \(-0.0403903\pi\) |
−0.605575 | + | 0.795788i | \(0.707057\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.500000 | + | 0.866025i | −0.0296174 | + | 0.0512989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000 | − | 3.46410i | 0.236113 | − | 0.204479i | ||||
\(288\) | 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 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.0000 | −0.873334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.50000 | − | 12.9904i | −0.435194 | − | 0.753778i | ||||
\(298\) | 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 | ||||||||
\(303\) | 1.50000 | − | 2.59808i | 0.0861727 | − | 0.149256i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.50000 | − | 4.33013i | −0.143150 | − | 0.247942i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 0.500000 | − | 0.866025i | 0.0282617 | − | 0.0489506i | −0.851549 | − | 0.524276i | \(-0.824336\pi\) |
0.879810 | + | 0.475325i | \(0.157669\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.00000 | + | 1.73205i | 0.281718 | + | 0.0975900i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.50000 | + | 2.59808i | −0.0842484 | + | 0.145922i | −0.905071 | − | 0.425261i | \(-0.860182\pi\) |
0.820822 | + | 0.571184i | \(0.193516\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | − | 5.19615i | −0.167968 | − | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.00000 | −0.502331 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.00000 | −0.278207 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0000 | − | 20.7846i | −0.665640 | − | 1.15292i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.50000 | + | 4.33013i | −0.138250 | + | 0.239457i | ||||
\(328\) | 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 | ||||||||
\(333\) | 3.00000 | + | 5.19615i | 0.164399 | + | 0.284747i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.00000 | 0.491723 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.50000 | − | 6.06218i | 0.188434 | − | 0.326377i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.50000 | − | 12.9904i | −0.402621 | − | 0.697360i | 0.591420 | − | 0.806363i | \(-0.298567\pi\) |
−0.994041 | + | 0.109003i | \(0.965234\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −30.0000 | −1.60128 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.50000 | − | 2.59808i | −0.0798369 | − | 0.138282i | 0.823343 | − | 0.567545i | \(-0.192107\pi\) |
−0.903179 | + | 0.429263i | \(0.858773\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.50000 | − | 12.9904i | −0.132314 | − | 0.687524i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.5000 | + | 18.1865i | −0.554169 | + | 0.959849i | 0.443799 | + | 0.896126i | \(0.353630\pi\) |
−0.997968 | + | 0.0637221i | \(0.979703\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.00000 | −0.366397 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.5000 | − | 19.9186i | −0.600295 | − | 1.03974i | −0.992776 | − | 0.119982i | \(-0.961716\pi\) |
0.392481 | − | 0.919760i | \(-0.371617\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | −5.50000 | + | 9.52628i | −0.284779 | + | 0.493252i | −0.972556 | − | 0.232671i | \(-0.925254\pi\) |
0.687776 | + | 0.725923i | \(0.258587\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.50000 | + | 7.79423i | 0.232379 | + | 0.402492i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0000 | 1.23280 | 0.616399 | − | 0.787434i | \(-0.288591\pi\) | ||||
0.616399 | + | 0.787434i | \(0.288591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.00000 | + | 6.92820i | 0.204926 | + | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.50000 | − | 2.59808i | 0.0766464 | − | 0.132755i | −0.825155 | − | 0.564907i | \(-0.808912\pi\) |
0.901801 | + | 0.432151i | \(0.142245\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | − | 5.19615i | 0.305788 | − | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00000 | + | 6.92820i | −0.203331 | + | 0.352180i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.5000 | + | 25.1147i | 0.735179 | + | 1.27337i | 0.954645 | + | 0.297747i | \(0.0962353\pi\) |
−0.219465 | + | 0.975620i | \(0.570431\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35.0000 | 1.77003 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.00000 | −0.252217 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.500000 | + | 0.866025i | 0.0251577 | + | 0.0435745i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.50000 | − | 14.7224i | 0.426603 | − | 0.738898i | −0.569966 | − | 0.821668i | \(-0.693044\pi\) |
0.996569 | + | 0.0827707i | \(0.0263769\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | −15.0000 | − | 25.9808i | −0.747203 | − | 1.29419i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.00000 | 0.446113 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.5000 | − | 23.3827i | −0.667532 | − | 1.15620i | −0.978592 | − | 0.205809i | \(-0.934017\pi\) |
0.311060 | − | 0.950390i | \(-0.399316\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.50000 | − | 9.52628i | 0.271295 | − | 0.469897i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 37.5000 | + | 12.9904i | 1.84525 | + | 0.639215i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | − | 10.3923i | 0.294528 | − | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.00000 | − | 10.3923i | −0.293821 | − | 0.508913i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.0000 | 0.977064 | 0.488532 | − | 0.872546i | \(-0.337533\pi\) | ||||
0.488532 | + | 0.872546i | \(0.337533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0000 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.00000 | + | 8.66025i | 0.243108 | + | 0.421076i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.0000 | + | 17.3205i | −0.485071 | + | 0.840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.50000 | + | 12.9904i | 0.120983 | + | 0.628649i | ||||
\(428\) | 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 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.00000 | 0.0958927 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.50000 | + | 6.06218i | 0.167428 | + | 0.289993i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.5000 | + | 18.1865i | −0.501138 | + | 0.867996i | 0.498861 | + | 0.866682i | \(0.333752\pi\) |
−0.999999 | + | 0.00131415i | \(0.999582\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.0000 | − | 8.66025i | −0.523810 | − | 0.412393i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.5000 | − | 26.8468i | 0.736427 | − | 1.27553i | −0.217667 | − | 0.976023i | \(-0.569845\pi\) |
0.954094 | − | 0.299506i | \(-0.0968220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.50000 | + | 6.06218i | 0.165916 | + | 0.287375i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.0000 | 0.804072 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.0000 | −1.22702 | −0.613508 | − | 0.789689i | \(-0.710242\pi\) | ||||
−0.613508 | + | 0.789689i | \(0.710242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.00000 | + | 5.19615i | 0.141264 | + | 0.244677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.50000 | + | 4.33013i | −0.117460 | + | 0.203447i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.00000 | − | 15.5885i | −0.140642 | − | 0.730798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.50000 | − | 14.7224i | 0.397613 | − | 0.688686i | −0.595818 | − | 0.803120i | \(-0.703172\pi\) |
0.993431 | + | 0.114433i | \(0.0365053\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.50000 | + | 4.33013i | 0.115935 | + | 0.200805i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.50000 | − | 2.59808i | 0.0694117 | − | 0.120225i | −0.829231 | − | 0.558906i | \(-0.811221\pi\) |
0.898642 | + | 0.438682i | \(0.144554\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | 6.00000 | + | 10.3923i | 0.275880 | + | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.5000 | − | 26.8468i | −0.708213 | − | 1.22666i | −0.965519 | − | 0.260331i | \(-0.916168\pi\) |
0.257306 | − | 0.966330i | \(-0.417165\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.00000 | − | 15.5885i | 0.410365 | − | 0.710772i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.0000 | + | 12.1244i | −0.637022 | + | 0.551677i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.00000 | + | 1.73205i | −0.0454077 | + | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.50000 | − | 6.06218i | −0.158600 | − | 0.274703i | 0.775764 | − | 0.631023i | \(-0.217365\pi\) |
−0.934364 | + | 0.356320i | \(0.884031\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 5.00000 | + | 8.66025i | 0.225189 | + | 0.390038i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.00000 | + | 5.19615i | −0.134840 | + | 0.233550i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.5000 | − | 30.3109i | 0.783408 | − | 1.35690i | −0.146538 | − | 0.989205i | \(-0.546813\pi\) |
0.929946 | − | 0.367697i | \(-0.119854\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | − | 10.3923i | −0.268060 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.0000 | −1.42681 | −0.713405 | − | 0.700752i | \(-0.752848\pi\) | ||||
−0.713405 | + | 0.700752i | \(0.752848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.00000 | −0.133498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.5000 | + | 19.9186i | 0.510733 | + | 0.884615i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.50000 | − | 7.79423i | 0.199459 | − | 0.345473i | −0.748894 | − | 0.662690i | \(-0.769415\pi\) |
0.948353 | + | 0.317217i | \(0.102748\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.5000 | + | 6.06218i | 0.774154 | + | 0.268175i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.50000 | + | 4.33013i | −0.110378 | + | 0.191180i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.50000 | − | 12.9904i | −0.330489 | − | 0.572425i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.0000 | 0.659699 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 3.50000 | − | 6.06218i | 0.153044 | − | 0.265081i | −0.779301 | − | 0.626650i | \(-0.784426\pi\) |
0.932345 | + | 0.361569i | \(0.117759\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.00000 | − | 10.3923i | −0.0872872 | − | 0.453557i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.5000 | + | 21.6506i | −0.544509 | + | 0.943116i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | − | 22.5167i | −0.565217 | − | 0.978985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30.0000 | −1.30189 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.50000 | + | 7.79423i | 0.194552 | + | 0.336974i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.50000 | + | 11.2583i | −0.280496 | + | 0.485833i | ||||
\(538\) | 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 | ||||||||
\(543\) | −5.00000 | − | 8.66025i | −0.214571 | − | 0.371647i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.00000 | 0.214176 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | −0.500000 | − | 2.59808i | −0.0212622 | − | 0.110481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.50000 | + | 2.59808i | −0.0636715 | + | 0.110282i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.50000 | + | 4.33013i | 0.105928 | + | 0.183473i | 0.914117 | − | 0.405450i | \(-0.132885\pi\) |
−0.808189 | + | 0.588924i | \(0.799552\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.0000 | 0.633300 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.5000 | + | 35.5070i | 0.863972 | + | 1.49644i | 0.868064 | + | 0.496452i | \(0.165364\pi\) |
−0.00409232 | + | 0.999992i | \(0.501303\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00000 | + | 15.5885i | −0.378633 | + | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.50000 | + | 0.866025i | 0.104990 | + | 0.0363696i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.5000 | − | 28.5788i | 0.691716 | − | 1.19809i | −0.279559 | − | 0.960128i | \(-0.590188\pi\) |
0.971275 | − | 0.237959i | \(-0.0764783\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 11.0000 | 0.459532 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.0000 | 1.16768 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.5000 | + | 28.5788i | 0.686904 | + | 1.18975i | 0.972834 | + | 0.231502i | \(0.0743641\pi\) |
−0.285930 | + | 0.958250i | \(0.592303\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | 1.50000 | − | 2.59808i | 0.0621237 | − | 0.107601i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.00000 | + | 10.3923i | 0.248069 | + | 0.429669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.0000 | −0.825488 | −0.412744 | − | 0.910847i | \(-0.635430\pi\) | ||||
−0.412744 | + | 0.910847i | \(0.635430\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | −0.206021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00000 | − | 5.19615i | −0.123404 | − | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.5000 | − | 38.9711i | 0.923964 | − | 1.60035i | 0.130746 | − | 0.991416i | \(-0.458263\pi\) |
0.793219 | − | 0.608937i | \(-0.208404\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.0000 | + | 8.66025i | −0.409960 | + | 0.355036i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.50000 | + | 11.2583i | −0.266027 | + | 0.460773i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.50000 | + | 14.7224i | 0.347301 | + | 0.601542i | 0.985769 | − | 0.168106i | \(-0.0537650\pi\) |
−0.638468 | + | 0.769648i | \(0.720432\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.0000 | 0.733017 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.50000 | + | 11.2583i | −0.263827 | + | 0.456962i | −0.967256 | − | 0.253804i | \(-0.918318\pi\) |
0.703429 | + | 0.710766i | \(0.251651\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | −21.5000 | − | 37.2391i | −0.868377 | − | 1.50407i | −0.863655 | − | 0.504084i | \(-0.831830\pi\) |
−0.00472215 | − | 0.999989i | \(-0.501503\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.0000 | 1.20775 | 0.603877 | − | 0.797077i | \(-0.293622\pi\) | ||||
0.603877 | + | 0.797077i | \(0.293622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.50000 | + | 7.79423i | 0.180870 | + | 0.313276i | 0.942177 | − | 0.335115i | \(-0.108775\pi\) |
−0.761307 | + | 0.648392i | \(0.775442\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.5000 | − | 30.3109i | 0.702251 | − | 1.21633i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.50000 | − | 18.1865i | −0.140225 | − | 0.728628i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.50000 | + | 2.59808i | 0.0599042 | + | 0.103757i | ||||
\(628\) | 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 | ||||||||
\(633\) | −2.00000 | − | 3.46410i | −0.0794929 | − | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000 | − | 6.92820i | 0.158735 | − | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.00000 | + | 41.5692i | −0.237729 | + | 1.64703i | ||||
\(638\) | 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 | ||||||||
\(643\) | −44.0000 | −1.73519 | −0.867595 | − | 0.497271i | \(-0.834335\pi\) | ||||
−0.867595 | + | 0.497271i | \(0.834335\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.00000 | −0.157500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.50000 | − | 12.9904i | −0.294855 | − | 0.510705i | 0.680096 | − | 0.733123i | \(-0.261938\pi\) |
−0.974951 | + | 0.222419i | \(0.928605\pi\) | |||||||
\(648\) | 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 | ||||||||
\(653\) | −17.5000 | + | 30.3109i | −0.684828 | + | 1.18616i | 0.288663 | + | 0.957431i | \(0.406789\pi\) |
−0.973491 | + | 0.228726i | \(0.926544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.50000 | + | 4.33013i | 0.0976831 | + | 0.169192i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.0000 | −0.546192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.0000 | 1.71400 | 0.856998 | − | 0.515319i | \(-0.172327\pi\) | ||||
0.856998 | + | 0.515319i | \(0.172327\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 15.0000 | − | 25.9808i | 0.582552 | − | 1.00901i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.50000 | − | 0.866025i | −0.0969458 | − | 0.0335830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.00000 | − | 12.1244i | 0.271041 | − | 0.469457i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.0000 | − | 20.7846i | −0.463947 | − | 0.803579i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0000 | −0.579069 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.0000 | −1.00223 | −0.501113 | − | 0.865382i | \(-0.667076\pi\) | ||||
−0.501113 | + | 0.865382i | \(0.667076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0000 | + | 17.3205i | 0.384900 | + | 0.666667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.5000 | + | 33.7750i | −0.749446 | + | 1.29808i | 0.198643 | + | 0.980072i | \(0.436347\pi\) |
−0.948089 | + | 0.318006i | \(0.896987\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | −13.5000 | − | 23.3827i | −0.516563 | − | 0.894714i | −0.999815 | − | 0.0192323i | \(-0.993878\pi\) |
0.483252 | − | 0.875481i | \(-0.339456\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.0000 | −0.420288 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.0000 | −0.877505 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 12.0000 | − | 10.3923i | 0.455842 | − | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.00000 | + | 10.3923i | −0.227593 | + | 0.394203i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.00000 | − | 8.66025i | −0.189389 | − | 0.328031i | ||||
\(698\) | 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 | ||||||||
\(703\) | −1.50000 | − | 2.59808i | −0.0565736 | − | 0.0979883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.50000 | + | 4.33013i | −0.0941554 | + | 0.163082i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.50000 | + | 2.59808i | 0.282067 | + | 0.0977107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.5000 | − | 25.1147i | 0.544559 | − | 0.943204i | −0.454076 | − | 0.890963i | \(-0.650030\pi\) |
0.998635 | − | 0.0522406i | \(-0.0166363\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.00000 | + | 1.73205i | 0.0375029 | + | 0.0649570i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35.0000 | 1.31076 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.0000 | 0.673162 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.0000 | + | 17.3205i | 0.373457 | + | 0.646846i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.5000 | − | 33.7750i | 0.727227 | − | 1.25959i | −0.230823 | − | 0.972996i | \(-0.574142\pi\) |
0.958051 | − | 0.286599i | \(-0.0925247\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.50000 | + | 38.9711i | 0.279315 | + | 1.45136i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.50000 | + | 14.7224i | −0.316118 | + | 0.547533i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.00000 | + | 6.92820i | 0.148556 | + | 0.257307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.0000 | − | 17.3205i | −0.369863 | − | 0.640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.50000 | + | 16.4545i | −0.350891 | + | 0.607760i | −0.986406 | − | 0.164328i | \(-0.947454\pi\) |
0.635515 | + | 0.772088i | \(0.280788\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.00000 | − | 6.92820i | 0.0368856 | − | 0.255551i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.5000 | − | 23.3827i | 0.497279 | − | 0.861312i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.50000 | + | 4.33013i | 0.0919640 | + | 0.159286i | 0.908337 | − | 0.418238i | \(-0.137352\pi\) |
−0.816373 | + | 0.577524i | \(0.804019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.00000 | 0.220416 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.0000 | −0.586983 | −0.293492 | − | 0.955962i | \(-0.594817\pi\) | ||||
−0.293492 | + | 0.955962i | \(0.594817\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.50000 | − | 14.7224i | −0.311416 | − | 0.539388i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | − | 20.7846i | 0.439057 | − | 0.760469i | ||||
\(748\) | 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 | ||||||||
\(753\) | 8.00000 | + | 13.8564i | 0.291536 | + | 0.504956i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.00000 | 0.181969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −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 | ||||||||
\(763\) | −12.5000 | − | 4.33013i | −0.452530 | − | 0.156761i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.00000 | − | 8.66025i | 0.180775 | − | 0.313112i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 45.0000 | + | 77.9423i | 1.62486 | + | 2.81433i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.0000 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.0000 | 0.756297 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.50000 | − | 16.4545i | −0.341691 | − | 0.591827i | 0.643056 | − | 0.765819i | \(-0.277666\pi\) |
−0.984747 | + | 0.173993i | \(0.944333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.0000 | + | 17.3205i | −0.359211 | + | 0.622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.00000 | − | 5.19615i | 0.215249 | − | 0.186411i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.00000 | − | 1.73205i | 0.0358287 | − | 0.0620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.0000 | 0.357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.00000 | 0.321224 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.50000 | + | 14.7224i | 0.302992 | + | 0.524798i | 0.976812 | − | 0.214097i | \(-0.0686810\pi\) |
−0.673820 | + | 0.738896i | \(0.735348\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | −15.0000 | + | 25.9808i | −0.532666 | + | 0.922604i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.500000 | + | 0.866025i | 0.0177332 | + | 0.0307148i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.0000 | 0.637593 | 0.318796 | − | 0.947823i | \(-0.396721\pi\) | ||||
0.318796 | + | 0.947823i | \(0.396721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.0000 | −0.884436 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.00000 | + | 12.1244i | 0.247333 | + | 0.428393i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.5000 | + | 18.1865i | −0.370537 | + | 0.641789i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.5000 | + | 6.06218i | 0.616794 | + | 0.213664i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.50000 | + | 7.79423i | −0.158408 | + | 0.274370i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.5000 | − | 33.7750i | −0.685583 | − | 1.18747i | −0.973253 | − | 0.229736i | \(-0.926214\pi\) |
0.287670 | − | 0.957730i | \(-0.407120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.0000 | 0.421377 | 0.210688 | − | 0.977553i | \(-0.432429\pi\) | ||||
0.210688 | + | 0.977553i | \(0.432429\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.00000 | 0.245501 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.50000 | + | 11.2583i | 0.227685 | + | 0.394362i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | − | 3.46410i | 0.0699711 | − | 0.121194i | ||||
\(818\) | 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 | ||||||||
\(823\) | −23.5000 | − | 40.7032i | −0.819159 | − | 1.41882i | −0.906303 | − | 0.422628i | \(-0.861108\pi\) |
0.0871445 | − | 0.996196i | \(-0.472226\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.0000 | 0.417786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.0000 | −1.25184 | −0.625921 | − | 0.779886i | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.50000 | − | 9.52628i | −0.191023 | − | 0.330861i | 0.754567 | − | 0.656223i | \(-0.227847\pi\) |
−0.945589 | + | 0.325362i | \(0.894514\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.50000 | + | 14.7224i | −0.294862 | + | 0.510716i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.5000 | − | 12.9904i | 1.12606 | − | 0.450090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.00000 | + | 10.3923i | −0.207639 | + | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.5000 | + | 21.6506i | 0.432063 | + | 0.748355i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.00000 | + | 5.19615i | 0.103325 | + | 0.178965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.5000 | − | 19.9186i | 0.395612 | − | 0.685220i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | + | 5.19615i | 0.0343604 | + | 0.178542i | ||||
\(848\) | 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 | ||||||||
\(853\) | 34.0000 | 1.16414 | 0.582069 | − | 0.813139i | \(-0.302243\pi\) | ||||
0.582069 | + | 0.813139i | \(0.302243\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.00000 | 0.0683986 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.5000 | − | 33.7750i | −0.666107 | − | 1.15373i | −0.978984 | − | 0.203938i | \(-0.934626\pi\) |
0.312877 | − | 0.949794i | \(-0.398707\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.500000 | + | 0.866025i | −0.0170598 | + | 0.0295484i | −0.874429 | − | 0.485153i | \(-0.838764\pi\) |
0.857369 | + | 0.514701i | \(0.172097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.00000 | + | 1.73205i | 0.170400 | + | 0.0590281i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.50000 | + | 14.7224i | −0.289343 | + | 0.501157i | −0.973653 | − | 0.228034i | \(-0.926770\pi\) |
0.684310 | + | 0.729191i | \(0.260104\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.50000 | − | 11.2583i | −0.221007 | − | 0.382795i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.00000 | 0.101768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.0000 | − | 46.7654i | −0.914860 | − | 1.58458i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.00000 | + | 3.46410i | −0.0676897 | + | 0.117242i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.0000 | + | 15.5885i | −0.608511 | + | 0.526986i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.5000 | + | 19.9186i | −0.388327 | + | 0.672603i | −0.992225 | − | 0.124459i | \(-0.960280\pi\) |
0.603897 | + | 0.797062i | \(0.293614\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −20.0000 | −0.673054 | −0.336527 | − | 0.941674i | \(-0.609252\pi\) | ||||
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.50000 | − | 12.9904i | −0.252110 | − | 0.436667i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.50000 | − | 2.59808i | 0.0503651 | − | 0.0872349i | −0.839744 | − | 0.542983i | \(-0.817295\pi\) |
0.890109 | + | 0.455748i | \(0.150628\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | −2.50000 | − | 4.33013i | −0.0836593 | − | 0.144902i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.0000 | 0.434542 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.0000 | −1.40234 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | 10.0000 | + | 3.46410i | 0.332779 | + | 0.115278i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.00000 | + | 8.66025i | −0.166206 | + | 0.287877i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.500000 | + | 0.866025i | 0.0166022 | + | 0.0287559i | 0.874207 | − | 0.485553i | \(-0.161382\pi\) |
−0.857605 | + | 0.514309i | \(0.828048\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −18.0000 | − | 31.1769i | −0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.50000 | − | 4.33013i | 0.0826475 | − | 0.143150i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.50000 | − | 12.9904i | −0.0825573 | − | 0.428980i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.50000 | − | 9.52628i | 0.181428 | − | 0.314243i | −0.760939 | − | 0.648824i | \(-0.775261\pi\) |
0.942367 | + | 0.334581i | \(0.108595\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.00000 | + | 3.46410i | 0.0659022 | + | 0.114146i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0000 | −0.394558 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.0000 | − | 25.9808i | −0.492665 | − | 0.853320i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.50000 | + | 6.06218i | −0.114831 | + | 0.198894i | −0.917712 | − | 0.397246i | \(-0.869966\pi\) |
0.802881 | + | 0.596139i | \(0.203299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.50000 | + | 4.33013i | 0.180255 | + | 0.141914i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.50000 | − | 12.9904i | 0.245539 | − | 0.425286i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.50000 | − | 12.9904i | −0.245276 | − | 0.424831i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.00000 | −0.196011 | −0.0980057 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980057 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | −7.00000 | + | 12.1244i | −0.227951 | + | 0.394823i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.50000 | + | 12.9904i | 0.0813250 | + | 0.422577i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.5000 | + | 32.0429i | −0.601169 | + | 1.04126i | 0.391475 | + | 0.920189i | \(0.371965\pi\) |
−0.992644 | + | 0.121067i | \(0.961368\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.0000 | + | 36.3731i | 0.681689 | + | 1.18072i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.00000 | −0.0972817 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.0000 | 0.712650 | 0.356325 | − | 0.934362i | \(-0.384030\pi\) | ||||
0.356325 | + | 0.934362i | \(0.384030\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.50000 | − | 9.52628i | −0.177976 | − | 0.308263i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.00000 | − | 5.19615i | 0.0969762 | − | 0.167968i | ||||
\(958\) | 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 | ||||||||
\(963\) | 9.00000 | + | 15.5885i | 0.290021 | + | 0.502331i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.00000 | −0.0965734 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.0000 | 1.54358 | 0.771788 | − | 0.635880i | \(-0.219363\pi\) | ||||
0.771788 | + | 0.635880i | \(0.219363\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | 24.0000 | − | 20.7846i | 0.769405 | − | 0.666324i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.0000 | − | 20.7846i | 0.384308 | − | 0.665640i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.50000 | − | 2.59808i | −0.0479893 | − | 0.0831198i | 0.841033 | − | 0.540984i | \(-0.181948\pi\) |
−0.889022 | + | 0.457864i | \(0.848615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.0000 | 0.671163 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.5000 | + | 18.1865i | 0.334898 | + | 0.580060i | 0.983465 | − | 0.181097i | \(-0.0579648\pi\) |
−0.648567 | + | 0.761157i | \(0.724631\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.00000 | + | 5.19615i | −0.0955879 | + | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.0000 | − | 8.66025i | 0.318304 | − | 0.275659i | ||||
\(988\) | 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 | ||||||||
\(993\) | −29.0000 | −0.920287 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.0000 | 0.412128 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.5000 | + | 35.5070i | 0.649242 | + | 1.12452i | 0.983304 | + | 0.181968i | \(0.0582469\pi\) |
−0.334063 | + | 0.942551i | \(0.608420\pi\) | |||||||
\(998\) | 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 \(a_p\))