Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2305 |
Dual form | 3024.2.q.b.2881.1 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | 0.732294 | − | 0.680989i | \(-0.238450\pi\) |
−0.955901 | + | 0.293691i | \(0.905116\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.50000 | + | 4.33013i | −0.753778 | + | 1.30558i | 0.192201 | + | 0.981356i | \(0.438437\pi\) |
−0.945979 | + | 0.324227i | \(0.894896\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50000 | − | 4.33013i | 0.693375 | − | 1.20096i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) |
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 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 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.50000 | − | 2.59808i | −0.312772 | − | 0.541736i | 0.666190 | − | 0.745782i | \(-0.267924\pi\) |
−0.978961 | + | 0.204046i | \(0.934591\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.500000 | − | 0.866025i | −0.0928477 | − | 0.160817i | 0.815861 | − | 0.578249i | \(-0.196264\pi\) |
−0.908708 | + | 0.417432i | \(0.862930\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.50000 | + | 4.33013i | −0.390434 | + | 0.676252i | −0.992507 | − | 0.122189i | \(-0.961009\pi\) |
0.602072 | + | 0.798441i | \(0.294342\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | − | 0.866025i | −0.0762493 | − | 0.132068i | 0.825380 | − | 0.564578i | \(-0.190961\pi\) |
−0.901629 | + | 0.432511i | \(0.857628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.50000 | − | 7.79423i | −0.618123 | − | 1.07062i | −0.989828 | − | 0.142269i | \(-0.954560\pi\) |
0.371706 | − | 0.928351i | \(-0.378773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | 0.674200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.0000 | −1.79252 | −0.896258 | − | 0.443533i | \(-0.853725\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.00000 | −0.620174 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.50000 | − | 2.59808i | −0.175562 | − | 0.304082i | 0.764794 | − | 0.644275i | \(-0.222841\pi\) |
−0.940356 | + | 0.340193i | \(0.889507\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.5000 | − | 4.33013i | 1.42451 | − | 0.493464i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.50000 | + | 7.79423i | 0.493939 | + | 0.855528i | 0.999976 | − | 0.00698436i | \(-0.00222321\pi\) |
−0.506036 | + | 0.862512i | \(0.668890\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.50000 | − | 2.59808i | 0.162698 | − | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.50000 | + | 11.2583i | −0.688999 | + | 1.19338i | 0.283164 | + | 0.959072i | \(0.408616\pi\) |
−0.972162 | + | 0.234309i | \(0.924717\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.5000 | + | 4.33013i | −1.31036 | + | 0.453921i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.50000 | + | 7.79423i | 0.456906 | + | 0.791384i | 0.998796 | − | 0.0490655i | \(-0.0156243\pi\) |
−0.541890 | + | 0.840450i | \(0.682291\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.50000 | + | 14.7224i | −0.845782 | + | 1.46494i | 0.0391591 | + | 0.999233i | \(0.487532\pi\) |
−0.884941 | + | 0.465704i | \(0.845801\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.500000 | − | 0.866025i | −0.0492665 | − | 0.0853320i | 0.840341 | − | 0.542059i | \(-0.182355\pi\) |
−0.889607 | + | 0.456727i | \(0.849022\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.50000 | + | 14.7224i | −0.821726 | + | 1.42327i | 0.0826699 | + | 0.996577i | \(0.473655\pi\) |
−0.904396 | + | 0.426694i | \(0.859678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.50000 | + | 7.79423i | 0.431022 | + | 0.746552i | 0.996962 | − | 0.0778949i | \(-0.0248199\pi\) |
−0.565940 | + | 0.824447i | \(0.691487\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.500000 | + | 0.866025i | −0.0470360 | + | 0.0814688i | −0.888585 | − | 0.458712i | \(-0.848311\pi\) |
0.841549 | + | 0.540181i | \(0.181644\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.50000 | + | 2.59808i | −0.139876 | + | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.50000 | − | 7.79423i | 0.137505 | − | 0.714496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | − | 12.1244i | −0.636364 | − | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0000 | 1.06483 | 0.532414 | − | 0.846484i | \(-0.321285\pi\) | ||||
0.532414 | + | 0.846484i | \(0.321285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.500000 | + | 0.866025i | 0.0436852 | + | 0.0756650i | 0.887041 | − | 0.461690i | \(-0.152757\pi\) |
−0.843356 | + | 0.537355i | \(0.819423\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.50000 | + | 0.866025i | −0.216777 | + | 0.0750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.50000 | + | 7.79423i | −0.384461 | + | 0.665906i | −0.991694 | − | 0.128618i | \(-0.958946\pi\) |
0.607233 | + | 0.794524i | \(0.292279\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.50000 | − | 7.79423i | 0.381685 | − | 0.661098i | −0.609618 | − | 0.792695i | \(-0.708677\pi\) |
0.991303 | + | 0.131597i | \(0.0420106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.5000 | + | 21.6506i | 1.04530 | + | 1.81052i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.500000 | + | 0.866025i | −0.0415227 | + | 0.0719195i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.50000 | + | 2.59808i | 0.122885 | + | 0.212843i | 0.920904 | − | 0.389789i | \(-0.127452\pi\) |
−0.798019 | + | 0.602632i | \(0.794119\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.50000 | − | 4.33013i | 0.203447 | − | 0.352381i | −0.746190 | − | 0.665733i | \(-0.768119\pi\) |
0.949637 | + | 0.313353i | \(0.101452\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.50000 | + | 7.79423i | −0.118217 | + | 0.614271i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50000 | + | 9.52628i | −0.430793 | + | 0.746156i | −0.996942 | − | 0.0781474i | \(-0.975100\pi\) |
0.566149 | + | 0.824303i | \(0.308433\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.50000 | − | 16.4545i | 0.735132 | − | 1.27329i | −0.219533 | − | 0.975605i | \(-0.570453\pi\) |
0.954665 | − | 0.297681i | \(-0.0962132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | − | 10.3923i | −0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.0000 | 1.06440 | 0.532200 | − | 0.846619i | \(-0.321365\pi\) | ||||
0.532200 | + | 0.846619i | \(0.321365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0000 | + | 3.46410i | −0.755929 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.50000 | − | 16.4545i | −0.710063 | − | 1.22987i | −0.964833 | − | 0.262864i | \(-0.915333\pi\) |
0.254770 | − | 0.967002i | \(-0.418000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | 0.220564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.0000 | −1.09691 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | −0.719816 | −0.359908 | − | 0.932988i | \(-0.617192\pi\) | ||||
−0.359908 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | + | 2.59808i | 0.106332 | + | 0.184173i | 0.914282 | − | 0.405079i | \(-0.132756\pi\) |
−0.807950 | + | 0.589252i | \(0.799423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.500000 | + | 2.59808i | −0.0350931 | + | 0.182349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.00000 | 0.349215 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.50000 | + | 4.33013i | 0.172929 | + | 0.299521i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.50000 | − | 11.2583i | 0.447478 | − | 0.775055i | −0.550743 | − | 0.834675i | \(-0.685655\pi\) |
0.998221 | + | 0.0596196i | \(0.0189888\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.500000 | + | 0.866025i | −0.0340997 | + | 0.0590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.0000 | 1.00901 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.50000 | + | 16.4545i | 0.636167 | + | 1.10187i | 0.986267 | + | 0.165161i | \(0.0528144\pi\) |
−0.350100 | + | 0.936713i | \(0.613852\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.50000 | − | 2.59808i | 0.0995585 | − | 0.172440i | −0.811943 | − | 0.583736i | \(-0.801590\pi\) |
0.911502 | + | 0.411296i | \(0.134924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.500000 | + | 0.866025i | 0.0330409 | + | 0.0572286i | 0.882073 | − | 0.471113i | \(-0.156147\pi\) |
−0.849032 | + | 0.528341i | \(0.822814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.50000 | − | 2.59808i | 0.0982683 | − | 0.170206i | −0.812700 | − | 0.582683i | \(-0.802003\pi\) |
0.910968 | + | 0.412477i | \(0.135336\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.50000 | − | 12.9904i | 0.485135 | − | 0.840278i | −0.514719 | − | 0.857359i | \(-0.672104\pi\) |
0.999854 | + | 0.0170808i | \(0.00543724\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.50000 | + | 9.52628i | −0.354286 | + | 0.613642i | −0.986996 | − | 0.160748i | \(-0.948609\pi\) |
0.632709 | + | 0.774389i | \(0.281943\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.50000 | − | 4.33013i | 0.351382 | − | 0.276642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.50000 | − | 4.33013i | −0.159071 | − | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.0000 | −1.76734 | −0.883672 | − | 0.468106i | \(-0.844936\pi\) | ||||
−0.883672 | + | 0.468106i | \(0.844936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.0000 | 0.943042 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.5000 | − | 25.1147i | −0.904485 | − | 1.56661i | −0.821607 | − | 0.570055i | \(-0.806922\pi\) |
−0.0828783 | − | 0.996560i | \(-0.526411\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.50000 | − | 2.59808i | 0.466027 | − | 0.161437i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.50000 | + | 4.33013i | −0.154157 | + | 0.267007i | −0.932752 | − | 0.360520i | \(-0.882599\pi\) |
0.778595 | + | 0.627527i | \(0.215933\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.50000 | + | 7.79423i | −0.276433 | + | 0.478796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.50000 | + | 2.59808i | 0.0914566 | + | 0.158408i | 0.908124 | − | 0.418701i | \(-0.137514\pi\) |
−0.816668 | + | 0.577108i | \(0.804181\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.500000 | − | 0.866025i | 0.0303728 | − | 0.0526073i | −0.850439 | − | 0.526073i | \(-0.823664\pi\) |
0.880812 | + | 0.473466i | \(0.156997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0000 | + | 17.3205i | 0.603023 | + | 1.04447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.50000 | + | 16.4545i | −0.570800 | + | 0.988654i | 0.425684 | + | 0.904872i | \(0.360033\pi\) |
−0.996484 | + | 0.0837823i | \(0.973300\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.5000 | − | 25.1147i | −0.864997 | − | 1.49822i | −0.867050 | − | 0.498222i | \(-0.833987\pi\) |
0.00205220 | − | 0.999998i | \(-0.499347\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.0000 | −1.66443 | −0.832214 | − | 0.554455i | \(-0.812927\pi\) | ||||
−0.832214 | + | 0.554455i | \(0.812927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.5000 | − | 4.33013i | 0.737852 | − | 0.255599i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.50000 | + | 4.33013i | −0.146052 | + | 0.252969i | −0.929765 | − | 0.368154i | \(-0.879990\pi\) |
0.783713 | + | 0.621123i | \(0.213323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.0000 | −0.867472 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.500000 | + | 2.59808i | −0.0288195 | + | 0.149751i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.00000 | + | 12.1244i | 0.400819 | + | 0.694239i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.00000 | 0.279946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.00000 | 0.166924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.0000 | − | 17.3205i | −0.554700 | − | 0.960769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.00000 | + | 3.46410i | 0.109272 | + | 0.189264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5000 | − | 25.1147i | 0.789865 | − | 1.36809i | −0.136184 | − | 0.990684i | \(-0.543484\pi\) |
0.926049 | − | 0.377403i | \(-0.123183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.00000 | 0.214731 | 0.107366 | − | 0.994220i | \(-0.465758\pi\) | ||||
0.107366 | + | 0.994220i | \(0.465758\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.50000 | − | 16.4545i | −0.508523 | − | 0.880788i | −0.999951 | − | 0.00987003i | \(-0.996858\pi\) |
0.491428 | − | 0.870918i | \(-0.336475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.50000 | − | 9.52628i | 0.292735 | − | 0.507033i | −0.681720 | − | 0.731613i | \(-0.738768\pi\) |
0.974456 | + | 0.224580i | \(0.0721011\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | + | 10.3923i | 0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.50000 | − | 9.52628i | 0.290279 | − | 0.502778i | −0.683597 | − | 0.729860i | \(-0.739585\pi\) |
0.973876 | + | 0.227082i | \(0.0729186\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.50000 | + | 2.59808i | −0.0785136 | + | 0.135990i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50000 | + | 2.59808i | −0.0782994 | + | 0.135618i | −0.902516 | − | 0.430656i | \(-0.858282\pi\) |
0.824217 | + | 0.566274i | \(0.191616\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.50000 | + | 23.3827i | −0.233628 | + | 1.21397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5000 | + | 21.6506i | 0.647225 | + | 1.12103i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) |
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.00000 | −0.257513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | 0.616399 | 0.308199 | − | 0.951322i | \(-0.400274\pi\) | ||||
0.308199 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.5000 | − | 23.3827i | −0.689818 | − | 1.19480i | −0.971897 | − | 0.235408i | \(-0.924357\pi\) |
0.282079 | − | 0.959391i | \(-0.408976\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.0000 | − | 8.66025i | −0.509647 | − | 0.441367i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.50000 | + | 7.79423i | −0.228159 | + | 0.395183i | −0.957263 | − | 0.289220i | \(-0.906604\pi\) |
0.729103 | + | 0.684403i | \(0.239937\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.50000 | − | 7.79423i | 0.227575 | − | 0.394171i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000 | + | 6.92820i | 0.201262 | + | 0.348596i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.50000 | + | 12.9904i | −0.376414 | + | 0.651969i | −0.990538 | − | 0.137241i | \(-0.956176\pi\) |
0.614123 | + | 0.789210i | \(0.289510\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.50000 | + | 2.59808i | 0.0749064 | + | 0.129742i | 0.901046 | − | 0.433724i | \(-0.142801\pi\) |
−0.826139 | + | 0.563466i | \(0.809468\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.50000 | − | 12.9904i | −0.371761 | − | 0.643909i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000 | 0.692255 | 0.346128 | − | 0.938187i | \(-0.387496\pi\) | ||||
0.346128 | + | 0.938187i | \(0.387496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.50000 | − | 7.79423i | 0.220896 | − | 0.382604i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.50000 | + | 7.79423i | −0.219839 | + | 0.380773i | −0.954759 | − | 0.297382i | \(-0.903887\pi\) |
0.734919 | + | 0.678155i | \(0.237220\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.500000 | + | 0.866025i | 0.0243685 | + | 0.0422075i | 0.877952 | − | 0.478748i | \(-0.158909\pi\) |
−0.853584 | + | 0.520955i | \(0.825576\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.0000 | + | 24.2487i | 1.35501 | + | 1.17348i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.50000 | + | 7.79423i | 0.216757 | + | 0.375435i | 0.953815 | − | 0.300395i | \(-0.0971186\pi\) |
−0.737057 | + | 0.675830i | \(0.763785\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.00000 | −0.143509 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.0000 | 1.71041 | 0.855206 | − | 0.518289i | \(-0.173431\pi\) | ||||
0.855206 | + | 0.518289i | \(0.173431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.0000 | 0.616259 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.5000 | − | 21.6506i | −0.588602 | − | 1.01949i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.0000 | + | 8.66025i | 0.468807 | + | 0.405999i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0000 | 1.02912 | 0.514558 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514558 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.50000 | + | 16.4545i | 0.442459 | + | 0.766362i | 0.997871 | − | 0.0652135i | \(-0.0207728\pi\) |
−0.555412 | + | 0.831575i | \(0.687440\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.50000 | − | 11.2583i | 0.302081 | − | 0.523219i | −0.674526 | − | 0.738251i | \(-0.735652\pi\) |
0.976607 | + | 0.215032i | \(0.0689855\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.5000 | − | 23.3827i | 0.624705 | − | 1.08202i | −0.363892 | − | 0.931441i | \(-0.618552\pi\) |
0.988598 | − | 0.150581i | \(-0.0481143\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | + | 6.92820i | 0.369406 | + | 0.319915i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.00000 | 0.229900 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | − | 3.46410i | −0.0917663 | − | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.5000 | + | 21.6506i | −0.571140 | + | 0.989243i | 0.425310 | + | 0.905048i | \(0.360165\pi\) |
−0.996449 | + | 0.0841949i | \(0.973168\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.50000 | + | 12.9904i | 0.341971 | + | 0.592310i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.50000 | − | 7.79423i | 0.204334 | − | 0.353918i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.50000 | + | 16.4545i | 0.430486 | + | 0.745624i | 0.996915 | − | 0.0784867i | \(-0.0250088\pi\) |
−0.566429 | + | 0.824110i | \(0.691675\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.50000 | + | 11.2583i | −0.293341 | + | 0.508081i | −0.974598 | − | 0.223963i | \(-0.928100\pi\) |
0.681257 | + | 0.732045i | \(0.261434\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.50000 | − | 2.59808i | 0.0675566 | − | 0.117011i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.0000 | + | 20.7846i | 1.07655 | + | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5000 | + | 26.8468i | 0.693875 | + | 1.20183i | 0.970558 | + | 0.240866i | \(0.0774314\pi\) |
−0.276683 | + | 0.960961i | \(0.589235\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.0000 | 0.756490 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.5000 | − | 25.1147i | −0.642701 | − | 1.11319i | −0.984827 | − | 0.173537i | \(-0.944480\pi\) |
0.342126 | − | 0.939654i | \(-0.388853\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.50000 | + | 7.79423i | −0.0663561 | + | 0.344796i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.500000 | + | 0.866025i | −0.0220326 | + | 0.0381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.50000 | + | 2.59808i | 0.0657162 | + | 0.113824i | 0.897011 | − | 0.442007i | \(-0.145733\pi\) |
−0.831295 | + | 0.555831i | \(0.812400\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.500000 | − | 0.866025i | 0.0218635 | − | 0.0378686i | −0.854887 | − | 0.518815i | \(-0.826373\pi\) |
0.876750 | + | 0.480946i | \(0.159707\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.5000 | + | 21.6506i | 0.541435 | + | 0.937793i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.0000 | 0.734974 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −32.5000 | − | 12.9904i | −1.39987 | − | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | − | 21.6506i | 0.537417 | − | 0.930834i | −0.461625 | − | 0.887075i | \(-0.652733\pi\) |
0.999042 | − | 0.0437584i | \(-0.0139332\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.50000 | − | 7.79423i | 0.192759 | − | 0.333868i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.5000 | − | 25.1147i | −0.619975 | − | 1.07383i | −0.989490 | − | 0.144604i | \(-0.953809\pi\) |
0.369514 | − | 0.929225i | \(-0.379524\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.00000 | −0.0426014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000 | + | 13.8564i | 0.680389 | + | 0.589234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.5000 | − | 32.0429i | −0.783870 | − | 1.35770i | −0.929672 | − | 0.368389i | \(-0.879909\pi\) |
0.145802 | − | 0.989314i | \(-0.453424\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.00000 | −0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.0000 | −1.18006 | −0.590030 | − | 0.807382i | \(-0.700884\pi\) | ||||
−0.590030 | + | 0.807382i | \(0.700884\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.00000 | 0.0420703 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.0000 | 1.42535 | 0.712677 | − | 0.701492i | \(-0.247483\pi\) | ||||
0.712677 | + | 0.701492i | \(0.247483\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.0000 | −1.33916 | −0.669579 | − | 0.742741i | \(-0.733526\pi\) | ||||
−0.669579 | + | 0.742741i | \(0.733526\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | −0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.5000 | − | 26.8468i | −0.645273 | − | 1.11765i | −0.984238 | − | 0.176847i | \(-0.943410\pi\) |
0.338965 | − | 0.940799i | \(-0.389923\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.50000 | − | 23.3827i | 0.186691 | − | 0.970077i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.0000 | 1.86371 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.5000 | + | 32.0429i | 0.763577 | + | 1.32255i | 0.940996 | + | 0.338418i | \(0.109892\pi\) |
−0.177419 | + | 0.984135i | \(0.556775\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.50000 | − | 12.9904i | 0.307988 | − | 0.533451i | −0.669934 | − | 0.742421i | \(-0.733678\pi\) |
0.977922 | + | 0.208970i | \(0.0670110\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.50000 | + | 2.59808i | −0.307470 | + | 0.106511i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.50000 | + | 7.79423i | 0.183559 | + | 0.317933i | 0.943090 | − | 0.332538i | \(-0.107905\pi\) |
−0.759531 | + | 0.650471i | \(0.774572\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.00000 | + | 12.1244i | −0.284590 | + | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.500000 | − | 0.866025i | −0.0202944 | − | 0.0351509i | 0.855700 | − | 0.517472i | \(-0.173127\pi\) |
−0.875994 | + | 0.482322i | \(0.839794\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.50000 | − | 16.4545i | −0.383701 | − | 0.664590i | 0.607887 | − | 0.794024i | \(-0.292017\pi\) |
−0.991588 | + | 0.129433i | \(0.958684\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.5000 | − | 23.3827i | 0.543490 | − | 0.941351i | −0.455211 | − | 0.890384i | \(-0.650436\pi\) |
0.998700 | − | 0.0509678i | \(-0.0162306\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.5000 | − | 21.6506i | 0.502417 | − | 0.870212i | −0.497579 | − | 0.867419i | \(-0.665777\pi\) |
0.999996 | − | 0.00279365i | \(-0.000889247\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32.5000 | − | 11.2583i | 1.30209 | − | 0.451055i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.00000 | −0.358854 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.00000 | − | 10.3923i | −0.238103 | − | 0.412406i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.5000 | + | 12.9904i | 1.28770 | + | 0.514698i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.50000 | + | 7.79423i | −0.177739 | + | 0.307854i | −0.941106 | − | 0.338112i | \(-0.890212\pi\) |
0.763367 | + | 0.645966i | \(0.223545\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.50000 | + | 16.4545i | −0.374643 | + | 0.648901i | −0.990274 | − | 0.139134i | \(-0.955568\pi\) |
0.615630 | + | 0.788035i | \(0.288902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.5000 | − | 26.8468i | −0.609368 | − | 1.05546i | −0.991345 | − | 0.131284i | \(-0.958090\pi\) |
0.381977 | − | 0.924172i | \(-0.375243\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.50000 | + | 2.59808i | 0.0586995 | + | 0.101671i | 0.893882 | − | 0.448303i | \(-0.147971\pi\) |
−0.835182 | + | 0.549973i | \(0.814638\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.500000 | − | 0.866025i | 0.0195366 | − | 0.0338384i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.5000 | − | 23.3827i | −0.525885 | − | 0.910860i | −0.999545 | − | 0.0301523i | \(-0.990401\pi\) |
0.473660 | − | 0.880708i | \(-0.342933\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.0000 | −0.544537 | −0.272268 | − | 0.962221i | \(-0.587774\pi\) | ||||
−0.272268 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.00000 | + | 1.73205i | 0.0775567 | + | 0.0671660i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.50000 | + | 2.59808i | −0.0580802 | + | 0.100598i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.0000 | − | 60.6218i | 1.35116 | − | 2.34028i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5000 | + | 25.1147i | 0.558934 | + | 0.968102i | 0.997586 | + | 0.0694449i | \(0.0221228\pi\) |
−0.438652 | + | 0.898657i | \(0.644544\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.0000 | −1.61419 | −0.807096 | − | 0.590421i | \(-0.798962\pi\) | ||||
−0.807096 | + | 0.590421i | \(0.798962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.50000 | − | 23.3827i | 0.172694 | − | 0.897345i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.50000 | + | 7.79423i | 0.172188 | + | 0.298238i | 0.939184 | − | 0.343413i | \(-0.111583\pi\) |
−0.766997 | + | 0.641651i | \(0.778250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.00000 | 0.343872 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −45.0000 | −1.71436 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0000 | 1.06517 | 0.532585 | − | 0.846376i | \(-0.321221\pi\) | ||||
0.532585 | + | 0.846376i | \(0.321221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.00000 | −0.341389 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.0000 | −0.568166 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.50000 | + | 2.59808i | 0.0565736 | + | 0.0979883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 42.5000 | − | 14.7224i | 1.59838 | − | 0.553694i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.00000 | −0.225335 | −0.112667 | − | 0.993633i | \(-0.535939\pi\) | ||||
−0.112667 | + | 0.993633i | \(0.535939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.5000 | − | 21.6506i | 0.467473 | − | 0.809688i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.5000 | − | 23.3827i | 0.503465 | − | 0.872027i | −0.496527 | − | 0.868021i | \(-0.665392\pi\) |
0.999992 | − | 0.00400572i | \(-0.00127506\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.500000 | + | 2.59808i | −0.0186210 | + | 0.0967574i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.00000 | −0.148556 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.5000 | + | 40.7032i | 0.871567 | + | 1.50960i | 0.860376 | + | 0.509661i | \(0.170229\pi\) |
0.0111912 | + | 0.999937i | \(0.496438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.50000 | − | 2.59808i | 0.0554795 | − | 0.0960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.5000 | − | 23.3827i | −0.498634 | − | 0.863659i | 0.501365 | − | 0.865236i | \(-0.332831\pi\) |
−0.999999 | + | 0.00157675i | \(0.999498\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.0000 | − | 17.3205i | 0.368355 | − | 0.638009i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.50000 | − | 7.79423i | −0.165535 | − | 0.286715i | 0.771310 | − | 0.636460i | \(-0.219602\pi\) |
−0.936845 | + | 0.349744i | \(0.886268\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.50000 | − | 12.9904i | 0.275148 | − | 0.476571i | −0.695024 | − | 0.718986i | \(-0.744606\pi\) |
0.970173 | + | 0.242415i | \(0.0779397\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.50000 | − | 2.59808i | 0.0549557 | − | 0.0951861i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 42.5000 | − | 14.7224i | 1.55292 | − | 0.537946i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5000 | + | 26.8468i | 0.565603 | + | 0.979653i | 0.996993 | + | 0.0774878i | \(0.0246899\pi\) |
−0.431390 | + | 0.902165i | \(0.641977\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.00000 | −0.181969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.5000 | + | 23.3827i | 0.489375 | + | 0.847622i | 0.999925 | − | 0.0122260i | \(-0.00389175\pi\) |
−0.510551 | + | 0.859848i | \(0.670558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.50000 | − | 23.3827i | 0.162911 | − | 0.846510i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.5000 | + | 19.9186i | −0.414701 | + | 0.718283i | −0.995397 | − | 0.0958377i | \(-0.969447\pi\) |
0.580696 | + | 0.814120i | \(0.302780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.5000 | + | 26.8468i | 0.557496 | + | 0.965612i | 0.997705 | + | 0.0677162i | \(0.0215712\pi\) |
−0.440208 | + | 0.897896i | \(0.645095\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.50000 | + | 4.33013i | 0.0895718 | + | 0.155143i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.0000 | − | 51.9615i | 1.07348 | − | 1.85933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.00000 | + | 12.1244i | 0.249841 | + | 0.432737i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.0000 | −0.998092 | −0.499046 | − | 0.866575i | \(-0.666316\pi\) | ||||
−0.499046 | + | 0.866575i | \(0.666316\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.50000 | − | 0.866025i | 0.0888898 | − | 0.0307923i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.0000 | + | 60.6218i | −1.24289 | + | 2.15274i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.5000 | − | 19.9186i | 0.407351 | − | 0.705552i | −0.587241 | − | 0.809412i | \(-0.699786\pi\) |
0.994592 | + | 0.103860i | \(0.0331193\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.0000 | 0.529339 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.50000 | − | 2.59808i | 0.264340 | − | 0.0915702i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.50000 | − | 7.79423i | −0.158212 | − | 0.274030i | 0.776012 | − | 0.630718i | \(-0.217239\pi\) |
−0.934224 | + | 0.356687i | \(0.883906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.0000 | 0.385313 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.00000 | −0.0349856 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.0000 | −0.767805 | −0.383903 | − | 0.923374i | \(-0.625420\pi\) | ||||
−0.383903 | + | 0.923374i | \(0.625420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0000 | 0.836587 | 0.418294 | − | 0.908312i | \(-0.362628\pi\) | ||||
0.418294 | + | 0.908312i | \(0.362628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.5000 | + | 21.6506i | 0.434143 | + | 0.751958i | 0.997225 | − | 0.0744432i | \(-0.0237179\pi\) |
−0.563082 | + | 0.826401i | \(0.690385\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.5000 | + | 12.9904i | −0.571691 | + | 0.450090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.0000 | −0.657522 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.5000 | + | 32.0429i | 0.638691 | + | 1.10625i | 0.985720 | + | 0.168391i | \(0.0538571\pi\) |
−0.347029 | + | 0.937854i | \(0.612810\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | − | 24.2487i | 0.482759 | − | 0.836162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.00000 | + | 10.3923i | −0.206406 | + | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00000 | + | 36.3731i | −0.240523 | + | 1.24979i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.00000 | 0.308516 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.5000 | + | 32.0429i | 0.633428 | + | 1.09713i | 0.986846 | + | 0.161664i | \(0.0516860\pi\) |
−0.353418 | + | 0.935466i | \(0.614981\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.50000 | − | 9.52628i | 0.187876 | − | 0.325412i | −0.756666 | − | 0.653802i | \(-0.773173\pi\) |
0.944542 | + | 0.328391i | \(0.106506\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.500000 | − | 0.866025i | −0.0170598 | − | 0.0295484i | 0.857369 | − | 0.514701i | \(-0.172097\pi\) |
−0.874429 | + | 0.485153i | \(0.838764\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.5000 | − | 33.7750i | 0.663788 | − | 1.14971i | −0.315825 | − | 0.948818i | \(-0.602281\pi\) |
0.979612 | − | 0.200897i | \(-0.0643855\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.00000 | − | 12.1244i | −0.238007 | − | 0.412240i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.0000 | − | 34.6410i | 0.678454 | − | 1.17512i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.0000 | + | 17.3205i | −0.338837 | + | 0.586883i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.0000 | + | 15.5885i | 0.608511 | + | 0.526986i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.5000 | + | 45.8993i | 0.894841 | + | 1.54991i | 0.834001 | + | 0.551763i | \(0.186045\pi\) |
0.0608407 | + | 0.998147i | \(0.480622\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.5000 | + | 25.1147i | 0.486862 | + | 0.843270i | 0.999886 | − | 0.0151042i | \(-0.00480800\pi\) |
−0.513024 | + | 0.858375i | \(0.671475\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.0000 | − | 20.7846i | −0.804934 | − | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.50000 | + | 16.4545i | −0.317550 | + | 0.550013i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.5000 | − | 23.3827i | 0.449750 | − | 0.778990i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.00000 | + | 12.1244i | 0.232688 | + | 0.403027i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.50000 | − | 4.33013i | 0.0830111 | − | 0.143780i | −0.821531 | − | 0.570164i | \(-0.806880\pi\) |
0.904542 | + | 0.426385i | \(0.140213\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.5000 | − | 23.3827i | −0.447275 | − | 0.774703i | 0.550933 | − | 0.834550i | \(-0.314272\pi\) |
−0.998208 | + | 0.0598468i | \(0.980939\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.0000 | −1.48928 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.500000 | − | 2.59808i | 0.0165115 | − | 0.0857960i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.50000 | − | 14.7224i | 0.280389 | − | 0.485648i | −0.691091 | − | 0.722767i | \(-0.742870\pi\) |
0.971481 | + | 0.237119i | \(0.0762032\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.0000 | + | 51.9615i | −0.987462 | + | 1.71033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | + | 10.3923i | 0.197279 | + | 0.341697i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.0000 | 0.459325 | 0.229663 | − | 0.973270i | \(-0.426238\pi\) | ||||
0.229663 | + | 0.973270i | \(0.426238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.50000 | + | 2.59808i | 0.213029 | + | 0.0851485i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.50000 | + | 12.9904i | 0.245276 | + | 0.424831i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.0000 | 1.37208 | 0.686040 | − | 0.727564i | \(-0.259347\pi\) | ||||
0.686040 | + | 0.727564i | \(0.259347\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000 | 0.456387 | 0.228193 | − | 0.973616i | \(-0.426718\pi\) | ||||
0.228193 | + | 0.973616i | \(0.426718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.0000 | 0.488467 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.0000 | −0.649913 | −0.324956 | − | 0.945729i | \(-0.605350\pi\) | ||||
−0.324956 | + | 0.945729i | \(0.605350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0000 | −0.486921 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.0000 | 0.842223 | 0.421111 | − | 0.907009i | \(-0.361640\pi\) | ||||
0.421111 | + | 0.907009i | \(0.361640\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.00000 | − | 6.92820i | −0.129437 | − | 0.224191i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.5000 | − | 7.79423i | 0.726563 | − | 0.251689i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.00000 | + | 8.66025i | 0.160956 | + | 0.278783i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.50000 | − | 11.2583i | 0.209026 | − | 0.362043i | −0.742382 | − | 0.669977i | \(-0.766304\pi\) |
0.951408 | + | 0.307933i | \(0.0996374\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.5000 | + | 49.3634i | −0.914609 | + | 1.58415i | −0.107135 | + | 0.994244i | \(0.534168\pi\) |
−0.807473 | + | 0.589904i | \(0.799166\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.5000 | + | 7.79423i | −0.721317 | + | 0.249871i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.0000 | −0.575871 | −0.287936 | − | 0.957650i | \(-0.592969\pi\) | ||||
−0.287936 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.5000 | − | 56.2917i | −1.03870 | − | 1.79909i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.50000 | − | 2.59808i | 0.0478426 | − | 0.0828658i | −0.841112 | − | 0.540860i | \(-0.818099\pi\) |
0.888955 | + | 0.457995i | \(0.151432\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.00000 | + | 1.73205i | 0.0318626 | + | 0.0551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.50000 | + | 2.59808i | −0.0476972 | + | 0.0826140i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.5000 | − | 32.0429i | −0.587672 | − | 1.01788i | −0.994537 | − | 0.104389i | \(-0.966711\pi\) |
0.406865 | − | 0.913488i | \(-0.366622\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.50000 | − | 2.59808i | 0.0475532 | − | 0.0823646i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.50000 | − | 14.7224i | 0.269198 | − | 0.466264i | −0.699457 | − | 0.714675i | \(-0.746575\pi\) |
0.968655 | + | 0.248410i | \(0.0799082\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))