Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(961,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("2352.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(18.7808145554\) |
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: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.961 |
Dual form | 2352.2.q.r.1537.1 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | + | 3.46410i | 0.603023 | + | 1.04447i | 0.992361 | + | 0.123371i | \(0.0393705\pi\) |
−0.389338 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | + | 1.73205i | 0.242536 | + | 0.420084i | 0.961436 | − | 0.275029i | \(-0.0886875\pi\) |
−0.718900 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | − | 3.46410i | 0.458831 | − | 0.794719i | −0.540068 | − | 0.841621i | \(-0.681602\pi\) |
0.998899 | + | 0.0469020i | \(0.0149348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | + | 6.92820i | −0.834058 | + | 1.44463i | 0.0607377 | + | 0.998154i | \(0.480655\pi\) |
−0.894795 | + | 0.446476i | \(0.852679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | − | 6.92820i | −0.718421 | − | 1.24434i | −0.961625 | − | 0.274367i | \(-0.911532\pi\) |
0.243204 | − | 0.969975i | \(-0.421802\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | + | 3.46410i | −0.348155 | + | 0.603023i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | + | 5.19615i | −0.493197 | + | 0.854242i | −0.999969 | − | 0.00783774i | \(-0.997505\pi\) |
0.506772 | + | 0.862080i | \(0.330838\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | + | 1.73205i | 0.160128 | + | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | + | 1.73205i | −0.140028 | + | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | + | 1.73205i | 0.137361 | + | 0.237915i | 0.926497 | − | 0.376303i | \(-0.122805\pi\) |
−0.789136 | + | 0.614218i | \(0.789471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.00000 | −1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | − | 3.46410i | −0.260378 | − | 0.450988i | 0.705965 | − | 0.708247i | \(-0.250514\pi\) |
−0.966342 | + | 0.257260i | \(0.917180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | + | 1.73205i | −0.128037 | + | 0.221766i | −0.922916 | − | 0.385002i | \(-0.874201\pi\) |
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | + | 3.46410i | −0.248069 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | − | 3.46410i | −0.244339 | − | 0.423207i | 0.717607 | − | 0.696449i | \(-0.245238\pi\) |
−0.961946 | + | 0.273241i | \(0.911904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | + | 8.66025i | 0.585206 | + | 1.01361i | 0.994850 | + | 0.101361i | \(0.0323196\pi\) |
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.00000 | + | 5.19615i | 0.321634 | + | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000 | − | 6.92820i | 0.414781 | − | 0.718421i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | + | 6.92820i | 0.410391 | + | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | − | 15.5885i | −0.895533 | − | 1.55111i | −0.833143 | − | 0.553058i | \(-0.813461\pi\) |
−0.0623905 | − | 0.998052i | \(-0.519872\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | + | 13.8564i | −0.788263 | + | 1.36531i | 0.138767 | + | 0.990325i | \(0.455686\pi\) |
−0.927030 | + | 0.374987i | \(0.877647\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | + | 10.3923i | −0.580042 | + | 1.00466i | 0.415432 | + | 0.909624i | \(0.363630\pi\) |
−0.995474 | + | 0.0950377i | \(0.969703\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00000 | − | 13.8564i | −0.746004 | − | 1.29212i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | + | 1.73205i | −0.0924500 | + | 0.160128i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.00000 | + | 5.19615i | 0.270501 | + | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 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 | ||||||||
\(131\) | 2.00000 | − | 3.46410i | 0.174741 | − | 0.302660i | −0.765331 | − | 0.643637i | \(-0.777425\pi\) |
0.940072 | + | 0.340977i | \(0.110758\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | − | 1.73205i | 0.0860663 | − | 0.149071i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.00000 | + | 5.19615i | 0.256307 | + | 0.443937i | 0.965250 | − | 0.261329i | \(-0.0841608\pi\) |
−0.708942 | + | 0.705266i | \(0.750827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | + | 6.92820i | 0.334497 | + | 0.579365i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | + | 10.3923i | −0.498273 | + | 0.863034i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.00000 | + | 12.1244i | −0.573462 | + | 0.993266i | 0.422744 | + | 0.906249i | \(0.361067\pi\) |
−0.996207 | + | 0.0870170i | \(0.972267\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | − | 13.8564i | −0.651031 | − | 1.12762i | −0.982873 | − | 0.184284i | \(-0.941004\pi\) |
0.331842 | − | 0.943335i | \(-0.392330\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.0000 | 1.28515 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | − | 1.73205i | −0.0798087 | − | 0.138233i | 0.823359 | − | 0.567521i | \(-0.192098\pi\) |
−0.903167 | + | 0.429289i | \(0.858764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.00000 | + | 1.73205i | −0.0793052 | + | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | − | 10.3923i | 0.469956 | − | 0.813988i | −0.529454 | − | 0.848339i | \(-0.677603\pi\) |
0.999410 | + | 0.0343508i | \(0.0109363\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.00000 | − | 6.92820i | −0.311400 | − | 0.539360i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.0000 | 1.85718 | 0.928588 | − | 0.371113i | \(-0.121024\pi\) | ||||
0.928588 | + | 0.371113i | \(0.121024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | + | 3.46410i | 0.152944 | + | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.00000 | − | 3.46410i | 0.150329 | − | 0.260378i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000 | + | 10.3923i | 0.448461 | + | 0.776757i | 0.998286 | − | 0.0585225i | \(-0.0186389\pi\) |
−0.549825 | + | 0.835280i | \(0.685306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | − | 10.3923i | −0.441129 | − | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | + | 6.92820i | −0.292509 | + | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | − | 1.73205i | −0.0719816 | − | 0.124676i | 0.827788 | − | 0.561041i | \(-0.189599\pi\) |
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.00000 | −0.286446 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | − | 13.8564i | −0.567105 | − | 0.982255i | −0.996850 | − | 0.0793045i | \(-0.974730\pi\) |
0.429745 | − | 0.902950i | \(-0.358603\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | − | 3.46410i | 0.141069 | − | 0.244339i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | + | 10.3923i | −0.419058 | + | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | − | 6.92820i | −0.278019 | − | 0.481543i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.00000 | − | 6.92820i | −0.274075 | − | 0.474713i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | − | 6.92820i | 0.272798 | − | 0.472500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.00000 | + | 8.66025i | −0.337869 | + | 0.585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | + | 3.46410i | 0.134535 | + | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.00000 | − | 10.3923i | −0.398234 | − | 0.689761i | 0.595274 | − | 0.803523i | \(-0.297043\pi\) |
−0.993508 | + | 0.113761i | \(0.963710\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.0000 | − | 19.0526i | 0.726900 | − | 1.25903i | −0.231287 | − | 0.972886i | \(-0.574293\pi\) |
0.958187 | − | 0.286143i | \(-0.0923732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.00000 | + | 8.66025i | −0.327561 | + | 0.567352i | −0.982027 | − | 0.188739i | \(-0.939560\pi\) |
0.654466 | + | 0.756091i | \(0.272893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.00000 | + | 15.5885i | 0.579741 | + | 1.00414i | 0.995509 | + | 0.0946700i | \(0.0301796\pi\) |
−0.415768 | + | 0.909471i | \(0.636487\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | − | 6.92820i | 0.254514 | − | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.00000 | − | 3.46410i | −0.126745 | − | 0.219529i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.0000 | 1.26239 | 0.631194 | − | 0.775625i | \(-0.282565\pi\) | ||||
0.631194 | + | 0.775625i | \(0.282565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.0000 | −2.01182 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.00000 | − | 3.46410i | −0.125245 | − | 0.216930i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.00000 | − | 1.73205i | 0.0623783 | − | 0.108042i | −0.833150 | − | 0.553047i | \(-0.813465\pi\) |
0.895528 | + | 0.445005i | \(0.146798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | + | 5.19615i | −0.185695 | + | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.00000 | − | 6.92820i | −0.246651 | − | 0.427211i | 0.715944 | − | 0.698158i | \(-0.245997\pi\) |
−0.962594 | + | 0.270947i | \(0.912663\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | −0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.00000 | − | 8.66025i | −0.304855 | − | 0.528025i | 0.672374 | − | 0.740212i | \(-0.265275\pi\) |
−0.977229 | + | 0.212187i | \(0.931941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | + | 6.92820i | −0.242983 | + | 0.420858i | −0.961563 | − | 0.274586i | \(-0.911459\pi\) |
0.718580 | + | 0.695444i | \(0.244792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | + | 3.46410i | −0.120605 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0000 | + | 22.5167i | 0.781094 | + | 1.35290i | 0.931305 | + | 0.364241i | \(0.118672\pi\) |
−0.150210 | + | 0.988654i | \(0.547995\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0000 | 1.55103 | 0.775515 | − | 0.631329i | \(-0.217490\pi\) | ||||
0.775515 | + | 0.631329i | \(0.217490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0000 | + | 24.2487i | 0.832214 | + | 1.44144i | 0.896279 | + | 0.443491i | \(0.146260\pi\) |
−0.0640654 | + | 0.997946i | \(0.520407\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | + | 6.92820i | −0.236940 | + | 0.410391i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.00000 | − | 1.73205i | −0.0586210 | − | 0.101535i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.0000 | 1.05157 | 0.525786 | − | 0.850617i | \(-0.323771\pi\) | ||||
0.525786 | + | 0.850617i | \(0.323771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.00000 | − | 3.46410i | −0.116052 | − | 0.201008i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.00000 | + | 13.8564i | −0.462652 | + | 0.801337i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00000 | − | 15.5885i | 0.517036 | − | 0.895533i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00000 | − | 3.46410i | −0.114520 | − | 0.198354i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000 | 0.684876 | 0.342438 | − | 0.939540i | \(-0.388747\pi\) | ||||
0.342438 | + | 0.939540i | \(0.388747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.0000 | −0.910208 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | + | 20.7846i | 0.680458 | + | 1.17859i | 0.974841 | + | 0.222900i | \(0.0715523\pi\) |
−0.294384 | + | 0.955687i | \(0.595114\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.00000 | + | 5.19615i | −0.169570 | + | 0.293704i | −0.938269 | − | 0.345907i | \(-0.887571\pi\) |
0.768699 | + | 0.639611i | \(0.220905\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.00000 | + | 5.19615i | −0.168497 | + | 0.291845i | −0.937892 | − | 0.346929i | \(-0.887225\pi\) |
0.769395 | + | 0.638774i | \(0.220558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | + | 20.7846i | 0.671871 | + | 1.16371i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.0000 | −0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | + | 1.73205i | 0.0554700 | + | 0.0960769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.00000 | + | 1.73205i | −0.0553001 | + | 0.0957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | − | 17.3205i | 0.549650 | − | 0.952021i | −0.448649 | − | 0.893708i | \(-0.648095\pi\) |
0.998298 | − | 0.0583130i | \(-0.0185721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.00000 | − | 5.19615i | −0.164399 | − | 0.284747i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.00000 | + | 15.5885i | 0.488813 | + | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000 | − | 27.7128i | 0.866449 | − | 1.50073i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.00000 | − | 13.8564i | 0.430706 | − | 0.746004i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.00000 | − | 10.3923i | −0.322097 | − | 0.557888i | 0.658824 | − | 0.752297i | \(-0.271054\pi\) |
−0.980921 | + | 0.194409i | \(0.937721\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.0000 | −1.60586 | −0.802932 | − | 0.596071i | \(-0.796728\pi\) | ||||
−0.802932 | + | 0.596071i | \(0.796728\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.00000 | + | 1.73205i | 0.0532246 | + | 0.0921878i | 0.891410 | − | 0.453197i | \(-0.149717\pi\) |
−0.838186 | + | 0.545385i | \(0.816383\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | − | 13.8564i | 0.424596 | − | 0.735422i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0000 | + | 20.7846i | −0.633336 | + | 1.09697i | 0.353529 | + | 0.935423i | \(0.384981\pi\) |
−0.986865 | + | 0.161546i | \(0.948352\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.0000 | −1.04685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00000 | + | 6.92820i | 0.208798 | + | 0.361649i | 0.951336 | − | 0.308155i | \(-0.0997115\pi\) |
−0.742538 | + | 0.669804i | \(0.766378\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.00000 | + | 5.19615i | −0.156174 | + | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | − | 8.66025i | 0.258890 | − | 0.448411i | −0.707055 | − | 0.707159i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.00000 | − | 10.3923i | −0.309839 | − | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.00000 | + | 6.92820i | 0.204926 | + | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.00000 | − | 3.46410i | 0.101666 | − | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.00000 | + | 1.73205i | 0.0507020 | + | 0.0878185i | 0.890263 | − | 0.455448i | \(-0.150521\pi\) |
−0.839561 | + | 0.543266i | \(0.817187\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.00000 | − | 13.8564i | −0.402524 | − | 0.697191i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.00000 | − | 12.1244i | 0.351320 | − | 0.608504i | −0.635161 | − | 0.772380i | \(-0.719066\pi\) |
0.986481 | + | 0.163876i | \(0.0523996\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.0000 | − | 25.9808i | 0.749064 | − | 1.29742i | −0.199207 | − | 0.979957i | \(-0.563837\pi\) |
0.948272 | − | 0.317460i | \(-0.102830\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | − | 13.8564i | −0.398508 | − | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000 | 0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.0000 | −1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.00000 | − | 5.19615i | −0.148340 | − | 0.256933i | 0.782274 | − | 0.622935i | \(-0.214060\pi\) |
−0.930614 | + | 0.366002i | \(0.880726\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.00000 | + | 5.19615i | −0.147979 | + | 0.256307i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | − | 6.92820i | 0.196352 | − | 0.340092i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.00000 | − | 10.3923i | −0.293821 | − | 0.508913i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.00000 | + | 1.73205i | −0.0485071 | + | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | + | 6.92820i | −0.193122 | + | 0.334497i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | + | 27.7128i | 0.770693 | + | 1.33488i | 0.937184 | + | 0.348836i | \(0.113423\pi\) |
−0.166491 | + | 0.986043i | \(0.553244\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.0000 | −0.575356 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.0000 | + | 27.7128i | 0.765384 | + | 1.32568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0000 | − | 17.3205i | 0.475114 | − | 0.822922i | −0.524479 | − | 0.851423i | \(-0.675740\pi\) |
0.999594 | + | 0.0285009i | \(0.00907336\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | − | 10.3923i | −0.284427 | − | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.0000 | −0.662177 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | + | 20.7846i | 0.565058 | + | 0.978709i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.00000 | − | 13.8564i | 0.375873 | − | 0.651031i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0000 | − | 19.0526i | 0.514558 | − | 0.891241i | −0.485299 | − | 0.874348i | \(-0.661289\pi\) |
0.999857 | − | 0.0168929i | \(-0.00537742\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | − | 1.73205i | −0.0466760 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.0000 | 1.21094 | 0.605470 | − | 0.795868i | \(-0.292985\pi\) | ||||
0.605470 | + | 0.795868i | \(0.292985\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.00000 | + | 13.8564i | 0.370991 | + | 0.642575i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.0000 | − | 31.1769i | 0.832941 | − | 1.44270i | −0.0627555 | − | 0.998029i | \(-0.519989\pi\) |
0.895696 | − | 0.444667i | \(-0.146678\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.00000 | − | 1.73205i | 0.0460776 | − | 0.0798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.00000 | − | 13.8564i | −0.367840 | − | 0.637118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.00000 | + | 13.8564i | 0.365529 | + | 0.633115i | 0.988861 | − | 0.148842i | \(-0.0475547\pi\) |
−0.623332 | + | 0.781958i | \(0.714221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | + | 10.3923i | −0.273576 | + | 0.473848i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.00000 | − | 3.46410i | 0.0908153 | − | 0.157297i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0000 | − | 27.7128i | −0.725029 | − | 1.25579i | −0.958962 | − | 0.283535i | \(-0.908493\pi\) |
0.233933 | − | 0.972253i | \(-0.424840\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.00000 | + | 10.3923i | 0.270226 | + | 0.468046i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.00000 | − | 6.92820i | 0.179787 | − | 0.311400i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.00000 | − | 10.3923i | 0.268597 | − | 0.465223i | −0.699903 | − | 0.714238i | \(-0.746773\pi\) |
0.968500 | + | 0.249015i | \(0.0801067\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | + | 20.7846i | 0.536120 | + | 0.928588i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.50000 | − | 7.79423i | −0.199852 | − | 0.346154i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.00000 | − | 5.19615i | 0.132973 | − | 0.230315i | −0.791849 | − | 0.610718i | \(-0.790881\pi\) |
0.924821 | + | 0.380402i | \(0.124214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.00000 | + | 3.46410i | −0.0883022 | + | 0.152944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.0000 | − | 27.7128i | −0.705044 | − | 1.22117i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0000 | + | 22.5167i | 0.569540 | + | 0.986473i | 0.996611 | + | 0.0822547i | \(0.0262121\pi\) |
−0.427071 | + | 0.904218i | \(0.640455\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.00000 | + | 3.46410i | −0.0874539 | + | 0.151475i | −0.906434 | − | 0.422347i | \(-0.861206\pi\) |
0.818980 | + | 0.573822i | \(0.194540\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.00000 | − | 13.8564i | 0.348485 | − | 0.603595i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | − | 35.5070i | −0.891304 | − | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0000 | − | 20.7846i | −0.518805 | − | 0.898597i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.00000 | + | 10.3923i | −0.258919 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.00000 | − | 15.5885i | 0.386940 | − | 0.670200i | −0.605096 | − | 0.796152i | \(-0.706865\pi\) |
0.992036 | + | 0.125952i | \(0.0401986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.00000 | − | 5.19615i | −0.128742 | − | 0.222988i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.00000 | −0.171341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.0000 | −1.88130 | −0.940652 | − | 0.339372i | \(-0.889785\pi\) | ||||
−0.940652 | + | 0.339372i | \(0.889785\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000 | − | 20.7846i | 0.511217 | − | 0.885454i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.00000 | − | 10.3923i | 0.254686 | − | 0.441129i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.0000 | + | 22.5167i | 0.550828 | + | 0.954062i | 0.998215 | + | 0.0597213i | \(0.0190212\pi\) |
−0.447387 | + | 0.894340i | \(0.647645\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.0000 | − | 24.2487i | −0.590030 | − | 1.02196i | −0.994228 | − | 0.107290i | \(-0.965783\pi\) |
0.404198 | − | 0.914671i | \(-0.367551\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0000 | + | 31.1769i | −0.757266 | + | 1.31162i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.00000 | + | 8.66025i | −0.209611 | + | 0.363057i | −0.951592 | − | 0.307364i | \(-0.900553\pi\) |
0.741981 | + | 0.670421i | \(0.233886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.0000 | + | 31.1769i | 0.753277 | + | 1.30471i | 0.946227 | + | 0.323505i | \(0.104861\pi\) |
−0.192950 | + | 0.981209i | \(0.561806\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.00000 | −0.333623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.00000 | + | 1.73205i | 0.0416305 | + | 0.0721062i | 0.886090 | − | 0.463513i | \(-0.153411\pi\) |
−0.844459 | + | 0.535620i | \(0.820078\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.00000 | − | 1.73205i | 0.0415586 | − | 0.0719816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.00000 | + | 6.92820i | −0.165663 | + | 0.286937i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.00000 | − | 3.46410i | −0.0826898 | − | 0.143223i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.0000 | −1.81607 | −0.908037 | − | 0.418890i | \(-0.862419\pi\) | ||||
−0.908037 | + | 0.418890i | \(0.862419\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.0000 | −1.31854 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.00000 | − | 15.5885i | −0.370211 | − | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.00000 | + | 12.1244i | −0.287456 | + | 0.497888i | −0.973202 | − | 0.229953i | \(-0.926143\pi\) |
0.685746 | + | 0.727841i | \(0.259476\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.00000 | − | 13.8564i | 0.327418 | − | 0.567105i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | + | 20.7846i | 0.490307 | + | 0.849236i | 0.999938 | − | 0.0111569i | \(-0.00355143\pi\) |
−0.509631 | + | 0.860393i | \(0.670218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000 | 0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.00000 | − | 8.66025i | −0.203279 | − | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.0000 | − | 34.6410i | 0.811775 | − | 1.40604i | −0.0998457 | − | 0.995003i | \(-0.531835\pi\) |
0.911621 | − | 0.411033i | \(-0.134832\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0000 | − | 32.9090i | −0.767403 | − | 1.32918i | −0.938967 | − | 0.344008i | \(-0.888215\pi\) |
0.171564 | − | 0.985173i | \(-0.445118\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.0000 | −0.483887 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.0000 | 1.69086 | 0.845428 | − | 0.534089i | \(-0.179345\pi\) | ||||
0.845428 | + | 0.534089i | \(0.179345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0000 | + | 38.1051i | 0.884255 | + | 1.53157i | 0.846566 | + | 0.532284i | \(0.178666\pi\) |
0.0376891 | + | 0.999290i | \(0.488000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | − | 6.92820i | 0.160514 | − | 0.278019i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.00000 | + | 13.8564i | 0.319489 | + | 0.553372i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.0000 | + | 17.3205i | 0.397464 | + | 0.688428i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | + | 13.8564i | −0.317470 | + | 0.549875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.00000 | − | 6.92820i | 0.158238 | − | 0.274075i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.00000 | + | 12.1244i | 0.276483 | + | 0.478883i | 0.970508 | − | 0.241068i | \(-0.0774976\pi\) |
−0.694025 | + | 0.719951i | \(0.744164\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0000 | 0.473234 | 0.236617 | − | 0.971603i | \(-0.423961\pi\) | ||||
0.236617 | + | 0.971603i | \(0.423961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000 | 0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.00000 | − | 6.92820i | −0.157256 | − | 0.272376i | 0.776622 | − | 0.629967i | \(-0.216932\pi\) |
−0.933878 | + | 0.357591i | \(0.883598\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | − | 13.8564i | 0.314027 | − | 0.543912i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.00000 | + | 5.19615i | −0.117399 | + | 0.203341i | −0.918736 | − | 0.394872i | \(-0.870789\pi\) |
0.801337 | + | 0.598213i | \(0.204122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | + | 6.92820i | 0.156293 | + | 0.270707i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.0000 | −0.390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.00000 | − | 8.66025i | −0.194477 | − | 0.336845i | 0.752252 | − | 0.658876i | \(-0.228968\pi\) |
−0.946729 | + | 0.322031i | \(0.895634\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.00000 | + | 3.46410i | −0.0776736 | + | 0.134535i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.0000 | + | 41.5692i | −0.929284 | + | 1.60957i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.00000 | − | 6.92820i | −0.154649 | − | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.00000 | −0.308837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.00000 | + | 1.73205i | −0.0384331 | + | 0.0665681i | −0.884602 | − | 0.466347i | \(-0.845570\pi\) |
0.846169 | + | 0.532915i | \(0.178903\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | − | 10.3923i | 0.229920 | − | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.00000 | + | 3.46410i | 0.0765279 | + | 0.132550i | 0.901750 | − | 0.432259i | \(-0.142283\pi\) |
−0.825222 | + | 0.564809i | \(0.808950\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.0000 | 0.839352 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00000 | + | 3.46410i | 0.0761939 | + | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.00000 | − | 3.46410i | 0.0760836 | − | 0.131781i | −0.825473 | − | 0.564441i | \(-0.809092\pi\) |
0.901557 | + | 0.432660i | \(0.142425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.0000 | − | 20.7846i | 0.455186 | − | 0.788405i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.00000 | + | 10.3923i | 0.227266 | + | 0.393637i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.0000 | −0.378235 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | + | 20.7846i | 0.452589 | + | 0.783906i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | − | 8.66025i | 0.187779 | − | 0.325243i | −0.756730 | − | 0.653727i | \(-0.773204\pi\) |
0.944509 | + | 0.328484i | \(0.106538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | − | 6.92820i | −0.150012 | − | 0.259828i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 64.0000 | 2.39682 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.0000 | −0.598366 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.00000 | + | 13.8564i | 0.298765 | + | 0.517477i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.0000 | − | 27.7128i | 0.596699 | − | 1.03351i | −0.396605 | − | 0.917989i | \(-0.629812\pi\) |
0.993305 | − | 0.115524i | \(-0.0368548\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.00000 | + | 15.5885i | −0.334714 | + | 0.579741i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.00000 | + | 5.19615i | 0.111417 | + | 0.192980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.0000 | 1.78022 | 0.890111 | − | 0.455744i | \(-0.150627\pi\) | ||||
0.890111 | + | 0.455744i | \(0.150627\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | − | 6.92820i | −0.147945 | − | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.00000 | − | 12.1244i | 0.258551 | − | 0.447823i | −0.707303 | − | 0.706910i | \(-0.750088\pi\) |
0.965854 | + | 0.259087i | \(0.0834217\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.00000 | − | 13.8564i | 0.294684 | − | 0.510407i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.00000 | − | 3.46410i | −0.0735712 | − | 0.127429i | 0.826893 | − | 0.562360i | \(-0.190106\pi\) |
−0.900464 | + | 0.434930i | \(0.856773\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.00000 | 0.293887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.00000 | 0.293492 | 0.146746 | − | 0.989174i | \(-0.453120\pi\) | ||||
0.146746 | + | 0.989174i | \(0.453120\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.0000 | − | 24.2487i | −0.512920 | − | 0.888404i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.00000 | − | 3.46410i | 0.0731762 | − | 0.126745i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0000 | − | 20.7846i | 0.437886 | − | 0.758441i | −0.559640 | − | 0.828736i | \(-0.689061\pi\) |
0.997526 | + | 0.0702946i | \(0.0223939\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.0000 | + | 17.3205i | 0.364420 | + | 0.631194i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.0000 | 1.16460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.0000 | − | 27.7128i | −0.580763 | − | 1.00591i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.0000 | + | 19.0526i | −0.398750 | + | 0.690655i | −0.993572 | − | 0.113203i | \(-0.963889\pi\) |
0.594822 | + | 0.803857i | \(0.297222\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.00000 | − | 3.46410i | 0.0723102 | − | 0.125245i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00000 | − | 6.92820i | −0.144432 | − | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.00000 | −0.0721218 | −0.0360609 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360609 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.00000 | 0.0720282 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.00000 | − | 15.5885i | −0.323708 | − | 0.560678i | 0.657542 | − | 0.753418i | \(-0.271596\pi\) |
−0.981250 | + | 0.192740i | \(0.938263\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | − | 6.92820i | 0.143684 | − | 0.248868i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0000 | − | 20.7846i | 0.429945 | − | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0000 | − | 27.7128i | −0.572525 | − | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.00000 | −0.214423 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.00000 | 0.142766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0000 | − | 24.2487i | −0.499046 | − | 0.864373i | 0.500953 | − | 0.865474i | \(-0.332983\pi\) |
−0.999999 | + | 0.00110111i | \(0.999650\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.00000 | − | 6.92820i | 0.142404 | − | 0.246651i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.00000 | + | 3.46410i | −0.0710221 | + | 0.123014i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.00000 | − | 3.46410i | −0.0709327 | − | 0.122859i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.0000 | −0.779280 | −0.389640 | − | 0.920967i | \(-0.627401\pi\) | ||||
−0.389640 | + | 0.920967i | \(0.627401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | − | 5.19615i | −0.106000 | − | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.0000 | + | 34.6410i | −0.705785 | + | 1.22245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.00000 | − | 8.66025i | 0.176008 | − | 0.304855i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.0000 | − | 22.5167i | −0.457056 | − | 0.791644i | 0.541748 | − | 0.840541i | \(-0.317763\pi\) |
−0.998804 | + | 0.0488972i | \(0.984429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.00000 | 0.140459 | 0.0702295 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702295 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.00000 | −0.280572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0000 | + | 20.7846i | 0.420342 | + | 0.728053i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | + | 13.8564i | −0.279885 | + | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0000 | + | 25.9808i | −0.523504 | + | 0.906735i | 0.476122 | + | 0.879379i | \(0.342042\pi\) |
−0.999626 | + | 0.0273557i | \(0.991291\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | − | 13.8564i | −0.278862 | − | 0.483004i | 0.692240 | − | 0.721668i | \(-0.256624\pi\) |
−0.971102 | + | 0.238664i | \(0.923291\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.00000 | −0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.0000 | 0.973655 | 0.486828 | − | 0.873498i | \(-0.338154\pi\) | ||||
0.486828 | + | 0.873498i | \(0.338154\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.0000 | − | 43.3013i | −0.868286 | − | 1.50392i | −0.863747 | − | 0.503926i | \(-0.831889\pi\) |
−0.00453881 | − | 0.999990i | \(-0.501445\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.0000 | + | 22.5167i | −0.450965 | + | 0.781094i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.0000 | + | 41.5692i | −0.830554 | + | 1.43856i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.00000 | + | 6.92820i | 0.138260 | + | 0.239474i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.0000 | + | 22.5167i | 0.447744 | + | 0.775515i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.00000 | − | 15.5885i | 0.309609 | − | 0.536259i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.0000 | + | 24.2487i | −0.480479 | + | 0.832214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.0000 | − | 41.5692i | −0.822709 | − | 1.42497i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.0000 | 0.342393 | 0.171197 | − | 0.985237i | \(-0.445237\pi\) | ||||
0.171197 | + | 0.985237i | \(0.445237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.00000 | −0.273594 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0000 | + | 36.3731i | 0.717346 | + | 1.24248i | 0.962048 | + | 0.272882i | \(0.0879768\pi\) |
−0.244701 | + | 0.969599i | \(0.578690\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.00000 | − | 10.3923i | 0.204717 | − | 0.354581i | −0.745325 | − | 0.666701i | \(-0.767706\pi\) |
0.950043 | + | 0.312120i | \(0.101039\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.0000 | + | 27.7128i | −0.544646 | + | 0.943355i | 0.453983 | + | 0.891010i | \(0.350003\pi\) |
−0.998629 | + | 0.0523446i | \(0.983331\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.00000 | + | 10.3923i | 0.204006 | + | 0.353349i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.0000 | −1.08553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.00000 | − | 6.92820i | −0.135535 | − | 0.234753i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.00000 | − | 1.73205i | 0.0338449 | − | 0.0586210i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.00000 | − | 15.5885i | 0.303908 | − | 0.526385i | −0.673109 | − | 0.739543i | \(-0.735042\pi\) |
0.977018 | + | 0.213158i | \(0.0683750\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.00000 | + | 15.5885i | 0.303562 | + | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.0000 | −1.68454 | −0.842271 | − | 0.539054i | \(-0.818782\pi\) | ||||
−0.842271 | + | 0.539054i | \(0.818782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00000 | 0.134611 | 0.0673054 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673054 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.00000 | + | 6.92820i | 0.134459 | + | 0.232889i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.00000 | + | 6.92820i | −0.134307 | + | 0.232626i | −0.925332 | − | 0.379157i | \(-0.876214\pi\) |
0.791026 | + | 0.611783i | \(0.209547\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000 | − | 3.46410i | 0.0670025 | − | 0.116052i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.0000 | −0.802232 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.0000 | −0.534224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.0000 | − | 41.5692i | −0.800445 | − | 1.38641i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.00000 | + | 3.46410i | −0.0666297 | + | 0.115406i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.00000 | − | 10.3923i | 0.199447 | − | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.00000 | + | 3.46410i | 0.0664089 | + | 0.115024i | 0.897318 | − | 0.441384i | \(-0.145512\pi\) |
−0.830909 | + | 0.556408i | \(0.812179\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | − | 13.8564i | −0.264761 | − | 0.458580i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.00000 | − | 3.46410i | 0.0661180 | − | 0.114520i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | − | 13.8564i | 0.263896 | − | 0.457081i | −0.703378 | − | 0.710816i | \(-0.748326\pi\) |
0.967274 | + | 0.253735i | \(0.0816592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.00000 | + | 10.3923i | 0.197707 | + | 0.342438i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.0000 | −0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.00000 | − | 13.8564i | −0.262754 | − | 0.455104i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.0000 | − | 43.3013i | 0.820223 | − | 1.42067i | −0.0852924 | − | 0.996356i | \(-0.527182\pi\) |
0.905516 | − | 0.424313i | \(-0.139484\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.0000 | + | 20.7846i | −0.392862 | + | 0.680458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.00000 | − | 13.8564i | −0.261628 | − | 0.453153i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.0000 | −1.37208 | −0.686040 | − | 0.727564i | \(-0.740653\pi\) | ||||
−0.686040 | + | 0.727564i | \(0.740653\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.00000 | −0.195803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.00000 | + | 5.19615i | 0.0977972 | + | 0.169390i | 0.910773 | − | 0.412908i | \(-0.135487\pi\) |
−0.812975 | + | 0.582298i | \(0.802154\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0000 | + | 41.5692i | −0.781548 | + | 1.35368i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.00000 | − | 10.3923i | 0.194974 | − | 0.337705i | −0.751918 | − | 0.659256i | \(-0.770871\pi\) |
0.946892 | + | 0.321552i | \(0.104204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0000 | + | 17.3205i | 0.324614 | + | 0.562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.00000 | −0.194563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.0000 | −1.74923 | −0.874616 | − | 0.484817i | \(-0.838886\pi\) | ||||
−0.874616 | + | 0.484817i | \(0.838886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.0000 | + | 20.7846i | −0.387905 | + | 0.671871i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.00000 | − | 10.3923i | −0.193347 | − | 0.334887i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0000 | 0.514525 | 0.257263 | − | 0.966342i | \(-0.417179\pi\) | ||||
0.257263 | + | 0.966342i | \(0.417179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.00000 | + | 6.92820i | 0.128499 | + | 0.222566i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | + | 31.1769i | −0.577647 | + | 1.00051i | 0.418101 | + | 0.908401i | \(0.362696\pi\) |
−0.995748 | + | 0.0921142i | \(0.970638\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00000 | + | 1.73205i | −0.0320256 | + | 0.0554700i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.0000 | + | 25.9808i | 0.479893 | + | 0.831198i | 0.999734 | − | 0.0230645i | \(-0.00734232\pi\) |
−0.519841 | + | 0.854263i | \(0.674009\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.0000 | −0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.0000 | + | 20.7846i | 0.382741 | + | 0.662926i | 0.991453 | − | 0.130465i | \(-0.0416470\pi\) |
−0.608712 | + | 0.793391i | \(0.708314\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.0000 | − | 31.1769i | 0.573528 | − | 0.993379i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.0000 | − | 27.7128i | 0.508770 | − | 0.881216i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | + | 34.6410i | 0.635321 | + | 1.10041i | 0.986447 | + | 0.164080i | \(0.0524655\pi\) |
−0.351126 | + | 0.936328i | \(0.614201\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.0000 | 0.634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.0000 | 1.01447 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.0000 | − | 22.5167i | −0.411714 | − | 0.713110i | 0.583363 | − | 0.812211i | \(-0.301736\pi\) |
−0.995077 | + | 0.0991016i | \(0.968403\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.00000 | − | 5.19615i | 0.0949158 | − | 0.164399i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))