Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,2,Mod(2,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.2");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.k (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.311416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{12}]$ |
Embedding invariants
Embedding label | 32.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.32 |
Dual form | 39.2.k.a.11.1 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{12}\right)\) |
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 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(3\) | 0.866025 | − | 1.50000i | 0.500000 | − | 0.866025i | ||||
\(4\) | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | ||||
\(5\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.767949 | + | 2.86603i | −0.290258 | + | 1.08326i | 0.654654 | + | 0.755929i | \(0.272814\pi\) |
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(12\) | 3.46410i | 1.00000i | ||||||||
\(13\) | −2.59808 | − | 2.50000i | −0.720577 | − | 0.693375i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.83013 | + | 2.09808i | 1.79635 | + | 0.481332i | 0.993399 | − | 0.114708i | \(-0.0365932\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.63397 | + | 3.63397i | 0.792998 | + | 0.792998i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 5.00000i | − | 1.00000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | −1.53590 | − | 5.73205i | −0.290258 | − | 1.08326i | ||||
\(29\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.83013 | + | 7.83013i | −1.40633 | + | 1.40633i | −0.628619 | + | 0.777714i | \(0.716379\pi\) |
−0.777714 | + | 0.628619i | \(0.783621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.19615 | + | 3.00000i | 0.866025 | + | 0.500000i | ||||
\(37\) | 2.09808 | − | 0.562178i | 0.344922 | − | 0.0924215i | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) |
0.427121 | + | 0.904194i | \(0.359528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.00000 | + | 1.73205i | −0.960769 | + | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.50000 | + | 0.866025i | −0.228748 | + | 0.132068i | −0.609994 | − | 0.792406i | \(-0.708828\pi\) |
0.381246 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | −3.46410 | − | 6.00000i | −0.500000 | − | 0.866025i | ||||
\(49\) | −1.56218 | − | 0.901924i | −0.223168 | − | 0.128846i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.00000 | + | 1.73205i | 0.970725 | + | 0.240192i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.92820 | − | 9.92820i | 1.31502 | − | 1.31502i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.33013 | + | 7.50000i | 0.554416 | + | 0.960277i | 0.997949 | + | 0.0640184i | \(0.0203916\pi\) |
−0.443533 | + | 0.896258i | \(0.646275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.59808 | − | 2.30385i | 1.08326 | − | 0.290258i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.205771 | + | 0.767949i | 0.0251390 | + | 0.0938199i | 0.977356 | − | 0.211604i | \(-0.0678686\pi\) |
−0.952217 | + | 0.305424i | \(0.901202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.36603 | − | 9.36603i | −1.09621 | − | 1.09621i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
−0.101361 | − | 0.994850i | \(-0.532320\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.50000 | − | 4.33013i | −0.866025 | − | 0.500000i | ||||
\(76\) | −15.6603 | + | 4.19615i | −1.79635 | + | 0.481332i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.1244 | 1.36410 | 0.682048 | − | 0.731307i | \(-0.261089\pi\) | ||||
0.682048 | + | 0.731307i | \(0.261089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | −9.92820 | − | 2.66025i | −1.08326 | − | 0.290258i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.16025 | − | 5.52628i | 0.960256 | − | 0.579311i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.96410 | + | 18.5263i | 0.514753 | + | 1.92109i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.4282 | − | 4.40192i | −1.66803 | − | 0.446948i | −0.703452 | − | 0.710742i | \(-0.748359\pi\) |
−0.964579 | + | 0.263795i | \(0.915026\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000 | + | 8.66025i | 0.500000 | + | 0.866025i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.5885i | − | 1.53598i | −0.640464 | − | 0.767988i | \(-0.721258\pi\) | ||
0.640464 | − | 0.767988i | \(-0.278742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 9.00000 | − | 5.19615i | 0.866025 | − | 0.500000i | ||||
\(109\) | 5.16987 | − | 5.16987i | 0.495184 | − | 0.495184i | −0.414751 | − | 0.909935i | \(-0.636131\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.973721 | − | 3.63397i | 0.0924215 | − | 0.344922i | ||||
\(112\) | 8.39230 | + | 8.39230i | 0.792998 | + | 0.792998i | ||||
\(113\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.59808 | + | 10.5000i | −0.240192 | + | 0.970725i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.52628 | − | 5.50000i | 0.866025 | − | 0.500000i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.73205 | − | 21.3923i | 0.514753 | − | 1.92109i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.866025 | − | 0.500000i | −0.0768473 | − | 0.0443678i | 0.461084 | − | 0.887357i | \(-0.347461\pi\) |
−0.537931 | + | 0.842989i | \(0.680794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.00000i | 0.264135i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0263 | + | 20.8301i | −1.04281 | + | 1.80620i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.50000 | + | 6.06218i | 0.296866 | + | 0.514187i | 0.975417 | − | 0.220366i | \(-0.0707252\pi\) |
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.0000 | −1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.70577 | + | 1.56218i | −0.223168 | + | 0.128846i | ||||
\(148\) | −3.07180 | + | 3.07180i | −0.252500 | + | 0.252500i | ||||
\(149\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1244 | − | 14.1244i | −1.14942 | − | 1.14942i | −0.986666 | − | 0.162758i | \(-0.947961\pi\) |
−0.162758 | − | 0.986666i | \(-0.552039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 8.66025 | − | 9.00000i | 0.693375 | − | 0.720577i | ||||
\(157\) | −11.0000 | −0.877896 | −0.438948 | − | 0.898513i | \(-0.644649\pi\) | ||||
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.52628 | + | 20.6244i | −0.432852 | + | 1.61542i | 0.313304 | + | 0.949653i | \(0.398564\pi\) |
−0.746156 | + | 0.665771i | \(0.768103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | + | 12.9904i | 0.0384615 | + | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.29423 | − | 23.4904i | −0.481332 | − | 1.79635i | ||||
\(172\) | 1.73205 | − | 3.00000i | 0.132068 | − | 0.228748i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.3301 | + | 3.83975i | 1.08326 | + | 0.290258i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.92820i | 0.514969i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.0000 | 1.10883 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.99038 | − | 14.8923i | 0.290258 | − | 1.08326i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 12.0000 | + | 6.92820i | 0.866025 | + | 0.500000i | ||||
\(193\) | 26.3564 | − | 7.06218i | 1.89718 | − | 0.508347i | 0.899770 | − | 0.436365i | \(-0.143734\pi\) |
0.997406 | − | 0.0719816i | \(-0.0229323\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.60770 | 0.257693 | ||||||||
\(197\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.7224 | + | 8.50000i | −1.04365 | + | 0.602549i | −0.920864 | − | 0.389885i | \(-0.872515\pi\) |
−0.122782 | + | 0.992434i | \(0.539182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.33013 | + | 0.356406i | 0.0938199 | + | 0.0251390i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.8564 | + | 4.00000i | −0.960769 | + | 0.277350i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9904 | − | 22.5000i | 0.894295 | − | 1.54896i | 0.0596196 | − | 0.998221i | \(-0.481011\pi\) |
0.834675 | − | 0.550743i | \(-0.185655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.4282 | − | 28.4545i | −1.11522 | − | 1.93162i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −22.1603 | + | 5.93782i | −1.49745 | + | 0.401241i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.22243 | + | 12.0263i | 0.215790 | + | 0.805339i | 0.985887 | + | 0.167412i | \(0.0535411\pi\) |
−0.770097 | + | 0.637927i | \(0.779792\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.9904 | + | 7.50000i | −0.866025 | + | 0.500000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(228\) | −7.26795 | + | 27.1244i | −0.481332 | + | 1.79635i | ||||
\(229\) | 21.3923 | + | 21.3923i | 1.41364 | + | 1.41364i | 0.726900 | + | 0.686743i | \(0.240960\pi\) |
0.686743 | + | 0.726900i | \(0.259040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.5000 | − | 18.1865i | 0.682048 | − | 1.18134i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.50962 | + | 9.36603i | −0.161659 | + | 0.603319i | 0.836784 | + | 0.547533i | \(0.184433\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.79423 | + | 13.5000i | 0.500000 | + | 0.866025i | ||||
\(244\) | −15.0000 | − | 8.66025i | −0.960277 | − | 0.554416i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.0981 | − | 25.0263i | −0.960668 | − | 1.59238i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(252\) | −12.5885 | + | 12.5885i | −0.792998 | + | 0.792998i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.44486i | 0.400464i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.12436 | − | 1.12436i | −0.0686810 | − | 0.0686810i | ||||
\(269\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.16025 | + | 2.45448i | −0.556446 | + | 0.149099i | −0.526073 | − | 0.850439i | \(-0.676336\pi\) |
−0.0303728 | + | 0.999539i | \(0.509669\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.356406 | − | 18.5263i | −0.0215707 | − | 1.12126i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.0000 | − | 10.3923i | 1.08152 | − | 0.624413i | 0.150210 | − | 0.988654i | \(-0.452005\pi\) |
0.931305 | + | 0.364241i | \(0.118672\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 32.0885 | + | 8.59808i | 1.92109 | + | 0.514753i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.6506 | + | 12.5000i | 1.28700 | + | 0.743048i | 0.978117 | − | 0.208053i | \(-0.0667128\pi\) |
0.308879 | + | 0.951101i | \(0.400046\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.8301 | + | 20.8301i | −1.22108 | + | 1.22108i | ||||
\(292\) | 25.5885 | + | 6.85641i | 1.49745 | + | 0.401241i | ||||
\(293\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 17.3205 | 1.00000 | ||||||||
\(301\) | −1.33013 | − | 4.96410i | −0.0766672 | − | 0.286126i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 22.9282 | − | 22.9282i | 1.31502 | − | 1.31502i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.6340 | + | 16.6340i | 0.949351 | + | 0.949351i | 0.998778 | − | 0.0494267i | \(-0.0157394\pi\) |
−0.0494267 | + | 0.998778i | \(0.515739\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.3827 | − | 13.5000i | −1.33019 | − | 0.767988i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.9090 | −1.86012 | −0.930062 | − | 0.367402i | \(-0.880247\pi\) | ||||
−0.930062 | + | 0.367402i | \(0.880247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −21.0000 | + | 12.1244i | −1.18134 | + | 0.682048i | ||||
\(317\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 18.0000i | − | 1.00000i | ||||||
\(325\) | −12.5000 | + | 12.9904i | −0.693375 | + | 0.720577i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.27757 | − | 12.2321i | −0.181250 | − | 0.676434i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.1865 | − | 9.16025i | −1.87906 | − | 0.503493i | −0.999622 | − | 0.0274825i | \(-0.991251\pi\) |
−0.879440 | − | 0.476011i | \(-0.842082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.60770 | − | 4.60770i | −0.252500 | − | 0.252500i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 19.8564 | − | 5.32051i | 1.08326 | − | 0.290258i | ||||
\(337\) | 29.0000i | 1.57973i | 0.613280 | + | 0.789865i | \(0.289850\pi\) | ||||
−0.613280 | + | 0.789865i | \(0.710150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.9019 | + | 10.9019i | −0.588649 | + | 0.588649i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.40192 | + | 1.17949i | −0.235630 | + | 0.0631368i | −0.374701 | − | 0.927146i | \(-0.622255\pi\) |
0.139072 | + | 0.990282i | \(0.455588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.5000 | + | 12.9904i | 0.720577 | + | 0.693375i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.4545 | + | 23.3564i | 2.12918 | + | 1.22928i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 19.0526i | − | 1.00000i | ||||||
\(364\) | −10.3397 | + | 18.7321i | −0.541950 | + | 0.981826i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.5000 | + | 26.8468i | −0.809093 | + | 1.40139i | 0.104399 | + | 0.994535i | \(0.466708\pi\) |
−0.913493 | + | 0.406855i | \(0.866625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −27.1244 | − | 27.1244i | −1.40633 | − | 1.40633i | ||||
\(373\) | −18.1865 | − | 31.5000i | −0.941663 | − | 1.63101i | −0.762299 | − | 0.647225i | \(-0.775929\pi\) |
−0.179364 | − | 0.983783i | \(-0.557404\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.55256 | − | 16.9904i | −0.233849 | − | 0.872737i | −0.978664 | − | 0.205466i | \(-0.934129\pi\) |
0.744815 | − | 0.667271i | \(-0.232538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.50000 | + | 0.866025i | −0.0768473 | + | 0.0443678i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.50000 | + | 2.59808i | 0.228748 | + | 0.132068i | ||||
\(388\) | 32.8564 | − | 8.80385i | 1.66803 | − | 0.446948i | ||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.47372 | − | 27.8923i | 0.375095 | − | 1.39987i | −0.478110 | − | 0.878300i | \(-0.658678\pi\) |
0.853206 | − | 0.521575i | \(-0.174655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.8301 | + | 36.0788i | 1.04281 | + | 1.80620i | ||||
\(400\) | −17.3205 | − | 10.0000i | −0.866025 | − | 0.500000i | ||||
\(401\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 39.9186 | − | 0.767949i | 1.98849 | − | 0.0382543i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.42820 | − | 0.918584i | −0.169514 | − | 0.0454211i | 0.173064 | − | 0.984911i | \(-0.444633\pi\) |
−0.342578 | + | 0.939490i | \(0.611300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.5885 | + | 27.0000i | 0.767988 | + | 1.33019i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.1244 | 0.593732 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.6865 | − | 27.6865i | 1.34936 | − | 1.34936i | 0.463002 | − | 0.886357i | \(-0.346772\pi\) |
0.886357 | − | 0.463002i | \(-0.153228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.8205 | + | 6.65064i | −1.20115 | + | 0.321847i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(432\) | −10.3923 | + | 18.0000i | −0.500000 | + | 0.866025i | ||||
\(433\) | 30.3109 | − | 17.5000i | 1.45665 | − | 0.840996i | 0.457804 | − | 0.889053i | \(-0.348636\pi\) |
0.998845 | + | 0.0480569i | \(0.0153029\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.78461 | + | 14.1244i | −0.181250 | + | 0.676434i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.5000 | − | 19.9186i | −1.64660 | − | 0.950662i | −0.978412 | − | 0.206666i | \(-0.933739\pi\) |
−0.668184 | − | 0.743996i | \(-0.732928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.41154i | 0.257693i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | 1.94744 | + | 7.26795i | 0.0924215 | + | 0.344922i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −22.9282 | − | 6.14359i | −1.08326 | − | 0.290258i | ||||
\(449\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.4186 | + | 8.95448i | −1.57014 | + | 0.420718i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.72243 | + | 36.2846i | 0.454796 | + | 1.69732i | 0.688686 | + | 0.725059i | \(0.258188\pi\) |
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.3660 | − | 22.3660i | −1.03944 | − | 1.03944i | −0.999190 | − | 0.0402476i | \(-0.987185\pi\) |
−0.0402476 | − | 0.999190i | \(-0.512815\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | −6.00000 | − | 20.7846i | −0.277350 | − | 0.960769i | ||||
\(469\) | −2.35898 | −0.108928 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.52628 | + | 16.5000i | −0.438948 | + | 0.760280i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.4904 | − | 39.1506i | 0.481332 | − | 1.79635i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.85641 | − | 3.78461i | −0.312625 | − | 0.172563i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0000 | + | 19.0526i | −0.500000 | + | 0.866025i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.6865 | − | 7.41858i | −1.25460 | − | 0.336168i | −0.430486 | − | 0.902597i | \(-0.641658\pi\) |
−0.824110 | + | 0.566429i | \(0.808325\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 26.1506 | + | 26.1506i | 1.18257 | + | 1.18257i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.4641 | + | 42.7846i | 0.514753 | + | 1.92109i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.411543 | − | 0.411543i | 0.0184232 | − | 0.0184232i | −0.697835 | − | 0.716258i | \(-0.745853\pi\) |
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.9186 | + | 10.5000i | 0.884615 | + | 0.466321i | ||||
\(508\) | 2.00000 | 0.0887357 | ||||||||
\(509\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.0359 | − | 19.6506i | 1.50566 | − | 0.869293i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −40.6865 | − | 10.9019i | −1.79635 | − | 0.481332i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.00000 | − | 5.19615i | −0.132068 | − | 0.228748i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000 | − | 6.92820i | 0.174908 | − | 0.302949i | −0.765222 | − | 0.643767i | \(-0.777371\pi\) |
0.940129 | + | 0.340818i | \(0.110704\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.1699 | − | 18.1699i | 0.792998 | − | 0.792998i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 48.1051i | − | 2.08562i | ||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.1506 | + | 13.1506i | 0.565390 | + | 0.565390i | 0.930834 | − | 0.365444i | \(-0.119083\pi\) |
−0.365444 | + | 0.930834i | \(0.619083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3923 | + | 6.00000i | 0.445976 | + | 0.257485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.0000 | 1.75303 | 0.876517 | − | 0.481371i | \(-0.159861\pi\) | ||||
0.876517 | + | 0.481371i | \(0.159861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.9904 | − | 22.5000i | 0.554416 | − | 0.960277i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.31089 | + | 34.7487i | −0.395939 | + | 1.47767i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.1244 | − | 7.00000i | −0.514187 | − | 0.296866i | ||||
\(557\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.06218 | + | 1.50000i | 0.256403 | + | 0.0634432i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.8827 | − | 18.8827i | −0.792998 | − | 0.792998i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0000i | 0.669579i | 0.942293 | + | 0.334790i | \(0.108665\pi\) | ||||
−0.942293 | + | 0.334790i | \(0.891335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 20.7846 | − | 12.0000i | 0.866025 | − | 0.500000i | ||||
\(577\) | −16.0718 | + | 16.0718i | −0.669078 | + | 0.669078i | −0.957503 | − | 0.288425i | \(-0.906868\pi\) |
0.288425 | + | 0.957503i | \(0.406868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.2321 | − | 45.6506i | 0.508347 | − | 1.89718i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(588\) | 3.12436 | − | 5.41154i | 0.128846 | − | 0.223168i | ||||
\(589\) | −77.7391 | + | 44.8827i | −3.20318 | + | 1.84936i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.24871 | − | 8.39230i | 0.0924215 | − | 0.344922i | ||||
\(593\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.4449i | 1.20510i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.7846 | + | 36.0000i | −0.847822 | + | 1.46847i | 0.0353259 | + | 0.999376i | \(0.488753\pi\) |
−0.883148 | + | 0.469095i | \(0.844580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.68653 | − | 1.68653i | 0.0686810 | − | 0.0686810i | ||||
\(604\) | 38.5885 | + | 10.3397i | 1.57014 | + | 0.420718i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.0000 | + | 17.3205i | 0.405887 | + | 0.703018i | 0.994424 | − | 0.105453i | \(-0.0336291\pi\) |
−0.588537 | + | 0.808470i | \(0.700296\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.7942 | − | 47.7487i | −0.516754 | − | 1.92855i | −0.314806 | − | 0.949156i | \(-0.601939\pi\) |
−0.201948 | − | 0.979396i | \(-0.564727\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.8827 | − | 31.8827i | −1.28147 | − | 1.28147i | −0.939829 | − | 0.341644i | \(-0.889016\pi\) |
−0.341644 | − | 0.939829i | \(-0.610984\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.00000 | + | 24.2487i | −0.240192 | + | 0.970725i | ||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.0526 | − | 11.0000i | 0.760280 | − | 0.438948i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.00962 | + | 33.6244i | −0.358667 | + | 1.33856i | 0.517139 | + | 0.855901i | \(0.326997\pi\) |
−0.875806 | + | 0.482663i | \(0.839670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.5000 | − | 38.9711i | −0.894295 | − | 1.54896i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.80385 | + | 6.24871i | 0.0714710 | + | 0.247583i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.0885 | + | 5.11474i | 0.752775 | + | 0.201706i | 0.614749 | − | 0.788723i | \(-0.289257\pi\) |
0.138027 | + | 0.990429i | \(0.455924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −56.9090 | −2.23044 | ||||||||
\(652\) | −11.0526 | − | 41.2487i | −0.432852 | − | 1.61542i | ||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.2846 | + | 38.3827i | −0.401241 | + | 1.49745i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.1147 | − | 11.8205i | 1.71586 | − | 0.459764i | 0.739014 | − | 0.673690i | \(-0.235292\pi\) |
0.976850 | + | 0.213925i | \(0.0686249\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.8301 | + | 5.58142i | 0.805339 | + | 0.215790i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.5000 | + | 25.1147i | 1.67680 | + | 0.968102i | 0.963679 | + | 0.267063i | \(0.0860531\pi\) |
0.713123 | + | 0.701039i | \(0.247280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.9808i | 1.00000i | ||||||||
\(676\) | −13.8564 | − | 22.0000i | −0.532939 | − | 0.846154i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.2321 | − | 43.7032i | 0.968317 | − | 1.67717i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(684\) | 34.3923 | + | 34.3923i | 1.31502 | + | 1.31502i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 50.6147 | − | 13.5622i | 1.93107 | − | 0.517429i | ||||
\(688\) | 6.92820i | 0.264135i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.48076 | + | 5.52628i | 0.0563308 | + | 0.210230i | 0.988355 | − | 0.152167i | \(-0.0486252\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −28.6603 | + | 7.67949i | −1.08326 | + | 0.290258i | ||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.6077 | 0.664087 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.74871 | − | 32.6506i | 0.328565 | − | 1.22622i | −0.582115 | − | 0.813107i | \(-0.697775\pi\) |
0.910679 | − | 0.413114i | \(-0.135559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.1865 | − | 31.5000i | −0.682048 | − | 1.18134i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.6769 | + | 11.9711i | 1.66386 | + | 0.445829i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.8756 | + | 11.8756i | 0.441660 | + | 0.441660i | ||||
\(724\) | −6.92820 | − | 12.0000i | −0.257485 | − | 0.445976i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 49.0000i | − | 1.81731i | −0.417548 | − | 0.908655i | \(-0.637111\pi\) | ||
0.417548 | − | 0.908655i | \(-0.362889\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −25.9808 | + | 15.0000i | −0.960277 | + | 0.554416i | ||||
\(733\) | −30.3468 | + | 30.3468i | −1.12088 | + | 1.12088i | −0.129275 | + | 0.991609i | \(0.541265\pi\) |
−0.991609 | + | 0.129275i | \(0.958735\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.4186 | + | 12.4378i | −1.70754 | + | 0.457533i | −0.974818 | − | 0.223001i | \(-0.928415\pi\) |
−0.732717 | + | 0.680534i | \(0.761748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −50.6147 | + | 0.973721i | −1.85938 | + | 0.0357705i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.0000 | − | 8.66025i | −0.547358 | − | 0.316017i | 0.200698 | − | 0.979653i | \(-0.435679\pi\) |
−0.748056 | + | 0.663636i | \(0.769012\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 7.98076 | + | 29.7846i | 0.290258 | + | 1.08326i | ||||
\(757\) | 24.2487 | − | 42.0000i | 0.881334 | − | 1.52652i | 0.0314762 | − | 0.999505i | \(-0.489979\pi\) |
0.849858 | − | 0.527011i | \(-0.176688\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.8468 | + | 18.7872i | 0.392680 | + | 0.680142i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −27.7128 | −1.00000 | ||||||||
\(769\) | −9.77757 | − | 36.4904i | −0.352588 | − | 1.31588i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) |
0.530904 | − | 0.847432i | \(-0.321852\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −38.5885 | + | 38.5885i | −1.38883 | + | 1.38883i | ||||
\(773\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.1506 | + | 39.1506i | 1.40633 | + | 1.40633i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.66730 | + | 5.58142i | 0.346812 | + | 0.200232i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.24871 | + | 3.60770i | −0.223168 | + | 0.128846i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.7679 | + | 51.3827i | −0.490774 | + | 1.83159i | 0.0617409 | + | 0.998092i | \(0.480335\pi\) |
−0.552515 | + | 0.833503i | \(0.686332\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.50000 | − | 30.3109i | 0.266333 | − | 1.07637i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.0000 | − | 29.4449i | 0.602549 | − | 1.04365i | ||||
\(797\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −2.66025 | + | 0.712813i | −0.0938199 | + | 0.0251390i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.3468 | + | 17.3468i | −0.609128 | + | 0.609128i | −0.942718 | − | 0.333590i | \(-0.891740\pi\) |
0.333590 | + | 0.942718i | \(0.391740\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.25129 | + | 15.8660i | −0.149099 | + | 0.556446i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.5622 | + | 3.63397i | −0.474481 | + | 0.127137i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −28.0981 | − | 15.5096i | −0.981826 | − | 0.541950i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.0000 | + | 12.1244i | −0.732014 | + | 0.422628i | −0.819159 | − | 0.573567i | \(-0.805559\pi\) |
0.0871445 | + | 0.996196i | \(0.472226\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.8993 | − | 26.5000i | −1.59415 | − | 0.920383i | −0.992584 | − | 0.121560i | \(-0.961210\pi\) |
−0.601566 | − | 0.798823i | \(-0.705456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 36.0000i | − | 1.24883i | ||||||
\(832\) | 20.0000 | − | 20.7846i | 0.693375 | − | 0.720577i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 40.6865 | − | 40.6865i | 1.40633 | − | 1.40633i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | − | 25.1147i | −0.500000 | − | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 51.9615i | 1.78859i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.44744 | + | 31.5263i | 0.290258 | + | 1.08326i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37.5000 | − | 21.6506i | 1.28700 | − | 0.743048i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.88269 | − | 5.88269i | −0.201419 | − | 0.201419i | 0.599189 | − | 0.800608i | \(-0.295490\pi\) |
−0.800608 | + | 0.599189i | \(0.795490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 57.1577 | 1.95019 | 0.975097 | − | 0.221777i | \(-0.0711857\pi\) | ||||
0.975097 | + | 0.221777i | \(0.0711857\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.7224 | − | 25.5000i | −0.500000 | − | 0.866025i | ||||
\(868\) | 56.9090 | + | 32.8564i | 1.93162 | + | 1.11522i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.38526 | − | 2.50962i | 0.0469379 | − | 0.0850352i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.2058 | + | 49.2846i | 0.446948 | + | 1.66803i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 32.4449 | − | 32.4449i | 1.09621 | − | 1.09621i | ||||
\(877\) | 56.3468 | + | 15.0981i | 1.90270 | + | 0.509826i | 0.996144 | + | 0.0877308i | \(0.0279615\pi\) |
0.906552 | + | 0.422095i | \(0.138705\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.0000i | 1.85090i | 0.378873 | + | 0.925449i | \(0.376312\pi\) | ||||
−0.378873 | + | 0.925449i | \(0.623688\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.09808 | − | 2.09808i | 0.0703672 | − | 0.0703672i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17.6077 | − | 17.6077i | −0.589549 | − | 0.589549i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 15.0000 | − | 25.9808i | 0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.59808 | − | 2.30385i | −0.286126 | − | 0.0766672i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.6410 | − | 20.0000i | −1.15024 | − | 0.664089i | −0.201291 | − | 0.979531i | \(-0.564514\pi\) |
−0.948945 | + | 0.315442i | \(0.897847\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −14.5359 | − | 54.2487i | −0.481332 | − | 1.79635i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −58.4449 | − | 15.6603i | −1.93107 | − | 0.517429i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.5885 | + | 27.0000i | 0.514216 | + | 0.890648i | 0.999864 | + | 0.0164935i | \(0.00525028\pi\) |
−0.485648 | + | 0.874154i | \(0.661416\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.3564 | − | 10.5455i | 1.29684 | − | 0.347487i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.81089 | − | 10.4904i | −0.0924215 | − | 0.344922i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −40.5000 | + | 23.3827i | −1.33019 | + | 0.767988i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.3397 | − | 10.3397i | −0.338871 | − | 0.338871i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −55.4256 | −1.81068 | −0.905338 | − | 0.424691i | \(-0.860383\pi\) | ||||
−0.905338 | + | 0.424691i | \(0.860383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.5000 | + | 49.3634i | −0.930062 | + | 1.61092i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(948\) | 42.0000i | 1.36410i | ||||||||
\(949\) | 0.918584 | + | 47.7487i | 0.0298185 | + | 1.54999i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 91.6218i | − | 2.95554i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.01924 | − | 18.7321i | −0.161659 | − | 0.603319i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.4449 | − | 19.4449i | 0.625305 | − | 0.625305i | −0.321578 | − | 0.946883i | \(-0.604213\pi\) |
0.946883 | + | 0.321578i | \(0.104213\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(972\) | −27.0000 | − | 15.5885i | −0.866025 | − | 0.500000i | ||||
\(973\) | −20.0622 | + | 5.37564i | −0.643164 | + | 0.172335i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.66025 | + | 30.0000i | 0.277350 | + | 0.960769i | ||||
\(976\) | 34.6410 | 1.10883 | ||||||||
\(977\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.1865 | − | 5.67691i | −0.676434 | − | 0.181250i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 51.1769 | + | 28.2487i | 1.62815 | + | 0.898711i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0000 | + | 38.1051i | −0.698853 | + | 1.21045i | 0.270011 | + | 0.962857i | \(0.412973\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −43.3468 | + | 43.3468i | −1.37557 | + | 1.37557i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.5000 | + | 51.0955i | 0.934274 | + | 1.61821i | 0.775923 | + | 0.630828i | \(0.217285\pi\) |
0.158352 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.9019 | + | 2.92116i | −0.344922 | + | 0.0924215i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))