Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1201,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
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 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1201.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1201 |
Dual form | 2100.2.q.b.1801.1 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 2.59808i | −0.188982 | + | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | + | 1.73205i | −0.301511 | + | 0.522233i | −0.976478 | − | 0.215615i | \(-0.930824\pi\) |
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | 0.832050 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000 | − | 6.92820i | 0.970143 | − | 1.68034i | 0.275029 | − | 0.961436i | \(-0.411312\pi\) |
0.695113 | − | 0.718900i | \(-0.255354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | + | 0.866025i | 0.114708 | + | 0.198680i | 0.917663 | − | 0.397360i | \(-0.130073\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | − | 1.73205i | −0.436436 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | + | 6.92820i | 0.834058 | + | 1.44463i | 0.894795 | + | 0.446476i | \(0.147321\pi\) |
−0.0607377 | + | 0.998154i | \(0.519345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | + | 2.59808i | −0.269408 | + | 0.466628i | −0.968709 | − | 0.248199i | \(-0.920161\pi\) |
0.699301 | + | 0.714827i | \(0.253495\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | − | 1.73205i | −0.174078 | − | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.500000 | − | 0.866025i | −0.0821995 | − | 0.142374i | 0.821995 | − | 0.569495i | \(-0.192861\pi\) |
−0.904194 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.50000 | + | 2.59808i | −0.240192 | + | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.0000 | −1.67748 | −0.838742 | − | 0.544529i | \(-0.816708\pi\) | ||||
−0.838742 | + | 0.544529i | \(0.816708\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | + | 5.19615i | 0.437595 | + | 0.757937i | 0.997503 | − | 0.0706177i | \(-0.0224970\pi\) |
−0.559908 | + | 0.828554i | \(0.689164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | + | 6.92820i | 0.560112 | + | 0.970143i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | + | 10.3923i | −0.824163 | + | 1.42749i | 0.0783936 | + | 0.996922i | \(0.475021\pi\) |
−0.902557 | + | 0.430570i | \(0.858312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | + | 5.19615i | 0.384111 | + | 0.665299i | 0.991645 | − | 0.128994i | \(-0.0411748\pi\) |
−0.607535 | + | 0.794293i | \(0.707841\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.50000 | − | 0.866025i | 0.314970 | − | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.50000 | − | 11.2583i | 0.794101 | − | 1.37542i | −0.129307 | − | 0.991605i | \(-0.541275\pi\) |
0.923408 | − | 0.383819i | \(-0.125391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.0000 | −1.18678 | −0.593391 | − | 0.804914i | \(-0.702211\pi\) | ||||
−0.593391 | + | 0.804914i | \(0.702211\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.50000 | + | 9.52628i | −0.643726 | + | 1.11497i | 0.340868 | + | 0.940111i | \(0.389279\pi\) |
−0.984594 | + | 0.174855i | \(0.944054\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.00000 | − | 3.46410i | −0.455842 | − | 0.394771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50000 | + | 2.59808i | 0.168763 | + | 0.292306i | 0.937985 | − | 0.346675i | \(-0.112689\pi\) |
−0.769222 | + | 0.638982i | \(0.779356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.00000 | −0.219529 | −0.109764 | − | 0.993958i | \(-0.535010\pi\) | ||||
−0.109764 | + | 0.993958i | \(0.535010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | + | 3.46410i | −0.214423 | + | 0.371391i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.50000 | + | 7.79423i | −0.157243 | + | 0.817057i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | − | 2.59808i | −0.155543 | − | 0.269408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.00000 | + | 8.66025i | −0.497519 | + | 0.861727i | −0.999996 | − | 0.00286291i | \(-0.999089\pi\) |
0.502477 | + | 0.864590i | \(0.332422\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.50000 | + | 9.52628i | 0.541931 | + | 0.938652i | 0.998793 | + | 0.0491146i | \(0.0156400\pi\) |
−0.456862 | + | 0.889538i | \(0.651027\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.50000 | − | 9.52628i | 0.526804 | − | 0.912452i | −0.472708 | − | 0.881219i | \(-0.656723\pi\) |
0.999512 | − | 0.0312328i | \(-0.00994332\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.00000 | 0.0949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.50000 | − | 2.59808i | −0.138675 | − | 0.240192i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.0000 | + | 13.8564i | 1.46672 | + | 1.27021i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.00000 | + | 5.19615i | −0.270501 | + | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.00000 | −0.266207 | −0.133103 | − | 0.991102i | \(-0.542494\pi\) | ||||
−0.133103 | + | 0.991102i | \(0.542494\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.50000 | − | 9.52628i | 0.484248 | − | 0.838742i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.00000 | + | 1.73205i | 0.0873704 | + | 0.151330i | 0.906399 | − | 0.422423i | \(-0.138820\pi\) |
−0.819028 | + | 0.573753i | \(0.805487\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.50000 | + | 0.866025i | −0.216777 | + | 0.0750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | − | 3.46410i | 0.170872 | − | 0.295958i | −0.767853 | − | 0.640626i | \(-0.778675\pi\) |
0.938725 | + | 0.344668i | \(0.112008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.00000 | −0.424094 | −0.212047 | − | 0.977259i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977259i | \(0.568013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.00000 | + | 5.19615i | −0.250873 | + | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.50000 | − | 4.33013i | 0.453632 | − | 0.357143i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | + | 10.3923i | 0.491539 | + | 0.851371i | 0.999953 | − | 0.00974235i | \(-0.00310113\pi\) |
−0.508413 | + | 0.861113i | \(0.669768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | − | 6.92820i | 0.325515 | − | 0.563809i | −0.656101 | − | 0.754673i | \(-0.727796\pi\) |
0.981617 | + | 0.190864i | \(0.0611289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.00000 | −0.646762 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.00000 | − | 1.73205i | 0.0798087 | − | 0.138233i | −0.823359 | − | 0.567521i | \(-0.807902\pi\) |
0.903167 | + | 0.429289i | \(0.141236\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | − | 10.3923i | −0.475831 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.0000 | + | 6.92820i | −1.57622 | + | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | − | 3.46410i | −0.156652 | − | 0.271329i | 0.777007 | − | 0.629492i | \(-0.216737\pi\) |
−0.933659 | + | 0.358162i | \(0.883403\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.00000 | 0.154765 | 0.0773823 | − | 0.997001i | \(-0.475344\pi\) | ||||
0.0773823 | + | 0.997001i | \(0.475344\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | − | 0.866025i | 0.0382360 | − | 0.0662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.00000 | + | 13.8564i | 0.608229 | + | 1.05348i | 0.991532 | + | 0.129861i | \(0.0414530\pi\) |
−0.383304 | + | 0.923622i | \(0.625214\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.00000 | − | 3.46410i | −0.150329 | − | 0.260378i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.00000 | + | 5.19615i | −0.224231 | + | 0.388379i | −0.956088 | − | 0.293079i | \(-0.905320\pi\) |
0.731858 | + | 0.681457i | \(0.238654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0000 | −1.11494 | −0.557471 | − | 0.830197i | \(-0.688228\pi\) | ||||
−0.557471 | + | 0.830197i | \(0.688228\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | + | 13.8564i | 0.585018 | + | 1.01328i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.500000 | + | 2.59808i | −0.0363696 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | − | 5.19615i | −0.217072 | − | 0.375980i | 0.736839 | − | 0.676068i | \(-0.236317\pi\) |
−0.953912 | + | 0.300088i | \(0.902984\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50000 | − | 9.52628i | 0.395899 | − | 0.685717i | −0.597317 | − | 0.802005i | \(-0.703766\pi\) |
0.993215 | + | 0.116289i | \(0.0370998\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.00000 | −0.569976 | −0.284988 | − | 0.958531i | \(-0.591990\pi\) | ||||
−0.284988 | + | 0.958531i | \(0.591990\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | + | 6.92820i | −0.283552 | + | 0.491127i | −0.972257 | − | 0.233915i | \(-0.924846\pi\) |
0.688705 | + | 0.725042i | \(0.258180\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.50000 | + | 11.2583i | 0.458475 | + | 0.794101i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | + | 10.3923i | −0.140372 | + | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | − | 6.92820i | 0.278019 | − | 0.481543i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.00000 | − | 8.66025i | 0.342594 | − | 0.593391i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | − | 5.19615i | −0.407307 | − | 0.352738i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.50000 | − | 9.52628i | −0.371656 | − | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | − | 20.7846i | 0.807207 | − | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.00000 | + | 15.5885i | −0.597351 | + | 1.03464i | 0.395860 | + | 0.918311i | \(0.370447\pi\) |
−0.993210 | + | 0.116331i | \(0.962887\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.500000 | − | 0.866025i | −0.0330409 | − | 0.0572286i | 0.849032 | − | 0.528341i | \(-0.177186\pi\) |
−0.882073 | + | 0.471113i | \(0.843853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.00000 | − | 1.73205i | 0.328976 | − | 0.113961i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.00000 | + | 12.1244i | 0.458585 | + | 0.794293i | 0.998886 | − | 0.0471787i | \(-0.0150230\pi\) |
−0.540301 | + | 0.841472i | \(0.681690\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.00000 | −0.194871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.00000 | + | 12.1244i | −0.450910 | + | 0.780998i | −0.998443 | − | 0.0557856i | \(-0.982234\pi\) |
0.547533 | + | 0.836784i | \(0.315567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.50000 | + | 2.59808i | 0.0954427 | + | 0.165312i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.00000 | − | 1.73205i | 0.0633724 | − | 0.109764i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.0000 | −1.00591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.00000 | + | 15.5885i | 0.561405 | + | 0.972381i | 0.997374 | + | 0.0724199i | \(0.0230722\pi\) |
−0.435970 | + | 0.899961i | \(0.643595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.50000 | − | 0.866025i | 0.155342 | − | 0.0538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | − | 3.46410i | −0.123797 | − | 0.214423i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | − | 10.3923i | 0.369976 | − | 0.640817i | −0.619586 | − | 0.784929i | \(-0.712699\pi\) |
0.989561 | + | 0.144112i | \(0.0460326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.00000 | − | 1.73205i | 0.0609711 | − | 0.105605i | −0.833929 | − | 0.551872i | \(-0.813914\pi\) |
0.894900 | + | 0.446267i | \(0.147247\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | + | 20.7846i | 0.728948 | + | 1.26258i | 0.957328 | + | 0.289003i | \(0.0933238\pi\) |
−0.228380 | + | 0.973572i | \(0.573343\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.00000 | − | 5.19615i | −0.363137 | − | 0.314485i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.50000 | − | 14.7224i | 0.510716 | − | 0.884585i | −0.489207 | − | 0.872167i | \(-0.662714\pi\) |
0.999923 | − | 0.0124177i | \(-0.00395278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.00000 | 0.179605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0000 | 1.19310 | 0.596550 | − | 0.802576i | \(-0.296538\pi\) | ||||
0.596550 | + | 0.802576i | \(0.296538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.50000 | − | 16.4545i | 0.564716 | − | 0.978117i | −0.432360 | − | 0.901701i | \(-0.642319\pi\) |
0.997076 | − | 0.0764162i | \(-0.0243478\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.00000 | + | 15.5885i | −0.177084 | + | 0.920158i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −23.5000 | − | 40.7032i | −1.38235 | − | 2.39431i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | − | 8.66025i | 0.293105 | − | 0.507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.0000 | 1.40209 | 0.701047 | − | 0.713115i | \(-0.252716\pi\) | ||||
0.701047 | + | 0.713115i | \(0.252716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | + | 1.73205i | −0.0580259 | + | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0000 | + | 20.7846i | 0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.50000 | − | 28.5788i | 0.317015 | − | 1.64726i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.00000 | − | 8.66025i | −0.287242 | − | 0.497519i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.0000 | 1.31268 | 0.656340 | − | 0.754466i | \(-0.272104\pi\) | ||||
0.656340 | + | 0.754466i | \(0.272104\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.0000 | −0.625768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.00000 | − | 1.73205i | 0.0567048 | − | 0.0982156i | −0.836280 | − | 0.548303i | \(-0.815274\pi\) |
0.892984 | + | 0.450088i | \(0.148607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.50000 | − | 14.7224i | −0.480448 | − | 0.832161i | 0.519300 | − | 0.854592i | \(-0.326193\pi\) |
−0.999748 | + | 0.0224310i | \(0.992859\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.0000 | − | 20.7846i | −0.673987 | − | 1.16738i | −0.976764 | − | 0.214318i | \(-0.931247\pi\) |
0.302777 | − | 0.953062i | \(-0.402086\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | + | 6.92820i | −0.223957 | + | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.50000 | + | 9.52628i | 0.304151 | + | 0.526804i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.0000 | + | 5.19615i | −0.826977 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50000 | − | 14.7224i | −0.467202 | − | 0.809218i | 0.532096 | − | 0.846684i | \(-0.321405\pi\) |
−0.999298 | + | 0.0374662i | \(0.988071\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.500000 | + | 0.866025i | −0.0273998 | + | 0.0474579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.0000 | −1.14394 | −0.571971 | − | 0.820274i | \(-0.693821\pi\) | ||||
−0.571971 | + | 0.820274i | \(0.693821\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.00000 | + | 12.1244i | −0.380188 | + | 0.658505i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.00000 | − | 5.19615i | −0.162459 | − | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0000 | − | 20.7846i | 0.644194 | − | 1.11578i | −0.340293 | − | 0.940319i | \(-0.610526\pi\) |
0.984487 | − | 0.175457i | \(-0.0561403\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.00000 | 0.160128 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.00000 | + | 5.19615i | −0.159674 | + | 0.276563i | −0.934751 | − | 0.355303i | \(-0.884378\pi\) |
0.775077 | + | 0.631867i | \(0.217711\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.0000 | + | 6.92820i | −1.05851 | + | 0.366679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.0000 | + | 17.3205i | 0.527780 | + | 0.914141i | 0.999476 | + | 0.0323801i | \(0.0103087\pi\) |
−0.471696 | + | 0.881761i | \(0.656358\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.50000 | − | 4.33013i | 0.130499 | − | 0.226031i | −0.793370 | − | 0.608740i | \(-0.791675\pi\) |
0.923869 | + | 0.382709i | \(0.125009\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.00000 | − | 5.19615i | −0.156174 | − | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.0000 | − | 20.7846i | −1.24602 | − | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.50000 | − | 4.33013i | −0.129445 | − | 0.224205i | 0.794017 | − | 0.607896i | \(-0.207986\pi\) |
−0.923462 | + | 0.383691i | \(0.874653\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.0000 | 0.667765 | 0.333883 | − | 0.942615i | \(-0.391641\pi\) | ||||
0.333883 | + | 0.942615i | \(0.391641\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.50000 | − | 2.59808i | 0.0768473 | − | 0.133103i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.0000 | − | 24.2487i | −0.715367 | − | 1.23905i | −0.962818 | − | 0.270151i | \(-0.912926\pi\) |
0.247451 | − | 0.968900i | \(-0.420407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.50000 | + | 9.52628i | 0.279581 | + | 0.484248i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.00000 | + | 8.66025i | −0.253510 | + | 0.439092i | −0.964490 | − | 0.264120i | \(-0.914918\pi\) |
0.710980 | + | 0.703213i | \(0.248252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 64.0000 | 3.23662 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.00000 | −0.100887 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.50000 | + | 2.59808i | 0.0752828 | + | 0.130394i | 0.901209 | − | 0.433384i | \(-0.142681\pi\) |
−0.825926 | + | 0.563778i | \(0.809347\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.500000 | − | 2.59808i | 0.0250313 | − | 0.130066i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | + | 10.3923i | 0.299626 | + | 0.518967i | 0.976050 | − | 0.217545i | \(-0.0698049\pi\) |
−0.676425 | + | 0.736512i | \(0.736472\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.50000 | + | 7.79423i | −0.224161 | + | 0.388258i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.00000 | 0.0991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.50000 | − | 16.4545i | 0.469745 | − | 0.813622i | −0.529657 | − | 0.848212i | \(-0.677679\pi\) |
0.999402 | + | 0.0345902i | \(0.0110126\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00000 | + | 3.46410i | 0.0986527 | + | 0.170872i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.00000 | − | 6.92820i | −0.393654 | − | 0.340915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.50000 | − | 4.33013i | 0.122426 | − | 0.212047i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0000 | 0.879358 | 0.439679 | − | 0.898155i | \(-0.355092\pi\) | ||||
0.439679 | + | 0.898155i | \(0.355092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.0000 | −1.31590 | −0.657950 | − | 0.753062i | \(-0.728576\pi\) | ||||
−0.657950 | + | 0.753062i | \(0.728576\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00000 | − | 5.19615i | 0.145865 | − | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.0000 | + | 5.19615i | −0.725901 | + | 0.251459i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.00000 | − | 5.19615i | −0.144841 | − | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0000 | − | 25.9808i | 0.722525 | − | 1.25145i | −0.237460 | − | 0.971397i | \(-0.576315\pi\) |
0.959985 | − | 0.280052i | \(-0.0903517\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.0000 | 1.20142 | 0.600712 | − | 0.799466i | \(-0.294884\pi\) | ||||
0.600712 | + | 0.799466i | \(0.294884\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.00000 | + | 6.92820i | −0.191346 | + | 0.331421i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0000 | − | 20.7846i | −0.572729 | − | 0.991995i | −0.996284 | − | 0.0861252i | \(-0.972552\pi\) |
0.423556 | − | 0.905870i | \(-0.360782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.00000 | − | 3.46410i | −0.0950229 | − | 0.164584i | 0.814595 | − | 0.580030i | \(-0.196959\pi\) |
−0.909618 | + | 0.415445i | \(0.863626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.0000 | 1.03824 | 0.519122 | − | 0.854700i | \(-0.326259\pi\) | ||||
0.519122 | + | 0.854700i | \(0.326259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | + | 10.3923i | −0.282529 | + | 0.489355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.00000 | + | 6.92820i | 0.187936 | + | 0.325515i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.50000 | + | 11.2583i | 0.304057 | + | 0.526642i | 0.977051 | − | 0.213006i | \(-0.0683253\pi\) |
−0.672994 | + | 0.739648i | \(0.734992\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.00000 | − | 6.92820i | 0.186704 | − | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.00000 | 0.186299 | 0.0931493 | − | 0.995652i | \(-0.470307\pi\) | ||||
0.0931493 | + | 0.995652i | \(0.470307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0000 | 0.511213 | 0.255607 | − | 0.966781i | \(-0.417725\pi\) | ||||
0.255607 | + | 0.966781i | \(0.417725\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.0000 | + | 29.4449i | 0.786666 | + | 1.36255i | 0.927999 | + | 0.372584i | \(0.121528\pi\) |
−0.141332 | + | 0.989962i | \(0.545139\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.0000 | + | 22.5167i | 1.20057 | + | 1.03972i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.00000 | + | 1.73205i | 0.0460776 | + | 0.0798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.0000 | − | 19.0526i | 0.505781 | − | 0.876038i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0000 | − | 24.2487i | 0.639676 | − | 1.10795i | −0.345827 | − | 0.938298i | \(-0.612402\pi\) |
0.985504 | − | 0.169654i | \(-0.0542649\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.50000 | − | 2.59808i | −0.0683941 | − | 0.118462i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.00000 | − | 20.7846i | 0.182006 | − | 0.945732i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.50000 | + | 16.4545i | −0.430486 | + | 0.745624i | −0.996915 | − | 0.0784867i | \(-0.974991\pi\) |
0.566429 | + | 0.824110i | \(0.308325\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.0000 | − | 27.7128i | 0.720604 | − | 1.24812i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.00000 | − | 25.9808i | 0.224281 | − | 1.16540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.5000 | + | 25.1147i | 0.649109 | + | 1.12429i | 0.983336 | + | 0.181797i | \(0.0581915\pi\) |
−0.334227 | + | 0.942493i | \(0.608475\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | + | 1.73205i | −0.0446767 | + | 0.0773823i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.0000 | 1.33763 | 0.668817 | − | 0.743427i | \(-0.266801\pi\) | ||||
0.668817 | + | 0.743427i | \(0.266801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.00000 | − | 3.46410i | 0.0888231 | − | 0.153846i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.00000 | − | 15.5885i | −0.398918 | − | 0.690946i | 0.594675 | − | 0.803966i | \(-0.297281\pi\) |
−0.993593 | + | 0.113020i | \(0.963948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.0000 | − | 19.0526i | −0.973223 | − | 0.842836i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.500000 | + | 0.866025i | 0.0220755 | + | 0.0382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | −0.527759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.0000 | −0.702322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | − | 31.1769i | 0.788594 | − | 1.36589i | −0.138234 | − | 0.990400i | \(-0.544143\pi\) |
0.926828 | − | 0.375486i | \(-0.122524\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5000 | − | 26.8468i | −0.677768 | − | 1.17393i | −0.975652 | − | 0.219326i | \(-0.929614\pi\) |
0.297884 | − | 0.954602i | \(-0.403719\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0000 | + | 20.7846i | 0.522728 | + | 0.905392i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.0000 | 0.779667 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.00000 | − | 5.19615i | −0.129460 | − | 0.224231i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.0000 | − | 8.66025i | 0.473804 | − | 0.373024i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.50000 | + | 12.9904i | 0.322450 | + | 0.558500i | 0.980993 | − | 0.194043i | \(-0.0621602\pi\) |
−0.658543 | + | 0.752543i | \(0.728827\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.50000 | − | 12.9904i | 0.321856 | − | 0.557471i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.00000 | − | 5.19615i | 0.128037 | − | 0.221766i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00000 | + | 3.46410i | 0.0852029 | + | 0.147576i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.50000 | + | 2.59808i | −0.318932 | + | 0.110481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.0000 | − | 19.0526i | 0.466085 | − | 0.807283i | −0.533165 | − | 0.846011i | \(-0.678997\pi\) |
0.999250 | + | 0.0387286i | \(0.0123308\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.0000 | −1.39575 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.0000 | −0.675521 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.0000 | + | 39.8372i | −0.969334 | + | 1.67894i | −0.271846 | + | 0.962341i | \(0.587634\pi\) |
−0.697489 | + | 0.716596i | \(0.745699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.00000 | − | 1.73205i | −0.0839921 | − | 0.0727393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00000 | − | 5.19615i | −0.125767 | − | 0.217834i | 0.796266 | − | 0.604947i | \(-0.206806\pi\) |
−0.922032 | + | 0.387113i | \(0.873472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.5000 | − | 18.1865i | 0.439411 | − | 0.761083i | −0.558233 | − | 0.829684i | \(-0.688520\pi\) |
0.997644 | + | 0.0686016i | \(0.0218537\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.00000 | 0.250654 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.5000 | + | 35.5070i | −0.853426 | + | 1.47818i | 0.0246713 | + | 0.999696i | \(0.492146\pi\) |
−0.878097 | + | 0.478482i | \(0.841187\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.50000 | + | 9.52628i | 0.228572 | + | 0.395899i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.00000 | − | 5.19615i | 0.0414870 | − | 0.215573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | − | 20.7846i | −0.496989 | − | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.0000 | −1.32078 | −0.660391 | − | 0.750922i | \(-0.729609\pi\) | ||||
−0.660391 | + | 0.750922i | \(0.729609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.00000 | −0.123613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.00000 | − | 6.92820i | 0.164538 | − | 0.284988i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.00000 | − | 5.19615i | −0.123195 | − | 0.213380i | 0.797831 | − | 0.602881i | \(-0.205981\pi\) |
−0.921026 | + | 0.389501i | \(0.872647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.00000 | − | 6.92820i | −0.163709 | − | 0.283552i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.00000 | − | 10.3923i | 0.245153 | − | 0.424618i | −0.717021 | − | 0.697051i | \(-0.754495\pi\) |
0.962175 | + | 0.272433i | \(0.0878284\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00000 | −0.0407909 | −0.0203954 | − | 0.999792i | \(-0.506493\pi\) | ||||
−0.0203954 | + | 0.999792i | \(0.506493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.0000 | −0.529401 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.50000 | − | 2.59808i | −0.0608831 | − | 0.105453i | 0.833977 | − | 0.551799i | \(-0.186058\pi\) |
−0.894860 | + | 0.446346i | \(0.852725\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.00000 | − | 6.92820i | −0.324176 | − | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.00000 | + | 15.5885i | 0.364101 | + | 0.630641i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.0000 | + | 25.9808i | −0.605844 | + | 1.04935i | 0.386073 | + | 0.922468i | \(0.373831\pi\) |
−0.991917 | + | 0.126885i | \(0.959502\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.0000 | −1.04672 | −0.523360 | − | 0.852111i | \(-0.675322\pi\) | ||||
−0.523360 | + | 0.852111i | \(0.675322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.50000 | − | 9.52628i | 0.221064 | − | 0.382893i | −0.734068 | − | 0.679076i | \(-0.762380\pi\) |
0.955131 | + | 0.296183i | \(0.0957138\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | + | 6.92820i | 0.160514 | + | 0.278019i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.00000 | − | 1.73205i | 0.0399362 | − | 0.0691714i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.00000 | −0.318981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.00000 | − | 3.46410i | 0.0794929 | − | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.5000 | − | 7.79423i | −0.772618 | − | 0.308819i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.00000 | + | 8.66025i | 0.197797 | + | 0.342594i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.0000 | − | 34.6410i | 0.789953 | − | 1.36824i | −0.136043 | − | 0.990703i | \(-0.543438\pi\) |
0.925995 | − | 0.377535i | \(-0.123228\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.0000 | −1.38027 | −0.690133 | − | 0.723683i | \(-0.742448\pi\) | ||||
−0.690133 | + | 0.723683i | \(0.742448\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.00000 | − | 5.19615i | 0.117942 | − | 0.204282i | −0.801010 | − | 0.598651i | \(-0.795704\pi\) |
0.918952 | + | 0.394369i | \(0.129037\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00000 | − | 6.92820i | −0.157014 | − | 0.271956i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.50000 | − | 2.59808i | 0.293948 | − | 0.101827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.00000 | − | 5.19615i | −0.117399 | − | 0.203341i | 0.801337 | − | 0.598213i | \(-0.204122\pi\) |
−0.918736 | + | 0.394872i | \(0.870789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.0000 | 0.429151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.0000 | −1.09073 | −0.545363 | − | 0.838200i | \(-0.683608\pi\) | ||||
−0.545363 | + | 0.838200i | \(0.683608\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.5000 | − | 25.1147i | 0.563985 | − | 0.976850i | −0.433159 | − | 0.901318i | \(-0.642601\pi\) |
0.997143 | − | 0.0755324i | \(-0.0240656\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.0000 | + | 20.7846i | 0.466041 | + | 0.807207i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000 | + | 27.7128i | 0.619522 | + | 1.07304i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.00000 | − | 6.92820i | 0.154649 | − | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.00000 | 0.0385472 | 0.0192736 | − | 0.999814i | \(-0.493865\pi\) | ||||
0.0192736 | + | 0.999814i | \(0.493865\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.00000 | + | 10.3923i | 0.230599 | + | 0.399409i | 0.957984 | − | 0.286820i | \(-0.0925982\pi\) |
−0.727386 | + | 0.686229i | \(0.759265\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.00000 | − | 25.9808i | 0.191882 | − | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.00000 | − | 15.5885i | −0.344881 | − | 0.597351i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.0000 | − | 31.1769i | 0.688751 | − | 1.19295i | −0.283491 | − | 0.958975i | \(-0.591493\pi\) |
0.972242 | − | 0.233977i | \(-0.0751739\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.00000 | 0.0381524 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.0000 | + | 31.1769i | −0.685745 | + | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.5000 | + | 37.2391i | 0.817899 | + | 1.41664i | 0.907228 | + | 0.420640i | \(0.138194\pi\) |
−0.0893292 | + | 0.996002i | \(0.528472\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.00000 | + | 5.19615i | −0.0379869 | + | 0.197386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000 | − | 41.5692i | 0.909065 | − | 1.57455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.0000 | −0.529529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.00000 | −0.302156 | −0.151078 | − | 0.988522i | \(-0.548274\pi\) | ||||
−0.151078 | + | 0.988522i | \(0.548274\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.500000 | − | 0.866025i | 0.0188579 | − | 0.0326628i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.0000 | − | 17.3205i | −0.752177 | − | 0.651405i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.00000 | − | 12.1244i | −0.262891 | − | 0.455340i | 0.704118 | − | 0.710083i | \(-0.251342\pi\) |
−0.967009 | + | 0.254743i | \(0.918009\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.50000 | − | 2.59808i | 0.0562544 | − | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.0000 | −0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.00000 | + | 15.5885i | −0.336111 | + | 0.582162i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.00000 | + | 5.19615i | 0.111881 | + | 0.193784i | 0.916529 | − | 0.399969i | \(-0.130979\pi\) |
−0.804648 | + | 0.593753i | \(0.797646\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.5000 | + | 9.52628i | −1.02415 | + | 0.354777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.00000 | − | 12.1244i | −0.260333 | − | 0.450910i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.0000 | 0.853023 | 0.426511 | − | 0.904482i | \(-0.359742\pi\) | ||||
0.426511 | + | 0.904482i | \(0.359742\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44.0000 | + | 76.2102i | −1.62740 | + | 2.81874i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.5000 | + | 38.9711i | 0.831056 | + | 1.43943i | 0.897201 | + | 0.441622i | \(0.145597\pi\) |
−0.0661448 | + | 0.997810i | \(0.521070\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.0000 | + | 22.5167i | 0.478861 | + | 0.829412i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.50000 | − | 7.79423i | 0.165535 | − | 0.286715i | −0.771310 | − | 0.636460i | \(-0.780398\pi\) |
0.936845 | + | 0.349744i | \(0.113732\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.00000 | −0.110208 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0000 | 0.660356 | 0.330178 | − | 0.943919i | \(-0.392891\pi\) | ||||
0.330178 | + | 0.943919i | \(0.392891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.00000 | + | 1.73205i | 0.0365881 | + | 0.0633724i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.50000 | − | 12.9904i | −0.273679 | − | 0.474026i | 0.696122 | − | 0.717923i | \(-0.254907\pi\) |
−0.969801 | + | 0.243898i | \(0.921574\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.0000 | −1.52652 | −0.763258 | − | 0.646094i | \(-0.776401\pi\) | ||||
−0.763258 | + | 0.646094i | \(0.776401\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.00000 | − | 13.8564i | 0.290382 | − | 0.502956i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.00000 | − | 6.92820i | −0.145000 | − | 0.251147i | 0.784373 | − | 0.620289i | \(-0.212985\pi\) |
−0.929373 | + | 0.369142i | \(0.879652\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.0000 | + | 19.0526i | 0.796453 | + | 0.689749i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.00000 | + | 10.3923i | −0.216647 | + | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.0000 | 1.11789 | 0.558944 | − | 0.829205i | \(-0.311207\pi\) | ||||
0.558944 | + | 0.829205i | \(0.311207\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.0000 | − | 19.0526i | 0.395643 | − | 0.685273i | −0.597540 | − | 0.801839i | \(-0.703855\pi\) |
0.993183 | + | 0.116566i | \(0.0371886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.500000 | + | 2.59808i | −0.0179374 | + | 0.0932055i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.00000 | + | 5.19615i | 0.107486 | + | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | − | 17.3205i | 0.357828 | − | 0.619777i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.00000 | 0.142948 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.0000 | − | 20.7846i | 0.427754 | − | 0.740891i | −0.568919 | − | 0.822393i | \(-0.692638\pi\) |
0.996673 | + | 0.0815020i | \(0.0259717\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.00000 | + | 10.3923i | 0.213606 | + | 0.369976i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.00000 | + | 36.3731i | −0.248891 | + | 1.29328i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.00000 | + | 15.5885i | 0.319599 | + | 0.553562i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.0000 | 1.70025 | 0.850124 | − | 0.526583i | \(-0.176527\pi\) | ||||
0.850124 | + | 0.526583i | \(0.176527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.0000 | 1.69812 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.0000 | − | 19.0526i | −0.388182 | − | 0.672350i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.00000 | + | 1.73205i | 0.0352017 | + | 0.0609711i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.0000 | + | 19.0526i | −0.386739 | + | 0.669852i | −0.992009 | − | 0.126168i | \(-0.959732\pi\) |
0.605269 | + | 0.796021i | \(0.293065\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.0000 | −1.12367 | −0.561836 | − | 0.827249i | \(-0.689905\pi\) | ||||
−0.561836 | + | 0.827249i | \(0.689905\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.0000 | −0.841717 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.50000 | − | 9.52628i | −0.192421 | − | 0.333282i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.50000 | − | 2.59808i | 0.262071 | − | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.00000 | − | 1.73205i | −0.0349002 | − | 0.0604490i | 0.848048 | − | 0.529920i | \(-0.177778\pi\) |
−0.882948 | + | 0.469471i | \(0.844445\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | − | 34.6410i | 0.697156 | − | 1.20751i | −0.272292 | − | 0.962215i | \(-0.587782\pi\) |
0.969448 | − | 0.245295i | \(-0.0788849\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −54.0000 | −1.87776 | −0.938882 | − | 0.344239i | \(-0.888137\pi\) | ||||
−0.938882 | + | 0.344239i | \(0.888137\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.50000 | − | 9.52628i | 0.191023 | − | 0.330861i | −0.754567 | − | 0.656223i | \(-0.772153\pi\) |
0.945589 | + | 0.325362i | \(0.105486\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.50000 | + | 14.7224i | 0.294862 | + | 0.510716i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −44.0000 | + | 34.6410i | −1.52451 | + | 1.20024i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.50000 | + | 2.59808i | −0.0518476 | + | 0.0898027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.00000 | −0.138095 | −0.0690477 | − | 0.997613i | \(-0.521996\pi\) | ||||
−0.0690477 | + | 0.997613i | \(0.521996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.0000 | + | 17.3205i | −0.344418 | + | 0.596550i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.5000 | + | 6.06218i | −0.601307 | + | 0.208299i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.50000 | + | 16.4545i | 0.326039 | + | 0.564716i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | − | 6.92820i | 0.137118 | − | 0.237496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.0000 | −0.787505 | −0.393753 | − | 0.919216i | \(-0.628823\pi\) | ||||
−0.393753 | + | 0.919216i | \(0.628823\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | − | 6.92820i | −0.136478 | − | 0.236387i | 0.789683 | − | 0.613515i | \(-0.210245\pi\) |
−0.926161 | + | 0.377128i | \(0.876912\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | − | 10.3923i | −0.408959 | − | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.0000 | + | 39.8372i | 0.782929 | + | 1.35607i | 0.930228 | + | 0.366981i | \(0.119609\pi\) |
−0.147299 | + | 0.989092i | \(0.547058\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 47.0000 | 1.59620 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.00000 | −0.203536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5000 | − | 33.7750i | 0.660732 | − | 1.14442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.00000 | + | 8.66025i | 0.169224 | + | 0.293105i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.0000 | − | 32.9090i | −0.641584 | − | 1.11126i | −0.985079 | − | 0.172102i | \(-0.944944\pi\) |
0.343495 | − | 0.939155i | \(-0.388389\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.0000 | + | 20.7846i | −0.404750 | + | 0.701047i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.0000 | 1.61716 | 0.808581 | − | 0.588386i | \(-0.200236\pi\) | ||||
0.808581 | + | 0.588386i | \(0.200236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.0000 | −0.975928 | −0.487964 | − | 0.872864i | \(-0.662260\pi\) | ||||
−0.487964 | + | 0.872864i | \(0.662260\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.00000 | − | 5.19615i | −0.100730 | − | 0.174470i | 0.811256 | − | 0.584692i | \(-0.198785\pi\) |
−0.911986 | + | 0.410222i | \(0.865451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.50000 | − | 7.79423i | 0.0503084 | − | 0.261410i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | − | 1.73205i | −0.0335013 | − | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.00000 | + | 5.19615i | −0.100391 | + | 0.173883i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.0000 | −0.801337 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.00000 | + | 10.3923i | −0.200111 | + | 0.346603i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.0000 | + | 83.1384i | 1.59911 | + | 2.76974i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.0000 | + | 19.0526i | 0.732114 | + | 0.634029i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.5000 | − | 18.1865i | 0.348647 | − | 0.603874i | −0.637363 | − | 0.770564i | \(-0.719975\pi\) |
0.986009 | + | 0.166690i | \(0.0533080\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.0000 | 0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.00000 | − | 3.46410i | 0.0661903 | − | 0.114645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.00000 | + | 1.73205i | −0.165115 | + | 0.0571974i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.50000 | + | 9.52628i | 0.181428 | + | 0.314243i | 0.942367 | − | 0.334581i | \(-0.108595\pi\) |
−0.760939 | + | 0.648824i | \(0.775261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.5000 | + | 19.9186i | −0.378938 | + | 0.656340i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.0000 | −0.987462 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.50000 | − | 9.52628i | 0.180644 | − | 0.312884i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.00000 | − | 5.19615i | −0.0984268 | − | 0.170480i | 0.812607 | − | 0.582812i | \(-0.198048\pi\) |
−0.911034 | + | 0.412332i | \(0.864714\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | − | 6.92820i | −0.0327737 | − | 0.227063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.00000 | + | 1.73205i | 0.0327385 | + | 0.0567048i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.0000 | 1.60076 | 0.800380 | − | 0.599493i | \(-0.204631\pi\) | ||||
0.800380 | + | 0.599493i | \(0.204631\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.0000 | 0.554774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.0000 | + | 45.0333i | −0.847576 | + | 1.46804i | 0.0357896 | + | 0.999359i | \(0.488605\pi\) |
−0.883365 | + | 0.468685i | \(0.844728\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | + | 41.5692i | 0.781548 | + | 1.35368i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.00000 | + | 8.66025i | 0.162478 | + | 0.281420i | 0.935757 | − | 0.352646i | \(-0.114718\pi\) |
−0.773279 | + | 0.634066i | \(0.781385\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.5000 | + | 28.5788i | −0.535613 | + | 0.927708i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.0000 | 0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.0000 | 0.907009 | 0.453504 | − | 0.891254i | \(-0.350174\pi\) | ||||
0.453504 | + | 0.891254i | \(0.350174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.00000 | − | 6.92820i | −0.129302 | − | 0.223957i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.00000 | + | 6.92820i | 0.258333 | + | 0.223723i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | + | 19.0526i | 0.354839 | + | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.0000 | 0.996893 | 0.498446 | − | 0.866921i | \(-0.333904\pi\) | ||||
0.498446 | + | 0.866921i | \(0.333904\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.00000 | + | 6.92820i | −0.128499 | + | 0.222566i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | − | 31.1769i | −0.577647 | − | 1.00051i | −0.995748 | − | 0.0921142i | \(-0.970638\pi\) |
0.418101 | − | 0.908401i | \(-0.362696\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.50000 | − | 12.9904i | 0.0801463 | − | 0.416452i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.00000 | + | 15.5885i | −0.287936 | + | 0.498719i | −0.973317 | − | 0.229465i | \(-0.926302\pi\) |
0.685381 | + | 0.728184i | \(0.259636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.0000 | −0.351203 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.00000 | + | 10.3923i | −0.191370 | + | 0.331463i | −0.945705 | − | 0.325027i | \(-0.894626\pi\) |
0.754334 | + | 0.656490i | \(0.227960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.00000 | − | 15.5885i | 0.0954911 | − | 0.496186i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.0000 | − | 76.2102i | −1.39912 | − | 2.42334i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.50000 | + | 9.52628i | −0.174713 | + | 0.302612i | −0.940062 | − | 0.341004i | \(-0.889233\pi\) |
0.765349 | + | 0.643616i | \(0.222567\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.0000 | 0.539479 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.500000 | + | 0.866025i | −0.0158352 | + | 0.0274273i | −0.873834 | − | 0.486224i | \(-0.838374\pi\) |
0.857999 | + | 0.513651i | \(0.171707\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.500000 | − | 0.866025i | −0.0158193 | − | 0.0273998i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))