Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(191,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.p (of order \(6\), 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 959.1 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.959 |
Dual form | 1152.2.p.c.191.1 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.57313 | − | 0.724745i | −0.908248 | − | 0.418432i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.94949 | + | 2.28024i | 0.649830 | + | 0.760080i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.476756 | − | 0.275255i | 0.143747 | − | 0.0829925i | −0.426401 | − | 0.904534i | \(-0.640219\pi\) |
0.570149 | + | 0.821541i | \(0.306886\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.36773i | 0.574258i | 0.957892 | + | 0.287129i | \(0.0927008\pi\) | ||||
−0.957892 | + | 0.287129i | \(0.907299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.97469 | −1.37069 | −0.685344 | − | 0.728219i | \(-0.740348\pi\) | ||||
−0.685344 | + | 0.728219i | \(0.740348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | + | 4.33013i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.41421 | − | 5.00000i | −0.272166 | − | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.949490 | + | 0.0874863i | −0.165285 | + | 0.0152294i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.39898 | + | 5.42650i | 1.46787 | + | 0.847477i | 0.999353 | − | 0.0359748i | \(-0.0114536\pi\) |
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.20881 | + | 3.82577i | 0.336840 | + | 0.583424i | 0.983836 | − | 0.179069i | \(-0.0573086\pi\) |
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | + | 6.06218i | −0.500000 | + | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.71600 | − | 3.72474i | 0.240288 | − | 0.521569i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.39898 | + | 4.33013i | 1.24493 | + | 0.573539i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.2047 | + | 7.62372i | 1.71910 | + | 0.992524i | 0.920575 | + | 0.390567i | \(0.127721\pi\) |
0.798528 | + | 0.601958i | \(0.205612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.18350 | + | 14.1742i | −0.999773 | + | 1.73166i | −0.481452 | + | 0.876472i | \(0.659891\pi\) |
−0.518321 | + | 0.855186i | \(0.673443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.6969 | 1.83719 | 0.918594 | − | 0.395203i | \(-0.129326\pi\) | ||||
0.918594 | + | 0.395203i | \(0.129326\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.794593 | − | 8.62372i | −0.0917517 | − | 0.995782i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.39898 | + | 8.89060i | −0.155442 | + | 0.987845i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.5885 | − | 9.00000i | 1.71106 | − | 0.987878i | 0.777913 | − | 0.628372i | \(-0.216279\pi\) |
0.933143 | − | 0.359506i | \(-0.117055\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.65685i | 0.599625i | 0.953998 | + | 0.299813i | \(0.0969242\pi\) | ||||
−0.953998 | + | 0.299813i | \(0.903076\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.84847 | − | 8.39780i | −0.492287 | − | 0.852667i | 0.507673 | − | 0.861550i | \(-0.330506\pi\) |
−0.999961 | + | 0.00888289i | \(0.997172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.55708 | + | 0.550510i | 0.156492 | + | 0.0553284i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1464i | 1.36759i | 0.729676 | + | 0.683793i | \(0.239671\pi\) | ||||
−0.729676 | + | 0.683793i | \(0.760329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.79796 | − | 5.65685i | −0.921714 | − | 0.532152i | −0.0375328 | − | 0.999295i | \(-0.511950\pi\) |
−0.884182 | + | 0.467143i | \(0.845283\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.34847 | + | 9.26382i | −0.486224 | + | 0.842165i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.8530 | − | 15.3485i | −0.978583 | − | 1.38392i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.702041 | − | 7.61926i | −0.0618113 | − | 0.670838i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5885 | + | 9.00000i | 1.36197 | + | 0.786334i | 0.989886 | − | 0.141865i | \(-0.0453100\pi\) |
0.372084 | + | 0.928199i | \(0.378643\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.29796 | − | 3.05878i | 0.452635 | − | 0.261329i | −0.256307 | − | 0.966595i | \(-0.582506\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.40496 | + | 12.8258i | −0.628080 | + | 1.08787i | 0.359856 | + | 0.933008i | \(0.382826\pi\) |
−0.987937 | + | 0.154859i | \(0.950508\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.89949 | − | 7.00000i | 0.816497 | − | 0.577350i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.39898 | + | 4.61586i | −0.436482 | + | 0.373170i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −25.4558 | −1.99386 | −0.996928 | − | 0.0783260i | \(-0.975042\pi\) | ||||
−0.996928 | + | 0.0783260i | \(0.975042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.50000 | − | 11.2583i | −0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.6476 | − | 13.6237i | −0.890714 | − | 1.04183i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.2474 | − | 21.5631i | −1.14607 | − | 1.62079i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 18.0000i | − | 1.34538i | −0.739923 | − | 0.672692i | \(-0.765138\pi\) | ||
0.739923 | − | 0.672692i | \(-0.234862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.651729 | + | 1.12883i | 0.0476591 | + | 0.0825480i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.84847 | + | 3.20164i | −0.133056 | + | 0.230459i | −0.924853 | − | 0.380325i | \(-0.875812\pi\) |
0.791797 | + | 0.610784i | \(0.209146\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.1464 | − | 16.3670i | 1.63262 | − | 1.15444i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.84847 | + | 1.64456i | −0.197033 | + | 0.113757i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7279 | + | 22.0454i | −0.876226 | + | 1.51767i | −0.0207756 | + | 0.999784i | \(0.506614\pi\) |
−0.855451 | + | 0.517884i | \(0.826720\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.6934 | − | 11.3763i | −1.66862 | − | 0.768737i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.00000 | + | 14.1421i | −0.333333 | + | 0.942809i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.1117 | − | 8.72474i | 1.00300 | − | 0.579082i | 0.0938647 | − | 0.995585i | \(-0.470078\pi\) |
0.909134 | + | 0.416503i | \(0.136745\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 28.8092i | − | 1.88735i | −0.330870 | − | 0.943676i | \(-0.607342\pi\) | ||
0.330870 | − | 0.943676i | \(-0.392658\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.8485 | − | 23.9863i | −0.892058 | − | 1.54509i | −0.837404 | − | 0.546585i | \(-0.815928\pi\) |
−0.0546547 | − | 0.998505i | \(-0.517406\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.64420 | − | 12.9722i | 0.554526 | − | 0.832167i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −31.0454 | + | 2.86054i | −1.96742 | + | 0.181279i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.9444i | 1.89007i | 0.326965 | + | 0.945036i | \(0.393974\pi\) | ||||
−0.326965 | + | 0.945036i | \(0.606026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.6010 | − | 10.1620i | −1.09792 | − | 0.633885i | −0.162247 | − | 0.986750i | \(-0.551874\pi\) |
−0.935674 | + | 0.352865i | \(0.885208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.09978 | − | 8.89898i | 0.250902 | − | 0.544609i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.38378 | + | 1.37628i | 0.143747 | + | 0.0829925i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.4949 | + | 14.1421i | −1.46124 | + | 0.843649i | −0.999069 | − | 0.0431402i | \(-0.986264\pi\) |
−0.462174 | + | 0.886789i | \(0.652930\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.7279 | − | 22.0454i | 0.756596 | − | 1.31046i | −0.187980 | − | 0.982173i | \(-0.560194\pi\) |
0.944577 | − | 0.328291i | \(-0.106473\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.3939 | 0.670228 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.54102 | + | 16.7247i | 0.0903364 | + | 0.980422i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.05051 | − | 1.99451i | −0.118983 | − | 0.115733i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.2022 | −1.43837 | −0.719183 | − | 0.694820i | \(-0.755484\pi\) | ||||
−0.719183 | + | 0.694820i | \(0.755484\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.1969 | − | 29.7860i | −0.972028 | − | 1.68360i | −0.689412 | − | 0.724370i | \(-0.742131\pi\) |
−0.282617 | − | 0.959233i | \(-0.591202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.2526 | − | 22.2542i | 0.572242 | − | 1.24211i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 14.1464i | − | 0.787128i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.7279 | + | 22.0454i | 0.699590 | + | 1.21173i | 0.968609 | + | 0.248590i | \(0.0799673\pi\) |
−0.269019 | + | 0.963135i | \(0.586699\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.1969 | + | 19.3937i | −0.609936 | + | 1.05644i | 0.381314 | + | 0.924445i | \(0.375472\pi\) |
−0.991250 | + | 0.131995i | \(0.957862\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.3137 | + | 16.0000i | 0.614476 | + | 0.869001i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.9791 | + | 14.4217i | 1.34095 | + | 0.774197i | 0.986947 | − | 0.161048i | \(-0.0514875\pi\) |
0.354001 | + | 0.935245i | \(0.384821\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.2980 | − | 18.6472i | 1.71905 | − | 0.992492i | 0.798369 | − | 0.602168i | \(-0.205696\pi\) |
0.920677 | − | 0.390324i | \(-0.127637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.6969 | 0.878786 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.1278 | − | 10.6969i | 0.794001 | − | 0.561444i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.94949 | + | 32.0108i | 0.309718 | + | 1.66642i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.1516 | 1.90835 | 0.954175 | − | 0.299249i | \(-0.0967363\pi\) | ||||
0.954175 | + | 0.299249i | \(0.0967363\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.41761 | + | 12.4949i | −0.224560 | + | 0.635151i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.0000 | − | 25.4558i | −0.907980 | − | 1.28408i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.6464 | + | 7.30142i | 0.631532 | + | 0.364615i | 0.781345 | − | 0.624099i | \(-0.214534\pi\) |
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.1969 | + | 34.9821i | −0.998674 | + | 1.72975i | −0.454759 | + | 0.890614i | \(0.650275\pi\) |
−0.543915 | + | 0.839140i | \(0.683059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.5512 | + | 0.972194i | −0.520453 | + | 0.0479548i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.9444 | − | 14.8099i | 1.02565 | − | 0.725245i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.5885 | − | 9.00000i | −0.761546 | − | 0.439679i | 0.0683046 | − | 0.997665i | \(-0.478241\pi\) |
−0.829851 | + | 0.557986i | \(0.811574\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.2526 | + | 5.91931i | −0.497322 | + | 0.287129i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.6969 | 1.61937 | 0.809686 | − | 0.586864i | \(-0.199638\pi\) | ||||
0.809686 | + | 0.586864i | \(0.199638\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.6464 | + | 3.83732i | −0.983163 | + | 0.182729i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.0652 | + | 9.27526i | −0.763281 | + | 0.440681i | −0.830473 | − | 0.557059i | \(-0.811930\pi\) |
0.0671913 | + | 0.997740i | \(0.478596\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.5446i | 1.58307i | 0.611124 | + | 0.791535i | \(0.290718\pi\) | ||||
−0.611124 | + | 0.791535i | \(0.709282\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.97469 | 0.281337 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.19694 | − | 14.1975i | −0.383437 | − | 0.664132i | 0.608114 | − | 0.793849i | \(-0.291926\pi\) |
−0.991551 | + | 0.129718i | \(0.958593\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.8386 | − | 3.34847i | 0.552580 | − | 0.156293i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 11.9444i | − | 0.552720i | −0.961054 | − | 0.276360i | \(-0.910872\pi\) | ||
0.961054 | − | 0.276360i | \(-0.0891283\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.10612 | + | 1.21597i | 0.0968396 | + | 0.0559104i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.9367 | − | 25.8712i | −0.685344 | − | 1.18705i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.0454 | + | 18.4490i | 1.81092 | + | 0.834292i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.7931 | − | 16.6237i | −1.29942 | − | 0.750218i | −0.319113 | − | 0.947717i | \(-0.603385\pi\) |
−0.980303 | + | 0.197499i | \(0.936718\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.54442 | + | 7.87117i | −0.203436 | + | 0.352362i | −0.949633 | − | 0.313363i | \(-0.898544\pi\) |
0.746197 | + | 0.665725i | \(0.231878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.06594 | + | 22.4217i | 0.0917517 | + | 0.995782i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.44949 | + | 29.8735i | 0.373054 | + | 1.31895i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 27.8236i | − | 1.21897i | −0.792797 | − | 0.609486i | \(-0.791376\pi\) | ||
0.792797 | − | 0.609486i | \(-0.208624\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.4558 | 1.11311 | 0.556553 | − | 0.830812i | \(-0.312124\pi\) | ||||
0.556553 | + | 0.830812i | \(0.312124\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.35847 | + | 44.9722i | 0.362727 | + | 1.95163i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.0454 | + | 28.3164i | −0.562951 | + | 1.22194i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.85357i | 0.165985i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.7973 | − | 30.8258i | −0.760956 | − | 1.31801i | −0.942358 | − | 0.334606i | \(-0.891397\pi\) |
0.181402 | − | 0.983409i | \(-0.441936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.207144 | − | 2.24813i | −0.00874561 | − | 0.0949162i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.5675 | − | 23.4217i | −1.70972 | − | 0.987106i | −0.934892 | − | 0.354932i | \(-0.884504\pi\) |
−0.774826 | − | 0.632175i | \(-0.782163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.7020 | + | 12.5297i | −0.909797 | + | 0.525271i | −0.880366 | − | 0.474295i | \(-0.842703\pi\) |
−0.0294311 | + | 0.999567i | \(0.509370\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.1329 | − | 34.8712i | 0.842535 | − | 1.45931i | −0.0452101 | − | 0.998978i | \(-0.514396\pi\) |
0.887745 | − | 0.460336i | \(-0.152271\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.3939 | 1.93140 | 0.965701 | − | 0.259656i | \(-0.0836092\pi\) | ||||
0.965701 | + | 0.259656i | \(0.0836092\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.22826 | − | 3.69694i | 0.217279 | − | 0.153640i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.6605 | + | 22.3207i | −1.59569 | + | 0.921272i | −0.603386 | + | 0.797449i | \(0.706182\pi\) |
−0.992304 | + | 0.123823i | \(0.960484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 45.2548i | 1.85839i | 0.369586 | + | 0.929197i | \(0.379500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.15153 | + | 7.19066i | 0.169344 | + | 0.293313i | 0.938190 | − | 0.346122i | \(-0.112502\pi\) |
−0.768845 | + | 0.639435i | \(0.779168\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −48.2743 | + | 8.97219i | −1.96588 | + | 0.365376i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.6464 | + | 22.8899i | 1.59611 | + | 0.921512i | 0.992228 | + | 0.124434i | \(0.0397116\pi\) |
0.603877 | + | 0.797077i | \(0.293622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.651729 | − | 1.12883i | −0.0261952 | − | 0.0453714i | 0.852631 | − | 0.522514i | \(-0.175006\pi\) |
−0.878826 | + | 0.477143i | \(0.841672\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.67291 | − | 0.522704i | 0.226554 | − | 0.0208748i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 36.0000 | − | 25.4558i | 1.43087 | − | 1.01178i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.7474 | − | 25.2576i | 1.72792 | − | 0.997615i | 0.829450 | − | 0.558581i | \(-0.188654\pi\) |
0.898470 | − | 0.439034i | \(-0.144679\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.7720 | − | 41.1742i | 0.937474 | − | 1.62375i | 0.167313 | − | 0.985904i | \(-0.446491\pi\) |
0.770161 | − | 0.637850i | \(-0.220176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.39388 | 0.329488 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.6010 | + | 35.7928i | 1.19386 | + | 1.39641i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.5885 | + | 9.00000i | −0.607240 | + | 0.350590i | −0.771885 | − | 0.635763i | \(-0.780686\pi\) |
0.164644 | + | 0.986353i | \(0.447352\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.00000 | − | 8.66025i | −0.192736 | − | 0.333828i | 0.753420 | − | 0.657539i | \(-0.228403\pi\) |
−0.946156 | + | 0.323711i | \(0.895069\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.1151 | − | 18.6237i | 0.697251 | − | 0.716827i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.0959 | + | 2.77305i | −1.15328 | + | 0.106263i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 47.9444i | − | 1.83454i | −0.398265 | − | 0.917270i | \(-0.630387\pi\) | ||
0.398265 | − | 0.917270i | \(-0.369613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.7279 | + | 22.0454i | 0.484193 | + | 0.838647i | 0.999835 | − | 0.0181572i | \(-0.00577993\pi\) |
−0.515642 | + | 0.856804i | \(0.672447\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.8485 | + | 22.2542i | −0.486670 | + | 0.842938i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.8793 | + | 45.3207i | −0.789728 | + | 1.71418i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.40156 | + | 47.7702i | 0.163696 | + | 1.77659i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0000 | + | 14.1421i | −0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.05836 | + | 5.22985i | −0.335036 | + | 0.193433i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.01020i | 0.331895i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.6581 | 1.86349 | 0.931744 | − | 0.363117i | \(-0.118287\pi\) | ||||
0.931744 | + | 0.363117i | \(0.118287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 50.9117 | + | 18.0000i | 1.86276 | + | 0.658586i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.7020 | − | 47.1065i | 0.790866 | − | 1.71666i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.79796 | − | 5.65685i | −0.355176 | − | 0.205061i | 0.311787 | − | 0.950152i | \(-0.399073\pi\) |
−0.666962 | + | 0.745091i | \(0.732406\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.0000 | + | 19.0526i | −0.396670 | + | 0.687053i | −0.993313 | − | 0.115454i | \(-0.963168\pi\) |
0.596643 | + | 0.802507i | \(0.296501\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.3239 | + | 28.7423i | 0.731948 | + | 1.03513i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −56.1560 | − | 32.4217i | −2.01200 | − | 1.16163i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.7279 | − | 22.0454i | 0.453701 | − | 0.785834i | −0.544911 | − | 0.838494i | \(-0.683437\pi\) |
0.998613 | + | 0.0526599i | \(0.0167699\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.8990 | + | 11.0280i | −0.455763 | + | 0.389654i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.48361 | − | 4.32066i | 0.264091 | − | 0.152473i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.0881i | 0.811735i | 0.913932 | + | 0.405868i | \(0.133031\pi\) | ||||
−0.913932 | + | 0.405868i | \(0.866969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.6958 | −0.410694 | −0.205347 | − | 0.978689i | \(-0.565832\pi\) | ||||
−0.205347 | + | 0.978689i | \(0.565832\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.1969 | − | 22.8578i | −0.461702 | − | 0.799692i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.75255 | − | 3.89270i | −0.0958315 | − | 0.135526i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.0000i | 1.87776i | 0.344239 | + | 0.938882i | \(0.388137\pi\) | ||||
−0.344239 | + | 0.938882i | \(0.611863\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.3536 | − | 8.28704i | −0.497322 | − | 0.287129i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5000 | − | 25.1147i | 0.500000 | − | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 48.7832 | − | 4.49490i | 1.68018 | − | 0.154812i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −36.0000 | + | 25.4558i | −1.23552 | + | 0.873642i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.5959 | + | 11.3137i | −0.669384 | + | 0.386469i | −0.795843 | − | 0.605503i | \(-0.792972\pi\) |
0.126459 | + | 0.991972i | \(0.459639\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.9934 | − | 39.8258i | 0.784525 | − | 1.35884i | −0.144757 | − | 0.989467i | \(-0.546240\pi\) |
0.929282 | − | 0.369370i | \(-0.120427\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.9241 | − | 8.25765i | −0.608733 | − | 0.280445i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.69694 | − | 27.4271i | 0.328192 | − | 0.928266i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 56.5685i | − | 1.90584i | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||
0.303218 | − | 0.952921i | \(-0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.4305 | 1.05772 | 0.528861 | − | 0.848709i | \(-0.322619\pi\) | ||||
0.528861 | + | 0.848709i | \(0.322619\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.78021 | + | 4.62372i | 0.0596394 | + | 0.154901i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.5191 | + | 18.2196i | 0.349281 | + | 0.604973i | 0.986122 | − | 0.166022i | \(-0.0530924\pi\) |
−0.636841 | + | 0.770996i | \(0.719759\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.95459 | − | 8.58161i | 0.163973 | − | 0.284010i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.6464 | + | 18.2652i | 1.30639 | + | 0.601858i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.4949 | + | 14.1421i | −0.803652 | + | 0.463988i | −0.844746 | − | 0.535167i | \(-0.820249\pi\) |
0.0410949 | + | 0.999155i | \(0.486915\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.9114 | − | 36.2196i | 0.685344 | − | 1.18705i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.0000 | 1.11073 | 0.555366 | − | 0.831606i | \(-0.312578\pi\) | ||||
0.555366 | + | 0.831606i | \(0.312578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.46583 | + | 59.3207i | 0.178371 | + | 1.93586i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.2955 | + | 30.7702i | −1.73187 | + | 0.999896i | −0.858710 | + | 0.512461i | \(0.828734\pi\) |
−0.873160 | + | 0.487435i | \(0.837933\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 59.0005i | − | 1.91121i | −0.294646 | − | 0.955607i | \(-0.595202\pi\) | ||
0.294646 | − | 0.955607i | \(-0.404798\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.5000 | − | 26.8468i | −0.500000 | − | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −32.2572 | + | 27.5783i | −1.03947 | + | 0.888699i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.2526 | + | 22.2542i | −0.329359 | + | 0.714908i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 54.0000i | − | 1.73294i | −0.499227 | − | 0.866471i | \(-0.666383\pi\) | ||
0.499227 | − | 0.866471i | \(-0.333617\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.4444 | − | 18.1544i | −1.00600 | − | 0.580812i | −0.0959785 | − | 0.995383i | \(-0.530598\pi\) |
−0.910017 | + | 0.414572i | \(0.863931\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.55708 | + | 2.69694i | 0.0497644 | + | 0.0861945i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.04541 | − | 43.9048i | −0.128377 | − | 1.39328i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1152.2.p.c.959.1 | yes | 8 | |
3.2 | odd | 2 | 3456.2.p.c.2879.2 | 8 | |||
4.3 | odd | 2 | inner | 1152.2.p.c.959.4 | yes | 8 | |
8.3 | odd | 2 | CM | 1152.2.p.c.959.1 | yes | 8 | |
8.5 | even | 2 | inner | 1152.2.p.c.959.4 | yes | 8 | |
9.2 | odd | 6 | inner | 1152.2.p.c.191.1 | ✓ | 8 | |
9.7 | even | 3 | 3456.2.p.c.575.2 | 8 | |||
12.11 | even | 2 | 3456.2.p.c.2879.3 | 8 | |||
24.5 | odd | 2 | 3456.2.p.c.2879.3 | 8 | |||
24.11 | even | 2 | 3456.2.p.c.2879.2 | 8 | |||
36.7 | odd | 6 | 3456.2.p.c.575.3 | 8 | |||
36.11 | even | 6 | inner | 1152.2.p.c.191.4 | yes | 8 | |
72.11 | even | 6 | inner | 1152.2.p.c.191.1 | ✓ | 8 | |
72.29 | odd | 6 | inner | 1152.2.p.c.191.4 | yes | 8 | |
72.43 | odd | 6 | 3456.2.p.c.575.2 | 8 | |||
72.61 | even | 6 | 3456.2.p.c.575.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.p.c.191.1 | ✓ | 8 | 9.2 | odd | 6 | inner | |
1152.2.p.c.191.1 | ✓ | 8 | 72.11 | even | 6 | inner | |
1152.2.p.c.191.4 | yes | 8 | 36.11 | even | 6 | inner | |
1152.2.p.c.191.4 | yes | 8 | 72.29 | odd | 6 | inner | |
1152.2.p.c.959.1 | yes | 8 | 1.1 | even | 1 | trivial | |
1152.2.p.c.959.1 | yes | 8 | 8.3 | odd | 2 | CM | |
1152.2.p.c.959.4 | yes | 8 | 4.3 | odd | 2 | inner | |
1152.2.p.c.959.4 | yes | 8 | 8.5 | even | 2 | inner | |
3456.2.p.c.575.2 | 8 | 9.7 | even | 3 | |||
3456.2.p.c.575.2 | 8 | 72.43 | odd | 6 | |||
3456.2.p.c.575.3 | 8 | 36.7 | odd | 6 | |||
3456.2.p.c.575.3 | 8 | 72.61 | even | 6 | |||
3456.2.p.c.2879.2 | 8 | 3.2 | odd | 2 | |||
3456.2.p.c.2879.2 | 8 | 24.11 | even | 2 | |||
3456.2.p.c.2879.3 | 8 | 12.11 | even | 2 | |||
3456.2.p.c.2879.3 | 8 | 24.5 | odd | 2 |