Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(353,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.353");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.t (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: | \(9.70980888579\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 1185.1 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1185 |
Dual form | 1216.2.t.a.353.1 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −2.98735 | + | 1.72474i | −1.72474 | + | 0.995782i | −0.816497 | + | 0.577350i | \(0.804087\pi\) |
−0.908248 | + | 0.418432i | \(0.862580\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.44949 | − | 7.70674i | 1.48316 | − | 2.56891i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.550510i | 0.165985i | 0.996550 | + | 0.0829925i | \(0.0264478\pi\) | ||||
−0.996550 | + | 0.0829925i | \(0.973552\pi\) | |||||||
\(12\) | 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 | ||||||||
\(17\) | 3.00000 | + | 5.19615i | 0.727607 | + | 1.26025i | 0.957892 | + | 0.287129i | \(0.0927008\pi\) |
−0.230285 | + | 0.973123i | \(0.573966\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.98735 | + | 3.17423i | −0.685344 | + | 0.728219i | ||||
\(20\) | 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 | ||||||||
\(27\) | 20.3485i | 3.91606i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.949490 | − | 1.64456i | −0.165285 | − | 0.286282i | ||||
\(34\) | 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 | ||||||||
\(41\) | −6.39898 | − | 11.0834i | −0.999353 | − | 1.73093i | −0.530831 | − | 0.847477i | \(-0.678120\pi\) |
−0.468521 | − | 0.883452i | \(-0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.66025 | − | 5.00000i | 1.32068 | − | 0.762493i | 0.336840 | − | 0.941562i | \(-0.390642\pi\) |
0.983836 | + | 0.179069i | \(0.0573086\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −17.9241 | − | 10.3485i | −2.50987 | − | 1.44908i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.44949 | − | 14.6349i | 0.456896 | − | 1.93845i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00853 | + | 4.62372i | −1.04262 | + | 0.601958i | −0.920575 | − | 0.390567i | \(-0.872279\pi\) |
−0.122047 | + | 0.992524i | \(0.538946\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.4261 | − | 7.17423i | −1.51809 | − | 0.876472i | −0.999773 | − | 0.0212861i | \(-0.993224\pi\) |
−0.518321 | − | 0.855186i | \(-0.673443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.84847 | + | 13.5939i | 0.918594 | + | 1.59105i | 0.801553 | + | 0.597924i | \(0.204008\pi\) |
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 17.2474i | − | 1.99156i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −21.7474 | − | 37.6677i | −2.41638 | − | 4.18530i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.55051i | − | 0.719012i | −0.933143 | − | 0.359506i | \(-0.882945\pi\) | ||
0.933143 | − | 0.359506i | \(-0.117055\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | + | 15.5885i | −0.953998 | + | 1.65237i | −0.217354 | + | 0.976093i | \(0.569742\pi\) |
−0.736644 | + | 0.676280i | \(0.763591\pi\) | |||||||
\(90\) | 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 | ||||||||
\(99\) | 4.24264 | + | 2.44949i | 0.426401 | + | 0.246183i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.00000i | − | 0.580042i | −0.957020 | − | 0.290021i | \(-0.906338\pi\) | ||
0.957020 | − | 0.290021i | \(-0.0936623\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.7980 | −1.76836 | −0.884182 | − | 0.467143i | \(-0.845283\pi\) | ||||
−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 | ||||||||
\(121\) | 10.6969 | 0.972449 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 38.2319 | + | 22.0732i | 3.44726 | + | 1.99027i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.2474 | + | 29.8735i | −1.51855 | + | 2.63021i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.4008 | + | 10.6237i | −1.60769 | + | 0.928199i | −0.617802 | + | 0.786334i | \(0.711977\pi\) |
−0.989886 | + | 0.141865i | \(0.954690\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.2980 | + | 19.5686i | −0.965250 | + | 1.67186i | −0.256307 | + | 0.966595i | \(0.582506\pi\) |
−0.708942 | + | 0.705266i | \(0.750827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.8902 | − | 9.17423i | −1.34779 | − | 0.778148i | −0.359856 | − | 0.933008i | \(-0.617174\pi\) |
−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 | ||||||||
\(147\) | 20.9114 | − | 12.0732i | 1.72474 | − | 0.995782i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 53.3939 | 4.31664 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 23.0454i | − | 1.80506i | −0.430632 | − | 0.902528i | \(-0.641709\pi\) | ||
0.430632 | − | 0.902528i | \(-0.358291\pi\) | |||||||
\(164\) | 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 | ||||||||
\(171\) | 11.1708 | + | 37.1464i | 0.854256 | + | 2.84066i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.9495 | − | 27.6253i | 1.19884 | − | 2.07645i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.14643i | 0.608893i | 0.952529 | + | 0.304446i | \(0.0984714\pi\) | ||||
−0.952529 | + | 0.304446i | \(0.901529\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.86054 | + | 1.65153i | −0.209183 | + | 0.120772i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0000 | + | 19.0526i | 0.791797 | + | 1.37143i | 0.924853 | + | 0.380325i | \(0.124188\pi\) |
−0.133056 | + | 0.991109i | \(0.542479\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 49.4949 | 3.49110 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.74745 | − | 1.64456i | −0.120874 | − | 0.113757i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.1244 | + | 7.00000i | −0.834675 | + | 0.481900i | −0.855451 | − | 0.517884i | \(-0.826720\pi\) |
0.0207756 | + | 0.999784i | \(0.493386\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −46.8922 | − | 27.0732i | −3.16868 | − | 1.82944i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 22.2474 | + | 38.5337i | 1.48316 | + | 2.56891i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.4495i | 1.15816i | 0.815270 | + | 0.579082i | \(0.196589\pi\) | ||||
−0.815270 | + | 0.579082i | \(0.803411\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.94949 | − | 17.2330i | −0.651813 | − | 1.12897i | −0.982683 | − | 0.185296i | \(-0.940675\pi\) |
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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.848469 | + | 1.46959i | −0.0546547 | + | 0.0946647i | −0.892058 | − | 0.451920i | \(-0.850739\pi\) |
0.837404 | + | 0.546585i | \(0.184072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 77.0674 | + | 44.4949i | 4.94388 | + | 2.85435i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.2980 | + | 19.5686i | 0.715979 | + | 1.24011i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.7364 | + | 11.9722i | 1.30887 | + | 0.755678i | 0.981908 | − | 0.189358i | \(-0.0606408\pi\) |
0.326965 | + | 0.945036i | \(0.393974\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.60102 | + | 4.50510i | −0.162247 | + | 0.281020i | −0.935674 | − | 0.352865i | \(-0.885208\pi\) |
0.773427 | + | 0.633885i | \(0.218541\pi\) | |||||||
\(258\) | 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 | ||||||||
\(267\) | − | 62.0908i | − | 3.79990i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.38378 | − | 1.37628i | −0.143747 | − | 0.0829925i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.74745 | + | 13.4190i | −0.462174 | + | 0.800509i | −0.999069 | − | 0.0431402i | \(-0.986264\pi\) |
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.6182 | − | 16.5227i | 1.70117 | − | 0.982173i | 0.756596 | − | 0.653882i | \(-0.226861\pi\) |
0.944577 | − | 0.328291i | \(-0.106473\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.9681 | + | 16.7247i | 1.69814 | + | 0.980422i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.2020 | −0.650008 | ||||||||
\(298\) | 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 | ||||||||
\(307\) | −8.35847 | + | 4.82577i | −0.477043 | + | 0.275421i | −0.719183 | − | 0.694820i | \(-0.755484\pi\) |
0.242140 | + | 0.970241i | \(0.422151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.1969 | + | 21.1257i | −0.689412 | + | 1.19410i | 0.282617 | + | 0.959233i | \(0.408798\pi\) |
−0.972028 | + | 0.234863i | \(0.924536\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.3485 | + | 17.9241i | 0.577595 | + | 1.00042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.4558 | − | 6.00000i | −1.41640 | − | 0.333849i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.04541i | 0.497181i | 0.968609 | + | 0.248590i | \(0.0799673\pi\) | ||||
−0.968609 | + | 0.248590i | \(0.920033\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1969 | + | 19.3937i | 0.609936 | + | 1.05644i | 0.991250 | + | 0.131995i | \(0.0421382\pi\) |
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 56.1560 | − | 32.4217i | 3.04998 | − | 1.76090i | ||||
\(340\) | 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 | \(-0.948512\pi\) |
−0.354001 | + | 0.935245i | \(0.615179\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.59592 | −0.244616 | −0.122308 | − | 0.992492i | \(-0.539030\pi\) | ||||
−0.122308 | + | 0.992492i | \(0.539030\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.15153 | − | 18.9651i | −0.0606069 | − | 0.998162i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −31.9555 | + | 18.4495i | −1.67723 | + | 0.968347i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −113.889 | −5.92881 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 38.0000i | − | 1.95193i | −0.217930 | − | 0.975964i | \(-0.569930\pi\) | ||
0.217930 | − | 0.975964i | \(-0.430070\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 88.9898i | − | 4.52361i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.6464 | − | 63.4735i | 1.84857 | − | 3.20181i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.6464 | − | 32.2966i | −0.931158 | − | 1.61281i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
−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 | ||||||||
\(409\) | 9.19694 | − | 15.9296i | 0.454759 | − | 0.787666i | −0.543915 | − | 0.839140i | \(-0.683059\pi\) |
0.998674 | + | 0.0514740i | \(0.0163919\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 77.9444i | − | 3.84471i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 63.2929 | 3.09946 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0000i | 0.879358i | 0.898155 | + | 0.439679i | \(0.144908\pi\) | ||||
−0.898155 | + | 0.439679i | \(0.855092\pi\) | |||||||
\(420\) | 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 | ||||||||
\(425\) | −30.0000 | −1.45521 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.0000 | − | 32.9090i | 0.913082 | − | 1.58150i | 0.103396 | − | 0.994640i | \(-0.467029\pi\) |
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 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −31.1464 | + | 53.9472i | −1.48316 | + | 2.56891i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.0652 | + | 9.27526i | 0.763281 | + | 0.440681i | 0.830473 | − | 0.557059i | \(-0.188070\pi\) |
−0.0671913 | + | 0.997740i | \(0.521404\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.8990 | −1.22225 | −0.611124 | − | 0.791535i | \(-0.709282\pi\) | ||||
−0.611124 | + | 0.791535i | \(0.709282\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.10150 | − | 3.52270i | 0.287309 | − | 0.165878i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.3939 | 0.766873 | 0.383437 | − | 0.923567i | \(-0.374740\pi\) | ||||
0.383437 | + | 0.923567i | \(0.374740\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −105.734 | + | 61.0454i | −4.93523 | + | 2.84936i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.9444i | 1.94095i | 0.241192 | + | 0.970477i | \(0.422462\pi\) | ||||
−0.241192 | + | 0.970477i | \(0.577538\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.75255 | + | 4.76756i | 0.126562 | + | 0.219213i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.27647 | − | 20.8712i | −0.287984 | − | 0.957635i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 39.7474 | + | 68.8446i | 1.79744 | + | 3.11326i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.3731 | − | 21.0000i | 1.64149 | − | 0.947717i | 0.661190 | − | 0.750218i | \(-0.270052\pi\) |
0.980303 | − | 0.197499i | \(-0.0632818\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.7576 | + | 14.8712i | −1.15307 | + | 0.665725i | −0.949633 | − | 0.313363i | \(-0.898544\pi\) |
−0.203436 | + | 0.979088i | \(0.565211\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 38.8355 | + | 22.4217i | 1.72474 | + | 0.995782i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −64.5908 | − | 60.7879i | −2.85175 | − | 2.68385i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.1918 | −1.58559 | −0.792797 | − | 0.609486i | \(-0.791376\pi\) | ||||
−0.792797 | + | 0.609486i | \(0.791376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.9090 | + | 19.0000i | 1.43901 | + | 0.830812i | 0.997781 | − | 0.0665832i | \(-0.0212098\pi\) |
0.441228 | + | 0.897395i | \(0.354543\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | 82.2929i | 3.57121i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.0505 | − | 24.3362i | −0.606324 | − | 1.05018i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 3.85357i | − | 0.165985i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.8372 | + | 23.0000i | 1.70331 | + | 0.983409i | 0.942358 | + | 0.334606i | \(0.108603\pi\) |
0.760956 | + | 0.648803i | \(0.224730\pi\) | |||||||
\(548\) | 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 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.69694 | − | 9.86739i | 0.240525 | − | 0.416601i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 46.8434i | 1.97421i | 0.160066 | + | 0.987106i | \(0.448829\pi\) | ||||
−0.160066 | + | 0.987106i | \(0.551171\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.0000 | 1.76073 | 0.880366 | − | 0.474295i | \(-0.157297\pi\) | ||||
0.880366 | + | 0.474295i | \(0.157297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 25.7423i | − | 1.07728i | −0.842535 | − | 0.538642i | \(-0.818938\pi\) | ||
0.842535 | − | 0.538642i | \(-0.181062\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.3939 | 0.515964 | 0.257982 | − | 0.966150i | \(-0.416942\pi\) | ||||
0.257982 | + | 0.966150i | \(0.416942\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −65.7216 | − | 37.9444i | −2.73130 | − | 1.57691i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.19615 | + | 3.00000i | −0.214468 | + | 0.123823i | −0.603386 | − | 0.797449i | \(-0.706182\pi\) |
0.388918 | + | 0.921272i | \(0.372849\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.0959 | − | 41.7354i | 0.989501 | − | 1.71387i | 0.369586 | − | 0.929197i | \(-0.379500\pi\) |
0.619915 | − | 0.784669i | \(-0.287167\pi\) | |||||||
\(594\) | 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 | ||||||||
\(601\) | 37.6969 | 1.53769 | 0.768845 | − | 0.639435i | \(-0.220832\pi\) | ||||
0.768845 | + | 0.639435i | \(0.220832\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −110.580 | + | 63.8434i | −4.50316 | + | 2.59990i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.6464 | + | 42.6889i | −0.992228 | + | 1.71859i | −0.388351 | + | 0.921512i | \(0.626955\pi\) |
−0.603877 | + | 0.797077i | \(0.706378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.0000i | 1.04503i | 0.852631 | + | 0.522514i | \(0.175006\pi\) | ||||
−0.852631 | + | 0.522514i | \(0.824994\pi\) | |||||||
\(620\) | 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 | ||||||||
\(627\) | 8.05669 | + | 1.89898i | 0.321753 | + | 0.0758379i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.1464 | − | 41.8228i | 0.959734 | − | 1.66231i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.74745 | − | 3.02667i | −0.0690201 | − | 0.119546i | 0.829450 | − | 0.558581i | \(-0.188654\pi\) |
−0.898470 | + | 0.439034i | \(0.855321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.2867 | + | 8.82577i | −0.602848 | + | 0.348054i | −0.770161 | − | 0.637850i | \(-0.779824\pi\) |
0.167313 | + | 0.985904i | \(0.446491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.54541 | − | 4.40878i | −0.0999160 | − | 0.173060i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 139.687 | 5.44970 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.5885 | − | 9.00000i | −0.607240 | − | 0.350590i | 0.164644 | − | 0.986353i | \(-0.447352\pi\) |
−0.771885 | + | 0.635763i | \(0.780686\pi\) | |||||||
\(660\) | 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 | ||||||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −88.1115 | − | 50.8712i | −3.39141 | − | 1.95803i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.0959 | − | 52.1277i | −1.15328 | − | 1.99754i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.0000i | 1.60709i | 0.595247 | + | 0.803543i | \(0.297054\pi\) | ||||
−0.595247 | + | 0.803543i | \(0.702946\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 46.0000i | − | 1.74992i | −0.484193 | − | 0.874961i | \(-0.660887\pi\) | ||
0.484193 | − | 0.874961i | \(-0.339113\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.3939 | − | 66.5001i | 1.45427 | − | 2.51887i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 59.4451 | + | 34.3207i | 2.24842 | + | 1.29813i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(702\) | 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 | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(710\) | 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 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 5.85357i | − | 0.217697i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −176.485 | −6.53647 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 51.9615 | + | 30.0000i | 1.92187 | + | 1.10959i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.94949 | − | 6.84072i | 0.145481 | − | 0.251981i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.5422 | + | 26.8712i | −1.71208 | + | 0.988472i | −0.780340 | + | 0.625355i | \(0.784954\pi\) |
−0.931744 | + | 0.363117i | \(0.881713\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −50.4831 | − | 29.1464i | −1.84708 | − | 1.06641i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −82.5959 | −3.00996 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.2020 | 0.623574 | 0.311787 | − | 0.950152i | \(-0.399073\pi\) | ||||
0.311787 | + | 0.950152i | \(0.399073\pi\) | |||||||
\(762\) | 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 | −0.596643 | − | 0.802507i | \(-0.703499\pi\) |
0.993313 | + | 0.115454i | \(0.0368323\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 17.9444i | − | 0.646251i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 54.2971 | + | 12.7980i | 1.94540 | + | 0.458534i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 47.0454i | − | 1.67699i | −0.544911 | − | 0.838494i | \(-0.683437\pi\) | ||
0.544911 | − | 0.838494i | \(-0.316563\pi\) | |||||||
\(788\) | 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 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 80.0908 | + | 138.721i | 2.82987 | + | 4.90148i | ||||
\(802\) | 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 | ||||||||
\(809\) | −45.9898 | −1.61692 | −0.808458 | − | 0.588555i | \(-0.799697\pi\) | ||||
−0.808458 | + | 0.588555i | \(0.799697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.9090 | + | 19.0000i | 1.15559 | + | 0.667180i | 0.950243 | − | 0.311509i | \(-0.100834\pi\) |
0.205347 | + | 0.978689i | \(0.434168\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.0000 | + | 42.4264i | −0.349856 | + | 1.48431i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.49490 | 0.330570 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.53344 | − | 4.92679i | −0.296737 | − | 0.171321i | 0.344239 | − | 0.938882i | \(-0.388137\pi\) |
−0.640976 | + | 0.767561i | \(0.721470\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.0000 | − | 36.3731i | −0.727607 | − | 1.26025i | ||||
\(834\) | 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 | ||||||||
\(843\) | − | 53.4495i | − | 1.84090i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −56.9949 | + | 98.7181i | −1.95606 | + | 3.38799i | ||||
\(850\) | 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 | ||||||||
\(857\) | −23.2980 | − | 40.3532i | −0.795843 | − | 1.37844i | −0.922302 | − | 0.386469i | \(-0.873695\pi\) |
0.126459 | − | 0.991972i | \(-0.459639\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.4787 | + | 18.1742i | 1.07404 | + | 0.620097i | 0.929282 | − | 0.369370i | \(-0.120427\pi\) |
0.144757 | + | 0.989467i | \(0.453760\pi\) | |||||||
\(860\) | 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 | ||||||||
\(867\) | − | 65.5403i | − | 2.22587i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −86.2929 | −2.92057 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.9898 | 1.34729 | 0.673645 | − | 0.739055i | \(-0.264728\pi\) | ||||
0.673645 | + | 0.739055i | \(0.264728\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.4138 | + | 26.2196i | 1.52829 | + | 0.882361i | 0.999434 | + | 0.0336527i | \(0.0107140\pi\) |
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 | ||||||||
\(891\) | 20.7364 | − | 11.9722i | 0.694697 | − | 0.401084i | ||||
\(892\) | 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 | ||||||||
\(907\) | 40.2176 | − | 23.2196i | 1.33540 | − | 0.770996i | 0.349281 | − | 0.937018i | \(-0.386426\pi\) |
0.986122 | + | 0.166022i | \(0.0530924\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.60612 | 0.119345 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.6464 | − | 28.8325i | 0.548518 | − | 0.950062i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.7474 | − | 44.5959i | −0.844746 | − | 1.46314i | −0.885841 | − | 0.463988i | \(-0.846418\pi\) |
0.0410949 | − | 0.999155i | \(-0.486915\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.9114 | − | 22.2196i | 0.685344 | − | 0.728219i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.5454 | + | 23.4613i | −0.442509 | + | 0.766448i | −0.997875 | − | 0.0651578i | \(-0.979245\pi\) |
0.555366 | + | 0.831606i | \(0.312578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 84.1464i | − | 2.74601i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.9808 | + | 15.0000i | −0.844261 | + | 0.487435i | −0.858710 | − | 0.512461i | \(-0.828734\pi\) |
0.0144491 | + | 0.999896i | \(0.495401\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.09592 | − | 15.7546i | −0.294646 | − | 0.510341i | 0.680257 | − | 0.732974i | \(-0.261868\pi\) |
−0.974902 | + | 0.222633i | \(0.928535\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −46.2405 | − | 26.6969i | −1.49008 | − | 0.860297i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 86.3939 | − | 25.9808i | 2.77537 | − | 0.834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.0481621 | − | 0.0278064i | 0.00154560 | − | 0.000892350i | −0.499227 | − | 0.866471i | \(-0.666383\pi\) |
0.500773 | + | 0.865579i | \(0.333049\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56.8888 | 1.82003 | 0.910017 | − | 0.414572i | \(-0.136069\pi\) | ||||
0.910017 | + | 0.414572i | \(0.136069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.58161 | − | 4.95459i | −0.274269 | − | 0.158349i | ||||
\(980\) | 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 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.6010 | − | 27.0218i | −0.495083 | − | 0.857510i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(998\) | 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 | 1216.2.t.a.1185.1 | yes | 8 | |
4.3 | odd | 2 | inner | 1216.2.t.a.1185.4 | yes | 8 | |
8.3 | odd | 2 | CM | 1216.2.t.a.1185.1 | yes | 8 | |
8.5 | even | 2 | inner | 1216.2.t.a.1185.4 | yes | 8 | |
19.11 | even | 3 | inner | 1216.2.t.a.353.4 | yes | 8 | |
76.11 | odd | 6 | inner | 1216.2.t.a.353.1 | ✓ | 8 | |
152.11 | odd | 6 | inner | 1216.2.t.a.353.4 | yes | 8 | |
152.125 | even | 6 | inner | 1216.2.t.a.353.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.t.a.353.1 | ✓ | 8 | 76.11 | odd | 6 | inner | |
1216.2.t.a.353.1 | ✓ | 8 | 152.125 | even | 6 | inner | |
1216.2.t.a.353.4 | yes | 8 | 19.11 | even | 3 | inner | |
1216.2.t.a.353.4 | yes | 8 | 152.11 | odd | 6 | inner | |
1216.2.t.a.1185.1 | yes | 8 | 1.1 | even | 1 | trivial | |
1216.2.t.a.1185.1 | yes | 8 | 8.3 | odd | 2 | CM | |
1216.2.t.a.1185.4 | yes | 8 | 4.3 | odd | 2 | inner | |
1216.2.t.a.1185.4 | yes | 8 | 8.5 | even | 2 | inner |