Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(687,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.687");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 687.2 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.687 |
Dual form | 1568.3.g.f.687.1 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.333333 | 0.166667 | − | 0.986013i | \(-0.446700\pi\) | ||||
0.166667 | + | 0.986013i | \(0.446700\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.19615i | 1.03923i | 0.854400 | + | 0.519615i | \(0.173925\pi\) | ||||
−0.854400 | + | 0.519615i | \(0.826075\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.00000 | −0.888889 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.0000 | −1.54545 | −0.772727 | − | 0.634738i | \(-0.781108\pi\) | ||||
−0.772727 | + | 0.634738i | \(0.781108\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.8564i | 1.06588i | 0.846154 | + | 0.532939i | \(0.178912\pi\) | ||||
−0.846154 | + | 0.532939i | \(0.821088\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.19615i | 0.346410i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.0000 | 1.47059 | 0.735294 | − | 0.677748i | \(-0.237044\pi\) | ||||
0.735294 | + | 0.677748i | \(0.237044\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.00000 | −0.368421 | −0.184211 | − | 0.982887i | \(-0.558973\pi\) | ||||
−0.184211 | + | 0.982887i | \(0.558973\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 5.19615i | − 0.225920i | −0.993600 | − | 0.112960i | \(-0.963967\pi\) | ||||
0.993600 | − | 0.112960i | \(-0.0360331\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.0800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −17.0000 | −0.629630 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.8564i | 0.477807i | 0.971043 | + | 0.238904i | \(0.0767880\pi\) | ||||
−0.971043 | + | 0.238904i | \(0.923212\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 32.9090i | − 1.06158i | −0.847504 | − | 0.530790i | \(-0.821895\pi\) | ||||
0.847504 | − | 0.530790i | \(-0.178105\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.0000 | −0.515152 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.66025i | 0.234061i | 0.993128 | + | 0.117030i | \(0.0373375\pi\) | ||||
−0.993128 | + | 0.117030i | \(0.962662\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.8564i | 0.355292i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −26.0000 | −0.634146 | −0.317073 | − | 0.948401i | \(-0.602700\pi\) | ||||
−0.317073 | + | 0.948401i | \(0.602700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14.0000 | −0.325581 | −0.162791 | − | 0.986661i | \(-0.552050\pi\) | ||||
−0.162791 | + | 0.986661i | \(0.552050\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 41.5692i | − 0.923760i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 50.2295i | − 1.06871i | −0.845259 | − | 0.534356i | \(-0.820554\pi\) | ||||
0.845259 | − | 0.534356i | \(-0.179446\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 25.0000 | 0.490196 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 91.7987i | − 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 88.3346i | − 1.60608i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.00000 | −0.122807 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −55.0000 | −0.932203 | −0.466102 | − | 0.884731i | \(-0.654342\pi\) | ||||
−0.466102 | + | 0.884731i | \(0.654342\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 22.5167i | − 0.369126i | −0.982821 | − | 0.184563i | \(-0.940913\pi\) | ||||
0.982821 | − | 0.184563i | \(-0.0590869\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −72.0000 | −1.10769 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −17.0000 | −0.253731 | −0.126866 | − | 0.991920i | \(-0.540492\pi\) | ||||
−0.126866 | + | 0.991920i | \(0.540492\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 5.19615i | − 0.0753066i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −119.000 | −1.63014 | −0.815068 | − | 0.579365i | \(-0.803301\pi\) | ||||
−0.815068 | + | 0.579365i | \(0.803301\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.00000 | −0.0266667 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 74.4782i | − 0.942762i | −0.881930 | − | 0.471381i | \(-0.843756\pi\) | ||||
0.881930 | − | 0.471381i | \(-0.156244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 55.0000 | 0.679012 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 110.000 | 1.32530 | 0.662651 | − | 0.748929i | \(-0.269431\pi\) | ||||
0.662651 | + | 0.748929i | \(0.269431\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 129.904i | 1.52828i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.8564i | 0.159269i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −71.0000 | −0.797753 | −0.398876 | − | 0.917005i | \(-0.630600\pi\) | ||||
−0.398876 | + | 0.917005i | \(0.630600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 32.9090i | − 0.353860i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 36.3731i | − 0.382874i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 22.0000 | 0.226804 | 0.113402 | − | 0.993549i | \(-0.463825\pi\) | ||||
0.113402 | + | 0.993549i | \(0.463825\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 136.000 | 1.37374 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 77.9423i | 0.771706i | 0.922560 | + | 0.385853i | \(0.126093\pi\) | ||||
−0.922560 | + | 0.385853i | \(0.873907\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 161.081i | − 1.56389i | −0.623347 | − | 0.781945i | \(-0.714228\pi\) | ||||
0.623347 | − | 0.781945i | \(-0.285772\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −65.0000 | −0.607477 | −0.303738 | − | 0.952755i | \(-0.598235\pi\) | ||||
−0.303738 | + | 0.952755i | \(0.598235\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 8.66025i | − 0.0794519i | −0.999211 | − | 0.0397259i | \(-0.987352\pi\) | ||||
0.999211 | − | 0.0397259i | \(-0.0126485\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.66025i | 0.0780203i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 122.000 | 1.07965 | 0.539823 | − | 0.841779i | \(-0.318491\pi\) | ||||
0.539823 | + | 0.841779i | \(0.318491\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 27.0000 | 0.234783 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 110.851i | − 0.947447i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 168.000 | 1.38843 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −26.0000 | −0.211382 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 119.512i | 0.956092i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 166.277i | 1.30927i | 0.755947 | + | 0.654633i | \(0.227177\pi\) | ||||
−0.755947 | + | 0.654633i | \(0.772823\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.0000 | −0.108527 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.0000 | 0.129771 | 0.0648855 | − | 0.997893i | \(-0.479332\pi\) | ||||
0.0648855 | + | 0.997893i | \(0.479332\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 88.3346i | − 0.654330i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −145.000 | −1.05839 | −0.529197 | − | 0.848499i | \(-0.677507\pi\) | ||||
−0.529197 | + | 0.848499i | \(0.677507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −82.0000 | −0.589928 | −0.294964 | − | 0.955508i | \(-0.595308\pi\) | ||||
−0.294964 | + | 0.955508i | \(0.595308\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 50.2295i | − 0.356237i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 235.559i | − 1.64727i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −72.0000 | −0.496552 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 5.19615i | − 0.0348735i | −0.999848 | − | 0.0174368i | \(-0.994449\pi\) | ||||
0.999848 | − | 0.0174368i | \(-0.00555057\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 36.3731i | − 0.240881i | −0.992721 | − | 0.120441i | \(-0.961569\pi\) | ||||
0.992721 | − | 0.120441i | \(-0.0384307\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −200.000 | −1.30719 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 171.000 | 1.10323 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 310.037i | − 1.97476i | −0.158373 | − | 0.987379i | \(-0.550625\pi\) | ||||
0.158373 | − | 0.987379i | \(-0.449375\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 91.7987i | − 0.577350i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.0000 | −0.104294 | −0.0521472 | − | 0.998639i | \(-0.516607\pi\) | ||||
−0.0521472 | + | 0.998639i | \(0.516607\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 88.3346i | − 0.535361i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 13.8564i | − 0.0829725i | −0.999139 | − | 0.0414862i | \(-0.986791\pi\) | ||||
0.999139 | − | 0.0414862i | \(-0.0132093\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −0.136095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 56.0000 | 0.327485 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 105.655i | − 0.610723i | −0.952236 | − | 0.305362i | \(-0.901223\pi\) | ||||
0.952236 | − | 0.305362i | \(-0.0987773\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −55.0000 | −0.310734 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −89.0000 | −0.497207 | −0.248603 | − | 0.968605i | \(-0.579972\pi\) | ||||
−0.248603 | + | 0.968605i | \(0.579972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 249.415i | − 1.37799i | −0.724768 | − | 0.688993i | \(-0.758053\pi\) | ||||
0.724768 | − | 0.688993i | \(-0.241947\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 22.5167i | − 0.123042i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −45.0000 | −0.243243 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −425.000 | −2.27273 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 216.506i | 1.13354i | 0.823876 | + | 0.566771i | \(0.191807\pi\) | ||||
−0.823876 | + | 0.566771i | \(0.808193\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −73.0000 | −0.378238 | −0.189119 | − | 0.981954i | \(-0.560563\pi\) | ||||
−0.189119 | + | 0.981954i | \(0.560563\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −72.0000 | −0.369231 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 207.846i | 1.05506i | 0.849538 | + | 0.527528i | \(0.176881\pi\) | ||||
−0.849538 | + | 0.527528i | \(0.823119\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 64.0859i | 0.322040i | 0.986951 | + | 0.161020i | \(0.0514783\pi\) | ||||
−0.986951 | + | 0.161020i | \(0.948522\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.0000 | −0.0845771 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 135.100i | − 0.659024i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 41.5692i | 0.200817i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 119.000 | 0.569378 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −302.000 | −1.43128 | −0.715640 | − | 0.698470i | \(-0.753865\pi\) | ||||
−0.715640 | + | 0.698470i | \(0.753865\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 72.7461i | − 0.338354i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −119.000 | −0.543379 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 346.410i | 1.56747i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 138.564i | 0.621364i | 0.950514 | + | 0.310682i | \(0.100557\pi\) | ||||
−0.950514 | + | 0.310682i | \(0.899443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.0000 | 0.0711111 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −55.0000 | −0.242291 | −0.121145 | − | 0.992635i | \(-0.538657\pi\) | ||||
−0.121145 | + | 0.992635i | \(0.538657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 327.358i | − 1.42951i | −0.699375 | − | 0.714755i | \(-0.746538\pi\) | ||||
0.699375 | − | 0.714755i | \(-0.253462\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −385.000 | −1.65236 | −0.826180 | − | 0.563406i | \(-0.809491\pi\) | ||||
−0.826180 | + | 0.563406i | \(0.809491\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 261.000 | 1.11064 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 74.4782i | − 0.314254i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 429.549i | 1.79727i | 0.438693 | + | 0.898637i | \(0.355442\pi\) | ||||
−0.438693 | + | 0.898637i | \(0.644558\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 145.000 | 0.601660 | 0.300830 | − | 0.953678i | \(-0.402736\pi\) | ||||
0.300830 | + | 0.953678i | \(0.402736\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 208.000 | 0.855967 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 96.9948i | − 0.392692i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 110.000 | 0.441767 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −58.0000 | −0.231076 | −0.115538 | − | 0.993303i | \(-0.536859\pi\) | ||||
−0.115538 | + | 0.993303i | \(0.536859\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 88.3346i | 0.349149i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 129.904i | 0.509427i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −119.000 | −0.463035 | −0.231518 | − | 0.972831i | \(-0.574369\pi\) | ||||
−0.231518 | + | 0.972831i | \(0.574369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 110.851i | − 0.424717i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 327.358i | − 1.24471i | −0.782737 | − | 0.622353i | \(-0.786177\pi\) | ||||
0.782737 | − | 0.622353i | \(-0.213823\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 477.000 | 1.80000 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −71.0000 | −0.265918 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 133.368i | 0.495791i | 0.968787 | + | 0.247896i | \(0.0797390\pi\) | ||||
−0.968787 | + | 0.247896i | \(0.920261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 434.745i | 1.60422i | 0.597174 | + | 0.802112i | \(0.296290\pi\) | ||||
−0.597174 | + | 0.802112i | \(0.703710\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 34.0000 | 0.123636 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 202.650i | − 0.731588i | −0.930696 | − | 0.365794i | \(-0.880797\pi\) | ||||
0.930696 | − | 0.365794i | \(-0.119203\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 263.272i | 0.943626i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 74.0000 | 0.263345 | 0.131673 | − | 0.991293i | \(-0.457965\pi\) | ||||
0.131673 | + | 0.991293i | \(0.457965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −463.000 | −1.63604 | −0.818021 | − | 0.575188i | \(-0.804929\pi\) | ||||
−0.818021 | + | 0.575188i | \(0.804929\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 36.3731i | − 0.127625i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 336.000 | 1.16263 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.0000 | 0.0756014 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 110.851i | − 0.378332i | −0.981945 | − | 0.189166i | \(-0.939422\pi\) | ||||
0.981945 | − | 0.189166i | \(-0.0605784\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 285.788i | − 0.968774i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 289.000 | 0.973064 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 72.0000 | 0.240803 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 77.9423i | 0.257235i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 117.000 | 0.383607 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −274.000 | −0.892508 | −0.446254 | − | 0.894906i | \(-0.647242\pi\) | ||||
−0.446254 | + | 0.894906i | \(0.647242\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 161.081i | − 0.521297i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 50.2295i | 0.161510i | 0.996734 | + | 0.0807548i | \(0.0257331\pi\) | ||||
−0.996734 | + | 0.0807548i | \(0.974267\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 409.000 | 1.30671 | 0.653355 | − | 0.757052i | \(-0.273361\pi\) | ||||
0.653355 | + | 0.757052i | \(0.273361\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 188.794i | 0.595563i | 0.954634 | + | 0.297782i | \(0.0962467\pi\) | ||||
−0.954634 | + | 0.297782i | \(0.903753\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 235.559i | − 0.738429i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −65.0000 | −0.202492 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −175.000 | −0.541796 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 27.7128i | − 0.0852702i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 8.66025i | − 0.0264840i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 295.000 | 0.891239 | 0.445619 | − | 0.895223i | \(-0.352983\pi\) | ||||
0.445619 | + | 0.895223i | \(0.352983\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 69.2820i | − 0.208054i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 88.3346i | − 0.263685i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0000 | 0.0771513 | 0.0385757 | − | 0.999256i | \(-0.487718\pi\) | ||||
0.0385757 | + | 0.999256i | \(0.487718\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 122.000 | 0.359882 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 559.452i | 1.64062i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 27.0000 | 0.0782609 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −377.000 | −1.08646 | −0.543228 | − | 0.839585i | \(-0.682798\pi\) | ||||
−0.543228 | + | 0.839585i | \(0.682798\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 96.9948i | − 0.277922i | −0.990298 | − | 0.138961i | \(-0.955624\pi\) | ||||
0.990298 | − | 0.138961i | \(-0.0443763\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 235.559i | − 0.671108i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −503.000 | −1.42493 | −0.712465 | − | 0.701708i | \(-0.752421\pi\) | ||||
−0.712465 | + | 0.701708i | \(0.752421\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 185.329i | − 0.516238i | −0.966113 | − | 0.258119i | \(-0.916897\pi\) | ||||
0.966113 | − | 0.258119i | \(-0.0831027\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −312.000 | −0.864266 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 168.000 | 0.462810 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 618.342i | − 1.69409i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 296.181i | − 0.807032i | −0.914973 | − | 0.403516i | \(-0.867788\pi\) | ||||
0.914973 | − | 0.403516i | \(-0.132212\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 208.000 | 0.563686 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 119.512i | 0.320406i | 0.987084 | + | 0.160203i | \(0.0512149\pi\) | ||||
−0.987084 | + | 0.160203i | \(0.948785\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 119.512i | 0.318697i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −192.000 | −0.509284 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 634.000 | 1.67282 | 0.836412 | − | 0.548102i | \(-0.184649\pi\) | ||||
0.836412 | + | 0.548102i | \(0.184649\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 166.277i | 0.436422i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 244.219i | − 0.637648i | −0.947814 | − | 0.318824i | \(-0.896712\pi\) | ||||
0.947814 | − | 0.318824i | \(-0.103288\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 112.000 | 0.289406 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 587.165i | 1.50942i | 0.656057 | + | 0.754711i | \(0.272223\pi\) | ||||
−0.656057 | + | 0.754711i | \(0.727777\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 129.904i | − 0.332235i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.0000 | 0.0432570 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 387.000 | 0.979747 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 240.755i | 0.606436i | 0.952921 | + | 0.303218i | \(0.0980610\pi\) | ||||
−0.952921 | + | 0.303218i | \(0.901939\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 119.000 | 0.296758 | 0.148379 | − | 0.988931i | \(-0.452594\pi\) | ||||
0.148379 | + | 0.988931i | \(0.452594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 456.000 | 1.13151 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 285.788i | 0.705650i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 147.224i | − 0.361731i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 145.000 | 0.354523 | 0.177262 | − | 0.984164i | \(-0.443276\pi\) | ||||
0.177262 | + | 0.984164i | \(0.443276\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −145.000 | −0.352798 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 571.577i | 1.37729i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −82.0000 | −0.196643 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 302.000 | 0.720764 | 0.360382 | − | 0.932805i | \(-0.382646\pi\) | ||||
0.360382 | + | 0.932805i | \(0.382646\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 401.836i | − 0.954479i | −0.878773 | − | 0.477240i | \(-0.841637\pi\) | ||||
0.878773 | − | 0.477240i | \(-0.158363\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 401.836i | 0.949966i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −50.0000 | −0.117647 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 235.559i | − 0.549088i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 808.868i | 1.87672i | 0.345655 | + | 0.938362i | \(0.387657\pi\) | ||||
−0.345655 | + | 0.938362i | \(0.612343\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −410.000 | −0.946882 | −0.473441 | − | 0.880825i | \(-0.656988\pi\) | ||||
−0.473441 | + | 0.880825i | \(0.656988\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −72.0000 | −0.165517 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.3731i | 0.0832336i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 490.170i | 1.11656i | 0.829652 | + | 0.558281i | \(0.188539\pi\) | ||||
−0.829652 | + | 0.558281i | \(0.811461\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −401.000 | −0.905192 | −0.452596 | − | 0.891716i | \(-0.649502\pi\) | ||||
−0.452596 | + | 0.891716i | \(0.649502\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 368.927i | − 0.829049i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 5.19615i | − 0.0116245i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −310.000 | −0.690423 | −0.345212 | − | 0.938525i | \(-0.612193\pi\) | ||||
−0.345212 | + | 0.938525i | \(0.612193\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 442.000 | 0.980044 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 36.3731i | − 0.0802937i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 167.000 | 0.365427 | 0.182713 | − | 0.983166i | \(-0.441512\pi\) | ||||
0.182713 | + | 0.983166i | \(0.441512\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −425.000 | −0.925926 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 13.8564i | − 0.0300573i | −0.999887 | − | 0.0150286i | \(-0.995216\pi\) | ||||
0.999887 | − | 0.0150286i | \(-0.00478394\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 609.682i | − 1.31681i | −0.752665 | − | 0.658404i | \(-0.771232\pi\) | ||||
0.752665 | − | 0.658404i | \(-0.228768\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 171.000 | 0.367742 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 785.000 | 1.68094 | 0.840471 | − | 0.541856i | \(-0.182278\pi\) | ||||
0.840471 | + | 0.541856i | \(0.182278\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 310.037i | − 0.658253i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 238.000 | 0.503171 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.0000 | 0.0294737 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 734.390i | 1.53960i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 618.342i | 1.29090i | 0.763802 | + | 0.645451i | \(0.223331\pi\) | ||||
−0.763802 | + | 0.645451i | \(0.776669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −120.000 | −0.249480 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 114.315i | 0.235702i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 393.176i | 0.807342i | 0.914904 | + | 0.403671i | \(0.132266\pi\) | ||||
−0.914904 | + | 0.403671i | \(0.867734\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.0000 | −0.0347648 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −422.000 | −0.859470 | −0.429735 | − | 0.902955i | \(-0.641393\pi\) | ||||
−0.429735 | + | 0.902955i | \(0.641393\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 346.410i | 0.702658i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 706.677i | 1.42763i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −65.0000 | −0.130261 | −0.0651303 | − | 0.997877i | \(-0.520746\pi\) | ||||
−0.0651303 | + | 0.997877i | \(0.520746\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 13.8564i | − 0.0276575i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 249.415i | − 0.495855i | −0.968779 | − | 0.247928i | \(-0.920250\pi\) | ||||
0.968779 | − | 0.247928i | \(-0.0797496\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −405.000 | −0.801980 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.0000 | −0.0453649 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 545.596i | 1.07190i | 0.844250 | + | 0.535949i | \(0.180046\pi\) | ||||
−0.844250 | + | 0.535949i | \(0.819954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 119.000 | 0.231969 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 837.000 | 1.62524 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 853.901i | 1.65165i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 105.655i | − 0.203574i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.0000 | 0.0479846 | 0.0239923 | − | 0.999712i | \(-0.492362\pi\) | ||||
0.0239923 | + | 0.999712i | \(0.492362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 593.000 | 1.13384 | 0.566922 | − | 0.823772i | \(-0.308134\pi\) | ||||
0.566922 | + | 0.823772i | \(0.308134\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 822.724i | − 1.56115i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 502.000 | 0.948960 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 440.000 | 0.828625 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 360.267i | − 0.675922i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 337.750i | − 0.631308i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −89.0000 | −0.165736 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 756.906i | 1.39909i | 0.714590 | + | 0.699544i | \(0.246613\pi\) | ||||
−0.714590 | + | 0.699544i | \(0.753387\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 249.415i | − 0.459328i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 45.0000 | 0.0825688 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −662.000 | −1.21024 | −0.605119 | − | 0.796135i | \(-0.706874\pi\) | ||||
−0.605119 | + | 0.796135i | \(0.706874\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 180.133i | 0.328112i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 96.9948i | − 0.176034i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −45.0000 | −0.0810811 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 590.629i | − 1.06038i | −0.847880 | − | 0.530188i | \(-0.822121\pi\) | ||||
0.847880 | − | 0.530188i | \(-0.177879\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 193.990i | − 0.347030i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −425.000 | −0.757576 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 737.000 | 1.30906 | 0.654529 | − | 0.756037i | \(-0.272867\pi\) | ||||
0.654529 | + | 0.756037i | \(0.272867\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 633.931i | 1.12200i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −121.000 | −0.212654 | −0.106327 | − | 0.994331i | \(-0.533909\pi\) | ||||
−0.106327 | + | 0.994331i | \(0.533909\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −737.000 | −1.29072 | −0.645359 | − | 0.763879i | \(-0.723292\pi\) | ||||
−0.645359 | + | 0.763879i | \(0.723292\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 216.506i | 0.377847i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.3923i | 0.0180736i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −47.0000 | −0.0814558 | −0.0407279 | − | 0.999170i | \(-0.512968\pi\) | ||||
−0.0407279 | + | 0.999170i | \(0.512968\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −73.0000 | −0.126079 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1560.58i | 2.67681i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 576.000 | 0.984615 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 446.000 | 0.759796 | 0.379898 | − | 0.925028i | \(-0.375959\pi\) | ||||
0.379898 | + | 0.925028i | \(0.375959\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 230.363i | 0.391108i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 207.846i | 0.351685i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −215.000 | −0.362563 | −0.181282 | − | 0.983431i | \(-0.558025\pi\) | ||||
−0.181282 | + | 0.983431i | \(0.558025\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 64.0859i | 0.107347i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 282.324i | 0.471326i | 0.971835 | + | 0.235663i | \(0.0757262\pi\) | ||||
−0.971835 | + | 0.235663i | \(0.924274\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −266.000 | −0.442596 | −0.221298 | − | 0.975206i | \(-0.571029\pi\) | ||||
−0.221298 | + | 0.975206i | \(0.571029\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 136.000 | 0.225539 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 872.954i | 1.44290i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 659.911i | − 1.08717i | −0.839355 | − | 0.543584i | \(-0.817067\pi\) | ||||
0.839355 | − | 0.543584i | \(-0.182933\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 696.000 | 1.13912 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 698.016i | 1.13869i | 0.822099 | + | 0.569345i | \(0.192803\pi\) | ||||
−0.822099 | + | 0.569345i | \(0.807197\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 135.100i | − 0.219675i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −118.000 | −0.191248 | −0.0956240 | − | 0.995418i | \(-0.530485\pi\) | ||||
−0.0956240 | + | 0.995418i | \(0.530485\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −919.000 | −1.48465 | −0.742326 | − | 0.670039i | \(-0.766278\pi\) | ||||
−0.742326 | + | 0.670039i | \(0.766278\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 88.3346i | 0.142246i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −671.000 | −1.07360 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 119.000 | 0.189793 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 216.506i | 0.344207i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 166.277i | 0.263513i | 0.991282 | + | 0.131757i | \(0.0420617\pi\) | ||||
−0.991282 | + | 0.131757i | \(0.957938\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −302.000 | −0.477093 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −864.000 | −1.36063 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.00000 | −0.00156006 | −0.000780031 | − | 1.00000i | \(-0.500248\pi\) | ||||
−0.000780031 | 1.00000i | \(0.500248\pi\) | ||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −514.000 | −0.799378 | −0.399689 | − | 0.916651i | \(-0.630882\pi\) | ||||
−0.399689 | + | 0.916651i | \(0.630882\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 72.7461i | − 0.112785i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 60.6218i | − 0.0936967i | −0.998902 | − | 0.0468484i | \(-0.985082\pi\) | ||||
0.998902 | − | 0.0468484i | \(-0.0149178\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 935.000 | 1.44068 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 327.358i | 0.501313i | 0.968076 | + | 0.250657i | \(0.0806465\pi\) | ||||
−0.968076 | + | 0.250657i | \(0.919353\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 88.3346i | 0.134862i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 952.000 | 1.44901 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −542.000 | −0.822458 | −0.411229 | − | 0.911532i | \(-0.634900\pi\) | ||||
−0.411229 | + | 0.911532i | \(0.634900\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1182.99i | − 1.78970i | −0.446368 | − | 0.894849i | \(-0.647283\pi\) | ||||
0.446368 | − | 0.894849i | \(-0.352717\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 346.410i | 0.522489i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 72.0000 | 0.107946 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 138.564i | 0.207121i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 382.783i | 0.570467i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 218.000 | 0.323923 | 0.161961 | − | 0.986797i | \(-0.448218\pi\) | ||||
0.161961 | + | 0.986797i | \(0.448218\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 34.0000 | 0.0503704 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 642.591i | 0.949174i | 0.880209 | + | 0.474587i | \(0.157403\pi\) | ||||
−0.880209 | + | 0.474587i | \(0.842597\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −55.0000 | −0.0807636 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 367.000 | 0.537335 | 0.268668 | − | 0.963233i | \(-0.413417\pi\) | ||||
0.268668 | + | 0.963233i | \(0.413417\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 753.442i | − 1.09992i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 327.358i | − 0.476503i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1272.00 | 1.84615 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 497.000 | 0.719247 | 0.359624 | − | 0.933097i | \(-0.382905\pi\) | ||||
0.359624 | + | 0.933097i | \(0.382905\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 426.084i | − 0.613071i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −650.000 | −0.932568 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −385.000 | −0.550787 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 332.554i | − 0.474399i | −0.971461 | − | 0.237200i | \(-0.923770\pi\) | ||||
0.971461 | − | 0.237200i | \(-0.0762295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 60.6218i | − 0.0862330i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 261.000 | 0.370213 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 396.640i | 0.559435i | 0.960082 | + | 0.279718i | \(0.0902409\pi\) | ||||
−0.960082 | + | 0.279718i | \(0.909759\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 595.825i | 0.838011i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −171.000 | −0.239832 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1224.00 | 1.71189 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 429.549i | 0.599091i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 64.0859i | − 0.0891320i | −0.999006 | − | 0.0445660i | \(-0.985810\pi\) | ||||
0.999006 | − | 0.0445660i | \(-0.0141905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 145.000 | 0.200553 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 27.7128i | − 0.0382246i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 55.4256i | 0.0762388i | 0.999273 | + | 0.0381194i | \(0.0121367\pi\) | ||||
−0.999273 | + | 0.0381194i | \(0.987863\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −287.000 | −0.393690 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −350.000 | −0.478796 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 826.188i | − 1.12713i | −0.826071 | − | 0.563566i | \(-0.809429\pi\) | ||||
0.826071 | − | 0.563566i | \(-0.190571\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 289.000 | 0.392130 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −713.000 | −0.964817 | −0.482409 | − | 0.875946i | \(-0.660238\pi\) | ||||
−0.482409 | + | 0.875946i | \(0.660238\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 96.9948i | − 0.130897i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 637.395i | 0.857866i | 0.903336 | + | 0.428933i | \(0.141110\pi\) | ||||
−0.903336 | + | 0.428933i | \(0.858890\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.0000 | 0.0362416 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −880.000 | −1.17805 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1169.13i | − 1.55677i | −0.627787 | − | 0.778385i | \(-0.716039\pi\) | ||||
0.627787 | − | 0.778385i | \(-0.283961\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −58.0000 | −0.0770252 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 189.000 | 0.250331 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1039.23i | − 1.37283i | −0.727211 | − | 0.686414i | \(-0.759184\pi\) | ||||
0.727211 | − | 0.686414i | \(-0.240816\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 88.3346i | 0.116383i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −863.000 | −1.13403 | −0.567017 | − | 0.823706i | \(-0.691903\pi\) | ||||
−0.567017 | + | 0.823706i | \(0.691903\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1039.23i | − 1.35847i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 762.102i | − 0.993615i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −410.000 | −0.533160 | −0.266580 | − | 0.963813i | \(-0.585894\pi\) | ||||
−0.266580 | + | 0.963813i | \(0.585894\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −119.000 | −0.154345 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 798.475i | 1.03296i | 0.856300 | + | 0.516478i | \(0.172757\pi\) | ||||
−0.856300 | + | 0.516478i | \(0.827243\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 65.8179i | 0.0849264i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 182.000 | 0.233633 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 235.559i | − 0.300842i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1611.00 | 2.05223 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.0000 | −0.0393901 | −0.0196950 | − | 0.999806i | \(-0.506270\pi\) | ||||
−0.0196950 | + | 0.999806i | \(0.506270\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 327.358i | − 0.414902i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 312.000 | 0.393443 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 477.000 | 0.600000 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 595.825i | 0.747585i | 0.927512 | + | 0.373793i | \(0.121943\pi\) | ||||
−0.927512 | + | 0.373793i | \(0.878057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1255.74i | − 1.57164i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 568.000 | 0.709114 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2023.00 | 2.51930 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 133.368i | 0.165264i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −313.000 | −0.386897 | −0.193449 | − | 0.981110i | \(-0.561967\pi\) | ||||
−0.193449 | + | 0.981110i | \(0.561967\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1138.00 | −1.40321 | −0.701603 | − | 0.712568i | \(-0.747532\pi\) | ||||
−0.701603 | + | 0.712568i | \(0.747532\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 434.745i | 0.534741i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 88.3346i | − 0.108386i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 98.0000 | 0.119951 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1224.56i | − 1.49155i | −0.666200 | − | 0.745773i | \(-0.732080\pi\) | ||||
0.666200 | − | 0.745773i | \(-0.267920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 116.047i | 0.141005i | 0.997512 | + | 0.0705027i | \(0.0224603\pi\) | ||||
−0.997512 | + | 0.0705027i | \(0.977540\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 34.0000 | 0.0412121 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 754.000 | 0.911729 | 0.455865 | − | 0.890049i | \(-0.349330\pi\) | ||||
0.455865 | + | 0.890049i | \(0.349330\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 905.863i | − 1.09272i | −0.837551 | − | 0.546359i | \(-0.816014\pi\) | ||||
0.837551 | − | 0.546359i | \(-0.183986\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 202.650i | − 0.243863i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 72.0000 | 0.0862275 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 559.452i | 0.668402i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1053.09i | 1.25517i | 0.778548 | + | 0.627585i | \(0.215956\pi\) | ||||
−0.778548 | + | 0.627585i | \(0.784044\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 649.000 | 0.771700 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 74.0000 | 0.0877817 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 119.512i | − 0.141434i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −463.000 | −0.545347 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.0000 | 0.0528790 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 845.241i | − 0.990904i | −0.868635 | − | 0.495452i | \(-0.835003\pi\) | ||||
0.868635 | − | 0.495452i | \(-0.164997\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 290.985i | 0.340333i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −887.000 | −1.03501 | −0.517503 | − | 0.855681i | \(-0.673138\pi\) | ||||
−0.517503 | + | 0.855681i | \(0.673138\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1663.00 | −1.93597 | −0.967986 | − | 0.251004i | \(-0.919239\pi\) | ||||
−0.967986 | + | 0.251004i | \(0.919239\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 562.917i | 0.652279i | 0.945322 | + | 0.326139i | \(0.105748\pi\) | ||||
−0.945322 | + | 0.326139i | \(0.894252\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 549.000 | 0.634682 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 336.000 | 0.387543 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1266.13i | 1.45700i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 235.559i | − 0.270447i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −176.000 | −0.201604 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 119.512i | 0.136273i | 0.997676 | + | 0.0681365i | \(0.0217054\pi\) | ||||
−0.997676 | + | 0.0681365i | \(0.978295\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 110.851i | − 0.126111i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 574.000 | 0.651532 | 0.325766 | − | 0.945450i | \(-0.394378\pi\) | ||||
0.325766 | + | 0.945450i | \(0.394378\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1166.00 | −1.32050 | −0.660249 | − | 0.751047i | \(-0.729549\pi\) | ||||
−0.660249 | + | 0.751047i | \(0.729549\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 285.788i | − 0.322925i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 545.596i | 0.615103i | 0.951532 | + | 0.307551i | \(0.0995096\pi\) | ||||
−0.951532 | + | 0.307551i | \(0.900490\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −935.000 | −1.04938 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 351.606i | 0.393736i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 462.458i | − 0.516712i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 72.0000 | 0.0802676 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 456.000 | 0.507230 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2294.97i | − 2.54713i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1296.00 | 1.43204 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −521.000 | −0.574421 | −0.287211 | − | 0.957867i | \(-0.592728\pi\) | ||||
−0.287211 | + | 0.957867i | \(0.592728\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 623.538i | − 0.685961i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1191.65i | 1.30807i | 0.756465 | + | 0.654035i | \(0.226925\pi\) | ||||
−0.756465 | + | 0.654035i | \(0.773075\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1870.00 | −2.04819 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 117.000 | 0.127869 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1394.30i | 1.51719i | 0.651560 | + | 0.758597i | \(0.274115\pi\) | ||||
−0.651560 | + | 0.758597i | \(0.725885\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −274.000 | −0.297503 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 17.3205i | − 0.0187249i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1288.65i | 1.39012i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 961.000 | 1.03445 | 0.517223 | − | 0.855851i | \(-0.326966\pi\) | ||||
0.517223 | + | 0.855851i | \(0.326966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 50.2295i | 0.0538365i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 2208.36i | − 2.36189i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 142.000 | 0.151547 | 0.0757737 | − | 0.997125i | \(-0.475857\pi\) | ||||
0.0757737 | + | 0.997125i | \(0.475857\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 409.000 | 0.435570 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1224.56i | − 1.30134i | −0.759361 | − | 0.650669i | \(-0.774488\pi\) | ||||
0.759361 | − | 0.650669i | \(-0.225512\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 135.100i | 0.143266i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 175.000 | 0.184794 | 0.0923970 | − | 0.995722i | \(-0.470547\pi\) | ||||
0.0923970 | + | 0.995722i | \(0.470547\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1648.91i | − 1.73753i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 188.794i | 0.198521i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −454.000 | −0.476390 | −0.238195 | − | 0.971217i | \(-0.576556\pi\) | ||||
−0.238195 | + | 0.971217i | \(0.576556\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1125.00 | −1.17801 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 235.559i | − 0.246143i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −122.000 | −0.126951 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 520.000 | 0.539979 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 379.319i | − 0.393077i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 720.533i | 0.745122i | 0.928008 | + | 0.372561i | \(0.121520\pi\) | ||||
−0.928008 | + | 0.372561i | \(0.878480\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −175.000 | −0.180599 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1639.00 | −1.68795 | −0.843975 | − | 0.536382i | \(-0.819791\pi\) | ||||
−0.843975 | + | 0.536382i | \(0.819791\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 27.7128i | − 0.0284234i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −793.000 | −0.811668 | −0.405834 | − | 0.913947i | \(-0.633019\pi\) | ||||
−0.405834 | + | 0.913947i | \(0.633019\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1207.00 | 1.23289 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 69.2820i | 0.0706239i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1543.26i | − 1.56995i | −0.619530 | − | 0.784973i | \(-0.712677\pi\) | ||||
0.619530 | − | 0.784973i | \(-0.287323\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1080.00 | −1.09645 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 72.7461i | 0.0735552i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 895.470i | − 0.903603i | −0.892119 | − | 0.451801i | \(-0.850782\pi\) | ||||
0.892119 | − | 0.451801i | \(-0.149218\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 295.000 | 0.297080 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −333.000 | −0.334673 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 795.011i | − 0.797404i | −0.917081 | − | 0.398702i | \(-0.869461\pi\) | ||||
0.917081 | − | 0.398702i | \(-0.130539\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 147.224i | − 0.147372i |
(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 | 1568.3.g.f.687.2 | 2 | ||
4.3 | odd | 2 | 392.3.g.d.99.1 | 2 | |||
7.3 | odd | 6 | 224.3.o.b.79.1 | 2 | |||
7.5 | odd | 6 | 224.3.o.a.207.1 | 2 | |||
7.6 | odd | 2 | 1568.3.g.c.687.1 | 2 | |||
8.3 | odd | 2 | inner | 1568.3.g.f.687.1 | 2 | ||
8.5 | even | 2 | 392.3.g.d.99.2 | 2 | |||
28.3 | even | 6 | 56.3.k.b.51.1 | yes | 2 | ||
28.11 | odd | 6 | 392.3.k.c.275.1 | 2 | |||
28.19 | even | 6 | 56.3.k.a.11.1 | ✓ | 2 | ||
28.23 | odd | 6 | 392.3.k.a.67.1 | 2 | |||
28.27 | even | 2 | 392.3.g.e.99.1 | 2 | |||
56.3 | even | 6 | 224.3.o.a.79.1 | 2 | |||
56.5 | odd | 6 | 56.3.k.b.11.1 | yes | 2 | ||
56.13 | odd | 2 | 392.3.g.e.99.2 | 2 | |||
56.19 | even | 6 | 224.3.o.b.207.1 | 2 | |||
56.27 | even | 2 | 1568.3.g.c.687.2 | 2 | |||
56.37 | even | 6 | 392.3.k.c.67.1 | 2 | |||
56.45 | odd | 6 | 56.3.k.a.51.1 | yes | 2 | ||
56.53 | even | 6 | 392.3.k.a.275.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.k.a.11.1 | ✓ | 2 | 28.19 | even | 6 | ||
56.3.k.a.51.1 | yes | 2 | 56.45 | odd | 6 | ||
56.3.k.b.11.1 | yes | 2 | 56.5 | odd | 6 | ||
56.3.k.b.51.1 | yes | 2 | 28.3 | even | 6 | ||
224.3.o.a.79.1 | 2 | 56.3 | even | 6 | |||
224.3.o.a.207.1 | 2 | 7.5 | odd | 6 | |||
224.3.o.b.79.1 | 2 | 7.3 | odd | 6 | |||
224.3.o.b.207.1 | 2 | 56.19 | even | 6 | |||
392.3.g.d.99.1 | 2 | 4.3 | odd | 2 | |||
392.3.g.d.99.2 | 2 | 8.5 | even | 2 | |||
392.3.g.e.99.1 | 2 | 28.27 | even | 2 | |||
392.3.g.e.99.2 | 2 | 56.13 | odd | 2 | |||
392.3.k.a.67.1 | 2 | 28.23 | odd | 6 | |||
392.3.k.a.275.1 | 2 | 56.53 | even | 6 | |||
392.3.k.c.67.1 | 2 | 56.37 | even | 6 | |||
392.3.k.c.275.1 | 2 | 28.11 | odd | 6 | |||
1568.3.g.c.687.1 | 2 | 7.6 | odd | 2 | |||
1568.3.g.c.687.2 | 2 | 56.27 | even | 2 | |||
1568.3.g.f.687.1 | 2 | 8.3 | odd | 2 | inner | ||
1568.3.g.f.687.2 | 2 | 1.1 | even | 1 | trivial |